TSTP Solution File: ITP276^3 by cvc5---1.0.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : ITP276^3 : TPTP v8.1.2. Released v8.1.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n003.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 03:30:22 EDT 2023
% Result : Theorem 104.61s 105.05s
% Output : Proof 104.78s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 2.63/2.67 % Problem : ITP276^3 : TPTP v8.1.2. Released v8.1.0.
% 2.63/2.68 % Command : do_cvc5 %s %d
% 2.68/2.89 % Computer : n003.cluster.edu
% 2.68/2.89 % Model : x86_64 x86_64
% 2.68/2.89 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 2.68/2.89 % Memory : 8042.1875MB
% 2.68/2.89 % OS : Linux 3.10.0-693.el7.x86_64
% 2.68/2.89 % CPULimit : 300
% 2.68/2.89 % WCLimit : 300
% 2.68/2.89 % DateTime : Sun Aug 27 16:35:42 EDT 2023
% 2.75/2.89 % CPUTime :
% 5.13/5.44 %----Proving TH0
% 5.13/5.45 %------------------------------------------------------------------------------
% 5.13/5.45 % File : ITP276^3 : TPTP v8.1.2. Released v8.1.0.
% 5.13/5.45 % Domain : Interactive Theorem Proving
% 5.13/5.45 % Problem : Sledgehammer problem VEBT_Uniqueness 00216_013627
% 5.13/5.45 % Version : [Des22] axioms.
% 5.13/5.45 % English :
% 5.13/5.45
% 5.13/5.45 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 5.13/5.45 % : [Des22] Desharnais (2022), Email to Geoff Sutcliffe
% 5.13/5.45 % Source : [Des22]
% 5.13/5.45 % Names : 0075_VEBT_Uniqueness_00216_013627 [Des22]
% 5.13/5.45
% 5.13/5.45 % Status : ContradictoryAxioms
% 5.13/5.45 % Rating : 0.62 v8.1.0
% 5.13/5.45 % Syntax : Number of formulae : 11045 (5080 unt;1495 typ; 0 def)
% 5.13/5.45 % Number of atoms : 27536 (12178 equ; 0 cnn)
% 5.13/5.45 % Maximal formula atoms : 71 ( 2 avg)
% 5.13/5.45 % Number of connectives : 116044 (2818 ~; 487 |;2080 &;99931 @)
% 5.13/5.45 % ( 0 <=>;10728 =>; 0 <=; 0 <~>)
% 5.13/5.45 % Maximal formula depth : 39 ( 6 avg)
% 5.13/5.45 % Number of types : 212 ( 211 usr)
% 5.13/5.45 % Number of type conns : 4874 (4874 >; 0 *; 0 +; 0 <<)
% 5.13/5.45 % Number of symbols : 1287 (1284 usr; 72 con; 0-8 aty)
% 5.13/5.45 % Number of variables : 25413 (2067 ^;22644 !; 702 ?;25413 :)
% 5.13/5.45 % SPC : TH0_CAX_EQU_NAR
% 5.13/5.45
% 5.13/5.45 % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 5.13/5.45 % from the van Emde Boas Trees session in the Archive of Formal
% 5.13/5.45 % proofs -
% 5.13/5.45 % www.isa-afp.org/browser_info/current/AFP/Van_Emde_Boas_Trees
% 5.13/5.45 % 2022-02-18 15:42:08.029
% 5.13/5.45 %------------------------------------------------------------------------------
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% 5.13/5.45 thf(ty_n_t__List__Olist_It__List__Olist_It__Nat__Onat_J_J,type,
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% 5.13/5.45 thf(ty_n_t__List__Olist_It__List__Olist_It__Int__Oint_J_J,type,
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% 5.13/5.45 thf(ty_n_t__Set__Oset_It__List__Olist_It__Nat__Onat_J_J,type,
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% 5.13/5.45 thf(ty_n_t__Set__Oset_It__List__Olist_It__Int__Oint_J_J,type,
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% 5.13/5.45 thf(ty_n_t__Product____Type__Oprod_It__Nat__Onat_M_Eo_J,type,
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% 5.13/5.45 thf(ty_n_t__Product____Type__Oprod_I_Eo_Mt__Nat__Onat_J,type,
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% 5.13/5.45 thf(ty_n_t__Product____Type__Oprod_I_Eo_Mt__Int__Oint_J,type,
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% 5.13/5.45 thf(ty_n_t__List__Olist_It__Set__Oset_It__Nat__Onat_J_J,type,
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% 5.13/5.45 thf(ty_n_t__List__Olist_It__Complex__Ocomplex_J,type,
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% 5.13/5.45
% 5.13/5.45 thf(ty_n_t__Filter__Ofilter_It__Nat__Onat_J,type,
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% 5.13/5.45 thf(ty_n_t__Set__Oset_It__String__Ochar_J,type,
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% 5.13/5.45 thf(ty_n_t__Set__Oset_It__Real__Oreal_J,type,
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% 5.13/5.45 thf(ty_n_t__List__Olist_It__Num__Onum_J,type,
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% 5.13/5.45 thf(ty_n_t__Int__Oint,type,
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% 5.13/5.45 thf(sy_c_BNF__Cardinal__Order__Relation_OnatLess,type,
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% 5.13/5.45 thf(sy_c_BNF__Cardinal__Order__Relation_OrelChain_001t__Code____Numeral__Ointeger_001t__Num__Onum,type,
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% 5.13/5.45
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% 5.13/5.45
% 5.13/5.45 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001_062_It__Nat__Onat_M_Eo_J_001_062_It__Nat__Onat_M_Eo_J,type,
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% 5.13/5.45 bNF_re4705727531993890431at_o_o: ( nat > nat > $o ) > ( $o > $o > $o ) > ( nat > $o ) > ( nat > $o ) > $o ).
% 5.13/5.45
% 5.13/5.45 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat,type,
% 5.13/5.45 bNF_re5653821019739307937at_nat: ( nat > nat > $o ) > ( nat > nat > $o ) > ( nat > nat ) > ( nat > nat ) > $o ).
% 5.13/5.45
% 5.13/5.45 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint,type,
% 5.13/5.45 bNF_re6830278522597306478at_int: ( nat > nat > $o ) > ( product_prod_nat_nat > int > $o ) > ( nat > product_prod_nat_nat ) > ( nat > int ) > $o ).
% 5.13/5.45
% 5.13/5.45 thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001_062_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_001_062_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
% 5.13/5.45 bNF_re5228765855967844073nt_int: ( product_prod_int_int > product_prod_int_int > $o ) > ( ( product_prod_int_int > product_prod_int_int ) > ( product_prod_int_int > product_prod_int_int ) > $o ) > ( product_prod_int_int > product_prod_int_int > product_prod_int_int ) > ( product_prod_int_int > product_prod_int_int > product_prod_int_int ) > $o ).
% 5.13/5.45
% 5.13/5.45 thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001_Eo_001_Eo,type,
% 5.13/5.45 bNF_re8699439704749558557nt_o_o: ( product_prod_int_int > product_prod_int_int > $o ) > ( $o > $o > $o ) > ( product_prod_int_int > $o ) > ( product_prod_int_int > $o ) > $o ).
% 5.13/5.45
% 5.13/5.45 thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 5.13/5.45 bNF_re7145576690424134365nt_int: ( product_prod_int_int > product_prod_int_int > $o ) > ( product_prod_int_int > product_prod_int_int > $o ) > ( product_prod_int_int > product_prod_int_int ) > ( product_prod_int_int > product_prod_int_int ) > $o ).
% 5.13/5.45
% 5.13/5.45 thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Rat__Orat_001_062_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_001_062_It__Rat__Orat_Mt__Rat__Orat_J,type,
% 5.13/5.45 bNF_re7627151682743391978at_rat: ( product_prod_int_int > rat > $o ) > ( ( product_prod_int_int > product_prod_int_int ) > ( rat > rat ) > $o ) > ( product_prod_int_int > product_prod_int_int > product_prod_int_int ) > ( rat > rat > rat ) > $o ).
% 5.13/5.45
% 5.13/5.45 thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Rat__Orat_001_Eo_001_Eo,type,
% 5.13/5.45 bNF_re1494630372529172596at_o_o: ( product_prod_int_int > rat > $o ) > ( $o > $o > $o ) > ( product_prod_int_int > $o ) > ( rat > $o ) > $o ).
% 5.13/5.45
% 5.13/5.45 thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Rat__Orat_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Rat__Orat,type,
% 5.13/5.45 bNF_re8279943556446156061nt_rat: ( product_prod_int_int > rat > $o ) > ( product_prod_int_int > rat > $o ) > ( product_prod_int_int > product_prod_int_int ) > ( rat > rat ) > $o ).
% 5.13/5.45
% 5.13/5.45 thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint_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,
% 5.13/5.45 bNF_re717283939379294677_int_o: ( product_prod_nat_nat > int > $o ) > ( ( product_prod_nat_nat > $o ) > ( int > $o ) > $o ) > ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( int > int > $o ) > $o ).
% 5.13/5.45
% 5.13/5.45 thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint_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,
% 5.13/5.45 bNF_re7408651293131936558nt_int: ( product_prod_nat_nat > int > $o ) > ( ( product_prod_nat_nat > product_prod_nat_nat ) > ( int > int ) > $o ) > ( product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ) > ( int > int > int ) > $o ).
% 5.13/5.45
% 5.13/5.45 thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint_001_Eo_001_Eo,type,
% 5.13/5.45 bNF_re6644619430987730960nt_o_o: ( product_prod_nat_nat > int > $o ) > ( $o > $o > $o ) > ( product_prod_nat_nat > $o ) > ( int > $o ) > $o ).
% 5.13/5.45
% 5.13/5.45 thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint,type,
% 5.13/5.45 bNF_re7400052026677387805at_int: ( product_prod_nat_nat > int > $o ) > ( product_prod_nat_nat > int > $o ) > ( product_prod_nat_nat > product_prod_nat_nat ) > ( int > int ) > $o ).
% 5.13/5.45
% 5.13/5.45 thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_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__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J,type,
% 5.13/5.45 bNF_re4202695980764964119_nat_o: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( ( product_prod_nat_nat > $o ) > ( product_prod_nat_nat > $o ) > $o ) > ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( product_prod_nat_nat > product_prod_nat_nat > $o ) > $o ).
% 5.13/5.45
% 5.13/5.45 thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_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__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 5.13/5.45 bNF_re3099431351363272937at_nat: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( ( product_prod_nat_nat > product_prod_nat_nat ) > ( product_prod_nat_nat > product_prod_nat_nat ) > $o ) > ( product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ) > ( product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ) > $o ).
% 5.13/5.45
% 5.13/5.45 thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001_Eo_001_Eo,type,
% 5.13/5.45 bNF_re3666534408544137501at_o_o: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( $o > $o > $o ) > ( product_prod_nat_nat > $o ) > ( product_prod_nat_nat > $o ) > $o ).
% 5.13/5.45
% 5.13/5.45 thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 5.13/5.45 bNF_re2241393799969408733at_nat: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( product_prod_nat_nat > product_prod_nat_nat ) > ( product_prod_nat_nat > product_prod_nat_nat ) > $o ).
% 5.13/5.45
% 5.13/5.45 thf(sy_c_BNF__Wellorder__Constructions_OordIso_001t__Nat__Onat_001t__Nat__Onat,type,
% 5.13/5.45 bNF_We5258908940166488438at_nat: set_Pr4329608150637261639at_nat ).
% 5.13/5.45
% 5.13/5.45 thf(sy_c_BNF__Wellorder__Relation_Owo__rel_001t__Nat__Onat,type,
% 5.13/5.45 bNF_We3818239936649020644el_nat: set_Pr1261947904930325089at_nat > $o ).
% 5.13/5.45
% 5.13/5.45 thf(sy_c_Binomial_Obinomial,type,
% 5.13/5.45 binomial: nat > nat > nat ).
% 5.13/5.45
% 5.13/5.45 thf(sy_c_Binomial_Ogbinomial_001t__Code____Numeral__Ointeger,type,
% 5.13/5.45 gbinom8545251970709558553nteger: code_integer > nat > code_integer ).
% 5.13/5.45
% 5.13/5.45 thf(sy_c_Binomial_Ogbinomial_001t__Complex__Ocomplex,type,
% 5.13/5.45 gbinomial_complex: complex > nat > complex ).
% 5.13/5.45
% 5.13/5.45 thf(sy_c_Binomial_Ogbinomial_001t__Int__Oint,type,
% 5.13/5.45 gbinomial_int: int > nat > int ).
% 5.13/5.45
% 5.13/5.45 thf(sy_c_Binomial_Ogbinomial_001t__Nat__Onat,type,
% 5.13/5.45 gbinomial_nat: nat > nat > nat ).
% 5.13/5.45
% 5.13/5.45 thf(sy_c_Binomial_Ogbinomial_001t__Rat__Orat,type,
% 5.13/5.45 gbinomial_rat: rat > nat > rat ).
% 5.13/5.45
% 5.13/5.45 thf(sy_c_Binomial_Ogbinomial_001t__Real__Oreal,type,
% 5.13/5.45 gbinomial_real: real > nat > real ).
% 5.13/5.45
% 5.13/5.45 thf(sy_c_Bit__Operations_Oand__int__rel,type,
% 5.13/5.45 bit_and_int_rel: product_prod_int_int > product_prod_int_int > $o ).
% 5.13/5.45
% 5.13/5.45 thf(sy_c_Bit__Operations_Oconcat__bit,type,
% 5.13/5.45 bit_concat_bit: nat > int > int > int ).
% 5.13/5.45
% 5.13/5.45 thf(sy_c_Bit__Operations_Oring__bit__operations__class_Onot_001t__Int__Oint,type,
% 5.13/5.45 bit_ri7919022796975470100ot_int: int > int ).
% 5.13/5.45
% 5.13/5.45 thf(sy_c_Bit__Operations_Oring__bit__operations__class_Osigned__take__bit_001t__Code____Numeral__Ointeger,type,
% 5.13/5.45 bit_ri6519982836138164636nteger: nat > code_integer > code_integer ).
% 5.13/5.45
% 5.13/5.45 thf(sy_c_Bit__Operations_Oring__bit__operations__class_Osigned__take__bit_001t__Int__Oint,type,
% 5.13/5.45 bit_ri631733984087533419it_int: nat > int > int ).
% 5.13/5.45
% 5.13/5.45 thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Oand_001t__Code____Numeral__Ointeger,type,
% 5.13/5.45 bit_se3949692690581998587nteger: code_integer > code_integer > code_integer ).
% 5.13/5.45
% 5.13/5.45 thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Oand_001t__Int__Oint,type,
% 5.13/5.45 bit_se725231765392027082nd_int: int > int > int ).
% 5.13/5.45
% 5.13/5.45 thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Oand_001t__Nat__Onat,type,
% 5.13/5.45 bit_se727722235901077358nd_nat: nat > nat > nat ).
% 5.13/5.45
% 5.13/5.45 thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Odrop__bit_001t__Int__Oint,type,
% 5.13/5.45 bit_se8568078237143864401it_int: nat > int > int ).
% 5.13/5.45
% 5.13/5.45 thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Odrop__bit_001t__Nat__Onat,type,
% 5.13/5.45 bit_se8570568707652914677it_nat: nat > nat > nat ).
% 5.13/5.45
% 5.13/5.45 thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Oflip__bit_001t__Code____Numeral__Ointeger,type,
% 5.13/5.45 bit_se1345352211410354436nteger: nat > code_integer > code_integer ).
% 5.13/5.45
% 5.13/5.45 thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Oflip__bit_001t__Code____Numeral__Onatural,type,
% 5.13/5.45 bit_se168947363167071951atural: nat > code_natural > code_natural ).
% 5.13/5.45
% 5.13/5.45 thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Oflip__bit_001t__Int__Oint,type,
% 5.13/5.45 bit_se2159334234014336723it_int: nat > int > int ).
% 5.13/5.45
% 5.13/5.45 thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Oflip__bit_001t__Nat__Onat,type,
% 5.13/5.45 bit_se2161824704523386999it_nat: nat > nat > nat ).
% 5.13/5.45
% 5.13/5.45 thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Omask_001t__Nat__Onat,type,
% 5.13/5.45 bit_se2002935070580805687sk_nat: nat > nat ).
% 5.13/5.45
% 5.13/5.45 thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Oor_001t__Int__Oint,type,
% 5.13/5.45 bit_se1409905431419307370or_int: int > int > int ).
% 5.13/5.45
% 5.13/5.45 thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Oor_001t__Nat__Onat,type,
% 5.13/5.45 bit_se1412395901928357646or_nat: nat > nat > nat ).
% 5.13/5.45
% 5.13/5.45 thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Opush__bit_001t__Int__Oint,type,
% 5.13/5.45 bit_se545348938243370406it_int: nat > int > int ).
% 5.13/5.45
% 5.13/5.45 thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Opush__bit_001t__Nat__Onat,type,
% 5.13/5.45 bit_se547839408752420682it_nat: nat > nat > nat ).
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% 5.13/5.45 thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Oset__bit_001t__Code____Numeral__Ointeger,type,
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% 5.13/5.45 thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Oset__bit_001t__Code____Numeral__Onatural,type,
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% 5.13/5.45
% 5.13/5.45 thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Oset__bit_001t__Int__Oint,type,
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% 5.13/5.45
% 5.13/5.45 thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Oset__bit_001t__Nat__Onat,type,
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% 5.13/5.45
% 5.13/5.45 thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Otake__bit_001t__Int__Oint,type,
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% 5.13/5.45
% 5.13/5.45 thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Otake__bit_001t__Nat__Onat,type,
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% 5.13/5.45 thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Ounset__bit_001t__Code____Numeral__Onatural,type,
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% 5.13/5.45 thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Ounset__bit_001t__Int__Oint,type,
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% 5.13/5.45 thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Ounset__bit_001t__Nat__Onat,type,
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% 5.13/5.45 thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Oxor_001t__Int__Oint,type,
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% 5.13/5.45 thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Oxor_001t__Nat__Onat,type,
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% 5.13/5.45
% 5.13/5.45 thf(sy_c_Bit__Operations_Osemiring__bits__class_Obit_001t__Int__Oint,type,
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% 5.13/5.45
% 5.13/5.45 thf(sy_c_Bit__Operations_Osemiring__bits__class_Obit_001t__Nat__Onat,type,
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% 5.13/5.45
% 5.13/5.45 thf(sy_c_Bit__Operations_Otake__bit__num,type,
% 5.13/5.45 bit_take_bit_num: nat > num > option_num ).
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% 5.13/5.45 thf(sy_c_Code__Numeral_OSuc,type,
% 5.13/5.45 code_Suc: code_natural > code_natural ).
% 5.13/5.45
% 5.13/5.45 thf(sy_c_Code__Numeral_Odivmod__abs,type,
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% 5.13/5.45
% 5.13/5.45 thf(sy_c_Code__Numeral_Odivmod__integer,type,
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% 5.13/5.45
% 5.13/5.45 thf(sy_c_Code__Numeral_Ointeger_Oint__of__integer,type,
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% 5.13/5.45
% 5.13/5.45 thf(sy_c_Code__Numeral_Ointeger_Ointeger__of__int,type,
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% 5.13/5.45
% 5.13/5.45 thf(sy_c_Code__Numeral_Ointeger__of__nat,type,
% 5.13/5.45 code_integer_of_nat: nat > code_integer ).
% 5.13/5.45
% 5.13/5.45 thf(sy_c_Code__Numeral_Onat__of__integer,type,
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% 5.13/5.45
% 5.13/5.45 thf(sy_c_Code__Numeral_Onatural_Onat__of__natural,type,
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% 5.13/5.45
% 5.13/5.45 thf(sy_c_Code__Numeral_Onatural_Onatural__of__nat,type,
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% 5.13/5.45
% 5.13/5.45 thf(sy_c_Complete__Lattices_OInf__class_OInf_001t__Set__Oset_It__Nat__Onat_J,type,
% 5.13/5.45 comple7806235888213564991et_nat: set_set_nat > set_nat ).
% 5.13/5.45
% 5.13/5.45 thf(sy_c_Complete__Lattices_OSup__class_OSup_001t__Nat__Onat,type,
% 5.13/5.45 complete_Sup_Sup_nat: set_nat > nat ).
% 5.13/5.45
% 5.13/5.45 thf(sy_c_Complete__Lattices_OSup__class_OSup_001t__Set__Oset_It__Nat__Onat_J,type,
% 5.13/5.45 comple7399068483239264473et_nat: set_set_nat > set_nat ).
% 5.13/5.45
% 5.13/5.45 thf(sy_c_Complex_OArg,type,
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% 5.13/5.46 comp_C8797469213163452608nteger: ( ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( code_integer > code_integer > code_integer ) > code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ).
% 5.13/5.46
% 5.13/5.46 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,
% 5.13/5.46 comp_C1593894019821074884nteger: ( code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( code_integer > code_integer ) > code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ).
% 5.13/5.46
% 5.13/5.46 thf(sy_c_Fun_Ocomp_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat,type,
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% 5.13/5.46 thf(sy_c_Fun_Oinj__on_001t__List__Olist_It__Nat__Onat_J_001t__Nat__Onat,type,
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% 5.13/5.46 thf(sy_c_Fun_Oinj__on_001t__Nat__Onat_001t__Nat__Onat,type,
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% 5.13/5.46 thf(sy_c_Fun_Oinj__on_001t__Real__Oreal_001t__Real__Oreal,type,
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% 5.13/5.46
% 5.13/5.46 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,
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% 5.13/5.46
% 5.13/5.46 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,
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% 5.13/5.46
% 5.13/5.46 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,
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% 5.13/5.46
% 5.13/5.46 thf(sy_c_Fun_Omap__fun_001t__Rat__Orat_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001_062_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_001_062_It__Rat__Orat_Mt__Rat__Orat_J,type,
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% 5.13/5.46
% 5.13/5.46 thf(sy_c_Fun_Omap__fun_001t__Rat__Orat_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001_Eo_001_Eo,type,
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% 5.13/5.46
% 5.13/5.46 thf(sy_c_Fun_Omap__fun_001t__Real__Oreal_001_062_It__Nat__Onat_Mt__Rat__Orat_J_001_Eo_001_Eo,type,
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% 5.13/5.46 thf(sy_c_Fun_Othe__inv__into_001t__Real__Oreal_001t__Real__Oreal,type,
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% 5.31/5.46 thf(sy_c_GCD_OGcd__class_OLcm_001t__Nat__Onat,type,
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% 5.31/5.46 thf(sy_c_GCD_Obezw,type,
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% 5.31/5.46 thf(sy_c_GCD_Obezw__rel,type,
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% 5.31/5.46 thf(sy_c_GCD_Ogcd__class_Ogcd_001t__Code____Numeral__Ointeger,type,
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% 5.31/5.46 thf(sy_c_GCD_Ogcd__class_Ogcd_001t__Nat__Onat,type,
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% 5.31/5.46 thf(sy_c_GCD_Ogcd__class_Olcm_001t__Nat__Onat,type,
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% 5.31/5.46 thf(sy_c_GCD_Ogcd__nat__rel,type,
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% 5.31/5.46 thf(sy_c_GCD_Osemiring__gcd__class_OGcd__fin_001t__Int__Oint,type,
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% 5.31/5.46 thf(sy_c_Groups_Oabs__class_Oabs_001t__Int__Oint,type,
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% 5.31/5.46 thf(sy_c_Groups_Oabs__class_Oabs_001t__Rat__Orat,type,
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% 5.31/5.46 thf(sy_c_Groups_Oabs__class_Oabs_001t__Real__Oreal,type,
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% 5.31/5.46 thf(sy_c_Groups_Ominus__class_Ominus_001t__Rat__Orat,type,
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% 5.31/5.46
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% 5.31/5.46
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% 5.31/5.46
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% 5.31/5.46
% 5.31/5.46 thf(sy_c_If_001t__List__Olist_It__Nat__Onat_J,type,
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% 5.31/5.46
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% 5.31/5.46
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% 5.31/5.46
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% 5.31/5.46
% 5.31/5.46 thf(sy_c_If_001t__Option__Ooption_It__Num__Onum_J,type,
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% 5.31/5.46
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% 5.31/5.46
% 5.31/5.46 thf(sy_c_If_001t__Rat__Orat,type,
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% 5.31/5.46
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% 5.31/5.46
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% 5.31/5.46
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% 5.31/5.46
% 5.31/5.46 thf(sy_c_Int_ORep__Integ,type,
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% 5.31/5.46
% 5.31/5.46 thf(sy_c_Int_Ointrel,type,
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% 5.31/5.46
% 5.31/5.46 thf(sy_c_Int_Onat,type,
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% 5.31/5.46
% 5.31/5.46 thf(sy_c_Int_Opcr__int,type,
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% 5.31/5.46
% 5.31/5.46 thf(sy_c_Int_Oring__1__class_OInts_001t__Real__Oreal,type,
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% 5.31/5.46
% 5.31/5.46 thf(sy_c_Int_Oring__1__class_Oof__int_001t__Rat__Orat,type,
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% 5.31/5.46
% 5.31/5.46 thf(sy_c_Int_Oring__1__class_Oof__int_001t__Real__Oreal,type,
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% 5.31/5.46
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% 5.31/5.46
% 5.31/5.46 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Nat__Onat,type,
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% 5.31/5.46
% 5.31/5.46 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Rat__Orat,type,
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% 5.31/5.46
% 5.31/5.46 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__Complex__Ocomplex_J,type,
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% 5.31/5.46
% 5.31/5.46 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__Int__Oint_J,type,
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% 5.31/5.46
% 5.31/5.46 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__Nat__Onat_J,type,
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% 5.31/5.46
% 5.31/5.46 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__Num__Onum_J,type,
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% 5.31/5.46
% 5.31/5.46 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
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% 5.31/5.46
% 5.31/5.46 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__Rat__Orat_J,type,
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% 5.31/5.46
% 5.31/5.46 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__Real__Oreal_J,type,
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% 5.31/5.46
% 5.31/5.46 thf(sy_c_Lattices_Osemilattice__neutr_001t__Nat__Onat,type,
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% 5.31/5.46
% 5.31/5.46 thf(sy_c_Lattices_Osemilattice__neutr__order_001t__Nat__Onat,type,
% 5.31/5.46 semila1623282765462674594er_nat: ( nat > nat > nat ) > nat > ( nat > nat > $o ) > ( nat > nat > $o ) > $o ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Lattices_Osup__class_Osup_001t__Int__Oint,type,
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% 5.31/5.46
% 5.31/5.46 thf(sy_c_Lattices_Osup__class_Osup_001t__Nat__Onat,type,
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% 5.31/5.46
% 5.31/5.46 thf(sy_c_Lattices_Osup__class_Osup_001t__Rat__Orat,type,
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% 5.31/5.46
% 5.31/5.46 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Complex__Ocomplex_J,type,
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% 5.31/5.46
% 5.31/5.46 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Int__Oint_J,type,
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% 5.31/5.46
% 5.31/5.46 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__List__Olist_It__Nat__Onat_J_J,type,
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% 5.31/5.46
% 5.31/5.46 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Nat__Onat_J,type,
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% 5.31/5.46
% 5.31/5.46 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Num__Onum_J,type,
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% 5.31/5.46
% 5.31/5.46 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 5.31/5.46 sup_su6327502436637775413at_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Rat__Orat_J,type,
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% 5.31/5.46
% 5.31/5.46 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Real__Oreal_J,type,
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% 5.31/5.46
% 5.31/5.46 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Set__Oset_It__Nat__Onat_J_J,type,
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% 5.31/5.46
% 5.31/5.46 thf(sy_c_Lattices__Big_Olinorder__class_OMax_001t__Nat__Onat,type,
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% 5.31/5.46
% 5.31/5.46 thf(sy_c_Lattices__Big_Oord__class_Oarg__min__on_001t__Complex__Ocomplex_001t__Nat__Onat,type,
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% 5.31/5.46
% 5.31/5.46 thf(sy_c_Lattices__Big_Oord__class_Oarg__min__on_001t__Complex__Ocomplex_001t__Num__Onum,type,
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% 5.31/5.46
% 5.31/5.46 thf(sy_c_Lattices__Big_Oord__class_Oarg__min__on_001t__Complex__Ocomplex_001t__Rat__Orat,type,
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% 5.31/5.46 thf(sy_c_Lattices__Big_Oord__class_Oarg__min__on_001t__Int__Oint_001t__Rat__Orat,type,
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% 5.31/5.46
% 5.31/5.46 thf(sy_c_Lattices__Big_Oord__class_Oarg__min__on_001t__Nat__Onat_001t__Nat__Onat,type,
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% 5.31/5.46
% 5.31/5.46 thf(sy_c_Lattices__Big_Oord__class_Oarg__min__on_001t__Nat__Onat_001t__Rat__Orat,type,
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% 5.31/5.46
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% 5.31/5.46
% 5.31/5.46 thf(sy_c_Lattices__Big_Osemilattice__neutr__set_OF_001t__Nat__Onat,type,
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% 5.31/5.46
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% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Oappend_001t__Nat__Onat,type,
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% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Oconcat_001_Eo,type,
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% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Oconcat_001t__Int__Oint,type,
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% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Oconcat_001t__Nat__Onat,type,
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% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Oconcat_001t__VEBT____Definitions__OVEBT,type,
% 5.31/5.46 concat_VEBT_VEBT: list_list_VEBT_VEBT > list_VEBT_VEBT ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Ocount__list_001_Eo,type,
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% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Ocount__list_001t__Complex__Ocomplex,type,
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% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Ocount__list_001t__Int__Oint,type,
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% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Ocount__list_001t__Nat__Onat,type,
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% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Ocount__list_001t__Real__Oreal,type,
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% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Ocount__list_001t__Set__Oset_It__Nat__Onat_J,type,
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% 5.31/5.46
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% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Odistinct_001_Eo,type,
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% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Odistinct_001t__Complex__Ocomplex,type,
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% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Odistinct_001t__Int__Oint,type,
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% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Odistinct_001t__List__Olist_It__Nat__Onat_J,type,
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% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Odistinct_001t__Nat__Onat,type,
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% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Odistinct_001t__Real__Oreal,type,
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% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Odistinct_001t__Set__Oset_It__Nat__Onat_J,type,
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% 5.31/5.46
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% 5.31/5.46
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% 5.31/5.46
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% 5.31/5.46
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% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Ofind_001_Eo,type,
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% 5.31/5.46 thf(sy_c_List_Ofind_001t__Int__Oint,type,
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% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Ofind_001t__Nat__Onat,type,
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% 5.31/5.46
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% 5.31/5.46 thf(sy_c_List_Ofold_001t__Nat__Onat_001t__Nat__Onat,type,
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% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Olenlex_001_Eo,type,
% 5.31/5.46 lenlex_o: set_Product_prod_o_o > set_Pr6227168374412355847list_o ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Olenlex_001t__Code____Numeral__Ointeger,type,
% 5.31/5.46 lenlex_Code_integer: set_Pr4811707699266497531nteger > set_Pr7565137564259432987nteger ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Olenlex_001t__Int__Oint,type,
% 5.31/5.46 lenlex_int: set_Pr958786334691620121nt_int > set_Pr765067013931698361st_int ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Olenlex_001t__Nat__Onat,type,
% 5.31/5.46 lenlex_nat: set_Pr1261947904930325089at_nat > set_Pr3451248702717554689st_nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Olenlex_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 5.31/5.46 lenlex325483962726685836at_nat: set_Pr8693737435421807431at_nat > set_Pr1542805901266377927at_nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Olenlex_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 5.31/5.46 lenlex1357538814655152620at_nat: set_Pr4329608150637261639at_nat > set_Pr4333006031979791559at_nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Olenlex_001t__VEBT____Definitions__OVEBT,type,
% 5.31/5.46 lenlex_VEBT_VEBT: set_Pr6192946355708809607T_VEBT > set_Pr1916528119006554503T_VEBT ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Olex_001_Eo,type,
% 5.31/5.46 lex_o: set_Product_prod_o_o > set_Pr6227168374412355847list_o ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Olex_001t__Code____Numeral__Ointeger,type,
% 5.31/5.46 lex_Code_integer: set_Pr4811707699266497531nteger > set_Pr7565137564259432987nteger ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Olex_001t__Int__Oint,type,
% 5.31/5.46 lex_int: set_Pr958786334691620121nt_int > set_Pr765067013931698361st_int ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Olex_001t__Nat__Onat,type,
% 5.31/5.46 lex_nat: set_Pr1261947904930325089at_nat > set_Pr3451248702717554689st_nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Olex_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 5.31/5.46 lex_Pr8571645452597969515at_nat: set_Pr8693737435421807431at_nat > set_Pr1542805901266377927at_nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Olex_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 5.31/5.46 lex_se2245640040323279819at_nat: set_Pr4329608150637261639at_nat > set_Pr4333006031979791559at_nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Olex_001t__VEBT____Definitions__OVEBT,type,
% 5.31/5.46 lex_VEBT_VEBT: set_Pr6192946355708809607T_VEBT > set_Pr1916528119006554503T_VEBT ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Olinorder__class_Osorted__list__of__set_001t__Nat__Onat,type,
% 5.31/5.46 linord2614967742042102400et_nat: set_nat > list_nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Olist_OCons_001_062_It__Code____Numeral__Ointeger_Mt__Nat__Onat_J,type,
% 5.31/5.46 cons_C1897838848541180310er_nat: ( code_integer > nat ) > list_C4705013386053401436er_nat > list_C4705013386053401436er_nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Olist_OCons_001_062_It__Int__Oint_Mt__Nat__Onat_J,type,
% 5.31/5.46 cons_int_nat: ( int > nat ) > list_int_nat > list_int_nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Olist_OCons_001_062_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 5.31/5.46 cons_nat_nat: ( nat > nat ) > list_nat_nat > list_nat_nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Olist_OCons_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Nat__Onat_J,type,
% 5.31/5.46 cons_P4861729644591583992at_nat: ( product_prod_nat_nat > nat ) > list_P9162950289778280392at_nat > list_P9162950289778280392at_nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Olist_OCons_001_062_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Nat__Onat_J,type,
% 5.31/5.46 cons_s2538900923071588440at_nat: ( set_Pr1261947904930325089at_nat > nat ) > list_s9130966667114977576at_nat > list_s9130966667114977576at_nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Olist_OCons_001_Eo,type,
% 5.31/5.46 cons_o: $o > list_o > list_o ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Olist_OCons_001t__Code____Numeral__Ointeger,type,
% 5.31/5.46 cons_Code_integer: code_integer > list_Code_integer > list_Code_integer ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Olist_OCons_001t__Complex__Ocomplex,type,
% 5.31/5.46 cons_complex: complex > list_complex > list_complex ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Olist_OCons_001t__Int__Oint,type,
% 5.31/5.46 cons_int: int > list_int > list_int ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Olist_OCons_001t__Nat__Onat,type,
% 5.31/5.46 cons_nat: nat > list_nat > list_nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Olist_OCons_001t__Num__Onum,type,
% 5.31/5.46 cons_num: num > list_num > list_num ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Olist_OCons_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
% 5.31/5.46 cons_P9044669534377732177nteger: produc8923325533196201883nteger > list_P5578671422887162913nteger > list_P5578671422887162913nteger ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Olist_OCons_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 5.31/5.46 cons_P3334398858971670639nt_int: product_prod_int_int > list_P5707943133018811711nt_int > list_P5707943133018811711nt_int ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Olist_OCons_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 5.31/5.46 cons_P6512896166579812791at_nat: product_prod_nat_nat > list_P6011104703257516679at_nat > list_P6011104703257516679at_nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Olist_OCons_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 5.31/5.46 cons_P8732206157123786781at_nat: produc859450856879609959at_nat > list_P8469869581646625389at_nat > list_P8469869581646625389at_nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Olist_OCons_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
% 5.31/5.46 cons_P3940603068885512221at_nat: produc3843707927480180839at_nat > list_P5464809261938338413at_nat > list_P5464809261938338413at_nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Olist_OCons_001t__Real__Oreal,type,
% 5.31/5.46 cons_real: real > list_real > list_real ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Olist_OCons_001t__Set__Oset_It__Nat__Onat_J,type,
% 5.31/5.46 cons_set_nat: set_nat > list_set_nat > list_set_nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Olist_OCons_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 5.31/5.46 cons_s6881495754146722583at_nat: set_Pr1261947904930325089at_nat > list_s1210847774152347623at_nat > list_s1210847774152347623at_nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Olist_OCons_001t__VEBT____Definitions__OVEBT,type,
% 5.31/5.46 cons_VEBT_VEBT: vEBT_VEBT > list_VEBT_VEBT > list_VEBT_VEBT ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Olist_ONil_001t__Nat__Onat,type,
% 5.31/5.46 nil_nat: list_nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Olist_Omap_001t__Nat__Onat_001t__Nat__Onat,type,
% 5.31/5.46 map_nat_nat: ( nat > nat ) > list_nat > list_nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Olist_Omap_001t__VEBT____Definitions__OVEBT_001t__VEBT____Definitions__OVEBT,type,
% 5.31/5.46 map_VE8901447254227204932T_VEBT: ( vEBT_VEBT > vEBT_VEBT ) > list_VEBT_VEBT > list_VEBT_VEBT ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Olist_Oset_001_Eo,type,
% 5.31/5.46 set_o2: list_o > set_o ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Olist_Oset_001t__Code____Numeral__Ointeger,type,
% 5.31/5.46 set_Code_integer2: list_Code_integer > set_Code_integer ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Olist_Oset_001t__Complex__Ocomplex,type,
% 5.31/5.46 set_complex2: list_complex > set_complex ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Olist_Oset_001t__Int__Oint,type,
% 5.31/5.46 set_int2: list_int > set_int ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Olist_Oset_001t__List__Olist_I_Eo_J,type,
% 5.31/5.46 set_list_o2: list_list_o > set_list_o ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Olist_Oset_001t__List__Olist_It__Int__Oint_J,type,
% 5.31/5.46 set_list_int2: list_list_int > set_list_int ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Olist_Oset_001t__List__Olist_It__Nat__Onat_J,type,
% 5.31/5.46 set_list_nat2: list_list_nat > set_list_nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Olist_Oset_001t__List__Olist_It__VEBT____Definitions__OVEBT_J,type,
% 5.31/5.46 set_list_VEBT_VEBT2: list_list_VEBT_VEBT > set_list_VEBT_VEBT ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Olist_Oset_001t__Nat__Onat,type,
% 5.31/5.46 set_nat2: list_nat > set_nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Olist_Oset_001t__Product____Type__Oprod_I_Eo_Mt__Complex__Ocomplex_J,type,
% 5.31/5.46 set_Pr1389080609085208608omplex: list_P3924974545808530565omplex > set_Pr5421754520313593387omplex ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Olist_Oset_001t__Product____Type__Oprod_I_Eo_Mt__Real__Oreal_J,type,
% 5.31/5.46 set_Pr2600826154070092190o_real: list_P5232166724548748803o_real > set_Pr6573716822653411497o_real ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Olist_Oset_001t__Product____Type__Oprod_I_Eo_Mt__VEBT____Definitions__OVEBT_J,type,
% 5.31/5.46 set_Pr655345902815428824T_VEBT: list_P7495141550334521929T_VEBT > set_Pr7543698050874017315T_VEBT ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Olist_Oset_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
% 5.31/5.46 set_Pr920681315882439344nteger: list_P5578671422887162913nteger > set_Pr4811707699266497531nteger ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Olist_Oset_001t__Product____Type__Oprod_It__Complex__Ocomplex_M_Eo_J,type,
% 5.31/5.46 set_Pr6829704231520703882plex_o: list_P7942624414058669295plex_o > set_Pr216032351708956309plex_o ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Olist_Oset_001t__Product____Type__Oprod_It__Complex__Ocomplex_Mt__Complex__Ocomplex_J,type,
% 5.31/5.46 set_Pr8199049879907524818omplex: list_P7664491975274850627omplex > set_Pr5085853215250843933omplex ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Olist_Oset_001t__Product____Type__Oprod_It__Complex__Ocomplex_Mt__Int__Oint_J,type,
% 5.31/5.46 set_Pr4995810437751016784ex_int: list_P2206113689347244737ex_int > set_Pr2254670189886740123ex_int ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Olist_Oset_001t__Product____Type__Oprod_It__Complex__Ocomplex_Mt__Nat__Onat_J,type,
% 5.31/5.46 set_Pr9173661457260213492ex_nat: list_P4696196834278971493ex_nat > set_Pr4744753334818466879ex_nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Olist_Oset_001t__Product____Type__Oprod_It__Complex__Ocomplex_Mt__Real__Oreal_J,type,
% 5.31/5.46 set_Pr1225976482156248400x_real: list_P7647014805210017729x_real > set_Pr1133549439701694107x_real ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Olist_Oset_001t__Product____Type__Oprod_It__Complex__Ocomplex_Mt__VEBT____Definitions__OVEBT_J,type,
% 5.31/5.46 set_Pr5158653123227461798T_VEBT: list_P7977503562704621835T_VEBT > set_Pr4085867452638698417T_VEBT ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Olist_Oset_001t__Product____Type__Oprod_It__Int__Oint_Mt__Complex__Ocomplex_J,type,
% 5.31/5.46 set_Pr3989287306472219216omplex: list_P1797514011394873281omplex > set_Pr1846070511934368667omplex ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Olist_Oset_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 5.31/5.46 set_Pr2470121279949933262nt_int: list_P5707943133018811711nt_int > set_Pr958786334691620121nt_int ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Olist_Oset_001t__Product____Type__Oprod_It__Int__Oint_Mt__Real__Oreal_J,type,
% 5.31/5.46 set_Pr112895574167722958t_real: list_P6863124054624500543t_real > set_Pr3538720872664544793t_real ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Olist_Oset_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 5.31/5.46 set_Pr5648618587558075414at_nat: list_P6011104703257516679at_nat > set_Pr1261947904930325089at_nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Olist_Oset_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 5.31/5.46 set_Pr5518436109238095868at_nat: list_P8469869581646625389at_nat > set_Pr8693737435421807431at_nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Olist_Oset_001t__Product____Type__Oprod_It__Real__Oreal_M_Eo_J,type,
% 5.31/5.46 set_Pr5196769464307566348real_o: list_P3595434254542482545real_o > set_Pr4936984352647145239real_o ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Olist_Oset_001t__Product____Type__Oprod_It__Real__Oreal_Mt__Complex__Ocomplex_J,type,
% 5.31/5.46 set_Pr8536649499196266448omplex: list_P3881527313128557121omplex > set_Pr6591433984475009307omplex ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Olist_Oset_001t__Product____Type__Oprod_It__Real__Oreal_Mt__Int__Oint_J,type,
% 5.31/5.46 set_Pr8219819362198175822al_int: list_P4344331454722006975al_int > set_Pr1019928272762051225al_int ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Olist_Oset_001t__Product____Type__Oprod_It__Real__Oreal_Mt__Nat__Onat_J,type,
% 5.31/5.46 set_Pr3174298344852596722al_nat: list_P6834414599653733731al_nat > set_Pr3510011417693777981al_nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Olist_Oset_001t__Product____Type__Oprod_It__Real__Oreal_Mt__Real__Oreal_J,type,
% 5.31/5.46 set_Pr5999470521830281550l_real: list_P8689742595348180415l_real > set_Pr6218003697084177305l_real ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Olist_Oset_001t__Product____Type__Oprod_It__Real__Oreal_Mt__VEBT____Definitions__OVEBT_J,type,
% 5.31/5.46 set_Pr8897343066327330088T_VEBT: list_P877281246627933069T_VEBT > set_Pr6019664923565264691T_VEBT ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Olist_Oset_001t__Product____Type__Oprod_It__Set__Oset_It__Nat__Onat_J_Mt__Set__Oset_It__Nat__Onat_J_J,type,
% 5.31/5.46 set_Pr9040384385603167362et_nat: list_P6254988961118846195et_nat > set_Pr5488025237498180813et_nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Olist_Oset_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
% 5.31/5.46 set_Pr3765526544606949372at_nat: list_P5464809261938338413at_nat > set_Pr4329608150637261639at_nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Olist_Oset_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_M_Eo_J,type,
% 5.31/5.46 set_Pr7708085864119495200VEBT_o: list_P3126845725202233233VEBT_o > set_Pr3175402225741728619VEBT_o ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Olist_Oset_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Complex__Ocomplex_J,type,
% 5.31/5.46 set_Pr6387300694196750780omplex: list_P4108580160459392801omplex > set_Pr216944050393469383omplex ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Olist_Oset_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Int__Oint_J,type,
% 5.31/5.46 set_Pr2853735649769556538BT_int: list_P4547456442757143711BT_int > set_Pr5066593544530342725BT_int ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Olist_Oset_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Nat__Onat_J,type,
% 5.31/5.46 set_Pr7031586669278753246BT_nat: list_P7037539587688870467BT_nat > set_Pr7556676689462069481BT_nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Olist_Oset_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Real__Oreal_J,type,
% 5.31/5.46 set_Pr1087130671499945274T_real: list_P2623026923184700063T_real > set_Pr7765410600122031685T_real ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Olist_Oset_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__VEBT____Definitions__OVEBT_J,type,
% 5.31/5.46 set_Pr9182192707038809660T_VEBT: list_P7413028617227757229T_VEBT > set_Pr6192946355708809607T_VEBT ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Olist_Oset_001t__Real__Oreal,type,
% 5.31/5.46 set_real2: list_real > set_real ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Olist_Oset_001t__Set__Oset_It__Nat__Onat_J,type,
% 5.31/5.46 set_set_nat2: list_set_nat > set_set_nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Olist_Oset_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 5.31/5.46 set_se5049602875457034614at_nat: list_s1210847774152347623at_nat > set_se7855581050983116737at_nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Olist_Oset_001t__VEBT____Definitions__OVEBT,type,
% 5.31/5.46 set_VEBT_VEBT2: list_VEBT_VEBT > set_VEBT_VEBT ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Olist_Osize__list_001t__Typerep__Otyperep,type,
% 5.31/5.46 size_list_typerep: ( typerep > nat ) > list_typerep > nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Olist_Osize__list_001t__VEBT____Definitions__OVEBT,type,
% 5.31/5.46 size_list_VEBT_VEBT: ( vEBT_VEBT > nat ) > list_VEBT_VEBT > nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Olist_Otl_001t__Nat__Onat,type,
% 5.31/5.46 tl_nat: list_nat > list_nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Olist__update_001_Eo,type,
% 5.31/5.46 list_update_o: list_o > nat > $o > list_o ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Olist__update_001t__Code____Numeral__Ointeger,type,
% 5.31/5.46 list_u5447711078246177391nteger: list_Code_integer > nat > code_integer > list_Code_integer ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Olist__update_001t__Complex__Ocomplex,type,
% 5.31/5.46 list_update_complex: list_complex > nat > complex > list_complex ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Olist__update_001t__Int__Oint,type,
% 5.31/5.46 list_update_int: list_int > nat > int > list_int ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Olist__update_001t__Nat__Onat,type,
% 5.31/5.46 list_update_nat: list_nat > nat > nat > list_nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Olist__update_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
% 5.31/5.46 list_u2254550707601501961nteger: list_P5578671422887162913nteger > nat > produc8923325533196201883nteger > list_P5578671422887162913nteger ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Olist__update_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 5.31/5.46 list_u3002344382305578791nt_int: list_P5707943133018811711nt_int > nat > product_prod_int_int > list_P5707943133018811711nt_int ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Olist__update_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 5.31/5.46 list_u6180841689913720943at_nat: list_P6011104703257516679at_nat > nat > product_prod_nat_nat > list_P6011104703257516679at_nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Olist__update_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 5.31/5.46 list_u5003261594476800725at_nat: list_P8469869581646625389at_nat > nat > produc859450856879609959at_nat > list_P8469869581646625389at_nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Olist__update_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
% 5.31/5.46 list_u4696772448584712917at_nat: list_P5464809261938338413at_nat > nat > produc3843707927480180839at_nat > list_P5464809261938338413at_nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Olist__update_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__VEBT____Definitions__OVEBT_J,type,
% 5.31/5.46 list_u6961636818849549845T_VEBT: list_P7413028617227757229T_VEBT > nat > produc8243902056947475879T_VEBT > list_P7413028617227757229T_VEBT ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Olist__update_001t__Real__Oreal,type,
% 5.31/5.46 list_update_real: list_real > nat > real > list_real ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Olist__update_001t__Set__Oset_It__Nat__Onat_J,type,
% 5.31/5.46 list_update_set_nat: list_set_nat > nat > set_nat > list_set_nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Olist__update_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 5.31/5.46 list_u8444657558853818831at_nat: list_s1210847774152347623at_nat > nat > set_Pr1261947904930325089at_nat > list_s1210847774152347623at_nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Olist__update_001t__VEBT____Definitions__OVEBT,type,
% 5.31/5.46 list_u1324408373059187874T_VEBT: list_VEBT_VEBT > nat > vEBT_VEBT > list_VEBT_VEBT ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Olistrel_001_Eo_001_Eo,type,
% 5.31/5.46 listrel_o_o: set_Product_prod_o_o > set_Pr6227168374412355847list_o ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Olistrel_001_Eo_001t__Int__Oint,type,
% 5.31/5.46 listrel_o_int: set_Pr8834758594704517033_o_int > set_Pr5001190662893202239st_int ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Olistrel_001_Eo_001t__Nat__Onat,type,
% 5.31/5.46 listrel_o_nat: set_Pr2101469702781467981_o_nat > set_Pr591367044826345187st_nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Olistrel_001_Eo_001t__VEBT____Definitions__OVEBT,type,
% 5.31/5.46 listrel_o_VEBT_VEBT: set_Pr7543698050874017315T_VEBT > set_Pr5170412164475753123T_VEBT ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Olistrel_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger,type,
% 5.31/5.46 listre5734910445319291053nteger: set_Pr4811707699266497531nteger > set_Pr7565137564259432987nteger ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Olistrel_001t__Int__Oint_001t__Int__Oint,type,
% 5.31/5.46 listrel_int_int: set_Pr958786334691620121nt_int > set_Pr765067013931698361st_int ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Olistrel_001t__Nat__Onat_001_Eo,type,
% 5.31/5.46 listrel_nat_o: set_Pr3149072824959771635_nat_o > set_Pr1150278048023938153list_o ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Olistrel_001t__Nat__Onat_001t__Nat__Onat,type,
% 5.31/5.46 listrel_nat_nat: set_Pr1261947904930325089at_nat > set_Pr3451248702717554689st_nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Olistrel_001t__Nat__Onat_001t__VEBT____Definitions__OVEBT,type,
% 5.31/5.46 listre5761932458788874033T_VEBT: set_Pr6167073792073659919T_VEBT > set_Pr1262583345697558789T_VEBT ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Olistrel_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 5.31/5.46 listre818007680106770737at_nat: set_Pr8693737435421807431at_nat > set_Pr1542805901266377927at_nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Olistrel_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 5.31/5.46 listre2047417242196832561at_nat: set_Pr4329608150637261639at_nat > set_Pr4333006031979791559at_nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Olistrel_001t__VEBT____Definitions__OVEBT_001_Eo,type,
% 5.31/5.46 listrel_VEBT_VEBT_o: set_Pr3175402225741728619VEBT_o > set_Pr7508168486584781291list_o ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Olistrel_001t__VEBT____Definitions__OVEBT_001t__Int__Oint,type,
% 5.31/5.46 listre5898179758603845167BT_int: set_Pr5066593544530342725BT_int > set_Pr4080907618048478043st_int ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Olistrel_001t__VEBT____Definitions__OVEBT_001t__Nat__Onat,type,
% 5.31/5.46 listre5900670229112895443BT_nat: set_Pr7556676689462069481BT_nat > set_Pr8894456036836396799st_nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Olistrel_001t__VEBT____Definitions__OVEBT_001t__VEBT____Definitions__OVEBT,type,
% 5.31/5.46 listre1230615542750757617T_VEBT: set_Pr6192946355708809607T_VEBT > set_Pr1916528119006554503T_VEBT ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Omeasures_001t__Code____Numeral__Ointeger,type,
% 5.31/5.46 measur8870801148506250077nteger: list_C4705013386053401436er_nat > set_Pr4811707699266497531nteger ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Omeasures_001t__Int__Oint,type,
% 5.31/5.46 measures_int: list_int_nat > set_Pr958786334691620121nt_int ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Omeasures_001t__Nat__Onat,type,
% 5.31/5.46 measures_nat: list_nat_nat > set_Pr1261947904930325089at_nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Omeasures_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 5.31/5.46 measur2679027848233739777at_nat: list_P9162950289778280392at_nat > set_Pr8693737435421807431at_nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Omeasures_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 5.31/5.46 measur2694323259624372065at_nat: list_s9130966667114977576at_nat > set_Pr4329608150637261639at_nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Onth_001_Eo,type,
% 5.31/5.46 nth_o: list_o > nat > $o ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Onth_001t__Code____Numeral__Ointeger,type,
% 5.31/5.46 nth_Code_integer: list_Code_integer > nat > code_integer ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Onth_001t__Complex__Ocomplex,type,
% 5.31/5.46 nth_complex: list_complex > nat > complex ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Onth_001t__Int__Oint,type,
% 5.31/5.46 nth_int: list_int > nat > int ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Onth_001t__Nat__Onat,type,
% 5.31/5.46 nth_nat: list_nat > nat > nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Onth_001t__Num__Onum,type,
% 5.31/5.46 nth_num: list_num > nat > num ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Onth_001t__Product____Type__Oprod_I_Eo_M_Eo_J,type,
% 5.31/5.46 nth_Product_prod_o_o: list_P4002435161011370285od_o_o > nat > product_prod_o_o ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Onth_001t__Product____Type__Oprod_I_Eo_Mt__Int__Oint_J,type,
% 5.31/5.46 nth_Pr1649062631805364268_o_int: list_P3795440434834930179_o_int > nat > product_prod_o_int ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Onth_001t__Product____Type__Oprod_I_Eo_Mt__Nat__Onat_J,type,
% 5.31/5.46 nth_Pr5826913651314560976_o_nat: list_P6285523579766656935_o_nat > nat > product_prod_o_nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Onth_001t__Product____Type__Oprod_I_Eo_Mt__VEBT____Definitions__OVEBT_J,type,
% 5.31/5.46 nth_Pr6777367263587873994T_VEBT: list_P7495141550334521929T_VEBT > nat > produc2504756804600209347T_VEBT ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
% 5.31/5.46 nth_Pr2304437835452373666nteger: list_P5578671422887162913nteger > nat > produc8923325533196201883nteger ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__Nat__Onat_M_Eo_J,type,
% 5.31/5.46 nth_Pr112076138515278198_nat_o: list_P7333126701944960589_nat_o > nat > product_prod_nat_o ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Int__Oint_J,type,
% 5.31/5.46 nth_Pr3440142176431000676at_int: list_P3521021558325789923at_int > nat > product_prod_nat_int ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 5.31/5.46 nth_Pr7617993195940197384at_nat: list_P6011104703257516679at_nat > nat > product_prod_nat_nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__Nat__Onat_Mt__VEBT____Definitions__OVEBT_J,type,
% 5.31/5.46 nth_Pr744662078594809490T_VEBT: list_P5647936690300460905T_VEBT > nat > produc8025551001238799321T_VEBT ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_M_Eo_J,type,
% 5.31/5.46 nth_Pr4606735188037164562VEBT_o: list_P3126845725202233233VEBT_o > nat > produc334124729049499915VEBT_o ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Int__Oint_J,type,
% 5.31/5.46 nth_Pr6837108013167703752BT_int: list_P4547456442757143711BT_int > nat > produc4894624898956917775BT_int ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Nat__Onat_J,type,
% 5.31/5.46 nth_Pr1791586995822124652BT_nat: list_P7037539587688870467BT_nat > nat > produc9072475918466114483BT_nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__VEBT____Definitions__OVEBT_J,type,
% 5.31/5.46 nth_Pr4953567300277697838T_VEBT: list_P7413028617227757229T_VEBT > nat > produc8243902056947475879T_VEBT ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Onth_001t__Real__Oreal,type,
% 5.31/5.46 nth_real: list_real > nat > real ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Onth_001t__Set__Oset_It__Nat__Onat_J,type,
% 5.31/5.46 nth_set_nat: list_set_nat > nat > set_nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Onth_001t__VEBT____Definitions__OVEBT,type,
% 5.31/5.46 nth_VEBT_VEBT: list_VEBT_VEBT > nat > vEBT_VEBT ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Oproduct_001_Eo_001_Eo,type,
% 5.31/5.46 product_o_o: list_o > list_o > list_P4002435161011370285od_o_o ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Oproduct_001_Eo_001t__Int__Oint,type,
% 5.31/5.46 product_o_int: list_o > list_int > list_P3795440434834930179_o_int ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Oproduct_001_Eo_001t__Nat__Onat,type,
% 5.31/5.46 product_o_nat: list_o > list_nat > list_P6285523579766656935_o_nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Oproduct_001_Eo_001t__VEBT____Definitions__OVEBT,type,
% 5.31/5.46 product_o_VEBT_VEBT: list_o > list_VEBT_VEBT > list_P7495141550334521929T_VEBT ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Oproduct_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger,type,
% 5.31/5.46 produc8792966785426426881nteger: list_Code_integer > list_Code_integer > list_P5578671422887162913nteger ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Oproduct_001t__Nat__Onat_001_Eo,type,
% 5.31/5.46 product_nat_o: list_nat > list_o > list_P7333126701944960589_nat_o ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Oproduct_001t__Nat__Onat_001t__VEBT____Definitions__OVEBT,type,
% 5.31/5.46 produc7156399406898700509T_VEBT: list_nat > list_VEBT_VEBT > list_P5647936690300460905T_VEBT ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Oproduct_001t__VEBT____Definitions__OVEBT_001_Eo,type,
% 5.31/5.46 product_VEBT_VEBT_o: list_VEBT_VEBT > list_o > list_P3126845725202233233VEBT_o ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Oproduct_001t__VEBT____Definitions__OVEBT_001t__Int__Oint,type,
% 5.31/5.46 produc7292646706713671643BT_int: list_VEBT_VEBT > list_int > list_P4547456442757143711BT_int ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Oproduct_001t__VEBT____Definitions__OVEBT_001t__Nat__Onat,type,
% 5.31/5.46 produc7295137177222721919BT_nat: list_VEBT_VEBT > list_nat > list_P7037539587688870467BT_nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Oproduct_001t__VEBT____Definitions__OVEBT_001t__VEBT____Definitions__OVEBT,type,
% 5.31/5.46 produc4743750530478302277T_VEBT: list_VEBT_VEBT > list_VEBT_VEBT > list_P7413028617227757229T_VEBT ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Oproduct__lists_001_Eo,type,
% 5.31/5.46 product_lists_o: list_list_o > list_list_o ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Oproduct__lists_001t__Int__Oint,type,
% 5.31/5.46 product_lists_int: list_list_int > list_list_int ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Oproduct__lists_001t__Nat__Onat,type,
% 5.31/5.46 product_lists_nat: list_list_nat > list_list_nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Oproduct__lists_001t__VEBT____Definitions__OVEBT,type,
% 5.31/5.46 produc3021084454716106787T_VEBT: list_list_VEBT_VEBT > list_list_VEBT_VEBT ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Oreplicate_001_Eo,type,
% 5.31/5.46 replicate_o: nat > $o > list_o ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Oreplicate_001t__Complex__Ocomplex,type,
% 5.31/5.46 replicate_complex: nat > complex > list_complex ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Oreplicate_001t__Int__Oint,type,
% 5.31/5.46 replicate_int: nat > int > list_int ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Oreplicate_001t__Nat__Onat,type,
% 5.31/5.46 replicate_nat: nat > nat > list_nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Oreplicate_001t__Real__Oreal,type,
% 5.31/5.46 replicate_real: nat > real > list_real ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Oreplicate_001t__Set__Oset_It__Nat__Onat_J,type,
% 5.31/5.46 replicate_set_nat: nat > set_nat > list_set_nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Oreplicate_001t__VEBT____Definitions__OVEBT,type,
% 5.31/5.46 replicate_VEBT_VEBT: nat > vEBT_VEBT > list_VEBT_VEBT ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Orotate1_001_Eo,type,
% 5.31/5.46 rotate1_o: list_o > list_o ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Orotate1_001t__Int__Oint,type,
% 5.31/5.46 rotate1_int: list_int > list_int ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Orotate1_001t__Nat__Onat,type,
% 5.31/5.46 rotate1_nat: list_nat > list_nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Orotate1_001t__VEBT____Definitions__OVEBT,type,
% 5.31/5.46 rotate1_VEBT_VEBT: list_VEBT_VEBT > list_VEBT_VEBT ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Osorted__wrt_001t__Nat__Onat,type,
% 5.31/5.46 sorted_wrt_nat: ( nat > nat > $o ) > list_nat > $o ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Otake_001t__Nat__Onat,type,
% 5.31/5.46 take_nat: nat > list_nat > list_nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Otake_001t__VEBT____Definitions__OVEBT,type,
% 5.31/5.46 take_VEBT_VEBT: nat > list_VEBT_VEBT > list_VEBT_VEBT ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Oupt,type,
% 5.31/5.46 upt: nat > nat > list_nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Oupto,type,
% 5.31/5.46 upto: int > int > list_int ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Ozip_001_Eo_001_Eo,type,
% 5.31/5.46 zip_o_o: list_o > list_o > list_P4002435161011370285od_o_o ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Ozip_001_Eo_001t__Complex__Ocomplex,type,
% 5.31/5.46 zip_o_complex: list_o > list_complex > list_P3924974545808530565omplex ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Ozip_001_Eo_001t__Int__Oint,type,
% 5.31/5.46 zip_o_int: list_o > list_int > list_P3795440434834930179_o_int ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Ozip_001_Eo_001t__Nat__Onat,type,
% 5.31/5.46 zip_o_nat: list_o > list_nat > list_P6285523579766656935_o_nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Ozip_001_Eo_001t__Real__Oreal,type,
% 5.31/5.46 zip_o_real: list_o > list_real > list_P5232166724548748803o_real ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Ozip_001_Eo_001t__VEBT____Definitions__OVEBT,type,
% 5.31/5.46 zip_o_VEBT_VEBT: list_o > list_VEBT_VEBT > list_P7495141550334521929T_VEBT ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Ozip_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger,type,
% 5.31/5.46 zip_Co3543743374963494515nteger: list_Code_integer > list_Code_integer > list_P5578671422887162913nteger ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Ozip_001t__Complex__Ocomplex_001_Eo,type,
% 5.31/5.46 zip_complex_o: list_complex > list_o > list_P7942624414058669295plex_o ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Ozip_001t__Complex__Ocomplex_001t__Complex__Ocomplex,type,
% 5.31/5.46 zip_complex_complex: list_complex > list_complex > list_P7664491975274850627omplex ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Ozip_001t__Complex__Ocomplex_001t__Int__Oint,type,
% 5.31/5.46 zip_complex_int: list_complex > list_int > list_P2206113689347244737ex_int ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Ozip_001t__Complex__Ocomplex_001t__Nat__Onat,type,
% 5.31/5.46 zip_complex_nat: list_complex > list_nat > list_P4696196834278971493ex_nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Ozip_001t__Complex__Ocomplex_001t__Real__Oreal,type,
% 5.31/5.46 zip_complex_real: list_complex > list_real > list_P7647014805210017729x_real ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Ozip_001t__Complex__Ocomplex_001t__VEBT____Definitions__OVEBT,type,
% 5.31/5.46 zip_co9157518722488180109T_VEBT: list_complex > list_VEBT_VEBT > list_P7977503562704621835T_VEBT ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Ozip_001t__Int__Oint_001t__Complex__Ocomplex,type,
% 5.31/5.46 zip_int_complex: list_int > list_complex > list_P1797514011394873281omplex ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Ozip_001t__Int__Oint_001t__Int__Oint,type,
% 5.31/5.46 zip_int_int: list_int > list_int > list_P5707943133018811711nt_int ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Ozip_001t__Int__Oint_001t__Real__Oreal,type,
% 5.31/5.46 zip_int_real: list_int > list_real > list_P6863124054624500543t_real ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Ozip_001t__Nat__Onat_001t__Nat__Onat,type,
% 5.31/5.46 zip_nat_nat: list_nat > list_nat > list_P6011104703257516679at_nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Ozip_001t__Nat__Onat_001t__VEBT____Definitions__OVEBT,type,
% 5.31/5.46 zip_nat_VEBT_VEBT: list_nat > list_VEBT_VEBT > list_P5647936690300460905T_VEBT ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Ozip_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 5.31/5.46 zip_Pr4664179122662387191at_nat: list_P6011104703257516679at_nat > list_P6011104703257516679at_nat > list_P8469869581646625389at_nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Ozip_001t__Real__Oreal_001_Eo,type,
% 5.31/5.46 zip_real_o: list_real > list_o > list_P3595434254542482545real_o ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Ozip_001t__Real__Oreal_001t__Complex__Ocomplex,type,
% 5.31/5.46 zip_real_complex: list_real > list_complex > list_P3881527313128557121omplex ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Ozip_001t__Real__Oreal_001t__Int__Oint,type,
% 5.31/5.46 zip_real_int: list_real > list_int > list_P4344331454722006975al_int ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Ozip_001t__Real__Oreal_001t__Nat__Onat,type,
% 5.31/5.46 zip_real_nat: list_real > list_nat > list_P6834414599653733731al_nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Ozip_001t__Real__Oreal_001t__Real__Oreal,type,
% 5.31/5.46 zip_real_real: list_real > list_real > list_P8689742595348180415l_real ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Ozip_001t__Real__Oreal_001t__VEBT____Definitions__OVEBT,type,
% 5.31/5.46 zip_real_VEBT_VEBT: list_real > list_VEBT_VEBT > list_P877281246627933069T_VEBT ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Ozip_001t__Set__Oset_It__Nat__Onat_J_001t__Set__Oset_It__Nat__Onat_J,type,
% 5.31/5.46 zip_set_nat_set_nat: list_set_nat > list_set_nat > list_P6254988961118846195et_nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Ozip_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 5.31/5.46 zip_se5600341670672612855at_nat: list_s1210847774152347623at_nat > list_s1210847774152347623at_nat > list_P5464809261938338413at_nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Ozip_001t__VEBT____Definitions__OVEBT_001_Eo,type,
% 5.31/5.46 zip_VEBT_VEBT_o: list_VEBT_VEBT > list_o > list_P3126845725202233233VEBT_o ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Ozip_001t__VEBT____Definitions__OVEBT_001t__Complex__Ocomplex,type,
% 5.31/5.46 zip_VE2794733401258833515omplex: list_VEBT_VEBT > list_complex > list_P4108580160459392801omplex ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Ozip_001t__VEBT____Definitions__OVEBT_001t__Int__Oint,type,
% 5.31/5.46 zip_VEBT_VEBT_int: list_VEBT_VEBT > list_int > list_P4547456442757143711BT_int ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Ozip_001t__VEBT____Definitions__OVEBT_001t__Nat__Onat,type,
% 5.31/5.46 zip_VEBT_VEBT_nat: list_VEBT_VEBT > list_nat > list_P7037539587688870467BT_nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Ozip_001t__VEBT____Definitions__OVEBT_001t__Real__Oreal,type,
% 5.31/5.46 zip_VEBT_VEBT_real: list_VEBT_VEBT > list_real > list_P2623026923184700063T_real ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_List_Ozip_001t__VEBT____Definitions__OVEBT_001t__VEBT____Definitions__OVEBT,type,
% 5.31/5.46 zip_VE537291747668921783T_VEBT: list_VEBT_VEBT > list_VEBT_VEBT > list_P7413028617227757229T_VEBT ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Nat_OSuc,type,
% 5.31/5.46 suc: nat > nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Nat_Ocompow_001_062_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 5.31/5.46 compow_nat_nat: nat > ( nat > nat ) > nat > nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Nat_Onat_Ocase__nat_001_Eo,type,
% 5.31/5.46 case_nat_o: $o > ( nat > $o ) > nat > $o ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Nat_Onat_Ocase__nat_001t__Nat__Onat,type,
% 5.31/5.46 case_nat_nat: nat > ( nat > nat ) > nat > nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Nat_Onat_Opred,type,
% 5.31/5.46 pred: nat > nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Code____Numeral__Ointeger,type,
% 5.31/5.46 semiri4939895301339042750nteger: nat > code_integer ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Code____Numeral__Onatural,type,
% 5.31/5.46 semiri3763490453095760265atural: nat > code_natural ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Complex__Ocomplex,type,
% 5.31/5.46 semiri8010041392384452111omplex: nat > complex ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Extended____Nat__Oenat,type,
% 5.31/5.46 semiri4216267220026989637d_enat: nat > extended_enat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Int__Oint,type,
% 5.31/5.46 semiri1314217659103216013at_int: nat > int ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Nat__Onat,type,
% 5.31/5.46 semiri1316708129612266289at_nat: nat > nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Rat__Orat,type,
% 5.31/5.46 semiri681578069525770553at_rat: nat > rat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Real__Oreal,type,
% 5.31/5.46 semiri5074537144036343181t_real: nat > real ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Nat_Osemiring__1__class_Oof__nat__aux_001t__Code____Numeral__Ointeger,type,
% 5.31/5.46 semiri4055485073559036834nteger: ( code_integer > code_integer ) > nat > code_integer > code_integer ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Nat_Osemiring__1__class_Oof__nat__aux_001t__Complex__Ocomplex,type,
% 5.31/5.46 semiri2816024913162550771omplex: ( complex > complex ) > nat > complex > complex ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Nat_Osemiring__1__class_Oof__nat__aux_001t__Int__Oint,type,
% 5.31/5.46 semiri8420488043553186161ux_int: ( int > int ) > nat > int > int ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Nat_Osemiring__1__class_Oof__nat__aux_001t__Nat__Onat,type,
% 5.31/5.46 semiri8422978514062236437ux_nat: ( nat > nat ) > nat > nat > nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Nat_Osemiring__1__class_Oof__nat__aux_001t__Rat__Orat,type,
% 5.31/5.46 semiri7787848453975740701ux_rat: ( rat > rat ) > nat > rat > rat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Nat_Osemiring__1__class_Oof__nat__aux_001t__Real__Oreal,type,
% 5.31/5.46 semiri7260567687927622513x_real: ( real > real ) > nat > real > real ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_I_Eo_J,type,
% 5.31/5.46 size_size_list_o: list_o > nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Code____Numeral__Ointeger_J,type,
% 5.31/5.46 size_s3445333598471063425nteger: list_Code_integer > nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Complex__Ocomplex_J,type,
% 5.31/5.46 size_s3451745648224563538omplex: list_complex > nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Int__Oint_J,type,
% 5.31/5.46 size_size_list_int: list_int > nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__List__Olist_I_Eo_J_J,type,
% 5.31/5.46 size_s2710708370519433104list_o: list_list_o > nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__List__Olist_It__Int__Oint_J_J,type,
% 5.31/5.46 size_s533118279054570080st_int: list_list_int > nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__List__Olist_It__Nat__Onat_J_J,type,
% 5.31/5.46 size_s3023201423986296836st_nat: list_list_nat > nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__List__Olist_It__VEBT____Definitions__OVEBT_J_J,type,
% 5.31/5.46 size_s8217280938318005548T_VEBT: list_list_VEBT_VEBT > nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Nat__Onat_J,type,
% 5.31/5.46 size_size_list_nat: list_nat > nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Num__Onum_J,type,
% 5.31/5.46 size_size_list_num: list_num > nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_I_Eo_M_Eo_J_J,type,
% 5.31/5.46 size_s1515746228057227161od_o_o: list_P4002435161011370285od_o_o > nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_I_Eo_Mt__Int__Oint_J_J,type,
% 5.31/5.46 size_s2953683556165314199_o_int: list_P3795440434834930179_o_int > nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_I_Eo_Mt__Nat__Onat_J_J,type,
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% 5.31/5.46
% 5.31/5.46 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_I_Eo_Mt__VEBT____Definitions__OVEBT_J_J,type,
% 5.31/5.46 size_s4313452262239582901T_VEBT: list_P7495141550334521929T_VEBT > nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__Nat__Onat_M_Eo_J_J,type,
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% 5.31/5.46
% 5.31/5.46 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__Nat__Onat_Mt__Int__Oint_J_J,type,
% 5.31/5.46 size_s2970893825323803983at_int: list_P3521021558325789923at_int > nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 5.31/5.46 size_s5460976970255530739at_nat: list_P6011104703257516679at_nat > nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__Nat__Onat_Mt__VEBT____Definitions__OVEBT_J_J,type,
% 5.31/5.46 size_s4762443039079500285T_VEBT: list_P5647936690300460905T_VEBT > nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_M_Eo_J_J,type,
% 5.31/5.46 size_s9168528473962070013VEBT_o: list_P3126845725202233233VEBT_o > nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Int__Oint_J_J,type,
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% 5.31/5.46
% 5.31/5.46 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Nat__Onat_J_J,type,
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% 5.31/5.46
% 5.31/5.46 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,
% 5.31/5.46 size_s7466405169056248089T_VEBT: list_P7413028617227757229T_VEBT > nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Real__Oreal_J,type,
% 5.31/5.46 size_size_list_real: list_real > nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Set__Oset_It__Nat__Onat_J_J,type,
% 5.31/5.46 size_s3254054031482475050et_nat: list_set_nat > nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
% 5.31/5.46 size_s8736152011456118867at_nat: list_s1210847774152347623at_nat > nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__VEBT____Definitions__OVEBT_J,type,
% 5.31/5.46 size_s6755466524823107622T_VEBT: list_VEBT_VEBT > nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Nat_Osize__class_Osize_001t__Num__Onum,type,
% 5.31/5.46 size_size_num: num > nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Nat_Osize__class_Osize_001t__Option__Ooption_It__Nat__Onat_J,type,
% 5.31/5.46 size_size_option_nat: option_nat > nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Nat_Osize__class_Osize_001t__Option__Ooption_It__Num__Onum_J,type,
% 5.31/5.46 size_size_option_num: option_num > nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Nat_Osize__class_Osize_001t__Option__Ooption_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 5.31/5.46 size_s170228958280169651at_nat: option4927543243414619207at_nat > nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Nat_Osize__class_Osize_001t__String__Ochar,type,
% 5.31/5.46 size_size_char: char > nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Nat_Osize__class_Osize_001t__Typerep__Otyperep,type,
% 5.31/5.46 size_size_typerep: typerep > nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Nat_Osize__class_Osize_001t__VEBT____Definitions__OVEBT,type,
% 5.31/5.46 size_size_VEBT_VEBT: vEBT_VEBT > nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Nat__Bijection_Oint__decode,type,
% 5.31/5.46 nat_int_decode: nat > int ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Nat__Bijection_Oint__encode,type,
% 5.31/5.46 nat_int_encode: int > nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Nat__Bijection_Olist__decode,type,
% 5.31/5.46 nat_list_decode: nat > list_nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Nat__Bijection_Olist__decode__rel,type,
% 5.31/5.46 nat_list_decode_rel: nat > nat > $o ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Nat__Bijection_Olist__encode,type,
% 5.31/5.46 nat_list_encode: list_nat > nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Nat__Bijection_Olist__encode__rel,type,
% 5.31/5.46 nat_list_encode_rel: list_nat > list_nat > $o ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Nat__Bijection_Oprod__decode,type,
% 5.31/5.46 nat_prod_decode: nat > product_prod_nat_nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Nat__Bijection_Oprod__decode__aux,type,
% 5.31/5.46 nat_prod_decode_aux: nat > nat > product_prod_nat_nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Nat__Bijection_Oprod__decode__aux__rel,type,
% 5.31/5.46 nat_pr5047031295181774490ux_rel: product_prod_nat_nat > product_prod_nat_nat > $o ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Nat__Bijection_Oprod__encode,type,
% 5.31/5.46 nat_prod_encode: product_prod_nat_nat > nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Nat__Bijection_Oset__decode,type,
% 5.31/5.46 nat_set_decode: nat > set_nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Nat__Bijection_Oset__encode,type,
% 5.31/5.46 nat_set_encode: set_nat > nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Nat__Bijection_Osum__decode,type,
% 5.31/5.46 nat_sum_decode: nat > sum_sum_nat_nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Nat__Bijection_Osum__encode,type,
% 5.31/5.46 nat_sum_encode: sum_sum_nat_nat > nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Nat__Bijection_Otriangle,type,
% 5.31/5.46 nat_triangle: nat > nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_NthRoot_Oroot,type,
% 5.31/5.46 root: nat > real > real ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_NthRoot_Osqrt,type,
% 5.31/5.46 sqrt: real > real ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Num_OBitM,type,
% 5.31/5.46 bitM: num > num ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Num_Oinc,type,
% 5.31/5.46 inc: num > num ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Num_Onat__of__num,type,
% 5.31/5.46 nat_of_num: num > nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Num_Oneg__numeral__class_Odbl_001t__Code____Numeral__Ointeger,type,
% 5.31/5.46 neg_nu8804712462038260780nteger: code_integer > code_integer ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Num_Oneg__numeral__class_Odbl_001t__Complex__Ocomplex,type,
% 5.31/5.46 neg_nu7009210354673126013omplex: complex > complex ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Num_Oneg__numeral__class_Odbl_001t__Int__Oint,type,
% 5.31/5.46 neg_numeral_dbl_int: int > int ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Num_Oneg__numeral__class_Odbl_001t__Rat__Orat,type,
% 5.31/5.46 neg_numeral_dbl_rat: rat > rat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Num_Oneg__numeral__class_Odbl_001t__Real__Oreal,type,
% 5.31/5.46 neg_numeral_dbl_real: real > real ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Num_Oneg__numeral__class_Odbl__dec_001t__Code____Numeral__Ointeger,type,
% 5.31/5.46 neg_nu7757733837767384882nteger: code_integer > code_integer ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Num_Oneg__numeral__class_Odbl__dec_001t__Complex__Ocomplex,type,
% 5.31/5.46 neg_nu6511756317524482435omplex: complex > complex ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Num_Oneg__numeral__class_Odbl__dec_001t__Int__Oint,type,
% 5.31/5.46 neg_nu3811975205180677377ec_int: int > int ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Num_Oneg__numeral__class_Odbl__dec_001t__Rat__Orat,type,
% 5.31/5.46 neg_nu3179335615603231917ec_rat: rat > rat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Num_Oneg__numeral__class_Odbl__dec_001t__Real__Oreal,type,
% 5.31/5.46 neg_nu6075765906172075777c_real: real > real ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Num_Oneg__numeral__class_Odbl__inc_001t__Code____Numeral__Ointeger,type,
% 5.31/5.46 neg_nu5831290666863070958nteger: code_integer > code_integer ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Num_Oneg__numeral__class_Odbl__inc_001t__Complex__Ocomplex,type,
% 5.31/5.46 neg_nu8557863876264182079omplex: complex > complex ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Num_Oneg__numeral__class_Odbl__inc_001t__Int__Oint,type,
% 5.31/5.46 neg_nu5851722552734809277nc_int: int > int ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Num_Oneg__numeral__class_Odbl__inc_001t__Rat__Orat,type,
% 5.31/5.46 neg_nu5219082963157363817nc_rat: rat > rat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Num_Oneg__numeral__class_Odbl__inc_001t__Real__Oreal,type,
% 5.31/5.46 neg_nu8295874005876285629c_real: real > real ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Num_Oneg__numeral__class_Osub_001t__Int__Oint,type,
% 5.31/5.46 neg_numeral_sub_int: num > num > int ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Num_Onum_OBit0,type,
% 5.31/5.46 bit0: num > num ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Num_Onum_OBit1,type,
% 5.31/5.46 bit1: num > num ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Num_Onum_OOne,type,
% 5.31/5.46 one: num ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Num_Onum_Osize__num,type,
% 5.31/5.46 size_num: num > nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Num_Onum__of__nat,type,
% 5.31/5.46 num_of_nat: nat > num ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Num_Onumeral__class_Onumeral_001t__Code____Numeral__Ointeger,type,
% 5.31/5.46 numera6620942414471956472nteger: num > code_integer ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Num_Onumeral__class_Onumeral_001t__Code____Numeral__Onatural,type,
% 5.31/5.46 numera5444537566228673987atural: num > code_natural ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Num_Onumeral__class_Onumeral_001t__Complex__Ocomplex,type,
% 5.31/5.46 numera6690914467698888265omplex: num > complex ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Num_Onumeral__class_Onumeral_001t__Extended____Nat__Oenat,type,
% 5.31/5.46 numera1916890842035813515d_enat: num > extended_enat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Num_Onumeral__class_Onumeral_001t__Int__Oint,type,
% 5.31/5.46 numeral_numeral_int: num > int ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Num_Onumeral__class_Onumeral_001t__Nat__Onat,type,
% 5.31/5.46 numeral_numeral_nat: num > nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Num_Onumeral__class_Onumeral_001t__Rat__Orat,type,
% 5.31/5.46 numeral_numeral_rat: num > rat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Num_Onumeral__class_Onumeral_001t__Real__Oreal,type,
% 5.31/5.46 numeral_numeral_real: num > real ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Num_Opow,type,
% 5.31/5.46 pow: num > num > num ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Num_Opred__numeral,type,
% 5.31/5.46 pred_numeral: num > nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Num_Osqr,type,
% 5.31/5.46 sqr: num > num ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Option_Ooption_ONone_001t__Nat__Onat,type,
% 5.31/5.46 none_nat: option_nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Option_Ooption_ONone_001t__Num__Onum,type,
% 5.31/5.46 none_num: option_num ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Option_Ooption_ONone_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 5.31/5.46 none_P5556105721700978146at_nat: option4927543243414619207at_nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Option_Ooption_OSome_001_Eo,type,
% 5.31/5.46 some_o: $o > option_o ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Option_Ooption_OSome_001t__Int__Oint,type,
% 5.31/5.46 some_int: int > option_int ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Option_Ooption_OSome_001t__Nat__Onat,type,
% 5.31/5.46 some_nat: nat > option_nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Option_Ooption_OSome_001t__Num__Onum,type,
% 5.31/5.46 some_num: num > option_num ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Option_Ooption_OSome_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 5.31/5.46 some_P7363390416028606310at_nat: product_prod_nat_nat > option4927543243414619207at_nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Option_Ooption_OSome_001t__VEBT____Definitions__OVEBT,type,
% 5.31/5.46 some_VEBT_VEBT: vEBT_VEBT > option_VEBT_VEBT ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Option_Ooption_Ocase__option_001_Eo_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 5.31/5.46 case_o184042715313410164at_nat: $o > ( product_prod_nat_nat > $o ) > option4927543243414619207at_nat > $o ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Option_Ooption_Ocase__option_001t__Num__Onum_001t__Num__Onum,type,
% 5.31/5.46 case_option_num_num: num > ( num > num ) > option_num > num ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Option_Ooption_Ocase__option_001t__Option__Ooption_It__Num__Onum_J_001t__Num__Onum,type,
% 5.31/5.46 case_o6005452278849405969um_num: option_num > ( num > option_num ) > option_num > option_num ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Option_Ooption_Osize__option_001t__Nat__Onat,type,
% 5.31/5.46 size_option_nat: ( nat > nat ) > option_nat > nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Option_Ooption_Osize__option_001t__Num__Onum,type,
% 5.31/5.46 size_option_num: ( num > nat ) > option_num > nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Option_Ooption_Osize__option_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
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% 5.31/5.46
% 5.31/5.46 thf(sy_c_Option_Ooption_Othe_001t__Nat__Onat,type,
% 5.31/5.46 the_nat: option_nat > nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Option_Ooption_Othe_001t__Num__Onum,type,
% 5.31/5.46 the_num: option_num > num ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Option_Ooption_Othe_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 5.31/5.46 the_Pr8591224930841456533at_nat: option4927543243414619207at_nat > product_prod_nat_nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Order__Relation_Olinear__order__on_001t__Nat__Onat,type,
% 5.31/5.46 order_4473980167227706203on_nat: set_nat > set_Pr1261947904930325089at_nat > $o ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Order__Relation_Opartial__order__on_001t__Nat__Onat,type,
% 5.31/5.46 order_5251275573222108571on_nat: set_nat > set_Pr1261947904930325089at_nat > $o ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Order__Relation_Opreorder__on_001t__Nat__Onat,type,
% 5.31/5.46 order_4861654808422542329on_nat: set_nat > set_Pr1261947904930325089at_nat > $o ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Order__Relation_OunderS_001t__Nat__Onat,type,
% 5.31/5.46 order_underS_nat: set_Pr1261947904930325089at_nat > nat > set_nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Order__Relation_Owell__order__on_001t__Nat__Onat,type,
% 5.31/5.46 order_2888998067076097458on_nat: set_nat > set_Pr1261947904930325089at_nat > $o ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Orderings_Obot__class_Obot_001t__Nat__Onat,type,
% 5.31/5.46 bot_bot_nat: nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_I_Eo_J,type,
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% 5.31/5.46
% 5.31/5.46 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Complex__Ocomplex_J,type,
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% 5.31/5.46
% 5.31/5.46 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Int__Oint_J,type,
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% 5.31/5.46
% 5.31/5.46 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__List__Olist_It__Nat__Onat_J_J,type,
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% 5.31/5.46
% 5.31/5.46 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Nat__Onat_J,type,
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% 5.31/5.46
% 5.31/5.46 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Num__Onum_J,type,
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% 5.31/5.46
% 5.31/5.46 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
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% 5.31/5.46
% 5.31/5.46 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Rat__Orat_J,type,
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% 5.31/5.46
% 5.31/5.46 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Real__Oreal_J,type,
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% 5.31/5.46
% 5.31/5.46 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Set__Oset_It__Nat__Onat_J_J,type,
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% 5.31/5.46
% 5.31/5.46 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__VEBT____Definitions__OVEBT_J,type,
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% 5.31/5.46
% 5.31/5.46 thf(sy_c_Orderings_Oord__class_OLeast_001t__Nat__Onat,type,
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% 5.31/5.46
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% 5.31/5.46 thf(sy_c_Orderings_Oord__class_Oless_001t__Extended____Nat__Oenat,type,
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% 5.31/5.46
% 5.31/5.46 thf(sy_c_Orderings_Oord__class_Oless_001t__Int__Oint,type,
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% 5.31/5.46
% 5.31/5.46 thf(sy_c_Orderings_Oord__class_Oless_001t__Nat__Onat,type,
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% 5.31/5.46
% 5.31/5.46 thf(sy_c_Orderings_Oord__class_Oless_001t__Num__Onum,type,
% 5.31/5.46 ord_less_num: num > num > $o ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Orderings_Oord__class_Oless_001t__Rat__Orat,type,
% 5.31/5.46 ord_less_rat: rat > rat > $o ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Orderings_Oord__class_Oless_001t__Real__Oreal,type,
% 5.31/5.46 ord_less_real: real > real > $o ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Orderings_Oord__class_Oless_001t__Set__Oset_It__Complex__Ocomplex_J,type,
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% 5.31/5.46
% 5.31/5.46 thf(sy_c_Orderings_Oord__class_Oless_001t__Set__Oset_It__Int__Oint_J,type,
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% 5.31/5.46 produc7128876500814652583st_nat: list_o > list_nat > produc4203922736317485613st_nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Product__Type_OPair_001t__List__Olist_I_Eo_J_001t__List__Olist_It__VEBT____Definitions__OVEBT_J,type,
% 5.31/5.46 produc6043759678074843571T_VEBT: list_o > list_VEBT_VEBT > produc1922972420619397443T_VEBT ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Product__Type_OPair_001t__List__Olist_It__Code____Numeral__Ointeger_J_001t__List__Olist_It__Code____Numeral__Ointeger_J,type,
% 5.31/5.46 produc750622340256944499nteger: list_Code_integer > list_Code_integer > produc862207588354017979nteger ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Product__Type_OPair_001t__List__Olist_It__Int__Oint_J_001t__List__Olist_It__Int__Oint_J,type,
% 5.31/5.46 produc364263696895485585st_int: list_int > list_int > produc1186641810826059865st_int ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Product__Type_OPair_001t__List__Olist_It__Nat__Onat_J_001t__List__Olist_I_Eo_J,type,
% 5.31/5.46 produc699922362453767013list_o: list_nat > list_o > produc149729814636038835list_o ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Product__Type_OPair_001t__List__Olist_It__Nat__Onat_J_001t__List__Olist_It__Nat__Onat_J,type,
% 5.31/5.46 produc2694037385005941721st_nat: list_nat > list_nat > produc1828647624359046049st_nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Product__Type_OPair_001t__List__Olist_It__Nat__Onat_J_001t__List__Olist_It__VEBT____Definitions__OVEBT_J,type,
% 5.31/5.46 produc8335345208264861441T_VEBT: list_nat > list_VEBT_VEBT > produc872621073311890639T_VEBT ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Product__Type_OPair_001t__List__Olist_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__List__Olist_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 5.31/5.46 produc5943733680697469783at_nat: list_P6011104703257516679at_nat > list_P6011104703257516679at_nat > produc6392793444374437607at_nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Product__Type_OPair_001t__List__Olist_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_001t__List__Olist_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
% 5.31/5.46 produc7536900900485677911at_nat: list_s1210847774152347623at_nat > list_s1210847774152347623at_nat > produc424102278133772007at_nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Product__Type_OPair_001t__List__Olist_It__VEBT____Definitions__OVEBT_J_001t__List__Olist_I_Eo_J,type,
% 5.31/5.46 produc2717590391345394939list_o: list_VEBT_VEBT > list_o > produc3962069817607390347list_o ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Product__Type_OPair_001t__List__Olist_It__VEBT____Definitions__OVEBT_J_001t__List__Olist_It__Int__Oint_J,type,
% 5.31/5.46 produc1392282695434103839st_int: list_VEBT_VEBT > list_int > produc7831203938951381541st_int ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Product__Type_OPair_001t__List__Olist_It__VEBT____Definitions__OVEBT_J_001t__List__Olist_It__Nat__Onat_J,type,
% 5.31/5.46 produc5570133714943300547st_nat: list_VEBT_VEBT > list_nat > produc1097915047028332489st_nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Product__Type_OPair_001t__List__Olist_It__VEBT____Definitions__OVEBT_J_001t__List__Olist_It__VEBT____Definitions__OVEBT_J,type,
% 5.31/5.46 produc3897820843166775703T_VEBT: list_VEBT_VEBT > list_VEBT_VEBT > produc9211091688327510695T_VEBT ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Product__Type_OPair_001t__Nat__Onat_001_Eo,type,
% 5.31/5.46 product_Pair_nat_o: nat > $o > product_prod_nat_o ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Product__Type_OPair_001t__Nat__Onat_001t__Int__Oint,type,
% 5.31/5.46 product_Pair_nat_int: nat > int > product_prod_nat_int ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Product__Type_OPair_001t__Nat__Onat_001t__Nat__Onat,type,
% 5.31/5.46 product_Pair_nat_nat: nat > nat > product_prod_nat_nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Product__Type_OPair_001t__Nat__Onat_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 5.31/5.46 produc487386426758144856at_nat: nat > product_prod_nat_nat > produc7248412053542808358at_nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Product__Type_OPair_001t__Nat__Onat_001t__VEBT____Definitions__OVEBT,type,
% 5.31/5.46 produc599794634098209291T_VEBT: nat > vEBT_VEBT > produc8025551001238799321T_VEBT ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Product__Type_OPair_001t__Option__Ooption_It__Nat__Onat_J_001t__Option__Ooption_It__Nat__Onat_J,type,
% 5.31/5.46 produc5098337634421038937on_nat: option_nat > option_nat > produc4953844613479565601on_nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Product__Type_OPair_001t__Option__Ooption_It__Num__Onum_J_001t__Option__Ooption_It__Num__Onum_J,type,
% 5.31/5.46 produc8585076106096196333on_num: option_num > option_num > produc3447558737645232053on_num ).
% 5.31/5.46
% 5.31/5.46 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,
% 5.31/5.46 produc488173922507101015at_nat: option4927543243414619207at_nat > option4927543243414619207at_nat > produc6121120109295599847at_nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 5.31/5.46 produc6161850002892822231at_nat: product_prod_nat_nat > product_prod_nat_nat > produc859450856879609959at_nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Product__Type_OPair_001t__Real__Oreal_001_Eo,type,
% 5.31/5.46 product_Pair_real_o: real > $o > product_prod_real_o ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Product__Type_OPair_001t__Real__Oreal_001t__Complex__Ocomplex,type,
% 5.31/5.46 produc1693001998875562995omplex: real > complex > produc6979889472282505531omplex ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Product__Type_OPair_001t__Real__Oreal_001t__Int__Oint,type,
% 5.31/5.46 produc3179012173361985393al_int: real > int > produc8786904178792722361al_int ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Product__Type_OPair_001t__Real__Oreal_001t__Nat__Onat,type,
% 5.31/5.46 produc3181502643871035669al_nat: real > nat > produc3741383161447143261al_nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Product__Type_OPair_001t__Real__Oreal_001t__Real__Oreal,type,
% 5.31/5.46 produc4511245868158468465l_real: real > real > produc2422161461964618553l_real ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Product__Type_OPair_001t__Real__Oreal_001t__VEBT____Definitions__OVEBT,type,
% 5.31/5.46 produc6931449550656315951T_VEBT: real > vEBT_VEBT > produc3757001726724277373T_VEBT ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Product__Type_OPair_001t__Set__Oset_It__Nat__Onat_J_001t__Set__Oset_It__Nat__Onat_J,type,
% 5.31/5.46 produc4532415448927165861et_nat: set_nat > set_nat > produc7819656566062154093et_nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Product__Type_OPair_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 5.31/5.46 produc2922128104949294807at_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > produc3843707927480180839at_nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Product__Type_OPair_001t__VEBT____Definitions__OVEBT_001_Eo,type,
% 5.31/5.46 produc8721562602347293563VEBT_o: vEBT_VEBT > $o > produc334124729049499915VEBT_o ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Product__Type_OPair_001t__VEBT____Definitions__OVEBT_001t__Complex__Ocomplex,type,
% 5.31/5.46 produc5617778602380981643omplex: vEBT_VEBT > complex > produc8380087813684007313omplex ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Product__Type_OPair_001t__VEBT____Definitions__OVEBT_001t__Extended____Nat__Oenat,type,
% 5.31/5.46 produc581526299967858633d_enat: vEBT_VEBT > extended_enat > produc7272778201969148633d_enat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Product__Type_OPair_001t__VEBT____Definitions__OVEBT_001t__Int__Oint,type,
% 5.31/5.46 produc736041933913180425BT_int: vEBT_VEBT > int > produc4894624898956917775BT_int ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Product__Type_OPair_001t__VEBT____Definitions__OVEBT_001t__Nat__Onat,type,
% 5.31/5.46 produc738532404422230701BT_nat: vEBT_VEBT > nat > produc9072475918466114483BT_nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Product__Type_OPair_001t__VEBT____Definitions__OVEBT_001t__Real__Oreal,type,
% 5.31/5.46 produc8117437818029410057T_real: vEBT_VEBT > real > produc5170161368751668367T_real ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Product__Type_OPair_001t__VEBT____Definitions__OVEBT_001t__VEBT____Definitions__OVEBT,type,
% 5.31/5.46 produc537772716801021591T_VEBT: vEBT_VEBT > vEBT_VEBT > produc8243902056947475879T_VEBT ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Product__Type_OSigma_001t__Nat__Onat_001t__Nat__Onat,type,
% 5.31/5.46 produc457027306803732586at_nat: set_nat > ( nat > set_nat ) > set_Pr1261947904930325089at_nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Product__Type_Oapsnd_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger,type,
% 5.31/5.46 produc6499014454317279255nteger: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__Int__Oint,type,
% 5.31/5.46 produc1553301316500091796er_int: ( code_integer > code_integer > int ) > produc8923325533196201883nteger > int ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__Nat__Onat,type,
% 5.31/5.46 produc1555791787009142072er_nat: ( code_integer > code_integer > nat ) > produc8923325533196201883nteger > nat ).
% 5.31/5.46
% 5.31/5.46 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,
% 5.31/5.46 produc6916734918728496179nteger: ( code_integer > code_integer > produc8923325533196201883nteger ) > produc8923325533196201883nteger > produc8923325533196201883nteger ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Int__Oint_001t__Int__Oint_001_Eo,type,
% 5.31/5.46 produc4947309494688390418_int_o: ( int > int > $o ) > product_prod_int_int > $o ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Int__Oint_001t__Int__Oint_001t__Int__Oint,type,
% 5.31/5.46 produc8211389475949308722nt_int: ( int > int > int ) > product_prod_int_int > int ).
% 5.31/5.46
% 5.31/5.46 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,
% 5.31/5.46 produc4245557441103728435nt_int: ( int > int > product_prod_int_int ) > product_prod_int_int > product_prod_int_int ).
% 5.31/5.46
% 5.31/5.46 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,
% 5.31/5.46 produc8739625826339149834_nat_o: ( nat > nat > product_prod_nat_nat > $o ) > product_prod_nat_nat > product_prod_nat_nat > $o ).
% 5.31/5.46
% 5.31/5.46 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,
% 5.31/5.46 produc27273713700761075at_nat: ( nat > nat > product_prod_nat_nat > product_prod_nat_nat ) > product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001_Eo,type,
% 5.31/5.46 produc6081775807080527818_nat_o: ( nat > nat > $o ) > product_prod_nat_nat > $o ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001t__List__Olist_It__Nat__Onat_J,type,
% 5.31/5.46 produc2761476792215241774st_nat: ( nat > nat > list_nat ) > product_prod_nat_nat > list_nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat,type,
% 5.31/5.46 produc6842872674320459806at_nat: ( nat > nat > nat ) > product_prod_nat_nat > nat ).
% 5.31/5.46
% 5.31/5.46 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,
% 5.31/5.46 produc2626176000494625587at_nat: ( nat > nat > product_prod_nat_nat ) > product_prod_nat_nat > product_prod_nat_nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001t__Rat__Orat,type,
% 5.31/5.46 produc6207742614233964070at_rat: ( nat > nat > rat ) > product_prod_nat_nat > rat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Product__Type_Oprod_Ofst_001t__Int__Oint_001t__Int__Oint,type,
% 5.31/5.46 product_fst_int_int: product_prod_int_int > int ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Product__Type_Oprod_Ofst_001t__Nat__Onat_001t__Nat__Onat,type,
% 5.31/5.46 product_fst_nat_nat: product_prod_nat_nat > nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Product__Type_Oprod_Osnd_001t__Int__Oint_001t__Int__Oint,type,
% 5.31/5.46 product_snd_int_int: product_prod_int_int > int ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Product__Type_Oprod_Osnd_001t__Nat__Onat_001t__Nat__Onat,type,
% 5.31/5.46 product_snd_nat_nat: product_prod_nat_nat > nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Product__Type_Oscomp_001t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_001t__Code____Numeral__Onatural_001t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_001t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_J,type,
% 5.31/5.46 produc5538323210962509403atural: ( produc7822875418678951345atural > produc5835291356934675326atural ) > ( code_natural > produc7822875418678951345atural > produc5835291356934675326atural ) > produc7822875418678951345atural > produc5835291356934675326atural ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Random_Oiterate_001t__Code____Numeral__Onatural_001t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J,type,
% 5.31/5.46 iterat8892046348760725948atural: code_natural > ( code_natural > produc7822875418678951345atural > produc5835291356934675326atural ) > code_natural > produc7822875418678951345atural > produc5835291356934675326atural ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Random_Olog,type,
% 5.31/5.46 log: code_natural > code_natural > code_natural ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Random_Ominus__shift,type,
% 5.31/5.46 minus_shift: code_natural > code_natural > code_natural > code_natural ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Random_Onext,type,
% 5.31/5.46 next: produc7822875418678951345atural > produc5835291356934675326atural ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Random_Orange,type,
% 5.31/5.46 range: code_natural > produc7822875418678951345atural > produc5835291356934675326atural ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Rat_OAbs__Rat,type,
% 5.31/5.46 abs_Rat: product_prod_int_int > rat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Rat_OFract,type,
% 5.31/5.46 fract: int > int > rat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Rat_ORep__Rat,type,
% 5.31/5.46 rep_Rat: rat > product_prod_int_int ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Rat_Ofield__char__0__class_ORats_001t__Real__Oreal,type,
% 5.31/5.46 field_5140801741446780682s_real: set_real ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Rat_Onormalize,type,
% 5.31/5.46 normalize: product_prod_int_int > product_prod_int_int ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Rat_Opcr__rat,type,
% 5.31/5.46 pcr_rat: product_prod_int_int > rat > $o ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Rat_Opositive,type,
% 5.31/5.46 positive: rat > $o ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Rat_Oquotient__of,type,
% 5.31/5.46 quotient_of: rat > product_prod_int_int ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Rat_Oratrel,type,
% 5.31/5.46 ratrel: product_prod_int_int > product_prod_int_int > $o ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Real_ORatreal,type,
% 5.31/5.46 ratreal: rat > real ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Real_OReal,type,
% 5.31/5.46 real2: ( nat > rat ) > real ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Real_Ocauchy,type,
% 5.31/5.46 cauchy: ( nat > rat ) > $o ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Real_Opcr__real,type,
% 5.31/5.46 pcr_real: ( nat > rat ) > real > $o ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Real_Opositive,type,
% 5.31/5.46 positive2: real > $o ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Real_Orealrel,type,
% 5.31/5.46 realrel: ( nat > rat ) > ( nat > rat ) > $o ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Real_Orep__real,type,
% 5.31/5.46 rep_real: real > nat > rat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Real_Ovanishes,type,
% 5.31/5.46 vanishes: ( nat > rat ) > $o ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Real__Vector__Spaces_OReals_001t__Complex__Ocomplex,type,
% 5.31/5.46 real_V2521375963428798218omplex: set_complex ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Real__Vector__Spaces_Obounded__linear_001t__Real__Oreal_001t__Real__Oreal,type,
% 5.31/5.46 real_V5970128139526366754l_real: ( real > real ) > $o ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Real__Vector__Spaces_Olinear_001t__Real__Oreal_001t__Real__Oreal,type,
% 5.31/5.46 real_V4572627801940501177l_real: ( real > real ) > $o ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Real__Vector__Spaces_Onorm__class_Onorm_001t__Complex__Ocomplex,type,
% 5.31/5.46 real_V1022390504157884413omplex: complex > real ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Real__Vector__Spaces_Onorm__class_Onorm_001t__Real__Oreal,type,
% 5.31/5.46 real_V7735802525324610683m_real: real > real ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Real__Vector__Spaces_Oof__real_001t__Complex__Ocomplex,type,
% 5.31/5.46 real_V4546457046886955230omplex: real > complex ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Real__Vector__Spaces_OscaleR__class_OscaleR_001t__Complex__Ocomplex,type,
% 5.31/5.46 real_V2046097035970521341omplex: real > complex > complex ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Real__Vector__Spaces_OscaleR__class_OscaleR_001t__Real__Oreal,type,
% 5.31/5.46 real_V1485227260804924795R_real: real > real > real ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Relation_OField_001t__Nat__Onat,type,
% 5.31/5.46 field_nat: set_Pr1261947904930325089at_nat > set_nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Relation_OId_001t__Nat__Onat,type,
% 5.31/5.46 id_nat2: set_Pr1261947904930325089at_nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Relation_Oantisym_001t__Nat__Onat,type,
% 5.31/5.46 antisym_nat: set_Pr1261947904930325089at_nat > $o ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Relation_Orefl__on_001t__Nat__Onat,type,
% 5.31/5.46 refl_on_nat: set_nat > set_Pr1261947904930325089at_nat > $o ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Relation_Ototal__on_001t__Nat__Onat,type,
% 5.31/5.46 total_on_nat: set_nat > set_Pr1261947904930325089at_nat > $o ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Relation_Otrans_001t__Nat__Onat,type,
% 5.31/5.46 trans_nat: set_Pr1261947904930325089at_nat > $o ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Rings_Oalgebraic__semidom__class_Ocoprime_001t__Int__Oint,type,
% 5.31/5.46 algebr932160517623751201me_int: int > int > $o ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Rings_Oalgebraic__semidom__class_Ocoprime_001t__Nat__Onat,type,
% 5.31/5.46 algebr934650988132801477me_nat: nat > nat > $o ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Rings_Odivide__class_Odivide_001t__Code____Numeral__Ointeger,type,
% 5.31/5.46 divide6298287555418463151nteger: code_integer > code_integer > code_integer ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Rings_Odivide__class_Odivide_001t__Code____Numeral__Onatural,type,
% 5.31/5.46 divide5121882707175180666atural: code_natural > code_natural > code_natural ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Rings_Odivide__class_Odivide_001t__Complex__Ocomplex,type,
% 5.31/5.46 divide1717551699836669952omplex: complex > complex > complex ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Rings_Odivide__class_Odivide_001t__Int__Oint,type,
% 5.31/5.46 divide_divide_int: int > int > int ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Rings_Odivide__class_Odivide_001t__Nat__Onat,type,
% 5.31/5.46 divide_divide_nat: nat > nat > nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Rings_Odivide__class_Odivide_001t__Rat__Orat,type,
% 5.31/5.46 divide_divide_rat: rat > rat > rat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Rings_Odivide__class_Odivide_001t__Real__Oreal,type,
% 5.31/5.46 divide_divide_real: real > real > real ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Rings_Odvd__class_Odvd_001t__Code____Numeral__Ointeger,type,
% 5.31/5.46 dvd_dvd_Code_integer: code_integer > code_integer > $o ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Rings_Odvd__class_Odvd_001t__Code____Numeral__Onatural,type,
% 5.31/5.46 dvd_dvd_Code_natural: code_natural > code_natural > $o ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Rings_Odvd__class_Odvd_001t__Complex__Ocomplex,type,
% 5.31/5.46 dvd_dvd_complex: complex > complex > $o ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Rings_Odvd__class_Odvd_001t__Int__Oint,type,
% 5.31/5.46 dvd_dvd_int: int > int > $o ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Rings_Odvd__class_Odvd_001t__Nat__Onat,type,
% 5.31/5.46 dvd_dvd_nat: nat > nat > $o ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Rings_Odvd__class_Odvd_001t__Rat__Orat,type,
% 5.31/5.46 dvd_dvd_rat: rat > rat > $o ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Rings_Odvd__class_Odvd_001t__Real__Oreal,type,
% 5.31/5.46 dvd_dvd_real: real > real > $o ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Rings_Omodulo__class_Omodulo_001t__Code____Numeral__Ointeger,type,
% 5.31/5.46 modulo364778990260209775nteger: code_integer > code_integer > code_integer ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Rings_Omodulo__class_Omodulo_001t__Code____Numeral__Onatural,type,
% 5.31/5.46 modulo8411746178871703098atural: code_natural > code_natural > code_natural ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Rings_Omodulo__class_Omodulo_001t__Int__Oint,type,
% 5.31/5.46 modulo_modulo_int: int > int > int ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Rings_Omodulo__class_Omodulo_001t__Nat__Onat,type,
% 5.31/5.46 modulo_modulo_nat: nat > nat > nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Rings_Ounit__factor__class_Ounit__factor_001t__Nat__Onat,type,
% 5.31/5.46 unit_f2748546683901255202or_nat: nat > nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Rings_Ozero__neq__one__class_Oof__bool_001t__Code____Numeral__Ointeger,type,
% 5.31/5.46 zero_n356916108424825756nteger: $o > code_integer ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Rings_Ozero__neq__one__class_Oof__bool_001t__Code____Numeral__Onatural,type,
% 5.31/5.46 zero_n8403883297036319079atural: $o > code_natural ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Rings_Ozero__neq__one__class_Oof__bool_001t__Complex__Ocomplex,type,
% 5.31/5.46 zero_n1201886186963655149omplex: $o > complex ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Rings_Ozero__neq__one__class_Oof__bool_001t__Int__Oint,type,
% 5.31/5.46 zero_n2684676970156552555ol_int: $o > int ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Rings_Ozero__neq__one__class_Oof__bool_001t__Nat__Onat,type,
% 5.31/5.46 zero_n2687167440665602831ol_nat: $o > nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Rings_Ozero__neq__one__class_Oof__bool_001t__Rat__Orat,type,
% 5.31/5.46 zero_n2052037380579107095ol_rat: $o > rat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Rings_Ozero__neq__one__class_Oof__bool_001t__Real__Oreal,type,
% 5.31/5.46 zero_n3304061248610475627l_real: $o > real ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Series_Osuminf_001t__Real__Oreal,type,
% 5.31/5.46 suminf_real: ( nat > real ) > real ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Series_Osummable_001t__Real__Oreal,type,
% 5.31/5.46 summable_real: ( nat > real ) > $o ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Series_Osums_001t__Complex__Ocomplex,type,
% 5.31/5.46 sums_complex: ( nat > complex ) > complex > $o ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Series_Osums_001t__Int__Oint,type,
% 5.31/5.46 sums_int: ( nat > int ) > int > $o ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Series_Osums_001t__Nat__Onat,type,
% 5.31/5.46 sums_nat: ( nat > nat ) > nat > $o ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Series_Osums_001t__Real__Oreal,type,
% 5.31/5.46 sums_real: ( nat > real ) > real > $o ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Set_OCollect_001t__Complex__Ocomplex,type,
% 5.31/5.46 collect_complex: ( complex > $o ) > set_complex ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Set_OCollect_001t__Int__Oint,type,
% 5.31/5.46 collect_int: ( int > $o ) > set_int ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Set_OCollect_001t__List__Olist_I_Eo_J,type,
% 5.31/5.46 collect_list_o: ( list_o > $o ) > set_list_o ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Set_OCollect_001t__List__Olist_It__Complex__Ocomplex_J,type,
% 5.31/5.46 collect_list_complex: ( list_complex > $o ) > set_list_complex ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Set_OCollect_001t__List__Olist_It__Int__Oint_J,type,
% 5.31/5.46 collect_list_int: ( list_int > $o ) > set_list_int ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Set_OCollect_001t__List__Olist_It__List__Olist_It__Nat__Onat_J_J,type,
% 5.31/5.46 collec5989764272469232197st_nat: ( list_list_nat > $o ) > set_list_list_nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Set_OCollect_001t__List__Olist_It__Nat__Onat_J,type,
% 5.31/5.46 collect_list_nat: ( list_nat > $o ) > set_list_nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Set_OCollect_001t__List__Olist_It__Set__Oset_It__Nat__Onat_J_J,type,
% 5.31/5.46 collect_list_set_nat: ( list_set_nat > $o ) > set_list_set_nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Set_OCollect_001t__List__Olist_It__VEBT____Definitions__OVEBT_J,type,
% 5.31/5.46 collec5608196760682091941T_VEBT: ( list_VEBT_VEBT > $o ) > set_list_VEBT_VEBT ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Set_OCollect_001t__Nat__Onat,type,
% 5.31/5.46 collect_nat: ( nat > $o ) > set_nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Set_OCollect_001t__Num__Onum,type,
% 5.31/5.46 collect_num: ( num > $o ) > set_num ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 5.31/5.46 collec3392354462482085612at_nat: ( product_prod_nat_nat > $o ) > set_Pr1261947904930325089at_nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Set_OCollect_001t__Rat__Orat,type,
% 5.31/5.46 collect_rat: ( rat > $o ) > set_rat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Set_OCollect_001t__Real__Oreal,type,
% 5.31/5.46 collect_real: ( real > $o ) > set_real ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Set_OCollect_001t__Set__Oset_It__Nat__Onat_J,type,
% 5.31/5.46 collect_set_nat: ( set_nat > $o ) > set_set_nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Set_OPow_001t__Nat__Onat,type,
% 5.31/5.46 pow_nat: set_nat > set_set_nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Set_Oimage_001t__Int__Oint_001t__Int__Oint,type,
% 5.31/5.46 image_int_int: ( int > int ) > set_int > set_int ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Set_Oimage_001t__Int__Oint_001t__Nat__Onat,type,
% 5.31/5.46 image_int_nat: ( int > nat ) > set_int > set_nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Set_Oimage_001t__List__Olist_It__Nat__Onat_J_001t__Nat__Onat,type,
% 5.31/5.46 image_list_nat_nat: ( list_nat > nat ) > set_list_nat > set_nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Set_Oimage_001t__Nat__Onat_001t__Int__Oint,type,
% 5.31/5.46 image_nat_int: ( nat > int ) > set_nat > set_int ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Set_Oimage_001t__Nat__Onat_001t__List__Olist_It__Nat__Onat_J,type,
% 5.31/5.46 image_nat_list_nat: ( nat > list_nat ) > set_nat > set_list_nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Set_Oimage_001t__Nat__Onat_001t__Nat__Onat,type,
% 5.31/5.46 image_nat_nat: ( nat > nat ) > set_nat > set_nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Set_Oimage_001t__Nat__Onat_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 5.31/5.46 image_5846123807819985514at_nat: ( nat > product_prod_nat_nat ) > set_nat > set_Pr1261947904930325089at_nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Set_Oimage_001t__Nat__Onat_001t__Set__Oset_It__Nat__Onat_J,type,
% 5.31/5.46 image_nat_set_nat: ( nat > set_nat ) > set_nat > set_set_nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Set_Oimage_001t__Nat__Onat_001t__String__Ochar,type,
% 5.31/5.46 image_nat_char: ( nat > char ) > set_nat > set_char ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Set_Oimage_001t__Nat__Onat_001t__Sum____Type__Osum_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 5.31/5.46 image_678696785212003926at_nat: ( nat > sum_sum_nat_nat ) > set_nat > set_Sum_sum_nat_nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Nat__Onat,type,
% 5.31/5.46 image_2486076414777270412at_nat: ( product_prod_nat_nat > nat ) > set_Pr1261947904930325089at_nat > set_nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Set_Oimage_001t__Real__Oreal_001t__Real__Oreal,type,
% 5.31/5.46 image_real_real: ( real > real ) > set_real > set_real ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Set_Oimage_001t__String__Ochar_001t__Nat__Onat,type,
% 5.31/5.46 image_char_nat: ( char > nat ) > set_char > set_nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Set_Oimage_001t__Sum____Type__Osum_It__Nat__Onat_Mt__Nat__Onat_J_001t__Nat__Onat,type,
% 5.31/5.46 image_1320371278474632150at_nat: ( sum_sum_nat_nat > nat ) > set_Sum_sum_nat_nat > set_nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Set_Oinsert_001_Eo,type,
% 5.31/5.46 insert_o: $o > set_o > set_o ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Set_Oinsert_001t__Complex__Ocomplex,type,
% 5.31/5.46 insert_complex: complex > set_complex > set_complex ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Set_Oinsert_001t__Int__Oint,type,
% 5.31/5.46 insert_int: int > set_int > set_int ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Set_Oinsert_001t__List__Olist_It__Nat__Onat_J,type,
% 5.31/5.46 insert_list_nat: list_nat > set_list_nat > set_list_nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Set_Oinsert_001t__Nat__Onat,type,
% 5.31/5.46 insert_nat: nat > set_nat > set_nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Set_Oinsert_001t__Num__Onum,type,
% 5.31/5.46 insert_num: num > set_num > set_num ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Set_Oinsert_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 5.31/5.46 insert8211810215607154385at_nat: product_prod_nat_nat > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Set_Oinsert_001t__Rat__Orat,type,
% 5.31/5.46 insert_rat: rat > set_rat > set_rat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Set_Oinsert_001t__Real__Oreal,type,
% 5.31/5.46 insert_real: real > set_real > set_real ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Set_Oinsert_001t__Set__Oset_It__Nat__Onat_J,type,
% 5.31/5.46 insert_set_nat: set_nat > set_set_nat > set_set_nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Set_Oinsert_001t__VEBT____Definitions__OVEBT,type,
% 5.31/5.46 insert_VEBT_VEBT: vEBT_VEBT > set_VEBT_VEBT > set_VEBT_VEBT ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Set_Ovimage_001t__Nat__Onat_001t__Nat__Onat,type,
% 5.31/5.46 vimage_nat_nat: ( nat > nat ) > set_nat > set_nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Set__Interval_Ofold__atLeastAtMost__nat_001t__Code____Numeral__Ointeger,type,
% 5.31/5.46 set_fo1084959871951514735nteger: ( nat > code_integer > code_integer ) > nat > nat > code_integer > code_integer ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Set__Interval_Ofold__atLeastAtMost__nat_001t__Complex__Ocomplex,type,
% 5.31/5.46 set_fo1517530859248394432omplex: ( nat > complex > complex ) > nat > nat > complex > complex ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Set__Interval_Ofold__atLeastAtMost__nat_001t__Int__Oint,type,
% 5.31/5.46 set_fo2581907887559384638at_int: ( nat > int > int ) > nat > nat > int > int ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Set__Interval_Ofold__atLeastAtMost__nat_001t__Nat__Onat,type,
% 5.31/5.46 set_fo2584398358068434914at_nat: ( nat > nat > nat ) > nat > nat > nat > nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Set__Interval_Ofold__atLeastAtMost__nat_001t__Rat__Orat,type,
% 5.31/5.46 set_fo1949268297981939178at_rat: ( nat > rat > rat ) > nat > nat > rat > rat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Set__Interval_Ofold__atLeastAtMost__nat_001t__Real__Oreal,type,
% 5.31/5.46 set_fo3111899725591712190t_real: ( nat > real > real ) > nat > nat > real > real ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Set__Interval_Oord__class_OatLeastAtMost_001t__Int__Oint,type,
% 5.31/5.46 set_or1266510415728281911st_int: int > int > set_int ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Set__Interval_Oord__class_OatLeastAtMost_001t__Nat__Onat,type,
% 5.31/5.46 set_or1269000886237332187st_nat: nat > nat > set_nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Set__Interval_Oord__class_OatLeastAtMost_001t__Num__Onum,type,
% 5.31/5.46 set_or7049704709247886629st_num: num > num > set_num ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Set__Interval_Oord__class_OatLeastAtMost_001t__Rat__Orat,type,
% 5.31/5.46 set_or633870826150836451st_rat: rat > rat > set_rat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Set__Interval_Oord__class_OatLeastAtMost_001t__Real__Oreal,type,
% 5.31/5.46 set_or1222579329274155063t_real: real > real > set_real ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Set__Interval_Oord__class_OatLeastAtMost_001t__Set__Oset_It__Nat__Onat_J,type,
% 5.31/5.46 set_or4548717258645045905et_nat: set_nat > set_nat > set_set_nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Set__Interval_Oord__class_OatLeastLessThan_001t__Int__Oint,type,
% 5.31/5.46 set_or4662586982721622107an_int: int > int > set_int ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Set__Interval_Oord__class_OatLeastLessThan_001t__Nat__Onat,type,
% 5.31/5.46 set_or4665077453230672383an_nat: nat > nat > set_nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Set__Interval_Oord__class_OatLeast_001t__Nat__Onat,type,
% 5.31/5.46 set_ord_atLeast_nat: nat > set_nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Set__Interval_Oord__class_OatMost_001t__Int__Oint,type,
% 5.31/5.46 set_ord_atMost_int: int > set_int ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Set__Interval_Oord__class_OatMost_001t__Nat__Onat,type,
% 5.31/5.46 set_ord_atMost_nat: nat > set_nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Set__Interval_Oord__class_OatMost_001t__Num__Onum,type,
% 5.31/5.46 set_ord_atMost_num: num > set_num ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Set__Interval_Oord__class_OatMost_001t__Rat__Orat,type,
% 5.31/5.46 set_ord_atMost_rat: rat > set_rat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Set__Interval_Oord__class_OatMost_001t__Real__Oreal,type,
% 5.31/5.46 set_ord_atMost_real: real > set_real ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Set__Interval_Oord__class_OatMost_001t__Set__Oset_It__Nat__Onat_J,type,
% 5.31/5.46 set_or4236626031148496127et_nat: set_nat > set_set_nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Set__Interval_Oord__class_OgreaterThanAtMost_001t__Int__Oint,type,
% 5.31/5.46 set_or6656581121297822940st_int: int > int > set_int ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Set__Interval_Oord__class_OgreaterThanAtMost_001t__Nat__Onat,type,
% 5.31/5.46 set_or6659071591806873216st_nat: nat > nat > set_nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Set__Interval_Oord__class_OgreaterThanLessThan_001t__Int__Oint,type,
% 5.31/5.46 set_or5832277885323065728an_int: int > int > set_int ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Set__Interval_Oord__class_OgreaterThanLessThan_001t__Nat__Onat,type,
% 5.31/5.46 set_or5834768355832116004an_nat: nat > nat > set_nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Set__Interval_Oord__class_OgreaterThanLessThan_001t__Real__Oreal,type,
% 5.31/5.46 set_or1633881224788618240n_real: real > real > set_real ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Set__Interval_Oord__class_OgreaterThan_001t__Nat__Onat,type,
% 5.31/5.46 set_or1210151606488870762an_nat: nat > set_nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Set__Interval_Oord__class_OgreaterThan_001t__Real__Oreal,type,
% 5.31/5.46 set_or5849166863359141190n_real: real > set_real ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Set__Interval_Oord__class_OlessThan_001t__Int__Oint,type,
% 5.31/5.46 set_ord_lessThan_int: int > set_int ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Set__Interval_Oord__class_OlessThan_001t__Nat__Onat,type,
% 5.31/5.46 set_ord_lessThan_nat: nat > set_nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Set__Interval_Oord__class_OlessThan_001t__Num__Onum,type,
% 5.31/5.46 set_ord_lessThan_num: num > set_num ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Set__Interval_Oord__class_OlessThan_001t__Rat__Orat,type,
% 5.31/5.46 set_ord_lessThan_rat: rat > set_rat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Set__Interval_Oord__class_OlessThan_001t__Real__Oreal,type,
% 5.31/5.46 set_or5984915006950818249n_real: real > set_real ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Set__Interval_Oord__class_OlessThan_001t__Set__Oset_It__Nat__Onat_J,type,
% 5.31/5.46 set_or890127255671739683et_nat: set_nat > set_set_nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_String_Ochar_OChar,type,
% 5.31/5.46 char2: $o > $o > $o > $o > $o > $o > $o > $o > char ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_String_Ochar_Osize__char,type,
% 5.31/5.46 size_char: char > nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_String_Ocomm__semiring__1__class_Oof__char_001t__Nat__Onat,type,
% 5.31/5.46 comm_s629917340098488124ar_nat: char > nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_String_Ointeger__of__char,type,
% 5.31/5.46 integer_of_char: char > code_integer ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_String_Ounique__euclidean__semiring__with__bit__operations__class_Ochar__of_001t__Nat__Onat,type,
% 5.31/5.46 unique3096191561947761185of_nat: nat > char ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Sum__Type_OInl_001t__Nat__Onat_001t__Nat__Onat,type,
% 5.31/5.46 sum_Inl_nat_nat: nat > sum_sum_nat_nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Sum__Type_OInr_001t__Nat__Onat_001t__Nat__Onat,type,
% 5.31/5.46 sum_Inr_nat_nat: nat > sum_sum_nat_nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Sum__Type_Osum_Ocase__sum_001t__Nat__Onat_001t__Int__Oint_001t__Nat__Onat,type,
% 5.31/5.46 sum_ca7763040182479039464nt_nat: ( nat > int ) > ( nat > int ) > sum_sum_nat_nat > int ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Sum__Type_Osum_Ocase__sum_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat,type,
% 5.31/5.46 sum_ca6763686470577984908at_nat: ( nat > nat ) > ( nat > nat ) > sum_sum_nat_nat > nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Topological__Spaces_Ocontinuous_001t__Real__Oreal_001t__Real__Oreal,type,
% 5.31/5.46 topolo4422821103128117721l_real: filter_real > ( real > real ) > $o ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Topological__Spaces_Ocontinuous__on_001t__Real__Oreal_001t__Real__Oreal,type,
% 5.31/5.46 topolo5044208981011980120l_real: set_real > ( real > real ) > $o ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Topological__Spaces_Omonoseq_001t__Real__Oreal,type,
% 5.31/5.46 topolo6980174941875973593q_real: ( nat > real ) > $o ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Topological__Spaces_Otopological__space__class_Oat__within_001t__Real__Oreal,type,
% 5.31/5.46 topolo2177554685111907308n_real: real > set_real > filter_real ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Topological__Spaces_Otopological__space__class_Oconvergent_001t__Real__Oreal,type,
% 5.31/5.46 topolo7531315842566124627t_real: ( nat > real ) > $o ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Topological__Spaces_Otopological__space__class_Onhds_001t__Real__Oreal,type,
% 5.31/5.46 topolo2815343760600316023s_real: real > filter_real ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Topological__Spaces_Ouniform__space__class_OCauchy_001t__Real__Oreal,type,
% 5.31/5.46 topolo4055970368930404560y_real: ( nat > real ) > $o ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Transcendental_Oarccos,type,
% 5.31/5.46 arccos: real > real ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Transcendental_Oarcosh_001t__Real__Oreal,type,
% 5.31/5.46 arcosh_real: real > real ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Transcendental_Oarctan,type,
% 5.31/5.46 arctan: real > real ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Transcendental_Oarsinh_001t__Real__Oreal,type,
% 5.31/5.46 arsinh_real: real > real ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Transcendental_Oartanh_001t__Real__Oreal,type,
% 5.31/5.46 artanh_real: real > real ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Transcendental_Ocos_001t__Complex__Ocomplex,type,
% 5.31/5.46 cos_complex: complex > complex ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Transcendental_Ocos_001t__Real__Oreal,type,
% 5.31/5.46 cos_real: real > real ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Transcendental_Ocos__coeff,type,
% 5.31/5.46 cos_coeff: nat > real ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Transcendental_Ocot_001t__Real__Oreal,type,
% 5.31/5.46 cot_real: real > real ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Transcendental_Oexp_001t__Complex__Ocomplex,type,
% 5.31/5.46 exp_complex: complex > complex ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Transcendental_Oexp_001t__Real__Oreal,type,
% 5.31/5.46 exp_real: real > real ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Transcendental_Oln__class_Oln_001t__Real__Oreal,type,
% 5.31/5.46 ln_ln_real: real > real ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Transcendental_Olog,type,
% 5.31/5.46 log2: real > real > real ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Transcendental_Opi,type,
% 5.31/5.46 pi: real ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Transcendental_Opowr_001t__Real__Oreal,type,
% 5.31/5.46 powr_real: real > real > real ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Transcendental_Osin_001t__Complex__Ocomplex,type,
% 5.31/5.46 sin_complex: complex > complex ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Transcendental_Osin_001t__Real__Oreal,type,
% 5.31/5.46 sin_real: real > real ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Transcendental_Osin__coeff,type,
% 5.31/5.46 sin_coeff: nat > real ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Transcendental_Otan_001t__Real__Oreal,type,
% 5.31/5.46 tan_real: real > real ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Transcendental_Otanh_001t__Real__Oreal,type,
% 5.31/5.46 tanh_real: real > real ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Transitive__Closure_Ortrancl_001t__Nat__Onat,type,
% 5.31/5.46 transi2905341329935302413cl_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ).
% 5.31/5.46
% 5.31/5.46 thf(sy_c_Transitive__Closure_Otrancl_001t__Nat__Onat,type,
% 5.31/5.47 transi6264000038957366511cl_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ).
% 5.31/5.47
% 5.31/5.47 thf(sy_c_Transitive__Closure_Otranclp_001t__Nat__Onat,type,
% 5.31/5.47 transi2163837189807498211lp_nat: ( nat > nat > $o ) > nat > nat > $o ).
% 5.31/5.47
% 5.31/5.47 thf(sy_c_Typerep_Otyperep_OTyperep,type,
% 5.31/5.47 typerep2: literal > list_typerep > typerep ).
% 5.31/5.47
% 5.31/5.47 thf(sy_c_Typerep_Otyperep_Osize__typerep,type,
% 5.31/5.47 size_typerep: typerep > nat ).
% 5.31/5.47
% 5.31/5.47 thf(sy_c_VEBT__Definitions_OVEBT_OLeaf,type,
% 5.31/5.47 vEBT_Leaf: $o > $o > vEBT_VEBT ).
% 5.31/5.47
% 5.31/5.47 thf(sy_c_VEBT__Definitions_OVEBT_ONode,type,
% 5.31/5.47 vEBT_Node: option4927543243414619207at_nat > nat > list_VEBT_VEBT > vEBT_VEBT > vEBT_VEBT ).
% 5.31/5.47
% 5.31/5.47 thf(sy_c_VEBT__Definitions_OVEBT_Osize__VEBT,type,
% 5.31/5.47 vEBT_size_VEBT: vEBT_VEBT > nat ).
% 5.31/5.47
% 5.31/5.47 thf(sy_c_VEBT__Definitions_OVEBT__internal_Oboth__member__options,type,
% 5.31/5.47 vEBT_V8194947554948674370ptions: vEBT_VEBT > nat > $o ).
% 5.31/5.47
% 5.31/5.47 thf(sy_c_VEBT__Definitions_OVEBT__internal_Oelim__dead,type,
% 5.31/5.47 vEBT_VEBT_elim_dead: vEBT_VEBT > extended_enat > vEBT_VEBT ).
% 5.31/5.47
% 5.31/5.47 thf(sy_c_VEBT__Definitions_OVEBT__internal_Oelim__dead__rel,type,
% 5.31/5.47 vEBT_V312737461966249ad_rel: produc7272778201969148633d_enat > produc7272778201969148633d_enat > $o ).
% 5.31/5.47
% 5.31/5.47 thf(sy_c_VEBT__Definitions_OVEBT__internal_Ohigh,type,
% 5.31/5.47 vEBT_VEBT_high: nat > nat > nat ).
% 5.31/5.47
% 5.31/5.47 thf(sy_c_VEBT__Definitions_OVEBT__internal_Oin__children,type,
% 5.31/5.47 vEBT_V5917875025757280293ildren: nat > list_VEBT_VEBT > nat > $o ).
% 5.31/5.47
% 5.31/5.47 thf(sy_c_VEBT__Definitions_OVEBT__internal_Olow,type,
% 5.31/5.47 vEBT_VEBT_low: nat > nat > nat ).
% 5.31/5.47
% 5.31/5.47 thf(sy_c_VEBT__Definitions_OVEBT__internal_Omembermima,type,
% 5.31/5.47 vEBT_VEBT_membermima: vEBT_VEBT > nat > $o ).
% 5.31/5.47
% 5.31/5.47 thf(sy_c_VEBT__Definitions_OVEBT__internal_Omembermima__rel,type,
% 5.31/5.47 vEBT_V4351362008482014158ma_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 5.31/5.47
% 5.31/5.47 thf(sy_c_VEBT__Definitions_OVEBT__internal_Onaive__member,type,
% 5.31/5.47 vEBT_V5719532721284313246member: vEBT_VEBT > nat > $o ).
% 5.31/5.47
% 5.31/5.47 thf(sy_c_VEBT__Definitions_OVEBT__internal_Onaive__member__rel,type,
% 5.31/5.47 vEBT_V5765760719290551771er_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 5.31/5.47
% 5.31/5.47 thf(sy_c_VEBT__Definitions_OVEBT__internal_Ovalid_H,type,
% 5.31/5.47 vEBT_VEBT_valid: vEBT_VEBT > nat > $o ).
% 5.31/5.47
% 5.31/5.47 thf(sy_c_VEBT__Definitions_OVEBT__internal_Ovalid_H__rel,type,
% 5.31/5.47 vEBT_VEBT_valid_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 5.31/5.47
% 5.31/5.47 thf(sy_c_VEBT__Definitions_Oinvar__vebt,type,
% 5.31/5.47 vEBT_invar_vebt: vEBT_VEBT > nat > $o ).
% 5.31/5.47
% 5.31/5.47 thf(sy_c_VEBT__Definitions_Oset__vebt,type,
% 5.31/5.47 vEBT_set_vebt: vEBT_VEBT > set_nat ).
% 5.31/5.47
% 5.31/5.47 thf(sy_c_VEBT__Definitions_Ovebt__buildup,type,
% 5.31/5.47 vEBT_vebt_buildup: nat > vEBT_VEBT ).
% 5.31/5.47
% 5.31/5.47 thf(sy_c_VEBT__Definitions_Ovebt__buildup__rel,type,
% 5.31/5.47 vEBT_v4011308405150292612up_rel: nat > nat > $o ).
% 5.31/5.47
% 5.31/5.47 thf(sy_c_VEBT__Delete_Ovebt__delete,type,
% 5.31/5.47 vEBT_vebt_delete: vEBT_VEBT > nat > vEBT_VEBT ).
% 5.31/5.47
% 5.31/5.47 thf(sy_c_VEBT__Delete_Ovebt__delete__rel,type,
% 5.31/5.47 vEBT_vebt_delete_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 5.31/5.47
% 5.31/5.47 thf(sy_c_VEBT__InsertCorrectness_OVEBT__internal_Oinsert_H,type,
% 5.31/5.47 vEBT_VEBT_insert: vEBT_VEBT > nat > vEBT_VEBT ).
% 5.31/5.47
% 5.31/5.47 thf(sy_c_VEBT__InsertCorrectness_OVEBT__internal_Oinsert_H__rel,type,
% 5.31/5.47 vEBT_VEBT_insert_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 5.31/5.47
% 5.31/5.47 thf(sy_c_VEBT__Insert_Ovebt__insert,type,
% 5.31/5.47 vEBT_vebt_insert: vEBT_VEBT > nat > vEBT_VEBT ).
% 5.31/5.47
% 5.31/5.47 thf(sy_c_VEBT__Insert_Ovebt__insert__rel,type,
% 5.31/5.47 vEBT_vebt_insert_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 5.31/5.47
% 5.31/5.47 thf(sy_c_VEBT__Member_OVEBT__internal_Obit__concat,type,
% 5.31/5.47 vEBT_VEBT_bit_concat: nat > nat > nat > nat ).
% 5.31/5.47
% 5.31/5.47 thf(sy_c_VEBT__Member_OVEBT__internal_OminNull,type,
% 5.31/5.47 vEBT_VEBT_minNull: vEBT_VEBT > $o ).
% 5.31/5.47
% 5.31/5.47 thf(sy_c_VEBT__Member_OVEBT__internal_OminNull__rel,type,
% 5.31/5.47 vEBT_V6963167321098673237ll_rel: vEBT_VEBT > vEBT_VEBT > $o ).
% 5.31/5.47
% 5.31/5.47 thf(sy_c_VEBT__Member_OVEBT__internal_Oset__vebt_H,type,
% 5.31/5.47 vEBT_VEBT_set_vebt: vEBT_VEBT > set_nat ).
% 5.31/5.47
% 5.31/5.47 thf(sy_c_VEBT__Member_Ovebt__member,type,
% 5.31/5.47 vEBT_vebt_member: vEBT_VEBT > nat > $o ).
% 5.31/5.47
% 5.31/5.47 thf(sy_c_VEBT__Member_Ovebt__member__rel,type,
% 5.31/5.47 vEBT_vebt_member_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 5.31/5.47
% 5.31/5.47 thf(sy_c_VEBT__MinMax_OVEBT__internal_Oadd,type,
% 5.31/5.47 vEBT_VEBT_add: option_nat > option_nat > option_nat ).
% 5.31/5.47
% 5.31/5.47 thf(sy_c_VEBT__MinMax_OVEBT__internal_Ogreater,type,
% 5.31/5.47 vEBT_VEBT_greater: option_nat > option_nat > $o ).
% 5.31/5.47
% 5.31/5.47 thf(sy_c_VEBT__MinMax_OVEBT__internal_Oless,type,
% 5.31/5.47 vEBT_VEBT_less: option_nat > option_nat > $o ).
% 5.31/5.47
% 5.31/5.47 thf(sy_c_VEBT__MinMax_OVEBT__internal_Olesseq,type,
% 5.31/5.47 vEBT_VEBT_lesseq: option_nat > option_nat > $o ).
% 5.31/5.47
% 5.31/5.47 thf(sy_c_VEBT__MinMax_OVEBT__internal_Omax__in__set,type,
% 5.31/5.47 vEBT_VEBT_max_in_set: set_nat > nat > $o ).
% 5.31/5.47
% 5.31/5.47 thf(sy_c_VEBT__MinMax_OVEBT__internal_Omin__in__set,type,
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% 5.31/5.47 member8277197624267554838et_nat: produc7819656566062154093et_nat > set_Pr5488025237498180813et_nat > $o ).
% 5.31/5.47
% 5.31/5.47 thf(sy_c_member_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
% 5.31/5.47 member8757157785044589968at_nat: produc3843707927480180839at_nat > set_Pr4329608150637261639at_nat > $o ).
% 5.31/5.47
% 5.31/5.47 thf(sy_c_member_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_M_Eo_J,type,
% 5.31/5.47 member3307348790968139188VEBT_o: produc334124729049499915VEBT_o > set_Pr3175402225741728619VEBT_o > $o ).
% 5.31/5.47
% 5.31/5.47 thf(sy_c_member_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Complex__Ocomplex_J,type,
% 5.31/5.47 member3207599676835851048omplex: produc8380087813684007313omplex > set_Pr216944050393469383omplex > $o ).
% 5.31/5.47
% 5.31/5.47 thf(sy_c_member_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Int__Oint_J,type,
% 5.31/5.47 member5419026705395827622BT_int: produc4894624898956917775BT_int > set_Pr5066593544530342725BT_int > $o ).
% 5.31/5.47
% 5.31/5.47 thf(sy_c_member_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Nat__Onat_J,type,
% 5.31/5.47 member373505688050248522BT_nat: produc9072475918466114483BT_nat > set_Pr7556676689462069481BT_nat > $o ).
% 5.31/5.47
% 5.31/5.47 thf(sy_c_member_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Real__Oreal_J,type,
% 5.31/5.47 member8675245146396747942T_real: produc5170161368751668367T_real > set_Pr7765410600122031685T_real > $o ).
% 5.31/5.47
% 5.31/5.47 thf(sy_c_member_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__VEBT____Definitions__OVEBT_J,type,
% 5.31/5.47 member568628332442017744T_VEBT: produc8243902056947475879T_VEBT > set_Pr6192946355708809607T_VEBT > $o ).
% 5.31/5.47
% 5.31/5.47 thf(sy_c_member_001t__Rat__Orat,type,
% 5.31/5.47 member_rat: rat > set_rat > $o ).
% 5.31/5.47
% 5.31/5.47 thf(sy_c_member_001t__Real__Oreal,type,
% 5.31/5.47 member_real: real > set_real > $o ).
% 5.31/5.47
% 5.31/5.47 thf(sy_c_member_001t__Set__Oset_It__Nat__Onat_J,type,
% 5.31/5.47 member_set_nat: set_nat > set_set_nat > $o ).
% 5.31/5.47
% 5.31/5.47 thf(sy_c_member_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 5.31/5.47 member2643936169264416010at_nat: set_Pr1261947904930325089at_nat > set_se7855581050983116737at_nat > $o ).
% 5.31/5.47
% 5.31/5.47 thf(sy_c_member_001t__VEBT____Definitions__OVEBT,type,
% 5.31/5.47 member_VEBT_VEBT: vEBT_VEBT > set_VEBT_VEBT > $o ).
% 5.31/5.47
% 5.31/5.47 thf(sy_v_a____,type,
% 5.31/5.47 a: $o ).
% 5.31/5.47
% 5.31/5.47 thf(sy_v_b____,type,
% 5.31/5.47 b: $o ).
% 5.31/5.47
% 5.31/5.47 thf(sy_v_deg____,type,
% 5.31/5.47 deg: nat ).
% 5.31/5.47
% 5.31/5.47 thf(sy_v_info____,type,
% 5.31/5.47 info: option4927543243414619207at_nat ).
% 5.31/5.47
% 5.31/5.47 thf(sy_v_m____,type,
% 5.31/5.47 m: nat ).
% 5.31/5.47
% 5.31/5.47 thf(sy_v_ma____,type,
% 5.31/5.47 ma: nat ).
% 5.31/5.47
% 5.31/5.47 thf(sy_v_mi____,type,
% 5.31/5.47 mi: nat ).
% 5.31/5.47
% 5.31/5.47 thf(sy_v_na____,type,
% 5.31/5.47 na: nat ).
% 5.31/5.47
% 5.31/5.47 thf(sy_v_sa____,type,
% 5.31/5.47 sa: vEBT_VEBT ).
% 5.31/5.47
% 5.31/5.47 thf(sy_v_summary_H____,type,
% 5.31/5.47 summary: vEBT_VEBT ).
% 5.31/5.47
% 5.31/5.47 thf(sy_v_summary____,type,
% 5.31/5.47 summary2: vEBT_VEBT ).
% 5.31/5.47
% 5.31/5.47 thf(sy_v_treeList_H____,type,
% 5.31/5.47 treeList: list_VEBT_VEBT ).
% 5.31/5.47
% 5.31/5.47 thf(sy_v_treeList____,type,
% 5.31/5.47 treeList2: list_VEBT_VEBT ).
% 5.31/5.47
% 5.31/5.47 % Relevant facts (9514)
% 5.31/5.47 thf(fact_0_case4_I9_J,axiom,
% 5.31/5.47 ord_less_eq_nat @ mi @ ma ).
% 5.31/5.47
% 5.31/5.47 % case4(9)
% 5.31/5.47 thf(fact_1_option_Oinject,axiom,
% 5.31/5.47 ! [X2: product_prod_nat_nat,Y2: product_prod_nat_nat] :
% 5.31/5.47 ( ( ( some_P7363390416028606310at_nat @ X2 )
% 5.31/5.47 = ( some_P7363390416028606310at_nat @ Y2 ) )
% 5.31/5.47 = ( X2 = Y2 ) ) ).
% 5.31/5.47
% 5.31/5.47 % option.inject
% 5.31/5.47 thf(fact_2_option_Oinject,axiom,
% 5.31/5.47 ! [X2: nat,Y2: nat] :
% 5.31/5.47 ( ( ( some_nat @ X2 )
% 5.31/5.47 = ( some_nat @ Y2 ) )
% 5.31/5.47 = ( X2 = Y2 ) ) ).
% 5.31/5.47
% 5.31/5.47 % option.inject
% 5.31/5.47 thf(fact_3_option_Oinject,axiom,
% 5.31/5.47 ! [X2: num,Y2: num] :
% 5.31/5.47 ( ( ( some_num @ X2 )
% 5.31/5.47 = ( some_num @ Y2 ) )
% 5.31/5.47 = ( X2 = Y2 ) ) ).
% 5.31/5.47
% 5.31/5.47 % option.inject
% 5.31/5.47 thf(fact_4_prod_Oinject,axiom,
% 5.31/5.47 ! [X1: code_integer,X2: code_integer,Y1: code_integer,Y2: code_integer] :
% 5.31/5.47 ( ( ( produc1086072967326762835nteger @ X1 @ X2 )
% 5.31/5.47 = ( produc1086072967326762835nteger @ Y1 @ Y2 ) )
% 5.31/5.47 = ( ( X1 = Y1 )
% 5.31/5.47 & ( X2 = Y2 ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % prod.inject
% 5.31/5.47 thf(fact_5_prod_Oinject,axiom,
% 5.31/5.47 ! [X1: product_prod_nat_nat,X2: product_prod_nat_nat,Y1: product_prod_nat_nat,Y2: product_prod_nat_nat] :
% 5.31/5.47 ( ( ( produc6161850002892822231at_nat @ X1 @ X2 )
% 5.31/5.47 = ( produc6161850002892822231at_nat @ Y1 @ Y2 ) )
% 5.31/5.47 = ( ( X1 = Y1 )
% 5.31/5.47 & ( X2 = Y2 ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % prod.inject
% 5.31/5.47 thf(fact_6_prod_Oinject,axiom,
% 5.31/5.47 ! [X1: set_Pr1261947904930325089at_nat,X2: set_Pr1261947904930325089at_nat,Y1: set_Pr1261947904930325089at_nat,Y2: set_Pr1261947904930325089at_nat] :
% 5.31/5.47 ( ( ( produc2922128104949294807at_nat @ X1 @ X2 )
% 5.31/5.47 = ( produc2922128104949294807at_nat @ Y1 @ Y2 ) )
% 5.31/5.47 = ( ( X1 = Y1 )
% 5.31/5.47 & ( X2 = Y2 ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % prod.inject
% 5.31/5.47 thf(fact_7_prod_Oinject,axiom,
% 5.31/5.47 ! [X1: nat,X2: nat,Y1: nat,Y2: nat] :
% 5.31/5.47 ( ( ( product_Pair_nat_nat @ X1 @ X2 )
% 5.31/5.47 = ( product_Pair_nat_nat @ Y1 @ Y2 ) )
% 5.31/5.47 = ( ( X1 = Y1 )
% 5.31/5.47 & ( X2 = Y2 ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % prod.inject
% 5.31/5.47 thf(fact_8_prod_Oinject,axiom,
% 5.31/5.47 ! [X1: int,X2: int,Y1: int,Y2: int] :
% 5.31/5.47 ( ( ( product_Pair_int_int @ X1 @ X2 )
% 5.31/5.47 = ( product_Pair_int_int @ Y1 @ Y2 ) )
% 5.31/5.47 = ( ( X1 = Y1 )
% 5.31/5.47 & ( X2 = Y2 ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % prod.inject
% 5.31/5.47 thf(fact_9_old_Oprod_Oinject,axiom,
% 5.31/5.47 ! [A: code_integer,B: code_integer,A2: code_integer,B2: code_integer] :
% 5.31/5.47 ( ( ( produc1086072967326762835nteger @ A @ B )
% 5.31/5.47 = ( produc1086072967326762835nteger @ A2 @ B2 ) )
% 5.31/5.47 = ( ( A = A2 )
% 5.31/5.47 & ( B = B2 ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % old.prod.inject
% 5.31/5.47 thf(fact_10_old_Oprod_Oinject,axiom,
% 5.31/5.47 ! [A: product_prod_nat_nat,B: product_prod_nat_nat,A2: product_prod_nat_nat,B2: product_prod_nat_nat] :
% 5.31/5.47 ( ( ( produc6161850002892822231at_nat @ A @ B )
% 5.31/5.47 = ( produc6161850002892822231at_nat @ A2 @ B2 ) )
% 5.31/5.47 = ( ( A = A2 )
% 5.31/5.47 & ( B = B2 ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % old.prod.inject
% 5.31/5.47 thf(fact_11_old_Oprod_Oinject,axiom,
% 5.31/5.47 ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat,A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 5.31/5.47 ( ( ( produc2922128104949294807at_nat @ A @ B )
% 5.31/5.47 = ( produc2922128104949294807at_nat @ A2 @ B2 ) )
% 5.31/5.47 = ( ( A = A2 )
% 5.31/5.47 & ( B = B2 ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % old.prod.inject
% 5.31/5.47 thf(fact_12_old_Oprod_Oinject,axiom,
% 5.31/5.47 ! [A: nat,B: nat,A2: nat,B2: nat] :
% 5.31/5.47 ( ( ( product_Pair_nat_nat @ A @ B )
% 5.31/5.47 = ( product_Pair_nat_nat @ A2 @ B2 ) )
% 5.31/5.47 = ( ( A = A2 )
% 5.31/5.47 & ( B = B2 ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % old.prod.inject
% 5.31/5.47 thf(fact_13_old_Oprod_Oinject,axiom,
% 5.31/5.47 ! [A: int,B: int,A2: int,B2: int] :
% 5.31/5.47 ( ( ( product_Pair_int_int @ A @ B )
% 5.31/5.47 = ( product_Pair_int_int @ A2 @ B2 ) )
% 5.31/5.47 = ( ( A = A2 )
% 5.31/5.47 & ( B = B2 ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % old.prod.inject
% 5.31/5.47 thf(fact_14_prod__decode__aux_Ocases,axiom,
% 5.31/5.47 ! [X: product_prod_nat_nat] :
% 5.31/5.47 ~ ! [K: nat,M: nat] :
% 5.31/5.47 ( X
% 5.31/5.47 != ( product_Pair_nat_nat @ K @ M ) ) ).
% 5.31/5.47
% 5.31/5.47 % prod_decode_aux.cases
% 5.31/5.47 thf(fact_15_old_Oprod_Oexhaust,axiom,
% 5.31/5.47 ! [Y: produc8923325533196201883nteger] :
% 5.31/5.47 ~ ! [A3: code_integer,B3: code_integer] :
% 5.31/5.47 ( Y
% 5.31/5.47 != ( produc1086072967326762835nteger @ A3 @ B3 ) ) ).
% 5.31/5.47
% 5.31/5.47 % old.prod.exhaust
% 5.31/5.47 thf(fact_16_old_Oprod_Oexhaust,axiom,
% 5.31/5.47 ! [Y: produc859450856879609959at_nat] :
% 5.31/5.47 ~ ! [A3: product_prod_nat_nat,B3: product_prod_nat_nat] :
% 5.31/5.47 ( Y
% 5.31/5.47 != ( produc6161850002892822231at_nat @ A3 @ B3 ) ) ).
% 5.31/5.47
% 5.31/5.47 % old.prod.exhaust
% 5.31/5.47 thf(fact_17_old_Oprod_Oexhaust,axiom,
% 5.31/5.47 ! [Y: produc3843707927480180839at_nat] :
% 5.31/5.47 ~ ! [A3: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat] :
% 5.31/5.47 ( Y
% 5.31/5.47 != ( produc2922128104949294807at_nat @ A3 @ B3 ) ) ).
% 5.31/5.47
% 5.31/5.47 % old.prod.exhaust
% 5.31/5.47 thf(fact_18_old_Oprod_Oexhaust,axiom,
% 5.31/5.47 ! [Y: product_prod_nat_nat] :
% 5.31/5.47 ~ ! [A3: nat,B3: nat] :
% 5.31/5.47 ( Y
% 5.31/5.47 != ( product_Pair_nat_nat @ A3 @ B3 ) ) ).
% 5.31/5.47
% 5.31/5.47 % old.prod.exhaust
% 5.31/5.47 thf(fact_19_old_Oprod_Oexhaust,axiom,
% 5.31/5.47 ! [Y: product_prod_int_int] :
% 5.31/5.47 ~ ! [A3: int,B3: int] :
% 5.31/5.47 ( Y
% 5.31/5.47 != ( product_Pair_int_int @ A3 @ B3 ) ) ).
% 5.31/5.47
% 5.31/5.47 % old.prod.exhaust
% 5.31/5.47 thf(fact_20_surj__pair,axiom,
% 5.31/5.47 ! [P: produc8923325533196201883nteger] :
% 5.31/5.47 ? [X3: code_integer,Y3: code_integer] :
% 5.31/5.47 ( P
% 5.31/5.47 = ( produc1086072967326762835nteger @ X3 @ Y3 ) ) ).
% 5.31/5.47
% 5.31/5.47 % surj_pair
% 5.31/5.47 thf(fact_21_surj__pair,axiom,
% 5.31/5.47 ! [P: produc859450856879609959at_nat] :
% 5.31/5.47 ? [X3: product_prod_nat_nat,Y3: product_prod_nat_nat] :
% 5.31/5.47 ( P
% 5.31/5.47 = ( produc6161850002892822231at_nat @ X3 @ Y3 ) ) ).
% 5.31/5.47
% 5.31/5.47 % surj_pair
% 5.31/5.47 thf(fact_22_surj__pair,axiom,
% 5.31/5.47 ! [P: produc3843707927480180839at_nat] :
% 5.31/5.47 ? [X3: set_Pr1261947904930325089at_nat,Y3: set_Pr1261947904930325089at_nat] :
% 5.31/5.47 ( P
% 5.31/5.47 = ( produc2922128104949294807at_nat @ X3 @ Y3 ) ) ).
% 5.31/5.47
% 5.31/5.47 % surj_pair
% 5.31/5.47 thf(fact_23_surj__pair,axiom,
% 5.31/5.47 ! [P: product_prod_nat_nat] :
% 5.31/5.47 ? [X3: nat,Y3: nat] :
% 5.31/5.47 ( P
% 5.31/5.47 = ( product_Pair_nat_nat @ X3 @ Y3 ) ) ).
% 5.31/5.47
% 5.31/5.47 % surj_pair
% 5.31/5.47 thf(fact_24_surj__pair,axiom,
% 5.31/5.47 ! [P: product_prod_int_int] :
% 5.31/5.47 ? [X3: int,Y3: int] :
% 5.31/5.47 ( P
% 5.31/5.47 = ( product_Pair_int_int @ X3 @ Y3 ) ) ).
% 5.31/5.47
% 5.31/5.47 % surj_pair
% 5.31/5.47 thf(fact_25_prod__cases,axiom,
% 5.31/5.47 ! [P2: produc8923325533196201883nteger > $o,P: produc8923325533196201883nteger] :
% 5.31/5.47 ( ! [A3: code_integer,B3: code_integer] : ( P2 @ ( produc1086072967326762835nteger @ A3 @ B3 ) )
% 5.31/5.47 => ( P2 @ P ) ) ).
% 5.31/5.47
% 5.31/5.47 % prod_cases
% 5.31/5.47 thf(fact_26_prod__cases,axiom,
% 5.31/5.47 ! [P2: produc859450856879609959at_nat > $o,P: produc859450856879609959at_nat] :
% 5.31/5.47 ( ! [A3: product_prod_nat_nat,B3: product_prod_nat_nat] : ( P2 @ ( produc6161850002892822231at_nat @ A3 @ B3 ) )
% 5.31/5.47 => ( P2 @ P ) ) ).
% 5.31/5.47
% 5.31/5.47 % prod_cases
% 5.31/5.47 thf(fact_27_prod__cases,axiom,
% 5.31/5.47 ! [P2: produc3843707927480180839at_nat > $o,P: produc3843707927480180839at_nat] :
% 5.31/5.47 ( ! [A3: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat] : ( P2 @ ( produc2922128104949294807at_nat @ A3 @ B3 ) )
% 5.31/5.47 => ( P2 @ P ) ) ).
% 5.31/5.47
% 5.31/5.47 % prod_cases
% 5.31/5.47 thf(fact_28_prod__cases,axiom,
% 5.31/5.47 ! [P2: product_prod_nat_nat > $o,P: product_prod_nat_nat] :
% 5.31/5.47 ( ! [A3: nat,B3: nat] : ( P2 @ ( product_Pair_nat_nat @ A3 @ B3 ) )
% 5.31/5.47 => ( P2 @ P ) ) ).
% 5.31/5.47
% 5.31/5.47 % prod_cases
% 5.31/5.47 thf(fact_29_prod__cases,axiom,
% 5.31/5.47 ! [P2: product_prod_int_int > $o,P: product_prod_int_int] :
% 5.31/5.47 ( ! [A3: int,B3: int] : ( P2 @ ( product_Pair_int_int @ A3 @ B3 ) )
% 5.31/5.47 => ( P2 @ P ) ) ).
% 5.31/5.47
% 5.31/5.47 % prod_cases
% 5.31/5.47 thf(fact_30_Pair__inject,axiom,
% 5.31/5.47 ! [A: code_integer,B: code_integer,A2: code_integer,B2: code_integer] :
% 5.31/5.47 ( ( ( produc1086072967326762835nteger @ A @ B )
% 5.31/5.47 = ( produc1086072967326762835nteger @ A2 @ B2 ) )
% 5.31/5.47 => ~ ( ( A = A2 )
% 5.31/5.47 => ( B != B2 ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % Pair_inject
% 5.31/5.47 thf(fact_31_Pair__inject,axiom,
% 5.31/5.47 ! [A: product_prod_nat_nat,B: product_prod_nat_nat,A2: product_prod_nat_nat,B2: product_prod_nat_nat] :
% 5.31/5.47 ( ( ( produc6161850002892822231at_nat @ A @ B )
% 5.31/5.47 = ( produc6161850002892822231at_nat @ A2 @ B2 ) )
% 5.31/5.47 => ~ ( ( A = A2 )
% 5.31/5.47 => ( B != B2 ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % Pair_inject
% 5.31/5.47 thf(fact_32_Pair__inject,axiom,
% 5.31/5.47 ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat,A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 5.31/5.47 ( ( ( produc2922128104949294807at_nat @ A @ B )
% 5.31/5.47 = ( produc2922128104949294807at_nat @ A2 @ B2 ) )
% 5.31/5.47 => ~ ( ( A = A2 )
% 5.31/5.47 => ( B != B2 ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % Pair_inject
% 5.31/5.47 thf(fact_33_Pair__inject,axiom,
% 5.31/5.47 ! [A: nat,B: nat,A2: nat,B2: nat] :
% 5.31/5.47 ( ( ( product_Pair_nat_nat @ A @ B )
% 5.31/5.47 = ( product_Pair_nat_nat @ A2 @ B2 ) )
% 5.31/5.47 => ~ ( ( A = A2 )
% 5.31/5.47 => ( B != B2 ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % Pair_inject
% 5.31/5.47 thf(fact_34_Pair__inject,axiom,
% 5.31/5.47 ! [A: int,B: int,A2: int,B2: int] :
% 5.31/5.47 ( ( ( product_Pair_int_int @ A @ B )
% 5.31/5.47 = ( product_Pair_int_int @ A2 @ B2 ) )
% 5.31/5.47 => ~ ( ( A = A2 )
% 5.31/5.47 => ( B != B2 ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % Pair_inject
% 5.31/5.47 thf(fact_35_prod__cases3,axiom,
% 5.31/5.47 ! [Y: produc859450856879609959at_nat] :
% 5.31/5.47 ~ ! [A3: product_prod_nat_nat,B3: nat,C: nat] :
% 5.31/5.47 ( Y
% 5.31/5.47 != ( produc6161850002892822231at_nat @ A3 @ ( product_Pair_nat_nat @ B3 @ C ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % prod_cases3
% 5.31/5.47 thf(fact_36_max__in__set__def,axiom,
% 5.31/5.47 ( vEBT_VEBT_max_in_set
% 5.31/5.47 = ( ^ [Xs: set_nat,X4: nat] :
% 5.31/5.47 ( ( member_nat @ X4 @ Xs )
% 5.31/5.47 & ! [Y4: nat] :
% 5.31/5.47 ( ( member_nat @ Y4 @ Xs )
% 5.31/5.47 => ( ord_less_eq_nat @ Y4 @ X4 ) ) ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % max_in_set_def
% 5.31/5.47 thf(fact_37_min__in__set__def,axiom,
% 5.31/5.47 ( vEBT_VEBT_min_in_set
% 5.31/5.47 = ( ^ [Xs: set_nat,X4: nat] :
% 5.31/5.47 ( ( member_nat @ X4 @ Xs )
% 5.31/5.47 & ! [Y4: nat] :
% 5.31/5.47 ( ( member_nat @ Y4 @ Xs )
% 5.31/5.47 => ( ord_less_eq_nat @ X4 @ Y4 ) ) ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % min_in_set_def
% 5.31/5.47 thf(fact_38_lesseq__shift,axiom,
% 5.31/5.47 ( ord_less_eq_nat
% 5.31/5.47 = ( ^ [X4: nat,Y4: nat] : ( vEBT_VEBT_lesseq @ ( some_nat @ X4 ) @ ( some_nat @ Y4 ) ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % lesseq_shift
% 5.31/5.47 thf(fact_39_prod__induct3,axiom,
% 5.31/5.47 ! [P2: produc859450856879609959at_nat > $o,X: produc859450856879609959at_nat] :
% 5.31/5.47 ( ! [A3: product_prod_nat_nat,B3: nat,C: nat] : ( P2 @ ( produc6161850002892822231at_nat @ A3 @ ( product_Pair_nat_nat @ B3 @ C ) ) )
% 5.31/5.47 => ( P2 @ X ) ) ).
% 5.31/5.47
% 5.31/5.47 % prod_induct3
% 5.31/5.47 thf(fact_40_order__refl,axiom,
% 5.31/5.47 ! [X: set_nat] : ( ord_less_eq_set_nat @ X @ X ) ).
% 5.31/5.47
% 5.31/5.47 % order_refl
% 5.31/5.47 thf(fact_41_order__refl,axiom,
% 5.31/5.47 ! [X: rat] : ( ord_less_eq_rat @ X @ X ) ).
% 5.31/5.47
% 5.31/5.47 % order_refl
% 5.31/5.47 thf(fact_42_order__refl,axiom,
% 5.31/5.47 ! [X: num] : ( ord_less_eq_num @ X @ X ) ).
% 5.31/5.47
% 5.31/5.47 % order_refl
% 5.31/5.47 thf(fact_43_order__refl,axiom,
% 5.31/5.47 ! [X: nat] : ( ord_less_eq_nat @ X @ X ) ).
% 5.31/5.47
% 5.31/5.47 % order_refl
% 5.31/5.47 thf(fact_44_order__refl,axiom,
% 5.31/5.47 ! [X: int] : ( ord_less_eq_int @ X @ X ) ).
% 5.31/5.47
% 5.31/5.47 % order_refl
% 5.31/5.47 thf(fact_45_dual__order_Orefl,axiom,
% 5.31/5.47 ! [A: set_nat] : ( ord_less_eq_set_nat @ A @ A ) ).
% 5.31/5.47
% 5.31/5.47 % dual_order.refl
% 5.31/5.47 thf(fact_46_dual__order_Orefl,axiom,
% 5.31/5.47 ! [A: rat] : ( ord_less_eq_rat @ A @ A ) ).
% 5.31/5.47
% 5.31/5.47 % dual_order.refl
% 5.31/5.47 thf(fact_47_dual__order_Orefl,axiom,
% 5.31/5.47 ! [A: num] : ( ord_less_eq_num @ A @ A ) ).
% 5.31/5.47
% 5.31/5.47 % dual_order.refl
% 5.31/5.47 thf(fact_48_dual__order_Orefl,axiom,
% 5.31/5.47 ! [A: nat] : ( ord_less_eq_nat @ A @ A ) ).
% 5.31/5.47
% 5.31/5.47 % dual_order.refl
% 5.31/5.47 thf(fact_49_dual__order_Orefl,axiom,
% 5.31/5.47 ! [A: int] : ( ord_less_eq_int @ A @ A ) ).
% 5.31/5.47
% 5.31/5.47 % dual_order.refl
% 5.31/5.47 thf(fact_50_relChain__def,axiom,
% 5.31/5.47 ( bNF_Ca8354645632395198811er_rat
% 5.31/5.47 = ( ^ [R: set_Pr4811707699266497531nteger,As: code_integer > rat] :
% 5.31/5.47 ! [I: code_integer,J: code_integer] :
% 5.31/5.47 ( ( member157494554546826820nteger @ ( produc1086072967326762835nteger @ I @ J ) @ R )
% 5.31/5.47 => ( ord_less_eq_rat @ ( As @ I ) @ ( As @ J ) ) ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % relChain_def
% 5.31/5.47 thf(fact_51_relChain__def,axiom,
% 5.31/5.47 ( bNF_Ca333620267926924494at_rat
% 5.31/5.47 = ( ^ [R: set_Pr1261947904930325089at_nat,As: nat > rat] :
% 5.31/5.47 ! [I: nat,J: nat] :
% 5.31/5.47 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ I @ J ) @ R )
% 5.31/5.47 => ( ord_less_eq_rat @ ( As @ I ) @ ( As @ J ) ) ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % relChain_def
% 5.31/5.47 thf(fact_52_relChain__def,axiom,
% 5.31/5.47 ( bNF_Ca1332973979827979050nt_rat
% 5.31/5.47 = ( ^ [R: set_Pr958786334691620121nt_int,As: int > rat] :
% 5.31/5.47 ! [I: int,J: int] :
% 5.31/5.47 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ I @ J ) @ R )
% 5.31/5.47 => ( ord_less_eq_rat @ ( As @ I ) @ ( As @ J ) ) ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % relChain_def
% 5.31/5.47 thf(fact_53_relChain__def,axiom,
% 5.31/5.47 ( bNF_Ca5547107478637473181er_num
% 5.31/5.47 = ( ^ [R: set_Pr4811707699266497531nteger,As: code_integer > num] :
% 5.31/5.47 ! [I: code_integer,J: code_integer] :
% 5.31/5.47 ( ( member157494554546826820nteger @ ( produc1086072967326762835nteger @ I @ J ) @ R )
% 5.31/5.47 => ( ord_less_eq_num @ ( As @ I ) @ ( As @ J ) ) ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % relChain_def
% 5.31/5.47 thf(fact_54_relChain__def,axiom,
% 5.31/5.47 ( bNF_Ca6749454151023974672at_num
% 5.31/5.47 = ( ^ [R: set_Pr1261947904930325089at_nat,As: nat > num] :
% 5.31/5.47 ! [I: nat,J: nat] :
% 5.31/5.47 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ I @ J ) @ R )
% 5.31/5.47 => ( ord_less_eq_num @ ( As @ I ) @ ( As @ J ) ) ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % relChain_def
% 5.31/5.47 thf(fact_55_relChain__def,axiom,
% 5.31/5.47 ( bNF_Ca7748807862925029228nt_num
% 5.31/5.47 = ( ^ [R: set_Pr958786334691620121nt_int,As: int > num] :
% 5.31/5.47 ! [I: int,J: int] :
% 5.31/5.47 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ I @ J ) @ R )
% 5.31/5.47 => ( ord_less_eq_num @ ( As @ I ) @ ( As @ J ) ) ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % relChain_def
% 5.31/5.47 thf(fact_56_relChain__def,axiom,
% 5.31/5.47 ( bNF_Ca8989775692481694547er_nat
% 5.31/5.47 = ( ^ [R: set_Pr4811707699266497531nteger,As: code_integer > nat] :
% 5.31/5.47 ! [I: code_integer,J: code_integer] :
% 5.31/5.47 ( ( member157494554546826820nteger @ ( produc1086072967326762835nteger @ I @ J ) @ R )
% 5.31/5.47 => ( ord_less_eq_nat @ ( As @ I ) @ ( As @ J ) ) ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % relChain_def
% 5.31/5.47 thf(fact_57_relChain__def,axiom,
% 5.31/5.47 ( bNF_Ca968750328013420230at_nat
% 5.31/5.47 = ( ^ [R: set_Pr1261947904930325089at_nat,As: nat > nat] :
% 5.31/5.47 ! [I: nat,J: nat] :
% 5.31/5.47 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ I @ J ) @ R )
% 5.31/5.47 => ( ord_less_eq_nat @ ( As @ I ) @ ( As @ J ) ) ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % relChain_def
% 5.31/5.47 thf(fact_58_relChain__def,axiom,
% 5.31/5.47 ( bNF_Ca1968104039914474786nt_nat
% 5.31/5.47 = ( ^ [R: set_Pr958786334691620121nt_int,As: int > nat] :
% 5.31/5.47 ! [I: int,J: int] :
% 5.31/5.47 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ I @ J ) @ R )
% 5.31/5.47 => ( ord_less_eq_nat @ ( As @ I ) @ ( As @ J ) ) ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % relChain_def
% 5.31/5.47 thf(fact_59_relChain__def,axiom,
% 5.31/5.47 ( bNF_Ca8987285221972644271er_int
% 5.31/5.47 = ( ^ [R: set_Pr4811707699266497531nteger,As: code_integer > int] :
% 5.31/5.47 ! [I: code_integer,J: code_integer] :
% 5.31/5.47 ( ( member157494554546826820nteger @ ( produc1086072967326762835nteger @ I @ J ) @ R )
% 5.31/5.47 => ( ord_less_eq_int @ ( As @ I ) @ ( As @ J ) ) ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % relChain_def
% 5.31/5.47 thf(fact_60_fold__atLeastAtMost__nat_Ocases,axiom,
% 5.31/5.47 ! [X: produc4471711990508489141at_nat] :
% 5.31/5.47 ~ ! [F: nat > nat > nat,A3: nat,B3: nat,Acc: nat] :
% 5.31/5.47 ( X
% 5.31/5.47 != ( produc3209952032786966637at_nat @ F @ ( produc487386426758144856at_nat @ A3 @ ( product_Pair_nat_nat @ B3 @ Acc ) ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % fold_atLeastAtMost_nat.cases
% 5.31/5.47 thf(fact_61_le__prod__encode__1,axiom,
% 5.31/5.47 ! [A: nat,B: nat] : ( ord_less_eq_nat @ A @ ( nat_prod_encode @ ( product_Pair_nat_nat @ A @ B ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % le_prod_encode_1
% 5.31/5.47 thf(fact_62_le__prod__encode__2,axiom,
% 5.31/5.47 ! [B: nat,A: nat] : ( ord_less_eq_nat @ B @ ( nat_prod_encode @ ( product_Pair_nat_nat @ A @ B ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % le_prod_encode_2
% 5.31/5.47 thf(fact_63_lift__Suc__mono__le,axiom,
% 5.31/5.47 ! [F2: nat > set_nat,N: nat,N2: nat] :
% 5.31/5.47 ( ! [N3: nat] : ( ord_less_eq_set_nat @ ( F2 @ N3 ) @ ( F2 @ ( suc @ N3 ) ) )
% 5.31/5.47 => ( ( ord_less_eq_nat @ N @ N2 )
% 5.31/5.47 => ( ord_less_eq_set_nat @ ( F2 @ N ) @ ( F2 @ N2 ) ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % lift_Suc_mono_le
% 5.31/5.47 thf(fact_64_lift__Suc__mono__le,axiom,
% 5.31/5.47 ! [F2: nat > rat,N: nat,N2: nat] :
% 5.31/5.47 ( ! [N3: nat] : ( ord_less_eq_rat @ ( F2 @ N3 ) @ ( F2 @ ( suc @ N3 ) ) )
% 5.31/5.47 => ( ( ord_less_eq_nat @ N @ N2 )
% 5.31/5.47 => ( ord_less_eq_rat @ ( F2 @ N ) @ ( F2 @ N2 ) ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % lift_Suc_mono_le
% 5.31/5.47 thf(fact_65_lift__Suc__mono__le,axiom,
% 5.31/5.47 ! [F2: nat > num,N: nat,N2: nat] :
% 5.31/5.47 ( ! [N3: nat] : ( ord_less_eq_num @ ( F2 @ N3 ) @ ( F2 @ ( suc @ N3 ) ) )
% 5.31/5.47 => ( ( ord_less_eq_nat @ N @ N2 )
% 5.31/5.47 => ( ord_less_eq_num @ ( F2 @ N ) @ ( F2 @ N2 ) ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % lift_Suc_mono_le
% 5.31/5.47 thf(fact_66_lift__Suc__mono__le,axiom,
% 5.31/5.47 ! [F2: nat > nat,N: nat,N2: nat] :
% 5.31/5.47 ( ! [N3: nat] : ( ord_less_eq_nat @ ( F2 @ N3 ) @ ( F2 @ ( suc @ N3 ) ) )
% 5.31/5.47 => ( ( ord_less_eq_nat @ N @ N2 )
% 5.31/5.47 => ( ord_less_eq_nat @ ( F2 @ N ) @ ( F2 @ N2 ) ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % lift_Suc_mono_le
% 5.31/5.47 thf(fact_67_lift__Suc__mono__le,axiom,
% 5.31/5.47 ! [F2: nat > int,N: nat,N2: nat] :
% 5.31/5.47 ( ! [N3: nat] : ( ord_less_eq_int @ ( F2 @ N3 ) @ ( F2 @ ( suc @ N3 ) ) )
% 5.31/5.47 => ( ( ord_less_eq_nat @ N @ N2 )
% 5.31/5.47 => ( ord_less_eq_int @ ( F2 @ N ) @ ( F2 @ N2 ) ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % lift_Suc_mono_le
% 5.31/5.47 thf(fact_68_lift__Suc__antimono__le,axiom,
% 5.31/5.47 ! [F2: nat > set_nat,N: nat,N2: nat] :
% 5.31/5.47 ( ! [N3: nat] : ( ord_less_eq_set_nat @ ( F2 @ ( suc @ N3 ) ) @ ( F2 @ N3 ) )
% 5.31/5.47 => ( ( ord_less_eq_nat @ N @ N2 )
% 5.31/5.47 => ( ord_less_eq_set_nat @ ( F2 @ N2 ) @ ( F2 @ N ) ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % lift_Suc_antimono_le
% 5.31/5.47 thf(fact_69_lift__Suc__antimono__le,axiom,
% 5.31/5.47 ! [F2: nat > rat,N: nat,N2: nat] :
% 5.31/5.47 ( ! [N3: nat] : ( ord_less_eq_rat @ ( F2 @ ( suc @ N3 ) ) @ ( F2 @ N3 ) )
% 5.31/5.47 => ( ( ord_less_eq_nat @ N @ N2 )
% 5.31/5.47 => ( ord_less_eq_rat @ ( F2 @ N2 ) @ ( F2 @ N ) ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % lift_Suc_antimono_le
% 5.31/5.47 thf(fact_70_lift__Suc__antimono__le,axiom,
% 5.31/5.47 ! [F2: nat > num,N: nat,N2: nat] :
% 5.31/5.47 ( ! [N3: nat] : ( ord_less_eq_num @ ( F2 @ ( suc @ N3 ) ) @ ( F2 @ N3 ) )
% 5.31/5.47 => ( ( ord_less_eq_nat @ N @ N2 )
% 5.31/5.47 => ( ord_less_eq_num @ ( F2 @ N2 ) @ ( F2 @ N ) ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % lift_Suc_antimono_le
% 5.31/5.47 thf(fact_71_lift__Suc__antimono__le,axiom,
% 5.31/5.47 ! [F2: nat > nat,N: nat,N2: nat] :
% 5.31/5.47 ( ! [N3: nat] : ( ord_less_eq_nat @ ( F2 @ ( suc @ N3 ) ) @ ( F2 @ N3 ) )
% 5.31/5.47 => ( ( ord_less_eq_nat @ N @ N2 )
% 5.31/5.47 => ( ord_less_eq_nat @ ( F2 @ N2 ) @ ( F2 @ N ) ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % lift_Suc_antimono_le
% 5.31/5.47 thf(fact_72_lift__Suc__antimono__le,axiom,
% 5.31/5.47 ! [F2: nat > int,N: nat,N2: nat] :
% 5.31/5.47 ( ! [N3: nat] : ( ord_less_eq_int @ ( F2 @ ( suc @ N3 ) ) @ ( F2 @ N3 ) )
% 5.31/5.47 => ( ( ord_less_eq_nat @ N @ N2 )
% 5.31/5.47 => ( ord_less_eq_int @ ( F2 @ N2 ) @ ( F2 @ N ) ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % lift_Suc_antimono_le
% 5.31/5.47 thf(fact_73_le__refl,axiom,
% 5.31/5.47 ! [N: nat] : ( ord_less_eq_nat @ N @ N ) ).
% 5.31/5.47
% 5.31/5.47 % le_refl
% 5.31/5.47 thf(fact_74_le__trans,axiom,
% 5.31/5.47 ! [I2: nat,J2: nat,K2: nat] :
% 5.31/5.47 ( ( ord_less_eq_nat @ I2 @ J2 )
% 5.31/5.47 => ( ( ord_less_eq_nat @ J2 @ K2 )
% 5.31/5.47 => ( ord_less_eq_nat @ I2 @ K2 ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % le_trans
% 5.31/5.47 thf(fact_75__C1_C_I2_J,axiom,
% 5.31/5.47 ( deg
% 5.31/5.47 = ( suc @ zero_zero_nat ) ) ).
% 5.31/5.47
% 5.31/5.47 % "1"(2)
% 5.31/5.47 thf(fact_76_old_Onat_Oinject,axiom,
% 5.31/5.47 ! [Nat: nat,Nat2: nat] :
% 5.31/5.47 ( ( ( suc @ Nat )
% 5.31/5.47 = ( suc @ Nat2 ) )
% 5.31/5.47 = ( Nat = Nat2 ) ) ).
% 5.31/5.47
% 5.31/5.47 % old.nat.inject
% 5.31/5.47 thf(fact_77_nat_Oinject,axiom,
% 5.31/5.47 ! [X2: nat,Y2: nat] :
% 5.31/5.47 ( ( ( suc @ X2 )
% 5.31/5.47 = ( suc @ Y2 ) )
% 5.31/5.47 = ( X2 = Y2 ) ) ).
% 5.31/5.47
% 5.31/5.47 % nat.inject
% 5.31/5.47 thf(fact_78_prod__encode__eq,axiom,
% 5.31/5.47 ! [X: product_prod_nat_nat,Y: product_prod_nat_nat] :
% 5.31/5.47 ( ( ( nat_prod_encode @ X )
% 5.31/5.47 = ( nat_prod_encode @ Y ) )
% 5.31/5.47 = ( X = Y ) ) ).
% 5.31/5.47
% 5.31/5.47 % prod_encode_eq
% 5.31/5.47 thf(fact_79_Suc__le__mono,axiom,
% 5.31/5.47 ! [N: nat,M2: nat] :
% 5.31/5.47 ( ( ord_less_eq_nat @ ( suc @ N ) @ ( suc @ M2 ) )
% 5.31/5.47 = ( ord_less_eq_nat @ N @ M2 ) ) ).
% 5.31/5.47
% 5.31/5.47 % Suc_le_mono
% 5.31/5.47 thf(fact_80_n__not__Suc__n,axiom,
% 5.31/5.47 ! [N: nat] :
% 5.31/5.47 ( N
% 5.31/5.47 != ( suc @ N ) ) ).
% 5.31/5.47
% 5.31/5.47 % n_not_Suc_n
% 5.31/5.47 thf(fact_81_Suc__inject,axiom,
% 5.31/5.47 ! [X: nat,Y: nat] :
% 5.31/5.47 ( ( ( suc @ X )
% 5.31/5.47 = ( suc @ Y ) )
% 5.31/5.47 => ( X = Y ) ) ).
% 5.31/5.47
% 5.31/5.47 % Suc_inject
% 5.31/5.47 thf(fact_82_transitive__stepwise__le,axiom,
% 5.31/5.47 ! [M2: nat,N: nat,R2: nat > nat > $o] :
% 5.31/5.47 ( ( ord_less_eq_nat @ M2 @ N )
% 5.31/5.47 => ( ! [X3: nat] : ( R2 @ X3 @ X3 )
% 5.31/5.47 => ( ! [X3: nat,Y3: nat,Z: nat] :
% 5.31/5.47 ( ( R2 @ X3 @ Y3 )
% 5.31/5.47 => ( ( R2 @ Y3 @ Z )
% 5.31/5.47 => ( R2 @ X3 @ Z ) ) )
% 5.31/5.47 => ( ! [N3: nat] : ( R2 @ N3 @ ( suc @ N3 ) )
% 5.31/5.47 => ( R2 @ M2 @ N ) ) ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % transitive_stepwise_le
% 5.31/5.47 thf(fact_83_nat__induct__at__least,axiom,
% 5.31/5.47 ! [M2: nat,N: nat,P2: nat > $o] :
% 5.31/5.47 ( ( ord_less_eq_nat @ M2 @ N )
% 5.31/5.47 => ( ( P2 @ M2 )
% 5.31/5.47 => ( ! [N3: nat] :
% 5.31/5.47 ( ( ord_less_eq_nat @ M2 @ N3 )
% 5.31/5.47 => ( ( P2 @ N3 )
% 5.31/5.47 => ( P2 @ ( suc @ N3 ) ) ) )
% 5.31/5.47 => ( P2 @ N ) ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % nat_induct_at_least
% 5.31/5.47 thf(fact_84_mem__Collect__eq,axiom,
% 5.31/5.47 ! [A: int,P2: int > $o] :
% 5.31/5.47 ( ( member_int @ A @ ( collect_int @ P2 ) )
% 5.31/5.47 = ( P2 @ A ) ) ).
% 5.31/5.47
% 5.31/5.47 % mem_Collect_eq
% 5.31/5.47 thf(fact_85_mem__Collect__eq,axiom,
% 5.31/5.47 ! [A: complex,P2: complex > $o] :
% 5.31/5.47 ( ( member_complex @ A @ ( collect_complex @ P2 ) )
% 5.31/5.47 = ( P2 @ A ) ) ).
% 5.31/5.47
% 5.31/5.47 % mem_Collect_eq
% 5.31/5.47 thf(fact_86_mem__Collect__eq,axiom,
% 5.31/5.47 ! [A: real,P2: real > $o] :
% 5.31/5.47 ( ( member_real @ A @ ( collect_real @ P2 ) )
% 5.31/5.47 = ( P2 @ A ) ) ).
% 5.31/5.47
% 5.31/5.47 % mem_Collect_eq
% 5.31/5.47 thf(fact_87_mem__Collect__eq,axiom,
% 5.31/5.47 ! [A: list_nat,P2: list_nat > $o] :
% 5.31/5.47 ( ( member_list_nat @ A @ ( collect_list_nat @ P2 ) )
% 5.31/5.47 = ( P2 @ A ) ) ).
% 5.31/5.47
% 5.31/5.47 % mem_Collect_eq
% 5.31/5.47 thf(fact_88_mem__Collect__eq,axiom,
% 5.31/5.47 ! [A: set_nat,P2: set_nat > $o] :
% 5.31/5.47 ( ( member_set_nat @ A @ ( collect_set_nat @ P2 ) )
% 5.31/5.47 = ( P2 @ A ) ) ).
% 5.31/5.47
% 5.31/5.47 % mem_Collect_eq
% 5.31/5.47 thf(fact_89_mem__Collect__eq,axiom,
% 5.31/5.47 ! [A: nat,P2: nat > $o] :
% 5.31/5.47 ( ( member_nat @ A @ ( collect_nat @ P2 ) )
% 5.31/5.47 = ( P2 @ A ) ) ).
% 5.31/5.47
% 5.31/5.47 % mem_Collect_eq
% 5.31/5.47 thf(fact_90_Collect__mem__eq,axiom,
% 5.31/5.47 ! [A4: set_int] :
% 5.31/5.47 ( ( collect_int
% 5.31/5.47 @ ^ [X4: int] : ( member_int @ X4 @ A4 ) )
% 5.31/5.47 = A4 ) ).
% 5.31/5.47
% 5.31/5.47 % Collect_mem_eq
% 5.31/5.47 thf(fact_91_Collect__mem__eq,axiom,
% 5.31/5.47 ! [A4: set_complex] :
% 5.31/5.47 ( ( collect_complex
% 5.31/5.47 @ ^ [X4: complex] : ( member_complex @ X4 @ A4 ) )
% 5.31/5.47 = A4 ) ).
% 5.31/5.47
% 5.31/5.47 % Collect_mem_eq
% 5.31/5.47 thf(fact_92_Collect__mem__eq,axiom,
% 5.31/5.47 ! [A4: set_real] :
% 5.31/5.47 ( ( collect_real
% 5.31/5.47 @ ^ [X4: real] : ( member_real @ X4 @ A4 ) )
% 5.31/5.47 = A4 ) ).
% 5.31/5.47
% 5.31/5.47 % Collect_mem_eq
% 5.31/5.47 thf(fact_93_Collect__mem__eq,axiom,
% 5.31/5.47 ! [A4: set_list_nat] :
% 5.31/5.47 ( ( collect_list_nat
% 5.31/5.47 @ ^ [X4: list_nat] : ( member_list_nat @ X4 @ A4 ) )
% 5.31/5.47 = A4 ) ).
% 5.31/5.47
% 5.31/5.47 % Collect_mem_eq
% 5.31/5.47 thf(fact_94_Collect__mem__eq,axiom,
% 5.31/5.47 ! [A4: set_set_nat] :
% 5.31/5.47 ( ( collect_set_nat
% 5.31/5.47 @ ^ [X4: set_nat] : ( member_set_nat @ X4 @ A4 ) )
% 5.31/5.47 = A4 ) ).
% 5.31/5.47
% 5.31/5.47 % Collect_mem_eq
% 5.31/5.47 thf(fact_95_Collect__mem__eq,axiom,
% 5.31/5.47 ! [A4: set_nat] :
% 5.31/5.47 ( ( collect_nat
% 5.31/5.47 @ ^ [X4: nat] : ( member_nat @ X4 @ A4 ) )
% 5.31/5.47 = A4 ) ).
% 5.31/5.47
% 5.31/5.47 % Collect_mem_eq
% 5.31/5.47 thf(fact_96_Collect__cong,axiom,
% 5.31/5.47 ! [P2: complex > $o,Q: complex > $o] :
% 5.31/5.47 ( ! [X3: complex] :
% 5.31/5.47 ( ( P2 @ X3 )
% 5.31/5.47 = ( Q @ X3 ) )
% 5.31/5.47 => ( ( collect_complex @ P2 )
% 5.31/5.47 = ( collect_complex @ Q ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % Collect_cong
% 5.31/5.47 thf(fact_97_Collect__cong,axiom,
% 5.31/5.47 ! [P2: real > $o,Q: real > $o] :
% 5.31/5.47 ( ! [X3: real] :
% 5.31/5.47 ( ( P2 @ X3 )
% 5.31/5.47 = ( Q @ X3 ) )
% 5.31/5.47 => ( ( collect_real @ P2 )
% 5.31/5.47 = ( collect_real @ Q ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % Collect_cong
% 5.31/5.47 thf(fact_98_Collect__cong,axiom,
% 5.31/5.47 ! [P2: list_nat > $o,Q: list_nat > $o] :
% 5.31/5.47 ( ! [X3: list_nat] :
% 5.31/5.47 ( ( P2 @ X3 )
% 5.31/5.47 = ( Q @ X3 ) )
% 5.31/5.47 => ( ( collect_list_nat @ P2 )
% 5.31/5.47 = ( collect_list_nat @ Q ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % Collect_cong
% 5.31/5.47 thf(fact_99_Collect__cong,axiom,
% 5.31/5.47 ! [P2: set_nat > $o,Q: set_nat > $o] :
% 5.31/5.47 ( ! [X3: set_nat] :
% 5.31/5.47 ( ( P2 @ X3 )
% 5.31/5.47 = ( Q @ X3 ) )
% 5.31/5.47 => ( ( collect_set_nat @ P2 )
% 5.31/5.47 = ( collect_set_nat @ Q ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % Collect_cong
% 5.31/5.47 thf(fact_100_Collect__cong,axiom,
% 5.31/5.47 ! [P2: nat > $o,Q: nat > $o] :
% 5.31/5.47 ( ! [X3: nat] :
% 5.31/5.47 ( ( P2 @ X3 )
% 5.31/5.47 = ( Q @ X3 ) )
% 5.31/5.47 => ( ( collect_nat @ P2 )
% 5.31/5.47 = ( collect_nat @ Q ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % Collect_cong
% 5.31/5.47 thf(fact_101_full__nat__induct,axiom,
% 5.31/5.47 ! [P2: nat > $o,N: nat] :
% 5.31/5.47 ( ! [N3: nat] :
% 5.31/5.47 ( ! [M3: nat] :
% 5.31/5.47 ( ( ord_less_eq_nat @ ( suc @ M3 ) @ N3 )
% 5.31/5.47 => ( P2 @ M3 ) )
% 5.31/5.47 => ( P2 @ N3 ) )
% 5.31/5.47 => ( P2 @ N ) ) ).
% 5.31/5.47
% 5.31/5.47 % full_nat_induct
% 5.31/5.47 thf(fact_102_not__less__eq__eq,axiom,
% 5.31/5.47 ! [M2: nat,N: nat] :
% 5.31/5.47 ( ( ~ ( ord_less_eq_nat @ M2 @ N ) )
% 5.31/5.47 = ( ord_less_eq_nat @ ( suc @ N ) @ M2 ) ) ).
% 5.31/5.47
% 5.31/5.47 % not_less_eq_eq
% 5.31/5.47 thf(fact_103_Suc__n__not__le__n,axiom,
% 5.31/5.47 ! [N: nat] :
% 5.31/5.47 ~ ( ord_less_eq_nat @ ( suc @ N ) @ N ) ).
% 5.31/5.47
% 5.31/5.47 % Suc_n_not_le_n
% 5.31/5.47 thf(fact_104_le__Suc__eq,axiom,
% 5.31/5.47 ! [M2: nat,N: nat] :
% 5.31/5.47 ( ( ord_less_eq_nat @ M2 @ ( suc @ N ) )
% 5.31/5.47 = ( ( ord_less_eq_nat @ M2 @ N )
% 5.31/5.47 | ( M2
% 5.31/5.47 = ( suc @ N ) ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % le_Suc_eq
% 5.31/5.47 thf(fact_105_Suc__le__D,axiom,
% 5.31/5.47 ! [N: nat,M4: nat] :
% 5.31/5.47 ( ( ord_less_eq_nat @ ( suc @ N ) @ M4 )
% 5.31/5.47 => ? [M: nat] :
% 5.31/5.47 ( M4
% 5.31/5.47 = ( suc @ M ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % Suc_le_D
% 5.31/5.47 thf(fact_106_le__SucI,axiom,
% 5.31/5.47 ! [M2: nat,N: nat] :
% 5.31/5.47 ( ( ord_less_eq_nat @ M2 @ N )
% 5.31/5.47 => ( ord_less_eq_nat @ M2 @ ( suc @ N ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % le_SucI
% 5.31/5.47 thf(fact_107_le__SucE,axiom,
% 5.31/5.47 ! [M2: nat,N: nat] :
% 5.31/5.47 ( ( ord_less_eq_nat @ M2 @ ( suc @ N ) )
% 5.31/5.47 => ( ~ ( ord_less_eq_nat @ M2 @ N )
% 5.31/5.47 => ( M2
% 5.31/5.47 = ( suc @ N ) ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % le_SucE
% 5.31/5.47 thf(fact_108_Suc__leD,axiom,
% 5.31/5.47 ! [M2: nat,N: nat] :
% 5.31/5.47 ( ( ord_less_eq_nat @ ( suc @ M2 ) @ N )
% 5.31/5.47 => ( ord_less_eq_nat @ M2 @ N ) ) ).
% 5.31/5.47
% 5.31/5.47 % Suc_leD
% 5.31/5.47 thf(fact_109_order__antisym__conv,axiom,
% 5.31/5.47 ! [Y: set_nat,X: set_nat] :
% 5.31/5.47 ( ( ord_less_eq_set_nat @ Y @ X )
% 5.31/5.47 => ( ( ord_less_eq_set_nat @ X @ Y )
% 5.31/5.47 = ( X = Y ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % order_antisym_conv
% 5.31/5.47 thf(fact_110_order__antisym__conv,axiom,
% 5.31/5.47 ! [Y: rat,X: rat] :
% 5.31/5.47 ( ( ord_less_eq_rat @ Y @ X )
% 5.31/5.47 => ( ( ord_less_eq_rat @ X @ Y )
% 5.31/5.47 = ( X = Y ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % order_antisym_conv
% 5.31/5.47 thf(fact_111_order__antisym__conv,axiom,
% 5.31/5.47 ! [Y: num,X: num] :
% 5.31/5.47 ( ( ord_less_eq_num @ Y @ X )
% 5.31/5.47 => ( ( ord_less_eq_num @ X @ Y )
% 5.31/5.47 = ( X = Y ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % order_antisym_conv
% 5.31/5.47 thf(fact_112_order__antisym__conv,axiom,
% 5.31/5.47 ! [Y: nat,X: nat] :
% 5.31/5.47 ( ( ord_less_eq_nat @ Y @ X )
% 5.31/5.47 => ( ( ord_less_eq_nat @ X @ Y )
% 5.31/5.47 = ( X = Y ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % order_antisym_conv
% 5.31/5.47 thf(fact_113_order__antisym__conv,axiom,
% 5.31/5.47 ! [Y: int,X: int] :
% 5.31/5.47 ( ( ord_less_eq_int @ Y @ X )
% 5.31/5.47 => ( ( ord_less_eq_int @ X @ Y )
% 5.31/5.47 = ( X = Y ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % order_antisym_conv
% 5.31/5.47 thf(fact_114_linorder__le__cases,axiom,
% 5.31/5.47 ! [X: rat,Y: rat] :
% 5.31/5.47 ( ~ ( ord_less_eq_rat @ X @ Y )
% 5.31/5.47 => ( ord_less_eq_rat @ Y @ X ) ) ).
% 5.31/5.47
% 5.31/5.47 % linorder_le_cases
% 5.31/5.47 thf(fact_115_linorder__le__cases,axiom,
% 5.31/5.47 ! [X: num,Y: num] :
% 5.31/5.47 ( ~ ( ord_less_eq_num @ X @ Y )
% 5.31/5.47 => ( ord_less_eq_num @ Y @ X ) ) ).
% 5.31/5.47
% 5.31/5.47 % linorder_le_cases
% 5.31/5.47 thf(fact_116_linorder__le__cases,axiom,
% 5.31/5.47 ! [X: nat,Y: nat] :
% 5.31/5.47 ( ~ ( ord_less_eq_nat @ X @ Y )
% 5.31/5.47 => ( ord_less_eq_nat @ Y @ X ) ) ).
% 5.31/5.47
% 5.31/5.47 % linorder_le_cases
% 5.31/5.47 thf(fact_117_linorder__le__cases,axiom,
% 5.31/5.47 ! [X: int,Y: int] :
% 5.31/5.47 ( ~ ( ord_less_eq_int @ X @ Y )
% 5.31/5.47 => ( ord_less_eq_int @ Y @ X ) ) ).
% 5.31/5.47
% 5.31/5.47 % linorder_le_cases
% 5.31/5.47 thf(fact_118_ord__le__eq__subst,axiom,
% 5.31/5.47 ! [A: rat,B: rat,F2: rat > rat,C2: rat] :
% 5.31/5.47 ( ( ord_less_eq_rat @ A @ B )
% 5.31/5.47 => ( ( ( F2 @ B )
% 5.31/5.47 = C2 )
% 5.31/5.47 => ( ! [X3: rat,Y3: rat] :
% 5.31/5.47 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 5.31/5.47 => ( ord_less_eq_rat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 5.31/5.47 => ( ord_less_eq_rat @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % ord_le_eq_subst
% 5.31/5.47 thf(fact_119_ord__le__eq__subst,axiom,
% 5.31/5.47 ! [A: rat,B: rat,F2: rat > num,C2: num] :
% 5.31/5.47 ( ( ord_less_eq_rat @ A @ B )
% 5.31/5.47 => ( ( ( F2 @ B )
% 5.31/5.47 = C2 )
% 5.31/5.47 => ( ! [X3: rat,Y3: rat] :
% 5.31/5.47 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 5.31/5.47 => ( ord_less_eq_num @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 5.31/5.47 => ( ord_less_eq_num @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % ord_le_eq_subst
% 5.31/5.47 thf(fact_120_ord__le__eq__subst,axiom,
% 5.31/5.47 ! [A: rat,B: rat,F2: rat > nat,C2: nat] :
% 5.31/5.47 ( ( ord_less_eq_rat @ A @ B )
% 5.31/5.47 => ( ( ( F2 @ B )
% 5.31/5.47 = C2 )
% 5.31/5.47 => ( ! [X3: rat,Y3: rat] :
% 5.31/5.47 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 5.31/5.47 => ( ord_less_eq_nat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 5.31/5.47 => ( ord_less_eq_nat @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % ord_le_eq_subst
% 5.31/5.47 thf(fact_121_ord__le__eq__subst,axiom,
% 5.31/5.47 ! [A: rat,B: rat,F2: rat > int,C2: int] :
% 5.31/5.47 ( ( ord_less_eq_rat @ A @ B )
% 5.31/5.47 => ( ( ( F2 @ B )
% 5.31/5.47 = C2 )
% 5.31/5.47 => ( ! [X3: rat,Y3: rat] :
% 5.31/5.47 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 5.31/5.47 => ( ord_less_eq_int @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 5.31/5.47 => ( ord_less_eq_int @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % ord_le_eq_subst
% 5.31/5.47 thf(fact_122_ord__le__eq__subst,axiom,
% 5.31/5.47 ! [A: num,B: num,F2: num > rat,C2: rat] :
% 5.31/5.47 ( ( ord_less_eq_num @ A @ B )
% 5.31/5.47 => ( ( ( F2 @ B )
% 5.31/5.47 = C2 )
% 5.31/5.47 => ( ! [X3: num,Y3: num] :
% 5.31/5.47 ( ( ord_less_eq_num @ X3 @ Y3 )
% 5.31/5.47 => ( ord_less_eq_rat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 5.31/5.47 => ( ord_less_eq_rat @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % ord_le_eq_subst
% 5.31/5.47 thf(fact_123_ord__le__eq__subst,axiom,
% 5.31/5.47 ! [A: num,B: num,F2: num > num,C2: num] :
% 5.31/5.47 ( ( ord_less_eq_num @ A @ B )
% 5.31/5.47 => ( ( ( F2 @ B )
% 5.31/5.47 = C2 )
% 5.31/5.47 => ( ! [X3: num,Y3: num] :
% 5.31/5.47 ( ( ord_less_eq_num @ X3 @ Y3 )
% 5.31/5.47 => ( ord_less_eq_num @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 5.31/5.47 => ( ord_less_eq_num @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % ord_le_eq_subst
% 5.31/5.47 thf(fact_124_ord__le__eq__subst,axiom,
% 5.31/5.47 ! [A: num,B: num,F2: num > nat,C2: nat] :
% 5.31/5.47 ( ( ord_less_eq_num @ A @ B )
% 5.31/5.47 => ( ( ( F2 @ B )
% 5.31/5.47 = C2 )
% 5.31/5.47 => ( ! [X3: num,Y3: num] :
% 5.31/5.47 ( ( ord_less_eq_num @ X3 @ Y3 )
% 5.31/5.47 => ( ord_less_eq_nat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 5.31/5.47 => ( ord_less_eq_nat @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % ord_le_eq_subst
% 5.31/5.47 thf(fact_125_ord__le__eq__subst,axiom,
% 5.31/5.47 ! [A: num,B: num,F2: num > int,C2: int] :
% 5.31/5.47 ( ( ord_less_eq_num @ A @ B )
% 5.31/5.47 => ( ( ( F2 @ B )
% 5.31/5.47 = C2 )
% 5.31/5.47 => ( ! [X3: num,Y3: num] :
% 5.31/5.47 ( ( ord_less_eq_num @ X3 @ Y3 )
% 5.31/5.47 => ( ord_less_eq_int @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 5.31/5.47 => ( ord_less_eq_int @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % ord_le_eq_subst
% 5.31/5.47 thf(fact_126_ord__le__eq__subst,axiom,
% 5.31/5.47 ! [A: nat,B: nat,F2: nat > rat,C2: rat] :
% 5.31/5.47 ( ( ord_less_eq_nat @ A @ B )
% 5.31/5.47 => ( ( ( F2 @ B )
% 5.31/5.47 = C2 )
% 5.31/5.47 => ( ! [X3: nat,Y3: nat] :
% 5.31/5.47 ( ( ord_less_eq_nat @ X3 @ Y3 )
% 5.31/5.47 => ( ord_less_eq_rat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 5.31/5.47 => ( ord_less_eq_rat @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % ord_le_eq_subst
% 5.31/5.47 thf(fact_127_ord__le__eq__subst,axiom,
% 5.31/5.47 ! [A: nat,B: nat,F2: nat > num,C2: num] :
% 5.31/5.47 ( ( ord_less_eq_nat @ A @ B )
% 5.31/5.47 => ( ( ( F2 @ B )
% 5.31/5.47 = C2 )
% 5.31/5.47 => ( ! [X3: nat,Y3: nat] :
% 5.31/5.47 ( ( ord_less_eq_nat @ X3 @ Y3 )
% 5.31/5.47 => ( ord_less_eq_num @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 5.31/5.47 => ( ord_less_eq_num @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % ord_le_eq_subst
% 5.31/5.47 thf(fact_128_ord__eq__le__subst,axiom,
% 5.31/5.47 ! [A: rat,F2: rat > rat,B: rat,C2: rat] :
% 5.31/5.47 ( ( A
% 5.31/5.47 = ( F2 @ B ) )
% 5.31/5.47 => ( ( ord_less_eq_rat @ B @ C2 )
% 5.31/5.47 => ( ! [X3: rat,Y3: rat] :
% 5.31/5.47 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 5.31/5.47 => ( ord_less_eq_rat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 5.31/5.47 => ( ord_less_eq_rat @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % ord_eq_le_subst
% 5.31/5.47 thf(fact_129_ord__eq__le__subst,axiom,
% 5.31/5.47 ! [A: num,F2: rat > num,B: rat,C2: rat] :
% 5.31/5.47 ( ( A
% 5.31/5.47 = ( F2 @ B ) )
% 5.31/5.47 => ( ( ord_less_eq_rat @ B @ C2 )
% 5.31/5.47 => ( ! [X3: rat,Y3: rat] :
% 5.31/5.47 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 5.31/5.47 => ( ord_less_eq_num @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 5.31/5.47 => ( ord_less_eq_num @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % ord_eq_le_subst
% 5.31/5.47 thf(fact_130_ord__eq__le__subst,axiom,
% 5.31/5.47 ! [A: nat,F2: rat > nat,B: rat,C2: rat] :
% 5.31/5.47 ( ( A
% 5.31/5.47 = ( F2 @ B ) )
% 5.31/5.47 => ( ( ord_less_eq_rat @ B @ C2 )
% 5.31/5.47 => ( ! [X3: rat,Y3: rat] :
% 5.31/5.47 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 5.31/5.47 => ( ord_less_eq_nat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 5.31/5.47 => ( ord_less_eq_nat @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % ord_eq_le_subst
% 5.31/5.47 thf(fact_131_ord__eq__le__subst,axiom,
% 5.31/5.47 ! [A: int,F2: rat > int,B: rat,C2: rat] :
% 5.31/5.47 ( ( A
% 5.31/5.47 = ( F2 @ B ) )
% 5.31/5.47 => ( ( ord_less_eq_rat @ B @ C2 )
% 5.31/5.47 => ( ! [X3: rat,Y3: rat] :
% 5.31/5.47 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 5.31/5.47 => ( ord_less_eq_int @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 5.31/5.47 => ( ord_less_eq_int @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % ord_eq_le_subst
% 5.31/5.47 thf(fact_132_ord__eq__le__subst,axiom,
% 5.31/5.47 ! [A: rat,F2: num > rat,B: num,C2: num] :
% 5.31/5.47 ( ( A
% 5.31/5.47 = ( F2 @ B ) )
% 5.31/5.47 => ( ( ord_less_eq_num @ B @ C2 )
% 5.31/5.47 => ( ! [X3: num,Y3: num] :
% 5.31/5.47 ( ( ord_less_eq_num @ X3 @ Y3 )
% 5.31/5.47 => ( ord_less_eq_rat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 5.31/5.47 => ( ord_less_eq_rat @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % ord_eq_le_subst
% 5.31/5.47 thf(fact_133_ord__eq__le__subst,axiom,
% 5.31/5.47 ! [A: num,F2: num > num,B: num,C2: num] :
% 5.31/5.47 ( ( A
% 5.31/5.47 = ( F2 @ B ) )
% 5.31/5.47 => ( ( ord_less_eq_num @ B @ C2 )
% 5.31/5.47 => ( ! [X3: num,Y3: num] :
% 5.31/5.47 ( ( ord_less_eq_num @ X3 @ Y3 )
% 5.31/5.47 => ( ord_less_eq_num @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 5.31/5.47 => ( ord_less_eq_num @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % ord_eq_le_subst
% 5.31/5.47 thf(fact_134_ord__eq__le__subst,axiom,
% 5.31/5.47 ! [A: nat,F2: num > nat,B: num,C2: num] :
% 5.31/5.47 ( ( A
% 5.31/5.47 = ( F2 @ B ) )
% 5.31/5.47 => ( ( ord_less_eq_num @ B @ C2 )
% 5.31/5.47 => ( ! [X3: num,Y3: num] :
% 5.31/5.47 ( ( ord_less_eq_num @ X3 @ Y3 )
% 5.31/5.47 => ( ord_less_eq_nat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 5.31/5.47 => ( ord_less_eq_nat @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % ord_eq_le_subst
% 5.31/5.47 thf(fact_135_ord__eq__le__subst,axiom,
% 5.31/5.47 ! [A: int,F2: num > int,B: num,C2: num] :
% 5.31/5.47 ( ( A
% 5.31/5.47 = ( F2 @ B ) )
% 5.31/5.47 => ( ( ord_less_eq_num @ B @ C2 )
% 5.31/5.47 => ( ! [X3: num,Y3: num] :
% 5.31/5.47 ( ( ord_less_eq_num @ X3 @ Y3 )
% 5.31/5.47 => ( ord_less_eq_int @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 5.31/5.47 => ( ord_less_eq_int @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % ord_eq_le_subst
% 5.31/5.47 thf(fact_136_ord__eq__le__subst,axiom,
% 5.31/5.47 ! [A: rat,F2: nat > rat,B: nat,C2: nat] :
% 5.31/5.47 ( ( A
% 5.31/5.47 = ( F2 @ B ) )
% 5.31/5.47 => ( ( ord_less_eq_nat @ B @ C2 )
% 5.31/5.47 => ( ! [X3: nat,Y3: nat] :
% 5.31/5.47 ( ( ord_less_eq_nat @ X3 @ Y3 )
% 5.31/5.47 => ( ord_less_eq_rat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 5.31/5.47 => ( ord_less_eq_rat @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % ord_eq_le_subst
% 5.31/5.47 thf(fact_137_ord__eq__le__subst,axiom,
% 5.31/5.47 ! [A: num,F2: nat > num,B: nat,C2: nat] :
% 5.31/5.47 ( ( A
% 5.31/5.47 = ( F2 @ B ) )
% 5.31/5.47 => ( ( ord_less_eq_nat @ B @ C2 )
% 5.31/5.47 => ( ! [X3: nat,Y3: nat] :
% 5.31/5.47 ( ( ord_less_eq_nat @ X3 @ Y3 )
% 5.31/5.47 => ( ord_less_eq_num @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 5.31/5.47 => ( ord_less_eq_num @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % ord_eq_le_subst
% 5.31/5.47 thf(fact_138_linorder__linear,axiom,
% 5.31/5.47 ! [X: rat,Y: rat] :
% 5.31/5.47 ( ( ord_less_eq_rat @ X @ Y )
% 5.31/5.47 | ( ord_less_eq_rat @ Y @ X ) ) ).
% 5.31/5.47
% 5.31/5.47 % linorder_linear
% 5.31/5.47 thf(fact_139_linorder__linear,axiom,
% 5.31/5.47 ! [X: num,Y: num] :
% 5.31/5.47 ( ( ord_less_eq_num @ X @ Y )
% 5.31/5.47 | ( ord_less_eq_num @ Y @ X ) ) ).
% 5.31/5.47
% 5.31/5.47 % linorder_linear
% 5.31/5.47 thf(fact_140_linorder__linear,axiom,
% 5.31/5.47 ! [X: nat,Y: nat] :
% 5.31/5.47 ( ( ord_less_eq_nat @ X @ Y )
% 5.31/5.47 | ( ord_less_eq_nat @ Y @ X ) ) ).
% 5.31/5.47
% 5.31/5.47 % linorder_linear
% 5.31/5.47 thf(fact_141_linorder__linear,axiom,
% 5.31/5.47 ! [X: int,Y: int] :
% 5.31/5.47 ( ( ord_less_eq_int @ X @ Y )
% 5.31/5.47 | ( ord_less_eq_int @ Y @ X ) ) ).
% 5.31/5.47
% 5.31/5.47 % linorder_linear
% 5.31/5.47 thf(fact_142_order__eq__refl,axiom,
% 5.31/5.47 ! [X: set_nat,Y: set_nat] :
% 5.31/5.47 ( ( X = Y )
% 5.31/5.47 => ( ord_less_eq_set_nat @ X @ Y ) ) ).
% 5.31/5.47
% 5.31/5.47 % order_eq_refl
% 5.31/5.47 thf(fact_143_order__eq__refl,axiom,
% 5.31/5.47 ! [X: rat,Y: rat] :
% 5.31/5.47 ( ( X = Y )
% 5.31/5.47 => ( ord_less_eq_rat @ X @ Y ) ) ).
% 5.31/5.47
% 5.31/5.47 % order_eq_refl
% 5.31/5.47 thf(fact_144_order__eq__refl,axiom,
% 5.31/5.47 ! [X: num,Y: num] :
% 5.31/5.47 ( ( X = Y )
% 5.31/5.47 => ( ord_less_eq_num @ X @ Y ) ) ).
% 5.31/5.47
% 5.31/5.47 % order_eq_refl
% 5.31/5.47 thf(fact_145_order__eq__refl,axiom,
% 5.31/5.47 ! [X: nat,Y: nat] :
% 5.31/5.47 ( ( X = Y )
% 5.31/5.47 => ( ord_less_eq_nat @ X @ Y ) ) ).
% 5.31/5.47
% 5.31/5.47 % order_eq_refl
% 5.31/5.47 thf(fact_146_order__eq__refl,axiom,
% 5.31/5.47 ! [X: int,Y: int] :
% 5.31/5.47 ( ( X = Y )
% 5.31/5.47 => ( ord_less_eq_int @ X @ Y ) ) ).
% 5.31/5.47
% 5.31/5.47 % order_eq_refl
% 5.31/5.47 thf(fact_147_order__subst2,axiom,
% 5.31/5.47 ! [A: rat,B: rat,F2: rat > rat,C2: rat] :
% 5.31/5.47 ( ( ord_less_eq_rat @ A @ B )
% 5.31/5.47 => ( ( ord_less_eq_rat @ ( F2 @ B ) @ C2 )
% 5.31/5.47 => ( ! [X3: rat,Y3: rat] :
% 5.31/5.47 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 5.31/5.47 => ( ord_less_eq_rat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 5.31/5.47 => ( ord_less_eq_rat @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % order_subst2
% 5.31/5.47 thf(fact_148_order__subst2,axiom,
% 5.31/5.47 ! [A: rat,B: rat,F2: rat > num,C2: num] :
% 5.31/5.47 ( ( ord_less_eq_rat @ A @ B )
% 5.31/5.47 => ( ( ord_less_eq_num @ ( F2 @ B ) @ C2 )
% 5.31/5.47 => ( ! [X3: rat,Y3: rat] :
% 5.31/5.47 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 5.31/5.47 => ( ord_less_eq_num @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 5.31/5.47 => ( ord_less_eq_num @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % order_subst2
% 5.31/5.47 thf(fact_149_order__subst2,axiom,
% 5.31/5.47 ! [A: rat,B: rat,F2: rat > nat,C2: nat] :
% 5.31/5.47 ( ( ord_less_eq_rat @ A @ B )
% 5.31/5.47 => ( ( ord_less_eq_nat @ ( F2 @ B ) @ C2 )
% 5.31/5.47 => ( ! [X3: rat,Y3: rat] :
% 5.31/5.47 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 5.31/5.47 => ( ord_less_eq_nat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 5.31/5.47 => ( ord_less_eq_nat @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % order_subst2
% 5.31/5.47 thf(fact_150_order__subst2,axiom,
% 5.31/5.47 ! [A: rat,B: rat,F2: rat > int,C2: int] :
% 5.31/5.47 ( ( ord_less_eq_rat @ A @ B )
% 5.31/5.47 => ( ( ord_less_eq_int @ ( F2 @ B ) @ C2 )
% 5.31/5.47 => ( ! [X3: rat,Y3: rat] :
% 5.31/5.47 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 5.31/5.47 => ( ord_less_eq_int @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 5.31/5.47 => ( ord_less_eq_int @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % order_subst2
% 5.31/5.47 thf(fact_151_order__subst2,axiom,
% 5.31/5.47 ! [A: num,B: num,F2: num > rat,C2: rat] :
% 5.31/5.47 ( ( ord_less_eq_num @ A @ B )
% 5.31/5.47 => ( ( ord_less_eq_rat @ ( F2 @ B ) @ C2 )
% 5.31/5.47 => ( ! [X3: num,Y3: num] :
% 5.31/5.47 ( ( ord_less_eq_num @ X3 @ Y3 )
% 5.31/5.47 => ( ord_less_eq_rat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 5.31/5.47 => ( ord_less_eq_rat @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % order_subst2
% 5.31/5.47 thf(fact_152_order__subst2,axiom,
% 5.31/5.47 ! [A: num,B: num,F2: num > num,C2: num] :
% 5.31/5.47 ( ( ord_less_eq_num @ A @ B )
% 5.31/5.47 => ( ( ord_less_eq_num @ ( F2 @ B ) @ C2 )
% 5.31/5.47 => ( ! [X3: num,Y3: num] :
% 5.31/5.47 ( ( ord_less_eq_num @ X3 @ Y3 )
% 5.31/5.47 => ( ord_less_eq_num @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 5.31/5.47 => ( ord_less_eq_num @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % order_subst2
% 5.31/5.47 thf(fact_153_order__subst2,axiom,
% 5.31/5.47 ! [A: num,B: num,F2: num > nat,C2: nat] :
% 5.31/5.47 ( ( ord_less_eq_num @ A @ B )
% 5.31/5.47 => ( ( ord_less_eq_nat @ ( F2 @ B ) @ C2 )
% 5.31/5.47 => ( ! [X3: num,Y3: num] :
% 5.31/5.47 ( ( ord_less_eq_num @ X3 @ Y3 )
% 5.31/5.47 => ( ord_less_eq_nat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 5.31/5.47 => ( ord_less_eq_nat @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % order_subst2
% 5.31/5.47 thf(fact_154_order__subst2,axiom,
% 5.31/5.47 ! [A: num,B: num,F2: num > int,C2: int] :
% 5.31/5.47 ( ( ord_less_eq_num @ A @ B )
% 5.31/5.47 => ( ( ord_less_eq_int @ ( F2 @ B ) @ C2 )
% 5.31/5.47 => ( ! [X3: num,Y3: num] :
% 5.31/5.47 ( ( ord_less_eq_num @ X3 @ Y3 )
% 5.31/5.47 => ( ord_less_eq_int @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 5.31/5.47 => ( ord_less_eq_int @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % order_subst2
% 5.31/5.47 thf(fact_155_order__subst2,axiom,
% 5.31/5.47 ! [A: nat,B: nat,F2: nat > rat,C2: rat] :
% 5.31/5.47 ( ( ord_less_eq_nat @ A @ B )
% 5.31/5.47 => ( ( ord_less_eq_rat @ ( F2 @ B ) @ C2 )
% 5.31/5.47 => ( ! [X3: nat,Y3: nat] :
% 5.31/5.47 ( ( ord_less_eq_nat @ X3 @ Y3 )
% 5.31/5.47 => ( ord_less_eq_rat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 5.31/5.47 => ( ord_less_eq_rat @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % order_subst2
% 5.31/5.47 thf(fact_156_order__subst2,axiom,
% 5.31/5.47 ! [A: nat,B: nat,F2: nat > num,C2: num] :
% 5.31/5.47 ( ( ord_less_eq_nat @ A @ B )
% 5.31/5.47 => ( ( ord_less_eq_num @ ( F2 @ B ) @ C2 )
% 5.31/5.47 => ( ! [X3: nat,Y3: nat] :
% 5.31/5.47 ( ( ord_less_eq_nat @ X3 @ Y3 )
% 5.31/5.47 => ( ord_less_eq_num @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 5.31/5.47 => ( ord_less_eq_num @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % order_subst2
% 5.31/5.47 thf(fact_157_order__subst1,axiom,
% 5.31/5.47 ! [A: rat,F2: rat > rat,B: rat,C2: rat] :
% 5.31/5.47 ( ( ord_less_eq_rat @ A @ ( F2 @ B ) )
% 5.31/5.47 => ( ( ord_less_eq_rat @ B @ C2 )
% 5.31/5.47 => ( ! [X3: rat,Y3: rat] :
% 5.31/5.47 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 5.31/5.47 => ( ord_less_eq_rat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 5.31/5.47 => ( ord_less_eq_rat @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % order_subst1
% 5.31/5.47 thf(fact_158_order__subst1,axiom,
% 5.31/5.47 ! [A: rat,F2: num > rat,B: num,C2: num] :
% 5.31/5.47 ( ( ord_less_eq_rat @ A @ ( F2 @ B ) )
% 5.31/5.47 => ( ( ord_less_eq_num @ B @ C2 )
% 5.31/5.47 => ( ! [X3: num,Y3: num] :
% 5.31/5.47 ( ( ord_less_eq_num @ X3 @ Y3 )
% 5.31/5.47 => ( ord_less_eq_rat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 5.31/5.47 => ( ord_less_eq_rat @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % order_subst1
% 5.31/5.47 thf(fact_159_order__subst1,axiom,
% 5.31/5.47 ! [A: rat,F2: nat > rat,B: nat,C2: nat] :
% 5.31/5.47 ( ( ord_less_eq_rat @ A @ ( F2 @ B ) )
% 5.31/5.47 => ( ( ord_less_eq_nat @ B @ C2 )
% 5.31/5.47 => ( ! [X3: nat,Y3: nat] :
% 5.31/5.47 ( ( ord_less_eq_nat @ X3 @ Y3 )
% 5.31/5.47 => ( ord_less_eq_rat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 5.31/5.47 => ( ord_less_eq_rat @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % order_subst1
% 5.31/5.47 thf(fact_160_order__subst1,axiom,
% 5.31/5.47 ! [A: rat,F2: int > rat,B: int,C2: int] :
% 5.31/5.47 ( ( ord_less_eq_rat @ A @ ( F2 @ B ) )
% 5.31/5.47 => ( ( ord_less_eq_int @ B @ C2 )
% 5.31/5.47 => ( ! [X3: int,Y3: int] :
% 5.31/5.47 ( ( ord_less_eq_int @ X3 @ Y3 )
% 5.31/5.47 => ( ord_less_eq_rat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 5.31/5.47 => ( ord_less_eq_rat @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % order_subst1
% 5.31/5.47 thf(fact_161_order__subst1,axiom,
% 5.31/5.47 ! [A: num,F2: rat > num,B: rat,C2: rat] :
% 5.31/5.47 ( ( ord_less_eq_num @ A @ ( F2 @ B ) )
% 5.31/5.47 => ( ( ord_less_eq_rat @ B @ C2 )
% 5.31/5.47 => ( ! [X3: rat,Y3: rat] :
% 5.31/5.47 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 5.31/5.47 => ( ord_less_eq_num @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 5.31/5.47 => ( ord_less_eq_num @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % order_subst1
% 5.31/5.47 thf(fact_162_order__subst1,axiom,
% 5.31/5.47 ! [A: num,F2: num > num,B: num,C2: num] :
% 5.31/5.47 ( ( ord_less_eq_num @ A @ ( F2 @ B ) )
% 5.31/5.47 => ( ( ord_less_eq_num @ B @ C2 )
% 5.31/5.47 => ( ! [X3: num,Y3: num] :
% 5.31/5.47 ( ( ord_less_eq_num @ X3 @ Y3 )
% 5.31/5.47 => ( ord_less_eq_num @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 5.31/5.47 => ( ord_less_eq_num @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % order_subst1
% 5.31/5.47 thf(fact_163_order__subst1,axiom,
% 5.31/5.47 ! [A: num,F2: nat > num,B: nat,C2: nat] :
% 5.31/5.47 ( ( ord_less_eq_num @ A @ ( F2 @ B ) )
% 5.31/5.47 => ( ( ord_less_eq_nat @ B @ C2 )
% 5.31/5.47 => ( ! [X3: nat,Y3: nat] :
% 5.31/5.47 ( ( ord_less_eq_nat @ X3 @ Y3 )
% 5.31/5.47 => ( ord_less_eq_num @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 5.31/5.47 => ( ord_less_eq_num @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % order_subst1
% 5.31/5.47 thf(fact_164_order__subst1,axiom,
% 5.31/5.47 ! [A: num,F2: int > num,B: int,C2: int] :
% 5.31/5.47 ( ( ord_less_eq_num @ A @ ( F2 @ B ) )
% 5.31/5.47 => ( ( ord_less_eq_int @ B @ C2 )
% 5.31/5.47 => ( ! [X3: int,Y3: int] :
% 5.31/5.47 ( ( ord_less_eq_int @ X3 @ Y3 )
% 5.31/5.47 => ( ord_less_eq_num @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 5.31/5.47 => ( ord_less_eq_num @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % order_subst1
% 5.31/5.47 thf(fact_165_order__subst1,axiom,
% 5.31/5.47 ! [A: nat,F2: rat > nat,B: rat,C2: rat] :
% 5.31/5.47 ( ( ord_less_eq_nat @ A @ ( F2 @ B ) )
% 5.31/5.47 => ( ( ord_less_eq_rat @ B @ C2 )
% 5.31/5.47 => ( ! [X3: rat,Y3: rat] :
% 5.31/5.47 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 5.31/5.47 => ( ord_less_eq_nat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 5.31/5.47 => ( ord_less_eq_nat @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % order_subst1
% 5.31/5.47 thf(fact_166_order__subst1,axiom,
% 5.31/5.47 ! [A: nat,F2: num > nat,B: num,C2: num] :
% 5.31/5.47 ( ( ord_less_eq_nat @ A @ ( F2 @ B ) )
% 5.31/5.47 => ( ( ord_less_eq_num @ B @ C2 )
% 5.31/5.47 => ( ! [X3: num,Y3: num] :
% 5.31/5.47 ( ( ord_less_eq_num @ X3 @ Y3 )
% 5.31/5.47 => ( ord_less_eq_nat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 5.31/5.47 => ( ord_less_eq_nat @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % order_subst1
% 5.31/5.47 thf(fact_167_Orderings_Oorder__eq__iff,axiom,
% 5.31/5.47 ( ( ^ [Y5: set_nat,Z2: set_nat] : ( Y5 = Z2 ) )
% 5.31/5.47 = ( ^ [A5: set_nat,B4: set_nat] :
% 5.31/5.47 ( ( ord_less_eq_set_nat @ A5 @ B4 )
% 5.31/5.47 & ( ord_less_eq_set_nat @ B4 @ A5 ) ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % Orderings.order_eq_iff
% 5.31/5.47 thf(fact_168_Orderings_Oorder__eq__iff,axiom,
% 5.31/5.47 ( ( ^ [Y5: rat,Z2: rat] : ( Y5 = Z2 ) )
% 5.31/5.47 = ( ^ [A5: rat,B4: rat] :
% 5.31/5.47 ( ( ord_less_eq_rat @ A5 @ B4 )
% 5.31/5.47 & ( ord_less_eq_rat @ B4 @ A5 ) ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % Orderings.order_eq_iff
% 5.31/5.47 thf(fact_169_Orderings_Oorder__eq__iff,axiom,
% 5.31/5.47 ( ( ^ [Y5: num,Z2: num] : ( Y5 = Z2 ) )
% 5.31/5.47 = ( ^ [A5: num,B4: num] :
% 5.31/5.47 ( ( ord_less_eq_num @ A5 @ B4 )
% 5.31/5.47 & ( ord_less_eq_num @ B4 @ A5 ) ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % Orderings.order_eq_iff
% 5.31/5.47 thf(fact_170_Orderings_Oorder__eq__iff,axiom,
% 5.31/5.47 ( ( ^ [Y5: nat,Z2: nat] : ( Y5 = Z2 ) )
% 5.31/5.47 = ( ^ [A5: nat,B4: nat] :
% 5.31/5.47 ( ( ord_less_eq_nat @ A5 @ B4 )
% 5.31/5.47 & ( ord_less_eq_nat @ B4 @ A5 ) ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % Orderings.order_eq_iff
% 5.31/5.47 thf(fact_171_Orderings_Oorder__eq__iff,axiom,
% 5.31/5.47 ( ( ^ [Y5: int,Z2: int] : ( Y5 = Z2 ) )
% 5.31/5.47 = ( ^ [A5: int,B4: int] :
% 5.31/5.47 ( ( ord_less_eq_int @ A5 @ B4 )
% 5.31/5.47 & ( ord_less_eq_int @ B4 @ A5 ) ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % Orderings.order_eq_iff
% 5.31/5.47 thf(fact_172_antisym,axiom,
% 5.31/5.47 ! [A: set_nat,B: set_nat] :
% 5.31/5.47 ( ( ord_less_eq_set_nat @ A @ B )
% 5.31/5.47 => ( ( ord_less_eq_set_nat @ B @ A )
% 5.31/5.47 => ( A = B ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % antisym
% 5.31/5.47 thf(fact_173_antisym,axiom,
% 5.31/5.47 ! [A: rat,B: rat] :
% 5.31/5.47 ( ( ord_less_eq_rat @ A @ B )
% 5.31/5.47 => ( ( ord_less_eq_rat @ B @ A )
% 5.31/5.47 => ( A = B ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % antisym
% 5.31/5.47 thf(fact_174_antisym,axiom,
% 5.31/5.47 ! [A: num,B: num] :
% 5.31/5.47 ( ( ord_less_eq_num @ A @ B )
% 5.31/5.47 => ( ( ord_less_eq_num @ B @ A )
% 5.31/5.47 => ( A = B ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % antisym
% 5.31/5.47 thf(fact_175_antisym,axiom,
% 5.31/5.47 ! [A: nat,B: nat] :
% 5.31/5.47 ( ( ord_less_eq_nat @ A @ B )
% 5.31/5.47 => ( ( ord_less_eq_nat @ B @ A )
% 5.31/5.47 => ( A = B ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % antisym
% 5.31/5.47 thf(fact_176_antisym,axiom,
% 5.31/5.47 ! [A: int,B: int] :
% 5.31/5.47 ( ( ord_less_eq_int @ A @ B )
% 5.31/5.47 => ( ( ord_less_eq_int @ B @ A )
% 5.31/5.47 => ( A = B ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % antisym
% 5.31/5.47 thf(fact_177_dual__order_Otrans,axiom,
% 5.31/5.47 ! [B: set_nat,A: set_nat,C2: set_nat] :
% 5.31/5.47 ( ( ord_less_eq_set_nat @ B @ A )
% 5.31/5.47 => ( ( ord_less_eq_set_nat @ C2 @ B )
% 5.31/5.47 => ( ord_less_eq_set_nat @ C2 @ A ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % dual_order.trans
% 5.31/5.47 thf(fact_178_dual__order_Otrans,axiom,
% 5.31/5.47 ! [B: rat,A: rat,C2: rat] :
% 5.31/5.47 ( ( ord_less_eq_rat @ B @ A )
% 5.31/5.47 => ( ( ord_less_eq_rat @ C2 @ B )
% 5.31/5.47 => ( ord_less_eq_rat @ C2 @ A ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % dual_order.trans
% 5.31/5.47 thf(fact_179_dual__order_Otrans,axiom,
% 5.31/5.47 ! [B: num,A: num,C2: num] :
% 5.31/5.47 ( ( ord_less_eq_num @ B @ A )
% 5.31/5.47 => ( ( ord_less_eq_num @ C2 @ B )
% 5.31/5.47 => ( ord_less_eq_num @ C2 @ A ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % dual_order.trans
% 5.31/5.47 thf(fact_180_dual__order_Otrans,axiom,
% 5.31/5.47 ! [B: nat,A: nat,C2: nat] :
% 5.31/5.47 ( ( ord_less_eq_nat @ B @ A )
% 5.31/5.47 => ( ( ord_less_eq_nat @ C2 @ B )
% 5.31/5.47 => ( ord_less_eq_nat @ C2 @ A ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % dual_order.trans
% 5.31/5.47 thf(fact_181_dual__order_Otrans,axiom,
% 5.31/5.47 ! [B: int,A: int,C2: int] :
% 5.31/5.47 ( ( ord_less_eq_int @ B @ A )
% 5.31/5.47 => ( ( ord_less_eq_int @ C2 @ B )
% 5.31/5.47 => ( ord_less_eq_int @ C2 @ A ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % dual_order.trans
% 5.31/5.47 thf(fact_182_dual__order_Oantisym,axiom,
% 5.31/5.47 ! [B: set_nat,A: set_nat] :
% 5.31/5.47 ( ( ord_less_eq_set_nat @ B @ A )
% 5.31/5.47 => ( ( ord_less_eq_set_nat @ A @ B )
% 5.31/5.47 => ( A = B ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % dual_order.antisym
% 5.31/5.47 thf(fact_183_dual__order_Oantisym,axiom,
% 5.31/5.47 ! [B: rat,A: rat] :
% 5.31/5.47 ( ( ord_less_eq_rat @ B @ A )
% 5.31/5.47 => ( ( ord_less_eq_rat @ A @ B )
% 5.31/5.47 => ( A = B ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % dual_order.antisym
% 5.31/5.47 thf(fact_184_dual__order_Oantisym,axiom,
% 5.31/5.47 ! [B: num,A: num] :
% 5.31/5.47 ( ( ord_less_eq_num @ B @ A )
% 5.31/5.47 => ( ( ord_less_eq_num @ A @ B )
% 5.31/5.47 => ( A = B ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % dual_order.antisym
% 5.31/5.47 thf(fact_185_dual__order_Oantisym,axiom,
% 5.31/5.47 ! [B: nat,A: nat] :
% 5.31/5.47 ( ( ord_less_eq_nat @ B @ A )
% 5.31/5.47 => ( ( ord_less_eq_nat @ A @ B )
% 5.31/5.47 => ( A = B ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % dual_order.antisym
% 5.31/5.47 thf(fact_186_dual__order_Oantisym,axiom,
% 5.31/5.47 ! [B: int,A: int] :
% 5.31/5.47 ( ( ord_less_eq_int @ B @ A )
% 5.31/5.47 => ( ( ord_less_eq_int @ A @ B )
% 5.31/5.47 => ( A = B ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % dual_order.antisym
% 5.31/5.47 thf(fact_187_dual__order_Oeq__iff,axiom,
% 5.31/5.47 ( ( ^ [Y5: set_nat,Z2: set_nat] : ( Y5 = Z2 ) )
% 5.31/5.47 = ( ^ [A5: set_nat,B4: set_nat] :
% 5.31/5.47 ( ( ord_less_eq_set_nat @ B4 @ A5 )
% 5.31/5.47 & ( ord_less_eq_set_nat @ A5 @ B4 ) ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % dual_order.eq_iff
% 5.31/5.47 thf(fact_188_dual__order_Oeq__iff,axiom,
% 5.31/5.47 ( ( ^ [Y5: rat,Z2: rat] : ( Y5 = Z2 ) )
% 5.31/5.47 = ( ^ [A5: rat,B4: rat] :
% 5.31/5.47 ( ( ord_less_eq_rat @ B4 @ A5 )
% 5.31/5.47 & ( ord_less_eq_rat @ A5 @ B4 ) ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % dual_order.eq_iff
% 5.31/5.47 thf(fact_189_dual__order_Oeq__iff,axiom,
% 5.31/5.47 ( ( ^ [Y5: num,Z2: num] : ( Y5 = Z2 ) )
% 5.31/5.47 = ( ^ [A5: num,B4: num] :
% 5.31/5.47 ( ( ord_less_eq_num @ B4 @ A5 )
% 5.31/5.47 & ( ord_less_eq_num @ A5 @ B4 ) ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % dual_order.eq_iff
% 5.31/5.47 thf(fact_190_dual__order_Oeq__iff,axiom,
% 5.31/5.47 ( ( ^ [Y5: nat,Z2: nat] : ( Y5 = Z2 ) )
% 5.31/5.47 = ( ^ [A5: nat,B4: nat] :
% 5.31/5.47 ( ( ord_less_eq_nat @ B4 @ A5 )
% 5.31/5.47 & ( ord_less_eq_nat @ A5 @ B4 ) ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % dual_order.eq_iff
% 5.31/5.47 thf(fact_191_dual__order_Oeq__iff,axiom,
% 5.31/5.47 ( ( ^ [Y5: int,Z2: int] : ( Y5 = Z2 ) )
% 5.31/5.47 = ( ^ [A5: int,B4: int] :
% 5.31/5.47 ( ( ord_less_eq_int @ B4 @ A5 )
% 5.31/5.47 & ( ord_less_eq_int @ A5 @ B4 ) ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % dual_order.eq_iff
% 5.31/5.47 thf(fact_192_linorder__wlog,axiom,
% 5.31/5.47 ! [P2: rat > rat > $o,A: rat,B: rat] :
% 5.31/5.47 ( ! [A3: rat,B3: rat] :
% 5.31/5.47 ( ( ord_less_eq_rat @ A3 @ B3 )
% 5.31/5.47 => ( P2 @ A3 @ B3 ) )
% 5.31/5.47 => ( ! [A3: rat,B3: rat] :
% 5.31/5.47 ( ( P2 @ B3 @ A3 )
% 5.31/5.47 => ( P2 @ A3 @ B3 ) )
% 5.31/5.47 => ( P2 @ A @ B ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % linorder_wlog
% 5.31/5.47 thf(fact_193_linorder__wlog,axiom,
% 5.31/5.47 ! [P2: num > num > $o,A: num,B: num] :
% 5.31/5.47 ( ! [A3: num,B3: num] :
% 5.31/5.47 ( ( ord_less_eq_num @ A3 @ B3 )
% 5.31/5.47 => ( P2 @ A3 @ B3 ) )
% 5.31/5.47 => ( ! [A3: num,B3: num] :
% 5.31/5.47 ( ( P2 @ B3 @ A3 )
% 5.31/5.47 => ( P2 @ A3 @ B3 ) )
% 5.31/5.47 => ( P2 @ A @ B ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % linorder_wlog
% 5.31/5.47 thf(fact_194_linorder__wlog,axiom,
% 5.31/5.47 ! [P2: nat > nat > $o,A: nat,B: nat] :
% 5.31/5.47 ( ! [A3: nat,B3: nat] :
% 5.31/5.47 ( ( ord_less_eq_nat @ A3 @ B3 )
% 5.31/5.47 => ( P2 @ A3 @ B3 ) )
% 5.31/5.47 => ( ! [A3: nat,B3: nat] :
% 5.31/5.47 ( ( P2 @ B3 @ A3 )
% 5.31/5.47 => ( P2 @ A3 @ B3 ) )
% 5.31/5.47 => ( P2 @ A @ B ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % linorder_wlog
% 5.31/5.47 thf(fact_195_linorder__wlog,axiom,
% 5.31/5.47 ! [P2: int > int > $o,A: int,B: int] :
% 5.31/5.47 ( ! [A3: int,B3: int] :
% 5.31/5.47 ( ( ord_less_eq_int @ A3 @ B3 )
% 5.31/5.47 => ( P2 @ A3 @ B3 ) )
% 5.31/5.47 => ( ! [A3: int,B3: int] :
% 5.31/5.47 ( ( P2 @ B3 @ A3 )
% 5.31/5.47 => ( P2 @ A3 @ B3 ) )
% 5.31/5.47 => ( P2 @ A @ B ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % linorder_wlog
% 5.31/5.47 thf(fact_196_order__trans,axiom,
% 5.31/5.47 ! [X: set_nat,Y: set_nat,Z3: set_nat] :
% 5.31/5.47 ( ( ord_less_eq_set_nat @ X @ Y )
% 5.31/5.47 => ( ( ord_less_eq_set_nat @ Y @ Z3 )
% 5.31/5.47 => ( ord_less_eq_set_nat @ X @ Z3 ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % order_trans
% 5.31/5.47 thf(fact_197_order__trans,axiom,
% 5.31/5.47 ! [X: rat,Y: rat,Z3: rat] :
% 5.31/5.47 ( ( ord_less_eq_rat @ X @ Y )
% 5.31/5.47 => ( ( ord_less_eq_rat @ Y @ Z3 )
% 5.31/5.47 => ( ord_less_eq_rat @ X @ Z3 ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % order_trans
% 5.31/5.47 thf(fact_198_order__trans,axiom,
% 5.31/5.47 ! [X: num,Y: num,Z3: num] :
% 5.31/5.47 ( ( ord_less_eq_num @ X @ Y )
% 5.31/5.47 => ( ( ord_less_eq_num @ Y @ Z3 )
% 5.31/5.47 => ( ord_less_eq_num @ X @ Z3 ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % order_trans
% 5.31/5.47 thf(fact_199_order__trans,axiom,
% 5.31/5.47 ! [X: nat,Y: nat,Z3: nat] :
% 5.31/5.47 ( ( ord_less_eq_nat @ X @ Y )
% 5.31/5.47 => ( ( ord_less_eq_nat @ Y @ Z3 )
% 5.31/5.47 => ( ord_less_eq_nat @ X @ Z3 ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % order_trans
% 5.31/5.47 thf(fact_200_order__trans,axiom,
% 5.31/5.47 ! [X: int,Y: int,Z3: int] :
% 5.31/5.47 ( ( ord_less_eq_int @ X @ Y )
% 5.31/5.47 => ( ( ord_less_eq_int @ Y @ Z3 )
% 5.31/5.47 => ( ord_less_eq_int @ X @ Z3 ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % order_trans
% 5.31/5.47 thf(fact_201_order_Otrans,axiom,
% 5.31/5.47 ! [A: set_nat,B: set_nat,C2: set_nat] :
% 5.31/5.47 ( ( ord_less_eq_set_nat @ A @ B )
% 5.31/5.47 => ( ( ord_less_eq_set_nat @ B @ C2 )
% 5.31/5.47 => ( ord_less_eq_set_nat @ A @ C2 ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % order.trans
% 5.31/5.47 thf(fact_202_order_Otrans,axiom,
% 5.31/5.47 ! [A: rat,B: rat,C2: rat] :
% 5.31/5.47 ( ( ord_less_eq_rat @ A @ B )
% 5.31/5.47 => ( ( ord_less_eq_rat @ B @ C2 )
% 5.31/5.47 => ( ord_less_eq_rat @ A @ C2 ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % order.trans
% 5.31/5.47 thf(fact_203_order_Otrans,axiom,
% 5.31/5.47 ! [A: num,B: num,C2: num] :
% 5.31/5.47 ( ( ord_less_eq_num @ A @ B )
% 5.31/5.47 => ( ( ord_less_eq_num @ B @ C2 )
% 5.31/5.47 => ( ord_less_eq_num @ A @ C2 ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % order.trans
% 5.31/5.47 thf(fact_204_order_Otrans,axiom,
% 5.31/5.47 ! [A: nat,B: nat,C2: nat] :
% 5.31/5.47 ( ( ord_less_eq_nat @ A @ B )
% 5.31/5.47 => ( ( ord_less_eq_nat @ B @ C2 )
% 5.31/5.47 => ( ord_less_eq_nat @ A @ C2 ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % order.trans
% 5.31/5.47 thf(fact_205_order_Otrans,axiom,
% 5.31/5.47 ! [A: int,B: int,C2: int] :
% 5.31/5.47 ( ( ord_less_eq_int @ A @ B )
% 5.31/5.47 => ( ( ord_less_eq_int @ B @ C2 )
% 5.31/5.47 => ( ord_less_eq_int @ A @ C2 ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % order.trans
% 5.31/5.47 thf(fact_206_order__antisym,axiom,
% 5.31/5.47 ! [X: set_nat,Y: set_nat] :
% 5.31/5.47 ( ( ord_less_eq_set_nat @ X @ Y )
% 5.31/5.47 => ( ( ord_less_eq_set_nat @ Y @ X )
% 5.31/5.47 => ( X = Y ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % order_antisym
% 5.31/5.47 thf(fact_207_order__antisym,axiom,
% 5.31/5.47 ! [X: rat,Y: rat] :
% 5.31/5.47 ( ( ord_less_eq_rat @ X @ Y )
% 5.31/5.47 => ( ( ord_less_eq_rat @ Y @ X )
% 5.31/5.47 => ( X = Y ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % order_antisym
% 5.31/5.47 thf(fact_208_order__antisym,axiom,
% 5.31/5.47 ! [X: num,Y: num] :
% 5.31/5.47 ( ( ord_less_eq_num @ X @ Y )
% 5.31/5.47 => ( ( ord_less_eq_num @ Y @ X )
% 5.31/5.47 => ( X = Y ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % order_antisym
% 5.31/5.47 thf(fact_209_order__antisym,axiom,
% 5.31/5.47 ! [X: nat,Y: nat] :
% 5.31/5.47 ( ( ord_less_eq_nat @ X @ Y )
% 5.31/5.47 => ( ( ord_less_eq_nat @ Y @ X )
% 5.31/5.47 => ( X = Y ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % order_antisym
% 5.31/5.47 thf(fact_210_order__antisym,axiom,
% 5.31/5.47 ! [X: int,Y: int] :
% 5.31/5.47 ( ( ord_less_eq_int @ X @ Y )
% 5.31/5.47 => ( ( ord_less_eq_int @ Y @ X )
% 5.31/5.47 => ( X = Y ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % order_antisym
% 5.31/5.47 thf(fact_211_ord__le__eq__trans,axiom,
% 5.31/5.47 ! [A: set_nat,B: set_nat,C2: set_nat] :
% 5.31/5.47 ( ( ord_less_eq_set_nat @ A @ B )
% 5.31/5.47 => ( ( B = C2 )
% 5.31/5.47 => ( ord_less_eq_set_nat @ A @ C2 ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % ord_le_eq_trans
% 5.31/5.47 thf(fact_212_ord__le__eq__trans,axiom,
% 5.31/5.47 ! [A: rat,B: rat,C2: rat] :
% 5.31/5.47 ( ( ord_less_eq_rat @ A @ B )
% 5.31/5.47 => ( ( B = C2 )
% 5.31/5.47 => ( ord_less_eq_rat @ A @ C2 ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % ord_le_eq_trans
% 5.31/5.47 thf(fact_213_ord__le__eq__trans,axiom,
% 5.31/5.47 ! [A: num,B: num,C2: num] :
% 5.31/5.47 ( ( ord_less_eq_num @ A @ B )
% 5.31/5.47 => ( ( B = C2 )
% 5.31/5.47 => ( ord_less_eq_num @ A @ C2 ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % ord_le_eq_trans
% 5.31/5.47 thf(fact_214_ord__le__eq__trans,axiom,
% 5.31/5.47 ! [A: nat,B: nat,C2: nat] :
% 5.31/5.47 ( ( ord_less_eq_nat @ A @ B )
% 5.31/5.47 => ( ( B = C2 )
% 5.31/5.47 => ( ord_less_eq_nat @ A @ C2 ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % ord_le_eq_trans
% 5.31/5.47 thf(fact_215_ord__le__eq__trans,axiom,
% 5.31/5.47 ! [A: int,B: int,C2: int] :
% 5.31/5.47 ( ( ord_less_eq_int @ A @ B )
% 5.31/5.47 => ( ( B = C2 )
% 5.31/5.47 => ( ord_less_eq_int @ A @ C2 ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % ord_le_eq_trans
% 5.31/5.47 thf(fact_216_ord__eq__le__trans,axiom,
% 5.31/5.47 ! [A: set_nat,B: set_nat,C2: set_nat] :
% 5.31/5.47 ( ( A = B )
% 5.31/5.47 => ( ( ord_less_eq_set_nat @ B @ C2 )
% 5.31/5.47 => ( ord_less_eq_set_nat @ A @ C2 ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % ord_eq_le_trans
% 5.31/5.47 thf(fact_217_ord__eq__le__trans,axiom,
% 5.31/5.47 ! [A: rat,B: rat,C2: rat] :
% 5.31/5.47 ( ( A = B )
% 5.31/5.47 => ( ( ord_less_eq_rat @ B @ C2 )
% 5.31/5.47 => ( ord_less_eq_rat @ A @ C2 ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % ord_eq_le_trans
% 5.31/5.47 thf(fact_218_ord__eq__le__trans,axiom,
% 5.31/5.47 ! [A: num,B: num,C2: num] :
% 5.31/5.47 ( ( A = B )
% 5.31/5.47 => ( ( ord_less_eq_num @ B @ C2 )
% 5.31/5.47 => ( ord_less_eq_num @ A @ C2 ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % ord_eq_le_trans
% 5.31/5.47 thf(fact_219_ord__eq__le__trans,axiom,
% 5.31/5.47 ! [A: nat,B: nat,C2: nat] :
% 5.31/5.47 ( ( A = B )
% 5.31/5.47 => ( ( ord_less_eq_nat @ B @ C2 )
% 5.31/5.47 => ( ord_less_eq_nat @ A @ C2 ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % ord_eq_le_trans
% 5.31/5.47 thf(fact_220_ord__eq__le__trans,axiom,
% 5.31/5.47 ! [A: int,B: int,C2: int] :
% 5.31/5.47 ( ( A = B )
% 5.31/5.47 => ( ( ord_less_eq_int @ B @ C2 )
% 5.31/5.47 => ( ord_less_eq_int @ A @ C2 ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % ord_eq_le_trans
% 5.31/5.47 thf(fact_221_order__class_Oorder__eq__iff,axiom,
% 5.31/5.47 ( ( ^ [Y5: set_nat,Z2: set_nat] : ( Y5 = Z2 ) )
% 5.31/5.47 = ( ^ [X4: set_nat,Y4: set_nat] :
% 5.31/5.47 ( ( ord_less_eq_set_nat @ X4 @ Y4 )
% 5.31/5.47 & ( ord_less_eq_set_nat @ Y4 @ X4 ) ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % order_class.order_eq_iff
% 5.31/5.47 thf(fact_222_order__class_Oorder__eq__iff,axiom,
% 5.31/5.47 ( ( ^ [Y5: rat,Z2: rat] : ( Y5 = Z2 ) )
% 5.31/5.47 = ( ^ [X4: rat,Y4: rat] :
% 5.31/5.47 ( ( ord_less_eq_rat @ X4 @ Y4 )
% 5.31/5.47 & ( ord_less_eq_rat @ Y4 @ X4 ) ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % order_class.order_eq_iff
% 5.31/5.47 thf(fact_223_order__class_Oorder__eq__iff,axiom,
% 5.31/5.47 ( ( ^ [Y5: num,Z2: num] : ( Y5 = Z2 ) )
% 5.31/5.47 = ( ^ [X4: num,Y4: num] :
% 5.31/5.47 ( ( ord_less_eq_num @ X4 @ Y4 )
% 5.31/5.47 & ( ord_less_eq_num @ Y4 @ X4 ) ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % order_class.order_eq_iff
% 5.31/5.47 thf(fact_224_order__class_Oorder__eq__iff,axiom,
% 5.31/5.47 ( ( ^ [Y5: nat,Z2: nat] : ( Y5 = Z2 ) )
% 5.31/5.47 = ( ^ [X4: nat,Y4: nat] :
% 5.31/5.47 ( ( ord_less_eq_nat @ X4 @ Y4 )
% 5.31/5.47 & ( ord_less_eq_nat @ Y4 @ X4 ) ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % order_class.order_eq_iff
% 5.31/5.47 thf(fact_225_order__class_Oorder__eq__iff,axiom,
% 5.31/5.47 ( ( ^ [Y5: int,Z2: int] : ( Y5 = Z2 ) )
% 5.31/5.47 = ( ^ [X4: int,Y4: int] :
% 5.31/5.47 ( ( ord_less_eq_int @ X4 @ Y4 )
% 5.31/5.47 & ( ord_less_eq_int @ Y4 @ X4 ) ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % order_class.order_eq_iff
% 5.31/5.47 thf(fact_226_le__cases3,axiom,
% 5.31/5.47 ! [X: rat,Y: rat,Z3: rat] :
% 5.31/5.47 ( ( ( ord_less_eq_rat @ X @ Y )
% 5.31/5.47 => ~ ( ord_less_eq_rat @ Y @ Z3 ) )
% 5.31/5.47 => ( ( ( ord_less_eq_rat @ Y @ X )
% 5.31/5.47 => ~ ( ord_less_eq_rat @ X @ Z3 ) )
% 5.31/5.47 => ( ( ( ord_less_eq_rat @ X @ Z3 )
% 5.31/5.47 => ~ ( ord_less_eq_rat @ Z3 @ Y ) )
% 5.31/5.47 => ( ( ( ord_less_eq_rat @ Z3 @ Y )
% 5.31/5.47 => ~ ( ord_less_eq_rat @ Y @ X ) )
% 5.31/5.47 => ( ( ( ord_less_eq_rat @ Y @ Z3 )
% 5.31/5.47 => ~ ( ord_less_eq_rat @ Z3 @ X ) )
% 5.31/5.47 => ~ ( ( ord_less_eq_rat @ Z3 @ X )
% 5.31/5.47 => ~ ( ord_less_eq_rat @ X @ Y ) ) ) ) ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % le_cases3
% 5.31/5.47 thf(fact_227_le__cases3,axiom,
% 5.31/5.47 ! [X: num,Y: num,Z3: num] :
% 5.31/5.47 ( ( ( ord_less_eq_num @ X @ Y )
% 5.31/5.47 => ~ ( ord_less_eq_num @ Y @ Z3 ) )
% 5.31/5.47 => ( ( ( ord_less_eq_num @ Y @ X )
% 5.31/5.47 => ~ ( ord_less_eq_num @ X @ Z3 ) )
% 5.31/5.47 => ( ( ( ord_less_eq_num @ X @ Z3 )
% 5.31/5.47 => ~ ( ord_less_eq_num @ Z3 @ Y ) )
% 5.31/5.47 => ( ( ( ord_less_eq_num @ Z3 @ Y )
% 5.31/5.47 => ~ ( ord_less_eq_num @ Y @ X ) )
% 5.31/5.47 => ( ( ( ord_less_eq_num @ Y @ Z3 )
% 5.31/5.47 => ~ ( ord_less_eq_num @ Z3 @ X ) )
% 5.31/5.47 => ~ ( ( ord_less_eq_num @ Z3 @ X )
% 5.31/5.47 => ~ ( ord_less_eq_num @ X @ Y ) ) ) ) ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % le_cases3
% 5.31/5.47 thf(fact_228_le__cases3,axiom,
% 5.31/5.47 ! [X: nat,Y: nat,Z3: nat] :
% 5.31/5.47 ( ( ( ord_less_eq_nat @ X @ Y )
% 5.31/5.47 => ~ ( ord_less_eq_nat @ Y @ Z3 ) )
% 5.31/5.47 => ( ( ( ord_less_eq_nat @ Y @ X )
% 5.31/5.47 => ~ ( ord_less_eq_nat @ X @ Z3 ) )
% 5.31/5.47 => ( ( ( ord_less_eq_nat @ X @ Z3 )
% 5.31/5.47 => ~ ( ord_less_eq_nat @ Z3 @ Y ) )
% 5.31/5.47 => ( ( ( ord_less_eq_nat @ Z3 @ Y )
% 5.31/5.47 => ~ ( ord_less_eq_nat @ Y @ X ) )
% 5.31/5.47 => ( ( ( ord_less_eq_nat @ Y @ Z3 )
% 5.31/5.47 => ~ ( ord_less_eq_nat @ Z3 @ X ) )
% 5.31/5.47 => ~ ( ( ord_less_eq_nat @ Z3 @ X )
% 5.31/5.47 => ~ ( ord_less_eq_nat @ X @ Y ) ) ) ) ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % le_cases3
% 5.31/5.47 thf(fact_229_le__cases3,axiom,
% 5.31/5.47 ! [X: int,Y: int,Z3: int] :
% 5.31/5.47 ( ( ( ord_less_eq_int @ X @ Y )
% 5.31/5.47 => ~ ( ord_less_eq_int @ Y @ Z3 ) )
% 5.31/5.47 => ( ( ( ord_less_eq_int @ Y @ X )
% 5.31/5.47 => ~ ( ord_less_eq_int @ X @ Z3 ) )
% 5.31/5.47 => ( ( ( ord_less_eq_int @ X @ Z3 )
% 5.31/5.47 => ~ ( ord_less_eq_int @ Z3 @ Y ) )
% 5.31/5.47 => ( ( ( ord_less_eq_int @ Z3 @ Y )
% 5.31/5.47 => ~ ( ord_less_eq_int @ Y @ X ) )
% 5.31/5.47 => ( ( ( ord_less_eq_int @ Y @ Z3 )
% 5.31/5.47 => ~ ( ord_less_eq_int @ Z3 @ X ) )
% 5.31/5.47 => ~ ( ( ord_less_eq_int @ Z3 @ X )
% 5.31/5.47 => ~ ( ord_less_eq_int @ X @ Y ) ) ) ) ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % le_cases3
% 5.31/5.47 thf(fact_230_nle__le,axiom,
% 5.31/5.47 ! [A: rat,B: rat] :
% 5.31/5.47 ( ( ~ ( ord_less_eq_rat @ A @ B ) )
% 5.31/5.47 = ( ( ord_less_eq_rat @ B @ A )
% 5.31/5.47 & ( B != A ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % nle_le
% 5.31/5.47 thf(fact_231_nle__le,axiom,
% 5.31/5.47 ! [A: num,B: num] :
% 5.31/5.47 ( ( ~ ( ord_less_eq_num @ A @ B ) )
% 5.31/5.47 = ( ( ord_less_eq_num @ B @ A )
% 5.31/5.47 & ( B != A ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % nle_le
% 5.31/5.47 thf(fact_232_nle__le,axiom,
% 5.31/5.47 ! [A: nat,B: nat] :
% 5.31/5.47 ( ( ~ ( ord_less_eq_nat @ A @ B ) )
% 5.31/5.47 = ( ( ord_less_eq_nat @ B @ A )
% 5.31/5.47 & ( B != A ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % nle_le
% 5.31/5.47 thf(fact_233_nle__le,axiom,
% 5.31/5.47 ! [A: int,B: int] :
% 5.31/5.47 ( ( ~ ( ord_less_eq_int @ A @ B ) )
% 5.31/5.47 = ( ( ord_less_eq_int @ B @ A )
% 5.31/5.47 & ( B != A ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % nle_le
% 5.31/5.47 thf(fact_234_bounded__Max__nat,axiom,
% 5.31/5.47 ! [P2: nat > $o,X: nat,M5: nat] :
% 5.31/5.47 ( ( P2 @ X )
% 5.31/5.47 => ( ! [X3: nat] :
% 5.31/5.47 ( ( P2 @ X3 )
% 5.31/5.47 => ( ord_less_eq_nat @ X3 @ M5 ) )
% 5.31/5.47 => ~ ! [M: nat] :
% 5.31/5.47 ( ( P2 @ M )
% 5.31/5.47 => ~ ! [X5: nat] :
% 5.31/5.47 ( ( P2 @ X5 )
% 5.31/5.47 => ( ord_less_eq_nat @ X5 @ M ) ) ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % bounded_Max_nat
% 5.31/5.47 thf(fact_235_Nat_Oex__has__greatest__nat,axiom,
% 5.31/5.47 ! [P2: nat > $o,K2: nat,B: nat] :
% 5.31/5.47 ( ( P2 @ K2 )
% 5.31/5.47 => ( ! [Y3: nat] :
% 5.31/5.47 ( ( P2 @ Y3 )
% 5.31/5.47 => ( ord_less_eq_nat @ Y3 @ B ) )
% 5.31/5.47 => ? [X3: nat] :
% 5.31/5.47 ( ( P2 @ X3 )
% 5.31/5.47 & ! [Y6: nat] :
% 5.31/5.47 ( ( P2 @ Y6 )
% 5.31/5.47 => ( ord_less_eq_nat @ Y6 @ X3 ) ) ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % Nat.ex_has_greatest_nat
% 5.31/5.47 thf(fact_236_nat__le__linear,axiom,
% 5.31/5.47 ! [M2: nat,N: nat] :
% 5.31/5.47 ( ( ord_less_eq_nat @ M2 @ N )
% 5.31/5.47 | ( ord_less_eq_nat @ N @ M2 ) ) ).
% 5.31/5.47
% 5.31/5.47 % nat_le_linear
% 5.31/5.47 thf(fact_237_le__antisym,axiom,
% 5.31/5.47 ! [M2: nat,N: nat] :
% 5.31/5.47 ( ( ord_less_eq_nat @ M2 @ N )
% 5.31/5.47 => ( ( ord_less_eq_nat @ N @ M2 )
% 5.31/5.47 => ( M2 = N ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % le_antisym
% 5.31/5.47 thf(fact_238_eq__imp__le,axiom,
% 5.31/5.47 ! [M2: nat,N: nat] :
% 5.31/5.47 ( ( M2 = N )
% 5.31/5.47 => ( ord_less_eq_nat @ M2 @ N ) ) ).
% 5.31/5.47
% 5.31/5.47 % eq_imp_le
% 5.31/5.47 thf(fact_239_le0,axiom,
% 5.31/5.47 ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N ) ).
% 5.31/5.47
% 5.31/5.47 % le0
% 5.31/5.47 thf(fact_240_bot__nat__0_Oextremum,axiom,
% 5.31/5.47 ! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ) ).
% 5.31/5.47
% 5.31/5.47 % bot_nat_0.extremum
% 5.31/5.47 thf(fact_241_le__0__eq,axiom,
% 5.31/5.47 ! [N: nat] :
% 5.31/5.47 ( ( ord_less_eq_nat @ N @ zero_zero_nat )
% 5.31/5.47 = ( N = zero_zero_nat ) ) ).
% 5.31/5.47
% 5.31/5.47 % le_0_eq
% 5.31/5.47 thf(fact_242_bot__nat__0_Oextremum__uniqueI,axiom,
% 5.31/5.47 ! [A: nat] :
% 5.31/5.47 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 5.31/5.47 => ( A = zero_zero_nat ) ) ).
% 5.31/5.47
% 5.31/5.47 % bot_nat_0.extremum_uniqueI
% 5.31/5.47 thf(fact_243_bot__nat__0_Oextremum__unique,axiom,
% 5.31/5.47 ! [A: nat] :
% 5.31/5.47 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 5.31/5.47 = ( A = zero_zero_nat ) ) ).
% 5.31/5.47
% 5.31/5.47 % bot_nat_0.extremum_unique
% 5.31/5.47 thf(fact_244_less__eq__nat_Osimps_I1_J,axiom,
% 5.31/5.47 ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N ) ).
% 5.31/5.47
% 5.31/5.47 % less_eq_nat.simps(1)
% 5.31/5.47 thf(fact_245_not0__implies__Suc,axiom,
% 5.31/5.47 ! [N: nat] :
% 5.31/5.47 ( ( N != zero_zero_nat )
% 5.31/5.47 => ? [M: nat] :
% 5.31/5.47 ( N
% 5.31/5.47 = ( suc @ M ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % not0_implies_Suc
% 5.31/5.47 thf(fact_246_Zero__not__Suc,axiom,
% 5.31/5.47 ! [M2: nat] :
% 5.31/5.47 ( zero_zero_nat
% 5.31/5.47 != ( suc @ M2 ) ) ).
% 5.31/5.47
% 5.31/5.47 % Zero_not_Suc
% 5.31/5.47 thf(fact_247_Zero__neq__Suc,axiom,
% 5.31/5.47 ! [M2: nat] :
% 5.31/5.47 ( zero_zero_nat
% 5.31/5.47 != ( suc @ M2 ) ) ).
% 5.31/5.47
% 5.31/5.47 % Zero_neq_Suc
% 5.31/5.47 thf(fact_248_Suc__neq__Zero,axiom,
% 5.31/5.47 ! [M2: nat] :
% 5.31/5.47 ( ( suc @ M2 )
% 5.31/5.47 != zero_zero_nat ) ).
% 5.31/5.47
% 5.31/5.47 % Suc_neq_Zero
% 5.31/5.47 thf(fact_249_zero__induct,axiom,
% 5.31/5.47 ! [P2: nat > $o,K2: nat] :
% 5.31/5.47 ( ( P2 @ K2 )
% 5.31/5.47 => ( ! [N3: nat] :
% 5.31/5.47 ( ( P2 @ ( suc @ N3 ) )
% 5.31/5.47 => ( P2 @ N3 ) )
% 5.31/5.47 => ( P2 @ zero_zero_nat ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % zero_induct
% 5.31/5.47 thf(fact_250_diff__induct,axiom,
% 5.31/5.47 ! [P2: nat > nat > $o,M2: nat,N: nat] :
% 5.31/5.47 ( ! [X3: nat] : ( P2 @ X3 @ zero_zero_nat )
% 5.31/5.47 => ( ! [Y3: nat] : ( P2 @ zero_zero_nat @ ( suc @ Y3 ) )
% 5.31/5.47 => ( ! [X3: nat,Y3: nat] :
% 5.31/5.47 ( ( P2 @ X3 @ Y3 )
% 5.31/5.47 => ( P2 @ ( suc @ X3 ) @ ( suc @ Y3 ) ) )
% 5.31/5.47 => ( P2 @ M2 @ N ) ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % diff_induct
% 5.31/5.47 thf(fact_251_list__decode_Ocases,axiom,
% 5.31/5.47 ! [X: nat] :
% 5.31/5.47 ( ( X != zero_zero_nat )
% 5.31/5.47 => ~ ! [N3: nat] :
% 5.31/5.47 ( X
% 5.31/5.47 != ( suc @ N3 ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % list_decode.cases
% 5.31/5.47 thf(fact_252_nat_Odistinct_I1_J,axiom,
% 5.31/5.47 ! [X2: nat] :
% 5.31/5.47 ( zero_zero_nat
% 5.31/5.47 != ( suc @ X2 ) ) ).
% 5.31/5.47
% 5.31/5.47 % nat.distinct(1)
% 5.31/5.47 thf(fact_253_old_Onat_Odistinct_I2_J,axiom,
% 5.31/5.47 ! [Nat2: nat] :
% 5.31/5.47 ( ( suc @ Nat2 )
% 5.31/5.47 != zero_zero_nat ) ).
% 5.31/5.47
% 5.31/5.47 % old.nat.distinct(2)
% 5.31/5.47 thf(fact_254_old_Onat_Odistinct_I1_J,axiom,
% 5.31/5.47 ! [Nat2: nat] :
% 5.31/5.47 ( zero_zero_nat
% 5.31/5.47 != ( suc @ Nat2 ) ) ).
% 5.31/5.47
% 5.31/5.47 % old.nat.distinct(1)
% 5.31/5.47 thf(fact_255_nat_OdiscI,axiom,
% 5.31/5.47 ! [Nat: nat,X2: nat] :
% 5.31/5.47 ( ( Nat
% 5.31/5.47 = ( suc @ X2 ) )
% 5.31/5.47 => ( Nat != zero_zero_nat ) ) ).
% 5.31/5.47
% 5.31/5.47 % nat.discI
% 5.31/5.47 thf(fact_256_old_Onat_Oexhaust,axiom,
% 5.31/5.47 ! [Y: nat] :
% 5.31/5.47 ( ( Y != zero_zero_nat )
% 5.31/5.47 => ~ ! [Nat3: nat] :
% 5.31/5.47 ( Y
% 5.31/5.47 != ( suc @ Nat3 ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % old.nat.exhaust
% 5.31/5.47 thf(fact_257_nat__induct,axiom,
% 5.31/5.47 ! [P2: nat > $o,N: nat] :
% 5.31/5.47 ( ( P2 @ zero_zero_nat )
% 5.31/5.47 => ( ! [N3: nat] :
% 5.31/5.47 ( ( P2 @ N3 )
% 5.31/5.47 => ( P2 @ ( suc @ N3 ) ) )
% 5.31/5.47 => ( P2 @ N ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % nat_induct
% 5.31/5.47 thf(fact_258_case4_I12_J,axiom,
% 5.31/5.47 vEBT_invar_vebt @ sa @ deg ).
% 5.31/5.47
% 5.31/5.47 % case4(12)
% 5.31/5.47 thf(fact_259_le__zero__eq,axiom,
% 5.31/5.47 ! [N: nat] :
% 5.31/5.47 ( ( ord_less_eq_nat @ N @ zero_zero_nat )
% 5.31/5.47 = ( N = zero_zero_nat ) ) ).
% 5.31/5.47
% 5.31/5.47 % le_zero_eq
% 5.31/5.47 thf(fact_260_option_Osize_I4_J,axiom,
% 5.31/5.47 ! [X2: product_prod_nat_nat] :
% 5.31/5.47 ( ( size_s170228958280169651at_nat @ ( some_P7363390416028606310at_nat @ X2 ) )
% 5.31/5.47 = ( suc @ zero_zero_nat ) ) ).
% 5.31/5.47
% 5.31/5.47 % option.size(4)
% 5.31/5.47 thf(fact_261_option_Osize_I4_J,axiom,
% 5.31/5.47 ! [X2: nat] :
% 5.31/5.47 ( ( size_size_option_nat @ ( some_nat @ X2 ) )
% 5.31/5.47 = ( suc @ zero_zero_nat ) ) ).
% 5.31/5.47
% 5.31/5.47 % option.size(4)
% 5.31/5.47 thf(fact_262_option_Osize_I4_J,axiom,
% 5.31/5.47 ! [X2: num] :
% 5.31/5.47 ( ( size_size_option_num @ ( some_num @ X2 ) )
% 5.31/5.47 = ( suc @ zero_zero_nat ) ) ).
% 5.31/5.47
% 5.31/5.47 % option.size(4)
% 5.31/5.47 thf(fact_263_vebt__buildup_Ocases,axiom,
% 5.31/5.47 ! [X: nat] :
% 5.31/5.47 ( ( X != zero_zero_nat )
% 5.31/5.47 => ( ( X
% 5.31/5.47 != ( suc @ zero_zero_nat ) )
% 5.31/5.47 => ~ ! [Va: nat] :
% 5.31/5.47 ( X
% 5.31/5.47 != ( suc @ ( suc @ Va ) ) ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % vebt_buildup.cases
% 5.31/5.47 thf(fact_264_exists__least__lemma,axiom,
% 5.31/5.47 ! [P2: nat > $o] :
% 5.31/5.47 ( ~ ( P2 @ zero_zero_nat )
% 5.31/5.47 => ( ? [X_1: nat] : ( P2 @ X_1 )
% 5.31/5.47 => ? [N3: nat] :
% 5.31/5.47 ( ~ ( P2 @ N3 )
% 5.31/5.47 & ( P2 @ ( suc @ N3 ) ) ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % exists_least_lemma
% 5.31/5.47 thf(fact_265_le__numeral__extra_I3_J,axiom,
% 5.31/5.47 ord_less_eq_real @ zero_zero_real @ zero_zero_real ).
% 5.31/5.47
% 5.31/5.47 % le_numeral_extra(3)
% 5.31/5.47 thf(fact_266_le__numeral__extra_I3_J,axiom,
% 5.31/5.47 ord_less_eq_rat @ zero_zero_rat @ zero_zero_rat ).
% 5.31/5.47
% 5.31/5.47 % le_numeral_extra(3)
% 5.31/5.47 thf(fact_267_le__numeral__extra_I3_J,axiom,
% 5.31/5.47 ord_less_eq_nat @ zero_zero_nat @ zero_zero_nat ).
% 5.31/5.47
% 5.31/5.47 % le_numeral_extra(3)
% 5.31/5.47 thf(fact_268_le__numeral__extra_I3_J,axiom,
% 5.31/5.47 ord_less_eq_int @ zero_zero_int @ zero_zero_int ).
% 5.31/5.47
% 5.31/5.47 % le_numeral_extra(3)
% 5.31/5.47 thf(fact_269_zero__le,axiom,
% 5.31/5.47 ! [X: nat] : ( ord_less_eq_nat @ zero_zero_nat @ X ) ).
% 5.31/5.47
% 5.31/5.47 % zero_le
% 5.31/5.47 thf(fact_270_divides__aux__eq,axiom,
% 5.31/5.47 ! [Q2: code_integer,R3: code_integer] :
% 5.31/5.47 ( ( unique5706413561485394159nteger @ ( produc1086072967326762835nteger @ Q2 @ R3 ) )
% 5.31/5.47 = ( R3 = zero_z3403309356797280102nteger ) ) ).
% 5.31/5.47
% 5.31/5.47 % divides_aux_eq
% 5.31/5.47 thf(fact_271_divides__aux__eq,axiom,
% 5.31/5.47 ! [Q2: nat,R3: nat] :
% 5.31/5.47 ( ( unique6322359934112328802ux_nat @ ( product_Pair_nat_nat @ Q2 @ R3 ) )
% 5.31/5.47 = ( R3 = zero_zero_nat ) ) ).
% 5.31/5.47
% 5.31/5.47 % divides_aux_eq
% 5.31/5.47 thf(fact_272_divides__aux__eq,axiom,
% 5.31/5.47 ! [Q2: int,R3: int] :
% 5.31/5.47 ( ( unique6319869463603278526ux_int @ ( product_Pair_int_int @ Q2 @ R3 ) )
% 5.31/5.47 = ( R3 = zero_zero_int ) ) ).
% 5.31/5.47
% 5.31/5.47 % divides_aux_eq
% 5.31/5.47 thf(fact_273_one__le__mult__iff,axiom,
% 5.31/5.47 ! [M2: nat,N: nat] :
% 5.31/5.47 ( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( times_times_nat @ M2 @ N ) )
% 5.31/5.47 = ( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ M2 )
% 5.31/5.47 & ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ N ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % one_le_mult_iff
% 5.31/5.47 thf(fact_274__C1_C_I1_J,axiom,
% 5.31/5.47 ( sa
% 5.31/5.47 = ( vEBT_Leaf @ a @ b ) ) ).
% 5.31/5.47
% 5.31/5.47 % "1"(1)
% 5.31/5.47 thf(fact_275_valid__tree__deg__neq__0,axiom,
% 5.31/5.47 ! [T: vEBT_VEBT] :
% 5.31/5.47 ~ ( vEBT_invar_vebt @ T @ zero_zero_nat ) ).
% 5.31/5.47
% 5.31/5.47 % valid_tree_deg_neq_0
% 5.31/5.47 thf(fact_276_valid__0__not,axiom,
% 5.31/5.47 ! [T: vEBT_VEBT] :
% 5.31/5.47 ~ ( vEBT_invar_vebt @ T @ zero_zero_nat ) ).
% 5.31/5.47
% 5.31/5.47 % valid_0_not
% 5.31/5.47 thf(fact_277_Leaf__0__not,axiom,
% 5.31/5.47 ! [A: $o,B: $o] :
% 5.31/5.47 ~ ( vEBT_invar_vebt @ ( vEBT_Leaf @ A @ B ) @ zero_zero_nat ) ).
% 5.31/5.47
% 5.31/5.47 % Leaf_0_not
% 5.31/5.47 thf(fact_278_prod__decode__eq,axiom,
% 5.31/5.47 ! [X: nat,Y: nat] :
% 5.31/5.47 ( ( ( nat_prod_decode @ X )
% 5.31/5.47 = ( nat_prod_decode @ Y ) )
% 5.31/5.47 = ( X = Y ) ) ).
% 5.31/5.47
% 5.31/5.47 % prod_decode_eq
% 5.31/5.47 thf(fact_279_insert_H__pres__valid,axiom,
% 5.31/5.47 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 5.31/5.47 ( ( vEBT_invar_vebt @ T @ N )
% 5.31/5.47 => ( vEBT_invar_vebt @ ( vEBT_VEBT_insert @ T @ X ) @ N ) ) ).
% 5.31/5.47
% 5.31/5.47 % insert'_pres_valid
% 5.31/5.47 thf(fact_280_mult__is__0,axiom,
% 5.31/5.47 ! [M2: nat,N: nat] :
% 5.31/5.47 ( ( ( times_times_nat @ M2 @ N )
% 5.31/5.47 = zero_zero_nat )
% 5.31/5.47 = ( ( M2 = zero_zero_nat )
% 5.31/5.47 | ( N = zero_zero_nat ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % mult_is_0
% 5.31/5.47 thf(fact_281_mult__0__right,axiom,
% 5.31/5.47 ! [M2: nat] :
% 5.31/5.47 ( ( times_times_nat @ M2 @ zero_zero_nat )
% 5.31/5.47 = zero_zero_nat ) ).
% 5.31/5.47
% 5.31/5.47 % mult_0_right
% 5.31/5.47 thf(fact_282_mult__cancel1,axiom,
% 5.31/5.47 ! [K2: nat,M2: nat,N: nat] :
% 5.31/5.47 ( ( ( times_times_nat @ K2 @ M2 )
% 5.31/5.47 = ( times_times_nat @ K2 @ N ) )
% 5.31/5.47 = ( ( M2 = N )
% 5.31/5.47 | ( K2 = zero_zero_nat ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % mult_cancel1
% 5.31/5.47 thf(fact_283_mult__cancel2,axiom,
% 5.31/5.47 ! [M2: nat,K2: nat,N: nat] :
% 5.31/5.47 ( ( ( times_times_nat @ M2 @ K2 )
% 5.31/5.47 = ( times_times_nat @ N @ K2 ) )
% 5.31/5.47 = ( ( M2 = N )
% 5.31/5.47 | ( K2 = zero_zero_nat ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % mult_cancel2
% 5.31/5.47 thf(fact_284_prod__decode__inverse,axiom,
% 5.31/5.47 ! [N: nat] :
% 5.31/5.47 ( ( nat_prod_encode @ ( nat_prod_decode @ N ) )
% 5.31/5.47 = N ) ).
% 5.31/5.47
% 5.31/5.47 % prod_decode_inverse
% 5.31/5.47 thf(fact_285_prod__encode__inverse,axiom,
% 5.31/5.47 ! [X: product_prod_nat_nat] :
% 5.31/5.47 ( ( nat_prod_decode @ ( nat_prod_encode @ X ) )
% 5.31/5.47 = X ) ).
% 5.31/5.47
% 5.31/5.47 % prod_encode_inverse
% 5.31/5.47 thf(fact_286_one__eq__mult__iff,axiom,
% 5.31/5.47 ! [M2: nat,N: nat] :
% 5.31/5.47 ( ( ( suc @ zero_zero_nat )
% 5.31/5.47 = ( times_times_nat @ M2 @ N ) )
% 5.31/5.47 = ( ( M2
% 5.31/5.47 = ( suc @ zero_zero_nat ) )
% 5.31/5.47 & ( N
% 5.31/5.47 = ( suc @ zero_zero_nat ) ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % one_eq_mult_iff
% 5.31/5.47 thf(fact_287_mult__eq__1__iff,axiom,
% 5.31/5.47 ! [M2: nat,N: nat] :
% 5.31/5.47 ( ( ( times_times_nat @ M2 @ N )
% 5.31/5.47 = ( suc @ zero_zero_nat ) )
% 5.31/5.47 = ( ( M2
% 5.31/5.47 = ( suc @ zero_zero_nat ) )
% 5.31/5.47 & ( N
% 5.31/5.47 = ( suc @ zero_zero_nat ) ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % mult_eq_1_iff
% 5.31/5.47 thf(fact_288_mult_Oleft__commute,axiom,
% 5.31/5.47 ! [B: real,A: real,C2: real] :
% 5.31/5.47 ( ( times_times_real @ B @ ( times_times_real @ A @ C2 ) )
% 5.31/5.47 = ( times_times_real @ A @ ( times_times_real @ B @ C2 ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % mult.left_commute
% 5.31/5.47 thf(fact_289_mult_Oleft__commute,axiom,
% 5.31/5.47 ! [B: rat,A: rat,C2: rat] :
% 5.31/5.47 ( ( times_times_rat @ B @ ( times_times_rat @ A @ C2 ) )
% 5.31/5.47 = ( times_times_rat @ A @ ( times_times_rat @ B @ C2 ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % mult.left_commute
% 5.31/5.47 thf(fact_290_mult_Oleft__commute,axiom,
% 5.31/5.47 ! [B: nat,A: nat,C2: nat] :
% 5.31/5.47 ( ( times_times_nat @ B @ ( times_times_nat @ A @ C2 ) )
% 5.31/5.47 = ( times_times_nat @ A @ ( times_times_nat @ B @ C2 ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % mult.left_commute
% 5.31/5.47 thf(fact_291_mult_Oleft__commute,axiom,
% 5.31/5.47 ! [B: int,A: int,C2: int] :
% 5.31/5.47 ( ( times_times_int @ B @ ( times_times_int @ A @ C2 ) )
% 5.31/5.47 = ( times_times_int @ A @ ( times_times_int @ B @ C2 ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % mult.left_commute
% 5.31/5.47 thf(fact_292_mult_Ocommute,axiom,
% 5.31/5.47 ( times_times_real
% 5.31/5.47 = ( ^ [A5: real,B4: real] : ( times_times_real @ B4 @ A5 ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % mult.commute
% 5.31/5.47 thf(fact_293_mult_Ocommute,axiom,
% 5.31/5.47 ( times_times_rat
% 5.31/5.47 = ( ^ [A5: rat,B4: rat] : ( times_times_rat @ B4 @ A5 ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % mult.commute
% 5.31/5.47 thf(fact_294_mult_Ocommute,axiom,
% 5.31/5.47 ( times_times_nat
% 5.31/5.47 = ( ^ [A5: nat,B4: nat] : ( times_times_nat @ B4 @ A5 ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % mult.commute
% 5.31/5.47 thf(fact_295_mult_Ocommute,axiom,
% 5.31/5.47 ( times_times_int
% 5.31/5.47 = ( ^ [A5: int,B4: int] : ( times_times_int @ B4 @ A5 ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % mult.commute
% 5.31/5.47 thf(fact_296_mult_Oassoc,axiom,
% 5.31/5.47 ! [A: real,B: real,C2: real] :
% 5.31/5.47 ( ( times_times_real @ ( times_times_real @ A @ B ) @ C2 )
% 5.31/5.47 = ( times_times_real @ A @ ( times_times_real @ B @ C2 ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % mult.assoc
% 5.31/5.47 thf(fact_297_mult_Oassoc,axiom,
% 5.31/5.47 ! [A: rat,B: rat,C2: rat] :
% 5.31/5.47 ( ( times_times_rat @ ( times_times_rat @ A @ B ) @ C2 )
% 5.31/5.47 = ( times_times_rat @ A @ ( times_times_rat @ B @ C2 ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % mult.assoc
% 5.31/5.47 thf(fact_298_mult_Oassoc,axiom,
% 5.31/5.47 ! [A: nat,B: nat,C2: nat] :
% 5.31/5.47 ( ( times_times_nat @ ( times_times_nat @ A @ B ) @ C2 )
% 5.31/5.47 = ( times_times_nat @ A @ ( times_times_nat @ B @ C2 ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % mult.assoc
% 5.31/5.47 thf(fact_299_mult_Oassoc,axiom,
% 5.31/5.47 ! [A: int,B: int,C2: int] :
% 5.31/5.47 ( ( times_times_int @ ( times_times_int @ A @ B ) @ C2 )
% 5.31/5.47 = ( times_times_int @ A @ ( times_times_int @ B @ C2 ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % mult.assoc
% 5.31/5.47 thf(fact_300_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 5.31/5.47 ! [A: real,B: real,C2: real] :
% 5.31/5.47 ( ( times_times_real @ ( times_times_real @ A @ B ) @ C2 )
% 5.31/5.47 = ( times_times_real @ A @ ( times_times_real @ B @ C2 ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % ab_semigroup_mult_class.mult_ac(1)
% 5.31/5.47 thf(fact_301_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 5.31/5.47 ! [A: rat,B: rat,C2: rat] :
% 5.31/5.47 ( ( times_times_rat @ ( times_times_rat @ A @ B ) @ C2 )
% 5.31/5.47 = ( times_times_rat @ A @ ( times_times_rat @ B @ C2 ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % ab_semigroup_mult_class.mult_ac(1)
% 5.31/5.47 thf(fact_302_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 5.31/5.47 ! [A: nat,B: nat,C2: nat] :
% 5.31/5.47 ( ( times_times_nat @ ( times_times_nat @ A @ B ) @ C2 )
% 5.31/5.47 = ( times_times_nat @ A @ ( times_times_nat @ B @ C2 ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % ab_semigroup_mult_class.mult_ac(1)
% 5.31/5.47 thf(fact_303_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 5.31/5.47 ! [A: int,B: int,C2: int] :
% 5.31/5.47 ( ( times_times_int @ ( times_times_int @ A @ B ) @ C2 )
% 5.31/5.47 = ( times_times_int @ A @ ( times_times_int @ B @ C2 ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % ab_semigroup_mult_class.mult_ac(1)
% 5.31/5.47 thf(fact_304_size__neq__size__imp__neq,axiom,
% 5.31/5.47 ! [X: list_VEBT_VEBT,Y: list_VEBT_VEBT] :
% 5.31/5.47 ( ( ( size_s6755466524823107622T_VEBT @ X )
% 5.31/5.47 != ( size_s6755466524823107622T_VEBT @ Y ) )
% 5.31/5.47 => ( X != Y ) ) ).
% 5.31/5.47
% 5.31/5.47 % size_neq_size_imp_neq
% 5.31/5.47 thf(fact_305_size__neq__size__imp__neq,axiom,
% 5.31/5.47 ! [X: list_o,Y: list_o] :
% 5.31/5.47 ( ( ( size_size_list_o @ X )
% 5.31/5.47 != ( size_size_list_o @ Y ) )
% 5.31/5.47 => ( X != Y ) ) ).
% 5.31/5.47
% 5.31/5.47 % size_neq_size_imp_neq
% 5.31/5.47 thf(fact_306_size__neq__size__imp__neq,axiom,
% 5.31/5.47 ! [X: list_nat,Y: list_nat] :
% 5.31/5.47 ( ( ( size_size_list_nat @ X )
% 5.31/5.47 != ( size_size_list_nat @ Y ) )
% 5.31/5.47 => ( X != Y ) ) ).
% 5.31/5.47
% 5.31/5.47 % size_neq_size_imp_neq
% 5.31/5.47 thf(fact_307_size__neq__size__imp__neq,axiom,
% 5.31/5.47 ! [X: list_int,Y: list_int] :
% 5.31/5.47 ( ( ( size_size_list_int @ X )
% 5.31/5.47 != ( size_size_list_int @ Y ) )
% 5.31/5.47 => ( X != Y ) ) ).
% 5.31/5.47
% 5.31/5.47 % size_neq_size_imp_neq
% 5.31/5.47 thf(fact_308_size__neq__size__imp__neq,axiom,
% 5.31/5.47 ! [X: num,Y: num] :
% 5.31/5.47 ( ( ( size_size_num @ X )
% 5.31/5.47 != ( size_size_num @ Y ) )
% 5.31/5.47 => ( X != Y ) ) ).
% 5.31/5.47
% 5.31/5.47 % size_neq_size_imp_neq
% 5.31/5.47 thf(fact_309_Suc__mult__cancel1,axiom,
% 5.31/5.47 ! [K2: nat,M2: nat,N: nat] :
% 5.31/5.47 ( ( ( times_times_nat @ ( suc @ K2 ) @ M2 )
% 5.31/5.47 = ( times_times_nat @ ( suc @ K2 ) @ N ) )
% 5.31/5.47 = ( M2 = N ) ) ).
% 5.31/5.47
% 5.31/5.47 % Suc_mult_cancel1
% 5.31/5.47 thf(fact_310_mult__0,axiom,
% 5.31/5.47 ! [N: nat] :
% 5.31/5.47 ( ( times_times_nat @ zero_zero_nat @ N )
% 5.31/5.47 = zero_zero_nat ) ).
% 5.31/5.47
% 5.31/5.47 % mult_0
% 5.31/5.47 thf(fact_311_mult__le__mono2,axiom,
% 5.31/5.47 ! [I2: nat,J2: nat,K2: nat] :
% 5.31/5.47 ( ( ord_less_eq_nat @ I2 @ J2 )
% 5.31/5.47 => ( ord_less_eq_nat @ ( times_times_nat @ K2 @ I2 ) @ ( times_times_nat @ K2 @ J2 ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % mult_le_mono2
% 5.31/5.47 thf(fact_312_mult__le__mono1,axiom,
% 5.31/5.47 ! [I2: nat,J2: nat,K2: nat] :
% 5.31/5.47 ( ( ord_less_eq_nat @ I2 @ J2 )
% 5.31/5.47 => ( ord_less_eq_nat @ ( times_times_nat @ I2 @ K2 ) @ ( times_times_nat @ J2 @ K2 ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % mult_le_mono1
% 5.31/5.47 thf(fact_313_mult__le__mono,axiom,
% 5.31/5.47 ! [I2: nat,J2: nat,K2: nat,L: nat] :
% 5.31/5.47 ( ( ord_less_eq_nat @ I2 @ J2 )
% 5.31/5.47 => ( ( ord_less_eq_nat @ K2 @ L )
% 5.31/5.47 => ( ord_less_eq_nat @ ( times_times_nat @ I2 @ K2 ) @ ( times_times_nat @ J2 @ L ) ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % mult_le_mono
% 5.31/5.47 thf(fact_314_le__square,axiom,
% 5.31/5.47 ! [M2: nat] : ( ord_less_eq_nat @ M2 @ ( times_times_nat @ M2 @ M2 ) ) ).
% 5.31/5.47
% 5.31/5.47 % le_square
% 5.31/5.47 thf(fact_315_le__cube,axiom,
% 5.31/5.47 ! [M2: nat] : ( ord_less_eq_nat @ M2 @ ( times_times_nat @ M2 @ ( times_times_nat @ M2 @ M2 ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % le_cube
% 5.31/5.47 thf(fact_316_Suc__mult__le__cancel1,axiom,
% 5.31/5.47 ! [K2: nat,M2: nat,N: nat] :
% 5.31/5.47 ( ( ord_less_eq_nat @ ( times_times_nat @ ( suc @ K2 ) @ M2 ) @ ( times_times_nat @ ( suc @ K2 ) @ N ) )
% 5.31/5.47 = ( ord_less_eq_nat @ M2 @ N ) ) ).
% 5.31/5.47
% 5.31/5.47 % Suc_mult_le_cancel1
% 5.31/5.47 thf(fact_317_zero__reorient,axiom,
% 5.31/5.47 ! [X: complex] :
% 5.31/5.47 ( ( zero_zero_complex = X )
% 5.31/5.47 = ( X = zero_zero_complex ) ) ).
% 5.31/5.47
% 5.31/5.47 % zero_reorient
% 5.31/5.47 thf(fact_318_zero__reorient,axiom,
% 5.31/5.47 ! [X: real] :
% 5.31/5.47 ( ( zero_zero_real = X )
% 5.31/5.47 = ( X = zero_zero_real ) ) ).
% 5.31/5.47
% 5.31/5.47 % zero_reorient
% 5.31/5.47 thf(fact_319_zero__reorient,axiom,
% 5.31/5.47 ! [X: rat] :
% 5.31/5.47 ( ( zero_zero_rat = X )
% 5.31/5.47 = ( X = zero_zero_rat ) ) ).
% 5.31/5.47
% 5.31/5.47 % zero_reorient
% 5.31/5.47 thf(fact_320_zero__reorient,axiom,
% 5.31/5.47 ! [X: nat] :
% 5.31/5.47 ( ( zero_zero_nat = X )
% 5.31/5.47 = ( X = zero_zero_nat ) ) ).
% 5.31/5.47
% 5.31/5.47 % zero_reorient
% 5.31/5.47 thf(fact_321_zero__reorient,axiom,
% 5.31/5.47 ! [X: int] :
% 5.31/5.47 ( ( zero_zero_int = X )
% 5.31/5.47 = ( X = zero_zero_int ) ) ).
% 5.31/5.47
% 5.31/5.47 % zero_reorient
% 5.31/5.47 thf(fact_322_mult__cancel__right,axiom,
% 5.31/5.47 ! [A: complex,C2: complex,B: complex] :
% 5.31/5.47 ( ( ( times_times_complex @ A @ C2 )
% 5.31/5.47 = ( times_times_complex @ B @ C2 ) )
% 5.31/5.47 = ( ( C2 = zero_zero_complex )
% 5.31/5.47 | ( A = B ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % mult_cancel_right
% 5.31/5.47 thf(fact_323_mult__cancel__right,axiom,
% 5.31/5.47 ! [A: real,C2: real,B: real] :
% 5.31/5.47 ( ( ( times_times_real @ A @ C2 )
% 5.31/5.47 = ( times_times_real @ B @ C2 ) )
% 5.31/5.47 = ( ( C2 = zero_zero_real )
% 5.31/5.47 | ( A = B ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % mult_cancel_right
% 5.31/5.47 thf(fact_324_mult__cancel__right,axiom,
% 5.31/5.47 ! [A: rat,C2: rat,B: rat] :
% 5.31/5.47 ( ( ( times_times_rat @ A @ C2 )
% 5.31/5.47 = ( times_times_rat @ B @ C2 ) )
% 5.31/5.47 = ( ( C2 = zero_zero_rat )
% 5.31/5.47 | ( A = B ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % mult_cancel_right
% 5.31/5.47 thf(fact_325_mult__cancel__right,axiom,
% 5.31/5.47 ! [A: nat,C2: nat,B: nat] :
% 5.31/5.47 ( ( ( times_times_nat @ A @ C2 )
% 5.31/5.47 = ( times_times_nat @ B @ C2 ) )
% 5.31/5.47 = ( ( C2 = zero_zero_nat )
% 5.31/5.47 | ( A = B ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % mult_cancel_right
% 5.31/5.47 thf(fact_326_mult__cancel__right,axiom,
% 5.31/5.47 ! [A: int,C2: int,B: int] :
% 5.31/5.47 ( ( ( times_times_int @ A @ C2 )
% 5.31/5.47 = ( times_times_int @ B @ C2 ) )
% 5.31/5.47 = ( ( C2 = zero_zero_int )
% 5.31/5.47 | ( A = B ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % mult_cancel_right
% 5.31/5.47 thf(fact_327_mult__cancel__left,axiom,
% 5.31/5.47 ! [C2: complex,A: complex,B: complex] :
% 5.31/5.47 ( ( ( times_times_complex @ C2 @ A )
% 5.31/5.47 = ( times_times_complex @ C2 @ B ) )
% 5.31/5.47 = ( ( C2 = zero_zero_complex )
% 5.31/5.47 | ( A = B ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % mult_cancel_left
% 5.31/5.47 thf(fact_328_mult__cancel__left,axiom,
% 5.31/5.47 ! [C2: real,A: real,B: real] :
% 5.31/5.47 ( ( ( times_times_real @ C2 @ A )
% 5.31/5.47 = ( times_times_real @ C2 @ B ) )
% 5.31/5.47 = ( ( C2 = zero_zero_real )
% 5.31/5.47 | ( A = B ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % mult_cancel_left
% 5.31/5.47 thf(fact_329_mult__cancel__left,axiom,
% 5.31/5.47 ! [C2: rat,A: rat,B: rat] :
% 5.31/5.47 ( ( ( times_times_rat @ C2 @ A )
% 5.31/5.47 = ( times_times_rat @ C2 @ B ) )
% 5.31/5.47 = ( ( C2 = zero_zero_rat )
% 5.31/5.47 | ( A = B ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % mult_cancel_left
% 5.31/5.47 thf(fact_330_mult__cancel__left,axiom,
% 5.31/5.47 ! [C2: nat,A: nat,B: nat] :
% 5.31/5.47 ( ( ( times_times_nat @ C2 @ A )
% 5.31/5.47 = ( times_times_nat @ C2 @ B ) )
% 5.31/5.47 = ( ( C2 = zero_zero_nat )
% 5.31/5.47 | ( A = B ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % mult_cancel_left
% 5.31/5.47 thf(fact_331_mult__cancel__left,axiom,
% 5.31/5.47 ! [C2: int,A: int,B: int] :
% 5.31/5.47 ( ( ( times_times_int @ C2 @ A )
% 5.31/5.47 = ( times_times_int @ C2 @ B ) )
% 5.31/5.47 = ( ( C2 = zero_zero_int )
% 5.31/5.47 | ( A = B ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % mult_cancel_left
% 5.31/5.47 thf(fact_332_mult__eq__0__iff,axiom,
% 5.31/5.47 ! [A: complex,B: complex] :
% 5.31/5.47 ( ( ( times_times_complex @ A @ B )
% 5.31/5.47 = zero_zero_complex )
% 5.31/5.47 = ( ( A = zero_zero_complex )
% 5.31/5.47 | ( B = zero_zero_complex ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % mult_eq_0_iff
% 5.31/5.47 thf(fact_333_mult__eq__0__iff,axiom,
% 5.31/5.47 ! [A: real,B: real] :
% 5.31/5.47 ( ( ( times_times_real @ A @ B )
% 5.31/5.47 = zero_zero_real )
% 5.31/5.47 = ( ( A = zero_zero_real )
% 5.31/5.47 | ( B = zero_zero_real ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % mult_eq_0_iff
% 5.31/5.47 thf(fact_334_mult__eq__0__iff,axiom,
% 5.31/5.47 ! [A: rat,B: rat] :
% 5.31/5.47 ( ( ( times_times_rat @ A @ B )
% 5.31/5.47 = zero_zero_rat )
% 5.31/5.47 = ( ( A = zero_zero_rat )
% 5.31/5.47 | ( B = zero_zero_rat ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % mult_eq_0_iff
% 5.31/5.47 thf(fact_335_mult__eq__0__iff,axiom,
% 5.31/5.47 ! [A: nat,B: nat] :
% 5.31/5.47 ( ( ( times_times_nat @ A @ B )
% 5.31/5.47 = zero_zero_nat )
% 5.31/5.47 = ( ( A = zero_zero_nat )
% 5.31/5.47 | ( B = zero_zero_nat ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % mult_eq_0_iff
% 5.31/5.47 thf(fact_336_mult__eq__0__iff,axiom,
% 5.31/5.47 ! [A: int,B: int] :
% 5.31/5.47 ( ( ( times_times_int @ A @ B )
% 5.31/5.47 = zero_zero_int )
% 5.31/5.47 = ( ( A = zero_zero_int )
% 5.31/5.47 | ( B = zero_zero_int ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % mult_eq_0_iff
% 5.31/5.47 thf(fact_337_mult__zero__right,axiom,
% 5.31/5.47 ! [A: complex] :
% 5.31/5.47 ( ( times_times_complex @ A @ zero_zero_complex )
% 5.31/5.47 = zero_zero_complex ) ).
% 5.31/5.47
% 5.31/5.47 % mult_zero_right
% 5.31/5.47 thf(fact_338_mult__zero__right,axiom,
% 5.31/5.47 ! [A: real] :
% 5.31/5.47 ( ( times_times_real @ A @ zero_zero_real )
% 5.31/5.47 = zero_zero_real ) ).
% 5.31/5.47
% 5.31/5.47 % mult_zero_right
% 5.31/5.47 thf(fact_339_mult__zero__right,axiom,
% 5.31/5.47 ! [A: rat] :
% 5.31/5.47 ( ( times_times_rat @ A @ zero_zero_rat )
% 5.31/5.47 = zero_zero_rat ) ).
% 5.31/5.47
% 5.31/5.47 % mult_zero_right
% 5.31/5.47 thf(fact_340_mult__zero__right,axiom,
% 5.31/5.47 ! [A: nat] :
% 5.31/5.47 ( ( times_times_nat @ A @ zero_zero_nat )
% 5.31/5.47 = zero_zero_nat ) ).
% 5.31/5.47
% 5.31/5.47 % mult_zero_right
% 5.31/5.47 thf(fact_341_mult__zero__right,axiom,
% 5.31/5.47 ! [A: int] :
% 5.31/5.47 ( ( times_times_int @ A @ zero_zero_int )
% 5.31/5.47 = zero_zero_int ) ).
% 5.31/5.47
% 5.31/5.47 % mult_zero_right
% 5.31/5.47 thf(fact_342_mult__zero__left,axiom,
% 5.31/5.47 ! [A: complex] :
% 5.31/5.47 ( ( times_times_complex @ zero_zero_complex @ A )
% 5.31/5.47 = zero_zero_complex ) ).
% 5.31/5.47
% 5.31/5.47 % mult_zero_left
% 5.31/5.47 thf(fact_343_mult__zero__left,axiom,
% 5.31/5.47 ! [A: real] :
% 5.31/5.47 ( ( times_times_real @ zero_zero_real @ A )
% 5.31/5.47 = zero_zero_real ) ).
% 5.31/5.47
% 5.31/5.47 % mult_zero_left
% 5.31/5.47 thf(fact_344_mult__zero__left,axiom,
% 5.31/5.47 ! [A: rat] :
% 5.31/5.47 ( ( times_times_rat @ zero_zero_rat @ A )
% 5.31/5.47 = zero_zero_rat ) ).
% 5.31/5.47
% 5.31/5.47 % mult_zero_left
% 5.31/5.47 thf(fact_345_mult__zero__left,axiom,
% 5.31/5.47 ! [A: nat] :
% 5.31/5.47 ( ( times_times_nat @ zero_zero_nat @ A )
% 5.31/5.47 = zero_zero_nat ) ).
% 5.31/5.47
% 5.31/5.47 % mult_zero_left
% 5.31/5.47 thf(fact_346_mult__zero__left,axiom,
% 5.31/5.47 ! [A: int] :
% 5.31/5.47 ( ( times_times_int @ zero_zero_int @ A )
% 5.31/5.47 = zero_zero_int ) ).
% 5.31/5.47
% 5.31/5.47 % mult_zero_left
% 5.31/5.47 thf(fact_347_mul__shift,axiom,
% 5.31/5.47 ! [X: nat,Y: nat,Z3: nat] :
% 5.31/5.47 ( ( ( times_times_nat @ X @ Y )
% 5.31/5.47 = Z3 )
% 5.31/5.47 = ( ( vEBT_VEBT_mul @ ( some_nat @ X ) @ ( some_nat @ Y ) )
% 5.31/5.47 = ( some_nat @ Z3 ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % mul_shift
% 5.31/5.47 thf(fact_348_invar__vebt_Ointros_I1_J,axiom,
% 5.31/5.47 ! [A: $o,B: $o] : ( vEBT_invar_vebt @ ( vEBT_Leaf @ A @ B ) @ ( suc @ zero_zero_nat ) ) ).
% 5.31/5.47
% 5.31/5.47 % invar_vebt.intros(1)
% 5.31/5.47 thf(fact_349_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 5.31/5.47 ! [A: real,B: real,C2: real] :
% 5.31/5.47 ( ( ord_less_eq_real @ A @ B )
% 5.31/5.47 => ( ( ord_less_eq_real @ zero_zero_real @ C2 )
% 5.31/5.47 => ( ord_less_eq_real @ ( times_times_real @ C2 @ A ) @ ( times_times_real @ C2 @ B ) ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % ordered_comm_semiring_class.comm_mult_left_mono
% 5.31/5.47 thf(fact_350_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 5.31/5.47 ! [A: rat,B: rat,C2: rat] :
% 5.31/5.47 ( ( ord_less_eq_rat @ A @ B )
% 5.31/5.47 => ( ( ord_less_eq_rat @ zero_zero_rat @ C2 )
% 5.31/5.47 => ( ord_less_eq_rat @ ( times_times_rat @ C2 @ A ) @ ( times_times_rat @ C2 @ B ) ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % ordered_comm_semiring_class.comm_mult_left_mono
% 5.31/5.47 thf(fact_351_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 5.31/5.47 ! [A: nat,B: nat,C2: nat] :
% 5.31/5.47 ( ( ord_less_eq_nat @ A @ B )
% 5.31/5.47 => ( ( ord_less_eq_nat @ zero_zero_nat @ C2 )
% 5.31/5.47 => ( ord_less_eq_nat @ ( times_times_nat @ C2 @ A ) @ ( times_times_nat @ C2 @ B ) ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % ordered_comm_semiring_class.comm_mult_left_mono
% 5.31/5.47 thf(fact_352_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 5.31/5.47 ! [A: int,B: int,C2: int] :
% 5.31/5.47 ( ( ord_less_eq_int @ A @ B )
% 5.31/5.47 => ( ( ord_less_eq_int @ zero_zero_int @ C2 )
% 5.31/5.47 => ( ord_less_eq_int @ ( times_times_int @ C2 @ A ) @ ( times_times_int @ C2 @ B ) ) ) ) ).
% 5.31/5.47
% 5.31/5.47 % ordered_comm_semiring_class.comm_mult_left_mono
% 5.31/5.47 thf(fact_353_zero__le__mult__iff,axiom,
% 5.31/5.47 ! [A: real,B: real] :
% 5.31/5.47 ( ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 5.31/5.47 = ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.31/5.47 & ( ord_less_eq_real @ zero_zero_real @ B ) )
% 5.31/5.47 | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.31/5.47 & ( ord_less_eq_real @ B @ zero_zero_real ) ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % zero_le_mult_iff
% 5.31/5.48 thf(fact_354_zero__le__mult__iff,axiom,
% 5.31/5.48 ! [A: rat,B: rat] :
% 5.31/5.48 ( ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 5.31/5.48 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.31/5.48 & ( ord_less_eq_rat @ zero_zero_rat @ B ) )
% 5.31/5.48 | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.31/5.48 & ( ord_less_eq_rat @ B @ zero_zero_rat ) ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % zero_le_mult_iff
% 5.31/5.48 thf(fact_355_zero__le__mult__iff,axiom,
% 5.31/5.48 ! [A: int,B: int] :
% 5.31/5.48 ( ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) )
% 5.31/5.48 = ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.31/5.48 & ( ord_less_eq_int @ zero_zero_int @ B ) )
% 5.31/5.48 | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.31/5.48 & ( ord_less_eq_int @ B @ zero_zero_int ) ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % zero_le_mult_iff
% 5.31/5.48 thf(fact_356_mult__nonneg__nonpos2,axiom,
% 5.31/5.48 ! [A: real,B: real] :
% 5.31/5.48 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.31/5.48 => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 5.31/5.48 => ( ord_less_eq_real @ ( times_times_real @ B @ A ) @ zero_zero_real ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % mult_nonneg_nonpos2
% 5.31/5.48 thf(fact_357_mult__nonneg__nonpos2,axiom,
% 5.31/5.48 ! [A: rat,B: rat] :
% 5.31/5.48 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.31/5.48 => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 5.31/5.48 => ( ord_less_eq_rat @ ( times_times_rat @ B @ A ) @ zero_zero_rat ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % mult_nonneg_nonpos2
% 5.31/5.48 thf(fact_358_mult__nonneg__nonpos2,axiom,
% 5.31/5.48 ! [A: nat,B: nat] :
% 5.31/5.48 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.31/5.48 => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 5.31/5.48 => ( ord_less_eq_nat @ ( times_times_nat @ B @ A ) @ zero_zero_nat ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % mult_nonneg_nonpos2
% 5.31/5.48 thf(fact_359_mult__nonneg__nonpos2,axiom,
% 5.31/5.48 ! [A: int,B: int] :
% 5.31/5.48 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.31/5.48 => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 5.31/5.48 => ( ord_less_eq_int @ ( times_times_int @ B @ A ) @ zero_zero_int ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % mult_nonneg_nonpos2
% 5.31/5.48 thf(fact_360_mult__nonpos__nonneg,axiom,
% 5.31/5.48 ! [A: real,B: real] :
% 5.31/5.48 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.31/5.48 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.31/5.48 => ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % mult_nonpos_nonneg
% 5.31/5.48 thf(fact_361_mult__nonpos__nonneg,axiom,
% 5.31/5.48 ! [A: rat,B: rat] :
% 5.31/5.48 ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.31/5.48 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.31/5.48 => ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % mult_nonpos_nonneg
% 5.31/5.48 thf(fact_362_mult__nonpos__nonneg,axiom,
% 5.31/5.48 ! [A: nat,B: nat] :
% 5.31/5.48 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 5.31/5.48 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.31/5.48 => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % mult_nonpos_nonneg
% 5.31/5.48 thf(fact_363_mult__nonpos__nonneg,axiom,
% 5.31/5.48 ! [A: int,B: int] :
% 5.31/5.48 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.31/5.48 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.31/5.48 => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % mult_nonpos_nonneg
% 5.31/5.48 thf(fact_364_mult__nonneg__nonpos,axiom,
% 5.31/5.48 ! [A: real,B: real] :
% 5.31/5.48 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.31/5.48 => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 5.31/5.48 => ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % mult_nonneg_nonpos
% 5.31/5.48 thf(fact_365_mult__nonneg__nonpos,axiom,
% 5.31/5.48 ! [A: rat,B: rat] :
% 5.31/5.48 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.31/5.48 => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 5.31/5.48 => ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % mult_nonneg_nonpos
% 5.31/5.48 thf(fact_366_mult__nonneg__nonpos,axiom,
% 5.31/5.48 ! [A: nat,B: nat] :
% 5.31/5.48 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.31/5.48 => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 5.31/5.48 => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % mult_nonneg_nonpos
% 5.31/5.48 thf(fact_367_mult__nonneg__nonpos,axiom,
% 5.31/5.48 ! [A: int,B: int] :
% 5.31/5.48 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.31/5.48 => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 5.31/5.48 => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % mult_nonneg_nonpos
% 5.31/5.48 thf(fact_368_VEBT_Oinject_I2_J,axiom,
% 5.31/5.48 ! [X21: $o,X22: $o,Y21: $o,Y22: $o] :
% 5.31/5.48 ( ( ( vEBT_Leaf @ X21 @ X22 )
% 5.31/5.48 = ( vEBT_Leaf @ Y21 @ Y22 ) )
% 5.31/5.48 = ( ( X21 = Y21 )
% 5.31/5.48 & ( X22 = Y22 ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % VEBT.inject(2)
% 5.31/5.48 thf(fact_369_mul__def,axiom,
% 5.31/5.48 ( vEBT_VEBT_mul
% 5.31/5.48 = ( vEBT_V4262088993061758097ft_nat @ times_times_nat ) ) ).
% 5.31/5.48
% 5.31/5.48 % mul_def
% 5.31/5.48 thf(fact_370_VEBT_Osize_I4_J,axiom,
% 5.31/5.48 ! [X21: $o,X22: $o] :
% 5.31/5.48 ( ( size_size_VEBT_VEBT @ ( vEBT_Leaf @ X21 @ X22 ) )
% 5.31/5.48 = zero_zero_nat ) ).
% 5.31/5.48
% 5.31/5.48 % VEBT.size(4)
% 5.31/5.48 thf(fact_371_mult__not__zero,axiom,
% 5.31/5.48 ! [A: complex,B: complex] :
% 5.31/5.48 ( ( ( times_times_complex @ A @ B )
% 5.31/5.48 != zero_zero_complex )
% 5.31/5.48 => ( ( A != zero_zero_complex )
% 5.31/5.48 & ( B != zero_zero_complex ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % mult_not_zero
% 5.31/5.48 thf(fact_372_mult__not__zero,axiom,
% 5.31/5.48 ! [A: real,B: real] :
% 5.31/5.48 ( ( ( times_times_real @ A @ B )
% 5.31/5.48 != zero_zero_real )
% 5.31/5.48 => ( ( A != zero_zero_real )
% 5.31/5.48 & ( B != zero_zero_real ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % mult_not_zero
% 5.31/5.48 thf(fact_373_mult__not__zero,axiom,
% 5.31/5.48 ! [A: rat,B: rat] :
% 5.31/5.48 ( ( ( times_times_rat @ A @ B )
% 5.31/5.48 != zero_zero_rat )
% 5.31/5.48 => ( ( A != zero_zero_rat )
% 5.31/5.48 & ( B != zero_zero_rat ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % mult_not_zero
% 5.31/5.48 thf(fact_374_mult__not__zero,axiom,
% 5.31/5.48 ! [A: nat,B: nat] :
% 5.31/5.48 ( ( ( times_times_nat @ A @ B )
% 5.31/5.48 != zero_zero_nat )
% 5.31/5.48 => ( ( A != zero_zero_nat )
% 5.31/5.48 & ( B != zero_zero_nat ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % mult_not_zero
% 5.31/5.48 thf(fact_375_mult__not__zero,axiom,
% 5.31/5.48 ! [A: int,B: int] :
% 5.31/5.48 ( ( ( times_times_int @ A @ B )
% 5.31/5.48 != zero_zero_int )
% 5.31/5.48 => ( ( A != zero_zero_int )
% 5.31/5.48 & ( B != zero_zero_int ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % mult_not_zero
% 5.31/5.48 thf(fact_376_divisors__zero,axiom,
% 5.31/5.48 ! [A: complex,B: complex] :
% 5.31/5.48 ( ( ( times_times_complex @ A @ B )
% 5.31/5.48 = zero_zero_complex )
% 5.31/5.48 => ( ( A = zero_zero_complex )
% 5.31/5.48 | ( B = zero_zero_complex ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % divisors_zero
% 5.31/5.48 thf(fact_377_divisors__zero,axiom,
% 5.31/5.48 ! [A: real,B: real] :
% 5.31/5.48 ( ( ( times_times_real @ A @ B )
% 5.31/5.48 = zero_zero_real )
% 5.31/5.48 => ( ( A = zero_zero_real )
% 5.31/5.48 | ( B = zero_zero_real ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % divisors_zero
% 5.31/5.48 thf(fact_378_divisors__zero,axiom,
% 5.31/5.48 ! [A: rat,B: rat] :
% 5.31/5.48 ( ( ( times_times_rat @ A @ B )
% 5.31/5.48 = zero_zero_rat )
% 5.31/5.48 => ( ( A = zero_zero_rat )
% 5.31/5.48 | ( B = zero_zero_rat ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % divisors_zero
% 5.31/5.48 thf(fact_379_divisors__zero,axiom,
% 5.31/5.48 ! [A: nat,B: nat] :
% 5.31/5.48 ( ( ( times_times_nat @ A @ B )
% 5.31/5.48 = zero_zero_nat )
% 5.31/5.48 => ( ( A = zero_zero_nat )
% 5.31/5.48 | ( B = zero_zero_nat ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % divisors_zero
% 5.31/5.48 thf(fact_380_divisors__zero,axiom,
% 5.31/5.48 ! [A: int,B: int] :
% 5.31/5.48 ( ( ( times_times_int @ A @ B )
% 5.31/5.48 = zero_zero_int )
% 5.31/5.48 => ( ( A = zero_zero_int )
% 5.31/5.48 | ( B = zero_zero_int ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % divisors_zero
% 5.31/5.48 thf(fact_381_no__zero__divisors,axiom,
% 5.31/5.48 ! [A: complex,B: complex] :
% 5.31/5.48 ( ( A != zero_zero_complex )
% 5.31/5.48 => ( ( B != zero_zero_complex )
% 5.31/5.48 => ( ( times_times_complex @ A @ B )
% 5.31/5.48 != zero_zero_complex ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % no_zero_divisors
% 5.31/5.48 thf(fact_382_no__zero__divisors,axiom,
% 5.31/5.48 ! [A: real,B: real] :
% 5.31/5.48 ( ( A != zero_zero_real )
% 5.31/5.48 => ( ( B != zero_zero_real )
% 5.31/5.48 => ( ( times_times_real @ A @ B )
% 5.31/5.48 != zero_zero_real ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % no_zero_divisors
% 5.31/5.48 thf(fact_383_no__zero__divisors,axiom,
% 5.31/5.48 ! [A: rat,B: rat] :
% 5.31/5.48 ( ( A != zero_zero_rat )
% 5.31/5.48 => ( ( B != zero_zero_rat )
% 5.31/5.48 => ( ( times_times_rat @ A @ B )
% 5.31/5.48 != zero_zero_rat ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % no_zero_divisors
% 5.31/5.48 thf(fact_384_no__zero__divisors,axiom,
% 5.31/5.48 ! [A: nat,B: nat] :
% 5.31/5.48 ( ( A != zero_zero_nat )
% 5.31/5.48 => ( ( B != zero_zero_nat )
% 5.31/5.48 => ( ( times_times_nat @ A @ B )
% 5.31/5.48 != zero_zero_nat ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % no_zero_divisors
% 5.31/5.48 thf(fact_385_no__zero__divisors,axiom,
% 5.31/5.48 ! [A: int,B: int] :
% 5.31/5.48 ( ( A != zero_zero_int )
% 5.31/5.48 => ( ( B != zero_zero_int )
% 5.31/5.48 => ( ( times_times_int @ A @ B )
% 5.31/5.48 != zero_zero_int ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % no_zero_divisors
% 5.31/5.48 thf(fact_386_mult__left__cancel,axiom,
% 5.31/5.48 ! [C2: complex,A: complex,B: complex] :
% 5.31/5.48 ( ( C2 != zero_zero_complex )
% 5.31/5.48 => ( ( ( times_times_complex @ C2 @ A )
% 5.31/5.48 = ( times_times_complex @ C2 @ B ) )
% 5.31/5.48 = ( A = B ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % mult_left_cancel
% 5.31/5.48 thf(fact_387_mult__left__cancel,axiom,
% 5.31/5.48 ! [C2: real,A: real,B: real] :
% 5.31/5.48 ( ( C2 != zero_zero_real )
% 5.31/5.48 => ( ( ( times_times_real @ C2 @ A )
% 5.31/5.48 = ( times_times_real @ C2 @ B ) )
% 5.31/5.48 = ( A = B ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % mult_left_cancel
% 5.31/5.48 thf(fact_388_mult__left__cancel,axiom,
% 5.31/5.48 ! [C2: rat,A: rat,B: rat] :
% 5.31/5.48 ( ( C2 != zero_zero_rat )
% 5.31/5.48 => ( ( ( times_times_rat @ C2 @ A )
% 5.31/5.48 = ( times_times_rat @ C2 @ B ) )
% 5.31/5.48 = ( A = B ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % mult_left_cancel
% 5.31/5.48 thf(fact_389_mult__left__cancel,axiom,
% 5.31/5.48 ! [C2: nat,A: nat,B: nat] :
% 5.31/5.48 ( ( C2 != zero_zero_nat )
% 5.31/5.48 => ( ( ( times_times_nat @ C2 @ A )
% 5.31/5.48 = ( times_times_nat @ C2 @ B ) )
% 5.31/5.48 = ( A = B ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % mult_left_cancel
% 5.31/5.48 thf(fact_390_mult__left__cancel,axiom,
% 5.31/5.48 ! [C2: int,A: int,B: int] :
% 5.31/5.48 ( ( C2 != zero_zero_int )
% 5.31/5.48 => ( ( ( times_times_int @ C2 @ A )
% 5.31/5.48 = ( times_times_int @ C2 @ B ) )
% 5.31/5.48 = ( A = B ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % mult_left_cancel
% 5.31/5.48 thf(fact_391_mult__right__cancel,axiom,
% 5.31/5.48 ! [C2: complex,A: complex,B: complex] :
% 5.31/5.48 ( ( C2 != zero_zero_complex )
% 5.31/5.48 => ( ( ( times_times_complex @ A @ C2 )
% 5.31/5.48 = ( times_times_complex @ B @ C2 ) )
% 5.31/5.48 = ( A = B ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % mult_right_cancel
% 5.31/5.48 thf(fact_392_mult__right__cancel,axiom,
% 5.31/5.48 ! [C2: real,A: real,B: real] :
% 5.31/5.48 ( ( C2 != zero_zero_real )
% 5.31/5.48 => ( ( ( times_times_real @ A @ C2 )
% 5.31/5.48 = ( times_times_real @ B @ C2 ) )
% 5.31/5.48 = ( A = B ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % mult_right_cancel
% 5.31/5.48 thf(fact_393_mult__right__cancel,axiom,
% 5.31/5.48 ! [C2: rat,A: rat,B: rat] :
% 5.31/5.48 ( ( C2 != zero_zero_rat )
% 5.31/5.48 => ( ( ( times_times_rat @ A @ C2 )
% 5.31/5.48 = ( times_times_rat @ B @ C2 ) )
% 5.31/5.48 = ( A = B ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % mult_right_cancel
% 5.31/5.48 thf(fact_394_mult__right__cancel,axiom,
% 5.31/5.48 ! [C2: nat,A: nat,B: nat] :
% 5.31/5.48 ( ( C2 != zero_zero_nat )
% 5.31/5.48 => ( ( ( times_times_nat @ A @ C2 )
% 5.31/5.48 = ( times_times_nat @ B @ C2 ) )
% 5.31/5.48 = ( A = B ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % mult_right_cancel
% 5.31/5.48 thf(fact_395_mult__right__cancel,axiom,
% 5.31/5.48 ! [C2: int,A: int,B: int] :
% 5.31/5.48 ( ( C2 != zero_zero_int )
% 5.31/5.48 => ( ( ( times_times_int @ A @ C2 )
% 5.31/5.48 = ( times_times_int @ B @ C2 ) )
% 5.31/5.48 = ( A = B ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % mult_right_cancel
% 5.31/5.48 thf(fact_396_mult__mono,axiom,
% 5.31/5.48 ! [A: real,B: real,C2: real,D: real] :
% 5.31/5.48 ( ( ord_less_eq_real @ A @ B )
% 5.31/5.48 => ( ( ord_less_eq_real @ C2 @ D )
% 5.31/5.48 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.31/5.48 => ( ( ord_less_eq_real @ zero_zero_real @ C2 )
% 5.31/5.48 => ( ord_less_eq_real @ ( times_times_real @ A @ C2 ) @ ( times_times_real @ B @ D ) ) ) ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % mult_mono
% 5.31/5.48 thf(fact_397_mult__mono,axiom,
% 5.31/5.48 ! [A: rat,B: rat,C2: rat,D: rat] :
% 5.31/5.48 ( ( ord_less_eq_rat @ A @ B )
% 5.31/5.48 => ( ( ord_less_eq_rat @ C2 @ D )
% 5.31/5.48 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.31/5.48 => ( ( ord_less_eq_rat @ zero_zero_rat @ C2 )
% 5.31/5.48 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C2 ) @ ( times_times_rat @ B @ D ) ) ) ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % mult_mono
% 5.31/5.48 thf(fact_398_mult__mono,axiom,
% 5.31/5.48 ! [A: nat,B: nat,C2: nat,D: nat] :
% 5.31/5.48 ( ( ord_less_eq_nat @ A @ B )
% 5.31/5.48 => ( ( ord_less_eq_nat @ C2 @ D )
% 5.31/5.48 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.31/5.48 => ( ( ord_less_eq_nat @ zero_zero_nat @ C2 )
% 5.31/5.48 => ( ord_less_eq_nat @ ( times_times_nat @ A @ C2 ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % mult_mono
% 5.31/5.48 thf(fact_399_mult__mono,axiom,
% 5.31/5.48 ! [A: int,B: int,C2: int,D: int] :
% 5.31/5.48 ( ( ord_less_eq_int @ A @ B )
% 5.31/5.48 => ( ( ord_less_eq_int @ C2 @ D )
% 5.31/5.48 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.31/5.48 => ( ( ord_less_eq_int @ zero_zero_int @ C2 )
% 5.31/5.48 => ( ord_less_eq_int @ ( times_times_int @ A @ C2 ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % mult_mono
% 5.31/5.48 thf(fact_400_mult__mono_H,axiom,
% 5.31/5.48 ! [A: real,B: real,C2: real,D: real] :
% 5.31/5.48 ( ( ord_less_eq_real @ A @ B )
% 5.31/5.48 => ( ( ord_less_eq_real @ C2 @ D )
% 5.31/5.48 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.31/5.48 => ( ( ord_less_eq_real @ zero_zero_real @ C2 )
% 5.31/5.48 => ( ord_less_eq_real @ ( times_times_real @ A @ C2 ) @ ( times_times_real @ B @ D ) ) ) ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % mult_mono'
% 5.31/5.48 thf(fact_401_mult__mono_H,axiom,
% 5.31/5.48 ! [A: rat,B: rat,C2: rat,D: rat] :
% 5.31/5.48 ( ( ord_less_eq_rat @ A @ B )
% 5.31/5.48 => ( ( ord_less_eq_rat @ C2 @ D )
% 5.31/5.48 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.31/5.48 => ( ( ord_less_eq_rat @ zero_zero_rat @ C2 )
% 5.31/5.48 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C2 ) @ ( times_times_rat @ B @ D ) ) ) ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % mult_mono'
% 5.31/5.48 thf(fact_402_mult__mono_H,axiom,
% 5.31/5.48 ! [A: nat,B: nat,C2: nat,D: nat] :
% 5.31/5.48 ( ( ord_less_eq_nat @ A @ B )
% 5.31/5.48 => ( ( ord_less_eq_nat @ C2 @ D )
% 5.31/5.48 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.31/5.48 => ( ( ord_less_eq_nat @ zero_zero_nat @ C2 )
% 5.31/5.48 => ( ord_less_eq_nat @ ( times_times_nat @ A @ C2 ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % mult_mono'
% 5.31/5.48 thf(fact_403_mult__mono_H,axiom,
% 5.31/5.48 ! [A: int,B: int,C2: int,D: int] :
% 5.31/5.48 ( ( ord_less_eq_int @ A @ B )
% 5.31/5.48 => ( ( ord_less_eq_int @ C2 @ D )
% 5.31/5.48 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.31/5.48 => ( ( ord_less_eq_int @ zero_zero_int @ C2 )
% 5.31/5.48 => ( ord_less_eq_int @ ( times_times_int @ A @ C2 ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % mult_mono'
% 5.31/5.48 thf(fact_404_zero__le__square,axiom,
% 5.31/5.48 ! [A: real] : ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ A ) ) ).
% 5.31/5.48
% 5.31/5.48 % zero_le_square
% 5.31/5.48 thf(fact_405_zero__le__square,axiom,
% 5.31/5.48 ! [A: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ A ) ) ).
% 5.31/5.48
% 5.31/5.48 % zero_le_square
% 5.31/5.48 thf(fact_406_zero__le__square,axiom,
% 5.31/5.48 ! [A: int] : ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ A ) ) ).
% 5.31/5.48
% 5.31/5.48 % zero_le_square
% 5.31/5.48 thf(fact_407_split__mult__pos__le,axiom,
% 5.31/5.48 ! [A: real,B: real] :
% 5.31/5.48 ( ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.31/5.48 & ( ord_less_eq_real @ zero_zero_real @ B ) )
% 5.31/5.48 | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.31/5.48 & ( ord_less_eq_real @ B @ zero_zero_real ) ) )
% 5.31/5.48 => ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % split_mult_pos_le
% 5.31/5.48 thf(fact_408_split__mult__pos__le,axiom,
% 5.31/5.48 ! [A: rat,B: rat] :
% 5.31/5.48 ( ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.31/5.48 & ( ord_less_eq_rat @ zero_zero_rat @ B ) )
% 5.31/5.48 | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.31/5.48 & ( ord_less_eq_rat @ B @ zero_zero_rat ) ) )
% 5.31/5.48 => ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % split_mult_pos_le
% 5.31/5.48 thf(fact_409_split__mult__pos__le,axiom,
% 5.31/5.48 ! [A: int,B: int] :
% 5.31/5.48 ( ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.31/5.48 & ( ord_less_eq_int @ zero_zero_int @ B ) )
% 5.31/5.48 | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.31/5.48 & ( ord_less_eq_int @ B @ zero_zero_int ) ) )
% 5.31/5.48 => ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % split_mult_pos_le
% 5.31/5.48 thf(fact_410_mult__left__mono__neg,axiom,
% 5.31/5.48 ! [B: real,A: real,C2: real] :
% 5.31/5.48 ( ( ord_less_eq_real @ B @ A )
% 5.31/5.48 => ( ( ord_less_eq_real @ C2 @ zero_zero_real )
% 5.31/5.48 => ( ord_less_eq_real @ ( times_times_real @ C2 @ A ) @ ( times_times_real @ C2 @ B ) ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % mult_left_mono_neg
% 5.31/5.48 thf(fact_411_mult__left__mono__neg,axiom,
% 5.31/5.48 ! [B: rat,A: rat,C2: rat] :
% 5.31/5.48 ( ( ord_less_eq_rat @ B @ A )
% 5.31/5.48 => ( ( ord_less_eq_rat @ C2 @ zero_zero_rat )
% 5.31/5.48 => ( ord_less_eq_rat @ ( times_times_rat @ C2 @ A ) @ ( times_times_rat @ C2 @ B ) ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % mult_left_mono_neg
% 5.31/5.48 thf(fact_412_mult__left__mono__neg,axiom,
% 5.31/5.48 ! [B: int,A: int,C2: int] :
% 5.31/5.48 ( ( ord_less_eq_int @ B @ A )
% 5.31/5.48 => ( ( ord_less_eq_int @ C2 @ zero_zero_int )
% 5.31/5.48 => ( ord_less_eq_int @ ( times_times_int @ C2 @ A ) @ ( times_times_int @ C2 @ B ) ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % mult_left_mono_neg
% 5.31/5.48 thf(fact_413_mult__nonpos__nonpos,axiom,
% 5.31/5.48 ! [A: real,B: real] :
% 5.31/5.48 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.31/5.48 => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 5.31/5.48 => ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % mult_nonpos_nonpos
% 5.31/5.48 thf(fact_414_mult__nonpos__nonpos,axiom,
% 5.31/5.48 ! [A: rat,B: rat] :
% 5.31/5.48 ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.31/5.48 => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 5.31/5.48 => ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % mult_nonpos_nonpos
% 5.31/5.48 thf(fact_415_mult__nonpos__nonpos,axiom,
% 5.31/5.48 ! [A: int,B: int] :
% 5.31/5.48 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.31/5.48 => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 5.31/5.48 => ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % mult_nonpos_nonpos
% 5.31/5.48 thf(fact_416_mult__left__mono,axiom,
% 5.31/5.48 ! [A: real,B: real,C2: real] :
% 5.31/5.48 ( ( ord_less_eq_real @ A @ B )
% 5.31/5.48 => ( ( ord_less_eq_real @ zero_zero_real @ C2 )
% 5.31/5.48 => ( ord_less_eq_real @ ( times_times_real @ C2 @ A ) @ ( times_times_real @ C2 @ B ) ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % mult_left_mono
% 5.31/5.48 thf(fact_417_mult__left__mono,axiom,
% 5.31/5.48 ! [A: rat,B: rat,C2: rat] :
% 5.31/5.48 ( ( ord_less_eq_rat @ A @ B )
% 5.31/5.48 => ( ( ord_less_eq_rat @ zero_zero_rat @ C2 )
% 5.31/5.48 => ( ord_less_eq_rat @ ( times_times_rat @ C2 @ A ) @ ( times_times_rat @ C2 @ B ) ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % mult_left_mono
% 5.31/5.48 thf(fact_418_mult__left__mono,axiom,
% 5.31/5.48 ! [A: nat,B: nat,C2: nat] :
% 5.31/5.48 ( ( ord_less_eq_nat @ A @ B )
% 5.31/5.48 => ( ( ord_less_eq_nat @ zero_zero_nat @ C2 )
% 5.31/5.48 => ( ord_less_eq_nat @ ( times_times_nat @ C2 @ A ) @ ( times_times_nat @ C2 @ B ) ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % mult_left_mono
% 5.31/5.48 thf(fact_419_mult__left__mono,axiom,
% 5.31/5.48 ! [A: int,B: int,C2: int] :
% 5.31/5.48 ( ( ord_less_eq_int @ A @ B )
% 5.31/5.48 => ( ( ord_less_eq_int @ zero_zero_int @ C2 )
% 5.31/5.48 => ( ord_less_eq_int @ ( times_times_int @ C2 @ A ) @ ( times_times_int @ C2 @ B ) ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % mult_left_mono
% 5.31/5.48 thf(fact_420_mult__right__mono__neg,axiom,
% 5.31/5.48 ! [B: real,A: real,C2: real] :
% 5.31/5.48 ( ( ord_less_eq_real @ B @ A )
% 5.31/5.48 => ( ( ord_less_eq_real @ C2 @ zero_zero_real )
% 5.31/5.48 => ( ord_less_eq_real @ ( times_times_real @ A @ C2 ) @ ( times_times_real @ B @ C2 ) ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % mult_right_mono_neg
% 5.31/5.48 thf(fact_421_mult__right__mono__neg,axiom,
% 5.31/5.48 ! [B: rat,A: rat,C2: rat] :
% 5.31/5.48 ( ( ord_less_eq_rat @ B @ A )
% 5.31/5.48 => ( ( ord_less_eq_rat @ C2 @ zero_zero_rat )
% 5.31/5.48 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C2 ) @ ( times_times_rat @ B @ C2 ) ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % mult_right_mono_neg
% 5.31/5.48 thf(fact_422_mult__right__mono__neg,axiom,
% 5.31/5.48 ! [B: int,A: int,C2: int] :
% 5.31/5.48 ( ( ord_less_eq_int @ B @ A )
% 5.31/5.48 => ( ( ord_less_eq_int @ C2 @ zero_zero_int )
% 5.31/5.48 => ( ord_less_eq_int @ ( times_times_int @ A @ C2 ) @ ( times_times_int @ B @ C2 ) ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % mult_right_mono_neg
% 5.31/5.48 thf(fact_423_mult__right__mono,axiom,
% 5.31/5.48 ! [A: real,B: real,C2: real] :
% 5.31/5.48 ( ( ord_less_eq_real @ A @ B )
% 5.31/5.48 => ( ( ord_less_eq_real @ zero_zero_real @ C2 )
% 5.31/5.48 => ( ord_less_eq_real @ ( times_times_real @ A @ C2 ) @ ( times_times_real @ B @ C2 ) ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % mult_right_mono
% 5.31/5.48 thf(fact_424_mult__right__mono,axiom,
% 5.31/5.48 ! [A: rat,B: rat,C2: rat] :
% 5.31/5.48 ( ( ord_less_eq_rat @ A @ B )
% 5.31/5.48 => ( ( ord_less_eq_rat @ zero_zero_rat @ C2 )
% 5.31/5.48 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C2 ) @ ( times_times_rat @ B @ C2 ) ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % mult_right_mono
% 5.31/5.48 thf(fact_425_mult__right__mono,axiom,
% 5.31/5.48 ! [A: nat,B: nat,C2: nat] :
% 5.31/5.48 ( ( ord_less_eq_nat @ A @ B )
% 5.31/5.48 => ( ( ord_less_eq_nat @ zero_zero_nat @ C2 )
% 5.31/5.48 => ( ord_less_eq_nat @ ( times_times_nat @ A @ C2 ) @ ( times_times_nat @ B @ C2 ) ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % mult_right_mono
% 5.31/5.48 thf(fact_426_mult__right__mono,axiom,
% 5.31/5.48 ! [A: int,B: int,C2: int] :
% 5.31/5.48 ( ( ord_less_eq_int @ A @ B )
% 5.31/5.48 => ( ( ord_less_eq_int @ zero_zero_int @ C2 )
% 5.31/5.48 => ( ord_less_eq_int @ ( times_times_int @ A @ C2 ) @ ( times_times_int @ B @ C2 ) ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % mult_right_mono
% 5.31/5.48 thf(fact_427_mult__le__0__iff,axiom,
% 5.31/5.48 ! [A: real,B: real] :
% 5.31/5.48 ( ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ zero_zero_real )
% 5.31/5.48 = ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.31/5.48 & ( ord_less_eq_real @ B @ zero_zero_real ) )
% 5.31/5.48 | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.31/5.48 & ( ord_less_eq_real @ zero_zero_real @ B ) ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % mult_le_0_iff
% 5.31/5.48 thf(fact_428_mult__le__0__iff,axiom,
% 5.31/5.48 ! [A: rat,B: rat] :
% 5.31/5.48 ( ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat )
% 5.31/5.48 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.31/5.48 & ( ord_less_eq_rat @ B @ zero_zero_rat ) )
% 5.31/5.48 | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.31/5.48 & ( ord_less_eq_rat @ zero_zero_rat @ B ) ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % mult_le_0_iff
% 5.31/5.48 thf(fact_429_mult__le__0__iff,axiom,
% 5.31/5.48 ! [A: int,B: int] :
% 5.31/5.48 ( ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int )
% 5.31/5.48 = ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.31/5.48 & ( ord_less_eq_int @ B @ zero_zero_int ) )
% 5.31/5.48 | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.31/5.48 & ( ord_less_eq_int @ zero_zero_int @ B ) ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % mult_le_0_iff
% 5.31/5.48 thf(fact_430_split__mult__neg__le,axiom,
% 5.31/5.48 ! [A: real,B: real] :
% 5.31/5.48 ( ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.31/5.48 & ( ord_less_eq_real @ B @ zero_zero_real ) )
% 5.31/5.48 | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.31/5.48 & ( ord_less_eq_real @ zero_zero_real @ B ) ) )
% 5.31/5.48 => ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ).
% 5.31/5.48
% 5.31/5.48 % split_mult_neg_le
% 5.31/5.48 thf(fact_431_split__mult__neg__le,axiom,
% 5.31/5.48 ! [A: rat,B: rat] :
% 5.31/5.48 ( ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.31/5.48 & ( ord_less_eq_rat @ B @ zero_zero_rat ) )
% 5.31/5.48 | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.31/5.48 & ( ord_less_eq_rat @ zero_zero_rat @ B ) ) )
% 5.31/5.48 => ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ).
% 5.31/5.48
% 5.31/5.48 % split_mult_neg_le
% 5.31/5.48 thf(fact_432_split__mult__neg__le,axiom,
% 5.31/5.48 ! [A: nat,B: nat] :
% 5.31/5.48 ( ( ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.31/5.48 & ( ord_less_eq_nat @ B @ zero_zero_nat ) )
% 5.31/5.48 | ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 5.31/5.48 & ( ord_less_eq_nat @ zero_zero_nat @ B ) ) )
% 5.31/5.48 => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ).
% 5.31/5.48
% 5.31/5.48 % split_mult_neg_le
% 5.31/5.48 thf(fact_433_split__mult__neg__le,axiom,
% 5.31/5.48 ! [A: int,B: int] :
% 5.31/5.48 ( ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.31/5.48 & ( ord_less_eq_int @ B @ zero_zero_int ) )
% 5.31/5.48 | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.31/5.48 & ( ord_less_eq_int @ zero_zero_int @ B ) ) )
% 5.31/5.48 => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ).
% 5.31/5.48
% 5.31/5.48 % split_mult_neg_le
% 5.31/5.48 thf(fact_434_mult__nonneg__nonneg,axiom,
% 5.31/5.48 ! [A: real,B: real] :
% 5.31/5.48 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.31/5.48 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.31/5.48 => ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % mult_nonneg_nonneg
% 5.31/5.48 thf(fact_435_mult__nonneg__nonneg,axiom,
% 5.31/5.48 ! [A: rat,B: rat] :
% 5.31/5.48 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.31/5.48 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.31/5.48 => ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % mult_nonneg_nonneg
% 5.31/5.48 thf(fact_436_mult__nonneg__nonneg,axiom,
% 5.31/5.48 ! [A: nat,B: nat] :
% 5.31/5.48 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.31/5.48 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.31/5.48 => ( ord_less_eq_nat @ zero_zero_nat @ ( times_times_nat @ A @ B ) ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % mult_nonneg_nonneg
% 5.31/5.48 thf(fact_437_mult__nonneg__nonneg,axiom,
% 5.31/5.48 ! [A: int,B: int] :
% 5.31/5.48 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.31/5.48 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.31/5.48 => ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % mult_nonneg_nonneg
% 5.31/5.48 thf(fact_438_valid__eq,axiom,
% 5.31/5.48 vEBT_VEBT_valid = vEBT_invar_vebt ).
% 5.31/5.48
% 5.31/5.48 % valid_eq
% 5.31/5.48 thf(fact_439_valid__eq1,axiom,
% 5.31/5.48 ! [T: vEBT_VEBT,D: nat] :
% 5.31/5.48 ( ( vEBT_invar_vebt @ T @ D )
% 5.31/5.48 => ( vEBT_VEBT_valid @ T @ D ) ) ).
% 5.31/5.48
% 5.31/5.48 % valid_eq1
% 5.31/5.48 thf(fact_440_valid__eq2,axiom,
% 5.31/5.48 ! [T: vEBT_VEBT,D: nat] :
% 5.31/5.48 ( ( vEBT_VEBT_valid @ T @ D )
% 5.31/5.48 => ( vEBT_invar_vebt @ T @ D ) ) ).
% 5.31/5.48
% 5.31/5.48 % valid_eq2
% 5.31/5.48 thf(fact_441_deg1Leaf,axiom,
% 5.31/5.48 ! [T: vEBT_VEBT] :
% 5.31/5.48 ( ( vEBT_invar_vebt @ T @ one_one_nat )
% 5.31/5.48 = ( ? [A5: $o,B4: $o] :
% 5.31/5.48 ( T
% 5.31/5.48 = ( vEBT_Leaf @ A5 @ B4 ) ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % deg1Leaf
% 5.31/5.48 thf(fact_442_deg__1__Leaf,axiom,
% 5.31/5.48 ! [T: vEBT_VEBT] :
% 5.31/5.48 ( ( vEBT_invar_vebt @ T @ one_one_nat )
% 5.31/5.48 => ? [A3: $o,B3: $o] :
% 5.31/5.48 ( T
% 5.31/5.48 = ( vEBT_Leaf @ A3 @ B3 ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % deg_1_Leaf
% 5.31/5.48 thf(fact_443_deg__1__Leafy,axiom,
% 5.31/5.48 ! [T: vEBT_VEBT,N: nat] :
% 5.31/5.48 ( ( vEBT_invar_vebt @ T @ N )
% 5.31/5.48 => ( ( N = one_one_nat )
% 5.31/5.48 => ? [A3: $o,B3: $o] :
% 5.31/5.48 ( T
% 5.31/5.48 = ( vEBT_Leaf @ A3 @ B3 ) ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % deg_1_Leafy
% 5.31/5.48 thf(fact_444_nat__mult__eq__cancel__disj,axiom,
% 5.31/5.48 ! [K2: nat,M2: nat,N: nat] :
% 5.31/5.48 ( ( ( times_times_nat @ K2 @ M2 )
% 5.31/5.48 = ( times_times_nat @ K2 @ N ) )
% 5.31/5.48 = ( ( K2 = zero_zero_nat )
% 5.31/5.48 | ( M2 = N ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % nat_mult_eq_cancel_disj
% 5.31/5.48 thf(fact_445_deg__not__0,axiom,
% 5.31/5.48 ! [T: vEBT_VEBT,N: nat] :
% 5.31/5.48 ( ( vEBT_invar_vebt @ T @ N )
% 5.31/5.48 => ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 5.31/5.48
% 5.31/5.48 % deg_not_0
% 5.31/5.48 thf(fact_446_VEBT_Osize__gen_I2_J,axiom,
% 5.31/5.48 ! [X21: $o,X22: $o] :
% 5.31/5.48 ( ( vEBT_size_VEBT @ ( vEBT_Leaf @ X21 @ X22 ) )
% 5.31/5.48 = zero_zero_nat ) ).
% 5.31/5.48
% 5.31/5.48 % VEBT.size_gen(2)
% 5.31/5.48 thf(fact_447_deg__SUcn__Node,axiom,
% 5.31/5.48 ! [Tree: vEBT_VEBT,N: nat] :
% 5.31/5.48 ( ( vEBT_invar_vebt @ Tree @ ( suc @ ( suc @ N ) ) )
% 5.31/5.48 => ? [Info: option4927543243414619207at_nat,TreeList: list_VEBT_VEBT,S: vEBT_VEBT] :
% 5.31/5.48 ( Tree
% 5.31/5.48 = ( vEBT_Node @ Info @ ( suc @ ( suc @ N ) ) @ TreeList @ S ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % deg_SUcn_Node
% 5.31/5.48 thf(fact_448_case4_I13_J,axiom,
% 5.31/5.48 ( ( vEBT_VEBT_set_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ deg @ treeList2 @ summary2 ) )
% 5.31/5.48 = ( vEBT_VEBT_set_vebt @ sa ) ) ).
% 5.31/5.48
% 5.31/5.48 % case4(13)
% 5.31/5.48 thf(fact_449_deg__deg__n,axiom,
% 5.31/5.48 ! [Info2: option4927543243414619207at_nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat] :
% 5.31/5.48 ( ( vEBT_invar_vebt @ ( vEBT_Node @ Info2 @ Deg @ TreeList2 @ Summary ) @ N )
% 5.31/5.48 => ( Deg = N ) ) ).
% 5.31/5.48
% 5.31/5.48 % deg_deg_n
% 5.31/5.48 thf(fact_450_VEBT_Oinject_I1_J,axiom,
% 5.31/5.48 ! [X11: option4927543243414619207at_nat,X12: nat,X13: list_VEBT_VEBT,X14: vEBT_VEBT,Y11: option4927543243414619207at_nat,Y12: nat,Y13: list_VEBT_VEBT,Y14: vEBT_VEBT] :
% 5.31/5.48 ( ( ( vEBT_Node @ X11 @ X12 @ X13 @ X14 )
% 5.31/5.48 = ( vEBT_Node @ Y11 @ Y12 @ Y13 @ Y14 ) )
% 5.31/5.48 = ( ( X11 = Y11 )
% 5.31/5.48 & ( X12 = Y12 )
% 5.31/5.48 & ( X13 = Y13 )
% 5.31/5.48 & ( X14 = Y14 ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % VEBT.inject(1)
% 5.31/5.48 thf(fact_451_not__gr__zero,axiom,
% 5.31/5.48 ! [N: nat] :
% 5.31/5.48 ( ( ~ ( ord_less_nat @ zero_zero_nat @ N ) )
% 5.31/5.48 = ( N = zero_zero_nat ) ) ).
% 5.31/5.48
% 5.31/5.48 % not_gr_zero
% 5.31/5.48 thf(fact_452_mult__1,axiom,
% 5.31/5.48 ! [A: code_integer] :
% 5.31/5.48 ( ( times_3573771949741848930nteger @ one_one_Code_integer @ A )
% 5.31/5.48 = A ) ).
% 5.31/5.48
% 5.31/5.48 % mult_1
% 5.31/5.48 thf(fact_453_mult__1,axiom,
% 5.31/5.48 ! [A: complex] :
% 5.31/5.48 ( ( times_times_complex @ one_one_complex @ A )
% 5.31/5.48 = A ) ).
% 5.31/5.48
% 5.31/5.48 % mult_1
% 5.31/5.48 thf(fact_454_mult__1,axiom,
% 5.31/5.48 ! [A: real] :
% 5.31/5.48 ( ( times_times_real @ one_one_real @ A )
% 5.31/5.48 = A ) ).
% 5.31/5.48
% 5.31/5.48 % mult_1
% 5.31/5.48 thf(fact_455_mult__1,axiom,
% 5.31/5.48 ! [A: rat] :
% 5.31/5.48 ( ( times_times_rat @ one_one_rat @ A )
% 5.31/5.48 = A ) ).
% 5.31/5.48
% 5.31/5.48 % mult_1
% 5.31/5.48 thf(fact_456_mult__1,axiom,
% 5.31/5.48 ! [A: nat] :
% 5.31/5.48 ( ( times_times_nat @ one_one_nat @ A )
% 5.31/5.48 = A ) ).
% 5.31/5.48
% 5.31/5.48 % mult_1
% 5.31/5.48 thf(fact_457_mult__1,axiom,
% 5.31/5.48 ! [A: int] :
% 5.31/5.48 ( ( times_times_int @ one_one_int @ A )
% 5.31/5.48 = A ) ).
% 5.31/5.48
% 5.31/5.48 % mult_1
% 5.31/5.48 thf(fact_458_mult_Oright__neutral,axiom,
% 5.31/5.48 ! [A: code_integer] :
% 5.31/5.48 ( ( times_3573771949741848930nteger @ A @ one_one_Code_integer )
% 5.31/5.48 = A ) ).
% 5.31/5.48
% 5.31/5.48 % mult.right_neutral
% 5.31/5.48 thf(fact_459_mult_Oright__neutral,axiom,
% 5.31/5.48 ! [A: complex] :
% 5.31/5.48 ( ( times_times_complex @ A @ one_one_complex )
% 5.31/5.48 = A ) ).
% 5.31/5.48
% 5.31/5.48 % mult.right_neutral
% 5.31/5.48 thf(fact_460_mult_Oright__neutral,axiom,
% 5.31/5.48 ! [A: real] :
% 5.31/5.48 ( ( times_times_real @ A @ one_one_real )
% 5.31/5.48 = A ) ).
% 5.31/5.48
% 5.31/5.48 % mult.right_neutral
% 5.31/5.48 thf(fact_461_mult_Oright__neutral,axiom,
% 5.31/5.48 ! [A: rat] :
% 5.31/5.48 ( ( times_times_rat @ A @ one_one_rat )
% 5.31/5.48 = A ) ).
% 5.31/5.48
% 5.31/5.48 % mult.right_neutral
% 5.31/5.48 thf(fact_462_mult_Oright__neutral,axiom,
% 5.31/5.48 ! [A: nat] :
% 5.31/5.48 ( ( times_times_nat @ A @ one_one_nat )
% 5.31/5.48 = A ) ).
% 5.31/5.48
% 5.31/5.48 % mult.right_neutral
% 5.31/5.48 thf(fact_463_mult_Oright__neutral,axiom,
% 5.31/5.48 ! [A: int] :
% 5.31/5.48 ( ( times_times_int @ A @ one_one_int )
% 5.31/5.48 = A ) ).
% 5.31/5.48
% 5.31/5.48 % mult.right_neutral
% 5.31/5.48 thf(fact_464_Suc__less__eq,axiom,
% 5.31/5.48 ! [M2: nat,N: nat] :
% 5.31/5.48 ( ( ord_less_nat @ ( suc @ M2 ) @ ( suc @ N ) )
% 5.31/5.48 = ( ord_less_nat @ M2 @ N ) ) ).
% 5.31/5.48
% 5.31/5.48 % Suc_less_eq
% 5.31/5.48 thf(fact_465_Suc__mono,axiom,
% 5.31/5.48 ! [M2: nat,N: nat] :
% 5.31/5.48 ( ( ord_less_nat @ M2 @ N )
% 5.31/5.48 => ( ord_less_nat @ ( suc @ M2 ) @ ( suc @ N ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % Suc_mono
% 5.31/5.48 thf(fact_466_lessI,axiom,
% 5.31/5.48 ! [N: nat] : ( ord_less_nat @ N @ ( suc @ N ) ) ).
% 5.31/5.48
% 5.31/5.48 % lessI
% 5.31/5.48 thf(fact_467_bot__nat__0_Onot__eq__extremum,axiom,
% 5.31/5.48 ! [A: nat] :
% 5.31/5.48 ( ( A != zero_zero_nat )
% 5.31/5.48 = ( ord_less_nat @ zero_zero_nat @ A ) ) ).
% 5.31/5.48
% 5.31/5.48 % bot_nat_0.not_eq_extremum
% 5.31/5.48 thf(fact_468_neq0__conv,axiom,
% 5.31/5.48 ! [N: nat] :
% 5.31/5.48 ( ( N != zero_zero_nat )
% 5.31/5.48 = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 5.31/5.48
% 5.31/5.48 % neq0_conv
% 5.31/5.48 thf(fact_469_less__nat__zero__code,axiom,
% 5.31/5.48 ! [N: nat] :
% 5.31/5.48 ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 5.31/5.48
% 5.31/5.48 % less_nat_zero_code
% 5.31/5.48 thf(fact_470_nat__1__eq__mult__iff,axiom,
% 5.31/5.48 ! [M2: nat,N: nat] :
% 5.31/5.48 ( ( one_one_nat
% 5.31/5.48 = ( times_times_nat @ M2 @ N ) )
% 5.31/5.48 = ( ( M2 = one_one_nat )
% 5.31/5.48 & ( N = one_one_nat ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % nat_1_eq_mult_iff
% 5.31/5.48 thf(fact_471_nat__mult__eq__1__iff,axiom,
% 5.31/5.48 ! [M2: nat,N: nat] :
% 5.31/5.48 ( ( ( times_times_nat @ M2 @ N )
% 5.31/5.48 = one_one_nat )
% 5.31/5.48 = ( ( M2 = one_one_nat )
% 5.31/5.48 & ( N = one_one_nat ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % nat_mult_eq_1_iff
% 5.31/5.48 thf(fact_472_case4_I3_J,axiom,
% 5.31/5.48 vEBT_invar_vebt @ summary2 @ m ).
% 5.31/5.48
% 5.31/5.48 % case4(3)
% 5.31/5.48 thf(fact_473_mult__cancel__left1,axiom,
% 5.31/5.48 ! [C2: code_integer,B: code_integer] :
% 5.31/5.48 ( ( C2
% 5.31/5.48 = ( times_3573771949741848930nteger @ C2 @ B ) )
% 5.31/5.48 = ( ( C2 = zero_z3403309356797280102nteger )
% 5.31/5.48 | ( B = one_one_Code_integer ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % mult_cancel_left1
% 5.31/5.48 thf(fact_474_mult__cancel__left1,axiom,
% 5.31/5.48 ! [C2: complex,B: complex] :
% 5.31/5.48 ( ( C2
% 5.31/5.48 = ( times_times_complex @ C2 @ B ) )
% 5.31/5.48 = ( ( C2 = zero_zero_complex )
% 5.31/5.48 | ( B = one_one_complex ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % mult_cancel_left1
% 5.31/5.48 thf(fact_475_mult__cancel__left1,axiom,
% 5.31/5.48 ! [C2: real,B: real] :
% 5.31/5.48 ( ( C2
% 5.31/5.48 = ( times_times_real @ C2 @ B ) )
% 5.31/5.48 = ( ( C2 = zero_zero_real )
% 5.31/5.48 | ( B = one_one_real ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % mult_cancel_left1
% 5.31/5.48 thf(fact_476_mult__cancel__left1,axiom,
% 5.31/5.48 ! [C2: rat,B: rat] :
% 5.31/5.48 ( ( C2
% 5.31/5.48 = ( times_times_rat @ C2 @ B ) )
% 5.31/5.48 = ( ( C2 = zero_zero_rat )
% 5.31/5.48 | ( B = one_one_rat ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % mult_cancel_left1
% 5.31/5.48 thf(fact_477_mult__cancel__left1,axiom,
% 5.31/5.48 ! [C2: int,B: int] :
% 5.31/5.48 ( ( C2
% 5.31/5.48 = ( times_times_int @ C2 @ B ) )
% 5.31/5.48 = ( ( C2 = zero_zero_int )
% 5.31/5.48 | ( B = one_one_int ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % mult_cancel_left1
% 5.31/5.48 thf(fact_478_mult__cancel__left2,axiom,
% 5.31/5.48 ! [C2: code_integer,A: code_integer] :
% 5.31/5.48 ( ( ( times_3573771949741848930nteger @ C2 @ A )
% 5.31/5.48 = C2 )
% 5.31/5.48 = ( ( C2 = zero_z3403309356797280102nteger )
% 5.31/5.48 | ( A = one_one_Code_integer ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % mult_cancel_left2
% 5.31/5.48 thf(fact_479_mult__cancel__left2,axiom,
% 5.31/5.48 ! [C2: complex,A: complex] :
% 5.31/5.48 ( ( ( times_times_complex @ C2 @ A )
% 5.31/5.48 = C2 )
% 5.31/5.48 = ( ( C2 = zero_zero_complex )
% 5.31/5.48 | ( A = one_one_complex ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % mult_cancel_left2
% 5.31/5.48 thf(fact_480_mult__cancel__left2,axiom,
% 5.31/5.48 ! [C2: real,A: real] :
% 5.31/5.48 ( ( ( times_times_real @ C2 @ A )
% 5.31/5.48 = C2 )
% 5.31/5.48 = ( ( C2 = zero_zero_real )
% 5.31/5.48 | ( A = one_one_real ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % mult_cancel_left2
% 5.31/5.48 thf(fact_481_mult__cancel__left2,axiom,
% 5.31/5.48 ! [C2: rat,A: rat] :
% 5.31/5.48 ( ( ( times_times_rat @ C2 @ A )
% 5.31/5.48 = C2 )
% 5.31/5.48 = ( ( C2 = zero_zero_rat )
% 5.31/5.48 | ( A = one_one_rat ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % mult_cancel_left2
% 5.31/5.48 thf(fact_482_mult__cancel__left2,axiom,
% 5.31/5.48 ! [C2: int,A: int] :
% 5.31/5.48 ( ( ( times_times_int @ C2 @ A )
% 5.31/5.48 = C2 )
% 5.31/5.48 = ( ( C2 = zero_zero_int )
% 5.31/5.48 | ( A = one_one_int ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % mult_cancel_left2
% 5.31/5.48 thf(fact_483_mult__cancel__right1,axiom,
% 5.31/5.48 ! [C2: code_integer,B: code_integer] :
% 5.31/5.48 ( ( C2
% 5.31/5.48 = ( times_3573771949741848930nteger @ B @ C2 ) )
% 5.31/5.48 = ( ( C2 = zero_z3403309356797280102nteger )
% 5.31/5.48 | ( B = one_one_Code_integer ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % mult_cancel_right1
% 5.31/5.48 thf(fact_484_mult__cancel__right1,axiom,
% 5.31/5.48 ! [C2: complex,B: complex] :
% 5.31/5.48 ( ( C2
% 5.31/5.48 = ( times_times_complex @ B @ C2 ) )
% 5.31/5.48 = ( ( C2 = zero_zero_complex )
% 5.31/5.48 | ( B = one_one_complex ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % mult_cancel_right1
% 5.31/5.48 thf(fact_485_mult__cancel__right1,axiom,
% 5.31/5.48 ! [C2: real,B: real] :
% 5.31/5.48 ( ( C2
% 5.31/5.48 = ( times_times_real @ B @ C2 ) )
% 5.31/5.48 = ( ( C2 = zero_zero_real )
% 5.31/5.48 | ( B = one_one_real ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % mult_cancel_right1
% 5.31/5.48 thf(fact_486_mult__cancel__right1,axiom,
% 5.31/5.48 ! [C2: rat,B: rat] :
% 5.31/5.48 ( ( C2
% 5.31/5.48 = ( times_times_rat @ B @ C2 ) )
% 5.31/5.48 = ( ( C2 = zero_zero_rat )
% 5.31/5.48 | ( B = one_one_rat ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % mult_cancel_right1
% 5.31/5.48 thf(fact_487_mult__cancel__right1,axiom,
% 5.31/5.48 ! [C2: int,B: int] :
% 5.31/5.48 ( ( C2
% 5.31/5.48 = ( times_times_int @ B @ C2 ) )
% 5.31/5.48 = ( ( C2 = zero_zero_int )
% 5.31/5.48 | ( B = one_one_int ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % mult_cancel_right1
% 5.31/5.48 thf(fact_488_mult__cancel__right2,axiom,
% 5.31/5.48 ! [A: code_integer,C2: code_integer] :
% 5.31/5.48 ( ( ( times_3573771949741848930nteger @ A @ C2 )
% 5.31/5.48 = C2 )
% 5.31/5.48 = ( ( C2 = zero_z3403309356797280102nteger )
% 5.31/5.48 | ( A = one_one_Code_integer ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % mult_cancel_right2
% 5.31/5.48 thf(fact_489_mult__cancel__right2,axiom,
% 5.31/5.48 ! [A: complex,C2: complex] :
% 5.31/5.48 ( ( ( times_times_complex @ A @ C2 )
% 5.31/5.48 = C2 )
% 5.31/5.48 = ( ( C2 = zero_zero_complex )
% 5.31/5.48 | ( A = one_one_complex ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % mult_cancel_right2
% 5.31/5.48 thf(fact_490_mult__cancel__right2,axiom,
% 5.31/5.48 ! [A: real,C2: real] :
% 5.31/5.48 ( ( ( times_times_real @ A @ C2 )
% 5.31/5.48 = C2 )
% 5.31/5.48 = ( ( C2 = zero_zero_real )
% 5.31/5.48 | ( A = one_one_real ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % mult_cancel_right2
% 5.31/5.48 thf(fact_491_mult__cancel__right2,axiom,
% 5.31/5.48 ! [A: rat,C2: rat] :
% 5.31/5.48 ( ( ( times_times_rat @ A @ C2 )
% 5.31/5.48 = C2 )
% 5.31/5.48 = ( ( C2 = zero_zero_rat )
% 5.31/5.48 | ( A = one_one_rat ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % mult_cancel_right2
% 5.31/5.48 thf(fact_492_mult__cancel__right2,axiom,
% 5.31/5.48 ! [A: int,C2: int] :
% 5.31/5.48 ( ( ( times_times_int @ A @ C2 )
% 5.31/5.48 = C2 )
% 5.31/5.48 = ( ( C2 = zero_zero_int )
% 5.31/5.48 | ( A = one_one_int ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % mult_cancel_right2
% 5.31/5.48 thf(fact_493_zero__less__Suc,axiom,
% 5.31/5.48 ! [N: nat] : ( ord_less_nat @ zero_zero_nat @ ( suc @ N ) ) ).
% 5.31/5.48
% 5.31/5.48 % zero_less_Suc
% 5.31/5.48 thf(fact_494_less__Suc0,axiom,
% 5.31/5.48 ! [N: nat] :
% 5.31/5.48 ( ( ord_less_nat @ N @ ( suc @ zero_zero_nat ) )
% 5.31/5.48 = ( N = zero_zero_nat ) ) ).
% 5.31/5.48
% 5.31/5.48 % less_Suc0
% 5.31/5.48 thf(fact_495_nat__mult__less__cancel__disj,axiom,
% 5.31/5.48 ! [K2: nat,M2: nat,N: nat] :
% 5.31/5.48 ( ( ord_less_nat @ ( times_times_nat @ K2 @ M2 ) @ ( times_times_nat @ K2 @ N ) )
% 5.31/5.48 = ( ( ord_less_nat @ zero_zero_nat @ K2 )
% 5.31/5.48 & ( ord_less_nat @ M2 @ N ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % nat_mult_less_cancel_disj
% 5.31/5.48 thf(fact_496_mult__less__cancel2,axiom,
% 5.31/5.48 ! [M2: nat,K2: nat,N: nat] :
% 5.31/5.48 ( ( ord_less_nat @ ( times_times_nat @ M2 @ K2 ) @ ( times_times_nat @ N @ K2 ) )
% 5.31/5.48 = ( ( ord_less_nat @ zero_zero_nat @ K2 )
% 5.31/5.48 & ( ord_less_nat @ M2 @ N ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % mult_less_cancel2
% 5.31/5.48 thf(fact_497_nat__0__less__mult__iff,axiom,
% 5.31/5.48 ! [M2: nat,N: nat] :
% 5.31/5.48 ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ M2 @ N ) )
% 5.31/5.48 = ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 5.31/5.48 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % nat_0_less_mult_iff
% 5.31/5.48 thf(fact_498_less__one,axiom,
% 5.31/5.48 ! [N: nat] :
% 5.31/5.48 ( ( ord_less_nat @ N @ one_one_nat )
% 5.31/5.48 = ( N = zero_zero_nat ) ) ).
% 5.31/5.48
% 5.31/5.48 % less_one
% 5.31/5.48 thf(fact_499_nat__mult__le__cancel__disj,axiom,
% 5.31/5.48 ! [K2: nat,M2: nat,N: nat] :
% 5.31/5.48 ( ( ord_less_eq_nat @ ( times_times_nat @ K2 @ M2 ) @ ( times_times_nat @ K2 @ N ) )
% 5.31/5.48 = ( ( ord_less_nat @ zero_zero_nat @ K2 )
% 5.31/5.48 => ( ord_less_eq_nat @ M2 @ N ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % nat_mult_le_cancel_disj
% 5.31/5.48 thf(fact_500_mult__le__cancel2,axiom,
% 5.31/5.48 ! [M2: nat,K2: nat,N: nat] :
% 5.31/5.48 ( ( ord_less_eq_nat @ ( times_times_nat @ M2 @ K2 ) @ ( times_times_nat @ N @ K2 ) )
% 5.31/5.48 = ( ( ord_less_nat @ zero_zero_nat @ K2 )
% 5.31/5.48 => ( ord_less_eq_nat @ M2 @ N ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % mult_le_cancel2
% 5.31/5.48 thf(fact_501_set__vebt__set__vebt_H__valid,axiom,
% 5.31/5.48 ! [T: vEBT_VEBT,N: nat] :
% 5.31/5.48 ( ( vEBT_invar_vebt @ T @ N )
% 5.31/5.48 => ( ( vEBT_set_vebt @ T )
% 5.31/5.48 = ( vEBT_VEBT_set_vebt @ T ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % set_vebt_set_vebt'_valid
% 5.31/5.48 thf(fact_502_linorder__neqE__linordered__idom,axiom,
% 5.31/5.48 ! [X: real,Y: real] :
% 5.31/5.48 ( ( X != Y )
% 5.31/5.48 => ( ~ ( ord_less_real @ X @ Y )
% 5.31/5.48 => ( ord_less_real @ Y @ X ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % linorder_neqE_linordered_idom
% 5.31/5.48 thf(fact_503_linorder__neqE__linordered__idom,axiom,
% 5.31/5.48 ! [X: rat,Y: rat] :
% 5.31/5.48 ( ( X != Y )
% 5.31/5.48 => ( ~ ( ord_less_rat @ X @ Y )
% 5.31/5.48 => ( ord_less_rat @ Y @ X ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % linorder_neqE_linordered_idom
% 5.31/5.48 thf(fact_504_linorder__neqE__linordered__idom,axiom,
% 5.31/5.48 ! [X: int,Y: int] :
% 5.31/5.48 ( ( X != Y )
% 5.31/5.48 => ( ~ ( ord_less_int @ X @ Y )
% 5.31/5.48 => ( ord_less_int @ Y @ X ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % linorder_neqE_linordered_idom
% 5.31/5.48 thf(fact_505_lt__ex,axiom,
% 5.31/5.48 ! [X: real] :
% 5.31/5.48 ? [Y3: real] : ( ord_less_real @ Y3 @ X ) ).
% 5.31/5.48
% 5.31/5.48 % lt_ex
% 5.31/5.48 thf(fact_506_lt__ex,axiom,
% 5.31/5.48 ! [X: rat] :
% 5.31/5.48 ? [Y3: rat] : ( ord_less_rat @ Y3 @ X ) ).
% 5.31/5.48
% 5.31/5.48 % lt_ex
% 5.31/5.48 thf(fact_507_lt__ex,axiom,
% 5.31/5.48 ! [X: int] :
% 5.31/5.48 ? [Y3: int] : ( ord_less_int @ Y3 @ X ) ).
% 5.31/5.48
% 5.31/5.48 % lt_ex
% 5.31/5.48 thf(fact_508_gt__ex,axiom,
% 5.31/5.48 ! [X: real] :
% 5.31/5.48 ? [X_12: real] : ( ord_less_real @ X @ X_12 ) ).
% 5.31/5.48
% 5.31/5.48 % gt_ex
% 5.31/5.48 thf(fact_509_gt__ex,axiom,
% 5.31/5.48 ! [X: rat] :
% 5.31/5.48 ? [X_12: rat] : ( ord_less_rat @ X @ X_12 ) ).
% 5.31/5.48
% 5.31/5.48 % gt_ex
% 5.31/5.48 thf(fact_510_gt__ex,axiom,
% 5.31/5.48 ! [X: nat] :
% 5.31/5.48 ? [X_12: nat] : ( ord_less_nat @ X @ X_12 ) ).
% 5.31/5.48
% 5.31/5.48 % gt_ex
% 5.31/5.48 thf(fact_511_gt__ex,axiom,
% 5.31/5.48 ! [X: int] :
% 5.31/5.48 ? [X_12: int] : ( ord_less_int @ X @ X_12 ) ).
% 5.31/5.48
% 5.31/5.48 % gt_ex
% 5.31/5.48 thf(fact_512_dense,axiom,
% 5.31/5.48 ! [X: real,Y: real] :
% 5.31/5.48 ( ( ord_less_real @ X @ Y )
% 5.31/5.48 => ? [Z: real] :
% 5.31/5.48 ( ( ord_less_real @ X @ Z )
% 5.31/5.48 & ( ord_less_real @ Z @ Y ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % dense
% 5.31/5.48 thf(fact_513_dense,axiom,
% 5.31/5.48 ! [X: rat,Y: rat] :
% 5.31/5.48 ( ( ord_less_rat @ X @ Y )
% 5.31/5.48 => ? [Z: rat] :
% 5.31/5.48 ( ( ord_less_rat @ X @ Z )
% 5.31/5.48 & ( ord_less_rat @ Z @ Y ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % dense
% 5.31/5.48 thf(fact_514_less__imp__neq,axiom,
% 5.31/5.48 ! [X: real,Y: real] :
% 5.31/5.48 ( ( ord_less_real @ X @ Y )
% 5.31/5.48 => ( X != Y ) ) ).
% 5.31/5.48
% 5.31/5.48 % less_imp_neq
% 5.31/5.48 thf(fact_515_less__imp__neq,axiom,
% 5.31/5.48 ! [X: rat,Y: rat] :
% 5.31/5.48 ( ( ord_less_rat @ X @ Y )
% 5.31/5.48 => ( X != Y ) ) ).
% 5.31/5.48
% 5.31/5.48 % less_imp_neq
% 5.31/5.48 thf(fact_516_less__imp__neq,axiom,
% 5.31/5.48 ! [X: num,Y: num] :
% 5.31/5.48 ( ( ord_less_num @ X @ Y )
% 5.31/5.48 => ( X != Y ) ) ).
% 5.31/5.48
% 5.31/5.48 % less_imp_neq
% 5.31/5.48 thf(fact_517_less__imp__neq,axiom,
% 5.31/5.48 ! [X: nat,Y: nat] :
% 5.31/5.48 ( ( ord_less_nat @ X @ Y )
% 5.31/5.48 => ( X != Y ) ) ).
% 5.31/5.48
% 5.31/5.48 % less_imp_neq
% 5.31/5.48 thf(fact_518_less__imp__neq,axiom,
% 5.31/5.48 ! [X: int,Y: int] :
% 5.31/5.48 ( ( ord_less_int @ X @ Y )
% 5.31/5.48 => ( X != Y ) ) ).
% 5.31/5.48
% 5.31/5.48 % less_imp_neq
% 5.31/5.48 thf(fact_519_order_Oasym,axiom,
% 5.31/5.48 ! [A: real,B: real] :
% 5.31/5.48 ( ( ord_less_real @ A @ B )
% 5.31/5.48 => ~ ( ord_less_real @ B @ A ) ) ).
% 5.31/5.48
% 5.31/5.48 % order.asym
% 5.31/5.48 thf(fact_520_order_Oasym,axiom,
% 5.31/5.48 ! [A: rat,B: rat] :
% 5.31/5.48 ( ( ord_less_rat @ A @ B )
% 5.31/5.48 => ~ ( ord_less_rat @ B @ A ) ) ).
% 5.31/5.48
% 5.31/5.48 % order.asym
% 5.31/5.48 thf(fact_521_order_Oasym,axiom,
% 5.31/5.48 ! [A: num,B: num] :
% 5.31/5.48 ( ( ord_less_num @ A @ B )
% 5.31/5.48 => ~ ( ord_less_num @ B @ A ) ) ).
% 5.31/5.48
% 5.31/5.48 % order.asym
% 5.31/5.48 thf(fact_522_order_Oasym,axiom,
% 5.31/5.48 ! [A: nat,B: nat] :
% 5.31/5.48 ( ( ord_less_nat @ A @ B )
% 5.31/5.48 => ~ ( ord_less_nat @ B @ A ) ) ).
% 5.31/5.48
% 5.31/5.48 % order.asym
% 5.31/5.48 thf(fact_523_order_Oasym,axiom,
% 5.31/5.48 ! [A: int,B: int] :
% 5.31/5.48 ( ( ord_less_int @ A @ B )
% 5.31/5.48 => ~ ( ord_less_int @ B @ A ) ) ).
% 5.31/5.48
% 5.31/5.48 % order.asym
% 5.31/5.48 thf(fact_524_ord__eq__less__trans,axiom,
% 5.31/5.48 ! [A: real,B: real,C2: real] :
% 5.31/5.48 ( ( A = B )
% 5.31/5.48 => ( ( ord_less_real @ B @ C2 )
% 5.31/5.48 => ( ord_less_real @ A @ C2 ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % ord_eq_less_trans
% 5.31/5.48 thf(fact_525_ord__eq__less__trans,axiom,
% 5.31/5.48 ! [A: rat,B: rat,C2: rat] :
% 5.31/5.48 ( ( A = B )
% 5.31/5.48 => ( ( ord_less_rat @ B @ C2 )
% 5.31/5.48 => ( ord_less_rat @ A @ C2 ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % ord_eq_less_trans
% 5.31/5.48 thf(fact_526_ord__eq__less__trans,axiom,
% 5.31/5.48 ! [A: num,B: num,C2: num] :
% 5.31/5.48 ( ( A = B )
% 5.31/5.48 => ( ( ord_less_num @ B @ C2 )
% 5.31/5.48 => ( ord_less_num @ A @ C2 ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % ord_eq_less_trans
% 5.31/5.48 thf(fact_527_ord__eq__less__trans,axiom,
% 5.31/5.48 ! [A: nat,B: nat,C2: nat] :
% 5.31/5.48 ( ( A = B )
% 5.31/5.48 => ( ( ord_less_nat @ B @ C2 )
% 5.31/5.48 => ( ord_less_nat @ A @ C2 ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % ord_eq_less_trans
% 5.31/5.48 thf(fact_528_ord__eq__less__trans,axiom,
% 5.31/5.48 ! [A: int,B: int,C2: int] :
% 5.31/5.48 ( ( A = B )
% 5.31/5.48 => ( ( ord_less_int @ B @ C2 )
% 5.31/5.48 => ( ord_less_int @ A @ C2 ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % ord_eq_less_trans
% 5.31/5.48 thf(fact_529_ord__less__eq__trans,axiom,
% 5.31/5.48 ! [A: real,B: real,C2: real] :
% 5.31/5.48 ( ( ord_less_real @ A @ B )
% 5.31/5.48 => ( ( B = C2 )
% 5.31/5.48 => ( ord_less_real @ A @ C2 ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % ord_less_eq_trans
% 5.31/5.48 thf(fact_530_ord__less__eq__trans,axiom,
% 5.31/5.48 ! [A: rat,B: rat,C2: rat] :
% 5.31/5.48 ( ( ord_less_rat @ A @ B )
% 5.31/5.48 => ( ( B = C2 )
% 5.31/5.48 => ( ord_less_rat @ A @ C2 ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % ord_less_eq_trans
% 5.31/5.48 thf(fact_531_ord__less__eq__trans,axiom,
% 5.31/5.48 ! [A: num,B: num,C2: num] :
% 5.31/5.48 ( ( ord_less_num @ A @ B )
% 5.31/5.48 => ( ( B = C2 )
% 5.31/5.48 => ( ord_less_num @ A @ C2 ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % ord_less_eq_trans
% 5.31/5.48 thf(fact_532_ord__less__eq__trans,axiom,
% 5.31/5.48 ! [A: nat,B: nat,C2: nat] :
% 5.31/5.48 ( ( ord_less_nat @ A @ B )
% 5.31/5.48 => ( ( B = C2 )
% 5.31/5.48 => ( ord_less_nat @ A @ C2 ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % ord_less_eq_trans
% 5.31/5.48 thf(fact_533_ord__less__eq__trans,axiom,
% 5.31/5.48 ! [A: int,B: int,C2: int] :
% 5.31/5.48 ( ( ord_less_int @ A @ B )
% 5.31/5.48 => ( ( B = C2 )
% 5.31/5.48 => ( ord_less_int @ A @ C2 ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % ord_less_eq_trans
% 5.31/5.48 thf(fact_534_less__induct,axiom,
% 5.31/5.48 ! [P2: nat > $o,A: nat] :
% 5.31/5.48 ( ! [X3: nat] :
% 5.31/5.48 ( ! [Y6: nat] :
% 5.31/5.48 ( ( ord_less_nat @ Y6 @ X3 )
% 5.31/5.48 => ( P2 @ Y6 ) )
% 5.31/5.48 => ( P2 @ X3 ) )
% 5.31/5.48 => ( P2 @ A ) ) ).
% 5.31/5.48
% 5.31/5.48 % less_induct
% 5.31/5.48 thf(fact_535_antisym__conv3,axiom,
% 5.31/5.48 ! [Y: real,X: real] :
% 5.31/5.48 ( ~ ( ord_less_real @ Y @ X )
% 5.31/5.48 => ( ( ~ ( ord_less_real @ X @ Y ) )
% 5.31/5.48 = ( X = Y ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % antisym_conv3
% 5.31/5.48 thf(fact_536_antisym__conv3,axiom,
% 5.31/5.48 ! [Y: rat,X: rat] :
% 5.31/5.48 ( ~ ( ord_less_rat @ Y @ X )
% 5.31/5.48 => ( ( ~ ( ord_less_rat @ X @ Y ) )
% 5.31/5.48 = ( X = Y ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % antisym_conv3
% 5.31/5.48 thf(fact_537_antisym__conv3,axiom,
% 5.31/5.48 ! [Y: num,X: num] :
% 5.31/5.48 ( ~ ( ord_less_num @ Y @ X )
% 5.31/5.48 => ( ( ~ ( ord_less_num @ X @ Y ) )
% 5.31/5.48 = ( X = Y ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % antisym_conv3
% 5.31/5.48 thf(fact_538_antisym__conv3,axiom,
% 5.31/5.48 ! [Y: nat,X: nat] :
% 5.31/5.48 ( ~ ( ord_less_nat @ Y @ X )
% 5.31/5.48 => ( ( ~ ( ord_less_nat @ X @ Y ) )
% 5.31/5.48 = ( X = Y ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % antisym_conv3
% 5.31/5.48 thf(fact_539_antisym__conv3,axiom,
% 5.31/5.48 ! [Y: int,X: int] :
% 5.31/5.48 ( ~ ( ord_less_int @ Y @ X )
% 5.31/5.48 => ( ( ~ ( ord_less_int @ X @ Y ) )
% 5.31/5.48 = ( X = Y ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % antisym_conv3
% 5.31/5.48 thf(fact_540_linorder__cases,axiom,
% 5.31/5.48 ! [X: real,Y: real] :
% 5.31/5.48 ( ~ ( ord_less_real @ X @ Y )
% 5.31/5.48 => ( ( X != Y )
% 5.31/5.48 => ( ord_less_real @ Y @ X ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % linorder_cases
% 5.31/5.48 thf(fact_541_linorder__cases,axiom,
% 5.31/5.48 ! [X: rat,Y: rat] :
% 5.31/5.48 ( ~ ( ord_less_rat @ X @ Y )
% 5.31/5.48 => ( ( X != Y )
% 5.31/5.48 => ( ord_less_rat @ Y @ X ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % linorder_cases
% 5.31/5.48 thf(fact_542_linorder__cases,axiom,
% 5.31/5.48 ! [X: num,Y: num] :
% 5.31/5.48 ( ~ ( ord_less_num @ X @ Y )
% 5.31/5.48 => ( ( X != Y )
% 5.31/5.48 => ( ord_less_num @ Y @ X ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % linorder_cases
% 5.31/5.48 thf(fact_543_linorder__cases,axiom,
% 5.31/5.48 ! [X: nat,Y: nat] :
% 5.31/5.48 ( ~ ( ord_less_nat @ X @ Y )
% 5.31/5.48 => ( ( X != Y )
% 5.31/5.48 => ( ord_less_nat @ Y @ X ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % linorder_cases
% 5.31/5.48 thf(fact_544_linorder__cases,axiom,
% 5.31/5.48 ! [X: int,Y: int] :
% 5.31/5.48 ( ~ ( ord_less_int @ X @ Y )
% 5.31/5.48 => ( ( X != Y )
% 5.31/5.48 => ( ord_less_int @ Y @ X ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % linorder_cases
% 5.31/5.48 thf(fact_545_dual__order_Oasym,axiom,
% 5.31/5.48 ! [B: real,A: real] :
% 5.31/5.48 ( ( ord_less_real @ B @ A )
% 5.31/5.48 => ~ ( ord_less_real @ A @ B ) ) ).
% 5.31/5.48
% 5.31/5.48 % dual_order.asym
% 5.31/5.48 thf(fact_546_dual__order_Oasym,axiom,
% 5.31/5.48 ! [B: rat,A: rat] :
% 5.31/5.48 ( ( ord_less_rat @ B @ A )
% 5.31/5.48 => ~ ( ord_less_rat @ A @ B ) ) ).
% 5.31/5.48
% 5.31/5.48 % dual_order.asym
% 5.31/5.48 thf(fact_547_dual__order_Oasym,axiom,
% 5.31/5.48 ! [B: num,A: num] :
% 5.31/5.48 ( ( ord_less_num @ B @ A )
% 5.31/5.48 => ~ ( ord_less_num @ A @ B ) ) ).
% 5.31/5.48
% 5.31/5.48 % dual_order.asym
% 5.31/5.48 thf(fact_548_dual__order_Oasym,axiom,
% 5.31/5.48 ! [B: nat,A: nat] :
% 5.31/5.48 ( ( ord_less_nat @ B @ A )
% 5.31/5.48 => ~ ( ord_less_nat @ A @ B ) ) ).
% 5.31/5.48
% 5.31/5.48 % dual_order.asym
% 5.31/5.48 thf(fact_549_dual__order_Oasym,axiom,
% 5.31/5.48 ! [B: int,A: int] :
% 5.31/5.48 ( ( ord_less_int @ B @ A )
% 5.31/5.48 => ~ ( ord_less_int @ A @ B ) ) ).
% 5.31/5.48
% 5.31/5.48 % dual_order.asym
% 5.31/5.48 thf(fact_550_dual__order_Oirrefl,axiom,
% 5.31/5.48 ! [A: real] :
% 5.31/5.48 ~ ( ord_less_real @ A @ A ) ).
% 5.31/5.48
% 5.31/5.48 % dual_order.irrefl
% 5.31/5.48 thf(fact_551_dual__order_Oirrefl,axiom,
% 5.31/5.48 ! [A: rat] :
% 5.31/5.48 ~ ( ord_less_rat @ A @ A ) ).
% 5.31/5.48
% 5.31/5.48 % dual_order.irrefl
% 5.31/5.48 thf(fact_552_dual__order_Oirrefl,axiom,
% 5.31/5.48 ! [A: num] :
% 5.31/5.48 ~ ( ord_less_num @ A @ A ) ).
% 5.31/5.48
% 5.31/5.48 % dual_order.irrefl
% 5.31/5.48 thf(fact_553_dual__order_Oirrefl,axiom,
% 5.31/5.48 ! [A: nat] :
% 5.31/5.48 ~ ( ord_less_nat @ A @ A ) ).
% 5.31/5.48
% 5.31/5.48 % dual_order.irrefl
% 5.31/5.48 thf(fact_554_dual__order_Oirrefl,axiom,
% 5.31/5.48 ! [A: int] :
% 5.31/5.48 ~ ( ord_less_int @ A @ A ) ).
% 5.31/5.48
% 5.31/5.48 % dual_order.irrefl
% 5.31/5.48 thf(fact_555_exists__least__iff,axiom,
% 5.31/5.48 ( ( ^ [P3: nat > $o] :
% 5.31/5.48 ? [X6: nat] : ( P3 @ X6 ) )
% 5.31/5.48 = ( ^ [P4: nat > $o] :
% 5.31/5.48 ? [N4: nat] :
% 5.31/5.48 ( ( P4 @ N4 )
% 5.31/5.48 & ! [M6: nat] :
% 5.31/5.48 ( ( ord_less_nat @ M6 @ N4 )
% 5.31/5.48 => ~ ( P4 @ M6 ) ) ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % exists_least_iff
% 5.31/5.48 thf(fact_556_linorder__less__wlog,axiom,
% 5.31/5.48 ! [P2: real > real > $o,A: real,B: real] :
% 5.31/5.48 ( ! [A3: real,B3: real] :
% 5.31/5.48 ( ( ord_less_real @ A3 @ B3 )
% 5.31/5.48 => ( P2 @ A3 @ B3 ) )
% 5.31/5.48 => ( ! [A3: real] : ( P2 @ A3 @ A3 )
% 5.31/5.48 => ( ! [A3: real,B3: real] :
% 5.31/5.48 ( ( P2 @ B3 @ A3 )
% 5.31/5.48 => ( P2 @ A3 @ B3 ) )
% 5.31/5.48 => ( P2 @ A @ B ) ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % linorder_less_wlog
% 5.31/5.48 thf(fact_557_linorder__less__wlog,axiom,
% 5.31/5.48 ! [P2: rat > rat > $o,A: rat,B: rat] :
% 5.31/5.48 ( ! [A3: rat,B3: rat] :
% 5.31/5.48 ( ( ord_less_rat @ A3 @ B3 )
% 5.31/5.48 => ( P2 @ A3 @ B3 ) )
% 5.31/5.48 => ( ! [A3: rat] : ( P2 @ A3 @ A3 )
% 5.31/5.48 => ( ! [A3: rat,B3: rat] :
% 5.31/5.48 ( ( P2 @ B3 @ A3 )
% 5.31/5.48 => ( P2 @ A3 @ B3 ) )
% 5.31/5.48 => ( P2 @ A @ B ) ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % linorder_less_wlog
% 5.31/5.48 thf(fact_558_linorder__less__wlog,axiom,
% 5.31/5.48 ! [P2: num > num > $o,A: num,B: num] :
% 5.31/5.48 ( ! [A3: num,B3: num] :
% 5.31/5.48 ( ( ord_less_num @ A3 @ B3 )
% 5.31/5.48 => ( P2 @ A3 @ B3 ) )
% 5.31/5.48 => ( ! [A3: num] : ( P2 @ A3 @ A3 )
% 5.31/5.48 => ( ! [A3: num,B3: num] :
% 5.31/5.48 ( ( P2 @ B3 @ A3 )
% 5.31/5.48 => ( P2 @ A3 @ B3 ) )
% 5.31/5.48 => ( P2 @ A @ B ) ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % linorder_less_wlog
% 5.31/5.48 thf(fact_559_linorder__less__wlog,axiom,
% 5.31/5.48 ! [P2: nat > nat > $o,A: nat,B: nat] :
% 5.31/5.48 ( ! [A3: nat,B3: nat] :
% 5.31/5.48 ( ( ord_less_nat @ A3 @ B3 )
% 5.31/5.48 => ( P2 @ A3 @ B3 ) )
% 5.31/5.48 => ( ! [A3: nat] : ( P2 @ A3 @ A3 )
% 5.31/5.48 => ( ! [A3: nat,B3: nat] :
% 5.31/5.48 ( ( P2 @ B3 @ A3 )
% 5.31/5.48 => ( P2 @ A3 @ B3 ) )
% 5.31/5.48 => ( P2 @ A @ B ) ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % linorder_less_wlog
% 5.31/5.48 thf(fact_560_linorder__less__wlog,axiom,
% 5.31/5.48 ! [P2: int > int > $o,A: int,B: int] :
% 5.31/5.48 ( ! [A3: int,B3: int] :
% 5.31/5.48 ( ( ord_less_int @ A3 @ B3 )
% 5.31/5.48 => ( P2 @ A3 @ B3 ) )
% 5.31/5.48 => ( ! [A3: int] : ( P2 @ A3 @ A3 )
% 5.31/5.48 => ( ! [A3: int,B3: int] :
% 5.31/5.48 ( ( P2 @ B3 @ A3 )
% 5.31/5.48 => ( P2 @ A3 @ B3 ) )
% 5.31/5.48 => ( P2 @ A @ B ) ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % linorder_less_wlog
% 5.31/5.48 thf(fact_561_order_Ostrict__trans,axiom,
% 5.31/5.48 ! [A: real,B: real,C2: real] :
% 5.31/5.48 ( ( ord_less_real @ A @ B )
% 5.31/5.48 => ( ( ord_less_real @ B @ C2 )
% 5.31/5.48 => ( ord_less_real @ A @ C2 ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % order.strict_trans
% 5.31/5.48 thf(fact_562_order_Ostrict__trans,axiom,
% 5.31/5.48 ! [A: rat,B: rat,C2: rat] :
% 5.31/5.48 ( ( ord_less_rat @ A @ B )
% 5.31/5.48 => ( ( ord_less_rat @ B @ C2 )
% 5.31/5.48 => ( ord_less_rat @ A @ C2 ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % order.strict_trans
% 5.31/5.48 thf(fact_563_order_Ostrict__trans,axiom,
% 5.31/5.48 ! [A: num,B: num,C2: num] :
% 5.31/5.48 ( ( ord_less_num @ A @ B )
% 5.31/5.48 => ( ( ord_less_num @ B @ C2 )
% 5.31/5.48 => ( ord_less_num @ A @ C2 ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % order.strict_trans
% 5.31/5.48 thf(fact_564_order_Ostrict__trans,axiom,
% 5.31/5.48 ! [A: nat,B: nat,C2: nat] :
% 5.31/5.48 ( ( ord_less_nat @ A @ B )
% 5.31/5.48 => ( ( ord_less_nat @ B @ C2 )
% 5.31/5.48 => ( ord_less_nat @ A @ C2 ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % order.strict_trans
% 5.31/5.48 thf(fact_565_order_Ostrict__trans,axiom,
% 5.31/5.48 ! [A: int,B: int,C2: int] :
% 5.31/5.48 ( ( ord_less_int @ A @ B )
% 5.31/5.48 => ( ( ord_less_int @ B @ C2 )
% 5.31/5.48 => ( ord_less_int @ A @ C2 ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % order.strict_trans
% 5.31/5.48 thf(fact_566_not__less__iff__gr__or__eq,axiom,
% 5.31/5.48 ! [X: real,Y: real] :
% 5.31/5.48 ( ( ~ ( ord_less_real @ X @ Y ) )
% 5.31/5.48 = ( ( ord_less_real @ Y @ X )
% 5.31/5.48 | ( X = Y ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % not_less_iff_gr_or_eq
% 5.31/5.48 thf(fact_567_not__less__iff__gr__or__eq,axiom,
% 5.31/5.48 ! [X: rat,Y: rat] :
% 5.31/5.48 ( ( ~ ( ord_less_rat @ X @ Y ) )
% 5.31/5.48 = ( ( ord_less_rat @ Y @ X )
% 5.31/5.48 | ( X = Y ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % not_less_iff_gr_or_eq
% 5.31/5.48 thf(fact_568_not__less__iff__gr__or__eq,axiom,
% 5.31/5.48 ! [X: num,Y: num] :
% 5.31/5.48 ( ( ~ ( ord_less_num @ X @ Y ) )
% 5.31/5.48 = ( ( ord_less_num @ Y @ X )
% 5.31/5.48 | ( X = Y ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % not_less_iff_gr_or_eq
% 5.31/5.48 thf(fact_569_not__less__iff__gr__or__eq,axiom,
% 5.31/5.48 ! [X: nat,Y: nat] :
% 5.31/5.48 ( ( ~ ( ord_less_nat @ X @ Y ) )
% 5.31/5.48 = ( ( ord_less_nat @ Y @ X )
% 5.31/5.48 | ( X = Y ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % not_less_iff_gr_or_eq
% 5.31/5.48 thf(fact_570_not__less__iff__gr__or__eq,axiom,
% 5.31/5.48 ! [X: int,Y: int] :
% 5.31/5.48 ( ( ~ ( ord_less_int @ X @ Y ) )
% 5.31/5.48 = ( ( ord_less_int @ Y @ X )
% 5.31/5.48 | ( X = Y ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % not_less_iff_gr_or_eq
% 5.31/5.48 thf(fact_571_dual__order_Ostrict__trans,axiom,
% 5.31/5.48 ! [B: real,A: real,C2: real] :
% 5.31/5.48 ( ( ord_less_real @ B @ A )
% 5.31/5.48 => ( ( ord_less_real @ C2 @ B )
% 5.31/5.48 => ( ord_less_real @ C2 @ A ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % dual_order.strict_trans
% 5.31/5.48 thf(fact_572_dual__order_Ostrict__trans,axiom,
% 5.31/5.48 ! [B: rat,A: rat,C2: rat] :
% 5.31/5.48 ( ( ord_less_rat @ B @ A )
% 5.31/5.48 => ( ( ord_less_rat @ C2 @ B )
% 5.31/5.48 => ( ord_less_rat @ C2 @ A ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % dual_order.strict_trans
% 5.31/5.48 thf(fact_573_dual__order_Ostrict__trans,axiom,
% 5.31/5.48 ! [B: num,A: num,C2: num] :
% 5.31/5.48 ( ( ord_less_num @ B @ A )
% 5.31/5.48 => ( ( ord_less_num @ C2 @ B )
% 5.31/5.48 => ( ord_less_num @ C2 @ A ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % dual_order.strict_trans
% 5.31/5.48 thf(fact_574_dual__order_Ostrict__trans,axiom,
% 5.31/5.48 ! [B: nat,A: nat,C2: nat] :
% 5.31/5.48 ( ( ord_less_nat @ B @ A )
% 5.31/5.48 => ( ( ord_less_nat @ C2 @ B )
% 5.31/5.48 => ( ord_less_nat @ C2 @ A ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % dual_order.strict_trans
% 5.31/5.48 thf(fact_575_dual__order_Ostrict__trans,axiom,
% 5.31/5.48 ! [B: int,A: int,C2: int] :
% 5.31/5.48 ( ( ord_less_int @ B @ A )
% 5.31/5.48 => ( ( ord_less_int @ C2 @ B )
% 5.31/5.48 => ( ord_less_int @ C2 @ A ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % dual_order.strict_trans
% 5.31/5.48 thf(fact_576_order_Ostrict__implies__not__eq,axiom,
% 5.31/5.48 ! [A: real,B: real] :
% 5.31/5.48 ( ( ord_less_real @ A @ B )
% 5.31/5.48 => ( A != B ) ) ).
% 5.31/5.48
% 5.31/5.48 % order.strict_implies_not_eq
% 5.31/5.48 thf(fact_577_order_Ostrict__implies__not__eq,axiom,
% 5.31/5.48 ! [A: rat,B: rat] :
% 5.31/5.48 ( ( ord_less_rat @ A @ B )
% 5.31/5.48 => ( A != B ) ) ).
% 5.31/5.48
% 5.31/5.48 % order.strict_implies_not_eq
% 5.31/5.48 thf(fact_578_order_Ostrict__implies__not__eq,axiom,
% 5.31/5.48 ! [A: num,B: num] :
% 5.31/5.48 ( ( ord_less_num @ A @ B )
% 5.31/5.48 => ( A != B ) ) ).
% 5.31/5.48
% 5.31/5.48 % order.strict_implies_not_eq
% 5.31/5.48 thf(fact_579_order_Ostrict__implies__not__eq,axiom,
% 5.31/5.48 ! [A: nat,B: nat] :
% 5.31/5.48 ( ( ord_less_nat @ A @ B )
% 5.31/5.48 => ( A != B ) ) ).
% 5.31/5.48
% 5.31/5.48 % order.strict_implies_not_eq
% 5.31/5.48 thf(fact_580_order_Ostrict__implies__not__eq,axiom,
% 5.31/5.48 ! [A: int,B: int] :
% 5.31/5.48 ( ( ord_less_int @ A @ B )
% 5.31/5.48 => ( A != B ) ) ).
% 5.31/5.48
% 5.31/5.48 % order.strict_implies_not_eq
% 5.31/5.48 thf(fact_581_dual__order_Ostrict__implies__not__eq,axiom,
% 5.31/5.48 ! [B: real,A: real] :
% 5.31/5.48 ( ( ord_less_real @ B @ A )
% 5.31/5.48 => ( A != B ) ) ).
% 5.31/5.48
% 5.31/5.48 % dual_order.strict_implies_not_eq
% 5.31/5.48 thf(fact_582_dual__order_Ostrict__implies__not__eq,axiom,
% 5.31/5.48 ! [B: rat,A: rat] :
% 5.31/5.48 ( ( ord_less_rat @ B @ A )
% 5.31/5.48 => ( A != B ) ) ).
% 5.31/5.48
% 5.31/5.48 % dual_order.strict_implies_not_eq
% 5.31/5.48 thf(fact_583_dual__order_Ostrict__implies__not__eq,axiom,
% 5.31/5.48 ! [B: num,A: num] :
% 5.31/5.48 ( ( ord_less_num @ B @ A )
% 5.31/5.48 => ( A != B ) ) ).
% 5.31/5.48
% 5.31/5.48 % dual_order.strict_implies_not_eq
% 5.31/5.48 thf(fact_584_dual__order_Ostrict__implies__not__eq,axiom,
% 5.31/5.48 ! [B: nat,A: nat] :
% 5.31/5.48 ( ( ord_less_nat @ B @ A )
% 5.31/5.48 => ( A != B ) ) ).
% 5.31/5.48
% 5.31/5.48 % dual_order.strict_implies_not_eq
% 5.31/5.48 thf(fact_585_dual__order_Ostrict__implies__not__eq,axiom,
% 5.31/5.48 ! [B: int,A: int] :
% 5.31/5.48 ( ( ord_less_int @ B @ A )
% 5.31/5.48 => ( A != B ) ) ).
% 5.31/5.48
% 5.31/5.48 % dual_order.strict_implies_not_eq
% 5.31/5.48 thf(fact_586_nat__neq__iff,axiom,
% 5.31/5.48 ! [M2: nat,N: nat] :
% 5.31/5.48 ( ( M2 != N )
% 5.31/5.48 = ( ( ord_less_nat @ M2 @ N )
% 5.31/5.48 | ( ord_less_nat @ N @ M2 ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % nat_neq_iff
% 5.31/5.48 thf(fact_587_less__not__refl,axiom,
% 5.31/5.48 ! [N: nat] :
% 5.31/5.48 ~ ( ord_less_nat @ N @ N ) ).
% 5.31/5.48
% 5.31/5.48 % less_not_refl
% 5.31/5.48 thf(fact_588_less__not__refl2,axiom,
% 5.31/5.48 ! [N: nat,M2: nat] :
% 5.31/5.48 ( ( ord_less_nat @ N @ M2 )
% 5.31/5.48 => ( M2 != N ) ) ).
% 5.31/5.48
% 5.31/5.48 % less_not_refl2
% 5.31/5.48 thf(fact_589_less__not__refl3,axiom,
% 5.31/5.48 ! [S2: nat,T: nat] :
% 5.31/5.48 ( ( ord_less_nat @ S2 @ T )
% 5.31/5.48 => ( S2 != T ) ) ).
% 5.31/5.48
% 5.31/5.48 % less_not_refl3
% 5.31/5.48 thf(fact_590_less__irrefl__nat,axiom,
% 5.31/5.48 ! [N: nat] :
% 5.31/5.48 ~ ( ord_less_nat @ N @ N ) ).
% 5.31/5.48
% 5.31/5.48 % less_irrefl_nat
% 5.31/5.48 thf(fact_591_nat__less__induct,axiom,
% 5.31/5.48 ! [P2: nat > $o,N: nat] :
% 5.31/5.48 ( ! [N3: nat] :
% 5.31/5.48 ( ! [M3: nat] :
% 5.31/5.48 ( ( ord_less_nat @ M3 @ N3 )
% 5.31/5.48 => ( P2 @ M3 ) )
% 5.31/5.48 => ( P2 @ N3 ) )
% 5.31/5.48 => ( P2 @ N ) ) ).
% 5.31/5.48
% 5.31/5.48 % nat_less_induct
% 5.31/5.48 thf(fact_592_infinite__descent,axiom,
% 5.31/5.48 ! [P2: nat > $o,N: nat] :
% 5.31/5.48 ( ! [N3: nat] :
% 5.31/5.48 ( ~ ( P2 @ N3 )
% 5.31/5.48 => ? [M3: nat] :
% 5.31/5.48 ( ( ord_less_nat @ M3 @ N3 )
% 5.31/5.48 & ~ ( P2 @ M3 ) ) )
% 5.31/5.48 => ( P2 @ N ) ) ).
% 5.31/5.48
% 5.31/5.48 % infinite_descent
% 5.31/5.48 thf(fact_593_linorder__neqE__nat,axiom,
% 5.31/5.48 ! [X: nat,Y: nat] :
% 5.31/5.48 ( ( X != Y )
% 5.31/5.48 => ( ~ ( ord_less_nat @ X @ Y )
% 5.31/5.48 => ( ord_less_nat @ Y @ X ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % linorder_neqE_nat
% 5.31/5.48 thf(fact_594_linorder__neqE,axiom,
% 5.31/5.48 ! [X: real,Y: real] :
% 5.31/5.48 ( ( X != Y )
% 5.31/5.48 => ( ~ ( ord_less_real @ X @ Y )
% 5.31/5.48 => ( ord_less_real @ Y @ X ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % linorder_neqE
% 5.31/5.48 thf(fact_595_linorder__neqE,axiom,
% 5.31/5.48 ! [X: rat,Y: rat] :
% 5.31/5.48 ( ( X != Y )
% 5.31/5.48 => ( ~ ( ord_less_rat @ X @ Y )
% 5.31/5.48 => ( ord_less_rat @ Y @ X ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % linorder_neqE
% 5.31/5.48 thf(fact_596_linorder__neqE,axiom,
% 5.31/5.48 ! [X: num,Y: num] :
% 5.31/5.48 ( ( X != Y )
% 5.31/5.48 => ( ~ ( ord_less_num @ X @ Y )
% 5.31/5.48 => ( ord_less_num @ Y @ X ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % linorder_neqE
% 5.31/5.48 thf(fact_597_linorder__neqE,axiom,
% 5.31/5.48 ! [X: nat,Y: nat] :
% 5.31/5.48 ( ( X != Y )
% 5.31/5.48 => ( ~ ( ord_less_nat @ X @ Y )
% 5.31/5.48 => ( ord_less_nat @ Y @ X ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % linorder_neqE
% 5.31/5.48 thf(fact_598_linorder__neqE,axiom,
% 5.31/5.48 ! [X: int,Y: int] :
% 5.31/5.48 ( ( X != Y )
% 5.31/5.48 => ( ~ ( ord_less_int @ X @ Y )
% 5.31/5.48 => ( ord_less_int @ Y @ X ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % linorder_neqE
% 5.31/5.48 thf(fact_599_order__less__asym,axiom,
% 5.31/5.48 ! [X: real,Y: real] :
% 5.31/5.48 ( ( ord_less_real @ X @ Y )
% 5.31/5.48 => ~ ( ord_less_real @ Y @ X ) ) ).
% 5.31/5.48
% 5.31/5.48 % order_less_asym
% 5.31/5.48 thf(fact_600_order__less__asym,axiom,
% 5.31/5.48 ! [X: rat,Y: rat] :
% 5.31/5.48 ( ( ord_less_rat @ X @ Y )
% 5.31/5.48 => ~ ( ord_less_rat @ Y @ X ) ) ).
% 5.31/5.48
% 5.31/5.48 % order_less_asym
% 5.31/5.48 thf(fact_601_order__less__asym,axiom,
% 5.31/5.48 ! [X: num,Y: num] :
% 5.31/5.48 ( ( ord_less_num @ X @ Y )
% 5.31/5.48 => ~ ( ord_less_num @ Y @ X ) ) ).
% 5.31/5.48
% 5.31/5.48 % order_less_asym
% 5.31/5.48 thf(fact_602_order__less__asym,axiom,
% 5.31/5.48 ! [X: nat,Y: nat] :
% 5.31/5.48 ( ( ord_less_nat @ X @ Y )
% 5.31/5.48 => ~ ( ord_less_nat @ Y @ X ) ) ).
% 5.31/5.48
% 5.31/5.48 % order_less_asym
% 5.31/5.48 thf(fact_603_order__less__asym,axiom,
% 5.31/5.48 ! [X: int,Y: int] :
% 5.31/5.48 ( ( ord_less_int @ X @ Y )
% 5.31/5.48 => ~ ( ord_less_int @ Y @ X ) ) ).
% 5.31/5.48
% 5.31/5.48 % order_less_asym
% 5.31/5.48 thf(fact_604_linorder__neq__iff,axiom,
% 5.31/5.48 ! [X: real,Y: real] :
% 5.31/5.48 ( ( X != Y )
% 5.31/5.48 = ( ( ord_less_real @ X @ Y )
% 5.31/5.48 | ( ord_less_real @ Y @ X ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % linorder_neq_iff
% 5.31/5.48 thf(fact_605_linorder__neq__iff,axiom,
% 5.31/5.48 ! [X: rat,Y: rat] :
% 5.31/5.48 ( ( X != Y )
% 5.31/5.48 = ( ( ord_less_rat @ X @ Y )
% 5.31/5.48 | ( ord_less_rat @ Y @ X ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % linorder_neq_iff
% 5.31/5.48 thf(fact_606_linorder__neq__iff,axiom,
% 5.31/5.48 ! [X: num,Y: num] :
% 5.31/5.48 ( ( X != Y )
% 5.31/5.48 = ( ( ord_less_num @ X @ Y )
% 5.31/5.48 | ( ord_less_num @ Y @ X ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % linorder_neq_iff
% 5.31/5.48 thf(fact_607_linorder__neq__iff,axiom,
% 5.31/5.48 ! [X: nat,Y: nat] :
% 5.31/5.48 ( ( X != Y )
% 5.31/5.48 = ( ( ord_less_nat @ X @ Y )
% 5.31/5.48 | ( ord_less_nat @ Y @ X ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % linorder_neq_iff
% 5.31/5.48 thf(fact_608_linorder__neq__iff,axiom,
% 5.31/5.48 ! [X: int,Y: int] :
% 5.31/5.48 ( ( X != Y )
% 5.31/5.48 = ( ( ord_less_int @ X @ Y )
% 5.31/5.48 | ( ord_less_int @ Y @ X ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % linorder_neq_iff
% 5.31/5.48 thf(fact_609_order__less__asym_H,axiom,
% 5.31/5.48 ! [A: real,B: real] :
% 5.31/5.48 ( ( ord_less_real @ A @ B )
% 5.31/5.48 => ~ ( ord_less_real @ B @ A ) ) ).
% 5.31/5.48
% 5.31/5.48 % order_less_asym'
% 5.31/5.48 thf(fact_610_order__less__asym_H,axiom,
% 5.31/5.48 ! [A: rat,B: rat] :
% 5.31/5.48 ( ( ord_less_rat @ A @ B )
% 5.31/5.48 => ~ ( ord_less_rat @ B @ A ) ) ).
% 5.31/5.48
% 5.31/5.48 % order_less_asym'
% 5.31/5.48 thf(fact_611_order__less__asym_H,axiom,
% 5.31/5.48 ! [A: num,B: num] :
% 5.31/5.48 ( ( ord_less_num @ A @ B )
% 5.31/5.48 => ~ ( ord_less_num @ B @ A ) ) ).
% 5.31/5.48
% 5.31/5.48 % order_less_asym'
% 5.31/5.48 thf(fact_612_order__less__asym_H,axiom,
% 5.31/5.48 ! [A: nat,B: nat] :
% 5.31/5.48 ( ( ord_less_nat @ A @ B )
% 5.31/5.48 => ~ ( ord_less_nat @ B @ A ) ) ).
% 5.31/5.48
% 5.31/5.48 % order_less_asym'
% 5.31/5.48 thf(fact_613_order__less__asym_H,axiom,
% 5.31/5.48 ! [A: int,B: int] :
% 5.31/5.48 ( ( ord_less_int @ A @ B )
% 5.31/5.48 => ~ ( ord_less_int @ B @ A ) ) ).
% 5.31/5.48
% 5.31/5.48 % order_less_asym'
% 5.31/5.48 thf(fact_614_order__less__trans,axiom,
% 5.31/5.48 ! [X: real,Y: real,Z3: real] :
% 5.31/5.48 ( ( ord_less_real @ X @ Y )
% 5.31/5.48 => ( ( ord_less_real @ Y @ Z3 )
% 5.31/5.48 => ( ord_less_real @ X @ Z3 ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % order_less_trans
% 5.31/5.48 thf(fact_615_order__less__trans,axiom,
% 5.31/5.48 ! [X: rat,Y: rat,Z3: rat] :
% 5.31/5.48 ( ( ord_less_rat @ X @ Y )
% 5.31/5.48 => ( ( ord_less_rat @ Y @ Z3 )
% 5.31/5.48 => ( ord_less_rat @ X @ Z3 ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % order_less_trans
% 5.31/5.48 thf(fact_616_order__less__trans,axiom,
% 5.31/5.48 ! [X: num,Y: num,Z3: num] :
% 5.31/5.48 ( ( ord_less_num @ X @ Y )
% 5.31/5.48 => ( ( ord_less_num @ Y @ Z3 )
% 5.31/5.48 => ( ord_less_num @ X @ Z3 ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % order_less_trans
% 5.31/5.48 thf(fact_617_order__less__trans,axiom,
% 5.31/5.48 ! [X: nat,Y: nat,Z3: nat] :
% 5.31/5.48 ( ( ord_less_nat @ X @ Y )
% 5.31/5.48 => ( ( ord_less_nat @ Y @ Z3 )
% 5.31/5.48 => ( ord_less_nat @ X @ Z3 ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % order_less_trans
% 5.31/5.48 thf(fact_618_order__less__trans,axiom,
% 5.31/5.48 ! [X: int,Y: int,Z3: int] :
% 5.31/5.48 ( ( ord_less_int @ X @ Y )
% 5.31/5.48 => ( ( ord_less_int @ Y @ Z3 )
% 5.31/5.48 => ( ord_less_int @ X @ Z3 ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % order_less_trans
% 5.31/5.48 thf(fact_619_ord__eq__less__subst,axiom,
% 5.31/5.48 ! [A: real,F2: real > real,B: real,C2: real] :
% 5.31/5.48 ( ( A
% 5.31/5.48 = ( F2 @ B ) )
% 5.31/5.48 => ( ( ord_less_real @ B @ C2 )
% 5.31/5.48 => ( ! [X3: real,Y3: real] :
% 5.31/5.48 ( ( ord_less_real @ X3 @ Y3 )
% 5.31/5.48 => ( ord_less_real @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 5.31/5.48 => ( ord_less_real @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % ord_eq_less_subst
% 5.31/5.48 thf(fact_620_ord__eq__less__subst,axiom,
% 5.31/5.48 ! [A: rat,F2: real > rat,B: real,C2: real] :
% 5.31/5.48 ( ( A
% 5.31/5.48 = ( F2 @ B ) )
% 5.31/5.48 => ( ( ord_less_real @ B @ C2 )
% 5.31/5.48 => ( ! [X3: real,Y3: real] :
% 5.31/5.48 ( ( ord_less_real @ X3 @ Y3 )
% 5.31/5.48 => ( ord_less_rat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 5.31/5.48 => ( ord_less_rat @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % ord_eq_less_subst
% 5.31/5.48 thf(fact_621_ord__eq__less__subst,axiom,
% 5.31/5.48 ! [A: num,F2: real > num,B: real,C2: real] :
% 5.31/5.48 ( ( A
% 5.31/5.48 = ( F2 @ B ) )
% 5.31/5.48 => ( ( ord_less_real @ B @ C2 )
% 5.31/5.48 => ( ! [X3: real,Y3: real] :
% 5.31/5.48 ( ( ord_less_real @ X3 @ Y3 )
% 5.31/5.48 => ( ord_less_num @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 5.31/5.48 => ( ord_less_num @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % ord_eq_less_subst
% 5.31/5.48 thf(fact_622_ord__eq__less__subst,axiom,
% 5.31/5.48 ! [A: nat,F2: real > nat,B: real,C2: real] :
% 5.31/5.48 ( ( A
% 5.31/5.48 = ( F2 @ B ) )
% 5.31/5.48 => ( ( ord_less_real @ B @ C2 )
% 5.31/5.48 => ( ! [X3: real,Y3: real] :
% 5.31/5.48 ( ( ord_less_real @ X3 @ Y3 )
% 5.31/5.48 => ( ord_less_nat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 5.31/5.48 => ( ord_less_nat @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % ord_eq_less_subst
% 5.31/5.48 thf(fact_623_ord__eq__less__subst,axiom,
% 5.31/5.48 ! [A: int,F2: real > int,B: real,C2: real] :
% 5.31/5.48 ( ( A
% 5.31/5.48 = ( F2 @ B ) )
% 5.31/5.48 => ( ( ord_less_real @ B @ C2 )
% 5.31/5.48 => ( ! [X3: real,Y3: real] :
% 5.31/5.48 ( ( ord_less_real @ X3 @ Y3 )
% 5.31/5.48 => ( ord_less_int @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 5.31/5.48 => ( ord_less_int @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % ord_eq_less_subst
% 5.31/5.48 thf(fact_624_ord__eq__less__subst,axiom,
% 5.31/5.48 ! [A: real,F2: rat > real,B: rat,C2: rat] :
% 5.31/5.48 ( ( A
% 5.31/5.48 = ( F2 @ B ) )
% 5.31/5.48 => ( ( ord_less_rat @ B @ C2 )
% 5.31/5.48 => ( ! [X3: rat,Y3: rat] :
% 5.31/5.48 ( ( ord_less_rat @ X3 @ Y3 )
% 5.31/5.48 => ( ord_less_real @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 5.31/5.48 => ( ord_less_real @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % ord_eq_less_subst
% 5.31/5.48 thf(fact_625_ord__eq__less__subst,axiom,
% 5.31/5.48 ! [A: rat,F2: rat > rat,B: rat,C2: rat] :
% 5.31/5.48 ( ( A
% 5.31/5.48 = ( F2 @ B ) )
% 5.31/5.48 => ( ( ord_less_rat @ B @ C2 )
% 5.31/5.48 => ( ! [X3: rat,Y3: rat] :
% 5.31/5.48 ( ( ord_less_rat @ X3 @ Y3 )
% 5.31/5.48 => ( ord_less_rat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 5.31/5.48 => ( ord_less_rat @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % ord_eq_less_subst
% 5.31/5.48 thf(fact_626_ord__eq__less__subst,axiom,
% 5.31/5.48 ! [A: num,F2: rat > num,B: rat,C2: rat] :
% 5.31/5.48 ( ( A
% 5.31/5.48 = ( F2 @ B ) )
% 5.31/5.48 => ( ( ord_less_rat @ B @ C2 )
% 5.31/5.48 => ( ! [X3: rat,Y3: rat] :
% 5.31/5.48 ( ( ord_less_rat @ X3 @ Y3 )
% 5.31/5.48 => ( ord_less_num @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 5.31/5.48 => ( ord_less_num @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % ord_eq_less_subst
% 5.31/5.48 thf(fact_627_ord__eq__less__subst,axiom,
% 5.31/5.48 ! [A: nat,F2: rat > nat,B: rat,C2: rat] :
% 5.31/5.48 ( ( A
% 5.31/5.48 = ( F2 @ B ) )
% 5.31/5.48 => ( ( ord_less_rat @ B @ C2 )
% 5.31/5.48 => ( ! [X3: rat,Y3: rat] :
% 5.31/5.48 ( ( ord_less_rat @ X3 @ Y3 )
% 5.31/5.48 => ( ord_less_nat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 5.31/5.48 => ( ord_less_nat @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % ord_eq_less_subst
% 5.31/5.48 thf(fact_628_ord__eq__less__subst,axiom,
% 5.31/5.48 ! [A: int,F2: rat > int,B: rat,C2: rat] :
% 5.31/5.48 ( ( A
% 5.31/5.48 = ( F2 @ B ) )
% 5.31/5.48 => ( ( ord_less_rat @ B @ C2 )
% 5.31/5.48 => ( ! [X3: rat,Y3: rat] :
% 5.31/5.48 ( ( ord_less_rat @ X3 @ Y3 )
% 5.31/5.48 => ( ord_less_int @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 5.31/5.48 => ( ord_less_int @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % ord_eq_less_subst
% 5.31/5.48 thf(fact_629_ord__less__eq__subst,axiom,
% 5.31/5.48 ! [A: real,B: real,F2: real > real,C2: real] :
% 5.31/5.48 ( ( ord_less_real @ A @ B )
% 5.31/5.48 => ( ( ( F2 @ B )
% 5.31/5.48 = C2 )
% 5.31/5.48 => ( ! [X3: real,Y3: real] :
% 5.31/5.48 ( ( ord_less_real @ X3 @ Y3 )
% 5.31/5.48 => ( ord_less_real @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 5.31/5.48 => ( ord_less_real @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % ord_less_eq_subst
% 5.31/5.48 thf(fact_630_ord__less__eq__subst,axiom,
% 5.31/5.48 ! [A: real,B: real,F2: real > rat,C2: rat] :
% 5.31/5.48 ( ( ord_less_real @ A @ B )
% 5.31/5.48 => ( ( ( F2 @ B )
% 5.31/5.48 = C2 )
% 5.31/5.48 => ( ! [X3: real,Y3: real] :
% 5.31/5.48 ( ( ord_less_real @ X3 @ Y3 )
% 5.31/5.48 => ( ord_less_rat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 5.31/5.48 => ( ord_less_rat @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % ord_less_eq_subst
% 5.31/5.48 thf(fact_631_ord__less__eq__subst,axiom,
% 5.31/5.48 ! [A: real,B: real,F2: real > num,C2: num] :
% 5.31/5.48 ( ( ord_less_real @ A @ B )
% 5.31/5.48 => ( ( ( F2 @ B )
% 5.31/5.48 = C2 )
% 5.31/5.48 => ( ! [X3: real,Y3: real] :
% 5.31/5.48 ( ( ord_less_real @ X3 @ Y3 )
% 5.31/5.48 => ( ord_less_num @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 5.31/5.48 => ( ord_less_num @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % ord_less_eq_subst
% 5.31/5.48 thf(fact_632_ord__less__eq__subst,axiom,
% 5.31/5.48 ! [A: real,B: real,F2: real > nat,C2: nat] :
% 5.31/5.48 ( ( ord_less_real @ A @ B )
% 5.31/5.48 => ( ( ( F2 @ B )
% 5.31/5.48 = C2 )
% 5.31/5.48 => ( ! [X3: real,Y3: real] :
% 5.31/5.48 ( ( ord_less_real @ X3 @ Y3 )
% 5.31/5.48 => ( ord_less_nat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 5.31/5.48 => ( ord_less_nat @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % ord_less_eq_subst
% 5.31/5.48 thf(fact_633_ord__less__eq__subst,axiom,
% 5.31/5.48 ! [A: real,B: real,F2: real > int,C2: int] :
% 5.31/5.48 ( ( ord_less_real @ A @ B )
% 5.31/5.48 => ( ( ( F2 @ B )
% 5.31/5.48 = C2 )
% 5.31/5.48 => ( ! [X3: real,Y3: real] :
% 5.31/5.48 ( ( ord_less_real @ X3 @ Y3 )
% 5.31/5.48 => ( ord_less_int @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 5.31/5.48 => ( ord_less_int @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % ord_less_eq_subst
% 5.31/5.48 thf(fact_634_ord__less__eq__subst,axiom,
% 5.31/5.48 ! [A: rat,B: rat,F2: rat > real,C2: real] :
% 5.31/5.48 ( ( ord_less_rat @ A @ B )
% 5.31/5.48 => ( ( ( F2 @ B )
% 5.31/5.48 = C2 )
% 5.31/5.48 => ( ! [X3: rat,Y3: rat] :
% 5.31/5.48 ( ( ord_less_rat @ X3 @ Y3 )
% 5.31/5.48 => ( ord_less_real @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 5.31/5.48 => ( ord_less_real @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % ord_less_eq_subst
% 5.31/5.48 thf(fact_635_ord__less__eq__subst,axiom,
% 5.31/5.48 ! [A: rat,B: rat,F2: rat > rat,C2: rat] :
% 5.31/5.48 ( ( ord_less_rat @ A @ B )
% 5.31/5.48 => ( ( ( F2 @ B )
% 5.31/5.48 = C2 )
% 5.31/5.48 => ( ! [X3: rat,Y3: rat] :
% 5.31/5.48 ( ( ord_less_rat @ X3 @ Y3 )
% 5.31/5.48 => ( ord_less_rat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 5.31/5.48 => ( ord_less_rat @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % ord_less_eq_subst
% 5.31/5.48 thf(fact_636_ord__less__eq__subst,axiom,
% 5.31/5.48 ! [A: rat,B: rat,F2: rat > num,C2: num] :
% 5.31/5.48 ( ( ord_less_rat @ A @ B )
% 5.31/5.48 => ( ( ( F2 @ B )
% 5.31/5.48 = C2 )
% 5.31/5.48 => ( ! [X3: rat,Y3: rat] :
% 5.31/5.48 ( ( ord_less_rat @ X3 @ Y3 )
% 5.31/5.48 => ( ord_less_num @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 5.31/5.48 => ( ord_less_num @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % ord_less_eq_subst
% 5.31/5.48 thf(fact_637_ord__less__eq__subst,axiom,
% 5.31/5.48 ! [A: rat,B: rat,F2: rat > nat,C2: nat] :
% 5.31/5.48 ( ( ord_less_rat @ A @ B )
% 5.31/5.48 => ( ( ( F2 @ B )
% 5.31/5.48 = C2 )
% 5.31/5.48 => ( ! [X3: rat,Y3: rat] :
% 5.31/5.48 ( ( ord_less_rat @ X3 @ Y3 )
% 5.31/5.48 => ( ord_less_nat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 5.31/5.48 => ( ord_less_nat @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % ord_less_eq_subst
% 5.31/5.48 thf(fact_638_ord__less__eq__subst,axiom,
% 5.31/5.48 ! [A: rat,B: rat,F2: rat > int,C2: int] :
% 5.31/5.48 ( ( ord_less_rat @ A @ B )
% 5.31/5.48 => ( ( ( F2 @ B )
% 5.31/5.48 = C2 )
% 5.31/5.48 => ( ! [X3: rat,Y3: rat] :
% 5.31/5.48 ( ( ord_less_rat @ X3 @ Y3 )
% 5.31/5.48 => ( ord_less_int @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 5.31/5.48 => ( ord_less_int @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % ord_less_eq_subst
% 5.31/5.48 thf(fact_639_order__less__irrefl,axiom,
% 5.31/5.48 ! [X: real] :
% 5.31/5.48 ~ ( ord_less_real @ X @ X ) ).
% 5.31/5.48
% 5.31/5.48 % order_less_irrefl
% 5.31/5.48 thf(fact_640_order__less__irrefl,axiom,
% 5.31/5.48 ! [X: rat] :
% 5.31/5.48 ~ ( ord_less_rat @ X @ X ) ).
% 5.31/5.48
% 5.31/5.48 % order_less_irrefl
% 5.31/5.48 thf(fact_641_order__less__irrefl,axiom,
% 5.31/5.48 ! [X: num] :
% 5.31/5.48 ~ ( ord_less_num @ X @ X ) ).
% 5.31/5.48
% 5.31/5.48 % order_less_irrefl
% 5.31/5.48 thf(fact_642_order__less__irrefl,axiom,
% 5.31/5.48 ! [X: nat] :
% 5.31/5.48 ~ ( ord_less_nat @ X @ X ) ).
% 5.31/5.48
% 5.31/5.48 % order_less_irrefl
% 5.31/5.48 thf(fact_643_order__less__irrefl,axiom,
% 5.31/5.48 ! [X: int] :
% 5.31/5.48 ~ ( ord_less_int @ X @ X ) ).
% 5.31/5.48
% 5.31/5.48 % order_less_irrefl
% 5.31/5.48 thf(fact_644_order__less__subst1,axiom,
% 5.31/5.48 ! [A: real,F2: real > real,B: real,C2: real] :
% 5.31/5.48 ( ( ord_less_real @ A @ ( F2 @ B ) )
% 5.31/5.48 => ( ( ord_less_real @ B @ C2 )
% 5.31/5.48 => ( ! [X3: real,Y3: real] :
% 5.31/5.48 ( ( ord_less_real @ X3 @ Y3 )
% 5.31/5.48 => ( ord_less_real @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 5.31/5.48 => ( ord_less_real @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % order_less_subst1
% 5.31/5.48 thf(fact_645_order__less__subst1,axiom,
% 5.31/5.48 ! [A: real,F2: rat > real,B: rat,C2: rat] :
% 5.31/5.48 ( ( ord_less_real @ A @ ( F2 @ B ) )
% 5.31/5.48 => ( ( ord_less_rat @ B @ C2 )
% 5.31/5.48 => ( ! [X3: rat,Y3: rat] :
% 5.31/5.48 ( ( ord_less_rat @ X3 @ Y3 )
% 5.31/5.48 => ( ord_less_real @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 5.31/5.48 => ( ord_less_real @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % order_less_subst1
% 5.31/5.48 thf(fact_646_order__less__subst1,axiom,
% 5.31/5.48 ! [A: real,F2: num > real,B: num,C2: num] :
% 5.31/5.48 ( ( ord_less_real @ A @ ( F2 @ B ) )
% 5.31/5.48 => ( ( ord_less_num @ B @ C2 )
% 5.31/5.48 => ( ! [X3: num,Y3: num] :
% 5.31/5.48 ( ( ord_less_num @ X3 @ Y3 )
% 5.31/5.48 => ( ord_less_real @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 5.31/5.48 => ( ord_less_real @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % order_less_subst1
% 5.31/5.48 thf(fact_647_order__less__subst1,axiom,
% 5.31/5.48 ! [A: real,F2: nat > real,B: nat,C2: nat] :
% 5.31/5.48 ( ( ord_less_real @ A @ ( F2 @ B ) )
% 5.31/5.48 => ( ( ord_less_nat @ B @ C2 )
% 5.31/5.48 => ( ! [X3: nat,Y3: nat] :
% 5.31/5.48 ( ( ord_less_nat @ X3 @ Y3 )
% 5.31/5.48 => ( ord_less_real @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 5.31/5.48 => ( ord_less_real @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % order_less_subst1
% 5.31/5.48 thf(fact_648_order__less__subst1,axiom,
% 5.31/5.48 ! [A: real,F2: int > real,B: int,C2: int] :
% 5.31/5.48 ( ( ord_less_real @ A @ ( F2 @ B ) )
% 5.31/5.48 => ( ( ord_less_int @ B @ C2 )
% 5.31/5.48 => ( ! [X3: int,Y3: int] :
% 5.31/5.48 ( ( ord_less_int @ X3 @ Y3 )
% 5.31/5.48 => ( ord_less_real @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 5.31/5.48 => ( ord_less_real @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % order_less_subst1
% 5.31/5.48 thf(fact_649_order__less__subst1,axiom,
% 5.31/5.48 ! [A: rat,F2: real > rat,B: real,C2: real] :
% 5.31/5.48 ( ( ord_less_rat @ A @ ( F2 @ B ) )
% 5.31/5.48 => ( ( ord_less_real @ B @ C2 )
% 5.31/5.48 => ( ! [X3: real,Y3: real] :
% 5.31/5.48 ( ( ord_less_real @ X3 @ Y3 )
% 5.31/5.48 => ( ord_less_rat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 5.31/5.48 => ( ord_less_rat @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % order_less_subst1
% 5.31/5.48 thf(fact_650_order__less__subst1,axiom,
% 5.31/5.48 ! [A: rat,F2: rat > rat,B: rat,C2: rat] :
% 5.31/5.48 ( ( ord_less_rat @ A @ ( F2 @ B ) )
% 5.31/5.48 => ( ( ord_less_rat @ B @ C2 )
% 5.31/5.48 => ( ! [X3: rat,Y3: rat] :
% 5.31/5.48 ( ( ord_less_rat @ X3 @ Y3 )
% 5.31/5.48 => ( ord_less_rat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 5.31/5.48 => ( ord_less_rat @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % order_less_subst1
% 5.31/5.48 thf(fact_651_order__less__subst1,axiom,
% 5.31/5.48 ! [A: rat,F2: num > rat,B: num,C2: num] :
% 5.31/5.48 ( ( ord_less_rat @ A @ ( F2 @ B ) )
% 5.31/5.48 => ( ( ord_less_num @ B @ C2 )
% 5.31/5.48 => ( ! [X3: num,Y3: num] :
% 5.31/5.48 ( ( ord_less_num @ X3 @ Y3 )
% 5.31/5.48 => ( ord_less_rat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 5.31/5.48 => ( ord_less_rat @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % order_less_subst1
% 5.31/5.48 thf(fact_652_order__less__subst1,axiom,
% 5.31/5.48 ! [A: rat,F2: nat > rat,B: nat,C2: nat] :
% 5.31/5.48 ( ( ord_less_rat @ A @ ( F2 @ B ) )
% 5.31/5.48 => ( ( ord_less_nat @ B @ C2 )
% 5.31/5.48 => ( ! [X3: nat,Y3: nat] :
% 5.31/5.48 ( ( ord_less_nat @ X3 @ Y3 )
% 5.31/5.48 => ( ord_less_rat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 5.31/5.48 => ( ord_less_rat @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % order_less_subst1
% 5.31/5.48 thf(fact_653_order__less__subst1,axiom,
% 5.31/5.48 ! [A: rat,F2: int > rat,B: int,C2: int] :
% 5.31/5.48 ( ( ord_less_rat @ A @ ( F2 @ B ) )
% 5.31/5.48 => ( ( ord_less_int @ B @ C2 )
% 5.31/5.48 => ( ! [X3: int,Y3: int] :
% 5.31/5.48 ( ( ord_less_int @ X3 @ Y3 )
% 5.31/5.48 => ( ord_less_rat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 5.31/5.48 => ( ord_less_rat @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % order_less_subst1
% 5.31/5.48 thf(fact_654_order__less__subst2,axiom,
% 5.31/5.48 ! [A: real,B: real,F2: real > real,C2: real] :
% 5.31/5.48 ( ( ord_less_real @ A @ B )
% 5.31/5.48 => ( ( ord_less_real @ ( F2 @ B ) @ C2 )
% 5.31/5.48 => ( ! [X3: real,Y3: real] :
% 5.31/5.48 ( ( ord_less_real @ X3 @ Y3 )
% 5.31/5.48 => ( ord_less_real @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 5.31/5.48 => ( ord_less_real @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % order_less_subst2
% 5.31/5.48 thf(fact_655_order__less__subst2,axiom,
% 5.31/5.48 ! [A: real,B: real,F2: real > rat,C2: rat] :
% 5.31/5.48 ( ( ord_less_real @ A @ B )
% 5.31/5.48 => ( ( ord_less_rat @ ( F2 @ B ) @ C2 )
% 5.31/5.48 => ( ! [X3: real,Y3: real] :
% 5.31/5.48 ( ( ord_less_real @ X3 @ Y3 )
% 5.31/5.48 => ( ord_less_rat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 5.31/5.48 => ( ord_less_rat @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % order_less_subst2
% 5.31/5.48 thf(fact_656_order__less__subst2,axiom,
% 5.31/5.48 ! [A: real,B: real,F2: real > num,C2: num] :
% 5.31/5.48 ( ( ord_less_real @ A @ B )
% 5.31/5.48 => ( ( ord_less_num @ ( F2 @ B ) @ C2 )
% 5.31/5.48 => ( ! [X3: real,Y3: real] :
% 5.31/5.48 ( ( ord_less_real @ X3 @ Y3 )
% 5.31/5.48 => ( ord_less_num @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 5.31/5.48 => ( ord_less_num @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % order_less_subst2
% 5.31/5.48 thf(fact_657_order__less__subst2,axiom,
% 5.31/5.48 ! [A: real,B: real,F2: real > nat,C2: nat] :
% 5.31/5.48 ( ( ord_less_real @ A @ B )
% 5.31/5.48 => ( ( ord_less_nat @ ( F2 @ B ) @ C2 )
% 5.31/5.48 => ( ! [X3: real,Y3: real] :
% 5.31/5.48 ( ( ord_less_real @ X3 @ Y3 )
% 5.31/5.48 => ( ord_less_nat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 5.31/5.48 => ( ord_less_nat @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % order_less_subst2
% 5.31/5.48 thf(fact_658_order__less__subst2,axiom,
% 5.31/5.48 ! [A: real,B: real,F2: real > int,C2: int] :
% 5.31/5.48 ( ( ord_less_real @ A @ B )
% 5.31/5.48 => ( ( ord_less_int @ ( F2 @ B ) @ C2 )
% 5.31/5.48 => ( ! [X3: real,Y3: real] :
% 5.31/5.48 ( ( ord_less_real @ X3 @ Y3 )
% 5.31/5.48 => ( ord_less_int @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 5.31/5.48 => ( ord_less_int @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % order_less_subst2
% 5.31/5.48 thf(fact_659_order__less__subst2,axiom,
% 5.31/5.48 ! [A: rat,B: rat,F2: rat > real,C2: real] :
% 5.31/5.48 ( ( ord_less_rat @ A @ B )
% 5.31/5.48 => ( ( ord_less_real @ ( F2 @ B ) @ C2 )
% 5.31/5.48 => ( ! [X3: rat,Y3: rat] :
% 5.31/5.48 ( ( ord_less_rat @ X3 @ Y3 )
% 5.31/5.48 => ( ord_less_real @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 5.31/5.48 => ( ord_less_real @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % order_less_subst2
% 5.31/5.48 thf(fact_660_order__less__subst2,axiom,
% 5.31/5.48 ! [A: rat,B: rat,F2: rat > rat,C2: rat] :
% 5.31/5.48 ( ( ord_less_rat @ A @ B )
% 5.31/5.48 => ( ( ord_less_rat @ ( F2 @ B ) @ C2 )
% 5.31/5.48 => ( ! [X3: rat,Y3: rat] :
% 5.31/5.48 ( ( ord_less_rat @ X3 @ Y3 )
% 5.31/5.48 => ( ord_less_rat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 5.31/5.48 => ( ord_less_rat @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % order_less_subst2
% 5.31/5.48 thf(fact_661_order__less__subst2,axiom,
% 5.31/5.48 ! [A: rat,B: rat,F2: rat > num,C2: num] :
% 5.31/5.48 ( ( ord_less_rat @ A @ B )
% 5.31/5.48 => ( ( ord_less_num @ ( F2 @ B ) @ C2 )
% 5.31/5.48 => ( ! [X3: rat,Y3: rat] :
% 5.31/5.48 ( ( ord_less_rat @ X3 @ Y3 )
% 5.31/5.48 => ( ord_less_num @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 5.31/5.48 => ( ord_less_num @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % order_less_subst2
% 5.31/5.48 thf(fact_662_order__less__subst2,axiom,
% 5.31/5.48 ! [A: rat,B: rat,F2: rat > nat,C2: nat] :
% 5.31/5.48 ( ( ord_less_rat @ A @ B )
% 5.31/5.48 => ( ( ord_less_nat @ ( F2 @ B ) @ C2 )
% 5.31/5.48 => ( ! [X3: rat,Y3: rat] :
% 5.31/5.48 ( ( ord_less_rat @ X3 @ Y3 )
% 5.31/5.48 => ( ord_less_nat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 5.31/5.48 => ( ord_less_nat @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % order_less_subst2
% 5.31/5.48 thf(fact_663_order__less__subst2,axiom,
% 5.31/5.48 ! [A: rat,B: rat,F2: rat > int,C2: int] :
% 5.31/5.48 ( ( ord_less_rat @ A @ B )
% 5.31/5.48 => ( ( ord_less_int @ ( F2 @ B ) @ C2 )
% 5.31/5.48 => ( ! [X3: rat,Y3: rat] :
% 5.31/5.48 ( ( ord_less_rat @ X3 @ Y3 )
% 5.31/5.48 => ( ord_less_int @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 5.31/5.48 => ( ord_less_int @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % order_less_subst2
% 5.31/5.48 thf(fact_664_order__less__not__sym,axiom,
% 5.31/5.48 ! [X: real,Y: real] :
% 5.31/5.48 ( ( ord_less_real @ X @ Y )
% 5.31/5.48 => ~ ( ord_less_real @ Y @ X ) ) ).
% 5.31/5.48
% 5.31/5.48 % order_less_not_sym
% 5.31/5.48 thf(fact_665_order__less__not__sym,axiom,
% 5.31/5.48 ! [X: rat,Y: rat] :
% 5.31/5.48 ( ( ord_less_rat @ X @ Y )
% 5.31/5.48 => ~ ( ord_less_rat @ Y @ X ) ) ).
% 5.31/5.48
% 5.31/5.48 % order_less_not_sym
% 5.31/5.48 thf(fact_666_order__less__not__sym,axiom,
% 5.31/5.48 ! [X: num,Y: num] :
% 5.31/5.48 ( ( ord_less_num @ X @ Y )
% 5.31/5.48 => ~ ( ord_less_num @ Y @ X ) ) ).
% 5.31/5.48
% 5.31/5.48 % order_less_not_sym
% 5.31/5.48 thf(fact_667_order__less__not__sym,axiom,
% 5.31/5.48 ! [X: nat,Y: nat] :
% 5.31/5.48 ( ( ord_less_nat @ X @ Y )
% 5.31/5.48 => ~ ( ord_less_nat @ Y @ X ) ) ).
% 5.31/5.48
% 5.31/5.48 % order_less_not_sym
% 5.31/5.48 thf(fact_668_order__less__not__sym,axiom,
% 5.31/5.48 ! [X: int,Y: int] :
% 5.31/5.48 ( ( ord_less_int @ X @ Y )
% 5.31/5.48 => ~ ( ord_less_int @ Y @ X ) ) ).
% 5.31/5.48
% 5.31/5.48 % order_less_not_sym
% 5.31/5.48 thf(fact_669_order__less__imp__triv,axiom,
% 5.31/5.48 ! [X: real,Y: real,P2: $o] :
% 5.31/5.48 ( ( ord_less_real @ X @ Y )
% 5.31/5.48 => ( ( ord_less_real @ Y @ X )
% 5.31/5.48 => P2 ) ) ).
% 5.31/5.48
% 5.31/5.48 % order_less_imp_triv
% 5.31/5.48 thf(fact_670_order__less__imp__triv,axiom,
% 5.31/5.48 ! [X: rat,Y: rat,P2: $o] :
% 5.31/5.48 ( ( ord_less_rat @ X @ Y )
% 5.31/5.48 => ( ( ord_less_rat @ Y @ X )
% 5.31/5.48 => P2 ) ) ).
% 5.31/5.48
% 5.31/5.48 % order_less_imp_triv
% 5.31/5.48 thf(fact_671_order__less__imp__triv,axiom,
% 5.31/5.48 ! [X: num,Y: num,P2: $o] :
% 5.31/5.48 ( ( ord_less_num @ X @ Y )
% 5.31/5.48 => ( ( ord_less_num @ Y @ X )
% 5.31/5.48 => P2 ) ) ).
% 5.31/5.48
% 5.31/5.48 % order_less_imp_triv
% 5.31/5.48 thf(fact_672_order__less__imp__triv,axiom,
% 5.31/5.48 ! [X: nat,Y: nat,P2: $o] :
% 5.31/5.48 ( ( ord_less_nat @ X @ Y )
% 5.31/5.48 => ( ( ord_less_nat @ Y @ X )
% 5.31/5.48 => P2 ) ) ).
% 5.31/5.48
% 5.31/5.48 % order_less_imp_triv
% 5.31/5.48 thf(fact_673_order__less__imp__triv,axiom,
% 5.31/5.48 ! [X: int,Y: int,P2: $o] :
% 5.31/5.48 ( ( ord_less_int @ X @ Y )
% 5.31/5.48 => ( ( ord_less_int @ Y @ X )
% 5.31/5.48 => P2 ) ) ).
% 5.31/5.48
% 5.31/5.48 % order_less_imp_triv
% 5.31/5.48 thf(fact_674_linorder__less__linear,axiom,
% 5.31/5.48 ! [X: real,Y: real] :
% 5.31/5.48 ( ( ord_less_real @ X @ Y )
% 5.31/5.48 | ( X = Y )
% 5.31/5.48 | ( ord_less_real @ Y @ X ) ) ).
% 5.31/5.48
% 5.31/5.48 % linorder_less_linear
% 5.31/5.48 thf(fact_675_linorder__less__linear,axiom,
% 5.31/5.48 ! [X: rat,Y: rat] :
% 5.31/5.48 ( ( ord_less_rat @ X @ Y )
% 5.31/5.48 | ( X = Y )
% 5.31/5.48 | ( ord_less_rat @ Y @ X ) ) ).
% 5.31/5.48
% 5.31/5.48 % linorder_less_linear
% 5.31/5.48 thf(fact_676_linorder__less__linear,axiom,
% 5.31/5.48 ! [X: num,Y: num] :
% 5.31/5.48 ( ( ord_less_num @ X @ Y )
% 5.31/5.48 | ( X = Y )
% 5.31/5.48 | ( ord_less_num @ Y @ X ) ) ).
% 5.31/5.48
% 5.31/5.48 % linorder_less_linear
% 5.31/5.48 thf(fact_677_linorder__less__linear,axiom,
% 5.31/5.48 ! [X: nat,Y: nat] :
% 5.31/5.48 ( ( ord_less_nat @ X @ Y )
% 5.31/5.48 | ( X = Y )
% 5.31/5.48 | ( ord_less_nat @ Y @ X ) ) ).
% 5.31/5.48
% 5.31/5.48 % linorder_less_linear
% 5.31/5.48 thf(fact_678_linorder__less__linear,axiom,
% 5.31/5.48 ! [X: int,Y: int] :
% 5.31/5.48 ( ( ord_less_int @ X @ Y )
% 5.31/5.48 | ( X = Y )
% 5.31/5.48 | ( ord_less_int @ Y @ X ) ) ).
% 5.31/5.48
% 5.31/5.48 % linorder_less_linear
% 5.31/5.48 thf(fact_679_order__less__imp__not__eq,axiom,
% 5.31/5.48 ! [X: real,Y: real] :
% 5.31/5.48 ( ( ord_less_real @ X @ Y )
% 5.31/5.48 => ( X != Y ) ) ).
% 5.31/5.48
% 5.31/5.48 % order_less_imp_not_eq
% 5.31/5.48 thf(fact_680_order__less__imp__not__eq,axiom,
% 5.31/5.48 ! [X: rat,Y: rat] :
% 5.31/5.48 ( ( ord_less_rat @ X @ Y )
% 5.31/5.48 => ( X != Y ) ) ).
% 5.31/5.48
% 5.31/5.48 % order_less_imp_not_eq
% 5.31/5.48 thf(fact_681_order__less__imp__not__eq,axiom,
% 5.31/5.48 ! [X: num,Y: num] :
% 5.31/5.48 ( ( ord_less_num @ X @ Y )
% 5.31/5.48 => ( X != Y ) ) ).
% 5.31/5.48
% 5.31/5.48 % order_less_imp_not_eq
% 5.31/5.48 thf(fact_682_order__less__imp__not__eq,axiom,
% 5.31/5.48 ! [X: nat,Y: nat] :
% 5.31/5.48 ( ( ord_less_nat @ X @ Y )
% 5.31/5.48 => ( X != Y ) ) ).
% 5.31/5.48
% 5.31/5.48 % order_less_imp_not_eq
% 5.31/5.48 thf(fact_683_order__less__imp__not__eq,axiom,
% 5.31/5.48 ! [X: int,Y: int] :
% 5.31/5.48 ( ( ord_less_int @ X @ Y )
% 5.31/5.48 => ( X != Y ) ) ).
% 5.31/5.48
% 5.31/5.48 % order_less_imp_not_eq
% 5.31/5.48 thf(fact_684_order__less__imp__not__eq2,axiom,
% 5.31/5.48 ! [X: real,Y: real] :
% 5.31/5.48 ( ( ord_less_real @ X @ Y )
% 5.31/5.48 => ( Y != X ) ) ).
% 5.31/5.48
% 5.31/5.48 % order_less_imp_not_eq2
% 5.31/5.48 thf(fact_685_order__less__imp__not__eq2,axiom,
% 5.31/5.48 ! [X: rat,Y: rat] :
% 5.31/5.48 ( ( ord_less_rat @ X @ Y )
% 5.31/5.48 => ( Y != X ) ) ).
% 5.31/5.48
% 5.31/5.48 % order_less_imp_not_eq2
% 5.31/5.48 thf(fact_686_order__less__imp__not__eq2,axiom,
% 5.31/5.48 ! [X: num,Y: num] :
% 5.31/5.48 ( ( ord_less_num @ X @ Y )
% 5.31/5.48 => ( Y != X ) ) ).
% 5.31/5.48
% 5.31/5.48 % order_less_imp_not_eq2
% 5.31/5.48 thf(fact_687_order__less__imp__not__eq2,axiom,
% 5.31/5.48 ! [X: nat,Y: nat] :
% 5.31/5.48 ( ( ord_less_nat @ X @ Y )
% 5.31/5.48 => ( Y != X ) ) ).
% 5.31/5.48
% 5.31/5.48 % order_less_imp_not_eq2
% 5.31/5.48 thf(fact_688_order__less__imp__not__eq2,axiom,
% 5.31/5.48 ! [X: int,Y: int] :
% 5.31/5.48 ( ( ord_less_int @ X @ Y )
% 5.31/5.48 => ( Y != X ) ) ).
% 5.31/5.48
% 5.31/5.48 % order_less_imp_not_eq2
% 5.31/5.48 thf(fact_689_order__less__imp__not__less,axiom,
% 5.31/5.48 ! [X: real,Y: real] :
% 5.31/5.48 ( ( ord_less_real @ X @ Y )
% 5.31/5.48 => ~ ( ord_less_real @ Y @ X ) ) ).
% 5.31/5.48
% 5.31/5.48 % order_less_imp_not_less
% 5.31/5.48 thf(fact_690_order__less__imp__not__less,axiom,
% 5.31/5.48 ! [X: rat,Y: rat] :
% 5.31/5.48 ( ( ord_less_rat @ X @ Y )
% 5.31/5.48 => ~ ( ord_less_rat @ Y @ X ) ) ).
% 5.31/5.48
% 5.31/5.48 % order_less_imp_not_less
% 5.31/5.48 thf(fact_691_order__less__imp__not__less,axiom,
% 5.31/5.48 ! [X: num,Y: num] :
% 5.31/5.48 ( ( ord_less_num @ X @ Y )
% 5.31/5.48 => ~ ( ord_less_num @ Y @ X ) ) ).
% 5.31/5.48
% 5.31/5.48 % order_less_imp_not_less
% 5.31/5.48 thf(fact_692_order__less__imp__not__less,axiom,
% 5.31/5.48 ! [X: nat,Y: nat] :
% 5.31/5.48 ( ( ord_less_nat @ X @ Y )
% 5.31/5.48 => ~ ( ord_less_nat @ Y @ X ) ) ).
% 5.31/5.48
% 5.31/5.48 % order_less_imp_not_less
% 5.31/5.48 thf(fact_693_order__less__imp__not__less,axiom,
% 5.31/5.48 ! [X: int,Y: int] :
% 5.31/5.48 ( ( ord_less_int @ X @ Y )
% 5.31/5.48 => ~ ( ord_less_int @ Y @ X ) ) ).
% 5.31/5.48
% 5.31/5.48 % order_less_imp_not_less
% 5.31/5.48 thf(fact_694_less__numeral__extra_I4_J,axiom,
% 5.31/5.48 ~ ( ord_le6747313008572928689nteger @ one_one_Code_integer @ one_one_Code_integer ) ).
% 5.31/5.48
% 5.31/5.48 % less_numeral_extra(4)
% 5.31/5.48 thf(fact_695_less__numeral__extra_I4_J,axiom,
% 5.31/5.48 ~ ( ord_less_real @ one_one_real @ one_one_real ) ).
% 5.31/5.48
% 5.31/5.48 % less_numeral_extra(4)
% 5.31/5.48 thf(fact_696_less__numeral__extra_I4_J,axiom,
% 5.31/5.48 ~ ( ord_less_rat @ one_one_rat @ one_one_rat ) ).
% 5.31/5.48
% 5.31/5.48 % less_numeral_extra(4)
% 5.31/5.48 thf(fact_697_less__numeral__extra_I4_J,axiom,
% 5.31/5.48 ~ ( ord_less_nat @ one_one_nat @ one_one_nat ) ).
% 5.31/5.48
% 5.31/5.48 % less_numeral_extra(4)
% 5.31/5.48 thf(fact_698_less__numeral__extra_I4_J,axiom,
% 5.31/5.48 ~ ( ord_less_int @ one_one_int @ one_one_int ) ).
% 5.31/5.48
% 5.31/5.48 % less_numeral_extra(4)
% 5.31/5.48 thf(fact_699_one__reorient,axiom,
% 5.31/5.48 ! [X: code_integer] :
% 5.31/5.48 ( ( one_one_Code_integer = X )
% 5.31/5.48 = ( X = one_one_Code_integer ) ) ).
% 5.31/5.48
% 5.31/5.48 % one_reorient
% 5.31/5.48 thf(fact_700_one__reorient,axiom,
% 5.31/5.48 ! [X: complex] :
% 5.31/5.48 ( ( one_one_complex = X )
% 5.31/5.48 = ( X = one_one_complex ) ) ).
% 5.31/5.48
% 5.31/5.48 % one_reorient
% 5.31/5.48 thf(fact_701_one__reorient,axiom,
% 5.31/5.48 ! [X: real] :
% 5.31/5.48 ( ( one_one_real = X )
% 5.31/5.48 = ( X = one_one_real ) ) ).
% 5.31/5.48
% 5.31/5.48 % one_reorient
% 5.31/5.48 thf(fact_702_one__reorient,axiom,
% 5.31/5.48 ! [X: nat] :
% 5.31/5.48 ( ( one_one_nat = X )
% 5.31/5.48 = ( X = one_one_nat ) ) ).
% 5.31/5.48
% 5.31/5.48 % one_reorient
% 5.31/5.48 thf(fact_703_one__reorient,axiom,
% 5.31/5.48 ! [X: int] :
% 5.31/5.48 ( ( one_one_int = X )
% 5.31/5.48 = ( X = one_one_int ) ) ).
% 5.31/5.48
% 5.31/5.48 % one_reorient
% 5.31/5.48 thf(fact_704_less__numeral__extra_I1_J,axiom,
% 5.31/5.48 ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ one_one_Code_integer ).
% 5.31/5.48
% 5.31/5.48 % less_numeral_extra(1)
% 5.31/5.48 thf(fact_705_less__numeral__extra_I1_J,axiom,
% 5.31/5.48 ord_less_real @ zero_zero_real @ one_one_real ).
% 5.31/5.48
% 5.31/5.48 % less_numeral_extra(1)
% 5.31/5.48 thf(fact_706_less__numeral__extra_I1_J,axiom,
% 5.31/5.48 ord_less_rat @ zero_zero_rat @ one_one_rat ).
% 5.31/5.48
% 5.31/5.48 % less_numeral_extra(1)
% 5.31/5.48 thf(fact_707_less__numeral__extra_I1_J,axiom,
% 5.31/5.48 ord_less_nat @ zero_zero_nat @ one_one_nat ).
% 5.31/5.48
% 5.31/5.48 % less_numeral_extra(1)
% 5.31/5.48 thf(fact_708_less__numeral__extra_I1_J,axiom,
% 5.31/5.48 ord_less_int @ zero_zero_int @ one_one_int ).
% 5.31/5.48
% 5.31/5.48 % less_numeral_extra(1)
% 5.31/5.48 thf(fact_709_not__one__less__zero,axiom,
% 5.31/5.48 ~ ( ord_le6747313008572928689nteger @ one_one_Code_integer @ zero_z3403309356797280102nteger ) ).
% 5.31/5.48
% 5.31/5.48 % not_one_less_zero
% 5.31/5.48 thf(fact_710_not__one__less__zero,axiom,
% 5.31/5.48 ~ ( ord_less_real @ one_one_real @ zero_zero_real ) ).
% 5.31/5.48
% 5.31/5.48 % not_one_less_zero
% 5.31/5.48 thf(fact_711_not__one__less__zero,axiom,
% 5.31/5.48 ~ ( ord_less_rat @ one_one_rat @ zero_zero_rat ) ).
% 5.31/5.48
% 5.31/5.48 % not_one_less_zero
% 5.31/5.48 thf(fact_712_not__one__less__zero,axiom,
% 5.31/5.48 ~ ( ord_less_nat @ one_one_nat @ zero_zero_nat ) ).
% 5.31/5.48
% 5.31/5.48 % not_one_less_zero
% 5.31/5.48 thf(fact_713_not__one__less__zero,axiom,
% 5.31/5.48 ~ ( ord_less_int @ one_one_int @ zero_zero_int ) ).
% 5.31/5.48
% 5.31/5.48 % not_one_less_zero
% 5.31/5.48 thf(fact_714_zero__less__one,axiom,
% 5.31/5.48 ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ one_one_Code_integer ).
% 5.31/5.48
% 5.31/5.48 % zero_less_one
% 5.31/5.48 thf(fact_715_zero__less__one,axiom,
% 5.31/5.48 ord_less_real @ zero_zero_real @ one_one_real ).
% 5.31/5.48
% 5.31/5.48 % zero_less_one
% 5.31/5.48 thf(fact_716_zero__less__one,axiom,
% 5.31/5.48 ord_less_rat @ zero_zero_rat @ one_one_rat ).
% 5.31/5.48
% 5.31/5.48 % zero_less_one
% 5.31/5.48 thf(fact_717_zero__less__one,axiom,
% 5.31/5.48 ord_less_nat @ zero_zero_nat @ one_one_nat ).
% 5.31/5.48
% 5.31/5.48 % zero_less_one
% 5.31/5.48 thf(fact_718_zero__less__one,axiom,
% 5.31/5.48 ord_less_int @ zero_zero_int @ one_one_int ).
% 5.31/5.48
% 5.31/5.48 % zero_less_one
% 5.31/5.48 thf(fact_719_lift__Suc__mono__less__iff,axiom,
% 5.31/5.48 ! [F2: nat > real,N: nat,M2: nat] :
% 5.31/5.48 ( ! [N3: nat] : ( ord_less_real @ ( F2 @ N3 ) @ ( F2 @ ( suc @ N3 ) ) )
% 5.31/5.48 => ( ( ord_less_real @ ( F2 @ N ) @ ( F2 @ M2 ) )
% 5.31/5.48 = ( ord_less_nat @ N @ M2 ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % lift_Suc_mono_less_iff
% 5.31/5.48 thf(fact_720_lift__Suc__mono__less__iff,axiom,
% 5.31/5.48 ! [F2: nat > rat,N: nat,M2: nat] :
% 5.31/5.48 ( ! [N3: nat] : ( ord_less_rat @ ( F2 @ N3 ) @ ( F2 @ ( suc @ N3 ) ) )
% 5.31/5.48 => ( ( ord_less_rat @ ( F2 @ N ) @ ( F2 @ M2 ) )
% 5.31/5.48 = ( ord_less_nat @ N @ M2 ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % lift_Suc_mono_less_iff
% 5.31/5.48 thf(fact_721_lift__Suc__mono__less__iff,axiom,
% 5.31/5.48 ! [F2: nat > num,N: nat,M2: nat] :
% 5.31/5.48 ( ! [N3: nat] : ( ord_less_num @ ( F2 @ N3 ) @ ( F2 @ ( suc @ N3 ) ) )
% 5.31/5.48 => ( ( ord_less_num @ ( F2 @ N ) @ ( F2 @ M2 ) )
% 5.31/5.48 = ( ord_less_nat @ N @ M2 ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % lift_Suc_mono_less_iff
% 5.31/5.48 thf(fact_722_lift__Suc__mono__less__iff,axiom,
% 5.31/5.48 ! [F2: nat > nat,N: nat,M2: nat] :
% 5.31/5.48 ( ! [N3: nat] : ( ord_less_nat @ ( F2 @ N3 ) @ ( F2 @ ( suc @ N3 ) ) )
% 5.31/5.48 => ( ( ord_less_nat @ ( F2 @ N ) @ ( F2 @ M2 ) )
% 5.31/5.48 = ( ord_less_nat @ N @ M2 ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % lift_Suc_mono_less_iff
% 5.31/5.48 thf(fact_723_lift__Suc__mono__less__iff,axiom,
% 5.31/5.48 ! [F2: nat > int,N: nat,M2: nat] :
% 5.31/5.48 ( ! [N3: nat] : ( ord_less_int @ ( F2 @ N3 ) @ ( F2 @ ( suc @ N3 ) ) )
% 5.31/5.48 => ( ( ord_less_int @ ( F2 @ N ) @ ( F2 @ M2 ) )
% 5.31/5.48 = ( ord_less_nat @ N @ M2 ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % lift_Suc_mono_less_iff
% 5.31/5.48 thf(fact_724_lift__Suc__mono__less,axiom,
% 5.31/5.48 ! [F2: nat > real,N: nat,N2: nat] :
% 5.31/5.48 ( ! [N3: nat] : ( ord_less_real @ ( F2 @ N3 ) @ ( F2 @ ( suc @ N3 ) ) )
% 5.31/5.48 => ( ( ord_less_nat @ N @ N2 )
% 5.31/5.48 => ( ord_less_real @ ( F2 @ N ) @ ( F2 @ N2 ) ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % lift_Suc_mono_less
% 5.31/5.48 thf(fact_725_lift__Suc__mono__less,axiom,
% 5.31/5.48 ! [F2: nat > rat,N: nat,N2: nat] :
% 5.31/5.48 ( ! [N3: nat] : ( ord_less_rat @ ( F2 @ N3 ) @ ( F2 @ ( suc @ N3 ) ) )
% 5.31/5.48 => ( ( ord_less_nat @ N @ N2 )
% 5.31/5.48 => ( ord_less_rat @ ( F2 @ N ) @ ( F2 @ N2 ) ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % lift_Suc_mono_less
% 5.31/5.48 thf(fact_726_lift__Suc__mono__less,axiom,
% 5.31/5.48 ! [F2: nat > num,N: nat,N2: nat] :
% 5.31/5.48 ( ! [N3: nat] : ( ord_less_num @ ( F2 @ N3 ) @ ( F2 @ ( suc @ N3 ) ) )
% 5.31/5.48 => ( ( ord_less_nat @ N @ N2 )
% 5.31/5.48 => ( ord_less_num @ ( F2 @ N ) @ ( F2 @ N2 ) ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % lift_Suc_mono_less
% 5.31/5.48 thf(fact_727_lift__Suc__mono__less,axiom,
% 5.31/5.48 ! [F2: nat > nat,N: nat,N2: nat] :
% 5.31/5.48 ( ! [N3: nat] : ( ord_less_nat @ ( F2 @ N3 ) @ ( F2 @ ( suc @ N3 ) ) )
% 5.31/5.48 => ( ( ord_less_nat @ N @ N2 )
% 5.31/5.48 => ( ord_less_nat @ ( F2 @ N ) @ ( F2 @ N2 ) ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % lift_Suc_mono_less
% 5.31/5.48 thf(fact_728_lift__Suc__mono__less,axiom,
% 5.31/5.48 ! [F2: nat > int,N: nat,N2: nat] :
% 5.31/5.48 ( ! [N3: nat] : ( ord_less_int @ ( F2 @ N3 ) @ ( F2 @ ( suc @ N3 ) ) )
% 5.31/5.48 => ( ( ord_less_nat @ N @ N2 )
% 5.31/5.48 => ( ord_less_int @ ( F2 @ N ) @ ( F2 @ N2 ) ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % lift_Suc_mono_less
% 5.31/5.48 thf(fact_729_less__1__mult,axiom,
% 5.31/5.48 ! [M2: code_integer,N: code_integer] :
% 5.31/5.48 ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ M2 )
% 5.31/5.48 => ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ N )
% 5.31/5.48 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( times_3573771949741848930nteger @ M2 @ N ) ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % less_1_mult
% 5.31/5.48 thf(fact_730_less__1__mult,axiom,
% 5.31/5.48 ! [M2: real,N: real] :
% 5.31/5.48 ( ( ord_less_real @ one_one_real @ M2 )
% 5.31/5.48 => ( ( ord_less_real @ one_one_real @ N )
% 5.31/5.48 => ( ord_less_real @ one_one_real @ ( times_times_real @ M2 @ N ) ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % less_1_mult
% 5.31/5.48 thf(fact_731_less__1__mult,axiom,
% 5.31/5.48 ! [M2: rat,N: rat] :
% 5.31/5.48 ( ( ord_less_rat @ one_one_rat @ M2 )
% 5.31/5.48 => ( ( ord_less_rat @ one_one_rat @ N )
% 5.31/5.48 => ( ord_less_rat @ one_one_rat @ ( times_times_rat @ M2 @ N ) ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % less_1_mult
% 5.31/5.48 thf(fact_732_less__1__mult,axiom,
% 5.31/5.48 ! [M2: nat,N: nat] :
% 5.31/5.48 ( ( ord_less_nat @ one_one_nat @ M2 )
% 5.31/5.48 => ( ( ord_less_nat @ one_one_nat @ N )
% 5.31/5.48 => ( ord_less_nat @ one_one_nat @ ( times_times_nat @ M2 @ N ) ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % less_1_mult
% 5.31/5.48 thf(fact_733_less__1__mult,axiom,
% 5.31/5.48 ! [M2: int,N: int] :
% 5.31/5.48 ( ( ord_less_int @ one_one_int @ M2 )
% 5.31/5.48 => ( ( ord_less_int @ one_one_int @ N )
% 5.31/5.48 => ( ord_less_int @ one_one_int @ ( times_times_int @ M2 @ N ) ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % less_1_mult
% 5.31/5.48 thf(fact_734_VEBT__internal_Ovalid_H_Osimps_I1_J,axiom,
% 5.31/5.48 ! [Uu: $o,Uv: $o,D: nat] :
% 5.31/5.48 ( ( vEBT_VEBT_valid @ ( vEBT_Leaf @ Uu @ Uv ) @ D )
% 5.31/5.48 = ( D = one_one_nat ) ) ).
% 5.31/5.48
% 5.31/5.48 % VEBT_internal.valid'.simps(1)
% 5.31/5.48 thf(fact_735_nat__induct__non__zero,axiom,
% 5.31/5.48 ! [N: nat,P2: nat > $o] :
% 5.31/5.48 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.48 => ( ( P2 @ one_one_nat )
% 5.31/5.48 => ( ! [N3: nat] :
% 5.31/5.48 ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 5.31/5.48 => ( ( P2 @ N3 )
% 5.31/5.48 => ( P2 @ ( suc @ N3 ) ) ) )
% 5.31/5.48 => ( P2 @ N ) ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % nat_induct_non_zero
% 5.31/5.48 thf(fact_736_order__le__imp__less__or__eq,axiom,
% 5.31/5.48 ! [X: real,Y: real] :
% 5.31/5.48 ( ( ord_less_eq_real @ X @ Y )
% 5.31/5.48 => ( ( ord_less_real @ X @ Y )
% 5.31/5.48 | ( X = Y ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % order_le_imp_less_or_eq
% 5.31/5.48 thf(fact_737_order__le__imp__less__or__eq,axiom,
% 5.31/5.48 ! [X: set_nat,Y: set_nat] :
% 5.31/5.48 ( ( ord_less_eq_set_nat @ X @ Y )
% 5.31/5.48 => ( ( ord_less_set_nat @ X @ Y )
% 5.31/5.48 | ( X = Y ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % order_le_imp_less_or_eq
% 5.31/5.48 thf(fact_738_order__le__imp__less__or__eq,axiom,
% 5.31/5.48 ! [X: rat,Y: rat] :
% 5.31/5.48 ( ( ord_less_eq_rat @ X @ Y )
% 5.31/5.48 => ( ( ord_less_rat @ X @ Y )
% 5.31/5.48 | ( X = Y ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % order_le_imp_less_or_eq
% 5.31/5.48 thf(fact_739_order__le__imp__less__or__eq,axiom,
% 5.31/5.48 ! [X: num,Y: num] :
% 5.31/5.48 ( ( ord_less_eq_num @ X @ Y )
% 5.31/5.48 => ( ( ord_less_num @ X @ Y )
% 5.31/5.48 | ( X = Y ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % order_le_imp_less_or_eq
% 5.31/5.48 thf(fact_740_order__le__imp__less__or__eq,axiom,
% 5.31/5.48 ! [X: nat,Y: nat] :
% 5.31/5.48 ( ( ord_less_eq_nat @ X @ Y )
% 5.31/5.48 => ( ( ord_less_nat @ X @ Y )
% 5.31/5.48 | ( X = Y ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % order_le_imp_less_or_eq
% 5.31/5.48 thf(fact_741_order__le__imp__less__or__eq,axiom,
% 5.31/5.48 ! [X: int,Y: int] :
% 5.31/5.48 ( ( ord_less_eq_int @ X @ Y )
% 5.31/5.48 => ( ( ord_less_int @ X @ Y )
% 5.31/5.48 | ( X = Y ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % order_le_imp_less_or_eq
% 5.31/5.48 thf(fact_742_linorder__le__less__linear,axiom,
% 5.31/5.48 ! [X: real,Y: real] :
% 5.31/5.48 ( ( ord_less_eq_real @ X @ Y )
% 5.31/5.48 | ( ord_less_real @ Y @ X ) ) ).
% 5.31/5.48
% 5.31/5.48 % linorder_le_less_linear
% 5.31/5.48 thf(fact_743_linorder__le__less__linear,axiom,
% 5.31/5.48 ! [X: rat,Y: rat] :
% 5.31/5.48 ( ( ord_less_eq_rat @ X @ Y )
% 5.31/5.48 | ( ord_less_rat @ Y @ X ) ) ).
% 5.31/5.48
% 5.31/5.48 % linorder_le_less_linear
% 5.31/5.48 thf(fact_744_linorder__le__less__linear,axiom,
% 5.31/5.48 ! [X: num,Y: num] :
% 5.31/5.48 ( ( ord_less_eq_num @ X @ Y )
% 5.31/5.48 | ( ord_less_num @ Y @ X ) ) ).
% 5.31/5.48
% 5.31/5.48 % linorder_le_less_linear
% 5.31/5.48 thf(fact_745_linorder__le__less__linear,axiom,
% 5.31/5.48 ! [X: nat,Y: nat] :
% 5.31/5.48 ( ( ord_less_eq_nat @ X @ Y )
% 5.31/5.48 | ( ord_less_nat @ Y @ X ) ) ).
% 5.31/5.48
% 5.31/5.48 % linorder_le_less_linear
% 5.31/5.48 thf(fact_746_linorder__le__less__linear,axiom,
% 5.31/5.48 ! [X: int,Y: int] :
% 5.31/5.48 ( ( ord_less_eq_int @ X @ Y )
% 5.31/5.48 | ( ord_less_int @ Y @ X ) ) ).
% 5.31/5.48
% 5.31/5.48 % linorder_le_less_linear
% 5.31/5.48 thf(fact_747_order__less__le__subst2,axiom,
% 5.31/5.48 ! [A: real,B: real,F2: real > real,C2: real] :
% 5.31/5.48 ( ( ord_less_real @ A @ B )
% 5.31/5.48 => ( ( ord_less_eq_real @ ( F2 @ B ) @ C2 )
% 5.31/5.48 => ( ! [X3: real,Y3: real] :
% 5.31/5.48 ( ( ord_less_real @ X3 @ Y3 )
% 5.31/5.48 => ( ord_less_real @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 5.31/5.48 => ( ord_less_real @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % order_less_le_subst2
% 5.31/5.48 thf(fact_748_order__less__le__subst2,axiom,
% 5.31/5.48 ! [A: rat,B: rat,F2: rat > real,C2: real] :
% 5.31/5.48 ( ( ord_less_rat @ A @ B )
% 5.31/5.48 => ( ( ord_less_eq_real @ ( F2 @ B ) @ C2 )
% 5.31/5.48 => ( ! [X3: rat,Y3: rat] :
% 5.31/5.48 ( ( ord_less_rat @ X3 @ Y3 )
% 5.31/5.48 => ( ord_less_real @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 5.31/5.48 => ( ord_less_real @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % order_less_le_subst2
% 5.31/5.48 thf(fact_749_order__less__le__subst2,axiom,
% 5.31/5.48 ! [A: num,B: num,F2: num > real,C2: real] :
% 5.31/5.48 ( ( ord_less_num @ A @ B )
% 5.31/5.48 => ( ( ord_less_eq_real @ ( F2 @ B ) @ C2 )
% 5.31/5.48 => ( ! [X3: num,Y3: num] :
% 5.31/5.48 ( ( ord_less_num @ X3 @ Y3 )
% 5.31/5.48 => ( ord_less_real @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 5.31/5.48 => ( ord_less_real @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % order_less_le_subst2
% 5.31/5.48 thf(fact_750_order__less__le__subst2,axiom,
% 5.31/5.48 ! [A: nat,B: nat,F2: nat > real,C2: real] :
% 5.31/5.48 ( ( ord_less_nat @ A @ B )
% 5.31/5.48 => ( ( ord_less_eq_real @ ( F2 @ B ) @ C2 )
% 5.31/5.48 => ( ! [X3: nat,Y3: nat] :
% 5.31/5.48 ( ( ord_less_nat @ X3 @ Y3 )
% 5.31/5.48 => ( ord_less_real @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 5.31/5.48 => ( ord_less_real @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % order_less_le_subst2
% 5.31/5.48 thf(fact_751_order__less__le__subst2,axiom,
% 5.31/5.48 ! [A: int,B: int,F2: int > real,C2: real] :
% 5.31/5.48 ( ( ord_less_int @ A @ B )
% 5.31/5.48 => ( ( ord_less_eq_real @ ( F2 @ B ) @ C2 )
% 5.31/5.48 => ( ! [X3: int,Y3: int] :
% 5.31/5.48 ( ( ord_less_int @ X3 @ Y3 )
% 5.31/5.48 => ( ord_less_real @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 5.31/5.48 => ( ord_less_real @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % order_less_le_subst2
% 5.31/5.48 thf(fact_752_order__less__le__subst2,axiom,
% 5.31/5.48 ! [A: real,B: real,F2: real > rat,C2: rat] :
% 5.31/5.48 ( ( ord_less_real @ A @ B )
% 5.31/5.48 => ( ( ord_less_eq_rat @ ( F2 @ B ) @ C2 )
% 5.31/5.48 => ( ! [X3: real,Y3: real] :
% 5.31/5.48 ( ( ord_less_real @ X3 @ Y3 )
% 5.31/5.48 => ( ord_less_rat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 5.31/5.48 => ( ord_less_rat @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % order_less_le_subst2
% 5.31/5.48 thf(fact_753_order__less__le__subst2,axiom,
% 5.31/5.48 ! [A: rat,B: rat,F2: rat > rat,C2: rat] :
% 5.31/5.48 ( ( ord_less_rat @ A @ B )
% 5.31/5.48 => ( ( ord_less_eq_rat @ ( F2 @ B ) @ C2 )
% 5.31/5.48 => ( ! [X3: rat,Y3: rat] :
% 5.31/5.48 ( ( ord_less_rat @ X3 @ Y3 )
% 5.31/5.48 => ( ord_less_rat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 5.31/5.48 => ( ord_less_rat @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % order_less_le_subst2
% 5.31/5.48 thf(fact_754_order__less__le__subst2,axiom,
% 5.31/5.48 ! [A: num,B: num,F2: num > rat,C2: rat] :
% 5.31/5.48 ( ( ord_less_num @ A @ B )
% 5.31/5.48 => ( ( ord_less_eq_rat @ ( F2 @ B ) @ C2 )
% 5.31/5.48 => ( ! [X3: num,Y3: num] :
% 5.31/5.48 ( ( ord_less_num @ X3 @ Y3 )
% 5.31/5.48 => ( ord_less_rat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 5.31/5.48 => ( ord_less_rat @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % order_less_le_subst2
% 5.31/5.48 thf(fact_755_order__less__le__subst2,axiom,
% 5.31/5.48 ! [A: nat,B: nat,F2: nat > rat,C2: rat] :
% 5.31/5.48 ( ( ord_less_nat @ A @ B )
% 5.31/5.48 => ( ( ord_less_eq_rat @ ( F2 @ B ) @ C2 )
% 5.31/5.48 => ( ! [X3: nat,Y3: nat] :
% 5.31/5.48 ( ( ord_less_nat @ X3 @ Y3 )
% 5.31/5.48 => ( ord_less_rat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 5.31/5.48 => ( ord_less_rat @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % order_less_le_subst2
% 5.31/5.48 thf(fact_756_order__less__le__subst2,axiom,
% 5.31/5.48 ! [A: int,B: int,F2: int > rat,C2: rat] :
% 5.31/5.48 ( ( ord_less_int @ A @ B )
% 5.31/5.48 => ( ( ord_less_eq_rat @ ( F2 @ B ) @ C2 )
% 5.31/5.48 => ( ! [X3: int,Y3: int] :
% 5.31/5.48 ( ( ord_less_int @ X3 @ Y3 )
% 5.31/5.48 => ( ord_less_rat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 5.31/5.48 => ( ord_less_rat @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % order_less_le_subst2
% 5.31/5.48 thf(fact_757_order__less__le__subst1,axiom,
% 5.31/5.48 ! [A: real,F2: rat > real,B: rat,C2: rat] :
% 5.31/5.48 ( ( ord_less_real @ A @ ( F2 @ B ) )
% 5.31/5.48 => ( ( ord_less_eq_rat @ B @ C2 )
% 5.31/5.48 => ( ! [X3: rat,Y3: rat] :
% 5.31/5.48 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 5.31/5.48 => ( ord_less_eq_real @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 5.31/5.48 => ( ord_less_real @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % order_less_le_subst1
% 5.31/5.48 thf(fact_758_order__less__le__subst1,axiom,
% 5.31/5.48 ! [A: rat,F2: rat > rat,B: rat,C2: rat] :
% 5.31/5.48 ( ( ord_less_rat @ A @ ( F2 @ B ) )
% 5.31/5.48 => ( ( ord_less_eq_rat @ B @ C2 )
% 5.31/5.48 => ( ! [X3: rat,Y3: rat] :
% 5.31/5.48 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 5.31/5.48 => ( ord_less_eq_rat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 5.31/5.48 => ( ord_less_rat @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % order_less_le_subst1
% 5.31/5.48 thf(fact_759_order__less__le__subst1,axiom,
% 5.31/5.48 ! [A: num,F2: rat > num,B: rat,C2: rat] :
% 5.31/5.48 ( ( ord_less_num @ A @ ( F2 @ B ) )
% 5.31/5.48 => ( ( ord_less_eq_rat @ B @ C2 )
% 5.31/5.48 => ( ! [X3: rat,Y3: rat] :
% 5.31/5.48 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 5.31/5.48 => ( ord_less_eq_num @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 5.31/5.48 => ( ord_less_num @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % order_less_le_subst1
% 5.31/5.48 thf(fact_760_order__less__le__subst1,axiom,
% 5.31/5.48 ! [A: nat,F2: rat > nat,B: rat,C2: rat] :
% 5.31/5.48 ( ( ord_less_nat @ A @ ( F2 @ B ) )
% 5.31/5.48 => ( ( ord_less_eq_rat @ B @ C2 )
% 5.31/5.48 => ( ! [X3: rat,Y3: rat] :
% 5.31/5.48 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 5.31/5.48 => ( ord_less_eq_nat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 5.31/5.48 => ( ord_less_nat @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % order_less_le_subst1
% 5.31/5.48 thf(fact_761_order__less__le__subst1,axiom,
% 5.31/5.48 ! [A: int,F2: rat > int,B: rat,C2: rat] :
% 5.31/5.48 ( ( ord_less_int @ A @ ( F2 @ B ) )
% 5.31/5.48 => ( ( ord_less_eq_rat @ B @ C2 )
% 5.31/5.48 => ( ! [X3: rat,Y3: rat] :
% 5.31/5.48 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 5.31/5.48 => ( ord_less_eq_int @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 5.31/5.48 => ( ord_less_int @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % order_less_le_subst1
% 5.31/5.48 thf(fact_762_order__less__le__subst1,axiom,
% 5.31/5.48 ! [A: real,F2: num > real,B: num,C2: num] :
% 5.31/5.48 ( ( ord_less_real @ A @ ( F2 @ B ) )
% 5.31/5.48 => ( ( ord_less_eq_num @ B @ C2 )
% 5.31/5.48 => ( ! [X3: num,Y3: num] :
% 5.31/5.48 ( ( ord_less_eq_num @ X3 @ Y3 )
% 5.31/5.48 => ( ord_less_eq_real @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 5.31/5.48 => ( ord_less_real @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % order_less_le_subst1
% 5.31/5.48 thf(fact_763_order__less__le__subst1,axiom,
% 5.31/5.48 ! [A: rat,F2: num > rat,B: num,C2: num] :
% 5.31/5.48 ( ( ord_less_rat @ A @ ( F2 @ B ) )
% 5.31/5.48 => ( ( ord_less_eq_num @ B @ C2 )
% 5.31/5.48 => ( ! [X3: num,Y3: num] :
% 5.31/5.48 ( ( ord_less_eq_num @ X3 @ Y3 )
% 5.31/5.48 => ( ord_less_eq_rat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 5.31/5.48 => ( ord_less_rat @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % order_less_le_subst1
% 5.31/5.48 thf(fact_764_order__less__le__subst1,axiom,
% 5.31/5.48 ! [A: num,F2: num > num,B: num,C2: num] :
% 5.31/5.48 ( ( ord_less_num @ A @ ( F2 @ B ) )
% 5.31/5.48 => ( ( ord_less_eq_num @ B @ C2 )
% 5.31/5.48 => ( ! [X3: num,Y3: num] :
% 5.31/5.48 ( ( ord_less_eq_num @ X3 @ Y3 )
% 5.31/5.48 => ( ord_less_eq_num @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 5.31/5.48 => ( ord_less_num @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % order_less_le_subst1
% 5.31/5.48 thf(fact_765_order__less__le__subst1,axiom,
% 5.31/5.48 ! [A: nat,F2: num > nat,B: num,C2: num] :
% 5.31/5.48 ( ( ord_less_nat @ A @ ( F2 @ B ) )
% 5.31/5.48 => ( ( ord_less_eq_num @ B @ C2 )
% 5.31/5.48 => ( ! [X3: num,Y3: num] :
% 5.31/5.48 ( ( ord_less_eq_num @ X3 @ Y3 )
% 5.31/5.48 => ( ord_less_eq_nat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 5.31/5.48 => ( ord_less_nat @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % order_less_le_subst1
% 5.31/5.48 thf(fact_766_order__less__le__subst1,axiom,
% 5.31/5.48 ! [A: int,F2: num > int,B: num,C2: num] :
% 5.31/5.48 ( ( ord_less_int @ A @ ( F2 @ B ) )
% 5.31/5.48 => ( ( ord_less_eq_num @ B @ C2 )
% 5.31/5.48 => ( ! [X3: num,Y3: num] :
% 5.31/5.48 ( ( ord_less_eq_num @ X3 @ Y3 )
% 5.31/5.48 => ( ord_less_eq_int @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 5.31/5.48 => ( ord_less_int @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % order_less_le_subst1
% 5.31/5.48 thf(fact_767_order__le__less__subst2,axiom,
% 5.31/5.48 ! [A: rat,B: rat,F2: rat > real,C2: real] :
% 5.31/5.48 ( ( ord_less_eq_rat @ A @ B )
% 5.31/5.48 => ( ( ord_less_real @ ( F2 @ B ) @ C2 )
% 5.31/5.48 => ( ! [X3: rat,Y3: rat] :
% 5.31/5.48 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 5.31/5.48 => ( ord_less_eq_real @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 5.31/5.48 => ( ord_less_real @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % order_le_less_subst2
% 5.31/5.48 thf(fact_768_order__le__less__subst2,axiom,
% 5.31/5.48 ! [A: rat,B: rat,F2: rat > rat,C2: rat] :
% 5.31/5.48 ( ( ord_less_eq_rat @ A @ B )
% 5.31/5.48 => ( ( ord_less_rat @ ( F2 @ B ) @ C2 )
% 5.31/5.48 => ( ! [X3: rat,Y3: rat] :
% 5.31/5.48 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 5.31/5.48 => ( ord_less_eq_rat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 5.31/5.48 => ( ord_less_rat @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % order_le_less_subst2
% 5.31/5.48 thf(fact_769_order__le__less__subst2,axiom,
% 5.31/5.48 ! [A: rat,B: rat,F2: rat > num,C2: num] :
% 5.31/5.48 ( ( ord_less_eq_rat @ A @ B )
% 5.31/5.48 => ( ( ord_less_num @ ( F2 @ B ) @ C2 )
% 5.31/5.48 => ( ! [X3: rat,Y3: rat] :
% 5.31/5.48 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 5.31/5.48 => ( ord_less_eq_num @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 5.31/5.48 => ( ord_less_num @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % order_le_less_subst2
% 5.31/5.48 thf(fact_770_order__le__less__subst2,axiom,
% 5.31/5.48 ! [A: rat,B: rat,F2: rat > nat,C2: nat] :
% 5.31/5.48 ( ( ord_less_eq_rat @ A @ B )
% 5.31/5.48 => ( ( ord_less_nat @ ( F2 @ B ) @ C2 )
% 5.31/5.48 => ( ! [X3: rat,Y3: rat] :
% 5.31/5.48 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 5.31/5.48 => ( ord_less_eq_nat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 5.31/5.48 => ( ord_less_nat @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % order_le_less_subst2
% 5.31/5.48 thf(fact_771_order__le__less__subst2,axiom,
% 5.31/5.48 ! [A: rat,B: rat,F2: rat > int,C2: int] :
% 5.31/5.48 ( ( ord_less_eq_rat @ A @ B )
% 5.31/5.48 => ( ( ord_less_int @ ( F2 @ B ) @ C2 )
% 5.31/5.48 => ( ! [X3: rat,Y3: rat] :
% 5.31/5.48 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 5.31/5.48 => ( ord_less_eq_int @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 5.31/5.48 => ( ord_less_int @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 5.31/5.48
% 5.31/5.48 % order_le_less_subst2
% 5.31/5.48 thf(fact_772_order__le__less__subst2,axiom,
% 5.31/5.48 ! [A: num,B: num,F2: num > real,C2: real] :
% 5.31/5.48 ( ( ord_less_eq_num @ A @ B )
% 5.31/5.48 => ( ( ord_less_real @ ( F2 @ B ) @ C2 )
% 5.31/5.48 => ( ! [X3: num,Y3: num] :
% 5.31/5.48 ( ( ord_less_eq_num @ X3 @ Y3 )
% 5.31/5.49 => ( ord_less_eq_real @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 5.31/5.49 => ( ord_less_real @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % order_le_less_subst2
% 5.31/5.49 thf(fact_773_order__le__less__subst2,axiom,
% 5.31/5.49 ! [A: num,B: num,F2: num > rat,C2: rat] :
% 5.31/5.49 ( ( ord_less_eq_num @ A @ B )
% 5.31/5.49 => ( ( ord_less_rat @ ( F2 @ B ) @ C2 )
% 5.31/5.49 => ( ! [X3: num,Y3: num] :
% 5.31/5.49 ( ( ord_less_eq_num @ X3 @ Y3 )
% 5.31/5.49 => ( ord_less_eq_rat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 5.31/5.49 => ( ord_less_rat @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % order_le_less_subst2
% 5.31/5.49 thf(fact_774_order__le__less__subst2,axiom,
% 5.31/5.49 ! [A: num,B: num,F2: num > num,C2: num] :
% 5.31/5.49 ( ( ord_less_eq_num @ A @ B )
% 5.31/5.49 => ( ( ord_less_num @ ( F2 @ B ) @ C2 )
% 5.31/5.49 => ( ! [X3: num,Y3: num] :
% 5.31/5.49 ( ( ord_less_eq_num @ X3 @ Y3 )
% 5.31/5.49 => ( ord_less_eq_num @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 5.31/5.49 => ( ord_less_num @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % order_le_less_subst2
% 5.31/5.49 thf(fact_775_order__le__less__subst2,axiom,
% 5.31/5.49 ! [A: num,B: num,F2: num > nat,C2: nat] :
% 5.31/5.49 ( ( ord_less_eq_num @ A @ B )
% 5.31/5.49 => ( ( ord_less_nat @ ( F2 @ B ) @ C2 )
% 5.31/5.49 => ( ! [X3: num,Y3: num] :
% 5.31/5.49 ( ( ord_less_eq_num @ X3 @ Y3 )
% 5.31/5.49 => ( ord_less_eq_nat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 5.31/5.49 => ( ord_less_nat @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % order_le_less_subst2
% 5.31/5.49 thf(fact_776_order__le__less__subst2,axiom,
% 5.31/5.49 ! [A: num,B: num,F2: num > int,C2: int] :
% 5.31/5.49 ( ( ord_less_eq_num @ A @ B )
% 5.31/5.49 => ( ( ord_less_int @ ( F2 @ B ) @ C2 )
% 5.31/5.49 => ( ! [X3: num,Y3: num] :
% 5.31/5.49 ( ( ord_less_eq_num @ X3 @ Y3 )
% 5.31/5.49 => ( ord_less_eq_int @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 5.31/5.49 => ( ord_less_int @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % order_le_less_subst2
% 5.31/5.49 thf(fact_777_order__le__less__subst1,axiom,
% 5.31/5.49 ! [A: real,F2: real > real,B: real,C2: real] :
% 5.31/5.49 ( ( ord_less_eq_real @ A @ ( F2 @ B ) )
% 5.31/5.49 => ( ( ord_less_real @ B @ C2 )
% 5.31/5.49 => ( ! [X3: real,Y3: real] :
% 5.31/5.49 ( ( ord_less_real @ X3 @ Y3 )
% 5.31/5.49 => ( ord_less_real @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 5.31/5.49 => ( ord_less_real @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % order_le_less_subst1
% 5.31/5.49 thf(fact_778_order__le__less__subst1,axiom,
% 5.31/5.49 ! [A: real,F2: rat > real,B: rat,C2: rat] :
% 5.31/5.49 ( ( ord_less_eq_real @ A @ ( F2 @ B ) )
% 5.31/5.49 => ( ( ord_less_rat @ B @ C2 )
% 5.31/5.49 => ( ! [X3: rat,Y3: rat] :
% 5.31/5.49 ( ( ord_less_rat @ X3 @ Y3 )
% 5.31/5.49 => ( ord_less_real @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 5.31/5.49 => ( ord_less_real @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % order_le_less_subst1
% 5.31/5.49 thf(fact_779_order__le__less__subst1,axiom,
% 5.31/5.49 ! [A: real,F2: num > real,B: num,C2: num] :
% 5.31/5.49 ( ( ord_less_eq_real @ A @ ( F2 @ B ) )
% 5.31/5.49 => ( ( ord_less_num @ B @ C2 )
% 5.31/5.49 => ( ! [X3: num,Y3: num] :
% 5.31/5.49 ( ( ord_less_num @ X3 @ Y3 )
% 5.31/5.49 => ( ord_less_real @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 5.31/5.49 => ( ord_less_real @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % order_le_less_subst1
% 5.31/5.49 thf(fact_780_order__le__less__subst1,axiom,
% 5.31/5.49 ! [A: real,F2: nat > real,B: nat,C2: nat] :
% 5.31/5.49 ( ( ord_less_eq_real @ A @ ( F2 @ B ) )
% 5.31/5.49 => ( ( ord_less_nat @ B @ C2 )
% 5.31/5.49 => ( ! [X3: nat,Y3: nat] :
% 5.31/5.49 ( ( ord_less_nat @ X3 @ Y3 )
% 5.31/5.49 => ( ord_less_real @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 5.31/5.49 => ( ord_less_real @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % order_le_less_subst1
% 5.31/5.49 thf(fact_781_order__le__less__subst1,axiom,
% 5.31/5.49 ! [A: real,F2: int > real,B: int,C2: int] :
% 5.31/5.49 ( ( ord_less_eq_real @ A @ ( F2 @ B ) )
% 5.31/5.49 => ( ( ord_less_int @ B @ C2 )
% 5.31/5.49 => ( ! [X3: int,Y3: int] :
% 5.31/5.49 ( ( ord_less_int @ X3 @ Y3 )
% 5.31/5.49 => ( ord_less_real @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 5.31/5.49 => ( ord_less_real @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % order_le_less_subst1
% 5.31/5.49 thf(fact_782_order__le__less__subst1,axiom,
% 5.31/5.49 ! [A: rat,F2: real > rat,B: real,C2: real] :
% 5.31/5.49 ( ( ord_less_eq_rat @ A @ ( F2 @ B ) )
% 5.31/5.49 => ( ( ord_less_real @ B @ C2 )
% 5.31/5.49 => ( ! [X3: real,Y3: real] :
% 5.31/5.49 ( ( ord_less_real @ X3 @ Y3 )
% 5.31/5.49 => ( ord_less_rat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 5.31/5.49 => ( ord_less_rat @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % order_le_less_subst1
% 5.31/5.49 thf(fact_783_order__le__less__subst1,axiom,
% 5.31/5.49 ! [A: rat,F2: rat > rat,B: rat,C2: rat] :
% 5.31/5.49 ( ( ord_less_eq_rat @ A @ ( F2 @ B ) )
% 5.31/5.49 => ( ( ord_less_rat @ B @ C2 )
% 5.31/5.49 => ( ! [X3: rat,Y3: rat] :
% 5.31/5.49 ( ( ord_less_rat @ X3 @ Y3 )
% 5.31/5.49 => ( ord_less_rat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 5.31/5.49 => ( ord_less_rat @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % order_le_less_subst1
% 5.31/5.49 thf(fact_784_order__le__less__subst1,axiom,
% 5.31/5.49 ! [A: rat,F2: num > rat,B: num,C2: num] :
% 5.31/5.49 ( ( ord_less_eq_rat @ A @ ( F2 @ B ) )
% 5.31/5.49 => ( ( ord_less_num @ B @ C2 )
% 5.31/5.49 => ( ! [X3: num,Y3: num] :
% 5.31/5.49 ( ( ord_less_num @ X3 @ Y3 )
% 5.31/5.49 => ( ord_less_rat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 5.31/5.49 => ( ord_less_rat @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % order_le_less_subst1
% 5.31/5.49 thf(fact_785_order__le__less__subst1,axiom,
% 5.31/5.49 ! [A: rat,F2: nat > rat,B: nat,C2: nat] :
% 5.31/5.49 ( ( ord_less_eq_rat @ A @ ( F2 @ B ) )
% 5.31/5.49 => ( ( ord_less_nat @ B @ C2 )
% 5.31/5.49 => ( ! [X3: nat,Y3: nat] :
% 5.31/5.49 ( ( ord_less_nat @ X3 @ Y3 )
% 5.31/5.49 => ( ord_less_rat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 5.31/5.49 => ( ord_less_rat @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % order_le_less_subst1
% 5.31/5.49 thf(fact_786_order__le__less__subst1,axiom,
% 5.31/5.49 ! [A: rat,F2: int > rat,B: int,C2: int] :
% 5.31/5.49 ( ( ord_less_eq_rat @ A @ ( F2 @ B ) )
% 5.31/5.49 => ( ( ord_less_int @ B @ C2 )
% 5.31/5.49 => ( ! [X3: int,Y3: int] :
% 5.31/5.49 ( ( ord_less_int @ X3 @ Y3 )
% 5.31/5.49 => ( ord_less_rat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 5.31/5.49 => ( ord_less_rat @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % order_le_less_subst1
% 5.31/5.49 thf(fact_787_order__less__le__trans,axiom,
% 5.31/5.49 ! [X: real,Y: real,Z3: real] :
% 5.31/5.49 ( ( ord_less_real @ X @ Y )
% 5.31/5.49 => ( ( ord_less_eq_real @ Y @ Z3 )
% 5.31/5.49 => ( ord_less_real @ X @ Z3 ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % order_less_le_trans
% 5.31/5.49 thf(fact_788_order__less__le__trans,axiom,
% 5.31/5.49 ! [X: set_nat,Y: set_nat,Z3: set_nat] :
% 5.31/5.49 ( ( ord_less_set_nat @ X @ Y )
% 5.31/5.49 => ( ( ord_less_eq_set_nat @ Y @ Z3 )
% 5.31/5.49 => ( ord_less_set_nat @ X @ Z3 ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % order_less_le_trans
% 5.31/5.49 thf(fact_789_order__less__le__trans,axiom,
% 5.31/5.49 ! [X: rat,Y: rat,Z3: rat] :
% 5.31/5.49 ( ( ord_less_rat @ X @ Y )
% 5.31/5.49 => ( ( ord_less_eq_rat @ Y @ Z3 )
% 5.31/5.49 => ( ord_less_rat @ X @ Z3 ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % order_less_le_trans
% 5.31/5.49 thf(fact_790_order__less__le__trans,axiom,
% 5.31/5.49 ! [X: num,Y: num,Z3: num] :
% 5.31/5.49 ( ( ord_less_num @ X @ Y )
% 5.31/5.49 => ( ( ord_less_eq_num @ Y @ Z3 )
% 5.31/5.49 => ( ord_less_num @ X @ Z3 ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % order_less_le_trans
% 5.31/5.49 thf(fact_791_order__less__le__trans,axiom,
% 5.31/5.49 ! [X: nat,Y: nat,Z3: nat] :
% 5.31/5.49 ( ( ord_less_nat @ X @ Y )
% 5.31/5.49 => ( ( ord_less_eq_nat @ Y @ Z3 )
% 5.31/5.49 => ( ord_less_nat @ X @ Z3 ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % order_less_le_trans
% 5.31/5.49 thf(fact_792_order__less__le__trans,axiom,
% 5.31/5.49 ! [X: int,Y: int,Z3: int] :
% 5.31/5.49 ( ( ord_less_int @ X @ Y )
% 5.31/5.49 => ( ( ord_less_eq_int @ Y @ Z3 )
% 5.31/5.49 => ( ord_less_int @ X @ Z3 ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % order_less_le_trans
% 5.31/5.49 thf(fact_793_order__le__less__trans,axiom,
% 5.31/5.49 ! [X: real,Y: real,Z3: real] :
% 5.31/5.49 ( ( ord_less_eq_real @ X @ Y )
% 5.31/5.49 => ( ( ord_less_real @ Y @ Z3 )
% 5.31/5.49 => ( ord_less_real @ X @ Z3 ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % order_le_less_trans
% 5.31/5.49 thf(fact_794_order__le__less__trans,axiom,
% 5.31/5.49 ! [X: set_nat,Y: set_nat,Z3: set_nat] :
% 5.31/5.49 ( ( ord_less_eq_set_nat @ X @ Y )
% 5.31/5.49 => ( ( ord_less_set_nat @ Y @ Z3 )
% 5.31/5.49 => ( ord_less_set_nat @ X @ Z3 ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % order_le_less_trans
% 5.31/5.49 thf(fact_795_order__le__less__trans,axiom,
% 5.31/5.49 ! [X: rat,Y: rat,Z3: rat] :
% 5.31/5.49 ( ( ord_less_eq_rat @ X @ Y )
% 5.31/5.49 => ( ( ord_less_rat @ Y @ Z3 )
% 5.31/5.49 => ( ord_less_rat @ X @ Z3 ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % order_le_less_trans
% 5.31/5.49 thf(fact_796_order__le__less__trans,axiom,
% 5.31/5.49 ! [X: num,Y: num,Z3: num] :
% 5.31/5.49 ( ( ord_less_eq_num @ X @ Y )
% 5.31/5.49 => ( ( ord_less_num @ Y @ Z3 )
% 5.31/5.49 => ( ord_less_num @ X @ Z3 ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % order_le_less_trans
% 5.31/5.49 thf(fact_797_order__le__less__trans,axiom,
% 5.31/5.49 ! [X: nat,Y: nat,Z3: nat] :
% 5.31/5.49 ( ( ord_less_eq_nat @ X @ Y )
% 5.31/5.49 => ( ( ord_less_nat @ Y @ Z3 )
% 5.31/5.49 => ( ord_less_nat @ X @ Z3 ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % order_le_less_trans
% 5.31/5.49 thf(fact_798_order__le__less__trans,axiom,
% 5.31/5.49 ! [X: int,Y: int,Z3: int] :
% 5.31/5.49 ( ( ord_less_eq_int @ X @ Y )
% 5.31/5.49 => ( ( ord_less_int @ Y @ Z3 )
% 5.31/5.49 => ( ord_less_int @ X @ Z3 ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % order_le_less_trans
% 5.31/5.49 thf(fact_799_order__neq__le__trans,axiom,
% 5.31/5.49 ! [A: real,B: real] :
% 5.31/5.49 ( ( A != B )
% 5.31/5.49 => ( ( ord_less_eq_real @ A @ B )
% 5.31/5.49 => ( ord_less_real @ A @ B ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % order_neq_le_trans
% 5.31/5.49 thf(fact_800_order__neq__le__trans,axiom,
% 5.31/5.49 ! [A: set_nat,B: set_nat] :
% 5.31/5.49 ( ( A != B )
% 5.31/5.49 => ( ( ord_less_eq_set_nat @ A @ B )
% 5.31/5.49 => ( ord_less_set_nat @ A @ B ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % order_neq_le_trans
% 5.31/5.49 thf(fact_801_order__neq__le__trans,axiom,
% 5.31/5.49 ! [A: rat,B: rat] :
% 5.31/5.49 ( ( A != B )
% 5.31/5.49 => ( ( ord_less_eq_rat @ A @ B )
% 5.31/5.49 => ( ord_less_rat @ A @ B ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % order_neq_le_trans
% 5.31/5.49 thf(fact_802_order__neq__le__trans,axiom,
% 5.31/5.49 ! [A: num,B: num] :
% 5.31/5.49 ( ( A != B )
% 5.31/5.49 => ( ( ord_less_eq_num @ A @ B )
% 5.31/5.49 => ( ord_less_num @ A @ B ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % order_neq_le_trans
% 5.31/5.49 thf(fact_803_order__neq__le__trans,axiom,
% 5.31/5.49 ! [A: nat,B: nat] :
% 5.31/5.49 ( ( A != B )
% 5.31/5.49 => ( ( ord_less_eq_nat @ A @ B )
% 5.31/5.49 => ( ord_less_nat @ A @ B ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % order_neq_le_trans
% 5.31/5.49 thf(fact_804_order__neq__le__trans,axiom,
% 5.31/5.49 ! [A: int,B: int] :
% 5.31/5.49 ( ( A != B )
% 5.31/5.49 => ( ( ord_less_eq_int @ A @ B )
% 5.31/5.49 => ( ord_less_int @ A @ B ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % order_neq_le_trans
% 5.31/5.49 thf(fact_805_order__le__neq__trans,axiom,
% 5.31/5.49 ! [A: real,B: real] :
% 5.31/5.49 ( ( ord_less_eq_real @ A @ B )
% 5.31/5.49 => ( ( A != B )
% 5.31/5.49 => ( ord_less_real @ A @ B ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % order_le_neq_trans
% 5.31/5.49 thf(fact_806_order__le__neq__trans,axiom,
% 5.31/5.49 ! [A: set_nat,B: set_nat] :
% 5.31/5.49 ( ( ord_less_eq_set_nat @ A @ B )
% 5.31/5.49 => ( ( A != B )
% 5.31/5.49 => ( ord_less_set_nat @ A @ B ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % order_le_neq_trans
% 5.31/5.49 thf(fact_807_order__le__neq__trans,axiom,
% 5.31/5.49 ! [A: rat,B: rat] :
% 5.31/5.49 ( ( ord_less_eq_rat @ A @ B )
% 5.31/5.49 => ( ( A != B )
% 5.31/5.49 => ( ord_less_rat @ A @ B ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % order_le_neq_trans
% 5.31/5.49 thf(fact_808_order__le__neq__trans,axiom,
% 5.31/5.49 ! [A: num,B: num] :
% 5.31/5.49 ( ( ord_less_eq_num @ A @ B )
% 5.31/5.49 => ( ( A != B )
% 5.31/5.49 => ( ord_less_num @ A @ B ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % order_le_neq_trans
% 5.31/5.49 thf(fact_809_order__le__neq__trans,axiom,
% 5.31/5.49 ! [A: nat,B: nat] :
% 5.31/5.49 ( ( ord_less_eq_nat @ A @ B )
% 5.31/5.49 => ( ( A != B )
% 5.31/5.49 => ( ord_less_nat @ A @ B ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % order_le_neq_trans
% 5.31/5.49 thf(fact_810_order__le__neq__trans,axiom,
% 5.31/5.49 ! [A: int,B: int] :
% 5.31/5.49 ( ( ord_less_eq_int @ A @ B )
% 5.31/5.49 => ( ( A != B )
% 5.31/5.49 => ( ord_less_int @ A @ B ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % order_le_neq_trans
% 5.31/5.49 thf(fact_811_order__less__imp__le,axiom,
% 5.31/5.49 ! [X: real,Y: real] :
% 5.31/5.49 ( ( ord_less_real @ X @ Y )
% 5.31/5.49 => ( ord_less_eq_real @ X @ Y ) ) ).
% 5.31/5.49
% 5.31/5.49 % order_less_imp_le
% 5.31/5.49 thf(fact_812_order__less__imp__le,axiom,
% 5.31/5.49 ! [X: set_nat,Y: set_nat] :
% 5.31/5.49 ( ( ord_less_set_nat @ X @ Y )
% 5.31/5.49 => ( ord_less_eq_set_nat @ X @ Y ) ) ).
% 5.31/5.49
% 5.31/5.49 % order_less_imp_le
% 5.31/5.49 thf(fact_813_order__less__imp__le,axiom,
% 5.31/5.49 ! [X: rat,Y: rat] :
% 5.31/5.49 ( ( ord_less_rat @ X @ Y )
% 5.31/5.49 => ( ord_less_eq_rat @ X @ Y ) ) ).
% 5.31/5.49
% 5.31/5.49 % order_less_imp_le
% 5.31/5.49 thf(fact_814_order__less__imp__le,axiom,
% 5.31/5.49 ! [X: num,Y: num] :
% 5.31/5.49 ( ( ord_less_num @ X @ Y )
% 5.31/5.49 => ( ord_less_eq_num @ X @ Y ) ) ).
% 5.31/5.49
% 5.31/5.49 % order_less_imp_le
% 5.31/5.49 thf(fact_815_order__less__imp__le,axiom,
% 5.31/5.49 ! [X: nat,Y: nat] :
% 5.31/5.49 ( ( ord_less_nat @ X @ Y )
% 5.31/5.49 => ( ord_less_eq_nat @ X @ Y ) ) ).
% 5.31/5.49
% 5.31/5.49 % order_less_imp_le
% 5.31/5.49 thf(fact_816_order__less__imp__le,axiom,
% 5.31/5.49 ! [X: int,Y: int] :
% 5.31/5.49 ( ( ord_less_int @ X @ Y )
% 5.31/5.49 => ( ord_less_eq_int @ X @ Y ) ) ).
% 5.31/5.49
% 5.31/5.49 % order_less_imp_le
% 5.31/5.49 thf(fact_817_linorder__not__less,axiom,
% 5.31/5.49 ! [X: real,Y: real] :
% 5.31/5.49 ( ( ~ ( ord_less_real @ X @ Y ) )
% 5.31/5.49 = ( ord_less_eq_real @ Y @ X ) ) ).
% 5.31/5.49
% 5.31/5.49 % linorder_not_less
% 5.31/5.49 thf(fact_818_linorder__not__less,axiom,
% 5.31/5.49 ! [X: rat,Y: rat] :
% 5.31/5.49 ( ( ~ ( ord_less_rat @ X @ Y ) )
% 5.31/5.49 = ( ord_less_eq_rat @ Y @ X ) ) ).
% 5.31/5.49
% 5.31/5.49 % linorder_not_less
% 5.31/5.49 thf(fact_819_linorder__not__less,axiom,
% 5.31/5.49 ! [X: num,Y: num] :
% 5.31/5.49 ( ( ~ ( ord_less_num @ X @ Y ) )
% 5.31/5.49 = ( ord_less_eq_num @ Y @ X ) ) ).
% 5.31/5.49
% 5.31/5.49 % linorder_not_less
% 5.31/5.49 thf(fact_820_linorder__not__less,axiom,
% 5.31/5.49 ! [X: nat,Y: nat] :
% 5.31/5.49 ( ( ~ ( ord_less_nat @ X @ Y ) )
% 5.31/5.49 = ( ord_less_eq_nat @ Y @ X ) ) ).
% 5.31/5.49
% 5.31/5.49 % linorder_not_less
% 5.31/5.49 thf(fact_821_linorder__not__less,axiom,
% 5.31/5.49 ! [X: int,Y: int] :
% 5.31/5.49 ( ( ~ ( ord_less_int @ X @ Y ) )
% 5.31/5.49 = ( ord_less_eq_int @ Y @ X ) ) ).
% 5.31/5.49
% 5.31/5.49 % linorder_not_less
% 5.31/5.49 thf(fact_822_linorder__not__le,axiom,
% 5.31/5.49 ! [X: real,Y: real] :
% 5.31/5.49 ( ( ~ ( ord_less_eq_real @ X @ Y ) )
% 5.31/5.49 = ( ord_less_real @ Y @ X ) ) ).
% 5.31/5.49
% 5.31/5.49 % linorder_not_le
% 5.31/5.49 thf(fact_823_linorder__not__le,axiom,
% 5.31/5.49 ! [X: rat,Y: rat] :
% 5.31/5.49 ( ( ~ ( ord_less_eq_rat @ X @ Y ) )
% 5.31/5.49 = ( ord_less_rat @ Y @ X ) ) ).
% 5.31/5.49
% 5.31/5.49 % linorder_not_le
% 5.31/5.49 thf(fact_824_linorder__not__le,axiom,
% 5.31/5.49 ! [X: num,Y: num] :
% 5.31/5.49 ( ( ~ ( ord_less_eq_num @ X @ Y ) )
% 5.31/5.49 = ( ord_less_num @ Y @ X ) ) ).
% 5.31/5.49
% 5.31/5.49 % linorder_not_le
% 5.31/5.49 thf(fact_825_linorder__not__le,axiom,
% 5.31/5.49 ! [X: nat,Y: nat] :
% 5.31/5.49 ( ( ~ ( ord_less_eq_nat @ X @ Y ) )
% 5.31/5.49 = ( ord_less_nat @ Y @ X ) ) ).
% 5.31/5.49
% 5.31/5.49 % linorder_not_le
% 5.31/5.49 thf(fact_826_linorder__not__le,axiom,
% 5.31/5.49 ! [X: int,Y: int] :
% 5.31/5.49 ( ( ~ ( ord_less_eq_int @ X @ Y ) )
% 5.31/5.49 = ( ord_less_int @ Y @ X ) ) ).
% 5.31/5.49
% 5.31/5.49 % linorder_not_le
% 5.31/5.49 thf(fact_827_order__less__le,axiom,
% 5.31/5.49 ( ord_less_real
% 5.31/5.49 = ( ^ [X4: real,Y4: real] :
% 5.31/5.49 ( ( ord_less_eq_real @ X4 @ Y4 )
% 5.31/5.49 & ( X4 != Y4 ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % order_less_le
% 5.31/5.49 thf(fact_828_order__less__le,axiom,
% 5.31/5.49 ( ord_less_set_nat
% 5.31/5.49 = ( ^ [X4: set_nat,Y4: set_nat] :
% 5.31/5.49 ( ( ord_less_eq_set_nat @ X4 @ Y4 )
% 5.31/5.49 & ( X4 != Y4 ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % order_less_le
% 5.31/5.49 thf(fact_829_order__less__le,axiom,
% 5.31/5.49 ( ord_less_rat
% 5.31/5.49 = ( ^ [X4: rat,Y4: rat] :
% 5.31/5.49 ( ( ord_less_eq_rat @ X4 @ Y4 )
% 5.31/5.49 & ( X4 != Y4 ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % order_less_le
% 5.31/5.49 thf(fact_830_order__less__le,axiom,
% 5.31/5.49 ( ord_less_num
% 5.31/5.49 = ( ^ [X4: num,Y4: num] :
% 5.31/5.49 ( ( ord_less_eq_num @ X4 @ Y4 )
% 5.31/5.49 & ( X4 != Y4 ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % order_less_le
% 5.31/5.49 thf(fact_831_order__less__le,axiom,
% 5.31/5.49 ( ord_less_nat
% 5.31/5.49 = ( ^ [X4: nat,Y4: nat] :
% 5.31/5.49 ( ( ord_less_eq_nat @ X4 @ Y4 )
% 5.31/5.49 & ( X4 != Y4 ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % order_less_le
% 5.31/5.49 thf(fact_832_order__less__le,axiom,
% 5.31/5.49 ( ord_less_int
% 5.31/5.49 = ( ^ [X4: int,Y4: int] :
% 5.31/5.49 ( ( ord_less_eq_int @ X4 @ Y4 )
% 5.31/5.49 & ( X4 != Y4 ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % order_less_le
% 5.31/5.49 thf(fact_833_order__le__less,axiom,
% 5.31/5.49 ( ord_less_eq_real
% 5.31/5.49 = ( ^ [X4: real,Y4: real] :
% 5.31/5.49 ( ( ord_less_real @ X4 @ Y4 )
% 5.31/5.49 | ( X4 = Y4 ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % order_le_less
% 5.31/5.49 thf(fact_834_order__le__less,axiom,
% 5.31/5.49 ( ord_less_eq_set_nat
% 5.31/5.49 = ( ^ [X4: set_nat,Y4: set_nat] :
% 5.31/5.49 ( ( ord_less_set_nat @ X4 @ Y4 )
% 5.31/5.49 | ( X4 = Y4 ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % order_le_less
% 5.31/5.49 thf(fact_835_order__le__less,axiom,
% 5.31/5.49 ( ord_less_eq_rat
% 5.31/5.49 = ( ^ [X4: rat,Y4: rat] :
% 5.31/5.49 ( ( ord_less_rat @ X4 @ Y4 )
% 5.31/5.49 | ( X4 = Y4 ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % order_le_less
% 5.31/5.49 thf(fact_836_order__le__less,axiom,
% 5.31/5.49 ( ord_less_eq_num
% 5.31/5.49 = ( ^ [X4: num,Y4: num] :
% 5.31/5.49 ( ( ord_less_num @ X4 @ Y4 )
% 5.31/5.49 | ( X4 = Y4 ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % order_le_less
% 5.31/5.49 thf(fact_837_order__le__less,axiom,
% 5.31/5.49 ( ord_less_eq_nat
% 5.31/5.49 = ( ^ [X4: nat,Y4: nat] :
% 5.31/5.49 ( ( ord_less_nat @ X4 @ Y4 )
% 5.31/5.49 | ( X4 = Y4 ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % order_le_less
% 5.31/5.49 thf(fact_838_order__le__less,axiom,
% 5.31/5.49 ( ord_less_eq_int
% 5.31/5.49 = ( ^ [X4: int,Y4: int] :
% 5.31/5.49 ( ( ord_less_int @ X4 @ Y4 )
% 5.31/5.49 | ( X4 = Y4 ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % order_le_less
% 5.31/5.49 thf(fact_839_dual__order_Ostrict__implies__order,axiom,
% 5.31/5.49 ! [B: real,A: real] :
% 5.31/5.49 ( ( ord_less_real @ B @ A )
% 5.31/5.49 => ( ord_less_eq_real @ B @ A ) ) ).
% 5.31/5.49
% 5.31/5.49 % dual_order.strict_implies_order
% 5.31/5.49 thf(fact_840_dual__order_Ostrict__implies__order,axiom,
% 5.31/5.49 ! [B: set_nat,A: set_nat] :
% 5.31/5.49 ( ( ord_less_set_nat @ B @ A )
% 5.31/5.49 => ( ord_less_eq_set_nat @ B @ A ) ) ).
% 5.31/5.49
% 5.31/5.49 % dual_order.strict_implies_order
% 5.31/5.49 thf(fact_841_dual__order_Ostrict__implies__order,axiom,
% 5.31/5.49 ! [B: rat,A: rat] :
% 5.31/5.49 ( ( ord_less_rat @ B @ A )
% 5.31/5.49 => ( ord_less_eq_rat @ B @ A ) ) ).
% 5.31/5.49
% 5.31/5.49 % dual_order.strict_implies_order
% 5.31/5.49 thf(fact_842_dual__order_Ostrict__implies__order,axiom,
% 5.31/5.49 ! [B: num,A: num] :
% 5.31/5.49 ( ( ord_less_num @ B @ A )
% 5.31/5.49 => ( ord_less_eq_num @ B @ A ) ) ).
% 5.31/5.49
% 5.31/5.49 % dual_order.strict_implies_order
% 5.31/5.49 thf(fact_843_dual__order_Ostrict__implies__order,axiom,
% 5.31/5.49 ! [B: nat,A: nat] :
% 5.31/5.49 ( ( ord_less_nat @ B @ A )
% 5.31/5.49 => ( ord_less_eq_nat @ B @ A ) ) ).
% 5.31/5.49
% 5.31/5.49 % dual_order.strict_implies_order
% 5.31/5.49 thf(fact_844_dual__order_Ostrict__implies__order,axiom,
% 5.31/5.49 ! [B: int,A: int] :
% 5.31/5.49 ( ( ord_less_int @ B @ A )
% 5.31/5.49 => ( ord_less_eq_int @ B @ A ) ) ).
% 5.31/5.49
% 5.31/5.49 % dual_order.strict_implies_order
% 5.31/5.49 thf(fact_845_order_Ostrict__implies__order,axiom,
% 5.31/5.49 ! [A: real,B: real] :
% 5.31/5.49 ( ( ord_less_real @ A @ B )
% 5.31/5.49 => ( ord_less_eq_real @ A @ B ) ) ).
% 5.31/5.49
% 5.31/5.49 % order.strict_implies_order
% 5.31/5.49 thf(fact_846_order_Ostrict__implies__order,axiom,
% 5.31/5.49 ! [A: set_nat,B: set_nat] :
% 5.31/5.49 ( ( ord_less_set_nat @ A @ B )
% 5.31/5.49 => ( ord_less_eq_set_nat @ A @ B ) ) ).
% 5.31/5.49
% 5.31/5.49 % order.strict_implies_order
% 5.31/5.49 thf(fact_847_order_Ostrict__implies__order,axiom,
% 5.31/5.49 ! [A: rat,B: rat] :
% 5.31/5.49 ( ( ord_less_rat @ A @ B )
% 5.31/5.49 => ( ord_less_eq_rat @ A @ B ) ) ).
% 5.31/5.49
% 5.31/5.49 % order.strict_implies_order
% 5.31/5.49 thf(fact_848_order_Ostrict__implies__order,axiom,
% 5.31/5.49 ! [A: num,B: num] :
% 5.31/5.49 ( ( ord_less_num @ A @ B )
% 5.31/5.49 => ( ord_less_eq_num @ A @ B ) ) ).
% 5.31/5.49
% 5.31/5.49 % order.strict_implies_order
% 5.31/5.49 thf(fact_849_order_Ostrict__implies__order,axiom,
% 5.31/5.49 ! [A: nat,B: nat] :
% 5.31/5.49 ( ( ord_less_nat @ A @ B )
% 5.31/5.49 => ( ord_less_eq_nat @ A @ B ) ) ).
% 5.31/5.49
% 5.31/5.49 % order.strict_implies_order
% 5.31/5.49 thf(fact_850_order_Ostrict__implies__order,axiom,
% 5.31/5.49 ! [A: int,B: int] :
% 5.31/5.49 ( ( ord_less_int @ A @ B )
% 5.31/5.49 => ( ord_less_eq_int @ A @ B ) ) ).
% 5.31/5.49
% 5.31/5.49 % order.strict_implies_order
% 5.31/5.49 thf(fact_851_dual__order_Ostrict__iff__not,axiom,
% 5.31/5.49 ( ord_less_real
% 5.31/5.49 = ( ^ [B4: real,A5: real] :
% 5.31/5.49 ( ( ord_less_eq_real @ B4 @ A5 )
% 5.31/5.49 & ~ ( ord_less_eq_real @ A5 @ B4 ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % dual_order.strict_iff_not
% 5.31/5.49 thf(fact_852_dual__order_Ostrict__iff__not,axiom,
% 5.31/5.49 ( ord_less_set_nat
% 5.31/5.49 = ( ^ [B4: set_nat,A5: set_nat] :
% 5.31/5.49 ( ( ord_less_eq_set_nat @ B4 @ A5 )
% 5.31/5.49 & ~ ( ord_less_eq_set_nat @ A5 @ B4 ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % dual_order.strict_iff_not
% 5.31/5.49 thf(fact_853_dual__order_Ostrict__iff__not,axiom,
% 5.31/5.49 ( ord_less_rat
% 5.31/5.49 = ( ^ [B4: rat,A5: rat] :
% 5.31/5.49 ( ( ord_less_eq_rat @ B4 @ A5 )
% 5.31/5.49 & ~ ( ord_less_eq_rat @ A5 @ B4 ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % dual_order.strict_iff_not
% 5.31/5.49 thf(fact_854_dual__order_Ostrict__iff__not,axiom,
% 5.31/5.49 ( ord_less_num
% 5.31/5.49 = ( ^ [B4: num,A5: num] :
% 5.31/5.49 ( ( ord_less_eq_num @ B4 @ A5 )
% 5.31/5.49 & ~ ( ord_less_eq_num @ A5 @ B4 ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % dual_order.strict_iff_not
% 5.31/5.49 thf(fact_855_dual__order_Ostrict__iff__not,axiom,
% 5.31/5.49 ( ord_less_nat
% 5.31/5.49 = ( ^ [B4: nat,A5: nat] :
% 5.31/5.49 ( ( ord_less_eq_nat @ B4 @ A5 )
% 5.31/5.49 & ~ ( ord_less_eq_nat @ A5 @ B4 ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % dual_order.strict_iff_not
% 5.31/5.49 thf(fact_856_dual__order_Ostrict__iff__not,axiom,
% 5.31/5.49 ( ord_less_int
% 5.31/5.49 = ( ^ [B4: int,A5: int] :
% 5.31/5.49 ( ( ord_less_eq_int @ B4 @ A5 )
% 5.31/5.49 & ~ ( ord_less_eq_int @ A5 @ B4 ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % dual_order.strict_iff_not
% 5.31/5.49 thf(fact_857_dual__order_Ostrict__trans2,axiom,
% 5.31/5.49 ! [B: real,A: real,C2: real] :
% 5.31/5.49 ( ( ord_less_real @ B @ A )
% 5.31/5.49 => ( ( ord_less_eq_real @ C2 @ B )
% 5.31/5.49 => ( ord_less_real @ C2 @ A ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % dual_order.strict_trans2
% 5.31/5.49 thf(fact_858_dual__order_Ostrict__trans2,axiom,
% 5.31/5.49 ! [B: set_nat,A: set_nat,C2: set_nat] :
% 5.31/5.49 ( ( ord_less_set_nat @ B @ A )
% 5.31/5.49 => ( ( ord_less_eq_set_nat @ C2 @ B )
% 5.31/5.49 => ( ord_less_set_nat @ C2 @ A ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % dual_order.strict_trans2
% 5.31/5.49 thf(fact_859_dual__order_Ostrict__trans2,axiom,
% 5.31/5.49 ! [B: rat,A: rat,C2: rat] :
% 5.31/5.49 ( ( ord_less_rat @ B @ A )
% 5.31/5.49 => ( ( ord_less_eq_rat @ C2 @ B )
% 5.31/5.49 => ( ord_less_rat @ C2 @ A ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % dual_order.strict_trans2
% 5.31/5.49 thf(fact_860_dual__order_Ostrict__trans2,axiom,
% 5.31/5.49 ! [B: num,A: num,C2: num] :
% 5.31/5.49 ( ( ord_less_num @ B @ A )
% 5.31/5.49 => ( ( ord_less_eq_num @ C2 @ B )
% 5.31/5.49 => ( ord_less_num @ C2 @ A ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % dual_order.strict_trans2
% 5.31/5.49 thf(fact_861_dual__order_Ostrict__trans2,axiom,
% 5.31/5.49 ! [B: nat,A: nat,C2: nat] :
% 5.31/5.49 ( ( ord_less_nat @ B @ A )
% 5.31/5.49 => ( ( ord_less_eq_nat @ C2 @ B )
% 5.31/5.49 => ( ord_less_nat @ C2 @ A ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % dual_order.strict_trans2
% 5.31/5.49 thf(fact_862_dual__order_Ostrict__trans2,axiom,
% 5.31/5.49 ! [B: int,A: int,C2: int] :
% 5.31/5.49 ( ( ord_less_int @ B @ A )
% 5.31/5.49 => ( ( ord_less_eq_int @ C2 @ B )
% 5.31/5.49 => ( ord_less_int @ C2 @ A ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % dual_order.strict_trans2
% 5.31/5.49 thf(fact_863_dual__order_Ostrict__trans1,axiom,
% 5.31/5.49 ! [B: real,A: real,C2: real] :
% 5.31/5.49 ( ( ord_less_eq_real @ B @ A )
% 5.31/5.49 => ( ( ord_less_real @ C2 @ B )
% 5.31/5.49 => ( ord_less_real @ C2 @ A ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % dual_order.strict_trans1
% 5.31/5.49 thf(fact_864_dual__order_Ostrict__trans1,axiom,
% 5.31/5.49 ! [B: set_nat,A: set_nat,C2: set_nat] :
% 5.31/5.49 ( ( ord_less_eq_set_nat @ B @ A )
% 5.31/5.49 => ( ( ord_less_set_nat @ C2 @ B )
% 5.31/5.49 => ( ord_less_set_nat @ C2 @ A ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % dual_order.strict_trans1
% 5.31/5.49 thf(fact_865_dual__order_Ostrict__trans1,axiom,
% 5.31/5.49 ! [B: rat,A: rat,C2: rat] :
% 5.31/5.49 ( ( ord_less_eq_rat @ B @ A )
% 5.31/5.49 => ( ( ord_less_rat @ C2 @ B )
% 5.31/5.49 => ( ord_less_rat @ C2 @ A ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % dual_order.strict_trans1
% 5.31/5.49 thf(fact_866_dual__order_Ostrict__trans1,axiom,
% 5.31/5.49 ! [B: num,A: num,C2: num] :
% 5.31/5.49 ( ( ord_less_eq_num @ B @ A )
% 5.31/5.49 => ( ( ord_less_num @ C2 @ B )
% 5.31/5.49 => ( ord_less_num @ C2 @ A ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % dual_order.strict_trans1
% 5.31/5.49 thf(fact_867_dual__order_Ostrict__trans1,axiom,
% 5.31/5.49 ! [B: nat,A: nat,C2: nat] :
% 5.31/5.49 ( ( ord_less_eq_nat @ B @ A )
% 5.31/5.49 => ( ( ord_less_nat @ C2 @ B )
% 5.31/5.49 => ( ord_less_nat @ C2 @ A ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % dual_order.strict_trans1
% 5.31/5.49 thf(fact_868_dual__order_Ostrict__trans1,axiom,
% 5.31/5.49 ! [B: int,A: int,C2: int] :
% 5.31/5.49 ( ( ord_less_eq_int @ B @ A )
% 5.31/5.49 => ( ( ord_less_int @ C2 @ B )
% 5.31/5.49 => ( ord_less_int @ C2 @ A ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % dual_order.strict_trans1
% 5.31/5.49 thf(fact_869_dual__order_Ostrict__iff__order,axiom,
% 5.31/5.49 ( ord_less_real
% 5.31/5.49 = ( ^ [B4: real,A5: real] :
% 5.31/5.49 ( ( ord_less_eq_real @ B4 @ A5 )
% 5.31/5.49 & ( A5 != B4 ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % dual_order.strict_iff_order
% 5.31/5.49 thf(fact_870_dual__order_Ostrict__iff__order,axiom,
% 5.31/5.49 ( ord_less_set_nat
% 5.31/5.49 = ( ^ [B4: set_nat,A5: set_nat] :
% 5.31/5.49 ( ( ord_less_eq_set_nat @ B4 @ A5 )
% 5.31/5.49 & ( A5 != B4 ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % dual_order.strict_iff_order
% 5.31/5.49 thf(fact_871_dual__order_Ostrict__iff__order,axiom,
% 5.31/5.49 ( ord_less_rat
% 5.31/5.49 = ( ^ [B4: rat,A5: rat] :
% 5.31/5.49 ( ( ord_less_eq_rat @ B4 @ A5 )
% 5.31/5.49 & ( A5 != B4 ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % dual_order.strict_iff_order
% 5.31/5.49 thf(fact_872_dual__order_Ostrict__iff__order,axiom,
% 5.31/5.49 ( ord_less_num
% 5.31/5.49 = ( ^ [B4: num,A5: num] :
% 5.31/5.49 ( ( ord_less_eq_num @ B4 @ A5 )
% 5.31/5.49 & ( A5 != B4 ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % dual_order.strict_iff_order
% 5.31/5.49 thf(fact_873_dual__order_Ostrict__iff__order,axiom,
% 5.31/5.49 ( ord_less_nat
% 5.31/5.49 = ( ^ [B4: nat,A5: nat] :
% 5.31/5.49 ( ( ord_less_eq_nat @ B4 @ A5 )
% 5.31/5.49 & ( A5 != B4 ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % dual_order.strict_iff_order
% 5.31/5.49 thf(fact_874_dual__order_Ostrict__iff__order,axiom,
% 5.31/5.49 ( ord_less_int
% 5.31/5.49 = ( ^ [B4: int,A5: int] :
% 5.31/5.49 ( ( ord_less_eq_int @ B4 @ A5 )
% 5.31/5.49 & ( A5 != B4 ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % dual_order.strict_iff_order
% 5.31/5.49 thf(fact_875_dual__order_Oorder__iff__strict,axiom,
% 5.31/5.49 ( ord_less_eq_real
% 5.31/5.49 = ( ^ [B4: real,A5: real] :
% 5.31/5.49 ( ( ord_less_real @ B4 @ A5 )
% 5.31/5.49 | ( A5 = B4 ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % dual_order.order_iff_strict
% 5.31/5.49 thf(fact_876_dual__order_Oorder__iff__strict,axiom,
% 5.31/5.49 ( ord_less_eq_set_nat
% 5.31/5.49 = ( ^ [B4: set_nat,A5: set_nat] :
% 5.31/5.49 ( ( ord_less_set_nat @ B4 @ A5 )
% 5.31/5.49 | ( A5 = B4 ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % dual_order.order_iff_strict
% 5.31/5.49 thf(fact_877_dual__order_Oorder__iff__strict,axiom,
% 5.31/5.49 ( ord_less_eq_rat
% 5.31/5.49 = ( ^ [B4: rat,A5: rat] :
% 5.31/5.49 ( ( ord_less_rat @ B4 @ A5 )
% 5.31/5.49 | ( A5 = B4 ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % dual_order.order_iff_strict
% 5.31/5.49 thf(fact_878_dual__order_Oorder__iff__strict,axiom,
% 5.31/5.49 ( ord_less_eq_num
% 5.31/5.49 = ( ^ [B4: num,A5: num] :
% 5.31/5.49 ( ( ord_less_num @ B4 @ A5 )
% 5.31/5.49 | ( A5 = B4 ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % dual_order.order_iff_strict
% 5.31/5.49 thf(fact_879_dual__order_Oorder__iff__strict,axiom,
% 5.31/5.49 ( ord_less_eq_nat
% 5.31/5.49 = ( ^ [B4: nat,A5: nat] :
% 5.31/5.49 ( ( ord_less_nat @ B4 @ A5 )
% 5.31/5.49 | ( A5 = B4 ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % dual_order.order_iff_strict
% 5.31/5.49 thf(fact_880_dual__order_Oorder__iff__strict,axiom,
% 5.31/5.49 ( ord_less_eq_int
% 5.31/5.49 = ( ^ [B4: int,A5: int] :
% 5.31/5.49 ( ( ord_less_int @ B4 @ A5 )
% 5.31/5.49 | ( A5 = B4 ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % dual_order.order_iff_strict
% 5.31/5.49 thf(fact_881_dense__le__bounded,axiom,
% 5.31/5.49 ! [X: real,Y: real,Z3: real] :
% 5.31/5.49 ( ( ord_less_real @ X @ Y )
% 5.31/5.49 => ( ! [W: real] :
% 5.31/5.49 ( ( ord_less_real @ X @ W )
% 5.31/5.49 => ( ( ord_less_real @ W @ Y )
% 5.31/5.49 => ( ord_less_eq_real @ W @ Z3 ) ) )
% 5.31/5.49 => ( ord_less_eq_real @ Y @ Z3 ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % dense_le_bounded
% 5.31/5.49 thf(fact_882_dense__le__bounded,axiom,
% 5.31/5.49 ! [X: rat,Y: rat,Z3: rat] :
% 5.31/5.49 ( ( ord_less_rat @ X @ Y )
% 5.31/5.49 => ( ! [W: rat] :
% 5.31/5.49 ( ( ord_less_rat @ X @ W )
% 5.31/5.49 => ( ( ord_less_rat @ W @ Y )
% 5.31/5.49 => ( ord_less_eq_rat @ W @ Z3 ) ) )
% 5.31/5.49 => ( ord_less_eq_rat @ Y @ Z3 ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % dense_le_bounded
% 5.31/5.49 thf(fact_883_dense__ge__bounded,axiom,
% 5.31/5.49 ! [Z3: real,X: real,Y: real] :
% 5.31/5.49 ( ( ord_less_real @ Z3 @ X )
% 5.31/5.49 => ( ! [W: real] :
% 5.31/5.49 ( ( ord_less_real @ Z3 @ W )
% 5.31/5.49 => ( ( ord_less_real @ W @ X )
% 5.31/5.49 => ( ord_less_eq_real @ Y @ W ) ) )
% 5.31/5.49 => ( ord_less_eq_real @ Y @ Z3 ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % dense_ge_bounded
% 5.31/5.49 thf(fact_884_dense__ge__bounded,axiom,
% 5.31/5.49 ! [Z3: rat,X: rat,Y: rat] :
% 5.31/5.49 ( ( ord_less_rat @ Z3 @ X )
% 5.31/5.49 => ( ! [W: rat] :
% 5.31/5.49 ( ( ord_less_rat @ Z3 @ W )
% 5.31/5.49 => ( ( ord_less_rat @ W @ X )
% 5.31/5.49 => ( ord_less_eq_rat @ Y @ W ) ) )
% 5.31/5.49 => ( ord_less_eq_rat @ Y @ Z3 ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % dense_ge_bounded
% 5.31/5.49 thf(fact_885_order_Ostrict__iff__not,axiom,
% 5.31/5.49 ( ord_less_real
% 5.31/5.49 = ( ^ [A5: real,B4: real] :
% 5.31/5.49 ( ( ord_less_eq_real @ A5 @ B4 )
% 5.31/5.49 & ~ ( ord_less_eq_real @ B4 @ A5 ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % order.strict_iff_not
% 5.31/5.49 thf(fact_886_order_Ostrict__iff__not,axiom,
% 5.31/5.49 ( ord_less_set_nat
% 5.31/5.49 = ( ^ [A5: set_nat,B4: set_nat] :
% 5.31/5.49 ( ( ord_less_eq_set_nat @ A5 @ B4 )
% 5.31/5.49 & ~ ( ord_less_eq_set_nat @ B4 @ A5 ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % order.strict_iff_not
% 5.31/5.49 thf(fact_887_order_Ostrict__iff__not,axiom,
% 5.31/5.49 ( ord_less_rat
% 5.31/5.49 = ( ^ [A5: rat,B4: rat] :
% 5.31/5.49 ( ( ord_less_eq_rat @ A5 @ B4 )
% 5.31/5.49 & ~ ( ord_less_eq_rat @ B4 @ A5 ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % order.strict_iff_not
% 5.31/5.49 thf(fact_888_order_Ostrict__iff__not,axiom,
% 5.31/5.49 ( ord_less_num
% 5.31/5.49 = ( ^ [A5: num,B4: num] :
% 5.31/5.49 ( ( ord_less_eq_num @ A5 @ B4 )
% 5.31/5.49 & ~ ( ord_less_eq_num @ B4 @ A5 ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % order.strict_iff_not
% 5.31/5.49 thf(fact_889_order_Ostrict__iff__not,axiom,
% 5.31/5.49 ( ord_less_nat
% 5.31/5.49 = ( ^ [A5: nat,B4: nat] :
% 5.31/5.49 ( ( ord_less_eq_nat @ A5 @ B4 )
% 5.31/5.49 & ~ ( ord_less_eq_nat @ B4 @ A5 ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % order.strict_iff_not
% 5.31/5.49 thf(fact_890_order_Ostrict__iff__not,axiom,
% 5.31/5.49 ( ord_less_int
% 5.31/5.49 = ( ^ [A5: int,B4: int] :
% 5.31/5.49 ( ( ord_less_eq_int @ A5 @ B4 )
% 5.31/5.49 & ~ ( ord_less_eq_int @ B4 @ A5 ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % order.strict_iff_not
% 5.31/5.49 thf(fact_891_order_Ostrict__trans2,axiom,
% 5.31/5.49 ! [A: real,B: real,C2: real] :
% 5.31/5.49 ( ( ord_less_real @ A @ B )
% 5.31/5.49 => ( ( ord_less_eq_real @ B @ C2 )
% 5.31/5.49 => ( ord_less_real @ A @ C2 ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % order.strict_trans2
% 5.31/5.49 thf(fact_892_order_Ostrict__trans2,axiom,
% 5.31/5.49 ! [A: set_nat,B: set_nat,C2: set_nat] :
% 5.31/5.49 ( ( ord_less_set_nat @ A @ B )
% 5.31/5.49 => ( ( ord_less_eq_set_nat @ B @ C2 )
% 5.31/5.49 => ( ord_less_set_nat @ A @ C2 ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % order.strict_trans2
% 5.31/5.49 thf(fact_893_order_Ostrict__trans2,axiom,
% 5.31/5.49 ! [A: rat,B: rat,C2: rat] :
% 5.31/5.49 ( ( ord_less_rat @ A @ B )
% 5.31/5.49 => ( ( ord_less_eq_rat @ B @ C2 )
% 5.31/5.49 => ( ord_less_rat @ A @ C2 ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % order.strict_trans2
% 5.31/5.49 thf(fact_894_order_Ostrict__trans2,axiom,
% 5.31/5.49 ! [A: num,B: num,C2: num] :
% 5.31/5.49 ( ( ord_less_num @ A @ B )
% 5.31/5.49 => ( ( ord_less_eq_num @ B @ C2 )
% 5.31/5.49 => ( ord_less_num @ A @ C2 ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % order.strict_trans2
% 5.31/5.49 thf(fact_895_order_Ostrict__trans2,axiom,
% 5.31/5.49 ! [A: nat,B: nat,C2: nat] :
% 5.31/5.49 ( ( ord_less_nat @ A @ B )
% 5.31/5.49 => ( ( ord_less_eq_nat @ B @ C2 )
% 5.31/5.49 => ( ord_less_nat @ A @ C2 ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % order.strict_trans2
% 5.31/5.49 thf(fact_896_order_Ostrict__trans2,axiom,
% 5.31/5.49 ! [A: int,B: int,C2: int] :
% 5.31/5.49 ( ( ord_less_int @ A @ B )
% 5.31/5.49 => ( ( ord_less_eq_int @ B @ C2 )
% 5.31/5.49 => ( ord_less_int @ A @ C2 ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % order.strict_trans2
% 5.31/5.49 thf(fact_897_order_Ostrict__trans1,axiom,
% 5.31/5.49 ! [A: real,B: real,C2: real] :
% 5.31/5.49 ( ( ord_less_eq_real @ A @ B )
% 5.31/5.49 => ( ( ord_less_real @ B @ C2 )
% 5.31/5.49 => ( ord_less_real @ A @ C2 ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % order.strict_trans1
% 5.31/5.49 thf(fact_898_order_Ostrict__trans1,axiom,
% 5.31/5.49 ! [A: set_nat,B: set_nat,C2: set_nat] :
% 5.31/5.49 ( ( ord_less_eq_set_nat @ A @ B )
% 5.31/5.49 => ( ( ord_less_set_nat @ B @ C2 )
% 5.31/5.49 => ( ord_less_set_nat @ A @ C2 ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % order.strict_trans1
% 5.31/5.49 thf(fact_899_order_Ostrict__trans1,axiom,
% 5.31/5.49 ! [A: rat,B: rat,C2: rat] :
% 5.31/5.49 ( ( ord_less_eq_rat @ A @ B )
% 5.31/5.49 => ( ( ord_less_rat @ B @ C2 )
% 5.31/5.49 => ( ord_less_rat @ A @ C2 ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % order.strict_trans1
% 5.31/5.49 thf(fact_900_order_Ostrict__trans1,axiom,
% 5.31/5.49 ! [A: num,B: num,C2: num] :
% 5.31/5.49 ( ( ord_less_eq_num @ A @ B )
% 5.31/5.49 => ( ( ord_less_num @ B @ C2 )
% 5.31/5.49 => ( ord_less_num @ A @ C2 ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % order.strict_trans1
% 5.31/5.49 thf(fact_901_order_Ostrict__trans1,axiom,
% 5.31/5.49 ! [A: nat,B: nat,C2: nat] :
% 5.31/5.49 ( ( ord_less_eq_nat @ A @ B )
% 5.31/5.49 => ( ( ord_less_nat @ B @ C2 )
% 5.31/5.49 => ( ord_less_nat @ A @ C2 ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % order.strict_trans1
% 5.31/5.49 thf(fact_902_order_Ostrict__trans1,axiom,
% 5.31/5.49 ! [A: int,B: int,C2: int] :
% 5.31/5.49 ( ( ord_less_eq_int @ A @ B )
% 5.31/5.49 => ( ( ord_less_int @ B @ C2 )
% 5.31/5.49 => ( ord_less_int @ A @ C2 ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % order.strict_trans1
% 5.31/5.49 thf(fact_903_order_Ostrict__iff__order,axiom,
% 5.31/5.49 ( ord_less_real
% 5.31/5.49 = ( ^ [A5: real,B4: real] :
% 5.31/5.49 ( ( ord_less_eq_real @ A5 @ B4 )
% 5.31/5.49 & ( A5 != B4 ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % order.strict_iff_order
% 5.31/5.49 thf(fact_904_order_Ostrict__iff__order,axiom,
% 5.31/5.49 ( ord_less_set_nat
% 5.31/5.49 = ( ^ [A5: set_nat,B4: set_nat] :
% 5.31/5.49 ( ( ord_less_eq_set_nat @ A5 @ B4 )
% 5.31/5.49 & ( A5 != B4 ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % order.strict_iff_order
% 5.31/5.49 thf(fact_905_order_Ostrict__iff__order,axiom,
% 5.31/5.49 ( ord_less_rat
% 5.31/5.49 = ( ^ [A5: rat,B4: rat] :
% 5.31/5.49 ( ( ord_less_eq_rat @ A5 @ B4 )
% 5.31/5.49 & ( A5 != B4 ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % order.strict_iff_order
% 5.31/5.49 thf(fact_906_order_Ostrict__iff__order,axiom,
% 5.31/5.49 ( ord_less_num
% 5.31/5.49 = ( ^ [A5: num,B4: num] :
% 5.31/5.49 ( ( ord_less_eq_num @ A5 @ B4 )
% 5.31/5.49 & ( A5 != B4 ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % order.strict_iff_order
% 5.31/5.49 thf(fact_907_order_Ostrict__iff__order,axiom,
% 5.31/5.49 ( ord_less_nat
% 5.31/5.49 = ( ^ [A5: nat,B4: nat] :
% 5.31/5.49 ( ( ord_less_eq_nat @ A5 @ B4 )
% 5.31/5.49 & ( A5 != B4 ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % order.strict_iff_order
% 5.31/5.49 thf(fact_908_order_Ostrict__iff__order,axiom,
% 5.31/5.49 ( ord_less_int
% 5.31/5.49 = ( ^ [A5: int,B4: int] :
% 5.31/5.49 ( ( ord_less_eq_int @ A5 @ B4 )
% 5.31/5.49 & ( A5 != B4 ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % order.strict_iff_order
% 5.31/5.49 thf(fact_909_order_Oorder__iff__strict,axiom,
% 5.31/5.49 ( ord_less_eq_real
% 5.31/5.49 = ( ^ [A5: real,B4: real] :
% 5.31/5.49 ( ( ord_less_real @ A5 @ B4 )
% 5.31/5.49 | ( A5 = B4 ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % order.order_iff_strict
% 5.31/5.49 thf(fact_910_order_Oorder__iff__strict,axiom,
% 5.31/5.49 ( ord_less_eq_set_nat
% 5.31/5.49 = ( ^ [A5: set_nat,B4: set_nat] :
% 5.31/5.49 ( ( ord_less_set_nat @ A5 @ B4 )
% 5.31/5.49 | ( A5 = B4 ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % order.order_iff_strict
% 5.31/5.49 thf(fact_911_order_Oorder__iff__strict,axiom,
% 5.31/5.49 ( ord_less_eq_rat
% 5.31/5.49 = ( ^ [A5: rat,B4: rat] :
% 5.31/5.49 ( ( ord_less_rat @ A5 @ B4 )
% 5.31/5.49 | ( A5 = B4 ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % order.order_iff_strict
% 5.31/5.49 thf(fact_912_order_Oorder__iff__strict,axiom,
% 5.31/5.49 ( ord_less_eq_num
% 5.31/5.49 = ( ^ [A5: num,B4: num] :
% 5.31/5.49 ( ( ord_less_num @ A5 @ B4 )
% 5.31/5.49 | ( A5 = B4 ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % order.order_iff_strict
% 5.31/5.49 thf(fact_913_order_Oorder__iff__strict,axiom,
% 5.31/5.49 ( ord_less_eq_nat
% 5.31/5.49 = ( ^ [A5: nat,B4: nat] :
% 5.31/5.49 ( ( ord_less_nat @ A5 @ B4 )
% 5.31/5.49 | ( A5 = B4 ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % order.order_iff_strict
% 5.31/5.49 thf(fact_914_order_Oorder__iff__strict,axiom,
% 5.31/5.49 ( ord_less_eq_int
% 5.31/5.49 = ( ^ [A5: int,B4: int] :
% 5.31/5.49 ( ( ord_less_int @ A5 @ B4 )
% 5.31/5.49 | ( A5 = B4 ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % order.order_iff_strict
% 5.31/5.49 thf(fact_915_not__le__imp__less,axiom,
% 5.31/5.49 ! [Y: real,X: real] :
% 5.31/5.49 ( ~ ( ord_less_eq_real @ Y @ X )
% 5.31/5.49 => ( ord_less_real @ X @ Y ) ) ).
% 5.31/5.49
% 5.31/5.49 % not_le_imp_less
% 5.31/5.49 thf(fact_916_not__le__imp__less,axiom,
% 5.31/5.49 ! [Y: rat,X: rat] :
% 5.31/5.49 ( ~ ( ord_less_eq_rat @ Y @ X )
% 5.31/5.49 => ( ord_less_rat @ X @ Y ) ) ).
% 5.31/5.49
% 5.31/5.49 % not_le_imp_less
% 5.31/5.49 thf(fact_917_not__le__imp__less,axiom,
% 5.31/5.49 ! [Y: num,X: num] :
% 5.31/5.49 ( ~ ( ord_less_eq_num @ Y @ X )
% 5.31/5.49 => ( ord_less_num @ X @ Y ) ) ).
% 5.31/5.49
% 5.31/5.49 % not_le_imp_less
% 5.31/5.49 thf(fact_918_not__le__imp__less,axiom,
% 5.31/5.49 ! [Y: nat,X: nat] :
% 5.31/5.49 ( ~ ( ord_less_eq_nat @ Y @ X )
% 5.31/5.49 => ( ord_less_nat @ X @ Y ) ) ).
% 5.31/5.49
% 5.31/5.49 % not_le_imp_less
% 5.31/5.49 thf(fact_919_not__le__imp__less,axiom,
% 5.31/5.49 ! [Y: int,X: int] :
% 5.31/5.49 ( ~ ( ord_less_eq_int @ Y @ X )
% 5.31/5.49 => ( ord_less_int @ X @ Y ) ) ).
% 5.31/5.49
% 5.31/5.49 % not_le_imp_less
% 5.31/5.49 thf(fact_920_less__le__not__le,axiom,
% 5.31/5.49 ( ord_less_real
% 5.31/5.49 = ( ^ [X4: real,Y4: real] :
% 5.31/5.49 ( ( ord_less_eq_real @ X4 @ Y4 )
% 5.31/5.49 & ~ ( ord_less_eq_real @ Y4 @ X4 ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % less_le_not_le
% 5.31/5.49 thf(fact_921_less__le__not__le,axiom,
% 5.31/5.49 ( ord_less_set_nat
% 5.31/5.49 = ( ^ [X4: set_nat,Y4: set_nat] :
% 5.31/5.49 ( ( ord_less_eq_set_nat @ X4 @ Y4 )
% 5.31/5.49 & ~ ( ord_less_eq_set_nat @ Y4 @ X4 ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % less_le_not_le
% 5.31/5.49 thf(fact_922_less__le__not__le,axiom,
% 5.31/5.49 ( ord_less_rat
% 5.31/5.49 = ( ^ [X4: rat,Y4: rat] :
% 5.31/5.49 ( ( ord_less_eq_rat @ X4 @ Y4 )
% 5.31/5.49 & ~ ( ord_less_eq_rat @ Y4 @ X4 ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % less_le_not_le
% 5.31/5.49 thf(fact_923_less__le__not__le,axiom,
% 5.31/5.49 ( ord_less_num
% 5.31/5.49 = ( ^ [X4: num,Y4: num] :
% 5.31/5.49 ( ( ord_less_eq_num @ X4 @ Y4 )
% 5.31/5.49 & ~ ( ord_less_eq_num @ Y4 @ X4 ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % less_le_not_le
% 5.31/5.49 thf(fact_924_less__le__not__le,axiom,
% 5.31/5.49 ( ord_less_nat
% 5.31/5.49 = ( ^ [X4: nat,Y4: nat] :
% 5.31/5.49 ( ( ord_less_eq_nat @ X4 @ Y4 )
% 5.31/5.49 & ~ ( ord_less_eq_nat @ Y4 @ X4 ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % less_le_not_le
% 5.31/5.49 thf(fact_925_less__le__not__le,axiom,
% 5.31/5.49 ( ord_less_int
% 5.31/5.49 = ( ^ [X4: int,Y4: int] :
% 5.31/5.49 ( ( ord_less_eq_int @ X4 @ Y4 )
% 5.31/5.49 & ~ ( ord_less_eq_int @ Y4 @ X4 ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % less_le_not_le
% 5.31/5.49 thf(fact_926_dense__le,axiom,
% 5.31/5.49 ! [Y: real,Z3: real] :
% 5.31/5.49 ( ! [X3: real] :
% 5.31/5.49 ( ( ord_less_real @ X3 @ Y )
% 5.31/5.49 => ( ord_less_eq_real @ X3 @ Z3 ) )
% 5.31/5.49 => ( ord_less_eq_real @ Y @ Z3 ) ) ).
% 5.31/5.49
% 5.31/5.49 % dense_le
% 5.31/5.49 thf(fact_927_dense__le,axiom,
% 5.31/5.49 ! [Y: rat,Z3: rat] :
% 5.31/5.49 ( ! [X3: rat] :
% 5.31/5.49 ( ( ord_less_rat @ X3 @ Y )
% 5.31/5.49 => ( ord_less_eq_rat @ X3 @ Z3 ) )
% 5.31/5.49 => ( ord_less_eq_rat @ Y @ Z3 ) ) ).
% 5.31/5.49
% 5.31/5.49 % dense_le
% 5.31/5.49 thf(fact_928_dense__ge,axiom,
% 5.31/5.49 ! [Z3: real,Y: real] :
% 5.31/5.49 ( ! [X3: real] :
% 5.31/5.49 ( ( ord_less_real @ Z3 @ X3 )
% 5.31/5.49 => ( ord_less_eq_real @ Y @ X3 ) )
% 5.31/5.49 => ( ord_less_eq_real @ Y @ Z3 ) ) ).
% 5.31/5.49
% 5.31/5.49 % dense_ge
% 5.31/5.49 thf(fact_929_dense__ge,axiom,
% 5.31/5.49 ! [Z3: rat,Y: rat] :
% 5.31/5.49 ( ! [X3: rat] :
% 5.31/5.49 ( ( ord_less_rat @ Z3 @ X3 )
% 5.31/5.49 => ( ord_less_eq_rat @ Y @ X3 ) )
% 5.31/5.49 => ( ord_less_eq_rat @ Y @ Z3 ) ) ).
% 5.31/5.49
% 5.31/5.49 % dense_ge
% 5.31/5.49 thf(fact_930_antisym__conv2,axiom,
% 5.31/5.49 ! [X: real,Y: real] :
% 5.31/5.49 ( ( ord_less_eq_real @ X @ Y )
% 5.31/5.49 => ( ( ~ ( ord_less_real @ X @ Y ) )
% 5.31/5.49 = ( X = Y ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % antisym_conv2
% 5.31/5.49 thf(fact_931_antisym__conv2,axiom,
% 5.31/5.49 ! [X: set_nat,Y: set_nat] :
% 5.31/5.49 ( ( ord_less_eq_set_nat @ X @ Y )
% 5.31/5.49 => ( ( ~ ( ord_less_set_nat @ X @ Y ) )
% 5.31/5.49 = ( X = Y ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % antisym_conv2
% 5.31/5.49 thf(fact_932_antisym__conv2,axiom,
% 5.31/5.49 ! [X: rat,Y: rat] :
% 5.31/5.49 ( ( ord_less_eq_rat @ X @ Y )
% 5.31/5.49 => ( ( ~ ( ord_less_rat @ X @ Y ) )
% 5.31/5.49 = ( X = Y ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % antisym_conv2
% 5.31/5.49 thf(fact_933_antisym__conv2,axiom,
% 5.31/5.49 ! [X: num,Y: num] :
% 5.31/5.49 ( ( ord_less_eq_num @ X @ Y )
% 5.31/5.49 => ( ( ~ ( ord_less_num @ X @ Y ) )
% 5.31/5.49 = ( X = Y ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % antisym_conv2
% 5.31/5.49 thf(fact_934_antisym__conv2,axiom,
% 5.31/5.49 ! [X: nat,Y: nat] :
% 5.31/5.49 ( ( ord_less_eq_nat @ X @ Y )
% 5.31/5.49 => ( ( ~ ( ord_less_nat @ X @ Y ) )
% 5.31/5.49 = ( X = Y ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % antisym_conv2
% 5.31/5.49 thf(fact_935_antisym__conv2,axiom,
% 5.31/5.49 ! [X: int,Y: int] :
% 5.31/5.49 ( ( ord_less_eq_int @ X @ Y )
% 5.31/5.49 => ( ( ~ ( ord_less_int @ X @ Y ) )
% 5.31/5.49 = ( X = Y ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % antisym_conv2
% 5.31/5.49 thf(fact_936_antisym__conv1,axiom,
% 5.31/5.49 ! [X: real,Y: real] :
% 5.31/5.49 ( ~ ( ord_less_real @ X @ Y )
% 5.31/5.49 => ( ( ord_less_eq_real @ X @ Y )
% 5.31/5.49 = ( X = Y ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % antisym_conv1
% 5.31/5.49 thf(fact_937_antisym__conv1,axiom,
% 5.31/5.49 ! [X: set_nat,Y: set_nat] :
% 5.31/5.49 ( ~ ( ord_less_set_nat @ X @ Y )
% 5.31/5.49 => ( ( ord_less_eq_set_nat @ X @ Y )
% 5.31/5.49 = ( X = Y ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % antisym_conv1
% 5.31/5.49 thf(fact_938_antisym__conv1,axiom,
% 5.31/5.49 ! [X: rat,Y: rat] :
% 5.31/5.49 ( ~ ( ord_less_rat @ X @ Y )
% 5.31/5.49 => ( ( ord_less_eq_rat @ X @ Y )
% 5.31/5.49 = ( X = Y ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % antisym_conv1
% 5.31/5.49 thf(fact_939_antisym__conv1,axiom,
% 5.31/5.49 ! [X: num,Y: num] :
% 5.31/5.49 ( ~ ( ord_less_num @ X @ Y )
% 5.31/5.49 => ( ( ord_less_eq_num @ X @ Y )
% 5.31/5.49 = ( X = Y ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % antisym_conv1
% 5.31/5.49 thf(fact_940_antisym__conv1,axiom,
% 5.31/5.49 ! [X: nat,Y: nat] :
% 5.31/5.49 ( ~ ( ord_less_nat @ X @ Y )
% 5.31/5.49 => ( ( ord_less_eq_nat @ X @ Y )
% 5.31/5.49 = ( X = Y ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % antisym_conv1
% 5.31/5.49 thf(fact_941_antisym__conv1,axiom,
% 5.31/5.49 ! [X: int,Y: int] :
% 5.31/5.49 ( ~ ( ord_less_int @ X @ Y )
% 5.31/5.49 => ( ( ord_less_eq_int @ X @ Y )
% 5.31/5.49 = ( X = Y ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % antisym_conv1
% 5.31/5.49 thf(fact_942_nless__le,axiom,
% 5.31/5.49 ! [A: real,B: real] :
% 5.31/5.49 ( ( ~ ( ord_less_real @ A @ B ) )
% 5.31/5.49 = ( ~ ( ord_less_eq_real @ A @ B )
% 5.31/5.49 | ( A = B ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % nless_le
% 5.31/5.49 thf(fact_943_nless__le,axiom,
% 5.31/5.49 ! [A: set_nat,B: set_nat] :
% 5.31/5.49 ( ( ~ ( ord_less_set_nat @ A @ B ) )
% 5.31/5.49 = ( ~ ( ord_less_eq_set_nat @ A @ B )
% 5.31/5.49 | ( A = B ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % nless_le
% 5.31/5.49 thf(fact_944_nless__le,axiom,
% 5.31/5.49 ! [A: rat,B: rat] :
% 5.31/5.49 ( ( ~ ( ord_less_rat @ A @ B ) )
% 5.31/5.49 = ( ~ ( ord_less_eq_rat @ A @ B )
% 5.31/5.49 | ( A = B ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % nless_le
% 5.31/5.49 thf(fact_945_nless__le,axiom,
% 5.31/5.49 ! [A: num,B: num] :
% 5.31/5.49 ( ( ~ ( ord_less_num @ A @ B ) )
% 5.31/5.49 = ( ~ ( ord_less_eq_num @ A @ B )
% 5.31/5.49 | ( A = B ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % nless_le
% 5.31/5.49 thf(fact_946_nless__le,axiom,
% 5.31/5.49 ! [A: nat,B: nat] :
% 5.31/5.49 ( ( ~ ( ord_less_nat @ A @ B ) )
% 5.31/5.49 = ( ~ ( ord_less_eq_nat @ A @ B )
% 5.31/5.49 | ( A = B ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % nless_le
% 5.31/5.49 thf(fact_947_nless__le,axiom,
% 5.31/5.49 ! [A: int,B: int] :
% 5.31/5.49 ( ( ~ ( ord_less_int @ A @ B ) )
% 5.31/5.49 = ( ~ ( ord_less_eq_int @ A @ B )
% 5.31/5.49 | ( A = B ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % nless_le
% 5.31/5.49 thf(fact_948_leI,axiom,
% 5.31/5.49 ! [X: real,Y: real] :
% 5.31/5.49 ( ~ ( ord_less_real @ X @ Y )
% 5.31/5.49 => ( ord_less_eq_real @ Y @ X ) ) ).
% 5.31/5.49
% 5.31/5.49 % leI
% 5.31/5.49 thf(fact_949_leI,axiom,
% 5.31/5.49 ! [X: rat,Y: rat] :
% 5.31/5.49 ( ~ ( ord_less_rat @ X @ Y )
% 5.31/5.49 => ( ord_less_eq_rat @ Y @ X ) ) ).
% 5.31/5.49
% 5.31/5.49 % leI
% 5.31/5.49 thf(fact_950_leI,axiom,
% 5.31/5.49 ! [X: num,Y: num] :
% 5.31/5.49 ( ~ ( ord_less_num @ X @ Y )
% 5.31/5.49 => ( ord_less_eq_num @ Y @ X ) ) ).
% 5.31/5.49
% 5.31/5.49 % leI
% 5.31/5.49 thf(fact_951_leI,axiom,
% 5.31/5.49 ! [X: nat,Y: nat] :
% 5.31/5.49 ( ~ ( ord_less_nat @ X @ Y )
% 5.31/5.49 => ( ord_less_eq_nat @ Y @ X ) ) ).
% 5.31/5.49
% 5.31/5.49 % leI
% 5.31/5.49 thf(fact_952_leI,axiom,
% 5.31/5.49 ! [X: int,Y: int] :
% 5.31/5.49 ( ~ ( ord_less_int @ X @ Y )
% 5.31/5.49 => ( ord_less_eq_int @ Y @ X ) ) ).
% 5.31/5.49
% 5.31/5.49 % leI
% 5.31/5.49 thf(fact_953_leD,axiom,
% 5.31/5.49 ! [Y: real,X: real] :
% 5.31/5.49 ( ( ord_less_eq_real @ Y @ X )
% 5.31/5.49 => ~ ( ord_less_real @ X @ Y ) ) ).
% 5.31/5.49
% 5.31/5.49 % leD
% 5.31/5.49 thf(fact_954_leD,axiom,
% 5.31/5.49 ! [Y: set_nat,X: set_nat] :
% 5.31/5.49 ( ( ord_less_eq_set_nat @ Y @ X )
% 5.31/5.49 => ~ ( ord_less_set_nat @ X @ Y ) ) ).
% 5.31/5.49
% 5.31/5.49 % leD
% 5.31/5.49 thf(fact_955_leD,axiom,
% 5.31/5.49 ! [Y: rat,X: rat] :
% 5.31/5.49 ( ( ord_less_eq_rat @ Y @ X )
% 5.31/5.49 => ~ ( ord_less_rat @ X @ Y ) ) ).
% 5.31/5.49
% 5.31/5.49 % leD
% 5.31/5.49 thf(fact_956_leD,axiom,
% 5.31/5.49 ! [Y: num,X: num] :
% 5.31/5.49 ( ( ord_less_eq_num @ Y @ X )
% 5.31/5.49 => ~ ( ord_less_num @ X @ Y ) ) ).
% 5.31/5.49
% 5.31/5.49 % leD
% 5.31/5.49 thf(fact_957_leD,axiom,
% 5.31/5.49 ! [Y: nat,X: nat] :
% 5.31/5.49 ( ( ord_less_eq_nat @ Y @ X )
% 5.31/5.49 => ~ ( ord_less_nat @ X @ Y ) ) ).
% 5.31/5.49
% 5.31/5.49 % leD
% 5.31/5.49 thf(fact_958_leD,axiom,
% 5.31/5.49 ! [Y: int,X: int] :
% 5.31/5.49 ( ( ord_less_eq_int @ Y @ X )
% 5.31/5.49 => ~ ( ord_less_int @ X @ Y ) ) ).
% 5.31/5.49
% 5.31/5.49 % leD
% 5.31/5.49 thf(fact_959_zero__less__iff__neq__zero,axiom,
% 5.31/5.49 ! [N: nat] :
% 5.31/5.49 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.49 = ( N != zero_zero_nat ) ) ).
% 5.31/5.49
% 5.31/5.49 % zero_less_iff_neq_zero
% 5.31/5.49 thf(fact_960_gr__implies__not__zero,axiom,
% 5.31/5.49 ! [M2: nat,N: nat] :
% 5.31/5.49 ( ( ord_less_nat @ M2 @ N )
% 5.31/5.49 => ( N != zero_zero_nat ) ) ).
% 5.31/5.49
% 5.31/5.49 % gr_implies_not_zero
% 5.31/5.49 thf(fact_961_not__less__zero,axiom,
% 5.31/5.49 ! [N: nat] :
% 5.31/5.49 ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 5.31/5.49
% 5.31/5.49 % not_less_zero
% 5.31/5.49 thf(fact_962_gr__zeroI,axiom,
% 5.31/5.49 ! [N: nat] :
% 5.31/5.49 ( ( N != zero_zero_nat )
% 5.31/5.49 => ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 5.31/5.49
% 5.31/5.49 % gr_zeroI
% 5.31/5.49 thf(fact_963_less__numeral__extra_I3_J,axiom,
% 5.31/5.49 ~ ( ord_less_real @ zero_zero_real @ zero_zero_real ) ).
% 5.31/5.49
% 5.31/5.49 % less_numeral_extra(3)
% 5.31/5.49 thf(fact_964_less__numeral__extra_I3_J,axiom,
% 5.31/5.49 ~ ( ord_less_rat @ zero_zero_rat @ zero_zero_rat ) ).
% 5.31/5.49
% 5.31/5.49 % less_numeral_extra(3)
% 5.31/5.49 thf(fact_965_less__numeral__extra_I3_J,axiom,
% 5.31/5.49 ~ ( ord_less_nat @ zero_zero_nat @ zero_zero_nat ) ).
% 5.31/5.49
% 5.31/5.49 % less_numeral_extra(3)
% 5.31/5.49 thf(fact_966_less__numeral__extra_I3_J,axiom,
% 5.31/5.49 ~ ( ord_less_int @ zero_zero_int @ zero_zero_int ) ).
% 5.31/5.49
% 5.31/5.49 % less_numeral_extra(3)
% 5.31/5.49 thf(fact_967_not__less__less__Suc__eq,axiom,
% 5.31/5.49 ! [N: nat,M2: nat] :
% 5.31/5.49 ( ~ ( ord_less_nat @ N @ M2 )
% 5.31/5.49 => ( ( ord_less_nat @ N @ ( suc @ M2 ) )
% 5.31/5.49 = ( N = M2 ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % not_less_less_Suc_eq
% 5.31/5.49 thf(fact_968_strict__inc__induct,axiom,
% 5.31/5.49 ! [I2: nat,J2: nat,P2: nat > $o] :
% 5.31/5.49 ( ( ord_less_nat @ I2 @ J2 )
% 5.31/5.49 => ( ! [I3: nat] :
% 5.31/5.49 ( ( J2
% 5.31/5.49 = ( suc @ I3 ) )
% 5.31/5.49 => ( P2 @ I3 ) )
% 5.31/5.49 => ( ! [I3: nat] :
% 5.31/5.49 ( ( ord_less_nat @ I3 @ J2 )
% 5.31/5.49 => ( ( P2 @ ( suc @ I3 ) )
% 5.31/5.49 => ( P2 @ I3 ) ) )
% 5.31/5.49 => ( P2 @ I2 ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % strict_inc_induct
% 5.31/5.49 thf(fact_969_less__Suc__induct,axiom,
% 5.31/5.49 ! [I2: nat,J2: nat,P2: nat > nat > $o] :
% 5.31/5.49 ( ( ord_less_nat @ I2 @ J2 )
% 5.31/5.49 => ( ! [I3: nat] : ( P2 @ I3 @ ( suc @ I3 ) )
% 5.31/5.49 => ( ! [I3: nat,J3: nat,K: nat] :
% 5.31/5.49 ( ( ord_less_nat @ I3 @ J3 )
% 5.31/5.49 => ( ( ord_less_nat @ J3 @ K )
% 5.31/5.49 => ( ( P2 @ I3 @ J3 )
% 5.31/5.49 => ( ( P2 @ J3 @ K )
% 5.31/5.49 => ( P2 @ I3 @ K ) ) ) ) )
% 5.31/5.49 => ( P2 @ I2 @ J2 ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % less_Suc_induct
% 5.31/5.49 thf(fact_970_less__trans__Suc,axiom,
% 5.31/5.49 ! [I2: nat,J2: nat,K2: nat] :
% 5.31/5.49 ( ( ord_less_nat @ I2 @ J2 )
% 5.31/5.49 => ( ( ord_less_nat @ J2 @ K2 )
% 5.31/5.49 => ( ord_less_nat @ ( suc @ I2 ) @ K2 ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % less_trans_Suc
% 5.31/5.49 thf(fact_971_Suc__less__SucD,axiom,
% 5.31/5.49 ! [M2: nat,N: nat] :
% 5.31/5.49 ( ( ord_less_nat @ ( suc @ M2 ) @ ( suc @ N ) )
% 5.31/5.49 => ( ord_less_nat @ M2 @ N ) ) ).
% 5.31/5.49
% 5.31/5.49 % Suc_less_SucD
% 5.31/5.49 thf(fact_972_less__antisym,axiom,
% 5.31/5.49 ! [N: nat,M2: nat] :
% 5.31/5.49 ( ~ ( ord_less_nat @ N @ M2 )
% 5.31/5.49 => ( ( ord_less_nat @ N @ ( suc @ M2 ) )
% 5.31/5.49 => ( M2 = N ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % less_antisym
% 5.31/5.49 thf(fact_973_Suc__less__eq2,axiom,
% 5.31/5.49 ! [N: nat,M2: nat] :
% 5.31/5.49 ( ( ord_less_nat @ ( suc @ N ) @ M2 )
% 5.31/5.49 = ( ? [M7: nat] :
% 5.31/5.49 ( ( M2
% 5.31/5.49 = ( suc @ M7 ) )
% 5.31/5.49 & ( ord_less_nat @ N @ M7 ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % Suc_less_eq2
% 5.31/5.49 thf(fact_974_All__less__Suc,axiom,
% 5.31/5.49 ! [N: nat,P2: nat > $o] :
% 5.31/5.49 ( ( ! [I: nat] :
% 5.31/5.49 ( ( ord_less_nat @ I @ ( suc @ N ) )
% 5.31/5.49 => ( P2 @ I ) ) )
% 5.31/5.49 = ( ( P2 @ N )
% 5.31/5.49 & ! [I: nat] :
% 5.31/5.49 ( ( ord_less_nat @ I @ N )
% 5.31/5.49 => ( P2 @ I ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % All_less_Suc
% 5.31/5.49 thf(fact_975_not__less__eq,axiom,
% 5.31/5.49 ! [M2: nat,N: nat] :
% 5.31/5.49 ( ( ~ ( ord_less_nat @ M2 @ N ) )
% 5.31/5.49 = ( ord_less_nat @ N @ ( suc @ M2 ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % not_less_eq
% 5.31/5.49 thf(fact_976_less__Suc__eq,axiom,
% 5.31/5.49 ! [M2: nat,N: nat] :
% 5.31/5.49 ( ( ord_less_nat @ M2 @ ( suc @ N ) )
% 5.31/5.49 = ( ( ord_less_nat @ M2 @ N )
% 5.31/5.49 | ( M2 = N ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % less_Suc_eq
% 5.31/5.49 thf(fact_977_Ex__less__Suc,axiom,
% 5.31/5.49 ! [N: nat,P2: nat > $o] :
% 5.31/5.49 ( ( ? [I: nat] :
% 5.31/5.49 ( ( ord_less_nat @ I @ ( suc @ N ) )
% 5.31/5.49 & ( P2 @ I ) ) )
% 5.31/5.49 = ( ( P2 @ N )
% 5.31/5.49 | ? [I: nat] :
% 5.31/5.49 ( ( ord_less_nat @ I @ N )
% 5.31/5.49 & ( P2 @ I ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % Ex_less_Suc
% 5.31/5.49 thf(fact_978_less__SucI,axiom,
% 5.31/5.49 ! [M2: nat,N: nat] :
% 5.31/5.49 ( ( ord_less_nat @ M2 @ N )
% 5.31/5.49 => ( ord_less_nat @ M2 @ ( suc @ N ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % less_SucI
% 5.31/5.49 thf(fact_979_less__SucE,axiom,
% 5.31/5.49 ! [M2: nat,N: nat] :
% 5.31/5.49 ( ( ord_less_nat @ M2 @ ( suc @ N ) )
% 5.31/5.49 => ( ~ ( ord_less_nat @ M2 @ N )
% 5.31/5.49 => ( M2 = N ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % less_SucE
% 5.31/5.49 thf(fact_980_Suc__lessI,axiom,
% 5.31/5.49 ! [M2: nat,N: nat] :
% 5.31/5.49 ( ( ord_less_nat @ M2 @ N )
% 5.31/5.49 => ( ( ( suc @ M2 )
% 5.31/5.49 != N )
% 5.31/5.49 => ( ord_less_nat @ ( suc @ M2 ) @ N ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % Suc_lessI
% 5.31/5.49 thf(fact_981_Suc__lessE,axiom,
% 5.31/5.49 ! [I2: nat,K2: nat] :
% 5.31/5.49 ( ( ord_less_nat @ ( suc @ I2 ) @ K2 )
% 5.31/5.49 => ~ ! [J3: nat] :
% 5.31/5.49 ( ( ord_less_nat @ I2 @ J3 )
% 5.31/5.49 => ( K2
% 5.31/5.49 != ( suc @ J3 ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % Suc_lessE
% 5.31/5.49 thf(fact_982_Suc__lessD,axiom,
% 5.31/5.49 ! [M2: nat,N: nat] :
% 5.31/5.49 ( ( ord_less_nat @ ( suc @ M2 ) @ N )
% 5.31/5.49 => ( ord_less_nat @ M2 @ N ) ) ).
% 5.31/5.49
% 5.31/5.49 % Suc_lessD
% 5.31/5.49 thf(fact_983_Nat_OlessE,axiom,
% 5.31/5.49 ! [I2: nat,K2: nat] :
% 5.31/5.49 ( ( ord_less_nat @ I2 @ K2 )
% 5.31/5.49 => ( ( K2
% 5.31/5.49 != ( suc @ I2 ) )
% 5.31/5.49 => ~ ! [J3: nat] :
% 5.31/5.49 ( ( ord_less_nat @ I2 @ J3 )
% 5.31/5.49 => ( K2
% 5.31/5.49 != ( suc @ J3 ) ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % Nat.lessE
% 5.31/5.49 thf(fact_984_VEBT_Odistinct_I1_J,axiom,
% 5.31/5.49 ! [X11: option4927543243414619207at_nat,X12: nat,X13: list_VEBT_VEBT,X14: vEBT_VEBT,X21: $o,X22: $o] :
% 5.31/5.49 ( ( vEBT_Node @ X11 @ X12 @ X13 @ X14 )
% 5.31/5.49 != ( vEBT_Leaf @ X21 @ X22 ) ) ).
% 5.31/5.49
% 5.31/5.49 % VEBT.distinct(1)
% 5.31/5.49 thf(fact_985_VEBT_Oexhaust,axiom,
% 5.31/5.49 ! [Y: vEBT_VEBT] :
% 5.31/5.49 ( ! [X112: option4927543243414619207at_nat,X122: nat,X132: list_VEBT_VEBT,X142: vEBT_VEBT] :
% 5.31/5.49 ( Y
% 5.31/5.49 != ( vEBT_Node @ X112 @ X122 @ X132 @ X142 ) )
% 5.31/5.49 => ~ ! [X212: $o,X222: $o] :
% 5.31/5.49 ( Y
% 5.31/5.49 != ( vEBT_Leaf @ X212 @ X222 ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % VEBT.exhaust
% 5.31/5.49 thf(fact_986_le__numeral__extra_I4_J,axiom,
% 5.31/5.49 ord_le3102999989581377725nteger @ one_one_Code_integer @ one_one_Code_integer ).
% 5.31/5.49
% 5.31/5.49 % le_numeral_extra(4)
% 5.31/5.49 thf(fact_987_le__numeral__extra_I4_J,axiom,
% 5.31/5.49 ord_less_eq_real @ one_one_real @ one_one_real ).
% 5.31/5.49
% 5.31/5.49 % le_numeral_extra(4)
% 5.31/5.49 thf(fact_988_le__numeral__extra_I4_J,axiom,
% 5.31/5.49 ord_less_eq_rat @ one_one_rat @ one_one_rat ).
% 5.31/5.49
% 5.31/5.49 % le_numeral_extra(4)
% 5.31/5.49 thf(fact_989_le__numeral__extra_I4_J,axiom,
% 5.31/5.49 ord_less_eq_nat @ one_one_nat @ one_one_nat ).
% 5.31/5.49
% 5.31/5.49 % le_numeral_extra(4)
% 5.31/5.49 thf(fact_990_le__numeral__extra_I4_J,axiom,
% 5.31/5.49 ord_less_eq_int @ one_one_int @ one_one_int ).
% 5.31/5.49
% 5.31/5.49 % le_numeral_extra(4)
% 5.31/5.49 thf(fact_991_zero__neq__one,axiom,
% 5.31/5.49 zero_z3403309356797280102nteger != one_one_Code_integer ).
% 5.31/5.49
% 5.31/5.49 % zero_neq_one
% 5.31/5.49 thf(fact_992_zero__neq__one,axiom,
% 5.31/5.49 zero_zero_complex != one_one_complex ).
% 5.31/5.49
% 5.31/5.49 % zero_neq_one
% 5.31/5.49 thf(fact_993_zero__neq__one,axiom,
% 5.31/5.49 zero_zero_real != one_one_real ).
% 5.31/5.49
% 5.31/5.49 % zero_neq_one
% 5.31/5.49 thf(fact_994_zero__neq__one,axiom,
% 5.31/5.49 zero_zero_rat != one_one_rat ).
% 5.31/5.49
% 5.31/5.49 % zero_neq_one
% 5.31/5.49 thf(fact_995_zero__neq__one,axiom,
% 5.31/5.49 zero_zero_nat != one_one_nat ).
% 5.31/5.49
% 5.31/5.49 % zero_neq_one
% 5.31/5.49 thf(fact_996_zero__neq__one,axiom,
% 5.31/5.49 zero_zero_int != one_one_int ).
% 5.31/5.49
% 5.31/5.49 % zero_neq_one
% 5.31/5.49 thf(fact_997_bot__nat__0_Oextremum__strict,axiom,
% 5.31/5.49 ! [A: nat] :
% 5.31/5.49 ~ ( ord_less_nat @ A @ zero_zero_nat ) ).
% 5.31/5.49
% 5.31/5.49 % bot_nat_0.extremum_strict
% 5.31/5.49 thf(fact_998_gr0I,axiom,
% 5.31/5.49 ! [N: nat] :
% 5.31/5.49 ( ( N != zero_zero_nat )
% 5.31/5.49 => ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 5.31/5.49
% 5.31/5.49 % gr0I
% 5.31/5.49 thf(fact_999_not__gr0,axiom,
% 5.31/5.49 ! [N: nat] :
% 5.31/5.49 ( ( ~ ( ord_less_nat @ zero_zero_nat @ N ) )
% 5.31/5.49 = ( N = zero_zero_nat ) ) ).
% 5.31/5.49
% 5.31/5.49 % not_gr0
% 5.31/5.49 thf(fact_1000_not__less0,axiom,
% 5.31/5.49 ! [N: nat] :
% 5.31/5.49 ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 5.31/5.49
% 5.31/5.49 % not_less0
% 5.31/5.49 thf(fact_1001_less__zeroE,axiom,
% 5.31/5.49 ! [N: nat] :
% 5.31/5.49 ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 5.31/5.49
% 5.31/5.49 % less_zeroE
% 5.31/5.49 thf(fact_1002_gr__implies__not0,axiom,
% 5.31/5.49 ! [M2: nat,N: nat] :
% 5.31/5.49 ( ( ord_less_nat @ M2 @ N )
% 5.31/5.49 => ( N != zero_zero_nat ) ) ).
% 5.31/5.49
% 5.31/5.49 % gr_implies_not0
% 5.31/5.49 thf(fact_1003_infinite__descent0,axiom,
% 5.31/5.49 ! [P2: nat > $o,N: nat] :
% 5.31/5.49 ( ( P2 @ zero_zero_nat )
% 5.31/5.49 => ( ! [N3: nat] :
% 5.31/5.49 ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 5.31/5.49 => ( ~ ( P2 @ N3 )
% 5.31/5.49 => ? [M3: nat] :
% 5.31/5.49 ( ( ord_less_nat @ M3 @ N3 )
% 5.31/5.49 & ~ ( P2 @ M3 ) ) ) )
% 5.31/5.49 => ( P2 @ N ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % infinite_descent0
% 5.31/5.49 thf(fact_1004_mult_Ocomm__neutral,axiom,
% 5.31/5.49 ! [A: code_integer] :
% 5.31/5.49 ( ( times_3573771949741848930nteger @ A @ one_one_Code_integer )
% 5.31/5.49 = A ) ).
% 5.31/5.49
% 5.31/5.49 % mult.comm_neutral
% 5.31/5.49 thf(fact_1005_mult_Ocomm__neutral,axiom,
% 5.31/5.49 ! [A: complex] :
% 5.31/5.49 ( ( times_times_complex @ A @ one_one_complex )
% 5.31/5.49 = A ) ).
% 5.31/5.49
% 5.31/5.49 % mult.comm_neutral
% 5.31/5.49 thf(fact_1006_mult_Ocomm__neutral,axiom,
% 5.31/5.49 ! [A: real] :
% 5.31/5.49 ( ( times_times_real @ A @ one_one_real )
% 5.31/5.49 = A ) ).
% 5.31/5.49
% 5.31/5.49 % mult.comm_neutral
% 5.31/5.49 thf(fact_1007_mult_Ocomm__neutral,axiom,
% 5.31/5.49 ! [A: rat] :
% 5.31/5.49 ( ( times_times_rat @ A @ one_one_rat )
% 5.31/5.49 = A ) ).
% 5.31/5.49
% 5.31/5.49 % mult.comm_neutral
% 5.31/5.49 thf(fact_1008_mult_Ocomm__neutral,axiom,
% 5.31/5.49 ! [A: nat] :
% 5.31/5.49 ( ( times_times_nat @ A @ one_one_nat )
% 5.31/5.49 = A ) ).
% 5.31/5.49
% 5.31/5.49 % mult.comm_neutral
% 5.31/5.49 thf(fact_1009_mult_Ocomm__neutral,axiom,
% 5.31/5.49 ! [A: int] :
% 5.31/5.49 ( ( times_times_int @ A @ one_one_int )
% 5.31/5.49 = A ) ).
% 5.31/5.49
% 5.31/5.49 % mult.comm_neutral
% 5.31/5.49 thf(fact_1010_comm__monoid__mult__class_Omult__1,axiom,
% 5.31/5.49 ! [A: code_integer] :
% 5.31/5.49 ( ( times_3573771949741848930nteger @ one_one_Code_integer @ A )
% 5.31/5.49 = A ) ).
% 5.31/5.49
% 5.31/5.49 % comm_monoid_mult_class.mult_1
% 5.31/5.49 thf(fact_1011_comm__monoid__mult__class_Omult__1,axiom,
% 5.31/5.49 ! [A: complex] :
% 5.31/5.49 ( ( times_times_complex @ one_one_complex @ A )
% 5.31/5.49 = A ) ).
% 5.31/5.49
% 5.31/5.49 % comm_monoid_mult_class.mult_1
% 5.31/5.49 thf(fact_1012_comm__monoid__mult__class_Omult__1,axiom,
% 5.31/5.49 ! [A: real] :
% 5.31/5.49 ( ( times_times_real @ one_one_real @ A )
% 5.31/5.49 = A ) ).
% 5.31/5.49
% 5.31/5.49 % comm_monoid_mult_class.mult_1
% 5.31/5.49 thf(fact_1013_comm__monoid__mult__class_Omult__1,axiom,
% 5.31/5.49 ! [A: rat] :
% 5.31/5.49 ( ( times_times_rat @ one_one_rat @ A )
% 5.31/5.49 = A ) ).
% 5.31/5.49
% 5.31/5.49 % comm_monoid_mult_class.mult_1
% 5.31/5.49 thf(fact_1014_comm__monoid__mult__class_Omult__1,axiom,
% 5.31/5.49 ! [A: nat] :
% 5.31/5.49 ( ( times_times_nat @ one_one_nat @ A )
% 5.31/5.49 = A ) ).
% 5.31/5.49
% 5.31/5.49 % comm_monoid_mult_class.mult_1
% 5.31/5.49 thf(fact_1015_comm__monoid__mult__class_Omult__1,axiom,
% 5.31/5.49 ! [A: int] :
% 5.31/5.49 ( ( times_times_int @ one_one_int @ A )
% 5.31/5.49 = A ) ).
% 5.31/5.49
% 5.31/5.49 % comm_monoid_mult_class.mult_1
% 5.31/5.49 thf(fact_1016_less__mono__imp__le__mono,axiom,
% 5.31/5.49 ! [F2: nat > nat,I2: nat,J2: nat] :
% 5.31/5.49 ( ! [I3: nat,J3: nat] :
% 5.31/5.49 ( ( ord_less_nat @ I3 @ J3 )
% 5.31/5.49 => ( ord_less_nat @ ( F2 @ I3 ) @ ( F2 @ J3 ) ) )
% 5.31/5.49 => ( ( ord_less_eq_nat @ I2 @ J2 )
% 5.31/5.49 => ( ord_less_eq_nat @ ( F2 @ I2 ) @ ( F2 @ J2 ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % less_mono_imp_le_mono
% 5.31/5.49 thf(fact_1017_le__neq__implies__less,axiom,
% 5.31/5.49 ! [M2: nat,N: nat] :
% 5.31/5.49 ( ( ord_less_eq_nat @ M2 @ N )
% 5.31/5.49 => ( ( M2 != N )
% 5.31/5.49 => ( ord_less_nat @ M2 @ N ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % le_neq_implies_less
% 5.31/5.49 thf(fact_1018_less__or__eq__imp__le,axiom,
% 5.31/5.49 ! [M2: nat,N: nat] :
% 5.31/5.49 ( ( ( ord_less_nat @ M2 @ N )
% 5.31/5.49 | ( M2 = N ) )
% 5.31/5.49 => ( ord_less_eq_nat @ M2 @ N ) ) ).
% 5.31/5.49
% 5.31/5.49 % less_or_eq_imp_le
% 5.31/5.49 thf(fact_1019_le__eq__less__or__eq,axiom,
% 5.31/5.49 ( ord_less_eq_nat
% 5.31/5.49 = ( ^ [M6: nat,N4: nat] :
% 5.31/5.49 ( ( ord_less_nat @ M6 @ N4 )
% 5.31/5.49 | ( M6 = N4 ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % le_eq_less_or_eq
% 5.31/5.49 thf(fact_1020_less__imp__le__nat,axiom,
% 5.31/5.49 ! [M2: nat,N: nat] :
% 5.31/5.49 ( ( ord_less_nat @ M2 @ N )
% 5.31/5.49 => ( ord_less_eq_nat @ M2 @ N ) ) ).
% 5.31/5.49
% 5.31/5.49 % less_imp_le_nat
% 5.31/5.49 thf(fact_1021_nat__less__le,axiom,
% 5.31/5.49 ( ord_less_nat
% 5.31/5.49 = ( ^ [M6: nat,N4: nat] :
% 5.31/5.49 ( ( ord_less_eq_nat @ M6 @ N4 )
% 5.31/5.49 & ( M6 != N4 ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % nat_less_le
% 5.31/5.49 thf(fact_1022_nat__mult__1,axiom,
% 5.31/5.49 ! [N: nat] :
% 5.31/5.49 ( ( times_times_nat @ one_one_nat @ N )
% 5.31/5.49 = N ) ).
% 5.31/5.49
% 5.31/5.49 % nat_mult_1
% 5.31/5.49 thf(fact_1023_nat__mult__1__right,axiom,
% 5.31/5.49 ! [N: nat] :
% 5.31/5.49 ( ( times_times_nat @ N @ one_one_nat )
% 5.31/5.49 = N ) ).
% 5.31/5.49
% 5.31/5.49 % nat_mult_1_right
% 5.31/5.49 thf(fact_1024_nat__mult__eq__cancel1,axiom,
% 5.31/5.49 ! [K2: nat,M2: nat,N: nat] :
% 5.31/5.49 ( ( ord_less_nat @ zero_zero_nat @ K2 )
% 5.31/5.49 => ( ( ( times_times_nat @ K2 @ M2 )
% 5.31/5.49 = ( times_times_nat @ K2 @ N ) )
% 5.31/5.49 = ( M2 = N ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % nat_mult_eq_cancel1
% 5.31/5.49 thf(fact_1025_nat__mult__less__cancel1,axiom,
% 5.31/5.49 ! [K2: nat,M2: nat,N: nat] :
% 5.31/5.49 ( ( ord_less_nat @ zero_zero_nat @ K2 )
% 5.31/5.49 => ( ( ord_less_nat @ ( times_times_nat @ K2 @ M2 ) @ ( times_times_nat @ K2 @ N ) )
% 5.31/5.49 = ( ord_less_nat @ M2 @ N ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % nat_mult_less_cancel1
% 5.31/5.49 thf(fact_1026_mult__less__cancel__right2,axiom,
% 5.31/5.49 ! [A: code_integer,C2: code_integer] :
% 5.31/5.49 ( ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ A @ C2 ) @ C2 )
% 5.31/5.49 = ( ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C2 )
% 5.31/5.49 => ( ord_le6747313008572928689nteger @ A @ one_one_Code_integer ) )
% 5.31/5.49 & ( ( ord_le3102999989581377725nteger @ C2 @ zero_z3403309356797280102nteger )
% 5.31/5.49 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ A ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % mult_less_cancel_right2
% 5.31/5.49 thf(fact_1027_mult__less__cancel__right2,axiom,
% 5.31/5.49 ! [A: real,C2: real] :
% 5.31/5.49 ( ( ord_less_real @ ( times_times_real @ A @ C2 ) @ C2 )
% 5.31/5.49 = ( ( ( ord_less_eq_real @ zero_zero_real @ C2 )
% 5.31/5.49 => ( ord_less_real @ A @ one_one_real ) )
% 5.31/5.49 & ( ( ord_less_eq_real @ C2 @ zero_zero_real )
% 5.31/5.49 => ( ord_less_real @ one_one_real @ A ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % mult_less_cancel_right2
% 5.31/5.49 thf(fact_1028_mult__less__cancel__right2,axiom,
% 5.31/5.49 ! [A: rat,C2: rat] :
% 5.31/5.49 ( ( ord_less_rat @ ( times_times_rat @ A @ C2 ) @ C2 )
% 5.31/5.49 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C2 )
% 5.31/5.49 => ( ord_less_rat @ A @ one_one_rat ) )
% 5.31/5.49 & ( ( ord_less_eq_rat @ C2 @ zero_zero_rat )
% 5.31/5.49 => ( ord_less_rat @ one_one_rat @ A ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % mult_less_cancel_right2
% 5.31/5.49 thf(fact_1029_mult__less__cancel__right2,axiom,
% 5.31/5.49 ! [A: int,C2: int] :
% 5.31/5.49 ( ( ord_less_int @ ( times_times_int @ A @ C2 ) @ C2 )
% 5.31/5.49 = ( ( ( ord_less_eq_int @ zero_zero_int @ C2 )
% 5.31/5.49 => ( ord_less_int @ A @ one_one_int ) )
% 5.31/5.49 & ( ( ord_less_eq_int @ C2 @ zero_zero_int )
% 5.31/5.49 => ( ord_less_int @ one_one_int @ A ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % mult_less_cancel_right2
% 5.31/5.49 thf(fact_1030_mult__less__cancel__right1,axiom,
% 5.31/5.49 ! [C2: code_integer,B: code_integer] :
% 5.31/5.49 ( ( ord_le6747313008572928689nteger @ C2 @ ( times_3573771949741848930nteger @ B @ C2 ) )
% 5.31/5.49 = ( ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C2 )
% 5.31/5.49 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ B ) )
% 5.31/5.49 & ( ( ord_le3102999989581377725nteger @ C2 @ zero_z3403309356797280102nteger )
% 5.31/5.49 => ( ord_le6747313008572928689nteger @ B @ one_one_Code_integer ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % mult_less_cancel_right1
% 5.31/5.49 thf(fact_1031_mult__less__cancel__right1,axiom,
% 5.31/5.49 ! [C2: real,B: real] :
% 5.31/5.49 ( ( ord_less_real @ C2 @ ( times_times_real @ B @ C2 ) )
% 5.31/5.49 = ( ( ( ord_less_eq_real @ zero_zero_real @ C2 )
% 5.31/5.49 => ( ord_less_real @ one_one_real @ B ) )
% 5.31/5.49 & ( ( ord_less_eq_real @ C2 @ zero_zero_real )
% 5.31/5.49 => ( ord_less_real @ B @ one_one_real ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % mult_less_cancel_right1
% 5.31/5.49 thf(fact_1032_mult__less__cancel__right1,axiom,
% 5.31/5.49 ! [C2: rat,B: rat] :
% 5.31/5.49 ( ( ord_less_rat @ C2 @ ( times_times_rat @ B @ C2 ) )
% 5.31/5.49 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C2 )
% 5.31/5.49 => ( ord_less_rat @ one_one_rat @ B ) )
% 5.31/5.49 & ( ( ord_less_eq_rat @ C2 @ zero_zero_rat )
% 5.31/5.49 => ( ord_less_rat @ B @ one_one_rat ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % mult_less_cancel_right1
% 5.31/5.49 thf(fact_1033_mult__less__cancel__right1,axiom,
% 5.31/5.49 ! [C2: int,B: int] :
% 5.31/5.49 ( ( ord_less_int @ C2 @ ( times_times_int @ B @ C2 ) )
% 5.31/5.49 = ( ( ( ord_less_eq_int @ zero_zero_int @ C2 )
% 5.31/5.49 => ( ord_less_int @ one_one_int @ B ) )
% 5.31/5.49 & ( ( ord_less_eq_int @ C2 @ zero_zero_int )
% 5.31/5.49 => ( ord_less_int @ B @ one_one_int ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % mult_less_cancel_right1
% 5.31/5.49 thf(fact_1034_mult__less__cancel__left2,axiom,
% 5.31/5.49 ! [C2: code_integer,A: code_integer] :
% 5.31/5.49 ( ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ C2 @ A ) @ C2 )
% 5.31/5.49 = ( ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C2 )
% 5.31/5.49 => ( ord_le6747313008572928689nteger @ A @ one_one_Code_integer ) )
% 5.31/5.49 & ( ( ord_le3102999989581377725nteger @ C2 @ zero_z3403309356797280102nteger )
% 5.31/5.49 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ A ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % mult_less_cancel_left2
% 5.31/5.49 thf(fact_1035_mult__less__cancel__left2,axiom,
% 5.31/5.49 ! [C2: real,A: real] :
% 5.31/5.49 ( ( ord_less_real @ ( times_times_real @ C2 @ A ) @ C2 )
% 5.31/5.49 = ( ( ( ord_less_eq_real @ zero_zero_real @ C2 )
% 5.31/5.49 => ( ord_less_real @ A @ one_one_real ) )
% 5.31/5.49 & ( ( ord_less_eq_real @ C2 @ zero_zero_real )
% 5.31/5.49 => ( ord_less_real @ one_one_real @ A ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % mult_less_cancel_left2
% 5.31/5.49 thf(fact_1036_mult__less__cancel__left2,axiom,
% 5.31/5.49 ! [C2: rat,A: rat] :
% 5.31/5.49 ( ( ord_less_rat @ ( times_times_rat @ C2 @ A ) @ C2 )
% 5.31/5.49 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C2 )
% 5.31/5.49 => ( ord_less_rat @ A @ one_one_rat ) )
% 5.31/5.49 & ( ( ord_less_eq_rat @ C2 @ zero_zero_rat )
% 5.31/5.49 => ( ord_less_rat @ one_one_rat @ A ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % mult_less_cancel_left2
% 5.31/5.49 thf(fact_1037_mult__less__cancel__left2,axiom,
% 5.31/5.49 ! [C2: int,A: int] :
% 5.31/5.49 ( ( ord_less_int @ ( times_times_int @ C2 @ A ) @ C2 )
% 5.31/5.49 = ( ( ( ord_less_eq_int @ zero_zero_int @ C2 )
% 5.31/5.49 => ( ord_less_int @ A @ one_one_int ) )
% 5.31/5.49 & ( ( ord_less_eq_int @ C2 @ zero_zero_int )
% 5.31/5.49 => ( ord_less_int @ one_one_int @ A ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % mult_less_cancel_left2
% 5.31/5.49 thf(fact_1038_mult__less__cancel__left1,axiom,
% 5.31/5.49 ! [C2: code_integer,B: code_integer] :
% 5.31/5.49 ( ( ord_le6747313008572928689nteger @ C2 @ ( times_3573771949741848930nteger @ C2 @ B ) )
% 5.31/5.49 = ( ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C2 )
% 5.31/5.49 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ B ) )
% 5.31/5.49 & ( ( ord_le3102999989581377725nteger @ C2 @ zero_z3403309356797280102nteger )
% 5.31/5.49 => ( ord_le6747313008572928689nteger @ B @ one_one_Code_integer ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % mult_less_cancel_left1
% 5.31/5.49 thf(fact_1039_mult__less__cancel__left1,axiom,
% 5.31/5.49 ! [C2: real,B: real] :
% 5.31/5.49 ( ( ord_less_real @ C2 @ ( times_times_real @ C2 @ B ) )
% 5.31/5.49 = ( ( ( ord_less_eq_real @ zero_zero_real @ C2 )
% 5.31/5.49 => ( ord_less_real @ one_one_real @ B ) )
% 5.31/5.49 & ( ( ord_less_eq_real @ C2 @ zero_zero_real )
% 5.31/5.49 => ( ord_less_real @ B @ one_one_real ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % mult_less_cancel_left1
% 5.31/5.49 thf(fact_1040_mult__less__cancel__left1,axiom,
% 5.31/5.49 ! [C2: rat,B: rat] :
% 5.31/5.49 ( ( ord_less_rat @ C2 @ ( times_times_rat @ C2 @ B ) )
% 5.31/5.49 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C2 )
% 5.31/5.49 => ( ord_less_rat @ one_one_rat @ B ) )
% 5.31/5.49 & ( ( ord_less_eq_rat @ C2 @ zero_zero_rat )
% 5.31/5.49 => ( ord_less_rat @ B @ one_one_rat ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % mult_less_cancel_left1
% 5.31/5.49 thf(fact_1041_mult__less__cancel__left1,axiom,
% 5.31/5.49 ! [C2: int,B: int] :
% 5.31/5.49 ( ( ord_less_int @ C2 @ ( times_times_int @ C2 @ B ) )
% 5.31/5.49 = ( ( ( ord_less_eq_int @ zero_zero_int @ C2 )
% 5.31/5.49 => ( ord_less_int @ one_one_int @ B ) )
% 5.31/5.49 & ( ( ord_less_eq_int @ C2 @ zero_zero_int )
% 5.31/5.49 => ( ord_less_int @ B @ one_one_int ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % mult_less_cancel_left1
% 5.31/5.49 thf(fact_1042_mult__le__cancel__right2,axiom,
% 5.31/5.49 ! [A: code_integer,C2: code_integer] :
% 5.31/5.49 ( ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ A @ C2 ) @ C2 )
% 5.31/5.49 = ( ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C2 )
% 5.31/5.49 => ( ord_le3102999989581377725nteger @ A @ one_one_Code_integer ) )
% 5.31/5.49 & ( ( ord_le6747313008572928689nteger @ C2 @ zero_z3403309356797280102nteger )
% 5.31/5.49 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ A ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % mult_le_cancel_right2
% 5.31/5.49 thf(fact_1043_mult__le__cancel__right2,axiom,
% 5.31/5.49 ! [A: real,C2: real] :
% 5.31/5.49 ( ( ord_less_eq_real @ ( times_times_real @ A @ C2 ) @ C2 )
% 5.31/5.49 = ( ( ( ord_less_real @ zero_zero_real @ C2 )
% 5.31/5.49 => ( ord_less_eq_real @ A @ one_one_real ) )
% 5.31/5.49 & ( ( ord_less_real @ C2 @ zero_zero_real )
% 5.31/5.49 => ( ord_less_eq_real @ one_one_real @ A ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % mult_le_cancel_right2
% 5.31/5.49 thf(fact_1044_mult__le__cancel__right2,axiom,
% 5.31/5.49 ! [A: rat,C2: rat] :
% 5.31/5.49 ( ( ord_less_eq_rat @ ( times_times_rat @ A @ C2 ) @ C2 )
% 5.31/5.49 = ( ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 5.31/5.49 => ( ord_less_eq_rat @ A @ one_one_rat ) )
% 5.31/5.49 & ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 5.31/5.49 => ( ord_less_eq_rat @ one_one_rat @ A ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % mult_le_cancel_right2
% 5.31/5.49 thf(fact_1045_mult__le__cancel__right2,axiom,
% 5.31/5.49 ! [A: int,C2: int] :
% 5.31/5.49 ( ( ord_less_eq_int @ ( times_times_int @ A @ C2 ) @ C2 )
% 5.31/5.49 = ( ( ( ord_less_int @ zero_zero_int @ C2 )
% 5.31/5.49 => ( ord_less_eq_int @ A @ one_one_int ) )
% 5.31/5.49 & ( ( ord_less_int @ C2 @ zero_zero_int )
% 5.31/5.49 => ( ord_less_eq_int @ one_one_int @ A ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % mult_le_cancel_right2
% 5.31/5.49 thf(fact_1046_mult__le__cancel__right1,axiom,
% 5.31/5.49 ! [C2: code_integer,B: code_integer] :
% 5.31/5.49 ( ( ord_le3102999989581377725nteger @ C2 @ ( times_3573771949741848930nteger @ B @ C2 ) )
% 5.31/5.49 = ( ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C2 )
% 5.31/5.49 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ B ) )
% 5.31/5.49 & ( ( ord_le6747313008572928689nteger @ C2 @ zero_z3403309356797280102nteger )
% 5.31/5.49 => ( ord_le3102999989581377725nteger @ B @ one_one_Code_integer ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % mult_le_cancel_right1
% 5.31/5.49 thf(fact_1047_mult__le__cancel__right1,axiom,
% 5.31/5.49 ! [C2: real,B: real] :
% 5.31/5.49 ( ( ord_less_eq_real @ C2 @ ( times_times_real @ B @ C2 ) )
% 5.31/5.49 = ( ( ( ord_less_real @ zero_zero_real @ C2 )
% 5.31/5.49 => ( ord_less_eq_real @ one_one_real @ B ) )
% 5.31/5.49 & ( ( ord_less_real @ C2 @ zero_zero_real )
% 5.31/5.49 => ( ord_less_eq_real @ B @ one_one_real ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % mult_le_cancel_right1
% 5.31/5.49 thf(fact_1048_mult__le__cancel__right1,axiom,
% 5.31/5.49 ! [C2: rat,B: rat] :
% 5.31/5.49 ( ( ord_less_eq_rat @ C2 @ ( times_times_rat @ B @ C2 ) )
% 5.31/5.49 = ( ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 5.31/5.49 => ( ord_less_eq_rat @ one_one_rat @ B ) )
% 5.31/5.49 & ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 5.31/5.49 => ( ord_less_eq_rat @ B @ one_one_rat ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % mult_le_cancel_right1
% 5.31/5.49 thf(fact_1049_mult__le__cancel__right1,axiom,
% 5.31/5.49 ! [C2: int,B: int] :
% 5.31/5.49 ( ( ord_less_eq_int @ C2 @ ( times_times_int @ B @ C2 ) )
% 5.31/5.49 = ( ( ( ord_less_int @ zero_zero_int @ C2 )
% 5.31/5.49 => ( ord_less_eq_int @ one_one_int @ B ) )
% 5.31/5.49 & ( ( ord_less_int @ C2 @ zero_zero_int )
% 5.31/5.49 => ( ord_less_eq_int @ B @ one_one_int ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % mult_le_cancel_right1
% 5.31/5.49 thf(fact_1050_mult__le__cancel__left2,axiom,
% 5.31/5.49 ! [C2: code_integer,A: code_integer] :
% 5.31/5.49 ( ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ C2 @ A ) @ C2 )
% 5.31/5.49 = ( ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C2 )
% 5.31/5.49 => ( ord_le3102999989581377725nteger @ A @ one_one_Code_integer ) )
% 5.31/5.49 & ( ( ord_le6747313008572928689nteger @ C2 @ zero_z3403309356797280102nteger )
% 5.31/5.49 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ A ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % mult_le_cancel_left2
% 5.31/5.49 thf(fact_1051_mult__le__cancel__left2,axiom,
% 5.31/5.49 ! [C2: real,A: real] :
% 5.31/5.49 ( ( ord_less_eq_real @ ( times_times_real @ C2 @ A ) @ C2 )
% 5.31/5.49 = ( ( ( ord_less_real @ zero_zero_real @ C2 )
% 5.31/5.49 => ( ord_less_eq_real @ A @ one_one_real ) )
% 5.31/5.49 & ( ( ord_less_real @ C2 @ zero_zero_real )
% 5.31/5.49 => ( ord_less_eq_real @ one_one_real @ A ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % mult_le_cancel_left2
% 5.31/5.49 thf(fact_1052_mult__le__cancel__left2,axiom,
% 5.31/5.49 ! [C2: rat,A: rat] :
% 5.31/5.49 ( ( ord_less_eq_rat @ ( times_times_rat @ C2 @ A ) @ C2 )
% 5.31/5.49 = ( ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 5.31/5.49 => ( ord_less_eq_rat @ A @ one_one_rat ) )
% 5.31/5.49 & ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 5.31/5.49 => ( ord_less_eq_rat @ one_one_rat @ A ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % mult_le_cancel_left2
% 5.31/5.49 thf(fact_1053_mult__le__cancel__left2,axiom,
% 5.31/5.49 ! [C2: int,A: int] :
% 5.31/5.49 ( ( ord_less_eq_int @ ( times_times_int @ C2 @ A ) @ C2 )
% 5.31/5.49 = ( ( ( ord_less_int @ zero_zero_int @ C2 )
% 5.31/5.49 => ( ord_less_eq_int @ A @ one_one_int ) )
% 5.31/5.49 & ( ( ord_less_int @ C2 @ zero_zero_int )
% 5.31/5.49 => ( ord_less_eq_int @ one_one_int @ A ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % mult_le_cancel_left2
% 5.31/5.49 thf(fact_1054_mult__le__cancel__left1,axiom,
% 5.31/5.49 ! [C2: code_integer,B: code_integer] :
% 5.31/5.49 ( ( ord_le3102999989581377725nteger @ C2 @ ( times_3573771949741848930nteger @ C2 @ B ) )
% 5.31/5.49 = ( ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C2 )
% 5.31/5.49 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ B ) )
% 5.31/5.49 & ( ( ord_le6747313008572928689nteger @ C2 @ zero_z3403309356797280102nteger )
% 5.31/5.49 => ( ord_le3102999989581377725nteger @ B @ one_one_Code_integer ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % mult_le_cancel_left1
% 5.31/5.49 thf(fact_1055_mult__le__cancel__left1,axiom,
% 5.31/5.49 ! [C2: real,B: real] :
% 5.31/5.49 ( ( ord_less_eq_real @ C2 @ ( times_times_real @ C2 @ B ) )
% 5.31/5.49 = ( ( ( ord_less_real @ zero_zero_real @ C2 )
% 5.31/5.49 => ( ord_less_eq_real @ one_one_real @ B ) )
% 5.31/5.49 & ( ( ord_less_real @ C2 @ zero_zero_real )
% 5.31/5.49 => ( ord_less_eq_real @ B @ one_one_real ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % mult_le_cancel_left1
% 5.31/5.49 thf(fact_1056_mult__le__cancel__left1,axiom,
% 5.31/5.49 ! [C2: rat,B: rat] :
% 5.31/5.49 ( ( ord_less_eq_rat @ C2 @ ( times_times_rat @ C2 @ B ) )
% 5.31/5.49 = ( ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 5.31/5.49 => ( ord_less_eq_rat @ one_one_rat @ B ) )
% 5.31/5.49 & ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 5.31/5.49 => ( ord_less_eq_rat @ B @ one_one_rat ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % mult_le_cancel_left1
% 5.31/5.49 thf(fact_1057_mult__le__cancel__left1,axiom,
% 5.31/5.49 ! [C2: int,B: int] :
% 5.31/5.49 ( ( ord_less_eq_int @ C2 @ ( times_times_int @ C2 @ B ) )
% 5.31/5.49 = ( ( ( ord_less_int @ zero_zero_int @ C2 )
% 5.31/5.49 => ( ord_less_eq_int @ one_one_int @ B ) )
% 5.31/5.49 & ( ( ord_less_int @ C2 @ zero_zero_int )
% 5.31/5.49 => ( ord_less_eq_int @ B @ one_one_int ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % mult_le_cancel_left1
% 5.31/5.49 thf(fact_1058_mult__neg__neg,axiom,
% 5.31/5.49 ! [A: real,B: real] :
% 5.31/5.49 ( ( ord_less_real @ A @ zero_zero_real )
% 5.31/5.49 => ( ( ord_less_real @ B @ zero_zero_real )
% 5.31/5.49 => ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % mult_neg_neg
% 5.31/5.49 thf(fact_1059_mult__neg__neg,axiom,
% 5.31/5.49 ! [A: rat,B: rat] :
% 5.31/5.49 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.31/5.49 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 5.31/5.49 => ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % mult_neg_neg
% 5.31/5.49 thf(fact_1060_mult__neg__neg,axiom,
% 5.31/5.49 ! [A: int,B: int] :
% 5.31/5.49 ( ( ord_less_int @ A @ zero_zero_int )
% 5.31/5.49 => ( ( ord_less_int @ B @ zero_zero_int )
% 5.31/5.49 => ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % mult_neg_neg
% 5.31/5.49 thf(fact_1061_not__square__less__zero,axiom,
% 5.31/5.49 ! [A: real] :
% 5.31/5.49 ~ ( ord_less_real @ ( times_times_real @ A @ A ) @ zero_zero_real ) ).
% 5.31/5.49
% 5.31/5.49 % not_square_less_zero
% 5.31/5.49 thf(fact_1062_not__square__less__zero,axiom,
% 5.31/5.49 ! [A: rat] :
% 5.31/5.49 ~ ( ord_less_rat @ ( times_times_rat @ A @ A ) @ zero_zero_rat ) ).
% 5.31/5.49
% 5.31/5.49 % not_square_less_zero
% 5.31/5.49 thf(fact_1063_not__square__less__zero,axiom,
% 5.31/5.49 ! [A: int] :
% 5.31/5.49 ~ ( ord_less_int @ ( times_times_int @ A @ A ) @ zero_zero_int ) ).
% 5.31/5.49
% 5.31/5.49 % not_square_less_zero
% 5.31/5.49 thf(fact_1064_mult__less__0__iff,axiom,
% 5.31/5.49 ! [A: real,B: real] :
% 5.31/5.49 ( ( ord_less_real @ ( times_times_real @ A @ B ) @ zero_zero_real )
% 5.31/5.49 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 5.31/5.49 & ( ord_less_real @ B @ zero_zero_real ) )
% 5.31/5.49 | ( ( ord_less_real @ A @ zero_zero_real )
% 5.31/5.49 & ( ord_less_real @ zero_zero_real @ B ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % mult_less_0_iff
% 5.31/5.49 thf(fact_1065_mult__less__0__iff,axiom,
% 5.31/5.49 ! [A: rat,B: rat] :
% 5.31/5.49 ( ( ord_less_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat )
% 5.31/5.49 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.31/5.49 & ( ord_less_rat @ B @ zero_zero_rat ) )
% 5.31/5.49 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.31/5.49 & ( ord_less_rat @ zero_zero_rat @ B ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % mult_less_0_iff
% 5.31/5.49 thf(fact_1066_mult__less__0__iff,axiom,
% 5.31/5.49 ! [A: int,B: int] :
% 5.31/5.49 ( ( ord_less_int @ ( times_times_int @ A @ B ) @ zero_zero_int )
% 5.31/5.49 = ( ( ( ord_less_int @ zero_zero_int @ A )
% 5.31/5.49 & ( ord_less_int @ B @ zero_zero_int ) )
% 5.31/5.49 | ( ( ord_less_int @ A @ zero_zero_int )
% 5.31/5.49 & ( ord_less_int @ zero_zero_int @ B ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % mult_less_0_iff
% 5.31/5.49 thf(fact_1067_mult__neg__pos,axiom,
% 5.31/5.49 ! [A: real,B: real] :
% 5.31/5.49 ( ( ord_less_real @ A @ zero_zero_real )
% 5.31/5.49 => ( ( ord_less_real @ zero_zero_real @ B )
% 5.31/5.49 => ( ord_less_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % mult_neg_pos
% 5.31/5.49 thf(fact_1068_mult__neg__pos,axiom,
% 5.31/5.49 ! [A: rat,B: rat] :
% 5.31/5.49 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.31/5.49 => ( ( ord_less_rat @ zero_zero_rat @ B )
% 5.31/5.49 => ( ord_less_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % mult_neg_pos
% 5.31/5.49 thf(fact_1069_mult__neg__pos,axiom,
% 5.31/5.49 ! [A: nat,B: nat] :
% 5.31/5.49 ( ( ord_less_nat @ A @ zero_zero_nat )
% 5.31/5.49 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.31/5.49 => ( ord_less_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % mult_neg_pos
% 5.31/5.49 thf(fact_1070_mult__neg__pos,axiom,
% 5.31/5.49 ! [A: int,B: int] :
% 5.31/5.49 ( ( ord_less_int @ A @ zero_zero_int )
% 5.31/5.49 => ( ( ord_less_int @ zero_zero_int @ B )
% 5.31/5.49 => ( ord_less_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % mult_neg_pos
% 5.31/5.49 thf(fact_1071_mult__pos__neg,axiom,
% 5.31/5.49 ! [A: real,B: real] :
% 5.31/5.49 ( ( ord_less_real @ zero_zero_real @ A )
% 5.31/5.49 => ( ( ord_less_real @ B @ zero_zero_real )
% 5.31/5.49 => ( ord_less_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % mult_pos_neg
% 5.31/5.49 thf(fact_1072_mult__pos__neg,axiom,
% 5.31/5.49 ! [A: rat,B: rat] :
% 5.31/5.49 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.31/5.49 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 5.31/5.49 => ( ord_less_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % mult_pos_neg
% 5.31/5.49 thf(fact_1073_mult__pos__neg,axiom,
% 5.31/5.49 ! [A: nat,B: nat] :
% 5.31/5.49 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.31/5.49 => ( ( ord_less_nat @ B @ zero_zero_nat )
% 5.31/5.49 => ( ord_less_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % mult_pos_neg
% 5.31/5.49 thf(fact_1074_mult__pos__neg,axiom,
% 5.31/5.49 ! [A: int,B: int] :
% 5.31/5.49 ( ( ord_less_int @ zero_zero_int @ A )
% 5.31/5.49 => ( ( ord_less_int @ B @ zero_zero_int )
% 5.31/5.49 => ( ord_less_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % mult_pos_neg
% 5.31/5.49 thf(fact_1075_mult__pos__pos,axiom,
% 5.31/5.49 ! [A: real,B: real] :
% 5.31/5.49 ( ( ord_less_real @ zero_zero_real @ A )
% 5.31/5.49 => ( ( ord_less_real @ zero_zero_real @ B )
% 5.31/5.49 => ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % mult_pos_pos
% 5.31/5.49 thf(fact_1076_mult__pos__pos,axiom,
% 5.31/5.49 ! [A: rat,B: rat] :
% 5.31/5.49 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.31/5.49 => ( ( ord_less_rat @ zero_zero_rat @ B )
% 5.31/5.49 => ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % mult_pos_pos
% 5.31/5.49 thf(fact_1077_mult__pos__pos,axiom,
% 5.31/5.49 ! [A: nat,B: nat] :
% 5.31/5.49 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.31/5.49 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.31/5.49 => ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ A @ B ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % mult_pos_pos
% 5.31/5.49 thf(fact_1078_mult__pos__pos,axiom,
% 5.31/5.49 ! [A: int,B: int] :
% 5.31/5.49 ( ( ord_less_int @ zero_zero_int @ A )
% 5.31/5.49 => ( ( ord_less_int @ zero_zero_int @ B )
% 5.31/5.49 => ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % mult_pos_pos
% 5.31/5.49 thf(fact_1079_mult__pos__neg2,axiom,
% 5.31/5.49 ! [A: real,B: real] :
% 5.31/5.49 ( ( ord_less_real @ zero_zero_real @ A )
% 5.31/5.49 => ( ( ord_less_real @ B @ zero_zero_real )
% 5.31/5.49 => ( ord_less_real @ ( times_times_real @ B @ A ) @ zero_zero_real ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % mult_pos_neg2
% 5.31/5.49 thf(fact_1080_mult__pos__neg2,axiom,
% 5.31/5.49 ! [A: rat,B: rat] :
% 5.31/5.49 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.31/5.49 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 5.31/5.49 => ( ord_less_rat @ ( times_times_rat @ B @ A ) @ zero_zero_rat ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % mult_pos_neg2
% 5.31/5.49 thf(fact_1081_mult__pos__neg2,axiom,
% 5.31/5.49 ! [A: nat,B: nat] :
% 5.31/5.49 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.31/5.49 => ( ( ord_less_nat @ B @ zero_zero_nat )
% 5.31/5.49 => ( ord_less_nat @ ( times_times_nat @ B @ A ) @ zero_zero_nat ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % mult_pos_neg2
% 5.31/5.49 thf(fact_1082_mult__pos__neg2,axiom,
% 5.31/5.49 ! [A: int,B: int] :
% 5.31/5.49 ( ( ord_less_int @ zero_zero_int @ A )
% 5.31/5.49 => ( ( ord_less_int @ B @ zero_zero_int )
% 5.31/5.49 => ( ord_less_int @ ( times_times_int @ B @ A ) @ zero_zero_int ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % mult_pos_neg2
% 5.31/5.49 thf(fact_1083_zero__less__mult__iff,axiom,
% 5.31/5.49 ! [A: real,B: real] :
% 5.31/5.49 ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 5.31/5.49 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 5.31/5.49 & ( ord_less_real @ zero_zero_real @ B ) )
% 5.31/5.49 | ( ( ord_less_real @ A @ zero_zero_real )
% 5.31/5.49 & ( ord_less_real @ B @ zero_zero_real ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % zero_less_mult_iff
% 5.31/5.49 thf(fact_1084_zero__less__mult__iff,axiom,
% 5.31/5.49 ! [A: rat,B: rat] :
% 5.31/5.49 ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 5.31/5.49 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.31/5.49 & ( ord_less_rat @ zero_zero_rat @ B ) )
% 5.31/5.49 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.31/5.49 & ( ord_less_rat @ B @ zero_zero_rat ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % zero_less_mult_iff
% 5.31/5.49 thf(fact_1085_zero__less__mult__iff,axiom,
% 5.31/5.49 ! [A: int,B: int] :
% 5.31/5.49 ( ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) )
% 5.31/5.49 = ( ( ( ord_less_int @ zero_zero_int @ A )
% 5.31/5.49 & ( ord_less_int @ zero_zero_int @ B ) )
% 5.31/5.49 | ( ( ord_less_int @ A @ zero_zero_int )
% 5.31/5.49 & ( ord_less_int @ B @ zero_zero_int ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % zero_less_mult_iff
% 5.31/5.49 thf(fact_1086_zero__less__mult__pos,axiom,
% 5.31/5.49 ! [A: real,B: real] :
% 5.31/5.49 ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 5.31/5.49 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.31/5.49 => ( ord_less_real @ zero_zero_real @ B ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % zero_less_mult_pos
% 5.31/5.49 thf(fact_1087_zero__less__mult__pos,axiom,
% 5.31/5.49 ! [A: rat,B: rat] :
% 5.31/5.49 ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 5.31/5.49 => ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.31/5.49 => ( ord_less_rat @ zero_zero_rat @ B ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % zero_less_mult_pos
% 5.31/5.49 thf(fact_1088_zero__less__mult__pos,axiom,
% 5.31/5.49 ! [A: nat,B: nat] :
% 5.31/5.49 ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ A @ B ) )
% 5.31/5.49 => ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.31/5.49 => ( ord_less_nat @ zero_zero_nat @ B ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % zero_less_mult_pos
% 5.31/5.49 thf(fact_1089_zero__less__mult__pos,axiom,
% 5.31/5.49 ! [A: int,B: int] :
% 5.31/5.49 ( ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) )
% 5.31/5.49 => ( ( ord_less_int @ zero_zero_int @ A )
% 5.31/5.49 => ( ord_less_int @ zero_zero_int @ B ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % zero_less_mult_pos
% 5.31/5.49 thf(fact_1090_zero__less__mult__pos2,axiom,
% 5.31/5.49 ! [B: real,A: real] :
% 5.31/5.49 ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ B @ A ) )
% 5.31/5.49 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.31/5.49 => ( ord_less_real @ zero_zero_real @ B ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % zero_less_mult_pos2
% 5.31/5.49 thf(fact_1091_zero__less__mult__pos2,axiom,
% 5.31/5.49 ! [B: rat,A: rat] :
% 5.31/5.49 ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ B @ A ) )
% 5.31/5.49 => ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.31/5.49 => ( ord_less_rat @ zero_zero_rat @ B ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % zero_less_mult_pos2
% 5.31/5.49 thf(fact_1092_zero__less__mult__pos2,axiom,
% 5.31/5.49 ! [B: nat,A: nat] :
% 5.31/5.49 ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ B @ A ) )
% 5.31/5.49 => ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.31/5.49 => ( ord_less_nat @ zero_zero_nat @ B ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % zero_less_mult_pos2
% 5.31/5.49 thf(fact_1093_zero__less__mult__pos2,axiom,
% 5.31/5.49 ! [B: int,A: int] :
% 5.31/5.49 ( ( ord_less_int @ zero_zero_int @ ( times_times_int @ B @ A ) )
% 5.31/5.49 => ( ( ord_less_int @ zero_zero_int @ A )
% 5.31/5.49 => ( ord_less_int @ zero_zero_int @ B ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % zero_less_mult_pos2
% 5.31/5.49 thf(fact_1094_mult__less__cancel__left__neg,axiom,
% 5.31/5.49 ! [C2: real,A: real,B: real] :
% 5.31/5.49 ( ( ord_less_real @ C2 @ zero_zero_real )
% 5.31/5.49 => ( ( ord_less_real @ ( times_times_real @ C2 @ A ) @ ( times_times_real @ C2 @ B ) )
% 5.31/5.49 = ( ord_less_real @ B @ A ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % mult_less_cancel_left_neg
% 5.31/5.49 thf(fact_1095_mult__less__cancel__left__neg,axiom,
% 5.31/5.49 ! [C2: rat,A: rat,B: rat] :
% 5.31/5.49 ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 5.31/5.49 => ( ( ord_less_rat @ ( times_times_rat @ C2 @ A ) @ ( times_times_rat @ C2 @ B ) )
% 5.31/5.49 = ( ord_less_rat @ B @ A ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % mult_less_cancel_left_neg
% 5.31/5.49 thf(fact_1096_mult__less__cancel__left__neg,axiom,
% 5.31/5.49 ! [C2: int,A: int,B: int] :
% 5.31/5.49 ( ( ord_less_int @ C2 @ zero_zero_int )
% 5.31/5.49 => ( ( ord_less_int @ ( times_times_int @ C2 @ A ) @ ( times_times_int @ C2 @ B ) )
% 5.31/5.49 = ( ord_less_int @ B @ A ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % mult_less_cancel_left_neg
% 5.31/5.49 thf(fact_1097_mult__less__cancel__left__pos,axiom,
% 5.31/5.49 ! [C2: real,A: real,B: real] :
% 5.31/5.49 ( ( ord_less_real @ zero_zero_real @ C2 )
% 5.31/5.49 => ( ( ord_less_real @ ( times_times_real @ C2 @ A ) @ ( times_times_real @ C2 @ B ) )
% 5.31/5.49 = ( ord_less_real @ A @ B ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % mult_less_cancel_left_pos
% 5.31/5.49 thf(fact_1098_mult__less__cancel__left__pos,axiom,
% 5.31/5.49 ! [C2: rat,A: rat,B: rat] :
% 5.31/5.49 ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 5.31/5.49 => ( ( ord_less_rat @ ( times_times_rat @ C2 @ A ) @ ( times_times_rat @ C2 @ B ) )
% 5.31/5.49 = ( ord_less_rat @ A @ B ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % mult_less_cancel_left_pos
% 5.31/5.49 thf(fact_1099_mult__less__cancel__left__pos,axiom,
% 5.31/5.49 ! [C2: int,A: int,B: int] :
% 5.31/5.49 ( ( ord_less_int @ zero_zero_int @ C2 )
% 5.31/5.49 => ( ( ord_less_int @ ( times_times_int @ C2 @ A ) @ ( times_times_int @ C2 @ B ) )
% 5.31/5.49 = ( ord_less_int @ A @ B ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % mult_less_cancel_left_pos
% 5.31/5.49 thf(fact_1100_mult__strict__left__mono__neg,axiom,
% 5.31/5.49 ! [B: real,A: real,C2: real] :
% 5.31/5.49 ( ( ord_less_real @ B @ A )
% 5.31/5.49 => ( ( ord_less_real @ C2 @ zero_zero_real )
% 5.31/5.49 => ( ord_less_real @ ( times_times_real @ C2 @ A ) @ ( times_times_real @ C2 @ B ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % mult_strict_left_mono_neg
% 5.31/5.49 thf(fact_1101_mult__strict__left__mono__neg,axiom,
% 5.31/5.49 ! [B: rat,A: rat,C2: rat] :
% 5.31/5.49 ( ( ord_less_rat @ B @ A )
% 5.31/5.49 => ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 5.31/5.49 => ( ord_less_rat @ ( times_times_rat @ C2 @ A ) @ ( times_times_rat @ C2 @ B ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % mult_strict_left_mono_neg
% 5.31/5.49 thf(fact_1102_mult__strict__left__mono__neg,axiom,
% 5.31/5.49 ! [B: int,A: int,C2: int] :
% 5.31/5.49 ( ( ord_less_int @ B @ A )
% 5.31/5.49 => ( ( ord_less_int @ C2 @ zero_zero_int )
% 5.31/5.49 => ( ord_less_int @ ( times_times_int @ C2 @ A ) @ ( times_times_int @ C2 @ B ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % mult_strict_left_mono_neg
% 5.31/5.49 thf(fact_1103_mult__strict__left__mono,axiom,
% 5.31/5.49 ! [A: real,B: real,C2: real] :
% 5.31/5.49 ( ( ord_less_real @ A @ B )
% 5.31/5.49 => ( ( ord_less_real @ zero_zero_real @ C2 )
% 5.31/5.49 => ( ord_less_real @ ( times_times_real @ C2 @ A ) @ ( times_times_real @ C2 @ B ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % mult_strict_left_mono
% 5.31/5.49 thf(fact_1104_mult__strict__left__mono,axiom,
% 5.31/5.49 ! [A: rat,B: rat,C2: rat] :
% 5.31/5.49 ( ( ord_less_rat @ A @ B )
% 5.31/5.49 => ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 5.31/5.49 => ( ord_less_rat @ ( times_times_rat @ C2 @ A ) @ ( times_times_rat @ C2 @ B ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % mult_strict_left_mono
% 5.31/5.49 thf(fact_1105_mult__strict__left__mono,axiom,
% 5.31/5.49 ! [A: nat,B: nat,C2: nat] :
% 5.31/5.49 ( ( ord_less_nat @ A @ B )
% 5.31/5.49 => ( ( ord_less_nat @ zero_zero_nat @ C2 )
% 5.31/5.49 => ( ord_less_nat @ ( times_times_nat @ C2 @ A ) @ ( times_times_nat @ C2 @ B ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % mult_strict_left_mono
% 5.31/5.49 thf(fact_1106_mult__strict__left__mono,axiom,
% 5.31/5.49 ! [A: int,B: int,C2: int] :
% 5.31/5.49 ( ( ord_less_int @ A @ B )
% 5.31/5.49 => ( ( ord_less_int @ zero_zero_int @ C2 )
% 5.31/5.49 => ( ord_less_int @ ( times_times_int @ C2 @ A ) @ ( times_times_int @ C2 @ B ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % mult_strict_left_mono
% 5.31/5.49 thf(fact_1107_mult__less__cancel__left__disj,axiom,
% 5.31/5.49 ! [C2: real,A: real,B: real] :
% 5.31/5.49 ( ( ord_less_real @ ( times_times_real @ C2 @ A ) @ ( times_times_real @ C2 @ B ) )
% 5.31/5.49 = ( ( ( ord_less_real @ zero_zero_real @ C2 )
% 5.31/5.49 & ( ord_less_real @ A @ B ) )
% 5.31/5.49 | ( ( ord_less_real @ C2 @ zero_zero_real )
% 5.31/5.49 & ( ord_less_real @ B @ A ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % mult_less_cancel_left_disj
% 5.31/5.49 thf(fact_1108_mult__less__cancel__left__disj,axiom,
% 5.31/5.49 ! [C2: rat,A: rat,B: rat] :
% 5.31/5.49 ( ( ord_less_rat @ ( times_times_rat @ C2 @ A ) @ ( times_times_rat @ C2 @ B ) )
% 5.31/5.49 = ( ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 5.31/5.49 & ( ord_less_rat @ A @ B ) )
% 5.31/5.49 | ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 5.31/5.49 & ( ord_less_rat @ B @ A ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % mult_less_cancel_left_disj
% 5.31/5.49 thf(fact_1109_mult__less__cancel__left__disj,axiom,
% 5.31/5.49 ! [C2: int,A: int,B: int] :
% 5.31/5.49 ( ( ord_less_int @ ( times_times_int @ C2 @ A ) @ ( times_times_int @ C2 @ B ) )
% 5.31/5.49 = ( ( ( ord_less_int @ zero_zero_int @ C2 )
% 5.31/5.49 & ( ord_less_int @ A @ B ) )
% 5.31/5.49 | ( ( ord_less_int @ C2 @ zero_zero_int )
% 5.31/5.49 & ( ord_less_int @ B @ A ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % mult_less_cancel_left_disj
% 5.31/5.49 thf(fact_1110_mult__strict__right__mono__neg,axiom,
% 5.31/5.49 ! [B: real,A: real,C2: real] :
% 5.31/5.49 ( ( ord_less_real @ B @ A )
% 5.31/5.49 => ( ( ord_less_real @ C2 @ zero_zero_real )
% 5.31/5.49 => ( ord_less_real @ ( times_times_real @ A @ C2 ) @ ( times_times_real @ B @ C2 ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % mult_strict_right_mono_neg
% 5.31/5.49 thf(fact_1111_mult__strict__right__mono__neg,axiom,
% 5.31/5.49 ! [B: rat,A: rat,C2: rat] :
% 5.31/5.49 ( ( ord_less_rat @ B @ A )
% 5.31/5.49 => ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 5.31/5.49 => ( ord_less_rat @ ( times_times_rat @ A @ C2 ) @ ( times_times_rat @ B @ C2 ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % mult_strict_right_mono_neg
% 5.31/5.49 thf(fact_1112_mult__strict__right__mono__neg,axiom,
% 5.31/5.49 ! [B: int,A: int,C2: int] :
% 5.31/5.49 ( ( ord_less_int @ B @ A )
% 5.31/5.49 => ( ( ord_less_int @ C2 @ zero_zero_int )
% 5.31/5.49 => ( ord_less_int @ ( times_times_int @ A @ C2 ) @ ( times_times_int @ B @ C2 ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % mult_strict_right_mono_neg
% 5.31/5.49 thf(fact_1113_mult__strict__right__mono,axiom,
% 5.31/5.49 ! [A: real,B: real,C2: real] :
% 5.31/5.49 ( ( ord_less_real @ A @ B )
% 5.31/5.49 => ( ( ord_less_real @ zero_zero_real @ C2 )
% 5.31/5.49 => ( ord_less_real @ ( times_times_real @ A @ C2 ) @ ( times_times_real @ B @ C2 ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % mult_strict_right_mono
% 5.31/5.49 thf(fact_1114_mult__strict__right__mono,axiom,
% 5.31/5.49 ! [A: rat,B: rat,C2: rat] :
% 5.31/5.49 ( ( ord_less_rat @ A @ B )
% 5.31/5.49 => ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 5.31/5.49 => ( ord_less_rat @ ( times_times_rat @ A @ C2 ) @ ( times_times_rat @ B @ C2 ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % mult_strict_right_mono
% 5.31/5.49 thf(fact_1115_mult__strict__right__mono,axiom,
% 5.31/5.49 ! [A: nat,B: nat,C2: nat] :
% 5.31/5.49 ( ( ord_less_nat @ A @ B )
% 5.31/5.49 => ( ( ord_less_nat @ zero_zero_nat @ C2 )
% 5.31/5.49 => ( ord_less_nat @ ( times_times_nat @ A @ C2 ) @ ( times_times_nat @ B @ C2 ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % mult_strict_right_mono
% 5.31/5.49 thf(fact_1116_mult__strict__right__mono,axiom,
% 5.31/5.49 ! [A: int,B: int,C2: int] :
% 5.31/5.49 ( ( ord_less_int @ A @ B )
% 5.31/5.49 => ( ( ord_less_int @ zero_zero_int @ C2 )
% 5.31/5.49 => ( ord_less_int @ ( times_times_int @ A @ C2 ) @ ( times_times_int @ B @ C2 ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % mult_strict_right_mono
% 5.31/5.49 thf(fact_1117_mult__less__cancel__right__disj,axiom,
% 5.31/5.49 ! [A: real,C2: real,B: real] :
% 5.31/5.49 ( ( ord_less_real @ ( times_times_real @ A @ C2 ) @ ( times_times_real @ B @ C2 ) )
% 5.31/5.49 = ( ( ( ord_less_real @ zero_zero_real @ C2 )
% 5.31/5.49 & ( ord_less_real @ A @ B ) )
% 5.31/5.49 | ( ( ord_less_real @ C2 @ zero_zero_real )
% 5.31/5.49 & ( ord_less_real @ B @ A ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % mult_less_cancel_right_disj
% 5.31/5.49 thf(fact_1118_mult__less__cancel__right__disj,axiom,
% 5.31/5.49 ! [A: rat,C2: rat,B: rat] :
% 5.31/5.49 ( ( ord_less_rat @ ( times_times_rat @ A @ C2 ) @ ( times_times_rat @ B @ C2 ) )
% 5.31/5.49 = ( ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 5.31/5.49 & ( ord_less_rat @ A @ B ) )
% 5.31/5.49 | ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 5.31/5.49 & ( ord_less_rat @ B @ A ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % mult_less_cancel_right_disj
% 5.31/5.49 thf(fact_1119_mult__less__cancel__right__disj,axiom,
% 5.31/5.49 ! [A: int,C2: int,B: int] :
% 5.31/5.49 ( ( ord_less_int @ ( times_times_int @ A @ C2 ) @ ( times_times_int @ B @ C2 ) )
% 5.31/5.49 = ( ( ( ord_less_int @ zero_zero_int @ C2 )
% 5.31/5.49 & ( ord_less_int @ A @ B ) )
% 5.31/5.49 | ( ( ord_less_int @ C2 @ zero_zero_int )
% 5.31/5.49 & ( ord_less_int @ B @ A ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % mult_less_cancel_right_disj
% 5.31/5.49 thf(fact_1120_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 5.31/5.49 ! [A: real,B: real,C2: real] :
% 5.31/5.49 ( ( ord_less_real @ A @ B )
% 5.31/5.49 => ( ( ord_less_real @ zero_zero_real @ C2 )
% 5.31/5.49 => ( ord_less_real @ ( times_times_real @ C2 @ A ) @ ( times_times_real @ C2 @ B ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
% 5.31/5.49 thf(fact_1121_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 5.31/5.49 ! [A: rat,B: rat,C2: rat] :
% 5.31/5.49 ( ( ord_less_rat @ A @ B )
% 5.31/5.49 => ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 5.31/5.49 => ( ord_less_rat @ ( times_times_rat @ C2 @ A ) @ ( times_times_rat @ C2 @ B ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
% 5.31/5.49 thf(fact_1122_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 5.31/5.49 ! [A: nat,B: nat,C2: nat] :
% 5.31/5.49 ( ( ord_less_nat @ A @ B )
% 5.31/5.49 => ( ( ord_less_nat @ zero_zero_nat @ C2 )
% 5.31/5.49 => ( ord_less_nat @ ( times_times_nat @ C2 @ A ) @ ( times_times_nat @ C2 @ B ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
% 5.31/5.49 thf(fact_1123_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 5.31/5.49 ! [A: int,B: int,C2: int] :
% 5.31/5.49 ( ( ord_less_int @ A @ B )
% 5.31/5.49 => ( ( ord_less_int @ zero_zero_int @ C2 )
% 5.31/5.49 => ( ord_less_int @ ( times_times_int @ C2 @ A ) @ ( times_times_int @ C2 @ B ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
% 5.31/5.49 thf(fact_1124_not__one__le__zero,axiom,
% 5.31/5.49 ~ ( ord_le3102999989581377725nteger @ one_one_Code_integer @ zero_z3403309356797280102nteger ) ).
% 5.31/5.49
% 5.31/5.49 % not_one_le_zero
% 5.31/5.49 thf(fact_1125_not__one__le__zero,axiom,
% 5.31/5.49 ~ ( ord_less_eq_real @ one_one_real @ zero_zero_real ) ).
% 5.31/5.49
% 5.31/5.49 % not_one_le_zero
% 5.31/5.49 thf(fact_1126_not__one__le__zero,axiom,
% 5.31/5.49 ~ ( ord_less_eq_rat @ one_one_rat @ zero_zero_rat ) ).
% 5.31/5.49
% 5.31/5.49 % not_one_le_zero
% 5.31/5.49 thf(fact_1127_not__one__le__zero,axiom,
% 5.31/5.49 ~ ( ord_less_eq_nat @ one_one_nat @ zero_zero_nat ) ).
% 5.31/5.49
% 5.31/5.49 % not_one_le_zero
% 5.31/5.49 thf(fact_1128_not__one__le__zero,axiom,
% 5.31/5.49 ~ ( ord_less_eq_int @ one_one_int @ zero_zero_int ) ).
% 5.31/5.49
% 5.31/5.49 % not_one_le_zero
% 5.31/5.49 thf(fact_1129_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 5.31/5.49 ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ one_one_Code_integer ).
% 5.31/5.49
% 5.31/5.49 % linordered_nonzero_semiring_class.zero_le_one
% 5.31/5.49 thf(fact_1130_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 5.31/5.49 ord_less_eq_real @ zero_zero_real @ one_one_real ).
% 5.31/5.49
% 5.31/5.49 % linordered_nonzero_semiring_class.zero_le_one
% 5.31/5.49 thf(fact_1131_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 5.31/5.49 ord_less_eq_rat @ zero_zero_rat @ one_one_rat ).
% 5.31/5.49
% 5.31/5.49 % linordered_nonzero_semiring_class.zero_le_one
% 5.31/5.49 thf(fact_1132_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 5.31/5.49 ord_less_eq_nat @ zero_zero_nat @ one_one_nat ).
% 5.31/5.49
% 5.31/5.49 % linordered_nonzero_semiring_class.zero_le_one
% 5.31/5.49 thf(fact_1133_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 5.31/5.49 ord_less_eq_int @ zero_zero_int @ one_one_int ).
% 5.31/5.49
% 5.31/5.49 % linordered_nonzero_semiring_class.zero_le_one
% 5.31/5.49 thf(fact_1134_zero__less__one__class_Ozero__le__one,axiom,
% 5.31/5.49 ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ one_one_Code_integer ).
% 5.31/5.49
% 5.31/5.49 % zero_less_one_class.zero_le_one
% 5.31/5.49 thf(fact_1135_zero__less__one__class_Ozero__le__one,axiom,
% 5.31/5.49 ord_less_eq_real @ zero_zero_real @ one_one_real ).
% 5.31/5.49
% 5.31/5.49 % zero_less_one_class.zero_le_one
% 5.31/5.49 thf(fact_1136_zero__less__one__class_Ozero__le__one,axiom,
% 5.31/5.49 ord_less_eq_rat @ zero_zero_rat @ one_one_rat ).
% 5.31/5.49
% 5.31/5.49 % zero_less_one_class.zero_le_one
% 5.31/5.49 thf(fact_1137_zero__less__one__class_Ozero__le__one,axiom,
% 5.31/5.49 ord_less_eq_nat @ zero_zero_nat @ one_one_nat ).
% 5.31/5.49
% 5.31/5.49 % zero_less_one_class.zero_le_one
% 5.31/5.49 thf(fact_1138_zero__less__one__class_Ozero__le__one,axiom,
% 5.31/5.49 ord_less_eq_int @ zero_zero_int @ one_one_int ).
% 5.31/5.49
% 5.31/5.49 % zero_less_one_class.zero_le_one
% 5.31/5.49 thf(fact_1139_nat__mult__le__cancel1,axiom,
% 5.31/5.49 ! [K2: nat,M2: nat,N: nat] :
% 5.31/5.49 ( ( ord_less_nat @ zero_zero_nat @ K2 )
% 5.31/5.49 => ( ( ord_less_eq_nat @ ( times_times_nat @ K2 @ M2 ) @ ( times_times_nat @ K2 @ N ) )
% 5.31/5.49 = ( ord_less_eq_nat @ M2 @ N ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % nat_mult_le_cancel1
% 5.31/5.49 thf(fact_1140_less__Suc__eq__0__disj,axiom,
% 5.31/5.49 ! [M2: nat,N: nat] :
% 5.31/5.49 ( ( ord_less_nat @ M2 @ ( suc @ N ) )
% 5.31/5.49 = ( ( M2 = zero_zero_nat )
% 5.31/5.49 | ? [J: nat] :
% 5.31/5.49 ( ( M2
% 5.31/5.49 = ( suc @ J ) )
% 5.31/5.49 & ( ord_less_nat @ J @ N ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % less_Suc_eq_0_disj
% 5.31/5.49 thf(fact_1141_gr0__implies__Suc,axiom,
% 5.31/5.49 ! [N: nat] :
% 5.31/5.49 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.49 => ? [M: nat] :
% 5.31/5.49 ( N
% 5.31/5.49 = ( suc @ M ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % gr0_implies_Suc
% 5.31/5.49 thf(fact_1142_All__less__Suc2,axiom,
% 5.31/5.49 ! [N: nat,P2: nat > $o] :
% 5.31/5.49 ( ( ! [I: nat] :
% 5.31/5.49 ( ( ord_less_nat @ I @ ( suc @ N ) )
% 5.31/5.49 => ( P2 @ I ) ) )
% 5.31/5.49 = ( ( P2 @ zero_zero_nat )
% 5.31/5.49 & ! [I: nat] :
% 5.31/5.49 ( ( ord_less_nat @ I @ N )
% 5.31/5.49 => ( P2 @ ( suc @ I ) ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % All_less_Suc2
% 5.31/5.49 thf(fact_1143_gr0__conv__Suc,axiom,
% 5.31/5.49 ! [N: nat] :
% 5.31/5.49 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.49 = ( ? [M6: nat] :
% 5.31/5.49 ( N
% 5.31/5.49 = ( suc @ M6 ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % gr0_conv_Suc
% 5.31/5.49 thf(fact_1144_Ex__less__Suc2,axiom,
% 5.31/5.49 ! [N: nat,P2: nat > $o] :
% 5.31/5.49 ( ( ? [I: nat] :
% 5.31/5.49 ( ( ord_less_nat @ I @ ( suc @ N ) )
% 5.31/5.49 & ( P2 @ I ) ) )
% 5.31/5.49 = ( ( P2 @ zero_zero_nat )
% 5.31/5.49 | ? [I: nat] :
% 5.31/5.49 ( ( ord_less_nat @ I @ N )
% 5.31/5.49 & ( P2 @ ( suc @ I ) ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % Ex_less_Suc2
% 5.31/5.49 thf(fact_1145_le__imp__less__Suc,axiom,
% 5.31/5.49 ! [M2: nat,N: nat] :
% 5.31/5.49 ( ( ord_less_eq_nat @ M2 @ N )
% 5.31/5.49 => ( ord_less_nat @ M2 @ ( suc @ N ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % le_imp_less_Suc
% 5.31/5.49 thf(fact_1146_less__eq__Suc__le,axiom,
% 5.31/5.49 ( ord_less_nat
% 5.31/5.49 = ( ^ [N4: nat] : ( ord_less_eq_nat @ ( suc @ N4 ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % less_eq_Suc_le
% 5.31/5.49 thf(fact_1147_less__Suc__eq__le,axiom,
% 5.31/5.49 ! [M2: nat,N: nat] :
% 5.31/5.49 ( ( ord_less_nat @ M2 @ ( suc @ N ) )
% 5.31/5.49 = ( ord_less_eq_nat @ M2 @ N ) ) ).
% 5.31/5.49
% 5.31/5.49 % less_Suc_eq_le
% 5.31/5.49 thf(fact_1148_le__less__Suc__eq,axiom,
% 5.31/5.49 ! [M2: nat,N: nat] :
% 5.31/5.49 ( ( ord_less_eq_nat @ M2 @ N )
% 5.31/5.49 => ( ( ord_less_nat @ N @ ( suc @ M2 ) )
% 5.31/5.49 = ( N = M2 ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % le_less_Suc_eq
% 5.31/5.49 thf(fact_1149_Suc__le__lessD,axiom,
% 5.31/5.49 ! [M2: nat,N: nat] :
% 5.31/5.49 ( ( ord_less_eq_nat @ ( suc @ M2 ) @ N )
% 5.31/5.49 => ( ord_less_nat @ M2 @ N ) ) ).
% 5.31/5.49
% 5.31/5.49 % Suc_le_lessD
% 5.31/5.49 thf(fact_1150_inc__induct,axiom,
% 5.31/5.49 ! [I2: nat,J2: nat,P2: nat > $o] :
% 5.31/5.49 ( ( ord_less_eq_nat @ I2 @ J2 )
% 5.31/5.49 => ( ( P2 @ J2 )
% 5.31/5.49 => ( ! [N3: nat] :
% 5.31/5.49 ( ( ord_less_eq_nat @ I2 @ N3 )
% 5.31/5.49 => ( ( ord_less_nat @ N3 @ J2 )
% 5.31/5.49 => ( ( P2 @ ( suc @ N3 ) )
% 5.31/5.49 => ( P2 @ N3 ) ) ) )
% 5.31/5.49 => ( P2 @ I2 ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % inc_induct
% 5.31/5.49 thf(fact_1151_dec__induct,axiom,
% 5.31/5.49 ! [I2: nat,J2: nat,P2: nat > $o] :
% 5.31/5.49 ( ( ord_less_eq_nat @ I2 @ J2 )
% 5.31/5.49 => ( ( P2 @ I2 )
% 5.31/5.49 => ( ! [N3: nat] :
% 5.31/5.49 ( ( ord_less_eq_nat @ I2 @ N3 )
% 5.31/5.49 => ( ( ord_less_nat @ N3 @ J2 )
% 5.31/5.49 => ( ( P2 @ N3 )
% 5.31/5.49 => ( P2 @ ( suc @ N3 ) ) ) ) )
% 5.31/5.49 => ( P2 @ J2 ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % dec_induct
% 5.31/5.49 thf(fact_1152_Suc__le__eq,axiom,
% 5.31/5.49 ! [M2: nat,N: nat] :
% 5.31/5.49 ( ( ord_less_eq_nat @ ( suc @ M2 ) @ N )
% 5.31/5.49 = ( ord_less_nat @ M2 @ N ) ) ).
% 5.31/5.49
% 5.31/5.49 % Suc_le_eq
% 5.31/5.49 thf(fact_1153_Suc__leI,axiom,
% 5.31/5.49 ! [M2: nat,N: nat] :
% 5.31/5.49 ( ( ord_less_nat @ M2 @ N )
% 5.31/5.49 => ( ord_less_eq_nat @ ( suc @ M2 ) @ N ) ) ).
% 5.31/5.49
% 5.31/5.49 % Suc_leI
% 5.31/5.49 thf(fact_1154_ex__least__nat__le,axiom,
% 5.31/5.49 ! [P2: nat > $o,N: nat] :
% 5.31/5.49 ( ( P2 @ N )
% 5.31/5.49 => ( ~ ( P2 @ zero_zero_nat )
% 5.31/5.49 => ? [K: nat] :
% 5.31/5.49 ( ( ord_less_eq_nat @ K @ N )
% 5.31/5.49 & ! [I4: nat] :
% 5.31/5.49 ( ( ord_less_nat @ I4 @ K )
% 5.31/5.49 => ~ ( P2 @ I4 ) )
% 5.31/5.49 & ( P2 @ K ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % ex_least_nat_le
% 5.31/5.49 thf(fact_1155_Suc__mult__less__cancel1,axiom,
% 5.31/5.49 ! [K2: nat,M2: nat,N: nat] :
% 5.31/5.49 ( ( ord_less_nat @ ( times_times_nat @ ( suc @ K2 ) @ M2 ) @ ( times_times_nat @ ( suc @ K2 ) @ N ) )
% 5.31/5.49 = ( ord_less_nat @ M2 @ N ) ) ).
% 5.31/5.49
% 5.31/5.49 % Suc_mult_less_cancel1
% 5.31/5.49 thf(fact_1156_mult__less__mono1,axiom,
% 5.31/5.49 ! [I2: nat,J2: nat,K2: nat] :
% 5.31/5.49 ( ( ord_less_nat @ I2 @ J2 )
% 5.31/5.49 => ( ( ord_less_nat @ zero_zero_nat @ K2 )
% 5.31/5.49 => ( ord_less_nat @ ( times_times_nat @ I2 @ K2 ) @ ( times_times_nat @ J2 @ K2 ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % mult_less_mono1
% 5.31/5.49 thf(fact_1157_mult__less__mono2,axiom,
% 5.31/5.49 ! [I2: nat,J2: nat,K2: nat] :
% 5.31/5.49 ( ( ord_less_nat @ I2 @ J2 )
% 5.31/5.49 => ( ( ord_less_nat @ zero_zero_nat @ K2 )
% 5.31/5.49 => ( ord_less_nat @ ( times_times_nat @ K2 @ I2 ) @ ( times_times_nat @ K2 @ J2 ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % mult_less_mono2
% 5.31/5.49 thf(fact_1158_One__nat__def,axiom,
% 5.31/5.49 ( one_one_nat
% 5.31/5.49 = ( suc @ zero_zero_nat ) ) ).
% 5.31/5.49
% 5.31/5.49 % One_nat_def
% 5.31/5.49 thf(fact_1159_mult__eq__self__implies__10,axiom,
% 5.31/5.49 ! [M2: nat,N: nat] :
% 5.31/5.49 ( ( M2
% 5.31/5.49 = ( times_times_nat @ M2 @ N ) )
% 5.31/5.49 => ( ( N = one_one_nat )
% 5.31/5.49 | ( M2 = zero_zero_nat ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % mult_eq_self_implies_10
% 5.31/5.49 thf(fact_1160_mult__less__le__imp__less,axiom,
% 5.31/5.49 ! [A: real,B: real,C2: real,D: real] :
% 5.31/5.49 ( ( ord_less_real @ A @ B )
% 5.31/5.49 => ( ( ord_less_eq_real @ C2 @ D )
% 5.31/5.49 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.31/5.49 => ( ( ord_less_real @ zero_zero_real @ C2 )
% 5.31/5.49 => ( ord_less_real @ ( times_times_real @ A @ C2 ) @ ( times_times_real @ B @ D ) ) ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % mult_less_le_imp_less
% 5.31/5.49 thf(fact_1161_mult__less__le__imp__less,axiom,
% 5.31/5.49 ! [A: rat,B: rat,C2: rat,D: rat] :
% 5.31/5.49 ( ( ord_less_rat @ A @ B )
% 5.31/5.49 => ( ( ord_less_eq_rat @ C2 @ D )
% 5.31/5.49 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.31/5.49 => ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 5.31/5.49 => ( ord_less_rat @ ( times_times_rat @ A @ C2 ) @ ( times_times_rat @ B @ D ) ) ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % mult_less_le_imp_less
% 5.31/5.49 thf(fact_1162_mult__less__le__imp__less,axiom,
% 5.31/5.49 ! [A: nat,B: nat,C2: nat,D: nat] :
% 5.31/5.49 ( ( ord_less_nat @ A @ B )
% 5.31/5.49 => ( ( ord_less_eq_nat @ C2 @ D )
% 5.31/5.49 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.31/5.49 => ( ( ord_less_nat @ zero_zero_nat @ C2 )
% 5.31/5.49 => ( ord_less_nat @ ( times_times_nat @ A @ C2 ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % mult_less_le_imp_less
% 5.31/5.49 thf(fact_1163_mult__less__le__imp__less,axiom,
% 5.31/5.49 ! [A: int,B: int,C2: int,D: int] :
% 5.31/5.49 ( ( ord_less_int @ A @ B )
% 5.31/5.49 => ( ( ord_less_eq_int @ C2 @ D )
% 5.31/5.49 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.31/5.49 => ( ( ord_less_int @ zero_zero_int @ C2 )
% 5.31/5.49 => ( ord_less_int @ ( times_times_int @ A @ C2 ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % mult_less_le_imp_less
% 5.31/5.49 thf(fact_1164_mult__le__less__imp__less,axiom,
% 5.31/5.49 ! [A: real,B: real,C2: real,D: real] :
% 5.31/5.49 ( ( ord_less_eq_real @ A @ B )
% 5.31/5.49 => ( ( ord_less_real @ C2 @ D )
% 5.31/5.49 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.31/5.49 => ( ( ord_less_eq_real @ zero_zero_real @ C2 )
% 5.31/5.49 => ( ord_less_real @ ( times_times_real @ A @ C2 ) @ ( times_times_real @ B @ D ) ) ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % mult_le_less_imp_less
% 5.31/5.49 thf(fact_1165_mult__le__less__imp__less,axiom,
% 5.31/5.49 ! [A: rat,B: rat,C2: rat,D: rat] :
% 5.31/5.49 ( ( ord_less_eq_rat @ A @ B )
% 5.31/5.49 => ( ( ord_less_rat @ C2 @ D )
% 5.31/5.49 => ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.31/5.49 => ( ( ord_less_eq_rat @ zero_zero_rat @ C2 )
% 5.31/5.49 => ( ord_less_rat @ ( times_times_rat @ A @ C2 ) @ ( times_times_rat @ B @ D ) ) ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % mult_le_less_imp_less
% 5.31/5.49 thf(fact_1166_mult__le__less__imp__less,axiom,
% 5.31/5.49 ! [A: nat,B: nat,C2: nat,D: nat] :
% 5.31/5.49 ( ( ord_less_eq_nat @ A @ B )
% 5.31/5.49 => ( ( ord_less_nat @ C2 @ D )
% 5.31/5.49 => ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.31/5.49 => ( ( ord_less_eq_nat @ zero_zero_nat @ C2 )
% 5.31/5.49 => ( ord_less_nat @ ( times_times_nat @ A @ C2 ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % mult_le_less_imp_less
% 5.31/5.49 thf(fact_1167_mult__le__less__imp__less,axiom,
% 5.31/5.49 ! [A: int,B: int,C2: int,D: int] :
% 5.31/5.49 ( ( ord_less_eq_int @ A @ B )
% 5.31/5.49 => ( ( ord_less_int @ C2 @ D )
% 5.31/5.49 => ( ( ord_less_int @ zero_zero_int @ A )
% 5.31/5.49 => ( ( ord_less_eq_int @ zero_zero_int @ C2 )
% 5.31/5.49 => ( ord_less_int @ ( times_times_int @ A @ C2 ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % mult_le_less_imp_less
% 5.31/5.49 thf(fact_1168_mult__right__le__imp__le,axiom,
% 5.31/5.49 ! [A: real,C2: real,B: real] :
% 5.31/5.49 ( ( ord_less_eq_real @ ( times_times_real @ A @ C2 ) @ ( times_times_real @ B @ C2 ) )
% 5.31/5.49 => ( ( ord_less_real @ zero_zero_real @ C2 )
% 5.31/5.49 => ( ord_less_eq_real @ A @ B ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % mult_right_le_imp_le
% 5.31/5.49 thf(fact_1169_mult__right__le__imp__le,axiom,
% 5.31/5.49 ! [A: rat,C2: rat,B: rat] :
% 5.31/5.49 ( ( ord_less_eq_rat @ ( times_times_rat @ A @ C2 ) @ ( times_times_rat @ B @ C2 ) )
% 5.31/5.49 => ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 5.31/5.49 => ( ord_less_eq_rat @ A @ B ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % mult_right_le_imp_le
% 5.31/5.49 thf(fact_1170_mult__right__le__imp__le,axiom,
% 5.31/5.49 ! [A: nat,C2: nat,B: nat] :
% 5.31/5.49 ( ( ord_less_eq_nat @ ( times_times_nat @ A @ C2 ) @ ( times_times_nat @ B @ C2 ) )
% 5.31/5.49 => ( ( ord_less_nat @ zero_zero_nat @ C2 )
% 5.31/5.49 => ( ord_less_eq_nat @ A @ B ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % mult_right_le_imp_le
% 5.31/5.49 thf(fact_1171_mult__right__le__imp__le,axiom,
% 5.31/5.49 ! [A: int,C2: int,B: int] :
% 5.31/5.49 ( ( ord_less_eq_int @ ( times_times_int @ A @ C2 ) @ ( times_times_int @ B @ C2 ) )
% 5.31/5.49 => ( ( ord_less_int @ zero_zero_int @ C2 )
% 5.31/5.49 => ( ord_less_eq_int @ A @ B ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % mult_right_le_imp_le
% 5.31/5.49 thf(fact_1172_mult__left__le__imp__le,axiom,
% 5.31/5.49 ! [C2: real,A: real,B: real] :
% 5.31/5.49 ( ( ord_less_eq_real @ ( times_times_real @ C2 @ A ) @ ( times_times_real @ C2 @ B ) )
% 5.31/5.49 => ( ( ord_less_real @ zero_zero_real @ C2 )
% 5.31/5.49 => ( ord_less_eq_real @ A @ B ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % mult_left_le_imp_le
% 5.31/5.49 thf(fact_1173_mult__left__le__imp__le,axiom,
% 5.31/5.49 ! [C2: rat,A: rat,B: rat] :
% 5.31/5.49 ( ( ord_less_eq_rat @ ( times_times_rat @ C2 @ A ) @ ( times_times_rat @ C2 @ B ) )
% 5.31/5.49 => ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 5.31/5.49 => ( ord_less_eq_rat @ A @ B ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % mult_left_le_imp_le
% 5.31/5.49 thf(fact_1174_mult__left__le__imp__le,axiom,
% 5.31/5.49 ! [C2: nat,A: nat,B: nat] :
% 5.31/5.49 ( ( ord_less_eq_nat @ ( times_times_nat @ C2 @ A ) @ ( times_times_nat @ C2 @ B ) )
% 5.31/5.49 => ( ( ord_less_nat @ zero_zero_nat @ C2 )
% 5.31/5.49 => ( ord_less_eq_nat @ A @ B ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % mult_left_le_imp_le
% 5.31/5.49 thf(fact_1175_mult__left__le__imp__le,axiom,
% 5.31/5.49 ! [C2: int,A: int,B: int] :
% 5.31/5.49 ( ( ord_less_eq_int @ ( times_times_int @ C2 @ A ) @ ( times_times_int @ C2 @ B ) )
% 5.31/5.49 => ( ( ord_less_int @ zero_zero_int @ C2 )
% 5.31/5.49 => ( ord_less_eq_int @ A @ B ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % mult_left_le_imp_le
% 5.31/5.49 thf(fact_1176_mult__le__cancel__left__pos,axiom,
% 5.31/5.49 ! [C2: real,A: real,B: real] :
% 5.31/5.49 ( ( ord_less_real @ zero_zero_real @ C2 )
% 5.31/5.49 => ( ( ord_less_eq_real @ ( times_times_real @ C2 @ A ) @ ( times_times_real @ C2 @ B ) )
% 5.31/5.49 = ( ord_less_eq_real @ A @ B ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % mult_le_cancel_left_pos
% 5.31/5.49 thf(fact_1177_mult__le__cancel__left__pos,axiom,
% 5.31/5.49 ! [C2: rat,A: rat,B: rat] :
% 5.31/5.49 ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 5.31/5.49 => ( ( ord_less_eq_rat @ ( times_times_rat @ C2 @ A ) @ ( times_times_rat @ C2 @ B ) )
% 5.31/5.49 = ( ord_less_eq_rat @ A @ B ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % mult_le_cancel_left_pos
% 5.31/5.49 thf(fact_1178_mult__le__cancel__left__pos,axiom,
% 5.31/5.49 ! [C2: int,A: int,B: int] :
% 5.31/5.49 ( ( ord_less_int @ zero_zero_int @ C2 )
% 5.31/5.49 => ( ( ord_less_eq_int @ ( times_times_int @ C2 @ A ) @ ( times_times_int @ C2 @ B ) )
% 5.31/5.49 = ( ord_less_eq_int @ A @ B ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % mult_le_cancel_left_pos
% 5.31/5.49 thf(fact_1179_mult__le__cancel__left__neg,axiom,
% 5.31/5.49 ! [C2: real,A: real,B: real] :
% 5.31/5.49 ( ( ord_less_real @ C2 @ zero_zero_real )
% 5.31/5.49 => ( ( ord_less_eq_real @ ( times_times_real @ C2 @ A ) @ ( times_times_real @ C2 @ B ) )
% 5.31/5.49 = ( ord_less_eq_real @ B @ A ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % mult_le_cancel_left_neg
% 5.31/5.49 thf(fact_1180_mult__le__cancel__left__neg,axiom,
% 5.31/5.49 ! [C2: rat,A: rat,B: rat] :
% 5.31/5.49 ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 5.31/5.49 => ( ( ord_less_eq_rat @ ( times_times_rat @ C2 @ A ) @ ( times_times_rat @ C2 @ B ) )
% 5.31/5.49 = ( ord_less_eq_rat @ B @ A ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % mult_le_cancel_left_neg
% 5.31/5.49 thf(fact_1181_mult__le__cancel__left__neg,axiom,
% 5.31/5.49 ! [C2: int,A: int,B: int] :
% 5.31/5.49 ( ( ord_less_int @ C2 @ zero_zero_int )
% 5.31/5.49 => ( ( ord_less_eq_int @ ( times_times_int @ C2 @ A ) @ ( times_times_int @ C2 @ B ) )
% 5.31/5.49 = ( ord_less_eq_int @ B @ A ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % mult_le_cancel_left_neg
% 5.31/5.49 thf(fact_1182_mult__less__cancel__right,axiom,
% 5.31/5.49 ! [A: real,C2: real,B: real] :
% 5.31/5.49 ( ( ord_less_real @ ( times_times_real @ A @ C2 ) @ ( times_times_real @ B @ C2 ) )
% 5.31/5.49 = ( ( ( ord_less_eq_real @ zero_zero_real @ C2 )
% 5.31/5.49 => ( ord_less_real @ A @ B ) )
% 5.31/5.49 & ( ( ord_less_eq_real @ C2 @ zero_zero_real )
% 5.31/5.49 => ( ord_less_real @ B @ A ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % mult_less_cancel_right
% 5.31/5.49 thf(fact_1183_mult__less__cancel__right,axiom,
% 5.31/5.49 ! [A: rat,C2: rat,B: rat] :
% 5.31/5.49 ( ( ord_less_rat @ ( times_times_rat @ A @ C2 ) @ ( times_times_rat @ B @ C2 ) )
% 5.31/5.49 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C2 )
% 5.31/5.49 => ( ord_less_rat @ A @ B ) )
% 5.31/5.49 & ( ( ord_less_eq_rat @ C2 @ zero_zero_rat )
% 5.31/5.49 => ( ord_less_rat @ B @ A ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % mult_less_cancel_right
% 5.31/5.49 thf(fact_1184_mult__less__cancel__right,axiom,
% 5.31/5.49 ! [A: int,C2: int,B: int] :
% 5.31/5.49 ( ( ord_less_int @ ( times_times_int @ A @ C2 ) @ ( times_times_int @ B @ C2 ) )
% 5.31/5.49 = ( ( ( ord_less_eq_int @ zero_zero_int @ C2 )
% 5.31/5.49 => ( ord_less_int @ A @ B ) )
% 5.31/5.49 & ( ( ord_less_eq_int @ C2 @ zero_zero_int )
% 5.31/5.49 => ( ord_less_int @ B @ A ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % mult_less_cancel_right
% 5.31/5.49 thf(fact_1185_mult__strict__mono_H,axiom,
% 5.31/5.49 ! [A: real,B: real,C2: real,D: real] :
% 5.31/5.49 ( ( ord_less_real @ A @ B )
% 5.31/5.49 => ( ( ord_less_real @ C2 @ D )
% 5.31/5.49 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.31/5.49 => ( ( ord_less_eq_real @ zero_zero_real @ C2 )
% 5.31/5.49 => ( ord_less_real @ ( times_times_real @ A @ C2 ) @ ( times_times_real @ B @ D ) ) ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % mult_strict_mono'
% 5.31/5.49 thf(fact_1186_mult__strict__mono_H,axiom,
% 5.31/5.49 ! [A: rat,B: rat,C2: rat,D: rat] :
% 5.31/5.49 ( ( ord_less_rat @ A @ B )
% 5.31/5.49 => ( ( ord_less_rat @ C2 @ D )
% 5.31/5.49 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.31/5.49 => ( ( ord_less_eq_rat @ zero_zero_rat @ C2 )
% 5.31/5.49 => ( ord_less_rat @ ( times_times_rat @ A @ C2 ) @ ( times_times_rat @ B @ D ) ) ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % mult_strict_mono'
% 5.31/5.49 thf(fact_1187_mult__strict__mono_H,axiom,
% 5.31/5.49 ! [A: nat,B: nat,C2: nat,D: nat] :
% 5.31/5.49 ( ( ord_less_nat @ A @ B )
% 5.31/5.49 => ( ( ord_less_nat @ C2 @ D )
% 5.31/5.49 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.31/5.49 => ( ( ord_less_eq_nat @ zero_zero_nat @ C2 )
% 5.31/5.49 => ( ord_less_nat @ ( times_times_nat @ A @ C2 ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % mult_strict_mono'
% 5.31/5.49 thf(fact_1188_mult__strict__mono_H,axiom,
% 5.31/5.49 ! [A: int,B: int,C2: int,D: int] :
% 5.31/5.49 ( ( ord_less_int @ A @ B )
% 5.31/5.49 => ( ( ord_less_int @ C2 @ D )
% 5.31/5.49 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.31/5.49 => ( ( ord_less_eq_int @ zero_zero_int @ C2 )
% 5.31/5.49 => ( ord_less_int @ ( times_times_int @ A @ C2 ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % mult_strict_mono'
% 5.31/5.49 thf(fact_1189_mult__right__less__imp__less,axiom,
% 5.31/5.49 ! [A: real,C2: real,B: real] :
% 5.31/5.49 ( ( ord_less_real @ ( times_times_real @ A @ C2 ) @ ( times_times_real @ B @ C2 ) )
% 5.31/5.49 => ( ( ord_less_eq_real @ zero_zero_real @ C2 )
% 5.31/5.49 => ( ord_less_real @ A @ B ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % mult_right_less_imp_less
% 5.31/5.49 thf(fact_1190_mult__right__less__imp__less,axiom,
% 5.31/5.49 ! [A: rat,C2: rat,B: rat] :
% 5.31/5.49 ( ( ord_less_rat @ ( times_times_rat @ A @ C2 ) @ ( times_times_rat @ B @ C2 ) )
% 5.31/5.49 => ( ( ord_less_eq_rat @ zero_zero_rat @ C2 )
% 5.31/5.49 => ( ord_less_rat @ A @ B ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % mult_right_less_imp_less
% 5.31/5.49 thf(fact_1191_mult__right__less__imp__less,axiom,
% 5.31/5.49 ! [A: nat,C2: nat,B: nat] :
% 5.31/5.49 ( ( ord_less_nat @ ( times_times_nat @ A @ C2 ) @ ( times_times_nat @ B @ C2 ) )
% 5.31/5.49 => ( ( ord_less_eq_nat @ zero_zero_nat @ C2 )
% 5.31/5.49 => ( ord_less_nat @ A @ B ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % mult_right_less_imp_less
% 5.31/5.49 thf(fact_1192_mult__right__less__imp__less,axiom,
% 5.31/5.49 ! [A: int,C2: int,B: int] :
% 5.31/5.49 ( ( ord_less_int @ ( times_times_int @ A @ C2 ) @ ( times_times_int @ B @ C2 ) )
% 5.31/5.49 => ( ( ord_less_eq_int @ zero_zero_int @ C2 )
% 5.31/5.49 => ( ord_less_int @ A @ B ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % mult_right_less_imp_less
% 5.31/5.49 thf(fact_1193_mult__less__cancel__left,axiom,
% 5.31/5.49 ! [C2: real,A: real,B: real] :
% 5.31/5.49 ( ( ord_less_real @ ( times_times_real @ C2 @ A ) @ ( times_times_real @ C2 @ B ) )
% 5.31/5.49 = ( ( ( ord_less_eq_real @ zero_zero_real @ C2 )
% 5.31/5.49 => ( ord_less_real @ A @ B ) )
% 5.31/5.49 & ( ( ord_less_eq_real @ C2 @ zero_zero_real )
% 5.31/5.49 => ( ord_less_real @ B @ A ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % mult_less_cancel_left
% 5.31/5.49 thf(fact_1194_mult__less__cancel__left,axiom,
% 5.31/5.49 ! [C2: rat,A: rat,B: rat] :
% 5.31/5.49 ( ( ord_less_rat @ ( times_times_rat @ C2 @ A ) @ ( times_times_rat @ C2 @ B ) )
% 5.31/5.49 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C2 )
% 5.31/5.49 => ( ord_less_rat @ A @ B ) )
% 5.31/5.49 & ( ( ord_less_eq_rat @ C2 @ zero_zero_rat )
% 5.31/5.49 => ( ord_less_rat @ B @ A ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % mult_less_cancel_left
% 5.31/5.49 thf(fact_1195_mult__less__cancel__left,axiom,
% 5.31/5.49 ! [C2: int,A: int,B: int] :
% 5.31/5.49 ( ( ord_less_int @ ( times_times_int @ C2 @ A ) @ ( times_times_int @ C2 @ B ) )
% 5.31/5.49 = ( ( ( ord_less_eq_int @ zero_zero_int @ C2 )
% 5.31/5.49 => ( ord_less_int @ A @ B ) )
% 5.31/5.49 & ( ( ord_less_eq_int @ C2 @ zero_zero_int )
% 5.31/5.49 => ( ord_less_int @ B @ A ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % mult_less_cancel_left
% 5.31/5.49 thf(fact_1196_mult__strict__mono,axiom,
% 5.31/5.49 ! [A: real,B: real,C2: real,D: real] :
% 5.31/5.49 ( ( ord_less_real @ A @ B )
% 5.31/5.49 => ( ( ord_less_real @ C2 @ D )
% 5.31/5.49 => ( ( ord_less_real @ zero_zero_real @ B )
% 5.31/5.49 => ( ( ord_less_eq_real @ zero_zero_real @ C2 )
% 5.31/5.49 => ( ord_less_real @ ( times_times_real @ A @ C2 ) @ ( times_times_real @ B @ D ) ) ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % mult_strict_mono
% 5.31/5.49 thf(fact_1197_mult__strict__mono,axiom,
% 5.31/5.49 ! [A: rat,B: rat,C2: rat,D: rat] :
% 5.31/5.49 ( ( ord_less_rat @ A @ B )
% 5.31/5.49 => ( ( ord_less_rat @ C2 @ D )
% 5.31/5.49 => ( ( ord_less_rat @ zero_zero_rat @ B )
% 5.31/5.49 => ( ( ord_less_eq_rat @ zero_zero_rat @ C2 )
% 5.31/5.49 => ( ord_less_rat @ ( times_times_rat @ A @ C2 ) @ ( times_times_rat @ B @ D ) ) ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % mult_strict_mono
% 5.31/5.49 thf(fact_1198_mult__strict__mono,axiom,
% 5.31/5.49 ! [A: nat,B: nat,C2: nat,D: nat] :
% 5.31/5.49 ( ( ord_less_nat @ A @ B )
% 5.31/5.49 => ( ( ord_less_nat @ C2 @ D )
% 5.31/5.49 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.31/5.49 => ( ( ord_less_eq_nat @ zero_zero_nat @ C2 )
% 5.31/5.49 => ( ord_less_nat @ ( times_times_nat @ A @ C2 ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % mult_strict_mono
% 5.31/5.49 thf(fact_1199_mult__strict__mono,axiom,
% 5.31/5.49 ! [A: int,B: int,C2: int,D: int] :
% 5.31/5.49 ( ( ord_less_int @ A @ B )
% 5.31/5.49 => ( ( ord_less_int @ C2 @ D )
% 5.31/5.49 => ( ( ord_less_int @ zero_zero_int @ B )
% 5.31/5.49 => ( ( ord_less_eq_int @ zero_zero_int @ C2 )
% 5.31/5.49 => ( ord_less_int @ ( times_times_int @ A @ C2 ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % mult_strict_mono
% 5.31/5.49 thf(fact_1200_mult__left__less__imp__less,axiom,
% 5.31/5.49 ! [C2: real,A: real,B: real] :
% 5.31/5.49 ( ( ord_less_real @ ( times_times_real @ C2 @ A ) @ ( times_times_real @ C2 @ B ) )
% 5.31/5.49 => ( ( ord_less_eq_real @ zero_zero_real @ C2 )
% 5.31/5.49 => ( ord_less_real @ A @ B ) ) ) ).
% 5.31/5.49
% 5.31/5.49 % mult_left_less_imp_less
% 5.31/5.49 thf(fact_1201_mult__left__less__imp__less,axiom,
% 5.31/5.49 ! [C2: rat,A: rat,B: rat] :
% 5.31/5.50 ( ( ord_less_rat @ ( times_times_rat @ C2 @ A ) @ ( times_times_rat @ C2 @ B ) )
% 5.31/5.50 => ( ( ord_less_eq_rat @ zero_zero_rat @ C2 )
% 5.31/5.50 => ( ord_less_rat @ A @ B ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % mult_left_less_imp_less
% 5.31/5.50 thf(fact_1202_mult__left__less__imp__less,axiom,
% 5.31/5.50 ! [C2: nat,A: nat,B: nat] :
% 5.31/5.50 ( ( ord_less_nat @ ( times_times_nat @ C2 @ A ) @ ( times_times_nat @ C2 @ B ) )
% 5.31/5.50 => ( ( ord_less_eq_nat @ zero_zero_nat @ C2 )
% 5.31/5.50 => ( ord_less_nat @ A @ B ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % mult_left_less_imp_less
% 5.31/5.50 thf(fact_1203_mult__left__less__imp__less,axiom,
% 5.31/5.50 ! [C2: int,A: int,B: int] :
% 5.31/5.50 ( ( ord_less_int @ ( times_times_int @ C2 @ A ) @ ( times_times_int @ C2 @ B ) )
% 5.31/5.50 => ( ( ord_less_eq_int @ zero_zero_int @ C2 )
% 5.31/5.50 => ( ord_less_int @ A @ B ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % mult_left_less_imp_less
% 5.31/5.50 thf(fact_1204_mult__le__cancel__right,axiom,
% 5.31/5.50 ! [A: real,C2: real,B: real] :
% 5.31/5.50 ( ( ord_less_eq_real @ ( times_times_real @ A @ C2 ) @ ( times_times_real @ B @ C2 ) )
% 5.31/5.50 = ( ( ( ord_less_real @ zero_zero_real @ C2 )
% 5.31/5.50 => ( ord_less_eq_real @ A @ B ) )
% 5.31/5.50 & ( ( ord_less_real @ C2 @ zero_zero_real )
% 5.31/5.50 => ( ord_less_eq_real @ B @ A ) ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % mult_le_cancel_right
% 5.31/5.50 thf(fact_1205_mult__le__cancel__right,axiom,
% 5.31/5.50 ! [A: rat,C2: rat,B: rat] :
% 5.31/5.50 ( ( ord_less_eq_rat @ ( times_times_rat @ A @ C2 ) @ ( times_times_rat @ B @ C2 ) )
% 5.31/5.50 = ( ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 5.31/5.50 => ( ord_less_eq_rat @ A @ B ) )
% 5.31/5.50 & ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 5.31/5.50 => ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % mult_le_cancel_right
% 5.31/5.50 thf(fact_1206_mult__le__cancel__right,axiom,
% 5.31/5.50 ! [A: int,C2: int,B: int] :
% 5.31/5.50 ( ( ord_less_eq_int @ ( times_times_int @ A @ C2 ) @ ( times_times_int @ B @ C2 ) )
% 5.31/5.50 = ( ( ( ord_less_int @ zero_zero_int @ C2 )
% 5.31/5.50 => ( ord_less_eq_int @ A @ B ) )
% 5.31/5.50 & ( ( ord_less_int @ C2 @ zero_zero_int )
% 5.31/5.50 => ( ord_less_eq_int @ B @ A ) ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % mult_le_cancel_right
% 5.31/5.50 thf(fact_1207_mult__le__cancel__left,axiom,
% 5.31/5.50 ! [C2: real,A: real,B: real] :
% 5.31/5.50 ( ( ord_less_eq_real @ ( times_times_real @ C2 @ A ) @ ( times_times_real @ C2 @ B ) )
% 5.31/5.50 = ( ( ( ord_less_real @ zero_zero_real @ C2 )
% 5.31/5.50 => ( ord_less_eq_real @ A @ B ) )
% 5.31/5.50 & ( ( ord_less_real @ C2 @ zero_zero_real )
% 5.31/5.50 => ( ord_less_eq_real @ B @ A ) ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % mult_le_cancel_left
% 5.31/5.50 thf(fact_1208_mult__le__cancel__left,axiom,
% 5.31/5.50 ! [C2: rat,A: rat,B: rat] :
% 5.31/5.50 ( ( ord_less_eq_rat @ ( times_times_rat @ C2 @ A ) @ ( times_times_rat @ C2 @ B ) )
% 5.31/5.50 = ( ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 5.31/5.50 => ( ord_less_eq_rat @ A @ B ) )
% 5.31/5.50 & ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 5.31/5.50 => ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % mult_le_cancel_left
% 5.31/5.50 thf(fact_1209_mult__le__cancel__left,axiom,
% 5.31/5.50 ! [C2: int,A: int,B: int] :
% 5.31/5.50 ( ( ord_less_eq_int @ ( times_times_int @ C2 @ A ) @ ( times_times_int @ C2 @ B ) )
% 5.31/5.50 = ( ( ( ord_less_int @ zero_zero_int @ C2 )
% 5.31/5.50 => ( ord_less_eq_int @ A @ B ) )
% 5.31/5.50 & ( ( ord_less_int @ C2 @ zero_zero_int )
% 5.31/5.50 => ( ord_less_eq_int @ B @ A ) ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % mult_le_cancel_left
% 5.31/5.50 thf(fact_1210_VEBT__internal_Onaive__member_Ocases,axiom,
% 5.31/5.50 ! [X: produc9072475918466114483BT_nat] :
% 5.31/5.50 ( ! [A3: $o,B3: $o,X3: nat] :
% 5.31/5.50 ( X
% 5.31/5.50 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ X3 ) )
% 5.31/5.50 => ( ! [Uu2: option4927543243414619207at_nat,Uv2: list_VEBT_VEBT,Uw: vEBT_VEBT,Ux: nat] :
% 5.31/5.50 ( X
% 5.31/5.50 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw ) @ Ux ) )
% 5.31/5.50 => ~ ! [Uy: option4927543243414619207at_nat,V: nat,TreeList: list_VEBT_VEBT,S: vEBT_VEBT,X3: nat] :
% 5.31/5.50 ( X
% 5.31/5.50 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uy @ ( suc @ V ) @ TreeList @ S ) @ X3 ) ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % VEBT_internal.naive_member.cases
% 5.31/5.50 thf(fact_1211_mult__left__le,axiom,
% 5.31/5.50 ! [C2: code_integer,A: code_integer] :
% 5.31/5.50 ( ( ord_le3102999989581377725nteger @ C2 @ one_one_Code_integer )
% 5.31/5.50 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 5.31/5.50 => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ A @ C2 ) @ A ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % mult_left_le
% 5.31/5.50 thf(fact_1212_mult__left__le,axiom,
% 5.31/5.50 ! [C2: real,A: real] :
% 5.31/5.50 ( ( ord_less_eq_real @ C2 @ one_one_real )
% 5.31/5.50 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.31/5.50 => ( ord_less_eq_real @ ( times_times_real @ A @ C2 ) @ A ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % mult_left_le
% 5.31/5.50 thf(fact_1213_mult__left__le,axiom,
% 5.31/5.50 ! [C2: rat,A: rat] :
% 5.31/5.50 ( ( ord_less_eq_rat @ C2 @ one_one_rat )
% 5.31/5.50 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.31/5.50 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C2 ) @ A ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % mult_left_le
% 5.31/5.50 thf(fact_1214_mult__left__le,axiom,
% 5.31/5.50 ! [C2: nat,A: nat] :
% 5.31/5.50 ( ( ord_less_eq_nat @ C2 @ one_one_nat )
% 5.31/5.50 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.31/5.50 => ( ord_less_eq_nat @ ( times_times_nat @ A @ C2 ) @ A ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % mult_left_le
% 5.31/5.50 thf(fact_1215_mult__left__le,axiom,
% 5.31/5.50 ! [C2: int,A: int] :
% 5.31/5.50 ( ( ord_less_eq_int @ C2 @ one_one_int )
% 5.31/5.50 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.31/5.50 => ( ord_less_eq_int @ ( times_times_int @ A @ C2 ) @ A ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % mult_left_le
% 5.31/5.50 thf(fact_1216_mult__le__one,axiom,
% 5.31/5.50 ! [A: code_integer,B: code_integer] :
% 5.31/5.50 ( ( ord_le3102999989581377725nteger @ A @ one_one_Code_integer )
% 5.31/5.50 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B )
% 5.31/5.50 => ( ( ord_le3102999989581377725nteger @ B @ one_one_Code_integer )
% 5.31/5.50 => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ A @ B ) @ one_one_Code_integer ) ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % mult_le_one
% 5.31/5.50 thf(fact_1217_mult__le__one,axiom,
% 5.31/5.50 ! [A: real,B: real] :
% 5.31/5.50 ( ( ord_less_eq_real @ A @ one_one_real )
% 5.31/5.50 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.31/5.50 => ( ( ord_less_eq_real @ B @ one_one_real )
% 5.31/5.50 => ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ one_one_real ) ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % mult_le_one
% 5.31/5.50 thf(fact_1218_mult__le__one,axiom,
% 5.31/5.50 ! [A: rat,B: rat] :
% 5.31/5.50 ( ( ord_less_eq_rat @ A @ one_one_rat )
% 5.31/5.50 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.31/5.50 => ( ( ord_less_eq_rat @ B @ one_one_rat )
% 5.31/5.50 => ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ one_one_rat ) ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % mult_le_one
% 5.31/5.50 thf(fact_1219_mult__le__one,axiom,
% 5.31/5.50 ! [A: nat,B: nat] :
% 5.31/5.50 ( ( ord_less_eq_nat @ A @ one_one_nat )
% 5.31/5.50 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.31/5.50 => ( ( ord_less_eq_nat @ B @ one_one_nat )
% 5.31/5.50 => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ one_one_nat ) ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % mult_le_one
% 5.31/5.50 thf(fact_1220_mult__le__one,axiom,
% 5.31/5.50 ! [A: int,B: int] :
% 5.31/5.50 ( ( ord_less_eq_int @ A @ one_one_int )
% 5.31/5.50 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.31/5.50 => ( ( ord_less_eq_int @ B @ one_one_int )
% 5.31/5.50 => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ one_one_int ) ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % mult_le_one
% 5.31/5.50 thf(fact_1221_mult__right__le__one__le,axiom,
% 5.31/5.50 ! [X: code_integer,Y: code_integer] :
% 5.31/5.50 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ X )
% 5.31/5.50 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ Y )
% 5.31/5.50 => ( ( ord_le3102999989581377725nteger @ Y @ one_one_Code_integer )
% 5.31/5.50 => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ X @ Y ) @ X ) ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % mult_right_le_one_le
% 5.31/5.50 thf(fact_1222_mult__right__le__one__le,axiom,
% 5.31/5.50 ! [X: real,Y: real] :
% 5.31/5.50 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.31/5.50 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.31/5.50 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.31/5.50 => ( ord_less_eq_real @ ( times_times_real @ X @ Y ) @ X ) ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % mult_right_le_one_le
% 5.31/5.50 thf(fact_1223_mult__right__le__one__le,axiom,
% 5.31/5.50 ! [X: rat,Y: rat] :
% 5.31/5.50 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 5.31/5.50 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 5.31/5.50 => ( ( ord_less_eq_rat @ Y @ one_one_rat )
% 5.31/5.50 => ( ord_less_eq_rat @ ( times_times_rat @ X @ Y ) @ X ) ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % mult_right_le_one_le
% 5.31/5.50 thf(fact_1224_mult__right__le__one__le,axiom,
% 5.31/5.50 ! [X: int,Y: int] :
% 5.31/5.50 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.31/5.50 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.31/5.50 => ( ( ord_less_eq_int @ Y @ one_one_int )
% 5.31/5.50 => ( ord_less_eq_int @ ( times_times_int @ X @ Y ) @ X ) ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % mult_right_le_one_le
% 5.31/5.50 thf(fact_1225_mult__left__le__one__le,axiom,
% 5.31/5.50 ! [X: code_integer,Y: code_integer] :
% 5.31/5.50 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ X )
% 5.31/5.50 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ Y )
% 5.31/5.50 => ( ( ord_le3102999989581377725nteger @ Y @ one_one_Code_integer )
% 5.31/5.50 => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ Y @ X ) @ X ) ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % mult_left_le_one_le
% 5.31/5.50 thf(fact_1226_mult__left__le__one__le,axiom,
% 5.31/5.50 ! [X: real,Y: real] :
% 5.31/5.50 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.31/5.50 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.31/5.50 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.31/5.50 => ( ord_less_eq_real @ ( times_times_real @ Y @ X ) @ X ) ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % mult_left_le_one_le
% 5.31/5.50 thf(fact_1227_mult__left__le__one__le,axiom,
% 5.31/5.50 ! [X: rat,Y: rat] :
% 5.31/5.50 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 5.31/5.50 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 5.31/5.50 => ( ( ord_less_eq_rat @ Y @ one_one_rat )
% 5.31/5.50 => ( ord_less_eq_rat @ ( times_times_rat @ Y @ X ) @ X ) ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % mult_left_le_one_le
% 5.31/5.50 thf(fact_1228_mult__left__le__one__le,axiom,
% 5.31/5.50 ! [X: int,Y: int] :
% 5.31/5.50 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.31/5.50 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.31/5.50 => ( ( ord_less_eq_int @ Y @ one_one_int )
% 5.31/5.50 => ( ord_less_eq_int @ ( times_times_int @ Y @ X ) @ X ) ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % mult_left_le_one_le
% 5.31/5.50 thf(fact_1229_ex__least__nat__less,axiom,
% 5.31/5.50 ! [P2: nat > $o,N: nat] :
% 5.31/5.50 ( ( P2 @ N )
% 5.31/5.50 => ( ~ ( P2 @ zero_zero_nat )
% 5.31/5.50 => ? [K: nat] :
% 5.31/5.50 ( ( ord_less_nat @ K @ N )
% 5.31/5.50 & ! [I4: nat] :
% 5.31/5.50 ( ( ord_less_eq_nat @ I4 @ K )
% 5.31/5.50 => ~ ( P2 @ I4 ) )
% 5.31/5.50 & ( P2 @ ( suc @ K ) ) ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % ex_least_nat_less
% 5.31/5.50 thf(fact_1230_n__less__n__mult__m,axiom,
% 5.31/5.50 ! [N: nat,M2: nat] :
% 5.31/5.50 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.50 => ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M2 )
% 5.31/5.50 => ( ord_less_nat @ N @ ( times_times_nat @ N @ M2 ) ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % n_less_n_mult_m
% 5.31/5.50 thf(fact_1231_n__less__m__mult__n,axiom,
% 5.31/5.50 ! [N: nat,M2: nat] :
% 5.31/5.50 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.50 => ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M2 )
% 5.31/5.50 => ( ord_less_nat @ N @ ( times_times_nat @ M2 @ N ) ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % n_less_m_mult_n
% 5.31/5.50 thf(fact_1232_one__less__mult,axiom,
% 5.31/5.50 ! [N: nat,M2: nat] :
% 5.31/5.50 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.31/5.50 => ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M2 )
% 5.31/5.50 => ( ord_less_nat @ ( suc @ zero_zero_nat ) @ ( times_times_nat @ M2 @ N ) ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % one_less_mult
% 5.31/5.50 thf(fact_1233_greater__shift,axiom,
% 5.31/5.50 ( ord_less_nat
% 5.31/5.50 = ( ^ [Y4: nat,X4: nat] : ( vEBT_VEBT_greater @ ( some_nat @ X4 ) @ ( some_nat @ Y4 ) ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % greater_shift
% 5.31/5.50 thf(fact_1234_less__shift,axiom,
% 5.31/5.50 ( ord_less_nat
% 5.31/5.50 = ( ^ [X4: nat,Y4: nat] : ( vEBT_VEBT_less @ ( some_nat @ X4 ) @ ( some_nat @ Y4 ) ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % less_shift
% 5.31/5.50 thf(fact_1235_buildup__gives__valid,axiom,
% 5.31/5.50 ! [N: nat] :
% 5.31/5.50 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.50 => ( vEBT_invar_vebt @ ( vEBT_vebt_buildup @ N ) @ N ) ) ).
% 5.31/5.50
% 5.31/5.50 % buildup_gives_valid
% 5.31/5.50 thf(fact_1236_field__le__mult__one__interval,axiom,
% 5.31/5.50 ! [X: real,Y: real] :
% 5.31/5.50 ( ! [Z: real] :
% 5.31/5.50 ( ( ord_less_real @ zero_zero_real @ Z )
% 5.31/5.50 => ( ( ord_less_real @ Z @ one_one_real )
% 5.31/5.50 => ( ord_less_eq_real @ ( times_times_real @ Z @ X ) @ Y ) ) )
% 5.31/5.50 => ( ord_less_eq_real @ X @ Y ) ) ).
% 5.31/5.50
% 5.31/5.50 % field_le_mult_one_interval
% 5.31/5.50 thf(fact_1237_field__le__mult__one__interval,axiom,
% 5.31/5.50 ! [X: rat,Y: rat] :
% 5.31/5.50 ( ! [Z: rat] :
% 5.31/5.50 ( ( ord_less_rat @ zero_zero_rat @ Z )
% 5.31/5.50 => ( ( ord_less_rat @ Z @ one_one_rat )
% 5.31/5.50 => ( ord_less_eq_rat @ ( times_times_rat @ Z @ X ) @ Y ) ) )
% 5.31/5.50 => ( ord_less_eq_rat @ X @ Y ) ) ).
% 5.31/5.50
% 5.31/5.50 % field_le_mult_one_interval
% 5.31/5.50 thf(fact_1238_case4_I2_J,axiom,
% 5.31/5.50 ! [S2: vEBT_VEBT] :
% 5.31/5.50 ( ( vEBT_invar_vebt @ S2 @ m )
% 5.31/5.50 => ( ( ( vEBT_VEBT_set_vebt @ summary2 )
% 5.31/5.50 = ( vEBT_VEBT_set_vebt @ S2 ) )
% 5.31/5.50 => ( S2 = summary2 ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % case4(2)
% 5.31/5.50 thf(fact_1239_maxt__corr,axiom,
% 5.31/5.50 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 5.31/5.50 ( ( vEBT_invar_vebt @ T @ N )
% 5.31/5.50 => ( ( ( vEBT_vebt_maxt @ T )
% 5.31/5.50 = ( some_nat @ X ) )
% 5.31/5.50 => ( vEBT_VEBT_max_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % maxt_corr
% 5.31/5.50 thf(fact_1240_maxt__sound,axiom,
% 5.31/5.50 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 5.31/5.50 ( ( vEBT_invar_vebt @ T @ N )
% 5.31/5.50 => ( ( vEBT_VEBT_max_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X )
% 5.31/5.50 => ( ( vEBT_vebt_maxt @ T )
% 5.31/5.50 = ( some_nat @ X ) ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % maxt_sound
% 5.31/5.50 thf(fact_1241_mint__corr,axiom,
% 5.31/5.50 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 5.31/5.50 ( ( vEBT_invar_vebt @ T @ N )
% 5.31/5.50 => ( ( ( vEBT_vebt_mint @ T )
% 5.31/5.50 = ( some_nat @ X ) )
% 5.31/5.50 => ( vEBT_VEBT_min_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % mint_corr
% 5.31/5.50 thf(fact_1242_mint__sound,axiom,
% 5.31/5.50 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 5.31/5.50 ( ( vEBT_invar_vebt @ T @ N )
% 5.31/5.50 => ( ( vEBT_VEBT_min_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X )
% 5.31/5.50 => ( ( vEBT_vebt_mint @ T )
% 5.31/5.50 = ( some_nat @ X ) ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % mint_sound
% 5.31/5.50 thf(fact_1243_mult__le__cancel__iff2,axiom,
% 5.31/5.50 ! [Z3: real,X: real,Y: real] :
% 5.31/5.50 ( ( ord_less_real @ zero_zero_real @ Z3 )
% 5.31/5.50 => ( ( ord_less_eq_real @ ( times_times_real @ Z3 @ X ) @ ( times_times_real @ Z3 @ Y ) )
% 5.31/5.50 = ( ord_less_eq_real @ X @ Y ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % mult_le_cancel_iff2
% 5.31/5.50 thf(fact_1244_mult__le__cancel__iff2,axiom,
% 5.31/5.50 ! [Z3: rat,X: rat,Y: rat] :
% 5.31/5.50 ( ( ord_less_rat @ zero_zero_rat @ Z3 )
% 5.31/5.50 => ( ( ord_less_eq_rat @ ( times_times_rat @ Z3 @ X ) @ ( times_times_rat @ Z3 @ Y ) )
% 5.31/5.50 = ( ord_less_eq_rat @ X @ Y ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % mult_le_cancel_iff2
% 5.31/5.50 thf(fact_1245_mult__le__cancel__iff2,axiom,
% 5.31/5.50 ! [Z3: int,X: int,Y: int] :
% 5.31/5.50 ( ( ord_less_int @ zero_zero_int @ Z3 )
% 5.31/5.50 => ( ( ord_less_eq_int @ ( times_times_int @ Z3 @ X ) @ ( times_times_int @ Z3 @ Y ) )
% 5.31/5.50 = ( ord_less_eq_int @ X @ Y ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % mult_le_cancel_iff2
% 5.31/5.50 thf(fact_1246_mult__le__cancel__iff1,axiom,
% 5.31/5.50 ! [Z3: real,X: real,Y: real] :
% 5.31/5.50 ( ( ord_less_real @ zero_zero_real @ Z3 )
% 5.31/5.50 => ( ( ord_less_eq_real @ ( times_times_real @ X @ Z3 ) @ ( times_times_real @ Y @ Z3 ) )
% 5.31/5.50 = ( ord_less_eq_real @ X @ Y ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % mult_le_cancel_iff1
% 5.31/5.50 thf(fact_1247_mult__le__cancel__iff1,axiom,
% 5.31/5.50 ! [Z3: rat,X: rat,Y: rat] :
% 5.31/5.50 ( ( ord_less_rat @ zero_zero_rat @ Z3 )
% 5.31/5.50 => ( ( ord_less_eq_rat @ ( times_times_rat @ X @ Z3 ) @ ( times_times_rat @ Y @ Z3 ) )
% 5.31/5.50 = ( ord_less_eq_rat @ X @ Y ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % mult_le_cancel_iff1
% 5.31/5.50 thf(fact_1248_mult__le__cancel__iff1,axiom,
% 5.31/5.50 ! [Z3: int,X: int,Y: int] :
% 5.31/5.50 ( ( ord_less_int @ zero_zero_int @ Z3 )
% 5.31/5.50 => ( ( ord_less_eq_int @ ( times_times_int @ X @ Z3 ) @ ( times_times_int @ Y @ Z3 ) )
% 5.31/5.50 = ( ord_less_eq_int @ X @ Y ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % mult_le_cancel_iff1
% 5.31/5.50 thf(fact_1249_ac,axiom,
% 5.31/5.50 ! [T: vEBT_VEBT,H: nat,K2: vEBT_VEBT] :
% 5.31/5.50 ( ( vEBT_invar_vebt @ T @ H )
% 5.31/5.50 => ( ( vEBT_invar_vebt @ K2 @ H )
% 5.31/5.50 => ( ( ( vEBT_VEBT_set_vebt @ T )
% 5.31/5.50 = ( vEBT_VEBT_set_vebt @ K2 ) )
% 5.31/5.50 => ( ( vEBT_vebt_mint @ T )
% 5.31/5.50 = ( vEBT_vebt_mint @ K2 ) ) ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % ac
% 5.31/5.50 thf(fact_1250_ad,axiom,
% 5.31/5.50 ! [T: vEBT_VEBT,H: nat,K2: vEBT_VEBT] :
% 5.31/5.50 ( ( vEBT_invar_vebt @ T @ H )
% 5.31/5.50 => ( ( vEBT_invar_vebt @ K2 @ H )
% 5.31/5.50 => ( ( ( vEBT_VEBT_set_vebt @ T )
% 5.31/5.50 = ( vEBT_VEBT_set_vebt @ K2 ) )
% 5.31/5.50 => ( ( vEBT_vebt_maxt @ T )
% 5.31/5.50 = ( vEBT_vebt_maxt @ K2 ) ) ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % ad
% 5.31/5.50 thf(fact_1251_case4_I5_J,axiom,
% 5.31/5.50 m = na ).
% 5.31/5.50
% 5.31/5.50 % case4(5)
% 5.31/5.50 thf(fact_1252_vebt__buildup_Osimps_I1_J,axiom,
% 5.31/5.50 ( ( vEBT_vebt_buildup @ zero_zero_nat )
% 5.31/5.50 = ( vEBT_Leaf @ $false @ $false ) ) ).
% 5.31/5.50
% 5.31/5.50 % vebt_buildup.simps(1)
% 5.31/5.50 thf(fact_1253_vebt__buildup_Osimps_I2_J,axiom,
% 5.31/5.50 ( ( vEBT_vebt_buildup @ ( suc @ zero_zero_nat ) )
% 5.31/5.50 = ( vEBT_Leaf @ $false @ $false ) ) ).
% 5.31/5.50
% 5.31/5.50 % vebt_buildup.simps(2)
% 5.31/5.50 thf(fact_1254_mult__less__iff1,axiom,
% 5.31/5.50 ! [Z3: real,X: real,Y: real] :
% 5.31/5.50 ( ( ord_less_real @ zero_zero_real @ Z3 )
% 5.31/5.50 => ( ( ord_less_real @ ( times_times_real @ X @ Z3 ) @ ( times_times_real @ Y @ Z3 ) )
% 5.31/5.50 = ( ord_less_real @ X @ Y ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % mult_less_iff1
% 5.31/5.50 thf(fact_1255_mult__less__iff1,axiom,
% 5.31/5.50 ! [Z3: rat,X: rat,Y: rat] :
% 5.31/5.50 ( ( ord_less_rat @ zero_zero_rat @ Z3 )
% 5.31/5.50 => ( ( ord_less_rat @ ( times_times_rat @ X @ Z3 ) @ ( times_times_rat @ Y @ Z3 ) )
% 5.31/5.50 = ( ord_less_rat @ X @ Y ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % mult_less_iff1
% 5.31/5.50 thf(fact_1256_mult__less__iff1,axiom,
% 5.31/5.50 ! [Z3: int,X: int,Y: int] :
% 5.31/5.50 ( ( ord_less_int @ zero_zero_int @ Z3 )
% 5.31/5.50 => ( ( ord_less_int @ ( times_times_int @ X @ Z3 ) @ ( times_times_int @ Y @ Z3 ) )
% 5.31/5.50 = ( ord_less_int @ X @ Y ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % mult_less_iff1
% 5.31/5.50 thf(fact_1257_vebt__maxt_Osimps_I3_J,axiom,
% 5.31/5.50 ! [Mi: nat,Ma: nat,Ux2: nat,Uy2: list_VEBT_VEBT,Uz: vEBT_VEBT] :
% 5.31/5.50 ( ( vEBT_vebt_maxt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Ux2 @ Uy2 @ Uz ) )
% 5.31/5.50 = ( some_nat @ Ma ) ) ).
% 5.31/5.50
% 5.31/5.50 % vebt_maxt.simps(3)
% 5.31/5.50 thf(fact_1258_vebt__mint_Osimps_I3_J,axiom,
% 5.31/5.50 ! [Mi: nat,Ma: nat,Ux2: nat,Uy2: list_VEBT_VEBT,Uz: vEBT_VEBT] :
% 5.31/5.50 ( ( vEBT_vebt_mint @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Ux2 @ Uy2 @ Uz ) )
% 5.31/5.50 = ( some_nat @ Mi ) ) ).
% 5.31/5.50
% 5.31/5.50 % vebt_mint.simps(3)
% 5.31/5.50 thf(fact_1259_maxt__corr__help,axiom,
% 5.31/5.50 ! [T: vEBT_VEBT,N: nat,Maxi: nat,X: nat] :
% 5.31/5.50 ( ( vEBT_invar_vebt @ T @ N )
% 5.31/5.50 => ( ( ( vEBT_vebt_maxt @ T )
% 5.31/5.50 = ( some_nat @ Maxi ) )
% 5.31/5.50 => ( ( vEBT_vebt_member @ T @ X )
% 5.31/5.50 => ( ord_less_eq_nat @ X @ Maxi ) ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % maxt_corr_help
% 5.31/5.50 thf(fact_1260_mint__corr__help,axiom,
% 5.31/5.50 ! [T: vEBT_VEBT,N: nat,Mini: nat,X: nat] :
% 5.31/5.50 ( ( vEBT_invar_vebt @ T @ N )
% 5.31/5.50 => ( ( ( vEBT_vebt_mint @ T )
% 5.31/5.50 = ( some_nat @ Mini ) )
% 5.31/5.50 => ( ( vEBT_vebt_member @ T @ X )
% 5.31/5.50 => ( ord_less_eq_nat @ Mini @ X ) ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % mint_corr_help
% 5.31/5.50 thf(fact_1261_buildup__nothing__in__leaf,axiom,
% 5.31/5.50 ! [N: nat,X: nat] :
% 5.31/5.50 ~ ( vEBT_V5719532721284313246member @ ( vEBT_vebt_buildup @ N ) @ X ) ).
% 5.31/5.50
% 5.31/5.50 % buildup_nothing_in_leaf
% 5.31/5.50 thf(fact_1262_maxt__member,axiom,
% 5.31/5.50 ! [T: vEBT_VEBT,N: nat,Maxi: nat] :
% 5.31/5.50 ( ( vEBT_invar_vebt @ T @ N )
% 5.31/5.50 => ( ( ( vEBT_vebt_maxt @ T )
% 5.31/5.50 = ( some_nat @ Maxi ) )
% 5.31/5.50 => ( vEBT_vebt_member @ T @ Maxi ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % maxt_member
% 5.31/5.50 thf(fact_1263_mint__member,axiom,
% 5.31/5.50 ! [T: vEBT_VEBT,N: nat,Maxi: nat] :
% 5.31/5.50 ( ( vEBT_invar_vebt @ T @ N )
% 5.31/5.50 => ( ( ( vEBT_vebt_mint @ T )
% 5.31/5.50 = ( some_nat @ Maxi ) )
% 5.31/5.50 => ( vEBT_vebt_member @ T @ Maxi ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % mint_member
% 5.31/5.50 thf(fact_1264_aa,axiom,
% 5.31/5.50 ord_less_eq_set_nat @ ( insert_nat @ mi @ ( insert_nat @ ma @ bot_bot_set_nat ) ) @ ( vEBT_VEBT_set_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ deg @ treeList2 @ summary2 ) ) ).
% 5.31/5.50
% 5.31/5.50 % aa
% 5.31/5.50 thf(fact_1265_VEBT__internal_Oinsert_H_Ocases,axiom,
% 5.31/5.50 ! [X: produc9072475918466114483BT_nat] :
% 5.31/5.50 ( ! [A3: $o,B3: $o,X3: nat] :
% 5.31/5.50 ( X
% 5.31/5.50 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ X3 ) )
% 5.31/5.50 => ~ ! [Info: option4927543243414619207at_nat,Deg2: nat,TreeList: list_VEBT_VEBT,Summary2: vEBT_VEBT,X3: nat] :
% 5.31/5.50 ( X
% 5.31/5.50 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info @ Deg2 @ TreeList @ Summary2 ) @ X3 ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % VEBT_internal.insert'.cases
% 5.31/5.50 thf(fact_1266_member__correct,axiom,
% 5.31/5.50 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 5.31/5.50 ( ( vEBT_invar_vebt @ T @ N )
% 5.31/5.50 => ( ( vEBT_vebt_member @ T @ X )
% 5.31/5.50 = ( member_nat @ X @ ( vEBT_set_vebt @ T ) ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % member_correct
% 5.31/5.50 thf(fact_1267_VEBT__internal_Ooption__shift_Osimps_I3_J,axiom,
% 5.31/5.50 ! [F2: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,A: product_prod_nat_nat,B: product_prod_nat_nat] :
% 5.31/5.50 ( ( vEBT_V1502963449132264192at_nat @ F2 @ ( some_P7363390416028606310at_nat @ A ) @ ( some_P7363390416028606310at_nat @ B ) )
% 5.31/5.50 = ( some_P7363390416028606310at_nat @ ( F2 @ A @ B ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % VEBT_internal.option_shift.simps(3)
% 5.31/5.50 thf(fact_1268_VEBT__internal_Ooption__shift_Osimps_I3_J,axiom,
% 5.31/5.50 ! [F2: num > num > num,A: num,B: num] :
% 5.31/5.50 ( ( vEBT_V819420779217536731ft_num @ F2 @ ( some_num @ A ) @ ( some_num @ B ) )
% 5.31/5.50 = ( some_num @ ( F2 @ A @ B ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % VEBT_internal.option_shift.simps(3)
% 5.31/5.50 thf(fact_1269_VEBT__internal_Ooption__shift_Osimps_I3_J,axiom,
% 5.31/5.50 ! [F2: nat > nat > nat,A: nat,B: nat] :
% 5.31/5.50 ( ( vEBT_V4262088993061758097ft_nat @ F2 @ ( some_nat @ A ) @ ( some_nat @ B ) )
% 5.31/5.50 = ( some_nat @ ( F2 @ A @ B ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % VEBT_internal.option_shift.simps(3)
% 5.31/5.50 thf(fact_1270_buildup__gives__empty,axiom,
% 5.31/5.50 ! [N: nat] :
% 5.31/5.50 ( ( vEBT_VEBT_set_vebt @ ( vEBT_vebt_buildup @ N ) )
% 5.31/5.50 = bot_bot_set_nat ) ).
% 5.31/5.50
% 5.31/5.50 % buildup_gives_empty
% 5.31/5.50 thf(fact_1271_pred__member,axiom,
% 5.31/5.50 ! [T: vEBT_VEBT,X: nat,Y: nat] :
% 5.31/5.50 ( ( vEBT_is_pred_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X @ Y )
% 5.31/5.50 = ( ( vEBT_vebt_member @ T @ Y )
% 5.31/5.50 & ( ord_less_nat @ Y @ X )
% 5.31/5.50 & ! [Z4: nat] :
% 5.31/5.50 ( ( ( vEBT_vebt_member @ T @ Z4 )
% 5.31/5.50 & ( ord_less_nat @ Z4 @ X ) )
% 5.31/5.50 => ( ord_less_eq_nat @ Z4 @ Y ) ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % pred_member
% 5.31/5.50 thf(fact_1272_succ__member,axiom,
% 5.31/5.50 ! [T: vEBT_VEBT,X: nat,Y: nat] :
% 5.31/5.50 ( ( vEBT_is_succ_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X @ Y )
% 5.31/5.50 = ( ( vEBT_vebt_member @ T @ Y )
% 5.31/5.50 & ( ord_less_nat @ X @ Y )
% 5.31/5.50 & ! [Z4: nat] :
% 5.31/5.50 ( ( ( vEBT_vebt_member @ T @ Z4 )
% 5.31/5.50 & ( ord_less_nat @ X @ Z4 ) )
% 5.31/5.50 => ( ord_less_eq_nat @ Y @ Z4 ) ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % succ_member
% 5.31/5.50 thf(fact_1273_case4_I6_J,axiom,
% 5.31/5.50 ( deg
% 5.31/5.50 = ( plus_plus_nat @ na @ m ) ) ).
% 5.31/5.50
% 5.31/5.50 % case4(6)
% 5.31/5.50 thf(fact_1274_case4_I1_J,axiom,
% 5.31/5.50 ! [X5: vEBT_VEBT] :
% 5.31/5.50 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ treeList2 ) )
% 5.31/5.50 => ( ( vEBT_invar_vebt @ X5 @ na )
% 5.31/5.50 & ! [Xa: vEBT_VEBT] :
% 5.31/5.50 ( ( vEBT_invar_vebt @ Xa @ na )
% 5.31/5.50 => ( ( ( vEBT_VEBT_set_vebt @ X5 )
% 5.31/5.50 = ( vEBT_VEBT_set_vebt @ Xa ) )
% 5.31/5.50 => ( Xa = X5 ) ) ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % case4(1)
% 5.31/5.50 thf(fact_1275_bot_Oextremum__uniqueI,axiom,
% 5.31/5.50 ! [A: set_int] :
% 5.31/5.50 ( ( ord_less_eq_set_int @ A @ bot_bot_set_int )
% 5.31/5.50 => ( A = bot_bot_set_int ) ) ).
% 5.31/5.50
% 5.31/5.50 % bot.extremum_uniqueI
% 5.31/5.50 thf(fact_1276_bot_Oextremum__uniqueI,axiom,
% 5.31/5.50 ! [A: set_real] :
% 5.31/5.50 ( ( ord_less_eq_set_real @ A @ bot_bot_set_real )
% 5.31/5.50 => ( A = bot_bot_set_real ) ) ).
% 5.31/5.50
% 5.31/5.50 % bot.extremum_uniqueI
% 5.31/5.50 thf(fact_1277_bot_Oextremum__uniqueI,axiom,
% 5.31/5.50 ! [A: set_nat] :
% 5.31/5.50 ( ( ord_less_eq_set_nat @ A @ bot_bot_set_nat )
% 5.31/5.50 => ( A = bot_bot_set_nat ) ) ).
% 5.31/5.50
% 5.31/5.50 % bot.extremum_uniqueI
% 5.31/5.50 thf(fact_1278_bot_Oextremum__uniqueI,axiom,
% 5.31/5.50 ! [A: nat] :
% 5.31/5.50 ( ( ord_less_eq_nat @ A @ bot_bot_nat )
% 5.31/5.50 => ( A = bot_bot_nat ) ) ).
% 5.31/5.50
% 5.31/5.50 % bot.extremum_uniqueI
% 5.31/5.50 thf(fact_1279_bot_Oextremum__unique,axiom,
% 5.31/5.50 ! [A: set_int] :
% 5.31/5.50 ( ( ord_less_eq_set_int @ A @ bot_bot_set_int )
% 5.31/5.50 = ( A = bot_bot_set_int ) ) ).
% 5.31/5.50
% 5.31/5.50 % bot.extremum_unique
% 5.31/5.50 thf(fact_1280_bot_Oextremum__unique,axiom,
% 5.31/5.50 ! [A: set_real] :
% 5.31/5.50 ( ( ord_less_eq_set_real @ A @ bot_bot_set_real )
% 5.31/5.50 = ( A = bot_bot_set_real ) ) ).
% 5.31/5.50
% 5.31/5.50 % bot.extremum_unique
% 5.31/5.50 thf(fact_1281_bot_Oextremum__unique,axiom,
% 5.31/5.50 ! [A: set_nat] :
% 5.31/5.50 ( ( ord_less_eq_set_nat @ A @ bot_bot_set_nat )
% 5.31/5.50 = ( A = bot_bot_set_nat ) ) ).
% 5.31/5.50
% 5.31/5.50 % bot.extremum_unique
% 5.31/5.50 thf(fact_1282_bot_Oextremum__unique,axiom,
% 5.31/5.50 ! [A: nat] :
% 5.31/5.50 ( ( ord_less_eq_nat @ A @ bot_bot_nat )
% 5.31/5.50 = ( A = bot_bot_nat ) ) ).
% 5.31/5.50
% 5.31/5.50 % bot.extremum_unique
% 5.31/5.50 thf(fact_1283_bot_Oextremum,axiom,
% 5.31/5.50 ! [A: set_int] : ( ord_less_eq_set_int @ bot_bot_set_int @ A ) ).
% 5.31/5.50
% 5.31/5.50 % bot.extremum
% 5.31/5.50 thf(fact_1284_bot_Oextremum,axiom,
% 5.31/5.50 ! [A: set_real] : ( ord_less_eq_set_real @ bot_bot_set_real @ A ) ).
% 5.31/5.50
% 5.31/5.50 % bot.extremum
% 5.31/5.50 thf(fact_1285_bot_Oextremum,axiom,
% 5.31/5.50 ! [A: set_nat] : ( ord_less_eq_set_nat @ bot_bot_set_nat @ A ) ).
% 5.31/5.50
% 5.31/5.50 % bot.extremum
% 5.31/5.50 thf(fact_1286_bot_Oextremum,axiom,
% 5.31/5.50 ! [A: nat] : ( ord_less_eq_nat @ bot_bot_nat @ A ) ).
% 5.31/5.50
% 5.31/5.50 % bot.extremum
% 5.31/5.50 thf(fact_1287_bot_Oextremum__strict,axiom,
% 5.31/5.50 ! [A: set_nat] :
% 5.31/5.50 ~ ( ord_less_set_nat @ A @ bot_bot_set_nat ) ).
% 5.31/5.50
% 5.31/5.50 % bot.extremum_strict
% 5.31/5.50 thf(fact_1288_bot_Oextremum__strict,axiom,
% 5.31/5.50 ! [A: set_int] :
% 5.31/5.50 ~ ( ord_less_set_int @ A @ bot_bot_set_int ) ).
% 5.31/5.50
% 5.31/5.50 % bot.extremum_strict
% 5.31/5.50 thf(fact_1289_bot_Oextremum__strict,axiom,
% 5.31/5.50 ! [A: set_real] :
% 5.31/5.50 ~ ( ord_less_set_real @ A @ bot_bot_set_real ) ).
% 5.31/5.50
% 5.31/5.50 % bot.extremum_strict
% 5.31/5.50 thf(fact_1290_bot_Oextremum__strict,axiom,
% 5.31/5.50 ! [A: nat] :
% 5.31/5.50 ~ ( ord_less_nat @ A @ bot_bot_nat ) ).
% 5.31/5.50
% 5.31/5.50 % bot.extremum_strict
% 5.31/5.50 thf(fact_1291_bot_Onot__eq__extremum,axiom,
% 5.31/5.50 ! [A: set_nat] :
% 5.31/5.50 ( ( A != bot_bot_set_nat )
% 5.31/5.50 = ( ord_less_set_nat @ bot_bot_set_nat @ A ) ) ).
% 5.31/5.50
% 5.31/5.50 % bot.not_eq_extremum
% 5.31/5.50 thf(fact_1292_bot_Onot__eq__extremum,axiom,
% 5.31/5.50 ! [A: set_int] :
% 5.31/5.50 ( ( A != bot_bot_set_int )
% 5.31/5.50 = ( ord_less_set_int @ bot_bot_set_int @ A ) ) ).
% 5.31/5.50
% 5.31/5.50 % bot.not_eq_extremum
% 5.31/5.50 thf(fact_1293_bot_Onot__eq__extremum,axiom,
% 5.31/5.50 ! [A: set_real] :
% 5.31/5.50 ( ( A != bot_bot_set_real )
% 5.31/5.50 = ( ord_less_set_real @ bot_bot_set_real @ A ) ) ).
% 5.31/5.50
% 5.31/5.50 % bot.not_eq_extremum
% 5.31/5.50 thf(fact_1294_bot_Onot__eq__extremum,axiom,
% 5.31/5.50 ! [A: nat] :
% 5.31/5.50 ( ( A != bot_bot_nat )
% 5.31/5.50 = ( ord_less_nat @ bot_bot_nat @ A ) ) ).
% 5.31/5.50
% 5.31/5.50 % bot.not_eq_extremum
% 5.31/5.50 thf(fact_1295_VEBT__internal_Onaive__member_Osimps_I2_J,axiom,
% 5.31/5.50 ! [Uu: option4927543243414619207at_nat,Uv: list_VEBT_VEBT,Uw2: vEBT_VEBT,Ux2: nat] :
% 5.31/5.50 ~ ( vEBT_V5719532721284313246member @ ( vEBT_Node @ Uu @ zero_zero_nat @ Uv @ Uw2 ) @ Ux2 ) ).
% 5.31/5.50
% 5.31/5.50 % VEBT_internal.naive_member.simps(2)
% 5.31/5.50 thf(fact_1296_VEBT__internal_Onaive__member_Osimps_I1_J,axiom,
% 5.31/5.50 ! [A: $o,B: $o,X: nat] :
% 5.31/5.50 ( ( vEBT_V5719532721284313246member @ ( vEBT_Leaf @ A @ B ) @ X )
% 5.31/5.50 = ( ( ( X = zero_zero_nat )
% 5.31/5.50 => A )
% 5.31/5.50 & ( ( X != zero_zero_nat )
% 5.31/5.50 => ( ( ( X = one_one_nat )
% 5.31/5.50 => B )
% 5.31/5.50 & ( X = one_one_nat ) ) ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % VEBT_internal.naive_member.simps(1)
% 5.31/5.50 thf(fact_1297_member__valid__both__member__options,axiom,
% 5.31/5.50 ! [Tree: vEBT_VEBT,N: nat,X: nat] :
% 5.31/5.50 ( ( vEBT_invar_vebt @ Tree @ N )
% 5.31/5.50 => ( ( vEBT_vebt_member @ Tree @ X )
% 5.31/5.50 => ( ( vEBT_V5719532721284313246member @ Tree @ X )
% 5.31/5.50 | ( vEBT_VEBT_membermima @ Tree @ X ) ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % member_valid_both_member_options
% 5.31/5.50 thf(fact_1298_vebt__member_Osimps_I4_J,axiom,
% 5.31/5.50 ! [V2: product_prod_nat_nat,Vb: list_VEBT_VEBT,Vc: vEBT_VEBT,X: nat] :
% 5.31/5.50 ~ ( vEBT_vebt_member @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb @ Vc ) @ X ) ).
% 5.31/5.50
% 5.31/5.50 % vebt_member.simps(4)
% 5.31/5.50 thf(fact_1299_vebt__member_Osimps_I1_J,axiom,
% 5.31/5.50 ! [A: $o,B: $o,X: nat] :
% 5.31/5.50 ( ( vEBT_vebt_member @ ( vEBT_Leaf @ A @ B ) @ X )
% 5.31/5.50 = ( ( ( X = zero_zero_nat )
% 5.31/5.50 => A )
% 5.31/5.50 & ( ( X != zero_zero_nat )
% 5.31/5.50 => ( ( ( X = one_one_nat )
% 5.31/5.50 => B )
% 5.31/5.50 & ( X = one_one_nat ) ) ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % vebt_member.simps(1)
% 5.31/5.50 thf(fact_1300_vebt__member_Osimps_I3_J,axiom,
% 5.31/5.50 ! [V2: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz: vEBT_VEBT,X: nat] :
% 5.31/5.50 ~ ( vEBT_vebt_member @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz ) @ X ) ).
% 5.31/5.50
% 5.31/5.50 % vebt_member.simps(3)
% 5.31/5.50 thf(fact_1301_maxt__corr__help__empty,axiom,
% 5.31/5.50 ! [T: vEBT_VEBT,N: nat] :
% 5.31/5.50 ( ( vEBT_invar_vebt @ T @ N )
% 5.31/5.50 => ( ( ( vEBT_vebt_maxt @ T )
% 5.31/5.50 = none_nat )
% 5.31/5.50 => ( ( vEBT_VEBT_set_vebt @ T )
% 5.31/5.50 = bot_bot_set_nat ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % maxt_corr_help_empty
% 5.31/5.50 thf(fact_1302_mint__corr__help__empty,axiom,
% 5.31/5.50 ! [T: vEBT_VEBT,N: nat] :
% 5.31/5.50 ( ( vEBT_invar_vebt @ T @ N )
% 5.31/5.50 => ( ( ( vEBT_vebt_mint @ T )
% 5.31/5.50 = none_nat )
% 5.31/5.50 => ( ( vEBT_VEBT_set_vebt @ T )
% 5.31/5.50 = bot_bot_set_nat ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % mint_corr_help_empty
% 5.31/5.50 thf(fact_1303_buildup__nothing__in__min__max,axiom,
% 5.31/5.50 ! [N: nat,X: nat] :
% 5.31/5.50 ~ ( vEBT_VEBT_membermima @ ( vEBT_vebt_buildup @ N ) @ X ) ).
% 5.31/5.50
% 5.31/5.50 % buildup_nothing_in_min_max
% 5.31/5.50 thf(fact_1304_dele__member__cont__corr,axiom,
% 5.31/5.50 ! [T: vEBT_VEBT,N: nat,X: nat,Y: nat] :
% 5.31/5.50 ( ( vEBT_invar_vebt @ T @ N )
% 5.31/5.50 => ( ( vEBT_vebt_member @ ( vEBT_vebt_delete @ T @ X ) @ Y )
% 5.31/5.50 = ( ( X != Y )
% 5.31/5.50 & ( vEBT_vebt_member @ T @ Y ) ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % dele_member_cont_corr
% 5.31/5.50 thf(fact_1305_VEBT__internal_Omembermima_Ocases,axiom,
% 5.31/5.50 ! [X: produc9072475918466114483BT_nat] :
% 5.31/5.50 ( ! [Uu2: $o,Uv2: $o,Uw: nat] :
% 5.31/5.50 ( X
% 5.31/5.50 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ Uw ) )
% 5.31/5.50 => ( ! [Ux: list_VEBT_VEBT,Uy: vEBT_VEBT,Uz2: nat] :
% 5.31/5.50 ( X
% 5.31/5.50 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux @ Uy ) @ Uz2 ) )
% 5.31/5.50 => ( ! [Mi2: nat,Ma2: nat,Va2: list_VEBT_VEBT,Vb2: vEBT_VEBT,X3: nat] :
% 5.31/5.50 ( X
% 5.31/5.50 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va2 @ Vb2 ) @ X3 ) )
% 5.31/5.50 => ( ! [Mi2: nat,Ma2: nat,V: nat,TreeList: list_VEBT_VEBT,Vc2: vEBT_VEBT,X3: nat] :
% 5.31/5.50 ( X
% 5.31/5.50 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V ) @ TreeList @ Vc2 ) @ X3 ) )
% 5.31/5.50 => ~ ! [V: nat,TreeList: list_VEBT_VEBT,Vd: vEBT_VEBT,X3: nat] :
% 5.31/5.50 ( X
% 5.31/5.50 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V ) @ TreeList @ Vd ) @ X3 ) ) ) ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % VEBT_internal.membermima.cases
% 5.31/5.50 thf(fact_1306_case4_I8_J,axiom,
% 5.31/5.50 ( ( mi = ma )
% 5.31/5.50 => ! [X5: vEBT_VEBT] :
% 5.31/5.50 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ treeList2 ) )
% 5.31/5.50 => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X5 @ X_1 ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % case4(8)
% 5.31/5.50 thf(fact_1307_even__odd__cases,axiom,
% 5.31/5.50 ! [X: nat] :
% 5.31/5.50 ( ! [N3: nat] :
% 5.31/5.50 ( X
% 5.31/5.50 != ( plus_plus_nat @ N3 @ N3 ) )
% 5.31/5.50 => ~ ! [N3: nat] :
% 5.31/5.50 ( X
% 5.31/5.50 != ( plus_plus_nat @ N3 @ ( suc @ N3 ) ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % even_odd_cases
% 5.31/5.50 thf(fact_1308_delete__pres__valid,axiom,
% 5.31/5.50 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 5.31/5.50 ( ( vEBT_invar_vebt @ T @ N )
% 5.31/5.50 => ( vEBT_invar_vebt @ ( vEBT_vebt_delete @ T @ X ) @ N ) ) ).
% 5.31/5.50
% 5.31/5.50 % delete_pres_valid
% 5.31/5.50 thf(fact_1309_maxbmo,axiom,
% 5.31/5.50 ! [T: vEBT_VEBT,X: nat] :
% 5.31/5.50 ( ( ( vEBT_vebt_maxt @ T )
% 5.31/5.50 = ( some_nat @ X ) )
% 5.31/5.50 => ( vEBT_V8194947554948674370ptions @ T @ X ) ) ).
% 5.31/5.50
% 5.31/5.50 % maxbmo
% 5.31/5.50 thf(fact_1310_dele__bmo__cont__corr,axiom,
% 5.31/5.50 ! [T: vEBT_VEBT,N: nat,X: nat,Y: nat] :
% 5.31/5.50 ( ( vEBT_invar_vebt @ T @ N )
% 5.31/5.50 => ( ( vEBT_V8194947554948674370ptions @ ( vEBT_vebt_delete @ T @ X ) @ Y )
% 5.31/5.50 = ( ( X != Y )
% 5.31/5.50 & ( vEBT_V8194947554948674370ptions @ T @ Y ) ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % dele_bmo_cont_corr
% 5.31/5.50 thf(fact_1311_both__member__options__equiv__member,axiom,
% 5.31/5.50 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 5.31/5.50 ( ( vEBT_invar_vebt @ T @ N )
% 5.31/5.50 => ( ( vEBT_V8194947554948674370ptions @ T @ X )
% 5.31/5.50 = ( vEBT_vebt_member @ T @ X ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % both_member_options_equiv_member
% 5.31/5.50 thf(fact_1312_valid__member__both__member__options,axiom,
% 5.31/5.50 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 5.31/5.50 ( ( vEBT_invar_vebt @ T @ N )
% 5.31/5.50 => ( ( vEBT_V8194947554948674370ptions @ T @ X )
% 5.31/5.50 => ( vEBT_vebt_member @ T @ X ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % valid_member_both_member_options
% 5.31/5.50 thf(fact_1313_both__member__options__def,axiom,
% 5.31/5.50 ( vEBT_V8194947554948674370ptions
% 5.31/5.50 = ( ^ [T2: vEBT_VEBT,X4: nat] :
% 5.31/5.50 ( ( vEBT_V5719532721284313246member @ T2 @ X4 )
% 5.31/5.50 | ( vEBT_VEBT_membermima @ T2 @ X4 ) ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % both_member_options_def
% 5.31/5.50 thf(fact_1314_add__right__cancel,axiom,
% 5.31/5.50 ! [B: real,A: real,C2: real] :
% 5.31/5.50 ( ( ( plus_plus_real @ B @ A )
% 5.31/5.50 = ( plus_plus_real @ C2 @ A ) )
% 5.31/5.50 = ( B = C2 ) ) ).
% 5.31/5.50
% 5.31/5.50 % add_right_cancel
% 5.31/5.50 thf(fact_1315_add__right__cancel,axiom,
% 5.31/5.50 ! [B: rat,A: rat,C2: rat] :
% 5.31/5.50 ( ( ( plus_plus_rat @ B @ A )
% 5.31/5.50 = ( plus_plus_rat @ C2 @ A ) )
% 5.31/5.50 = ( B = C2 ) ) ).
% 5.31/5.50
% 5.31/5.50 % add_right_cancel
% 5.31/5.50 thf(fact_1316_add__right__cancel,axiom,
% 5.31/5.50 ! [B: nat,A: nat,C2: nat] :
% 5.31/5.50 ( ( ( plus_plus_nat @ B @ A )
% 5.31/5.50 = ( plus_plus_nat @ C2 @ A ) )
% 5.31/5.50 = ( B = C2 ) ) ).
% 5.31/5.50
% 5.31/5.50 % add_right_cancel
% 5.31/5.50 thf(fact_1317_add__right__cancel,axiom,
% 5.31/5.50 ! [B: int,A: int,C2: int] :
% 5.31/5.50 ( ( ( plus_plus_int @ B @ A )
% 5.31/5.50 = ( plus_plus_int @ C2 @ A ) )
% 5.31/5.50 = ( B = C2 ) ) ).
% 5.31/5.50
% 5.31/5.50 % add_right_cancel
% 5.31/5.50 thf(fact_1318_add__left__cancel,axiom,
% 5.31/5.50 ! [A: real,B: real,C2: real] :
% 5.31/5.50 ( ( ( plus_plus_real @ A @ B )
% 5.31/5.50 = ( plus_plus_real @ A @ C2 ) )
% 5.31/5.50 = ( B = C2 ) ) ).
% 5.31/5.50
% 5.31/5.50 % add_left_cancel
% 5.31/5.50 thf(fact_1319_add__left__cancel,axiom,
% 5.31/5.50 ! [A: rat,B: rat,C2: rat] :
% 5.31/5.50 ( ( ( plus_plus_rat @ A @ B )
% 5.31/5.50 = ( plus_plus_rat @ A @ C2 ) )
% 5.31/5.50 = ( B = C2 ) ) ).
% 5.31/5.50
% 5.31/5.50 % add_left_cancel
% 5.31/5.50 thf(fact_1320_add__left__cancel,axiom,
% 5.31/5.50 ! [A: nat,B: nat,C2: nat] :
% 5.31/5.50 ( ( ( plus_plus_nat @ A @ B )
% 5.31/5.50 = ( plus_plus_nat @ A @ C2 ) )
% 5.31/5.50 = ( B = C2 ) ) ).
% 5.31/5.50
% 5.31/5.50 % add_left_cancel
% 5.31/5.50 thf(fact_1321_add__left__cancel,axiom,
% 5.31/5.50 ! [A: int,B: int,C2: int] :
% 5.31/5.50 ( ( ( plus_plus_int @ A @ B )
% 5.31/5.50 = ( plus_plus_int @ A @ C2 ) )
% 5.31/5.50 = ( B = C2 ) ) ).
% 5.31/5.50
% 5.31/5.50 % add_left_cancel
% 5.31/5.50 thf(fact_1322_mi__eq__ma__no__ch,axiom,
% 5.31/5.50 ! [Mi: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.31/5.50 ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ Deg )
% 5.31/5.50 => ( ( Mi = Ma )
% 5.31/5.50 => ( ! [X5: vEBT_VEBT] :
% 5.31/5.50 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.31/5.50 => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X5 @ X_1 ) )
% 5.31/5.50 & ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ Summary @ X_1 ) ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % mi_eq_ma_no_ch
% 5.31/5.50 thf(fact_1323_add__le__cancel__left,axiom,
% 5.31/5.50 ! [C2: real,A: real,B: real] :
% 5.31/5.50 ( ( ord_less_eq_real @ ( plus_plus_real @ C2 @ A ) @ ( plus_plus_real @ C2 @ B ) )
% 5.31/5.50 = ( ord_less_eq_real @ A @ B ) ) ).
% 5.31/5.50
% 5.31/5.50 % add_le_cancel_left
% 5.31/5.50 thf(fact_1324_add__le__cancel__left,axiom,
% 5.31/5.50 ! [C2: rat,A: rat,B: rat] :
% 5.31/5.50 ( ( ord_less_eq_rat @ ( plus_plus_rat @ C2 @ A ) @ ( plus_plus_rat @ C2 @ B ) )
% 5.31/5.50 = ( ord_less_eq_rat @ A @ B ) ) ).
% 5.31/5.50
% 5.31/5.50 % add_le_cancel_left
% 5.31/5.50 thf(fact_1325_add__le__cancel__left,axiom,
% 5.31/5.50 ! [C2: nat,A: nat,B: nat] :
% 5.31/5.50 ( ( ord_less_eq_nat @ ( plus_plus_nat @ C2 @ A ) @ ( plus_plus_nat @ C2 @ B ) )
% 5.31/5.50 = ( ord_less_eq_nat @ A @ B ) ) ).
% 5.31/5.50
% 5.31/5.50 % add_le_cancel_left
% 5.31/5.50 thf(fact_1326_add__le__cancel__left,axiom,
% 5.31/5.50 ! [C2: int,A: int,B: int] :
% 5.31/5.50 ( ( ord_less_eq_int @ ( plus_plus_int @ C2 @ A ) @ ( plus_plus_int @ C2 @ B ) )
% 5.31/5.50 = ( ord_less_eq_int @ A @ B ) ) ).
% 5.31/5.50
% 5.31/5.50 % add_le_cancel_left
% 5.31/5.50 thf(fact_1327_add__le__cancel__right,axiom,
% 5.31/5.50 ! [A: real,C2: real,B: real] :
% 5.31/5.50 ( ( ord_less_eq_real @ ( plus_plus_real @ A @ C2 ) @ ( plus_plus_real @ B @ C2 ) )
% 5.31/5.50 = ( ord_less_eq_real @ A @ B ) ) ).
% 5.31/5.50
% 5.31/5.50 % add_le_cancel_right
% 5.31/5.50 thf(fact_1328_add__le__cancel__right,axiom,
% 5.31/5.50 ! [A: rat,C2: rat,B: rat] :
% 5.31/5.50 ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C2 ) @ ( plus_plus_rat @ B @ C2 ) )
% 5.31/5.50 = ( ord_less_eq_rat @ A @ B ) ) ).
% 5.31/5.50
% 5.31/5.50 % add_le_cancel_right
% 5.31/5.50 thf(fact_1329_add__le__cancel__right,axiom,
% 5.31/5.50 ! [A: nat,C2: nat,B: nat] :
% 5.31/5.50 ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C2 ) @ ( plus_plus_nat @ B @ C2 ) )
% 5.31/5.50 = ( ord_less_eq_nat @ A @ B ) ) ).
% 5.31/5.50
% 5.31/5.50 % add_le_cancel_right
% 5.31/5.50 thf(fact_1330_add__le__cancel__right,axiom,
% 5.31/5.50 ! [A: int,C2: int,B: int] :
% 5.31/5.50 ( ( ord_less_eq_int @ ( plus_plus_int @ A @ C2 ) @ ( plus_plus_int @ B @ C2 ) )
% 5.31/5.50 = ( ord_less_eq_int @ A @ B ) ) ).
% 5.31/5.50
% 5.31/5.50 % add_le_cancel_right
% 5.31/5.50 thf(fact_1331_add_Oright__neutral,axiom,
% 5.31/5.50 ! [A: complex] :
% 5.31/5.50 ( ( plus_plus_complex @ A @ zero_zero_complex )
% 5.31/5.50 = A ) ).
% 5.31/5.50
% 5.31/5.50 % add.right_neutral
% 5.31/5.50 thf(fact_1332_add_Oright__neutral,axiom,
% 5.31/5.50 ! [A: real] :
% 5.31/5.50 ( ( plus_plus_real @ A @ zero_zero_real )
% 5.31/5.50 = A ) ).
% 5.31/5.50
% 5.31/5.50 % add.right_neutral
% 5.31/5.50 thf(fact_1333_add_Oright__neutral,axiom,
% 5.31/5.50 ! [A: rat] :
% 5.31/5.50 ( ( plus_plus_rat @ A @ zero_zero_rat )
% 5.31/5.50 = A ) ).
% 5.31/5.50
% 5.31/5.50 % add.right_neutral
% 5.31/5.50 thf(fact_1334_add_Oright__neutral,axiom,
% 5.31/5.50 ! [A: nat] :
% 5.31/5.50 ( ( plus_plus_nat @ A @ zero_zero_nat )
% 5.31/5.50 = A ) ).
% 5.31/5.50
% 5.31/5.50 % add.right_neutral
% 5.31/5.50 thf(fact_1335_add_Oright__neutral,axiom,
% 5.31/5.50 ! [A: int] :
% 5.31/5.50 ( ( plus_plus_int @ A @ zero_zero_int )
% 5.31/5.50 = A ) ).
% 5.31/5.50
% 5.31/5.50 % add.right_neutral
% 5.31/5.50 thf(fact_1336_double__zero__sym,axiom,
% 5.31/5.50 ! [A: real] :
% 5.31/5.50 ( ( zero_zero_real
% 5.31/5.50 = ( plus_plus_real @ A @ A ) )
% 5.31/5.50 = ( A = zero_zero_real ) ) ).
% 5.31/5.50
% 5.31/5.50 % double_zero_sym
% 5.31/5.50 thf(fact_1337_double__zero__sym,axiom,
% 5.31/5.50 ! [A: rat] :
% 5.31/5.50 ( ( zero_zero_rat
% 5.31/5.50 = ( plus_plus_rat @ A @ A ) )
% 5.31/5.50 = ( A = zero_zero_rat ) ) ).
% 5.31/5.50
% 5.31/5.50 % double_zero_sym
% 5.31/5.50 thf(fact_1338_double__zero__sym,axiom,
% 5.31/5.50 ! [A: int] :
% 5.31/5.50 ( ( zero_zero_int
% 5.31/5.50 = ( plus_plus_int @ A @ A ) )
% 5.31/5.50 = ( A = zero_zero_int ) ) ).
% 5.31/5.50
% 5.31/5.50 % double_zero_sym
% 5.31/5.50 thf(fact_1339_add__cancel__left__left,axiom,
% 5.31/5.50 ! [B: complex,A: complex] :
% 5.31/5.50 ( ( ( plus_plus_complex @ B @ A )
% 5.31/5.50 = A )
% 5.31/5.50 = ( B = zero_zero_complex ) ) ).
% 5.31/5.50
% 5.31/5.50 % add_cancel_left_left
% 5.31/5.50 thf(fact_1340_add__cancel__left__left,axiom,
% 5.31/5.50 ! [B: real,A: real] :
% 5.31/5.50 ( ( ( plus_plus_real @ B @ A )
% 5.31/5.50 = A )
% 5.31/5.50 = ( B = zero_zero_real ) ) ).
% 5.31/5.50
% 5.31/5.50 % add_cancel_left_left
% 5.31/5.50 thf(fact_1341_add__cancel__left__left,axiom,
% 5.31/5.50 ! [B: rat,A: rat] :
% 5.31/5.50 ( ( ( plus_plus_rat @ B @ A )
% 5.31/5.50 = A )
% 5.31/5.50 = ( B = zero_zero_rat ) ) ).
% 5.31/5.50
% 5.31/5.50 % add_cancel_left_left
% 5.31/5.50 thf(fact_1342_add__cancel__left__left,axiom,
% 5.31/5.50 ! [B: nat,A: nat] :
% 5.31/5.50 ( ( ( plus_plus_nat @ B @ A )
% 5.31/5.50 = A )
% 5.31/5.50 = ( B = zero_zero_nat ) ) ).
% 5.31/5.50
% 5.31/5.50 % add_cancel_left_left
% 5.31/5.50 thf(fact_1343_add__cancel__left__left,axiom,
% 5.31/5.50 ! [B: int,A: int] :
% 5.31/5.50 ( ( ( plus_plus_int @ B @ A )
% 5.31/5.50 = A )
% 5.31/5.50 = ( B = zero_zero_int ) ) ).
% 5.31/5.50
% 5.31/5.50 % add_cancel_left_left
% 5.31/5.50 thf(fact_1344_add__cancel__left__right,axiom,
% 5.31/5.50 ! [A: complex,B: complex] :
% 5.31/5.50 ( ( ( plus_plus_complex @ A @ B )
% 5.31/5.50 = A )
% 5.31/5.50 = ( B = zero_zero_complex ) ) ).
% 5.31/5.50
% 5.31/5.50 % add_cancel_left_right
% 5.31/5.50 thf(fact_1345_add__cancel__left__right,axiom,
% 5.31/5.50 ! [A: real,B: real] :
% 5.31/5.50 ( ( ( plus_plus_real @ A @ B )
% 5.31/5.50 = A )
% 5.31/5.50 = ( B = zero_zero_real ) ) ).
% 5.31/5.50
% 5.31/5.50 % add_cancel_left_right
% 5.31/5.50 thf(fact_1346_add__cancel__left__right,axiom,
% 5.31/5.50 ! [A: rat,B: rat] :
% 5.31/5.50 ( ( ( plus_plus_rat @ A @ B )
% 5.31/5.50 = A )
% 5.31/5.50 = ( B = zero_zero_rat ) ) ).
% 5.31/5.50
% 5.31/5.50 % add_cancel_left_right
% 5.31/5.50 thf(fact_1347_add__cancel__left__right,axiom,
% 5.31/5.50 ! [A: nat,B: nat] :
% 5.31/5.50 ( ( ( plus_plus_nat @ A @ B )
% 5.31/5.50 = A )
% 5.31/5.50 = ( B = zero_zero_nat ) ) ).
% 5.31/5.50
% 5.31/5.50 % add_cancel_left_right
% 5.31/5.50 thf(fact_1348_add__cancel__left__right,axiom,
% 5.31/5.50 ! [A: int,B: int] :
% 5.31/5.50 ( ( ( plus_plus_int @ A @ B )
% 5.31/5.50 = A )
% 5.31/5.50 = ( B = zero_zero_int ) ) ).
% 5.31/5.50
% 5.31/5.50 % add_cancel_left_right
% 5.31/5.50 thf(fact_1349_add__cancel__right__left,axiom,
% 5.31/5.50 ! [A: complex,B: complex] :
% 5.31/5.50 ( ( A
% 5.31/5.50 = ( plus_plus_complex @ B @ A ) )
% 5.31/5.50 = ( B = zero_zero_complex ) ) ).
% 5.31/5.50
% 5.31/5.50 % add_cancel_right_left
% 5.31/5.50 thf(fact_1350_add__cancel__right__left,axiom,
% 5.31/5.50 ! [A: real,B: real] :
% 5.31/5.50 ( ( A
% 5.31/5.50 = ( plus_plus_real @ B @ A ) )
% 5.31/5.50 = ( B = zero_zero_real ) ) ).
% 5.31/5.50
% 5.31/5.50 % add_cancel_right_left
% 5.31/5.50 thf(fact_1351_add__cancel__right__left,axiom,
% 5.31/5.50 ! [A: rat,B: rat] :
% 5.31/5.50 ( ( A
% 5.31/5.50 = ( plus_plus_rat @ B @ A ) )
% 5.31/5.50 = ( B = zero_zero_rat ) ) ).
% 5.31/5.50
% 5.31/5.50 % add_cancel_right_left
% 5.31/5.50 thf(fact_1352_add__cancel__right__left,axiom,
% 5.31/5.50 ! [A: nat,B: nat] :
% 5.31/5.50 ( ( A
% 5.31/5.50 = ( plus_plus_nat @ B @ A ) )
% 5.31/5.50 = ( B = zero_zero_nat ) ) ).
% 5.31/5.50
% 5.31/5.50 % add_cancel_right_left
% 5.31/5.50 thf(fact_1353_add__cancel__right__left,axiom,
% 5.31/5.50 ! [A: int,B: int] :
% 5.31/5.50 ( ( A
% 5.31/5.50 = ( plus_plus_int @ B @ A ) )
% 5.31/5.50 = ( B = zero_zero_int ) ) ).
% 5.31/5.50
% 5.31/5.50 % add_cancel_right_left
% 5.31/5.50 thf(fact_1354_add__cancel__right__right,axiom,
% 5.31/5.50 ! [A: complex,B: complex] :
% 5.31/5.50 ( ( A
% 5.31/5.50 = ( plus_plus_complex @ A @ B ) )
% 5.31/5.50 = ( B = zero_zero_complex ) ) ).
% 5.31/5.50
% 5.31/5.50 % add_cancel_right_right
% 5.31/5.50 thf(fact_1355_add__cancel__right__right,axiom,
% 5.31/5.50 ! [A: real,B: real] :
% 5.31/5.50 ( ( A
% 5.31/5.50 = ( plus_plus_real @ A @ B ) )
% 5.31/5.50 = ( B = zero_zero_real ) ) ).
% 5.31/5.50
% 5.31/5.50 % add_cancel_right_right
% 5.31/5.50 thf(fact_1356_add__cancel__right__right,axiom,
% 5.31/5.50 ! [A: rat,B: rat] :
% 5.31/5.50 ( ( A
% 5.31/5.50 = ( plus_plus_rat @ A @ B ) )
% 5.31/5.50 = ( B = zero_zero_rat ) ) ).
% 5.31/5.50
% 5.31/5.50 % add_cancel_right_right
% 5.31/5.50 thf(fact_1357_add__cancel__right__right,axiom,
% 5.31/5.50 ! [A: nat,B: nat] :
% 5.31/5.50 ( ( A
% 5.31/5.50 = ( plus_plus_nat @ A @ B ) )
% 5.31/5.50 = ( B = zero_zero_nat ) ) ).
% 5.31/5.50
% 5.31/5.50 % add_cancel_right_right
% 5.31/5.50 thf(fact_1358_add__cancel__right__right,axiom,
% 5.31/5.50 ! [A: int,B: int] :
% 5.31/5.50 ( ( A
% 5.31/5.50 = ( plus_plus_int @ A @ B ) )
% 5.31/5.50 = ( B = zero_zero_int ) ) ).
% 5.31/5.50
% 5.31/5.50 % add_cancel_right_right
% 5.31/5.50 thf(fact_1359_add__eq__0__iff__both__eq__0,axiom,
% 5.31/5.50 ! [X: nat,Y: nat] :
% 5.31/5.50 ( ( ( plus_plus_nat @ X @ Y )
% 5.31/5.50 = zero_zero_nat )
% 5.31/5.50 = ( ( X = zero_zero_nat )
% 5.31/5.50 & ( Y = zero_zero_nat ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % add_eq_0_iff_both_eq_0
% 5.31/5.50 thf(fact_1360_zero__eq__add__iff__both__eq__0,axiom,
% 5.31/5.50 ! [X: nat,Y: nat] :
% 5.31/5.50 ( ( zero_zero_nat
% 5.31/5.50 = ( plus_plus_nat @ X @ Y ) )
% 5.31/5.50 = ( ( X = zero_zero_nat )
% 5.31/5.50 & ( Y = zero_zero_nat ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % zero_eq_add_iff_both_eq_0
% 5.31/5.50 thf(fact_1361_add__0,axiom,
% 5.31/5.50 ! [A: complex] :
% 5.31/5.50 ( ( plus_plus_complex @ zero_zero_complex @ A )
% 5.31/5.50 = A ) ).
% 5.31/5.50
% 5.31/5.50 % add_0
% 5.31/5.50 thf(fact_1362_add__0,axiom,
% 5.31/5.50 ! [A: real] :
% 5.31/5.50 ( ( plus_plus_real @ zero_zero_real @ A )
% 5.31/5.50 = A ) ).
% 5.31/5.50
% 5.31/5.50 % add_0
% 5.31/5.50 thf(fact_1363_add__0,axiom,
% 5.31/5.50 ! [A: rat] :
% 5.31/5.50 ( ( plus_plus_rat @ zero_zero_rat @ A )
% 5.31/5.50 = A ) ).
% 5.31/5.50
% 5.31/5.50 % add_0
% 5.31/5.50 thf(fact_1364_add__0,axiom,
% 5.31/5.50 ! [A: nat] :
% 5.31/5.50 ( ( plus_plus_nat @ zero_zero_nat @ A )
% 5.31/5.50 = A ) ).
% 5.31/5.50
% 5.31/5.50 % add_0
% 5.31/5.50 thf(fact_1365_add__0,axiom,
% 5.31/5.50 ! [A: int] :
% 5.31/5.50 ( ( plus_plus_int @ zero_zero_int @ A )
% 5.31/5.50 = A ) ).
% 5.31/5.50
% 5.31/5.50 % add_0
% 5.31/5.50 thf(fact_1366_add__less__cancel__right,axiom,
% 5.31/5.50 ! [A: real,C2: real,B: real] :
% 5.31/5.50 ( ( ord_less_real @ ( plus_plus_real @ A @ C2 ) @ ( plus_plus_real @ B @ C2 ) )
% 5.31/5.50 = ( ord_less_real @ A @ B ) ) ).
% 5.31/5.50
% 5.31/5.50 % add_less_cancel_right
% 5.31/5.50 thf(fact_1367_add__less__cancel__right,axiom,
% 5.31/5.50 ! [A: rat,C2: rat,B: rat] :
% 5.31/5.50 ( ( ord_less_rat @ ( plus_plus_rat @ A @ C2 ) @ ( plus_plus_rat @ B @ C2 ) )
% 5.31/5.50 = ( ord_less_rat @ A @ B ) ) ).
% 5.31/5.50
% 5.31/5.50 % add_less_cancel_right
% 5.31/5.50 thf(fact_1368_add__less__cancel__right,axiom,
% 5.31/5.50 ! [A: nat,C2: nat,B: nat] :
% 5.31/5.50 ( ( ord_less_nat @ ( plus_plus_nat @ A @ C2 ) @ ( plus_plus_nat @ B @ C2 ) )
% 5.31/5.50 = ( ord_less_nat @ A @ B ) ) ).
% 5.31/5.50
% 5.31/5.50 % add_less_cancel_right
% 5.31/5.50 thf(fact_1369_add__less__cancel__right,axiom,
% 5.31/5.50 ! [A: int,C2: int,B: int] :
% 5.31/5.50 ( ( ord_less_int @ ( plus_plus_int @ A @ C2 ) @ ( plus_plus_int @ B @ C2 ) )
% 5.31/5.50 = ( ord_less_int @ A @ B ) ) ).
% 5.31/5.50
% 5.31/5.50 % add_less_cancel_right
% 5.31/5.50 thf(fact_1370_add__less__cancel__left,axiom,
% 5.31/5.50 ! [C2: real,A: real,B: real] :
% 5.31/5.50 ( ( ord_less_real @ ( plus_plus_real @ C2 @ A ) @ ( plus_plus_real @ C2 @ B ) )
% 5.31/5.50 = ( ord_less_real @ A @ B ) ) ).
% 5.31/5.50
% 5.31/5.50 % add_less_cancel_left
% 5.31/5.50 thf(fact_1371_add__less__cancel__left,axiom,
% 5.31/5.50 ! [C2: rat,A: rat,B: rat] :
% 5.31/5.50 ( ( ord_less_rat @ ( plus_plus_rat @ C2 @ A ) @ ( plus_plus_rat @ C2 @ B ) )
% 5.31/5.50 = ( ord_less_rat @ A @ B ) ) ).
% 5.31/5.50
% 5.31/5.50 % add_less_cancel_left
% 5.31/5.50 thf(fact_1372_add__less__cancel__left,axiom,
% 5.31/5.50 ! [C2: nat,A: nat,B: nat] :
% 5.31/5.50 ( ( ord_less_nat @ ( plus_plus_nat @ C2 @ A ) @ ( plus_plus_nat @ C2 @ B ) )
% 5.31/5.50 = ( ord_less_nat @ A @ B ) ) ).
% 5.31/5.50
% 5.31/5.50 % add_less_cancel_left
% 5.31/5.50 thf(fact_1373_add__less__cancel__left,axiom,
% 5.31/5.50 ! [C2: int,A: int,B: int] :
% 5.31/5.50 ( ( ord_less_int @ ( plus_plus_int @ C2 @ A ) @ ( plus_plus_int @ C2 @ B ) )
% 5.31/5.50 = ( ord_less_int @ A @ B ) ) ).
% 5.31/5.50
% 5.31/5.50 % add_less_cancel_left
% 5.31/5.50 thf(fact_1374_add__Suc__right,axiom,
% 5.31/5.50 ! [M2: nat,N: nat] :
% 5.31/5.50 ( ( plus_plus_nat @ M2 @ ( suc @ N ) )
% 5.31/5.50 = ( suc @ ( plus_plus_nat @ M2 @ N ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % add_Suc_right
% 5.31/5.50 thf(fact_1375_Nat_Oadd__0__right,axiom,
% 5.31/5.50 ! [M2: nat] :
% 5.31/5.50 ( ( plus_plus_nat @ M2 @ zero_zero_nat )
% 5.31/5.50 = M2 ) ).
% 5.31/5.50
% 5.31/5.50 % Nat.add_0_right
% 5.31/5.50 thf(fact_1376_add__is__0,axiom,
% 5.31/5.50 ! [M2: nat,N: nat] :
% 5.31/5.50 ( ( ( plus_plus_nat @ M2 @ N )
% 5.31/5.50 = zero_zero_nat )
% 5.31/5.50 = ( ( M2 = zero_zero_nat )
% 5.31/5.50 & ( N = zero_zero_nat ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % add_is_0
% 5.31/5.50 thf(fact_1377_nat__add__left__cancel__less,axiom,
% 5.31/5.50 ! [K2: nat,M2: nat,N: nat] :
% 5.31/5.50 ( ( ord_less_nat @ ( plus_plus_nat @ K2 @ M2 ) @ ( plus_plus_nat @ K2 @ N ) )
% 5.31/5.50 = ( ord_less_nat @ M2 @ N ) ) ).
% 5.31/5.50
% 5.31/5.50 % nat_add_left_cancel_less
% 5.31/5.50 thf(fact_1378_nat__add__left__cancel__le,axiom,
% 5.31/5.50 ! [K2: nat,M2: nat,N: nat] :
% 5.31/5.50 ( ( ord_less_eq_nat @ ( plus_plus_nat @ K2 @ M2 ) @ ( plus_plus_nat @ K2 @ N ) )
% 5.31/5.50 = ( ord_less_eq_nat @ M2 @ N ) ) ).
% 5.31/5.50
% 5.31/5.50 % nat_add_left_cancel_le
% 5.31/5.50 thf(fact_1379_not__Some__eq,axiom,
% 5.31/5.50 ! [X: option4927543243414619207at_nat] :
% 5.31/5.50 ( ( ! [Y4: product_prod_nat_nat] :
% 5.31/5.50 ( X
% 5.31/5.50 != ( some_P7363390416028606310at_nat @ Y4 ) ) )
% 5.31/5.50 = ( X = none_P5556105721700978146at_nat ) ) ).
% 5.31/5.50
% 5.31/5.50 % not_Some_eq
% 5.31/5.50 thf(fact_1380_not__Some__eq,axiom,
% 5.31/5.50 ! [X: option_nat] :
% 5.31/5.50 ( ( ! [Y4: nat] :
% 5.31/5.50 ( X
% 5.31/5.50 != ( some_nat @ Y4 ) ) )
% 5.31/5.50 = ( X = none_nat ) ) ).
% 5.31/5.50
% 5.31/5.50 % not_Some_eq
% 5.31/5.50 thf(fact_1381_not__Some__eq,axiom,
% 5.31/5.50 ! [X: option_num] :
% 5.31/5.50 ( ( ! [Y4: num] :
% 5.31/5.50 ( X
% 5.31/5.50 != ( some_num @ Y4 ) ) )
% 5.31/5.50 = ( X = none_num ) ) ).
% 5.31/5.50
% 5.31/5.50 % not_Some_eq
% 5.31/5.50 thf(fact_1382_not__None__eq,axiom,
% 5.31/5.50 ! [X: option4927543243414619207at_nat] :
% 5.31/5.50 ( ( X != none_P5556105721700978146at_nat )
% 5.31/5.50 = ( ? [Y4: product_prod_nat_nat] :
% 5.31/5.50 ( X
% 5.31/5.50 = ( some_P7363390416028606310at_nat @ Y4 ) ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % not_None_eq
% 5.31/5.50 thf(fact_1383_not__None__eq,axiom,
% 5.31/5.50 ! [X: option_nat] :
% 5.31/5.50 ( ( X != none_nat )
% 5.31/5.50 = ( ? [Y4: nat] :
% 5.31/5.50 ( X
% 5.31/5.50 = ( some_nat @ Y4 ) ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % not_None_eq
% 5.31/5.50 thf(fact_1384_not__None__eq,axiom,
% 5.31/5.50 ! [X: option_num] :
% 5.31/5.50 ( ( X != none_num )
% 5.31/5.50 = ( ? [Y4: num] :
% 5.31/5.50 ( X
% 5.31/5.50 = ( some_num @ Y4 ) ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % not_None_eq
% 5.31/5.50 thf(fact_1385_add__le__same__cancel1,axiom,
% 5.31/5.50 ! [B: real,A: real] :
% 5.31/5.50 ( ( ord_less_eq_real @ ( plus_plus_real @ B @ A ) @ B )
% 5.31/5.50 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 5.31/5.50
% 5.31/5.50 % add_le_same_cancel1
% 5.31/5.50 thf(fact_1386_add__le__same__cancel1,axiom,
% 5.31/5.50 ! [B: rat,A: rat] :
% 5.31/5.50 ( ( ord_less_eq_rat @ ( plus_plus_rat @ B @ A ) @ B )
% 5.31/5.50 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 5.31/5.50
% 5.31/5.50 % add_le_same_cancel1
% 5.31/5.50 thf(fact_1387_add__le__same__cancel1,axiom,
% 5.31/5.50 ! [B: nat,A: nat] :
% 5.31/5.50 ( ( ord_less_eq_nat @ ( plus_plus_nat @ B @ A ) @ B )
% 5.31/5.50 = ( ord_less_eq_nat @ A @ zero_zero_nat ) ) ).
% 5.31/5.50
% 5.31/5.50 % add_le_same_cancel1
% 5.31/5.50 thf(fact_1388_add__le__same__cancel1,axiom,
% 5.31/5.50 ! [B: int,A: int] :
% 5.31/5.50 ( ( ord_less_eq_int @ ( plus_plus_int @ B @ A ) @ B )
% 5.31/5.50 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 5.31/5.50
% 5.31/5.50 % add_le_same_cancel1
% 5.31/5.50 thf(fact_1389_add__le__same__cancel2,axiom,
% 5.31/5.50 ! [A: real,B: real] :
% 5.31/5.50 ( ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ B )
% 5.31/5.50 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 5.31/5.50
% 5.31/5.50 % add_le_same_cancel2
% 5.31/5.50 thf(fact_1390_add__le__same__cancel2,axiom,
% 5.31/5.50 ! [A: rat,B: rat] :
% 5.31/5.50 ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ B ) @ B )
% 5.31/5.50 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 5.31/5.50
% 5.31/5.50 % add_le_same_cancel2
% 5.31/5.50 thf(fact_1391_add__le__same__cancel2,axiom,
% 5.31/5.50 ! [A: nat,B: nat] :
% 5.31/5.50 ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 5.31/5.50 = ( ord_less_eq_nat @ A @ zero_zero_nat ) ) ).
% 5.31/5.50
% 5.31/5.50 % add_le_same_cancel2
% 5.31/5.50 thf(fact_1392_add__le__same__cancel2,axiom,
% 5.31/5.50 ! [A: int,B: int] :
% 5.31/5.50 ( ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ B )
% 5.31/5.50 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 5.31/5.50
% 5.31/5.50 % add_le_same_cancel2
% 5.31/5.50 thf(fact_1393_le__add__same__cancel1,axiom,
% 5.31/5.50 ! [A: real,B: real] :
% 5.31/5.50 ( ( ord_less_eq_real @ A @ ( plus_plus_real @ A @ B ) )
% 5.31/5.50 = ( ord_less_eq_real @ zero_zero_real @ B ) ) ).
% 5.31/5.50
% 5.31/5.50 % le_add_same_cancel1
% 5.31/5.50 thf(fact_1394_le__add__same__cancel1,axiom,
% 5.31/5.50 ! [A: rat,B: rat] :
% 5.31/5.50 ( ( ord_less_eq_rat @ A @ ( plus_plus_rat @ A @ B ) )
% 5.31/5.50 = ( ord_less_eq_rat @ zero_zero_rat @ B ) ) ).
% 5.31/5.50
% 5.31/5.50 % le_add_same_cancel1
% 5.31/5.50 thf(fact_1395_le__add__same__cancel1,axiom,
% 5.31/5.50 ! [A: nat,B: nat] :
% 5.31/5.50 ( ( ord_less_eq_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 5.31/5.50 = ( ord_less_eq_nat @ zero_zero_nat @ B ) ) ).
% 5.31/5.50
% 5.31/5.50 % le_add_same_cancel1
% 5.31/5.50 thf(fact_1396_le__add__same__cancel1,axiom,
% 5.31/5.50 ! [A: int,B: int] :
% 5.31/5.50 ( ( ord_less_eq_int @ A @ ( plus_plus_int @ A @ B ) )
% 5.31/5.50 = ( ord_less_eq_int @ zero_zero_int @ B ) ) ).
% 5.31/5.50
% 5.31/5.50 % le_add_same_cancel1
% 5.31/5.50 thf(fact_1397_le__add__same__cancel2,axiom,
% 5.31/5.50 ! [A: real,B: real] :
% 5.31/5.50 ( ( ord_less_eq_real @ A @ ( plus_plus_real @ B @ A ) )
% 5.31/5.50 = ( ord_less_eq_real @ zero_zero_real @ B ) ) ).
% 5.31/5.50
% 5.31/5.50 % le_add_same_cancel2
% 5.31/5.50 thf(fact_1398_le__add__same__cancel2,axiom,
% 5.31/5.50 ! [A: rat,B: rat] :
% 5.31/5.50 ( ( ord_less_eq_rat @ A @ ( plus_plus_rat @ B @ A ) )
% 5.31/5.50 = ( ord_less_eq_rat @ zero_zero_rat @ B ) ) ).
% 5.31/5.50
% 5.31/5.50 % le_add_same_cancel2
% 5.31/5.50 thf(fact_1399_le__add__same__cancel2,axiom,
% 5.31/5.50 ! [A: nat,B: nat] :
% 5.31/5.50 ( ( ord_less_eq_nat @ A @ ( plus_plus_nat @ B @ A ) )
% 5.31/5.50 = ( ord_less_eq_nat @ zero_zero_nat @ B ) ) ).
% 5.31/5.50
% 5.31/5.50 % le_add_same_cancel2
% 5.31/5.50 thf(fact_1400_le__add__same__cancel2,axiom,
% 5.31/5.50 ! [A: int,B: int] :
% 5.31/5.50 ( ( ord_less_eq_int @ A @ ( plus_plus_int @ B @ A ) )
% 5.31/5.50 = ( ord_less_eq_int @ zero_zero_int @ B ) ) ).
% 5.31/5.50
% 5.31/5.50 % le_add_same_cancel2
% 5.31/5.50 thf(fact_1401_double__add__le__zero__iff__single__add__le__zero,axiom,
% 5.31/5.50 ! [A: real] :
% 5.31/5.50 ( ( ord_less_eq_real @ ( plus_plus_real @ A @ A ) @ zero_zero_real )
% 5.31/5.50 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 5.31/5.50
% 5.31/5.50 % double_add_le_zero_iff_single_add_le_zero
% 5.31/5.50 thf(fact_1402_double__add__le__zero__iff__single__add__le__zero,axiom,
% 5.31/5.50 ! [A: rat] :
% 5.31/5.50 ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ A ) @ zero_zero_rat )
% 5.31/5.50 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 5.31/5.50
% 5.31/5.50 % double_add_le_zero_iff_single_add_le_zero
% 5.31/5.50 thf(fact_1403_double__add__le__zero__iff__single__add__le__zero,axiom,
% 5.31/5.50 ! [A: int] :
% 5.31/5.50 ( ( ord_less_eq_int @ ( plus_plus_int @ A @ A ) @ zero_zero_int )
% 5.31/5.50 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 5.31/5.50
% 5.31/5.50 % double_add_le_zero_iff_single_add_le_zero
% 5.31/5.50 thf(fact_1404_zero__le__double__add__iff__zero__le__single__add,axiom,
% 5.31/5.50 ! [A: real] :
% 5.31/5.50 ( ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ A @ A ) )
% 5.31/5.50 = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 5.31/5.50
% 5.31/5.50 % zero_le_double_add_iff_zero_le_single_add
% 5.31/5.50 thf(fact_1405_zero__le__double__add__iff__zero__le__single__add,axiom,
% 5.31/5.50 ! [A: rat] :
% 5.31/5.50 ( ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ A ) )
% 5.31/5.50 = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 5.31/5.50
% 5.31/5.50 % zero_le_double_add_iff_zero_le_single_add
% 5.31/5.50 thf(fact_1406_zero__le__double__add__iff__zero__le__single__add,axiom,
% 5.31/5.50 ! [A: int] :
% 5.31/5.50 ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ A @ A ) )
% 5.31/5.50 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 5.31/5.50
% 5.31/5.50 % zero_le_double_add_iff_zero_le_single_add
% 5.31/5.50 thf(fact_1407_zero__less__double__add__iff__zero__less__single__add,axiom,
% 5.31/5.50 ! [A: real] :
% 5.31/5.50 ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ A ) )
% 5.31/5.50 = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 5.31/5.50
% 5.31/5.50 % zero_less_double_add_iff_zero_less_single_add
% 5.31/5.50 thf(fact_1408_zero__less__double__add__iff__zero__less__single__add,axiom,
% 5.31/5.50 ! [A: rat] :
% 5.31/5.50 ( ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ A ) )
% 5.31/5.50 = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 5.31/5.50
% 5.31/5.50 % zero_less_double_add_iff_zero_less_single_add
% 5.31/5.50 thf(fact_1409_zero__less__double__add__iff__zero__less__single__add,axiom,
% 5.31/5.50 ! [A: int] :
% 5.31/5.50 ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ A ) )
% 5.31/5.50 = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 5.31/5.50
% 5.31/5.50 % zero_less_double_add_iff_zero_less_single_add
% 5.31/5.50 thf(fact_1410_double__add__less__zero__iff__single__add__less__zero,axiom,
% 5.31/5.50 ! [A: real] :
% 5.31/5.50 ( ( ord_less_real @ ( plus_plus_real @ A @ A ) @ zero_zero_real )
% 5.31/5.50 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 5.31/5.50
% 5.31/5.50 % double_add_less_zero_iff_single_add_less_zero
% 5.31/5.50 thf(fact_1411_double__add__less__zero__iff__single__add__less__zero,axiom,
% 5.31/5.50 ! [A: rat] :
% 5.31/5.50 ( ( ord_less_rat @ ( plus_plus_rat @ A @ A ) @ zero_zero_rat )
% 5.31/5.50 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 5.31/5.50
% 5.31/5.50 % double_add_less_zero_iff_single_add_less_zero
% 5.31/5.50 thf(fact_1412_double__add__less__zero__iff__single__add__less__zero,axiom,
% 5.31/5.50 ! [A: int] :
% 5.31/5.50 ( ( ord_less_int @ ( plus_plus_int @ A @ A ) @ zero_zero_int )
% 5.31/5.50 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 5.31/5.50
% 5.31/5.50 % double_add_less_zero_iff_single_add_less_zero
% 5.31/5.50 thf(fact_1413_less__add__same__cancel2,axiom,
% 5.31/5.50 ! [A: real,B: real] :
% 5.31/5.50 ( ( ord_less_real @ A @ ( plus_plus_real @ B @ A ) )
% 5.31/5.50 = ( ord_less_real @ zero_zero_real @ B ) ) ).
% 5.31/5.50
% 5.31/5.50 % less_add_same_cancel2
% 5.31/5.50 thf(fact_1414_less__add__same__cancel2,axiom,
% 5.31/5.50 ! [A: rat,B: rat] :
% 5.31/5.50 ( ( ord_less_rat @ A @ ( plus_plus_rat @ B @ A ) )
% 5.31/5.50 = ( ord_less_rat @ zero_zero_rat @ B ) ) ).
% 5.31/5.50
% 5.31/5.50 % less_add_same_cancel2
% 5.31/5.50 thf(fact_1415_less__add__same__cancel2,axiom,
% 5.31/5.50 ! [A: nat,B: nat] :
% 5.31/5.50 ( ( ord_less_nat @ A @ ( plus_plus_nat @ B @ A ) )
% 5.31/5.50 = ( ord_less_nat @ zero_zero_nat @ B ) ) ).
% 5.31/5.50
% 5.31/5.50 % less_add_same_cancel2
% 5.31/5.50 thf(fact_1416_less__add__same__cancel2,axiom,
% 5.31/5.50 ! [A: int,B: int] :
% 5.31/5.50 ( ( ord_less_int @ A @ ( plus_plus_int @ B @ A ) )
% 5.31/5.50 = ( ord_less_int @ zero_zero_int @ B ) ) ).
% 5.31/5.50
% 5.31/5.50 % less_add_same_cancel2
% 5.31/5.50 thf(fact_1417_less__add__same__cancel1,axiom,
% 5.31/5.50 ! [A: real,B: real] :
% 5.31/5.50 ( ( ord_less_real @ A @ ( plus_plus_real @ A @ B ) )
% 5.31/5.50 = ( ord_less_real @ zero_zero_real @ B ) ) ).
% 5.31/5.50
% 5.31/5.50 % less_add_same_cancel1
% 5.31/5.50 thf(fact_1418_less__add__same__cancel1,axiom,
% 5.31/5.50 ! [A: rat,B: rat] :
% 5.31/5.50 ( ( ord_less_rat @ A @ ( plus_plus_rat @ A @ B ) )
% 5.31/5.50 = ( ord_less_rat @ zero_zero_rat @ B ) ) ).
% 5.31/5.50
% 5.31/5.50 % less_add_same_cancel1
% 5.31/5.50 thf(fact_1419_less__add__same__cancel1,axiom,
% 5.31/5.50 ! [A: nat,B: nat] :
% 5.31/5.50 ( ( ord_less_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 5.31/5.50 = ( ord_less_nat @ zero_zero_nat @ B ) ) ).
% 5.31/5.50
% 5.31/5.50 % less_add_same_cancel1
% 5.31/5.50 thf(fact_1420_less__add__same__cancel1,axiom,
% 5.31/5.50 ! [A: int,B: int] :
% 5.31/5.50 ( ( ord_less_int @ A @ ( plus_plus_int @ A @ B ) )
% 5.31/5.50 = ( ord_less_int @ zero_zero_int @ B ) ) ).
% 5.31/5.50
% 5.31/5.50 % less_add_same_cancel1
% 5.31/5.50 thf(fact_1421_add__less__same__cancel2,axiom,
% 5.31/5.50 ! [A: real,B: real] :
% 5.31/5.50 ( ( ord_less_real @ ( plus_plus_real @ A @ B ) @ B )
% 5.31/5.50 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 5.31/5.50
% 5.31/5.50 % add_less_same_cancel2
% 5.31/5.50 thf(fact_1422_add__less__same__cancel2,axiom,
% 5.31/5.50 ! [A: rat,B: rat] :
% 5.31/5.50 ( ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ B )
% 5.31/5.50 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 5.31/5.50
% 5.31/5.50 % add_less_same_cancel2
% 5.31/5.50 thf(fact_1423_add__less__same__cancel2,axiom,
% 5.31/5.50 ! [A: nat,B: nat] :
% 5.31/5.50 ( ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 5.31/5.50 = ( ord_less_nat @ A @ zero_zero_nat ) ) ).
% 5.31/5.50
% 5.31/5.50 % add_less_same_cancel2
% 5.31/5.50 thf(fact_1424_add__less__same__cancel2,axiom,
% 5.31/5.50 ! [A: int,B: int] :
% 5.31/5.50 ( ( ord_less_int @ ( plus_plus_int @ A @ B ) @ B )
% 5.31/5.50 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 5.31/5.50
% 5.31/5.50 % add_less_same_cancel2
% 5.31/5.50 thf(fact_1425_add__less__same__cancel1,axiom,
% 5.31/5.50 ! [B: real,A: real] :
% 5.31/5.50 ( ( ord_less_real @ ( plus_plus_real @ B @ A ) @ B )
% 5.31/5.50 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 5.31/5.50
% 5.31/5.50 % add_less_same_cancel1
% 5.31/5.50 thf(fact_1426_add__less__same__cancel1,axiom,
% 5.31/5.50 ! [B: rat,A: rat] :
% 5.31/5.50 ( ( ord_less_rat @ ( plus_plus_rat @ B @ A ) @ B )
% 5.31/5.50 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 5.31/5.50
% 5.31/5.50 % add_less_same_cancel1
% 5.31/5.50 thf(fact_1427_add__less__same__cancel1,axiom,
% 5.31/5.50 ! [B: nat,A: nat] :
% 5.31/5.50 ( ( ord_less_nat @ ( plus_plus_nat @ B @ A ) @ B )
% 5.31/5.50 = ( ord_less_nat @ A @ zero_zero_nat ) ) ).
% 5.31/5.50
% 5.31/5.50 % add_less_same_cancel1
% 5.31/5.50 thf(fact_1428_add__less__same__cancel1,axiom,
% 5.31/5.50 ! [B: int,A: int] :
% 5.31/5.50 ( ( ord_less_int @ ( plus_plus_int @ B @ A ) @ B )
% 5.31/5.50 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 5.31/5.50
% 5.31/5.50 % add_less_same_cancel1
% 5.31/5.50 thf(fact_1429_add__gr__0,axiom,
% 5.31/5.50 ! [M2: nat,N: nat] :
% 5.31/5.50 ( ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ M2 @ N ) )
% 5.31/5.50 = ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 5.31/5.50 | ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % add_gr_0
% 5.31/5.50 thf(fact_1430_mult__Suc__right,axiom,
% 5.31/5.50 ! [M2: nat,N: nat] :
% 5.31/5.50 ( ( times_times_nat @ M2 @ ( suc @ N ) )
% 5.31/5.50 = ( plus_plus_nat @ M2 @ ( times_times_nat @ M2 @ N ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % mult_Suc_right
% 5.31/5.50 thf(fact_1431_add__right__imp__eq,axiom,
% 5.31/5.50 ! [B: real,A: real,C2: real] :
% 5.31/5.50 ( ( ( plus_plus_real @ B @ A )
% 5.31/5.50 = ( plus_plus_real @ C2 @ A ) )
% 5.31/5.50 => ( B = C2 ) ) ).
% 5.31/5.50
% 5.31/5.50 % add_right_imp_eq
% 5.31/5.50 thf(fact_1432_add__right__imp__eq,axiom,
% 5.31/5.50 ! [B: rat,A: rat,C2: rat] :
% 5.31/5.50 ( ( ( plus_plus_rat @ B @ A )
% 5.31/5.50 = ( plus_plus_rat @ C2 @ A ) )
% 5.31/5.50 => ( B = C2 ) ) ).
% 5.31/5.50
% 5.31/5.50 % add_right_imp_eq
% 5.31/5.50 thf(fact_1433_add__right__imp__eq,axiom,
% 5.31/5.50 ! [B: nat,A: nat,C2: nat] :
% 5.31/5.50 ( ( ( plus_plus_nat @ B @ A )
% 5.31/5.50 = ( plus_plus_nat @ C2 @ A ) )
% 5.31/5.50 => ( B = C2 ) ) ).
% 5.31/5.50
% 5.31/5.50 % add_right_imp_eq
% 5.31/5.50 thf(fact_1434_add__right__imp__eq,axiom,
% 5.31/5.50 ! [B: int,A: int,C2: int] :
% 5.31/5.50 ( ( ( plus_plus_int @ B @ A )
% 5.31/5.50 = ( plus_plus_int @ C2 @ A ) )
% 5.31/5.50 => ( B = C2 ) ) ).
% 5.31/5.50
% 5.31/5.50 % add_right_imp_eq
% 5.31/5.50 thf(fact_1435_add__left__imp__eq,axiom,
% 5.31/5.50 ! [A: real,B: real,C2: real] :
% 5.31/5.50 ( ( ( plus_plus_real @ A @ B )
% 5.31/5.50 = ( plus_plus_real @ A @ C2 ) )
% 5.31/5.50 => ( B = C2 ) ) ).
% 5.31/5.50
% 5.31/5.50 % add_left_imp_eq
% 5.31/5.50 thf(fact_1436_add__left__imp__eq,axiom,
% 5.31/5.50 ! [A: rat,B: rat,C2: rat] :
% 5.31/5.50 ( ( ( plus_plus_rat @ A @ B )
% 5.31/5.50 = ( plus_plus_rat @ A @ C2 ) )
% 5.31/5.50 => ( B = C2 ) ) ).
% 5.31/5.50
% 5.31/5.50 % add_left_imp_eq
% 5.31/5.50 thf(fact_1437_add__left__imp__eq,axiom,
% 5.31/5.50 ! [A: nat,B: nat,C2: nat] :
% 5.31/5.50 ( ( ( plus_plus_nat @ A @ B )
% 5.31/5.50 = ( plus_plus_nat @ A @ C2 ) )
% 5.31/5.50 => ( B = C2 ) ) ).
% 5.31/5.50
% 5.31/5.50 % add_left_imp_eq
% 5.31/5.50 thf(fact_1438_add__left__imp__eq,axiom,
% 5.31/5.50 ! [A: int,B: int,C2: int] :
% 5.31/5.50 ( ( ( plus_plus_int @ A @ B )
% 5.31/5.50 = ( plus_plus_int @ A @ C2 ) )
% 5.31/5.50 => ( B = C2 ) ) ).
% 5.31/5.50
% 5.31/5.50 % add_left_imp_eq
% 5.31/5.50 thf(fact_1439_add_Oleft__commute,axiom,
% 5.31/5.50 ! [B: real,A: real,C2: real] :
% 5.31/5.50 ( ( plus_plus_real @ B @ ( plus_plus_real @ A @ C2 ) )
% 5.31/5.50 = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C2 ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % add.left_commute
% 5.31/5.50 thf(fact_1440_add_Oleft__commute,axiom,
% 5.31/5.50 ! [B: rat,A: rat,C2: rat] :
% 5.31/5.50 ( ( plus_plus_rat @ B @ ( plus_plus_rat @ A @ C2 ) )
% 5.31/5.50 = ( plus_plus_rat @ A @ ( plus_plus_rat @ B @ C2 ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % add.left_commute
% 5.31/5.50 thf(fact_1441_add_Oleft__commute,axiom,
% 5.31/5.50 ! [B: nat,A: nat,C2: nat] :
% 5.31/5.50 ( ( plus_plus_nat @ B @ ( plus_plus_nat @ A @ C2 ) )
% 5.31/5.50 = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C2 ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % add.left_commute
% 5.31/5.50 thf(fact_1442_add_Oleft__commute,axiom,
% 5.31/5.50 ! [B: int,A: int,C2: int] :
% 5.31/5.50 ( ( plus_plus_int @ B @ ( plus_plus_int @ A @ C2 ) )
% 5.31/5.50 = ( plus_plus_int @ A @ ( plus_plus_int @ B @ C2 ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % add.left_commute
% 5.31/5.50 thf(fact_1443_add_Ocommute,axiom,
% 5.31/5.50 ( plus_plus_real
% 5.31/5.50 = ( ^ [A5: real,B4: real] : ( plus_plus_real @ B4 @ A5 ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % add.commute
% 5.31/5.50 thf(fact_1444_add_Ocommute,axiom,
% 5.31/5.50 ( plus_plus_rat
% 5.31/5.50 = ( ^ [A5: rat,B4: rat] : ( plus_plus_rat @ B4 @ A5 ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % add.commute
% 5.31/5.50 thf(fact_1445_add_Ocommute,axiom,
% 5.31/5.50 ( plus_plus_nat
% 5.31/5.50 = ( ^ [A5: nat,B4: nat] : ( plus_plus_nat @ B4 @ A5 ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % add.commute
% 5.31/5.50 thf(fact_1446_add_Ocommute,axiom,
% 5.31/5.50 ( plus_plus_int
% 5.31/5.50 = ( ^ [A5: int,B4: int] : ( plus_plus_int @ B4 @ A5 ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % add.commute
% 5.31/5.50 thf(fact_1447_add_Oright__cancel,axiom,
% 5.31/5.50 ! [B: real,A: real,C2: real] :
% 5.31/5.50 ( ( ( plus_plus_real @ B @ A )
% 5.31/5.50 = ( plus_plus_real @ C2 @ A ) )
% 5.31/5.50 = ( B = C2 ) ) ).
% 5.31/5.50
% 5.31/5.50 % add.right_cancel
% 5.31/5.50 thf(fact_1448_add_Oright__cancel,axiom,
% 5.31/5.50 ! [B: rat,A: rat,C2: rat] :
% 5.31/5.50 ( ( ( plus_plus_rat @ B @ A )
% 5.31/5.50 = ( plus_plus_rat @ C2 @ A ) )
% 5.31/5.50 = ( B = C2 ) ) ).
% 5.31/5.50
% 5.31/5.50 % add.right_cancel
% 5.31/5.50 thf(fact_1449_add_Oright__cancel,axiom,
% 5.31/5.50 ! [B: int,A: int,C2: int] :
% 5.31/5.50 ( ( ( plus_plus_int @ B @ A )
% 5.31/5.50 = ( plus_plus_int @ C2 @ A ) )
% 5.31/5.50 = ( B = C2 ) ) ).
% 5.31/5.50
% 5.31/5.50 % add.right_cancel
% 5.31/5.50 thf(fact_1450_add_Oleft__cancel,axiom,
% 5.31/5.50 ! [A: real,B: real,C2: real] :
% 5.31/5.50 ( ( ( plus_plus_real @ A @ B )
% 5.31/5.50 = ( plus_plus_real @ A @ C2 ) )
% 5.31/5.50 = ( B = C2 ) ) ).
% 5.31/5.50
% 5.31/5.50 % add.left_cancel
% 5.31/5.50 thf(fact_1451_add_Oleft__cancel,axiom,
% 5.31/5.50 ! [A: rat,B: rat,C2: rat] :
% 5.31/5.50 ( ( ( plus_plus_rat @ A @ B )
% 5.31/5.50 = ( plus_plus_rat @ A @ C2 ) )
% 5.31/5.50 = ( B = C2 ) ) ).
% 5.31/5.50
% 5.31/5.50 % add.left_cancel
% 5.31/5.50 thf(fact_1452_add_Oleft__cancel,axiom,
% 5.31/5.50 ! [A: int,B: int,C2: int] :
% 5.31/5.50 ( ( ( plus_plus_int @ A @ B )
% 5.31/5.50 = ( plus_plus_int @ A @ C2 ) )
% 5.31/5.50 = ( B = C2 ) ) ).
% 5.31/5.50
% 5.31/5.50 % add.left_cancel
% 5.31/5.50 thf(fact_1453_add_Oassoc,axiom,
% 5.31/5.50 ! [A: real,B: real,C2: real] :
% 5.31/5.50 ( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C2 )
% 5.31/5.50 = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C2 ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % add.assoc
% 5.31/5.50 thf(fact_1454_add_Oassoc,axiom,
% 5.31/5.50 ! [A: rat,B: rat,C2: rat] :
% 5.31/5.50 ( ( plus_plus_rat @ ( plus_plus_rat @ A @ B ) @ C2 )
% 5.31/5.50 = ( plus_plus_rat @ A @ ( plus_plus_rat @ B @ C2 ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % add.assoc
% 5.31/5.50 thf(fact_1455_add_Oassoc,axiom,
% 5.31/5.50 ! [A: nat,B: nat,C2: nat] :
% 5.31/5.50 ( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C2 )
% 5.31/5.50 = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C2 ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % add.assoc
% 5.31/5.50 thf(fact_1456_add_Oassoc,axiom,
% 5.31/5.50 ! [A: int,B: int,C2: int] :
% 5.31/5.50 ( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C2 )
% 5.31/5.50 = ( plus_plus_int @ A @ ( plus_plus_int @ B @ C2 ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % add.assoc
% 5.31/5.50 thf(fact_1457_group__cancel_Oadd2,axiom,
% 5.31/5.50 ! [B5: real,K2: real,B: real,A: real] :
% 5.31/5.50 ( ( B5
% 5.31/5.50 = ( plus_plus_real @ K2 @ B ) )
% 5.31/5.50 => ( ( plus_plus_real @ A @ B5 )
% 5.31/5.50 = ( plus_plus_real @ K2 @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % group_cancel.add2
% 5.31/5.50 thf(fact_1458_group__cancel_Oadd2,axiom,
% 5.31/5.50 ! [B5: rat,K2: rat,B: rat,A: rat] :
% 5.31/5.50 ( ( B5
% 5.31/5.50 = ( plus_plus_rat @ K2 @ B ) )
% 5.31/5.50 => ( ( plus_plus_rat @ A @ B5 )
% 5.31/5.50 = ( plus_plus_rat @ K2 @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % group_cancel.add2
% 5.31/5.50 thf(fact_1459_group__cancel_Oadd2,axiom,
% 5.31/5.50 ! [B5: nat,K2: nat,B: nat,A: nat] :
% 5.31/5.50 ( ( B5
% 5.31/5.50 = ( plus_plus_nat @ K2 @ B ) )
% 5.31/5.50 => ( ( plus_plus_nat @ A @ B5 )
% 5.31/5.50 = ( plus_plus_nat @ K2 @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % group_cancel.add2
% 5.31/5.50 thf(fact_1460_group__cancel_Oadd2,axiom,
% 5.31/5.50 ! [B5: int,K2: int,B: int,A: int] :
% 5.31/5.50 ( ( B5
% 5.31/5.50 = ( plus_plus_int @ K2 @ B ) )
% 5.31/5.50 => ( ( plus_plus_int @ A @ B5 )
% 5.31/5.50 = ( plus_plus_int @ K2 @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % group_cancel.add2
% 5.31/5.50 thf(fact_1461_group__cancel_Oadd1,axiom,
% 5.31/5.50 ! [A4: real,K2: real,A: real,B: real] :
% 5.31/5.50 ( ( A4
% 5.31/5.50 = ( plus_plus_real @ K2 @ A ) )
% 5.31/5.50 => ( ( plus_plus_real @ A4 @ B )
% 5.31/5.50 = ( plus_plus_real @ K2 @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % group_cancel.add1
% 5.31/5.50 thf(fact_1462_group__cancel_Oadd1,axiom,
% 5.31/5.50 ! [A4: rat,K2: rat,A: rat,B: rat] :
% 5.31/5.50 ( ( A4
% 5.31/5.50 = ( plus_plus_rat @ K2 @ A ) )
% 5.31/5.50 => ( ( plus_plus_rat @ A4 @ B )
% 5.31/5.50 = ( plus_plus_rat @ K2 @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % group_cancel.add1
% 5.31/5.50 thf(fact_1463_group__cancel_Oadd1,axiom,
% 5.31/5.50 ! [A4: nat,K2: nat,A: nat,B: nat] :
% 5.31/5.50 ( ( A4
% 5.31/5.50 = ( plus_plus_nat @ K2 @ A ) )
% 5.31/5.50 => ( ( plus_plus_nat @ A4 @ B )
% 5.31/5.50 = ( plus_plus_nat @ K2 @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % group_cancel.add1
% 5.31/5.50 thf(fact_1464_group__cancel_Oadd1,axiom,
% 5.31/5.50 ! [A4: int,K2: int,A: int,B: int] :
% 5.31/5.50 ( ( A4
% 5.31/5.50 = ( plus_plus_int @ K2 @ A ) )
% 5.31/5.50 => ( ( plus_plus_int @ A4 @ B )
% 5.31/5.50 = ( plus_plus_int @ K2 @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % group_cancel.add1
% 5.31/5.50 thf(fact_1465_add__mono__thms__linordered__semiring_I4_J,axiom,
% 5.31/5.50 ! [I2: real,J2: real,K2: real,L: real] :
% 5.31/5.50 ( ( ( I2 = J2 )
% 5.31/5.50 & ( K2 = L ) )
% 5.31/5.50 => ( ( plus_plus_real @ I2 @ K2 )
% 5.31/5.50 = ( plus_plus_real @ J2 @ L ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % add_mono_thms_linordered_semiring(4)
% 5.31/5.50 thf(fact_1466_add__mono__thms__linordered__semiring_I4_J,axiom,
% 5.31/5.50 ! [I2: rat,J2: rat,K2: rat,L: rat] :
% 5.31/5.50 ( ( ( I2 = J2 )
% 5.31/5.50 & ( K2 = L ) )
% 5.31/5.50 => ( ( plus_plus_rat @ I2 @ K2 )
% 5.31/5.50 = ( plus_plus_rat @ J2 @ L ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % add_mono_thms_linordered_semiring(4)
% 5.31/5.50 thf(fact_1467_add__mono__thms__linordered__semiring_I4_J,axiom,
% 5.31/5.50 ! [I2: nat,J2: nat,K2: nat,L: nat] :
% 5.31/5.50 ( ( ( I2 = J2 )
% 5.31/5.50 & ( K2 = L ) )
% 5.31/5.50 => ( ( plus_plus_nat @ I2 @ K2 )
% 5.31/5.50 = ( plus_plus_nat @ J2 @ L ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % add_mono_thms_linordered_semiring(4)
% 5.31/5.50 thf(fact_1468_add__mono__thms__linordered__semiring_I4_J,axiom,
% 5.31/5.50 ! [I2: int,J2: int,K2: int,L: int] :
% 5.31/5.50 ( ( ( I2 = J2 )
% 5.31/5.50 & ( K2 = L ) )
% 5.31/5.50 => ( ( plus_plus_int @ I2 @ K2 )
% 5.31/5.50 = ( plus_plus_int @ J2 @ L ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % add_mono_thms_linordered_semiring(4)
% 5.31/5.50 thf(fact_1469_is__num__normalize_I1_J,axiom,
% 5.31/5.50 ! [A: real,B: real,C2: real] :
% 5.31/5.50 ( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C2 )
% 5.31/5.50 = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C2 ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % is_num_normalize(1)
% 5.31/5.50 thf(fact_1470_is__num__normalize_I1_J,axiom,
% 5.31/5.50 ! [A: rat,B: rat,C2: rat] :
% 5.31/5.50 ( ( plus_plus_rat @ ( plus_plus_rat @ A @ B ) @ C2 )
% 5.31/5.50 = ( plus_plus_rat @ A @ ( plus_plus_rat @ B @ C2 ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % is_num_normalize(1)
% 5.31/5.50 thf(fact_1471_is__num__normalize_I1_J,axiom,
% 5.31/5.50 ! [A: int,B: int,C2: int] :
% 5.31/5.50 ( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C2 )
% 5.31/5.50 = ( plus_plus_int @ A @ ( plus_plus_int @ B @ C2 ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % is_num_normalize(1)
% 5.31/5.50 thf(fact_1472_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 5.31/5.50 ! [A: real,B: real,C2: real] :
% 5.31/5.50 ( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C2 )
% 5.31/5.50 = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C2 ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % ab_semigroup_add_class.add_ac(1)
% 5.31/5.50 thf(fact_1473_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 5.31/5.50 ! [A: rat,B: rat,C2: rat] :
% 5.31/5.50 ( ( plus_plus_rat @ ( plus_plus_rat @ A @ B ) @ C2 )
% 5.31/5.50 = ( plus_plus_rat @ A @ ( plus_plus_rat @ B @ C2 ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % ab_semigroup_add_class.add_ac(1)
% 5.31/5.50 thf(fact_1474_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 5.31/5.50 ! [A: nat,B: nat,C2: nat] :
% 5.31/5.50 ( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C2 )
% 5.31/5.50 = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C2 ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % ab_semigroup_add_class.add_ac(1)
% 5.31/5.50 thf(fact_1475_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 5.31/5.50 ! [A: int,B: int,C2: int] :
% 5.31/5.50 ( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C2 )
% 5.31/5.50 = ( plus_plus_int @ A @ ( plus_plus_int @ B @ C2 ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % ab_semigroup_add_class.add_ac(1)
% 5.31/5.50 thf(fact_1476_bot__nat__def,axiom,
% 5.31/5.50 bot_bot_nat = zero_zero_nat ).
% 5.31/5.50
% 5.31/5.50 % bot_nat_def
% 5.31/5.50 thf(fact_1477_VEBT__internal_Omembermima_Osimps_I2_J,axiom,
% 5.31/5.50 ! [Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT,Uz: nat] :
% 5.31/5.50 ~ ( vEBT_VEBT_membermima @ ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) @ Uz ) ).
% 5.31/5.50
% 5.31/5.50 % VEBT_internal.membermima.simps(2)
% 5.31/5.50 thf(fact_1478_add__mono__thms__linordered__semiring_I3_J,axiom,
% 5.31/5.50 ! [I2: real,J2: real,K2: real,L: real] :
% 5.31/5.50 ( ( ( ord_less_eq_real @ I2 @ J2 )
% 5.31/5.50 & ( K2 = L ) )
% 5.31/5.50 => ( ord_less_eq_real @ ( plus_plus_real @ I2 @ K2 ) @ ( plus_plus_real @ J2 @ L ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % add_mono_thms_linordered_semiring(3)
% 5.31/5.50 thf(fact_1479_add__mono__thms__linordered__semiring_I3_J,axiom,
% 5.31/5.50 ! [I2: rat,J2: rat,K2: rat,L: rat] :
% 5.31/5.50 ( ( ( ord_less_eq_rat @ I2 @ J2 )
% 5.31/5.50 & ( K2 = L ) )
% 5.31/5.50 => ( ord_less_eq_rat @ ( plus_plus_rat @ I2 @ K2 ) @ ( plus_plus_rat @ J2 @ L ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % add_mono_thms_linordered_semiring(3)
% 5.31/5.50 thf(fact_1480_add__mono__thms__linordered__semiring_I3_J,axiom,
% 5.31/5.50 ! [I2: nat,J2: nat,K2: nat,L: nat] :
% 5.31/5.50 ( ( ( ord_less_eq_nat @ I2 @ J2 )
% 5.31/5.50 & ( K2 = L ) )
% 5.31/5.50 => ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K2 ) @ ( plus_plus_nat @ J2 @ L ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % add_mono_thms_linordered_semiring(3)
% 5.31/5.50 thf(fact_1481_add__mono__thms__linordered__semiring_I3_J,axiom,
% 5.31/5.50 ! [I2: int,J2: int,K2: int,L: int] :
% 5.31/5.50 ( ( ( ord_less_eq_int @ I2 @ J2 )
% 5.31/5.50 & ( K2 = L ) )
% 5.31/5.50 => ( ord_less_eq_int @ ( plus_plus_int @ I2 @ K2 ) @ ( plus_plus_int @ J2 @ L ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % add_mono_thms_linordered_semiring(3)
% 5.31/5.50 thf(fact_1482_add__mono__thms__linordered__semiring_I2_J,axiom,
% 5.31/5.50 ! [I2: real,J2: real,K2: real,L: real] :
% 5.31/5.50 ( ( ( I2 = J2 )
% 5.31/5.50 & ( ord_less_eq_real @ K2 @ L ) )
% 5.31/5.50 => ( ord_less_eq_real @ ( plus_plus_real @ I2 @ K2 ) @ ( plus_plus_real @ J2 @ L ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % add_mono_thms_linordered_semiring(2)
% 5.31/5.50 thf(fact_1483_add__mono__thms__linordered__semiring_I2_J,axiom,
% 5.31/5.50 ! [I2: rat,J2: rat,K2: rat,L: rat] :
% 5.31/5.50 ( ( ( I2 = J2 )
% 5.31/5.50 & ( ord_less_eq_rat @ K2 @ L ) )
% 5.31/5.50 => ( ord_less_eq_rat @ ( plus_plus_rat @ I2 @ K2 ) @ ( plus_plus_rat @ J2 @ L ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % add_mono_thms_linordered_semiring(2)
% 5.31/5.50 thf(fact_1484_add__mono__thms__linordered__semiring_I2_J,axiom,
% 5.31/5.50 ! [I2: nat,J2: nat,K2: nat,L: nat] :
% 5.31/5.50 ( ( ( I2 = J2 )
% 5.31/5.50 & ( ord_less_eq_nat @ K2 @ L ) )
% 5.31/5.50 => ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K2 ) @ ( plus_plus_nat @ J2 @ L ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % add_mono_thms_linordered_semiring(2)
% 5.31/5.50 thf(fact_1485_add__mono__thms__linordered__semiring_I2_J,axiom,
% 5.31/5.50 ! [I2: int,J2: int,K2: int,L: int] :
% 5.31/5.50 ( ( ( I2 = J2 )
% 5.31/5.50 & ( ord_less_eq_int @ K2 @ L ) )
% 5.31/5.50 => ( ord_less_eq_int @ ( plus_plus_int @ I2 @ K2 ) @ ( plus_plus_int @ J2 @ L ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % add_mono_thms_linordered_semiring(2)
% 5.31/5.50 thf(fact_1486_add__mono__thms__linordered__semiring_I1_J,axiom,
% 5.31/5.50 ! [I2: real,J2: real,K2: real,L: real] :
% 5.31/5.50 ( ( ( ord_less_eq_real @ I2 @ J2 )
% 5.31/5.50 & ( ord_less_eq_real @ K2 @ L ) )
% 5.31/5.50 => ( ord_less_eq_real @ ( plus_plus_real @ I2 @ K2 ) @ ( plus_plus_real @ J2 @ L ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % add_mono_thms_linordered_semiring(1)
% 5.31/5.50 thf(fact_1487_add__mono__thms__linordered__semiring_I1_J,axiom,
% 5.31/5.50 ! [I2: rat,J2: rat,K2: rat,L: rat] :
% 5.31/5.50 ( ( ( ord_less_eq_rat @ I2 @ J2 )
% 5.31/5.50 & ( ord_less_eq_rat @ K2 @ L ) )
% 5.31/5.50 => ( ord_less_eq_rat @ ( plus_plus_rat @ I2 @ K2 ) @ ( plus_plus_rat @ J2 @ L ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % add_mono_thms_linordered_semiring(1)
% 5.31/5.50 thf(fact_1488_add__mono__thms__linordered__semiring_I1_J,axiom,
% 5.31/5.50 ! [I2: nat,J2: nat,K2: nat,L: nat] :
% 5.31/5.50 ( ( ( ord_less_eq_nat @ I2 @ J2 )
% 5.31/5.50 & ( ord_less_eq_nat @ K2 @ L ) )
% 5.31/5.50 => ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K2 ) @ ( plus_plus_nat @ J2 @ L ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % add_mono_thms_linordered_semiring(1)
% 5.31/5.50 thf(fact_1489_add__mono__thms__linordered__semiring_I1_J,axiom,
% 5.31/5.50 ! [I2: int,J2: int,K2: int,L: int] :
% 5.31/5.50 ( ( ( ord_less_eq_int @ I2 @ J2 )
% 5.31/5.50 & ( ord_less_eq_int @ K2 @ L ) )
% 5.31/5.50 => ( ord_less_eq_int @ ( plus_plus_int @ I2 @ K2 ) @ ( plus_plus_int @ J2 @ L ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % add_mono_thms_linordered_semiring(1)
% 5.31/5.50 thf(fact_1490_add__mono,axiom,
% 5.31/5.50 ! [A: real,B: real,C2: real,D: real] :
% 5.31/5.50 ( ( ord_less_eq_real @ A @ B )
% 5.31/5.50 => ( ( ord_less_eq_real @ C2 @ D )
% 5.31/5.50 => ( ord_less_eq_real @ ( plus_plus_real @ A @ C2 ) @ ( plus_plus_real @ B @ D ) ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % add_mono
% 5.31/5.50 thf(fact_1491_add__mono,axiom,
% 5.31/5.50 ! [A: rat,B: rat,C2: rat,D: rat] :
% 5.31/5.50 ( ( ord_less_eq_rat @ A @ B )
% 5.31/5.50 => ( ( ord_less_eq_rat @ C2 @ D )
% 5.31/5.50 => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C2 ) @ ( plus_plus_rat @ B @ D ) ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % add_mono
% 5.31/5.50 thf(fact_1492_add__mono,axiom,
% 5.31/5.50 ! [A: nat,B: nat,C2: nat,D: nat] :
% 5.31/5.50 ( ( ord_less_eq_nat @ A @ B )
% 5.31/5.50 => ( ( ord_less_eq_nat @ C2 @ D )
% 5.31/5.50 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C2 ) @ ( plus_plus_nat @ B @ D ) ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % add_mono
% 5.31/5.50 thf(fact_1493_add__mono,axiom,
% 5.31/5.50 ! [A: int,B: int,C2: int,D: int] :
% 5.31/5.50 ( ( ord_less_eq_int @ A @ B )
% 5.31/5.50 => ( ( ord_less_eq_int @ C2 @ D )
% 5.31/5.50 => ( ord_less_eq_int @ ( plus_plus_int @ A @ C2 ) @ ( plus_plus_int @ B @ D ) ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % add_mono
% 5.31/5.50 thf(fact_1494_add__left__mono,axiom,
% 5.31/5.50 ! [A: real,B: real,C2: real] :
% 5.31/5.50 ( ( ord_less_eq_real @ A @ B )
% 5.31/5.50 => ( ord_less_eq_real @ ( plus_plus_real @ C2 @ A ) @ ( plus_plus_real @ C2 @ B ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % add_left_mono
% 5.31/5.50 thf(fact_1495_add__left__mono,axiom,
% 5.31/5.50 ! [A: rat,B: rat,C2: rat] :
% 5.31/5.50 ( ( ord_less_eq_rat @ A @ B )
% 5.31/5.50 => ( ord_less_eq_rat @ ( plus_plus_rat @ C2 @ A ) @ ( plus_plus_rat @ C2 @ B ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % add_left_mono
% 5.31/5.50 thf(fact_1496_add__left__mono,axiom,
% 5.31/5.50 ! [A: nat,B: nat,C2: nat] :
% 5.31/5.50 ( ( ord_less_eq_nat @ A @ B )
% 5.31/5.50 => ( ord_less_eq_nat @ ( plus_plus_nat @ C2 @ A ) @ ( plus_plus_nat @ C2 @ B ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % add_left_mono
% 5.31/5.50 thf(fact_1497_add__left__mono,axiom,
% 5.31/5.50 ! [A: int,B: int,C2: int] :
% 5.31/5.50 ( ( ord_less_eq_int @ A @ B )
% 5.31/5.50 => ( ord_less_eq_int @ ( plus_plus_int @ C2 @ A ) @ ( plus_plus_int @ C2 @ B ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % add_left_mono
% 5.31/5.50 thf(fact_1498_less__eqE,axiom,
% 5.31/5.50 ! [A: nat,B: nat] :
% 5.31/5.50 ( ( ord_less_eq_nat @ A @ B )
% 5.31/5.50 => ~ ! [C: nat] :
% 5.31/5.50 ( B
% 5.31/5.50 != ( plus_plus_nat @ A @ C ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % less_eqE
% 5.31/5.50 thf(fact_1499_add__right__mono,axiom,
% 5.31/5.50 ! [A: real,B: real,C2: real] :
% 5.31/5.50 ( ( ord_less_eq_real @ A @ B )
% 5.31/5.50 => ( ord_less_eq_real @ ( plus_plus_real @ A @ C2 ) @ ( plus_plus_real @ B @ C2 ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % add_right_mono
% 5.31/5.50 thf(fact_1500_add__right__mono,axiom,
% 5.31/5.50 ! [A: rat,B: rat,C2: rat] :
% 5.31/5.50 ( ( ord_less_eq_rat @ A @ B )
% 5.31/5.50 => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C2 ) @ ( plus_plus_rat @ B @ C2 ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % add_right_mono
% 5.31/5.50 thf(fact_1501_add__right__mono,axiom,
% 5.31/5.50 ! [A: nat,B: nat,C2: nat] :
% 5.31/5.50 ( ( ord_less_eq_nat @ A @ B )
% 5.31/5.50 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C2 ) @ ( plus_plus_nat @ B @ C2 ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % add_right_mono
% 5.31/5.50 thf(fact_1502_add__right__mono,axiom,
% 5.31/5.50 ! [A: int,B: int,C2: int] :
% 5.31/5.50 ( ( ord_less_eq_int @ A @ B )
% 5.31/5.50 => ( ord_less_eq_int @ ( plus_plus_int @ A @ C2 ) @ ( plus_plus_int @ B @ C2 ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % add_right_mono
% 5.31/5.50 thf(fact_1503_le__iff__add,axiom,
% 5.31/5.50 ( ord_less_eq_nat
% 5.31/5.50 = ( ^ [A5: nat,B4: nat] :
% 5.31/5.50 ? [C3: nat] :
% 5.31/5.50 ( B4
% 5.31/5.50 = ( plus_plus_nat @ A5 @ C3 ) ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % le_iff_add
% 5.31/5.50 thf(fact_1504_add__le__imp__le__left,axiom,
% 5.31/5.50 ! [C2: real,A: real,B: real] :
% 5.31/5.50 ( ( ord_less_eq_real @ ( plus_plus_real @ C2 @ A ) @ ( plus_plus_real @ C2 @ B ) )
% 5.31/5.50 => ( ord_less_eq_real @ A @ B ) ) ).
% 5.31/5.50
% 5.31/5.50 % add_le_imp_le_left
% 5.31/5.50 thf(fact_1505_add__le__imp__le__left,axiom,
% 5.31/5.50 ! [C2: rat,A: rat,B: rat] :
% 5.31/5.50 ( ( ord_less_eq_rat @ ( plus_plus_rat @ C2 @ A ) @ ( plus_plus_rat @ C2 @ B ) )
% 5.31/5.50 => ( ord_less_eq_rat @ A @ B ) ) ).
% 5.31/5.50
% 5.31/5.50 % add_le_imp_le_left
% 5.31/5.50 thf(fact_1506_add__le__imp__le__left,axiom,
% 5.31/5.50 ! [C2: nat,A: nat,B: nat] :
% 5.31/5.50 ( ( ord_less_eq_nat @ ( plus_plus_nat @ C2 @ A ) @ ( plus_plus_nat @ C2 @ B ) )
% 5.31/5.50 => ( ord_less_eq_nat @ A @ B ) ) ).
% 5.31/5.50
% 5.31/5.50 % add_le_imp_le_left
% 5.31/5.50 thf(fact_1507_add__le__imp__le__left,axiom,
% 5.31/5.50 ! [C2: int,A: int,B: int] :
% 5.31/5.50 ( ( ord_less_eq_int @ ( plus_plus_int @ C2 @ A ) @ ( plus_plus_int @ C2 @ B ) )
% 5.31/5.50 => ( ord_less_eq_int @ A @ B ) ) ).
% 5.31/5.50
% 5.31/5.50 % add_le_imp_le_left
% 5.31/5.50 thf(fact_1508_add__le__imp__le__right,axiom,
% 5.31/5.50 ! [A: real,C2: real,B: real] :
% 5.31/5.50 ( ( ord_less_eq_real @ ( plus_plus_real @ A @ C2 ) @ ( plus_plus_real @ B @ C2 ) )
% 5.31/5.50 => ( ord_less_eq_real @ A @ B ) ) ).
% 5.31/5.50
% 5.31/5.50 % add_le_imp_le_right
% 5.31/5.50 thf(fact_1509_add__le__imp__le__right,axiom,
% 5.31/5.50 ! [A: rat,C2: rat,B: rat] :
% 5.31/5.50 ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C2 ) @ ( plus_plus_rat @ B @ C2 ) )
% 5.31/5.50 => ( ord_less_eq_rat @ A @ B ) ) ).
% 5.31/5.50
% 5.31/5.50 % add_le_imp_le_right
% 5.31/5.50 thf(fact_1510_add__le__imp__le__right,axiom,
% 5.31/5.50 ! [A: nat,C2: nat,B: nat] :
% 5.31/5.50 ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C2 ) @ ( plus_plus_nat @ B @ C2 ) )
% 5.31/5.50 => ( ord_less_eq_nat @ A @ B ) ) ).
% 5.31/5.50
% 5.31/5.50 % add_le_imp_le_right
% 5.31/5.50 thf(fact_1511_add__le__imp__le__right,axiom,
% 5.31/5.50 ! [A: int,C2: int,B: int] :
% 5.31/5.50 ( ( ord_less_eq_int @ ( plus_plus_int @ A @ C2 ) @ ( plus_plus_int @ B @ C2 ) )
% 5.31/5.50 => ( ord_less_eq_int @ A @ B ) ) ).
% 5.31/5.50
% 5.31/5.50 % add_le_imp_le_right
% 5.31/5.50 thf(fact_1512_comm__monoid__add__class_Oadd__0,axiom,
% 5.31/5.50 ! [A: complex] :
% 5.31/5.50 ( ( plus_plus_complex @ zero_zero_complex @ A )
% 5.31/5.50 = A ) ).
% 5.31/5.50
% 5.31/5.50 % comm_monoid_add_class.add_0
% 5.31/5.50 thf(fact_1513_comm__monoid__add__class_Oadd__0,axiom,
% 5.31/5.50 ! [A: real] :
% 5.31/5.50 ( ( plus_plus_real @ zero_zero_real @ A )
% 5.31/5.50 = A ) ).
% 5.31/5.50
% 5.31/5.50 % comm_monoid_add_class.add_0
% 5.31/5.50 thf(fact_1514_comm__monoid__add__class_Oadd__0,axiom,
% 5.31/5.50 ! [A: rat] :
% 5.31/5.50 ( ( plus_plus_rat @ zero_zero_rat @ A )
% 5.31/5.50 = A ) ).
% 5.31/5.50
% 5.31/5.50 % comm_monoid_add_class.add_0
% 5.31/5.50 thf(fact_1515_comm__monoid__add__class_Oadd__0,axiom,
% 5.31/5.50 ! [A: nat] :
% 5.31/5.50 ( ( plus_plus_nat @ zero_zero_nat @ A )
% 5.31/5.50 = A ) ).
% 5.31/5.50
% 5.31/5.50 % comm_monoid_add_class.add_0
% 5.31/5.50 thf(fact_1516_comm__monoid__add__class_Oadd__0,axiom,
% 5.31/5.50 ! [A: int] :
% 5.31/5.50 ( ( plus_plus_int @ zero_zero_int @ A )
% 5.31/5.50 = A ) ).
% 5.31/5.50
% 5.31/5.50 % comm_monoid_add_class.add_0
% 5.31/5.50 thf(fact_1517_add_Ocomm__neutral,axiom,
% 5.31/5.50 ! [A: complex] :
% 5.31/5.50 ( ( plus_plus_complex @ A @ zero_zero_complex )
% 5.31/5.50 = A ) ).
% 5.31/5.50
% 5.31/5.50 % add.comm_neutral
% 5.31/5.50 thf(fact_1518_add_Ocomm__neutral,axiom,
% 5.31/5.50 ! [A: real] :
% 5.31/5.50 ( ( plus_plus_real @ A @ zero_zero_real )
% 5.31/5.50 = A ) ).
% 5.31/5.50
% 5.31/5.50 % add.comm_neutral
% 5.31/5.50 thf(fact_1519_add_Ocomm__neutral,axiom,
% 5.31/5.50 ! [A: rat] :
% 5.31/5.50 ( ( plus_plus_rat @ A @ zero_zero_rat )
% 5.31/5.50 = A ) ).
% 5.31/5.50
% 5.31/5.50 % add.comm_neutral
% 5.31/5.50 thf(fact_1520_add_Ocomm__neutral,axiom,
% 5.31/5.50 ! [A: nat] :
% 5.31/5.50 ( ( plus_plus_nat @ A @ zero_zero_nat )
% 5.31/5.50 = A ) ).
% 5.31/5.50
% 5.31/5.50 % add.comm_neutral
% 5.31/5.50 thf(fact_1521_add_Ocomm__neutral,axiom,
% 5.31/5.50 ! [A: int] :
% 5.31/5.50 ( ( plus_plus_int @ A @ zero_zero_int )
% 5.31/5.50 = A ) ).
% 5.31/5.50
% 5.31/5.50 % add.comm_neutral
% 5.31/5.50 thf(fact_1522_add_Ogroup__left__neutral,axiom,
% 5.31/5.50 ! [A: complex] :
% 5.31/5.50 ( ( plus_plus_complex @ zero_zero_complex @ A )
% 5.31/5.50 = A ) ).
% 5.31/5.50
% 5.31/5.50 % add.group_left_neutral
% 5.31/5.50 thf(fact_1523_add_Ogroup__left__neutral,axiom,
% 5.31/5.50 ! [A: real] :
% 5.31/5.50 ( ( plus_plus_real @ zero_zero_real @ A )
% 5.31/5.50 = A ) ).
% 5.31/5.50
% 5.31/5.50 % add.group_left_neutral
% 5.31/5.50 thf(fact_1524_add_Ogroup__left__neutral,axiom,
% 5.31/5.50 ! [A: rat] :
% 5.31/5.50 ( ( plus_plus_rat @ zero_zero_rat @ A )
% 5.31/5.50 = A ) ).
% 5.31/5.50
% 5.31/5.50 % add.group_left_neutral
% 5.31/5.50 thf(fact_1525_add_Ogroup__left__neutral,axiom,
% 5.31/5.50 ! [A: int] :
% 5.31/5.50 ( ( plus_plus_int @ zero_zero_int @ A )
% 5.31/5.50 = A ) ).
% 5.31/5.50
% 5.31/5.50 % add.group_left_neutral
% 5.31/5.50 thf(fact_1526_add__less__imp__less__right,axiom,
% 5.31/5.50 ! [A: real,C2: real,B: real] :
% 5.31/5.50 ( ( ord_less_real @ ( plus_plus_real @ A @ C2 ) @ ( plus_plus_real @ B @ C2 ) )
% 5.31/5.50 => ( ord_less_real @ A @ B ) ) ).
% 5.31/5.50
% 5.31/5.50 % add_less_imp_less_right
% 5.31/5.50 thf(fact_1527_add__less__imp__less__right,axiom,
% 5.31/5.50 ! [A: rat,C2: rat,B: rat] :
% 5.31/5.50 ( ( ord_less_rat @ ( plus_plus_rat @ A @ C2 ) @ ( plus_plus_rat @ B @ C2 ) )
% 5.31/5.50 => ( ord_less_rat @ A @ B ) ) ).
% 5.31/5.50
% 5.31/5.50 % add_less_imp_less_right
% 5.31/5.50 thf(fact_1528_add__less__imp__less__right,axiom,
% 5.31/5.50 ! [A: nat,C2: nat,B: nat] :
% 5.31/5.50 ( ( ord_less_nat @ ( plus_plus_nat @ A @ C2 ) @ ( plus_plus_nat @ B @ C2 ) )
% 5.31/5.50 => ( ord_less_nat @ A @ B ) ) ).
% 5.31/5.50
% 5.31/5.50 % add_less_imp_less_right
% 5.31/5.50 thf(fact_1529_add__less__imp__less__right,axiom,
% 5.31/5.50 ! [A: int,C2: int,B: int] :
% 5.31/5.50 ( ( ord_less_int @ ( plus_plus_int @ A @ C2 ) @ ( plus_plus_int @ B @ C2 ) )
% 5.31/5.50 => ( ord_less_int @ A @ B ) ) ).
% 5.31/5.50
% 5.31/5.50 % add_less_imp_less_right
% 5.31/5.50 thf(fact_1530_add__less__imp__less__left,axiom,
% 5.31/5.50 ! [C2: real,A: real,B: real] :
% 5.31/5.50 ( ( ord_less_real @ ( plus_plus_real @ C2 @ A ) @ ( plus_plus_real @ C2 @ B ) )
% 5.31/5.50 => ( ord_less_real @ A @ B ) ) ).
% 5.31/5.50
% 5.31/5.50 % add_less_imp_less_left
% 5.31/5.50 thf(fact_1531_add__less__imp__less__left,axiom,
% 5.31/5.50 ! [C2: rat,A: rat,B: rat] :
% 5.31/5.50 ( ( ord_less_rat @ ( plus_plus_rat @ C2 @ A ) @ ( plus_plus_rat @ C2 @ B ) )
% 5.31/5.50 => ( ord_less_rat @ A @ B ) ) ).
% 5.31/5.50
% 5.31/5.50 % add_less_imp_less_left
% 5.31/5.50 thf(fact_1532_add__less__imp__less__left,axiom,
% 5.31/5.50 ! [C2: nat,A: nat,B: nat] :
% 5.31/5.50 ( ( ord_less_nat @ ( plus_plus_nat @ C2 @ A ) @ ( plus_plus_nat @ C2 @ B ) )
% 5.31/5.50 => ( ord_less_nat @ A @ B ) ) ).
% 5.31/5.50
% 5.31/5.50 % add_less_imp_less_left
% 5.31/5.50 thf(fact_1533_add__less__imp__less__left,axiom,
% 5.31/5.50 ! [C2: int,A: int,B: int] :
% 5.31/5.50 ( ( ord_less_int @ ( plus_plus_int @ C2 @ A ) @ ( plus_plus_int @ C2 @ B ) )
% 5.31/5.50 => ( ord_less_int @ A @ B ) ) ).
% 5.31/5.50
% 5.31/5.50 % add_less_imp_less_left
% 5.31/5.50 thf(fact_1534_add__strict__right__mono,axiom,
% 5.31/5.50 ! [A: real,B: real,C2: real] :
% 5.31/5.50 ( ( ord_less_real @ A @ B )
% 5.31/5.50 => ( ord_less_real @ ( plus_plus_real @ A @ C2 ) @ ( plus_plus_real @ B @ C2 ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % add_strict_right_mono
% 5.31/5.50 thf(fact_1535_add__strict__right__mono,axiom,
% 5.31/5.50 ! [A: rat,B: rat,C2: rat] :
% 5.31/5.50 ( ( ord_less_rat @ A @ B )
% 5.31/5.50 => ( ord_less_rat @ ( plus_plus_rat @ A @ C2 ) @ ( plus_plus_rat @ B @ C2 ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % add_strict_right_mono
% 5.31/5.50 thf(fact_1536_add__strict__right__mono,axiom,
% 5.31/5.50 ! [A: nat,B: nat,C2: nat] :
% 5.31/5.50 ( ( ord_less_nat @ A @ B )
% 5.31/5.50 => ( ord_less_nat @ ( plus_plus_nat @ A @ C2 ) @ ( plus_plus_nat @ B @ C2 ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % add_strict_right_mono
% 5.31/5.50 thf(fact_1537_add__strict__right__mono,axiom,
% 5.31/5.50 ! [A: int,B: int,C2: int] :
% 5.31/5.50 ( ( ord_less_int @ A @ B )
% 5.31/5.50 => ( ord_less_int @ ( plus_plus_int @ A @ C2 ) @ ( plus_plus_int @ B @ C2 ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % add_strict_right_mono
% 5.31/5.50 thf(fact_1538_add__strict__left__mono,axiom,
% 5.31/5.50 ! [A: real,B: real,C2: real] :
% 5.31/5.50 ( ( ord_less_real @ A @ B )
% 5.31/5.50 => ( ord_less_real @ ( plus_plus_real @ C2 @ A ) @ ( plus_plus_real @ C2 @ B ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % add_strict_left_mono
% 5.31/5.50 thf(fact_1539_add__strict__left__mono,axiom,
% 5.31/5.50 ! [A: rat,B: rat,C2: rat] :
% 5.31/5.50 ( ( ord_less_rat @ A @ B )
% 5.31/5.50 => ( ord_less_rat @ ( plus_plus_rat @ C2 @ A ) @ ( plus_plus_rat @ C2 @ B ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % add_strict_left_mono
% 5.31/5.50 thf(fact_1540_add__strict__left__mono,axiom,
% 5.31/5.50 ! [A: nat,B: nat,C2: nat] :
% 5.31/5.50 ( ( ord_less_nat @ A @ B )
% 5.31/5.50 => ( ord_less_nat @ ( plus_plus_nat @ C2 @ A ) @ ( plus_plus_nat @ C2 @ B ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % add_strict_left_mono
% 5.31/5.50 thf(fact_1541_add__strict__left__mono,axiom,
% 5.31/5.50 ! [A: int,B: int,C2: int] :
% 5.31/5.50 ( ( ord_less_int @ A @ B )
% 5.31/5.50 => ( ord_less_int @ ( plus_plus_int @ C2 @ A ) @ ( plus_plus_int @ C2 @ B ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % add_strict_left_mono
% 5.31/5.50 thf(fact_1542_add__strict__mono,axiom,
% 5.31/5.50 ! [A: real,B: real,C2: real,D: real] :
% 5.31/5.50 ( ( ord_less_real @ A @ B )
% 5.31/5.50 => ( ( ord_less_real @ C2 @ D )
% 5.31/5.50 => ( ord_less_real @ ( plus_plus_real @ A @ C2 ) @ ( plus_plus_real @ B @ D ) ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % add_strict_mono
% 5.31/5.50 thf(fact_1543_add__strict__mono,axiom,
% 5.31/5.50 ! [A: rat,B: rat,C2: rat,D: rat] :
% 5.31/5.50 ( ( ord_less_rat @ A @ B )
% 5.31/5.50 => ( ( ord_less_rat @ C2 @ D )
% 5.31/5.50 => ( ord_less_rat @ ( plus_plus_rat @ A @ C2 ) @ ( plus_plus_rat @ B @ D ) ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % add_strict_mono
% 5.31/5.50 thf(fact_1544_add__strict__mono,axiom,
% 5.31/5.50 ! [A: nat,B: nat,C2: nat,D: nat] :
% 5.31/5.50 ( ( ord_less_nat @ A @ B )
% 5.31/5.50 => ( ( ord_less_nat @ C2 @ D )
% 5.31/5.50 => ( ord_less_nat @ ( plus_plus_nat @ A @ C2 ) @ ( plus_plus_nat @ B @ D ) ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % add_strict_mono
% 5.31/5.50 thf(fact_1545_add__strict__mono,axiom,
% 5.31/5.50 ! [A: int,B: int,C2: int,D: int] :
% 5.31/5.50 ( ( ord_less_int @ A @ B )
% 5.31/5.50 => ( ( ord_less_int @ C2 @ D )
% 5.31/5.50 => ( ord_less_int @ ( plus_plus_int @ A @ C2 ) @ ( plus_plus_int @ B @ D ) ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % add_strict_mono
% 5.31/5.50 thf(fact_1546_add__mono__thms__linordered__field_I1_J,axiom,
% 5.31/5.50 ! [I2: real,J2: real,K2: real,L: real] :
% 5.31/5.50 ( ( ( ord_less_real @ I2 @ J2 )
% 5.31/5.50 & ( K2 = L ) )
% 5.31/5.50 => ( ord_less_real @ ( plus_plus_real @ I2 @ K2 ) @ ( plus_plus_real @ J2 @ L ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % add_mono_thms_linordered_field(1)
% 5.31/5.50 thf(fact_1547_add__mono__thms__linordered__field_I1_J,axiom,
% 5.31/5.50 ! [I2: rat,J2: rat,K2: rat,L: rat] :
% 5.31/5.50 ( ( ( ord_less_rat @ I2 @ J2 )
% 5.31/5.50 & ( K2 = L ) )
% 5.31/5.50 => ( ord_less_rat @ ( plus_plus_rat @ I2 @ K2 ) @ ( plus_plus_rat @ J2 @ L ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % add_mono_thms_linordered_field(1)
% 5.31/5.50 thf(fact_1548_add__mono__thms__linordered__field_I1_J,axiom,
% 5.31/5.50 ! [I2: nat,J2: nat,K2: nat,L: nat] :
% 5.31/5.50 ( ( ( ord_less_nat @ I2 @ J2 )
% 5.31/5.50 & ( K2 = L ) )
% 5.31/5.50 => ( ord_less_nat @ ( plus_plus_nat @ I2 @ K2 ) @ ( plus_plus_nat @ J2 @ L ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % add_mono_thms_linordered_field(1)
% 5.31/5.50 thf(fact_1549_add__mono__thms__linordered__field_I1_J,axiom,
% 5.31/5.50 ! [I2: int,J2: int,K2: int,L: int] :
% 5.31/5.50 ( ( ( ord_less_int @ I2 @ J2 )
% 5.31/5.50 & ( K2 = L ) )
% 5.31/5.50 => ( ord_less_int @ ( plus_plus_int @ I2 @ K2 ) @ ( plus_plus_int @ J2 @ L ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % add_mono_thms_linordered_field(1)
% 5.31/5.50 thf(fact_1550_add__mono__thms__linordered__field_I2_J,axiom,
% 5.31/5.50 ! [I2: real,J2: real,K2: real,L: real] :
% 5.31/5.50 ( ( ( I2 = J2 )
% 5.31/5.50 & ( ord_less_real @ K2 @ L ) )
% 5.31/5.50 => ( ord_less_real @ ( plus_plus_real @ I2 @ K2 ) @ ( plus_plus_real @ J2 @ L ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % add_mono_thms_linordered_field(2)
% 5.31/5.50 thf(fact_1551_add__mono__thms__linordered__field_I2_J,axiom,
% 5.31/5.50 ! [I2: rat,J2: rat,K2: rat,L: rat] :
% 5.31/5.50 ( ( ( I2 = J2 )
% 5.31/5.50 & ( ord_less_rat @ K2 @ L ) )
% 5.31/5.50 => ( ord_less_rat @ ( plus_plus_rat @ I2 @ K2 ) @ ( plus_plus_rat @ J2 @ L ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % add_mono_thms_linordered_field(2)
% 5.31/5.50 thf(fact_1552_add__mono__thms__linordered__field_I2_J,axiom,
% 5.31/5.50 ! [I2: nat,J2: nat,K2: nat,L: nat] :
% 5.31/5.50 ( ( ( I2 = J2 )
% 5.31/5.50 & ( ord_less_nat @ K2 @ L ) )
% 5.31/5.50 => ( ord_less_nat @ ( plus_plus_nat @ I2 @ K2 ) @ ( plus_plus_nat @ J2 @ L ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % add_mono_thms_linordered_field(2)
% 5.31/5.50 thf(fact_1553_add__mono__thms__linordered__field_I2_J,axiom,
% 5.31/5.50 ! [I2: int,J2: int,K2: int,L: int] :
% 5.31/5.50 ( ( ( I2 = J2 )
% 5.31/5.50 & ( ord_less_int @ K2 @ L ) )
% 5.31/5.50 => ( ord_less_int @ ( plus_plus_int @ I2 @ K2 ) @ ( plus_plus_int @ J2 @ L ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % add_mono_thms_linordered_field(2)
% 5.31/5.50 thf(fact_1554_add__mono__thms__linordered__field_I5_J,axiom,
% 5.31/5.50 ! [I2: real,J2: real,K2: real,L: real] :
% 5.31/5.50 ( ( ( ord_less_real @ I2 @ J2 )
% 5.31/5.50 & ( ord_less_real @ K2 @ L ) )
% 5.31/5.50 => ( ord_less_real @ ( plus_plus_real @ I2 @ K2 ) @ ( plus_plus_real @ J2 @ L ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % add_mono_thms_linordered_field(5)
% 5.31/5.50 thf(fact_1555_add__mono__thms__linordered__field_I5_J,axiom,
% 5.31/5.50 ! [I2: rat,J2: rat,K2: rat,L: rat] :
% 5.31/5.50 ( ( ( ord_less_rat @ I2 @ J2 )
% 5.31/5.50 & ( ord_less_rat @ K2 @ L ) )
% 5.31/5.50 => ( ord_less_rat @ ( plus_plus_rat @ I2 @ K2 ) @ ( plus_plus_rat @ J2 @ L ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % add_mono_thms_linordered_field(5)
% 5.31/5.50 thf(fact_1556_add__mono__thms__linordered__field_I5_J,axiom,
% 5.31/5.50 ! [I2: nat,J2: nat,K2: nat,L: nat] :
% 5.31/5.50 ( ( ( ord_less_nat @ I2 @ J2 )
% 5.31/5.50 & ( ord_less_nat @ K2 @ L ) )
% 5.31/5.50 => ( ord_less_nat @ ( plus_plus_nat @ I2 @ K2 ) @ ( plus_plus_nat @ J2 @ L ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % add_mono_thms_linordered_field(5)
% 5.31/5.50 thf(fact_1557_add__mono__thms__linordered__field_I5_J,axiom,
% 5.31/5.50 ! [I2: int,J2: int,K2: int,L: int] :
% 5.31/5.50 ( ( ( ord_less_int @ I2 @ J2 )
% 5.31/5.50 & ( ord_less_int @ K2 @ L ) )
% 5.31/5.50 => ( ord_less_int @ ( plus_plus_int @ I2 @ K2 ) @ ( plus_plus_int @ J2 @ L ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % add_mono_thms_linordered_field(5)
% 5.31/5.50 thf(fact_1558_ring__class_Oring__distribs_I2_J,axiom,
% 5.31/5.50 ! [A: real,B: real,C2: real] :
% 5.31/5.50 ( ( times_times_real @ ( plus_plus_real @ A @ B ) @ C2 )
% 5.31/5.50 = ( plus_plus_real @ ( times_times_real @ A @ C2 ) @ ( times_times_real @ B @ C2 ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % ring_class.ring_distribs(2)
% 5.31/5.50 thf(fact_1559_ring__class_Oring__distribs_I2_J,axiom,
% 5.31/5.50 ! [A: rat,B: rat,C2: rat] :
% 5.31/5.50 ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ C2 )
% 5.31/5.50 = ( plus_plus_rat @ ( times_times_rat @ A @ C2 ) @ ( times_times_rat @ B @ C2 ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % ring_class.ring_distribs(2)
% 5.31/5.50 thf(fact_1560_ring__class_Oring__distribs_I2_J,axiom,
% 5.31/5.50 ! [A: int,B: int,C2: int] :
% 5.31/5.50 ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C2 )
% 5.31/5.50 = ( plus_plus_int @ ( times_times_int @ A @ C2 ) @ ( times_times_int @ B @ C2 ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % ring_class.ring_distribs(2)
% 5.31/5.50 thf(fact_1561_ring__class_Oring__distribs_I1_J,axiom,
% 5.31/5.50 ! [A: real,B: real,C2: real] :
% 5.31/5.50 ( ( times_times_real @ A @ ( plus_plus_real @ B @ C2 ) )
% 5.31/5.50 = ( plus_plus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C2 ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % ring_class.ring_distribs(1)
% 5.31/5.50 thf(fact_1562_ring__class_Oring__distribs_I1_J,axiom,
% 5.31/5.50 ! [A: rat,B: rat,C2: rat] :
% 5.31/5.50 ( ( times_times_rat @ A @ ( plus_plus_rat @ B @ C2 ) )
% 5.31/5.50 = ( plus_plus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C2 ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % ring_class.ring_distribs(1)
% 5.31/5.50 thf(fact_1563_ring__class_Oring__distribs_I1_J,axiom,
% 5.31/5.50 ! [A: int,B: int,C2: int] :
% 5.31/5.50 ( ( times_times_int @ A @ ( plus_plus_int @ B @ C2 ) )
% 5.31/5.50 = ( plus_plus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C2 ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % ring_class.ring_distribs(1)
% 5.31/5.50 thf(fact_1564_comm__semiring__class_Odistrib,axiom,
% 5.31/5.50 ! [A: real,B: real,C2: real] :
% 5.31/5.50 ( ( times_times_real @ ( plus_plus_real @ A @ B ) @ C2 )
% 5.31/5.50 = ( plus_plus_real @ ( times_times_real @ A @ C2 ) @ ( times_times_real @ B @ C2 ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % comm_semiring_class.distrib
% 5.31/5.50 thf(fact_1565_comm__semiring__class_Odistrib,axiom,
% 5.31/5.50 ! [A: rat,B: rat,C2: rat] :
% 5.31/5.50 ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ C2 )
% 5.31/5.50 = ( plus_plus_rat @ ( times_times_rat @ A @ C2 ) @ ( times_times_rat @ B @ C2 ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % comm_semiring_class.distrib
% 5.31/5.50 thf(fact_1566_comm__semiring__class_Odistrib,axiom,
% 5.31/5.50 ! [A: nat,B: nat,C2: nat] :
% 5.31/5.50 ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ C2 )
% 5.31/5.50 = ( plus_plus_nat @ ( times_times_nat @ A @ C2 ) @ ( times_times_nat @ B @ C2 ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % comm_semiring_class.distrib
% 5.31/5.50 thf(fact_1567_comm__semiring__class_Odistrib,axiom,
% 5.31/5.50 ! [A: int,B: int,C2: int] :
% 5.31/5.50 ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C2 )
% 5.31/5.50 = ( plus_plus_int @ ( times_times_int @ A @ C2 ) @ ( times_times_int @ B @ C2 ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % comm_semiring_class.distrib
% 5.31/5.50 thf(fact_1568_distrib__left,axiom,
% 5.31/5.50 ! [A: real,B: real,C2: real] :
% 5.31/5.50 ( ( times_times_real @ A @ ( plus_plus_real @ B @ C2 ) )
% 5.31/5.50 = ( plus_plus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C2 ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % distrib_left
% 5.31/5.50 thf(fact_1569_distrib__left,axiom,
% 5.31/5.50 ! [A: rat,B: rat,C2: rat] :
% 5.31/5.50 ( ( times_times_rat @ A @ ( plus_plus_rat @ B @ C2 ) )
% 5.31/5.50 = ( plus_plus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C2 ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % distrib_left
% 5.31/5.50 thf(fact_1570_distrib__left,axiom,
% 5.31/5.50 ! [A: nat,B: nat,C2: nat] :
% 5.31/5.50 ( ( times_times_nat @ A @ ( plus_plus_nat @ B @ C2 ) )
% 5.31/5.50 = ( plus_plus_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C2 ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % distrib_left
% 5.31/5.50 thf(fact_1571_distrib__left,axiom,
% 5.31/5.50 ! [A: int,B: int,C2: int] :
% 5.31/5.50 ( ( times_times_int @ A @ ( plus_plus_int @ B @ C2 ) )
% 5.31/5.50 = ( plus_plus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C2 ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % distrib_left
% 5.31/5.50 thf(fact_1572_distrib__right,axiom,
% 5.31/5.50 ! [A: real,B: real,C2: real] :
% 5.31/5.50 ( ( times_times_real @ ( plus_plus_real @ A @ B ) @ C2 )
% 5.31/5.50 = ( plus_plus_real @ ( times_times_real @ A @ C2 ) @ ( times_times_real @ B @ C2 ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % distrib_right
% 5.31/5.50 thf(fact_1573_distrib__right,axiom,
% 5.31/5.50 ! [A: rat,B: rat,C2: rat] :
% 5.31/5.50 ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ C2 )
% 5.31/5.50 = ( plus_plus_rat @ ( times_times_rat @ A @ C2 ) @ ( times_times_rat @ B @ C2 ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % distrib_right
% 5.31/5.50 thf(fact_1574_distrib__right,axiom,
% 5.31/5.50 ! [A: nat,B: nat,C2: nat] :
% 5.31/5.50 ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ C2 )
% 5.31/5.50 = ( plus_plus_nat @ ( times_times_nat @ A @ C2 ) @ ( times_times_nat @ B @ C2 ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % distrib_right
% 5.31/5.50 thf(fact_1575_distrib__right,axiom,
% 5.31/5.50 ! [A: int,B: int,C2: int] :
% 5.31/5.50 ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C2 )
% 5.31/5.50 = ( plus_plus_int @ ( times_times_int @ A @ C2 ) @ ( times_times_int @ B @ C2 ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % distrib_right
% 5.31/5.50 thf(fact_1576_combine__common__factor,axiom,
% 5.31/5.50 ! [A: real,E: real,B: real,C2: real] :
% 5.31/5.50 ( ( plus_plus_real @ ( times_times_real @ A @ E ) @ ( plus_plus_real @ ( times_times_real @ B @ E ) @ C2 ) )
% 5.31/5.50 = ( plus_plus_real @ ( times_times_real @ ( plus_plus_real @ A @ B ) @ E ) @ C2 ) ) ).
% 5.31/5.50
% 5.31/5.50 % combine_common_factor
% 5.31/5.50 thf(fact_1577_combine__common__factor,axiom,
% 5.31/5.50 ! [A: rat,E: rat,B: rat,C2: rat] :
% 5.31/5.50 ( ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ C2 ) )
% 5.31/5.50 = ( plus_plus_rat @ ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ E ) @ C2 ) ) ).
% 5.31/5.50
% 5.31/5.50 % combine_common_factor
% 5.31/5.50 thf(fact_1578_combine__common__factor,axiom,
% 5.31/5.50 ! [A: nat,E: nat,B: nat,C2: nat] :
% 5.31/5.50 ( ( plus_plus_nat @ ( times_times_nat @ A @ E ) @ ( plus_plus_nat @ ( times_times_nat @ B @ E ) @ C2 ) )
% 5.31/5.50 = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ E ) @ C2 ) ) ).
% 5.31/5.50
% 5.31/5.50 % combine_common_factor
% 5.31/5.50 thf(fact_1579_combine__common__factor,axiom,
% 5.31/5.50 ! [A: int,E: int,B: int,C2: int] :
% 5.31/5.50 ( ( plus_plus_int @ ( times_times_int @ A @ E ) @ ( plus_plus_int @ ( times_times_int @ B @ E ) @ C2 ) )
% 5.31/5.50 = ( plus_plus_int @ ( times_times_int @ ( plus_plus_int @ A @ B ) @ E ) @ C2 ) ) ).
% 5.31/5.50
% 5.31/5.50 % combine_common_factor
% 5.31/5.50 thf(fact_1580_combine__options__cases,axiom,
% 5.31/5.50 ! [X: option4927543243414619207at_nat,P2: option4927543243414619207at_nat > option4927543243414619207at_nat > $o,Y: option4927543243414619207at_nat] :
% 5.31/5.50 ( ( ( X = none_P5556105721700978146at_nat )
% 5.31/5.50 => ( P2 @ X @ Y ) )
% 5.31/5.50 => ( ( ( Y = none_P5556105721700978146at_nat )
% 5.31/5.50 => ( P2 @ X @ Y ) )
% 5.31/5.50 => ( ! [A3: product_prod_nat_nat,B3: product_prod_nat_nat] :
% 5.31/5.50 ( ( X
% 5.31/5.50 = ( some_P7363390416028606310at_nat @ A3 ) )
% 5.31/5.50 => ( ( Y
% 5.31/5.50 = ( some_P7363390416028606310at_nat @ B3 ) )
% 5.31/5.50 => ( P2 @ X @ Y ) ) )
% 5.31/5.50 => ( P2 @ X @ Y ) ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % combine_options_cases
% 5.31/5.50 thf(fact_1581_combine__options__cases,axiom,
% 5.31/5.50 ! [X: option4927543243414619207at_nat,P2: option4927543243414619207at_nat > option_nat > $o,Y: option_nat] :
% 5.31/5.50 ( ( ( X = none_P5556105721700978146at_nat )
% 5.31/5.50 => ( P2 @ X @ Y ) )
% 5.31/5.50 => ( ( ( Y = none_nat )
% 5.31/5.50 => ( P2 @ X @ Y ) )
% 5.31/5.50 => ( ! [A3: product_prod_nat_nat,B3: nat] :
% 5.31/5.50 ( ( X
% 5.31/5.50 = ( some_P7363390416028606310at_nat @ A3 ) )
% 5.31/5.50 => ( ( Y
% 5.31/5.50 = ( some_nat @ B3 ) )
% 5.31/5.50 => ( P2 @ X @ Y ) ) )
% 5.31/5.50 => ( P2 @ X @ Y ) ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % combine_options_cases
% 5.31/5.50 thf(fact_1582_combine__options__cases,axiom,
% 5.31/5.50 ! [X: option4927543243414619207at_nat,P2: option4927543243414619207at_nat > option_num > $o,Y: option_num] :
% 5.31/5.50 ( ( ( X = none_P5556105721700978146at_nat )
% 5.31/5.50 => ( P2 @ X @ Y ) )
% 5.31/5.50 => ( ( ( Y = none_num )
% 5.31/5.50 => ( P2 @ X @ Y ) )
% 5.31/5.50 => ( ! [A3: product_prod_nat_nat,B3: num] :
% 5.31/5.50 ( ( X
% 5.31/5.50 = ( some_P7363390416028606310at_nat @ A3 ) )
% 5.31/5.50 => ( ( Y
% 5.31/5.50 = ( some_num @ B3 ) )
% 5.31/5.50 => ( P2 @ X @ Y ) ) )
% 5.31/5.50 => ( P2 @ X @ Y ) ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % combine_options_cases
% 5.31/5.50 thf(fact_1583_combine__options__cases,axiom,
% 5.31/5.50 ! [X: option_nat,P2: option_nat > option4927543243414619207at_nat > $o,Y: option4927543243414619207at_nat] :
% 5.31/5.50 ( ( ( X = none_nat )
% 5.31/5.50 => ( P2 @ X @ Y ) )
% 5.31/5.50 => ( ( ( Y = none_P5556105721700978146at_nat )
% 5.31/5.50 => ( P2 @ X @ Y ) )
% 5.31/5.50 => ( ! [A3: nat,B3: product_prod_nat_nat] :
% 5.31/5.50 ( ( X
% 5.31/5.50 = ( some_nat @ A3 ) )
% 5.31/5.50 => ( ( Y
% 5.31/5.50 = ( some_P7363390416028606310at_nat @ B3 ) )
% 5.31/5.50 => ( P2 @ X @ Y ) ) )
% 5.31/5.50 => ( P2 @ X @ Y ) ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % combine_options_cases
% 5.31/5.50 thf(fact_1584_combine__options__cases,axiom,
% 5.31/5.50 ! [X: option_nat,P2: option_nat > option_nat > $o,Y: option_nat] :
% 5.31/5.50 ( ( ( X = none_nat )
% 5.31/5.50 => ( P2 @ X @ Y ) )
% 5.31/5.50 => ( ( ( Y = none_nat )
% 5.31/5.50 => ( P2 @ X @ Y ) )
% 5.31/5.50 => ( ! [A3: nat,B3: nat] :
% 5.31/5.50 ( ( X
% 5.31/5.50 = ( some_nat @ A3 ) )
% 5.31/5.50 => ( ( Y
% 5.31/5.50 = ( some_nat @ B3 ) )
% 5.31/5.50 => ( P2 @ X @ Y ) ) )
% 5.31/5.50 => ( P2 @ X @ Y ) ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % combine_options_cases
% 5.31/5.50 thf(fact_1585_combine__options__cases,axiom,
% 5.31/5.50 ! [X: option_nat,P2: option_nat > option_num > $o,Y: option_num] :
% 5.31/5.50 ( ( ( X = none_nat )
% 5.31/5.50 => ( P2 @ X @ Y ) )
% 5.31/5.50 => ( ( ( Y = none_num )
% 5.31/5.50 => ( P2 @ X @ Y ) )
% 5.31/5.50 => ( ! [A3: nat,B3: num] :
% 5.31/5.50 ( ( X
% 5.31/5.50 = ( some_nat @ A3 ) )
% 5.31/5.50 => ( ( Y
% 5.31/5.50 = ( some_num @ B3 ) )
% 5.31/5.50 => ( P2 @ X @ Y ) ) )
% 5.31/5.50 => ( P2 @ X @ Y ) ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % combine_options_cases
% 5.31/5.50 thf(fact_1586_combine__options__cases,axiom,
% 5.31/5.50 ! [X: option_num,P2: option_num > option4927543243414619207at_nat > $o,Y: option4927543243414619207at_nat] :
% 5.31/5.50 ( ( ( X = none_num )
% 5.31/5.50 => ( P2 @ X @ Y ) )
% 5.31/5.50 => ( ( ( Y = none_P5556105721700978146at_nat )
% 5.31/5.50 => ( P2 @ X @ Y ) )
% 5.31/5.50 => ( ! [A3: num,B3: product_prod_nat_nat] :
% 5.31/5.50 ( ( X
% 5.31/5.50 = ( some_num @ A3 ) )
% 5.31/5.50 => ( ( Y
% 5.31/5.50 = ( some_P7363390416028606310at_nat @ B3 ) )
% 5.31/5.50 => ( P2 @ X @ Y ) ) )
% 5.31/5.50 => ( P2 @ X @ Y ) ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % combine_options_cases
% 5.31/5.50 thf(fact_1587_combine__options__cases,axiom,
% 5.31/5.50 ! [X: option_num,P2: option_num > option_nat > $o,Y: option_nat] :
% 5.31/5.50 ( ( ( X = none_num )
% 5.31/5.50 => ( P2 @ X @ Y ) )
% 5.31/5.50 => ( ( ( Y = none_nat )
% 5.31/5.50 => ( P2 @ X @ Y ) )
% 5.31/5.50 => ( ! [A3: num,B3: nat] :
% 5.31/5.50 ( ( X
% 5.31/5.50 = ( some_num @ A3 ) )
% 5.31/5.50 => ( ( Y
% 5.31/5.50 = ( some_nat @ B3 ) )
% 5.31/5.50 => ( P2 @ X @ Y ) ) )
% 5.31/5.50 => ( P2 @ X @ Y ) ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % combine_options_cases
% 5.31/5.50 thf(fact_1588_combine__options__cases,axiom,
% 5.31/5.50 ! [X: option_num,P2: option_num > option_num > $o,Y: option_num] :
% 5.31/5.50 ( ( ( X = none_num )
% 5.31/5.50 => ( P2 @ X @ Y ) )
% 5.31/5.50 => ( ( ( Y = none_num )
% 5.31/5.50 => ( P2 @ X @ Y ) )
% 5.31/5.50 => ( ! [A3: num,B3: num] :
% 5.31/5.50 ( ( X
% 5.31/5.50 = ( some_num @ A3 ) )
% 5.31/5.50 => ( ( Y
% 5.31/5.50 = ( some_num @ B3 ) )
% 5.31/5.50 => ( P2 @ X @ Y ) ) )
% 5.31/5.50 => ( P2 @ X @ Y ) ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % combine_options_cases
% 5.31/5.50 thf(fact_1589_split__option__all,axiom,
% 5.31/5.50 ( ( ^ [P3: option4927543243414619207at_nat > $o] :
% 5.31/5.50 ! [X6: option4927543243414619207at_nat] : ( P3 @ X6 ) )
% 5.31/5.50 = ( ^ [P4: option4927543243414619207at_nat > $o] :
% 5.31/5.50 ( ( P4 @ none_P5556105721700978146at_nat )
% 5.31/5.50 & ! [X4: product_prod_nat_nat] : ( P4 @ ( some_P7363390416028606310at_nat @ X4 ) ) ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % split_option_all
% 5.31/5.50 thf(fact_1590_split__option__all,axiom,
% 5.31/5.50 ( ( ^ [P3: option_nat > $o] :
% 5.31/5.50 ! [X6: option_nat] : ( P3 @ X6 ) )
% 5.31/5.50 = ( ^ [P4: option_nat > $o] :
% 5.31/5.50 ( ( P4 @ none_nat )
% 5.31/5.50 & ! [X4: nat] : ( P4 @ ( some_nat @ X4 ) ) ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % split_option_all
% 5.31/5.50 thf(fact_1591_split__option__all,axiom,
% 5.31/5.50 ( ( ^ [P3: option_num > $o] :
% 5.31/5.50 ! [X6: option_num] : ( P3 @ X6 ) )
% 5.31/5.50 = ( ^ [P4: option_num > $o] :
% 5.31/5.50 ( ( P4 @ none_num )
% 5.31/5.50 & ! [X4: num] : ( P4 @ ( some_num @ X4 ) ) ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % split_option_all
% 5.31/5.50 thf(fact_1592_split__option__ex,axiom,
% 5.31/5.50 ( ( ^ [P3: option4927543243414619207at_nat > $o] :
% 5.31/5.50 ? [X6: option4927543243414619207at_nat] : ( P3 @ X6 ) )
% 5.31/5.50 = ( ^ [P4: option4927543243414619207at_nat > $o] :
% 5.31/5.50 ( ( P4 @ none_P5556105721700978146at_nat )
% 5.31/5.50 | ? [X4: product_prod_nat_nat] : ( P4 @ ( some_P7363390416028606310at_nat @ X4 ) ) ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % split_option_ex
% 5.31/5.50 thf(fact_1593_split__option__ex,axiom,
% 5.31/5.50 ( ( ^ [P3: option_nat > $o] :
% 5.31/5.50 ? [X6: option_nat] : ( P3 @ X6 ) )
% 5.31/5.50 = ( ^ [P4: option_nat > $o] :
% 5.31/5.50 ( ( P4 @ none_nat )
% 5.31/5.50 | ? [X4: nat] : ( P4 @ ( some_nat @ X4 ) ) ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % split_option_ex
% 5.31/5.50 thf(fact_1594_split__option__ex,axiom,
% 5.31/5.50 ( ( ^ [P3: option_num > $o] :
% 5.31/5.50 ? [X6: option_num] : ( P3 @ X6 ) )
% 5.31/5.50 = ( ^ [P4: option_num > $o] :
% 5.31/5.50 ( ( P4 @ none_num )
% 5.31/5.50 | ? [X4: num] : ( P4 @ ( some_num @ X4 ) ) ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % split_option_ex
% 5.31/5.50 thf(fact_1595_option_Oexhaust,axiom,
% 5.31/5.50 ! [Y: option4927543243414619207at_nat] :
% 5.31/5.50 ( ( Y != none_P5556105721700978146at_nat )
% 5.31/5.50 => ~ ! [X23: product_prod_nat_nat] :
% 5.31/5.50 ( Y
% 5.31/5.50 != ( some_P7363390416028606310at_nat @ X23 ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % option.exhaust
% 5.31/5.50 thf(fact_1596_option_Oexhaust,axiom,
% 5.31/5.50 ! [Y: option_nat] :
% 5.31/5.50 ( ( Y != none_nat )
% 5.31/5.50 => ~ ! [X23: nat] :
% 5.31/5.50 ( Y
% 5.31/5.50 != ( some_nat @ X23 ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % option.exhaust
% 5.31/5.50 thf(fact_1597_option_Oexhaust,axiom,
% 5.31/5.50 ! [Y: option_num] :
% 5.31/5.50 ( ( Y != none_num )
% 5.31/5.50 => ~ ! [X23: num] :
% 5.31/5.50 ( Y
% 5.31/5.50 != ( some_num @ X23 ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % option.exhaust
% 5.31/5.50 thf(fact_1598_option_OdiscI,axiom,
% 5.31/5.50 ! [Option: option4927543243414619207at_nat,X2: product_prod_nat_nat] :
% 5.31/5.50 ( ( Option
% 5.31/5.50 = ( some_P7363390416028606310at_nat @ X2 ) )
% 5.31/5.50 => ( Option != none_P5556105721700978146at_nat ) ) ).
% 5.31/5.50
% 5.31/5.50 % option.discI
% 5.31/5.50 thf(fact_1599_option_OdiscI,axiom,
% 5.31/5.50 ! [Option: option_nat,X2: nat] :
% 5.31/5.50 ( ( Option
% 5.31/5.50 = ( some_nat @ X2 ) )
% 5.31/5.50 => ( Option != none_nat ) ) ).
% 5.31/5.50
% 5.31/5.50 % option.discI
% 5.31/5.50 thf(fact_1600_option_OdiscI,axiom,
% 5.31/5.50 ! [Option: option_num,X2: num] :
% 5.31/5.50 ( ( Option
% 5.31/5.50 = ( some_num @ X2 ) )
% 5.31/5.50 => ( Option != none_num ) ) ).
% 5.31/5.50
% 5.31/5.50 % option.discI
% 5.31/5.50 thf(fact_1601_option_Odistinct_I1_J,axiom,
% 5.31/5.50 ! [X2: product_prod_nat_nat] :
% 5.31/5.50 ( none_P5556105721700978146at_nat
% 5.31/5.50 != ( some_P7363390416028606310at_nat @ X2 ) ) ).
% 5.31/5.50
% 5.31/5.50 % option.distinct(1)
% 5.31/5.50 thf(fact_1602_option_Odistinct_I1_J,axiom,
% 5.31/5.50 ! [X2: nat] :
% 5.31/5.50 ( none_nat
% 5.31/5.50 != ( some_nat @ X2 ) ) ).
% 5.31/5.50
% 5.31/5.50 % option.distinct(1)
% 5.31/5.50 thf(fact_1603_option_Odistinct_I1_J,axiom,
% 5.31/5.50 ! [X2: num] :
% 5.31/5.50 ( none_num
% 5.31/5.50 != ( some_num @ X2 ) ) ).
% 5.31/5.50
% 5.31/5.50 % option.distinct(1)
% 5.31/5.50 thf(fact_1604_VEBT__internal_Ooption__shift_Ocases,axiom,
% 5.31/5.50 ! [X: produc5542196010084753463at_nat] :
% 5.31/5.50 ( ! [Uu2: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,Uv2: option4927543243414619207at_nat] :
% 5.31/5.50 ( X
% 5.31/5.50 != ( produc2899441246263362727at_nat @ Uu2 @ ( produc488173922507101015at_nat @ none_P5556105721700978146at_nat @ Uv2 ) ) )
% 5.31/5.50 => ( ! [Uw: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,V: product_prod_nat_nat] :
% 5.31/5.50 ( X
% 5.31/5.50 != ( produc2899441246263362727at_nat @ Uw @ ( produc488173922507101015at_nat @ ( some_P7363390416028606310at_nat @ V ) @ none_P5556105721700978146at_nat ) ) )
% 5.31/5.50 => ~ ! [F: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,A3: product_prod_nat_nat,B3: product_prod_nat_nat] :
% 5.31/5.50 ( X
% 5.31/5.50 != ( produc2899441246263362727at_nat @ F @ ( produc488173922507101015at_nat @ ( some_P7363390416028606310at_nat @ A3 ) @ ( some_P7363390416028606310at_nat @ B3 ) ) ) ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % VEBT_internal.option_shift.cases
% 5.31/5.50 thf(fact_1605_VEBT__internal_Ooption__shift_Ocases,axiom,
% 5.31/5.50 ! [X: produc8306885398267862888on_nat] :
% 5.31/5.50 ( ! [Uu2: nat > nat > nat,Uv2: option_nat] :
% 5.31/5.50 ( X
% 5.31/5.50 != ( produc8929957630744042906on_nat @ Uu2 @ ( produc5098337634421038937on_nat @ none_nat @ Uv2 ) ) )
% 5.31/5.50 => ( ! [Uw: nat > nat > nat,V: nat] :
% 5.31/5.50 ( X
% 5.31/5.50 != ( produc8929957630744042906on_nat @ Uw @ ( produc5098337634421038937on_nat @ ( some_nat @ V ) @ none_nat ) ) )
% 5.31/5.50 => ~ ! [F: nat > nat > nat,A3: nat,B3: nat] :
% 5.31/5.50 ( X
% 5.31/5.50 != ( produc8929957630744042906on_nat @ F @ ( produc5098337634421038937on_nat @ ( some_nat @ A3 ) @ ( some_nat @ B3 ) ) ) ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % VEBT_internal.option_shift.cases
% 5.31/5.50 thf(fact_1606_VEBT__internal_Ooption__shift_Ocases,axiom,
% 5.31/5.50 ! [X: produc1193250871479095198on_num] :
% 5.31/5.50 ( ! [Uu2: num > num > num,Uv2: option_num] :
% 5.31/5.50 ( X
% 5.31/5.50 != ( produc5778274026573060048on_num @ Uu2 @ ( produc8585076106096196333on_num @ none_num @ Uv2 ) ) )
% 5.31/5.50 => ( ! [Uw: num > num > num,V: num] :
% 5.31/5.50 ( X
% 5.31/5.50 != ( produc5778274026573060048on_num @ Uw @ ( produc8585076106096196333on_num @ ( some_num @ V ) @ none_num ) ) )
% 5.31/5.50 => ~ ! [F: num > num > num,A3: num,B3: num] :
% 5.31/5.50 ( X
% 5.31/5.50 != ( produc5778274026573060048on_num @ F @ ( produc8585076106096196333on_num @ ( some_num @ A3 ) @ ( some_num @ B3 ) ) ) ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % VEBT_internal.option_shift.cases
% 5.31/5.50 thf(fact_1607_VEBT__internal_Ooption__comp__shift_Ocases,axiom,
% 5.31/5.50 ! [X: produc5491161045314408544at_nat] :
% 5.31/5.50 ( ! [Uu2: product_prod_nat_nat > product_prod_nat_nat > $o,Uv2: option4927543243414619207at_nat] :
% 5.31/5.50 ( X
% 5.31/5.50 != ( produc3994169339658061776at_nat @ Uu2 @ ( produc488173922507101015at_nat @ none_P5556105721700978146at_nat @ Uv2 ) ) )
% 5.31/5.50 => ( ! [Uw: product_prod_nat_nat > product_prod_nat_nat > $o,V: product_prod_nat_nat] :
% 5.31/5.50 ( X
% 5.31/5.50 != ( produc3994169339658061776at_nat @ Uw @ ( produc488173922507101015at_nat @ ( some_P7363390416028606310at_nat @ V ) @ none_P5556105721700978146at_nat ) ) )
% 5.31/5.50 => ~ ! [F: product_prod_nat_nat > product_prod_nat_nat > $o,X3: product_prod_nat_nat,Y3: product_prod_nat_nat] :
% 5.31/5.50 ( X
% 5.31/5.50 != ( produc3994169339658061776at_nat @ F @ ( produc488173922507101015at_nat @ ( some_P7363390416028606310at_nat @ X3 ) @ ( some_P7363390416028606310at_nat @ Y3 ) ) ) ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % VEBT_internal.option_comp_shift.cases
% 5.31/5.50 thf(fact_1608_VEBT__internal_Ooption__comp__shift_Ocases,axiom,
% 5.31/5.50 ! [X: produc2233624965454879586on_nat] :
% 5.31/5.50 ( ! [Uu2: nat > nat > $o,Uv2: option_nat] :
% 5.31/5.50 ( X
% 5.31/5.50 != ( produc4035269172776083154on_nat @ Uu2 @ ( produc5098337634421038937on_nat @ none_nat @ Uv2 ) ) )
% 5.31/5.50 => ( ! [Uw: nat > nat > $o,V: nat] :
% 5.31/5.50 ( X
% 5.31/5.50 != ( produc4035269172776083154on_nat @ Uw @ ( produc5098337634421038937on_nat @ ( some_nat @ V ) @ none_nat ) ) )
% 5.31/5.50 => ~ ! [F: nat > nat > $o,X3: nat,Y3: nat] :
% 5.31/5.50 ( X
% 5.31/5.50 != ( produc4035269172776083154on_nat @ F @ ( produc5098337634421038937on_nat @ ( some_nat @ X3 ) @ ( some_nat @ Y3 ) ) ) ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % VEBT_internal.option_comp_shift.cases
% 5.31/5.50 thf(fact_1609_VEBT__internal_Ooption__comp__shift_Ocases,axiom,
% 5.31/5.50 ! [X: produc7036089656553540234on_num] :
% 5.31/5.50 ( ! [Uu2: num > num > $o,Uv2: option_num] :
% 5.31/5.50 ( X
% 5.31/5.50 != ( produc3576312749637752826on_num @ Uu2 @ ( produc8585076106096196333on_num @ none_num @ Uv2 ) ) )
% 5.31/5.50 => ( ! [Uw: num > num > $o,V: num] :
% 5.31/5.50 ( X
% 5.31/5.50 != ( produc3576312749637752826on_num @ Uw @ ( produc8585076106096196333on_num @ ( some_num @ V ) @ none_num ) ) )
% 5.31/5.50 => ~ ! [F: num > num > $o,X3: num,Y3: num] :
% 5.31/5.50 ( X
% 5.31/5.50 != ( produc3576312749637752826on_num @ F @ ( produc8585076106096196333on_num @ ( some_num @ X3 ) @ ( some_num @ Y3 ) ) ) ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % VEBT_internal.option_comp_shift.cases
% 5.31/5.50 thf(fact_1610_nat__arith_Osuc1,axiom,
% 5.31/5.50 ! [A4: nat,K2: nat,A: nat] :
% 5.31/5.50 ( ( A4
% 5.31/5.50 = ( plus_plus_nat @ K2 @ A ) )
% 5.31/5.50 => ( ( suc @ A4 )
% 5.31/5.50 = ( plus_plus_nat @ K2 @ ( suc @ A ) ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % nat_arith.suc1
% 5.31/5.50 thf(fact_1611_add__Suc,axiom,
% 5.31/5.50 ! [M2: nat,N: nat] :
% 5.31/5.50 ( ( plus_plus_nat @ ( suc @ M2 ) @ N )
% 5.31/5.50 = ( suc @ ( plus_plus_nat @ M2 @ N ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % add_Suc
% 5.31/5.50 thf(fact_1612_add__Suc__shift,axiom,
% 5.31/5.50 ! [M2: nat,N: nat] :
% 5.31/5.50 ( ( plus_plus_nat @ ( suc @ M2 ) @ N )
% 5.31/5.50 = ( plus_plus_nat @ M2 @ ( suc @ N ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % add_Suc_shift
% 5.31/5.50 thf(fact_1613_add__eq__self__zero,axiom,
% 5.31/5.50 ! [M2: nat,N: nat] :
% 5.31/5.50 ( ( ( plus_plus_nat @ M2 @ N )
% 5.31/5.50 = M2 )
% 5.31/5.50 => ( N = zero_zero_nat ) ) ).
% 5.31/5.50
% 5.31/5.50 % add_eq_self_zero
% 5.31/5.50 thf(fact_1614_plus__nat_Oadd__0,axiom,
% 5.31/5.50 ! [N: nat] :
% 5.31/5.50 ( ( plus_plus_nat @ zero_zero_nat @ N )
% 5.31/5.50 = N ) ).
% 5.31/5.50
% 5.31/5.50 % plus_nat.add_0
% 5.31/5.50 thf(fact_1615_less__add__eq__less,axiom,
% 5.31/5.50 ! [K2: nat,L: nat,M2: nat,N: nat] :
% 5.31/5.50 ( ( ord_less_nat @ K2 @ L )
% 5.31/5.50 => ( ( ( plus_plus_nat @ M2 @ L )
% 5.31/5.50 = ( plus_plus_nat @ K2 @ N ) )
% 5.31/5.50 => ( ord_less_nat @ M2 @ N ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % less_add_eq_less
% 5.31/5.50 thf(fact_1616_trans__less__add2,axiom,
% 5.31/5.50 ! [I2: nat,J2: nat,M2: nat] :
% 5.31/5.50 ( ( ord_less_nat @ I2 @ J2 )
% 5.31/5.50 => ( ord_less_nat @ I2 @ ( plus_plus_nat @ M2 @ J2 ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % trans_less_add2
% 5.31/5.50 thf(fact_1617_trans__less__add1,axiom,
% 5.31/5.50 ! [I2: nat,J2: nat,M2: nat] :
% 5.31/5.50 ( ( ord_less_nat @ I2 @ J2 )
% 5.31/5.50 => ( ord_less_nat @ I2 @ ( plus_plus_nat @ J2 @ M2 ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % trans_less_add1
% 5.31/5.50 thf(fact_1618_add__less__mono1,axiom,
% 5.31/5.50 ! [I2: nat,J2: nat,K2: nat] :
% 5.31/5.50 ( ( ord_less_nat @ I2 @ J2 )
% 5.31/5.50 => ( ord_less_nat @ ( plus_plus_nat @ I2 @ K2 ) @ ( plus_plus_nat @ J2 @ K2 ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % add_less_mono1
% 5.31/5.50 thf(fact_1619_not__add__less2,axiom,
% 5.31/5.50 ! [J2: nat,I2: nat] :
% 5.31/5.50 ~ ( ord_less_nat @ ( plus_plus_nat @ J2 @ I2 ) @ I2 ) ).
% 5.31/5.50
% 5.31/5.50 % not_add_less2
% 5.31/5.50 thf(fact_1620_not__add__less1,axiom,
% 5.31/5.50 ! [I2: nat,J2: nat] :
% 5.31/5.50 ~ ( ord_less_nat @ ( plus_plus_nat @ I2 @ J2 ) @ I2 ) ).
% 5.31/5.50
% 5.31/5.50 % not_add_less1
% 5.31/5.50 thf(fact_1621_add__less__mono,axiom,
% 5.31/5.50 ! [I2: nat,J2: nat,K2: nat,L: nat] :
% 5.31/5.50 ( ( ord_less_nat @ I2 @ J2 )
% 5.31/5.50 => ( ( ord_less_nat @ K2 @ L )
% 5.31/5.50 => ( ord_less_nat @ ( plus_plus_nat @ I2 @ K2 ) @ ( plus_plus_nat @ J2 @ L ) ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % add_less_mono
% 5.31/5.50 thf(fact_1622_add__lessD1,axiom,
% 5.31/5.50 ! [I2: nat,J2: nat,K2: nat] :
% 5.31/5.50 ( ( ord_less_nat @ ( plus_plus_nat @ I2 @ J2 ) @ K2 )
% 5.31/5.50 => ( ord_less_nat @ I2 @ K2 ) ) ).
% 5.31/5.50
% 5.31/5.50 % add_lessD1
% 5.31/5.50 thf(fact_1623_add__leE,axiom,
% 5.31/5.50 ! [M2: nat,K2: nat,N: nat] :
% 5.31/5.50 ( ( ord_less_eq_nat @ ( plus_plus_nat @ M2 @ K2 ) @ N )
% 5.31/5.50 => ~ ( ( ord_less_eq_nat @ M2 @ N )
% 5.31/5.50 => ~ ( ord_less_eq_nat @ K2 @ N ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % add_leE
% 5.31/5.50 thf(fact_1624_le__add1,axiom,
% 5.31/5.50 ! [N: nat,M2: nat] : ( ord_less_eq_nat @ N @ ( plus_plus_nat @ N @ M2 ) ) ).
% 5.31/5.50
% 5.31/5.50 % le_add1
% 5.31/5.50 thf(fact_1625_le__add2,axiom,
% 5.31/5.50 ! [N: nat,M2: nat] : ( ord_less_eq_nat @ N @ ( plus_plus_nat @ M2 @ N ) ) ).
% 5.31/5.50
% 5.31/5.50 % le_add2
% 5.31/5.50 thf(fact_1626_add__leD1,axiom,
% 5.31/5.50 ! [M2: nat,K2: nat,N: nat] :
% 5.31/5.50 ( ( ord_less_eq_nat @ ( plus_plus_nat @ M2 @ K2 ) @ N )
% 5.31/5.50 => ( ord_less_eq_nat @ M2 @ N ) ) ).
% 5.31/5.50
% 5.31/5.50 % add_leD1
% 5.31/5.50 thf(fact_1627_add__leD2,axiom,
% 5.31/5.50 ! [M2: nat,K2: nat,N: nat] :
% 5.31/5.50 ( ( ord_less_eq_nat @ ( plus_plus_nat @ M2 @ K2 ) @ N )
% 5.31/5.50 => ( ord_less_eq_nat @ K2 @ N ) ) ).
% 5.31/5.50
% 5.31/5.50 % add_leD2
% 5.31/5.50 thf(fact_1628_le__Suc__ex,axiom,
% 5.31/5.50 ! [K2: nat,L: nat] :
% 5.31/5.50 ( ( ord_less_eq_nat @ K2 @ L )
% 5.31/5.50 => ? [N3: nat] :
% 5.31/5.50 ( L
% 5.31/5.50 = ( plus_plus_nat @ K2 @ N3 ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % le_Suc_ex
% 5.31/5.50 thf(fact_1629_add__le__mono,axiom,
% 5.31/5.50 ! [I2: nat,J2: nat,K2: nat,L: nat] :
% 5.31/5.50 ( ( ord_less_eq_nat @ I2 @ J2 )
% 5.31/5.50 => ( ( ord_less_eq_nat @ K2 @ L )
% 5.31/5.50 => ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K2 ) @ ( plus_plus_nat @ J2 @ L ) ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % add_le_mono
% 5.31/5.50 thf(fact_1630_add__le__mono1,axiom,
% 5.31/5.50 ! [I2: nat,J2: nat,K2: nat] :
% 5.31/5.50 ( ( ord_less_eq_nat @ I2 @ J2 )
% 5.31/5.50 => ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K2 ) @ ( plus_plus_nat @ J2 @ K2 ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % add_le_mono1
% 5.31/5.50 thf(fact_1631_trans__le__add1,axiom,
% 5.31/5.50 ! [I2: nat,J2: nat,M2: nat] :
% 5.31/5.50 ( ( ord_less_eq_nat @ I2 @ J2 )
% 5.31/5.50 => ( ord_less_eq_nat @ I2 @ ( plus_plus_nat @ J2 @ M2 ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % trans_le_add1
% 5.31/5.50 thf(fact_1632_trans__le__add2,axiom,
% 5.31/5.50 ! [I2: nat,J2: nat,M2: nat] :
% 5.31/5.50 ( ( ord_less_eq_nat @ I2 @ J2 )
% 5.31/5.50 => ( ord_less_eq_nat @ I2 @ ( plus_plus_nat @ M2 @ J2 ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % trans_le_add2
% 5.31/5.50 thf(fact_1633_nat__le__iff__add,axiom,
% 5.31/5.50 ( ord_less_eq_nat
% 5.31/5.50 = ( ^ [M6: nat,N4: nat] :
% 5.31/5.50 ? [K3: nat] :
% 5.31/5.50 ( N4
% 5.31/5.50 = ( plus_plus_nat @ M6 @ K3 ) ) ) ) ).
% 5.31/5.50
% 5.31/5.50 % nat_le_iff_add
% 5.31/5.50 thf(fact_1634_add__mult__distrib2,axiom,
% 5.31/5.50 ! [K2: nat,M2: nat,N: nat] :
% 5.31/5.51 ( ( times_times_nat @ K2 @ ( plus_plus_nat @ M2 @ N ) )
% 5.31/5.51 = ( plus_plus_nat @ ( times_times_nat @ K2 @ M2 ) @ ( times_times_nat @ K2 @ N ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % add_mult_distrib2
% 5.31/5.51 thf(fact_1635_add__mult__distrib,axiom,
% 5.31/5.51 ! [M2: nat,N: nat,K2: nat] :
% 5.31/5.51 ( ( times_times_nat @ ( plus_plus_nat @ M2 @ N ) @ K2 )
% 5.31/5.51 = ( plus_plus_nat @ ( times_times_nat @ M2 @ K2 ) @ ( times_times_nat @ N @ K2 ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % add_mult_distrib
% 5.31/5.51 thf(fact_1636_left__add__mult__distrib,axiom,
% 5.31/5.51 ! [I2: nat,U: nat,J2: nat,K2: nat] :
% 5.31/5.51 ( ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ ( plus_plus_nat @ ( times_times_nat @ J2 @ U ) @ K2 ) )
% 5.31/5.51 = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ I2 @ J2 ) @ U ) @ K2 ) ) ).
% 5.31/5.51
% 5.31/5.51 % left_add_mult_distrib
% 5.31/5.51 thf(fact_1637_VEBT__internal_Omembermima_Osimps_I1_J,axiom,
% 5.31/5.51 ! [Uu: $o,Uv: $o,Uw2: nat] :
% 5.31/5.51 ~ ( vEBT_VEBT_membermima @ ( vEBT_Leaf @ Uu @ Uv ) @ Uw2 ) ).
% 5.31/5.51
% 5.31/5.51 % VEBT_internal.membermima.simps(1)
% 5.31/5.51 thf(fact_1638_add__decreasing,axiom,
% 5.31/5.51 ! [A: real,C2: real,B: real] :
% 5.31/5.51 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.31/5.51 => ( ( ord_less_eq_real @ C2 @ B )
% 5.31/5.51 => ( ord_less_eq_real @ ( plus_plus_real @ A @ C2 ) @ B ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % add_decreasing
% 5.31/5.51 thf(fact_1639_add__decreasing,axiom,
% 5.31/5.51 ! [A: rat,C2: rat,B: rat] :
% 5.31/5.51 ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.31/5.51 => ( ( ord_less_eq_rat @ C2 @ B )
% 5.31/5.51 => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C2 ) @ B ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % add_decreasing
% 5.31/5.51 thf(fact_1640_add__decreasing,axiom,
% 5.31/5.51 ! [A: nat,C2: nat,B: nat] :
% 5.31/5.51 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 5.31/5.51 => ( ( ord_less_eq_nat @ C2 @ B )
% 5.31/5.51 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C2 ) @ B ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % add_decreasing
% 5.31/5.51 thf(fact_1641_add__decreasing,axiom,
% 5.31/5.51 ! [A: int,C2: int,B: int] :
% 5.31/5.51 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.31/5.51 => ( ( ord_less_eq_int @ C2 @ B )
% 5.31/5.51 => ( ord_less_eq_int @ ( plus_plus_int @ A @ C2 ) @ B ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % add_decreasing
% 5.31/5.51 thf(fact_1642_add__increasing,axiom,
% 5.31/5.51 ! [A: real,B: real,C2: real] :
% 5.31/5.51 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.31/5.51 => ( ( ord_less_eq_real @ B @ C2 )
% 5.31/5.51 => ( ord_less_eq_real @ B @ ( plus_plus_real @ A @ C2 ) ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % add_increasing
% 5.31/5.51 thf(fact_1643_add__increasing,axiom,
% 5.31/5.51 ! [A: rat,B: rat,C2: rat] :
% 5.31/5.51 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.31/5.51 => ( ( ord_less_eq_rat @ B @ C2 )
% 5.31/5.51 => ( ord_less_eq_rat @ B @ ( plus_plus_rat @ A @ C2 ) ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % add_increasing
% 5.31/5.51 thf(fact_1644_add__increasing,axiom,
% 5.31/5.51 ! [A: nat,B: nat,C2: nat] :
% 5.31/5.51 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.31/5.51 => ( ( ord_less_eq_nat @ B @ C2 )
% 5.31/5.51 => ( ord_less_eq_nat @ B @ ( plus_plus_nat @ A @ C2 ) ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % add_increasing
% 5.31/5.51 thf(fact_1645_add__increasing,axiom,
% 5.31/5.51 ! [A: int,B: int,C2: int] :
% 5.31/5.51 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.31/5.51 => ( ( ord_less_eq_int @ B @ C2 )
% 5.31/5.51 => ( ord_less_eq_int @ B @ ( plus_plus_int @ A @ C2 ) ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % add_increasing
% 5.31/5.51 thf(fact_1646_add__decreasing2,axiom,
% 5.31/5.51 ! [C2: real,A: real,B: real] :
% 5.31/5.51 ( ( ord_less_eq_real @ C2 @ zero_zero_real )
% 5.31/5.51 => ( ( ord_less_eq_real @ A @ B )
% 5.31/5.51 => ( ord_less_eq_real @ ( plus_plus_real @ A @ C2 ) @ B ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % add_decreasing2
% 5.31/5.51 thf(fact_1647_add__decreasing2,axiom,
% 5.31/5.51 ! [C2: rat,A: rat,B: rat] :
% 5.31/5.51 ( ( ord_less_eq_rat @ C2 @ zero_zero_rat )
% 5.31/5.51 => ( ( ord_less_eq_rat @ A @ B )
% 5.31/5.51 => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C2 ) @ B ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % add_decreasing2
% 5.31/5.51 thf(fact_1648_add__decreasing2,axiom,
% 5.31/5.51 ! [C2: nat,A: nat,B: nat] :
% 5.31/5.51 ( ( ord_less_eq_nat @ C2 @ zero_zero_nat )
% 5.31/5.51 => ( ( ord_less_eq_nat @ A @ B )
% 5.31/5.51 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C2 ) @ B ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % add_decreasing2
% 5.31/5.51 thf(fact_1649_add__decreasing2,axiom,
% 5.31/5.51 ! [C2: int,A: int,B: int] :
% 5.31/5.51 ( ( ord_less_eq_int @ C2 @ zero_zero_int )
% 5.31/5.51 => ( ( ord_less_eq_int @ A @ B )
% 5.31/5.51 => ( ord_less_eq_int @ ( plus_plus_int @ A @ C2 ) @ B ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % add_decreasing2
% 5.31/5.51 thf(fact_1650_add__increasing2,axiom,
% 5.31/5.51 ! [C2: real,B: real,A: real] :
% 5.31/5.51 ( ( ord_less_eq_real @ zero_zero_real @ C2 )
% 5.31/5.51 => ( ( ord_less_eq_real @ B @ A )
% 5.31/5.51 => ( ord_less_eq_real @ B @ ( plus_plus_real @ A @ C2 ) ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % add_increasing2
% 5.31/5.51 thf(fact_1651_add__increasing2,axiom,
% 5.31/5.51 ! [C2: rat,B: rat,A: rat] :
% 5.31/5.51 ( ( ord_less_eq_rat @ zero_zero_rat @ C2 )
% 5.31/5.51 => ( ( ord_less_eq_rat @ B @ A )
% 5.31/5.51 => ( ord_less_eq_rat @ B @ ( plus_plus_rat @ A @ C2 ) ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % add_increasing2
% 5.31/5.51 thf(fact_1652_add__increasing2,axiom,
% 5.31/5.51 ! [C2: nat,B: nat,A: nat] :
% 5.31/5.51 ( ( ord_less_eq_nat @ zero_zero_nat @ C2 )
% 5.31/5.51 => ( ( ord_less_eq_nat @ B @ A )
% 5.31/5.51 => ( ord_less_eq_nat @ B @ ( plus_plus_nat @ A @ C2 ) ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % add_increasing2
% 5.31/5.51 thf(fact_1653_add__increasing2,axiom,
% 5.31/5.51 ! [C2: int,B: int,A: int] :
% 5.31/5.51 ( ( ord_less_eq_int @ zero_zero_int @ C2 )
% 5.31/5.51 => ( ( ord_less_eq_int @ B @ A )
% 5.31/5.51 => ( ord_less_eq_int @ B @ ( plus_plus_int @ A @ C2 ) ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % add_increasing2
% 5.31/5.51 thf(fact_1654_add__nonneg__nonneg,axiom,
% 5.31/5.51 ! [A: real,B: real] :
% 5.31/5.51 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.31/5.51 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.31/5.51 => ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % add_nonneg_nonneg
% 5.31/5.51 thf(fact_1655_add__nonneg__nonneg,axiom,
% 5.31/5.51 ! [A: rat,B: rat] :
% 5.31/5.51 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.31/5.51 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.31/5.51 => ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % add_nonneg_nonneg
% 5.31/5.51 thf(fact_1656_add__nonneg__nonneg,axiom,
% 5.31/5.51 ! [A: nat,B: nat] :
% 5.31/5.51 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.31/5.51 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.31/5.51 => ( ord_less_eq_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % add_nonneg_nonneg
% 5.31/5.51 thf(fact_1657_add__nonneg__nonneg,axiom,
% 5.31/5.51 ! [A: int,B: int] :
% 5.31/5.51 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.31/5.51 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.31/5.51 => ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % add_nonneg_nonneg
% 5.31/5.51 thf(fact_1658_add__nonpos__nonpos,axiom,
% 5.31/5.51 ! [A: real,B: real] :
% 5.31/5.51 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.31/5.51 => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 5.31/5.51 => ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % add_nonpos_nonpos
% 5.31/5.51 thf(fact_1659_add__nonpos__nonpos,axiom,
% 5.31/5.51 ! [A: rat,B: rat] :
% 5.31/5.51 ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.31/5.51 => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 5.31/5.51 => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % add_nonpos_nonpos
% 5.31/5.51 thf(fact_1660_add__nonpos__nonpos,axiom,
% 5.31/5.51 ! [A: nat,B: nat] :
% 5.31/5.51 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 5.31/5.51 => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 5.31/5.51 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % add_nonpos_nonpos
% 5.31/5.51 thf(fact_1661_add__nonpos__nonpos,axiom,
% 5.31/5.51 ! [A: int,B: int] :
% 5.31/5.51 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.31/5.51 => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 5.31/5.51 => ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % add_nonpos_nonpos
% 5.31/5.51 thf(fact_1662_add__nonneg__eq__0__iff,axiom,
% 5.31/5.51 ! [X: real,Y: real] :
% 5.31/5.51 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.31/5.51 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.31/5.51 => ( ( ( plus_plus_real @ X @ Y )
% 5.31/5.51 = zero_zero_real )
% 5.31/5.51 = ( ( X = zero_zero_real )
% 5.31/5.51 & ( Y = zero_zero_real ) ) ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % add_nonneg_eq_0_iff
% 5.31/5.51 thf(fact_1663_add__nonneg__eq__0__iff,axiom,
% 5.31/5.51 ! [X: rat,Y: rat] :
% 5.31/5.51 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 5.31/5.51 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 5.31/5.51 => ( ( ( plus_plus_rat @ X @ Y )
% 5.31/5.51 = zero_zero_rat )
% 5.31/5.51 = ( ( X = zero_zero_rat )
% 5.31/5.51 & ( Y = zero_zero_rat ) ) ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % add_nonneg_eq_0_iff
% 5.31/5.51 thf(fact_1664_add__nonneg__eq__0__iff,axiom,
% 5.31/5.51 ! [X: nat,Y: nat] :
% 5.31/5.51 ( ( ord_less_eq_nat @ zero_zero_nat @ X )
% 5.31/5.51 => ( ( ord_less_eq_nat @ zero_zero_nat @ Y )
% 5.31/5.51 => ( ( ( plus_plus_nat @ X @ Y )
% 5.31/5.51 = zero_zero_nat )
% 5.31/5.51 = ( ( X = zero_zero_nat )
% 5.31/5.51 & ( Y = zero_zero_nat ) ) ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % add_nonneg_eq_0_iff
% 5.31/5.51 thf(fact_1665_add__nonneg__eq__0__iff,axiom,
% 5.31/5.51 ! [X: int,Y: int] :
% 5.31/5.51 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.31/5.51 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.31/5.51 => ( ( ( plus_plus_int @ X @ Y )
% 5.31/5.51 = zero_zero_int )
% 5.31/5.51 = ( ( X = zero_zero_int )
% 5.31/5.51 & ( Y = zero_zero_int ) ) ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % add_nonneg_eq_0_iff
% 5.31/5.51 thf(fact_1666_add__nonpos__eq__0__iff,axiom,
% 5.31/5.51 ! [X: real,Y: real] :
% 5.31/5.51 ( ( ord_less_eq_real @ X @ zero_zero_real )
% 5.31/5.51 => ( ( ord_less_eq_real @ Y @ zero_zero_real )
% 5.31/5.51 => ( ( ( plus_plus_real @ X @ Y )
% 5.31/5.51 = zero_zero_real )
% 5.31/5.51 = ( ( X = zero_zero_real )
% 5.31/5.51 & ( Y = zero_zero_real ) ) ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % add_nonpos_eq_0_iff
% 5.31/5.51 thf(fact_1667_add__nonpos__eq__0__iff,axiom,
% 5.31/5.51 ! [X: rat,Y: rat] :
% 5.31/5.51 ( ( ord_less_eq_rat @ X @ zero_zero_rat )
% 5.31/5.51 => ( ( ord_less_eq_rat @ Y @ zero_zero_rat )
% 5.31/5.51 => ( ( ( plus_plus_rat @ X @ Y )
% 5.31/5.51 = zero_zero_rat )
% 5.31/5.51 = ( ( X = zero_zero_rat )
% 5.31/5.51 & ( Y = zero_zero_rat ) ) ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % add_nonpos_eq_0_iff
% 5.31/5.51 thf(fact_1668_add__nonpos__eq__0__iff,axiom,
% 5.31/5.51 ! [X: nat,Y: nat] :
% 5.31/5.51 ( ( ord_less_eq_nat @ X @ zero_zero_nat )
% 5.31/5.51 => ( ( ord_less_eq_nat @ Y @ zero_zero_nat )
% 5.31/5.51 => ( ( ( plus_plus_nat @ X @ Y )
% 5.31/5.51 = zero_zero_nat )
% 5.31/5.51 = ( ( X = zero_zero_nat )
% 5.31/5.51 & ( Y = zero_zero_nat ) ) ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % add_nonpos_eq_0_iff
% 5.31/5.51 thf(fact_1669_add__nonpos__eq__0__iff,axiom,
% 5.31/5.51 ! [X: int,Y: int] :
% 5.31/5.51 ( ( ord_less_eq_int @ X @ zero_zero_int )
% 5.31/5.51 => ( ( ord_less_eq_int @ Y @ zero_zero_int )
% 5.31/5.51 => ( ( ( plus_plus_int @ X @ Y )
% 5.31/5.51 = zero_zero_int )
% 5.31/5.51 = ( ( X = zero_zero_int )
% 5.31/5.51 & ( Y = zero_zero_int ) ) ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % add_nonpos_eq_0_iff
% 5.31/5.51 thf(fact_1670_add__less__le__mono,axiom,
% 5.31/5.51 ! [A: real,B: real,C2: real,D: real] :
% 5.31/5.51 ( ( ord_less_real @ A @ B )
% 5.31/5.51 => ( ( ord_less_eq_real @ C2 @ D )
% 5.31/5.51 => ( ord_less_real @ ( plus_plus_real @ A @ C2 ) @ ( plus_plus_real @ B @ D ) ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % add_less_le_mono
% 5.31/5.51 thf(fact_1671_add__less__le__mono,axiom,
% 5.31/5.51 ! [A: rat,B: rat,C2: rat,D: rat] :
% 5.31/5.51 ( ( ord_less_rat @ A @ B )
% 5.31/5.51 => ( ( ord_less_eq_rat @ C2 @ D )
% 5.31/5.51 => ( ord_less_rat @ ( plus_plus_rat @ A @ C2 ) @ ( plus_plus_rat @ B @ D ) ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % add_less_le_mono
% 5.31/5.51 thf(fact_1672_add__less__le__mono,axiom,
% 5.31/5.51 ! [A: nat,B: nat,C2: nat,D: nat] :
% 5.31/5.51 ( ( ord_less_nat @ A @ B )
% 5.31/5.51 => ( ( ord_less_eq_nat @ C2 @ D )
% 5.31/5.51 => ( ord_less_nat @ ( plus_plus_nat @ A @ C2 ) @ ( plus_plus_nat @ B @ D ) ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % add_less_le_mono
% 5.31/5.51 thf(fact_1673_add__less__le__mono,axiom,
% 5.31/5.51 ! [A: int,B: int,C2: int,D: int] :
% 5.31/5.51 ( ( ord_less_int @ A @ B )
% 5.31/5.51 => ( ( ord_less_eq_int @ C2 @ D )
% 5.31/5.51 => ( ord_less_int @ ( plus_plus_int @ A @ C2 ) @ ( plus_plus_int @ B @ D ) ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % add_less_le_mono
% 5.31/5.51 thf(fact_1674_add__le__less__mono,axiom,
% 5.31/5.51 ! [A: real,B: real,C2: real,D: real] :
% 5.31/5.51 ( ( ord_less_eq_real @ A @ B )
% 5.31/5.51 => ( ( ord_less_real @ C2 @ D )
% 5.31/5.51 => ( ord_less_real @ ( plus_plus_real @ A @ C2 ) @ ( plus_plus_real @ B @ D ) ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % add_le_less_mono
% 5.31/5.51 thf(fact_1675_add__le__less__mono,axiom,
% 5.31/5.51 ! [A: rat,B: rat,C2: rat,D: rat] :
% 5.31/5.51 ( ( ord_less_eq_rat @ A @ B )
% 5.31/5.51 => ( ( ord_less_rat @ C2 @ D )
% 5.31/5.51 => ( ord_less_rat @ ( plus_plus_rat @ A @ C2 ) @ ( plus_plus_rat @ B @ D ) ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % add_le_less_mono
% 5.31/5.51 thf(fact_1676_add__le__less__mono,axiom,
% 5.31/5.51 ! [A: nat,B: nat,C2: nat,D: nat] :
% 5.31/5.51 ( ( ord_less_eq_nat @ A @ B )
% 5.31/5.51 => ( ( ord_less_nat @ C2 @ D )
% 5.31/5.51 => ( ord_less_nat @ ( plus_plus_nat @ A @ C2 ) @ ( plus_plus_nat @ B @ D ) ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % add_le_less_mono
% 5.31/5.51 thf(fact_1677_add__le__less__mono,axiom,
% 5.31/5.51 ! [A: int,B: int,C2: int,D: int] :
% 5.31/5.51 ( ( ord_less_eq_int @ A @ B )
% 5.31/5.51 => ( ( ord_less_int @ C2 @ D )
% 5.31/5.51 => ( ord_less_int @ ( plus_plus_int @ A @ C2 ) @ ( plus_plus_int @ B @ D ) ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % add_le_less_mono
% 5.31/5.51 thf(fact_1678_add__mono__thms__linordered__field_I3_J,axiom,
% 5.31/5.51 ! [I2: real,J2: real,K2: real,L: real] :
% 5.31/5.51 ( ( ( ord_less_real @ I2 @ J2 )
% 5.31/5.51 & ( ord_less_eq_real @ K2 @ L ) )
% 5.31/5.51 => ( ord_less_real @ ( plus_plus_real @ I2 @ K2 ) @ ( plus_plus_real @ J2 @ L ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % add_mono_thms_linordered_field(3)
% 5.31/5.51 thf(fact_1679_add__mono__thms__linordered__field_I3_J,axiom,
% 5.31/5.51 ! [I2: rat,J2: rat,K2: rat,L: rat] :
% 5.31/5.51 ( ( ( ord_less_rat @ I2 @ J2 )
% 5.31/5.51 & ( ord_less_eq_rat @ K2 @ L ) )
% 5.31/5.51 => ( ord_less_rat @ ( plus_plus_rat @ I2 @ K2 ) @ ( plus_plus_rat @ J2 @ L ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % add_mono_thms_linordered_field(3)
% 5.31/5.51 thf(fact_1680_add__mono__thms__linordered__field_I3_J,axiom,
% 5.31/5.51 ! [I2: nat,J2: nat,K2: nat,L: nat] :
% 5.31/5.51 ( ( ( ord_less_nat @ I2 @ J2 )
% 5.31/5.51 & ( ord_less_eq_nat @ K2 @ L ) )
% 5.31/5.51 => ( ord_less_nat @ ( plus_plus_nat @ I2 @ K2 ) @ ( plus_plus_nat @ J2 @ L ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % add_mono_thms_linordered_field(3)
% 5.31/5.51 thf(fact_1681_add__mono__thms__linordered__field_I3_J,axiom,
% 5.31/5.51 ! [I2: int,J2: int,K2: int,L: int] :
% 5.31/5.51 ( ( ( ord_less_int @ I2 @ J2 )
% 5.31/5.51 & ( ord_less_eq_int @ K2 @ L ) )
% 5.31/5.51 => ( ord_less_int @ ( plus_plus_int @ I2 @ K2 ) @ ( plus_plus_int @ J2 @ L ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % add_mono_thms_linordered_field(3)
% 5.31/5.51 thf(fact_1682_add__mono__thms__linordered__field_I4_J,axiom,
% 5.31/5.51 ! [I2: real,J2: real,K2: real,L: real] :
% 5.31/5.51 ( ( ( ord_less_eq_real @ I2 @ J2 )
% 5.31/5.51 & ( ord_less_real @ K2 @ L ) )
% 5.31/5.51 => ( ord_less_real @ ( plus_plus_real @ I2 @ K2 ) @ ( plus_plus_real @ J2 @ L ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % add_mono_thms_linordered_field(4)
% 5.31/5.51 thf(fact_1683_add__mono__thms__linordered__field_I4_J,axiom,
% 5.31/5.51 ! [I2: rat,J2: rat,K2: rat,L: rat] :
% 5.31/5.51 ( ( ( ord_less_eq_rat @ I2 @ J2 )
% 5.31/5.51 & ( ord_less_rat @ K2 @ L ) )
% 5.31/5.51 => ( ord_less_rat @ ( plus_plus_rat @ I2 @ K2 ) @ ( plus_plus_rat @ J2 @ L ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % add_mono_thms_linordered_field(4)
% 5.31/5.51 thf(fact_1684_add__mono__thms__linordered__field_I4_J,axiom,
% 5.31/5.51 ! [I2: nat,J2: nat,K2: nat,L: nat] :
% 5.31/5.51 ( ( ( ord_less_eq_nat @ I2 @ J2 )
% 5.31/5.51 & ( ord_less_nat @ K2 @ L ) )
% 5.31/5.51 => ( ord_less_nat @ ( plus_plus_nat @ I2 @ K2 ) @ ( plus_plus_nat @ J2 @ L ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % add_mono_thms_linordered_field(4)
% 5.31/5.51 thf(fact_1685_add__mono__thms__linordered__field_I4_J,axiom,
% 5.31/5.51 ! [I2: int,J2: int,K2: int,L: int] :
% 5.31/5.51 ( ( ( ord_less_eq_int @ I2 @ J2 )
% 5.31/5.51 & ( ord_less_int @ K2 @ L ) )
% 5.31/5.51 => ( ord_less_int @ ( plus_plus_int @ I2 @ K2 ) @ ( plus_plus_int @ J2 @ L ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % add_mono_thms_linordered_field(4)
% 5.31/5.51 thf(fact_1686_add__less__zeroD,axiom,
% 5.31/5.51 ! [X: real,Y: real] :
% 5.31/5.51 ( ( ord_less_real @ ( plus_plus_real @ X @ Y ) @ zero_zero_real )
% 5.31/5.51 => ( ( ord_less_real @ X @ zero_zero_real )
% 5.31/5.51 | ( ord_less_real @ Y @ zero_zero_real ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % add_less_zeroD
% 5.31/5.51 thf(fact_1687_add__less__zeroD,axiom,
% 5.31/5.51 ! [X: rat,Y: rat] :
% 5.31/5.51 ( ( ord_less_rat @ ( plus_plus_rat @ X @ Y ) @ zero_zero_rat )
% 5.31/5.51 => ( ( ord_less_rat @ X @ zero_zero_rat )
% 5.31/5.51 | ( ord_less_rat @ Y @ zero_zero_rat ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % add_less_zeroD
% 5.31/5.51 thf(fact_1688_add__less__zeroD,axiom,
% 5.31/5.51 ! [X: int,Y: int] :
% 5.31/5.51 ( ( ord_less_int @ ( plus_plus_int @ X @ Y ) @ zero_zero_int )
% 5.31/5.51 => ( ( ord_less_int @ X @ zero_zero_int )
% 5.31/5.51 | ( ord_less_int @ Y @ zero_zero_int ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % add_less_zeroD
% 5.31/5.51 thf(fact_1689_pos__add__strict,axiom,
% 5.31/5.51 ! [A: real,B: real,C2: real] :
% 5.31/5.51 ( ( ord_less_real @ zero_zero_real @ A )
% 5.31/5.51 => ( ( ord_less_real @ B @ C2 )
% 5.31/5.51 => ( ord_less_real @ B @ ( plus_plus_real @ A @ C2 ) ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % pos_add_strict
% 5.31/5.51 thf(fact_1690_pos__add__strict,axiom,
% 5.31/5.51 ! [A: rat,B: rat,C2: rat] :
% 5.31/5.51 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.31/5.51 => ( ( ord_less_rat @ B @ C2 )
% 5.31/5.51 => ( ord_less_rat @ B @ ( plus_plus_rat @ A @ C2 ) ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % pos_add_strict
% 5.31/5.51 thf(fact_1691_pos__add__strict,axiom,
% 5.31/5.51 ! [A: nat,B: nat,C2: nat] :
% 5.31/5.51 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.31/5.51 => ( ( ord_less_nat @ B @ C2 )
% 5.31/5.51 => ( ord_less_nat @ B @ ( plus_plus_nat @ A @ C2 ) ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % pos_add_strict
% 5.31/5.51 thf(fact_1692_pos__add__strict,axiom,
% 5.31/5.51 ! [A: int,B: int,C2: int] :
% 5.31/5.51 ( ( ord_less_int @ zero_zero_int @ A )
% 5.31/5.51 => ( ( ord_less_int @ B @ C2 )
% 5.31/5.51 => ( ord_less_int @ B @ ( plus_plus_int @ A @ C2 ) ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % pos_add_strict
% 5.31/5.51 thf(fact_1693_canonically__ordered__monoid__add__class_OlessE,axiom,
% 5.31/5.51 ! [A: nat,B: nat] :
% 5.31/5.51 ( ( ord_less_nat @ A @ B )
% 5.31/5.51 => ~ ! [C: nat] :
% 5.31/5.51 ( ( B
% 5.31/5.51 = ( plus_plus_nat @ A @ C ) )
% 5.31/5.51 => ( C = zero_zero_nat ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % canonically_ordered_monoid_add_class.lessE
% 5.31/5.51 thf(fact_1694_add__pos__pos,axiom,
% 5.31/5.51 ! [A: real,B: real] :
% 5.31/5.51 ( ( ord_less_real @ zero_zero_real @ A )
% 5.31/5.51 => ( ( ord_less_real @ zero_zero_real @ B )
% 5.31/5.51 => ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % add_pos_pos
% 5.31/5.51 thf(fact_1695_add__pos__pos,axiom,
% 5.31/5.51 ! [A: rat,B: rat] :
% 5.31/5.51 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.31/5.51 => ( ( ord_less_rat @ zero_zero_rat @ B )
% 5.31/5.51 => ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % add_pos_pos
% 5.31/5.51 thf(fact_1696_add__pos__pos,axiom,
% 5.31/5.51 ! [A: nat,B: nat] :
% 5.31/5.51 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.31/5.51 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.31/5.51 => ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % add_pos_pos
% 5.31/5.51 thf(fact_1697_add__pos__pos,axiom,
% 5.31/5.51 ! [A: int,B: int] :
% 5.31/5.51 ( ( ord_less_int @ zero_zero_int @ A )
% 5.31/5.51 => ( ( ord_less_int @ zero_zero_int @ B )
% 5.31/5.51 => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % add_pos_pos
% 5.31/5.51 thf(fact_1698_add__neg__neg,axiom,
% 5.31/5.51 ! [A: real,B: real] :
% 5.31/5.51 ( ( ord_less_real @ A @ zero_zero_real )
% 5.31/5.51 => ( ( ord_less_real @ B @ zero_zero_real )
% 5.31/5.51 => ( ord_less_real @ ( plus_plus_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % add_neg_neg
% 5.31/5.51 thf(fact_1699_add__neg__neg,axiom,
% 5.31/5.51 ! [A: rat,B: rat] :
% 5.31/5.51 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.31/5.51 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 5.31/5.51 => ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % add_neg_neg
% 5.31/5.51 thf(fact_1700_add__neg__neg,axiom,
% 5.31/5.51 ! [A: nat,B: nat] :
% 5.31/5.51 ( ( ord_less_nat @ A @ zero_zero_nat )
% 5.31/5.51 => ( ( ord_less_nat @ B @ zero_zero_nat )
% 5.31/5.51 => ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % add_neg_neg
% 5.31/5.51 thf(fact_1701_add__neg__neg,axiom,
% 5.31/5.51 ! [A: int,B: int] :
% 5.31/5.51 ( ( ord_less_int @ A @ zero_zero_int )
% 5.31/5.51 => ( ( ord_less_int @ B @ zero_zero_int )
% 5.31/5.51 => ( ord_less_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % add_neg_neg
% 5.31/5.51 thf(fact_1702_add__mono1,axiom,
% 5.31/5.51 ! [A: code_integer,B: code_integer] :
% 5.31/5.51 ( ( ord_le6747313008572928689nteger @ A @ B )
% 5.31/5.51 => ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ A @ one_one_Code_integer ) @ ( plus_p5714425477246183910nteger @ B @ one_one_Code_integer ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % add_mono1
% 5.31/5.51 thf(fact_1703_add__mono1,axiom,
% 5.31/5.51 ! [A: real,B: real] :
% 5.31/5.51 ( ( ord_less_real @ A @ B )
% 5.31/5.51 => ( ord_less_real @ ( plus_plus_real @ A @ one_one_real ) @ ( plus_plus_real @ B @ one_one_real ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % add_mono1
% 5.31/5.51 thf(fact_1704_add__mono1,axiom,
% 5.31/5.51 ! [A: rat,B: rat] :
% 5.31/5.51 ( ( ord_less_rat @ A @ B )
% 5.31/5.51 => ( ord_less_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( plus_plus_rat @ B @ one_one_rat ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % add_mono1
% 5.31/5.51 thf(fact_1705_add__mono1,axiom,
% 5.31/5.51 ! [A: nat,B: nat] :
% 5.31/5.51 ( ( ord_less_nat @ A @ B )
% 5.31/5.51 => ( ord_less_nat @ ( plus_plus_nat @ A @ one_one_nat ) @ ( plus_plus_nat @ B @ one_one_nat ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % add_mono1
% 5.31/5.51 thf(fact_1706_add__mono1,axiom,
% 5.31/5.51 ! [A: int,B: int] :
% 5.31/5.51 ( ( ord_less_int @ A @ B )
% 5.31/5.51 => ( ord_less_int @ ( plus_plus_int @ A @ one_one_int ) @ ( plus_plus_int @ B @ one_one_int ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % add_mono1
% 5.31/5.51 thf(fact_1707_less__add__one,axiom,
% 5.31/5.51 ! [A: code_integer] : ( ord_le6747313008572928689nteger @ A @ ( plus_p5714425477246183910nteger @ A @ one_one_Code_integer ) ) ).
% 5.31/5.51
% 5.31/5.51 % less_add_one
% 5.31/5.51 thf(fact_1708_less__add__one,axiom,
% 5.31/5.51 ! [A: real] : ( ord_less_real @ A @ ( plus_plus_real @ A @ one_one_real ) ) ).
% 5.31/5.51
% 5.31/5.51 % less_add_one
% 5.31/5.51 thf(fact_1709_less__add__one,axiom,
% 5.31/5.51 ! [A: rat] : ( ord_less_rat @ A @ ( plus_plus_rat @ A @ one_one_rat ) ) ).
% 5.31/5.51
% 5.31/5.51 % less_add_one
% 5.31/5.51 thf(fact_1710_less__add__one,axiom,
% 5.31/5.51 ! [A: nat] : ( ord_less_nat @ A @ ( plus_plus_nat @ A @ one_one_nat ) ) ).
% 5.31/5.51
% 5.31/5.51 % less_add_one
% 5.31/5.51 thf(fact_1711_less__add__one,axiom,
% 5.31/5.51 ! [A: int] : ( ord_less_int @ A @ ( plus_plus_int @ A @ one_one_int ) ) ).
% 5.31/5.51
% 5.31/5.51 % less_add_one
% 5.31/5.51 thf(fact_1712_add__is__1,axiom,
% 5.31/5.51 ! [M2: nat,N: nat] :
% 5.31/5.51 ( ( ( plus_plus_nat @ M2 @ N )
% 5.31/5.51 = ( suc @ zero_zero_nat ) )
% 5.31/5.51 = ( ( ( M2
% 5.31/5.51 = ( suc @ zero_zero_nat ) )
% 5.31/5.51 & ( N = zero_zero_nat ) )
% 5.31/5.51 | ( ( M2 = zero_zero_nat )
% 5.31/5.51 & ( N
% 5.31/5.51 = ( suc @ zero_zero_nat ) ) ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % add_is_1
% 5.31/5.51 thf(fact_1713_one__is__add,axiom,
% 5.31/5.51 ! [M2: nat,N: nat] :
% 5.31/5.51 ( ( ( suc @ zero_zero_nat )
% 5.31/5.51 = ( plus_plus_nat @ M2 @ N ) )
% 5.31/5.51 = ( ( ( M2
% 5.31/5.51 = ( suc @ zero_zero_nat ) )
% 5.31/5.51 & ( N = zero_zero_nat ) )
% 5.31/5.51 | ( ( M2 = zero_zero_nat )
% 5.31/5.51 & ( N
% 5.31/5.51 = ( suc @ zero_zero_nat ) ) ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % one_is_add
% 5.31/5.51 thf(fact_1714_less__natE,axiom,
% 5.31/5.51 ! [M2: nat,N: nat] :
% 5.31/5.51 ( ( ord_less_nat @ M2 @ N )
% 5.31/5.51 => ~ ! [Q3: nat] :
% 5.31/5.51 ( N
% 5.31/5.51 != ( suc @ ( plus_plus_nat @ M2 @ Q3 ) ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % less_natE
% 5.31/5.51 thf(fact_1715_less__add__Suc1,axiom,
% 5.31/5.51 ! [I2: nat,M2: nat] : ( ord_less_nat @ I2 @ ( suc @ ( plus_plus_nat @ I2 @ M2 ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % less_add_Suc1
% 5.31/5.51 thf(fact_1716_less__add__Suc2,axiom,
% 5.31/5.51 ! [I2: nat,M2: nat] : ( ord_less_nat @ I2 @ ( suc @ ( plus_plus_nat @ M2 @ I2 ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % less_add_Suc2
% 5.31/5.51 thf(fact_1717_less__iff__Suc__add,axiom,
% 5.31/5.51 ( ord_less_nat
% 5.31/5.51 = ( ^ [M6: nat,N4: nat] :
% 5.31/5.51 ? [K3: nat] :
% 5.31/5.51 ( N4
% 5.31/5.51 = ( suc @ ( plus_plus_nat @ M6 @ K3 ) ) ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % less_iff_Suc_add
% 5.31/5.51 thf(fact_1718_less__imp__Suc__add,axiom,
% 5.31/5.51 ! [M2: nat,N: nat] :
% 5.31/5.51 ( ( ord_less_nat @ M2 @ N )
% 5.31/5.51 => ? [K: nat] :
% 5.31/5.51 ( N
% 5.31/5.51 = ( suc @ ( plus_plus_nat @ M2 @ K ) ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % less_imp_Suc_add
% 5.31/5.51 thf(fact_1719_less__imp__add__positive,axiom,
% 5.31/5.51 ! [I2: nat,J2: nat] :
% 5.31/5.51 ( ( ord_less_nat @ I2 @ J2 )
% 5.31/5.51 => ? [K: nat] :
% 5.31/5.51 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.31/5.51 & ( ( plus_plus_nat @ I2 @ K )
% 5.31/5.51 = J2 ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % less_imp_add_positive
% 5.31/5.51 thf(fact_1720_mono__nat__linear__lb,axiom,
% 5.31/5.51 ! [F2: nat > nat,M2: nat,K2: nat] :
% 5.31/5.51 ( ! [M: nat,N3: nat] :
% 5.31/5.51 ( ( ord_less_nat @ M @ N3 )
% 5.31/5.51 => ( ord_less_nat @ ( F2 @ M ) @ ( F2 @ N3 ) ) )
% 5.31/5.51 => ( ord_less_eq_nat @ ( plus_plus_nat @ ( F2 @ M2 ) @ K2 ) @ ( F2 @ ( plus_plus_nat @ M2 @ K2 ) ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % mono_nat_linear_lb
% 5.31/5.51 thf(fact_1721_mult__Suc,axiom,
% 5.31/5.51 ! [M2: nat,N: nat] :
% 5.31/5.51 ( ( times_times_nat @ ( suc @ M2 ) @ N )
% 5.31/5.51 = ( plus_plus_nat @ N @ ( times_times_nat @ M2 @ N ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % mult_Suc
% 5.31/5.51 thf(fact_1722_Suc__eq__plus1,axiom,
% 5.31/5.51 ( suc
% 5.31/5.51 = ( ^ [N4: nat] : ( plus_plus_nat @ N4 @ one_one_nat ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % Suc_eq_plus1
% 5.31/5.51 thf(fact_1723_plus__1__eq__Suc,axiom,
% 5.31/5.51 ( ( plus_plus_nat @ one_one_nat )
% 5.31/5.51 = suc ) ).
% 5.31/5.51
% 5.31/5.51 % plus_1_eq_Suc
% 5.31/5.51 thf(fact_1724_Suc__eq__plus1__left,axiom,
% 5.31/5.51 ( suc
% 5.31/5.51 = ( plus_plus_nat @ one_one_nat ) ) ).
% 5.31/5.51
% 5.31/5.51 % Suc_eq_plus1_left
% 5.31/5.51 thf(fact_1725_VEBT__internal_OminNull_Ocases,axiom,
% 5.31/5.51 ! [X: vEBT_VEBT] :
% 5.31/5.51 ( ( X
% 5.31/5.51 != ( vEBT_Leaf @ $false @ $false ) )
% 5.31/5.51 => ( ! [Uv2: $o] :
% 5.31/5.51 ( X
% 5.31/5.51 != ( vEBT_Leaf @ $true @ Uv2 ) )
% 5.31/5.51 => ( ! [Uu2: $o] :
% 5.31/5.51 ( X
% 5.31/5.51 != ( vEBT_Leaf @ Uu2 @ $true ) )
% 5.31/5.51 => ( ! [Uw: nat,Ux: list_VEBT_VEBT,Uy: vEBT_VEBT] :
% 5.31/5.51 ( X
% 5.31/5.51 != ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw @ Ux @ Uy ) )
% 5.31/5.51 => ~ ! [Uz2: product_prod_nat_nat,Va2: nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.31/5.51 ( X
% 5.31/5.51 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va2 @ Vb2 @ Vc2 ) ) ) ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % VEBT_internal.minNull.cases
% 5.31/5.51 thf(fact_1726_VEBT__internal_Ooption__shift_Osimps_I2_J,axiom,
% 5.31/5.51 ! [Uw2: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,V2: product_prod_nat_nat] :
% 5.31/5.51 ( ( vEBT_V1502963449132264192at_nat @ Uw2 @ ( some_P7363390416028606310at_nat @ V2 ) @ none_P5556105721700978146at_nat )
% 5.31/5.51 = none_P5556105721700978146at_nat ) ).
% 5.31/5.51
% 5.31/5.51 % VEBT_internal.option_shift.simps(2)
% 5.31/5.51 thf(fact_1727_VEBT__internal_Ooption__shift_Osimps_I2_J,axiom,
% 5.31/5.51 ! [Uw2: num > num > num,V2: num] :
% 5.31/5.51 ( ( vEBT_V819420779217536731ft_num @ Uw2 @ ( some_num @ V2 ) @ none_num )
% 5.31/5.51 = none_num ) ).
% 5.31/5.51
% 5.31/5.51 % VEBT_internal.option_shift.simps(2)
% 5.31/5.51 thf(fact_1728_VEBT__internal_Ooption__shift_Osimps_I2_J,axiom,
% 5.31/5.51 ! [Uw2: nat > nat > nat,V2: nat] :
% 5.31/5.51 ( ( vEBT_V4262088993061758097ft_nat @ Uw2 @ ( some_nat @ V2 ) @ none_nat )
% 5.31/5.51 = none_nat ) ).
% 5.31/5.51
% 5.31/5.51 % VEBT_internal.option_shift.simps(2)
% 5.31/5.51 thf(fact_1729_VEBT__internal_Ooption__shift_Oelims,axiom,
% 5.31/5.51 ! [X: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,Xa2: option4927543243414619207at_nat,Xb: option4927543243414619207at_nat,Y: option4927543243414619207at_nat] :
% 5.31/5.51 ( ( ( vEBT_V1502963449132264192at_nat @ X @ Xa2 @ Xb )
% 5.31/5.51 = Y )
% 5.31/5.51 => ( ( ( Xa2 = none_P5556105721700978146at_nat )
% 5.31/5.51 => ( Y != none_P5556105721700978146at_nat ) )
% 5.31/5.51 => ( ( ? [V: product_prod_nat_nat] :
% 5.31/5.51 ( Xa2
% 5.31/5.51 = ( some_P7363390416028606310at_nat @ V ) )
% 5.31/5.51 => ( ( Xb = none_P5556105721700978146at_nat )
% 5.31/5.51 => ( Y != none_P5556105721700978146at_nat ) ) )
% 5.31/5.51 => ~ ! [A3: product_prod_nat_nat] :
% 5.31/5.51 ( ( Xa2
% 5.31/5.51 = ( some_P7363390416028606310at_nat @ A3 ) )
% 5.31/5.51 => ! [B3: product_prod_nat_nat] :
% 5.31/5.51 ( ( Xb
% 5.31/5.51 = ( some_P7363390416028606310at_nat @ B3 ) )
% 5.31/5.51 => ( Y
% 5.31/5.51 != ( some_P7363390416028606310at_nat @ ( X @ A3 @ B3 ) ) ) ) ) ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % VEBT_internal.option_shift.elims
% 5.31/5.51 thf(fact_1730_VEBT__internal_Ooption__shift_Oelims,axiom,
% 5.31/5.51 ! [X: num > num > num,Xa2: option_num,Xb: option_num,Y: option_num] :
% 5.31/5.51 ( ( ( vEBT_V819420779217536731ft_num @ X @ Xa2 @ Xb )
% 5.31/5.51 = Y )
% 5.31/5.51 => ( ( ( Xa2 = none_num )
% 5.31/5.51 => ( Y != none_num ) )
% 5.31/5.51 => ( ( ? [V: num] :
% 5.31/5.51 ( Xa2
% 5.31/5.51 = ( some_num @ V ) )
% 5.31/5.51 => ( ( Xb = none_num )
% 5.31/5.51 => ( Y != none_num ) ) )
% 5.31/5.51 => ~ ! [A3: num] :
% 5.31/5.51 ( ( Xa2
% 5.31/5.51 = ( some_num @ A3 ) )
% 5.31/5.51 => ! [B3: num] :
% 5.31/5.51 ( ( Xb
% 5.31/5.51 = ( some_num @ B3 ) )
% 5.31/5.51 => ( Y
% 5.31/5.51 != ( some_num @ ( X @ A3 @ B3 ) ) ) ) ) ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % VEBT_internal.option_shift.elims
% 5.31/5.51 thf(fact_1731_VEBT__internal_Ooption__shift_Oelims,axiom,
% 5.31/5.51 ! [X: nat > nat > nat,Xa2: option_nat,Xb: option_nat,Y: option_nat] :
% 5.31/5.51 ( ( ( vEBT_V4262088993061758097ft_nat @ X @ Xa2 @ Xb )
% 5.31/5.51 = Y )
% 5.31/5.51 => ( ( ( Xa2 = none_nat )
% 5.31/5.51 => ( Y != none_nat ) )
% 5.31/5.51 => ( ( ? [V: nat] :
% 5.31/5.51 ( Xa2
% 5.31/5.51 = ( some_nat @ V ) )
% 5.31/5.51 => ( ( Xb = none_nat )
% 5.31/5.51 => ( Y != none_nat ) ) )
% 5.31/5.51 => ~ ! [A3: nat] :
% 5.31/5.51 ( ( Xa2
% 5.31/5.51 = ( some_nat @ A3 ) )
% 5.31/5.51 => ! [B3: nat] :
% 5.31/5.51 ( ( Xb
% 5.31/5.51 = ( some_nat @ B3 ) )
% 5.31/5.51 => ( Y
% 5.31/5.51 != ( some_nat @ ( X @ A3 @ B3 ) ) ) ) ) ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % VEBT_internal.option_shift.elims
% 5.31/5.51 thf(fact_1732_field__le__epsilon,axiom,
% 5.31/5.51 ! [X: real,Y: real] :
% 5.31/5.51 ( ! [E2: real] :
% 5.31/5.51 ( ( ord_less_real @ zero_zero_real @ E2 )
% 5.31/5.51 => ( ord_less_eq_real @ X @ ( plus_plus_real @ Y @ E2 ) ) )
% 5.31/5.51 => ( ord_less_eq_real @ X @ Y ) ) ).
% 5.31/5.51
% 5.31/5.51 % field_le_epsilon
% 5.31/5.51 thf(fact_1733_field__le__epsilon,axiom,
% 5.31/5.51 ! [X: rat,Y: rat] :
% 5.31/5.51 ( ! [E2: rat] :
% 5.31/5.51 ( ( ord_less_rat @ zero_zero_rat @ E2 )
% 5.31/5.51 => ( ord_less_eq_rat @ X @ ( plus_plus_rat @ Y @ E2 ) ) )
% 5.31/5.51 => ( ord_less_eq_rat @ X @ Y ) ) ).
% 5.31/5.51
% 5.31/5.51 % field_le_epsilon
% 5.31/5.51 thf(fact_1734_add__neg__nonpos,axiom,
% 5.31/5.51 ! [A: real,B: real] :
% 5.31/5.51 ( ( ord_less_real @ A @ zero_zero_real )
% 5.31/5.51 => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 5.31/5.51 => ( ord_less_real @ ( plus_plus_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % add_neg_nonpos
% 5.31/5.51 thf(fact_1735_add__neg__nonpos,axiom,
% 5.31/5.51 ! [A: rat,B: rat] :
% 5.31/5.51 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.31/5.51 => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 5.31/5.51 => ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % add_neg_nonpos
% 5.31/5.51 thf(fact_1736_add__neg__nonpos,axiom,
% 5.31/5.51 ! [A: nat,B: nat] :
% 5.31/5.51 ( ( ord_less_nat @ A @ zero_zero_nat )
% 5.31/5.51 => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 5.31/5.51 => ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % add_neg_nonpos
% 5.31/5.51 thf(fact_1737_add__neg__nonpos,axiom,
% 5.31/5.51 ! [A: int,B: int] :
% 5.31/5.51 ( ( ord_less_int @ A @ zero_zero_int )
% 5.31/5.51 => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 5.31/5.51 => ( ord_less_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % add_neg_nonpos
% 5.31/5.51 thf(fact_1738_add__nonneg__pos,axiom,
% 5.31/5.51 ! [A: real,B: real] :
% 5.31/5.51 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.31/5.51 => ( ( ord_less_real @ zero_zero_real @ B )
% 5.31/5.51 => ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % add_nonneg_pos
% 5.31/5.51 thf(fact_1739_add__nonneg__pos,axiom,
% 5.31/5.51 ! [A: rat,B: rat] :
% 5.31/5.51 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.31/5.51 => ( ( ord_less_rat @ zero_zero_rat @ B )
% 5.31/5.51 => ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % add_nonneg_pos
% 5.31/5.51 thf(fact_1740_add__nonneg__pos,axiom,
% 5.31/5.51 ! [A: nat,B: nat] :
% 5.31/5.51 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.31/5.51 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.31/5.51 => ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % add_nonneg_pos
% 5.31/5.51 thf(fact_1741_add__nonneg__pos,axiom,
% 5.31/5.51 ! [A: int,B: int] :
% 5.31/5.51 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.31/5.51 => ( ( ord_less_int @ zero_zero_int @ B )
% 5.31/5.51 => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % add_nonneg_pos
% 5.31/5.51 thf(fact_1742_add__nonpos__neg,axiom,
% 5.31/5.51 ! [A: real,B: real] :
% 5.31/5.51 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.31/5.51 => ( ( ord_less_real @ B @ zero_zero_real )
% 5.31/5.51 => ( ord_less_real @ ( plus_plus_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % add_nonpos_neg
% 5.31/5.51 thf(fact_1743_add__nonpos__neg,axiom,
% 5.31/5.51 ! [A: rat,B: rat] :
% 5.31/5.51 ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.31/5.51 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 5.31/5.51 => ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % add_nonpos_neg
% 5.31/5.51 thf(fact_1744_add__nonpos__neg,axiom,
% 5.31/5.51 ! [A: nat,B: nat] :
% 5.31/5.51 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 5.31/5.51 => ( ( ord_less_nat @ B @ zero_zero_nat )
% 5.31/5.51 => ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % add_nonpos_neg
% 5.31/5.51 thf(fact_1745_add__nonpos__neg,axiom,
% 5.31/5.51 ! [A: int,B: int] :
% 5.31/5.51 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.31/5.51 => ( ( ord_less_int @ B @ zero_zero_int )
% 5.31/5.51 => ( ord_less_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % add_nonpos_neg
% 5.31/5.51 thf(fact_1746_add__pos__nonneg,axiom,
% 5.31/5.51 ! [A: real,B: real] :
% 5.31/5.51 ( ( ord_less_real @ zero_zero_real @ A )
% 5.31/5.51 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.31/5.51 => ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % add_pos_nonneg
% 5.31/5.51 thf(fact_1747_add__pos__nonneg,axiom,
% 5.31/5.51 ! [A: rat,B: rat] :
% 5.31/5.51 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.31/5.51 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.31/5.51 => ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % add_pos_nonneg
% 5.31/5.51 thf(fact_1748_add__pos__nonneg,axiom,
% 5.31/5.51 ! [A: nat,B: nat] :
% 5.31/5.51 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.31/5.51 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.31/5.51 => ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % add_pos_nonneg
% 5.31/5.51 thf(fact_1749_add__pos__nonneg,axiom,
% 5.31/5.51 ! [A: int,B: int] :
% 5.31/5.51 ( ( ord_less_int @ zero_zero_int @ A )
% 5.31/5.51 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.31/5.51 => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % add_pos_nonneg
% 5.31/5.51 thf(fact_1750_add__strict__increasing,axiom,
% 5.31/5.51 ! [A: real,B: real,C2: real] :
% 5.31/5.51 ( ( ord_less_real @ zero_zero_real @ A )
% 5.31/5.51 => ( ( ord_less_eq_real @ B @ C2 )
% 5.31/5.51 => ( ord_less_real @ B @ ( plus_plus_real @ A @ C2 ) ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % add_strict_increasing
% 5.31/5.51 thf(fact_1751_add__strict__increasing,axiom,
% 5.31/5.51 ! [A: rat,B: rat,C2: rat] :
% 5.31/5.51 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.31/5.51 => ( ( ord_less_eq_rat @ B @ C2 )
% 5.31/5.51 => ( ord_less_rat @ B @ ( plus_plus_rat @ A @ C2 ) ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % add_strict_increasing
% 5.31/5.51 thf(fact_1752_add__strict__increasing,axiom,
% 5.31/5.51 ! [A: nat,B: nat,C2: nat] :
% 5.31/5.51 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.31/5.51 => ( ( ord_less_eq_nat @ B @ C2 )
% 5.31/5.51 => ( ord_less_nat @ B @ ( plus_plus_nat @ A @ C2 ) ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % add_strict_increasing
% 5.31/5.51 thf(fact_1753_add__strict__increasing,axiom,
% 5.31/5.51 ! [A: int,B: int,C2: int] :
% 5.31/5.51 ( ( ord_less_int @ zero_zero_int @ A )
% 5.31/5.51 => ( ( ord_less_eq_int @ B @ C2 )
% 5.31/5.51 => ( ord_less_int @ B @ ( plus_plus_int @ A @ C2 ) ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % add_strict_increasing
% 5.31/5.51 thf(fact_1754_add__strict__increasing2,axiom,
% 5.31/5.51 ! [A: real,B: real,C2: real] :
% 5.31/5.51 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.31/5.51 => ( ( ord_less_real @ B @ C2 )
% 5.31/5.51 => ( ord_less_real @ B @ ( plus_plus_real @ A @ C2 ) ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % add_strict_increasing2
% 5.31/5.51 thf(fact_1755_add__strict__increasing2,axiom,
% 5.31/5.51 ! [A: rat,B: rat,C2: rat] :
% 5.31/5.51 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.31/5.51 => ( ( ord_less_rat @ B @ C2 )
% 5.31/5.51 => ( ord_less_rat @ B @ ( plus_plus_rat @ A @ C2 ) ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % add_strict_increasing2
% 5.31/5.51 thf(fact_1756_add__strict__increasing2,axiom,
% 5.31/5.51 ! [A: nat,B: nat,C2: nat] :
% 5.31/5.51 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.31/5.51 => ( ( ord_less_nat @ B @ C2 )
% 5.31/5.51 => ( ord_less_nat @ B @ ( plus_plus_nat @ A @ C2 ) ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % add_strict_increasing2
% 5.31/5.51 thf(fact_1757_add__strict__increasing2,axiom,
% 5.31/5.51 ! [A: int,B: int,C2: int] :
% 5.31/5.51 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.31/5.51 => ( ( ord_less_int @ B @ C2 )
% 5.31/5.51 => ( ord_less_int @ B @ ( plus_plus_int @ A @ C2 ) ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % add_strict_increasing2
% 5.31/5.51 thf(fact_1758_sum__squares__ge__zero,axiom,
% 5.31/5.51 ! [X: real,Y: real] : ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ ( times_times_real @ X @ X ) @ ( times_times_real @ Y @ Y ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % sum_squares_ge_zero
% 5.31/5.51 thf(fact_1759_sum__squares__ge__zero,axiom,
% 5.31/5.51 ! [X: rat,Y: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ ( times_times_rat @ X @ X ) @ ( times_times_rat @ Y @ Y ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % sum_squares_ge_zero
% 5.31/5.51 thf(fact_1760_sum__squares__ge__zero,axiom,
% 5.31/5.51 ! [X: int,Y: int] : ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y @ Y ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % sum_squares_ge_zero
% 5.31/5.51 thf(fact_1761_not__sum__squares__lt__zero,axiom,
% 5.31/5.51 ! [X: real,Y: real] :
% 5.31/5.51 ~ ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ X @ X ) @ ( times_times_real @ Y @ Y ) ) @ zero_zero_real ) ).
% 5.31/5.51
% 5.31/5.51 % not_sum_squares_lt_zero
% 5.31/5.51 thf(fact_1762_not__sum__squares__lt__zero,axiom,
% 5.31/5.51 ! [X: rat,Y: rat] :
% 5.31/5.51 ~ ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ X @ X ) @ ( times_times_rat @ Y @ Y ) ) @ zero_zero_rat ) ).
% 5.31/5.51
% 5.31/5.51 % not_sum_squares_lt_zero
% 5.31/5.51 thf(fact_1763_not__sum__squares__lt__zero,axiom,
% 5.31/5.51 ! [X: int,Y: int] :
% 5.31/5.51 ~ ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y @ Y ) ) @ zero_zero_int ) ).
% 5.31/5.51
% 5.31/5.51 % not_sum_squares_lt_zero
% 5.31/5.51 thf(fact_1764_discrete,axiom,
% 5.31/5.51 ( ord_le6747313008572928689nteger
% 5.31/5.51 = ( ^ [A5: code_integer] : ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ A5 @ one_one_Code_integer ) ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % discrete
% 5.31/5.51 thf(fact_1765_discrete,axiom,
% 5.31/5.51 ( ord_less_nat
% 5.31/5.51 = ( ^ [A5: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ A5 @ one_one_nat ) ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % discrete
% 5.31/5.51 thf(fact_1766_discrete,axiom,
% 5.31/5.51 ( ord_less_int
% 5.31/5.51 = ( ^ [A5: int] : ( ord_less_eq_int @ ( plus_plus_int @ A5 @ one_one_int ) ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % discrete
% 5.31/5.51 thf(fact_1767_zero__less__two,axiom,
% 5.31/5.51 ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ one_one_Code_integer ) ).
% 5.31/5.51
% 5.31/5.51 % zero_less_two
% 5.31/5.51 thf(fact_1768_zero__less__two,axiom,
% 5.31/5.51 ord_less_real @ zero_zero_real @ ( plus_plus_real @ one_one_real @ one_one_real ) ).
% 5.31/5.51
% 5.31/5.51 % zero_less_two
% 5.31/5.51 thf(fact_1769_zero__less__two,axiom,
% 5.31/5.51 ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ one_one_rat @ one_one_rat ) ).
% 5.31/5.51
% 5.31/5.51 % zero_less_two
% 5.31/5.51 thf(fact_1770_zero__less__two,axiom,
% 5.31/5.51 ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ).
% 5.31/5.51
% 5.31/5.51 % zero_less_two
% 5.31/5.51 thf(fact_1771_zero__less__two,axiom,
% 5.31/5.51 ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ one_one_int ) ).
% 5.31/5.51
% 5.31/5.51 % zero_less_two
% 5.31/5.51 thf(fact_1772_option_Osize_I3_J,axiom,
% 5.31/5.51 ( ( size_size_option_nat @ none_nat )
% 5.31/5.51 = ( suc @ zero_zero_nat ) ) ).
% 5.31/5.51
% 5.31/5.51 % option.size(3)
% 5.31/5.51 thf(fact_1773_option_Osize_I3_J,axiom,
% 5.31/5.51 ( ( size_s170228958280169651at_nat @ none_P5556105721700978146at_nat )
% 5.31/5.51 = ( suc @ zero_zero_nat ) ) ).
% 5.31/5.51
% 5.31/5.51 % option.size(3)
% 5.31/5.51 thf(fact_1774_option_Osize_I3_J,axiom,
% 5.31/5.51 ( ( size_size_option_num @ none_num )
% 5.31/5.51 = ( suc @ zero_zero_nat ) ) ).
% 5.31/5.51
% 5.31/5.51 % option.size(3)
% 5.31/5.51 thf(fact_1775_convex__bound__le,axiom,
% 5.31/5.51 ! [X: code_integer,A: code_integer,Y: code_integer,U: code_integer,V2: code_integer] :
% 5.31/5.51 ( ( ord_le3102999989581377725nteger @ X @ A )
% 5.31/5.51 => ( ( ord_le3102999989581377725nteger @ Y @ A )
% 5.31/5.51 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ U )
% 5.31/5.51 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ V2 )
% 5.31/5.51 => ( ( ( plus_p5714425477246183910nteger @ U @ V2 )
% 5.31/5.51 = one_one_Code_integer )
% 5.31/5.51 => ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ U @ X ) @ ( times_3573771949741848930nteger @ V2 @ Y ) ) @ A ) ) ) ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % convex_bound_le
% 5.31/5.51 thf(fact_1776_convex__bound__le,axiom,
% 5.31/5.51 ! [X: real,A: real,Y: real,U: real,V2: real] :
% 5.31/5.51 ( ( ord_less_eq_real @ X @ A )
% 5.31/5.51 => ( ( ord_less_eq_real @ Y @ A )
% 5.31/5.51 => ( ( ord_less_eq_real @ zero_zero_real @ U )
% 5.31/5.51 => ( ( ord_less_eq_real @ zero_zero_real @ V2 )
% 5.31/5.51 => ( ( ( plus_plus_real @ U @ V2 )
% 5.31/5.51 = one_one_real )
% 5.31/5.51 => ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ U @ X ) @ ( times_times_real @ V2 @ Y ) ) @ A ) ) ) ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % convex_bound_le
% 5.31/5.51 thf(fact_1777_convex__bound__le,axiom,
% 5.31/5.51 ! [X: rat,A: rat,Y: rat,U: rat,V2: rat] :
% 5.31/5.51 ( ( ord_less_eq_rat @ X @ A )
% 5.31/5.51 => ( ( ord_less_eq_rat @ Y @ A )
% 5.31/5.51 => ( ( ord_less_eq_rat @ zero_zero_rat @ U )
% 5.31/5.51 => ( ( ord_less_eq_rat @ zero_zero_rat @ V2 )
% 5.31/5.51 => ( ( ( plus_plus_rat @ U @ V2 )
% 5.31/5.51 = one_one_rat )
% 5.31/5.51 => ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ U @ X ) @ ( times_times_rat @ V2 @ Y ) ) @ A ) ) ) ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % convex_bound_le
% 5.31/5.51 thf(fact_1778_convex__bound__le,axiom,
% 5.31/5.51 ! [X: int,A: int,Y: int,U: int,V2: int] :
% 5.31/5.51 ( ( ord_less_eq_int @ X @ A )
% 5.31/5.51 => ( ( ord_less_eq_int @ Y @ A )
% 5.31/5.51 => ( ( ord_less_eq_int @ zero_zero_int @ U )
% 5.31/5.51 => ( ( ord_less_eq_int @ zero_zero_int @ V2 )
% 5.31/5.51 => ( ( ( plus_plus_int @ U @ V2 )
% 5.31/5.51 = one_one_int )
% 5.31/5.51 => ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ U @ X ) @ ( times_times_int @ V2 @ Y ) ) @ A ) ) ) ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % convex_bound_le
% 5.31/5.51 thf(fact_1779_vebt__mint_Oelims,axiom,
% 5.31/5.51 ! [X: vEBT_VEBT,Y: option_nat] :
% 5.31/5.51 ( ( ( vEBT_vebt_mint @ X )
% 5.31/5.51 = Y )
% 5.31/5.51 => ( ! [A3: $o,B3: $o] :
% 5.31/5.51 ( ( X
% 5.31/5.51 = ( vEBT_Leaf @ A3 @ B3 ) )
% 5.31/5.51 => ~ ( ( A3
% 5.31/5.51 => ( Y
% 5.31/5.51 = ( some_nat @ zero_zero_nat ) ) )
% 5.31/5.51 & ( ~ A3
% 5.31/5.51 => ( ( B3
% 5.31/5.51 => ( Y
% 5.31/5.51 = ( some_nat @ one_one_nat ) ) )
% 5.31/5.51 & ( ~ B3
% 5.31/5.51 => ( Y = none_nat ) ) ) ) ) )
% 5.31/5.51 => ( ( ? [Uu2: nat,Uv2: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 5.31/5.51 ( X
% 5.31/5.51 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw ) )
% 5.31/5.51 => ( Y != none_nat ) )
% 5.31/5.51 => ~ ! [Mi2: nat] :
% 5.31/5.51 ( ? [Ma2: nat,Ux: nat,Uy: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.31/5.51 ( X
% 5.31/5.51 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux @ Uy @ Uz2 ) )
% 5.31/5.51 => ( Y
% 5.31/5.51 != ( some_nat @ Mi2 ) ) ) ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % vebt_mint.elims
% 5.31/5.51 thf(fact_1780_vebt__maxt_Oelims,axiom,
% 5.31/5.51 ! [X: vEBT_VEBT,Y: option_nat] :
% 5.31/5.51 ( ( ( vEBT_vebt_maxt @ X )
% 5.31/5.51 = Y )
% 5.31/5.51 => ( ! [A3: $o,B3: $o] :
% 5.31/5.51 ( ( X
% 5.31/5.51 = ( vEBT_Leaf @ A3 @ B3 ) )
% 5.31/5.51 => ~ ( ( B3
% 5.31/5.51 => ( Y
% 5.31/5.51 = ( some_nat @ one_one_nat ) ) )
% 5.31/5.51 & ( ~ B3
% 5.31/5.51 => ( ( A3
% 5.31/5.51 => ( Y
% 5.31/5.51 = ( some_nat @ zero_zero_nat ) ) )
% 5.31/5.51 & ( ~ A3
% 5.31/5.51 => ( Y = none_nat ) ) ) ) ) )
% 5.31/5.51 => ( ( ? [Uu2: nat,Uv2: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 5.31/5.51 ( X
% 5.31/5.51 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw ) )
% 5.31/5.51 => ( Y != none_nat ) )
% 5.31/5.51 => ~ ! [Mi2: nat,Ma2: nat] :
% 5.31/5.51 ( ? [Ux: nat,Uy: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.31/5.51 ( X
% 5.31/5.51 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux @ Uy @ Uz2 ) )
% 5.31/5.51 => ( Y
% 5.31/5.51 != ( some_nat @ Ma2 ) ) ) ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % vebt_maxt.elims
% 5.31/5.51 thf(fact_1781_vebt__mint_Ocases,axiom,
% 5.31/5.51 ! [X: vEBT_VEBT] :
% 5.31/5.51 ( ! [A3: $o,B3: $o] :
% 5.31/5.51 ( X
% 5.31/5.51 != ( vEBT_Leaf @ A3 @ B3 ) )
% 5.31/5.51 => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 5.31/5.51 ( X
% 5.31/5.51 != ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw ) )
% 5.31/5.51 => ~ ! [Mi2: nat,Ma2: nat,Ux: nat,Uy: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.31/5.51 ( X
% 5.31/5.51 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux @ Uy @ Uz2 ) ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % vebt_mint.cases
% 5.31/5.51 thf(fact_1782_convex__bound__lt,axiom,
% 5.31/5.51 ! [X: code_integer,A: code_integer,Y: code_integer,U: code_integer,V2: code_integer] :
% 5.31/5.51 ( ( ord_le6747313008572928689nteger @ X @ A )
% 5.31/5.51 => ( ( ord_le6747313008572928689nteger @ Y @ A )
% 5.31/5.51 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ U )
% 5.31/5.51 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ V2 )
% 5.31/5.51 => ( ( ( plus_p5714425477246183910nteger @ U @ V2 )
% 5.31/5.51 = one_one_Code_integer )
% 5.31/5.51 => ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ U @ X ) @ ( times_3573771949741848930nteger @ V2 @ Y ) ) @ A ) ) ) ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % convex_bound_lt
% 5.31/5.51 thf(fact_1783_convex__bound__lt,axiom,
% 5.31/5.51 ! [X: real,A: real,Y: real,U: real,V2: real] :
% 5.31/5.51 ( ( ord_less_real @ X @ A )
% 5.31/5.51 => ( ( ord_less_real @ Y @ A )
% 5.31/5.51 => ( ( ord_less_eq_real @ zero_zero_real @ U )
% 5.31/5.51 => ( ( ord_less_eq_real @ zero_zero_real @ V2 )
% 5.31/5.51 => ( ( ( plus_plus_real @ U @ V2 )
% 5.31/5.51 = one_one_real )
% 5.31/5.51 => ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ U @ X ) @ ( times_times_real @ V2 @ Y ) ) @ A ) ) ) ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % convex_bound_lt
% 5.31/5.51 thf(fact_1784_convex__bound__lt,axiom,
% 5.31/5.51 ! [X: rat,A: rat,Y: rat,U: rat,V2: rat] :
% 5.31/5.51 ( ( ord_less_rat @ X @ A )
% 5.31/5.51 => ( ( ord_less_rat @ Y @ A )
% 5.31/5.51 => ( ( ord_less_eq_rat @ zero_zero_rat @ U )
% 5.31/5.51 => ( ( ord_less_eq_rat @ zero_zero_rat @ V2 )
% 5.31/5.51 => ( ( ( plus_plus_rat @ U @ V2 )
% 5.31/5.51 = one_one_rat )
% 5.31/5.51 => ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ U @ X ) @ ( times_times_rat @ V2 @ Y ) ) @ A ) ) ) ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % convex_bound_lt
% 5.31/5.51 thf(fact_1785_convex__bound__lt,axiom,
% 5.31/5.51 ! [X: int,A: int,Y: int,U: int,V2: int] :
% 5.31/5.51 ( ( ord_less_int @ X @ A )
% 5.31/5.51 => ( ( ord_less_int @ Y @ A )
% 5.31/5.51 => ( ( ord_less_eq_int @ zero_zero_int @ U )
% 5.31/5.51 => ( ( ord_less_eq_int @ zero_zero_int @ V2 )
% 5.31/5.51 => ( ( ( plus_plus_int @ U @ V2 )
% 5.31/5.51 = one_one_int )
% 5.31/5.51 => ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ U @ X ) @ ( times_times_int @ V2 @ Y ) ) @ A ) ) ) ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % convex_bound_lt
% 5.31/5.51 thf(fact_1786_VEBT__internal_Omembermima_Osimps_I3_J,axiom,
% 5.31/5.51 ! [Mi: nat,Ma: nat,Va3: list_VEBT_VEBT,Vb: vEBT_VEBT,X: nat] :
% 5.31/5.51 ( ( vEBT_VEBT_membermima @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ zero_zero_nat @ Va3 @ Vb ) @ X )
% 5.31/5.51 = ( ( X = Mi )
% 5.31/5.51 | ( X = Ma ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % VEBT_internal.membermima.simps(3)
% 5.31/5.51 thf(fact_1787_vebt__member_Ocases,axiom,
% 5.31/5.51 ! [X: produc9072475918466114483BT_nat] :
% 5.31/5.51 ( ! [A3: $o,B3: $o,X3: nat] :
% 5.31/5.51 ( X
% 5.31/5.51 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ X3 ) )
% 5.31/5.51 => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw: vEBT_VEBT,X3: nat] :
% 5.31/5.51 ( X
% 5.31/5.51 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw ) @ X3 ) )
% 5.31/5.51 => ( ! [V: product_prod_nat_nat,Uy: list_VEBT_VEBT,Uz2: vEBT_VEBT,X3: nat] :
% 5.31/5.51 ( X
% 5.31/5.51 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Uy @ Uz2 ) @ X3 ) )
% 5.31/5.51 => ( ! [V: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT,X3: nat] :
% 5.31/5.51 ( X
% 5.31/5.51 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) @ X3 ) )
% 5.31/5.51 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList: list_VEBT_VEBT,Summary2: vEBT_VEBT,X3: nat] :
% 5.31/5.51 ( X
% 5.31/5.51 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary2 ) @ X3 ) ) ) ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % vebt_member.cases
% 5.31/5.51 thf(fact_1788_vebt__mint_Osimps_I1_J,axiom,
% 5.31/5.51 ! [A: $o,B: $o] :
% 5.31/5.51 ( ( A
% 5.31/5.51 => ( ( vEBT_vebt_mint @ ( vEBT_Leaf @ A @ B ) )
% 5.31/5.51 = ( some_nat @ zero_zero_nat ) ) )
% 5.31/5.51 & ( ~ A
% 5.31/5.51 => ( ( B
% 5.31/5.51 => ( ( vEBT_vebt_mint @ ( vEBT_Leaf @ A @ B ) )
% 5.31/5.51 = ( some_nat @ one_one_nat ) ) )
% 5.31/5.51 & ( ~ B
% 5.31/5.51 => ( ( vEBT_vebt_mint @ ( vEBT_Leaf @ A @ B ) )
% 5.31/5.51 = none_nat ) ) ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % vebt_mint.simps(1)
% 5.31/5.51 thf(fact_1789_vebt__maxt_Osimps_I1_J,axiom,
% 5.31/5.51 ! [B: $o,A: $o] :
% 5.31/5.51 ( ( B
% 5.31/5.51 => ( ( vEBT_vebt_maxt @ ( vEBT_Leaf @ A @ B ) )
% 5.31/5.51 = ( some_nat @ one_one_nat ) ) )
% 5.31/5.51 & ( ~ B
% 5.31/5.51 => ( ( A
% 5.31/5.51 => ( ( vEBT_vebt_maxt @ ( vEBT_Leaf @ A @ B ) )
% 5.31/5.51 = ( some_nat @ zero_zero_nat ) ) )
% 5.31/5.51 & ( ~ A
% 5.31/5.51 => ( ( vEBT_vebt_maxt @ ( vEBT_Leaf @ A @ B ) )
% 5.31/5.51 = none_nat ) ) ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % vebt_maxt.simps(1)
% 5.31/5.51 thf(fact_1790_geqmaxNone,axiom,
% 5.31/5.51 ! [Mi: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat,X: nat] :
% 5.31/5.51 ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ N )
% 5.31/5.51 => ( ( ord_less_eq_nat @ Ma @ X )
% 5.31/5.51 => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 5.31/5.51 = none_nat ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % geqmaxNone
% 5.31/5.51 thf(fact_1791_vebt__pred_Ocases,axiom,
% 5.31/5.51 ! [X: produc9072475918466114483BT_nat] :
% 5.31/5.51 ( ! [Uu2: $o,Uv2: $o] :
% 5.31/5.51 ( X
% 5.31/5.51 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ zero_zero_nat ) )
% 5.31/5.51 => ( ! [A3: $o,Uw: $o] :
% 5.31/5.51 ( X
% 5.31/5.51 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ Uw ) @ ( suc @ zero_zero_nat ) ) )
% 5.31/5.51 => ( ! [A3: $o,B3: $o,Va: nat] :
% 5.31/5.51 ( X
% 5.31/5.51 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ ( suc @ ( suc @ Va ) ) ) )
% 5.31/5.51 => ( ! [Uy: nat,Uz2: list_VEBT_VEBT,Va2: vEBT_VEBT,Vb2: nat] :
% 5.31/5.51 ( X
% 5.31/5.51 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy @ Uz2 @ Va2 ) @ Vb2 ) )
% 5.31/5.51 => ( ! [V: product_prod_nat_nat,Vd: list_VEBT_VEBT,Ve: vEBT_VEBT,Vf: nat] :
% 5.31/5.51 ( X
% 5.31/5.51 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Vd @ Ve ) @ Vf ) )
% 5.31/5.51 => ( ! [V: product_prod_nat_nat,Vh: list_VEBT_VEBT,Vi: vEBT_VEBT,Vj: nat] :
% 5.31/5.51 ( X
% 5.31/5.51 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vh @ Vi ) @ Vj ) )
% 5.31/5.51 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList: list_VEBT_VEBT,Summary2: vEBT_VEBT,X3: nat] :
% 5.31/5.51 ( X
% 5.31/5.51 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary2 ) @ X3 ) ) ) ) ) ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % vebt_pred.cases
% 5.31/5.51 thf(fact_1792_vebt__succ_Ocases,axiom,
% 5.31/5.51 ! [X: produc9072475918466114483BT_nat] :
% 5.31/5.51 ( ! [Uu2: $o,B3: $o] :
% 5.31/5.51 ( X
% 5.31/5.51 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ B3 ) @ zero_zero_nat ) )
% 5.31/5.51 => ( ! [Uv2: $o,Uw: $o,N3: nat] :
% 5.31/5.51 ( X
% 5.31/5.51 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uv2 @ Uw ) @ ( suc @ N3 ) ) )
% 5.31/5.51 => ( ! [Ux: nat,Uy: list_VEBT_VEBT,Uz2: vEBT_VEBT,Va2: nat] :
% 5.31/5.51 ( X
% 5.31/5.51 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux @ Uy @ Uz2 ) @ Va2 ) )
% 5.31/5.51 => ( ! [V: product_prod_nat_nat,Vc2: list_VEBT_VEBT,Vd: vEBT_VEBT,Ve: nat] :
% 5.31/5.51 ( X
% 5.31/5.51 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Vc2 @ Vd ) @ Ve ) )
% 5.31/5.51 => ( ! [V: product_prod_nat_nat,Vg: list_VEBT_VEBT,Vh: vEBT_VEBT,Vi: nat] :
% 5.31/5.51 ( X
% 5.31/5.51 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vg @ Vh ) @ Vi ) )
% 5.31/5.51 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList: list_VEBT_VEBT,Summary2: vEBT_VEBT,X3: nat] :
% 5.31/5.51 ( X
% 5.31/5.51 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary2 ) @ X3 ) ) ) ) ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % vebt_succ.cases
% 5.31/5.51 thf(fact_1793_vebt__delete_Ocases,axiom,
% 5.31/5.51 ! [X: produc9072475918466114483BT_nat] :
% 5.31/5.51 ( ! [A3: $o,B3: $o] :
% 5.31/5.51 ( X
% 5.31/5.51 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ zero_zero_nat ) )
% 5.31/5.51 => ( ! [A3: $o,B3: $o] :
% 5.31/5.51 ( X
% 5.31/5.51 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ ( suc @ zero_zero_nat ) ) )
% 5.31/5.51 => ( ! [A3: $o,B3: $o,N3: nat] :
% 5.31/5.51 ( X
% 5.31/5.51 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ ( suc @ ( suc @ N3 ) ) ) )
% 5.31/5.51 => ( ! [Deg2: nat,TreeList: list_VEBT_VEBT,Summary2: vEBT_VEBT,Uu2: nat] :
% 5.31/5.51 ( X
% 5.31/5.51 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList @ Summary2 ) @ Uu2 ) )
% 5.31/5.51 => ( ! [Mi2: nat,Ma2: nat,TrLst: list_VEBT_VEBT,Smry: vEBT_VEBT,X3: nat] :
% 5.31/5.51 ( X
% 5.31/5.51 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ TrLst @ Smry ) @ X3 ) )
% 5.31/5.51 => ( ! [Mi2: nat,Ma2: nat,Tr: list_VEBT_VEBT,Sm: vEBT_VEBT,X3: nat] :
% 5.31/5.51 ( X
% 5.31/5.51 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ zero_zero_nat ) @ Tr @ Sm ) @ X3 ) )
% 5.31/5.51 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList: list_VEBT_VEBT,Summary2: vEBT_VEBT,X3: nat] :
% 5.31/5.51 ( X
% 5.31/5.51 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary2 ) @ X3 ) ) ) ) ) ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % vebt_delete.cases
% 5.31/5.51 thf(fact_1794_vebt__insert_Ocases,axiom,
% 5.31/5.51 ! [X: produc9072475918466114483BT_nat] :
% 5.31/5.51 ( ! [A3: $o,B3: $o,X3: nat] :
% 5.31/5.51 ( X
% 5.31/5.51 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ X3 ) )
% 5.31/5.51 => ( ! [Info: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S: vEBT_VEBT,X3: nat] :
% 5.31/5.51 ( X
% 5.31/5.51 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info @ zero_zero_nat @ Ts @ S ) @ X3 ) )
% 5.31/5.51 => ( ! [Info: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S: vEBT_VEBT,X3: nat] :
% 5.31/5.51 ( X
% 5.31/5.51 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info @ ( suc @ zero_zero_nat ) @ Ts @ S ) @ X3 ) )
% 5.31/5.51 => ( ! [V: nat,TreeList: list_VEBT_VEBT,Summary2: vEBT_VEBT,X3: nat] :
% 5.31/5.51 ( X
% 5.31/5.51 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V ) ) @ TreeList @ Summary2 ) @ X3 ) )
% 5.31/5.51 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList: list_VEBT_VEBT,Summary2: vEBT_VEBT,X3: nat] :
% 5.31/5.51 ( X
% 5.31/5.51 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary2 ) @ X3 ) ) ) ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % vebt_insert.cases
% 5.31/5.51 thf(fact_1795_succ__correct,axiom,
% 5.31/5.51 ! [T: vEBT_VEBT,N: nat,X: nat,Sx: nat] :
% 5.31/5.51 ( ( vEBT_invar_vebt @ T @ N )
% 5.31/5.51 => ( ( ( vEBT_vebt_succ @ T @ X )
% 5.31/5.51 = ( some_nat @ Sx ) )
% 5.31/5.51 = ( vEBT_is_succ_in_set @ ( vEBT_set_vebt @ T ) @ X @ Sx ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % succ_correct
% 5.31/5.51 thf(fact_1796_pred__correct,axiom,
% 5.31/5.51 ! [T: vEBT_VEBT,N: nat,X: nat,Sx: nat] :
% 5.31/5.51 ( ( vEBT_invar_vebt @ T @ N )
% 5.31/5.51 => ( ( ( vEBT_vebt_pred @ T @ X )
% 5.31/5.51 = ( some_nat @ Sx ) )
% 5.31/5.51 = ( vEBT_is_pred_in_set @ ( vEBT_set_vebt @ T ) @ X @ Sx ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % pred_correct
% 5.31/5.51 thf(fact_1797_pred__corr,axiom,
% 5.31/5.51 ! [T: vEBT_VEBT,N: nat,X: nat,Px: nat] :
% 5.31/5.51 ( ( vEBT_invar_vebt @ T @ N )
% 5.31/5.51 => ( ( ( vEBT_vebt_pred @ T @ X )
% 5.31/5.51 = ( some_nat @ Px ) )
% 5.31/5.51 = ( vEBT_is_pred_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X @ Px ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % pred_corr
% 5.31/5.51 thf(fact_1798_succ__corr,axiom,
% 5.31/5.51 ! [T: vEBT_VEBT,N: nat,X: nat,Sx: nat] :
% 5.31/5.51 ( ( vEBT_invar_vebt @ T @ N )
% 5.31/5.51 => ( ( ( vEBT_vebt_succ @ T @ X )
% 5.31/5.51 = ( some_nat @ Sx ) )
% 5.31/5.51 = ( vEBT_is_succ_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X @ Sx ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % succ_corr
% 5.31/5.51 thf(fact_1799_sum__squares__eq__zero__iff,axiom,
% 5.31/5.51 ! [X: real,Y: real] :
% 5.31/5.51 ( ( ( plus_plus_real @ ( times_times_real @ X @ X ) @ ( times_times_real @ Y @ Y ) )
% 5.31/5.51 = zero_zero_real )
% 5.31/5.51 = ( ( X = zero_zero_real )
% 5.31/5.51 & ( Y = zero_zero_real ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % sum_squares_eq_zero_iff
% 5.31/5.51 thf(fact_1800_sum__squares__eq__zero__iff,axiom,
% 5.31/5.51 ! [X: rat,Y: rat] :
% 5.31/5.51 ( ( ( plus_plus_rat @ ( times_times_rat @ X @ X ) @ ( times_times_rat @ Y @ Y ) )
% 5.31/5.51 = zero_zero_rat )
% 5.31/5.51 = ( ( X = zero_zero_rat )
% 5.31/5.51 & ( Y = zero_zero_rat ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % sum_squares_eq_zero_iff
% 5.31/5.51 thf(fact_1801_sum__squares__eq__zero__iff,axiom,
% 5.31/5.51 ! [X: int,Y: int] :
% 5.31/5.51 ( ( ( plus_plus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y @ Y ) )
% 5.31/5.51 = zero_zero_int )
% 5.31/5.51 = ( ( X = zero_zero_int )
% 5.31/5.51 & ( Y = zero_zero_int ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % sum_squares_eq_zero_iff
% 5.31/5.51 thf(fact_1802_vebt__succ_Osimps_I2_J,axiom,
% 5.31/5.51 ! [Uv: $o,Uw2: $o,N: nat] :
% 5.31/5.51 ( ( vEBT_vebt_succ @ ( vEBT_Leaf @ Uv @ Uw2 ) @ ( suc @ N ) )
% 5.31/5.51 = none_nat ) ).
% 5.31/5.51
% 5.31/5.51 % vebt_succ.simps(2)
% 5.31/5.51 thf(fact_1803_vebt__pred_Osimps_I1_J,axiom,
% 5.31/5.51 ! [Uu: $o,Uv: $o] :
% 5.31/5.51 ( ( vEBT_vebt_pred @ ( vEBT_Leaf @ Uu @ Uv ) @ zero_zero_nat )
% 5.31/5.51 = none_nat ) ).
% 5.31/5.51
% 5.31/5.51 % vebt_pred.simps(1)
% 5.31/5.51 thf(fact_1804_vebt__succ_Osimps_I4_J,axiom,
% 5.31/5.51 ! [V2: product_prod_nat_nat,Vc: list_VEBT_VEBT,Vd2: vEBT_VEBT,Ve2: nat] :
% 5.31/5.51 ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vc @ Vd2 ) @ Ve2 )
% 5.31/5.51 = none_nat ) ).
% 5.31/5.51
% 5.31/5.51 % vebt_succ.simps(4)
% 5.31/5.51 thf(fact_1805_vebt__pred_Osimps_I5_J,axiom,
% 5.31/5.51 ! [V2: product_prod_nat_nat,Vd2: list_VEBT_VEBT,Ve2: vEBT_VEBT,Vf2: nat] :
% 5.31/5.51 ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vd2 @ Ve2 ) @ Vf2 )
% 5.31/5.51 = none_nat ) ).
% 5.31/5.51
% 5.31/5.51 % vebt_pred.simps(5)
% 5.31/5.51 thf(fact_1806_vebt__pred_Osimps_I6_J,axiom,
% 5.31/5.51 ! [V2: product_prod_nat_nat,Vh2: list_VEBT_VEBT,Vi2: vEBT_VEBT,Vj2: nat] :
% 5.31/5.51 ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vh2 @ Vi2 ) @ Vj2 )
% 5.31/5.51 = none_nat ) ).
% 5.31/5.51
% 5.31/5.51 % vebt_pred.simps(6)
% 5.31/5.51 thf(fact_1807_vebt__succ_Osimps_I5_J,axiom,
% 5.31/5.51 ! [V2: product_prod_nat_nat,Vg2: list_VEBT_VEBT,Vh2: vEBT_VEBT,Vi2: nat] :
% 5.31/5.51 ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vg2 @ Vh2 ) @ Vi2 )
% 5.31/5.51 = none_nat ) ).
% 5.31/5.51
% 5.31/5.51 % vebt_succ.simps(5)
% 5.31/5.51 thf(fact_1808_vebt__pred_Osimps_I2_J,axiom,
% 5.31/5.51 ! [A: $o,Uw2: $o] :
% 5.31/5.51 ( ( A
% 5.31/5.51 => ( ( vEBT_vebt_pred @ ( vEBT_Leaf @ A @ Uw2 ) @ ( suc @ zero_zero_nat ) )
% 5.31/5.51 = ( some_nat @ zero_zero_nat ) ) )
% 5.31/5.51 & ( ~ A
% 5.31/5.51 => ( ( vEBT_vebt_pred @ ( vEBT_Leaf @ A @ Uw2 ) @ ( suc @ zero_zero_nat ) )
% 5.31/5.51 = none_nat ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % vebt_pred.simps(2)
% 5.31/5.51 thf(fact_1809_vebt__succ_Osimps_I1_J,axiom,
% 5.31/5.51 ! [B: $o,Uu: $o] :
% 5.31/5.51 ( ( B
% 5.31/5.51 => ( ( vEBT_vebt_succ @ ( vEBT_Leaf @ Uu @ B ) @ zero_zero_nat )
% 5.31/5.51 = ( some_nat @ one_one_nat ) ) )
% 5.31/5.51 & ( ~ B
% 5.31/5.51 => ( ( vEBT_vebt_succ @ ( vEBT_Leaf @ Uu @ B ) @ zero_zero_nat )
% 5.31/5.51 = none_nat ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % vebt_succ.simps(1)
% 5.31/5.51 thf(fact_1810_vebt__pred_Osimps_I3_J,axiom,
% 5.31/5.51 ! [B: $o,A: $o,Va3: nat] :
% 5.31/5.51 ( ( B
% 5.31/5.51 => ( ( vEBT_vebt_pred @ ( vEBT_Leaf @ A @ B ) @ ( suc @ ( suc @ Va3 ) ) )
% 5.31/5.51 = ( some_nat @ one_one_nat ) ) )
% 5.31/5.51 & ( ~ B
% 5.31/5.51 => ( ( A
% 5.31/5.51 => ( ( vEBT_vebt_pred @ ( vEBT_Leaf @ A @ B ) @ ( suc @ ( suc @ Va3 ) ) )
% 5.31/5.51 = ( some_nat @ zero_zero_nat ) ) )
% 5.31/5.51 & ( ~ A
% 5.31/5.51 => ( ( vEBT_vebt_pred @ ( vEBT_Leaf @ A @ B ) @ ( suc @ ( suc @ Va3 ) ) )
% 5.31/5.51 = none_nat ) ) ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % vebt_pred.simps(3)
% 5.31/5.51 thf(fact_1811_vebt__delete_Osimps_I3_J,axiom,
% 5.31/5.51 ! [A: $o,B: $o,N: nat] :
% 5.31/5.51 ( ( vEBT_vebt_delete @ ( vEBT_Leaf @ A @ B ) @ ( suc @ ( suc @ N ) ) )
% 5.31/5.51 = ( vEBT_Leaf @ A @ B ) ) ).
% 5.31/5.51
% 5.31/5.51 % vebt_delete.simps(3)
% 5.31/5.51 thf(fact_1812_vebt__delete_Osimps_I1_J,axiom,
% 5.31/5.51 ! [A: $o,B: $o] :
% 5.31/5.51 ( ( vEBT_vebt_delete @ ( vEBT_Leaf @ A @ B ) @ zero_zero_nat )
% 5.31/5.51 = ( vEBT_Leaf @ $false @ B ) ) ).
% 5.31/5.51
% 5.31/5.51 % vebt_delete.simps(1)
% 5.31/5.51 thf(fact_1813_is__pred__in__set__def,axiom,
% 5.31/5.51 ( vEBT_is_pred_in_set
% 5.31/5.51 = ( ^ [Xs: set_nat,X4: nat,Y4: nat] :
% 5.31/5.51 ( ( member_nat @ Y4 @ Xs )
% 5.31/5.51 & ( ord_less_nat @ Y4 @ X4 )
% 5.31/5.51 & ! [Z4: nat] :
% 5.31/5.51 ( ( member_nat @ Z4 @ Xs )
% 5.31/5.51 => ( ( ord_less_nat @ Z4 @ X4 )
% 5.31/5.51 => ( ord_less_eq_nat @ Z4 @ Y4 ) ) ) ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % is_pred_in_set_def
% 5.31/5.51 thf(fact_1814_is__succ__in__set__def,axiom,
% 5.31/5.51 ( vEBT_is_succ_in_set
% 5.31/5.51 = ( ^ [Xs: set_nat,X4: nat,Y4: nat] :
% 5.31/5.51 ( ( member_nat @ Y4 @ Xs )
% 5.31/5.51 & ( ord_less_nat @ X4 @ Y4 )
% 5.31/5.51 & ! [Z4: nat] :
% 5.31/5.51 ( ( member_nat @ Z4 @ Xs )
% 5.31/5.51 => ( ( ord_less_nat @ X4 @ Z4 )
% 5.31/5.51 => ( ord_less_eq_nat @ Y4 @ Z4 ) ) ) ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % is_succ_in_set_def
% 5.31/5.51 thf(fact_1815_sum__squares__le__zero__iff,axiom,
% 5.31/5.51 ! [X: real,Y: real] :
% 5.31/5.51 ( ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ X @ X ) @ ( times_times_real @ Y @ Y ) ) @ zero_zero_real )
% 5.31/5.51 = ( ( X = zero_zero_real )
% 5.31/5.51 & ( Y = zero_zero_real ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % sum_squares_le_zero_iff
% 5.31/5.51 thf(fact_1816_sum__squares__le__zero__iff,axiom,
% 5.31/5.51 ! [X: rat,Y: rat] :
% 5.31/5.51 ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ X @ X ) @ ( times_times_rat @ Y @ Y ) ) @ zero_zero_rat )
% 5.31/5.51 = ( ( X = zero_zero_rat )
% 5.31/5.51 & ( Y = zero_zero_rat ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % sum_squares_le_zero_iff
% 5.31/5.51 thf(fact_1817_sum__squares__le__zero__iff,axiom,
% 5.31/5.51 ! [X: int,Y: int] :
% 5.31/5.51 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y @ Y ) ) @ zero_zero_int )
% 5.31/5.51 = ( ( X = zero_zero_int )
% 5.31/5.51 & ( Y = zero_zero_int ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % sum_squares_le_zero_iff
% 5.31/5.51 thf(fact_1818_sum__squares__gt__zero__iff,axiom,
% 5.31/5.51 ! [X: real,Y: real] :
% 5.31/5.51 ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( times_times_real @ X @ X ) @ ( times_times_real @ Y @ Y ) ) )
% 5.31/5.51 = ( ( X != zero_zero_real )
% 5.31/5.51 | ( Y != zero_zero_real ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % sum_squares_gt_zero_iff
% 5.31/5.51 thf(fact_1819_sum__squares__gt__zero__iff,axiom,
% 5.31/5.51 ! [X: rat,Y: rat] :
% 5.31/5.51 ( ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ ( times_times_rat @ X @ X ) @ ( times_times_rat @ Y @ Y ) ) )
% 5.31/5.51 = ( ( X != zero_zero_rat )
% 5.31/5.51 | ( Y != zero_zero_rat ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % sum_squares_gt_zero_iff
% 5.31/5.51 thf(fact_1820_sum__squares__gt__zero__iff,axiom,
% 5.31/5.51 ! [X: int,Y: int] :
% 5.31/5.51 ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y @ Y ) ) )
% 5.31/5.51 = ( ( X != zero_zero_int )
% 5.31/5.51 | ( Y != zero_zero_int ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % sum_squares_gt_zero_iff
% 5.31/5.51 thf(fact_1821_vebt__delete_Osimps_I2_J,axiom,
% 5.31/5.51 ! [A: $o,B: $o] :
% 5.31/5.51 ( ( vEBT_vebt_delete @ ( vEBT_Leaf @ A @ B ) @ ( suc @ zero_zero_nat ) )
% 5.31/5.51 = ( vEBT_Leaf @ A @ $false ) ) ).
% 5.31/5.51
% 5.31/5.51 % vebt_delete.simps(2)
% 5.31/5.51 thf(fact_1822_vebt__delete_Osimps_I5_J,axiom,
% 5.31/5.51 ! [Mi: nat,Ma: nat,TrLst2: list_VEBT_VEBT,Smry2: vEBT_VEBT,X: nat] :
% 5.31/5.51 ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ zero_zero_nat @ TrLst2 @ Smry2 ) @ X )
% 5.31/5.51 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ zero_zero_nat @ TrLst2 @ Smry2 ) ) ).
% 5.31/5.51
% 5.31/5.51 % vebt_delete.simps(5)
% 5.31/5.51 thf(fact_1823_vebt__delete_Osimps_I6_J,axiom,
% 5.31/5.51 ! [Mi: nat,Ma: nat,Tr2: list_VEBT_VEBT,Sm2: vEBT_VEBT,X: nat] :
% 5.31/5.51 ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ zero_zero_nat ) @ Tr2 @ Sm2 ) @ X )
% 5.31/5.51 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ zero_zero_nat ) @ Tr2 @ Sm2 ) ) ).
% 5.31/5.51
% 5.31/5.51 % vebt_delete.simps(6)
% 5.31/5.51 thf(fact_1824_add__def,axiom,
% 5.31/5.51 ( vEBT_VEBT_add
% 5.31/5.51 = ( vEBT_V4262088993061758097ft_nat @ plus_plus_nat ) ) ).
% 5.31/5.51
% 5.31/5.51 % add_def
% 5.31/5.51 thf(fact_1825_delete__correct,axiom,
% 5.31/5.51 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 5.31/5.51 ( ( vEBT_invar_vebt @ T @ N )
% 5.31/5.51 => ( ( vEBT_VEBT_set_vebt @ ( vEBT_vebt_delete @ T @ X ) )
% 5.31/5.51 = ( minus_minus_set_nat @ ( vEBT_set_vebt @ T ) @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % delete_correct
% 5.31/5.51 thf(fact_1826_double__eq__0__iff,axiom,
% 5.31/5.51 ! [A: real] :
% 5.31/5.51 ( ( ( plus_plus_real @ A @ A )
% 5.31/5.51 = zero_zero_real )
% 5.31/5.51 = ( A = zero_zero_real ) ) ).
% 5.31/5.51
% 5.31/5.51 % double_eq_0_iff
% 5.31/5.51 thf(fact_1827_double__eq__0__iff,axiom,
% 5.31/5.51 ! [A: rat] :
% 5.31/5.51 ( ( ( plus_plus_rat @ A @ A )
% 5.31/5.51 = zero_zero_rat )
% 5.31/5.51 = ( A = zero_zero_rat ) ) ).
% 5.31/5.51
% 5.31/5.51 % double_eq_0_iff
% 5.31/5.51 thf(fact_1828_double__eq__0__iff,axiom,
% 5.31/5.51 ! [A: int] :
% 5.31/5.51 ( ( ( plus_plus_int @ A @ A )
% 5.31/5.51 = zero_zero_int )
% 5.31/5.51 = ( A = zero_zero_int ) ) ).
% 5.31/5.51
% 5.31/5.51 % double_eq_0_iff
% 5.31/5.51 thf(fact_1829_add__shift,axiom,
% 5.31/5.51 ! [X: nat,Y: nat,Z3: nat] :
% 5.31/5.51 ( ( ( plus_plus_nat @ X @ Y )
% 5.31/5.51 = Z3 )
% 5.31/5.51 = ( ( vEBT_VEBT_add @ ( some_nat @ X ) @ ( some_nat @ Y ) )
% 5.31/5.51 = ( some_nat @ Z3 ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % add_shift
% 5.31/5.51 thf(fact_1830_delete__correct_H,axiom,
% 5.31/5.51 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 5.31/5.51 ( ( vEBT_invar_vebt @ T @ N )
% 5.31/5.51 => ( ( vEBT_VEBT_set_vebt @ ( vEBT_vebt_delete @ T @ X ) )
% 5.31/5.51 = ( minus_minus_set_nat @ ( vEBT_VEBT_set_vebt @ T ) @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % delete_correct'
% 5.31/5.51 thf(fact_1831_obtain__set__succ,axiom,
% 5.31/5.51 ! [X: nat,Z3: nat,A4: set_nat,B5: set_nat] :
% 5.31/5.51 ( ( ord_less_nat @ X @ Z3 )
% 5.31/5.51 => ( ( vEBT_VEBT_max_in_set @ A4 @ Z3 )
% 5.31/5.51 => ( ( finite_finite_nat @ B5 )
% 5.31/5.51 => ( ( A4 = B5 )
% 5.31/5.51 => ? [X_12: nat] : ( vEBT_is_succ_in_set @ A4 @ X @ X_12 ) ) ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % obtain_set_succ
% 5.31/5.51 thf(fact_1832_obtain__set__pred,axiom,
% 5.31/5.51 ! [Z3: nat,X: nat,A4: set_nat] :
% 5.31/5.51 ( ( ord_less_nat @ Z3 @ X )
% 5.31/5.51 => ( ( vEBT_VEBT_min_in_set @ A4 @ Z3 )
% 5.31/5.51 => ( ( finite_finite_nat @ A4 )
% 5.31/5.51 => ? [X_12: nat] : ( vEBT_is_pred_in_set @ A4 @ X @ X_12 ) ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % obtain_set_pred
% 5.31/5.51 thf(fact_1833_length__pos__if__in__set,axiom,
% 5.31/5.51 ! [X: complex,Xs2: list_complex] :
% 5.31/5.51 ( ( member_complex @ X @ ( set_complex2 @ Xs2 ) )
% 5.31/5.51 => ( ord_less_nat @ zero_zero_nat @ ( size_s3451745648224563538omplex @ Xs2 ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % length_pos_if_in_set
% 5.31/5.51 thf(fact_1834_length__pos__if__in__set,axiom,
% 5.31/5.51 ! [X: real,Xs2: list_real] :
% 5.31/5.51 ( ( member_real @ X @ ( set_real2 @ Xs2 ) )
% 5.31/5.51 => ( ord_less_nat @ zero_zero_nat @ ( size_size_list_real @ Xs2 ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % length_pos_if_in_set
% 5.31/5.51 thf(fact_1835_length__pos__if__in__set,axiom,
% 5.31/5.51 ! [X: set_nat,Xs2: list_set_nat] :
% 5.31/5.51 ( ( member_set_nat @ X @ ( set_set_nat2 @ Xs2 ) )
% 5.31/5.51 => ( ord_less_nat @ zero_zero_nat @ ( size_s3254054031482475050et_nat @ Xs2 ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % length_pos_if_in_set
% 5.31/5.51 thf(fact_1836_length__pos__if__in__set,axiom,
% 5.31/5.51 ! [X: vEBT_VEBT,Xs2: list_VEBT_VEBT] :
% 5.31/5.51 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 5.31/5.51 => ( ord_less_nat @ zero_zero_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % length_pos_if_in_set
% 5.31/5.51 thf(fact_1837_length__pos__if__in__set,axiom,
% 5.31/5.51 ! [X: $o,Xs2: list_o] :
% 5.31/5.51 ( ( member_o @ X @ ( set_o2 @ Xs2 ) )
% 5.31/5.51 => ( ord_less_nat @ zero_zero_nat @ ( size_size_list_o @ Xs2 ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % length_pos_if_in_set
% 5.31/5.51 thf(fact_1838_length__pos__if__in__set,axiom,
% 5.31/5.51 ! [X: nat,Xs2: list_nat] :
% 5.31/5.51 ( ( member_nat @ X @ ( set_nat2 @ Xs2 ) )
% 5.31/5.51 => ( ord_less_nat @ zero_zero_nat @ ( size_size_list_nat @ Xs2 ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % length_pos_if_in_set
% 5.31/5.51 thf(fact_1839_length__pos__if__in__set,axiom,
% 5.31/5.51 ! [X: int,Xs2: list_int] :
% 5.31/5.51 ( ( member_int @ X @ ( set_int2 @ Xs2 ) )
% 5.31/5.51 => ( ord_less_nat @ zero_zero_nat @ ( size_size_list_int @ Xs2 ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % length_pos_if_in_set
% 5.31/5.51 thf(fact_1840_option_Osize__gen_I2_J,axiom,
% 5.31/5.51 ! [X: product_prod_nat_nat > nat,X2: product_prod_nat_nat] :
% 5.31/5.51 ( ( size_o8335143837870341156at_nat @ X @ ( some_P7363390416028606310at_nat @ X2 ) )
% 5.31/5.51 = ( plus_plus_nat @ ( X @ X2 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % option.size_gen(2)
% 5.31/5.51 thf(fact_1841_option_Osize__gen_I2_J,axiom,
% 5.31/5.51 ! [X: nat > nat,X2: nat] :
% 5.31/5.51 ( ( size_option_nat @ X @ ( some_nat @ X2 ) )
% 5.31/5.51 = ( plus_plus_nat @ ( X @ X2 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % option.size_gen(2)
% 5.31/5.51 thf(fact_1842_option_Osize__gen_I2_J,axiom,
% 5.31/5.51 ! [X: num > nat,X2: num] :
% 5.31/5.51 ( ( size_option_num @ X @ ( some_num @ X2 ) )
% 5.31/5.51 = ( plus_plus_nat @ ( X @ X2 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % option.size_gen(2)
% 5.31/5.51 thf(fact_1843_add__scale__eq__noteq,axiom,
% 5.31/5.51 ! [R3: complex,A: complex,B: complex,C2: complex,D: complex] :
% 5.31/5.51 ( ( R3 != zero_zero_complex )
% 5.31/5.51 => ( ( ( A = B )
% 5.31/5.51 & ( C2 != D ) )
% 5.31/5.51 => ( ( plus_plus_complex @ A @ ( times_times_complex @ R3 @ C2 ) )
% 5.31/5.51 != ( plus_plus_complex @ B @ ( times_times_complex @ R3 @ D ) ) ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % add_scale_eq_noteq
% 5.31/5.51 thf(fact_1844_add__scale__eq__noteq,axiom,
% 5.31/5.51 ! [R3: real,A: real,B: real,C2: real,D: real] :
% 5.31/5.51 ( ( R3 != zero_zero_real )
% 5.31/5.51 => ( ( ( A = B )
% 5.31/5.51 & ( C2 != D ) )
% 5.31/5.51 => ( ( plus_plus_real @ A @ ( times_times_real @ R3 @ C2 ) )
% 5.31/5.51 != ( plus_plus_real @ B @ ( times_times_real @ R3 @ D ) ) ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % add_scale_eq_noteq
% 5.31/5.51 thf(fact_1845_add__scale__eq__noteq,axiom,
% 5.31/5.51 ! [R3: rat,A: rat,B: rat,C2: rat,D: rat] :
% 5.31/5.51 ( ( R3 != zero_zero_rat )
% 5.31/5.51 => ( ( ( A = B )
% 5.31/5.51 & ( C2 != D ) )
% 5.31/5.51 => ( ( plus_plus_rat @ A @ ( times_times_rat @ R3 @ C2 ) )
% 5.31/5.51 != ( plus_plus_rat @ B @ ( times_times_rat @ R3 @ D ) ) ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % add_scale_eq_noteq
% 5.31/5.51 thf(fact_1846_add__scale__eq__noteq,axiom,
% 5.31/5.51 ! [R3: nat,A: nat,B: nat,C2: nat,D: nat] :
% 5.31/5.51 ( ( R3 != zero_zero_nat )
% 5.31/5.51 => ( ( ( A = B )
% 5.31/5.51 & ( C2 != D ) )
% 5.31/5.51 => ( ( plus_plus_nat @ A @ ( times_times_nat @ R3 @ C2 ) )
% 5.31/5.51 != ( plus_plus_nat @ B @ ( times_times_nat @ R3 @ D ) ) ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % add_scale_eq_noteq
% 5.31/5.51 thf(fact_1847_add__scale__eq__noteq,axiom,
% 5.31/5.51 ! [R3: int,A: int,B: int,C2: int,D: int] :
% 5.31/5.51 ( ( R3 != zero_zero_int )
% 5.31/5.51 => ( ( ( A = B )
% 5.31/5.51 & ( C2 != D ) )
% 5.31/5.51 => ( ( plus_plus_int @ A @ ( times_times_int @ R3 @ C2 ) )
% 5.31/5.51 != ( plus_plus_int @ B @ ( times_times_int @ R3 @ D ) ) ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % add_scale_eq_noteq
% 5.31/5.51 thf(fact_1848_set__vebt__finite,axiom,
% 5.31/5.51 ! [T: vEBT_VEBT,N: nat] :
% 5.31/5.51 ( ( vEBT_invar_vebt @ T @ N )
% 5.31/5.51 => ( finite_finite_nat @ ( vEBT_VEBT_set_vebt @ T ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % set_vebt_finite
% 5.31/5.51 thf(fact_1849_pred__none__empty,axiom,
% 5.31/5.51 ! [Xs2: set_nat,A: nat] :
% 5.31/5.51 ( ~ ? [X_12: nat] : ( vEBT_is_pred_in_set @ Xs2 @ A @ X_12 )
% 5.31/5.51 => ( ( finite_finite_nat @ Xs2 )
% 5.31/5.51 => ~ ? [X5: nat] :
% 5.31/5.51 ( ( member_nat @ X5 @ Xs2 )
% 5.31/5.51 & ( ord_less_nat @ X5 @ A ) ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % pred_none_empty
% 5.31/5.51 thf(fact_1850_succ__none__empty,axiom,
% 5.31/5.51 ! [Xs2: set_nat,A: nat] :
% 5.31/5.51 ( ~ ? [X_12: nat] : ( vEBT_is_succ_in_set @ Xs2 @ A @ X_12 )
% 5.31/5.51 => ( ( finite_finite_nat @ Xs2 )
% 5.31/5.51 => ~ ? [X5: nat] :
% 5.31/5.51 ( ( member_nat @ X5 @ Xs2 )
% 5.31/5.51 & ( ord_less_nat @ A @ X5 ) ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % succ_none_empty
% 5.31/5.51 thf(fact_1851_diff__self,axiom,
% 5.31/5.51 ! [A: complex] :
% 5.31/5.51 ( ( minus_minus_complex @ A @ A )
% 5.31/5.51 = zero_zero_complex ) ).
% 5.31/5.51
% 5.31/5.51 % diff_self
% 5.31/5.51 thf(fact_1852_diff__self,axiom,
% 5.31/5.51 ! [A: real] :
% 5.31/5.51 ( ( minus_minus_real @ A @ A )
% 5.31/5.51 = zero_zero_real ) ).
% 5.31/5.51
% 5.31/5.51 % diff_self
% 5.31/5.51 thf(fact_1853_diff__self,axiom,
% 5.31/5.51 ! [A: rat] :
% 5.31/5.51 ( ( minus_minus_rat @ A @ A )
% 5.31/5.51 = zero_zero_rat ) ).
% 5.31/5.51
% 5.31/5.51 % diff_self
% 5.31/5.51 thf(fact_1854_diff__self,axiom,
% 5.31/5.51 ! [A: int] :
% 5.31/5.51 ( ( minus_minus_int @ A @ A )
% 5.31/5.51 = zero_zero_int ) ).
% 5.31/5.51
% 5.31/5.51 % diff_self
% 5.31/5.51 thf(fact_1855_diff__0__right,axiom,
% 5.31/5.51 ! [A: complex] :
% 5.31/5.51 ( ( minus_minus_complex @ A @ zero_zero_complex )
% 5.31/5.51 = A ) ).
% 5.31/5.51
% 5.31/5.51 % diff_0_right
% 5.31/5.51 thf(fact_1856_diff__0__right,axiom,
% 5.31/5.51 ! [A: real] :
% 5.31/5.51 ( ( minus_minus_real @ A @ zero_zero_real )
% 5.31/5.51 = A ) ).
% 5.31/5.51
% 5.31/5.51 % diff_0_right
% 5.31/5.51 thf(fact_1857_diff__0__right,axiom,
% 5.31/5.51 ! [A: rat] :
% 5.31/5.51 ( ( minus_minus_rat @ A @ zero_zero_rat )
% 5.31/5.51 = A ) ).
% 5.31/5.51
% 5.31/5.51 % diff_0_right
% 5.31/5.51 thf(fact_1858_diff__0__right,axiom,
% 5.31/5.51 ! [A: int] :
% 5.31/5.51 ( ( minus_minus_int @ A @ zero_zero_int )
% 5.31/5.51 = A ) ).
% 5.31/5.51
% 5.31/5.51 % diff_0_right
% 5.31/5.51 thf(fact_1859_zero__diff,axiom,
% 5.31/5.51 ! [A: nat] :
% 5.31/5.51 ( ( minus_minus_nat @ zero_zero_nat @ A )
% 5.31/5.51 = zero_zero_nat ) ).
% 5.31/5.51
% 5.31/5.51 % zero_diff
% 5.31/5.51 thf(fact_1860_diff__zero,axiom,
% 5.31/5.51 ! [A: complex] :
% 5.31/5.51 ( ( minus_minus_complex @ A @ zero_zero_complex )
% 5.31/5.51 = A ) ).
% 5.31/5.51
% 5.31/5.51 % diff_zero
% 5.31/5.51 thf(fact_1861_diff__zero,axiom,
% 5.31/5.51 ! [A: real] :
% 5.31/5.51 ( ( minus_minus_real @ A @ zero_zero_real )
% 5.31/5.51 = A ) ).
% 5.31/5.51
% 5.31/5.51 % diff_zero
% 5.31/5.51 thf(fact_1862_diff__zero,axiom,
% 5.31/5.51 ! [A: rat] :
% 5.31/5.51 ( ( minus_minus_rat @ A @ zero_zero_rat )
% 5.31/5.51 = A ) ).
% 5.31/5.51
% 5.31/5.51 % diff_zero
% 5.31/5.51 thf(fact_1863_diff__zero,axiom,
% 5.31/5.51 ! [A: nat] :
% 5.31/5.51 ( ( minus_minus_nat @ A @ zero_zero_nat )
% 5.31/5.51 = A ) ).
% 5.31/5.51
% 5.31/5.51 % diff_zero
% 5.31/5.51 thf(fact_1864_diff__zero,axiom,
% 5.31/5.51 ! [A: int] :
% 5.31/5.51 ( ( minus_minus_int @ A @ zero_zero_int )
% 5.31/5.51 = A ) ).
% 5.31/5.51
% 5.31/5.51 % diff_zero
% 5.31/5.51 thf(fact_1865_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 5.31/5.51 ! [A: complex] :
% 5.31/5.51 ( ( minus_minus_complex @ A @ A )
% 5.31/5.51 = zero_zero_complex ) ).
% 5.31/5.51
% 5.31/5.51 % cancel_comm_monoid_add_class.diff_cancel
% 5.31/5.51 thf(fact_1866_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 5.31/5.51 ! [A: real] :
% 5.31/5.51 ( ( minus_minus_real @ A @ A )
% 5.31/5.51 = zero_zero_real ) ).
% 5.31/5.51
% 5.31/5.51 % cancel_comm_monoid_add_class.diff_cancel
% 5.31/5.51 thf(fact_1867_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 5.31/5.51 ! [A: rat] :
% 5.31/5.51 ( ( minus_minus_rat @ A @ A )
% 5.31/5.51 = zero_zero_rat ) ).
% 5.31/5.51
% 5.31/5.51 % cancel_comm_monoid_add_class.diff_cancel
% 5.31/5.51 thf(fact_1868_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 5.31/5.51 ! [A: nat] :
% 5.31/5.51 ( ( minus_minus_nat @ A @ A )
% 5.31/5.51 = zero_zero_nat ) ).
% 5.31/5.51
% 5.31/5.51 % cancel_comm_monoid_add_class.diff_cancel
% 5.31/5.51 thf(fact_1869_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 5.31/5.51 ! [A: int] :
% 5.31/5.51 ( ( minus_minus_int @ A @ A )
% 5.31/5.51 = zero_zero_int ) ).
% 5.31/5.51
% 5.31/5.51 % cancel_comm_monoid_add_class.diff_cancel
% 5.31/5.51 thf(fact_1870_add__diff__cancel__right_H,axiom,
% 5.31/5.51 ! [A: real,B: real] :
% 5.31/5.51 ( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ B )
% 5.31/5.51 = A ) ).
% 5.31/5.51
% 5.31/5.51 % add_diff_cancel_right'
% 5.31/5.51 thf(fact_1871_add__diff__cancel__right_H,axiom,
% 5.31/5.51 ! [A: rat,B: rat] :
% 5.31/5.51 ( ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ B )
% 5.31/5.51 = A ) ).
% 5.31/5.51
% 5.31/5.51 % add_diff_cancel_right'
% 5.31/5.51 thf(fact_1872_add__diff__cancel__right_H,axiom,
% 5.31/5.51 ! [A: nat,B: nat] :
% 5.31/5.51 ( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 5.31/5.51 = A ) ).
% 5.31/5.51
% 5.31/5.51 % add_diff_cancel_right'
% 5.31/5.51 thf(fact_1873_add__diff__cancel__right_H,axiom,
% 5.31/5.51 ! [A: int,B: int] :
% 5.31/5.51 ( ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ B )
% 5.31/5.51 = A ) ).
% 5.31/5.51
% 5.31/5.51 % add_diff_cancel_right'
% 5.31/5.51 thf(fact_1874_add__diff__cancel__right,axiom,
% 5.31/5.51 ! [A: real,C2: real,B: real] :
% 5.31/5.51 ( ( minus_minus_real @ ( plus_plus_real @ A @ C2 ) @ ( plus_plus_real @ B @ C2 ) )
% 5.31/5.51 = ( minus_minus_real @ A @ B ) ) ).
% 5.31/5.51
% 5.31/5.51 % add_diff_cancel_right
% 5.31/5.51 thf(fact_1875_add__diff__cancel__right,axiom,
% 5.31/5.51 ! [A: rat,C2: rat,B: rat] :
% 5.31/5.51 ( ( minus_minus_rat @ ( plus_plus_rat @ A @ C2 ) @ ( plus_plus_rat @ B @ C2 ) )
% 5.31/5.51 = ( minus_minus_rat @ A @ B ) ) ).
% 5.31/5.51
% 5.31/5.51 % add_diff_cancel_right
% 5.31/5.51 thf(fact_1876_add__diff__cancel__right,axiom,
% 5.31/5.51 ! [A: nat,C2: nat,B: nat] :
% 5.31/5.51 ( ( minus_minus_nat @ ( plus_plus_nat @ A @ C2 ) @ ( plus_plus_nat @ B @ C2 ) )
% 5.31/5.51 = ( minus_minus_nat @ A @ B ) ) ).
% 5.31/5.51
% 5.31/5.51 % add_diff_cancel_right
% 5.31/5.51 thf(fact_1877_add__diff__cancel__right,axiom,
% 5.31/5.51 ! [A: int,C2: int,B: int] :
% 5.31/5.51 ( ( minus_minus_int @ ( plus_plus_int @ A @ C2 ) @ ( plus_plus_int @ B @ C2 ) )
% 5.31/5.51 = ( minus_minus_int @ A @ B ) ) ).
% 5.31/5.51
% 5.31/5.51 % add_diff_cancel_right
% 5.31/5.51 thf(fact_1878_add__diff__cancel__left_H,axiom,
% 5.31/5.51 ! [A: real,B: real] :
% 5.31/5.51 ( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ A )
% 5.31/5.51 = B ) ).
% 5.31/5.51
% 5.31/5.51 % add_diff_cancel_left'
% 5.31/5.51 thf(fact_1879_add__diff__cancel__left_H,axiom,
% 5.31/5.51 ! [A: rat,B: rat] :
% 5.31/5.51 ( ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ A )
% 5.31/5.51 = B ) ).
% 5.31/5.51
% 5.31/5.51 % add_diff_cancel_left'
% 5.31/5.51 thf(fact_1880_add__diff__cancel__left_H,axiom,
% 5.31/5.51 ! [A: nat,B: nat] :
% 5.31/5.51 ( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ A )
% 5.31/5.51 = B ) ).
% 5.31/5.51
% 5.31/5.51 % add_diff_cancel_left'
% 5.31/5.51 thf(fact_1881_add__diff__cancel__left_H,axiom,
% 5.31/5.51 ! [A: int,B: int] :
% 5.31/5.51 ( ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ A )
% 5.31/5.51 = B ) ).
% 5.31/5.51
% 5.31/5.51 % add_diff_cancel_left'
% 5.31/5.51 thf(fact_1882_add__diff__cancel__left,axiom,
% 5.31/5.51 ! [C2: real,A: real,B: real] :
% 5.31/5.51 ( ( minus_minus_real @ ( plus_plus_real @ C2 @ A ) @ ( plus_plus_real @ C2 @ B ) )
% 5.31/5.51 = ( minus_minus_real @ A @ B ) ) ).
% 5.31/5.51
% 5.31/5.51 % add_diff_cancel_left
% 5.31/5.51 thf(fact_1883_add__diff__cancel__left,axiom,
% 5.31/5.51 ! [C2: rat,A: rat,B: rat] :
% 5.31/5.51 ( ( minus_minus_rat @ ( plus_plus_rat @ C2 @ A ) @ ( plus_plus_rat @ C2 @ B ) )
% 5.31/5.51 = ( minus_minus_rat @ A @ B ) ) ).
% 5.31/5.51
% 5.31/5.51 % add_diff_cancel_left
% 5.31/5.51 thf(fact_1884_add__diff__cancel__left,axiom,
% 5.31/5.51 ! [C2: nat,A: nat,B: nat] :
% 5.31/5.51 ( ( minus_minus_nat @ ( plus_plus_nat @ C2 @ A ) @ ( plus_plus_nat @ C2 @ B ) )
% 5.31/5.51 = ( minus_minus_nat @ A @ B ) ) ).
% 5.31/5.51
% 5.31/5.51 % add_diff_cancel_left
% 5.31/5.51 thf(fact_1885_add__diff__cancel__left,axiom,
% 5.31/5.51 ! [C2: int,A: int,B: int] :
% 5.31/5.51 ( ( minus_minus_int @ ( plus_plus_int @ C2 @ A ) @ ( plus_plus_int @ C2 @ B ) )
% 5.31/5.51 = ( minus_minus_int @ A @ B ) ) ).
% 5.31/5.51
% 5.31/5.51 % add_diff_cancel_left
% 5.31/5.51 thf(fact_1886_diff__add__cancel,axiom,
% 5.31/5.51 ! [A: real,B: real] :
% 5.31/5.51 ( ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ B )
% 5.31/5.51 = A ) ).
% 5.31/5.51
% 5.31/5.51 % diff_add_cancel
% 5.31/5.51 thf(fact_1887_diff__add__cancel,axiom,
% 5.31/5.51 ! [A: rat,B: rat] :
% 5.31/5.51 ( ( plus_plus_rat @ ( minus_minus_rat @ A @ B ) @ B )
% 5.31/5.51 = A ) ).
% 5.31/5.51
% 5.31/5.51 % diff_add_cancel
% 5.31/5.51 thf(fact_1888_diff__add__cancel,axiom,
% 5.31/5.51 ! [A: int,B: int] :
% 5.31/5.51 ( ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ B )
% 5.31/5.51 = A ) ).
% 5.31/5.51
% 5.31/5.51 % diff_add_cancel
% 5.31/5.51 thf(fact_1889_add__diff__cancel,axiom,
% 5.31/5.51 ! [A: real,B: real] :
% 5.31/5.51 ( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ B )
% 5.31/5.51 = A ) ).
% 5.31/5.51
% 5.31/5.51 % add_diff_cancel
% 5.31/5.51 thf(fact_1890_add__diff__cancel,axiom,
% 5.31/5.51 ! [A: rat,B: rat] :
% 5.31/5.51 ( ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ B )
% 5.31/5.51 = A ) ).
% 5.31/5.51
% 5.31/5.51 % add_diff_cancel
% 5.31/5.51 thf(fact_1891_add__diff__cancel,axiom,
% 5.31/5.51 ! [A: int,B: int] :
% 5.31/5.51 ( ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ B )
% 5.31/5.51 = A ) ).
% 5.31/5.51
% 5.31/5.51 % add_diff_cancel
% 5.31/5.51 thf(fact_1892_diff__ge__0__iff__ge,axiom,
% 5.31/5.51 ! [A: real,B: real] :
% 5.31/5.51 ( ( ord_less_eq_real @ zero_zero_real @ ( minus_minus_real @ A @ B ) )
% 5.31/5.51 = ( ord_less_eq_real @ B @ A ) ) ).
% 5.31/5.51
% 5.31/5.51 % diff_ge_0_iff_ge
% 5.31/5.51 thf(fact_1893_diff__ge__0__iff__ge,axiom,
% 5.31/5.51 ! [A: rat,B: rat] :
% 5.31/5.51 ( ( ord_less_eq_rat @ zero_zero_rat @ ( minus_minus_rat @ A @ B ) )
% 5.31/5.51 = ( ord_less_eq_rat @ B @ A ) ) ).
% 5.31/5.51
% 5.31/5.51 % diff_ge_0_iff_ge
% 5.31/5.51 thf(fact_1894_diff__ge__0__iff__ge,axiom,
% 5.31/5.51 ! [A: int,B: int] :
% 5.31/5.51 ( ( ord_less_eq_int @ zero_zero_int @ ( minus_minus_int @ A @ B ) )
% 5.31/5.51 = ( ord_less_eq_int @ B @ A ) ) ).
% 5.31/5.51
% 5.31/5.51 % diff_ge_0_iff_ge
% 5.31/5.51 thf(fact_1895_diff__gt__0__iff__gt,axiom,
% 5.31/5.51 ! [A: real,B: real] :
% 5.31/5.51 ( ( ord_less_real @ zero_zero_real @ ( minus_minus_real @ A @ B ) )
% 5.31/5.51 = ( ord_less_real @ B @ A ) ) ).
% 5.31/5.51
% 5.31/5.51 % diff_gt_0_iff_gt
% 5.31/5.51 thf(fact_1896_diff__gt__0__iff__gt,axiom,
% 5.31/5.51 ! [A: rat,B: rat] :
% 5.31/5.51 ( ( ord_less_rat @ zero_zero_rat @ ( minus_minus_rat @ A @ B ) )
% 5.31/5.51 = ( ord_less_rat @ B @ A ) ) ).
% 5.31/5.51
% 5.31/5.51 % diff_gt_0_iff_gt
% 5.31/5.51 thf(fact_1897_diff__gt__0__iff__gt,axiom,
% 5.31/5.51 ! [A: int,B: int] :
% 5.31/5.51 ( ( ord_less_int @ zero_zero_int @ ( minus_minus_int @ A @ B ) )
% 5.31/5.51 = ( ord_less_int @ B @ A ) ) ).
% 5.31/5.51
% 5.31/5.51 % diff_gt_0_iff_gt
% 5.31/5.51 thf(fact_1898_le__add__diff__inverse2,axiom,
% 5.31/5.51 ! [B: real,A: real] :
% 5.31/5.51 ( ( ord_less_eq_real @ B @ A )
% 5.31/5.51 => ( ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ B )
% 5.31/5.51 = A ) ) ).
% 5.31/5.51
% 5.31/5.51 % le_add_diff_inverse2
% 5.31/5.51 thf(fact_1899_le__add__diff__inverse2,axiom,
% 5.31/5.51 ! [B: rat,A: rat] :
% 5.31/5.51 ( ( ord_less_eq_rat @ B @ A )
% 5.31/5.51 => ( ( plus_plus_rat @ ( minus_minus_rat @ A @ B ) @ B )
% 5.31/5.51 = A ) ) ).
% 5.31/5.51
% 5.31/5.51 % le_add_diff_inverse2
% 5.31/5.51 thf(fact_1900_le__add__diff__inverse2,axiom,
% 5.31/5.51 ! [B: nat,A: nat] :
% 5.31/5.51 ( ( ord_less_eq_nat @ B @ A )
% 5.31/5.51 => ( ( plus_plus_nat @ ( minus_minus_nat @ A @ B ) @ B )
% 5.31/5.51 = A ) ) ).
% 5.31/5.51
% 5.31/5.51 % le_add_diff_inverse2
% 5.31/5.51 thf(fact_1901_le__add__diff__inverse2,axiom,
% 5.31/5.51 ! [B: int,A: int] :
% 5.31/5.51 ( ( ord_less_eq_int @ B @ A )
% 5.31/5.51 => ( ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ B )
% 5.31/5.51 = A ) ) ).
% 5.31/5.51
% 5.31/5.51 % le_add_diff_inverse2
% 5.31/5.51 thf(fact_1902_le__add__diff__inverse,axiom,
% 5.31/5.51 ! [B: real,A: real] :
% 5.31/5.51 ( ( ord_less_eq_real @ B @ A )
% 5.31/5.51 => ( ( plus_plus_real @ B @ ( minus_minus_real @ A @ B ) )
% 5.31/5.51 = A ) ) ).
% 5.31/5.51
% 5.31/5.51 % le_add_diff_inverse
% 5.31/5.51 thf(fact_1903_le__add__diff__inverse,axiom,
% 5.31/5.51 ! [B: rat,A: rat] :
% 5.31/5.51 ( ( ord_less_eq_rat @ B @ A )
% 5.31/5.51 => ( ( plus_plus_rat @ B @ ( minus_minus_rat @ A @ B ) )
% 5.31/5.51 = A ) ) ).
% 5.31/5.51
% 5.31/5.51 % le_add_diff_inverse
% 5.31/5.51 thf(fact_1904_le__add__diff__inverse,axiom,
% 5.31/5.51 ! [B: nat,A: nat] :
% 5.31/5.51 ( ( ord_less_eq_nat @ B @ A )
% 5.31/5.51 => ( ( plus_plus_nat @ B @ ( minus_minus_nat @ A @ B ) )
% 5.31/5.51 = A ) ) ).
% 5.31/5.51
% 5.31/5.51 % le_add_diff_inverse
% 5.31/5.51 thf(fact_1905_le__add__diff__inverse,axiom,
% 5.31/5.51 ! [B: int,A: int] :
% 5.31/5.51 ( ( ord_less_eq_int @ B @ A )
% 5.31/5.51 => ( ( plus_plus_int @ B @ ( minus_minus_int @ A @ B ) )
% 5.31/5.51 = A ) ) ).
% 5.31/5.51
% 5.31/5.51 % le_add_diff_inverse
% 5.31/5.51 thf(fact_1906_diff__add__zero,axiom,
% 5.31/5.51 ! [A: nat,B: nat] :
% 5.31/5.51 ( ( minus_minus_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 5.31/5.51 = zero_zero_nat ) ).
% 5.31/5.51
% 5.31/5.51 % diff_add_zero
% 5.31/5.51 thf(fact_1907_diff__numeral__special_I9_J,axiom,
% 5.31/5.51 ( ( minus_8373710615458151222nteger @ one_one_Code_integer @ one_one_Code_integer )
% 5.31/5.51 = zero_z3403309356797280102nteger ) ).
% 5.31/5.51
% 5.31/5.51 % diff_numeral_special(9)
% 5.31/5.51 thf(fact_1908_diff__numeral__special_I9_J,axiom,
% 5.31/5.51 ( ( minus_minus_complex @ one_one_complex @ one_one_complex )
% 5.31/5.51 = zero_zero_complex ) ).
% 5.31/5.51
% 5.31/5.51 % diff_numeral_special(9)
% 5.31/5.51 thf(fact_1909_diff__numeral__special_I9_J,axiom,
% 5.31/5.51 ( ( minus_minus_real @ one_one_real @ one_one_real )
% 5.31/5.51 = zero_zero_real ) ).
% 5.31/5.51
% 5.31/5.51 % diff_numeral_special(9)
% 5.31/5.51 thf(fact_1910_diff__numeral__special_I9_J,axiom,
% 5.31/5.51 ( ( minus_minus_rat @ one_one_rat @ one_one_rat )
% 5.31/5.51 = zero_zero_rat ) ).
% 5.31/5.51
% 5.31/5.51 % diff_numeral_special(9)
% 5.31/5.51 thf(fact_1911_diff__numeral__special_I9_J,axiom,
% 5.31/5.51 ( ( minus_minus_int @ one_one_int @ one_one_int )
% 5.31/5.51 = zero_zero_int ) ).
% 5.31/5.51
% 5.31/5.51 % diff_numeral_special(9)
% 5.31/5.51 thf(fact_1912_neq__if__length__neq,axiom,
% 5.31/5.51 ! [Xs2: list_VEBT_VEBT,Ys: list_VEBT_VEBT] :
% 5.31/5.51 ( ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 5.31/5.51 != ( size_s6755466524823107622T_VEBT @ Ys ) )
% 5.31/5.51 => ( Xs2 != Ys ) ) ).
% 5.31/5.51
% 5.31/5.51 % neq_if_length_neq
% 5.31/5.51 thf(fact_1913_neq__if__length__neq,axiom,
% 5.31/5.51 ! [Xs2: list_o,Ys: list_o] :
% 5.31/5.51 ( ( ( size_size_list_o @ Xs2 )
% 5.31/5.51 != ( size_size_list_o @ Ys ) )
% 5.31/5.51 => ( Xs2 != Ys ) ) ).
% 5.31/5.51
% 5.31/5.51 % neq_if_length_neq
% 5.31/5.51 thf(fact_1914_neq__if__length__neq,axiom,
% 5.31/5.51 ! [Xs2: list_nat,Ys: list_nat] :
% 5.31/5.51 ( ( ( size_size_list_nat @ Xs2 )
% 5.31/5.51 != ( size_size_list_nat @ Ys ) )
% 5.31/5.51 => ( Xs2 != Ys ) ) ).
% 5.31/5.51
% 5.31/5.51 % neq_if_length_neq
% 5.31/5.51 thf(fact_1915_neq__if__length__neq,axiom,
% 5.31/5.51 ! [Xs2: list_int,Ys: list_int] :
% 5.31/5.51 ( ( ( size_size_list_int @ Xs2 )
% 5.31/5.51 != ( size_size_list_int @ Ys ) )
% 5.31/5.51 => ( Xs2 != Ys ) ) ).
% 5.31/5.51
% 5.31/5.51 % neq_if_length_neq
% 5.31/5.51 thf(fact_1916_Ex__list__of__length,axiom,
% 5.31/5.51 ! [N: nat] :
% 5.31/5.51 ? [Xs3: list_VEBT_VEBT] :
% 5.31/5.51 ( ( size_s6755466524823107622T_VEBT @ Xs3 )
% 5.31/5.51 = N ) ).
% 5.31/5.51
% 5.31/5.51 % Ex_list_of_length
% 5.31/5.51 thf(fact_1917_Ex__list__of__length,axiom,
% 5.31/5.51 ! [N: nat] :
% 5.31/5.51 ? [Xs3: list_o] :
% 5.31/5.51 ( ( size_size_list_o @ Xs3 )
% 5.31/5.51 = N ) ).
% 5.31/5.51
% 5.31/5.51 % Ex_list_of_length
% 5.31/5.51 thf(fact_1918_Ex__list__of__length,axiom,
% 5.31/5.51 ! [N: nat] :
% 5.31/5.51 ? [Xs3: list_nat] :
% 5.31/5.51 ( ( size_size_list_nat @ Xs3 )
% 5.31/5.51 = N ) ).
% 5.31/5.51
% 5.31/5.51 % Ex_list_of_length
% 5.31/5.51 thf(fact_1919_Ex__list__of__length,axiom,
% 5.31/5.51 ! [N: nat] :
% 5.31/5.51 ? [Xs3: list_int] :
% 5.31/5.51 ( ( size_size_list_int @ Xs3 )
% 5.31/5.51 = N ) ).
% 5.31/5.51
% 5.31/5.51 % Ex_list_of_length
% 5.31/5.51 thf(fact_1920_diff__right__commute,axiom,
% 5.31/5.51 ! [A: rat,C2: rat,B: rat] :
% 5.31/5.51 ( ( minus_minus_rat @ ( minus_minus_rat @ A @ C2 ) @ B )
% 5.31/5.51 = ( minus_minus_rat @ ( minus_minus_rat @ A @ B ) @ C2 ) ) ).
% 5.31/5.51
% 5.31/5.51 % diff_right_commute
% 5.31/5.51 thf(fact_1921_diff__right__commute,axiom,
% 5.31/5.51 ! [A: nat,C2: nat,B: nat] :
% 5.31/5.51 ( ( minus_minus_nat @ ( minus_minus_nat @ A @ C2 ) @ B )
% 5.31/5.51 = ( minus_minus_nat @ ( minus_minus_nat @ A @ B ) @ C2 ) ) ).
% 5.31/5.51
% 5.31/5.51 % diff_right_commute
% 5.31/5.51 thf(fact_1922_diff__right__commute,axiom,
% 5.31/5.51 ! [A: int,C2: int,B: int] :
% 5.31/5.51 ( ( minus_minus_int @ ( minus_minus_int @ A @ C2 ) @ B )
% 5.31/5.51 = ( minus_minus_int @ ( minus_minus_int @ A @ B ) @ C2 ) ) ).
% 5.31/5.51
% 5.31/5.51 % diff_right_commute
% 5.31/5.51 thf(fact_1923_diff__eq__diff__eq,axiom,
% 5.31/5.51 ! [A: rat,B: rat,C2: rat,D: rat] :
% 5.31/5.51 ( ( ( minus_minus_rat @ A @ B )
% 5.31/5.51 = ( minus_minus_rat @ C2 @ D ) )
% 5.31/5.51 => ( ( A = B )
% 5.31/5.51 = ( C2 = D ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % diff_eq_diff_eq
% 5.31/5.51 thf(fact_1924_diff__eq__diff__eq,axiom,
% 5.31/5.51 ! [A: int,B: int,C2: int,D: int] :
% 5.31/5.51 ( ( ( minus_minus_int @ A @ B )
% 5.31/5.51 = ( minus_minus_int @ C2 @ D ) )
% 5.31/5.51 => ( ( A = B )
% 5.31/5.51 = ( C2 = D ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % diff_eq_diff_eq
% 5.31/5.51 thf(fact_1925_diff__mono,axiom,
% 5.31/5.51 ! [A: rat,B: rat,D: rat,C2: rat] :
% 5.31/5.51 ( ( ord_less_eq_rat @ A @ B )
% 5.31/5.51 => ( ( ord_less_eq_rat @ D @ C2 )
% 5.31/5.51 => ( ord_less_eq_rat @ ( minus_minus_rat @ A @ C2 ) @ ( minus_minus_rat @ B @ D ) ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % diff_mono
% 5.31/5.51 thf(fact_1926_diff__mono,axiom,
% 5.31/5.51 ! [A: int,B: int,D: int,C2: int] :
% 5.31/5.51 ( ( ord_less_eq_int @ A @ B )
% 5.31/5.51 => ( ( ord_less_eq_int @ D @ C2 )
% 5.31/5.51 => ( ord_less_eq_int @ ( minus_minus_int @ A @ C2 ) @ ( minus_minus_int @ B @ D ) ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % diff_mono
% 5.31/5.51 thf(fact_1927_diff__left__mono,axiom,
% 5.31/5.51 ! [B: rat,A: rat,C2: rat] :
% 5.31/5.51 ( ( ord_less_eq_rat @ B @ A )
% 5.31/5.51 => ( ord_less_eq_rat @ ( minus_minus_rat @ C2 @ A ) @ ( minus_minus_rat @ C2 @ B ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % diff_left_mono
% 5.31/5.51 thf(fact_1928_diff__left__mono,axiom,
% 5.31/5.51 ! [B: int,A: int,C2: int] :
% 5.31/5.51 ( ( ord_less_eq_int @ B @ A )
% 5.31/5.51 => ( ord_less_eq_int @ ( minus_minus_int @ C2 @ A ) @ ( minus_minus_int @ C2 @ B ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % diff_left_mono
% 5.31/5.51 thf(fact_1929_diff__right__mono,axiom,
% 5.31/5.51 ! [A: rat,B: rat,C2: rat] :
% 5.31/5.51 ( ( ord_less_eq_rat @ A @ B )
% 5.31/5.51 => ( ord_less_eq_rat @ ( minus_minus_rat @ A @ C2 ) @ ( minus_minus_rat @ B @ C2 ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % diff_right_mono
% 5.31/5.51 thf(fact_1930_diff__right__mono,axiom,
% 5.31/5.51 ! [A: int,B: int,C2: int] :
% 5.31/5.51 ( ( ord_less_eq_int @ A @ B )
% 5.31/5.51 => ( ord_less_eq_int @ ( minus_minus_int @ A @ C2 ) @ ( minus_minus_int @ B @ C2 ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % diff_right_mono
% 5.31/5.51 thf(fact_1931_diff__eq__diff__less__eq,axiom,
% 5.31/5.51 ! [A: rat,B: rat,C2: rat,D: rat] :
% 5.31/5.51 ( ( ( minus_minus_rat @ A @ B )
% 5.31/5.51 = ( minus_minus_rat @ C2 @ D ) )
% 5.31/5.51 => ( ( ord_less_eq_rat @ A @ B )
% 5.31/5.51 = ( ord_less_eq_rat @ C2 @ D ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % diff_eq_diff_less_eq
% 5.31/5.51 thf(fact_1932_diff__eq__diff__less__eq,axiom,
% 5.31/5.51 ! [A: int,B: int,C2: int,D: int] :
% 5.31/5.51 ( ( ( minus_minus_int @ A @ B )
% 5.31/5.51 = ( minus_minus_int @ C2 @ D ) )
% 5.31/5.51 => ( ( ord_less_eq_int @ A @ B )
% 5.31/5.51 = ( ord_less_eq_int @ C2 @ D ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % diff_eq_diff_less_eq
% 5.31/5.51 thf(fact_1933_eq__iff__diff__eq__0,axiom,
% 5.31/5.51 ( ( ^ [Y5: complex,Z2: complex] : ( Y5 = Z2 ) )
% 5.31/5.51 = ( ^ [A5: complex,B4: complex] :
% 5.31/5.51 ( ( minus_minus_complex @ A5 @ B4 )
% 5.31/5.51 = zero_zero_complex ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % eq_iff_diff_eq_0
% 5.31/5.51 thf(fact_1934_eq__iff__diff__eq__0,axiom,
% 5.31/5.51 ( ( ^ [Y5: real,Z2: real] : ( Y5 = Z2 ) )
% 5.31/5.51 = ( ^ [A5: real,B4: real] :
% 5.31/5.51 ( ( minus_minus_real @ A5 @ B4 )
% 5.31/5.51 = zero_zero_real ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % eq_iff_diff_eq_0
% 5.31/5.51 thf(fact_1935_eq__iff__diff__eq__0,axiom,
% 5.31/5.51 ( ( ^ [Y5: rat,Z2: rat] : ( Y5 = Z2 ) )
% 5.31/5.51 = ( ^ [A5: rat,B4: rat] :
% 5.31/5.51 ( ( minus_minus_rat @ A5 @ B4 )
% 5.31/5.51 = zero_zero_rat ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % eq_iff_diff_eq_0
% 5.31/5.51 thf(fact_1936_eq__iff__diff__eq__0,axiom,
% 5.31/5.51 ( ( ^ [Y5: int,Z2: int] : ( Y5 = Z2 ) )
% 5.31/5.51 = ( ^ [A5: int,B4: int] :
% 5.31/5.51 ( ( minus_minus_int @ A5 @ B4 )
% 5.31/5.51 = zero_zero_int ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % eq_iff_diff_eq_0
% 5.31/5.51 thf(fact_1937_diff__strict__right__mono,axiom,
% 5.31/5.51 ! [A: real,B: real,C2: real] :
% 5.31/5.51 ( ( ord_less_real @ A @ B )
% 5.31/5.51 => ( ord_less_real @ ( minus_minus_real @ A @ C2 ) @ ( minus_minus_real @ B @ C2 ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % diff_strict_right_mono
% 5.31/5.51 thf(fact_1938_diff__strict__right__mono,axiom,
% 5.31/5.51 ! [A: rat,B: rat,C2: rat] :
% 5.31/5.51 ( ( ord_less_rat @ A @ B )
% 5.31/5.51 => ( ord_less_rat @ ( minus_minus_rat @ A @ C2 ) @ ( minus_minus_rat @ B @ C2 ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % diff_strict_right_mono
% 5.31/5.51 thf(fact_1939_diff__strict__right__mono,axiom,
% 5.31/5.51 ! [A: int,B: int,C2: int] :
% 5.31/5.51 ( ( ord_less_int @ A @ B )
% 5.31/5.51 => ( ord_less_int @ ( minus_minus_int @ A @ C2 ) @ ( minus_minus_int @ B @ C2 ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % diff_strict_right_mono
% 5.31/5.51 thf(fact_1940_diff__strict__left__mono,axiom,
% 5.31/5.51 ! [B: real,A: real,C2: real] :
% 5.31/5.51 ( ( ord_less_real @ B @ A )
% 5.31/5.51 => ( ord_less_real @ ( minus_minus_real @ C2 @ A ) @ ( minus_minus_real @ C2 @ B ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % diff_strict_left_mono
% 5.31/5.51 thf(fact_1941_diff__strict__left__mono,axiom,
% 5.31/5.51 ! [B: rat,A: rat,C2: rat] :
% 5.31/5.51 ( ( ord_less_rat @ B @ A )
% 5.31/5.51 => ( ord_less_rat @ ( minus_minus_rat @ C2 @ A ) @ ( minus_minus_rat @ C2 @ B ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % diff_strict_left_mono
% 5.31/5.51 thf(fact_1942_diff__strict__left__mono,axiom,
% 5.31/5.51 ! [B: int,A: int,C2: int] :
% 5.31/5.51 ( ( ord_less_int @ B @ A )
% 5.31/5.51 => ( ord_less_int @ ( minus_minus_int @ C2 @ A ) @ ( minus_minus_int @ C2 @ B ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % diff_strict_left_mono
% 5.31/5.51 thf(fact_1943_diff__eq__diff__less,axiom,
% 5.31/5.51 ! [A: real,B: real,C2: real,D: real] :
% 5.31/5.51 ( ( ( minus_minus_real @ A @ B )
% 5.31/5.51 = ( minus_minus_real @ C2 @ D ) )
% 5.31/5.51 => ( ( ord_less_real @ A @ B )
% 5.31/5.51 = ( ord_less_real @ C2 @ D ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % diff_eq_diff_less
% 5.31/5.51 thf(fact_1944_diff__eq__diff__less,axiom,
% 5.31/5.51 ! [A: rat,B: rat,C2: rat,D: rat] :
% 5.31/5.51 ( ( ( minus_minus_rat @ A @ B )
% 5.31/5.51 = ( minus_minus_rat @ C2 @ D ) )
% 5.31/5.51 => ( ( ord_less_rat @ A @ B )
% 5.31/5.51 = ( ord_less_rat @ C2 @ D ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % diff_eq_diff_less
% 5.31/5.51 thf(fact_1945_diff__eq__diff__less,axiom,
% 5.31/5.51 ! [A: int,B: int,C2: int,D: int] :
% 5.31/5.51 ( ( ( minus_minus_int @ A @ B )
% 5.31/5.51 = ( minus_minus_int @ C2 @ D ) )
% 5.31/5.51 => ( ( ord_less_int @ A @ B )
% 5.31/5.51 = ( ord_less_int @ C2 @ D ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % diff_eq_diff_less
% 5.31/5.51 thf(fact_1946_diff__strict__mono,axiom,
% 5.31/5.51 ! [A: real,B: real,D: real,C2: real] :
% 5.31/5.51 ( ( ord_less_real @ A @ B )
% 5.31/5.51 => ( ( ord_less_real @ D @ C2 )
% 5.31/5.51 => ( ord_less_real @ ( minus_minus_real @ A @ C2 ) @ ( minus_minus_real @ B @ D ) ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % diff_strict_mono
% 5.31/5.51 thf(fact_1947_diff__strict__mono,axiom,
% 5.31/5.51 ! [A: rat,B: rat,D: rat,C2: rat] :
% 5.31/5.51 ( ( ord_less_rat @ A @ B )
% 5.31/5.51 => ( ( ord_less_rat @ D @ C2 )
% 5.31/5.51 => ( ord_less_rat @ ( minus_minus_rat @ A @ C2 ) @ ( minus_minus_rat @ B @ D ) ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % diff_strict_mono
% 5.31/5.51 thf(fact_1948_diff__strict__mono,axiom,
% 5.31/5.51 ! [A: int,B: int,D: int,C2: int] :
% 5.31/5.51 ( ( ord_less_int @ A @ B )
% 5.31/5.51 => ( ( ord_less_int @ D @ C2 )
% 5.31/5.51 => ( ord_less_int @ ( minus_minus_int @ A @ C2 ) @ ( minus_minus_int @ B @ D ) ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % diff_strict_mono
% 5.31/5.51 thf(fact_1949_left__diff__distrib,axiom,
% 5.31/5.51 ! [A: real,B: real,C2: real] :
% 5.31/5.51 ( ( times_times_real @ ( minus_minus_real @ A @ B ) @ C2 )
% 5.31/5.51 = ( minus_minus_real @ ( times_times_real @ A @ C2 ) @ ( times_times_real @ B @ C2 ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % left_diff_distrib
% 5.31/5.51 thf(fact_1950_left__diff__distrib,axiom,
% 5.31/5.51 ! [A: rat,B: rat,C2: rat] :
% 5.31/5.51 ( ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ C2 )
% 5.31/5.51 = ( minus_minus_rat @ ( times_times_rat @ A @ C2 ) @ ( times_times_rat @ B @ C2 ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % left_diff_distrib
% 5.31/5.51 thf(fact_1951_left__diff__distrib,axiom,
% 5.31/5.51 ! [A: int,B: int,C2: int] :
% 5.31/5.51 ( ( times_times_int @ ( minus_minus_int @ A @ B ) @ C2 )
% 5.31/5.51 = ( minus_minus_int @ ( times_times_int @ A @ C2 ) @ ( times_times_int @ B @ C2 ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % left_diff_distrib
% 5.31/5.51 thf(fact_1952_right__diff__distrib,axiom,
% 5.31/5.51 ! [A: real,B: real,C2: real] :
% 5.31/5.51 ( ( times_times_real @ A @ ( minus_minus_real @ B @ C2 ) )
% 5.31/5.51 = ( minus_minus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C2 ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % right_diff_distrib
% 5.31/5.51 thf(fact_1953_right__diff__distrib,axiom,
% 5.31/5.51 ! [A: rat,B: rat,C2: rat] :
% 5.31/5.51 ( ( times_times_rat @ A @ ( minus_minus_rat @ B @ C2 ) )
% 5.31/5.51 = ( minus_minus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C2 ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % right_diff_distrib
% 5.31/5.51 thf(fact_1954_right__diff__distrib,axiom,
% 5.31/5.51 ! [A: int,B: int,C2: int] :
% 5.31/5.51 ( ( times_times_int @ A @ ( minus_minus_int @ B @ C2 ) )
% 5.31/5.51 = ( minus_minus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C2 ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % right_diff_distrib
% 5.31/5.51 thf(fact_1955_left__diff__distrib_H,axiom,
% 5.31/5.51 ! [B: real,C2: real,A: real] :
% 5.31/5.51 ( ( times_times_real @ ( minus_minus_real @ B @ C2 ) @ A )
% 5.31/5.51 = ( minus_minus_real @ ( times_times_real @ B @ A ) @ ( times_times_real @ C2 @ A ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % left_diff_distrib'
% 5.31/5.51 thf(fact_1956_left__diff__distrib_H,axiom,
% 5.31/5.51 ! [B: rat,C2: rat,A: rat] :
% 5.31/5.51 ( ( times_times_rat @ ( minus_minus_rat @ B @ C2 ) @ A )
% 5.31/5.51 = ( minus_minus_rat @ ( times_times_rat @ B @ A ) @ ( times_times_rat @ C2 @ A ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % left_diff_distrib'
% 5.31/5.51 thf(fact_1957_left__diff__distrib_H,axiom,
% 5.31/5.51 ! [B: nat,C2: nat,A: nat] :
% 5.31/5.51 ( ( times_times_nat @ ( minus_minus_nat @ B @ C2 ) @ A )
% 5.31/5.51 = ( minus_minus_nat @ ( times_times_nat @ B @ A ) @ ( times_times_nat @ C2 @ A ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % left_diff_distrib'
% 5.31/5.51 thf(fact_1958_left__diff__distrib_H,axiom,
% 5.31/5.51 ! [B: int,C2: int,A: int] :
% 5.31/5.51 ( ( times_times_int @ ( minus_minus_int @ B @ C2 ) @ A )
% 5.31/5.51 = ( minus_minus_int @ ( times_times_int @ B @ A ) @ ( times_times_int @ C2 @ A ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % left_diff_distrib'
% 5.31/5.51 thf(fact_1959_right__diff__distrib_H,axiom,
% 5.31/5.51 ! [A: real,B: real,C2: real] :
% 5.31/5.51 ( ( times_times_real @ A @ ( minus_minus_real @ B @ C2 ) )
% 5.31/5.51 = ( minus_minus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C2 ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % right_diff_distrib'
% 5.31/5.51 thf(fact_1960_right__diff__distrib_H,axiom,
% 5.31/5.51 ! [A: rat,B: rat,C2: rat] :
% 5.31/5.51 ( ( times_times_rat @ A @ ( minus_minus_rat @ B @ C2 ) )
% 5.31/5.51 = ( minus_minus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C2 ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % right_diff_distrib'
% 5.31/5.51 thf(fact_1961_right__diff__distrib_H,axiom,
% 5.31/5.51 ! [A: nat,B: nat,C2: nat] :
% 5.31/5.51 ( ( times_times_nat @ A @ ( minus_minus_nat @ B @ C2 ) )
% 5.31/5.51 = ( minus_minus_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C2 ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % right_diff_distrib'
% 5.31/5.51 thf(fact_1962_right__diff__distrib_H,axiom,
% 5.31/5.51 ! [A: int,B: int,C2: int] :
% 5.31/5.51 ( ( times_times_int @ A @ ( minus_minus_int @ B @ C2 ) )
% 5.31/5.51 = ( minus_minus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C2 ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % right_diff_distrib'
% 5.31/5.51 thf(fact_1963_diff__diff__eq,axiom,
% 5.31/5.51 ! [A: real,B: real,C2: real] :
% 5.31/5.51 ( ( minus_minus_real @ ( minus_minus_real @ A @ B ) @ C2 )
% 5.31/5.51 = ( minus_minus_real @ A @ ( plus_plus_real @ B @ C2 ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % diff_diff_eq
% 5.31/5.51 thf(fact_1964_diff__diff__eq,axiom,
% 5.31/5.51 ! [A: rat,B: rat,C2: rat] :
% 5.31/5.51 ( ( minus_minus_rat @ ( minus_minus_rat @ A @ B ) @ C2 )
% 5.31/5.51 = ( minus_minus_rat @ A @ ( plus_plus_rat @ B @ C2 ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % diff_diff_eq
% 5.31/5.51 thf(fact_1965_diff__diff__eq,axiom,
% 5.31/5.51 ! [A: nat,B: nat,C2: nat] :
% 5.31/5.51 ( ( minus_minus_nat @ ( minus_minus_nat @ A @ B ) @ C2 )
% 5.31/5.51 = ( minus_minus_nat @ A @ ( plus_plus_nat @ B @ C2 ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % diff_diff_eq
% 5.31/5.51 thf(fact_1966_diff__diff__eq,axiom,
% 5.31/5.51 ! [A: int,B: int,C2: int] :
% 5.31/5.51 ( ( minus_minus_int @ ( minus_minus_int @ A @ B ) @ C2 )
% 5.31/5.51 = ( minus_minus_int @ A @ ( plus_plus_int @ B @ C2 ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % diff_diff_eq
% 5.31/5.51 thf(fact_1967_add__implies__diff,axiom,
% 5.31/5.51 ! [C2: real,B: real,A: real] :
% 5.31/5.51 ( ( ( plus_plus_real @ C2 @ B )
% 5.31/5.51 = A )
% 5.31/5.51 => ( C2
% 5.31/5.51 = ( minus_minus_real @ A @ B ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % add_implies_diff
% 5.31/5.51 thf(fact_1968_add__implies__diff,axiom,
% 5.31/5.51 ! [C2: rat,B: rat,A: rat] :
% 5.31/5.51 ( ( ( plus_plus_rat @ C2 @ B )
% 5.31/5.51 = A )
% 5.31/5.51 => ( C2
% 5.31/5.51 = ( minus_minus_rat @ A @ B ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % add_implies_diff
% 5.31/5.51 thf(fact_1969_add__implies__diff,axiom,
% 5.31/5.51 ! [C2: nat,B: nat,A: nat] :
% 5.31/5.51 ( ( ( plus_plus_nat @ C2 @ B )
% 5.31/5.51 = A )
% 5.31/5.51 => ( C2
% 5.31/5.51 = ( minus_minus_nat @ A @ B ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % add_implies_diff
% 5.31/5.51 thf(fact_1970_add__implies__diff,axiom,
% 5.31/5.51 ! [C2: int,B: int,A: int] :
% 5.31/5.51 ( ( ( plus_plus_int @ C2 @ B )
% 5.31/5.51 = A )
% 5.31/5.51 => ( C2
% 5.31/5.51 = ( minus_minus_int @ A @ B ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % add_implies_diff
% 5.31/5.51 thf(fact_1971_diff__add__eq__diff__diff__swap,axiom,
% 5.31/5.51 ! [A: real,B: real,C2: real] :
% 5.31/5.51 ( ( minus_minus_real @ A @ ( plus_plus_real @ B @ C2 ) )
% 5.31/5.51 = ( minus_minus_real @ ( minus_minus_real @ A @ C2 ) @ B ) ) ).
% 5.31/5.51
% 5.31/5.51 % diff_add_eq_diff_diff_swap
% 5.31/5.51 thf(fact_1972_diff__add__eq__diff__diff__swap,axiom,
% 5.31/5.51 ! [A: rat,B: rat,C2: rat] :
% 5.31/5.51 ( ( minus_minus_rat @ A @ ( plus_plus_rat @ B @ C2 ) )
% 5.31/5.51 = ( minus_minus_rat @ ( minus_minus_rat @ A @ C2 ) @ B ) ) ).
% 5.31/5.51
% 5.31/5.51 % diff_add_eq_diff_diff_swap
% 5.31/5.51 thf(fact_1973_diff__add__eq__diff__diff__swap,axiom,
% 5.31/5.51 ! [A: int,B: int,C2: int] :
% 5.31/5.51 ( ( minus_minus_int @ A @ ( plus_plus_int @ B @ C2 ) )
% 5.31/5.51 = ( minus_minus_int @ ( minus_minus_int @ A @ C2 ) @ B ) ) ).
% 5.31/5.51
% 5.31/5.51 % diff_add_eq_diff_diff_swap
% 5.31/5.51 thf(fact_1974_diff__add__eq,axiom,
% 5.31/5.51 ! [A: real,B: real,C2: real] :
% 5.31/5.51 ( ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ C2 )
% 5.31/5.51 = ( minus_minus_real @ ( plus_plus_real @ A @ C2 ) @ B ) ) ).
% 5.31/5.51
% 5.31/5.51 % diff_add_eq
% 5.31/5.51 thf(fact_1975_diff__add__eq,axiom,
% 5.31/5.51 ! [A: rat,B: rat,C2: rat] :
% 5.31/5.51 ( ( plus_plus_rat @ ( minus_minus_rat @ A @ B ) @ C2 )
% 5.31/5.51 = ( minus_minus_rat @ ( plus_plus_rat @ A @ C2 ) @ B ) ) ).
% 5.31/5.51
% 5.31/5.51 % diff_add_eq
% 5.31/5.51 thf(fact_1976_diff__add__eq,axiom,
% 5.31/5.51 ! [A: int,B: int,C2: int] :
% 5.31/5.51 ( ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ C2 )
% 5.31/5.51 = ( minus_minus_int @ ( plus_plus_int @ A @ C2 ) @ B ) ) ).
% 5.31/5.51
% 5.31/5.51 % diff_add_eq
% 5.31/5.51 thf(fact_1977_diff__diff__eq2,axiom,
% 5.31/5.51 ! [A: real,B: real,C2: real] :
% 5.31/5.51 ( ( minus_minus_real @ A @ ( minus_minus_real @ B @ C2 ) )
% 5.31/5.51 = ( minus_minus_real @ ( plus_plus_real @ A @ C2 ) @ B ) ) ).
% 5.31/5.51
% 5.31/5.51 % diff_diff_eq2
% 5.31/5.51 thf(fact_1978_diff__diff__eq2,axiom,
% 5.31/5.51 ! [A: rat,B: rat,C2: rat] :
% 5.31/5.51 ( ( minus_minus_rat @ A @ ( minus_minus_rat @ B @ C2 ) )
% 5.31/5.51 = ( minus_minus_rat @ ( plus_plus_rat @ A @ C2 ) @ B ) ) ).
% 5.31/5.51
% 5.31/5.51 % diff_diff_eq2
% 5.31/5.51 thf(fact_1979_diff__diff__eq2,axiom,
% 5.31/5.51 ! [A: int,B: int,C2: int] :
% 5.31/5.51 ( ( minus_minus_int @ A @ ( minus_minus_int @ B @ C2 ) )
% 5.31/5.51 = ( minus_minus_int @ ( plus_plus_int @ A @ C2 ) @ B ) ) ).
% 5.31/5.51
% 5.31/5.51 % diff_diff_eq2
% 5.31/5.51 thf(fact_1980_add__diff__eq,axiom,
% 5.31/5.51 ! [A: real,B: real,C2: real] :
% 5.31/5.51 ( ( plus_plus_real @ A @ ( minus_minus_real @ B @ C2 ) )
% 5.31/5.51 = ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ C2 ) ) ).
% 5.31/5.51
% 5.31/5.51 % add_diff_eq
% 5.31/5.51 thf(fact_1981_add__diff__eq,axiom,
% 5.31/5.51 ! [A: rat,B: rat,C2: rat] :
% 5.31/5.51 ( ( plus_plus_rat @ A @ ( minus_minus_rat @ B @ C2 ) )
% 5.31/5.51 = ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ C2 ) ) ).
% 5.31/5.51
% 5.31/5.51 % add_diff_eq
% 5.31/5.51 thf(fact_1982_add__diff__eq,axiom,
% 5.31/5.51 ! [A: int,B: int,C2: int] :
% 5.31/5.51 ( ( plus_plus_int @ A @ ( minus_minus_int @ B @ C2 ) )
% 5.31/5.51 = ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ C2 ) ) ).
% 5.31/5.51
% 5.31/5.51 % add_diff_eq
% 5.31/5.51 thf(fact_1983_eq__diff__eq,axiom,
% 5.31/5.51 ! [A: real,C2: real,B: real] :
% 5.31/5.51 ( ( A
% 5.31/5.51 = ( minus_minus_real @ C2 @ B ) )
% 5.31/5.51 = ( ( plus_plus_real @ A @ B )
% 5.31/5.51 = C2 ) ) ).
% 5.31/5.51
% 5.31/5.51 % eq_diff_eq
% 5.31/5.51 thf(fact_1984_eq__diff__eq,axiom,
% 5.31/5.51 ! [A: rat,C2: rat,B: rat] :
% 5.31/5.51 ( ( A
% 5.31/5.51 = ( minus_minus_rat @ C2 @ B ) )
% 5.31/5.51 = ( ( plus_plus_rat @ A @ B )
% 5.31/5.51 = C2 ) ) ).
% 5.31/5.51
% 5.31/5.51 % eq_diff_eq
% 5.31/5.51 thf(fact_1985_eq__diff__eq,axiom,
% 5.31/5.51 ! [A: int,C2: int,B: int] :
% 5.31/5.51 ( ( A
% 5.31/5.51 = ( minus_minus_int @ C2 @ B ) )
% 5.31/5.51 = ( ( plus_plus_int @ A @ B )
% 5.31/5.51 = C2 ) ) ).
% 5.31/5.51
% 5.31/5.51 % eq_diff_eq
% 5.31/5.51 thf(fact_1986_diff__eq__eq,axiom,
% 5.31/5.51 ! [A: real,B: real,C2: real] :
% 5.31/5.51 ( ( ( minus_minus_real @ A @ B )
% 5.31/5.51 = C2 )
% 5.31/5.51 = ( A
% 5.31/5.51 = ( plus_plus_real @ C2 @ B ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % diff_eq_eq
% 5.31/5.51 thf(fact_1987_diff__eq__eq,axiom,
% 5.31/5.51 ! [A: rat,B: rat,C2: rat] :
% 5.31/5.51 ( ( ( minus_minus_rat @ A @ B )
% 5.31/5.51 = C2 )
% 5.31/5.51 = ( A
% 5.31/5.51 = ( plus_plus_rat @ C2 @ B ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % diff_eq_eq
% 5.31/5.51 thf(fact_1988_diff__eq__eq,axiom,
% 5.31/5.51 ! [A: int,B: int,C2: int] :
% 5.31/5.51 ( ( ( minus_minus_int @ A @ B )
% 5.31/5.51 = C2 )
% 5.31/5.51 = ( A
% 5.31/5.51 = ( plus_plus_int @ C2 @ B ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % diff_eq_eq
% 5.31/5.51 thf(fact_1989_group__cancel_Osub1,axiom,
% 5.31/5.51 ! [A4: real,K2: real,A: real,B: real] :
% 5.31/5.51 ( ( A4
% 5.31/5.51 = ( plus_plus_real @ K2 @ A ) )
% 5.31/5.51 => ( ( minus_minus_real @ A4 @ B )
% 5.31/5.51 = ( plus_plus_real @ K2 @ ( minus_minus_real @ A @ B ) ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % group_cancel.sub1
% 5.31/5.51 thf(fact_1990_group__cancel_Osub1,axiom,
% 5.31/5.51 ! [A4: rat,K2: rat,A: rat,B: rat] :
% 5.31/5.51 ( ( A4
% 5.31/5.51 = ( plus_plus_rat @ K2 @ A ) )
% 5.31/5.51 => ( ( minus_minus_rat @ A4 @ B )
% 5.31/5.51 = ( plus_plus_rat @ K2 @ ( minus_minus_rat @ A @ B ) ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % group_cancel.sub1
% 5.31/5.51 thf(fact_1991_group__cancel_Osub1,axiom,
% 5.31/5.51 ! [A4: int,K2: int,A: int,B: int] :
% 5.31/5.51 ( ( A4
% 5.31/5.51 = ( plus_plus_int @ K2 @ A ) )
% 5.31/5.51 => ( ( minus_minus_int @ A4 @ B )
% 5.31/5.51 = ( plus_plus_int @ K2 @ ( minus_minus_int @ A @ B ) ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % group_cancel.sub1
% 5.31/5.51 thf(fact_1992_finite__nat__set__iff__bounded,axiom,
% 5.31/5.51 ( finite_finite_nat
% 5.31/5.51 = ( ^ [N5: set_nat] :
% 5.31/5.51 ? [M6: nat] :
% 5.31/5.51 ! [X4: nat] :
% 5.31/5.51 ( ( member_nat @ X4 @ N5 )
% 5.31/5.51 => ( ord_less_nat @ X4 @ M6 ) ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % finite_nat_set_iff_bounded
% 5.31/5.51 thf(fact_1993_bounded__nat__set__is__finite,axiom,
% 5.31/5.51 ! [N6: set_nat,N: nat] :
% 5.31/5.51 ( ! [X3: nat] :
% 5.31/5.51 ( ( member_nat @ X3 @ N6 )
% 5.31/5.51 => ( ord_less_nat @ X3 @ N ) )
% 5.31/5.51 => ( finite_finite_nat @ N6 ) ) ).
% 5.31/5.51
% 5.31/5.51 % bounded_nat_set_is_finite
% 5.31/5.51 thf(fact_1994_finite__nat__set__iff__bounded__le,axiom,
% 5.31/5.51 ( finite_finite_nat
% 5.31/5.51 = ( ^ [N5: set_nat] :
% 5.31/5.51 ? [M6: nat] :
% 5.31/5.51 ! [X4: nat] :
% 5.31/5.51 ( ( member_nat @ X4 @ N5 )
% 5.31/5.51 => ( ord_less_eq_nat @ X4 @ M6 ) ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % finite_nat_set_iff_bounded_le
% 5.31/5.51 thf(fact_1995_le__iff__diff__le__0,axiom,
% 5.31/5.51 ( ord_less_eq_real
% 5.31/5.51 = ( ^ [A5: real,B4: real] : ( ord_less_eq_real @ ( minus_minus_real @ A5 @ B4 ) @ zero_zero_real ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % le_iff_diff_le_0
% 5.31/5.51 thf(fact_1996_le__iff__diff__le__0,axiom,
% 5.31/5.51 ( ord_less_eq_rat
% 5.31/5.51 = ( ^ [A5: rat,B4: rat] : ( ord_less_eq_rat @ ( minus_minus_rat @ A5 @ B4 ) @ zero_zero_rat ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % le_iff_diff_le_0
% 5.31/5.51 thf(fact_1997_le__iff__diff__le__0,axiom,
% 5.31/5.51 ( ord_less_eq_int
% 5.31/5.51 = ( ^ [A5: int,B4: int] : ( ord_less_eq_int @ ( minus_minus_int @ A5 @ B4 ) @ zero_zero_int ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % le_iff_diff_le_0
% 5.31/5.51 thf(fact_1998_less__iff__diff__less__0,axiom,
% 5.31/5.51 ( ord_less_real
% 5.31/5.51 = ( ^ [A5: real,B4: real] : ( ord_less_real @ ( minus_minus_real @ A5 @ B4 ) @ zero_zero_real ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % less_iff_diff_less_0
% 5.31/5.51 thf(fact_1999_less__iff__diff__less__0,axiom,
% 5.31/5.51 ( ord_less_rat
% 5.31/5.51 = ( ^ [A5: rat,B4: rat] : ( ord_less_rat @ ( minus_minus_rat @ A5 @ B4 ) @ zero_zero_rat ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % less_iff_diff_less_0
% 5.31/5.51 thf(fact_2000_less__iff__diff__less__0,axiom,
% 5.31/5.51 ( ord_less_int
% 5.31/5.51 = ( ^ [A5: int,B4: int] : ( ord_less_int @ ( minus_minus_int @ A5 @ B4 ) @ zero_zero_int ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % less_iff_diff_less_0
% 5.31/5.51 thf(fact_2001_add__le__add__imp__diff__le,axiom,
% 5.31/5.51 ! [I2: real,K2: real,N: real,J2: real] :
% 5.31/5.51 ( ( ord_less_eq_real @ ( plus_plus_real @ I2 @ K2 ) @ N )
% 5.31/5.51 => ( ( ord_less_eq_real @ N @ ( plus_plus_real @ J2 @ K2 ) )
% 5.31/5.51 => ( ( ord_less_eq_real @ ( plus_plus_real @ I2 @ K2 ) @ N )
% 5.31/5.51 => ( ( ord_less_eq_real @ N @ ( plus_plus_real @ J2 @ K2 ) )
% 5.31/5.51 => ( ord_less_eq_real @ ( minus_minus_real @ N @ K2 ) @ J2 ) ) ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % add_le_add_imp_diff_le
% 5.31/5.51 thf(fact_2002_add__le__add__imp__diff__le,axiom,
% 5.31/5.51 ! [I2: rat,K2: rat,N: rat,J2: rat] :
% 5.31/5.51 ( ( ord_less_eq_rat @ ( plus_plus_rat @ I2 @ K2 ) @ N )
% 5.31/5.51 => ( ( ord_less_eq_rat @ N @ ( plus_plus_rat @ J2 @ K2 ) )
% 5.31/5.51 => ( ( ord_less_eq_rat @ ( plus_plus_rat @ I2 @ K2 ) @ N )
% 5.31/5.51 => ( ( ord_less_eq_rat @ N @ ( plus_plus_rat @ J2 @ K2 ) )
% 5.31/5.51 => ( ord_less_eq_rat @ ( minus_minus_rat @ N @ K2 ) @ J2 ) ) ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % add_le_add_imp_diff_le
% 5.31/5.51 thf(fact_2003_add__le__add__imp__diff__le,axiom,
% 5.31/5.51 ! [I2: nat,K2: nat,N: nat,J2: nat] :
% 5.31/5.51 ( ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K2 ) @ N )
% 5.31/5.51 => ( ( ord_less_eq_nat @ N @ ( plus_plus_nat @ J2 @ K2 ) )
% 5.31/5.51 => ( ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K2 ) @ N )
% 5.31/5.51 => ( ( ord_less_eq_nat @ N @ ( plus_plus_nat @ J2 @ K2 ) )
% 5.31/5.51 => ( ord_less_eq_nat @ ( minus_minus_nat @ N @ K2 ) @ J2 ) ) ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % add_le_add_imp_diff_le
% 5.31/5.51 thf(fact_2004_add__le__add__imp__diff__le,axiom,
% 5.31/5.51 ! [I2: int,K2: int,N: int,J2: int] :
% 5.31/5.51 ( ( ord_less_eq_int @ ( plus_plus_int @ I2 @ K2 ) @ N )
% 5.31/5.51 => ( ( ord_less_eq_int @ N @ ( plus_plus_int @ J2 @ K2 ) )
% 5.31/5.51 => ( ( ord_less_eq_int @ ( plus_plus_int @ I2 @ K2 ) @ N )
% 5.31/5.51 => ( ( ord_less_eq_int @ N @ ( plus_plus_int @ J2 @ K2 ) )
% 5.31/5.51 => ( ord_less_eq_int @ ( minus_minus_int @ N @ K2 ) @ J2 ) ) ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % add_le_add_imp_diff_le
% 5.31/5.51 thf(fact_2005_add__le__imp__le__diff,axiom,
% 5.31/5.51 ! [I2: real,K2: real,N: real] :
% 5.31/5.51 ( ( ord_less_eq_real @ ( plus_plus_real @ I2 @ K2 ) @ N )
% 5.31/5.51 => ( ord_less_eq_real @ I2 @ ( minus_minus_real @ N @ K2 ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % add_le_imp_le_diff
% 5.31/5.51 thf(fact_2006_add__le__imp__le__diff,axiom,
% 5.31/5.51 ! [I2: rat,K2: rat,N: rat] :
% 5.31/5.51 ( ( ord_less_eq_rat @ ( plus_plus_rat @ I2 @ K2 ) @ N )
% 5.31/5.51 => ( ord_less_eq_rat @ I2 @ ( minus_minus_rat @ N @ K2 ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % add_le_imp_le_diff
% 5.31/5.51 thf(fact_2007_add__le__imp__le__diff,axiom,
% 5.31/5.51 ! [I2: nat,K2: nat,N: nat] :
% 5.31/5.51 ( ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K2 ) @ N )
% 5.31/5.51 => ( ord_less_eq_nat @ I2 @ ( minus_minus_nat @ N @ K2 ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % add_le_imp_le_diff
% 5.31/5.51 thf(fact_2008_add__le__imp__le__diff,axiom,
% 5.31/5.51 ! [I2: int,K2: int,N: int] :
% 5.31/5.51 ( ( ord_less_eq_int @ ( plus_plus_int @ I2 @ K2 ) @ N )
% 5.31/5.51 => ( ord_less_eq_int @ I2 @ ( minus_minus_int @ N @ K2 ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % add_le_imp_le_diff
% 5.31/5.51 thf(fact_2009_ordered__cancel__comm__monoid__diff__class_Ole__imp__diff__is__add,axiom,
% 5.31/5.51 ! [A: nat,B: nat,C2: nat] :
% 5.31/5.51 ( ( ord_less_eq_nat @ A @ B )
% 5.31/5.51 => ( ( ord_less_eq_nat @ A @ B )
% 5.31/5.51 => ( ( ( minus_minus_nat @ B @ A )
% 5.31/5.51 = C2 )
% 5.31/5.51 = ( B
% 5.31/5.51 = ( plus_plus_nat @ C2 @ A ) ) ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % ordered_cancel_comm_monoid_diff_class.le_imp_diff_is_add
% 5.31/5.51 thf(fact_2010_ordered__cancel__comm__monoid__diff__class_Oadd__diff__inverse,axiom,
% 5.31/5.51 ! [A: nat,B: nat] :
% 5.31/5.51 ( ( ord_less_eq_nat @ A @ B )
% 5.31/5.51 => ( ( plus_plus_nat @ A @ ( minus_minus_nat @ B @ A ) )
% 5.31/5.51 = B ) ) ).
% 5.31/5.51
% 5.31/5.51 % ordered_cancel_comm_monoid_diff_class.add_diff_inverse
% 5.31/5.51 thf(fact_2011_ordered__cancel__comm__monoid__diff__class_Odiff__diff__right,axiom,
% 5.31/5.51 ! [A: nat,B: nat,C2: nat] :
% 5.31/5.51 ( ( ord_less_eq_nat @ A @ B )
% 5.31/5.51 => ( ( minus_minus_nat @ C2 @ ( minus_minus_nat @ B @ A ) )
% 5.31/5.51 = ( minus_minus_nat @ ( plus_plus_nat @ C2 @ A ) @ B ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % ordered_cancel_comm_monoid_diff_class.diff_diff_right
% 5.31/5.51 thf(fact_2012_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc2,axiom,
% 5.31/5.51 ! [A: nat,B: nat,C2: nat] :
% 5.31/5.51 ( ( ord_less_eq_nat @ A @ B )
% 5.31/5.51 => ( ( minus_minus_nat @ ( plus_plus_nat @ B @ C2 ) @ A )
% 5.31/5.51 = ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ C2 ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % ordered_cancel_comm_monoid_diff_class.diff_add_assoc2
% 5.31/5.51 thf(fact_2013_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc2,axiom,
% 5.31/5.51 ! [A: nat,B: nat,C2: nat] :
% 5.31/5.51 ( ( ord_less_eq_nat @ A @ B )
% 5.31/5.51 => ( ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ C2 )
% 5.31/5.51 = ( minus_minus_nat @ ( plus_plus_nat @ B @ C2 ) @ A ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % ordered_cancel_comm_monoid_diff_class.add_diff_assoc2
% 5.31/5.51 thf(fact_2014_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc,axiom,
% 5.31/5.51 ! [A: nat,B: nat,C2: nat] :
% 5.31/5.51 ( ( ord_less_eq_nat @ A @ B )
% 5.31/5.51 => ( ( minus_minus_nat @ ( plus_plus_nat @ C2 @ B ) @ A )
% 5.31/5.51 = ( plus_plus_nat @ C2 @ ( minus_minus_nat @ B @ A ) ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % ordered_cancel_comm_monoid_diff_class.diff_add_assoc
% 5.31/5.51 thf(fact_2015_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc,axiom,
% 5.31/5.51 ! [A: nat,B: nat,C2: nat] :
% 5.31/5.51 ( ( ord_less_eq_nat @ A @ B )
% 5.31/5.51 => ( ( plus_plus_nat @ C2 @ ( minus_minus_nat @ B @ A ) )
% 5.31/5.51 = ( minus_minus_nat @ ( plus_plus_nat @ C2 @ B ) @ A ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % ordered_cancel_comm_monoid_diff_class.add_diff_assoc
% 5.31/5.51 thf(fact_2016_ordered__cancel__comm__monoid__diff__class_Ole__diff__conv2,axiom,
% 5.31/5.51 ! [A: nat,B: nat,C2: nat] :
% 5.31/5.51 ( ( ord_less_eq_nat @ A @ B )
% 5.31/5.51 => ( ( ord_less_eq_nat @ C2 @ ( minus_minus_nat @ B @ A ) )
% 5.31/5.51 = ( ord_less_eq_nat @ ( plus_plus_nat @ C2 @ A ) @ B ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % ordered_cancel_comm_monoid_diff_class.le_diff_conv2
% 5.31/5.51 thf(fact_2017_le__add__diff,axiom,
% 5.31/5.51 ! [A: nat,B: nat,C2: nat] :
% 5.31/5.51 ( ( ord_less_eq_nat @ A @ B )
% 5.31/5.51 => ( ord_less_eq_nat @ C2 @ ( minus_minus_nat @ ( plus_plus_nat @ B @ C2 ) @ A ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % le_add_diff
% 5.31/5.51 thf(fact_2018_diff__add,axiom,
% 5.31/5.51 ! [A: nat,B: nat] :
% 5.31/5.51 ( ( ord_less_eq_nat @ A @ B )
% 5.31/5.51 => ( ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ A )
% 5.31/5.51 = B ) ) ).
% 5.31/5.51
% 5.31/5.51 % diff_add
% 5.31/5.51 thf(fact_2019_le__diff__eq,axiom,
% 5.31/5.51 ! [A: real,C2: real,B: real] :
% 5.31/5.51 ( ( ord_less_eq_real @ A @ ( minus_minus_real @ C2 @ B ) )
% 5.31/5.51 = ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ C2 ) ) ).
% 5.31/5.51
% 5.31/5.51 % le_diff_eq
% 5.31/5.51 thf(fact_2020_le__diff__eq,axiom,
% 5.31/5.51 ! [A: rat,C2: rat,B: rat] :
% 5.31/5.51 ( ( ord_less_eq_rat @ A @ ( minus_minus_rat @ C2 @ B ) )
% 5.31/5.51 = ( ord_less_eq_rat @ ( plus_plus_rat @ A @ B ) @ C2 ) ) ).
% 5.31/5.51
% 5.31/5.51 % le_diff_eq
% 5.31/5.51 thf(fact_2021_le__diff__eq,axiom,
% 5.31/5.51 ! [A: int,C2: int,B: int] :
% 5.31/5.51 ( ( ord_less_eq_int @ A @ ( minus_minus_int @ C2 @ B ) )
% 5.31/5.51 = ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ C2 ) ) ).
% 5.31/5.51
% 5.31/5.51 % le_diff_eq
% 5.31/5.51 thf(fact_2022_diff__le__eq,axiom,
% 5.31/5.51 ! [A: real,B: real,C2: real] :
% 5.31/5.51 ( ( ord_less_eq_real @ ( minus_minus_real @ A @ B ) @ C2 )
% 5.31/5.51 = ( ord_less_eq_real @ A @ ( plus_plus_real @ C2 @ B ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % diff_le_eq
% 5.31/5.51 thf(fact_2023_diff__le__eq,axiom,
% 5.31/5.51 ! [A: rat,B: rat,C2: rat] :
% 5.31/5.51 ( ( ord_less_eq_rat @ ( minus_minus_rat @ A @ B ) @ C2 )
% 5.31/5.51 = ( ord_less_eq_rat @ A @ ( plus_plus_rat @ C2 @ B ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % diff_le_eq
% 5.31/5.51 thf(fact_2024_diff__le__eq,axiom,
% 5.31/5.51 ! [A: int,B: int,C2: int] :
% 5.31/5.51 ( ( ord_less_eq_int @ ( minus_minus_int @ A @ B ) @ C2 )
% 5.31/5.51 = ( ord_less_eq_int @ A @ ( plus_plus_int @ C2 @ B ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % diff_le_eq
% 5.31/5.51 thf(fact_2025_less__diff__eq,axiom,
% 5.31/5.51 ! [A: real,C2: real,B: real] :
% 5.31/5.51 ( ( ord_less_real @ A @ ( minus_minus_real @ C2 @ B ) )
% 5.31/5.51 = ( ord_less_real @ ( plus_plus_real @ A @ B ) @ C2 ) ) ).
% 5.31/5.51
% 5.31/5.51 % less_diff_eq
% 5.31/5.51 thf(fact_2026_less__diff__eq,axiom,
% 5.31/5.51 ! [A: rat,C2: rat,B: rat] :
% 5.31/5.51 ( ( ord_less_rat @ A @ ( minus_minus_rat @ C2 @ B ) )
% 5.31/5.51 = ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ C2 ) ) ).
% 5.31/5.51
% 5.31/5.51 % less_diff_eq
% 5.31/5.51 thf(fact_2027_less__diff__eq,axiom,
% 5.31/5.51 ! [A: int,C2: int,B: int] :
% 5.31/5.51 ( ( ord_less_int @ A @ ( minus_minus_int @ C2 @ B ) )
% 5.31/5.51 = ( ord_less_int @ ( plus_plus_int @ A @ B ) @ C2 ) ) ).
% 5.31/5.51
% 5.31/5.51 % less_diff_eq
% 5.31/5.51 thf(fact_2028_diff__less__eq,axiom,
% 5.31/5.51 ! [A: real,B: real,C2: real] :
% 5.31/5.51 ( ( ord_less_real @ ( minus_minus_real @ A @ B ) @ C2 )
% 5.31/5.51 = ( ord_less_real @ A @ ( plus_plus_real @ C2 @ B ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % diff_less_eq
% 5.31/5.51 thf(fact_2029_diff__less__eq,axiom,
% 5.31/5.51 ! [A: rat,B: rat,C2: rat] :
% 5.31/5.51 ( ( ord_less_rat @ ( minus_minus_rat @ A @ B ) @ C2 )
% 5.31/5.51 = ( ord_less_rat @ A @ ( plus_plus_rat @ C2 @ B ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % diff_less_eq
% 5.31/5.51 thf(fact_2030_diff__less__eq,axiom,
% 5.31/5.51 ! [A: int,B: int,C2: int] :
% 5.31/5.51 ( ( ord_less_int @ ( minus_minus_int @ A @ B ) @ C2 )
% 5.31/5.51 = ( ord_less_int @ A @ ( plus_plus_int @ C2 @ B ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % diff_less_eq
% 5.31/5.51 thf(fact_2031_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 5.31/5.51 ! [A: real,B: real] :
% 5.31/5.51 ( ~ ( ord_less_real @ A @ B )
% 5.31/5.51 => ( ( plus_plus_real @ B @ ( minus_minus_real @ A @ B ) )
% 5.31/5.51 = A ) ) ).
% 5.31/5.51
% 5.31/5.51 % linordered_semidom_class.add_diff_inverse
% 5.31/5.51 thf(fact_2032_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 5.31/5.51 ! [A: rat,B: rat] :
% 5.31/5.51 ( ~ ( ord_less_rat @ A @ B )
% 5.31/5.51 => ( ( plus_plus_rat @ B @ ( minus_minus_rat @ A @ B ) )
% 5.31/5.51 = A ) ) ).
% 5.31/5.51
% 5.31/5.51 % linordered_semidom_class.add_diff_inverse
% 5.31/5.51 thf(fact_2033_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 5.31/5.51 ! [A: nat,B: nat] :
% 5.31/5.51 ( ~ ( ord_less_nat @ A @ B )
% 5.31/5.51 => ( ( plus_plus_nat @ B @ ( minus_minus_nat @ A @ B ) )
% 5.31/5.51 = A ) ) ).
% 5.31/5.51
% 5.31/5.51 % linordered_semidom_class.add_diff_inverse
% 5.31/5.51 thf(fact_2034_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 5.31/5.51 ! [A: int,B: int] :
% 5.31/5.51 ( ~ ( ord_less_int @ A @ B )
% 5.31/5.51 => ( ( plus_plus_int @ B @ ( minus_minus_int @ A @ B ) )
% 5.31/5.51 = A ) ) ).
% 5.31/5.51
% 5.31/5.51 % linordered_semidom_class.add_diff_inverse
% 5.31/5.51 thf(fact_2035_square__diff__square__factored,axiom,
% 5.31/5.51 ! [X: real,Y: real] :
% 5.31/5.51 ( ( minus_minus_real @ ( times_times_real @ X @ X ) @ ( times_times_real @ Y @ Y ) )
% 5.31/5.51 = ( times_times_real @ ( plus_plus_real @ X @ Y ) @ ( minus_minus_real @ X @ Y ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % square_diff_square_factored
% 5.31/5.51 thf(fact_2036_square__diff__square__factored,axiom,
% 5.31/5.51 ! [X: rat,Y: rat] :
% 5.31/5.51 ( ( minus_minus_rat @ ( times_times_rat @ X @ X ) @ ( times_times_rat @ Y @ Y ) )
% 5.31/5.51 = ( times_times_rat @ ( plus_plus_rat @ X @ Y ) @ ( minus_minus_rat @ X @ Y ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % square_diff_square_factored
% 5.31/5.51 thf(fact_2037_square__diff__square__factored,axiom,
% 5.31/5.51 ! [X: int,Y: int] :
% 5.31/5.51 ( ( minus_minus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y @ Y ) )
% 5.31/5.51 = ( times_times_int @ ( plus_plus_int @ X @ Y ) @ ( minus_minus_int @ X @ Y ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % square_diff_square_factored
% 5.31/5.51 thf(fact_2038_eq__add__iff2,axiom,
% 5.31/5.51 ! [A: real,E: real,C2: real,B: real,D: real] :
% 5.31/5.51 ( ( ( plus_plus_real @ ( times_times_real @ A @ E ) @ C2 )
% 5.31/5.51 = ( plus_plus_real @ ( times_times_real @ B @ E ) @ D ) )
% 5.31/5.51 = ( C2
% 5.31/5.51 = ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ B @ A ) @ E ) @ D ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % eq_add_iff2
% 5.31/5.51 thf(fact_2039_eq__add__iff2,axiom,
% 5.31/5.51 ! [A: rat,E: rat,C2: rat,B: rat,D: rat] :
% 5.31/5.51 ( ( ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ C2 )
% 5.31/5.51 = ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ D ) )
% 5.31/5.51 = ( C2
% 5.31/5.51 = ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ B @ A ) @ E ) @ D ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % eq_add_iff2
% 5.31/5.51 thf(fact_2040_eq__add__iff2,axiom,
% 5.31/5.51 ! [A: int,E: int,C2: int,B: int,D: int] :
% 5.31/5.51 ( ( ( plus_plus_int @ ( times_times_int @ A @ E ) @ C2 )
% 5.31/5.51 = ( plus_plus_int @ ( times_times_int @ B @ E ) @ D ) )
% 5.31/5.51 = ( C2
% 5.31/5.51 = ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ B @ A ) @ E ) @ D ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % eq_add_iff2
% 5.31/5.51 thf(fact_2041_eq__add__iff1,axiom,
% 5.31/5.51 ! [A: real,E: real,C2: real,B: real,D: real] :
% 5.31/5.51 ( ( ( plus_plus_real @ ( times_times_real @ A @ E ) @ C2 )
% 5.31/5.51 = ( plus_plus_real @ ( times_times_real @ B @ E ) @ D ) )
% 5.31/5.51 = ( ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ A @ B ) @ E ) @ C2 )
% 5.31/5.51 = D ) ) ).
% 5.31/5.51
% 5.31/5.51 % eq_add_iff1
% 5.31/5.51 thf(fact_2042_eq__add__iff1,axiom,
% 5.31/5.51 ! [A: rat,E: rat,C2: rat,B: rat,D: rat] :
% 5.31/5.51 ( ( ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ C2 )
% 5.31/5.51 = ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ D ) )
% 5.31/5.51 = ( ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ E ) @ C2 )
% 5.31/5.51 = D ) ) ).
% 5.31/5.51
% 5.31/5.51 % eq_add_iff1
% 5.31/5.51 thf(fact_2043_eq__add__iff1,axiom,
% 5.31/5.51 ! [A: int,E: int,C2: int,B: int,D: int] :
% 5.31/5.51 ( ( ( plus_plus_int @ ( times_times_int @ A @ E ) @ C2 )
% 5.31/5.51 = ( plus_plus_int @ ( times_times_int @ B @ E ) @ D ) )
% 5.31/5.51 = ( ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A @ B ) @ E ) @ C2 )
% 5.31/5.51 = D ) ) ).
% 5.31/5.51
% 5.31/5.51 % eq_add_iff1
% 5.31/5.51 thf(fact_2044_ordered__ring__class_Ole__add__iff2,axiom,
% 5.31/5.51 ! [A: real,E: real,C2: real,B: real,D: real] :
% 5.31/5.51 ( ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ A @ E ) @ C2 ) @ ( plus_plus_real @ ( times_times_real @ B @ E ) @ D ) )
% 5.31/5.51 = ( ord_less_eq_real @ C2 @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ B @ A ) @ E ) @ D ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % ordered_ring_class.le_add_iff2
% 5.31/5.51 thf(fact_2045_ordered__ring__class_Ole__add__iff2,axiom,
% 5.31/5.51 ! [A: rat,E: rat,C2: rat,B: rat,D: rat] :
% 5.31/5.51 ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ C2 ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ D ) )
% 5.31/5.51 = ( ord_less_eq_rat @ C2 @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ B @ A ) @ E ) @ D ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % ordered_ring_class.le_add_iff2
% 5.31/5.51 thf(fact_2046_ordered__ring__class_Ole__add__iff2,axiom,
% 5.31/5.51 ! [A: int,E: int,C2: int,B: int,D: int] :
% 5.31/5.51 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ A @ E ) @ C2 ) @ ( plus_plus_int @ ( times_times_int @ B @ E ) @ D ) )
% 5.31/5.51 = ( ord_less_eq_int @ C2 @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ B @ A ) @ E ) @ D ) ) ) ).
% 5.31/5.51
% 5.31/5.51 % ordered_ring_class.le_add_iff2
% 5.31/5.51 thf(fact_2047_ordered__ring__class_Ole__add__iff1,axiom,
% 5.31/5.51 ! [A: real,E: real,C2: real,B: real,D: real] :
% 5.31/5.51 ( ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ A @ E ) @ C2 ) @ ( plus_plus_real @ ( times_times_real @ B @ E ) @ D ) )
% 5.31/5.51 = ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ A @ B ) @ E ) @ C2 ) @ D ) ) ).
% 5.31/5.51
% 5.31/5.51 % ordered_ring_class.le_add_iff1
% 5.31/5.51 thf(fact_2048_ordered__ring__class_Ole__add__iff1,axiom,
% 5.31/5.51 ! [A: rat,E: rat,C2: rat,B: rat,D: rat] :
% 5.31/5.51 ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ C2 ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ D ) )
% 5.31/5.51 = ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ E ) @ C2 ) @ D ) ) ).
% 5.31/5.51
% 5.31/5.51 % ordered_ring_class.le_add_iff1
% 5.31/5.51 thf(fact_2049_ordered__ring__class_Ole__add__iff1,axiom,
% 5.31/5.51 ! [A: int,E: int,C2: int,B: int,D: int] :
% 5.31/5.51 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ A @ E ) @ C2 ) @ ( plus_plus_int @ ( times_times_int @ B @ E ) @ D ) )
% 5.31/5.51 = ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A @ B ) @ E ) @ C2 ) @ D ) ) ).
% 5.31/5.52
% 5.31/5.52 % ordered_ring_class.le_add_iff1
% 5.31/5.52 thf(fact_2050_less__add__iff1,axiom,
% 5.31/5.52 ! [A: real,E: real,C2: real,B: real,D: real] :
% 5.31/5.52 ( ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ A @ E ) @ C2 ) @ ( plus_plus_real @ ( times_times_real @ B @ E ) @ D ) )
% 5.31/5.52 = ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ A @ B ) @ E ) @ C2 ) @ D ) ) ).
% 5.31/5.52
% 5.31/5.52 % less_add_iff1
% 5.31/5.52 thf(fact_2051_less__add__iff1,axiom,
% 5.31/5.52 ! [A: rat,E: rat,C2: rat,B: rat,D: rat] :
% 5.31/5.52 ( ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ C2 ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ D ) )
% 5.31/5.52 = ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ E ) @ C2 ) @ D ) ) ).
% 5.31/5.52
% 5.31/5.52 % less_add_iff1
% 5.31/5.52 thf(fact_2052_less__add__iff1,axiom,
% 5.31/5.52 ! [A: int,E: int,C2: int,B: int,D: int] :
% 5.31/5.52 ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ A @ E ) @ C2 ) @ ( plus_plus_int @ ( times_times_int @ B @ E ) @ D ) )
% 5.31/5.52 = ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A @ B ) @ E ) @ C2 ) @ D ) ) ).
% 5.31/5.52
% 5.31/5.52 % less_add_iff1
% 5.31/5.52 thf(fact_2053_less__add__iff2,axiom,
% 5.31/5.52 ! [A: real,E: real,C2: real,B: real,D: real] :
% 5.31/5.52 ( ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ A @ E ) @ C2 ) @ ( plus_plus_real @ ( times_times_real @ B @ E ) @ D ) )
% 5.31/5.52 = ( ord_less_real @ C2 @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ B @ A ) @ E ) @ D ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % less_add_iff2
% 5.31/5.52 thf(fact_2054_less__add__iff2,axiom,
% 5.31/5.52 ! [A: rat,E: rat,C2: rat,B: rat,D: rat] :
% 5.31/5.52 ( ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ C2 ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ D ) )
% 5.31/5.52 = ( ord_less_rat @ C2 @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ B @ A ) @ E ) @ D ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % less_add_iff2
% 5.31/5.52 thf(fact_2055_less__add__iff2,axiom,
% 5.31/5.52 ! [A: int,E: int,C2: int,B: int,D: int] :
% 5.31/5.52 ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ A @ E ) @ C2 ) @ ( plus_plus_int @ ( times_times_int @ B @ E ) @ D ) )
% 5.31/5.52 = ( ord_less_int @ C2 @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ B @ A ) @ E ) @ D ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % less_add_iff2
% 5.31/5.52 thf(fact_2056_square__diff__one__factored,axiom,
% 5.31/5.52 ! [X: code_integer] :
% 5.31/5.52 ( ( minus_8373710615458151222nteger @ ( times_3573771949741848930nteger @ X @ X ) @ one_one_Code_integer )
% 5.31/5.52 = ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ X @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ X @ one_one_Code_integer ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % square_diff_one_factored
% 5.31/5.52 thf(fact_2057_square__diff__one__factored,axiom,
% 5.31/5.52 ! [X: complex] :
% 5.31/5.52 ( ( minus_minus_complex @ ( times_times_complex @ X @ X ) @ one_one_complex )
% 5.31/5.52 = ( times_times_complex @ ( plus_plus_complex @ X @ one_one_complex ) @ ( minus_minus_complex @ X @ one_one_complex ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % square_diff_one_factored
% 5.31/5.52 thf(fact_2058_square__diff__one__factored,axiom,
% 5.31/5.52 ! [X: real] :
% 5.31/5.52 ( ( minus_minus_real @ ( times_times_real @ X @ X ) @ one_one_real )
% 5.31/5.52 = ( times_times_real @ ( plus_plus_real @ X @ one_one_real ) @ ( minus_minus_real @ X @ one_one_real ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % square_diff_one_factored
% 5.31/5.52 thf(fact_2059_square__diff__one__factored,axiom,
% 5.31/5.52 ! [X: rat] :
% 5.31/5.52 ( ( minus_minus_rat @ ( times_times_rat @ X @ X ) @ one_one_rat )
% 5.31/5.52 = ( times_times_rat @ ( plus_plus_rat @ X @ one_one_rat ) @ ( minus_minus_rat @ X @ one_one_rat ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % square_diff_one_factored
% 5.31/5.52 thf(fact_2060_square__diff__one__factored,axiom,
% 5.31/5.52 ! [X: int] :
% 5.31/5.52 ( ( minus_minus_int @ ( times_times_int @ X @ X ) @ one_one_int )
% 5.31/5.52 = ( times_times_int @ ( plus_plus_int @ X @ one_one_int ) @ ( minus_minus_int @ X @ one_one_int ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % square_diff_one_factored
% 5.31/5.52 thf(fact_2061_finite__ranking__induct,axiom,
% 5.31/5.52 ! [S3: set_complex,P2: set_complex > $o,F2: complex > rat] :
% 5.31/5.52 ( ( finite3207457112153483333omplex @ S3 )
% 5.31/5.52 => ( ( P2 @ bot_bot_set_complex )
% 5.31/5.52 => ( ! [X3: complex,S4: set_complex] :
% 5.31/5.52 ( ( finite3207457112153483333omplex @ S4 )
% 5.31/5.52 => ( ! [Y6: complex] :
% 5.31/5.52 ( ( member_complex @ Y6 @ S4 )
% 5.31/5.52 => ( ord_less_eq_rat @ ( F2 @ Y6 ) @ ( F2 @ X3 ) ) )
% 5.31/5.52 => ( ( P2 @ S4 )
% 5.31/5.52 => ( P2 @ ( insert_complex @ X3 @ S4 ) ) ) ) )
% 5.31/5.52 => ( P2 @ S3 ) ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % finite_ranking_induct
% 5.31/5.52 thf(fact_2062_finite__ranking__induct,axiom,
% 5.31/5.52 ! [S3: set_nat,P2: set_nat > $o,F2: nat > rat] :
% 5.31/5.52 ( ( finite_finite_nat @ S3 )
% 5.31/5.52 => ( ( P2 @ bot_bot_set_nat )
% 5.31/5.52 => ( ! [X3: nat,S4: set_nat] :
% 5.31/5.52 ( ( finite_finite_nat @ S4 )
% 5.31/5.52 => ( ! [Y6: nat] :
% 5.31/5.52 ( ( member_nat @ Y6 @ S4 )
% 5.31/5.52 => ( ord_less_eq_rat @ ( F2 @ Y6 ) @ ( F2 @ X3 ) ) )
% 5.31/5.52 => ( ( P2 @ S4 )
% 5.31/5.52 => ( P2 @ ( insert_nat @ X3 @ S4 ) ) ) ) )
% 5.31/5.52 => ( P2 @ S3 ) ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % finite_ranking_induct
% 5.31/5.52 thf(fact_2063_finite__ranking__induct,axiom,
% 5.31/5.52 ! [S3: set_int,P2: set_int > $o,F2: int > rat] :
% 5.31/5.52 ( ( finite_finite_int @ S3 )
% 5.31/5.52 => ( ( P2 @ bot_bot_set_int )
% 5.31/5.52 => ( ! [X3: int,S4: set_int] :
% 5.31/5.52 ( ( finite_finite_int @ S4 )
% 5.31/5.52 => ( ! [Y6: int] :
% 5.31/5.52 ( ( member_int @ Y6 @ S4 )
% 5.31/5.52 => ( ord_less_eq_rat @ ( F2 @ Y6 ) @ ( F2 @ X3 ) ) )
% 5.31/5.52 => ( ( P2 @ S4 )
% 5.31/5.52 => ( P2 @ ( insert_int @ X3 @ S4 ) ) ) ) )
% 5.31/5.52 => ( P2 @ S3 ) ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % finite_ranking_induct
% 5.31/5.52 thf(fact_2064_finite__ranking__induct,axiom,
% 5.31/5.52 ! [S3: set_real,P2: set_real > $o,F2: real > rat] :
% 5.31/5.52 ( ( finite_finite_real @ S3 )
% 5.31/5.52 => ( ( P2 @ bot_bot_set_real )
% 5.31/5.52 => ( ! [X3: real,S4: set_real] :
% 5.31/5.52 ( ( finite_finite_real @ S4 )
% 5.31/5.52 => ( ! [Y6: real] :
% 5.31/5.52 ( ( member_real @ Y6 @ S4 )
% 5.31/5.52 => ( ord_less_eq_rat @ ( F2 @ Y6 ) @ ( F2 @ X3 ) ) )
% 5.31/5.52 => ( ( P2 @ S4 )
% 5.31/5.52 => ( P2 @ ( insert_real @ X3 @ S4 ) ) ) ) )
% 5.31/5.52 => ( P2 @ S3 ) ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % finite_ranking_induct
% 5.31/5.52 thf(fact_2065_finite__ranking__induct,axiom,
% 5.31/5.52 ! [S3: set_complex,P2: set_complex > $o,F2: complex > num] :
% 5.31/5.52 ( ( finite3207457112153483333omplex @ S3 )
% 5.31/5.52 => ( ( P2 @ bot_bot_set_complex )
% 5.31/5.52 => ( ! [X3: complex,S4: set_complex] :
% 5.31/5.52 ( ( finite3207457112153483333omplex @ S4 )
% 5.31/5.52 => ( ! [Y6: complex] :
% 5.31/5.52 ( ( member_complex @ Y6 @ S4 )
% 5.31/5.52 => ( ord_less_eq_num @ ( F2 @ Y6 ) @ ( F2 @ X3 ) ) )
% 5.31/5.52 => ( ( P2 @ S4 )
% 5.31/5.52 => ( P2 @ ( insert_complex @ X3 @ S4 ) ) ) ) )
% 5.31/5.52 => ( P2 @ S3 ) ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % finite_ranking_induct
% 5.31/5.52 thf(fact_2066_finite__ranking__induct,axiom,
% 5.31/5.52 ! [S3: set_nat,P2: set_nat > $o,F2: nat > num] :
% 5.31/5.52 ( ( finite_finite_nat @ S3 )
% 5.31/5.52 => ( ( P2 @ bot_bot_set_nat )
% 5.31/5.52 => ( ! [X3: nat,S4: set_nat] :
% 5.31/5.52 ( ( finite_finite_nat @ S4 )
% 5.31/5.52 => ( ! [Y6: nat] :
% 5.31/5.52 ( ( member_nat @ Y6 @ S4 )
% 5.31/5.52 => ( ord_less_eq_num @ ( F2 @ Y6 ) @ ( F2 @ X3 ) ) )
% 5.31/5.52 => ( ( P2 @ S4 )
% 5.31/5.52 => ( P2 @ ( insert_nat @ X3 @ S4 ) ) ) ) )
% 5.31/5.52 => ( P2 @ S3 ) ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % finite_ranking_induct
% 5.31/5.52 thf(fact_2067_finite__ranking__induct,axiom,
% 5.31/5.52 ! [S3: set_int,P2: set_int > $o,F2: int > num] :
% 5.31/5.52 ( ( finite_finite_int @ S3 )
% 5.31/5.52 => ( ( P2 @ bot_bot_set_int )
% 5.31/5.52 => ( ! [X3: int,S4: set_int] :
% 5.31/5.52 ( ( finite_finite_int @ S4 )
% 5.31/5.52 => ( ! [Y6: int] :
% 5.31/5.52 ( ( member_int @ Y6 @ S4 )
% 5.31/5.52 => ( ord_less_eq_num @ ( F2 @ Y6 ) @ ( F2 @ X3 ) ) )
% 5.31/5.52 => ( ( P2 @ S4 )
% 5.31/5.52 => ( P2 @ ( insert_int @ X3 @ S4 ) ) ) ) )
% 5.31/5.52 => ( P2 @ S3 ) ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % finite_ranking_induct
% 5.31/5.52 thf(fact_2068_finite__ranking__induct,axiom,
% 5.31/5.52 ! [S3: set_real,P2: set_real > $o,F2: real > num] :
% 5.31/5.52 ( ( finite_finite_real @ S3 )
% 5.31/5.52 => ( ( P2 @ bot_bot_set_real )
% 5.31/5.52 => ( ! [X3: real,S4: set_real] :
% 5.31/5.52 ( ( finite_finite_real @ S4 )
% 5.31/5.52 => ( ! [Y6: real] :
% 5.31/5.52 ( ( member_real @ Y6 @ S4 )
% 5.31/5.52 => ( ord_less_eq_num @ ( F2 @ Y6 ) @ ( F2 @ X3 ) ) )
% 5.31/5.52 => ( ( P2 @ S4 )
% 5.31/5.52 => ( P2 @ ( insert_real @ X3 @ S4 ) ) ) ) )
% 5.31/5.52 => ( P2 @ S3 ) ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % finite_ranking_induct
% 5.31/5.52 thf(fact_2069_finite__ranking__induct,axiom,
% 5.31/5.52 ! [S3: set_complex,P2: set_complex > $o,F2: complex > nat] :
% 5.31/5.52 ( ( finite3207457112153483333omplex @ S3 )
% 5.31/5.52 => ( ( P2 @ bot_bot_set_complex )
% 5.31/5.52 => ( ! [X3: complex,S4: set_complex] :
% 5.31/5.52 ( ( finite3207457112153483333omplex @ S4 )
% 5.31/5.52 => ( ! [Y6: complex] :
% 5.31/5.52 ( ( member_complex @ Y6 @ S4 )
% 5.31/5.52 => ( ord_less_eq_nat @ ( F2 @ Y6 ) @ ( F2 @ X3 ) ) )
% 5.31/5.52 => ( ( P2 @ S4 )
% 5.31/5.52 => ( P2 @ ( insert_complex @ X3 @ S4 ) ) ) ) )
% 5.31/5.52 => ( P2 @ S3 ) ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % finite_ranking_induct
% 5.31/5.52 thf(fact_2070_finite__ranking__induct,axiom,
% 5.31/5.52 ! [S3: set_nat,P2: set_nat > $o,F2: nat > nat] :
% 5.31/5.52 ( ( finite_finite_nat @ S3 )
% 5.31/5.52 => ( ( P2 @ bot_bot_set_nat )
% 5.31/5.52 => ( ! [X3: nat,S4: set_nat] :
% 5.31/5.52 ( ( finite_finite_nat @ S4 )
% 5.31/5.52 => ( ! [Y6: nat] :
% 5.31/5.52 ( ( member_nat @ Y6 @ S4 )
% 5.31/5.52 => ( ord_less_eq_nat @ ( F2 @ Y6 ) @ ( F2 @ X3 ) ) )
% 5.31/5.52 => ( ( P2 @ S4 )
% 5.31/5.52 => ( P2 @ ( insert_nat @ X3 @ S4 ) ) ) ) )
% 5.31/5.52 => ( P2 @ S3 ) ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % finite_ranking_induct
% 5.31/5.52 thf(fact_2071_length__induct,axiom,
% 5.31/5.52 ! [P2: list_VEBT_VEBT > $o,Xs2: list_VEBT_VEBT] :
% 5.31/5.52 ( ! [Xs3: list_VEBT_VEBT] :
% 5.31/5.52 ( ! [Ys2: list_VEBT_VEBT] :
% 5.31/5.52 ( ( ord_less_nat @ ( size_s6755466524823107622T_VEBT @ Ys2 ) @ ( size_s6755466524823107622T_VEBT @ Xs3 ) )
% 5.31/5.52 => ( P2 @ Ys2 ) )
% 5.31/5.52 => ( P2 @ Xs3 ) )
% 5.31/5.52 => ( P2 @ Xs2 ) ) ).
% 5.31/5.52
% 5.31/5.52 % length_induct
% 5.31/5.52 thf(fact_2072_length__induct,axiom,
% 5.31/5.52 ! [P2: list_o > $o,Xs2: list_o] :
% 5.31/5.52 ( ! [Xs3: list_o] :
% 5.31/5.52 ( ! [Ys2: list_o] :
% 5.31/5.52 ( ( ord_less_nat @ ( size_size_list_o @ Ys2 ) @ ( size_size_list_o @ Xs3 ) )
% 5.31/5.52 => ( P2 @ Ys2 ) )
% 5.31/5.52 => ( P2 @ Xs3 ) )
% 5.31/5.52 => ( P2 @ Xs2 ) ) ).
% 5.31/5.52
% 5.31/5.52 % length_induct
% 5.31/5.52 thf(fact_2073_length__induct,axiom,
% 5.31/5.52 ! [P2: list_nat > $o,Xs2: list_nat] :
% 5.31/5.52 ( ! [Xs3: list_nat] :
% 5.31/5.52 ( ! [Ys2: list_nat] :
% 5.31/5.52 ( ( ord_less_nat @ ( size_size_list_nat @ Ys2 ) @ ( size_size_list_nat @ Xs3 ) )
% 5.31/5.52 => ( P2 @ Ys2 ) )
% 5.31/5.52 => ( P2 @ Xs3 ) )
% 5.31/5.52 => ( P2 @ Xs2 ) ) ).
% 5.31/5.52
% 5.31/5.52 % length_induct
% 5.31/5.52 thf(fact_2074_length__induct,axiom,
% 5.31/5.52 ! [P2: list_int > $o,Xs2: list_int] :
% 5.31/5.52 ( ! [Xs3: list_int] :
% 5.31/5.52 ( ! [Ys2: list_int] :
% 5.31/5.52 ( ( ord_less_nat @ ( size_size_list_int @ Ys2 ) @ ( size_size_list_int @ Xs3 ) )
% 5.31/5.52 => ( P2 @ Ys2 ) )
% 5.31/5.52 => ( P2 @ Xs3 ) )
% 5.31/5.52 => ( P2 @ Xs2 ) ) ).
% 5.31/5.52
% 5.31/5.52 % length_induct
% 5.31/5.52 thf(fact_2075_add__0__iff,axiom,
% 5.31/5.52 ! [B: complex,A: complex] :
% 5.31/5.52 ( ( B
% 5.31/5.52 = ( plus_plus_complex @ B @ A ) )
% 5.31/5.52 = ( A = zero_zero_complex ) ) ).
% 5.31/5.52
% 5.31/5.52 % add_0_iff
% 5.31/5.52 thf(fact_2076_add__0__iff,axiom,
% 5.31/5.52 ! [B: real,A: real] :
% 5.31/5.52 ( ( B
% 5.31/5.52 = ( plus_plus_real @ B @ A ) )
% 5.31/5.52 = ( A = zero_zero_real ) ) ).
% 5.31/5.52
% 5.31/5.52 % add_0_iff
% 5.31/5.52 thf(fact_2077_add__0__iff,axiom,
% 5.31/5.52 ! [B: rat,A: rat] :
% 5.31/5.52 ( ( B
% 5.31/5.52 = ( plus_plus_rat @ B @ A ) )
% 5.31/5.52 = ( A = zero_zero_rat ) ) ).
% 5.31/5.52
% 5.31/5.52 % add_0_iff
% 5.31/5.52 thf(fact_2078_add__0__iff,axiom,
% 5.31/5.52 ! [B: nat,A: nat] :
% 5.31/5.52 ( ( B
% 5.31/5.52 = ( plus_plus_nat @ B @ A ) )
% 5.31/5.52 = ( A = zero_zero_nat ) ) ).
% 5.31/5.52
% 5.31/5.52 % add_0_iff
% 5.31/5.52 thf(fact_2079_add__0__iff,axiom,
% 5.31/5.52 ! [B: int,A: int] :
% 5.31/5.52 ( ( B
% 5.31/5.52 = ( plus_plus_int @ B @ A ) )
% 5.31/5.52 = ( A = zero_zero_int ) ) ).
% 5.31/5.52
% 5.31/5.52 % add_0_iff
% 5.31/5.52 thf(fact_2080_crossproduct__eq,axiom,
% 5.31/5.52 ! [W2: real,Y: real,X: real,Z3: real] :
% 5.31/5.52 ( ( ( plus_plus_real @ ( times_times_real @ W2 @ Y ) @ ( times_times_real @ X @ Z3 ) )
% 5.31/5.52 = ( plus_plus_real @ ( times_times_real @ W2 @ Z3 ) @ ( times_times_real @ X @ Y ) ) )
% 5.31/5.52 = ( ( W2 = X )
% 5.31/5.52 | ( Y = Z3 ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % crossproduct_eq
% 5.31/5.52 thf(fact_2081_crossproduct__eq,axiom,
% 5.31/5.52 ! [W2: rat,Y: rat,X: rat,Z3: rat] :
% 5.31/5.52 ( ( ( plus_plus_rat @ ( times_times_rat @ W2 @ Y ) @ ( times_times_rat @ X @ Z3 ) )
% 5.31/5.52 = ( plus_plus_rat @ ( times_times_rat @ W2 @ Z3 ) @ ( times_times_rat @ X @ Y ) ) )
% 5.31/5.52 = ( ( W2 = X )
% 5.31/5.52 | ( Y = Z3 ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % crossproduct_eq
% 5.31/5.52 thf(fact_2082_crossproduct__eq,axiom,
% 5.31/5.52 ! [W2: nat,Y: nat,X: nat,Z3: nat] :
% 5.31/5.52 ( ( ( plus_plus_nat @ ( times_times_nat @ W2 @ Y ) @ ( times_times_nat @ X @ Z3 ) )
% 5.31/5.52 = ( plus_plus_nat @ ( times_times_nat @ W2 @ Z3 ) @ ( times_times_nat @ X @ Y ) ) )
% 5.31/5.52 = ( ( W2 = X )
% 5.31/5.52 | ( Y = Z3 ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % crossproduct_eq
% 5.31/5.52 thf(fact_2083_crossproduct__eq,axiom,
% 5.31/5.52 ! [W2: int,Y: int,X: int,Z3: int] :
% 5.31/5.52 ( ( ( plus_plus_int @ ( times_times_int @ W2 @ Y ) @ ( times_times_int @ X @ Z3 ) )
% 5.31/5.52 = ( plus_plus_int @ ( times_times_int @ W2 @ Z3 ) @ ( times_times_int @ X @ Y ) ) )
% 5.31/5.52 = ( ( W2 = X )
% 5.31/5.52 | ( Y = Z3 ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % crossproduct_eq
% 5.31/5.52 thf(fact_2084_crossproduct__noteq,axiom,
% 5.31/5.52 ! [A: real,B: real,C2: real,D: real] :
% 5.31/5.52 ( ( ( A != B )
% 5.31/5.52 & ( C2 != D ) )
% 5.31/5.52 = ( ( plus_plus_real @ ( times_times_real @ A @ C2 ) @ ( times_times_real @ B @ D ) )
% 5.31/5.52 != ( plus_plus_real @ ( times_times_real @ A @ D ) @ ( times_times_real @ B @ C2 ) ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % crossproduct_noteq
% 5.31/5.52 thf(fact_2085_crossproduct__noteq,axiom,
% 5.31/5.52 ! [A: rat,B: rat,C2: rat,D: rat] :
% 5.31/5.52 ( ( ( A != B )
% 5.31/5.52 & ( C2 != D ) )
% 5.31/5.52 = ( ( plus_plus_rat @ ( times_times_rat @ A @ C2 ) @ ( times_times_rat @ B @ D ) )
% 5.31/5.52 != ( plus_plus_rat @ ( times_times_rat @ A @ D ) @ ( times_times_rat @ B @ C2 ) ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % crossproduct_noteq
% 5.31/5.52 thf(fact_2086_crossproduct__noteq,axiom,
% 5.31/5.52 ! [A: nat,B: nat,C2: nat,D: nat] :
% 5.31/5.52 ( ( ( A != B )
% 5.31/5.52 & ( C2 != D ) )
% 5.31/5.52 = ( ( plus_plus_nat @ ( times_times_nat @ A @ C2 ) @ ( times_times_nat @ B @ D ) )
% 5.31/5.52 != ( plus_plus_nat @ ( times_times_nat @ A @ D ) @ ( times_times_nat @ B @ C2 ) ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % crossproduct_noteq
% 5.31/5.52 thf(fact_2087_crossproduct__noteq,axiom,
% 5.31/5.52 ! [A: int,B: int,C2: int,D: int] :
% 5.31/5.52 ( ( ( A != B )
% 5.31/5.52 & ( C2 != D ) )
% 5.31/5.52 = ( ( plus_plus_int @ ( times_times_int @ A @ C2 ) @ ( times_times_int @ B @ D ) )
% 5.31/5.52 != ( plus_plus_int @ ( times_times_int @ A @ D ) @ ( times_times_int @ B @ C2 ) ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % crossproduct_noteq
% 5.31/5.52 thf(fact_2088_option_Osize__gen_I1_J,axiom,
% 5.31/5.52 ! [X: nat > nat] :
% 5.31/5.52 ( ( size_option_nat @ X @ none_nat )
% 5.31/5.52 = ( suc @ zero_zero_nat ) ) ).
% 5.31/5.52
% 5.31/5.52 % option.size_gen(1)
% 5.31/5.52 thf(fact_2089_option_Osize__gen_I1_J,axiom,
% 5.31/5.52 ! [X: product_prod_nat_nat > nat] :
% 5.31/5.52 ( ( size_o8335143837870341156at_nat @ X @ none_P5556105721700978146at_nat )
% 5.31/5.52 = ( suc @ zero_zero_nat ) ) ).
% 5.31/5.52
% 5.31/5.52 % option.size_gen(1)
% 5.31/5.52 thf(fact_2090_option_Osize__gen_I1_J,axiom,
% 5.31/5.52 ! [X: num > nat] :
% 5.31/5.52 ( ( size_option_num @ X @ none_num )
% 5.31/5.52 = ( suc @ zero_zero_nat ) ) ).
% 5.31/5.52
% 5.31/5.52 % option.size_gen(1)
% 5.31/5.52 thf(fact_2091_finite__has__minimal,axiom,
% 5.31/5.52 ! [A4: set_real] :
% 5.31/5.52 ( ( finite_finite_real @ A4 )
% 5.31/5.52 => ( ( A4 != bot_bot_set_real )
% 5.31/5.52 => ? [X3: real] :
% 5.31/5.52 ( ( member_real @ X3 @ A4 )
% 5.31/5.52 & ! [Xa: real] :
% 5.31/5.52 ( ( member_real @ Xa @ A4 )
% 5.31/5.52 => ( ( ord_less_eq_real @ Xa @ X3 )
% 5.31/5.52 => ( X3 = Xa ) ) ) ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % finite_has_minimal
% 5.31/5.52 thf(fact_2092_finite__has__minimal,axiom,
% 5.31/5.52 ! [A4: set_set_nat] :
% 5.31/5.52 ( ( finite1152437895449049373et_nat @ A4 )
% 5.31/5.52 => ( ( A4 != bot_bot_set_set_nat )
% 5.31/5.52 => ? [X3: set_nat] :
% 5.31/5.52 ( ( member_set_nat @ X3 @ A4 )
% 5.31/5.52 & ! [Xa: set_nat] :
% 5.31/5.52 ( ( member_set_nat @ Xa @ A4 )
% 5.31/5.52 => ( ( ord_less_eq_set_nat @ Xa @ X3 )
% 5.31/5.52 => ( X3 = Xa ) ) ) ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % finite_has_minimal
% 5.31/5.52 thf(fact_2093_finite__has__minimal,axiom,
% 5.31/5.52 ! [A4: set_rat] :
% 5.31/5.52 ( ( finite_finite_rat @ A4 )
% 5.31/5.52 => ( ( A4 != bot_bot_set_rat )
% 5.31/5.52 => ? [X3: rat] :
% 5.31/5.52 ( ( member_rat @ X3 @ A4 )
% 5.31/5.52 & ! [Xa: rat] :
% 5.31/5.52 ( ( member_rat @ Xa @ A4 )
% 5.31/5.52 => ( ( ord_less_eq_rat @ Xa @ X3 )
% 5.31/5.52 => ( X3 = Xa ) ) ) ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % finite_has_minimal
% 5.31/5.52 thf(fact_2094_finite__has__minimal,axiom,
% 5.31/5.52 ! [A4: set_num] :
% 5.31/5.52 ( ( finite_finite_num @ A4 )
% 5.31/5.52 => ( ( A4 != bot_bot_set_num )
% 5.31/5.52 => ? [X3: num] :
% 5.31/5.52 ( ( member_num @ X3 @ A4 )
% 5.31/5.52 & ! [Xa: num] :
% 5.31/5.52 ( ( member_num @ Xa @ A4 )
% 5.31/5.52 => ( ( ord_less_eq_num @ Xa @ X3 )
% 5.31/5.52 => ( X3 = Xa ) ) ) ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % finite_has_minimal
% 5.31/5.52 thf(fact_2095_finite__has__minimal,axiom,
% 5.31/5.52 ! [A4: set_nat] :
% 5.31/5.52 ( ( finite_finite_nat @ A4 )
% 5.31/5.52 => ( ( A4 != bot_bot_set_nat )
% 5.31/5.52 => ? [X3: nat] :
% 5.31/5.52 ( ( member_nat @ X3 @ A4 )
% 5.31/5.52 & ! [Xa: nat] :
% 5.31/5.52 ( ( member_nat @ Xa @ A4 )
% 5.31/5.52 => ( ( ord_less_eq_nat @ Xa @ X3 )
% 5.31/5.52 => ( X3 = Xa ) ) ) ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % finite_has_minimal
% 5.31/5.52 thf(fact_2096_finite__has__minimal,axiom,
% 5.31/5.52 ! [A4: set_int] :
% 5.31/5.52 ( ( finite_finite_int @ A4 )
% 5.31/5.52 => ( ( A4 != bot_bot_set_int )
% 5.31/5.52 => ? [X3: int] :
% 5.31/5.52 ( ( member_int @ X3 @ A4 )
% 5.31/5.52 & ! [Xa: int] :
% 5.31/5.52 ( ( member_int @ Xa @ A4 )
% 5.31/5.52 => ( ( ord_less_eq_int @ Xa @ X3 )
% 5.31/5.52 => ( X3 = Xa ) ) ) ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % finite_has_minimal
% 5.31/5.52 thf(fact_2097_finite__has__maximal,axiom,
% 5.31/5.52 ! [A4: set_real] :
% 5.31/5.52 ( ( finite_finite_real @ A4 )
% 5.31/5.52 => ( ( A4 != bot_bot_set_real )
% 5.31/5.52 => ? [X3: real] :
% 5.31/5.52 ( ( member_real @ X3 @ A4 )
% 5.31/5.52 & ! [Xa: real] :
% 5.31/5.52 ( ( member_real @ Xa @ A4 )
% 5.31/5.52 => ( ( ord_less_eq_real @ X3 @ Xa )
% 5.31/5.52 => ( X3 = Xa ) ) ) ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % finite_has_maximal
% 5.31/5.52 thf(fact_2098_finite__has__maximal,axiom,
% 5.31/5.52 ! [A4: set_set_nat] :
% 5.31/5.52 ( ( finite1152437895449049373et_nat @ A4 )
% 5.31/5.52 => ( ( A4 != bot_bot_set_set_nat )
% 5.31/5.52 => ? [X3: set_nat] :
% 5.31/5.52 ( ( member_set_nat @ X3 @ A4 )
% 5.31/5.52 & ! [Xa: set_nat] :
% 5.31/5.52 ( ( member_set_nat @ Xa @ A4 )
% 5.31/5.52 => ( ( ord_less_eq_set_nat @ X3 @ Xa )
% 5.31/5.52 => ( X3 = Xa ) ) ) ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % finite_has_maximal
% 5.31/5.52 thf(fact_2099_finite__has__maximal,axiom,
% 5.31/5.52 ! [A4: set_rat] :
% 5.31/5.52 ( ( finite_finite_rat @ A4 )
% 5.31/5.52 => ( ( A4 != bot_bot_set_rat )
% 5.31/5.52 => ? [X3: rat] :
% 5.31/5.52 ( ( member_rat @ X3 @ A4 )
% 5.31/5.52 & ! [Xa: rat] :
% 5.31/5.52 ( ( member_rat @ Xa @ A4 )
% 5.31/5.52 => ( ( ord_less_eq_rat @ X3 @ Xa )
% 5.31/5.52 => ( X3 = Xa ) ) ) ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % finite_has_maximal
% 5.31/5.52 thf(fact_2100_finite__has__maximal,axiom,
% 5.31/5.52 ! [A4: set_num] :
% 5.31/5.52 ( ( finite_finite_num @ A4 )
% 5.31/5.52 => ( ( A4 != bot_bot_set_num )
% 5.31/5.52 => ? [X3: num] :
% 5.31/5.52 ( ( member_num @ X3 @ A4 )
% 5.31/5.52 & ! [Xa: num] :
% 5.31/5.52 ( ( member_num @ Xa @ A4 )
% 5.31/5.52 => ( ( ord_less_eq_num @ X3 @ Xa )
% 5.31/5.52 => ( X3 = Xa ) ) ) ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % finite_has_maximal
% 5.31/5.52 thf(fact_2101_finite__has__maximal,axiom,
% 5.31/5.52 ! [A4: set_nat] :
% 5.31/5.52 ( ( finite_finite_nat @ A4 )
% 5.31/5.52 => ( ( A4 != bot_bot_set_nat )
% 5.31/5.52 => ? [X3: nat] :
% 5.31/5.52 ( ( member_nat @ X3 @ A4 )
% 5.31/5.52 & ! [Xa: nat] :
% 5.31/5.52 ( ( member_nat @ Xa @ A4 )
% 5.31/5.52 => ( ( ord_less_eq_nat @ X3 @ Xa )
% 5.31/5.52 => ( X3 = Xa ) ) ) ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % finite_has_maximal
% 5.31/5.52 thf(fact_2102_finite__has__maximal,axiom,
% 5.31/5.52 ! [A4: set_int] :
% 5.31/5.52 ( ( finite_finite_int @ A4 )
% 5.31/5.52 => ( ( A4 != bot_bot_set_int )
% 5.31/5.52 => ? [X3: int] :
% 5.31/5.52 ( ( member_int @ X3 @ A4 )
% 5.31/5.52 & ! [Xa: int] :
% 5.31/5.52 ( ( member_int @ Xa @ A4 )
% 5.31/5.52 => ( ( ord_less_eq_int @ X3 @ Xa )
% 5.31/5.52 => ( X3 = Xa ) ) ) ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % finite_has_maximal
% 5.31/5.52 thf(fact_2103_mult__diff__mult,axiom,
% 5.31/5.52 ! [X: real,Y: real,A: real,B: real] :
% 5.31/5.52 ( ( minus_minus_real @ ( times_times_real @ X @ Y ) @ ( times_times_real @ A @ B ) )
% 5.31/5.52 = ( plus_plus_real @ ( times_times_real @ X @ ( minus_minus_real @ Y @ B ) ) @ ( times_times_real @ ( minus_minus_real @ X @ A ) @ B ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % mult_diff_mult
% 5.31/5.52 thf(fact_2104_mult__diff__mult,axiom,
% 5.31/5.52 ! [X: rat,Y: rat,A: rat,B: rat] :
% 5.31/5.52 ( ( minus_minus_rat @ ( times_times_rat @ X @ Y ) @ ( times_times_rat @ A @ B ) )
% 5.31/5.52 = ( plus_plus_rat @ ( times_times_rat @ X @ ( minus_minus_rat @ Y @ B ) ) @ ( times_times_rat @ ( minus_minus_rat @ X @ A ) @ B ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % mult_diff_mult
% 5.31/5.52 thf(fact_2105_mult__diff__mult,axiom,
% 5.31/5.52 ! [X: int,Y: int,A: int,B: int] :
% 5.31/5.52 ( ( minus_minus_int @ ( times_times_int @ X @ Y ) @ ( times_times_int @ A @ B ) )
% 5.31/5.52 = ( plus_plus_int @ ( times_times_int @ X @ ( minus_minus_int @ Y @ B ) ) @ ( times_times_int @ ( minus_minus_int @ X @ A ) @ B ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % mult_diff_mult
% 5.31/5.52 thf(fact_2106_diff__shunt__var,axiom,
% 5.31/5.52 ! [X: set_int,Y: set_int] :
% 5.31/5.52 ( ( ( minus_minus_set_int @ X @ Y )
% 5.31/5.52 = bot_bot_set_int )
% 5.31/5.52 = ( ord_less_eq_set_int @ X @ Y ) ) ).
% 5.31/5.52
% 5.31/5.52 % diff_shunt_var
% 5.31/5.52 thf(fact_2107_diff__shunt__var,axiom,
% 5.31/5.52 ! [X: set_real,Y: set_real] :
% 5.31/5.52 ( ( ( minus_minus_set_real @ X @ Y )
% 5.31/5.52 = bot_bot_set_real )
% 5.31/5.52 = ( ord_less_eq_set_real @ X @ Y ) ) ).
% 5.31/5.52
% 5.31/5.52 % diff_shunt_var
% 5.31/5.52 thf(fact_2108_diff__shunt__var,axiom,
% 5.31/5.52 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] :
% 5.31/5.52 ( ( ( minus_1356011639430497352at_nat @ X @ Y )
% 5.31/5.52 = bot_bo2099793752762293965at_nat )
% 5.31/5.52 = ( ord_le3146513528884898305at_nat @ X @ Y ) ) ).
% 5.31/5.52
% 5.31/5.52 % diff_shunt_var
% 5.31/5.52 thf(fact_2109_diff__shunt__var,axiom,
% 5.31/5.52 ! [X: set_nat,Y: set_nat] :
% 5.31/5.52 ( ( ( minus_minus_set_nat @ X @ Y )
% 5.31/5.52 = bot_bot_set_nat )
% 5.31/5.52 = ( ord_less_eq_set_nat @ X @ Y ) ) ).
% 5.31/5.52
% 5.31/5.52 % diff_shunt_var
% 5.31/5.52 thf(fact_2110_minNullmin,axiom,
% 5.31/5.52 ! [T: vEBT_VEBT] :
% 5.31/5.52 ( ( vEBT_VEBT_minNull @ T )
% 5.31/5.52 => ( ( vEBT_vebt_mint @ T )
% 5.31/5.52 = none_nat ) ) ).
% 5.31/5.52
% 5.31/5.52 % minNullmin
% 5.31/5.52 thf(fact_2111_minminNull,axiom,
% 5.31/5.52 ! [T: vEBT_VEBT] :
% 5.31/5.52 ( ( ( vEBT_vebt_mint @ T )
% 5.31/5.52 = none_nat )
% 5.31/5.52 => ( vEBT_VEBT_minNull @ T ) ) ).
% 5.31/5.52
% 5.31/5.52 % minminNull
% 5.31/5.52 thf(fact_2112_vebt__maxt_Opelims,axiom,
% 5.31/5.52 ! [X: vEBT_VEBT,Y: option_nat] :
% 5.31/5.52 ( ( ( vEBT_vebt_maxt @ X )
% 5.31/5.52 = Y )
% 5.31/5.52 => ( ( accp_VEBT_VEBT @ vEBT_vebt_maxt_rel @ X )
% 5.31/5.52 => ( ! [A3: $o,B3: $o] :
% 5.31/5.52 ( ( X
% 5.31/5.52 = ( vEBT_Leaf @ A3 @ B3 ) )
% 5.31/5.52 => ( ( ( B3
% 5.31/5.52 => ( Y
% 5.31/5.52 = ( some_nat @ one_one_nat ) ) )
% 5.31/5.52 & ( ~ B3
% 5.31/5.52 => ( ( A3
% 5.31/5.52 => ( Y
% 5.31/5.52 = ( some_nat @ zero_zero_nat ) ) )
% 5.31/5.52 & ( ~ A3
% 5.31/5.52 => ( Y = none_nat ) ) ) ) )
% 5.31/5.52 => ~ ( accp_VEBT_VEBT @ vEBT_vebt_maxt_rel @ ( vEBT_Leaf @ A3 @ B3 ) ) ) )
% 5.31/5.52 => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 5.31/5.52 ( ( X
% 5.31/5.52 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw ) )
% 5.31/5.52 => ( ( Y = none_nat )
% 5.31/5.52 => ~ ( accp_VEBT_VEBT @ vEBT_vebt_maxt_rel @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw ) ) ) )
% 5.31/5.52 => ~ ! [Mi2: nat,Ma2: nat,Ux: nat,Uy: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.31/5.52 ( ( X
% 5.31/5.52 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux @ Uy @ Uz2 ) )
% 5.31/5.52 => ( ( Y
% 5.31/5.52 = ( some_nat @ Ma2 ) )
% 5.31/5.52 => ~ ( accp_VEBT_VEBT @ vEBT_vebt_maxt_rel @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux @ Uy @ Uz2 ) ) ) ) ) ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % vebt_maxt.pelims
% 5.31/5.52 thf(fact_2113_vebt__mint_Opelims,axiom,
% 5.31/5.52 ! [X: vEBT_VEBT,Y: option_nat] :
% 5.31/5.52 ( ( ( vEBT_vebt_mint @ X )
% 5.31/5.52 = Y )
% 5.31/5.52 => ( ( accp_VEBT_VEBT @ vEBT_vebt_mint_rel @ X )
% 5.31/5.52 => ( ! [A3: $o,B3: $o] :
% 5.31/5.52 ( ( X
% 5.31/5.52 = ( vEBT_Leaf @ A3 @ B3 ) )
% 5.31/5.52 => ( ( ( A3
% 5.31/5.52 => ( Y
% 5.31/5.52 = ( some_nat @ zero_zero_nat ) ) )
% 5.31/5.52 & ( ~ A3
% 5.31/5.52 => ( ( B3
% 5.31/5.52 => ( Y
% 5.31/5.52 = ( some_nat @ one_one_nat ) ) )
% 5.31/5.52 & ( ~ B3
% 5.31/5.52 => ( Y = none_nat ) ) ) ) )
% 5.31/5.52 => ~ ( accp_VEBT_VEBT @ vEBT_vebt_mint_rel @ ( vEBT_Leaf @ A3 @ B3 ) ) ) )
% 5.31/5.52 => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 5.31/5.52 ( ( X
% 5.31/5.52 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw ) )
% 5.31/5.52 => ( ( Y = none_nat )
% 5.31/5.52 => ~ ( accp_VEBT_VEBT @ vEBT_vebt_mint_rel @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw ) ) ) )
% 5.31/5.52 => ~ ! [Mi2: nat,Ma2: nat,Ux: nat,Uy: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.31/5.52 ( ( X
% 5.31/5.52 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux @ Uy @ Uz2 ) )
% 5.31/5.52 => ( ( Y
% 5.31/5.52 = ( some_nat @ Mi2 ) )
% 5.31/5.52 => ~ ( accp_VEBT_VEBT @ vEBT_vebt_mint_rel @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux @ Uy @ Uz2 ) ) ) ) ) ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % vebt_mint.pelims
% 5.31/5.52 thf(fact_2114_infinite__nat__iff__unbounded__le,axiom,
% 5.31/5.52 ! [S3: set_nat] :
% 5.31/5.52 ( ( ~ ( finite_finite_nat @ S3 ) )
% 5.31/5.52 = ( ! [M6: nat] :
% 5.31/5.52 ? [N4: nat] :
% 5.31/5.52 ( ( ord_less_eq_nat @ M6 @ N4 )
% 5.31/5.52 & ( member_nat @ N4 @ S3 ) ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % infinite_nat_iff_unbounded_le
% 5.31/5.52 thf(fact_2115_inthall,axiom,
% 5.31/5.52 ! [Xs2: list_complex,P2: complex > $o,N: nat] :
% 5.31/5.52 ( ! [X3: complex] :
% 5.31/5.52 ( ( member_complex @ X3 @ ( set_complex2 @ Xs2 ) )
% 5.31/5.52 => ( P2 @ X3 ) )
% 5.31/5.52 => ( ( ord_less_nat @ N @ ( size_s3451745648224563538omplex @ Xs2 ) )
% 5.31/5.52 => ( P2 @ ( nth_complex @ Xs2 @ N ) ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % inthall
% 5.31/5.52 thf(fact_2116_inthall,axiom,
% 5.31/5.52 ! [Xs2: list_real,P2: real > $o,N: nat] :
% 5.31/5.52 ( ! [X3: real] :
% 5.31/5.52 ( ( member_real @ X3 @ ( set_real2 @ Xs2 ) )
% 5.31/5.52 => ( P2 @ X3 ) )
% 5.31/5.52 => ( ( ord_less_nat @ N @ ( size_size_list_real @ Xs2 ) )
% 5.31/5.52 => ( P2 @ ( nth_real @ Xs2 @ N ) ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % inthall
% 5.31/5.52 thf(fact_2117_inthall,axiom,
% 5.31/5.52 ! [Xs2: list_set_nat,P2: set_nat > $o,N: nat] :
% 5.31/5.52 ( ! [X3: set_nat] :
% 5.31/5.52 ( ( member_set_nat @ X3 @ ( set_set_nat2 @ Xs2 ) )
% 5.31/5.52 => ( P2 @ X3 ) )
% 5.31/5.52 => ( ( ord_less_nat @ N @ ( size_s3254054031482475050et_nat @ Xs2 ) )
% 5.31/5.52 => ( P2 @ ( nth_set_nat @ Xs2 @ N ) ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % inthall
% 5.31/5.52 thf(fact_2118_inthall,axiom,
% 5.31/5.52 ! [Xs2: list_VEBT_VEBT,P2: vEBT_VEBT > $o,N: nat] :
% 5.31/5.52 ( ! [X3: vEBT_VEBT] :
% 5.31/5.52 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 5.31/5.52 => ( P2 @ X3 ) )
% 5.31/5.52 => ( ( ord_less_nat @ N @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 5.31/5.52 => ( P2 @ ( nth_VEBT_VEBT @ Xs2 @ N ) ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % inthall
% 5.31/5.52 thf(fact_2119_inthall,axiom,
% 5.31/5.52 ! [Xs2: list_o,P2: $o > $o,N: nat] :
% 5.31/5.52 ( ! [X3: $o] :
% 5.31/5.52 ( ( member_o @ X3 @ ( set_o2 @ Xs2 ) )
% 5.31/5.52 => ( P2 @ X3 ) )
% 5.31/5.52 => ( ( ord_less_nat @ N @ ( size_size_list_o @ Xs2 ) )
% 5.31/5.52 => ( P2 @ ( nth_o @ Xs2 @ N ) ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % inthall
% 5.31/5.52 thf(fact_2120_inthall,axiom,
% 5.31/5.52 ! [Xs2: list_nat,P2: nat > $o,N: nat] :
% 5.31/5.52 ( ! [X3: nat] :
% 5.31/5.52 ( ( member_nat @ X3 @ ( set_nat2 @ Xs2 ) )
% 5.31/5.52 => ( P2 @ X3 ) )
% 5.31/5.52 => ( ( ord_less_nat @ N @ ( size_size_list_nat @ Xs2 ) )
% 5.31/5.52 => ( P2 @ ( nth_nat @ Xs2 @ N ) ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % inthall
% 5.31/5.52 thf(fact_2121_inthall,axiom,
% 5.31/5.52 ! [Xs2: list_int,P2: int > $o,N: nat] :
% 5.31/5.52 ( ! [X3: int] :
% 5.31/5.52 ( ( member_int @ X3 @ ( set_int2 @ Xs2 ) )
% 5.31/5.52 => ( P2 @ X3 ) )
% 5.31/5.52 => ( ( ord_less_nat @ N @ ( size_size_list_int @ Xs2 ) )
% 5.31/5.52 => ( P2 @ ( nth_int @ Xs2 @ N ) ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % inthall
% 5.31/5.52 thf(fact_2122_not__min__Null__member,axiom,
% 5.31/5.52 ! [T: vEBT_VEBT] :
% 5.31/5.52 ( ~ ( vEBT_VEBT_minNull @ T )
% 5.31/5.52 => ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ T @ X_12 ) ) ).
% 5.31/5.52
% 5.31/5.52 % not_min_Null_member
% 5.31/5.52 thf(fact_2123_min__Null__member,axiom,
% 5.31/5.52 ! [T: vEBT_VEBT,X: nat] :
% 5.31/5.52 ( ( vEBT_VEBT_minNull @ T )
% 5.31/5.52 => ~ ( vEBT_vebt_member @ T @ X ) ) ).
% 5.31/5.52
% 5.31/5.52 % min_Null_member
% 5.31/5.52 thf(fact_2124_Suc__diff__diff,axiom,
% 5.31/5.52 ! [M2: nat,N: nat,K2: nat] :
% 5.31/5.52 ( ( minus_minus_nat @ ( minus_minus_nat @ ( suc @ M2 ) @ N ) @ ( suc @ K2 ) )
% 5.31/5.52 = ( minus_minus_nat @ ( minus_minus_nat @ M2 @ N ) @ K2 ) ) ).
% 5.31/5.52
% 5.31/5.52 % Suc_diff_diff
% 5.31/5.52 thf(fact_2125_diff__Suc__Suc,axiom,
% 5.31/5.52 ! [M2: nat,N: nat] :
% 5.31/5.52 ( ( minus_minus_nat @ ( suc @ M2 ) @ ( suc @ N ) )
% 5.31/5.52 = ( minus_minus_nat @ M2 @ N ) ) ).
% 5.31/5.52
% 5.31/5.52 % diff_Suc_Suc
% 5.31/5.52 thf(fact_2126_diff__0__eq__0,axiom,
% 5.31/5.52 ! [N: nat] :
% 5.31/5.52 ( ( minus_minus_nat @ zero_zero_nat @ N )
% 5.31/5.52 = zero_zero_nat ) ).
% 5.31/5.52
% 5.31/5.52 % diff_0_eq_0
% 5.31/5.52 thf(fact_2127_diff__self__eq__0,axiom,
% 5.31/5.52 ! [M2: nat] :
% 5.31/5.52 ( ( minus_minus_nat @ M2 @ M2 )
% 5.31/5.52 = zero_zero_nat ) ).
% 5.31/5.52
% 5.31/5.52 % diff_self_eq_0
% 5.31/5.52 thf(fact_2128_diff__diff__cancel,axiom,
% 5.31/5.52 ! [I2: nat,N: nat] :
% 5.31/5.52 ( ( ord_less_eq_nat @ I2 @ N )
% 5.31/5.52 => ( ( minus_minus_nat @ N @ ( minus_minus_nat @ N @ I2 ) )
% 5.31/5.52 = I2 ) ) ).
% 5.31/5.52
% 5.31/5.52 % diff_diff_cancel
% 5.31/5.52 thf(fact_2129_diff__diff__left,axiom,
% 5.31/5.52 ! [I2: nat,J2: nat,K2: nat] :
% 5.31/5.52 ( ( minus_minus_nat @ ( minus_minus_nat @ I2 @ J2 ) @ K2 )
% 5.31/5.52 = ( minus_minus_nat @ I2 @ ( plus_plus_nat @ J2 @ K2 ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % diff_diff_left
% 5.31/5.52 thf(fact_2130_zero__less__diff,axiom,
% 5.31/5.52 ! [N: nat,M2: nat] :
% 5.31/5.52 ( ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ N @ M2 ) )
% 5.31/5.52 = ( ord_less_nat @ M2 @ N ) ) ).
% 5.31/5.52
% 5.31/5.52 % zero_less_diff
% 5.31/5.52 thf(fact_2131_diff__is__0__eq_H,axiom,
% 5.31/5.52 ! [M2: nat,N: nat] :
% 5.31/5.52 ( ( ord_less_eq_nat @ M2 @ N )
% 5.31/5.52 => ( ( minus_minus_nat @ M2 @ N )
% 5.31/5.52 = zero_zero_nat ) ) ).
% 5.31/5.52
% 5.31/5.52 % diff_is_0_eq'
% 5.31/5.52 thf(fact_2132_diff__is__0__eq,axiom,
% 5.31/5.52 ! [M2: nat,N: nat] :
% 5.31/5.52 ( ( ( minus_minus_nat @ M2 @ N )
% 5.31/5.52 = zero_zero_nat )
% 5.31/5.52 = ( ord_less_eq_nat @ M2 @ N ) ) ).
% 5.31/5.52
% 5.31/5.52 % diff_is_0_eq
% 5.31/5.52 thf(fact_2133_Nat_Oadd__diff__assoc,axiom,
% 5.31/5.52 ! [K2: nat,J2: nat,I2: nat] :
% 5.31/5.52 ( ( ord_less_eq_nat @ K2 @ J2 )
% 5.31/5.52 => ( ( plus_plus_nat @ I2 @ ( minus_minus_nat @ J2 @ K2 ) )
% 5.31/5.52 = ( minus_minus_nat @ ( plus_plus_nat @ I2 @ J2 ) @ K2 ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % Nat.add_diff_assoc
% 5.31/5.52 thf(fact_2134_Nat_Oadd__diff__assoc2,axiom,
% 5.31/5.52 ! [K2: nat,J2: nat,I2: nat] :
% 5.31/5.52 ( ( ord_less_eq_nat @ K2 @ J2 )
% 5.31/5.52 => ( ( plus_plus_nat @ ( minus_minus_nat @ J2 @ K2 ) @ I2 )
% 5.31/5.52 = ( minus_minus_nat @ ( plus_plus_nat @ J2 @ I2 ) @ K2 ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % Nat.add_diff_assoc2
% 5.31/5.52 thf(fact_2135_Nat_Odiff__diff__right,axiom,
% 5.31/5.52 ! [K2: nat,J2: nat,I2: nat] :
% 5.31/5.52 ( ( ord_less_eq_nat @ K2 @ J2 )
% 5.31/5.52 => ( ( minus_minus_nat @ I2 @ ( minus_minus_nat @ J2 @ K2 ) )
% 5.31/5.52 = ( minus_minus_nat @ ( plus_plus_nat @ I2 @ K2 ) @ J2 ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % Nat.diff_diff_right
% 5.31/5.52 thf(fact_2136_diff__Suc__1,axiom,
% 5.31/5.52 ! [N: nat] :
% 5.31/5.52 ( ( minus_minus_nat @ ( suc @ N ) @ one_one_nat )
% 5.31/5.52 = N ) ).
% 5.31/5.52
% 5.31/5.52 % diff_Suc_1
% 5.31/5.52 thf(fact_2137_Suc__pred,axiom,
% 5.31/5.52 ! [N: nat] :
% 5.31/5.52 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.52 => ( ( suc @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) )
% 5.31/5.52 = N ) ) ).
% 5.31/5.52
% 5.31/5.52 % Suc_pred
% 5.31/5.52 thf(fact_2138_diff__Suc__diff__eq1,axiom,
% 5.31/5.52 ! [K2: nat,J2: nat,I2: nat] :
% 5.31/5.52 ( ( ord_less_eq_nat @ K2 @ J2 )
% 5.31/5.52 => ( ( minus_minus_nat @ I2 @ ( suc @ ( minus_minus_nat @ J2 @ K2 ) ) )
% 5.31/5.52 = ( minus_minus_nat @ ( plus_plus_nat @ I2 @ K2 ) @ ( suc @ J2 ) ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % diff_Suc_diff_eq1
% 5.31/5.52 thf(fact_2139_diff__Suc__diff__eq2,axiom,
% 5.31/5.52 ! [K2: nat,J2: nat,I2: nat] :
% 5.31/5.52 ( ( ord_less_eq_nat @ K2 @ J2 )
% 5.31/5.52 => ( ( minus_minus_nat @ ( suc @ ( minus_minus_nat @ J2 @ K2 ) ) @ I2 )
% 5.31/5.52 = ( minus_minus_nat @ ( suc @ J2 ) @ ( plus_plus_nat @ K2 @ I2 ) ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % diff_Suc_diff_eq2
% 5.31/5.52 thf(fact_2140_Suc__diff__1,axiom,
% 5.31/5.52 ! [N: nat] :
% 5.31/5.52 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.52 => ( ( suc @ ( minus_minus_nat @ N @ one_one_nat ) )
% 5.31/5.52 = N ) ) ).
% 5.31/5.52
% 5.31/5.52 % Suc_diff_1
% 5.31/5.52 thf(fact_2141_zero__induct__lemma,axiom,
% 5.31/5.52 ! [P2: nat > $o,K2: nat,I2: nat] :
% 5.31/5.52 ( ( P2 @ K2 )
% 5.31/5.52 => ( ! [N3: nat] :
% 5.31/5.52 ( ( P2 @ ( suc @ N3 ) )
% 5.31/5.52 => ( P2 @ N3 ) )
% 5.31/5.52 => ( P2 @ ( minus_minus_nat @ K2 @ I2 ) ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % zero_induct_lemma
% 5.31/5.52 thf(fact_2142_minus__nat_Odiff__0,axiom,
% 5.31/5.52 ! [M2: nat] :
% 5.31/5.52 ( ( minus_minus_nat @ M2 @ zero_zero_nat )
% 5.31/5.52 = M2 ) ).
% 5.31/5.52
% 5.31/5.52 % minus_nat.diff_0
% 5.31/5.52 thf(fact_2143_diffs0__imp__equal,axiom,
% 5.31/5.52 ! [M2: nat,N: nat] :
% 5.31/5.52 ( ( ( minus_minus_nat @ M2 @ N )
% 5.31/5.52 = zero_zero_nat )
% 5.31/5.52 => ( ( ( minus_minus_nat @ N @ M2 )
% 5.31/5.52 = zero_zero_nat )
% 5.31/5.52 => ( M2 = N ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % diffs0_imp_equal
% 5.31/5.52 thf(fact_2144_diff__less__mono2,axiom,
% 5.31/5.52 ! [M2: nat,N: nat,L: nat] :
% 5.31/5.52 ( ( ord_less_nat @ M2 @ N )
% 5.31/5.52 => ( ( ord_less_nat @ M2 @ L )
% 5.31/5.52 => ( ord_less_nat @ ( minus_minus_nat @ L @ N ) @ ( minus_minus_nat @ L @ M2 ) ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % diff_less_mono2
% 5.31/5.52 thf(fact_2145_less__imp__diff__less,axiom,
% 5.31/5.52 ! [J2: nat,K2: nat,N: nat] :
% 5.31/5.52 ( ( ord_less_nat @ J2 @ K2 )
% 5.31/5.52 => ( ord_less_nat @ ( minus_minus_nat @ J2 @ N ) @ K2 ) ) ).
% 5.31/5.52
% 5.31/5.52 % less_imp_diff_less
% 5.31/5.52 thf(fact_2146_diff__le__mono2,axiom,
% 5.31/5.52 ! [M2: nat,N: nat,L: nat] :
% 5.31/5.52 ( ( ord_less_eq_nat @ M2 @ N )
% 5.31/5.52 => ( ord_less_eq_nat @ ( minus_minus_nat @ L @ N ) @ ( minus_minus_nat @ L @ M2 ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % diff_le_mono2
% 5.31/5.52 thf(fact_2147_le__diff__iff_H,axiom,
% 5.31/5.52 ! [A: nat,C2: nat,B: nat] :
% 5.31/5.52 ( ( ord_less_eq_nat @ A @ C2 )
% 5.31/5.52 => ( ( ord_less_eq_nat @ B @ C2 )
% 5.31/5.52 => ( ( ord_less_eq_nat @ ( minus_minus_nat @ C2 @ A ) @ ( minus_minus_nat @ C2 @ B ) )
% 5.31/5.52 = ( ord_less_eq_nat @ B @ A ) ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % le_diff_iff'
% 5.31/5.52 thf(fact_2148_diff__le__self,axiom,
% 5.31/5.52 ! [M2: nat,N: nat] : ( ord_less_eq_nat @ ( minus_minus_nat @ M2 @ N ) @ M2 ) ).
% 5.31/5.52
% 5.31/5.52 % diff_le_self
% 5.31/5.52 thf(fact_2149_diff__le__mono,axiom,
% 5.31/5.52 ! [M2: nat,N: nat,L: nat] :
% 5.31/5.52 ( ( ord_less_eq_nat @ M2 @ N )
% 5.31/5.52 => ( ord_less_eq_nat @ ( minus_minus_nat @ M2 @ L ) @ ( minus_minus_nat @ N @ L ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % diff_le_mono
% 5.31/5.52 thf(fact_2150_Nat_Odiff__diff__eq,axiom,
% 5.31/5.52 ! [K2: nat,M2: nat,N: nat] :
% 5.31/5.52 ( ( ord_less_eq_nat @ K2 @ M2 )
% 5.31/5.52 => ( ( ord_less_eq_nat @ K2 @ N )
% 5.31/5.52 => ( ( minus_minus_nat @ ( minus_minus_nat @ M2 @ K2 ) @ ( minus_minus_nat @ N @ K2 ) )
% 5.31/5.52 = ( minus_minus_nat @ M2 @ N ) ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % Nat.diff_diff_eq
% 5.31/5.52 thf(fact_2151_le__diff__iff,axiom,
% 5.31/5.52 ! [K2: nat,M2: nat,N: nat] :
% 5.31/5.52 ( ( ord_less_eq_nat @ K2 @ M2 )
% 5.31/5.52 => ( ( ord_less_eq_nat @ K2 @ N )
% 5.31/5.52 => ( ( ord_less_eq_nat @ ( minus_minus_nat @ M2 @ K2 ) @ ( minus_minus_nat @ N @ K2 ) )
% 5.31/5.52 = ( ord_less_eq_nat @ M2 @ N ) ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % le_diff_iff
% 5.31/5.52 thf(fact_2152_eq__diff__iff,axiom,
% 5.31/5.52 ! [K2: nat,M2: nat,N: nat] :
% 5.31/5.52 ( ( ord_less_eq_nat @ K2 @ M2 )
% 5.31/5.52 => ( ( ord_less_eq_nat @ K2 @ N )
% 5.31/5.52 => ( ( ( minus_minus_nat @ M2 @ K2 )
% 5.31/5.52 = ( minus_minus_nat @ N @ K2 ) )
% 5.31/5.52 = ( M2 = N ) ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % eq_diff_iff
% 5.31/5.52 thf(fact_2153_Nat_Odiff__cancel,axiom,
% 5.31/5.52 ! [K2: nat,M2: nat,N: nat] :
% 5.31/5.52 ( ( minus_minus_nat @ ( plus_plus_nat @ K2 @ M2 ) @ ( plus_plus_nat @ K2 @ N ) )
% 5.31/5.52 = ( minus_minus_nat @ M2 @ N ) ) ).
% 5.31/5.52
% 5.31/5.52 % Nat.diff_cancel
% 5.31/5.52 thf(fact_2154_diff__cancel2,axiom,
% 5.31/5.52 ! [M2: nat,K2: nat,N: nat] :
% 5.31/5.52 ( ( minus_minus_nat @ ( plus_plus_nat @ M2 @ K2 ) @ ( plus_plus_nat @ N @ K2 ) )
% 5.31/5.52 = ( minus_minus_nat @ M2 @ N ) ) ).
% 5.31/5.52
% 5.31/5.52 % diff_cancel2
% 5.31/5.52 thf(fact_2155_diff__add__inverse,axiom,
% 5.31/5.52 ! [N: nat,M2: nat] :
% 5.31/5.52 ( ( minus_minus_nat @ ( plus_plus_nat @ N @ M2 ) @ N )
% 5.31/5.52 = M2 ) ).
% 5.31/5.52
% 5.31/5.52 % diff_add_inverse
% 5.31/5.52 thf(fact_2156_diff__add__inverse2,axiom,
% 5.31/5.52 ! [M2: nat,N: nat] :
% 5.31/5.52 ( ( minus_minus_nat @ ( plus_plus_nat @ M2 @ N ) @ N )
% 5.31/5.52 = M2 ) ).
% 5.31/5.52
% 5.31/5.52 % diff_add_inverse2
% 5.31/5.52 thf(fact_2157_diff__mult__distrib,axiom,
% 5.31/5.52 ! [M2: nat,N: nat,K2: nat] :
% 5.31/5.52 ( ( times_times_nat @ ( minus_minus_nat @ M2 @ N ) @ K2 )
% 5.31/5.52 = ( minus_minus_nat @ ( times_times_nat @ M2 @ K2 ) @ ( times_times_nat @ N @ K2 ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % diff_mult_distrib
% 5.31/5.52 thf(fact_2158_diff__mult__distrib2,axiom,
% 5.31/5.52 ! [K2: nat,M2: nat,N: nat] :
% 5.31/5.52 ( ( times_times_nat @ K2 @ ( minus_minus_nat @ M2 @ N ) )
% 5.31/5.52 = ( minus_minus_nat @ ( times_times_nat @ K2 @ M2 ) @ ( times_times_nat @ K2 @ N ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % diff_mult_distrib2
% 5.31/5.52 thf(fact_2159_VEBT__internal_OminNull_Osimps_I1_J,axiom,
% 5.31/5.52 vEBT_VEBT_minNull @ ( vEBT_Leaf @ $false @ $false ) ).
% 5.31/5.52
% 5.31/5.52 % VEBT_internal.minNull.simps(1)
% 5.31/5.52 thf(fact_2160_VEBT__internal_OminNull_Osimps_I2_J,axiom,
% 5.31/5.52 ! [Uv: $o] :
% 5.31/5.52 ~ ( vEBT_VEBT_minNull @ ( vEBT_Leaf @ $true @ Uv ) ) ).
% 5.31/5.52
% 5.31/5.52 % VEBT_internal.minNull.simps(2)
% 5.31/5.52 thf(fact_2161_VEBT__internal_OminNull_Osimps_I3_J,axiom,
% 5.31/5.52 ! [Uu: $o] :
% 5.31/5.52 ~ ( vEBT_VEBT_minNull @ ( vEBT_Leaf @ Uu @ $true ) ) ).
% 5.31/5.52
% 5.31/5.52 % VEBT_internal.minNull.simps(3)
% 5.31/5.52 thf(fact_2162_list__eq__iff__nth__eq,axiom,
% 5.31/5.52 ( ( ^ [Y5: list_VEBT_VEBT,Z2: list_VEBT_VEBT] : ( Y5 = Z2 ) )
% 5.31/5.52 = ( ^ [Xs: list_VEBT_VEBT,Ys3: list_VEBT_VEBT] :
% 5.31/5.52 ( ( ( size_s6755466524823107622T_VEBT @ Xs )
% 5.31/5.52 = ( size_s6755466524823107622T_VEBT @ Ys3 ) )
% 5.31/5.52 & ! [I: nat] :
% 5.31/5.52 ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 5.31/5.52 => ( ( nth_VEBT_VEBT @ Xs @ I )
% 5.31/5.52 = ( nth_VEBT_VEBT @ Ys3 @ I ) ) ) ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % list_eq_iff_nth_eq
% 5.31/5.52 thf(fact_2163_list__eq__iff__nth__eq,axiom,
% 5.31/5.52 ( ( ^ [Y5: list_o,Z2: list_o] : ( Y5 = Z2 ) )
% 5.31/5.52 = ( ^ [Xs: list_o,Ys3: list_o] :
% 5.31/5.52 ( ( ( size_size_list_o @ Xs )
% 5.31/5.52 = ( size_size_list_o @ Ys3 ) )
% 5.31/5.52 & ! [I: nat] :
% 5.31/5.52 ( ( ord_less_nat @ I @ ( size_size_list_o @ Xs ) )
% 5.31/5.52 => ( ( nth_o @ Xs @ I )
% 5.31/5.52 = ( nth_o @ Ys3 @ I ) ) ) ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % list_eq_iff_nth_eq
% 5.31/5.52 thf(fact_2164_list__eq__iff__nth__eq,axiom,
% 5.31/5.52 ( ( ^ [Y5: list_nat,Z2: list_nat] : ( Y5 = Z2 ) )
% 5.31/5.52 = ( ^ [Xs: list_nat,Ys3: list_nat] :
% 5.31/5.52 ( ( ( size_size_list_nat @ Xs )
% 5.31/5.52 = ( size_size_list_nat @ Ys3 ) )
% 5.31/5.52 & ! [I: nat] :
% 5.31/5.52 ( ( ord_less_nat @ I @ ( size_size_list_nat @ Xs ) )
% 5.31/5.52 => ( ( nth_nat @ Xs @ I )
% 5.31/5.52 = ( nth_nat @ Ys3 @ I ) ) ) ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % list_eq_iff_nth_eq
% 5.31/5.52 thf(fact_2165_list__eq__iff__nth__eq,axiom,
% 5.31/5.52 ( ( ^ [Y5: list_int,Z2: list_int] : ( Y5 = Z2 ) )
% 5.31/5.52 = ( ^ [Xs: list_int,Ys3: list_int] :
% 5.31/5.52 ( ( ( size_size_list_int @ Xs )
% 5.31/5.52 = ( size_size_list_int @ Ys3 ) )
% 5.31/5.52 & ! [I: nat] :
% 5.31/5.52 ( ( ord_less_nat @ I @ ( size_size_list_int @ Xs ) )
% 5.31/5.52 => ( ( nth_int @ Xs @ I )
% 5.31/5.52 = ( nth_int @ Ys3 @ I ) ) ) ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % list_eq_iff_nth_eq
% 5.31/5.52 thf(fact_2166_Skolem__list__nth,axiom,
% 5.31/5.52 ! [K2: nat,P2: nat > vEBT_VEBT > $o] :
% 5.31/5.52 ( ( ! [I: nat] :
% 5.31/5.52 ( ( ord_less_nat @ I @ K2 )
% 5.31/5.52 => ? [X7: vEBT_VEBT] : ( P2 @ I @ X7 ) ) )
% 5.31/5.52 = ( ? [Xs: list_VEBT_VEBT] :
% 5.31/5.52 ( ( ( size_s6755466524823107622T_VEBT @ Xs )
% 5.31/5.52 = K2 )
% 5.31/5.52 & ! [I: nat] :
% 5.31/5.52 ( ( ord_less_nat @ I @ K2 )
% 5.31/5.52 => ( P2 @ I @ ( nth_VEBT_VEBT @ Xs @ I ) ) ) ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % Skolem_list_nth
% 5.31/5.52 thf(fact_2167_Skolem__list__nth,axiom,
% 5.31/5.52 ! [K2: nat,P2: nat > $o > $o] :
% 5.31/5.52 ( ( ! [I: nat] :
% 5.31/5.52 ( ( ord_less_nat @ I @ K2 )
% 5.31/5.52 => ? [X7: $o] : ( P2 @ I @ X7 ) ) )
% 5.31/5.52 = ( ? [Xs: list_o] :
% 5.31/5.52 ( ( ( size_size_list_o @ Xs )
% 5.31/5.52 = K2 )
% 5.31/5.52 & ! [I: nat] :
% 5.31/5.52 ( ( ord_less_nat @ I @ K2 )
% 5.31/5.52 => ( P2 @ I @ ( nth_o @ Xs @ I ) ) ) ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % Skolem_list_nth
% 5.31/5.52 thf(fact_2168_Skolem__list__nth,axiom,
% 5.31/5.52 ! [K2: nat,P2: nat > nat > $o] :
% 5.31/5.52 ( ( ! [I: nat] :
% 5.31/5.52 ( ( ord_less_nat @ I @ K2 )
% 5.31/5.52 => ? [X7: nat] : ( P2 @ I @ X7 ) ) )
% 5.31/5.52 = ( ? [Xs: list_nat] :
% 5.31/5.52 ( ( ( size_size_list_nat @ Xs )
% 5.31/5.52 = K2 )
% 5.31/5.52 & ! [I: nat] :
% 5.31/5.52 ( ( ord_less_nat @ I @ K2 )
% 5.31/5.52 => ( P2 @ I @ ( nth_nat @ Xs @ I ) ) ) ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % Skolem_list_nth
% 5.31/5.52 thf(fact_2169_Skolem__list__nth,axiom,
% 5.31/5.52 ! [K2: nat,P2: nat > int > $o] :
% 5.31/5.52 ( ( ! [I: nat] :
% 5.31/5.52 ( ( ord_less_nat @ I @ K2 )
% 5.31/5.52 => ? [X7: int] : ( P2 @ I @ X7 ) ) )
% 5.31/5.52 = ( ? [Xs: list_int] :
% 5.31/5.52 ( ( ( size_size_list_int @ Xs )
% 5.31/5.52 = K2 )
% 5.31/5.52 & ! [I: nat] :
% 5.31/5.52 ( ( ord_less_nat @ I @ K2 )
% 5.31/5.52 => ( P2 @ I @ ( nth_int @ Xs @ I ) ) ) ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % Skolem_list_nth
% 5.31/5.52 thf(fact_2170_nth__equalityI,axiom,
% 5.31/5.52 ! [Xs2: list_VEBT_VEBT,Ys: list_VEBT_VEBT] :
% 5.31/5.52 ( ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 5.31/5.52 = ( size_s6755466524823107622T_VEBT @ Ys ) )
% 5.31/5.52 => ( ! [I3: nat] :
% 5.31/5.52 ( ( ord_less_nat @ I3 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 5.31/5.52 => ( ( nth_VEBT_VEBT @ Xs2 @ I3 )
% 5.31/5.52 = ( nth_VEBT_VEBT @ Ys @ I3 ) ) )
% 5.31/5.52 => ( Xs2 = Ys ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % nth_equalityI
% 5.31/5.52 thf(fact_2171_nth__equalityI,axiom,
% 5.31/5.52 ! [Xs2: list_o,Ys: list_o] :
% 5.31/5.52 ( ( ( size_size_list_o @ Xs2 )
% 5.31/5.52 = ( size_size_list_o @ Ys ) )
% 5.31/5.52 => ( ! [I3: nat] :
% 5.31/5.52 ( ( ord_less_nat @ I3 @ ( size_size_list_o @ Xs2 ) )
% 5.31/5.52 => ( ( nth_o @ Xs2 @ I3 )
% 5.31/5.52 = ( nth_o @ Ys @ I3 ) ) )
% 5.31/5.52 => ( Xs2 = Ys ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % nth_equalityI
% 5.31/5.52 thf(fact_2172_nth__equalityI,axiom,
% 5.31/5.52 ! [Xs2: list_nat,Ys: list_nat] :
% 5.31/5.52 ( ( ( size_size_list_nat @ Xs2 )
% 5.31/5.52 = ( size_size_list_nat @ Ys ) )
% 5.31/5.52 => ( ! [I3: nat] :
% 5.31/5.52 ( ( ord_less_nat @ I3 @ ( size_size_list_nat @ Xs2 ) )
% 5.31/5.52 => ( ( nth_nat @ Xs2 @ I3 )
% 5.31/5.52 = ( nth_nat @ Ys @ I3 ) ) )
% 5.31/5.52 => ( Xs2 = Ys ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % nth_equalityI
% 5.31/5.52 thf(fact_2173_nth__equalityI,axiom,
% 5.31/5.52 ! [Xs2: list_int,Ys: list_int] :
% 5.31/5.52 ( ( ( size_size_list_int @ Xs2 )
% 5.31/5.52 = ( size_size_list_int @ Ys ) )
% 5.31/5.52 => ( ! [I3: nat] :
% 5.31/5.52 ( ( ord_less_nat @ I3 @ ( size_size_list_int @ Xs2 ) )
% 5.31/5.52 => ( ( nth_int @ Xs2 @ I3 )
% 5.31/5.52 = ( nth_int @ Ys @ I3 ) ) )
% 5.31/5.52 => ( Xs2 = Ys ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % nth_equalityI
% 5.31/5.52 thf(fact_2174_diff__less__Suc,axiom,
% 5.31/5.52 ! [M2: nat,N: nat] : ( ord_less_nat @ ( minus_minus_nat @ M2 @ N ) @ ( suc @ M2 ) ) ).
% 5.31/5.52
% 5.31/5.52 % diff_less_Suc
% 5.31/5.52 thf(fact_2175_Suc__diff__Suc,axiom,
% 5.31/5.52 ! [N: nat,M2: nat] :
% 5.31/5.52 ( ( ord_less_nat @ N @ M2 )
% 5.31/5.52 => ( ( suc @ ( minus_minus_nat @ M2 @ ( suc @ N ) ) )
% 5.31/5.52 = ( minus_minus_nat @ M2 @ N ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % Suc_diff_Suc
% 5.31/5.52 thf(fact_2176_diff__less,axiom,
% 5.31/5.52 ! [N: nat,M2: nat] :
% 5.31/5.52 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.52 => ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 5.31/5.52 => ( ord_less_nat @ ( minus_minus_nat @ M2 @ N ) @ M2 ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % diff_less
% 5.31/5.52 thf(fact_2177_Suc__diff__le,axiom,
% 5.31/5.52 ! [N: nat,M2: nat] :
% 5.31/5.52 ( ( ord_less_eq_nat @ N @ M2 )
% 5.31/5.52 => ( ( minus_minus_nat @ ( suc @ M2 ) @ N )
% 5.31/5.52 = ( suc @ ( minus_minus_nat @ M2 @ N ) ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % Suc_diff_le
% 5.31/5.52 thf(fact_2178_less__diff__iff,axiom,
% 5.31/5.52 ! [K2: nat,M2: nat,N: nat] :
% 5.31/5.52 ( ( ord_less_eq_nat @ K2 @ M2 )
% 5.31/5.52 => ( ( ord_less_eq_nat @ K2 @ N )
% 5.31/5.52 => ( ( ord_less_nat @ ( minus_minus_nat @ M2 @ K2 ) @ ( minus_minus_nat @ N @ K2 ) )
% 5.31/5.52 = ( ord_less_nat @ M2 @ N ) ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % less_diff_iff
% 5.31/5.52 thf(fact_2179_diff__less__mono,axiom,
% 5.31/5.52 ! [A: nat,B: nat,C2: nat] :
% 5.31/5.52 ( ( ord_less_nat @ A @ B )
% 5.31/5.52 => ( ( ord_less_eq_nat @ C2 @ A )
% 5.31/5.52 => ( ord_less_nat @ ( minus_minus_nat @ A @ C2 ) @ ( minus_minus_nat @ B @ C2 ) ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % diff_less_mono
% 5.31/5.52 thf(fact_2180_diff__add__0,axiom,
% 5.31/5.52 ! [N: nat,M2: nat] :
% 5.31/5.52 ( ( minus_minus_nat @ N @ ( plus_plus_nat @ N @ M2 ) )
% 5.31/5.52 = zero_zero_nat ) ).
% 5.31/5.52
% 5.31/5.52 % diff_add_0
% 5.31/5.52 thf(fact_2181_finite__maxlen,axiom,
% 5.31/5.52 ! [M5: set_list_VEBT_VEBT] :
% 5.31/5.52 ( ( finite3004134309566078307T_VEBT @ M5 )
% 5.31/5.52 => ? [N3: nat] :
% 5.31/5.52 ! [X5: list_VEBT_VEBT] :
% 5.31/5.52 ( ( member2936631157270082147T_VEBT @ X5 @ M5 )
% 5.31/5.52 => ( ord_less_nat @ ( size_s6755466524823107622T_VEBT @ X5 ) @ N3 ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % finite_maxlen
% 5.31/5.52 thf(fact_2182_finite__maxlen,axiom,
% 5.31/5.52 ! [M5: set_list_o] :
% 5.31/5.52 ( ( finite_finite_list_o @ M5 )
% 5.31/5.52 => ? [N3: nat] :
% 5.31/5.52 ! [X5: list_o] :
% 5.31/5.52 ( ( member_list_o @ X5 @ M5 )
% 5.31/5.52 => ( ord_less_nat @ ( size_size_list_o @ X5 ) @ N3 ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % finite_maxlen
% 5.31/5.52 thf(fact_2183_finite__maxlen,axiom,
% 5.31/5.52 ! [M5: set_list_nat] :
% 5.31/5.52 ( ( finite8100373058378681591st_nat @ M5 )
% 5.31/5.52 => ? [N3: nat] :
% 5.31/5.52 ! [X5: list_nat] :
% 5.31/5.52 ( ( member_list_nat @ X5 @ M5 )
% 5.31/5.52 => ( ord_less_nat @ ( size_size_list_nat @ X5 ) @ N3 ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % finite_maxlen
% 5.31/5.52 thf(fact_2184_finite__maxlen,axiom,
% 5.31/5.52 ! [M5: set_list_int] :
% 5.31/5.52 ( ( finite3922522038869484883st_int @ M5 )
% 5.31/5.52 => ? [N3: nat] :
% 5.31/5.52 ! [X5: list_int] :
% 5.31/5.52 ( ( member_list_int @ X5 @ M5 )
% 5.31/5.52 => ( ord_less_nat @ ( size_size_list_int @ X5 ) @ N3 ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % finite_maxlen
% 5.31/5.52 thf(fact_2185_less__diff__conv,axiom,
% 5.31/5.52 ! [I2: nat,J2: nat,K2: nat] :
% 5.31/5.52 ( ( ord_less_nat @ I2 @ ( minus_minus_nat @ J2 @ K2 ) )
% 5.31/5.52 = ( ord_less_nat @ ( plus_plus_nat @ I2 @ K2 ) @ J2 ) ) ).
% 5.31/5.52
% 5.31/5.52 % less_diff_conv
% 5.31/5.52 thf(fact_2186_add__diff__inverse__nat,axiom,
% 5.31/5.52 ! [M2: nat,N: nat] :
% 5.31/5.52 ( ~ ( ord_less_nat @ M2 @ N )
% 5.31/5.52 => ( ( plus_plus_nat @ N @ ( minus_minus_nat @ M2 @ N ) )
% 5.31/5.52 = M2 ) ) ).
% 5.31/5.52
% 5.31/5.52 % add_diff_inverse_nat
% 5.31/5.52 thf(fact_2187_le__diff__conv,axiom,
% 5.31/5.52 ! [J2: nat,K2: nat,I2: nat] :
% 5.31/5.52 ( ( ord_less_eq_nat @ ( minus_minus_nat @ J2 @ K2 ) @ I2 )
% 5.31/5.52 = ( ord_less_eq_nat @ J2 @ ( plus_plus_nat @ I2 @ K2 ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % le_diff_conv
% 5.31/5.52 thf(fact_2188_Nat_Ole__diff__conv2,axiom,
% 5.31/5.52 ! [K2: nat,J2: nat,I2: nat] :
% 5.31/5.52 ( ( ord_less_eq_nat @ K2 @ J2 )
% 5.31/5.52 => ( ( ord_less_eq_nat @ I2 @ ( minus_minus_nat @ J2 @ K2 ) )
% 5.31/5.52 = ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K2 ) @ J2 ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % Nat.le_diff_conv2
% 5.31/5.52 thf(fact_2189_Nat_Odiff__add__assoc,axiom,
% 5.31/5.52 ! [K2: nat,J2: nat,I2: nat] :
% 5.31/5.52 ( ( ord_less_eq_nat @ K2 @ J2 )
% 5.31/5.52 => ( ( minus_minus_nat @ ( plus_plus_nat @ I2 @ J2 ) @ K2 )
% 5.31/5.52 = ( plus_plus_nat @ I2 @ ( minus_minus_nat @ J2 @ K2 ) ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % Nat.diff_add_assoc
% 5.31/5.52 thf(fact_2190_Nat_Odiff__add__assoc2,axiom,
% 5.31/5.52 ! [K2: nat,J2: nat,I2: nat] :
% 5.31/5.52 ( ( ord_less_eq_nat @ K2 @ J2 )
% 5.31/5.52 => ( ( minus_minus_nat @ ( plus_plus_nat @ J2 @ I2 ) @ K2 )
% 5.31/5.52 = ( plus_plus_nat @ ( minus_minus_nat @ J2 @ K2 ) @ I2 ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % Nat.diff_add_assoc2
% 5.31/5.52 thf(fact_2191_Nat_Ole__imp__diff__is__add,axiom,
% 5.31/5.52 ! [I2: nat,J2: nat,K2: nat] :
% 5.31/5.52 ( ( ord_less_eq_nat @ I2 @ J2 )
% 5.31/5.52 => ( ( ( minus_minus_nat @ J2 @ I2 )
% 5.31/5.52 = K2 )
% 5.31/5.52 = ( J2
% 5.31/5.52 = ( plus_plus_nat @ K2 @ I2 ) ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % Nat.le_imp_diff_is_add
% 5.31/5.52 thf(fact_2192_diff__Suc__eq__diff__pred,axiom,
% 5.31/5.52 ! [M2: nat,N: nat] :
% 5.31/5.52 ( ( minus_minus_nat @ M2 @ ( suc @ N ) )
% 5.31/5.52 = ( minus_minus_nat @ ( minus_minus_nat @ M2 @ one_one_nat ) @ N ) ) ).
% 5.31/5.52
% 5.31/5.52 % diff_Suc_eq_diff_pred
% 5.31/5.52 thf(fact_2193_VEBT__internal_OminNull_Osimps_I5_J,axiom,
% 5.31/5.52 ! [Uz: product_prod_nat_nat,Va3: nat,Vb: list_VEBT_VEBT,Vc: vEBT_VEBT] :
% 5.31/5.52 ~ ( vEBT_VEBT_minNull @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz ) @ Va3 @ Vb @ Vc ) ) ).
% 5.31/5.52
% 5.31/5.52 % VEBT_internal.minNull.simps(5)
% 5.31/5.52 thf(fact_2194_nth__mem,axiom,
% 5.31/5.52 ! [N: nat,Xs2: list_complex] :
% 5.31/5.52 ( ( ord_less_nat @ N @ ( size_s3451745648224563538omplex @ Xs2 ) )
% 5.31/5.52 => ( member_complex @ ( nth_complex @ Xs2 @ N ) @ ( set_complex2 @ Xs2 ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % nth_mem
% 5.31/5.52 thf(fact_2195_nth__mem,axiom,
% 5.31/5.52 ! [N: nat,Xs2: list_real] :
% 5.31/5.52 ( ( ord_less_nat @ N @ ( size_size_list_real @ Xs2 ) )
% 5.31/5.52 => ( member_real @ ( nth_real @ Xs2 @ N ) @ ( set_real2 @ Xs2 ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % nth_mem
% 5.31/5.52 thf(fact_2196_nth__mem,axiom,
% 5.31/5.52 ! [N: nat,Xs2: list_set_nat] :
% 5.31/5.52 ( ( ord_less_nat @ N @ ( size_s3254054031482475050et_nat @ Xs2 ) )
% 5.31/5.52 => ( member_set_nat @ ( nth_set_nat @ Xs2 @ N ) @ ( set_set_nat2 @ Xs2 ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % nth_mem
% 5.31/5.52 thf(fact_2197_nth__mem,axiom,
% 5.31/5.52 ! [N: nat,Xs2: list_VEBT_VEBT] :
% 5.31/5.52 ( ( ord_less_nat @ N @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 5.31/5.52 => ( member_VEBT_VEBT @ ( nth_VEBT_VEBT @ Xs2 @ N ) @ ( set_VEBT_VEBT2 @ Xs2 ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % nth_mem
% 5.31/5.52 thf(fact_2198_nth__mem,axiom,
% 5.31/5.52 ! [N: nat,Xs2: list_o] :
% 5.31/5.52 ( ( ord_less_nat @ N @ ( size_size_list_o @ Xs2 ) )
% 5.31/5.52 => ( member_o @ ( nth_o @ Xs2 @ N ) @ ( set_o2 @ Xs2 ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % nth_mem
% 5.31/5.52 thf(fact_2199_nth__mem,axiom,
% 5.31/5.52 ! [N: nat,Xs2: list_nat] :
% 5.31/5.52 ( ( ord_less_nat @ N @ ( size_size_list_nat @ Xs2 ) )
% 5.31/5.52 => ( member_nat @ ( nth_nat @ Xs2 @ N ) @ ( set_nat2 @ Xs2 ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % nth_mem
% 5.31/5.52 thf(fact_2200_nth__mem,axiom,
% 5.31/5.52 ! [N: nat,Xs2: list_int] :
% 5.31/5.52 ( ( ord_less_nat @ N @ ( size_size_list_int @ Xs2 ) )
% 5.31/5.52 => ( member_int @ ( nth_int @ Xs2 @ N ) @ ( set_int2 @ Xs2 ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % nth_mem
% 5.31/5.52 thf(fact_2201_list__ball__nth,axiom,
% 5.31/5.52 ! [N: nat,Xs2: list_VEBT_VEBT,P2: vEBT_VEBT > $o] :
% 5.31/5.52 ( ( ord_less_nat @ N @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 5.31/5.52 => ( ! [X3: vEBT_VEBT] :
% 5.31/5.52 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 5.31/5.52 => ( P2 @ X3 ) )
% 5.31/5.52 => ( P2 @ ( nth_VEBT_VEBT @ Xs2 @ N ) ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % list_ball_nth
% 5.31/5.52 thf(fact_2202_list__ball__nth,axiom,
% 5.31/5.52 ! [N: nat,Xs2: list_o,P2: $o > $o] :
% 5.31/5.52 ( ( ord_less_nat @ N @ ( size_size_list_o @ Xs2 ) )
% 5.31/5.52 => ( ! [X3: $o] :
% 5.31/5.52 ( ( member_o @ X3 @ ( set_o2 @ Xs2 ) )
% 5.31/5.52 => ( P2 @ X3 ) )
% 5.31/5.52 => ( P2 @ ( nth_o @ Xs2 @ N ) ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % list_ball_nth
% 5.31/5.52 thf(fact_2203_list__ball__nth,axiom,
% 5.31/5.52 ! [N: nat,Xs2: list_nat,P2: nat > $o] :
% 5.31/5.52 ( ( ord_less_nat @ N @ ( size_size_list_nat @ Xs2 ) )
% 5.31/5.52 => ( ! [X3: nat] :
% 5.31/5.52 ( ( member_nat @ X3 @ ( set_nat2 @ Xs2 ) )
% 5.31/5.52 => ( P2 @ X3 ) )
% 5.31/5.52 => ( P2 @ ( nth_nat @ Xs2 @ N ) ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % list_ball_nth
% 5.31/5.52 thf(fact_2204_list__ball__nth,axiom,
% 5.31/5.52 ! [N: nat,Xs2: list_int,P2: int > $o] :
% 5.31/5.52 ( ( ord_less_nat @ N @ ( size_size_list_int @ Xs2 ) )
% 5.31/5.52 => ( ! [X3: int] :
% 5.31/5.52 ( ( member_int @ X3 @ ( set_int2 @ Xs2 ) )
% 5.31/5.52 => ( P2 @ X3 ) )
% 5.31/5.52 => ( P2 @ ( nth_int @ Xs2 @ N ) ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % list_ball_nth
% 5.31/5.52 thf(fact_2205_in__set__conv__nth,axiom,
% 5.31/5.52 ! [X: complex,Xs2: list_complex] :
% 5.31/5.52 ( ( member_complex @ X @ ( set_complex2 @ Xs2 ) )
% 5.31/5.52 = ( ? [I: nat] :
% 5.31/5.52 ( ( ord_less_nat @ I @ ( size_s3451745648224563538omplex @ Xs2 ) )
% 5.31/5.52 & ( ( nth_complex @ Xs2 @ I )
% 5.31/5.52 = X ) ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % in_set_conv_nth
% 5.31/5.52 thf(fact_2206_in__set__conv__nth,axiom,
% 5.31/5.52 ! [X: real,Xs2: list_real] :
% 5.31/5.52 ( ( member_real @ X @ ( set_real2 @ Xs2 ) )
% 5.31/5.52 = ( ? [I: nat] :
% 5.31/5.52 ( ( ord_less_nat @ I @ ( size_size_list_real @ Xs2 ) )
% 5.31/5.52 & ( ( nth_real @ Xs2 @ I )
% 5.31/5.52 = X ) ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % in_set_conv_nth
% 5.31/5.52 thf(fact_2207_in__set__conv__nth,axiom,
% 5.31/5.52 ! [X: set_nat,Xs2: list_set_nat] :
% 5.31/5.52 ( ( member_set_nat @ X @ ( set_set_nat2 @ Xs2 ) )
% 5.31/5.52 = ( ? [I: nat] :
% 5.31/5.52 ( ( ord_less_nat @ I @ ( size_s3254054031482475050et_nat @ Xs2 ) )
% 5.31/5.52 & ( ( nth_set_nat @ Xs2 @ I )
% 5.31/5.52 = X ) ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % in_set_conv_nth
% 5.31/5.52 thf(fact_2208_in__set__conv__nth,axiom,
% 5.31/5.52 ! [X: vEBT_VEBT,Xs2: list_VEBT_VEBT] :
% 5.31/5.52 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 5.31/5.52 = ( ? [I: nat] :
% 5.31/5.52 ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 5.31/5.52 & ( ( nth_VEBT_VEBT @ Xs2 @ I )
% 5.31/5.52 = X ) ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % in_set_conv_nth
% 5.31/5.52 thf(fact_2209_in__set__conv__nth,axiom,
% 5.31/5.52 ! [X: $o,Xs2: list_o] :
% 5.31/5.52 ( ( member_o @ X @ ( set_o2 @ Xs2 ) )
% 5.31/5.52 = ( ? [I: nat] :
% 5.31/5.52 ( ( ord_less_nat @ I @ ( size_size_list_o @ Xs2 ) )
% 5.31/5.52 & ( ( nth_o @ Xs2 @ I )
% 5.31/5.52 = X ) ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % in_set_conv_nth
% 5.31/5.52 thf(fact_2210_in__set__conv__nth,axiom,
% 5.31/5.52 ! [X: nat,Xs2: list_nat] :
% 5.31/5.52 ( ( member_nat @ X @ ( set_nat2 @ Xs2 ) )
% 5.31/5.52 = ( ? [I: nat] :
% 5.31/5.52 ( ( ord_less_nat @ I @ ( size_size_list_nat @ Xs2 ) )
% 5.31/5.52 & ( ( nth_nat @ Xs2 @ I )
% 5.31/5.52 = X ) ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % in_set_conv_nth
% 5.31/5.52 thf(fact_2211_in__set__conv__nth,axiom,
% 5.31/5.52 ! [X: int,Xs2: list_int] :
% 5.31/5.52 ( ( member_int @ X @ ( set_int2 @ Xs2 ) )
% 5.31/5.52 = ( ? [I: nat] :
% 5.31/5.52 ( ( ord_less_nat @ I @ ( size_size_list_int @ Xs2 ) )
% 5.31/5.52 & ( ( nth_int @ Xs2 @ I )
% 5.31/5.52 = X ) ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % in_set_conv_nth
% 5.31/5.52 thf(fact_2212_all__nth__imp__all__set,axiom,
% 5.31/5.52 ! [Xs2: list_complex,P2: complex > $o,X: complex] :
% 5.31/5.52 ( ! [I3: nat] :
% 5.31/5.52 ( ( ord_less_nat @ I3 @ ( size_s3451745648224563538omplex @ Xs2 ) )
% 5.31/5.52 => ( P2 @ ( nth_complex @ Xs2 @ I3 ) ) )
% 5.31/5.52 => ( ( member_complex @ X @ ( set_complex2 @ Xs2 ) )
% 5.31/5.52 => ( P2 @ X ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % all_nth_imp_all_set
% 5.31/5.52 thf(fact_2213_all__nth__imp__all__set,axiom,
% 5.31/5.52 ! [Xs2: list_real,P2: real > $o,X: real] :
% 5.31/5.52 ( ! [I3: nat] :
% 5.31/5.52 ( ( ord_less_nat @ I3 @ ( size_size_list_real @ Xs2 ) )
% 5.31/5.52 => ( P2 @ ( nth_real @ Xs2 @ I3 ) ) )
% 5.31/5.52 => ( ( member_real @ X @ ( set_real2 @ Xs2 ) )
% 5.31/5.52 => ( P2 @ X ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % all_nth_imp_all_set
% 5.31/5.52 thf(fact_2214_all__nth__imp__all__set,axiom,
% 5.31/5.52 ! [Xs2: list_set_nat,P2: set_nat > $o,X: set_nat] :
% 5.31/5.52 ( ! [I3: nat] :
% 5.31/5.52 ( ( ord_less_nat @ I3 @ ( size_s3254054031482475050et_nat @ Xs2 ) )
% 5.31/5.52 => ( P2 @ ( nth_set_nat @ Xs2 @ I3 ) ) )
% 5.31/5.52 => ( ( member_set_nat @ X @ ( set_set_nat2 @ Xs2 ) )
% 5.31/5.52 => ( P2 @ X ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % all_nth_imp_all_set
% 5.31/5.52 thf(fact_2215_all__nth__imp__all__set,axiom,
% 5.31/5.52 ! [Xs2: list_VEBT_VEBT,P2: vEBT_VEBT > $o,X: vEBT_VEBT] :
% 5.31/5.52 ( ! [I3: nat] :
% 5.31/5.52 ( ( ord_less_nat @ I3 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 5.31/5.52 => ( P2 @ ( nth_VEBT_VEBT @ Xs2 @ I3 ) ) )
% 5.31/5.52 => ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 5.31/5.52 => ( P2 @ X ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % all_nth_imp_all_set
% 5.31/5.52 thf(fact_2216_all__nth__imp__all__set,axiom,
% 5.31/5.52 ! [Xs2: list_o,P2: $o > $o,X: $o] :
% 5.31/5.52 ( ! [I3: nat] :
% 5.31/5.52 ( ( ord_less_nat @ I3 @ ( size_size_list_o @ Xs2 ) )
% 5.31/5.52 => ( P2 @ ( nth_o @ Xs2 @ I3 ) ) )
% 5.31/5.52 => ( ( member_o @ X @ ( set_o2 @ Xs2 ) )
% 5.31/5.52 => ( P2 @ X ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % all_nth_imp_all_set
% 5.31/5.52 thf(fact_2217_all__nth__imp__all__set,axiom,
% 5.31/5.52 ! [Xs2: list_nat,P2: nat > $o,X: nat] :
% 5.31/5.52 ( ! [I3: nat] :
% 5.31/5.52 ( ( ord_less_nat @ I3 @ ( size_size_list_nat @ Xs2 ) )
% 5.31/5.52 => ( P2 @ ( nth_nat @ Xs2 @ I3 ) ) )
% 5.31/5.52 => ( ( member_nat @ X @ ( set_nat2 @ Xs2 ) )
% 5.31/5.52 => ( P2 @ X ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % all_nth_imp_all_set
% 5.31/5.52 thf(fact_2218_all__nth__imp__all__set,axiom,
% 5.31/5.52 ! [Xs2: list_int,P2: int > $o,X: int] :
% 5.31/5.52 ( ! [I3: nat] :
% 5.31/5.52 ( ( ord_less_nat @ I3 @ ( size_size_list_int @ Xs2 ) )
% 5.31/5.52 => ( P2 @ ( nth_int @ Xs2 @ I3 ) ) )
% 5.31/5.52 => ( ( member_int @ X @ ( set_int2 @ Xs2 ) )
% 5.31/5.52 => ( P2 @ X ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % all_nth_imp_all_set
% 5.31/5.52 thf(fact_2219_all__set__conv__all__nth,axiom,
% 5.31/5.52 ! [Xs2: list_VEBT_VEBT,P2: vEBT_VEBT > $o] :
% 5.31/5.52 ( ( ! [X4: vEBT_VEBT] :
% 5.31/5.52 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 5.31/5.52 => ( P2 @ X4 ) ) )
% 5.31/5.52 = ( ! [I: nat] :
% 5.31/5.52 ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 5.31/5.52 => ( P2 @ ( nth_VEBT_VEBT @ Xs2 @ I ) ) ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % all_set_conv_all_nth
% 5.31/5.52 thf(fact_2220_all__set__conv__all__nth,axiom,
% 5.31/5.52 ! [Xs2: list_o,P2: $o > $o] :
% 5.31/5.52 ( ( ! [X4: $o] :
% 5.31/5.52 ( ( member_o @ X4 @ ( set_o2 @ Xs2 ) )
% 5.31/5.52 => ( P2 @ X4 ) ) )
% 5.31/5.52 = ( ! [I: nat] :
% 5.31/5.52 ( ( ord_less_nat @ I @ ( size_size_list_o @ Xs2 ) )
% 5.31/5.52 => ( P2 @ ( nth_o @ Xs2 @ I ) ) ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % all_set_conv_all_nth
% 5.31/5.52 thf(fact_2221_all__set__conv__all__nth,axiom,
% 5.31/5.52 ! [Xs2: list_nat,P2: nat > $o] :
% 5.31/5.52 ( ( ! [X4: nat] :
% 5.31/5.52 ( ( member_nat @ X4 @ ( set_nat2 @ Xs2 ) )
% 5.31/5.52 => ( P2 @ X4 ) ) )
% 5.31/5.52 = ( ! [I: nat] :
% 5.31/5.52 ( ( ord_less_nat @ I @ ( size_size_list_nat @ Xs2 ) )
% 5.31/5.52 => ( P2 @ ( nth_nat @ Xs2 @ I ) ) ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % all_set_conv_all_nth
% 5.31/5.52 thf(fact_2222_all__set__conv__all__nth,axiom,
% 5.31/5.52 ! [Xs2: list_int,P2: int > $o] :
% 5.31/5.52 ( ( ! [X4: int] :
% 5.31/5.52 ( ( member_int @ X4 @ ( set_int2 @ Xs2 ) )
% 5.31/5.52 => ( P2 @ X4 ) ) )
% 5.31/5.52 = ( ! [I: nat] :
% 5.31/5.52 ( ( ord_less_nat @ I @ ( size_size_list_int @ Xs2 ) )
% 5.31/5.52 => ( P2 @ ( nth_int @ Xs2 @ I ) ) ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % all_set_conv_all_nth
% 5.31/5.52 thf(fact_2223_diff__Suc__less,axiom,
% 5.31/5.52 ! [N: nat,I2: nat] :
% 5.31/5.52 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.52 => ( ord_less_nat @ ( minus_minus_nat @ N @ ( suc @ I2 ) ) @ N ) ) ).
% 5.31/5.52
% 5.31/5.52 % diff_Suc_less
% 5.31/5.52 thf(fact_2224_nat__diff__split,axiom,
% 5.31/5.52 ! [P2: nat > $o,A: nat,B: nat] :
% 5.31/5.52 ( ( P2 @ ( minus_minus_nat @ A @ B ) )
% 5.31/5.52 = ( ( ( ord_less_nat @ A @ B )
% 5.31/5.52 => ( P2 @ zero_zero_nat ) )
% 5.31/5.52 & ! [D2: nat] :
% 5.31/5.52 ( ( A
% 5.31/5.52 = ( plus_plus_nat @ B @ D2 ) )
% 5.31/5.52 => ( P2 @ D2 ) ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % nat_diff_split
% 5.31/5.52 thf(fact_2225_nat__diff__split__asm,axiom,
% 5.31/5.52 ! [P2: nat > $o,A: nat,B: nat] :
% 5.31/5.52 ( ( P2 @ ( minus_minus_nat @ A @ B ) )
% 5.31/5.52 = ( ~ ( ( ( ord_less_nat @ A @ B )
% 5.31/5.52 & ~ ( P2 @ zero_zero_nat ) )
% 5.31/5.52 | ? [D2: nat] :
% 5.31/5.52 ( ( A
% 5.31/5.52 = ( plus_plus_nat @ B @ D2 ) )
% 5.31/5.52 & ~ ( P2 @ D2 ) ) ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % nat_diff_split_asm
% 5.31/5.52 thf(fact_2226_less__diff__conv2,axiom,
% 5.31/5.52 ! [K2: nat,J2: nat,I2: nat] :
% 5.31/5.52 ( ( ord_less_eq_nat @ K2 @ J2 )
% 5.31/5.52 => ( ( ord_less_nat @ ( minus_minus_nat @ J2 @ K2 ) @ I2 )
% 5.31/5.52 = ( ord_less_nat @ J2 @ ( plus_plus_nat @ I2 @ K2 ) ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % less_diff_conv2
% 5.31/5.52 thf(fact_2227_nat__eq__add__iff1,axiom,
% 5.31/5.52 ! [J2: nat,I2: nat,U: nat,M2: nat,N: nat] :
% 5.31/5.52 ( ( ord_less_eq_nat @ J2 @ I2 )
% 5.31/5.52 => ( ( ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ M2 )
% 5.31/5.52 = ( plus_plus_nat @ ( times_times_nat @ J2 @ U ) @ N ) )
% 5.31/5.52 = ( ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I2 @ J2 ) @ U ) @ M2 )
% 5.31/5.52 = N ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % nat_eq_add_iff1
% 5.31/5.52 thf(fact_2228_nat__eq__add__iff2,axiom,
% 5.31/5.52 ! [I2: nat,J2: nat,U: nat,M2: nat,N: nat] :
% 5.31/5.52 ( ( ord_less_eq_nat @ I2 @ J2 )
% 5.31/5.52 => ( ( ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ M2 )
% 5.31/5.52 = ( plus_plus_nat @ ( times_times_nat @ J2 @ U ) @ N ) )
% 5.31/5.52 = ( M2
% 5.31/5.52 = ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J2 @ I2 ) @ U ) @ N ) ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % nat_eq_add_iff2
% 5.31/5.52 thf(fact_2229_nat__le__add__iff1,axiom,
% 5.31/5.52 ! [J2: nat,I2: nat,U: nat,M2: nat,N: nat] :
% 5.31/5.52 ( ( ord_less_eq_nat @ J2 @ I2 )
% 5.31/5.52 => ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ M2 ) @ ( plus_plus_nat @ ( times_times_nat @ J2 @ U ) @ N ) )
% 5.31/5.52 = ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I2 @ J2 ) @ U ) @ M2 ) @ N ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % nat_le_add_iff1
% 5.31/5.52 thf(fact_2230_nat__le__add__iff2,axiom,
% 5.31/5.52 ! [I2: nat,J2: nat,U: nat,M2: nat,N: nat] :
% 5.31/5.52 ( ( ord_less_eq_nat @ I2 @ J2 )
% 5.31/5.52 => ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ M2 ) @ ( plus_plus_nat @ ( times_times_nat @ J2 @ U ) @ N ) )
% 5.31/5.52 = ( ord_less_eq_nat @ M2 @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J2 @ I2 ) @ U ) @ N ) ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % nat_le_add_iff2
% 5.31/5.52 thf(fact_2231_nat__diff__add__eq1,axiom,
% 5.31/5.52 ! [J2: nat,I2: nat,U: nat,M2: nat,N: nat] :
% 5.31/5.52 ( ( ord_less_eq_nat @ J2 @ I2 )
% 5.31/5.52 => ( ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ M2 ) @ ( plus_plus_nat @ ( times_times_nat @ J2 @ U ) @ N ) )
% 5.31/5.52 = ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I2 @ J2 ) @ U ) @ M2 ) @ N ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % nat_diff_add_eq1
% 5.31/5.52 thf(fact_2232_nat__diff__add__eq2,axiom,
% 5.31/5.52 ! [I2: nat,J2: nat,U: nat,M2: nat,N: nat] :
% 5.31/5.52 ( ( ord_less_eq_nat @ I2 @ J2 )
% 5.31/5.52 => ( ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ M2 ) @ ( plus_plus_nat @ ( times_times_nat @ J2 @ U ) @ N ) )
% 5.31/5.52 = ( minus_minus_nat @ M2 @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J2 @ I2 ) @ U ) @ N ) ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % nat_diff_add_eq2
% 5.31/5.52 thf(fact_2233_VEBT__internal_OminNull_Oelims_I3_J,axiom,
% 5.31/5.52 ! [X: vEBT_VEBT] :
% 5.31/5.52 ( ~ ( vEBT_VEBT_minNull @ X )
% 5.31/5.52 => ( ! [Uv2: $o] :
% 5.31/5.52 ( X
% 5.31/5.52 != ( vEBT_Leaf @ $true @ Uv2 ) )
% 5.31/5.52 => ( ! [Uu2: $o] :
% 5.31/5.52 ( X
% 5.31/5.52 != ( vEBT_Leaf @ Uu2 @ $true ) )
% 5.31/5.52 => ~ ! [Uz2: product_prod_nat_nat,Va2: nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.31/5.52 ( X
% 5.31/5.52 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va2 @ Vb2 @ Vc2 ) ) ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % VEBT_internal.minNull.elims(3)
% 5.31/5.52 thf(fact_2234_VEBT__internal_OminNull_Oelims_I2_J,axiom,
% 5.31/5.52 ! [X: vEBT_VEBT] :
% 5.31/5.52 ( ( vEBT_VEBT_minNull @ X )
% 5.31/5.52 => ( ( X
% 5.31/5.52 != ( vEBT_Leaf @ $false @ $false ) )
% 5.31/5.52 => ~ ! [Uw: nat,Ux: list_VEBT_VEBT,Uy: vEBT_VEBT] :
% 5.31/5.52 ( X
% 5.31/5.52 != ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw @ Ux @ Uy ) ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % VEBT_internal.minNull.elims(2)
% 5.31/5.52 thf(fact_2235_Suc__pred_H,axiom,
% 5.31/5.52 ! [N: nat] :
% 5.31/5.52 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.52 => ( N
% 5.31/5.52 = ( suc @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % Suc_pred'
% 5.31/5.52 thf(fact_2236_Suc__diff__eq__diff__pred,axiom,
% 5.31/5.52 ! [N: nat,M2: nat] :
% 5.31/5.52 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.52 => ( ( minus_minus_nat @ ( suc @ M2 ) @ N )
% 5.31/5.52 = ( minus_minus_nat @ M2 @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % Suc_diff_eq_diff_pred
% 5.31/5.52 thf(fact_2237_add__eq__if,axiom,
% 5.31/5.52 ( plus_plus_nat
% 5.31/5.52 = ( ^ [M6: nat,N4: nat] : ( if_nat @ ( M6 = zero_zero_nat ) @ N4 @ ( suc @ ( plus_plus_nat @ ( minus_minus_nat @ M6 @ one_one_nat ) @ N4 ) ) ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % add_eq_if
% 5.31/5.52 thf(fact_2238_nat__less__add__iff1,axiom,
% 5.31/5.52 ! [J2: nat,I2: nat,U: nat,M2: nat,N: nat] :
% 5.31/5.52 ( ( ord_less_eq_nat @ J2 @ I2 )
% 5.31/5.52 => ( ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ M2 ) @ ( plus_plus_nat @ ( times_times_nat @ J2 @ U ) @ N ) )
% 5.31/5.52 = ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I2 @ J2 ) @ U ) @ M2 ) @ N ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % nat_less_add_iff1
% 5.31/5.52 thf(fact_2239_nat__less__add__iff2,axiom,
% 5.31/5.52 ! [I2: nat,J2: nat,U: nat,M2: nat,N: nat] :
% 5.31/5.52 ( ( ord_less_eq_nat @ I2 @ J2 )
% 5.31/5.52 => ( ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ M2 ) @ ( plus_plus_nat @ ( times_times_nat @ J2 @ U ) @ N ) )
% 5.31/5.52 = ( ord_less_nat @ M2 @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J2 @ I2 ) @ U ) @ N ) ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % nat_less_add_iff2
% 5.31/5.52 thf(fact_2240_mult__eq__if,axiom,
% 5.31/5.52 ( times_times_nat
% 5.31/5.52 = ( ^ [M6: nat,N4: nat] : ( if_nat @ ( M6 = zero_zero_nat ) @ zero_zero_nat @ ( plus_plus_nat @ N4 @ ( times_times_nat @ ( minus_minus_nat @ M6 @ one_one_nat ) @ N4 ) ) ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % mult_eq_if
% 5.31/5.52 thf(fact_2241_VEBT__internal_OminNull_Oelims_I1_J,axiom,
% 5.31/5.52 ! [X: vEBT_VEBT,Y: $o] :
% 5.31/5.52 ( ( ( vEBT_VEBT_minNull @ X )
% 5.31/5.52 = Y )
% 5.31/5.52 => ( ( ( X
% 5.31/5.52 = ( vEBT_Leaf @ $false @ $false ) )
% 5.31/5.52 => ~ Y )
% 5.31/5.52 => ( ( ? [Uv2: $o] :
% 5.31/5.52 ( X
% 5.31/5.52 = ( vEBT_Leaf @ $true @ Uv2 ) )
% 5.31/5.52 => Y )
% 5.31/5.52 => ( ( ? [Uu2: $o] :
% 5.31/5.52 ( X
% 5.31/5.52 = ( vEBT_Leaf @ Uu2 @ $true ) )
% 5.31/5.52 => Y )
% 5.31/5.52 => ( ( ? [Uw: nat,Ux: list_VEBT_VEBT,Uy: vEBT_VEBT] :
% 5.31/5.52 ( X
% 5.31/5.52 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw @ Ux @ Uy ) )
% 5.31/5.52 => ~ Y )
% 5.31/5.52 => ~ ( ? [Uz2: product_prod_nat_nat,Va2: nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.31/5.52 ( X
% 5.31/5.52 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va2 @ Vb2 @ Vc2 ) )
% 5.31/5.52 => Y ) ) ) ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % VEBT_internal.minNull.elims(1)
% 5.31/5.52 thf(fact_2242_field__lbound__gt__zero,axiom,
% 5.31/5.52 ! [D1: real,D22: real] :
% 5.31/5.52 ( ( ord_less_real @ zero_zero_real @ D1 )
% 5.31/5.52 => ( ( ord_less_real @ zero_zero_real @ D22 )
% 5.31/5.52 => ? [E2: real] :
% 5.31/5.52 ( ( ord_less_real @ zero_zero_real @ E2 )
% 5.31/5.52 & ( ord_less_real @ E2 @ D1 )
% 5.31/5.52 & ( ord_less_real @ E2 @ D22 ) ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % field_lbound_gt_zero
% 5.31/5.52 thf(fact_2243_field__lbound__gt__zero,axiom,
% 5.31/5.52 ! [D1: rat,D22: rat] :
% 5.31/5.52 ( ( ord_less_rat @ zero_zero_rat @ D1 )
% 5.31/5.52 => ( ( ord_less_rat @ zero_zero_rat @ D22 )
% 5.31/5.52 => ? [E2: rat] :
% 5.31/5.52 ( ( ord_less_rat @ zero_zero_rat @ E2 )
% 5.31/5.52 & ( ord_less_rat @ E2 @ D1 )
% 5.31/5.52 & ( ord_less_rat @ E2 @ D22 ) ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % field_lbound_gt_zero
% 5.31/5.52 thf(fact_2244_finite__has__minimal2,axiom,
% 5.31/5.52 ! [A4: set_real,A: real] :
% 5.31/5.52 ( ( finite_finite_real @ A4 )
% 5.31/5.52 => ( ( member_real @ A @ A4 )
% 5.31/5.52 => ? [X3: real] :
% 5.31/5.52 ( ( member_real @ X3 @ A4 )
% 5.31/5.52 & ( ord_less_eq_real @ X3 @ A )
% 5.31/5.52 & ! [Xa: real] :
% 5.31/5.52 ( ( member_real @ Xa @ A4 )
% 5.31/5.52 => ( ( ord_less_eq_real @ Xa @ X3 )
% 5.31/5.52 => ( X3 = Xa ) ) ) ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % finite_has_minimal2
% 5.31/5.52 thf(fact_2245_finite__has__minimal2,axiom,
% 5.31/5.52 ! [A4: set_set_nat,A: set_nat] :
% 5.31/5.52 ( ( finite1152437895449049373et_nat @ A4 )
% 5.31/5.52 => ( ( member_set_nat @ A @ A4 )
% 5.31/5.52 => ? [X3: set_nat] :
% 5.31/5.52 ( ( member_set_nat @ X3 @ A4 )
% 5.31/5.52 & ( ord_less_eq_set_nat @ X3 @ A )
% 5.31/5.52 & ! [Xa: set_nat] :
% 5.31/5.52 ( ( member_set_nat @ Xa @ A4 )
% 5.31/5.52 => ( ( ord_less_eq_set_nat @ Xa @ X3 )
% 5.31/5.52 => ( X3 = Xa ) ) ) ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % finite_has_minimal2
% 5.31/5.52 thf(fact_2246_finite__has__minimal2,axiom,
% 5.31/5.52 ! [A4: set_rat,A: rat] :
% 5.31/5.52 ( ( finite_finite_rat @ A4 )
% 5.31/5.52 => ( ( member_rat @ A @ A4 )
% 5.31/5.52 => ? [X3: rat] :
% 5.31/5.52 ( ( member_rat @ X3 @ A4 )
% 5.31/5.52 & ( ord_less_eq_rat @ X3 @ A )
% 5.31/5.52 & ! [Xa: rat] :
% 5.31/5.52 ( ( member_rat @ Xa @ A4 )
% 5.31/5.52 => ( ( ord_less_eq_rat @ Xa @ X3 )
% 5.31/5.52 => ( X3 = Xa ) ) ) ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % finite_has_minimal2
% 5.31/5.52 thf(fact_2247_finite__has__minimal2,axiom,
% 5.31/5.52 ! [A4: set_num,A: num] :
% 5.31/5.52 ( ( finite_finite_num @ A4 )
% 5.31/5.52 => ( ( member_num @ A @ A4 )
% 5.31/5.52 => ? [X3: num] :
% 5.31/5.52 ( ( member_num @ X3 @ A4 )
% 5.31/5.52 & ( ord_less_eq_num @ X3 @ A )
% 5.31/5.52 & ! [Xa: num] :
% 5.31/5.52 ( ( member_num @ Xa @ A4 )
% 5.31/5.52 => ( ( ord_less_eq_num @ Xa @ X3 )
% 5.31/5.52 => ( X3 = Xa ) ) ) ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % finite_has_minimal2
% 5.31/5.52 thf(fact_2248_finite__has__minimal2,axiom,
% 5.31/5.52 ! [A4: set_nat,A: nat] :
% 5.31/5.52 ( ( finite_finite_nat @ A4 )
% 5.31/5.52 => ( ( member_nat @ A @ A4 )
% 5.31/5.52 => ? [X3: nat] :
% 5.31/5.52 ( ( member_nat @ X3 @ A4 )
% 5.31/5.52 & ( ord_less_eq_nat @ X3 @ A )
% 5.31/5.52 & ! [Xa: nat] :
% 5.31/5.52 ( ( member_nat @ Xa @ A4 )
% 5.31/5.52 => ( ( ord_less_eq_nat @ Xa @ X3 )
% 5.31/5.52 => ( X3 = Xa ) ) ) ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % finite_has_minimal2
% 5.31/5.52 thf(fact_2249_finite__has__minimal2,axiom,
% 5.31/5.52 ! [A4: set_int,A: int] :
% 5.31/5.52 ( ( finite_finite_int @ A4 )
% 5.31/5.52 => ( ( member_int @ A @ A4 )
% 5.31/5.52 => ? [X3: int] :
% 5.31/5.52 ( ( member_int @ X3 @ A4 )
% 5.31/5.52 & ( ord_less_eq_int @ X3 @ A )
% 5.31/5.52 & ! [Xa: int] :
% 5.31/5.52 ( ( member_int @ Xa @ A4 )
% 5.31/5.52 => ( ( ord_less_eq_int @ Xa @ X3 )
% 5.31/5.52 => ( X3 = Xa ) ) ) ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % finite_has_minimal2
% 5.31/5.52 thf(fact_2250_finite__has__maximal2,axiom,
% 5.31/5.52 ! [A4: set_real,A: real] :
% 5.31/5.52 ( ( finite_finite_real @ A4 )
% 5.31/5.52 => ( ( member_real @ A @ A4 )
% 5.31/5.52 => ? [X3: real] :
% 5.31/5.52 ( ( member_real @ X3 @ A4 )
% 5.31/5.52 & ( ord_less_eq_real @ A @ X3 )
% 5.31/5.52 & ! [Xa: real] :
% 5.31/5.52 ( ( member_real @ Xa @ A4 )
% 5.31/5.52 => ( ( ord_less_eq_real @ X3 @ Xa )
% 5.31/5.52 => ( X3 = Xa ) ) ) ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % finite_has_maximal2
% 5.31/5.52 thf(fact_2251_finite__has__maximal2,axiom,
% 5.31/5.52 ! [A4: set_set_nat,A: set_nat] :
% 5.31/5.52 ( ( finite1152437895449049373et_nat @ A4 )
% 5.31/5.52 => ( ( member_set_nat @ A @ A4 )
% 5.31/5.52 => ? [X3: set_nat] :
% 5.31/5.52 ( ( member_set_nat @ X3 @ A4 )
% 5.31/5.52 & ( ord_less_eq_set_nat @ A @ X3 )
% 5.31/5.52 & ! [Xa: set_nat] :
% 5.31/5.52 ( ( member_set_nat @ Xa @ A4 )
% 5.31/5.52 => ( ( ord_less_eq_set_nat @ X3 @ Xa )
% 5.31/5.52 => ( X3 = Xa ) ) ) ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % finite_has_maximal2
% 5.31/5.52 thf(fact_2252_finite__has__maximal2,axiom,
% 5.31/5.52 ! [A4: set_rat,A: rat] :
% 5.31/5.52 ( ( finite_finite_rat @ A4 )
% 5.31/5.52 => ( ( member_rat @ A @ A4 )
% 5.31/5.52 => ? [X3: rat] :
% 5.31/5.52 ( ( member_rat @ X3 @ A4 )
% 5.31/5.52 & ( ord_less_eq_rat @ A @ X3 )
% 5.31/5.52 & ! [Xa: rat] :
% 5.31/5.52 ( ( member_rat @ Xa @ A4 )
% 5.31/5.52 => ( ( ord_less_eq_rat @ X3 @ Xa )
% 5.31/5.52 => ( X3 = Xa ) ) ) ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % finite_has_maximal2
% 5.31/5.52 thf(fact_2253_finite__has__maximal2,axiom,
% 5.31/5.52 ! [A4: set_num,A: num] :
% 5.31/5.52 ( ( finite_finite_num @ A4 )
% 5.31/5.52 => ( ( member_num @ A @ A4 )
% 5.31/5.52 => ? [X3: num] :
% 5.31/5.52 ( ( member_num @ X3 @ A4 )
% 5.31/5.52 & ( ord_less_eq_num @ A @ X3 )
% 5.31/5.52 & ! [Xa: num] :
% 5.31/5.52 ( ( member_num @ Xa @ A4 )
% 5.31/5.52 => ( ( ord_less_eq_num @ X3 @ Xa )
% 5.31/5.52 => ( X3 = Xa ) ) ) ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % finite_has_maximal2
% 5.31/5.52 thf(fact_2254_finite__has__maximal2,axiom,
% 5.31/5.52 ! [A4: set_nat,A: nat] :
% 5.31/5.52 ( ( finite_finite_nat @ A4 )
% 5.31/5.52 => ( ( member_nat @ A @ A4 )
% 5.31/5.52 => ? [X3: nat] :
% 5.31/5.52 ( ( member_nat @ X3 @ A4 )
% 5.31/5.52 & ( ord_less_eq_nat @ A @ X3 )
% 5.31/5.52 & ! [Xa: nat] :
% 5.31/5.52 ( ( member_nat @ Xa @ A4 )
% 5.31/5.52 => ( ( ord_less_eq_nat @ X3 @ Xa )
% 5.31/5.52 => ( X3 = Xa ) ) ) ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % finite_has_maximal2
% 5.31/5.52 thf(fact_2255_finite__has__maximal2,axiom,
% 5.31/5.52 ! [A4: set_int,A: int] :
% 5.31/5.52 ( ( finite_finite_int @ A4 )
% 5.31/5.52 => ( ( member_int @ A @ A4 )
% 5.31/5.52 => ? [X3: int] :
% 5.31/5.52 ( ( member_int @ X3 @ A4 )
% 5.31/5.52 & ( ord_less_eq_int @ A @ X3 )
% 5.31/5.52 & ! [Xa: int] :
% 5.31/5.52 ( ( member_int @ Xa @ A4 )
% 5.31/5.52 => ( ( ord_less_eq_int @ X3 @ Xa )
% 5.31/5.52 => ( X3 = Xa ) ) ) ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % finite_has_maximal2
% 5.31/5.52 thf(fact_2256_VEBT__internal_OminNull_Opelims_I1_J,axiom,
% 5.31/5.52 ! [X: vEBT_VEBT,Y: $o] :
% 5.31/5.52 ( ( ( vEBT_VEBT_minNull @ X )
% 5.31/5.52 = Y )
% 5.31/5.52 => ( ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ X )
% 5.31/5.52 => ( ( ( X
% 5.31/5.52 = ( vEBT_Leaf @ $false @ $false ) )
% 5.31/5.52 => ( Y
% 5.31/5.52 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Leaf @ $false @ $false ) ) ) )
% 5.31/5.52 => ( ! [Uv2: $o] :
% 5.31/5.52 ( ( X
% 5.31/5.52 = ( vEBT_Leaf @ $true @ Uv2 ) )
% 5.31/5.52 => ( ~ Y
% 5.31/5.52 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Leaf @ $true @ Uv2 ) ) ) )
% 5.31/5.52 => ( ! [Uu2: $o] :
% 5.31/5.52 ( ( X
% 5.31/5.52 = ( vEBT_Leaf @ Uu2 @ $true ) )
% 5.31/5.52 => ( ~ Y
% 5.31/5.52 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Leaf @ Uu2 @ $true ) ) ) )
% 5.31/5.52 => ( ! [Uw: nat,Ux: list_VEBT_VEBT,Uy: vEBT_VEBT] :
% 5.31/5.52 ( ( X
% 5.31/5.52 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw @ Ux @ Uy ) )
% 5.31/5.52 => ( Y
% 5.31/5.52 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw @ Ux @ Uy ) ) ) )
% 5.31/5.52 => ~ ! [Uz2: product_prod_nat_nat,Va2: nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.31/5.52 ( ( X
% 5.31/5.52 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va2 @ Vb2 @ Vc2 ) )
% 5.31/5.52 => ( ~ Y
% 5.31/5.52 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va2 @ Vb2 @ Vc2 ) ) ) ) ) ) ) ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % VEBT_internal.minNull.pelims(1)
% 5.31/5.52 thf(fact_2257_VEBT__internal_OminNull_Opelims_I2_J,axiom,
% 5.31/5.52 ! [X: vEBT_VEBT] :
% 5.31/5.52 ( ( vEBT_VEBT_minNull @ X )
% 5.31/5.52 => ( ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ X )
% 5.31/5.52 => ( ( ( X
% 5.31/5.52 = ( vEBT_Leaf @ $false @ $false ) )
% 5.31/5.52 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Leaf @ $false @ $false ) ) )
% 5.31/5.52 => ~ ! [Uw: nat,Ux: list_VEBT_VEBT,Uy: vEBT_VEBT] :
% 5.31/5.52 ( ( X
% 5.31/5.52 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw @ Ux @ Uy ) )
% 5.31/5.52 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw @ Ux @ Uy ) ) ) ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % VEBT_internal.minNull.pelims(2)
% 5.31/5.52 thf(fact_2258_VEBT__internal_OminNull_Opelims_I3_J,axiom,
% 5.31/5.52 ! [X: vEBT_VEBT] :
% 5.31/5.52 ( ~ ( vEBT_VEBT_minNull @ X )
% 5.31/5.52 => ( ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ X )
% 5.31/5.52 => ( ! [Uv2: $o] :
% 5.31/5.52 ( ( X
% 5.31/5.52 = ( vEBT_Leaf @ $true @ Uv2 ) )
% 5.31/5.52 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Leaf @ $true @ Uv2 ) ) )
% 5.31/5.52 => ( ! [Uu2: $o] :
% 5.31/5.52 ( ( X
% 5.31/5.52 = ( vEBT_Leaf @ Uu2 @ $true ) )
% 5.31/5.52 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Leaf @ Uu2 @ $true ) ) )
% 5.31/5.52 => ~ ! [Uz2: product_prod_nat_nat,Va2: nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.31/5.52 ( ( X
% 5.31/5.52 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va2 @ Vb2 @ Vc2 ) )
% 5.31/5.52 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va2 @ Vb2 @ Vc2 ) ) ) ) ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % VEBT_internal.minNull.pelims(3)
% 5.31/5.52 thf(fact_2259_nth__enumerate__eq,axiom,
% 5.31/5.52 ! [M2: nat,Xs2: list_VEBT_VEBT,N: nat] :
% 5.31/5.52 ( ( ord_less_nat @ M2 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 5.31/5.52 => ( ( nth_Pr744662078594809490T_VEBT @ ( enumerate_VEBT_VEBT @ N @ Xs2 ) @ M2 )
% 5.31/5.52 = ( produc599794634098209291T_VEBT @ ( plus_plus_nat @ N @ M2 ) @ ( nth_VEBT_VEBT @ Xs2 @ M2 ) ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % nth_enumerate_eq
% 5.31/5.52 thf(fact_2260_nth__enumerate__eq,axiom,
% 5.31/5.52 ! [M2: nat,Xs2: list_o,N: nat] :
% 5.31/5.52 ( ( ord_less_nat @ M2 @ ( size_size_list_o @ Xs2 ) )
% 5.31/5.52 => ( ( nth_Pr112076138515278198_nat_o @ ( enumerate_o @ N @ Xs2 ) @ M2 )
% 5.31/5.52 = ( product_Pair_nat_o @ ( plus_plus_nat @ N @ M2 ) @ ( nth_o @ Xs2 @ M2 ) ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % nth_enumerate_eq
% 5.31/5.52 thf(fact_2261_nth__enumerate__eq,axiom,
% 5.31/5.52 ! [M2: nat,Xs2: list_nat,N: nat] :
% 5.31/5.52 ( ( ord_less_nat @ M2 @ ( size_size_list_nat @ Xs2 ) )
% 5.31/5.52 => ( ( nth_Pr7617993195940197384at_nat @ ( enumerate_nat @ N @ Xs2 ) @ M2 )
% 5.31/5.52 = ( product_Pair_nat_nat @ ( plus_plus_nat @ N @ M2 ) @ ( nth_nat @ Xs2 @ M2 ) ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % nth_enumerate_eq
% 5.31/5.52 thf(fact_2262_nth__enumerate__eq,axiom,
% 5.31/5.52 ! [M2: nat,Xs2: list_int,N: nat] :
% 5.31/5.52 ( ( ord_less_nat @ M2 @ ( size_size_list_int @ Xs2 ) )
% 5.31/5.52 => ( ( nth_Pr3440142176431000676at_int @ ( enumerate_int @ N @ Xs2 ) @ M2 )
% 5.31/5.52 = ( product_Pair_nat_int @ ( plus_plus_nat @ N @ M2 ) @ ( nth_int @ Xs2 @ M2 ) ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % nth_enumerate_eq
% 5.31/5.52 thf(fact_2263_arg__min__least,axiom,
% 5.31/5.52 ! [S3: set_complex,Y: complex,F2: complex > rat] :
% 5.31/5.52 ( ( finite3207457112153483333omplex @ S3 )
% 5.31/5.52 => ( ( S3 != bot_bot_set_complex )
% 5.31/5.52 => ( ( member_complex @ Y @ S3 )
% 5.31/5.52 => ( ord_less_eq_rat @ ( F2 @ ( lattic4729654577720512673ex_rat @ F2 @ S3 ) ) @ ( F2 @ Y ) ) ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % arg_min_least
% 5.31/5.52 thf(fact_2264_arg__min__least,axiom,
% 5.31/5.52 ! [S3: set_nat,Y: nat,F2: nat > rat] :
% 5.31/5.52 ( ( finite_finite_nat @ S3 )
% 5.31/5.52 => ( ( S3 != bot_bot_set_nat )
% 5.31/5.52 => ( ( member_nat @ Y @ S3 )
% 5.31/5.52 => ( ord_less_eq_rat @ ( F2 @ ( lattic6811802900495863747at_rat @ F2 @ S3 ) ) @ ( F2 @ Y ) ) ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % arg_min_least
% 5.31/5.52 thf(fact_2265_arg__min__least,axiom,
% 5.31/5.52 ! [S3: set_int,Y: int,F2: int > rat] :
% 5.31/5.52 ( ( finite_finite_int @ S3 )
% 5.31/5.52 => ( ( S3 != bot_bot_set_int )
% 5.31/5.52 => ( ( member_int @ Y @ S3 )
% 5.31/5.52 => ( ord_less_eq_rat @ ( F2 @ ( lattic7811156612396918303nt_rat @ F2 @ S3 ) ) @ ( F2 @ Y ) ) ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % arg_min_least
% 5.31/5.52 thf(fact_2266_arg__min__least,axiom,
% 5.31/5.52 ! [S3: set_real,Y: real,F2: real > rat] :
% 5.31/5.52 ( ( finite_finite_real @ S3 )
% 5.31/5.52 => ( ( S3 != bot_bot_set_real )
% 5.31/5.52 => ( ( member_real @ Y @ S3 )
% 5.31/5.52 => ( ord_less_eq_rat @ ( F2 @ ( lattic4420706379359479199al_rat @ F2 @ S3 ) ) @ ( F2 @ Y ) ) ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % arg_min_least
% 5.31/5.52 thf(fact_2267_arg__min__least,axiom,
% 5.31/5.52 ! [S3: set_complex,Y: complex,F2: complex > num] :
% 5.31/5.52 ( ( finite3207457112153483333omplex @ S3 )
% 5.31/5.52 => ( ( S3 != bot_bot_set_complex )
% 5.31/5.52 => ( ( member_complex @ Y @ S3 )
% 5.31/5.52 => ( ord_less_eq_num @ ( F2 @ ( lattic1922116423962787043ex_num @ F2 @ S3 ) ) @ ( F2 @ Y ) ) ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % arg_min_least
% 5.31/5.52 thf(fact_2268_arg__min__least,axiom,
% 5.31/5.52 ! [S3: set_nat,Y: nat,F2: nat > num] :
% 5.31/5.52 ( ( finite_finite_nat @ S3 )
% 5.31/5.52 => ( ( S3 != bot_bot_set_nat )
% 5.31/5.52 => ( ( member_nat @ Y @ S3 )
% 5.31/5.52 => ( ord_less_eq_num @ ( F2 @ ( lattic4004264746738138117at_num @ F2 @ S3 ) ) @ ( F2 @ Y ) ) ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % arg_min_least
% 5.31/5.52 thf(fact_2269_arg__min__least,axiom,
% 5.31/5.52 ! [S3: set_int,Y: int,F2: int > num] :
% 5.31/5.52 ( ( finite_finite_int @ S3 )
% 5.31/5.52 => ( ( S3 != bot_bot_set_int )
% 5.31/5.52 => ( ( member_int @ Y @ S3 )
% 5.31/5.52 => ( ord_less_eq_num @ ( F2 @ ( lattic5003618458639192673nt_num @ F2 @ S3 ) ) @ ( F2 @ Y ) ) ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % arg_min_least
% 5.31/5.52 thf(fact_2270_arg__min__least,axiom,
% 5.31/5.52 ! [S3: set_real,Y: real,F2: real > num] :
% 5.31/5.52 ( ( finite_finite_real @ S3 )
% 5.31/5.52 => ( ( S3 != bot_bot_set_real )
% 5.31/5.52 => ( ( member_real @ Y @ S3 )
% 5.31/5.52 => ( ord_less_eq_num @ ( F2 @ ( lattic1613168225601753569al_num @ F2 @ S3 ) ) @ ( F2 @ Y ) ) ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % arg_min_least
% 5.31/5.52 thf(fact_2271_arg__min__least,axiom,
% 5.31/5.52 ! [S3: set_complex,Y: complex,F2: complex > nat] :
% 5.31/5.52 ( ( finite3207457112153483333omplex @ S3 )
% 5.31/5.52 => ( ( S3 != bot_bot_set_complex )
% 5.31/5.52 => ( ( member_complex @ Y @ S3 )
% 5.31/5.52 => ( ord_less_eq_nat @ ( F2 @ ( lattic5364784637807008409ex_nat @ F2 @ S3 ) ) @ ( F2 @ Y ) ) ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % arg_min_least
% 5.31/5.52 thf(fact_2272_arg__min__least,axiom,
% 5.31/5.52 ! [S3: set_nat,Y: nat,F2: nat > nat] :
% 5.31/5.52 ( ( finite_finite_nat @ S3 )
% 5.31/5.52 => ( ( S3 != bot_bot_set_nat )
% 5.31/5.52 => ( ( member_nat @ Y @ S3 )
% 5.31/5.52 => ( ord_less_eq_nat @ ( F2 @ ( lattic7446932960582359483at_nat @ F2 @ S3 ) ) @ ( F2 @ Y ) ) ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % arg_min_least
% 5.31/5.52 thf(fact_2273_Euclid__induct,axiom,
% 5.31/5.52 ! [P2: nat > nat > $o,A: nat,B: nat] :
% 5.31/5.52 ( ! [A3: nat,B3: nat] :
% 5.31/5.52 ( ( P2 @ A3 @ B3 )
% 5.31/5.52 = ( P2 @ B3 @ A3 ) )
% 5.31/5.52 => ( ! [A3: nat] : ( P2 @ A3 @ zero_zero_nat )
% 5.31/5.52 => ( ! [A3: nat,B3: nat] :
% 5.31/5.52 ( ( P2 @ A3 @ B3 )
% 5.31/5.52 => ( P2 @ A3 @ ( plus_plus_nat @ A3 @ B3 ) ) )
% 5.31/5.52 => ( P2 @ A @ B ) ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % Euclid_induct
% 5.31/5.52 thf(fact_2274_nat__descend__induct,axiom,
% 5.31/5.52 ! [N: nat,P2: nat > $o,M2: nat] :
% 5.31/5.52 ( ! [K: nat] :
% 5.31/5.52 ( ( ord_less_nat @ N @ K )
% 5.31/5.52 => ( P2 @ K ) )
% 5.31/5.52 => ( ! [K: nat] :
% 5.31/5.52 ( ( ord_less_eq_nat @ K @ N )
% 5.31/5.52 => ( ! [I4: nat] :
% 5.31/5.52 ( ( ord_less_nat @ K @ I4 )
% 5.31/5.52 => ( P2 @ I4 ) )
% 5.31/5.52 => ( P2 @ K ) ) )
% 5.31/5.52 => ( P2 @ M2 ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % nat_descend_induct
% 5.31/5.52 thf(fact_2275_length__mul__elem,axiom,
% 5.31/5.52 ! [Xs2: list_list_VEBT_VEBT,N: nat] :
% 5.31/5.52 ( ! [X3: list_VEBT_VEBT] :
% 5.31/5.52 ( ( member2936631157270082147T_VEBT @ X3 @ ( set_list_VEBT_VEBT2 @ Xs2 ) )
% 5.31/5.52 => ( ( size_s6755466524823107622T_VEBT @ X3 )
% 5.31/5.52 = N ) )
% 5.31/5.52 => ( ( size_s6755466524823107622T_VEBT @ ( concat_VEBT_VEBT @ Xs2 ) )
% 5.31/5.52 = ( times_times_nat @ ( size_s8217280938318005548T_VEBT @ Xs2 ) @ N ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % length_mul_elem
% 5.31/5.52 thf(fact_2276_length__mul__elem,axiom,
% 5.31/5.52 ! [Xs2: list_list_o,N: nat] :
% 5.31/5.52 ( ! [X3: list_o] :
% 5.31/5.52 ( ( member_list_o @ X3 @ ( set_list_o2 @ Xs2 ) )
% 5.31/5.52 => ( ( size_size_list_o @ X3 )
% 5.31/5.52 = N ) )
% 5.31/5.52 => ( ( size_size_list_o @ ( concat_o @ Xs2 ) )
% 5.31/5.52 = ( times_times_nat @ ( size_s2710708370519433104list_o @ Xs2 ) @ N ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % length_mul_elem
% 5.31/5.52 thf(fact_2277_length__mul__elem,axiom,
% 5.31/5.52 ! [Xs2: list_list_nat,N: nat] :
% 5.31/5.52 ( ! [X3: list_nat] :
% 5.31/5.52 ( ( member_list_nat @ X3 @ ( set_list_nat2 @ Xs2 ) )
% 5.31/5.52 => ( ( size_size_list_nat @ X3 )
% 5.31/5.52 = N ) )
% 5.31/5.52 => ( ( size_size_list_nat @ ( concat_nat @ Xs2 ) )
% 5.31/5.52 = ( times_times_nat @ ( size_s3023201423986296836st_nat @ Xs2 ) @ N ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % length_mul_elem
% 5.31/5.52 thf(fact_2278_length__mul__elem,axiom,
% 5.31/5.52 ! [Xs2: list_list_int,N: nat] :
% 5.31/5.52 ( ! [X3: list_int] :
% 5.31/5.52 ( ( member_list_int @ X3 @ ( set_list_int2 @ Xs2 ) )
% 5.31/5.52 => ( ( size_size_list_int @ X3 )
% 5.31/5.52 = N ) )
% 5.31/5.52 => ( ( size_size_list_int @ ( concat_int @ Xs2 ) )
% 5.31/5.52 = ( times_times_nat @ ( size_s533118279054570080st_int @ Xs2 ) @ N ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % length_mul_elem
% 5.31/5.52 thf(fact_2279_triangle__Suc,axiom,
% 5.31/5.52 ! [N: nat] :
% 5.31/5.52 ( ( nat_triangle @ ( suc @ N ) )
% 5.31/5.52 = ( plus_plus_nat @ ( nat_triangle @ N ) @ ( suc @ N ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % triangle_Suc
% 5.31/5.52 thf(fact_2280_length__enumerate,axiom,
% 5.31/5.52 ! [N: nat,Xs2: list_VEBT_VEBT] :
% 5.31/5.52 ( ( size_s4762443039079500285T_VEBT @ ( enumerate_VEBT_VEBT @ N @ Xs2 ) )
% 5.31/5.52 = ( size_s6755466524823107622T_VEBT @ Xs2 ) ) ).
% 5.31/5.52
% 5.31/5.52 % length_enumerate
% 5.31/5.52 thf(fact_2281_length__enumerate,axiom,
% 5.31/5.52 ! [N: nat,Xs2: list_o] :
% 5.31/5.52 ( ( size_s6491369823275344609_nat_o @ ( enumerate_o @ N @ Xs2 ) )
% 5.31/5.52 = ( size_size_list_o @ Xs2 ) ) ).
% 5.31/5.52
% 5.31/5.52 % length_enumerate
% 5.31/5.52 thf(fact_2282_length__enumerate,axiom,
% 5.31/5.52 ! [N: nat,Xs2: list_nat] :
% 5.31/5.52 ( ( size_s5460976970255530739at_nat @ ( enumerate_nat @ N @ Xs2 ) )
% 5.31/5.52 = ( size_size_list_nat @ Xs2 ) ) ).
% 5.31/5.52
% 5.31/5.52 % length_enumerate
% 5.31/5.52 thf(fact_2283_length__enumerate,axiom,
% 5.31/5.52 ! [N: nat,Xs2: list_int] :
% 5.31/5.52 ( ( size_s2970893825323803983at_int @ ( enumerate_int @ N @ Xs2 ) )
% 5.31/5.52 = ( size_size_list_int @ Xs2 ) ) ).
% 5.31/5.52
% 5.31/5.52 % length_enumerate
% 5.31/5.52 thf(fact_2284_triangle__0,axiom,
% 5.31/5.52 ( ( nat_triangle @ zero_zero_nat )
% 5.31/5.52 = zero_zero_nat ) ).
% 5.31/5.52
% 5.31/5.52 % triangle_0
% 5.31/5.52 thf(fact_2285_diff__commute,axiom,
% 5.31/5.52 ! [I2: nat,J2: nat,K2: nat] :
% 5.31/5.52 ( ( minus_minus_nat @ ( minus_minus_nat @ I2 @ J2 ) @ K2 )
% 5.31/5.52 = ( minus_minus_nat @ ( minus_minus_nat @ I2 @ K2 ) @ J2 ) ) ).
% 5.31/5.52
% 5.31/5.52 % diff_commute
% 5.31/5.52 thf(fact_2286_prod__decode__aux_Oelims,axiom,
% 5.31/5.52 ! [X: nat,Xa2: nat,Y: product_prod_nat_nat] :
% 5.31/5.52 ( ( ( nat_prod_decode_aux @ X @ Xa2 )
% 5.31/5.52 = Y )
% 5.31/5.52 => ( ( ( ord_less_eq_nat @ Xa2 @ X )
% 5.31/5.52 => ( Y
% 5.31/5.52 = ( product_Pair_nat_nat @ Xa2 @ ( minus_minus_nat @ X @ Xa2 ) ) ) )
% 5.31/5.52 & ( ~ ( ord_less_eq_nat @ Xa2 @ X )
% 5.31/5.52 => ( Y
% 5.31/5.52 = ( nat_prod_decode_aux @ ( suc @ X ) @ ( minus_minus_nat @ Xa2 @ ( suc @ X ) ) ) ) ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % prod_decode_aux.elims
% 5.31/5.52 thf(fact_2287_prod__decode__aux_Osimps,axiom,
% 5.31/5.52 ( nat_prod_decode_aux
% 5.31/5.52 = ( ^ [K3: nat,M6: nat] : ( if_Pro6206227464963214023at_nat @ ( ord_less_eq_nat @ M6 @ K3 ) @ ( product_Pair_nat_nat @ M6 @ ( minus_minus_nat @ K3 @ M6 ) ) @ ( nat_prod_decode_aux @ ( suc @ K3 ) @ ( minus_minus_nat @ M6 @ ( suc @ K3 ) ) ) ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % prod_decode_aux.simps
% 5.31/5.52 thf(fact_2288_prod__encode__prod__decode__aux,axiom,
% 5.31/5.52 ! [K2: nat,M2: nat] :
% 5.31/5.52 ( ( nat_prod_encode @ ( nat_prod_decode_aux @ K2 @ M2 ) )
% 5.31/5.52 = ( plus_plus_nat @ ( nat_triangle @ K2 ) @ M2 ) ) ).
% 5.31/5.52
% 5.31/5.52 % prod_encode_prod_decode_aux
% 5.31/5.52 thf(fact_2289_prod__decode__triangle__add,axiom,
% 5.31/5.52 ! [K2: nat,M2: nat] :
% 5.31/5.52 ( ( nat_prod_decode @ ( plus_plus_nat @ ( nat_triangle @ K2 ) @ M2 ) )
% 5.31/5.52 = ( nat_prod_decode_aux @ K2 @ M2 ) ) ).
% 5.31/5.52
% 5.31/5.52 % prod_decode_triangle_add
% 5.31/5.52 thf(fact_2290_in__set__product__lists__length,axiom,
% 5.31/5.52 ! [Xs2: list_VEBT_VEBT,Xss: list_list_VEBT_VEBT] :
% 5.31/5.52 ( ( member2936631157270082147T_VEBT @ Xs2 @ ( set_list_VEBT_VEBT2 @ ( produc3021084454716106787T_VEBT @ Xss ) ) )
% 5.31/5.52 => ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 5.31/5.52 = ( size_s8217280938318005548T_VEBT @ Xss ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % in_set_product_lists_length
% 5.31/5.52 thf(fact_2291_in__set__product__lists__length,axiom,
% 5.31/5.52 ! [Xs2: list_o,Xss: list_list_o] :
% 5.31/5.52 ( ( member_list_o @ Xs2 @ ( set_list_o2 @ ( product_lists_o @ Xss ) ) )
% 5.31/5.52 => ( ( size_size_list_o @ Xs2 )
% 5.31/5.52 = ( size_s2710708370519433104list_o @ Xss ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % in_set_product_lists_length
% 5.31/5.52 thf(fact_2292_in__set__product__lists__length,axiom,
% 5.31/5.52 ! [Xs2: list_nat,Xss: list_list_nat] :
% 5.31/5.52 ( ( member_list_nat @ Xs2 @ ( set_list_nat2 @ ( product_lists_nat @ Xss ) ) )
% 5.31/5.52 => ( ( size_size_list_nat @ Xs2 )
% 5.31/5.52 = ( size_s3023201423986296836st_nat @ Xss ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % in_set_product_lists_length
% 5.31/5.52 thf(fact_2293_in__set__product__lists__length,axiom,
% 5.31/5.52 ! [Xs2: list_int,Xss: list_list_int] :
% 5.31/5.52 ( ( member_list_int @ Xs2 @ ( set_list_int2 @ ( product_lists_int @ Xss ) ) )
% 5.31/5.52 => ( ( size_size_list_int @ Xs2 )
% 5.31/5.52 = ( size_s533118279054570080st_int @ Xss ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % in_set_product_lists_length
% 5.31/5.52 thf(fact_2294_Gcd__remove0__nat,axiom,
% 5.31/5.52 ! [M5: set_nat] :
% 5.31/5.52 ( ( finite_finite_nat @ M5 )
% 5.31/5.52 => ( ( gcd_Gcd_nat @ M5 )
% 5.31/5.52 = ( gcd_Gcd_nat @ ( minus_minus_set_nat @ M5 @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % Gcd_remove0_nat
% 5.31/5.52 thf(fact_2295_inf__period_I2_J,axiom,
% 5.31/5.52 ! [P2: real > $o,D3: real,Q: real > $o] :
% 5.31/5.52 ( ! [X3: real,K: real] :
% 5.31/5.52 ( ( P2 @ X3 )
% 5.31/5.52 = ( P2 @ ( minus_minus_real @ X3 @ ( times_times_real @ K @ D3 ) ) ) )
% 5.31/5.52 => ( ! [X3: real,K: real] :
% 5.31/5.52 ( ( Q @ X3 )
% 5.31/5.52 = ( Q @ ( minus_minus_real @ X3 @ ( times_times_real @ K @ D3 ) ) ) )
% 5.31/5.52 => ! [X5: real,K4: real] :
% 5.31/5.52 ( ( ( P2 @ X5 )
% 5.31/5.52 | ( Q @ X5 ) )
% 5.31/5.52 = ( ( P2 @ ( minus_minus_real @ X5 @ ( times_times_real @ K4 @ D3 ) ) )
% 5.31/5.52 | ( Q @ ( minus_minus_real @ X5 @ ( times_times_real @ K4 @ D3 ) ) ) ) ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % inf_period(2)
% 5.31/5.52 thf(fact_2296_inf__period_I2_J,axiom,
% 5.31/5.52 ! [P2: rat > $o,D3: rat,Q: rat > $o] :
% 5.31/5.52 ( ! [X3: rat,K: rat] :
% 5.31/5.52 ( ( P2 @ X3 )
% 5.31/5.52 = ( P2 @ ( minus_minus_rat @ X3 @ ( times_times_rat @ K @ D3 ) ) ) )
% 5.31/5.52 => ( ! [X3: rat,K: rat] :
% 5.31/5.52 ( ( Q @ X3 )
% 5.31/5.52 = ( Q @ ( minus_minus_rat @ X3 @ ( times_times_rat @ K @ D3 ) ) ) )
% 5.31/5.52 => ! [X5: rat,K4: rat] :
% 5.31/5.52 ( ( ( P2 @ X5 )
% 5.31/5.52 | ( Q @ X5 ) )
% 5.31/5.52 = ( ( P2 @ ( minus_minus_rat @ X5 @ ( times_times_rat @ K4 @ D3 ) ) )
% 5.31/5.52 | ( Q @ ( minus_minus_rat @ X5 @ ( times_times_rat @ K4 @ D3 ) ) ) ) ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % inf_period(2)
% 5.31/5.52 thf(fact_2297_inf__period_I2_J,axiom,
% 5.31/5.52 ! [P2: int > $o,D3: int,Q: int > $o] :
% 5.31/5.52 ( ! [X3: int,K: int] :
% 5.31/5.52 ( ( P2 @ X3 )
% 5.31/5.52 = ( P2 @ ( minus_minus_int @ X3 @ ( times_times_int @ K @ D3 ) ) ) )
% 5.31/5.52 => ( ! [X3: int,K: int] :
% 5.31/5.52 ( ( Q @ X3 )
% 5.31/5.52 = ( Q @ ( minus_minus_int @ X3 @ ( times_times_int @ K @ D3 ) ) ) )
% 5.31/5.52 => ! [X5: int,K4: int] :
% 5.31/5.52 ( ( ( P2 @ X5 )
% 5.31/5.52 | ( Q @ X5 ) )
% 5.31/5.52 = ( ( P2 @ ( minus_minus_int @ X5 @ ( times_times_int @ K4 @ D3 ) ) )
% 5.31/5.52 | ( Q @ ( minus_minus_int @ X5 @ ( times_times_int @ K4 @ D3 ) ) ) ) ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % inf_period(2)
% 5.31/5.52 thf(fact_2298_inf__period_I1_J,axiom,
% 5.31/5.52 ! [P2: real > $o,D3: real,Q: real > $o] :
% 5.31/5.52 ( ! [X3: real,K: real] :
% 5.31/5.52 ( ( P2 @ X3 )
% 5.31/5.52 = ( P2 @ ( minus_minus_real @ X3 @ ( times_times_real @ K @ D3 ) ) ) )
% 5.31/5.52 => ( ! [X3: real,K: real] :
% 5.31/5.52 ( ( Q @ X3 )
% 5.31/5.52 = ( Q @ ( minus_minus_real @ X3 @ ( times_times_real @ K @ D3 ) ) ) )
% 5.31/5.52 => ! [X5: real,K4: real] :
% 5.31/5.52 ( ( ( P2 @ X5 )
% 5.31/5.52 & ( Q @ X5 ) )
% 5.31/5.52 = ( ( P2 @ ( minus_minus_real @ X5 @ ( times_times_real @ K4 @ D3 ) ) )
% 5.31/5.52 & ( Q @ ( minus_minus_real @ X5 @ ( times_times_real @ K4 @ D3 ) ) ) ) ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % inf_period(1)
% 5.31/5.52 thf(fact_2299_inf__period_I1_J,axiom,
% 5.31/5.52 ! [P2: rat > $o,D3: rat,Q: rat > $o] :
% 5.31/5.52 ( ! [X3: rat,K: rat] :
% 5.31/5.52 ( ( P2 @ X3 )
% 5.31/5.52 = ( P2 @ ( minus_minus_rat @ X3 @ ( times_times_rat @ K @ D3 ) ) ) )
% 5.31/5.52 => ( ! [X3: rat,K: rat] :
% 5.31/5.52 ( ( Q @ X3 )
% 5.31/5.52 = ( Q @ ( minus_minus_rat @ X3 @ ( times_times_rat @ K @ D3 ) ) ) )
% 5.31/5.52 => ! [X5: rat,K4: rat] :
% 5.31/5.52 ( ( ( P2 @ X5 )
% 5.31/5.52 & ( Q @ X5 ) )
% 5.31/5.52 = ( ( P2 @ ( minus_minus_rat @ X5 @ ( times_times_rat @ K4 @ D3 ) ) )
% 5.31/5.52 & ( Q @ ( minus_minus_rat @ X5 @ ( times_times_rat @ K4 @ D3 ) ) ) ) ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % inf_period(1)
% 5.31/5.52 thf(fact_2300_inf__period_I1_J,axiom,
% 5.31/5.52 ! [P2: int > $o,D3: int,Q: int > $o] :
% 5.31/5.52 ( ! [X3: int,K: int] :
% 5.31/5.52 ( ( P2 @ X3 )
% 5.31/5.52 = ( P2 @ ( minus_minus_int @ X3 @ ( times_times_int @ K @ D3 ) ) ) )
% 5.31/5.52 => ( ! [X3: int,K: int] :
% 5.31/5.52 ( ( Q @ X3 )
% 5.31/5.52 = ( Q @ ( minus_minus_int @ X3 @ ( times_times_int @ K @ D3 ) ) ) )
% 5.31/5.52 => ! [X5: int,K4: int] :
% 5.31/5.52 ( ( ( P2 @ X5 )
% 5.31/5.52 & ( Q @ X5 ) )
% 5.31/5.52 = ( ( P2 @ ( minus_minus_int @ X5 @ ( times_times_int @ K4 @ D3 ) ) )
% 5.31/5.52 & ( Q @ ( minus_minus_int @ X5 @ ( times_times_int @ K4 @ D3 ) ) ) ) ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % inf_period(1)
% 5.31/5.52 thf(fact_2301_verit__sum__simplify,axiom,
% 5.31/5.52 ! [A: complex] :
% 5.31/5.52 ( ( plus_plus_complex @ A @ zero_zero_complex )
% 5.31/5.52 = A ) ).
% 5.31/5.52
% 5.31/5.52 % verit_sum_simplify
% 5.31/5.52 thf(fact_2302_verit__sum__simplify,axiom,
% 5.31/5.52 ! [A: real] :
% 5.31/5.52 ( ( plus_plus_real @ A @ zero_zero_real )
% 5.31/5.52 = A ) ).
% 5.31/5.52
% 5.31/5.52 % verit_sum_simplify
% 5.31/5.52 thf(fact_2303_verit__sum__simplify,axiom,
% 5.31/5.52 ! [A: rat] :
% 5.31/5.52 ( ( plus_plus_rat @ A @ zero_zero_rat )
% 5.31/5.52 = A ) ).
% 5.31/5.52
% 5.31/5.52 % verit_sum_simplify
% 5.31/5.52 thf(fact_2304_verit__sum__simplify,axiom,
% 5.31/5.52 ! [A: nat] :
% 5.31/5.52 ( ( plus_plus_nat @ A @ zero_zero_nat )
% 5.31/5.52 = A ) ).
% 5.31/5.52
% 5.31/5.52 % verit_sum_simplify
% 5.31/5.52 thf(fact_2305_verit__sum__simplify,axiom,
% 5.31/5.52 ! [A: int] :
% 5.31/5.52 ( ( plus_plus_int @ A @ zero_zero_int )
% 5.31/5.52 = A ) ).
% 5.31/5.52
% 5.31/5.52 % verit_sum_simplify
% 5.31/5.52 thf(fact_2306_Gcd__empty,axiom,
% 5.31/5.52 ( ( gcd_Gcd_nat @ bot_bot_set_nat )
% 5.31/5.52 = zero_zero_nat ) ).
% 5.31/5.52
% 5.31/5.52 % Gcd_empty
% 5.31/5.52 thf(fact_2307_Gcd__empty,axiom,
% 5.31/5.52 ( ( gcd_Gcd_int @ bot_bot_set_int )
% 5.31/5.52 = zero_zero_int ) ).
% 5.31/5.52
% 5.31/5.52 % Gcd_empty
% 5.31/5.52 thf(fact_2308_Gcd__0__iff,axiom,
% 5.31/5.52 ! [A4: set_int] :
% 5.31/5.52 ( ( ( gcd_Gcd_int @ A4 )
% 5.31/5.52 = zero_zero_int )
% 5.31/5.52 = ( ord_less_eq_set_int @ A4 @ ( insert_int @ zero_zero_int @ bot_bot_set_int ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % Gcd_0_iff
% 5.31/5.52 thf(fact_2309_Gcd__0__iff,axiom,
% 5.31/5.52 ! [A4: set_nat] :
% 5.31/5.52 ( ( ( gcd_Gcd_nat @ A4 )
% 5.31/5.52 = zero_zero_nat )
% 5.31/5.52 = ( ord_less_eq_set_nat @ A4 @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % Gcd_0_iff
% 5.31/5.52 thf(fact_2310_verit__la__disequality,axiom,
% 5.31/5.52 ! [A: rat,B: rat] :
% 5.31/5.52 ( ( A = B )
% 5.31/5.52 | ~ ( ord_less_eq_rat @ A @ B )
% 5.31/5.52 | ~ ( ord_less_eq_rat @ B @ A ) ) ).
% 5.31/5.52
% 5.31/5.52 % verit_la_disequality
% 5.31/5.52 thf(fact_2311_verit__la__disequality,axiom,
% 5.31/5.52 ! [A: num,B: num] :
% 5.31/5.52 ( ( A = B )
% 5.31/5.52 | ~ ( ord_less_eq_num @ A @ B )
% 5.31/5.52 | ~ ( ord_less_eq_num @ B @ A ) ) ).
% 5.31/5.52
% 5.31/5.52 % verit_la_disequality
% 5.31/5.52 thf(fact_2312_verit__la__disequality,axiom,
% 5.31/5.52 ! [A: nat,B: nat] :
% 5.31/5.52 ( ( A = B )
% 5.31/5.52 | ~ ( ord_less_eq_nat @ A @ B )
% 5.31/5.52 | ~ ( ord_less_eq_nat @ B @ A ) ) ).
% 5.31/5.52
% 5.31/5.52 % verit_la_disequality
% 5.31/5.52 thf(fact_2313_verit__la__disequality,axiom,
% 5.31/5.52 ! [A: int,B: int] :
% 5.31/5.52 ( ( A = B )
% 5.31/5.52 | ~ ( ord_less_eq_int @ A @ B )
% 5.31/5.52 | ~ ( ord_less_eq_int @ B @ A ) ) ).
% 5.31/5.52
% 5.31/5.52 % verit_la_disequality
% 5.31/5.52 thf(fact_2314_verit__comp__simplify1_I2_J,axiom,
% 5.31/5.52 ! [A: set_nat] : ( ord_less_eq_set_nat @ A @ A ) ).
% 5.31/5.52
% 5.31/5.52 % verit_comp_simplify1(2)
% 5.31/5.52 thf(fact_2315_verit__comp__simplify1_I2_J,axiom,
% 5.31/5.52 ! [A: rat] : ( ord_less_eq_rat @ A @ A ) ).
% 5.31/5.52
% 5.31/5.52 % verit_comp_simplify1(2)
% 5.31/5.52 thf(fact_2316_verit__comp__simplify1_I2_J,axiom,
% 5.31/5.52 ! [A: num] : ( ord_less_eq_num @ A @ A ) ).
% 5.31/5.52
% 5.31/5.52 % verit_comp_simplify1(2)
% 5.31/5.52 thf(fact_2317_verit__comp__simplify1_I2_J,axiom,
% 5.31/5.52 ! [A: nat] : ( ord_less_eq_nat @ A @ A ) ).
% 5.31/5.52
% 5.31/5.52 % verit_comp_simplify1(2)
% 5.31/5.52 thf(fact_2318_verit__comp__simplify1_I2_J,axiom,
% 5.31/5.52 ! [A: int] : ( ord_less_eq_int @ A @ A ) ).
% 5.31/5.52
% 5.31/5.52 % verit_comp_simplify1(2)
% 5.31/5.52 thf(fact_2319_prod__decode__def,axiom,
% 5.31/5.52 ( nat_prod_decode
% 5.31/5.52 = ( nat_prod_decode_aux @ zero_zero_nat ) ) ).
% 5.31/5.52
% 5.31/5.52 % prod_decode_def
% 5.31/5.52 thf(fact_2320_verit__comp__simplify1_I3_J,axiom,
% 5.31/5.52 ! [B2: real,A2: real] :
% 5.31/5.52 ( ( ~ ( ord_less_eq_real @ B2 @ A2 ) )
% 5.31/5.52 = ( ord_less_real @ A2 @ B2 ) ) ).
% 5.31/5.52
% 5.31/5.52 % verit_comp_simplify1(3)
% 5.31/5.52 thf(fact_2321_verit__comp__simplify1_I3_J,axiom,
% 5.31/5.52 ! [B2: rat,A2: rat] :
% 5.31/5.52 ( ( ~ ( ord_less_eq_rat @ B2 @ A2 ) )
% 5.31/5.52 = ( ord_less_rat @ A2 @ B2 ) ) ).
% 5.31/5.52
% 5.31/5.52 % verit_comp_simplify1(3)
% 5.31/5.52 thf(fact_2322_verit__comp__simplify1_I3_J,axiom,
% 5.31/5.52 ! [B2: num,A2: num] :
% 5.31/5.52 ( ( ~ ( ord_less_eq_num @ B2 @ A2 ) )
% 5.31/5.52 = ( ord_less_num @ A2 @ B2 ) ) ).
% 5.31/5.52
% 5.31/5.52 % verit_comp_simplify1(3)
% 5.31/5.52 thf(fact_2323_verit__comp__simplify1_I3_J,axiom,
% 5.31/5.52 ! [B2: nat,A2: nat] :
% 5.31/5.52 ( ( ~ ( ord_less_eq_nat @ B2 @ A2 ) )
% 5.31/5.52 = ( ord_less_nat @ A2 @ B2 ) ) ).
% 5.31/5.52
% 5.31/5.52 % verit_comp_simplify1(3)
% 5.31/5.52 thf(fact_2324_verit__comp__simplify1_I3_J,axiom,
% 5.31/5.52 ! [B2: int,A2: int] :
% 5.31/5.52 ( ( ~ ( ord_less_eq_int @ B2 @ A2 ) )
% 5.31/5.52 = ( ord_less_int @ A2 @ B2 ) ) ).
% 5.31/5.52
% 5.31/5.52 % verit_comp_simplify1(3)
% 5.31/5.52 thf(fact_2325_pinf_I6_J,axiom,
% 5.31/5.52 ! [T: real] :
% 5.31/5.52 ? [Z: real] :
% 5.31/5.52 ! [X5: real] :
% 5.31/5.52 ( ( ord_less_real @ Z @ X5 )
% 5.31/5.52 => ~ ( ord_less_eq_real @ X5 @ T ) ) ).
% 5.31/5.52
% 5.31/5.52 % pinf(6)
% 5.31/5.52 thf(fact_2326_pinf_I6_J,axiom,
% 5.31/5.52 ! [T: rat] :
% 5.31/5.52 ? [Z: rat] :
% 5.31/5.52 ! [X5: rat] :
% 5.31/5.52 ( ( ord_less_rat @ Z @ X5 )
% 5.31/5.52 => ~ ( ord_less_eq_rat @ X5 @ T ) ) ).
% 5.31/5.52
% 5.31/5.52 % pinf(6)
% 5.31/5.52 thf(fact_2327_pinf_I6_J,axiom,
% 5.31/5.52 ! [T: num] :
% 5.31/5.52 ? [Z: num] :
% 5.31/5.52 ! [X5: num] :
% 5.31/5.52 ( ( ord_less_num @ Z @ X5 )
% 5.31/5.52 => ~ ( ord_less_eq_num @ X5 @ T ) ) ).
% 5.31/5.52
% 5.31/5.52 % pinf(6)
% 5.31/5.52 thf(fact_2328_pinf_I6_J,axiom,
% 5.31/5.52 ! [T: nat] :
% 5.31/5.52 ? [Z: nat] :
% 5.31/5.52 ! [X5: nat] :
% 5.31/5.52 ( ( ord_less_nat @ Z @ X5 )
% 5.31/5.52 => ~ ( ord_less_eq_nat @ X5 @ T ) ) ).
% 5.31/5.52
% 5.31/5.52 % pinf(6)
% 5.31/5.52 thf(fact_2329_pinf_I6_J,axiom,
% 5.31/5.52 ! [T: int] :
% 5.31/5.52 ? [Z: int] :
% 5.31/5.52 ! [X5: int] :
% 5.31/5.52 ( ( ord_less_int @ Z @ X5 )
% 5.31/5.52 => ~ ( ord_less_eq_int @ X5 @ T ) ) ).
% 5.31/5.52
% 5.31/5.52 % pinf(6)
% 5.31/5.52 thf(fact_2330_pinf_I8_J,axiom,
% 5.31/5.52 ! [T: real] :
% 5.31/5.52 ? [Z: real] :
% 5.31/5.52 ! [X5: real] :
% 5.31/5.52 ( ( ord_less_real @ Z @ X5 )
% 5.31/5.52 => ( ord_less_eq_real @ T @ X5 ) ) ).
% 5.31/5.52
% 5.31/5.52 % pinf(8)
% 5.31/5.52 thf(fact_2331_pinf_I8_J,axiom,
% 5.31/5.52 ! [T: rat] :
% 5.31/5.52 ? [Z: rat] :
% 5.31/5.52 ! [X5: rat] :
% 5.31/5.52 ( ( ord_less_rat @ Z @ X5 )
% 5.31/5.52 => ( ord_less_eq_rat @ T @ X5 ) ) ).
% 5.31/5.52
% 5.31/5.52 % pinf(8)
% 5.31/5.52 thf(fact_2332_pinf_I8_J,axiom,
% 5.31/5.52 ! [T: num] :
% 5.31/5.52 ? [Z: num] :
% 5.31/5.52 ! [X5: num] :
% 5.31/5.52 ( ( ord_less_num @ Z @ X5 )
% 5.31/5.52 => ( ord_less_eq_num @ T @ X5 ) ) ).
% 5.31/5.52
% 5.31/5.52 % pinf(8)
% 5.31/5.52 thf(fact_2333_pinf_I8_J,axiom,
% 5.31/5.52 ! [T: nat] :
% 5.31/5.52 ? [Z: nat] :
% 5.31/5.52 ! [X5: nat] :
% 5.31/5.52 ( ( ord_less_nat @ Z @ X5 )
% 5.31/5.52 => ( ord_less_eq_nat @ T @ X5 ) ) ).
% 5.31/5.52
% 5.31/5.52 % pinf(8)
% 5.31/5.52 thf(fact_2334_pinf_I8_J,axiom,
% 5.31/5.52 ! [T: int] :
% 5.31/5.52 ? [Z: int] :
% 5.31/5.52 ! [X5: int] :
% 5.31/5.52 ( ( ord_less_int @ Z @ X5 )
% 5.31/5.52 => ( ord_less_eq_int @ T @ X5 ) ) ).
% 5.31/5.52
% 5.31/5.52 % pinf(8)
% 5.31/5.52 thf(fact_2335_minf_I6_J,axiom,
% 5.31/5.52 ! [T: real] :
% 5.31/5.52 ? [Z: real] :
% 5.31/5.52 ! [X5: real] :
% 5.31/5.52 ( ( ord_less_real @ X5 @ Z )
% 5.31/5.52 => ( ord_less_eq_real @ X5 @ T ) ) ).
% 5.31/5.52
% 5.31/5.52 % minf(6)
% 5.31/5.52 thf(fact_2336_minf_I6_J,axiom,
% 5.31/5.52 ! [T: rat] :
% 5.31/5.52 ? [Z: rat] :
% 5.31/5.52 ! [X5: rat] :
% 5.31/5.52 ( ( ord_less_rat @ X5 @ Z )
% 5.31/5.52 => ( ord_less_eq_rat @ X5 @ T ) ) ).
% 5.31/5.52
% 5.31/5.52 % minf(6)
% 5.31/5.52 thf(fact_2337_minf_I6_J,axiom,
% 5.31/5.52 ! [T: num] :
% 5.31/5.52 ? [Z: num] :
% 5.31/5.52 ! [X5: num] :
% 5.31/5.52 ( ( ord_less_num @ X5 @ Z )
% 5.31/5.52 => ( ord_less_eq_num @ X5 @ T ) ) ).
% 5.31/5.52
% 5.31/5.52 % minf(6)
% 5.31/5.52 thf(fact_2338_minf_I6_J,axiom,
% 5.31/5.52 ! [T: nat] :
% 5.31/5.52 ? [Z: nat] :
% 5.31/5.52 ! [X5: nat] :
% 5.31/5.52 ( ( ord_less_nat @ X5 @ Z )
% 5.31/5.52 => ( ord_less_eq_nat @ X5 @ T ) ) ).
% 5.31/5.52
% 5.31/5.52 % minf(6)
% 5.31/5.52 thf(fact_2339_minf_I6_J,axiom,
% 5.31/5.52 ! [T: int] :
% 5.31/5.52 ? [Z: int] :
% 5.31/5.52 ! [X5: int] :
% 5.31/5.52 ( ( ord_less_int @ X5 @ Z )
% 5.31/5.52 => ( ord_less_eq_int @ X5 @ T ) ) ).
% 5.31/5.52
% 5.31/5.52 % minf(6)
% 5.31/5.52 thf(fact_2340_minf_I8_J,axiom,
% 5.31/5.52 ! [T: real] :
% 5.31/5.52 ? [Z: real] :
% 5.31/5.52 ! [X5: real] :
% 5.31/5.52 ( ( ord_less_real @ X5 @ Z )
% 5.31/5.52 => ~ ( ord_less_eq_real @ T @ X5 ) ) ).
% 5.31/5.52
% 5.31/5.52 % minf(8)
% 5.31/5.52 thf(fact_2341_minf_I8_J,axiom,
% 5.31/5.52 ! [T: rat] :
% 5.31/5.52 ? [Z: rat] :
% 5.31/5.52 ! [X5: rat] :
% 5.31/5.52 ( ( ord_less_rat @ X5 @ Z )
% 5.31/5.52 => ~ ( ord_less_eq_rat @ T @ X5 ) ) ).
% 5.31/5.52
% 5.31/5.52 % minf(8)
% 5.31/5.52 thf(fact_2342_minf_I8_J,axiom,
% 5.31/5.52 ! [T: num] :
% 5.31/5.52 ? [Z: num] :
% 5.31/5.52 ! [X5: num] :
% 5.31/5.52 ( ( ord_less_num @ X5 @ Z )
% 5.31/5.52 => ~ ( ord_less_eq_num @ T @ X5 ) ) ).
% 5.31/5.52
% 5.31/5.52 % minf(8)
% 5.31/5.52 thf(fact_2343_minf_I8_J,axiom,
% 5.31/5.52 ! [T: nat] :
% 5.31/5.52 ? [Z: nat] :
% 5.31/5.52 ! [X5: nat] :
% 5.31/5.52 ( ( ord_less_nat @ X5 @ Z )
% 5.31/5.52 => ~ ( ord_less_eq_nat @ T @ X5 ) ) ).
% 5.31/5.52
% 5.31/5.52 % minf(8)
% 5.31/5.52 thf(fact_2344_minf_I8_J,axiom,
% 5.31/5.52 ! [T: int] :
% 5.31/5.52 ? [Z: int] :
% 5.31/5.52 ! [X5: int] :
% 5.31/5.52 ( ( ord_less_int @ X5 @ Z )
% 5.31/5.52 => ~ ( ord_less_eq_int @ T @ X5 ) ) ).
% 5.31/5.52
% 5.31/5.52 % minf(8)
% 5.31/5.52 thf(fact_2345_length__product,axiom,
% 5.31/5.52 ! [Xs2: list_VEBT_VEBT,Ys: list_VEBT_VEBT] :
% 5.31/5.52 ( ( size_s7466405169056248089T_VEBT @ ( produc4743750530478302277T_VEBT @ Xs2 @ Ys ) )
% 5.31/5.52 = ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % length_product
% 5.31/5.52 thf(fact_2346_length__product,axiom,
% 5.31/5.52 ! [Xs2: list_VEBT_VEBT,Ys: list_o] :
% 5.31/5.52 ( ( size_s9168528473962070013VEBT_o @ ( product_VEBT_VEBT_o @ Xs2 @ Ys ) )
% 5.31/5.52 = ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) @ ( size_size_list_o @ Ys ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % length_product
% 5.31/5.52 thf(fact_2347_length__product,axiom,
% 5.31/5.52 ! [Xs2: list_VEBT_VEBT,Ys: list_nat] :
% 5.31/5.52 ( ( size_s6152045936467909847BT_nat @ ( produc7295137177222721919BT_nat @ Xs2 @ Ys ) )
% 5.31/5.52 = ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) @ ( size_size_list_nat @ Ys ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % length_product
% 5.31/5.52 thf(fact_2348_length__product,axiom,
% 5.31/5.52 ! [Xs2: list_VEBT_VEBT,Ys: list_int] :
% 5.31/5.52 ( ( size_s3661962791536183091BT_int @ ( produc7292646706713671643BT_int @ Xs2 @ Ys ) )
% 5.31/5.52 = ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) @ ( size_size_list_int @ Ys ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % length_product
% 5.31/5.52 thf(fact_2349_length__product,axiom,
% 5.31/5.52 ! [Xs2: list_o,Ys: list_VEBT_VEBT] :
% 5.31/5.52 ( ( size_s4313452262239582901T_VEBT @ ( product_o_VEBT_VEBT @ Xs2 @ Ys ) )
% 5.31/5.52 = ( times_times_nat @ ( size_size_list_o @ Xs2 ) @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % length_product
% 5.31/5.52 thf(fact_2350_length__product,axiom,
% 5.31/5.52 ! [Xs2: list_o,Ys: list_o] :
% 5.31/5.52 ( ( size_s1515746228057227161od_o_o @ ( product_o_o @ Xs2 @ Ys ) )
% 5.31/5.52 = ( times_times_nat @ ( size_size_list_o @ Xs2 ) @ ( size_size_list_o @ Ys ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % length_product
% 5.31/5.52 thf(fact_2351_length__product,axiom,
% 5.31/5.52 ! [Xs2: list_o,Ys: list_nat] :
% 5.31/5.52 ( ( size_s5443766701097040955_o_nat @ ( product_o_nat @ Xs2 @ Ys ) )
% 5.31/5.52 = ( times_times_nat @ ( size_size_list_o @ Xs2 ) @ ( size_size_list_nat @ Ys ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % length_product
% 5.31/5.52 thf(fact_2352_length__product,axiom,
% 5.31/5.52 ! [Xs2: list_o,Ys: list_int] :
% 5.31/5.52 ( ( size_s2953683556165314199_o_int @ ( product_o_int @ Xs2 @ Ys ) )
% 5.31/5.52 = ( times_times_nat @ ( size_size_list_o @ Xs2 ) @ ( size_size_list_int @ Ys ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % length_product
% 5.31/5.52 thf(fact_2353_length__product,axiom,
% 5.31/5.52 ! [Xs2: list_nat,Ys: list_VEBT_VEBT] :
% 5.31/5.52 ( ( size_s4762443039079500285T_VEBT @ ( produc7156399406898700509T_VEBT @ Xs2 @ Ys ) )
% 5.31/5.52 = ( times_times_nat @ ( size_size_list_nat @ Xs2 ) @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % length_product
% 5.31/5.52 thf(fact_2354_length__product,axiom,
% 5.31/5.52 ! [Xs2: list_nat,Ys: list_o] :
% 5.31/5.52 ( ( size_s6491369823275344609_nat_o @ ( product_nat_o @ Xs2 @ Ys ) )
% 5.31/5.52 = ( times_times_nat @ ( size_size_list_nat @ Xs2 ) @ ( size_size_list_o @ Ys ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % length_product
% 5.31/5.52 thf(fact_2355_complete__interval,axiom,
% 5.31/5.52 ! [A: real,B: real,P2: real > $o] :
% 5.31/5.52 ( ( ord_less_real @ A @ B )
% 5.31/5.52 => ( ( P2 @ A )
% 5.31/5.52 => ( ~ ( P2 @ B )
% 5.31/5.52 => ? [C: real] :
% 5.31/5.52 ( ( ord_less_eq_real @ A @ C )
% 5.31/5.52 & ( ord_less_eq_real @ C @ B )
% 5.31/5.52 & ! [X5: real] :
% 5.31/5.52 ( ( ( ord_less_eq_real @ A @ X5 )
% 5.31/5.52 & ( ord_less_real @ X5 @ C ) )
% 5.31/5.52 => ( P2 @ X5 ) )
% 5.31/5.52 & ! [D4: real] :
% 5.31/5.52 ( ! [X3: real] :
% 5.31/5.52 ( ( ( ord_less_eq_real @ A @ X3 )
% 5.31/5.52 & ( ord_less_real @ X3 @ D4 ) )
% 5.31/5.52 => ( P2 @ X3 ) )
% 5.31/5.52 => ( ord_less_eq_real @ D4 @ C ) ) ) ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % complete_interval
% 5.31/5.52 thf(fact_2356_complete__interval,axiom,
% 5.31/5.52 ! [A: nat,B: nat,P2: nat > $o] :
% 5.31/5.52 ( ( ord_less_nat @ A @ B )
% 5.31/5.52 => ( ( P2 @ A )
% 5.31/5.52 => ( ~ ( P2 @ B )
% 5.31/5.52 => ? [C: nat] :
% 5.31/5.52 ( ( ord_less_eq_nat @ A @ C )
% 5.31/5.52 & ( ord_less_eq_nat @ C @ B )
% 5.31/5.52 & ! [X5: nat] :
% 5.31/5.52 ( ( ( ord_less_eq_nat @ A @ X5 )
% 5.31/5.52 & ( ord_less_nat @ X5 @ C ) )
% 5.31/5.52 => ( P2 @ X5 ) )
% 5.31/5.52 & ! [D4: nat] :
% 5.31/5.52 ( ! [X3: nat] :
% 5.31/5.52 ( ( ( ord_less_eq_nat @ A @ X3 )
% 5.31/5.52 & ( ord_less_nat @ X3 @ D4 ) )
% 5.31/5.52 => ( P2 @ X3 ) )
% 5.31/5.52 => ( ord_less_eq_nat @ D4 @ C ) ) ) ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % complete_interval
% 5.31/5.52 thf(fact_2357_complete__interval,axiom,
% 5.31/5.52 ! [A: int,B: int,P2: int > $o] :
% 5.31/5.52 ( ( ord_less_int @ A @ B )
% 5.31/5.52 => ( ( P2 @ A )
% 5.31/5.52 => ( ~ ( P2 @ B )
% 5.31/5.52 => ? [C: int] :
% 5.31/5.52 ( ( ord_less_eq_int @ A @ C )
% 5.31/5.52 & ( ord_less_eq_int @ C @ B )
% 5.31/5.52 & ! [X5: int] :
% 5.31/5.52 ( ( ( ord_less_eq_int @ A @ X5 )
% 5.31/5.52 & ( ord_less_int @ X5 @ C ) )
% 5.31/5.52 => ( P2 @ X5 ) )
% 5.31/5.52 & ! [D4: int] :
% 5.31/5.52 ( ! [X3: int] :
% 5.31/5.52 ( ( ( ord_less_eq_int @ A @ X3 )
% 5.31/5.52 & ( ord_less_int @ X3 @ D4 ) )
% 5.31/5.52 => ( P2 @ X3 ) )
% 5.31/5.52 => ( ord_less_eq_int @ D4 @ C ) ) ) ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % complete_interval
% 5.31/5.52 thf(fact_2358_vebt__insert_Osimps_I4_J,axiom,
% 5.31/5.52 ! [V2: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 5.31/5.52 ( ( vEBT_vebt_insert @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V2 ) ) @ TreeList2 @ Summary ) @ X )
% 5.31/5.52 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ X @ X ) ) @ ( suc @ ( suc @ V2 ) ) @ TreeList2 @ Summary ) ) ).
% 5.31/5.52
% 5.31/5.52 % vebt_insert.simps(4)
% 5.31/5.52 thf(fact_2359_nth__zip,axiom,
% 5.31/5.52 ! [I2: nat,Xs2: list_Code_integer,Ys: list_Code_integer] :
% 5.31/5.52 ( ( ord_less_nat @ I2 @ ( size_s3445333598471063425nteger @ Xs2 ) )
% 5.31/5.52 => ( ( ord_less_nat @ I2 @ ( size_s3445333598471063425nteger @ Ys ) )
% 5.31/5.52 => ( ( nth_Pr2304437835452373666nteger @ ( zip_Co3543743374963494515nteger @ Xs2 @ Ys ) @ I2 )
% 5.31/5.52 = ( produc1086072967326762835nteger @ ( nth_Code_integer @ Xs2 @ I2 ) @ ( nth_Code_integer @ Ys @ I2 ) ) ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % nth_zip
% 5.31/5.52 thf(fact_2360_nth__zip,axiom,
% 5.31/5.52 ! [I2: nat,Xs2: list_VEBT_VEBT,Ys: list_VEBT_VEBT] :
% 5.31/5.52 ( ( ord_less_nat @ I2 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 5.31/5.52 => ( ( ord_less_nat @ I2 @ ( size_s6755466524823107622T_VEBT @ Ys ) )
% 5.31/5.52 => ( ( nth_Pr4953567300277697838T_VEBT @ ( zip_VE537291747668921783T_VEBT @ Xs2 @ Ys ) @ I2 )
% 5.31/5.52 = ( produc537772716801021591T_VEBT @ ( nth_VEBT_VEBT @ Xs2 @ I2 ) @ ( nth_VEBT_VEBT @ Ys @ I2 ) ) ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % nth_zip
% 5.31/5.52 thf(fact_2361_nth__zip,axiom,
% 5.31/5.52 ! [I2: nat,Xs2: list_VEBT_VEBT,Ys: list_o] :
% 5.31/5.52 ( ( ord_less_nat @ I2 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 5.31/5.52 => ( ( ord_less_nat @ I2 @ ( size_size_list_o @ Ys ) )
% 5.31/5.52 => ( ( nth_Pr4606735188037164562VEBT_o @ ( zip_VEBT_VEBT_o @ Xs2 @ Ys ) @ I2 )
% 5.31/5.52 = ( produc8721562602347293563VEBT_o @ ( nth_VEBT_VEBT @ Xs2 @ I2 ) @ ( nth_o @ Ys @ I2 ) ) ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % nth_zip
% 5.31/5.52 thf(fact_2362_nth__zip,axiom,
% 5.31/5.52 ! [I2: nat,Xs2: list_VEBT_VEBT,Ys: list_nat] :
% 5.31/5.52 ( ( ord_less_nat @ I2 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 5.31/5.52 => ( ( ord_less_nat @ I2 @ ( size_size_list_nat @ Ys ) )
% 5.31/5.52 => ( ( nth_Pr1791586995822124652BT_nat @ ( zip_VEBT_VEBT_nat @ Xs2 @ Ys ) @ I2 )
% 5.31/5.52 = ( produc738532404422230701BT_nat @ ( nth_VEBT_VEBT @ Xs2 @ I2 ) @ ( nth_nat @ Ys @ I2 ) ) ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % nth_zip
% 5.31/5.52 thf(fact_2363_nth__zip,axiom,
% 5.31/5.52 ! [I2: nat,Xs2: list_VEBT_VEBT,Ys: list_int] :
% 5.31/5.52 ( ( ord_less_nat @ I2 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 5.31/5.52 => ( ( ord_less_nat @ I2 @ ( size_size_list_int @ Ys ) )
% 5.31/5.52 => ( ( nth_Pr6837108013167703752BT_int @ ( zip_VEBT_VEBT_int @ Xs2 @ Ys ) @ I2 )
% 5.31/5.52 = ( produc736041933913180425BT_int @ ( nth_VEBT_VEBT @ Xs2 @ I2 ) @ ( nth_int @ Ys @ I2 ) ) ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % nth_zip
% 5.31/5.52 thf(fact_2364_nth__zip,axiom,
% 5.31/5.52 ! [I2: nat,Xs2: list_o,Ys: list_VEBT_VEBT] :
% 5.31/5.52 ( ( ord_less_nat @ I2 @ ( size_size_list_o @ Xs2 ) )
% 5.31/5.52 => ( ( ord_less_nat @ I2 @ ( size_s6755466524823107622T_VEBT @ Ys ) )
% 5.31/5.52 => ( ( nth_Pr6777367263587873994T_VEBT @ ( zip_o_VEBT_VEBT @ Xs2 @ Ys ) @ I2 )
% 5.31/5.52 = ( produc2982872950893828659T_VEBT @ ( nth_o @ Xs2 @ I2 ) @ ( nth_VEBT_VEBT @ Ys @ I2 ) ) ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % nth_zip
% 5.31/5.52 thf(fact_2365_nth__zip,axiom,
% 5.31/5.52 ! [I2: nat,Xs2: list_o,Ys: list_o] :
% 5.31/5.52 ( ( ord_less_nat @ I2 @ ( size_size_list_o @ Xs2 ) )
% 5.31/5.52 => ( ( ord_less_nat @ I2 @ ( size_size_list_o @ Ys ) )
% 5.31/5.52 => ( ( nth_Product_prod_o_o @ ( zip_o_o @ Xs2 @ Ys ) @ I2 )
% 5.31/5.52 = ( product_Pair_o_o @ ( nth_o @ Xs2 @ I2 ) @ ( nth_o @ Ys @ I2 ) ) ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % nth_zip
% 5.31/5.52 thf(fact_2366_nth__zip,axiom,
% 5.31/5.52 ! [I2: nat,Xs2: list_o,Ys: list_nat] :
% 5.31/5.52 ( ( ord_less_nat @ I2 @ ( size_size_list_o @ Xs2 ) )
% 5.31/5.52 => ( ( ord_less_nat @ I2 @ ( size_size_list_nat @ Ys ) )
% 5.31/5.52 => ( ( nth_Pr5826913651314560976_o_nat @ ( zip_o_nat @ Xs2 @ Ys ) @ I2 )
% 5.31/5.52 = ( product_Pair_o_nat @ ( nth_o @ Xs2 @ I2 ) @ ( nth_nat @ Ys @ I2 ) ) ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % nth_zip
% 5.31/5.52 thf(fact_2367_nth__zip,axiom,
% 5.31/5.52 ! [I2: nat,Xs2: list_o,Ys: list_int] :
% 5.31/5.52 ( ( ord_less_nat @ I2 @ ( size_size_list_o @ Xs2 ) )
% 5.31/5.52 => ( ( ord_less_nat @ I2 @ ( size_size_list_int @ Ys ) )
% 5.31/5.52 => ( ( nth_Pr1649062631805364268_o_int @ ( zip_o_int @ Xs2 @ Ys ) @ I2 )
% 5.31/5.52 = ( product_Pair_o_int @ ( nth_o @ Xs2 @ I2 ) @ ( nth_int @ Ys @ I2 ) ) ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % nth_zip
% 5.31/5.52 thf(fact_2368_nth__zip,axiom,
% 5.31/5.52 ! [I2: nat,Xs2: list_nat,Ys: list_VEBT_VEBT] :
% 5.31/5.52 ( ( ord_less_nat @ I2 @ ( size_size_list_nat @ Xs2 ) )
% 5.31/5.52 => ( ( ord_less_nat @ I2 @ ( size_s6755466524823107622T_VEBT @ Ys ) )
% 5.31/5.52 => ( ( nth_Pr744662078594809490T_VEBT @ ( zip_nat_VEBT_VEBT @ Xs2 @ Ys ) @ I2 )
% 5.31/5.52 = ( produc599794634098209291T_VEBT @ ( nth_nat @ Xs2 @ I2 ) @ ( nth_VEBT_VEBT @ Ys @ I2 ) ) ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % nth_zip
% 5.31/5.52 thf(fact_2369_find__Some__iff2,axiom,
% 5.31/5.52 ! [X: product_prod_nat_nat,P2: product_prod_nat_nat > $o,Xs2: list_P6011104703257516679at_nat] :
% 5.31/5.52 ( ( ( some_P7363390416028606310at_nat @ X )
% 5.31/5.52 = ( find_P8199882355184865565at_nat @ P2 @ Xs2 ) )
% 5.31/5.52 = ( ? [I: nat] :
% 5.31/5.52 ( ( ord_less_nat @ I @ ( size_s5460976970255530739at_nat @ Xs2 ) )
% 5.31/5.52 & ( P2 @ ( nth_Pr7617993195940197384at_nat @ Xs2 @ I ) )
% 5.31/5.52 & ( X
% 5.31/5.52 = ( nth_Pr7617993195940197384at_nat @ Xs2 @ I ) )
% 5.31/5.52 & ! [J: nat] :
% 5.31/5.52 ( ( ord_less_nat @ J @ I )
% 5.31/5.52 => ~ ( P2 @ ( nth_Pr7617993195940197384at_nat @ Xs2 @ J ) ) ) ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % find_Some_iff2
% 5.31/5.52 thf(fact_2370_find__Some__iff2,axiom,
% 5.31/5.52 ! [X: num,P2: num > $o,Xs2: list_num] :
% 5.31/5.52 ( ( ( some_num @ X )
% 5.31/5.52 = ( find_num @ P2 @ Xs2 ) )
% 5.31/5.52 = ( ? [I: nat] :
% 5.31/5.52 ( ( ord_less_nat @ I @ ( size_size_list_num @ Xs2 ) )
% 5.31/5.52 & ( P2 @ ( nth_num @ Xs2 @ I ) )
% 5.31/5.52 & ( X
% 5.31/5.52 = ( nth_num @ Xs2 @ I ) )
% 5.31/5.52 & ! [J: nat] :
% 5.31/5.52 ( ( ord_less_nat @ J @ I )
% 5.31/5.52 => ~ ( P2 @ ( nth_num @ Xs2 @ J ) ) ) ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % find_Some_iff2
% 5.31/5.52 thf(fact_2371_find__Some__iff2,axiom,
% 5.31/5.52 ! [X: vEBT_VEBT,P2: vEBT_VEBT > $o,Xs2: list_VEBT_VEBT] :
% 5.31/5.52 ( ( ( some_VEBT_VEBT @ X )
% 5.31/5.52 = ( find_VEBT_VEBT @ P2 @ Xs2 ) )
% 5.31/5.52 = ( ? [I: nat] :
% 5.31/5.52 ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 5.31/5.52 & ( P2 @ ( nth_VEBT_VEBT @ Xs2 @ I ) )
% 5.31/5.52 & ( X
% 5.31/5.52 = ( nth_VEBT_VEBT @ Xs2 @ I ) )
% 5.31/5.52 & ! [J: nat] :
% 5.31/5.52 ( ( ord_less_nat @ J @ I )
% 5.31/5.52 => ~ ( P2 @ ( nth_VEBT_VEBT @ Xs2 @ J ) ) ) ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % find_Some_iff2
% 5.31/5.52 thf(fact_2372_find__Some__iff2,axiom,
% 5.31/5.52 ! [X: $o,P2: $o > $o,Xs2: list_o] :
% 5.31/5.52 ( ( ( some_o @ X )
% 5.31/5.52 = ( find_o @ P2 @ Xs2 ) )
% 5.31/5.52 = ( ? [I: nat] :
% 5.31/5.52 ( ( ord_less_nat @ I @ ( size_size_list_o @ Xs2 ) )
% 5.31/5.52 & ( P2 @ ( nth_o @ Xs2 @ I ) )
% 5.31/5.52 & ( X
% 5.31/5.52 = ( nth_o @ Xs2 @ I ) )
% 5.31/5.52 & ! [J: nat] :
% 5.31/5.52 ( ( ord_less_nat @ J @ I )
% 5.31/5.52 => ~ ( P2 @ ( nth_o @ Xs2 @ J ) ) ) ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % find_Some_iff2
% 5.31/5.52 thf(fact_2373_find__Some__iff2,axiom,
% 5.31/5.52 ! [X: nat,P2: nat > $o,Xs2: list_nat] :
% 5.31/5.52 ( ( ( some_nat @ X )
% 5.31/5.52 = ( find_nat @ P2 @ Xs2 ) )
% 5.31/5.52 = ( ? [I: nat] :
% 5.31/5.52 ( ( ord_less_nat @ I @ ( size_size_list_nat @ Xs2 ) )
% 5.31/5.52 & ( P2 @ ( nth_nat @ Xs2 @ I ) )
% 5.31/5.52 & ( X
% 5.31/5.52 = ( nth_nat @ Xs2 @ I ) )
% 5.31/5.52 & ! [J: nat] :
% 5.31/5.52 ( ( ord_less_nat @ J @ I )
% 5.31/5.52 => ~ ( P2 @ ( nth_nat @ Xs2 @ J ) ) ) ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % find_Some_iff2
% 5.31/5.52 thf(fact_2374_find__Some__iff2,axiom,
% 5.31/5.52 ! [X: int,P2: int > $o,Xs2: list_int] :
% 5.31/5.52 ( ( ( some_int @ X )
% 5.31/5.52 = ( find_int @ P2 @ Xs2 ) )
% 5.31/5.52 = ( ? [I: nat] :
% 5.31/5.52 ( ( ord_less_nat @ I @ ( size_size_list_int @ Xs2 ) )
% 5.31/5.52 & ( P2 @ ( nth_int @ Xs2 @ I ) )
% 5.31/5.52 & ( X
% 5.31/5.52 = ( nth_int @ Xs2 @ I ) )
% 5.31/5.52 & ! [J: nat] :
% 5.31/5.52 ( ( ord_less_nat @ J @ I )
% 5.31/5.52 => ~ ( P2 @ ( nth_int @ Xs2 @ J ) ) ) ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % find_Some_iff2
% 5.31/5.52 thf(fact_2375_find__Some__iff,axiom,
% 5.31/5.52 ! [P2: product_prod_nat_nat > $o,Xs2: list_P6011104703257516679at_nat,X: product_prod_nat_nat] :
% 5.31/5.52 ( ( ( find_P8199882355184865565at_nat @ P2 @ Xs2 )
% 5.31/5.52 = ( some_P7363390416028606310at_nat @ X ) )
% 5.31/5.52 = ( ? [I: nat] :
% 5.31/5.52 ( ( ord_less_nat @ I @ ( size_s5460976970255530739at_nat @ Xs2 ) )
% 5.31/5.52 & ( P2 @ ( nth_Pr7617993195940197384at_nat @ Xs2 @ I ) )
% 5.31/5.52 & ( X
% 5.31/5.52 = ( nth_Pr7617993195940197384at_nat @ Xs2 @ I ) )
% 5.31/5.52 & ! [J: nat] :
% 5.31/5.52 ( ( ord_less_nat @ J @ I )
% 5.31/5.52 => ~ ( P2 @ ( nth_Pr7617993195940197384at_nat @ Xs2 @ J ) ) ) ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % find_Some_iff
% 5.31/5.52 thf(fact_2376_find__Some__iff,axiom,
% 5.31/5.52 ! [P2: num > $o,Xs2: list_num,X: num] :
% 5.31/5.52 ( ( ( find_num @ P2 @ Xs2 )
% 5.31/5.52 = ( some_num @ X ) )
% 5.31/5.52 = ( ? [I: nat] :
% 5.31/5.52 ( ( ord_less_nat @ I @ ( size_size_list_num @ Xs2 ) )
% 5.31/5.52 & ( P2 @ ( nth_num @ Xs2 @ I ) )
% 5.31/5.52 & ( X
% 5.31/5.52 = ( nth_num @ Xs2 @ I ) )
% 5.31/5.52 & ! [J: nat] :
% 5.31/5.52 ( ( ord_less_nat @ J @ I )
% 5.31/5.52 => ~ ( P2 @ ( nth_num @ Xs2 @ J ) ) ) ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % find_Some_iff
% 5.31/5.52 thf(fact_2377_find__Some__iff,axiom,
% 5.31/5.52 ! [P2: vEBT_VEBT > $o,Xs2: list_VEBT_VEBT,X: vEBT_VEBT] :
% 5.31/5.52 ( ( ( find_VEBT_VEBT @ P2 @ Xs2 )
% 5.31/5.52 = ( some_VEBT_VEBT @ X ) )
% 5.31/5.52 = ( ? [I: nat] :
% 5.31/5.52 ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 5.31/5.52 & ( P2 @ ( nth_VEBT_VEBT @ Xs2 @ I ) )
% 5.31/5.52 & ( X
% 5.31/5.52 = ( nth_VEBT_VEBT @ Xs2 @ I ) )
% 5.31/5.52 & ! [J: nat] :
% 5.31/5.52 ( ( ord_less_nat @ J @ I )
% 5.31/5.52 => ~ ( P2 @ ( nth_VEBT_VEBT @ Xs2 @ J ) ) ) ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % find_Some_iff
% 5.31/5.52 thf(fact_2378_find__Some__iff,axiom,
% 5.31/5.52 ! [P2: $o > $o,Xs2: list_o,X: $o] :
% 5.31/5.52 ( ( ( find_o @ P2 @ Xs2 )
% 5.31/5.52 = ( some_o @ X ) )
% 5.31/5.52 = ( ? [I: nat] :
% 5.31/5.52 ( ( ord_less_nat @ I @ ( size_size_list_o @ Xs2 ) )
% 5.31/5.52 & ( P2 @ ( nth_o @ Xs2 @ I ) )
% 5.31/5.52 & ( X
% 5.31/5.52 = ( nth_o @ Xs2 @ I ) )
% 5.31/5.52 & ! [J: nat] :
% 5.31/5.52 ( ( ord_less_nat @ J @ I )
% 5.31/5.52 => ~ ( P2 @ ( nth_o @ Xs2 @ J ) ) ) ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % find_Some_iff
% 5.31/5.52 thf(fact_2379_find__Some__iff,axiom,
% 5.31/5.52 ! [P2: nat > $o,Xs2: list_nat,X: nat] :
% 5.31/5.52 ( ( ( find_nat @ P2 @ Xs2 )
% 5.31/5.52 = ( some_nat @ X ) )
% 5.31/5.52 = ( ? [I: nat] :
% 5.31/5.52 ( ( ord_less_nat @ I @ ( size_size_list_nat @ Xs2 ) )
% 5.31/5.52 & ( P2 @ ( nth_nat @ Xs2 @ I ) )
% 5.31/5.52 & ( X
% 5.31/5.52 = ( nth_nat @ Xs2 @ I ) )
% 5.31/5.52 & ! [J: nat] :
% 5.31/5.52 ( ( ord_less_nat @ J @ I )
% 5.31/5.52 => ~ ( P2 @ ( nth_nat @ Xs2 @ J ) ) ) ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % find_Some_iff
% 5.31/5.52 thf(fact_2380_find__Some__iff,axiom,
% 5.31/5.52 ! [P2: int > $o,Xs2: list_int,X: int] :
% 5.31/5.52 ( ( ( find_int @ P2 @ Xs2 )
% 5.31/5.52 = ( some_int @ X ) )
% 5.31/5.52 = ( ? [I: nat] :
% 5.31/5.52 ( ( ord_less_nat @ I @ ( size_size_list_int @ Xs2 ) )
% 5.31/5.52 & ( P2 @ ( nth_int @ Xs2 @ I ) )
% 5.31/5.52 & ( X
% 5.31/5.52 = ( nth_int @ Xs2 @ I ) )
% 5.31/5.52 & ! [J: nat] :
% 5.31/5.52 ( ( ord_less_nat @ J @ I )
% 5.31/5.52 => ~ ( P2 @ ( nth_int @ Xs2 @ J ) ) ) ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % find_Some_iff
% 5.31/5.52 thf(fact_2381_nth__Cons__pos,axiom,
% 5.31/5.52 ! [N: nat,X: vEBT_VEBT,Xs2: list_VEBT_VEBT] :
% 5.31/5.52 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.52 => ( ( nth_VEBT_VEBT @ ( cons_VEBT_VEBT @ X @ Xs2 ) @ N )
% 5.31/5.52 = ( nth_VEBT_VEBT @ Xs2 @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % nth_Cons_pos
% 5.31/5.52 thf(fact_2382_nth__Cons__pos,axiom,
% 5.31/5.52 ! [N: nat,X: nat,Xs2: list_nat] :
% 5.31/5.52 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.52 => ( ( nth_nat @ ( cons_nat @ X @ Xs2 ) @ N )
% 5.31/5.52 = ( nth_nat @ Xs2 @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % nth_Cons_pos
% 5.31/5.52 thf(fact_2383_rotate1__length01,axiom,
% 5.31/5.52 ! [Xs2: list_VEBT_VEBT] :
% 5.31/5.52 ( ( ord_less_eq_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) @ one_one_nat )
% 5.31/5.52 => ( ( rotate1_VEBT_VEBT @ Xs2 )
% 5.31/5.52 = Xs2 ) ) ).
% 5.31/5.52
% 5.31/5.52 % rotate1_length01
% 5.31/5.52 thf(fact_2384_rotate1__length01,axiom,
% 5.31/5.52 ! [Xs2: list_o] :
% 5.31/5.52 ( ( ord_less_eq_nat @ ( size_size_list_o @ Xs2 ) @ one_one_nat )
% 5.31/5.52 => ( ( rotate1_o @ Xs2 )
% 5.31/5.52 = Xs2 ) ) ).
% 5.31/5.52
% 5.31/5.52 % rotate1_length01
% 5.31/5.52 thf(fact_2385_rotate1__length01,axiom,
% 5.31/5.52 ! [Xs2: list_nat] :
% 5.31/5.52 ( ( ord_less_eq_nat @ ( size_size_list_nat @ Xs2 ) @ one_one_nat )
% 5.31/5.52 => ( ( rotate1_nat @ Xs2 )
% 5.31/5.52 = Xs2 ) ) ).
% 5.31/5.52
% 5.31/5.52 % rotate1_length01
% 5.31/5.52 thf(fact_2386_rotate1__length01,axiom,
% 5.31/5.52 ! [Xs2: list_int] :
% 5.31/5.52 ( ( ord_less_eq_nat @ ( size_size_list_int @ Xs2 ) @ one_one_nat )
% 5.31/5.52 => ( ( rotate1_int @ Xs2 )
% 5.31/5.52 = Xs2 ) ) ).
% 5.31/5.52
% 5.31/5.52 % rotate1_length01
% 5.31/5.52 thf(fact_2387_length__rotate1,axiom,
% 5.31/5.52 ! [Xs2: list_VEBT_VEBT] :
% 5.31/5.52 ( ( size_s6755466524823107622T_VEBT @ ( rotate1_VEBT_VEBT @ Xs2 ) )
% 5.31/5.52 = ( size_s6755466524823107622T_VEBT @ Xs2 ) ) ).
% 5.31/5.52
% 5.31/5.52 % length_rotate1
% 5.31/5.52 thf(fact_2388_length__rotate1,axiom,
% 5.31/5.52 ! [Xs2: list_o] :
% 5.31/5.52 ( ( size_size_list_o @ ( rotate1_o @ Xs2 ) )
% 5.31/5.52 = ( size_size_list_o @ Xs2 ) ) ).
% 5.31/5.52
% 5.31/5.52 % length_rotate1
% 5.31/5.52 thf(fact_2389_length__rotate1,axiom,
% 5.31/5.52 ! [Xs2: list_nat] :
% 5.31/5.52 ( ( size_size_list_nat @ ( rotate1_nat @ Xs2 ) )
% 5.31/5.52 = ( size_size_list_nat @ Xs2 ) ) ).
% 5.31/5.52
% 5.31/5.52 % length_rotate1
% 5.31/5.52 thf(fact_2390_length__rotate1,axiom,
% 5.31/5.52 ! [Xs2: list_int] :
% 5.31/5.52 ( ( size_size_list_int @ ( rotate1_int @ Xs2 ) )
% 5.31/5.52 = ( size_size_list_int @ Xs2 ) ) ).
% 5.31/5.52
% 5.31/5.52 % length_rotate1
% 5.31/5.52 thf(fact_2391_nth__Cons__Suc,axiom,
% 5.31/5.52 ! [X: vEBT_VEBT,Xs2: list_VEBT_VEBT,N: nat] :
% 5.31/5.52 ( ( nth_VEBT_VEBT @ ( cons_VEBT_VEBT @ X @ Xs2 ) @ ( suc @ N ) )
% 5.31/5.52 = ( nth_VEBT_VEBT @ Xs2 @ N ) ) ).
% 5.31/5.52
% 5.31/5.52 % nth_Cons_Suc
% 5.31/5.52 thf(fact_2392_nth__Cons__Suc,axiom,
% 5.31/5.52 ! [X: nat,Xs2: list_nat,N: nat] :
% 5.31/5.52 ( ( nth_nat @ ( cons_nat @ X @ Xs2 ) @ ( suc @ N ) )
% 5.31/5.52 = ( nth_nat @ Xs2 @ N ) ) ).
% 5.31/5.52
% 5.31/5.52 % nth_Cons_Suc
% 5.31/5.52 thf(fact_2393_nth__Cons__0,axiom,
% 5.31/5.52 ! [X: vEBT_VEBT,Xs2: list_VEBT_VEBT] :
% 5.31/5.52 ( ( nth_VEBT_VEBT @ ( cons_VEBT_VEBT @ X @ Xs2 ) @ zero_zero_nat )
% 5.31/5.52 = X ) ).
% 5.31/5.52
% 5.31/5.52 % nth_Cons_0
% 5.31/5.52 thf(fact_2394_nth__Cons__0,axiom,
% 5.31/5.52 ! [X: nat,Xs2: list_nat] :
% 5.31/5.52 ( ( nth_nat @ ( cons_nat @ X @ Xs2 ) @ zero_zero_nat )
% 5.31/5.52 = X ) ).
% 5.31/5.52
% 5.31/5.52 % nth_Cons_0
% 5.31/5.52 thf(fact_2395_zip__Cons__Cons,axiom,
% 5.31/5.52 ! [X: code_integer,Xs2: list_Code_integer,Y: code_integer,Ys: list_Code_integer] :
% 5.31/5.52 ( ( zip_Co3543743374963494515nteger @ ( cons_Code_integer @ X @ Xs2 ) @ ( cons_Code_integer @ Y @ Ys ) )
% 5.31/5.52 = ( cons_P9044669534377732177nteger @ ( produc1086072967326762835nteger @ X @ Y ) @ ( zip_Co3543743374963494515nteger @ Xs2 @ Ys ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % zip_Cons_Cons
% 5.31/5.52 thf(fact_2396_zip__Cons__Cons,axiom,
% 5.31/5.52 ! [X: product_prod_nat_nat,Xs2: list_P6011104703257516679at_nat,Y: product_prod_nat_nat,Ys: list_P6011104703257516679at_nat] :
% 5.31/5.52 ( ( zip_Pr4664179122662387191at_nat @ ( cons_P6512896166579812791at_nat @ X @ Xs2 ) @ ( cons_P6512896166579812791at_nat @ Y @ Ys ) )
% 5.31/5.52 = ( cons_P8732206157123786781at_nat @ ( produc6161850002892822231at_nat @ X @ Y ) @ ( zip_Pr4664179122662387191at_nat @ Xs2 @ Ys ) ) ) ).
% 5.31/5.52
% 5.31/5.52 % zip_Cons_Cons
% 5.31/5.52 thf(fact_2397_zip__Cons__Cons,axiom,
% 5.31/5.52 ! [X: set_Pr1261947904930325089at_nat,Xs2: list_s1210847774152347623at_nat,Y: set_Pr1261947904930325089at_nat,Ys: list_s1210847774152347623at_nat] :
% 5.31/5.53 ( ( zip_se5600341670672612855at_nat @ ( cons_s6881495754146722583at_nat @ X @ Xs2 ) @ ( cons_s6881495754146722583at_nat @ Y @ Ys ) )
% 5.31/5.53 = ( cons_P3940603068885512221at_nat @ ( produc2922128104949294807at_nat @ X @ Y ) @ ( zip_se5600341670672612855at_nat @ Xs2 @ Ys ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % zip_Cons_Cons
% 5.31/5.53 thf(fact_2398_zip__Cons__Cons,axiom,
% 5.31/5.53 ! [X: nat,Xs2: list_nat,Y: nat,Ys: list_nat] :
% 5.31/5.53 ( ( zip_nat_nat @ ( cons_nat @ X @ Xs2 ) @ ( cons_nat @ Y @ Ys ) )
% 5.31/5.53 = ( cons_P6512896166579812791at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ ( zip_nat_nat @ Xs2 @ Ys ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % zip_Cons_Cons
% 5.31/5.53 thf(fact_2399_zip__Cons__Cons,axiom,
% 5.31/5.53 ! [X: int,Xs2: list_int,Y: int,Ys: list_int] :
% 5.31/5.53 ( ( zip_int_int @ ( cons_int @ X @ Xs2 ) @ ( cons_int @ Y @ Ys ) )
% 5.31/5.53 = ( cons_P3334398858971670639nt_int @ ( product_Pair_int_int @ X @ Y ) @ ( zip_int_int @ Xs2 @ Ys ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % zip_Cons_Cons
% 5.31/5.53 thf(fact_2400_enumerate__simps_I2_J,axiom,
% 5.31/5.53 ! [N: nat,X: nat,Xs2: list_nat] :
% 5.31/5.53 ( ( enumerate_nat @ N @ ( cons_nat @ X @ Xs2 ) )
% 5.31/5.53 = ( cons_P6512896166579812791at_nat @ ( product_Pair_nat_nat @ N @ X ) @ ( enumerate_nat @ ( suc @ N ) @ Xs2 ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % enumerate_simps(2)
% 5.31/5.53 thf(fact_2401_zip__eq__ConsE,axiom,
% 5.31/5.53 ! [Xs2: list_Code_integer,Ys: list_Code_integer,Xy: produc8923325533196201883nteger,Xys: list_P5578671422887162913nteger] :
% 5.31/5.53 ( ( ( zip_Co3543743374963494515nteger @ Xs2 @ Ys )
% 5.31/5.53 = ( cons_P9044669534377732177nteger @ Xy @ Xys ) )
% 5.31/5.53 => ~ ! [X3: code_integer,Xs4: list_Code_integer] :
% 5.31/5.53 ( ( Xs2
% 5.31/5.53 = ( cons_Code_integer @ X3 @ Xs4 ) )
% 5.31/5.53 => ! [Y3: code_integer,Ys4: list_Code_integer] :
% 5.31/5.53 ( ( Ys
% 5.31/5.53 = ( cons_Code_integer @ Y3 @ Ys4 ) )
% 5.31/5.53 => ( ( Xy
% 5.31/5.53 = ( produc1086072967326762835nteger @ X3 @ Y3 ) )
% 5.31/5.53 => ( Xys
% 5.31/5.53 != ( zip_Co3543743374963494515nteger @ Xs4 @ Ys4 ) ) ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % zip_eq_ConsE
% 5.31/5.53 thf(fact_2402_zip__eq__ConsE,axiom,
% 5.31/5.53 ! [Xs2: list_P6011104703257516679at_nat,Ys: list_P6011104703257516679at_nat,Xy: produc859450856879609959at_nat,Xys: list_P8469869581646625389at_nat] :
% 5.31/5.53 ( ( ( zip_Pr4664179122662387191at_nat @ Xs2 @ Ys )
% 5.31/5.53 = ( cons_P8732206157123786781at_nat @ Xy @ Xys ) )
% 5.31/5.53 => ~ ! [X3: product_prod_nat_nat,Xs4: list_P6011104703257516679at_nat] :
% 5.31/5.53 ( ( Xs2
% 5.31/5.53 = ( cons_P6512896166579812791at_nat @ X3 @ Xs4 ) )
% 5.31/5.53 => ! [Y3: product_prod_nat_nat,Ys4: list_P6011104703257516679at_nat] :
% 5.31/5.53 ( ( Ys
% 5.31/5.53 = ( cons_P6512896166579812791at_nat @ Y3 @ Ys4 ) )
% 5.31/5.53 => ( ( Xy
% 5.31/5.53 = ( produc6161850002892822231at_nat @ X3 @ Y3 ) )
% 5.31/5.53 => ( Xys
% 5.31/5.53 != ( zip_Pr4664179122662387191at_nat @ Xs4 @ Ys4 ) ) ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % zip_eq_ConsE
% 5.31/5.53 thf(fact_2403_zip__eq__ConsE,axiom,
% 5.31/5.53 ! [Xs2: list_s1210847774152347623at_nat,Ys: list_s1210847774152347623at_nat,Xy: produc3843707927480180839at_nat,Xys: list_P5464809261938338413at_nat] :
% 5.31/5.53 ( ( ( zip_se5600341670672612855at_nat @ Xs2 @ Ys )
% 5.31/5.53 = ( cons_P3940603068885512221at_nat @ Xy @ Xys ) )
% 5.31/5.53 => ~ ! [X3: set_Pr1261947904930325089at_nat,Xs4: list_s1210847774152347623at_nat] :
% 5.31/5.53 ( ( Xs2
% 5.31/5.53 = ( cons_s6881495754146722583at_nat @ X3 @ Xs4 ) )
% 5.31/5.53 => ! [Y3: set_Pr1261947904930325089at_nat,Ys4: list_s1210847774152347623at_nat] :
% 5.31/5.53 ( ( Ys
% 5.31/5.53 = ( cons_s6881495754146722583at_nat @ Y3 @ Ys4 ) )
% 5.31/5.53 => ( ( Xy
% 5.31/5.53 = ( produc2922128104949294807at_nat @ X3 @ Y3 ) )
% 5.31/5.53 => ( Xys
% 5.31/5.53 != ( zip_se5600341670672612855at_nat @ Xs4 @ Ys4 ) ) ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % zip_eq_ConsE
% 5.31/5.53 thf(fact_2404_zip__eq__ConsE,axiom,
% 5.31/5.53 ! [Xs2: list_nat,Ys: list_nat,Xy: product_prod_nat_nat,Xys: list_P6011104703257516679at_nat] :
% 5.31/5.53 ( ( ( zip_nat_nat @ Xs2 @ Ys )
% 5.31/5.53 = ( cons_P6512896166579812791at_nat @ Xy @ Xys ) )
% 5.31/5.53 => ~ ! [X3: nat,Xs4: list_nat] :
% 5.31/5.53 ( ( Xs2
% 5.31/5.53 = ( cons_nat @ X3 @ Xs4 ) )
% 5.31/5.53 => ! [Y3: nat,Ys4: list_nat] :
% 5.31/5.53 ( ( Ys
% 5.31/5.53 = ( cons_nat @ Y3 @ Ys4 ) )
% 5.31/5.53 => ( ( Xy
% 5.31/5.53 = ( product_Pair_nat_nat @ X3 @ Y3 ) )
% 5.31/5.53 => ( Xys
% 5.31/5.53 != ( zip_nat_nat @ Xs4 @ Ys4 ) ) ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % zip_eq_ConsE
% 5.31/5.53 thf(fact_2405_zip__eq__ConsE,axiom,
% 5.31/5.53 ! [Xs2: list_int,Ys: list_int,Xy: product_prod_int_int,Xys: list_P5707943133018811711nt_int] :
% 5.31/5.53 ( ( ( zip_int_int @ Xs2 @ Ys )
% 5.31/5.53 = ( cons_P3334398858971670639nt_int @ Xy @ Xys ) )
% 5.31/5.53 => ~ ! [X3: int,Xs4: list_int] :
% 5.31/5.53 ( ( Xs2
% 5.31/5.53 = ( cons_int @ X3 @ Xs4 ) )
% 5.31/5.53 => ! [Y3: int,Ys4: list_int] :
% 5.31/5.53 ( ( Ys
% 5.31/5.53 = ( cons_int @ Y3 @ Ys4 ) )
% 5.31/5.53 => ( ( Xy
% 5.31/5.53 = ( product_Pair_int_int @ X3 @ Y3 ) )
% 5.31/5.53 => ( Xys
% 5.31/5.53 != ( zip_int_int @ Xs4 @ Ys4 ) ) ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % zip_eq_ConsE
% 5.31/5.53 thf(fact_2406_find_Osimps_I2_J,axiom,
% 5.31/5.53 ! [P2: product_prod_nat_nat > $o,X: product_prod_nat_nat,Xs2: list_P6011104703257516679at_nat] :
% 5.31/5.53 ( ( ( P2 @ X )
% 5.31/5.53 => ( ( find_P8199882355184865565at_nat @ P2 @ ( cons_P6512896166579812791at_nat @ X @ Xs2 ) )
% 5.31/5.53 = ( some_P7363390416028606310at_nat @ X ) ) )
% 5.31/5.53 & ( ~ ( P2 @ X )
% 5.31/5.53 => ( ( find_P8199882355184865565at_nat @ P2 @ ( cons_P6512896166579812791at_nat @ X @ Xs2 ) )
% 5.31/5.53 = ( find_P8199882355184865565at_nat @ P2 @ Xs2 ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % find.simps(2)
% 5.31/5.53 thf(fact_2407_find_Osimps_I2_J,axiom,
% 5.31/5.53 ! [P2: nat > $o,X: nat,Xs2: list_nat] :
% 5.31/5.53 ( ( ( P2 @ X )
% 5.31/5.53 => ( ( find_nat @ P2 @ ( cons_nat @ X @ Xs2 ) )
% 5.31/5.53 = ( some_nat @ X ) ) )
% 5.31/5.53 & ( ~ ( P2 @ X )
% 5.31/5.53 => ( ( find_nat @ P2 @ ( cons_nat @ X @ Xs2 ) )
% 5.31/5.53 = ( find_nat @ P2 @ Xs2 ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % find.simps(2)
% 5.31/5.53 thf(fact_2408_find_Osimps_I2_J,axiom,
% 5.31/5.53 ! [P2: num > $o,X: num,Xs2: list_num] :
% 5.31/5.53 ( ( ( P2 @ X )
% 5.31/5.53 => ( ( find_num @ P2 @ ( cons_num @ X @ Xs2 ) )
% 5.31/5.53 = ( some_num @ X ) ) )
% 5.31/5.53 & ( ~ ( P2 @ X )
% 5.31/5.53 => ( ( find_num @ P2 @ ( cons_num @ X @ Xs2 ) )
% 5.31/5.53 = ( find_num @ P2 @ Xs2 ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % find.simps(2)
% 5.31/5.53 thf(fact_2409_set__zip__rightD,axiom,
% 5.31/5.53 ! [X: code_integer,Y: code_integer,Xs2: list_Code_integer,Ys: list_Code_integer] :
% 5.31/5.53 ( ( member157494554546826820nteger @ ( produc1086072967326762835nteger @ X @ Y ) @ ( set_Pr920681315882439344nteger @ ( zip_Co3543743374963494515nteger @ Xs2 @ Ys ) ) )
% 5.31/5.53 => ( member_Code_integer @ Y @ ( set_Code_integer2 @ Ys ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % set_zip_rightD
% 5.31/5.53 thf(fact_2410_set__zip__rightD,axiom,
% 5.31/5.53 ! [X: product_prod_nat_nat,Y: product_prod_nat_nat,Xs2: list_P6011104703257516679at_nat,Ys: list_P6011104703257516679at_nat] :
% 5.31/5.53 ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X @ Y ) @ ( set_Pr5518436109238095868at_nat @ ( zip_Pr4664179122662387191at_nat @ Xs2 @ Ys ) ) )
% 5.31/5.53 => ( member8440522571783428010at_nat @ Y @ ( set_Pr5648618587558075414at_nat @ Ys ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % set_zip_rightD
% 5.31/5.53 thf(fact_2411_set__zip__rightD,axiom,
% 5.31/5.53 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,Xs2: list_s1210847774152347623at_nat,Ys: list_s1210847774152347623at_nat] :
% 5.31/5.53 ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X @ Y ) @ ( set_Pr3765526544606949372at_nat @ ( zip_se5600341670672612855at_nat @ Xs2 @ Ys ) ) )
% 5.31/5.53 => ( member2643936169264416010at_nat @ Y @ ( set_se5049602875457034614at_nat @ Ys ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % set_zip_rightD
% 5.31/5.53 thf(fact_2412_set__zip__rightD,axiom,
% 5.31/5.53 ! [X: nat,Y: nat,Xs2: list_nat,Ys: list_nat] :
% 5.31/5.53 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ ( set_Pr5648618587558075414at_nat @ ( zip_nat_nat @ Xs2 @ Ys ) ) )
% 5.31/5.53 => ( member_nat @ Y @ ( set_nat2 @ Ys ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % set_zip_rightD
% 5.31/5.53 thf(fact_2413_set__zip__rightD,axiom,
% 5.31/5.53 ! [X: int,Y: int,Xs2: list_int,Ys: list_int] :
% 5.31/5.53 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y ) @ ( set_Pr2470121279949933262nt_int @ ( zip_int_int @ Xs2 @ Ys ) ) )
% 5.31/5.53 => ( member_int @ Y @ ( set_int2 @ Ys ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % set_zip_rightD
% 5.31/5.53 thf(fact_2414_set__zip__leftD,axiom,
% 5.31/5.53 ! [X: code_integer,Y: code_integer,Xs2: list_Code_integer,Ys: list_Code_integer] :
% 5.31/5.53 ( ( member157494554546826820nteger @ ( produc1086072967326762835nteger @ X @ Y ) @ ( set_Pr920681315882439344nteger @ ( zip_Co3543743374963494515nteger @ Xs2 @ Ys ) ) )
% 5.31/5.53 => ( member_Code_integer @ X @ ( set_Code_integer2 @ Xs2 ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % set_zip_leftD
% 5.31/5.53 thf(fact_2415_set__zip__leftD,axiom,
% 5.31/5.53 ! [X: product_prod_nat_nat,Y: product_prod_nat_nat,Xs2: list_P6011104703257516679at_nat,Ys: list_P6011104703257516679at_nat] :
% 5.31/5.53 ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X @ Y ) @ ( set_Pr5518436109238095868at_nat @ ( zip_Pr4664179122662387191at_nat @ Xs2 @ Ys ) ) )
% 5.31/5.53 => ( member8440522571783428010at_nat @ X @ ( set_Pr5648618587558075414at_nat @ Xs2 ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % set_zip_leftD
% 5.31/5.53 thf(fact_2416_set__zip__leftD,axiom,
% 5.31/5.53 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,Xs2: list_s1210847774152347623at_nat,Ys: list_s1210847774152347623at_nat] :
% 5.31/5.53 ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X @ Y ) @ ( set_Pr3765526544606949372at_nat @ ( zip_se5600341670672612855at_nat @ Xs2 @ Ys ) ) )
% 5.31/5.53 => ( member2643936169264416010at_nat @ X @ ( set_se5049602875457034614at_nat @ Xs2 ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % set_zip_leftD
% 5.31/5.53 thf(fact_2417_set__zip__leftD,axiom,
% 5.31/5.53 ! [X: nat,Y: nat,Xs2: list_nat,Ys: list_nat] :
% 5.31/5.53 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ ( set_Pr5648618587558075414at_nat @ ( zip_nat_nat @ Xs2 @ Ys ) ) )
% 5.31/5.53 => ( member_nat @ X @ ( set_nat2 @ Xs2 ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % set_zip_leftD
% 5.31/5.53 thf(fact_2418_set__zip__leftD,axiom,
% 5.31/5.53 ! [X: int,Y: int,Xs2: list_int,Ys: list_int] :
% 5.31/5.53 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y ) @ ( set_Pr2470121279949933262nt_int @ ( zip_int_int @ Xs2 @ Ys ) ) )
% 5.31/5.53 => ( member_int @ X @ ( set_int2 @ Xs2 ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % set_zip_leftD
% 5.31/5.53 thf(fact_2419_in__set__zipE,axiom,
% 5.31/5.53 ! [X: complex,Y: complex,Xs2: list_complex,Ys: list_complex] :
% 5.31/5.53 ( ( member5793383173714906214omplex @ ( produc101793102246108661omplex @ X @ Y ) @ ( set_Pr8199049879907524818omplex @ ( zip_complex_complex @ Xs2 @ Ys ) ) )
% 5.31/5.53 => ~ ( ( member_complex @ X @ ( set_complex2 @ Xs2 ) )
% 5.31/5.53 => ~ ( member_complex @ Y @ ( set_complex2 @ Ys ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % in_set_zipE
% 5.31/5.53 thf(fact_2420_in__set__zipE,axiom,
% 5.31/5.53 ! [X: complex,Y: real,Xs2: list_complex,Ys: list_real] :
% 5.31/5.53 ( ( member47443559803733732x_real @ ( produc1746590499379883635x_real @ X @ Y ) @ ( set_Pr1225976482156248400x_real @ ( zip_complex_real @ Xs2 @ Ys ) ) )
% 5.31/5.53 => ~ ( ( member_complex @ X @ ( set_complex2 @ Xs2 ) )
% 5.31/5.53 => ~ ( member_real @ Y @ ( set_real2 @ Ys ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % in_set_zipE
% 5.31/5.53 thf(fact_2421_in__set__zipE,axiom,
% 5.31/5.53 ! [X: complex,Y: int,Xs2: list_complex,Ys: list_int] :
% 5.31/5.53 ( ( member595073364599660772ex_int @ ( produc1367138851071493491ex_int @ X @ Y ) @ ( set_Pr4995810437751016784ex_int @ ( zip_complex_int @ Xs2 @ Ys ) ) )
% 5.31/5.53 => ~ ( ( member_complex @ X @ ( set_complex2 @ Xs2 ) )
% 5.31/5.53 => ~ ( member_int @ Y @ ( set_int2 @ Ys ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % in_set_zipE
% 5.31/5.53 thf(fact_2422_in__set__zipE,axiom,
% 5.31/5.53 ! [X: real,Y: complex,Xs2: list_real,Ys: list_complex] :
% 5.31/5.53 ( ( member7358116576843751780omplex @ ( produc1693001998875562995omplex @ X @ Y ) @ ( set_Pr8536649499196266448omplex @ ( zip_real_complex @ Xs2 @ Ys ) ) )
% 5.31/5.53 => ~ ( ( member_real @ X @ ( set_real2 @ Xs2 ) )
% 5.31/5.53 => ~ ( member_complex @ Y @ ( set_complex2 @ Ys ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % in_set_zipE
% 5.31/5.53 thf(fact_2423_in__set__zipE,axiom,
% 5.31/5.53 ! [X: real,Y: real,Xs2: list_real,Ys: list_real] :
% 5.31/5.53 ( ( member7849222048561428706l_real @ ( produc4511245868158468465l_real @ X @ Y ) @ ( set_Pr5999470521830281550l_real @ ( zip_real_real @ Xs2 @ Ys ) ) )
% 5.31/5.53 => ~ ( ( member_real @ X @ ( set_real2 @ Xs2 ) )
% 5.31/5.53 => ~ ( member_real @ Y @ ( set_real2 @ Ys ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % in_set_zipE
% 5.31/5.53 thf(fact_2424_in__set__zipE,axiom,
% 5.31/5.53 ! [X: real,Y: int,Xs2: list_real,Ys: list_int] :
% 5.31/5.53 ( ( member1627681773268152802al_int @ ( produc3179012173361985393al_int @ X @ Y ) @ ( set_Pr8219819362198175822al_int @ ( zip_real_int @ Xs2 @ Ys ) ) )
% 5.31/5.53 => ~ ( ( member_real @ X @ ( set_real2 @ Xs2 ) )
% 5.31/5.53 => ~ ( member_int @ Y @ ( set_int2 @ Ys ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % in_set_zipE
% 5.31/5.53 thf(fact_2425_in__set__zipE,axiom,
% 5.31/5.53 ! [X: int,Y: complex,Xs2: list_int,Ys: list_complex] :
% 5.31/5.53 ( ( member8811922270175639012omplex @ ( produc7948753499206759283omplex @ X @ Y ) @ ( set_Pr3989287306472219216omplex @ ( zip_int_complex @ Xs2 @ Ys ) ) )
% 5.31/5.53 => ~ ( ( member_int @ X @ ( set_int2 @ Xs2 ) )
% 5.31/5.53 => ~ ( member_complex @ Y @ ( set_complex2 @ Ys ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % in_set_zipE
% 5.31/5.53 thf(fact_2426_in__set__zipE,axiom,
% 5.31/5.53 ! [X: int,Y: real,Xs2: list_int,Ys: list_real] :
% 5.31/5.53 ( ( member2744130022092475746t_real @ ( produc801115645435158769t_real @ X @ Y ) @ ( set_Pr112895574167722958t_real @ ( zip_int_real @ Xs2 @ Ys ) ) )
% 5.31/5.53 => ~ ( ( member_int @ X @ ( set_int2 @ Xs2 ) )
% 5.31/5.53 => ~ ( member_real @ Y @ ( set_real2 @ Ys ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % in_set_zipE
% 5.31/5.53 thf(fact_2427_in__set__zipE,axiom,
% 5.31/5.53 ! [X: complex,Y: vEBT_VEBT,Xs2: list_complex,Ys: list_VEBT_VEBT] :
% 5.31/5.53 ( ( member1978952105866562066T_VEBT @ ( produc2757191886755552429T_VEBT @ X @ Y ) @ ( set_Pr5158653123227461798T_VEBT @ ( zip_co9157518722488180109T_VEBT @ Xs2 @ Ys ) ) )
% 5.31/5.53 => ~ ( ( member_complex @ X @ ( set_complex2 @ Xs2 ) )
% 5.31/5.53 => ~ ( member_VEBT_VEBT @ Y @ ( set_VEBT_VEBT2 @ Ys ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % in_set_zipE
% 5.31/5.53 thf(fact_2428_in__set__zipE,axiom,
% 5.31/5.53 ! [X: real,Y: vEBT_VEBT,Xs2: list_real,Ys: list_VEBT_VEBT] :
% 5.31/5.53 ( ( member7262085504369356948T_VEBT @ ( produc6931449550656315951T_VEBT @ X @ Y ) @ ( set_Pr8897343066327330088T_VEBT @ ( zip_real_VEBT_VEBT @ Xs2 @ Ys ) ) )
% 5.31/5.53 => ~ ( ( member_real @ X @ ( set_real2 @ Xs2 ) )
% 5.31/5.53 => ~ ( member_VEBT_VEBT @ Y @ ( set_VEBT_VEBT2 @ Ys ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % in_set_zipE
% 5.31/5.53 thf(fact_2429_zip__same,axiom,
% 5.31/5.53 ! [A: complex,B: complex,Xs2: list_complex] :
% 5.31/5.53 ( ( member5793383173714906214omplex @ ( produc101793102246108661omplex @ A @ B ) @ ( set_Pr8199049879907524818omplex @ ( zip_complex_complex @ Xs2 @ Xs2 ) ) )
% 5.31/5.53 = ( ( member_complex @ A @ ( set_complex2 @ Xs2 ) )
% 5.31/5.53 & ( A = B ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % zip_same
% 5.31/5.53 thf(fact_2430_zip__same,axiom,
% 5.31/5.53 ! [A: real,B: real,Xs2: list_real] :
% 5.31/5.53 ( ( member7849222048561428706l_real @ ( produc4511245868158468465l_real @ A @ B ) @ ( set_Pr5999470521830281550l_real @ ( zip_real_real @ Xs2 @ Xs2 ) ) )
% 5.31/5.53 = ( ( member_real @ A @ ( set_real2 @ Xs2 ) )
% 5.31/5.53 & ( A = B ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % zip_same
% 5.31/5.53 thf(fact_2431_zip__same,axiom,
% 5.31/5.53 ! [A: set_nat,B: set_nat,Xs2: list_set_nat] :
% 5.31/5.53 ( ( member8277197624267554838et_nat @ ( produc4532415448927165861et_nat @ A @ B ) @ ( set_Pr9040384385603167362et_nat @ ( zip_set_nat_set_nat @ Xs2 @ Xs2 ) ) )
% 5.31/5.53 = ( ( member_set_nat @ A @ ( set_set_nat2 @ Xs2 ) )
% 5.31/5.53 & ( A = B ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % zip_same
% 5.31/5.53 thf(fact_2432_zip__same,axiom,
% 5.31/5.53 ! [A: vEBT_VEBT,B: vEBT_VEBT,Xs2: list_VEBT_VEBT] :
% 5.31/5.53 ( ( member568628332442017744T_VEBT @ ( produc537772716801021591T_VEBT @ A @ B ) @ ( set_Pr9182192707038809660T_VEBT @ ( zip_VE537291747668921783T_VEBT @ Xs2 @ Xs2 ) ) )
% 5.31/5.53 = ( ( member_VEBT_VEBT @ A @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 5.31/5.53 & ( A = B ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % zip_same
% 5.31/5.53 thf(fact_2433_zip__same,axiom,
% 5.31/5.53 ! [A: code_integer,B: code_integer,Xs2: list_Code_integer] :
% 5.31/5.53 ( ( member157494554546826820nteger @ ( produc1086072967326762835nteger @ A @ B ) @ ( set_Pr920681315882439344nteger @ ( zip_Co3543743374963494515nteger @ Xs2 @ Xs2 ) ) )
% 5.31/5.53 = ( ( member_Code_integer @ A @ ( set_Code_integer2 @ Xs2 ) )
% 5.31/5.53 & ( A = B ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % zip_same
% 5.31/5.53 thf(fact_2434_zip__same,axiom,
% 5.31/5.53 ! [A: product_prod_nat_nat,B: product_prod_nat_nat,Xs2: list_P6011104703257516679at_nat] :
% 5.31/5.53 ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ A @ B ) @ ( set_Pr5518436109238095868at_nat @ ( zip_Pr4664179122662387191at_nat @ Xs2 @ Xs2 ) ) )
% 5.31/5.53 = ( ( member8440522571783428010at_nat @ A @ ( set_Pr5648618587558075414at_nat @ Xs2 ) )
% 5.31/5.53 & ( A = B ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % zip_same
% 5.31/5.53 thf(fact_2435_zip__same,axiom,
% 5.31/5.53 ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat,Xs2: list_s1210847774152347623at_nat] :
% 5.31/5.53 ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A @ B ) @ ( set_Pr3765526544606949372at_nat @ ( zip_se5600341670672612855at_nat @ Xs2 @ Xs2 ) ) )
% 5.31/5.53 = ( ( member2643936169264416010at_nat @ A @ ( set_se5049602875457034614at_nat @ Xs2 ) )
% 5.31/5.53 & ( A = B ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % zip_same
% 5.31/5.53 thf(fact_2436_zip__same,axiom,
% 5.31/5.53 ! [A: nat,B: nat,Xs2: list_nat] :
% 5.31/5.53 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ B ) @ ( set_Pr5648618587558075414at_nat @ ( zip_nat_nat @ Xs2 @ Xs2 ) ) )
% 5.31/5.53 = ( ( member_nat @ A @ ( set_nat2 @ Xs2 ) )
% 5.31/5.53 & ( A = B ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % zip_same
% 5.31/5.53 thf(fact_2437_zip__same,axiom,
% 5.31/5.53 ! [A: int,B: int,Xs2: list_int] :
% 5.31/5.53 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A @ B ) @ ( set_Pr2470121279949933262nt_int @ ( zip_int_int @ Xs2 @ Xs2 ) ) )
% 5.31/5.53 = ( ( member_int @ A @ ( set_int2 @ Xs2 ) )
% 5.31/5.53 & ( A = B ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % zip_same
% 5.31/5.53 thf(fact_2438_Suc__length__conv,axiom,
% 5.31/5.53 ! [N: nat,Xs2: list_VEBT_VEBT] :
% 5.31/5.53 ( ( ( suc @ N )
% 5.31/5.53 = ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 5.31/5.53 = ( ? [Y4: vEBT_VEBT,Ys3: list_VEBT_VEBT] :
% 5.31/5.53 ( ( Xs2
% 5.31/5.53 = ( cons_VEBT_VEBT @ Y4 @ Ys3 ) )
% 5.31/5.53 & ( ( size_s6755466524823107622T_VEBT @ Ys3 )
% 5.31/5.53 = N ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % Suc_length_conv
% 5.31/5.53 thf(fact_2439_Suc__length__conv,axiom,
% 5.31/5.53 ! [N: nat,Xs2: list_o] :
% 5.31/5.53 ( ( ( suc @ N )
% 5.31/5.53 = ( size_size_list_o @ Xs2 ) )
% 5.31/5.53 = ( ? [Y4: $o,Ys3: list_o] :
% 5.31/5.53 ( ( Xs2
% 5.31/5.53 = ( cons_o @ Y4 @ Ys3 ) )
% 5.31/5.53 & ( ( size_size_list_o @ Ys3 )
% 5.31/5.53 = N ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % Suc_length_conv
% 5.31/5.53 thf(fact_2440_Suc__length__conv,axiom,
% 5.31/5.53 ! [N: nat,Xs2: list_nat] :
% 5.31/5.53 ( ( ( suc @ N )
% 5.31/5.53 = ( size_size_list_nat @ Xs2 ) )
% 5.31/5.53 = ( ? [Y4: nat,Ys3: list_nat] :
% 5.31/5.53 ( ( Xs2
% 5.31/5.53 = ( cons_nat @ Y4 @ Ys3 ) )
% 5.31/5.53 & ( ( size_size_list_nat @ Ys3 )
% 5.31/5.53 = N ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % Suc_length_conv
% 5.31/5.53 thf(fact_2441_Suc__length__conv,axiom,
% 5.31/5.53 ! [N: nat,Xs2: list_int] :
% 5.31/5.53 ( ( ( suc @ N )
% 5.31/5.53 = ( size_size_list_int @ Xs2 ) )
% 5.31/5.53 = ( ? [Y4: int,Ys3: list_int] :
% 5.31/5.53 ( ( Xs2
% 5.31/5.53 = ( cons_int @ Y4 @ Ys3 ) )
% 5.31/5.53 & ( ( size_size_list_int @ Ys3 )
% 5.31/5.53 = N ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % Suc_length_conv
% 5.31/5.53 thf(fact_2442_length__Suc__conv,axiom,
% 5.31/5.53 ! [Xs2: list_VEBT_VEBT,N: nat] :
% 5.31/5.53 ( ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 5.31/5.53 = ( suc @ N ) )
% 5.31/5.53 = ( ? [Y4: vEBT_VEBT,Ys3: list_VEBT_VEBT] :
% 5.31/5.53 ( ( Xs2
% 5.31/5.53 = ( cons_VEBT_VEBT @ Y4 @ Ys3 ) )
% 5.31/5.53 & ( ( size_s6755466524823107622T_VEBT @ Ys3 )
% 5.31/5.53 = N ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % length_Suc_conv
% 5.31/5.53 thf(fact_2443_length__Suc__conv,axiom,
% 5.31/5.53 ! [Xs2: list_o,N: nat] :
% 5.31/5.53 ( ( ( size_size_list_o @ Xs2 )
% 5.31/5.53 = ( suc @ N ) )
% 5.31/5.53 = ( ? [Y4: $o,Ys3: list_o] :
% 5.31/5.53 ( ( Xs2
% 5.31/5.53 = ( cons_o @ Y4 @ Ys3 ) )
% 5.31/5.53 & ( ( size_size_list_o @ Ys3 )
% 5.31/5.53 = N ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % length_Suc_conv
% 5.31/5.53 thf(fact_2444_length__Suc__conv,axiom,
% 5.31/5.53 ! [Xs2: list_nat,N: nat] :
% 5.31/5.53 ( ( ( size_size_list_nat @ Xs2 )
% 5.31/5.53 = ( suc @ N ) )
% 5.31/5.53 = ( ? [Y4: nat,Ys3: list_nat] :
% 5.31/5.53 ( ( Xs2
% 5.31/5.53 = ( cons_nat @ Y4 @ Ys3 ) )
% 5.31/5.53 & ( ( size_size_list_nat @ Ys3 )
% 5.31/5.53 = N ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % length_Suc_conv
% 5.31/5.53 thf(fact_2445_length__Suc__conv,axiom,
% 5.31/5.53 ! [Xs2: list_int,N: nat] :
% 5.31/5.53 ( ( ( size_size_list_int @ Xs2 )
% 5.31/5.53 = ( suc @ N ) )
% 5.31/5.53 = ( ? [Y4: int,Ys3: list_int] :
% 5.31/5.53 ( ( Xs2
% 5.31/5.53 = ( cons_int @ Y4 @ Ys3 ) )
% 5.31/5.53 & ( ( size_size_list_int @ Ys3 )
% 5.31/5.53 = N ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % length_Suc_conv
% 5.31/5.53 thf(fact_2446_impossible__Cons,axiom,
% 5.31/5.53 ! [Xs2: list_VEBT_VEBT,Ys: list_VEBT_VEBT,X: vEBT_VEBT] :
% 5.31/5.53 ( ( ord_less_eq_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) @ ( size_s6755466524823107622T_VEBT @ Ys ) )
% 5.31/5.53 => ( Xs2
% 5.31/5.53 != ( cons_VEBT_VEBT @ X @ Ys ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % impossible_Cons
% 5.31/5.53 thf(fact_2447_impossible__Cons,axiom,
% 5.31/5.53 ! [Xs2: list_o,Ys: list_o,X: $o] :
% 5.31/5.53 ( ( ord_less_eq_nat @ ( size_size_list_o @ Xs2 ) @ ( size_size_list_o @ Ys ) )
% 5.31/5.53 => ( Xs2
% 5.31/5.53 != ( cons_o @ X @ Ys ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % impossible_Cons
% 5.31/5.53 thf(fact_2448_impossible__Cons,axiom,
% 5.31/5.53 ! [Xs2: list_nat,Ys: list_nat,X: nat] :
% 5.31/5.53 ( ( ord_less_eq_nat @ ( size_size_list_nat @ Xs2 ) @ ( size_size_list_nat @ Ys ) )
% 5.31/5.53 => ( Xs2
% 5.31/5.53 != ( cons_nat @ X @ Ys ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % impossible_Cons
% 5.31/5.53 thf(fact_2449_impossible__Cons,axiom,
% 5.31/5.53 ! [Xs2: list_int,Ys: list_int,X: int] :
% 5.31/5.53 ( ( ord_less_eq_nat @ ( size_size_list_int @ Xs2 ) @ ( size_size_list_int @ Ys ) )
% 5.31/5.53 => ( Xs2
% 5.31/5.53 != ( cons_int @ X @ Ys ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % impossible_Cons
% 5.31/5.53 thf(fact_2450_vebt__insert_Osimps_I2_J,axiom,
% 5.31/5.53 ! [Info2: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S2: vEBT_VEBT,X: nat] :
% 5.31/5.53 ( ( vEBT_vebt_insert @ ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts2 @ S2 ) @ X )
% 5.31/5.53 = ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts2 @ S2 ) ) ).
% 5.31/5.53
% 5.31/5.53 % vebt_insert.simps(2)
% 5.31/5.53 thf(fact_2451_in__set__impl__in__set__zip1,axiom,
% 5.31/5.53 ! [Xs2: list_Code_integer,Ys: list_Code_integer,X: code_integer] :
% 5.31/5.53 ( ( ( size_s3445333598471063425nteger @ Xs2 )
% 5.31/5.53 = ( size_s3445333598471063425nteger @ Ys ) )
% 5.31/5.53 => ( ( member_Code_integer @ X @ ( set_Code_integer2 @ Xs2 ) )
% 5.31/5.53 => ~ ! [Y3: code_integer] :
% 5.31/5.53 ~ ( member157494554546826820nteger @ ( produc1086072967326762835nteger @ X @ Y3 ) @ ( set_Pr920681315882439344nteger @ ( zip_Co3543743374963494515nteger @ Xs2 @ Ys ) ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % in_set_impl_in_set_zip1
% 5.31/5.53 thf(fact_2452_in__set__impl__in__set__zip1,axiom,
% 5.31/5.53 ! [Xs2: list_complex,Ys: list_VEBT_VEBT,X: complex] :
% 5.31/5.53 ( ( ( size_s3451745648224563538omplex @ Xs2 )
% 5.31/5.53 = ( size_s6755466524823107622T_VEBT @ Ys ) )
% 5.31/5.53 => ( ( member_complex @ X @ ( set_complex2 @ Xs2 ) )
% 5.31/5.53 => ~ ! [Y3: vEBT_VEBT] :
% 5.31/5.53 ~ ( member1978952105866562066T_VEBT @ ( produc2757191886755552429T_VEBT @ X @ Y3 ) @ ( set_Pr5158653123227461798T_VEBT @ ( zip_co9157518722488180109T_VEBT @ Xs2 @ Ys ) ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % in_set_impl_in_set_zip1
% 5.31/5.53 thf(fact_2453_in__set__impl__in__set__zip1,axiom,
% 5.31/5.53 ! [Xs2: list_real,Ys: list_VEBT_VEBT,X: real] :
% 5.31/5.53 ( ( ( size_size_list_real @ Xs2 )
% 5.31/5.53 = ( size_s6755466524823107622T_VEBT @ Ys ) )
% 5.31/5.53 => ( ( member_real @ X @ ( set_real2 @ Xs2 ) )
% 5.31/5.53 => ~ ! [Y3: vEBT_VEBT] :
% 5.31/5.53 ~ ( member7262085504369356948T_VEBT @ ( produc6931449550656315951T_VEBT @ X @ Y3 ) @ ( set_Pr8897343066327330088T_VEBT @ ( zip_real_VEBT_VEBT @ Xs2 @ Ys ) ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % in_set_impl_in_set_zip1
% 5.31/5.53 thf(fact_2454_in__set__impl__in__set__zip1,axiom,
% 5.31/5.53 ! [Xs2: list_complex,Ys: list_o,X: complex] :
% 5.31/5.53 ( ( ( size_s3451745648224563538omplex @ Xs2 )
% 5.31/5.53 = ( size_size_list_o @ Ys ) )
% 5.31/5.53 => ( ( member_complex @ X @ ( set_complex2 @ Xs2 ) )
% 5.31/5.53 => ~ ! [Y3: $o] :
% 5.31/5.53 ~ ( member6487239523555734774plex_o @ ( produc2908979694703026321plex_o @ X @ Y3 ) @ ( set_Pr6829704231520703882plex_o @ ( zip_complex_o @ Xs2 @ Ys ) ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % in_set_impl_in_set_zip1
% 5.31/5.53 thf(fact_2455_in__set__impl__in__set__zip1,axiom,
% 5.31/5.53 ! [Xs2: list_real,Ys: list_o,X: real] :
% 5.31/5.53 ( ( ( size_size_list_real @ Xs2 )
% 5.31/5.53 = ( size_size_list_o @ Ys ) )
% 5.31/5.53 => ( ( member_real @ X @ ( set_real2 @ Xs2 ) )
% 5.31/5.53 => ~ ! [Y3: $o] :
% 5.31/5.53 ~ ( member772602641336174712real_o @ ( product_Pair_real_o @ X @ Y3 ) @ ( set_Pr5196769464307566348real_o @ ( zip_real_o @ Xs2 @ Ys ) ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % in_set_impl_in_set_zip1
% 5.31/5.53 thf(fact_2456_in__set__impl__in__set__zip1,axiom,
% 5.31/5.53 ! [Xs2: list_complex,Ys: list_nat,X: complex] :
% 5.31/5.53 ( ( ( size_s3451745648224563538omplex @ Xs2 )
% 5.31/5.53 = ( size_size_list_nat @ Ys ) )
% 5.31/5.53 => ( ( member_complex @ X @ ( set_complex2 @ Xs2 ) )
% 5.31/5.53 => ~ ! [Y3: nat] :
% 5.31/5.53 ~ ( member4772924384108857480ex_nat @ ( produc1369629321580543767ex_nat @ X @ Y3 ) @ ( set_Pr9173661457260213492ex_nat @ ( zip_complex_nat @ Xs2 @ Ys ) ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % in_set_impl_in_set_zip1
% 5.31/5.53 thf(fact_2457_in__set__impl__in__set__zip1,axiom,
% 5.31/5.53 ! [Xs2: list_real,Ys: list_nat,X: real] :
% 5.31/5.53 ( ( ( size_size_list_real @ Xs2 )
% 5.31/5.53 = ( size_size_list_nat @ Ys ) )
% 5.31/5.53 => ( ( member_real @ X @ ( set_real2 @ Xs2 ) )
% 5.31/5.53 => ~ ! [Y3: nat] :
% 5.31/5.53 ~ ( member5805532792777349510al_nat @ ( produc3181502643871035669al_nat @ X @ Y3 ) @ ( set_Pr3174298344852596722al_nat @ ( zip_real_nat @ Xs2 @ Ys ) ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % in_set_impl_in_set_zip1
% 5.31/5.53 thf(fact_2458_in__set__impl__in__set__zip1,axiom,
% 5.31/5.53 ! [Xs2: list_complex,Ys: list_int,X: complex] :
% 5.31/5.53 ( ( ( size_s3451745648224563538omplex @ Xs2 )
% 5.31/5.53 = ( size_size_list_int @ Ys ) )
% 5.31/5.53 => ( ( member_complex @ X @ ( set_complex2 @ Xs2 ) )
% 5.31/5.53 => ~ ! [Y3: int] :
% 5.31/5.53 ~ ( member595073364599660772ex_int @ ( produc1367138851071493491ex_int @ X @ Y3 ) @ ( set_Pr4995810437751016784ex_int @ ( zip_complex_int @ Xs2 @ Ys ) ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % in_set_impl_in_set_zip1
% 5.31/5.53 thf(fact_2459_in__set__impl__in__set__zip1,axiom,
% 5.31/5.53 ! [Xs2: list_real,Ys: list_int,X: real] :
% 5.31/5.53 ( ( ( size_size_list_real @ Xs2 )
% 5.31/5.53 = ( size_size_list_int @ Ys ) )
% 5.31/5.53 => ( ( member_real @ X @ ( set_real2 @ Xs2 ) )
% 5.31/5.53 => ~ ! [Y3: int] :
% 5.31/5.53 ~ ( member1627681773268152802al_int @ ( produc3179012173361985393al_int @ X @ Y3 ) @ ( set_Pr8219819362198175822al_int @ ( zip_real_int @ Xs2 @ Ys ) ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % in_set_impl_in_set_zip1
% 5.31/5.53 thf(fact_2460_in__set__impl__in__set__zip1,axiom,
% 5.31/5.53 ! [Xs2: list_VEBT_VEBT,Ys: list_VEBT_VEBT,X: vEBT_VEBT] :
% 5.31/5.53 ( ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 5.31/5.53 = ( size_s6755466524823107622T_VEBT @ Ys ) )
% 5.31/5.53 => ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 5.31/5.53 => ~ ! [Y3: vEBT_VEBT] :
% 5.31/5.53 ~ ( member568628332442017744T_VEBT @ ( produc537772716801021591T_VEBT @ X @ Y3 ) @ ( set_Pr9182192707038809660T_VEBT @ ( zip_VE537291747668921783T_VEBT @ Xs2 @ Ys ) ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % in_set_impl_in_set_zip1
% 5.31/5.53 thf(fact_2461_in__set__impl__in__set__zip2,axiom,
% 5.31/5.53 ! [Xs2: list_Code_integer,Ys: list_Code_integer,Y: code_integer] :
% 5.31/5.53 ( ( ( size_s3445333598471063425nteger @ Xs2 )
% 5.31/5.53 = ( size_s3445333598471063425nteger @ Ys ) )
% 5.31/5.53 => ( ( member_Code_integer @ Y @ ( set_Code_integer2 @ Ys ) )
% 5.31/5.53 => ~ ! [X3: code_integer] :
% 5.31/5.53 ~ ( member157494554546826820nteger @ ( produc1086072967326762835nteger @ X3 @ Y ) @ ( set_Pr920681315882439344nteger @ ( zip_Co3543743374963494515nteger @ Xs2 @ Ys ) ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % in_set_impl_in_set_zip2
% 5.31/5.53 thf(fact_2462_in__set__impl__in__set__zip2,axiom,
% 5.31/5.53 ! [Xs2: list_VEBT_VEBT,Ys: list_complex,Y: complex] :
% 5.31/5.53 ( ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 5.31/5.53 = ( size_s3451745648224563538omplex @ Ys ) )
% 5.31/5.53 => ( ( member_complex @ Y @ ( set_complex2 @ Ys ) )
% 5.31/5.53 => ~ ! [X3: vEBT_VEBT] :
% 5.31/5.53 ~ ( member3207599676835851048omplex @ ( produc5617778602380981643omplex @ X3 @ Y ) @ ( set_Pr6387300694196750780omplex @ ( zip_VE2794733401258833515omplex @ Xs2 @ Ys ) ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % in_set_impl_in_set_zip2
% 5.31/5.53 thf(fact_2463_in__set__impl__in__set__zip2,axiom,
% 5.31/5.53 ! [Xs2: list_VEBT_VEBT,Ys: list_real,Y: real] :
% 5.31/5.53 ( ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 5.31/5.53 = ( size_size_list_real @ Ys ) )
% 5.31/5.53 => ( ( member_real @ Y @ ( set_real2 @ Ys ) )
% 5.31/5.53 => ~ ! [X3: vEBT_VEBT] :
% 5.31/5.53 ~ ( member8675245146396747942T_real @ ( produc8117437818029410057T_real @ X3 @ Y ) @ ( set_Pr1087130671499945274T_real @ ( zip_VEBT_VEBT_real @ Xs2 @ Ys ) ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % in_set_impl_in_set_zip2
% 5.31/5.53 thf(fact_2464_in__set__impl__in__set__zip2,axiom,
% 5.31/5.53 ! [Xs2: list_VEBT_VEBT,Ys: list_VEBT_VEBT,Y: vEBT_VEBT] :
% 5.31/5.53 ( ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 5.31/5.53 = ( size_s6755466524823107622T_VEBT @ Ys ) )
% 5.31/5.53 => ( ( member_VEBT_VEBT @ Y @ ( set_VEBT_VEBT2 @ Ys ) )
% 5.31/5.53 => ~ ! [X3: vEBT_VEBT] :
% 5.31/5.53 ~ ( member568628332442017744T_VEBT @ ( produc537772716801021591T_VEBT @ X3 @ Y ) @ ( set_Pr9182192707038809660T_VEBT @ ( zip_VE537291747668921783T_VEBT @ Xs2 @ Ys ) ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % in_set_impl_in_set_zip2
% 5.31/5.53 thf(fact_2465_in__set__impl__in__set__zip2,axiom,
% 5.31/5.53 ! [Xs2: list_VEBT_VEBT,Ys: list_o,Y: $o] :
% 5.31/5.53 ( ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 5.31/5.53 = ( size_size_list_o @ Ys ) )
% 5.31/5.53 => ( ( member_o @ Y @ ( set_o2 @ Ys ) )
% 5.31/5.53 => ~ ! [X3: vEBT_VEBT] :
% 5.31/5.53 ~ ( member3307348790968139188VEBT_o @ ( produc8721562602347293563VEBT_o @ X3 @ Y ) @ ( set_Pr7708085864119495200VEBT_o @ ( zip_VEBT_VEBT_o @ Xs2 @ Ys ) ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % in_set_impl_in_set_zip2
% 5.31/5.53 thf(fact_2466_in__set__impl__in__set__zip2,axiom,
% 5.31/5.53 ! [Xs2: list_VEBT_VEBT,Ys: list_nat,Y: nat] :
% 5.31/5.53 ( ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 5.31/5.53 = ( size_size_list_nat @ Ys ) )
% 5.31/5.53 => ( ( member_nat @ Y @ ( set_nat2 @ Ys ) )
% 5.31/5.53 => ~ ! [X3: vEBT_VEBT] :
% 5.31/5.53 ~ ( member373505688050248522BT_nat @ ( produc738532404422230701BT_nat @ X3 @ Y ) @ ( set_Pr7031586669278753246BT_nat @ ( zip_VEBT_VEBT_nat @ Xs2 @ Ys ) ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % in_set_impl_in_set_zip2
% 5.31/5.53 thf(fact_2467_in__set__impl__in__set__zip2,axiom,
% 5.31/5.53 ! [Xs2: list_VEBT_VEBT,Ys: list_int,Y: int] :
% 5.31/5.53 ( ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 5.31/5.53 = ( size_size_list_int @ Ys ) )
% 5.31/5.53 => ( ( member_int @ Y @ ( set_int2 @ Ys ) )
% 5.31/5.53 => ~ ! [X3: vEBT_VEBT] :
% 5.31/5.53 ~ ( member5419026705395827622BT_int @ ( produc736041933913180425BT_int @ X3 @ Y ) @ ( set_Pr2853735649769556538BT_int @ ( zip_VEBT_VEBT_int @ Xs2 @ Ys ) ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % in_set_impl_in_set_zip2
% 5.31/5.53 thf(fact_2468_in__set__impl__in__set__zip2,axiom,
% 5.31/5.53 ! [Xs2: list_o,Ys: list_complex,Y: complex] :
% 5.31/5.53 ( ( ( size_size_list_o @ Xs2 )
% 5.31/5.53 = ( size_s3451745648224563538omplex @ Ys ) )
% 5.31/5.53 => ( ( member_complex @ Y @ ( set_complex2 @ Ys ) )
% 5.31/5.53 => ~ ! [X3: $o] :
% 5.31/5.53 ~ ( member1046615901120239500omplex @ ( produc414345526774272751omplex @ X3 @ Y ) @ ( set_Pr1389080609085208608omplex @ ( zip_o_complex @ Xs2 @ Ys ) ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % in_set_impl_in_set_zip2
% 5.31/5.53 thf(fact_2469_in__set__impl__in__set__zip2,axiom,
% 5.31/5.53 ! [Xs2: list_o,Ys: list_real,Y: real] :
% 5.31/5.53 ( ( ( size_size_list_o @ Xs2 )
% 5.31/5.53 = ( size_size_list_real @ Ys ) )
% 5.31/5.53 => ( ( member_real @ Y @ ( set_real2 @ Ys ) )
% 5.31/5.53 => ~ ! [X3: $o] :
% 5.31/5.53 ~ ( member7400031367953476362o_real @ ( product_Pair_o_real @ X3 @ Y ) @ ( set_Pr2600826154070092190o_real @ ( zip_o_real @ Xs2 @ Ys ) ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % in_set_impl_in_set_zip2
% 5.31/5.53 thf(fact_2470_in__set__impl__in__set__zip2,axiom,
% 5.31/5.53 ! [Xs2: list_o,Ys: list_VEBT_VEBT,Y: vEBT_VEBT] :
% 5.31/5.53 ( ( ( size_size_list_o @ Xs2 )
% 5.31/5.53 = ( size_s6755466524823107622T_VEBT @ Ys ) )
% 5.31/5.53 => ( ( member_VEBT_VEBT @ Y @ ( set_VEBT_VEBT2 @ Ys ) )
% 5.31/5.53 => ~ ! [X3: $o] :
% 5.31/5.53 ~ ( member5477980866518848620T_VEBT @ ( produc2982872950893828659T_VEBT @ X3 @ Y ) @ ( set_Pr655345902815428824T_VEBT @ ( zip_o_VEBT_VEBT @ Xs2 @ Ys ) ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % in_set_impl_in_set_zip2
% 5.31/5.53 thf(fact_2471_Suc__le__length__iff,axiom,
% 5.31/5.53 ! [N: nat,Xs2: list_VEBT_VEBT] :
% 5.31/5.53 ( ( ord_less_eq_nat @ ( suc @ N ) @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 5.31/5.53 = ( ? [X4: vEBT_VEBT,Ys3: list_VEBT_VEBT] :
% 5.31/5.53 ( ( Xs2
% 5.31/5.53 = ( cons_VEBT_VEBT @ X4 @ Ys3 ) )
% 5.31/5.53 & ( ord_less_eq_nat @ N @ ( size_s6755466524823107622T_VEBT @ Ys3 ) ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % Suc_le_length_iff
% 5.31/5.53 thf(fact_2472_Suc__le__length__iff,axiom,
% 5.31/5.53 ! [N: nat,Xs2: list_o] :
% 5.31/5.53 ( ( ord_less_eq_nat @ ( suc @ N ) @ ( size_size_list_o @ Xs2 ) )
% 5.31/5.53 = ( ? [X4: $o,Ys3: list_o] :
% 5.31/5.53 ( ( Xs2
% 5.31/5.53 = ( cons_o @ X4 @ Ys3 ) )
% 5.31/5.53 & ( ord_less_eq_nat @ N @ ( size_size_list_o @ Ys3 ) ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % Suc_le_length_iff
% 5.31/5.53 thf(fact_2473_Suc__le__length__iff,axiom,
% 5.31/5.53 ! [N: nat,Xs2: list_nat] :
% 5.31/5.53 ( ( ord_less_eq_nat @ ( suc @ N ) @ ( size_size_list_nat @ Xs2 ) )
% 5.31/5.53 = ( ? [X4: nat,Ys3: list_nat] :
% 5.31/5.53 ( ( Xs2
% 5.31/5.53 = ( cons_nat @ X4 @ Ys3 ) )
% 5.31/5.53 & ( ord_less_eq_nat @ N @ ( size_size_list_nat @ Ys3 ) ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % Suc_le_length_iff
% 5.31/5.53 thf(fact_2474_Suc__le__length__iff,axiom,
% 5.31/5.53 ! [N: nat,Xs2: list_int] :
% 5.31/5.53 ( ( ord_less_eq_nat @ ( suc @ N ) @ ( size_size_list_int @ Xs2 ) )
% 5.31/5.53 = ( ? [X4: int,Ys3: list_int] :
% 5.31/5.53 ( ( Xs2
% 5.31/5.53 = ( cons_int @ X4 @ Ys3 ) )
% 5.31/5.53 & ( ord_less_eq_nat @ N @ ( size_size_list_int @ Ys3 ) ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % Suc_le_length_iff
% 5.31/5.53 thf(fact_2475_VEBT__internal_Oinsert_H_Osimps_I1_J,axiom,
% 5.31/5.53 ! [A: $o,B: $o,X: nat] :
% 5.31/5.53 ( ( vEBT_VEBT_insert @ ( vEBT_Leaf @ A @ B ) @ X )
% 5.31/5.53 = ( vEBT_vebt_insert @ ( vEBT_Leaf @ A @ B ) @ X ) ) ).
% 5.31/5.53
% 5.31/5.53 % VEBT_internal.insert'.simps(1)
% 5.31/5.53 thf(fact_2476_vebt__insert_Osimps_I3_J,axiom,
% 5.31/5.53 ! [Info2: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S2: vEBT_VEBT,X: nat] :
% 5.31/5.53 ( ( vEBT_vebt_insert @ ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts2 @ S2 ) @ X )
% 5.31/5.53 = ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts2 @ S2 ) ) ).
% 5.31/5.53
% 5.31/5.53 % vebt_insert.simps(3)
% 5.31/5.53 thf(fact_2477_vebt__insert_Osimps_I1_J,axiom,
% 5.31/5.53 ! [X: nat,A: $o,B: $o] :
% 5.31/5.53 ( ( ( X = zero_zero_nat )
% 5.31/5.53 => ( ( vEBT_vebt_insert @ ( vEBT_Leaf @ A @ B ) @ X )
% 5.31/5.53 = ( vEBT_Leaf @ $true @ B ) ) )
% 5.31/5.53 & ( ( X != zero_zero_nat )
% 5.31/5.53 => ( ( ( X = one_one_nat )
% 5.31/5.53 => ( ( vEBT_vebt_insert @ ( vEBT_Leaf @ A @ B ) @ X )
% 5.31/5.53 = ( vEBT_Leaf @ A @ $true ) ) )
% 5.31/5.53 & ( ( X != one_one_nat )
% 5.31/5.53 => ( ( vEBT_vebt_insert @ ( vEBT_Leaf @ A @ B ) @ X )
% 5.31/5.53 = ( vEBT_Leaf @ A @ B ) ) ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % vebt_insert.simps(1)
% 5.31/5.53 thf(fact_2478_list_Osize_I4_J,axiom,
% 5.31/5.53 ! [X21: vEBT_VEBT,X22: list_VEBT_VEBT] :
% 5.31/5.53 ( ( size_s6755466524823107622T_VEBT @ ( cons_VEBT_VEBT @ X21 @ X22 ) )
% 5.31/5.53 = ( plus_plus_nat @ ( size_s6755466524823107622T_VEBT @ X22 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % list.size(4)
% 5.31/5.53 thf(fact_2479_list_Osize_I4_J,axiom,
% 5.31/5.53 ! [X21: $o,X22: list_o] :
% 5.31/5.53 ( ( size_size_list_o @ ( cons_o @ X21 @ X22 ) )
% 5.31/5.53 = ( plus_plus_nat @ ( size_size_list_o @ X22 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % list.size(4)
% 5.31/5.53 thf(fact_2480_list_Osize_I4_J,axiom,
% 5.31/5.53 ! [X21: nat,X22: list_nat] :
% 5.31/5.53 ( ( size_size_list_nat @ ( cons_nat @ X21 @ X22 ) )
% 5.31/5.53 = ( plus_plus_nat @ ( size_size_list_nat @ X22 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % list.size(4)
% 5.31/5.53 thf(fact_2481_list_Osize_I4_J,axiom,
% 5.31/5.53 ! [X21: int,X22: list_int] :
% 5.31/5.53 ( ( size_size_list_int @ ( cons_int @ X21 @ X22 ) )
% 5.31/5.53 = ( plus_plus_nat @ ( size_size_list_int @ X22 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % list.size(4)
% 5.31/5.53 thf(fact_2482_nth__Cons_H,axiom,
% 5.31/5.53 ! [N: nat,X: vEBT_VEBT,Xs2: list_VEBT_VEBT] :
% 5.31/5.53 ( ( ( N = zero_zero_nat )
% 5.31/5.53 => ( ( nth_VEBT_VEBT @ ( cons_VEBT_VEBT @ X @ Xs2 ) @ N )
% 5.31/5.53 = X ) )
% 5.31/5.53 & ( ( N != zero_zero_nat )
% 5.31/5.53 => ( ( nth_VEBT_VEBT @ ( cons_VEBT_VEBT @ X @ Xs2 ) @ N )
% 5.31/5.53 = ( nth_VEBT_VEBT @ Xs2 @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % nth_Cons'
% 5.31/5.53 thf(fact_2483_nth__Cons_H,axiom,
% 5.31/5.53 ! [N: nat,X: nat,Xs2: list_nat] :
% 5.31/5.53 ( ( ( N = zero_zero_nat )
% 5.31/5.53 => ( ( nth_nat @ ( cons_nat @ X @ Xs2 ) @ N )
% 5.31/5.53 = X ) )
% 5.31/5.53 & ( ( N != zero_zero_nat )
% 5.31/5.53 => ( ( nth_nat @ ( cons_nat @ X @ Xs2 ) @ N )
% 5.31/5.53 = ( nth_nat @ Xs2 @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % nth_Cons'
% 5.31/5.53 thf(fact_2484_nth__equal__first__eq,axiom,
% 5.31/5.53 ! [X: complex,Xs2: list_complex,N: nat] :
% 5.31/5.53 ( ~ ( member_complex @ X @ ( set_complex2 @ Xs2 ) )
% 5.31/5.53 => ( ( ord_less_eq_nat @ N @ ( size_s3451745648224563538omplex @ Xs2 ) )
% 5.31/5.53 => ( ( ( nth_complex @ ( cons_complex @ X @ Xs2 ) @ N )
% 5.31/5.53 = X )
% 5.31/5.53 = ( N = zero_zero_nat ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % nth_equal_first_eq
% 5.31/5.53 thf(fact_2485_nth__equal__first__eq,axiom,
% 5.31/5.53 ! [X: real,Xs2: list_real,N: nat] :
% 5.31/5.53 ( ~ ( member_real @ X @ ( set_real2 @ Xs2 ) )
% 5.31/5.53 => ( ( ord_less_eq_nat @ N @ ( size_size_list_real @ Xs2 ) )
% 5.31/5.53 => ( ( ( nth_real @ ( cons_real @ X @ Xs2 ) @ N )
% 5.31/5.53 = X )
% 5.31/5.53 = ( N = zero_zero_nat ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % nth_equal_first_eq
% 5.31/5.53 thf(fact_2486_nth__equal__first__eq,axiom,
% 5.31/5.53 ! [X: set_nat,Xs2: list_set_nat,N: nat] :
% 5.31/5.53 ( ~ ( member_set_nat @ X @ ( set_set_nat2 @ Xs2 ) )
% 5.31/5.53 => ( ( ord_less_eq_nat @ N @ ( size_s3254054031482475050et_nat @ Xs2 ) )
% 5.31/5.53 => ( ( ( nth_set_nat @ ( cons_set_nat @ X @ Xs2 ) @ N )
% 5.31/5.53 = X )
% 5.31/5.53 = ( N = zero_zero_nat ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % nth_equal_first_eq
% 5.31/5.53 thf(fact_2487_nth__equal__first__eq,axiom,
% 5.31/5.53 ! [X: vEBT_VEBT,Xs2: list_VEBT_VEBT,N: nat] :
% 5.31/5.53 ( ~ ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 5.31/5.53 => ( ( ord_less_eq_nat @ N @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 5.31/5.53 => ( ( ( nth_VEBT_VEBT @ ( cons_VEBT_VEBT @ X @ Xs2 ) @ N )
% 5.31/5.53 = X )
% 5.31/5.53 = ( N = zero_zero_nat ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % nth_equal_first_eq
% 5.31/5.53 thf(fact_2488_nth__equal__first__eq,axiom,
% 5.31/5.53 ! [X: $o,Xs2: list_o,N: nat] :
% 5.31/5.53 ( ~ ( member_o @ X @ ( set_o2 @ Xs2 ) )
% 5.31/5.53 => ( ( ord_less_eq_nat @ N @ ( size_size_list_o @ Xs2 ) )
% 5.31/5.53 => ( ( ( nth_o @ ( cons_o @ X @ Xs2 ) @ N )
% 5.31/5.53 = X )
% 5.31/5.53 = ( N = zero_zero_nat ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % nth_equal_first_eq
% 5.31/5.53 thf(fact_2489_nth__equal__first__eq,axiom,
% 5.31/5.53 ! [X: nat,Xs2: list_nat,N: nat] :
% 5.31/5.53 ( ~ ( member_nat @ X @ ( set_nat2 @ Xs2 ) )
% 5.31/5.53 => ( ( ord_less_eq_nat @ N @ ( size_size_list_nat @ Xs2 ) )
% 5.31/5.53 => ( ( ( nth_nat @ ( cons_nat @ X @ Xs2 ) @ N )
% 5.31/5.53 = X )
% 5.31/5.53 = ( N = zero_zero_nat ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % nth_equal_first_eq
% 5.31/5.53 thf(fact_2490_nth__equal__first__eq,axiom,
% 5.31/5.53 ! [X: int,Xs2: list_int,N: nat] :
% 5.31/5.53 ( ~ ( member_int @ X @ ( set_int2 @ Xs2 ) )
% 5.31/5.53 => ( ( ord_less_eq_nat @ N @ ( size_size_list_int @ Xs2 ) )
% 5.31/5.53 => ( ( ( nth_int @ ( cons_int @ X @ Xs2 ) @ N )
% 5.31/5.53 = X )
% 5.31/5.53 = ( N = zero_zero_nat ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % nth_equal_first_eq
% 5.31/5.53 thf(fact_2491_nth__non__equal__first__eq,axiom,
% 5.31/5.53 ! [X: vEBT_VEBT,Y: vEBT_VEBT,Xs2: list_VEBT_VEBT,N: nat] :
% 5.31/5.53 ( ( X != Y )
% 5.31/5.53 => ( ( ( nth_VEBT_VEBT @ ( cons_VEBT_VEBT @ X @ Xs2 ) @ N )
% 5.31/5.53 = Y )
% 5.31/5.53 = ( ( ( nth_VEBT_VEBT @ Xs2 @ ( minus_minus_nat @ N @ one_one_nat ) )
% 5.31/5.53 = Y )
% 5.31/5.53 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % nth_non_equal_first_eq
% 5.31/5.53 thf(fact_2492_nth__non__equal__first__eq,axiom,
% 5.31/5.53 ! [X: nat,Y: nat,Xs2: list_nat,N: nat] :
% 5.31/5.53 ( ( X != Y )
% 5.31/5.53 => ( ( ( nth_nat @ ( cons_nat @ X @ Xs2 ) @ N )
% 5.31/5.53 = Y )
% 5.31/5.53 = ( ( ( nth_nat @ Xs2 @ ( minus_minus_nat @ N @ one_one_nat ) )
% 5.31/5.53 = Y )
% 5.31/5.53 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % nth_non_equal_first_eq
% 5.31/5.53 thf(fact_2493_length__Cons,axiom,
% 5.31/5.53 ! [X: vEBT_VEBT,Xs2: list_VEBT_VEBT] :
% 5.31/5.53 ( ( size_s6755466524823107622T_VEBT @ ( cons_VEBT_VEBT @ X @ Xs2 ) )
% 5.31/5.53 = ( suc @ ( size_s6755466524823107622T_VEBT @ Xs2 ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % length_Cons
% 5.31/5.53 thf(fact_2494_length__Cons,axiom,
% 5.31/5.53 ! [X: $o,Xs2: list_o] :
% 5.31/5.53 ( ( size_size_list_o @ ( cons_o @ X @ Xs2 ) )
% 5.31/5.53 = ( suc @ ( size_size_list_o @ Xs2 ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % length_Cons
% 5.31/5.53 thf(fact_2495_length__Cons,axiom,
% 5.31/5.53 ! [X: nat,Xs2: list_nat] :
% 5.31/5.53 ( ( size_size_list_nat @ ( cons_nat @ X @ Xs2 ) )
% 5.31/5.53 = ( suc @ ( size_size_list_nat @ Xs2 ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % length_Cons
% 5.31/5.53 thf(fact_2496_length__Cons,axiom,
% 5.31/5.53 ! [X: int,Xs2: list_int] :
% 5.31/5.53 ( ( size_size_list_int @ ( cons_int @ X @ Xs2 ) )
% 5.31/5.53 = ( suc @ ( size_size_list_int @ Xs2 ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % length_Cons
% 5.31/5.53 thf(fact_2497_dbl__inc__simps_I2_J,axiom,
% 5.31/5.53 ( ( neg_nu5831290666863070958nteger @ zero_z3403309356797280102nteger )
% 5.31/5.53 = one_one_Code_integer ) ).
% 5.31/5.53
% 5.31/5.53 % dbl_inc_simps(2)
% 5.31/5.53 thf(fact_2498_dbl__inc__simps_I2_J,axiom,
% 5.31/5.53 ( ( neg_nu8557863876264182079omplex @ zero_zero_complex )
% 5.31/5.53 = one_one_complex ) ).
% 5.31/5.53
% 5.31/5.53 % dbl_inc_simps(2)
% 5.31/5.53 thf(fact_2499_dbl__inc__simps_I2_J,axiom,
% 5.31/5.53 ( ( neg_nu8295874005876285629c_real @ zero_zero_real )
% 5.31/5.53 = one_one_real ) ).
% 5.31/5.53
% 5.31/5.53 % dbl_inc_simps(2)
% 5.31/5.53 thf(fact_2500_dbl__inc__simps_I2_J,axiom,
% 5.31/5.53 ( ( neg_nu5219082963157363817nc_rat @ zero_zero_rat )
% 5.31/5.53 = one_one_rat ) ).
% 5.31/5.53
% 5.31/5.53 % dbl_inc_simps(2)
% 5.31/5.53 thf(fact_2501_dbl__inc__simps_I2_J,axiom,
% 5.31/5.53 ( ( neg_nu5851722552734809277nc_int @ zero_zero_int )
% 5.31/5.53 = one_one_int ) ).
% 5.31/5.53
% 5.31/5.53 % dbl_inc_simps(2)
% 5.31/5.53 thf(fact_2502_enumerate__Suc_H,axiom,
% 5.31/5.53 ! [S3: set_nat,N: nat] :
% 5.31/5.53 ( ( infini8530281810654367211te_nat @ S3 @ ( suc @ N ) )
% 5.31/5.53 = ( infini8530281810654367211te_nat @ ( minus_minus_set_nat @ S3 @ ( insert_nat @ ( infini8530281810654367211te_nat @ S3 @ zero_zero_nat ) @ bot_bot_set_nat ) ) @ N ) ) ).
% 5.31/5.53
% 5.31/5.53 % enumerate_Suc'
% 5.31/5.53 thf(fact_2503_dbl__dec__def,axiom,
% 5.31/5.53 ( neg_nu7757733837767384882nteger
% 5.31/5.53 = ( ^ [X4: code_integer] : ( minus_8373710615458151222nteger @ ( plus_p5714425477246183910nteger @ X4 @ X4 ) @ one_one_Code_integer ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % dbl_dec_def
% 5.31/5.53 thf(fact_2504_dbl__dec__def,axiom,
% 5.31/5.53 ( neg_nu6511756317524482435omplex
% 5.31/5.53 = ( ^ [X4: complex] : ( minus_minus_complex @ ( plus_plus_complex @ X4 @ X4 ) @ one_one_complex ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % dbl_dec_def
% 5.31/5.53 thf(fact_2505_dbl__dec__def,axiom,
% 5.31/5.53 ( neg_nu6075765906172075777c_real
% 5.31/5.53 = ( ^ [X4: real] : ( minus_minus_real @ ( plus_plus_real @ X4 @ X4 ) @ one_one_real ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % dbl_dec_def
% 5.31/5.53 thf(fact_2506_dbl__dec__def,axiom,
% 5.31/5.53 ( neg_nu3179335615603231917ec_rat
% 5.31/5.53 = ( ^ [X4: rat] : ( minus_minus_rat @ ( plus_plus_rat @ X4 @ X4 ) @ one_one_rat ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % dbl_dec_def
% 5.31/5.53 thf(fact_2507_dbl__dec__def,axiom,
% 5.31/5.53 ( neg_nu3811975205180677377ec_int
% 5.31/5.53 = ( ^ [X4: int] : ( minus_minus_int @ ( plus_plus_int @ X4 @ X4 ) @ one_one_int ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % dbl_dec_def
% 5.31/5.53 thf(fact_2508_Gcd__fin__0__iff,axiom,
% 5.31/5.53 ! [A4: set_int] :
% 5.31/5.53 ( ( ( semiri4256215615220890538in_int @ A4 )
% 5.31/5.53 = zero_zero_int )
% 5.31/5.53 = ( ( ord_less_eq_set_int @ A4 @ ( insert_int @ zero_zero_int @ bot_bot_set_int ) )
% 5.31/5.53 & ( finite_finite_int @ A4 ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % Gcd_fin_0_iff
% 5.31/5.53 thf(fact_2509_Gcd__fin__0__iff,axiom,
% 5.31/5.53 ! [A4: set_nat] :
% 5.31/5.53 ( ( ( semiri4258706085729940814in_nat @ A4 )
% 5.31/5.53 = zero_zero_nat )
% 5.31/5.53 = ( ( ord_less_eq_set_nat @ A4 @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) )
% 5.31/5.53 & ( finite_finite_nat @ A4 ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % Gcd_fin_0_iff
% 5.31/5.53 thf(fact_2510_power__decreasing__iff,axiom,
% 5.31/5.53 ! [B: code_integer,M2: nat,N: nat] :
% 5.31/5.53 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 5.31/5.53 => ( ( ord_le6747313008572928689nteger @ B @ one_one_Code_integer )
% 5.31/5.53 => ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ B @ M2 ) @ ( power_8256067586552552935nteger @ B @ N ) )
% 5.31/5.53 = ( ord_less_eq_nat @ N @ M2 ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % power_decreasing_iff
% 5.31/5.53 thf(fact_2511_power__decreasing__iff,axiom,
% 5.31/5.53 ! [B: real,M2: nat,N: nat] :
% 5.31/5.53 ( ( ord_less_real @ zero_zero_real @ B )
% 5.31/5.53 => ( ( ord_less_real @ B @ one_one_real )
% 5.31/5.53 => ( ( ord_less_eq_real @ ( power_power_real @ B @ M2 ) @ ( power_power_real @ B @ N ) )
% 5.31/5.53 = ( ord_less_eq_nat @ N @ M2 ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % power_decreasing_iff
% 5.31/5.53 thf(fact_2512_power__decreasing__iff,axiom,
% 5.31/5.53 ! [B: rat,M2: nat,N: nat] :
% 5.31/5.53 ( ( ord_less_rat @ zero_zero_rat @ B )
% 5.31/5.53 => ( ( ord_less_rat @ B @ one_one_rat )
% 5.31/5.53 => ( ( ord_less_eq_rat @ ( power_power_rat @ B @ M2 ) @ ( power_power_rat @ B @ N ) )
% 5.31/5.53 = ( ord_less_eq_nat @ N @ M2 ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % power_decreasing_iff
% 5.31/5.53 thf(fact_2513_power__decreasing__iff,axiom,
% 5.31/5.53 ! [B: nat,M2: nat,N: nat] :
% 5.31/5.53 ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.31/5.53 => ( ( ord_less_nat @ B @ one_one_nat )
% 5.31/5.53 => ( ( ord_less_eq_nat @ ( power_power_nat @ B @ M2 ) @ ( power_power_nat @ B @ N ) )
% 5.31/5.53 = ( ord_less_eq_nat @ N @ M2 ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % power_decreasing_iff
% 5.31/5.53 thf(fact_2514_power__decreasing__iff,axiom,
% 5.31/5.53 ! [B: int,M2: nat,N: nat] :
% 5.31/5.53 ( ( ord_less_int @ zero_zero_int @ B )
% 5.31/5.53 => ( ( ord_less_int @ B @ one_one_int )
% 5.31/5.53 => ( ( ord_less_eq_int @ ( power_power_int @ B @ M2 ) @ ( power_power_int @ B @ N ) )
% 5.31/5.53 = ( ord_less_eq_nat @ N @ M2 ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % power_decreasing_iff
% 5.31/5.53 thf(fact_2515_card__insert__le__m1,axiom,
% 5.31/5.53 ! [N: nat,Y: set_real,X: real] :
% 5.31/5.53 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.53 => ( ( ord_less_eq_nat @ ( finite_card_real @ Y ) @ ( minus_minus_nat @ N @ one_one_nat ) )
% 5.31/5.53 => ( ord_less_eq_nat @ ( finite_card_real @ ( insert_real @ X @ Y ) ) @ N ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % card_insert_le_m1
% 5.31/5.53 thf(fact_2516_card__insert__le__m1,axiom,
% 5.31/5.53 ! [N: nat,Y: set_nat,X: nat] :
% 5.31/5.53 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.53 => ( ( ord_less_eq_nat @ ( finite_card_nat @ Y ) @ ( minus_minus_nat @ N @ one_one_nat ) )
% 5.31/5.53 => ( ord_less_eq_nat @ ( finite_card_nat @ ( insert_nat @ X @ Y ) ) @ N ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % card_insert_le_m1
% 5.31/5.53 thf(fact_2517_card__insert__le__m1,axiom,
% 5.31/5.53 ! [N: nat,Y: set_complex,X: complex] :
% 5.31/5.53 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.53 => ( ( ord_less_eq_nat @ ( finite_card_complex @ Y ) @ ( minus_minus_nat @ N @ one_one_nat ) )
% 5.31/5.53 => ( ord_less_eq_nat @ ( finite_card_complex @ ( insert_complex @ X @ Y ) ) @ N ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % card_insert_le_m1
% 5.31/5.53 thf(fact_2518_card__insert__le__m1,axiom,
% 5.31/5.53 ! [N: nat,Y: set_int,X: int] :
% 5.31/5.53 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.53 => ( ( ord_less_eq_nat @ ( finite_card_int @ Y ) @ ( minus_minus_nat @ N @ one_one_nat ) )
% 5.31/5.53 => ( ord_less_eq_nat @ ( finite_card_int @ ( insert_int @ X @ Y ) ) @ N ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % card_insert_le_m1
% 5.31/5.53 thf(fact_2519_card__insert__le__m1,axiom,
% 5.31/5.53 ! [N: nat,Y: set_list_nat,X: list_nat] :
% 5.31/5.53 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.53 => ( ( ord_less_eq_nat @ ( finite_card_list_nat @ Y ) @ ( minus_minus_nat @ N @ one_one_nat ) )
% 5.31/5.53 => ( ord_less_eq_nat @ ( finite_card_list_nat @ ( insert_list_nat @ X @ Y ) ) @ N ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % card_insert_le_m1
% 5.31/5.53 thf(fact_2520_card__insert__le__m1,axiom,
% 5.31/5.53 ! [N: nat,Y: set_set_nat,X: set_nat] :
% 5.31/5.53 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.53 => ( ( ord_less_eq_nat @ ( finite_card_set_nat @ Y ) @ ( minus_minus_nat @ N @ one_one_nat ) )
% 5.31/5.53 => ( ord_less_eq_nat @ ( finite_card_set_nat @ ( insert_set_nat @ X @ Y ) ) @ N ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % card_insert_le_m1
% 5.31/5.53 thf(fact_2521_count__notin,axiom,
% 5.31/5.53 ! [X: complex,Xs2: list_complex] :
% 5.31/5.53 ( ~ ( member_complex @ X @ ( set_complex2 @ Xs2 ) )
% 5.31/5.53 => ( ( count_list_complex @ Xs2 @ X )
% 5.31/5.53 = zero_zero_nat ) ) ).
% 5.31/5.53
% 5.31/5.53 % count_notin
% 5.31/5.53 thf(fact_2522_count__notin,axiom,
% 5.31/5.53 ! [X: real,Xs2: list_real] :
% 5.31/5.53 ( ~ ( member_real @ X @ ( set_real2 @ Xs2 ) )
% 5.31/5.53 => ( ( count_list_real @ Xs2 @ X )
% 5.31/5.53 = zero_zero_nat ) ) ).
% 5.31/5.53
% 5.31/5.53 % count_notin
% 5.31/5.53 thf(fact_2523_count__notin,axiom,
% 5.31/5.53 ! [X: set_nat,Xs2: list_set_nat] :
% 5.31/5.53 ( ~ ( member_set_nat @ X @ ( set_set_nat2 @ Xs2 ) )
% 5.31/5.53 => ( ( count_list_set_nat @ Xs2 @ X )
% 5.31/5.53 = zero_zero_nat ) ) ).
% 5.31/5.53
% 5.31/5.53 % count_notin
% 5.31/5.53 thf(fact_2524_count__notin,axiom,
% 5.31/5.53 ! [X: int,Xs2: list_int] :
% 5.31/5.53 ( ~ ( member_int @ X @ ( set_int2 @ Xs2 ) )
% 5.31/5.53 => ( ( count_list_int @ Xs2 @ X )
% 5.31/5.53 = zero_zero_nat ) ) ).
% 5.31/5.53
% 5.31/5.53 % count_notin
% 5.31/5.53 thf(fact_2525_count__notin,axiom,
% 5.31/5.53 ! [X: vEBT_VEBT,Xs2: list_VEBT_VEBT] :
% 5.31/5.53 ( ~ ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 5.31/5.53 => ( ( count_list_VEBT_VEBT @ Xs2 @ X )
% 5.31/5.53 = zero_zero_nat ) ) ).
% 5.31/5.53
% 5.31/5.53 % count_notin
% 5.31/5.53 thf(fact_2526_count__notin,axiom,
% 5.31/5.53 ! [X: nat,Xs2: list_nat] :
% 5.31/5.53 ( ~ ( member_nat @ X @ ( set_nat2 @ Xs2 ) )
% 5.31/5.53 => ( ( count_list_nat @ Xs2 @ X )
% 5.31/5.53 = zero_zero_nat ) ) ).
% 5.31/5.53
% 5.31/5.53 % count_notin
% 5.31/5.53 thf(fact_2527_Cons__lenlex__iff,axiom,
% 5.31/5.53 ! [M2: code_integer,Ms: list_Code_integer,N: code_integer,Ns: list_Code_integer,R3: set_Pr4811707699266497531nteger] :
% 5.31/5.53 ( ( member749217712838834276nteger @ ( produc750622340256944499nteger @ ( cons_Code_integer @ M2 @ Ms ) @ ( cons_Code_integer @ N @ Ns ) ) @ ( lenlex_Code_integer @ R3 ) )
% 5.31/5.53 = ( ( ord_less_nat @ ( size_s3445333598471063425nteger @ Ms ) @ ( size_s3445333598471063425nteger @ Ns ) )
% 5.31/5.53 | ( ( ( size_s3445333598471063425nteger @ Ms )
% 5.31/5.53 = ( size_s3445333598471063425nteger @ Ns ) )
% 5.31/5.53 & ( member157494554546826820nteger @ ( produc1086072967326762835nteger @ M2 @ N ) @ R3 ) )
% 5.31/5.53 | ( ( M2 = N )
% 5.31/5.53 & ( member749217712838834276nteger @ ( produc750622340256944499nteger @ Ms @ Ns ) @ ( lenlex_Code_integer @ R3 ) ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % Cons_lenlex_iff
% 5.31/5.53 thf(fact_2528_Cons__lenlex__iff,axiom,
% 5.31/5.53 ! [M2: product_prod_nat_nat,Ms: list_P6011104703257516679at_nat,N: product_prod_nat_nat,Ns: list_P6011104703257516679at_nat,R3: set_Pr8693737435421807431at_nat] :
% 5.31/5.53 ( ( member6693912407220327184at_nat @ ( produc5943733680697469783at_nat @ ( cons_P6512896166579812791at_nat @ M2 @ Ms ) @ ( cons_P6512896166579812791at_nat @ N @ Ns ) ) @ ( lenlex325483962726685836at_nat @ R3 ) )
% 5.31/5.53 = ( ( ord_less_nat @ ( size_s5460976970255530739at_nat @ Ms ) @ ( size_s5460976970255530739at_nat @ Ns ) )
% 5.31/5.53 | ( ( ( size_s5460976970255530739at_nat @ Ms )
% 5.31/5.53 = ( size_s5460976970255530739at_nat @ Ns ) )
% 5.31/5.53 & ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ M2 @ N ) @ R3 ) )
% 5.31/5.53 | ( ( M2 = N )
% 5.31/5.53 & ( member6693912407220327184at_nat @ ( produc5943733680697469783at_nat @ Ms @ Ns ) @ ( lenlex325483962726685836at_nat @ R3 ) ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % Cons_lenlex_iff
% 5.31/5.53 thf(fact_2529_Cons__lenlex__iff,axiom,
% 5.31/5.53 ! [M2: set_Pr1261947904930325089at_nat,Ms: list_s1210847774152347623at_nat,N: set_Pr1261947904930325089at_nat,Ns: list_s1210847774152347623at_nat,R3: set_Pr4329608150637261639at_nat] :
% 5.31/5.53 ( ( member4080735728053443344at_nat @ ( produc7536900900485677911at_nat @ ( cons_s6881495754146722583at_nat @ M2 @ Ms ) @ ( cons_s6881495754146722583at_nat @ N @ Ns ) ) @ ( lenlex1357538814655152620at_nat @ R3 ) )
% 5.31/5.53 = ( ( ord_less_nat @ ( size_s8736152011456118867at_nat @ Ms ) @ ( size_s8736152011456118867at_nat @ Ns ) )
% 5.31/5.53 | ( ( ( size_s8736152011456118867at_nat @ Ms )
% 5.31/5.53 = ( size_s8736152011456118867at_nat @ Ns ) )
% 5.31/5.53 & ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ M2 @ N ) @ R3 ) )
% 5.31/5.53 | ( ( M2 = N )
% 5.31/5.53 & ( member4080735728053443344at_nat @ ( produc7536900900485677911at_nat @ Ms @ Ns ) @ ( lenlex1357538814655152620at_nat @ R3 ) ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % Cons_lenlex_iff
% 5.31/5.53 thf(fact_2530_Cons__lenlex__iff,axiom,
% 5.31/5.53 ! [M2: vEBT_VEBT,Ms: list_VEBT_VEBT,N: vEBT_VEBT,Ns: list_VEBT_VEBT,R3: set_Pr6192946355708809607T_VEBT] :
% 5.31/5.53 ( ( member4439316823752958928T_VEBT @ ( produc3897820843166775703T_VEBT @ ( cons_VEBT_VEBT @ M2 @ Ms ) @ ( cons_VEBT_VEBT @ N @ Ns ) ) @ ( lenlex_VEBT_VEBT @ R3 ) )
% 5.31/5.53 = ( ( ord_less_nat @ ( size_s6755466524823107622T_VEBT @ Ms ) @ ( size_s6755466524823107622T_VEBT @ Ns ) )
% 5.31/5.53 | ( ( ( size_s6755466524823107622T_VEBT @ Ms )
% 5.31/5.53 = ( size_s6755466524823107622T_VEBT @ Ns ) )
% 5.31/5.53 & ( member568628332442017744T_VEBT @ ( produc537772716801021591T_VEBT @ M2 @ N ) @ R3 ) )
% 5.31/5.53 | ( ( M2 = N )
% 5.31/5.53 & ( member4439316823752958928T_VEBT @ ( produc3897820843166775703T_VEBT @ Ms @ Ns ) @ ( lenlex_VEBT_VEBT @ R3 ) ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % Cons_lenlex_iff
% 5.31/5.53 thf(fact_2531_Cons__lenlex__iff,axiom,
% 5.31/5.53 ! [M2: $o,Ms: list_o,N: $o,Ns: list_o,R3: set_Product_prod_o_o] :
% 5.31/5.53 ( ( member4159035015898711888list_o @ ( produc8435520187683070743list_o @ ( cons_o @ M2 @ Ms ) @ ( cons_o @ N @ Ns ) ) @ ( lenlex_o @ R3 ) )
% 5.31/5.53 = ( ( ord_less_nat @ ( size_size_list_o @ Ms ) @ ( size_size_list_o @ Ns ) )
% 5.31/5.53 | ( ( ( size_size_list_o @ Ms )
% 5.31/5.53 = ( size_size_list_o @ Ns ) )
% 5.31/5.53 & ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ M2 @ N ) @ R3 ) )
% 5.31/5.53 | ( ( M2 = N )
% 5.31/5.53 & ( member4159035015898711888list_o @ ( produc8435520187683070743list_o @ Ms @ Ns ) @ ( lenlex_o @ R3 ) ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % Cons_lenlex_iff
% 5.31/5.53 thf(fact_2532_Cons__lenlex__iff,axiom,
% 5.31/5.53 ! [M2: nat,Ms: list_nat,N: nat,Ns: list_nat,R3: set_Pr1261947904930325089at_nat] :
% 5.31/5.53 ( ( member7340969449405702474st_nat @ ( produc2694037385005941721st_nat @ ( cons_nat @ M2 @ Ms ) @ ( cons_nat @ N @ Ns ) ) @ ( lenlex_nat @ R3 ) )
% 5.31/5.53 = ( ( ord_less_nat @ ( size_size_list_nat @ Ms ) @ ( size_size_list_nat @ Ns ) )
% 5.31/5.53 | ( ( ( size_size_list_nat @ Ms )
% 5.31/5.53 = ( size_size_list_nat @ Ns ) )
% 5.31/5.53 & ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ M2 @ N ) @ R3 ) )
% 5.31/5.53 | ( ( M2 = N )
% 5.31/5.53 & ( member7340969449405702474st_nat @ ( produc2694037385005941721st_nat @ Ms @ Ns ) @ ( lenlex_nat @ R3 ) ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % Cons_lenlex_iff
% 5.31/5.53 thf(fact_2533_Cons__lenlex__iff,axiom,
% 5.31/5.53 ! [M2: int,Ms: list_int,N: int,Ns: list_int,R3: set_Pr958786334691620121nt_int] :
% 5.31/5.53 ( ( member6698963635872716290st_int @ ( produc364263696895485585st_int @ ( cons_int @ M2 @ Ms ) @ ( cons_int @ N @ Ns ) ) @ ( lenlex_int @ R3 ) )
% 5.31/5.53 = ( ( ord_less_nat @ ( size_size_list_int @ Ms ) @ ( size_size_list_int @ Ns ) )
% 5.31/5.53 | ( ( ( size_size_list_int @ Ms )
% 5.31/5.53 = ( size_size_list_int @ Ns ) )
% 5.31/5.53 & ( member5262025264175285858nt_int @ ( product_Pair_int_int @ M2 @ N ) @ R3 ) )
% 5.31/5.53 | ( ( M2 = N )
% 5.31/5.53 & ( member6698963635872716290st_int @ ( produc364263696895485585st_int @ Ms @ Ns ) @ ( lenlex_int @ R3 ) ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % Cons_lenlex_iff
% 5.31/5.53 thf(fact_2534_power__shift,axiom,
% 5.31/5.53 ! [X: nat,Y: nat,Z3: nat] :
% 5.31/5.53 ( ( ( power_power_nat @ X @ Y )
% 5.31/5.53 = Z3 )
% 5.31/5.53 = ( ( vEBT_VEBT_power @ ( some_nat @ X ) @ ( some_nat @ Y ) )
% 5.31/5.53 = ( some_nat @ Z3 ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % power_shift
% 5.31/5.53 thf(fact_2535_local_Opower__def,axiom,
% 5.31/5.53 ( vEBT_VEBT_power
% 5.31/5.53 = ( vEBT_V4262088993061758097ft_nat @ power_power_nat ) ) ).
% 5.31/5.53
% 5.31/5.53 % local.power_def
% 5.31/5.53 thf(fact_2536_nat__power__eq__Suc__0__iff,axiom,
% 5.31/5.53 ! [X: nat,M2: nat] :
% 5.31/5.53 ( ( ( power_power_nat @ X @ M2 )
% 5.31/5.53 = ( suc @ zero_zero_nat ) )
% 5.31/5.53 = ( ( M2 = zero_zero_nat )
% 5.31/5.53 | ( X
% 5.31/5.53 = ( suc @ zero_zero_nat ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % nat_power_eq_Suc_0_iff
% 5.31/5.53 thf(fact_2537_power__Suc__0,axiom,
% 5.31/5.53 ! [N: nat] :
% 5.31/5.53 ( ( power_power_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.31/5.53 = ( suc @ zero_zero_nat ) ) ).
% 5.31/5.53
% 5.31/5.53 % power_Suc_0
% 5.31/5.53 thf(fact_2538_nat__zero__less__power__iff,axiom,
% 5.31/5.53 ! [X: nat,N: nat] :
% 5.31/5.53 ( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ X @ N ) )
% 5.31/5.53 = ( ( ord_less_nat @ zero_zero_nat @ X )
% 5.31/5.53 | ( N = zero_zero_nat ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % nat_zero_less_power_iff
% 5.31/5.53 thf(fact_2539_dbl__dec__simps_I3_J,axiom,
% 5.31/5.53 ( ( neg_nu7757733837767384882nteger @ one_one_Code_integer )
% 5.31/5.53 = one_one_Code_integer ) ).
% 5.31/5.53
% 5.31/5.53 % dbl_dec_simps(3)
% 5.31/5.53 thf(fact_2540_dbl__dec__simps_I3_J,axiom,
% 5.31/5.53 ( ( neg_nu6511756317524482435omplex @ one_one_complex )
% 5.31/5.53 = one_one_complex ) ).
% 5.31/5.53
% 5.31/5.53 % dbl_dec_simps(3)
% 5.31/5.53 thf(fact_2541_dbl__dec__simps_I3_J,axiom,
% 5.31/5.53 ( ( neg_nu6075765906172075777c_real @ one_one_real )
% 5.31/5.53 = one_one_real ) ).
% 5.31/5.53
% 5.31/5.53 % dbl_dec_simps(3)
% 5.31/5.53 thf(fact_2542_dbl__dec__simps_I3_J,axiom,
% 5.31/5.53 ( ( neg_nu3811975205180677377ec_int @ one_one_int )
% 5.31/5.53 = one_one_int ) ).
% 5.31/5.53
% 5.31/5.53 % dbl_dec_simps(3)
% 5.31/5.53 thf(fact_2543_power__0__Suc,axiom,
% 5.31/5.53 ! [N: nat] :
% 5.31/5.53 ( ( power_power_rat @ zero_zero_rat @ ( suc @ N ) )
% 5.31/5.53 = zero_zero_rat ) ).
% 5.31/5.53
% 5.31/5.53 % power_0_Suc
% 5.31/5.53 thf(fact_2544_power__0__Suc,axiom,
% 5.31/5.53 ! [N: nat] :
% 5.31/5.53 ( ( power_power_nat @ zero_zero_nat @ ( suc @ N ) )
% 5.31/5.53 = zero_zero_nat ) ).
% 5.31/5.53
% 5.31/5.53 % power_0_Suc
% 5.31/5.53 thf(fact_2545_power__0__Suc,axiom,
% 5.31/5.53 ! [N: nat] :
% 5.31/5.53 ( ( power_power_real @ zero_zero_real @ ( suc @ N ) )
% 5.31/5.53 = zero_zero_real ) ).
% 5.31/5.53
% 5.31/5.53 % power_0_Suc
% 5.31/5.53 thf(fact_2546_power__0__Suc,axiom,
% 5.31/5.53 ! [N: nat] :
% 5.31/5.53 ( ( power_power_int @ zero_zero_int @ ( suc @ N ) )
% 5.31/5.53 = zero_zero_int ) ).
% 5.31/5.53
% 5.31/5.53 % power_0_Suc
% 5.31/5.53 thf(fact_2547_power__0__Suc,axiom,
% 5.31/5.53 ! [N: nat] :
% 5.31/5.53 ( ( power_power_complex @ zero_zero_complex @ ( suc @ N ) )
% 5.31/5.53 = zero_zero_complex ) ).
% 5.31/5.53
% 5.31/5.53 % power_0_Suc
% 5.31/5.53 thf(fact_2548_power__Suc0__right,axiom,
% 5.31/5.53 ! [A: nat] :
% 5.31/5.53 ( ( power_power_nat @ A @ ( suc @ zero_zero_nat ) )
% 5.31/5.53 = A ) ).
% 5.31/5.53
% 5.31/5.53 % power_Suc0_right
% 5.31/5.53 thf(fact_2549_power__Suc0__right,axiom,
% 5.31/5.53 ! [A: real] :
% 5.31/5.53 ( ( power_power_real @ A @ ( suc @ zero_zero_nat ) )
% 5.31/5.53 = A ) ).
% 5.31/5.53
% 5.31/5.53 % power_Suc0_right
% 5.31/5.53 thf(fact_2550_power__Suc0__right,axiom,
% 5.31/5.53 ! [A: int] :
% 5.31/5.53 ( ( power_power_int @ A @ ( suc @ zero_zero_nat ) )
% 5.31/5.53 = A ) ).
% 5.31/5.53
% 5.31/5.53 % power_Suc0_right
% 5.31/5.53 thf(fact_2551_power__Suc0__right,axiom,
% 5.31/5.53 ! [A: complex] :
% 5.31/5.53 ( ( power_power_complex @ A @ ( suc @ zero_zero_nat ) )
% 5.31/5.53 = A ) ).
% 5.31/5.53
% 5.31/5.53 % power_Suc0_right
% 5.31/5.53 thf(fact_2552_card_Oempty,axiom,
% 5.31/5.53 ( ( finite_card_complex @ bot_bot_set_complex )
% 5.31/5.53 = zero_zero_nat ) ).
% 5.31/5.53
% 5.31/5.53 % card.empty
% 5.31/5.53 thf(fact_2553_card_Oempty,axiom,
% 5.31/5.53 ( ( finite_card_list_nat @ bot_bot_set_list_nat )
% 5.31/5.53 = zero_zero_nat ) ).
% 5.31/5.53
% 5.31/5.53 % card.empty
% 5.31/5.53 thf(fact_2554_card_Oempty,axiom,
% 5.31/5.53 ( ( finite_card_set_nat @ bot_bot_set_set_nat )
% 5.31/5.53 = zero_zero_nat ) ).
% 5.31/5.53
% 5.31/5.53 % card.empty
% 5.31/5.53 thf(fact_2555_card_Oempty,axiom,
% 5.31/5.53 ( ( finite_card_nat @ bot_bot_set_nat )
% 5.31/5.53 = zero_zero_nat ) ).
% 5.31/5.53
% 5.31/5.53 % card.empty
% 5.31/5.53 thf(fact_2556_card_Oempty,axiom,
% 5.31/5.53 ( ( finite_card_int @ bot_bot_set_int )
% 5.31/5.53 = zero_zero_nat ) ).
% 5.31/5.53
% 5.31/5.53 % card.empty
% 5.31/5.53 thf(fact_2557_card_Oempty,axiom,
% 5.31/5.53 ( ( finite_card_real @ bot_bot_set_real )
% 5.31/5.53 = zero_zero_nat ) ).
% 5.31/5.53
% 5.31/5.53 % card.empty
% 5.31/5.53 thf(fact_2558_card_Oinfinite,axiom,
% 5.31/5.53 ! [A4: set_list_nat] :
% 5.31/5.53 ( ~ ( finite8100373058378681591st_nat @ A4 )
% 5.31/5.53 => ( ( finite_card_list_nat @ A4 )
% 5.31/5.53 = zero_zero_nat ) ) ).
% 5.31/5.53
% 5.31/5.53 % card.infinite
% 5.31/5.53 thf(fact_2559_card_Oinfinite,axiom,
% 5.31/5.53 ! [A4: set_set_nat] :
% 5.31/5.53 ( ~ ( finite1152437895449049373et_nat @ A4 )
% 5.31/5.53 => ( ( finite_card_set_nat @ A4 )
% 5.31/5.53 = zero_zero_nat ) ) ).
% 5.31/5.53
% 5.31/5.53 % card.infinite
% 5.31/5.53 thf(fact_2560_card_Oinfinite,axiom,
% 5.31/5.53 ! [A4: set_nat] :
% 5.31/5.53 ( ~ ( finite_finite_nat @ A4 )
% 5.31/5.53 => ( ( finite_card_nat @ A4 )
% 5.31/5.53 = zero_zero_nat ) ) ).
% 5.31/5.53
% 5.31/5.53 % card.infinite
% 5.31/5.53 thf(fact_2561_card_Oinfinite,axiom,
% 5.31/5.53 ! [A4: set_int] :
% 5.31/5.53 ( ~ ( finite_finite_int @ A4 )
% 5.31/5.53 => ( ( finite_card_int @ A4 )
% 5.31/5.53 = zero_zero_nat ) ) ).
% 5.31/5.53
% 5.31/5.53 % card.infinite
% 5.31/5.53 thf(fact_2562_card_Oinfinite,axiom,
% 5.31/5.53 ! [A4: set_complex] :
% 5.31/5.53 ( ~ ( finite3207457112153483333omplex @ A4 )
% 5.31/5.53 => ( ( finite_card_complex @ A4 )
% 5.31/5.53 = zero_zero_nat ) ) ).
% 5.31/5.53
% 5.31/5.53 % card.infinite
% 5.31/5.53 thf(fact_2563_Gcd__fin_Oempty,axiom,
% 5.31/5.53 ( ( semiri4258706085729940814in_nat @ bot_bot_set_nat )
% 5.31/5.53 = zero_zero_nat ) ).
% 5.31/5.53
% 5.31/5.53 % Gcd_fin.empty
% 5.31/5.53 thf(fact_2564_Gcd__fin_Oempty,axiom,
% 5.31/5.53 ( ( semiri4256215615220890538in_int @ bot_bot_set_int )
% 5.31/5.53 = zero_zero_int ) ).
% 5.31/5.53
% 5.31/5.53 % Gcd_fin.empty
% 5.31/5.53 thf(fact_2565_power__eq__0__iff,axiom,
% 5.31/5.53 ! [A: rat,N: nat] :
% 5.31/5.53 ( ( ( power_power_rat @ A @ N )
% 5.31/5.53 = zero_zero_rat )
% 5.31/5.53 = ( ( A = zero_zero_rat )
% 5.31/5.53 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % power_eq_0_iff
% 5.31/5.53 thf(fact_2566_power__eq__0__iff,axiom,
% 5.31/5.53 ! [A: nat,N: nat] :
% 5.31/5.53 ( ( ( power_power_nat @ A @ N )
% 5.31/5.53 = zero_zero_nat )
% 5.31/5.53 = ( ( A = zero_zero_nat )
% 5.31/5.53 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % power_eq_0_iff
% 5.31/5.53 thf(fact_2567_power__eq__0__iff,axiom,
% 5.31/5.53 ! [A: real,N: nat] :
% 5.31/5.53 ( ( ( power_power_real @ A @ N )
% 5.31/5.53 = zero_zero_real )
% 5.31/5.53 = ( ( A = zero_zero_real )
% 5.31/5.53 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % power_eq_0_iff
% 5.31/5.53 thf(fact_2568_power__eq__0__iff,axiom,
% 5.31/5.53 ! [A: int,N: nat] :
% 5.31/5.53 ( ( ( power_power_int @ A @ N )
% 5.31/5.53 = zero_zero_int )
% 5.31/5.53 = ( ( A = zero_zero_int )
% 5.31/5.53 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % power_eq_0_iff
% 5.31/5.53 thf(fact_2569_power__eq__0__iff,axiom,
% 5.31/5.53 ! [A: complex,N: nat] :
% 5.31/5.53 ( ( ( power_power_complex @ A @ N )
% 5.31/5.53 = zero_zero_complex )
% 5.31/5.53 = ( ( A = zero_zero_complex )
% 5.31/5.53 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % power_eq_0_iff
% 5.31/5.53 thf(fact_2570_card__0__eq,axiom,
% 5.31/5.53 ! [A4: set_list_nat] :
% 5.31/5.53 ( ( finite8100373058378681591st_nat @ A4 )
% 5.31/5.53 => ( ( ( finite_card_list_nat @ A4 )
% 5.31/5.53 = zero_zero_nat )
% 5.31/5.53 = ( A4 = bot_bot_set_list_nat ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % card_0_eq
% 5.31/5.53 thf(fact_2571_card__0__eq,axiom,
% 5.31/5.53 ! [A4: set_set_nat] :
% 5.31/5.53 ( ( finite1152437895449049373et_nat @ A4 )
% 5.31/5.53 => ( ( ( finite_card_set_nat @ A4 )
% 5.31/5.53 = zero_zero_nat )
% 5.31/5.53 = ( A4 = bot_bot_set_set_nat ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % card_0_eq
% 5.31/5.53 thf(fact_2572_card__0__eq,axiom,
% 5.31/5.53 ! [A4: set_complex] :
% 5.31/5.53 ( ( finite3207457112153483333omplex @ A4 )
% 5.31/5.53 => ( ( ( finite_card_complex @ A4 )
% 5.31/5.53 = zero_zero_nat )
% 5.31/5.53 = ( A4 = bot_bot_set_complex ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % card_0_eq
% 5.31/5.53 thf(fact_2573_card__0__eq,axiom,
% 5.31/5.53 ! [A4: set_nat] :
% 5.31/5.53 ( ( finite_finite_nat @ A4 )
% 5.31/5.53 => ( ( ( finite_card_nat @ A4 )
% 5.31/5.53 = zero_zero_nat )
% 5.31/5.53 = ( A4 = bot_bot_set_nat ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % card_0_eq
% 5.31/5.53 thf(fact_2574_card__0__eq,axiom,
% 5.31/5.53 ! [A4: set_int] :
% 5.31/5.53 ( ( finite_finite_int @ A4 )
% 5.31/5.53 => ( ( ( finite_card_int @ A4 )
% 5.31/5.53 = zero_zero_nat )
% 5.31/5.53 = ( A4 = bot_bot_set_int ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % card_0_eq
% 5.31/5.53 thf(fact_2575_card__0__eq,axiom,
% 5.31/5.53 ! [A4: set_real] :
% 5.31/5.53 ( ( finite_finite_real @ A4 )
% 5.31/5.53 => ( ( ( finite_card_real @ A4 )
% 5.31/5.53 = zero_zero_nat )
% 5.31/5.53 = ( A4 = bot_bot_set_real ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % card_0_eq
% 5.31/5.53 thf(fact_2576_card__insert__disjoint,axiom,
% 5.31/5.53 ! [A4: set_real,X: real] :
% 5.31/5.53 ( ( finite_finite_real @ A4 )
% 5.31/5.53 => ( ~ ( member_real @ X @ A4 )
% 5.31/5.53 => ( ( finite_card_real @ ( insert_real @ X @ A4 ) )
% 5.31/5.53 = ( suc @ ( finite_card_real @ A4 ) ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % card_insert_disjoint
% 5.31/5.53 thf(fact_2577_card__insert__disjoint,axiom,
% 5.31/5.53 ! [A4: set_list_nat,X: list_nat] :
% 5.31/5.53 ( ( finite8100373058378681591st_nat @ A4 )
% 5.31/5.53 => ( ~ ( member_list_nat @ X @ A4 )
% 5.31/5.53 => ( ( finite_card_list_nat @ ( insert_list_nat @ X @ A4 ) )
% 5.31/5.53 = ( suc @ ( finite_card_list_nat @ A4 ) ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % card_insert_disjoint
% 5.31/5.53 thf(fact_2578_card__insert__disjoint,axiom,
% 5.31/5.53 ! [A4: set_set_nat,X: set_nat] :
% 5.31/5.53 ( ( finite1152437895449049373et_nat @ A4 )
% 5.31/5.53 => ( ~ ( member_set_nat @ X @ A4 )
% 5.31/5.53 => ( ( finite_card_set_nat @ ( insert_set_nat @ X @ A4 ) )
% 5.31/5.53 = ( suc @ ( finite_card_set_nat @ A4 ) ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % card_insert_disjoint
% 5.31/5.53 thf(fact_2579_card__insert__disjoint,axiom,
% 5.31/5.53 ! [A4: set_nat,X: nat] :
% 5.31/5.53 ( ( finite_finite_nat @ A4 )
% 5.31/5.53 => ( ~ ( member_nat @ X @ A4 )
% 5.31/5.53 => ( ( finite_card_nat @ ( insert_nat @ X @ A4 ) )
% 5.31/5.53 = ( suc @ ( finite_card_nat @ A4 ) ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % card_insert_disjoint
% 5.31/5.53 thf(fact_2580_card__insert__disjoint,axiom,
% 5.31/5.53 ! [A4: set_int,X: int] :
% 5.31/5.53 ( ( finite_finite_int @ A4 )
% 5.31/5.53 => ( ~ ( member_int @ X @ A4 )
% 5.31/5.53 => ( ( finite_card_int @ ( insert_int @ X @ A4 ) )
% 5.31/5.53 = ( suc @ ( finite_card_int @ A4 ) ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % card_insert_disjoint
% 5.31/5.53 thf(fact_2581_card__insert__disjoint,axiom,
% 5.31/5.53 ! [A4: set_complex,X: complex] :
% 5.31/5.53 ( ( finite3207457112153483333omplex @ A4 )
% 5.31/5.53 => ( ~ ( member_complex @ X @ A4 )
% 5.31/5.53 => ( ( finite_card_complex @ ( insert_complex @ X @ A4 ) )
% 5.31/5.53 = ( suc @ ( finite_card_complex @ A4 ) ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % card_insert_disjoint
% 5.31/5.53 thf(fact_2582_power__strict__decreasing__iff,axiom,
% 5.31/5.53 ! [B: code_integer,M2: nat,N: nat] :
% 5.31/5.53 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 5.31/5.53 => ( ( ord_le6747313008572928689nteger @ B @ one_one_Code_integer )
% 5.31/5.53 => ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ B @ M2 ) @ ( power_8256067586552552935nteger @ B @ N ) )
% 5.31/5.53 = ( ord_less_nat @ N @ M2 ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % power_strict_decreasing_iff
% 5.31/5.53 thf(fact_2583_power__strict__decreasing__iff,axiom,
% 5.31/5.53 ! [B: real,M2: nat,N: nat] :
% 5.31/5.53 ( ( ord_less_real @ zero_zero_real @ B )
% 5.31/5.53 => ( ( ord_less_real @ B @ one_one_real )
% 5.31/5.53 => ( ( ord_less_real @ ( power_power_real @ B @ M2 ) @ ( power_power_real @ B @ N ) )
% 5.31/5.53 = ( ord_less_nat @ N @ M2 ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % power_strict_decreasing_iff
% 5.31/5.53 thf(fact_2584_power__strict__decreasing__iff,axiom,
% 5.31/5.53 ! [B: rat,M2: nat,N: nat] :
% 5.31/5.53 ( ( ord_less_rat @ zero_zero_rat @ B )
% 5.31/5.53 => ( ( ord_less_rat @ B @ one_one_rat )
% 5.31/5.53 => ( ( ord_less_rat @ ( power_power_rat @ B @ M2 ) @ ( power_power_rat @ B @ N ) )
% 5.31/5.53 = ( ord_less_nat @ N @ M2 ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % power_strict_decreasing_iff
% 5.31/5.53 thf(fact_2585_power__strict__decreasing__iff,axiom,
% 5.31/5.53 ! [B: nat,M2: nat,N: nat] :
% 5.31/5.53 ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.31/5.53 => ( ( ord_less_nat @ B @ one_one_nat )
% 5.31/5.53 => ( ( ord_less_nat @ ( power_power_nat @ B @ M2 ) @ ( power_power_nat @ B @ N ) )
% 5.31/5.53 = ( ord_less_nat @ N @ M2 ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % power_strict_decreasing_iff
% 5.31/5.53 thf(fact_2586_power__strict__decreasing__iff,axiom,
% 5.31/5.53 ! [B: int,M2: nat,N: nat] :
% 5.31/5.53 ( ( ord_less_int @ zero_zero_int @ B )
% 5.31/5.53 => ( ( ord_less_int @ B @ one_one_int )
% 5.31/5.53 => ( ( ord_less_int @ ( power_power_int @ B @ M2 ) @ ( power_power_int @ B @ N ) )
% 5.31/5.53 = ( ord_less_nat @ N @ M2 ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % power_strict_decreasing_iff
% 5.31/5.53 thf(fact_2587_power__increasing__iff,axiom,
% 5.31/5.53 ! [B: code_integer,X: nat,Y: nat] :
% 5.31/5.53 ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ B )
% 5.31/5.53 => ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ B @ X ) @ ( power_8256067586552552935nteger @ B @ Y ) )
% 5.31/5.53 = ( ord_less_eq_nat @ X @ Y ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % power_increasing_iff
% 5.31/5.53 thf(fact_2588_power__increasing__iff,axiom,
% 5.31/5.53 ! [B: real,X: nat,Y: nat] :
% 5.31/5.53 ( ( ord_less_real @ one_one_real @ B )
% 5.31/5.53 => ( ( ord_less_eq_real @ ( power_power_real @ B @ X ) @ ( power_power_real @ B @ Y ) )
% 5.31/5.53 = ( ord_less_eq_nat @ X @ Y ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % power_increasing_iff
% 5.31/5.53 thf(fact_2589_power__increasing__iff,axiom,
% 5.31/5.53 ! [B: rat,X: nat,Y: nat] :
% 5.31/5.53 ( ( ord_less_rat @ one_one_rat @ B )
% 5.31/5.53 => ( ( ord_less_eq_rat @ ( power_power_rat @ B @ X ) @ ( power_power_rat @ B @ Y ) )
% 5.31/5.53 = ( ord_less_eq_nat @ X @ Y ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % power_increasing_iff
% 5.31/5.53 thf(fact_2590_power__increasing__iff,axiom,
% 5.31/5.53 ! [B: nat,X: nat,Y: nat] :
% 5.31/5.53 ( ( ord_less_nat @ one_one_nat @ B )
% 5.31/5.53 => ( ( ord_less_eq_nat @ ( power_power_nat @ B @ X ) @ ( power_power_nat @ B @ Y ) )
% 5.31/5.53 = ( ord_less_eq_nat @ X @ Y ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % power_increasing_iff
% 5.31/5.53 thf(fact_2591_power__increasing__iff,axiom,
% 5.31/5.53 ! [B: int,X: nat,Y: nat] :
% 5.31/5.53 ( ( ord_less_int @ one_one_int @ B )
% 5.31/5.53 => ( ( ord_less_eq_int @ ( power_power_int @ B @ X ) @ ( power_power_int @ B @ Y ) )
% 5.31/5.53 = ( ord_less_eq_nat @ X @ Y ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % power_increasing_iff
% 5.31/5.53 thf(fact_2592_power__mono__iff,axiom,
% 5.31/5.53 ! [A: real,B: real,N: nat] :
% 5.31/5.53 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.31/5.53 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.31/5.53 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.53 => ( ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) )
% 5.31/5.53 = ( ord_less_eq_real @ A @ B ) ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % power_mono_iff
% 5.31/5.53 thf(fact_2593_power__mono__iff,axiom,
% 5.31/5.53 ! [A: rat,B: rat,N: nat] :
% 5.31/5.53 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.31/5.53 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.31/5.53 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.53 => ( ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) )
% 5.31/5.53 = ( ord_less_eq_rat @ A @ B ) ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % power_mono_iff
% 5.31/5.53 thf(fact_2594_power__mono__iff,axiom,
% 5.31/5.53 ! [A: nat,B: nat,N: nat] :
% 5.31/5.53 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.31/5.53 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.31/5.53 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.53 => ( ( ord_less_eq_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) )
% 5.31/5.53 = ( ord_less_eq_nat @ A @ B ) ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % power_mono_iff
% 5.31/5.53 thf(fact_2595_power__mono__iff,axiom,
% 5.31/5.53 ! [A: int,B: int,N: nat] :
% 5.31/5.53 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.31/5.53 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.31/5.53 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.53 => ( ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) )
% 5.31/5.53 = ( ord_less_eq_int @ A @ B ) ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % power_mono_iff
% 5.31/5.53 thf(fact_2596_power__not__zero,axiom,
% 5.31/5.53 ! [A: rat,N: nat] :
% 5.31/5.53 ( ( A != zero_zero_rat )
% 5.31/5.53 => ( ( power_power_rat @ A @ N )
% 5.31/5.53 != zero_zero_rat ) ) ).
% 5.31/5.53
% 5.31/5.53 % power_not_zero
% 5.31/5.53 thf(fact_2597_power__not__zero,axiom,
% 5.31/5.53 ! [A: nat,N: nat] :
% 5.31/5.53 ( ( A != zero_zero_nat )
% 5.31/5.53 => ( ( power_power_nat @ A @ N )
% 5.31/5.53 != zero_zero_nat ) ) ).
% 5.31/5.53
% 5.31/5.53 % power_not_zero
% 5.31/5.53 thf(fact_2598_power__not__zero,axiom,
% 5.31/5.53 ! [A: real,N: nat] :
% 5.31/5.53 ( ( A != zero_zero_real )
% 5.31/5.53 => ( ( power_power_real @ A @ N )
% 5.31/5.53 != zero_zero_real ) ) ).
% 5.31/5.53
% 5.31/5.53 % power_not_zero
% 5.31/5.53 thf(fact_2599_power__not__zero,axiom,
% 5.31/5.53 ! [A: int,N: nat] :
% 5.31/5.53 ( ( A != zero_zero_int )
% 5.31/5.53 => ( ( power_power_int @ A @ N )
% 5.31/5.53 != zero_zero_int ) ) ).
% 5.31/5.53
% 5.31/5.53 % power_not_zero
% 5.31/5.53 thf(fact_2600_power__not__zero,axiom,
% 5.31/5.53 ! [A: complex,N: nat] :
% 5.31/5.53 ( ( A != zero_zero_complex )
% 5.31/5.53 => ( ( power_power_complex @ A @ N )
% 5.31/5.53 != zero_zero_complex ) ) ).
% 5.31/5.53
% 5.31/5.53 % power_not_zero
% 5.31/5.53 thf(fact_2601_power__commuting__commutes,axiom,
% 5.31/5.53 ! [X: complex,Y: complex,N: nat] :
% 5.31/5.53 ( ( ( times_times_complex @ X @ Y )
% 5.31/5.53 = ( times_times_complex @ Y @ X ) )
% 5.31/5.53 => ( ( times_times_complex @ ( power_power_complex @ X @ N ) @ Y )
% 5.31/5.53 = ( times_times_complex @ Y @ ( power_power_complex @ X @ N ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % power_commuting_commutes
% 5.31/5.53 thf(fact_2602_power__commuting__commutes,axiom,
% 5.31/5.53 ! [X: real,Y: real,N: nat] :
% 5.31/5.53 ( ( ( times_times_real @ X @ Y )
% 5.31/5.53 = ( times_times_real @ Y @ X ) )
% 5.31/5.53 => ( ( times_times_real @ ( power_power_real @ X @ N ) @ Y )
% 5.31/5.53 = ( times_times_real @ Y @ ( power_power_real @ X @ N ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % power_commuting_commutes
% 5.31/5.53 thf(fact_2603_power__commuting__commutes,axiom,
% 5.31/5.53 ! [X: rat,Y: rat,N: nat] :
% 5.31/5.53 ( ( ( times_times_rat @ X @ Y )
% 5.31/5.53 = ( times_times_rat @ Y @ X ) )
% 5.31/5.53 => ( ( times_times_rat @ ( power_power_rat @ X @ N ) @ Y )
% 5.31/5.53 = ( times_times_rat @ Y @ ( power_power_rat @ X @ N ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % power_commuting_commutes
% 5.31/5.53 thf(fact_2604_power__commuting__commutes,axiom,
% 5.31/5.53 ! [X: nat,Y: nat,N: nat] :
% 5.31/5.53 ( ( ( times_times_nat @ X @ Y )
% 5.31/5.53 = ( times_times_nat @ Y @ X ) )
% 5.31/5.53 => ( ( times_times_nat @ ( power_power_nat @ X @ N ) @ Y )
% 5.31/5.53 = ( times_times_nat @ Y @ ( power_power_nat @ X @ N ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % power_commuting_commutes
% 5.31/5.53 thf(fact_2605_power__commuting__commutes,axiom,
% 5.31/5.53 ! [X: int,Y: int,N: nat] :
% 5.31/5.53 ( ( ( times_times_int @ X @ Y )
% 5.31/5.53 = ( times_times_int @ Y @ X ) )
% 5.31/5.53 => ( ( times_times_int @ ( power_power_int @ X @ N ) @ Y )
% 5.31/5.53 = ( times_times_int @ Y @ ( power_power_int @ X @ N ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % power_commuting_commutes
% 5.31/5.53 thf(fact_2606_power__mult__distrib,axiom,
% 5.31/5.53 ! [A: complex,B: complex,N: nat] :
% 5.31/5.53 ( ( power_power_complex @ ( times_times_complex @ A @ B ) @ N )
% 5.31/5.53 = ( times_times_complex @ ( power_power_complex @ A @ N ) @ ( power_power_complex @ B @ N ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % power_mult_distrib
% 5.31/5.53 thf(fact_2607_power__mult__distrib,axiom,
% 5.31/5.53 ! [A: real,B: real,N: nat] :
% 5.31/5.53 ( ( power_power_real @ ( times_times_real @ A @ B ) @ N )
% 5.31/5.53 = ( times_times_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % power_mult_distrib
% 5.31/5.53 thf(fact_2608_power__mult__distrib,axiom,
% 5.31/5.53 ! [A: rat,B: rat,N: nat] :
% 5.31/5.53 ( ( power_power_rat @ ( times_times_rat @ A @ B ) @ N )
% 5.31/5.53 = ( times_times_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % power_mult_distrib
% 5.31/5.53 thf(fact_2609_power__mult__distrib,axiom,
% 5.31/5.53 ! [A: nat,B: nat,N: nat] :
% 5.31/5.53 ( ( power_power_nat @ ( times_times_nat @ A @ B ) @ N )
% 5.31/5.53 = ( times_times_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % power_mult_distrib
% 5.31/5.53 thf(fact_2610_power__mult__distrib,axiom,
% 5.31/5.53 ! [A: int,B: int,N: nat] :
% 5.31/5.53 ( ( power_power_int @ ( times_times_int @ A @ B ) @ N )
% 5.31/5.53 = ( times_times_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % power_mult_distrib
% 5.31/5.53 thf(fact_2611_power__commutes,axiom,
% 5.31/5.53 ! [A: complex,N: nat] :
% 5.31/5.53 ( ( times_times_complex @ ( power_power_complex @ A @ N ) @ A )
% 5.31/5.53 = ( times_times_complex @ A @ ( power_power_complex @ A @ N ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % power_commutes
% 5.31/5.53 thf(fact_2612_power__commutes,axiom,
% 5.31/5.53 ! [A: real,N: nat] :
% 5.31/5.53 ( ( times_times_real @ ( power_power_real @ A @ N ) @ A )
% 5.31/5.53 = ( times_times_real @ A @ ( power_power_real @ A @ N ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % power_commutes
% 5.31/5.53 thf(fact_2613_power__commutes,axiom,
% 5.31/5.53 ! [A: rat,N: nat] :
% 5.31/5.53 ( ( times_times_rat @ ( power_power_rat @ A @ N ) @ A )
% 5.31/5.53 = ( times_times_rat @ A @ ( power_power_rat @ A @ N ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % power_commutes
% 5.31/5.53 thf(fact_2614_power__commutes,axiom,
% 5.31/5.53 ! [A: nat,N: nat] :
% 5.31/5.53 ( ( times_times_nat @ ( power_power_nat @ A @ N ) @ A )
% 5.31/5.53 = ( times_times_nat @ A @ ( power_power_nat @ A @ N ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % power_commutes
% 5.31/5.53 thf(fact_2615_power__commutes,axiom,
% 5.31/5.53 ! [A: int,N: nat] :
% 5.31/5.53 ( ( times_times_int @ ( power_power_int @ A @ N ) @ A )
% 5.31/5.53 = ( times_times_int @ A @ ( power_power_int @ A @ N ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % power_commutes
% 5.31/5.53 thf(fact_2616_power__mult,axiom,
% 5.31/5.53 ! [A: nat,M2: nat,N: nat] :
% 5.31/5.53 ( ( power_power_nat @ A @ ( times_times_nat @ M2 @ N ) )
% 5.31/5.53 = ( power_power_nat @ ( power_power_nat @ A @ M2 ) @ N ) ) ).
% 5.31/5.53
% 5.31/5.53 % power_mult
% 5.31/5.53 thf(fact_2617_power__mult,axiom,
% 5.31/5.53 ! [A: real,M2: nat,N: nat] :
% 5.31/5.53 ( ( power_power_real @ A @ ( times_times_nat @ M2 @ N ) )
% 5.31/5.53 = ( power_power_real @ ( power_power_real @ A @ M2 ) @ N ) ) ).
% 5.31/5.53
% 5.31/5.53 % power_mult
% 5.31/5.53 thf(fact_2618_power__mult,axiom,
% 5.31/5.53 ! [A: int,M2: nat,N: nat] :
% 5.31/5.53 ( ( power_power_int @ A @ ( times_times_nat @ M2 @ N ) )
% 5.31/5.53 = ( power_power_int @ ( power_power_int @ A @ M2 ) @ N ) ) ).
% 5.31/5.53
% 5.31/5.53 % power_mult
% 5.31/5.53 thf(fact_2619_power__mult,axiom,
% 5.31/5.53 ! [A: complex,M2: nat,N: nat] :
% 5.31/5.53 ( ( power_power_complex @ A @ ( times_times_nat @ M2 @ N ) )
% 5.31/5.53 = ( power_power_complex @ ( power_power_complex @ A @ M2 ) @ N ) ) ).
% 5.31/5.53
% 5.31/5.53 % power_mult
% 5.31/5.53 thf(fact_2620_finite__le__enumerate,axiom,
% 5.31/5.53 ! [S3: set_nat,N: nat] :
% 5.31/5.53 ( ( finite_finite_nat @ S3 )
% 5.31/5.53 => ( ( ord_less_nat @ N @ ( finite_card_nat @ S3 ) )
% 5.31/5.53 => ( ord_less_eq_nat @ N @ ( infini8530281810654367211te_nat @ S3 @ N ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % finite_le_enumerate
% 5.31/5.53 thf(fact_2621_lenlex__irreflexive,axiom,
% 5.31/5.53 ! [R3: set_Pr4811707699266497531nteger,Xs2: list_Code_integer] :
% 5.31/5.53 ( ! [X3: code_integer] :
% 5.31/5.53 ~ ( member157494554546826820nteger @ ( produc1086072967326762835nteger @ X3 @ X3 ) @ R3 )
% 5.31/5.53 => ~ ( member749217712838834276nteger @ ( produc750622340256944499nteger @ Xs2 @ Xs2 ) @ ( lenlex_Code_integer @ R3 ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % lenlex_irreflexive
% 5.31/5.53 thf(fact_2622_lenlex__irreflexive,axiom,
% 5.31/5.53 ! [R3: set_Pr8693737435421807431at_nat,Xs2: list_P6011104703257516679at_nat] :
% 5.31/5.53 ( ! [X3: product_prod_nat_nat] :
% 5.31/5.53 ~ ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X3 @ X3 ) @ R3 )
% 5.31/5.53 => ~ ( member6693912407220327184at_nat @ ( produc5943733680697469783at_nat @ Xs2 @ Xs2 ) @ ( lenlex325483962726685836at_nat @ R3 ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % lenlex_irreflexive
% 5.31/5.53 thf(fact_2623_lenlex__irreflexive,axiom,
% 5.31/5.53 ! [R3: set_Pr4329608150637261639at_nat,Xs2: list_s1210847774152347623at_nat] :
% 5.31/5.53 ( ! [X3: set_Pr1261947904930325089at_nat] :
% 5.31/5.53 ~ ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X3 @ X3 ) @ R3 )
% 5.31/5.53 => ~ ( member4080735728053443344at_nat @ ( produc7536900900485677911at_nat @ Xs2 @ Xs2 ) @ ( lenlex1357538814655152620at_nat @ R3 ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % lenlex_irreflexive
% 5.31/5.53 thf(fact_2624_lenlex__irreflexive,axiom,
% 5.31/5.53 ! [R3: set_Pr1261947904930325089at_nat,Xs2: list_nat] :
% 5.31/5.53 ( ! [X3: nat] :
% 5.31/5.53 ~ ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X3 @ X3 ) @ R3 )
% 5.31/5.53 => ~ ( member7340969449405702474st_nat @ ( produc2694037385005941721st_nat @ Xs2 @ Xs2 ) @ ( lenlex_nat @ R3 ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % lenlex_irreflexive
% 5.31/5.53 thf(fact_2625_lenlex__irreflexive,axiom,
% 5.31/5.53 ! [R3: set_Pr958786334691620121nt_int,Xs2: list_int] :
% 5.31/5.53 ( ! [X3: int] :
% 5.31/5.53 ~ ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X3 @ X3 ) @ R3 )
% 5.31/5.53 => ~ ( member6698963635872716290st_int @ ( produc364263696895485585st_int @ Xs2 @ Xs2 ) @ ( lenlex_int @ R3 ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % lenlex_irreflexive
% 5.31/5.53 thf(fact_2626_zero__le__power,axiom,
% 5.31/5.53 ! [A: real,N: nat] :
% 5.31/5.53 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.31/5.53 => ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ N ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % zero_le_power
% 5.31/5.53 thf(fact_2627_zero__le__power,axiom,
% 5.31/5.53 ! [A: rat,N: nat] :
% 5.31/5.53 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.31/5.53 => ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ N ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % zero_le_power
% 5.31/5.53 thf(fact_2628_zero__le__power,axiom,
% 5.31/5.53 ! [A: nat,N: nat] :
% 5.31/5.53 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.31/5.53 => ( ord_less_eq_nat @ zero_zero_nat @ ( power_power_nat @ A @ N ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % zero_le_power
% 5.31/5.53 thf(fact_2629_zero__le__power,axiom,
% 5.31/5.53 ! [A: int,N: nat] :
% 5.31/5.53 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.31/5.53 => ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ N ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % zero_le_power
% 5.31/5.53 thf(fact_2630_power__mono,axiom,
% 5.31/5.53 ! [A: real,B: real,N: nat] :
% 5.31/5.53 ( ( ord_less_eq_real @ A @ B )
% 5.31/5.53 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.31/5.53 => ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % power_mono
% 5.31/5.53 thf(fact_2631_power__mono,axiom,
% 5.31/5.53 ! [A: rat,B: rat,N: nat] :
% 5.31/5.53 ( ( ord_less_eq_rat @ A @ B )
% 5.31/5.53 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.31/5.53 => ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % power_mono
% 5.31/5.53 thf(fact_2632_power__mono,axiom,
% 5.31/5.53 ! [A: nat,B: nat,N: nat] :
% 5.31/5.53 ( ( ord_less_eq_nat @ A @ B )
% 5.31/5.53 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.31/5.53 => ( ord_less_eq_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % power_mono
% 5.31/5.53 thf(fact_2633_power__mono,axiom,
% 5.31/5.53 ! [A: int,B: int,N: nat] :
% 5.31/5.53 ( ( ord_less_eq_int @ A @ B )
% 5.31/5.53 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.31/5.53 => ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % power_mono
% 5.31/5.53 thf(fact_2634_finite__enumerate__step,axiom,
% 5.31/5.53 ! [S3: set_nat,N: nat] :
% 5.31/5.53 ( ( finite_finite_nat @ S3 )
% 5.31/5.53 => ( ( ord_less_nat @ ( suc @ N ) @ ( finite_card_nat @ S3 ) )
% 5.31/5.53 => ( ord_less_nat @ ( infini8530281810654367211te_nat @ S3 @ N ) @ ( infini8530281810654367211te_nat @ S3 @ ( suc @ N ) ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % finite_enumerate_step
% 5.31/5.53 thf(fact_2635_card__le__if__inj__on__rel,axiom,
% 5.31/5.53 ! [B5: set_real,A4: set_real,R3: real > real > $o] :
% 5.31/5.53 ( ( finite_finite_real @ B5 )
% 5.31/5.53 => ( ! [A3: real] :
% 5.31/5.53 ( ( member_real @ A3 @ A4 )
% 5.31/5.53 => ? [B6: real] :
% 5.31/5.53 ( ( member_real @ B6 @ B5 )
% 5.31/5.53 & ( R3 @ A3 @ B6 ) ) )
% 5.31/5.53 => ( ! [A1: real,A22: real,B3: real] :
% 5.31/5.53 ( ( member_real @ A1 @ A4 )
% 5.31/5.53 => ( ( member_real @ A22 @ A4 )
% 5.31/5.53 => ( ( member_real @ B3 @ B5 )
% 5.31/5.53 => ( ( R3 @ A1 @ B3 )
% 5.31/5.53 => ( ( R3 @ A22 @ B3 )
% 5.31/5.53 => ( A1 = A22 ) ) ) ) ) )
% 5.31/5.53 => ( ord_less_eq_nat @ ( finite_card_real @ A4 ) @ ( finite_card_real @ B5 ) ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % card_le_if_inj_on_rel
% 5.31/5.53 thf(fact_2636_card__le__if__inj__on__rel,axiom,
% 5.31/5.53 ! [B5: set_real,A4: set_nat,R3: nat > real > $o] :
% 5.31/5.53 ( ( finite_finite_real @ B5 )
% 5.31/5.53 => ( ! [A3: nat] :
% 5.31/5.53 ( ( member_nat @ A3 @ A4 )
% 5.31/5.53 => ? [B6: real] :
% 5.31/5.53 ( ( member_real @ B6 @ B5 )
% 5.31/5.53 & ( R3 @ A3 @ B6 ) ) )
% 5.31/5.53 => ( ! [A1: nat,A22: nat,B3: real] :
% 5.31/5.53 ( ( member_nat @ A1 @ A4 )
% 5.31/5.53 => ( ( member_nat @ A22 @ A4 )
% 5.31/5.53 => ( ( member_real @ B3 @ B5 )
% 5.31/5.53 => ( ( R3 @ A1 @ B3 )
% 5.31/5.53 => ( ( R3 @ A22 @ B3 )
% 5.31/5.53 => ( A1 = A22 ) ) ) ) ) )
% 5.31/5.53 => ( ord_less_eq_nat @ ( finite_card_nat @ A4 ) @ ( finite_card_real @ B5 ) ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % card_le_if_inj_on_rel
% 5.31/5.53 thf(fact_2637_card__le__if__inj__on__rel,axiom,
% 5.31/5.53 ! [B5: set_real,A4: set_complex,R3: complex > real > $o] :
% 5.31/5.53 ( ( finite_finite_real @ B5 )
% 5.31/5.53 => ( ! [A3: complex] :
% 5.31/5.53 ( ( member_complex @ A3 @ A4 )
% 5.31/5.53 => ? [B6: real] :
% 5.31/5.53 ( ( member_real @ B6 @ B5 )
% 5.31/5.53 & ( R3 @ A3 @ B6 ) ) )
% 5.31/5.53 => ( ! [A1: complex,A22: complex,B3: real] :
% 5.31/5.53 ( ( member_complex @ A1 @ A4 )
% 5.31/5.53 => ( ( member_complex @ A22 @ A4 )
% 5.31/5.53 => ( ( member_real @ B3 @ B5 )
% 5.31/5.53 => ( ( R3 @ A1 @ B3 )
% 5.31/5.53 => ( ( R3 @ A22 @ B3 )
% 5.31/5.53 => ( A1 = A22 ) ) ) ) ) )
% 5.31/5.53 => ( ord_less_eq_nat @ ( finite_card_complex @ A4 ) @ ( finite_card_real @ B5 ) ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % card_le_if_inj_on_rel
% 5.31/5.53 thf(fact_2638_card__le__if__inj__on__rel,axiom,
% 5.31/5.53 ! [B5: set_real,A4: set_int,R3: int > real > $o] :
% 5.31/5.53 ( ( finite_finite_real @ B5 )
% 5.31/5.53 => ( ! [A3: int] :
% 5.31/5.53 ( ( member_int @ A3 @ A4 )
% 5.31/5.53 => ? [B6: real] :
% 5.31/5.53 ( ( member_real @ B6 @ B5 )
% 5.31/5.53 & ( R3 @ A3 @ B6 ) ) )
% 5.31/5.53 => ( ! [A1: int,A22: int,B3: real] :
% 5.31/5.53 ( ( member_int @ A1 @ A4 )
% 5.31/5.53 => ( ( member_int @ A22 @ A4 )
% 5.31/5.53 => ( ( member_real @ B3 @ B5 )
% 5.31/5.53 => ( ( R3 @ A1 @ B3 )
% 5.31/5.53 => ( ( R3 @ A22 @ B3 )
% 5.31/5.53 => ( A1 = A22 ) ) ) ) ) )
% 5.31/5.53 => ( ord_less_eq_nat @ ( finite_card_int @ A4 ) @ ( finite_card_real @ B5 ) ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % card_le_if_inj_on_rel
% 5.31/5.53 thf(fact_2639_card__le__if__inj__on__rel,axiom,
% 5.31/5.53 ! [B5: set_nat,A4: set_real,R3: real > nat > $o] :
% 5.31/5.53 ( ( finite_finite_nat @ B5 )
% 5.31/5.53 => ( ! [A3: real] :
% 5.31/5.53 ( ( member_real @ A3 @ A4 )
% 5.31/5.53 => ? [B6: nat] :
% 5.31/5.53 ( ( member_nat @ B6 @ B5 )
% 5.31/5.53 & ( R3 @ A3 @ B6 ) ) )
% 5.31/5.53 => ( ! [A1: real,A22: real,B3: nat] :
% 5.31/5.53 ( ( member_real @ A1 @ A4 )
% 5.31/5.53 => ( ( member_real @ A22 @ A4 )
% 5.31/5.53 => ( ( member_nat @ B3 @ B5 )
% 5.31/5.53 => ( ( R3 @ A1 @ B3 )
% 5.31/5.53 => ( ( R3 @ A22 @ B3 )
% 5.31/5.53 => ( A1 = A22 ) ) ) ) ) )
% 5.31/5.53 => ( ord_less_eq_nat @ ( finite_card_real @ A4 ) @ ( finite_card_nat @ B5 ) ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % card_le_if_inj_on_rel
% 5.31/5.53 thf(fact_2640_card__le__if__inj__on__rel,axiom,
% 5.31/5.53 ! [B5: set_nat,A4: set_nat,R3: nat > nat > $o] :
% 5.31/5.53 ( ( finite_finite_nat @ B5 )
% 5.31/5.53 => ( ! [A3: nat] :
% 5.31/5.53 ( ( member_nat @ A3 @ A4 )
% 5.31/5.53 => ? [B6: nat] :
% 5.31/5.53 ( ( member_nat @ B6 @ B5 )
% 5.31/5.53 & ( R3 @ A3 @ B6 ) ) )
% 5.31/5.53 => ( ! [A1: nat,A22: nat,B3: nat] :
% 5.31/5.53 ( ( member_nat @ A1 @ A4 )
% 5.31/5.53 => ( ( member_nat @ A22 @ A4 )
% 5.31/5.53 => ( ( member_nat @ B3 @ B5 )
% 5.31/5.53 => ( ( R3 @ A1 @ B3 )
% 5.31/5.53 => ( ( R3 @ A22 @ B3 )
% 5.31/5.53 => ( A1 = A22 ) ) ) ) ) )
% 5.31/5.53 => ( ord_less_eq_nat @ ( finite_card_nat @ A4 ) @ ( finite_card_nat @ B5 ) ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % card_le_if_inj_on_rel
% 5.31/5.53 thf(fact_2641_card__le__if__inj__on__rel,axiom,
% 5.31/5.53 ! [B5: set_nat,A4: set_complex,R3: complex > nat > $o] :
% 5.31/5.53 ( ( finite_finite_nat @ B5 )
% 5.31/5.53 => ( ! [A3: complex] :
% 5.31/5.53 ( ( member_complex @ A3 @ A4 )
% 5.31/5.53 => ? [B6: nat] :
% 5.31/5.53 ( ( member_nat @ B6 @ B5 )
% 5.31/5.53 & ( R3 @ A3 @ B6 ) ) )
% 5.31/5.53 => ( ! [A1: complex,A22: complex,B3: nat] :
% 5.31/5.53 ( ( member_complex @ A1 @ A4 )
% 5.31/5.53 => ( ( member_complex @ A22 @ A4 )
% 5.31/5.53 => ( ( member_nat @ B3 @ B5 )
% 5.31/5.53 => ( ( R3 @ A1 @ B3 )
% 5.31/5.53 => ( ( R3 @ A22 @ B3 )
% 5.31/5.53 => ( A1 = A22 ) ) ) ) ) )
% 5.31/5.53 => ( ord_less_eq_nat @ ( finite_card_complex @ A4 ) @ ( finite_card_nat @ B5 ) ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % card_le_if_inj_on_rel
% 5.31/5.53 thf(fact_2642_card__le__if__inj__on__rel,axiom,
% 5.31/5.53 ! [B5: set_nat,A4: set_int,R3: int > nat > $o] :
% 5.31/5.53 ( ( finite_finite_nat @ B5 )
% 5.31/5.53 => ( ! [A3: int] :
% 5.31/5.53 ( ( member_int @ A3 @ A4 )
% 5.31/5.53 => ? [B6: nat] :
% 5.31/5.53 ( ( member_nat @ B6 @ B5 )
% 5.31/5.53 & ( R3 @ A3 @ B6 ) ) )
% 5.31/5.53 => ( ! [A1: int,A22: int,B3: nat] :
% 5.31/5.53 ( ( member_int @ A1 @ A4 )
% 5.31/5.53 => ( ( member_int @ A22 @ A4 )
% 5.31/5.53 => ( ( member_nat @ B3 @ B5 )
% 5.31/5.53 => ( ( R3 @ A1 @ B3 )
% 5.31/5.53 => ( ( R3 @ A22 @ B3 )
% 5.31/5.53 => ( A1 = A22 ) ) ) ) ) )
% 5.31/5.53 => ( ord_less_eq_nat @ ( finite_card_int @ A4 ) @ ( finite_card_nat @ B5 ) ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % card_le_if_inj_on_rel
% 5.31/5.53 thf(fact_2643_card__le__if__inj__on__rel,axiom,
% 5.31/5.53 ! [B5: set_int,A4: set_real,R3: real > int > $o] :
% 5.31/5.53 ( ( finite_finite_int @ B5 )
% 5.31/5.53 => ( ! [A3: real] :
% 5.31/5.53 ( ( member_real @ A3 @ A4 )
% 5.31/5.53 => ? [B6: int] :
% 5.31/5.53 ( ( member_int @ B6 @ B5 )
% 5.31/5.53 & ( R3 @ A3 @ B6 ) ) )
% 5.31/5.53 => ( ! [A1: real,A22: real,B3: int] :
% 5.31/5.53 ( ( member_real @ A1 @ A4 )
% 5.31/5.53 => ( ( member_real @ A22 @ A4 )
% 5.31/5.53 => ( ( member_int @ B3 @ B5 )
% 5.31/5.53 => ( ( R3 @ A1 @ B3 )
% 5.31/5.53 => ( ( R3 @ A22 @ B3 )
% 5.31/5.53 => ( A1 = A22 ) ) ) ) ) )
% 5.31/5.53 => ( ord_less_eq_nat @ ( finite_card_real @ A4 ) @ ( finite_card_int @ B5 ) ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % card_le_if_inj_on_rel
% 5.31/5.53 thf(fact_2644_card__le__if__inj__on__rel,axiom,
% 5.31/5.53 ! [B5: set_int,A4: set_nat,R3: nat > int > $o] :
% 5.31/5.53 ( ( finite_finite_int @ B5 )
% 5.31/5.53 => ( ! [A3: nat] :
% 5.31/5.53 ( ( member_nat @ A3 @ A4 )
% 5.31/5.53 => ? [B6: int] :
% 5.31/5.53 ( ( member_int @ B6 @ B5 )
% 5.31/5.53 & ( R3 @ A3 @ B6 ) ) )
% 5.31/5.53 => ( ! [A1: nat,A22: nat,B3: int] :
% 5.31/5.53 ( ( member_nat @ A1 @ A4 )
% 5.31/5.53 => ( ( member_nat @ A22 @ A4 )
% 5.31/5.53 => ( ( member_int @ B3 @ B5 )
% 5.31/5.53 => ( ( R3 @ A1 @ B3 )
% 5.31/5.53 => ( ( R3 @ A22 @ B3 )
% 5.31/5.53 => ( A1 = A22 ) ) ) ) ) )
% 5.31/5.53 => ( ord_less_eq_nat @ ( finite_card_nat @ A4 ) @ ( finite_card_int @ B5 ) ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % card_le_if_inj_on_rel
% 5.31/5.53 thf(fact_2645_zero__less__power,axiom,
% 5.31/5.53 ! [A: real,N: nat] :
% 5.31/5.53 ( ( ord_less_real @ zero_zero_real @ A )
% 5.31/5.53 => ( ord_less_real @ zero_zero_real @ ( power_power_real @ A @ N ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % zero_less_power
% 5.31/5.53 thf(fact_2646_zero__less__power,axiom,
% 5.31/5.53 ! [A: rat,N: nat] :
% 5.31/5.53 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.31/5.53 => ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ A @ N ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % zero_less_power
% 5.31/5.53 thf(fact_2647_zero__less__power,axiom,
% 5.31/5.53 ! [A: nat,N: nat] :
% 5.31/5.53 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.31/5.53 => ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ A @ N ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % zero_less_power
% 5.31/5.53 thf(fact_2648_zero__less__power,axiom,
% 5.31/5.53 ! [A: int,N: nat] :
% 5.31/5.53 ( ( ord_less_int @ zero_zero_int @ A )
% 5.31/5.53 => ( ord_less_int @ zero_zero_int @ ( power_power_int @ A @ N ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % zero_less_power
% 5.31/5.53 thf(fact_2649_card__insert__le,axiom,
% 5.31/5.53 ! [A4: set_real,X: real] : ( ord_less_eq_nat @ ( finite_card_real @ A4 ) @ ( finite_card_real @ ( insert_real @ X @ A4 ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % card_insert_le
% 5.31/5.53 thf(fact_2650_card__insert__le,axiom,
% 5.31/5.53 ! [A4: set_nat,X: nat] : ( ord_less_eq_nat @ ( finite_card_nat @ A4 ) @ ( finite_card_nat @ ( insert_nat @ X @ A4 ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % card_insert_le
% 5.31/5.53 thf(fact_2651_card__insert__le,axiom,
% 5.31/5.53 ! [A4: set_complex,X: complex] : ( ord_less_eq_nat @ ( finite_card_complex @ A4 ) @ ( finite_card_complex @ ( insert_complex @ X @ A4 ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % card_insert_le
% 5.31/5.53 thf(fact_2652_card__insert__le,axiom,
% 5.31/5.53 ! [A4: set_int,X: int] : ( ord_less_eq_nat @ ( finite_card_int @ A4 ) @ ( finite_card_int @ ( insert_int @ X @ A4 ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % card_insert_le
% 5.31/5.53 thf(fact_2653_card__insert__le,axiom,
% 5.31/5.53 ! [A4: set_list_nat,X: list_nat] : ( ord_less_eq_nat @ ( finite_card_list_nat @ A4 ) @ ( finite_card_list_nat @ ( insert_list_nat @ X @ A4 ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % card_insert_le
% 5.31/5.53 thf(fact_2654_card__insert__le,axiom,
% 5.31/5.53 ! [A4: set_set_nat,X: set_nat] : ( ord_less_eq_nat @ ( finite_card_set_nat @ A4 ) @ ( finite_card_set_nat @ ( insert_set_nat @ X @ A4 ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % card_insert_le
% 5.31/5.53 thf(fact_2655_one__le__power,axiom,
% 5.31/5.53 ! [A: code_integer,N: nat] :
% 5.31/5.53 ( ( ord_le3102999989581377725nteger @ one_one_Code_integer @ A )
% 5.31/5.53 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ A @ N ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % one_le_power
% 5.31/5.53 thf(fact_2656_one__le__power,axiom,
% 5.31/5.53 ! [A: real,N: nat] :
% 5.31/5.53 ( ( ord_less_eq_real @ one_one_real @ A )
% 5.31/5.53 => ( ord_less_eq_real @ one_one_real @ ( power_power_real @ A @ N ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % one_le_power
% 5.31/5.53 thf(fact_2657_one__le__power,axiom,
% 5.31/5.53 ! [A: rat,N: nat] :
% 5.31/5.53 ( ( ord_less_eq_rat @ one_one_rat @ A )
% 5.31/5.53 => ( ord_less_eq_rat @ one_one_rat @ ( power_power_rat @ A @ N ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % one_le_power
% 5.31/5.53 thf(fact_2658_one__le__power,axiom,
% 5.31/5.53 ! [A: nat,N: nat] :
% 5.31/5.53 ( ( ord_less_eq_nat @ one_one_nat @ A )
% 5.31/5.53 => ( ord_less_eq_nat @ one_one_nat @ ( power_power_nat @ A @ N ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % one_le_power
% 5.31/5.53 thf(fact_2659_one__le__power,axiom,
% 5.31/5.53 ! [A: int,N: nat] :
% 5.31/5.53 ( ( ord_less_eq_int @ one_one_int @ A )
% 5.31/5.53 => ( ord_less_eq_int @ one_one_int @ ( power_power_int @ A @ N ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % one_le_power
% 5.31/5.53 thf(fact_2660_left__right__inverse__power,axiom,
% 5.31/5.53 ! [X: code_integer,Y: code_integer,N: nat] :
% 5.31/5.53 ( ( ( times_3573771949741848930nteger @ X @ Y )
% 5.31/5.53 = one_one_Code_integer )
% 5.31/5.53 => ( ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ X @ N ) @ ( power_8256067586552552935nteger @ Y @ N ) )
% 5.31/5.53 = one_one_Code_integer ) ) ).
% 5.31/5.53
% 5.31/5.53 % left_right_inverse_power
% 5.31/5.53 thf(fact_2661_left__right__inverse__power,axiom,
% 5.31/5.53 ! [X: complex,Y: complex,N: nat] :
% 5.31/5.53 ( ( ( times_times_complex @ X @ Y )
% 5.31/5.53 = one_one_complex )
% 5.31/5.53 => ( ( times_times_complex @ ( power_power_complex @ X @ N ) @ ( power_power_complex @ Y @ N ) )
% 5.31/5.53 = one_one_complex ) ) ).
% 5.31/5.53
% 5.31/5.53 % left_right_inverse_power
% 5.31/5.53 thf(fact_2662_left__right__inverse__power,axiom,
% 5.31/5.53 ! [X: real,Y: real,N: nat] :
% 5.31/5.53 ( ( ( times_times_real @ X @ Y )
% 5.31/5.53 = one_one_real )
% 5.31/5.53 => ( ( times_times_real @ ( power_power_real @ X @ N ) @ ( power_power_real @ Y @ N ) )
% 5.31/5.53 = one_one_real ) ) ).
% 5.31/5.53
% 5.31/5.53 % left_right_inverse_power
% 5.31/5.53 thf(fact_2663_left__right__inverse__power,axiom,
% 5.31/5.53 ! [X: rat,Y: rat,N: nat] :
% 5.31/5.53 ( ( ( times_times_rat @ X @ Y )
% 5.31/5.53 = one_one_rat )
% 5.31/5.53 => ( ( times_times_rat @ ( power_power_rat @ X @ N ) @ ( power_power_rat @ Y @ N ) )
% 5.31/5.53 = one_one_rat ) ) ).
% 5.31/5.53
% 5.31/5.53 % left_right_inverse_power
% 5.31/5.53 thf(fact_2664_left__right__inverse__power,axiom,
% 5.31/5.53 ! [X: nat,Y: nat,N: nat] :
% 5.31/5.53 ( ( ( times_times_nat @ X @ Y )
% 5.31/5.53 = one_one_nat )
% 5.31/5.53 => ( ( times_times_nat @ ( power_power_nat @ X @ N ) @ ( power_power_nat @ Y @ N ) )
% 5.31/5.53 = one_one_nat ) ) ).
% 5.31/5.53
% 5.31/5.53 % left_right_inverse_power
% 5.31/5.53 thf(fact_2665_left__right__inverse__power,axiom,
% 5.31/5.53 ! [X: int,Y: int,N: nat] :
% 5.31/5.53 ( ( ( times_times_int @ X @ Y )
% 5.31/5.53 = one_one_int )
% 5.31/5.53 => ( ( times_times_int @ ( power_power_int @ X @ N ) @ ( power_power_int @ Y @ N ) )
% 5.31/5.53 = one_one_int ) ) ).
% 5.31/5.53
% 5.31/5.53 % left_right_inverse_power
% 5.31/5.53 thf(fact_2666_finite__enum__subset,axiom,
% 5.31/5.53 ! [X8: set_nat,Y7: set_nat] :
% 5.31/5.53 ( ! [I3: nat] :
% 5.31/5.53 ( ( ord_less_nat @ I3 @ ( finite_card_nat @ X8 ) )
% 5.31/5.53 => ( ( infini8530281810654367211te_nat @ X8 @ I3 )
% 5.31/5.53 = ( infini8530281810654367211te_nat @ Y7 @ I3 ) ) )
% 5.31/5.53 => ( ( finite_finite_nat @ X8 )
% 5.31/5.53 => ( ( finite_finite_nat @ Y7 )
% 5.31/5.53 => ( ( ord_less_eq_nat @ ( finite_card_nat @ X8 ) @ ( finite_card_nat @ Y7 ) )
% 5.31/5.53 => ( ord_less_eq_set_nat @ X8 @ Y7 ) ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % finite_enum_subset
% 5.31/5.53 thf(fact_2667_power__Suc,axiom,
% 5.31/5.53 ! [A: complex,N: nat] :
% 5.31/5.53 ( ( power_power_complex @ A @ ( suc @ N ) )
% 5.31/5.53 = ( times_times_complex @ A @ ( power_power_complex @ A @ N ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % power_Suc
% 5.31/5.53 thf(fact_2668_power__Suc,axiom,
% 5.31/5.53 ! [A: real,N: nat] :
% 5.31/5.53 ( ( power_power_real @ A @ ( suc @ N ) )
% 5.31/5.53 = ( times_times_real @ A @ ( power_power_real @ A @ N ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % power_Suc
% 5.31/5.53 thf(fact_2669_power__Suc,axiom,
% 5.31/5.53 ! [A: rat,N: nat] :
% 5.31/5.53 ( ( power_power_rat @ A @ ( suc @ N ) )
% 5.31/5.53 = ( times_times_rat @ A @ ( power_power_rat @ A @ N ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % power_Suc
% 5.31/5.53 thf(fact_2670_power__Suc,axiom,
% 5.31/5.53 ! [A: nat,N: nat] :
% 5.31/5.53 ( ( power_power_nat @ A @ ( suc @ N ) )
% 5.31/5.53 = ( times_times_nat @ A @ ( power_power_nat @ A @ N ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % power_Suc
% 5.31/5.53 thf(fact_2671_power__Suc,axiom,
% 5.31/5.53 ! [A: int,N: nat] :
% 5.31/5.53 ( ( power_power_int @ A @ ( suc @ N ) )
% 5.31/5.53 = ( times_times_int @ A @ ( power_power_int @ A @ N ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % power_Suc
% 5.31/5.53 thf(fact_2672_power__Suc2,axiom,
% 5.31/5.53 ! [A: complex,N: nat] :
% 5.31/5.53 ( ( power_power_complex @ A @ ( suc @ N ) )
% 5.31/5.53 = ( times_times_complex @ ( power_power_complex @ A @ N ) @ A ) ) ).
% 5.31/5.53
% 5.31/5.53 % power_Suc2
% 5.31/5.53 thf(fact_2673_power__Suc2,axiom,
% 5.31/5.53 ! [A: real,N: nat] :
% 5.31/5.53 ( ( power_power_real @ A @ ( suc @ N ) )
% 5.31/5.53 = ( times_times_real @ ( power_power_real @ A @ N ) @ A ) ) ).
% 5.31/5.53
% 5.31/5.53 % power_Suc2
% 5.31/5.53 thf(fact_2674_power__Suc2,axiom,
% 5.31/5.53 ! [A: rat,N: nat] :
% 5.31/5.53 ( ( power_power_rat @ A @ ( suc @ N ) )
% 5.31/5.53 = ( times_times_rat @ ( power_power_rat @ A @ N ) @ A ) ) ).
% 5.31/5.53
% 5.31/5.53 % power_Suc2
% 5.31/5.53 thf(fact_2675_power__Suc2,axiom,
% 5.31/5.53 ! [A: nat,N: nat] :
% 5.31/5.53 ( ( power_power_nat @ A @ ( suc @ N ) )
% 5.31/5.53 = ( times_times_nat @ ( power_power_nat @ A @ N ) @ A ) ) ).
% 5.31/5.53
% 5.31/5.53 % power_Suc2
% 5.31/5.53 thf(fact_2676_power__Suc2,axiom,
% 5.31/5.53 ! [A: int,N: nat] :
% 5.31/5.53 ( ( power_power_int @ A @ ( suc @ N ) )
% 5.31/5.53 = ( times_times_int @ ( power_power_int @ A @ N ) @ A ) ) ).
% 5.31/5.53
% 5.31/5.53 % power_Suc2
% 5.31/5.53 thf(fact_2677_power__0,axiom,
% 5.31/5.53 ! [A: code_integer] :
% 5.31/5.53 ( ( power_8256067586552552935nteger @ A @ zero_zero_nat )
% 5.31/5.53 = one_one_Code_integer ) ).
% 5.31/5.53
% 5.31/5.53 % power_0
% 5.31/5.53 thf(fact_2678_power__0,axiom,
% 5.31/5.53 ! [A: nat] :
% 5.31/5.53 ( ( power_power_nat @ A @ zero_zero_nat )
% 5.31/5.53 = one_one_nat ) ).
% 5.31/5.53
% 5.31/5.53 % power_0
% 5.31/5.53 thf(fact_2679_power__0,axiom,
% 5.31/5.53 ! [A: real] :
% 5.31/5.53 ( ( power_power_real @ A @ zero_zero_nat )
% 5.31/5.53 = one_one_real ) ).
% 5.31/5.53
% 5.31/5.53 % power_0
% 5.31/5.53 thf(fact_2680_power__0,axiom,
% 5.31/5.53 ! [A: int] :
% 5.31/5.53 ( ( power_power_int @ A @ zero_zero_nat )
% 5.31/5.53 = one_one_int ) ).
% 5.31/5.53
% 5.31/5.53 % power_0
% 5.31/5.53 thf(fact_2681_power__0,axiom,
% 5.31/5.53 ! [A: complex] :
% 5.31/5.53 ( ( power_power_complex @ A @ zero_zero_nat )
% 5.31/5.53 = one_one_complex ) ).
% 5.31/5.53
% 5.31/5.53 % power_0
% 5.31/5.53 thf(fact_2682_power__add,axiom,
% 5.31/5.53 ! [A: complex,M2: nat,N: nat] :
% 5.31/5.53 ( ( power_power_complex @ A @ ( plus_plus_nat @ M2 @ N ) )
% 5.31/5.53 = ( times_times_complex @ ( power_power_complex @ A @ M2 ) @ ( power_power_complex @ A @ N ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % power_add
% 5.31/5.53 thf(fact_2683_power__add,axiom,
% 5.31/5.53 ! [A: real,M2: nat,N: nat] :
% 5.31/5.53 ( ( power_power_real @ A @ ( plus_plus_nat @ M2 @ N ) )
% 5.31/5.53 = ( times_times_real @ ( power_power_real @ A @ M2 ) @ ( power_power_real @ A @ N ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % power_add
% 5.31/5.53 thf(fact_2684_power__add,axiom,
% 5.31/5.53 ! [A: rat,M2: nat,N: nat] :
% 5.31/5.53 ( ( power_power_rat @ A @ ( plus_plus_nat @ M2 @ N ) )
% 5.31/5.53 = ( times_times_rat @ ( power_power_rat @ A @ M2 ) @ ( power_power_rat @ A @ N ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % power_add
% 5.31/5.53 thf(fact_2685_power__add,axiom,
% 5.31/5.53 ! [A: nat,M2: nat,N: nat] :
% 5.31/5.53 ( ( power_power_nat @ A @ ( plus_plus_nat @ M2 @ N ) )
% 5.31/5.53 = ( times_times_nat @ ( power_power_nat @ A @ M2 ) @ ( power_power_nat @ A @ N ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % power_add
% 5.31/5.53 thf(fact_2686_power__add,axiom,
% 5.31/5.53 ! [A: int,M2: nat,N: nat] :
% 5.31/5.53 ( ( power_power_int @ A @ ( plus_plus_nat @ M2 @ N ) )
% 5.31/5.53 = ( times_times_int @ ( power_power_int @ A @ M2 ) @ ( power_power_int @ A @ N ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % power_add
% 5.31/5.53 thf(fact_2687_nat__power__less__imp__less,axiom,
% 5.31/5.53 ! [I2: nat,M2: nat,N: nat] :
% 5.31/5.53 ( ( ord_less_nat @ zero_zero_nat @ I2 )
% 5.31/5.53 => ( ( ord_less_nat @ ( power_power_nat @ I2 @ M2 ) @ ( power_power_nat @ I2 @ N ) )
% 5.31/5.53 => ( ord_less_nat @ M2 @ N ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % nat_power_less_imp_less
% 5.31/5.53 thf(fact_2688_le__enumerate,axiom,
% 5.31/5.53 ! [S3: set_nat,N: nat] :
% 5.31/5.53 ( ~ ( finite_finite_nat @ S3 )
% 5.31/5.53 => ( ord_less_eq_nat @ N @ ( infini8530281810654367211te_nat @ S3 @ N ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % le_enumerate
% 5.31/5.53 thf(fact_2689_card__eq__0__iff,axiom,
% 5.31/5.53 ! [A4: set_list_nat] :
% 5.31/5.53 ( ( ( finite_card_list_nat @ A4 )
% 5.31/5.53 = zero_zero_nat )
% 5.31/5.53 = ( ( A4 = bot_bot_set_list_nat )
% 5.31/5.53 | ~ ( finite8100373058378681591st_nat @ A4 ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % card_eq_0_iff
% 5.31/5.53 thf(fact_2690_card__eq__0__iff,axiom,
% 5.31/5.53 ! [A4: set_set_nat] :
% 5.31/5.53 ( ( ( finite_card_set_nat @ A4 )
% 5.31/5.53 = zero_zero_nat )
% 5.31/5.53 = ( ( A4 = bot_bot_set_set_nat )
% 5.31/5.53 | ~ ( finite1152437895449049373et_nat @ A4 ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % card_eq_0_iff
% 5.31/5.53 thf(fact_2691_card__eq__0__iff,axiom,
% 5.31/5.53 ! [A4: set_complex] :
% 5.31/5.53 ( ( ( finite_card_complex @ A4 )
% 5.31/5.53 = zero_zero_nat )
% 5.31/5.53 = ( ( A4 = bot_bot_set_complex )
% 5.31/5.53 | ~ ( finite3207457112153483333omplex @ A4 ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % card_eq_0_iff
% 5.31/5.53 thf(fact_2692_card__eq__0__iff,axiom,
% 5.31/5.53 ! [A4: set_nat] :
% 5.31/5.53 ( ( ( finite_card_nat @ A4 )
% 5.31/5.53 = zero_zero_nat )
% 5.31/5.53 = ( ( A4 = bot_bot_set_nat )
% 5.31/5.53 | ~ ( finite_finite_nat @ A4 ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % card_eq_0_iff
% 5.31/5.53 thf(fact_2693_card__eq__0__iff,axiom,
% 5.31/5.53 ! [A4: set_int] :
% 5.31/5.53 ( ( ( finite_card_int @ A4 )
% 5.31/5.53 = zero_zero_nat )
% 5.31/5.53 = ( ( A4 = bot_bot_set_int )
% 5.31/5.53 | ~ ( finite_finite_int @ A4 ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % card_eq_0_iff
% 5.31/5.53 thf(fact_2694_card__eq__0__iff,axiom,
% 5.31/5.53 ! [A4: set_real] :
% 5.31/5.53 ( ( ( finite_card_real @ A4 )
% 5.31/5.53 = zero_zero_nat )
% 5.31/5.53 = ( ( A4 = bot_bot_set_real )
% 5.31/5.53 | ~ ( finite_finite_real @ A4 ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % card_eq_0_iff
% 5.31/5.53 thf(fact_2695_card__ge__0__finite,axiom,
% 5.31/5.53 ! [A4: set_list_nat] :
% 5.31/5.53 ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_list_nat @ A4 ) )
% 5.31/5.53 => ( finite8100373058378681591st_nat @ A4 ) ) ).
% 5.31/5.53
% 5.31/5.53 % card_ge_0_finite
% 5.31/5.53 thf(fact_2696_card__ge__0__finite,axiom,
% 5.31/5.53 ! [A4: set_set_nat] :
% 5.31/5.53 ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_set_nat @ A4 ) )
% 5.31/5.53 => ( finite1152437895449049373et_nat @ A4 ) ) ).
% 5.31/5.53
% 5.31/5.53 % card_ge_0_finite
% 5.31/5.53 thf(fact_2697_card__ge__0__finite,axiom,
% 5.31/5.53 ! [A4: set_nat] :
% 5.31/5.53 ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_nat @ A4 ) )
% 5.31/5.53 => ( finite_finite_nat @ A4 ) ) ).
% 5.31/5.53
% 5.31/5.53 % card_ge_0_finite
% 5.31/5.53 thf(fact_2698_card__ge__0__finite,axiom,
% 5.31/5.53 ! [A4: set_int] :
% 5.31/5.53 ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_int @ A4 ) )
% 5.31/5.53 => ( finite_finite_int @ A4 ) ) ).
% 5.31/5.53
% 5.31/5.53 % card_ge_0_finite
% 5.31/5.53 thf(fact_2699_card__ge__0__finite,axiom,
% 5.31/5.53 ! [A4: set_complex] :
% 5.31/5.53 ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_complex @ A4 ) )
% 5.31/5.53 => ( finite3207457112153483333omplex @ A4 ) ) ).
% 5.31/5.53
% 5.31/5.53 % card_ge_0_finite
% 5.31/5.53 thf(fact_2700_card__insert__if,axiom,
% 5.31/5.53 ! [A4: set_real,X: real] :
% 5.31/5.53 ( ( finite_finite_real @ A4 )
% 5.31/5.53 => ( ( ( member_real @ X @ A4 )
% 5.31/5.53 => ( ( finite_card_real @ ( insert_real @ X @ A4 ) )
% 5.31/5.53 = ( finite_card_real @ A4 ) ) )
% 5.31/5.53 & ( ~ ( member_real @ X @ A4 )
% 5.31/5.53 => ( ( finite_card_real @ ( insert_real @ X @ A4 ) )
% 5.31/5.53 = ( suc @ ( finite_card_real @ A4 ) ) ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % card_insert_if
% 5.31/5.53 thf(fact_2701_card__insert__if,axiom,
% 5.31/5.53 ! [A4: set_list_nat,X: list_nat] :
% 5.31/5.53 ( ( finite8100373058378681591st_nat @ A4 )
% 5.31/5.53 => ( ( ( member_list_nat @ X @ A4 )
% 5.31/5.53 => ( ( finite_card_list_nat @ ( insert_list_nat @ X @ A4 ) )
% 5.31/5.53 = ( finite_card_list_nat @ A4 ) ) )
% 5.31/5.53 & ( ~ ( member_list_nat @ X @ A4 )
% 5.31/5.53 => ( ( finite_card_list_nat @ ( insert_list_nat @ X @ A4 ) )
% 5.31/5.53 = ( suc @ ( finite_card_list_nat @ A4 ) ) ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % card_insert_if
% 5.31/5.53 thf(fact_2702_card__insert__if,axiom,
% 5.31/5.53 ! [A4: set_set_nat,X: set_nat] :
% 5.31/5.53 ( ( finite1152437895449049373et_nat @ A4 )
% 5.31/5.53 => ( ( ( member_set_nat @ X @ A4 )
% 5.31/5.53 => ( ( finite_card_set_nat @ ( insert_set_nat @ X @ A4 ) )
% 5.31/5.53 = ( finite_card_set_nat @ A4 ) ) )
% 5.31/5.53 & ( ~ ( member_set_nat @ X @ A4 )
% 5.31/5.53 => ( ( finite_card_set_nat @ ( insert_set_nat @ X @ A4 ) )
% 5.31/5.53 = ( suc @ ( finite_card_set_nat @ A4 ) ) ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % card_insert_if
% 5.31/5.53 thf(fact_2703_card__insert__if,axiom,
% 5.31/5.53 ! [A4: set_nat,X: nat] :
% 5.31/5.53 ( ( finite_finite_nat @ A4 )
% 5.31/5.53 => ( ( ( member_nat @ X @ A4 )
% 5.31/5.53 => ( ( finite_card_nat @ ( insert_nat @ X @ A4 ) )
% 5.31/5.53 = ( finite_card_nat @ A4 ) ) )
% 5.31/5.53 & ( ~ ( member_nat @ X @ A4 )
% 5.31/5.53 => ( ( finite_card_nat @ ( insert_nat @ X @ A4 ) )
% 5.31/5.53 = ( suc @ ( finite_card_nat @ A4 ) ) ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % card_insert_if
% 5.31/5.53 thf(fact_2704_card__insert__if,axiom,
% 5.31/5.53 ! [A4: set_int,X: int] :
% 5.31/5.53 ( ( finite_finite_int @ A4 )
% 5.31/5.53 => ( ( ( member_int @ X @ A4 )
% 5.31/5.53 => ( ( finite_card_int @ ( insert_int @ X @ A4 ) )
% 5.31/5.53 = ( finite_card_int @ A4 ) ) )
% 5.31/5.53 & ( ~ ( member_int @ X @ A4 )
% 5.31/5.53 => ( ( finite_card_int @ ( insert_int @ X @ A4 ) )
% 5.31/5.53 = ( suc @ ( finite_card_int @ A4 ) ) ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % card_insert_if
% 5.31/5.53 thf(fact_2705_card__insert__if,axiom,
% 5.31/5.53 ! [A4: set_complex,X: complex] :
% 5.31/5.53 ( ( finite3207457112153483333omplex @ A4 )
% 5.31/5.53 => ( ( ( member_complex @ X @ A4 )
% 5.31/5.53 => ( ( finite_card_complex @ ( insert_complex @ X @ A4 ) )
% 5.31/5.53 = ( finite_card_complex @ A4 ) ) )
% 5.31/5.53 & ( ~ ( member_complex @ X @ A4 )
% 5.31/5.53 => ( ( finite_card_complex @ ( insert_complex @ X @ A4 ) )
% 5.31/5.53 = ( suc @ ( finite_card_complex @ A4 ) ) ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % card_insert_if
% 5.31/5.53 thf(fact_2706_card__Suc__eq__finite,axiom,
% 5.31/5.53 ! [A4: set_real,K2: nat] :
% 5.31/5.53 ( ( ( finite_card_real @ A4 )
% 5.31/5.53 = ( suc @ K2 ) )
% 5.31/5.53 = ( ? [B4: real,B7: set_real] :
% 5.31/5.53 ( ( A4
% 5.31/5.53 = ( insert_real @ B4 @ B7 ) )
% 5.31/5.53 & ~ ( member_real @ B4 @ B7 )
% 5.31/5.53 & ( ( finite_card_real @ B7 )
% 5.31/5.53 = K2 )
% 5.31/5.53 & ( finite_finite_real @ B7 ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % card_Suc_eq_finite
% 5.31/5.53 thf(fact_2707_card__Suc__eq__finite,axiom,
% 5.31/5.53 ! [A4: set_list_nat,K2: nat] :
% 5.31/5.53 ( ( ( finite_card_list_nat @ A4 )
% 5.31/5.53 = ( suc @ K2 ) )
% 5.31/5.53 = ( ? [B4: list_nat,B7: set_list_nat] :
% 5.31/5.53 ( ( A4
% 5.31/5.53 = ( insert_list_nat @ B4 @ B7 ) )
% 5.31/5.53 & ~ ( member_list_nat @ B4 @ B7 )
% 5.31/5.53 & ( ( finite_card_list_nat @ B7 )
% 5.31/5.53 = K2 )
% 5.31/5.53 & ( finite8100373058378681591st_nat @ B7 ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % card_Suc_eq_finite
% 5.31/5.53 thf(fact_2708_card__Suc__eq__finite,axiom,
% 5.31/5.53 ! [A4: set_set_nat,K2: nat] :
% 5.31/5.53 ( ( ( finite_card_set_nat @ A4 )
% 5.31/5.53 = ( suc @ K2 ) )
% 5.31/5.53 = ( ? [B4: set_nat,B7: set_set_nat] :
% 5.31/5.53 ( ( A4
% 5.31/5.53 = ( insert_set_nat @ B4 @ B7 ) )
% 5.31/5.53 & ~ ( member_set_nat @ B4 @ B7 )
% 5.31/5.53 & ( ( finite_card_set_nat @ B7 )
% 5.31/5.53 = K2 )
% 5.31/5.53 & ( finite1152437895449049373et_nat @ B7 ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % card_Suc_eq_finite
% 5.31/5.53 thf(fact_2709_card__Suc__eq__finite,axiom,
% 5.31/5.53 ! [A4: set_nat,K2: nat] :
% 5.31/5.53 ( ( ( finite_card_nat @ A4 )
% 5.31/5.53 = ( suc @ K2 ) )
% 5.31/5.53 = ( ? [B4: nat,B7: set_nat] :
% 5.31/5.53 ( ( A4
% 5.31/5.53 = ( insert_nat @ B4 @ B7 ) )
% 5.31/5.53 & ~ ( member_nat @ B4 @ B7 )
% 5.31/5.53 & ( ( finite_card_nat @ B7 )
% 5.31/5.53 = K2 )
% 5.31/5.53 & ( finite_finite_nat @ B7 ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % card_Suc_eq_finite
% 5.31/5.53 thf(fact_2710_card__Suc__eq__finite,axiom,
% 5.31/5.53 ! [A4: set_int,K2: nat] :
% 5.31/5.53 ( ( ( finite_card_int @ A4 )
% 5.31/5.53 = ( suc @ K2 ) )
% 5.31/5.53 = ( ? [B4: int,B7: set_int] :
% 5.31/5.53 ( ( A4
% 5.31/5.53 = ( insert_int @ B4 @ B7 ) )
% 5.31/5.53 & ~ ( member_int @ B4 @ B7 )
% 5.31/5.53 & ( ( finite_card_int @ B7 )
% 5.31/5.53 = K2 )
% 5.31/5.53 & ( finite_finite_int @ B7 ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % card_Suc_eq_finite
% 5.31/5.53 thf(fact_2711_card__Suc__eq__finite,axiom,
% 5.31/5.53 ! [A4: set_complex,K2: nat] :
% 5.31/5.53 ( ( ( finite_card_complex @ A4 )
% 5.31/5.53 = ( suc @ K2 ) )
% 5.31/5.53 = ( ? [B4: complex,B7: set_complex] :
% 5.31/5.53 ( ( A4
% 5.31/5.53 = ( insert_complex @ B4 @ B7 ) )
% 5.31/5.53 & ~ ( member_complex @ B4 @ B7 )
% 5.31/5.53 & ( ( finite_card_complex @ B7 )
% 5.31/5.53 = K2 )
% 5.31/5.53 & ( finite3207457112153483333omplex @ B7 ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % card_Suc_eq_finite
% 5.31/5.53 thf(fact_2712_power__less__imp__less__base,axiom,
% 5.31/5.53 ! [A: real,N: nat,B: real] :
% 5.31/5.53 ( ( ord_less_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) )
% 5.31/5.53 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.31/5.53 => ( ord_less_real @ A @ B ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % power_less_imp_less_base
% 5.31/5.53 thf(fact_2713_power__less__imp__less__base,axiom,
% 5.31/5.53 ! [A: rat,N: nat,B: rat] :
% 5.31/5.53 ( ( ord_less_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) )
% 5.31/5.53 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.31/5.53 => ( ord_less_rat @ A @ B ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % power_less_imp_less_base
% 5.31/5.53 thf(fact_2714_power__less__imp__less__base,axiom,
% 5.31/5.53 ! [A: nat,N: nat,B: nat] :
% 5.31/5.53 ( ( ord_less_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) )
% 5.31/5.53 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.31/5.53 => ( ord_less_nat @ A @ B ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % power_less_imp_less_base
% 5.31/5.53 thf(fact_2715_power__less__imp__less__base,axiom,
% 5.31/5.53 ! [A: int,N: nat,B: int] :
% 5.31/5.53 ( ( ord_less_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) )
% 5.31/5.53 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.31/5.53 => ( ord_less_int @ A @ B ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % power_less_imp_less_base
% 5.31/5.53 thf(fact_2716_card__mono,axiom,
% 5.31/5.53 ! [B5: set_list_nat,A4: set_list_nat] :
% 5.31/5.53 ( ( finite8100373058378681591st_nat @ B5 )
% 5.31/5.53 => ( ( ord_le6045566169113846134st_nat @ A4 @ B5 )
% 5.31/5.53 => ( ord_less_eq_nat @ ( finite_card_list_nat @ A4 ) @ ( finite_card_list_nat @ B5 ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % card_mono
% 5.31/5.53 thf(fact_2717_card__mono,axiom,
% 5.31/5.53 ! [B5: set_set_nat,A4: set_set_nat] :
% 5.31/5.53 ( ( finite1152437895449049373et_nat @ B5 )
% 5.31/5.53 => ( ( ord_le6893508408891458716et_nat @ A4 @ B5 )
% 5.31/5.53 => ( ord_less_eq_nat @ ( finite_card_set_nat @ A4 ) @ ( finite_card_set_nat @ B5 ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % card_mono
% 5.31/5.53 thf(fact_2718_card__mono,axiom,
% 5.31/5.53 ! [B5: set_int,A4: set_int] :
% 5.31/5.53 ( ( finite_finite_int @ B5 )
% 5.31/5.53 => ( ( ord_less_eq_set_int @ A4 @ B5 )
% 5.31/5.53 => ( ord_less_eq_nat @ ( finite_card_int @ A4 ) @ ( finite_card_int @ B5 ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % card_mono
% 5.31/5.53 thf(fact_2719_card__mono,axiom,
% 5.31/5.53 ! [B5: set_complex,A4: set_complex] :
% 5.31/5.53 ( ( finite3207457112153483333omplex @ B5 )
% 5.31/5.53 => ( ( ord_le211207098394363844omplex @ A4 @ B5 )
% 5.31/5.53 => ( ord_less_eq_nat @ ( finite_card_complex @ A4 ) @ ( finite_card_complex @ B5 ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % card_mono
% 5.31/5.53 thf(fact_2720_card__mono,axiom,
% 5.31/5.53 ! [B5: set_nat,A4: set_nat] :
% 5.31/5.53 ( ( finite_finite_nat @ B5 )
% 5.31/5.53 => ( ( ord_less_eq_set_nat @ A4 @ B5 )
% 5.31/5.53 => ( ord_less_eq_nat @ ( finite_card_nat @ A4 ) @ ( finite_card_nat @ B5 ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % card_mono
% 5.31/5.53 thf(fact_2721_card__seteq,axiom,
% 5.31/5.53 ! [B5: set_list_nat,A4: set_list_nat] :
% 5.31/5.53 ( ( finite8100373058378681591st_nat @ B5 )
% 5.31/5.53 => ( ( ord_le6045566169113846134st_nat @ A4 @ B5 )
% 5.31/5.53 => ( ( ord_less_eq_nat @ ( finite_card_list_nat @ B5 ) @ ( finite_card_list_nat @ A4 ) )
% 5.31/5.53 => ( A4 = B5 ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % card_seteq
% 5.31/5.53 thf(fact_2722_card__seteq,axiom,
% 5.31/5.53 ! [B5: set_set_nat,A4: set_set_nat] :
% 5.31/5.53 ( ( finite1152437895449049373et_nat @ B5 )
% 5.31/5.53 => ( ( ord_le6893508408891458716et_nat @ A4 @ B5 )
% 5.31/5.53 => ( ( ord_less_eq_nat @ ( finite_card_set_nat @ B5 ) @ ( finite_card_set_nat @ A4 ) )
% 5.31/5.53 => ( A4 = B5 ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % card_seteq
% 5.31/5.53 thf(fact_2723_card__seteq,axiom,
% 5.31/5.53 ! [B5: set_int,A4: set_int] :
% 5.31/5.53 ( ( finite_finite_int @ B5 )
% 5.31/5.53 => ( ( ord_less_eq_set_int @ A4 @ B5 )
% 5.31/5.53 => ( ( ord_less_eq_nat @ ( finite_card_int @ B5 ) @ ( finite_card_int @ A4 ) )
% 5.31/5.53 => ( A4 = B5 ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % card_seteq
% 5.31/5.53 thf(fact_2724_card__seteq,axiom,
% 5.31/5.53 ! [B5: set_complex,A4: set_complex] :
% 5.31/5.53 ( ( finite3207457112153483333omplex @ B5 )
% 5.31/5.53 => ( ( ord_le211207098394363844omplex @ A4 @ B5 )
% 5.31/5.53 => ( ( ord_less_eq_nat @ ( finite_card_complex @ B5 ) @ ( finite_card_complex @ A4 ) )
% 5.31/5.53 => ( A4 = B5 ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % card_seteq
% 5.31/5.53 thf(fact_2725_card__seteq,axiom,
% 5.31/5.53 ! [B5: set_nat,A4: set_nat] :
% 5.31/5.53 ( ( finite_finite_nat @ B5 )
% 5.31/5.53 => ( ( ord_less_eq_set_nat @ A4 @ B5 )
% 5.31/5.53 => ( ( ord_less_eq_nat @ ( finite_card_nat @ B5 ) @ ( finite_card_nat @ A4 ) )
% 5.31/5.53 => ( A4 = B5 ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % card_seteq
% 5.31/5.53 thf(fact_2726_finite__if__finite__subsets__card__bdd,axiom,
% 5.31/5.53 ! [F3: set_list_nat,C4: nat] :
% 5.31/5.53 ( ! [G: set_list_nat] :
% 5.31/5.53 ( ( ord_le6045566169113846134st_nat @ G @ F3 )
% 5.31/5.53 => ( ( finite8100373058378681591st_nat @ G )
% 5.31/5.53 => ( ord_less_eq_nat @ ( finite_card_list_nat @ G ) @ C4 ) ) )
% 5.31/5.53 => ( ( finite8100373058378681591st_nat @ F3 )
% 5.31/5.53 & ( ord_less_eq_nat @ ( finite_card_list_nat @ F3 ) @ C4 ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % finite_if_finite_subsets_card_bdd
% 5.31/5.53 thf(fact_2727_finite__if__finite__subsets__card__bdd,axiom,
% 5.31/5.53 ! [F3: set_set_nat,C4: nat] :
% 5.31/5.53 ( ! [G: set_set_nat] :
% 5.31/5.53 ( ( ord_le6893508408891458716et_nat @ G @ F3 )
% 5.31/5.53 => ( ( finite1152437895449049373et_nat @ G )
% 5.31/5.53 => ( ord_less_eq_nat @ ( finite_card_set_nat @ G ) @ C4 ) ) )
% 5.31/5.53 => ( ( finite1152437895449049373et_nat @ F3 )
% 5.31/5.53 & ( ord_less_eq_nat @ ( finite_card_set_nat @ F3 ) @ C4 ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % finite_if_finite_subsets_card_bdd
% 5.31/5.53 thf(fact_2728_finite__if__finite__subsets__card__bdd,axiom,
% 5.31/5.53 ! [F3: set_int,C4: nat] :
% 5.31/5.53 ( ! [G: set_int] :
% 5.31/5.53 ( ( ord_less_eq_set_int @ G @ F3 )
% 5.31/5.53 => ( ( finite_finite_int @ G )
% 5.31/5.53 => ( ord_less_eq_nat @ ( finite_card_int @ G ) @ C4 ) ) )
% 5.31/5.53 => ( ( finite_finite_int @ F3 )
% 5.31/5.53 & ( ord_less_eq_nat @ ( finite_card_int @ F3 ) @ C4 ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % finite_if_finite_subsets_card_bdd
% 5.31/5.53 thf(fact_2729_finite__if__finite__subsets__card__bdd,axiom,
% 5.31/5.53 ! [F3: set_complex,C4: nat] :
% 5.31/5.53 ( ! [G: set_complex] :
% 5.31/5.53 ( ( ord_le211207098394363844omplex @ G @ F3 )
% 5.31/5.53 => ( ( finite3207457112153483333omplex @ G )
% 5.31/5.53 => ( ord_less_eq_nat @ ( finite_card_complex @ G ) @ C4 ) ) )
% 5.31/5.53 => ( ( finite3207457112153483333omplex @ F3 )
% 5.31/5.53 & ( ord_less_eq_nat @ ( finite_card_complex @ F3 ) @ C4 ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % finite_if_finite_subsets_card_bdd
% 5.31/5.53 thf(fact_2730_finite__if__finite__subsets__card__bdd,axiom,
% 5.31/5.53 ! [F3: set_nat,C4: nat] :
% 5.31/5.53 ( ! [G: set_nat] :
% 5.31/5.53 ( ( ord_less_eq_set_nat @ G @ F3 )
% 5.31/5.53 => ( ( finite_finite_nat @ G )
% 5.31/5.53 => ( ord_less_eq_nat @ ( finite_card_nat @ G ) @ C4 ) ) )
% 5.31/5.53 => ( ( finite_finite_nat @ F3 )
% 5.31/5.53 & ( ord_less_eq_nat @ ( finite_card_nat @ F3 ) @ C4 ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % finite_if_finite_subsets_card_bdd
% 5.31/5.53 thf(fact_2731_obtain__subset__with__card__n,axiom,
% 5.31/5.53 ! [N: nat,S3: set_list_nat] :
% 5.31/5.53 ( ( ord_less_eq_nat @ N @ ( finite_card_list_nat @ S3 ) )
% 5.31/5.53 => ~ ! [T3: set_list_nat] :
% 5.31/5.53 ( ( ord_le6045566169113846134st_nat @ T3 @ S3 )
% 5.31/5.53 => ( ( ( finite_card_list_nat @ T3 )
% 5.31/5.53 = N )
% 5.31/5.53 => ~ ( finite8100373058378681591st_nat @ T3 ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % obtain_subset_with_card_n
% 5.31/5.53 thf(fact_2732_obtain__subset__with__card__n,axiom,
% 5.31/5.53 ! [N: nat,S3: set_set_nat] :
% 5.31/5.53 ( ( ord_less_eq_nat @ N @ ( finite_card_set_nat @ S3 ) )
% 5.31/5.53 => ~ ! [T3: set_set_nat] :
% 5.31/5.53 ( ( ord_le6893508408891458716et_nat @ T3 @ S3 )
% 5.31/5.53 => ( ( ( finite_card_set_nat @ T3 )
% 5.31/5.53 = N )
% 5.31/5.53 => ~ ( finite1152437895449049373et_nat @ T3 ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % obtain_subset_with_card_n
% 5.31/5.53 thf(fact_2733_obtain__subset__with__card__n,axiom,
% 5.31/5.53 ! [N: nat,S3: set_int] :
% 5.31/5.53 ( ( ord_less_eq_nat @ N @ ( finite_card_int @ S3 ) )
% 5.31/5.53 => ~ ! [T3: set_int] :
% 5.31/5.53 ( ( ord_less_eq_set_int @ T3 @ S3 )
% 5.31/5.53 => ( ( ( finite_card_int @ T3 )
% 5.31/5.53 = N )
% 5.31/5.53 => ~ ( finite_finite_int @ T3 ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % obtain_subset_with_card_n
% 5.31/5.53 thf(fact_2734_obtain__subset__with__card__n,axiom,
% 5.31/5.53 ! [N: nat,S3: set_complex] :
% 5.31/5.53 ( ( ord_less_eq_nat @ N @ ( finite_card_complex @ S3 ) )
% 5.31/5.53 => ~ ! [T3: set_complex] :
% 5.31/5.53 ( ( ord_le211207098394363844omplex @ T3 @ S3 )
% 5.31/5.53 => ( ( ( finite_card_complex @ T3 )
% 5.31/5.53 = N )
% 5.31/5.53 => ~ ( finite3207457112153483333omplex @ T3 ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % obtain_subset_with_card_n
% 5.31/5.53 thf(fact_2735_obtain__subset__with__card__n,axiom,
% 5.31/5.53 ! [N: nat,S3: set_nat] :
% 5.31/5.53 ( ( ord_less_eq_nat @ N @ ( finite_card_nat @ S3 ) )
% 5.31/5.53 => ~ ! [T3: set_nat] :
% 5.31/5.53 ( ( ord_less_eq_set_nat @ T3 @ S3 )
% 5.31/5.53 => ( ( ( finite_card_nat @ T3 )
% 5.31/5.53 = N )
% 5.31/5.53 => ~ ( finite_finite_nat @ T3 ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % obtain_subset_with_card_n
% 5.31/5.53 thf(fact_2736_power__le__one,axiom,
% 5.31/5.53 ! [A: code_integer,N: nat] :
% 5.31/5.53 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 5.31/5.53 => ( ( ord_le3102999989581377725nteger @ A @ one_one_Code_integer )
% 5.31/5.53 => ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ A @ N ) @ one_one_Code_integer ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % power_le_one
% 5.31/5.53 thf(fact_2737_power__le__one,axiom,
% 5.31/5.53 ! [A: real,N: nat] :
% 5.31/5.53 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.31/5.53 => ( ( ord_less_eq_real @ A @ one_one_real )
% 5.31/5.53 => ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ one_one_real ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % power_le_one
% 5.31/5.53 thf(fact_2738_power__le__one,axiom,
% 5.31/5.53 ! [A: rat,N: nat] :
% 5.31/5.53 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.31/5.53 => ( ( ord_less_eq_rat @ A @ one_one_rat )
% 5.31/5.53 => ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ one_one_rat ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % power_le_one
% 5.31/5.53 thf(fact_2739_power__le__one,axiom,
% 5.31/5.53 ! [A: nat,N: nat] :
% 5.31/5.53 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.31/5.53 => ( ( ord_less_eq_nat @ A @ one_one_nat )
% 5.31/5.53 => ( ord_less_eq_nat @ ( power_power_nat @ A @ N ) @ one_one_nat ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % power_le_one
% 5.31/5.53 thf(fact_2740_power__le__one,axiom,
% 5.31/5.53 ! [A: int,N: nat] :
% 5.31/5.53 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.31/5.53 => ( ( ord_less_eq_int @ A @ one_one_int )
% 5.31/5.53 => ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ one_one_int ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % power_le_one
% 5.31/5.53 thf(fact_2741_power__inject__base,axiom,
% 5.31/5.53 ! [A: real,N: nat,B: real] :
% 5.31/5.53 ( ( ( power_power_real @ A @ ( suc @ N ) )
% 5.31/5.53 = ( power_power_real @ B @ ( suc @ N ) ) )
% 5.31/5.53 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.31/5.53 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.31/5.53 => ( A = B ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % power_inject_base
% 5.31/5.53 thf(fact_2742_power__inject__base,axiom,
% 5.31/5.53 ! [A: rat,N: nat,B: rat] :
% 5.31/5.53 ( ( ( power_power_rat @ A @ ( suc @ N ) )
% 5.31/5.53 = ( power_power_rat @ B @ ( suc @ N ) ) )
% 5.31/5.53 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.31/5.53 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.31/5.53 => ( A = B ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % power_inject_base
% 5.31/5.53 thf(fact_2743_power__inject__base,axiom,
% 5.31/5.53 ! [A: nat,N: nat,B: nat] :
% 5.31/5.53 ( ( ( power_power_nat @ A @ ( suc @ N ) )
% 5.31/5.53 = ( power_power_nat @ B @ ( suc @ N ) ) )
% 5.31/5.53 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.31/5.53 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.31/5.53 => ( A = B ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % power_inject_base
% 5.31/5.53 thf(fact_2744_power__inject__base,axiom,
% 5.31/5.53 ! [A: int,N: nat,B: int] :
% 5.31/5.53 ( ( ( power_power_int @ A @ ( suc @ N ) )
% 5.31/5.53 = ( power_power_int @ B @ ( suc @ N ) ) )
% 5.31/5.53 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.31/5.53 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.31/5.53 => ( A = B ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % power_inject_base
% 5.31/5.53 thf(fact_2745_power__le__imp__le__base,axiom,
% 5.31/5.53 ! [A: real,N: nat,B: real] :
% 5.31/5.53 ( ( ord_less_eq_real @ ( power_power_real @ A @ ( suc @ N ) ) @ ( power_power_real @ B @ ( suc @ N ) ) )
% 5.31/5.53 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.31/5.53 => ( ord_less_eq_real @ A @ B ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % power_le_imp_le_base
% 5.31/5.53 thf(fact_2746_power__le__imp__le__base,axiom,
% 5.31/5.53 ! [A: rat,N: nat,B: rat] :
% 5.31/5.53 ( ( ord_less_eq_rat @ ( power_power_rat @ A @ ( suc @ N ) ) @ ( power_power_rat @ B @ ( suc @ N ) ) )
% 5.31/5.53 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.31/5.53 => ( ord_less_eq_rat @ A @ B ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % power_le_imp_le_base
% 5.31/5.53 thf(fact_2747_power__le__imp__le__base,axiom,
% 5.31/5.53 ! [A: nat,N: nat,B: nat] :
% 5.31/5.53 ( ( ord_less_eq_nat @ ( power_power_nat @ A @ ( suc @ N ) ) @ ( power_power_nat @ B @ ( suc @ N ) ) )
% 5.31/5.53 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.31/5.53 => ( ord_less_eq_nat @ A @ B ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % power_le_imp_le_base
% 5.31/5.53 thf(fact_2748_power__le__imp__le__base,axiom,
% 5.31/5.53 ! [A: int,N: nat,B: int] :
% 5.31/5.53 ( ( ord_less_eq_int @ ( power_power_int @ A @ ( suc @ N ) ) @ ( power_power_int @ B @ ( suc @ N ) ) )
% 5.31/5.53 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.31/5.53 => ( ord_less_eq_int @ A @ B ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % power_le_imp_le_base
% 5.31/5.53 thf(fact_2749_power__less__power__Suc,axiom,
% 5.31/5.53 ! [A: code_integer,N: nat] :
% 5.31/5.53 ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ A )
% 5.31/5.53 => ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ A @ N ) @ ( times_3573771949741848930nteger @ A @ ( power_8256067586552552935nteger @ A @ N ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % power_less_power_Suc
% 5.31/5.53 thf(fact_2750_power__less__power__Suc,axiom,
% 5.31/5.53 ! [A: real,N: nat] :
% 5.31/5.53 ( ( ord_less_real @ one_one_real @ A )
% 5.31/5.53 => ( ord_less_real @ ( power_power_real @ A @ N ) @ ( times_times_real @ A @ ( power_power_real @ A @ N ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % power_less_power_Suc
% 5.31/5.53 thf(fact_2751_power__less__power__Suc,axiom,
% 5.31/5.53 ! [A: rat,N: nat] :
% 5.31/5.53 ( ( ord_less_rat @ one_one_rat @ A )
% 5.31/5.53 => ( ord_less_rat @ ( power_power_rat @ A @ N ) @ ( times_times_rat @ A @ ( power_power_rat @ A @ N ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % power_less_power_Suc
% 5.31/5.53 thf(fact_2752_power__less__power__Suc,axiom,
% 5.31/5.53 ! [A: nat,N: nat] :
% 5.31/5.53 ( ( ord_less_nat @ one_one_nat @ A )
% 5.31/5.53 => ( ord_less_nat @ ( power_power_nat @ A @ N ) @ ( times_times_nat @ A @ ( power_power_nat @ A @ N ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % power_less_power_Suc
% 5.31/5.53 thf(fact_2753_power__less__power__Suc,axiom,
% 5.31/5.53 ! [A: int,N: nat] :
% 5.31/5.53 ( ( ord_less_int @ one_one_int @ A )
% 5.31/5.53 => ( ord_less_int @ ( power_power_int @ A @ N ) @ ( times_times_int @ A @ ( power_power_int @ A @ N ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % power_less_power_Suc
% 5.31/5.53 thf(fact_2754_power__gt1__lemma,axiom,
% 5.31/5.53 ! [A: code_integer,N: nat] :
% 5.31/5.53 ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ A )
% 5.31/5.53 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( times_3573771949741848930nteger @ A @ ( power_8256067586552552935nteger @ A @ N ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % power_gt1_lemma
% 5.31/5.53 thf(fact_2755_power__gt1__lemma,axiom,
% 5.31/5.53 ! [A: real,N: nat] :
% 5.31/5.53 ( ( ord_less_real @ one_one_real @ A )
% 5.31/5.53 => ( ord_less_real @ one_one_real @ ( times_times_real @ A @ ( power_power_real @ A @ N ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % power_gt1_lemma
% 5.31/5.53 thf(fact_2756_power__gt1__lemma,axiom,
% 5.31/5.53 ! [A: rat,N: nat] :
% 5.31/5.53 ( ( ord_less_rat @ one_one_rat @ A )
% 5.31/5.53 => ( ord_less_rat @ one_one_rat @ ( times_times_rat @ A @ ( power_power_rat @ A @ N ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % power_gt1_lemma
% 5.31/5.53 thf(fact_2757_power__gt1__lemma,axiom,
% 5.31/5.53 ! [A: nat,N: nat] :
% 5.31/5.53 ( ( ord_less_nat @ one_one_nat @ A )
% 5.31/5.53 => ( ord_less_nat @ one_one_nat @ ( times_times_nat @ A @ ( power_power_nat @ A @ N ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % power_gt1_lemma
% 5.31/5.53 thf(fact_2758_power__gt1__lemma,axiom,
% 5.31/5.53 ! [A: int,N: nat] :
% 5.31/5.53 ( ( ord_less_int @ one_one_int @ A )
% 5.31/5.53 => ( ord_less_int @ one_one_int @ ( times_times_int @ A @ ( power_power_int @ A @ N ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % power_gt1_lemma
% 5.31/5.53 thf(fact_2759_card__le__sym__Diff,axiom,
% 5.31/5.53 ! [A4: set_list_nat,B5: set_list_nat] :
% 5.31/5.53 ( ( finite8100373058378681591st_nat @ A4 )
% 5.31/5.53 => ( ( finite8100373058378681591st_nat @ B5 )
% 5.31/5.53 => ( ( ord_less_eq_nat @ ( finite_card_list_nat @ A4 ) @ ( finite_card_list_nat @ B5 ) )
% 5.31/5.53 => ( ord_less_eq_nat @ ( finite_card_list_nat @ ( minus_7954133019191499631st_nat @ A4 @ B5 ) ) @ ( finite_card_list_nat @ ( minus_7954133019191499631st_nat @ B5 @ A4 ) ) ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % card_le_sym_Diff
% 5.31/5.53 thf(fact_2760_card__le__sym__Diff,axiom,
% 5.31/5.53 ! [A4: set_set_nat,B5: set_set_nat] :
% 5.31/5.53 ( ( finite1152437895449049373et_nat @ A4 )
% 5.31/5.53 => ( ( finite1152437895449049373et_nat @ B5 )
% 5.31/5.53 => ( ( ord_less_eq_nat @ ( finite_card_set_nat @ A4 ) @ ( finite_card_set_nat @ B5 ) )
% 5.31/5.53 => ( ord_less_eq_nat @ ( finite_card_set_nat @ ( minus_2163939370556025621et_nat @ A4 @ B5 ) ) @ ( finite_card_set_nat @ ( minus_2163939370556025621et_nat @ B5 @ A4 ) ) ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % card_le_sym_Diff
% 5.31/5.53 thf(fact_2761_card__le__sym__Diff,axiom,
% 5.31/5.53 ! [A4: set_int,B5: set_int] :
% 5.31/5.53 ( ( finite_finite_int @ A4 )
% 5.31/5.53 => ( ( finite_finite_int @ B5 )
% 5.31/5.53 => ( ( ord_less_eq_nat @ ( finite_card_int @ A4 ) @ ( finite_card_int @ B5 ) )
% 5.31/5.53 => ( ord_less_eq_nat @ ( finite_card_int @ ( minus_minus_set_int @ A4 @ B5 ) ) @ ( finite_card_int @ ( minus_minus_set_int @ B5 @ A4 ) ) ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % card_le_sym_Diff
% 5.31/5.53 thf(fact_2762_card__le__sym__Diff,axiom,
% 5.31/5.53 ! [A4: set_complex,B5: set_complex] :
% 5.31/5.53 ( ( finite3207457112153483333omplex @ A4 )
% 5.31/5.53 => ( ( finite3207457112153483333omplex @ B5 )
% 5.31/5.53 => ( ( ord_less_eq_nat @ ( finite_card_complex @ A4 ) @ ( finite_card_complex @ B5 ) )
% 5.31/5.53 => ( ord_less_eq_nat @ ( finite_card_complex @ ( minus_811609699411566653omplex @ A4 @ B5 ) ) @ ( finite_card_complex @ ( minus_811609699411566653omplex @ B5 @ A4 ) ) ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % card_le_sym_Diff
% 5.31/5.53 thf(fact_2763_card__le__sym__Diff,axiom,
% 5.31/5.53 ! [A4: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat] :
% 5.31/5.53 ( ( finite6177210948735845034at_nat @ A4 )
% 5.31/5.53 => ( ( finite6177210948735845034at_nat @ B5 )
% 5.31/5.53 => ( ( ord_less_eq_nat @ ( finite711546835091564841at_nat @ A4 ) @ ( finite711546835091564841at_nat @ B5 ) )
% 5.31/5.53 => ( ord_less_eq_nat @ ( finite711546835091564841at_nat @ ( minus_1356011639430497352at_nat @ A4 @ B5 ) ) @ ( finite711546835091564841at_nat @ ( minus_1356011639430497352at_nat @ B5 @ A4 ) ) ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % card_le_sym_Diff
% 5.31/5.53 thf(fact_2764_card__le__sym__Diff,axiom,
% 5.31/5.53 ! [A4: set_nat,B5: set_nat] :
% 5.31/5.53 ( ( finite_finite_nat @ A4 )
% 5.31/5.53 => ( ( finite_finite_nat @ B5 )
% 5.31/5.53 => ( ( ord_less_eq_nat @ ( finite_card_nat @ A4 ) @ ( finite_card_nat @ B5 ) )
% 5.31/5.53 => ( ord_less_eq_nat @ ( finite_card_nat @ ( minus_minus_set_nat @ A4 @ B5 ) ) @ ( finite_card_nat @ ( minus_minus_set_nat @ B5 @ A4 ) ) ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % card_le_sym_Diff
% 5.31/5.53 thf(fact_2765_card__length,axiom,
% 5.31/5.53 ! [Xs2: list_complex] : ( ord_less_eq_nat @ ( finite_card_complex @ ( set_complex2 @ Xs2 ) ) @ ( size_s3451745648224563538omplex @ Xs2 ) ) ).
% 5.31/5.53
% 5.31/5.53 % card_length
% 5.31/5.53 thf(fact_2766_card__length,axiom,
% 5.31/5.53 ! [Xs2: list_list_nat] : ( ord_less_eq_nat @ ( finite_card_list_nat @ ( set_list_nat2 @ Xs2 ) ) @ ( size_s3023201423986296836st_nat @ Xs2 ) ) ).
% 5.31/5.53
% 5.31/5.53 % card_length
% 5.31/5.53 thf(fact_2767_card__length,axiom,
% 5.31/5.53 ! [Xs2: list_set_nat] : ( ord_less_eq_nat @ ( finite_card_set_nat @ ( set_set_nat2 @ Xs2 ) ) @ ( size_s3254054031482475050et_nat @ Xs2 ) ) ).
% 5.31/5.53
% 5.31/5.53 % card_length
% 5.31/5.53 thf(fact_2768_card__length,axiom,
% 5.31/5.53 ! [Xs2: list_VEBT_VEBT] : ( ord_less_eq_nat @ ( finite7802652506058667612T_VEBT @ ( set_VEBT_VEBT2 @ Xs2 ) ) @ ( size_s6755466524823107622T_VEBT @ Xs2 ) ) ).
% 5.31/5.53
% 5.31/5.53 % card_length
% 5.31/5.53 thf(fact_2769_card__length,axiom,
% 5.31/5.53 ! [Xs2: list_o] : ( ord_less_eq_nat @ ( finite_card_o @ ( set_o2 @ Xs2 ) ) @ ( size_size_list_o @ Xs2 ) ) ).
% 5.31/5.53
% 5.31/5.53 % card_length
% 5.31/5.53 thf(fact_2770_card__length,axiom,
% 5.31/5.53 ! [Xs2: list_nat] : ( ord_less_eq_nat @ ( finite_card_nat @ ( set_nat2 @ Xs2 ) ) @ ( size_size_list_nat @ Xs2 ) ) ).
% 5.31/5.53
% 5.31/5.53 % card_length
% 5.31/5.53 thf(fact_2771_card__length,axiom,
% 5.31/5.53 ! [Xs2: list_int] : ( ord_less_eq_nat @ ( finite_card_int @ ( set_int2 @ Xs2 ) ) @ ( size_size_list_int @ Xs2 ) ) ).
% 5.31/5.53
% 5.31/5.53 % card_length
% 5.31/5.53 thf(fact_2772_power__gt1,axiom,
% 5.31/5.53 ! [A: code_integer,N: nat] :
% 5.31/5.53 ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ A )
% 5.31/5.53 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ A @ ( suc @ N ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % power_gt1
% 5.31/5.53 thf(fact_2773_power__gt1,axiom,
% 5.31/5.53 ! [A: real,N: nat] :
% 5.31/5.53 ( ( ord_less_real @ one_one_real @ A )
% 5.31/5.53 => ( ord_less_real @ one_one_real @ ( power_power_real @ A @ ( suc @ N ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % power_gt1
% 5.31/5.53 thf(fact_2774_power__gt1,axiom,
% 5.31/5.53 ! [A: rat,N: nat] :
% 5.31/5.53 ( ( ord_less_rat @ one_one_rat @ A )
% 5.31/5.53 => ( ord_less_rat @ one_one_rat @ ( power_power_rat @ A @ ( suc @ N ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % power_gt1
% 5.31/5.53 thf(fact_2775_power__gt1,axiom,
% 5.31/5.53 ! [A: nat,N: nat] :
% 5.31/5.53 ( ( ord_less_nat @ one_one_nat @ A )
% 5.31/5.53 => ( ord_less_nat @ one_one_nat @ ( power_power_nat @ A @ ( suc @ N ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % power_gt1
% 5.31/5.53 thf(fact_2776_power__gt1,axiom,
% 5.31/5.53 ! [A: int,N: nat] :
% 5.31/5.53 ( ( ord_less_int @ one_one_int @ A )
% 5.31/5.53 => ( ord_less_int @ one_one_int @ ( power_power_int @ A @ ( suc @ N ) ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % power_gt1
% 5.31/5.53 thf(fact_2777_power__0__left,axiom,
% 5.31/5.53 ! [N: nat] :
% 5.31/5.53 ( ( ( N = zero_zero_nat )
% 5.31/5.53 => ( ( power_8256067586552552935nteger @ zero_z3403309356797280102nteger @ N )
% 5.31/5.53 = one_one_Code_integer ) )
% 5.31/5.53 & ( ( N != zero_zero_nat )
% 5.31/5.53 => ( ( power_8256067586552552935nteger @ zero_z3403309356797280102nteger @ N )
% 5.31/5.53 = zero_z3403309356797280102nteger ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % power_0_left
% 5.31/5.53 thf(fact_2778_power__0__left,axiom,
% 5.31/5.53 ! [N: nat] :
% 5.31/5.53 ( ( ( N = zero_zero_nat )
% 5.31/5.53 => ( ( power_power_rat @ zero_zero_rat @ N )
% 5.31/5.53 = one_one_rat ) )
% 5.31/5.53 & ( ( N != zero_zero_nat )
% 5.31/5.53 => ( ( power_power_rat @ zero_zero_rat @ N )
% 5.31/5.53 = zero_zero_rat ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % power_0_left
% 5.31/5.53 thf(fact_2779_power__0__left,axiom,
% 5.31/5.53 ! [N: nat] :
% 5.31/5.53 ( ( ( N = zero_zero_nat )
% 5.31/5.53 => ( ( power_power_nat @ zero_zero_nat @ N )
% 5.31/5.53 = one_one_nat ) )
% 5.31/5.53 & ( ( N != zero_zero_nat )
% 5.31/5.53 => ( ( power_power_nat @ zero_zero_nat @ N )
% 5.31/5.53 = zero_zero_nat ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % power_0_left
% 5.31/5.53 thf(fact_2780_power__0__left,axiom,
% 5.31/5.53 ! [N: nat] :
% 5.31/5.53 ( ( ( N = zero_zero_nat )
% 5.31/5.53 => ( ( power_power_real @ zero_zero_real @ N )
% 5.31/5.53 = one_one_real ) )
% 5.31/5.53 & ( ( N != zero_zero_nat )
% 5.31/5.53 => ( ( power_power_real @ zero_zero_real @ N )
% 5.31/5.53 = zero_zero_real ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % power_0_left
% 5.31/5.53 thf(fact_2781_power__0__left,axiom,
% 5.31/5.53 ! [N: nat] :
% 5.31/5.53 ( ( ( N = zero_zero_nat )
% 5.31/5.53 => ( ( power_power_int @ zero_zero_int @ N )
% 5.31/5.53 = one_one_int ) )
% 5.31/5.53 & ( ( N != zero_zero_nat )
% 5.31/5.53 => ( ( power_power_int @ zero_zero_int @ N )
% 5.31/5.53 = zero_zero_int ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % power_0_left
% 5.31/5.53 thf(fact_2782_power__0__left,axiom,
% 5.31/5.53 ! [N: nat] :
% 5.31/5.53 ( ( ( N = zero_zero_nat )
% 5.31/5.53 => ( ( power_power_complex @ zero_zero_complex @ N )
% 5.31/5.53 = one_one_complex ) )
% 5.31/5.53 & ( ( N != zero_zero_nat )
% 5.31/5.53 => ( ( power_power_complex @ zero_zero_complex @ N )
% 5.31/5.53 = zero_zero_complex ) ) ) ).
% 5.31/5.53
% 5.31/5.53 % power_0_left
% 5.31/5.53 thf(fact_2783_power__increasing,axiom,
% 5.31/5.54 ! [N: nat,N6: nat,A: code_integer] :
% 5.31/5.54 ( ( ord_less_eq_nat @ N @ N6 )
% 5.31/5.54 => ( ( ord_le3102999989581377725nteger @ one_one_Code_integer @ A )
% 5.31/5.54 => ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ A @ N ) @ ( power_8256067586552552935nteger @ A @ N6 ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % power_increasing
% 5.31/5.54 thf(fact_2784_power__increasing,axiom,
% 5.31/5.54 ! [N: nat,N6: nat,A: real] :
% 5.31/5.54 ( ( ord_less_eq_nat @ N @ N6 )
% 5.31/5.54 => ( ( ord_less_eq_real @ one_one_real @ A )
% 5.31/5.54 => ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ A @ N6 ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % power_increasing
% 5.31/5.54 thf(fact_2785_power__increasing,axiom,
% 5.31/5.54 ! [N: nat,N6: nat,A: rat] :
% 5.31/5.54 ( ( ord_less_eq_nat @ N @ N6 )
% 5.31/5.54 => ( ( ord_less_eq_rat @ one_one_rat @ A )
% 5.31/5.54 => ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ A @ N6 ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % power_increasing
% 5.31/5.54 thf(fact_2786_power__increasing,axiom,
% 5.31/5.54 ! [N: nat,N6: nat,A: nat] :
% 5.31/5.54 ( ( ord_less_eq_nat @ N @ N6 )
% 5.31/5.54 => ( ( ord_less_eq_nat @ one_one_nat @ A )
% 5.31/5.54 => ( ord_less_eq_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ A @ N6 ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % power_increasing
% 5.31/5.54 thf(fact_2787_power__increasing,axiom,
% 5.31/5.54 ! [N: nat,N6: nat,A: int] :
% 5.31/5.54 ( ( ord_less_eq_nat @ N @ N6 )
% 5.31/5.54 => ( ( ord_less_eq_int @ one_one_int @ A )
% 5.31/5.54 => ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ A @ N6 ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % power_increasing
% 5.31/5.54 thf(fact_2788_zero__power,axiom,
% 5.31/5.54 ! [N: nat] :
% 5.31/5.54 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.54 => ( ( power_power_rat @ zero_zero_rat @ N )
% 5.31/5.54 = zero_zero_rat ) ) ).
% 5.31/5.54
% 5.31/5.54 % zero_power
% 5.31/5.54 thf(fact_2789_zero__power,axiom,
% 5.31/5.54 ! [N: nat] :
% 5.31/5.54 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.54 => ( ( power_power_nat @ zero_zero_nat @ N )
% 5.31/5.54 = zero_zero_nat ) ) ).
% 5.31/5.54
% 5.31/5.54 % zero_power
% 5.31/5.54 thf(fact_2790_zero__power,axiom,
% 5.31/5.54 ! [N: nat] :
% 5.31/5.54 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.54 => ( ( power_power_real @ zero_zero_real @ N )
% 5.31/5.54 = zero_zero_real ) ) ).
% 5.31/5.54
% 5.31/5.54 % zero_power
% 5.31/5.54 thf(fact_2791_zero__power,axiom,
% 5.31/5.54 ! [N: nat] :
% 5.31/5.54 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.54 => ( ( power_power_int @ zero_zero_int @ N )
% 5.31/5.54 = zero_zero_int ) ) ).
% 5.31/5.54
% 5.31/5.54 % zero_power
% 5.31/5.54 thf(fact_2792_zero__power,axiom,
% 5.31/5.54 ! [N: nat] :
% 5.31/5.54 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.54 => ( ( power_power_complex @ zero_zero_complex @ N )
% 5.31/5.54 = zero_zero_complex ) ) ).
% 5.31/5.54
% 5.31/5.54 % zero_power
% 5.31/5.54 thf(fact_2793_lenlex__length,axiom,
% 5.31/5.54 ! [Ms: list_VEBT_VEBT,Ns: list_VEBT_VEBT,R3: set_Pr6192946355708809607T_VEBT] :
% 5.31/5.54 ( ( member4439316823752958928T_VEBT @ ( produc3897820843166775703T_VEBT @ Ms @ Ns ) @ ( lenlex_VEBT_VEBT @ R3 ) )
% 5.31/5.54 => ( ord_less_eq_nat @ ( size_s6755466524823107622T_VEBT @ Ms ) @ ( size_s6755466524823107622T_VEBT @ Ns ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % lenlex_length
% 5.31/5.54 thf(fact_2794_lenlex__length,axiom,
% 5.31/5.54 ! [Ms: list_o,Ns: list_o,R3: set_Product_prod_o_o] :
% 5.31/5.54 ( ( member4159035015898711888list_o @ ( produc8435520187683070743list_o @ Ms @ Ns ) @ ( lenlex_o @ R3 ) )
% 5.31/5.54 => ( ord_less_eq_nat @ ( size_size_list_o @ Ms ) @ ( size_size_list_o @ Ns ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % lenlex_length
% 5.31/5.54 thf(fact_2795_lenlex__length,axiom,
% 5.31/5.54 ! [Ms: list_nat,Ns: list_nat,R3: set_Pr1261947904930325089at_nat] :
% 5.31/5.54 ( ( member7340969449405702474st_nat @ ( produc2694037385005941721st_nat @ Ms @ Ns ) @ ( lenlex_nat @ R3 ) )
% 5.31/5.54 => ( ord_less_eq_nat @ ( size_size_list_nat @ Ms ) @ ( size_size_list_nat @ Ns ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % lenlex_length
% 5.31/5.54 thf(fact_2796_lenlex__length,axiom,
% 5.31/5.54 ! [Ms: list_int,Ns: list_int,R3: set_Pr958786334691620121nt_int] :
% 5.31/5.54 ( ( member6698963635872716290st_int @ ( produc364263696895485585st_int @ Ms @ Ns ) @ ( lenlex_int @ R3 ) )
% 5.31/5.54 => ( ord_less_eq_nat @ ( size_size_list_int @ Ms ) @ ( size_size_list_int @ Ns ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % lenlex_length
% 5.31/5.54 thf(fact_2797_power__gt__expt,axiom,
% 5.31/5.54 ! [N: nat,K2: nat] :
% 5.31/5.54 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.31/5.54 => ( ord_less_nat @ K2 @ ( power_power_nat @ N @ K2 ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % power_gt_expt
% 5.31/5.54 thf(fact_2798_nat__one__le__power,axiom,
% 5.31/5.54 ! [I2: nat,N: nat] :
% 5.31/5.54 ( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ I2 )
% 5.31/5.54 => ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( power_power_nat @ I2 @ N ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % nat_one_le_power
% 5.31/5.54 thf(fact_2799_enumerate__step,axiom,
% 5.31/5.54 ! [S3: set_nat,N: nat] :
% 5.31/5.54 ( ~ ( finite_finite_nat @ S3 )
% 5.31/5.54 => ( ord_less_nat @ ( infini8530281810654367211te_nat @ S3 @ N ) @ ( infini8530281810654367211te_nat @ S3 @ ( suc @ N ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % enumerate_step
% 5.31/5.54 thf(fact_2800_card__gt__0__iff,axiom,
% 5.31/5.54 ! [A4: set_list_nat] :
% 5.31/5.54 ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_list_nat @ A4 ) )
% 5.31/5.54 = ( ( A4 != bot_bot_set_list_nat )
% 5.31/5.54 & ( finite8100373058378681591st_nat @ A4 ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % card_gt_0_iff
% 5.31/5.54 thf(fact_2801_card__gt__0__iff,axiom,
% 5.31/5.54 ! [A4: set_set_nat] :
% 5.31/5.54 ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_set_nat @ A4 ) )
% 5.31/5.54 = ( ( A4 != bot_bot_set_set_nat )
% 5.31/5.54 & ( finite1152437895449049373et_nat @ A4 ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % card_gt_0_iff
% 5.31/5.54 thf(fact_2802_card__gt__0__iff,axiom,
% 5.31/5.54 ! [A4: set_complex] :
% 5.31/5.54 ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_complex @ A4 ) )
% 5.31/5.54 = ( ( A4 != bot_bot_set_complex )
% 5.31/5.54 & ( finite3207457112153483333omplex @ A4 ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % card_gt_0_iff
% 5.31/5.54 thf(fact_2803_card__gt__0__iff,axiom,
% 5.31/5.54 ! [A4: set_nat] :
% 5.31/5.54 ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_nat @ A4 ) )
% 5.31/5.54 = ( ( A4 != bot_bot_set_nat )
% 5.31/5.54 & ( finite_finite_nat @ A4 ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % card_gt_0_iff
% 5.31/5.54 thf(fact_2804_card__gt__0__iff,axiom,
% 5.31/5.54 ! [A4: set_int] :
% 5.31/5.54 ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_int @ A4 ) )
% 5.31/5.54 = ( ( A4 != bot_bot_set_int )
% 5.31/5.54 & ( finite_finite_int @ A4 ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % card_gt_0_iff
% 5.31/5.54 thf(fact_2805_card__gt__0__iff,axiom,
% 5.31/5.54 ! [A4: set_real] :
% 5.31/5.54 ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_real @ A4 ) )
% 5.31/5.54 = ( ( A4 != bot_bot_set_real )
% 5.31/5.54 & ( finite_finite_real @ A4 ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % card_gt_0_iff
% 5.31/5.54 thf(fact_2806_card__1__singleton__iff,axiom,
% 5.31/5.54 ! [A4: set_complex] :
% 5.31/5.54 ( ( ( finite_card_complex @ A4 )
% 5.31/5.54 = ( suc @ zero_zero_nat ) )
% 5.31/5.54 = ( ? [X4: complex] :
% 5.31/5.54 ( A4
% 5.31/5.54 = ( insert_complex @ X4 @ bot_bot_set_complex ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % card_1_singleton_iff
% 5.31/5.54 thf(fact_2807_card__1__singleton__iff,axiom,
% 5.31/5.54 ! [A4: set_list_nat] :
% 5.31/5.54 ( ( ( finite_card_list_nat @ A4 )
% 5.31/5.54 = ( suc @ zero_zero_nat ) )
% 5.31/5.54 = ( ? [X4: list_nat] :
% 5.31/5.54 ( A4
% 5.31/5.54 = ( insert_list_nat @ X4 @ bot_bot_set_list_nat ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % card_1_singleton_iff
% 5.31/5.54 thf(fact_2808_card__1__singleton__iff,axiom,
% 5.31/5.54 ! [A4: set_set_nat] :
% 5.31/5.54 ( ( ( finite_card_set_nat @ A4 )
% 5.31/5.54 = ( suc @ zero_zero_nat ) )
% 5.31/5.54 = ( ? [X4: set_nat] :
% 5.31/5.54 ( A4
% 5.31/5.54 = ( insert_set_nat @ X4 @ bot_bot_set_set_nat ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % card_1_singleton_iff
% 5.31/5.54 thf(fact_2809_card__1__singleton__iff,axiom,
% 5.31/5.54 ! [A4: set_nat] :
% 5.31/5.54 ( ( ( finite_card_nat @ A4 )
% 5.31/5.54 = ( suc @ zero_zero_nat ) )
% 5.31/5.54 = ( ? [X4: nat] :
% 5.31/5.54 ( A4
% 5.31/5.54 = ( insert_nat @ X4 @ bot_bot_set_nat ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % card_1_singleton_iff
% 5.31/5.54 thf(fact_2810_card__1__singleton__iff,axiom,
% 5.31/5.54 ! [A4: set_int] :
% 5.31/5.54 ( ( ( finite_card_int @ A4 )
% 5.31/5.54 = ( suc @ zero_zero_nat ) )
% 5.31/5.54 = ( ? [X4: int] :
% 5.31/5.54 ( A4
% 5.31/5.54 = ( insert_int @ X4 @ bot_bot_set_int ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % card_1_singleton_iff
% 5.31/5.54 thf(fact_2811_card__1__singleton__iff,axiom,
% 5.31/5.54 ! [A4: set_real] :
% 5.31/5.54 ( ( ( finite_card_real @ A4 )
% 5.31/5.54 = ( suc @ zero_zero_nat ) )
% 5.31/5.54 = ( ? [X4: real] :
% 5.31/5.54 ( A4
% 5.31/5.54 = ( insert_real @ X4 @ bot_bot_set_real ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % card_1_singleton_iff
% 5.31/5.54 thf(fact_2812_card__eq__SucD,axiom,
% 5.31/5.54 ! [A4: set_complex,K2: nat] :
% 5.31/5.54 ( ( ( finite_card_complex @ A4 )
% 5.31/5.54 = ( suc @ K2 ) )
% 5.31/5.54 => ? [B3: complex,B8: set_complex] :
% 5.31/5.54 ( ( A4
% 5.31/5.54 = ( insert_complex @ B3 @ B8 ) )
% 5.31/5.54 & ~ ( member_complex @ B3 @ B8 )
% 5.31/5.54 & ( ( finite_card_complex @ B8 )
% 5.31/5.54 = K2 )
% 5.31/5.54 & ( ( K2 = zero_zero_nat )
% 5.31/5.54 => ( B8 = bot_bot_set_complex ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % card_eq_SucD
% 5.31/5.54 thf(fact_2813_card__eq__SucD,axiom,
% 5.31/5.54 ! [A4: set_list_nat,K2: nat] :
% 5.31/5.54 ( ( ( finite_card_list_nat @ A4 )
% 5.31/5.54 = ( suc @ K2 ) )
% 5.31/5.54 => ? [B3: list_nat,B8: set_list_nat] :
% 5.31/5.54 ( ( A4
% 5.31/5.54 = ( insert_list_nat @ B3 @ B8 ) )
% 5.31/5.54 & ~ ( member_list_nat @ B3 @ B8 )
% 5.31/5.54 & ( ( finite_card_list_nat @ B8 )
% 5.31/5.54 = K2 )
% 5.31/5.54 & ( ( K2 = zero_zero_nat )
% 5.31/5.54 => ( B8 = bot_bot_set_list_nat ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % card_eq_SucD
% 5.31/5.54 thf(fact_2814_card__eq__SucD,axiom,
% 5.31/5.54 ! [A4: set_set_nat,K2: nat] :
% 5.31/5.54 ( ( ( finite_card_set_nat @ A4 )
% 5.31/5.54 = ( suc @ K2 ) )
% 5.31/5.54 => ? [B3: set_nat,B8: set_set_nat] :
% 5.31/5.54 ( ( A4
% 5.31/5.54 = ( insert_set_nat @ B3 @ B8 ) )
% 5.31/5.54 & ~ ( member_set_nat @ B3 @ B8 )
% 5.31/5.54 & ( ( finite_card_set_nat @ B8 )
% 5.31/5.54 = K2 )
% 5.31/5.54 & ( ( K2 = zero_zero_nat )
% 5.31/5.54 => ( B8 = bot_bot_set_set_nat ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % card_eq_SucD
% 5.31/5.54 thf(fact_2815_card__eq__SucD,axiom,
% 5.31/5.54 ! [A4: set_nat,K2: nat] :
% 5.31/5.54 ( ( ( finite_card_nat @ A4 )
% 5.31/5.54 = ( suc @ K2 ) )
% 5.31/5.54 => ? [B3: nat,B8: set_nat] :
% 5.31/5.54 ( ( A4
% 5.31/5.54 = ( insert_nat @ B3 @ B8 ) )
% 5.31/5.54 & ~ ( member_nat @ B3 @ B8 )
% 5.31/5.54 & ( ( finite_card_nat @ B8 )
% 5.31/5.54 = K2 )
% 5.31/5.54 & ( ( K2 = zero_zero_nat )
% 5.31/5.54 => ( B8 = bot_bot_set_nat ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % card_eq_SucD
% 5.31/5.54 thf(fact_2816_card__eq__SucD,axiom,
% 5.31/5.54 ! [A4: set_int,K2: nat] :
% 5.31/5.54 ( ( ( finite_card_int @ A4 )
% 5.31/5.54 = ( suc @ K2 ) )
% 5.31/5.54 => ? [B3: int,B8: set_int] :
% 5.31/5.54 ( ( A4
% 5.31/5.54 = ( insert_int @ B3 @ B8 ) )
% 5.31/5.54 & ~ ( member_int @ B3 @ B8 )
% 5.31/5.54 & ( ( finite_card_int @ B8 )
% 5.31/5.54 = K2 )
% 5.31/5.54 & ( ( K2 = zero_zero_nat )
% 5.31/5.54 => ( B8 = bot_bot_set_int ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % card_eq_SucD
% 5.31/5.54 thf(fact_2817_card__eq__SucD,axiom,
% 5.31/5.54 ! [A4: set_real,K2: nat] :
% 5.31/5.54 ( ( ( finite_card_real @ A4 )
% 5.31/5.54 = ( suc @ K2 ) )
% 5.31/5.54 => ? [B3: real,B8: set_real] :
% 5.31/5.54 ( ( A4
% 5.31/5.54 = ( insert_real @ B3 @ B8 ) )
% 5.31/5.54 & ~ ( member_real @ B3 @ B8 )
% 5.31/5.54 & ( ( finite_card_real @ B8 )
% 5.31/5.54 = K2 )
% 5.31/5.54 & ( ( K2 = zero_zero_nat )
% 5.31/5.54 => ( B8 = bot_bot_set_real ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % card_eq_SucD
% 5.31/5.54 thf(fact_2818_card__Suc__eq,axiom,
% 5.31/5.54 ! [A4: set_complex,K2: nat] :
% 5.31/5.54 ( ( ( finite_card_complex @ A4 )
% 5.31/5.54 = ( suc @ K2 ) )
% 5.31/5.54 = ( ? [B4: complex,B7: set_complex] :
% 5.31/5.54 ( ( A4
% 5.31/5.54 = ( insert_complex @ B4 @ B7 ) )
% 5.31/5.54 & ~ ( member_complex @ B4 @ B7 )
% 5.31/5.54 & ( ( finite_card_complex @ B7 )
% 5.31/5.54 = K2 )
% 5.31/5.54 & ( ( K2 = zero_zero_nat )
% 5.31/5.54 => ( B7 = bot_bot_set_complex ) ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % card_Suc_eq
% 5.31/5.54 thf(fact_2819_card__Suc__eq,axiom,
% 5.31/5.54 ! [A4: set_list_nat,K2: nat] :
% 5.31/5.54 ( ( ( finite_card_list_nat @ A4 )
% 5.31/5.54 = ( suc @ K2 ) )
% 5.31/5.54 = ( ? [B4: list_nat,B7: set_list_nat] :
% 5.31/5.54 ( ( A4
% 5.31/5.54 = ( insert_list_nat @ B4 @ B7 ) )
% 5.31/5.54 & ~ ( member_list_nat @ B4 @ B7 )
% 5.31/5.54 & ( ( finite_card_list_nat @ B7 )
% 5.31/5.54 = K2 )
% 5.31/5.54 & ( ( K2 = zero_zero_nat )
% 5.31/5.54 => ( B7 = bot_bot_set_list_nat ) ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % card_Suc_eq
% 5.31/5.54 thf(fact_2820_card__Suc__eq,axiom,
% 5.31/5.54 ! [A4: set_set_nat,K2: nat] :
% 5.31/5.54 ( ( ( finite_card_set_nat @ A4 )
% 5.31/5.54 = ( suc @ K2 ) )
% 5.31/5.54 = ( ? [B4: set_nat,B7: set_set_nat] :
% 5.31/5.54 ( ( A4
% 5.31/5.54 = ( insert_set_nat @ B4 @ B7 ) )
% 5.31/5.54 & ~ ( member_set_nat @ B4 @ B7 )
% 5.31/5.54 & ( ( finite_card_set_nat @ B7 )
% 5.31/5.54 = K2 )
% 5.31/5.54 & ( ( K2 = zero_zero_nat )
% 5.31/5.54 => ( B7 = bot_bot_set_set_nat ) ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % card_Suc_eq
% 5.31/5.54 thf(fact_2821_card__Suc__eq,axiom,
% 5.31/5.54 ! [A4: set_nat,K2: nat] :
% 5.31/5.54 ( ( ( finite_card_nat @ A4 )
% 5.31/5.54 = ( suc @ K2 ) )
% 5.31/5.54 = ( ? [B4: nat,B7: set_nat] :
% 5.31/5.54 ( ( A4
% 5.31/5.54 = ( insert_nat @ B4 @ B7 ) )
% 5.31/5.54 & ~ ( member_nat @ B4 @ B7 )
% 5.31/5.54 & ( ( finite_card_nat @ B7 )
% 5.31/5.54 = K2 )
% 5.31/5.54 & ( ( K2 = zero_zero_nat )
% 5.31/5.54 => ( B7 = bot_bot_set_nat ) ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % card_Suc_eq
% 5.31/5.54 thf(fact_2822_card__Suc__eq,axiom,
% 5.31/5.54 ! [A4: set_int,K2: nat] :
% 5.31/5.54 ( ( ( finite_card_int @ A4 )
% 5.31/5.54 = ( suc @ K2 ) )
% 5.31/5.54 = ( ? [B4: int,B7: set_int] :
% 5.31/5.54 ( ( A4
% 5.31/5.54 = ( insert_int @ B4 @ B7 ) )
% 5.31/5.54 & ~ ( member_int @ B4 @ B7 )
% 5.31/5.54 & ( ( finite_card_int @ B7 )
% 5.31/5.54 = K2 )
% 5.31/5.54 & ( ( K2 = zero_zero_nat )
% 5.31/5.54 => ( B7 = bot_bot_set_int ) ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % card_Suc_eq
% 5.31/5.54 thf(fact_2823_card__Suc__eq,axiom,
% 5.31/5.54 ! [A4: set_real,K2: nat] :
% 5.31/5.54 ( ( ( finite_card_real @ A4 )
% 5.31/5.54 = ( suc @ K2 ) )
% 5.31/5.54 = ( ? [B4: real,B7: set_real] :
% 5.31/5.54 ( ( A4
% 5.31/5.54 = ( insert_real @ B4 @ B7 ) )
% 5.31/5.54 & ~ ( member_real @ B4 @ B7 )
% 5.31/5.54 & ( ( finite_card_real @ B7 )
% 5.31/5.54 = K2 )
% 5.31/5.54 & ( ( K2 = zero_zero_nat )
% 5.31/5.54 => ( B7 = bot_bot_set_real ) ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % card_Suc_eq
% 5.31/5.54 thf(fact_2824_card__le__Suc0__iff__eq,axiom,
% 5.31/5.54 ! [A4: set_list_nat] :
% 5.31/5.54 ( ( finite8100373058378681591st_nat @ A4 )
% 5.31/5.54 => ( ( ord_less_eq_nat @ ( finite_card_list_nat @ A4 ) @ ( suc @ zero_zero_nat ) )
% 5.31/5.54 = ( ! [X4: list_nat] :
% 5.31/5.54 ( ( member_list_nat @ X4 @ A4 )
% 5.31/5.54 => ! [Y4: list_nat] :
% 5.31/5.54 ( ( member_list_nat @ Y4 @ A4 )
% 5.31/5.54 => ( X4 = Y4 ) ) ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % card_le_Suc0_iff_eq
% 5.31/5.54 thf(fact_2825_card__le__Suc0__iff__eq,axiom,
% 5.31/5.54 ! [A4: set_set_nat] :
% 5.31/5.54 ( ( finite1152437895449049373et_nat @ A4 )
% 5.31/5.54 => ( ( ord_less_eq_nat @ ( finite_card_set_nat @ A4 ) @ ( suc @ zero_zero_nat ) )
% 5.31/5.54 = ( ! [X4: set_nat] :
% 5.31/5.54 ( ( member_set_nat @ X4 @ A4 )
% 5.31/5.54 => ! [Y4: set_nat] :
% 5.31/5.54 ( ( member_set_nat @ Y4 @ A4 )
% 5.31/5.54 => ( X4 = Y4 ) ) ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % card_le_Suc0_iff_eq
% 5.31/5.54 thf(fact_2826_card__le__Suc0__iff__eq,axiom,
% 5.31/5.54 ! [A4: set_nat] :
% 5.31/5.54 ( ( finite_finite_nat @ A4 )
% 5.31/5.54 => ( ( ord_less_eq_nat @ ( finite_card_nat @ A4 ) @ ( suc @ zero_zero_nat ) )
% 5.31/5.54 = ( ! [X4: nat] :
% 5.31/5.54 ( ( member_nat @ X4 @ A4 )
% 5.31/5.54 => ! [Y4: nat] :
% 5.31/5.54 ( ( member_nat @ Y4 @ A4 )
% 5.31/5.54 => ( X4 = Y4 ) ) ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % card_le_Suc0_iff_eq
% 5.31/5.54 thf(fact_2827_card__le__Suc0__iff__eq,axiom,
% 5.31/5.54 ! [A4: set_int] :
% 5.31/5.54 ( ( finite_finite_int @ A4 )
% 5.31/5.54 => ( ( ord_less_eq_nat @ ( finite_card_int @ A4 ) @ ( suc @ zero_zero_nat ) )
% 5.31/5.54 = ( ! [X4: int] :
% 5.31/5.54 ( ( member_int @ X4 @ A4 )
% 5.31/5.54 => ! [Y4: int] :
% 5.31/5.54 ( ( member_int @ Y4 @ A4 )
% 5.31/5.54 => ( X4 = Y4 ) ) ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % card_le_Suc0_iff_eq
% 5.31/5.54 thf(fact_2828_card__le__Suc0__iff__eq,axiom,
% 5.31/5.54 ! [A4: set_complex] :
% 5.31/5.54 ( ( finite3207457112153483333omplex @ A4 )
% 5.31/5.54 => ( ( ord_less_eq_nat @ ( finite_card_complex @ A4 ) @ ( suc @ zero_zero_nat ) )
% 5.31/5.54 = ( ! [X4: complex] :
% 5.31/5.54 ( ( member_complex @ X4 @ A4 )
% 5.31/5.54 => ! [Y4: complex] :
% 5.31/5.54 ( ( member_complex @ Y4 @ A4 )
% 5.31/5.54 => ( X4 = Y4 ) ) ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % card_le_Suc0_iff_eq
% 5.31/5.54 thf(fact_2829_card__le__Suc__iff,axiom,
% 5.31/5.54 ! [N: nat,A4: set_real] :
% 5.31/5.54 ( ( ord_less_eq_nat @ ( suc @ N ) @ ( finite_card_real @ A4 ) )
% 5.31/5.54 = ( ? [A5: real,B7: set_real] :
% 5.31/5.54 ( ( A4
% 5.31/5.54 = ( insert_real @ A5 @ B7 ) )
% 5.31/5.54 & ~ ( member_real @ A5 @ B7 )
% 5.31/5.54 & ( ord_less_eq_nat @ N @ ( finite_card_real @ B7 ) )
% 5.31/5.54 & ( finite_finite_real @ B7 ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % card_le_Suc_iff
% 5.31/5.54 thf(fact_2830_card__le__Suc__iff,axiom,
% 5.31/5.54 ! [N: nat,A4: set_list_nat] :
% 5.31/5.54 ( ( ord_less_eq_nat @ ( suc @ N ) @ ( finite_card_list_nat @ A4 ) )
% 5.31/5.54 = ( ? [A5: list_nat,B7: set_list_nat] :
% 5.31/5.54 ( ( A4
% 5.31/5.54 = ( insert_list_nat @ A5 @ B7 ) )
% 5.31/5.54 & ~ ( member_list_nat @ A5 @ B7 )
% 5.31/5.54 & ( ord_less_eq_nat @ N @ ( finite_card_list_nat @ B7 ) )
% 5.31/5.54 & ( finite8100373058378681591st_nat @ B7 ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % card_le_Suc_iff
% 5.31/5.54 thf(fact_2831_card__le__Suc__iff,axiom,
% 5.31/5.54 ! [N: nat,A4: set_set_nat] :
% 5.31/5.54 ( ( ord_less_eq_nat @ ( suc @ N ) @ ( finite_card_set_nat @ A4 ) )
% 5.31/5.54 = ( ? [A5: set_nat,B7: set_set_nat] :
% 5.31/5.54 ( ( A4
% 5.31/5.54 = ( insert_set_nat @ A5 @ B7 ) )
% 5.31/5.54 & ~ ( member_set_nat @ A5 @ B7 )
% 5.31/5.54 & ( ord_less_eq_nat @ N @ ( finite_card_set_nat @ B7 ) )
% 5.31/5.54 & ( finite1152437895449049373et_nat @ B7 ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % card_le_Suc_iff
% 5.31/5.54 thf(fact_2832_card__le__Suc__iff,axiom,
% 5.31/5.54 ! [N: nat,A4: set_nat] :
% 5.31/5.54 ( ( ord_less_eq_nat @ ( suc @ N ) @ ( finite_card_nat @ A4 ) )
% 5.31/5.54 = ( ? [A5: nat,B7: set_nat] :
% 5.31/5.54 ( ( A4
% 5.31/5.54 = ( insert_nat @ A5 @ B7 ) )
% 5.31/5.54 & ~ ( member_nat @ A5 @ B7 )
% 5.31/5.54 & ( ord_less_eq_nat @ N @ ( finite_card_nat @ B7 ) )
% 5.31/5.54 & ( finite_finite_nat @ B7 ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % card_le_Suc_iff
% 5.31/5.54 thf(fact_2833_card__le__Suc__iff,axiom,
% 5.31/5.54 ! [N: nat,A4: set_int] :
% 5.31/5.54 ( ( ord_less_eq_nat @ ( suc @ N ) @ ( finite_card_int @ A4 ) )
% 5.31/5.54 = ( ? [A5: int,B7: set_int] :
% 5.31/5.54 ( ( A4
% 5.31/5.54 = ( insert_int @ A5 @ B7 ) )
% 5.31/5.54 & ~ ( member_int @ A5 @ B7 )
% 5.31/5.54 & ( ord_less_eq_nat @ N @ ( finite_card_int @ B7 ) )
% 5.31/5.54 & ( finite_finite_int @ B7 ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % card_le_Suc_iff
% 5.31/5.54 thf(fact_2834_card__le__Suc__iff,axiom,
% 5.31/5.54 ! [N: nat,A4: set_complex] :
% 5.31/5.54 ( ( ord_less_eq_nat @ ( suc @ N ) @ ( finite_card_complex @ A4 ) )
% 5.31/5.54 = ( ? [A5: complex,B7: set_complex] :
% 5.31/5.54 ( ( A4
% 5.31/5.54 = ( insert_complex @ A5 @ B7 ) )
% 5.31/5.54 & ~ ( member_complex @ A5 @ B7 )
% 5.31/5.54 & ( ord_less_eq_nat @ N @ ( finite_card_complex @ B7 ) )
% 5.31/5.54 & ( finite3207457112153483333omplex @ B7 ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % card_le_Suc_iff
% 5.31/5.54 thf(fact_2835_power__Suc__less,axiom,
% 5.31/5.54 ! [A: code_integer,N: nat] :
% 5.31/5.54 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 5.31/5.54 => ( ( ord_le6747313008572928689nteger @ A @ one_one_Code_integer )
% 5.31/5.54 => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ A @ ( power_8256067586552552935nteger @ A @ N ) ) @ ( power_8256067586552552935nteger @ A @ N ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % power_Suc_less
% 5.31/5.54 thf(fact_2836_power__Suc__less,axiom,
% 5.31/5.54 ! [A: real,N: nat] :
% 5.31/5.54 ( ( ord_less_real @ zero_zero_real @ A )
% 5.31/5.54 => ( ( ord_less_real @ A @ one_one_real )
% 5.31/5.54 => ( ord_less_real @ ( times_times_real @ A @ ( power_power_real @ A @ N ) ) @ ( power_power_real @ A @ N ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % power_Suc_less
% 5.31/5.54 thf(fact_2837_power__Suc__less,axiom,
% 5.31/5.54 ! [A: rat,N: nat] :
% 5.31/5.54 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.31/5.54 => ( ( ord_less_rat @ A @ one_one_rat )
% 5.31/5.54 => ( ord_less_rat @ ( times_times_rat @ A @ ( power_power_rat @ A @ N ) ) @ ( power_power_rat @ A @ N ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % power_Suc_less
% 5.31/5.54 thf(fact_2838_power__Suc__less,axiom,
% 5.31/5.54 ! [A: nat,N: nat] :
% 5.31/5.54 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.31/5.54 => ( ( ord_less_nat @ A @ one_one_nat )
% 5.31/5.54 => ( ord_less_nat @ ( times_times_nat @ A @ ( power_power_nat @ A @ N ) ) @ ( power_power_nat @ A @ N ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % power_Suc_less
% 5.31/5.54 thf(fact_2839_power__Suc__less,axiom,
% 5.31/5.54 ! [A: int,N: nat] :
% 5.31/5.54 ( ( ord_less_int @ zero_zero_int @ A )
% 5.31/5.54 => ( ( ord_less_int @ A @ one_one_int )
% 5.31/5.54 => ( ord_less_int @ ( times_times_int @ A @ ( power_power_int @ A @ N ) ) @ ( power_power_int @ A @ N ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % power_Suc_less
% 5.31/5.54 thf(fact_2840_power__Suc__le__self,axiom,
% 5.31/5.54 ! [A: code_integer,N: nat] :
% 5.31/5.54 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 5.31/5.54 => ( ( ord_le3102999989581377725nteger @ A @ one_one_Code_integer )
% 5.31/5.54 => ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ A @ ( suc @ N ) ) @ A ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % power_Suc_le_self
% 5.31/5.54 thf(fact_2841_power__Suc__le__self,axiom,
% 5.31/5.54 ! [A: real,N: nat] :
% 5.31/5.54 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.31/5.54 => ( ( ord_less_eq_real @ A @ one_one_real )
% 5.31/5.54 => ( ord_less_eq_real @ ( power_power_real @ A @ ( suc @ N ) ) @ A ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % power_Suc_le_self
% 5.31/5.54 thf(fact_2842_power__Suc__le__self,axiom,
% 5.31/5.54 ! [A: rat,N: nat] :
% 5.31/5.54 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.31/5.54 => ( ( ord_less_eq_rat @ A @ one_one_rat )
% 5.31/5.54 => ( ord_less_eq_rat @ ( power_power_rat @ A @ ( suc @ N ) ) @ A ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % power_Suc_le_self
% 5.31/5.54 thf(fact_2843_power__Suc__le__self,axiom,
% 5.31/5.54 ! [A: nat,N: nat] :
% 5.31/5.54 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.31/5.54 => ( ( ord_less_eq_nat @ A @ one_one_nat )
% 5.31/5.54 => ( ord_less_eq_nat @ ( power_power_nat @ A @ ( suc @ N ) ) @ A ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % power_Suc_le_self
% 5.31/5.54 thf(fact_2844_power__Suc__le__self,axiom,
% 5.31/5.54 ! [A: int,N: nat] :
% 5.31/5.54 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.31/5.54 => ( ( ord_less_eq_int @ A @ one_one_int )
% 5.31/5.54 => ( ord_less_eq_int @ ( power_power_int @ A @ ( suc @ N ) ) @ A ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % power_Suc_le_self
% 5.31/5.54 thf(fact_2845_power__Suc__less__one,axiom,
% 5.31/5.54 ! [A: code_integer,N: nat] :
% 5.31/5.54 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 5.31/5.54 => ( ( ord_le6747313008572928689nteger @ A @ one_one_Code_integer )
% 5.31/5.54 => ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ A @ ( suc @ N ) ) @ one_one_Code_integer ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % power_Suc_less_one
% 5.31/5.54 thf(fact_2846_power__Suc__less__one,axiom,
% 5.31/5.54 ! [A: real,N: nat] :
% 5.31/5.54 ( ( ord_less_real @ zero_zero_real @ A )
% 5.31/5.54 => ( ( ord_less_real @ A @ one_one_real )
% 5.31/5.54 => ( ord_less_real @ ( power_power_real @ A @ ( suc @ N ) ) @ one_one_real ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % power_Suc_less_one
% 5.31/5.54 thf(fact_2847_power__Suc__less__one,axiom,
% 5.31/5.54 ! [A: rat,N: nat] :
% 5.31/5.54 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.31/5.54 => ( ( ord_less_rat @ A @ one_one_rat )
% 5.31/5.54 => ( ord_less_rat @ ( power_power_rat @ A @ ( suc @ N ) ) @ one_one_rat ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % power_Suc_less_one
% 5.31/5.54 thf(fact_2848_power__Suc__less__one,axiom,
% 5.31/5.54 ! [A: nat,N: nat] :
% 5.31/5.54 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.31/5.54 => ( ( ord_less_nat @ A @ one_one_nat )
% 5.31/5.54 => ( ord_less_nat @ ( power_power_nat @ A @ ( suc @ N ) ) @ one_one_nat ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % power_Suc_less_one
% 5.31/5.54 thf(fact_2849_power__Suc__less__one,axiom,
% 5.31/5.54 ! [A: int,N: nat] :
% 5.31/5.54 ( ( ord_less_int @ zero_zero_int @ A )
% 5.31/5.54 => ( ( ord_less_int @ A @ one_one_int )
% 5.31/5.54 => ( ord_less_int @ ( power_power_int @ A @ ( suc @ N ) ) @ one_one_int ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % power_Suc_less_one
% 5.31/5.54 thf(fact_2850_card__Diff1__le,axiom,
% 5.31/5.54 ! [A4: set_complex,X: complex] : ( ord_less_eq_nat @ ( finite_card_complex @ ( minus_811609699411566653omplex @ A4 @ ( insert_complex @ X @ bot_bot_set_complex ) ) ) @ ( finite_card_complex @ A4 ) ) ).
% 5.31/5.54
% 5.31/5.54 % card_Diff1_le
% 5.31/5.54 thf(fact_2851_card__Diff1__le,axiom,
% 5.31/5.54 ! [A4: set_list_nat,X: list_nat] : ( ord_less_eq_nat @ ( finite_card_list_nat @ ( minus_7954133019191499631st_nat @ A4 @ ( insert_list_nat @ X @ bot_bot_set_list_nat ) ) ) @ ( finite_card_list_nat @ A4 ) ) ).
% 5.31/5.54
% 5.31/5.54 % card_Diff1_le
% 5.31/5.54 thf(fact_2852_card__Diff1__le,axiom,
% 5.31/5.54 ! [A4: set_set_nat,X: set_nat] : ( ord_less_eq_nat @ ( finite_card_set_nat @ ( minus_2163939370556025621et_nat @ A4 @ ( insert_set_nat @ X @ bot_bot_set_set_nat ) ) ) @ ( finite_card_set_nat @ A4 ) ) ).
% 5.31/5.54
% 5.31/5.54 % card_Diff1_le
% 5.31/5.54 thf(fact_2853_card__Diff1__le,axiom,
% 5.31/5.54 ! [A4: set_int,X: int] : ( ord_less_eq_nat @ ( finite_card_int @ ( minus_minus_set_int @ A4 @ ( insert_int @ X @ bot_bot_set_int ) ) ) @ ( finite_card_int @ A4 ) ) ).
% 5.31/5.54
% 5.31/5.54 % card_Diff1_le
% 5.31/5.54 thf(fact_2854_card__Diff1__le,axiom,
% 5.31/5.54 ! [A4: set_real,X: real] : ( ord_less_eq_nat @ ( finite_card_real @ ( minus_minus_set_real @ A4 @ ( insert_real @ X @ bot_bot_set_real ) ) ) @ ( finite_card_real @ A4 ) ) ).
% 5.31/5.54
% 5.31/5.54 % card_Diff1_le
% 5.31/5.54 thf(fact_2855_card__Diff1__le,axiom,
% 5.31/5.54 ! [A4: set_Pr1261947904930325089at_nat,X: product_prod_nat_nat] : ( ord_less_eq_nat @ ( finite711546835091564841at_nat @ ( minus_1356011639430497352at_nat @ A4 @ ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat ) ) ) @ ( finite711546835091564841at_nat @ A4 ) ) ).
% 5.31/5.54
% 5.31/5.54 % card_Diff1_le
% 5.31/5.54 thf(fact_2856_card__Diff1__le,axiom,
% 5.31/5.54 ! [A4: set_nat,X: nat] : ( ord_less_eq_nat @ ( finite_card_nat @ ( minus_minus_set_nat @ A4 @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) @ ( finite_card_nat @ A4 ) ) ).
% 5.31/5.54
% 5.31/5.54 % card_Diff1_le
% 5.31/5.54 thf(fact_2857_power__strict__decreasing,axiom,
% 5.31/5.54 ! [N: nat,N6: nat,A: code_integer] :
% 5.31/5.54 ( ( ord_less_nat @ N @ N6 )
% 5.31/5.54 => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 5.31/5.54 => ( ( ord_le6747313008572928689nteger @ A @ one_one_Code_integer )
% 5.31/5.54 => ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ A @ N6 ) @ ( power_8256067586552552935nteger @ A @ N ) ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % power_strict_decreasing
% 5.31/5.54 thf(fact_2858_power__strict__decreasing,axiom,
% 5.31/5.54 ! [N: nat,N6: nat,A: real] :
% 5.31/5.54 ( ( ord_less_nat @ N @ N6 )
% 5.31/5.54 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.31/5.54 => ( ( ord_less_real @ A @ one_one_real )
% 5.31/5.54 => ( ord_less_real @ ( power_power_real @ A @ N6 ) @ ( power_power_real @ A @ N ) ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % power_strict_decreasing
% 5.31/5.54 thf(fact_2859_power__strict__decreasing,axiom,
% 5.31/5.54 ! [N: nat,N6: nat,A: rat] :
% 5.31/5.54 ( ( ord_less_nat @ N @ N6 )
% 5.31/5.54 => ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.31/5.54 => ( ( ord_less_rat @ A @ one_one_rat )
% 5.31/5.54 => ( ord_less_rat @ ( power_power_rat @ A @ N6 ) @ ( power_power_rat @ A @ N ) ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % power_strict_decreasing
% 5.31/5.54 thf(fact_2860_power__strict__decreasing,axiom,
% 5.31/5.54 ! [N: nat,N6: nat,A: nat] :
% 5.31/5.54 ( ( ord_less_nat @ N @ N6 )
% 5.31/5.54 => ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.31/5.54 => ( ( ord_less_nat @ A @ one_one_nat )
% 5.31/5.54 => ( ord_less_nat @ ( power_power_nat @ A @ N6 ) @ ( power_power_nat @ A @ N ) ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % power_strict_decreasing
% 5.31/5.54 thf(fact_2861_power__strict__decreasing,axiom,
% 5.31/5.54 ! [N: nat,N6: nat,A: int] :
% 5.31/5.54 ( ( ord_less_nat @ N @ N6 )
% 5.31/5.54 => ( ( ord_less_int @ zero_zero_int @ A )
% 5.31/5.54 => ( ( ord_less_int @ A @ one_one_int )
% 5.31/5.54 => ( ord_less_int @ ( power_power_int @ A @ N6 ) @ ( power_power_int @ A @ N ) ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % power_strict_decreasing
% 5.31/5.54 thf(fact_2862_power__decreasing,axiom,
% 5.31/5.54 ! [N: nat,N6: nat,A: code_integer] :
% 5.31/5.54 ( ( ord_less_eq_nat @ N @ N6 )
% 5.31/5.54 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 5.31/5.54 => ( ( ord_le3102999989581377725nteger @ A @ one_one_Code_integer )
% 5.31/5.54 => ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ A @ N6 ) @ ( power_8256067586552552935nteger @ A @ N ) ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % power_decreasing
% 5.31/5.54 thf(fact_2863_power__decreasing,axiom,
% 5.31/5.54 ! [N: nat,N6: nat,A: real] :
% 5.31/5.54 ( ( ord_less_eq_nat @ N @ N6 )
% 5.31/5.54 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.31/5.54 => ( ( ord_less_eq_real @ A @ one_one_real )
% 5.31/5.54 => ( ord_less_eq_real @ ( power_power_real @ A @ N6 ) @ ( power_power_real @ A @ N ) ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % power_decreasing
% 5.31/5.54 thf(fact_2864_power__decreasing,axiom,
% 5.31/5.54 ! [N: nat,N6: nat,A: rat] :
% 5.31/5.54 ( ( ord_less_eq_nat @ N @ N6 )
% 5.31/5.54 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.31/5.54 => ( ( ord_less_eq_rat @ A @ one_one_rat )
% 5.31/5.54 => ( ord_less_eq_rat @ ( power_power_rat @ A @ N6 ) @ ( power_power_rat @ A @ N ) ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % power_decreasing
% 5.31/5.54 thf(fact_2865_power__decreasing,axiom,
% 5.31/5.54 ! [N: nat,N6: nat,A: nat] :
% 5.31/5.54 ( ( ord_less_eq_nat @ N @ N6 )
% 5.31/5.54 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.31/5.54 => ( ( ord_less_eq_nat @ A @ one_one_nat )
% 5.31/5.54 => ( ord_less_eq_nat @ ( power_power_nat @ A @ N6 ) @ ( power_power_nat @ A @ N ) ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % power_decreasing
% 5.31/5.54 thf(fact_2866_power__decreasing,axiom,
% 5.31/5.54 ! [N: nat,N6: nat,A: int] :
% 5.31/5.54 ( ( ord_less_eq_nat @ N @ N6 )
% 5.31/5.54 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.31/5.54 => ( ( ord_less_eq_int @ A @ one_one_int )
% 5.31/5.54 => ( ord_less_eq_int @ ( power_power_int @ A @ N6 ) @ ( power_power_int @ A @ N ) ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % power_decreasing
% 5.31/5.54 thf(fact_2867_power__le__imp__le__exp,axiom,
% 5.31/5.54 ! [A: code_integer,M2: nat,N: nat] :
% 5.31/5.54 ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ A )
% 5.31/5.54 => ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ A @ M2 ) @ ( power_8256067586552552935nteger @ A @ N ) )
% 5.31/5.54 => ( ord_less_eq_nat @ M2 @ N ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % power_le_imp_le_exp
% 5.31/5.54 thf(fact_2868_power__le__imp__le__exp,axiom,
% 5.31/5.54 ! [A: real,M2: nat,N: nat] :
% 5.31/5.54 ( ( ord_less_real @ one_one_real @ A )
% 5.31/5.54 => ( ( ord_less_eq_real @ ( power_power_real @ A @ M2 ) @ ( power_power_real @ A @ N ) )
% 5.31/5.54 => ( ord_less_eq_nat @ M2 @ N ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % power_le_imp_le_exp
% 5.31/5.54 thf(fact_2869_power__le__imp__le__exp,axiom,
% 5.31/5.54 ! [A: rat,M2: nat,N: nat] :
% 5.31/5.54 ( ( ord_less_rat @ one_one_rat @ A )
% 5.31/5.54 => ( ( ord_less_eq_rat @ ( power_power_rat @ A @ M2 ) @ ( power_power_rat @ A @ N ) )
% 5.31/5.54 => ( ord_less_eq_nat @ M2 @ N ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % power_le_imp_le_exp
% 5.31/5.54 thf(fact_2870_power__le__imp__le__exp,axiom,
% 5.31/5.54 ! [A: nat,M2: nat,N: nat] :
% 5.31/5.54 ( ( ord_less_nat @ one_one_nat @ A )
% 5.31/5.54 => ( ( ord_less_eq_nat @ ( power_power_nat @ A @ M2 ) @ ( power_power_nat @ A @ N ) )
% 5.31/5.54 => ( ord_less_eq_nat @ M2 @ N ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % power_le_imp_le_exp
% 5.31/5.54 thf(fact_2871_power__le__imp__le__exp,axiom,
% 5.31/5.54 ! [A: int,M2: nat,N: nat] :
% 5.31/5.54 ( ( ord_less_int @ one_one_int @ A )
% 5.31/5.54 => ( ( ord_less_eq_int @ ( power_power_int @ A @ M2 ) @ ( power_power_int @ A @ N ) )
% 5.31/5.54 => ( ord_less_eq_nat @ M2 @ N ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % power_le_imp_le_exp
% 5.31/5.54 thf(fact_2872_power__eq__iff__eq__base,axiom,
% 5.31/5.54 ! [N: nat,A: real,B: real] :
% 5.31/5.54 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.54 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.31/5.54 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.31/5.54 => ( ( ( power_power_real @ A @ N )
% 5.31/5.54 = ( power_power_real @ B @ N ) )
% 5.31/5.54 = ( A = B ) ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % power_eq_iff_eq_base
% 5.31/5.54 thf(fact_2873_power__eq__iff__eq__base,axiom,
% 5.31/5.54 ! [N: nat,A: rat,B: rat] :
% 5.31/5.54 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.54 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.31/5.54 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.31/5.54 => ( ( ( power_power_rat @ A @ N )
% 5.31/5.54 = ( power_power_rat @ B @ N ) )
% 5.31/5.54 = ( A = B ) ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % power_eq_iff_eq_base
% 5.31/5.54 thf(fact_2874_power__eq__iff__eq__base,axiom,
% 5.31/5.54 ! [N: nat,A: nat,B: nat] :
% 5.31/5.54 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.54 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.31/5.54 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.31/5.54 => ( ( ( power_power_nat @ A @ N )
% 5.31/5.54 = ( power_power_nat @ B @ N ) )
% 5.31/5.54 = ( A = B ) ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % power_eq_iff_eq_base
% 5.31/5.54 thf(fact_2875_power__eq__iff__eq__base,axiom,
% 5.31/5.54 ! [N: nat,A: int,B: int] :
% 5.31/5.54 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.54 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.31/5.54 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.31/5.54 => ( ( ( power_power_int @ A @ N )
% 5.31/5.54 = ( power_power_int @ B @ N ) )
% 5.31/5.54 = ( A = B ) ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % power_eq_iff_eq_base
% 5.31/5.54 thf(fact_2876_power__eq__imp__eq__base,axiom,
% 5.31/5.54 ! [A: real,N: nat,B: real] :
% 5.31/5.54 ( ( ( power_power_real @ A @ N )
% 5.31/5.54 = ( power_power_real @ B @ N ) )
% 5.31/5.54 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.31/5.54 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.31/5.54 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.54 => ( A = B ) ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % power_eq_imp_eq_base
% 5.31/5.54 thf(fact_2877_power__eq__imp__eq__base,axiom,
% 5.31/5.54 ! [A: rat,N: nat,B: rat] :
% 5.31/5.54 ( ( ( power_power_rat @ A @ N )
% 5.31/5.54 = ( power_power_rat @ B @ N ) )
% 5.31/5.54 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.31/5.54 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.31/5.54 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.54 => ( A = B ) ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % power_eq_imp_eq_base
% 5.31/5.54 thf(fact_2878_power__eq__imp__eq__base,axiom,
% 5.31/5.54 ! [A: nat,N: nat,B: nat] :
% 5.31/5.54 ( ( ( power_power_nat @ A @ N )
% 5.31/5.54 = ( power_power_nat @ B @ N ) )
% 5.31/5.54 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.31/5.54 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.31/5.54 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.54 => ( A = B ) ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % power_eq_imp_eq_base
% 5.31/5.54 thf(fact_2879_power__eq__imp__eq__base,axiom,
% 5.31/5.54 ! [A: int,N: nat,B: int] :
% 5.31/5.54 ( ( ( power_power_int @ A @ N )
% 5.31/5.54 = ( power_power_int @ B @ N ) )
% 5.31/5.54 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.31/5.54 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.31/5.54 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.54 => ( A = B ) ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % power_eq_imp_eq_base
% 5.31/5.54 thf(fact_2880_diff__card__le__card__Diff,axiom,
% 5.31/5.54 ! [B5: set_list_nat,A4: set_list_nat] :
% 5.31/5.54 ( ( finite8100373058378681591st_nat @ B5 )
% 5.31/5.54 => ( ord_less_eq_nat @ ( minus_minus_nat @ ( finite_card_list_nat @ A4 ) @ ( finite_card_list_nat @ B5 ) ) @ ( finite_card_list_nat @ ( minus_7954133019191499631st_nat @ A4 @ B5 ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % diff_card_le_card_Diff
% 5.31/5.54 thf(fact_2881_diff__card__le__card__Diff,axiom,
% 5.31/5.54 ! [B5: set_set_nat,A4: set_set_nat] :
% 5.31/5.54 ( ( finite1152437895449049373et_nat @ B5 )
% 5.31/5.54 => ( ord_less_eq_nat @ ( minus_minus_nat @ ( finite_card_set_nat @ A4 ) @ ( finite_card_set_nat @ B5 ) ) @ ( finite_card_set_nat @ ( minus_2163939370556025621et_nat @ A4 @ B5 ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % diff_card_le_card_Diff
% 5.31/5.54 thf(fact_2882_diff__card__le__card__Diff,axiom,
% 5.31/5.54 ! [B5: set_int,A4: set_int] :
% 5.31/5.54 ( ( finite_finite_int @ B5 )
% 5.31/5.54 => ( ord_less_eq_nat @ ( minus_minus_nat @ ( finite_card_int @ A4 ) @ ( finite_card_int @ B5 ) ) @ ( finite_card_int @ ( minus_minus_set_int @ A4 @ B5 ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % diff_card_le_card_Diff
% 5.31/5.54 thf(fact_2883_diff__card__le__card__Diff,axiom,
% 5.31/5.54 ! [B5: set_complex,A4: set_complex] :
% 5.31/5.54 ( ( finite3207457112153483333omplex @ B5 )
% 5.31/5.54 => ( ord_less_eq_nat @ ( minus_minus_nat @ ( finite_card_complex @ A4 ) @ ( finite_card_complex @ B5 ) ) @ ( finite_card_complex @ ( minus_811609699411566653omplex @ A4 @ B5 ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % diff_card_le_card_Diff
% 5.31/5.54 thf(fact_2884_diff__card__le__card__Diff,axiom,
% 5.31/5.54 ! [B5: set_Pr1261947904930325089at_nat,A4: set_Pr1261947904930325089at_nat] :
% 5.31/5.54 ( ( finite6177210948735845034at_nat @ B5 )
% 5.31/5.54 => ( ord_less_eq_nat @ ( minus_minus_nat @ ( finite711546835091564841at_nat @ A4 ) @ ( finite711546835091564841at_nat @ B5 ) ) @ ( finite711546835091564841at_nat @ ( minus_1356011639430497352at_nat @ A4 @ B5 ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % diff_card_le_card_Diff
% 5.31/5.54 thf(fact_2885_diff__card__le__card__Diff,axiom,
% 5.31/5.54 ! [B5: set_nat,A4: set_nat] :
% 5.31/5.54 ( ( finite_finite_nat @ B5 )
% 5.31/5.54 => ( ord_less_eq_nat @ ( minus_minus_nat @ ( finite_card_nat @ A4 ) @ ( finite_card_nat @ B5 ) ) @ ( finite_card_nat @ ( minus_minus_set_nat @ A4 @ B5 ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % diff_card_le_card_Diff
% 5.31/5.54 thf(fact_2886_self__le__power,axiom,
% 5.31/5.54 ! [A: code_integer,N: nat] :
% 5.31/5.54 ( ( ord_le3102999989581377725nteger @ one_one_Code_integer @ A )
% 5.31/5.54 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.54 => ( ord_le3102999989581377725nteger @ A @ ( power_8256067586552552935nteger @ A @ N ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % self_le_power
% 5.31/5.54 thf(fact_2887_self__le__power,axiom,
% 5.31/5.54 ! [A: real,N: nat] :
% 5.31/5.54 ( ( ord_less_eq_real @ one_one_real @ A )
% 5.31/5.54 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.54 => ( ord_less_eq_real @ A @ ( power_power_real @ A @ N ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % self_le_power
% 5.31/5.54 thf(fact_2888_self__le__power,axiom,
% 5.31/5.54 ! [A: rat,N: nat] :
% 5.31/5.54 ( ( ord_less_eq_rat @ one_one_rat @ A )
% 5.31/5.54 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.54 => ( ord_less_eq_rat @ A @ ( power_power_rat @ A @ N ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % self_le_power
% 5.31/5.54 thf(fact_2889_self__le__power,axiom,
% 5.31/5.54 ! [A: nat,N: nat] :
% 5.31/5.54 ( ( ord_less_eq_nat @ one_one_nat @ A )
% 5.31/5.54 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.54 => ( ord_less_eq_nat @ A @ ( power_power_nat @ A @ N ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % self_le_power
% 5.31/5.54 thf(fact_2890_self__le__power,axiom,
% 5.31/5.54 ! [A: int,N: nat] :
% 5.31/5.54 ( ( ord_less_eq_int @ one_one_int @ A )
% 5.31/5.54 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.54 => ( ord_less_eq_int @ A @ ( power_power_int @ A @ N ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % self_le_power
% 5.31/5.54 thf(fact_2891_one__less__power,axiom,
% 5.31/5.54 ! [A: code_integer,N: nat] :
% 5.31/5.54 ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ A )
% 5.31/5.54 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.54 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ A @ N ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % one_less_power
% 5.31/5.54 thf(fact_2892_one__less__power,axiom,
% 5.31/5.54 ! [A: real,N: nat] :
% 5.31/5.54 ( ( ord_less_real @ one_one_real @ A )
% 5.31/5.54 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.54 => ( ord_less_real @ one_one_real @ ( power_power_real @ A @ N ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % one_less_power
% 5.31/5.54 thf(fact_2893_one__less__power,axiom,
% 5.31/5.54 ! [A: rat,N: nat] :
% 5.31/5.54 ( ( ord_less_rat @ one_one_rat @ A )
% 5.31/5.54 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.54 => ( ord_less_rat @ one_one_rat @ ( power_power_rat @ A @ N ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % one_less_power
% 5.31/5.54 thf(fact_2894_one__less__power,axiom,
% 5.31/5.54 ! [A: nat,N: nat] :
% 5.31/5.54 ( ( ord_less_nat @ one_one_nat @ A )
% 5.31/5.54 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.54 => ( ord_less_nat @ one_one_nat @ ( power_power_nat @ A @ N ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % one_less_power
% 5.31/5.54 thf(fact_2895_one__less__power,axiom,
% 5.31/5.54 ! [A: int,N: nat] :
% 5.31/5.54 ( ( ord_less_int @ one_one_int @ A )
% 5.31/5.54 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.54 => ( ord_less_int @ one_one_int @ ( power_power_int @ A @ N ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % one_less_power
% 5.31/5.54 thf(fact_2896_count__le__length,axiom,
% 5.31/5.54 ! [Xs2: list_VEBT_VEBT,X: vEBT_VEBT] : ( ord_less_eq_nat @ ( count_list_VEBT_VEBT @ Xs2 @ X ) @ ( size_s6755466524823107622T_VEBT @ Xs2 ) ) ).
% 5.31/5.54
% 5.31/5.54 % count_le_length
% 5.31/5.54 thf(fact_2897_count__le__length,axiom,
% 5.31/5.54 ! [Xs2: list_o,X: $o] : ( ord_less_eq_nat @ ( count_list_o @ Xs2 @ X ) @ ( size_size_list_o @ Xs2 ) ) ).
% 5.31/5.54
% 5.31/5.54 % count_le_length
% 5.31/5.54 thf(fact_2898_count__le__length,axiom,
% 5.31/5.54 ! [Xs2: list_nat,X: nat] : ( ord_less_eq_nat @ ( count_list_nat @ Xs2 @ X ) @ ( size_size_list_nat @ Xs2 ) ) ).
% 5.31/5.54
% 5.31/5.54 % count_le_length
% 5.31/5.54 thf(fact_2899_count__le__length,axiom,
% 5.31/5.54 ! [Xs2: list_int,X: int] : ( ord_less_eq_nat @ ( count_list_int @ Xs2 @ X ) @ ( size_size_list_int @ Xs2 ) ) ).
% 5.31/5.54
% 5.31/5.54 % count_le_length
% 5.31/5.54 thf(fact_2900_dbl__inc__def,axiom,
% 5.31/5.54 ( neg_nu5831290666863070958nteger
% 5.31/5.54 = ( ^ [X4: code_integer] : ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ X4 @ X4 ) @ one_one_Code_integer ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % dbl_inc_def
% 5.31/5.54 thf(fact_2901_dbl__inc__def,axiom,
% 5.31/5.54 ( neg_nu8557863876264182079omplex
% 5.31/5.54 = ( ^ [X4: complex] : ( plus_plus_complex @ ( plus_plus_complex @ X4 @ X4 ) @ one_one_complex ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % dbl_inc_def
% 5.31/5.54 thf(fact_2902_dbl__inc__def,axiom,
% 5.31/5.54 ( neg_nu8295874005876285629c_real
% 5.31/5.54 = ( ^ [X4: real] : ( plus_plus_real @ ( plus_plus_real @ X4 @ X4 ) @ one_one_real ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % dbl_inc_def
% 5.31/5.54 thf(fact_2903_dbl__inc__def,axiom,
% 5.31/5.54 ( neg_nu5219082963157363817nc_rat
% 5.31/5.54 = ( ^ [X4: rat] : ( plus_plus_rat @ ( plus_plus_rat @ X4 @ X4 ) @ one_one_rat ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % dbl_inc_def
% 5.31/5.54 thf(fact_2904_dbl__inc__def,axiom,
% 5.31/5.54 ( neg_nu5851722552734809277nc_int
% 5.31/5.54 = ( ^ [X4: int] : ( plus_plus_int @ ( plus_plus_int @ X4 @ X4 ) @ one_one_int ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % dbl_inc_def
% 5.31/5.54 thf(fact_2905_card_Oremove,axiom,
% 5.31/5.54 ! [A4: set_list_nat,X: list_nat] :
% 5.31/5.54 ( ( finite8100373058378681591st_nat @ A4 )
% 5.31/5.54 => ( ( member_list_nat @ X @ A4 )
% 5.31/5.54 => ( ( finite_card_list_nat @ A4 )
% 5.31/5.54 = ( suc @ ( finite_card_list_nat @ ( minus_7954133019191499631st_nat @ A4 @ ( insert_list_nat @ X @ bot_bot_set_list_nat ) ) ) ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % card.remove
% 5.31/5.54 thf(fact_2906_card_Oremove,axiom,
% 5.31/5.54 ! [A4: set_set_nat,X: set_nat] :
% 5.31/5.54 ( ( finite1152437895449049373et_nat @ A4 )
% 5.31/5.54 => ( ( member_set_nat @ X @ A4 )
% 5.31/5.54 => ( ( finite_card_set_nat @ A4 )
% 5.31/5.54 = ( suc @ ( finite_card_set_nat @ ( minus_2163939370556025621et_nat @ A4 @ ( insert_set_nat @ X @ bot_bot_set_set_nat ) ) ) ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % card.remove
% 5.31/5.54 thf(fact_2907_card_Oremove,axiom,
% 5.31/5.54 ! [A4: set_complex,X: complex] :
% 5.31/5.54 ( ( finite3207457112153483333omplex @ A4 )
% 5.31/5.54 => ( ( member_complex @ X @ A4 )
% 5.31/5.54 => ( ( finite_card_complex @ A4 )
% 5.31/5.54 = ( suc @ ( finite_card_complex @ ( minus_811609699411566653omplex @ A4 @ ( insert_complex @ X @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % card.remove
% 5.31/5.54 thf(fact_2908_card_Oremove,axiom,
% 5.31/5.54 ! [A4: set_int,X: int] :
% 5.31/5.54 ( ( finite_finite_int @ A4 )
% 5.31/5.54 => ( ( member_int @ X @ A4 )
% 5.31/5.54 => ( ( finite_card_int @ A4 )
% 5.31/5.54 = ( suc @ ( finite_card_int @ ( minus_minus_set_int @ A4 @ ( insert_int @ X @ bot_bot_set_int ) ) ) ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % card.remove
% 5.31/5.54 thf(fact_2909_card_Oremove,axiom,
% 5.31/5.54 ! [A4: set_real,X: real] :
% 5.31/5.54 ( ( finite_finite_real @ A4 )
% 5.31/5.54 => ( ( member_real @ X @ A4 )
% 5.31/5.54 => ( ( finite_card_real @ A4 )
% 5.31/5.54 = ( suc @ ( finite_card_real @ ( minus_minus_set_real @ A4 @ ( insert_real @ X @ bot_bot_set_real ) ) ) ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % card.remove
% 5.31/5.54 thf(fact_2910_card_Oremove,axiom,
% 5.31/5.54 ! [A4: set_Pr1261947904930325089at_nat,X: product_prod_nat_nat] :
% 5.31/5.54 ( ( finite6177210948735845034at_nat @ A4 )
% 5.31/5.54 => ( ( member8440522571783428010at_nat @ X @ A4 )
% 5.31/5.54 => ( ( finite711546835091564841at_nat @ A4 )
% 5.31/5.54 = ( suc @ ( finite711546835091564841at_nat @ ( minus_1356011639430497352at_nat @ A4 @ ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat ) ) ) ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % card.remove
% 5.31/5.54 thf(fact_2911_card_Oremove,axiom,
% 5.31/5.54 ! [A4: set_nat,X: nat] :
% 5.31/5.54 ( ( finite_finite_nat @ A4 )
% 5.31/5.54 => ( ( member_nat @ X @ A4 )
% 5.31/5.54 => ( ( finite_card_nat @ A4 )
% 5.31/5.54 = ( suc @ ( finite_card_nat @ ( minus_minus_set_nat @ A4 @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % card.remove
% 5.31/5.54 thf(fact_2912_card_Oinsert__remove,axiom,
% 5.31/5.54 ! [A4: set_list_nat,X: list_nat] :
% 5.31/5.54 ( ( finite8100373058378681591st_nat @ A4 )
% 5.31/5.54 => ( ( finite_card_list_nat @ ( insert_list_nat @ X @ A4 ) )
% 5.31/5.54 = ( suc @ ( finite_card_list_nat @ ( minus_7954133019191499631st_nat @ A4 @ ( insert_list_nat @ X @ bot_bot_set_list_nat ) ) ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % card.insert_remove
% 5.31/5.54 thf(fact_2913_card_Oinsert__remove,axiom,
% 5.31/5.54 ! [A4: set_set_nat,X: set_nat] :
% 5.31/5.54 ( ( finite1152437895449049373et_nat @ A4 )
% 5.31/5.54 => ( ( finite_card_set_nat @ ( insert_set_nat @ X @ A4 ) )
% 5.31/5.54 = ( suc @ ( finite_card_set_nat @ ( minus_2163939370556025621et_nat @ A4 @ ( insert_set_nat @ X @ bot_bot_set_set_nat ) ) ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % card.insert_remove
% 5.31/5.54 thf(fact_2914_card_Oinsert__remove,axiom,
% 5.31/5.54 ! [A4: set_complex,X: complex] :
% 5.31/5.54 ( ( finite3207457112153483333omplex @ A4 )
% 5.31/5.54 => ( ( finite_card_complex @ ( insert_complex @ X @ A4 ) )
% 5.31/5.54 = ( suc @ ( finite_card_complex @ ( minus_811609699411566653omplex @ A4 @ ( insert_complex @ X @ bot_bot_set_complex ) ) ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % card.insert_remove
% 5.31/5.54 thf(fact_2915_card_Oinsert__remove,axiom,
% 5.31/5.54 ! [A4: set_int,X: int] :
% 5.31/5.54 ( ( finite_finite_int @ A4 )
% 5.31/5.54 => ( ( finite_card_int @ ( insert_int @ X @ A4 ) )
% 5.31/5.54 = ( suc @ ( finite_card_int @ ( minus_minus_set_int @ A4 @ ( insert_int @ X @ bot_bot_set_int ) ) ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % card.insert_remove
% 5.31/5.54 thf(fact_2916_card_Oinsert__remove,axiom,
% 5.31/5.54 ! [A4: set_real,X: real] :
% 5.31/5.54 ( ( finite_finite_real @ A4 )
% 5.31/5.54 => ( ( finite_card_real @ ( insert_real @ X @ A4 ) )
% 5.31/5.54 = ( suc @ ( finite_card_real @ ( minus_minus_set_real @ A4 @ ( insert_real @ X @ bot_bot_set_real ) ) ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % card.insert_remove
% 5.31/5.54 thf(fact_2917_card_Oinsert__remove,axiom,
% 5.31/5.54 ! [A4: set_Pr1261947904930325089at_nat,X: product_prod_nat_nat] :
% 5.31/5.54 ( ( finite6177210948735845034at_nat @ A4 )
% 5.31/5.54 => ( ( finite711546835091564841at_nat @ ( insert8211810215607154385at_nat @ X @ A4 ) )
% 5.31/5.54 = ( suc @ ( finite711546835091564841at_nat @ ( minus_1356011639430497352at_nat @ A4 @ ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat ) ) ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % card.insert_remove
% 5.31/5.54 thf(fact_2918_card_Oinsert__remove,axiom,
% 5.31/5.54 ! [A4: set_nat,X: nat] :
% 5.31/5.54 ( ( finite_finite_nat @ A4 )
% 5.31/5.54 => ( ( finite_card_nat @ ( insert_nat @ X @ A4 ) )
% 5.31/5.54 = ( suc @ ( finite_card_nat @ ( minus_minus_set_nat @ A4 @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % card.insert_remove
% 5.31/5.54 thf(fact_2919_card__Suc__Diff1,axiom,
% 5.31/5.54 ! [A4: set_list_nat,X: list_nat] :
% 5.31/5.54 ( ( finite8100373058378681591st_nat @ A4 )
% 5.31/5.54 => ( ( member_list_nat @ X @ A4 )
% 5.31/5.54 => ( ( suc @ ( finite_card_list_nat @ ( minus_7954133019191499631st_nat @ A4 @ ( insert_list_nat @ X @ bot_bot_set_list_nat ) ) ) )
% 5.31/5.54 = ( finite_card_list_nat @ A4 ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % card_Suc_Diff1
% 5.31/5.54 thf(fact_2920_card__Suc__Diff1,axiom,
% 5.31/5.54 ! [A4: set_set_nat,X: set_nat] :
% 5.31/5.54 ( ( finite1152437895449049373et_nat @ A4 )
% 5.31/5.54 => ( ( member_set_nat @ X @ A4 )
% 5.31/5.54 => ( ( suc @ ( finite_card_set_nat @ ( minus_2163939370556025621et_nat @ A4 @ ( insert_set_nat @ X @ bot_bot_set_set_nat ) ) ) )
% 5.31/5.54 = ( finite_card_set_nat @ A4 ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % card_Suc_Diff1
% 5.31/5.54 thf(fact_2921_card__Suc__Diff1,axiom,
% 5.31/5.54 ! [A4: set_complex,X: complex] :
% 5.31/5.54 ( ( finite3207457112153483333omplex @ A4 )
% 5.31/5.54 => ( ( member_complex @ X @ A4 )
% 5.31/5.54 => ( ( suc @ ( finite_card_complex @ ( minus_811609699411566653omplex @ A4 @ ( insert_complex @ X @ bot_bot_set_complex ) ) ) )
% 5.31/5.54 = ( finite_card_complex @ A4 ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % card_Suc_Diff1
% 5.31/5.54 thf(fact_2922_card__Suc__Diff1,axiom,
% 5.31/5.54 ! [A4: set_int,X: int] :
% 5.31/5.54 ( ( finite_finite_int @ A4 )
% 5.31/5.54 => ( ( member_int @ X @ A4 )
% 5.31/5.54 => ( ( suc @ ( finite_card_int @ ( minus_minus_set_int @ A4 @ ( insert_int @ X @ bot_bot_set_int ) ) ) )
% 5.31/5.54 = ( finite_card_int @ A4 ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % card_Suc_Diff1
% 5.31/5.54 thf(fact_2923_card__Suc__Diff1,axiom,
% 5.31/5.54 ! [A4: set_real,X: real] :
% 5.31/5.54 ( ( finite_finite_real @ A4 )
% 5.31/5.54 => ( ( member_real @ X @ A4 )
% 5.31/5.54 => ( ( suc @ ( finite_card_real @ ( minus_minus_set_real @ A4 @ ( insert_real @ X @ bot_bot_set_real ) ) ) )
% 5.31/5.54 = ( finite_card_real @ A4 ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % card_Suc_Diff1
% 5.31/5.54 thf(fact_2924_card__Suc__Diff1,axiom,
% 5.31/5.54 ! [A4: set_Pr1261947904930325089at_nat,X: product_prod_nat_nat] :
% 5.31/5.54 ( ( finite6177210948735845034at_nat @ A4 )
% 5.31/5.54 => ( ( member8440522571783428010at_nat @ X @ A4 )
% 5.31/5.54 => ( ( suc @ ( finite711546835091564841at_nat @ ( minus_1356011639430497352at_nat @ A4 @ ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat ) ) ) )
% 5.31/5.54 = ( finite711546835091564841at_nat @ A4 ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % card_Suc_Diff1
% 5.31/5.54 thf(fact_2925_card__Suc__Diff1,axiom,
% 5.31/5.54 ! [A4: set_nat,X: nat] :
% 5.31/5.54 ( ( finite_finite_nat @ A4 )
% 5.31/5.54 => ( ( member_nat @ X @ A4 )
% 5.31/5.54 => ( ( suc @ ( finite_card_nat @ ( minus_minus_set_nat @ A4 @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) )
% 5.31/5.54 = ( finite_card_nat @ A4 ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % card_Suc_Diff1
% 5.31/5.54 thf(fact_2926_power__strict__mono,axiom,
% 5.31/5.54 ! [A: real,B: real,N: nat] :
% 5.31/5.54 ( ( ord_less_real @ A @ B )
% 5.31/5.54 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.31/5.54 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.54 => ( ord_less_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % power_strict_mono
% 5.31/5.54 thf(fact_2927_power__strict__mono,axiom,
% 5.31/5.54 ! [A: rat,B: rat,N: nat] :
% 5.31/5.54 ( ( ord_less_rat @ A @ B )
% 5.31/5.54 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.31/5.54 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.54 => ( ord_less_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % power_strict_mono
% 5.31/5.54 thf(fact_2928_power__strict__mono,axiom,
% 5.31/5.54 ! [A: nat,B: nat,N: nat] :
% 5.31/5.54 ( ( ord_less_nat @ A @ B )
% 5.31/5.54 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.31/5.54 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.54 => ( ord_less_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % power_strict_mono
% 5.31/5.54 thf(fact_2929_power__strict__mono,axiom,
% 5.31/5.54 ! [A: int,B: int,N: nat] :
% 5.31/5.54 ( ( ord_less_int @ A @ B )
% 5.31/5.54 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.31/5.54 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.54 => ( ord_less_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % power_strict_mono
% 5.31/5.54 thf(fact_2930_power__eq__if,axiom,
% 5.31/5.54 ( power_8256067586552552935nteger
% 5.31/5.54 = ( ^ [P5: code_integer,M6: nat] : ( if_Code_integer @ ( M6 = zero_zero_nat ) @ one_one_Code_integer @ ( times_3573771949741848930nteger @ P5 @ ( power_8256067586552552935nteger @ P5 @ ( minus_minus_nat @ M6 @ one_one_nat ) ) ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % power_eq_if
% 5.31/5.54 thf(fact_2931_power__eq__if,axiom,
% 5.31/5.54 ( power_power_complex
% 5.31/5.54 = ( ^ [P5: complex,M6: nat] : ( if_complex @ ( M6 = zero_zero_nat ) @ one_one_complex @ ( times_times_complex @ P5 @ ( power_power_complex @ P5 @ ( minus_minus_nat @ M6 @ one_one_nat ) ) ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % power_eq_if
% 5.31/5.54 thf(fact_2932_power__eq__if,axiom,
% 5.31/5.54 ( power_power_real
% 5.31/5.54 = ( ^ [P5: real,M6: nat] : ( if_real @ ( M6 = zero_zero_nat ) @ one_one_real @ ( times_times_real @ P5 @ ( power_power_real @ P5 @ ( minus_minus_nat @ M6 @ one_one_nat ) ) ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % power_eq_if
% 5.31/5.54 thf(fact_2933_power__eq__if,axiom,
% 5.31/5.54 ( power_power_rat
% 5.31/5.54 = ( ^ [P5: rat,M6: nat] : ( if_rat @ ( M6 = zero_zero_nat ) @ one_one_rat @ ( times_times_rat @ P5 @ ( power_power_rat @ P5 @ ( minus_minus_nat @ M6 @ one_one_nat ) ) ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % power_eq_if
% 5.31/5.54 thf(fact_2934_power__eq__if,axiom,
% 5.31/5.54 ( power_power_nat
% 5.31/5.54 = ( ^ [P5: nat,M6: nat] : ( if_nat @ ( M6 = zero_zero_nat ) @ one_one_nat @ ( times_times_nat @ P5 @ ( power_power_nat @ P5 @ ( minus_minus_nat @ M6 @ one_one_nat ) ) ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % power_eq_if
% 5.31/5.54 thf(fact_2935_power__eq__if,axiom,
% 5.31/5.54 ( power_power_int
% 5.31/5.54 = ( ^ [P5: int,M6: nat] : ( if_int @ ( M6 = zero_zero_nat ) @ one_one_int @ ( times_times_int @ P5 @ ( power_power_int @ P5 @ ( minus_minus_nat @ M6 @ one_one_nat ) ) ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % power_eq_if
% 5.31/5.54 thf(fact_2936_power__minus__mult,axiom,
% 5.31/5.54 ! [N: nat,A: complex] :
% 5.31/5.54 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.54 => ( ( times_times_complex @ ( power_power_complex @ A @ ( minus_minus_nat @ N @ one_one_nat ) ) @ A )
% 5.31/5.54 = ( power_power_complex @ A @ N ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % power_minus_mult
% 5.31/5.54 thf(fact_2937_power__minus__mult,axiom,
% 5.31/5.54 ! [N: nat,A: real] :
% 5.31/5.54 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.54 => ( ( times_times_real @ ( power_power_real @ A @ ( minus_minus_nat @ N @ one_one_nat ) ) @ A )
% 5.31/5.54 = ( power_power_real @ A @ N ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % power_minus_mult
% 5.31/5.54 thf(fact_2938_power__minus__mult,axiom,
% 5.31/5.54 ! [N: nat,A: rat] :
% 5.31/5.54 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.54 => ( ( times_times_rat @ ( power_power_rat @ A @ ( minus_minus_nat @ N @ one_one_nat ) ) @ A )
% 5.31/5.54 = ( power_power_rat @ A @ N ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % power_minus_mult
% 5.31/5.54 thf(fact_2939_power__minus__mult,axiom,
% 5.31/5.54 ! [N: nat,A: nat] :
% 5.31/5.54 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.54 => ( ( times_times_nat @ ( power_power_nat @ A @ ( minus_minus_nat @ N @ one_one_nat ) ) @ A )
% 5.31/5.54 = ( power_power_nat @ A @ N ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % power_minus_mult
% 5.31/5.54 thf(fact_2940_power__minus__mult,axiom,
% 5.31/5.54 ! [N: nat,A: int] :
% 5.31/5.54 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.54 => ( ( times_times_int @ ( power_power_int @ A @ ( minus_minus_nat @ N @ one_one_nat ) ) @ A )
% 5.31/5.54 = ( power_power_int @ A @ N ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % power_minus_mult
% 5.31/5.54 thf(fact_2941_Cons__in__lex,axiom,
% 5.31/5.54 ! [X: code_integer,Xs2: list_Code_integer,Y: code_integer,Ys: list_Code_integer,R3: set_Pr4811707699266497531nteger] :
% 5.31/5.54 ( ( member749217712838834276nteger @ ( produc750622340256944499nteger @ ( cons_Code_integer @ X @ Xs2 ) @ ( cons_Code_integer @ Y @ Ys ) ) @ ( lex_Code_integer @ R3 ) )
% 5.31/5.54 = ( ( ( member157494554546826820nteger @ ( produc1086072967326762835nteger @ X @ Y ) @ R3 )
% 5.31/5.54 & ( ( size_s3445333598471063425nteger @ Xs2 )
% 5.31/5.54 = ( size_s3445333598471063425nteger @ Ys ) ) )
% 5.31/5.54 | ( ( X = Y )
% 5.31/5.54 & ( member749217712838834276nteger @ ( produc750622340256944499nteger @ Xs2 @ Ys ) @ ( lex_Code_integer @ R3 ) ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % Cons_in_lex
% 5.31/5.54 thf(fact_2942_Cons__in__lex,axiom,
% 5.31/5.54 ! [X: product_prod_nat_nat,Xs2: list_P6011104703257516679at_nat,Y: product_prod_nat_nat,Ys: list_P6011104703257516679at_nat,R3: set_Pr8693737435421807431at_nat] :
% 5.31/5.54 ( ( member6693912407220327184at_nat @ ( produc5943733680697469783at_nat @ ( cons_P6512896166579812791at_nat @ X @ Xs2 ) @ ( cons_P6512896166579812791at_nat @ Y @ Ys ) ) @ ( lex_Pr8571645452597969515at_nat @ R3 ) )
% 5.31/5.54 = ( ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X @ Y ) @ R3 )
% 5.31/5.54 & ( ( size_s5460976970255530739at_nat @ Xs2 )
% 5.31/5.54 = ( size_s5460976970255530739at_nat @ Ys ) ) )
% 5.31/5.54 | ( ( X = Y )
% 5.31/5.54 & ( member6693912407220327184at_nat @ ( produc5943733680697469783at_nat @ Xs2 @ Ys ) @ ( lex_Pr8571645452597969515at_nat @ R3 ) ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % Cons_in_lex
% 5.31/5.54 thf(fact_2943_Cons__in__lex,axiom,
% 5.31/5.54 ! [X: set_Pr1261947904930325089at_nat,Xs2: list_s1210847774152347623at_nat,Y: set_Pr1261947904930325089at_nat,Ys: list_s1210847774152347623at_nat,R3: set_Pr4329608150637261639at_nat] :
% 5.31/5.54 ( ( member4080735728053443344at_nat @ ( produc7536900900485677911at_nat @ ( cons_s6881495754146722583at_nat @ X @ Xs2 ) @ ( cons_s6881495754146722583at_nat @ Y @ Ys ) ) @ ( lex_se2245640040323279819at_nat @ R3 ) )
% 5.31/5.54 = ( ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X @ Y ) @ R3 )
% 5.31/5.54 & ( ( size_s8736152011456118867at_nat @ Xs2 )
% 5.31/5.54 = ( size_s8736152011456118867at_nat @ Ys ) ) )
% 5.31/5.54 | ( ( X = Y )
% 5.31/5.54 & ( member4080735728053443344at_nat @ ( produc7536900900485677911at_nat @ Xs2 @ Ys ) @ ( lex_se2245640040323279819at_nat @ R3 ) ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % Cons_in_lex
% 5.31/5.54 thf(fact_2944_Cons__in__lex,axiom,
% 5.31/5.54 ! [X: vEBT_VEBT,Xs2: list_VEBT_VEBT,Y: vEBT_VEBT,Ys: list_VEBT_VEBT,R3: set_Pr6192946355708809607T_VEBT] :
% 5.31/5.54 ( ( member4439316823752958928T_VEBT @ ( produc3897820843166775703T_VEBT @ ( cons_VEBT_VEBT @ X @ Xs2 ) @ ( cons_VEBT_VEBT @ Y @ Ys ) ) @ ( lex_VEBT_VEBT @ R3 ) )
% 5.31/5.54 = ( ( ( member568628332442017744T_VEBT @ ( produc537772716801021591T_VEBT @ X @ Y ) @ R3 )
% 5.31/5.54 & ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 5.31/5.54 = ( size_s6755466524823107622T_VEBT @ Ys ) ) )
% 5.31/5.54 | ( ( X = Y )
% 5.31/5.54 & ( member4439316823752958928T_VEBT @ ( produc3897820843166775703T_VEBT @ Xs2 @ Ys ) @ ( lex_VEBT_VEBT @ R3 ) ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % Cons_in_lex
% 5.31/5.54 thf(fact_2945_Cons__in__lex,axiom,
% 5.31/5.54 ! [X: $o,Xs2: list_o,Y: $o,Ys: list_o,R3: set_Product_prod_o_o] :
% 5.31/5.54 ( ( member4159035015898711888list_o @ ( produc8435520187683070743list_o @ ( cons_o @ X @ Xs2 ) @ ( cons_o @ Y @ Ys ) ) @ ( lex_o @ R3 ) )
% 5.31/5.54 = ( ( ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ X @ Y ) @ R3 )
% 5.31/5.54 & ( ( size_size_list_o @ Xs2 )
% 5.31/5.54 = ( size_size_list_o @ Ys ) ) )
% 5.31/5.54 | ( ( X = Y )
% 5.31/5.54 & ( member4159035015898711888list_o @ ( produc8435520187683070743list_o @ Xs2 @ Ys ) @ ( lex_o @ R3 ) ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % Cons_in_lex
% 5.31/5.54 thf(fact_2946_Cons__in__lex,axiom,
% 5.31/5.54 ! [X: nat,Xs2: list_nat,Y: nat,Ys: list_nat,R3: set_Pr1261947904930325089at_nat] :
% 5.31/5.54 ( ( member7340969449405702474st_nat @ ( produc2694037385005941721st_nat @ ( cons_nat @ X @ Xs2 ) @ ( cons_nat @ Y @ Ys ) ) @ ( lex_nat @ R3 ) )
% 5.31/5.54 = ( ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ R3 )
% 5.31/5.54 & ( ( size_size_list_nat @ Xs2 )
% 5.31/5.54 = ( size_size_list_nat @ Ys ) ) )
% 5.31/5.54 | ( ( X = Y )
% 5.31/5.54 & ( member7340969449405702474st_nat @ ( produc2694037385005941721st_nat @ Xs2 @ Ys ) @ ( lex_nat @ R3 ) ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % Cons_in_lex
% 5.31/5.54 thf(fact_2947_Cons__in__lex,axiom,
% 5.31/5.54 ! [X: int,Xs2: list_int,Y: int,Ys: list_int,R3: set_Pr958786334691620121nt_int] :
% 5.31/5.54 ( ( member6698963635872716290st_int @ ( produc364263696895485585st_int @ ( cons_int @ X @ Xs2 ) @ ( cons_int @ Y @ Ys ) ) @ ( lex_int @ R3 ) )
% 5.31/5.54 = ( ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y ) @ R3 )
% 5.31/5.54 & ( ( size_size_list_int @ Xs2 )
% 5.31/5.54 = ( size_size_list_int @ Ys ) ) )
% 5.31/5.54 | ( ( X = Y )
% 5.31/5.54 & ( member6698963635872716290st_int @ ( produc364263696895485585st_int @ Xs2 @ Ys ) @ ( lex_int @ R3 ) ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % Cons_in_lex
% 5.31/5.54 thf(fact_2948_realpow__pos__nth__unique,axiom,
% 5.31/5.54 ! [N: nat,A: real] :
% 5.31/5.54 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.54 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.31/5.54 => ? [X3: real] :
% 5.31/5.54 ( ( ord_less_real @ zero_zero_real @ X3 )
% 5.31/5.54 & ( ( power_power_real @ X3 @ N )
% 5.31/5.54 = A )
% 5.31/5.54 & ! [Y6: real] :
% 5.31/5.54 ( ( ( ord_less_real @ zero_zero_real @ Y6 )
% 5.31/5.54 & ( ( power_power_real @ Y6 @ N )
% 5.31/5.54 = A ) )
% 5.31/5.54 => ( Y6 = X3 ) ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % realpow_pos_nth_unique
% 5.31/5.54 thf(fact_2949_realpow__pos__nth,axiom,
% 5.31/5.54 ! [N: nat,A: real] :
% 5.31/5.54 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.54 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.31/5.54 => ? [R4: real] :
% 5.31/5.54 ( ( ord_less_real @ zero_zero_real @ R4 )
% 5.31/5.54 & ( ( power_power_real @ R4 @ N )
% 5.31/5.54 = A ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % realpow_pos_nth
% 5.31/5.54 thf(fact_2950_sprop1,axiom,
% 5.31/5.54 ( ( sa
% 5.31/5.54 = ( vEBT_Node @ info @ deg @ treeList @ summary ) )
% 5.31/5.54 & ( deg
% 5.31/5.54 = ( plus_plus_nat @ na @ m ) )
% 5.31/5.54 & ( ( size_s6755466524823107622T_VEBT @ treeList )
% 5.31/5.54 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) )
% 5.31/5.54 & ( vEBT_invar_vebt @ summary @ m )
% 5.31/5.54 & ! [X5: vEBT_VEBT] :
% 5.31/5.54 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ treeList ) )
% 5.31/5.54 => ( vEBT_invar_vebt @ X5 @ na ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % sprop1
% 5.31/5.54 thf(fact_2951_listrel__iff__nth,axiom,
% 5.31/5.54 ! [Xs2: list_Code_integer,Ys: list_Code_integer,R3: set_Pr4811707699266497531nteger] :
% 5.31/5.54 ( ( member749217712838834276nteger @ ( produc750622340256944499nteger @ Xs2 @ Ys ) @ ( listre5734910445319291053nteger @ R3 ) )
% 5.31/5.54 = ( ( ( size_s3445333598471063425nteger @ Xs2 )
% 5.31/5.54 = ( size_s3445333598471063425nteger @ Ys ) )
% 5.31/5.54 & ! [N4: nat] :
% 5.31/5.54 ( ( ord_less_nat @ N4 @ ( size_s3445333598471063425nteger @ Xs2 ) )
% 5.31/5.54 => ( member157494554546826820nteger @ ( produc1086072967326762835nteger @ ( nth_Code_integer @ Xs2 @ N4 ) @ ( nth_Code_integer @ Ys @ N4 ) ) @ R3 ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % listrel_iff_nth
% 5.31/5.54 thf(fact_2952_listrel__iff__nth,axiom,
% 5.31/5.54 ! [Xs2: list_VEBT_VEBT,Ys: list_VEBT_VEBT,R3: set_Pr6192946355708809607T_VEBT] :
% 5.31/5.54 ( ( member4439316823752958928T_VEBT @ ( produc3897820843166775703T_VEBT @ Xs2 @ Ys ) @ ( listre1230615542750757617T_VEBT @ R3 ) )
% 5.31/5.54 = ( ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 5.31/5.54 = ( size_s6755466524823107622T_VEBT @ Ys ) )
% 5.31/5.54 & ! [N4: nat] :
% 5.31/5.54 ( ( ord_less_nat @ N4 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 5.31/5.54 => ( member568628332442017744T_VEBT @ ( produc537772716801021591T_VEBT @ ( nth_VEBT_VEBT @ Xs2 @ N4 ) @ ( nth_VEBT_VEBT @ Ys @ N4 ) ) @ R3 ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % listrel_iff_nth
% 5.31/5.54 thf(fact_2953_listrel__iff__nth,axiom,
% 5.31/5.54 ! [Xs2: list_VEBT_VEBT,Ys: list_o,R3: set_Pr3175402225741728619VEBT_o] :
% 5.31/5.54 ( ( member3126162362653435956list_o @ ( produc2717590391345394939list_o @ Xs2 @ Ys ) @ ( listrel_VEBT_VEBT_o @ R3 ) )
% 5.31/5.54 = ( ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 5.31/5.54 = ( size_size_list_o @ Ys ) )
% 5.31/5.54 & ! [N4: nat] :
% 5.31/5.54 ( ( ord_less_nat @ N4 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 5.31/5.54 => ( member3307348790968139188VEBT_o @ ( produc8721562602347293563VEBT_o @ ( nth_VEBT_VEBT @ Xs2 @ N4 ) @ ( nth_o @ Ys @ N4 ) ) @ R3 ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % listrel_iff_nth
% 5.31/5.54 thf(fact_2954_listrel__iff__nth,axiom,
% 5.31/5.54 ! [Xs2: list_VEBT_VEBT,Ys: list_nat,R3: set_Pr7556676689462069481BT_nat] :
% 5.31/5.54 ( ( member6193324644334088288st_nat @ ( produc5570133714943300547st_nat @ Xs2 @ Ys ) @ ( listre5900670229112895443BT_nat @ R3 ) )
% 5.31/5.54 = ( ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 5.31/5.54 = ( size_size_list_nat @ Ys ) )
% 5.31/5.54 & ! [N4: nat] :
% 5.31/5.54 ( ( ord_less_nat @ N4 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 5.31/5.54 => ( member373505688050248522BT_nat @ ( produc738532404422230701BT_nat @ ( nth_VEBT_VEBT @ Xs2 @ N4 ) @ ( nth_nat @ Ys @ N4 ) ) @ R3 ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % listrel_iff_nth
% 5.31/5.54 thf(fact_2955_listrel__iff__nth,axiom,
% 5.31/5.54 ! [Xs2: list_VEBT_VEBT,Ys: list_int,R3: set_Pr5066593544530342725BT_int] :
% 5.31/5.54 ( ( member3703241499402361532st_int @ ( produc1392282695434103839st_int @ Xs2 @ Ys ) @ ( listre5898179758603845167BT_int @ R3 ) )
% 5.31/5.54 = ( ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 5.31/5.54 = ( size_size_list_int @ Ys ) )
% 5.31/5.54 & ! [N4: nat] :
% 5.31/5.54 ( ( ord_less_nat @ N4 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 5.31/5.54 => ( member5419026705395827622BT_int @ ( produc736041933913180425BT_int @ ( nth_VEBT_VEBT @ Xs2 @ N4 ) @ ( nth_int @ Ys @ N4 ) ) @ R3 ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % listrel_iff_nth
% 5.31/5.54 thf(fact_2956_listrel__iff__nth,axiom,
% 5.31/5.54 ! [Xs2: list_o,Ys: list_VEBT_VEBT,R3: set_Pr7543698050874017315T_VEBT] :
% 5.31/5.54 ( ( member1087064965665443052T_VEBT @ ( produc6043759678074843571T_VEBT @ Xs2 @ Ys ) @ ( listrel_o_VEBT_VEBT @ R3 ) )
% 5.31/5.54 = ( ( ( size_size_list_o @ Xs2 )
% 5.31/5.54 = ( size_s6755466524823107622T_VEBT @ Ys ) )
% 5.31/5.54 & ! [N4: nat] :
% 5.31/5.54 ( ( ord_less_nat @ N4 @ ( size_size_list_o @ Xs2 ) )
% 5.31/5.54 => ( member5477980866518848620T_VEBT @ ( produc2982872950893828659T_VEBT @ ( nth_o @ Xs2 @ N4 ) @ ( nth_VEBT_VEBT @ Ys @ N4 ) ) @ R3 ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % listrel_iff_nth
% 5.31/5.54 thf(fact_2957_listrel__iff__nth,axiom,
% 5.31/5.54 ! [Xs2: list_o,Ys: list_o,R3: set_Product_prod_o_o] :
% 5.31/5.54 ( ( member4159035015898711888list_o @ ( produc8435520187683070743list_o @ Xs2 @ Ys ) @ ( listrel_o_o @ R3 ) )
% 5.31/5.54 = ( ( ( size_size_list_o @ Xs2 )
% 5.31/5.54 = ( size_size_list_o @ Ys ) )
% 5.31/5.54 & ! [N4: nat] :
% 5.31/5.54 ( ( ord_less_nat @ N4 @ ( size_size_list_o @ Xs2 ) )
% 5.31/5.54 => ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ ( nth_o @ Xs2 @ N4 ) @ ( nth_o @ Ys @ N4 ) ) @ R3 ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % listrel_iff_nth
% 5.31/5.54 thf(fact_2958_listrel__iff__nth,axiom,
% 5.31/5.54 ! [Xs2: list_o,Ys: list_nat,R3: set_Pr2101469702781467981_o_nat] :
% 5.31/5.54 ( ( member1519744053835550788st_nat @ ( produc7128876500814652583st_nat @ Xs2 @ Ys ) @ ( listrel_o_nat @ R3 ) )
% 5.31/5.54 = ( ( ( size_size_list_o @ Xs2 )
% 5.31/5.54 = ( size_size_list_nat @ Ys ) )
% 5.31/5.54 & ! [N4: nat] :
% 5.31/5.54 ( ( ord_less_nat @ N4 @ ( size_size_list_o @ Xs2 ) )
% 5.31/5.54 => ( member2802428098988154798_o_nat @ ( product_Pair_o_nat @ ( nth_o @ Xs2 @ N4 ) @ ( nth_nat @ Ys @ N4 ) ) @ R3 ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % listrel_iff_nth
% 5.31/5.54 thf(fact_2959_listrel__iff__nth,axiom,
% 5.31/5.54 ! [Xs2: list_o,Ys: list_int,R3: set_Pr8834758594704517033_o_int] :
% 5.31/5.54 ( ( member8253032945758599840st_int @ ( produc2951025481305455875st_int @ Xs2 @ Ys ) @ ( listrel_o_int @ R3 ) )
% 5.31/5.54 = ( ( ( size_size_list_o @ Xs2 )
% 5.31/5.54 = ( size_size_list_int @ Ys ) )
% 5.31/5.54 & ! [N4: nat] :
% 5.31/5.54 ( ( ord_less_nat @ N4 @ ( size_size_list_o @ Xs2 ) )
% 5.31/5.54 => ( member7847949116333733898_o_int @ ( product_Pair_o_int @ ( nth_o @ Xs2 @ N4 ) @ ( nth_int @ Ys @ N4 ) ) @ R3 ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % listrel_iff_nth
% 5.31/5.54 thf(fact_2960_listrel__iff__nth,axiom,
% 5.31/5.54 ! [Xs2: list_nat,Ys: list_VEBT_VEBT,R3: set_Pr6167073792073659919T_VEBT] :
% 5.31/5.54 ( ( member5968030670617646438T_VEBT @ ( produc8335345208264861441T_VEBT @ Xs2 @ Ys ) @ ( listre5761932458788874033T_VEBT @ R3 ) )
% 5.31/5.54 = ( ( ( size_size_list_nat @ Xs2 )
% 5.31/5.54 = ( size_s6755466524823107622T_VEBT @ Ys ) )
% 5.31/5.54 & ! [N4: nat] :
% 5.31/5.54 ( ( ord_less_nat @ N4 @ ( size_size_list_nat @ Xs2 ) )
% 5.31/5.54 => ( member8549952807677709168T_VEBT @ ( produc599794634098209291T_VEBT @ ( nth_nat @ Xs2 @ N4 ) @ ( nth_VEBT_VEBT @ Ys @ N4 ) ) @ R3 ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % listrel_iff_nth
% 5.31/5.54 thf(fact_2961_in__measures_I2_J,axiom,
% 5.31/5.54 ! [X: code_integer,Y: code_integer,F2: code_integer > nat,Fs: list_C4705013386053401436er_nat] :
% 5.31/5.54 ( ( member157494554546826820nteger @ ( produc1086072967326762835nteger @ X @ Y ) @ ( measur8870801148506250077nteger @ ( cons_C1897838848541180310er_nat @ F2 @ Fs ) ) )
% 5.31/5.54 = ( ( ord_less_nat @ ( F2 @ X ) @ ( F2 @ Y ) )
% 5.31/5.54 | ( ( ( F2 @ X )
% 5.31/5.54 = ( F2 @ Y ) )
% 5.31/5.54 & ( member157494554546826820nteger @ ( produc1086072967326762835nteger @ X @ Y ) @ ( measur8870801148506250077nteger @ Fs ) ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % in_measures(2)
% 5.31/5.54 thf(fact_2962_in__measures_I2_J,axiom,
% 5.31/5.54 ! [X: product_prod_nat_nat,Y: product_prod_nat_nat,F2: product_prod_nat_nat > nat,Fs: list_P9162950289778280392at_nat] :
% 5.31/5.54 ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X @ Y ) @ ( measur2679027848233739777at_nat @ ( cons_P4861729644591583992at_nat @ F2 @ Fs ) ) )
% 5.31/5.54 = ( ( ord_less_nat @ ( F2 @ X ) @ ( F2 @ Y ) )
% 5.31/5.54 | ( ( ( F2 @ X )
% 5.31/5.54 = ( F2 @ Y ) )
% 5.31/5.54 & ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X @ Y ) @ ( measur2679027848233739777at_nat @ Fs ) ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % in_measures(2)
% 5.31/5.54 thf(fact_2963_in__measures_I2_J,axiom,
% 5.31/5.54 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,F2: set_Pr1261947904930325089at_nat > nat,Fs: list_s9130966667114977576at_nat] :
% 5.31/5.54 ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X @ Y ) @ ( measur2694323259624372065at_nat @ ( cons_s2538900923071588440at_nat @ F2 @ Fs ) ) )
% 5.31/5.54 = ( ( ord_less_nat @ ( F2 @ X ) @ ( F2 @ Y ) )
% 5.31/5.54 | ( ( ( F2 @ X )
% 5.31/5.54 = ( F2 @ Y ) )
% 5.31/5.54 & ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X @ Y ) @ ( measur2694323259624372065at_nat @ Fs ) ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % in_measures(2)
% 5.31/5.54 thf(fact_2964_in__measures_I2_J,axiom,
% 5.31/5.54 ! [X: nat,Y: nat,F2: nat > nat,Fs: list_nat_nat] :
% 5.31/5.54 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ ( measures_nat @ ( cons_nat_nat @ F2 @ Fs ) ) )
% 5.31/5.54 = ( ( ord_less_nat @ ( F2 @ X ) @ ( F2 @ Y ) )
% 5.31/5.54 | ( ( ( F2 @ X )
% 5.31/5.54 = ( F2 @ Y ) )
% 5.31/5.54 & ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ ( measures_nat @ Fs ) ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % in_measures(2)
% 5.31/5.54 thf(fact_2965_in__measures_I2_J,axiom,
% 5.31/5.54 ! [X: int,Y: int,F2: int > nat,Fs: list_int_nat] :
% 5.31/5.54 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y ) @ ( measures_int @ ( cons_int_nat @ F2 @ Fs ) ) )
% 5.31/5.54 = ( ( ord_less_nat @ ( F2 @ X ) @ ( F2 @ Y ) )
% 5.31/5.54 | ( ( ( F2 @ X )
% 5.31/5.54 = ( F2 @ Y ) )
% 5.31/5.54 & ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y ) @ ( measures_int @ Fs ) ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % in_measures(2)
% 5.31/5.54 thf(fact_2966_of__nat__zero__less__power__iff,axiom,
% 5.31/5.54 ! [X: nat,N: nat] :
% 5.31/5.54 ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ ( semiri681578069525770553at_rat @ X ) @ N ) )
% 5.31/5.54 = ( ( ord_less_nat @ zero_zero_nat @ X )
% 5.31/5.54 | ( N = zero_zero_nat ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % of_nat_zero_less_power_iff
% 5.31/5.54 thf(fact_2967_of__nat__zero__less__power__iff,axiom,
% 5.31/5.54 ! [X: nat,N: nat] :
% 5.31/5.54 ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ ( semiri5074537144036343181t_real @ X ) @ N ) )
% 5.31/5.54 = ( ( ord_less_nat @ zero_zero_nat @ X )
% 5.31/5.54 | ( N = zero_zero_nat ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % of_nat_zero_less_power_iff
% 5.31/5.54 thf(fact_2968_of__nat__zero__less__power__iff,axiom,
% 5.31/5.54 ! [X: nat,N: nat] :
% 5.31/5.54 ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ ( semiri1314217659103216013at_int @ X ) @ N ) )
% 5.31/5.54 = ( ( ord_less_nat @ zero_zero_nat @ X )
% 5.31/5.54 | ( N = zero_zero_nat ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % of_nat_zero_less_power_iff
% 5.31/5.54 thf(fact_2969_of__nat__zero__less__power__iff,axiom,
% 5.31/5.54 ! [X: nat,N: nat] :
% 5.31/5.54 ( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ X ) @ N ) )
% 5.31/5.54 = ( ( ord_less_nat @ zero_zero_nat @ X )
% 5.31/5.54 | ( N = zero_zero_nat ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % of_nat_zero_less_power_iff
% 5.31/5.54 thf(fact_2970__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062treeList_H_Asummary_H_Ainfo_O_As_A_061_ANode_Ainfo_Adeg_AtreeList_H_Asummary_H_A_092_060and_062_Adeg_A_061_An_A_L_Am_A_092_060and_062_Alength_AtreeList_H_A_061_A2_A_094_Am_A_092_060and_062_Ainvar__vebt_Asummary_H_Am_A_092_060and_062_A_I_092_060forall_062t_092_060in_062set_AtreeList_H_O_Ainvar__vebt_At_An_J_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
% 5.31/5.54 ~ ! [TreeList3: list_VEBT_VEBT,Summary3: vEBT_VEBT,Info: option4927543243414619207at_nat] :
% 5.31/5.54 ~ ( ( sa
% 5.31/5.54 = ( vEBT_Node @ Info @ deg @ TreeList3 @ Summary3 ) )
% 5.31/5.54 & ( deg
% 5.31/5.54 = ( plus_plus_nat @ na @ m ) )
% 5.31/5.54 & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 5.31/5.54 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) )
% 5.31/5.54 & ( vEBT_invar_vebt @ Summary3 @ m )
% 5.31/5.54 & ! [X5: vEBT_VEBT] :
% 5.31/5.54 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.31/5.54 => ( vEBT_invar_vebt @ X5 @ na ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % \<open>\<And>thesis. (\<And>treeList' summary' info. s = Node info deg treeList' summary' \<and> deg = n + m \<and> length treeList' = 2 ^ m \<and> invar_vebt summary' m \<and> (\<forall>t\<in>set treeList'. invar_vebt t n) \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
% 5.31/5.54 thf(fact_2971_intind,axiom,
% 5.31/5.54 ! [I2: nat,N: nat,P2: nat > $o,X: nat] :
% 5.31/5.54 ( ( ord_less_nat @ I2 @ N )
% 5.31/5.54 => ( ( P2 @ X )
% 5.31/5.54 => ( P2 @ ( nth_nat @ ( replicate_nat @ N @ X ) @ I2 ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % intind
% 5.31/5.54 thf(fact_2972_intind,axiom,
% 5.31/5.54 ! [I2: nat,N: nat,P2: vEBT_VEBT > $o,X: vEBT_VEBT] :
% 5.31/5.54 ( ( ord_less_nat @ I2 @ N )
% 5.31/5.54 => ( ( P2 @ X )
% 5.31/5.54 => ( P2 @ ( nth_VEBT_VEBT @ ( replicate_VEBT_VEBT @ N @ X ) @ I2 ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % intind
% 5.31/5.54 thf(fact_2973_numeral__eq__iff,axiom,
% 5.31/5.54 ! [M2: num,N: num] :
% 5.31/5.54 ( ( ( numera1916890842035813515d_enat @ M2 )
% 5.31/5.54 = ( numera1916890842035813515d_enat @ N ) )
% 5.31/5.54 = ( M2 = N ) ) ).
% 5.31/5.54
% 5.31/5.54 % numeral_eq_iff
% 5.31/5.54 thf(fact_2974_numeral__eq__iff,axiom,
% 5.31/5.54 ! [M2: num,N: num] :
% 5.31/5.54 ( ( ( numera6690914467698888265omplex @ M2 )
% 5.31/5.54 = ( numera6690914467698888265omplex @ N ) )
% 5.31/5.54 = ( M2 = N ) ) ).
% 5.31/5.54
% 5.31/5.54 % numeral_eq_iff
% 5.31/5.54 thf(fact_2975_numeral__eq__iff,axiom,
% 5.31/5.54 ! [M2: num,N: num] :
% 5.31/5.54 ( ( ( numeral_numeral_real @ M2 )
% 5.31/5.54 = ( numeral_numeral_real @ N ) )
% 5.31/5.54 = ( M2 = N ) ) ).
% 5.31/5.54
% 5.31/5.54 % numeral_eq_iff
% 5.31/5.54 thf(fact_2976_numeral__eq__iff,axiom,
% 5.31/5.54 ! [M2: num,N: num] :
% 5.31/5.54 ( ( ( numeral_numeral_nat @ M2 )
% 5.31/5.54 = ( numeral_numeral_nat @ N ) )
% 5.31/5.54 = ( M2 = N ) ) ).
% 5.31/5.54
% 5.31/5.54 % numeral_eq_iff
% 5.31/5.54 thf(fact_2977_numeral__eq__iff,axiom,
% 5.31/5.54 ! [M2: num,N: num] :
% 5.31/5.54 ( ( ( numeral_numeral_int @ M2 )
% 5.31/5.54 = ( numeral_numeral_int @ N ) )
% 5.31/5.54 = ( M2 = N ) ) ).
% 5.31/5.54
% 5.31/5.54 % numeral_eq_iff
% 5.31/5.54 thf(fact_2978_semiring__norm_I13_J,axiom,
% 5.31/5.54 ! [M2: num,N: num] :
% 5.31/5.54 ( ( times_times_num @ ( bit0 @ M2 ) @ ( bit0 @ N ) )
% 5.31/5.54 = ( bit0 @ ( bit0 @ ( times_times_num @ M2 @ N ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % semiring_norm(13)
% 5.31/5.54 thf(fact_2979_semiring__norm_I11_J,axiom,
% 5.31/5.54 ! [M2: num] :
% 5.31/5.54 ( ( times_times_num @ M2 @ one )
% 5.31/5.54 = M2 ) ).
% 5.31/5.54
% 5.31/5.54 % semiring_norm(11)
% 5.31/5.54 thf(fact_2980_semiring__norm_I12_J,axiom,
% 5.31/5.54 ! [N: num] :
% 5.31/5.54 ( ( times_times_num @ one @ N )
% 5.31/5.54 = N ) ).
% 5.31/5.54
% 5.31/5.54 % semiring_norm(12)
% 5.31/5.54 thf(fact_2981_case4_I10_J,axiom,
% 5.31/5.54 ord_less_nat @ ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ deg ) ).
% 5.31/5.54
% 5.31/5.54 % case4(10)
% 5.31/5.54 thf(fact_2982_case4_I4_J,axiom,
% 5.31/5.54 ( ( size_s6755466524823107622T_VEBT @ treeList2 )
% 5.31/5.54 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) ) ).
% 5.31/5.54
% 5.31/5.54 % case4(4)
% 5.31/5.54 thf(fact_2983_of__nat__eq__iff,axiom,
% 5.31/5.54 ! [M2: nat,N: nat] :
% 5.31/5.54 ( ( ( semiri5074537144036343181t_real @ M2 )
% 5.31/5.54 = ( semiri5074537144036343181t_real @ N ) )
% 5.31/5.54 = ( M2 = N ) ) ).
% 5.31/5.54
% 5.31/5.54 % of_nat_eq_iff
% 5.31/5.54 thf(fact_2984_of__nat__eq__iff,axiom,
% 5.31/5.54 ! [M2: nat,N: nat] :
% 5.31/5.54 ( ( ( semiri1314217659103216013at_int @ M2 )
% 5.31/5.54 = ( semiri1314217659103216013at_int @ N ) )
% 5.31/5.54 = ( M2 = N ) ) ).
% 5.31/5.54
% 5.31/5.54 % of_nat_eq_iff
% 5.31/5.54 thf(fact_2985_of__nat__eq__iff,axiom,
% 5.31/5.54 ! [M2: nat,N: nat] :
% 5.31/5.54 ( ( ( semiri1316708129612266289at_nat @ M2 )
% 5.31/5.54 = ( semiri1316708129612266289at_nat @ N ) )
% 5.31/5.54 = ( M2 = N ) ) ).
% 5.31/5.54
% 5.31/5.54 % of_nat_eq_iff
% 5.31/5.54 thf(fact_2986_a0,axiom,
% 5.31/5.54 ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ deg ).
% 5.31/5.54
% 5.31/5.54 % a0
% 5.31/5.54 thf(fact_2987_case4_I7_J,axiom,
% 5.31/5.54 ! [I4: nat] :
% 5.31/5.54 ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) )
% 5.31/5.54 => ( ( ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList2 @ I4 ) @ X7 ) )
% 5.31/5.54 = ( vEBT_V8194947554948674370ptions @ summary2 @ I4 ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % case4(7)
% 5.31/5.54 thf(fact_2988_member__bound,axiom,
% 5.31/5.54 ! [Tree: vEBT_VEBT,X: nat,N: nat] :
% 5.31/5.54 ( ( vEBT_vebt_member @ Tree @ X )
% 5.31/5.54 => ( ( vEBT_invar_vebt @ Tree @ N )
% 5.31/5.54 => ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % member_bound
% 5.31/5.54 thf(fact_2989_valid__pres__insert,axiom,
% 5.31/5.54 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 5.31/5.54 ( ( vEBT_invar_vebt @ T @ N )
% 5.31/5.54 => ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.31/5.54 => ( vEBT_invar_vebt @ ( vEBT_vebt_insert @ T @ X ) @ N ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % valid_pres_insert
% 5.31/5.54 thf(fact_2990_numeral__le__iff,axiom,
% 5.31/5.54 ! [M2: num,N: num] :
% 5.31/5.54 ( ( ord_le2932123472753598470d_enat @ ( numera1916890842035813515d_enat @ M2 ) @ ( numera1916890842035813515d_enat @ N ) )
% 5.31/5.54 = ( ord_less_eq_num @ M2 @ N ) ) ).
% 5.31/5.54
% 5.31/5.54 % numeral_le_iff
% 5.31/5.54 thf(fact_2991_numeral__le__iff,axiom,
% 5.31/5.54 ! [M2: num,N: num] :
% 5.31/5.54 ( ( ord_less_eq_real @ ( numeral_numeral_real @ M2 ) @ ( numeral_numeral_real @ N ) )
% 5.31/5.54 = ( ord_less_eq_num @ M2 @ N ) ) ).
% 5.31/5.54
% 5.31/5.54 % numeral_le_iff
% 5.31/5.54 thf(fact_2992_numeral__le__iff,axiom,
% 5.31/5.54 ! [M2: num,N: num] :
% 5.31/5.54 ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ M2 ) @ ( numeral_numeral_rat @ N ) )
% 5.31/5.54 = ( ord_less_eq_num @ M2 @ N ) ) ).
% 5.31/5.54
% 5.31/5.54 % numeral_le_iff
% 5.31/5.54 thf(fact_2993_numeral__le__iff,axiom,
% 5.31/5.54 ! [M2: num,N: num] :
% 5.31/5.54 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ M2 ) @ ( numeral_numeral_nat @ N ) )
% 5.31/5.54 = ( ord_less_eq_num @ M2 @ N ) ) ).
% 5.31/5.54
% 5.31/5.54 % numeral_le_iff
% 5.31/5.54 thf(fact_2994_numeral__le__iff,axiom,
% 5.31/5.54 ! [M2: num,N: num] :
% 5.31/5.54 ( ( ord_less_eq_int @ ( numeral_numeral_int @ M2 ) @ ( numeral_numeral_int @ N ) )
% 5.31/5.54 = ( ord_less_eq_num @ M2 @ N ) ) ).
% 5.31/5.54
% 5.31/5.54 % numeral_le_iff
% 5.31/5.54 thf(fact_2995_numeral__less__iff,axiom,
% 5.31/5.54 ! [M2: num,N: num] :
% 5.31/5.54 ( ( ord_less_rat @ ( numeral_numeral_rat @ M2 ) @ ( numeral_numeral_rat @ N ) )
% 5.31/5.54 = ( ord_less_num @ M2 @ N ) ) ).
% 5.31/5.54
% 5.31/5.54 % numeral_less_iff
% 5.31/5.54 thf(fact_2996_numeral__less__iff,axiom,
% 5.31/5.54 ! [M2: num,N: num] :
% 5.31/5.54 ( ( ord_le72135733267957522d_enat @ ( numera1916890842035813515d_enat @ M2 ) @ ( numera1916890842035813515d_enat @ N ) )
% 5.31/5.54 = ( ord_less_num @ M2 @ N ) ) ).
% 5.31/5.54
% 5.31/5.54 % numeral_less_iff
% 5.31/5.54 thf(fact_2997_numeral__less__iff,axiom,
% 5.31/5.54 ! [M2: num,N: num] :
% 5.31/5.54 ( ( ord_less_real @ ( numeral_numeral_real @ M2 ) @ ( numeral_numeral_real @ N ) )
% 5.31/5.54 = ( ord_less_num @ M2 @ N ) ) ).
% 5.31/5.54
% 5.31/5.54 % numeral_less_iff
% 5.31/5.54 thf(fact_2998_numeral__less__iff,axiom,
% 5.31/5.54 ! [M2: num,N: num] :
% 5.31/5.54 ( ( ord_less_nat @ ( numeral_numeral_nat @ M2 ) @ ( numeral_numeral_nat @ N ) )
% 5.31/5.54 = ( ord_less_num @ M2 @ N ) ) ).
% 5.31/5.54
% 5.31/5.54 % numeral_less_iff
% 5.31/5.54 thf(fact_2999_numeral__less__iff,axiom,
% 5.31/5.54 ! [M2: num,N: num] :
% 5.31/5.54 ( ( ord_less_int @ ( numeral_numeral_int @ M2 ) @ ( numeral_numeral_int @ N ) )
% 5.31/5.54 = ( ord_less_num @ M2 @ N ) ) ).
% 5.31/5.54
% 5.31/5.54 % numeral_less_iff
% 5.31/5.54 thf(fact_3000_numeral__times__numeral,axiom,
% 5.31/5.54 ! [M2: num,N: num] :
% 5.31/5.54 ( ( times_times_rat @ ( numeral_numeral_rat @ M2 ) @ ( numeral_numeral_rat @ N ) )
% 5.31/5.54 = ( numeral_numeral_rat @ ( times_times_num @ M2 @ N ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % numeral_times_numeral
% 5.31/5.54 thf(fact_3001_numeral__times__numeral,axiom,
% 5.31/5.54 ! [M2: num,N: num] :
% 5.31/5.54 ( ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ M2 ) @ ( numera1916890842035813515d_enat @ N ) )
% 5.31/5.54 = ( numera1916890842035813515d_enat @ ( times_times_num @ M2 @ N ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % numeral_times_numeral
% 5.31/5.54 thf(fact_3002_numeral__times__numeral,axiom,
% 5.31/5.54 ! [M2: num,N: num] :
% 5.31/5.54 ( ( times_times_complex @ ( numera6690914467698888265omplex @ M2 ) @ ( numera6690914467698888265omplex @ N ) )
% 5.31/5.54 = ( numera6690914467698888265omplex @ ( times_times_num @ M2 @ N ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % numeral_times_numeral
% 5.31/5.54 thf(fact_3003_numeral__times__numeral,axiom,
% 5.31/5.54 ! [M2: num,N: num] :
% 5.31/5.54 ( ( times_times_real @ ( numeral_numeral_real @ M2 ) @ ( numeral_numeral_real @ N ) )
% 5.31/5.54 = ( numeral_numeral_real @ ( times_times_num @ M2 @ N ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % numeral_times_numeral
% 5.31/5.54 thf(fact_3004_numeral__times__numeral,axiom,
% 5.31/5.54 ! [M2: num,N: num] :
% 5.31/5.54 ( ( times_times_nat @ ( numeral_numeral_nat @ M2 ) @ ( numeral_numeral_nat @ N ) )
% 5.31/5.54 = ( numeral_numeral_nat @ ( times_times_num @ M2 @ N ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % numeral_times_numeral
% 5.31/5.54 thf(fact_3005_numeral__times__numeral,axiom,
% 5.31/5.54 ! [M2: num,N: num] :
% 5.31/5.54 ( ( times_times_int @ ( numeral_numeral_int @ M2 ) @ ( numeral_numeral_int @ N ) )
% 5.31/5.54 = ( numeral_numeral_int @ ( times_times_num @ M2 @ N ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % numeral_times_numeral
% 5.31/5.54 thf(fact_3006_mult__numeral__left__semiring__numeral,axiom,
% 5.31/5.54 ! [V2: num,W2: num,Z3: rat] :
% 5.31/5.54 ( ( times_times_rat @ ( numeral_numeral_rat @ V2 ) @ ( times_times_rat @ ( numeral_numeral_rat @ W2 ) @ Z3 ) )
% 5.31/5.54 = ( times_times_rat @ ( numeral_numeral_rat @ ( times_times_num @ V2 @ W2 ) ) @ Z3 ) ) ).
% 5.31/5.54
% 5.31/5.54 % mult_numeral_left_semiring_numeral
% 5.31/5.54 thf(fact_3007_mult__numeral__left__semiring__numeral,axiom,
% 5.31/5.54 ! [V2: num,W2: num,Z3: extended_enat] :
% 5.31/5.54 ( ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ V2 ) @ ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ W2 ) @ Z3 ) )
% 5.31/5.54 = ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ ( times_times_num @ V2 @ W2 ) ) @ Z3 ) ) ).
% 5.31/5.54
% 5.31/5.54 % mult_numeral_left_semiring_numeral
% 5.31/5.54 thf(fact_3008_mult__numeral__left__semiring__numeral,axiom,
% 5.31/5.54 ! [V2: num,W2: num,Z3: complex] :
% 5.31/5.54 ( ( times_times_complex @ ( numera6690914467698888265omplex @ V2 ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ W2 ) @ Z3 ) )
% 5.31/5.54 = ( times_times_complex @ ( numera6690914467698888265omplex @ ( times_times_num @ V2 @ W2 ) ) @ Z3 ) ) ).
% 5.31/5.54
% 5.31/5.54 % mult_numeral_left_semiring_numeral
% 5.31/5.54 thf(fact_3009_mult__numeral__left__semiring__numeral,axiom,
% 5.31/5.54 ! [V2: num,W2: num,Z3: real] :
% 5.31/5.54 ( ( times_times_real @ ( numeral_numeral_real @ V2 ) @ ( times_times_real @ ( numeral_numeral_real @ W2 ) @ Z3 ) )
% 5.31/5.54 = ( times_times_real @ ( numeral_numeral_real @ ( times_times_num @ V2 @ W2 ) ) @ Z3 ) ) ).
% 5.31/5.54
% 5.31/5.54 % mult_numeral_left_semiring_numeral
% 5.31/5.54 thf(fact_3010_mult__numeral__left__semiring__numeral,axiom,
% 5.31/5.54 ! [V2: num,W2: num,Z3: nat] :
% 5.31/5.54 ( ( times_times_nat @ ( numeral_numeral_nat @ V2 ) @ ( times_times_nat @ ( numeral_numeral_nat @ W2 ) @ Z3 ) )
% 5.31/5.54 = ( times_times_nat @ ( numeral_numeral_nat @ ( times_times_num @ V2 @ W2 ) ) @ Z3 ) ) ).
% 5.31/5.54
% 5.31/5.54 % mult_numeral_left_semiring_numeral
% 5.31/5.54 thf(fact_3011_mult__numeral__left__semiring__numeral,axiom,
% 5.31/5.54 ! [V2: num,W2: num,Z3: int] :
% 5.31/5.54 ( ( times_times_int @ ( numeral_numeral_int @ V2 ) @ ( times_times_int @ ( numeral_numeral_int @ W2 ) @ Z3 ) )
% 5.31/5.54 = ( times_times_int @ ( numeral_numeral_int @ ( times_times_num @ V2 @ W2 ) ) @ Z3 ) ) ).
% 5.31/5.54
% 5.31/5.54 % mult_numeral_left_semiring_numeral
% 5.31/5.54 thf(fact_3012_add__numeral__left,axiom,
% 5.31/5.54 ! [V2: num,W2: num,Z3: rat] :
% 5.31/5.54 ( ( plus_plus_rat @ ( numeral_numeral_rat @ V2 ) @ ( plus_plus_rat @ ( numeral_numeral_rat @ W2 ) @ Z3 ) )
% 5.31/5.54 = ( plus_plus_rat @ ( numeral_numeral_rat @ ( plus_plus_num @ V2 @ W2 ) ) @ Z3 ) ) ).
% 5.31/5.54
% 5.31/5.54 % add_numeral_left
% 5.31/5.54 thf(fact_3013_add__numeral__left,axiom,
% 5.31/5.54 ! [V2: num,W2: num,Z3: extended_enat] :
% 5.31/5.54 ( ( plus_p3455044024723400733d_enat @ ( numera1916890842035813515d_enat @ V2 ) @ ( plus_p3455044024723400733d_enat @ ( numera1916890842035813515d_enat @ W2 ) @ Z3 ) )
% 5.31/5.54 = ( plus_p3455044024723400733d_enat @ ( numera1916890842035813515d_enat @ ( plus_plus_num @ V2 @ W2 ) ) @ Z3 ) ) ).
% 5.31/5.54
% 5.31/5.54 % add_numeral_left
% 5.31/5.54 thf(fact_3014_add__numeral__left,axiom,
% 5.31/5.54 ! [V2: num,W2: num,Z3: complex] :
% 5.31/5.54 ( ( plus_plus_complex @ ( numera6690914467698888265omplex @ V2 ) @ ( plus_plus_complex @ ( numera6690914467698888265omplex @ W2 ) @ Z3 ) )
% 5.31/5.54 = ( plus_plus_complex @ ( numera6690914467698888265omplex @ ( plus_plus_num @ V2 @ W2 ) ) @ Z3 ) ) ).
% 5.31/5.54
% 5.31/5.54 % add_numeral_left
% 5.31/5.54 thf(fact_3015_add__numeral__left,axiom,
% 5.31/5.54 ! [V2: num,W2: num,Z3: real] :
% 5.31/5.54 ( ( plus_plus_real @ ( numeral_numeral_real @ V2 ) @ ( plus_plus_real @ ( numeral_numeral_real @ W2 ) @ Z3 ) )
% 5.31/5.54 = ( plus_plus_real @ ( numeral_numeral_real @ ( plus_plus_num @ V2 @ W2 ) ) @ Z3 ) ) ).
% 5.31/5.54
% 5.31/5.54 % add_numeral_left
% 5.31/5.54 thf(fact_3016_add__numeral__left,axiom,
% 5.31/5.54 ! [V2: num,W2: num,Z3: nat] :
% 5.31/5.54 ( ( plus_plus_nat @ ( numeral_numeral_nat @ V2 ) @ ( plus_plus_nat @ ( numeral_numeral_nat @ W2 ) @ Z3 ) )
% 5.31/5.54 = ( plus_plus_nat @ ( numeral_numeral_nat @ ( plus_plus_num @ V2 @ W2 ) ) @ Z3 ) ) ).
% 5.31/5.54
% 5.31/5.54 % add_numeral_left
% 5.31/5.54 thf(fact_3017_add__numeral__left,axiom,
% 5.31/5.54 ! [V2: num,W2: num,Z3: int] :
% 5.31/5.54 ( ( plus_plus_int @ ( numeral_numeral_int @ V2 ) @ ( plus_plus_int @ ( numeral_numeral_int @ W2 ) @ Z3 ) )
% 5.31/5.54 = ( plus_plus_int @ ( numeral_numeral_int @ ( plus_plus_num @ V2 @ W2 ) ) @ Z3 ) ) ).
% 5.31/5.54
% 5.31/5.54 % add_numeral_left
% 5.31/5.54 thf(fact_3018_numeral__plus__numeral,axiom,
% 5.31/5.54 ! [M2: num,N: num] :
% 5.31/5.54 ( ( plus_plus_rat @ ( numeral_numeral_rat @ M2 ) @ ( numeral_numeral_rat @ N ) )
% 5.31/5.54 = ( numeral_numeral_rat @ ( plus_plus_num @ M2 @ N ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % numeral_plus_numeral
% 5.31/5.54 thf(fact_3019_numeral__plus__numeral,axiom,
% 5.31/5.54 ! [M2: num,N: num] :
% 5.31/5.54 ( ( plus_p3455044024723400733d_enat @ ( numera1916890842035813515d_enat @ M2 ) @ ( numera1916890842035813515d_enat @ N ) )
% 5.31/5.54 = ( numera1916890842035813515d_enat @ ( plus_plus_num @ M2 @ N ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % numeral_plus_numeral
% 5.31/5.54 thf(fact_3020_numeral__plus__numeral,axiom,
% 5.31/5.54 ! [M2: num,N: num] :
% 5.31/5.54 ( ( plus_plus_complex @ ( numera6690914467698888265omplex @ M2 ) @ ( numera6690914467698888265omplex @ N ) )
% 5.31/5.54 = ( numera6690914467698888265omplex @ ( plus_plus_num @ M2 @ N ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % numeral_plus_numeral
% 5.31/5.54 thf(fact_3021_numeral__plus__numeral,axiom,
% 5.31/5.54 ! [M2: num,N: num] :
% 5.31/5.54 ( ( plus_plus_real @ ( numeral_numeral_real @ M2 ) @ ( numeral_numeral_real @ N ) )
% 5.31/5.54 = ( numeral_numeral_real @ ( plus_plus_num @ M2 @ N ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % numeral_plus_numeral
% 5.31/5.54 thf(fact_3022_numeral__plus__numeral,axiom,
% 5.31/5.54 ! [M2: num,N: num] :
% 5.31/5.54 ( ( plus_plus_nat @ ( numeral_numeral_nat @ M2 ) @ ( numeral_numeral_nat @ N ) )
% 5.31/5.54 = ( numeral_numeral_nat @ ( plus_plus_num @ M2 @ N ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % numeral_plus_numeral
% 5.31/5.54 thf(fact_3023_numeral__plus__numeral,axiom,
% 5.31/5.54 ! [M2: num,N: num] :
% 5.31/5.54 ( ( plus_plus_int @ ( numeral_numeral_int @ M2 ) @ ( numeral_numeral_int @ N ) )
% 5.31/5.54 = ( numeral_numeral_int @ ( plus_plus_num @ M2 @ N ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % numeral_plus_numeral
% 5.31/5.54 thf(fact_3024_num__double,axiom,
% 5.31/5.54 ! [N: num] :
% 5.31/5.54 ( ( times_times_num @ ( bit0 @ one ) @ N )
% 5.31/5.54 = ( bit0 @ N ) ) ).
% 5.31/5.54
% 5.31/5.54 % num_double
% 5.31/5.54 thf(fact_3025_power__mult__numeral,axiom,
% 5.31/5.54 ! [A: nat,M2: num,N: num] :
% 5.31/5.54 ( ( power_power_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ M2 ) ) @ ( numeral_numeral_nat @ N ) )
% 5.31/5.54 = ( power_power_nat @ A @ ( numeral_numeral_nat @ ( times_times_num @ M2 @ N ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % power_mult_numeral
% 5.31/5.54 thf(fact_3026_power__mult__numeral,axiom,
% 5.31/5.54 ! [A: real,M2: num,N: num] :
% 5.31/5.54 ( ( power_power_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ M2 ) ) @ ( numeral_numeral_nat @ N ) )
% 5.31/5.54 = ( power_power_real @ A @ ( numeral_numeral_nat @ ( times_times_num @ M2 @ N ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % power_mult_numeral
% 5.31/5.54 thf(fact_3027_power__mult__numeral,axiom,
% 5.31/5.54 ! [A: int,M2: num,N: num] :
% 5.31/5.54 ( ( power_power_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ M2 ) ) @ ( numeral_numeral_nat @ N ) )
% 5.31/5.54 = ( power_power_int @ A @ ( numeral_numeral_nat @ ( times_times_num @ M2 @ N ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % power_mult_numeral
% 5.31/5.54 thf(fact_3028_power__mult__numeral,axiom,
% 5.31/5.54 ! [A: complex,M2: num,N: num] :
% 5.31/5.54 ( ( power_power_complex @ ( power_power_complex @ A @ ( numeral_numeral_nat @ M2 ) ) @ ( numeral_numeral_nat @ N ) )
% 5.31/5.54 = ( power_power_complex @ A @ ( numeral_numeral_nat @ ( times_times_num @ M2 @ N ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % power_mult_numeral
% 5.31/5.54 thf(fact_3029_insert__simp__mima,axiom,
% 5.31/5.54 ! [X: nat,Mi: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.31/5.54 ( ( ( X = Mi )
% 5.31/5.54 | ( X = Ma ) )
% 5.31/5.54 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.31/5.54 => ( ( vEBT_vebt_insert @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 5.31/5.54 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % insert_simp_mima
% 5.31/5.54 thf(fact_3030_misiz,axiom,
% 5.31/5.54 ! [T: vEBT_VEBT,N: nat,M2: nat] :
% 5.31/5.54 ( ( vEBT_invar_vebt @ T @ N )
% 5.31/5.54 => ( ( ( some_nat @ M2 )
% 5.31/5.54 = ( vEBT_vebt_mint @ T ) )
% 5.31/5.54 => ( ord_less_nat @ M2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % misiz
% 5.31/5.54 thf(fact_3031_not__real__square__gt__zero,axiom,
% 5.31/5.54 ! [X: real] :
% 5.31/5.54 ( ( ~ ( ord_less_real @ zero_zero_real @ ( times_times_real @ X @ X ) ) )
% 5.31/5.54 = ( X = zero_zero_real ) ) ).
% 5.31/5.54
% 5.31/5.54 % not_real_square_gt_zero
% 5.31/5.54 thf(fact_3032_valid__insert__both__member__options__add,axiom,
% 5.31/5.54 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 5.31/5.54 ( ( vEBT_invar_vebt @ T @ N )
% 5.31/5.54 => ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.31/5.54 => ( vEBT_V8194947554948674370ptions @ ( vEBT_vebt_insert @ T @ X ) @ X ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % valid_insert_both_member_options_add
% 5.31/5.54 thf(fact_3033_valid__insert__both__member__options__pres,axiom,
% 5.31/5.54 ! [T: vEBT_VEBT,N: nat,X: nat,Y: nat] :
% 5.31/5.54 ( ( vEBT_invar_vebt @ T @ N )
% 5.31/5.54 => ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.31/5.54 => ( ( ord_less_nat @ Y @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.31/5.54 => ( ( vEBT_V8194947554948674370ptions @ T @ X )
% 5.31/5.54 => ( vEBT_V8194947554948674370ptions @ ( vEBT_vebt_insert @ T @ Y ) @ X ) ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % valid_insert_both_member_options_pres
% 5.31/5.54 thf(fact_3034_helpypredd,axiom,
% 5.31/5.54 ! [T: vEBT_VEBT,N: nat,X: nat,Y: nat] :
% 5.31/5.54 ( ( vEBT_invar_vebt @ T @ N )
% 5.31/5.54 => ( ( ( vEBT_vebt_pred @ T @ X )
% 5.31/5.54 = ( some_nat @ Y ) )
% 5.31/5.54 => ( ord_less_nat @ Y @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % helpypredd
% 5.31/5.54 thf(fact_3035_helpyd,axiom,
% 5.31/5.54 ! [T: vEBT_VEBT,N: nat,X: nat,Y: nat] :
% 5.31/5.54 ( ( vEBT_invar_vebt @ T @ N )
% 5.31/5.54 => ( ( ( vEBT_vebt_succ @ T @ X )
% 5.31/5.54 = ( some_nat @ Y ) )
% 5.31/5.54 => ( ord_less_nat @ Y @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % helpyd
% 5.31/5.54 thf(fact_3036_post__member__pre__member,axiom,
% 5.31/5.54 ! [T: vEBT_VEBT,N: nat,X: nat,Y: nat] :
% 5.31/5.54 ( ( vEBT_invar_vebt @ T @ N )
% 5.31/5.54 => ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.31/5.54 => ( ( ord_less_nat @ Y @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.31/5.54 => ( ( vEBT_vebt_member @ ( vEBT_vebt_insert @ T @ X ) @ Y )
% 5.31/5.54 => ( ( vEBT_vebt_member @ T @ Y )
% 5.31/5.54 | ( X = Y ) ) ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % post_member_pre_member
% 5.31/5.54 thf(fact_3037_replicate__eq__replicate,axiom,
% 5.31/5.54 ! [M2: nat,X: vEBT_VEBT,N: nat,Y: vEBT_VEBT] :
% 5.31/5.54 ( ( ( replicate_VEBT_VEBT @ M2 @ X )
% 5.31/5.54 = ( replicate_VEBT_VEBT @ N @ Y ) )
% 5.31/5.54 = ( ( M2 = N )
% 5.31/5.54 & ( ( M2 != zero_zero_nat )
% 5.31/5.54 => ( X = Y ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % replicate_eq_replicate
% 5.31/5.54 thf(fact_3038_length__replicate,axiom,
% 5.31/5.54 ! [N: nat,X: vEBT_VEBT] :
% 5.31/5.54 ( ( size_s6755466524823107622T_VEBT @ ( replicate_VEBT_VEBT @ N @ X ) )
% 5.31/5.54 = N ) ).
% 5.31/5.54
% 5.31/5.54 % length_replicate
% 5.31/5.54 thf(fact_3039_length__replicate,axiom,
% 5.31/5.54 ! [N: nat,X: $o] :
% 5.31/5.54 ( ( size_size_list_o @ ( replicate_o @ N @ X ) )
% 5.31/5.54 = N ) ).
% 5.31/5.54
% 5.31/5.54 % length_replicate
% 5.31/5.54 thf(fact_3040_length__replicate,axiom,
% 5.31/5.54 ! [N: nat,X: nat] :
% 5.31/5.54 ( ( size_size_list_nat @ ( replicate_nat @ N @ X ) )
% 5.31/5.54 = N ) ).
% 5.31/5.54
% 5.31/5.54 % length_replicate
% 5.31/5.54 thf(fact_3041_length__replicate,axiom,
% 5.31/5.54 ! [N: nat,X: int] :
% 5.31/5.54 ( ( size_size_list_int @ ( replicate_int @ N @ X ) )
% 5.31/5.54 = N ) ).
% 5.31/5.54
% 5.31/5.54 % length_replicate
% 5.31/5.54 thf(fact_3042_delt__out__of__range,axiom,
% 5.31/5.54 ! [X: nat,Mi: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.31/5.54 ( ( ( ord_less_nat @ X @ Mi )
% 5.31/5.54 | ( ord_less_nat @ Ma @ X ) )
% 5.31/5.54 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.31/5.54 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 5.31/5.54 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % delt_out_of_range
% 5.31/5.54 thf(fact_3043_del__single__cont,axiom,
% 5.31/5.54 ! [X: nat,Mi: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.31/5.54 ( ( ( X = Mi )
% 5.31/5.54 & ( X = Ma ) )
% 5.31/5.54 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.31/5.54 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 5.31/5.54 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg @ TreeList2 @ Summary ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % del_single_cont
% 5.31/5.54 thf(fact_3044_set__n__deg__not__0,axiom,
% 5.31/5.54 ! [TreeList2: list_VEBT_VEBT,N: nat,M2: nat] :
% 5.31/5.54 ( ! [X3: vEBT_VEBT] :
% 5.31/5.54 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.31/5.54 => ( vEBT_invar_vebt @ X3 @ N ) )
% 5.31/5.54 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 5.31/5.54 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) )
% 5.31/5.54 => ( ord_less_eq_nat @ one_one_nat @ N ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % set_n_deg_not_0
% 5.31/5.54 thf(fact_3045_mi__ma__2__deg,axiom,
% 5.31/5.54 ! [Mi: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat] :
% 5.31/5.54 ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ N )
% 5.31/5.54 => ( ( ord_less_eq_nat @ Mi @ Ma )
% 5.31/5.54 & ( ord_less_nat @ Ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % mi_ma_2_deg
% 5.31/5.54 thf(fact_3046_pred__max,axiom,
% 5.31/5.54 ! [Deg: nat,Ma: nat,X: nat,Mi: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.31/5.54 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.31/5.54 => ( ( ord_less_nat @ Ma @ X )
% 5.31/5.54 => ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 5.31/5.54 = ( some_nat @ Ma ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % pred_max
% 5.31/5.54 thf(fact_3047_succ__min,axiom,
% 5.31/5.54 ! [Deg: nat,X: nat,Mi: nat,Ma: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.31/5.54 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.31/5.54 => ( ( ord_less_nat @ X @ Mi )
% 5.31/5.54 => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 5.31/5.54 = ( some_nat @ Mi ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % succ_min
% 5.31/5.54 thf(fact_3048_bit__concat__def,axiom,
% 5.31/5.54 ( vEBT_VEBT_bit_concat
% 5.31/5.54 = ( ^ [H2: nat,L2: nat,D2: nat] : ( plus_plus_nat @ ( times_times_nat @ H2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ D2 ) ) @ L2 ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % bit_concat_def
% 5.31/5.54 thf(fact_3049_distrib__left__numeral,axiom,
% 5.31/5.54 ! [V2: num,B: rat,C2: rat] :
% 5.31/5.54 ( ( times_times_rat @ ( numeral_numeral_rat @ V2 ) @ ( plus_plus_rat @ B @ C2 ) )
% 5.31/5.54 = ( plus_plus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ V2 ) @ B ) @ ( times_times_rat @ ( numeral_numeral_rat @ V2 ) @ C2 ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % distrib_left_numeral
% 5.31/5.54 thf(fact_3050_distrib__left__numeral,axiom,
% 5.31/5.54 ! [V2: num,B: extended_enat,C2: extended_enat] :
% 5.31/5.54 ( ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ V2 ) @ ( plus_p3455044024723400733d_enat @ B @ C2 ) )
% 5.31/5.54 = ( plus_p3455044024723400733d_enat @ ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ V2 ) @ B ) @ ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ V2 ) @ C2 ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % distrib_left_numeral
% 5.31/5.54 thf(fact_3051_distrib__left__numeral,axiom,
% 5.31/5.54 ! [V2: num,B: complex,C2: complex] :
% 5.31/5.54 ( ( times_times_complex @ ( numera6690914467698888265omplex @ V2 ) @ ( plus_plus_complex @ B @ C2 ) )
% 5.31/5.54 = ( plus_plus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ V2 ) @ B ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ V2 ) @ C2 ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % distrib_left_numeral
% 5.31/5.54 thf(fact_3052_distrib__left__numeral,axiom,
% 5.31/5.54 ! [V2: num,B: real,C2: real] :
% 5.31/5.54 ( ( times_times_real @ ( numeral_numeral_real @ V2 ) @ ( plus_plus_real @ B @ C2 ) )
% 5.31/5.54 = ( plus_plus_real @ ( times_times_real @ ( numeral_numeral_real @ V2 ) @ B ) @ ( times_times_real @ ( numeral_numeral_real @ V2 ) @ C2 ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % distrib_left_numeral
% 5.31/5.54 thf(fact_3053_distrib__left__numeral,axiom,
% 5.31/5.54 ! [V2: num,B: nat,C2: nat] :
% 5.31/5.54 ( ( times_times_nat @ ( numeral_numeral_nat @ V2 ) @ ( plus_plus_nat @ B @ C2 ) )
% 5.31/5.54 = ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ V2 ) @ B ) @ ( times_times_nat @ ( numeral_numeral_nat @ V2 ) @ C2 ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % distrib_left_numeral
% 5.31/5.54 thf(fact_3054_distrib__left__numeral,axiom,
% 5.31/5.54 ! [V2: num,B: int,C2: int] :
% 5.31/5.54 ( ( times_times_int @ ( numeral_numeral_int @ V2 ) @ ( plus_plus_int @ B @ C2 ) )
% 5.31/5.54 = ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ V2 ) @ B ) @ ( times_times_int @ ( numeral_numeral_int @ V2 ) @ C2 ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % distrib_left_numeral
% 5.31/5.54 thf(fact_3055_distrib__right__numeral,axiom,
% 5.31/5.54 ! [A: rat,B: rat,V2: num] :
% 5.31/5.54 ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ ( numeral_numeral_rat @ V2 ) )
% 5.31/5.54 = ( plus_plus_rat @ ( times_times_rat @ A @ ( numeral_numeral_rat @ V2 ) ) @ ( times_times_rat @ B @ ( numeral_numeral_rat @ V2 ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % distrib_right_numeral
% 5.31/5.54 thf(fact_3056_distrib__right__numeral,axiom,
% 5.31/5.54 ! [A: extended_enat,B: extended_enat,V2: num] :
% 5.31/5.54 ( ( times_7803423173614009249d_enat @ ( plus_p3455044024723400733d_enat @ A @ B ) @ ( numera1916890842035813515d_enat @ V2 ) )
% 5.31/5.54 = ( plus_p3455044024723400733d_enat @ ( times_7803423173614009249d_enat @ A @ ( numera1916890842035813515d_enat @ V2 ) ) @ ( times_7803423173614009249d_enat @ B @ ( numera1916890842035813515d_enat @ V2 ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % distrib_right_numeral
% 5.31/5.54 thf(fact_3057_distrib__right__numeral,axiom,
% 5.31/5.54 ! [A: complex,B: complex,V2: num] :
% 5.31/5.54 ( ( times_times_complex @ ( plus_plus_complex @ A @ B ) @ ( numera6690914467698888265omplex @ V2 ) )
% 5.31/5.54 = ( plus_plus_complex @ ( times_times_complex @ A @ ( numera6690914467698888265omplex @ V2 ) ) @ ( times_times_complex @ B @ ( numera6690914467698888265omplex @ V2 ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % distrib_right_numeral
% 5.31/5.54 thf(fact_3058_distrib__right__numeral,axiom,
% 5.31/5.54 ! [A: real,B: real,V2: num] :
% 5.31/5.54 ( ( times_times_real @ ( plus_plus_real @ A @ B ) @ ( numeral_numeral_real @ V2 ) )
% 5.31/5.54 = ( plus_plus_real @ ( times_times_real @ A @ ( numeral_numeral_real @ V2 ) ) @ ( times_times_real @ B @ ( numeral_numeral_real @ V2 ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % distrib_right_numeral
% 5.31/5.54 thf(fact_3059_distrib__right__numeral,axiom,
% 5.31/5.54 ! [A: nat,B: nat,V2: num] :
% 5.31/5.54 ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ ( numeral_numeral_nat @ V2 ) )
% 5.31/5.54 = ( plus_plus_nat @ ( times_times_nat @ A @ ( numeral_numeral_nat @ V2 ) ) @ ( times_times_nat @ B @ ( numeral_numeral_nat @ V2 ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % distrib_right_numeral
% 5.31/5.54 thf(fact_3060_distrib__right__numeral,axiom,
% 5.31/5.54 ! [A: int,B: int,V2: num] :
% 5.31/5.54 ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ ( numeral_numeral_int @ V2 ) )
% 5.31/5.54 = ( plus_plus_int @ ( times_times_int @ A @ ( numeral_numeral_int @ V2 ) ) @ ( times_times_int @ B @ ( numeral_numeral_int @ V2 ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % distrib_right_numeral
% 5.31/5.54 thf(fact_3061_numeral__eq__one__iff,axiom,
% 5.31/5.54 ! [N: num] :
% 5.31/5.54 ( ( ( numera6620942414471956472nteger @ N )
% 5.31/5.54 = one_one_Code_integer )
% 5.31/5.54 = ( N = one ) ) ).
% 5.31/5.54
% 5.31/5.54 % numeral_eq_one_iff
% 5.31/5.54 thf(fact_3062_numeral__eq__one__iff,axiom,
% 5.31/5.54 ! [N: num] :
% 5.31/5.54 ( ( ( numera1916890842035813515d_enat @ N )
% 5.31/5.54 = one_on7984719198319812577d_enat )
% 5.31/5.54 = ( N = one ) ) ).
% 5.31/5.54
% 5.31/5.54 % numeral_eq_one_iff
% 5.31/5.54 thf(fact_3063_numeral__eq__one__iff,axiom,
% 5.31/5.54 ! [N: num] :
% 5.31/5.54 ( ( ( numera6690914467698888265omplex @ N )
% 5.31/5.54 = one_one_complex )
% 5.31/5.54 = ( N = one ) ) ).
% 5.31/5.54
% 5.31/5.54 % numeral_eq_one_iff
% 5.31/5.54 thf(fact_3064_numeral__eq__one__iff,axiom,
% 5.31/5.54 ! [N: num] :
% 5.31/5.54 ( ( ( numeral_numeral_real @ N )
% 5.31/5.54 = one_one_real )
% 5.31/5.54 = ( N = one ) ) ).
% 5.31/5.54
% 5.31/5.54 % numeral_eq_one_iff
% 5.31/5.54 thf(fact_3065_numeral__eq__one__iff,axiom,
% 5.31/5.54 ! [N: num] :
% 5.31/5.54 ( ( ( numeral_numeral_nat @ N )
% 5.31/5.54 = one_one_nat )
% 5.31/5.54 = ( N = one ) ) ).
% 5.31/5.54
% 5.31/5.54 % numeral_eq_one_iff
% 5.31/5.54 thf(fact_3066_numeral__eq__one__iff,axiom,
% 5.31/5.54 ! [N: num] :
% 5.31/5.54 ( ( ( numeral_numeral_int @ N )
% 5.31/5.54 = one_one_int )
% 5.31/5.54 = ( N = one ) ) ).
% 5.31/5.54
% 5.31/5.54 % numeral_eq_one_iff
% 5.31/5.54 thf(fact_3067_one__eq__numeral__iff,axiom,
% 5.31/5.54 ! [N: num] :
% 5.31/5.54 ( ( one_one_Code_integer
% 5.31/5.54 = ( numera6620942414471956472nteger @ N ) )
% 5.31/5.54 = ( one = N ) ) ).
% 5.31/5.54
% 5.31/5.54 % one_eq_numeral_iff
% 5.31/5.54 thf(fact_3068_one__eq__numeral__iff,axiom,
% 5.31/5.54 ! [N: num] :
% 5.31/5.54 ( ( one_on7984719198319812577d_enat
% 5.31/5.54 = ( numera1916890842035813515d_enat @ N ) )
% 5.31/5.54 = ( one = N ) ) ).
% 5.31/5.54
% 5.31/5.54 % one_eq_numeral_iff
% 5.31/5.54 thf(fact_3069_one__eq__numeral__iff,axiom,
% 5.31/5.54 ! [N: num] :
% 5.31/5.54 ( ( one_one_complex
% 5.31/5.54 = ( numera6690914467698888265omplex @ N ) )
% 5.31/5.54 = ( one = N ) ) ).
% 5.31/5.54
% 5.31/5.54 % one_eq_numeral_iff
% 5.31/5.54 thf(fact_3070_one__eq__numeral__iff,axiom,
% 5.31/5.54 ! [N: num] :
% 5.31/5.54 ( ( one_one_real
% 5.31/5.54 = ( numeral_numeral_real @ N ) )
% 5.31/5.54 = ( one = N ) ) ).
% 5.31/5.54
% 5.31/5.54 % one_eq_numeral_iff
% 5.31/5.54 thf(fact_3071_one__eq__numeral__iff,axiom,
% 5.31/5.54 ! [N: num] :
% 5.31/5.54 ( ( one_one_nat
% 5.31/5.54 = ( numeral_numeral_nat @ N ) )
% 5.31/5.54 = ( one = N ) ) ).
% 5.31/5.54
% 5.31/5.54 % one_eq_numeral_iff
% 5.31/5.54 thf(fact_3072_one__eq__numeral__iff,axiom,
% 5.31/5.54 ! [N: num] :
% 5.31/5.54 ( ( one_one_int
% 5.31/5.54 = ( numeral_numeral_int @ N ) )
% 5.31/5.54 = ( one = N ) ) ).
% 5.31/5.54
% 5.31/5.54 % one_eq_numeral_iff
% 5.31/5.54 thf(fact_3073_left__diff__distrib__numeral,axiom,
% 5.31/5.54 ! [A: rat,B: rat,V2: num] :
% 5.31/5.54 ( ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ ( numeral_numeral_rat @ V2 ) )
% 5.31/5.54 = ( minus_minus_rat @ ( times_times_rat @ A @ ( numeral_numeral_rat @ V2 ) ) @ ( times_times_rat @ B @ ( numeral_numeral_rat @ V2 ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % left_diff_distrib_numeral
% 5.31/5.54 thf(fact_3074_left__diff__distrib__numeral,axiom,
% 5.31/5.54 ! [A: complex,B: complex,V2: num] :
% 5.31/5.54 ( ( times_times_complex @ ( minus_minus_complex @ A @ B ) @ ( numera6690914467698888265omplex @ V2 ) )
% 5.31/5.54 = ( minus_minus_complex @ ( times_times_complex @ A @ ( numera6690914467698888265omplex @ V2 ) ) @ ( times_times_complex @ B @ ( numera6690914467698888265omplex @ V2 ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % left_diff_distrib_numeral
% 5.31/5.54 thf(fact_3075_left__diff__distrib__numeral,axiom,
% 5.31/5.54 ! [A: real,B: real,V2: num] :
% 5.31/5.54 ( ( times_times_real @ ( minus_minus_real @ A @ B ) @ ( numeral_numeral_real @ V2 ) )
% 5.31/5.54 = ( minus_minus_real @ ( times_times_real @ A @ ( numeral_numeral_real @ V2 ) ) @ ( times_times_real @ B @ ( numeral_numeral_real @ V2 ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % left_diff_distrib_numeral
% 5.31/5.54 thf(fact_3076_left__diff__distrib__numeral,axiom,
% 5.31/5.54 ! [A: int,B: int,V2: num] :
% 5.31/5.54 ( ( times_times_int @ ( minus_minus_int @ A @ B ) @ ( numeral_numeral_int @ V2 ) )
% 5.31/5.54 = ( minus_minus_int @ ( times_times_int @ A @ ( numeral_numeral_int @ V2 ) ) @ ( times_times_int @ B @ ( numeral_numeral_int @ V2 ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % left_diff_distrib_numeral
% 5.31/5.54 thf(fact_3077_right__diff__distrib__numeral,axiom,
% 5.31/5.54 ! [V2: num,B: rat,C2: rat] :
% 5.31/5.54 ( ( times_times_rat @ ( numeral_numeral_rat @ V2 ) @ ( minus_minus_rat @ B @ C2 ) )
% 5.31/5.54 = ( minus_minus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ V2 ) @ B ) @ ( times_times_rat @ ( numeral_numeral_rat @ V2 ) @ C2 ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % right_diff_distrib_numeral
% 5.31/5.54 thf(fact_3078_right__diff__distrib__numeral,axiom,
% 5.31/5.54 ! [V2: num,B: complex,C2: complex] :
% 5.31/5.54 ( ( times_times_complex @ ( numera6690914467698888265omplex @ V2 ) @ ( minus_minus_complex @ B @ C2 ) )
% 5.31/5.54 = ( minus_minus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ V2 ) @ B ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ V2 ) @ C2 ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % right_diff_distrib_numeral
% 5.31/5.54 thf(fact_3079_right__diff__distrib__numeral,axiom,
% 5.31/5.54 ! [V2: num,B: real,C2: real] :
% 5.31/5.54 ( ( times_times_real @ ( numeral_numeral_real @ V2 ) @ ( minus_minus_real @ B @ C2 ) )
% 5.31/5.54 = ( minus_minus_real @ ( times_times_real @ ( numeral_numeral_real @ V2 ) @ B ) @ ( times_times_real @ ( numeral_numeral_real @ V2 ) @ C2 ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % right_diff_distrib_numeral
% 5.31/5.54 thf(fact_3080_right__diff__distrib__numeral,axiom,
% 5.31/5.54 ! [V2: num,B: int,C2: int] :
% 5.31/5.54 ( ( times_times_int @ ( numeral_numeral_int @ V2 ) @ ( minus_minus_int @ B @ C2 ) )
% 5.31/5.54 = ( minus_minus_int @ ( times_times_int @ ( numeral_numeral_int @ V2 ) @ B ) @ ( times_times_int @ ( numeral_numeral_int @ V2 ) @ C2 ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % right_diff_distrib_numeral
% 5.31/5.54 thf(fact_3081_power__zero__numeral,axiom,
% 5.31/5.54 ! [K2: num] :
% 5.31/5.54 ( ( power_power_rat @ zero_zero_rat @ ( numeral_numeral_nat @ K2 ) )
% 5.31/5.54 = zero_zero_rat ) ).
% 5.31/5.54
% 5.31/5.54 % power_zero_numeral
% 5.31/5.54 thf(fact_3082_power__zero__numeral,axiom,
% 5.31/5.54 ! [K2: num] :
% 5.31/5.54 ( ( power_power_nat @ zero_zero_nat @ ( numeral_numeral_nat @ K2 ) )
% 5.31/5.54 = zero_zero_nat ) ).
% 5.31/5.54
% 5.31/5.54 % power_zero_numeral
% 5.31/5.54 thf(fact_3083_power__zero__numeral,axiom,
% 5.31/5.54 ! [K2: num] :
% 5.31/5.54 ( ( power_power_real @ zero_zero_real @ ( numeral_numeral_nat @ K2 ) )
% 5.31/5.54 = zero_zero_real ) ).
% 5.31/5.54
% 5.31/5.54 % power_zero_numeral
% 5.31/5.54 thf(fact_3084_power__zero__numeral,axiom,
% 5.31/5.54 ! [K2: num] :
% 5.31/5.54 ( ( power_power_int @ zero_zero_int @ ( numeral_numeral_nat @ K2 ) )
% 5.31/5.54 = zero_zero_int ) ).
% 5.31/5.54
% 5.31/5.54 % power_zero_numeral
% 5.31/5.54 thf(fact_3085_power__zero__numeral,axiom,
% 5.31/5.54 ! [K2: num] :
% 5.31/5.54 ( ( power_power_complex @ zero_zero_complex @ ( numeral_numeral_nat @ K2 ) )
% 5.31/5.54 = zero_zero_complex ) ).
% 5.31/5.54
% 5.31/5.54 % power_zero_numeral
% 5.31/5.54 thf(fact_3086_Suc__numeral,axiom,
% 5.31/5.54 ! [N: num] :
% 5.31/5.54 ( ( suc @ ( numeral_numeral_nat @ N ) )
% 5.31/5.54 = ( numeral_numeral_nat @ ( plus_plus_num @ N @ one ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % Suc_numeral
% 5.31/5.54 thf(fact_3087_power__add__numeral,axiom,
% 5.31/5.54 ! [A: complex,M2: num,N: num] :
% 5.31/5.54 ( ( times_times_complex @ ( power_power_complex @ A @ ( numeral_numeral_nat @ M2 ) ) @ ( power_power_complex @ A @ ( numeral_numeral_nat @ N ) ) )
% 5.31/5.54 = ( power_power_complex @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M2 @ N ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % power_add_numeral
% 5.31/5.54 thf(fact_3088_power__add__numeral,axiom,
% 5.31/5.54 ! [A: real,M2: num,N: num] :
% 5.31/5.54 ( ( times_times_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ M2 ) ) @ ( power_power_real @ A @ ( numeral_numeral_nat @ N ) ) )
% 5.31/5.54 = ( power_power_real @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M2 @ N ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % power_add_numeral
% 5.31/5.54 thf(fact_3089_power__add__numeral,axiom,
% 5.31/5.54 ! [A: rat,M2: num,N: num] :
% 5.31/5.54 ( ( times_times_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ M2 ) ) @ ( power_power_rat @ A @ ( numeral_numeral_nat @ N ) ) )
% 5.31/5.54 = ( power_power_rat @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M2 @ N ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % power_add_numeral
% 5.31/5.54 thf(fact_3090_power__add__numeral,axiom,
% 5.31/5.54 ! [A: nat,M2: num,N: num] :
% 5.31/5.54 ( ( times_times_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ M2 ) ) @ ( power_power_nat @ A @ ( numeral_numeral_nat @ N ) ) )
% 5.31/5.54 = ( power_power_nat @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M2 @ N ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % power_add_numeral
% 5.31/5.54 thf(fact_3091_power__add__numeral,axiom,
% 5.31/5.54 ! [A: int,M2: num,N: num] :
% 5.31/5.54 ( ( times_times_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ M2 ) ) @ ( power_power_int @ A @ ( numeral_numeral_nat @ N ) ) )
% 5.31/5.54 = ( power_power_int @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M2 @ N ) ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % power_add_numeral
% 5.31/5.54 thf(fact_3092_power__add__numeral2,axiom,
% 5.31/5.54 ! [A: complex,M2: num,N: num,B: complex] :
% 5.31/5.54 ( ( times_times_complex @ ( power_power_complex @ A @ ( numeral_numeral_nat @ M2 ) ) @ ( times_times_complex @ ( power_power_complex @ A @ ( numeral_numeral_nat @ N ) ) @ B ) )
% 5.31/5.54 = ( times_times_complex @ ( power_power_complex @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M2 @ N ) ) ) @ B ) ) ).
% 5.31/5.54
% 5.31/5.54 % power_add_numeral2
% 5.31/5.54 thf(fact_3093_power__add__numeral2,axiom,
% 5.31/5.54 ! [A: real,M2: num,N: num,B: real] :
% 5.31/5.54 ( ( times_times_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ M2 ) ) @ ( times_times_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ N ) ) @ B ) )
% 5.31/5.54 = ( times_times_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M2 @ N ) ) ) @ B ) ) ).
% 5.31/5.54
% 5.31/5.54 % power_add_numeral2
% 5.31/5.54 thf(fact_3094_power__add__numeral2,axiom,
% 5.31/5.54 ! [A: rat,M2: num,N: num,B: rat] :
% 5.31/5.54 ( ( times_times_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ M2 ) ) @ ( times_times_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ N ) ) @ B ) )
% 5.31/5.54 = ( times_times_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M2 @ N ) ) ) @ B ) ) ).
% 5.31/5.54
% 5.31/5.54 % power_add_numeral2
% 5.31/5.54 thf(fact_3095_power__add__numeral2,axiom,
% 5.31/5.54 ! [A: nat,M2: num,N: num,B: nat] :
% 5.31/5.54 ( ( times_times_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ M2 ) ) @ ( times_times_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ N ) ) @ B ) )
% 5.31/5.54 = ( times_times_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M2 @ N ) ) ) @ B ) ) ).
% 5.31/5.54
% 5.31/5.54 % power_add_numeral2
% 5.31/5.54 thf(fact_3096_power__add__numeral2,axiom,
% 5.31/5.54 ! [A: int,M2: num,N: num,B: int] :
% 5.31/5.54 ( ( times_times_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ M2 ) ) @ ( times_times_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ N ) ) @ B ) )
% 5.31/5.54 = ( times_times_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M2 @ N ) ) ) @ B ) ) ).
% 5.31/5.54
% 5.31/5.54 % power_add_numeral2
% 5.31/5.54 thf(fact_3097_of__nat__eq__0__iff,axiom,
% 5.31/5.54 ! [M2: nat] :
% 5.31/5.54 ( ( ( semiri8010041392384452111omplex @ M2 )
% 5.31/5.54 = zero_zero_complex )
% 5.31/5.54 = ( M2 = zero_zero_nat ) ) ).
% 5.31/5.54
% 5.31/5.54 % of_nat_eq_0_iff
% 5.31/5.54 thf(fact_3098_of__nat__eq__0__iff,axiom,
% 5.31/5.54 ! [M2: nat] :
% 5.31/5.54 ( ( ( semiri681578069525770553at_rat @ M2 )
% 5.31/5.54 = zero_zero_rat )
% 5.31/5.54 = ( M2 = zero_zero_nat ) ) ).
% 5.31/5.54
% 5.31/5.54 % of_nat_eq_0_iff
% 5.31/5.54 thf(fact_3099_of__nat__eq__0__iff,axiom,
% 5.31/5.54 ! [M2: nat] :
% 5.31/5.54 ( ( ( semiri5074537144036343181t_real @ M2 )
% 5.31/5.54 = zero_zero_real )
% 5.31/5.54 = ( M2 = zero_zero_nat ) ) ).
% 5.31/5.54
% 5.31/5.54 % of_nat_eq_0_iff
% 5.31/5.54 thf(fact_3100_of__nat__eq__0__iff,axiom,
% 5.31/5.54 ! [M2: nat] :
% 5.31/5.54 ( ( ( semiri1314217659103216013at_int @ M2 )
% 5.31/5.54 = zero_zero_int )
% 5.31/5.54 = ( M2 = zero_zero_nat ) ) ).
% 5.31/5.54
% 5.31/5.54 % of_nat_eq_0_iff
% 5.31/5.54 thf(fact_3101_of__nat__eq__0__iff,axiom,
% 5.31/5.54 ! [M2: nat] :
% 5.31/5.54 ( ( ( semiri1316708129612266289at_nat @ M2 )
% 5.31/5.54 = zero_zero_nat )
% 5.31/5.54 = ( M2 = zero_zero_nat ) ) ).
% 5.31/5.54
% 5.31/5.54 % of_nat_eq_0_iff
% 5.31/5.54 thf(fact_3102_of__nat__0__eq__iff,axiom,
% 5.31/5.54 ! [N: nat] :
% 5.31/5.54 ( ( zero_zero_complex
% 5.31/5.54 = ( semiri8010041392384452111omplex @ N ) )
% 5.31/5.54 = ( zero_zero_nat = N ) ) ).
% 5.31/5.54
% 5.31/5.54 % of_nat_0_eq_iff
% 5.31/5.54 thf(fact_3103_of__nat__0__eq__iff,axiom,
% 5.31/5.54 ! [N: nat] :
% 5.31/5.54 ( ( zero_zero_rat
% 5.31/5.54 = ( semiri681578069525770553at_rat @ N ) )
% 5.31/5.54 = ( zero_zero_nat = N ) ) ).
% 5.31/5.54
% 5.31/5.54 % of_nat_0_eq_iff
% 5.31/5.54 thf(fact_3104_of__nat__0__eq__iff,axiom,
% 5.31/5.54 ! [N: nat] :
% 5.31/5.54 ( ( zero_zero_real
% 5.31/5.54 = ( semiri5074537144036343181t_real @ N ) )
% 5.31/5.54 = ( zero_zero_nat = N ) ) ).
% 5.31/5.54
% 5.31/5.54 % of_nat_0_eq_iff
% 5.31/5.54 thf(fact_3105_of__nat__0__eq__iff,axiom,
% 5.31/5.54 ! [N: nat] :
% 5.31/5.54 ( ( zero_zero_int
% 5.31/5.54 = ( semiri1314217659103216013at_int @ N ) )
% 5.31/5.54 = ( zero_zero_nat = N ) ) ).
% 5.31/5.54
% 5.31/5.54 % of_nat_0_eq_iff
% 5.31/5.54 thf(fact_3106_of__nat__0__eq__iff,axiom,
% 5.31/5.54 ! [N: nat] :
% 5.31/5.54 ( ( zero_zero_nat
% 5.31/5.54 = ( semiri1316708129612266289at_nat @ N ) )
% 5.31/5.54 = ( zero_zero_nat = N ) ) ).
% 5.31/5.54
% 5.31/5.54 % of_nat_0_eq_iff
% 5.31/5.54 thf(fact_3107_of__nat__0,axiom,
% 5.31/5.54 ( ( semiri8010041392384452111omplex @ zero_zero_nat )
% 5.31/5.54 = zero_zero_complex ) ).
% 5.31/5.54
% 5.31/5.54 % of_nat_0
% 5.31/5.54 thf(fact_3108_of__nat__0,axiom,
% 5.31/5.54 ( ( semiri681578069525770553at_rat @ zero_zero_nat )
% 5.31/5.54 = zero_zero_rat ) ).
% 5.31/5.54
% 5.31/5.54 % of_nat_0
% 5.31/5.54 thf(fact_3109_of__nat__0,axiom,
% 5.31/5.54 ( ( semiri5074537144036343181t_real @ zero_zero_nat )
% 5.31/5.54 = zero_zero_real ) ).
% 5.31/5.54
% 5.31/5.54 % of_nat_0
% 5.31/5.54 thf(fact_3110_of__nat__0,axiom,
% 5.31/5.54 ( ( semiri1314217659103216013at_int @ zero_zero_nat )
% 5.31/5.54 = zero_zero_int ) ).
% 5.31/5.54
% 5.31/5.54 % of_nat_0
% 5.31/5.54 thf(fact_3111_of__nat__0,axiom,
% 5.31/5.54 ( ( semiri1316708129612266289at_nat @ zero_zero_nat )
% 5.31/5.54 = zero_zero_nat ) ).
% 5.31/5.54
% 5.31/5.54 % of_nat_0
% 5.31/5.54 thf(fact_3112_of__nat__less__iff,axiom,
% 5.31/5.54 ! [M2: nat,N: nat] :
% 5.31/5.54 ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ M2 ) @ ( semiri681578069525770553at_rat @ N ) )
% 5.31/5.54 = ( ord_less_nat @ M2 @ N ) ) ).
% 5.31/5.54
% 5.31/5.54 % of_nat_less_iff
% 5.31/5.54 thf(fact_3113_of__nat__less__iff,axiom,
% 5.31/5.54 ! [M2: nat,N: nat] :
% 5.31/5.54 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ M2 ) @ ( semiri5074537144036343181t_real @ N ) )
% 5.31/5.54 = ( ord_less_nat @ M2 @ N ) ) ).
% 5.31/5.54
% 5.31/5.54 % of_nat_less_iff
% 5.31/5.54 thf(fact_3114_of__nat__less__iff,axiom,
% 5.31/5.54 ! [M2: nat,N: nat] :
% 5.31/5.54 ( ( ord_less_int @ ( semiri1314217659103216013at_int @ M2 ) @ ( semiri1314217659103216013at_int @ N ) )
% 5.31/5.54 = ( ord_less_nat @ M2 @ N ) ) ).
% 5.31/5.54
% 5.31/5.54 % of_nat_less_iff
% 5.31/5.54 thf(fact_3115_of__nat__less__iff,axiom,
% 5.31/5.54 ! [M2: nat,N: nat] :
% 5.31/5.54 ( ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M2 ) @ ( semiri1316708129612266289at_nat @ N ) )
% 5.31/5.54 = ( ord_less_nat @ M2 @ N ) ) ).
% 5.31/5.54
% 5.31/5.54 % of_nat_less_iff
% 5.31/5.54 thf(fact_3116_of__nat__numeral,axiom,
% 5.31/5.54 ! [N: num] :
% 5.31/5.54 ( ( semiri4216267220026989637d_enat @ ( numeral_numeral_nat @ N ) )
% 5.31/5.54 = ( numera1916890842035813515d_enat @ N ) ) ).
% 5.31/5.54
% 5.31/5.54 % of_nat_numeral
% 5.31/5.54 thf(fact_3117_of__nat__numeral,axiom,
% 5.31/5.54 ! [N: num] :
% 5.31/5.54 ( ( semiri8010041392384452111omplex @ ( numeral_numeral_nat @ N ) )
% 5.31/5.54 = ( numera6690914467698888265omplex @ N ) ) ).
% 5.31/5.54
% 5.31/5.54 % of_nat_numeral
% 5.31/5.54 thf(fact_3118_of__nat__numeral,axiom,
% 5.31/5.54 ! [N: num] :
% 5.31/5.54 ( ( semiri5074537144036343181t_real @ ( numeral_numeral_nat @ N ) )
% 5.31/5.54 = ( numeral_numeral_real @ N ) ) ).
% 5.31/5.54
% 5.31/5.54 % of_nat_numeral
% 5.31/5.54 thf(fact_3119_of__nat__numeral,axiom,
% 5.31/5.54 ! [N: num] :
% 5.31/5.54 ( ( semiri1314217659103216013at_int @ ( numeral_numeral_nat @ N ) )
% 5.31/5.54 = ( numeral_numeral_int @ N ) ) ).
% 5.31/5.54
% 5.31/5.54 % of_nat_numeral
% 5.31/5.54 thf(fact_3120_of__nat__numeral,axiom,
% 5.31/5.54 ! [N: num] :
% 5.31/5.54 ( ( semiri1316708129612266289at_nat @ ( numeral_numeral_nat @ N ) )
% 5.31/5.54 = ( numeral_numeral_nat @ N ) ) ).
% 5.31/5.54
% 5.31/5.54 % of_nat_numeral
% 5.31/5.54 thf(fact_3121_of__nat__le__iff,axiom,
% 5.31/5.54 ! [M2: nat,N: nat] :
% 5.31/5.54 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ M2 ) @ ( semiri5074537144036343181t_real @ N ) )
% 5.31/5.54 = ( ord_less_eq_nat @ M2 @ N ) ) ).
% 5.31/5.54
% 5.31/5.54 % of_nat_le_iff
% 5.31/5.54 thf(fact_3122_of__nat__le__iff,axiom,
% 5.31/5.54 ! [M2: nat,N: nat] :
% 5.31/5.54 ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ M2 ) @ ( semiri681578069525770553at_rat @ N ) )
% 5.31/5.54 = ( ord_less_eq_nat @ M2 @ N ) ) ).
% 5.31/5.54
% 5.31/5.54 % of_nat_le_iff
% 5.31/5.54 thf(fact_3123_of__nat__le__iff,axiom,
% 5.31/5.54 ! [M2: nat,N: nat] :
% 5.31/5.54 ( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ M2 ) @ ( semiri1316708129612266289at_nat @ N ) )
% 5.31/5.54 = ( ord_less_eq_nat @ M2 @ N ) ) ).
% 5.31/5.54
% 5.31/5.54 % of_nat_le_iff
% 5.31/5.54 thf(fact_3124_of__nat__le__iff,axiom,
% 5.31/5.54 ! [M2: nat,N: nat] :
% 5.31/5.54 ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ M2 ) @ ( semiri1314217659103216013at_int @ N ) )
% 5.31/5.54 = ( ord_less_eq_nat @ M2 @ N ) ) ).
% 5.31/5.54
% 5.31/5.54 % of_nat_le_iff
% 5.31/5.54 thf(fact_3125_of__nat__add,axiom,
% 5.31/5.54 ! [M2: nat,N: nat] :
% 5.31/5.54 ( ( semiri681578069525770553at_rat @ ( plus_plus_nat @ M2 @ N ) )
% 5.31/5.54 = ( plus_plus_rat @ ( semiri681578069525770553at_rat @ M2 ) @ ( semiri681578069525770553at_rat @ N ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % of_nat_add
% 5.31/5.54 thf(fact_3126_of__nat__add,axiom,
% 5.31/5.54 ! [M2: nat,N: nat] :
% 5.31/5.54 ( ( semiri5074537144036343181t_real @ ( plus_plus_nat @ M2 @ N ) )
% 5.31/5.54 = ( plus_plus_real @ ( semiri5074537144036343181t_real @ M2 ) @ ( semiri5074537144036343181t_real @ N ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % of_nat_add
% 5.31/5.54 thf(fact_3127_of__nat__add,axiom,
% 5.31/5.54 ! [M2: nat,N: nat] :
% 5.31/5.54 ( ( semiri1314217659103216013at_int @ ( plus_plus_nat @ M2 @ N ) )
% 5.31/5.54 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ M2 ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % of_nat_add
% 5.31/5.54 thf(fact_3128_of__nat__add,axiom,
% 5.31/5.54 ! [M2: nat,N: nat] :
% 5.31/5.54 ( ( semiri1316708129612266289at_nat @ ( plus_plus_nat @ M2 @ N ) )
% 5.31/5.54 = ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ M2 ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % of_nat_add
% 5.31/5.54 thf(fact_3129_of__nat__mult,axiom,
% 5.31/5.54 ! [M2: nat,N: nat] :
% 5.31/5.54 ( ( semiri681578069525770553at_rat @ ( times_times_nat @ M2 @ N ) )
% 5.31/5.54 = ( times_times_rat @ ( semiri681578069525770553at_rat @ M2 ) @ ( semiri681578069525770553at_rat @ N ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % of_nat_mult
% 5.31/5.54 thf(fact_3130_of__nat__mult,axiom,
% 5.31/5.54 ! [M2: nat,N: nat] :
% 5.31/5.54 ( ( semiri5074537144036343181t_real @ ( times_times_nat @ M2 @ N ) )
% 5.31/5.54 = ( times_times_real @ ( semiri5074537144036343181t_real @ M2 ) @ ( semiri5074537144036343181t_real @ N ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % of_nat_mult
% 5.31/5.54 thf(fact_3131_of__nat__mult,axiom,
% 5.31/5.54 ! [M2: nat,N: nat] :
% 5.31/5.54 ( ( semiri1314217659103216013at_int @ ( times_times_nat @ M2 @ N ) )
% 5.31/5.54 = ( times_times_int @ ( semiri1314217659103216013at_int @ M2 ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % of_nat_mult
% 5.31/5.54 thf(fact_3132_of__nat__mult,axiom,
% 5.31/5.54 ! [M2: nat,N: nat] :
% 5.31/5.54 ( ( semiri1316708129612266289at_nat @ ( times_times_nat @ M2 @ N ) )
% 5.31/5.54 = ( times_times_nat @ ( semiri1316708129612266289at_nat @ M2 ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % of_nat_mult
% 5.31/5.54 thf(fact_3133_of__nat__eq__1__iff,axiom,
% 5.31/5.54 ! [N: nat] :
% 5.31/5.54 ( ( ( semiri4939895301339042750nteger @ N )
% 5.31/5.54 = one_one_Code_integer )
% 5.31/5.54 = ( N = one_one_nat ) ) ).
% 5.31/5.54
% 5.31/5.54 % of_nat_eq_1_iff
% 5.31/5.54 thf(fact_3134_of__nat__eq__1__iff,axiom,
% 5.31/5.54 ! [N: nat] :
% 5.31/5.54 ( ( ( semiri8010041392384452111omplex @ N )
% 5.31/5.54 = one_one_complex )
% 5.31/5.54 = ( N = one_one_nat ) ) ).
% 5.31/5.54
% 5.31/5.54 % of_nat_eq_1_iff
% 5.31/5.54 thf(fact_3135_of__nat__eq__1__iff,axiom,
% 5.31/5.54 ! [N: nat] :
% 5.31/5.54 ( ( ( semiri5074537144036343181t_real @ N )
% 5.31/5.54 = one_one_real )
% 5.31/5.54 = ( N = one_one_nat ) ) ).
% 5.31/5.54
% 5.31/5.54 % of_nat_eq_1_iff
% 5.31/5.54 thf(fact_3136_of__nat__eq__1__iff,axiom,
% 5.31/5.54 ! [N: nat] :
% 5.31/5.54 ( ( ( semiri1314217659103216013at_int @ N )
% 5.31/5.54 = one_one_int )
% 5.31/5.54 = ( N = one_one_nat ) ) ).
% 5.31/5.54
% 5.31/5.54 % of_nat_eq_1_iff
% 5.31/5.54 thf(fact_3137_of__nat__eq__1__iff,axiom,
% 5.31/5.54 ! [N: nat] :
% 5.31/5.54 ( ( ( semiri1316708129612266289at_nat @ N )
% 5.31/5.54 = one_one_nat )
% 5.31/5.54 = ( N = one_one_nat ) ) ).
% 5.31/5.54
% 5.31/5.54 % of_nat_eq_1_iff
% 5.31/5.54 thf(fact_3138_of__nat__1__eq__iff,axiom,
% 5.31/5.54 ! [N: nat] :
% 5.31/5.54 ( ( one_one_Code_integer
% 5.31/5.54 = ( semiri4939895301339042750nteger @ N ) )
% 5.31/5.54 = ( N = one_one_nat ) ) ).
% 5.31/5.54
% 5.31/5.54 % of_nat_1_eq_iff
% 5.31/5.54 thf(fact_3139_of__nat__1__eq__iff,axiom,
% 5.31/5.54 ! [N: nat] :
% 5.31/5.54 ( ( one_one_complex
% 5.31/5.54 = ( semiri8010041392384452111omplex @ N ) )
% 5.31/5.54 = ( N = one_one_nat ) ) ).
% 5.31/5.54
% 5.31/5.54 % of_nat_1_eq_iff
% 5.31/5.54 thf(fact_3140_of__nat__1__eq__iff,axiom,
% 5.31/5.54 ! [N: nat] :
% 5.31/5.54 ( ( one_one_real
% 5.31/5.54 = ( semiri5074537144036343181t_real @ N ) )
% 5.31/5.54 = ( N = one_one_nat ) ) ).
% 5.31/5.54
% 5.31/5.54 % of_nat_1_eq_iff
% 5.31/5.54 thf(fact_3141_of__nat__1__eq__iff,axiom,
% 5.31/5.54 ! [N: nat] :
% 5.31/5.54 ( ( one_one_int
% 5.31/5.54 = ( semiri1314217659103216013at_int @ N ) )
% 5.31/5.54 = ( N = one_one_nat ) ) ).
% 5.31/5.54
% 5.31/5.54 % of_nat_1_eq_iff
% 5.31/5.54 thf(fact_3142_of__nat__1__eq__iff,axiom,
% 5.31/5.54 ! [N: nat] :
% 5.31/5.54 ( ( one_one_nat
% 5.31/5.54 = ( semiri1316708129612266289at_nat @ N ) )
% 5.31/5.54 = ( N = one_one_nat ) ) ).
% 5.31/5.54
% 5.31/5.54 % of_nat_1_eq_iff
% 5.31/5.54 thf(fact_3143_of__nat__1,axiom,
% 5.31/5.54 ( ( semiri4939895301339042750nteger @ one_one_nat )
% 5.31/5.54 = one_one_Code_integer ) ).
% 5.31/5.54
% 5.31/5.54 % of_nat_1
% 5.31/5.54 thf(fact_3144_of__nat__1,axiom,
% 5.31/5.54 ( ( semiri8010041392384452111omplex @ one_one_nat )
% 5.31/5.54 = one_one_complex ) ).
% 5.31/5.54
% 5.31/5.54 % of_nat_1
% 5.31/5.54 thf(fact_3145_of__nat__1,axiom,
% 5.31/5.54 ( ( semiri5074537144036343181t_real @ one_one_nat )
% 5.31/5.54 = one_one_real ) ).
% 5.31/5.54
% 5.31/5.54 % of_nat_1
% 5.31/5.54 thf(fact_3146_of__nat__1,axiom,
% 5.31/5.54 ( ( semiri1314217659103216013at_int @ one_one_nat )
% 5.31/5.54 = one_one_int ) ).
% 5.31/5.54
% 5.31/5.54 % of_nat_1
% 5.31/5.54 thf(fact_3147_of__nat__1,axiom,
% 5.31/5.54 ( ( semiri1316708129612266289at_nat @ one_one_nat )
% 5.31/5.54 = one_one_nat ) ).
% 5.31/5.54
% 5.31/5.54 % of_nat_1
% 5.31/5.54 thf(fact_3148_in__set__replicate,axiom,
% 5.31/5.54 ! [X: complex,N: nat,Y: complex] :
% 5.31/5.54 ( ( member_complex @ X @ ( set_complex2 @ ( replicate_complex @ N @ Y ) ) )
% 5.31/5.54 = ( ( X = Y )
% 5.31/5.54 & ( N != zero_zero_nat ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % in_set_replicate
% 5.31/5.54 thf(fact_3149_in__set__replicate,axiom,
% 5.31/5.54 ! [X: real,N: nat,Y: real] :
% 5.31/5.54 ( ( member_real @ X @ ( set_real2 @ ( replicate_real @ N @ Y ) ) )
% 5.31/5.54 = ( ( X = Y )
% 5.31/5.54 & ( N != zero_zero_nat ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % in_set_replicate
% 5.31/5.54 thf(fact_3150_in__set__replicate,axiom,
% 5.31/5.54 ! [X: set_nat,N: nat,Y: set_nat] :
% 5.31/5.54 ( ( member_set_nat @ X @ ( set_set_nat2 @ ( replicate_set_nat @ N @ Y ) ) )
% 5.31/5.54 = ( ( X = Y )
% 5.31/5.54 & ( N != zero_zero_nat ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % in_set_replicate
% 5.31/5.54 thf(fact_3151_in__set__replicate,axiom,
% 5.31/5.54 ! [X: int,N: nat,Y: int] :
% 5.31/5.54 ( ( member_int @ X @ ( set_int2 @ ( replicate_int @ N @ Y ) ) )
% 5.31/5.54 = ( ( X = Y )
% 5.31/5.54 & ( N != zero_zero_nat ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % in_set_replicate
% 5.31/5.54 thf(fact_3152_in__set__replicate,axiom,
% 5.31/5.54 ! [X: nat,N: nat,Y: nat] :
% 5.31/5.54 ( ( member_nat @ X @ ( set_nat2 @ ( replicate_nat @ N @ Y ) ) )
% 5.31/5.54 = ( ( X = Y )
% 5.31/5.54 & ( N != zero_zero_nat ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % in_set_replicate
% 5.31/5.54 thf(fact_3153_in__set__replicate,axiom,
% 5.31/5.54 ! [X: vEBT_VEBT,N: nat,Y: vEBT_VEBT] :
% 5.31/5.54 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ N @ Y ) ) )
% 5.31/5.54 = ( ( X = Y )
% 5.31/5.54 & ( N != zero_zero_nat ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % in_set_replicate
% 5.31/5.54 thf(fact_3154_Bex__set__replicate,axiom,
% 5.31/5.54 ! [N: nat,A: nat,P2: nat > $o] :
% 5.31/5.54 ( ( ? [X4: nat] :
% 5.31/5.54 ( ( member_nat @ X4 @ ( set_nat2 @ ( replicate_nat @ N @ A ) ) )
% 5.31/5.54 & ( P2 @ X4 ) ) )
% 5.31/5.54 = ( ( P2 @ A )
% 5.31/5.54 & ( N != zero_zero_nat ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % Bex_set_replicate
% 5.31/5.54 thf(fact_3155_Bex__set__replicate,axiom,
% 5.31/5.54 ! [N: nat,A: vEBT_VEBT,P2: vEBT_VEBT > $o] :
% 5.31/5.54 ( ( ? [X4: vEBT_VEBT] :
% 5.31/5.54 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ N @ A ) ) )
% 5.31/5.54 & ( P2 @ X4 ) ) )
% 5.31/5.54 = ( ( P2 @ A )
% 5.31/5.54 & ( N != zero_zero_nat ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % Bex_set_replicate
% 5.31/5.54 thf(fact_3156_Ball__set__replicate,axiom,
% 5.31/5.54 ! [N: nat,A: nat,P2: nat > $o] :
% 5.31/5.54 ( ( ! [X4: nat] :
% 5.31/5.54 ( ( member_nat @ X4 @ ( set_nat2 @ ( replicate_nat @ N @ A ) ) )
% 5.31/5.54 => ( P2 @ X4 ) ) )
% 5.31/5.54 = ( ( P2 @ A )
% 5.31/5.54 | ( N = zero_zero_nat ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % Ball_set_replicate
% 5.31/5.54 thf(fact_3157_Ball__set__replicate,axiom,
% 5.31/5.54 ! [N: nat,A: vEBT_VEBT,P2: vEBT_VEBT > $o] :
% 5.31/5.54 ( ( ! [X4: vEBT_VEBT] :
% 5.31/5.54 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ N @ A ) ) )
% 5.31/5.54 => ( P2 @ X4 ) ) )
% 5.31/5.54 = ( ( P2 @ A )
% 5.31/5.54 | ( N = zero_zero_nat ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % Ball_set_replicate
% 5.31/5.54 thf(fact_3158_numeral__le__one__iff,axiom,
% 5.31/5.54 ! [N: num] :
% 5.31/5.54 ( ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ N ) @ one_one_Code_integer )
% 5.31/5.54 = ( ord_less_eq_num @ N @ one ) ) ).
% 5.31/5.54
% 5.31/5.54 % numeral_le_one_iff
% 5.31/5.54 thf(fact_3159_numeral__le__one__iff,axiom,
% 5.31/5.54 ! [N: num] :
% 5.31/5.54 ( ( ord_le2932123472753598470d_enat @ ( numera1916890842035813515d_enat @ N ) @ one_on7984719198319812577d_enat )
% 5.31/5.54 = ( ord_less_eq_num @ N @ one ) ) ).
% 5.31/5.54
% 5.31/5.54 % numeral_le_one_iff
% 5.31/5.54 thf(fact_3160_numeral__le__one__iff,axiom,
% 5.31/5.54 ! [N: num] :
% 5.31/5.54 ( ( ord_less_eq_real @ ( numeral_numeral_real @ N ) @ one_one_real )
% 5.31/5.54 = ( ord_less_eq_num @ N @ one ) ) ).
% 5.31/5.54
% 5.31/5.54 % numeral_le_one_iff
% 5.31/5.54 thf(fact_3161_numeral__le__one__iff,axiom,
% 5.31/5.54 ! [N: num] :
% 5.31/5.54 ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ N ) @ one_one_rat )
% 5.31/5.54 = ( ord_less_eq_num @ N @ one ) ) ).
% 5.31/5.54
% 5.31/5.54 % numeral_le_one_iff
% 5.31/5.54 thf(fact_3162_numeral__le__one__iff,axiom,
% 5.31/5.54 ! [N: num] :
% 5.31/5.54 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ N ) @ one_one_nat )
% 5.31/5.54 = ( ord_less_eq_num @ N @ one ) ) ).
% 5.31/5.54
% 5.31/5.54 % numeral_le_one_iff
% 5.31/5.54 thf(fact_3163_numeral__le__one__iff,axiom,
% 5.31/5.54 ! [N: num] :
% 5.31/5.54 ( ( ord_less_eq_int @ ( numeral_numeral_int @ N ) @ one_one_int )
% 5.31/5.54 = ( ord_less_eq_num @ N @ one ) ) ).
% 5.31/5.54
% 5.31/5.54 % numeral_le_one_iff
% 5.31/5.54 thf(fact_3164_one__less__numeral__iff,axiom,
% 5.31/5.54 ! [N: num] :
% 5.31/5.54 ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ N ) )
% 5.31/5.54 = ( ord_less_num @ one @ N ) ) ).
% 5.31/5.54
% 5.31/5.54 % one_less_numeral_iff
% 5.31/5.54 thf(fact_3165_one__less__numeral__iff,axiom,
% 5.31/5.54 ! [N: num] :
% 5.31/5.54 ( ( ord_less_rat @ one_one_rat @ ( numeral_numeral_rat @ N ) )
% 5.31/5.54 = ( ord_less_num @ one @ N ) ) ).
% 5.31/5.54
% 5.31/5.54 % one_less_numeral_iff
% 5.31/5.54 thf(fact_3166_one__less__numeral__iff,axiom,
% 5.31/5.54 ! [N: num] :
% 5.31/5.54 ( ( ord_le72135733267957522d_enat @ one_on7984719198319812577d_enat @ ( numera1916890842035813515d_enat @ N ) )
% 5.31/5.54 = ( ord_less_num @ one @ N ) ) ).
% 5.31/5.54
% 5.31/5.54 % one_less_numeral_iff
% 5.31/5.54 thf(fact_3167_one__less__numeral__iff,axiom,
% 5.31/5.54 ! [N: num] :
% 5.31/5.54 ( ( ord_less_real @ one_one_real @ ( numeral_numeral_real @ N ) )
% 5.31/5.54 = ( ord_less_num @ one @ N ) ) ).
% 5.31/5.54
% 5.31/5.54 % one_less_numeral_iff
% 5.31/5.54 thf(fact_3168_one__less__numeral__iff,axiom,
% 5.31/5.54 ! [N: num] :
% 5.31/5.54 ( ( ord_less_nat @ one_one_nat @ ( numeral_numeral_nat @ N ) )
% 5.31/5.54 = ( ord_less_num @ one @ N ) ) ).
% 5.31/5.54
% 5.31/5.54 % one_less_numeral_iff
% 5.31/5.54 thf(fact_3169_one__less__numeral__iff,axiom,
% 5.31/5.54 ! [N: num] :
% 5.31/5.54 ( ( ord_less_int @ one_one_int @ ( numeral_numeral_int @ N ) )
% 5.31/5.54 = ( ord_less_num @ one @ N ) ) ).
% 5.31/5.54
% 5.31/5.54 % one_less_numeral_iff
% 5.31/5.54 thf(fact_3170_one__plus__numeral,axiom,
% 5.31/5.54 ! [N: num] :
% 5.31/5.54 ( ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ N ) )
% 5.31/5.54 = ( numera6620942414471956472nteger @ ( plus_plus_num @ one @ N ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % one_plus_numeral
% 5.31/5.54 thf(fact_3171_one__plus__numeral,axiom,
% 5.31/5.54 ! [N: num] :
% 5.31/5.54 ( ( plus_plus_rat @ one_one_rat @ ( numeral_numeral_rat @ N ) )
% 5.31/5.54 = ( numeral_numeral_rat @ ( plus_plus_num @ one @ N ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % one_plus_numeral
% 5.31/5.54 thf(fact_3172_one__plus__numeral,axiom,
% 5.31/5.54 ! [N: num] :
% 5.31/5.54 ( ( plus_p3455044024723400733d_enat @ one_on7984719198319812577d_enat @ ( numera1916890842035813515d_enat @ N ) )
% 5.31/5.54 = ( numera1916890842035813515d_enat @ ( plus_plus_num @ one @ N ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % one_plus_numeral
% 5.31/5.54 thf(fact_3173_one__plus__numeral,axiom,
% 5.31/5.54 ! [N: num] :
% 5.31/5.54 ( ( plus_plus_complex @ one_one_complex @ ( numera6690914467698888265omplex @ N ) )
% 5.31/5.54 = ( numera6690914467698888265omplex @ ( plus_plus_num @ one @ N ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % one_plus_numeral
% 5.31/5.54 thf(fact_3174_one__plus__numeral,axiom,
% 5.31/5.54 ! [N: num] :
% 5.31/5.54 ( ( plus_plus_real @ one_one_real @ ( numeral_numeral_real @ N ) )
% 5.31/5.54 = ( numeral_numeral_real @ ( plus_plus_num @ one @ N ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % one_plus_numeral
% 5.31/5.54 thf(fact_3175_one__plus__numeral,axiom,
% 5.31/5.54 ! [N: num] :
% 5.31/5.54 ( ( plus_plus_nat @ one_one_nat @ ( numeral_numeral_nat @ N ) )
% 5.31/5.54 = ( numeral_numeral_nat @ ( plus_plus_num @ one @ N ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % one_plus_numeral
% 5.31/5.54 thf(fact_3176_one__plus__numeral,axiom,
% 5.31/5.54 ! [N: num] :
% 5.31/5.54 ( ( plus_plus_int @ one_one_int @ ( numeral_numeral_int @ N ) )
% 5.31/5.54 = ( numeral_numeral_int @ ( plus_plus_num @ one @ N ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % one_plus_numeral
% 5.31/5.54 thf(fact_3177_numeral__plus__one,axiom,
% 5.31/5.54 ! [N: num] :
% 5.31/5.54 ( ( plus_p5714425477246183910nteger @ ( numera6620942414471956472nteger @ N ) @ one_one_Code_integer )
% 5.31/5.54 = ( numera6620942414471956472nteger @ ( plus_plus_num @ N @ one ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % numeral_plus_one
% 5.31/5.54 thf(fact_3178_numeral__plus__one,axiom,
% 5.31/5.54 ! [N: num] :
% 5.31/5.54 ( ( plus_plus_rat @ ( numeral_numeral_rat @ N ) @ one_one_rat )
% 5.31/5.54 = ( numeral_numeral_rat @ ( plus_plus_num @ N @ one ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % numeral_plus_one
% 5.31/5.54 thf(fact_3179_numeral__plus__one,axiom,
% 5.31/5.54 ! [N: num] :
% 5.31/5.54 ( ( plus_p3455044024723400733d_enat @ ( numera1916890842035813515d_enat @ N ) @ one_on7984719198319812577d_enat )
% 5.31/5.54 = ( numera1916890842035813515d_enat @ ( plus_plus_num @ N @ one ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % numeral_plus_one
% 5.31/5.54 thf(fact_3180_numeral__plus__one,axiom,
% 5.31/5.54 ! [N: num] :
% 5.31/5.54 ( ( plus_plus_complex @ ( numera6690914467698888265omplex @ N ) @ one_one_complex )
% 5.31/5.54 = ( numera6690914467698888265omplex @ ( plus_plus_num @ N @ one ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % numeral_plus_one
% 5.31/5.54 thf(fact_3181_numeral__plus__one,axiom,
% 5.31/5.54 ! [N: num] :
% 5.31/5.54 ( ( plus_plus_real @ ( numeral_numeral_real @ N ) @ one_one_real )
% 5.31/5.54 = ( numeral_numeral_real @ ( plus_plus_num @ N @ one ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % numeral_plus_one
% 5.31/5.54 thf(fact_3182_numeral__plus__one,axiom,
% 5.31/5.54 ! [N: num] :
% 5.31/5.54 ( ( plus_plus_nat @ ( numeral_numeral_nat @ N ) @ one_one_nat )
% 5.31/5.54 = ( numeral_numeral_nat @ ( plus_plus_num @ N @ one ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % numeral_plus_one
% 5.31/5.54 thf(fact_3183_numeral__plus__one,axiom,
% 5.31/5.54 ! [N: num] :
% 5.31/5.54 ( ( plus_plus_int @ ( numeral_numeral_int @ N ) @ one_one_int )
% 5.31/5.54 = ( numeral_numeral_int @ ( plus_plus_num @ N @ one ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % numeral_plus_one
% 5.31/5.54 thf(fact_3184_of__nat__le__0__iff,axiom,
% 5.31/5.54 ! [M2: nat] :
% 5.31/5.54 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ M2 ) @ zero_zero_real )
% 5.31/5.54 = ( M2 = zero_zero_nat ) ) ).
% 5.31/5.54
% 5.31/5.54 % of_nat_le_0_iff
% 5.31/5.54 thf(fact_3185_of__nat__le__0__iff,axiom,
% 5.31/5.54 ! [M2: nat] :
% 5.31/5.54 ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ M2 ) @ zero_zero_rat )
% 5.31/5.54 = ( M2 = zero_zero_nat ) ) ).
% 5.31/5.54
% 5.31/5.54 % of_nat_le_0_iff
% 5.31/5.54 thf(fact_3186_of__nat__le__0__iff,axiom,
% 5.31/5.54 ! [M2: nat] :
% 5.31/5.54 ( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ M2 ) @ zero_zero_nat )
% 5.31/5.54 = ( M2 = zero_zero_nat ) ) ).
% 5.31/5.54
% 5.31/5.54 % of_nat_le_0_iff
% 5.31/5.54 thf(fact_3187_of__nat__le__0__iff,axiom,
% 5.31/5.54 ! [M2: nat] :
% 5.31/5.54 ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ M2 ) @ zero_zero_int )
% 5.31/5.54 = ( M2 = zero_zero_nat ) ) ).
% 5.31/5.54
% 5.31/5.54 % of_nat_le_0_iff
% 5.31/5.54 thf(fact_3188_of__nat__Suc,axiom,
% 5.31/5.54 ! [M2: nat] :
% 5.31/5.54 ( ( semiri4939895301339042750nteger @ ( suc @ M2 ) )
% 5.31/5.54 = ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( semiri4939895301339042750nteger @ M2 ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % of_nat_Suc
% 5.31/5.54 thf(fact_3189_of__nat__Suc,axiom,
% 5.31/5.54 ! [M2: nat] :
% 5.31/5.54 ( ( semiri8010041392384452111omplex @ ( suc @ M2 ) )
% 5.31/5.54 = ( plus_plus_complex @ one_one_complex @ ( semiri8010041392384452111omplex @ M2 ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % of_nat_Suc
% 5.31/5.54 thf(fact_3190_of__nat__Suc,axiom,
% 5.31/5.54 ! [M2: nat] :
% 5.31/5.54 ( ( semiri681578069525770553at_rat @ ( suc @ M2 ) )
% 5.31/5.54 = ( plus_plus_rat @ one_one_rat @ ( semiri681578069525770553at_rat @ M2 ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % of_nat_Suc
% 5.31/5.54 thf(fact_3191_of__nat__Suc,axiom,
% 5.31/5.54 ! [M2: nat] :
% 5.31/5.54 ( ( semiri5074537144036343181t_real @ ( suc @ M2 ) )
% 5.31/5.54 = ( plus_plus_real @ one_one_real @ ( semiri5074537144036343181t_real @ M2 ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % of_nat_Suc
% 5.31/5.54 thf(fact_3192_of__nat__Suc,axiom,
% 5.31/5.54 ! [M2: nat] :
% 5.31/5.54 ( ( semiri1314217659103216013at_int @ ( suc @ M2 ) )
% 5.31/5.54 = ( plus_plus_int @ one_one_int @ ( semiri1314217659103216013at_int @ M2 ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % of_nat_Suc
% 5.31/5.54 thf(fact_3193_of__nat__Suc,axiom,
% 5.31/5.54 ! [M2: nat] :
% 5.31/5.54 ( ( semiri1316708129612266289at_nat @ ( suc @ M2 ) )
% 5.31/5.54 = ( plus_plus_nat @ one_one_nat @ ( semiri1316708129612266289at_nat @ M2 ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % of_nat_Suc
% 5.31/5.54 thf(fact_3194_one__add__one,axiom,
% 5.31/5.54 ( ( plus_p5714425477246183910nteger @ one_one_Code_integer @ one_one_Code_integer )
% 5.31/5.54 = ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % one_add_one
% 5.31/5.54 thf(fact_3195_one__add__one,axiom,
% 5.31/5.54 ( ( plus_plus_rat @ one_one_rat @ one_one_rat )
% 5.31/5.54 = ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % one_add_one
% 5.31/5.54 thf(fact_3196_one__add__one,axiom,
% 5.31/5.54 ( ( plus_p3455044024723400733d_enat @ one_on7984719198319812577d_enat @ one_on7984719198319812577d_enat )
% 5.31/5.54 = ( numera1916890842035813515d_enat @ ( bit0 @ one ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % one_add_one
% 5.31/5.54 thf(fact_3197_one__add__one,axiom,
% 5.31/5.54 ( ( plus_plus_complex @ one_one_complex @ one_one_complex )
% 5.31/5.54 = ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % one_add_one
% 5.31/5.54 thf(fact_3198_one__add__one,axiom,
% 5.31/5.54 ( ( plus_plus_real @ one_one_real @ one_one_real )
% 5.31/5.54 = ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % one_add_one
% 5.31/5.54 thf(fact_3199_one__add__one,axiom,
% 5.31/5.54 ( ( plus_plus_nat @ one_one_nat @ one_one_nat )
% 5.31/5.54 = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % one_add_one
% 5.31/5.54 thf(fact_3200_one__add__one,axiom,
% 5.31/5.54 ( ( plus_plus_int @ one_one_int @ one_one_int )
% 5.31/5.54 = ( numeral_numeral_int @ ( bit0 @ one ) ) ) ).
% 5.31/5.54
% 5.31/5.54 % one_add_one
% 5.31/5.54 thf(fact_3201_zero__eq__power2,axiom,
% 5.31/5.54 ! [A: rat] :
% 5.31/5.54 ( ( ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.31/5.54 = zero_zero_rat )
% 5.31/5.54 = ( A = zero_zero_rat ) ) ).
% 5.31/5.54
% 5.31/5.54 % zero_eq_power2
% 5.31/5.54 thf(fact_3202_zero__eq__power2,axiom,
% 5.31/5.54 ! [A: nat] :
% 5.31/5.54 ( ( ( power_power_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.31/5.54 = zero_zero_nat )
% 5.31/5.54 = ( A = zero_zero_nat ) ) ).
% 5.31/5.54
% 5.31/5.54 % zero_eq_power2
% 5.31/5.54 thf(fact_3203_zero__eq__power2,axiom,
% 5.31/5.54 ! [A: real] :
% 5.31/5.54 ( ( ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.31/5.54 = zero_zero_real )
% 5.31/5.54 = ( A = zero_zero_real ) ) ).
% 5.31/5.54
% 5.31/5.54 % zero_eq_power2
% 5.31/5.54 thf(fact_3204_zero__eq__power2,axiom,
% 5.31/5.54 ! [A: int] :
% 5.31/5.54 ( ( ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.31/5.54 = zero_zero_int )
% 5.31/5.54 = ( A = zero_zero_int ) ) ).
% 5.31/5.54
% 5.31/5.54 % zero_eq_power2
% 5.31/5.54 thf(fact_3205_zero__eq__power2,axiom,
% 5.31/5.54 ! [A: complex] :
% 5.31/5.54 ( ( ( power_power_complex @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.31/5.54 = zero_zero_complex )
% 5.31/5.54 = ( A = zero_zero_complex ) ) ).
% 5.31/5.54
% 5.31/5.54 % zero_eq_power2
% 5.31/5.54 thf(fact_3206_of__nat__0__less__iff,axiom,
% 5.31/5.54 ! [N: nat] :
% 5.31/5.54 ( ( ord_less_rat @ zero_zero_rat @ ( semiri681578069525770553at_rat @ N ) )
% 5.31/5.54 = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 5.31/5.54
% 5.31/5.54 % of_nat_0_less_iff
% 5.31/5.54 thf(fact_3207_of__nat__0__less__iff,axiom,
% 5.31/5.55 ! [N: nat] :
% 5.31/5.55 ( ( ord_less_real @ zero_zero_real @ ( semiri5074537144036343181t_real @ N ) )
% 5.31/5.55 = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 5.31/5.55
% 5.31/5.55 % of_nat_0_less_iff
% 5.31/5.55 thf(fact_3208_of__nat__0__less__iff,axiom,
% 5.31/5.55 ! [N: nat] :
% 5.31/5.55 ( ( ord_less_int @ zero_zero_int @ ( semiri1314217659103216013at_int @ N ) )
% 5.31/5.55 = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 5.31/5.55
% 5.31/5.55 % of_nat_0_less_iff
% 5.31/5.55 thf(fact_3209_of__nat__0__less__iff,axiom,
% 5.31/5.55 ! [N: nat] :
% 5.31/5.55 ( ( ord_less_nat @ zero_zero_nat @ ( semiri1316708129612266289at_nat @ N ) )
% 5.31/5.55 = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 5.31/5.55
% 5.31/5.55 % of_nat_0_less_iff
% 5.31/5.55 thf(fact_3210_add__2__eq__Suc,axiom,
% 5.31/5.55 ! [N: nat] :
% 5.31/5.55 ( ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.31/5.55 = ( suc @ ( suc @ N ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % add_2_eq_Suc
% 5.31/5.55 thf(fact_3211_add__2__eq__Suc_H,axiom,
% 5.31/5.55 ! [N: nat] :
% 5.31/5.55 ( ( plus_plus_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.31/5.55 = ( suc @ ( suc @ N ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % add_2_eq_Suc'
% 5.31/5.55 thf(fact_3212_Suc__1,axiom,
% 5.31/5.55 ( ( suc @ one_one_nat )
% 5.31/5.55 = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % Suc_1
% 5.31/5.55 thf(fact_3213_of__nat__le__of__nat__power__cancel__iff,axiom,
% 5.31/5.55 ! [B: nat,W2: nat,X: nat] :
% 5.31/5.55 ( ( ord_less_eq_real @ ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W2 ) @ ( semiri5074537144036343181t_real @ X ) )
% 5.31/5.55 = ( ord_less_eq_nat @ ( power_power_nat @ B @ W2 ) @ X ) ) ).
% 5.31/5.55
% 5.31/5.55 % of_nat_le_of_nat_power_cancel_iff
% 5.31/5.55 thf(fact_3214_of__nat__le__of__nat__power__cancel__iff,axiom,
% 5.31/5.55 ! [B: nat,W2: nat,X: nat] :
% 5.31/5.55 ( ( ord_less_eq_rat @ ( power_power_rat @ ( semiri681578069525770553at_rat @ B ) @ W2 ) @ ( semiri681578069525770553at_rat @ X ) )
% 5.31/5.55 = ( ord_less_eq_nat @ ( power_power_nat @ B @ W2 ) @ X ) ) ).
% 5.31/5.55
% 5.31/5.55 % of_nat_le_of_nat_power_cancel_iff
% 5.31/5.55 thf(fact_3215_of__nat__le__of__nat__power__cancel__iff,axiom,
% 5.31/5.55 ! [B: nat,W2: nat,X: nat] :
% 5.31/5.55 ( ( ord_less_eq_nat @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W2 ) @ ( semiri1316708129612266289at_nat @ X ) )
% 5.31/5.55 = ( ord_less_eq_nat @ ( power_power_nat @ B @ W2 ) @ X ) ) ).
% 5.31/5.55
% 5.31/5.55 % of_nat_le_of_nat_power_cancel_iff
% 5.31/5.55 thf(fact_3216_of__nat__le__of__nat__power__cancel__iff,axiom,
% 5.31/5.55 ! [B: nat,W2: nat,X: nat] :
% 5.31/5.55 ( ( ord_less_eq_int @ ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W2 ) @ ( semiri1314217659103216013at_int @ X ) )
% 5.31/5.55 = ( ord_less_eq_nat @ ( power_power_nat @ B @ W2 ) @ X ) ) ).
% 5.31/5.55
% 5.31/5.55 % of_nat_le_of_nat_power_cancel_iff
% 5.31/5.55 thf(fact_3217_of__nat__power__le__of__nat__cancel__iff,axiom,
% 5.31/5.55 ! [X: nat,B: nat,W2: nat] :
% 5.31/5.55 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ X ) @ ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W2 ) )
% 5.31/5.55 = ( ord_less_eq_nat @ X @ ( power_power_nat @ B @ W2 ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % of_nat_power_le_of_nat_cancel_iff
% 5.31/5.55 thf(fact_3218_of__nat__power__le__of__nat__cancel__iff,axiom,
% 5.31/5.55 ! [X: nat,B: nat,W2: nat] :
% 5.31/5.55 ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ X ) @ ( power_power_rat @ ( semiri681578069525770553at_rat @ B ) @ W2 ) )
% 5.31/5.55 = ( ord_less_eq_nat @ X @ ( power_power_nat @ B @ W2 ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % of_nat_power_le_of_nat_cancel_iff
% 5.31/5.55 thf(fact_3219_of__nat__power__le__of__nat__cancel__iff,axiom,
% 5.31/5.55 ! [X: nat,B: nat,W2: nat] :
% 5.31/5.55 ( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ X ) @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W2 ) )
% 5.31/5.55 = ( ord_less_eq_nat @ X @ ( power_power_nat @ B @ W2 ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % of_nat_power_le_of_nat_cancel_iff
% 5.31/5.55 thf(fact_3220_of__nat__power__le__of__nat__cancel__iff,axiom,
% 5.31/5.55 ! [X: nat,B: nat,W2: nat] :
% 5.31/5.55 ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ X ) @ ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W2 ) )
% 5.31/5.55 = ( ord_less_eq_nat @ X @ ( power_power_nat @ B @ W2 ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % of_nat_power_le_of_nat_cancel_iff
% 5.31/5.55 thf(fact_3221_set__replicate,axiom,
% 5.31/5.55 ! [N: nat,X: vEBT_VEBT] :
% 5.31/5.55 ( ( N != zero_zero_nat )
% 5.31/5.55 => ( ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ N @ X ) )
% 5.31/5.55 = ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % set_replicate
% 5.31/5.55 thf(fact_3222_set__replicate,axiom,
% 5.31/5.55 ! [N: nat,X: nat] :
% 5.31/5.55 ( ( N != zero_zero_nat )
% 5.31/5.55 => ( ( set_nat2 @ ( replicate_nat @ N @ X ) )
% 5.31/5.55 = ( insert_nat @ X @ bot_bot_set_nat ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % set_replicate
% 5.31/5.55 thf(fact_3223_set__replicate,axiom,
% 5.31/5.55 ! [N: nat,X: int] :
% 5.31/5.55 ( ( N != zero_zero_nat )
% 5.31/5.55 => ( ( set_int2 @ ( replicate_int @ N @ X ) )
% 5.31/5.55 = ( insert_int @ X @ bot_bot_set_int ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % set_replicate
% 5.31/5.55 thf(fact_3224_set__replicate,axiom,
% 5.31/5.55 ! [N: nat,X: real] :
% 5.31/5.55 ( ( N != zero_zero_nat )
% 5.31/5.55 => ( ( set_real2 @ ( replicate_real @ N @ X ) )
% 5.31/5.55 = ( insert_real @ X @ bot_bot_set_real ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % set_replicate
% 5.31/5.55 thf(fact_3225_power2__eq__iff__nonneg,axiom,
% 5.31/5.55 ! [X: real,Y: real] :
% 5.31/5.55 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.31/5.55 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.31/5.55 => ( ( ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.31/5.55 = ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.31/5.55 = ( X = Y ) ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % power2_eq_iff_nonneg
% 5.31/5.55 thf(fact_3226_power2__eq__iff__nonneg,axiom,
% 5.31/5.55 ! [X: rat,Y: rat] :
% 5.31/5.55 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 5.31/5.55 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 5.31/5.55 => ( ( ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.31/5.55 = ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.31/5.55 = ( X = Y ) ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % power2_eq_iff_nonneg
% 5.31/5.55 thf(fact_3227_power2__eq__iff__nonneg,axiom,
% 5.31/5.55 ! [X: nat,Y: nat] :
% 5.31/5.55 ( ( ord_less_eq_nat @ zero_zero_nat @ X )
% 5.31/5.55 => ( ( ord_less_eq_nat @ zero_zero_nat @ Y )
% 5.31/5.55 => ( ( ( power_power_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.31/5.55 = ( power_power_nat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.31/5.55 = ( X = Y ) ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % power2_eq_iff_nonneg
% 5.31/5.55 thf(fact_3228_power2__eq__iff__nonneg,axiom,
% 5.31/5.55 ! [X: int,Y: int] :
% 5.31/5.55 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.31/5.55 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.31/5.55 => ( ( ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.31/5.55 = ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.31/5.55 = ( X = Y ) ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % power2_eq_iff_nonneg
% 5.31/5.55 thf(fact_3229_power2__less__eq__zero__iff,axiom,
% 5.31/5.55 ! [A: real] :
% 5.31/5.55 ( ( ord_less_eq_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_real )
% 5.31/5.55 = ( A = zero_zero_real ) ) ).
% 5.31/5.55
% 5.31/5.55 % power2_less_eq_zero_iff
% 5.31/5.55 thf(fact_3230_power2__less__eq__zero__iff,axiom,
% 5.31/5.55 ! [A: rat] :
% 5.31/5.55 ( ( ord_less_eq_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_rat )
% 5.31/5.55 = ( A = zero_zero_rat ) ) ).
% 5.31/5.55
% 5.31/5.55 % power2_less_eq_zero_iff
% 5.31/5.55 thf(fact_3231_power2__less__eq__zero__iff,axiom,
% 5.31/5.55 ! [A: int] :
% 5.31/5.55 ( ( ord_less_eq_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_int )
% 5.31/5.55 = ( A = zero_zero_int ) ) ).
% 5.31/5.55
% 5.31/5.55 % power2_less_eq_zero_iff
% 5.31/5.55 thf(fact_3232_zero__less__power2,axiom,
% 5.31/5.55 ! [A: real] :
% 5.31/5.55 ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.31/5.55 = ( A != zero_zero_real ) ) ).
% 5.31/5.55
% 5.31/5.55 % zero_less_power2
% 5.31/5.55 thf(fact_3233_zero__less__power2,axiom,
% 5.31/5.55 ! [A: rat] :
% 5.31/5.55 ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.31/5.55 = ( A != zero_zero_rat ) ) ).
% 5.31/5.55
% 5.31/5.55 % zero_less_power2
% 5.31/5.55 thf(fact_3234_zero__less__power2,axiom,
% 5.31/5.55 ! [A: int] :
% 5.31/5.55 ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.31/5.55 = ( A != zero_zero_int ) ) ).
% 5.31/5.55
% 5.31/5.55 % zero_less_power2
% 5.31/5.55 thf(fact_3235_sum__power2__eq__zero__iff,axiom,
% 5.31/5.55 ! [X: rat,Y: rat] :
% 5.31/5.55 ( ( ( plus_plus_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.31/5.55 = zero_zero_rat )
% 5.31/5.55 = ( ( X = zero_zero_rat )
% 5.31/5.55 & ( Y = zero_zero_rat ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % sum_power2_eq_zero_iff
% 5.31/5.55 thf(fact_3236_sum__power2__eq__zero__iff,axiom,
% 5.31/5.55 ! [X: real,Y: real] :
% 5.31/5.55 ( ( ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.31/5.55 = zero_zero_real )
% 5.31/5.55 = ( ( X = zero_zero_real )
% 5.31/5.55 & ( Y = zero_zero_real ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % sum_power2_eq_zero_iff
% 5.31/5.55 thf(fact_3237_sum__power2__eq__zero__iff,axiom,
% 5.31/5.55 ! [X: int,Y: int] :
% 5.31/5.55 ( ( ( plus_plus_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.31/5.55 = zero_zero_int )
% 5.31/5.55 = ( ( X = zero_zero_int )
% 5.31/5.55 & ( Y = zero_zero_int ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % sum_power2_eq_zero_iff
% 5.31/5.55 thf(fact_3238_numeral__power__le__of__nat__cancel__iff,axiom,
% 5.31/5.55 ! [I2: num,N: nat,X: nat] :
% 5.31/5.55 ( ( ord_less_eq_real @ ( power_power_real @ ( numeral_numeral_real @ I2 ) @ N ) @ ( semiri5074537144036343181t_real @ X ) )
% 5.31/5.55 = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N ) @ X ) ) ).
% 5.31/5.55
% 5.31/5.55 % numeral_power_le_of_nat_cancel_iff
% 5.31/5.55 thf(fact_3239_numeral__power__le__of__nat__cancel__iff,axiom,
% 5.31/5.55 ! [I2: num,N: nat,X: nat] :
% 5.31/5.55 ( ( ord_less_eq_rat @ ( power_power_rat @ ( numeral_numeral_rat @ I2 ) @ N ) @ ( semiri681578069525770553at_rat @ X ) )
% 5.31/5.55 = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N ) @ X ) ) ).
% 5.31/5.55
% 5.31/5.55 % numeral_power_le_of_nat_cancel_iff
% 5.31/5.55 thf(fact_3240_numeral__power__le__of__nat__cancel__iff,axiom,
% 5.31/5.55 ! [I2: num,N: nat,X: nat] :
% 5.31/5.55 ( ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N ) @ ( semiri1316708129612266289at_nat @ X ) )
% 5.31/5.55 = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N ) @ X ) ) ).
% 5.31/5.55
% 5.31/5.55 % numeral_power_le_of_nat_cancel_iff
% 5.31/5.55 thf(fact_3241_numeral__power__le__of__nat__cancel__iff,axiom,
% 5.31/5.55 ! [I2: num,N: nat,X: nat] :
% 5.31/5.55 ( ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ I2 ) @ N ) @ ( semiri1314217659103216013at_int @ X ) )
% 5.31/5.55 = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N ) @ X ) ) ).
% 5.31/5.55
% 5.31/5.55 % numeral_power_le_of_nat_cancel_iff
% 5.31/5.55 thf(fact_3242_of__nat__le__numeral__power__cancel__iff,axiom,
% 5.31/5.55 ! [X: nat,I2: num,N: nat] :
% 5.31/5.55 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ X ) @ ( power_power_real @ ( numeral_numeral_real @ I2 ) @ N ) )
% 5.31/5.55 = ( ord_less_eq_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % of_nat_le_numeral_power_cancel_iff
% 5.31/5.55 thf(fact_3243_of__nat__le__numeral__power__cancel__iff,axiom,
% 5.31/5.55 ! [X: nat,I2: num,N: nat] :
% 5.31/5.55 ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ X ) @ ( power_power_rat @ ( numeral_numeral_rat @ I2 ) @ N ) )
% 5.31/5.55 = ( ord_less_eq_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % of_nat_le_numeral_power_cancel_iff
% 5.31/5.55 thf(fact_3244_of__nat__le__numeral__power__cancel__iff,axiom,
% 5.31/5.55 ! [X: nat,I2: num,N: nat] :
% 5.31/5.55 ( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ X ) @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N ) )
% 5.31/5.55 = ( ord_less_eq_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % of_nat_le_numeral_power_cancel_iff
% 5.31/5.55 thf(fact_3245_of__nat__le__numeral__power__cancel__iff,axiom,
% 5.31/5.55 ! [X: nat,I2: num,N: nat] :
% 5.31/5.55 ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ X ) @ ( power_power_int @ ( numeral_numeral_int @ I2 ) @ N ) )
% 5.31/5.55 = ( ord_less_eq_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % of_nat_le_numeral_power_cancel_iff
% 5.31/5.55 thf(fact_3246_power2__nat__le__imp__le,axiom,
% 5.31/5.55 ! [M2: nat,N: nat] :
% 5.31/5.55 ( ( ord_less_eq_nat @ ( power_power_nat @ M2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ N )
% 5.31/5.55 => ( ord_less_eq_nat @ M2 @ N ) ) ).
% 5.31/5.55
% 5.31/5.55 % power2_nat_le_imp_le
% 5.31/5.55 thf(fact_3247_power2__nat__le__eq__le,axiom,
% 5.31/5.55 ! [M2: nat,N: nat] :
% 5.31/5.55 ( ( ord_less_eq_nat @ ( power_power_nat @ M2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.31/5.55 = ( ord_less_eq_nat @ M2 @ N ) ) ).
% 5.31/5.55
% 5.31/5.55 % power2_nat_le_eq_le
% 5.31/5.55 thf(fact_3248_self__le__ge2__pow,axiom,
% 5.31/5.55 ! [K2: nat,M2: nat] :
% 5.31/5.55 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K2 )
% 5.31/5.55 => ( ord_less_eq_nat @ M2 @ ( power_power_nat @ K2 @ M2 ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % self_le_ge2_pow
% 5.31/5.55 thf(fact_3249_card__2__iff_H,axiom,
% 5.31/5.55 ! [S3: set_nat] :
% 5.31/5.55 ( ( ( finite_card_nat @ S3 )
% 5.31/5.55 = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.31/5.55 = ( ? [X4: nat] :
% 5.31/5.55 ( ( member_nat @ X4 @ S3 )
% 5.31/5.55 & ? [Y4: nat] :
% 5.31/5.55 ( ( member_nat @ Y4 @ S3 )
% 5.31/5.55 & ( X4 != Y4 )
% 5.31/5.55 & ! [Z4: nat] :
% 5.31/5.55 ( ( member_nat @ Z4 @ S3 )
% 5.31/5.55 => ( ( Z4 = X4 )
% 5.31/5.55 | ( Z4 = Y4 ) ) ) ) ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % card_2_iff'
% 5.31/5.55 thf(fact_3250_card__2__iff_H,axiom,
% 5.31/5.55 ! [S3: set_complex] :
% 5.31/5.55 ( ( ( finite_card_complex @ S3 )
% 5.31/5.55 = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.31/5.55 = ( ? [X4: complex] :
% 5.31/5.55 ( ( member_complex @ X4 @ S3 )
% 5.31/5.55 & ? [Y4: complex] :
% 5.31/5.55 ( ( member_complex @ Y4 @ S3 )
% 5.31/5.55 & ( X4 != Y4 )
% 5.31/5.55 & ! [Z4: complex] :
% 5.31/5.55 ( ( member_complex @ Z4 @ S3 )
% 5.31/5.55 => ( ( Z4 = X4 )
% 5.31/5.55 | ( Z4 = Y4 ) ) ) ) ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % card_2_iff'
% 5.31/5.55 thf(fact_3251_card__2__iff_H,axiom,
% 5.31/5.55 ! [S3: set_int] :
% 5.31/5.55 ( ( ( finite_card_int @ S3 )
% 5.31/5.55 = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.31/5.55 = ( ? [X4: int] :
% 5.31/5.55 ( ( member_int @ X4 @ S3 )
% 5.31/5.55 & ? [Y4: int] :
% 5.31/5.55 ( ( member_int @ Y4 @ S3 )
% 5.31/5.55 & ( X4 != Y4 )
% 5.31/5.55 & ! [Z4: int] :
% 5.31/5.55 ( ( member_int @ Z4 @ S3 )
% 5.31/5.55 => ( ( Z4 = X4 )
% 5.31/5.55 | ( Z4 = Y4 ) ) ) ) ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % card_2_iff'
% 5.31/5.55 thf(fact_3252_card__2__iff_H,axiom,
% 5.31/5.55 ! [S3: set_list_nat] :
% 5.31/5.55 ( ( ( finite_card_list_nat @ S3 )
% 5.31/5.55 = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.31/5.55 = ( ? [X4: list_nat] :
% 5.31/5.55 ( ( member_list_nat @ X4 @ S3 )
% 5.31/5.55 & ? [Y4: list_nat] :
% 5.31/5.55 ( ( member_list_nat @ Y4 @ S3 )
% 5.31/5.55 & ( X4 != Y4 )
% 5.31/5.55 & ! [Z4: list_nat] :
% 5.31/5.55 ( ( member_list_nat @ Z4 @ S3 )
% 5.31/5.55 => ( ( Z4 = X4 )
% 5.31/5.55 | ( Z4 = Y4 ) ) ) ) ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % card_2_iff'
% 5.31/5.55 thf(fact_3253_card__2__iff_H,axiom,
% 5.31/5.55 ! [S3: set_set_nat] :
% 5.31/5.55 ( ( ( finite_card_set_nat @ S3 )
% 5.31/5.55 = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.31/5.55 = ( ? [X4: set_nat] :
% 5.31/5.55 ( ( member_set_nat @ X4 @ S3 )
% 5.31/5.55 & ? [Y4: set_nat] :
% 5.31/5.55 ( ( member_set_nat @ Y4 @ S3 )
% 5.31/5.55 & ( X4 != Y4 )
% 5.31/5.55 & ! [Z4: set_nat] :
% 5.31/5.55 ( ( member_set_nat @ Z4 @ S3 )
% 5.31/5.55 => ( ( Z4 = X4 )
% 5.31/5.55 | ( Z4 = Y4 ) ) ) ) ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % card_2_iff'
% 5.31/5.55 thf(fact_3254_reals__Archimedean3,axiom,
% 5.31/5.55 ! [X: real] :
% 5.31/5.55 ( ( ord_less_real @ zero_zero_real @ X )
% 5.31/5.55 => ! [Y6: real] :
% 5.31/5.55 ? [N3: nat] : ( ord_less_real @ Y6 @ ( times_times_real @ ( semiri5074537144036343181t_real @ N3 ) @ X ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % reals_Archimedean3
% 5.31/5.55 thf(fact_3255_add__One__commute,axiom,
% 5.31/5.55 ! [N: num] :
% 5.31/5.55 ( ( plus_plus_num @ one @ N )
% 5.31/5.55 = ( plus_plus_num @ N @ one ) ) ).
% 5.31/5.55
% 5.31/5.55 % add_One_commute
% 5.31/5.55 thf(fact_3256_numeral__Bit0,axiom,
% 5.31/5.55 ! [N: num] :
% 5.31/5.55 ( ( numeral_numeral_rat @ ( bit0 @ N ) )
% 5.31/5.55 = ( plus_plus_rat @ ( numeral_numeral_rat @ N ) @ ( numeral_numeral_rat @ N ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % numeral_Bit0
% 5.31/5.55 thf(fact_3257_numeral__Bit0,axiom,
% 5.31/5.55 ! [N: num] :
% 5.31/5.55 ( ( numera1916890842035813515d_enat @ ( bit0 @ N ) )
% 5.31/5.55 = ( plus_p3455044024723400733d_enat @ ( numera1916890842035813515d_enat @ N ) @ ( numera1916890842035813515d_enat @ N ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % numeral_Bit0
% 5.31/5.55 thf(fact_3258_numeral__Bit0,axiom,
% 5.31/5.55 ! [N: num] :
% 5.31/5.55 ( ( numera6690914467698888265omplex @ ( bit0 @ N ) )
% 5.31/5.55 = ( plus_plus_complex @ ( numera6690914467698888265omplex @ N ) @ ( numera6690914467698888265omplex @ N ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % numeral_Bit0
% 5.31/5.55 thf(fact_3259_numeral__Bit0,axiom,
% 5.31/5.55 ! [N: num] :
% 5.31/5.55 ( ( numeral_numeral_real @ ( bit0 @ N ) )
% 5.31/5.55 = ( plus_plus_real @ ( numeral_numeral_real @ N ) @ ( numeral_numeral_real @ N ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % numeral_Bit0
% 5.31/5.55 thf(fact_3260_numeral__Bit0,axiom,
% 5.31/5.55 ! [N: num] :
% 5.31/5.55 ( ( numeral_numeral_nat @ ( bit0 @ N ) )
% 5.31/5.55 = ( plus_plus_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ N ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % numeral_Bit0
% 5.31/5.55 thf(fact_3261_numeral__Bit0,axiom,
% 5.31/5.55 ! [N: num] :
% 5.31/5.55 ( ( numeral_numeral_int @ ( bit0 @ N ) )
% 5.31/5.55 = ( plus_plus_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ N ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % numeral_Bit0
% 5.31/5.55 thf(fact_3262_mult__numeral__1__right,axiom,
% 5.31/5.55 ! [A: rat] :
% 5.31/5.55 ( ( times_times_rat @ A @ ( numeral_numeral_rat @ one ) )
% 5.31/5.55 = A ) ).
% 5.31/5.55
% 5.31/5.55 % mult_numeral_1_right
% 5.31/5.55 thf(fact_3263_mult__numeral__1__right,axiom,
% 5.31/5.55 ! [A: extended_enat] :
% 5.31/5.55 ( ( times_7803423173614009249d_enat @ A @ ( numera1916890842035813515d_enat @ one ) )
% 5.31/5.55 = A ) ).
% 5.31/5.55
% 5.31/5.55 % mult_numeral_1_right
% 5.31/5.55 thf(fact_3264_mult__numeral__1__right,axiom,
% 5.31/5.55 ! [A: complex] :
% 5.31/5.55 ( ( times_times_complex @ A @ ( numera6690914467698888265omplex @ one ) )
% 5.31/5.55 = A ) ).
% 5.31/5.55
% 5.31/5.55 % mult_numeral_1_right
% 5.31/5.55 thf(fact_3265_mult__numeral__1__right,axiom,
% 5.31/5.55 ! [A: real] :
% 5.31/5.55 ( ( times_times_real @ A @ ( numeral_numeral_real @ one ) )
% 5.31/5.55 = A ) ).
% 5.31/5.55
% 5.31/5.55 % mult_numeral_1_right
% 5.31/5.55 thf(fact_3266_mult__numeral__1__right,axiom,
% 5.31/5.55 ! [A: nat] :
% 5.31/5.55 ( ( times_times_nat @ A @ ( numeral_numeral_nat @ one ) )
% 5.31/5.55 = A ) ).
% 5.31/5.55
% 5.31/5.55 % mult_numeral_1_right
% 5.31/5.55 thf(fact_3267_mult__numeral__1__right,axiom,
% 5.31/5.55 ! [A: int] :
% 5.31/5.55 ( ( times_times_int @ A @ ( numeral_numeral_int @ one ) )
% 5.31/5.55 = A ) ).
% 5.31/5.55
% 5.31/5.55 % mult_numeral_1_right
% 5.31/5.55 thf(fact_3268_mult__numeral__1,axiom,
% 5.31/5.55 ! [A: rat] :
% 5.31/5.55 ( ( times_times_rat @ ( numeral_numeral_rat @ one ) @ A )
% 5.31/5.55 = A ) ).
% 5.31/5.55
% 5.31/5.55 % mult_numeral_1
% 5.31/5.55 thf(fact_3269_mult__numeral__1,axiom,
% 5.31/5.55 ! [A: extended_enat] :
% 5.31/5.55 ( ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ one ) @ A )
% 5.31/5.55 = A ) ).
% 5.31/5.55
% 5.31/5.55 % mult_numeral_1
% 5.31/5.55 thf(fact_3270_mult__numeral__1,axiom,
% 5.31/5.55 ! [A: complex] :
% 5.31/5.55 ( ( times_times_complex @ ( numera6690914467698888265omplex @ one ) @ A )
% 5.31/5.55 = A ) ).
% 5.31/5.55
% 5.31/5.55 % mult_numeral_1
% 5.31/5.55 thf(fact_3271_mult__numeral__1,axiom,
% 5.31/5.55 ! [A: real] :
% 5.31/5.55 ( ( times_times_real @ ( numeral_numeral_real @ one ) @ A )
% 5.31/5.55 = A ) ).
% 5.31/5.55
% 5.31/5.55 % mult_numeral_1
% 5.31/5.55 thf(fact_3272_mult__numeral__1,axiom,
% 5.31/5.55 ! [A: nat] :
% 5.31/5.55 ( ( times_times_nat @ ( numeral_numeral_nat @ one ) @ A )
% 5.31/5.55 = A ) ).
% 5.31/5.55
% 5.31/5.55 % mult_numeral_1
% 5.31/5.55 thf(fact_3273_mult__numeral__1,axiom,
% 5.31/5.55 ! [A: int] :
% 5.31/5.55 ( ( times_times_int @ ( numeral_numeral_int @ one ) @ A )
% 5.31/5.55 = A ) ).
% 5.31/5.55
% 5.31/5.55 % mult_numeral_1
% 5.31/5.55 thf(fact_3274_numeral__One,axiom,
% 5.31/5.55 ( ( numera6620942414471956472nteger @ one )
% 5.31/5.55 = one_one_Code_integer ) ).
% 5.31/5.55
% 5.31/5.55 % numeral_One
% 5.31/5.55 thf(fact_3275_numeral__One,axiom,
% 5.31/5.55 ( ( numera1916890842035813515d_enat @ one )
% 5.31/5.55 = one_on7984719198319812577d_enat ) ).
% 5.31/5.55
% 5.31/5.55 % numeral_One
% 5.31/5.55 thf(fact_3276_numeral__One,axiom,
% 5.31/5.55 ( ( numera6690914467698888265omplex @ one )
% 5.31/5.55 = one_one_complex ) ).
% 5.31/5.55
% 5.31/5.55 % numeral_One
% 5.31/5.55 thf(fact_3277_numeral__One,axiom,
% 5.31/5.55 ( ( numeral_numeral_real @ one )
% 5.31/5.55 = one_one_real ) ).
% 5.31/5.55
% 5.31/5.55 % numeral_One
% 5.31/5.55 thf(fact_3278_numeral__One,axiom,
% 5.31/5.55 ( ( numeral_numeral_nat @ one )
% 5.31/5.55 = one_one_nat ) ).
% 5.31/5.55
% 5.31/5.55 % numeral_One
% 5.31/5.55 thf(fact_3279_numeral__One,axiom,
% 5.31/5.55 ( ( numeral_numeral_int @ one )
% 5.31/5.55 = one_one_int ) ).
% 5.31/5.55
% 5.31/5.55 % numeral_One
% 5.31/5.55 thf(fact_3280_pos2,axiom,
% 5.31/5.55 ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ).
% 5.31/5.55
% 5.31/5.55 % pos2
% 5.31/5.55 thf(fact_3281_numerals_I1_J,axiom,
% 5.31/5.55 ( ( numeral_numeral_nat @ one )
% 5.31/5.55 = one_one_nat ) ).
% 5.31/5.55
% 5.31/5.55 % numerals(1)
% 5.31/5.55 thf(fact_3282_le__num__One__iff,axiom,
% 5.31/5.55 ! [X: num] :
% 5.31/5.55 ( ( ord_less_eq_num @ X @ one )
% 5.31/5.55 = ( X = one ) ) ).
% 5.31/5.55
% 5.31/5.55 % le_num_One_iff
% 5.31/5.55 thf(fact_3283_mult__2,axiom,
% 5.31/5.55 ! [Z3: rat] :
% 5.31/5.55 ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ Z3 )
% 5.31/5.55 = ( plus_plus_rat @ Z3 @ Z3 ) ) ).
% 5.31/5.55
% 5.31/5.55 % mult_2
% 5.31/5.55 thf(fact_3284_mult__2,axiom,
% 5.31/5.55 ! [Z3: extended_enat] :
% 5.31/5.55 ( ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ ( bit0 @ one ) ) @ Z3 )
% 5.31/5.55 = ( plus_p3455044024723400733d_enat @ Z3 @ Z3 ) ) ).
% 5.31/5.55
% 5.31/5.55 % mult_2
% 5.31/5.55 thf(fact_3285_mult__2,axiom,
% 5.31/5.55 ! [Z3: complex] :
% 5.31/5.55 ( ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ Z3 )
% 5.31/5.55 = ( plus_plus_complex @ Z3 @ Z3 ) ) ).
% 5.31/5.55
% 5.31/5.55 % mult_2
% 5.31/5.55 thf(fact_3286_mult__2,axiom,
% 5.31/5.55 ! [Z3: real] :
% 5.31/5.55 ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ Z3 )
% 5.31/5.55 = ( plus_plus_real @ Z3 @ Z3 ) ) ).
% 5.31/5.55
% 5.31/5.55 % mult_2
% 5.31/5.55 thf(fact_3287_mult__2,axiom,
% 5.31/5.55 ! [Z3: nat] :
% 5.31/5.55 ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Z3 )
% 5.31/5.55 = ( plus_plus_nat @ Z3 @ Z3 ) ) ).
% 5.31/5.55
% 5.31/5.55 % mult_2
% 5.31/5.55 thf(fact_3288_mult__2,axiom,
% 5.31/5.55 ! [Z3: int] :
% 5.31/5.55 ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Z3 )
% 5.31/5.55 = ( plus_plus_int @ Z3 @ Z3 ) ) ).
% 5.31/5.55
% 5.31/5.55 % mult_2
% 5.31/5.55 thf(fact_3289_mult__2__right,axiom,
% 5.31/5.55 ! [Z3: rat] :
% 5.31/5.55 ( ( times_times_rat @ Z3 @ ( numeral_numeral_rat @ ( bit0 @ one ) ) )
% 5.31/5.55 = ( plus_plus_rat @ Z3 @ Z3 ) ) ).
% 5.31/5.55
% 5.31/5.55 % mult_2_right
% 5.31/5.55 thf(fact_3290_mult__2__right,axiom,
% 5.31/5.55 ! [Z3: extended_enat] :
% 5.31/5.55 ( ( times_7803423173614009249d_enat @ Z3 @ ( numera1916890842035813515d_enat @ ( bit0 @ one ) ) )
% 5.31/5.55 = ( plus_p3455044024723400733d_enat @ Z3 @ Z3 ) ) ).
% 5.31/5.55
% 5.31/5.55 % mult_2_right
% 5.31/5.55 thf(fact_3291_mult__2__right,axiom,
% 5.31/5.55 ! [Z3: complex] :
% 5.31/5.55 ( ( times_times_complex @ Z3 @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) )
% 5.31/5.55 = ( plus_plus_complex @ Z3 @ Z3 ) ) ).
% 5.31/5.55
% 5.31/5.55 % mult_2_right
% 5.31/5.55 thf(fact_3292_mult__2__right,axiom,
% 5.31/5.55 ! [Z3: real] :
% 5.31/5.55 ( ( times_times_real @ Z3 @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.31/5.55 = ( plus_plus_real @ Z3 @ Z3 ) ) ).
% 5.31/5.55
% 5.31/5.55 % mult_2_right
% 5.31/5.55 thf(fact_3293_mult__2__right,axiom,
% 5.31/5.55 ! [Z3: nat] :
% 5.31/5.55 ( ( times_times_nat @ Z3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.31/5.55 = ( plus_plus_nat @ Z3 @ Z3 ) ) ).
% 5.31/5.55
% 5.31/5.55 % mult_2_right
% 5.31/5.55 thf(fact_3294_mult__2__right,axiom,
% 5.31/5.55 ! [Z3: int] :
% 5.31/5.55 ( ( times_times_int @ Z3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.31/5.55 = ( plus_plus_int @ Z3 @ Z3 ) ) ).
% 5.31/5.55
% 5.31/5.55 % mult_2_right
% 5.31/5.55 thf(fact_3295_left__add__twice,axiom,
% 5.31/5.55 ! [A: rat,B: rat] :
% 5.31/5.55 ( ( plus_plus_rat @ A @ ( plus_plus_rat @ A @ B ) )
% 5.31/5.55 = ( plus_plus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 5.31/5.55
% 5.31/5.55 % left_add_twice
% 5.31/5.55 thf(fact_3296_left__add__twice,axiom,
% 5.31/5.55 ! [A: extended_enat,B: extended_enat] :
% 5.31/5.55 ( ( plus_p3455044024723400733d_enat @ A @ ( plus_p3455044024723400733d_enat @ A @ B ) )
% 5.31/5.55 = ( plus_p3455044024723400733d_enat @ ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 5.31/5.55
% 5.31/5.55 % left_add_twice
% 5.31/5.55 thf(fact_3297_left__add__twice,axiom,
% 5.31/5.55 ! [A: complex,B: complex] :
% 5.31/5.55 ( ( plus_plus_complex @ A @ ( plus_plus_complex @ A @ B ) )
% 5.31/5.55 = ( plus_plus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 5.31/5.55
% 5.31/5.55 % left_add_twice
% 5.31/5.55 thf(fact_3298_left__add__twice,axiom,
% 5.31/5.55 ! [A: real,B: real] :
% 5.31/5.55 ( ( plus_plus_real @ A @ ( plus_plus_real @ A @ B ) )
% 5.31/5.55 = ( plus_plus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 5.31/5.55
% 5.31/5.55 % left_add_twice
% 5.31/5.55 thf(fact_3299_left__add__twice,axiom,
% 5.31/5.55 ! [A: nat,B: nat] :
% 5.31/5.55 ( ( plus_plus_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 5.31/5.55 = ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 5.31/5.55
% 5.31/5.55 % left_add_twice
% 5.31/5.55 thf(fact_3300_left__add__twice,axiom,
% 5.31/5.55 ! [A: int,B: int] :
% 5.31/5.55 ( ( plus_plus_int @ A @ ( plus_plus_int @ A @ B ) )
% 5.31/5.55 = ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 5.31/5.55
% 5.31/5.55 % left_add_twice
% 5.31/5.55 thf(fact_3301_zero__power2,axiom,
% 5.31/5.55 ( ( power_power_rat @ zero_zero_rat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.31/5.55 = zero_zero_rat ) ).
% 5.31/5.55
% 5.31/5.55 % zero_power2
% 5.31/5.55 thf(fact_3302_zero__power2,axiom,
% 5.31/5.55 ( ( power_power_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.31/5.55 = zero_zero_nat ) ).
% 5.31/5.55
% 5.31/5.55 % zero_power2
% 5.31/5.55 thf(fact_3303_zero__power2,axiom,
% 5.31/5.55 ( ( power_power_real @ zero_zero_real @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.31/5.55 = zero_zero_real ) ).
% 5.31/5.55
% 5.31/5.55 % zero_power2
% 5.31/5.55 thf(fact_3304_zero__power2,axiom,
% 5.31/5.55 ( ( power_power_int @ zero_zero_int @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.31/5.55 = zero_zero_int ) ).
% 5.31/5.55
% 5.31/5.55 % zero_power2
% 5.31/5.55 thf(fact_3305_zero__power2,axiom,
% 5.31/5.55 ( ( power_power_complex @ zero_zero_complex @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.31/5.55 = zero_zero_complex ) ).
% 5.31/5.55
% 5.31/5.55 % zero_power2
% 5.31/5.55 thf(fact_3306_power2__eq__square,axiom,
% 5.31/5.55 ! [A: complex] :
% 5.31/5.55 ( ( power_power_complex @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.31/5.55 = ( times_times_complex @ A @ A ) ) ).
% 5.31/5.55
% 5.31/5.55 % power2_eq_square
% 5.31/5.55 thf(fact_3307_power2__eq__square,axiom,
% 5.31/5.55 ! [A: real] :
% 5.31/5.55 ( ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.31/5.55 = ( times_times_real @ A @ A ) ) ).
% 5.31/5.55
% 5.31/5.55 % power2_eq_square
% 5.31/5.55 thf(fact_3308_power2__eq__square,axiom,
% 5.31/5.55 ! [A: rat] :
% 5.31/5.55 ( ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.31/5.55 = ( times_times_rat @ A @ A ) ) ).
% 5.31/5.55
% 5.31/5.55 % power2_eq_square
% 5.31/5.55 thf(fact_3309_power2__eq__square,axiom,
% 5.31/5.55 ! [A: nat] :
% 5.31/5.55 ( ( power_power_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.31/5.55 = ( times_times_nat @ A @ A ) ) ).
% 5.31/5.55
% 5.31/5.55 % power2_eq_square
% 5.31/5.55 thf(fact_3310_power2__eq__square,axiom,
% 5.31/5.55 ! [A: int] :
% 5.31/5.55 ( ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.31/5.55 = ( times_times_int @ A @ A ) ) ).
% 5.31/5.55
% 5.31/5.55 % power2_eq_square
% 5.31/5.55 thf(fact_3311_power4__eq__xxxx,axiom,
% 5.31/5.55 ! [X: complex] :
% 5.31/5.55 ( ( power_power_complex @ X @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.31/5.55 = ( times_times_complex @ ( times_times_complex @ ( times_times_complex @ X @ X ) @ X ) @ X ) ) ).
% 5.31/5.55
% 5.31/5.55 % power4_eq_xxxx
% 5.31/5.55 thf(fact_3312_power4__eq__xxxx,axiom,
% 5.31/5.55 ! [X: real] :
% 5.31/5.55 ( ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.31/5.55 = ( times_times_real @ ( times_times_real @ ( times_times_real @ X @ X ) @ X ) @ X ) ) ).
% 5.31/5.55
% 5.31/5.55 % power4_eq_xxxx
% 5.31/5.55 thf(fact_3313_power4__eq__xxxx,axiom,
% 5.31/5.55 ! [X: rat] :
% 5.31/5.55 ( ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.31/5.55 = ( times_times_rat @ ( times_times_rat @ ( times_times_rat @ X @ X ) @ X ) @ X ) ) ).
% 5.31/5.55
% 5.31/5.55 % power4_eq_xxxx
% 5.31/5.55 thf(fact_3314_power4__eq__xxxx,axiom,
% 5.31/5.55 ! [X: nat] :
% 5.31/5.55 ( ( power_power_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.31/5.55 = ( times_times_nat @ ( times_times_nat @ ( times_times_nat @ X @ X ) @ X ) @ X ) ) ).
% 5.31/5.55
% 5.31/5.55 % power4_eq_xxxx
% 5.31/5.55 thf(fact_3315_power4__eq__xxxx,axiom,
% 5.31/5.55 ! [X: int] :
% 5.31/5.55 ( ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.31/5.55 = ( times_times_int @ ( times_times_int @ ( times_times_int @ X @ X ) @ X ) @ X ) ) ).
% 5.31/5.55
% 5.31/5.55 % power4_eq_xxxx
% 5.31/5.55 thf(fact_3316_numeral__2__eq__2,axiom,
% 5.31/5.55 ( ( numeral_numeral_nat @ ( bit0 @ one ) )
% 5.31/5.55 = ( suc @ ( suc @ zero_zero_nat ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % numeral_2_eq_2
% 5.31/5.55 thf(fact_3317_power__even__eq,axiom,
% 5.31/5.55 ! [A: nat,N: nat] :
% 5.31/5.55 ( ( power_power_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.31/5.55 = ( power_power_nat @ ( power_power_nat @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % power_even_eq
% 5.31/5.55 thf(fact_3318_power__even__eq,axiom,
% 5.31/5.55 ! [A: real,N: nat] :
% 5.31/5.55 ( ( power_power_real @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.31/5.55 = ( power_power_real @ ( power_power_real @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % power_even_eq
% 5.31/5.55 thf(fact_3319_power__even__eq,axiom,
% 5.31/5.55 ! [A: int,N: nat] :
% 5.31/5.55 ( ( power_power_int @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.31/5.55 = ( power_power_int @ ( power_power_int @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % power_even_eq
% 5.31/5.55 thf(fact_3320_power__even__eq,axiom,
% 5.31/5.55 ! [A: complex,N: nat] :
% 5.31/5.55 ( ( power_power_complex @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.31/5.55 = ( power_power_complex @ ( power_power_complex @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % power_even_eq
% 5.31/5.55 thf(fact_3321_diff__le__diff__pow,axiom,
% 5.31/5.55 ! [K2: nat,M2: nat,N: nat] :
% 5.31/5.55 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K2 )
% 5.31/5.55 => ( ord_less_eq_nat @ ( minus_minus_nat @ M2 @ N ) @ ( minus_minus_nat @ ( power_power_nat @ K2 @ M2 ) @ ( power_power_nat @ K2 @ N ) ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % diff_le_diff_pow
% 5.31/5.55 thf(fact_3322_nat__1__add__1,axiom,
% 5.31/5.55 ( ( plus_plus_nat @ one_one_nat @ one_one_nat )
% 5.31/5.55 = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % nat_1_add_1
% 5.31/5.55 thf(fact_3323_power2__sum,axiom,
% 5.31/5.55 ! [X: rat,Y: rat] :
% 5.31/5.55 ( ( power_power_rat @ ( plus_plus_rat @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.31/5.55 = ( 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 ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % power2_sum
% 5.31/5.55 thf(fact_3324_power2__sum,axiom,
% 5.31/5.55 ! [X: extended_enat,Y: extended_enat] :
% 5.31/5.55 ( ( power_8040749407984259932d_enat @ ( plus_p3455044024723400733d_enat @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.31/5.55 = ( plus_p3455044024723400733d_enat @ ( plus_p3455044024723400733d_enat @ ( power_8040749407984259932d_enat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_8040749407984259932d_enat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_7803423173614009249d_enat @ ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ ( bit0 @ one ) ) @ X ) @ Y ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % power2_sum
% 5.31/5.55 thf(fact_3325_power2__sum,axiom,
% 5.31/5.55 ! [X: complex,Y: complex] :
% 5.31/5.55 ( ( power_power_complex @ ( plus_plus_complex @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.31/5.55 = ( 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 ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % power2_sum
% 5.31/5.55 thf(fact_3326_power2__sum,axiom,
% 5.31/5.55 ! [X: real,Y: real] :
% 5.31/5.55 ( ( power_power_real @ ( plus_plus_real @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.31/5.55 = ( 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 ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % power2_sum
% 5.31/5.55 thf(fact_3327_power2__sum,axiom,
% 5.31/5.55 ! [X: nat,Y: nat] :
% 5.31/5.55 ( ( power_power_nat @ ( plus_plus_nat @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.31/5.55 = ( 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 ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % power2_sum
% 5.31/5.55 thf(fact_3328_power2__sum,axiom,
% 5.31/5.55 ! [X: int,Y: int] :
% 5.31/5.55 ( ( power_power_int @ ( plus_plus_int @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.31/5.55 = ( 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 ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % power2_sum
% 5.31/5.55 thf(fact_3329_sum__squares__bound,axiom,
% 5.31/5.55 ! [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 ) ) ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % sum_squares_bound
% 5.31/5.55 thf(fact_3330_sum__squares__bound,axiom,
% 5.31/5.55 ! [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 ) ) ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % sum_squares_bound
% 5.31/5.55 thf(fact_3331_power2__diff,axiom,
% 5.31/5.55 ! [X: rat,Y: rat] :
% 5.31/5.55 ( ( power_power_rat @ ( minus_minus_rat @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.31/5.55 = ( 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 ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % power2_diff
% 5.31/5.55 thf(fact_3332_power2__diff,axiom,
% 5.31/5.55 ! [X: complex,Y: complex] :
% 5.31/5.55 ( ( power_power_complex @ ( minus_minus_complex @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.31/5.55 = ( 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 ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % power2_diff
% 5.31/5.55 thf(fact_3333_power2__diff,axiom,
% 5.31/5.55 ! [X: real,Y: real] :
% 5.31/5.55 ( ( power_power_real @ ( minus_minus_real @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.31/5.55 = ( 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 ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % power2_diff
% 5.31/5.55 thf(fact_3334_power2__diff,axiom,
% 5.31/5.55 ! [X: int,Y: int] :
% 5.31/5.55 ( ( power_power_int @ ( minus_minus_int @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.31/5.55 = ( 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 ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % power2_diff
% 5.31/5.55 thf(fact_3335_power2__le__imp__le,axiom,
% 5.31/5.55 ! [X: real,Y: real] :
% 5.31/5.55 ( ( ord_less_eq_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.31/5.55 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.31/5.55 => ( ord_less_eq_real @ X @ Y ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % power2_le_imp_le
% 5.31/5.55 thf(fact_3336_power2__le__imp__le,axiom,
% 5.31/5.55 ! [X: rat,Y: rat] :
% 5.31/5.55 ( ( ord_less_eq_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.31/5.55 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 5.31/5.55 => ( ord_less_eq_rat @ X @ Y ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % power2_le_imp_le
% 5.31/5.55 thf(fact_3337_power2__le__imp__le,axiom,
% 5.31/5.55 ! [X: nat,Y: nat] :
% 5.31/5.55 ( ( ord_less_eq_nat @ ( power_power_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.31/5.55 => ( ( ord_less_eq_nat @ zero_zero_nat @ Y )
% 5.31/5.55 => ( ord_less_eq_nat @ X @ Y ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % power2_le_imp_le
% 5.31/5.55 thf(fact_3338_power2__le__imp__le,axiom,
% 5.31/5.55 ! [X: int,Y: int] :
% 5.31/5.55 ( ( ord_less_eq_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.31/5.55 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.31/5.55 => ( ord_less_eq_int @ X @ Y ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % power2_le_imp_le
% 5.31/5.55 thf(fact_3339_power2__eq__imp__eq,axiom,
% 5.31/5.55 ! [X: real,Y: real] :
% 5.31/5.55 ( ( ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.31/5.55 = ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.31/5.55 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.31/5.55 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.31/5.55 => ( X = Y ) ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % power2_eq_imp_eq
% 5.31/5.55 thf(fact_3340_power2__eq__imp__eq,axiom,
% 5.31/5.55 ! [X: rat,Y: rat] :
% 5.31/5.55 ( ( ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.31/5.55 = ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.31/5.55 => ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 5.31/5.55 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 5.31/5.55 => ( X = Y ) ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % power2_eq_imp_eq
% 5.31/5.55 thf(fact_3341_power2__eq__imp__eq,axiom,
% 5.31/5.55 ! [X: nat,Y: nat] :
% 5.31/5.55 ( ( ( power_power_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.31/5.55 = ( power_power_nat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.31/5.55 => ( ( ord_less_eq_nat @ zero_zero_nat @ X )
% 5.31/5.55 => ( ( ord_less_eq_nat @ zero_zero_nat @ Y )
% 5.31/5.55 => ( X = Y ) ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % power2_eq_imp_eq
% 5.31/5.55 thf(fact_3342_power2__eq__imp__eq,axiom,
% 5.31/5.55 ! [X: int,Y: int] :
% 5.31/5.55 ( ( ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.31/5.55 = ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.31/5.55 => ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.31/5.55 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.31/5.55 => ( X = Y ) ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % power2_eq_imp_eq
% 5.31/5.55 thf(fact_3343_zero__le__power2,axiom,
% 5.31/5.55 ! [A: real] : ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % zero_le_power2
% 5.31/5.55 thf(fact_3344_zero__le__power2,axiom,
% 5.31/5.55 ! [A: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % zero_le_power2
% 5.31/5.55 thf(fact_3345_zero__le__power2,axiom,
% 5.31/5.55 ! [A: int] : ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % zero_le_power2
% 5.31/5.55 thf(fact_3346_power2__less__0,axiom,
% 5.31/5.55 ! [A: real] :
% 5.31/5.55 ~ ( ord_less_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_real ) ).
% 5.31/5.55
% 5.31/5.55 % power2_less_0
% 5.31/5.55 thf(fact_3347_power2__less__0,axiom,
% 5.31/5.55 ! [A: rat] :
% 5.31/5.55 ~ ( ord_less_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_rat ) ).
% 5.31/5.55
% 5.31/5.55 % power2_less_0
% 5.31/5.55 thf(fact_3348_power2__less__0,axiom,
% 5.31/5.55 ! [A: int] :
% 5.31/5.55 ~ ( ord_less_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_int ) ).
% 5.31/5.55
% 5.31/5.55 % power2_less_0
% 5.31/5.55 thf(fact_3349_less__2__cases,axiom,
% 5.31/5.55 ! [N: nat] :
% 5.31/5.55 ( ( ord_less_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.31/5.55 => ( ( N = zero_zero_nat )
% 5.31/5.55 | ( N
% 5.31/5.55 = ( suc @ zero_zero_nat ) ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % less_2_cases
% 5.31/5.55 thf(fact_3350_less__2__cases__iff,axiom,
% 5.31/5.55 ! [N: nat] :
% 5.31/5.55 ( ( ord_less_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.31/5.55 = ( ( N = zero_zero_nat )
% 5.31/5.55 | ( N
% 5.31/5.55 = ( suc @ zero_zero_nat ) ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % less_2_cases_iff
% 5.31/5.55 thf(fact_3351_card__2__iff,axiom,
% 5.31/5.55 ! [S3: set_complex] :
% 5.31/5.55 ( ( ( finite_card_complex @ S3 )
% 5.31/5.55 = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.31/5.55 = ( ? [X4: complex,Y4: complex] :
% 5.31/5.55 ( ( S3
% 5.31/5.55 = ( insert_complex @ X4 @ ( insert_complex @ Y4 @ bot_bot_set_complex ) ) )
% 5.31/5.55 & ( X4 != Y4 ) ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % card_2_iff
% 5.31/5.55 thf(fact_3352_card__2__iff,axiom,
% 5.31/5.55 ! [S3: set_list_nat] :
% 5.31/5.55 ( ( ( finite_card_list_nat @ S3 )
% 5.31/5.55 = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.31/5.55 = ( ? [X4: list_nat,Y4: list_nat] :
% 5.31/5.55 ( ( S3
% 5.31/5.55 = ( insert_list_nat @ X4 @ ( insert_list_nat @ Y4 @ bot_bot_set_list_nat ) ) )
% 5.31/5.55 & ( X4 != Y4 ) ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % card_2_iff
% 5.31/5.55 thf(fact_3353_card__2__iff,axiom,
% 5.31/5.55 ! [S3: set_set_nat] :
% 5.31/5.55 ( ( ( finite_card_set_nat @ S3 )
% 5.31/5.55 = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.31/5.55 = ( ? [X4: set_nat,Y4: set_nat] :
% 5.31/5.55 ( ( S3
% 5.31/5.55 = ( insert_set_nat @ X4 @ ( insert_set_nat @ Y4 @ bot_bot_set_set_nat ) ) )
% 5.31/5.55 & ( X4 != Y4 ) ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % card_2_iff
% 5.31/5.55 thf(fact_3354_card__2__iff,axiom,
% 5.31/5.55 ! [S3: set_nat] :
% 5.31/5.55 ( ( ( finite_card_nat @ S3 )
% 5.31/5.55 = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.31/5.55 = ( ? [X4: nat,Y4: nat] :
% 5.31/5.55 ( ( S3
% 5.31/5.55 = ( insert_nat @ X4 @ ( insert_nat @ Y4 @ bot_bot_set_nat ) ) )
% 5.31/5.55 & ( X4 != Y4 ) ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % card_2_iff
% 5.31/5.55 thf(fact_3355_card__2__iff,axiom,
% 5.31/5.55 ! [S3: set_int] :
% 5.31/5.55 ( ( ( finite_card_int @ S3 )
% 5.31/5.55 = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.31/5.55 = ( ? [X4: int,Y4: int] :
% 5.31/5.55 ( ( S3
% 5.31/5.55 = ( insert_int @ X4 @ ( insert_int @ Y4 @ bot_bot_set_int ) ) )
% 5.31/5.55 & ( X4 != Y4 ) ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % card_2_iff
% 5.31/5.55 thf(fact_3356_card__2__iff,axiom,
% 5.31/5.55 ! [S3: set_real] :
% 5.31/5.55 ( ( ( finite_card_real @ S3 )
% 5.31/5.55 = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.31/5.55 = ( ? [X4: real,Y4: real] :
% 5.31/5.55 ( ( S3
% 5.31/5.55 = ( insert_real @ X4 @ ( insert_real @ Y4 @ bot_bot_set_real ) ) )
% 5.31/5.55 & ( X4 != Y4 ) ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % card_2_iff
% 5.31/5.55 thf(fact_3357_numeral__1__eq__Suc__0,axiom,
% 5.31/5.55 ( ( numeral_numeral_nat @ one )
% 5.31/5.55 = ( suc @ zero_zero_nat ) ) ).
% 5.31/5.55
% 5.31/5.55 % numeral_1_eq_Suc_0
% 5.31/5.55 thf(fact_3358_Suc__nat__number__of__add,axiom,
% 5.31/5.55 ! [V2: num,N: nat] :
% 5.31/5.55 ( ( suc @ ( plus_plus_nat @ ( numeral_numeral_nat @ V2 ) @ N ) )
% 5.31/5.55 = ( plus_plus_nat @ ( numeral_numeral_nat @ ( plus_plus_num @ V2 @ one ) ) @ N ) ) ).
% 5.31/5.55
% 5.31/5.55 % Suc_nat_number_of_add
% 5.31/5.55 thf(fact_3359_real__arch__simple,axiom,
% 5.31/5.55 ! [X: real] :
% 5.31/5.55 ? [N3: nat] : ( ord_less_eq_real @ X @ ( semiri5074537144036343181t_real @ N3 ) ) ).
% 5.31/5.55
% 5.31/5.55 % real_arch_simple
% 5.31/5.55 thf(fact_3360_real__arch__simple,axiom,
% 5.31/5.55 ! [X: rat] :
% 5.31/5.55 ? [N3: nat] : ( ord_less_eq_rat @ X @ ( semiri681578069525770553at_rat @ N3 ) ) ).
% 5.31/5.55
% 5.31/5.55 % real_arch_simple
% 5.31/5.55 thf(fact_3361_reals__Archimedean2,axiom,
% 5.31/5.55 ! [X: rat] :
% 5.31/5.55 ? [N3: nat] : ( ord_less_rat @ X @ ( semiri681578069525770553at_rat @ N3 ) ) ).
% 5.31/5.55
% 5.31/5.55 % reals_Archimedean2
% 5.31/5.55 thf(fact_3362_reals__Archimedean2,axiom,
% 5.31/5.55 ! [X: real] :
% 5.31/5.55 ? [N3: nat] : ( ord_less_real @ X @ ( semiri5074537144036343181t_real @ N3 ) ) ).
% 5.31/5.55
% 5.31/5.55 % reals_Archimedean2
% 5.31/5.55 thf(fact_3363_mult__of__nat__commute,axiom,
% 5.31/5.55 ! [X: nat,Y: rat] :
% 5.31/5.55 ( ( times_times_rat @ ( semiri681578069525770553at_rat @ X ) @ Y )
% 5.31/5.55 = ( times_times_rat @ Y @ ( semiri681578069525770553at_rat @ X ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % mult_of_nat_commute
% 5.31/5.55 thf(fact_3364_mult__of__nat__commute,axiom,
% 5.31/5.55 ! [X: nat,Y: real] :
% 5.31/5.55 ( ( times_times_real @ ( semiri5074537144036343181t_real @ X ) @ Y )
% 5.31/5.55 = ( times_times_real @ Y @ ( semiri5074537144036343181t_real @ X ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % mult_of_nat_commute
% 5.31/5.55 thf(fact_3365_mult__of__nat__commute,axiom,
% 5.31/5.55 ! [X: nat,Y: int] :
% 5.31/5.55 ( ( times_times_int @ ( semiri1314217659103216013at_int @ X ) @ Y )
% 5.31/5.55 = ( times_times_int @ Y @ ( semiri1314217659103216013at_int @ X ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % mult_of_nat_commute
% 5.31/5.55 thf(fact_3366_mult__of__nat__commute,axiom,
% 5.31/5.55 ! [X: nat,Y: nat] :
% 5.31/5.55 ( ( times_times_nat @ ( semiri1316708129612266289at_nat @ X ) @ Y )
% 5.31/5.55 = ( times_times_nat @ Y @ ( semiri1316708129612266289at_nat @ X ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % mult_of_nat_commute
% 5.31/5.55 thf(fact_3367_zless__iff__Suc__zadd,axiom,
% 5.31/5.55 ( ord_less_int
% 5.31/5.55 = ( ^ [W3: int,Z4: int] :
% 5.31/5.55 ? [N4: nat] :
% 5.31/5.55 ( Z4
% 5.31/5.55 = ( plus_plus_int @ W3 @ ( semiri1314217659103216013at_int @ ( suc @ N4 ) ) ) ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % zless_iff_Suc_zadd
% 5.31/5.55 thf(fact_3368_int__Suc,axiom,
% 5.31/5.55 ! [N: nat] :
% 5.31/5.55 ( ( semiri1314217659103216013at_int @ ( suc @ N ) )
% 5.31/5.55 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) ) ).
% 5.31/5.55
% 5.31/5.55 % int_Suc
% 5.31/5.55 thf(fact_3369_int__ops_I4_J,axiom,
% 5.31/5.55 ! [A: nat] :
% 5.31/5.55 ( ( semiri1314217659103216013at_int @ ( suc @ A ) )
% 5.31/5.55 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ A ) @ one_one_int ) ) ).
% 5.31/5.55
% 5.31/5.55 % int_ops(4)
% 5.31/5.55 thf(fact_3370_zero__neq__numeral,axiom,
% 5.31/5.55 ! [N: num] :
% 5.31/5.55 ( zero_zero_rat
% 5.31/5.55 != ( numeral_numeral_rat @ N ) ) ).
% 5.31/5.55
% 5.31/5.55 % zero_neq_numeral
% 5.31/5.55 thf(fact_3371_zero__neq__numeral,axiom,
% 5.31/5.55 ! [N: num] :
% 5.31/5.55 ( zero_z5237406670263579293d_enat
% 5.31/5.55 != ( numera1916890842035813515d_enat @ N ) ) ).
% 5.31/5.55
% 5.31/5.55 % zero_neq_numeral
% 5.31/5.55 thf(fact_3372_zero__neq__numeral,axiom,
% 5.31/5.55 ! [N: num] :
% 5.31/5.55 ( zero_zero_complex
% 5.31/5.55 != ( numera6690914467698888265omplex @ N ) ) ).
% 5.31/5.55
% 5.31/5.55 % zero_neq_numeral
% 5.31/5.55 thf(fact_3373_zero__neq__numeral,axiom,
% 5.31/5.55 ! [N: num] :
% 5.31/5.55 ( zero_zero_real
% 5.31/5.55 != ( numeral_numeral_real @ N ) ) ).
% 5.31/5.55
% 5.31/5.55 % zero_neq_numeral
% 5.31/5.55 thf(fact_3374_zero__neq__numeral,axiom,
% 5.31/5.55 ! [N: num] :
% 5.31/5.55 ( zero_zero_nat
% 5.31/5.55 != ( numeral_numeral_nat @ N ) ) ).
% 5.31/5.55
% 5.31/5.55 % zero_neq_numeral
% 5.31/5.55 thf(fact_3375_zero__neq__numeral,axiom,
% 5.31/5.55 ! [N: num] :
% 5.31/5.55 ( zero_zero_int
% 5.31/5.55 != ( numeral_numeral_int @ N ) ) ).
% 5.31/5.55
% 5.31/5.55 % zero_neq_numeral
% 5.31/5.55 thf(fact_3376_int__ops_I1_J,axiom,
% 5.31/5.55 ( ( semiri1314217659103216013at_int @ zero_zero_nat )
% 5.31/5.55 = zero_zero_int ) ).
% 5.31/5.55
% 5.31/5.55 % int_ops(1)
% 5.31/5.55 thf(fact_3377_nat__le__real__less,axiom,
% 5.31/5.55 ( ord_less_eq_nat
% 5.31/5.55 = ( ^ [N4: nat,M6: nat] : ( ord_less_real @ ( semiri5074537144036343181t_real @ N4 ) @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ M6 ) @ one_one_real ) ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % nat_le_real_less
% 5.31/5.55 thf(fact_3378_zle__int,axiom,
% 5.31/5.55 ! [M2: nat,N: nat] :
% 5.31/5.55 ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ M2 ) @ ( semiri1314217659103216013at_int @ N ) )
% 5.31/5.55 = ( ord_less_eq_nat @ M2 @ N ) ) ).
% 5.31/5.55
% 5.31/5.55 % zle_int
% 5.31/5.55 thf(fact_3379_nat__int__comparison_I3_J,axiom,
% 5.31/5.55 ( ord_less_eq_nat
% 5.31/5.55 = ( ^ [A5: nat,B4: nat] : ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ A5 ) @ ( semiri1314217659103216013at_int @ B4 ) ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % nat_int_comparison(3)
% 5.31/5.55 thf(fact_3380_int__ops_I7_J,axiom,
% 5.31/5.55 ! [A: nat,B: nat] :
% 5.31/5.55 ( ( semiri1314217659103216013at_int @ ( times_times_nat @ A @ B ) )
% 5.31/5.55 = ( times_times_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % int_ops(7)
% 5.31/5.55 thf(fact_3381_power2__less__imp__less,axiom,
% 5.31/5.55 ! [X: real,Y: real] :
% 5.31/5.55 ( ( ord_less_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.31/5.55 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.31/5.55 => ( ord_less_real @ X @ Y ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % power2_less_imp_less
% 5.31/5.55 thf(fact_3382_power2__less__imp__less,axiom,
% 5.31/5.55 ! [X: rat,Y: rat] :
% 5.31/5.55 ( ( ord_less_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.31/5.55 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 5.31/5.55 => ( ord_less_rat @ X @ Y ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % power2_less_imp_less
% 5.31/5.55 thf(fact_3383_power2__less__imp__less,axiom,
% 5.31/5.55 ! [X: nat,Y: nat] :
% 5.31/5.55 ( ( ord_less_nat @ ( power_power_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.31/5.55 => ( ( ord_less_eq_nat @ zero_zero_nat @ Y )
% 5.31/5.55 => ( ord_less_nat @ X @ Y ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % power2_less_imp_less
% 5.31/5.55 thf(fact_3384_power2__less__imp__less,axiom,
% 5.31/5.55 ! [X: int,Y: int] :
% 5.31/5.55 ( ( ord_less_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.31/5.55 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.31/5.55 => ( ord_less_int @ X @ Y ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % power2_less_imp_less
% 5.31/5.55 thf(fact_3385_sum__power2__le__zero__iff,axiom,
% 5.31/5.55 ! [X: real,Y: real] :
% 5.31/5.55 ( ( 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 )
% 5.31/5.55 = ( ( X = zero_zero_real )
% 5.31/5.55 & ( Y = zero_zero_real ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % sum_power2_le_zero_iff
% 5.31/5.55 thf(fact_3386_sum__power2__le__zero__iff,axiom,
% 5.31/5.55 ! [X: rat,Y: rat] :
% 5.31/5.55 ( ( 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 )
% 5.31/5.55 = ( ( X = zero_zero_rat )
% 5.31/5.55 & ( Y = zero_zero_rat ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % sum_power2_le_zero_iff
% 5.31/5.55 thf(fact_3387_sum__power2__le__zero__iff,axiom,
% 5.31/5.55 ! [X: int,Y: int] :
% 5.31/5.55 ( ( 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 )
% 5.31/5.55 = ( ( X = zero_zero_int )
% 5.31/5.55 & ( Y = zero_zero_int ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % sum_power2_le_zero_iff
% 5.31/5.55 thf(fact_3388_sum__power2__ge__zero,axiom,
% 5.31/5.55 ! [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 ) ) ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % sum_power2_ge_zero
% 5.31/5.55 thf(fact_3389_sum__power2__ge__zero,axiom,
% 5.31/5.55 ! [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 ) ) ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % sum_power2_ge_zero
% 5.31/5.55 thf(fact_3390_sum__power2__ge__zero,axiom,
% 5.31/5.55 ! [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 ) ) ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % sum_power2_ge_zero
% 5.31/5.55 thf(fact_3391_sum__power2__gt__zero__iff,axiom,
% 5.31/5.55 ! [X: real,Y: real] :
% 5.31/5.55 ( ( 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 ) ) ) ) )
% 5.31/5.55 = ( ( X != zero_zero_real )
% 5.31/5.55 | ( Y != zero_zero_real ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % sum_power2_gt_zero_iff
% 5.31/5.55 thf(fact_3392_sum__power2__gt__zero__iff,axiom,
% 5.31/5.55 ! [X: rat,Y: rat] :
% 5.31/5.55 ( ( 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 ) ) ) ) )
% 5.31/5.55 = ( ( X != zero_zero_rat )
% 5.31/5.55 | ( Y != zero_zero_rat ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % sum_power2_gt_zero_iff
% 5.31/5.55 thf(fact_3393_sum__power2__gt__zero__iff,axiom,
% 5.31/5.55 ! [X: int,Y: int] :
% 5.31/5.55 ( ( 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 ) ) ) ) )
% 5.31/5.55 = ( ( X != zero_zero_int )
% 5.31/5.55 | ( Y != zero_zero_int ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % sum_power2_gt_zero_iff
% 5.31/5.55 thf(fact_3394_not__sum__power2__lt__zero,axiom,
% 5.31/5.55 ! [X: real,Y: real] :
% 5.31/5.55 ~ ( 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 ) ).
% 5.31/5.55
% 5.31/5.55 % not_sum_power2_lt_zero
% 5.31/5.55 thf(fact_3395_not__sum__power2__lt__zero,axiom,
% 5.31/5.55 ! [X: rat,Y: rat] :
% 5.31/5.55 ~ ( 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 ) ).
% 5.31/5.55
% 5.31/5.55 % not_sum_power2_lt_zero
% 5.31/5.55 thf(fact_3396_not__sum__power2__lt__zero,axiom,
% 5.31/5.55 ! [X: int,Y: int] :
% 5.31/5.55 ~ ( 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 ) ).
% 5.31/5.55
% 5.31/5.55 % not_sum_power2_lt_zero
% 5.31/5.55 thf(fact_3397_num_Osize_I4_J,axiom,
% 5.31/5.55 ( ( size_size_num @ one )
% 5.31/5.55 = zero_zero_nat ) ).
% 5.31/5.55
% 5.31/5.55 % num.size(4)
% 5.31/5.55 thf(fact_3398_zero__le__even__power_H,axiom,
% 5.31/5.55 ! [A: real,N: nat] : ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % zero_le_even_power'
% 5.31/5.55 thf(fact_3399_zero__le__even__power_H,axiom,
% 5.31/5.55 ! [A: rat,N: nat] : ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % zero_le_even_power'
% 5.31/5.55 thf(fact_3400_zero__le__even__power_H,axiom,
% 5.31/5.55 ! [A: int,N: nat] : ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % zero_le_even_power'
% 5.31/5.55 thf(fact_3401_power__odd__eq,axiom,
% 5.31/5.55 ! [A: complex,N: nat] :
% 5.31/5.55 ( ( power_power_complex @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.31/5.55 = ( times_times_complex @ A @ ( power_power_complex @ ( power_power_complex @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % power_odd_eq
% 5.31/5.55 thf(fact_3402_power__odd__eq,axiom,
% 5.31/5.55 ! [A: real,N: nat] :
% 5.31/5.55 ( ( power_power_real @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.31/5.55 = ( times_times_real @ A @ ( power_power_real @ ( power_power_real @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % power_odd_eq
% 5.31/5.55 thf(fact_3403_power__odd__eq,axiom,
% 5.31/5.55 ! [A: rat,N: nat] :
% 5.31/5.55 ( ( power_power_rat @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.31/5.55 = ( times_times_rat @ A @ ( power_power_rat @ ( power_power_rat @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % power_odd_eq
% 5.31/5.55 thf(fact_3404_power__odd__eq,axiom,
% 5.31/5.55 ! [A: nat,N: nat] :
% 5.31/5.55 ( ( power_power_nat @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.31/5.55 = ( times_times_nat @ A @ ( power_power_nat @ ( power_power_nat @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % power_odd_eq
% 5.31/5.55 thf(fact_3405_power__odd__eq,axiom,
% 5.31/5.55 ! [A: int,N: nat] :
% 5.31/5.55 ( ( power_power_int @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.31/5.55 = ( times_times_int @ A @ ( power_power_int @ ( power_power_int @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % power_odd_eq
% 5.31/5.55 thf(fact_3406_ex__power__ivl1,axiom,
% 5.31/5.55 ! [B: nat,K2: nat] :
% 5.31/5.55 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 5.31/5.55 => ( ( ord_less_eq_nat @ one_one_nat @ K2 )
% 5.31/5.55 => ? [N3: nat] :
% 5.31/5.55 ( ( ord_less_eq_nat @ ( power_power_nat @ B @ N3 ) @ K2 )
% 5.31/5.55 & ( ord_less_nat @ K2 @ ( power_power_nat @ B @ ( plus_plus_nat @ N3 @ one_one_nat ) ) ) ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % ex_power_ivl1
% 5.31/5.55 thf(fact_3407_ex__power__ivl2,axiom,
% 5.31/5.55 ! [B: nat,K2: nat] :
% 5.31/5.55 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 5.31/5.55 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K2 )
% 5.31/5.55 => ? [N3: nat] :
% 5.31/5.55 ( ( ord_less_nat @ ( power_power_nat @ B @ N3 ) @ K2 )
% 5.31/5.55 & ( ord_less_eq_nat @ K2 @ ( power_power_nat @ B @ ( plus_plus_nat @ N3 @ one_one_nat ) ) ) ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % ex_power_ivl2
% 5.31/5.55 thf(fact_3408_VEBT__internal_Oinsert_H_Osimps_I2_J,axiom,
% 5.31/5.55 ! [Deg: nat,X: nat,Info2: option4927543243414619207at_nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.31/5.55 ( ( ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) @ X )
% 5.31/5.55 => ( ( vEBT_VEBT_insert @ ( vEBT_Node @ Info2 @ Deg @ TreeList2 @ Summary ) @ X )
% 5.31/5.55 = ( vEBT_Node @ Info2 @ Deg @ TreeList2 @ Summary ) ) )
% 5.31/5.55 & ( ~ ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) @ X )
% 5.31/5.55 => ( ( vEBT_VEBT_insert @ ( vEBT_Node @ Info2 @ Deg @ TreeList2 @ Summary ) @ X )
% 5.31/5.55 = ( vEBT_vebt_insert @ ( vEBT_Node @ Info2 @ Deg @ TreeList2 @ Summary ) @ X ) ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % VEBT_internal.insert'.simps(2)
% 5.31/5.55 thf(fact_3409_odd__0__le__power__imp__0__le,axiom,
% 5.31/5.55 ! [A: real,N: nat] :
% 5.31/5.55 ( ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 5.31/5.55 => ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 5.31/5.55
% 5.31/5.55 % odd_0_le_power_imp_0_le
% 5.31/5.55 thf(fact_3410_odd__0__le__power__imp__0__le,axiom,
% 5.31/5.55 ! [A: rat,N: nat] :
% 5.31/5.55 ( ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 5.31/5.55 => ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 5.31/5.55
% 5.31/5.55 % odd_0_le_power_imp_0_le
% 5.31/5.55 thf(fact_3411_odd__0__le__power__imp__0__le,axiom,
% 5.31/5.55 ! [A: int,N: nat] :
% 5.31/5.55 ( ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 5.31/5.55 => ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 5.31/5.55
% 5.31/5.55 % odd_0_le_power_imp_0_le
% 5.31/5.55 thf(fact_3412_odd__power__less__zero,axiom,
% 5.31/5.55 ! [A: real,N: nat] :
% 5.31/5.55 ( ( ord_less_real @ A @ zero_zero_real )
% 5.31/5.55 => ( ord_less_real @ ( power_power_real @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) @ zero_zero_real ) ) ).
% 5.31/5.55
% 5.31/5.55 % odd_power_less_zero
% 5.31/5.55 thf(fact_3413_odd__power__less__zero,axiom,
% 5.31/5.55 ! [A: rat,N: nat] :
% 5.31/5.55 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.31/5.55 => ( ord_less_rat @ ( power_power_rat @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) @ zero_zero_rat ) ) ).
% 5.31/5.55
% 5.31/5.55 % odd_power_less_zero
% 5.31/5.55 thf(fact_3414_odd__power__less__zero,axiom,
% 5.31/5.55 ! [A: int,N: nat] :
% 5.31/5.55 ( ( ord_less_int @ A @ zero_zero_int )
% 5.31/5.55 => ( ord_less_int @ ( power_power_int @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) @ zero_zero_int ) ) ).
% 5.31/5.55
% 5.31/5.55 % odd_power_less_zero
% 5.31/5.55 thf(fact_3415_VEBT__internal_Oinsert_H_Oelims,axiom,
% 5.31/5.55 ! [X: vEBT_VEBT,Xa2: nat,Y: vEBT_VEBT] :
% 5.31/5.55 ( ( ( vEBT_VEBT_insert @ X @ Xa2 )
% 5.31/5.55 = Y )
% 5.31/5.55 => ( ! [A3: $o,B3: $o] :
% 5.31/5.55 ( ( X
% 5.31/5.55 = ( vEBT_Leaf @ A3 @ B3 ) )
% 5.31/5.55 => ( Y
% 5.31/5.55 != ( vEBT_vebt_insert @ ( vEBT_Leaf @ A3 @ B3 ) @ Xa2 ) ) )
% 5.31/5.55 => ~ ! [Info: option4927543243414619207at_nat,Deg2: nat,TreeList: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.31/5.55 ( ( X
% 5.31/5.55 = ( vEBT_Node @ Info @ Deg2 @ TreeList @ Summary2 ) )
% 5.31/5.55 => ~ ( ( ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) @ Xa2 )
% 5.31/5.55 => ( Y
% 5.31/5.55 = ( vEBT_Node @ Info @ Deg2 @ TreeList @ Summary2 ) ) )
% 5.31/5.55 & ( ~ ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) @ Xa2 )
% 5.31/5.55 => ( Y
% 5.31/5.55 = ( vEBT_vebt_insert @ ( vEBT_Node @ Info @ Deg2 @ TreeList @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % VEBT_internal.insert'.elims
% 5.31/5.55 thf(fact_3416_of__nat__0__le__iff,axiom,
% 5.31/5.55 ! [N: nat] : ( ord_less_eq_real @ zero_zero_real @ ( semiri5074537144036343181t_real @ N ) ) ).
% 5.31/5.55
% 5.31/5.55 % of_nat_0_le_iff
% 5.31/5.55 thf(fact_3417_of__nat__0__le__iff,axiom,
% 5.31/5.55 ! [N: nat] : ( ord_less_eq_rat @ zero_zero_rat @ ( semiri681578069525770553at_rat @ N ) ) ).
% 5.31/5.55
% 5.31/5.55 % of_nat_0_le_iff
% 5.31/5.55 thf(fact_3418_of__nat__0__le__iff,axiom,
% 5.31/5.55 ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( semiri1316708129612266289at_nat @ N ) ) ).
% 5.31/5.55
% 5.31/5.55 % of_nat_0_le_iff
% 5.31/5.55 thf(fact_3419_of__nat__0__le__iff,axiom,
% 5.31/5.55 ! [N: nat] : ( ord_less_eq_int @ zero_zero_int @ ( semiri1314217659103216013at_int @ N ) ) ).
% 5.31/5.55
% 5.31/5.55 % of_nat_0_le_iff
% 5.31/5.55 thf(fact_3420_of__nat__less__0__iff,axiom,
% 5.31/5.55 ! [M2: nat] :
% 5.31/5.55 ~ ( ord_less_rat @ ( semiri681578069525770553at_rat @ M2 ) @ zero_zero_rat ) ).
% 5.31/5.55
% 5.31/5.55 % of_nat_less_0_iff
% 5.31/5.55 thf(fact_3421_of__nat__less__0__iff,axiom,
% 5.31/5.55 ! [M2: nat] :
% 5.31/5.55 ~ ( ord_less_real @ ( semiri5074537144036343181t_real @ M2 ) @ zero_zero_real ) ).
% 5.31/5.55
% 5.31/5.55 % of_nat_less_0_iff
% 5.31/5.55 thf(fact_3422_of__nat__less__0__iff,axiom,
% 5.31/5.55 ! [M2: nat] :
% 5.31/5.55 ~ ( ord_less_int @ ( semiri1314217659103216013at_int @ M2 ) @ zero_zero_int ) ).
% 5.31/5.55
% 5.31/5.55 % of_nat_less_0_iff
% 5.31/5.55 thf(fact_3423_of__nat__less__0__iff,axiom,
% 5.31/5.55 ! [M2: nat] :
% 5.31/5.55 ~ ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M2 ) @ zero_zero_nat ) ).
% 5.31/5.55
% 5.31/5.55 % of_nat_less_0_iff
% 5.31/5.55 thf(fact_3424_of__nat__neq__0,axiom,
% 5.31/5.55 ! [N: nat] :
% 5.31/5.55 ( ( semiri8010041392384452111omplex @ ( suc @ N ) )
% 5.31/5.55 != zero_zero_complex ) ).
% 5.31/5.55
% 5.31/5.55 % of_nat_neq_0
% 5.31/5.55 thf(fact_3425_of__nat__neq__0,axiom,
% 5.31/5.55 ! [N: nat] :
% 5.31/5.55 ( ( semiri681578069525770553at_rat @ ( suc @ N ) )
% 5.31/5.55 != zero_zero_rat ) ).
% 5.31/5.55
% 5.31/5.55 % of_nat_neq_0
% 5.31/5.55 thf(fact_3426_of__nat__neq__0,axiom,
% 5.31/5.55 ! [N: nat] :
% 5.31/5.55 ( ( semiri5074537144036343181t_real @ ( suc @ N ) )
% 5.31/5.55 != zero_zero_real ) ).
% 5.31/5.55
% 5.31/5.55 % of_nat_neq_0
% 5.31/5.55 thf(fact_3427_of__nat__neq__0,axiom,
% 5.31/5.55 ! [N: nat] :
% 5.31/5.55 ( ( semiri1314217659103216013at_int @ ( suc @ N ) )
% 5.31/5.55 != zero_zero_int ) ).
% 5.31/5.55
% 5.31/5.55 % of_nat_neq_0
% 5.31/5.55 thf(fact_3428_of__nat__neq__0,axiom,
% 5.31/5.55 ! [N: nat] :
% 5.31/5.55 ( ( semiri1316708129612266289at_nat @ ( suc @ N ) )
% 5.31/5.55 != zero_zero_nat ) ).
% 5.31/5.55
% 5.31/5.55 % of_nat_neq_0
% 5.31/5.55 thf(fact_3429_of__nat__less__imp__less,axiom,
% 5.31/5.55 ! [M2: nat,N: nat] :
% 5.31/5.55 ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ M2 ) @ ( semiri681578069525770553at_rat @ N ) )
% 5.31/5.55 => ( ord_less_nat @ M2 @ N ) ) ).
% 5.31/5.55
% 5.31/5.55 % of_nat_less_imp_less
% 5.31/5.55 thf(fact_3430_of__nat__less__imp__less,axiom,
% 5.31/5.55 ! [M2: nat,N: nat] :
% 5.31/5.55 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ M2 ) @ ( semiri5074537144036343181t_real @ N ) )
% 5.31/5.55 => ( ord_less_nat @ M2 @ N ) ) ).
% 5.31/5.55
% 5.31/5.55 % of_nat_less_imp_less
% 5.31/5.55 thf(fact_3431_of__nat__less__imp__less,axiom,
% 5.31/5.55 ! [M2: nat,N: nat] :
% 5.31/5.55 ( ( ord_less_int @ ( semiri1314217659103216013at_int @ M2 ) @ ( semiri1314217659103216013at_int @ N ) )
% 5.31/5.55 => ( ord_less_nat @ M2 @ N ) ) ).
% 5.31/5.55
% 5.31/5.55 % of_nat_less_imp_less
% 5.31/5.55 thf(fact_3432_of__nat__less__imp__less,axiom,
% 5.31/5.55 ! [M2: nat,N: nat] :
% 5.31/5.55 ( ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M2 ) @ ( semiri1316708129612266289at_nat @ N ) )
% 5.31/5.55 => ( ord_less_nat @ M2 @ N ) ) ).
% 5.31/5.55
% 5.31/5.55 % of_nat_less_imp_less
% 5.31/5.55 thf(fact_3433_less__imp__of__nat__less,axiom,
% 5.31/5.55 ! [M2: nat,N: nat] :
% 5.31/5.55 ( ( ord_less_nat @ M2 @ N )
% 5.31/5.55 => ( ord_less_rat @ ( semiri681578069525770553at_rat @ M2 ) @ ( semiri681578069525770553at_rat @ N ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % less_imp_of_nat_less
% 5.31/5.55 thf(fact_3434_less__imp__of__nat__less,axiom,
% 5.31/5.55 ! [M2: nat,N: nat] :
% 5.31/5.55 ( ( ord_less_nat @ M2 @ N )
% 5.31/5.55 => ( ord_less_real @ ( semiri5074537144036343181t_real @ M2 ) @ ( semiri5074537144036343181t_real @ N ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % less_imp_of_nat_less
% 5.31/5.55 thf(fact_3435_less__imp__of__nat__less,axiom,
% 5.31/5.55 ! [M2: nat,N: nat] :
% 5.31/5.55 ( ( ord_less_nat @ M2 @ N )
% 5.31/5.55 => ( ord_less_int @ ( semiri1314217659103216013at_int @ M2 ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % less_imp_of_nat_less
% 5.31/5.55 thf(fact_3436_less__imp__of__nat__less,axiom,
% 5.31/5.55 ! [M2: nat,N: nat] :
% 5.31/5.55 ( ( ord_less_nat @ M2 @ N )
% 5.31/5.55 => ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M2 ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % less_imp_of_nat_less
% 5.31/5.55 thf(fact_3437_of__nat__mono,axiom,
% 5.31/5.55 ! [I2: nat,J2: nat] :
% 5.31/5.55 ( ( ord_less_eq_nat @ I2 @ J2 )
% 5.31/5.55 => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ I2 ) @ ( semiri5074537144036343181t_real @ J2 ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % of_nat_mono
% 5.31/5.55 thf(fact_3438_of__nat__mono,axiom,
% 5.31/5.55 ! [I2: nat,J2: nat] :
% 5.31/5.55 ( ( ord_less_eq_nat @ I2 @ J2 )
% 5.31/5.55 => ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ I2 ) @ ( semiri681578069525770553at_rat @ J2 ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % of_nat_mono
% 5.31/5.55 thf(fact_3439_of__nat__mono,axiom,
% 5.31/5.55 ! [I2: nat,J2: nat] :
% 5.31/5.55 ( ( ord_less_eq_nat @ I2 @ J2 )
% 5.31/5.55 => ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ I2 ) @ ( semiri1316708129612266289at_nat @ J2 ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % of_nat_mono
% 5.31/5.55 thf(fact_3440_of__nat__mono,axiom,
% 5.31/5.55 ! [I2: nat,J2: nat] :
% 5.31/5.55 ( ( ord_less_eq_nat @ I2 @ J2 )
% 5.31/5.55 => ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ I2 ) @ ( semiri1314217659103216013at_int @ J2 ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % of_nat_mono
% 5.31/5.55 thf(fact_3441_zero__le__numeral,axiom,
% 5.31/5.55 ! [N: num] : ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ ( numera1916890842035813515d_enat @ N ) ) ).
% 5.31/5.55
% 5.31/5.55 % zero_le_numeral
% 5.31/5.55 thf(fact_3442_zero__le__numeral,axiom,
% 5.31/5.55 ! [N: num] : ( ord_less_eq_real @ zero_zero_real @ ( numeral_numeral_real @ N ) ) ).
% 5.31/5.55
% 5.31/5.55 % zero_le_numeral
% 5.31/5.55 thf(fact_3443_zero__le__numeral,axiom,
% 5.31/5.55 ! [N: num] : ( ord_less_eq_rat @ zero_zero_rat @ ( numeral_numeral_rat @ N ) ) ).
% 5.31/5.55
% 5.31/5.55 % zero_le_numeral
% 5.31/5.55 thf(fact_3444_zero__le__numeral,axiom,
% 5.31/5.55 ! [N: num] : ( ord_less_eq_nat @ zero_zero_nat @ ( numeral_numeral_nat @ N ) ) ).
% 5.31/5.55
% 5.31/5.55 % zero_le_numeral
% 5.31/5.55 thf(fact_3445_zero__le__numeral,axiom,
% 5.31/5.55 ! [N: num] : ( ord_less_eq_int @ zero_zero_int @ ( numeral_numeral_int @ N ) ) ).
% 5.31/5.55
% 5.31/5.55 % zero_le_numeral
% 5.31/5.55 thf(fact_3446_not__numeral__le__zero,axiom,
% 5.31/5.55 ! [N: num] :
% 5.31/5.55 ~ ( ord_le2932123472753598470d_enat @ ( numera1916890842035813515d_enat @ N ) @ zero_z5237406670263579293d_enat ) ).
% 5.31/5.55
% 5.31/5.55 % not_numeral_le_zero
% 5.31/5.55 thf(fact_3447_not__numeral__le__zero,axiom,
% 5.31/5.55 ! [N: num] :
% 5.31/5.55 ~ ( ord_less_eq_real @ ( numeral_numeral_real @ N ) @ zero_zero_real ) ).
% 5.31/5.55
% 5.31/5.55 % not_numeral_le_zero
% 5.31/5.55 thf(fact_3448_not__numeral__le__zero,axiom,
% 5.31/5.55 ! [N: num] :
% 5.31/5.55 ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ N ) @ zero_zero_rat ) ).
% 5.31/5.55
% 5.31/5.55 % not_numeral_le_zero
% 5.31/5.55 thf(fact_3449_not__numeral__le__zero,axiom,
% 5.31/5.55 ! [N: num] :
% 5.31/5.55 ~ ( ord_less_eq_nat @ ( numeral_numeral_nat @ N ) @ zero_zero_nat ) ).
% 5.31/5.55
% 5.31/5.55 % not_numeral_le_zero
% 5.31/5.55 thf(fact_3450_not__numeral__le__zero,axiom,
% 5.31/5.55 ! [N: num] :
% 5.31/5.55 ~ ( ord_less_eq_int @ ( numeral_numeral_int @ N ) @ zero_zero_int ) ).
% 5.31/5.55
% 5.31/5.55 % not_numeral_le_zero
% 5.31/5.55 thf(fact_3451_not__numeral__less__zero,axiom,
% 5.31/5.55 ! [N: num] :
% 5.31/5.55 ~ ( ord_less_rat @ ( numeral_numeral_rat @ N ) @ zero_zero_rat ) ).
% 5.31/5.55
% 5.31/5.55 % not_numeral_less_zero
% 5.31/5.55 thf(fact_3452_not__numeral__less__zero,axiom,
% 5.31/5.55 ! [N: num] :
% 5.31/5.55 ~ ( ord_le72135733267957522d_enat @ ( numera1916890842035813515d_enat @ N ) @ zero_z5237406670263579293d_enat ) ).
% 5.31/5.55
% 5.31/5.55 % not_numeral_less_zero
% 5.31/5.55 thf(fact_3453_not__numeral__less__zero,axiom,
% 5.31/5.55 ! [N: num] :
% 5.31/5.55 ~ ( ord_less_real @ ( numeral_numeral_real @ N ) @ zero_zero_real ) ).
% 5.31/5.55
% 5.31/5.55 % not_numeral_less_zero
% 5.31/5.55 thf(fact_3454_not__numeral__less__zero,axiom,
% 5.31/5.55 ! [N: num] :
% 5.31/5.55 ~ ( ord_less_nat @ ( numeral_numeral_nat @ N ) @ zero_zero_nat ) ).
% 5.31/5.55
% 5.31/5.55 % not_numeral_less_zero
% 5.31/5.55 thf(fact_3455_not__numeral__less__zero,axiom,
% 5.31/5.55 ! [N: num] :
% 5.31/5.55 ~ ( ord_less_int @ ( numeral_numeral_int @ N ) @ zero_zero_int ) ).
% 5.31/5.55
% 5.31/5.55 % not_numeral_less_zero
% 5.31/5.55 thf(fact_3456_zero__less__numeral,axiom,
% 5.31/5.55 ! [N: num] : ( ord_less_rat @ zero_zero_rat @ ( numeral_numeral_rat @ N ) ) ).
% 5.31/5.55
% 5.31/5.55 % zero_less_numeral
% 5.31/5.55 thf(fact_3457_zero__less__numeral,axiom,
% 5.31/5.55 ! [N: num] : ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ ( numera1916890842035813515d_enat @ N ) ) ).
% 5.31/5.55
% 5.31/5.55 % zero_less_numeral
% 5.31/5.55 thf(fact_3458_zero__less__numeral,axiom,
% 5.31/5.55 ! [N: num] : ( ord_less_real @ zero_zero_real @ ( numeral_numeral_real @ N ) ) ).
% 5.31/5.55
% 5.31/5.55 % zero_less_numeral
% 5.31/5.55 thf(fact_3459_zero__less__numeral,axiom,
% 5.31/5.55 ! [N: num] : ( ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ N ) ) ).
% 5.31/5.55
% 5.31/5.55 % zero_less_numeral
% 5.31/5.55 thf(fact_3460_zero__less__numeral,axiom,
% 5.31/5.55 ! [N: num] : ( ord_less_int @ zero_zero_int @ ( numeral_numeral_int @ N ) ) ).
% 5.31/5.55
% 5.31/5.55 % zero_less_numeral
% 5.31/5.55 thf(fact_3461_replicate__Suc,axiom,
% 5.31/5.55 ! [N: nat,X: nat] :
% 5.31/5.55 ( ( replicate_nat @ ( suc @ N ) @ X )
% 5.31/5.55 = ( cons_nat @ X @ ( replicate_nat @ N @ X ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % replicate_Suc
% 5.31/5.55 thf(fact_3462_replicate__Suc,axiom,
% 5.31/5.55 ! [N: nat,X: vEBT_VEBT] :
% 5.31/5.55 ( ( replicate_VEBT_VEBT @ ( suc @ N ) @ X )
% 5.31/5.55 = ( cons_VEBT_VEBT @ X @ ( replicate_VEBT_VEBT @ N @ X ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % replicate_Suc
% 5.31/5.55 thf(fact_3463_real__archimedian__rdiv__eq__0,axiom,
% 5.31/5.55 ! [X: real,C2: real] :
% 5.31/5.55 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.31/5.55 => ( ( ord_less_eq_real @ zero_zero_real @ C2 )
% 5.31/5.55 => ( ! [M: nat] :
% 5.31/5.55 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.31/5.55 => ( ord_less_eq_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ M ) @ X ) @ C2 ) )
% 5.31/5.55 => ( X = zero_zero_real ) ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % real_archimedian_rdiv_eq_0
% 5.31/5.55 thf(fact_3464_one__le__numeral,axiom,
% 5.31/5.55 ! [N: num] : ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ N ) ) ).
% 5.31/5.55
% 5.31/5.55 % one_le_numeral
% 5.31/5.55 thf(fact_3465_one__le__numeral,axiom,
% 5.31/5.55 ! [N: num] : ( ord_le2932123472753598470d_enat @ one_on7984719198319812577d_enat @ ( numera1916890842035813515d_enat @ N ) ) ).
% 5.31/5.55
% 5.31/5.55 % one_le_numeral
% 5.31/5.55 thf(fact_3466_one__le__numeral,axiom,
% 5.31/5.55 ! [N: num] : ( ord_less_eq_real @ one_one_real @ ( numeral_numeral_real @ N ) ) ).
% 5.31/5.55
% 5.31/5.55 % one_le_numeral
% 5.31/5.55 thf(fact_3467_one__le__numeral,axiom,
% 5.31/5.55 ! [N: num] : ( ord_less_eq_rat @ one_one_rat @ ( numeral_numeral_rat @ N ) ) ).
% 5.31/5.55
% 5.31/5.55 % one_le_numeral
% 5.31/5.55 thf(fact_3468_one__le__numeral,axiom,
% 5.31/5.55 ! [N: num] : ( ord_less_eq_nat @ one_one_nat @ ( numeral_numeral_nat @ N ) ) ).
% 5.31/5.55
% 5.31/5.55 % one_le_numeral
% 5.31/5.55 thf(fact_3469_one__le__numeral,axiom,
% 5.31/5.55 ! [N: num] : ( ord_less_eq_int @ one_one_int @ ( numeral_numeral_int @ N ) ) ).
% 5.31/5.55
% 5.31/5.55 % one_le_numeral
% 5.31/5.55 thf(fact_3470_pos__int__cases,axiom,
% 5.31/5.55 ! [K2: int] :
% 5.31/5.55 ( ( ord_less_int @ zero_zero_int @ K2 )
% 5.31/5.55 => ~ ! [N3: nat] :
% 5.31/5.55 ( ( K2
% 5.31/5.55 = ( semiri1314217659103216013at_int @ N3 ) )
% 5.31/5.55 => ~ ( ord_less_nat @ zero_zero_nat @ N3 ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % pos_int_cases
% 5.31/5.55 thf(fact_3471_zero__less__imp__eq__int,axiom,
% 5.31/5.55 ! [K2: int] :
% 5.31/5.55 ( ( ord_less_int @ zero_zero_int @ K2 )
% 5.31/5.55 => ? [N3: nat] :
% 5.31/5.55 ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 5.31/5.55 & ( K2
% 5.31/5.55 = ( semiri1314217659103216013at_int @ N3 ) ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % zero_less_imp_eq_int
% 5.31/5.55 thf(fact_3472_zmult__zless__mono2__lemma,axiom,
% 5.31/5.55 ! [I2: int,J2: int,K2: nat] :
% 5.31/5.55 ( ( ord_less_int @ I2 @ J2 )
% 5.31/5.55 => ( ( ord_less_nat @ zero_zero_nat @ K2 )
% 5.31/5.55 => ( ord_less_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ K2 ) @ I2 ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ K2 ) @ J2 ) ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % zmult_zless_mono2_lemma
% 5.31/5.55 thf(fact_3473_not__numeral__less__one,axiom,
% 5.31/5.55 ! [N: num] :
% 5.31/5.55 ~ ( ord_le6747313008572928689nteger @ ( numera6620942414471956472nteger @ N ) @ one_one_Code_integer ) ).
% 5.31/5.55
% 5.31/5.55 % not_numeral_less_one
% 5.31/5.55 thf(fact_3474_not__numeral__less__one,axiom,
% 5.31/5.55 ! [N: num] :
% 5.31/5.55 ~ ( ord_less_rat @ ( numeral_numeral_rat @ N ) @ one_one_rat ) ).
% 5.31/5.55
% 5.31/5.55 % not_numeral_less_one
% 5.31/5.55 thf(fact_3475_not__numeral__less__one,axiom,
% 5.31/5.55 ! [N: num] :
% 5.31/5.55 ~ ( ord_le72135733267957522d_enat @ ( numera1916890842035813515d_enat @ N ) @ one_on7984719198319812577d_enat ) ).
% 5.31/5.55
% 5.31/5.55 % not_numeral_less_one
% 5.31/5.55 thf(fact_3476_not__numeral__less__one,axiom,
% 5.31/5.55 ! [N: num] :
% 5.31/5.55 ~ ( ord_less_real @ ( numeral_numeral_real @ N ) @ one_one_real ) ).
% 5.31/5.55
% 5.31/5.55 % not_numeral_less_one
% 5.31/5.55 thf(fact_3477_not__numeral__less__one,axiom,
% 5.31/5.55 ! [N: num] :
% 5.31/5.55 ~ ( ord_less_nat @ ( numeral_numeral_nat @ N ) @ one_one_nat ) ).
% 5.31/5.55
% 5.31/5.55 % not_numeral_less_one
% 5.31/5.55 thf(fact_3478_not__numeral__less__one,axiom,
% 5.31/5.55 ! [N: num] :
% 5.31/5.55 ~ ( ord_less_int @ ( numeral_numeral_int @ N ) @ one_one_int ) ).
% 5.31/5.55
% 5.31/5.55 % not_numeral_less_one
% 5.31/5.55 thf(fact_3479_one__plus__numeral__commute,axiom,
% 5.31/5.55 ! [X: num] :
% 5.31/5.55 ( ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ X ) )
% 5.31/5.55 = ( plus_p5714425477246183910nteger @ ( numera6620942414471956472nteger @ X ) @ one_one_Code_integer ) ) ).
% 5.31/5.55
% 5.31/5.55 % one_plus_numeral_commute
% 5.31/5.55 thf(fact_3480_one__plus__numeral__commute,axiom,
% 5.31/5.55 ! [X: num] :
% 5.31/5.55 ( ( plus_plus_rat @ one_one_rat @ ( numeral_numeral_rat @ X ) )
% 5.31/5.55 = ( plus_plus_rat @ ( numeral_numeral_rat @ X ) @ one_one_rat ) ) ).
% 5.31/5.55
% 5.31/5.55 % one_plus_numeral_commute
% 5.31/5.55 thf(fact_3481_one__plus__numeral__commute,axiom,
% 5.31/5.55 ! [X: num] :
% 5.31/5.55 ( ( plus_p3455044024723400733d_enat @ one_on7984719198319812577d_enat @ ( numera1916890842035813515d_enat @ X ) )
% 5.31/5.55 = ( plus_p3455044024723400733d_enat @ ( numera1916890842035813515d_enat @ X ) @ one_on7984719198319812577d_enat ) ) ).
% 5.31/5.55
% 5.31/5.55 % one_plus_numeral_commute
% 5.31/5.55 thf(fact_3482_one__plus__numeral__commute,axiom,
% 5.31/5.55 ! [X: num] :
% 5.31/5.55 ( ( plus_plus_complex @ one_one_complex @ ( numera6690914467698888265omplex @ X ) )
% 5.31/5.55 = ( plus_plus_complex @ ( numera6690914467698888265omplex @ X ) @ one_one_complex ) ) ).
% 5.31/5.55
% 5.31/5.55 % one_plus_numeral_commute
% 5.31/5.55 thf(fact_3483_one__plus__numeral__commute,axiom,
% 5.31/5.55 ! [X: num] :
% 5.31/5.55 ( ( plus_plus_real @ one_one_real @ ( numeral_numeral_real @ X ) )
% 5.31/5.55 = ( plus_plus_real @ ( numeral_numeral_real @ X ) @ one_one_real ) ) ).
% 5.31/5.55
% 5.31/5.55 % one_plus_numeral_commute
% 5.31/5.55 thf(fact_3484_one__plus__numeral__commute,axiom,
% 5.31/5.55 ! [X: num] :
% 5.31/5.55 ( ( plus_plus_nat @ one_one_nat @ ( numeral_numeral_nat @ X ) )
% 5.31/5.55 = ( plus_plus_nat @ ( numeral_numeral_nat @ X ) @ one_one_nat ) ) ).
% 5.31/5.55
% 5.31/5.55 % one_plus_numeral_commute
% 5.31/5.55 thf(fact_3485_one__plus__numeral__commute,axiom,
% 5.31/5.55 ! [X: num] :
% 5.31/5.55 ( ( plus_plus_int @ one_one_int @ ( numeral_numeral_int @ X ) )
% 5.31/5.55 = ( plus_plus_int @ ( numeral_numeral_int @ X ) @ one_one_int ) ) ).
% 5.31/5.55
% 5.31/5.55 % one_plus_numeral_commute
% 5.31/5.55 thf(fact_3486_replicate__length__same,axiom,
% 5.31/5.55 ! [Xs2: list_VEBT_VEBT,X: vEBT_VEBT] :
% 5.31/5.55 ( ! [X3: vEBT_VEBT] :
% 5.31/5.55 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 5.31/5.55 => ( X3 = X ) )
% 5.31/5.55 => ( ( replicate_VEBT_VEBT @ ( size_s6755466524823107622T_VEBT @ Xs2 ) @ X )
% 5.31/5.55 = Xs2 ) ) ).
% 5.31/5.55
% 5.31/5.55 % replicate_length_same
% 5.31/5.55 thf(fact_3487_replicate__length__same,axiom,
% 5.31/5.55 ! [Xs2: list_o,X: $o] :
% 5.31/5.55 ( ! [X3: $o] :
% 5.31/5.55 ( ( member_o @ X3 @ ( set_o2 @ Xs2 ) )
% 5.31/5.55 => ( X3 = X ) )
% 5.31/5.55 => ( ( replicate_o @ ( size_size_list_o @ Xs2 ) @ X )
% 5.31/5.55 = Xs2 ) ) ).
% 5.31/5.55
% 5.31/5.55 % replicate_length_same
% 5.31/5.55 thf(fact_3488_replicate__length__same,axiom,
% 5.31/5.55 ! [Xs2: list_nat,X: nat] :
% 5.31/5.55 ( ! [X3: nat] :
% 5.31/5.55 ( ( member_nat @ X3 @ ( set_nat2 @ Xs2 ) )
% 5.31/5.55 => ( X3 = X ) )
% 5.31/5.55 => ( ( replicate_nat @ ( size_size_list_nat @ Xs2 ) @ X )
% 5.31/5.55 = Xs2 ) ) ).
% 5.31/5.55
% 5.31/5.55 % replicate_length_same
% 5.31/5.55 thf(fact_3489_replicate__length__same,axiom,
% 5.31/5.55 ! [Xs2: list_int,X: int] :
% 5.31/5.55 ( ! [X3: int] :
% 5.31/5.55 ( ( member_int @ X3 @ ( set_int2 @ Xs2 ) )
% 5.31/5.55 => ( X3 = X ) )
% 5.31/5.55 => ( ( replicate_int @ ( size_size_list_int @ Xs2 ) @ X )
% 5.31/5.55 = Xs2 ) ) ).
% 5.31/5.55
% 5.31/5.55 % replicate_length_same
% 5.31/5.55 thf(fact_3490_replicate__eqI,axiom,
% 5.31/5.55 ! [Xs2: list_complex,N: nat,X: complex] :
% 5.31/5.55 ( ( ( size_s3451745648224563538omplex @ Xs2 )
% 5.31/5.55 = N )
% 5.31/5.55 => ( ! [Y3: complex] :
% 5.31/5.55 ( ( member_complex @ Y3 @ ( set_complex2 @ Xs2 ) )
% 5.31/5.55 => ( Y3 = X ) )
% 5.31/5.55 => ( Xs2
% 5.31/5.55 = ( replicate_complex @ N @ X ) ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % replicate_eqI
% 5.31/5.55 thf(fact_3491_replicate__eqI,axiom,
% 5.31/5.55 ! [Xs2: list_real,N: nat,X: real] :
% 5.31/5.55 ( ( ( size_size_list_real @ Xs2 )
% 5.31/5.55 = N )
% 5.31/5.55 => ( ! [Y3: real] :
% 5.31/5.55 ( ( member_real @ Y3 @ ( set_real2 @ Xs2 ) )
% 5.31/5.55 => ( Y3 = X ) )
% 5.31/5.55 => ( Xs2
% 5.31/5.55 = ( replicate_real @ N @ X ) ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % replicate_eqI
% 5.31/5.55 thf(fact_3492_replicate__eqI,axiom,
% 5.31/5.55 ! [Xs2: list_set_nat,N: nat,X: set_nat] :
% 5.31/5.55 ( ( ( size_s3254054031482475050et_nat @ Xs2 )
% 5.31/5.55 = N )
% 5.31/5.55 => ( ! [Y3: set_nat] :
% 5.31/5.55 ( ( member_set_nat @ Y3 @ ( set_set_nat2 @ Xs2 ) )
% 5.31/5.55 => ( Y3 = X ) )
% 5.31/5.55 => ( Xs2
% 5.31/5.55 = ( replicate_set_nat @ N @ X ) ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % replicate_eqI
% 5.31/5.55 thf(fact_3493_replicate__eqI,axiom,
% 5.31/5.55 ! [Xs2: list_VEBT_VEBT,N: nat,X: vEBT_VEBT] :
% 5.31/5.55 ( ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 5.31/5.55 = N )
% 5.31/5.55 => ( ! [Y3: vEBT_VEBT] :
% 5.31/5.55 ( ( member_VEBT_VEBT @ Y3 @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 5.31/5.55 => ( Y3 = X ) )
% 5.31/5.55 => ( Xs2
% 5.31/5.55 = ( replicate_VEBT_VEBT @ N @ X ) ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % replicate_eqI
% 5.31/5.55 thf(fact_3494_replicate__eqI,axiom,
% 5.31/5.55 ! [Xs2: list_o,N: nat,X: $o] :
% 5.31/5.55 ( ( ( size_size_list_o @ Xs2 )
% 5.31/5.55 = N )
% 5.31/5.55 => ( ! [Y3: $o] :
% 5.31/5.55 ( ( member_o @ Y3 @ ( set_o2 @ Xs2 ) )
% 5.31/5.55 => ( Y3 = X ) )
% 5.31/5.55 => ( Xs2
% 5.31/5.55 = ( replicate_o @ N @ X ) ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % replicate_eqI
% 5.31/5.55 thf(fact_3495_replicate__eqI,axiom,
% 5.31/5.55 ! [Xs2: list_nat,N: nat,X: nat] :
% 5.31/5.55 ( ( ( size_size_list_nat @ Xs2 )
% 5.31/5.55 = N )
% 5.31/5.55 => ( ! [Y3: nat] :
% 5.31/5.55 ( ( member_nat @ Y3 @ ( set_nat2 @ Xs2 ) )
% 5.31/5.55 => ( Y3 = X ) )
% 5.31/5.55 => ( Xs2
% 5.31/5.55 = ( replicate_nat @ N @ X ) ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % replicate_eqI
% 5.31/5.55 thf(fact_3496_replicate__eqI,axiom,
% 5.31/5.55 ! [Xs2: list_int,N: nat,X: int] :
% 5.31/5.55 ( ( ( size_size_list_int @ Xs2 )
% 5.31/5.55 = N )
% 5.31/5.55 => ( ! [Y3: int] :
% 5.31/5.55 ( ( member_int @ Y3 @ ( set_int2 @ Xs2 ) )
% 5.31/5.55 => ( Y3 = X ) )
% 5.31/5.55 => ( Xs2
% 5.31/5.55 = ( replicate_int @ N @ X ) ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % replicate_eqI
% 5.31/5.55 thf(fact_3497_invar__vebt_Ointros_I2_J,axiom,
% 5.31/5.55 ! [TreeList2: list_VEBT_VEBT,N: nat,Summary: vEBT_VEBT,M2: nat,Deg: nat] :
% 5.31/5.55 ( ! [X3: vEBT_VEBT] :
% 5.31/5.55 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.31/5.55 => ( vEBT_invar_vebt @ X3 @ N ) )
% 5.31/5.55 => ( ( vEBT_invar_vebt @ Summary @ M2 )
% 5.31/5.55 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 5.31/5.55 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) )
% 5.31/5.55 => ( ( M2 = N )
% 5.31/5.55 => ( ( Deg
% 5.31/5.55 = ( plus_plus_nat @ N @ M2 ) )
% 5.31/5.55 => ( ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ Summary @ X_12 )
% 5.31/5.55 => ( ! [X3: vEBT_VEBT] :
% 5.31/5.55 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.31/5.55 => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X_12 ) )
% 5.31/5.55 => ( vEBT_invar_vebt @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg @ TreeList2 @ Summary ) @ Deg ) ) ) ) ) ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % invar_vebt.intros(2)
% 5.31/5.55 thf(fact_3498_invar__vebt_Ointros_I3_J,axiom,
% 5.31/5.55 ! [TreeList2: list_VEBT_VEBT,N: nat,Summary: vEBT_VEBT,M2: nat,Deg: nat] :
% 5.31/5.55 ( ! [X3: vEBT_VEBT] :
% 5.31/5.55 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.31/5.55 => ( vEBT_invar_vebt @ X3 @ N ) )
% 5.31/5.55 => ( ( vEBT_invar_vebt @ Summary @ M2 )
% 5.31/5.55 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 5.31/5.55 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) )
% 5.31/5.55 => ( ( M2
% 5.31/5.55 = ( suc @ N ) )
% 5.31/5.55 => ( ( Deg
% 5.31/5.55 = ( plus_plus_nat @ N @ M2 ) )
% 5.31/5.55 => ( ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ Summary @ X_12 )
% 5.31/5.55 => ( ! [X3: vEBT_VEBT] :
% 5.31/5.55 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.31/5.55 => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X_12 ) )
% 5.31/5.55 => ( vEBT_invar_vebt @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg @ TreeList2 @ Summary ) @ Deg ) ) ) ) ) ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % invar_vebt.intros(3)
% 5.31/5.55 thf(fact_3499_listrel__eq__len,axiom,
% 5.31/5.55 ! [Xs2: list_VEBT_VEBT,Ys: list_VEBT_VEBT,R3: set_Pr6192946355708809607T_VEBT] :
% 5.31/5.55 ( ( member4439316823752958928T_VEBT @ ( produc3897820843166775703T_VEBT @ Xs2 @ Ys ) @ ( listre1230615542750757617T_VEBT @ R3 ) )
% 5.31/5.55 => ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 5.31/5.55 = ( size_s6755466524823107622T_VEBT @ Ys ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % listrel_eq_len
% 5.31/5.55 thf(fact_3500_listrel__eq__len,axiom,
% 5.31/5.55 ! [Xs2: list_VEBT_VEBT,Ys: list_o,R3: set_Pr3175402225741728619VEBT_o] :
% 5.31/5.55 ( ( member3126162362653435956list_o @ ( produc2717590391345394939list_o @ Xs2 @ Ys ) @ ( listrel_VEBT_VEBT_o @ R3 ) )
% 5.31/5.55 => ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 5.31/5.55 = ( size_size_list_o @ Ys ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % listrel_eq_len
% 5.31/5.55 thf(fact_3501_listrel__eq__len,axiom,
% 5.31/5.55 ! [Xs2: list_VEBT_VEBT,Ys: list_nat,R3: set_Pr7556676689462069481BT_nat] :
% 5.31/5.55 ( ( member6193324644334088288st_nat @ ( produc5570133714943300547st_nat @ Xs2 @ Ys ) @ ( listre5900670229112895443BT_nat @ R3 ) )
% 5.31/5.55 => ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 5.31/5.55 = ( size_size_list_nat @ Ys ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % listrel_eq_len
% 5.31/5.55 thf(fact_3502_listrel__eq__len,axiom,
% 5.31/5.55 ! [Xs2: list_VEBT_VEBT,Ys: list_int,R3: set_Pr5066593544530342725BT_int] :
% 5.31/5.55 ( ( member3703241499402361532st_int @ ( produc1392282695434103839st_int @ Xs2 @ Ys ) @ ( listre5898179758603845167BT_int @ R3 ) )
% 5.31/5.55 => ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 5.31/5.55 = ( size_size_list_int @ Ys ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % listrel_eq_len
% 5.31/5.55 thf(fact_3503_listrel__eq__len,axiom,
% 5.31/5.55 ! [Xs2: list_o,Ys: list_VEBT_VEBT,R3: set_Pr7543698050874017315T_VEBT] :
% 5.31/5.55 ( ( member1087064965665443052T_VEBT @ ( produc6043759678074843571T_VEBT @ Xs2 @ Ys ) @ ( listrel_o_VEBT_VEBT @ R3 ) )
% 5.31/5.55 => ( ( size_size_list_o @ Xs2 )
% 5.31/5.55 = ( size_s6755466524823107622T_VEBT @ Ys ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % listrel_eq_len
% 5.31/5.55 thf(fact_3504_listrel__eq__len,axiom,
% 5.31/5.55 ! [Xs2: list_o,Ys: list_o,R3: set_Product_prod_o_o] :
% 5.31/5.55 ( ( member4159035015898711888list_o @ ( produc8435520187683070743list_o @ Xs2 @ Ys ) @ ( listrel_o_o @ R3 ) )
% 5.31/5.55 => ( ( size_size_list_o @ Xs2 )
% 5.31/5.55 = ( size_size_list_o @ Ys ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % listrel_eq_len
% 5.31/5.55 thf(fact_3505_listrel__eq__len,axiom,
% 5.31/5.55 ! [Xs2: list_o,Ys: list_nat,R3: set_Pr2101469702781467981_o_nat] :
% 5.31/5.55 ( ( member1519744053835550788st_nat @ ( produc7128876500814652583st_nat @ Xs2 @ Ys ) @ ( listrel_o_nat @ R3 ) )
% 5.31/5.55 => ( ( size_size_list_o @ Xs2 )
% 5.31/5.55 = ( size_size_list_nat @ Ys ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % listrel_eq_len
% 5.31/5.55 thf(fact_3506_listrel__eq__len,axiom,
% 5.31/5.55 ! [Xs2: list_o,Ys: list_int,R3: set_Pr8834758594704517033_o_int] :
% 5.31/5.55 ( ( member8253032945758599840st_int @ ( produc2951025481305455875st_int @ Xs2 @ Ys ) @ ( listrel_o_int @ R3 ) )
% 5.31/5.55 => ( ( size_size_list_o @ Xs2 )
% 5.31/5.55 = ( size_size_list_int @ Ys ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % listrel_eq_len
% 5.31/5.55 thf(fact_3507_listrel__eq__len,axiom,
% 5.31/5.55 ! [Xs2: list_nat,Ys: list_VEBT_VEBT,R3: set_Pr6167073792073659919T_VEBT] :
% 5.31/5.55 ( ( member5968030670617646438T_VEBT @ ( produc8335345208264861441T_VEBT @ Xs2 @ Ys ) @ ( listre5761932458788874033T_VEBT @ R3 ) )
% 5.31/5.55 => ( ( size_size_list_nat @ Xs2 )
% 5.31/5.55 = ( size_s6755466524823107622T_VEBT @ Ys ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % listrel_eq_len
% 5.31/5.55 thf(fact_3508_listrel__eq__len,axiom,
% 5.31/5.55 ! [Xs2: list_nat,Ys: list_o,R3: set_Pr3149072824959771635_nat_o] :
% 5.31/5.55 ( ( member6688923169008879818list_o @ ( produc699922362453767013list_o @ Xs2 @ Ys ) @ ( listrel_nat_o @ R3 ) )
% 5.31/5.55 => ( ( size_size_list_nat @ Xs2 )
% 5.31/5.55 = ( size_size_list_o @ Ys ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % listrel_eq_len
% 5.31/5.55 thf(fact_3509_ex__less__of__nat__mult,axiom,
% 5.31/5.55 ! [X: rat,Y: rat] :
% 5.31/5.55 ( ( ord_less_rat @ zero_zero_rat @ X )
% 5.31/5.55 => ? [N3: nat] : ( ord_less_rat @ Y @ ( times_times_rat @ ( semiri681578069525770553at_rat @ N3 ) @ X ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % ex_less_of_nat_mult
% 5.31/5.55 thf(fact_3510_ex__less__of__nat__mult,axiom,
% 5.31/5.55 ! [X: real,Y: real] :
% 5.31/5.55 ( ( ord_less_real @ zero_zero_real @ X )
% 5.31/5.55 => ? [N3: nat] : ( ord_less_real @ Y @ ( times_times_real @ ( semiri5074537144036343181t_real @ N3 ) @ X ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % ex_less_of_nat_mult
% 5.31/5.55 thf(fact_3511_of__nat__diff,axiom,
% 5.31/5.55 ! [N: nat,M2: nat] :
% 5.31/5.55 ( ( ord_less_eq_nat @ N @ M2 )
% 5.31/5.55 => ( ( semiri681578069525770553at_rat @ ( minus_minus_nat @ M2 @ N ) )
% 5.31/5.55 = ( minus_minus_rat @ ( semiri681578069525770553at_rat @ M2 ) @ ( semiri681578069525770553at_rat @ N ) ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % of_nat_diff
% 5.31/5.55 thf(fact_3512_of__nat__diff,axiom,
% 5.31/5.55 ! [N: nat,M2: nat] :
% 5.31/5.55 ( ( ord_less_eq_nat @ N @ M2 )
% 5.31/5.55 => ( ( semiri5074537144036343181t_real @ ( minus_minus_nat @ M2 @ N ) )
% 5.31/5.55 = ( minus_minus_real @ ( semiri5074537144036343181t_real @ M2 ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % of_nat_diff
% 5.31/5.55 thf(fact_3513_of__nat__diff,axiom,
% 5.31/5.55 ! [N: nat,M2: nat] :
% 5.31/5.55 ( ( ord_less_eq_nat @ N @ M2 )
% 5.31/5.55 => ( ( semiri1314217659103216013at_int @ ( minus_minus_nat @ M2 @ N ) )
% 5.31/5.55 = ( minus_minus_int @ ( semiri1314217659103216013at_int @ M2 ) @ ( semiri1314217659103216013at_int @ N ) ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % of_nat_diff
% 5.31/5.55 thf(fact_3514_of__nat__diff,axiom,
% 5.31/5.55 ! [N: nat,M2: nat] :
% 5.31/5.55 ( ( ord_less_eq_nat @ N @ M2 )
% 5.31/5.55 => ( ( semiri1316708129612266289at_nat @ ( minus_minus_nat @ M2 @ N ) )
% 5.31/5.55 = ( minus_minus_nat @ ( semiri1316708129612266289at_nat @ M2 ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % of_nat_diff
% 5.31/5.55 thf(fact_3515_zdiff__int__split,axiom,
% 5.31/5.55 ! [P2: int > $o,X: nat,Y: nat] :
% 5.31/5.55 ( ( P2 @ ( semiri1314217659103216013at_int @ ( minus_minus_nat @ X @ Y ) ) )
% 5.31/5.55 = ( ( ( ord_less_eq_nat @ Y @ X )
% 5.31/5.55 => ( P2 @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ X ) @ ( semiri1314217659103216013at_int @ Y ) ) ) )
% 5.31/5.55 & ( ( ord_less_nat @ X @ Y )
% 5.31/5.55 => ( P2 @ zero_zero_int ) ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % zdiff_int_split
% 5.31/5.55 thf(fact_3516_num_Osize_I5_J,axiom,
% 5.31/5.55 ! [X2: num] :
% 5.31/5.55 ( ( size_size_num @ ( bit0 @ X2 ) )
% 5.31/5.55 = ( plus_plus_nat @ ( size_size_num @ X2 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % num.size(5)
% 5.31/5.55 thf(fact_3517_realpow__pos__nth2,axiom,
% 5.31/5.55 ! [A: real,N: nat] :
% 5.31/5.55 ( ( ord_less_real @ zero_zero_real @ A )
% 5.31/5.55 => ? [R4: real] :
% 5.31/5.55 ( ( ord_less_real @ zero_zero_real @ R4 )
% 5.31/5.55 & ( ( power_power_real @ R4 @ ( suc @ N ) )
% 5.31/5.55 = A ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % realpow_pos_nth2
% 5.31/5.55 thf(fact_3518_listrel__Cons2,axiom,
% 5.31/5.55 ! [Xs2: list_Code_integer,Y: code_integer,Ys: list_Code_integer,R3: set_Pr4811707699266497531nteger] :
% 5.31/5.55 ( ( member749217712838834276nteger @ ( produc750622340256944499nteger @ Xs2 @ ( cons_Code_integer @ Y @ Ys ) ) @ ( listre5734910445319291053nteger @ R3 ) )
% 5.31/5.55 => ~ ! [X3: code_integer,Xs3: list_Code_integer] :
% 5.31/5.55 ( ( Xs2
% 5.31/5.55 = ( cons_Code_integer @ X3 @ Xs3 ) )
% 5.31/5.55 => ( ( member157494554546826820nteger @ ( produc1086072967326762835nteger @ X3 @ Y ) @ R3 )
% 5.31/5.55 => ~ ( member749217712838834276nteger @ ( produc750622340256944499nteger @ Xs3 @ Ys ) @ ( listre5734910445319291053nteger @ R3 ) ) ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % listrel_Cons2
% 5.31/5.55 thf(fact_3519_listrel__Cons2,axiom,
% 5.31/5.55 ! [Xs2: list_P6011104703257516679at_nat,Y: product_prod_nat_nat,Ys: list_P6011104703257516679at_nat,R3: set_Pr8693737435421807431at_nat] :
% 5.31/5.55 ( ( member6693912407220327184at_nat @ ( produc5943733680697469783at_nat @ Xs2 @ ( cons_P6512896166579812791at_nat @ Y @ Ys ) ) @ ( listre818007680106770737at_nat @ R3 ) )
% 5.31/5.55 => ~ ! [X3: product_prod_nat_nat,Xs3: list_P6011104703257516679at_nat] :
% 5.31/5.55 ( ( Xs2
% 5.31/5.55 = ( cons_P6512896166579812791at_nat @ X3 @ Xs3 ) )
% 5.31/5.55 => ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X3 @ Y ) @ R3 )
% 5.31/5.55 => ~ ( member6693912407220327184at_nat @ ( produc5943733680697469783at_nat @ Xs3 @ Ys ) @ ( listre818007680106770737at_nat @ R3 ) ) ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % listrel_Cons2
% 5.31/5.55 thf(fact_3520_listrel__Cons2,axiom,
% 5.31/5.55 ! [Xs2: list_s1210847774152347623at_nat,Y: set_Pr1261947904930325089at_nat,Ys: list_s1210847774152347623at_nat,R3: set_Pr4329608150637261639at_nat] :
% 5.31/5.55 ( ( member4080735728053443344at_nat @ ( produc7536900900485677911at_nat @ Xs2 @ ( cons_s6881495754146722583at_nat @ Y @ Ys ) ) @ ( listre2047417242196832561at_nat @ R3 ) )
% 5.31/5.55 => ~ ! [X3: set_Pr1261947904930325089at_nat,Xs3: list_s1210847774152347623at_nat] :
% 5.31/5.55 ( ( Xs2
% 5.31/5.55 = ( cons_s6881495754146722583at_nat @ X3 @ Xs3 ) )
% 5.31/5.55 => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X3 @ Y ) @ R3 )
% 5.31/5.55 => ~ ( member4080735728053443344at_nat @ ( produc7536900900485677911at_nat @ Xs3 @ Ys ) @ ( listre2047417242196832561at_nat @ R3 ) ) ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % listrel_Cons2
% 5.31/5.55 thf(fact_3521_listrel__Cons2,axiom,
% 5.31/5.55 ! [Xs2: list_nat,Y: nat,Ys: list_nat,R3: set_Pr1261947904930325089at_nat] :
% 5.31/5.55 ( ( member7340969449405702474st_nat @ ( produc2694037385005941721st_nat @ Xs2 @ ( cons_nat @ Y @ Ys ) ) @ ( listrel_nat_nat @ R3 ) )
% 5.31/5.55 => ~ ! [X3: nat,Xs3: list_nat] :
% 5.31/5.55 ( ( Xs2
% 5.31/5.55 = ( cons_nat @ X3 @ Xs3 ) )
% 5.31/5.55 => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X3 @ Y ) @ R3 )
% 5.31/5.55 => ~ ( member7340969449405702474st_nat @ ( produc2694037385005941721st_nat @ Xs3 @ Ys ) @ ( listrel_nat_nat @ R3 ) ) ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % listrel_Cons2
% 5.31/5.55 thf(fact_3522_listrel__Cons2,axiom,
% 5.31/5.55 ! [Xs2: list_int,Y: int,Ys: list_int,R3: set_Pr958786334691620121nt_int] :
% 5.31/5.55 ( ( member6698963635872716290st_int @ ( produc364263696895485585st_int @ Xs2 @ ( cons_int @ Y @ Ys ) ) @ ( listrel_int_int @ R3 ) )
% 5.31/5.55 => ~ ! [X3: int,Xs3: list_int] :
% 5.31/5.55 ( ( Xs2
% 5.31/5.55 = ( cons_int @ X3 @ Xs3 ) )
% 5.31/5.55 => ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X3 @ Y ) @ R3 )
% 5.31/5.55 => ~ ( member6698963635872716290st_int @ ( produc364263696895485585st_int @ Xs3 @ Ys ) @ ( listrel_int_int @ R3 ) ) ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % listrel_Cons2
% 5.31/5.55 thf(fact_3523_listrel__Cons1,axiom,
% 5.31/5.55 ! [Y: code_integer,Ys: list_Code_integer,Xs2: list_Code_integer,R3: set_Pr4811707699266497531nteger] :
% 5.31/5.55 ( ( member749217712838834276nteger @ ( produc750622340256944499nteger @ ( cons_Code_integer @ Y @ Ys ) @ Xs2 ) @ ( listre5734910445319291053nteger @ R3 ) )
% 5.31/5.55 => ~ ! [Y3: code_integer,Ys5: list_Code_integer] :
% 5.31/5.55 ( ( Xs2
% 5.31/5.55 = ( cons_Code_integer @ Y3 @ Ys5 ) )
% 5.31/5.55 => ( ( member157494554546826820nteger @ ( produc1086072967326762835nteger @ Y @ Y3 ) @ R3 )
% 5.31/5.55 => ~ ( member749217712838834276nteger @ ( produc750622340256944499nteger @ Ys @ Ys5 ) @ ( listre5734910445319291053nteger @ R3 ) ) ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % listrel_Cons1
% 5.31/5.55 thf(fact_3524_listrel__Cons1,axiom,
% 5.31/5.55 ! [Y: product_prod_nat_nat,Ys: list_P6011104703257516679at_nat,Xs2: list_P6011104703257516679at_nat,R3: set_Pr8693737435421807431at_nat] :
% 5.31/5.55 ( ( member6693912407220327184at_nat @ ( produc5943733680697469783at_nat @ ( cons_P6512896166579812791at_nat @ Y @ Ys ) @ Xs2 ) @ ( listre818007680106770737at_nat @ R3 ) )
% 5.31/5.55 => ~ ! [Y3: product_prod_nat_nat,Ys5: list_P6011104703257516679at_nat] :
% 5.31/5.55 ( ( Xs2
% 5.31/5.55 = ( cons_P6512896166579812791at_nat @ Y3 @ Ys5 ) )
% 5.31/5.55 => ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ Y @ Y3 ) @ R3 )
% 5.31/5.55 => ~ ( member6693912407220327184at_nat @ ( produc5943733680697469783at_nat @ Ys @ Ys5 ) @ ( listre818007680106770737at_nat @ R3 ) ) ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % listrel_Cons1
% 5.31/5.55 thf(fact_3525_listrel__Cons1,axiom,
% 5.31/5.55 ! [Y: set_Pr1261947904930325089at_nat,Ys: list_s1210847774152347623at_nat,Xs2: list_s1210847774152347623at_nat,R3: set_Pr4329608150637261639at_nat] :
% 5.31/5.55 ( ( member4080735728053443344at_nat @ ( produc7536900900485677911at_nat @ ( cons_s6881495754146722583at_nat @ Y @ Ys ) @ Xs2 ) @ ( listre2047417242196832561at_nat @ R3 ) )
% 5.31/5.55 => ~ ! [Y3: set_Pr1261947904930325089at_nat,Ys5: list_s1210847774152347623at_nat] :
% 5.31/5.55 ( ( Xs2
% 5.31/5.55 = ( cons_s6881495754146722583at_nat @ Y3 @ Ys5 ) )
% 5.31/5.55 => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ Y @ Y3 ) @ R3 )
% 5.31/5.55 => ~ ( member4080735728053443344at_nat @ ( produc7536900900485677911at_nat @ Ys @ Ys5 ) @ ( listre2047417242196832561at_nat @ R3 ) ) ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % listrel_Cons1
% 5.31/5.55 thf(fact_3526_listrel__Cons1,axiom,
% 5.31/5.55 ! [Y: nat,Ys: list_nat,Xs2: list_nat,R3: set_Pr1261947904930325089at_nat] :
% 5.31/5.55 ( ( member7340969449405702474st_nat @ ( produc2694037385005941721st_nat @ ( cons_nat @ Y @ Ys ) @ Xs2 ) @ ( listrel_nat_nat @ R3 ) )
% 5.31/5.55 => ~ ! [Y3: nat,Ys5: list_nat] :
% 5.31/5.55 ( ( Xs2
% 5.31/5.55 = ( cons_nat @ Y3 @ Ys5 ) )
% 5.31/5.55 => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ Y @ Y3 ) @ R3 )
% 5.31/5.55 => ~ ( member7340969449405702474st_nat @ ( produc2694037385005941721st_nat @ Ys @ Ys5 ) @ ( listrel_nat_nat @ R3 ) ) ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % listrel_Cons1
% 5.31/5.55 thf(fact_3527_listrel__Cons1,axiom,
% 5.31/5.55 ! [Y: int,Ys: list_int,Xs2: list_int,R3: set_Pr958786334691620121nt_int] :
% 5.31/5.55 ( ( member6698963635872716290st_int @ ( produc364263696895485585st_int @ ( cons_int @ Y @ Ys ) @ Xs2 ) @ ( listrel_int_int @ R3 ) )
% 5.31/5.55 => ~ ! [Y3: int,Ys5: list_int] :
% 5.31/5.55 ( ( Xs2
% 5.31/5.55 = ( cons_int @ Y3 @ Ys5 ) )
% 5.31/5.55 => ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ Y @ Y3 ) @ R3 )
% 5.31/5.55 => ~ ( member6698963635872716290st_int @ ( produc364263696895485585st_int @ Ys @ Ys5 ) @ ( listrel_int_int @ R3 ) ) ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % listrel_Cons1
% 5.31/5.55 thf(fact_3528_listrel_OCons,axiom,
% 5.31/5.55 ! [X: code_integer,Y: code_integer,R3: set_Pr4811707699266497531nteger,Xs2: list_Code_integer,Ys: list_Code_integer] :
% 5.31/5.55 ( ( member157494554546826820nteger @ ( produc1086072967326762835nteger @ X @ Y ) @ R3 )
% 5.31/5.55 => ( ( member749217712838834276nteger @ ( produc750622340256944499nteger @ Xs2 @ Ys ) @ ( listre5734910445319291053nteger @ R3 ) )
% 5.31/5.55 => ( member749217712838834276nteger @ ( produc750622340256944499nteger @ ( cons_Code_integer @ X @ Xs2 ) @ ( cons_Code_integer @ Y @ Ys ) ) @ ( listre5734910445319291053nteger @ R3 ) ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % listrel.Cons
% 5.31/5.55 thf(fact_3529_listrel_OCons,axiom,
% 5.31/5.55 ! [X: product_prod_nat_nat,Y: product_prod_nat_nat,R3: set_Pr8693737435421807431at_nat,Xs2: list_P6011104703257516679at_nat,Ys: list_P6011104703257516679at_nat] :
% 5.31/5.55 ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X @ Y ) @ R3 )
% 5.31/5.55 => ( ( member6693912407220327184at_nat @ ( produc5943733680697469783at_nat @ Xs2 @ Ys ) @ ( listre818007680106770737at_nat @ R3 ) )
% 5.31/5.55 => ( member6693912407220327184at_nat @ ( produc5943733680697469783at_nat @ ( cons_P6512896166579812791at_nat @ X @ Xs2 ) @ ( cons_P6512896166579812791at_nat @ Y @ Ys ) ) @ ( listre818007680106770737at_nat @ R3 ) ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % listrel.Cons
% 5.31/5.55 thf(fact_3530_listrel_OCons,axiom,
% 5.31/5.55 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,R3: set_Pr4329608150637261639at_nat,Xs2: list_s1210847774152347623at_nat,Ys: list_s1210847774152347623at_nat] :
% 5.31/5.55 ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X @ Y ) @ R3 )
% 5.31/5.55 => ( ( member4080735728053443344at_nat @ ( produc7536900900485677911at_nat @ Xs2 @ Ys ) @ ( listre2047417242196832561at_nat @ R3 ) )
% 5.31/5.55 => ( member4080735728053443344at_nat @ ( produc7536900900485677911at_nat @ ( cons_s6881495754146722583at_nat @ X @ Xs2 ) @ ( cons_s6881495754146722583at_nat @ Y @ Ys ) ) @ ( listre2047417242196832561at_nat @ R3 ) ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % listrel.Cons
% 5.31/5.55 thf(fact_3531_listrel_OCons,axiom,
% 5.31/5.55 ! [X: nat,Y: nat,R3: set_Pr1261947904930325089at_nat,Xs2: list_nat,Ys: list_nat] :
% 5.31/5.55 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ R3 )
% 5.31/5.55 => ( ( member7340969449405702474st_nat @ ( produc2694037385005941721st_nat @ Xs2 @ Ys ) @ ( listrel_nat_nat @ R3 ) )
% 5.31/5.55 => ( member7340969449405702474st_nat @ ( produc2694037385005941721st_nat @ ( cons_nat @ X @ Xs2 ) @ ( cons_nat @ Y @ Ys ) ) @ ( listrel_nat_nat @ R3 ) ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % listrel.Cons
% 5.31/5.55 thf(fact_3532_listrel_OCons,axiom,
% 5.31/5.55 ! [X: int,Y: int,R3: set_Pr958786334691620121nt_int,Xs2: list_int,Ys: list_int] :
% 5.31/5.55 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y ) @ R3 )
% 5.31/5.55 => ( ( member6698963635872716290st_int @ ( produc364263696895485585st_int @ Xs2 @ Ys ) @ ( listrel_int_int @ R3 ) )
% 5.31/5.55 => ( member6698963635872716290st_int @ ( produc364263696895485585st_int @ ( cons_int @ X @ Xs2 ) @ ( cons_int @ Y @ Ys ) ) @ ( listrel_int_int @ R3 ) ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % listrel.Cons
% 5.31/5.55 thf(fact_3533_measures__less,axiom,
% 5.31/5.55 ! [F2: code_integer > nat,X: code_integer,Y: code_integer,Fs: list_C4705013386053401436er_nat] :
% 5.31/5.55 ( ( ord_less_nat @ ( F2 @ X ) @ ( F2 @ Y ) )
% 5.31/5.55 => ( member157494554546826820nteger @ ( produc1086072967326762835nteger @ X @ Y ) @ ( measur8870801148506250077nteger @ ( cons_C1897838848541180310er_nat @ F2 @ Fs ) ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % measures_less
% 5.31/5.55 thf(fact_3534_measures__less,axiom,
% 5.31/5.55 ! [F2: product_prod_nat_nat > nat,X: product_prod_nat_nat,Y: product_prod_nat_nat,Fs: list_P9162950289778280392at_nat] :
% 5.31/5.55 ( ( ord_less_nat @ ( F2 @ X ) @ ( F2 @ Y ) )
% 5.31/5.55 => ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X @ Y ) @ ( measur2679027848233739777at_nat @ ( cons_P4861729644591583992at_nat @ F2 @ Fs ) ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % measures_less
% 5.31/5.55 thf(fact_3535_measures__less,axiom,
% 5.31/5.55 ! [F2: set_Pr1261947904930325089at_nat > nat,X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,Fs: list_s9130966667114977576at_nat] :
% 5.31/5.55 ( ( ord_less_nat @ ( F2 @ X ) @ ( F2 @ Y ) )
% 5.31/5.55 => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X @ Y ) @ ( measur2694323259624372065at_nat @ ( cons_s2538900923071588440at_nat @ F2 @ Fs ) ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % measures_less
% 5.31/5.55 thf(fact_3536_measures__less,axiom,
% 5.31/5.55 ! [F2: nat > nat,X: nat,Y: nat,Fs: list_nat_nat] :
% 5.31/5.55 ( ( ord_less_nat @ ( F2 @ X ) @ ( F2 @ Y ) )
% 5.31/5.55 => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ ( measures_nat @ ( cons_nat_nat @ F2 @ Fs ) ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % measures_less
% 5.31/5.55 thf(fact_3537_measures__less,axiom,
% 5.31/5.55 ! [F2: int > nat,X: int,Y: int,Fs: list_int_nat] :
% 5.31/5.55 ( ( ord_less_nat @ ( F2 @ X ) @ ( F2 @ Y ) )
% 5.31/5.55 => ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y ) @ ( measures_int @ ( cons_int_nat @ F2 @ Fs ) ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % measures_less
% 5.31/5.55 thf(fact_3538_measures__lesseq,axiom,
% 5.31/5.55 ! [F2: code_integer > nat,X: code_integer,Y: code_integer,Fs: list_C4705013386053401436er_nat] :
% 5.31/5.55 ( ( ord_less_eq_nat @ ( F2 @ X ) @ ( F2 @ Y ) )
% 5.31/5.55 => ( ( member157494554546826820nteger @ ( produc1086072967326762835nteger @ X @ Y ) @ ( measur8870801148506250077nteger @ Fs ) )
% 5.31/5.55 => ( member157494554546826820nteger @ ( produc1086072967326762835nteger @ X @ Y ) @ ( measur8870801148506250077nteger @ ( cons_C1897838848541180310er_nat @ F2 @ Fs ) ) ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % measures_lesseq
% 5.31/5.55 thf(fact_3539_measures__lesseq,axiom,
% 5.31/5.55 ! [F2: product_prod_nat_nat > nat,X: product_prod_nat_nat,Y: product_prod_nat_nat,Fs: list_P9162950289778280392at_nat] :
% 5.31/5.55 ( ( ord_less_eq_nat @ ( F2 @ X ) @ ( F2 @ Y ) )
% 5.31/5.55 => ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X @ Y ) @ ( measur2679027848233739777at_nat @ Fs ) )
% 5.31/5.55 => ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X @ Y ) @ ( measur2679027848233739777at_nat @ ( cons_P4861729644591583992at_nat @ F2 @ Fs ) ) ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % measures_lesseq
% 5.31/5.55 thf(fact_3540_measures__lesseq,axiom,
% 5.31/5.55 ! [F2: set_Pr1261947904930325089at_nat > nat,X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,Fs: list_s9130966667114977576at_nat] :
% 5.31/5.55 ( ( ord_less_eq_nat @ ( F2 @ X ) @ ( F2 @ Y ) )
% 5.31/5.55 => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X @ Y ) @ ( measur2694323259624372065at_nat @ Fs ) )
% 5.31/5.55 => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X @ Y ) @ ( measur2694323259624372065at_nat @ ( cons_s2538900923071588440at_nat @ F2 @ Fs ) ) ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % measures_lesseq
% 5.31/5.55 thf(fact_3541_measures__lesseq,axiom,
% 5.31/5.55 ! [F2: nat > nat,X: nat,Y: nat,Fs: list_nat_nat] :
% 5.31/5.55 ( ( ord_less_eq_nat @ ( F2 @ X ) @ ( F2 @ Y ) )
% 5.31/5.55 => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ ( measures_nat @ Fs ) )
% 5.31/5.55 => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ ( measures_nat @ ( cons_nat_nat @ F2 @ Fs ) ) ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % measures_lesseq
% 5.31/5.55 thf(fact_3542_measures__lesseq,axiom,
% 5.31/5.55 ! [F2: int > nat,X: int,Y: int,Fs: list_int_nat] :
% 5.31/5.55 ( ( ord_less_eq_nat @ ( F2 @ X ) @ ( F2 @ Y ) )
% 5.31/5.55 => ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y ) @ ( measures_int @ Fs ) )
% 5.31/5.55 => ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y ) @ ( measures_int @ ( cons_int_nat @ F2 @ Fs ) ) ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % measures_lesseq
% 5.31/5.55 thf(fact_3543_set__replicate__Suc,axiom,
% 5.31/5.55 ! [N: nat,X: vEBT_VEBT] :
% 5.31/5.55 ( ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ ( suc @ N ) @ X ) )
% 5.31/5.55 = ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) ) ).
% 5.31/5.55
% 5.31/5.55 % set_replicate_Suc
% 5.31/5.55 thf(fact_3544_set__replicate__Suc,axiom,
% 5.31/5.55 ! [N: nat,X: nat] :
% 5.31/5.55 ( ( set_nat2 @ ( replicate_nat @ ( suc @ N ) @ X ) )
% 5.31/5.55 = ( insert_nat @ X @ bot_bot_set_nat ) ) ).
% 5.31/5.55
% 5.31/5.55 % set_replicate_Suc
% 5.31/5.55 thf(fact_3545_set__replicate__Suc,axiom,
% 5.31/5.55 ! [N: nat,X: int] :
% 5.31/5.55 ( ( set_int2 @ ( replicate_int @ ( suc @ N ) @ X ) )
% 5.31/5.55 = ( insert_int @ X @ bot_bot_set_int ) ) ).
% 5.31/5.55
% 5.31/5.55 % set_replicate_Suc
% 5.31/5.55 thf(fact_3546_set__replicate__Suc,axiom,
% 5.31/5.55 ! [N: nat,X: real] :
% 5.31/5.55 ( ( set_real2 @ ( replicate_real @ ( suc @ N ) @ X ) )
% 5.31/5.55 = ( insert_real @ X @ bot_bot_set_real ) ) ).
% 5.31/5.55
% 5.31/5.55 % set_replicate_Suc
% 5.31/5.55 thf(fact_3547_set__replicate__conv__if,axiom,
% 5.31/5.55 ! [N: nat,X: vEBT_VEBT] :
% 5.31/5.55 ( ( ( N = zero_zero_nat )
% 5.31/5.55 => ( ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ N @ X ) )
% 5.31/5.55 = bot_bo8194388402131092736T_VEBT ) )
% 5.31/5.55 & ( ( N != zero_zero_nat )
% 5.31/5.55 => ( ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ N @ X ) )
% 5.31/5.55 = ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % set_replicate_conv_if
% 5.31/5.55 thf(fact_3548_set__replicate__conv__if,axiom,
% 5.31/5.55 ! [N: nat,X: nat] :
% 5.31/5.55 ( ( ( N = zero_zero_nat )
% 5.31/5.55 => ( ( set_nat2 @ ( replicate_nat @ N @ X ) )
% 5.31/5.55 = bot_bot_set_nat ) )
% 5.31/5.55 & ( ( N != zero_zero_nat )
% 5.31/5.55 => ( ( set_nat2 @ ( replicate_nat @ N @ X ) )
% 5.31/5.55 = ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % set_replicate_conv_if
% 5.31/5.55 thf(fact_3549_set__replicate__conv__if,axiom,
% 5.31/5.55 ! [N: nat,X: int] :
% 5.31/5.55 ( ( ( N = zero_zero_nat )
% 5.31/5.55 => ( ( set_int2 @ ( replicate_int @ N @ X ) )
% 5.31/5.55 = bot_bot_set_int ) )
% 5.31/5.55 & ( ( N != zero_zero_nat )
% 5.31/5.55 => ( ( set_int2 @ ( replicate_int @ N @ X ) )
% 5.31/5.55 = ( insert_int @ X @ bot_bot_set_int ) ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % set_replicate_conv_if
% 5.31/5.55 thf(fact_3550_set__replicate__conv__if,axiom,
% 5.31/5.55 ! [N: nat,X: real] :
% 5.31/5.55 ( ( ( N = zero_zero_nat )
% 5.31/5.55 => ( ( set_real2 @ ( replicate_real @ N @ X ) )
% 5.31/5.55 = bot_bot_set_real ) )
% 5.31/5.55 & ( ( N != zero_zero_nat )
% 5.31/5.55 => ( ( set_real2 @ ( replicate_real @ N @ X ) )
% 5.31/5.55 = ( insert_real @ X @ bot_bot_set_real ) ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % set_replicate_conv_if
% 5.31/5.55 thf(fact_3551_Cons__replicate__eq,axiom,
% 5.31/5.55 ! [X: nat,Xs2: list_nat,N: nat,Y: nat] :
% 5.31/5.55 ( ( ( cons_nat @ X @ Xs2 )
% 5.31/5.55 = ( replicate_nat @ N @ Y ) )
% 5.31/5.55 = ( ( X = Y )
% 5.31/5.55 & ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.55 & ( Xs2
% 5.31/5.55 = ( replicate_nat @ ( minus_minus_nat @ N @ one_one_nat ) @ X ) ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % Cons_replicate_eq
% 5.31/5.55 thf(fact_3552_Cons__replicate__eq,axiom,
% 5.31/5.55 ! [X: vEBT_VEBT,Xs2: list_VEBT_VEBT,N: nat,Y: vEBT_VEBT] :
% 5.31/5.55 ( ( ( cons_VEBT_VEBT @ X @ Xs2 )
% 5.31/5.55 = ( replicate_VEBT_VEBT @ N @ Y ) )
% 5.31/5.55 = ( ( X = Y )
% 5.31/5.55 & ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.55 & ( Xs2
% 5.31/5.55 = ( replicate_VEBT_VEBT @ ( minus_minus_nat @ N @ one_one_nat ) @ X ) ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % Cons_replicate_eq
% 5.31/5.55 thf(fact_3553_divmod__step__eq,axiom,
% 5.31/5.55 ! [L: num,R3: nat,Q2: nat] :
% 5.31/5.55 ( ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ L ) @ R3 )
% 5.31/5.55 => ( ( unique5026877609467782581ep_nat @ L @ ( product_Pair_nat_nat @ Q2 @ R3 ) )
% 5.31/5.55 = ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q2 ) @ one_one_nat ) @ ( minus_minus_nat @ R3 @ ( numeral_numeral_nat @ L ) ) ) ) )
% 5.31/5.55 & ( ~ ( ord_less_eq_nat @ ( numeral_numeral_nat @ L ) @ R3 )
% 5.31/5.55 => ( ( unique5026877609467782581ep_nat @ L @ ( product_Pair_nat_nat @ Q2 @ R3 ) )
% 5.31/5.55 = ( product_Pair_nat_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q2 ) @ R3 ) ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % divmod_step_eq
% 5.31/5.55 thf(fact_3554_divmod__step__eq,axiom,
% 5.31/5.55 ! [L: num,R3: int,Q2: int] :
% 5.31/5.55 ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ L ) @ R3 )
% 5.31/5.55 => ( ( unique5024387138958732305ep_int @ L @ ( product_Pair_int_int @ Q2 @ R3 ) )
% 5.31/5.55 = ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q2 ) @ one_one_int ) @ ( minus_minus_int @ R3 @ ( numeral_numeral_int @ L ) ) ) ) )
% 5.31/5.55 & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ L ) @ R3 )
% 5.31/5.55 => ( ( unique5024387138958732305ep_int @ L @ ( product_Pair_int_int @ Q2 @ R3 ) )
% 5.31/5.55 = ( product_Pair_int_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q2 ) @ R3 ) ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % divmod_step_eq
% 5.31/5.55 thf(fact_3555_divmod__step__eq,axiom,
% 5.31/5.55 ! [L: num,R3: code_integer,Q2: code_integer] :
% 5.31/5.55 ( ( ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ L ) @ R3 )
% 5.31/5.55 => ( ( unique4921790084139445826nteger @ L @ ( produc1086072967326762835nteger @ Q2 @ R3 ) )
% 5.31/5.55 = ( produc1086072967326762835nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q2 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ R3 @ ( numera6620942414471956472nteger @ L ) ) ) ) )
% 5.31/5.55 & ( ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ L ) @ R3 )
% 5.31/5.55 => ( ( unique4921790084139445826nteger @ L @ ( produc1086072967326762835nteger @ Q2 @ R3 ) )
% 5.31/5.55 = ( produc1086072967326762835nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q2 ) @ R3 ) ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % divmod_step_eq
% 5.31/5.55 thf(fact_3556_mintlistlength,axiom,
% 5.31/5.55 ! [Mi: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat] :
% 5.31/5.55 ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ N )
% 5.31/5.55 => ( ( Mi != Ma )
% 5.31/5.55 => ( ( ord_less_nat @ Mi @ Ma )
% 5.31/5.55 & ? [M: nat] :
% 5.31/5.55 ( ( ( some_nat @ M )
% 5.31/5.55 = ( vEBT_vebt_mint @ Summary ) )
% 5.31/5.55 & ( ord_less_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % mintlistlength
% 5.31/5.55 thf(fact_3557_insert__correct,axiom,
% 5.31/5.55 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 5.31/5.55 ( ( vEBT_invar_vebt @ T @ N )
% 5.31/5.55 => ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.31/5.55 => ( ( sup_sup_set_nat @ ( vEBT_set_vebt @ T ) @ ( insert_nat @ X @ bot_bot_set_nat ) )
% 5.31/5.55 = ( vEBT_set_vebt @ ( vEBT_vebt_insert @ T @ X ) ) ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % insert_correct
% 5.31/5.55 thf(fact_3558_insert__corr,axiom,
% 5.31/5.55 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 5.31/5.55 ( ( vEBT_invar_vebt @ T @ N )
% 5.31/5.55 => ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.31/5.55 => ( ( sup_sup_set_nat @ ( vEBT_VEBT_set_vebt @ T ) @ ( insert_nat @ X @ bot_bot_set_nat ) )
% 5.31/5.55 = ( vEBT_VEBT_set_vebt @ ( vEBT_vebt_insert @ T @ X ) ) ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % insert_corr
% 5.31/5.55 thf(fact_3559_inrange,axiom,
% 5.31/5.55 ! [T: vEBT_VEBT,N: nat] :
% 5.31/5.55 ( ( vEBT_invar_vebt @ T @ N )
% 5.31/5.55 => ( 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 ) ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % inrange
% 5.31/5.55 thf(fact_3560_nat__bit__induct,axiom,
% 5.31/5.55 ! [P2: nat > $o,N: nat] :
% 5.31/5.55 ( ( P2 @ zero_zero_nat )
% 5.31/5.55 => ( ! [N3: nat] :
% 5.31/5.55 ( ( P2 @ N3 )
% 5.31/5.55 => ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 5.31/5.55 => ( P2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) ) ) )
% 5.31/5.55 => ( ! [N3: nat] :
% 5.31/5.55 ( ( P2 @ N3 )
% 5.31/5.55 => ( P2 @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) ) ) )
% 5.31/5.55 => ( P2 @ N ) ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % nat_bit_induct
% 5.31/5.55 thf(fact_3561_nat__induct2,axiom,
% 5.31/5.55 ! [P2: nat > $o,N: nat] :
% 5.31/5.55 ( ( P2 @ zero_zero_nat )
% 5.31/5.55 => ( ( P2 @ one_one_nat )
% 5.31/5.55 => ( ! [N3: nat] :
% 5.31/5.55 ( ( P2 @ N3 )
% 5.31/5.55 => ( P2 @ ( plus_plus_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.31/5.55 => ( P2 @ N ) ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % nat_induct2
% 5.31/5.55 thf(fact_3562_exp__not__zero__imp__exp__diff__not__zero,axiom,
% 5.31/5.55 ! [N: nat,M2: nat] :
% 5.31/5.55 ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.31/5.55 != zero_zero_nat )
% 5.31/5.55 => ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M2 ) )
% 5.31/5.55 != zero_zero_nat ) ) ).
% 5.31/5.55
% 5.31/5.55 % exp_not_zero_imp_exp_diff_not_zero
% 5.31/5.55 thf(fact_3563_exp__not__zero__imp__exp__diff__not__zero,axiom,
% 5.31/5.55 ! [N: nat,M2: nat] :
% 5.31/5.55 ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 5.31/5.55 != zero_zero_int )
% 5.31/5.55 => ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M2 ) )
% 5.31/5.55 != zero_zero_int ) ) ).
% 5.31/5.55
% 5.31/5.55 % exp_not_zero_imp_exp_diff_not_zero
% 5.31/5.55 thf(fact_3564_exp__add__not__zero__imp__left,axiom,
% 5.31/5.55 ! [M2: nat,N: nat] :
% 5.31/5.55 ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M2 @ N ) )
% 5.31/5.55 != zero_zero_nat )
% 5.31/5.55 => ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 )
% 5.31/5.55 != zero_zero_nat ) ) ).
% 5.31/5.55
% 5.31/5.55 % exp_add_not_zero_imp_left
% 5.31/5.55 thf(fact_3565_exp__add__not__zero__imp__left,axiom,
% 5.31/5.55 ! [M2: nat,N: nat] :
% 5.31/5.55 ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M2 @ N ) )
% 5.31/5.55 != zero_zero_int )
% 5.31/5.55 => ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M2 )
% 5.31/5.55 != zero_zero_int ) ) ).
% 5.31/5.55
% 5.31/5.55 % exp_add_not_zero_imp_left
% 5.31/5.55 thf(fact_3566_pow__sum,axiom,
% 5.31/5.55 ! [A: nat,B: nat] :
% 5.31/5.55 ( ( 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 ) )
% 5.31/5.55 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ).
% 5.31/5.55
% 5.31/5.55 % pow_sum
% 5.31/5.55 thf(fact_3567_power__minus__is__div,axiom,
% 5.31/5.55 ! [B: nat,A: nat] :
% 5.31/5.55 ( ( ord_less_eq_nat @ B @ A )
% 5.31/5.55 => ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ A @ B ) )
% 5.31/5.55 = ( divide_divide_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % power_minus_is_div
% 5.31/5.55 thf(fact_3568_bits__div__by__0,axiom,
% 5.31/5.55 ! [A: nat] :
% 5.31/5.55 ( ( divide_divide_nat @ A @ zero_zero_nat )
% 5.31/5.55 = zero_zero_nat ) ).
% 5.31/5.55
% 5.31/5.55 % bits_div_by_0
% 5.31/5.55 thf(fact_3569_bits__div__by__0,axiom,
% 5.31/5.55 ! [A: int] :
% 5.31/5.55 ( ( divide_divide_int @ A @ zero_zero_int )
% 5.31/5.55 = zero_zero_int ) ).
% 5.31/5.55
% 5.31/5.55 % bits_div_by_0
% 5.31/5.55 thf(fact_3570_bits__div__0,axiom,
% 5.31/5.55 ! [A: nat] :
% 5.31/5.55 ( ( divide_divide_nat @ zero_zero_nat @ A )
% 5.31/5.55 = zero_zero_nat ) ).
% 5.31/5.55
% 5.31/5.55 % bits_div_0
% 5.31/5.55 thf(fact_3571_bits__div__0,axiom,
% 5.31/5.55 ! [A: int] :
% 5.31/5.55 ( ( divide_divide_int @ zero_zero_int @ A )
% 5.31/5.55 = zero_zero_int ) ).
% 5.31/5.55
% 5.31/5.55 % bits_div_0
% 5.31/5.55 thf(fact_3572_div__by__0,axiom,
% 5.31/5.55 ! [A: complex] :
% 5.31/5.55 ( ( divide1717551699836669952omplex @ A @ zero_zero_complex )
% 5.31/5.55 = zero_zero_complex ) ).
% 5.31/5.55
% 5.31/5.55 % div_by_0
% 5.31/5.55 thf(fact_3573_div__by__0,axiom,
% 5.31/5.55 ! [A: real] :
% 5.31/5.55 ( ( divide_divide_real @ A @ zero_zero_real )
% 5.31/5.55 = zero_zero_real ) ).
% 5.31/5.55
% 5.31/5.55 % div_by_0
% 5.31/5.55 thf(fact_3574_div__by__0,axiom,
% 5.31/5.55 ! [A: rat] :
% 5.31/5.55 ( ( divide_divide_rat @ A @ zero_zero_rat )
% 5.31/5.55 = zero_zero_rat ) ).
% 5.31/5.55
% 5.31/5.55 % div_by_0
% 5.31/5.55 thf(fact_3575_div__by__0,axiom,
% 5.31/5.55 ! [A: nat] :
% 5.31/5.55 ( ( divide_divide_nat @ A @ zero_zero_nat )
% 5.31/5.55 = zero_zero_nat ) ).
% 5.31/5.55
% 5.31/5.55 % div_by_0
% 5.31/5.55 thf(fact_3576_div__by__0,axiom,
% 5.31/5.55 ! [A: int] :
% 5.31/5.55 ( ( divide_divide_int @ A @ zero_zero_int )
% 5.31/5.55 = zero_zero_int ) ).
% 5.31/5.55
% 5.31/5.55 % div_by_0
% 5.31/5.55 thf(fact_3577_div__0,axiom,
% 5.31/5.55 ! [A: complex] :
% 5.31/5.55 ( ( divide1717551699836669952omplex @ zero_zero_complex @ A )
% 5.31/5.55 = zero_zero_complex ) ).
% 5.31/5.55
% 5.31/5.55 % div_0
% 5.31/5.55 thf(fact_3578_div__0,axiom,
% 5.31/5.55 ! [A: real] :
% 5.31/5.55 ( ( divide_divide_real @ zero_zero_real @ A )
% 5.31/5.55 = zero_zero_real ) ).
% 5.31/5.55
% 5.31/5.55 % div_0
% 5.31/5.55 thf(fact_3579_div__0,axiom,
% 5.31/5.55 ! [A: rat] :
% 5.31/5.55 ( ( divide_divide_rat @ zero_zero_rat @ A )
% 5.31/5.55 = zero_zero_rat ) ).
% 5.31/5.55
% 5.31/5.55 % div_0
% 5.31/5.55 thf(fact_3580_div__0,axiom,
% 5.31/5.55 ! [A: nat] :
% 5.31/5.55 ( ( divide_divide_nat @ zero_zero_nat @ A )
% 5.31/5.55 = zero_zero_nat ) ).
% 5.31/5.55
% 5.31/5.55 % div_0
% 5.31/5.55 thf(fact_3581_div__0,axiom,
% 5.31/5.55 ! [A: int] :
% 5.31/5.55 ( ( divide_divide_int @ zero_zero_int @ A )
% 5.31/5.55 = zero_zero_int ) ).
% 5.31/5.55
% 5.31/5.55 % div_0
% 5.31/5.55 thf(fact_3582_division__ring__divide__zero,axiom,
% 5.31/5.55 ! [A: complex] :
% 5.31/5.55 ( ( divide1717551699836669952omplex @ A @ zero_zero_complex )
% 5.31/5.55 = zero_zero_complex ) ).
% 5.31/5.55
% 5.31/5.55 % division_ring_divide_zero
% 5.31/5.55 thf(fact_3583_division__ring__divide__zero,axiom,
% 5.31/5.55 ! [A: real] :
% 5.31/5.55 ( ( divide_divide_real @ A @ zero_zero_real )
% 5.31/5.55 = zero_zero_real ) ).
% 5.31/5.55
% 5.31/5.55 % division_ring_divide_zero
% 5.31/5.55 thf(fact_3584_division__ring__divide__zero,axiom,
% 5.31/5.55 ! [A: rat] :
% 5.31/5.55 ( ( divide_divide_rat @ A @ zero_zero_rat )
% 5.31/5.55 = zero_zero_rat ) ).
% 5.31/5.55
% 5.31/5.55 % division_ring_divide_zero
% 5.31/5.55 thf(fact_3585_divide__cancel__right,axiom,
% 5.31/5.55 ! [A: complex,C2: complex,B: complex] :
% 5.31/5.55 ( ( ( divide1717551699836669952omplex @ A @ C2 )
% 5.31/5.55 = ( divide1717551699836669952omplex @ B @ C2 ) )
% 5.31/5.55 = ( ( C2 = zero_zero_complex )
% 5.31/5.55 | ( A = B ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % divide_cancel_right
% 5.31/5.55 thf(fact_3586_divide__cancel__right,axiom,
% 5.31/5.55 ! [A: real,C2: real,B: real] :
% 5.31/5.55 ( ( ( divide_divide_real @ A @ C2 )
% 5.31/5.55 = ( divide_divide_real @ B @ C2 ) )
% 5.31/5.55 = ( ( C2 = zero_zero_real )
% 5.31/5.55 | ( A = B ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % divide_cancel_right
% 5.31/5.55 thf(fact_3587_divide__cancel__right,axiom,
% 5.31/5.55 ! [A: rat,C2: rat,B: rat] :
% 5.31/5.55 ( ( ( divide_divide_rat @ A @ C2 )
% 5.31/5.55 = ( divide_divide_rat @ B @ C2 ) )
% 5.31/5.55 = ( ( C2 = zero_zero_rat )
% 5.31/5.55 | ( A = B ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % divide_cancel_right
% 5.31/5.55 thf(fact_3588_divide__cancel__left,axiom,
% 5.31/5.55 ! [C2: complex,A: complex,B: complex] :
% 5.31/5.55 ( ( ( divide1717551699836669952omplex @ C2 @ A )
% 5.31/5.55 = ( divide1717551699836669952omplex @ C2 @ B ) )
% 5.31/5.55 = ( ( C2 = zero_zero_complex )
% 5.31/5.55 | ( A = B ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % divide_cancel_left
% 5.31/5.55 thf(fact_3589_divide__cancel__left,axiom,
% 5.31/5.55 ! [C2: real,A: real,B: real] :
% 5.31/5.55 ( ( ( divide_divide_real @ C2 @ A )
% 5.31/5.55 = ( divide_divide_real @ C2 @ B ) )
% 5.31/5.55 = ( ( C2 = zero_zero_real )
% 5.31/5.55 | ( A = B ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % divide_cancel_left
% 5.31/5.55 thf(fact_3590_divide__cancel__left,axiom,
% 5.31/5.55 ! [C2: rat,A: rat,B: rat] :
% 5.31/5.55 ( ( ( divide_divide_rat @ C2 @ A )
% 5.31/5.55 = ( divide_divide_rat @ C2 @ B ) )
% 5.31/5.55 = ( ( C2 = zero_zero_rat )
% 5.31/5.55 | ( A = B ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % divide_cancel_left
% 5.31/5.55 thf(fact_3591_divide__eq__0__iff,axiom,
% 5.31/5.55 ! [A: complex,B: complex] :
% 5.31/5.55 ( ( ( divide1717551699836669952omplex @ A @ B )
% 5.31/5.55 = zero_zero_complex )
% 5.31/5.55 = ( ( A = zero_zero_complex )
% 5.31/5.55 | ( B = zero_zero_complex ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % divide_eq_0_iff
% 5.31/5.55 thf(fact_3592_divide__eq__0__iff,axiom,
% 5.31/5.55 ! [A: real,B: real] :
% 5.31/5.55 ( ( ( divide_divide_real @ A @ B )
% 5.31/5.55 = zero_zero_real )
% 5.31/5.55 = ( ( A = zero_zero_real )
% 5.31/5.55 | ( B = zero_zero_real ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % divide_eq_0_iff
% 5.31/5.55 thf(fact_3593_divide__eq__0__iff,axiom,
% 5.31/5.55 ! [A: rat,B: rat] :
% 5.31/5.55 ( ( ( divide_divide_rat @ A @ B )
% 5.31/5.55 = zero_zero_rat )
% 5.31/5.55 = ( ( A = zero_zero_rat )
% 5.31/5.55 | ( B = zero_zero_rat ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % divide_eq_0_iff
% 5.31/5.55 thf(fact_3594_times__divide__eq__right,axiom,
% 5.31/5.55 ! [A: complex,B: complex,C2: complex] :
% 5.31/5.55 ( ( times_times_complex @ A @ ( divide1717551699836669952omplex @ B @ C2 ) )
% 5.31/5.55 = ( divide1717551699836669952omplex @ ( times_times_complex @ A @ B ) @ C2 ) ) ).
% 5.31/5.55
% 5.31/5.55 % times_divide_eq_right
% 5.31/5.55 thf(fact_3595_times__divide__eq__right,axiom,
% 5.31/5.55 ! [A: real,B: real,C2: real] :
% 5.31/5.55 ( ( times_times_real @ A @ ( divide_divide_real @ B @ C2 ) )
% 5.31/5.55 = ( divide_divide_real @ ( times_times_real @ A @ B ) @ C2 ) ) ).
% 5.31/5.55
% 5.31/5.55 % times_divide_eq_right
% 5.31/5.55 thf(fact_3596_times__divide__eq__right,axiom,
% 5.31/5.55 ! [A: rat,B: rat,C2: rat] :
% 5.31/5.55 ( ( times_times_rat @ A @ ( divide_divide_rat @ B @ C2 ) )
% 5.31/5.55 = ( divide_divide_rat @ ( times_times_rat @ A @ B ) @ C2 ) ) ).
% 5.31/5.55
% 5.31/5.55 % times_divide_eq_right
% 5.31/5.55 thf(fact_3597_divide__divide__eq__right,axiom,
% 5.31/5.55 ! [A: complex,B: complex,C2: complex] :
% 5.31/5.55 ( ( divide1717551699836669952omplex @ A @ ( divide1717551699836669952omplex @ B @ C2 ) )
% 5.31/5.55 = ( divide1717551699836669952omplex @ ( times_times_complex @ A @ C2 ) @ B ) ) ).
% 5.31/5.55
% 5.31/5.55 % divide_divide_eq_right
% 5.31/5.55 thf(fact_3598_divide__divide__eq__right,axiom,
% 5.31/5.55 ! [A: real,B: real,C2: real] :
% 5.31/5.55 ( ( divide_divide_real @ A @ ( divide_divide_real @ B @ C2 ) )
% 5.31/5.55 = ( divide_divide_real @ ( times_times_real @ A @ C2 ) @ B ) ) ).
% 5.31/5.55
% 5.31/5.55 % divide_divide_eq_right
% 5.31/5.55 thf(fact_3599_divide__divide__eq__right,axiom,
% 5.31/5.55 ! [A: rat,B: rat,C2: rat] :
% 5.31/5.55 ( ( divide_divide_rat @ A @ ( divide_divide_rat @ B @ C2 ) )
% 5.31/5.55 = ( divide_divide_rat @ ( times_times_rat @ A @ C2 ) @ B ) ) ).
% 5.31/5.55
% 5.31/5.55 % divide_divide_eq_right
% 5.31/5.55 thf(fact_3600_divide__divide__eq__left,axiom,
% 5.31/5.55 ! [A: complex,B: complex,C2: complex] :
% 5.31/5.55 ( ( divide1717551699836669952omplex @ ( divide1717551699836669952omplex @ A @ B ) @ C2 )
% 5.31/5.55 = ( divide1717551699836669952omplex @ A @ ( times_times_complex @ B @ C2 ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % divide_divide_eq_left
% 5.31/5.55 thf(fact_3601_divide__divide__eq__left,axiom,
% 5.31/5.55 ! [A: real,B: real,C2: real] :
% 5.31/5.55 ( ( divide_divide_real @ ( divide_divide_real @ A @ B ) @ C2 )
% 5.31/5.55 = ( divide_divide_real @ A @ ( times_times_real @ B @ C2 ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % divide_divide_eq_left
% 5.31/5.55 thf(fact_3602_divide__divide__eq__left,axiom,
% 5.31/5.55 ! [A: rat,B: rat,C2: rat] :
% 5.31/5.55 ( ( divide_divide_rat @ ( divide_divide_rat @ A @ B ) @ C2 )
% 5.31/5.55 = ( divide_divide_rat @ A @ ( times_times_rat @ B @ C2 ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % divide_divide_eq_left
% 5.31/5.55 thf(fact_3603_times__divide__eq__left,axiom,
% 5.31/5.55 ! [B: complex,C2: complex,A: complex] :
% 5.31/5.55 ( ( times_times_complex @ ( divide1717551699836669952omplex @ B @ C2 ) @ A )
% 5.31/5.55 = ( divide1717551699836669952omplex @ ( times_times_complex @ B @ A ) @ C2 ) ) ).
% 5.31/5.55
% 5.31/5.55 % times_divide_eq_left
% 5.31/5.55 thf(fact_3604_times__divide__eq__left,axiom,
% 5.31/5.55 ! [B: real,C2: real,A: real] :
% 5.31/5.55 ( ( times_times_real @ ( divide_divide_real @ B @ C2 ) @ A )
% 5.31/5.55 = ( divide_divide_real @ ( times_times_real @ B @ A ) @ C2 ) ) ).
% 5.31/5.55
% 5.31/5.55 % times_divide_eq_left
% 5.31/5.55 thf(fact_3605_times__divide__eq__left,axiom,
% 5.31/5.55 ! [B: rat,C2: rat,A: rat] :
% 5.31/5.55 ( ( times_times_rat @ ( divide_divide_rat @ B @ C2 ) @ A )
% 5.31/5.55 = ( divide_divide_rat @ ( times_times_rat @ B @ A ) @ C2 ) ) ).
% 5.31/5.55
% 5.31/5.55 % times_divide_eq_left
% 5.31/5.55 thf(fact_3606_div__by__1,axiom,
% 5.31/5.55 ! [A: code_integer] :
% 5.31/5.55 ( ( divide6298287555418463151nteger @ A @ one_one_Code_integer )
% 5.31/5.55 = A ) ).
% 5.31/5.55
% 5.31/5.55 % div_by_1
% 5.31/5.55 thf(fact_3607_div__by__1,axiom,
% 5.31/5.55 ! [A: complex] :
% 5.31/5.55 ( ( divide1717551699836669952omplex @ A @ one_one_complex )
% 5.31/5.55 = A ) ).
% 5.31/5.55
% 5.31/5.55 % div_by_1
% 5.31/5.55 thf(fact_3608_div__by__1,axiom,
% 5.31/5.55 ! [A: real] :
% 5.31/5.55 ( ( divide_divide_real @ A @ one_one_real )
% 5.31/5.55 = A ) ).
% 5.31/5.55
% 5.31/5.55 % div_by_1
% 5.31/5.55 thf(fact_3609_div__by__1,axiom,
% 5.31/5.55 ! [A: rat] :
% 5.31/5.55 ( ( divide_divide_rat @ A @ one_one_rat )
% 5.31/5.55 = A ) ).
% 5.31/5.55
% 5.31/5.55 % div_by_1
% 5.31/5.55 thf(fact_3610_div__by__1,axiom,
% 5.31/5.55 ! [A: nat] :
% 5.31/5.55 ( ( divide_divide_nat @ A @ one_one_nat )
% 5.31/5.55 = A ) ).
% 5.31/5.55
% 5.31/5.55 % div_by_1
% 5.31/5.55 thf(fact_3611_div__by__1,axiom,
% 5.31/5.55 ! [A: int] :
% 5.31/5.55 ( ( divide_divide_int @ A @ one_one_int )
% 5.31/5.55 = A ) ).
% 5.31/5.55
% 5.31/5.55 % div_by_1
% 5.31/5.55 thf(fact_3612_atLeastAtMost__iff,axiom,
% 5.31/5.55 ! [I2: set_nat,L: set_nat,U: set_nat] :
% 5.31/5.55 ( ( member_set_nat @ I2 @ ( set_or4548717258645045905et_nat @ L @ U ) )
% 5.31/5.55 = ( ( ord_less_eq_set_nat @ L @ I2 )
% 5.31/5.55 & ( ord_less_eq_set_nat @ I2 @ U ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % atLeastAtMost_iff
% 5.31/5.55 thf(fact_3613_atLeastAtMost__iff,axiom,
% 5.31/5.55 ! [I2: rat,L: rat,U: rat] :
% 5.31/5.55 ( ( member_rat @ I2 @ ( set_or633870826150836451st_rat @ L @ U ) )
% 5.31/5.55 = ( ( ord_less_eq_rat @ L @ I2 )
% 5.31/5.55 & ( ord_less_eq_rat @ I2 @ U ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % atLeastAtMost_iff
% 5.31/5.55 thf(fact_3614_atLeastAtMost__iff,axiom,
% 5.31/5.55 ! [I2: num,L: num,U: num] :
% 5.31/5.55 ( ( member_num @ I2 @ ( set_or7049704709247886629st_num @ L @ U ) )
% 5.31/5.55 = ( ( ord_less_eq_num @ L @ I2 )
% 5.31/5.55 & ( ord_less_eq_num @ I2 @ U ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % atLeastAtMost_iff
% 5.31/5.55 thf(fact_3615_atLeastAtMost__iff,axiom,
% 5.31/5.55 ! [I2: nat,L: nat,U: nat] :
% 5.31/5.55 ( ( member_nat @ I2 @ ( set_or1269000886237332187st_nat @ L @ U ) )
% 5.31/5.55 = ( ( ord_less_eq_nat @ L @ I2 )
% 5.31/5.55 & ( ord_less_eq_nat @ I2 @ U ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % atLeastAtMost_iff
% 5.31/5.55 thf(fact_3616_atLeastAtMost__iff,axiom,
% 5.31/5.55 ! [I2: int,L: int,U: int] :
% 5.31/5.55 ( ( member_int @ I2 @ ( set_or1266510415728281911st_int @ L @ U ) )
% 5.31/5.55 = ( ( ord_less_eq_int @ L @ I2 )
% 5.31/5.55 & ( ord_less_eq_int @ I2 @ U ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % atLeastAtMost_iff
% 5.31/5.55 thf(fact_3617_atLeastAtMost__iff,axiom,
% 5.31/5.55 ! [I2: real,L: real,U: real] :
% 5.31/5.55 ( ( member_real @ I2 @ ( set_or1222579329274155063t_real @ L @ U ) )
% 5.31/5.55 = ( ( ord_less_eq_real @ L @ I2 )
% 5.31/5.55 & ( ord_less_eq_real @ I2 @ U ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % atLeastAtMost_iff
% 5.31/5.55 thf(fact_3618_Icc__eq__Icc,axiom,
% 5.31/5.55 ! [L: set_nat,H: set_nat,L3: set_nat,H3: set_nat] :
% 5.31/5.55 ( ( ( set_or4548717258645045905et_nat @ L @ H )
% 5.31/5.55 = ( set_or4548717258645045905et_nat @ L3 @ H3 ) )
% 5.31/5.55 = ( ( ( L = L3 )
% 5.31/5.55 & ( H = H3 ) )
% 5.31/5.55 | ( ~ ( ord_less_eq_set_nat @ L @ H )
% 5.31/5.55 & ~ ( ord_less_eq_set_nat @ L3 @ H3 ) ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % Icc_eq_Icc
% 5.31/5.55 thf(fact_3619_Icc__eq__Icc,axiom,
% 5.31/5.55 ! [L: rat,H: rat,L3: rat,H3: rat] :
% 5.31/5.55 ( ( ( set_or633870826150836451st_rat @ L @ H )
% 5.31/5.55 = ( set_or633870826150836451st_rat @ L3 @ H3 ) )
% 5.31/5.55 = ( ( ( L = L3 )
% 5.31/5.55 & ( H = H3 ) )
% 5.31/5.55 | ( ~ ( ord_less_eq_rat @ L @ H )
% 5.31/5.55 & ~ ( ord_less_eq_rat @ L3 @ H3 ) ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % Icc_eq_Icc
% 5.31/5.55 thf(fact_3620_Icc__eq__Icc,axiom,
% 5.31/5.55 ! [L: num,H: num,L3: num,H3: num] :
% 5.31/5.55 ( ( ( set_or7049704709247886629st_num @ L @ H )
% 5.31/5.55 = ( set_or7049704709247886629st_num @ L3 @ H3 ) )
% 5.31/5.55 = ( ( ( L = L3 )
% 5.31/5.55 & ( H = H3 ) )
% 5.31/5.55 | ( ~ ( ord_less_eq_num @ L @ H )
% 5.31/5.55 & ~ ( ord_less_eq_num @ L3 @ H3 ) ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % Icc_eq_Icc
% 5.31/5.55 thf(fact_3621_Icc__eq__Icc,axiom,
% 5.31/5.55 ! [L: nat,H: nat,L3: nat,H3: nat] :
% 5.31/5.55 ( ( ( set_or1269000886237332187st_nat @ L @ H )
% 5.31/5.55 = ( set_or1269000886237332187st_nat @ L3 @ H3 ) )
% 5.31/5.55 = ( ( ( L = L3 )
% 5.31/5.55 & ( H = H3 ) )
% 5.31/5.55 | ( ~ ( ord_less_eq_nat @ L @ H )
% 5.31/5.55 & ~ ( ord_less_eq_nat @ L3 @ H3 ) ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % Icc_eq_Icc
% 5.31/5.55 thf(fact_3622_Icc__eq__Icc,axiom,
% 5.31/5.55 ! [L: int,H: int,L3: int,H3: int] :
% 5.31/5.55 ( ( ( set_or1266510415728281911st_int @ L @ H )
% 5.31/5.55 = ( set_or1266510415728281911st_int @ L3 @ H3 ) )
% 5.31/5.55 = ( ( ( L = L3 )
% 5.31/5.55 & ( H = H3 ) )
% 5.31/5.55 | ( ~ ( ord_less_eq_int @ L @ H )
% 5.31/5.55 & ~ ( ord_less_eq_int @ L3 @ H3 ) ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % Icc_eq_Icc
% 5.31/5.55 thf(fact_3623_Icc__eq__Icc,axiom,
% 5.31/5.55 ! [L: real,H: real,L3: real,H3: real] :
% 5.31/5.55 ( ( ( set_or1222579329274155063t_real @ L @ H )
% 5.31/5.55 = ( set_or1222579329274155063t_real @ L3 @ H3 ) )
% 5.31/5.55 = ( ( ( L = L3 )
% 5.31/5.55 & ( H = H3 ) )
% 5.31/5.55 | ( ~ ( ord_less_eq_real @ L @ H )
% 5.31/5.55 & ~ ( ord_less_eq_real @ L3 @ H3 ) ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % Icc_eq_Icc
% 5.31/5.55 thf(fact_3624_finite__atLeastAtMost,axiom,
% 5.31/5.55 ! [L: nat,U: nat] : ( finite_finite_nat @ ( set_or1269000886237332187st_nat @ L @ U ) ) ).
% 5.31/5.55
% 5.31/5.55 % finite_atLeastAtMost
% 5.31/5.55 thf(fact_3625_nonzero__mult__div__cancel__left,axiom,
% 5.31/5.55 ! [A: complex,B: complex] :
% 5.31/5.55 ( ( A != zero_zero_complex )
% 5.31/5.55 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ A @ B ) @ A )
% 5.31/5.55 = B ) ) ).
% 5.31/5.55
% 5.31/5.55 % nonzero_mult_div_cancel_left
% 5.31/5.55 thf(fact_3626_nonzero__mult__div__cancel__left,axiom,
% 5.31/5.55 ! [A: real,B: real] :
% 5.31/5.55 ( ( A != zero_zero_real )
% 5.31/5.55 => ( ( divide_divide_real @ ( times_times_real @ A @ B ) @ A )
% 5.31/5.55 = B ) ) ).
% 5.31/5.55
% 5.31/5.55 % nonzero_mult_div_cancel_left
% 5.31/5.55 thf(fact_3627_nonzero__mult__div__cancel__left,axiom,
% 5.31/5.55 ! [A: rat,B: rat] :
% 5.31/5.55 ( ( A != zero_zero_rat )
% 5.31/5.55 => ( ( divide_divide_rat @ ( times_times_rat @ A @ B ) @ A )
% 5.31/5.55 = B ) ) ).
% 5.31/5.55
% 5.31/5.55 % nonzero_mult_div_cancel_left
% 5.31/5.55 thf(fact_3628_nonzero__mult__div__cancel__left,axiom,
% 5.31/5.55 ! [A: nat,B: nat] :
% 5.31/5.55 ( ( A != zero_zero_nat )
% 5.31/5.55 => ( ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ A )
% 5.31/5.55 = B ) ) ).
% 5.31/5.55
% 5.31/5.55 % nonzero_mult_div_cancel_left
% 5.31/5.55 thf(fact_3629_nonzero__mult__div__cancel__left,axiom,
% 5.31/5.55 ! [A: int,B: int] :
% 5.31/5.55 ( ( A != zero_zero_int )
% 5.31/5.55 => ( ( divide_divide_int @ ( times_times_int @ A @ B ) @ A )
% 5.31/5.55 = B ) ) ).
% 5.31/5.55
% 5.31/5.55 % nonzero_mult_div_cancel_left
% 5.31/5.55 thf(fact_3630_nonzero__mult__div__cancel__right,axiom,
% 5.31/5.55 ! [B: complex,A: complex] :
% 5.31/5.55 ( ( B != zero_zero_complex )
% 5.31/5.55 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ A @ B ) @ B )
% 5.31/5.55 = A ) ) ).
% 5.31/5.55
% 5.31/5.55 % nonzero_mult_div_cancel_right
% 5.31/5.55 thf(fact_3631_nonzero__mult__div__cancel__right,axiom,
% 5.31/5.55 ! [B: real,A: real] :
% 5.31/5.55 ( ( B != zero_zero_real )
% 5.31/5.55 => ( ( divide_divide_real @ ( times_times_real @ A @ B ) @ B )
% 5.31/5.55 = A ) ) ).
% 5.31/5.55
% 5.31/5.55 % nonzero_mult_div_cancel_right
% 5.31/5.55 thf(fact_3632_nonzero__mult__div__cancel__right,axiom,
% 5.31/5.55 ! [B: rat,A: rat] :
% 5.31/5.55 ( ( B != zero_zero_rat )
% 5.31/5.55 => ( ( divide_divide_rat @ ( times_times_rat @ A @ B ) @ B )
% 5.31/5.55 = A ) ) ).
% 5.31/5.55
% 5.31/5.55 % nonzero_mult_div_cancel_right
% 5.31/5.55 thf(fact_3633_nonzero__mult__div__cancel__right,axiom,
% 5.31/5.55 ! [B: nat,A: nat] :
% 5.31/5.55 ( ( B != zero_zero_nat )
% 5.31/5.55 => ( ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ B )
% 5.31/5.55 = A ) ) ).
% 5.31/5.55
% 5.31/5.55 % nonzero_mult_div_cancel_right
% 5.31/5.55 thf(fact_3634_nonzero__mult__div__cancel__right,axiom,
% 5.31/5.55 ! [B: int,A: int] :
% 5.31/5.55 ( ( B != zero_zero_int )
% 5.31/5.55 => ( ( divide_divide_int @ ( times_times_int @ A @ B ) @ B )
% 5.31/5.55 = A ) ) ).
% 5.31/5.55
% 5.31/5.55 % nonzero_mult_div_cancel_right
% 5.31/5.55 thf(fact_3635_mult__divide__mult__cancel__left__if,axiom,
% 5.31/5.55 ! [C2: complex,A: complex,B: complex] :
% 5.31/5.55 ( ( ( C2 = zero_zero_complex )
% 5.31/5.55 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ C2 @ A ) @ ( times_times_complex @ C2 @ B ) )
% 5.31/5.55 = zero_zero_complex ) )
% 5.31/5.55 & ( ( C2 != zero_zero_complex )
% 5.31/5.55 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ C2 @ A ) @ ( times_times_complex @ C2 @ B ) )
% 5.31/5.55 = ( divide1717551699836669952omplex @ A @ B ) ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % mult_divide_mult_cancel_left_if
% 5.31/5.55 thf(fact_3636_mult__divide__mult__cancel__left__if,axiom,
% 5.31/5.55 ! [C2: real,A: real,B: real] :
% 5.31/5.55 ( ( ( C2 = zero_zero_real )
% 5.31/5.55 => ( ( divide_divide_real @ ( times_times_real @ C2 @ A ) @ ( times_times_real @ C2 @ B ) )
% 5.31/5.55 = zero_zero_real ) )
% 5.31/5.55 & ( ( C2 != zero_zero_real )
% 5.31/5.55 => ( ( divide_divide_real @ ( times_times_real @ C2 @ A ) @ ( times_times_real @ C2 @ B ) )
% 5.31/5.55 = ( divide_divide_real @ A @ B ) ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % mult_divide_mult_cancel_left_if
% 5.31/5.55 thf(fact_3637_mult__divide__mult__cancel__left__if,axiom,
% 5.31/5.55 ! [C2: rat,A: rat,B: rat] :
% 5.31/5.55 ( ( ( C2 = zero_zero_rat )
% 5.31/5.55 => ( ( divide_divide_rat @ ( times_times_rat @ C2 @ A ) @ ( times_times_rat @ C2 @ B ) )
% 5.31/5.55 = zero_zero_rat ) )
% 5.31/5.55 & ( ( C2 != zero_zero_rat )
% 5.31/5.55 => ( ( divide_divide_rat @ ( times_times_rat @ C2 @ A ) @ ( times_times_rat @ C2 @ B ) )
% 5.31/5.55 = ( divide_divide_rat @ A @ B ) ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % mult_divide_mult_cancel_left_if
% 5.31/5.55 thf(fact_3638_nonzero__mult__divide__mult__cancel__left,axiom,
% 5.31/5.55 ! [C2: complex,A: complex,B: complex] :
% 5.31/5.55 ( ( C2 != zero_zero_complex )
% 5.31/5.55 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ C2 @ A ) @ ( times_times_complex @ C2 @ B ) )
% 5.31/5.55 = ( divide1717551699836669952omplex @ A @ B ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % nonzero_mult_divide_mult_cancel_left
% 5.31/5.55 thf(fact_3639_nonzero__mult__divide__mult__cancel__left,axiom,
% 5.31/5.55 ! [C2: real,A: real,B: real] :
% 5.31/5.55 ( ( C2 != zero_zero_real )
% 5.31/5.55 => ( ( divide_divide_real @ ( times_times_real @ C2 @ A ) @ ( times_times_real @ C2 @ B ) )
% 5.31/5.55 = ( divide_divide_real @ A @ B ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % nonzero_mult_divide_mult_cancel_left
% 5.31/5.55 thf(fact_3640_nonzero__mult__divide__mult__cancel__left,axiom,
% 5.31/5.55 ! [C2: rat,A: rat,B: rat] :
% 5.31/5.55 ( ( C2 != zero_zero_rat )
% 5.31/5.55 => ( ( divide_divide_rat @ ( times_times_rat @ C2 @ A ) @ ( times_times_rat @ C2 @ B ) )
% 5.31/5.55 = ( divide_divide_rat @ A @ B ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % nonzero_mult_divide_mult_cancel_left
% 5.31/5.55 thf(fact_3641_nonzero__mult__divide__mult__cancel__left2,axiom,
% 5.31/5.55 ! [C2: complex,A: complex,B: complex] :
% 5.31/5.55 ( ( C2 != zero_zero_complex )
% 5.31/5.55 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ C2 @ A ) @ ( times_times_complex @ B @ C2 ) )
% 5.31/5.55 = ( divide1717551699836669952omplex @ A @ B ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % nonzero_mult_divide_mult_cancel_left2
% 5.31/5.55 thf(fact_3642_nonzero__mult__divide__mult__cancel__left2,axiom,
% 5.31/5.55 ! [C2: real,A: real,B: real] :
% 5.31/5.55 ( ( C2 != zero_zero_real )
% 5.31/5.55 => ( ( divide_divide_real @ ( times_times_real @ C2 @ A ) @ ( times_times_real @ B @ C2 ) )
% 5.31/5.55 = ( divide_divide_real @ A @ B ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % nonzero_mult_divide_mult_cancel_left2
% 5.31/5.55 thf(fact_3643_nonzero__mult__divide__mult__cancel__left2,axiom,
% 5.31/5.55 ! [C2: rat,A: rat,B: rat] :
% 5.31/5.55 ( ( C2 != zero_zero_rat )
% 5.31/5.55 => ( ( divide_divide_rat @ ( times_times_rat @ C2 @ A ) @ ( times_times_rat @ B @ C2 ) )
% 5.31/5.55 = ( divide_divide_rat @ A @ B ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % nonzero_mult_divide_mult_cancel_left2
% 5.31/5.55 thf(fact_3644_nonzero__mult__divide__mult__cancel__right,axiom,
% 5.31/5.55 ! [C2: complex,A: complex,B: complex] :
% 5.31/5.55 ( ( C2 != zero_zero_complex )
% 5.31/5.55 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ A @ C2 ) @ ( times_times_complex @ B @ C2 ) )
% 5.31/5.55 = ( divide1717551699836669952omplex @ A @ B ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % nonzero_mult_divide_mult_cancel_right
% 5.31/5.55 thf(fact_3645_nonzero__mult__divide__mult__cancel__right,axiom,
% 5.31/5.55 ! [C2: real,A: real,B: real] :
% 5.31/5.55 ( ( C2 != zero_zero_real )
% 5.31/5.55 => ( ( divide_divide_real @ ( times_times_real @ A @ C2 ) @ ( times_times_real @ B @ C2 ) )
% 5.31/5.55 = ( divide_divide_real @ A @ B ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % nonzero_mult_divide_mult_cancel_right
% 5.31/5.55 thf(fact_3646_nonzero__mult__divide__mult__cancel__right,axiom,
% 5.31/5.55 ! [C2: rat,A: rat,B: rat] :
% 5.31/5.55 ( ( C2 != zero_zero_rat )
% 5.31/5.55 => ( ( divide_divide_rat @ ( times_times_rat @ A @ C2 ) @ ( times_times_rat @ B @ C2 ) )
% 5.31/5.55 = ( divide_divide_rat @ A @ B ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % nonzero_mult_divide_mult_cancel_right
% 5.31/5.55 thf(fact_3647_nonzero__mult__divide__mult__cancel__right2,axiom,
% 5.31/5.55 ! [C2: complex,A: complex,B: complex] :
% 5.31/5.55 ( ( C2 != zero_zero_complex )
% 5.31/5.55 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ A @ C2 ) @ ( times_times_complex @ C2 @ B ) )
% 5.31/5.55 = ( divide1717551699836669952omplex @ A @ B ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % nonzero_mult_divide_mult_cancel_right2
% 5.31/5.55 thf(fact_3648_nonzero__mult__divide__mult__cancel__right2,axiom,
% 5.31/5.55 ! [C2: real,A: real,B: real] :
% 5.31/5.55 ( ( C2 != zero_zero_real )
% 5.31/5.55 => ( ( divide_divide_real @ ( times_times_real @ A @ C2 ) @ ( times_times_real @ C2 @ B ) )
% 5.31/5.55 = ( divide_divide_real @ A @ B ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % nonzero_mult_divide_mult_cancel_right2
% 5.31/5.55 thf(fact_3649_nonzero__mult__divide__mult__cancel__right2,axiom,
% 5.31/5.55 ! [C2: rat,A: rat,B: rat] :
% 5.31/5.55 ( ( C2 != zero_zero_rat )
% 5.31/5.55 => ( ( divide_divide_rat @ ( times_times_rat @ A @ C2 ) @ ( times_times_rat @ C2 @ B ) )
% 5.31/5.55 = ( divide_divide_rat @ A @ B ) ) ) ).
% 5.31/5.55
% 5.31/5.55 % nonzero_mult_divide_mult_cancel_right2
% 5.31/5.55 thf(fact_3650_div__self,axiom,
% 5.31/5.55 ! [A: code_integer] :
% 5.31/5.55 ( ( A != zero_z3403309356797280102nteger )
% 5.31/5.55 => ( ( divide6298287555418463151nteger @ A @ A )
% 5.31/5.55 = one_one_Code_integer ) ) ).
% 5.31/5.55
% 5.31/5.55 % div_self
% 5.31/5.55 thf(fact_3651_div__self,axiom,
% 5.31/5.55 ! [A: complex] :
% 5.31/5.55 ( ( A != zero_zero_complex )
% 5.31/5.55 => ( ( divide1717551699836669952omplex @ A @ A )
% 5.31/5.55 = one_one_complex ) ) ).
% 5.31/5.55
% 5.31/5.55 % div_self
% 5.31/5.55 thf(fact_3652_div__self,axiom,
% 5.31/5.55 ! [A: real] :
% 5.31/5.55 ( ( A != zero_zero_real )
% 5.31/5.55 => ( ( divide_divide_real @ A @ A )
% 5.31/5.55 = one_one_real ) ) ).
% 5.31/5.55
% 5.31/5.55 % div_self
% 5.31/5.55 thf(fact_3653_div__self,axiom,
% 5.31/5.55 ! [A: rat] :
% 5.31/5.55 ( ( A != zero_zero_rat )
% 5.31/5.55 => ( ( divide_divide_rat @ A @ A )
% 5.31/5.55 = one_one_rat ) ) ).
% 5.31/5.55
% 5.31/5.55 % div_self
% 5.31/5.55 thf(fact_3654_div__self,axiom,
% 5.31/5.55 ! [A: nat] :
% 5.31/5.55 ( ( A != zero_zero_nat )
% 5.31/5.55 => ( ( divide_divide_nat @ A @ A )
% 5.31/5.55 = one_one_nat ) ) ).
% 5.31/5.55
% 5.31/5.55 % div_self
% 5.31/5.55 thf(fact_3655_div__self,axiom,
% 5.31/5.55 ! [A: int] :
% 5.31/5.55 ( ( A != zero_zero_int )
% 5.31/5.55 => ( ( divide_divide_int @ A @ A )
% 5.31/5.55 = one_one_int ) ) ).
% 5.31/5.56
% 5.31/5.56 % div_self
% 5.31/5.56 thf(fact_3656_zero__eq__1__divide__iff,axiom,
% 5.31/5.56 ! [A: real] :
% 5.31/5.56 ( ( zero_zero_real
% 5.31/5.56 = ( divide_divide_real @ one_one_real @ A ) )
% 5.31/5.56 = ( A = zero_zero_real ) ) ).
% 5.31/5.56
% 5.31/5.56 % zero_eq_1_divide_iff
% 5.31/5.56 thf(fact_3657_zero__eq__1__divide__iff,axiom,
% 5.31/5.56 ! [A: rat] :
% 5.31/5.56 ( ( zero_zero_rat
% 5.31/5.56 = ( divide_divide_rat @ one_one_rat @ A ) )
% 5.31/5.56 = ( A = zero_zero_rat ) ) ).
% 5.31/5.56
% 5.31/5.56 % zero_eq_1_divide_iff
% 5.31/5.56 thf(fact_3658_one__divide__eq__0__iff,axiom,
% 5.31/5.56 ! [A: real] :
% 5.31/5.56 ( ( ( divide_divide_real @ one_one_real @ A )
% 5.31/5.56 = zero_zero_real )
% 5.31/5.56 = ( A = zero_zero_real ) ) ).
% 5.31/5.56
% 5.31/5.56 % one_divide_eq_0_iff
% 5.31/5.56 thf(fact_3659_one__divide__eq__0__iff,axiom,
% 5.31/5.56 ! [A: rat] :
% 5.31/5.56 ( ( ( divide_divide_rat @ one_one_rat @ A )
% 5.31/5.56 = zero_zero_rat )
% 5.31/5.56 = ( A = zero_zero_rat ) ) ).
% 5.31/5.56
% 5.31/5.56 % one_divide_eq_0_iff
% 5.31/5.56 thf(fact_3660_eq__divide__eq__1,axiom,
% 5.31/5.56 ! [B: real,A: real] :
% 5.31/5.56 ( ( one_one_real
% 5.31/5.56 = ( divide_divide_real @ B @ A ) )
% 5.31/5.56 = ( ( A != zero_zero_real )
% 5.31/5.56 & ( A = B ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % eq_divide_eq_1
% 5.31/5.56 thf(fact_3661_eq__divide__eq__1,axiom,
% 5.31/5.56 ! [B: rat,A: rat] :
% 5.31/5.56 ( ( one_one_rat
% 5.31/5.56 = ( divide_divide_rat @ B @ A ) )
% 5.31/5.56 = ( ( A != zero_zero_rat )
% 5.31/5.56 & ( A = B ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % eq_divide_eq_1
% 5.31/5.56 thf(fact_3662_divide__eq__eq__1,axiom,
% 5.31/5.56 ! [B: real,A: real] :
% 5.31/5.56 ( ( ( divide_divide_real @ B @ A )
% 5.31/5.56 = one_one_real )
% 5.31/5.56 = ( ( A != zero_zero_real )
% 5.31/5.56 & ( A = B ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % divide_eq_eq_1
% 5.31/5.56 thf(fact_3663_divide__eq__eq__1,axiom,
% 5.31/5.56 ! [B: rat,A: rat] :
% 5.31/5.56 ( ( ( divide_divide_rat @ B @ A )
% 5.31/5.56 = one_one_rat )
% 5.31/5.56 = ( ( A != zero_zero_rat )
% 5.31/5.56 & ( A = B ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % divide_eq_eq_1
% 5.31/5.56 thf(fact_3664_divide__self__if,axiom,
% 5.31/5.56 ! [A: complex] :
% 5.31/5.56 ( ( ( A = zero_zero_complex )
% 5.31/5.56 => ( ( divide1717551699836669952omplex @ A @ A )
% 5.31/5.56 = zero_zero_complex ) )
% 5.31/5.56 & ( ( A != zero_zero_complex )
% 5.31/5.56 => ( ( divide1717551699836669952omplex @ A @ A )
% 5.31/5.56 = one_one_complex ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % divide_self_if
% 5.31/5.56 thf(fact_3665_divide__self__if,axiom,
% 5.31/5.56 ! [A: real] :
% 5.31/5.56 ( ( ( A = zero_zero_real )
% 5.31/5.56 => ( ( divide_divide_real @ A @ A )
% 5.31/5.56 = zero_zero_real ) )
% 5.31/5.56 & ( ( A != zero_zero_real )
% 5.31/5.56 => ( ( divide_divide_real @ A @ A )
% 5.31/5.56 = one_one_real ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % divide_self_if
% 5.31/5.56 thf(fact_3666_divide__self__if,axiom,
% 5.31/5.56 ! [A: rat] :
% 5.31/5.56 ( ( ( A = zero_zero_rat )
% 5.31/5.56 => ( ( divide_divide_rat @ A @ A )
% 5.31/5.56 = zero_zero_rat ) )
% 5.31/5.56 & ( ( A != zero_zero_rat )
% 5.31/5.56 => ( ( divide_divide_rat @ A @ A )
% 5.31/5.56 = one_one_rat ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % divide_self_if
% 5.31/5.56 thf(fact_3667_divide__self,axiom,
% 5.31/5.56 ! [A: complex] :
% 5.31/5.56 ( ( A != zero_zero_complex )
% 5.31/5.56 => ( ( divide1717551699836669952omplex @ A @ A )
% 5.31/5.56 = one_one_complex ) ) ).
% 5.31/5.56
% 5.31/5.56 % divide_self
% 5.31/5.56 thf(fact_3668_divide__self,axiom,
% 5.31/5.56 ! [A: real] :
% 5.31/5.56 ( ( A != zero_zero_real )
% 5.31/5.56 => ( ( divide_divide_real @ A @ A )
% 5.31/5.56 = one_one_real ) ) ).
% 5.31/5.56
% 5.31/5.56 % divide_self
% 5.31/5.56 thf(fact_3669_divide__self,axiom,
% 5.31/5.56 ! [A: rat] :
% 5.31/5.56 ( ( A != zero_zero_rat )
% 5.31/5.56 => ( ( divide_divide_rat @ A @ A )
% 5.31/5.56 = one_one_rat ) ) ).
% 5.31/5.56
% 5.31/5.56 % divide_self
% 5.31/5.56 thf(fact_3670_one__eq__divide__iff,axiom,
% 5.31/5.56 ! [A: complex,B: complex] :
% 5.31/5.56 ( ( one_one_complex
% 5.31/5.56 = ( divide1717551699836669952omplex @ A @ B ) )
% 5.31/5.56 = ( ( B != zero_zero_complex )
% 5.31/5.56 & ( A = B ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % one_eq_divide_iff
% 5.31/5.56 thf(fact_3671_one__eq__divide__iff,axiom,
% 5.31/5.56 ! [A: real,B: real] :
% 5.31/5.56 ( ( one_one_real
% 5.31/5.56 = ( divide_divide_real @ A @ B ) )
% 5.31/5.56 = ( ( B != zero_zero_real )
% 5.31/5.56 & ( A = B ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % one_eq_divide_iff
% 5.31/5.56 thf(fact_3672_one__eq__divide__iff,axiom,
% 5.31/5.56 ! [A: rat,B: rat] :
% 5.31/5.56 ( ( one_one_rat
% 5.31/5.56 = ( divide_divide_rat @ A @ B ) )
% 5.31/5.56 = ( ( B != zero_zero_rat )
% 5.31/5.56 & ( A = B ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % one_eq_divide_iff
% 5.31/5.56 thf(fact_3673_divide__eq__1__iff,axiom,
% 5.31/5.56 ! [A: complex,B: complex] :
% 5.31/5.56 ( ( ( divide1717551699836669952omplex @ A @ B )
% 5.31/5.56 = one_one_complex )
% 5.31/5.56 = ( ( B != zero_zero_complex )
% 5.31/5.56 & ( A = B ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % divide_eq_1_iff
% 5.31/5.56 thf(fact_3674_divide__eq__1__iff,axiom,
% 5.31/5.56 ! [A: real,B: real] :
% 5.31/5.56 ( ( ( divide_divide_real @ A @ B )
% 5.31/5.56 = one_one_real )
% 5.31/5.56 = ( ( B != zero_zero_real )
% 5.31/5.56 & ( A = B ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % divide_eq_1_iff
% 5.31/5.56 thf(fact_3675_divide__eq__1__iff,axiom,
% 5.31/5.56 ! [A: rat,B: rat] :
% 5.31/5.56 ( ( ( divide_divide_rat @ A @ B )
% 5.31/5.56 = one_one_rat )
% 5.31/5.56 = ( ( B != zero_zero_rat )
% 5.31/5.56 & ( A = B ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % divide_eq_1_iff
% 5.31/5.56 thf(fact_3676_atLeastatMost__empty__iff,axiom,
% 5.31/5.56 ! [A: set_nat,B: set_nat] :
% 5.31/5.56 ( ( ( set_or4548717258645045905et_nat @ A @ B )
% 5.31/5.56 = bot_bot_set_set_nat )
% 5.31/5.56 = ( ~ ( ord_less_eq_set_nat @ A @ B ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % atLeastatMost_empty_iff
% 5.31/5.56 thf(fact_3677_atLeastatMost__empty__iff,axiom,
% 5.31/5.56 ! [A: rat,B: rat] :
% 5.31/5.56 ( ( ( set_or633870826150836451st_rat @ A @ B )
% 5.31/5.56 = bot_bot_set_rat )
% 5.31/5.56 = ( ~ ( ord_less_eq_rat @ A @ B ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % atLeastatMost_empty_iff
% 5.31/5.56 thf(fact_3678_atLeastatMost__empty__iff,axiom,
% 5.31/5.56 ! [A: num,B: num] :
% 5.31/5.56 ( ( ( set_or7049704709247886629st_num @ A @ B )
% 5.31/5.56 = bot_bot_set_num )
% 5.31/5.56 = ( ~ ( ord_less_eq_num @ A @ B ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % atLeastatMost_empty_iff
% 5.31/5.56 thf(fact_3679_atLeastatMost__empty__iff,axiom,
% 5.31/5.56 ! [A: nat,B: nat] :
% 5.31/5.56 ( ( ( set_or1269000886237332187st_nat @ A @ B )
% 5.31/5.56 = bot_bot_set_nat )
% 5.31/5.56 = ( ~ ( ord_less_eq_nat @ A @ B ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % atLeastatMost_empty_iff
% 5.31/5.56 thf(fact_3680_atLeastatMost__empty__iff,axiom,
% 5.31/5.56 ! [A: int,B: int] :
% 5.31/5.56 ( ( ( set_or1266510415728281911st_int @ A @ B )
% 5.31/5.56 = bot_bot_set_int )
% 5.31/5.56 = ( ~ ( ord_less_eq_int @ A @ B ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % atLeastatMost_empty_iff
% 5.31/5.56 thf(fact_3681_atLeastatMost__empty__iff,axiom,
% 5.31/5.56 ! [A: real,B: real] :
% 5.31/5.56 ( ( ( set_or1222579329274155063t_real @ A @ B )
% 5.31/5.56 = bot_bot_set_real )
% 5.31/5.56 = ( ~ ( ord_less_eq_real @ A @ B ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % atLeastatMost_empty_iff
% 5.31/5.56 thf(fact_3682_atLeastatMost__empty__iff2,axiom,
% 5.31/5.56 ! [A: set_nat,B: set_nat] :
% 5.31/5.56 ( ( bot_bot_set_set_nat
% 5.31/5.56 = ( set_or4548717258645045905et_nat @ A @ B ) )
% 5.31/5.56 = ( ~ ( ord_less_eq_set_nat @ A @ B ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % atLeastatMost_empty_iff2
% 5.31/5.56 thf(fact_3683_atLeastatMost__empty__iff2,axiom,
% 5.31/5.56 ! [A: rat,B: rat] :
% 5.31/5.56 ( ( bot_bot_set_rat
% 5.31/5.56 = ( set_or633870826150836451st_rat @ A @ B ) )
% 5.31/5.56 = ( ~ ( ord_less_eq_rat @ A @ B ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % atLeastatMost_empty_iff2
% 5.31/5.56 thf(fact_3684_atLeastatMost__empty__iff2,axiom,
% 5.31/5.56 ! [A: num,B: num] :
% 5.31/5.56 ( ( bot_bot_set_num
% 5.31/5.56 = ( set_or7049704709247886629st_num @ A @ B ) )
% 5.31/5.56 = ( ~ ( ord_less_eq_num @ A @ B ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % atLeastatMost_empty_iff2
% 5.31/5.56 thf(fact_3685_atLeastatMost__empty__iff2,axiom,
% 5.31/5.56 ! [A: nat,B: nat] :
% 5.31/5.56 ( ( bot_bot_set_nat
% 5.31/5.56 = ( set_or1269000886237332187st_nat @ A @ B ) )
% 5.31/5.56 = ( ~ ( ord_less_eq_nat @ A @ B ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % atLeastatMost_empty_iff2
% 5.31/5.56 thf(fact_3686_atLeastatMost__empty__iff2,axiom,
% 5.31/5.56 ! [A: int,B: int] :
% 5.31/5.56 ( ( bot_bot_set_int
% 5.31/5.56 = ( set_or1266510415728281911st_int @ A @ B ) )
% 5.31/5.56 = ( ~ ( ord_less_eq_int @ A @ B ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % atLeastatMost_empty_iff2
% 5.31/5.56 thf(fact_3687_atLeastatMost__empty__iff2,axiom,
% 5.31/5.56 ! [A: real,B: real] :
% 5.31/5.56 ( ( bot_bot_set_real
% 5.31/5.56 = ( set_or1222579329274155063t_real @ A @ B ) )
% 5.31/5.56 = ( ~ ( ord_less_eq_real @ A @ B ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % atLeastatMost_empty_iff2
% 5.31/5.56 thf(fact_3688_atLeastatMost__subset__iff,axiom,
% 5.31/5.56 ! [A: set_nat,B: set_nat,C2: set_nat,D: set_nat] :
% 5.31/5.56 ( ( ord_le6893508408891458716et_nat @ ( set_or4548717258645045905et_nat @ A @ B ) @ ( set_or4548717258645045905et_nat @ C2 @ D ) )
% 5.31/5.56 = ( ~ ( ord_less_eq_set_nat @ A @ B )
% 5.31/5.56 | ( ( ord_less_eq_set_nat @ C2 @ A )
% 5.31/5.56 & ( ord_less_eq_set_nat @ B @ D ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % atLeastatMost_subset_iff
% 5.31/5.56 thf(fact_3689_atLeastatMost__subset__iff,axiom,
% 5.31/5.56 ! [A: rat,B: rat,C2: rat,D: rat] :
% 5.31/5.56 ( ( ord_less_eq_set_rat @ ( set_or633870826150836451st_rat @ A @ B ) @ ( set_or633870826150836451st_rat @ C2 @ D ) )
% 5.31/5.56 = ( ~ ( ord_less_eq_rat @ A @ B )
% 5.31/5.56 | ( ( ord_less_eq_rat @ C2 @ A )
% 5.31/5.56 & ( ord_less_eq_rat @ B @ D ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % atLeastatMost_subset_iff
% 5.31/5.56 thf(fact_3690_atLeastatMost__subset__iff,axiom,
% 5.31/5.56 ! [A: num,B: num,C2: num,D: num] :
% 5.31/5.56 ( ( ord_less_eq_set_num @ ( set_or7049704709247886629st_num @ A @ B ) @ ( set_or7049704709247886629st_num @ C2 @ D ) )
% 5.31/5.56 = ( ~ ( ord_less_eq_num @ A @ B )
% 5.31/5.56 | ( ( ord_less_eq_num @ C2 @ A )
% 5.31/5.56 & ( ord_less_eq_num @ B @ D ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % atLeastatMost_subset_iff
% 5.31/5.56 thf(fact_3691_atLeastatMost__subset__iff,axiom,
% 5.31/5.56 ! [A: nat,B: nat,C2: nat,D: nat] :
% 5.31/5.56 ( ( ord_less_eq_set_nat @ ( set_or1269000886237332187st_nat @ A @ B ) @ ( set_or1269000886237332187st_nat @ C2 @ D ) )
% 5.31/5.56 = ( ~ ( ord_less_eq_nat @ A @ B )
% 5.31/5.56 | ( ( ord_less_eq_nat @ C2 @ A )
% 5.31/5.56 & ( ord_less_eq_nat @ B @ D ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % atLeastatMost_subset_iff
% 5.31/5.56 thf(fact_3692_atLeastatMost__subset__iff,axiom,
% 5.31/5.56 ! [A: int,B: int,C2: int,D: int] :
% 5.31/5.56 ( ( ord_less_eq_set_int @ ( set_or1266510415728281911st_int @ A @ B ) @ ( set_or1266510415728281911st_int @ C2 @ D ) )
% 5.31/5.56 = ( ~ ( ord_less_eq_int @ A @ B )
% 5.31/5.56 | ( ( ord_less_eq_int @ C2 @ A )
% 5.31/5.56 & ( ord_less_eq_int @ B @ D ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % atLeastatMost_subset_iff
% 5.31/5.56 thf(fact_3693_atLeastatMost__subset__iff,axiom,
% 5.31/5.56 ! [A: real,B: real,C2: real,D: real] :
% 5.31/5.56 ( ( ord_less_eq_set_real @ ( set_or1222579329274155063t_real @ A @ B ) @ ( set_or1222579329274155063t_real @ C2 @ D ) )
% 5.31/5.56 = ( ~ ( ord_less_eq_real @ A @ B )
% 5.31/5.56 | ( ( ord_less_eq_real @ C2 @ A )
% 5.31/5.56 & ( ord_less_eq_real @ B @ D ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % atLeastatMost_subset_iff
% 5.31/5.56 thf(fact_3694_atLeastatMost__empty,axiom,
% 5.31/5.56 ! [B: rat,A: rat] :
% 5.31/5.56 ( ( ord_less_rat @ B @ A )
% 5.31/5.56 => ( ( set_or633870826150836451st_rat @ A @ B )
% 5.31/5.56 = bot_bot_set_rat ) ) ).
% 5.31/5.56
% 5.31/5.56 % atLeastatMost_empty
% 5.31/5.56 thf(fact_3695_atLeastatMost__empty,axiom,
% 5.31/5.56 ! [B: num,A: num] :
% 5.31/5.56 ( ( ord_less_num @ B @ A )
% 5.31/5.56 => ( ( set_or7049704709247886629st_num @ A @ B )
% 5.31/5.56 = bot_bot_set_num ) ) ).
% 5.31/5.56
% 5.31/5.56 % atLeastatMost_empty
% 5.31/5.56 thf(fact_3696_atLeastatMost__empty,axiom,
% 5.31/5.56 ! [B: nat,A: nat] :
% 5.31/5.56 ( ( ord_less_nat @ B @ A )
% 5.31/5.56 => ( ( set_or1269000886237332187st_nat @ A @ B )
% 5.31/5.56 = bot_bot_set_nat ) ) ).
% 5.31/5.56
% 5.31/5.56 % atLeastatMost_empty
% 5.31/5.56 thf(fact_3697_atLeastatMost__empty,axiom,
% 5.31/5.56 ! [B: int,A: int] :
% 5.31/5.56 ( ( ord_less_int @ B @ A )
% 5.31/5.56 => ( ( set_or1266510415728281911st_int @ A @ B )
% 5.31/5.56 = bot_bot_set_int ) ) ).
% 5.31/5.56
% 5.31/5.56 % atLeastatMost_empty
% 5.31/5.56 thf(fact_3698_atLeastatMost__empty,axiom,
% 5.31/5.56 ! [B: real,A: real] :
% 5.31/5.56 ( ( ord_less_real @ B @ A )
% 5.31/5.56 => ( ( set_or1222579329274155063t_real @ A @ B )
% 5.31/5.56 = bot_bot_set_real ) ) ).
% 5.31/5.56
% 5.31/5.56 % atLeastatMost_empty
% 5.31/5.56 thf(fact_3699_infinite__Icc__iff,axiom,
% 5.31/5.56 ! [A: rat,B: rat] :
% 5.31/5.56 ( ( ~ ( finite_finite_rat @ ( set_or633870826150836451st_rat @ A @ B ) ) )
% 5.31/5.56 = ( ord_less_rat @ A @ B ) ) ).
% 5.31/5.56
% 5.31/5.56 % infinite_Icc_iff
% 5.31/5.56 thf(fact_3700_infinite__Icc__iff,axiom,
% 5.31/5.56 ! [A: real,B: real] :
% 5.31/5.56 ( ( ~ ( finite_finite_real @ ( set_or1222579329274155063t_real @ A @ B ) ) )
% 5.31/5.56 = ( ord_less_real @ A @ B ) ) ).
% 5.31/5.56
% 5.31/5.56 % infinite_Icc_iff
% 5.31/5.56 thf(fact_3701_atLeastAtMost__singleton,axiom,
% 5.31/5.56 ! [A: nat] :
% 5.31/5.56 ( ( set_or1269000886237332187st_nat @ A @ A )
% 5.31/5.56 = ( insert_nat @ A @ bot_bot_set_nat ) ) ).
% 5.31/5.56
% 5.31/5.56 % atLeastAtMost_singleton
% 5.31/5.56 thf(fact_3702_atLeastAtMost__singleton,axiom,
% 5.31/5.56 ! [A: int] :
% 5.31/5.56 ( ( set_or1266510415728281911st_int @ A @ A )
% 5.31/5.56 = ( insert_int @ A @ bot_bot_set_int ) ) ).
% 5.31/5.56
% 5.31/5.56 % atLeastAtMost_singleton
% 5.31/5.56 thf(fact_3703_atLeastAtMost__singleton,axiom,
% 5.31/5.56 ! [A: real] :
% 5.31/5.56 ( ( set_or1222579329274155063t_real @ A @ A )
% 5.31/5.56 = ( insert_real @ A @ bot_bot_set_real ) ) ).
% 5.31/5.56
% 5.31/5.56 % atLeastAtMost_singleton
% 5.31/5.56 thf(fact_3704_atLeastAtMost__singleton__iff,axiom,
% 5.31/5.56 ! [A: nat,B: nat,C2: nat] :
% 5.31/5.56 ( ( ( set_or1269000886237332187st_nat @ A @ B )
% 5.31/5.56 = ( insert_nat @ C2 @ bot_bot_set_nat ) )
% 5.31/5.56 = ( ( A = B )
% 5.31/5.56 & ( B = C2 ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % atLeastAtMost_singleton_iff
% 5.31/5.56 thf(fact_3705_atLeastAtMost__singleton__iff,axiom,
% 5.31/5.56 ! [A: int,B: int,C2: int] :
% 5.31/5.56 ( ( ( set_or1266510415728281911st_int @ A @ B )
% 5.31/5.56 = ( insert_int @ C2 @ bot_bot_set_int ) )
% 5.31/5.56 = ( ( A = B )
% 5.31/5.56 & ( B = C2 ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % atLeastAtMost_singleton_iff
% 5.31/5.56 thf(fact_3706_atLeastAtMost__singleton__iff,axiom,
% 5.31/5.56 ! [A: real,B: real,C2: real] :
% 5.31/5.56 ( ( ( set_or1222579329274155063t_real @ A @ B )
% 5.31/5.56 = ( insert_real @ C2 @ bot_bot_set_real ) )
% 5.31/5.56 = ( ( A = B )
% 5.31/5.56 & ( B = C2 ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % atLeastAtMost_singleton_iff
% 5.31/5.56 thf(fact_3707_nat__mult__div__cancel__disj,axiom,
% 5.31/5.56 ! [K2: nat,M2: nat,N: nat] :
% 5.31/5.56 ( ( ( K2 = zero_zero_nat )
% 5.31/5.56 => ( ( divide_divide_nat @ ( times_times_nat @ K2 @ M2 ) @ ( times_times_nat @ K2 @ N ) )
% 5.31/5.56 = zero_zero_nat ) )
% 5.31/5.56 & ( ( K2 != zero_zero_nat )
% 5.31/5.56 => ( ( divide_divide_nat @ ( times_times_nat @ K2 @ M2 ) @ ( times_times_nat @ K2 @ N ) )
% 5.31/5.56 = ( divide_divide_nat @ M2 @ N ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % nat_mult_div_cancel_disj
% 5.31/5.56 thf(fact_3708_zero__le__divide__1__iff,axiom,
% 5.31/5.56 ! [A: real] :
% 5.31/5.56 ( ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ one_one_real @ A ) )
% 5.31/5.56 = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 5.31/5.56
% 5.31/5.56 % zero_le_divide_1_iff
% 5.31/5.56 thf(fact_3709_zero__le__divide__1__iff,axiom,
% 5.31/5.56 ! [A: rat] :
% 5.31/5.56 ( ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ one_one_rat @ A ) )
% 5.31/5.56 = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 5.31/5.56
% 5.31/5.56 % zero_le_divide_1_iff
% 5.31/5.56 thf(fact_3710_divide__le__0__1__iff,axiom,
% 5.31/5.56 ! [A: real] :
% 5.31/5.56 ( ( ord_less_eq_real @ ( divide_divide_real @ one_one_real @ A ) @ zero_zero_real )
% 5.31/5.56 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 5.31/5.56
% 5.31/5.56 % divide_le_0_1_iff
% 5.31/5.56 thf(fact_3711_divide__le__0__1__iff,axiom,
% 5.31/5.56 ! [A: rat] :
% 5.31/5.56 ( ( ord_less_eq_rat @ ( divide_divide_rat @ one_one_rat @ A ) @ zero_zero_rat )
% 5.31/5.56 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 5.31/5.56
% 5.31/5.56 % divide_le_0_1_iff
% 5.31/5.56 thf(fact_3712_zero__less__divide__1__iff,axiom,
% 5.31/5.56 ! [A: real] :
% 5.31/5.56 ( ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ one_one_real @ A ) )
% 5.31/5.56 = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 5.31/5.56
% 5.31/5.56 % zero_less_divide_1_iff
% 5.31/5.56 thf(fact_3713_zero__less__divide__1__iff,axiom,
% 5.31/5.56 ! [A: rat] :
% 5.31/5.56 ( ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ one_one_rat @ A ) )
% 5.31/5.56 = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 5.31/5.56
% 5.31/5.56 % zero_less_divide_1_iff
% 5.31/5.56 thf(fact_3714_less__divide__eq__1__pos,axiom,
% 5.31/5.56 ! [A: real,B: real] :
% 5.31/5.56 ( ( ord_less_real @ zero_zero_real @ A )
% 5.31/5.56 => ( ( ord_less_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 5.31/5.56 = ( ord_less_real @ A @ B ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % less_divide_eq_1_pos
% 5.31/5.56 thf(fact_3715_less__divide__eq__1__pos,axiom,
% 5.31/5.56 ! [A: rat,B: rat] :
% 5.31/5.56 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.31/5.56 => ( ( ord_less_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 5.31/5.56 = ( ord_less_rat @ A @ B ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % less_divide_eq_1_pos
% 5.31/5.56 thf(fact_3716_less__divide__eq__1__neg,axiom,
% 5.31/5.56 ! [A: real,B: real] :
% 5.31/5.56 ( ( ord_less_real @ A @ zero_zero_real )
% 5.31/5.56 => ( ( ord_less_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 5.31/5.56 = ( ord_less_real @ B @ A ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % less_divide_eq_1_neg
% 5.31/5.56 thf(fact_3717_less__divide__eq__1__neg,axiom,
% 5.31/5.56 ! [A: rat,B: rat] :
% 5.31/5.56 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.31/5.56 => ( ( ord_less_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 5.31/5.56 = ( ord_less_rat @ B @ A ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % less_divide_eq_1_neg
% 5.31/5.56 thf(fact_3718_divide__less__eq__1__pos,axiom,
% 5.31/5.56 ! [A: real,B: real] :
% 5.31/5.56 ( ( ord_less_real @ zero_zero_real @ A )
% 5.31/5.56 => ( ( ord_less_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 5.31/5.56 = ( ord_less_real @ B @ A ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % divide_less_eq_1_pos
% 5.31/5.56 thf(fact_3719_divide__less__eq__1__pos,axiom,
% 5.31/5.56 ! [A: rat,B: rat] :
% 5.31/5.56 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.31/5.56 => ( ( ord_less_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 5.31/5.56 = ( ord_less_rat @ B @ A ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % divide_less_eq_1_pos
% 5.31/5.56 thf(fact_3720_divide__less__eq__1__neg,axiom,
% 5.31/5.56 ! [A: real,B: real] :
% 5.31/5.56 ( ( ord_less_real @ A @ zero_zero_real )
% 5.31/5.56 => ( ( ord_less_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 5.31/5.56 = ( ord_less_real @ A @ B ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % divide_less_eq_1_neg
% 5.31/5.56 thf(fact_3721_divide__less__eq__1__neg,axiom,
% 5.31/5.56 ! [A: rat,B: rat] :
% 5.31/5.56 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.31/5.56 => ( ( ord_less_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 5.31/5.56 = ( ord_less_rat @ A @ B ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % divide_less_eq_1_neg
% 5.31/5.56 thf(fact_3722_divide__less__0__1__iff,axiom,
% 5.31/5.56 ! [A: real] :
% 5.31/5.56 ( ( ord_less_real @ ( divide_divide_real @ one_one_real @ A ) @ zero_zero_real )
% 5.31/5.56 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 5.31/5.56
% 5.31/5.56 % divide_less_0_1_iff
% 5.31/5.56 thf(fact_3723_divide__less__0__1__iff,axiom,
% 5.31/5.56 ! [A: rat] :
% 5.31/5.56 ( ( ord_less_rat @ ( divide_divide_rat @ one_one_rat @ A ) @ zero_zero_rat )
% 5.31/5.56 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 5.31/5.56
% 5.31/5.56 % divide_less_0_1_iff
% 5.31/5.56 thf(fact_3724_divide__le__eq__numeral1_I1_J,axiom,
% 5.31/5.56 ! [B: real,W2: num,A: real] :
% 5.31/5.56 ( ( ord_less_eq_real @ ( divide_divide_real @ B @ ( numeral_numeral_real @ W2 ) ) @ A )
% 5.31/5.56 = ( ord_less_eq_real @ B @ ( times_times_real @ A @ ( numeral_numeral_real @ W2 ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % divide_le_eq_numeral1(1)
% 5.31/5.56 thf(fact_3725_divide__le__eq__numeral1_I1_J,axiom,
% 5.31/5.56 ! [B: rat,W2: num,A: rat] :
% 5.31/5.56 ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W2 ) ) @ A )
% 5.31/5.56 = ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ ( numeral_numeral_rat @ W2 ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % divide_le_eq_numeral1(1)
% 5.31/5.56 thf(fact_3726_le__divide__eq__numeral1_I1_J,axiom,
% 5.31/5.56 ! [A: real,B: real,W2: num] :
% 5.31/5.56 ( ( ord_less_eq_real @ A @ ( divide_divide_real @ B @ ( numeral_numeral_real @ W2 ) ) )
% 5.31/5.56 = ( ord_less_eq_real @ ( times_times_real @ A @ ( numeral_numeral_real @ W2 ) ) @ B ) ) ).
% 5.31/5.56
% 5.31/5.56 % le_divide_eq_numeral1(1)
% 5.31/5.56 thf(fact_3727_le__divide__eq__numeral1_I1_J,axiom,
% 5.31/5.56 ! [A: rat,B: rat,W2: num] :
% 5.31/5.56 ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W2 ) ) )
% 5.31/5.56 = ( ord_less_eq_rat @ ( times_times_rat @ A @ ( numeral_numeral_rat @ W2 ) ) @ B ) ) ).
% 5.31/5.56
% 5.31/5.56 % le_divide_eq_numeral1(1)
% 5.31/5.56 thf(fact_3728_divide__eq__eq__numeral1_I1_J,axiom,
% 5.31/5.56 ! [B: complex,W2: num,A: complex] :
% 5.31/5.56 ( ( ( divide1717551699836669952omplex @ B @ ( numera6690914467698888265omplex @ W2 ) )
% 5.31/5.56 = A )
% 5.31/5.56 = ( ( ( ( numera6690914467698888265omplex @ W2 )
% 5.31/5.56 != zero_zero_complex )
% 5.31/5.56 => ( B
% 5.31/5.56 = ( times_times_complex @ A @ ( numera6690914467698888265omplex @ W2 ) ) ) )
% 5.31/5.56 & ( ( ( numera6690914467698888265omplex @ W2 )
% 5.31/5.56 = zero_zero_complex )
% 5.31/5.56 => ( A = zero_zero_complex ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % divide_eq_eq_numeral1(1)
% 5.31/5.56 thf(fact_3729_divide__eq__eq__numeral1_I1_J,axiom,
% 5.31/5.56 ! [B: real,W2: num,A: real] :
% 5.31/5.56 ( ( ( divide_divide_real @ B @ ( numeral_numeral_real @ W2 ) )
% 5.31/5.56 = A )
% 5.31/5.56 = ( ( ( ( numeral_numeral_real @ W2 )
% 5.31/5.56 != zero_zero_real )
% 5.31/5.56 => ( B
% 5.31/5.56 = ( times_times_real @ A @ ( numeral_numeral_real @ W2 ) ) ) )
% 5.31/5.56 & ( ( ( numeral_numeral_real @ W2 )
% 5.31/5.56 = zero_zero_real )
% 5.31/5.56 => ( A = zero_zero_real ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % divide_eq_eq_numeral1(1)
% 5.31/5.56 thf(fact_3730_divide__eq__eq__numeral1_I1_J,axiom,
% 5.31/5.56 ! [B: rat,W2: num,A: rat] :
% 5.31/5.56 ( ( ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W2 ) )
% 5.31/5.56 = A )
% 5.31/5.56 = ( ( ( ( numeral_numeral_rat @ W2 )
% 5.31/5.56 != zero_zero_rat )
% 5.31/5.56 => ( B
% 5.31/5.56 = ( times_times_rat @ A @ ( numeral_numeral_rat @ W2 ) ) ) )
% 5.31/5.56 & ( ( ( numeral_numeral_rat @ W2 )
% 5.31/5.56 = zero_zero_rat )
% 5.31/5.56 => ( A = zero_zero_rat ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % divide_eq_eq_numeral1(1)
% 5.31/5.56 thf(fact_3731_eq__divide__eq__numeral1_I1_J,axiom,
% 5.31/5.56 ! [A: complex,B: complex,W2: num] :
% 5.31/5.56 ( ( A
% 5.31/5.56 = ( divide1717551699836669952omplex @ B @ ( numera6690914467698888265omplex @ W2 ) ) )
% 5.31/5.56 = ( ( ( ( numera6690914467698888265omplex @ W2 )
% 5.31/5.56 != zero_zero_complex )
% 5.31/5.56 => ( ( times_times_complex @ A @ ( numera6690914467698888265omplex @ W2 ) )
% 5.31/5.56 = B ) )
% 5.31/5.56 & ( ( ( numera6690914467698888265omplex @ W2 )
% 5.31/5.56 = zero_zero_complex )
% 5.31/5.56 => ( A = zero_zero_complex ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % eq_divide_eq_numeral1(1)
% 5.31/5.56 thf(fact_3732_eq__divide__eq__numeral1_I1_J,axiom,
% 5.31/5.56 ! [A: real,B: real,W2: num] :
% 5.31/5.56 ( ( A
% 5.31/5.56 = ( divide_divide_real @ B @ ( numeral_numeral_real @ W2 ) ) )
% 5.31/5.56 = ( ( ( ( numeral_numeral_real @ W2 )
% 5.31/5.56 != zero_zero_real )
% 5.31/5.56 => ( ( times_times_real @ A @ ( numeral_numeral_real @ W2 ) )
% 5.31/5.56 = B ) )
% 5.31/5.56 & ( ( ( numeral_numeral_real @ W2 )
% 5.31/5.56 = zero_zero_real )
% 5.31/5.56 => ( A = zero_zero_real ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % eq_divide_eq_numeral1(1)
% 5.31/5.56 thf(fact_3733_eq__divide__eq__numeral1_I1_J,axiom,
% 5.31/5.56 ! [A: rat,B: rat,W2: num] :
% 5.31/5.56 ( ( A
% 5.31/5.56 = ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W2 ) ) )
% 5.31/5.56 = ( ( ( ( numeral_numeral_rat @ W2 )
% 5.31/5.56 != zero_zero_rat )
% 5.31/5.56 => ( ( times_times_rat @ A @ ( numeral_numeral_rat @ W2 ) )
% 5.31/5.56 = B ) )
% 5.31/5.56 & ( ( ( numeral_numeral_rat @ W2 )
% 5.31/5.56 = zero_zero_rat )
% 5.31/5.56 => ( A = zero_zero_rat ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % eq_divide_eq_numeral1(1)
% 5.31/5.56 thf(fact_3734_less__divide__eq__numeral1_I1_J,axiom,
% 5.31/5.56 ! [A: real,B: real,W2: num] :
% 5.31/5.56 ( ( ord_less_real @ A @ ( divide_divide_real @ B @ ( numeral_numeral_real @ W2 ) ) )
% 5.31/5.56 = ( ord_less_real @ ( times_times_real @ A @ ( numeral_numeral_real @ W2 ) ) @ B ) ) ).
% 5.31/5.56
% 5.31/5.56 % less_divide_eq_numeral1(1)
% 5.31/5.56 thf(fact_3735_less__divide__eq__numeral1_I1_J,axiom,
% 5.31/5.56 ! [A: rat,B: rat,W2: num] :
% 5.31/5.56 ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W2 ) ) )
% 5.31/5.56 = ( ord_less_rat @ ( times_times_rat @ A @ ( numeral_numeral_rat @ W2 ) ) @ B ) ) ).
% 5.31/5.56
% 5.31/5.56 % less_divide_eq_numeral1(1)
% 5.31/5.56 thf(fact_3736_divide__less__eq__numeral1_I1_J,axiom,
% 5.31/5.56 ! [B: real,W2: num,A: real] :
% 5.31/5.56 ( ( ord_less_real @ ( divide_divide_real @ B @ ( numeral_numeral_real @ W2 ) ) @ A )
% 5.31/5.56 = ( ord_less_real @ B @ ( times_times_real @ A @ ( numeral_numeral_real @ W2 ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % divide_less_eq_numeral1(1)
% 5.31/5.56 thf(fact_3737_divide__less__eq__numeral1_I1_J,axiom,
% 5.31/5.56 ! [B: rat,W2: num,A: rat] :
% 5.31/5.56 ( ( ord_less_rat @ ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W2 ) ) @ A )
% 5.31/5.56 = ( ord_less_rat @ B @ ( times_times_rat @ A @ ( numeral_numeral_rat @ W2 ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % divide_less_eq_numeral1(1)
% 5.31/5.56 thf(fact_3738_nonzero__divide__mult__cancel__left,axiom,
% 5.31/5.56 ! [A: complex,B: complex] :
% 5.31/5.56 ( ( A != zero_zero_complex )
% 5.31/5.56 => ( ( divide1717551699836669952omplex @ A @ ( times_times_complex @ A @ B ) )
% 5.31/5.56 = ( divide1717551699836669952omplex @ one_one_complex @ B ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % nonzero_divide_mult_cancel_left
% 5.31/5.56 thf(fact_3739_nonzero__divide__mult__cancel__left,axiom,
% 5.31/5.56 ! [A: real,B: real] :
% 5.31/5.56 ( ( A != zero_zero_real )
% 5.31/5.56 => ( ( divide_divide_real @ A @ ( times_times_real @ A @ B ) )
% 5.31/5.56 = ( divide_divide_real @ one_one_real @ B ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % nonzero_divide_mult_cancel_left
% 5.31/5.56 thf(fact_3740_nonzero__divide__mult__cancel__left,axiom,
% 5.31/5.56 ! [A: rat,B: rat] :
% 5.31/5.56 ( ( A != zero_zero_rat )
% 5.31/5.56 => ( ( divide_divide_rat @ A @ ( times_times_rat @ A @ B ) )
% 5.31/5.56 = ( divide_divide_rat @ one_one_rat @ B ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % nonzero_divide_mult_cancel_left
% 5.31/5.56 thf(fact_3741_nonzero__divide__mult__cancel__right,axiom,
% 5.31/5.56 ! [B: complex,A: complex] :
% 5.31/5.56 ( ( B != zero_zero_complex )
% 5.31/5.56 => ( ( divide1717551699836669952omplex @ B @ ( times_times_complex @ A @ B ) )
% 5.31/5.56 = ( divide1717551699836669952omplex @ one_one_complex @ A ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % nonzero_divide_mult_cancel_right
% 5.31/5.56 thf(fact_3742_nonzero__divide__mult__cancel__right,axiom,
% 5.31/5.56 ! [B: real,A: real] :
% 5.31/5.56 ( ( B != zero_zero_real )
% 5.31/5.56 => ( ( divide_divide_real @ B @ ( times_times_real @ A @ B ) )
% 5.31/5.56 = ( divide_divide_real @ one_one_real @ A ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % nonzero_divide_mult_cancel_right
% 5.31/5.56 thf(fact_3743_nonzero__divide__mult__cancel__right,axiom,
% 5.31/5.56 ! [B: rat,A: rat] :
% 5.31/5.56 ( ( B != zero_zero_rat )
% 5.31/5.56 => ( ( divide_divide_rat @ B @ ( times_times_rat @ A @ B ) )
% 5.31/5.56 = ( divide_divide_rat @ one_one_rat @ A ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % nonzero_divide_mult_cancel_right
% 5.31/5.56 thf(fact_3744_numeral__le__real__of__nat__iff,axiom,
% 5.31/5.56 ! [N: num,M2: nat] :
% 5.31/5.56 ( ( ord_less_eq_real @ ( numeral_numeral_real @ N ) @ ( semiri5074537144036343181t_real @ M2 ) )
% 5.31/5.56 = ( ord_less_eq_nat @ ( numeral_numeral_nat @ N ) @ M2 ) ) ).
% 5.31/5.56
% 5.31/5.56 % numeral_le_real_of_nat_iff
% 5.31/5.56 thf(fact_3745_card__atLeastAtMost,axiom,
% 5.31/5.56 ! [L: nat,U: nat] :
% 5.31/5.56 ( ( finite_card_nat @ ( set_or1269000886237332187st_nat @ L @ U ) )
% 5.31/5.56 = ( minus_minus_nat @ ( suc @ U ) @ L ) ) ).
% 5.31/5.56
% 5.31/5.56 % card_atLeastAtMost
% 5.31/5.56 thf(fact_3746_le__divide__eq__1__pos,axiom,
% 5.31/5.56 ! [A: real,B: real] :
% 5.31/5.56 ( ( ord_less_real @ zero_zero_real @ A )
% 5.31/5.56 => ( ( ord_less_eq_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 5.31/5.56 = ( ord_less_eq_real @ A @ B ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % le_divide_eq_1_pos
% 5.31/5.56 thf(fact_3747_le__divide__eq__1__pos,axiom,
% 5.31/5.56 ! [A: rat,B: rat] :
% 5.31/5.56 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.31/5.56 => ( ( ord_less_eq_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 5.31/5.56 = ( ord_less_eq_rat @ A @ B ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % le_divide_eq_1_pos
% 5.31/5.56 thf(fact_3748_le__divide__eq__1__neg,axiom,
% 5.31/5.56 ! [A: real,B: real] :
% 5.31/5.56 ( ( ord_less_real @ A @ zero_zero_real )
% 5.31/5.56 => ( ( ord_less_eq_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 5.31/5.56 = ( ord_less_eq_real @ B @ A ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % le_divide_eq_1_neg
% 5.31/5.56 thf(fact_3749_le__divide__eq__1__neg,axiom,
% 5.31/5.56 ! [A: rat,B: rat] :
% 5.31/5.56 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.31/5.56 => ( ( ord_less_eq_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 5.31/5.56 = ( ord_less_eq_rat @ B @ A ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % le_divide_eq_1_neg
% 5.31/5.56 thf(fact_3750_divide__le__eq__1__pos,axiom,
% 5.31/5.56 ! [A: real,B: real] :
% 5.31/5.56 ( ( ord_less_real @ zero_zero_real @ A )
% 5.31/5.56 => ( ( ord_less_eq_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 5.31/5.56 = ( ord_less_eq_real @ B @ A ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % divide_le_eq_1_pos
% 5.31/5.56 thf(fact_3751_divide__le__eq__1__pos,axiom,
% 5.31/5.56 ! [A: rat,B: rat] :
% 5.31/5.56 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.31/5.56 => ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 5.31/5.56 = ( ord_less_eq_rat @ B @ A ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % divide_le_eq_1_pos
% 5.31/5.56 thf(fact_3752_divide__le__eq__1__neg,axiom,
% 5.31/5.56 ! [A: real,B: real] :
% 5.31/5.56 ( ( ord_less_real @ A @ zero_zero_real )
% 5.31/5.56 => ( ( ord_less_eq_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 5.31/5.56 = ( ord_less_eq_real @ A @ B ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % divide_le_eq_1_neg
% 5.31/5.56 thf(fact_3753_divide__le__eq__1__neg,axiom,
% 5.31/5.56 ! [A: rat,B: rat] :
% 5.31/5.56 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.31/5.56 => ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 5.31/5.56 = ( ord_less_eq_rat @ A @ B ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % divide_le_eq_1_neg
% 5.31/5.56 thf(fact_3754_bits__1__div__2,axiom,
% 5.31/5.56 ( ( divide6298287555418463151nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.31/5.56 = zero_z3403309356797280102nteger ) ).
% 5.31/5.56
% 5.31/5.56 % bits_1_div_2
% 5.31/5.56 thf(fact_3755_bits__1__div__2,axiom,
% 5.31/5.56 ( ( divide_divide_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.31/5.56 = zero_zero_nat ) ).
% 5.31/5.56
% 5.31/5.56 % bits_1_div_2
% 5.31/5.56 thf(fact_3756_bits__1__div__2,axiom,
% 5.31/5.56 ( ( divide_divide_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.31/5.56 = zero_zero_int ) ).
% 5.31/5.56
% 5.31/5.56 % bits_1_div_2
% 5.31/5.56 thf(fact_3757_decr__mult__lemma,axiom,
% 5.31/5.56 ! [D: int,P2: int > $o,K2: int] :
% 5.31/5.56 ( ( ord_less_int @ zero_zero_int @ D )
% 5.31/5.56 => ( ! [X3: int] :
% 5.31/5.56 ( ( P2 @ X3 )
% 5.31/5.56 => ( P2 @ ( minus_minus_int @ X3 @ D ) ) )
% 5.31/5.56 => ( ( ord_less_eq_int @ zero_zero_int @ K2 )
% 5.31/5.56 => ! [X5: int] :
% 5.31/5.56 ( ( P2 @ X5 )
% 5.31/5.56 => ( P2 @ ( minus_minus_int @ X5 @ ( times_times_int @ K2 @ D ) ) ) ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % decr_mult_lemma
% 5.31/5.56 thf(fact_3758_minusinfinity,axiom,
% 5.31/5.56 ! [D: int,P1: int > $o,P2: int > $o] :
% 5.31/5.56 ( ( ord_less_int @ zero_zero_int @ D )
% 5.31/5.56 => ( ! [X3: int,K: int] :
% 5.31/5.56 ( ( P1 @ X3 )
% 5.31/5.56 = ( P1 @ ( minus_minus_int @ X3 @ ( times_times_int @ K @ D ) ) ) )
% 5.31/5.56 => ( ? [Z5: int] :
% 5.31/5.56 ! [X3: int] :
% 5.31/5.56 ( ( ord_less_int @ X3 @ Z5 )
% 5.31/5.56 => ( ( P2 @ X3 )
% 5.31/5.56 = ( P1 @ X3 ) ) )
% 5.31/5.56 => ( ? [X_1: int] : ( P1 @ X_1 )
% 5.31/5.56 => ? [X_12: int] : ( P2 @ X_12 ) ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % minusinfinity
% 5.31/5.56 thf(fact_3759_plusinfinity,axiom,
% 5.31/5.56 ! [D: int,P6: int > $o,P2: int > $o] :
% 5.31/5.56 ( ( ord_less_int @ zero_zero_int @ D )
% 5.31/5.56 => ( ! [X3: int,K: int] :
% 5.31/5.56 ( ( P6 @ X3 )
% 5.31/5.56 = ( P6 @ ( minus_minus_int @ X3 @ ( times_times_int @ K @ D ) ) ) )
% 5.31/5.56 => ( ? [Z5: int] :
% 5.31/5.56 ! [X3: int] :
% 5.31/5.56 ( ( ord_less_int @ Z5 @ X3 )
% 5.31/5.56 => ( ( P2 @ X3 )
% 5.31/5.56 = ( P6 @ X3 ) ) )
% 5.31/5.56 => ( ? [X_1: int] : ( P6 @ X_1 )
% 5.31/5.56 => ? [X_12: int] : ( P2 @ X_12 ) ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % plusinfinity
% 5.31/5.56 thf(fact_3760_times__int__code_I2_J,axiom,
% 5.31/5.56 ! [L: int] :
% 5.31/5.56 ( ( times_times_int @ zero_zero_int @ L )
% 5.31/5.56 = zero_zero_int ) ).
% 5.31/5.56
% 5.31/5.56 % times_int_code(2)
% 5.31/5.56 thf(fact_3761_times__int__code_I1_J,axiom,
% 5.31/5.56 ! [K2: int] :
% 5.31/5.56 ( ( times_times_int @ K2 @ zero_zero_int )
% 5.31/5.56 = zero_zero_int ) ).
% 5.31/5.56
% 5.31/5.56 % times_int_code(1)
% 5.31/5.56 thf(fact_3762_pos__zmult__eq__1__iff,axiom,
% 5.31/5.56 ! [M2: int,N: int] :
% 5.31/5.56 ( ( ord_less_int @ zero_zero_int @ M2 )
% 5.31/5.56 => ( ( ( times_times_int @ M2 @ N )
% 5.31/5.56 = one_one_int )
% 5.31/5.56 = ( ( M2 = one_one_int )
% 5.31/5.56 & ( N = one_one_int ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % pos_zmult_eq_1_iff
% 5.31/5.56 thf(fact_3763_zmult__zless__mono2,axiom,
% 5.31/5.56 ! [I2: int,J2: int,K2: int] :
% 5.31/5.56 ( ( ord_less_int @ I2 @ J2 )
% 5.31/5.56 => ( ( ord_less_int @ zero_zero_int @ K2 )
% 5.31/5.56 => ( ord_less_int @ ( times_times_int @ K2 @ I2 ) @ ( times_times_int @ K2 @ J2 ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % zmult_zless_mono2
% 5.31/5.56 thf(fact_3764_unique__quotient__lemma__neg,axiom,
% 5.31/5.56 ! [B: int,Q4: int,R5: int,Q2: int,R3: int] :
% 5.31/5.56 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ B @ Q4 ) @ R5 ) @ ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R3 ) )
% 5.31/5.56 => ( ( ord_less_eq_int @ R3 @ zero_zero_int )
% 5.31/5.56 => ( ( ord_less_int @ B @ R3 )
% 5.31/5.56 => ( ( ord_less_int @ B @ R5 )
% 5.31/5.56 => ( ord_less_eq_int @ Q2 @ Q4 ) ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % unique_quotient_lemma_neg
% 5.31/5.56 thf(fact_3765_unique__quotient__lemma,axiom,
% 5.31/5.56 ! [B: int,Q4: int,R5: int,Q2: int,R3: int] :
% 5.31/5.56 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ B @ Q4 ) @ R5 ) @ ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R3 ) )
% 5.31/5.56 => ( ( ord_less_eq_int @ zero_zero_int @ R5 )
% 5.31/5.56 => ( ( ord_less_int @ R5 @ B )
% 5.31/5.56 => ( ( ord_less_int @ R3 @ B )
% 5.31/5.56 => ( ord_less_eq_int @ Q4 @ Q2 ) ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % unique_quotient_lemma
% 5.31/5.56 thf(fact_3766_zdiv__mono2__neg__lemma,axiom,
% 5.31/5.56 ! [B: int,Q2: int,R3: int,B2: int,Q4: int,R5: int] :
% 5.31/5.56 ( ( ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R3 )
% 5.31/5.56 = ( plus_plus_int @ ( times_times_int @ B2 @ Q4 ) @ R5 ) )
% 5.31/5.56 => ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ B2 @ Q4 ) @ R5 ) @ zero_zero_int )
% 5.31/5.56 => ( ( ord_less_int @ R3 @ B )
% 5.31/5.56 => ( ( ord_less_eq_int @ zero_zero_int @ R5 )
% 5.31/5.56 => ( ( ord_less_int @ zero_zero_int @ B2 )
% 5.31/5.56 => ( ( ord_less_eq_int @ B2 @ B )
% 5.31/5.56 => ( ord_less_eq_int @ Q4 @ Q2 ) ) ) ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % zdiv_mono2_neg_lemma
% 5.31/5.56 thf(fact_3767_zdiv__mono2__lemma,axiom,
% 5.31/5.56 ! [B: int,Q2: int,R3: int,B2: int,Q4: int,R5: int] :
% 5.31/5.56 ( ( ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R3 )
% 5.31/5.56 = ( plus_plus_int @ ( times_times_int @ B2 @ Q4 ) @ R5 ) )
% 5.31/5.56 => ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ B2 @ Q4 ) @ R5 ) )
% 5.31/5.56 => ( ( ord_less_int @ R5 @ B2 )
% 5.31/5.56 => ( ( ord_less_eq_int @ zero_zero_int @ R3 )
% 5.31/5.56 => ( ( ord_less_int @ zero_zero_int @ B2 )
% 5.31/5.56 => ( ( ord_less_eq_int @ B2 @ B )
% 5.31/5.56 => ( ord_less_eq_int @ Q2 @ Q4 ) ) ) ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % zdiv_mono2_lemma
% 5.31/5.56 thf(fact_3768_q__pos__lemma,axiom,
% 5.31/5.56 ! [B2: int,Q4: int,R5: int] :
% 5.31/5.56 ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ B2 @ Q4 ) @ R5 ) )
% 5.31/5.56 => ( ( ord_less_int @ R5 @ B2 )
% 5.31/5.56 => ( ( ord_less_int @ zero_zero_int @ B2 )
% 5.31/5.56 => ( ord_less_eq_int @ zero_zero_int @ Q4 ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % q_pos_lemma
% 5.31/5.56 thf(fact_3769_incr__mult__lemma,axiom,
% 5.31/5.56 ! [D: int,P2: int > $o,K2: int] :
% 5.31/5.56 ( ( ord_less_int @ zero_zero_int @ D )
% 5.31/5.56 => ( ! [X3: int] :
% 5.31/5.56 ( ( P2 @ X3 )
% 5.31/5.56 => ( P2 @ ( plus_plus_int @ X3 @ D ) ) )
% 5.31/5.56 => ( ( ord_less_eq_int @ zero_zero_int @ K2 )
% 5.31/5.56 => ! [X5: int] :
% 5.31/5.56 ( ( P2 @ X5 )
% 5.31/5.56 => ( P2 @ ( plus_plus_int @ X5 @ ( times_times_int @ K2 @ D ) ) ) ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % incr_mult_lemma
% 5.31/5.56 thf(fact_3770_ivl__disj__un__two__touch_I4_J,axiom,
% 5.31/5.56 ! [L: rat,M2: rat,U: rat] :
% 5.31/5.56 ( ( ord_less_eq_rat @ L @ M2 )
% 5.31/5.56 => ( ( ord_less_eq_rat @ M2 @ U )
% 5.31/5.56 => ( ( sup_sup_set_rat @ ( set_or633870826150836451st_rat @ L @ M2 ) @ ( set_or633870826150836451st_rat @ M2 @ U ) )
% 5.31/5.56 = ( set_or633870826150836451st_rat @ L @ U ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % ivl_disj_un_two_touch(4)
% 5.31/5.56 thf(fact_3771_ivl__disj__un__two__touch_I4_J,axiom,
% 5.31/5.56 ! [L: num,M2: num,U: num] :
% 5.31/5.56 ( ( ord_less_eq_num @ L @ M2 )
% 5.31/5.56 => ( ( ord_less_eq_num @ M2 @ U )
% 5.31/5.56 => ( ( sup_sup_set_num @ ( set_or7049704709247886629st_num @ L @ M2 ) @ ( set_or7049704709247886629st_num @ M2 @ U ) )
% 5.31/5.56 = ( set_or7049704709247886629st_num @ L @ U ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % ivl_disj_un_two_touch(4)
% 5.31/5.56 thf(fact_3772_ivl__disj__un__two__touch_I4_J,axiom,
% 5.31/5.56 ! [L: nat,M2: nat,U: nat] :
% 5.31/5.56 ( ( ord_less_eq_nat @ L @ M2 )
% 5.31/5.56 => ( ( ord_less_eq_nat @ M2 @ U )
% 5.31/5.56 => ( ( sup_sup_set_nat @ ( set_or1269000886237332187st_nat @ L @ M2 ) @ ( set_or1269000886237332187st_nat @ M2 @ U ) )
% 5.31/5.56 = ( set_or1269000886237332187st_nat @ L @ U ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % ivl_disj_un_two_touch(4)
% 5.31/5.56 thf(fact_3773_ivl__disj__un__two__touch_I4_J,axiom,
% 5.31/5.56 ! [L: int,M2: int,U: int] :
% 5.31/5.56 ( ( ord_less_eq_int @ L @ M2 )
% 5.31/5.56 => ( ( ord_less_eq_int @ M2 @ U )
% 5.31/5.56 => ( ( sup_sup_set_int @ ( set_or1266510415728281911st_int @ L @ M2 ) @ ( set_or1266510415728281911st_int @ M2 @ U ) )
% 5.31/5.56 = ( set_or1266510415728281911st_int @ L @ U ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % ivl_disj_un_two_touch(4)
% 5.31/5.56 thf(fact_3774_ivl__disj__un__two__touch_I4_J,axiom,
% 5.31/5.56 ! [L: real,M2: real,U: real] :
% 5.31/5.56 ( ( ord_less_eq_real @ L @ M2 )
% 5.31/5.56 => ( ( ord_less_eq_real @ M2 @ U )
% 5.31/5.56 => ( ( sup_sup_set_real @ ( set_or1222579329274155063t_real @ L @ M2 ) @ ( set_or1222579329274155063t_real @ M2 @ U ) )
% 5.31/5.56 = ( set_or1222579329274155063t_real @ L @ U ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % ivl_disj_un_two_touch(4)
% 5.31/5.56 thf(fact_3775_int__distrib_I2_J,axiom,
% 5.31/5.56 ! [W2: int,Z1: int,Z22: int] :
% 5.31/5.56 ( ( times_times_int @ W2 @ ( plus_plus_int @ Z1 @ Z22 ) )
% 5.31/5.56 = ( plus_plus_int @ ( times_times_int @ W2 @ Z1 ) @ ( times_times_int @ W2 @ Z22 ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % int_distrib(2)
% 5.31/5.56 thf(fact_3776_int__distrib_I1_J,axiom,
% 5.31/5.56 ! [Z1: int,Z22: int,W2: int] :
% 5.31/5.56 ( ( times_times_int @ ( plus_plus_int @ Z1 @ Z22 ) @ W2 )
% 5.31/5.56 = ( plus_plus_int @ ( times_times_int @ Z1 @ W2 ) @ ( times_times_int @ Z22 @ W2 ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % int_distrib(1)
% 5.31/5.56 thf(fact_3777_int__distrib_I3_J,axiom,
% 5.31/5.56 ! [Z1: int,Z22: int,W2: int] :
% 5.31/5.56 ( ( times_times_int @ ( minus_minus_int @ Z1 @ Z22 ) @ W2 )
% 5.31/5.56 = ( minus_minus_int @ ( times_times_int @ Z1 @ W2 ) @ ( times_times_int @ Z22 @ W2 ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % int_distrib(3)
% 5.31/5.56 thf(fact_3778_int__distrib_I4_J,axiom,
% 5.31/5.56 ! [W2: int,Z1: int,Z22: int] :
% 5.31/5.56 ( ( times_times_int @ W2 @ ( minus_minus_int @ Z1 @ Z22 ) )
% 5.31/5.56 = ( minus_minus_int @ ( times_times_int @ W2 @ Z1 ) @ ( times_times_int @ W2 @ Z22 ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % int_distrib(4)
% 5.31/5.56 thf(fact_3779_divide__divide__eq__left_H,axiom,
% 5.31/5.56 ! [A: complex,B: complex,C2: complex] :
% 5.31/5.56 ( ( divide1717551699836669952omplex @ ( divide1717551699836669952omplex @ A @ B ) @ C2 )
% 5.31/5.56 = ( divide1717551699836669952omplex @ A @ ( times_times_complex @ C2 @ B ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % divide_divide_eq_left'
% 5.31/5.56 thf(fact_3780_divide__divide__eq__left_H,axiom,
% 5.31/5.56 ! [A: real,B: real,C2: real] :
% 5.31/5.56 ( ( divide_divide_real @ ( divide_divide_real @ A @ B ) @ C2 )
% 5.31/5.56 = ( divide_divide_real @ A @ ( times_times_real @ C2 @ B ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % divide_divide_eq_left'
% 5.31/5.56 thf(fact_3781_divide__divide__eq__left_H,axiom,
% 5.31/5.56 ! [A: rat,B: rat,C2: rat] :
% 5.31/5.56 ( ( divide_divide_rat @ ( divide_divide_rat @ A @ B ) @ C2 )
% 5.31/5.56 = ( divide_divide_rat @ A @ ( times_times_rat @ C2 @ B ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % divide_divide_eq_left'
% 5.31/5.56 thf(fact_3782_divide__divide__times__eq,axiom,
% 5.31/5.56 ! [X: complex,Y: complex,Z3: complex,W2: complex] :
% 5.31/5.56 ( ( divide1717551699836669952omplex @ ( divide1717551699836669952omplex @ X @ Y ) @ ( divide1717551699836669952omplex @ Z3 @ W2 ) )
% 5.31/5.56 = ( divide1717551699836669952omplex @ ( times_times_complex @ X @ W2 ) @ ( times_times_complex @ Y @ Z3 ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % divide_divide_times_eq
% 5.31/5.56 thf(fact_3783_divide__divide__times__eq,axiom,
% 5.31/5.56 ! [X: real,Y: real,Z3: real,W2: real] :
% 5.31/5.56 ( ( divide_divide_real @ ( divide_divide_real @ X @ Y ) @ ( divide_divide_real @ Z3 @ W2 ) )
% 5.31/5.56 = ( divide_divide_real @ ( times_times_real @ X @ W2 ) @ ( times_times_real @ Y @ Z3 ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % divide_divide_times_eq
% 5.31/5.56 thf(fact_3784_divide__divide__times__eq,axiom,
% 5.31/5.56 ! [X: rat,Y: rat,Z3: rat,W2: rat] :
% 5.31/5.56 ( ( divide_divide_rat @ ( divide_divide_rat @ X @ Y ) @ ( divide_divide_rat @ Z3 @ W2 ) )
% 5.31/5.56 = ( divide_divide_rat @ ( times_times_rat @ X @ W2 ) @ ( times_times_rat @ Y @ Z3 ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % divide_divide_times_eq
% 5.31/5.56 thf(fact_3785_times__divide__times__eq,axiom,
% 5.31/5.56 ! [X: complex,Y: complex,Z3: complex,W2: complex] :
% 5.31/5.56 ( ( times_times_complex @ ( divide1717551699836669952omplex @ X @ Y ) @ ( divide1717551699836669952omplex @ Z3 @ W2 ) )
% 5.31/5.56 = ( divide1717551699836669952omplex @ ( times_times_complex @ X @ Z3 ) @ ( times_times_complex @ Y @ W2 ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % times_divide_times_eq
% 5.31/5.56 thf(fact_3786_times__divide__times__eq,axiom,
% 5.31/5.56 ! [X: real,Y: real,Z3: real,W2: real] :
% 5.31/5.56 ( ( times_times_real @ ( divide_divide_real @ X @ Y ) @ ( divide_divide_real @ Z3 @ W2 ) )
% 5.31/5.56 = ( divide_divide_real @ ( times_times_real @ X @ Z3 ) @ ( times_times_real @ Y @ W2 ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % times_divide_times_eq
% 5.31/5.56 thf(fact_3787_times__divide__times__eq,axiom,
% 5.31/5.56 ! [X: rat,Y: rat,Z3: rat,W2: rat] :
% 5.31/5.56 ( ( times_times_rat @ ( divide_divide_rat @ X @ Y ) @ ( divide_divide_rat @ Z3 @ W2 ) )
% 5.31/5.56 = ( divide_divide_rat @ ( times_times_rat @ X @ Z3 ) @ ( times_times_rat @ Y @ W2 ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % times_divide_times_eq
% 5.31/5.56 thf(fact_3788_atLeastatMost__psubset__iff,axiom,
% 5.31/5.56 ! [A: set_nat,B: set_nat,C2: set_nat,D: set_nat] :
% 5.31/5.56 ( ( ord_less_set_set_nat @ ( set_or4548717258645045905et_nat @ A @ B ) @ ( set_or4548717258645045905et_nat @ C2 @ D ) )
% 5.31/5.56 = ( ( ~ ( ord_less_eq_set_nat @ A @ B )
% 5.31/5.56 | ( ( ord_less_eq_set_nat @ C2 @ A )
% 5.31/5.56 & ( ord_less_eq_set_nat @ B @ D )
% 5.31/5.56 & ( ( ord_less_set_nat @ C2 @ A )
% 5.31/5.56 | ( ord_less_set_nat @ B @ D ) ) ) )
% 5.31/5.56 & ( ord_less_eq_set_nat @ C2 @ D ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % atLeastatMost_psubset_iff
% 5.31/5.56 thf(fact_3789_atLeastatMost__psubset__iff,axiom,
% 5.31/5.56 ! [A: rat,B: rat,C2: rat,D: rat] :
% 5.31/5.56 ( ( ord_less_set_rat @ ( set_or633870826150836451st_rat @ A @ B ) @ ( set_or633870826150836451st_rat @ C2 @ D ) )
% 5.31/5.56 = ( ( ~ ( ord_less_eq_rat @ A @ B )
% 5.31/5.56 | ( ( ord_less_eq_rat @ C2 @ A )
% 5.31/5.56 & ( ord_less_eq_rat @ B @ D )
% 5.31/5.56 & ( ( ord_less_rat @ C2 @ A )
% 5.31/5.56 | ( ord_less_rat @ B @ D ) ) ) )
% 5.31/5.56 & ( ord_less_eq_rat @ C2 @ D ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % atLeastatMost_psubset_iff
% 5.31/5.56 thf(fact_3790_atLeastatMost__psubset__iff,axiom,
% 5.31/5.56 ! [A: num,B: num,C2: num,D: num] :
% 5.31/5.56 ( ( ord_less_set_num @ ( set_or7049704709247886629st_num @ A @ B ) @ ( set_or7049704709247886629st_num @ C2 @ D ) )
% 5.31/5.56 = ( ( ~ ( ord_less_eq_num @ A @ B )
% 5.31/5.56 | ( ( ord_less_eq_num @ C2 @ A )
% 5.31/5.56 & ( ord_less_eq_num @ B @ D )
% 5.31/5.56 & ( ( ord_less_num @ C2 @ A )
% 5.31/5.56 | ( ord_less_num @ B @ D ) ) ) )
% 5.31/5.56 & ( ord_less_eq_num @ C2 @ D ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % atLeastatMost_psubset_iff
% 5.31/5.56 thf(fact_3791_atLeastatMost__psubset__iff,axiom,
% 5.31/5.56 ! [A: nat,B: nat,C2: nat,D: nat] :
% 5.31/5.56 ( ( ord_less_set_nat @ ( set_or1269000886237332187st_nat @ A @ B ) @ ( set_or1269000886237332187st_nat @ C2 @ D ) )
% 5.31/5.56 = ( ( ~ ( ord_less_eq_nat @ A @ B )
% 5.31/5.56 | ( ( ord_less_eq_nat @ C2 @ A )
% 5.31/5.56 & ( ord_less_eq_nat @ B @ D )
% 5.31/5.56 & ( ( ord_less_nat @ C2 @ A )
% 5.31/5.56 | ( ord_less_nat @ B @ D ) ) ) )
% 5.31/5.56 & ( ord_less_eq_nat @ C2 @ D ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % atLeastatMost_psubset_iff
% 5.31/5.56 thf(fact_3792_atLeastatMost__psubset__iff,axiom,
% 5.31/5.56 ! [A: int,B: int,C2: int,D: int] :
% 5.31/5.56 ( ( ord_less_set_int @ ( set_or1266510415728281911st_int @ A @ B ) @ ( set_or1266510415728281911st_int @ C2 @ D ) )
% 5.31/5.56 = ( ( ~ ( ord_less_eq_int @ A @ B )
% 5.31/5.56 | ( ( ord_less_eq_int @ C2 @ A )
% 5.31/5.56 & ( ord_less_eq_int @ B @ D )
% 5.31/5.56 & ( ( ord_less_int @ C2 @ A )
% 5.31/5.56 | ( ord_less_int @ B @ D ) ) ) )
% 5.31/5.56 & ( ord_less_eq_int @ C2 @ D ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % atLeastatMost_psubset_iff
% 5.31/5.56 thf(fact_3793_atLeastatMost__psubset__iff,axiom,
% 5.31/5.56 ! [A: real,B: real,C2: real,D: real] :
% 5.31/5.56 ( ( ord_less_set_real @ ( set_or1222579329274155063t_real @ A @ B ) @ ( set_or1222579329274155063t_real @ C2 @ D ) )
% 5.31/5.56 = ( ( ~ ( ord_less_eq_real @ A @ B )
% 5.31/5.56 | ( ( ord_less_eq_real @ C2 @ A )
% 5.31/5.56 & ( ord_less_eq_real @ B @ D )
% 5.31/5.56 & ( ( ord_less_real @ C2 @ A )
% 5.31/5.56 | ( ord_less_real @ B @ D ) ) ) )
% 5.31/5.56 & ( ord_less_eq_real @ C2 @ D ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % atLeastatMost_psubset_iff
% 5.31/5.56 thf(fact_3794_infinite__Icc,axiom,
% 5.31/5.56 ! [A: rat,B: rat] :
% 5.31/5.56 ( ( ord_less_rat @ A @ B )
% 5.31/5.56 => ~ ( finite_finite_rat @ ( set_or633870826150836451st_rat @ A @ B ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % infinite_Icc
% 5.31/5.56 thf(fact_3795_infinite__Icc,axiom,
% 5.31/5.56 ! [A: real,B: real] :
% 5.31/5.56 ( ( ord_less_real @ A @ B )
% 5.31/5.56 => ~ ( finite_finite_real @ ( set_or1222579329274155063t_real @ A @ B ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % infinite_Icc
% 5.31/5.56 thf(fact_3796_atLeastAtMost__singleton_H,axiom,
% 5.31/5.56 ! [A: nat,B: nat] :
% 5.31/5.56 ( ( A = B )
% 5.31/5.56 => ( ( set_or1269000886237332187st_nat @ A @ B )
% 5.31/5.56 = ( insert_nat @ A @ bot_bot_set_nat ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % atLeastAtMost_singleton'
% 5.31/5.56 thf(fact_3797_atLeastAtMost__singleton_H,axiom,
% 5.31/5.56 ! [A: int,B: int] :
% 5.31/5.56 ( ( A = B )
% 5.31/5.56 => ( ( set_or1266510415728281911st_int @ A @ B )
% 5.31/5.56 = ( insert_int @ A @ bot_bot_set_int ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % atLeastAtMost_singleton'
% 5.31/5.56 thf(fact_3798_atLeastAtMost__singleton_H,axiom,
% 5.31/5.56 ! [A: real,B: real] :
% 5.31/5.56 ( ( A = B )
% 5.31/5.56 => ( ( set_or1222579329274155063t_real @ A @ B )
% 5.31/5.56 = ( insert_real @ A @ bot_bot_set_real ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % atLeastAtMost_singleton'
% 5.31/5.56 thf(fact_3799_divide__right__mono__neg,axiom,
% 5.31/5.56 ! [A: real,B: real,C2: real] :
% 5.31/5.56 ( ( ord_less_eq_real @ A @ B )
% 5.31/5.56 => ( ( ord_less_eq_real @ C2 @ zero_zero_real )
% 5.31/5.56 => ( ord_less_eq_real @ ( divide_divide_real @ B @ C2 ) @ ( divide_divide_real @ A @ C2 ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % divide_right_mono_neg
% 5.31/5.56 thf(fact_3800_divide__right__mono__neg,axiom,
% 5.31/5.56 ! [A: rat,B: rat,C2: rat] :
% 5.31/5.56 ( ( ord_less_eq_rat @ A @ B )
% 5.31/5.56 => ( ( ord_less_eq_rat @ C2 @ zero_zero_rat )
% 5.31/5.56 => ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C2 ) @ ( divide_divide_rat @ A @ C2 ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % divide_right_mono_neg
% 5.31/5.56 thf(fact_3801_divide__nonpos__nonpos,axiom,
% 5.31/5.56 ! [X: real,Y: real] :
% 5.31/5.56 ( ( ord_less_eq_real @ X @ zero_zero_real )
% 5.31/5.56 => ( ( ord_less_eq_real @ Y @ zero_zero_real )
% 5.31/5.56 => ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ X @ Y ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % divide_nonpos_nonpos
% 5.31/5.56 thf(fact_3802_divide__nonpos__nonpos,axiom,
% 5.31/5.56 ! [X: rat,Y: rat] :
% 5.31/5.56 ( ( ord_less_eq_rat @ X @ zero_zero_rat )
% 5.31/5.56 => ( ( ord_less_eq_rat @ Y @ zero_zero_rat )
% 5.31/5.56 => ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ X @ Y ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % divide_nonpos_nonpos
% 5.31/5.56 thf(fact_3803_divide__nonpos__nonneg,axiom,
% 5.31/5.56 ! [X: real,Y: real] :
% 5.31/5.56 ( ( ord_less_eq_real @ X @ zero_zero_real )
% 5.31/5.56 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.31/5.56 => ( ord_less_eq_real @ ( divide_divide_real @ X @ Y ) @ zero_zero_real ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % divide_nonpos_nonneg
% 5.31/5.56 thf(fact_3804_divide__nonpos__nonneg,axiom,
% 5.31/5.56 ! [X: rat,Y: rat] :
% 5.31/5.56 ( ( ord_less_eq_rat @ X @ zero_zero_rat )
% 5.31/5.56 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 5.31/5.56 => ( ord_less_eq_rat @ ( divide_divide_rat @ X @ Y ) @ zero_zero_rat ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % divide_nonpos_nonneg
% 5.31/5.56 thf(fact_3805_divide__nonneg__nonpos,axiom,
% 5.31/5.56 ! [X: real,Y: real] :
% 5.31/5.56 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.31/5.56 => ( ( ord_less_eq_real @ Y @ zero_zero_real )
% 5.31/5.56 => ( ord_less_eq_real @ ( divide_divide_real @ X @ Y ) @ zero_zero_real ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % divide_nonneg_nonpos
% 5.31/5.56 thf(fact_3806_divide__nonneg__nonpos,axiom,
% 5.31/5.56 ! [X: rat,Y: rat] :
% 5.31/5.56 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 5.31/5.56 => ( ( ord_less_eq_rat @ Y @ zero_zero_rat )
% 5.31/5.56 => ( ord_less_eq_rat @ ( divide_divide_rat @ X @ Y ) @ zero_zero_rat ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % divide_nonneg_nonpos
% 5.31/5.56 thf(fact_3807_divide__nonneg__nonneg,axiom,
% 5.31/5.56 ! [X: real,Y: real] :
% 5.31/5.56 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.31/5.56 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.31/5.56 => ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ X @ Y ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % divide_nonneg_nonneg
% 5.31/5.56 thf(fact_3808_divide__nonneg__nonneg,axiom,
% 5.31/5.56 ! [X: rat,Y: rat] :
% 5.31/5.56 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 5.31/5.56 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 5.31/5.56 => ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ X @ Y ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % divide_nonneg_nonneg
% 5.31/5.56 thf(fact_3809_zero__le__divide__iff,axiom,
% 5.31/5.56 ! [A: real,B: real] :
% 5.31/5.56 ( ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ A @ B ) )
% 5.31/5.56 = ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.31/5.56 & ( ord_less_eq_real @ zero_zero_real @ B ) )
% 5.31/5.56 | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.31/5.56 & ( ord_less_eq_real @ B @ zero_zero_real ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % zero_le_divide_iff
% 5.31/5.56 thf(fact_3810_zero__le__divide__iff,axiom,
% 5.31/5.56 ! [A: rat,B: rat] :
% 5.31/5.56 ( ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ B ) )
% 5.31/5.56 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.31/5.56 & ( ord_less_eq_rat @ zero_zero_rat @ B ) )
% 5.31/5.56 | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.31/5.56 & ( ord_less_eq_rat @ B @ zero_zero_rat ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % zero_le_divide_iff
% 5.31/5.56 thf(fact_3811_divide__right__mono,axiom,
% 5.31/5.56 ! [A: real,B: real,C2: real] :
% 5.31/5.56 ( ( ord_less_eq_real @ A @ B )
% 5.31/5.56 => ( ( ord_less_eq_real @ zero_zero_real @ C2 )
% 5.31/5.56 => ( ord_less_eq_real @ ( divide_divide_real @ A @ C2 ) @ ( divide_divide_real @ B @ C2 ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % divide_right_mono
% 5.31/5.56 thf(fact_3812_divide__right__mono,axiom,
% 5.31/5.56 ! [A: rat,B: rat,C2: rat] :
% 5.31/5.56 ( ( ord_less_eq_rat @ A @ B )
% 5.31/5.56 => ( ( ord_less_eq_rat @ zero_zero_rat @ C2 )
% 5.31/5.56 => ( ord_less_eq_rat @ ( divide_divide_rat @ A @ C2 ) @ ( divide_divide_rat @ B @ C2 ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % divide_right_mono
% 5.31/5.56 thf(fact_3813_divide__le__0__iff,axiom,
% 5.31/5.56 ! [A: real,B: real] :
% 5.31/5.56 ( ( ord_less_eq_real @ ( divide_divide_real @ A @ B ) @ zero_zero_real )
% 5.31/5.56 = ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.31/5.56 & ( ord_less_eq_real @ B @ zero_zero_real ) )
% 5.31/5.56 | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.31/5.56 & ( ord_less_eq_real @ zero_zero_real @ B ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % divide_le_0_iff
% 5.31/5.56 thf(fact_3814_divide__le__0__iff,axiom,
% 5.31/5.56 ! [A: rat,B: rat] :
% 5.31/5.56 ( ( ord_less_eq_rat @ ( divide_divide_rat @ A @ B ) @ zero_zero_rat )
% 5.31/5.56 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.31/5.56 & ( ord_less_eq_rat @ B @ zero_zero_rat ) )
% 5.31/5.56 | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.31/5.56 & ( ord_less_eq_rat @ zero_zero_rat @ B ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % divide_le_0_iff
% 5.31/5.56 thf(fact_3815_divide__strict__right__mono__neg,axiom,
% 5.31/5.56 ! [B: real,A: real,C2: real] :
% 5.31/5.56 ( ( ord_less_real @ B @ A )
% 5.31/5.56 => ( ( ord_less_real @ C2 @ zero_zero_real )
% 5.31/5.56 => ( ord_less_real @ ( divide_divide_real @ A @ C2 ) @ ( divide_divide_real @ B @ C2 ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % divide_strict_right_mono_neg
% 5.31/5.56 thf(fact_3816_divide__strict__right__mono__neg,axiom,
% 5.31/5.56 ! [B: rat,A: rat,C2: rat] :
% 5.31/5.56 ( ( ord_less_rat @ B @ A )
% 5.31/5.56 => ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 5.31/5.56 => ( ord_less_rat @ ( divide_divide_rat @ A @ C2 ) @ ( divide_divide_rat @ B @ C2 ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % divide_strict_right_mono_neg
% 5.31/5.56 thf(fact_3817_divide__strict__right__mono,axiom,
% 5.31/5.56 ! [A: real,B: real,C2: real] :
% 5.31/5.56 ( ( ord_less_real @ A @ B )
% 5.31/5.56 => ( ( ord_less_real @ zero_zero_real @ C2 )
% 5.31/5.56 => ( ord_less_real @ ( divide_divide_real @ A @ C2 ) @ ( divide_divide_real @ B @ C2 ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % divide_strict_right_mono
% 5.31/5.56 thf(fact_3818_divide__strict__right__mono,axiom,
% 5.31/5.56 ! [A: rat,B: rat,C2: rat] :
% 5.31/5.56 ( ( ord_less_rat @ A @ B )
% 5.31/5.56 => ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 5.31/5.56 => ( ord_less_rat @ ( divide_divide_rat @ A @ C2 ) @ ( divide_divide_rat @ B @ C2 ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % divide_strict_right_mono
% 5.31/5.56 thf(fact_3819_zero__less__divide__iff,axiom,
% 5.31/5.56 ! [A: real,B: real] :
% 5.31/5.56 ( ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ A @ B ) )
% 5.31/5.56 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 5.31/5.56 & ( ord_less_real @ zero_zero_real @ B ) )
% 5.31/5.56 | ( ( ord_less_real @ A @ zero_zero_real )
% 5.31/5.56 & ( ord_less_real @ B @ zero_zero_real ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % zero_less_divide_iff
% 5.31/5.56 thf(fact_3820_zero__less__divide__iff,axiom,
% 5.31/5.56 ! [A: rat,B: rat] :
% 5.31/5.56 ( ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ B ) )
% 5.31/5.56 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.31/5.56 & ( ord_less_rat @ zero_zero_rat @ B ) )
% 5.31/5.56 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.31/5.56 & ( ord_less_rat @ B @ zero_zero_rat ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % zero_less_divide_iff
% 5.31/5.56 thf(fact_3821_divide__less__cancel,axiom,
% 5.31/5.56 ! [A: real,C2: real,B: real] :
% 5.31/5.56 ( ( ord_less_real @ ( divide_divide_real @ A @ C2 ) @ ( divide_divide_real @ B @ C2 ) )
% 5.31/5.56 = ( ( ( ord_less_real @ zero_zero_real @ C2 )
% 5.31/5.56 => ( ord_less_real @ A @ B ) )
% 5.31/5.56 & ( ( ord_less_real @ C2 @ zero_zero_real )
% 5.31/5.56 => ( ord_less_real @ B @ A ) )
% 5.31/5.56 & ( C2 != zero_zero_real ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % divide_less_cancel
% 5.31/5.56 thf(fact_3822_divide__less__cancel,axiom,
% 5.31/5.56 ! [A: rat,C2: rat,B: rat] :
% 5.31/5.56 ( ( ord_less_rat @ ( divide_divide_rat @ A @ C2 ) @ ( divide_divide_rat @ B @ C2 ) )
% 5.31/5.56 = ( ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 5.31/5.56 => ( ord_less_rat @ A @ B ) )
% 5.31/5.56 & ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 5.31/5.56 => ( ord_less_rat @ B @ A ) )
% 5.31/5.56 & ( C2 != zero_zero_rat ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % divide_less_cancel
% 5.31/5.56 thf(fact_3823_divide__less__0__iff,axiom,
% 5.31/5.56 ! [A: real,B: real] :
% 5.31/5.56 ( ( ord_less_real @ ( divide_divide_real @ A @ B ) @ zero_zero_real )
% 5.31/5.56 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 5.31/5.56 & ( ord_less_real @ B @ zero_zero_real ) )
% 5.31/5.56 | ( ( ord_less_real @ A @ zero_zero_real )
% 5.31/5.56 & ( ord_less_real @ zero_zero_real @ B ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % divide_less_0_iff
% 5.31/5.56 thf(fact_3824_divide__less__0__iff,axiom,
% 5.31/5.56 ! [A: rat,B: rat] :
% 5.31/5.56 ( ( ord_less_rat @ ( divide_divide_rat @ A @ B ) @ zero_zero_rat )
% 5.31/5.56 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.31/5.56 & ( ord_less_rat @ B @ zero_zero_rat ) )
% 5.31/5.56 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.31/5.56 & ( ord_less_rat @ zero_zero_rat @ B ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % divide_less_0_iff
% 5.31/5.56 thf(fact_3825_divide__pos__pos,axiom,
% 5.31/5.56 ! [X: real,Y: real] :
% 5.31/5.56 ( ( ord_less_real @ zero_zero_real @ X )
% 5.31/5.56 => ( ( ord_less_real @ zero_zero_real @ Y )
% 5.31/5.56 => ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ X @ Y ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % divide_pos_pos
% 5.31/5.56 thf(fact_3826_divide__pos__pos,axiom,
% 5.31/5.56 ! [X: rat,Y: rat] :
% 5.31/5.56 ( ( ord_less_rat @ zero_zero_rat @ X )
% 5.31/5.56 => ( ( ord_less_rat @ zero_zero_rat @ Y )
% 5.31/5.56 => ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ X @ Y ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % divide_pos_pos
% 5.31/5.56 thf(fact_3827_divide__pos__neg,axiom,
% 5.31/5.56 ! [X: real,Y: real] :
% 5.31/5.56 ( ( ord_less_real @ zero_zero_real @ X )
% 5.31/5.56 => ( ( ord_less_real @ Y @ zero_zero_real )
% 5.31/5.56 => ( ord_less_real @ ( divide_divide_real @ X @ Y ) @ zero_zero_real ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % divide_pos_neg
% 5.31/5.56 thf(fact_3828_divide__pos__neg,axiom,
% 5.31/5.56 ! [X: rat,Y: rat] :
% 5.31/5.56 ( ( ord_less_rat @ zero_zero_rat @ X )
% 5.31/5.56 => ( ( ord_less_rat @ Y @ zero_zero_rat )
% 5.31/5.56 => ( ord_less_rat @ ( divide_divide_rat @ X @ Y ) @ zero_zero_rat ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % divide_pos_neg
% 5.31/5.56 thf(fact_3829_divide__neg__pos,axiom,
% 5.31/5.56 ! [X: real,Y: real] :
% 5.31/5.56 ( ( ord_less_real @ X @ zero_zero_real )
% 5.31/5.56 => ( ( ord_less_real @ zero_zero_real @ Y )
% 5.31/5.56 => ( ord_less_real @ ( divide_divide_real @ X @ Y ) @ zero_zero_real ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % divide_neg_pos
% 5.31/5.56 thf(fact_3830_divide__neg__pos,axiom,
% 5.31/5.56 ! [X: rat,Y: rat] :
% 5.31/5.56 ( ( ord_less_rat @ X @ zero_zero_rat )
% 5.31/5.56 => ( ( ord_less_rat @ zero_zero_rat @ Y )
% 5.31/5.56 => ( ord_less_rat @ ( divide_divide_rat @ X @ Y ) @ zero_zero_rat ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % divide_neg_pos
% 5.31/5.56 thf(fact_3831_divide__neg__neg,axiom,
% 5.31/5.56 ! [X: real,Y: real] :
% 5.31/5.56 ( ( ord_less_real @ X @ zero_zero_real )
% 5.31/5.56 => ( ( ord_less_real @ Y @ zero_zero_real )
% 5.31/5.56 => ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ X @ Y ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % divide_neg_neg
% 5.31/5.56 thf(fact_3832_divide__neg__neg,axiom,
% 5.31/5.56 ! [X: rat,Y: rat] :
% 5.31/5.56 ( ( ord_less_rat @ X @ zero_zero_rat )
% 5.31/5.56 => ( ( ord_less_rat @ Y @ zero_zero_rat )
% 5.31/5.56 => ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ X @ Y ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % divide_neg_neg
% 5.31/5.56 thf(fact_3833_all__nat__less,axiom,
% 5.31/5.56 ! [N: nat,P2: nat > $o] :
% 5.31/5.56 ( ( ! [M6: nat] :
% 5.31/5.56 ( ( ord_less_eq_nat @ M6 @ N )
% 5.31/5.56 => ( P2 @ M6 ) ) )
% 5.31/5.56 = ( ! [X4: nat] :
% 5.31/5.56 ( ( member_nat @ X4 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 5.31/5.56 => ( P2 @ X4 ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % all_nat_less
% 5.31/5.56 thf(fact_3834_ex__nat__less,axiom,
% 5.31/5.56 ! [N: nat,P2: nat > $o] :
% 5.31/5.56 ( ( ? [M6: nat] :
% 5.31/5.56 ( ( ord_less_eq_nat @ M6 @ N )
% 5.31/5.56 & ( P2 @ M6 ) ) )
% 5.31/5.56 = ( ? [X4: nat] :
% 5.31/5.56 ( ( member_nat @ X4 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 5.31/5.56 & ( P2 @ X4 ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % ex_nat_less
% 5.31/5.56 thf(fact_3835_frac__eq__eq,axiom,
% 5.31/5.56 ! [Y: complex,Z3: complex,X: complex,W2: complex] :
% 5.31/5.56 ( ( Y != zero_zero_complex )
% 5.31/5.56 => ( ( Z3 != zero_zero_complex )
% 5.31/5.56 => ( ( ( divide1717551699836669952omplex @ X @ Y )
% 5.31/5.56 = ( divide1717551699836669952omplex @ W2 @ Z3 ) )
% 5.31/5.56 = ( ( times_times_complex @ X @ Z3 )
% 5.31/5.56 = ( times_times_complex @ W2 @ Y ) ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % frac_eq_eq
% 5.31/5.56 thf(fact_3836_frac__eq__eq,axiom,
% 5.31/5.56 ! [Y: real,Z3: real,X: real,W2: real] :
% 5.31/5.56 ( ( Y != zero_zero_real )
% 5.31/5.56 => ( ( Z3 != zero_zero_real )
% 5.31/5.56 => ( ( ( divide_divide_real @ X @ Y )
% 5.31/5.56 = ( divide_divide_real @ W2 @ Z3 ) )
% 5.31/5.56 = ( ( times_times_real @ X @ Z3 )
% 5.31/5.56 = ( times_times_real @ W2 @ Y ) ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % frac_eq_eq
% 5.31/5.56 thf(fact_3837_frac__eq__eq,axiom,
% 5.31/5.56 ! [Y: rat,Z3: rat,X: rat,W2: rat] :
% 5.31/5.56 ( ( Y != zero_zero_rat )
% 5.31/5.56 => ( ( Z3 != zero_zero_rat )
% 5.31/5.56 => ( ( ( divide_divide_rat @ X @ Y )
% 5.31/5.56 = ( divide_divide_rat @ W2 @ Z3 ) )
% 5.31/5.56 = ( ( times_times_rat @ X @ Z3 )
% 5.31/5.56 = ( times_times_rat @ W2 @ Y ) ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % frac_eq_eq
% 5.31/5.56 thf(fact_3838_divide__eq__eq,axiom,
% 5.31/5.56 ! [B: complex,C2: complex,A: complex] :
% 5.31/5.56 ( ( ( divide1717551699836669952omplex @ B @ C2 )
% 5.31/5.56 = A )
% 5.31/5.56 = ( ( ( C2 != zero_zero_complex )
% 5.31/5.56 => ( B
% 5.31/5.56 = ( times_times_complex @ A @ C2 ) ) )
% 5.31/5.56 & ( ( C2 = zero_zero_complex )
% 5.31/5.56 => ( A = zero_zero_complex ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % divide_eq_eq
% 5.31/5.56 thf(fact_3839_divide__eq__eq,axiom,
% 5.31/5.56 ! [B: real,C2: real,A: real] :
% 5.31/5.56 ( ( ( divide_divide_real @ B @ C2 )
% 5.31/5.56 = A )
% 5.31/5.56 = ( ( ( C2 != zero_zero_real )
% 5.31/5.56 => ( B
% 5.31/5.56 = ( times_times_real @ A @ C2 ) ) )
% 5.31/5.56 & ( ( C2 = zero_zero_real )
% 5.31/5.56 => ( A = zero_zero_real ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % divide_eq_eq
% 5.31/5.56 thf(fact_3840_divide__eq__eq,axiom,
% 5.31/5.56 ! [B: rat,C2: rat,A: rat] :
% 5.31/5.56 ( ( ( divide_divide_rat @ B @ C2 )
% 5.31/5.56 = A )
% 5.31/5.56 = ( ( ( C2 != zero_zero_rat )
% 5.31/5.56 => ( B
% 5.31/5.56 = ( times_times_rat @ A @ C2 ) ) )
% 5.31/5.56 & ( ( C2 = zero_zero_rat )
% 5.31/5.56 => ( A = zero_zero_rat ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % divide_eq_eq
% 5.31/5.56 thf(fact_3841_eq__divide__eq,axiom,
% 5.31/5.56 ! [A: complex,B: complex,C2: complex] :
% 5.31/5.56 ( ( A
% 5.31/5.56 = ( divide1717551699836669952omplex @ B @ C2 ) )
% 5.31/5.56 = ( ( ( C2 != zero_zero_complex )
% 5.31/5.56 => ( ( times_times_complex @ A @ C2 )
% 5.31/5.56 = B ) )
% 5.31/5.56 & ( ( C2 = zero_zero_complex )
% 5.31/5.56 => ( A = zero_zero_complex ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % eq_divide_eq
% 5.31/5.56 thf(fact_3842_eq__divide__eq,axiom,
% 5.31/5.56 ! [A: real,B: real,C2: real] :
% 5.31/5.56 ( ( A
% 5.31/5.56 = ( divide_divide_real @ B @ C2 ) )
% 5.31/5.56 = ( ( ( C2 != zero_zero_real )
% 5.31/5.56 => ( ( times_times_real @ A @ C2 )
% 5.31/5.56 = B ) )
% 5.31/5.56 & ( ( C2 = zero_zero_real )
% 5.31/5.56 => ( A = zero_zero_real ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % eq_divide_eq
% 5.31/5.56 thf(fact_3843_eq__divide__eq,axiom,
% 5.31/5.56 ! [A: rat,B: rat,C2: rat] :
% 5.31/5.56 ( ( A
% 5.31/5.56 = ( divide_divide_rat @ B @ C2 ) )
% 5.31/5.56 = ( ( ( C2 != zero_zero_rat )
% 5.31/5.56 => ( ( times_times_rat @ A @ C2 )
% 5.31/5.56 = B ) )
% 5.31/5.56 & ( ( C2 = zero_zero_rat )
% 5.31/5.56 => ( A = zero_zero_rat ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % eq_divide_eq
% 5.31/5.56 thf(fact_3844_divide__eq__imp,axiom,
% 5.31/5.56 ! [C2: complex,B: complex,A: complex] :
% 5.31/5.56 ( ( C2 != zero_zero_complex )
% 5.31/5.56 => ( ( B
% 5.31/5.56 = ( times_times_complex @ A @ C2 ) )
% 5.31/5.56 => ( ( divide1717551699836669952omplex @ B @ C2 )
% 5.31/5.56 = A ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % divide_eq_imp
% 5.31/5.56 thf(fact_3845_divide__eq__imp,axiom,
% 5.31/5.56 ! [C2: real,B: real,A: real] :
% 5.31/5.56 ( ( C2 != zero_zero_real )
% 5.31/5.56 => ( ( B
% 5.31/5.56 = ( times_times_real @ A @ C2 ) )
% 5.31/5.56 => ( ( divide_divide_real @ B @ C2 )
% 5.31/5.56 = A ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % divide_eq_imp
% 5.31/5.56 thf(fact_3846_divide__eq__imp,axiom,
% 5.31/5.56 ! [C2: rat,B: rat,A: rat] :
% 5.31/5.56 ( ( C2 != zero_zero_rat )
% 5.31/5.56 => ( ( B
% 5.31/5.56 = ( times_times_rat @ A @ C2 ) )
% 5.31/5.56 => ( ( divide_divide_rat @ B @ C2 )
% 5.31/5.56 = A ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % divide_eq_imp
% 5.31/5.56 thf(fact_3847_eq__divide__imp,axiom,
% 5.31/5.56 ! [C2: complex,A: complex,B: complex] :
% 5.31/5.56 ( ( C2 != zero_zero_complex )
% 5.31/5.56 => ( ( ( times_times_complex @ A @ C2 )
% 5.31/5.56 = B )
% 5.31/5.56 => ( A
% 5.31/5.56 = ( divide1717551699836669952omplex @ B @ C2 ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % eq_divide_imp
% 5.31/5.56 thf(fact_3848_eq__divide__imp,axiom,
% 5.31/5.56 ! [C2: real,A: real,B: real] :
% 5.31/5.56 ( ( C2 != zero_zero_real )
% 5.31/5.56 => ( ( ( times_times_real @ A @ C2 )
% 5.31/5.56 = B )
% 5.31/5.56 => ( A
% 5.31/5.56 = ( divide_divide_real @ B @ C2 ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % eq_divide_imp
% 5.31/5.56 thf(fact_3849_eq__divide__imp,axiom,
% 5.31/5.56 ! [C2: rat,A: rat,B: rat] :
% 5.31/5.56 ( ( C2 != zero_zero_rat )
% 5.31/5.56 => ( ( ( times_times_rat @ A @ C2 )
% 5.31/5.56 = B )
% 5.31/5.56 => ( A
% 5.31/5.56 = ( divide_divide_rat @ B @ C2 ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % eq_divide_imp
% 5.31/5.56 thf(fact_3850_nonzero__divide__eq__eq,axiom,
% 5.31/5.56 ! [C2: complex,B: complex,A: complex] :
% 5.31/5.56 ( ( C2 != zero_zero_complex )
% 5.31/5.56 => ( ( ( divide1717551699836669952omplex @ B @ C2 )
% 5.31/5.56 = A )
% 5.31/5.56 = ( B
% 5.31/5.56 = ( times_times_complex @ A @ C2 ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % nonzero_divide_eq_eq
% 5.31/5.56 thf(fact_3851_nonzero__divide__eq__eq,axiom,
% 5.31/5.56 ! [C2: real,B: real,A: real] :
% 5.31/5.56 ( ( C2 != zero_zero_real )
% 5.31/5.56 => ( ( ( divide_divide_real @ B @ C2 )
% 5.31/5.56 = A )
% 5.31/5.56 = ( B
% 5.31/5.56 = ( times_times_real @ A @ C2 ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % nonzero_divide_eq_eq
% 5.31/5.56 thf(fact_3852_nonzero__divide__eq__eq,axiom,
% 5.31/5.56 ! [C2: rat,B: rat,A: rat] :
% 5.31/5.56 ( ( C2 != zero_zero_rat )
% 5.31/5.56 => ( ( ( divide_divide_rat @ B @ C2 )
% 5.31/5.56 = A )
% 5.31/5.56 = ( B
% 5.31/5.56 = ( times_times_rat @ A @ C2 ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % nonzero_divide_eq_eq
% 5.31/5.56 thf(fact_3853_nonzero__eq__divide__eq,axiom,
% 5.31/5.56 ! [C2: complex,A: complex,B: complex] :
% 5.31/5.56 ( ( C2 != zero_zero_complex )
% 5.31/5.56 => ( ( A
% 5.31/5.56 = ( divide1717551699836669952omplex @ B @ C2 ) )
% 5.31/5.56 = ( ( times_times_complex @ A @ C2 )
% 5.31/5.56 = B ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % nonzero_eq_divide_eq
% 5.31/5.56 thf(fact_3854_nonzero__eq__divide__eq,axiom,
% 5.31/5.56 ! [C2: real,A: real,B: real] :
% 5.31/5.56 ( ( C2 != zero_zero_real )
% 5.31/5.56 => ( ( A
% 5.31/5.56 = ( divide_divide_real @ B @ C2 ) )
% 5.31/5.56 = ( ( times_times_real @ A @ C2 )
% 5.31/5.56 = B ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % nonzero_eq_divide_eq
% 5.31/5.56 thf(fact_3855_nonzero__eq__divide__eq,axiom,
% 5.31/5.56 ! [C2: rat,A: rat,B: rat] :
% 5.31/5.56 ( ( C2 != zero_zero_rat )
% 5.31/5.56 => ( ( A
% 5.31/5.56 = ( divide_divide_rat @ B @ C2 ) )
% 5.31/5.56 = ( ( times_times_rat @ A @ C2 )
% 5.31/5.56 = B ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % nonzero_eq_divide_eq
% 5.31/5.56 thf(fact_3856_right__inverse__eq,axiom,
% 5.31/5.56 ! [B: complex,A: complex] :
% 5.31/5.56 ( ( B != zero_zero_complex )
% 5.31/5.56 => ( ( ( divide1717551699836669952omplex @ A @ B )
% 5.31/5.56 = one_one_complex )
% 5.31/5.56 = ( A = B ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % right_inverse_eq
% 5.31/5.56 thf(fact_3857_right__inverse__eq,axiom,
% 5.31/5.56 ! [B: real,A: real] :
% 5.31/5.56 ( ( B != zero_zero_real )
% 5.31/5.56 => ( ( ( divide_divide_real @ A @ B )
% 5.31/5.56 = one_one_real )
% 5.31/5.56 = ( A = B ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % right_inverse_eq
% 5.31/5.56 thf(fact_3858_right__inverse__eq,axiom,
% 5.31/5.56 ! [B: rat,A: rat] :
% 5.31/5.56 ( ( B != zero_zero_rat )
% 5.31/5.56 => ( ( ( divide_divide_rat @ A @ B )
% 5.31/5.56 = one_one_rat )
% 5.31/5.56 = ( A = B ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % right_inverse_eq
% 5.31/5.56 thf(fact_3859_divide__numeral__1,axiom,
% 5.31/5.56 ! [A: complex] :
% 5.31/5.56 ( ( divide1717551699836669952omplex @ A @ ( numera6690914467698888265omplex @ one ) )
% 5.31/5.56 = A ) ).
% 5.31/5.56
% 5.31/5.56 % divide_numeral_1
% 5.31/5.56 thf(fact_3860_divide__numeral__1,axiom,
% 5.31/5.56 ! [A: real] :
% 5.31/5.56 ( ( divide_divide_real @ A @ ( numeral_numeral_real @ one ) )
% 5.31/5.56 = A ) ).
% 5.31/5.56
% 5.31/5.56 % divide_numeral_1
% 5.31/5.56 thf(fact_3861_divide__numeral__1,axiom,
% 5.31/5.56 ! [A: rat] :
% 5.31/5.56 ( ( divide_divide_rat @ A @ ( numeral_numeral_rat @ one ) )
% 5.31/5.56 = A ) ).
% 5.31/5.56
% 5.31/5.56 % divide_numeral_1
% 5.31/5.56 thf(fact_3862_div__positive,axiom,
% 5.31/5.56 ! [B: nat,A: nat] :
% 5.31/5.56 ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.31/5.56 => ( ( ord_less_eq_nat @ B @ A )
% 5.31/5.56 => ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % div_positive
% 5.31/5.56 thf(fact_3863_div__positive,axiom,
% 5.31/5.56 ! [B: int,A: int] :
% 5.31/5.56 ( ( ord_less_int @ zero_zero_int @ B )
% 5.31/5.56 => ( ( ord_less_eq_int @ B @ A )
% 5.31/5.56 => ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % div_positive
% 5.31/5.56 thf(fact_3864_unique__euclidean__semiring__numeral__class_Odiv__less,axiom,
% 5.31/5.56 ! [A: nat,B: nat] :
% 5.31/5.56 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.31/5.56 => ( ( ord_less_nat @ A @ B )
% 5.31/5.56 => ( ( divide_divide_nat @ A @ B )
% 5.31/5.56 = zero_zero_nat ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % unique_euclidean_semiring_numeral_class.div_less
% 5.31/5.56 thf(fact_3865_unique__euclidean__semiring__numeral__class_Odiv__less,axiom,
% 5.31/5.56 ! [A: int,B: int] :
% 5.31/5.56 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.31/5.56 => ( ( ord_less_int @ A @ B )
% 5.31/5.56 => ( ( divide_divide_int @ A @ B )
% 5.31/5.56 = zero_zero_int ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % unique_euclidean_semiring_numeral_class.div_less
% 5.31/5.56 thf(fact_3866_divide__nonpos__pos,axiom,
% 5.31/5.56 ! [X: real,Y: real] :
% 5.31/5.56 ( ( ord_less_eq_real @ X @ zero_zero_real )
% 5.31/5.56 => ( ( ord_less_real @ zero_zero_real @ Y )
% 5.31/5.56 => ( ord_less_eq_real @ ( divide_divide_real @ X @ Y ) @ zero_zero_real ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % divide_nonpos_pos
% 5.31/5.56 thf(fact_3867_divide__nonpos__pos,axiom,
% 5.31/5.56 ! [X: rat,Y: rat] :
% 5.31/5.56 ( ( ord_less_eq_rat @ X @ zero_zero_rat )
% 5.31/5.56 => ( ( ord_less_rat @ zero_zero_rat @ Y )
% 5.31/5.56 => ( ord_less_eq_rat @ ( divide_divide_rat @ X @ Y ) @ zero_zero_rat ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % divide_nonpos_pos
% 5.31/5.56 thf(fact_3868_divide__nonpos__neg,axiom,
% 5.31/5.56 ! [X: real,Y: real] :
% 5.31/5.56 ( ( ord_less_eq_real @ X @ zero_zero_real )
% 5.31/5.56 => ( ( ord_less_real @ Y @ zero_zero_real )
% 5.31/5.56 => ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ X @ Y ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % divide_nonpos_neg
% 5.31/5.56 thf(fact_3869_divide__nonpos__neg,axiom,
% 5.31/5.56 ! [X: rat,Y: rat] :
% 5.31/5.56 ( ( ord_less_eq_rat @ X @ zero_zero_rat )
% 5.31/5.56 => ( ( ord_less_rat @ Y @ zero_zero_rat )
% 5.31/5.56 => ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ X @ Y ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % divide_nonpos_neg
% 5.31/5.56 thf(fact_3870_divide__nonneg__pos,axiom,
% 5.31/5.56 ! [X: real,Y: real] :
% 5.31/5.56 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.31/5.56 => ( ( ord_less_real @ zero_zero_real @ Y )
% 5.31/5.56 => ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ X @ Y ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % divide_nonneg_pos
% 5.31/5.56 thf(fact_3871_divide__nonneg__pos,axiom,
% 5.31/5.56 ! [X: rat,Y: rat] :
% 5.31/5.56 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 5.31/5.56 => ( ( ord_less_rat @ zero_zero_rat @ Y )
% 5.31/5.56 => ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ X @ Y ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % divide_nonneg_pos
% 5.31/5.56 thf(fact_3872_divide__nonneg__neg,axiom,
% 5.31/5.56 ! [X: real,Y: real] :
% 5.31/5.56 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.31/5.56 => ( ( ord_less_real @ Y @ zero_zero_real )
% 5.31/5.56 => ( ord_less_eq_real @ ( divide_divide_real @ X @ Y ) @ zero_zero_real ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % divide_nonneg_neg
% 5.31/5.56 thf(fact_3873_divide__nonneg__neg,axiom,
% 5.31/5.56 ! [X: rat,Y: rat] :
% 5.31/5.56 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 5.31/5.56 => ( ( ord_less_rat @ Y @ zero_zero_rat )
% 5.31/5.56 => ( ord_less_eq_rat @ ( divide_divide_rat @ X @ Y ) @ zero_zero_rat ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % divide_nonneg_neg
% 5.31/5.56 thf(fact_3874_divide__le__cancel,axiom,
% 5.31/5.56 ! [A: real,C2: real,B: real] :
% 5.31/5.56 ( ( ord_less_eq_real @ ( divide_divide_real @ A @ C2 ) @ ( divide_divide_real @ B @ C2 ) )
% 5.31/5.56 = ( ( ( ord_less_real @ zero_zero_real @ C2 )
% 5.31/5.56 => ( ord_less_eq_real @ A @ B ) )
% 5.31/5.56 & ( ( ord_less_real @ C2 @ zero_zero_real )
% 5.31/5.56 => ( ord_less_eq_real @ B @ A ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % divide_le_cancel
% 5.31/5.56 thf(fact_3875_divide__le__cancel,axiom,
% 5.31/5.56 ! [A: rat,C2: rat,B: rat] :
% 5.31/5.56 ( ( ord_less_eq_rat @ ( divide_divide_rat @ A @ C2 ) @ ( divide_divide_rat @ B @ C2 ) )
% 5.31/5.56 = ( ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 5.31/5.56 => ( ord_less_eq_rat @ A @ B ) )
% 5.31/5.56 & ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 5.31/5.56 => ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % divide_le_cancel
% 5.31/5.56 thf(fact_3876_frac__less2,axiom,
% 5.31/5.56 ! [X: real,Y: real,W2: real,Z3: real] :
% 5.31/5.56 ( ( ord_less_real @ zero_zero_real @ X )
% 5.31/5.56 => ( ( ord_less_eq_real @ X @ Y )
% 5.31/5.56 => ( ( ord_less_real @ zero_zero_real @ W2 )
% 5.31/5.56 => ( ( ord_less_real @ W2 @ Z3 )
% 5.31/5.56 => ( ord_less_real @ ( divide_divide_real @ X @ Z3 ) @ ( divide_divide_real @ Y @ W2 ) ) ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % frac_less2
% 5.31/5.56 thf(fact_3877_frac__less2,axiom,
% 5.31/5.56 ! [X: rat,Y: rat,W2: rat,Z3: rat] :
% 5.31/5.56 ( ( ord_less_rat @ zero_zero_rat @ X )
% 5.31/5.56 => ( ( ord_less_eq_rat @ X @ Y )
% 5.31/5.56 => ( ( ord_less_rat @ zero_zero_rat @ W2 )
% 5.31/5.56 => ( ( ord_less_rat @ W2 @ Z3 )
% 5.31/5.56 => ( ord_less_rat @ ( divide_divide_rat @ X @ Z3 ) @ ( divide_divide_rat @ Y @ W2 ) ) ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % frac_less2
% 5.31/5.56 thf(fact_3878_frac__less,axiom,
% 5.31/5.56 ! [X: real,Y: real,W2: real,Z3: real] :
% 5.31/5.56 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.31/5.56 => ( ( ord_less_real @ X @ Y )
% 5.31/5.56 => ( ( ord_less_real @ zero_zero_real @ W2 )
% 5.31/5.56 => ( ( ord_less_eq_real @ W2 @ Z3 )
% 5.31/5.56 => ( ord_less_real @ ( divide_divide_real @ X @ Z3 ) @ ( divide_divide_real @ Y @ W2 ) ) ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % frac_less
% 5.31/5.56 thf(fact_3879_frac__less,axiom,
% 5.31/5.56 ! [X: rat,Y: rat,W2: rat,Z3: rat] :
% 5.31/5.56 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 5.31/5.56 => ( ( ord_less_rat @ X @ Y )
% 5.31/5.56 => ( ( ord_less_rat @ zero_zero_rat @ W2 )
% 5.31/5.56 => ( ( ord_less_eq_rat @ W2 @ Z3 )
% 5.31/5.56 => ( ord_less_rat @ ( divide_divide_rat @ X @ Z3 ) @ ( divide_divide_rat @ Y @ W2 ) ) ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % frac_less
% 5.31/5.56 thf(fact_3880_frac__le,axiom,
% 5.31/5.56 ! [Y: real,X: real,W2: real,Z3: real] :
% 5.31/5.56 ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.31/5.56 => ( ( ord_less_eq_real @ X @ Y )
% 5.31/5.56 => ( ( ord_less_real @ zero_zero_real @ W2 )
% 5.31/5.56 => ( ( ord_less_eq_real @ W2 @ Z3 )
% 5.31/5.56 => ( ord_less_eq_real @ ( divide_divide_real @ X @ Z3 ) @ ( divide_divide_real @ Y @ W2 ) ) ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % frac_le
% 5.31/5.56 thf(fact_3881_frac__le,axiom,
% 5.31/5.56 ! [Y: rat,X: rat,W2: rat,Z3: rat] :
% 5.31/5.56 ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 5.31/5.56 => ( ( ord_less_eq_rat @ X @ Y )
% 5.31/5.56 => ( ( ord_less_rat @ zero_zero_rat @ W2 )
% 5.31/5.56 => ( ( ord_less_eq_rat @ W2 @ Z3 )
% 5.31/5.56 => ( ord_less_eq_rat @ ( divide_divide_rat @ X @ Z3 ) @ ( divide_divide_rat @ Y @ W2 ) ) ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % frac_le
% 5.31/5.56 thf(fact_3882_unique__euclidean__semiring__numeral__class_Odiv__mult2__eq,axiom,
% 5.31/5.56 ! [C2: nat,A: nat,B: nat] :
% 5.31/5.56 ( ( ord_less_eq_nat @ zero_zero_nat @ C2 )
% 5.31/5.56 => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ C2 ) )
% 5.31/5.56 = ( divide_divide_nat @ ( divide_divide_nat @ A @ B ) @ C2 ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % unique_euclidean_semiring_numeral_class.div_mult2_eq
% 5.31/5.56 thf(fact_3883_unique__euclidean__semiring__numeral__class_Odiv__mult2__eq,axiom,
% 5.31/5.56 ! [C2: int,A: int,B: int] :
% 5.31/5.56 ( ( ord_less_eq_int @ zero_zero_int @ C2 )
% 5.31/5.56 => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C2 ) )
% 5.31/5.56 = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C2 ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % unique_euclidean_semiring_numeral_class.div_mult2_eq
% 5.31/5.56 thf(fact_3884_divide__less__eq,axiom,
% 5.31/5.56 ! [B: real,C2: real,A: real] :
% 5.31/5.56 ( ( ord_less_real @ ( divide_divide_real @ B @ C2 ) @ A )
% 5.31/5.56 = ( ( ( ord_less_real @ zero_zero_real @ C2 )
% 5.31/5.56 => ( ord_less_real @ B @ ( times_times_real @ A @ C2 ) ) )
% 5.31/5.56 & ( ~ ( ord_less_real @ zero_zero_real @ C2 )
% 5.31/5.56 => ( ( ( ord_less_real @ C2 @ zero_zero_real )
% 5.31/5.56 => ( ord_less_real @ ( times_times_real @ A @ C2 ) @ B ) )
% 5.31/5.56 & ( ~ ( ord_less_real @ C2 @ zero_zero_real )
% 5.31/5.56 => ( ord_less_real @ zero_zero_real @ A ) ) ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % divide_less_eq
% 5.31/5.56 thf(fact_3885_divide__less__eq,axiom,
% 5.31/5.56 ! [B: rat,C2: rat,A: rat] :
% 5.31/5.56 ( ( ord_less_rat @ ( divide_divide_rat @ B @ C2 ) @ A )
% 5.31/5.56 = ( ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 5.31/5.56 => ( ord_less_rat @ B @ ( times_times_rat @ A @ C2 ) ) )
% 5.31/5.56 & ( ~ ( ord_less_rat @ zero_zero_rat @ C2 )
% 5.31/5.56 => ( ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 5.31/5.56 => ( ord_less_rat @ ( times_times_rat @ A @ C2 ) @ B ) )
% 5.31/5.56 & ( ~ ( ord_less_rat @ C2 @ zero_zero_rat )
% 5.31/5.56 => ( ord_less_rat @ zero_zero_rat @ A ) ) ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % divide_less_eq
% 5.31/5.56 thf(fact_3886_less__divide__eq,axiom,
% 5.31/5.56 ! [A: real,B: real,C2: real] :
% 5.31/5.56 ( ( ord_less_real @ A @ ( divide_divide_real @ B @ C2 ) )
% 5.31/5.56 = ( ( ( ord_less_real @ zero_zero_real @ C2 )
% 5.31/5.56 => ( ord_less_real @ ( times_times_real @ A @ C2 ) @ B ) )
% 5.31/5.56 & ( ~ ( ord_less_real @ zero_zero_real @ C2 )
% 5.31/5.56 => ( ( ( ord_less_real @ C2 @ zero_zero_real )
% 5.31/5.56 => ( ord_less_real @ B @ ( times_times_real @ A @ C2 ) ) )
% 5.31/5.56 & ( ~ ( ord_less_real @ C2 @ zero_zero_real )
% 5.31/5.56 => ( ord_less_real @ A @ zero_zero_real ) ) ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % less_divide_eq
% 5.31/5.56 thf(fact_3887_less__divide__eq,axiom,
% 5.31/5.56 ! [A: rat,B: rat,C2: rat] :
% 5.31/5.56 ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ C2 ) )
% 5.31/5.56 = ( ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 5.31/5.56 => ( ord_less_rat @ ( times_times_rat @ A @ C2 ) @ B ) )
% 5.31/5.56 & ( ~ ( ord_less_rat @ zero_zero_rat @ C2 )
% 5.31/5.56 => ( ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 5.31/5.56 => ( ord_less_rat @ B @ ( times_times_rat @ A @ C2 ) ) )
% 5.31/5.56 & ( ~ ( ord_less_rat @ C2 @ zero_zero_rat )
% 5.31/5.56 => ( ord_less_rat @ A @ zero_zero_rat ) ) ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % less_divide_eq
% 5.31/5.56 thf(fact_3888_neg__divide__less__eq,axiom,
% 5.31/5.56 ! [C2: real,B: real,A: real] :
% 5.31/5.56 ( ( ord_less_real @ C2 @ zero_zero_real )
% 5.31/5.56 => ( ( ord_less_real @ ( divide_divide_real @ B @ C2 ) @ A )
% 5.31/5.56 = ( ord_less_real @ ( times_times_real @ A @ C2 ) @ B ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % neg_divide_less_eq
% 5.31/5.56 thf(fact_3889_neg__divide__less__eq,axiom,
% 5.31/5.56 ! [C2: rat,B: rat,A: rat] :
% 5.31/5.56 ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 5.31/5.56 => ( ( ord_less_rat @ ( divide_divide_rat @ B @ C2 ) @ A )
% 5.31/5.56 = ( ord_less_rat @ ( times_times_rat @ A @ C2 ) @ B ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % neg_divide_less_eq
% 5.31/5.56 thf(fact_3890_neg__less__divide__eq,axiom,
% 5.31/5.56 ! [C2: real,A: real,B: real] :
% 5.31/5.56 ( ( ord_less_real @ C2 @ zero_zero_real )
% 5.31/5.56 => ( ( ord_less_real @ A @ ( divide_divide_real @ B @ C2 ) )
% 5.31/5.56 = ( ord_less_real @ B @ ( times_times_real @ A @ C2 ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % neg_less_divide_eq
% 5.31/5.56 thf(fact_3891_neg__less__divide__eq,axiom,
% 5.31/5.56 ! [C2: rat,A: rat,B: rat] :
% 5.31/5.56 ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 5.31/5.56 => ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ C2 ) )
% 5.31/5.56 = ( ord_less_rat @ B @ ( times_times_rat @ A @ C2 ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % neg_less_divide_eq
% 5.31/5.56 thf(fact_3892_pos__divide__less__eq,axiom,
% 5.31/5.56 ! [C2: real,B: real,A: real] :
% 5.31/5.56 ( ( ord_less_real @ zero_zero_real @ C2 )
% 5.31/5.56 => ( ( ord_less_real @ ( divide_divide_real @ B @ C2 ) @ A )
% 5.31/5.56 = ( ord_less_real @ B @ ( times_times_real @ A @ C2 ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % pos_divide_less_eq
% 5.31/5.56 thf(fact_3893_pos__divide__less__eq,axiom,
% 5.31/5.56 ! [C2: rat,B: rat,A: rat] :
% 5.31/5.56 ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 5.31/5.56 => ( ( ord_less_rat @ ( divide_divide_rat @ B @ C2 ) @ A )
% 5.31/5.56 = ( ord_less_rat @ B @ ( times_times_rat @ A @ C2 ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % pos_divide_less_eq
% 5.31/5.56 thf(fact_3894_pos__less__divide__eq,axiom,
% 5.31/5.56 ! [C2: real,A: real,B: real] :
% 5.31/5.56 ( ( ord_less_real @ zero_zero_real @ C2 )
% 5.31/5.56 => ( ( ord_less_real @ A @ ( divide_divide_real @ B @ C2 ) )
% 5.31/5.56 = ( ord_less_real @ ( times_times_real @ A @ C2 ) @ B ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % pos_less_divide_eq
% 5.31/5.56 thf(fact_3895_pos__less__divide__eq,axiom,
% 5.31/5.56 ! [C2: rat,A: rat,B: rat] :
% 5.31/5.56 ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 5.31/5.56 => ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ C2 ) )
% 5.31/5.56 = ( ord_less_rat @ ( times_times_rat @ A @ C2 ) @ B ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % pos_less_divide_eq
% 5.31/5.56 thf(fact_3896_mult__imp__div__pos__less,axiom,
% 5.31/5.56 ! [Y: real,X: real,Z3: real] :
% 5.31/5.56 ( ( ord_less_real @ zero_zero_real @ Y )
% 5.31/5.56 => ( ( ord_less_real @ X @ ( times_times_real @ Z3 @ Y ) )
% 5.31/5.56 => ( ord_less_real @ ( divide_divide_real @ X @ Y ) @ Z3 ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % mult_imp_div_pos_less
% 5.31/5.56 thf(fact_3897_mult__imp__div__pos__less,axiom,
% 5.31/5.56 ! [Y: rat,X: rat,Z3: rat] :
% 5.31/5.56 ( ( ord_less_rat @ zero_zero_rat @ Y )
% 5.31/5.56 => ( ( ord_less_rat @ X @ ( times_times_rat @ Z3 @ Y ) )
% 5.31/5.56 => ( ord_less_rat @ ( divide_divide_rat @ X @ Y ) @ Z3 ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % mult_imp_div_pos_less
% 5.31/5.56 thf(fact_3898_mult__imp__less__div__pos,axiom,
% 5.31/5.56 ! [Y: real,Z3: real,X: real] :
% 5.31/5.56 ( ( ord_less_real @ zero_zero_real @ Y )
% 5.31/5.56 => ( ( ord_less_real @ ( times_times_real @ Z3 @ Y ) @ X )
% 5.31/5.56 => ( ord_less_real @ Z3 @ ( divide_divide_real @ X @ Y ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % mult_imp_less_div_pos
% 5.31/5.56 thf(fact_3899_mult__imp__less__div__pos,axiom,
% 5.31/5.56 ! [Y: rat,Z3: rat,X: rat] :
% 5.31/5.56 ( ( ord_less_rat @ zero_zero_rat @ Y )
% 5.31/5.56 => ( ( ord_less_rat @ ( times_times_rat @ Z3 @ Y ) @ X )
% 5.31/5.56 => ( ord_less_rat @ Z3 @ ( divide_divide_rat @ X @ Y ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % mult_imp_less_div_pos
% 5.31/5.56 thf(fact_3900_divide__strict__left__mono,axiom,
% 5.31/5.56 ! [B: real,A: real,C2: real] :
% 5.31/5.56 ( ( ord_less_real @ B @ A )
% 5.31/5.56 => ( ( ord_less_real @ zero_zero_real @ C2 )
% 5.31/5.56 => ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 5.31/5.56 => ( ord_less_real @ ( divide_divide_real @ C2 @ A ) @ ( divide_divide_real @ C2 @ B ) ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % divide_strict_left_mono
% 5.31/5.56 thf(fact_3901_divide__strict__left__mono,axiom,
% 5.31/5.56 ! [B: rat,A: rat,C2: rat] :
% 5.31/5.56 ( ( ord_less_rat @ B @ A )
% 5.31/5.56 => ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 5.31/5.56 => ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 5.31/5.56 => ( ord_less_rat @ ( divide_divide_rat @ C2 @ A ) @ ( divide_divide_rat @ C2 @ B ) ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % divide_strict_left_mono
% 5.31/5.56 thf(fact_3902_divide__strict__left__mono__neg,axiom,
% 5.31/5.56 ! [A: real,B: real,C2: real] :
% 5.31/5.56 ( ( ord_less_real @ A @ B )
% 5.31/5.56 => ( ( ord_less_real @ C2 @ zero_zero_real )
% 5.31/5.56 => ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 5.31/5.56 => ( ord_less_real @ ( divide_divide_real @ C2 @ A ) @ ( divide_divide_real @ C2 @ B ) ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % divide_strict_left_mono_neg
% 5.31/5.56 thf(fact_3903_divide__strict__left__mono__neg,axiom,
% 5.31/5.56 ! [A: rat,B: rat,C2: rat] :
% 5.31/5.56 ( ( ord_less_rat @ A @ B )
% 5.31/5.56 => ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 5.31/5.56 => ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 5.31/5.56 => ( ord_less_rat @ ( divide_divide_rat @ C2 @ A ) @ ( divide_divide_rat @ C2 @ B ) ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % divide_strict_left_mono_neg
% 5.31/5.56 thf(fact_3904_less__divide__eq__1,axiom,
% 5.31/5.56 ! [B: real,A: real] :
% 5.31/5.56 ( ( ord_less_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 5.31/5.56 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 5.31/5.56 & ( ord_less_real @ A @ B ) )
% 5.31/5.56 | ( ( ord_less_real @ A @ zero_zero_real )
% 5.31/5.56 & ( ord_less_real @ B @ A ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % less_divide_eq_1
% 5.31/5.56 thf(fact_3905_less__divide__eq__1,axiom,
% 5.31/5.56 ! [B: rat,A: rat] :
% 5.31/5.56 ( ( ord_less_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 5.31/5.56 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.31/5.56 & ( ord_less_rat @ A @ B ) )
% 5.31/5.56 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.31/5.56 & ( ord_less_rat @ B @ A ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % less_divide_eq_1
% 5.31/5.56 thf(fact_3906_divide__less__eq__1,axiom,
% 5.31/5.56 ! [B: real,A: real] :
% 5.31/5.56 ( ( ord_less_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 5.31/5.56 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 5.31/5.56 & ( ord_less_real @ B @ A ) )
% 5.31/5.56 | ( ( ord_less_real @ A @ zero_zero_real )
% 5.31/5.56 & ( ord_less_real @ A @ B ) )
% 5.31/5.56 | ( A = zero_zero_real ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % divide_less_eq_1
% 5.31/5.56 thf(fact_3907_divide__less__eq__1,axiom,
% 5.31/5.56 ! [B: rat,A: rat] :
% 5.31/5.56 ( ( ord_less_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 5.31/5.56 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.31/5.56 & ( ord_less_rat @ B @ A ) )
% 5.31/5.56 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.31/5.56 & ( ord_less_rat @ A @ B ) )
% 5.31/5.56 | ( A = zero_zero_rat ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % divide_less_eq_1
% 5.31/5.56 thf(fact_3908_divide__eq__eq__numeral_I1_J,axiom,
% 5.31/5.56 ! [B: complex,C2: complex,W2: num] :
% 5.31/5.56 ( ( ( divide1717551699836669952omplex @ B @ C2 )
% 5.31/5.56 = ( numera6690914467698888265omplex @ W2 ) )
% 5.31/5.56 = ( ( ( C2 != zero_zero_complex )
% 5.31/5.56 => ( B
% 5.31/5.56 = ( times_times_complex @ ( numera6690914467698888265omplex @ W2 ) @ C2 ) ) )
% 5.31/5.56 & ( ( C2 = zero_zero_complex )
% 5.31/5.56 => ( ( numera6690914467698888265omplex @ W2 )
% 5.31/5.56 = zero_zero_complex ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % divide_eq_eq_numeral(1)
% 5.31/5.56 thf(fact_3909_divide__eq__eq__numeral_I1_J,axiom,
% 5.31/5.56 ! [B: real,C2: real,W2: num] :
% 5.31/5.56 ( ( ( divide_divide_real @ B @ C2 )
% 5.31/5.56 = ( numeral_numeral_real @ W2 ) )
% 5.31/5.56 = ( ( ( C2 != zero_zero_real )
% 5.31/5.56 => ( B
% 5.31/5.56 = ( times_times_real @ ( numeral_numeral_real @ W2 ) @ C2 ) ) )
% 5.31/5.56 & ( ( C2 = zero_zero_real )
% 5.31/5.56 => ( ( numeral_numeral_real @ W2 )
% 5.31/5.56 = zero_zero_real ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % divide_eq_eq_numeral(1)
% 5.31/5.56 thf(fact_3910_divide__eq__eq__numeral_I1_J,axiom,
% 5.31/5.56 ! [B: rat,C2: rat,W2: num] :
% 5.31/5.56 ( ( ( divide_divide_rat @ B @ C2 )
% 5.31/5.56 = ( numeral_numeral_rat @ W2 ) )
% 5.31/5.56 = ( ( ( C2 != zero_zero_rat )
% 5.31/5.56 => ( B
% 5.31/5.56 = ( times_times_rat @ ( numeral_numeral_rat @ W2 ) @ C2 ) ) )
% 5.31/5.56 & ( ( C2 = zero_zero_rat )
% 5.31/5.56 => ( ( numeral_numeral_rat @ W2 )
% 5.31/5.56 = zero_zero_rat ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % divide_eq_eq_numeral(1)
% 5.31/5.56 thf(fact_3911_eq__divide__eq__numeral_I1_J,axiom,
% 5.31/5.56 ! [W2: num,B: complex,C2: complex] :
% 5.31/5.56 ( ( ( numera6690914467698888265omplex @ W2 )
% 5.31/5.56 = ( divide1717551699836669952omplex @ B @ C2 ) )
% 5.31/5.56 = ( ( ( C2 != zero_zero_complex )
% 5.31/5.56 => ( ( times_times_complex @ ( numera6690914467698888265omplex @ W2 ) @ C2 )
% 5.31/5.56 = B ) )
% 5.31/5.56 & ( ( C2 = zero_zero_complex )
% 5.31/5.56 => ( ( numera6690914467698888265omplex @ W2 )
% 5.31/5.56 = zero_zero_complex ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % eq_divide_eq_numeral(1)
% 5.31/5.56 thf(fact_3912_eq__divide__eq__numeral_I1_J,axiom,
% 5.31/5.56 ! [W2: num,B: real,C2: real] :
% 5.31/5.56 ( ( ( numeral_numeral_real @ W2 )
% 5.31/5.56 = ( divide_divide_real @ B @ C2 ) )
% 5.31/5.56 = ( ( ( C2 != zero_zero_real )
% 5.31/5.56 => ( ( times_times_real @ ( numeral_numeral_real @ W2 ) @ C2 )
% 5.31/5.56 = B ) )
% 5.31/5.56 & ( ( C2 = zero_zero_real )
% 5.31/5.56 => ( ( numeral_numeral_real @ W2 )
% 5.31/5.56 = zero_zero_real ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % eq_divide_eq_numeral(1)
% 5.31/5.56 thf(fact_3913_eq__divide__eq__numeral_I1_J,axiom,
% 5.31/5.56 ! [W2: num,B: rat,C2: rat] :
% 5.31/5.56 ( ( ( numeral_numeral_rat @ W2 )
% 5.31/5.56 = ( divide_divide_rat @ B @ C2 ) )
% 5.31/5.56 = ( ( ( C2 != zero_zero_rat )
% 5.31/5.56 => ( ( times_times_rat @ ( numeral_numeral_rat @ W2 ) @ C2 )
% 5.31/5.56 = B ) )
% 5.31/5.56 & ( ( C2 = zero_zero_rat )
% 5.31/5.56 => ( ( numeral_numeral_rat @ W2 )
% 5.31/5.56 = zero_zero_rat ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % eq_divide_eq_numeral(1)
% 5.31/5.56 thf(fact_3914_add__divide__eq__if__simps_I2_J,axiom,
% 5.31/5.56 ! [Z3: complex,A: complex,B: complex] :
% 5.31/5.56 ( ( ( Z3 = zero_zero_complex )
% 5.31/5.56 => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ A @ Z3 ) @ B )
% 5.31/5.56 = B ) )
% 5.31/5.56 & ( ( Z3 != zero_zero_complex )
% 5.31/5.56 => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ A @ Z3 ) @ B )
% 5.31/5.56 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ A @ ( times_times_complex @ B @ Z3 ) ) @ Z3 ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % add_divide_eq_if_simps(2)
% 5.31/5.56 thf(fact_3915_add__divide__eq__if__simps_I2_J,axiom,
% 5.31/5.56 ! [Z3: real,A: real,B: real] :
% 5.31/5.56 ( ( ( Z3 = zero_zero_real )
% 5.31/5.56 => ( ( plus_plus_real @ ( divide_divide_real @ A @ Z3 ) @ B )
% 5.31/5.56 = B ) )
% 5.31/5.56 & ( ( Z3 != zero_zero_real )
% 5.31/5.56 => ( ( plus_plus_real @ ( divide_divide_real @ A @ Z3 ) @ B )
% 5.31/5.56 = ( divide_divide_real @ ( plus_plus_real @ A @ ( times_times_real @ B @ Z3 ) ) @ Z3 ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % add_divide_eq_if_simps(2)
% 5.31/5.56 thf(fact_3916_add__divide__eq__if__simps_I2_J,axiom,
% 5.31/5.56 ! [Z3: rat,A: rat,B: rat] :
% 5.31/5.56 ( ( ( Z3 = zero_zero_rat )
% 5.31/5.56 => ( ( plus_plus_rat @ ( divide_divide_rat @ A @ Z3 ) @ B )
% 5.31/5.56 = B ) )
% 5.31/5.56 & ( ( Z3 != zero_zero_rat )
% 5.31/5.56 => ( ( plus_plus_rat @ ( divide_divide_rat @ A @ Z3 ) @ B )
% 5.31/5.56 = ( divide_divide_rat @ ( plus_plus_rat @ A @ ( times_times_rat @ B @ Z3 ) ) @ Z3 ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % add_divide_eq_if_simps(2)
% 5.31/5.56 thf(fact_3917_add__divide__eq__if__simps_I1_J,axiom,
% 5.31/5.56 ! [Z3: complex,A: complex,B: complex] :
% 5.31/5.56 ( ( ( Z3 = zero_zero_complex )
% 5.31/5.56 => ( ( plus_plus_complex @ A @ ( divide1717551699836669952omplex @ B @ Z3 ) )
% 5.31/5.56 = A ) )
% 5.31/5.56 & ( ( Z3 != zero_zero_complex )
% 5.31/5.56 => ( ( plus_plus_complex @ A @ ( divide1717551699836669952omplex @ B @ Z3 ) )
% 5.31/5.56 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( times_times_complex @ A @ Z3 ) @ B ) @ Z3 ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % add_divide_eq_if_simps(1)
% 5.31/5.56 thf(fact_3918_add__divide__eq__if__simps_I1_J,axiom,
% 5.31/5.56 ! [Z3: real,A: real,B: real] :
% 5.31/5.56 ( ( ( Z3 = zero_zero_real )
% 5.31/5.56 => ( ( plus_plus_real @ A @ ( divide_divide_real @ B @ Z3 ) )
% 5.31/5.56 = A ) )
% 5.31/5.56 & ( ( Z3 != zero_zero_real )
% 5.31/5.56 => ( ( plus_plus_real @ A @ ( divide_divide_real @ B @ Z3 ) )
% 5.31/5.56 = ( divide_divide_real @ ( plus_plus_real @ ( times_times_real @ A @ Z3 ) @ B ) @ Z3 ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % add_divide_eq_if_simps(1)
% 5.31/5.56 thf(fact_3919_add__divide__eq__if__simps_I1_J,axiom,
% 5.31/5.56 ! [Z3: rat,A: rat,B: rat] :
% 5.31/5.56 ( ( ( Z3 = zero_zero_rat )
% 5.31/5.56 => ( ( plus_plus_rat @ A @ ( divide_divide_rat @ B @ Z3 ) )
% 5.31/5.56 = A ) )
% 5.31/5.56 & ( ( Z3 != zero_zero_rat )
% 5.31/5.56 => ( ( plus_plus_rat @ A @ ( divide_divide_rat @ B @ Z3 ) )
% 5.31/5.56 = ( divide_divide_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ Z3 ) @ B ) @ Z3 ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % add_divide_eq_if_simps(1)
% 5.31/5.56 thf(fact_3920_add__frac__eq,axiom,
% 5.31/5.56 ! [Y: complex,Z3: complex,X: complex,W2: complex] :
% 5.31/5.56 ( ( Y != zero_zero_complex )
% 5.31/5.56 => ( ( Z3 != zero_zero_complex )
% 5.31/5.56 => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ X @ Y ) @ ( divide1717551699836669952omplex @ W2 @ Z3 ) )
% 5.31/5.56 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( times_times_complex @ X @ Z3 ) @ ( times_times_complex @ W2 @ Y ) ) @ ( times_times_complex @ Y @ Z3 ) ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % add_frac_eq
% 5.31/5.56 thf(fact_3921_add__frac__eq,axiom,
% 5.31/5.56 ! [Y: real,Z3: real,X: real,W2: real] :
% 5.31/5.56 ( ( Y != zero_zero_real )
% 5.31/5.56 => ( ( Z3 != zero_zero_real )
% 5.31/5.56 => ( ( plus_plus_real @ ( divide_divide_real @ X @ Y ) @ ( divide_divide_real @ W2 @ Z3 ) )
% 5.31/5.56 = ( divide_divide_real @ ( plus_plus_real @ ( times_times_real @ X @ Z3 ) @ ( times_times_real @ W2 @ Y ) ) @ ( times_times_real @ Y @ Z3 ) ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % add_frac_eq
% 5.31/5.56 thf(fact_3922_add__frac__eq,axiom,
% 5.31/5.56 ! [Y: rat,Z3: rat,X: rat,W2: rat] :
% 5.31/5.56 ( ( Y != zero_zero_rat )
% 5.31/5.56 => ( ( Z3 != zero_zero_rat )
% 5.31/5.56 => ( ( plus_plus_rat @ ( divide_divide_rat @ X @ Y ) @ ( divide_divide_rat @ W2 @ Z3 ) )
% 5.31/5.56 = ( divide_divide_rat @ ( plus_plus_rat @ ( times_times_rat @ X @ Z3 ) @ ( times_times_rat @ W2 @ Y ) ) @ ( times_times_rat @ Y @ Z3 ) ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % add_frac_eq
% 5.31/5.56 thf(fact_3923_add__frac__num,axiom,
% 5.31/5.56 ! [Y: complex,X: complex,Z3: complex] :
% 5.31/5.56 ( ( Y != zero_zero_complex )
% 5.31/5.56 => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ X @ Y ) @ Z3 )
% 5.31/5.56 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ X @ ( times_times_complex @ Z3 @ Y ) ) @ Y ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % add_frac_num
% 5.31/5.56 thf(fact_3924_add__frac__num,axiom,
% 5.31/5.56 ! [Y: real,X: real,Z3: real] :
% 5.31/5.56 ( ( Y != zero_zero_real )
% 5.31/5.56 => ( ( plus_plus_real @ ( divide_divide_real @ X @ Y ) @ Z3 )
% 5.31/5.56 = ( divide_divide_real @ ( plus_plus_real @ X @ ( times_times_real @ Z3 @ Y ) ) @ Y ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % add_frac_num
% 5.31/5.56 thf(fact_3925_add__frac__num,axiom,
% 5.31/5.56 ! [Y: rat,X: rat,Z3: rat] :
% 5.31/5.56 ( ( Y != zero_zero_rat )
% 5.31/5.56 => ( ( plus_plus_rat @ ( divide_divide_rat @ X @ Y ) @ Z3 )
% 5.31/5.56 = ( divide_divide_rat @ ( plus_plus_rat @ X @ ( times_times_rat @ Z3 @ Y ) ) @ Y ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % add_frac_num
% 5.31/5.56 thf(fact_3926_add__num__frac,axiom,
% 5.31/5.56 ! [Y: complex,Z3: complex,X: complex] :
% 5.31/5.56 ( ( Y != zero_zero_complex )
% 5.31/5.56 => ( ( plus_plus_complex @ Z3 @ ( divide1717551699836669952omplex @ X @ Y ) )
% 5.31/5.56 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ X @ ( times_times_complex @ Z3 @ Y ) ) @ Y ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % add_num_frac
% 5.31/5.56 thf(fact_3927_add__num__frac,axiom,
% 5.31/5.56 ! [Y: real,Z3: real,X: real] :
% 5.31/5.56 ( ( Y != zero_zero_real )
% 5.31/5.56 => ( ( plus_plus_real @ Z3 @ ( divide_divide_real @ X @ Y ) )
% 5.31/5.56 = ( divide_divide_real @ ( plus_plus_real @ X @ ( times_times_real @ Z3 @ Y ) ) @ Y ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % add_num_frac
% 5.31/5.56 thf(fact_3928_add__num__frac,axiom,
% 5.31/5.56 ! [Y: rat,Z3: rat,X: rat] :
% 5.31/5.56 ( ( Y != zero_zero_rat )
% 5.31/5.56 => ( ( plus_plus_rat @ Z3 @ ( divide_divide_rat @ X @ Y ) )
% 5.31/5.56 = ( divide_divide_rat @ ( plus_plus_rat @ X @ ( times_times_rat @ Z3 @ Y ) ) @ Y ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % add_num_frac
% 5.31/5.56 thf(fact_3929_add__divide__eq__iff,axiom,
% 5.31/5.56 ! [Z3: complex,X: complex,Y: complex] :
% 5.31/5.56 ( ( Z3 != zero_zero_complex )
% 5.31/5.56 => ( ( plus_plus_complex @ X @ ( divide1717551699836669952omplex @ Y @ Z3 ) )
% 5.31/5.56 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( times_times_complex @ X @ Z3 ) @ Y ) @ Z3 ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % add_divide_eq_iff
% 5.31/5.56 thf(fact_3930_add__divide__eq__iff,axiom,
% 5.31/5.56 ! [Z3: real,X: real,Y: real] :
% 5.31/5.56 ( ( Z3 != zero_zero_real )
% 5.31/5.56 => ( ( plus_plus_real @ X @ ( divide_divide_real @ Y @ Z3 ) )
% 5.31/5.56 = ( divide_divide_real @ ( plus_plus_real @ ( times_times_real @ X @ Z3 ) @ Y ) @ Z3 ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % add_divide_eq_iff
% 5.31/5.56 thf(fact_3931_add__divide__eq__iff,axiom,
% 5.31/5.56 ! [Z3: rat,X: rat,Y: rat] :
% 5.31/5.56 ( ( Z3 != zero_zero_rat )
% 5.31/5.56 => ( ( plus_plus_rat @ X @ ( divide_divide_rat @ Y @ Z3 ) )
% 5.31/5.56 = ( divide_divide_rat @ ( plus_plus_rat @ ( times_times_rat @ X @ Z3 ) @ Y ) @ Z3 ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % add_divide_eq_iff
% 5.31/5.56 thf(fact_3932_divide__add__eq__iff,axiom,
% 5.31/5.56 ! [Z3: complex,X: complex,Y: complex] :
% 5.31/5.56 ( ( Z3 != zero_zero_complex )
% 5.31/5.56 => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ X @ Z3 ) @ Y )
% 5.31/5.56 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ X @ ( times_times_complex @ Y @ Z3 ) ) @ Z3 ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % divide_add_eq_iff
% 5.31/5.56 thf(fact_3933_divide__add__eq__iff,axiom,
% 5.31/5.56 ! [Z3: real,X: real,Y: real] :
% 5.31/5.56 ( ( Z3 != zero_zero_real )
% 5.31/5.56 => ( ( plus_plus_real @ ( divide_divide_real @ X @ Z3 ) @ Y )
% 5.31/5.56 = ( divide_divide_real @ ( plus_plus_real @ X @ ( times_times_real @ Y @ Z3 ) ) @ Z3 ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % divide_add_eq_iff
% 5.31/5.56 thf(fact_3934_divide__add__eq__iff,axiom,
% 5.31/5.56 ! [Z3: rat,X: rat,Y: rat] :
% 5.31/5.56 ( ( Z3 != zero_zero_rat )
% 5.31/5.56 => ( ( plus_plus_rat @ ( divide_divide_rat @ X @ Z3 ) @ Y )
% 5.31/5.56 = ( divide_divide_rat @ ( plus_plus_rat @ X @ ( times_times_rat @ Y @ Z3 ) ) @ Z3 ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % divide_add_eq_iff
% 5.31/5.56 thf(fact_3935_add__divide__eq__if__simps_I4_J,axiom,
% 5.31/5.56 ! [Z3: complex,A: complex,B: complex] :
% 5.31/5.56 ( ( ( Z3 = zero_zero_complex )
% 5.31/5.56 => ( ( minus_minus_complex @ A @ ( divide1717551699836669952omplex @ B @ Z3 ) )
% 5.31/5.56 = A ) )
% 5.31/5.56 & ( ( Z3 != zero_zero_complex )
% 5.31/5.56 => ( ( minus_minus_complex @ A @ ( divide1717551699836669952omplex @ B @ Z3 ) )
% 5.31/5.56 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( times_times_complex @ A @ Z3 ) @ B ) @ Z3 ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % add_divide_eq_if_simps(4)
% 5.31/5.56 thf(fact_3936_add__divide__eq__if__simps_I4_J,axiom,
% 5.31/5.56 ! [Z3: real,A: real,B: real] :
% 5.31/5.56 ( ( ( Z3 = zero_zero_real )
% 5.31/5.56 => ( ( minus_minus_real @ A @ ( divide_divide_real @ B @ Z3 ) )
% 5.31/5.56 = A ) )
% 5.31/5.56 & ( ( Z3 != zero_zero_real )
% 5.31/5.56 => ( ( minus_minus_real @ A @ ( divide_divide_real @ B @ Z3 ) )
% 5.31/5.56 = ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ A @ Z3 ) @ B ) @ Z3 ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % add_divide_eq_if_simps(4)
% 5.31/5.56 thf(fact_3937_add__divide__eq__if__simps_I4_J,axiom,
% 5.31/5.56 ! [Z3: rat,A: rat,B: rat] :
% 5.31/5.56 ( ( ( Z3 = zero_zero_rat )
% 5.31/5.56 => ( ( minus_minus_rat @ A @ ( divide_divide_rat @ B @ Z3 ) )
% 5.31/5.56 = A ) )
% 5.31/5.56 & ( ( Z3 != zero_zero_rat )
% 5.31/5.56 => ( ( minus_minus_rat @ A @ ( divide_divide_rat @ B @ Z3 ) )
% 5.31/5.56 = ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ A @ Z3 ) @ B ) @ Z3 ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % add_divide_eq_if_simps(4)
% 5.31/5.56 thf(fact_3938_diff__frac__eq,axiom,
% 5.31/5.56 ! [Y: complex,Z3: complex,X: complex,W2: complex] :
% 5.31/5.56 ( ( Y != zero_zero_complex )
% 5.31/5.56 => ( ( Z3 != zero_zero_complex )
% 5.31/5.56 => ( ( minus_minus_complex @ ( divide1717551699836669952omplex @ X @ Y ) @ ( divide1717551699836669952omplex @ W2 @ Z3 ) )
% 5.31/5.56 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( times_times_complex @ X @ Z3 ) @ ( times_times_complex @ W2 @ Y ) ) @ ( times_times_complex @ Y @ Z3 ) ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % diff_frac_eq
% 5.31/5.56 thf(fact_3939_diff__frac__eq,axiom,
% 5.31/5.56 ! [Y: real,Z3: real,X: real,W2: real] :
% 5.31/5.56 ( ( Y != zero_zero_real )
% 5.31/5.56 => ( ( Z3 != zero_zero_real )
% 5.31/5.56 => ( ( minus_minus_real @ ( divide_divide_real @ X @ Y ) @ ( divide_divide_real @ W2 @ Z3 ) )
% 5.31/5.56 = ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ X @ Z3 ) @ ( times_times_real @ W2 @ Y ) ) @ ( times_times_real @ Y @ Z3 ) ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % diff_frac_eq
% 5.31/5.56 thf(fact_3940_diff__frac__eq,axiom,
% 5.31/5.56 ! [Y: rat,Z3: rat,X: rat,W2: rat] :
% 5.31/5.56 ( ( Y != zero_zero_rat )
% 5.31/5.56 => ( ( Z3 != zero_zero_rat )
% 5.31/5.56 => ( ( minus_minus_rat @ ( divide_divide_rat @ X @ Y ) @ ( divide_divide_rat @ W2 @ Z3 ) )
% 5.31/5.56 = ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ X @ Z3 ) @ ( times_times_rat @ W2 @ Y ) ) @ ( times_times_rat @ Y @ Z3 ) ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % diff_frac_eq
% 5.31/5.56 thf(fact_3941_diff__divide__eq__iff,axiom,
% 5.31/5.56 ! [Z3: complex,X: complex,Y: complex] :
% 5.31/5.56 ( ( Z3 != zero_zero_complex )
% 5.31/5.56 => ( ( minus_minus_complex @ X @ ( divide1717551699836669952omplex @ Y @ Z3 ) )
% 5.31/5.56 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( times_times_complex @ X @ Z3 ) @ Y ) @ Z3 ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % diff_divide_eq_iff
% 5.31/5.56 thf(fact_3942_diff__divide__eq__iff,axiom,
% 5.31/5.56 ! [Z3: real,X: real,Y: real] :
% 5.31/5.56 ( ( Z3 != zero_zero_real )
% 5.31/5.56 => ( ( minus_minus_real @ X @ ( divide_divide_real @ Y @ Z3 ) )
% 5.31/5.56 = ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ X @ Z3 ) @ Y ) @ Z3 ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % diff_divide_eq_iff
% 5.31/5.56 thf(fact_3943_diff__divide__eq__iff,axiom,
% 5.31/5.56 ! [Z3: rat,X: rat,Y: rat] :
% 5.31/5.56 ( ( Z3 != zero_zero_rat )
% 5.31/5.56 => ( ( minus_minus_rat @ X @ ( divide_divide_rat @ Y @ Z3 ) )
% 5.31/5.56 = ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ X @ Z3 ) @ Y ) @ Z3 ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % diff_divide_eq_iff
% 5.31/5.56 thf(fact_3944_divide__diff__eq__iff,axiom,
% 5.31/5.56 ! [Z3: complex,X: complex,Y: complex] :
% 5.31/5.56 ( ( Z3 != zero_zero_complex )
% 5.31/5.56 => ( ( minus_minus_complex @ ( divide1717551699836669952omplex @ X @ Z3 ) @ Y )
% 5.31/5.56 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ X @ ( times_times_complex @ Y @ Z3 ) ) @ Z3 ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % divide_diff_eq_iff
% 5.31/5.56 thf(fact_3945_divide__diff__eq__iff,axiom,
% 5.31/5.56 ! [Z3: real,X: real,Y: real] :
% 5.31/5.56 ( ( Z3 != zero_zero_real )
% 5.31/5.56 => ( ( minus_minus_real @ ( divide_divide_real @ X @ Z3 ) @ Y )
% 5.31/5.56 = ( divide_divide_real @ ( minus_minus_real @ X @ ( times_times_real @ Y @ Z3 ) ) @ Z3 ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % divide_diff_eq_iff
% 5.31/5.56 thf(fact_3946_divide__diff__eq__iff,axiom,
% 5.31/5.56 ! [Z3: rat,X: rat,Y: rat] :
% 5.31/5.56 ( ( Z3 != zero_zero_rat )
% 5.31/5.56 => ( ( minus_minus_rat @ ( divide_divide_rat @ X @ Z3 ) @ Y )
% 5.31/5.56 = ( divide_divide_rat @ ( minus_minus_rat @ X @ ( times_times_rat @ Y @ Z3 ) ) @ Z3 ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % divide_diff_eq_iff
% 5.31/5.56 thf(fact_3947_card__Un__le,axiom,
% 5.31/5.56 ! [A4: set_complex,B5: set_complex] : ( ord_less_eq_nat @ ( finite_card_complex @ ( sup_sup_set_complex @ A4 @ B5 ) ) @ ( plus_plus_nat @ ( finite_card_complex @ A4 ) @ ( finite_card_complex @ B5 ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % card_Un_le
% 5.31/5.56 thf(fact_3948_card__Un__le,axiom,
% 5.31/5.56 ! [A4: set_int,B5: set_int] : ( ord_less_eq_nat @ ( finite_card_int @ ( sup_sup_set_int @ A4 @ B5 ) ) @ ( plus_plus_nat @ ( finite_card_int @ A4 ) @ ( finite_card_int @ B5 ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % card_Un_le
% 5.31/5.56 thf(fact_3949_card__Un__le,axiom,
% 5.31/5.56 ! [A4: set_list_nat,B5: set_list_nat] : ( ord_less_eq_nat @ ( finite_card_list_nat @ ( sup_sup_set_list_nat @ A4 @ B5 ) ) @ ( plus_plus_nat @ ( finite_card_list_nat @ A4 ) @ ( finite_card_list_nat @ B5 ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % card_Un_le
% 5.31/5.56 thf(fact_3950_card__Un__le,axiom,
% 5.31/5.56 ! [A4: set_set_nat,B5: set_set_nat] : ( ord_less_eq_nat @ ( finite_card_set_nat @ ( sup_sup_set_set_nat @ A4 @ B5 ) ) @ ( plus_plus_nat @ ( finite_card_set_nat @ A4 ) @ ( finite_card_set_nat @ B5 ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % card_Un_le
% 5.31/5.56 thf(fact_3951_card__Un__le,axiom,
% 5.31/5.56 ! [A4: set_nat,B5: set_nat] : ( ord_less_eq_nat @ ( finite_card_nat @ ( sup_sup_set_nat @ A4 @ B5 ) ) @ ( plus_plus_nat @ ( finite_card_nat @ A4 ) @ ( finite_card_nat @ B5 ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % card_Un_le
% 5.31/5.56 thf(fact_3952_atLeast0__atMost__Suc,axiom,
% 5.31/5.56 ! [N: nat] :
% 5.31/5.56 ( ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) )
% 5.31/5.56 = ( insert_nat @ ( suc @ N ) @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % atLeast0_atMost_Suc
% 5.31/5.56 thf(fact_3953_nat__mult__div__cancel1,axiom,
% 5.31/5.56 ! [K2: nat,M2: nat,N: nat] :
% 5.31/5.56 ( ( ord_less_nat @ zero_zero_nat @ K2 )
% 5.31/5.56 => ( ( divide_divide_nat @ ( times_times_nat @ K2 @ M2 ) @ ( times_times_nat @ K2 @ N ) )
% 5.31/5.56 = ( divide_divide_nat @ M2 @ N ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % nat_mult_div_cancel1
% 5.31/5.56 thf(fact_3954_Icc__eq__insert__lb__nat,axiom,
% 5.31/5.56 ! [M2: nat,N: nat] :
% 5.31/5.56 ( ( ord_less_eq_nat @ M2 @ N )
% 5.31/5.56 => ( ( set_or1269000886237332187st_nat @ M2 @ N )
% 5.31/5.56 = ( insert_nat @ M2 @ ( set_or1269000886237332187st_nat @ ( suc @ M2 ) @ N ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % Icc_eq_insert_lb_nat
% 5.31/5.56 thf(fact_3955_atLeastAtMostSuc__conv,axiom,
% 5.31/5.56 ! [M2: nat,N: nat] :
% 5.31/5.56 ( ( ord_less_eq_nat @ M2 @ ( suc @ N ) )
% 5.31/5.56 => ( ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N ) )
% 5.31/5.56 = ( insert_nat @ ( suc @ N ) @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % atLeastAtMostSuc_conv
% 5.31/5.56 thf(fact_3956_atLeastAtMost__insertL,axiom,
% 5.31/5.56 ! [M2: nat,N: nat] :
% 5.31/5.56 ( ( ord_less_eq_nat @ M2 @ N )
% 5.31/5.56 => ( ( insert_nat @ M2 @ ( set_or1269000886237332187st_nat @ ( suc @ M2 ) @ N ) )
% 5.31/5.56 = ( set_or1269000886237332187st_nat @ M2 @ N ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % atLeastAtMost_insertL
% 5.31/5.56 thf(fact_3957_subset__eq__atLeast0__atMost__finite,axiom,
% 5.31/5.56 ! [N6: set_nat,N: nat] :
% 5.31/5.56 ( ( ord_less_eq_set_nat @ N6 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 5.31/5.56 => ( finite_finite_nat @ N6 ) ) ).
% 5.31/5.56
% 5.31/5.56 % subset_eq_atLeast0_atMost_finite
% 5.31/5.56 thf(fact_3958_divide__le__eq,axiom,
% 5.31/5.56 ! [B: real,C2: real,A: real] :
% 5.31/5.56 ( ( ord_less_eq_real @ ( divide_divide_real @ B @ C2 ) @ A )
% 5.31/5.56 = ( ( ( ord_less_real @ zero_zero_real @ C2 )
% 5.31/5.56 => ( ord_less_eq_real @ B @ ( times_times_real @ A @ C2 ) ) )
% 5.31/5.56 & ( ~ ( ord_less_real @ zero_zero_real @ C2 )
% 5.31/5.56 => ( ( ( ord_less_real @ C2 @ zero_zero_real )
% 5.31/5.56 => ( ord_less_eq_real @ ( times_times_real @ A @ C2 ) @ B ) )
% 5.31/5.56 & ( ~ ( ord_less_real @ C2 @ zero_zero_real )
% 5.31/5.56 => ( ord_less_eq_real @ zero_zero_real @ A ) ) ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % divide_le_eq
% 5.31/5.56 thf(fact_3959_divide__le__eq,axiom,
% 5.31/5.56 ! [B: rat,C2: rat,A: rat] :
% 5.31/5.56 ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C2 ) @ A )
% 5.31/5.56 = ( ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 5.31/5.56 => ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ C2 ) ) )
% 5.31/5.56 & ( ~ ( ord_less_rat @ zero_zero_rat @ C2 )
% 5.31/5.56 => ( ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 5.31/5.56 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C2 ) @ B ) )
% 5.31/5.56 & ( ~ ( ord_less_rat @ C2 @ zero_zero_rat )
% 5.31/5.56 => ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % divide_le_eq
% 5.31/5.56 thf(fact_3960_le__divide__eq,axiom,
% 5.31/5.56 ! [A: real,B: real,C2: real] :
% 5.31/5.56 ( ( ord_less_eq_real @ A @ ( divide_divide_real @ B @ C2 ) )
% 5.31/5.56 = ( ( ( ord_less_real @ zero_zero_real @ C2 )
% 5.31/5.56 => ( ord_less_eq_real @ ( times_times_real @ A @ C2 ) @ B ) )
% 5.31/5.56 & ( ~ ( ord_less_real @ zero_zero_real @ C2 )
% 5.31/5.56 => ( ( ( ord_less_real @ C2 @ zero_zero_real )
% 5.31/5.56 => ( ord_less_eq_real @ B @ ( times_times_real @ A @ C2 ) ) )
% 5.31/5.56 & ( ~ ( ord_less_real @ C2 @ zero_zero_real )
% 5.31/5.56 => ( ord_less_eq_real @ A @ zero_zero_real ) ) ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % le_divide_eq
% 5.31/5.56 thf(fact_3961_le__divide__eq,axiom,
% 5.31/5.56 ! [A: rat,B: rat,C2: rat] :
% 5.31/5.56 ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ C2 ) )
% 5.31/5.56 = ( ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 5.31/5.56 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C2 ) @ B ) )
% 5.31/5.56 & ( ~ ( ord_less_rat @ zero_zero_rat @ C2 )
% 5.31/5.56 => ( ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 5.31/5.56 => ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ C2 ) ) )
% 5.31/5.56 & ( ~ ( ord_less_rat @ C2 @ zero_zero_rat )
% 5.31/5.56 => ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % le_divide_eq
% 5.31/5.56 thf(fact_3962_divide__left__mono,axiom,
% 5.31/5.56 ! [B: real,A: real,C2: real] :
% 5.31/5.56 ( ( ord_less_eq_real @ B @ A )
% 5.31/5.56 => ( ( ord_less_eq_real @ zero_zero_real @ C2 )
% 5.31/5.56 => ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 5.31/5.56 => ( ord_less_eq_real @ ( divide_divide_real @ C2 @ A ) @ ( divide_divide_real @ C2 @ B ) ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % divide_left_mono
% 5.31/5.56 thf(fact_3963_divide__left__mono,axiom,
% 5.31/5.56 ! [B: rat,A: rat,C2: rat] :
% 5.31/5.56 ( ( ord_less_eq_rat @ B @ A )
% 5.31/5.56 => ( ( ord_less_eq_rat @ zero_zero_rat @ C2 )
% 5.31/5.56 => ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 5.31/5.56 => ( ord_less_eq_rat @ ( divide_divide_rat @ C2 @ A ) @ ( divide_divide_rat @ C2 @ B ) ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % divide_left_mono
% 5.31/5.56 thf(fact_3964_neg__divide__le__eq,axiom,
% 5.31/5.56 ! [C2: real,B: real,A: real] :
% 5.31/5.56 ( ( ord_less_real @ C2 @ zero_zero_real )
% 5.31/5.56 => ( ( ord_less_eq_real @ ( divide_divide_real @ B @ C2 ) @ A )
% 5.31/5.56 = ( ord_less_eq_real @ ( times_times_real @ A @ C2 ) @ B ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % neg_divide_le_eq
% 5.31/5.56 thf(fact_3965_neg__divide__le__eq,axiom,
% 5.31/5.56 ! [C2: rat,B: rat,A: rat] :
% 5.31/5.56 ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 5.31/5.56 => ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C2 ) @ A )
% 5.31/5.56 = ( ord_less_eq_rat @ ( times_times_rat @ A @ C2 ) @ B ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % neg_divide_le_eq
% 5.31/5.56 thf(fact_3966_neg__le__divide__eq,axiom,
% 5.31/5.56 ! [C2: real,A: real,B: real] :
% 5.31/5.56 ( ( ord_less_real @ C2 @ zero_zero_real )
% 5.31/5.56 => ( ( ord_less_eq_real @ A @ ( divide_divide_real @ B @ C2 ) )
% 5.31/5.56 = ( ord_less_eq_real @ B @ ( times_times_real @ A @ C2 ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % neg_le_divide_eq
% 5.31/5.56 thf(fact_3967_neg__le__divide__eq,axiom,
% 5.31/5.56 ! [C2: rat,A: rat,B: rat] :
% 5.31/5.56 ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 5.31/5.56 => ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ C2 ) )
% 5.31/5.56 = ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ C2 ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % neg_le_divide_eq
% 5.31/5.56 thf(fact_3968_pos__divide__le__eq,axiom,
% 5.31/5.56 ! [C2: real,B: real,A: real] :
% 5.31/5.56 ( ( ord_less_real @ zero_zero_real @ C2 )
% 5.31/5.56 => ( ( ord_less_eq_real @ ( divide_divide_real @ B @ C2 ) @ A )
% 5.31/5.56 = ( ord_less_eq_real @ B @ ( times_times_real @ A @ C2 ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % pos_divide_le_eq
% 5.31/5.56 thf(fact_3969_pos__divide__le__eq,axiom,
% 5.31/5.56 ! [C2: rat,B: rat,A: rat] :
% 5.31/5.56 ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 5.31/5.56 => ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C2 ) @ A )
% 5.31/5.56 = ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ C2 ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % pos_divide_le_eq
% 5.31/5.56 thf(fact_3970_pos__le__divide__eq,axiom,
% 5.31/5.56 ! [C2: real,A: real,B: real] :
% 5.31/5.56 ( ( ord_less_real @ zero_zero_real @ C2 )
% 5.31/5.56 => ( ( ord_less_eq_real @ A @ ( divide_divide_real @ B @ C2 ) )
% 5.31/5.56 = ( ord_less_eq_real @ ( times_times_real @ A @ C2 ) @ B ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % pos_le_divide_eq
% 5.31/5.56 thf(fact_3971_pos__le__divide__eq,axiom,
% 5.31/5.56 ! [C2: rat,A: rat,B: rat] :
% 5.31/5.56 ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 5.31/5.56 => ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ C2 ) )
% 5.31/5.56 = ( ord_less_eq_rat @ ( times_times_rat @ A @ C2 ) @ B ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % pos_le_divide_eq
% 5.31/5.56 thf(fact_3972_mult__imp__div__pos__le,axiom,
% 5.31/5.56 ! [Y: real,X: real,Z3: real] :
% 5.31/5.56 ( ( ord_less_real @ zero_zero_real @ Y )
% 5.31/5.56 => ( ( ord_less_eq_real @ X @ ( times_times_real @ Z3 @ Y ) )
% 5.31/5.56 => ( ord_less_eq_real @ ( divide_divide_real @ X @ Y ) @ Z3 ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % mult_imp_div_pos_le
% 5.31/5.56 thf(fact_3973_mult__imp__div__pos__le,axiom,
% 5.31/5.56 ! [Y: rat,X: rat,Z3: rat] :
% 5.31/5.56 ( ( ord_less_rat @ zero_zero_rat @ Y )
% 5.31/5.56 => ( ( ord_less_eq_rat @ X @ ( times_times_rat @ Z3 @ Y ) )
% 5.31/5.56 => ( ord_less_eq_rat @ ( divide_divide_rat @ X @ Y ) @ Z3 ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % mult_imp_div_pos_le
% 5.31/5.56 thf(fact_3974_mult__imp__le__div__pos,axiom,
% 5.31/5.56 ! [Y: real,Z3: real,X: real] :
% 5.31/5.56 ( ( ord_less_real @ zero_zero_real @ Y )
% 5.31/5.56 => ( ( ord_less_eq_real @ ( times_times_real @ Z3 @ Y ) @ X )
% 5.31/5.56 => ( ord_less_eq_real @ Z3 @ ( divide_divide_real @ X @ Y ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % mult_imp_le_div_pos
% 5.31/5.56 thf(fact_3975_mult__imp__le__div__pos,axiom,
% 5.31/5.56 ! [Y: rat,Z3: rat,X: rat] :
% 5.31/5.56 ( ( ord_less_rat @ zero_zero_rat @ Y )
% 5.31/5.56 => ( ( ord_less_eq_rat @ ( times_times_rat @ Z3 @ Y ) @ X )
% 5.31/5.56 => ( ord_less_eq_rat @ Z3 @ ( divide_divide_rat @ X @ Y ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % mult_imp_le_div_pos
% 5.31/5.56 thf(fact_3976_divide__left__mono__neg,axiom,
% 5.31/5.56 ! [A: real,B: real,C2: real] :
% 5.31/5.56 ( ( ord_less_eq_real @ A @ B )
% 5.31/5.56 => ( ( ord_less_eq_real @ C2 @ zero_zero_real )
% 5.31/5.56 => ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 5.31/5.56 => ( ord_less_eq_real @ ( divide_divide_real @ C2 @ A ) @ ( divide_divide_real @ C2 @ B ) ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % divide_left_mono_neg
% 5.31/5.56 thf(fact_3977_divide__left__mono__neg,axiom,
% 5.31/5.56 ! [A: rat,B: rat,C2: rat] :
% 5.31/5.56 ( ( ord_less_eq_rat @ A @ B )
% 5.31/5.56 => ( ( ord_less_eq_rat @ C2 @ zero_zero_rat )
% 5.31/5.56 => ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 5.31/5.56 => ( ord_less_eq_rat @ ( divide_divide_rat @ C2 @ A ) @ ( divide_divide_rat @ C2 @ B ) ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % divide_left_mono_neg
% 5.31/5.56 thf(fact_3978_divide__le__eq__1,axiom,
% 5.31/5.56 ! [B: real,A: real] :
% 5.31/5.56 ( ( ord_less_eq_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 5.31/5.56 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 5.31/5.56 & ( ord_less_eq_real @ B @ A ) )
% 5.31/5.56 | ( ( ord_less_real @ A @ zero_zero_real )
% 5.31/5.56 & ( ord_less_eq_real @ A @ B ) )
% 5.31/5.56 | ( A = zero_zero_real ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % divide_le_eq_1
% 5.31/5.56 thf(fact_3979_divide__le__eq__1,axiom,
% 5.31/5.56 ! [B: rat,A: rat] :
% 5.31/5.56 ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 5.31/5.56 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.31/5.56 & ( ord_less_eq_rat @ B @ A ) )
% 5.31/5.56 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.31/5.56 & ( ord_less_eq_rat @ A @ B ) )
% 5.31/5.56 | ( A = zero_zero_rat ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % divide_le_eq_1
% 5.31/5.56 thf(fact_3980_le__divide__eq__1,axiom,
% 5.31/5.56 ! [B: real,A: real] :
% 5.31/5.56 ( ( ord_less_eq_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 5.31/5.56 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 5.31/5.56 & ( ord_less_eq_real @ A @ B ) )
% 5.31/5.56 | ( ( ord_less_real @ A @ zero_zero_real )
% 5.31/5.56 & ( ord_less_eq_real @ B @ A ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % le_divide_eq_1
% 5.31/5.56 thf(fact_3981_le__divide__eq__1,axiom,
% 5.31/5.56 ! [B: rat,A: rat] :
% 5.31/5.56 ( ( ord_less_eq_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 5.31/5.56 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.31/5.56 & ( ord_less_eq_rat @ A @ B ) )
% 5.31/5.56 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.31/5.56 & ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % le_divide_eq_1
% 5.31/5.56 thf(fact_3982_divide__less__eq__numeral_I1_J,axiom,
% 5.31/5.56 ! [B: real,C2: real,W2: num] :
% 5.31/5.56 ( ( ord_less_real @ ( divide_divide_real @ B @ C2 ) @ ( numeral_numeral_real @ W2 ) )
% 5.31/5.56 = ( ( ( ord_less_real @ zero_zero_real @ C2 )
% 5.31/5.56 => ( ord_less_real @ B @ ( times_times_real @ ( numeral_numeral_real @ W2 ) @ C2 ) ) )
% 5.31/5.56 & ( ~ ( ord_less_real @ zero_zero_real @ C2 )
% 5.31/5.56 => ( ( ( ord_less_real @ C2 @ zero_zero_real )
% 5.31/5.56 => ( ord_less_real @ ( times_times_real @ ( numeral_numeral_real @ W2 ) @ C2 ) @ B ) )
% 5.31/5.56 & ( ~ ( ord_less_real @ C2 @ zero_zero_real )
% 5.31/5.56 => ( ord_less_real @ zero_zero_real @ ( numeral_numeral_real @ W2 ) ) ) ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % divide_less_eq_numeral(1)
% 5.31/5.56 thf(fact_3983_divide__less__eq__numeral_I1_J,axiom,
% 5.31/5.56 ! [B: rat,C2: rat,W2: num] :
% 5.31/5.56 ( ( ord_less_rat @ ( divide_divide_rat @ B @ C2 ) @ ( numeral_numeral_rat @ W2 ) )
% 5.31/5.56 = ( ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 5.31/5.56 => ( ord_less_rat @ B @ ( times_times_rat @ ( numeral_numeral_rat @ W2 ) @ C2 ) ) )
% 5.31/5.56 & ( ~ ( ord_less_rat @ zero_zero_rat @ C2 )
% 5.31/5.56 => ( ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 5.31/5.56 => ( ord_less_rat @ ( times_times_rat @ ( numeral_numeral_rat @ W2 ) @ C2 ) @ B ) )
% 5.31/5.56 & ( ~ ( ord_less_rat @ C2 @ zero_zero_rat )
% 5.31/5.56 => ( ord_less_rat @ zero_zero_rat @ ( numeral_numeral_rat @ W2 ) ) ) ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % divide_less_eq_numeral(1)
% 5.31/5.56 thf(fact_3984_less__divide__eq__numeral_I1_J,axiom,
% 5.31/5.56 ! [W2: num,B: real,C2: real] :
% 5.31/5.56 ( ( ord_less_real @ ( numeral_numeral_real @ W2 ) @ ( divide_divide_real @ B @ C2 ) )
% 5.31/5.56 = ( ( ( ord_less_real @ zero_zero_real @ C2 )
% 5.31/5.56 => ( ord_less_real @ ( times_times_real @ ( numeral_numeral_real @ W2 ) @ C2 ) @ B ) )
% 5.31/5.56 & ( ~ ( ord_less_real @ zero_zero_real @ C2 )
% 5.31/5.56 => ( ( ( ord_less_real @ C2 @ zero_zero_real )
% 5.31/5.56 => ( ord_less_real @ B @ ( times_times_real @ ( numeral_numeral_real @ W2 ) @ C2 ) ) )
% 5.31/5.56 & ( ~ ( ord_less_real @ C2 @ zero_zero_real )
% 5.31/5.56 => ( ord_less_real @ ( numeral_numeral_real @ W2 ) @ zero_zero_real ) ) ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % less_divide_eq_numeral(1)
% 5.31/5.56 thf(fact_3985_less__divide__eq__numeral_I1_J,axiom,
% 5.31/5.56 ! [W2: num,B: rat,C2: rat] :
% 5.31/5.56 ( ( ord_less_rat @ ( numeral_numeral_rat @ W2 ) @ ( divide_divide_rat @ B @ C2 ) )
% 5.31/5.56 = ( ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 5.31/5.56 => ( ord_less_rat @ ( times_times_rat @ ( numeral_numeral_rat @ W2 ) @ C2 ) @ B ) )
% 5.31/5.56 & ( ~ ( ord_less_rat @ zero_zero_rat @ C2 )
% 5.31/5.56 => ( ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 5.31/5.56 => ( ord_less_rat @ B @ ( times_times_rat @ ( numeral_numeral_rat @ W2 ) @ C2 ) ) )
% 5.31/5.56 & ( ~ ( ord_less_rat @ C2 @ zero_zero_rat )
% 5.31/5.56 => ( ord_less_rat @ ( numeral_numeral_rat @ W2 ) @ zero_zero_rat ) ) ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % less_divide_eq_numeral(1)
% 5.31/5.56 thf(fact_3986_frac__le__eq,axiom,
% 5.31/5.56 ! [Y: real,Z3: real,X: real,W2: real] :
% 5.31/5.56 ( ( Y != zero_zero_real )
% 5.31/5.56 => ( ( Z3 != zero_zero_real )
% 5.31/5.56 => ( ( ord_less_eq_real @ ( divide_divide_real @ X @ Y ) @ ( divide_divide_real @ W2 @ Z3 ) )
% 5.31/5.56 = ( ord_less_eq_real @ ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ X @ Z3 ) @ ( times_times_real @ W2 @ Y ) ) @ ( times_times_real @ Y @ Z3 ) ) @ zero_zero_real ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % frac_le_eq
% 5.31/5.56 thf(fact_3987_frac__le__eq,axiom,
% 5.31/5.56 ! [Y: rat,Z3: rat,X: rat,W2: rat] :
% 5.31/5.56 ( ( Y != zero_zero_rat )
% 5.31/5.56 => ( ( Z3 != zero_zero_rat )
% 5.31/5.56 => ( ( ord_less_eq_rat @ ( divide_divide_rat @ X @ Y ) @ ( divide_divide_rat @ W2 @ Z3 ) )
% 5.31/5.56 = ( ord_less_eq_rat @ ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ X @ Z3 ) @ ( times_times_rat @ W2 @ Y ) ) @ ( times_times_rat @ Y @ Z3 ) ) @ zero_zero_rat ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % frac_le_eq
% 5.31/5.56 thf(fact_3988_frac__less__eq,axiom,
% 5.31/5.56 ! [Y: real,Z3: real,X: real,W2: real] :
% 5.31/5.56 ( ( Y != zero_zero_real )
% 5.31/5.56 => ( ( Z3 != zero_zero_real )
% 5.31/5.56 => ( ( ord_less_real @ ( divide_divide_real @ X @ Y ) @ ( divide_divide_real @ W2 @ Z3 ) )
% 5.31/5.56 = ( ord_less_real @ ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ X @ Z3 ) @ ( times_times_real @ W2 @ Y ) ) @ ( times_times_real @ Y @ Z3 ) ) @ zero_zero_real ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % frac_less_eq
% 5.31/5.56 thf(fact_3989_frac__less__eq,axiom,
% 5.31/5.56 ! [Y: rat,Z3: rat,X: rat,W2: rat] :
% 5.31/5.56 ( ( Y != zero_zero_rat )
% 5.31/5.56 => ( ( Z3 != zero_zero_rat )
% 5.31/5.56 => ( ( ord_less_rat @ ( divide_divide_rat @ X @ Y ) @ ( divide_divide_rat @ W2 @ Z3 ) )
% 5.31/5.56 = ( ord_less_rat @ ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ X @ Z3 ) @ ( times_times_rat @ W2 @ Y ) ) @ ( times_times_rat @ Y @ Z3 ) ) @ zero_zero_rat ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % frac_less_eq
% 5.31/5.56 thf(fact_3990_power__diff,axiom,
% 5.31/5.56 ! [A: complex,N: nat,M2: nat] :
% 5.31/5.56 ( ( A != zero_zero_complex )
% 5.31/5.56 => ( ( ord_less_eq_nat @ N @ M2 )
% 5.31/5.56 => ( ( power_power_complex @ A @ ( minus_minus_nat @ M2 @ N ) )
% 5.31/5.56 = ( divide1717551699836669952omplex @ ( power_power_complex @ A @ M2 ) @ ( power_power_complex @ A @ N ) ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % power_diff
% 5.31/5.56 thf(fact_3991_power__diff,axiom,
% 5.31/5.56 ! [A: real,N: nat,M2: nat] :
% 5.31/5.56 ( ( A != zero_zero_real )
% 5.31/5.56 => ( ( ord_less_eq_nat @ N @ M2 )
% 5.31/5.56 => ( ( power_power_real @ A @ ( minus_minus_nat @ M2 @ N ) )
% 5.31/5.56 = ( divide_divide_real @ ( power_power_real @ A @ M2 ) @ ( power_power_real @ A @ N ) ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % power_diff
% 5.31/5.56 thf(fact_3992_power__diff,axiom,
% 5.31/5.56 ! [A: rat,N: nat,M2: nat] :
% 5.31/5.56 ( ( A != zero_zero_rat )
% 5.31/5.56 => ( ( ord_less_eq_nat @ N @ M2 )
% 5.31/5.56 => ( ( power_power_rat @ A @ ( minus_minus_nat @ M2 @ N ) )
% 5.31/5.56 = ( divide_divide_rat @ ( power_power_rat @ A @ M2 ) @ ( power_power_rat @ A @ N ) ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % power_diff
% 5.31/5.56 thf(fact_3993_power__diff,axiom,
% 5.31/5.56 ! [A: nat,N: nat,M2: nat] :
% 5.31/5.56 ( ( A != zero_zero_nat )
% 5.31/5.56 => ( ( ord_less_eq_nat @ N @ M2 )
% 5.31/5.56 => ( ( power_power_nat @ A @ ( minus_minus_nat @ M2 @ N ) )
% 5.31/5.56 = ( divide_divide_nat @ ( power_power_nat @ A @ M2 ) @ ( power_power_nat @ A @ N ) ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % power_diff
% 5.31/5.56 thf(fact_3994_power__diff,axiom,
% 5.31/5.56 ! [A: int,N: nat,M2: nat] :
% 5.31/5.56 ( ( A != zero_zero_int )
% 5.31/5.56 => ( ( ord_less_eq_nat @ N @ M2 )
% 5.31/5.56 => ( ( power_power_int @ A @ ( minus_minus_nat @ M2 @ N ) )
% 5.31/5.56 = ( divide_divide_int @ ( power_power_int @ A @ M2 ) @ ( power_power_int @ A @ N ) ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % power_diff
% 5.31/5.56 thf(fact_3995_div__geq,axiom,
% 5.31/5.56 ! [N: nat,M2: nat] :
% 5.31/5.56 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.56 => ( ~ ( ord_less_nat @ M2 @ N )
% 5.31/5.56 => ( ( divide_divide_nat @ M2 @ N )
% 5.31/5.56 = ( suc @ ( divide_divide_nat @ ( minus_minus_nat @ M2 @ N ) @ N ) ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % div_geq
% 5.31/5.56 thf(fact_3996_four__x__squared,axiom,
% 5.31/5.56 ! [X: real] :
% 5.31/5.56 ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.31/5.56 = ( power_power_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % four_x_squared
% 5.31/5.56 thf(fact_3997_L2__set__mult__ineq__lemma,axiom,
% 5.31/5.56 ! [A: real,C2: real,B: real,D: real] : ( ord_less_eq_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( times_times_real @ A @ C2 ) ) @ ( 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 @ C2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % L2_set_mult_ineq_lemma
% 5.31/5.56 thf(fact_3998_divide__le__eq__numeral_I1_J,axiom,
% 5.31/5.56 ! [B: real,C2: real,W2: num] :
% 5.31/5.56 ( ( ord_less_eq_real @ ( divide_divide_real @ B @ C2 ) @ ( numeral_numeral_real @ W2 ) )
% 5.31/5.56 = ( ( ( ord_less_real @ zero_zero_real @ C2 )
% 5.31/5.56 => ( ord_less_eq_real @ B @ ( times_times_real @ ( numeral_numeral_real @ W2 ) @ C2 ) ) )
% 5.31/5.56 & ( ~ ( ord_less_real @ zero_zero_real @ C2 )
% 5.31/5.56 => ( ( ( ord_less_real @ C2 @ zero_zero_real )
% 5.31/5.56 => ( ord_less_eq_real @ ( times_times_real @ ( numeral_numeral_real @ W2 ) @ C2 ) @ B ) )
% 5.31/5.56 & ( ~ ( ord_less_real @ C2 @ zero_zero_real )
% 5.31/5.56 => ( ord_less_eq_real @ zero_zero_real @ ( numeral_numeral_real @ W2 ) ) ) ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % divide_le_eq_numeral(1)
% 5.31/5.56 thf(fact_3999_divide__le__eq__numeral_I1_J,axiom,
% 5.31/5.56 ! [B: rat,C2: rat,W2: num] :
% 5.31/5.56 ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C2 ) @ ( numeral_numeral_rat @ W2 ) )
% 5.31/5.56 = ( ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 5.31/5.56 => ( ord_less_eq_rat @ B @ ( times_times_rat @ ( numeral_numeral_rat @ W2 ) @ C2 ) ) )
% 5.31/5.56 & ( ~ ( ord_less_rat @ zero_zero_rat @ C2 )
% 5.31/5.56 => ( ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 5.31/5.56 => ( ord_less_eq_rat @ ( times_times_rat @ ( numeral_numeral_rat @ W2 ) @ C2 ) @ B ) )
% 5.31/5.56 & ( ~ ( ord_less_rat @ C2 @ zero_zero_rat )
% 5.31/5.56 => ( ord_less_eq_rat @ zero_zero_rat @ ( numeral_numeral_rat @ W2 ) ) ) ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % divide_le_eq_numeral(1)
% 5.31/5.56 thf(fact_4000_le__divide__eq__numeral_I1_J,axiom,
% 5.31/5.56 ! [W2: num,B: real,C2: real] :
% 5.31/5.56 ( ( ord_less_eq_real @ ( numeral_numeral_real @ W2 ) @ ( divide_divide_real @ B @ C2 ) )
% 5.31/5.56 = ( ( ( ord_less_real @ zero_zero_real @ C2 )
% 5.31/5.56 => ( ord_less_eq_real @ ( times_times_real @ ( numeral_numeral_real @ W2 ) @ C2 ) @ B ) )
% 5.31/5.56 & ( ~ ( ord_less_real @ zero_zero_real @ C2 )
% 5.31/5.56 => ( ( ( ord_less_real @ C2 @ zero_zero_real )
% 5.31/5.56 => ( ord_less_eq_real @ B @ ( times_times_real @ ( numeral_numeral_real @ W2 ) @ C2 ) ) )
% 5.31/5.56 & ( ~ ( ord_less_real @ C2 @ zero_zero_real )
% 5.31/5.56 => ( ord_less_eq_real @ ( numeral_numeral_real @ W2 ) @ zero_zero_real ) ) ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % le_divide_eq_numeral(1)
% 5.31/5.56 thf(fact_4001_le__divide__eq__numeral_I1_J,axiom,
% 5.31/5.56 ! [W2: num,B: rat,C2: rat] :
% 5.31/5.56 ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ W2 ) @ ( divide_divide_rat @ B @ C2 ) )
% 5.31/5.56 = ( ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 5.31/5.56 => ( ord_less_eq_rat @ ( times_times_rat @ ( numeral_numeral_rat @ W2 ) @ C2 ) @ B ) )
% 5.31/5.56 & ( ~ ( ord_less_rat @ zero_zero_rat @ C2 )
% 5.31/5.56 => ( ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 5.31/5.56 => ( ord_less_eq_rat @ B @ ( times_times_rat @ ( numeral_numeral_rat @ W2 ) @ C2 ) ) )
% 5.31/5.56 & ( ~ ( ord_less_rat @ C2 @ zero_zero_rat )
% 5.31/5.56 => ( ord_less_eq_rat @ ( numeral_numeral_rat @ W2 ) @ zero_zero_rat ) ) ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % le_divide_eq_numeral(1)
% 5.31/5.56 thf(fact_4002_half__gt__zero,axiom,
% 5.31/5.56 ! [A: real] :
% 5.31/5.56 ( ( ord_less_real @ zero_zero_real @ A )
% 5.31/5.56 => ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ A @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % half_gt_zero
% 5.31/5.56 thf(fact_4003_half__gt__zero,axiom,
% 5.31/5.56 ! [A: rat] :
% 5.31/5.56 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.31/5.56 => ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % half_gt_zero
% 5.31/5.56 thf(fact_4004_half__gt__zero__iff,axiom,
% 5.31/5.56 ! [A: real] :
% 5.31/5.56 ( ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ A @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.31/5.56 = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 5.31/5.56
% 5.31/5.56 % half_gt_zero_iff
% 5.31/5.56 thf(fact_4005_half__gt__zero__iff,axiom,
% 5.31/5.56 ! [A: rat] :
% 5.31/5.56 ( ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) )
% 5.31/5.56 = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 5.31/5.56
% 5.31/5.56 % half_gt_zero_iff
% 5.31/5.56 thf(fact_4006_scaling__mono,axiom,
% 5.31/5.56 ! [U: real,V2: real,R3: real,S2: real] :
% 5.31/5.56 ( ( ord_less_eq_real @ U @ V2 )
% 5.31/5.56 => ( ( ord_less_eq_real @ zero_zero_real @ R3 )
% 5.31/5.56 => ( ( ord_less_eq_real @ R3 @ S2 )
% 5.31/5.56 => ( ord_less_eq_real @ ( plus_plus_real @ U @ ( divide_divide_real @ ( times_times_real @ R3 @ ( minus_minus_real @ V2 @ U ) ) @ S2 ) ) @ V2 ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % scaling_mono
% 5.31/5.56 thf(fact_4007_scaling__mono,axiom,
% 5.31/5.56 ! [U: rat,V2: rat,R3: rat,S2: rat] :
% 5.31/5.56 ( ( ord_less_eq_rat @ U @ V2 )
% 5.31/5.56 => ( ( ord_less_eq_rat @ zero_zero_rat @ R3 )
% 5.31/5.56 => ( ( ord_less_eq_rat @ R3 @ S2 )
% 5.31/5.56 => ( ord_less_eq_rat @ ( plus_plus_rat @ U @ ( divide_divide_rat @ ( times_times_rat @ R3 @ ( minus_minus_rat @ V2 @ U ) ) @ S2 ) ) @ V2 ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % scaling_mono
% 5.31/5.56 thf(fact_4008_nat__approx__posE,axiom,
% 5.31/5.56 ! [E: rat] :
% 5.31/5.56 ( ( ord_less_rat @ zero_zero_rat @ E )
% 5.31/5.56 => ~ ! [N3: nat] :
% 5.31/5.56 ~ ( ord_less_rat @ ( divide_divide_rat @ one_one_rat @ ( semiri681578069525770553at_rat @ ( suc @ N3 ) ) ) @ E ) ) ).
% 5.31/5.56
% 5.31/5.56 % nat_approx_posE
% 5.31/5.56 thf(fact_4009_nat__approx__posE,axiom,
% 5.31/5.56 ! [E: real] :
% 5.31/5.56 ( ( ord_less_real @ zero_zero_real @ E )
% 5.31/5.56 => ~ ! [N3: nat] :
% 5.31/5.56 ~ ( ord_less_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( suc @ N3 ) ) ) @ E ) ) ).
% 5.31/5.56
% 5.31/5.56 % nat_approx_posE
% 5.31/5.56 thf(fact_4010_inverse__of__nat__le,axiom,
% 5.31/5.56 ! [N: nat,M2: nat] :
% 5.31/5.56 ( ( ord_less_eq_nat @ N @ M2 )
% 5.31/5.56 => ( ( N != zero_zero_nat )
% 5.31/5.56 => ( ord_less_eq_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ M2 ) ) @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % inverse_of_nat_le
% 5.31/5.56 thf(fact_4011_inverse__of__nat__le,axiom,
% 5.31/5.56 ! [N: nat,M2: nat] :
% 5.31/5.56 ( ( ord_less_eq_nat @ N @ M2 )
% 5.31/5.56 => ( ( N != zero_zero_nat )
% 5.31/5.56 => ( ord_less_eq_rat @ ( divide_divide_rat @ one_one_rat @ ( semiri681578069525770553at_rat @ M2 ) ) @ ( divide_divide_rat @ one_one_rat @ ( semiri681578069525770553at_rat @ N ) ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % inverse_of_nat_le
% 5.31/5.56 thf(fact_4012_triangle__def,axiom,
% 5.31/5.56 ( nat_triangle
% 5.31/5.56 = ( ^ [N4: nat] : ( divide_divide_nat @ ( times_times_nat @ N4 @ ( suc @ N4 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % triangle_def
% 5.31/5.56 thf(fact_4013_arith__geo__mean,axiom,
% 5.31/5.56 ! [U: real,X: real,Y: real] :
% 5.31/5.56 ( ( ( power_power_real @ U @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.31/5.56 = ( times_times_real @ X @ Y ) )
% 5.31/5.56 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.31/5.56 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.31/5.56 => ( ord_less_eq_real @ U @ ( divide_divide_real @ ( plus_plus_real @ X @ Y ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % arith_geo_mean
% 5.31/5.56 thf(fact_4014_arith__geo__mean,axiom,
% 5.31/5.56 ! [U: rat,X: rat,Y: rat] :
% 5.31/5.56 ( ( ( power_power_rat @ U @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.31/5.56 = ( times_times_rat @ X @ Y ) )
% 5.31/5.56 => ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 5.31/5.56 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 5.31/5.56 => ( ord_less_eq_rat @ U @ ( divide_divide_rat @ ( plus_plus_rat @ X @ Y ) @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % arith_geo_mean
% 5.31/5.56 thf(fact_4015_double__not__eq__Suc__double,axiom,
% 5.31/5.56 ! [M2: nat,N: nat] :
% 5.31/5.56 ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 )
% 5.31/5.56 != ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % double_not_eq_Suc_double
% 5.31/5.56 thf(fact_4016_Suc__double__not__eq__double,axiom,
% 5.31/5.56 ! [M2: nat,N: nat] :
% 5.31/5.56 ( ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) )
% 5.31/5.56 != ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.31/5.56
% 5.31/5.56 % Suc_double_not_eq_double
% 5.31/5.56 thf(fact_4017_exp__add__not__zero__imp__right,axiom,
% 5.31/5.56 ! [M2: nat,N: nat] :
% 5.31/5.56 ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M2 @ N ) )
% 5.31/5.56 != zero_zero_nat )
% 5.31/5.56 => ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.31/5.56 != zero_zero_nat ) ) ).
% 5.31/5.56
% 5.31/5.56 % exp_add_not_zero_imp_right
% 5.31/5.56 thf(fact_4018_exp__add__not__zero__imp__right,axiom,
% 5.31/5.56 ! [M2: nat,N: nat] :
% 5.31/5.56 ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M2 @ N ) )
% 5.31/5.56 != zero_zero_int )
% 5.31/5.56 => ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 5.31/5.56 != zero_zero_int ) ) ).
% 5.31/5.56
% 5.31/5.56 % exp_add_not_zero_imp_right
% 5.31/5.56 thf(fact_4019_one__div__two__eq__zero,axiom,
% 5.31/5.56 ( ( divide6298287555418463151nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.31/5.56 = zero_z3403309356797280102nteger ) ).
% 5.31/5.56
% 5.31/5.56 % one_div_two_eq_zero
% 5.31/5.56 thf(fact_4020_one__div__two__eq__zero,axiom,
% 5.31/5.56 ( ( divide_divide_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.31/5.56 = zero_zero_nat ) ).
% 5.31/5.56
% 5.31/5.56 % one_div_two_eq_zero
% 5.31/5.56 thf(fact_4021_one__div__two__eq__zero,axiom,
% 5.31/5.56 ( ( divide_divide_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.31/5.56 = zero_zero_int ) ).
% 5.31/5.56
% 5.31/5.56 % one_div_two_eq_zero
% 5.31/5.56 thf(fact_4022_div2__Suc__Suc,axiom,
% 5.31/5.56 ! [M2: nat] :
% 5.31/5.56 ( ( divide_divide_nat @ ( suc @ ( suc @ M2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.31/5.56 = ( suc @ ( divide_divide_nat @ M2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % div2_Suc_Suc
% 5.31/5.56 thf(fact_4023_insert_H__correct,axiom,
% 5.31/5.56 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 5.31/5.56 ( ( vEBT_invar_vebt @ T @ N )
% 5.31/5.56 => ( ( vEBT_set_vebt @ ( vEBT_VEBT_insert @ T @ X ) )
% 5.31/5.56 = ( inf_inf_set_nat @ ( sup_sup_set_nat @ ( vEBT_set_vebt @ T ) @ ( insert_nat @ X @ bot_bot_set_nat ) ) @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % insert'_correct
% 5.31/5.56 thf(fact_4024_div__mult__self__is__m,axiom,
% 5.31/5.56 ! [N: nat,M2: nat] :
% 5.31/5.56 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.56 => ( ( divide_divide_nat @ ( times_times_nat @ M2 @ N ) @ N )
% 5.31/5.56 = M2 ) ) ).
% 5.31/5.56
% 5.31/5.56 % div_mult_self_is_m
% 5.31/5.56 thf(fact_4025_div__mult__self1__is__m,axiom,
% 5.31/5.56 ! [N: nat,M2: nat] :
% 5.31/5.56 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.56 => ( ( divide_divide_nat @ ( times_times_nat @ N @ M2 ) @ N )
% 5.31/5.56 = M2 ) ) ).
% 5.31/5.56
% 5.31/5.56 % div_mult_self1_is_m
% 5.31/5.56 thf(fact_4026_div__mult__self1,axiom,
% 5.31/5.56 ! [B: nat,A: nat,C2: nat] :
% 5.31/5.56 ( ( B != zero_zero_nat )
% 5.31/5.56 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ C2 @ B ) ) @ B )
% 5.31/5.56 = ( plus_plus_nat @ C2 @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % div_mult_self1
% 5.31/5.56 thf(fact_4027_div__mult__self1,axiom,
% 5.31/5.56 ! [B: int,A: int,C2: int] :
% 5.31/5.56 ( ( B != zero_zero_int )
% 5.31/5.56 => ( ( divide_divide_int @ ( plus_plus_int @ A @ ( times_times_int @ C2 @ B ) ) @ B )
% 5.31/5.56 = ( plus_plus_int @ C2 @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % div_mult_self1
% 5.31/5.56 thf(fact_4028_div__mult__self2,axiom,
% 5.31/5.56 ! [B: nat,A: nat,C2: nat] :
% 5.31/5.56 ( ( B != zero_zero_nat )
% 5.31/5.56 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ B @ C2 ) ) @ B )
% 5.31/5.56 = ( plus_plus_nat @ C2 @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % div_mult_self2
% 5.31/5.56 thf(fact_4029_div__mult__self2,axiom,
% 5.31/5.56 ! [B: int,A: int,C2: int] :
% 5.31/5.56 ( ( B != zero_zero_int )
% 5.31/5.56 => ( ( divide_divide_int @ ( plus_plus_int @ A @ ( times_times_int @ B @ C2 ) ) @ B )
% 5.31/5.56 = ( plus_plus_int @ C2 @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % div_mult_self2
% 5.31/5.56 thf(fact_4030_div__mult__self3,axiom,
% 5.31/5.56 ! [B: nat,C2: nat,A: nat] :
% 5.31/5.56 ( ( B != zero_zero_nat )
% 5.31/5.56 => ( ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ C2 @ B ) @ A ) @ B )
% 5.31/5.56 = ( plus_plus_nat @ C2 @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % div_mult_self3
% 5.31/5.56 thf(fact_4031_div__mult__self3,axiom,
% 5.31/5.56 ! [B: int,C2: int,A: int] :
% 5.31/5.56 ( ( B != zero_zero_int )
% 5.31/5.56 => ( ( divide_divide_int @ ( plus_plus_int @ ( times_times_int @ C2 @ B ) @ A ) @ B )
% 5.31/5.56 = ( plus_plus_int @ C2 @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % div_mult_self3
% 5.31/5.56 thf(fact_4032_zdiv__numeral__Bit0,axiom,
% 5.31/5.56 ! [V2: num,W2: num] :
% 5.31/5.56 ( ( divide_divide_int @ ( numeral_numeral_int @ ( bit0 @ V2 ) ) @ ( numeral_numeral_int @ ( bit0 @ W2 ) ) )
% 5.31/5.56 = ( divide_divide_int @ ( numeral_numeral_int @ V2 ) @ ( numeral_numeral_int @ W2 ) ) ) ).
% 5.31/5.56
% 5.31/5.56 % zdiv_numeral_Bit0
% 5.31/5.56 thf(fact_4033_real__divide__square__eq,axiom,
% 5.31/5.56 ! [R3: real,A: real] :
% 5.31/5.56 ( ( divide_divide_real @ ( times_times_real @ R3 @ A ) @ ( times_times_real @ R3 @ R3 ) )
% 5.31/5.56 = ( divide_divide_real @ A @ R3 ) ) ).
% 5.31/5.56
% 5.31/5.56 % real_divide_square_eq
% 5.31/5.56 thf(fact_4034_div__mult__mult1__if,axiom,
% 5.31/5.57 ! [C2: nat,A: nat,B: nat] :
% 5.31/5.57 ( ( ( C2 = zero_zero_nat )
% 5.31/5.57 => ( ( divide_divide_nat @ ( times_times_nat @ C2 @ A ) @ ( times_times_nat @ C2 @ B ) )
% 5.31/5.57 = zero_zero_nat ) )
% 5.31/5.57 & ( ( C2 != zero_zero_nat )
% 5.31/5.57 => ( ( divide_divide_nat @ ( times_times_nat @ C2 @ A ) @ ( times_times_nat @ C2 @ B ) )
% 5.31/5.57 = ( divide_divide_nat @ A @ B ) ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % div_mult_mult1_if
% 5.31/5.57 thf(fact_4035_div__mult__mult1__if,axiom,
% 5.31/5.57 ! [C2: int,A: int,B: int] :
% 5.31/5.57 ( ( ( C2 = zero_zero_int )
% 5.31/5.57 => ( ( divide_divide_int @ ( times_times_int @ C2 @ A ) @ ( times_times_int @ C2 @ B ) )
% 5.31/5.57 = zero_zero_int ) )
% 5.31/5.57 & ( ( C2 != zero_zero_int )
% 5.31/5.57 => ( ( divide_divide_int @ ( times_times_int @ C2 @ A ) @ ( times_times_int @ C2 @ B ) )
% 5.31/5.57 = ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % div_mult_mult1_if
% 5.31/5.57 thf(fact_4036_div__mult__mult2,axiom,
% 5.31/5.57 ! [C2: nat,A: nat,B: nat] :
% 5.31/5.57 ( ( C2 != zero_zero_nat )
% 5.31/5.57 => ( ( divide_divide_nat @ ( times_times_nat @ A @ C2 ) @ ( times_times_nat @ B @ C2 ) )
% 5.31/5.57 = ( divide_divide_nat @ A @ B ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % div_mult_mult2
% 5.31/5.57 thf(fact_4037_div__mult__mult2,axiom,
% 5.31/5.57 ! [C2: int,A: int,B: int] :
% 5.31/5.57 ( ( C2 != zero_zero_int )
% 5.31/5.57 => ( ( divide_divide_int @ ( times_times_int @ A @ C2 ) @ ( times_times_int @ B @ C2 ) )
% 5.31/5.57 = ( divide_divide_int @ A @ B ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % div_mult_mult2
% 5.31/5.57 thf(fact_4038_div__mult__mult1,axiom,
% 5.31/5.57 ! [C2: nat,A: nat,B: nat] :
% 5.31/5.57 ( ( C2 != zero_zero_nat )
% 5.31/5.57 => ( ( divide_divide_nat @ ( times_times_nat @ C2 @ A ) @ ( times_times_nat @ C2 @ B ) )
% 5.31/5.57 = ( divide_divide_nat @ A @ B ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % div_mult_mult1
% 5.31/5.57 thf(fact_4039_div__mult__mult1,axiom,
% 5.31/5.57 ! [C2: int,A: int,B: int] :
% 5.31/5.57 ( ( C2 != zero_zero_int )
% 5.31/5.57 => ( ( divide_divide_int @ ( times_times_int @ C2 @ A ) @ ( times_times_int @ C2 @ B ) )
% 5.31/5.57 = ( divide_divide_int @ A @ B ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % div_mult_mult1
% 5.31/5.57 thf(fact_4040_div__by__Suc__0,axiom,
% 5.31/5.57 ! [M2: nat] :
% 5.31/5.57 ( ( divide_divide_nat @ M2 @ ( suc @ zero_zero_nat ) )
% 5.31/5.57 = M2 ) ).
% 5.31/5.57
% 5.31/5.57 % div_by_Suc_0
% 5.31/5.57 thf(fact_4041_div__less,axiom,
% 5.31/5.57 ! [M2: nat,N: nat] :
% 5.31/5.57 ( ( ord_less_nat @ M2 @ N )
% 5.31/5.57 => ( ( divide_divide_nat @ M2 @ N )
% 5.31/5.57 = zero_zero_nat ) ) ).
% 5.31/5.57
% 5.31/5.57 % div_less
% 5.31/5.57 thf(fact_4042_div__mult__self4,axiom,
% 5.31/5.57 ! [B: nat,C2: nat,A: nat] :
% 5.31/5.57 ( ( B != zero_zero_nat )
% 5.31/5.57 => ( ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ B @ C2 ) @ A ) @ B )
% 5.31/5.57 = ( plus_plus_nat @ C2 @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % div_mult_self4
% 5.31/5.57 thf(fact_4043_div__mult__self4,axiom,
% 5.31/5.57 ! [B: int,C2: int,A: int] :
% 5.31/5.57 ( ( B != zero_zero_int )
% 5.31/5.57 => ( ( divide_divide_int @ ( plus_plus_int @ ( times_times_int @ B @ C2 ) @ A ) @ B )
% 5.31/5.57 = ( plus_plus_int @ C2 @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % div_mult_self4
% 5.31/5.57 thf(fact_4044_zdiv__zmult2__eq,axiom,
% 5.31/5.57 ! [C2: int,A: int,B: int] :
% 5.31/5.57 ( ( ord_less_eq_int @ zero_zero_int @ C2 )
% 5.31/5.57 => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C2 ) )
% 5.31/5.57 = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C2 ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % zdiv_zmult2_eq
% 5.31/5.57 thf(fact_4045_div__neg__pos__less0,axiom,
% 5.31/5.57 ! [A: int,B: int] :
% 5.31/5.57 ( ( ord_less_int @ A @ zero_zero_int )
% 5.31/5.57 => ( ( ord_less_int @ zero_zero_int @ B )
% 5.31/5.57 => ( ord_less_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % div_neg_pos_less0
% 5.31/5.57 thf(fact_4046_neg__imp__zdiv__neg__iff,axiom,
% 5.31/5.57 ! [B: int,A: int] :
% 5.31/5.57 ( ( ord_less_int @ B @ zero_zero_int )
% 5.31/5.57 => ( ( ord_less_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int )
% 5.31/5.57 = ( ord_less_int @ zero_zero_int @ A ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % neg_imp_zdiv_neg_iff
% 5.31/5.57 thf(fact_4047_pos__imp__zdiv__neg__iff,axiom,
% 5.31/5.57 ! [B: int,A: int] :
% 5.31/5.57 ( ( ord_less_int @ zero_zero_int @ B )
% 5.31/5.57 => ( ( ord_less_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int )
% 5.31/5.57 = ( ord_less_int @ A @ zero_zero_int ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % pos_imp_zdiv_neg_iff
% 5.31/5.57 thf(fact_4048_zdiv__int,axiom,
% 5.31/5.57 ! [A: nat,B: nat] :
% 5.31/5.57 ( ( semiri1314217659103216013at_int @ ( divide_divide_nat @ A @ B ) )
% 5.31/5.57 = ( divide_divide_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % zdiv_int
% 5.31/5.57 thf(fact_4049_atLeastAtMostPlus1__int__conv,axiom,
% 5.31/5.57 ! [M2: int,N: int] :
% 5.31/5.57 ( ( ord_less_eq_int @ M2 @ ( plus_plus_int @ one_one_int @ N ) )
% 5.31/5.57 => ( ( set_or1266510415728281911st_int @ M2 @ ( plus_plus_int @ one_one_int @ N ) )
% 5.31/5.57 = ( insert_int @ ( plus_plus_int @ one_one_int @ N ) @ ( set_or1266510415728281911st_int @ M2 @ N ) ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % atLeastAtMostPlus1_int_conv
% 5.31/5.57 thf(fact_4050_nonneg1__imp__zdiv__pos__iff,axiom,
% 5.31/5.57 ! [A: int,B: int] :
% 5.31/5.57 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.31/5.57 => ( ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ A @ B ) )
% 5.31/5.57 = ( ( ord_less_eq_int @ B @ A )
% 5.31/5.57 & ( ord_less_int @ zero_zero_int @ B ) ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % nonneg1_imp_zdiv_pos_iff
% 5.31/5.57 thf(fact_4051_pos__imp__zdiv__nonneg__iff,axiom,
% 5.31/5.57 ! [B: int,A: int] :
% 5.31/5.57 ( ( ord_less_int @ zero_zero_int @ B )
% 5.31/5.57 => ( ( ord_less_eq_int @ zero_zero_int @ ( divide_divide_int @ A @ B ) )
% 5.31/5.57 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % pos_imp_zdiv_nonneg_iff
% 5.31/5.57 thf(fact_4052_neg__imp__zdiv__nonneg__iff,axiom,
% 5.31/5.57 ! [B: int,A: int] :
% 5.31/5.57 ( ( ord_less_int @ B @ zero_zero_int )
% 5.31/5.57 => ( ( ord_less_eq_int @ zero_zero_int @ ( divide_divide_int @ A @ B ) )
% 5.31/5.57 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % neg_imp_zdiv_nonneg_iff
% 5.31/5.57 thf(fact_4053_pos__imp__zdiv__pos__iff,axiom,
% 5.31/5.57 ! [K2: int,I2: int] :
% 5.31/5.57 ( ( ord_less_int @ zero_zero_int @ K2 )
% 5.31/5.57 => ( ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ I2 @ K2 ) )
% 5.31/5.57 = ( ord_less_eq_int @ K2 @ I2 ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % pos_imp_zdiv_pos_iff
% 5.31/5.57 thf(fact_4054_div__nonpos__pos__le0,axiom,
% 5.31/5.57 ! [A: int,B: int] :
% 5.31/5.57 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.31/5.57 => ( ( ord_less_int @ zero_zero_int @ B )
% 5.31/5.57 => ( ord_less_eq_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % div_nonpos_pos_le0
% 5.31/5.57 thf(fact_4055_div__nonneg__neg__le0,axiom,
% 5.31/5.57 ! [A: int,B: int] :
% 5.31/5.57 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.31/5.57 => ( ( ord_less_int @ B @ zero_zero_int )
% 5.31/5.57 => ( ord_less_eq_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % div_nonneg_neg_le0
% 5.31/5.57 thf(fact_4056_div__positive__int,axiom,
% 5.31/5.57 ! [L: int,K2: int] :
% 5.31/5.57 ( ( ord_less_eq_int @ L @ K2 )
% 5.31/5.57 => ( ( ord_less_int @ zero_zero_int @ L )
% 5.31/5.57 => ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ K2 @ L ) ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % div_positive_int
% 5.31/5.57 thf(fact_4057_div__int__pos__iff,axiom,
% 5.31/5.57 ! [K2: int,L: int] :
% 5.31/5.57 ( ( ord_less_eq_int @ zero_zero_int @ ( divide_divide_int @ K2 @ L ) )
% 5.31/5.57 = ( ( K2 = zero_zero_int )
% 5.31/5.57 | ( L = zero_zero_int )
% 5.31/5.57 | ( ( ord_less_eq_int @ zero_zero_int @ K2 )
% 5.31/5.57 & ( ord_less_eq_int @ zero_zero_int @ L ) )
% 5.31/5.57 | ( ( ord_less_int @ K2 @ zero_zero_int )
% 5.31/5.57 & ( ord_less_int @ L @ zero_zero_int ) ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % div_int_pos_iff
% 5.31/5.57 thf(fact_4058_zdiv__mono2__neg,axiom,
% 5.31/5.57 ! [A: int,B2: int,B: int] :
% 5.31/5.57 ( ( ord_less_int @ A @ zero_zero_int )
% 5.31/5.57 => ( ( ord_less_int @ zero_zero_int @ B2 )
% 5.31/5.57 => ( ( ord_less_eq_int @ B2 @ B )
% 5.31/5.57 => ( ord_less_eq_int @ ( divide_divide_int @ A @ B2 ) @ ( divide_divide_int @ A @ B ) ) ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % zdiv_mono2_neg
% 5.31/5.57 thf(fact_4059_zdiv__mono1__neg,axiom,
% 5.31/5.57 ! [A: int,A2: int,B: int] :
% 5.31/5.57 ( ( ord_less_eq_int @ A @ A2 )
% 5.31/5.57 => ( ( ord_less_int @ B @ zero_zero_int )
% 5.31/5.57 => ( ord_less_eq_int @ ( divide_divide_int @ A2 @ B ) @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % zdiv_mono1_neg
% 5.31/5.57 thf(fact_4060_zdiv__eq__0__iff,axiom,
% 5.31/5.57 ! [I2: int,K2: int] :
% 5.31/5.57 ( ( ( divide_divide_int @ I2 @ K2 )
% 5.31/5.57 = zero_zero_int )
% 5.31/5.57 = ( ( K2 = zero_zero_int )
% 5.31/5.57 | ( ( ord_less_eq_int @ zero_zero_int @ I2 )
% 5.31/5.57 & ( ord_less_int @ I2 @ K2 ) )
% 5.31/5.57 | ( ( ord_less_eq_int @ I2 @ zero_zero_int )
% 5.31/5.57 & ( ord_less_int @ K2 @ I2 ) ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % zdiv_eq_0_iff
% 5.31/5.57 thf(fact_4061_zdiv__mono2,axiom,
% 5.31/5.57 ! [A: int,B2: int,B: int] :
% 5.31/5.57 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.31/5.57 => ( ( ord_less_int @ zero_zero_int @ B2 )
% 5.31/5.57 => ( ( ord_less_eq_int @ B2 @ B )
% 5.31/5.57 => ( ord_less_eq_int @ ( divide_divide_int @ A @ B ) @ ( divide_divide_int @ A @ B2 ) ) ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % zdiv_mono2
% 5.31/5.57 thf(fact_4062_zdiv__mono1,axiom,
% 5.31/5.57 ! [A: int,A2: int,B: int] :
% 5.31/5.57 ( ( ord_less_eq_int @ A @ A2 )
% 5.31/5.57 => ( ( ord_less_int @ zero_zero_int @ B )
% 5.31/5.57 => ( ord_less_eq_int @ ( divide_divide_int @ A @ B ) @ ( divide_divide_int @ A2 @ B ) ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % zdiv_mono1
% 5.31/5.57 thf(fact_4063_int__div__less__self,axiom,
% 5.31/5.57 ! [X: int,K2: int] :
% 5.31/5.57 ( ( ord_less_int @ zero_zero_int @ X )
% 5.31/5.57 => ( ( ord_less_int @ one_one_int @ K2 )
% 5.31/5.57 => ( ord_less_int @ ( divide_divide_int @ X @ K2 ) @ X ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % int_div_less_self
% 5.31/5.57 thf(fact_4064_periodic__finite__ex,axiom,
% 5.31/5.57 ! [D: int,P2: int > $o] :
% 5.31/5.57 ( ( ord_less_int @ zero_zero_int @ D )
% 5.31/5.57 => ( ! [X3: int,K: int] :
% 5.31/5.57 ( ( P2 @ X3 )
% 5.31/5.57 = ( P2 @ ( minus_minus_int @ X3 @ ( times_times_int @ K @ D ) ) ) )
% 5.31/5.57 => ( ( ? [X7: int] : ( P2 @ X7 ) )
% 5.31/5.57 = ( ? [X4: int] :
% 5.31/5.57 ( ( member_int @ X4 @ ( set_or1266510415728281911st_int @ one_one_int @ D ) )
% 5.31/5.57 & ( P2 @ X4 ) ) ) ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % periodic_finite_ex
% 5.31/5.57 thf(fact_4065_split__zdiv,axiom,
% 5.31/5.57 ! [P2: int > $o,N: int,K2: int] :
% 5.31/5.57 ( ( P2 @ ( divide_divide_int @ N @ K2 ) )
% 5.31/5.57 = ( ( ( K2 = zero_zero_int )
% 5.31/5.57 => ( P2 @ zero_zero_int ) )
% 5.31/5.57 & ( ( ord_less_int @ zero_zero_int @ K2 )
% 5.31/5.57 => ! [I: int,J: int] :
% 5.31/5.57 ( ( ( ord_less_eq_int @ zero_zero_int @ J )
% 5.31/5.57 & ( ord_less_int @ J @ K2 )
% 5.31/5.57 & ( N
% 5.31/5.57 = ( plus_plus_int @ ( times_times_int @ K2 @ I ) @ J ) ) )
% 5.31/5.57 => ( P2 @ I ) ) )
% 5.31/5.57 & ( ( ord_less_int @ K2 @ zero_zero_int )
% 5.31/5.57 => ! [I: int,J: int] :
% 5.31/5.57 ( ( ( ord_less_int @ K2 @ J )
% 5.31/5.57 & ( ord_less_eq_int @ J @ zero_zero_int )
% 5.31/5.57 & ( N
% 5.31/5.57 = ( plus_plus_int @ ( times_times_int @ K2 @ I ) @ J ) ) )
% 5.31/5.57 => ( P2 @ I ) ) ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % split_zdiv
% 5.31/5.57 thf(fact_4066_int__div__neg__eq,axiom,
% 5.31/5.57 ! [A: int,B: int,Q2: int,R3: int] :
% 5.31/5.57 ( ( A
% 5.31/5.57 = ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R3 ) )
% 5.31/5.57 => ( ( ord_less_eq_int @ R3 @ zero_zero_int )
% 5.31/5.57 => ( ( ord_less_int @ B @ R3 )
% 5.31/5.57 => ( ( divide_divide_int @ A @ B )
% 5.31/5.57 = Q2 ) ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % int_div_neg_eq
% 5.31/5.57 thf(fact_4067_int__div__pos__eq,axiom,
% 5.31/5.57 ! [A: int,B: int,Q2: int,R3: int] :
% 5.31/5.57 ( ( A
% 5.31/5.57 = ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R3 ) )
% 5.31/5.57 => ( ( ord_less_eq_int @ zero_zero_int @ R3 )
% 5.31/5.57 => ( ( ord_less_int @ R3 @ B )
% 5.31/5.57 => ( ( divide_divide_int @ A @ B )
% 5.31/5.57 = Q2 ) ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % int_div_pos_eq
% 5.31/5.57 thf(fact_4068_cpmi,axiom,
% 5.31/5.57 ! [D3: int,P2: int > $o,P6: int > $o,B5: set_int] :
% 5.31/5.57 ( ( ord_less_int @ zero_zero_int @ D3 )
% 5.31/5.57 => ( ? [Z5: int] :
% 5.31/5.57 ! [X3: int] :
% 5.31/5.57 ( ( ord_less_int @ X3 @ Z5 )
% 5.31/5.57 => ( ( P2 @ X3 )
% 5.31/5.57 = ( P6 @ X3 ) ) )
% 5.31/5.57 => ( ! [X3: int] :
% 5.31/5.57 ( ! [Xa: int] :
% 5.31/5.57 ( ( member_int @ Xa @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 5.31/5.57 => ! [Xb2: int] :
% 5.31/5.57 ( ( member_int @ Xb2 @ B5 )
% 5.31/5.57 => ( X3
% 5.31/5.57 != ( plus_plus_int @ Xb2 @ Xa ) ) ) )
% 5.31/5.57 => ( ( P2 @ X3 )
% 5.31/5.57 => ( P2 @ ( minus_minus_int @ X3 @ D3 ) ) ) )
% 5.31/5.57 => ( ! [X3: int,K: int] :
% 5.31/5.57 ( ( P6 @ X3 )
% 5.31/5.57 = ( P6 @ ( minus_minus_int @ X3 @ ( times_times_int @ K @ D3 ) ) ) )
% 5.31/5.57 => ( ( ? [X7: int] : ( P2 @ X7 ) )
% 5.31/5.57 = ( ? [X4: int] :
% 5.31/5.57 ( ( member_int @ X4 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 5.31/5.57 & ( P6 @ X4 ) )
% 5.31/5.57 | ? [X4: int] :
% 5.31/5.57 ( ( member_int @ X4 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 5.31/5.57 & ? [Y4: int] :
% 5.31/5.57 ( ( member_int @ Y4 @ B5 )
% 5.31/5.57 & ( P2 @ ( plus_plus_int @ Y4 @ X4 ) ) ) ) ) ) ) ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % cpmi
% 5.31/5.57 thf(fact_4069_cppi,axiom,
% 5.31/5.57 ! [D3: int,P2: int > $o,P6: int > $o,A4: set_int] :
% 5.31/5.57 ( ( ord_less_int @ zero_zero_int @ D3 )
% 5.31/5.57 => ( ? [Z5: int] :
% 5.31/5.57 ! [X3: int] :
% 5.31/5.57 ( ( ord_less_int @ Z5 @ X3 )
% 5.31/5.57 => ( ( P2 @ X3 )
% 5.31/5.57 = ( P6 @ X3 ) ) )
% 5.31/5.57 => ( ! [X3: int] :
% 5.31/5.57 ( ! [Xa: int] :
% 5.31/5.57 ( ( member_int @ Xa @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 5.31/5.57 => ! [Xb2: int] :
% 5.31/5.57 ( ( member_int @ Xb2 @ A4 )
% 5.31/5.57 => ( X3
% 5.31/5.57 != ( minus_minus_int @ Xb2 @ Xa ) ) ) )
% 5.31/5.57 => ( ( P2 @ X3 )
% 5.31/5.57 => ( P2 @ ( plus_plus_int @ X3 @ D3 ) ) ) )
% 5.31/5.57 => ( ! [X3: int,K: int] :
% 5.31/5.57 ( ( P6 @ X3 )
% 5.31/5.57 = ( P6 @ ( minus_minus_int @ X3 @ ( times_times_int @ K @ D3 ) ) ) )
% 5.31/5.57 => ( ( ? [X7: int] : ( P2 @ X7 ) )
% 5.31/5.57 = ( ? [X4: int] :
% 5.31/5.57 ( ( member_int @ X4 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 5.31/5.57 & ( P6 @ X4 ) )
% 5.31/5.57 | ? [X4: int] :
% 5.31/5.57 ( ( member_int @ X4 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 5.31/5.57 & ? [Y4: int] :
% 5.31/5.57 ( ( member_int @ Y4 @ A4 )
% 5.31/5.57 & ( P2 @ ( minus_minus_int @ Y4 @ X4 ) ) ) ) ) ) ) ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % cppi
% 5.31/5.57 thf(fact_4070_int__power__div__base,axiom,
% 5.31/5.57 ! [M2: nat,K2: int] :
% 5.31/5.57 ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 5.31/5.57 => ( ( ord_less_int @ zero_zero_int @ K2 )
% 5.31/5.57 => ( ( divide_divide_int @ ( power_power_int @ K2 @ M2 ) @ K2 )
% 5.31/5.57 = ( power_power_int @ K2 @ ( minus_minus_nat @ M2 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % int_power_div_base
% 5.31/5.57 thf(fact_4071_div__pos__geq,axiom,
% 5.31/5.57 ! [L: int,K2: int] :
% 5.31/5.57 ( ( ord_less_int @ zero_zero_int @ L )
% 5.31/5.57 => ( ( ord_less_eq_int @ L @ K2 )
% 5.31/5.57 => ( ( divide_divide_int @ K2 @ L )
% 5.31/5.57 = ( plus_plus_int @ ( divide_divide_int @ ( minus_minus_int @ K2 @ L ) @ L ) @ one_one_int ) ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % div_pos_geq
% 5.31/5.57 thf(fact_4072_div__le__dividend,axiom,
% 5.31/5.57 ! [M2: nat,N: nat] : ( ord_less_eq_nat @ ( divide_divide_nat @ M2 @ N ) @ M2 ) ).
% 5.31/5.57
% 5.31/5.57 % div_le_dividend
% 5.31/5.57 thf(fact_4073_div__le__mono,axiom,
% 5.31/5.57 ! [M2: nat,N: nat,K2: nat] :
% 5.31/5.57 ( ( ord_less_eq_nat @ M2 @ N )
% 5.31/5.57 => ( ord_less_eq_nat @ ( divide_divide_nat @ M2 @ K2 ) @ ( divide_divide_nat @ N @ K2 ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % div_le_mono
% 5.31/5.57 thf(fact_4074_div__mult2__eq,axiom,
% 5.31/5.57 ! [M2: nat,N: nat,Q2: nat] :
% 5.31/5.57 ( ( divide_divide_nat @ M2 @ ( times_times_nat @ N @ Q2 ) )
% 5.31/5.57 = ( divide_divide_nat @ ( divide_divide_nat @ M2 @ N ) @ Q2 ) ) ).
% 5.31/5.57
% 5.31/5.57 % div_mult2_eq
% 5.31/5.57 thf(fact_4075_pos__zdiv__mult__2,axiom,
% 5.31/5.57 ! [A: int,B: int] :
% 5.31/5.57 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.31/5.57 => ( ( 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 ) )
% 5.31/5.57 = ( divide_divide_int @ B @ A ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % pos_zdiv_mult_2
% 5.31/5.57 thf(fact_4076_neg__zdiv__mult__2,axiom,
% 5.31/5.57 ! [A: int,B: int] :
% 5.31/5.57 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.31/5.57 => ( ( 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 ) )
% 5.31/5.57 = ( divide_divide_int @ ( plus_plus_int @ B @ one_one_int ) @ A ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % neg_zdiv_mult_2
% 5.31/5.57 thf(fact_4077_div__mult2__eq_H,axiom,
% 5.31/5.57 ! [A: int,M2: nat,N: nat] :
% 5.31/5.57 ( ( divide_divide_int @ A @ ( times_times_int @ ( semiri1314217659103216013at_int @ M2 ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 5.31/5.57 = ( divide_divide_int @ ( divide_divide_int @ A @ ( semiri1314217659103216013at_int @ M2 ) ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % div_mult2_eq'
% 5.31/5.57 thf(fact_4078_div__mult2__eq_H,axiom,
% 5.31/5.57 ! [A: nat,M2: nat,N: nat] :
% 5.31/5.57 ( ( divide_divide_nat @ A @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ M2 ) @ ( semiri1316708129612266289at_nat @ N ) ) )
% 5.31/5.57 = ( divide_divide_nat @ ( divide_divide_nat @ A @ ( semiri1316708129612266289at_nat @ M2 ) ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % div_mult2_eq'
% 5.31/5.57 thf(fact_4079_Euclidean__Division_Odiv__eq__0__iff,axiom,
% 5.31/5.57 ! [M2: nat,N: nat] :
% 5.31/5.57 ( ( ( divide_divide_nat @ M2 @ N )
% 5.31/5.57 = zero_zero_nat )
% 5.31/5.57 = ( ( ord_less_nat @ M2 @ N )
% 5.31/5.57 | ( N = zero_zero_nat ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % Euclidean_Division.div_eq_0_iff
% 5.31/5.57 thf(fact_4080_Suc__div__le__mono,axiom,
% 5.31/5.57 ! [M2: nat,N: nat] : ( ord_less_eq_nat @ ( divide_divide_nat @ M2 @ N ) @ ( divide_divide_nat @ ( suc @ M2 ) @ N ) ) ).
% 5.31/5.57
% 5.31/5.57 % Suc_div_le_mono
% 5.31/5.57 thf(fact_4081_less__mult__imp__div__less,axiom,
% 5.31/5.57 ! [M2: nat,I2: nat,N: nat] :
% 5.31/5.57 ( ( ord_less_nat @ M2 @ ( times_times_nat @ I2 @ N ) )
% 5.31/5.57 => ( ord_less_nat @ ( divide_divide_nat @ M2 @ N ) @ I2 ) ) ).
% 5.31/5.57
% 5.31/5.57 % less_mult_imp_div_less
% 5.31/5.57 thf(fact_4082_times__div__less__eq__dividend,axiom,
% 5.31/5.57 ! [N: nat,M2: nat] : ( ord_less_eq_nat @ ( times_times_nat @ N @ ( divide_divide_nat @ M2 @ N ) ) @ M2 ) ).
% 5.31/5.57
% 5.31/5.57 % times_div_less_eq_dividend
% 5.31/5.57 thf(fact_4083_div__times__less__eq__dividend,axiom,
% 5.31/5.57 ! [M2: nat,N: nat] : ( ord_less_eq_nat @ ( times_times_nat @ ( divide_divide_nat @ M2 @ N ) @ N ) @ M2 ) ).
% 5.31/5.57
% 5.31/5.57 % div_times_less_eq_dividend
% 5.31/5.57 thf(fact_4084_div__mult2__numeral__eq,axiom,
% 5.31/5.57 ! [A: nat,K2: num,L: num] :
% 5.31/5.57 ( ( divide_divide_nat @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ K2 ) ) @ ( numeral_numeral_nat @ L ) )
% 5.31/5.57 = ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( times_times_num @ K2 @ L ) ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % div_mult2_numeral_eq
% 5.31/5.57 thf(fact_4085_div__mult2__numeral__eq,axiom,
% 5.31/5.57 ! [A: int,K2: num,L: num] :
% 5.31/5.57 ( ( divide_divide_int @ ( divide_divide_int @ A @ ( numeral_numeral_int @ K2 ) ) @ ( numeral_numeral_int @ L ) )
% 5.31/5.57 = ( divide_divide_int @ A @ ( numeral_numeral_int @ ( times_times_num @ K2 @ L ) ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % div_mult2_numeral_eq
% 5.31/5.57 thf(fact_4086_div__add__self1,axiom,
% 5.31/5.57 ! [B: code_integer,A: code_integer] :
% 5.31/5.57 ( ( B != zero_z3403309356797280102nteger )
% 5.31/5.57 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ B @ A ) @ B )
% 5.31/5.57 = ( plus_p5714425477246183910nteger @ ( divide6298287555418463151nteger @ A @ B ) @ one_one_Code_integer ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % div_add_self1
% 5.31/5.57 thf(fact_4087_div__add__self1,axiom,
% 5.31/5.57 ! [B: nat,A: nat] :
% 5.31/5.57 ( ( B != zero_zero_nat )
% 5.31/5.57 => ( ( divide_divide_nat @ ( plus_plus_nat @ B @ A ) @ B )
% 5.31/5.57 = ( plus_plus_nat @ ( divide_divide_nat @ A @ B ) @ one_one_nat ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % div_add_self1
% 5.31/5.57 thf(fact_4088_div__add__self1,axiom,
% 5.31/5.57 ! [B: int,A: int] :
% 5.31/5.57 ( ( B != zero_zero_int )
% 5.31/5.57 => ( ( divide_divide_int @ ( plus_plus_int @ B @ A ) @ B )
% 5.31/5.57 = ( plus_plus_int @ ( divide_divide_int @ A @ B ) @ one_one_int ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % div_add_self1
% 5.31/5.57 thf(fact_4089_div__add__self2,axiom,
% 5.31/5.57 ! [B: code_integer,A: code_integer] :
% 5.31/5.57 ( ( B != zero_z3403309356797280102nteger )
% 5.31/5.57 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ B )
% 5.31/5.57 = ( plus_p5714425477246183910nteger @ ( divide6298287555418463151nteger @ A @ B ) @ one_one_Code_integer ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % div_add_self2
% 5.31/5.57 thf(fact_4090_div__add__self2,axiom,
% 5.31/5.57 ! [B: nat,A: nat] :
% 5.31/5.57 ( ( B != zero_zero_nat )
% 5.31/5.57 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 5.31/5.57 = ( plus_plus_nat @ ( divide_divide_nat @ A @ B ) @ one_one_nat ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % div_add_self2
% 5.31/5.57 thf(fact_4091_div__add__self2,axiom,
% 5.31/5.57 ! [B: int,A: int] :
% 5.31/5.57 ( ( B != zero_zero_int )
% 5.31/5.57 => ( ( divide_divide_int @ ( plus_plus_int @ A @ B ) @ B )
% 5.31/5.57 = ( plus_plus_int @ ( divide_divide_int @ A @ B ) @ one_one_int ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % div_add_self2
% 5.31/5.57 thf(fact_4092_div__le__mono2,axiom,
% 5.31/5.57 ! [M2: nat,N: nat,K2: nat] :
% 5.31/5.57 ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 5.31/5.57 => ( ( ord_less_eq_nat @ M2 @ N )
% 5.31/5.57 => ( ord_less_eq_nat @ ( divide_divide_nat @ K2 @ N ) @ ( divide_divide_nat @ K2 @ M2 ) ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % div_le_mono2
% 5.31/5.57 thf(fact_4093_div__greater__zero__iff,axiom,
% 5.31/5.57 ! [M2: nat,N: nat] :
% 5.31/5.57 ( ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ M2 @ N ) )
% 5.31/5.57 = ( ( ord_less_eq_nat @ N @ M2 )
% 5.31/5.57 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % div_greater_zero_iff
% 5.31/5.57 thf(fact_4094_div__less__iff__less__mult,axiom,
% 5.31/5.57 ! [Q2: nat,M2: nat,N: nat] :
% 5.31/5.57 ( ( ord_less_nat @ zero_zero_nat @ Q2 )
% 5.31/5.57 => ( ( ord_less_nat @ ( divide_divide_nat @ M2 @ Q2 ) @ N )
% 5.31/5.57 = ( ord_less_nat @ M2 @ ( times_times_nat @ N @ Q2 ) ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % div_less_iff_less_mult
% 5.31/5.57 thf(fact_4095_div__less__dividend,axiom,
% 5.31/5.57 ! [N: nat,M2: nat] :
% 5.31/5.57 ( ( ord_less_nat @ one_one_nat @ N )
% 5.31/5.57 => ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 5.31/5.57 => ( ord_less_nat @ ( divide_divide_nat @ M2 @ N ) @ M2 ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % div_less_dividend
% 5.31/5.57 thf(fact_4096_div__eq__dividend__iff,axiom,
% 5.31/5.57 ! [M2: nat,N: nat] :
% 5.31/5.57 ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 5.31/5.57 => ( ( ( divide_divide_nat @ M2 @ N )
% 5.31/5.57 = M2 )
% 5.31/5.57 = ( N = one_one_nat ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % div_eq_dividend_iff
% 5.31/5.57 thf(fact_4097_div__if,axiom,
% 5.31/5.57 ( divide_divide_nat
% 5.31/5.57 = ( ^ [M6: nat,N4: nat] :
% 5.31/5.57 ( if_nat
% 5.31/5.57 @ ( ( ord_less_nat @ M6 @ N4 )
% 5.31/5.57 | ( N4 = zero_zero_nat ) )
% 5.31/5.57 @ zero_zero_nat
% 5.31/5.57 @ ( suc @ ( divide_divide_nat @ ( minus_minus_nat @ M6 @ N4 ) @ N4 ) ) ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % div_if
% 5.31/5.57 thf(fact_4098_div__nat__eqI,axiom,
% 5.31/5.57 ! [N: nat,Q2: nat,M2: nat] :
% 5.31/5.57 ( ( ord_less_eq_nat @ ( times_times_nat @ N @ Q2 ) @ M2 )
% 5.31/5.57 => ( ( ord_less_nat @ M2 @ ( times_times_nat @ N @ ( suc @ Q2 ) ) )
% 5.31/5.57 => ( ( divide_divide_nat @ M2 @ N )
% 5.31/5.57 = Q2 ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % div_nat_eqI
% 5.31/5.57 thf(fact_4099_less__eq__div__iff__mult__less__eq,axiom,
% 5.31/5.57 ! [Q2: nat,M2: nat,N: nat] :
% 5.31/5.57 ( ( ord_less_nat @ zero_zero_nat @ Q2 )
% 5.31/5.57 => ( ( ord_less_eq_nat @ M2 @ ( divide_divide_nat @ N @ Q2 ) )
% 5.31/5.57 = ( ord_less_eq_nat @ ( times_times_nat @ M2 @ Q2 ) @ N ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % less_eq_div_iff_mult_less_eq
% 5.31/5.57 thf(fact_4100_dividend__less__times__div,axiom,
% 5.31/5.57 ! [N: nat,M2: nat] :
% 5.31/5.57 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.57 => ( ord_less_nat @ M2 @ ( plus_plus_nat @ N @ ( times_times_nat @ N @ ( divide_divide_nat @ M2 @ N ) ) ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % dividend_less_times_div
% 5.31/5.57 thf(fact_4101_dividend__less__div__times,axiom,
% 5.31/5.57 ! [N: nat,M2: nat] :
% 5.31/5.57 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.57 => ( ord_less_nat @ M2 @ ( plus_plus_nat @ N @ ( times_times_nat @ ( divide_divide_nat @ M2 @ N ) @ N ) ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % dividend_less_div_times
% 5.31/5.57 thf(fact_4102_split__div,axiom,
% 5.31/5.57 ! [P2: nat > $o,M2: nat,N: nat] :
% 5.31/5.57 ( ( P2 @ ( divide_divide_nat @ M2 @ N ) )
% 5.31/5.57 = ( ( ( N = zero_zero_nat )
% 5.31/5.57 => ( P2 @ zero_zero_nat ) )
% 5.31/5.57 & ( ( N != zero_zero_nat )
% 5.31/5.57 => ! [I: nat,J: nat] :
% 5.31/5.57 ( ( ord_less_nat @ J @ N )
% 5.31/5.57 => ( ( M2
% 5.31/5.57 = ( plus_plus_nat @ ( times_times_nat @ N @ I ) @ J ) )
% 5.31/5.57 => ( P2 @ I ) ) ) ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % split_div
% 5.31/5.57 thf(fact_4103_power__diff__power__eq,axiom,
% 5.31/5.57 ! [A: code_integer,N: nat,M2: nat] :
% 5.31/5.57 ( ( A != zero_z3403309356797280102nteger )
% 5.31/5.57 => ( ( ( ord_less_eq_nat @ N @ M2 )
% 5.31/5.57 => ( ( divide6298287555418463151nteger @ ( power_8256067586552552935nteger @ A @ M2 ) @ ( power_8256067586552552935nteger @ A @ N ) )
% 5.31/5.57 = ( power_8256067586552552935nteger @ A @ ( minus_minus_nat @ M2 @ N ) ) ) )
% 5.31/5.57 & ( ~ ( ord_less_eq_nat @ N @ M2 )
% 5.31/5.57 => ( ( divide6298287555418463151nteger @ ( power_8256067586552552935nteger @ A @ M2 ) @ ( power_8256067586552552935nteger @ A @ N ) )
% 5.31/5.57 = ( divide6298287555418463151nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ A @ ( minus_minus_nat @ N @ M2 ) ) ) ) ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % power_diff_power_eq
% 5.31/5.57 thf(fact_4104_power__diff__power__eq,axiom,
% 5.31/5.57 ! [A: nat,N: nat,M2: nat] :
% 5.31/5.57 ( ( A != zero_zero_nat )
% 5.31/5.57 => ( ( ( ord_less_eq_nat @ N @ M2 )
% 5.31/5.57 => ( ( divide_divide_nat @ ( power_power_nat @ A @ M2 ) @ ( power_power_nat @ A @ N ) )
% 5.31/5.57 = ( power_power_nat @ A @ ( minus_minus_nat @ M2 @ N ) ) ) )
% 5.31/5.57 & ( ~ ( ord_less_eq_nat @ N @ M2 )
% 5.31/5.57 => ( ( divide_divide_nat @ ( power_power_nat @ A @ M2 ) @ ( power_power_nat @ A @ N ) )
% 5.31/5.57 = ( divide_divide_nat @ one_one_nat @ ( power_power_nat @ A @ ( minus_minus_nat @ N @ M2 ) ) ) ) ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % power_diff_power_eq
% 5.31/5.57 thf(fact_4105_power__diff__power__eq,axiom,
% 5.31/5.57 ! [A: int,N: nat,M2: nat] :
% 5.31/5.57 ( ( A != zero_zero_int )
% 5.31/5.57 => ( ( ( ord_less_eq_nat @ N @ M2 )
% 5.31/5.57 => ( ( divide_divide_int @ ( power_power_int @ A @ M2 ) @ ( power_power_int @ A @ N ) )
% 5.31/5.57 = ( power_power_int @ A @ ( minus_minus_nat @ M2 @ N ) ) ) )
% 5.31/5.57 & ( ~ ( ord_less_eq_nat @ N @ M2 )
% 5.31/5.57 => ( ( divide_divide_int @ ( power_power_int @ A @ M2 ) @ ( power_power_int @ A @ N ) )
% 5.31/5.57 = ( divide_divide_int @ one_one_int @ ( power_power_int @ A @ ( minus_minus_nat @ N @ M2 ) ) ) ) ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % power_diff_power_eq
% 5.31/5.57 thf(fact_4106_le__div__geq,axiom,
% 5.31/5.57 ! [N: nat,M2: nat] :
% 5.31/5.57 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.57 => ( ( ord_less_eq_nat @ N @ M2 )
% 5.31/5.57 => ( ( divide_divide_nat @ M2 @ N )
% 5.31/5.57 = ( suc @ ( divide_divide_nat @ ( minus_minus_nat @ M2 @ N ) @ N ) ) ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % le_div_geq
% 5.31/5.57 thf(fact_4107_split__div_H,axiom,
% 5.31/5.57 ! [P2: nat > $o,M2: nat,N: nat] :
% 5.31/5.57 ( ( P2 @ ( divide_divide_nat @ M2 @ N ) )
% 5.31/5.57 = ( ( ( N = zero_zero_nat )
% 5.31/5.57 & ( P2 @ zero_zero_nat ) )
% 5.31/5.57 | ? [Q5: nat] :
% 5.31/5.57 ( ( ord_less_eq_nat @ ( times_times_nat @ N @ Q5 ) @ M2 )
% 5.31/5.57 & ( ord_less_nat @ M2 @ ( times_times_nat @ N @ ( suc @ Q5 ) ) )
% 5.31/5.57 & ( P2 @ Q5 ) ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % split_div'
% 5.31/5.57 thf(fact_4108_div__2__gt__zero,axiom,
% 5.31/5.57 ! [N: nat] :
% 5.31/5.57 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.31/5.57 => ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % div_2_gt_zero
% 5.31/5.57 thf(fact_4109_Suc__n__div__2__gt__zero,axiom,
% 5.31/5.57 ! [N: nat] :
% 5.31/5.57 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.57 => ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % Suc_n_div_2_gt_zero
% 5.31/5.57 thf(fact_4110_linear__plus__1__le__power,axiom,
% 5.31/5.57 ! [X: real,N: nat] :
% 5.31/5.57 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.31/5.57 => ( 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 ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % linear_plus_1_le_power
% 5.31/5.57 thf(fact_4111_succ__list__to__short,axiom,
% 5.31/5.57 ! [Deg: nat,Mi: nat,X: nat,TreeList2: list_VEBT_VEBT,Ma: nat,Summary: vEBT_VEBT] :
% 5.31/5.57 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.31/5.57 => ( ( ord_less_eq_nat @ Mi @ X )
% 5.31/5.57 => ( ( ord_less_eq_nat @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.31/5.57 => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 5.31/5.57 = none_nat ) ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % succ_list_to_short
% 5.31/5.57 thf(fact_4112_pred__list__to__short,axiom,
% 5.31/5.57 ! [Deg: nat,X: nat,Ma: nat,TreeList2: list_VEBT_VEBT,Mi: nat,Summary: vEBT_VEBT] :
% 5.31/5.57 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.31/5.57 => ( ( ord_less_eq_nat @ X @ Ma )
% 5.31/5.57 => ( ( ord_less_eq_nat @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.31/5.57 => ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 5.31/5.57 = none_nat ) ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % pred_list_to_short
% 5.31/5.57 thf(fact_4113_set__bit__0,axiom,
% 5.31/5.57 ! [A: code_integer] :
% 5.31/5.57 ( ( bit_se2793503036327961859nteger @ zero_zero_nat @ A )
% 5.31/5.57 = ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % set_bit_0
% 5.31/5.57 thf(fact_4114_set__bit__0,axiom,
% 5.31/5.57 ! [A: nat] :
% 5.31/5.57 ( ( bit_se7882103937844011126it_nat @ zero_zero_nat @ A )
% 5.31/5.57 = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % set_bit_0
% 5.31/5.57 thf(fact_4115_set__bit__0,axiom,
% 5.31/5.57 ! [A: int] :
% 5.31/5.57 ( ( bit_se7879613467334960850it_int @ zero_zero_nat @ A )
% 5.31/5.57 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % set_bit_0
% 5.31/5.57 thf(fact_4116_case4_I11_J,axiom,
% 5.31/5.57 ( ( mi != ma )
% 5.31/5.57 => ! [I4: nat] :
% 5.31/5.57 ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) )
% 5.31/5.57 => ( ( ( ( vEBT_VEBT_high @ ma @ na )
% 5.31/5.57 = I4 )
% 5.31/5.57 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList2 @ I4 ) @ ( vEBT_VEBT_low @ ma @ na ) ) )
% 5.31/5.57 & ! [X5: nat] :
% 5.31/5.57 ( ( ( ( vEBT_VEBT_high @ X5 @ na )
% 5.31/5.57 = I4 )
% 5.31/5.57 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList2 @ I4 ) @ ( vEBT_VEBT_low @ X5 @ na ) ) )
% 5.31/5.57 => ( ( ord_less_nat @ mi @ X5 )
% 5.31/5.57 & ( ord_less_eq_nat @ X5 @ ma ) ) ) ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % case4(11)
% 5.31/5.57 thf(fact_4117_enat__ord__number_I1_J,axiom,
% 5.31/5.57 ! [M2: num,N: num] :
% 5.31/5.57 ( ( ord_le2932123472753598470d_enat @ ( numera1916890842035813515d_enat @ M2 ) @ ( numera1916890842035813515d_enat @ N ) )
% 5.31/5.57 = ( ord_less_eq_nat @ ( numeral_numeral_nat @ M2 ) @ ( numeral_numeral_nat @ N ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % enat_ord_number(1)
% 5.31/5.57 thf(fact_4118_le__sup__iff,axiom,
% 5.31/5.57 ! [X: set_nat,Y: set_nat,Z3: set_nat] :
% 5.31/5.57 ( ( ord_less_eq_set_nat @ ( sup_sup_set_nat @ X @ Y ) @ Z3 )
% 5.31/5.57 = ( ( ord_less_eq_set_nat @ X @ Z3 )
% 5.31/5.57 & ( ord_less_eq_set_nat @ Y @ Z3 ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % le_sup_iff
% 5.31/5.57 thf(fact_4119_le__sup__iff,axiom,
% 5.31/5.57 ! [X: rat,Y: rat,Z3: rat] :
% 5.31/5.57 ( ( ord_less_eq_rat @ ( sup_sup_rat @ X @ Y ) @ Z3 )
% 5.31/5.57 = ( ( ord_less_eq_rat @ X @ Z3 )
% 5.31/5.57 & ( ord_less_eq_rat @ Y @ Z3 ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % le_sup_iff
% 5.31/5.57 thf(fact_4120_le__sup__iff,axiom,
% 5.31/5.57 ! [X: nat,Y: nat,Z3: nat] :
% 5.31/5.57 ( ( ord_less_eq_nat @ ( sup_sup_nat @ X @ Y ) @ Z3 )
% 5.31/5.57 = ( ( ord_less_eq_nat @ X @ Z3 )
% 5.31/5.57 & ( ord_less_eq_nat @ Y @ Z3 ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % le_sup_iff
% 5.31/5.57 thf(fact_4121_le__sup__iff,axiom,
% 5.31/5.57 ! [X: int,Y: int,Z3: int] :
% 5.31/5.57 ( ( ord_less_eq_int @ ( sup_sup_int @ X @ Y ) @ Z3 )
% 5.31/5.57 = ( ( ord_less_eq_int @ X @ Z3 )
% 5.31/5.57 & ( ord_less_eq_int @ Y @ Z3 ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % le_sup_iff
% 5.31/5.57 thf(fact_4122_sup_Obounded__iff,axiom,
% 5.31/5.57 ! [B: set_nat,C2: set_nat,A: set_nat] :
% 5.31/5.57 ( ( ord_less_eq_set_nat @ ( sup_sup_set_nat @ B @ C2 ) @ A )
% 5.31/5.57 = ( ( ord_less_eq_set_nat @ B @ A )
% 5.31/5.57 & ( ord_less_eq_set_nat @ C2 @ A ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % sup.bounded_iff
% 5.31/5.57 thf(fact_4123_sup_Obounded__iff,axiom,
% 5.31/5.57 ! [B: rat,C2: rat,A: rat] :
% 5.31/5.57 ( ( ord_less_eq_rat @ ( sup_sup_rat @ B @ C2 ) @ A )
% 5.31/5.57 = ( ( ord_less_eq_rat @ B @ A )
% 5.31/5.57 & ( ord_less_eq_rat @ C2 @ A ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % sup.bounded_iff
% 5.31/5.57 thf(fact_4124_sup_Obounded__iff,axiom,
% 5.31/5.57 ! [B: nat,C2: nat,A: nat] :
% 5.31/5.57 ( ( ord_less_eq_nat @ ( sup_sup_nat @ B @ C2 ) @ A )
% 5.31/5.57 = ( ( ord_less_eq_nat @ B @ A )
% 5.31/5.57 & ( ord_less_eq_nat @ C2 @ A ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % sup.bounded_iff
% 5.31/5.57 thf(fact_4125_sup_Obounded__iff,axiom,
% 5.31/5.57 ! [B: int,C2: int,A: int] :
% 5.31/5.57 ( ( ord_less_eq_int @ ( sup_sup_int @ B @ C2 ) @ A )
% 5.31/5.57 = ( ( ord_less_eq_int @ B @ A )
% 5.31/5.57 & ( ord_less_eq_int @ C2 @ A ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % sup.bounded_iff
% 5.31/5.57 thf(fact_4126_bit__split__inv,axiom,
% 5.31/5.57 ! [X: nat,D: nat] :
% 5.31/5.57 ( ( vEBT_VEBT_bit_concat @ ( vEBT_VEBT_high @ X @ D ) @ ( vEBT_VEBT_low @ X @ D ) @ D )
% 5.31/5.57 = X ) ).
% 5.31/5.57
% 5.31/5.57 % bit_split_inv
% 5.31/5.57 thf(fact_4127_finite__atLeastAtMost__int,axiom,
% 5.31/5.57 ! [L: int,U: int] : ( finite_finite_int @ ( set_or1266510415728281911st_int @ L @ U ) ) ).
% 5.31/5.57
% 5.31/5.57 % finite_atLeastAtMost_int
% 5.31/5.57 thf(fact_4128_high__def,axiom,
% 5.31/5.57 ( vEBT_VEBT_high
% 5.31/5.57 = ( ^ [X4: nat,N4: nat] : ( divide_divide_nat @ X4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % high_def
% 5.31/5.57 thf(fact_4129_high__bound__aux,axiom,
% 5.31/5.57 ! [Ma: nat,N: nat,M2: nat] :
% 5.31/5.57 ( ( ord_less_nat @ Ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N @ M2 ) ) )
% 5.31/5.57 => ( ord_less_nat @ ( vEBT_VEBT_high @ Ma @ N ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % high_bound_aux
% 5.31/5.57 thf(fact_4130_high__inv,axiom,
% 5.31/5.57 ! [X: nat,N: nat,Y: nat] :
% 5.31/5.57 ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.31/5.57 => ( ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ Y @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) @ X ) @ N )
% 5.31/5.57 = Y ) ) ).
% 5.31/5.57
% 5.31/5.57 % high_inv
% 5.31/5.57 thf(fact_4131_low__inv,axiom,
% 5.31/5.57 ! [X: nat,N: nat,Y: nat] :
% 5.31/5.57 ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.31/5.57 => ( ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ Y @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) @ X ) @ N )
% 5.31/5.57 = X ) ) ).
% 5.31/5.57
% 5.31/5.57 % low_inv
% 5.31/5.57 thf(fact_4132_le__inf__iff,axiom,
% 5.31/5.57 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,Z3: set_Pr1261947904930325089at_nat] :
% 5.31/5.57 ( ( ord_le3146513528884898305at_nat @ X @ ( inf_in2572325071724192079at_nat @ Y @ Z3 ) )
% 5.31/5.57 = ( ( ord_le3146513528884898305at_nat @ X @ Y )
% 5.31/5.57 & ( ord_le3146513528884898305at_nat @ X @ Z3 ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % le_inf_iff
% 5.31/5.57 thf(fact_4133_le__inf__iff,axiom,
% 5.31/5.57 ! [X: set_nat,Y: set_nat,Z3: set_nat] :
% 5.31/5.57 ( ( ord_less_eq_set_nat @ X @ ( inf_inf_set_nat @ Y @ Z3 ) )
% 5.31/5.57 = ( ( ord_less_eq_set_nat @ X @ Y )
% 5.31/5.57 & ( ord_less_eq_set_nat @ X @ Z3 ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % le_inf_iff
% 5.31/5.57 thf(fact_4134_le__inf__iff,axiom,
% 5.31/5.57 ! [X: rat,Y: rat,Z3: rat] :
% 5.31/5.57 ( ( ord_less_eq_rat @ X @ ( inf_inf_rat @ Y @ Z3 ) )
% 5.31/5.57 = ( ( ord_less_eq_rat @ X @ Y )
% 5.31/5.57 & ( ord_less_eq_rat @ X @ Z3 ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % le_inf_iff
% 5.31/5.57 thf(fact_4135_le__inf__iff,axiom,
% 5.31/5.57 ! [X: nat,Y: nat,Z3: nat] :
% 5.31/5.57 ( ( ord_less_eq_nat @ X @ ( inf_inf_nat @ Y @ Z3 ) )
% 5.31/5.57 = ( ( ord_less_eq_nat @ X @ Y )
% 5.31/5.57 & ( ord_less_eq_nat @ X @ Z3 ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % le_inf_iff
% 5.31/5.57 thf(fact_4136_le__inf__iff,axiom,
% 5.31/5.57 ! [X: int,Y: int,Z3: int] :
% 5.31/5.57 ( ( ord_less_eq_int @ X @ ( inf_inf_int @ Y @ Z3 ) )
% 5.31/5.57 = ( ( ord_less_eq_int @ X @ Y )
% 5.31/5.57 & ( ord_less_eq_int @ X @ Z3 ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % le_inf_iff
% 5.31/5.57 thf(fact_4137_inf_Obounded__iff,axiom,
% 5.31/5.57 ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat,C2: set_Pr1261947904930325089at_nat] :
% 5.31/5.57 ( ( ord_le3146513528884898305at_nat @ A @ ( inf_in2572325071724192079at_nat @ B @ C2 ) )
% 5.31/5.57 = ( ( ord_le3146513528884898305at_nat @ A @ B )
% 5.31/5.57 & ( ord_le3146513528884898305at_nat @ A @ C2 ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % inf.bounded_iff
% 5.31/5.57 thf(fact_4138_inf_Obounded__iff,axiom,
% 5.31/5.57 ! [A: set_nat,B: set_nat,C2: set_nat] :
% 5.31/5.57 ( ( ord_less_eq_set_nat @ A @ ( inf_inf_set_nat @ B @ C2 ) )
% 5.31/5.57 = ( ( ord_less_eq_set_nat @ A @ B )
% 5.31/5.57 & ( ord_less_eq_set_nat @ A @ C2 ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % inf.bounded_iff
% 5.31/5.57 thf(fact_4139_inf_Obounded__iff,axiom,
% 5.31/5.57 ! [A: rat,B: rat,C2: rat] :
% 5.31/5.57 ( ( ord_less_eq_rat @ A @ ( inf_inf_rat @ B @ C2 ) )
% 5.31/5.57 = ( ( ord_less_eq_rat @ A @ B )
% 5.31/5.57 & ( ord_less_eq_rat @ A @ C2 ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % inf.bounded_iff
% 5.31/5.57 thf(fact_4140_inf_Obounded__iff,axiom,
% 5.31/5.57 ! [A: nat,B: nat,C2: nat] :
% 5.31/5.57 ( ( ord_less_eq_nat @ A @ ( inf_inf_nat @ B @ C2 ) )
% 5.31/5.57 = ( ( ord_less_eq_nat @ A @ B )
% 5.31/5.57 & ( ord_less_eq_nat @ A @ C2 ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % inf.bounded_iff
% 5.31/5.57 thf(fact_4141_inf_Obounded__iff,axiom,
% 5.31/5.57 ! [A: int,B: int,C2: int] :
% 5.31/5.57 ( ( ord_less_eq_int @ A @ ( inf_inf_int @ B @ C2 ) )
% 5.31/5.57 = ( ( ord_less_eq_int @ A @ B )
% 5.31/5.57 & ( ord_less_eq_int @ A @ C2 ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % inf.bounded_iff
% 5.31/5.57 thf(fact_4142_both__member__options__ding,axiom,
% 5.31/5.57 ! [Info2: option4927543243414619207at_nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat,X: nat] :
% 5.31/5.57 ( ( vEBT_invar_vebt @ ( vEBT_Node @ Info2 @ Deg @ TreeList2 @ Summary ) @ N )
% 5.31/5.57 => ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 5.31/5.57 => ( ( 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 ) ) ) ) )
% 5.31/5.57 => ( vEBT_V8194947554948674370ptions @ ( vEBT_Node @ Info2 @ Deg @ TreeList2 @ Summary ) @ X ) ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % both_member_options_ding
% 5.31/5.57 thf(fact_4143_both__member__options__from__complete__tree__to__child,axiom,
% 5.31/5.57 ! [Deg: nat,Mi: nat,Ma: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 5.31/5.57 ( ( ord_less_eq_nat @ one_one_nat @ Deg )
% 5.31/5.57 => ( ( vEBT_V8194947554948674370ptions @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 5.31/5.57 => ( ( 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 ) ) ) ) )
% 5.31/5.57 | ( X = Mi )
% 5.31/5.57 | ( X = Ma ) ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % both_member_options_from_complete_tree_to_child
% 5.31/5.57 thf(fact_4144_member__inv,axiom,
% 5.31/5.57 ! [Mi: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 5.31/5.57 ( ( vEBT_vebt_member @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 5.31/5.57 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.31/5.57 & ( ( X = Mi )
% 5.31/5.57 | ( X = Ma )
% 5.31/5.57 | ( ( ord_less_nat @ X @ Ma )
% 5.31/5.57 & ( ord_less_nat @ Mi @ X )
% 5.31/5.57 & ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.31/5.57 & ( 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 ) ) ) ) ) ) ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % member_inv
% 5.31/5.57 thf(fact_4145_both__member__options__from__chilf__to__complete__tree,axiom,
% 5.31/5.57 ! [X: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Mi: nat,Ma: nat,Summary: vEBT_VEBT] :
% 5.31/5.57 ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.31/5.57 => ( ( ord_less_eq_nat @ one_one_nat @ Deg )
% 5.31/5.57 => ( ( 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 ) ) ) ) )
% 5.31/5.57 => ( vEBT_V8194947554948674370ptions @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X ) ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % both_member_options_from_chilf_to_complete_tree
% 5.31/5.57 thf(fact_4146_VEBT__internal_Oexp__split__high__low_I2_J,axiom,
% 5.31/5.57 ! [X: nat,N: nat,M2: nat] :
% 5.31/5.57 ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N @ M2 ) ) )
% 5.31/5.57 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.57 => ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 5.31/5.57 => ( ord_less_nat @ ( vEBT_VEBT_low @ X @ N ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % VEBT_internal.exp_split_high_low(2)
% 5.31/5.57 thf(fact_4147_VEBT__internal_Oexp__split__high__low_I1_J,axiom,
% 5.31/5.57 ! [X: nat,N: nat,M2: nat] :
% 5.31/5.57 ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N @ M2 ) ) )
% 5.31/5.57 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.57 => ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 5.31/5.57 => ( ord_less_nat @ ( vEBT_VEBT_high @ X @ N ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) ) ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % VEBT_internal.exp_split_high_low(1)
% 5.31/5.57 thf(fact_4148_inf__sup__ord_I2_J,axiom,
% 5.31/5.57 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] : ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ X @ Y ) @ Y ) ).
% 5.31/5.57
% 5.31/5.57 % inf_sup_ord(2)
% 5.31/5.57 thf(fact_4149_inf__sup__ord_I2_J,axiom,
% 5.31/5.57 ! [X: set_nat,Y: set_nat] : ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ X @ Y ) @ Y ) ).
% 5.31/5.57
% 5.31/5.57 % inf_sup_ord(2)
% 5.31/5.57 thf(fact_4150_inf__sup__ord_I2_J,axiom,
% 5.31/5.57 ! [X: rat,Y: rat] : ( ord_less_eq_rat @ ( inf_inf_rat @ X @ Y ) @ Y ) ).
% 5.31/5.57
% 5.31/5.57 % inf_sup_ord(2)
% 5.31/5.57 thf(fact_4151_inf__sup__ord_I2_J,axiom,
% 5.31/5.57 ! [X: nat,Y: nat] : ( ord_less_eq_nat @ ( inf_inf_nat @ X @ Y ) @ Y ) ).
% 5.31/5.57
% 5.31/5.57 % inf_sup_ord(2)
% 5.31/5.57 thf(fact_4152_inf__sup__ord_I2_J,axiom,
% 5.31/5.57 ! [X: int,Y: int] : ( ord_less_eq_int @ ( inf_inf_int @ X @ Y ) @ Y ) ).
% 5.31/5.57
% 5.31/5.57 % inf_sup_ord(2)
% 5.31/5.57 thf(fact_4153_inf__sup__ord_I1_J,axiom,
% 5.31/5.57 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] : ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ X @ Y ) @ X ) ).
% 5.31/5.57
% 5.31/5.57 % inf_sup_ord(1)
% 5.31/5.57 thf(fact_4154_inf__sup__ord_I1_J,axiom,
% 5.31/5.57 ! [X: set_nat,Y: set_nat] : ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ X @ Y ) @ X ) ).
% 5.31/5.57
% 5.31/5.57 % inf_sup_ord(1)
% 5.31/5.57 thf(fact_4155_inf__sup__ord_I1_J,axiom,
% 5.31/5.57 ! [X: rat,Y: rat] : ( ord_less_eq_rat @ ( inf_inf_rat @ X @ Y ) @ X ) ).
% 5.31/5.57
% 5.31/5.57 % inf_sup_ord(1)
% 5.31/5.57 thf(fact_4156_inf__sup__ord_I1_J,axiom,
% 5.31/5.57 ! [X: nat,Y: nat] : ( ord_less_eq_nat @ ( inf_inf_nat @ X @ Y ) @ X ) ).
% 5.31/5.57
% 5.31/5.57 % inf_sup_ord(1)
% 5.31/5.57 thf(fact_4157_inf__sup__ord_I1_J,axiom,
% 5.31/5.57 ! [X: int,Y: int] : ( ord_less_eq_int @ ( inf_inf_int @ X @ Y ) @ X ) ).
% 5.31/5.57
% 5.31/5.57 % inf_sup_ord(1)
% 5.31/5.57 thf(fact_4158_inf__le1,axiom,
% 5.31/5.57 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] : ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ X @ Y ) @ X ) ).
% 5.31/5.57
% 5.31/5.57 % inf_le1
% 5.31/5.57 thf(fact_4159_inf__le1,axiom,
% 5.31/5.57 ! [X: set_nat,Y: set_nat] : ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ X @ Y ) @ X ) ).
% 5.31/5.57
% 5.31/5.57 % inf_le1
% 5.31/5.57 thf(fact_4160_inf__le1,axiom,
% 5.31/5.57 ! [X: rat,Y: rat] : ( ord_less_eq_rat @ ( inf_inf_rat @ X @ Y ) @ X ) ).
% 5.31/5.57
% 5.31/5.57 % inf_le1
% 5.31/5.57 thf(fact_4161_inf__le1,axiom,
% 5.31/5.57 ! [X: nat,Y: nat] : ( ord_less_eq_nat @ ( inf_inf_nat @ X @ Y ) @ X ) ).
% 5.31/5.57
% 5.31/5.57 % inf_le1
% 5.31/5.57 thf(fact_4162_inf__le1,axiom,
% 5.31/5.57 ! [X: int,Y: int] : ( ord_less_eq_int @ ( inf_inf_int @ X @ Y ) @ X ) ).
% 5.31/5.57
% 5.31/5.57 % inf_le1
% 5.31/5.57 thf(fact_4163_inf__le2,axiom,
% 5.31/5.57 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] : ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ X @ Y ) @ Y ) ).
% 5.31/5.57
% 5.31/5.57 % inf_le2
% 5.31/5.57 thf(fact_4164_inf__le2,axiom,
% 5.31/5.57 ! [X: set_nat,Y: set_nat] : ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ X @ Y ) @ Y ) ).
% 5.31/5.57
% 5.31/5.57 % inf_le2
% 5.31/5.57 thf(fact_4165_inf__le2,axiom,
% 5.31/5.57 ! [X: rat,Y: rat] : ( ord_less_eq_rat @ ( inf_inf_rat @ X @ Y ) @ Y ) ).
% 5.31/5.57
% 5.31/5.57 % inf_le2
% 5.31/5.57 thf(fact_4166_inf__le2,axiom,
% 5.31/5.57 ! [X: nat,Y: nat] : ( ord_less_eq_nat @ ( inf_inf_nat @ X @ Y ) @ Y ) ).
% 5.31/5.57
% 5.31/5.57 % inf_le2
% 5.31/5.57 thf(fact_4167_inf__le2,axiom,
% 5.31/5.57 ! [X: int,Y: int] : ( ord_less_eq_int @ ( inf_inf_int @ X @ Y ) @ Y ) ).
% 5.31/5.57
% 5.31/5.57 % inf_le2
% 5.31/5.57 thf(fact_4168_le__infE,axiom,
% 5.31/5.57 ! [X: set_Pr1261947904930325089at_nat,A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 5.31/5.57 ( ( ord_le3146513528884898305at_nat @ X @ ( inf_in2572325071724192079at_nat @ A @ B ) )
% 5.31/5.57 => ~ ( ( ord_le3146513528884898305at_nat @ X @ A )
% 5.31/5.57 => ~ ( ord_le3146513528884898305at_nat @ X @ B ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % le_infE
% 5.31/5.57 thf(fact_4169_le__infE,axiom,
% 5.31/5.57 ! [X: set_nat,A: set_nat,B: set_nat] :
% 5.31/5.57 ( ( ord_less_eq_set_nat @ X @ ( inf_inf_set_nat @ A @ B ) )
% 5.31/5.57 => ~ ( ( ord_less_eq_set_nat @ X @ A )
% 5.31/5.57 => ~ ( ord_less_eq_set_nat @ X @ B ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % le_infE
% 5.31/5.57 thf(fact_4170_le__infE,axiom,
% 5.31/5.57 ! [X: rat,A: rat,B: rat] :
% 5.31/5.57 ( ( ord_less_eq_rat @ X @ ( inf_inf_rat @ A @ B ) )
% 5.31/5.57 => ~ ( ( ord_less_eq_rat @ X @ A )
% 5.31/5.57 => ~ ( ord_less_eq_rat @ X @ B ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % le_infE
% 5.31/5.57 thf(fact_4171_le__infE,axiom,
% 5.31/5.57 ! [X: nat,A: nat,B: nat] :
% 5.31/5.57 ( ( ord_less_eq_nat @ X @ ( inf_inf_nat @ A @ B ) )
% 5.31/5.57 => ~ ( ( ord_less_eq_nat @ X @ A )
% 5.31/5.57 => ~ ( ord_less_eq_nat @ X @ B ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % le_infE
% 5.31/5.57 thf(fact_4172_le__infE,axiom,
% 5.31/5.57 ! [X: int,A: int,B: int] :
% 5.31/5.57 ( ( ord_less_eq_int @ X @ ( inf_inf_int @ A @ B ) )
% 5.31/5.57 => ~ ( ( ord_less_eq_int @ X @ A )
% 5.31/5.57 => ~ ( ord_less_eq_int @ X @ B ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % le_infE
% 5.31/5.57 thf(fact_4173_le__infI,axiom,
% 5.31/5.57 ! [X: set_Pr1261947904930325089at_nat,A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 5.31/5.57 ( ( ord_le3146513528884898305at_nat @ X @ A )
% 5.31/5.57 => ( ( ord_le3146513528884898305at_nat @ X @ B )
% 5.31/5.57 => ( ord_le3146513528884898305at_nat @ X @ ( inf_in2572325071724192079at_nat @ A @ B ) ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % le_infI
% 5.31/5.57 thf(fact_4174_le__infI,axiom,
% 5.31/5.57 ! [X: set_nat,A: set_nat,B: set_nat] :
% 5.31/5.57 ( ( ord_less_eq_set_nat @ X @ A )
% 5.31/5.57 => ( ( ord_less_eq_set_nat @ X @ B )
% 5.31/5.57 => ( ord_less_eq_set_nat @ X @ ( inf_inf_set_nat @ A @ B ) ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % le_infI
% 5.31/5.57 thf(fact_4175_le__infI,axiom,
% 5.31/5.57 ! [X: rat,A: rat,B: rat] :
% 5.31/5.57 ( ( ord_less_eq_rat @ X @ A )
% 5.31/5.57 => ( ( ord_less_eq_rat @ X @ B )
% 5.31/5.57 => ( ord_less_eq_rat @ X @ ( inf_inf_rat @ A @ B ) ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % le_infI
% 5.31/5.57 thf(fact_4176_le__infI,axiom,
% 5.31/5.57 ! [X: nat,A: nat,B: nat] :
% 5.31/5.57 ( ( ord_less_eq_nat @ X @ A )
% 5.31/5.57 => ( ( ord_less_eq_nat @ X @ B )
% 5.31/5.57 => ( ord_less_eq_nat @ X @ ( inf_inf_nat @ A @ B ) ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % le_infI
% 5.31/5.57 thf(fact_4177_le__infI,axiom,
% 5.31/5.57 ! [X: int,A: int,B: int] :
% 5.31/5.57 ( ( ord_less_eq_int @ X @ A )
% 5.31/5.57 => ( ( ord_less_eq_int @ X @ B )
% 5.31/5.57 => ( ord_less_eq_int @ X @ ( inf_inf_int @ A @ B ) ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % le_infI
% 5.31/5.57 thf(fact_4178_inf__mono,axiom,
% 5.31/5.57 ! [A: set_Pr1261947904930325089at_nat,C2: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat,D: set_Pr1261947904930325089at_nat] :
% 5.31/5.57 ( ( ord_le3146513528884898305at_nat @ A @ C2 )
% 5.31/5.57 => ( ( ord_le3146513528884898305at_nat @ B @ D )
% 5.31/5.57 => ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ A @ B ) @ ( inf_in2572325071724192079at_nat @ C2 @ D ) ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % inf_mono
% 5.31/5.57 thf(fact_4179_inf__mono,axiom,
% 5.31/5.57 ! [A: set_nat,C2: set_nat,B: set_nat,D: set_nat] :
% 5.31/5.57 ( ( ord_less_eq_set_nat @ A @ C2 )
% 5.31/5.57 => ( ( ord_less_eq_set_nat @ B @ D )
% 5.31/5.57 => ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ A @ B ) @ ( inf_inf_set_nat @ C2 @ D ) ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % inf_mono
% 5.31/5.57 thf(fact_4180_inf__mono,axiom,
% 5.31/5.57 ! [A: rat,C2: rat,B: rat,D: rat] :
% 5.31/5.57 ( ( ord_less_eq_rat @ A @ C2 )
% 5.31/5.57 => ( ( ord_less_eq_rat @ B @ D )
% 5.31/5.57 => ( ord_less_eq_rat @ ( inf_inf_rat @ A @ B ) @ ( inf_inf_rat @ C2 @ D ) ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % inf_mono
% 5.31/5.57 thf(fact_4181_inf__mono,axiom,
% 5.31/5.57 ! [A: nat,C2: nat,B: nat,D: nat] :
% 5.31/5.57 ( ( ord_less_eq_nat @ A @ C2 )
% 5.31/5.57 => ( ( ord_less_eq_nat @ B @ D )
% 5.31/5.57 => ( ord_less_eq_nat @ ( inf_inf_nat @ A @ B ) @ ( inf_inf_nat @ C2 @ D ) ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % inf_mono
% 5.31/5.57 thf(fact_4182_inf__mono,axiom,
% 5.31/5.57 ! [A: int,C2: int,B: int,D: int] :
% 5.31/5.57 ( ( ord_less_eq_int @ A @ C2 )
% 5.31/5.57 => ( ( ord_less_eq_int @ B @ D )
% 5.31/5.57 => ( ord_less_eq_int @ ( inf_inf_int @ A @ B ) @ ( inf_inf_int @ C2 @ D ) ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % inf_mono
% 5.31/5.57 thf(fact_4183_le__infI1,axiom,
% 5.31/5.57 ! [A: set_Pr1261947904930325089at_nat,X: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 5.31/5.57 ( ( ord_le3146513528884898305at_nat @ A @ X )
% 5.31/5.57 => ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ A @ B ) @ X ) ) ).
% 5.31/5.57
% 5.31/5.57 % le_infI1
% 5.31/5.57 thf(fact_4184_le__infI1,axiom,
% 5.31/5.57 ! [A: set_nat,X: set_nat,B: set_nat] :
% 5.31/5.57 ( ( ord_less_eq_set_nat @ A @ X )
% 5.31/5.57 => ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ A @ B ) @ X ) ) ).
% 5.31/5.57
% 5.31/5.57 % le_infI1
% 5.31/5.57 thf(fact_4185_le__infI1,axiom,
% 5.31/5.57 ! [A: rat,X: rat,B: rat] :
% 5.31/5.57 ( ( ord_less_eq_rat @ A @ X )
% 5.31/5.57 => ( ord_less_eq_rat @ ( inf_inf_rat @ A @ B ) @ X ) ) ).
% 5.31/5.57
% 5.31/5.57 % le_infI1
% 5.31/5.57 thf(fact_4186_le__infI1,axiom,
% 5.31/5.57 ! [A: nat,X: nat,B: nat] :
% 5.31/5.57 ( ( ord_less_eq_nat @ A @ X )
% 5.31/5.57 => ( ord_less_eq_nat @ ( inf_inf_nat @ A @ B ) @ X ) ) ).
% 5.31/5.57
% 5.31/5.57 % le_infI1
% 5.31/5.57 thf(fact_4187_le__infI1,axiom,
% 5.31/5.57 ! [A: int,X: int,B: int] :
% 5.31/5.57 ( ( ord_less_eq_int @ A @ X )
% 5.31/5.57 => ( ord_less_eq_int @ ( inf_inf_int @ A @ B ) @ X ) ) ).
% 5.31/5.57
% 5.31/5.57 % le_infI1
% 5.31/5.57 thf(fact_4188_le__infI2,axiom,
% 5.31/5.57 ! [B: set_Pr1261947904930325089at_nat,X: set_Pr1261947904930325089at_nat,A: set_Pr1261947904930325089at_nat] :
% 5.31/5.57 ( ( ord_le3146513528884898305at_nat @ B @ X )
% 5.31/5.57 => ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ A @ B ) @ X ) ) ).
% 5.31/5.57
% 5.31/5.57 % le_infI2
% 5.31/5.57 thf(fact_4189_le__infI2,axiom,
% 5.31/5.57 ! [B: set_nat,X: set_nat,A: set_nat] :
% 5.31/5.57 ( ( ord_less_eq_set_nat @ B @ X )
% 5.31/5.57 => ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ A @ B ) @ X ) ) ).
% 5.31/5.57
% 5.31/5.57 % le_infI2
% 5.31/5.57 thf(fact_4190_le__infI2,axiom,
% 5.31/5.57 ! [B: rat,X: rat,A: rat] :
% 5.31/5.57 ( ( ord_less_eq_rat @ B @ X )
% 5.31/5.57 => ( ord_less_eq_rat @ ( inf_inf_rat @ A @ B ) @ X ) ) ).
% 5.31/5.57
% 5.31/5.57 % le_infI2
% 5.31/5.57 thf(fact_4191_le__infI2,axiom,
% 5.31/5.57 ! [B: nat,X: nat,A: nat] :
% 5.31/5.57 ( ( ord_less_eq_nat @ B @ X )
% 5.31/5.57 => ( ord_less_eq_nat @ ( inf_inf_nat @ A @ B ) @ X ) ) ).
% 5.31/5.57
% 5.31/5.57 % le_infI2
% 5.31/5.57 thf(fact_4192_le__infI2,axiom,
% 5.31/5.57 ! [B: int,X: int,A: int] :
% 5.31/5.57 ( ( ord_less_eq_int @ B @ X )
% 5.31/5.57 => ( ord_less_eq_int @ ( inf_inf_int @ A @ B ) @ X ) ) ).
% 5.31/5.57
% 5.31/5.57 % le_infI2
% 5.31/5.57 thf(fact_4193_inf_OorderE,axiom,
% 5.31/5.57 ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 5.31/5.57 ( ( ord_le3146513528884898305at_nat @ A @ B )
% 5.31/5.57 => ( A
% 5.31/5.57 = ( inf_in2572325071724192079at_nat @ A @ B ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % inf.orderE
% 5.31/5.57 thf(fact_4194_inf_OorderE,axiom,
% 5.31/5.57 ! [A: set_nat,B: set_nat] :
% 5.31/5.57 ( ( ord_less_eq_set_nat @ A @ B )
% 5.31/5.57 => ( A
% 5.31/5.57 = ( inf_inf_set_nat @ A @ B ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % inf.orderE
% 5.31/5.57 thf(fact_4195_inf_OorderE,axiom,
% 5.31/5.57 ! [A: rat,B: rat] :
% 5.31/5.57 ( ( ord_less_eq_rat @ A @ B )
% 5.31/5.57 => ( A
% 5.31/5.57 = ( inf_inf_rat @ A @ B ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % inf.orderE
% 5.31/5.57 thf(fact_4196_inf_OorderE,axiom,
% 5.31/5.57 ! [A: nat,B: nat] :
% 5.31/5.57 ( ( ord_less_eq_nat @ A @ B )
% 5.31/5.57 => ( A
% 5.31/5.57 = ( inf_inf_nat @ A @ B ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % inf.orderE
% 5.31/5.57 thf(fact_4197_inf_OorderE,axiom,
% 5.31/5.57 ! [A: int,B: int] :
% 5.31/5.57 ( ( ord_less_eq_int @ A @ B )
% 5.31/5.57 => ( A
% 5.31/5.57 = ( inf_inf_int @ A @ B ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % inf.orderE
% 5.31/5.57 thf(fact_4198_inf_OorderI,axiom,
% 5.31/5.57 ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 5.31/5.57 ( ( A
% 5.31/5.57 = ( inf_in2572325071724192079at_nat @ A @ B ) )
% 5.31/5.57 => ( ord_le3146513528884898305at_nat @ A @ B ) ) ).
% 5.31/5.57
% 5.31/5.57 % inf.orderI
% 5.31/5.57 thf(fact_4199_inf_OorderI,axiom,
% 5.31/5.57 ! [A: set_nat,B: set_nat] :
% 5.31/5.57 ( ( A
% 5.31/5.57 = ( inf_inf_set_nat @ A @ B ) )
% 5.31/5.57 => ( ord_less_eq_set_nat @ A @ B ) ) ).
% 5.31/5.57
% 5.31/5.57 % inf.orderI
% 5.31/5.57 thf(fact_4200_inf_OorderI,axiom,
% 5.31/5.57 ! [A: rat,B: rat] :
% 5.31/5.57 ( ( A
% 5.31/5.57 = ( inf_inf_rat @ A @ B ) )
% 5.31/5.57 => ( ord_less_eq_rat @ A @ B ) ) ).
% 5.31/5.57
% 5.31/5.57 % inf.orderI
% 5.31/5.57 thf(fact_4201_inf_OorderI,axiom,
% 5.31/5.57 ! [A: nat,B: nat] :
% 5.31/5.57 ( ( A
% 5.31/5.57 = ( inf_inf_nat @ A @ B ) )
% 5.31/5.57 => ( ord_less_eq_nat @ A @ B ) ) ).
% 5.31/5.57
% 5.31/5.57 % inf.orderI
% 5.31/5.57 thf(fact_4202_inf_OorderI,axiom,
% 5.31/5.57 ! [A: int,B: int] :
% 5.31/5.57 ( ( A
% 5.31/5.57 = ( inf_inf_int @ A @ B ) )
% 5.31/5.57 => ( ord_less_eq_int @ A @ B ) ) ).
% 5.31/5.57
% 5.31/5.57 % inf.orderI
% 5.31/5.57 thf(fact_4203_inf__unique,axiom,
% 5.31/5.57 ! [F2: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat,X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] :
% 5.31/5.57 ( ! [X3: set_Pr1261947904930325089at_nat,Y3: set_Pr1261947904930325089at_nat] : ( ord_le3146513528884898305at_nat @ ( F2 @ X3 @ Y3 ) @ X3 )
% 5.31/5.57 => ( ! [X3: set_Pr1261947904930325089at_nat,Y3: set_Pr1261947904930325089at_nat] : ( ord_le3146513528884898305at_nat @ ( F2 @ X3 @ Y3 ) @ Y3 )
% 5.31/5.57 => ( ! [X3: set_Pr1261947904930325089at_nat,Y3: set_Pr1261947904930325089at_nat,Z: set_Pr1261947904930325089at_nat] :
% 5.31/5.57 ( ( ord_le3146513528884898305at_nat @ X3 @ Y3 )
% 5.31/5.57 => ( ( ord_le3146513528884898305at_nat @ X3 @ Z )
% 5.31/5.57 => ( ord_le3146513528884898305at_nat @ X3 @ ( F2 @ Y3 @ Z ) ) ) )
% 5.31/5.57 => ( ( inf_in2572325071724192079at_nat @ X @ Y )
% 5.31/5.57 = ( F2 @ X @ Y ) ) ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % inf_unique
% 5.31/5.57 thf(fact_4204_inf__unique,axiom,
% 5.31/5.57 ! [F2: set_nat > set_nat > set_nat,X: set_nat,Y: set_nat] :
% 5.31/5.57 ( ! [X3: set_nat,Y3: set_nat] : ( ord_less_eq_set_nat @ ( F2 @ X3 @ Y3 ) @ X3 )
% 5.31/5.57 => ( ! [X3: set_nat,Y3: set_nat] : ( ord_less_eq_set_nat @ ( F2 @ X3 @ Y3 ) @ Y3 )
% 5.31/5.57 => ( ! [X3: set_nat,Y3: set_nat,Z: set_nat] :
% 5.31/5.57 ( ( ord_less_eq_set_nat @ X3 @ Y3 )
% 5.31/5.57 => ( ( ord_less_eq_set_nat @ X3 @ Z )
% 5.31/5.57 => ( ord_less_eq_set_nat @ X3 @ ( F2 @ Y3 @ Z ) ) ) )
% 5.31/5.57 => ( ( inf_inf_set_nat @ X @ Y )
% 5.31/5.57 = ( F2 @ X @ Y ) ) ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % inf_unique
% 5.31/5.57 thf(fact_4205_inf__unique,axiom,
% 5.31/5.57 ! [F2: rat > rat > rat,X: rat,Y: rat] :
% 5.31/5.57 ( ! [X3: rat,Y3: rat] : ( ord_less_eq_rat @ ( F2 @ X3 @ Y3 ) @ X3 )
% 5.31/5.57 => ( ! [X3: rat,Y3: rat] : ( ord_less_eq_rat @ ( F2 @ X3 @ Y3 ) @ Y3 )
% 5.31/5.57 => ( ! [X3: rat,Y3: rat,Z: rat] :
% 5.31/5.57 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 5.31/5.57 => ( ( ord_less_eq_rat @ X3 @ Z )
% 5.31/5.57 => ( ord_less_eq_rat @ X3 @ ( F2 @ Y3 @ Z ) ) ) )
% 5.31/5.57 => ( ( inf_inf_rat @ X @ Y )
% 5.31/5.57 = ( F2 @ X @ Y ) ) ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % inf_unique
% 5.31/5.57 thf(fact_4206_inf__unique,axiom,
% 5.31/5.57 ! [F2: nat > nat > nat,X: nat,Y: nat] :
% 5.31/5.57 ( ! [X3: nat,Y3: nat] : ( ord_less_eq_nat @ ( F2 @ X3 @ Y3 ) @ X3 )
% 5.31/5.57 => ( ! [X3: nat,Y3: nat] : ( ord_less_eq_nat @ ( F2 @ X3 @ Y3 ) @ Y3 )
% 5.31/5.57 => ( ! [X3: nat,Y3: nat,Z: nat] :
% 5.31/5.57 ( ( ord_less_eq_nat @ X3 @ Y3 )
% 5.31/5.57 => ( ( ord_less_eq_nat @ X3 @ Z )
% 5.31/5.57 => ( ord_less_eq_nat @ X3 @ ( F2 @ Y3 @ Z ) ) ) )
% 5.31/5.57 => ( ( inf_inf_nat @ X @ Y )
% 5.31/5.57 = ( F2 @ X @ Y ) ) ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % inf_unique
% 5.31/5.57 thf(fact_4207_inf__unique,axiom,
% 5.31/5.57 ! [F2: int > int > int,X: int,Y: int] :
% 5.31/5.57 ( ! [X3: int,Y3: int] : ( ord_less_eq_int @ ( F2 @ X3 @ Y3 ) @ X3 )
% 5.31/5.57 => ( ! [X3: int,Y3: int] : ( ord_less_eq_int @ ( F2 @ X3 @ Y3 ) @ Y3 )
% 5.31/5.57 => ( ! [X3: int,Y3: int,Z: int] :
% 5.31/5.57 ( ( ord_less_eq_int @ X3 @ Y3 )
% 5.31/5.57 => ( ( ord_less_eq_int @ X3 @ Z )
% 5.31/5.57 => ( ord_less_eq_int @ X3 @ ( F2 @ Y3 @ Z ) ) ) )
% 5.31/5.57 => ( ( inf_inf_int @ X @ Y )
% 5.31/5.57 = ( F2 @ X @ Y ) ) ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % inf_unique
% 5.31/5.57 thf(fact_4208_le__iff__inf,axiom,
% 5.31/5.57 ( ord_le3146513528884898305at_nat
% 5.31/5.57 = ( ^ [X4: set_Pr1261947904930325089at_nat,Y4: set_Pr1261947904930325089at_nat] :
% 5.31/5.57 ( ( inf_in2572325071724192079at_nat @ X4 @ Y4 )
% 5.31/5.57 = X4 ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % le_iff_inf
% 5.31/5.57 thf(fact_4209_le__iff__inf,axiom,
% 5.31/5.57 ( ord_less_eq_set_nat
% 5.31/5.57 = ( ^ [X4: set_nat,Y4: set_nat] :
% 5.31/5.57 ( ( inf_inf_set_nat @ X4 @ Y4 )
% 5.31/5.57 = X4 ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % le_iff_inf
% 5.31/5.57 thf(fact_4210_le__iff__inf,axiom,
% 5.31/5.57 ( ord_less_eq_rat
% 5.31/5.57 = ( ^ [X4: rat,Y4: rat] :
% 5.31/5.57 ( ( inf_inf_rat @ X4 @ Y4 )
% 5.31/5.57 = X4 ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % le_iff_inf
% 5.31/5.57 thf(fact_4211_le__iff__inf,axiom,
% 5.31/5.57 ( ord_less_eq_nat
% 5.31/5.57 = ( ^ [X4: nat,Y4: nat] :
% 5.31/5.57 ( ( inf_inf_nat @ X4 @ Y4 )
% 5.31/5.57 = X4 ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % le_iff_inf
% 5.31/5.57 thf(fact_4212_le__iff__inf,axiom,
% 5.31/5.57 ( ord_less_eq_int
% 5.31/5.57 = ( ^ [X4: int,Y4: int] :
% 5.31/5.57 ( ( inf_inf_int @ X4 @ Y4 )
% 5.31/5.57 = X4 ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % le_iff_inf
% 5.31/5.57 thf(fact_4213_inf_Oabsorb1,axiom,
% 5.31/5.57 ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 5.31/5.57 ( ( ord_le3146513528884898305at_nat @ A @ B )
% 5.31/5.57 => ( ( inf_in2572325071724192079at_nat @ A @ B )
% 5.31/5.57 = A ) ) ).
% 5.31/5.57
% 5.31/5.57 % inf.absorb1
% 5.31/5.57 thf(fact_4214_inf_Oabsorb1,axiom,
% 5.31/5.57 ! [A: set_nat,B: set_nat] :
% 5.31/5.57 ( ( ord_less_eq_set_nat @ A @ B )
% 5.31/5.57 => ( ( inf_inf_set_nat @ A @ B )
% 5.31/5.57 = A ) ) ).
% 5.31/5.57
% 5.31/5.57 % inf.absorb1
% 5.31/5.57 thf(fact_4215_inf_Oabsorb1,axiom,
% 5.31/5.57 ! [A: rat,B: rat] :
% 5.31/5.57 ( ( ord_less_eq_rat @ A @ B )
% 5.31/5.57 => ( ( inf_inf_rat @ A @ B )
% 5.31/5.57 = A ) ) ).
% 5.31/5.57
% 5.31/5.57 % inf.absorb1
% 5.31/5.57 thf(fact_4216_inf_Oabsorb1,axiom,
% 5.31/5.57 ! [A: nat,B: nat] :
% 5.31/5.57 ( ( ord_less_eq_nat @ A @ B )
% 5.31/5.57 => ( ( inf_inf_nat @ A @ B )
% 5.31/5.57 = A ) ) ).
% 5.31/5.57
% 5.31/5.57 % inf.absorb1
% 5.31/5.57 thf(fact_4217_inf_Oabsorb1,axiom,
% 5.31/5.57 ! [A: int,B: int] :
% 5.31/5.57 ( ( ord_less_eq_int @ A @ B )
% 5.31/5.57 => ( ( inf_inf_int @ A @ B )
% 5.31/5.57 = A ) ) ).
% 5.31/5.57
% 5.31/5.57 % inf.absorb1
% 5.31/5.57 thf(fact_4218_inf_Oabsorb2,axiom,
% 5.31/5.57 ! [B: set_Pr1261947904930325089at_nat,A: set_Pr1261947904930325089at_nat] :
% 5.31/5.57 ( ( ord_le3146513528884898305at_nat @ B @ A )
% 5.31/5.57 => ( ( inf_in2572325071724192079at_nat @ A @ B )
% 5.31/5.57 = B ) ) ).
% 5.31/5.57
% 5.31/5.57 % inf.absorb2
% 5.31/5.57 thf(fact_4219_inf_Oabsorb2,axiom,
% 5.31/5.57 ! [B: set_nat,A: set_nat] :
% 5.31/5.57 ( ( ord_less_eq_set_nat @ B @ A )
% 5.31/5.57 => ( ( inf_inf_set_nat @ A @ B )
% 5.31/5.57 = B ) ) ).
% 5.31/5.57
% 5.31/5.57 % inf.absorb2
% 5.31/5.57 thf(fact_4220_inf_Oabsorb2,axiom,
% 5.31/5.57 ! [B: rat,A: rat] :
% 5.31/5.57 ( ( ord_less_eq_rat @ B @ A )
% 5.31/5.57 => ( ( inf_inf_rat @ A @ B )
% 5.31/5.57 = B ) ) ).
% 5.31/5.57
% 5.31/5.57 % inf.absorb2
% 5.31/5.57 thf(fact_4221_inf_Oabsorb2,axiom,
% 5.31/5.57 ! [B: nat,A: nat] :
% 5.31/5.57 ( ( ord_less_eq_nat @ B @ A )
% 5.31/5.57 => ( ( inf_inf_nat @ A @ B )
% 5.31/5.57 = B ) ) ).
% 5.31/5.57
% 5.31/5.57 % inf.absorb2
% 5.31/5.57 thf(fact_4222_inf_Oabsorb2,axiom,
% 5.31/5.57 ! [B: int,A: int] :
% 5.31/5.57 ( ( ord_less_eq_int @ B @ A )
% 5.31/5.57 => ( ( inf_inf_int @ A @ B )
% 5.31/5.57 = B ) ) ).
% 5.31/5.57
% 5.31/5.57 % inf.absorb2
% 5.31/5.57 thf(fact_4223_inf__absorb1,axiom,
% 5.31/5.57 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] :
% 5.31/5.57 ( ( ord_le3146513528884898305at_nat @ X @ Y )
% 5.31/5.57 => ( ( inf_in2572325071724192079at_nat @ X @ Y )
% 5.31/5.57 = X ) ) ).
% 5.31/5.57
% 5.31/5.57 % inf_absorb1
% 5.31/5.57 thf(fact_4224_inf__absorb1,axiom,
% 5.31/5.57 ! [X: set_nat,Y: set_nat] :
% 5.31/5.57 ( ( ord_less_eq_set_nat @ X @ Y )
% 5.31/5.57 => ( ( inf_inf_set_nat @ X @ Y )
% 5.31/5.57 = X ) ) ).
% 5.31/5.57
% 5.31/5.57 % inf_absorb1
% 5.31/5.57 thf(fact_4225_inf__absorb1,axiom,
% 5.31/5.57 ! [X: rat,Y: rat] :
% 5.31/5.57 ( ( ord_less_eq_rat @ X @ Y )
% 5.31/5.57 => ( ( inf_inf_rat @ X @ Y )
% 5.31/5.57 = X ) ) ).
% 5.31/5.57
% 5.31/5.57 % inf_absorb1
% 5.31/5.57 thf(fact_4226_inf__absorb1,axiom,
% 5.31/5.57 ! [X: nat,Y: nat] :
% 5.31/5.57 ( ( ord_less_eq_nat @ X @ Y )
% 5.31/5.57 => ( ( inf_inf_nat @ X @ Y )
% 5.31/5.57 = X ) ) ).
% 5.31/5.57
% 5.31/5.57 % inf_absorb1
% 5.31/5.57 thf(fact_4227_inf__absorb1,axiom,
% 5.31/5.57 ! [X: int,Y: int] :
% 5.31/5.57 ( ( ord_less_eq_int @ X @ Y )
% 5.31/5.57 => ( ( inf_inf_int @ X @ Y )
% 5.31/5.57 = X ) ) ).
% 5.31/5.57
% 5.31/5.57 % inf_absorb1
% 5.31/5.57 thf(fact_4228_inf__absorb2,axiom,
% 5.31/5.57 ! [Y: set_Pr1261947904930325089at_nat,X: set_Pr1261947904930325089at_nat] :
% 5.31/5.57 ( ( ord_le3146513528884898305at_nat @ Y @ X )
% 5.31/5.57 => ( ( inf_in2572325071724192079at_nat @ X @ Y )
% 5.31/5.57 = Y ) ) ).
% 5.31/5.57
% 5.31/5.57 % inf_absorb2
% 5.31/5.57 thf(fact_4229_inf__absorb2,axiom,
% 5.31/5.57 ! [Y: set_nat,X: set_nat] :
% 5.31/5.57 ( ( ord_less_eq_set_nat @ Y @ X )
% 5.31/5.57 => ( ( inf_inf_set_nat @ X @ Y )
% 5.31/5.57 = Y ) ) ).
% 5.31/5.57
% 5.31/5.57 % inf_absorb2
% 5.31/5.57 thf(fact_4230_inf__absorb2,axiom,
% 5.31/5.57 ! [Y: rat,X: rat] :
% 5.31/5.57 ( ( ord_less_eq_rat @ Y @ X )
% 5.31/5.57 => ( ( inf_inf_rat @ X @ Y )
% 5.31/5.57 = Y ) ) ).
% 5.31/5.57
% 5.31/5.57 % inf_absorb2
% 5.31/5.57 thf(fact_4231_inf__absorb2,axiom,
% 5.31/5.57 ! [Y: nat,X: nat] :
% 5.31/5.57 ( ( ord_less_eq_nat @ Y @ X )
% 5.31/5.57 => ( ( inf_inf_nat @ X @ Y )
% 5.31/5.57 = Y ) ) ).
% 5.31/5.57
% 5.31/5.57 % inf_absorb2
% 5.31/5.57 thf(fact_4232_inf__absorb2,axiom,
% 5.31/5.57 ! [Y: int,X: int] :
% 5.31/5.57 ( ( ord_less_eq_int @ Y @ X )
% 5.31/5.57 => ( ( inf_inf_int @ X @ Y )
% 5.31/5.57 = Y ) ) ).
% 5.31/5.57
% 5.31/5.57 % inf_absorb2
% 5.31/5.57 thf(fact_4233_inf_OboundedE,axiom,
% 5.31/5.57 ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat,C2: set_Pr1261947904930325089at_nat] :
% 5.31/5.57 ( ( ord_le3146513528884898305at_nat @ A @ ( inf_in2572325071724192079at_nat @ B @ C2 ) )
% 5.31/5.57 => ~ ( ( ord_le3146513528884898305at_nat @ A @ B )
% 5.31/5.57 => ~ ( ord_le3146513528884898305at_nat @ A @ C2 ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % inf.boundedE
% 5.31/5.57 thf(fact_4234_inf_OboundedE,axiom,
% 5.31/5.57 ! [A: set_nat,B: set_nat,C2: set_nat] :
% 5.31/5.57 ( ( ord_less_eq_set_nat @ A @ ( inf_inf_set_nat @ B @ C2 ) )
% 5.31/5.57 => ~ ( ( ord_less_eq_set_nat @ A @ B )
% 5.31/5.57 => ~ ( ord_less_eq_set_nat @ A @ C2 ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % inf.boundedE
% 5.31/5.57 thf(fact_4235_inf_OboundedE,axiom,
% 5.31/5.57 ! [A: rat,B: rat,C2: rat] :
% 5.31/5.57 ( ( ord_less_eq_rat @ A @ ( inf_inf_rat @ B @ C2 ) )
% 5.31/5.57 => ~ ( ( ord_less_eq_rat @ A @ B )
% 5.31/5.57 => ~ ( ord_less_eq_rat @ A @ C2 ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % inf.boundedE
% 5.31/5.57 thf(fact_4236_inf_OboundedE,axiom,
% 5.31/5.57 ! [A: nat,B: nat,C2: nat] :
% 5.31/5.57 ( ( ord_less_eq_nat @ A @ ( inf_inf_nat @ B @ C2 ) )
% 5.31/5.57 => ~ ( ( ord_less_eq_nat @ A @ B )
% 5.31/5.57 => ~ ( ord_less_eq_nat @ A @ C2 ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % inf.boundedE
% 5.31/5.57 thf(fact_4237_inf_OboundedE,axiom,
% 5.31/5.57 ! [A: int,B: int,C2: int] :
% 5.31/5.57 ( ( ord_less_eq_int @ A @ ( inf_inf_int @ B @ C2 ) )
% 5.31/5.57 => ~ ( ( ord_less_eq_int @ A @ B )
% 5.31/5.57 => ~ ( ord_less_eq_int @ A @ C2 ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % inf.boundedE
% 5.31/5.57 thf(fact_4238_inf_OboundedI,axiom,
% 5.31/5.57 ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat,C2: set_Pr1261947904930325089at_nat] :
% 5.31/5.57 ( ( ord_le3146513528884898305at_nat @ A @ B )
% 5.31/5.57 => ( ( ord_le3146513528884898305at_nat @ A @ C2 )
% 5.31/5.57 => ( ord_le3146513528884898305at_nat @ A @ ( inf_in2572325071724192079at_nat @ B @ C2 ) ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % inf.boundedI
% 5.31/5.57 thf(fact_4239_inf_OboundedI,axiom,
% 5.31/5.57 ! [A: set_nat,B: set_nat,C2: set_nat] :
% 5.31/5.57 ( ( ord_less_eq_set_nat @ A @ B )
% 5.31/5.57 => ( ( ord_less_eq_set_nat @ A @ C2 )
% 5.31/5.57 => ( ord_less_eq_set_nat @ A @ ( inf_inf_set_nat @ B @ C2 ) ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % inf.boundedI
% 5.31/5.57 thf(fact_4240_inf_OboundedI,axiom,
% 5.31/5.57 ! [A: rat,B: rat,C2: rat] :
% 5.31/5.57 ( ( ord_less_eq_rat @ A @ B )
% 5.31/5.57 => ( ( ord_less_eq_rat @ A @ C2 )
% 5.31/5.57 => ( ord_less_eq_rat @ A @ ( inf_inf_rat @ B @ C2 ) ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % inf.boundedI
% 5.31/5.57 thf(fact_4241_inf_OboundedI,axiom,
% 5.31/5.57 ! [A: nat,B: nat,C2: nat] :
% 5.31/5.57 ( ( ord_less_eq_nat @ A @ B )
% 5.31/5.57 => ( ( ord_less_eq_nat @ A @ C2 )
% 5.31/5.57 => ( ord_less_eq_nat @ A @ ( inf_inf_nat @ B @ C2 ) ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % inf.boundedI
% 5.31/5.57 thf(fact_4242_inf_OboundedI,axiom,
% 5.31/5.57 ! [A: int,B: int,C2: int] :
% 5.31/5.57 ( ( ord_less_eq_int @ A @ B )
% 5.31/5.57 => ( ( ord_less_eq_int @ A @ C2 )
% 5.31/5.57 => ( ord_less_eq_int @ A @ ( inf_inf_int @ B @ C2 ) ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % inf.boundedI
% 5.31/5.57 thf(fact_4243_inf__greatest,axiom,
% 5.31/5.57 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,Z3: set_Pr1261947904930325089at_nat] :
% 5.31/5.57 ( ( ord_le3146513528884898305at_nat @ X @ Y )
% 5.31/5.57 => ( ( ord_le3146513528884898305at_nat @ X @ Z3 )
% 5.31/5.57 => ( ord_le3146513528884898305at_nat @ X @ ( inf_in2572325071724192079at_nat @ Y @ Z3 ) ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % inf_greatest
% 5.31/5.57 thf(fact_4244_inf__greatest,axiom,
% 5.31/5.57 ! [X: set_nat,Y: set_nat,Z3: set_nat] :
% 5.31/5.57 ( ( ord_less_eq_set_nat @ X @ Y )
% 5.31/5.57 => ( ( ord_less_eq_set_nat @ X @ Z3 )
% 5.31/5.57 => ( ord_less_eq_set_nat @ X @ ( inf_inf_set_nat @ Y @ Z3 ) ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % inf_greatest
% 5.31/5.57 thf(fact_4245_inf__greatest,axiom,
% 5.31/5.57 ! [X: rat,Y: rat,Z3: rat] :
% 5.31/5.57 ( ( ord_less_eq_rat @ X @ Y )
% 5.31/5.57 => ( ( ord_less_eq_rat @ X @ Z3 )
% 5.31/5.57 => ( ord_less_eq_rat @ X @ ( inf_inf_rat @ Y @ Z3 ) ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % inf_greatest
% 5.31/5.57 thf(fact_4246_inf__greatest,axiom,
% 5.31/5.57 ! [X: nat,Y: nat,Z3: nat] :
% 5.31/5.57 ( ( ord_less_eq_nat @ X @ Y )
% 5.31/5.57 => ( ( ord_less_eq_nat @ X @ Z3 )
% 5.31/5.57 => ( ord_less_eq_nat @ X @ ( inf_inf_nat @ Y @ Z3 ) ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % inf_greatest
% 5.31/5.57 thf(fact_4247_inf__greatest,axiom,
% 5.31/5.57 ! [X: int,Y: int,Z3: int] :
% 5.31/5.57 ( ( ord_less_eq_int @ X @ Y )
% 5.31/5.57 => ( ( ord_less_eq_int @ X @ Z3 )
% 5.31/5.57 => ( ord_less_eq_int @ X @ ( inf_inf_int @ Y @ Z3 ) ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % inf_greatest
% 5.31/5.57 thf(fact_4248_inf_Oorder__iff,axiom,
% 5.31/5.57 ( ord_le3146513528884898305at_nat
% 5.31/5.57 = ( ^ [A5: set_Pr1261947904930325089at_nat,B4: set_Pr1261947904930325089at_nat] :
% 5.31/5.57 ( A5
% 5.31/5.57 = ( inf_in2572325071724192079at_nat @ A5 @ B4 ) ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % inf.order_iff
% 5.31/5.57 thf(fact_4249_inf_Oorder__iff,axiom,
% 5.31/5.57 ( ord_less_eq_set_nat
% 5.31/5.57 = ( ^ [A5: set_nat,B4: set_nat] :
% 5.31/5.57 ( A5
% 5.31/5.57 = ( inf_inf_set_nat @ A5 @ B4 ) ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % inf.order_iff
% 5.31/5.57 thf(fact_4250_inf_Oorder__iff,axiom,
% 5.31/5.57 ( ord_less_eq_rat
% 5.31/5.57 = ( ^ [A5: rat,B4: rat] :
% 5.31/5.57 ( A5
% 5.31/5.57 = ( inf_inf_rat @ A5 @ B4 ) ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % inf.order_iff
% 5.31/5.57 thf(fact_4251_inf_Oorder__iff,axiom,
% 5.31/5.57 ( ord_less_eq_nat
% 5.31/5.57 = ( ^ [A5: nat,B4: nat] :
% 5.31/5.57 ( A5
% 5.31/5.57 = ( inf_inf_nat @ A5 @ B4 ) ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % inf.order_iff
% 5.31/5.57 thf(fact_4252_inf_Oorder__iff,axiom,
% 5.31/5.57 ( ord_less_eq_int
% 5.31/5.57 = ( ^ [A5: int,B4: int] :
% 5.31/5.57 ( A5
% 5.31/5.57 = ( inf_inf_int @ A5 @ B4 ) ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % inf.order_iff
% 5.31/5.57 thf(fact_4253_inf_Ocobounded1,axiom,
% 5.31/5.57 ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] : ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ A @ B ) @ A ) ).
% 5.31/5.57
% 5.31/5.57 % inf.cobounded1
% 5.31/5.57 thf(fact_4254_inf_Ocobounded1,axiom,
% 5.31/5.57 ! [A: set_nat,B: set_nat] : ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ A @ B ) @ A ) ).
% 5.31/5.57
% 5.31/5.57 % inf.cobounded1
% 5.31/5.57 thf(fact_4255_inf_Ocobounded1,axiom,
% 5.31/5.57 ! [A: rat,B: rat] : ( ord_less_eq_rat @ ( inf_inf_rat @ A @ B ) @ A ) ).
% 5.31/5.57
% 5.31/5.57 % inf.cobounded1
% 5.31/5.57 thf(fact_4256_inf_Ocobounded1,axiom,
% 5.31/5.57 ! [A: nat,B: nat] : ( ord_less_eq_nat @ ( inf_inf_nat @ A @ B ) @ A ) ).
% 5.31/5.57
% 5.31/5.57 % inf.cobounded1
% 5.31/5.57 thf(fact_4257_inf_Ocobounded1,axiom,
% 5.31/5.57 ! [A: int,B: int] : ( ord_less_eq_int @ ( inf_inf_int @ A @ B ) @ A ) ).
% 5.31/5.57
% 5.31/5.57 % inf.cobounded1
% 5.31/5.57 thf(fact_4258_inf_Ocobounded2,axiom,
% 5.31/5.57 ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] : ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ A @ B ) @ B ) ).
% 5.31/5.57
% 5.31/5.57 % inf.cobounded2
% 5.31/5.57 thf(fact_4259_inf_Ocobounded2,axiom,
% 5.31/5.57 ! [A: set_nat,B: set_nat] : ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ A @ B ) @ B ) ).
% 5.31/5.57
% 5.31/5.57 % inf.cobounded2
% 5.31/5.57 thf(fact_4260_inf_Ocobounded2,axiom,
% 5.31/5.57 ! [A: rat,B: rat] : ( ord_less_eq_rat @ ( inf_inf_rat @ A @ B ) @ B ) ).
% 5.31/5.57
% 5.31/5.57 % inf.cobounded2
% 5.31/5.57 thf(fact_4261_inf_Ocobounded2,axiom,
% 5.31/5.57 ! [A: nat,B: nat] : ( ord_less_eq_nat @ ( inf_inf_nat @ A @ B ) @ B ) ).
% 5.31/5.57
% 5.31/5.57 % inf.cobounded2
% 5.31/5.57 thf(fact_4262_inf_Ocobounded2,axiom,
% 5.31/5.57 ! [A: int,B: int] : ( ord_less_eq_int @ ( inf_inf_int @ A @ B ) @ B ) ).
% 5.31/5.57
% 5.31/5.57 % inf.cobounded2
% 5.31/5.57 thf(fact_4263_inf_Oabsorb__iff1,axiom,
% 5.31/5.57 ( ord_le3146513528884898305at_nat
% 5.31/5.57 = ( ^ [A5: set_Pr1261947904930325089at_nat,B4: set_Pr1261947904930325089at_nat] :
% 5.31/5.57 ( ( inf_in2572325071724192079at_nat @ A5 @ B4 )
% 5.31/5.57 = A5 ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % inf.absorb_iff1
% 5.31/5.57 thf(fact_4264_inf_Oabsorb__iff1,axiom,
% 5.31/5.57 ( ord_less_eq_set_nat
% 5.31/5.57 = ( ^ [A5: set_nat,B4: set_nat] :
% 5.31/5.57 ( ( inf_inf_set_nat @ A5 @ B4 )
% 5.31/5.57 = A5 ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % inf.absorb_iff1
% 5.31/5.57 thf(fact_4265_inf_Oabsorb__iff1,axiom,
% 5.31/5.57 ( ord_less_eq_rat
% 5.31/5.57 = ( ^ [A5: rat,B4: rat] :
% 5.31/5.57 ( ( inf_inf_rat @ A5 @ B4 )
% 5.31/5.57 = A5 ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % inf.absorb_iff1
% 5.31/5.57 thf(fact_4266_inf_Oabsorb__iff1,axiom,
% 5.31/5.57 ( ord_less_eq_nat
% 5.31/5.57 = ( ^ [A5: nat,B4: nat] :
% 5.31/5.57 ( ( inf_inf_nat @ A5 @ B4 )
% 5.31/5.57 = A5 ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % inf.absorb_iff1
% 5.31/5.57 thf(fact_4267_inf_Oabsorb__iff1,axiom,
% 5.31/5.57 ( ord_less_eq_int
% 5.31/5.57 = ( ^ [A5: int,B4: int] :
% 5.31/5.57 ( ( inf_inf_int @ A5 @ B4 )
% 5.31/5.57 = A5 ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % inf.absorb_iff1
% 5.31/5.57 thf(fact_4268_inf_Oabsorb__iff2,axiom,
% 5.31/5.57 ( ord_le3146513528884898305at_nat
% 5.31/5.57 = ( ^ [B4: set_Pr1261947904930325089at_nat,A5: set_Pr1261947904930325089at_nat] :
% 5.31/5.57 ( ( inf_in2572325071724192079at_nat @ A5 @ B4 )
% 5.31/5.57 = B4 ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % inf.absorb_iff2
% 5.31/5.57 thf(fact_4269_inf_Oabsorb__iff2,axiom,
% 5.31/5.57 ( ord_less_eq_set_nat
% 5.31/5.57 = ( ^ [B4: set_nat,A5: set_nat] :
% 5.31/5.57 ( ( inf_inf_set_nat @ A5 @ B4 )
% 5.31/5.57 = B4 ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % inf.absorb_iff2
% 5.31/5.57 thf(fact_4270_inf_Oabsorb__iff2,axiom,
% 5.31/5.57 ( ord_less_eq_rat
% 5.31/5.57 = ( ^ [B4: rat,A5: rat] :
% 5.31/5.57 ( ( inf_inf_rat @ A5 @ B4 )
% 5.31/5.57 = B4 ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % inf.absorb_iff2
% 5.31/5.57 thf(fact_4271_inf_Oabsorb__iff2,axiom,
% 5.31/5.57 ( ord_less_eq_nat
% 5.31/5.57 = ( ^ [B4: nat,A5: nat] :
% 5.31/5.57 ( ( inf_inf_nat @ A5 @ B4 )
% 5.31/5.57 = B4 ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % inf.absorb_iff2
% 5.31/5.57 thf(fact_4272_inf_Oabsorb__iff2,axiom,
% 5.31/5.57 ( ord_less_eq_int
% 5.31/5.57 = ( ^ [B4: int,A5: int] :
% 5.31/5.57 ( ( inf_inf_int @ A5 @ B4 )
% 5.31/5.57 = B4 ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % inf.absorb_iff2
% 5.31/5.57 thf(fact_4273_inf_OcoboundedI1,axiom,
% 5.31/5.57 ! [A: set_Pr1261947904930325089at_nat,C2: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 5.31/5.57 ( ( ord_le3146513528884898305at_nat @ A @ C2 )
% 5.31/5.57 => ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ A @ B ) @ C2 ) ) ).
% 5.31/5.57
% 5.31/5.57 % inf.coboundedI1
% 5.31/5.57 thf(fact_4274_inf_OcoboundedI1,axiom,
% 5.31/5.57 ! [A: set_nat,C2: set_nat,B: set_nat] :
% 5.31/5.57 ( ( ord_less_eq_set_nat @ A @ C2 )
% 5.31/5.57 => ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ A @ B ) @ C2 ) ) ).
% 5.31/5.57
% 5.31/5.57 % inf.coboundedI1
% 5.31/5.57 thf(fact_4275_inf_OcoboundedI1,axiom,
% 5.31/5.57 ! [A: rat,C2: rat,B: rat] :
% 5.31/5.57 ( ( ord_less_eq_rat @ A @ C2 )
% 5.31/5.57 => ( ord_less_eq_rat @ ( inf_inf_rat @ A @ B ) @ C2 ) ) ).
% 5.31/5.57
% 5.31/5.57 % inf.coboundedI1
% 5.31/5.57 thf(fact_4276_inf_OcoboundedI1,axiom,
% 5.31/5.57 ! [A: nat,C2: nat,B: nat] :
% 5.31/5.57 ( ( ord_less_eq_nat @ A @ C2 )
% 5.31/5.57 => ( ord_less_eq_nat @ ( inf_inf_nat @ A @ B ) @ C2 ) ) ).
% 5.31/5.57
% 5.31/5.57 % inf.coboundedI1
% 5.31/5.57 thf(fact_4277_inf_OcoboundedI1,axiom,
% 5.31/5.57 ! [A: int,C2: int,B: int] :
% 5.31/5.57 ( ( ord_less_eq_int @ A @ C2 )
% 5.31/5.57 => ( ord_less_eq_int @ ( inf_inf_int @ A @ B ) @ C2 ) ) ).
% 5.31/5.57
% 5.31/5.57 % inf.coboundedI1
% 5.31/5.57 thf(fact_4278_inf_OcoboundedI2,axiom,
% 5.31/5.57 ! [B: set_Pr1261947904930325089at_nat,C2: set_Pr1261947904930325089at_nat,A: set_Pr1261947904930325089at_nat] :
% 5.31/5.57 ( ( ord_le3146513528884898305at_nat @ B @ C2 )
% 5.31/5.57 => ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ A @ B ) @ C2 ) ) ).
% 5.31/5.57
% 5.31/5.57 % inf.coboundedI2
% 5.31/5.57 thf(fact_4279_inf_OcoboundedI2,axiom,
% 5.31/5.57 ! [B: set_nat,C2: set_nat,A: set_nat] :
% 5.31/5.57 ( ( ord_less_eq_set_nat @ B @ C2 )
% 5.31/5.57 => ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ A @ B ) @ C2 ) ) ).
% 5.31/5.57
% 5.31/5.57 % inf.coboundedI2
% 5.31/5.57 thf(fact_4280_inf_OcoboundedI2,axiom,
% 5.31/5.57 ! [B: rat,C2: rat,A: rat] :
% 5.31/5.57 ( ( ord_less_eq_rat @ B @ C2 )
% 5.31/5.57 => ( ord_less_eq_rat @ ( inf_inf_rat @ A @ B ) @ C2 ) ) ).
% 5.31/5.57
% 5.31/5.57 % inf.coboundedI2
% 5.31/5.57 thf(fact_4281_inf_OcoboundedI2,axiom,
% 5.31/5.57 ! [B: nat,C2: nat,A: nat] :
% 5.31/5.57 ( ( ord_less_eq_nat @ B @ C2 )
% 5.31/5.57 => ( ord_less_eq_nat @ ( inf_inf_nat @ A @ B ) @ C2 ) ) ).
% 5.31/5.57
% 5.31/5.57 % inf.coboundedI2
% 5.31/5.57 thf(fact_4282_inf_OcoboundedI2,axiom,
% 5.31/5.57 ! [B: int,C2: int,A: int] :
% 5.31/5.57 ( ( ord_less_eq_int @ B @ C2 )
% 5.31/5.57 => ( ord_less_eq_int @ ( inf_inf_int @ A @ B ) @ C2 ) ) ).
% 5.31/5.57
% 5.31/5.57 % inf.coboundedI2
% 5.31/5.57 thf(fact_4283_sup_OcoboundedI2,axiom,
% 5.31/5.57 ! [C2: set_nat,B: set_nat,A: set_nat] :
% 5.31/5.57 ( ( ord_less_eq_set_nat @ C2 @ B )
% 5.31/5.57 => ( ord_less_eq_set_nat @ C2 @ ( sup_sup_set_nat @ A @ B ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % sup.coboundedI2
% 5.31/5.57 thf(fact_4284_sup_OcoboundedI2,axiom,
% 5.31/5.57 ! [C2: rat,B: rat,A: rat] :
% 5.31/5.57 ( ( ord_less_eq_rat @ C2 @ B )
% 5.31/5.57 => ( ord_less_eq_rat @ C2 @ ( sup_sup_rat @ A @ B ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % sup.coboundedI2
% 5.31/5.57 thf(fact_4285_sup_OcoboundedI2,axiom,
% 5.31/5.57 ! [C2: nat,B: nat,A: nat] :
% 5.31/5.57 ( ( ord_less_eq_nat @ C2 @ B )
% 5.31/5.57 => ( ord_less_eq_nat @ C2 @ ( sup_sup_nat @ A @ B ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % sup.coboundedI2
% 5.31/5.57 thf(fact_4286_sup_OcoboundedI2,axiom,
% 5.31/5.57 ! [C2: int,B: int,A: int] :
% 5.31/5.57 ( ( ord_less_eq_int @ C2 @ B )
% 5.31/5.57 => ( ord_less_eq_int @ C2 @ ( sup_sup_int @ A @ B ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % sup.coboundedI2
% 5.31/5.57 thf(fact_4287_sup_OcoboundedI1,axiom,
% 5.31/5.57 ! [C2: set_nat,A: set_nat,B: set_nat] :
% 5.31/5.57 ( ( ord_less_eq_set_nat @ C2 @ A )
% 5.31/5.57 => ( ord_less_eq_set_nat @ C2 @ ( sup_sup_set_nat @ A @ B ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % sup.coboundedI1
% 5.31/5.57 thf(fact_4288_sup_OcoboundedI1,axiom,
% 5.31/5.57 ! [C2: rat,A: rat,B: rat] :
% 5.31/5.57 ( ( ord_less_eq_rat @ C2 @ A )
% 5.31/5.57 => ( ord_less_eq_rat @ C2 @ ( sup_sup_rat @ A @ B ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % sup.coboundedI1
% 5.31/5.57 thf(fact_4289_sup_OcoboundedI1,axiom,
% 5.31/5.57 ! [C2: nat,A: nat,B: nat] :
% 5.31/5.57 ( ( ord_less_eq_nat @ C2 @ A )
% 5.31/5.57 => ( ord_less_eq_nat @ C2 @ ( sup_sup_nat @ A @ B ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % sup.coboundedI1
% 5.31/5.57 thf(fact_4290_sup_OcoboundedI1,axiom,
% 5.31/5.57 ! [C2: int,A: int,B: int] :
% 5.31/5.57 ( ( ord_less_eq_int @ C2 @ A )
% 5.31/5.57 => ( ord_less_eq_int @ C2 @ ( sup_sup_int @ A @ B ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % sup.coboundedI1
% 5.31/5.57 thf(fact_4291_sup_Oabsorb__iff2,axiom,
% 5.31/5.57 ( ord_less_eq_set_nat
% 5.31/5.57 = ( ^ [A5: set_nat,B4: set_nat] :
% 5.31/5.57 ( ( sup_sup_set_nat @ A5 @ B4 )
% 5.31/5.57 = B4 ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % sup.absorb_iff2
% 5.31/5.57 thf(fact_4292_sup_Oabsorb__iff2,axiom,
% 5.31/5.57 ( ord_less_eq_rat
% 5.31/5.57 = ( ^ [A5: rat,B4: rat] :
% 5.31/5.57 ( ( sup_sup_rat @ A5 @ B4 )
% 5.31/5.57 = B4 ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % sup.absorb_iff2
% 5.31/5.57 thf(fact_4293_sup_Oabsorb__iff2,axiom,
% 5.31/5.57 ( ord_less_eq_nat
% 5.31/5.57 = ( ^ [A5: nat,B4: nat] :
% 5.31/5.57 ( ( sup_sup_nat @ A5 @ B4 )
% 5.31/5.57 = B4 ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % sup.absorb_iff2
% 5.31/5.57 thf(fact_4294_sup_Oabsorb__iff2,axiom,
% 5.31/5.57 ( ord_less_eq_int
% 5.31/5.57 = ( ^ [A5: int,B4: int] :
% 5.31/5.57 ( ( sup_sup_int @ A5 @ B4 )
% 5.31/5.57 = B4 ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % sup.absorb_iff2
% 5.31/5.57 thf(fact_4295_sup_Oabsorb__iff1,axiom,
% 5.31/5.57 ( ord_less_eq_set_nat
% 5.31/5.57 = ( ^ [B4: set_nat,A5: set_nat] :
% 5.31/5.57 ( ( sup_sup_set_nat @ A5 @ B4 )
% 5.31/5.57 = A5 ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % sup.absorb_iff1
% 5.31/5.57 thf(fact_4296_sup_Oabsorb__iff1,axiom,
% 5.31/5.57 ( ord_less_eq_rat
% 5.31/5.57 = ( ^ [B4: rat,A5: rat] :
% 5.31/5.57 ( ( sup_sup_rat @ A5 @ B4 )
% 5.31/5.57 = A5 ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % sup.absorb_iff1
% 5.31/5.57 thf(fact_4297_sup_Oabsorb__iff1,axiom,
% 5.31/5.57 ( ord_less_eq_nat
% 5.31/5.57 = ( ^ [B4: nat,A5: nat] :
% 5.31/5.57 ( ( sup_sup_nat @ A5 @ B4 )
% 5.31/5.57 = A5 ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % sup.absorb_iff1
% 5.31/5.57 thf(fact_4298_sup_Oabsorb__iff1,axiom,
% 5.31/5.57 ( ord_less_eq_int
% 5.31/5.57 = ( ^ [B4: int,A5: int] :
% 5.31/5.57 ( ( sup_sup_int @ A5 @ B4 )
% 5.31/5.57 = A5 ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % sup.absorb_iff1
% 5.31/5.57 thf(fact_4299_sup_Ocobounded2,axiom,
% 5.31/5.57 ! [B: set_nat,A: set_nat] : ( ord_less_eq_set_nat @ B @ ( sup_sup_set_nat @ A @ B ) ) ).
% 5.31/5.57
% 5.31/5.57 % sup.cobounded2
% 5.31/5.57 thf(fact_4300_sup_Ocobounded2,axiom,
% 5.31/5.57 ! [B: rat,A: rat] : ( ord_less_eq_rat @ B @ ( sup_sup_rat @ A @ B ) ) ).
% 5.31/5.57
% 5.31/5.57 % sup.cobounded2
% 5.31/5.57 thf(fact_4301_sup_Ocobounded2,axiom,
% 5.31/5.57 ! [B: nat,A: nat] : ( ord_less_eq_nat @ B @ ( sup_sup_nat @ A @ B ) ) ).
% 5.31/5.57
% 5.31/5.57 % sup.cobounded2
% 5.31/5.57 thf(fact_4302_sup_Ocobounded2,axiom,
% 5.31/5.57 ! [B: int,A: int] : ( ord_less_eq_int @ B @ ( sup_sup_int @ A @ B ) ) ).
% 5.31/5.57
% 5.31/5.57 % sup.cobounded2
% 5.31/5.57 thf(fact_4303_sup_Ocobounded1,axiom,
% 5.31/5.57 ! [A: set_nat,B: set_nat] : ( ord_less_eq_set_nat @ A @ ( sup_sup_set_nat @ A @ B ) ) ).
% 5.31/5.57
% 5.31/5.57 % sup.cobounded1
% 5.31/5.57 thf(fact_4304_sup_Ocobounded1,axiom,
% 5.31/5.57 ! [A: rat,B: rat] : ( ord_less_eq_rat @ A @ ( sup_sup_rat @ A @ B ) ) ).
% 5.31/5.57
% 5.31/5.57 % sup.cobounded1
% 5.31/5.57 thf(fact_4305_sup_Ocobounded1,axiom,
% 5.31/5.57 ! [A: nat,B: nat] : ( ord_less_eq_nat @ A @ ( sup_sup_nat @ A @ B ) ) ).
% 5.31/5.57
% 5.31/5.57 % sup.cobounded1
% 5.31/5.57 thf(fact_4306_sup_Ocobounded1,axiom,
% 5.31/5.57 ! [A: int,B: int] : ( ord_less_eq_int @ A @ ( sup_sup_int @ A @ B ) ) ).
% 5.31/5.57
% 5.31/5.57 % sup.cobounded1
% 5.31/5.57 thf(fact_4307_sup_Oorder__iff,axiom,
% 5.31/5.57 ( ord_less_eq_set_nat
% 5.31/5.57 = ( ^ [B4: set_nat,A5: set_nat] :
% 5.31/5.57 ( A5
% 5.31/5.57 = ( sup_sup_set_nat @ A5 @ B4 ) ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % sup.order_iff
% 5.31/5.57 thf(fact_4308_sup_Oorder__iff,axiom,
% 5.31/5.57 ( ord_less_eq_rat
% 5.31/5.57 = ( ^ [B4: rat,A5: rat] :
% 5.31/5.57 ( A5
% 5.31/5.57 = ( sup_sup_rat @ A5 @ B4 ) ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % sup.order_iff
% 5.31/5.57 thf(fact_4309_sup_Oorder__iff,axiom,
% 5.31/5.57 ( ord_less_eq_nat
% 5.31/5.57 = ( ^ [B4: nat,A5: nat] :
% 5.31/5.57 ( A5
% 5.31/5.57 = ( sup_sup_nat @ A5 @ B4 ) ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % sup.order_iff
% 5.31/5.57 thf(fact_4310_sup_Oorder__iff,axiom,
% 5.31/5.57 ( ord_less_eq_int
% 5.31/5.57 = ( ^ [B4: int,A5: int] :
% 5.31/5.57 ( A5
% 5.31/5.57 = ( sup_sup_int @ A5 @ B4 ) ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % sup.order_iff
% 5.31/5.57 thf(fact_4311_sup_OboundedI,axiom,
% 5.31/5.57 ! [B: set_nat,A: set_nat,C2: set_nat] :
% 5.31/5.57 ( ( ord_less_eq_set_nat @ B @ A )
% 5.31/5.57 => ( ( ord_less_eq_set_nat @ C2 @ A )
% 5.31/5.57 => ( ord_less_eq_set_nat @ ( sup_sup_set_nat @ B @ C2 ) @ A ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % sup.boundedI
% 5.31/5.57 thf(fact_4312_sup_OboundedI,axiom,
% 5.31/5.57 ! [B: rat,A: rat,C2: rat] :
% 5.31/5.57 ( ( ord_less_eq_rat @ B @ A )
% 5.31/5.57 => ( ( ord_less_eq_rat @ C2 @ A )
% 5.31/5.57 => ( ord_less_eq_rat @ ( sup_sup_rat @ B @ C2 ) @ A ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % sup.boundedI
% 5.31/5.57 thf(fact_4313_sup_OboundedI,axiom,
% 5.31/5.57 ! [B: nat,A: nat,C2: nat] :
% 5.31/5.57 ( ( ord_less_eq_nat @ B @ A )
% 5.31/5.57 => ( ( ord_less_eq_nat @ C2 @ A )
% 5.31/5.57 => ( ord_less_eq_nat @ ( sup_sup_nat @ B @ C2 ) @ A ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % sup.boundedI
% 5.31/5.57 thf(fact_4314_sup_OboundedI,axiom,
% 5.31/5.57 ! [B: int,A: int,C2: int] :
% 5.31/5.57 ( ( ord_less_eq_int @ B @ A )
% 5.31/5.57 => ( ( ord_less_eq_int @ C2 @ A )
% 5.31/5.57 => ( ord_less_eq_int @ ( sup_sup_int @ B @ C2 ) @ A ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % sup.boundedI
% 5.31/5.57 thf(fact_4315_sup_OboundedE,axiom,
% 5.31/5.57 ! [B: set_nat,C2: set_nat,A: set_nat] :
% 5.31/5.57 ( ( ord_less_eq_set_nat @ ( sup_sup_set_nat @ B @ C2 ) @ A )
% 5.31/5.57 => ~ ( ( ord_less_eq_set_nat @ B @ A )
% 5.31/5.57 => ~ ( ord_less_eq_set_nat @ C2 @ A ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % sup.boundedE
% 5.31/5.57 thf(fact_4316_sup_OboundedE,axiom,
% 5.31/5.57 ! [B: rat,C2: rat,A: rat] :
% 5.31/5.57 ( ( ord_less_eq_rat @ ( sup_sup_rat @ B @ C2 ) @ A )
% 5.31/5.57 => ~ ( ( ord_less_eq_rat @ B @ A )
% 5.31/5.57 => ~ ( ord_less_eq_rat @ C2 @ A ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % sup.boundedE
% 5.31/5.57 thf(fact_4317_sup_OboundedE,axiom,
% 5.31/5.57 ! [B: nat,C2: nat,A: nat] :
% 5.31/5.57 ( ( ord_less_eq_nat @ ( sup_sup_nat @ B @ C2 ) @ A )
% 5.31/5.57 => ~ ( ( ord_less_eq_nat @ B @ A )
% 5.31/5.57 => ~ ( ord_less_eq_nat @ C2 @ A ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % sup.boundedE
% 5.31/5.57 thf(fact_4318_sup_OboundedE,axiom,
% 5.31/5.57 ! [B: int,C2: int,A: int] :
% 5.31/5.57 ( ( ord_less_eq_int @ ( sup_sup_int @ B @ C2 ) @ A )
% 5.31/5.57 => ~ ( ( ord_less_eq_int @ B @ A )
% 5.31/5.57 => ~ ( ord_less_eq_int @ C2 @ A ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % sup.boundedE
% 5.31/5.57 thf(fact_4319_sup__absorb2,axiom,
% 5.31/5.57 ! [X: set_nat,Y: set_nat] :
% 5.31/5.57 ( ( ord_less_eq_set_nat @ X @ Y )
% 5.31/5.57 => ( ( sup_sup_set_nat @ X @ Y )
% 5.31/5.57 = Y ) ) ).
% 5.31/5.57
% 5.31/5.57 % sup_absorb2
% 5.31/5.57 thf(fact_4320_sup__absorb2,axiom,
% 5.31/5.57 ! [X: rat,Y: rat] :
% 5.31/5.57 ( ( ord_less_eq_rat @ X @ Y )
% 5.31/5.57 => ( ( sup_sup_rat @ X @ Y )
% 5.31/5.57 = Y ) ) ).
% 5.31/5.57
% 5.31/5.57 % sup_absorb2
% 5.31/5.57 thf(fact_4321_sup__absorb2,axiom,
% 5.31/5.57 ! [X: nat,Y: nat] :
% 5.31/5.57 ( ( ord_less_eq_nat @ X @ Y )
% 5.31/5.57 => ( ( sup_sup_nat @ X @ Y )
% 5.31/5.57 = Y ) ) ).
% 5.31/5.57
% 5.31/5.57 % sup_absorb2
% 5.31/5.57 thf(fact_4322_sup__absorb2,axiom,
% 5.31/5.57 ! [X: int,Y: int] :
% 5.31/5.57 ( ( ord_less_eq_int @ X @ Y )
% 5.31/5.57 => ( ( sup_sup_int @ X @ Y )
% 5.31/5.57 = Y ) ) ).
% 5.31/5.57
% 5.31/5.57 % sup_absorb2
% 5.31/5.57 thf(fact_4323_sup__absorb1,axiom,
% 5.31/5.57 ! [Y: set_nat,X: set_nat] :
% 5.31/5.57 ( ( ord_less_eq_set_nat @ Y @ X )
% 5.31/5.57 => ( ( sup_sup_set_nat @ X @ Y )
% 5.31/5.57 = X ) ) ).
% 5.31/5.57
% 5.31/5.57 % sup_absorb1
% 5.31/5.57 thf(fact_4324_sup__absorb1,axiom,
% 5.31/5.57 ! [Y: rat,X: rat] :
% 5.31/5.57 ( ( ord_less_eq_rat @ Y @ X )
% 5.31/5.57 => ( ( sup_sup_rat @ X @ Y )
% 5.31/5.57 = X ) ) ).
% 5.31/5.57
% 5.31/5.57 % sup_absorb1
% 5.31/5.57 thf(fact_4325_sup__absorb1,axiom,
% 5.31/5.57 ! [Y: nat,X: nat] :
% 5.31/5.57 ( ( ord_less_eq_nat @ Y @ X )
% 5.31/5.57 => ( ( sup_sup_nat @ X @ Y )
% 5.31/5.57 = X ) ) ).
% 5.31/5.57
% 5.31/5.57 % sup_absorb1
% 5.31/5.57 thf(fact_4326_sup__absorb1,axiom,
% 5.31/5.57 ! [Y: int,X: int] :
% 5.31/5.57 ( ( ord_less_eq_int @ Y @ X )
% 5.31/5.57 => ( ( sup_sup_int @ X @ Y )
% 5.31/5.57 = X ) ) ).
% 5.31/5.57
% 5.31/5.57 % sup_absorb1
% 5.31/5.57 thf(fact_4327_sup_Oabsorb2,axiom,
% 5.31/5.57 ! [A: set_nat,B: set_nat] :
% 5.31/5.57 ( ( ord_less_eq_set_nat @ A @ B )
% 5.31/5.57 => ( ( sup_sup_set_nat @ A @ B )
% 5.31/5.57 = B ) ) ).
% 5.31/5.57
% 5.31/5.57 % sup.absorb2
% 5.31/5.57 thf(fact_4328_sup_Oabsorb2,axiom,
% 5.31/5.57 ! [A: rat,B: rat] :
% 5.31/5.57 ( ( ord_less_eq_rat @ A @ B )
% 5.31/5.57 => ( ( sup_sup_rat @ A @ B )
% 5.31/5.57 = B ) ) ).
% 5.31/5.57
% 5.31/5.57 % sup.absorb2
% 5.31/5.57 thf(fact_4329_sup_Oabsorb2,axiom,
% 5.31/5.57 ! [A: nat,B: nat] :
% 5.31/5.57 ( ( ord_less_eq_nat @ A @ B )
% 5.31/5.57 => ( ( sup_sup_nat @ A @ B )
% 5.31/5.57 = B ) ) ).
% 5.31/5.57
% 5.31/5.57 % sup.absorb2
% 5.31/5.57 thf(fact_4330_sup_Oabsorb2,axiom,
% 5.31/5.57 ! [A: int,B: int] :
% 5.31/5.57 ( ( ord_less_eq_int @ A @ B )
% 5.31/5.57 => ( ( sup_sup_int @ A @ B )
% 5.31/5.57 = B ) ) ).
% 5.31/5.57
% 5.31/5.57 % sup.absorb2
% 5.31/5.57 thf(fact_4331_sup_Oabsorb1,axiom,
% 5.31/5.57 ! [B: set_nat,A: set_nat] :
% 5.31/5.57 ( ( ord_less_eq_set_nat @ B @ A )
% 5.31/5.57 => ( ( sup_sup_set_nat @ A @ B )
% 5.31/5.57 = A ) ) ).
% 5.31/5.57
% 5.31/5.57 % sup.absorb1
% 5.31/5.57 thf(fact_4332_sup_Oabsorb1,axiom,
% 5.31/5.57 ! [B: rat,A: rat] :
% 5.31/5.57 ( ( ord_less_eq_rat @ B @ A )
% 5.31/5.57 => ( ( sup_sup_rat @ A @ B )
% 5.31/5.57 = A ) ) ).
% 5.31/5.57
% 5.31/5.57 % sup.absorb1
% 5.31/5.57 thf(fact_4333_sup_Oabsorb1,axiom,
% 5.31/5.57 ! [B: nat,A: nat] :
% 5.31/5.57 ( ( ord_less_eq_nat @ B @ A )
% 5.31/5.57 => ( ( sup_sup_nat @ A @ B )
% 5.31/5.57 = A ) ) ).
% 5.31/5.57
% 5.31/5.57 % sup.absorb1
% 5.31/5.57 thf(fact_4334_sup_Oabsorb1,axiom,
% 5.31/5.57 ! [B: int,A: int] :
% 5.31/5.57 ( ( ord_less_eq_int @ B @ A )
% 5.31/5.57 => ( ( sup_sup_int @ A @ B )
% 5.31/5.57 = A ) ) ).
% 5.31/5.57
% 5.31/5.57 % sup.absorb1
% 5.31/5.57 thf(fact_4335_sup__unique,axiom,
% 5.31/5.57 ! [F2: set_nat > set_nat > set_nat,X: set_nat,Y: set_nat] :
% 5.31/5.57 ( ! [X3: set_nat,Y3: set_nat] : ( ord_less_eq_set_nat @ X3 @ ( F2 @ X3 @ Y3 ) )
% 5.31/5.57 => ( ! [X3: set_nat,Y3: set_nat] : ( ord_less_eq_set_nat @ Y3 @ ( F2 @ X3 @ Y3 ) )
% 5.31/5.57 => ( ! [X3: set_nat,Y3: set_nat,Z: set_nat] :
% 5.31/5.57 ( ( ord_less_eq_set_nat @ Y3 @ X3 )
% 5.31/5.57 => ( ( ord_less_eq_set_nat @ Z @ X3 )
% 5.31/5.57 => ( ord_less_eq_set_nat @ ( F2 @ Y3 @ Z ) @ X3 ) ) )
% 5.31/5.57 => ( ( sup_sup_set_nat @ X @ Y )
% 5.31/5.57 = ( F2 @ X @ Y ) ) ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % sup_unique
% 5.31/5.57 thf(fact_4336_sup__unique,axiom,
% 5.31/5.57 ! [F2: rat > rat > rat,X: rat,Y: rat] :
% 5.31/5.57 ( ! [X3: rat,Y3: rat] : ( ord_less_eq_rat @ X3 @ ( F2 @ X3 @ Y3 ) )
% 5.31/5.57 => ( ! [X3: rat,Y3: rat] : ( ord_less_eq_rat @ Y3 @ ( F2 @ X3 @ Y3 ) )
% 5.31/5.57 => ( ! [X3: rat,Y3: rat,Z: rat] :
% 5.31/5.57 ( ( ord_less_eq_rat @ Y3 @ X3 )
% 5.31/5.57 => ( ( ord_less_eq_rat @ Z @ X3 )
% 5.31/5.57 => ( ord_less_eq_rat @ ( F2 @ Y3 @ Z ) @ X3 ) ) )
% 5.31/5.57 => ( ( sup_sup_rat @ X @ Y )
% 5.31/5.57 = ( F2 @ X @ Y ) ) ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % sup_unique
% 5.31/5.57 thf(fact_4337_sup__unique,axiom,
% 5.31/5.57 ! [F2: nat > nat > nat,X: nat,Y: nat] :
% 5.31/5.57 ( ! [X3: nat,Y3: nat] : ( ord_less_eq_nat @ X3 @ ( F2 @ X3 @ Y3 ) )
% 5.31/5.57 => ( ! [X3: nat,Y3: nat] : ( ord_less_eq_nat @ Y3 @ ( F2 @ X3 @ Y3 ) )
% 5.31/5.57 => ( ! [X3: nat,Y3: nat,Z: nat] :
% 5.31/5.57 ( ( ord_less_eq_nat @ Y3 @ X3 )
% 5.31/5.57 => ( ( ord_less_eq_nat @ Z @ X3 )
% 5.31/5.57 => ( ord_less_eq_nat @ ( F2 @ Y3 @ Z ) @ X3 ) ) )
% 5.31/5.57 => ( ( sup_sup_nat @ X @ Y )
% 5.31/5.57 = ( F2 @ X @ Y ) ) ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % sup_unique
% 5.31/5.57 thf(fact_4338_sup__unique,axiom,
% 5.31/5.57 ! [F2: int > int > int,X: int,Y: int] :
% 5.31/5.57 ( ! [X3: int,Y3: int] : ( ord_less_eq_int @ X3 @ ( F2 @ X3 @ Y3 ) )
% 5.31/5.57 => ( ! [X3: int,Y3: int] : ( ord_less_eq_int @ Y3 @ ( F2 @ X3 @ Y3 ) )
% 5.31/5.57 => ( ! [X3: int,Y3: int,Z: int] :
% 5.31/5.57 ( ( ord_less_eq_int @ Y3 @ X3 )
% 5.31/5.57 => ( ( ord_less_eq_int @ Z @ X3 )
% 5.31/5.57 => ( ord_less_eq_int @ ( F2 @ Y3 @ Z ) @ X3 ) ) )
% 5.31/5.57 => ( ( sup_sup_int @ X @ Y )
% 5.31/5.57 = ( F2 @ X @ Y ) ) ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % sup_unique
% 5.31/5.57 thf(fact_4339_sup_OorderI,axiom,
% 5.31/5.57 ! [A: set_nat,B: set_nat] :
% 5.31/5.57 ( ( A
% 5.31/5.57 = ( sup_sup_set_nat @ A @ B ) )
% 5.31/5.57 => ( ord_less_eq_set_nat @ B @ A ) ) ).
% 5.31/5.57
% 5.31/5.57 % sup.orderI
% 5.31/5.57 thf(fact_4340_sup_OorderI,axiom,
% 5.31/5.57 ! [A: rat,B: rat] :
% 5.31/5.57 ( ( A
% 5.31/5.57 = ( sup_sup_rat @ A @ B ) )
% 5.31/5.57 => ( ord_less_eq_rat @ B @ A ) ) ).
% 5.31/5.57
% 5.31/5.57 % sup.orderI
% 5.31/5.57 thf(fact_4341_sup_OorderI,axiom,
% 5.31/5.57 ! [A: nat,B: nat] :
% 5.31/5.57 ( ( A
% 5.31/5.57 = ( sup_sup_nat @ A @ B ) )
% 5.31/5.57 => ( ord_less_eq_nat @ B @ A ) ) ).
% 5.31/5.57
% 5.31/5.57 % sup.orderI
% 5.31/5.57 thf(fact_4342_sup_OorderI,axiom,
% 5.31/5.57 ! [A: int,B: int] :
% 5.31/5.57 ( ( A
% 5.31/5.57 = ( sup_sup_int @ A @ B ) )
% 5.31/5.57 => ( ord_less_eq_int @ B @ A ) ) ).
% 5.31/5.57
% 5.31/5.57 % sup.orderI
% 5.31/5.57 thf(fact_4343_sup_OorderE,axiom,
% 5.31/5.57 ! [B: set_nat,A: set_nat] :
% 5.31/5.57 ( ( ord_less_eq_set_nat @ B @ A )
% 5.31/5.57 => ( A
% 5.31/5.57 = ( sup_sup_set_nat @ A @ B ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % sup.orderE
% 5.31/5.57 thf(fact_4344_sup_OorderE,axiom,
% 5.31/5.57 ! [B: rat,A: rat] :
% 5.31/5.57 ( ( ord_less_eq_rat @ B @ A )
% 5.31/5.57 => ( A
% 5.31/5.57 = ( sup_sup_rat @ A @ B ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % sup.orderE
% 5.31/5.57 thf(fact_4345_sup_OorderE,axiom,
% 5.31/5.57 ! [B: nat,A: nat] :
% 5.31/5.57 ( ( ord_less_eq_nat @ B @ A )
% 5.31/5.57 => ( A
% 5.31/5.57 = ( sup_sup_nat @ A @ B ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % sup.orderE
% 5.31/5.57 thf(fact_4346_sup_OorderE,axiom,
% 5.31/5.57 ! [B: int,A: int] :
% 5.31/5.57 ( ( ord_less_eq_int @ B @ A )
% 5.31/5.57 => ( A
% 5.31/5.57 = ( sup_sup_int @ A @ B ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % sup.orderE
% 5.31/5.57 thf(fact_4347_le__iff__sup,axiom,
% 5.31/5.57 ( ord_less_eq_set_nat
% 5.31/5.57 = ( ^ [X4: set_nat,Y4: set_nat] :
% 5.31/5.57 ( ( sup_sup_set_nat @ X4 @ Y4 )
% 5.31/5.57 = Y4 ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % le_iff_sup
% 5.31/5.57 thf(fact_4348_le__iff__sup,axiom,
% 5.31/5.57 ( ord_less_eq_rat
% 5.31/5.57 = ( ^ [X4: rat,Y4: rat] :
% 5.31/5.57 ( ( sup_sup_rat @ X4 @ Y4 )
% 5.31/5.57 = Y4 ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % le_iff_sup
% 5.31/5.57 thf(fact_4349_le__iff__sup,axiom,
% 5.31/5.57 ( ord_less_eq_nat
% 5.31/5.57 = ( ^ [X4: nat,Y4: nat] :
% 5.31/5.57 ( ( sup_sup_nat @ X4 @ Y4 )
% 5.31/5.57 = Y4 ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % le_iff_sup
% 5.31/5.57 thf(fact_4350_le__iff__sup,axiom,
% 5.31/5.57 ( ord_less_eq_int
% 5.31/5.57 = ( ^ [X4: int,Y4: int] :
% 5.31/5.57 ( ( sup_sup_int @ X4 @ Y4 )
% 5.31/5.57 = Y4 ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % le_iff_sup
% 5.31/5.57 thf(fact_4351_sup__least,axiom,
% 5.31/5.57 ! [Y: set_nat,X: set_nat,Z3: set_nat] :
% 5.31/5.57 ( ( ord_less_eq_set_nat @ Y @ X )
% 5.31/5.57 => ( ( ord_less_eq_set_nat @ Z3 @ X )
% 5.31/5.57 => ( ord_less_eq_set_nat @ ( sup_sup_set_nat @ Y @ Z3 ) @ X ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % sup_least
% 5.31/5.57 thf(fact_4352_sup__least,axiom,
% 5.31/5.57 ! [Y: rat,X: rat,Z3: rat] :
% 5.31/5.57 ( ( ord_less_eq_rat @ Y @ X )
% 5.31/5.57 => ( ( ord_less_eq_rat @ Z3 @ X )
% 5.31/5.57 => ( ord_less_eq_rat @ ( sup_sup_rat @ Y @ Z3 ) @ X ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % sup_least
% 5.31/5.57 thf(fact_4353_sup__least,axiom,
% 5.31/5.57 ! [Y: nat,X: nat,Z3: nat] :
% 5.31/5.57 ( ( ord_less_eq_nat @ Y @ X )
% 5.31/5.57 => ( ( ord_less_eq_nat @ Z3 @ X )
% 5.31/5.57 => ( ord_less_eq_nat @ ( sup_sup_nat @ Y @ Z3 ) @ X ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % sup_least
% 5.31/5.57 thf(fact_4354_sup__least,axiom,
% 5.31/5.57 ! [Y: int,X: int,Z3: int] :
% 5.31/5.57 ( ( ord_less_eq_int @ Y @ X )
% 5.31/5.57 => ( ( ord_less_eq_int @ Z3 @ X )
% 5.31/5.57 => ( ord_less_eq_int @ ( sup_sup_int @ Y @ Z3 ) @ X ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % sup_least
% 5.31/5.57 thf(fact_4355_sup__mono,axiom,
% 5.31/5.57 ! [A: set_nat,C2: set_nat,B: set_nat,D: set_nat] :
% 5.31/5.57 ( ( ord_less_eq_set_nat @ A @ C2 )
% 5.31/5.57 => ( ( ord_less_eq_set_nat @ B @ D )
% 5.31/5.57 => ( ord_less_eq_set_nat @ ( sup_sup_set_nat @ A @ B ) @ ( sup_sup_set_nat @ C2 @ D ) ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % sup_mono
% 5.31/5.57 thf(fact_4356_sup__mono,axiom,
% 5.31/5.57 ! [A: rat,C2: rat,B: rat,D: rat] :
% 5.31/5.57 ( ( ord_less_eq_rat @ A @ C2 )
% 5.31/5.57 => ( ( ord_less_eq_rat @ B @ D )
% 5.31/5.57 => ( ord_less_eq_rat @ ( sup_sup_rat @ A @ B ) @ ( sup_sup_rat @ C2 @ D ) ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % sup_mono
% 5.31/5.57 thf(fact_4357_sup__mono,axiom,
% 5.31/5.57 ! [A: nat,C2: nat,B: nat,D: nat] :
% 5.31/5.57 ( ( ord_less_eq_nat @ A @ C2 )
% 5.31/5.57 => ( ( ord_less_eq_nat @ B @ D )
% 5.31/5.57 => ( ord_less_eq_nat @ ( sup_sup_nat @ A @ B ) @ ( sup_sup_nat @ C2 @ D ) ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % sup_mono
% 5.31/5.57 thf(fact_4358_sup__mono,axiom,
% 5.31/5.57 ! [A: int,C2: int,B: int,D: int] :
% 5.31/5.57 ( ( ord_less_eq_int @ A @ C2 )
% 5.31/5.57 => ( ( ord_less_eq_int @ B @ D )
% 5.31/5.57 => ( ord_less_eq_int @ ( sup_sup_int @ A @ B ) @ ( sup_sup_int @ C2 @ D ) ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % sup_mono
% 5.31/5.57 thf(fact_4359_sup_Omono,axiom,
% 5.31/5.57 ! [C2: set_nat,A: set_nat,D: set_nat,B: set_nat] :
% 5.31/5.57 ( ( ord_less_eq_set_nat @ C2 @ A )
% 5.31/5.57 => ( ( ord_less_eq_set_nat @ D @ B )
% 5.31/5.57 => ( ord_less_eq_set_nat @ ( sup_sup_set_nat @ C2 @ D ) @ ( sup_sup_set_nat @ A @ B ) ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % sup.mono
% 5.31/5.57 thf(fact_4360_sup_Omono,axiom,
% 5.31/5.57 ! [C2: rat,A: rat,D: rat,B: rat] :
% 5.31/5.57 ( ( ord_less_eq_rat @ C2 @ A )
% 5.31/5.57 => ( ( ord_less_eq_rat @ D @ B )
% 5.31/5.57 => ( ord_less_eq_rat @ ( sup_sup_rat @ C2 @ D ) @ ( sup_sup_rat @ A @ B ) ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % sup.mono
% 5.31/5.57 thf(fact_4361_sup_Omono,axiom,
% 5.31/5.57 ! [C2: nat,A: nat,D: nat,B: nat] :
% 5.31/5.57 ( ( ord_less_eq_nat @ C2 @ A )
% 5.31/5.57 => ( ( ord_less_eq_nat @ D @ B )
% 5.31/5.57 => ( ord_less_eq_nat @ ( sup_sup_nat @ C2 @ D ) @ ( sup_sup_nat @ A @ B ) ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % sup.mono
% 5.31/5.57 thf(fact_4362_sup_Omono,axiom,
% 5.31/5.57 ! [C2: int,A: int,D: int,B: int] :
% 5.31/5.57 ( ( ord_less_eq_int @ C2 @ A )
% 5.31/5.57 => ( ( ord_less_eq_int @ D @ B )
% 5.31/5.57 => ( ord_less_eq_int @ ( sup_sup_int @ C2 @ D ) @ ( sup_sup_int @ A @ B ) ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % sup.mono
% 5.31/5.57 thf(fact_4363_le__supI2,axiom,
% 5.31/5.57 ! [X: set_nat,B: set_nat,A: set_nat] :
% 5.31/5.57 ( ( ord_less_eq_set_nat @ X @ B )
% 5.31/5.57 => ( ord_less_eq_set_nat @ X @ ( sup_sup_set_nat @ A @ B ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % le_supI2
% 5.31/5.57 thf(fact_4364_le__supI2,axiom,
% 5.31/5.57 ! [X: rat,B: rat,A: rat] :
% 5.31/5.57 ( ( ord_less_eq_rat @ X @ B )
% 5.31/5.57 => ( ord_less_eq_rat @ X @ ( sup_sup_rat @ A @ B ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % le_supI2
% 5.31/5.57 thf(fact_4365_le__supI2,axiom,
% 5.31/5.57 ! [X: nat,B: nat,A: nat] :
% 5.31/5.57 ( ( ord_less_eq_nat @ X @ B )
% 5.31/5.57 => ( ord_less_eq_nat @ X @ ( sup_sup_nat @ A @ B ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % le_supI2
% 5.31/5.57 thf(fact_4366_le__supI2,axiom,
% 5.31/5.57 ! [X: int,B: int,A: int] :
% 5.31/5.57 ( ( ord_less_eq_int @ X @ B )
% 5.31/5.57 => ( ord_less_eq_int @ X @ ( sup_sup_int @ A @ B ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % le_supI2
% 5.31/5.57 thf(fact_4367_le__supI1,axiom,
% 5.31/5.57 ! [X: set_nat,A: set_nat,B: set_nat] :
% 5.31/5.57 ( ( ord_less_eq_set_nat @ X @ A )
% 5.31/5.57 => ( ord_less_eq_set_nat @ X @ ( sup_sup_set_nat @ A @ B ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % le_supI1
% 5.31/5.57 thf(fact_4368_le__supI1,axiom,
% 5.31/5.57 ! [X: rat,A: rat,B: rat] :
% 5.31/5.57 ( ( ord_less_eq_rat @ X @ A )
% 5.31/5.57 => ( ord_less_eq_rat @ X @ ( sup_sup_rat @ A @ B ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % le_supI1
% 5.31/5.57 thf(fact_4369_le__supI1,axiom,
% 5.31/5.57 ! [X: nat,A: nat,B: nat] :
% 5.31/5.57 ( ( ord_less_eq_nat @ X @ A )
% 5.31/5.57 => ( ord_less_eq_nat @ X @ ( sup_sup_nat @ A @ B ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % le_supI1
% 5.31/5.57 thf(fact_4370_le__supI1,axiom,
% 5.31/5.57 ! [X: int,A: int,B: int] :
% 5.31/5.57 ( ( ord_less_eq_int @ X @ A )
% 5.31/5.57 => ( ord_less_eq_int @ X @ ( sup_sup_int @ A @ B ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % le_supI1
% 5.31/5.57 thf(fact_4371_sup__ge2,axiom,
% 5.31/5.57 ! [Y: set_nat,X: set_nat] : ( ord_less_eq_set_nat @ Y @ ( sup_sup_set_nat @ X @ Y ) ) ).
% 5.31/5.57
% 5.31/5.57 % sup_ge2
% 5.31/5.57 thf(fact_4372_sup__ge2,axiom,
% 5.31/5.57 ! [Y: rat,X: rat] : ( ord_less_eq_rat @ Y @ ( sup_sup_rat @ X @ Y ) ) ).
% 5.31/5.57
% 5.31/5.57 % sup_ge2
% 5.31/5.57 thf(fact_4373_sup__ge2,axiom,
% 5.31/5.57 ! [Y: nat,X: nat] : ( ord_less_eq_nat @ Y @ ( sup_sup_nat @ X @ Y ) ) ).
% 5.31/5.57
% 5.31/5.57 % sup_ge2
% 5.31/5.57 thf(fact_4374_sup__ge2,axiom,
% 5.31/5.57 ! [Y: int,X: int] : ( ord_less_eq_int @ Y @ ( sup_sup_int @ X @ Y ) ) ).
% 5.31/5.57
% 5.31/5.57 % sup_ge2
% 5.31/5.57 thf(fact_4375_sup__ge1,axiom,
% 5.31/5.57 ! [X: set_nat,Y: set_nat] : ( ord_less_eq_set_nat @ X @ ( sup_sup_set_nat @ X @ Y ) ) ).
% 5.31/5.57
% 5.31/5.57 % sup_ge1
% 5.31/5.57 thf(fact_4376_sup__ge1,axiom,
% 5.31/5.57 ! [X: rat,Y: rat] : ( ord_less_eq_rat @ X @ ( sup_sup_rat @ X @ Y ) ) ).
% 5.31/5.57
% 5.31/5.57 % sup_ge1
% 5.31/5.57 thf(fact_4377_sup__ge1,axiom,
% 5.31/5.57 ! [X: nat,Y: nat] : ( ord_less_eq_nat @ X @ ( sup_sup_nat @ X @ Y ) ) ).
% 5.31/5.57
% 5.31/5.57 % sup_ge1
% 5.31/5.57 thf(fact_4378_sup__ge1,axiom,
% 5.31/5.57 ! [X: int,Y: int] : ( ord_less_eq_int @ X @ ( sup_sup_int @ X @ Y ) ) ).
% 5.31/5.57
% 5.31/5.57 % sup_ge1
% 5.31/5.57 thf(fact_4379_le__supI,axiom,
% 5.31/5.57 ! [A: set_nat,X: set_nat,B: set_nat] :
% 5.31/5.57 ( ( ord_less_eq_set_nat @ A @ X )
% 5.31/5.57 => ( ( ord_less_eq_set_nat @ B @ X )
% 5.31/5.57 => ( ord_less_eq_set_nat @ ( sup_sup_set_nat @ A @ B ) @ X ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % le_supI
% 5.31/5.57 thf(fact_4380_le__supI,axiom,
% 5.31/5.57 ! [A: rat,X: rat,B: rat] :
% 5.31/5.57 ( ( ord_less_eq_rat @ A @ X )
% 5.31/5.57 => ( ( ord_less_eq_rat @ B @ X )
% 5.31/5.57 => ( ord_less_eq_rat @ ( sup_sup_rat @ A @ B ) @ X ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % le_supI
% 5.31/5.57 thf(fact_4381_le__supI,axiom,
% 5.31/5.57 ! [A: nat,X: nat,B: nat] :
% 5.31/5.57 ( ( ord_less_eq_nat @ A @ X )
% 5.31/5.57 => ( ( ord_less_eq_nat @ B @ X )
% 5.31/5.57 => ( ord_less_eq_nat @ ( sup_sup_nat @ A @ B ) @ X ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % le_supI
% 5.31/5.57 thf(fact_4382_le__supI,axiom,
% 5.31/5.57 ! [A: int,X: int,B: int] :
% 5.31/5.57 ( ( ord_less_eq_int @ A @ X )
% 5.31/5.57 => ( ( ord_less_eq_int @ B @ X )
% 5.31/5.57 => ( ord_less_eq_int @ ( sup_sup_int @ A @ B ) @ X ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % le_supI
% 5.31/5.57 thf(fact_4383_le__supE,axiom,
% 5.31/5.57 ! [A: set_nat,B: set_nat,X: set_nat] :
% 5.31/5.57 ( ( ord_less_eq_set_nat @ ( sup_sup_set_nat @ A @ B ) @ X )
% 5.31/5.57 => ~ ( ( ord_less_eq_set_nat @ A @ X )
% 5.31/5.57 => ~ ( ord_less_eq_set_nat @ B @ X ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % le_supE
% 5.31/5.57 thf(fact_4384_le__supE,axiom,
% 5.31/5.57 ! [A: rat,B: rat,X: rat] :
% 5.31/5.57 ( ( ord_less_eq_rat @ ( sup_sup_rat @ A @ B ) @ X )
% 5.31/5.57 => ~ ( ( ord_less_eq_rat @ A @ X )
% 5.31/5.57 => ~ ( ord_less_eq_rat @ B @ X ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % le_supE
% 5.31/5.57 thf(fact_4385_le__supE,axiom,
% 5.31/5.57 ! [A: nat,B: nat,X: nat] :
% 5.31/5.57 ( ( ord_less_eq_nat @ ( sup_sup_nat @ A @ B ) @ X )
% 5.31/5.57 => ~ ( ( ord_less_eq_nat @ A @ X )
% 5.31/5.57 => ~ ( ord_less_eq_nat @ B @ X ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % le_supE
% 5.31/5.57 thf(fact_4386_le__supE,axiom,
% 5.31/5.57 ! [A: int,B: int,X: int] :
% 5.31/5.57 ( ( ord_less_eq_int @ ( sup_sup_int @ A @ B ) @ X )
% 5.31/5.57 => ~ ( ( ord_less_eq_int @ A @ X )
% 5.31/5.57 => ~ ( ord_less_eq_int @ B @ X ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % le_supE
% 5.31/5.57 thf(fact_4387_inf__sup__ord_I3_J,axiom,
% 5.31/5.57 ! [X: set_nat,Y: set_nat] : ( ord_less_eq_set_nat @ X @ ( sup_sup_set_nat @ X @ Y ) ) ).
% 5.31/5.57
% 5.31/5.57 % inf_sup_ord(3)
% 5.31/5.57 thf(fact_4388_inf__sup__ord_I3_J,axiom,
% 5.31/5.57 ! [X: rat,Y: rat] : ( ord_less_eq_rat @ X @ ( sup_sup_rat @ X @ Y ) ) ).
% 5.31/5.57
% 5.31/5.57 % inf_sup_ord(3)
% 5.31/5.57 thf(fact_4389_inf__sup__ord_I3_J,axiom,
% 5.31/5.57 ! [X: nat,Y: nat] : ( ord_less_eq_nat @ X @ ( sup_sup_nat @ X @ Y ) ) ).
% 5.31/5.57
% 5.31/5.57 % inf_sup_ord(3)
% 5.31/5.57 thf(fact_4390_inf__sup__ord_I3_J,axiom,
% 5.31/5.57 ! [X: int,Y: int] : ( ord_less_eq_int @ X @ ( sup_sup_int @ X @ Y ) ) ).
% 5.31/5.57
% 5.31/5.57 % inf_sup_ord(3)
% 5.31/5.57 thf(fact_4391_inf__sup__ord_I4_J,axiom,
% 5.31/5.57 ! [Y: set_nat,X: set_nat] : ( ord_less_eq_set_nat @ Y @ ( sup_sup_set_nat @ X @ Y ) ) ).
% 5.31/5.57
% 5.31/5.57 % inf_sup_ord(4)
% 5.31/5.57 thf(fact_4392_inf__sup__ord_I4_J,axiom,
% 5.31/5.57 ! [Y: rat,X: rat] : ( ord_less_eq_rat @ Y @ ( sup_sup_rat @ X @ Y ) ) ).
% 5.31/5.57
% 5.31/5.57 % inf_sup_ord(4)
% 5.31/5.57 thf(fact_4393_inf__sup__ord_I4_J,axiom,
% 5.31/5.57 ! [Y: nat,X: nat] : ( ord_less_eq_nat @ Y @ ( sup_sup_nat @ X @ Y ) ) ).
% 5.31/5.57
% 5.31/5.57 % inf_sup_ord(4)
% 5.31/5.57 thf(fact_4394_inf__sup__ord_I4_J,axiom,
% 5.31/5.57 ! [Y: int,X: int] : ( ord_less_eq_int @ Y @ ( sup_sup_int @ X @ Y ) ) ).
% 5.31/5.57
% 5.31/5.57 % inf_sup_ord(4)
% 5.31/5.57 thf(fact_4395_invar__vebt_Ointros_I4_J,axiom,
% 5.31/5.57 ! [TreeList2: list_VEBT_VEBT,N: nat,Summary: vEBT_VEBT,M2: nat,Deg: nat,Mi: nat,Ma: nat] :
% 5.31/5.57 ( ! [X3: vEBT_VEBT] :
% 5.31/5.57 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.31/5.57 => ( vEBT_invar_vebt @ X3 @ N ) )
% 5.31/5.57 => ( ( vEBT_invar_vebt @ Summary @ M2 )
% 5.31/5.57 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 5.31/5.57 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) )
% 5.31/5.57 => ( ( M2 = N )
% 5.31/5.57 => ( ( Deg
% 5.31/5.57 = ( plus_plus_nat @ N @ M2 ) )
% 5.31/5.57 => ( ! [I3: nat] :
% 5.31/5.57 ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) )
% 5.31/5.57 => ( ( ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I3 ) @ X7 ) )
% 5.31/5.57 = ( vEBT_V8194947554948674370ptions @ Summary @ I3 ) ) )
% 5.31/5.57 => ( ( ( Mi = Ma )
% 5.31/5.57 => ! [X3: vEBT_VEBT] :
% 5.31/5.57 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.31/5.57 => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X_12 ) ) )
% 5.31/5.57 => ( ( ord_less_eq_nat @ Mi @ Ma )
% 5.31/5.57 => ( ( ord_less_nat @ Ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 5.31/5.57 => ( ( ( Mi != Ma )
% 5.31/5.57 => ! [I3: nat] :
% 5.31/5.57 ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) )
% 5.31/5.57 => ( ( ( ( vEBT_VEBT_high @ Ma @ N )
% 5.31/5.57 = I3 )
% 5.31/5.57 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I3 ) @ ( vEBT_VEBT_low @ Ma @ N ) ) )
% 5.31/5.57 & ! [X3: nat] :
% 5.31/5.57 ( ( ( ( vEBT_VEBT_high @ X3 @ N )
% 5.31/5.57 = I3 )
% 5.31/5.57 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I3 ) @ ( vEBT_VEBT_low @ X3 @ N ) ) )
% 5.31/5.57 => ( ( ord_less_nat @ Mi @ X3 )
% 5.31/5.57 & ( ord_less_eq_nat @ X3 @ Ma ) ) ) ) ) )
% 5.31/5.57 => ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ Deg ) ) ) ) ) ) ) ) ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % invar_vebt.intros(4)
% 5.31/5.57 thf(fact_4396_invar__vebt_Ointros_I5_J,axiom,
% 5.31/5.57 ! [TreeList2: list_VEBT_VEBT,N: nat,Summary: vEBT_VEBT,M2: nat,Deg: nat,Mi: nat,Ma: nat] :
% 5.31/5.57 ( ! [X3: vEBT_VEBT] :
% 5.31/5.57 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.31/5.57 => ( vEBT_invar_vebt @ X3 @ N ) )
% 5.31/5.57 => ( ( vEBT_invar_vebt @ Summary @ M2 )
% 5.31/5.57 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 5.31/5.57 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) )
% 5.31/5.57 => ( ( M2
% 5.31/5.57 = ( suc @ N ) )
% 5.31/5.57 => ( ( Deg
% 5.31/5.57 = ( plus_plus_nat @ N @ M2 ) )
% 5.31/5.57 => ( ! [I3: nat] :
% 5.31/5.57 ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) )
% 5.31/5.57 => ( ( ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I3 ) @ X7 ) )
% 5.31/5.57 = ( vEBT_V8194947554948674370ptions @ Summary @ I3 ) ) )
% 5.31/5.57 => ( ( ( Mi = Ma )
% 5.31/5.57 => ! [X3: vEBT_VEBT] :
% 5.31/5.57 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.31/5.57 => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X_12 ) ) )
% 5.31/5.57 => ( ( ord_less_eq_nat @ Mi @ Ma )
% 5.31/5.57 => ( ( ord_less_nat @ Ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 5.31/5.57 => ( ( ( Mi != Ma )
% 5.31/5.57 => ! [I3: nat] :
% 5.31/5.57 ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) )
% 5.31/5.57 => ( ( ( ( vEBT_VEBT_high @ Ma @ N )
% 5.31/5.57 = I3 )
% 5.31/5.57 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I3 ) @ ( vEBT_VEBT_low @ Ma @ N ) ) )
% 5.31/5.57 & ! [X3: nat] :
% 5.31/5.57 ( ( ( ( vEBT_VEBT_high @ X3 @ N )
% 5.31/5.57 = I3 )
% 5.31/5.57 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I3 ) @ ( vEBT_VEBT_low @ X3 @ N ) ) )
% 5.31/5.57 => ( ( ord_less_nat @ Mi @ X3 )
% 5.31/5.57 & ( ord_less_eq_nat @ X3 @ Ma ) ) ) ) ) )
% 5.31/5.57 => ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ Deg ) ) ) ) ) ) ) ) ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % invar_vebt.intros(5)
% 5.31/5.57 thf(fact_4397_invar__vebt_Ocases,axiom,
% 5.31/5.57 ! [A12: vEBT_VEBT,A23: nat] :
% 5.31/5.57 ( ( vEBT_invar_vebt @ A12 @ A23 )
% 5.31/5.57 => ( ( ? [A3: $o,B3: $o] :
% 5.31/5.57 ( A12
% 5.31/5.57 = ( vEBT_Leaf @ A3 @ B3 ) )
% 5.31/5.57 => ( A23
% 5.31/5.57 != ( suc @ zero_zero_nat ) ) )
% 5.31/5.57 => ( ! [TreeList: list_VEBT_VEBT,N3: nat,Summary2: vEBT_VEBT,M: nat,Deg2: nat] :
% 5.31/5.57 ( ( A12
% 5.31/5.57 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList @ Summary2 ) )
% 5.31/5.57 => ( ( A23 = Deg2 )
% 5.31/5.57 => ( ! [X5: vEBT_VEBT] :
% 5.31/5.57 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.31/5.57 => ( vEBT_invar_vebt @ X5 @ N3 ) )
% 5.31/5.57 => ( ( vEBT_invar_vebt @ Summary2 @ M )
% 5.31/5.57 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 5.31/5.57 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.31/5.57 => ( ( M = N3 )
% 5.31/5.57 => ( ( Deg2
% 5.31/5.57 = ( plus_plus_nat @ N3 @ M ) )
% 5.31/5.57 => ( ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X_1 )
% 5.31/5.57 => ~ ! [X5: vEBT_VEBT] :
% 5.31/5.57 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.31/5.57 => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X5 @ X_1 ) ) ) ) ) ) ) ) ) )
% 5.31/5.57 => ( ! [TreeList: list_VEBT_VEBT,N3: nat,Summary2: vEBT_VEBT,M: nat,Deg2: nat] :
% 5.31/5.57 ( ( A12
% 5.31/5.57 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList @ Summary2 ) )
% 5.31/5.57 => ( ( A23 = Deg2 )
% 5.31/5.57 => ( ! [X5: vEBT_VEBT] :
% 5.31/5.57 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.31/5.57 => ( vEBT_invar_vebt @ X5 @ N3 ) )
% 5.31/5.57 => ( ( vEBT_invar_vebt @ Summary2 @ M )
% 5.31/5.57 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 5.31/5.57 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.31/5.57 => ( ( M
% 5.31/5.57 = ( suc @ N3 ) )
% 5.31/5.57 => ( ( Deg2
% 5.31/5.57 = ( plus_plus_nat @ N3 @ M ) )
% 5.31/5.57 => ( ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X_1 )
% 5.31/5.57 => ~ ! [X5: vEBT_VEBT] :
% 5.31/5.57 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.31/5.57 => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X5 @ X_1 ) ) ) ) ) ) ) ) ) )
% 5.31/5.57 => ( ! [TreeList: list_VEBT_VEBT,N3: nat,Summary2: vEBT_VEBT,M: nat,Deg2: nat,Mi2: nat,Ma2: nat] :
% 5.31/5.57 ( ( A12
% 5.31/5.57 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Deg2 @ TreeList @ Summary2 ) )
% 5.31/5.57 => ( ( A23 = Deg2 )
% 5.31/5.57 => ( ! [X5: vEBT_VEBT] :
% 5.31/5.57 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.31/5.57 => ( vEBT_invar_vebt @ X5 @ N3 ) )
% 5.31/5.57 => ( ( vEBT_invar_vebt @ Summary2 @ M )
% 5.31/5.57 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 5.31/5.57 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.31/5.57 => ( ( M = N3 )
% 5.31/5.57 => ( ( Deg2
% 5.31/5.57 = ( plus_plus_nat @ N3 @ M ) )
% 5.31/5.57 => ( ! [I4: nat] :
% 5.31/5.57 ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.31/5.57 => ( ( ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I4 ) @ X7 ) )
% 5.31/5.57 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I4 ) ) )
% 5.31/5.57 => ( ( ( Mi2 = Ma2 )
% 5.31/5.57 => ! [X5: vEBT_VEBT] :
% 5.31/5.57 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.31/5.57 => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X5 @ X_1 ) ) )
% 5.31/5.57 => ( ( ord_less_eq_nat @ Mi2 @ Ma2 )
% 5.31/5.57 => ( ( ord_less_nat @ Ma2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.31/5.57 => ~ ( ( Mi2 != Ma2 )
% 5.31/5.57 => ! [I4: nat] :
% 5.31/5.57 ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.31/5.57 => ( ( ( ( vEBT_VEBT_high @ Ma2 @ N3 )
% 5.31/5.57 = I4 )
% 5.31/5.57 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I4 ) @ ( vEBT_VEBT_low @ Ma2 @ N3 ) ) )
% 5.31/5.57 & ! [X5: nat] :
% 5.31/5.57 ( ( ( ( vEBT_VEBT_high @ X5 @ N3 )
% 5.31/5.57 = I4 )
% 5.31/5.57 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I4 ) @ ( vEBT_VEBT_low @ X5 @ N3 ) ) )
% 5.31/5.57 => ( ( ord_less_nat @ Mi2 @ X5 )
% 5.31/5.57 & ( ord_less_eq_nat @ X5 @ Ma2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
% 5.31/5.57 => ~ ! [TreeList: list_VEBT_VEBT,N3: nat,Summary2: vEBT_VEBT,M: nat,Deg2: nat,Mi2: nat,Ma2: nat] :
% 5.31/5.57 ( ( A12
% 5.31/5.57 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Deg2 @ TreeList @ Summary2 ) )
% 5.31/5.57 => ( ( A23 = Deg2 )
% 5.31/5.57 => ( ! [X5: vEBT_VEBT] :
% 5.31/5.57 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.31/5.57 => ( vEBT_invar_vebt @ X5 @ N3 ) )
% 5.31/5.57 => ( ( vEBT_invar_vebt @ Summary2 @ M )
% 5.31/5.57 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 5.31/5.57 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.31/5.57 => ( ( M
% 5.31/5.57 = ( suc @ N3 ) )
% 5.31/5.57 => ( ( Deg2
% 5.31/5.57 = ( plus_plus_nat @ N3 @ M ) )
% 5.31/5.57 => ( ! [I4: nat] :
% 5.31/5.57 ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.31/5.57 => ( ( ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I4 ) @ X7 ) )
% 5.31/5.57 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I4 ) ) )
% 5.31/5.57 => ( ( ( Mi2 = Ma2 )
% 5.31/5.57 => ! [X5: vEBT_VEBT] :
% 5.31/5.57 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.31/5.57 => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X5 @ X_1 ) ) )
% 5.31/5.57 => ( ( ord_less_eq_nat @ Mi2 @ Ma2 )
% 5.31/5.57 => ( ( ord_less_nat @ Ma2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.31/5.57 => ~ ( ( Mi2 != Ma2 )
% 5.31/5.57 => ! [I4: nat] :
% 5.31/5.57 ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.31/5.57 => ( ( ( ( vEBT_VEBT_high @ Ma2 @ N3 )
% 5.31/5.57 = I4 )
% 5.31/5.57 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I4 ) @ ( vEBT_VEBT_low @ Ma2 @ N3 ) ) )
% 5.31/5.57 & ! [X5: nat] :
% 5.31/5.57 ( ( ( ( vEBT_VEBT_high @ X5 @ N3 )
% 5.31/5.57 = I4 )
% 5.31/5.57 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I4 ) @ ( vEBT_VEBT_low @ X5 @ N3 ) ) )
% 5.31/5.57 => ( ( ord_less_nat @ Mi2 @ X5 )
% 5.31/5.57 & ( ord_less_eq_nat @ X5 @ Ma2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % invar_vebt.cases
% 5.31/5.57 thf(fact_4398_invar__vebt_Osimps,axiom,
% 5.31/5.57 ( vEBT_invar_vebt
% 5.31/5.57 = ( ^ [A13: vEBT_VEBT,A24: nat] :
% 5.31/5.57 ( ( ? [A5: $o,B4: $o] :
% 5.31/5.57 ( A13
% 5.31/5.57 = ( vEBT_Leaf @ A5 @ B4 ) )
% 5.31/5.57 & ( A24
% 5.31/5.57 = ( suc @ zero_zero_nat ) ) )
% 5.31/5.57 | ? [TreeList4: list_VEBT_VEBT,N4: nat,Summary4: vEBT_VEBT] :
% 5.31/5.57 ( ( A13
% 5.31/5.57 = ( vEBT_Node @ none_P5556105721700978146at_nat @ A24 @ TreeList4 @ Summary4 ) )
% 5.31/5.57 & ! [X4: vEBT_VEBT] :
% 5.31/5.57 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList4 ) )
% 5.31/5.57 => ( vEBT_invar_vebt @ X4 @ N4 ) )
% 5.31/5.57 & ( vEBT_invar_vebt @ Summary4 @ N4 )
% 5.31/5.57 & ( ( size_s6755466524823107622T_VEBT @ TreeList4 )
% 5.31/5.57 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) )
% 5.31/5.57 & ( A24
% 5.31/5.57 = ( plus_plus_nat @ N4 @ N4 ) )
% 5.31/5.57 & ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ Summary4 @ X7 )
% 5.31/5.57 & ! [X4: vEBT_VEBT] :
% 5.31/5.57 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList4 ) )
% 5.31/5.57 => ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X7 ) ) )
% 5.31/5.57 | ? [TreeList4: list_VEBT_VEBT,N4: nat,Summary4: vEBT_VEBT] :
% 5.31/5.57 ( ( A13
% 5.31/5.57 = ( vEBT_Node @ none_P5556105721700978146at_nat @ A24 @ TreeList4 @ Summary4 ) )
% 5.31/5.57 & ! [X4: vEBT_VEBT] :
% 5.31/5.57 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList4 ) )
% 5.31/5.57 => ( vEBT_invar_vebt @ X4 @ N4 ) )
% 5.31/5.57 & ( vEBT_invar_vebt @ Summary4 @ ( suc @ N4 ) )
% 5.31/5.57 & ( ( size_s6755466524823107622T_VEBT @ TreeList4 )
% 5.31/5.57 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N4 ) ) )
% 5.31/5.57 & ( A24
% 5.31/5.57 = ( plus_plus_nat @ N4 @ ( suc @ N4 ) ) )
% 5.31/5.57 & ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ Summary4 @ X7 )
% 5.31/5.57 & ! [X4: vEBT_VEBT] :
% 5.31/5.57 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList4 ) )
% 5.31/5.57 => ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X7 ) ) )
% 5.31/5.57 | ? [TreeList4: list_VEBT_VEBT,N4: nat,Summary4: vEBT_VEBT,Mi3: nat,Ma3: nat] :
% 5.31/5.57 ( ( A13
% 5.31/5.57 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma3 ) ) @ A24 @ TreeList4 @ Summary4 ) )
% 5.31/5.57 & ! [X4: vEBT_VEBT] :
% 5.31/5.57 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList4 ) )
% 5.31/5.57 => ( vEBT_invar_vebt @ X4 @ N4 ) )
% 5.31/5.57 & ( vEBT_invar_vebt @ Summary4 @ N4 )
% 5.31/5.57 & ( ( size_s6755466524823107622T_VEBT @ TreeList4 )
% 5.31/5.57 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) )
% 5.31/5.57 & ( A24
% 5.31/5.57 = ( plus_plus_nat @ N4 @ N4 ) )
% 5.31/5.57 & ! [I: nat] :
% 5.31/5.57 ( ( ord_less_nat @ I @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) )
% 5.31/5.57 => ( ( ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList4 @ I ) @ X7 ) )
% 5.31/5.57 = ( vEBT_V8194947554948674370ptions @ Summary4 @ I ) ) )
% 5.31/5.57 & ( ( Mi3 = Ma3 )
% 5.31/5.57 => ! [X4: vEBT_VEBT] :
% 5.31/5.57 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList4 ) )
% 5.31/5.57 => ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X7 ) ) )
% 5.31/5.57 & ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 5.31/5.57 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A24 ) )
% 5.31/5.57 & ( ( Mi3 != Ma3 )
% 5.31/5.57 => ! [I: nat] :
% 5.31/5.57 ( ( ord_less_nat @ I @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) )
% 5.31/5.57 => ( ( ( ( vEBT_VEBT_high @ Ma3 @ N4 )
% 5.31/5.57 = I )
% 5.31/5.57 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList4 @ I ) @ ( vEBT_VEBT_low @ Ma3 @ N4 ) ) )
% 5.31/5.57 & ! [X4: nat] :
% 5.31/5.57 ( ( ( ( vEBT_VEBT_high @ X4 @ N4 )
% 5.31/5.57 = I )
% 5.31/5.57 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList4 @ I ) @ ( vEBT_VEBT_low @ X4 @ N4 ) ) )
% 5.31/5.57 => ( ( ord_less_nat @ Mi3 @ X4 )
% 5.31/5.57 & ( ord_less_eq_nat @ X4 @ Ma3 ) ) ) ) ) ) )
% 5.31/5.57 | ? [TreeList4: list_VEBT_VEBT,N4: nat,Summary4: vEBT_VEBT,Mi3: nat,Ma3: nat] :
% 5.31/5.57 ( ( A13
% 5.31/5.57 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma3 ) ) @ A24 @ TreeList4 @ Summary4 ) )
% 5.31/5.57 & ! [X4: vEBT_VEBT] :
% 5.31/5.57 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList4 ) )
% 5.31/5.57 => ( vEBT_invar_vebt @ X4 @ N4 ) )
% 5.31/5.57 & ( vEBT_invar_vebt @ Summary4 @ ( suc @ N4 ) )
% 5.31/5.57 & ( ( size_s6755466524823107622T_VEBT @ TreeList4 )
% 5.31/5.57 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N4 ) ) )
% 5.31/5.57 & ( A24
% 5.31/5.57 = ( plus_plus_nat @ N4 @ ( suc @ N4 ) ) )
% 5.31/5.57 & ! [I: nat] :
% 5.31/5.57 ( ( ord_less_nat @ I @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N4 ) ) )
% 5.31/5.57 => ( ( ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList4 @ I ) @ X7 ) )
% 5.31/5.57 = ( vEBT_V8194947554948674370ptions @ Summary4 @ I ) ) )
% 5.31/5.57 & ( ( Mi3 = Ma3 )
% 5.31/5.57 => ! [X4: vEBT_VEBT] :
% 5.31/5.57 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList4 ) )
% 5.31/5.57 => ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X7 ) ) )
% 5.31/5.57 & ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 5.31/5.57 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A24 ) )
% 5.31/5.57 & ( ( Mi3 != Ma3 )
% 5.31/5.57 => ! [I: nat] :
% 5.31/5.57 ( ( ord_less_nat @ I @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N4 ) ) )
% 5.31/5.57 => ( ( ( ( vEBT_VEBT_high @ Ma3 @ N4 )
% 5.31/5.57 = I )
% 5.31/5.57 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList4 @ I ) @ ( vEBT_VEBT_low @ Ma3 @ N4 ) ) )
% 5.31/5.57 & ! [X4: nat] :
% 5.31/5.57 ( ( ( ( vEBT_VEBT_high @ X4 @ N4 )
% 5.31/5.57 = I )
% 5.31/5.57 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList4 @ I ) @ ( vEBT_VEBT_low @ X4 @ N4 ) ) )
% 5.31/5.57 => ( ( ord_less_nat @ Mi3 @ X4 )
% 5.31/5.57 & ( ord_less_eq_nat @ X4 @ Ma3 ) ) ) ) ) ) ) ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % invar_vebt.simps
% 5.31/5.57 thf(fact_4399_distrib__inf__le,axiom,
% 5.31/5.57 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,Z3: set_Pr1261947904930325089at_nat] : ( ord_le3146513528884898305at_nat @ ( sup_su6327502436637775413at_nat @ ( inf_in2572325071724192079at_nat @ X @ Y ) @ ( inf_in2572325071724192079at_nat @ X @ Z3 ) ) @ ( inf_in2572325071724192079at_nat @ X @ ( sup_su6327502436637775413at_nat @ Y @ Z3 ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % distrib_inf_le
% 5.31/5.57 thf(fact_4400_distrib__inf__le,axiom,
% 5.31/5.57 ! [X: set_nat,Y: set_nat,Z3: set_nat] : ( ord_less_eq_set_nat @ ( sup_sup_set_nat @ ( inf_inf_set_nat @ X @ Y ) @ ( inf_inf_set_nat @ X @ Z3 ) ) @ ( inf_inf_set_nat @ X @ ( sup_sup_set_nat @ Y @ Z3 ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % distrib_inf_le
% 5.31/5.57 thf(fact_4401_distrib__inf__le,axiom,
% 5.31/5.57 ! [X: rat,Y: rat,Z3: rat] : ( ord_less_eq_rat @ ( sup_sup_rat @ ( inf_inf_rat @ X @ Y ) @ ( inf_inf_rat @ X @ Z3 ) ) @ ( inf_inf_rat @ X @ ( sup_sup_rat @ Y @ Z3 ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % distrib_inf_le
% 5.31/5.57 thf(fact_4402_distrib__inf__le,axiom,
% 5.31/5.57 ! [X: nat,Y: nat,Z3: nat] : ( ord_less_eq_nat @ ( sup_sup_nat @ ( inf_inf_nat @ X @ Y ) @ ( inf_inf_nat @ X @ Z3 ) ) @ ( inf_inf_nat @ X @ ( sup_sup_nat @ Y @ Z3 ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % distrib_inf_le
% 5.31/5.57 thf(fact_4403_distrib__inf__le,axiom,
% 5.31/5.57 ! [X: int,Y: int,Z3: int] : ( ord_less_eq_int @ ( sup_sup_int @ ( inf_inf_int @ X @ Y ) @ ( inf_inf_int @ X @ Z3 ) ) @ ( inf_inf_int @ X @ ( sup_sup_int @ Y @ Z3 ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % distrib_inf_le
% 5.31/5.57 thf(fact_4404_distrib__sup__le,axiom,
% 5.31/5.57 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,Z3: set_Pr1261947904930325089at_nat] : ( ord_le3146513528884898305at_nat @ ( sup_su6327502436637775413at_nat @ X @ ( inf_in2572325071724192079at_nat @ Y @ Z3 ) ) @ ( inf_in2572325071724192079at_nat @ ( sup_su6327502436637775413at_nat @ X @ Y ) @ ( sup_su6327502436637775413at_nat @ X @ Z3 ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % distrib_sup_le
% 5.31/5.57 thf(fact_4405_distrib__sup__le,axiom,
% 5.31/5.57 ! [X: set_nat,Y: set_nat,Z3: set_nat] : ( ord_less_eq_set_nat @ ( sup_sup_set_nat @ X @ ( inf_inf_set_nat @ Y @ Z3 ) ) @ ( inf_inf_set_nat @ ( sup_sup_set_nat @ X @ Y ) @ ( sup_sup_set_nat @ X @ Z3 ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % distrib_sup_le
% 5.31/5.57 thf(fact_4406_distrib__sup__le,axiom,
% 5.31/5.57 ! [X: rat,Y: rat,Z3: rat] : ( ord_less_eq_rat @ ( sup_sup_rat @ X @ ( inf_inf_rat @ Y @ Z3 ) ) @ ( inf_inf_rat @ ( sup_sup_rat @ X @ Y ) @ ( sup_sup_rat @ X @ Z3 ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % distrib_sup_le
% 5.31/5.57 thf(fact_4407_distrib__sup__le,axiom,
% 5.31/5.57 ! [X: nat,Y: nat,Z3: nat] : ( ord_less_eq_nat @ ( sup_sup_nat @ X @ ( inf_inf_nat @ Y @ Z3 ) ) @ ( inf_inf_nat @ ( sup_sup_nat @ X @ Y ) @ ( sup_sup_nat @ X @ Z3 ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % distrib_sup_le
% 5.31/5.57 thf(fact_4408_distrib__sup__le,axiom,
% 5.31/5.57 ! [X: int,Y: int,Z3: int] : ( ord_less_eq_int @ ( sup_sup_int @ X @ ( inf_inf_int @ Y @ Z3 ) ) @ ( inf_inf_int @ ( sup_sup_int @ X @ Y ) @ ( sup_sup_int @ X @ Z3 ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % distrib_sup_le
% 5.31/5.57 thf(fact_4409_in__children__def,axiom,
% 5.31/5.57 ( vEBT_V5917875025757280293ildren
% 5.31/5.57 = ( ^ [N4: nat,TreeList4: list_VEBT_VEBT,X4: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList4 @ ( vEBT_VEBT_high @ X4 @ N4 ) ) @ ( vEBT_VEBT_low @ X4 @ N4 ) ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % in_children_def
% 5.31/5.57 thf(fact_4410_nested__mint,axiom,
% 5.31/5.57 ! [Mi: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat,Va3: nat] :
% 5.31/5.57 ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ N )
% 5.31/5.57 => ( ( N
% 5.31/5.57 = ( suc @ ( suc @ Va3 ) ) )
% 5.31/5.57 => ( ~ ( ord_less_nat @ Ma @ Mi )
% 5.31/5.57 => ( ( Ma != Mi )
% 5.31/5.57 => ( 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 @ Va3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( suc @ ( divide_divide_nat @ Va3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % nested_mint
% 5.31/5.57 thf(fact_4411_summaxma,axiom,
% 5.31/5.57 ! [Mi: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.31/5.57 ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ Deg )
% 5.31/5.57 => ( ( Mi != Ma )
% 5.31/5.57 => ( ( the_nat @ ( vEBT_vebt_maxt @ Summary ) )
% 5.31/5.57 = ( vEBT_VEBT_high @ Ma @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % summaxma
% 5.31/5.57 thf(fact_4412_set__encode__insert,axiom,
% 5.31/5.57 ! [A4: set_nat,N: nat] :
% 5.31/5.57 ( ( finite_finite_nat @ A4 )
% 5.31/5.57 => ( ~ ( member_nat @ N @ A4 )
% 5.31/5.57 => ( ( nat_set_encode @ ( insert_nat @ N @ A4 ) )
% 5.31/5.57 = ( plus_plus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ ( nat_set_encode @ A4 ) ) ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % set_encode_insert
% 5.31/5.57 thf(fact_4413_unset__bit__0,axiom,
% 5.31/5.57 ! [A: nat] :
% 5.31/5.57 ( ( bit_se4205575877204974255it_nat @ zero_zero_nat @ A )
% 5.31/5.57 = ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % unset_bit_0
% 5.31/5.57 thf(fact_4414_unset__bit__0,axiom,
% 5.31/5.57 ! [A: int] :
% 5.31/5.57 ( ( bit_se4203085406695923979it_int @ zero_zero_nat @ A )
% 5.31/5.57 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % unset_bit_0
% 5.31/5.57 thf(fact_4415_del__x__mi__lets__in__not__minNull,axiom,
% 5.31/5.57 ! [X: nat,Mi: nat,Ma: nat,Deg: nat,Xn: nat,H: nat,Summary: vEBT_VEBT,TreeList2: list_VEBT_VEBT,L: nat,Newnode: vEBT_VEBT,Newlist: list_VEBT_VEBT] :
% 5.31/5.57 ( ( ( X = Mi )
% 5.31/5.57 & ( ord_less_nat @ X @ Ma ) )
% 5.31/5.57 => ( ( Mi != Ma )
% 5.31/5.57 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.31/5.57 => ( ( ( vEBT_VEBT_high @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.31/5.57 = H )
% 5.31/5.57 => ( ( Xn
% 5.31/5.57 = ( 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 ) ) ) ) ) ) )
% 5.31/5.57 => ( ( ( vEBT_VEBT_low @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.31/5.57 = L )
% 5.31/5.57 => ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.31/5.57 => ( ( Newnode
% 5.31/5.57 = ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ H ) @ L ) )
% 5.31/5.57 => ( ( Newlist
% 5.31/5.57 = ( list_u1324408373059187874T_VEBT @ TreeList2 @ H @ Newnode ) )
% 5.31/5.57 => ( ~ ( vEBT_VEBT_minNull @ Newnode )
% 5.31/5.57 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 5.31/5.57 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Xn @ ( if_nat @ ( Xn = Ma ) @ ( plus_plus_nat @ ( times_times_nat @ H @ ( 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 @ H ) ) ) ) @ Ma ) ) ) @ Deg @ Newlist @ Summary ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % del_x_mi_lets_in_not_minNull
% 5.31/5.57 thf(fact_4416_del__x__not__mi__newnode__not__nil,axiom,
% 5.31/5.57 ! [Mi: nat,X: nat,Ma: nat,Deg: nat,H: nat,L: nat,Newnode: vEBT_VEBT,TreeList2: list_VEBT_VEBT,Newlist: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.31/5.57 ( ( ( ord_less_nat @ Mi @ X )
% 5.31/5.57 & ( ord_less_eq_nat @ X @ Ma ) )
% 5.31/5.57 => ( ( Mi != Ma )
% 5.31/5.57 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.31/5.57 => ( ( ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.31/5.57 = H )
% 5.31/5.57 => ( ( ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.31/5.57 = L )
% 5.31/5.57 => ( ( Newnode
% 5.31/5.57 = ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ H ) @ L ) )
% 5.31/5.57 => ( ~ ( vEBT_VEBT_minNull @ Newnode )
% 5.31/5.57 => ( ( Newlist
% 5.31/5.57 = ( list_u1324408373059187874T_VEBT @ TreeList2 @ H @ Newnode ) )
% 5.31/5.57 => ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.31/5.57 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 5.31/5.57 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ ( if_nat @ ( X = Ma ) @ ( plus_plus_nat @ ( times_times_nat @ H @ ( 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 @ H ) ) ) ) @ Ma ) ) ) @ Deg @ Newlist @ Summary ) ) ) ) ) ) ) ) ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % del_x_not_mi_newnode_not_nil
% 5.31/5.57 thf(fact_4417_neg__eucl__rel__int__mult__2,axiom,
% 5.31/5.57 ! [B: int,A: int,Q2: int,R3: int] :
% 5.31/5.57 ( ( ord_less_eq_int @ B @ zero_zero_int )
% 5.31/5.57 => ( ( eucl_rel_int @ ( plus_plus_int @ A @ one_one_int ) @ B @ ( product_Pair_int_int @ Q2 @ R3 ) )
% 5.31/5.57 => ( 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 ) ) @ R3 ) @ one_one_int ) ) ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % neg_eucl_rel_int_mult_2
% 5.31/5.57 thf(fact_4418_length__list__update,axiom,
% 5.31/5.57 ! [Xs2: list_VEBT_VEBT,I2: nat,X: vEBT_VEBT] :
% 5.31/5.57 ( ( size_s6755466524823107622T_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs2 @ I2 @ X ) )
% 5.31/5.57 = ( size_s6755466524823107622T_VEBT @ Xs2 ) ) ).
% 5.31/5.57
% 5.31/5.57 % length_list_update
% 5.31/5.57 thf(fact_4419_length__list__update,axiom,
% 5.31/5.57 ! [Xs2: list_o,I2: nat,X: $o] :
% 5.31/5.57 ( ( size_size_list_o @ ( list_update_o @ Xs2 @ I2 @ X ) )
% 5.31/5.57 = ( size_size_list_o @ Xs2 ) ) ).
% 5.31/5.57
% 5.31/5.57 % length_list_update
% 5.31/5.57 thf(fact_4420_length__list__update,axiom,
% 5.31/5.57 ! [Xs2: list_nat,I2: nat,X: nat] :
% 5.31/5.57 ( ( size_size_list_nat @ ( list_update_nat @ Xs2 @ I2 @ X ) )
% 5.31/5.57 = ( size_size_list_nat @ Xs2 ) ) ).
% 5.31/5.57
% 5.31/5.57 % length_list_update
% 5.31/5.57 thf(fact_4421_length__list__update,axiom,
% 5.31/5.57 ! [Xs2: list_int,I2: nat,X: int] :
% 5.31/5.57 ( ( size_size_list_int @ ( list_update_int @ Xs2 @ I2 @ X ) )
% 5.31/5.57 = ( size_size_list_int @ Xs2 ) ) ).
% 5.31/5.57
% 5.31/5.57 % length_list_update
% 5.31/5.57 thf(fact_4422_option_Ocollapse,axiom,
% 5.31/5.57 ! [Option: option4927543243414619207at_nat] :
% 5.31/5.57 ( ( Option != none_P5556105721700978146at_nat )
% 5.31/5.57 => ( ( some_P7363390416028606310at_nat @ ( the_Pr8591224930841456533at_nat @ Option ) )
% 5.31/5.57 = Option ) ) ).
% 5.31/5.57
% 5.31/5.57 % option.collapse
% 5.31/5.57 thf(fact_4423_option_Ocollapse,axiom,
% 5.31/5.57 ! [Option: option_nat] :
% 5.31/5.57 ( ( Option != none_nat )
% 5.31/5.57 => ( ( some_nat @ ( the_nat @ Option ) )
% 5.31/5.57 = Option ) ) ).
% 5.31/5.57
% 5.31/5.57 % option.collapse
% 5.31/5.57 thf(fact_4424_option_Ocollapse,axiom,
% 5.31/5.57 ! [Option: option_num] :
% 5.31/5.57 ( ( Option != none_num )
% 5.31/5.57 => ( ( some_num @ ( the_num @ Option ) )
% 5.31/5.57 = Option ) ) ).
% 5.31/5.57
% 5.31/5.57 % option.collapse
% 5.31/5.57 thf(fact_4425_list__update__beyond,axiom,
% 5.31/5.57 ! [Xs2: list_VEBT_VEBT,I2: nat,X: vEBT_VEBT] :
% 5.31/5.57 ( ( ord_less_eq_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) @ I2 )
% 5.31/5.57 => ( ( list_u1324408373059187874T_VEBT @ Xs2 @ I2 @ X )
% 5.31/5.57 = Xs2 ) ) ).
% 5.31/5.57
% 5.31/5.57 % list_update_beyond
% 5.31/5.57 thf(fact_4426_list__update__beyond,axiom,
% 5.31/5.57 ! [Xs2: list_o,I2: nat,X: $o] :
% 5.31/5.57 ( ( ord_less_eq_nat @ ( size_size_list_o @ Xs2 ) @ I2 )
% 5.31/5.57 => ( ( list_update_o @ Xs2 @ I2 @ X )
% 5.31/5.57 = Xs2 ) ) ).
% 5.31/5.57
% 5.31/5.57 % list_update_beyond
% 5.31/5.57 thf(fact_4427_list__update__beyond,axiom,
% 5.31/5.57 ! [Xs2: list_nat,I2: nat,X: nat] :
% 5.31/5.57 ( ( ord_less_eq_nat @ ( size_size_list_nat @ Xs2 ) @ I2 )
% 5.31/5.57 => ( ( list_update_nat @ Xs2 @ I2 @ X )
% 5.31/5.57 = Xs2 ) ) ).
% 5.31/5.57
% 5.31/5.57 % list_update_beyond
% 5.31/5.57 thf(fact_4428_list__update__beyond,axiom,
% 5.31/5.57 ! [Xs2: list_int,I2: nat,X: int] :
% 5.31/5.57 ( ( ord_less_eq_nat @ ( size_size_list_int @ Xs2 ) @ I2 )
% 5.31/5.57 => ( ( list_update_int @ Xs2 @ I2 @ X )
% 5.31/5.57 = Xs2 ) ) ).
% 5.31/5.57
% 5.31/5.57 % list_update_beyond
% 5.31/5.57 thf(fact_4429_set__encode__empty,axiom,
% 5.31/5.57 ( ( nat_set_encode @ bot_bot_set_nat )
% 5.31/5.57 = zero_zero_nat ) ).
% 5.31/5.57
% 5.31/5.57 % set_encode_empty
% 5.31/5.57 thf(fact_4430_nth__list__update__eq,axiom,
% 5.31/5.57 ! [I2: nat,Xs2: list_VEBT_VEBT,X: vEBT_VEBT] :
% 5.31/5.57 ( ( ord_less_nat @ I2 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 5.31/5.57 => ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs2 @ I2 @ X ) @ I2 )
% 5.31/5.57 = X ) ) ).
% 5.31/5.57
% 5.31/5.57 % nth_list_update_eq
% 5.31/5.57 thf(fact_4431_nth__list__update__eq,axiom,
% 5.31/5.57 ! [I2: nat,Xs2: list_o,X: $o] :
% 5.31/5.57 ( ( ord_less_nat @ I2 @ ( size_size_list_o @ Xs2 ) )
% 5.31/5.57 => ( ( nth_o @ ( list_update_o @ Xs2 @ I2 @ X ) @ I2 )
% 5.31/5.57 = X ) ) ).
% 5.31/5.57
% 5.31/5.57 % nth_list_update_eq
% 5.31/5.57 thf(fact_4432_nth__list__update__eq,axiom,
% 5.31/5.57 ! [I2: nat,Xs2: list_nat,X: nat] :
% 5.31/5.57 ( ( ord_less_nat @ I2 @ ( size_size_list_nat @ Xs2 ) )
% 5.31/5.57 => ( ( nth_nat @ ( list_update_nat @ Xs2 @ I2 @ X ) @ I2 )
% 5.31/5.57 = X ) ) ).
% 5.31/5.57
% 5.31/5.57 % nth_list_update_eq
% 5.31/5.57 thf(fact_4433_nth__list__update__eq,axiom,
% 5.31/5.57 ! [I2: nat,Xs2: list_int,X: int] :
% 5.31/5.57 ( ( ord_less_nat @ I2 @ ( size_size_list_int @ Xs2 ) )
% 5.31/5.57 => ( ( nth_int @ ( list_update_int @ Xs2 @ I2 @ X ) @ I2 )
% 5.31/5.57 = X ) ) ).
% 5.31/5.57
% 5.31/5.57 % nth_list_update_eq
% 5.31/5.57 thf(fact_4434_set__swap,axiom,
% 5.31/5.57 ! [I2: nat,Xs2: list_VEBT_VEBT,J2: nat] :
% 5.31/5.57 ( ( ord_less_nat @ I2 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 5.31/5.57 => ( ( ord_less_nat @ J2 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 5.31/5.57 => ( ( set_VEBT_VEBT2 @ ( list_u1324408373059187874T_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs2 @ I2 @ ( nth_VEBT_VEBT @ Xs2 @ J2 ) ) @ J2 @ ( nth_VEBT_VEBT @ Xs2 @ I2 ) ) )
% 5.31/5.57 = ( set_VEBT_VEBT2 @ Xs2 ) ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % set_swap
% 5.31/5.57 thf(fact_4435_set__swap,axiom,
% 5.31/5.57 ! [I2: nat,Xs2: list_o,J2: nat] :
% 5.31/5.57 ( ( ord_less_nat @ I2 @ ( size_size_list_o @ Xs2 ) )
% 5.31/5.57 => ( ( ord_less_nat @ J2 @ ( size_size_list_o @ Xs2 ) )
% 5.31/5.57 => ( ( set_o2 @ ( list_update_o @ ( list_update_o @ Xs2 @ I2 @ ( nth_o @ Xs2 @ J2 ) ) @ J2 @ ( nth_o @ Xs2 @ I2 ) ) )
% 5.31/5.57 = ( set_o2 @ Xs2 ) ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % set_swap
% 5.31/5.57 thf(fact_4436_set__swap,axiom,
% 5.31/5.57 ! [I2: nat,Xs2: list_nat,J2: nat] :
% 5.31/5.57 ( ( ord_less_nat @ I2 @ ( size_size_list_nat @ Xs2 ) )
% 5.31/5.57 => ( ( ord_less_nat @ J2 @ ( size_size_list_nat @ Xs2 ) )
% 5.31/5.57 => ( ( set_nat2 @ ( list_update_nat @ ( list_update_nat @ Xs2 @ I2 @ ( nth_nat @ Xs2 @ J2 ) ) @ J2 @ ( nth_nat @ Xs2 @ I2 ) ) )
% 5.31/5.57 = ( set_nat2 @ Xs2 ) ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % set_swap
% 5.31/5.57 thf(fact_4437_set__swap,axiom,
% 5.31/5.57 ! [I2: nat,Xs2: list_int,J2: nat] :
% 5.31/5.57 ( ( ord_less_nat @ I2 @ ( size_size_list_int @ Xs2 ) )
% 5.31/5.57 => ( ( ord_less_nat @ J2 @ ( size_size_list_int @ Xs2 ) )
% 5.31/5.57 => ( ( set_int2 @ ( list_update_int @ ( list_update_int @ Xs2 @ I2 @ ( nth_int @ Xs2 @ J2 ) ) @ J2 @ ( nth_int @ Xs2 @ I2 ) ) )
% 5.31/5.57 = ( set_int2 @ Xs2 ) ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % set_swap
% 5.31/5.57 thf(fact_4438_unique__quotient,axiom,
% 5.31/5.57 ! [A: int,B: int,Q2: int,R3: int,Q4: int,R5: int] :
% 5.31/5.57 ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q2 @ R3 ) )
% 5.31/5.57 => ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q4 @ R5 ) )
% 5.31/5.57 => ( Q2 = Q4 ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % unique_quotient
% 5.31/5.57 thf(fact_4439_unique__remainder,axiom,
% 5.31/5.57 ! [A: int,B: int,Q2: int,R3: int,Q4: int,R5: int] :
% 5.31/5.57 ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q2 @ R3 ) )
% 5.31/5.57 => ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q4 @ R5 ) )
% 5.31/5.57 => ( R3 = R5 ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % unique_remainder
% 5.31/5.57 thf(fact_4440_zip__update,axiom,
% 5.31/5.57 ! [Xs2: list_VEBT_VEBT,I2: nat,X: vEBT_VEBT,Ys: list_VEBT_VEBT,Y: vEBT_VEBT] :
% 5.31/5.57 ( ( zip_VE537291747668921783T_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs2 @ I2 @ X ) @ ( list_u1324408373059187874T_VEBT @ Ys @ I2 @ Y ) )
% 5.31/5.57 = ( list_u6961636818849549845T_VEBT @ ( zip_VE537291747668921783T_VEBT @ Xs2 @ Ys ) @ I2 @ ( produc537772716801021591T_VEBT @ X @ Y ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % zip_update
% 5.31/5.57 thf(fact_4441_zip__update,axiom,
% 5.31/5.57 ! [Xs2: list_Code_integer,I2: nat,X: code_integer,Ys: list_Code_integer,Y: code_integer] :
% 5.31/5.57 ( ( zip_Co3543743374963494515nteger @ ( list_u5447711078246177391nteger @ Xs2 @ I2 @ X ) @ ( list_u5447711078246177391nteger @ Ys @ I2 @ Y ) )
% 5.31/5.57 = ( list_u2254550707601501961nteger @ ( zip_Co3543743374963494515nteger @ Xs2 @ Ys ) @ I2 @ ( produc1086072967326762835nteger @ X @ Y ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % zip_update
% 5.31/5.57 thf(fact_4442_zip__update,axiom,
% 5.31/5.57 ! [Xs2: list_P6011104703257516679at_nat,I2: nat,X: product_prod_nat_nat,Ys: list_P6011104703257516679at_nat,Y: product_prod_nat_nat] :
% 5.31/5.57 ( ( zip_Pr4664179122662387191at_nat @ ( list_u6180841689913720943at_nat @ Xs2 @ I2 @ X ) @ ( list_u6180841689913720943at_nat @ Ys @ I2 @ Y ) )
% 5.31/5.57 = ( list_u5003261594476800725at_nat @ ( zip_Pr4664179122662387191at_nat @ Xs2 @ Ys ) @ I2 @ ( produc6161850002892822231at_nat @ X @ Y ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % zip_update
% 5.31/5.57 thf(fact_4443_zip__update,axiom,
% 5.31/5.57 ! [Xs2: list_s1210847774152347623at_nat,I2: nat,X: set_Pr1261947904930325089at_nat,Ys: list_s1210847774152347623at_nat,Y: set_Pr1261947904930325089at_nat] :
% 5.31/5.57 ( ( zip_se5600341670672612855at_nat @ ( list_u8444657558853818831at_nat @ Xs2 @ I2 @ X ) @ ( list_u8444657558853818831at_nat @ Ys @ I2 @ Y ) )
% 5.31/5.57 = ( list_u4696772448584712917at_nat @ ( zip_se5600341670672612855at_nat @ Xs2 @ Ys ) @ I2 @ ( produc2922128104949294807at_nat @ X @ Y ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % zip_update
% 5.31/5.57 thf(fact_4444_zip__update,axiom,
% 5.31/5.57 ! [Xs2: list_nat,I2: nat,X: nat,Ys: list_nat,Y: nat] :
% 5.31/5.57 ( ( zip_nat_nat @ ( list_update_nat @ Xs2 @ I2 @ X ) @ ( list_update_nat @ Ys @ I2 @ Y ) )
% 5.31/5.57 = ( list_u6180841689913720943at_nat @ ( zip_nat_nat @ Xs2 @ Ys ) @ I2 @ ( product_Pair_nat_nat @ X @ Y ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % zip_update
% 5.31/5.57 thf(fact_4445_zip__update,axiom,
% 5.31/5.57 ! [Xs2: list_int,I2: nat,X: int,Ys: list_int,Y: int] :
% 5.31/5.57 ( ( zip_int_int @ ( list_update_int @ Xs2 @ I2 @ X ) @ ( list_update_int @ Ys @ I2 @ Y ) )
% 5.31/5.57 = ( list_u3002344382305578791nt_int @ ( zip_int_int @ Xs2 @ Ys ) @ I2 @ ( product_Pair_int_int @ X @ Y ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % zip_update
% 5.31/5.57 thf(fact_4446_option_Osel,axiom,
% 5.31/5.57 ! [X2: product_prod_nat_nat] :
% 5.31/5.57 ( ( the_Pr8591224930841456533at_nat @ ( some_P7363390416028606310at_nat @ X2 ) )
% 5.31/5.57 = X2 ) ).
% 5.31/5.57
% 5.31/5.57 % option.sel
% 5.31/5.57 thf(fact_4447_option_Osel,axiom,
% 5.31/5.57 ! [X2: nat] :
% 5.31/5.57 ( ( the_nat @ ( some_nat @ X2 ) )
% 5.31/5.57 = X2 ) ).
% 5.31/5.57
% 5.31/5.57 % option.sel
% 5.31/5.57 thf(fact_4448_option_Osel,axiom,
% 5.31/5.57 ! [X2: num] :
% 5.31/5.57 ( ( the_num @ ( some_num @ X2 ) )
% 5.31/5.57 = X2 ) ).
% 5.31/5.57
% 5.31/5.57 % option.sel
% 5.31/5.57 thf(fact_4449_option_Oexpand,axiom,
% 5.31/5.57 ! [Option: option_nat,Option2: option_nat] :
% 5.31/5.57 ( ( ( Option = none_nat )
% 5.31/5.57 = ( Option2 = none_nat ) )
% 5.31/5.57 => ( ( ( Option != none_nat )
% 5.31/5.57 => ( ( Option2 != none_nat )
% 5.31/5.57 => ( ( the_nat @ Option )
% 5.31/5.57 = ( the_nat @ Option2 ) ) ) )
% 5.31/5.57 => ( Option = Option2 ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % option.expand
% 5.31/5.57 thf(fact_4450_option_Oexpand,axiom,
% 5.31/5.57 ! [Option: option4927543243414619207at_nat,Option2: option4927543243414619207at_nat] :
% 5.31/5.57 ( ( ( Option = none_P5556105721700978146at_nat )
% 5.31/5.57 = ( Option2 = none_P5556105721700978146at_nat ) )
% 5.31/5.57 => ( ( ( Option != none_P5556105721700978146at_nat )
% 5.31/5.57 => ( ( Option2 != none_P5556105721700978146at_nat )
% 5.31/5.57 => ( ( the_Pr8591224930841456533at_nat @ Option )
% 5.31/5.57 = ( the_Pr8591224930841456533at_nat @ Option2 ) ) ) )
% 5.31/5.57 => ( Option = Option2 ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % option.expand
% 5.31/5.57 thf(fact_4451_option_Oexpand,axiom,
% 5.31/5.57 ! [Option: option_num,Option2: option_num] :
% 5.31/5.57 ( ( ( Option = none_num )
% 5.31/5.57 = ( Option2 = none_num ) )
% 5.31/5.57 => ( ( ( Option != none_num )
% 5.31/5.57 => ( ( Option2 != none_num )
% 5.31/5.57 => ( ( the_num @ Option )
% 5.31/5.57 = ( the_num @ Option2 ) ) ) )
% 5.31/5.57 => ( Option = Option2 ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % option.expand
% 5.31/5.57 thf(fact_4452_eucl__rel__int__by0,axiom,
% 5.31/5.57 ! [K2: int] : ( eucl_rel_int @ K2 @ zero_zero_int @ ( product_Pair_int_int @ zero_zero_int @ K2 ) ) ).
% 5.31/5.57
% 5.31/5.57 % eucl_rel_int_by0
% 5.31/5.57 thf(fact_4453_div__int__unique,axiom,
% 5.31/5.57 ! [K2: int,L: int,Q2: int,R3: int] :
% 5.31/5.57 ( ( eucl_rel_int @ K2 @ L @ ( product_Pair_int_int @ Q2 @ R3 ) )
% 5.31/5.57 => ( ( divide_divide_int @ K2 @ L )
% 5.31/5.57 = Q2 ) ) ).
% 5.31/5.57
% 5.31/5.57 % div_int_unique
% 5.31/5.57 thf(fact_4454_list__update__code_I3_J,axiom,
% 5.31/5.57 ! [X: nat,Xs2: list_nat,I2: nat,Y: nat] :
% 5.31/5.57 ( ( list_update_nat @ ( cons_nat @ X @ Xs2 ) @ ( suc @ I2 ) @ Y )
% 5.31/5.57 = ( cons_nat @ X @ ( list_update_nat @ Xs2 @ I2 @ Y ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % list_update_code(3)
% 5.31/5.57 thf(fact_4455_list__update__code_I3_J,axiom,
% 5.31/5.57 ! [X: vEBT_VEBT,Xs2: list_VEBT_VEBT,I2: nat,Y: vEBT_VEBT] :
% 5.31/5.57 ( ( list_u1324408373059187874T_VEBT @ ( cons_VEBT_VEBT @ X @ Xs2 ) @ ( suc @ I2 ) @ Y )
% 5.31/5.57 = ( cons_VEBT_VEBT @ X @ ( list_u1324408373059187874T_VEBT @ Xs2 @ I2 @ Y ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % list_update_code(3)
% 5.31/5.57 thf(fact_4456_list__update__code_I2_J,axiom,
% 5.31/5.57 ! [X: nat,Xs2: list_nat,Y: nat] :
% 5.31/5.57 ( ( list_update_nat @ ( cons_nat @ X @ Xs2 ) @ zero_zero_nat @ Y )
% 5.31/5.57 = ( cons_nat @ Y @ Xs2 ) ) ).
% 5.31/5.57
% 5.31/5.57 % list_update_code(2)
% 5.31/5.57 thf(fact_4457_list__update__code_I2_J,axiom,
% 5.31/5.57 ! [X: vEBT_VEBT,Xs2: list_VEBT_VEBT,Y: vEBT_VEBT] :
% 5.31/5.57 ( ( list_u1324408373059187874T_VEBT @ ( cons_VEBT_VEBT @ X @ Xs2 ) @ zero_zero_nat @ Y )
% 5.31/5.57 = ( cons_VEBT_VEBT @ Y @ Xs2 ) ) ).
% 5.31/5.57
% 5.31/5.57 % list_update_code(2)
% 5.31/5.57 thf(fact_4458_set__encode__eq,axiom,
% 5.31/5.57 ! [A4: set_nat,B5: set_nat] :
% 5.31/5.57 ( ( finite_finite_nat @ A4 )
% 5.31/5.57 => ( ( finite_finite_nat @ B5 )
% 5.31/5.57 => ( ( ( nat_set_encode @ A4 )
% 5.31/5.57 = ( nat_set_encode @ B5 ) )
% 5.31/5.57 = ( A4 = B5 ) ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % set_encode_eq
% 5.31/5.57 thf(fact_4459_option_Oexhaust__sel,axiom,
% 5.31/5.57 ! [Option: option4927543243414619207at_nat] :
% 5.31/5.57 ( ( Option != none_P5556105721700978146at_nat )
% 5.31/5.57 => ( Option
% 5.31/5.57 = ( some_P7363390416028606310at_nat @ ( the_Pr8591224930841456533at_nat @ Option ) ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % option.exhaust_sel
% 5.31/5.57 thf(fact_4460_option_Oexhaust__sel,axiom,
% 5.31/5.57 ! [Option: option_nat] :
% 5.31/5.57 ( ( Option != none_nat )
% 5.31/5.57 => ( Option
% 5.31/5.57 = ( some_nat @ ( the_nat @ Option ) ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % option.exhaust_sel
% 5.31/5.57 thf(fact_4461_option_Oexhaust__sel,axiom,
% 5.31/5.57 ! [Option: option_num] :
% 5.31/5.57 ( ( Option != none_num )
% 5.31/5.57 => ( Option
% 5.31/5.57 = ( some_num @ ( the_num @ Option ) ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % option.exhaust_sel
% 5.31/5.57 thf(fact_4462_eucl__rel__int__dividesI,axiom,
% 5.31/5.57 ! [L: int,K2: int,Q2: int] :
% 5.31/5.57 ( ( L != zero_zero_int )
% 5.31/5.57 => ( ( K2
% 5.31/5.57 = ( times_times_int @ Q2 @ L ) )
% 5.31/5.57 => ( eucl_rel_int @ K2 @ L @ ( product_Pair_int_int @ Q2 @ zero_zero_int ) ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % eucl_rel_int_dividesI
% 5.31/5.57 thf(fact_4463_set__update__memI,axiom,
% 5.31/5.57 ! [N: nat,Xs2: list_complex,X: complex] :
% 5.31/5.57 ( ( ord_less_nat @ N @ ( size_s3451745648224563538omplex @ Xs2 ) )
% 5.31/5.57 => ( member_complex @ X @ ( set_complex2 @ ( list_update_complex @ Xs2 @ N @ X ) ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % set_update_memI
% 5.31/5.57 thf(fact_4464_set__update__memI,axiom,
% 5.31/5.57 ! [N: nat,Xs2: list_real,X: real] :
% 5.31/5.57 ( ( ord_less_nat @ N @ ( size_size_list_real @ Xs2 ) )
% 5.31/5.57 => ( member_real @ X @ ( set_real2 @ ( list_update_real @ Xs2 @ N @ X ) ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % set_update_memI
% 5.31/5.57 thf(fact_4465_set__update__memI,axiom,
% 5.31/5.57 ! [N: nat,Xs2: list_set_nat,X: set_nat] :
% 5.31/5.57 ( ( ord_less_nat @ N @ ( size_s3254054031482475050et_nat @ Xs2 ) )
% 5.31/5.57 => ( member_set_nat @ X @ ( set_set_nat2 @ ( list_update_set_nat @ Xs2 @ N @ X ) ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % set_update_memI
% 5.31/5.57 thf(fact_4466_set__update__memI,axiom,
% 5.31/5.57 ! [N: nat,Xs2: list_VEBT_VEBT,X: vEBT_VEBT] :
% 5.31/5.57 ( ( ord_less_nat @ N @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 5.31/5.57 => ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ ( list_u1324408373059187874T_VEBT @ Xs2 @ N @ X ) ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % set_update_memI
% 5.31/5.57 thf(fact_4467_set__update__memI,axiom,
% 5.31/5.57 ! [N: nat,Xs2: list_o,X: $o] :
% 5.31/5.57 ( ( ord_less_nat @ N @ ( size_size_list_o @ Xs2 ) )
% 5.31/5.57 => ( member_o @ X @ ( set_o2 @ ( list_update_o @ Xs2 @ N @ X ) ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % set_update_memI
% 5.31/5.57 thf(fact_4468_set__update__memI,axiom,
% 5.31/5.57 ! [N: nat,Xs2: list_nat,X: nat] :
% 5.31/5.57 ( ( ord_less_nat @ N @ ( size_size_list_nat @ Xs2 ) )
% 5.31/5.57 => ( member_nat @ X @ ( set_nat2 @ ( list_update_nat @ Xs2 @ N @ X ) ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % set_update_memI
% 5.31/5.57 thf(fact_4469_set__update__memI,axiom,
% 5.31/5.57 ! [N: nat,Xs2: list_int,X: int] :
% 5.31/5.57 ( ( ord_less_nat @ N @ ( size_size_list_int @ Xs2 ) )
% 5.31/5.57 => ( member_int @ X @ ( set_int2 @ ( list_update_int @ Xs2 @ N @ X ) ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % set_update_memI
% 5.31/5.57 thf(fact_4470_list__update__same__conv,axiom,
% 5.31/5.57 ! [I2: nat,Xs2: list_VEBT_VEBT,X: vEBT_VEBT] :
% 5.31/5.57 ( ( ord_less_nat @ I2 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 5.31/5.57 => ( ( ( list_u1324408373059187874T_VEBT @ Xs2 @ I2 @ X )
% 5.31/5.57 = Xs2 )
% 5.31/5.57 = ( ( nth_VEBT_VEBT @ Xs2 @ I2 )
% 5.31/5.57 = X ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % list_update_same_conv
% 5.31/5.57 thf(fact_4471_list__update__same__conv,axiom,
% 5.31/5.57 ! [I2: nat,Xs2: list_o,X: $o] :
% 5.31/5.57 ( ( ord_less_nat @ I2 @ ( size_size_list_o @ Xs2 ) )
% 5.31/5.57 => ( ( ( list_update_o @ Xs2 @ I2 @ X )
% 5.31/5.57 = Xs2 )
% 5.31/5.57 = ( ( nth_o @ Xs2 @ I2 )
% 5.31/5.57 = X ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % list_update_same_conv
% 5.31/5.57 thf(fact_4472_list__update__same__conv,axiom,
% 5.31/5.57 ! [I2: nat,Xs2: list_nat,X: nat] :
% 5.31/5.57 ( ( ord_less_nat @ I2 @ ( size_size_list_nat @ Xs2 ) )
% 5.31/5.57 => ( ( ( list_update_nat @ Xs2 @ I2 @ X )
% 5.31/5.57 = Xs2 )
% 5.31/5.57 = ( ( nth_nat @ Xs2 @ I2 )
% 5.31/5.57 = X ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % list_update_same_conv
% 5.31/5.57 thf(fact_4473_list__update__same__conv,axiom,
% 5.31/5.57 ! [I2: nat,Xs2: list_int,X: int] :
% 5.31/5.57 ( ( ord_less_nat @ I2 @ ( size_size_list_int @ Xs2 ) )
% 5.31/5.57 => ( ( ( list_update_int @ Xs2 @ I2 @ X )
% 5.31/5.57 = Xs2 )
% 5.31/5.57 = ( ( nth_int @ Xs2 @ I2 )
% 5.31/5.57 = X ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % list_update_same_conv
% 5.31/5.57 thf(fact_4474_nth__list__update,axiom,
% 5.31/5.57 ! [I2: nat,Xs2: list_VEBT_VEBT,J2: nat,X: vEBT_VEBT] :
% 5.31/5.57 ( ( ord_less_nat @ I2 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 5.31/5.57 => ( ( ( I2 = J2 )
% 5.31/5.57 => ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs2 @ I2 @ X ) @ J2 )
% 5.31/5.57 = X ) )
% 5.31/5.57 & ( ( I2 != J2 )
% 5.31/5.57 => ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs2 @ I2 @ X ) @ J2 )
% 5.31/5.57 = ( nth_VEBT_VEBT @ Xs2 @ J2 ) ) ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % nth_list_update
% 5.31/5.57 thf(fact_4475_nth__list__update,axiom,
% 5.31/5.57 ! [I2: nat,Xs2: list_o,X: $o,J2: nat] :
% 5.31/5.57 ( ( ord_less_nat @ I2 @ ( size_size_list_o @ Xs2 ) )
% 5.31/5.57 => ( ( nth_o @ ( list_update_o @ Xs2 @ I2 @ X ) @ J2 )
% 5.31/5.57 = ( ( ( I2 = J2 )
% 5.31/5.57 => X )
% 5.31/5.57 & ( ( I2 != J2 )
% 5.31/5.57 => ( nth_o @ Xs2 @ J2 ) ) ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % nth_list_update
% 5.31/5.57 thf(fact_4476_nth__list__update,axiom,
% 5.31/5.57 ! [I2: nat,Xs2: list_nat,J2: nat,X: nat] :
% 5.31/5.57 ( ( ord_less_nat @ I2 @ ( size_size_list_nat @ Xs2 ) )
% 5.31/5.57 => ( ( ( I2 = J2 )
% 5.31/5.57 => ( ( nth_nat @ ( list_update_nat @ Xs2 @ I2 @ X ) @ J2 )
% 5.31/5.57 = X ) )
% 5.31/5.57 & ( ( I2 != J2 )
% 5.31/5.57 => ( ( nth_nat @ ( list_update_nat @ Xs2 @ I2 @ X ) @ J2 )
% 5.31/5.57 = ( nth_nat @ Xs2 @ J2 ) ) ) ) ) ).
% 5.31/5.57
% 5.31/5.57 % nth_list_update
% 5.31/5.57 thf(fact_4477_nth__list__update,axiom,
% 5.31/5.57 ! [I2: nat,Xs2: list_int,J2: nat,X: int] :
% 5.31/5.58 ( ( ord_less_nat @ I2 @ ( size_size_list_int @ Xs2 ) )
% 5.31/5.58 => ( ( ( I2 = J2 )
% 5.31/5.58 => ( ( nth_int @ ( list_update_int @ Xs2 @ I2 @ X ) @ J2 )
% 5.31/5.58 = X ) )
% 5.31/5.58 & ( ( I2 != J2 )
% 5.31/5.58 => ( ( nth_int @ ( list_update_int @ Xs2 @ I2 @ X ) @ J2 )
% 5.31/5.58 = ( nth_int @ Xs2 @ J2 ) ) ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % nth_list_update
% 5.31/5.58 thf(fact_4478_set__encode__inf,axiom,
% 5.31/5.58 ! [A4: set_nat] :
% 5.31/5.58 ( ~ ( finite_finite_nat @ A4 )
% 5.31/5.58 => ( ( nat_set_encode @ A4 )
% 5.31/5.58 = zero_zero_nat ) ) ).
% 5.31/5.58
% 5.31/5.58 % set_encode_inf
% 5.31/5.58 thf(fact_4479_eucl__rel__int__iff,axiom,
% 5.31/5.58 ! [K2: int,L: int,Q2: int,R3: int] :
% 5.31/5.58 ( ( eucl_rel_int @ K2 @ L @ ( product_Pair_int_int @ Q2 @ R3 ) )
% 5.31/5.58 = ( ( K2
% 5.31/5.58 = ( plus_plus_int @ ( times_times_int @ L @ Q2 ) @ R3 ) )
% 5.31/5.58 & ( ( ord_less_int @ zero_zero_int @ L )
% 5.31/5.58 => ( ( ord_less_eq_int @ zero_zero_int @ R3 )
% 5.31/5.58 & ( ord_less_int @ R3 @ L ) ) )
% 5.31/5.58 & ( ~ ( ord_less_int @ zero_zero_int @ L )
% 5.31/5.58 => ( ( ( ord_less_int @ L @ zero_zero_int )
% 5.31/5.58 => ( ( ord_less_int @ L @ R3 )
% 5.31/5.58 & ( ord_less_eq_int @ R3 @ zero_zero_int ) ) )
% 5.31/5.58 & ( ~ ( ord_less_int @ L @ zero_zero_int )
% 5.31/5.58 => ( Q2 = zero_zero_int ) ) ) ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % eucl_rel_int_iff
% 5.31/5.58 thf(fact_4480_pos__eucl__rel__int__mult__2,axiom,
% 5.31/5.58 ! [B: int,A: int,Q2: int,R3: int] :
% 5.31/5.58 ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.31/5.58 => ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q2 @ R3 ) )
% 5.31/5.58 => ( 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 ) ) @ R3 ) ) ) ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % pos_eucl_rel_int_mult_2
% 5.31/5.58 thf(fact_4481_insert__simp__excp,axiom,
% 5.31/5.58 ! [Mi: nat,Deg: nat,TreeList2: list_VEBT_VEBT,X: nat,Ma: nat,Summary: vEBT_VEBT] :
% 5.31/5.58 ( ( ord_less_nat @ ( vEBT_VEBT_high @ Mi @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.31/5.58 => ( ( ord_less_nat @ X @ Mi )
% 5.31/5.58 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.31/5.58 => ( ( X != Ma )
% 5.31/5.58 => ( ( vEBT_vebt_insert @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 5.31/5.58 = ( 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 ) ) ) ) ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % insert_simp_excp
% 5.31/5.58 thf(fact_4482_insert__simp__norm,axiom,
% 5.31/5.58 ! [X: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Mi: nat,Ma: nat,Summary: vEBT_VEBT] :
% 5.31/5.58 ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.31/5.58 => ( ( ord_less_nat @ Mi @ X )
% 5.31/5.58 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.31/5.58 => ( ( X != Ma )
% 5.31/5.58 => ( ( vEBT_vebt_insert @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 5.31/5.58 = ( 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 ) ) ) ) ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % insert_simp_norm
% 5.31/5.58 thf(fact_4483_pred__less__length__list,axiom,
% 5.31/5.58 ! [Deg: nat,X: nat,Ma: nat,TreeList2: list_VEBT_VEBT,Mi: nat,Summary: vEBT_VEBT] :
% 5.31/5.58 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.31/5.58 => ( ( ord_less_eq_nat @ X @ Ma )
% 5.31/5.58 => ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.31/5.58 => ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 5.31/5.58 = ( if_option_nat
% 5.31/5.58 @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.31/5.58 != none_nat )
% 5.31/5.58 & ( 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 ) ) ) ) ) ) ) )
% 5.31/5.58 @ ( 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 ) ) ) ) ) )
% 5.31/5.58 @ ( if_option_nat
% 5.31/5.58 @ ( ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.31/5.58 = none_nat )
% 5.31/5.58 @ ( if_option_nat @ ( ord_less_nat @ Mi @ X ) @ ( some_nat @ Mi ) @ none_nat )
% 5.31/5.58 @ ( 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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % pred_less_length_list
% 5.31/5.58 thf(fact_4484_pred__lesseq__max,axiom,
% 5.31/5.58 ! [Deg: nat,X: nat,Ma: nat,Mi: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.31/5.58 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.31/5.58 => ( ( ord_less_eq_nat @ X @ Ma )
% 5.31/5.58 => ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 5.31/5.58 = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.31/5.58 @ ( if_option_nat
% 5.31/5.58 @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.31/5.58 != none_nat )
% 5.31/5.58 & ( 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 ) ) ) ) ) ) ) )
% 5.31/5.58 @ ( 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 ) ) ) ) ) )
% 5.31/5.58 @ ( if_option_nat
% 5.31/5.58 @ ( ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.31/5.58 = none_nat )
% 5.31/5.58 @ ( if_option_nat @ ( ord_less_nat @ Mi @ X ) @ ( some_nat @ Mi ) @ none_nat )
% 5.31/5.58 @ ( 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 ) ) ) ) ) ) ) ) ) ) )
% 5.31/5.58 @ none_nat ) ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % pred_lesseq_max
% 5.31/5.58 thf(fact_4485_succ__greatereq__min,axiom,
% 5.31/5.58 ! [Deg: nat,Mi: nat,X: nat,Ma: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.31/5.58 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.31/5.58 => ( ( ord_less_eq_nat @ Mi @ X )
% 5.31/5.58 => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 5.31/5.58 = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.31/5.58 @ ( if_option_nat
% 5.31/5.58 @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.31/5.58 != none_nat )
% 5.31/5.58 & ( 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 ) ) ) ) ) ) ) )
% 5.31/5.58 @ ( 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 ) ) ) ) ) )
% 5.31/5.58 @ ( if_option_nat
% 5.31/5.58 @ ( ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.31/5.58 = none_nat )
% 5.31/5.58 @ none_nat
% 5.31/5.58 @ ( 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 ) ) ) ) ) ) ) ) ) ) )
% 5.31/5.58 @ none_nat ) ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % succ_greatereq_min
% 5.31/5.58 thf(fact_4486_succ__less__length__list,axiom,
% 5.31/5.58 ! [Deg: nat,Mi: nat,X: nat,TreeList2: list_VEBT_VEBT,Ma: nat,Summary: vEBT_VEBT] :
% 5.31/5.58 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.31/5.58 => ( ( ord_less_eq_nat @ Mi @ X )
% 5.31/5.58 => ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.31/5.58 => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 5.31/5.58 = ( if_option_nat
% 5.31/5.58 @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.31/5.58 != none_nat )
% 5.31/5.58 & ( 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 ) ) ) ) ) ) ) )
% 5.31/5.58 @ ( 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 ) ) ) ) ) )
% 5.31/5.58 @ ( if_option_nat
% 5.31/5.58 @ ( ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.31/5.58 = none_nat )
% 5.31/5.58 @ none_nat
% 5.31/5.58 @ ( 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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % succ_less_length_list
% 5.31/5.58 thf(fact_4487_del__in__range,axiom,
% 5.31/5.58 ! [Mi: nat,X: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.31/5.58 ( ( ( ord_less_eq_nat @ Mi @ X )
% 5.31/5.58 & ( ord_less_eq_nat @ X @ Ma ) )
% 5.31/5.58 => ( ( Mi != Ma )
% 5.31/5.58 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.31/5.58 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 5.31/5.58 = ( 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 ) )
% 5.31/5.58 @ ( 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 ) ) ) ) ) )
% 5.31/5.58 @ ( vEBT_Node
% 5.31/5.58 @ ( some_P7363390416028606310at_nat
% 5.31/5.58 @ ( 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 )
% 5.31/5.58 @ ( if_nat
% 5.31/5.58 @ ( ( ( X = Mi )
% 5.31/5.58 => ( ( 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 ) ) ) ) ) )
% 5.31/5.58 = Ma ) )
% 5.31/5.58 & ( ( X != Mi )
% 5.31/5.58 => ( X = Ma ) ) )
% 5.31/5.58 @ ( if_nat
% 5.31/5.58 @ ( ( 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 ) ) ) ) ) )
% 5.31/5.58 = none_nat )
% 5.31/5.58 @ ( 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 )
% 5.31/5.58 @ ( 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 ) ) ) ) ) ) ) ) ) ) ) )
% 5.31/5.58 @ Ma ) ) )
% 5.31/5.58 @ Deg
% 5.31/5.58 @ ( 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 ) ) ) ) ) )
% 5.31/5.58 @ ( 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 ) ) ) ) ) )
% 5.31/5.58 @ ( vEBT_Node
% 5.31/5.58 @ ( some_P7363390416028606310at_nat
% 5.31/5.58 @ ( 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 )
% 5.31/5.58 @ ( if_nat
% 5.31/5.58 @ ( ( ( X = Mi )
% 5.31/5.58 => ( ( 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 ) ) ) ) ) )
% 5.31/5.58 = Ma ) )
% 5.31/5.58 & ( ( X != Mi )
% 5.31/5.58 => ( X = Ma ) ) )
% 5.31/5.58 @ ( 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 ) ) ) ) ) ) ) )
% 5.31/5.58 @ Ma ) ) )
% 5.31/5.58 @ Deg
% 5.31/5.58 @ ( 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 ) ) ) ) ) )
% 5.31/5.58 @ Summary ) )
% 5.31/5.58 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) ) ) ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % del_in_range
% 5.31/5.58 thf(fact_4488_del__x__mi,axiom,
% 5.31/5.58 ! [X: nat,Mi: nat,Ma: nat,Deg: nat,Xn: nat,H: nat,Summary: vEBT_VEBT,TreeList2: list_VEBT_VEBT,L: nat] :
% 5.31/5.58 ( ( ( X = Mi )
% 5.31/5.58 & ( ord_less_nat @ X @ Ma ) )
% 5.31/5.58 => ( ( Mi != Ma )
% 5.31/5.58 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.31/5.58 => ( ( ( vEBT_VEBT_high @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.31/5.58 = H )
% 5.31/5.58 => ( ( Xn
% 5.31/5.58 = ( 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 ) ) ) ) ) ) )
% 5.31/5.58 => ( ( ( vEBT_VEBT_low @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.31/5.58 = L )
% 5.31/5.58 => ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.31/5.58 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 5.31/5.58 = ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ H ) @ L ) )
% 5.31/5.58 @ ( vEBT_Node
% 5.31/5.58 @ ( some_P7363390416028606310at_nat
% 5.31/5.58 @ ( product_Pair_nat_nat @ Xn
% 5.31/5.58 @ ( if_nat @ ( Xn = Ma )
% 5.31/5.58 @ ( if_nat
% 5.31/5.58 @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H ) )
% 5.31/5.58 = none_nat )
% 5.31/5.58 @ Xn
% 5.31/5.58 @ ( 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 @ H ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ H @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ H ) @ L ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H ) ) ) ) ) ) ) )
% 5.31/5.58 @ Ma ) ) )
% 5.31/5.58 @ Deg
% 5.31/5.58 @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ H @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ H ) @ L ) )
% 5.31/5.58 @ ( vEBT_vebt_delete @ Summary @ H ) )
% 5.31/5.58 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Xn @ ( if_nat @ ( Xn = Ma ) @ ( plus_plus_nat @ ( times_times_nat @ H @ ( 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 @ H @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ H ) @ L ) ) @ H ) ) ) ) @ Ma ) ) ) @ Deg @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ H @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ H ) @ L ) ) @ Summary ) ) ) ) ) ) ) ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % del_x_mi
% 5.31/5.58 thf(fact_4489_set__vebt_H__def,axiom,
% 5.31/5.58 ( vEBT_VEBT_set_vebt
% 5.31/5.58 = ( ^ [T2: vEBT_VEBT] : ( collect_nat @ ( vEBT_vebt_member @ T2 ) ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % set_vebt'_def
% 5.31/5.58 thf(fact_4490_pred__empty,axiom,
% 5.31/5.58 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 5.31/5.58 ( ( vEBT_invar_vebt @ T @ N )
% 5.31/5.58 => ( ( ( vEBT_vebt_pred @ T @ X )
% 5.31/5.58 = none_nat )
% 5.31/5.58 = ( ( collect_nat
% 5.31/5.58 @ ^ [Y4: nat] :
% 5.31/5.58 ( ( vEBT_vebt_member @ T @ Y4 )
% 5.31/5.58 & ( ord_less_nat @ Y4 @ X ) ) )
% 5.31/5.58 = bot_bot_set_nat ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % pred_empty
% 5.31/5.58 thf(fact_4491_succ__empty,axiom,
% 5.31/5.58 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 5.31/5.58 ( ( vEBT_invar_vebt @ T @ N )
% 5.31/5.58 => ( ( ( vEBT_vebt_succ @ T @ X )
% 5.31/5.58 = none_nat )
% 5.31/5.58 = ( ( collect_nat
% 5.31/5.58 @ ^ [Y4: nat] :
% 5.31/5.58 ( ( vEBT_vebt_member @ T @ Y4 )
% 5.31/5.58 & ( ord_less_nat @ X @ Y4 ) ) )
% 5.31/5.58 = bot_bot_set_nat ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % succ_empty
% 5.31/5.58 thf(fact_4492_max_Obounded__iff,axiom,
% 5.31/5.58 ! [B: rat,C2: rat,A: rat] :
% 5.31/5.58 ( ( ord_less_eq_rat @ ( ord_max_rat @ B @ C2 ) @ A )
% 5.31/5.58 = ( ( ord_less_eq_rat @ B @ A )
% 5.31/5.58 & ( ord_less_eq_rat @ C2 @ A ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % max.bounded_iff
% 5.31/5.58 thf(fact_4493_max_Obounded__iff,axiom,
% 5.31/5.58 ! [B: num,C2: num,A: num] :
% 5.31/5.58 ( ( ord_less_eq_num @ ( ord_max_num @ B @ C2 ) @ A )
% 5.31/5.58 = ( ( ord_less_eq_num @ B @ A )
% 5.31/5.58 & ( ord_less_eq_num @ C2 @ A ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % max.bounded_iff
% 5.31/5.58 thf(fact_4494_max_Obounded__iff,axiom,
% 5.31/5.58 ! [B: nat,C2: nat,A: nat] :
% 5.31/5.58 ( ( ord_less_eq_nat @ ( ord_max_nat @ B @ C2 ) @ A )
% 5.31/5.58 = ( ( ord_less_eq_nat @ B @ A )
% 5.31/5.58 & ( ord_less_eq_nat @ C2 @ A ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % max.bounded_iff
% 5.31/5.58 thf(fact_4495_max_Obounded__iff,axiom,
% 5.31/5.58 ! [B: int,C2: int,A: int] :
% 5.31/5.58 ( ( ord_less_eq_int @ ( ord_max_int @ B @ C2 ) @ A )
% 5.31/5.58 = ( ( ord_less_eq_int @ B @ A )
% 5.31/5.58 & ( ord_less_eq_int @ C2 @ A ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % max.bounded_iff
% 5.31/5.58 thf(fact_4496_max_Oabsorb2,axiom,
% 5.31/5.58 ! [A: rat,B: rat] :
% 5.31/5.58 ( ( ord_less_eq_rat @ A @ B )
% 5.31/5.58 => ( ( ord_max_rat @ A @ B )
% 5.31/5.58 = B ) ) ).
% 5.31/5.58
% 5.31/5.58 % max.absorb2
% 5.31/5.58 thf(fact_4497_max_Oabsorb2,axiom,
% 5.31/5.58 ! [A: num,B: num] :
% 5.31/5.58 ( ( ord_less_eq_num @ A @ B )
% 5.31/5.58 => ( ( ord_max_num @ A @ B )
% 5.31/5.58 = B ) ) ).
% 5.31/5.58
% 5.31/5.58 % max.absorb2
% 5.31/5.58 thf(fact_4498_max_Oabsorb2,axiom,
% 5.31/5.58 ! [A: nat,B: nat] :
% 5.31/5.58 ( ( ord_less_eq_nat @ A @ B )
% 5.31/5.58 => ( ( ord_max_nat @ A @ B )
% 5.31/5.58 = B ) ) ).
% 5.31/5.58
% 5.31/5.58 % max.absorb2
% 5.31/5.58 thf(fact_4499_max_Oabsorb2,axiom,
% 5.31/5.58 ! [A: int,B: int] :
% 5.31/5.58 ( ( ord_less_eq_int @ A @ B )
% 5.31/5.58 => ( ( ord_max_int @ A @ B )
% 5.31/5.58 = B ) ) ).
% 5.31/5.58
% 5.31/5.58 % max.absorb2
% 5.31/5.58 thf(fact_4500_max_Oabsorb1,axiom,
% 5.31/5.58 ! [B: rat,A: rat] :
% 5.31/5.58 ( ( ord_less_eq_rat @ B @ A )
% 5.31/5.58 => ( ( ord_max_rat @ A @ B )
% 5.31/5.58 = A ) ) ).
% 5.31/5.58
% 5.31/5.58 % max.absorb1
% 5.31/5.58 thf(fact_4501_max_Oabsorb1,axiom,
% 5.31/5.58 ! [B: num,A: num] :
% 5.31/5.58 ( ( ord_less_eq_num @ B @ A )
% 5.31/5.58 => ( ( ord_max_num @ A @ B )
% 5.31/5.58 = A ) ) ).
% 5.31/5.58
% 5.31/5.58 % max.absorb1
% 5.31/5.58 thf(fact_4502_max_Oabsorb1,axiom,
% 5.31/5.58 ! [B: nat,A: nat] :
% 5.31/5.58 ( ( ord_less_eq_nat @ B @ A )
% 5.31/5.58 => ( ( ord_max_nat @ A @ B )
% 5.31/5.58 = A ) ) ).
% 5.31/5.58
% 5.31/5.58 % max.absorb1
% 5.31/5.58 thf(fact_4503_max_Oabsorb1,axiom,
% 5.31/5.58 ! [B: int,A: int] :
% 5.31/5.58 ( ( ord_less_eq_int @ B @ A )
% 5.31/5.58 => ( ( ord_max_int @ A @ B )
% 5.31/5.58 = A ) ) ).
% 5.31/5.58
% 5.31/5.58 % max.absorb1
% 5.31/5.58 thf(fact_4504_max__bot,axiom,
% 5.31/5.58 ! [X: set_nat] :
% 5.31/5.58 ( ( ord_max_set_nat @ bot_bot_set_nat @ X )
% 5.31/5.58 = X ) ).
% 5.31/5.58
% 5.31/5.58 % max_bot
% 5.31/5.58 thf(fact_4505_max__bot,axiom,
% 5.31/5.58 ! [X: set_int] :
% 5.31/5.58 ( ( ord_max_set_int @ bot_bot_set_int @ X )
% 5.31/5.58 = X ) ).
% 5.31/5.58
% 5.31/5.58 % max_bot
% 5.31/5.58 thf(fact_4506_max__bot,axiom,
% 5.31/5.58 ! [X: set_real] :
% 5.31/5.58 ( ( ord_max_set_real @ bot_bot_set_real @ X )
% 5.31/5.58 = X ) ).
% 5.31/5.58
% 5.31/5.58 % max_bot
% 5.31/5.58 thf(fact_4507_max__bot,axiom,
% 5.31/5.58 ! [X: nat] :
% 5.31/5.58 ( ( ord_max_nat @ bot_bot_nat @ X )
% 5.31/5.58 = X ) ).
% 5.31/5.58
% 5.31/5.58 % max_bot
% 5.31/5.58 thf(fact_4508_max__bot2,axiom,
% 5.31/5.58 ! [X: set_nat] :
% 5.31/5.58 ( ( ord_max_set_nat @ X @ bot_bot_set_nat )
% 5.31/5.58 = X ) ).
% 5.31/5.58
% 5.31/5.58 % max_bot2
% 5.31/5.58 thf(fact_4509_max__bot2,axiom,
% 5.31/5.58 ! [X: set_int] :
% 5.31/5.58 ( ( ord_max_set_int @ X @ bot_bot_set_int )
% 5.31/5.58 = X ) ).
% 5.31/5.58
% 5.31/5.58 % max_bot2
% 5.31/5.58 thf(fact_4510_max__bot2,axiom,
% 5.31/5.58 ! [X: set_real] :
% 5.31/5.58 ( ( ord_max_set_real @ X @ bot_bot_set_real )
% 5.31/5.58 = X ) ).
% 5.31/5.58
% 5.31/5.58 % max_bot2
% 5.31/5.58 thf(fact_4511_max__bot2,axiom,
% 5.31/5.58 ! [X: nat] :
% 5.31/5.58 ( ( ord_max_nat @ X @ bot_bot_nat )
% 5.31/5.58 = X ) ).
% 5.31/5.58
% 5.31/5.58 % max_bot2
% 5.31/5.58 thf(fact_4512_max__Suc__Suc,axiom,
% 5.31/5.58 ! [M2: nat,N: nat] :
% 5.31/5.58 ( ( ord_max_nat @ ( suc @ M2 ) @ ( suc @ N ) )
% 5.31/5.58 = ( suc @ ( ord_max_nat @ M2 @ N ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % max_Suc_Suc
% 5.31/5.58 thf(fact_4513_max__nat_Oeq__neutr__iff,axiom,
% 5.31/5.58 ! [A: nat,B: nat] :
% 5.31/5.58 ( ( ( ord_max_nat @ A @ B )
% 5.31/5.58 = zero_zero_nat )
% 5.31/5.58 = ( ( A = zero_zero_nat )
% 5.31/5.58 & ( B = zero_zero_nat ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % max_nat.eq_neutr_iff
% 5.31/5.58 thf(fact_4514_max__nat_Oleft__neutral,axiom,
% 5.31/5.58 ! [A: nat] :
% 5.31/5.58 ( ( ord_max_nat @ zero_zero_nat @ A )
% 5.31/5.58 = A ) ).
% 5.31/5.58
% 5.31/5.58 % max_nat.left_neutral
% 5.31/5.58 thf(fact_4515_max__nat_Oneutr__eq__iff,axiom,
% 5.31/5.58 ! [A: nat,B: nat] :
% 5.31/5.58 ( ( zero_zero_nat
% 5.31/5.58 = ( ord_max_nat @ A @ B ) )
% 5.31/5.58 = ( ( A = zero_zero_nat )
% 5.31/5.58 & ( B = zero_zero_nat ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % max_nat.neutr_eq_iff
% 5.31/5.58 thf(fact_4516_max__nat_Oright__neutral,axiom,
% 5.31/5.58 ! [A: nat] :
% 5.31/5.58 ( ( ord_max_nat @ A @ zero_zero_nat )
% 5.31/5.58 = A ) ).
% 5.31/5.58
% 5.31/5.58 % max_nat.right_neutral
% 5.31/5.58 thf(fact_4517_max__0L,axiom,
% 5.31/5.58 ! [N: nat] :
% 5.31/5.58 ( ( ord_max_nat @ zero_zero_nat @ N )
% 5.31/5.58 = N ) ).
% 5.31/5.58
% 5.31/5.58 % max_0L
% 5.31/5.58 thf(fact_4518_max__0R,axiom,
% 5.31/5.58 ! [N: nat] :
% 5.31/5.58 ( ( ord_max_nat @ N @ zero_zero_nat )
% 5.31/5.58 = N ) ).
% 5.31/5.58
% 5.31/5.58 % max_0R
% 5.31/5.58 thf(fact_4519_finite__Collect__le__nat,axiom,
% 5.31/5.58 ! [K2: nat] :
% 5.31/5.58 ( finite_finite_nat
% 5.31/5.58 @ ( collect_nat
% 5.31/5.58 @ ^ [N4: nat] : ( ord_less_eq_nat @ N4 @ K2 ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % finite_Collect_le_nat
% 5.31/5.58 thf(fact_4520_max__number__of_I1_J,axiom,
% 5.31/5.58 ! [U: num,V2: num] :
% 5.31/5.58 ( ( ( ord_le2932123472753598470d_enat @ ( numera1916890842035813515d_enat @ U ) @ ( numera1916890842035813515d_enat @ V2 ) )
% 5.31/5.58 => ( ( ord_ma741700101516333627d_enat @ ( numera1916890842035813515d_enat @ U ) @ ( numera1916890842035813515d_enat @ V2 ) )
% 5.31/5.58 = ( numera1916890842035813515d_enat @ V2 ) ) )
% 5.31/5.58 & ( ~ ( ord_le2932123472753598470d_enat @ ( numera1916890842035813515d_enat @ U ) @ ( numera1916890842035813515d_enat @ V2 ) )
% 5.31/5.58 => ( ( ord_ma741700101516333627d_enat @ ( numera1916890842035813515d_enat @ U ) @ ( numera1916890842035813515d_enat @ V2 ) )
% 5.31/5.58 = ( numera1916890842035813515d_enat @ U ) ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % max_number_of(1)
% 5.31/5.58 thf(fact_4521_max__number__of_I1_J,axiom,
% 5.31/5.58 ! [U: num,V2: num] :
% 5.31/5.58 ( ( ( ord_less_eq_real @ ( numeral_numeral_real @ U ) @ ( numeral_numeral_real @ V2 ) )
% 5.31/5.58 => ( ( ord_max_real @ ( numeral_numeral_real @ U ) @ ( numeral_numeral_real @ V2 ) )
% 5.31/5.58 = ( numeral_numeral_real @ V2 ) ) )
% 5.31/5.58 & ( ~ ( ord_less_eq_real @ ( numeral_numeral_real @ U ) @ ( numeral_numeral_real @ V2 ) )
% 5.31/5.58 => ( ( ord_max_real @ ( numeral_numeral_real @ U ) @ ( numeral_numeral_real @ V2 ) )
% 5.31/5.58 = ( numeral_numeral_real @ U ) ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % max_number_of(1)
% 5.31/5.58 thf(fact_4522_max__number__of_I1_J,axiom,
% 5.31/5.58 ! [U: num,V2: num] :
% 5.31/5.58 ( ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ U ) @ ( numeral_numeral_rat @ V2 ) )
% 5.31/5.58 => ( ( ord_max_rat @ ( numeral_numeral_rat @ U ) @ ( numeral_numeral_rat @ V2 ) )
% 5.31/5.58 = ( numeral_numeral_rat @ V2 ) ) )
% 5.31/5.58 & ( ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ U ) @ ( numeral_numeral_rat @ V2 ) )
% 5.31/5.58 => ( ( ord_max_rat @ ( numeral_numeral_rat @ U ) @ ( numeral_numeral_rat @ V2 ) )
% 5.31/5.58 = ( numeral_numeral_rat @ U ) ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % max_number_of(1)
% 5.31/5.58 thf(fact_4523_max__number__of_I1_J,axiom,
% 5.31/5.58 ! [U: num,V2: num] :
% 5.31/5.58 ( ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ U ) @ ( numeral_numeral_nat @ V2 ) )
% 5.31/5.58 => ( ( ord_max_nat @ ( numeral_numeral_nat @ U ) @ ( numeral_numeral_nat @ V2 ) )
% 5.31/5.58 = ( numeral_numeral_nat @ V2 ) ) )
% 5.31/5.58 & ( ~ ( ord_less_eq_nat @ ( numeral_numeral_nat @ U ) @ ( numeral_numeral_nat @ V2 ) )
% 5.31/5.58 => ( ( ord_max_nat @ ( numeral_numeral_nat @ U ) @ ( numeral_numeral_nat @ V2 ) )
% 5.31/5.58 = ( numeral_numeral_nat @ U ) ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % max_number_of(1)
% 5.31/5.58 thf(fact_4524_max__number__of_I1_J,axiom,
% 5.31/5.58 ! [U: num,V2: num] :
% 5.31/5.58 ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ U ) @ ( numeral_numeral_int @ V2 ) )
% 5.31/5.58 => ( ( ord_max_int @ ( numeral_numeral_int @ U ) @ ( numeral_numeral_int @ V2 ) )
% 5.31/5.58 = ( numeral_numeral_int @ V2 ) ) )
% 5.31/5.58 & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ U ) @ ( numeral_numeral_int @ V2 ) )
% 5.31/5.58 => ( ( ord_max_int @ ( numeral_numeral_int @ U ) @ ( numeral_numeral_int @ V2 ) )
% 5.31/5.58 = ( numeral_numeral_int @ U ) ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % max_number_of(1)
% 5.31/5.58 thf(fact_4525_max__0__1_I3_J,axiom,
% 5.31/5.58 ! [X: num] :
% 5.31/5.58 ( ( ord_max_rat @ zero_zero_rat @ ( numeral_numeral_rat @ X ) )
% 5.31/5.58 = ( numeral_numeral_rat @ X ) ) ).
% 5.31/5.58
% 5.31/5.58 % max_0_1(3)
% 5.31/5.58 thf(fact_4526_max__0__1_I3_J,axiom,
% 5.31/5.58 ! [X: num] :
% 5.31/5.58 ( ( ord_ma741700101516333627d_enat @ zero_z5237406670263579293d_enat @ ( numera1916890842035813515d_enat @ X ) )
% 5.31/5.58 = ( numera1916890842035813515d_enat @ X ) ) ).
% 5.31/5.58
% 5.31/5.58 % max_0_1(3)
% 5.31/5.58 thf(fact_4527_max__0__1_I3_J,axiom,
% 5.31/5.58 ! [X: num] :
% 5.31/5.58 ( ( ord_max_real @ zero_zero_real @ ( numeral_numeral_real @ X ) )
% 5.31/5.58 = ( numeral_numeral_real @ X ) ) ).
% 5.31/5.58
% 5.31/5.58 % max_0_1(3)
% 5.31/5.58 thf(fact_4528_max__0__1_I3_J,axiom,
% 5.31/5.58 ! [X: num] :
% 5.31/5.58 ( ( ord_max_nat @ zero_zero_nat @ ( numeral_numeral_nat @ X ) )
% 5.31/5.58 = ( numeral_numeral_nat @ X ) ) ).
% 5.31/5.58
% 5.31/5.58 % max_0_1(3)
% 5.31/5.58 thf(fact_4529_max__0__1_I3_J,axiom,
% 5.31/5.58 ! [X: num] :
% 5.31/5.58 ( ( ord_max_int @ zero_zero_int @ ( numeral_numeral_int @ X ) )
% 5.31/5.58 = ( numeral_numeral_int @ X ) ) ).
% 5.31/5.58
% 5.31/5.58 % max_0_1(3)
% 5.31/5.58 thf(fact_4530_max__0__1_I4_J,axiom,
% 5.31/5.58 ! [X: num] :
% 5.31/5.58 ( ( ord_max_rat @ ( numeral_numeral_rat @ X ) @ zero_zero_rat )
% 5.31/5.58 = ( numeral_numeral_rat @ X ) ) ).
% 5.31/5.58
% 5.31/5.58 % max_0_1(4)
% 5.31/5.58 thf(fact_4531_max__0__1_I4_J,axiom,
% 5.31/5.58 ! [X: num] :
% 5.31/5.58 ( ( ord_ma741700101516333627d_enat @ ( numera1916890842035813515d_enat @ X ) @ zero_z5237406670263579293d_enat )
% 5.31/5.58 = ( numera1916890842035813515d_enat @ X ) ) ).
% 5.31/5.58
% 5.31/5.58 % max_0_1(4)
% 5.31/5.58 thf(fact_4532_max__0__1_I4_J,axiom,
% 5.31/5.58 ! [X: num] :
% 5.31/5.58 ( ( ord_max_real @ ( numeral_numeral_real @ X ) @ zero_zero_real )
% 5.31/5.58 = ( numeral_numeral_real @ X ) ) ).
% 5.31/5.58
% 5.31/5.58 % max_0_1(4)
% 5.31/5.58 thf(fact_4533_max__0__1_I4_J,axiom,
% 5.31/5.58 ! [X: num] :
% 5.31/5.58 ( ( ord_max_nat @ ( numeral_numeral_nat @ X ) @ zero_zero_nat )
% 5.31/5.58 = ( numeral_numeral_nat @ X ) ) ).
% 5.31/5.58
% 5.31/5.58 % max_0_1(4)
% 5.31/5.58 thf(fact_4534_max__0__1_I4_J,axiom,
% 5.31/5.58 ! [X: num] :
% 5.31/5.58 ( ( ord_max_int @ ( numeral_numeral_int @ X ) @ zero_zero_int )
% 5.31/5.58 = ( numeral_numeral_int @ X ) ) ).
% 5.31/5.58
% 5.31/5.58 % max_0_1(4)
% 5.31/5.58 thf(fact_4535_max__0__1_I2_J,axiom,
% 5.31/5.58 ( ( ord_max_Code_integer @ one_one_Code_integer @ zero_z3403309356797280102nteger )
% 5.31/5.58 = one_one_Code_integer ) ).
% 5.31/5.58
% 5.31/5.58 % max_0_1(2)
% 5.31/5.58 thf(fact_4536_max__0__1_I2_J,axiom,
% 5.31/5.58 ( ( ord_max_real @ one_one_real @ zero_zero_real )
% 5.31/5.58 = one_one_real ) ).
% 5.31/5.58
% 5.31/5.58 % max_0_1(2)
% 5.31/5.58 thf(fact_4537_max__0__1_I2_J,axiom,
% 5.31/5.58 ( ( ord_max_rat @ one_one_rat @ zero_zero_rat )
% 5.31/5.58 = one_one_rat ) ).
% 5.31/5.58
% 5.31/5.58 % max_0_1(2)
% 5.31/5.58 thf(fact_4538_max__0__1_I2_J,axiom,
% 5.31/5.58 ( ( ord_max_nat @ one_one_nat @ zero_zero_nat )
% 5.31/5.58 = one_one_nat ) ).
% 5.31/5.58
% 5.31/5.58 % max_0_1(2)
% 5.31/5.58 thf(fact_4539_max__0__1_I2_J,axiom,
% 5.31/5.58 ( ( ord_max_int @ one_one_int @ zero_zero_int )
% 5.31/5.58 = one_one_int ) ).
% 5.31/5.58
% 5.31/5.58 % max_0_1(2)
% 5.31/5.58 thf(fact_4540_max__0__1_I1_J,axiom,
% 5.31/5.58 ( ( ord_max_Code_integer @ zero_z3403309356797280102nteger @ one_one_Code_integer )
% 5.31/5.58 = one_one_Code_integer ) ).
% 5.31/5.58
% 5.31/5.58 % max_0_1(1)
% 5.31/5.58 thf(fact_4541_max__0__1_I1_J,axiom,
% 5.31/5.58 ( ( ord_max_real @ zero_zero_real @ one_one_real )
% 5.31/5.58 = one_one_real ) ).
% 5.31/5.58
% 5.31/5.58 % max_0_1(1)
% 5.31/5.58 thf(fact_4542_max__0__1_I1_J,axiom,
% 5.31/5.58 ( ( ord_max_rat @ zero_zero_rat @ one_one_rat )
% 5.31/5.58 = one_one_rat ) ).
% 5.31/5.58
% 5.31/5.58 % max_0_1(1)
% 5.31/5.58 thf(fact_4543_max__0__1_I1_J,axiom,
% 5.31/5.58 ( ( ord_max_nat @ zero_zero_nat @ one_one_nat )
% 5.31/5.58 = one_one_nat ) ).
% 5.31/5.58
% 5.31/5.58 % max_0_1(1)
% 5.31/5.58 thf(fact_4544_max__0__1_I1_J,axiom,
% 5.31/5.58 ( ( ord_max_int @ zero_zero_int @ one_one_int )
% 5.31/5.58 = one_one_int ) ).
% 5.31/5.58
% 5.31/5.58 % max_0_1(1)
% 5.31/5.58 thf(fact_4545_max__0__1_I5_J,axiom,
% 5.31/5.58 ! [X: num] :
% 5.31/5.58 ( ( ord_max_Code_integer @ one_one_Code_integer @ ( numera6620942414471956472nteger @ X ) )
% 5.31/5.58 = ( numera6620942414471956472nteger @ X ) ) ).
% 5.31/5.58
% 5.31/5.58 % max_0_1(5)
% 5.31/5.58 thf(fact_4546_max__0__1_I5_J,axiom,
% 5.31/5.58 ! [X: num] :
% 5.31/5.58 ( ( ord_ma741700101516333627d_enat @ one_on7984719198319812577d_enat @ ( numera1916890842035813515d_enat @ X ) )
% 5.31/5.58 = ( numera1916890842035813515d_enat @ X ) ) ).
% 5.31/5.58
% 5.31/5.58 % max_0_1(5)
% 5.31/5.58 thf(fact_4547_max__0__1_I5_J,axiom,
% 5.31/5.58 ! [X: num] :
% 5.31/5.58 ( ( ord_max_real @ one_one_real @ ( numeral_numeral_real @ X ) )
% 5.31/5.58 = ( numeral_numeral_real @ X ) ) ).
% 5.31/5.58
% 5.31/5.58 % max_0_1(5)
% 5.31/5.58 thf(fact_4548_max__0__1_I5_J,axiom,
% 5.31/5.58 ! [X: num] :
% 5.31/5.58 ( ( ord_max_nat @ one_one_nat @ ( numeral_numeral_nat @ X ) )
% 5.31/5.58 = ( numeral_numeral_nat @ X ) ) ).
% 5.31/5.58
% 5.31/5.58 % max_0_1(5)
% 5.31/5.58 thf(fact_4549_max__0__1_I5_J,axiom,
% 5.31/5.58 ! [X: num] :
% 5.31/5.58 ( ( ord_max_int @ one_one_int @ ( numeral_numeral_int @ X ) )
% 5.31/5.58 = ( numeral_numeral_int @ X ) ) ).
% 5.31/5.58
% 5.31/5.58 % max_0_1(5)
% 5.31/5.58 thf(fact_4550_max__0__1_I6_J,axiom,
% 5.31/5.58 ! [X: num] :
% 5.31/5.58 ( ( ord_max_Code_integer @ ( numera6620942414471956472nteger @ X ) @ one_one_Code_integer )
% 5.31/5.58 = ( numera6620942414471956472nteger @ X ) ) ).
% 5.31/5.58
% 5.31/5.58 % max_0_1(6)
% 5.31/5.58 thf(fact_4551_max__0__1_I6_J,axiom,
% 5.31/5.58 ! [X: num] :
% 5.31/5.58 ( ( ord_ma741700101516333627d_enat @ ( numera1916890842035813515d_enat @ X ) @ one_on7984719198319812577d_enat )
% 5.31/5.58 = ( numera1916890842035813515d_enat @ X ) ) ).
% 5.31/5.58
% 5.31/5.58 % max_0_1(6)
% 5.31/5.58 thf(fact_4552_max__0__1_I6_J,axiom,
% 5.31/5.58 ! [X: num] :
% 5.31/5.58 ( ( ord_max_real @ ( numeral_numeral_real @ X ) @ one_one_real )
% 5.31/5.58 = ( numeral_numeral_real @ X ) ) ).
% 5.31/5.58
% 5.31/5.58 % max_0_1(6)
% 5.31/5.58 thf(fact_4553_max__0__1_I6_J,axiom,
% 5.31/5.58 ! [X: num] :
% 5.31/5.58 ( ( ord_max_nat @ ( numeral_numeral_nat @ X ) @ one_one_nat )
% 5.31/5.58 = ( numeral_numeral_nat @ X ) ) ).
% 5.31/5.58
% 5.31/5.58 % max_0_1(6)
% 5.31/5.58 thf(fact_4554_max__0__1_I6_J,axiom,
% 5.31/5.58 ! [X: num] :
% 5.31/5.58 ( ( ord_max_int @ ( numeral_numeral_int @ X ) @ one_one_int )
% 5.31/5.58 = ( numeral_numeral_int @ X ) ) ).
% 5.31/5.58
% 5.31/5.58 % max_0_1(6)
% 5.31/5.58 thf(fact_4555_card__Collect__le__nat,axiom,
% 5.31/5.58 ! [N: nat] :
% 5.31/5.58 ( ( finite_card_nat
% 5.31/5.58 @ ( collect_nat
% 5.31/5.58 @ ^ [I: nat] : ( ord_less_eq_nat @ I @ N ) ) )
% 5.31/5.58 = ( suc @ N ) ) ).
% 5.31/5.58
% 5.31/5.58 % card_Collect_le_nat
% 5.31/5.58 thf(fact_4556_del__x__not__mia,axiom,
% 5.31/5.58 ! [Mi: nat,X: nat,Ma: nat,Deg: nat,H: nat,L: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.31/5.58 ( ( ( ord_less_nat @ Mi @ X )
% 5.31/5.58 & ( ord_less_eq_nat @ X @ Ma ) )
% 5.31/5.58 => ( ( Mi != Ma )
% 5.31/5.58 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.31/5.58 => ( ( ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.31/5.58 = H )
% 5.31/5.58 => ( ( ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.31/5.58 = L )
% 5.31/5.58 => ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.31/5.58 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 5.31/5.58 = ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ H ) @ L ) )
% 5.31/5.58 @ ( vEBT_Node
% 5.31/5.58 @ ( some_P7363390416028606310at_nat
% 5.31/5.58 @ ( product_Pair_nat_nat @ Mi
% 5.31/5.58 @ ( if_nat @ ( X = Ma )
% 5.31/5.58 @ ( if_nat
% 5.31/5.58 @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H ) )
% 5.31/5.58 = none_nat )
% 5.31/5.58 @ Mi
% 5.31/5.58 @ ( 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 @ H ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ H @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ H ) @ L ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H ) ) ) ) ) ) ) )
% 5.31/5.58 @ Ma ) ) )
% 5.31/5.58 @ Deg
% 5.31/5.58 @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ H @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ H ) @ L ) )
% 5.31/5.58 @ ( vEBT_vebt_delete @ Summary @ H ) )
% 5.31/5.58 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ ( if_nat @ ( X = Ma ) @ ( plus_plus_nat @ ( times_times_nat @ H @ ( 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 @ H @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ H ) @ L ) ) @ H ) ) ) ) @ Ma ) ) ) @ Deg @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ H @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ H ) @ L ) ) @ Summary ) ) ) ) ) ) ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % del_x_not_mia
% 5.31/5.58 thf(fact_4557_del__x__not__mi__new__node__nil,axiom,
% 5.31/5.58 ! [Mi: nat,X: nat,Ma: nat,Deg: nat,H: nat,L: nat,Newnode: vEBT_VEBT,TreeList2: list_VEBT_VEBT,Sn: vEBT_VEBT,Summary: vEBT_VEBT,Newlist: list_VEBT_VEBT] :
% 5.31/5.58 ( ( ( ord_less_nat @ Mi @ X )
% 5.31/5.58 & ( ord_less_eq_nat @ X @ Ma ) )
% 5.31/5.58 => ( ( Mi != Ma )
% 5.31/5.58 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.31/5.58 => ( ( ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.31/5.58 = H )
% 5.31/5.58 => ( ( ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.31/5.58 = L )
% 5.31/5.58 => ( ( Newnode
% 5.31/5.58 = ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ H ) @ L ) )
% 5.31/5.58 => ( ( vEBT_VEBT_minNull @ Newnode )
% 5.31/5.58 => ( ( Sn
% 5.31/5.58 = ( vEBT_vebt_delete @ Summary @ H ) )
% 5.31/5.58 => ( ( Newlist
% 5.31/5.58 = ( list_u1324408373059187874T_VEBT @ TreeList2 @ H @ Newnode ) )
% 5.31/5.58 => ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.31/5.58 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 5.31/5.58 = ( vEBT_Node
% 5.31/5.58 @ ( some_P7363390416028606310at_nat
% 5.31/5.58 @ ( product_Pair_nat_nat @ Mi
% 5.31/5.58 @ ( if_nat @ ( X = Ma )
% 5.31/5.58 @ ( if_nat
% 5.31/5.58 @ ( ( vEBT_vebt_maxt @ Sn )
% 5.31/5.58 = none_nat )
% 5.31/5.58 @ Mi
% 5.31/5.58 @ ( 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 ) ) ) ) ) ) )
% 5.31/5.58 @ Ma ) ) )
% 5.31/5.58 @ Deg
% 5.31/5.58 @ Newlist
% 5.31/5.58 @ Sn ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % del_x_not_mi_new_node_nil
% 5.31/5.58 thf(fact_4558_del__x__not__mi,axiom,
% 5.31/5.58 ! [Mi: nat,X: nat,Ma: nat,Deg: nat,H: nat,L: nat,Newnode: vEBT_VEBT,TreeList2: list_VEBT_VEBT,Newlist: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.31/5.58 ( ( ( ord_less_nat @ Mi @ X )
% 5.31/5.58 & ( ord_less_eq_nat @ X @ Ma ) )
% 5.31/5.58 => ( ( Mi != Ma )
% 5.31/5.58 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.31/5.58 => ( ( ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.31/5.58 = H )
% 5.31/5.58 => ( ( ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.31/5.58 = L )
% 5.31/5.58 => ( ( Newnode
% 5.31/5.58 = ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ H ) @ L ) )
% 5.31/5.58 => ( ( Newlist
% 5.31/5.58 = ( list_u1324408373059187874T_VEBT @ TreeList2 @ H @ Newnode ) )
% 5.31/5.58 => ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.31/5.58 => ( ( ( vEBT_VEBT_minNull @ Newnode )
% 5.31/5.58 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 5.31/5.58 = ( vEBT_Node
% 5.31/5.58 @ ( some_P7363390416028606310at_nat
% 5.31/5.58 @ ( product_Pair_nat_nat @ Mi
% 5.31/5.58 @ ( if_nat @ ( X = Ma )
% 5.31/5.58 @ ( if_nat
% 5.31/5.58 @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H ) )
% 5.31/5.58 = none_nat )
% 5.31/5.58 @ Mi
% 5.31/5.58 @ ( 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 @ H ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ Newlist @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H ) ) ) ) ) ) ) )
% 5.31/5.58 @ Ma ) ) )
% 5.31/5.58 @ Deg
% 5.31/5.58 @ Newlist
% 5.31/5.58 @ ( vEBT_vebt_delete @ Summary @ H ) ) ) )
% 5.31/5.58 & ( ~ ( vEBT_VEBT_minNull @ Newnode )
% 5.31/5.58 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 5.31/5.58 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ ( if_nat @ ( X = Ma ) @ ( plus_plus_nat @ ( times_times_nat @ H @ ( 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 @ H ) ) ) ) @ Ma ) ) ) @ Deg @ Newlist @ Summary ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % del_x_not_mi
% 5.31/5.58 thf(fact_4559_del__x__mia,axiom,
% 5.31/5.58 ! [X: nat,Mi: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.31/5.58 ( ( ( X = Mi )
% 5.31/5.58 & ( ord_less_nat @ X @ Ma ) )
% 5.31/5.58 => ( ( Mi != Ma )
% 5.31/5.58 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.31/5.58 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 5.31/5.58 = ( 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 ) )
% 5.31/5.58 @ ( 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 ) ) ) ) ) )
% 5.31/5.58 @ ( vEBT_Node
% 5.31/5.58 @ ( some_P7363390416028606310at_nat
% 5.31/5.58 @ ( 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 ) ) ) ) ) )
% 5.31/5.58 @ ( if_nat
% 5.31/5.58 @ ( ( 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 ) ) ) ) ) )
% 5.31/5.58 = Ma )
% 5.31/5.58 @ ( if_nat
% 5.31/5.58 @ ( ( 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 ) ) ) ) ) )
% 5.31/5.58 = none_nat )
% 5.31/5.58 @ ( 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 ) ) ) ) ) )
% 5.31/5.58 @ ( 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 ) ) ) ) ) ) ) ) ) ) ) )
% 5.31/5.58 @ Ma ) ) )
% 5.31/5.58 @ Deg
% 5.31/5.58 @ ( 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 ) ) ) ) ) )
% 5.31/5.58 @ ( 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 ) ) ) ) ) )
% 5.31/5.58 @ ( vEBT_Node
% 5.31/5.58 @ ( some_P7363390416028606310at_nat
% 5.31/5.58 @ ( 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 ) ) ) ) ) )
% 5.31/5.58 @ ( if_nat
% 5.31/5.58 @ ( ( 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 ) ) ) ) ) )
% 5.31/5.58 = Ma )
% 5.31/5.58 @ ( 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 ) ) ) ) ) ) ) )
% 5.31/5.58 @ Ma ) ) )
% 5.31/5.58 @ Deg
% 5.31/5.58 @ ( 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 ) ) ) ) ) )
% 5.31/5.58 @ Summary ) )
% 5.31/5.58 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) ) ) ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % del_x_mia
% 5.31/5.58 thf(fact_4560_del__x__mi__lets__in__minNull,axiom,
% 5.31/5.58 ! [X: nat,Mi: nat,Ma: nat,Deg: nat,Xn: nat,H: nat,Summary: vEBT_VEBT,TreeList2: list_VEBT_VEBT,L: nat,Newnode: vEBT_VEBT,Newlist: list_VEBT_VEBT,Sn: vEBT_VEBT] :
% 5.31/5.58 ( ( ( X = Mi )
% 5.31/5.58 & ( ord_less_nat @ X @ Ma ) )
% 5.31/5.58 => ( ( Mi != Ma )
% 5.31/5.58 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.31/5.58 => ( ( ( vEBT_VEBT_high @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.31/5.58 = H )
% 5.31/5.58 => ( ( Xn
% 5.31/5.58 = ( 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 ) ) ) ) ) ) )
% 5.31/5.58 => ( ( ( vEBT_VEBT_low @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.31/5.58 = L )
% 5.31/5.58 => ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.31/5.58 => ( ( Newnode
% 5.31/5.58 = ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ H ) @ L ) )
% 5.31/5.58 => ( ( Newlist
% 5.31/5.58 = ( list_u1324408373059187874T_VEBT @ TreeList2 @ H @ Newnode ) )
% 5.31/5.58 => ( ( vEBT_VEBT_minNull @ Newnode )
% 5.31/5.58 => ( ( Sn
% 5.31/5.58 = ( vEBT_vebt_delete @ Summary @ H ) )
% 5.31/5.58 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 5.31/5.58 = ( vEBT_Node
% 5.31/5.58 @ ( some_P7363390416028606310at_nat
% 5.31/5.58 @ ( product_Pair_nat_nat @ Xn
% 5.31/5.58 @ ( if_nat @ ( Xn = Ma )
% 5.31/5.58 @ ( if_nat
% 5.31/5.58 @ ( ( vEBT_vebt_maxt @ Sn )
% 5.31/5.58 = none_nat )
% 5.31/5.58 @ Xn
% 5.31/5.58 @ ( 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 ) ) ) ) ) ) )
% 5.31/5.58 @ Ma ) ) )
% 5.31/5.58 @ Deg
% 5.31/5.58 @ Newlist
% 5.31/5.58 @ Sn ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % del_x_mi_lets_in_minNull
% 5.31/5.58 thf(fact_4561_del__x__mi__lets__in,axiom,
% 5.31/5.58 ! [X: nat,Mi: nat,Ma: nat,Deg: nat,Xn: nat,H: nat,Summary: vEBT_VEBT,TreeList2: list_VEBT_VEBT,L: nat,Newnode: vEBT_VEBT,Newlist: list_VEBT_VEBT] :
% 5.31/5.58 ( ( ( X = Mi )
% 5.31/5.58 & ( ord_less_nat @ X @ Ma ) )
% 5.31/5.58 => ( ( Mi != Ma )
% 5.31/5.58 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.31/5.58 => ( ( ( vEBT_VEBT_high @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.31/5.58 = H )
% 5.31/5.58 => ( ( Xn
% 5.31/5.58 = ( 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 ) ) ) ) ) ) )
% 5.31/5.58 => ( ( ( vEBT_VEBT_low @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.31/5.58 = L )
% 5.31/5.58 => ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.31/5.58 => ( ( Newnode
% 5.31/5.58 = ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ H ) @ L ) )
% 5.31/5.58 => ( ( Newlist
% 5.31/5.58 = ( list_u1324408373059187874T_VEBT @ TreeList2 @ H @ Newnode ) )
% 5.31/5.58 => ( ( ( vEBT_VEBT_minNull @ Newnode )
% 5.31/5.58 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 5.31/5.58 = ( vEBT_Node
% 5.31/5.58 @ ( some_P7363390416028606310at_nat
% 5.31/5.58 @ ( product_Pair_nat_nat @ Xn
% 5.31/5.58 @ ( if_nat @ ( Xn = Ma )
% 5.31/5.58 @ ( if_nat
% 5.31/5.58 @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H ) )
% 5.31/5.58 = none_nat )
% 5.31/5.58 @ Xn
% 5.31/5.58 @ ( 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 @ H ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ Newlist @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H ) ) ) ) ) ) ) )
% 5.31/5.58 @ Ma ) ) )
% 5.31/5.58 @ Deg
% 5.31/5.58 @ Newlist
% 5.31/5.58 @ ( vEBT_vebt_delete @ Summary @ H ) ) ) )
% 5.31/5.58 & ( ~ ( vEBT_VEBT_minNull @ Newnode )
% 5.31/5.58 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 5.31/5.58 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Xn @ ( if_nat @ ( Xn = Ma ) @ ( plus_plus_nat @ ( times_times_nat @ H @ ( 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 @ H ) ) ) ) @ Ma ) ) ) @ Deg @ Newlist @ Summary ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % del_x_mi_lets_in
% 5.31/5.58 thf(fact_4562_of__nat__max,axiom,
% 5.31/5.58 ! [X: nat,Y: nat] :
% 5.31/5.58 ( ( semiri5074537144036343181t_real @ ( ord_max_nat @ X @ Y ) )
% 5.31/5.58 = ( ord_max_real @ ( semiri5074537144036343181t_real @ X ) @ ( semiri5074537144036343181t_real @ Y ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % of_nat_max
% 5.31/5.58 thf(fact_4563_of__nat__max,axiom,
% 5.31/5.58 ! [X: nat,Y: nat] :
% 5.31/5.58 ( ( semiri1314217659103216013at_int @ ( ord_max_nat @ X @ Y ) )
% 5.31/5.58 = ( ord_max_int @ ( semiri1314217659103216013at_int @ X ) @ ( semiri1314217659103216013at_int @ Y ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % of_nat_max
% 5.31/5.58 thf(fact_4564_of__nat__max,axiom,
% 5.31/5.58 ! [X: nat,Y: nat] :
% 5.31/5.58 ( ( semiri1316708129612266289at_nat @ ( ord_max_nat @ X @ Y ) )
% 5.31/5.58 = ( ord_max_nat @ ( semiri1316708129612266289at_nat @ X ) @ ( semiri1316708129612266289at_nat @ Y ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % of_nat_max
% 5.31/5.58 thf(fact_4565_max__def__raw,axiom,
% 5.31/5.58 ( ord_max_set_nat
% 5.31/5.58 = ( ^ [A5: set_nat,B4: set_nat] : ( if_set_nat @ ( ord_less_eq_set_nat @ A5 @ B4 ) @ B4 @ A5 ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % max_def_raw
% 5.31/5.58 thf(fact_4566_max__def__raw,axiom,
% 5.31/5.58 ( ord_max_rat
% 5.31/5.58 = ( ^ [A5: rat,B4: rat] : ( if_rat @ ( ord_less_eq_rat @ A5 @ B4 ) @ B4 @ A5 ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % max_def_raw
% 5.31/5.58 thf(fact_4567_max__def__raw,axiom,
% 5.31/5.58 ( ord_max_num
% 5.31/5.58 = ( ^ [A5: num,B4: num] : ( if_num @ ( ord_less_eq_num @ A5 @ B4 ) @ B4 @ A5 ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % max_def_raw
% 5.31/5.58 thf(fact_4568_max__def__raw,axiom,
% 5.31/5.58 ( ord_max_nat
% 5.31/5.58 = ( ^ [A5: nat,B4: nat] : ( if_nat @ ( ord_less_eq_nat @ A5 @ B4 ) @ B4 @ A5 ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % max_def_raw
% 5.31/5.58 thf(fact_4569_max__def__raw,axiom,
% 5.31/5.58 ( ord_max_int
% 5.31/5.58 = ( ^ [A5: int,B4: int] : ( if_int @ ( ord_less_eq_int @ A5 @ B4 ) @ B4 @ A5 ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % max_def_raw
% 5.31/5.58 thf(fact_4570_sup__nat__def,axiom,
% 5.31/5.58 sup_sup_nat = ord_max_nat ).
% 5.31/5.58
% 5.31/5.58 % sup_nat_def
% 5.31/5.58 thf(fact_4571_lambda__zero,axiom,
% 5.31/5.58 ( ( ^ [H2: complex] : zero_zero_complex )
% 5.31/5.58 = ( times_times_complex @ zero_zero_complex ) ) ).
% 5.31/5.58
% 5.31/5.58 % lambda_zero
% 5.31/5.58 thf(fact_4572_lambda__zero,axiom,
% 5.31/5.58 ( ( ^ [H2: real] : zero_zero_real )
% 5.31/5.58 = ( times_times_real @ zero_zero_real ) ) ).
% 5.31/5.58
% 5.31/5.58 % lambda_zero
% 5.31/5.58 thf(fact_4573_lambda__zero,axiom,
% 5.31/5.58 ( ( ^ [H2: rat] : zero_zero_rat )
% 5.31/5.58 = ( times_times_rat @ zero_zero_rat ) ) ).
% 5.31/5.58
% 5.31/5.58 % lambda_zero
% 5.31/5.58 thf(fact_4574_lambda__zero,axiom,
% 5.31/5.58 ( ( ^ [H2: nat] : zero_zero_nat )
% 5.31/5.58 = ( times_times_nat @ zero_zero_nat ) ) ).
% 5.31/5.58
% 5.31/5.58 % lambda_zero
% 5.31/5.58 thf(fact_4575_lambda__zero,axiom,
% 5.31/5.58 ( ( ^ [H2: int] : zero_zero_int )
% 5.31/5.58 = ( times_times_int @ zero_zero_int ) ) ).
% 5.31/5.58
% 5.31/5.58 % lambda_zero
% 5.31/5.58 thf(fact_4576_lambda__one,axiom,
% 5.31/5.58 ( ( ^ [X4: code_integer] : X4 )
% 5.31/5.58 = ( times_3573771949741848930nteger @ one_one_Code_integer ) ) ).
% 5.31/5.58
% 5.31/5.58 % lambda_one
% 5.31/5.58 thf(fact_4577_lambda__one,axiom,
% 5.31/5.58 ( ( ^ [X4: complex] : X4 )
% 5.31/5.58 = ( times_times_complex @ one_one_complex ) ) ).
% 5.31/5.58
% 5.31/5.58 % lambda_one
% 5.31/5.58 thf(fact_4578_lambda__one,axiom,
% 5.31/5.58 ( ( ^ [X4: real] : X4 )
% 5.31/5.58 = ( times_times_real @ one_one_real ) ) ).
% 5.31/5.58
% 5.31/5.58 % lambda_one
% 5.31/5.58 thf(fact_4579_lambda__one,axiom,
% 5.31/5.58 ( ( ^ [X4: rat] : X4 )
% 5.31/5.58 = ( times_times_rat @ one_one_rat ) ) ).
% 5.31/5.58
% 5.31/5.58 % lambda_one
% 5.31/5.58 thf(fact_4580_lambda__one,axiom,
% 5.31/5.58 ( ( ^ [X4: nat] : X4 )
% 5.31/5.58 = ( times_times_nat @ one_one_nat ) ) ).
% 5.31/5.58
% 5.31/5.58 % lambda_one
% 5.31/5.58 thf(fact_4581_lambda__one,axiom,
% 5.31/5.58 ( ( ^ [X4: int] : X4 )
% 5.31/5.58 = ( times_times_int @ one_one_int ) ) ).
% 5.31/5.58
% 5.31/5.58 % lambda_one
% 5.31/5.58 thf(fact_4582_finite__M__bounded__by__nat,axiom,
% 5.31/5.58 ! [P2: nat > $o,I2: nat] :
% 5.31/5.58 ( finite_finite_nat
% 5.31/5.58 @ ( collect_nat
% 5.31/5.58 @ ^ [K3: nat] :
% 5.31/5.58 ( ( P2 @ K3 )
% 5.31/5.58 & ( ord_less_nat @ K3 @ I2 ) ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % finite_M_bounded_by_nat
% 5.31/5.58 thf(fact_4583_finite__less__ub,axiom,
% 5.31/5.58 ! [F2: nat > nat,U: nat] :
% 5.31/5.58 ( ! [N3: nat] : ( ord_less_eq_nat @ N3 @ ( F2 @ N3 ) )
% 5.31/5.58 => ( finite_finite_nat
% 5.31/5.58 @ ( collect_nat
% 5.31/5.58 @ ^ [N4: nat] : ( ord_less_eq_nat @ ( F2 @ N4 ) @ U ) ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % finite_less_ub
% 5.31/5.58 thf(fact_4584_max_Omono,axiom,
% 5.31/5.58 ! [C2: rat,A: rat,D: rat,B: rat] :
% 5.31/5.58 ( ( ord_less_eq_rat @ C2 @ A )
% 5.31/5.58 => ( ( ord_less_eq_rat @ D @ B )
% 5.31/5.58 => ( ord_less_eq_rat @ ( ord_max_rat @ C2 @ D ) @ ( ord_max_rat @ A @ B ) ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % max.mono
% 5.31/5.58 thf(fact_4585_max_Omono,axiom,
% 5.31/5.58 ! [C2: num,A: num,D: num,B: num] :
% 5.31/5.58 ( ( ord_less_eq_num @ C2 @ A )
% 5.31/5.58 => ( ( ord_less_eq_num @ D @ B )
% 5.31/5.58 => ( ord_less_eq_num @ ( ord_max_num @ C2 @ D ) @ ( ord_max_num @ A @ B ) ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % max.mono
% 5.31/5.58 thf(fact_4586_max_Omono,axiom,
% 5.31/5.58 ! [C2: nat,A: nat,D: nat,B: nat] :
% 5.31/5.58 ( ( ord_less_eq_nat @ C2 @ A )
% 5.31/5.58 => ( ( ord_less_eq_nat @ D @ B )
% 5.31/5.58 => ( ord_less_eq_nat @ ( ord_max_nat @ C2 @ D ) @ ( ord_max_nat @ A @ B ) ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % max.mono
% 5.31/5.58 thf(fact_4587_max_Omono,axiom,
% 5.31/5.58 ! [C2: int,A: int,D: int,B: int] :
% 5.31/5.58 ( ( ord_less_eq_int @ C2 @ A )
% 5.31/5.58 => ( ( ord_less_eq_int @ D @ B )
% 5.31/5.58 => ( ord_less_eq_int @ ( ord_max_int @ C2 @ D ) @ ( ord_max_int @ A @ B ) ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % max.mono
% 5.31/5.58 thf(fact_4588_max_OorderE,axiom,
% 5.31/5.58 ! [B: rat,A: rat] :
% 5.31/5.58 ( ( ord_less_eq_rat @ B @ A )
% 5.31/5.58 => ( A
% 5.31/5.58 = ( ord_max_rat @ A @ B ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % max.orderE
% 5.31/5.58 thf(fact_4589_max_OorderE,axiom,
% 5.31/5.58 ! [B: num,A: num] :
% 5.31/5.58 ( ( ord_less_eq_num @ B @ A )
% 5.31/5.58 => ( A
% 5.31/5.58 = ( ord_max_num @ A @ B ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % max.orderE
% 5.31/5.58 thf(fact_4590_max_OorderE,axiom,
% 5.31/5.58 ! [B: nat,A: nat] :
% 5.31/5.58 ( ( ord_less_eq_nat @ B @ A )
% 5.31/5.58 => ( A
% 5.31/5.58 = ( ord_max_nat @ A @ B ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % max.orderE
% 5.31/5.58 thf(fact_4591_max_OorderE,axiom,
% 5.31/5.58 ! [B: int,A: int] :
% 5.31/5.58 ( ( ord_less_eq_int @ B @ A )
% 5.31/5.58 => ( A
% 5.31/5.58 = ( ord_max_int @ A @ B ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % max.orderE
% 5.31/5.58 thf(fact_4592_max_OorderI,axiom,
% 5.31/5.58 ! [A: rat,B: rat] :
% 5.31/5.58 ( ( A
% 5.31/5.58 = ( ord_max_rat @ A @ B ) )
% 5.31/5.58 => ( ord_less_eq_rat @ B @ A ) ) ).
% 5.31/5.58
% 5.31/5.58 % max.orderI
% 5.31/5.58 thf(fact_4593_max_OorderI,axiom,
% 5.31/5.58 ! [A: num,B: num] :
% 5.31/5.58 ( ( A
% 5.31/5.58 = ( ord_max_num @ A @ B ) )
% 5.31/5.58 => ( ord_less_eq_num @ B @ A ) ) ).
% 5.31/5.58
% 5.31/5.58 % max.orderI
% 5.31/5.58 thf(fact_4594_max_OorderI,axiom,
% 5.31/5.58 ! [A: nat,B: nat] :
% 5.31/5.58 ( ( A
% 5.31/5.58 = ( ord_max_nat @ A @ B ) )
% 5.31/5.58 => ( ord_less_eq_nat @ B @ A ) ) ).
% 5.31/5.58
% 5.31/5.58 % max.orderI
% 5.31/5.58 thf(fact_4595_max_OorderI,axiom,
% 5.31/5.58 ! [A: int,B: int] :
% 5.31/5.58 ( ( A
% 5.31/5.58 = ( ord_max_int @ A @ B ) )
% 5.31/5.58 => ( ord_less_eq_int @ B @ A ) ) ).
% 5.31/5.58
% 5.31/5.58 % max.orderI
% 5.31/5.58 thf(fact_4596_max_OboundedE,axiom,
% 5.31/5.58 ! [B: rat,C2: rat,A: rat] :
% 5.31/5.58 ( ( ord_less_eq_rat @ ( ord_max_rat @ B @ C2 ) @ A )
% 5.31/5.58 => ~ ( ( ord_less_eq_rat @ B @ A )
% 5.31/5.58 => ~ ( ord_less_eq_rat @ C2 @ A ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % max.boundedE
% 5.31/5.58 thf(fact_4597_max_OboundedE,axiom,
% 5.31/5.58 ! [B: num,C2: num,A: num] :
% 5.31/5.58 ( ( ord_less_eq_num @ ( ord_max_num @ B @ C2 ) @ A )
% 5.31/5.58 => ~ ( ( ord_less_eq_num @ B @ A )
% 5.31/5.58 => ~ ( ord_less_eq_num @ C2 @ A ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % max.boundedE
% 5.31/5.58 thf(fact_4598_max_OboundedE,axiom,
% 5.31/5.58 ! [B: nat,C2: nat,A: nat] :
% 5.31/5.58 ( ( ord_less_eq_nat @ ( ord_max_nat @ B @ C2 ) @ A )
% 5.31/5.58 => ~ ( ( ord_less_eq_nat @ B @ A )
% 5.31/5.58 => ~ ( ord_less_eq_nat @ C2 @ A ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % max.boundedE
% 5.31/5.58 thf(fact_4599_max_OboundedE,axiom,
% 5.31/5.58 ! [B: int,C2: int,A: int] :
% 5.31/5.58 ( ( ord_less_eq_int @ ( ord_max_int @ B @ C2 ) @ A )
% 5.31/5.58 => ~ ( ( ord_less_eq_int @ B @ A )
% 5.31/5.58 => ~ ( ord_less_eq_int @ C2 @ A ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % max.boundedE
% 5.31/5.58 thf(fact_4600_max_OboundedI,axiom,
% 5.31/5.58 ! [B: rat,A: rat,C2: rat] :
% 5.31/5.58 ( ( ord_less_eq_rat @ B @ A )
% 5.31/5.58 => ( ( ord_less_eq_rat @ C2 @ A )
% 5.31/5.58 => ( ord_less_eq_rat @ ( ord_max_rat @ B @ C2 ) @ A ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % max.boundedI
% 5.31/5.58 thf(fact_4601_max_OboundedI,axiom,
% 5.31/5.58 ! [B: num,A: num,C2: num] :
% 5.31/5.58 ( ( ord_less_eq_num @ B @ A )
% 5.31/5.58 => ( ( ord_less_eq_num @ C2 @ A )
% 5.31/5.58 => ( ord_less_eq_num @ ( ord_max_num @ B @ C2 ) @ A ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % max.boundedI
% 5.31/5.58 thf(fact_4602_max_OboundedI,axiom,
% 5.31/5.58 ! [B: nat,A: nat,C2: nat] :
% 5.31/5.58 ( ( ord_less_eq_nat @ B @ A )
% 5.31/5.58 => ( ( ord_less_eq_nat @ C2 @ A )
% 5.31/5.58 => ( ord_less_eq_nat @ ( ord_max_nat @ B @ C2 ) @ A ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % max.boundedI
% 5.31/5.58 thf(fact_4603_max_OboundedI,axiom,
% 5.31/5.58 ! [B: int,A: int,C2: int] :
% 5.31/5.58 ( ( ord_less_eq_int @ B @ A )
% 5.31/5.58 => ( ( ord_less_eq_int @ C2 @ A )
% 5.31/5.58 => ( ord_less_eq_int @ ( ord_max_int @ B @ C2 ) @ A ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % max.boundedI
% 5.31/5.58 thf(fact_4604_max_Oorder__iff,axiom,
% 5.31/5.58 ( ord_less_eq_rat
% 5.31/5.58 = ( ^ [B4: rat,A5: rat] :
% 5.31/5.58 ( A5
% 5.31/5.58 = ( ord_max_rat @ A5 @ B4 ) ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % max.order_iff
% 5.31/5.58 thf(fact_4605_max_Oorder__iff,axiom,
% 5.31/5.58 ( ord_less_eq_num
% 5.31/5.58 = ( ^ [B4: num,A5: num] :
% 5.31/5.58 ( A5
% 5.31/5.58 = ( ord_max_num @ A5 @ B4 ) ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % max.order_iff
% 5.31/5.58 thf(fact_4606_max_Oorder__iff,axiom,
% 5.31/5.58 ( ord_less_eq_nat
% 5.31/5.58 = ( ^ [B4: nat,A5: nat] :
% 5.31/5.58 ( A5
% 5.31/5.58 = ( ord_max_nat @ A5 @ B4 ) ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % max.order_iff
% 5.31/5.58 thf(fact_4607_max_Oorder__iff,axiom,
% 5.31/5.58 ( ord_less_eq_int
% 5.31/5.58 = ( ^ [B4: int,A5: int] :
% 5.31/5.58 ( A5
% 5.31/5.58 = ( ord_max_int @ A5 @ B4 ) ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % max.order_iff
% 5.31/5.58 thf(fact_4608_max_Ocobounded1,axiom,
% 5.31/5.58 ! [A: rat,B: rat] : ( ord_less_eq_rat @ A @ ( ord_max_rat @ A @ B ) ) ).
% 5.31/5.58
% 5.31/5.58 % max.cobounded1
% 5.31/5.58 thf(fact_4609_max_Ocobounded1,axiom,
% 5.31/5.58 ! [A: num,B: num] : ( ord_less_eq_num @ A @ ( ord_max_num @ A @ B ) ) ).
% 5.31/5.58
% 5.31/5.58 % max.cobounded1
% 5.31/5.58 thf(fact_4610_max_Ocobounded1,axiom,
% 5.31/5.58 ! [A: nat,B: nat] : ( ord_less_eq_nat @ A @ ( ord_max_nat @ A @ B ) ) ).
% 5.31/5.58
% 5.31/5.58 % max.cobounded1
% 5.31/5.58 thf(fact_4611_max_Ocobounded1,axiom,
% 5.31/5.58 ! [A: int,B: int] : ( ord_less_eq_int @ A @ ( ord_max_int @ A @ B ) ) ).
% 5.31/5.58
% 5.31/5.58 % max.cobounded1
% 5.31/5.58 thf(fact_4612_max_Ocobounded2,axiom,
% 5.31/5.58 ! [B: rat,A: rat] : ( ord_less_eq_rat @ B @ ( ord_max_rat @ A @ B ) ) ).
% 5.31/5.58
% 5.31/5.58 % max.cobounded2
% 5.31/5.58 thf(fact_4613_max_Ocobounded2,axiom,
% 5.31/5.58 ! [B: num,A: num] : ( ord_less_eq_num @ B @ ( ord_max_num @ A @ B ) ) ).
% 5.31/5.58
% 5.31/5.58 % max.cobounded2
% 5.31/5.58 thf(fact_4614_max_Ocobounded2,axiom,
% 5.31/5.58 ! [B: nat,A: nat] : ( ord_less_eq_nat @ B @ ( ord_max_nat @ A @ B ) ) ).
% 5.31/5.58
% 5.31/5.58 % max.cobounded2
% 5.31/5.58 thf(fact_4615_max_Ocobounded2,axiom,
% 5.31/5.58 ! [B: int,A: int] : ( ord_less_eq_int @ B @ ( ord_max_int @ A @ B ) ) ).
% 5.31/5.58
% 5.31/5.58 % max.cobounded2
% 5.31/5.58 thf(fact_4616_le__max__iff__disj,axiom,
% 5.31/5.58 ! [Z3: rat,X: rat,Y: rat] :
% 5.31/5.58 ( ( ord_less_eq_rat @ Z3 @ ( ord_max_rat @ X @ Y ) )
% 5.31/5.58 = ( ( ord_less_eq_rat @ Z3 @ X )
% 5.31/5.58 | ( ord_less_eq_rat @ Z3 @ Y ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % le_max_iff_disj
% 5.31/5.58 thf(fact_4617_le__max__iff__disj,axiom,
% 5.31/5.58 ! [Z3: num,X: num,Y: num] :
% 5.31/5.58 ( ( ord_less_eq_num @ Z3 @ ( ord_max_num @ X @ Y ) )
% 5.31/5.58 = ( ( ord_less_eq_num @ Z3 @ X )
% 5.31/5.58 | ( ord_less_eq_num @ Z3 @ Y ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % le_max_iff_disj
% 5.31/5.58 thf(fact_4618_le__max__iff__disj,axiom,
% 5.31/5.58 ! [Z3: nat,X: nat,Y: nat] :
% 5.31/5.58 ( ( ord_less_eq_nat @ Z3 @ ( ord_max_nat @ X @ Y ) )
% 5.31/5.58 = ( ( ord_less_eq_nat @ Z3 @ X )
% 5.31/5.58 | ( ord_less_eq_nat @ Z3 @ Y ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % le_max_iff_disj
% 5.31/5.58 thf(fact_4619_le__max__iff__disj,axiom,
% 5.31/5.58 ! [Z3: int,X: int,Y: int] :
% 5.31/5.58 ( ( ord_less_eq_int @ Z3 @ ( ord_max_int @ X @ Y ) )
% 5.31/5.58 = ( ( ord_less_eq_int @ Z3 @ X )
% 5.31/5.58 | ( ord_less_eq_int @ Z3 @ Y ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % le_max_iff_disj
% 5.31/5.58 thf(fact_4620_max_Oabsorb__iff1,axiom,
% 5.31/5.58 ( ord_less_eq_rat
% 5.31/5.58 = ( ^ [B4: rat,A5: rat] :
% 5.31/5.58 ( ( ord_max_rat @ A5 @ B4 )
% 5.31/5.58 = A5 ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % max.absorb_iff1
% 5.31/5.58 thf(fact_4621_max_Oabsorb__iff1,axiom,
% 5.31/5.58 ( ord_less_eq_num
% 5.31/5.58 = ( ^ [B4: num,A5: num] :
% 5.31/5.58 ( ( ord_max_num @ A5 @ B4 )
% 5.31/5.58 = A5 ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % max.absorb_iff1
% 5.31/5.58 thf(fact_4622_max_Oabsorb__iff1,axiom,
% 5.31/5.58 ( ord_less_eq_nat
% 5.31/5.58 = ( ^ [B4: nat,A5: nat] :
% 5.31/5.58 ( ( ord_max_nat @ A5 @ B4 )
% 5.31/5.58 = A5 ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % max.absorb_iff1
% 5.31/5.58 thf(fact_4623_max_Oabsorb__iff1,axiom,
% 5.31/5.58 ( ord_less_eq_int
% 5.31/5.58 = ( ^ [B4: int,A5: int] :
% 5.31/5.58 ( ( ord_max_int @ A5 @ B4 )
% 5.31/5.58 = A5 ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % max.absorb_iff1
% 5.31/5.58 thf(fact_4624_max_Oabsorb__iff2,axiom,
% 5.31/5.58 ( ord_less_eq_rat
% 5.31/5.58 = ( ^ [A5: rat,B4: rat] :
% 5.31/5.58 ( ( ord_max_rat @ A5 @ B4 )
% 5.31/5.58 = B4 ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % max.absorb_iff2
% 5.31/5.58 thf(fact_4625_max_Oabsorb__iff2,axiom,
% 5.31/5.58 ( ord_less_eq_num
% 5.31/5.58 = ( ^ [A5: num,B4: num] :
% 5.31/5.58 ( ( ord_max_num @ A5 @ B4 )
% 5.31/5.58 = B4 ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % max.absorb_iff2
% 5.31/5.58 thf(fact_4626_max_Oabsorb__iff2,axiom,
% 5.31/5.58 ( ord_less_eq_nat
% 5.31/5.58 = ( ^ [A5: nat,B4: nat] :
% 5.31/5.58 ( ( ord_max_nat @ A5 @ B4 )
% 5.31/5.58 = B4 ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % max.absorb_iff2
% 5.31/5.58 thf(fact_4627_max_Oabsorb__iff2,axiom,
% 5.31/5.58 ( ord_less_eq_int
% 5.31/5.58 = ( ^ [A5: int,B4: int] :
% 5.31/5.58 ( ( ord_max_int @ A5 @ B4 )
% 5.31/5.58 = B4 ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % max.absorb_iff2
% 5.31/5.58 thf(fact_4628_max_OcoboundedI1,axiom,
% 5.31/5.58 ! [C2: rat,A: rat,B: rat] :
% 5.31/5.58 ( ( ord_less_eq_rat @ C2 @ A )
% 5.31/5.58 => ( ord_less_eq_rat @ C2 @ ( ord_max_rat @ A @ B ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % max.coboundedI1
% 5.31/5.58 thf(fact_4629_max_OcoboundedI1,axiom,
% 5.31/5.58 ! [C2: num,A: num,B: num] :
% 5.31/5.58 ( ( ord_less_eq_num @ C2 @ A )
% 5.31/5.58 => ( ord_less_eq_num @ C2 @ ( ord_max_num @ A @ B ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % max.coboundedI1
% 5.31/5.58 thf(fact_4630_max_OcoboundedI1,axiom,
% 5.31/5.58 ! [C2: nat,A: nat,B: nat] :
% 5.31/5.58 ( ( ord_less_eq_nat @ C2 @ A )
% 5.31/5.58 => ( ord_less_eq_nat @ C2 @ ( ord_max_nat @ A @ B ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % max.coboundedI1
% 5.31/5.58 thf(fact_4631_max_OcoboundedI1,axiom,
% 5.31/5.58 ! [C2: int,A: int,B: int] :
% 5.31/5.58 ( ( ord_less_eq_int @ C2 @ A )
% 5.31/5.58 => ( ord_less_eq_int @ C2 @ ( ord_max_int @ A @ B ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % max.coboundedI1
% 5.31/5.58 thf(fact_4632_max_OcoboundedI2,axiom,
% 5.31/5.58 ! [C2: rat,B: rat,A: rat] :
% 5.31/5.58 ( ( ord_less_eq_rat @ C2 @ B )
% 5.31/5.58 => ( ord_less_eq_rat @ C2 @ ( ord_max_rat @ A @ B ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % max.coboundedI2
% 5.31/5.58 thf(fact_4633_max_OcoboundedI2,axiom,
% 5.31/5.58 ! [C2: num,B: num,A: num] :
% 5.31/5.58 ( ( ord_less_eq_num @ C2 @ B )
% 5.31/5.58 => ( ord_less_eq_num @ C2 @ ( ord_max_num @ A @ B ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % max.coboundedI2
% 5.31/5.58 thf(fact_4634_max_OcoboundedI2,axiom,
% 5.31/5.58 ! [C2: nat,B: nat,A: nat] :
% 5.31/5.58 ( ( ord_less_eq_nat @ C2 @ B )
% 5.31/5.58 => ( ord_less_eq_nat @ C2 @ ( ord_max_nat @ A @ B ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % max.coboundedI2
% 5.31/5.58 thf(fact_4635_max_OcoboundedI2,axiom,
% 5.31/5.58 ! [C2: int,B: int,A: int] :
% 5.31/5.58 ( ( ord_less_eq_int @ C2 @ B )
% 5.31/5.58 => ( ord_less_eq_int @ C2 @ ( ord_max_int @ A @ B ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % max.coboundedI2
% 5.31/5.58 thf(fact_4636_max__absorb2,axiom,
% 5.31/5.58 ! [X: set_nat,Y: set_nat] :
% 5.31/5.58 ( ( ord_less_eq_set_nat @ X @ Y )
% 5.31/5.58 => ( ( ord_max_set_nat @ X @ Y )
% 5.31/5.58 = Y ) ) ).
% 5.31/5.58
% 5.31/5.58 % max_absorb2
% 5.31/5.58 thf(fact_4637_max__absorb2,axiom,
% 5.31/5.58 ! [X: rat,Y: rat] :
% 5.31/5.58 ( ( ord_less_eq_rat @ X @ Y )
% 5.31/5.58 => ( ( ord_max_rat @ X @ Y )
% 5.31/5.58 = Y ) ) ).
% 5.31/5.58
% 5.31/5.58 % max_absorb2
% 5.31/5.58 thf(fact_4638_max__absorb2,axiom,
% 5.31/5.58 ! [X: num,Y: num] :
% 5.31/5.58 ( ( ord_less_eq_num @ X @ Y )
% 5.31/5.58 => ( ( ord_max_num @ X @ Y )
% 5.31/5.58 = Y ) ) ).
% 5.31/5.58
% 5.31/5.58 % max_absorb2
% 5.31/5.58 thf(fact_4639_max__absorb2,axiom,
% 5.31/5.58 ! [X: nat,Y: nat] :
% 5.31/5.58 ( ( ord_less_eq_nat @ X @ Y )
% 5.31/5.58 => ( ( ord_max_nat @ X @ Y )
% 5.31/5.58 = Y ) ) ).
% 5.31/5.58
% 5.31/5.58 % max_absorb2
% 5.31/5.58 thf(fact_4640_max__absorb2,axiom,
% 5.31/5.58 ! [X: int,Y: int] :
% 5.31/5.58 ( ( ord_less_eq_int @ X @ Y )
% 5.31/5.58 => ( ( ord_max_int @ X @ Y )
% 5.31/5.58 = Y ) ) ).
% 5.31/5.58
% 5.31/5.58 % max_absorb2
% 5.31/5.58 thf(fact_4641_max__absorb1,axiom,
% 5.31/5.58 ! [Y: set_nat,X: set_nat] :
% 5.31/5.58 ( ( ord_less_eq_set_nat @ Y @ X )
% 5.31/5.58 => ( ( ord_max_set_nat @ X @ Y )
% 5.31/5.58 = X ) ) ).
% 5.31/5.58
% 5.31/5.58 % max_absorb1
% 5.31/5.58 thf(fact_4642_max__absorb1,axiom,
% 5.31/5.58 ! [Y: rat,X: rat] :
% 5.31/5.58 ( ( ord_less_eq_rat @ Y @ X )
% 5.31/5.58 => ( ( ord_max_rat @ X @ Y )
% 5.31/5.58 = X ) ) ).
% 5.31/5.58
% 5.31/5.58 % max_absorb1
% 5.31/5.58 thf(fact_4643_max__absorb1,axiom,
% 5.31/5.58 ! [Y: num,X: num] :
% 5.31/5.58 ( ( ord_less_eq_num @ Y @ X )
% 5.31/5.58 => ( ( ord_max_num @ X @ Y )
% 5.31/5.58 = X ) ) ).
% 5.31/5.58
% 5.31/5.58 % max_absorb1
% 5.31/5.58 thf(fact_4644_max__absorb1,axiom,
% 5.31/5.58 ! [Y: nat,X: nat] :
% 5.31/5.58 ( ( ord_less_eq_nat @ Y @ X )
% 5.31/5.58 => ( ( ord_max_nat @ X @ Y )
% 5.31/5.58 = X ) ) ).
% 5.31/5.58
% 5.31/5.58 % max_absorb1
% 5.31/5.58 thf(fact_4645_max__absorb1,axiom,
% 5.31/5.58 ! [Y: int,X: int] :
% 5.31/5.58 ( ( ord_less_eq_int @ Y @ X )
% 5.31/5.58 => ( ( ord_max_int @ X @ Y )
% 5.31/5.58 = X ) ) ).
% 5.31/5.58
% 5.31/5.58 % max_absorb1
% 5.31/5.58 thf(fact_4646_max__def,axiom,
% 5.31/5.58 ( ord_max_set_nat
% 5.31/5.58 = ( ^ [A5: set_nat,B4: set_nat] : ( if_set_nat @ ( ord_less_eq_set_nat @ A5 @ B4 ) @ B4 @ A5 ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % max_def
% 5.31/5.58 thf(fact_4647_max__def,axiom,
% 5.31/5.58 ( ord_max_rat
% 5.31/5.58 = ( ^ [A5: rat,B4: rat] : ( if_rat @ ( ord_less_eq_rat @ A5 @ B4 ) @ B4 @ A5 ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % max_def
% 5.31/5.58 thf(fact_4648_max__def,axiom,
% 5.31/5.58 ( ord_max_num
% 5.31/5.58 = ( ^ [A5: num,B4: num] : ( if_num @ ( ord_less_eq_num @ A5 @ B4 ) @ B4 @ A5 ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % max_def
% 5.31/5.58 thf(fact_4649_max__def,axiom,
% 5.31/5.58 ( ord_max_nat
% 5.31/5.58 = ( ^ [A5: nat,B4: nat] : ( if_nat @ ( ord_less_eq_nat @ A5 @ B4 ) @ B4 @ A5 ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % max_def
% 5.31/5.58 thf(fact_4650_max__def,axiom,
% 5.31/5.58 ( ord_max_int
% 5.31/5.58 = ( ^ [A5: int,B4: int] : ( if_int @ ( ord_less_eq_int @ A5 @ B4 ) @ B4 @ A5 ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % max_def
% 5.31/5.58 thf(fact_4651_max__add__distrib__left,axiom,
% 5.31/5.58 ! [X: real,Y: real,Z3: real] :
% 5.31/5.58 ( ( plus_plus_real @ ( ord_max_real @ X @ Y ) @ Z3 )
% 5.31/5.58 = ( ord_max_real @ ( plus_plus_real @ X @ Z3 ) @ ( plus_plus_real @ Y @ Z3 ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % max_add_distrib_left
% 5.31/5.58 thf(fact_4652_max__add__distrib__left,axiom,
% 5.31/5.58 ! [X: rat,Y: rat,Z3: rat] :
% 5.31/5.58 ( ( plus_plus_rat @ ( ord_max_rat @ X @ Y ) @ Z3 )
% 5.31/5.58 = ( ord_max_rat @ ( plus_plus_rat @ X @ Z3 ) @ ( plus_plus_rat @ Y @ Z3 ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % max_add_distrib_left
% 5.31/5.58 thf(fact_4653_max__add__distrib__left,axiom,
% 5.31/5.58 ! [X: nat,Y: nat,Z3: nat] :
% 5.31/5.58 ( ( plus_plus_nat @ ( ord_max_nat @ X @ Y ) @ Z3 )
% 5.31/5.58 = ( ord_max_nat @ ( plus_plus_nat @ X @ Z3 ) @ ( plus_plus_nat @ Y @ Z3 ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % max_add_distrib_left
% 5.31/5.58 thf(fact_4654_max__add__distrib__left,axiom,
% 5.31/5.58 ! [X: int,Y: int,Z3: int] :
% 5.31/5.58 ( ( plus_plus_int @ ( ord_max_int @ X @ Y ) @ Z3 )
% 5.31/5.58 = ( ord_max_int @ ( plus_plus_int @ X @ Z3 ) @ ( plus_plus_int @ Y @ Z3 ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % max_add_distrib_left
% 5.31/5.58 thf(fact_4655_max__add__distrib__right,axiom,
% 5.31/5.58 ! [X: real,Y: real,Z3: real] :
% 5.31/5.58 ( ( plus_plus_real @ X @ ( ord_max_real @ Y @ Z3 ) )
% 5.31/5.58 = ( ord_max_real @ ( plus_plus_real @ X @ Y ) @ ( plus_plus_real @ X @ Z3 ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % max_add_distrib_right
% 5.31/5.58 thf(fact_4656_max__add__distrib__right,axiom,
% 5.31/5.58 ! [X: rat,Y: rat,Z3: rat] :
% 5.31/5.58 ( ( plus_plus_rat @ X @ ( ord_max_rat @ Y @ Z3 ) )
% 5.31/5.58 = ( ord_max_rat @ ( plus_plus_rat @ X @ Y ) @ ( plus_plus_rat @ X @ Z3 ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % max_add_distrib_right
% 5.31/5.58 thf(fact_4657_max__add__distrib__right,axiom,
% 5.31/5.58 ! [X: nat,Y: nat,Z3: nat] :
% 5.31/5.58 ( ( plus_plus_nat @ X @ ( ord_max_nat @ Y @ Z3 ) )
% 5.31/5.58 = ( ord_max_nat @ ( plus_plus_nat @ X @ Y ) @ ( plus_plus_nat @ X @ Z3 ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % max_add_distrib_right
% 5.31/5.58 thf(fact_4658_max__add__distrib__right,axiom,
% 5.31/5.58 ! [X: int,Y: int,Z3: int] :
% 5.31/5.58 ( ( plus_plus_int @ X @ ( ord_max_int @ Y @ Z3 ) )
% 5.31/5.58 = ( ord_max_int @ ( plus_plus_int @ X @ Y ) @ ( plus_plus_int @ X @ Z3 ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % max_add_distrib_right
% 5.31/5.58 thf(fact_4659_max__diff__distrib__left,axiom,
% 5.31/5.58 ! [X: rat,Y: rat,Z3: rat] :
% 5.31/5.58 ( ( minus_minus_rat @ ( ord_max_rat @ X @ Y ) @ Z3 )
% 5.31/5.58 = ( ord_max_rat @ ( minus_minus_rat @ X @ Z3 ) @ ( minus_minus_rat @ Y @ Z3 ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % max_diff_distrib_left
% 5.31/5.58 thf(fact_4660_max__diff__distrib__left,axiom,
% 5.31/5.58 ! [X: int,Y: int,Z3: int] :
% 5.31/5.58 ( ( minus_minus_int @ ( ord_max_int @ X @ Y ) @ Z3 )
% 5.31/5.58 = ( ord_max_int @ ( minus_minus_int @ X @ Z3 ) @ ( minus_minus_int @ Y @ Z3 ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % max_diff_distrib_left
% 5.31/5.58 thf(fact_4661_nat__add__max__left,axiom,
% 5.31/5.58 ! [M2: nat,N: nat,Q2: nat] :
% 5.31/5.58 ( ( plus_plus_nat @ ( ord_max_nat @ M2 @ N ) @ Q2 )
% 5.31/5.58 = ( ord_max_nat @ ( plus_plus_nat @ M2 @ Q2 ) @ ( plus_plus_nat @ N @ Q2 ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % nat_add_max_left
% 5.31/5.58 thf(fact_4662_nat__add__max__right,axiom,
% 5.31/5.58 ! [M2: nat,N: nat,Q2: nat] :
% 5.31/5.58 ( ( plus_plus_nat @ M2 @ ( ord_max_nat @ N @ Q2 ) )
% 5.31/5.58 = ( ord_max_nat @ ( plus_plus_nat @ M2 @ N ) @ ( plus_plus_nat @ M2 @ Q2 ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % nat_add_max_right
% 5.31/5.58 thf(fact_4663_set__vebt__def,axiom,
% 5.31/5.58 ( vEBT_set_vebt
% 5.31/5.58 = ( ^ [T2: vEBT_VEBT] : ( collect_nat @ ( vEBT_V8194947554948674370ptions @ T2 ) ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % set_vebt_def
% 5.31/5.58 thf(fact_4664_nat__mult__max__left,axiom,
% 5.31/5.58 ! [M2: nat,N: nat,Q2: nat] :
% 5.31/5.58 ( ( times_times_nat @ ( ord_max_nat @ M2 @ N ) @ Q2 )
% 5.31/5.58 = ( ord_max_nat @ ( times_times_nat @ M2 @ Q2 ) @ ( times_times_nat @ N @ Q2 ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % nat_mult_max_left
% 5.31/5.58 thf(fact_4665_nat__mult__max__right,axiom,
% 5.31/5.58 ! [M2: nat,N: nat,Q2: nat] :
% 5.31/5.58 ( ( times_times_nat @ M2 @ ( ord_max_nat @ N @ Q2 ) )
% 5.31/5.58 = ( ord_max_nat @ ( times_times_nat @ M2 @ N ) @ ( times_times_nat @ M2 @ Q2 ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % nat_mult_max_right
% 5.31/5.58 thf(fact_4666_numeral__code_I2_J,axiom,
% 5.31/5.58 ! [N: num] :
% 5.31/5.58 ( ( numeral_numeral_rat @ ( bit0 @ N ) )
% 5.31/5.58 = ( plus_plus_rat @ ( numeral_numeral_rat @ N ) @ ( numeral_numeral_rat @ N ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % numeral_code(2)
% 5.31/5.58 thf(fact_4667_numeral__code_I2_J,axiom,
% 5.31/5.58 ! [N: num] :
% 5.31/5.58 ( ( numera1916890842035813515d_enat @ ( bit0 @ N ) )
% 5.31/5.58 = ( plus_p3455044024723400733d_enat @ ( numera1916890842035813515d_enat @ N ) @ ( numera1916890842035813515d_enat @ N ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % numeral_code(2)
% 5.31/5.58 thf(fact_4668_numeral__code_I2_J,axiom,
% 5.31/5.58 ! [N: num] :
% 5.31/5.58 ( ( numera6690914467698888265omplex @ ( bit0 @ N ) )
% 5.31/5.58 = ( plus_plus_complex @ ( numera6690914467698888265omplex @ N ) @ ( numera6690914467698888265omplex @ N ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % numeral_code(2)
% 5.31/5.58 thf(fact_4669_numeral__code_I2_J,axiom,
% 5.31/5.58 ! [N: num] :
% 5.31/5.58 ( ( numeral_numeral_real @ ( bit0 @ N ) )
% 5.31/5.58 = ( plus_plus_real @ ( numeral_numeral_real @ N ) @ ( numeral_numeral_real @ N ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % numeral_code(2)
% 5.31/5.58 thf(fact_4670_numeral__code_I2_J,axiom,
% 5.31/5.58 ! [N: num] :
% 5.31/5.58 ( ( numeral_numeral_nat @ ( bit0 @ N ) )
% 5.31/5.58 = ( plus_plus_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ N ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % numeral_code(2)
% 5.31/5.58 thf(fact_4671_numeral__code_I2_J,axiom,
% 5.31/5.58 ! [N: num] :
% 5.31/5.58 ( ( numeral_numeral_int @ ( bit0 @ N ) )
% 5.31/5.58 = ( plus_plus_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ N ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % numeral_code(2)
% 5.31/5.58 thf(fact_4672_nat__leq__as__int,axiom,
% 5.31/5.58 ( ord_less_eq_nat
% 5.31/5.58 = ( ^ [A5: nat,B4: nat] : ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ A5 ) @ ( semiri1314217659103216013at_int @ B4 ) ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % nat_leq_as_int
% 5.31/5.58 thf(fact_4673_power__numeral__even,axiom,
% 5.31/5.58 ! [Z3: complex,W2: num] :
% 5.31/5.58 ( ( power_power_complex @ Z3 @ ( numeral_numeral_nat @ ( bit0 @ W2 ) ) )
% 5.31/5.58 = ( times_times_complex @ ( power_power_complex @ Z3 @ ( numeral_numeral_nat @ W2 ) ) @ ( power_power_complex @ Z3 @ ( numeral_numeral_nat @ W2 ) ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % power_numeral_even
% 5.31/5.58 thf(fact_4674_power__numeral__even,axiom,
% 5.31/5.58 ! [Z3: real,W2: num] :
% 5.31/5.58 ( ( power_power_real @ Z3 @ ( numeral_numeral_nat @ ( bit0 @ W2 ) ) )
% 5.31/5.58 = ( times_times_real @ ( power_power_real @ Z3 @ ( numeral_numeral_nat @ W2 ) ) @ ( power_power_real @ Z3 @ ( numeral_numeral_nat @ W2 ) ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % power_numeral_even
% 5.31/5.58 thf(fact_4675_power__numeral__even,axiom,
% 5.31/5.58 ! [Z3: rat,W2: num] :
% 5.31/5.58 ( ( power_power_rat @ Z3 @ ( numeral_numeral_nat @ ( bit0 @ W2 ) ) )
% 5.31/5.58 = ( times_times_rat @ ( power_power_rat @ Z3 @ ( numeral_numeral_nat @ W2 ) ) @ ( power_power_rat @ Z3 @ ( numeral_numeral_nat @ W2 ) ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % power_numeral_even
% 5.31/5.58 thf(fact_4676_power__numeral__even,axiom,
% 5.31/5.58 ! [Z3: nat,W2: num] :
% 5.31/5.58 ( ( power_power_nat @ Z3 @ ( numeral_numeral_nat @ ( bit0 @ W2 ) ) )
% 5.31/5.58 = ( times_times_nat @ ( power_power_nat @ Z3 @ ( numeral_numeral_nat @ W2 ) ) @ ( power_power_nat @ Z3 @ ( numeral_numeral_nat @ W2 ) ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % power_numeral_even
% 5.31/5.58 thf(fact_4677_power__numeral__even,axiom,
% 5.31/5.58 ! [Z3: int,W2: num] :
% 5.31/5.58 ( ( power_power_int @ Z3 @ ( numeral_numeral_nat @ ( bit0 @ W2 ) ) )
% 5.31/5.58 = ( times_times_int @ ( power_power_int @ Z3 @ ( numeral_numeral_nat @ W2 ) ) @ ( power_power_int @ Z3 @ ( numeral_numeral_nat @ W2 ) ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % power_numeral_even
% 5.31/5.58 thf(fact_4678_card__less,axiom,
% 5.31/5.58 ! [M5: set_nat,I2: nat] :
% 5.31/5.58 ( ( member_nat @ zero_zero_nat @ M5 )
% 5.31/5.58 => ( ( finite_card_nat
% 5.31/5.58 @ ( collect_nat
% 5.31/5.58 @ ^ [K3: nat] :
% 5.31/5.58 ( ( member_nat @ K3 @ M5 )
% 5.31/5.58 & ( ord_less_nat @ K3 @ ( suc @ I2 ) ) ) ) )
% 5.31/5.58 != zero_zero_nat ) ) ).
% 5.31/5.58
% 5.31/5.58 % card_less
% 5.31/5.58 thf(fact_4679_card__less__Suc,axiom,
% 5.31/5.58 ! [M5: set_nat,I2: nat] :
% 5.31/5.58 ( ( member_nat @ zero_zero_nat @ M5 )
% 5.31/5.58 => ( ( suc
% 5.31/5.58 @ ( finite_card_nat
% 5.31/5.58 @ ( collect_nat
% 5.31/5.58 @ ^ [K3: nat] :
% 5.31/5.58 ( ( member_nat @ ( suc @ K3 ) @ M5 )
% 5.31/5.58 & ( ord_less_nat @ K3 @ I2 ) ) ) ) )
% 5.31/5.58 = ( finite_card_nat
% 5.31/5.58 @ ( collect_nat
% 5.31/5.58 @ ^ [K3: nat] :
% 5.31/5.58 ( ( member_nat @ K3 @ M5 )
% 5.31/5.58 & ( ord_less_nat @ K3 @ ( suc @ I2 ) ) ) ) ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % card_less_Suc
% 5.31/5.58 thf(fact_4680_card__less__Suc2,axiom,
% 5.31/5.58 ! [M5: set_nat,I2: nat] :
% 5.31/5.58 ( ~ ( member_nat @ zero_zero_nat @ M5 )
% 5.31/5.58 => ( ( finite_card_nat
% 5.31/5.58 @ ( collect_nat
% 5.31/5.58 @ ^ [K3: nat] :
% 5.31/5.58 ( ( member_nat @ ( suc @ K3 ) @ M5 )
% 5.31/5.58 & ( ord_less_nat @ K3 @ I2 ) ) ) )
% 5.31/5.58 = ( finite_card_nat
% 5.31/5.58 @ ( collect_nat
% 5.31/5.58 @ ^ [K3: nat] :
% 5.31/5.58 ( ( member_nat @ K3 @ M5 )
% 5.31/5.58 & ( ord_less_nat @ K3 @ ( suc @ I2 ) ) ) ) ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % card_less_Suc2
% 5.31/5.58 thf(fact_4681_nat__minus__add__max,axiom,
% 5.31/5.58 ! [N: nat,M2: nat] :
% 5.31/5.58 ( ( plus_plus_nat @ ( minus_minus_nat @ N @ M2 ) @ M2 )
% 5.31/5.58 = ( ord_max_nat @ N @ M2 ) ) ).
% 5.31/5.58
% 5.31/5.58 % nat_minus_add_max
% 5.31/5.58 thf(fact_4682_finite__lists__length__eq,axiom,
% 5.31/5.58 ! [A4: set_complex,N: nat] :
% 5.31/5.58 ( ( finite3207457112153483333omplex @ A4 )
% 5.31/5.58 => ( finite8712137658972009173omplex
% 5.31/5.58 @ ( collect_list_complex
% 5.31/5.58 @ ^ [Xs: list_complex] :
% 5.31/5.58 ( ( ord_le211207098394363844omplex @ ( set_complex2 @ Xs ) @ A4 )
% 5.31/5.58 & ( ( size_s3451745648224563538omplex @ Xs )
% 5.31/5.58 = N ) ) ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % finite_lists_length_eq
% 5.31/5.58 thf(fact_4683_finite__lists__length__eq,axiom,
% 5.31/5.58 ! [A4: set_VEBT_VEBT,N: nat] :
% 5.31/5.58 ( ( finite5795047828879050333T_VEBT @ A4 )
% 5.31/5.58 => ( finite3004134309566078307T_VEBT
% 5.31/5.58 @ ( collec5608196760682091941T_VEBT
% 5.31/5.58 @ ^ [Xs: list_VEBT_VEBT] :
% 5.31/5.58 ( ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ Xs ) @ A4 )
% 5.31/5.58 & ( ( size_s6755466524823107622T_VEBT @ Xs )
% 5.31/5.58 = N ) ) ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % finite_lists_length_eq
% 5.31/5.58 thf(fact_4684_finite__lists__length__eq,axiom,
% 5.31/5.58 ! [A4: set_o,N: nat] :
% 5.31/5.58 ( ( finite_finite_o @ A4 )
% 5.31/5.58 => ( finite_finite_list_o
% 5.31/5.58 @ ( collect_list_o
% 5.31/5.58 @ ^ [Xs: list_o] :
% 5.31/5.58 ( ( ord_less_eq_set_o @ ( set_o2 @ Xs ) @ A4 )
% 5.31/5.58 & ( ( size_size_list_o @ Xs )
% 5.31/5.58 = N ) ) ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % finite_lists_length_eq
% 5.31/5.58 thf(fact_4685_finite__lists__length__eq,axiom,
% 5.31/5.58 ! [A4: set_int,N: nat] :
% 5.31/5.58 ( ( finite_finite_int @ A4 )
% 5.31/5.58 => ( finite3922522038869484883st_int
% 5.31/5.58 @ ( collect_list_int
% 5.31/5.58 @ ^ [Xs: list_int] :
% 5.31/5.58 ( ( ord_less_eq_set_int @ ( set_int2 @ Xs ) @ A4 )
% 5.31/5.58 & ( ( size_size_list_int @ Xs )
% 5.31/5.58 = N ) ) ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % finite_lists_length_eq
% 5.31/5.58 thf(fact_4686_finite__lists__length__eq,axiom,
% 5.31/5.58 ! [A4: set_nat,N: nat] :
% 5.31/5.58 ( ( finite_finite_nat @ A4 )
% 5.31/5.58 => ( finite8100373058378681591st_nat
% 5.31/5.58 @ ( collect_list_nat
% 5.31/5.58 @ ^ [Xs: list_nat] :
% 5.31/5.58 ( ( ord_less_eq_set_nat @ ( set_nat2 @ Xs ) @ A4 )
% 5.31/5.58 & ( ( size_size_list_nat @ Xs )
% 5.31/5.58 = N ) ) ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % finite_lists_length_eq
% 5.31/5.58 thf(fact_4687_card__lists__length__eq,axiom,
% 5.31/5.58 ! [A4: set_list_nat,N: nat] :
% 5.31/5.58 ( ( finite8100373058378681591st_nat @ A4 )
% 5.31/5.58 => ( ( finite7325466520557071688st_nat
% 5.31/5.58 @ ( collec5989764272469232197st_nat
% 5.31/5.58 @ ^ [Xs: list_list_nat] :
% 5.31/5.58 ( ( ord_le6045566169113846134st_nat @ ( set_list_nat2 @ Xs ) @ A4 )
% 5.31/5.58 & ( ( size_s3023201423986296836st_nat @ Xs )
% 5.31/5.58 = N ) ) ) )
% 5.31/5.58 = ( power_power_nat @ ( finite_card_list_nat @ A4 ) @ N ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % card_lists_length_eq
% 5.31/5.58 thf(fact_4688_card__lists__length__eq,axiom,
% 5.31/5.58 ! [A4: set_set_nat,N: nat] :
% 5.31/5.58 ( ( finite1152437895449049373et_nat @ A4 )
% 5.31/5.58 => ( ( finite5631907774883551598et_nat
% 5.31/5.58 @ ( collect_list_set_nat
% 5.31/5.58 @ ^ [Xs: list_set_nat] :
% 5.31/5.58 ( ( ord_le6893508408891458716et_nat @ ( set_set_nat2 @ Xs ) @ A4 )
% 5.31/5.58 & ( ( size_s3254054031482475050et_nat @ Xs )
% 5.31/5.58 = N ) ) ) )
% 5.31/5.58 = ( power_power_nat @ ( finite_card_set_nat @ A4 ) @ N ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % card_lists_length_eq
% 5.31/5.58 thf(fact_4689_card__lists__length__eq,axiom,
% 5.31/5.58 ! [A4: set_complex,N: nat] :
% 5.31/5.58 ( ( finite3207457112153483333omplex @ A4 )
% 5.31/5.58 => ( ( finite5120063068150530198omplex
% 5.31/5.58 @ ( collect_list_complex
% 5.31/5.58 @ ^ [Xs: list_complex] :
% 5.31/5.58 ( ( ord_le211207098394363844omplex @ ( set_complex2 @ Xs ) @ A4 )
% 5.31/5.58 & ( ( size_s3451745648224563538omplex @ Xs )
% 5.31/5.58 = N ) ) ) )
% 5.31/5.58 = ( power_power_nat @ ( finite_card_complex @ A4 ) @ N ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % card_lists_length_eq
% 5.31/5.58 thf(fact_4690_card__lists__length__eq,axiom,
% 5.31/5.58 ! [A4: set_VEBT_VEBT,N: nat] :
% 5.31/5.58 ( ( finite5795047828879050333T_VEBT @ A4 )
% 5.31/5.58 => ( ( finite5915292604075114978T_VEBT
% 5.31/5.58 @ ( collec5608196760682091941T_VEBT
% 5.31/5.58 @ ^ [Xs: list_VEBT_VEBT] :
% 5.31/5.58 ( ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ Xs ) @ A4 )
% 5.31/5.58 & ( ( size_s6755466524823107622T_VEBT @ Xs )
% 5.31/5.58 = N ) ) ) )
% 5.31/5.58 = ( power_power_nat @ ( finite7802652506058667612T_VEBT @ A4 ) @ N ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % card_lists_length_eq
% 5.31/5.58 thf(fact_4691_card__lists__length__eq,axiom,
% 5.31/5.58 ! [A4: set_o,N: nat] :
% 5.31/5.58 ( ( finite_finite_o @ A4 )
% 5.31/5.58 => ( ( finite_card_list_o
% 5.31/5.58 @ ( collect_list_o
% 5.31/5.58 @ ^ [Xs: list_o] :
% 5.31/5.58 ( ( ord_less_eq_set_o @ ( set_o2 @ Xs ) @ A4 )
% 5.31/5.58 & ( ( size_size_list_o @ Xs )
% 5.31/5.58 = N ) ) ) )
% 5.31/5.58 = ( power_power_nat @ ( finite_card_o @ A4 ) @ N ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % card_lists_length_eq
% 5.31/5.58 thf(fact_4692_card__lists__length__eq,axiom,
% 5.31/5.58 ! [A4: set_int,N: nat] :
% 5.31/5.58 ( ( finite_finite_int @ A4 )
% 5.31/5.58 => ( ( finite_card_list_int
% 5.31/5.58 @ ( collect_list_int
% 5.31/5.58 @ ^ [Xs: list_int] :
% 5.31/5.58 ( ( ord_less_eq_set_int @ ( set_int2 @ Xs ) @ A4 )
% 5.31/5.58 & ( ( size_size_list_int @ Xs )
% 5.31/5.58 = N ) ) ) )
% 5.31/5.58 = ( power_power_nat @ ( finite_card_int @ A4 ) @ N ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % card_lists_length_eq
% 5.31/5.58 thf(fact_4693_card__lists__length__eq,axiom,
% 5.31/5.58 ! [A4: set_nat,N: nat] :
% 5.31/5.58 ( ( finite_finite_nat @ A4 )
% 5.31/5.58 => ( ( finite_card_list_nat
% 5.31/5.58 @ ( collect_list_nat
% 5.31/5.58 @ ^ [Xs: list_nat] :
% 5.31/5.58 ( ( ord_less_eq_set_nat @ ( set_nat2 @ Xs ) @ A4 )
% 5.31/5.58 & ( ( size_size_list_nat @ Xs )
% 5.31/5.58 = N ) ) ) )
% 5.31/5.58 = ( power_power_nat @ ( finite_card_nat @ A4 ) @ N ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % card_lists_length_eq
% 5.31/5.58 thf(fact_4694_finite__lists__length__le,axiom,
% 5.31/5.58 ! [A4: set_complex,N: nat] :
% 5.31/5.58 ( ( finite3207457112153483333omplex @ A4 )
% 5.31/5.58 => ( finite8712137658972009173omplex
% 5.31/5.58 @ ( collect_list_complex
% 5.31/5.58 @ ^ [Xs: list_complex] :
% 5.31/5.58 ( ( ord_le211207098394363844omplex @ ( set_complex2 @ Xs ) @ A4 )
% 5.31/5.58 & ( ord_less_eq_nat @ ( size_s3451745648224563538omplex @ Xs ) @ N ) ) ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % finite_lists_length_le
% 5.31/5.58 thf(fact_4695_finite__lists__length__le,axiom,
% 5.31/5.58 ! [A4: set_VEBT_VEBT,N: nat] :
% 5.31/5.58 ( ( finite5795047828879050333T_VEBT @ A4 )
% 5.31/5.58 => ( finite3004134309566078307T_VEBT
% 5.31/5.58 @ ( collec5608196760682091941T_VEBT
% 5.31/5.58 @ ^ [Xs: list_VEBT_VEBT] :
% 5.31/5.58 ( ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ Xs ) @ A4 )
% 5.31/5.58 & ( ord_less_eq_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ N ) ) ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % finite_lists_length_le
% 5.31/5.58 thf(fact_4696_finite__lists__length__le,axiom,
% 5.31/5.58 ! [A4: set_o,N: nat] :
% 5.31/5.58 ( ( finite_finite_o @ A4 )
% 5.31/5.58 => ( finite_finite_list_o
% 5.31/5.58 @ ( collect_list_o
% 5.31/5.58 @ ^ [Xs: list_o] :
% 5.31/5.58 ( ( ord_less_eq_set_o @ ( set_o2 @ Xs ) @ A4 )
% 5.31/5.58 & ( ord_less_eq_nat @ ( size_size_list_o @ Xs ) @ N ) ) ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % finite_lists_length_le
% 5.31/5.58 thf(fact_4697_finite__lists__length__le,axiom,
% 5.31/5.58 ! [A4: set_int,N: nat] :
% 5.31/5.58 ( ( finite_finite_int @ A4 )
% 5.31/5.58 => ( finite3922522038869484883st_int
% 5.31/5.58 @ ( collect_list_int
% 5.31/5.58 @ ^ [Xs: list_int] :
% 5.31/5.58 ( ( ord_less_eq_set_int @ ( set_int2 @ Xs ) @ A4 )
% 5.31/5.58 & ( ord_less_eq_nat @ ( size_size_list_int @ Xs ) @ N ) ) ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % finite_lists_length_le
% 5.31/5.58 thf(fact_4698_finite__lists__length__le,axiom,
% 5.31/5.58 ! [A4: set_nat,N: nat] :
% 5.31/5.58 ( ( finite_finite_nat @ A4 )
% 5.31/5.58 => ( finite8100373058378681591st_nat
% 5.31/5.58 @ ( collect_list_nat
% 5.31/5.58 @ ^ [Xs: list_nat] :
% 5.31/5.58 ( ( ord_less_eq_set_nat @ ( set_nat2 @ Xs ) @ A4 )
% 5.31/5.58 & ( ord_less_eq_nat @ ( size_size_list_nat @ Xs ) @ N ) ) ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % finite_lists_length_le
% 5.31/5.58 thf(fact_4699_vebt__insert_Osimps_I5_J,axiom,
% 5.31/5.58 ! [Mi: nat,Ma: nat,Va3: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 5.31/5.58 ( ( vEBT_vebt_insert @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary ) @ X )
% 5.31/5.58 = ( if_VEBT_VEBT
% 5.31/5.58 @ ( ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.31/5.58 & ~ ( ( X = Mi )
% 5.31/5.58 | ( X = Ma ) ) )
% 5.31/5.58 @ ( 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 @ Va3 ) ) @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( 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 @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( 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 @ Va3 ) ) @ ( 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 @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ Summary ) )
% 5.31/5.58 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % vebt_insert.simps(5)
% 5.31/5.58 thf(fact_4700_VEBT__internal_Onaive__member_Osimps_I3_J,axiom,
% 5.31/5.58 ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList2: list_VEBT_VEBT,S2: vEBT_VEBT,X: nat] :
% 5.31/5.58 ( ( vEBT_V5719532721284313246member @ ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList2 @ S2 ) @ X )
% 5.31/5.58 = ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.31/5.58 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.31/5.58 & ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % VEBT_internal.naive_member.simps(3)
% 5.31/5.58 thf(fact_4701_VEBT__internal_Omembermima_Osimps_I5_J,axiom,
% 5.31/5.58 ! [V2: nat,TreeList2: list_VEBT_VEBT,Vd2: vEBT_VEBT,X: nat] :
% 5.31/5.58 ( ( vEBT_VEBT_membermima @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList2 @ Vd2 ) @ X )
% 5.31/5.58 = ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.31/5.58 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.31/5.58 & ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % VEBT_internal.membermima.simps(5)
% 5.31/5.58 thf(fact_4702_vebt__insert_Oelims,axiom,
% 5.31/5.58 ! [X: vEBT_VEBT,Xa2: nat,Y: vEBT_VEBT] :
% 5.31/5.58 ( ( ( vEBT_vebt_insert @ X @ Xa2 )
% 5.31/5.58 = Y )
% 5.31/5.58 => ( ! [A3: $o,B3: $o] :
% 5.31/5.58 ( ( X
% 5.31/5.58 = ( vEBT_Leaf @ A3 @ B3 ) )
% 5.31/5.58 => ~ ( ( ( Xa2 = zero_zero_nat )
% 5.31/5.58 => ( Y
% 5.31/5.58 = ( vEBT_Leaf @ $true @ B3 ) ) )
% 5.31/5.58 & ( ( Xa2 != zero_zero_nat )
% 5.31/5.58 => ( ( ( Xa2 = one_one_nat )
% 5.31/5.58 => ( Y
% 5.31/5.58 = ( vEBT_Leaf @ A3 @ $true ) ) )
% 5.31/5.58 & ( ( Xa2 != one_one_nat )
% 5.31/5.58 => ( Y
% 5.31/5.58 = ( vEBT_Leaf @ A3 @ B3 ) ) ) ) ) ) )
% 5.31/5.58 => ( ! [Info: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S: vEBT_VEBT] :
% 5.31/5.58 ( ( X
% 5.31/5.58 = ( vEBT_Node @ Info @ zero_zero_nat @ Ts @ S ) )
% 5.31/5.58 => ( Y
% 5.31/5.58 != ( vEBT_Node @ Info @ zero_zero_nat @ Ts @ S ) ) )
% 5.31/5.58 => ( ! [Info: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S: vEBT_VEBT] :
% 5.31/5.58 ( ( X
% 5.31/5.58 = ( vEBT_Node @ Info @ ( suc @ zero_zero_nat ) @ Ts @ S ) )
% 5.31/5.58 => ( Y
% 5.31/5.58 != ( vEBT_Node @ Info @ ( suc @ zero_zero_nat ) @ Ts @ S ) ) )
% 5.31/5.58 => ( ! [V: nat,TreeList: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.31/5.58 ( ( X
% 5.31/5.58 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V ) ) @ TreeList @ Summary2 ) )
% 5.31/5.58 => ( Y
% 5.31/5.58 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Xa2 @ Xa2 ) ) @ ( suc @ ( suc @ V ) ) @ TreeList @ Summary2 ) ) )
% 5.31/5.58 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.31/5.58 ( ( X
% 5.31/5.58 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary2 ) )
% 5.31/5.58 => ( Y
% 5.31/5.58 != ( if_VEBT_VEBT
% 5.31/5.58 @ ( ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.31/5.58 & ~ ( ( Xa2 = Mi2 )
% 5.31/5.58 | ( Xa2 = Ma2 ) ) )
% 5.31/5.58 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Xa2 @ Mi2 ) @ ( ord_max_nat @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ Ma2 ) ) ) @ ( suc @ ( suc @ Va ) ) @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_insert @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ Summary2 ) )
% 5.31/5.58 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary2 ) ) ) ) ) ) ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % vebt_insert.elims
% 5.31/5.58 thf(fact_4703_vebt__member_Osimps_I5_J,axiom,
% 5.31/5.58 ! [Mi: nat,Ma: nat,Va3: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 5.31/5.58 ( ( vEBT_vebt_member @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary ) @ X )
% 5.31/5.58 = ( ( X != Mi )
% 5.31/5.58 => ( ( X != Ma )
% 5.31/5.58 => ( ~ ( ord_less_nat @ X @ Mi )
% 5.31/5.58 & ( ~ ( ord_less_nat @ X @ Mi )
% 5.31/5.58 => ( ~ ( ord_less_nat @ Ma @ X )
% 5.31/5.58 & ( ~ ( ord_less_nat @ Ma @ X )
% 5.31/5.58 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.31/5.58 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.31/5.58 & ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % vebt_member.simps(5)
% 5.31/5.58 thf(fact_4704_VEBT__internal_Omembermima_Osimps_I4_J,axiom,
% 5.31/5.58 ! [Mi: nat,Ma: nat,V2: nat,TreeList2: list_VEBT_VEBT,Vc: vEBT_VEBT,X: nat] :
% 5.31/5.58 ( ( vEBT_VEBT_membermima @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ V2 ) @ TreeList2 @ Vc ) @ X )
% 5.31/5.58 = ( ( X = Mi )
% 5.31/5.58 | ( X = Ma )
% 5.31/5.58 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.31/5.58 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.31/5.58 & ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % VEBT_internal.membermima.simps(4)
% 5.31/5.58 thf(fact_4705_VEBT__internal_Onaive__member_Oelims_I3_J,axiom,
% 5.31/5.58 ! [X: vEBT_VEBT,Xa2: nat] :
% 5.31/5.58 ( ~ ( vEBT_V5719532721284313246member @ X @ Xa2 )
% 5.31/5.58 => ( ! [A3: $o,B3: $o] :
% 5.31/5.58 ( ( X
% 5.31/5.58 = ( vEBT_Leaf @ A3 @ B3 ) )
% 5.31/5.58 => ( ( ( Xa2 = zero_zero_nat )
% 5.31/5.58 => A3 )
% 5.31/5.58 & ( ( Xa2 != zero_zero_nat )
% 5.31/5.58 => ( ( ( Xa2 = one_one_nat )
% 5.31/5.58 => B3 )
% 5.31/5.58 & ( Xa2 = one_one_nat ) ) ) ) )
% 5.31/5.58 => ( ! [Uu2: option4927543243414619207at_nat,Uv2: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 5.31/5.58 ( X
% 5.31/5.58 != ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw ) )
% 5.31/5.58 => ~ ! [Uy: option4927543243414619207at_nat,V: nat,TreeList: list_VEBT_VEBT] :
% 5.31/5.58 ( ? [S: vEBT_VEBT] :
% 5.31/5.58 ( X
% 5.31/5.58 = ( vEBT_Node @ Uy @ ( suc @ V ) @ TreeList @ S ) )
% 5.31/5.58 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.31/5.58 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.31/5.58 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % VEBT_internal.naive_member.elims(3)
% 5.31/5.58 thf(fact_4706_VEBT__internal_Onaive__member_Oelims_I2_J,axiom,
% 5.31/5.58 ! [X: vEBT_VEBT,Xa2: nat] :
% 5.31/5.58 ( ( vEBT_V5719532721284313246member @ X @ Xa2 )
% 5.31/5.58 => ( ! [A3: $o,B3: $o] :
% 5.31/5.58 ( ( X
% 5.31/5.58 = ( vEBT_Leaf @ A3 @ B3 ) )
% 5.31/5.58 => ~ ( ( ( Xa2 = zero_zero_nat )
% 5.31/5.58 => A3 )
% 5.31/5.58 & ( ( Xa2 != zero_zero_nat )
% 5.31/5.58 => ( ( ( Xa2 = one_one_nat )
% 5.31/5.58 => B3 )
% 5.31/5.58 & ( Xa2 = one_one_nat ) ) ) ) )
% 5.31/5.58 => ~ ! [Uy: option4927543243414619207at_nat,V: nat,TreeList: list_VEBT_VEBT] :
% 5.31/5.58 ( ? [S: vEBT_VEBT] :
% 5.31/5.58 ( X
% 5.31/5.58 = ( vEBT_Node @ Uy @ ( suc @ V ) @ TreeList @ S ) )
% 5.31/5.58 => ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.31/5.58 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.31/5.58 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % VEBT_internal.naive_member.elims(2)
% 5.31/5.58 thf(fact_4707_VEBT__internal_Onaive__member_Oelims_I1_J,axiom,
% 5.31/5.58 ! [X: vEBT_VEBT,Xa2: nat,Y: $o] :
% 5.31/5.58 ( ( ( vEBT_V5719532721284313246member @ X @ Xa2 )
% 5.31/5.58 = Y )
% 5.31/5.58 => ( ! [A3: $o,B3: $o] :
% 5.31/5.58 ( ( X
% 5.31/5.58 = ( vEBT_Leaf @ A3 @ B3 ) )
% 5.31/5.58 => ( Y
% 5.31/5.58 = ( ~ ( ( ( Xa2 = zero_zero_nat )
% 5.31/5.58 => A3 )
% 5.31/5.58 & ( ( Xa2 != zero_zero_nat )
% 5.31/5.58 => ( ( ( Xa2 = one_one_nat )
% 5.31/5.58 => B3 )
% 5.31/5.58 & ( Xa2 = one_one_nat ) ) ) ) ) ) )
% 5.31/5.58 => ( ( ? [Uu2: option4927543243414619207at_nat,Uv2: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 5.31/5.58 ( X
% 5.31/5.58 = ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw ) )
% 5.31/5.58 => Y )
% 5.31/5.58 => ~ ! [Uy: option4927543243414619207at_nat,V: nat,TreeList: list_VEBT_VEBT] :
% 5.31/5.58 ( ? [S: vEBT_VEBT] :
% 5.31/5.58 ( X
% 5.31/5.58 = ( vEBT_Node @ Uy @ ( suc @ V ) @ TreeList @ S ) )
% 5.31/5.58 => ( Y
% 5.31/5.58 = ( ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.31/5.58 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.31/5.58 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) ) ) ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % VEBT_internal.naive_member.elims(1)
% 5.31/5.58 thf(fact_4708_VEBT__internal_Omembermima_Oelims_I2_J,axiom,
% 5.31/5.58 ! [X: vEBT_VEBT,Xa2: nat] :
% 5.31/5.58 ( ( vEBT_VEBT_membermima @ X @ Xa2 )
% 5.31/5.58 => ( ! [Mi2: nat,Ma2: nat] :
% 5.31/5.58 ( ? [Va2: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 5.31/5.58 ( X
% 5.31/5.58 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va2 @ Vb2 ) )
% 5.31/5.58 => ~ ( ( Xa2 = Mi2 )
% 5.31/5.58 | ( Xa2 = Ma2 ) ) )
% 5.31/5.58 => ( ! [Mi2: nat,Ma2: nat,V: nat,TreeList: list_VEBT_VEBT] :
% 5.31/5.58 ( ? [Vc2: vEBT_VEBT] :
% 5.31/5.58 ( X
% 5.31/5.58 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V ) @ TreeList @ Vc2 ) )
% 5.31/5.58 => ~ ( ( Xa2 = Mi2 )
% 5.31/5.58 | ( Xa2 = Ma2 )
% 5.31/5.58 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.31/5.58 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.31/5.58 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) )
% 5.31/5.58 => ~ ! [V: nat,TreeList: list_VEBT_VEBT] :
% 5.31/5.58 ( ? [Vd: vEBT_VEBT] :
% 5.31/5.58 ( X
% 5.31/5.58 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V ) @ TreeList @ Vd ) )
% 5.31/5.58 => ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.31/5.58 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.31/5.58 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % VEBT_internal.membermima.elims(2)
% 5.31/5.58 thf(fact_4709_vebt__member_Oelims_I2_J,axiom,
% 5.31/5.58 ! [X: vEBT_VEBT,Xa2: nat] :
% 5.31/5.58 ( ( vEBT_vebt_member @ X @ Xa2 )
% 5.31/5.58 => ( ! [A3: $o,B3: $o] :
% 5.31/5.58 ( ( X
% 5.31/5.58 = ( vEBT_Leaf @ A3 @ B3 ) )
% 5.31/5.58 => ~ ( ( ( Xa2 = zero_zero_nat )
% 5.31/5.58 => A3 )
% 5.31/5.58 & ( ( Xa2 != zero_zero_nat )
% 5.31/5.58 => ( ( ( Xa2 = one_one_nat )
% 5.31/5.58 => B3 )
% 5.31/5.58 & ( Xa2 = one_one_nat ) ) ) ) )
% 5.31/5.58 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList: list_VEBT_VEBT] :
% 5.31/5.58 ( ? [Summary2: vEBT_VEBT] :
% 5.31/5.58 ( X
% 5.31/5.58 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary2 ) )
% 5.31/5.58 => ~ ( ( Xa2 != Mi2 )
% 5.31/5.58 => ( ( Xa2 != Ma2 )
% 5.31/5.58 => ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.31/5.58 & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.31/5.58 => ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.31/5.58 & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.31/5.58 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.31/5.58 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.31/5.58 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % vebt_member.elims(2)
% 5.31/5.58 thf(fact_4710_VEBT__internal_Omembermima_Oelims_I3_J,axiom,
% 5.31/5.58 ! [X: vEBT_VEBT,Xa2: nat] :
% 5.31/5.58 ( ~ ( vEBT_VEBT_membermima @ X @ Xa2 )
% 5.31/5.58 => ( ! [Uu2: $o,Uv2: $o] :
% 5.31/5.58 ( X
% 5.31/5.58 != ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 5.31/5.58 => ( ! [Ux: list_VEBT_VEBT,Uy: vEBT_VEBT] :
% 5.31/5.58 ( X
% 5.31/5.58 != ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux @ Uy ) )
% 5.31/5.58 => ( ! [Mi2: nat,Ma2: nat] :
% 5.31/5.58 ( ? [Va2: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 5.31/5.58 ( X
% 5.31/5.58 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va2 @ Vb2 ) )
% 5.31/5.58 => ( ( Xa2 = Mi2 )
% 5.31/5.58 | ( Xa2 = Ma2 ) ) )
% 5.31/5.58 => ( ! [Mi2: nat,Ma2: nat,V: nat,TreeList: list_VEBT_VEBT] :
% 5.31/5.58 ( ? [Vc2: vEBT_VEBT] :
% 5.31/5.58 ( X
% 5.31/5.58 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V ) @ TreeList @ Vc2 ) )
% 5.31/5.58 => ( ( Xa2 = Mi2 )
% 5.31/5.58 | ( Xa2 = Ma2 )
% 5.31/5.58 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.31/5.58 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.31/5.58 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) )
% 5.31/5.58 => ~ ! [V: nat,TreeList: list_VEBT_VEBT] :
% 5.31/5.58 ( ? [Vd: vEBT_VEBT] :
% 5.31/5.58 ( X
% 5.31/5.58 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V ) @ TreeList @ Vd ) )
% 5.31/5.58 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.31/5.58 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.31/5.58 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) ) ) ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % VEBT_internal.membermima.elims(3)
% 5.31/5.58 thf(fact_4711_VEBT__internal_Omembermima_Oelims_I1_J,axiom,
% 5.31/5.58 ! [X: vEBT_VEBT,Xa2: nat,Y: $o] :
% 5.31/5.58 ( ( ( vEBT_VEBT_membermima @ X @ Xa2 )
% 5.31/5.58 = Y )
% 5.31/5.58 => ( ( ? [Uu2: $o,Uv2: $o] :
% 5.31/5.58 ( X
% 5.31/5.58 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 5.31/5.58 => Y )
% 5.31/5.58 => ( ( ? [Ux: list_VEBT_VEBT,Uy: vEBT_VEBT] :
% 5.31/5.58 ( X
% 5.31/5.58 = ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux @ Uy ) )
% 5.31/5.58 => Y )
% 5.31/5.58 => ( ! [Mi2: nat,Ma2: nat] :
% 5.31/5.58 ( ? [Va2: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 5.31/5.58 ( X
% 5.31/5.58 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va2 @ Vb2 ) )
% 5.31/5.58 => ( Y
% 5.31/5.58 = ( ~ ( ( Xa2 = Mi2 )
% 5.31/5.58 | ( Xa2 = Ma2 ) ) ) ) )
% 5.31/5.58 => ( ! [Mi2: nat,Ma2: nat,V: nat,TreeList: list_VEBT_VEBT] :
% 5.31/5.58 ( ? [Vc2: vEBT_VEBT] :
% 5.31/5.58 ( X
% 5.31/5.58 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V ) @ TreeList @ Vc2 ) )
% 5.31/5.58 => ( Y
% 5.31/5.58 = ( ~ ( ( Xa2 = Mi2 )
% 5.31/5.58 | ( Xa2 = Ma2 )
% 5.31/5.58 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.31/5.58 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.31/5.58 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) ) ) )
% 5.31/5.58 => ~ ! [V: nat,TreeList: list_VEBT_VEBT] :
% 5.31/5.58 ( ? [Vd: vEBT_VEBT] :
% 5.31/5.58 ( X
% 5.31/5.58 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V ) @ TreeList @ Vd ) )
% 5.31/5.58 => ( Y
% 5.31/5.58 = ( ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.31/5.58 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.31/5.58 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) ) ) ) ) ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % VEBT_internal.membermima.elims(1)
% 5.31/5.58 thf(fact_4712_vebt__member_Oelims_I3_J,axiom,
% 5.31/5.58 ! [X: vEBT_VEBT,Xa2: nat] :
% 5.31/5.58 ( ~ ( vEBT_vebt_member @ X @ Xa2 )
% 5.31/5.58 => ( ! [A3: $o,B3: $o] :
% 5.31/5.58 ( ( X
% 5.31/5.58 = ( vEBT_Leaf @ A3 @ B3 ) )
% 5.31/5.58 => ( ( ( Xa2 = zero_zero_nat )
% 5.31/5.58 => A3 )
% 5.31/5.58 & ( ( Xa2 != zero_zero_nat )
% 5.31/5.58 => ( ( ( Xa2 = one_one_nat )
% 5.31/5.58 => B3 )
% 5.31/5.58 & ( Xa2 = one_one_nat ) ) ) ) )
% 5.31/5.58 => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 5.31/5.58 ( X
% 5.31/5.58 != ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw ) )
% 5.31/5.58 => ( ! [V: product_prod_nat_nat,Uy: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.31/5.58 ( X
% 5.31/5.58 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Uy @ Uz2 ) )
% 5.31/5.58 => ( ! [V: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.31/5.58 ( X
% 5.31/5.58 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) )
% 5.31/5.58 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList: list_VEBT_VEBT] :
% 5.31/5.58 ( ? [Summary2: vEBT_VEBT] :
% 5.31/5.58 ( X
% 5.31/5.58 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary2 ) )
% 5.31/5.58 => ( ( Xa2 != Mi2 )
% 5.31/5.58 => ( ( Xa2 != Ma2 )
% 5.31/5.58 => ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.31/5.58 & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.31/5.58 => ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.31/5.58 & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.31/5.58 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.31/5.58 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.31/5.58 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % vebt_member.elims(3)
% 5.31/5.58 thf(fact_4713_vebt__member_Oelims_I1_J,axiom,
% 5.31/5.58 ! [X: vEBT_VEBT,Xa2: nat,Y: $o] :
% 5.31/5.58 ( ( ( vEBT_vebt_member @ X @ Xa2 )
% 5.31/5.58 = Y )
% 5.31/5.58 => ( ! [A3: $o,B3: $o] :
% 5.31/5.58 ( ( X
% 5.31/5.58 = ( vEBT_Leaf @ A3 @ B3 ) )
% 5.31/5.58 => ( Y
% 5.31/5.58 = ( ~ ( ( ( Xa2 = zero_zero_nat )
% 5.31/5.58 => A3 )
% 5.31/5.58 & ( ( Xa2 != zero_zero_nat )
% 5.31/5.58 => ( ( ( Xa2 = one_one_nat )
% 5.31/5.58 => B3 )
% 5.31/5.58 & ( Xa2 = one_one_nat ) ) ) ) ) ) )
% 5.31/5.58 => ( ( ? [Uu2: nat,Uv2: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 5.31/5.58 ( X
% 5.31/5.58 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw ) )
% 5.31/5.58 => Y )
% 5.31/5.58 => ( ( ? [V: product_prod_nat_nat,Uy: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.31/5.58 ( X
% 5.31/5.58 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Uy @ Uz2 ) )
% 5.31/5.58 => Y )
% 5.31/5.58 => ( ( ? [V: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.31/5.58 ( X
% 5.31/5.58 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) )
% 5.31/5.58 => Y )
% 5.31/5.58 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList: list_VEBT_VEBT] :
% 5.31/5.58 ( ? [Summary2: vEBT_VEBT] :
% 5.31/5.58 ( X
% 5.31/5.58 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary2 ) )
% 5.31/5.58 => ( Y
% 5.31/5.58 = ( ~ ( ( Xa2 != Mi2 )
% 5.31/5.58 => ( ( Xa2 != Ma2 )
% 5.31/5.58 => ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.31/5.58 & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.31/5.58 => ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.31/5.58 & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.31/5.58 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.31/5.58 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.31/5.58 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % vebt_member.elims(1)
% 5.31/5.58 thf(fact_4714_vebt__pred_Osimps_I7_J,axiom,
% 5.31/5.58 ! [Ma: nat,X: nat,Mi: nat,Va3: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.31/5.58 ( ( ( ord_less_nat @ Ma @ X )
% 5.31/5.58 => ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary ) @ X )
% 5.31/5.58 = ( some_nat @ Ma ) ) )
% 5.31/5.58 & ( ~ ( ord_less_nat @ Ma @ X )
% 5.31/5.58 => ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary ) @ X )
% 5.31/5.58 = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.31/5.58 @ ( if_option_nat
% 5.31/5.58 @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.31/5.58 != none_nat )
% 5.31/5.58 & ( vEBT_VEBT_greater @ ( some_nat @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 5.31/5.58 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( some_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_pred @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.31/5.58 @ ( if_option_nat
% 5.31/5.58 @ ( ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.31/5.58 = none_nat )
% 5.31/5.58 @ ( if_option_nat @ ( ord_less_nat @ Mi @ X ) @ ( some_nat @ Mi ) @ none_nat )
% 5.31/5.58 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( 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 @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 5.31/5.58 @ none_nat ) ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % vebt_pred.simps(7)
% 5.31/5.58 thf(fact_4715_vebt__succ_Osimps_I6_J,axiom,
% 5.31/5.58 ! [X: nat,Mi: nat,Ma: nat,Va3: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.31/5.58 ( ( ( ord_less_nat @ X @ Mi )
% 5.31/5.58 => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary ) @ X )
% 5.31/5.58 = ( some_nat @ Mi ) ) )
% 5.31/5.58 & ( ~ ( ord_less_nat @ X @ Mi )
% 5.31/5.58 => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary ) @ X )
% 5.31/5.58 = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.31/5.58 @ ( if_option_nat
% 5.31/5.58 @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.31/5.58 != none_nat )
% 5.31/5.58 & ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 5.31/5.58 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( some_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_succ @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.31/5.58 @ ( if_option_nat
% 5.31/5.58 @ ( ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.31/5.58 = none_nat )
% 5.31/5.58 @ none_nat
% 5.31/5.58 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( 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 @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 5.31/5.58 @ none_nat ) ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % vebt_succ.simps(6)
% 5.31/5.58 thf(fact_4716_vebt__delete_Osimps_I7_J,axiom,
% 5.31/5.58 ! [X: nat,Mi: nat,Ma: nat,Va3: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.31/5.58 ( ( ( ( ord_less_nat @ X @ Mi )
% 5.31/5.58 | ( ord_less_nat @ Ma @ X ) )
% 5.31/5.58 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary ) @ X )
% 5.31/5.58 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary ) ) )
% 5.31/5.58 & ( ~ ( ( ord_less_nat @ X @ Mi )
% 5.31/5.58 | ( ord_less_nat @ Ma @ X ) )
% 5.31/5.58 => ( ( ( ( X = Mi )
% 5.31/5.58 & ( X = Ma ) )
% 5.31/5.58 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary ) @ X )
% 5.31/5.58 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary ) ) )
% 5.31/5.58 & ( ~ ( ( X = Mi )
% 5.31/5.58 & ( X = Ma ) )
% 5.31/5.58 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary ) @ X )
% 5.31/5.58 = ( 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 @ Va3 ) ) @ ( 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 @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.31/5.58 @ ( 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 @ Va3 ) ) @ ( 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 @ Va3 ) ) @ ( 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 @ Va3 ) ) @ ( 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 @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.31/5.58 @ ( vEBT_Node
% 5.31/5.58 @ ( some_P7363390416028606310at_nat
% 5.31/5.58 @ ( 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 @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ Mi )
% 5.31/5.58 @ ( if_nat
% 5.31/5.58 @ ( ( ( X = Mi )
% 5.31/5.58 => ( ( 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 @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) )
% 5.31/5.58 = Ma ) )
% 5.31/5.58 & ( ( X != Mi )
% 5.31/5.58 => ( X = Ma ) ) )
% 5.31/5.58 @ ( if_nat
% 5.31/5.58 @ ( ( 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 @ Va3 ) ) @ ( 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 @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.31/5.58 = none_nat )
% 5.31/5.58 @ ( 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 @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ Mi )
% 5.31/5.58 @ ( plus_plus_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( 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 @ Va3 ) ) @ ( 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 @ Va3 ) ) @ ( 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 @ Va3 ) ) @ ( 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 @ Va3 ) ) @ ( 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 @ Va3 ) ) @ ( 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 @ Va3 ) ) @ ( 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 @ Va3 ) ) @ ( 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 @ Va3 ) ) @ ( 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 @ Va3 ) ) @ ( 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 @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) )
% 5.31/5.58 @ Ma ) ) )
% 5.31/5.58 @ ( suc @ ( suc @ Va3 ) )
% 5.31/5.58 @ ( 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 @ Va3 ) ) @ ( 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 @ Va3 ) ) @ ( 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 @ Va3 ) ) @ ( 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 @ Va3 ) ) @ ( 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 @ Va3 ) ) @ ( 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 @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.31/5.58 @ ( 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 @ Va3 ) ) @ ( 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 @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.31/5.58 @ ( vEBT_Node
% 5.31/5.58 @ ( some_P7363390416028606310at_nat
% 5.31/5.58 @ ( 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 @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ Mi )
% 5.31/5.58 @ ( if_nat
% 5.31/5.58 @ ( ( ( X = Mi )
% 5.31/5.58 => ( ( 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 @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) )
% 5.31/5.58 = Ma ) )
% 5.31/5.58 & ( ( X != Mi )
% 5.31/5.58 => ( X = Ma ) ) )
% 5.31/5.58 @ ( 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 @ Va3 ) ) @ ( 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 @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( 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 @ Va3 ) ) @ ( 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 @ Va3 ) ) @ ( 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 @ Va3 ) ) @ ( 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 @ Va3 ) ) @ ( 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 @ Va3 ) ) @ ( 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 @ Va3 ) ) @ ( 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 @ Va3 ) ) @ ( 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 @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 5.31/5.58 @ Ma ) ) )
% 5.31/5.58 @ ( suc @ ( suc @ Va3 ) )
% 5.31/5.58 @ ( 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 @ Va3 ) ) @ ( 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 @ Va3 ) ) @ ( 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 @ Va3 ) ) @ ( 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 @ Va3 ) ) @ ( 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 @ Va3 ) ) @ ( 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 @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.31/5.58 @ Summary ) )
% 5.31/5.58 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary ) ) ) ) ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % vebt_delete.simps(7)
% 5.31/5.58 thf(fact_4717_vebt__delete_Oelims,axiom,
% 5.31/5.58 ! [X: vEBT_VEBT,Xa2: nat,Y: vEBT_VEBT] :
% 5.31/5.58 ( ( ( vEBT_vebt_delete @ X @ Xa2 )
% 5.31/5.58 = Y )
% 5.31/5.58 => ( ! [A3: $o,B3: $o] :
% 5.31/5.58 ( ( X
% 5.31/5.58 = ( vEBT_Leaf @ A3 @ B3 ) )
% 5.31/5.58 => ( ( Xa2 = zero_zero_nat )
% 5.31/5.58 => ( Y
% 5.31/5.58 != ( vEBT_Leaf @ $false @ B3 ) ) ) )
% 5.31/5.58 => ( ! [A3: $o] :
% 5.31/5.58 ( ? [B3: $o] :
% 5.31/5.58 ( X
% 5.31/5.58 = ( vEBT_Leaf @ A3 @ B3 ) )
% 5.31/5.58 => ( ( Xa2
% 5.31/5.58 = ( suc @ zero_zero_nat ) )
% 5.31/5.58 => ( Y
% 5.31/5.58 != ( vEBT_Leaf @ A3 @ $false ) ) ) )
% 5.31/5.58 => ( ! [A3: $o,B3: $o] :
% 5.31/5.58 ( ( X
% 5.31/5.58 = ( vEBT_Leaf @ A3 @ B3 ) )
% 5.31/5.58 => ( ? [N3: nat] :
% 5.31/5.58 ( Xa2
% 5.31/5.58 = ( suc @ ( suc @ N3 ) ) )
% 5.31/5.58 => ( Y
% 5.31/5.58 != ( vEBT_Leaf @ A3 @ B3 ) ) ) )
% 5.31/5.58 => ( ! [Deg2: nat,TreeList: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.31/5.58 ( ( X
% 5.31/5.58 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList @ Summary2 ) )
% 5.31/5.58 => ( Y
% 5.31/5.58 != ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList @ Summary2 ) ) )
% 5.31/5.58 => ( ! [Mi2: nat,Ma2: nat,TrLst: list_VEBT_VEBT,Smry: vEBT_VEBT] :
% 5.31/5.58 ( ( X
% 5.31/5.58 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ TrLst @ Smry ) )
% 5.31/5.58 => ( Y
% 5.31/5.58 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ TrLst @ Smry ) ) )
% 5.31/5.58 => ( ! [Mi2: nat,Ma2: nat,Tr: list_VEBT_VEBT,Sm: vEBT_VEBT] :
% 5.31/5.58 ( ( X
% 5.31/5.58 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ zero_zero_nat ) @ Tr @ Sm ) )
% 5.31/5.58 => ( Y
% 5.31/5.58 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ zero_zero_nat ) @ Tr @ Sm ) ) )
% 5.31/5.58 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.31/5.58 ( ( X
% 5.31/5.58 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary2 ) )
% 5.31/5.58 => ~ ( ( ( ( ord_less_nat @ Xa2 @ Mi2 )
% 5.31/5.58 | ( ord_less_nat @ Ma2 @ Xa2 ) )
% 5.31/5.58 => ( Y
% 5.31/5.58 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary2 ) ) )
% 5.31/5.58 & ( ~ ( ( ord_less_nat @ Xa2 @ Mi2 )
% 5.31/5.58 | ( ord_less_nat @ Ma2 @ Xa2 ) )
% 5.31/5.58 => ( ( ( ( Xa2 = Mi2 )
% 5.31/5.58 & ( Xa2 = Ma2 ) )
% 5.31/5.58 => ( Y
% 5.31/5.58 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary2 ) ) )
% 5.31/5.58 & ( ~ ( ( Xa2 = Mi2 )
% 5.31/5.58 & ( Xa2 = Ma2 ) )
% 5.31/5.58 => ( Y
% 5.31/5.58 = ( 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 @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.31/5.58 @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( 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 @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( 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 @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.31/5.58 @ ( vEBT_Node
% 5.31/5.58 @ ( some_P7363390416028606310at_nat
% 5.31/5.58 @ ( 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 @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ Mi2 )
% 5.31/5.58 @ ( if_nat
% 5.31/5.58 @ ( ( ( Xa2 = Mi2 )
% 5.31/5.58 => ( ( 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 @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) )
% 5.31/5.58 = Ma2 ) )
% 5.31/5.58 & ( ( Xa2 != Mi2 )
% 5.31/5.58 => ( Xa2 = Ma2 ) ) )
% 5.31/5.58 @ ( if_nat
% 5.31/5.58 @ ( ( 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 @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.31/5.58 = none_nat )
% 5.31/5.58 @ ( 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 @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ Mi2 )
% 5.31/5.58 @ ( 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 @ 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 @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( 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 @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( 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 @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( 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 @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( 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 @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) )
% 5.31/5.58 @ Ma2 ) ) )
% 5.31/5.58 @ ( suc @ ( suc @ Va ) )
% 5.31/5.58 @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( 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 @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( 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 @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( 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 @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.31/5.58 @ ( 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 @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.31/5.58 @ ( vEBT_Node
% 5.31/5.58 @ ( some_P7363390416028606310at_nat
% 5.31/5.58 @ ( 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 @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ Mi2 )
% 5.31/5.58 @ ( if_nat
% 5.31/5.58 @ ( ( ( Xa2 = Mi2 )
% 5.31/5.58 => ( ( 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 @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) )
% 5.31/5.58 = Ma2 ) )
% 5.31/5.58 & ( ( Xa2 != Mi2 )
% 5.31/5.58 => ( Xa2 = Ma2 ) ) )
% 5.31/5.58 @ ( 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 @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( 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 @ TreeList @ ( 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 @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( 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 @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( 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 @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( 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 @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 5.31/5.58 @ Ma2 ) ) )
% 5.31/5.58 @ ( suc @ ( suc @ Va ) )
% 5.31/5.58 @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( 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 @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( 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 @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( 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 @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.31/5.58 @ Summary2 ) )
% 5.31/5.58 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % vebt_delete.elims
% 5.31/5.58 thf(fact_4718_vebt__succ_Oelims,axiom,
% 5.31/5.58 ! [X: vEBT_VEBT,Xa2: nat,Y: option_nat] :
% 5.31/5.58 ( ( ( vEBT_vebt_succ @ X @ Xa2 )
% 5.31/5.58 = Y )
% 5.31/5.58 => ( ! [Uu2: $o,B3: $o] :
% 5.31/5.58 ( ( X
% 5.31/5.58 = ( vEBT_Leaf @ Uu2 @ B3 ) )
% 5.31/5.58 => ( ( Xa2 = zero_zero_nat )
% 5.31/5.58 => ~ ( ( B3
% 5.31/5.58 => ( Y
% 5.31/5.58 = ( some_nat @ one_one_nat ) ) )
% 5.31/5.58 & ( ~ B3
% 5.31/5.58 => ( Y = none_nat ) ) ) ) )
% 5.31/5.58 => ( ( ? [Uv2: $o,Uw: $o] :
% 5.31/5.58 ( X
% 5.31/5.58 = ( vEBT_Leaf @ Uv2 @ Uw ) )
% 5.31/5.58 => ( ? [N3: nat] :
% 5.31/5.58 ( Xa2
% 5.31/5.58 = ( suc @ N3 ) )
% 5.31/5.58 => ( Y != none_nat ) ) )
% 5.31/5.58 => ( ( ? [Ux: nat,Uy: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.31/5.58 ( X
% 5.31/5.58 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux @ Uy @ Uz2 ) )
% 5.31/5.58 => ( Y != none_nat ) )
% 5.31/5.58 => ( ( ? [V: product_prod_nat_nat,Vc2: list_VEBT_VEBT,Vd: vEBT_VEBT] :
% 5.31/5.58 ( X
% 5.31/5.58 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Vc2 @ Vd ) )
% 5.31/5.58 => ( Y != none_nat ) )
% 5.31/5.58 => ( ( ? [V: product_prod_nat_nat,Vg: list_VEBT_VEBT,Vh: vEBT_VEBT] :
% 5.31/5.58 ( X
% 5.31/5.58 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vg @ Vh ) )
% 5.31/5.58 => ( Y != none_nat ) )
% 5.31/5.58 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.31/5.58 ( ( X
% 5.31/5.58 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary2 ) )
% 5.31/5.58 => ~ ( ( ( ord_less_nat @ Xa2 @ Mi2 )
% 5.31/5.58 => ( Y
% 5.31/5.58 = ( some_nat @ Mi2 ) ) )
% 5.31/5.58 & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.31/5.58 => ( Y
% 5.31/5.58 = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.31/5.58 @ ( if_option_nat
% 5.31/5.58 @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.31/5.58 != none_nat )
% 5.31/5.58 & ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 5.31/5.58 @ ( 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 @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_succ @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.31/5.58 @ ( if_option_nat
% 5.31/5.58 @ ( ( vEBT_vebt_succ @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.31/5.58 = none_nat )
% 5.31/5.58 @ none_nat
% 5.31/5.58 @ ( 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 @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_succ @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 5.31/5.58 @ none_nat ) ) ) ) ) ) ) ) ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % vebt_succ.elims
% 5.31/5.58 thf(fact_4719_vebt__pred_Oelims,axiom,
% 5.31/5.58 ! [X: vEBT_VEBT,Xa2: nat,Y: option_nat] :
% 5.31/5.58 ( ( ( vEBT_vebt_pred @ X @ Xa2 )
% 5.31/5.58 = Y )
% 5.31/5.58 => ( ( ? [Uu2: $o,Uv2: $o] :
% 5.31/5.58 ( X
% 5.31/5.58 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 5.31/5.58 => ( ( Xa2 = zero_zero_nat )
% 5.31/5.58 => ( Y != none_nat ) ) )
% 5.31/5.58 => ( ! [A3: $o] :
% 5.31/5.58 ( ? [Uw: $o] :
% 5.31/5.58 ( X
% 5.31/5.58 = ( vEBT_Leaf @ A3 @ Uw ) )
% 5.31/5.58 => ( ( Xa2
% 5.31/5.58 = ( suc @ zero_zero_nat ) )
% 5.31/5.58 => ~ ( ( A3
% 5.31/5.58 => ( Y
% 5.31/5.58 = ( some_nat @ zero_zero_nat ) ) )
% 5.31/5.58 & ( ~ A3
% 5.31/5.58 => ( Y = none_nat ) ) ) ) )
% 5.31/5.58 => ( ! [A3: $o,B3: $o] :
% 5.31/5.58 ( ( X
% 5.31/5.58 = ( vEBT_Leaf @ A3 @ B3 ) )
% 5.31/5.58 => ( ? [Va: nat] :
% 5.31/5.58 ( Xa2
% 5.31/5.58 = ( suc @ ( suc @ Va ) ) )
% 5.31/5.58 => ~ ( ( B3
% 5.31/5.58 => ( Y
% 5.31/5.58 = ( some_nat @ one_one_nat ) ) )
% 5.31/5.58 & ( ~ B3
% 5.31/5.58 => ( ( A3
% 5.31/5.58 => ( Y
% 5.31/5.58 = ( some_nat @ zero_zero_nat ) ) )
% 5.31/5.58 & ( ~ A3
% 5.31/5.58 => ( Y = none_nat ) ) ) ) ) ) )
% 5.31/5.58 => ( ( ? [Uy: nat,Uz2: list_VEBT_VEBT,Va2: vEBT_VEBT] :
% 5.31/5.58 ( X
% 5.31/5.58 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy @ Uz2 @ Va2 ) )
% 5.31/5.58 => ( Y != none_nat ) )
% 5.31/5.58 => ( ( ? [V: product_prod_nat_nat,Vd: list_VEBT_VEBT,Ve: vEBT_VEBT] :
% 5.31/5.58 ( X
% 5.31/5.58 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Vd @ Ve ) )
% 5.31/5.58 => ( Y != none_nat ) )
% 5.31/5.58 => ( ( ? [V: product_prod_nat_nat,Vh: list_VEBT_VEBT,Vi: vEBT_VEBT] :
% 5.31/5.58 ( X
% 5.31/5.58 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vh @ Vi ) )
% 5.31/5.58 => ( Y != none_nat ) )
% 5.31/5.58 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.31/5.58 ( ( X
% 5.31/5.58 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary2 ) )
% 5.31/5.58 => ~ ( ( ( ord_less_nat @ Ma2 @ Xa2 )
% 5.31/5.58 => ( Y
% 5.31/5.58 = ( some_nat @ Ma2 ) ) )
% 5.31/5.58 & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.31/5.58 => ( Y
% 5.31/5.58 = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.31/5.58 @ ( if_option_nat
% 5.31/5.58 @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.31/5.58 != none_nat )
% 5.31/5.58 & ( vEBT_VEBT_greater @ ( some_nat @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 5.31/5.58 @ ( 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 @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_pred @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.31/5.58 @ ( if_option_nat
% 5.31/5.58 @ ( ( vEBT_vebt_pred @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.31/5.58 = none_nat )
% 5.31/5.58 @ ( if_option_nat @ ( ord_less_nat @ Mi2 @ Xa2 ) @ ( some_nat @ Mi2 ) @ none_nat )
% 5.31/5.58 @ ( 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 @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_pred @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 5.31/5.58 @ none_nat ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % vebt_pred.elims
% 5.31/5.58 thf(fact_4720_finite__nth__roots,axiom,
% 5.31/5.58 ! [N: nat,C2: complex] :
% 5.31/5.58 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.58 => ( finite3207457112153483333omplex
% 5.31/5.58 @ ( collect_complex
% 5.31/5.58 @ ^ [Z4: complex] :
% 5.31/5.58 ( ( power_power_complex @ Z4 @ N )
% 5.31/5.58 = C2 ) ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % finite_nth_roots
% 5.31/5.58 thf(fact_4721_card__roots__unity,axiom,
% 5.31/5.58 ! [N: nat] :
% 5.31/5.58 ( ( ord_less_eq_nat @ one_one_nat @ N )
% 5.31/5.58 => ( ord_less_eq_nat
% 5.31/5.58 @ ( finite_card_real
% 5.31/5.58 @ ( collect_real
% 5.31/5.58 @ ^ [Z4: real] :
% 5.31/5.58 ( ( power_power_real @ Z4 @ N )
% 5.31/5.58 = one_one_real ) ) )
% 5.31/5.58 @ N ) ) ).
% 5.31/5.58
% 5.31/5.58 % card_roots_unity
% 5.31/5.58 thf(fact_4722_card__roots__unity,axiom,
% 5.31/5.58 ! [N: nat] :
% 5.31/5.58 ( ( ord_less_eq_nat @ one_one_nat @ N )
% 5.31/5.58 => ( ord_less_eq_nat
% 5.31/5.58 @ ( finite_card_complex
% 5.31/5.58 @ ( collect_complex
% 5.31/5.58 @ ^ [Z4: complex] :
% 5.31/5.58 ( ( power_power_complex @ Z4 @ N )
% 5.31/5.58 = one_one_complex ) ) )
% 5.31/5.58 @ N ) ) ).
% 5.31/5.58
% 5.31/5.58 % card_roots_unity
% 5.31/5.58 thf(fact_4723_finite__roots__unity,axiom,
% 5.31/5.58 ! [N: nat] :
% 5.31/5.58 ( ( ord_less_eq_nat @ one_one_nat @ N )
% 5.31/5.58 => ( finite_finite_real
% 5.31/5.58 @ ( collect_real
% 5.31/5.58 @ ^ [Z4: real] :
% 5.31/5.58 ( ( power_power_real @ Z4 @ N )
% 5.31/5.58 = one_one_real ) ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % finite_roots_unity
% 5.31/5.58 thf(fact_4724_finite__roots__unity,axiom,
% 5.31/5.58 ! [N: nat] :
% 5.31/5.58 ( ( ord_less_eq_nat @ one_one_nat @ N )
% 5.31/5.58 => ( finite3207457112153483333omplex
% 5.31/5.58 @ ( collect_complex
% 5.31/5.58 @ ^ [Z4: complex] :
% 5.31/5.58 ( ( power_power_complex @ Z4 @ N )
% 5.31/5.58 = one_one_complex ) ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % finite_roots_unity
% 5.31/5.58 thf(fact_4725_vebt__succ_Opelims,axiom,
% 5.31/5.58 ! [X: vEBT_VEBT,Xa2: nat,Y: option_nat] :
% 5.31/5.58 ( ( ( vEBT_vebt_succ @ X @ Xa2 )
% 5.31/5.58 = Y )
% 5.31/5.58 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 5.31/5.58 => ( ! [Uu2: $o,B3: $o] :
% 5.31/5.58 ( ( X
% 5.31/5.58 = ( vEBT_Leaf @ Uu2 @ B3 ) )
% 5.31/5.58 => ( ( Xa2 = zero_zero_nat )
% 5.31/5.58 => ( ( ( B3
% 5.31/5.58 => ( Y
% 5.31/5.58 = ( some_nat @ one_one_nat ) ) )
% 5.31/5.58 & ( ~ B3
% 5.31/5.58 => ( Y = none_nat ) ) )
% 5.31/5.58 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ B3 ) @ zero_zero_nat ) ) ) ) )
% 5.31/5.58 => ( ! [Uv2: $o,Uw: $o] :
% 5.31/5.58 ( ( X
% 5.31/5.58 = ( vEBT_Leaf @ Uv2 @ Uw ) )
% 5.31/5.58 => ! [N3: nat] :
% 5.31/5.58 ( ( Xa2
% 5.31/5.58 = ( suc @ N3 ) )
% 5.31/5.58 => ( ( Y = none_nat )
% 5.31/5.58 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uv2 @ Uw ) @ ( suc @ N3 ) ) ) ) ) )
% 5.31/5.58 => ( ! [Ux: nat,Uy: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.31/5.58 ( ( X
% 5.31/5.58 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux @ Uy @ Uz2 ) )
% 5.31/5.58 => ( ( Y = none_nat )
% 5.31/5.58 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux @ Uy @ Uz2 ) @ Xa2 ) ) ) )
% 5.31/5.58 => ( ! [V: product_prod_nat_nat,Vc2: list_VEBT_VEBT,Vd: vEBT_VEBT] :
% 5.31/5.58 ( ( X
% 5.31/5.58 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Vc2 @ Vd ) )
% 5.31/5.58 => ( ( Y = none_nat )
% 5.31/5.58 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Vc2 @ Vd ) @ Xa2 ) ) ) )
% 5.31/5.58 => ( ! [V: product_prod_nat_nat,Vg: list_VEBT_VEBT,Vh: vEBT_VEBT] :
% 5.31/5.58 ( ( X
% 5.31/5.58 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vg @ Vh ) )
% 5.31/5.58 => ( ( Y = none_nat )
% 5.31/5.58 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vg @ Vh ) @ Xa2 ) ) ) )
% 5.31/5.58 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.31/5.58 ( ( X
% 5.31/5.58 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary2 ) )
% 5.31/5.58 => ( ( ( ( ord_less_nat @ Xa2 @ Mi2 )
% 5.31/5.58 => ( Y
% 5.31/5.58 = ( some_nat @ Mi2 ) ) )
% 5.31/5.58 & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.31/5.58 => ( Y
% 5.31/5.58 = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.31/5.58 @ ( if_option_nat
% 5.31/5.58 @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.31/5.58 != none_nat )
% 5.31/5.58 & ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 5.31/5.58 @ ( 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 @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_succ @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.31/5.58 @ ( if_option_nat
% 5.31/5.58 @ ( ( vEBT_vebt_succ @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.31/5.58 = none_nat )
% 5.31/5.58 @ none_nat
% 5.31/5.58 @ ( 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 @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_succ @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 5.31/5.58 @ none_nat ) ) ) )
% 5.31/5.58 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % vebt_succ.pelims
% 5.31/5.58 thf(fact_4726_vebt__pred_Opelims,axiom,
% 5.31/5.58 ! [X: vEBT_VEBT,Xa2: nat,Y: option_nat] :
% 5.31/5.58 ( ( ( vEBT_vebt_pred @ X @ Xa2 )
% 5.31/5.58 = Y )
% 5.31/5.58 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 5.31/5.58 => ( ! [Uu2: $o,Uv2: $o] :
% 5.31/5.58 ( ( X
% 5.31/5.58 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 5.31/5.58 => ( ( Xa2 = zero_zero_nat )
% 5.31/5.58 => ( ( Y = none_nat )
% 5.31/5.58 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ zero_zero_nat ) ) ) ) )
% 5.31/5.58 => ( ! [A3: $o,Uw: $o] :
% 5.31/5.58 ( ( X
% 5.31/5.58 = ( vEBT_Leaf @ A3 @ Uw ) )
% 5.31/5.58 => ( ( Xa2
% 5.31/5.58 = ( suc @ zero_zero_nat ) )
% 5.31/5.58 => ( ( ( A3
% 5.31/5.58 => ( Y
% 5.31/5.58 = ( some_nat @ zero_zero_nat ) ) )
% 5.31/5.58 & ( ~ A3
% 5.31/5.58 => ( Y = none_nat ) ) )
% 5.31/5.58 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ Uw ) @ ( suc @ zero_zero_nat ) ) ) ) ) )
% 5.31/5.58 => ( ! [A3: $o,B3: $o] :
% 5.31/5.58 ( ( X
% 5.31/5.58 = ( vEBT_Leaf @ A3 @ B3 ) )
% 5.31/5.58 => ! [Va: nat] :
% 5.31/5.58 ( ( Xa2
% 5.31/5.58 = ( suc @ ( suc @ Va ) ) )
% 5.31/5.58 => ( ( ( B3
% 5.31/5.58 => ( Y
% 5.31/5.58 = ( some_nat @ one_one_nat ) ) )
% 5.31/5.58 & ( ~ B3
% 5.31/5.58 => ( ( A3
% 5.31/5.58 => ( Y
% 5.31/5.58 = ( some_nat @ zero_zero_nat ) ) )
% 5.31/5.58 & ( ~ A3
% 5.31/5.58 => ( Y = none_nat ) ) ) ) )
% 5.31/5.58 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ ( suc @ ( suc @ Va ) ) ) ) ) ) )
% 5.31/5.58 => ( ! [Uy: nat,Uz2: list_VEBT_VEBT,Va2: vEBT_VEBT] :
% 5.31/5.58 ( ( X
% 5.31/5.58 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy @ Uz2 @ Va2 ) )
% 5.31/5.58 => ( ( Y = none_nat )
% 5.31/5.58 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy @ Uz2 @ Va2 ) @ Xa2 ) ) ) )
% 5.31/5.58 => ( ! [V: product_prod_nat_nat,Vd: list_VEBT_VEBT,Ve: vEBT_VEBT] :
% 5.31/5.58 ( ( X
% 5.31/5.58 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Vd @ Ve ) )
% 5.31/5.58 => ( ( Y = none_nat )
% 5.31/5.58 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Vd @ Ve ) @ Xa2 ) ) ) )
% 5.31/5.58 => ( ! [V: product_prod_nat_nat,Vh: list_VEBT_VEBT,Vi: vEBT_VEBT] :
% 5.31/5.58 ( ( X
% 5.31/5.58 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vh @ Vi ) )
% 5.31/5.58 => ( ( Y = none_nat )
% 5.31/5.58 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vh @ Vi ) @ Xa2 ) ) ) )
% 5.31/5.58 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.31/5.58 ( ( X
% 5.31/5.58 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary2 ) )
% 5.31/5.58 => ( ( ( ( ord_less_nat @ Ma2 @ Xa2 )
% 5.31/5.58 => ( Y
% 5.31/5.58 = ( some_nat @ Ma2 ) ) )
% 5.31/5.58 & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.31/5.58 => ( Y
% 5.31/5.58 = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.31/5.58 @ ( if_option_nat
% 5.31/5.58 @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.31/5.58 != none_nat )
% 5.31/5.58 & ( vEBT_VEBT_greater @ ( some_nat @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 5.31/5.58 @ ( 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 @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_pred @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.31/5.58 @ ( if_option_nat
% 5.31/5.58 @ ( ( vEBT_vebt_pred @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.31/5.58 = none_nat )
% 5.31/5.58 @ ( if_option_nat @ ( ord_less_nat @ Mi2 @ Xa2 ) @ ( some_nat @ Mi2 ) @ none_nat )
% 5.31/5.58 @ ( 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 @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_pred @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 5.31/5.58 @ none_nat ) ) ) )
% 5.31/5.58 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % vebt_pred.pelims
% 5.31/5.58 thf(fact_4727_vebt__delete_Opelims,axiom,
% 5.31/5.58 ! [X: vEBT_VEBT,Xa2: nat,Y: vEBT_VEBT] :
% 5.31/5.58 ( ( ( vEBT_vebt_delete @ X @ Xa2 )
% 5.31/5.58 = Y )
% 5.31/5.58 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_delete_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 5.31/5.58 => ( ! [A3: $o,B3: $o] :
% 5.31/5.58 ( ( X
% 5.31/5.58 = ( vEBT_Leaf @ A3 @ B3 ) )
% 5.31/5.58 => ( ( Xa2 = zero_zero_nat )
% 5.31/5.58 => ( ( Y
% 5.31/5.58 = ( vEBT_Leaf @ $false @ B3 ) )
% 5.31/5.58 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_delete_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ zero_zero_nat ) ) ) ) )
% 5.31/5.58 => ( ! [A3: $o,B3: $o] :
% 5.31/5.58 ( ( X
% 5.31/5.58 = ( vEBT_Leaf @ A3 @ B3 ) )
% 5.31/5.58 => ( ( Xa2
% 5.31/5.58 = ( suc @ zero_zero_nat ) )
% 5.31/5.58 => ( ( Y
% 5.31/5.58 = ( vEBT_Leaf @ A3 @ $false ) )
% 5.31/5.58 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_delete_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ ( suc @ zero_zero_nat ) ) ) ) ) )
% 5.31/5.58 => ( ! [A3: $o,B3: $o] :
% 5.31/5.58 ( ( X
% 5.31/5.58 = ( vEBT_Leaf @ A3 @ B3 ) )
% 5.31/5.58 => ! [N3: nat] :
% 5.31/5.58 ( ( Xa2
% 5.31/5.58 = ( suc @ ( suc @ N3 ) ) )
% 5.31/5.58 => ( ( Y
% 5.31/5.58 = ( vEBT_Leaf @ A3 @ B3 ) )
% 5.31/5.58 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_delete_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ ( suc @ ( suc @ N3 ) ) ) ) ) ) )
% 5.31/5.58 => ( ! [Deg2: nat,TreeList: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.31/5.58 ( ( X
% 5.31/5.58 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList @ Summary2 ) )
% 5.31/5.58 => ( ( Y
% 5.31/5.58 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList @ Summary2 ) )
% 5.31/5.58 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_delete_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList @ Summary2 ) @ Xa2 ) ) ) )
% 5.31/5.58 => ( ! [Mi2: nat,Ma2: nat,TrLst: list_VEBT_VEBT,Smry: vEBT_VEBT] :
% 5.31/5.58 ( ( X
% 5.31/5.58 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ TrLst @ Smry ) )
% 5.31/5.58 => ( ( Y
% 5.31/5.58 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ TrLst @ Smry ) )
% 5.31/5.58 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_delete_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ TrLst @ Smry ) @ Xa2 ) ) ) )
% 5.31/5.58 => ( ! [Mi2: nat,Ma2: nat,Tr: list_VEBT_VEBT,Sm: vEBT_VEBT] :
% 5.31/5.58 ( ( X
% 5.31/5.58 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ zero_zero_nat ) @ Tr @ Sm ) )
% 5.31/5.58 => ( ( Y
% 5.31/5.58 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ zero_zero_nat ) @ Tr @ Sm ) )
% 5.31/5.58 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_delete_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ zero_zero_nat ) @ Tr @ Sm ) @ Xa2 ) ) ) )
% 5.31/5.58 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.31/5.58 ( ( X
% 5.31/5.58 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary2 ) )
% 5.31/5.58 => ( ( ( ( ( ord_less_nat @ Xa2 @ Mi2 )
% 5.31/5.58 | ( ord_less_nat @ Ma2 @ Xa2 ) )
% 5.31/5.58 => ( Y
% 5.31/5.58 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary2 ) ) )
% 5.31/5.58 & ( ~ ( ( ord_less_nat @ Xa2 @ Mi2 )
% 5.31/5.58 | ( ord_less_nat @ Ma2 @ Xa2 ) )
% 5.31/5.58 => ( ( ( ( Xa2 = Mi2 )
% 5.31/5.58 & ( Xa2 = Ma2 ) )
% 5.31/5.58 => ( Y
% 5.31/5.58 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary2 ) ) )
% 5.31/5.58 & ( ~ ( ( Xa2 = Mi2 )
% 5.31/5.58 & ( Xa2 = Ma2 ) )
% 5.31/5.58 => ( Y
% 5.31/5.58 = ( 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 @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.31/5.58 @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( 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 @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( 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 @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.31/5.58 @ ( vEBT_Node
% 5.31/5.58 @ ( some_P7363390416028606310at_nat
% 5.31/5.58 @ ( 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 @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ Mi2 )
% 5.31/5.58 @ ( if_nat
% 5.31/5.58 @ ( ( ( Xa2 = Mi2 )
% 5.31/5.58 => ( ( 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 @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) )
% 5.31/5.58 = Ma2 ) )
% 5.31/5.58 & ( ( Xa2 != Mi2 )
% 5.31/5.58 => ( Xa2 = Ma2 ) ) )
% 5.31/5.58 @ ( if_nat
% 5.31/5.58 @ ( ( 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 @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.31/5.58 = none_nat )
% 5.31/5.58 @ ( 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 @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ Mi2 )
% 5.31/5.58 @ ( 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 @ 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 @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( 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 @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( 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 @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( 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 @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( 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 @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) )
% 5.31/5.58 @ Ma2 ) ) )
% 5.31/5.58 @ ( suc @ ( suc @ Va ) )
% 5.31/5.58 @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( 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 @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( 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 @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( 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 @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.31/5.58 @ ( 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 @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.31/5.58 @ ( vEBT_Node
% 5.31/5.58 @ ( some_P7363390416028606310at_nat
% 5.31/5.58 @ ( 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 @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ Mi2 )
% 5.31/5.58 @ ( if_nat
% 5.31/5.58 @ ( ( ( Xa2 = Mi2 )
% 5.31/5.58 => ( ( 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 @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) )
% 5.31/5.58 = Ma2 ) )
% 5.31/5.58 & ( ( Xa2 != Mi2 )
% 5.31/5.58 => ( Xa2 = Ma2 ) ) )
% 5.31/5.58 @ ( 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 @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( 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 @ TreeList @ ( 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 @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( 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 @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( 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 @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( 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 @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 5.31/5.58 @ Ma2 ) ) )
% 5.31/5.58 @ ( suc @ ( suc @ Va ) )
% 5.31/5.58 @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( 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 @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( 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 @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( 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 @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.31/5.58 @ Summary2 ) )
% 5.31/5.58 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary2 ) ) ) ) ) ) )
% 5.31/5.58 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_delete_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % vebt_delete.pelims
% 5.31/5.58 thf(fact_4728_vebt__insert_Opelims,axiom,
% 5.31/5.58 ! [X: vEBT_VEBT,Xa2: nat,Y: vEBT_VEBT] :
% 5.31/5.58 ( ( ( vEBT_vebt_insert @ X @ Xa2 )
% 5.31/5.58 = Y )
% 5.31/5.58 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 5.31/5.58 => ( ! [A3: $o,B3: $o] :
% 5.31/5.58 ( ( X
% 5.31/5.58 = ( vEBT_Leaf @ A3 @ B3 ) )
% 5.31/5.58 => ( ( ( ( Xa2 = zero_zero_nat )
% 5.31/5.58 => ( Y
% 5.31/5.58 = ( vEBT_Leaf @ $true @ B3 ) ) )
% 5.31/5.58 & ( ( Xa2 != zero_zero_nat )
% 5.31/5.58 => ( ( ( Xa2 = one_one_nat )
% 5.31/5.58 => ( Y
% 5.31/5.58 = ( vEBT_Leaf @ A3 @ $true ) ) )
% 5.31/5.58 & ( ( Xa2 != one_one_nat )
% 5.31/5.58 => ( Y
% 5.31/5.58 = ( vEBT_Leaf @ A3 @ B3 ) ) ) ) ) )
% 5.31/5.58 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ Xa2 ) ) ) )
% 5.31/5.58 => ( ! [Info: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S: vEBT_VEBT] :
% 5.31/5.58 ( ( X
% 5.31/5.58 = ( vEBT_Node @ Info @ zero_zero_nat @ Ts @ S ) )
% 5.31/5.58 => ( ( Y
% 5.31/5.58 = ( vEBT_Node @ Info @ zero_zero_nat @ Ts @ S ) )
% 5.31/5.58 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info @ zero_zero_nat @ Ts @ S ) @ Xa2 ) ) ) )
% 5.31/5.58 => ( ! [Info: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S: vEBT_VEBT] :
% 5.31/5.58 ( ( X
% 5.31/5.58 = ( vEBT_Node @ Info @ ( suc @ zero_zero_nat ) @ Ts @ S ) )
% 5.31/5.58 => ( ( Y
% 5.31/5.58 = ( vEBT_Node @ Info @ ( suc @ zero_zero_nat ) @ Ts @ S ) )
% 5.31/5.58 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info @ ( suc @ zero_zero_nat ) @ Ts @ S ) @ Xa2 ) ) ) )
% 5.31/5.58 => ( ! [V: nat,TreeList: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.31/5.58 ( ( X
% 5.31/5.58 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V ) ) @ TreeList @ Summary2 ) )
% 5.31/5.58 => ( ( Y
% 5.31/5.58 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Xa2 @ Xa2 ) ) @ ( suc @ ( suc @ V ) ) @ TreeList @ Summary2 ) )
% 5.31/5.58 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V ) ) @ TreeList @ Summary2 ) @ Xa2 ) ) ) )
% 5.31/5.58 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.31/5.58 ( ( X
% 5.31/5.58 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary2 ) )
% 5.31/5.58 => ( ( Y
% 5.31/5.58 = ( if_VEBT_VEBT
% 5.31/5.58 @ ( ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.31/5.58 & ~ ( ( Xa2 = Mi2 )
% 5.31/5.58 | ( Xa2 = Ma2 ) ) )
% 5.31/5.58 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Xa2 @ Mi2 ) @ ( ord_max_nat @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ Ma2 ) ) ) @ ( suc @ ( suc @ Va ) ) @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_insert @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ Summary2 ) )
% 5.31/5.58 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary2 ) ) )
% 5.31/5.58 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % vebt_insert.pelims
% 5.31/5.58 thf(fact_4729_low__def,axiom,
% 5.31/5.58 ( vEBT_VEBT_low
% 5.31/5.58 = ( ^ [X4: nat,N4: nat] : ( modulo_modulo_nat @ X4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % low_def
% 5.31/5.58 thf(fact_4730_mod__0,axiom,
% 5.31/5.58 ! [A: nat] :
% 5.31/5.58 ( ( modulo_modulo_nat @ zero_zero_nat @ A )
% 5.31/5.58 = zero_zero_nat ) ).
% 5.31/5.58
% 5.31/5.58 % mod_0
% 5.31/5.58 thf(fact_4731_mod__0,axiom,
% 5.31/5.58 ! [A: int] :
% 5.31/5.58 ( ( modulo_modulo_int @ zero_zero_int @ A )
% 5.31/5.58 = zero_zero_int ) ).
% 5.31/5.58
% 5.31/5.58 % mod_0
% 5.31/5.58 thf(fact_4732_mod__0,axiom,
% 5.31/5.58 ! [A: code_natural] :
% 5.31/5.58 ( ( modulo8411746178871703098atural @ zero_z2226904508553997617atural @ A )
% 5.31/5.58 = zero_z2226904508553997617atural ) ).
% 5.31/5.58
% 5.31/5.58 % mod_0
% 5.31/5.58 thf(fact_4733_mod__by__0,axiom,
% 5.31/5.58 ! [A: nat] :
% 5.31/5.58 ( ( modulo_modulo_nat @ A @ zero_zero_nat )
% 5.31/5.58 = A ) ).
% 5.31/5.58
% 5.31/5.58 % mod_by_0
% 5.31/5.58 thf(fact_4734_mod__by__0,axiom,
% 5.31/5.58 ! [A: int] :
% 5.31/5.58 ( ( modulo_modulo_int @ A @ zero_zero_int )
% 5.31/5.58 = A ) ).
% 5.31/5.58
% 5.31/5.58 % mod_by_0
% 5.31/5.58 thf(fact_4735_mod__by__0,axiom,
% 5.31/5.58 ! [A: code_natural] :
% 5.31/5.58 ( ( modulo8411746178871703098atural @ A @ zero_z2226904508553997617atural )
% 5.31/5.58 = A ) ).
% 5.31/5.58
% 5.31/5.58 % mod_by_0
% 5.31/5.58 thf(fact_4736_mod__self,axiom,
% 5.31/5.58 ! [A: nat] :
% 5.31/5.58 ( ( modulo_modulo_nat @ A @ A )
% 5.31/5.58 = zero_zero_nat ) ).
% 5.31/5.58
% 5.31/5.58 % mod_self
% 5.31/5.58 thf(fact_4737_mod__self,axiom,
% 5.31/5.58 ! [A: int] :
% 5.31/5.58 ( ( modulo_modulo_int @ A @ A )
% 5.31/5.58 = zero_zero_int ) ).
% 5.31/5.58
% 5.31/5.58 % mod_self
% 5.31/5.58 thf(fact_4738_mod__self,axiom,
% 5.31/5.58 ! [A: code_natural] :
% 5.31/5.58 ( ( modulo8411746178871703098atural @ A @ A )
% 5.31/5.58 = zero_z2226904508553997617atural ) ).
% 5.31/5.58
% 5.31/5.58 % mod_self
% 5.31/5.58 thf(fact_4739_bits__mod__0,axiom,
% 5.31/5.58 ! [A: nat] :
% 5.31/5.58 ( ( modulo_modulo_nat @ zero_zero_nat @ A )
% 5.31/5.58 = zero_zero_nat ) ).
% 5.31/5.58
% 5.31/5.58 % bits_mod_0
% 5.31/5.58 thf(fact_4740_bits__mod__0,axiom,
% 5.31/5.58 ! [A: int] :
% 5.31/5.58 ( ( modulo_modulo_int @ zero_zero_int @ A )
% 5.31/5.58 = zero_zero_int ) ).
% 5.31/5.58
% 5.31/5.58 % bits_mod_0
% 5.31/5.58 thf(fact_4741_bits__mod__0,axiom,
% 5.31/5.58 ! [A: code_natural] :
% 5.31/5.58 ( ( modulo8411746178871703098atural @ zero_z2226904508553997617atural @ A )
% 5.31/5.58 = zero_z2226904508553997617atural ) ).
% 5.31/5.58
% 5.31/5.58 % bits_mod_0
% 5.31/5.58 thf(fact_4742_mod__mult__self2__is__0,axiom,
% 5.31/5.58 ! [A: nat,B: nat] :
% 5.31/5.58 ( ( modulo_modulo_nat @ ( times_times_nat @ A @ B ) @ B )
% 5.31/5.58 = zero_zero_nat ) ).
% 5.31/5.58
% 5.31/5.58 % mod_mult_self2_is_0
% 5.31/5.58 thf(fact_4743_mod__mult__self2__is__0,axiom,
% 5.31/5.58 ! [A: int,B: int] :
% 5.31/5.58 ( ( modulo_modulo_int @ ( times_times_int @ A @ B ) @ B )
% 5.31/5.58 = zero_zero_int ) ).
% 5.31/5.58
% 5.31/5.58 % mod_mult_self2_is_0
% 5.31/5.58 thf(fact_4744_mod__mult__self2__is__0,axiom,
% 5.31/5.58 ! [A: code_natural,B: code_natural] :
% 5.31/5.58 ( ( modulo8411746178871703098atural @ ( times_2397367101498566445atural @ A @ B ) @ B )
% 5.31/5.58 = zero_z2226904508553997617atural ) ).
% 5.31/5.58
% 5.31/5.58 % mod_mult_self2_is_0
% 5.31/5.58 thf(fact_4745_mod__mult__self1__is__0,axiom,
% 5.31/5.58 ! [B: nat,A: nat] :
% 5.31/5.58 ( ( modulo_modulo_nat @ ( times_times_nat @ B @ A ) @ B )
% 5.31/5.58 = zero_zero_nat ) ).
% 5.31/5.58
% 5.31/5.58 % mod_mult_self1_is_0
% 5.31/5.58 thf(fact_4746_mod__mult__self1__is__0,axiom,
% 5.31/5.58 ! [B: int,A: int] :
% 5.31/5.58 ( ( modulo_modulo_int @ ( times_times_int @ B @ A ) @ B )
% 5.31/5.58 = zero_zero_int ) ).
% 5.31/5.58
% 5.31/5.58 % mod_mult_self1_is_0
% 5.31/5.58 thf(fact_4747_mod__mult__self1__is__0,axiom,
% 5.31/5.58 ! [B: code_natural,A: code_natural] :
% 5.31/5.58 ( ( modulo8411746178871703098atural @ ( times_2397367101498566445atural @ B @ A ) @ B )
% 5.31/5.58 = zero_z2226904508553997617atural ) ).
% 5.31/5.58
% 5.31/5.58 % mod_mult_self1_is_0
% 5.31/5.58 thf(fact_4748_mod__by__1,axiom,
% 5.31/5.58 ! [A: code_integer] :
% 5.31/5.58 ( ( modulo364778990260209775nteger @ A @ one_one_Code_integer )
% 5.31/5.58 = zero_z3403309356797280102nteger ) ).
% 5.31/5.58
% 5.31/5.58 % mod_by_1
% 5.31/5.58 thf(fact_4749_mod__by__1,axiom,
% 5.31/5.58 ! [A: nat] :
% 5.31/5.58 ( ( modulo_modulo_nat @ A @ one_one_nat )
% 5.31/5.58 = zero_zero_nat ) ).
% 5.31/5.58
% 5.31/5.58 % mod_by_1
% 5.31/5.58 thf(fact_4750_mod__by__1,axiom,
% 5.31/5.58 ! [A: int] :
% 5.31/5.58 ( ( modulo_modulo_int @ A @ one_one_int )
% 5.31/5.58 = zero_zero_int ) ).
% 5.31/5.58
% 5.31/5.58 % mod_by_1
% 5.31/5.58 thf(fact_4751_mod__by__1,axiom,
% 5.31/5.58 ! [A: code_natural] :
% 5.31/5.58 ( ( modulo8411746178871703098atural @ A @ one_one_Code_natural )
% 5.31/5.58 = zero_z2226904508553997617atural ) ).
% 5.31/5.58
% 5.31/5.58 % mod_by_1
% 5.31/5.58 thf(fact_4752_bits__mod__by__1,axiom,
% 5.31/5.58 ! [A: code_integer] :
% 5.31/5.58 ( ( modulo364778990260209775nteger @ A @ one_one_Code_integer )
% 5.31/5.58 = zero_z3403309356797280102nteger ) ).
% 5.31/5.58
% 5.31/5.58 % bits_mod_by_1
% 5.31/5.58 thf(fact_4753_bits__mod__by__1,axiom,
% 5.31/5.58 ! [A: nat] :
% 5.31/5.58 ( ( modulo_modulo_nat @ A @ one_one_nat )
% 5.31/5.58 = zero_zero_nat ) ).
% 5.31/5.58
% 5.31/5.58 % bits_mod_by_1
% 5.31/5.58 thf(fact_4754_bits__mod__by__1,axiom,
% 5.31/5.58 ! [A: int] :
% 5.31/5.58 ( ( modulo_modulo_int @ A @ one_one_int )
% 5.31/5.58 = zero_zero_int ) ).
% 5.31/5.58
% 5.31/5.58 % bits_mod_by_1
% 5.31/5.58 thf(fact_4755_bits__mod__by__1,axiom,
% 5.31/5.58 ! [A: code_natural] :
% 5.31/5.58 ( ( modulo8411746178871703098atural @ A @ one_one_Code_natural )
% 5.31/5.58 = zero_z2226904508553997617atural ) ).
% 5.31/5.58
% 5.31/5.58 % bits_mod_by_1
% 5.31/5.58 thf(fact_4756_mod__div__trivial,axiom,
% 5.31/5.58 ! [A: nat,B: nat] :
% 5.31/5.58 ( ( divide_divide_nat @ ( modulo_modulo_nat @ A @ B ) @ B )
% 5.31/5.58 = zero_zero_nat ) ).
% 5.31/5.58
% 5.31/5.58 % mod_div_trivial
% 5.31/5.58 thf(fact_4757_mod__div__trivial,axiom,
% 5.31/5.58 ! [A: int,B: int] :
% 5.31/5.58 ( ( divide_divide_int @ ( modulo_modulo_int @ A @ B ) @ B )
% 5.31/5.58 = zero_zero_int ) ).
% 5.31/5.58
% 5.31/5.58 % mod_div_trivial
% 5.31/5.58 thf(fact_4758_mod__div__trivial,axiom,
% 5.31/5.58 ! [A: code_natural,B: code_natural] :
% 5.31/5.58 ( ( divide5121882707175180666atural @ ( modulo8411746178871703098atural @ A @ B ) @ B )
% 5.31/5.58 = zero_z2226904508553997617atural ) ).
% 5.31/5.58
% 5.31/5.58 % mod_div_trivial
% 5.31/5.58 thf(fact_4759_bits__mod__div__trivial,axiom,
% 5.31/5.58 ! [A: nat,B: nat] :
% 5.31/5.58 ( ( divide_divide_nat @ ( modulo_modulo_nat @ A @ B ) @ B )
% 5.31/5.58 = zero_zero_nat ) ).
% 5.31/5.58
% 5.31/5.58 % bits_mod_div_trivial
% 5.31/5.58 thf(fact_4760_bits__mod__div__trivial,axiom,
% 5.31/5.58 ! [A: int,B: int] :
% 5.31/5.58 ( ( divide_divide_int @ ( modulo_modulo_int @ A @ B ) @ B )
% 5.31/5.58 = zero_zero_int ) ).
% 5.31/5.58
% 5.31/5.58 % bits_mod_div_trivial
% 5.31/5.58 thf(fact_4761_bits__mod__div__trivial,axiom,
% 5.31/5.58 ! [A: code_natural,B: code_natural] :
% 5.31/5.58 ( ( divide5121882707175180666atural @ ( modulo8411746178871703098atural @ A @ B ) @ B )
% 5.31/5.58 = zero_z2226904508553997617atural ) ).
% 5.31/5.58
% 5.31/5.58 % bits_mod_div_trivial
% 5.31/5.58 thf(fact_4762_mod__mult__self1,axiom,
% 5.31/5.58 ! [A: nat,C2: nat,B: nat] :
% 5.31/5.58 ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ C2 @ B ) ) @ B )
% 5.31/5.58 = ( modulo_modulo_nat @ A @ B ) ) ).
% 5.31/5.58
% 5.31/5.58 % mod_mult_self1
% 5.31/5.58 thf(fact_4763_mod__mult__self1,axiom,
% 5.31/5.58 ! [A: int,C2: int,B: int] :
% 5.31/5.58 ( ( modulo_modulo_int @ ( plus_plus_int @ A @ ( times_times_int @ C2 @ B ) ) @ B )
% 5.31/5.58 = ( modulo_modulo_int @ A @ B ) ) ).
% 5.31/5.58
% 5.31/5.58 % mod_mult_self1
% 5.31/5.58 thf(fact_4764_mod__mult__self1,axiom,
% 5.31/5.58 ! [A: code_natural,C2: code_natural,B: code_natural] :
% 5.31/5.58 ( ( modulo8411746178871703098atural @ ( plus_p4538020629002901425atural @ A @ ( times_2397367101498566445atural @ C2 @ B ) ) @ B )
% 5.31/5.58 = ( modulo8411746178871703098atural @ A @ B ) ) ).
% 5.31/5.58
% 5.31/5.58 % mod_mult_self1
% 5.31/5.58 thf(fact_4765_mod__mult__self2,axiom,
% 5.31/5.58 ! [A: nat,B: nat,C2: nat] :
% 5.31/5.58 ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ B @ C2 ) ) @ B )
% 5.31/5.58 = ( modulo_modulo_nat @ A @ B ) ) ).
% 5.31/5.58
% 5.31/5.58 % mod_mult_self2
% 5.31/5.58 thf(fact_4766_mod__mult__self2,axiom,
% 5.31/5.58 ! [A: int,B: int,C2: int] :
% 5.31/5.58 ( ( modulo_modulo_int @ ( plus_plus_int @ A @ ( times_times_int @ B @ C2 ) ) @ B )
% 5.31/5.58 = ( modulo_modulo_int @ A @ B ) ) ).
% 5.31/5.58
% 5.31/5.58 % mod_mult_self2
% 5.31/5.58 thf(fact_4767_mod__mult__self2,axiom,
% 5.31/5.58 ! [A: code_natural,B: code_natural,C2: code_natural] :
% 5.31/5.58 ( ( modulo8411746178871703098atural @ ( plus_p4538020629002901425atural @ A @ ( times_2397367101498566445atural @ B @ C2 ) ) @ B )
% 5.31/5.58 = ( modulo8411746178871703098atural @ A @ B ) ) ).
% 5.31/5.58
% 5.31/5.58 % mod_mult_self2
% 5.31/5.58 thf(fact_4768_mod__mult__self3,axiom,
% 5.31/5.58 ! [C2: nat,B: nat,A: nat] :
% 5.31/5.58 ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( times_times_nat @ C2 @ B ) @ A ) @ B )
% 5.31/5.58 = ( modulo_modulo_nat @ A @ B ) ) ).
% 5.31/5.58
% 5.31/5.58 % mod_mult_self3
% 5.31/5.58 thf(fact_4769_mod__mult__self3,axiom,
% 5.31/5.58 ! [C2: int,B: int,A: int] :
% 5.31/5.58 ( ( modulo_modulo_int @ ( plus_plus_int @ ( times_times_int @ C2 @ B ) @ A ) @ B )
% 5.31/5.58 = ( modulo_modulo_int @ A @ B ) ) ).
% 5.31/5.58
% 5.31/5.58 % mod_mult_self3
% 5.31/5.58 thf(fact_4770_mod__mult__self3,axiom,
% 5.31/5.58 ! [C2: code_natural,B: code_natural,A: code_natural] :
% 5.31/5.58 ( ( modulo8411746178871703098atural @ ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ C2 @ B ) @ A ) @ B )
% 5.31/5.58 = ( modulo8411746178871703098atural @ A @ B ) ) ).
% 5.31/5.58
% 5.31/5.58 % mod_mult_self3
% 5.31/5.58 thf(fact_4771_mod__mult__self4,axiom,
% 5.31/5.58 ! [B: nat,C2: nat,A: nat] :
% 5.31/5.58 ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( times_times_nat @ B @ C2 ) @ A ) @ B )
% 5.31/5.58 = ( modulo_modulo_nat @ A @ B ) ) ).
% 5.31/5.58
% 5.31/5.58 % mod_mult_self4
% 5.31/5.58 thf(fact_4772_mod__mult__self4,axiom,
% 5.31/5.58 ! [B: int,C2: int,A: int] :
% 5.31/5.58 ( ( modulo_modulo_int @ ( plus_plus_int @ ( times_times_int @ B @ C2 ) @ A ) @ B )
% 5.31/5.58 = ( modulo_modulo_int @ A @ B ) ) ).
% 5.31/5.58
% 5.31/5.58 % mod_mult_self4
% 5.31/5.58 thf(fact_4773_mod__mult__self4,axiom,
% 5.31/5.58 ! [B: code_natural,C2: code_natural,A: code_natural] :
% 5.31/5.58 ( ( modulo8411746178871703098atural @ ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ B @ C2 ) @ A ) @ B )
% 5.31/5.58 = ( modulo8411746178871703098atural @ A @ B ) ) ).
% 5.31/5.58
% 5.31/5.58 % mod_mult_self4
% 5.31/5.58 thf(fact_4774_mod__by__Suc__0,axiom,
% 5.31/5.58 ! [M2: nat] :
% 5.31/5.58 ( ( modulo_modulo_nat @ M2 @ ( suc @ zero_zero_nat ) )
% 5.31/5.58 = zero_zero_nat ) ).
% 5.31/5.58
% 5.31/5.58 % mod_by_Suc_0
% 5.31/5.58 thf(fact_4775_Suc__mod__mult__self4,axiom,
% 5.31/5.58 ! [N: nat,K2: nat,M2: nat] :
% 5.31/5.58 ( ( modulo_modulo_nat @ ( suc @ ( plus_plus_nat @ ( times_times_nat @ N @ K2 ) @ M2 ) ) @ N )
% 5.31/5.58 = ( modulo_modulo_nat @ ( suc @ M2 ) @ N ) ) ).
% 5.31/5.58
% 5.31/5.58 % Suc_mod_mult_self4
% 5.31/5.58 thf(fact_4776_Suc__mod__mult__self3,axiom,
% 5.31/5.58 ! [K2: nat,N: nat,M2: nat] :
% 5.31/5.58 ( ( modulo_modulo_nat @ ( suc @ ( plus_plus_nat @ ( times_times_nat @ K2 @ N ) @ M2 ) ) @ N )
% 5.31/5.58 = ( modulo_modulo_nat @ ( suc @ M2 ) @ N ) ) ).
% 5.31/5.58
% 5.31/5.58 % Suc_mod_mult_self3
% 5.31/5.58 thf(fact_4777_Suc__mod__mult__self2,axiom,
% 5.31/5.58 ! [M2: nat,N: nat,K2: nat] :
% 5.31/5.58 ( ( modulo_modulo_nat @ ( suc @ ( plus_plus_nat @ M2 @ ( times_times_nat @ N @ K2 ) ) ) @ N )
% 5.31/5.58 = ( modulo_modulo_nat @ ( suc @ M2 ) @ N ) ) ).
% 5.31/5.58
% 5.31/5.58 % Suc_mod_mult_self2
% 5.31/5.58 thf(fact_4778_Suc__mod__mult__self1,axiom,
% 5.31/5.58 ! [M2: nat,K2: nat,N: nat] :
% 5.31/5.58 ( ( modulo_modulo_nat @ ( suc @ ( plus_plus_nat @ M2 @ ( times_times_nat @ K2 @ N ) ) ) @ N )
% 5.31/5.58 = ( modulo_modulo_nat @ ( suc @ M2 ) @ N ) ) ).
% 5.31/5.58
% 5.31/5.58 % Suc_mod_mult_self1
% 5.31/5.58 thf(fact_4779_mod2__Suc__Suc,axiom,
% 5.31/5.58 ! [M2: nat] :
% 5.31/5.58 ( ( modulo_modulo_nat @ ( suc @ ( suc @ M2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.31/5.58 = ( modulo_modulo_nat @ M2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % mod2_Suc_Suc
% 5.31/5.58 thf(fact_4780_Suc__times__numeral__mod__eq,axiom,
% 5.31/5.58 ! [K2: num,N: nat] :
% 5.31/5.58 ( ( ( numeral_numeral_nat @ K2 )
% 5.31/5.58 != one_one_nat )
% 5.31/5.58 => ( ( modulo_modulo_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ K2 ) @ N ) ) @ ( numeral_numeral_nat @ K2 ) )
% 5.31/5.58 = one_one_nat ) ) ).
% 5.31/5.58
% 5.31/5.58 % Suc_times_numeral_mod_eq
% 5.31/5.58 thf(fact_4781_not__mod__2__eq__0__eq__1,axiom,
% 5.31/5.58 ! [A: code_integer] :
% 5.31/5.58 ( ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.31/5.58 != zero_z3403309356797280102nteger )
% 5.31/5.58 = ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.31/5.58 = one_one_Code_integer ) ) ).
% 5.31/5.58
% 5.31/5.58 % not_mod_2_eq_0_eq_1
% 5.31/5.58 thf(fact_4782_not__mod__2__eq__0__eq__1,axiom,
% 5.31/5.58 ! [A: nat] :
% 5.31/5.58 ( ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.31/5.58 != zero_zero_nat )
% 5.31/5.58 = ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.31/5.58 = one_one_nat ) ) ).
% 5.31/5.58
% 5.31/5.58 % not_mod_2_eq_0_eq_1
% 5.31/5.58 thf(fact_4783_not__mod__2__eq__0__eq__1,axiom,
% 5.31/5.58 ! [A: int] :
% 5.31/5.58 ( ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.31/5.58 != zero_zero_int )
% 5.31/5.58 = ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.31/5.58 = one_one_int ) ) ).
% 5.31/5.58
% 5.31/5.58 % not_mod_2_eq_0_eq_1
% 5.31/5.58 thf(fact_4784_not__mod__2__eq__0__eq__1,axiom,
% 5.31/5.58 ! [A: code_natural] :
% 5.31/5.58 ( ( ( modulo8411746178871703098atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 5.31/5.58 != zero_z2226904508553997617atural )
% 5.31/5.58 = ( ( modulo8411746178871703098atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 5.31/5.58 = one_one_Code_natural ) ) ).
% 5.31/5.58
% 5.31/5.58 % not_mod_2_eq_0_eq_1
% 5.31/5.58 thf(fact_4785_not__mod__2__eq__1__eq__0,axiom,
% 5.31/5.58 ! [A: code_integer] :
% 5.31/5.58 ( ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.31/5.58 != one_one_Code_integer )
% 5.31/5.58 = ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.31/5.58 = zero_z3403309356797280102nteger ) ) ).
% 5.31/5.58
% 5.31/5.58 % not_mod_2_eq_1_eq_0
% 5.31/5.58 thf(fact_4786_not__mod__2__eq__1__eq__0,axiom,
% 5.31/5.58 ! [A: nat] :
% 5.31/5.58 ( ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.31/5.58 != one_one_nat )
% 5.31/5.58 = ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.31/5.58 = zero_zero_nat ) ) ).
% 5.31/5.58
% 5.31/5.58 % not_mod_2_eq_1_eq_0
% 5.31/5.58 thf(fact_4787_not__mod__2__eq__1__eq__0,axiom,
% 5.31/5.58 ! [A: int] :
% 5.31/5.58 ( ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.31/5.58 != one_one_int )
% 5.31/5.58 = ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.31/5.58 = zero_zero_int ) ) ).
% 5.31/5.58
% 5.31/5.58 % not_mod_2_eq_1_eq_0
% 5.31/5.58 thf(fact_4788_not__mod__2__eq__1__eq__0,axiom,
% 5.31/5.58 ! [A: code_natural] :
% 5.31/5.58 ( ( ( modulo8411746178871703098atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 5.31/5.58 != one_one_Code_natural )
% 5.31/5.58 = ( ( modulo8411746178871703098atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 5.31/5.58 = zero_z2226904508553997617atural ) ) ).
% 5.31/5.58
% 5.31/5.58 % not_mod_2_eq_1_eq_0
% 5.31/5.58 thf(fact_4789_not__mod2__eq__Suc__0__eq__0,axiom,
% 5.31/5.58 ! [N: nat] :
% 5.31/5.58 ( ( ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.31/5.58 != ( suc @ zero_zero_nat ) )
% 5.31/5.58 = ( ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.31/5.58 = zero_zero_nat ) ) ).
% 5.31/5.58
% 5.31/5.58 % not_mod2_eq_Suc_0_eq_0
% 5.31/5.58 thf(fact_4790_add__self__mod__2,axiom,
% 5.31/5.58 ! [M2: nat] :
% 5.31/5.58 ( ( modulo_modulo_nat @ ( plus_plus_nat @ M2 @ M2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.31/5.58 = zero_zero_nat ) ).
% 5.31/5.58
% 5.31/5.58 % add_self_mod_2
% 5.31/5.58 thf(fact_4791_mod2__gr__0,axiom,
% 5.31/5.58 ! [M2: nat] :
% 5.31/5.58 ( ( ord_less_nat @ zero_zero_nat @ ( modulo_modulo_nat @ M2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.31/5.58 = ( ( modulo_modulo_nat @ M2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.31/5.58 = one_one_nat ) ) ).
% 5.31/5.58
% 5.31/5.58 % mod2_gr_0
% 5.31/5.58 thf(fact_4792_mod__mult__eq,axiom,
% 5.31/5.58 ! [A: nat,C2: nat,B: nat] :
% 5.31/5.58 ( ( modulo_modulo_nat @ ( times_times_nat @ ( modulo_modulo_nat @ A @ C2 ) @ ( modulo_modulo_nat @ B @ C2 ) ) @ C2 )
% 5.31/5.58 = ( modulo_modulo_nat @ ( times_times_nat @ A @ B ) @ C2 ) ) ).
% 5.31/5.58
% 5.31/5.58 % mod_mult_eq
% 5.31/5.58 thf(fact_4793_mod__mult__eq,axiom,
% 5.31/5.58 ! [A: int,C2: int,B: int] :
% 5.31/5.58 ( ( modulo_modulo_int @ ( times_times_int @ ( modulo_modulo_int @ A @ C2 ) @ ( modulo_modulo_int @ B @ C2 ) ) @ C2 )
% 5.31/5.58 = ( modulo_modulo_int @ ( times_times_int @ A @ B ) @ C2 ) ) ).
% 5.31/5.58
% 5.31/5.58 % mod_mult_eq
% 5.31/5.58 thf(fact_4794_mod__mult__eq,axiom,
% 5.31/5.58 ! [A: code_natural,C2: code_natural,B: code_natural] :
% 5.31/5.58 ( ( modulo8411746178871703098atural @ ( times_2397367101498566445atural @ ( modulo8411746178871703098atural @ A @ C2 ) @ ( modulo8411746178871703098atural @ B @ C2 ) ) @ C2 )
% 5.31/5.58 = ( modulo8411746178871703098atural @ ( times_2397367101498566445atural @ A @ B ) @ C2 ) ) ).
% 5.31/5.58
% 5.31/5.58 % mod_mult_eq
% 5.31/5.58 thf(fact_4795_mod__mult__cong,axiom,
% 5.31/5.58 ! [A: nat,C2: nat,A2: nat,B: nat,B2: nat] :
% 5.31/5.58 ( ( ( modulo_modulo_nat @ A @ C2 )
% 5.31/5.58 = ( modulo_modulo_nat @ A2 @ C2 ) )
% 5.31/5.58 => ( ( ( modulo_modulo_nat @ B @ C2 )
% 5.31/5.58 = ( modulo_modulo_nat @ B2 @ C2 ) )
% 5.31/5.58 => ( ( modulo_modulo_nat @ ( times_times_nat @ A @ B ) @ C2 )
% 5.31/5.58 = ( modulo_modulo_nat @ ( times_times_nat @ A2 @ B2 ) @ C2 ) ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % mod_mult_cong
% 5.31/5.58 thf(fact_4796_mod__mult__cong,axiom,
% 5.31/5.58 ! [A: int,C2: int,A2: int,B: int,B2: int] :
% 5.31/5.58 ( ( ( modulo_modulo_int @ A @ C2 )
% 5.31/5.58 = ( modulo_modulo_int @ A2 @ C2 ) )
% 5.31/5.58 => ( ( ( modulo_modulo_int @ B @ C2 )
% 5.31/5.58 = ( modulo_modulo_int @ B2 @ C2 ) )
% 5.31/5.58 => ( ( modulo_modulo_int @ ( times_times_int @ A @ B ) @ C2 )
% 5.31/5.58 = ( modulo_modulo_int @ ( times_times_int @ A2 @ B2 ) @ C2 ) ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % mod_mult_cong
% 5.31/5.58 thf(fact_4797_mod__mult__cong,axiom,
% 5.31/5.58 ! [A: code_natural,C2: code_natural,A2: code_natural,B: code_natural,B2: code_natural] :
% 5.31/5.58 ( ( ( modulo8411746178871703098atural @ A @ C2 )
% 5.31/5.58 = ( modulo8411746178871703098atural @ A2 @ C2 ) )
% 5.31/5.58 => ( ( ( modulo8411746178871703098atural @ B @ C2 )
% 5.31/5.58 = ( modulo8411746178871703098atural @ B2 @ C2 ) )
% 5.31/5.58 => ( ( modulo8411746178871703098atural @ ( times_2397367101498566445atural @ A @ B ) @ C2 )
% 5.31/5.58 = ( modulo8411746178871703098atural @ ( times_2397367101498566445atural @ A2 @ B2 ) @ C2 ) ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % mod_mult_cong
% 5.31/5.58 thf(fact_4798_mod__mult__mult2,axiom,
% 5.31/5.58 ! [A: nat,C2: nat,B: nat] :
% 5.31/5.58 ( ( modulo_modulo_nat @ ( times_times_nat @ A @ C2 ) @ ( times_times_nat @ B @ C2 ) )
% 5.31/5.58 = ( times_times_nat @ ( modulo_modulo_nat @ A @ B ) @ C2 ) ) ).
% 5.31/5.58
% 5.31/5.58 % mod_mult_mult2
% 5.31/5.58 thf(fact_4799_mod__mult__mult2,axiom,
% 5.31/5.58 ! [A: int,C2: int,B: int] :
% 5.31/5.58 ( ( modulo_modulo_int @ ( times_times_int @ A @ C2 ) @ ( times_times_int @ B @ C2 ) )
% 5.31/5.58 = ( times_times_int @ ( modulo_modulo_int @ A @ B ) @ C2 ) ) ).
% 5.31/5.58
% 5.31/5.58 % mod_mult_mult2
% 5.31/5.58 thf(fact_4800_mod__mult__mult2,axiom,
% 5.31/5.58 ! [A: code_natural,C2: code_natural,B: code_natural] :
% 5.31/5.58 ( ( modulo8411746178871703098atural @ ( times_2397367101498566445atural @ A @ C2 ) @ ( times_2397367101498566445atural @ B @ C2 ) )
% 5.31/5.58 = ( times_2397367101498566445atural @ ( modulo8411746178871703098atural @ A @ B ) @ C2 ) ) ).
% 5.31/5.58
% 5.31/5.58 % mod_mult_mult2
% 5.31/5.58 thf(fact_4801_mult__mod__right,axiom,
% 5.31/5.58 ! [C2: nat,A: nat,B: nat] :
% 5.31/5.58 ( ( times_times_nat @ C2 @ ( modulo_modulo_nat @ A @ B ) )
% 5.31/5.58 = ( modulo_modulo_nat @ ( times_times_nat @ C2 @ A ) @ ( times_times_nat @ C2 @ B ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % mult_mod_right
% 5.31/5.58 thf(fact_4802_mult__mod__right,axiom,
% 5.31/5.58 ! [C2: int,A: int,B: int] :
% 5.31/5.58 ( ( times_times_int @ C2 @ ( modulo_modulo_int @ A @ B ) )
% 5.31/5.58 = ( modulo_modulo_int @ ( times_times_int @ C2 @ A ) @ ( times_times_int @ C2 @ B ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % mult_mod_right
% 5.31/5.58 thf(fact_4803_mult__mod__right,axiom,
% 5.31/5.58 ! [C2: code_natural,A: code_natural,B: code_natural] :
% 5.31/5.58 ( ( times_2397367101498566445atural @ C2 @ ( modulo8411746178871703098atural @ A @ B ) )
% 5.31/5.58 = ( modulo8411746178871703098atural @ ( times_2397367101498566445atural @ C2 @ A ) @ ( times_2397367101498566445atural @ C2 @ B ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % mult_mod_right
% 5.31/5.58 thf(fact_4804_mod__mult__left__eq,axiom,
% 5.31/5.58 ! [A: nat,C2: nat,B: nat] :
% 5.31/5.58 ( ( modulo_modulo_nat @ ( times_times_nat @ ( modulo_modulo_nat @ A @ C2 ) @ B ) @ C2 )
% 5.31/5.58 = ( modulo_modulo_nat @ ( times_times_nat @ A @ B ) @ C2 ) ) ).
% 5.31/5.58
% 5.31/5.58 % mod_mult_left_eq
% 5.31/5.58 thf(fact_4805_mod__mult__left__eq,axiom,
% 5.31/5.58 ! [A: int,C2: int,B: int] :
% 5.31/5.58 ( ( modulo_modulo_int @ ( times_times_int @ ( modulo_modulo_int @ A @ C2 ) @ B ) @ C2 )
% 5.31/5.58 = ( modulo_modulo_int @ ( times_times_int @ A @ B ) @ C2 ) ) ).
% 5.31/5.58
% 5.31/5.58 % mod_mult_left_eq
% 5.31/5.58 thf(fact_4806_mod__mult__left__eq,axiom,
% 5.31/5.58 ! [A: code_natural,C2: code_natural,B: code_natural] :
% 5.31/5.58 ( ( modulo8411746178871703098atural @ ( times_2397367101498566445atural @ ( modulo8411746178871703098atural @ A @ C2 ) @ B ) @ C2 )
% 5.31/5.58 = ( modulo8411746178871703098atural @ ( times_2397367101498566445atural @ A @ B ) @ C2 ) ) ).
% 5.31/5.58
% 5.31/5.58 % mod_mult_left_eq
% 5.31/5.58 thf(fact_4807_mod__mult__right__eq,axiom,
% 5.31/5.58 ! [A: nat,B: nat,C2: nat] :
% 5.31/5.58 ( ( modulo_modulo_nat @ ( times_times_nat @ A @ ( modulo_modulo_nat @ B @ C2 ) ) @ C2 )
% 5.31/5.58 = ( modulo_modulo_nat @ ( times_times_nat @ A @ B ) @ C2 ) ) ).
% 5.31/5.58
% 5.31/5.58 % mod_mult_right_eq
% 5.31/5.58 thf(fact_4808_mod__mult__right__eq,axiom,
% 5.31/5.58 ! [A: int,B: int,C2: int] :
% 5.31/5.58 ( ( modulo_modulo_int @ ( times_times_int @ A @ ( modulo_modulo_int @ B @ C2 ) ) @ C2 )
% 5.31/5.58 = ( modulo_modulo_int @ ( times_times_int @ A @ B ) @ C2 ) ) ).
% 5.31/5.58
% 5.31/5.58 % mod_mult_right_eq
% 5.31/5.58 thf(fact_4809_mod__mult__right__eq,axiom,
% 5.31/5.58 ! [A: code_natural,B: code_natural,C2: code_natural] :
% 5.31/5.58 ( ( modulo8411746178871703098atural @ ( times_2397367101498566445atural @ A @ ( modulo8411746178871703098atural @ B @ C2 ) ) @ C2 )
% 5.31/5.58 = ( modulo8411746178871703098atural @ ( times_2397367101498566445atural @ A @ B ) @ C2 ) ) ).
% 5.31/5.58
% 5.31/5.58 % mod_mult_right_eq
% 5.31/5.58 thf(fact_4810_mod__Suc__Suc__eq,axiom,
% 5.31/5.58 ! [M2: nat,N: nat] :
% 5.31/5.58 ( ( modulo_modulo_nat @ ( suc @ ( suc @ ( modulo_modulo_nat @ M2 @ N ) ) ) @ N )
% 5.31/5.58 = ( modulo_modulo_nat @ ( suc @ ( suc @ M2 ) ) @ N ) ) ).
% 5.31/5.58
% 5.31/5.58 % mod_Suc_Suc_eq
% 5.31/5.58 thf(fact_4811_mod__Suc__eq,axiom,
% 5.31/5.58 ! [M2: nat,N: nat] :
% 5.31/5.58 ( ( modulo_modulo_nat @ ( suc @ ( modulo_modulo_nat @ M2 @ N ) ) @ N )
% 5.31/5.58 = ( modulo_modulo_nat @ ( suc @ M2 ) @ N ) ) ).
% 5.31/5.58
% 5.31/5.58 % mod_Suc_eq
% 5.31/5.58 thf(fact_4812_mod__less__eq__dividend,axiom,
% 5.31/5.58 ! [M2: nat,N: nat] : ( ord_less_eq_nat @ ( modulo_modulo_nat @ M2 @ N ) @ M2 ) ).
% 5.31/5.58
% 5.31/5.58 % mod_less_eq_dividend
% 5.31/5.58 thf(fact_4813_unique__euclidean__semiring__numeral__class_Omod__less__eq__dividend,axiom,
% 5.31/5.58 ! [A: nat,B: nat] :
% 5.31/5.58 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.31/5.58 => ( ord_less_eq_nat @ ( modulo_modulo_nat @ A @ B ) @ A ) ) ).
% 5.31/5.58
% 5.31/5.58 % unique_euclidean_semiring_numeral_class.mod_less_eq_dividend
% 5.31/5.58 thf(fact_4814_unique__euclidean__semiring__numeral__class_Omod__less__eq__dividend,axiom,
% 5.31/5.58 ! [A: int,B: int] :
% 5.31/5.58 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.31/5.58 => ( ord_less_eq_int @ ( modulo_modulo_int @ A @ B ) @ A ) ) ).
% 5.31/5.58
% 5.31/5.58 % unique_euclidean_semiring_numeral_class.mod_less_eq_dividend
% 5.31/5.58 thf(fact_4815_unique__euclidean__semiring__numeral__class_Opos__mod__bound,axiom,
% 5.31/5.58 ! [B: nat,A: nat] :
% 5.31/5.58 ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.31/5.58 => ( ord_less_nat @ ( modulo_modulo_nat @ A @ B ) @ B ) ) ).
% 5.31/5.58
% 5.31/5.58 % unique_euclidean_semiring_numeral_class.pos_mod_bound
% 5.31/5.58 thf(fact_4816_unique__euclidean__semiring__numeral__class_Opos__mod__bound,axiom,
% 5.31/5.58 ! [B: int,A: int] :
% 5.31/5.58 ( ( ord_less_int @ zero_zero_int @ B )
% 5.31/5.58 => ( ord_less_int @ ( modulo_modulo_int @ A @ B ) @ B ) ) ).
% 5.31/5.58
% 5.31/5.58 % unique_euclidean_semiring_numeral_class.pos_mod_bound
% 5.31/5.58 thf(fact_4817_mod__eq__self__iff__div__eq__0,axiom,
% 5.31/5.58 ! [A: nat,B: nat] :
% 5.31/5.58 ( ( ( modulo_modulo_nat @ A @ B )
% 5.31/5.58 = A )
% 5.31/5.58 = ( ( divide_divide_nat @ A @ B )
% 5.31/5.58 = zero_zero_nat ) ) ).
% 5.31/5.58
% 5.31/5.58 % mod_eq_self_iff_div_eq_0
% 5.31/5.58 thf(fact_4818_mod__eq__self__iff__div__eq__0,axiom,
% 5.31/5.58 ! [A: int,B: int] :
% 5.31/5.58 ( ( ( modulo_modulo_int @ A @ B )
% 5.31/5.58 = A )
% 5.31/5.58 = ( ( divide_divide_int @ A @ B )
% 5.31/5.58 = zero_zero_int ) ) ).
% 5.31/5.58
% 5.31/5.58 % mod_eq_self_iff_div_eq_0
% 5.31/5.58 thf(fact_4819_mod__eq__self__iff__div__eq__0,axiom,
% 5.31/5.58 ! [A: code_natural,B: code_natural] :
% 5.31/5.58 ( ( ( modulo8411746178871703098atural @ A @ B )
% 5.31/5.58 = A )
% 5.31/5.58 = ( ( divide5121882707175180666atural @ A @ B )
% 5.31/5.58 = zero_z2226904508553997617atural ) ) ).
% 5.31/5.58
% 5.31/5.58 % mod_eq_self_iff_div_eq_0
% 5.31/5.58 thf(fact_4820_cong__exp__iff__simps_I9_J,axiom,
% 5.31/5.58 ! [M2: num,Q2: num,N: num] :
% 5.31/5.58 ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ M2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 5.31/5.58 = ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) )
% 5.31/5.58 = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ M2 ) @ ( numeral_numeral_nat @ Q2 ) )
% 5.31/5.58 = ( modulo_modulo_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ Q2 ) ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % cong_exp_iff_simps(9)
% 5.31/5.58 thf(fact_4821_cong__exp__iff__simps_I9_J,axiom,
% 5.31/5.58 ! [M2: num,Q2: num,N: num] :
% 5.31/5.58 ( ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ M2 ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 5.31/5.58 = ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) ) )
% 5.31/5.58 = ( ( modulo_modulo_int @ ( numeral_numeral_int @ M2 ) @ ( numeral_numeral_int @ Q2 ) )
% 5.31/5.58 = ( modulo_modulo_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ Q2 ) ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % cong_exp_iff_simps(9)
% 5.31/5.58 thf(fact_4822_cong__exp__iff__simps_I4_J,axiom,
% 5.31/5.58 ! [M2: num,N: num] :
% 5.31/5.58 ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ M2 ) @ ( numeral_numeral_nat @ one ) )
% 5.31/5.58 = ( modulo_modulo_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ one ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % cong_exp_iff_simps(4)
% 5.31/5.58 thf(fact_4823_cong__exp__iff__simps_I4_J,axiom,
% 5.31/5.58 ! [M2: num,N: num] :
% 5.31/5.58 ( ( modulo_modulo_int @ ( numeral_numeral_int @ M2 ) @ ( numeral_numeral_int @ one ) )
% 5.31/5.58 = ( modulo_modulo_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ one ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % cong_exp_iff_simps(4)
% 5.31/5.58 thf(fact_4824_mod__eqE,axiom,
% 5.31/5.58 ! [A: int,C2: int,B: int] :
% 5.31/5.58 ( ( ( modulo_modulo_int @ A @ C2 )
% 5.31/5.58 = ( modulo_modulo_int @ B @ C2 ) )
% 5.31/5.58 => ~ ! [D5: int] :
% 5.31/5.58 ( B
% 5.31/5.58 != ( plus_plus_int @ A @ ( times_times_int @ C2 @ D5 ) ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % mod_eqE
% 5.31/5.58 thf(fact_4825_mod__Suc,axiom,
% 5.31/5.58 ! [M2: nat,N: nat] :
% 5.31/5.58 ( ( ( ( suc @ ( modulo_modulo_nat @ M2 @ N ) )
% 5.31/5.58 = N )
% 5.31/5.58 => ( ( modulo_modulo_nat @ ( suc @ M2 ) @ N )
% 5.31/5.58 = zero_zero_nat ) )
% 5.31/5.58 & ( ( ( suc @ ( modulo_modulo_nat @ M2 @ N ) )
% 5.31/5.58 != N )
% 5.31/5.58 => ( ( modulo_modulo_nat @ ( suc @ M2 ) @ N )
% 5.31/5.58 = ( suc @ ( modulo_modulo_nat @ M2 @ N ) ) ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % mod_Suc
% 5.31/5.58 thf(fact_4826_mod__induct,axiom,
% 5.31/5.58 ! [P2: nat > $o,N: nat,P: nat,M2: nat] :
% 5.31/5.58 ( ( P2 @ N )
% 5.31/5.58 => ( ( ord_less_nat @ N @ P )
% 5.31/5.58 => ( ( ord_less_nat @ M2 @ P )
% 5.31/5.58 => ( ! [N3: nat] :
% 5.31/5.58 ( ( ord_less_nat @ N3 @ P )
% 5.31/5.58 => ( ( P2 @ N3 )
% 5.31/5.58 => ( P2 @ ( modulo_modulo_nat @ ( suc @ N3 ) @ P ) ) ) )
% 5.31/5.58 => ( P2 @ M2 ) ) ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % mod_induct
% 5.31/5.58 thf(fact_4827_mod__less__divisor,axiom,
% 5.31/5.58 ! [N: nat,M2: nat] :
% 5.31/5.58 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.58 => ( ord_less_nat @ ( modulo_modulo_nat @ M2 @ N ) @ N ) ) ).
% 5.31/5.58
% 5.31/5.58 % mod_less_divisor
% 5.31/5.58 thf(fact_4828_gcd__nat__induct,axiom,
% 5.31/5.58 ! [P2: nat > nat > $o,M2: nat,N: nat] :
% 5.31/5.58 ( ! [M: nat] : ( P2 @ M @ zero_zero_nat )
% 5.31/5.58 => ( ! [M: nat,N3: nat] :
% 5.31/5.58 ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 5.31/5.58 => ( ( P2 @ N3 @ ( modulo_modulo_nat @ M @ N3 ) )
% 5.31/5.58 => ( P2 @ M @ N3 ) ) )
% 5.31/5.58 => ( P2 @ M2 @ N ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % gcd_nat_induct
% 5.31/5.58 thf(fact_4829_mod__Suc__le__divisor,axiom,
% 5.31/5.58 ! [M2: nat,N: nat] : ( ord_less_eq_nat @ ( modulo_modulo_nat @ M2 @ ( suc @ N ) ) @ N ) ).
% 5.31/5.58
% 5.31/5.58 % mod_Suc_le_divisor
% 5.31/5.58 thf(fact_4830_mod__eq__0D,axiom,
% 5.31/5.58 ! [M2: nat,D: nat] :
% 5.31/5.58 ( ( ( modulo_modulo_nat @ M2 @ D )
% 5.31/5.58 = zero_zero_nat )
% 5.31/5.58 => ? [Q3: nat] :
% 5.31/5.58 ( M2
% 5.31/5.58 = ( times_times_nat @ D @ Q3 ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % mod_eq_0D
% 5.31/5.58 thf(fact_4831_mod__geq,axiom,
% 5.31/5.58 ! [M2: nat,N: nat] :
% 5.31/5.58 ( ~ ( ord_less_nat @ M2 @ N )
% 5.31/5.58 => ( ( modulo_modulo_nat @ M2 @ N )
% 5.31/5.58 = ( modulo_modulo_nat @ ( minus_minus_nat @ M2 @ N ) @ N ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % mod_geq
% 5.31/5.58 thf(fact_4832_le__mod__geq,axiom,
% 5.31/5.58 ! [N: nat,M2: nat] :
% 5.31/5.58 ( ( ord_less_eq_nat @ N @ M2 )
% 5.31/5.58 => ( ( modulo_modulo_nat @ M2 @ N )
% 5.31/5.58 = ( modulo_modulo_nat @ ( minus_minus_nat @ M2 @ N ) @ N ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % le_mod_geq
% 5.31/5.58 thf(fact_4833_nat__mod__eq__iff,axiom,
% 5.31/5.58 ! [X: nat,N: nat,Y: nat] :
% 5.31/5.58 ( ( ( modulo_modulo_nat @ X @ N )
% 5.31/5.58 = ( modulo_modulo_nat @ Y @ N ) )
% 5.31/5.58 = ( ? [Q1: nat,Q22: nat] :
% 5.31/5.58 ( ( plus_plus_nat @ X @ ( times_times_nat @ N @ Q1 ) )
% 5.31/5.58 = ( plus_plus_nat @ Y @ ( times_times_nat @ N @ Q22 ) ) ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % nat_mod_eq_iff
% 5.31/5.58 thf(fact_4834_unique__euclidean__semiring__numeral__class_Omod__less,axiom,
% 5.31/5.58 ! [A: nat,B: nat] :
% 5.31/5.58 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.31/5.58 => ( ( ord_less_nat @ A @ B )
% 5.31/5.58 => ( ( modulo_modulo_nat @ A @ B )
% 5.31/5.58 = A ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % unique_euclidean_semiring_numeral_class.mod_less
% 5.31/5.58 thf(fact_4835_unique__euclidean__semiring__numeral__class_Omod__less,axiom,
% 5.31/5.58 ! [A: int,B: int] :
% 5.31/5.58 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.31/5.58 => ( ( ord_less_int @ A @ B )
% 5.31/5.58 => ( ( modulo_modulo_int @ A @ B )
% 5.31/5.58 = A ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % unique_euclidean_semiring_numeral_class.mod_less
% 5.31/5.58 thf(fact_4836_unique__euclidean__semiring__numeral__class_Opos__mod__sign,axiom,
% 5.31/5.58 ! [B: nat,A: nat] :
% 5.31/5.58 ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.31/5.58 => ( ord_less_eq_nat @ zero_zero_nat @ ( modulo_modulo_nat @ A @ B ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % unique_euclidean_semiring_numeral_class.pos_mod_sign
% 5.31/5.58 thf(fact_4837_unique__euclidean__semiring__numeral__class_Opos__mod__sign,axiom,
% 5.31/5.58 ! [B: int,A: int] :
% 5.31/5.58 ( ( ord_less_int @ zero_zero_int @ B )
% 5.31/5.58 => ( ord_less_eq_int @ zero_zero_int @ ( modulo_modulo_int @ A @ B ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % unique_euclidean_semiring_numeral_class.pos_mod_sign
% 5.31/5.58 thf(fact_4838_cong__exp__iff__simps_I2_J,axiom,
% 5.31/5.58 ! [N: num,Q2: num] :
% 5.31/5.58 ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 5.31/5.58 = zero_zero_nat )
% 5.31/5.58 = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ Q2 ) )
% 5.31/5.58 = zero_zero_nat ) ) ).
% 5.31/5.58
% 5.31/5.58 % cong_exp_iff_simps(2)
% 5.31/5.58 thf(fact_4839_cong__exp__iff__simps_I2_J,axiom,
% 5.31/5.58 ! [N: num,Q2: num] :
% 5.31/5.58 ( ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 5.31/5.58 = zero_zero_int )
% 5.31/5.58 = ( ( modulo_modulo_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ Q2 ) )
% 5.31/5.58 = zero_zero_int ) ) ).
% 5.31/5.58
% 5.31/5.58 % cong_exp_iff_simps(2)
% 5.31/5.58 thf(fact_4840_cong__exp__iff__simps_I1_J,axiom,
% 5.31/5.58 ! [N: num] :
% 5.31/5.58 ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ one ) )
% 5.31/5.58 = zero_zero_nat ) ).
% 5.31/5.58
% 5.31/5.58 % cong_exp_iff_simps(1)
% 5.31/5.58 thf(fact_4841_cong__exp__iff__simps_I1_J,axiom,
% 5.31/5.58 ! [N: num] :
% 5.31/5.58 ( ( modulo_modulo_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ one ) )
% 5.31/5.58 = zero_zero_int ) ).
% 5.31/5.58
% 5.31/5.58 % cong_exp_iff_simps(1)
% 5.31/5.58 thf(fact_4842_cong__exp__iff__simps_I6_J,axiom,
% 5.31/5.58 ! [Q2: num,N: num] :
% 5.31/5.58 ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ one ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 5.31/5.58 != ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % cong_exp_iff_simps(6)
% 5.31/5.58 thf(fact_4843_cong__exp__iff__simps_I6_J,axiom,
% 5.31/5.58 ! [Q2: num,N: num] :
% 5.31/5.58 ( ( modulo_modulo_int @ ( numeral_numeral_int @ one ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 5.31/5.58 != ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % cong_exp_iff_simps(6)
% 5.31/5.58 thf(fact_4844_cong__exp__iff__simps_I8_J,axiom,
% 5.31/5.58 ! [M2: num,Q2: num] :
% 5.31/5.58 ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ M2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 5.31/5.58 != ( modulo_modulo_nat @ ( numeral_numeral_nat @ one ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % cong_exp_iff_simps(8)
% 5.31/5.58 thf(fact_4845_cong__exp__iff__simps_I8_J,axiom,
% 5.31/5.58 ! [M2: num,Q2: num] :
% 5.31/5.58 ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ M2 ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 5.31/5.58 != ( modulo_modulo_int @ ( numeral_numeral_int @ one ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % cong_exp_iff_simps(8)
% 5.31/5.58 thf(fact_4846_div__mult1__eq,axiom,
% 5.31/5.58 ! [A: nat,B: nat,C2: nat] :
% 5.31/5.58 ( ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ C2 )
% 5.31/5.58 = ( plus_plus_nat @ ( times_times_nat @ A @ ( divide_divide_nat @ B @ C2 ) ) @ ( divide_divide_nat @ ( times_times_nat @ A @ ( modulo_modulo_nat @ B @ C2 ) ) @ C2 ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % div_mult1_eq
% 5.31/5.58 thf(fact_4847_div__mult1__eq,axiom,
% 5.31/5.58 ! [A: int,B: int,C2: int] :
% 5.31/5.58 ( ( divide_divide_int @ ( times_times_int @ A @ B ) @ C2 )
% 5.31/5.58 = ( plus_plus_int @ ( times_times_int @ A @ ( divide_divide_int @ B @ C2 ) ) @ ( divide_divide_int @ ( times_times_int @ A @ ( modulo_modulo_int @ B @ C2 ) ) @ C2 ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % div_mult1_eq
% 5.31/5.58 thf(fact_4848_div__mult1__eq,axiom,
% 5.31/5.58 ! [A: code_natural,B: code_natural,C2: code_natural] :
% 5.31/5.58 ( ( divide5121882707175180666atural @ ( times_2397367101498566445atural @ A @ B ) @ C2 )
% 5.31/5.58 = ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ A @ ( divide5121882707175180666atural @ B @ C2 ) ) @ ( divide5121882707175180666atural @ ( times_2397367101498566445atural @ A @ ( modulo8411746178871703098atural @ B @ C2 ) ) @ C2 ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % div_mult1_eq
% 5.31/5.58 thf(fact_4849_cancel__div__mod__rules_I2_J,axiom,
% 5.31/5.58 ! [B: nat,A: nat,C2: nat] :
% 5.31/5.58 ( ( plus_plus_nat @ ( plus_plus_nat @ ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) @ ( modulo_modulo_nat @ A @ B ) ) @ C2 )
% 5.31/5.58 = ( plus_plus_nat @ A @ C2 ) ) ).
% 5.31/5.58
% 5.31/5.58 % cancel_div_mod_rules(2)
% 5.31/5.58 thf(fact_4850_cancel__div__mod__rules_I2_J,axiom,
% 5.31/5.58 ! [B: int,A: int,C2: int] :
% 5.31/5.58 ( ( plus_plus_int @ ( plus_plus_int @ ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) @ ( modulo_modulo_int @ A @ B ) ) @ C2 )
% 5.31/5.58 = ( plus_plus_int @ A @ C2 ) ) ).
% 5.31/5.58
% 5.31/5.58 % cancel_div_mod_rules(2)
% 5.31/5.58 thf(fact_4851_cancel__div__mod__rules_I2_J,axiom,
% 5.31/5.58 ! [B: code_natural,A: code_natural,C2: code_natural] :
% 5.31/5.58 ( ( plus_p4538020629002901425atural @ ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ B @ ( divide5121882707175180666atural @ A @ B ) ) @ ( modulo8411746178871703098atural @ A @ B ) ) @ C2 )
% 5.31/5.58 = ( plus_p4538020629002901425atural @ A @ C2 ) ) ).
% 5.31/5.58
% 5.31/5.58 % cancel_div_mod_rules(2)
% 5.31/5.58 thf(fact_4852_cancel__div__mod__rules_I1_J,axiom,
% 5.31/5.58 ! [A: nat,B: nat,C2: nat] :
% 5.31/5.58 ( ( plus_plus_nat @ ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) @ ( modulo_modulo_nat @ A @ B ) ) @ C2 )
% 5.31/5.58 = ( plus_plus_nat @ A @ C2 ) ) ).
% 5.31/5.58
% 5.31/5.58 % cancel_div_mod_rules(1)
% 5.31/5.58 thf(fact_4853_cancel__div__mod__rules_I1_J,axiom,
% 5.31/5.58 ! [A: int,B: int,C2: int] :
% 5.31/5.58 ( ( plus_plus_int @ ( plus_plus_int @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) @ ( modulo_modulo_int @ A @ B ) ) @ C2 )
% 5.31/5.58 = ( plus_plus_int @ A @ C2 ) ) ).
% 5.31/5.58
% 5.31/5.58 % cancel_div_mod_rules(1)
% 5.31/5.58 thf(fact_4854_cancel__div__mod__rules_I1_J,axiom,
% 5.31/5.58 ! [A: code_natural,B: code_natural,C2: code_natural] :
% 5.31/5.58 ( ( plus_p4538020629002901425atural @ ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ ( divide5121882707175180666atural @ A @ B ) @ B ) @ ( modulo8411746178871703098atural @ A @ B ) ) @ C2 )
% 5.31/5.58 = ( plus_p4538020629002901425atural @ A @ C2 ) ) ).
% 5.31/5.58
% 5.31/5.58 % cancel_div_mod_rules(1)
% 5.31/5.58 thf(fact_4855_mod__div__decomp,axiom,
% 5.31/5.58 ! [A: nat,B: nat] :
% 5.31/5.58 ( A
% 5.31/5.58 = ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) @ ( modulo_modulo_nat @ A @ B ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % mod_div_decomp
% 5.31/5.58 thf(fact_4856_mod__div__decomp,axiom,
% 5.31/5.58 ! [A: int,B: int] :
% 5.31/5.58 ( A
% 5.31/5.58 = ( plus_plus_int @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) @ ( modulo_modulo_int @ A @ B ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % mod_div_decomp
% 5.31/5.58 thf(fact_4857_mod__div__decomp,axiom,
% 5.31/5.58 ! [A: code_natural,B: code_natural] :
% 5.31/5.58 ( A
% 5.31/5.58 = ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ ( divide5121882707175180666atural @ A @ B ) @ B ) @ ( modulo8411746178871703098atural @ A @ B ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % mod_div_decomp
% 5.31/5.58 thf(fact_4858_div__mult__mod__eq,axiom,
% 5.31/5.58 ! [A: nat,B: nat] :
% 5.31/5.58 ( ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) @ ( modulo_modulo_nat @ A @ B ) )
% 5.31/5.58 = A ) ).
% 5.31/5.58
% 5.31/5.58 % div_mult_mod_eq
% 5.31/5.58 thf(fact_4859_div__mult__mod__eq,axiom,
% 5.31/5.58 ! [A: int,B: int] :
% 5.31/5.58 ( ( plus_plus_int @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) @ ( modulo_modulo_int @ A @ B ) )
% 5.31/5.58 = A ) ).
% 5.31/5.58
% 5.31/5.58 % div_mult_mod_eq
% 5.31/5.58 thf(fact_4860_div__mult__mod__eq,axiom,
% 5.31/5.58 ! [A: code_natural,B: code_natural] :
% 5.31/5.58 ( ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ ( divide5121882707175180666atural @ A @ B ) @ B ) @ ( modulo8411746178871703098atural @ A @ B ) )
% 5.31/5.58 = A ) ).
% 5.31/5.58
% 5.31/5.58 % div_mult_mod_eq
% 5.31/5.58 thf(fact_4861_mod__div__mult__eq,axiom,
% 5.31/5.58 ! [A: nat,B: nat] :
% 5.31/5.58 ( ( plus_plus_nat @ ( modulo_modulo_nat @ A @ B ) @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) )
% 5.31/5.58 = A ) ).
% 5.31/5.58
% 5.31/5.58 % mod_div_mult_eq
% 5.31/5.58 thf(fact_4862_mod__div__mult__eq,axiom,
% 5.31/5.58 ! [A: int,B: int] :
% 5.31/5.58 ( ( plus_plus_int @ ( modulo_modulo_int @ A @ B ) @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) )
% 5.31/5.58 = A ) ).
% 5.31/5.58
% 5.31/5.58 % mod_div_mult_eq
% 5.31/5.58 thf(fact_4863_mod__div__mult__eq,axiom,
% 5.31/5.58 ! [A: code_natural,B: code_natural] :
% 5.31/5.58 ( ( plus_p4538020629002901425atural @ ( modulo8411746178871703098atural @ A @ B ) @ ( times_2397367101498566445atural @ ( divide5121882707175180666atural @ A @ B ) @ B ) )
% 5.31/5.58 = A ) ).
% 5.31/5.58
% 5.31/5.58 % mod_div_mult_eq
% 5.31/5.58 thf(fact_4864_mod__mult__div__eq,axiom,
% 5.31/5.58 ! [A: nat,B: nat] :
% 5.31/5.58 ( ( plus_plus_nat @ ( modulo_modulo_nat @ A @ B ) @ ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) )
% 5.31/5.58 = A ) ).
% 5.31/5.58
% 5.31/5.58 % mod_mult_div_eq
% 5.31/5.58 thf(fact_4865_mod__mult__div__eq,axiom,
% 5.31/5.58 ! [A: int,B: int] :
% 5.31/5.58 ( ( plus_plus_int @ ( modulo_modulo_int @ A @ B ) @ ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) )
% 5.31/5.58 = A ) ).
% 5.31/5.58
% 5.31/5.58 % mod_mult_div_eq
% 5.31/5.58 thf(fact_4866_mod__mult__div__eq,axiom,
% 5.31/5.58 ! [A: code_natural,B: code_natural] :
% 5.31/5.58 ( ( plus_p4538020629002901425atural @ ( modulo8411746178871703098atural @ A @ B ) @ ( times_2397367101498566445atural @ B @ ( divide5121882707175180666atural @ A @ B ) ) )
% 5.31/5.58 = A ) ).
% 5.31/5.58
% 5.31/5.58 % mod_mult_div_eq
% 5.31/5.58 thf(fact_4867_mult__div__mod__eq,axiom,
% 5.31/5.58 ! [B: nat,A: nat] :
% 5.31/5.58 ( ( plus_plus_nat @ ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) @ ( modulo_modulo_nat @ A @ B ) )
% 5.31/5.58 = A ) ).
% 5.31/5.58
% 5.31/5.58 % mult_div_mod_eq
% 5.31/5.58 thf(fact_4868_mult__div__mod__eq,axiom,
% 5.31/5.58 ! [B: int,A: int] :
% 5.31/5.58 ( ( plus_plus_int @ ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) @ ( modulo_modulo_int @ A @ B ) )
% 5.31/5.58 = A ) ).
% 5.31/5.58
% 5.31/5.58 % mult_div_mod_eq
% 5.31/5.58 thf(fact_4869_mult__div__mod__eq,axiom,
% 5.31/5.58 ! [B: code_natural,A: code_natural] :
% 5.31/5.58 ( ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ B @ ( divide5121882707175180666atural @ A @ B ) ) @ ( modulo8411746178871703098atural @ A @ B ) )
% 5.31/5.58 = A ) ).
% 5.31/5.58
% 5.31/5.58 % mult_div_mod_eq
% 5.31/5.58 thf(fact_4870_minus__div__mult__eq__mod,axiom,
% 5.31/5.58 ! [A: nat,B: nat] :
% 5.31/5.58 ( ( minus_minus_nat @ A @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) )
% 5.31/5.58 = ( modulo_modulo_nat @ A @ B ) ) ).
% 5.31/5.58
% 5.31/5.58 % minus_div_mult_eq_mod
% 5.31/5.58 thf(fact_4871_minus__div__mult__eq__mod,axiom,
% 5.31/5.58 ! [A: int,B: int] :
% 5.31/5.58 ( ( minus_minus_int @ A @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) )
% 5.31/5.58 = ( modulo_modulo_int @ A @ B ) ) ).
% 5.31/5.58
% 5.31/5.58 % minus_div_mult_eq_mod
% 5.31/5.58 thf(fact_4872_minus__div__mult__eq__mod,axiom,
% 5.31/5.58 ! [A: code_natural,B: code_natural] :
% 5.31/5.58 ( ( minus_7197305767214868737atural @ A @ ( times_2397367101498566445atural @ ( divide5121882707175180666atural @ A @ B ) @ B ) )
% 5.31/5.58 = ( modulo8411746178871703098atural @ A @ B ) ) ).
% 5.31/5.58
% 5.31/5.58 % minus_div_mult_eq_mod
% 5.31/5.58 thf(fact_4873_minus__mod__eq__div__mult,axiom,
% 5.31/5.58 ! [A: nat,B: nat] :
% 5.31/5.58 ( ( minus_minus_nat @ A @ ( modulo_modulo_nat @ A @ B ) )
% 5.31/5.58 = ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) ) ).
% 5.31/5.58
% 5.31/5.58 % minus_mod_eq_div_mult
% 5.31/5.58 thf(fact_4874_minus__mod__eq__div__mult,axiom,
% 5.31/5.58 ! [A: int,B: int] :
% 5.31/5.58 ( ( minus_minus_int @ A @ ( modulo_modulo_int @ A @ B ) )
% 5.31/5.58 = ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) ) ).
% 5.31/5.58
% 5.31/5.58 % minus_mod_eq_div_mult
% 5.31/5.58 thf(fact_4875_minus__mod__eq__div__mult,axiom,
% 5.31/5.58 ! [A: code_natural,B: code_natural] :
% 5.31/5.58 ( ( minus_7197305767214868737atural @ A @ ( modulo8411746178871703098atural @ A @ B ) )
% 5.31/5.58 = ( times_2397367101498566445atural @ ( divide5121882707175180666atural @ A @ B ) @ B ) ) ).
% 5.31/5.58
% 5.31/5.58 % minus_mod_eq_div_mult
% 5.31/5.58 thf(fact_4876_minus__mod__eq__mult__div,axiom,
% 5.31/5.58 ! [A: nat,B: nat] :
% 5.31/5.58 ( ( minus_minus_nat @ A @ ( modulo_modulo_nat @ A @ B ) )
% 5.31/5.58 = ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % minus_mod_eq_mult_div
% 5.31/5.58 thf(fact_4877_minus__mod__eq__mult__div,axiom,
% 5.31/5.58 ! [A: int,B: int] :
% 5.31/5.58 ( ( minus_minus_int @ A @ ( modulo_modulo_int @ A @ B ) )
% 5.31/5.58 = ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % minus_mod_eq_mult_div
% 5.31/5.58 thf(fact_4878_minus__mod__eq__mult__div,axiom,
% 5.31/5.58 ! [A: code_natural,B: code_natural] :
% 5.31/5.58 ( ( minus_7197305767214868737atural @ A @ ( modulo8411746178871703098atural @ A @ B ) )
% 5.31/5.58 = ( times_2397367101498566445atural @ B @ ( divide5121882707175180666atural @ A @ B ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % minus_mod_eq_mult_div
% 5.31/5.58 thf(fact_4879_minus__mult__div__eq__mod,axiom,
% 5.31/5.58 ! [A: nat,B: nat] :
% 5.31/5.58 ( ( minus_minus_nat @ A @ ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) )
% 5.31/5.58 = ( modulo_modulo_nat @ A @ B ) ) ).
% 5.31/5.58
% 5.31/5.58 % minus_mult_div_eq_mod
% 5.31/5.58 thf(fact_4880_minus__mult__div__eq__mod,axiom,
% 5.31/5.58 ! [A: int,B: int] :
% 5.31/5.58 ( ( minus_minus_int @ A @ ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) )
% 5.31/5.58 = ( modulo_modulo_int @ A @ B ) ) ).
% 5.31/5.58
% 5.31/5.58 % minus_mult_div_eq_mod
% 5.31/5.58 thf(fact_4881_minus__mult__div__eq__mod,axiom,
% 5.31/5.58 ! [A: code_natural,B: code_natural] :
% 5.31/5.58 ( ( minus_7197305767214868737atural @ A @ ( times_2397367101498566445atural @ B @ ( divide5121882707175180666atural @ A @ B ) ) )
% 5.31/5.58 = ( modulo8411746178871703098atural @ A @ B ) ) ).
% 5.31/5.58
% 5.31/5.58 % minus_mult_div_eq_mod
% 5.31/5.58 thf(fact_4882_mod__le__divisor,axiom,
% 5.31/5.58 ! [N: nat,M2: nat] :
% 5.31/5.58 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.58 => ( ord_less_eq_nat @ ( modulo_modulo_nat @ M2 @ N ) @ N ) ) ).
% 5.31/5.58
% 5.31/5.58 % mod_le_divisor
% 5.31/5.58 thf(fact_4883_div__less__mono,axiom,
% 5.31/5.58 ! [A4: nat,B5: nat,N: nat] :
% 5.31/5.58 ( ( ord_less_nat @ A4 @ B5 )
% 5.31/5.58 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.58 => ( ( ( modulo_modulo_nat @ A4 @ N )
% 5.31/5.58 = zero_zero_nat )
% 5.31/5.58 => ( ( ( modulo_modulo_nat @ B5 @ N )
% 5.31/5.58 = zero_zero_nat )
% 5.31/5.58 => ( ord_less_nat @ ( divide_divide_nat @ A4 @ N ) @ ( divide_divide_nat @ B5 @ N ) ) ) ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % div_less_mono
% 5.31/5.58 thf(fact_4884_nat__mod__eq__lemma,axiom,
% 5.31/5.58 ! [X: nat,N: nat,Y: nat] :
% 5.31/5.58 ( ( ( modulo_modulo_nat @ X @ N )
% 5.31/5.58 = ( modulo_modulo_nat @ Y @ N ) )
% 5.31/5.58 => ( ( ord_less_eq_nat @ Y @ X )
% 5.31/5.58 => ? [Q3: nat] :
% 5.31/5.58 ( X
% 5.31/5.58 = ( plus_plus_nat @ Y @ ( times_times_nat @ N @ Q3 ) ) ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % nat_mod_eq_lemma
% 5.31/5.58 thf(fact_4885_mod__eq__nat2E,axiom,
% 5.31/5.58 ! [M2: nat,Q2: nat,N: nat] :
% 5.31/5.58 ( ( ( modulo_modulo_nat @ M2 @ Q2 )
% 5.31/5.58 = ( modulo_modulo_nat @ N @ Q2 ) )
% 5.31/5.58 => ( ( ord_less_eq_nat @ M2 @ N )
% 5.31/5.58 => ~ ! [S: nat] :
% 5.31/5.58 ( N
% 5.31/5.58 != ( plus_plus_nat @ M2 @ ( times_times_nat @ Q2 @ S ) ) ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % mod_eq_nat2E
% 5.31/5.58 thf(fact_4886_mod__eq__nat1E,axiom,
% 5.31/5.58 ! [M2: nat,Q2: nat,N: nat] :
% 5.31/5.58 ( ( ( modulo_modulo_nat @ M2 @ Q2 )
% 5.31/5.58 = ( modulo_modulo_nat @ N @ Q2 ) )
% 5.31/5.58 => ( ( ord_less_eq_nat @ N @ M2 )
% 5.31/5.58 => ~ ! [S: nat] :
% 5.31/5.58 ( M2
% 5.31/5.58 != ( plus_plus_nat @ N @ ( times_times_nat @ Q2 @ S ) ) ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % mod_eq_nat1E
% 5.31/5.58 thf(fact_4887_mod__mult2__eq,axiom,
% 5.31/5.58 ! [M2: nat,N: nat,Q2: nat] :
% 5.31/5.58 ( ( modulo_modulo_nat @ M2 @ ( times_times_nat @ N @ Q2 ) )
% 5.31/5.58 = ( plus_plus_nat @ ( times_times_nat @ N @ ( modulo_modulo_nat @ ( divide_divide_nat @ M2 @ N ) @ Q2 ) ) @ ( modulo_modulo_nat @ M2 @ N ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % mod_mult2_eq
% 5.31/5.58 thf(fact_4888_div__mod__decomp,axiom,
% 5.31/5.58 ! [A4: nat,N: nat] :
% 5.31/5.58 ( A4
% 5.31/5.58 = ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A4 @ N ) @ N ) @ ( modulo_modulo_nat @ A4 @ N ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % div_mod_decomp
% 5.31/5.58 thf(fact_4889_modulo__nat__def,axiom,
% 5.31/5.58 ( modulo_modulo_nat
% 5.31/5.58 = ( ^ [M6: nat,N4: nat] : ( minus_minus_nat @ M6 @ ( times_times_nat @ ( divide_divide_nat @ M6 @ N4 ) @ N4 ) ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % modulo_nat_def
% 5.31/5.58 thf(fact_4890_mod__mult2__eq_H,axiom,
% 5.31/5.58 ! [A: code_natural,M2: nat,N: nat] :
% 5.31/5.58 ( ( modulo8411746178871703098atural @ A @ ( times_2397367101498566445atural @ ( semiri3763490453095760265atural @ M2 ) @ ( semiri3763490453095760265atural @ N ) ) )
% 5.31/5.58 = ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ ( semiri3763490453095760265atural @ M2 ) @ ( modulo8411746178871703098atural @ ( divide5121882707175180666atural @ A @ ( semiri3763490453095760265atural @ M2 ) ) @ ( semiri3763490453095760265atural @ N ) ) ) @ ( modulo8411746178871703098atural @ A @ ( semiri3763490453095760265atural @ M2 ) ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % mod_mult2_eq'
% 5.31/5.58 thf(fact_4891_mod__mult2__eq_H,axiom,
% 5.31/5.58 ! [A: int,M2: nat,N: nat] :
% 5.31/5.58 ( ( modulo_modulo_int @ A @ ( times_times_int @ ( semiri1314217659103216013at_int @ M2 ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 5.31/5.58 = ( plus_plus_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ M2 ) @ ( modulo_modulo_int @ ( divide_divide_int @ A @ ( semiri1314217659103216013at_int @ M2 ) ) @ ( semiri1314217659103216013at_int @ N ) ) ) @ ( modulo_modulo_int @ A @ ( semiri1314217659103216013at_int @ M2 ) ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % mod_mult2_eq'
% 5.31/5.58 thf(fact_4892_mod__mult2__eq_H,axiom,
% 5.31/5.58 ! [A: nat,M2: nat,N: nat] :
% 5.31/5.58 ( ( modulo_modulo_nat @ A @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ M2 ) @ ( semiri1316708129612266289at_nat @ N ) ) )
% 5.31/5.58 = ( plus_plus_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ M2 ) @ ( modulo_modulo_nat @ ( divide_divide_nat @ A @ ( semiri1316708129612266289at_nat @ M2 ) ) @ ( semiri1316708129612266289at_nat @ N ) ) ) @ ( modulo_modulo_nat @ A @ ( semiri1316708129612266289at_nat @ M2 ) ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % mod_mult2_eq'
% 5.31/5.58 thf(fact_4893_split__mod,axiom,
% 5.31/5.58 ! [P2: nat > $o,M2: nat,N: nat] :
% 5.31/5.58 ( ( P2 @ ( modulo_modulo_nat @ M2 @ N ) )
% 5.31/5.58 = ( ( ( N = zero_zero_nat )
% 5.31/5.58 => ( P2 @ M2 ) )
% 5.31/5.58 & ( ( N != zero_zero_nat )
% 5.31/5.58 => ! [I: nat,J: nat] :
% 5.31/5.58 ( ( ord_less_nat @ J @ N )
% 5.31/5.58 => ( ( M2
% 5.31/5.58 = ( plus_plus_nat @ ( times_times_nat @ N @ I ) @ J ) )
% 5.31/5.58 => ( P2 @ J ) ) ) ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % split_mod
% 5.31/5.58 thf(fact_4894_unique__euclidean__semiring__numeral__class_Omod__mult2__eq,axiom,
% 5.31/5.58 ! [C2: nat,A: nat,B: nat] :
% 5.31/5.58 ( ( ord_less_eq_nat @ zero_zero_nat @ C2 )
% 5.31/5.58 => ( ( modulo_modulo_nat @ A @ ( times_times_nat @ B @ C2 ) )
% 5.31/5.58 = ( plus_plus_nat @ ( times_times_nat @ B @ ( modulo_modulo_nat @ ( divide_divide_nat @ A @ B ) @ C2 ) ) @ ( modulo_modulo_nat @ A @ B ) ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % unique_euclidean_semiring_numeral_class.mod_mult2_eq
% 5.31/5.58 thf(fact_4895_unique__euclidean__semiring__numeral__class_Omod__mult2__eq,axiom,
% 5.31/5.58 ! [C2: int,A: int,B: int] :
% 5.31/5.58 ( ( ord_less_eq_int @ zero_zero_int @ C2 )
% 5.31/5.58 => ( ( modulo_modulo_int @ A @ ( times_times_int @ B @ C2 ) )
% 5.31/5.58 = ( plus_plus_int @ ( times_times_int @ B @ ( modulo_modulo_int @ ( divide_divide_int @ A @ B ) @ C2 ) ) @ ( modulo_modulo_int @ A @ B ) ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % unique_euclidean_semiring_numeral_class.mod_mult2_eq
% 5.31/5.58 thf(fact_4896_Suc__times__mod__eq,axiom,
% 5.31/5.58 ! [M2: nat,N: nat] :
% 5.31/5.58 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M2 )
% 5.31/5.58 => ( ( modulo_modulo_nat @ ( suc @ ( times_times_nat @ M2 @ N ) ) @ M2 )
% 5.31/5.58 = one_one_nat ) ) ).
% 5.31/5.58
% 5.31/5.58 % Suc_times_mod_eq
% 5.31/5.58 thf(fact_4897_nth__rotate1,axiom,
% 5.31/5.58 ! [N: nat,Xs2: list_VEBT_VEBT] :
% 5.31/5.58 ( ( ord_less_nat @ N @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 5.31/5.58 => ( ( nth_VEBT_VEBT @ ( rotate1_VEBT_VEBT @ Xs2 ) @ N )
% 5.31/5.58 = ( nth_VEBT_VEBT @ Xs2 @ ( modulo_modulo_nat @ ( suc @ N ) @ ( size_s6755466524823107622T_VEBT @ Xs2 ) ) ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % nth_rotate1
% 5.31/5.58 thf(fact_4898_nth__rotate1,axiom,
% 5.31/5.58 ! [N: nat,Xs2: list_o] :
% 5.31/5.58 ( ( ord_less_nat @ N @ ( size_size_list_o @ Xs2 ) )
% 5.31/5.58 => ( ( nth_o @ ( rotate1_o @ Xs2 ) @ N )
% 5.31/5.58 = ( nth_o @ Xs2 @ ( modulo_modulo_nat @ ( suc @ N ) @ ( size_size_list_o @ Xs2 ) ) ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % nth_rotate1
% 5.31/5.58 thf(fact_4899_nth__rotate1,axiom,
% 5.31/5.58 ! [N: nat,Xs2: list_nat] :
% 5.31/5.58 ( ( ord_less_nat @ N @ ( size_size_list_nat @ Xs2 ) )
% 5.31/5.58 => ( ( nth_nat @ ( rotate1_nat @ Xs2 ) @ N )
% 5.31/5.58 = ( nth_nat @ Xs2 @ ( modulo_modulo_nat @ ( suc @ N ) @ ( size_size_list_nat @ Xs2 ) ) ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % nth_rotate1
% 5.31/5.58 thf(fact_4900_nth__rotate1,axiom,
% 5.31/5.58 ! [N: nat,Xs2: list_int] :
% 5.31/5.58 ( ( ord_less_nat @ N @ ( size_size_list_int @ Xs2 ) )
% 5.31/5.58 => ( ( nth_int @ ( rotate1_int @ Xs2 ) @ N )
% 5.31/5.58 = ( nth_int @ Xs2 @ ( modulo_modulo_nat @ ( suc @ N ) @ ( size_size_list_int @ Xs2 ) ) ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % nth_rotate1
% 5.31/5.58 thf(fact_4901_divmod__digit__0_I2_J,axiom,
% 5.31/5.58 ! [B: nat,A: nat] :
% 5.31/5.58 ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.31/5.58 => ( ( ord_less_nat @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) @ B )
% 5.31/5.58 => ( ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) )
% 5.31/5.58 = ( modulo_modulo_nat @ A @ B ) ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % divmod_digit_0(2)
% 5.31/5.58 thf(fact_4902_divmod__digit__0_I2_J,axiom,
% 5.31/5.58 ! [B: int,A: int] :
% 5.31/5.58 ( ( ord_less_int @ zero_zero_int @ B )
% 5.31/5.58 => ( ( ord_less_int @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ B )
% 5.31/5.58 => ( ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) )
% 5.31/5.58 = ( modulo_modulo_int @ A @ B ) ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % divmod_digit_0(2)
% 5.31/5.58 thf(fact_4903_bits__stable__imp__add__self,axiom,
% 5.31/5.58 ! [A: nat] :
% 5.31/5.58 ( ( ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.31/5.58 = A )
% 5.31/5.58 => ( ( plus_plus_nat @ A @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.31/5.58 = zero_zero_nat ) ) ).
% 5.31/5.58
% 5.31/5.58 % bits_stable_imp_add_self
% 5.31/5.58 thf(fact_4904_bits__stable__imp__add__self,axiom,
% 5.31/5.58 ! [A: int] :
% 5.31/5.58 ( ( ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.31/5.58 = A )
% 5.31/5.58 => ( ( plus_plus_int @ A @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) )
% 5.31/5.58 = zero_zero_int ) ) ).
% 5.31/5.58
% 5.31/5.58 % bits_stable_imp_add_self
% 5.31/5.58 thf(fact_4905_bits__stable__imp__add__self,axiom,
% 5.31/5.58 ! [A: code_natural] :
% 5.31/5.58 ( ( ( divide5121882707175180666atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 5.31/5.58 = A )
% 5.31/5.58 => ( ( plus_p4538020629002901425atural @ A @ ( modulo8411746178871703098atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) )
% 5.31/5.58 = zero_z2226904508553997617atural ) ) ).
% 5.31/5.58
% 5.31/5.58 % bits_stable_imp_add_self
% 5.31/5.58 thf(fact_4906_verit__le__mono__div,axiom,
% 5.31/5.58 ! [A4: nat,B5: nat,N: nat] :
% 5.31/5.58 ( ( ord_less_nat @ A4 @ B5 )
% 5.31/5.58 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.58 => ( ord_less_eq_nat
% 5.31/5.58 @ ( plus_plus_nat @ ( divide_divide_nat @ A4 @ N )
% 5.31/5.58 @ ( if_nat
% 5.31/5.58 @ ( ( modulo_modulo_nat @ B5 @ N )
% 5.31/5.58 = zero_zero_nat )
% 5.31/5.58 @ one_one_nat
% 5.31/5.58 @ zero_zero_nat ) )
% 5.31/5.58 @ ( divide_divide_nat @ B5 @ N ) ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % verit_le_mono_div
% 5.31/5.58 thf(fact_4907_divmod__digit__0_I1_J,axiom,
% 5.31/5.58 ! [B: nat,A: nat] :
% 5.31/5.58 ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.31/5.58 => ( ( ord_less_nat @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) @ B )
% 5.31/5.58 => ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) )
% 5.31/5.58 = ( divide_divide_nat @ A @ B ) ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % divmod_digit_0(1)
% 5.31/5.58 thf(fact_4908_divmod__digit__0_I1_J,axiom,
% 5.31/5.58 ! [B: int,A: int] :
% 5.31/5.58 ( ( ord_less_int @ zero_zero_int @ B )
% 5.31/5.58 => ( ( ord_less_int @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ B )
% 5.31/5.58 => ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) )
% 5.31/5.58 = ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % divmod_digit_0(1)
% 5.31/5.58 thf(fact_4909_mult__exp__mod__exp__eq,axiom,
% 5.31/5.58 ! [M2: nat,N: nat,A: nat] :
% 5.31/5.58 ( ( ord_less_eq_nat @ M2 @ N )
% 5.31/5.58 => ( ( modulo_modulo_nat @ ( times_times_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.31/5.58 = ( times_times_nat @ ( modulo_modulo_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M2 ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % mult_exp_mod_exp_eq
% 5.31/5.58 thf(fact_4910_mult__exp__mod__exp__eq,axiom,
% 5.31/5.58 ! [M2: nat,N: nat,A: int] :
% 5.31/5.58 ( ( ord_less_eq_nat @ M2 @ N )
% 5.31/5.58 => ( ( modulo_modulo_int @ ( times_times_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M2 ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.31/5.58 = ( times_times_int @ ( modulo_modulo_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M2 ) ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M2 ) ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % mult_exp_mod_exp_eq
% 5.31/5.58 thf(fact_4911_mult__exp__mod__exp__eq,axiom,
% 5.31/5.58 ! [M2: nat,N: nat,A: code_natural] :
% 5.31/5.58 ( ( ord_less_eq_nat @ M2 @ N )
% 5.31/5.58 => ( ( modulo8411746178871703098atural @ ( times_2397367101498566445atural @ A @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ M2 ) ) @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N ) )
% 5.31/5.58 = ( times_2397367101498566445atural @ ( modulo8411746178871703098atural @ A @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M2 ) ) ) @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ M2 ) ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % mult_exp_mod_exp_eq
% 5.31/5.58 thf(fact_4912_mod__double__modulus,axiom,
% 5.31/5.58 ! [M2: nat,X: nat] :
% 5.31/5.58 ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 5.31/5.58 => ( ( ord_less_eq_nat @ zero_zero_nat @ X )
% 5.31/5.58 => ( ( ( modulo_modulo_nat @ X @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) )
% 5.31/5.58 = ( modulo_modulo_nat @ X @ M2 ) )
% 5.31/5.58 | ( ( modulo_modulo_nat @ X @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) )
% 5.31/5.58 = ( plus_plus_nat @ ( modulo_modulo_nat @ X @ M2 ) @ M2 ) ) ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % mod_double_modulus
% 5.31/5.58 thf(fact_4913_mod__double__modulus,axiom,
% 5.31/5.58 ! [M2: int,X: int] :
% 5.31/5.58 ( ( ord_less_int @ zero_zero_int @ M2 )
% 5.31/5.58 => ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.31/5.58 => ( ( ( modulo_modulo_int @ X @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M2 ) )
% 5.31/5.58 = ( modulo_modulo_int @ X @ M2 ) )
% 5.31/5.58 | ( ( modulo_modulo_int @ X @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M2 ) )
% 5.31/5.58 = ( plus_plus_int @ ( modulo_modulo_int @ X @ M2 ) @ M2 ) ) ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % mod_double_modulus
% 5.31/5.58 thf(fact_4914_divmod__digit__1_I2_J,axiom,
% 5.31/5.58 ! [A: nat,B: nat] :
% 5.31/5.58 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.31/5.58 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.31/5.58 => ( ( ord_less_eq_nat @ B @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) )
% 5.31/5.58 => ( ( minus_minus_nat @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) @ B )
% 5.31/5.58 = ( modulo_modulo_nat @ A @ B ) ) ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % divmod_digit_1(2)
% 5.31/5.58 thf(fact_4915_divmod__digit__1_I2_J,axiom,
% 5.31/5.58 ! [A: int,B: int] :
% 5.31/5.58 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.31/5.58 => ( ( ord_less_int @ zero_zero_int @ B )
% 5.31/5.58 => ( ( ord_less_eq_int @ B @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) )
% 5.31/5.58 => ( ( minus_minus_int @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ B )
% 5.31/5.58 = ( modulo_modulo_int @ A @ B ) ) ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % divmod_digit_1(2)
% 5.31/5.58 thf(fact_4916_unset__bit__Suc,axiom,
% 5.31/5.58 ! [N: nat,A: nat] :
% 5.31/5.58 ( ( bit_se4205575877204974255it_nat @ ( suc @ N ) @ A )
% 5.31/5.58 = ( 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 ) ) ) ) ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % unset_bit_Suc
% 5.31/5.58 thf(fact_4917_unset__bit__Suc,axiom,
% 5.31/5.58 ! [N: nat,A: code_natural] :
% 5.31/5.58 ( ( bit_se7083795435491715335atural @ ( suc @ N ) @ A )
% 5.31/5.58 = ( plus_p4538020629002901425atural @ ( modulo8411746178871703098atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( bit_se7083795435491715335atural @ N @ ( divide5121882707175180666atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % unset_bit_Suc
% 5.31/5.58 thf(fact_4918_unset__bit__Suc,axiom,
% 5.31/5.58 ! [N: nat,A: int] :
% 5.31/5.58 ( ( bit_se4203085406695923979it_int @ ( suc @ N ) @ A )
% 5.31/5.58 = ( 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 ) ) ) ) ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % unset_bit_Suc
% 5.31/5.58 thf(fact_4919_set__bit__Suc,axiom,
% 5.31/5.58 ! [N: nat,A: nat] :
% 5.31/5.58 ( ( bit_se7882103937844011126it_nat @ ( suc @ N ) @ A )
% 5.31/5.58 = ( 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 ) ) ) ) ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % set_bit_Suc
% 5.31/5.58 thf(fact_4920_set__bit__Suc,axiom,
% 5.31/5.58 ! [N: nat,A: code_natural] :
% 5.31/5.58 ( ( bit_se1617098188084679374atural @ ( suc @ N ) @ A )
% 5.31/5.58 = ( plus_p4538020629002901425atural @ ( modulo8411746178871703098atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( bit_se1617098188084679374atural @ N @ ( divide5121882707175180666atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % set_bit_Suc
% 5.31/5.58 thf(fact_4921_set__bit__Suc,axiom,
% 5.31/5.58 ! [N: nat,A: int] :
% 5.31/5.58 ( ( bit_se7879613467334960850it_int @ ( suc @ N ) @ A )
% 5.31/5.58 = ( 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 ) ) ) ) ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % set_bit_Suc
% 5.31/5.58 thf(fact_4922_card__roots__unity__eq,axiom,
% 5.31/5.58 ! [N: nat] :
% 5.31/5.58 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.58 => ( ( finite_card_complex
% 5.31/5.58 @ ( collect_complex
% 5.31/5.58 @ ^ [Z4: complex] :
% 5.31/5.58 ( ( power_power_complex @ Z4 @ N )
% 5.31/5.58 = one_one_complex ) ) )
% 5.31/5.58 = N ) ) ).
% 5.31/5.58
% 5.31/5.58 % card_roots_unity_eq
% 5.31/5.58 thf(fact_4923_card__nth__roots,axiom,
% 5.31/5.58 ! [C2: complex,N: nat] :
% 5.31/5.58 ( ( C2 != zero_zero_complex )
% 5.31/5.58 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.58 => ( ( finite_card_complex
% 5.31/5.58 @ ( collect_complex
% 5.31/5.58 @ ^ [Z4: complex] :
% 5.31/5.58 ( ( power_power_complex @ Z4 @ N )
% 5.31/5.58 = C2 ) ) )
% 5.31/5.58 = N ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % card_nth_roots
% 5.31/5.58 thf(fact_4924_product__nth,axiom,
% 5.31/5.58 ! [N: nat,Xs2: list_Code_integer,Ys: list_Code_integer] :
% 5.31/5.58 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_s3445333598471063425nteger @ Xs2 ) @ ( size_s3445333598471063425nteger @ Ys ) ) )
% 5.31/5.58 => ( ( nth_Pr2304437835452373666nteger @ ( produc8792966785426426881nteger @ Xs2 @ Ys ) @ N )
% 5.31/5.58 = ( produc1086072967326762835nteger @ ( nth_Code_integer @ Xs2 @ ( divide_divide_nat @ N @ ( size_s3445333598471063425nteger @ Ys ) ) ) @ ( nth_Code_integer @ Ys @ ( modulo_modulo_nat @ N @ ( size_s3445333598471063425nteger @ Ys ) ) ) ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % product_nth
% 5.31/5.58 thf(fact_4925_product__nth,axiom,
% 5.31/5.58 ! [N: nat,Xs2: list_VEBT_VEBT,Ys: list_VEBT_VEBT] :
% 5.31/5.58 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) @ ( size_s6755466524823107622T_VEBT @ Ys ) ) )
% 5.31/5.58 => ( ( nth_Pr4953567300277697838T_VEBT @ ( produc4743750530478302277T_VEBT @ Xs2 @ Ys ) @ N )
% 5.31/5.58 = ( produc537772716801021591T_VEBT @ ( nth_VEBT_VEBT @ Xs2 @ ( divide_divide_nat @ N @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) @ ( nth_VEBT_VEBT @ Ys @ ( modulo_modulo_nat @ N @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % product_nth
% 5.31/5.58 thf(fact_4926_product__nth,axiom,
% 5.31/5.58 ! [N: nat,Xs2: list_VEBT_VEBT,Ys: list_o] :
% 5.31/5.58 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) @ ( size_size_list_o @ Ys ) ) )
% 5.31/5.58 => ( ( nth_Pr4606735188037164562VEBT_o @ ( product_VEBT_VEBT_o @ Xs2 @ Ys ) @ N )
% 5.31/5.58 = ( produc8721562602347293563VEBT_o @ ( nth_VEBT_VEBT @ Xs2 @ ( divide_divide_nat @ N @ ( size_size_list_o @ Ys ) ) ) @ ( nth_o @ Ys @ ( modulo_modulo_nat @ N @ ( size_size_list_o @ Ys ) ) ) ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % product_nth
% 5.31/5.58 thf(fact_4927_product__nth,axiom,
% 5.31/5.58 ! [N: nat,Xs2: list_VEBT_VEBT,Ys: list_nat] :
% 5.31/5.58 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) @ ( size_size_list_nat @ Ys ) ) )
% 5.31/5.58 => ( ( nth_Pr1791586995822124652BT_nat @ ( produc7295137177222721919BT_nat @ Xs2 @ Ys ) @ N )
% 5.31/5.58 = ( produc738532404422230701BT_nat @ ( nth_VEBT_VEBT @ Xs2 @ ( divide_divide_nat @ N @ ( size_size_list_nat @ Ys ) ) ) @ ( nth_nat @ Ys @ ( modulo_modulo_nat @ N @ ( size_size_list_nat @ Ys ) ) ) ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % product_nth
% 5.31/5.58 thf(fact_4928_product__nth,axiom,
% 5.31/5.58 ! [N: nat,Xs2: list_VEBT_VEBT,Ys: list_int] :
% 5.31/5.58 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) @ ( size_size_list_int @ Ys ) ) )
% 5.31/5.58 => ( ( nth_Pr6837108013167703752BT_int @ ( produc7292646706713671643BT_int @ Xs2 @ Ys ) @ N )
% 5.31/5.58 = ( produc736041933913180425BT_int @ ( nth_VEBT_VEBT @ Xs2 @ ( divide_divide_nat @ N @ ( size_size_list_int @ Ys ) ) ) @ ( nth_int @ Ys @ ( modulo_modulo_nat @ N @ ( size_size_list_int @ Ys ) ) ) ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % product_nth
% 5.31/5.58 thf(fact_4929_product__nth,axiom,
% 5.31/5.58 ! [N: nat,Xs2: list_o,Ys: list_VEBT_VEBT] :
% 5.31/5.58 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_size_list_o @ Xs2 ) @ ( size_s6755466524823107622T_VEBT @ Ys ) ) )
% 5.31/5.58 => ( ( nth_Pr6777367263587873994T_VEBT @ ( product_o_VEBT_VEBT @ Xs2 @ Ys ) @ N )
% 5.31/5.58 = ( produc2982872950893828659T_VEBT @ ( nth_o @ Xs2 @ ( divide_divide_nat @ N @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) @ ( nth_VEBT_VEBT @ Ys @ ( modulo_modulo_nat @ N @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) ) ) ) ).
% 5.31/5.58
% 5.31/5.58 % product_nth
% 5.31/5.58 thf(fact_4930_product__nth,axiom,
% 5.31/5.58 ! [N: nat,Xs2: list_o,Ys: list_o] :
% 5.31/5.58 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_size_list_o @ Xs2 ) @ ( size_size_list_o @ Ys ) ) )
% 5.31/5.58 => ( ( nth_Product_prod_o_o @ ( product_o_o @ Xs2 @ Ys ) @ N )
% 5.31/5.58 = ( product_Pair_o_o @ ( nth_o @ Xs2 @ ( divide_divide_nat @ N @ ( size_size_list_o @ Ys ) ) ) @ ( nth_o @ Ys @ ( modulo_modulo_nat @ N @ ( size_size_list_o @ Ys ) ) ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % product_nth
% 5.31/5.59 thf(fact_4931_product__nth,axiom,
% 5.31/5.59 ! [N: nat,Xs2: list_o,Ys: list_nat] :
% 5.31/5.59 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_size_list_o @ Xs2 ) @ ( size_size_list_nat @ Ys ) ) )
% 5.31/5.59 => ( ( nth_Pr5826913651314560976_o_nat @ ( product_o_nat @ Xs2 @ Ys ) @ N )
% 5.31/5.59 = ( product_Pair_o_nat @ ( nth_o @ Xs2 @ ( divide_divide_nat @ N @ ( size_size_list_nat @ Ys ) ) ) @ ( nth_nat @ Ys @ ( modulo_modulo_nat @ N @ ( size_size_list_nat @ Ys ) ) ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % product_nth
% 5.31/5.59 thf(fact_4932_product__nth,axiom,
% 5.31/5.59 ! [N: nat,Xs2: list_o,Ys: list_int] :
% 5.31/5.59 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_size_list_o @ Xs2 ) @ ( size_size_list_int @ Ys ) ) )
% 5.31/5.59 => ( ( nth_Pr1649062631805364268_o_int @ ( product_o_int @ Xs2 @ Ys ) @ N )
% 5.31/5.59 = ( product_Pair_o_int @ ( nth_o @ Xs2 @ ( divide_divide_nat @ N @ ( size_size_list_int @ Ys ) ) ) @ ( nth_int @ Ys @ ( modulo_modulo_nat @ N @ ( size_size_list_int @ Ys ) ) ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % product_nth
% 5.31/5.59 thf(fact_4933_product__nth,axiom,
% 5.31/5.59 ! [N: nat,Xs2: list_nat,Ys: list_VEBT_VEBT] :
% 5.31/5.59 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_size_list_nat @ Xs2 ) @ ( size_s6755466524823107622T_VEBT @ Ys ) ) )
% 5.31/5.59 => ( ( nth_Pr744662078594809490T_VEBT @ ( produc7156399406898700509T_VEBT @ Xs2 @ Ys ) @ N )
% 5.31/5.59 = ( produc599794634098209291T_VEBT @ ( nth_nat @ Xs2 @ ( divide_divide_nat @ N @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) @ ( nth_VEBT_VEBT @ Ys @ ( modulo_modulo_nat @ N @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % product_nth
% 5.31/5.59 thf(fact_4934_divmod__digit__1_I1_J,axiom,
% 5.31/5.59 ! [A: code_integer,B: code_integer] :
% 5.31/5.59 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 5.31/5.59 => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 5.31/5.59 => ( ( ord_le3102999989581377725nteger @ B @ ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) )
% 5.31/5.59 => ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) ) @ one_one_Code_integer )
% 5.31/5.59 = ( divide6298287555418463151nteger @ A @ B ) ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % divmod_digit_1(1)
% 5.31/5.59 thf(fact_4935_divmod__digit__1_I1_J,axiom,
% 5.31/5.59 ! [A: nat,B: nat] :
% 5.31/5.59 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.31/5.59 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.31/5.59 => ( ( ord_less_eq_nat @ B @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) )
% 5.31/5.59 => ( ( 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 )
% 5.31/5.59 = ( divide_divide_nat @ A @ B ) ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % divmod_digit_1(1)
% 5.31/5.59 thf(fact_4936_divmod__digit__1_I1_J,axiom,
% 5.31/5.59 ! [A: int,B: int] :
% 5.31/5.59 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.31/5.59 => ( ( ord_less_int @ zero_zero_int @ B )
% 5.31/5.59 => ( ( ord_less_eq_int @ B @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) )
% 5.31/5.59 => ( ( 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 )
% 5.31/5.59 = ( divide_divide_int @ A @ B ) ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % divmod_digit_1(1)
% 5.31/5.59 thf(fact_4937_VEBT__internal_Oinsert_H_Opelims,axiom,
% 5.31/5.59 ! [X: vEBT_VEBT,Xa2: nat,Y: vEBT_VEBT] :
% 5.31/5.59 ( ( ( vEBT_VEBT_insert @ X @ Xa2 )
% 5.31/5.59 = Y )
% 5.31/5.59 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_insert_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 5.31/5.59 => ( ! [A3: $o,B3: $o] :
% 5.31/5.59 ( ( X
% 5.31/5.59 = ( vEBT_Leaf @ A3 @ B3 ) )
% 5.31/5.59 => ( ( Y
% 5.31/5.59 = ( vEBT_vebt_insert @ ( vEBT_Leaf @ A3 @ B3 ) @ Xa2 ) )
% 5.31/5.59 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ Xa2 ) ) ) )
% 5.31/5.59 => ~ ! [Info: option4927543243414619207at_nat,Deg2: nat,TreeList: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.31/5.59 ( ( X
% 5.31/5.59 = ( vEBT_Node @ Info @ Deg2 @ TreeList @ Summary2 ) )
% 5.31/5.59 => ( ( ( ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) @ Xa2 )
% 5.31/5.59 => ( Y
% 5.31/5.59 = ( vEBT_Node @ Info @ Deg2 @ TreeList @ Summary2 ) ) )
% 5.31/5.59 & ( ~ ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) @ Xa2 )
% 5.31/5.59 => ( Y
% 5.31/5.59 = ( vEBT_vebt_insert @ ( vEBT_Node @ Info @ Deg2 @ TreeList @ Summary2 ) @ Xa2 ) ) ) )
% 5.31/5.59 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info @ Deg2 @ TreeList @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % VEBT_internal.insert'.pelims
% 5.31/5.59 thf(fact_4938_vebt__member_Opelims_I1_J,axiom,
% 5.31/5.59 ! [X: vEBT_VEBT,Xa2: nat,Y: $o] :
% 5.31/5.59 ( ( ( vEBT_vebt_member @ X @ Xa2 )
% 5.31/5.59 = Y )
% 5.31/5.59 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 5.31/5.59 => ( ! [A3: $o,B3: $o] :
% 5.31/5.59 ( ( X
% 5.31/5.59 = ( vEBT_Leaf @ A3 @ B3 ) )
% 5.31/5.59 => ( ( Y
% 5.31/5.59 = ( ( ( Xa2 = zero_zero_nat )
% 5.31/5.59 => A3 )
% 5.31/5.59 & ( ( Xa2 != zero_zero_nat )
% 5.31/5.59 => ( ( ( Xa2 = one_one_nat )
% 5.31/5.59 => B3 )
% 5.31/5.59 & ( Xa2 = one_one_nat ) ) ) ) )
% 5.31/5.59 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ Xa2 ) ) ) )
% 5.31/5.59 => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 5.31/5.59 ( ( X
% 5.31/5.59 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw ) )
% 5.31/5.59 => ( ~ Y
% 5.31/5.59 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw ) @ Xa2 ) ) ) )
% 5.31/5.59 => ( ! [V: product_prod_nat_nat,Uy: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.31/5.59 ( ( X
% 5.31/5.59 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Uy @ Uz2 ) )
% 5.31/5.59 => ( ~ Y
% 5.31/5.59 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Uy @ Uz2 ) @ Xa2 ) ) ) )
% 5.31/5.59 => ( ! [V: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.31/5.59 ( ( X
% 5.31/5.59 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) )
% 5.31/5.59 => ( ~ Y
% 5.31/5.59 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) @ Xa2 ) ) ) )
% 5.31/5.59 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.31/5.59 ( ( X
% 5.31/5.59 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary2 ) )
% 5.31/5.59 => ( ( Y
% 5.31/5.59 = ( ( Xa2 != Mi2 )
% 5.31/5.59 => ( ( Xa2 != Ma2 )
% 5.31/5.59 => ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.31/5.59 & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.31/5.59 => ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.31/5.59 & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.31/5.59 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.31/5.59 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.31/5.59 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) ) ) ) ) ) )
% 5.31/5.59 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % vebt_member.pelims(1)
% 5.31/5.59 thf(fact_4939_vebt__member_Opelims_I3_J,axiom,
% 5.31/5.59 ! [X: vEBT_VEBT,Xa2: nat] :
% 5.31/5.59 ( ~ ( vEBT_vebt_member @ X @ Xa2 )
% 5.31/5.59 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 5.31/5.59 => ( ! [A3: $o,B3: $o] :
% 5.31/5.59 ( ( X
% 5.31/5.59 = ( vEBT_Leaf @ A3 @ B3 ) )
% 5.31/5.59 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ Xa2 ) )
% 5.31/5.59 => ( ( ( Xa2 = zero_zero_nat )
% 5.31/5.59 => A3 )
% 5.31/5.59 & ( ( Xa2 != zero_zero_nat )
% 5.31/5.59 => ( ( ( Xa2 = one_one_nat )
% 5.31/5.59 => B3 )
% 5.31/5.59 & ( Xa2 = one_one_nat ) ) ) ) ) )
% 5.31/5.59 => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 5.31/5.59 ( ( X
% 5.31/5.59 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw ) )
% 5.31/5.59 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw ) @ Xa2 ) ) )
% 5.31/5.59 => ( ! [V: product_prod_nat_nat,Uy: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.31/5.59 ( ( X
% 5.31/5.59 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Uy @ Uz2 ) )
% 5.31/5.59 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Uy @ Uz2 ) @ Xa2 ) ) )
% 5.31/5.59 => ( ! [V: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.31/5.59 ( ( X
% 5.31/5.59 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) )
% 5.31/5.59 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) @ Xa2 ) ) )
% 5.31/5.59 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.31/5.59 ( ( X
% 5.31/5.59 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary2 ) )
% 5.31/5.59 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary2 ) @ Xa2 ) )
% 5.31/5.59 => ( ( Xa2 != Mi2 )
% 5.31/5.59 => ( ( Xa2 != Ma2 )
% 5.31/5.59 => ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.31/5.59 & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.31/5.59 => ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.31/5.59 & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.31/5.59 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.31/5.59 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.31/5.59 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % vebt_member.pelims(3)
% 5.31/5.59 thf(fact_4940_VEBT__internal_Onaive__member_Opelims_I1_J,axiom,
% 5.31/5.59 ! [X: vEBT_VEBT,Xa2: nat,Y: $o] :
% 5.31/5.59 ( ( ( vEBT_V5719532721284313246member @ X @ Xa2 )
% 5.31/5.59 = Y )
% 5.31/5.59 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 5.31/5.59 => ( ! [A3: $o,B3: $o] :
% 5.31/5.59 ( ( X
% 5.31/5.59 = ( vEBT_Leaf @ A3 @ B3 ) )
% 5.31/5.59 => ( ( Y
% 5.31/5.59 = ( ( ( Xa2 = zero_zero_nat )
% 5.31/5.59 => A3 )
% 5.31/5.59 & ( ( Xa2 != zero_zero_nat )
% 5.31/5.59 => ( ( ( Xa2 = one_one_nat )
% 5.31/5.59 => B3 )
% 5.31/5.59 & ( Xa2 = one_one_nat ) ) ) ) )
% 5.31/5.59 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ Xa2 ) ) ) )
% 5.31/5.59 => ( ! [Uu2: option4927543243414619207at_nat,Uv2: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 5.31/5.59 ( ( X
% 5.31/5.59 = ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw ) )
% 5.31/5.59 => ( ~ Y
% 5.31/5.59 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw ) @ Xa2 ) ) ) )
% 5.31/5.59 => ~ ! [Uy: option4927543243414619207at_nat,V: nat,TreeList: list_VEBT_VEBT,S: vEBT_VEBT] :
% 5.31/5.59 ( ( X
% 5.31/5.59 = ( vEBT_Node @ Uy @ ( suc @ V ) @ TreeList @ S ) )
% 5.31/5.59 => ( ( Y
% 5.31/5.59 = ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.31/5.59 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.31/5.59 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) )
% 5.31/5.59 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uy @ ( suc @ V ) @ TreeList @ S ) @ Xa2 ) ) ) ) ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % VEBT_internal.naive_member.pelims(1)
% 5.31/5.59 thf(fact_4941_VEBT__internal_Onaive__member_Opelims_I2_J,axiom,
% 5.31/5.59 ! [X: vEBT_VEBT,Xa2: nat] :
% 5.31/5.59 ( ( vEBT_V5719532721284313246member @ X @ Xa2 )
% 5.31/5.59 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 5.31/5.59 => ( ! [A3: $o,B3: $o] :
% 5.31/5.59 ( ( X
% 5.31/5.59 = ( vEBT_Leaf @ A3 @ B3 ) )
% 5.31/5.59 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ Xa2 ) )
% 5.31/5.59 => ~ ( ( ( Xa2 = zero_zero_nat )
% 5.31/5.59 => A3 )
% 5.31/5.59 & ( ( Xa2 != zero_zero_nat )
% 5.31/5.59 => ( ( ( Xa2 = one_one_nat )
% 5.31/5.59 => B3 )
% 5.31/5.59 & ( Xa2 = one_one_nat ) ) ) ) ) )
% 5.31/5.59 => ~ ! [Uy: option4927543243414619207at_nat,V: nat,TreeList: list_VEBT_VEBT,S: vEBT_VEBT] :
% 5.31/5.59 ( ( X
% 5.31/5.59 = ( vEBT_Node @ Uy @ ( suc @ V ) @ TreeList @ S ) )
% 5.31/5.59 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uy @ ( suc @ V ) @ TreeList @ S ) @ Xa2 ) )
% 5.31/5.59 => ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.31/5.59 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.31/5.59 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % VEBT_internal.naive_member.pelims(2)
% 5.31/5.59 thf(fact_4942_VEBT__internal_Onaive__member_Opelims_I3_J,axiom,
% 5.31/5.59 ! [X: vEBT_VEBT,Xa2: nat] :
% 5.31/5.59 ( ~ ( vEBT_V5719532721284313246member @ X @ Xa2 )
% 5.31/5.59 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 5.31/5.59 => ( ! [A3: $o,B3: $o] :
% 5.31/5.59 ( ( X
% 5.31/5.59 = ( vEBT_Leaf @ A3 @ B3 ) )
% 5.31/5.59 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ Xa2 ) )
% 5.31/5.59 => ( ( ( Xa2 = zero_zero_nat )
% 5.31/5.59 => A3 )
% 5.31/5.59 & ( ( Xa2 != zero_zero_nat )
% 5.31/5.59 => ( ( ( Xa2 = one_one_nat )
% 5.31/5.59 => B3 )
% 5.31/5.59 & ( Xa2 = one_one_nat ) ) ) ) ) )
% 5.31/5.59 => ( ! [Uu2: option4927543243414619207at_nat,Uv2: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 5.31/5.59 ( ( X
% 5.31/5.59 = ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw ) )
% 5.31/5.59 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw ) @ Xa2 ) ) )
% 5.31/5.59 => ~ ! [Uy: option4927543243414619207at_nat,V: nat,TreeList: list_VEBT_VEBT,S: vEBT_VEBT] :
% 5.31/5.59 ( ( X
% 5.31/5.59 = ( vEBT_Node @ Uy @ ( suc @ V ) @ TreeList @ S ) )
% 5.31/5.59 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uy @ ( suc @ V ) @ TreeList @ S ) @ Xa2 ) )
% 5.31/5.59 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.31/5.59 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.31/5.59 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) ) ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % VEBT_internal.naive_member.pelims(3)
% 5.31/5.59 thf(fact_4943_vebt__member_Opelims_I2_J,axiom,
% 5.31/5.59 ! [X: vEBT_VEBT,Xa2: nat] :
% 5.31/5.59 ( ( vEBT_vebt_member @ X @ Xa2 )
% 5.31/5.59 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 5.31/5.59 => ( ! [A3: $o,B3: $o] :
% 5.31/5.59 ( ( X
% 5.31/5.59 = ( vEBT_Leaf @ A3 @ B3 ) )
% 5.31/5.59 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ Xa2 ) )
% 5.31/5.59 => ~ ( ( ( Xa2 = zero_zero_nat )
% 5.31/5.59 => A3 )
% 5.31/5.59 & ( ( Xa2 != zero_zero_nat )
% 5.31/5.59 => ( ( ( Xa2 = one_one_nat )
% 5.31/5.59 => B3 )
% 5.31/5.59 & ( Xa2 = one_one_nat ) ) ) ) ) )
% 5.31/5.59 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.31/5.59 ( ( X
% 5.31/5.59 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary2 ) )
% 5.31/5.59 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary2 ) @ Xa2 ) )
% 5.31/5.59 => ~ ( ( Xa2 != Mi2 )
% 5.31/5.59 => ( ( Xa2 != Ma2 )
% 5.31/5.59 => ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.31/5.59 & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.31/5.59 => ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.31/5.59 & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.31/5.59 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.31/5.59 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.31/5.59 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % vebt_member.pelims(2)
% 5.31/5.59 thf(fact_4944_zmod__numeral__Bit0,axiom,
% 5.31/5.59 ! [V2: num,W2: num] :
% 5.31/5.59 ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ V2 ) ) @ ( numeral_numeral_int @ ( bit0 @ W2 ) ) )
% 5.31/5.59 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( modulo_modulo_int @ ( numeral_numeral_int @ V2 ) @ ( numeral_numeral_int @ W2 ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % zmod_numeral_Bit0
% 5.31/5.59 thf(fact_4945_zmod__le__nonneg__dividend,axiom,
% 5.31/5.59 ! [M2: int,K2: int] :
% 5.31/5.59 ( ( ord_less_eq_int @ zero_zero_int @ M2 )
% 5.31/5.59 => ( ord_less_eq_int @ ( modulo_modulo_int @ M2 @ K2 ) @ M2 ) ) ).
% 5.31/5.59
% 5.31/5.59 % zmod_le_nonneg_dividend
% 5.31/5.59 thf(fact_4946_zmod__eq__0__iff,axiom,
% 5.31/5.59 ! [M2: int,D: int] :
% 5.31/5.59 ( ( ( modulo_modulo_int @ M2 @ D )
% 5.31/5.59 = zero_zero_int )
% 5.31/5.59 = ( ? [Q5: int] :
% 5.31/5.59 ( M2
% 5.31/5.59 = ( times_times_int @ D @ Q5 ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % zmod_eq_0_iff
% 5.31/5.59 thf(fact_4947_zmod__eq__0D,axiom,
% 5.31/5.59 ! [M2: int,D: int] :
% 5.31/5.59 ( ( ( modulo_modulo_int @ M2 @ D )
% 5.31/5.59 = zero_zero_int )
% 5.31/5.59 => ? [Q3: int] :
% 5.31/5.59 ( M2
% 5.31/5.59 = ( times_times_int @ D @ Q3 ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % zmod_eq_0D
% 5.31/5.59 thf(fact_4948_zmod__int,axiom,
% 5.31/5.59 ! [A: nat,B: nat] :
% 5.31/5.59 ( ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ A @ B ) )
% 5.31/5.59 = ( modulo_modulo_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % zmod_int
% 5.31/5.59 thf(fact_4949_mod__int__unique,axiom,
% 5.31/5.59 ! [K2: int,L: int,Q2: int,R3: int] :
% 5.31/5.59 ( ( eucl_rel_int @ K2 @ L @ ( product_Pair_int_int @ Q2 @ R3 ) )
% 5.31/5.59 => ( ( modulo_modulo_int @ K2 @ L )
% 5.31/5.59 = R3 ) ) ).
% 5.31/5.59
% 5.31/5.59 % mod_int_unique
% 5.31/5.59 thf(fact_4950_neg__mod__conj,axiom,
% 5.31/5.59 ! [B: int,A: int] :
% 5.31/5.59 ( ( ord_less_int @ B @ zero_zero_int )
% 5.31/5.59 => ( ( ord_less_eq_int @ ( modulo_modulo_int @ A @ B ) @ zero_zero_int )
% 5.31/5.59 & ( ord_less_int @ B @ ( modulo_modulo_int @ A @ B ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % neg_mod_conj
% 5.31/5.59 thf(fact_4951_pos__mod__conj,axiom,
% 5.31/5.59 ! [B: int,A: int] :
% 5.31/5.59 ( ( ord_less_int @ zero_zero_int @ B )
% 5.31/5.59 => ( ( ord_less_eq_int @ zero_zero_int @ ( modulo_modulo_int @ A @ B ) )
% 5.31/5.59 & ( ord_less_int @ ( modulo_modulo_int @ A @ B ) @ B ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % pos_mod_conj
% 5.31/5.59 thf(fact_4952_zmod__trivial__iff,axiom,
% 5.31/5.59 ! [I2: int,K2: int] :
% 5.31/5.59 ( ( ( modulo_modulo_int @ I2 @ K2 )
% 5.31/5.59 = I2 )
% 5.31/5.59 = ( ( K2 = zero_zero_int )
% 5.31/5.59 | ( ( ord_less_eq_int @ zero_zero_int @ I2 )
% 5.31/5.59 & ( ord_less_int @ I2 @ K2 ) )
% 5.31/5.59 | ( ( ord_less_eq_int @ I2 @ zero_zero_int )
% 5.31/5.59 & ( ord_less_int @ K2 @ I2 ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % zmod_trivial_iff
% 5.31/5.59 thf(fact_4953_div__mod__decomp__int,axiom,
% 5.31/5.59 ! [A4: int,N: int] :
% 5.31/5.59 ( A4
% 5.31/5.59 = ( plus_plus_int @ ( times_times_int @ ( divide_divide_int @ A4 @ N ) @ N ) @ ( modulo_modulo_int @ A4 @ N ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % div_mod_decomp_int
% 5.31/5.59 thf(fact_4954_eucl__rel__int,axiom,
% 5.31/5.59 ! [K2: int,L: int] : ( eucl_rel_int @ K2 @ L @ ( product_Pair_int_int @ ( divide_divide_int @ K2 @ L ) @ ( modulo_modulo_int @ K2 @ L ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % eucl_rel_int
% 5.31/5.59 thf(fact_4955_mod__pos__geq,axiom,
% 5.31/5.59 ! [L: int,K2: int] :
% 5.31/5.59 ( ( ord_less_int @ zero_zero_int @ L )
% 5.31/5.59 => ( ( ord_less_eq_int @ L @ K2 )
% 5.31/5.59 => ( ( modulo_modulo_int @ K2 @ L )
% 5.31/5.59 = ( modulo_modulo_int @ ( minus_minus_int @ K2 @ L ) @ L ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % mod_pos_geq
% 5.31/5.59 thf(fact_4956_int__mod__pos__eq,axiom,
% 5.31/5.59 ! [A: int,B: int,Q2: int,R3: int] :
% 5.31/5.59 ( ( A
% 5.31/5.59 = ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R3 ) )
% 5.31/5.59 => ( ( ord_less_eq_int @ zero_zero_int @ R3 )
% 5.31/5.59 => ( ( ord_less_int @ R3 @ B )
% 5.31/5.59 => ( ( modulo_modulo_int @ A @ B )
% 5.31/5.59 = R3 ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % int_mod_pos_eq
% 5.31/5.59 thf(fact_4957_int__mod__neg__eq,axiom,
% 5.31/5.59 ! [A: int,B: int,Q2: int,R3: int] :
% 5.31/5.59 ( ( A
% 5.31/5.59 = ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R3 ) )
% 5.31/5.59 => ( ( ord_less_eq_int @ R3 @ zero_zero_int )
% 5.31/5.59 => ( ( ord_less_int @ B @ R3 )
% 5.31/5.59 => ( ( modulo_modulo_int @ A @ B )
% 5.31/5.59 = R3 ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % int_mod_neg_eq
% 5.31/5.59 thf(fact_4958_split__zmod,axiom,
% 5.31/5.59 ! [P2: int > $o,N: int,K2: int] :
% 5.31/5.59 ( ( P2 @ ( modulo_modulo_int @ N @ K2 ) )
% 5.31/5.59 = ( ( ( K2 = zero_zero_int )
% 5.31/5.59 => ( P2 @ N ) )
% 5.31/5.59 & ( ( ord_less_int @ zero_zero_int @ K2 )
% 5.31/5.59 => ! [I: int,J: int] :
% 5.31/5.59 ( ( ( ord_less_eq_int @ zero_zero_int @ J )
% 5.31/5.59 & ( ord_less_int @ J @ K2 )
% 5.31/5.59 & ( N
% 5.31/5.59 = ( plus_plus_int @ ( times_times_int @ K2 @ I ) @ J ) ) )
% 5.31/5.59 => ( P2 @ J ) ) )
% 5.31/5.59 & ( ( ord_less_int @ K2 @ zero_zero_int )
% 5.31/5.59 => ! [I: int,J: int] :
% 5.31/5.59 ( ( ( ord_less_int @ K2 @ J )
% 5.31/5.59 & ( ord_less_eq_int @ J @ zero_zero_int )
% 5.31/5.59 & ( N
% 5.31/5.59 = ( plus_plus_int @ ( times_times_int @ K2 @ I ) @ J ) ) )
% 5.31/5.59 => ( P2 @ J ) ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % split_zmod
% 5.31/5.59 thf(fact_4959_zmod__zmult2__eq,axiom,
% 5.31/5.59 ! [C2: int,A: int,B: int] :
% 5.31/5.59 ( ( ord_less_eq_int @ zero_zero_int @ C2 )
% 5.31/5.59 => ( ( modulo_modulo_int @ A @ ( times_times_int @ B @ C2 ) )
% 5.31/5.59 = ( plus_plus_int @ ( times_times_int @ B @ ( modulo_modulo_int @ ( divide_divide_int @ A @ B ) @ C2 ) ) @ ( modulo_modulo_int @ A @ B ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % zmod_zmult2_eq
% 5.31/5.59 thf(fact_4960_split__pos__lemma,axiom,
% 5.31/5.59 ! [K2: int,P2: int > int > $o,N: int] :
% 5.31/5.59 ( ( ord_less_int @ zero_zero_int @ K2 )
% 5.31/5.59 => ( ( P2 @ ( divide_divide_int @ N @ K2 ) @ ( modulo_modulo_int @ N @ K2 ) )
% 5.31/5.59 = ( ! [I: int,J: int] :
% 5.31/5.59 ( ( ( ord_less_eq_int @ zero_zero_int @ J )
% 5.31/5.59 & ( ord_less_int @ J @ K2 )
% 5.31/5.59 & ( N
% 5.31/5.59 = ( plus_plus_int @ ( times_times_int @ K2 @ I ) @ J ) ) )
% 5.31/5.59 => ( P2 @ I @ J ) ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % split_pos_lemma
% 5.31/5.59 thf(fact_4961_split__neg__lemma,axiom,
% 5.31/5.59 ! [K2: int,P2: int > int > $o,N: int] :
% 5.31/5.59 ( ( ord_less_int @ K2 @ zero_zero_int )
% 5.31/5.59 => ( ( P2 @ ( divide_divide_int @ N @ K2 ) @ ( modulo_modulo_int @ N @ K2 ) )
% 5.31/5.59 = ( ! [I: int,J: int] :
% 5.31/5.59 ( ( ( ord_less_int @ K2 @ J )
% 5.31/5.59 & ( ord_less_eq_int @ J @ zero_zero_int )
% 5.31/5.59 & ( N
% 5.31/5.59 = ( plus_plus_int @ ( times_times_int @ K2 @ I ) @ J ) ) )
% 5.31/5.59 => ( P2 @ I @ J ) ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % split_neg_lemma
% 5.31/5.59 thf(fact_4962_pos__zmod__mult__2,axiom,
% 5.31/5.59 ! [A: int,B: int] :
% 5.31/5.59 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.31/5.59 => ( ( 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 ) )
% 5.31/5.59 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( modulo_modulo_int @ B @ A ) ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % pos_zmod_mult_2
% 5.31/5.59 thf(fact_4963_neg__zmod__mult__2,axiom,
% 5.31/5.59 ! [A: int,B: int] :
% 5.31/5.59 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.31/5.59 => ( ( 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 ) )
% 5.31/5.59 = ( 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 ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % neg_zmod_mult_2
% 5.31/5.59 thf(fact_4964_VEBT__internal_Omembermima_Opelims_I1_J,axiom,
% 5.31/5.59 ! [X: vEBT_VEBT,Xa2: nat,Y: $o] :
% 5.31/5.59 ( ( ( vEBT_VEBT_membermima @ X @ Xa2 )
% 5.31/5.59 = Y )
% 5.31/5.59 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 5.31/5.59 => ( ! [Uu2: $o,Uv2: $o] :
% 5.31/5.59 ( ( X
% 5.31/5.59 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 5.31/5.59 => ( ~ Y
% 5.31/5.59 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ Xa2 ) ) ) )
% 5.31/5.59 => ( ! [Ux: list_VEBT_VEBT,Uy: vEBT_VEBT] :
% 5.31/5.59 ( ( X
% 5.31/5.59 = ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux @ Uy ) )
% 5.31/5.59 => ( ~ Y
% 5.31/5.59 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux @ Uy ) @ Xa2 ) ) ) )
% 5.31/5.59 => ( ! [Mi2: nat,Ma2: nat,Va2: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 5.31/5.59 ( ( X
% 5.31/5.59 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va2 @ Vb2 ) )
% 5.31/5.59 => ( ( Y
% 5.31/5.59 = ( ( Xa2 = Mi2 )
% 5.31/5.59 | ( Xa2 = Ma2 ) ) )
% 5.31/5.59 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va2 @ Vb2 ) @ Xa2 ) ) ) )
% 5.31/5.59 => ( ! [Mi2: nat,Ma2: nat,V: nat,TreeList: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.31/5.59 ( ( X
% 5.31/5.59 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V ) @ TreeList @ Vc2 ) )
% 5.31/5.59 => ( ( Y
% 5.31/5.59 = ( ( Xa2 = Mi2 )
% 5.31/5.59 | ( Xa2 = Ma2 )
% 5.31/5.59 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.31/5.59 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.31/5.59 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) )
% 5.31/5.59 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V ) @ TreeList @ Vc2 ) @ Xa2 ) ) ) )
% 5.31/5.59 => ~ ! [V: nat,TreeList: list_VEBT_VEBT,Vd: vEBT_VEBT] :
% 5.31/5.59 ( ( X
% 5.31/5.59 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V ) @ TreeList @ Vd ) )
% 5.31/5.59 => ( ( Y
% 5.31/5.59 = ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.31/5.59 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.31/5.59 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) )
% 5.31/5.59 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V ) @ TreeList @ Vd ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % VEBT_internal.membermima.pelims(1)
% 5.31/5.59 thf(fact_4965_VEBT__internal_Omembermima_Opelims_I3_J,axiom,
% 5.31/5.59 ! [X: vEBT_VEBT,Xa2: nat] :
% 5.31/5.59 ( ~ ( vEBT_VEBT_membermima @ X @ Xa2 )
% 5.31/5.59 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 5.31/5.59 => ( ! [Uu2: $o,Uv2: $o] :
% 5.31/5.59 ( ( X
% 5.31/5.59 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 5.31/5.59 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ Xa2 ) ) )
% 5.31/5.59 => ( ! [Ux: list_VEBT_VEBT,Uy: vEBT_VEBT] :
% 5.31/5.59 ( ( X
% 5.31/5.59 = ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux @ Uy ) )
% 5.31/5.59 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux @ Uy ) @ Xa2 ) ) )
% 5.31/5.59 => ( ! [Mi2: nat,Ma2: nat,Va2: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 5.31/5.59 ( ( X
% 5.31/5.59 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va2 @ Vb2 ) )
% 5.31/5.59 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va2 @ Vb2 ) @ Xa2 ) )
% 5.31/5.59 => ( ( Xa2 = Mi2 )
% 5.31/5.59 | ( Xa2 = Ma2 ) ) ) )
% 5.31/5.59 => ( ! [Mi2: nat,Ma2: nat,V: nat,TreeList: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.31/5.59 ( ( X
% 5.31/5.59 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V ) @ TreeList @ Vc2 ) )
% 5.31/5.59 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V ) @ TreeList @ Vc2 ) @ Xa2 ) )
% 5.31/5.59 => ( ( Xa2 = Mi2 )
% 5.31/5.59 | ( Xa2 = Ma2 )
% 5.31/5.59 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.31/5.59 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.31/5.59 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) ) )
% 5.31/5.59 => ~ ! [V: nat,TreeList: list_VEBT_VEBT,Vd: vEBT_VEBT] :
% 5.31/5.59 ( ( X
% 5.31/5.59 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V ) @ TreeList @ Vd ) )
% 5.31/5.59 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V ) @ TreeList @ Vd ) @ Xa2 ) )
% 5.31/5.59 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.31/5.59 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.31/5.59 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) ) ) ) ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % VEBT_internal.membermima.pelims(3)
% 5.31/5.59 thf(fact_4966_VEBT__internal_Omembermima_Opelims_I2_J,axiom,
% 5.31/5.59 ! [X: vEBT_VEBT,Xa2: nat] :
% 5.31/5.59 ( ( vEBT_VEBT_membermima @ X @ Xa2 )
% 5.31/5.59 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 5.31/5.59 => ( ! [Mi2: nat,Ma2: nat,Va2: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 5.31/5.59 ( ( X
% 5.31/5.59 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va2 @ Vb2 ) )
% 5.31/5.59 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va2 @ Vb2 ) @ Xa2 ) )
% 5.31/5.59 => ~ ( ( Xa2 = Mi2 )
% 5.31/5.59 | ( Xa2 = Ma2 ) ) ) )
% 5.31/5.59 => ( ! [Mi2: nat,Ma2: nat,V: nat,TreeList: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.31/5.59 ( ( X
% 5.31/5.59 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V ) @ TreeList @ Vc2 ) )
% 5.31/5.59 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V ) @ TreeList @ Vc2 ) @ Xa2 ) )
% 5.31/5.59 => ~ ( ( Xa2 = Mi2 )
% 5.31/5.59 | ( Xa2 = Ma2 )
% 5.31/5.59 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.31/5.59 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.31/5.59 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) ) )
% 5.31/5.59 => ~ ! [V: nat,TreeList: list_VEBT_VEBT,Vd: vEBT_VEBT] :
% 5.31/5.59 ( ( X
% 5.31/5.59 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V ) @ TreeList @ Vd ) )
% 5.31/5.59 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V ) @ TreeList @ Vd ) @ Xa2 ) )
% 5.31/5.59 => ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.31/5.59 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.31/5.59 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) ) ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % VEBT_internal.membermima.pelims(2)
% 5.31/5.59 thf(fact_4967_arcosh__1,axiom,
% 5.31/5.59 ( ( arcosh_real @ one_one_real )
% 5.31/5.59 = zero_zero_real ) ).
% 5.31/5.59
% 5.31/5.59 % arcosh_1
% 5.31/5.59 thf(fact_4968_lemma__termdiff3,axiom,
% 5.31/5.59 ! [H: real,Z3: real,K5: real,N: nat] :
% 5.31/5.59 ( ( H != zero_zero_real )
% 5.31/5.59 => ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ Z3 ) @ K5 )
% 5.31/5.59 => ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ Z3 @ H ) ) @ K5 )
% 5.31/5.59 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( divide_divide_real @ ( minus_minus_real @ ( power_power_real @ ( plus_plus_real @ Z3 @ H ) @ N ) @ ( power_power_real @ Z3 @ N ) ) @ H ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ Z3 @ ( 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 @ H ) ) ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % lemma_termdiff3
% 5.31/5.59 thf(fact_4969_lemma__termdiff3,axiom,
% 5.31/5.59 ! [H: complex,Z3: complex,K5: real,N: nat] :
% 5.31/5.59 ( ( H != zero_zero_complex )
% 5.31/5.59 => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ Z3 ) @ K5 )
% 5.31/5.59 => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ Z3 @ H ) ) @ K5 )
% 5.31/5.59 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( power_power_complex @ ( plus_plus_complex @ Z3 @ H ) @ N ) @ ( power_power_complex @ Z3 @ N ) ) @ H ) @ ( times_times_complex @ ( semiri8010041392384452111omplex @ N ) @ ( power_power_complex @ Z3 @ ( 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 @ H ) ) ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % lemma_termdiff3
% 5.31/5.59 thf(fact_4970_flip__bit__Suc,axiom,
% 5.31/5.59 ! [N: nat,A: nat] :
% 5.31/5.59 ( ( bit_se2161824704523386999it_nat @ ( suc @ N ) @ A )
% 5.31/5.59 = ( 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 ) ) ) ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % flip_bit_Suc
% 5.31/5.59 thf(fact_4971_flip__bit__Suc,axiom,
% 5.31/5.59 ! [N: nat,A: int] :
% 5.31/5.59 ( ( bit_se2159334234014336723it_int @ ( suc @ N ) @ A )
% 5.31/5.59 = ( 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 ) ) ) ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % flip_bit_Suc
% 5.31/5.59 thf(fact_4972_flip__bit__Suc,axiom,
% 5.31/5.59 ! [N: nat,A: code_natural] :
% 5.31/5.59 ( ( bit_se168947363167071951atural @ ( suc @ N ) @ A )
% 5.31/5.59 = ( plus_p4538020629002901425atural @ ( modulo8411746178871703098atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( bit_se168947363167071951atural @ N @ ( divide5121882707175180666atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % flip_bit_Suc
% 5.31/5.59 thf(fact_4973_artanh__0,axiom,
% 5.31/5.59 ( ( artanh_real @ zero_zero_real )
% 5.31/5.59 = zero_zero_real ) ).
% 5.31/5.59
% 5.31/5.59 % artanh_0
% 5.31/5.59 thf(fact_4974_norm__mult__numeral1,axiom,
% 5.31/5.59 ! [W2: num,A: real] :
% 5.31/5.59 ( ( real_V7735802525324610683m_real @ ( times_times_real @ ( numeral_numeral_real @ W2 ) @ A ) )
% 5.31/5.59 = ( times_times_real @ ( numeral_numeral_real @ W2 ) @ ( real_V7735802525324610683m_real @ A ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % norm_mult_numeral1
% 5.31/5.59 thf(fact_4975_norm__mult__numeral1,axiom,
% 5.31/5.59 ! [W2: num,A: complex] :
% 5.31/5.59 ( ( real_V1022390504157884413omplex @ ( times_times_complex @ ( numera6690914467698888265omplex @ W2 ) @ A ) )
% 5.31/5.59 = ( times_times_real @ ( numeral_numeral_real @ W2 ) @ ( real_V1022390504157884413omplex @ A ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % norm_mult_numeral1
% 5.31/5.59 thf(fact_4976_norm__mult__numeral2,axiom,
% 5.31/5.59 ! [A: real,W2: num] :
% 5.31/5.59 ( ( real_V7735802525324610683m_real @ ( times_times_real @ A @ ( numeral_numeral_real @ W2 ) ) )
% 5.31/5.59 = ( times_times_real @ ( real_V7735802525324610683m_real @ A ) @ ( numeral_numeral_real @ W2 ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % norm_mult_numeral2
% 5.31/5.59 thf(fact_4977_norm__mult__numeral2,axiom,
% 5.31/5.59 ! [A: complex,W2: num] :
% 5.31/5.59 ( ( real_V1022390504157884413omplex @ ( times_times_complex @ A @ ( numera6690914467698888265omplex @ W2 ) ) )
% 5.31/5.59 = ( times_times_real @ ( real_V1022390504157884413omplex @ A ) @ ( numeral_numeral_real @ W2 ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % norm_mult_numeral2
% 5.31/5.59 thf(fact_4978_norm__le__zero__iff,axiom,
% 5.31/5.59 ! [X: real] :
% 5.31/5.59 ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ X ) @ zero_zero_real )
% 5.31/5.59 = ( X = zero_zero_real ) ) ).
% 5.31/5.59
% 5.31/5.59 % norm_le_zero_iff
% 5.31/5.59 thf(fact_4979_norm__le__zero__iff,axiom,
% 5.31/5.59 ! [X: complex] :
% 5.31/5.59 ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ X ) @ zero_zero_real )
% 5.31/5.59 = ( X = zero_zero_complex ) ) ).
% 5.31/5.59
% 5.31/5.59 % norm_le_zero_iff
% 5.31/5.59 thf(fact_4980_zero__less__norm__iff,axiom,
% 5.31/5.59 ! [X: real] :
% 5.31/5.59 ( ( ord_less_real @ zero_zero_real @ ( real_V7735802525324610683m_real @ X ) )
% 5.31/5.59 = ( X != zero_zero_real ) ) ).
% 5.31/5.59
% 5.31/5.59 % zero_less_norm_iff
% 5.31/5.59 thf(fact_4981_zero__less__norm__iff,axiom,
% 5.31/5.59 ! [X: complex] :
% 5.31/5.59 ( ( ord_less_real @ zero_zero_real @ ( real_V1022390504157884413omplex @ X ) )
% 5.31/5.59 = ( X != zero_zero_complex ) ) ).
% 5.31/5.59
% 5.31/5.59 % zero_less_norm_iff
% 5.31/5.59 thf(fact_4982_norm__zero,axiom,
% 5.31/5.59 ( ( real_V7735802525324610683m_real @ zero_zero_real )
% 5.31/5.59 = zero_zero_real ) ).
% 5.31/5.59
% 5.31/5.59 % norm_zero
% 5.31/5.59 thf(fact_4983_norm__zero,axiom,
% 5.31/5.59 ( ( real_V1022390504157884413omplex @ zero_zero_complex )
% 5.31/5.59 = zero_zero_real ) ).
% 5.31/5.59
% 5.31/5.59 % norm_zero
% 5.31/5.59 thf(fact_4984_norm__eq__zero,axiom,
% 5.31/5.59 ! [X: real] :
% 5.31/5.59 ( ( ( real_V7735802525324610683m_real @ X )
% 5.31/5.59 = zero_zero_real )
% 5.31/5.59 = ( X = zero_zero_real ) ) ).
% 5.31/5.59
% 5.31/5.59 % norm_eq_zero
% 5.31/5.59 thf(fact_4985_norm__eq__zero,axiom,
% 5.31/5.59 ! [X: complex] :
% 5.31/5.59 ( ( ( real_V1022390504157884413omplex @ X )
% 5.31/5.59 = zero_zero_real )
% 5.31/5.59 = ( X = zero_zero_complex ) ) ).
% 5.31/5.59
% 5.31/5.59 % norm_eq_zero
% 5.31/5.59 thf(fact_4986_norm__power__diff,axiom,
% 5.31/5.59 ! [Z3: real,W2: real,M2: nat] :
% 5.31/5.59 ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ Z3 ) @ one_one_real )
% 5.31/5.59 => ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ W2 ) @ one_one_real )
% 5.31/5.59 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( power_power_real @ Z3 @ M2 ) @ ( power_power_real @ W2 @ M2 ) ) ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ M2 ) @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ Z3 @ W2 ) ) ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % norm_power_diff
% 5.31/5.59 thf(fact_4987_norm__power__diff,axiom,
% 5.31/5.59 ! [Z3: complex,W2: complex,M2: nat] :
% 5.31/5.59 ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ Z3 ) @ one_one_real )
% 5.31/5.59 => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ W2 ) @ one_one_real )
% 5.31/5.59 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( power_power_complex @ Z3 @ M2 ) @ ( power_power_complex @ W2 @ M2 ) ) ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ M2 ) @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ Z3 @ W2 ) ) ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % norm_power_diff
% 5.31/5.59 thf(fact_4988_norm__mult,axiom,
% 5.31/5.59 ! [X: real,Y: real] :
% 5.31/5.59 ( ( real_V7735802525324610683m_real @ ( times_times_real @ X @ Y ) )
% 5.31/5.59 = ( times_times_real @ ( real_V7735802525324610683m_real @ X ) @ ( real_V7735802525324610683m_real @ Y ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % norm_mult
% 5.31/5.59 thf(fact_4989_norm__mult,axiom,
% 5.31/5.59 ! [X: complex,Y: complex] :
% 5.31/5.59 ( ( real_V1022390504157884413omplex @ ( times_times_complex @ X @ Y ) )
% 5.31/5.59 = ( times_times_real @ ( real_V1022390504157884413omplex @ X ) @ ( real_V1022390504157884413omplex @ Y ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % norm_mult
% 5.31/5.59 thf(fact_4990_nonzero__norm__divide,axiom,
% 5.31/5.59 ! [B: real,A: real] :
% 5.31/5.59 ( ( B != zero_zero_real )
% 5.31/5.59 => ( ( real_V7735802525324610683m_real @ ( divide_divide_real @ A @ B ) )
% 5.31/5.59 = ( divide_divide_real @ ( real_V7735802525324610683m_real @ A ) @ ( real_V7735802525324610683m_real @ B ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % nonzero_norm_divide
% 5.31/5.59 thf(fact_4991_nonzero__norm__divide,axiom,
% 5.31/5.59 ! [B: complex,A: complex] :
% 5.31/5.59 ( ( B != zero_zero_complex )
% 5.31/5.59 => ( ( real_V1022390504157884413omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 5.31/5.59 = ( divide_divide_real @ ( real_V1022390504157884413omplex @ A ) @ ( real_V1022390504157884413omplex @ B ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % nonzero_norm_divide
% 5.31/5.59 thf(fact_4992_power__eq__imp__eq__norm,axiom,
% 5.31/5.59 ! [W2: real,N: nat,Z3: real] :
% 5.31/5.59 ( ( ( power_power_real @ W2 @ N )
% 5.31/5.59 = ( power_power_real @ Z3 @ N ) )
% 5.31/5.59 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.59 => ( ( real_V7735802525324610683m_real @ W2 )
% 5.31/5.59 = ( real_V7735802525324610683m_real @ Z3 ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % power_eq_imp_eq_norm
% 5.31/5.59 thf(fact_4993_power__eq__imp__eq__norm,axiom,
% 5.31/5.59 ! [W2: complex,N: nat,Z3: complex] :
% 5.31/5.59 ( ( ( power_power_complex @ W2 @ N )
% 5.31/5.59 = ( power_power_complex @ Z3 @ N ) )
% 5.31/5.59 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.59 => ( ( real_V1022390504157884413omplex @ W2 )
% 5.31/5.59 = ( real_V1022390504157884413omplex @ Z3 ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % power_eq_imp_eq_norm
% 5.31/5.59 thf(fact_4994_norm__mult__less,axiom,
% 5.31/5.59 ! [X: real,R3: real,Y: real,S2: real] :
% 5.31/5.59 ( ( ord_less_real @ ( real_V7735802525324610683m_real @ X ) @ R3 )
% 5.31/5.59 => ( ( ord_less_real @ ( real_V7735802525324610683m_real @ Y ) @ S2 )
% 5.31/5.59 => ( ord_less_real @ ( real_V7735802525324610683m_real @ ( times_times_real @ X @ Y ) ) @ ( times_times_real @ R3 @ S2 ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % norm_mult_less
% 5.31/5.59 thf(fact_4995_norm__mult__less,axiom,
% 5.31/5.59 ! [X: complex,R3: real,Y: complex,S2: real] :
% 5.31/5.59 ( ( ord_less_real @ ( real_V1022390504157884413omplex @ X ) @ R3 )
% 5.31/5.59 => ( ( ord_less_real @ ( real_V1022390504157884413omplex @ Y ) @ S2 )
% 5.31/5.59 => ( ord_less_real @ ( real_V1022390504157884413omplex @ ( times_times_complex @ X @ Y ) ) @ ( times_times_real @ R3 @ S2 ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % norm_mult_less
% 5.31/5.59 thf(fact_4996_norm__mult__ineq,axiom,
% 5.31/5.59 ! [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 ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % norm_mult_ineq
% 5.31/5.59 thf(fact_4997_norm__mult__ineq,axiom,
% 5.31/5.59 ! [X: complex,Y: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( times_times_complex @ X @ Y ) ) @ ( times_times_real @ ( real_V1022390504157884413omplex @ X ) @ ( real_V1022390504157884413omplex @ Y ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % norm_mult_ineq
% 5.31/5.59 thf(fact_4998_power__eq__1__iff,axiom,
% 5.31/5.59 ! [W2: real,N: nat] :
% 5.31/5.59 ( ( ( power_power_real @ W2 @ N )
% 5.31/5.59 = one_one_real )
% 5.31/5.59 => ( ( ( real_V7735802525324610683m_real @ W2 )
% 5.31/5.59 = one_one_real )
% 5.31/5.59 | ( N = zero_zero_nat ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % power_eq_1_iff
% 5.31/5.59 thf(fact_4999_power__eq__1__iff,axiom,
% 5.31/5.59 ! [W2: complex,N: nat] :
% 5.31/5.59 ( ( ( power_power_complex @ W2 @ N )
% 5.31/5.59 = one_one_complex )
% 5.31/5.59 => ( ( ( real_V1022390504157884413omplex @ W2 )
% 5.31/5.59 = one_one_real )
% 5.31/5.59 | ( N = zero_zero_nat ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % power_eq_1_iff
% 5.31/5.59 thf(fact_5000_arsinh__0,axiom,
% 5.31/5.59 ( ( arsinh_real @ zero_zero_real )
% 5.31/5.59 = zero_zero_real ) ).
% 5.31/5.59
% 5.31/5.59 % arsinh_0
% 5.31/5.59 thf(fact_5001_vebt__buildup_Oelims,axiom,
% 5.31/5.59 ! [X: nat,Y: vEBT_VEBT] :
% 5.31/5.59 ( ( ( vEBT_vebt_buildup @ X )
% 5.31/5.59 = Y )
% 5.31/5.59 => ( ( ( X = zero_zero_nat )
% 5.31/5.59 => ( Y
% 5.31/5.59 != ( vEBT_Leaf @ $false @ $false ) ) )
% 5.31/5.59 => ( ( ( X
% 5.31/5.59 = ( suc @ zero_zero_nat ) )
% 5.31/5.59 => ( Y
% 5.31/5.59 != ( vEBT_Leaf @ $false @ $false ) ) )
% 5.31/5.59 => ~ ! [Va: nat] :
% 5.31/5.59 ( ( X
% 5.31/5.59 = ( suc @ ( suc @ Va ) ) )
% 5.31/5.59 => ~ ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va ) ) )
% 5.31/5.59 => ( Y
% 5.31/5.59 = ( 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 ) ) ) ) ) ) )
% 5.31/5.59 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va ) ) )
% 5.31/5.59 => ( Y
% 5.31/5.59 = ( 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 ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % vebt_buildup.elims
% 5.31/5.59 thf(fact_5002_prod_Ofinite__Collect__op,axiom,
% 5.31/5.59 ! [I5: set_real,X: real > code_integer,Y: real > code_integer] :
% 5.31/5.59 ( ( finite_finite_real
% 5.31/5.59 @ ( collect_real
% 5.31/5.59 @ ^ [I: real] :
% 5.31/5.59 ( ( member_real @ I @ I5 )
% 5.31/5.59 & ( ( X @ I )
% 5.31/5.59 != one_one_Code_integer ) ) ) )
% 5.31/5.59 => ( ( finite_finite_real
% 5.31/5.59 @ ( collect_real
% 5.31/5.59 @ ^ [I: real] :
% 5.31/5.59 ( ( member_real @ I @ I5 )
% 5.31/5.59 & ( ( Y @ I )
% 5.31/5.59 != one_one_Code_integer ) ) ) )
% 5.31/5.59 => ( finite_finite_real
% 5.31/5.59 @ ( collect_real
% 5.31/5.59 @ ^ [I: real] :
% 5.31/5.59 ( ( member_real @ I @ I5 )
% 5.31/5.59 & ( ( times_3573771949741848930nteger @ ( X @ I ) @ ( Y @ I ) )
% 5.31/5.59 != one_one_Code_integer ) ) ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % prod.finite_Collect_op
% 5.31/5.59 thf(fact_5003_prod_Ofinite__Collect__op,axiom,
% 5.31/5.59 ! [I5: set_nat,X: nat > code_integer,Y: nat > code_integer] :
% 5.31/5.59 ( ( finite_finite_nat
% 5.31/5.59 @ ( collect_nat
% 5.31/5.59 @ ^ [I: nat] :
% 5.31/5.59 ( ( member_nat @ I @ I5 )
% 5.31/5.59 & ( ( X @ I )
% 5.31/5.59 != one_one_Code_integer ) ) ) )
% 5.31/5.59 => ( ( finite_finite_nat
% 5.31/5.59 @ ( collect_nat
% 5.31/5.59 @ ^ [I: nat] :
% 5.31/5.59 ( ( member_nat @ I @ I5 )
% 5.31/5.59 & ( ( Y @ I )
% 5.31/5.59 != one_one_Code_integer ) ) ) )
% 5.31/5.59 => ( finite_finite_nat
% 5.31/5.59 @ ( collect_nat
% 5.31/5.59 @ ^ [I: nat] :
% 5.31/5.59 ( ( member_nat @ I @ I5 )
% 5.31/5.59 & ( ( times_3573771949741848930nteger @ ( X @ I ) @ ( Y @ I ) )
% 5.31/5.59 != one_one_Code_integer ) ) ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % prod.finite_Collect_op
% 5.31/5.59 thf(fact_5004_prod_Ofinite__Collect__op,axiom,
% 5.31/5.59 ! [I5: set_int,X: int > code_integer,Y: int > code_integer] :
% 5.31/5.59 ( ( finite_finite_int
% 5.31/5.59 @ ( collect_int
% 5.31/5.59 @ ^ [I: int] :
% 5.31/5.59 ( ( member_int @ I @ I5 )
% 5.31/5.59 & ( ( X @ I )
% 5.31/5.59 != one_one_Code_integer ) ) ) )
% 5.31/5.59 => ( ( finite_finite_int
% 5.31/5.59 @ ( collect_int
% 5.31/5.59 @ ^ [I: int] :
% 5.31/5.59 ( ( member_int @ I @ I5 )
% 5.31/5.59 & ( ( Y @ I )
% 5.31/5.59 != one_one_Code_integer ) ) ) )
% 5.31/5.59 => ( finite_finite_int
% 5.31/5.59 @ ( collect_int
% 5.31/5.59 @ ^ [I: int] :
% 5.31/5.59 ( ( member_int @ I @ I5 )
% 5.31/5.59 & ( ( times_3573771949741848930nteger @ ( X @ I ) @ ( Y @ I ) )
% 5.31/5.59 != one_one_Code_integer ) ) ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % prod.finite_Collect_op
% 5.31/5.59 thf(fact_5005_prod_Ofinite__Collect__op,axiom,
% 5.31/5.59 ! [I5: set_complex,X: complex > code_integer,Y: complex > code_integer] :
% 5.31/5.59 ( ( finite3207457112153483333omplex
% 5.31/5.59 @ ( collect_complex
% 5.31/5.59 @ ^ [I: complex] :
% 5.31/5.59 ( ( member_complex @ I @ I5 )
% 5.31/5.59 & ( ( X @ I )
% 5.31/5.59 != one_one_Code_integer ) ) ) )
% 5.31/5.59 => ( ( finite3207457112153483333omplex
% 5.31/5.59 @ ( collect_complex
% 5.31/5.59 @ ^ [I: complex] :
% 5.31/5.59 ( ( member_complex @ I @ I5 )
% 5.31/5.59 & ( ( Y @ I )
% 5.31/5.59 != one_one_Code_integer ) ) ) )
% 5.31/5.59 => ( finite3207457112153483333omplex
% 5.31/5.59 @ ( collect_complex
% 5.31/5.59 @ ^ [I: complex] :
% 5.31/5.59 ( ( member_complex @ I @ I5 )
% 5.31/5.59 & ( ( times_3573771949741848930nteger @ ( X @ I ) @ ( Y @ I ) )
% 5.31/5.59 != one_one_Code_integer ) ) ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % prod.finite_Collect_op
% 5.31/5.59 thf(fact_5006_prod_Ofinite__Collect__op,axiom,
% 5.31/5.59 ! [I5: set_real,X: real > complex,Y: real > complex] :
% 5.31/5.59 ( ( finite_finite_real
% 5.31/5.59 @ ( collect_real
% 5.31/5.59 @ ^ [I: real] :
% 5.31/5.59 ( ( member_real @ I @ I5 )
% 5.31/5.59 & ( ( X @ I )
% 5.31/5.59 != one_one_complex ) ) ) )
% 5.31/5.59 => ( ( finite_finite_real
% 5.31/5.59 @ ( collect_real
% 5.31/5.59 @ ^ [I: real] :
% 5.31/5.59 ( ( member_real @ I @ I5 )
% 5.31/5.59 & ( ( Y @ I )
% 5.31/5.59 != one_one_complex ) ) ) )
% 5.31/5.59 => ( finite_finite_real
% 5.31/5.59 @ ( collect_real
% 5.31/5.59 @ ^ [I: real] :
% 5.31/5.59 ( ( member_real @ I @ I5 )
% 5.31/5.59 & ( ( times_times_complex @ ( X @ I ) @ ( Y @ I ) )
% 5.31/5.59 != one_one_complex ) ) ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % prod.finite_Collect_op
% 5.31/5.59 thf(fact_5007_prod_Ofinite__Collect__op,axiom,
% 5.31/5.59 ! [I5: set_nat,X: nat > complex,Y: nat > complex] :
% 5.31/5.59 ( ( finite_finite_nat
% 5.31/5.59 @ ( collect_nat
% 5.31/5.59 @ ^ [I: nat] :
% 5.31/5.59 ( ( member_nat @ I @ I5 )
% 5.31/5.59 & ( ( X @ I )
% 5.31/5.59 != one_one_complex ) ) ) )
% 5.31/5.59 => ( ( finite_finite_nat
% 5.31/5.59 @ ( collect_nat
% 5.31/5.59 @ ^ [I: nat] :
% 5.31/5.59 ( ( member_nat @ I @ I5 )
% 5.31/5.59 & ( ( Y @ I )
% 5.31/5.59 != one_one_complex ) ) ) )
% 5.31/5.59 => ( finite_finite_nat
% 5.31/5.59 @ ( collect_nat
% 5.31/5.59 @ ^ [I: nat] :
% 5.31/5.59 ( ( member_nat @ I @ I5 )
% 5.31/5.59 & ( ( times_times_complex @ ( X @ I ) @ ( Y @ I ) )
% 5.31/5.59 != one_one_complex ) ) ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % prod.finite_Collect_op
% 5.31/5.59 thf(fact_5008_prod_Ofinite__Collect__op,axiom,
% 5.31/5.59 ! [I5: set_int,X: int > complex,Y: int > complex] :
% 5.31/5.59 ( ( finite_finite_int
% 5.31/5.59 @ ( collect_int
% 5.31/5.59 @ ^ [I: int] :
% 5.31/5.59 ( ( member_int @ I @ I5 )
% 5.31/5.59 & ( ( X @ I )
% 5.31/5.59 != one_one_complex ) ) ) )
% 5.31/5.59 => ( ( finite_finite_int
% 5.31/5.59 @ ( collect_int
% 5.31/5.59 @ ^ [I: int] :
% 5.31/5.59 ( ( member_int @ I @ I5 )
% 5.31/5.59 & ( ( Y @ I )
% 5.31/5.59 != one_one_complex ) ) ) )
% 5.31/5.59 => ( finite_finite_int
% 5.31/5.59 @ ( collect_int
% 5.31/5.59 @ ^ [I: int] :
% 5.31/5.59 ( ( member_int @ I @ I5 )
% 5.31/5.59 & ( ( times_times_complex @ ( X @ I ) @ ( Y @ I ) )
% 5.31/5.59 != one_one_complex ) ) ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % prod.finite_Collect_op
% 5.31/5.59 thf(fact_5009_prod_Ofinite__Collect__op,axiom,
% 5.31/5.59 ! [I5: set_complex,X: complex > complex,Y: complex > complex] :
% 5.31/5.59 ( ( finite3207457112153483333omplex
% 5.31/5.59 @ ( collect_complex
% 5.31/5.59 @ ^ [I: complex] :
% 5.31/5.59 ( ( member_complex @ I @ I5 )
% 5.31/5.59 & ( ( X @ I )
% 5.31/5.59 != one_one_complex ) ) ) )
% 5.31/5.59 => ( ( finite3207457112153483333omplex
% 5.31/5.59 @ ( collect_complex
% 5.31/5.59 @ ^ [I: complex] :
% 5.31/5.59 ( ( member_complex @ I @ I5 )
% 5.31/5.59 & ( ( Y @ I )
% 5.31/5.59 != one_one_complex ) ) ) )
% 5.31/5.59 => ( finite3207457112153483333omplex
% 5.31/5.59 @ ( collect_complex
% 5.31/5.59 @ ^ [I: complex] :
% 5.31/5.59 ( ( member_complex @ I @ I5 )
% 5.31/5.59 & ( ( times_times_complex @ ( X @ I ) @ ( Y @ I ) )
% 5.31/5.59 != one_one_complex ) ) ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % prod.finite_Collect_op
% 5.31/5.59 thf(fact_5010_prod_Ofinite__Collect__op,axiom,
% 5.31/5.59 ! [I5: set_real,X: real > real,Y: real > real] :
% 5.31/5.59 ( ( finite_finite_real
% 5.31/5.59 @ ( collect_real
% 5.31/5.59 @ ^ [I: real] :
% 5.31/5.59 ( ( member_real @ I @ I5 )
% 5.31/5.59 & ( ( X @ I )
% 5.31/5.59 != one_one_real ) ) ) )
% 5.31/5.59 => ( ( finite_finite_real
% 5.31/5.59 @ ( collect_real
% 5.31/5.59 @ ^ [I: real] :
% 5.31/5.59 ( ( member_real @ I @ I5 )
% 5.31/5.59 & ( ( Y @ I )
% 5.31/5.59 != one_one_real ) ) ) )
% 5.31/5.59 => ( finite_finite_real
% 5.31/5.59 @ ( collect_real
% 5.31/5.59 @ ^ [I: real] :
% 5.31/5.59 ( ( member_real @ I @ I5 )
% 5.31/5.59 & ( ( times_times_real @ ( X @ I ) @ ( Y @ I ) )
% 5.31/5.59 != one_one_real ) ) ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % prod.finite_Collect_op
% 5.31/5.59 thf(fact_5011_prod_Ofinite__Collect__op,axiom,
% 5.31/5.59 ! [I5: set_nat,X: nat > real,Y: nat > real] :
% 5.31/5.59 ( ( finite_finite_nat
% 5.31/5.59 @ ( collect_nat
% 5.31/5.59 @ ^ [I: nat] :
% 5.31/5.59 ( ( member_nat @ I @ I5 )
% 5.31/5.59 & ( ( X @ I )
% 5.31/5.59 != one_one_real ) ) ) )
% 5.31/5.59 => ( ( finite_finite_nat
% 5.31/5.59 @ ( collect_nat
% 5.31/5.59 @ ^ [I: nat] :
% 5.31/5.59 ( ( member_nat @ I @ I5 )
% 5.31/5.59 & ( ( Y @ I )
% 5.31/5.59 != one_one_real ) ) ) )
% 5.31/5.59 => ( finite_finite_nat
% 5.31/5.59 @ ( collect_nat
% 5.31/5.59 @ ^ [I: nat] :
% 5.31/5.59 ( ( member_nat @ I @ I5 )
% 5.31/5.59 & ( ( times_times_real @ ( X @ I ) @ ( Y @ I ) )
% 5.31/5.59 != one_one_real ) ) ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % prod.finite_Collect_op
% 5.31/5.59 thf(fact_5012_sum__gp,axiom,
% 5.31/5.59 ! [N: nat,M2: nat,X: complex] :
% 5.31/5.59 ( ( ( ord_less_nat @ N @ M2 )
% 5.31/5.59 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_or1269000886237332187st_nat @ M2 @ N ) )
% 5.31/5.59 = zero_zero_complex ) )
% 5.31/5.59 & ( ~ ( ord_less_nat @ N @ M2 )
% 5.31/5.59 => ( ( ( X = one_one_complex )
% 5.31/5.59 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_or1269000886237332187st_nat @ M2 @ N ) )
% 5.31/5.59 = ( semiri8010041392384452111omplex @ ( minus_minus_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ M2 ) ) ) )
% 5.31/5.59 & ( ( X != one_one_complex )
% 5.31/5.59 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_or1269000886237332187st_nat @ M2 @ N ) )
% 5.31/5.59 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( power_power_complex @ X @ M2 ) @ ( power_power_complex @ X @ ( suc @ N ) ) ) @ ( minus_minus_complex @ one_one_complex @ X ) ) ) ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum_gp
% 5.31/5.59 thf(fact_5013_sum__gp,axiom,
% 5.31/5.59 ! [N: nat,M2: nat,X: rat] :
% 5.31/5.59 ( ( ( ord_less_nat @ N @ M2 )
% 5.31/5.59 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_or1269000886237332187st_nat @ M2 @ N ) )
% 5.31/5.59 = zero_zero_rat ) )
% 5.31/5.59 & ( ~ ( ord_less_nat @ N @ M2 )
% 5.31/5.59 => ( ( ( X = one_one_rat )
% 5.31/5.59 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_or1269000886237332187st_nat @ M2 @ N ) )
% 5.31/5.59 = ( semiri681578069525770553at_rat @ ( minus_minus_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ M2 ) ) ) )
% 5.31/5.59 & ( ( X != one_one_rat )
% 5.31/5.59 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_or1269000886237332187st_nat @ M2 @ N ) )
% 5.31/5.59 = ( divide_divide_rat @ ( minus_minus_rat @ ( power_power_rat @ X @ M2 ) @ ( power_power_rat @ X @ ( suc @ N ) ) ) @ ( minus_minus_rat @ one_one_rat @ X ) ) ) ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum_gp
% 5.31/5.59 thf(fact_5014_sum__gp,axiom,
% 5.31/5.59 ! [N: nat,M2: nat,X: real] :
% 5.31/5.59 ( ( ( ord_less_nat @ N @ M2 )
% 5.31/5.59 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_or1269000886237332187st_nat @ M2 @ N ) )
% 5.31/5.59 = zero_zero_real ) )
% 5.31/5.59 & ( ~ ( ord_less_nat @ N @ M2 )
% 5.31/5.59 => ( ( ( X = one_one_real )
% 5.31/5.59 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_or1269000886237332187st_nat @ M2 @ N ) )
% 5.31/5.59 = ( semiri5074537144036343181t_real @ ( minus_minus_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ M2 ) ) ) )
% 5.31/5.59 & ( ( X != one_one_real )
% 5.31/5.59 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_or1269000886237332187st_nat @ M2 @ N ) )
% 5.31/5.59 = ( divide_divide_real @ ( minus_minus_real @ ( power_power_real @ X @ M2 ) @ ( power_power_real @ X @ ( suc @ N ) ) ) @ ( minus_minus_real @ one_one_real @ X ) ) ) ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum_gp
% 5.31/5.59 thf(fact_5015_sum_Ofinite__Collect__op,axiom,
% 5.31/5.59 ! [I5: set_real,X: real > complex,Y: real > complex] :
% 5.31/5.59 ( ( finite_finite_real
% 5.31/5.59 @ ( collect_real
% 5.31/5.59 @ ^ [I: real] :
% 5.31/5.59 ( ( member_real @ I @ I5 )
% 5.31/5.59 & ( ( X @ I )
% 5.31/5.59 != zero_zero_complex ) ) ) )
% 5.31/5.59 => ( ( finite_finite_real
% 5.31/5.59 @ ( collect_real
% 5.31/5.59 @ ^ [I: real] :
% 5.31/5.59 ( ( member_real @ I @ I5 )
% 5.31/5.59 & ( ( Y @ I )
% 5.31/5.59 != zero_zero_complex ) ) ) )
% 5.31/5.59 => ( finite_finite_real
% 5.31/5.59 @ ( collect_real
% 5.31/5.59 @ ^ [I: real] :
% 5.31/5.59 ( ( member_real @ I @ I5 )
% 5.31/5.59 & ( ( plus_plus_complex @ ( X @ I ) @ ( Y @ I ) )
% 5.31/5.59 != zero_zero_complex ) ) ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum.finite_Collect_op
% 5.31/5.59 thf(fact_5016_sum_Ofinite__Collect__op,axiom,
% 5.31/5.59 ! [I5: set_nat,X: nat > complex,Y: nat > complex] :
% 5.31/5.59 ( ( finite_finite_nat
% 5.31/5.59 @ ( collect_nat
% 5.31/5.59 @ ^ [I: nat] :
% 5.31/5.59 ( ( member_nat @ I @ I5 )
% 5.31/5.59 & ( ( X @ I )
% 5.31/5.59 != zero_zero_complex ) ) ) )
% 5.31/5.59 => ( ( finite_finite_nat
% 5.31/5.59 @ ( collect_nat
% 5.31/5.59 @ ^ [I: nat] :
% 5.31/5.59 ( ( member_nat @ I @ I5 )
% 5.31/5.59 & ( ( Y @ I )
% 5.31/5.59 != zero_zero_complex ) ) ) )
% 5.31/5.59 => ( finite_finite_nat
% 5.31/5.59 @ ( collect_nat
% 5.31/5.59 @ ^ [I: nat] :
% 5.31/5.59 ( ( member_nat @ I @ I5 )
% 5.31/5.59 & ( ( plus_plus_complex @ ( X @ I ) @ ( Y @ I ) )
% 5.31/5.59 != zero_zero_complex ) ) ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum.finite_Collect_op
% 5.31/5.59 thf(fact_5017_sum_Ofinite__Collect__op,axiom,
% 5.31/5.59 ! [I5: set_int,X: int > complex,Y: int > complex] :
% 5.31/5.59 ( ( finite_finite_int
% 5.31/5.59 @ ( collect_int
% 5.31/5.59 @ ^ [I: int] :
% 5.31/5.59 ( ( member_int @ I @ I5 )
% 5.31/5.59 & ( ( X @ I )
% 5.31/5.59 != zero_zero_complex ) ) ) )
% 5.31/5.59 => ( ( finite_finite_int
% 5.31/5.59 @ ( collect_int
% 5.31/5.59 @ ^ [I: int] :
% 5.31/5.59 ( ( member_int @ I @ I5 )
% 5.31/5.59 & ( ( Y @ I )
% 5.31/5.59 != zero_zero_complex ) ) ) )
% 5.31/5.59 => ( finite_finite_int
% 5.31/5.59 @ ( collect_int
% 5.31/5.59 @ ^ [I: int] :
% 5.31/5.59 ( ( member_int @ I @ I5 )
% 5.31/5.59 & ( ( plus_plus_complex @ ( X @ I ) @ ( Y @ I ) )
% 5.31/5.59 != zero_zero_complex ) ) ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum.finite_Collect_op
% 5.31/5.59 thf(fact_5018_sum_Ofinite__Collect__op,axiom,
% 5.31/5.59 ! [I5: set_complex,X: complex > complex,Y: complex > complex] :
% 5.31/5.59 ( ( finite3207457112153483333omplex
% 5.31/5.59 @ ( collect_complex
% 5.31/5.59 @ ^ [I: complex] :
% 5.31/5.59 ( ( member_complex @ I @ I5 )
% 5.31/5.59 & ( ( X @ I )
% 5.31/5.59 != zero_zero_complex ) ) ) )
% 5.31/5.59 => ( ( finite3207457112153483333omplex
% 5.31/5.59 @ ( collect_complex
% 5.31/5.59 @ ^ [I: complex] :
% 5.31/5.59 ( ( member_complex @ I @ I5 )
% 5.31/5.59 & ( ( Y @ I )
% 5.31/5.59 != zero_zero_complex ) ) ) )
% 5.31/5.59 => ( finite3207457112153483333omplex
% 5.31/5.59 @ ( collect_complex
% 5.31/5.59 @ ^ [I: complex] :
% 5.31/5.59 ( ( member_complex @ I @ I5 )
% 5.31/5.59 & ( ( plus_plus_complex @ ( X @ I ) @ ( Y @ I ) )
% 5.31/5.59 != zero_zero_complex ) ) ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum.finite_Collect_op
% 5.31/5.59 thf(fact_5019_sum_Ofinite__Collect__op,axiom,
% 5.31/5.59 ! [I5: set_real,X: real > real,Y: real > real] :
% 5.31/5.59 ( ( finite_finite_real
% 5.31/5.59 @ ( collect_real
% 5.31/5.59 @ ^ [I: real] :
% 5.31/5.59 ( ( member_real @ I @ I5 )
% 5.31/5.59 & ( ( X @ I )
% 5.31/5.59 != zero_zero_real ) ) ) )
% 5.31/5.59 => ( ( finite_finite_real
% 5.31/5.59 @ ( collect_real
% 5.31/5.59 @ ^ [I: real] :
% 5.31/5.59 ( ( member_real @ I @ I5 )
% 5.31/5.59 & ( ( Y @ I )
% 5.31/5.59 != zero_zero_real ) ) ) )
% 5.31/5.59 => ( finite_finite_real
% 5.31/5.59 @ ( collect_real
% 5.31/5.59 @ ^ [I: real] :
% 5.31/5.59 ( ( member_real @ I @ I5 )
% 5.31/5.59 & ( ( plus_plus_real @ ( X @ I ) @ ( Y @ I ) )
% 5.31/5.59 != zero_zero_real ) ) ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum.finite_Collect_op
% 5.31/5.59 thf(fact_5020_sum_Ofinite__Collect__op,axiom,
% 5.31/5.59 ! [I5: set_nat,X: nat > real,Y: nat > real] :
% 5.31/5.59 ( ( finite_finite_nat
% 5.31/5.59 @ ( collect_nat
% 5.31/5.59 @ ^ [I: nat] :
% 5.31/5.59 ( ( member_nat @ I @ I5 )
% 5.31/5.59 & ( ( X @ I )
% 5.31/5.59 != zero_zero_real ) ) ) )
% 5.31/5.59 => ( ( finite_finite_nat
% 5.31/5.59 @ ( collect_nat
% 5.31/5.59 @ ^ [I: nat] :
% 5.31/5.59 ( ( member_nat @ I @ I5 )
% 5.31/5.59 & ( ( Y @ I )
% 5.31/5.59 != zero_zero_real ) ) ) )
% 5.31/5.59 => ( finite_finite_nat
% 5.31/5.59 @ ( collect_nat
% 5.31/5.59 @ ^ [I: nat] :
% 5.31/5.59 ( ( member_nat @ I @ I5 )
% 5.31/5.59 & ( ( plus_plus_real @ ( X @ I ) @ ( Y @ I ) )
% 5.31/5.59 != zero_zero_real ) ) ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum.finite_Collect_op
% 5.31/5.59 thf(fact_5021_sum_Ofinite__Collect__op,axiom,
% 5.31/5.59 ! [I5: set_int,X: int > real,Y: int > real] :
% 5.31/5.59 ( ( finite_finite_int
% 5.31/5.59 @ ( collect_int
% 5.31/5.59 @ ^ [I: int] :
% 5.31/5.59 ( ( member_int @ I @ I5 )
% 5.31/5.59 & ( ( X @ I )
% 5.31/5.59 != zero_zero_real ) ) ) )
% 5.31/5.59 => ( ( finite_finite_int
% 5.31/5.59 @ ( collect_int
% 5.31/5.59 @ ^ [I: int] :
% 5.31/5.59 ( ( member_int @ I @ I5 )
% 5.31/5.59 & ( ( Y @ I )
% 5.31/5.59 != zero_zero_real ) ) ) )
% 5.31/5.59 => ( finite_finite_int
% 5.31/5.59 @ ( collect_int
% 5.31/5.59 @ ^ [I: int] :
% 5.31/5.59 ( ( member_int @ I @ I5 )
% 5.31/5.59 & ( ( plus_plus_real @ ( X @ I ) @ ( Y @ I ) )
% 5.31/5.59 != zero_zero_real ) ) ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum.finite_Collect_op
% 5.31/5.59 thf(fact_5022_sum_Ofinite__Collect__op,axiom,
% 5.31/5.59 ! [I5: set_complex,X: complex > real,Y: complex > real] :
% 5.31/5.59 ( ( finite3207457112153483333omplex
% 5.31/5.59 @ ( collect_complex
% 5.31/5.59 @ ^ [I: complex] :
% 5.31/5.59 ( ( member_complex @ I @ I5 )
% 5.31/5.59 & ( ( X @ I )
% 5.31/5.59 != zero_zero_real ) ) ) )
% 5.31/5.59 => ( ( finite3207457112153483333omplex
% 5.31/5.59 @ ( collect_complex
% 5.31/5.59 @ ^ [I: complex] :
% 5.31/5.59 ( ( member_complex @ I @ I5 )
% 5.31/5.59 & ( ( Y @ I )
% 5.31/5.59 != zero_zero_real ) ) ) )
% 5.31/5.59 => ( finite3207457112153483333omplex
% 5.31/5.59 @ ( collect_complex
% 5.31/5.59 @ ^ [I: complex] :
% 5.31/5.59 ( ( member_complex @ I @ I5 )
% 5.31/5.59 & ( ( plus_plus_real @ ( X @ I ) @ ( Y @ I ) )
% 5.31/5.59 != zero_zero_real ) ) ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum.finite_Collect_op
% 5.31/5.59 thf(fact_5023_sum_Ofinite__Collect__op,axiom,
% 5.31/5.59 ! [I5: set_real,X: real > rat,Y: real > rat] :
% 5.31/5.59 ( ( finite_finite_real
% 5.31/5.59 @ ( collect_real
% 5.31/5.59 @ ^ [I: real] :
% 5.31/5.59 ( ( member_real @ I @ I5 )
% 5.31/5.59 & ( ( X @ I )
% 5.31/5.59 != zero_zero_rat ) ) ) )
% 5.31/5.59 => ( ( finite_finite_real
% 5.31/5.59 @ ( collect_real
% 5.31/5.59 @ ^ [I: real] :
% 5.31/5.59 ( ( member_real @ I @ I5 )
% 5.31/5.59 & ( ( Y @ I )
% 5.31/5.59 != zero_zero_rat ) ) ) )
% 5.31/5.59 => ( finite_finite_real
% 5.31/5.59 @ ( collect_real
% 5.31/5.59 @ ^ [I: real] :
% 5.31/5.59 ( ( member_real @ I @ I5 )
% 5.31/5.59 & ( ( plus_plus_rat @ ( X @ I ) @ ( Y @ I ) )
% 5.31/5.59 != zero_zero_rat ) ) ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum.finite_Collect_op
% 5.31/5.59 thf(fact_5024_sum_Ofinite__Collect__op,axiom,
% 5.31/5.59 ! [I5: set_nat,X: nat > rat,Y: nat > rat] :
% 5.31/5.59 ( ( finite_finite_nat
% 5.31/5.59 @ ( collect_nat
% 5.31/5.59 @ ^ [I: nat] :
% 5.31/5.59 ( ( member_nat @ I @ I5 )
% 5.31/5.59 & ( ( X @ I )
% 5.31/5.59 != zero_zero_rat ) ) ) )
% 5.31/5.59 => ( ( finite_finite_nat
% 5.31/5.59 @ ( collect_nat
% 5.31/5.59 @ ^ [I: nat] :
% 5.31/5.59 ( ( member_nat @ I @ I5 )
% 5.31/5.59 & ( ( Y @ I )
% 5.31/5.59 != zero_zero_rat ) ) ) )
% 5.31/5.59 => ( finite_finite_nat
% 5.31/5.59 @ ( collect_nat
% 5.31/5.59 @ ^ [I: nat] :
% 5.31/5.59 ( ( member_nat @ I @ I5 )
% 5.31/5.59 & ( ( plus_plus_rat @ ( X @ I ) @ ( Y @ I ) )
% 5.31/5.59 != zero_zero_rat ) ) ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum.finite_Collect_op
% 5.31/5.59 thf(fact_5025_geometric__deriv__sums,axiom,
% 5.31/5.59 ! [Z3: real] :
% 5.31/5.59 ( ( ord_less_real @ ( real_V7735802525324610683m_real @ Z3 ) @ one_one_real )
% 5.31/5.59 => ( sums_real
% 5.31/5.59 @ ^ [N4: nat] : ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ N4 ) ) @ ( power_power_real @ Z3 @ N4 ) )
% 5.31/5.59 @ ( divide_divide_real @ one_one_real @ ( power_power_real @ ( minus_minus_real @ one_one_real @ Z3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % geometric_deriv_sums
% 5.31/5.59 thf(fact_5026_geometric__deriv__sums,axiom,
% 5.31/5.59 ! [Z3: complex] :
% 5.31/5.59 ( ( ord_less_real @ ( real_V1022390504157884413omplex @ Z3 ) @ one_one_real )
% 5.31/5.59 => ( sums_complex
% 5.31/5.59 @ ^ [N4: nat] : ( times_times_complex @ ( semiri8010041392384452111omplex @ ( suc @ N4 ) ) @ ( power_power_complex @ Z3 @ N4 ) )
% 5.31/5.59 @ ( divide1717551699836669952omplex @ one_one_complex @ ( power_power_complex @ ( minus_minus_complex @ one_one_complex @ Z3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % geometric_deriv_sums
% 5.31/5.59 thf(fact_5027_pochhammer__double,axiom,
% 5.31/5.59 ! [Z3: complex,N: nat] :
% 5.31/5.59 ( ( comm_s2602460028002588243omplex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ Z3 ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.31/5.59 = ( times_times_complex @ ( times_times_complex @ ( semiri8010041392384452111omplex @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) @ ( comm_s2602460028002588243omplex @ Z3 @ N ) ) @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ Z3 @ ( divide1717551699836669952omplex @ one_one_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) @ N ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % pochhammer_double
% 5.31/5.59 thf(fact_5028_pochhammer__double,axiom,
% 5.31/5.59 ! [Z3: rat,N: nat] :
% 5.31/5.59 ( ( comm_s4028243227959126397er_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ Z3 ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.31/5.59 = ( times_times_rat @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) @ ( comm_s4028243227959126397er_rat @ Z3 @ N ) ) @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ Z3 @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) @ N ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % pochhammer_double
% 5.31/5.59 thf(fact_5029_pochhammer__double,axiom,
% 5.31/5.59 ! [Z3: real,N: nat] :
% 5.31/5.59 ( ( comm_s7457072308508201937r_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ Z3 ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.31/5.59 = ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) @ ( comm_s7457072308508201937r_real @ Z3 @ N ) ) @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ Z3 @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ N ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % pochhammer_double
% 5.31/5.59 thf(fact_5030_dvd__0__right,axiom,
% 5.31/5.59 ! [A: complex] : ( dvd_dvd_complex @ A @ zero_zero_complex ) ).
% 5.31/5.59
% 5.31/5.59 % dvd_0_right
% 5.31/5.59 thf(fact_5031_dvd__0__right,axiom,
% 5.31/5.59 ! [A: real] : ( dvd_dvd_real @ A @ zero_zero_real ) ).
% 5.31/5.59
% 5.31/5.59 % dvd_0_right
% 5.31/5.59 thf(fact_5032_dvd__0__right,axiom,
% 5.31/5.59 ! [A: rat] : ( dvd_dvd_rat @ A @ zero_zero_rat ) ).
% 5.31/5.59
% 5.31/5.59 % dvd_0_right
% 5.31/5.59 thf(fact_5033_dvd__0__right,axiom,
% 5.31/5.59 ! [A: nat] : ( dvd_dvd_nat @ A @ zero_zero_nat ) ).
% 5.31/5.59
% 5.31/5.59 % dvd_0_right
% 5.31/5.59 thf(fact_5034_dvd__0__right,axiom,
% 5.31/5.59 ! [A: int] : ( dvd_dvd_int @ A @ zero_zero_int ) ).
% 5.31/5.59
% 5.31/5.59 % dvd_0_right
% 5.31/5.59 thf(fact_5035_dvd__0__left__iff,axiom,
% 5.31/5.59 ! [A: complex] :
% 5.31/5.59 ( ( dvd_dvd_complex @ zero_zero_complex @ A )
% 5.31/5.59 = ( A = zero_zero_complex ) ) ).
% 5.31/5.59
% 5.31/5.59 % dvd_0_left_iff
% 5.31/5.59 thf(fact_5036_dvd__0__left__iff,axiom,
% 5.31/5.59 ! [A: real] :
% 5.31/5.59 ( ( dvd_dvd_real @ zero_zero_real @ A )
% 5.31/5.59 = ( A = zero_zero_real ) ) ).
% 5.31/5.59
% 5.31/5.59 % dvd_0_left_iff
% 5.31/5.59 thf(fact_5037_dvd__0__left__iff,axiom,
% 5.31/5.59 ! [A: rat] :
% 5.31/5.59 ( ( dvd_dvd_rat @ zero_zero_rat @ A )
% 5.31/5.59 = ( A = zero_zero_rat ) ) ).
% 5.31/5.59
% 5.31/5.59 % dvd_0_left_iff
% 5.31/5.59 thf(fact_5038_dvd__0__left__iff,axiom,
% 5.31/5.59 ! [A: nat] :
% 5.31/5.59 ( ( dvd_dvd_nat @ zero_zero_nat @ A )
% 5.31/5.59 = ( A = zero_zero_nat ) ) ).
% 5.31/5.59
% 5.31/5.59 % dvd_0_left_iff
% 5.31/5.59 thf(fact_5039_dvd__0__left__iff,axiom,
% 5.31/5.59 ! [A: int] :
% 5.31/5.59 ( ( dvd_dvd_int @ zero_zero_int @ A )
% 5.31/5.59 = ( A = zero_zero_int ) ) ).
% 5.31/5.59
% 5.31/5.59 % dvd_0_left_iff
% 5.31/5.59 thf(fact_5040_dvd__add__triv__right__iff,axiom,
% 5.31/5.59 ! [A: real,B: real] :
% 5.31/5.59 ( ( dvd_dvd_real @ A @ ( plus_plus_real @ B @ A ) )
% 5.31/5.59 = ( dvd_dvd_real @ A @ B ) ) ).
% 5.31/5.59
% 5.31/5.59 % dvd_add_triv_right_iff
% 5.31/5.59 thf(fact_5041_dvd__add__triv__right__iff,axiom,
% 5.31/5.59 ! [A: rat,B: rat] :
% 5.31/5.59 ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ B @ A ) )
% 5.31/5.59 = ( dvd_dvd_rat @ A @ B ) ) ).
% 5.31/5.59
% 5.31/5.59 % dvd_add_triv_right_iff
% 5.31/5.59 thf(fact_5042_dvd__add__triv__right__iff,axiom,
% 5.31/5.59 ! [A: nat,B: nat] :
% 5.31/5.59 ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ A ) )
% 5.31/5.59 = ( dvd_dvd_nat @ A @ B ) ) ).
% 5.31/5.59
% 5.31/5.59 % dvd_add_triv_right_iff
% 5.31/5.59 thf(fact_5043_dvd__add__triv__right__iff,axiom,
% 5.31/5.59 ! [A: int,B: int] :
% 5.31/5.59 ( ( dvd_dvd_int @ A @ ( plus_plus_int @ B @ A ) )
% 5.31/5.59 = ( dvd_dvd_int @ A @ B ) ) ).
% 5.31/5.59
% 5.31/5.59 % dvd_add_triv_right_iff
% 5.31/5.59 thf(fact_5044_dvd__add__triv__left__iff,axiom,
% 5.31/5.59 ! [A: real,B: real] :
% 5.31/5.59 ( ( dvd_dvd_real @ A @ ( plus_plus_real @ A @ B ) )
% 5.31/5.59 = ( dvd_dvd_real @ A @ B ) ) ).
% 5.31/5.59
% 5.31/5.59 % dvd_add_triv_left_iff
% 5.31/5.59 thf(fact_5045_dvd__add__triv__left__iff,axiom,
% 5.31/5.59 ! [A: rat,B: rat] :
% 5.31/5.59 ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ A @ B ) )
% 5.31/5.59 = ( dvd_dvd_rat @ A @ B ) ) ).
% 5.31/5.59
% 5.31/5.59 % dvd_add_triv_left_iff
% 5.31/5.59 thf(fact_5046_dvd__add__triv__left__iff,axiom,
% 5.31/5.59 ! [A: nat,B: nat] :
% 5.31/5.59 ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 5.31/5.59 = ( dvd_dvd_nat @ A @ B ) ) ).
% 5.31/5.59
% 5.31/5.59 % dvd_add_triv_left_iff
% 5.31/5.59 thf(fact_5047_dvd__add__triv__left__iff,axiom,
% 5.31/5.59 ! [A: int,B: int] :
% 5.31/5.59 ( ( dvd_dvd_int @ A @ ( plus_plus_int @ A @ B ) )
% 5.31/5.59 = ( dvd_dvd_int @ A @ B ) ) ).
% 5.31/5.59
% 5.31/5.59 % dvd_add_triv_left_iff
% 5.31/5.59 thf(fact_5048_div__dvd__div,axiom,
% 5.31/5.59 ! [A: nat,B: nat,C2: nat] :
% 5.31/5.59 ( ( dvd_dvd_nat @ A @ B )
% 5.31/5.59 => ( ( dvd_dvd_nat @ A @ C2 )
% 5.31/5.59 => ( ( dvd_dvd_nat @ ( divide_divide_nat @ B @ A ) @ ( divide_divide_nat @ C2 @ A ) )
% 5.31/5.59 = ( dvd_dvd_nat @ B @ C2 ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % div_dvd_div
% 5.31/5.59 thf(fact_5049_div__dvd__div,axiom,
% 5.31/5.59 ! [A: int,B: int,C2: int] :
% 5.31/5.59 ( ( dvd_dvd_int @ A @ B )
% 5.31/5.59 => ( ( dvd_dvd_int @ A @ C2 )
% 5.31/5.59 => ( ( dvd_dvd_int @ ( divide_divide_int @ B @ A ) @ ( divide_divide_int @ C2 @ A ) )
% 5.31/5.59 = ( dvd_dvd_int @ B @ C2 ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % div_dvd_div
% 5.31/5.59 thf(fact_5050_nat__dvd__1__iff__1,axiom,
% 5.31/5.59 ! [M2: nat] :
% 5.31/5.59 ( ( dvd_dvd_nat @ M2 @ one_one_nat )
% 5.31/5.59 = ( M2 = one_one_nat ) ) ).
% 5.31/5.59
% 5.31/5.59 % nat_dvd_1_iff_1
% 5.31/5.59 thf(fact_5051_sum_Oneutral__const,axiom,
% 5.31/5.59 ! [A4: set_nat] :
% 5.31/5.59 ( ( groups3542108847815614940at_nat
% 5.31/5.59 @ ^ [Uu3: nat] : zero_zero_nat
% 5.31/5.59 @ A4 )
% 5.31/5.59 = zero_zero_nat ) ).
% 5.31/5.59
% 5.31/5.59 % sum.neutral_const
% 5.31/5.59 thf(fact_5052_sum_Oneutral__const,axiom,
% 5.31/5.59 ! [A4: set_int] :
% 5.31/5.59 ( ( groups4538972089207619220nt_int
% 5.31/5.59 @ ^ [Uu3: int] : zero_zero_int
% 5.31/5.59 @ A4 )
% 5.31/5.59 = zero_zero_int ) ).
% 5.31/5.59
% 5.31/5.59 % sum.neutral_const
% 5.31/5.59 thf(fact_5053_sum_Oneutral__const,axiom,
% 5.31/5.59 ! [A4: set_nat] :
% 5.31/5.59 ( ( groups6591440286371151544t_real
% 5.31/5.59 @ ^ [Uu3: nat] : zero_zero_real
% 5.31/5.59 @ A4 )
% 5.31/5.59 = zero_zero_real ) ).
% 5.31/5.59
% 5.31/5.59 % sum.neutral_const
% 5.31/5.59 thf(fact_5054_dvd__times__right__cancel__iff,axiom,
% 5.31/5.59 ! [A: nat,B: nat,C2: nat] :
% 5.31/5.59 ( ( A != zero_zero_nat )
% 5.31/5.59 => ( ( dvd_dvd_nat @ ( times_times_nat @ B @ A ) @ ( times_times_nat @ C2 @ A ) )
% 5.31/5.59 = ( dvd_dvd_nat @ B @ C2 ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % dvd_times_right_cancel_iff
% 5.31/5.59 thf(fact_5055_dvd__times__right__cancel__iff,axiom,
% 5.31/5.59 ! [A: int,B: int,C2: int] :
% 5.31/5.59 ( ( A != zero_zero_int )
% 5.31/5.59 => ( ( dvd_dvd_int @ ( times_times_int @ B @ A ) @ ( times_times_int @ C2 @ A ) )
% 5.31/5.59 = ( dvd_dvd_int @ B @ C2 ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % dvd_times_right_cancel_iff
% 5.31/5.59 thf(fact_5056_dvd__times__left__cancel__iff,axiom,
% 5.31/5.59 ! [A: nat,B: nat,C2: nat] :
% 5.31/5.59 ( ( A != zero_zero_nat )
% 5.31/5.59 => ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C2 ) )
% 5.31/5.59 = ( dvd_dvd_nat @ B @ C2 ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % dvd_times_left_cancel_iff
% 5.31/5.59 thf(fact_5057_dvd__times__left__cancel__iff,axiom,
% 5.31/5.59 ! [A: int,B: int,C2: int] :
% 5.31/5.59 ( ( A != zero_zero_int )
% 5.31/5.59 => ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C2 ) )
% 5.31/5.59 = ( dvd_dvd_int @ B @ C2 ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % dvd_times_left_cancel_iff
% 5.31/5.59 thf(fact_5058_dvd__mult__cancel__right,axiom,
% 5.31/5.59 ! [A: complex,C2: complex,B: complex] :
% 5.31/5.59 ( ( dvd_dvd_complex @ ( times_times_complex @ A @ C2 ) @ ( times_times_complex @ B @ C2 ) )
% 5.31/5.59 = ( ( C2 = zero_zero_complex )
% 5.31/5.59 | ( dvd_dvd_complex @ A @ B ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % dvd_mult_cancel_right
% 5.31/5.59 thf(fact_5059_dvd__mult__cancel__right,axiom,
% 5.31/5.59 ! [A: real,C2: real,B: real] :
% 5.31/5.59 ( ( dvd_dvd_real @ ( times_times_real @ A @ C2 ) @ ( times_times_real @ B @ C2 ) )
% 5.31/5.59 = ( ( C2 = zero_zero_real )
% 5.31/5.59 | ( dvd_dvd_real @ A @ B ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % dvd_mult_cancel_right
% 5.31/5.59 thf(fact_5060_dvd__mult__cancel__right,axiom,
% 5.31/5.59 ! [A: rat,C2: rat,B: rat] :
% 5.31/5.59 ( ( dvd_dvd_rat @ ( times_times_rat @ A @ C2 ) @ ( times_times_rat @ B @ C2 ) )
% 5.31/5.59 = ( ( C2 = zero_zero_rat )
% 5.31/5.59 | ( dvd_dvd_rat @ A @ B ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % dvd_mult_cancel_right
% 5.31/5.59 thf(fact_5061_dvd__mult__cancel__right,axiom,
% 5.31/5.59 ! [A: int,C2: int,B: int] :
% 5.31/5.59 ( ( dvd_dvd_int @ ( times_times_int @ A @ C2 ) @ ( times_times_int @ B @ C2 ) )
% 5.31/5.59 = ( ( C2 = zero_zero_int )
% 5.31/5.59 | ( dvd_dvd_int @ A @ B ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % dvd_mult_cancel_right
% 5.31/5.59 thf(fact_5062_dvd__mult__cancel__left,axiom,
% 5.31/5.59 ! [C2: complex,A: complex,B: complex] :
% 5.31/5.59 ( ( dvd_dvd_complex @ ( times_times_complex @ C2 @ A ) @ ( times_times_complex @ C2 @ B ) )
% 5.31/5.59 = ( ( C2 = zero_zero_complex )
% 5.31/5.59 | ( dvd_dvd_complex @ A @ B ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % dvd_mult_cancel_left
% 5.31/5.59 thf(fact_5063_dvd__mult__cancel__left,axiom,
% 5.31/5.59 ! [C2: real,A: real,B: real] :
% 5.31/5.59 ( ( dvd_dvd_real @ ( times_times_real @ C2 @ A ) @ ( times_times_real @ C2 @ B ) )
% 5.31/5.59 = ( ( C2 = zero_zero_real )
% 5.31/5.59 | ( dvd_dvd_real @ A @ B ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % dvd_mult_cancel_left
% 5.31/5.59 thf(fact_5064_dvd__mult__cancel__left,axiom,
% 5.31/5.59 ! [C2: rat,A: rat,B: rat] :
% 5.31/5.59 ( ( dvd_dvd_rat @ ( times_times_rat @ C2 @ A ) @ ( times_times_rat @ C2 @ B ) )
% 5.31/5.59 = ( ( C2 = zero_zero_rat )
% 5.31/5.59 | ( dvd_dvd_rat @ A @ B ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % dvd_mult_cancel_left
% 5.31/5.59 thf(fact_5065_dvd__mult__cancel__left,axiom,
% 5.31/5.59 ! [C2: int,A: int,B: int] :
% 5.31/5.59 ( ( dvd_dvd_int @ ( times_times_int @ C2 @ A ) @ ( times_times_int @ C2 @ B ) )
% 5.31/5.59 = ( ( C2 = zero_zero_int )
% 5.31/5.59 | ( dvd_dvd_int @ A @ B ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % dvd_mult_cancel_left
% 5.31/5.59 thf(fact_5066_dvd__add__times__triv__right__iff,axiom,
% 5.31/5.59 ! [A: real,B: real,C2: real] :
% 5.31/5.59 ( ( dvd_dvd_real @ A @ ( plus_plus_real @ B @ ( times_times_real @ C2 @ A ) ) )
% 5.31/5.59 = ( dvd_dvd_real @ A @ B ) ) ).
% 5.31/5.59
% 5.31/5.59 % dvd_add_times_triv_right_iff
% 5.31/5.59 thf(fact_5067_dvd__add__times__triv__right__iff,axiom,
% 5.31/5.59 ! [A: rat,B: rat,C2: rat] :
% 5.31/5.59 ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ B @ ( times_times_rat @ C2 @ A ) ) )
% 5.31/5.59 = ( dvd_dvd_rat @ A @ B ) ) ).
% 5.31/5.59
% 5.31/5.59 % dvd_add_times_triv_right_iff
% 5.31/5.59 thf(fact_5068_dvd__add__times__triv__right__iff,axiom,
% 5.31/5.59 ! [A: nat,B: nat,C2: nat] :
% 5.31/5.59 ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ ( times_times_nat @ C2 @ A ) ) )
% 5.31/5.59 = ( dvd_dvd_nat @ A @ B ) ) ).
% 5.31/5.59
% 5.31/5.59 % dvd_add_times_triv_right_iff
% 5.31/5.59 thf(fact_5069_dvd__add__times__triv__right__iff,axiom,
% 5.31/5.59 ! [A: int,B: int,C2: int] :
% 5.31/5.59 ( ( dvd_dvd_int @ A @ ( plus_plus_int @ B @ ( times_times_int @ C2 @ A ) ) )
% 5.31/5.59 = ( dvd_dvd_int @ A @ B ) ) ).
% 5.31/5.59
% 5.31/5.59 % dvd_add_times_triv_right_iff
% 5.31/5.59 thf(fact_5070_dvd__add__times__triv__left__iff,axiom,
% 5.31/5.59 ! [A: real,C2: real,B: real] :
% 5.31/5.59 ( ( dvd_dvd_real @ A @ ( plus_plus_real @ ( times_times_real @ C2 @ A ) @ B ) )
% 5.31/5.59 = ( dvd_dvd_real @ A @ B ) ) ).
% 5.31/5.59
% 5.31/5.59 % dvd_add_times_triv_left_iff
% 5.31/5.59 thf(fact_5071_dvd__add__times__triv__left__iff,axiom,
% 5.31/5.59 ! [A: rat,C2: rat,B: rat] :
% 5.31/5.59 ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ ( times_times_rat @ C2 @ A ) @ B ) )
% 5.31/5.59 = ( dvd_dvd_rat @ A @ B ) ) ).
% 5.31/5.59
% 5.31/5.59 % dvd_add_times_triv_left_iff
% 5.31/5.59 thf(fact_5072_dvd__add__times__triv__left__iff,axiom,
% 5.31/5.59 ! [A: nat,C2: nat,B: nat] :
% 5.31/5.59 ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ ( times_times_nat @ C2 @ A ) @ B ) )
% 5.31/5.59 = ( dvd_dvd_nat @ A @ B ) ) ).
% 5.31/5.59
% 5.31/5.59 % dvd_add_times_triv_left_iff
% 5.31/5.59 thf(fact_5073_dvd__add__times__triv__left__iff,axiom,
% 5.31/5.59 ! [A: int,C2: int,B: int] :
% 5.31/5.59 ( ( dvd_dvd_int @ A @ ( plus_plus_int @ ( times_times_int @ C2 @ A ) @ B ) )
% 5.31/5.59 = ( dvd_dvd_int @ A @ B ) ) ).
% 5.31/5.59
% 5.31/5.59 % dvd_add_times_triv_left_iff
% 5.31/5.59 thf(fact_5074_unit__prod,axiom,
% 5.31/5.59 ! [A: code_integer,B: code_integer] :
% 5.31/5.59 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.31/5.59 => ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.31/5.59 => ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ one_one_Code_integer ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % unit_prod
% 5.31/5.59 thf(fact_5075_unit__prod,axiom,
% 5.31/5.59 ! [A: nat,B: nat] :
% 5.31/5.59 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.31/5.59 => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.31/5.59 => ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ one_one_nat ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % unit_prod
% 5.31/5.59 thf(fact_5076_unit__prod,axiom,
% 5.31/5.59 ! [A: int,B: int] :
% 5.31/5.59 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.31/5.59 => ( ( dvd_dvd_int @ B @ one_one_int )
% 5.31/5.59 => ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ one_one_int ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % unit_prod
% 5.31/5.59 thf(fact_5077_dvd__div__mult__self,axiom,
% 5.31/5.59 ! [A: nat,B: nat] :
% 5.31/5.59 ( ( dvd_dvd_nat @ A @ B )
% 5.31/5.59 => ( ( times_times_nat @ ( divide_divide_nat @ B @ A ) @ A )
% 5.31/5.59 = B ) ) ).
% 5.31/5.59
% 5.31/5.59 % dvd_div_mult_self
% 5.31/5.59 thf(fact_5078_dvd__div__mult__self,axiom,
% 5.31/5.59 ! [A: int,B: int] :
% 5.31/5.59 ( ( dvd_dvd_int @ A @ B )
% 5.31/5.59 => ( ( times_times_int @ ( divide_divide_int @ B @ A ) @ A )
% 5.31/5.59 = B ) ) ).
% 5.31/5.59
% 5.31/5.59 % dvd_div_mult_self
% 5.31/5.59 thf(fact_5079_dvd__mult__div__cancel,axiom,
% 5.31/5.59 ! [A: nat,B: nat] :
% 5.31/5.59 ( ( dvd_dvd_nat @ A @ B )
% 5.31/5.59 => ( ( times_times_nat @ A @ ( divide_divide_nat @ B @ A ) )
% 5.31/5.59 = B ) ) ).
% 5.31/5.59
% 5.31/5.59 % dvd_mult_div_cancel
% 5.31/5.59 thf(fact_5080_dvd__mult__div__cancel,axiom,
% 5.31/5.59 ! [A: int,B: int] :
% 5.31/5.59 ( ( dvd_dvd_int @ A @ B )
% 5.31/5.59 => ( ( times_times_int @ A @ ( divide_divide_int @ B @ A ) )
% 5.31/5.59 = B ) ) ).
% 5.31/5.59
% 5.31/5.59 % dvd_mult_div_cancel
% 5.31/5.59 thf(fact_5081_div__add,axiom,
% 5.31/5.59 ! [C2: nat,A: nat,B: nat] :
% 5.31/5.59 ( ( dvd_dvd_nat @ C2 @ A )
% 5.31/5.59 => ( ( dvd_dvd_nat @ C2 @ B )
% 5.31/5.59 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B ) @ C2 )
% 5.31/5.59 = ( plus_plus_nat @ ( divide_divide_nat @ A @ C2 ) @ ( divide_divide_nat @ B @ C2 ) ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % div_add
% 5.31/5.59 thf(fact_5082_div__add,axiom,
% 5.31/5.59 ! [C2: int,A: int,B: int] :
% 5.31/5.59 ( ( dvd_dvd_int @ C2 @ A )
% 5.31/5.59 => ( ( dvd_dvd_int @ C2 @ B )
% 5.31/5.59 => ( ( divide_divide_int @ ( plus_plus_int @ A @ B ) @ C2 )
% 5.31/5.59 = ( plus_plus_int @ ( divide_divide_int @ A @ C2 ) @ ( divide_divide_int @ B @ C2 ) ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % div_add
% 5.31/5.59 thf(fact_5083_unit__div,axiom,
% 5.31/5.59 ! [A: code_integer,B: code_integer] :
% 5.31/5.59 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.31/5.59 => ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.31/5.59 => ( dvd_dvd_Code_integer @ ( divide6298287555418463151nteger @ A @ B ) @ one_one_Code_integer ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % unit_div
% 5.31/5.59 thf(fact_5084_unit__div,axiom,
% 5.31/5.59 ! [A: nat,B: nat] :
% 5.31/5.59 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.31/5.59 => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.31/5.59 => ( dvd_dvd_nat @ ( divide_divide_nat @ A @ B ) @ one_one_nat ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % unit_div
% 5.31/5.59 thf(fact_5085_unit__div,axiom,
% 5.31/5.59 ! [A: int,B: int] :
% 5.31/5.59 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.31/5.59 => ( ( dvd_dvd_int @ B @ one_one_int )
% 5.31/5.59 => ( dvd_dvd_int @ ( divide_divide_int @ A @ B ) @ one_one_int ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % unit_div
% 5.31/5.59 thf(fact_5086_unit__div__1__unit,axiom,
% 5.31/5.59 ! [A: code_integer] :
% 5.31/5.59 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.31/5.59 => ( dvd_dvd_Code_integer @ ( divide6298287555418463151nteger @ one_one_Code_integer @ A ) @ one_one_Code_integer ) ) ).
% 5.31/5.59
% 5.31/5.59 % unit_div_1_unit
% 5.31/5.59 thf(fact_5087_unit__div__1__unit,axiom,
% 5.31/5.59 ! [A: nat] :
% 5.31/5.59 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.31/5.59 => ( dvd_dvd_nat @ ( divide_divide_nat @ one_one_nat @ A ) @ one_one_nat ) ) ).
% 5.31/5.59
% 5.31/5.59 % unit_div_1_unit
% 5.31/5.59 thf(fact_5088_unit__div__1__unit,axiom,
% 5.31/5.59 ! [A: int] :
% 5.31/5.59 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.31/5.59 => ( dvd_dvd_int @ ( divide_divide_int @ one_one_int @ A ) @ one_one_int ) ) ).
% 5.31/5.59
% 5.31/5.59 % unit_div_1_unit
% 5.31/5.59 thf(fact_5089_unit__div__1__div__1,axiom,
% 5.31/5.59 ! [A: code_integer] :
% 5.31/5.59 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.31/5.59 => ( ( divide6298287555418463151nteger @ one_one_Code_integer @ ( divide6298287555418463151nteger @ one_one_Code_integer @ A ) )
% 5.31/5.59 = A ) ) ).
% 5.31/5.59
% 5.31/5.59 % unit_div_1_div_1
% 5.31/5.59 thf(fact_5090_unit__div__1__div__1,axiom,
% 5.31/5.59 ! [A: nat] :
% 5.31/5.59 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.31/5.59 => ( ( divide_divide_nat @ one_one_nat @ ( divide_divide_nat @ one_one_nat @ A ) )
% 5.31/5.59 = A ) ) ).
% 5.31/5.59
% 5.31/5.59 % unit_div_1_div_1
% 5.31/5.59 thf(fact_5091_unit__div__1__div__1,axiom,
% 5.31/5.59 ! [A: int] :
% 5.31/5.59 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.31/5.59 => ( ( divide_divide_int @ one_one_int @ ( divide_divide_int @ one_one_int @ A ) )
% 5.31/5.59 = A ) ) ).
% 5.31/5.59
% 5.31/5.59 % unit_div_1_div_1
% 5.31/5.59 thf(fact_5092_sum_Oempty,axiom,
% 5.31/5.59 ! [G2: nat > complex] :
% 5.31/5.59 ( ( groups2073611262835488442omplex @ G2 @ bot_bot_set_nat )
% 5.31/5.59 = zero_zero_complex ) ).
% 5.31/5.59
% 5.31/5.59 % sum.empty
% 5.31/5.59 thf(fact_5093_sum_Oempty,axiom,
% 5.31/5.59 ! [G2: nat > rat] :
% 5.31/5.59 ( ( groups2906978787729119204at_rat @ G2 @ bot_bot_set_nat )
% 5.31/5.59 = zero_zero_rat ) ).
% 5.31/5.59
% 5.31/5.59 % sum.empty
% 5.31/5.59 thf(fact_5094_sum_Oempty,axiom,
% 5.31/5.59 ! [G2: nat > int] :
% 5.31/5.59 ( ( groups3539618377306564664at_int @ G2 @ bot_bot_set_nat )
% 5.31/5.59 = zero_zero_int ) ).
% 5.31/5.59
% 5.31/5.59 % sum.empty
% 5.31/5.59 thf(fact_5095_sum_Oempty,axiom,
% 5.31/5.59 ! [G2: int > complex] :
% 5.31/5.59 ( ( groups3049146728041665814omplex @ G2 @ bot_bot_set_int )
% 5.31/5.59 = zero_zero_complex ) ).
% 5.31/5.59
% 5.31/5.59 % sum.empty
% 5.31/5.59 thf(fact_5096_sum_Oempty,axiom,
% 5.31/5.59 ! [G2: int > real] :
% 5.31/5.59 ( ( groups8778361861064173332t_real @ G2 @ bot_bot_set_int )
% 5.31/5.59 = zero_zero_real ) ).
% 5.31/5.59
% 5.31/5.59 % sum.empty
% 5.31/5.59 thf(fact_5097_sum_Oempty,axiom,
% 5.31/5.59 ! [G2: int > rat] :
% 5.31/5.59 ( ( groups3906332499630173760nt_rat @ G2 @ bot_bot_set_int )
% 5.31/5.59 = zero_zero_rat ) ).
% 5.31/5.59
% 5.31/5.59 % sum.empty
% 5.31/5.59 thf(fact_5098_sum_Oempty,axiom,
% 5.31/5.59 ! [G2: int > nat] :
% 5.31/5.59 ( ( groups4541462559716669496nt_nat @ G2 @ bot_bot_set_int )
% 5.31/5.59 = zero_zero_nat ) ).
% 5.31/5.59
% 5.31/5.59 % sum.empty
% 5.31/5.59 thf(fact_5099_sum_Oempty,axiom,
% 5.31/5.59 ! [G2: real > complex] :
% 5.31/5.59 ( ( groups5754745047067104278omplex @ G2 @ bot_bot_set_real )
% 5.31/5.59 = zero_zero_complex ) ).
% 5.31/5.59
% 5.31/5.59 % sum.empty
% 5.31/5.59 thf(fact_5100_sum_Oempty,axiom,
% 5.31/5.59 ! [G2: real > real] :
% 5.31/5.59 ( ( groups8097168146408367636l_real @ G2 @ bot_bot_set_real )
% 5.31/5.59 = zero_zero_real ) ).
% 5.31/5.59
% 5.31/5.59 % sum.empty
% 5.31/5.59 thf(fact_5101_sum_Oempty,axiom,
% 5.31/5.59 ! [G2: real > rat] :
% 5.31/5.59 ( ( groups1300246762558778688al_rat @ G2 @ bot_bot_set_real )
% 5.31/5.59 = zero_zero_rat ) ).
% 5.31/5.59
% 5.31/5.59 % sum.empty
% 5.31/5.59 thf(fact_5102_sum_Oinfinite,axiom,
% 5.31/5.59 ! [A4: set_nat,G2: nat > complex] :
% 5.31/5.59 ( ~ ( finite_finite_nat @ A4 )
% 5.31/5.59 => ( ( groups2073611262835488442omplex @ G2 @ A4 )
% 5.31/5.59 = zero_zero_complex ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum.infinite
% 5.31/5.59 thf(fact_5103_sum_Oinfinite,axiom,
% 5.31/5.59 ! [A4: set_int,G2: int > complex] :
% 5.31/5.59 ( ~ ( finite_finite_int @ A4 )
% 5.31/5.59 => ( ( groups3049146728041665814omplex @ G2 @ A4 )
% 5.31/5.59 = zero_zero_complex ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum.infinite
% 5.31/5.59 thf(fact_5104_sum_Oinfinite,axiom,
% 5.31/5.59 ! [A4: set_complex,G2: complex > complex] :
% 5.31/5.59 ( ~ ( finite3207457112153483333omplex @ A4 )
% 5.31/5.59 => ( ( groups7754918857620584856omplex @ G2 @ A4 )
% 5.31/5.59 = zero_zero_complex ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum.infinite
% 5.31/5.59 thf(fact_5105_sum_Oinfinite,axiom,
% 5.31/5.59 ! [A4: set_int,G2: int > real] :
% 5.31/5.59 ( ~ ( finite_finite_int @ A4 )
% 5.31/5.59 => ( ( groups8778361861064173332t_real @ G2 @ A4 )
% 5.31/5.59 = zero_zero_real ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum.infinite
% 5.31/5.59 thf(fact_5106_sum_Oinfinite,axiom,
% 5.31/5.59 ! [A4: set_complex,G2: complex > real] :
% 5.31/5.59 ( ~ ( finite3207457112153483333omplex @ A4 )
% 5.31/5.59 => ( ( groups5808333547571424918x_real @ G2 @ A4 )
% 5.31/5.59 = zero_zero_real ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum.infinite
% 5.31/5.59 thf(fact_5107_sum_Oinfinite,axiom,
% 5.31/5.59 ! [A4: set_nat,G2: nat > rat] :
% 5.31/5.59 ( ~ ( finite_finite_nat @ A4 )
% 5.31/5.59 => ( ( groups2906978787729119204at_rat @ G2 @ A4 )
% 5.31/5.59 = zero_zero_rat ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum.infinite
% 5.31/5.59 thf(fact_5108_sum_Oinfinite,axiom,
% 5.31/5.59 ! [A4: set_int,G2: int > rat] :
% 5.31/5.59 ( ~ ( finite_finite_int @ A4 )
% 5.31/5.59 => ( ( groups3906332499630173760nt_rat @ G2 @ A4 )
% 5.31/5.59 = zero_zero_rat ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum.infinite
% 5.31/5.59 thf(fact_5109_sum_Oinfinite,axiom,
% 5.31/5.59 ! [A4: set_complex,G2: complex > rat] :
% 5.31/5.59 ( ~ ( finite3207457112153483333omplex @ A4 )
% 5.31/5.59 => ( ( groups5058264527183730370ex_rat @ G2 @ A4 )
% 5.31/5.59 = zero_zero_rat ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum.infinite
% 5.31/5.59 thf(fact_5110_sum_Oinfinite,axiom,
% 5.31/5.59 ! [A4: set_int,G2: int > nat] :
% 5.31/5.59 ( ~ ( finite_finite_int @ A4 )
% 5.31/5.59 => ( ( groups4541462559716669496nt_nat @ G2 @ A4 )
% 5.31/5.59 = zero_zero_nat ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum.infinite
% 5.31/5.59 thf(fact_5111_sum_Oinfinite,axiom,
% 5.31/5.59 ! [A4: set_complex,G2: complex > nat] :
% 5.31/5.59 ( ~ ( finite3207457112153483333omplex @ A4 )
% 5.31/5.59 => ( ( groups5693394587270226106ex_nat @ G2 @ A4 )
% 5.31/5.59 = zero_zero_nat ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum.infinite
% 5.31/5.59 thf(fact_5112_sum__eq__0__iff,axiom,
% 5.31/5.59 ! [F3: set_int,F2: int > nat] :
% 5.31/5.59 ( ( finite_finite_int @ F3 )
% 5.31/5.59 => ( ( ( groups4541462559716669496nt_nat @ F2 @ F3 )
% 5.31/5.59 = zero_zero_nat )
% 5.31/5.59 = ( ! [X4: int] :
% 5.31/5.59 ( ( member_int @ X4 @ F3 )
% 5.31/5.59 => ( ( F2 @ X4 )
% 5.31/5.59 = zero_zero_nat ) ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum_eq_0_iff
% 5.31/5.59 thf(fact_5113_sum__eq__0__iff,axiom,
% 5.31/5.59 ! [F3: set_complex,F2: complex > nat] :
% 5.31/5.59 ( ( finite3207457112153483333omplex @ F3 )
% 5.31/5.59 => ( ( ( groups5693394587270226106ex_nat @ F2 @ F3 )
% 5.31/5.59 = zero_zero_nat )
% 5.31/5.59 = ( ! [X4: complex] :
% 5.31/5.59 ( ( member_complex @ X4 @ F3 )
% 5.31/5.59 => ( ( F2 @ X4 )
% 5.31/5.59 = zero_zero_nat ) ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum_eq_0_iff
% 5.31/5.59 thf(fact_5114_sum__eq__0__iff,axiom,
% 5.31/5.59 ! [F3: set_nat,F2: nat > nat] :
% 5.31/5.59 ( ( finite_finite_nat @ F3 )
% 5.31/5.59 => ( ( ( groups3542108847815614940at_nat @ F2 @ F3 )
% 5.31/5.59 = zero_zero_nat )
% 5.31/5.59 = ( ! [X4: nat] :
% 5.31/5.59 ( ( member_nat @ X4 @ F3 )
% 5.31/5.59 => ( ( F2 @ X4 )
% 5.31/5.59 = zero_zero_nat ) ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum_eq_0_iff
% 5.31/5.59 thf(fact_5115_div__diff,axiom,
% 5.31/5.59 ! [C2: int,A: int,B: int] :
% 5.31/5.59 ( ( dvd_dvd_int @ C2 @ A )
% 5.31/5.59 => ( ( dvd_dvd_int @ C2 @ B )
% 5.31/5.59 => ( ( divide_divide_int @ ( minus_minus_int @ A @ B ) @ C2 )
% 5.31/5.59 = ( minus_minus_int @ ( divide_divide_int @ A @ C2 ) @ ( divide_divide_int @ B @ C2 ) ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % div_diff
% 5.31/5.59 thf(fact_5116_dvd__imp__mod__0,axiom,
% 5.31/5.59 ! [A: nat,B: nat] :
% 5.31/5.59 ( ( dvd_dvd_nat @ A @ B )
% 5.31/5.59 => ( ( modulo_modulo_nat @ B @ A )
% 5.31/5.59 = zero_zero_nat ) ) ).
% 5.31/5.59
% 5.31/5.59 % dvd_imp_mod_0
% 5.31/5.59 thf(fact_5117_dvd__imp__mod__0,axiom,
% 5.31/5.59 ! [A: int,B: int] :
% 5.31/5.59 ( ( dvd_dvd_int @ A @ B )
% 5.31/5.59 => ( ( modulo_modulo_int @ B @ A )
% 5.31/5.59 = zero_zero_int ) ) ).
% 5.31/5.59
% 5.31/5.59 % dvd_imp_mod_0
% 5.31/5.59 thf(fact_5118_dvd__imp__mod__0,axiom,
% 5.31/5.59 ! [A: code_natural,B: code_natural] :
% 5.31/5.59 ( ( dvd_dvd_Code_natural @ A @ B )
% 5.31/5.59 => ( ( modulo8411746178871703098atural @ B @ A )
% 5.31/5.59 = zero_z2226904508553997617atural ) ) ).
% 5.31/5.59
% 5.31/5.59 % dvd_imp_mod_0
% 5.31/5.59 thf(fact_5119_dvd__1__left,axiom,
% 5.31/5.59 ! [K2: nat] : ( dvd_dvd_nat @ ( suc @ zero_zero_nat ) @ K2 ) ).
% 5.31/5.59
% 5.31/5.59 % dvd_1_left
% 5.31/5.59 thf(fact_5120_dvd__1__iff__1,axiom,
% 5.31/5.59 ! [M2: nat] :
% 5.31/5.59 ( ( dvd_dvd_nat @ M2 @ ( suc @ zero_zero_nat ) )
% 5.31/5.59 = ( M2
% 5.31/5.59 = ( suc @ zero_zero_nat ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % dvd_1_iff_1
% 5.31/5.59 thf(fact_5121_nat__mult__dvd__cancel__disj,axiom,
% 5.31/5.59 ! [K2: nat,M2: nat,N: nat] :
% 5.31/5.59 ( ( dvd_dvd_nat @ ( times_times_nat @ K2 @ M2 ) @ ( times_times_nat @ K2 @ N ) )
% 5.31/5.59 = ( ( K2 = zero_zero_nat )
% 5.31/5.59 | ( dvd_dvd_nat @ M2 @ N ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % nat_mult_dvd_cancel_disj
% 5.31/5.59 thf(fact_5122_pochhammer__0,axiom,
% 5.31/5.59 ! [A: code_integer] :
% 5.31/5.59 ( ( comm_s8582702949713902594nteger @ A @ zero_zero_nat )
% 5.31/5.59 = one_one_Code_integer ) ).
% 5.31/5.59
% 5.31/5.59 % pochhammer_0
% 5.31/5.59 thf(fact_5123_pochhammer__0,axiom,
% 5.31/5.59 ! [A: complex] :
% 5.31/5.59 ( ( comm_s2602460028002588243omplex @ A @ zero_zero_nat )
% 5.31/5.59 = one_one_complex ) ).
% 5.31/5.59
% 5.31/5.59 % pochhammer_0
% 5.31/5.59 thf(fact_5124_pochhammer__0,axiom,
% 5.31/5.59 ! [A: real] :
% 5.31/5.59 ( ( comm_s7457072308508201937r_real @ A @ zero_zero_nat )
% 5.31/5.59 = one_one_real ) ).
% 5.31/5.59
% 5.31/5.59 % pochhammer_0
% 5.31/5.59 thf(fact_5125_pochhammer__0,axiom,
% 5.31/5.59 ! [A: nat] :
% 5.31/5.59 ( ( comm_s4663373288045622133er_nat @ A @ zero_zero_nat )
% 5.31/5.59 = one_one_nat ) ).
% 5.31/5.59
% 5.31/5.59 % pochhammer_0
% 5.31/5.59 thf(fact_5126_pochhammer__0,axiom,
% 5.31/5.59 ! [A: int] :
% 5.31/5.59 ( ( comm_s4660882817536571857er_int @ A @ zero_zero_nat )
% 5.31/5.59 = one_one_int ) ).
% 5.31/5.59
% 5.31/5.59 % pochhammer_0
% 5.31/5.59 thf(fact_5127_sum_Odelta,axiom,
% 5.31/5.59 ! [S3: set_real,A: real,B: real > complex] :
% 5.31/5.59 ( ( finite_finite_real @ S3 )
% 5.31/5.59 => ( ( ( member_real @ A @ S3 )
% 5.31/5.59 => ( ( groups5754745047067104278omplex
% 5.31/5.59 @ ^ [K3: real] : ( if_complex @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_complex )
% 5.31/5.59 @ S3 )
% 5.31/5.59 = ( B @ A ) ) )
% 5.31/5.59 & ( ~ ( member_real @ A @ S3 )
% 5.31/5.59 => ( ( groups5754745047067104278omplex
% 5.31/5.59 @ ^ [K3: real] : ( if_complex @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_complex )
% 5.31/5.59 @ S3 )
% 5.31/5.59 = zero_zero_complex ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum.delta
% 5.31/5.59 thf(fact_5128_sum_Odelta,axiom,
% 5.31/5.59 ! [S3: set_nat,A: nat,B: nat > complex] :
% 5.31/5.59 ( ( finite_finite_nat @ S3 )
% 5.31/5.59 => ( ( ( member_nat @ A @ S3 )
% 5.31/5.59 => ( ( groups2073611262835488442omplex
% 5.31/5.59 @ ^ [K3: nat] : ( if_complex @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_complex )
% 5.31/5.59 @ S3 )
% 5.31/5.59 = ( B @ A ) ) )
% 5.31/5.59 & ( ~ ( member_nat @ A @ S3 )
% 5.31/5.59 => ( ( groups2073611262835488442omplex
% 5.31/5.59 @ ^ [K3: nat] : ( if_complex @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_complex )
% 5.31/5.59 @ S3 )
% 5.31/5.59 = zero_zero_complex ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum.delta
% 5.31/5.59 thf(fact_5129_sum_Odelta,axiom,
% 5.31/5.59 ! [S3: set_int,A: int,B: int > complex] :
% 5.31/5.59 ( ( finite_finite_int @ S3 )
% 5.31/5.59 => ( ( ( member_int @ A @ S3 )
% 5.31/5.59 => ( ( groups3049146728041665814omplex
% 5.31/5.59 @ ^ [K3: int] : ( if_complex @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_complex )
% 5.31/5.59 @ S3 )
% 5.31/5.59 = ( B @ A ) ) )
% 5.31/5.59 & ( ~ ( member_int @ A @ S3 )
% 5.31/5.59 => ( ( groups3049146728041665814omplex
% 5.31/5.59 @ ^ [K3: int] : ( if_complex @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_complex )
% 5.31/5.59 @ S3 )
% 5.31/5.59 = zero_zero_complex ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum.delta
% 5.31/5.59 thf(fact_5130_sum_Odelta,axiom,
% 5.31/5.59 ! [S3: set_complex,A: complex,B: complex > complex] :
% 5.31/5.59 ( ( finite3207457112153483333omplex @ S3 )
% 5.31/5.59 => ( ( ( member_complex @ A @ S3 )
% 5.31/5.59 => ( ( groups7754918857620584856omplex
% 5.31/5.59 @ ^ [K3: complex] : ( if_complex @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_complex )
% 5.31/5.59 @ S3 )
% 5.31/5.59 = ( B @ A ) ) )
% 5.31/5.59 & ( ~ ( member_complex @ A @ S3 )
% 5.31/5.59 => ( ( groups7754918857620584856omplex
% 5.31/5.59 @ ^ [K3: complex] : ( if_complex @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_complex )
% 5.31/5.59 @ S3 )
% 5.31/5.59 = zero_zero_complex ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum.delta
% 5.31/5.59 thf(fact_5131_sum_Odelta,axiom,
% 5.31/5.59 ! [S3: set_real,A: real,B: real > real] :
% 5.31/5.59 ( ( finite_finite_real @ S3 )
% 5.31/5.59 => ( ( ( member_real @ A @ S3 )
% 5.31/5.59 => ( ( groups8097168146408367636l_real
% 5.31/5.59 @ ^ [K3: real] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_real )
% 5.31/5.59 @ S3 )
% 5.31/5.59 = ( B @ A ) ) )
% 5.31/5.59 & ( ~ ( member_real @ A @ S3 )
% 5.31/5.59 => ( ( groups8097168146408367636l_real
% 5.31/5.59 @ ^ [K3: real] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_real )
% 5.31/5.59 @ S3 )
% 5.31/5.59 = zero_zero_real ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum.delta
% 5.31/5.59 thf(fact_5132_sum_Odelta,axiom,
% 5.31/5.59 ! [S3: set_int,A: int,B: int > real] :
% 5.31/5.59 ( ( finite_finite_int @ S3 )
% 5.31/5.59 => ( ( ( member_int @ A @ S3 )
% 5.31/5.59 => ( ( groups8778361861064173332t_real
% 5.31/5.59 @ ^ [K3: int] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_real )
% 5.31/5.59 @ S3 )
% 5.31/5.59 = ( B @ A ) ) )
% 5.31/5.59 & ( ~ ( member_int @ A @ S3 )
% 5.31/5.59 => ( ( groups8778361861064173332t_real
% 5.31/5.59 @ ^ [K3: int] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_real )
% 5.31/5.59 @ S3 )
% 5.31/5.59 = zero_zero_real ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum.delta
% 5.31/5.59 thf(fact_5133_sum_Odelta,axiom,
% 5.31/5.59 ! [S3: set_complex,A: complex,B: complex > real] :
% 5.31/5.59 ( ( finite3207457112153483333omplex @ S3 )
% 5.31/5.59 => ( ( ( member_complex @ A @ S3 )
% 5.31/5.59 => ( ( groups5808333547571424918x_real
% 5.31/5.59 @ ^ [K3: complex] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_real )
% 5.31/5.59 @ S3 )
% 5.31/5.59 = ( B @ A ) ) )
% 5.31/5.59 & ( ~ ( member_complex @ A @ S3 )
% 5.31/5.59 => ( ( groups5808333547571424918x_real
% 5.31/5.59 @ ^ [K3: complex] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_real )
% 5.31/5.59 @ S3 )
% 5.31/5.59 = zero_zero_real ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum.delta
% 5.31/5.59 thf(fact_5134_sum_Odelta,axiom,
% 5.31/5.59 ! [S3: set_real,A: real,B: real > rat] :
% 5.31/5.59 ( ( finite_finite_real @ S3 )
% 5.31/5.59 => ( ( ( member_real @ A @ S3 )
% 5.31/5.59 => ( ( groups1300246762558778688al_rat
% 5.31/5.59 @ ^ [K3: real] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_rat )
% 5.31/5.59 @ S3 )
% 5.31/5.59 = ( B @ A ) ) )
% 5.31/5.59 & ( ~ ( member_real @ A @ S3 )
% 5.31/5.59 => ( ( groups1300246762558778688al_rat
% 5.31/5.59 @ ^ [K3: real] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_rat )
% 5.31/5.59 @ S3 )
% 5.31/5.59 = zero_zero_rat ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum.delta
% 5.31/5.59 thf(fact_5135_sum_Odelta,axiom,
% 5.31/5.59 ! [S3: set_nat,A: nat,B: nat > rat] :
% 5.31/5.59 ( ( finite_finite_nat @ S3 )
% 5.31/5.59 => ( ( ( member_nat @ A @ S3 )
% 5.31/5.59 => ( ( groups2906978787729119204at_rat
% 5.31/5.59 @ ^ [K3: nat] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_rat )
% 5.31/5.59 @ S3 )
% 5.31/5.59 = ( B @ A ) ) )
% 5.31/5.59 & ( ~ ( member_nat @ A @ S3 )
% 5.31/5.59 => ( ( groups2906978787729119204at_rat
% 5.31/5.59 @ ^ [K3: nat] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_rat )
% 5.31/5.59 @ S3 )
% 5.31/5.59 = zero_zero_rat ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum.delta
% 5.31/5.59 thf(fact_5136_sum_Odelta,axiom,
% 5.31/5.59 ! [S3: set_int,A: int,B: int > rat] :
% 5.31/5.59 ( ( finite_finite_int @ S3 )
% 5.31/5.59 => ( ( ( member_int @ A @ S3 )
% 5.31/5.59 => ( ( groups3906332499630173760nt_rat
% 5.31/5.59 @ ^ [K3: int] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_rat )
% 5.31/5.59 @ S3 )
% 5.31/5.59 = ( B @ A ) ) )
% 5.31/5.59 & ( ~ ( member_int @ A @ S3 )
% 5.31/5.59 => ( ( groups3906332499630173760nt_rat
% 5.31/5.59 @ ^ [K3: int] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_rat )
% 5.31/5.59 @ S3 )
% 5.31/5.59 = zero_zero_rat ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum.delta
% 5.31/5.59 thf(fact_5137_sum_Odelta_H,axiom,
% 5.31/5.59 ! [S3: set_real,A: real,B: real > complex] :
% 5.31/5.59 ( ( finite_finite_real @ S3 )
% 5.31/5.59 => ( ( ( member_real @ A @ S3 )
% 5.31/5.59 => ( ( groups5754745047067104278omplex
% 5.31/5.59 @ ^ [K3: real] : ( if_complex @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_complex )
% 5.31/5.59 @ S3 )
% 5.31/5.59 = ( B @ A ) ) )
% 5.31/5.59 & ( ~ ( member_real @ A @ S3 )
% 5.31/5.59 => ( ( groups5754745047067104278omplex
% 5.31/5.59 @ ^ [K3: real] : ( if_complex @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_complex )
% 5.31/5.59 @ S3 )
% 5.31/5.59 = zero_zero_complex ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum.delta'
% 5.31/5.59 thf(fact_5138_sum_Odelta_H,axiom,
% 5.31/5.59 ! [S3: set_nat,A: nat,B: nat > complex] :
% 5.31/5.59 ( ( finite_finite_nat @ S3 )
% 5.31/5.59 => ( ( ( member_nat @ A @ S3 )
% 5.31/5.59 => ( ( groups2073611262835488442omplex
% 5.31/5.59 @ ^ [K3: nat] : ( if_complex @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_complex )
% 5.31/5.59 @ S3 )
% 5.31/5.59 = ( B @ A ) ) )
% 5.31/5.59 & ( ~ ( member_nat @ A @ S3 )
% 5.31/5.59 => ( ( groups2073611262835488442omplex
% 5.31/5.59 @ ^ [K3: nat] : ( if_complex @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_complex )
% 5.31/5.59 @ S3 )
% 5.31/5.59 = zero_zero_complex ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum.delta'
% 5.31/5.59 thf(fact_5139_sum_Odelta_H,axiom,
% 5.31/5.59 ! [S3: set_int,A: int,B: int > complex] :
% 5.31/5.59 ( ( finite_finite_int @ S3 )
% 5.31/5.59 => ( ( ( member_int @ A @ S3 )
% 5.31/5.59 => ( ( groups3049146728041665814omplex
% 5.31/5.59 @ ^ [K3: int] : ( if_complex @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_complex )
% 5.31/5.59 @ S3 )
% 5.31/5.59 = ( B @ A ) ) )
% 5.31/5.59 & ( ~ ( member_int @ A @ S3 )
% 5.31/5.59 => ( ( groups3049146728041665814omplex
% 5.31/5.59 @ ^ [K3: int] : ( if_complex @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_complex )
% 5.31/5.59 @ S3 )
% 5.31/5.59 = zero_zero_complex ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum.delta'
% 5.31/5.59 thf(fact_5140_sum_Odelta_H,axiom,
% 5.31/5.59 ! [S3: set_complex,A: complex,B: complex > complex] :
% 5.31/5.59 ( ( finite3207457112153483333omplex @ S3 )
% 5.31/5.59 => ( ( ( member_complex @ A @ S3 )
% 5.31/5.59 => ( ( groups7754918857620584856omplex
% 5.31/5.59 @ ^ [K3: complex] : ( if_complex @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_complex )
% 5.31/5.59 @ S3 )
% 5.31/5.59 = ( B @ A ) ) )
% 5.31/5.59 & ( ~ ( member_complex @ A @ S3 )
% 5.31/5.59 => ( ( groups7754918857620584856omplex
% 5.31/5.59 @ ^ [K3: complex] : ( if_complex @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_complex )
% 5.31/5.59 @ S3 )
% 5.31/5.59 = zero_zero_complex ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum.delta'
% 5.31/5.59 thf(fact_5141_sum_Odelta_H,axiom,
% 5.31/5.59 ! [S3: set_real,A: real,B: real > real] :
% 5.31/5.59 ( ( finite_finite_real @ S3 )
% 5.31/5.59 => ( ( ( member_real @ A @ S3 )
% 5.31/5.59 => ( ( groups8097168146408367636l_real
% 5.31/5.59 @ ^ [K3: real] : ( if_real @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_real )
% 5.31/5.59 @ S3 )
% 5.31/5.59 = ( B @ A ) ) )
% 5.31/5.59 & ( ~ ( member_real @ A @ S3 )
% 5.31/5.59 => ( ( groups8097168146408367636l_real
% 5.31/5.59 @ ^ [K3: real] : ( if_real @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_real )
% 5.31/5.59 @ S3 )
% 5.31/5.59 = zero_zero_real ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum.delta'
% 5.31/5.59 thf(fact_5142_sum_Odelta_H,axiom,
% 5.31/5.59 ! [S3: set_int,A: int,B: int > real] :
% 5.31/5.59 ( ( finite_finite_int @ S3 )
% 5.31/5.59 => ( ( ( member_int @ A @ S3 )
% 5.31/5.59 => ( ( groups8778361861064173332t_real
% 5.31/5.59 @ ^ [K3: int] : ( if_real @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_real )
% 5.31/5.59 @ S3 )
% 5.31/5.59 = ( B @ A ) ) )
% 5.31/5.59 & ( ~ ( member_int @ A @ S3 )
% 5.31/5.59 => ( ( groups8778361861064173332t_real
% 5.31/5.59 @ ^ [K3: int] : ( if_real @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_real )
% 5.31/5.59 @ S3 )
% 5.31/5.59 = zero_zero_real ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum.delta'
% 5.31/5.59 thf(fact_5143_sum_Odelta_H,axiom,
% 5.31/5.59 ! [S3: set_complex,A: complex,B: complex > real] :
% 5.31/5.59 ( ( finite3207457112153483333omplex @ S3 )
% 5.31/5.59 => ( ( ( member_complex @ A @ S3 )
% 5.31/5.59 => ( ( groups5808333547571424918x_real
% 5.31/5.59 @ ^ [K3: complex] : ( if_real @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_real )
% 5.31/5.59 @ S3 )
% 5.31/5.59 = ( B @ A ) ) )
% 5.31/5.59 & ( ~ ( member_complex @ A @ S3 )
% 5.31/5.59 => ( ( groups5808333547571424918x_real
% 5.31/5.59 @ ^ [K3: complex] : ( if_real @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_real )
% 5.31/5.59 @ S3 )
% 5.31/5.59 = zero_zero_real ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum.delta'
% 5.31/5.59 thf(fact_5144_sum_Odelta_H,axiom,
% 5.31/5.59 ! [S3: set_real,A: real,B: real > rat] :
% 5.31/5.59 ( ( finite_finite_real @ S3 )
% 5.31/5.59 => ( ( ( member_real @ A @ S3 )
% 5.31/5.59 => ( ( groups1300246762558778688al_rat
% 5.31/5.59 @ ^ [K3: real] : ( if_rat @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_rat )
% 5.31/5.59 @ S3 )
% 5.31/5.59 = ( B @ A ) ) )
% 5.31/5.59 & ( ~ ( member_real @ A @ S3 )
% 5.31/5.59 => ( ( groups1300246762558778688al_rat
% 5.31/5.59 @ ^ [K3: real] : ( if_rat @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_rat )
% 5.31/5.59 @ S3 )
% 5.31/5.59 = zero_zero_rat ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum.delta'
% 5.31/5.59 thf(fact_5145_sum_Odelta_H,axiom,
% 5.31/5.59 ! [S3: set_nat,A: nat,B: nat > rat] :
% 5.31/5.59 ( ( finite_finite_nat @ S3 )
% 5.31/5.59 => ( ( ( member_nat @ A @ S3 )
% 5.31/5.59 => ( ( groups2906978787729119204at_rat
% 5.31/5.59 @ ^ [K3: nat] : ( if_rat @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_rat )
% 5.31/5.59 @ S3 )
% 5.31/5.59 = ( B @ A ) ) )
% 5.31/5.59 & ( ~ ( member_nat @ A @ S3 )
% 5.31/5.59 => ( ( groups2906978787729119204at_rat
% 5.31/5.59 @ ^ [K3: nat] : ( if_rat @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_rat )
% 5.31/5.59 @ S3 )
% 5.31/5.59 = zero_zero_rat ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum.delta'
% 5.31/5.59 thf(fact_5146_sum_Odelta_H,axiom,
% 5.31/5.59 ! [S3: set_int,A: int,B: int > rat] :
% 5.31/5.59 ( ( finite_finite_int @ S3 )
% 5.31/5.59 => ( ( ( member_int @ A @ S3 )
% 5.31/5.59 => ( ( groups3906332499630173760nt_rat
% 5.31/5.59 @ ^ [K3: int] : ( if_rat @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_rat )
% 5.31/5.59 @ S3 )
% 5.31/5.59 = ( B @ A ) ) )
% 5.31/5.59 & ( ~ ( member_int @ A @ S3 )
% 5.31/5.59 => ( ( groups3906332499630173760nt_rat
% 5.31/5.59 @ ^ [K3: int] : ( if_rat @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_rat )
% 5.31/5.59 @ S3 )
% 5.31/5.59 = zero_zero_rat ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum.delta'
% 5.31/5.59 thf(fact_5147_unit__mult__div__div,axiom,
% 5.31/5.59 ! [A: code_integer,B: code_integer] :
% 5.31/5.59 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.31/5.59 => ( ( times_3573771949741848930nteger @ B @ ( divide6298287555418463151nteger @ one_one_Code_integer @ A ) )
% 5.31/5.59 = ( divide6298287555418463151nteger @ B @ A ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % unit_mult_div_div
% 5.31/5.59 thf(fact_5148_unit__mult__div__div,axiom,
% 5.31/5.59 ! [A: nat,B: nat] :
% 5.31/5.59 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.31/5.59 => ( ( times_times_nat @ B @ ( divide_divide_nat @ one_one_nat @ A ) )
% 5.31/5.59 = ( divide_divide_nat @ B @ A ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % unit_mult_div_div
% 5.31/5.59 thf(fact_5149_unit__mult__div__div,axiom,
% 5.31/5.59 ! [A: int,B: int] :
% 5.31/5.59 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.31/5.59 => ( ( times_times_int @ B @ ( divide_divide_int @ one_one_int @ A ) )
% 5.31/5.59 = ( divide_divide_int @ B @ A ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % unit_mult_div_div
% 5.31/5.59 thf(fact_5150_unit__div__mult__self,axiom,
% 5.31/5.59 ! [A: code_integer,B: code_integer] :
% 5.31/5.59 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.31/5.59 => ( ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ B @ A ) @ A )
% 5.31/5.59 = B ) ) ).
% 5.31/5.59
% 5.31/5.59 % unit_div_mult_self
% 5.31/5.59 thf(fact_5151_unit__div__mult__self,axiom,
% 5.31/5.59 ! [A: nat,B: nat] :
% 5.31/5.59 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.31/5.59 => ( ( times_times_nat @ ( divide_divide_nat @ B @ A ) @ A )
% 5.31/5.59 = B ) ) ).
% 5.31/5.59
% 5.31/5.59 % unit_div_mult_self
% 5.31/5.59 thf(fact_5152_unit__div__mult__self,axiom,
% 5.31/5.59 ! [A: int,B: int] :
% 5.31/5.59 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.31/5.59 => ( ( times_times_int @ ( divide_divide_int @ B @ A ) @ A )
% 5.31/5.59 = B ) ) ).
% 5.31/5.59
% 5.31/5.59 % unit_div_mult_self
% 5.31/5.59 thf(fact_5153_pow__divides__pow__iff,axiom,
% 5.31/5.59 ! [N: nat,A: nat,B: nat] :
% 5.31/5.59 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.59 => ( ( dvd_dvd_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) )
% 5.31/5.59 = ( dvd_dvd_nat @ A @ B ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % pow_divides_pow_iff
% 5.31/5.59 thf(fact_5154_pow__divides__pow__iff,axiom,
% 5.31/5.59 ! [N: nat,A: int,B: int] :
% 5.31/5.59 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.59 => ( ( dvd_dvd_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) )
% 5.31/5.59 = ( dvd_dvd_int @ A @ B ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % pow_divides_pow_iff
% 5.31/5.59 thf(fact_5155_sum__constant,axiom,
% 5.31/5.59 ! [Y: rat,A4: set_nat] :
% 5.31/5.59 ( ( groups2906978787729119204at_rat
% 5.31/5.59 @ ^ [X4: nat] : Y
% 5.31/5.59 @ A4 )
% 5.31/5.59 = ( times_times_rat @ ( semiri681578069525770553at_rat @ ( finite_card_nat @ A4 ) ) @ Y ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum_constant
% 5.31/5.59 thf(fact_5156_sum__constant,axiom,
% 5.31/5.59 ! [Y: rat,A4: set_complex] :
% 5.31/5.59 ( ( groups5058264527183730370ex_rat
% 5.31/5.59 @ ^ [X4: complex] : Y
% 5.31/5.59 @ A4 )
% 5.31/5.59 = ( times_times_rat @ ( semiri681578069525770553at_rat @ ( finite_card_complex @ A4 ) ) @ Y ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum_constant
% 5.31/5.59 thf(fact_5157_sum__constant,axiom,
% 5.31/5.59 ! [Y: rat,A4: set_int] :
% 5.31/5.59 ( ( groups3906332499630173760nt_rat
% 5.31/5.59 @ ^ [X4: int] : Y
% 5.31/5.59 @ A4 )
% 5.31/5.59 = ( times_times_rat @ ( semiri681578069525770553at_rat @ ( finite_card_int @ A4 ) ) @ Y ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum_constant
% 5.31/5.59 thf(fact_5158_sum__constant,axiom,
% 5.31/5.59 ! [Y: real,A4: set_complex] :
% 5.31/5.59 ( ( groups5808333547571424918x_real
% 5.31/5.59 @ ^ [X4: complex] : Y
% 5.31/5.59 @ A4 )
% 5.31/5.59 = ( times_times_real @ ( semiri5074537144036343181t_real @ ( finite_card_complex @ A4 ) ) @ Y ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum_constant
% 5.31/5.59 thf(fact_5159_sum__constant,axiom,
% 5.31/5.59 ! [Y: real,A4: set_int] :
% 5.31/5.59 ( ( groups8778361861064173332t_real
% 5.31/5.59 @ ^ [X4: int] : Y
% 5.31/5.59 @ A4 )
% 5.31/5.59 = ( times_times_real @ ( semiri5074537144036343181t_real @ ( finite_card_int @ A4 ) ) @ Y ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum_constant
% 5.31/5.59 thf(fact_5160_sum__constant,axiom,
% 5.31/5.59 ! [Y: int,A4: set_nat] :
% 5.31/5.59 ( ( groups3539618377306564664at_int
% 5.31/5.59 @ ^ [X4: nat] : Y
% 5.31/5.59 @ A4 )
% 5.31/5.59 = ( times_times_int @ ( semiri1314217659103216013at_int @ ( finite_card_nat @ A4 ) ) @ Y ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum_constant
% 5.31/5.59 thf(fact_5161_sum__constant,axiom,
% 5.31/5.59 ! [Y: int,A4: set_complex] :
% 5.31/5.59 ( ( groups5690904116761175830ex_int
% 5.31/5.59 @ ^ [X4: complex] : Y
% 5.31/5.59 @ A4 )
% 5.31/5.59 = ( times_times_int @ ( semiri1314217659103216013at_int @ ( finite_card_complex @ A4 ) ) @ Y ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum_constant
% 5.31/5.59 thf(fact_5162_sum__constant,axiom,
% 5.31/5.59 ! [Y: nat,A4: set_complex] :
% 5.31/5.59 ( ( groups5693394587270226106ex_nat
% 5.31/5.59 @ ^ [X4: complex] : Y
% 5.31/5.59 @ A4 )
% 5.31/5.59 = ( times_times_nat @ ( semiri1316708129612266289at_nat @ ( finite_card_complex @ A4 ) ) @ Y ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum_constant
% 5.31/5.59 thf(fact_5163_sum__constant,axiom,
% 5.31/5.59 ! [Y: nat,A4: set_int] :
% 5.31/5.59 ( ( groups4541462559716669496nt_nat
% 5.31/5.59 @ ^ [X4: int] : Y
% 5.31/5.59 @ A4 )
% 5.31/5.59 = ( times_times_nat @ ( semiri1316708129612266289at_nat @ ( finite_card_int @ A4 ) ) @ Y ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum_constant
% 5.31/5.59 thf(fact_5164_sum__constant,axiom,
% 5.31/5.59 ! [Y: nat,A4: set_nat] :
% 5.31/5.59 ( ( groups3542108847815614940at_nat
% 5.31/5.59 @ ^ [X4: nat] : Y
% 5.31/5.59 @ A4 )
% 5.31/5.59 = ( times_times_nat @ ( semiri1316708129612266289at_nat @ ( finite_card_nat @ A4 ) ) @ Y ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum_constant
% 5.31/5.59 thf(fact_5165_even__mult__iff,axiom,
% 5.31/5.59 ! [A: nat,B: nat] :
% 5.31/5.59 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ A @ B ) )
% 5.31/5.59 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.31/5.59 | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % even_mult_iff
% 5.31/5.59 thf(fact_5166_even__mult__iff,axiom,
% 5.31/5.59 ! [A: int,B: int] :
% 5.31/5.59 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( times_times_int @ A @ B ) )
% 5.31/5.59 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.31/5.59 | ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % even_mult_iff
% 5.31/5.59 thf(fact_5167_even__Suc__Suc__iff,axiom,
% 5.31/5.59 ! [N: nat] :
% 5.31/5.59 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ N ) ) )
% 5.31/5.59 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.31/5.59
% 5.31/5.59 % even_Suc_Suc_iff
% 5.31/5.59 thf(fact_5168_even__Suc,axiom,
% 5.31/5.59 ! [N: nat] :
% 5.31/5.59 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N ) )
% 5.31/5.59 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % even_Suc
% 5.31/5.59 thf(fact_5169_powser__sums__zero__iff,axiom,
% 5.31/5.59 ! [A: nat > complex,X: complex] :
% 5.31/5.59 ( ( sums_complex
% 5.31/5.59 @ ^ [N4: nat] : ( times_times_complex @ ( A @ N4 ) @ ( power_power_complex @ zero_zero_complex @ N4 ) )
% 5.31/5.59 @ X )
% 5.31/5.59 = ( ( A @ zero_zero_nat )
% 5.31/5.59 = X ) ) ).
% 5.31/5.59
% 5.31/5.59 % powser_sums_zero_iff
% 5.31/5.59 thf(fact_5170_powser__sums__zero__iff,axiom,
% 5.31/5.59 ! [A: nat > real,X: real] :
% 5.31/5.59 ( ( sums_real
% 5.31/5.59 @ ^ [N4: nat] : ( times_times_real @ ( A @ N4 ) @ ( power_power_real @ zero_zero_real @ N4 ) )
% 5.31/5.59 @ X )
% 5.31/5.59 = ( ( A @ zero_zero_nat )
% 5.31/5.59 = X ) ) ).
% 5.31/5.59
% 5.31/5.59 % powser_sums_zero_iff
% 5.31/5.59 thf(fact_5171_even__Suc__div__two,axiom,
% 5.31/5.59 ! [N: nat] :
% 5.31/5.59 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.31/5.59 => ( ( divide_divide_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.31/5.59 = ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % even_Suc_div_two
% 5.31/5.59 thf(fact_5172_odd__Suc__div__two,axiom,
% 5.31/5.59 ! [N: nat] :
% 5.31/5.59 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.31/5.59 => ( ( divide_divide_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.31/5.59 = ( suc @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % odd_Suc_div_two
% 5.31/5.59 thf(fact_5173_sum_Ocl__ivl__Suc,axiom,
% 5.31/5.59 ! [N: nat,M2: nat,G2: nat > complex] :
% 5.31/5.59 ( ( ( ord_less_nat @ ( suc @ N ) @ M2 )
% 5.31/5.59 => ( ( groups2073611262835488442omplex @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N ) ) )
% 5.31/5.59 = zero_zero_complex ) )
% 5.31/5.59 & ( ~ ( ord_less_nat @ ( suc @ N ) @ M2 )
% 5.31/5.59 => ( ( groups2073611262835488442omplex @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N ) ) )
% 5.31/5.59 = ( plus_plus_complex @ ( groups2073611262835488442omplex @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) @ ( G2 @ ( suc @ N ) ) ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum.cl_ivl_Suc
% 5.31/5.59 thf(fact_5174_sum_Ocl__ivl__Suc,axiom,
% 5.31/5.59 ! [N: nat,M2: nat,G2: nat > rat] :
% 5.31/5.59 ( ( ( ord_less_nat @ ( suc @ N ) @ M2 )
% 5.31/5.59 => ( ( groups2906978787729119204at_rat @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N ) ) )
% 5.31/5.59 = zero_zero_rat ) )
% 5.31/5.59 & ( ~ ( ord_less_nat @ ( suc @ N ) @ M2 )
% 5.31/5.59 => ( ( groups2906978787729119204at_rat @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N ) ) )
% 5.31/5.59 = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) @ ( G2 @ ( suc @ N ) ) ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum.cl_ivl_Suc
% 5.31/5.59 thf(fact_5175_sum_Ocl__ivl__Suc,axiom,
% 5.31/5.59 ! [N: nat,M2: nat,G2: nat > int] :
% 5.31/5.59 ( ( ( ord_less_nat @ ( suc @ N ) @ M2 )
% 5.31/5.59 => ( ( groups3539618377306564664at_int @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N ) ) )
% 5.31/5.59 = zero_zero_int ) )
% 5.31/5.59 & ( ~ ( ord_less_nat @ ( suc @ N ) @ M2 )
% 5.31/5.59 => ( ( groups3539618377306564664at_int @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N ) ) )
% 5.31/5.59 = ( plus_plus_int @ ( groups3539618377306564664at_int @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) @ ( G2 @ ( suc @ N ) ) ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum.cl_ivl_Suc
% 5.31/5.59 thf(fact_5176_sum_Ocl__ivl__Suc,axiom,
% 5.31/5.59 ! [N: nat,M2: nat,G2: nat > nat] :
% 5.31/5.59 ( ( ( ord_less_nat @ ( suc @ N ) @ M2 )
% 5.31/5.59 => ( ( groups3542108847815614940at_nat @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N ) ) )
% 5.31/5.59 = zero_zero_nat ) )
% 5.31/5.59 & ( ~ ( ord_less_nat @ ( suc @ N ) @ M2 )
% 5.31/5.59 => ( ( groups3542108847815614940at_nat @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N ) ) )
% 5.31/5.59 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) @ ( G2 @ ( suc @ N ) ) ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum.cl_ivl_Suc
% 5.31/5.59 thf(fact_5177_sum_Ocl__ivl__Suc,axiom,
% 5.31/5.59 ! [N: nat,M2: nat,G2: nat > real] :
% 5.31/5.59 ( ( ( ord_less_nat @ ( suc @ N ) @ M2 )
% 5.31/5.59 => ( ( groups6591440286371151544t_real @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N ) ) )
% 5.31/5.59 = zero_zero_real ) )
% 5.31/5.59 & ( ~ ( ord_less_nat @ ( suc @ N ) @ M2 )
% 5.31/5.59 => ( ( groups6591440286371151544t_real @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N ) ) )
% 5.31/5.59 = ( plus_plus_real @ ( groups6591440286371151544t_real @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) @ ( G2 @ ( suc @ N ) ) ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum.cl_ivl_Suc
% 5.31/5.59 thf(fact_5178_sum__zero__power,axiom,
% 5.31/5.59 ! [A4: set_nat,C2: nat > complex] :
% 5.31/5.59 ( ( ( ( finite_finite_nat @ A4 )
% 5.31/5.59 & ( member_nat @ zero_zero_nat @ A4 ) )
% 5.31/5.59 => ( ( groups2073611262835488442omplex
% 5.31/5.59 @ ^ [I: nat] : ( times_times_complex @ ( C2 @ I ) @ ( power_power_complex @ zero_zero_complex @ I ) )
% 5.31/5.59 @ A4 )
% 5.31/5.59 = ( C2 @ zero_zero_nat ) ) )
% 5.31/5.59 & ( ~ ( ( finite_finite_nat @ A4 )
% 5.31/5.59 & ( member_nat @ zero_zero_nat @ A4 ) )
% 5.31/5.59 => ( ( groups2073611262835488442omplex
% 5.31/5.59 @ ^ [I: nat] : ( times_times_complex @ ( C2 @ I ) @ ( power_power_complex @ zero_zero_complex @ I ) )
% 5.31/5.59 @ A4 )
% 5.31/5.59 = zero_zero_complex ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum_zero_power
% 5.31/5.59 thf(fact_5179_sum__zero__power,axiom,
% 5.31/5.59 ! [A4: set_nat,C2: nat > rat] :
% 5.31/5.59 ( ( ( ( finite_finite_nat @ A4 )
% 5.31/5.59 & ( member_nat @ zero_zero_nat @ A4 ) )
% 5.31/5.59 => ( ( groups2906978787729119204at_rat
% 5.31/5.59 @ ^ [I: nat] : ( times_times_rat @ ( C2 @ I ) @ ( power_power_rat @ zero_zero_rat @ I ) )
% 5.31/5.59 @ A4 )
% 5.31/5.59 = ( C2 @ zero_zero_nat ) ) )
% 5.31/5.59 & ( ~ ( ( finite_finite_nat @ A4 )
% 5.31/5.59 & ( member_nat @ zero_zero_nat @ A4 ) )
% 5.31/5.59 => ( ( groups2906978787729119204at_rat
% 5.31/5.59 @ ^ [I: nat] : ( times_times_rat @ ( C2 @ I ) @ ( power_power_rat @ zero_zero_rat @ I ) )
% 5.31/5.59 @ A4 )
% 5.31/5.59 = zero_zero_rat ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum_zero_power
% 5.31/5.59 thf(fact_5180_sum__zero__power,axiom,
% 5.31/5.59 ! [A4: set_nat,C2: nat > real] :
% 5.31/5.59 ( ( ( ( finite_finite_nat @ A4 )
% 5.31/5.59 & ( member_nat @ zero_zero_nat @ A4 ) )
% 5.31/5.59 => ( ( groups6591440286371151544t_real
% 5.31/5.59 @ ^ [I: nat] : ( times_times_real @ ( C2 @ I ) @ ( power_power_real @ zero_zero_real @ I ) )
% 5.31/5.59 @ A4 )
% 5.31/5.59 = ( C2 @ zero_zero_nat ) ) )
% 5.31/5.59 & ( ~ ( ( finite_finite_nat @ A4 )
% 5.31/5.59 & ( member_nat @ zero_zero_nat @ A4 ) )
% 5.31/5.59 => ( ( groups6591440286371151544t_real
% 5.31/5.59 @ ^ [I: nat] : ( times_times_real @ ( C2 @ I ) @ ( power_power_real @ zero_zero_real @ I ) )
% 5.31/5.59 @ A4 )
% 5.31/5.59 = zero_zero_real ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum_zero_power
% 5.31/5.59 thf(fact_5181_zero__le__power__eq__numeral,axiom,
% 5.31/5.59 ! [A: real,W2: num] :
% 5.31/5.59 ( ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ W2 ) ) )
% 5.31/5.59 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 5.31/5.59 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 5.31/5.59 & ( ord_less_eq_real @ zero_zero_real @ A ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % zero_le_power_eq_numeral
% 5.31/5.59 thf(fact_5182_zero__le__power__eq__numeral,axiom,
% 5.31/5.59 ! [A: rat,W2: num] :
% 5.31/5.59 ( ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ W2 ) ) )
% 5.31/5.59 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 5.31/5.59 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 5.31/5.59 & ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % zero_le_power_eq_numeral
% 5.31/5.59 thf(fact_5183_zero__le__power__eq__numeral,axiom,
% 5.31/5.59 ! [A: int,W2: num] :
% 5.31/5.59 ( ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ W2 ) ) )
% 5.31/5.59 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 5.31/5.59 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 5.31/5.59 & ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % zero_le_power_eq_numeral
% 5.31/5.59 thf(fact_5184_even__power,axiom,
% 5.31/5.59 ! [A: nat,N: nat] :
% 5.31/5.59 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( power_power_nat @ A @ N ) )
% 5.31/5.59 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.31/5.59 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % even_power
% 5.31/5.59 thf(fact_5185_even__power,axiom,
% 5.31/5.59 ! [A: int,N: nat] :
% 5.31/5.59 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( power_power_int @ A @ N ) )
% 5.31/5.59 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.31/5.59 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % even_power
% 5.31/5.59 thf(fact_5186_power__less__zero__eq,axiom,
% 5.31/5.59 ! [A: real,N: nat] :
% 5.31/5.59 ( ( ord_less_real @ ( power_power_real @ A @ N ) @ zero_zero_real )
% 5.31/5.59 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.31/5.59 & ( ord_less_real @ A @ zero_zero_real ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % power_less_zero_eq
% 5.31/5.59 thf(fact_5187_power__less__zero__eq,axiom,
% 5.31/5.59 ! [A: rat,N: nat] :
% 5.31/5.59 ( ( ord_less_rat @ ( power_power_rat @ A @ N ) @ zero_zero_rat )
% 5.31/5.59 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.31/5.59 & ( ord_less_rat @ A @ zero_zero_rat ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % power_less_zero_eq
% 5.31/5.59 thf(fact_5188_power__less__zero__eq,axiom,
% 5.31/5.59 ! [A: int,N: nat] :
% 5.31/5.59 ( ( ord_less_int @ ( power_power_int @ A @ N ) @ zero_zero_int )
% 5.31/5.59 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.31/5.59 & ( ord_less_int @ A @ zero_zero_int ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % power_less_zero_eq
% 5.31/5.59 thf(fact_5189_power__less__zero__eq__numeral,axiom,
% 5.31/5.59 ! [A: real,W2: num] :
% 5.31/5.59 ( ( ord_less_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ W2 ) ) @ zero_zero_real )
% 5.31/5.59 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 5.31/5.59 & ( ord_less_real @ A @ zero_zero_real ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % power_less_zero_eq_numeral
% 5.31/5.59 thf(fact_5190_power__less__zero__eq__numeral,axiom,
% 5.31/5.59 ! [A: rat,W2: num] :
% 5.31/5.59 ( ( ord_less_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ W2 ) ) @ zero_zero_rat )
% 5.31/5.59 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 5.31/5.59 & ( ord_less_rat @ A @ zero_zero_rat ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % power_less_zero_eq_numeral
% 5.31/5.59 thf(fact_5191_power__less__zero__eq__numeral,axiom,
% 5.31/5.59 ! [A: int,W2: num] :
% 5.31/5.59 ( ( ord_less_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ W2 ) ) @ zero_zero_int )
% 5.31/5.59 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 5.31/5.59 & ( ord_less_int @ A @ zero_zero_int ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % power_less_zero_eq_numeral
% 5.31/5.59 thf(fact_5192_odd__Suc__minus__one,axiom,
% 5.31/5.59 ! [N: nat] :
% 5.31/5.59 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.31/5.59 => ( ( suc @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) )
% 5.31/5.59 = N ) ) ).
% 5.31/5.59
% 5.31/5.59 % odd_Suc_minus_one
% 5.31/5.59 thf(fact_5193_sum__zero__power_H,axiom,
% 5.31/5.59 ! [A4: set_nat,C2: nat > complex,D: nat > complex] :
% 5.31/5.59 ( ( ( ( finite_finite_nat @ A4 )
% 5.31/5.59 & ( member_nat @ zero_zero_nat @ A4 ) )
% 5.31/5.59 => ( ( groups2073611262835488442omplex
% 5.31/5.59 @ ^ [I: nat] : ( divide1717551699836669952omplex @ ( times_times_complex @ ( C2 @ I ) @ ( power_power_complex @ zero_zero_complex @ I ) ) @ ( D @ I ) )
% 5.31/5.59 @ A4 )
% 5.31/5.59 = ( divide1717551699836669952omplex @ ( C2 @ zero_zero_nat ) @ ( D @ zero_zero_nat ) ) ) )
% 5.31/5.59 & ( ~ ( ( finite_finite_nat @ A4 )
% 5.31/5.59 & ( member_nat @ zero_zero_nat @ A4 ) )
% 5.31/5.59 => ( ( groups2073611262835488442omplex
% 5.31/5.59 @ ^ [I: nat] : ( divide1717551699836669952omplex @ ( times_times_complex @ ( C2 @ I ) @ ( power_power_complex @ zero_zero_complex @ I ) ) @ ( D @ I ) )
% 5.31/5.59 @ A4 )
% 5.31/5.59 = zero_zero_complex ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum_zero_power'
% 5.31/5.59 thf(fact_5194_sum__zero__power_H,axiom,
% 5.31/5.59 ! [A4: set_nat,C2: nat > rat,D: nat > rat] :
% 5.31/5.59 ( ( ( ( finite_finite_nat @ A4 )
% 5.31/5.59 & ( member_nat @ zero_zero_nat @ A4 ) )
% 5.31/5.59 => ( ( groups2906978787729119204at_rat
% 5.31/5.59 @ ^ [I: nat] : ( divide_divide_rat @ ( times_times_rat @ ( C2 @ I ) @ ( power_power_rat @ zero_zero_rat @ I ) ) @ ( D @ I ) )
% 5.31/5.59 @ A4 )
% 5.31/5.59 = ( divide_divide_rat @ ( C2 @ zero_zero_nat ) @ ( D @ zero_zero_nat ) ) ) )
% 5.31/5.59 & ( ~ ( ( finite_finite_nat @ A4 )
% 5.31/5.59 & ( member_nat @ zero_zero_nat @ A4 ) )
% 5.31/5.59 => ( ( groups2906978787729119204at_rat
% 5.31/5.59 @ ^ [I: nat] : ( divide_divide_rat @ ( times_times_rat @ ( C2 @ I ) @ ( power_power_rat @ zero_zero_rat @ I ) ) @ ( D @ I ) )
% 5.31/5.59 @ A4 )
% 5.31/5.59 = zero_zero_rat ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum_zero_power'
% 5.31/5.59 thf(fact_5195_sum__zero__power_H,axiom,
% 5.31/5.59 ! [A4: set_nat,C2: nat > real,D: nat > real] :
% 5.31/5.59 ( ( ( ( finite_finite_nat @ A4 )
% 5.31/5.59 & ( member_nat @ zero_zero_nat @ A4 ) )
% 5.31/5.59 => ( ( groups6591440286371151544t_real
% 5.31/5.59 @ ^ [I: nat] : ( divide_divide_real @ ( times_times_real @ ( C2 @ I ) @ ( power_power_real @ zero_zero_real @ I ) ) @ ( D @ I ) )
% 5.31/5.59 @ A4 )
% 5.31/5.59 = ( divide_divide_real @ ( C2 @ zero_zero_nat ) @ ( D @ zero_zero_nat ) ) ) )
% 5.31/5.59 & ( ~ ( ( finite_finite_nat @ A4 )
% 5.31/5.59 & ( member_nat @ zero_zero_nat @ A4 ) )
% 5.31/5.59 => ( ( groups6591440286371151544t_real
% 5.31/5.59 @ ^ [I: nat] : ( divide_divide_real @ ( times_times_real @ ( C2 @ I ) @ ( power_power_real @ zero_zero_real @ I ) ) @ ( D @ I ) )
% 5.31/5.59 @ A4 )
% 5.31/5.59 = zero_zero_real ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum_zero_power'
% 5.31/5.59 thf(fact_5196_odd__two__times__div__two__succ,axiom,
% 5.31/5.59 ! [A: code_integer] :
% 5.31/5.59 ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.31/5.59 => ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) @ one_one_Code_integer )
% 5.31/5.59 = A ) ) ).
% 5.31/5.59
% 5.31/5.59 % odd_two_times_div_two_succ
% 5.31/5.59 thf(fact_5197_odd__two__times__div__two__succ,axiom,
% 5.31/5.59 ! [A: nat] :
% 5.31/5.59 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.31/5.59 => ( ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ one_one_nat )
% 5.31/5.59 = A ) ) ).
% 5.31/5.59
% 5.31/5.59 % odd_two_times_div_two_succ
% 5.31/5.59 thf(fact_5198_odd__two__times__div__two__succ,axiom,
% 5.31/5.59 ! [A: int] :
% 5.31/5.59 ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.31/5.59 => ( ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ one_one_int )
% 5.31/5.59 = A ) ) ).
% 5.31/5.59
% 5.31/5.59 % odd_two_times_div_two_succ
% 5.31/5.59 thf(fact_5199_semiring__parity__class_Oeven__mask__iff,axiom,
% 5.31/5.59 ! [N: nat] :
% 5.31/5.59 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) @ one_one_Code_integer ) )
% 5.31/5.59 = ( N = zero_zero_nat ) ) ).
% 5.31/5.59
% 5.31/5.59 % semiring_parity_class.even_mask_iff
% 5.31/5.59 thf(fact_5200_semiring__parity__class_Oeven__mask__iff,axiom,
% 5.31/5.59 ! [N: nat] :
% 5.31/5.59 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) )
% 5.31/5.59 = ( N = zero_zero_nat ) ) ).
% 5.31/5.59
% 5.31/5.59 % semiring_parity_class.even_mask_iff
% 5.31/5.59 thf(fact_5201_semiring__parity__class_Oeven__mask__iff,axiom,
% 5.31/5.59 ! [N: nat] :
% 5.31/5.59 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ one_one_int ) )
% 5.31/5.59 = ( N = zero_zero_nat ) ) ).
% 5.31/5.59
% 5.31/5.59 % semiring_parity_class.even_mask_iff
% 5.31/5.59 thf(fact_5202_zero__less__power__eq__numeral,axiom,
% 5.31/5.59 ! [A: real,W2: num] :
% 5.31/5.59 ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ W2 ) ) )
% 5.31/5.59 = ( ( ( numeral_numeral_nat @ W2 )
% 5.31/5.59 = zero_zero_nat )
% 5.31/5.59 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 5.31/5.59 & ( A != zero_zero_real ) )
% 5.31/5.59 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 5.31/5.59 & ( ord_less_real @ zero_zero_real @ A ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % zero_less_power_eq_numeral
% 5.31/5.59 thf(fact_5203_zero__less__power__eq__numeral,axiom,
% 5.31/5.59 ! [A: rat,W2: num] :
% 5.31/5.59 ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ W2 ) ) )
% 5.31/5.59 = ( ( ( numeral_numeral_nat @ W2 )
% 5.31/5.59 = zero_zero_nat )
% 5.31/5.59 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 5.31/5.59 & ( A != zero_zero_rat ) )
% 5.31/5.59 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 5.31/5.59 & ( ord_less_rat @ zero_zero_rat @ A ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % zero_less_power_eq_numeral
% 5.31/5.59 thf(fact_5204_zero__less__power__eq__numeral,axiom,
% 5.31/5.59 ! [A: int,W2: num] :
% 5.31/5.59 ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ W2 ) ) )
% 5.31/5.59 = ( ( ( numeral_numeral_nat @ W2 )
% 5.31/5.59 = zero_zero_nat )
% 5.31/5.59 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 5.31/5.59 & ( A != zero_zero_int ) )
% 5.31/5.59 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 5.31/5.59 & ( ord_less_int @ zero_zero_int @ A ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % zero_less_power_eq_numeral
% 5.31/5.59 thf(fact_5205_odd__two__times__div__two__nat,axiom,
% 5.31/5.59 ! [N: nat] :
% 5.31/5.59 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.31/5.59 => ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.31/5.59 = ( minus_minus_nat @ N @ one_one_nat ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % odd_two_times_div_two_nat
% 5.31/5.59 thf(fact_5206_power__le__zero__eq__numeral,axiom,
% 5.31/5.59 ! [A: real,W2: num] :
% 5.31/5.59 ( ( ord_less_eq_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ W2 ) ) @ zero_zero_real )
% 5.31/5.59 = ( ( ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ W2 ) )
% 5.31/5.59 & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 5.31/5.59 & ( ord_less_eq_real @ A @ zero_zero_real ) )
% 5.31/5.59 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 5.31/5.59 & ( A = zero_zero_real ) ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % power_le_zero_eq_numeral
% 5.31/5.59 thf(fact_5207_power__le__zero__eq__numeral,axiom,
% 5.31/5.59 ! [A: rat,W2: num] :
% 5.31/5.59 ( ( ord_less_eq_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ W2 ) ) @ zero_zero_rat )
% 5.31/5.59 = ( ( ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ W2 ) )
% 5.31/5.59 & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 5.31/5.59 & ( ord_less_eq_rat @ A @ zero_zero_rat ) )
% 5.31/5.59 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 5.31/5.59 & ( A = zero_zero_rat ) ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % power_le_zero_eq_numeral
% 5.31/5.59 thf(fact_5208_power__le__zero__eq__numeral,axiom,
% 5.31/5.59 ! [A: int,W2: num] :
% 5.31/5.59 ( ( ord_less_eq_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ W2 ) ) @ zero_zero_int )
% 5.31/5.59 = ( ( ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ W2 ) )
% 5.31/5.59 & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 5.31/5.59 & ( ord_less_eq_int @ A @ zero_zero_int ) )
% 5.31/5.59 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 5.31/5.59 & ( A = zero_zero_int ) ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % power_le_zero_eq_numeral
% 5.31/5.59 thf(fact_5209_even__succ__div__exp,axiom,
% 5.31/5.59 ! [A: code_integer,N: nat] :
% 5.31/5.59 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.31/5.59 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.59 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ A ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 5.31/5.59 = ( divide6298287555418463151nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % even_succ_div_exp
% 5.31/5.59 thf(fact_5210_even__succ__div__exp,axiom,
% 5.31/5.59 ! [A: nat,N: nat] :
% 5.31/5.59 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.31/5.59 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.59 => ( ( divide_divide_nat @ ( plus_plus_nat @ one_one_nat @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.31/5.59 = ( divide_divide_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % even_succ_div_exp
% 5.31/5.59 thf(fact_5211_even__succ__div__exp,axiom,
% 5.31/5.59 ! [A: int,N: nat] :
% 5.31/5.59 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.31/5.59 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.59 => ( ( divide_divide_int @ ( plus_plus_int @ one_one_int @ A ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.31/5.59 = ( divide_divide_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % even_succ_div_exp
% 5.31/5.59 thf(fact_5212_even__succ__mod__exp,axiom,
% 5.31/5.59 ! [A: code_integer,N: nat] :
% 5.31/5.59 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.31/5.59 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.59 => ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ A ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 5.31/5.59 = ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( modulo364778990260209775nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % even_succ_mod_exp
% 5.31/5.59 thf(fact_5213_even__succ__mod__exp,axiom,
% 5.31/5.59 ! [A: nat,N: nat] :
% 5.31/5.59 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.31/5.59 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.59 => ( ( modulo_modulo_nat @ ( plus_plus_nat @ one_one_nat @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.31/5.59 = ( plus_plus_nat @ one_one_nat @ ( modulo_modulo_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % even_succ_mod_exp
% 5.31/5.59 thf(fact_5214_even__succ__mod__exp,axiom,
% 5.31/5.59 ! [A: int,N: nat] :
% 5.31/5.59 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.31/5.59 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.59 => ( ( modulo_modulo_int @ ( plus_plus_int @ one_one_int @ A ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.31/5.59 = ( plus_plus_int @ one_one_int @ ( modulo_modulo_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % even_succ_mod_exp
% 5.31/5.59 thf(fact_5215_even__succ__mod__exp,axiom,
% 5.31/5.59 ! [A: code_natural,N: nat] :
% 5.31/5.59 ( ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A )
% 5.31/5.59 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.59 => ( ( modulo8411746178871703098atural @ ( plus_p4538020629002901425atural @ one_one_Code_natural @ A ) @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N ) )
% 5.31/5.59 = ( plus_p4538020629002901425atural @ one_one_Code_natural @ ( modulo8411746178871703098atural @ A @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N ) ) ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % even_succ_mod_exp
% 5.31/5.59 thf(fact_5216_sum_Oneutral,axiom,
% 5.31/5.59 ! [A4: set_nat,G2: nat > nat] :
% 5.31/5.59 ( ! [X3: nat] :
% 5.31/5.59 ( ( member_nat @ X3 @ A4 )
% 5.31/5.59 => ( ( G2 @ X3 )
% 5.31/5.59 = zero_zero_nat ) )
% 5.31/5.59 => ( ( groups3542108847815614940at_nat @ G2 @ A4 )
% 5.31/5.59 = zero_zero_nat ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum.neutral
% 5.31/5.59 thf(fact_5217_sum_Oneutral,axiom,
% 5.31/5.59 ! [A4: set_int,G2: int > int] :
% 5.31/5.59 ( ! [X3: int] :
% 5.31/5.59 ( ( member_int @ X3 @ A4 )
% 5.31/5.59 => ( ( G2 @ X3 )
% 5.31/5.59 = zero_zero_int ) )
% 5.31/5.59 => ( ( groups4538972089207619220nt_int @ G2 @ A4 )
% 5.31/5.59 = zero_zero_int ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum.neutral
% 5.31/5.59 thf(fact_5218_sum_Oneutral,axiom,
% 5.31/5.59 ! [A4: set_nat,G2: nat > real] :
% 5.31/5.59 ( ! [X3: nat] :
% 5.31/5.59 ( ( member_nat @ X3 @ A4 )
% 5.31/5.59 => ( ( G2 @ X3 )
% 5.31/5.59 = zero_zero_real ) )
% 5.31/5.59 => ( ( groups6591440286371151544t_real @ G2 @ A4 )
% 5.31/5.59 = zero_zero_real ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum.neutral
% 5.31/5.59 thf(fact_5219_sum_Onot__neutral__contains__not__neutral,axiom,
% 5.31/5.59 ! [G2: complex > complex,A4: set_complex] :
% 5.31/5.59 ( ( ( groups7754918857620584856omplex @ G2 @ A4 )
% 5.31/5.59 != zero_zero_complex )
% 5.31/5.59 => ~ ! [A3: complex] :
% 5.31/5.59 ( ( member_complex @ A3 @ A4 )
% 5.31/5.59 => ( ( G2 @ A3 )
% 5.31/5.59 = zero_zero_complex ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum.not_neutral_contains_not_neutral
% 5.31/5.59 thf(fact_5220_sum_Onot__neutral__contains__not__neutral,axiom,
% 5.31/5.59 ! [G2: real > complex,A4: set_real] :
% 5.31/5.59 ( ( ( groups5754745047067104278omplex @ G2 @ A4 )
% 5.31/5.59 != zero_zero_complex )
% 5.31/5.59 => ~ ! [A3: real] :
% 5.31/5.59 ( ( member_real @ A3 @ A4 )
% 5.31/5.59 => ( ( G2 @ A3 )
% 5.31/5.59 = zero_zero_complex ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum.not_neutral_contains_not_neutral
% 5.31/5.59 thf(fact_5221_sum_Onot__neutral__contains__not__neutral,axiom,
% 5.31/5.59 ! [G2: nat > complex,A4: set_nat] :
% 5.31/5.59 ( ( ( groups2073611262835488442omplex @ G2 @ A4 )
% 5.31/5.59 != zero_zero_complex )
% 5.31/5.59 => ~ ! [A3: nat] :
% 5.31/5.59 ( ( member_nat @ A3 @ A4 )
% 5.31/5.59 => ( ( G2 @ A3 )
% 5.31/5.59 = zero_zero_complex ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum.not_neutral_contains_not_neutral
% 5.31/5.59 thf(fact_5222_sum_Onot__neutral__contains__not__neutral,axiom,
% 5.31/5.59 ! [G2: int > complex,A4: set_int] :
% 5.31/5.59 ( ( ( groups3049146728041665814omplex @ G2 @ A4 )
% 5.31/5.59 != zero_zero_complex )
% 5.31/5.59 => ~ ! [A3: int] :
% 5.31/5.59 ( ( member_int @ A3 @ A4 )
% 5.31/5.59 => ( ( G2 @ A3 )
% 5.31/5.59 = zero_zero_complex ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum.not_neutral_contains_not_neutral
% 5.31/5.59 thf(fact_5223_sum_Onot__neutral__contains__not__neutral,axiom,
% 5.31/5.59 ! [G2: complex > real,A4: set_complex] :
% 5.31/5.59 ( ( ( groups5808333547571424918x_real @ G2 @ A4 )
% 5.31/5.59 != zero_zero_real )
% 5.31/5.59 => ~ ! [A3: complex] :
% 5.31/5.59 ( ( member_complex @ A3 @ A4 )
% 5.31/5.59 => ( ( G2 @ A3 )
% 5.31/5.59 = zero_zero_real ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum.not_neutral_contains_not_neutral
% 5.31/5.59 thf(fact_5224_sum_Onot__neutral__contains__not__neutral,axiom,
% 5.31/5.59 ! [G2: real > real,A4: set_real] :
% 5.31/5.59 ( ( ( groups8097168146408367636l_real @ G2 @ A4 )
% 5.31/5.59 != zero_zero_real )
% 5.31/5.59 => ~ ! [A3: real] :
% 5.31/5.59 ( ( member_real @ A3 @ A4 )
% 5.31/5.59 => ( ( G2 @ A3 )
% 5.31/5.59 = zero_zero_real ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum.not_neutral_contains_not_neutral
% 5.31/5.59 thf(fact_5225_sum_Onot__neutral__contains__not__neutral,axiom,
% 5.31/5.59 ! [G2: int > real,A4: set_int] :
% 5.31/5.59 ( ( ( groups8778361861064173332t_real @ G2 @ A4 )
% 5.31/5.59 != zero_zero_real )
% 5.31/5.59 => ~ ! [A3: int] :
% 5.31/5.59 ( ( member_int @ A3 @ A4 )
% 5.31/5.59 => ( ( G2 @ A3 )
% 5.31/5.59 = zero_zero_real ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum.not_neutral_contains_not_neutral
% 5.31/5.59 thf(fact_5226_sum_Onot__neutral__contains__not__neutral,axiom,
% 5.31/5.59 ! [G2: complex > rat,A4: set_complex] :
% 5.31/5.59 ( ( ( groups5058264527183730370ex_rat @ G2 @ A4 )
% 5.31/5.59 != zero_zero_rat )
% 5.31/5.59 => ~ ! [A3: complex] :
% 5.31/5.59 ( ( member_complex @ A3 @ A4 )
% 5.31/5.59 => ( ( G2 @ A3 )
% 5.31/5.59 = zero_zero_rat ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum.not_neutral_contains_not_neutral
% 5.31/5.59 thf(fact_5227_sum_Onot__neutral__contains__not__neutral,axiom,
% 5.31/5.59 ! [G2: real > rat,A4: set_real] :
% 5.31/5.59 ( ( ( groups1300246762558778688al_rat @ G2 @ A4 )
% 5.31/5.59 != zero_zero_rat )
% 5.31/5.59 => ~ ! [A3: real] :
% 5.31/5.59 ( ( member_real @ A3 @ A4 )
% 5.31/5.59 => ( ( G2 @ A3 )
% 5.31/5.59 = zero_zero_rat ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum.not_neutral_contains_not_neutral
% 5.31/5.59 thf(fact_5228_sum_Onot__neutral__contains__not__neutral,axiom,
% 5.31/5.59 ! [G2: nat > rat,A4: set_nat] :
% 5.31/5.59 ( ( ( groups2906978787729119204at_rat @ G2 @ A4 )
% 5.31/5.59 != zero_zero_rat )
% 5.31/5.59 => ~ ! [A3: nat] :
% 5.31/5.59 ( ( member_nat @ A3 @ A4 )
% 5.31/5.59 => ( ( G2 @ A3 )
% 5.31/5.59 = zero_zero_rat ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum.not_neutral_contains_not_neutral
% 5.31/5.59 thf(fact_5229_sum__mono,axiom,
% 5.31/5.59 ! [K5: set_complex,F2: complex > rat,G2: complex > rat] :
% 5.31/5.59 ( ! [I3: complex] :
% 5.31/5.59 ( ( member_complex @ I3 @ K5 )
% 5.31/5.59 => ( ord_less_eq_rat @ ( F2 @ I3 ) @ ( G2 @ I3 ) ) )
% 5.31/5.59 => ( ord_less_eq_rat @ ( groups5058264527183730370ex_rat @ F2 @ K5 ) @ ( groups5058264527183730370ex_rat @ G2 @ K5 ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum_mono
% 5.31/5.59 thf(fact_5230_sum__mono,axiom,
% 5.31/5.59 ! [K5: set_real,F2: real > rat,G2: real > rat] :
% 5.31/5.59 ( ! [I3: real] :
% 5.31/5.59 ( ( member_real @ I3 @ K5 )
% 5.31/5.59 => ( ord_less_eq_rat @ ( F2 @ I3 ) @ ( G2 @ I3 ) ) )
% 5.31/5.59 => ( ord_less_eq_rat @ ( groups1300246762558778688al_rat @ F2 @ K5 ) @ ( groups1300246762558778688al_rat @ G2 @ K5 ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum_mono
% 5.31/5.59 thf(fact_5231_sum__mono,axiom,
% 5.31/5.59 ! [K5: set_nat,F2: nat > rat,G2: nat > rat] :
% 5.31/5.59 ( ! [I3: nat] :
% 5.31/5.59 ( ( member_nat @ I3 @ K5 )
% 5.31/5.59 => ( ord_less_eq_rat @ ( F2 @ I3 ) @ ( G2 @ I3 ) ) )
% 5.31/5.59 => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F2 @ K5 ) @ ( groups2906978787729119204at_rat @ G2 @ K5 ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum_mono
% 5.31/5.59 thf(fact_5232_sum__mono,axiom,
% 5.31/5.59 ! [K5: set_int,F2: int > rat,G2: int > rat] :
% 5.31/5.59 ( ! [I3: int] :
% 5.31/5.59 ( ( member_int @ I3 @ K5 )
% 5.31/5.59 => ( ord_less_eq_rat @ ( F2 @ I3 ) @ ( G2 @ I3 ) ) )
% 5.31/5.59 => ( ord_less_eq_rat @ ( groups3906332499630173760nt_rat @ F2 @ K5 ) @ ( groups3906332499630173760nt_rat @ G2 @ K5 ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum_mono
% 5.31/5.59 thf(fact_5233_sum__mono,axiom,
% 5.31/5.59 ! [K5: set_complex,F2: complex > nat,G2: complex > nat] :
% 5.31/5.59 ( ! [I3: complex] :
% 5.31/5.59 ( ( member_complex @ I3 @ K5 )
% 5.31/5.59 => ( ord_less_eq_nat @ ( F2 @ I3 ) @ ( G2 @ I3 ) ) )
% 5.31/5.59 => ( ord_less_eq_nat @ ( groups5693394587270226106ex_nat @ F2 @ K5 ) @ ( groups5693394587270226106ex_nat @ G2 @ K5 ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum_mono
% 5.31/5.59 thf(fact_5234_sum__mono,axiom,
% 5.31/5.59 ! [K5: set_real,F2: real > nat,G2: real > nat] :
% 5.31/5.59 ( ! [I3: real] :
% 5.31/5.59 ( ( member_real @ I3 @ K5 )
% 5.31/5.59 => ( ord_less_eq_nat @ ( F2 @ I3 ) @ ( G2 @ I3 ) ) )
% 5.31/5.59 => ( ord_less_eq_nat @ ( groups1935376822645274424al_nat @ F2 @ K5 ) @ ( groups1935376822645274424al_nat @ G2 @ K5 ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum_mono
% 5.31/5.59 thf(fact_5235_sum__mono,axiom,
% 5.31/5.59 ! [K5: set_int,F2: int > nat,G2: int > nat] :
% 5.31/5.59 ( ! [I3: int] :
% 5.31/5.59 ( ( member_int @ I3 @ K5 )
% 5.31/5.59 => ( ord_less_eq_nat @ ( F2 @ I3 ) @ ( G2 @ I3 ) ) )
% 5.31/5.59 => ( ord_less_eq_nat @ ( groups4541462559716669496nt_nat @ F2 @ K5 ) @ ( groups4541462559716669496nt_nat @ G2 @ K5 ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum_mono
% 5.31/5.59 thf(fact_5236_sum__mono,axiom,
% 5.31/5.59 ! [K5: set_complex,F2: complex > int,G2: complex > int] :
% 5.31/5.59 ( ! [I3: complex] :
% 5.31/5.59 ( ( member_complex @ I3 @ K5 )
% 5.31/5.59 => ( ord_less_eq_int @ ( F2 @ I3 ) @ ( G2 @ I3 ) ) )
% 5.31/5.59 => ( ord_less_eq_int @ ( groups5690904116761175830ex_int @ F2 @ K5 ) @ ( groups5690904116761175830ex_int @ G2 @ K5 ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum_mono
% 5.31/5.59 thf(fact_5237_sum__mono,axiom,
% 5.31/5.59 ! [K5: set_real,F2: real > int,G2: real > int] :
% 5.31/5.59 ( ! [I3: real] :
% 5.31/5.59 ( ( member_real @ I3 @ K5 )
% 5.31/5.59 => ( ord_less_eq_int @ ( F2 @ I3 ) @ ( G2 @ I3 ) ) )
% 5.31/5.59 => ( ord_less_eq_int @ ( groups1932886352136224148al_int @ F2 @ K5 ) @ ( groups1932886352136224148al_int @ G2 @ K5 ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum_mono
% 5.31/5.59 thf(fact_5238_sum__mono,axiom,
% 5.31/5.59 ! [K5: set_nat,F2: nat > int,G2: nat > int] :
% 5.31/5.59 ( ! [I3: nat] :
% 5.31/5.59 ( ( member_nat @ I3 @ K5 )
% 5.31/5.59 => ( ord_less_eq_int @ ( F2 @ I3 ) @ ( G2 @ I3 ) ) )
% 5.31/5.59 => ( ord_less_eq_int @ ( groups3539618377306564664at_int @ F2 @ K5 ) @ ( groups3539618377306564664at_int @ G2 @ K5 ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum_mono
% 5.31/5.59 thf(fact_5239_sum__distrib__left,axiom,
% 5.31/5.59 ! [R3: nat,F2: nat > nat,A4: set_nat] :
% 5.31/5.59 ( ( times_times_nat @ R3 @ ( groups3542108847815614940at_nat @ F2 @ A4 ) )
% 5.31/5.59 = ( groups3542108847815614940at_nat
% 5.31/5.59 @ ^ [N4: nat] : ( times_times_nat @ R3 @ ( F2 @ N4 ) )
% 5.31/5.59 @ A4 ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum_distrib_left
% 5.31/5.59 thf(fact_5240_sum__distrib__left,axiom,
% 5.31/5.59 ! [R3: int,F2: int > int,A4: set_int] :
% 5.31/5.59 ( ( times_times_int @ R3 @ ( groups4538972089207619220nt_int @ F2 @ A4 ) )
% 5.31/5.59 = ( groups4538972089207619220nt_int
% 5.31/5.59 @ ^ [N4: int] : ( times_times_int @ R3 @ ( F2 @ N4 ) )
% 5.31/5.59 @ A4 ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum_distrib_left
% 5.31/5.59 thf(fact_5241_sum__distrib__left,axiom,
% 5.31/5.59 ! [R3: real,F2: nat > real,A4: set_nat] :
% 5.31/5.59 ( ( times_times_real @ R3 @ ( groups6591440286371151544t_real @ F2 @ A4 ) )
% 5.31/5.59 = ( groups6591440286371151544t_real
% 5.31/5.59 @ ^ [N4: nat] : ( times_times_real @ R3 @ ( F2 @ N4 ) )
% 5.31/5.59 @ A4 ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum_distrib_left
% 5.31/5.59 thf(fact_5242_sum__distrib__right,axiom,
% 5.31/5.59 ! [F2: nat > nat,A4: set_nat,R3: nat] :
% 5.31/5.59 ( ( times_times_nat @ ( groups3542108847815614940at_nat @ F2 @ A4 ) @ R3 )
% 5.31/5.59 = ( groups3542108847815614940at_nat
% 5.31/5.59 @ ^ [N4: nat] : ( times_times_nat @ ( F2 @ N4 ) @ R3 )
% 5.31/5.59 @ A4 ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum_distrib_right
% 5.31/5.59 thf(fact_5243_sum__distrib__right,axiom,
% 5.31/5.59 ! [F2: int > int,A4: set_int,R3: int] :
% 5.31/5.59 ( ( times_times_int @ ( groups4538972089207619220nt_int @ F2 @ A4 ) @ R3 )
% 5.31/5.59 = ( groups4538972089207619220nt_int
% 5.31/5.59 @ ^ [N4: int] : ( times_times_int @ ( F2 @ N4 ) @ R3 )
% 5.31/5.59 @ A4 ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum_distrib_right
% 5.31/5.59 thf(fact_5244_sum__distrib__right,axiom,
% 5.31/5.59 ! [F2: nat > real,A4: set_nat,R3: real] :
% 5.31/5.59 ( ( times_times_real @ ( groups6591440286371151544t_real @ F2 @ A4 ) @ R3 )
% 5.31/5.59 = ( groups6591440286371151544t_real
% 5.31/5.59 @ ^ [N4: nat] : ( times_times_real @ ( F2 @ N4 ) @ R3 )
% 5.31/5.59 @ A4 ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum_distrib_right
% 5.31/5.59 thf(fact_5245_sum__product,axiom,
% 5.31/5.59 ! [F2: nat > nat,A4: set_nat,G2: nat > nat,B5: set_nat] :
% 5.31/5.59 ( ( times_times_nat @ ( groups3542108847815614940at_nat @ F2 @ A4 ) @ ( groups3542108847815614940at_nat @ G2 @ B5 ) )
% 5.31/5.59 = ( groups3542108847815614940at_nat
% 5.31/5.59 @ ^ [I: nat] :
% 5.31/5.59 ( groups3542108847815614940at_nat
% 5.31/5.59 @ ^ [J: nat] : ( times_times_nat @ ( F2 @ I ) @ ( G2 @ J ) )
% 5.31/5.59 @ B5 )
% 5.31/5.59 @ A4 ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum_product
% 5.31/5.59 thf(fact_5246_sum__product,axiom,
% 5.31/5.59 ! [F2: int > int,A4: set_int,G2: int > int,B5: set_int] :
% 5.31/5.59 ( ( times_times_int @ ( groups4538972089207619220nt_int @ F2 @ A4 ) @ ( groups4538972089207619220nt_int @ G2 @ B5 ) )
% 5.31/5.59 = ( groups4538972089207619220nt_int
% 5.31/5.59 @ ^ [I: int] :
% 5.31/5.59 ( groups4538972089207619220nt_int
% 5.31/5.59 @ ^ [J: int] : ( times_times_int @ ( F2 @ I ) @ ( G2 @ J ) )
% 5.31/5.59 @ B5 )
% 5.31/5.59 @ A4 ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum_product
% 5.31/5.59 thf(fact_5247_sum__product,axiom,
% 5.31/5.59 ! [F2: nat > real,A4: set_nat,G2: nat > real,B5: set_nat] :
% 5.31/5.59 ( ( times_times_real @ ( groups6591440286371151544t_real @ F2 @ A4 ) @ ( groups6591440286371151544t_real @ G2 @ B5 ) )
% 5.31/5.59 = ( groups6591440286371151544t_real
% 5.31/5.59 @ ^ [I: nat] :
% 5.31/5.59 ( groups6591440286371151544t_real
% 5.31/5.59 @ ^ [J: nat] : ( times_times_real @ ( F2 @ I ) @ ( G2 @ J ) )
% 5.31/5.59 @ B5 )
% 5.31/5.59 @ A4 ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum_product
% 5.31/5.59 thf(fact_5248_dvd__antisym,axiom,
% 5.31/5.59 ! [M2: nat,N: nat] :
% 5.31/5.59 ( ( dvd_dvd_nat @ M2 @ N )
% 5.31/5.59 => ( ( dvd_dvd_nat @ N @ M2 )
% 5.31/5.59 => ( M2 = N ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % dvd_antisym
% 5.31/5.59 thf(fact_5249_dvd__trans,axiom,
% 5.31/5.59 ! [A: nat,B: nat,C2: nat] :
% 5.31/5.59 ( ( dvd_dvd_nat @ A @ B )
% 5.31/5.59 => ( ( dvd_dvd_nat @ B @ C2 )
% 5.31/5.59 => ( dvd_dvd_nat @ A @ C2 ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % dvd_trans
% 5.31/5.59 thf(fact_5250_dvd__trans,axiom,
% 5.31/5.59 ! [A: int,B: int,C2: int] :
% 5.31/5.59 ( ( dvd_dvd_int @ A @ B )
% 5.31/5.59 => ( ( dvd_dvd_int @ B @ C2 )
% 5.31/5.59 => ( dvd_dvd_int @ A @ C2 ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % dvd_trans
% 5.31/5.59 thf(fact_5251_dvd__refl,axiom,
% 5.31/5.59 ! [A: nat] : ( dvd_dvd_nat @ A @ A ) ).
% 5.31/5.59
% 5.31/5.59 % dvd_refl
% 5.31/5.59 thf(fact_5252_dvd__refl,axiom,
% 5.31/5.59 ! [A: int] : ( dvd_dvd_int @ A @ A ) ).
% 5.31/5.59
% 5.31/5.59 % dvd_refl
% 5.31/5.59 thf(fact_5253_dvd__field__iff,axiom,
% 5.31/5.59 ( dvd_dvd_complex
% 5.31/5.59 = ( ^ [A5: complex,B4: complex] :
% 5.31/5.59 ( ( A5 = zero_zero_complex )
% 5.31/5.59 => ( B4 = zero_zero_complex ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % dvd_field_iff
% 5.31/5.59 thf(fact_5254_dvd__field__iff,axiom,
% 5.31/5.59 ( dvd_dvd_real
% 5.31/5.59 = ( ^ [A5: real,B4: real] :
% 5.31/5.59 ( ( A5 = zero_zero_real )
% 5.31/5.59 => ( B4 = zero_zero_real ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % dvd_field_iff
% 5.31/5.59 thf(fact_5255_dvd__field__iff,axiom,
% 5.31/5.59 ( dvd_dvd_rat
% 5.31/5.59 = ( ^ [A5: rat,B4: rat] :
% 5.31/5.59 ( ( A5 = zero_zero_rat )
% 5.31/5.59 => ( B4 = zero_zero_rat ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % dvd_field_iff
% 5.31/5.59 thf(fact_5256_dvd__0__left,axiom,
% 5.31/5.59 ! [A: complex] :
% 5.31/5.59 ( ( dvd_dvd_complex @ zero_zero_complex @ A )
% 5.31/5.59 => ( A = zero_zero_complex ) ) ).
% 5.31/5.59
% 5.31/5.59 % dvd_0_left
% 5.31/5.59 thf(fact_5257_dvd__0__left,axiom,
% 5.31/5.59 ! [A: real] :
% 5.31/5.59 ( ( dvd_dvd_real @ zero_zero_real @ A )
% 5.31/5.59 => ( A = zero_zero_real ) ) ).
% 5.31/5.59
% 5.31/5.59 % dvd_0_left
% 5.31/5.59 thf(fact_5258_dvd__0__left,axiom,
% 5.31/5.59 ! [A: rat] :
% 5.31/5.59 ( ( dvd_dvd_rat @ zero_zero_rat @ A )
% 5.31/5.59 => ( A = zero_zero_rat ) ) ).
% 5.31/5.59
% 5.31/5.59 % dvd_0_left
% 5.31/5.59 thf(fact_5259_dvd__0__left,axiom,
% 5.31/5.59 ! [A: nat] :
% 5.31/5.59 ( ( dvd_dvd_nat @ zero_zero_nat @ A )
% 5.31/5.59 => ( A = zero_zero_nat ) ) ).
% 5.31/5.59
% 5.31/5.59 % dvd_0_left
% 5.31/5.59 thf(fact_5260_dvd__0__left,axiom,
% 5.31/5.59 ! [A: int] :
% 5.31/5.59 ( ( dvd_dvd_int @ zero_zero_int @ A )
% 5.31/5.59 => ( A = zero_zero_int ) ) ).
% 5.31/5.59
% 5.31/5.59 % dvd_0_left
% 5.31/5.59 thf(fact_5261_dvd__productE,axiom,
% 5.31/5.59 ! [P: nat,A: nat,B: nat] :
% 5.31/5.59 ( ( dvd_dvd_nat @ P @ ( times_times_nat @ A @ B ) )
% 5.31/5.59 => ~ ! [X3: nat,Y3: nat] :
% 5.31/5.59 ( ( P
% 5.31/5.59 = ( times_times_nat @ X3 @ Y3 ) )
% 5.31/5.59 => ( ( dvd_dvd_nat @ X3 @ A )
% 5.31/5.59 => ~ ( dvd_dvd_nat @ Y3 @ B ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % dvd_productE
% 5.31/5.59 thf(fact_5262_dvd__productE,axiom,
% 5.31/5.59 ! [P: int,A: int,B: int] :
% 5.31/5.59 ( ( dvd_dvd_int @ P @ ( times_times_int @ A @ B ) )
% 5.31/5.59 => ~ ! [X3: int,Y3: int] :
% 5.31/5.59 ( ( P
% 5.31/5.59 = ( times_times_int @ X3 @ Y3 ) )
% 5.31/5.59 => ( ( dvd_dvd_int @ X3 @ A )
% 5.31/5.59 => ~ ( dvd_dvd_int @ Y3 @ B ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % dvd_productE
% 5.31/5.59 thf(fact_5263_division__decomp,axiom,
% 5.31/5.59 ! [A: nat,B: nat,C2: nat] :
% 5.31/5.59 ( ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ C2 ) )
% 5.31/5.59 => ? [B9: nat,C5: nat] :
% 5.31/5.59 ( ( A
% 5.31/5.59 = ( times_times_nat @ B9 @ C5 ) )
% 5.31/5.59 & ( dvd_dvd_nat @ B9 @ B )
% 5.31/5.59 & ( dvd_dvd_nat @ C5 @ C2 ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % division_decomp
% 5.31/5.59 thf(fact_5264_division__decomp,axiom,
% 5.31/5.59 ! [A: int,B: int,C2: int] :
% 5.31/5.59 ( ( dvd_dvd_int @ A @ ( times_times_int @ B @ C2 ) )
% 5.31/5.59 => ? [B9: int,C5: int] :
% 5.31/5.59 ( ( A
% 5.31/5.59 = ( times_times_int @ B9 @ C5 ) )
% 5.31/5.59 & ( dvd_dvd_int @ B9 @ B )
% 5.31/5.59 & ( dvd_dvd_int @ C5 @ C2 ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % division_decomp
% 5.31/5.59 thf(fact_5265_dvdE,axiom,
% 5.31/5.59 ! [B: real,A: real] :
% 5.31/5.59 ( ( dvd_dvd_real @ B @ A )
% 5.31/5.59 => ~ ! [K: real] :
% 5.31/5.59 ( A
% 5.31/5.59 != ( times_times_real @ B @ K ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % dvdE
% 5.31/5.59 thf(fact_5266_dvdE,axiom,
% 5.31/5.59 ! [B: rat,A: rat] :
% 5.31/5.59 ( ( dvd_dvd_rat @ B @ A )
% 5.31/5.59 => ~ ! [K: rat] :
% 5.31/5.59 ( A
% 5.31/5.59 != ( times_times_rat @ B @ K ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % dvdE
% 5.31/5.59 thf(fact_5267_dvdE,axiom,
% 5.31/5.59 ! [B: nat,A: nat] :
% 5.31/5.59 ( ( dvd_dvd_nat @ B @ A )
% 5.31/5.59 => ~ ! [K: nat] :
% 5.31/5.59 ( A
% 5.31/5.59 != ( times_times_nat @ B @ K ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % dvdE
% 5.31/5.59 thf(fact_5268_dvdE,axiom,
% 5.31/5.59 ! [B: int,A: int] :
% 5.31/5.59 ( ( dvd_dvd_int @ B @ A )
% 5.31/5.59 => ~ ! [K: int] :
% 5.31/5.59 ( A
% 5.31/5.59 != ( times_times_int @ B @ K ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % dvdE
% 5.31/5.59 thf(fact_5269_dvdI,axiom,
% 5.31/5.59 ! [A: real,B: real,K2: real] :
% 5.31/5.59 ( ( A
% 5.31/5.59 = ( times_times_real @ B @ K2 ) )
% 5.31/5.59 => ( dvd_dvd_real @ B @ A ) ) ).
% 5.31/5.59
% 5.31/5.59 % dvdI
% 5.31/5.59 thf(fact_5270_dvdI,axiom,
% 5.31/5.59 ! [A: rat,B: rat,K2: rat] :
% 5.31/5.59 ( ( A
% 5.31/5.59 = ( times_times_rat @ B @ K2 ) )
% 5.31/5.59 => ( dvd_dvd_rat @ B @ A ) ) ).
% 5.31/5.59
% 5.31/5.59 % dvdI
% 5.31/5.59 thf(fact_5271_dvdI,axiom,
% 5.31/5.59 ! [A: nat,B: nat,K2: nat] :
% 5.31/5.59 ( ( A
% 5.31/5.59 = ( times_times_nat @ B @ K2 ) )
% 5.31/5.59 => ( dvd_dvd_nat @ B @ A ) ) ).
% 5.31/5.59
% 5.31/5.59 % dvdI
% 5.31/5.59 thf(fact_5272_dvdI,axiom,
% 5.31/5.59 ! [A: int,B: int,K2: int] :
% 5.31/5.59 ( ( A
% 5.31/5.59 = ( times_times_int @ B @ K2 ) )
% 5.31/5.59 => ( dvd_dvd_int @ B @ A ) ) ).
% 5.31/5.59
% 5.31/5.59 % dvdI
% 5.31/5.59 thf(fact_5273_dvd__def,axiom,
% 5.31/5.59 ( dvd_dvd_real
% 5.31/5.59 = ( ^ [B4: real,A5: real] :
% 5.31/5.59 ? [K3: real] :
% 5.31/5.59 ( A5
% 5.31/5.59 = ( times_times_real @ B4 @ K3 ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % dvd_def
% 5.31/5.59 thf(fact_5274_dvd__def,axiom,
% 5.31/5.59 ( dvd_dvd_rat
% 5.31/5.59 = ( ^ [B4: rat,A5: rat] :
% 5.31/5.59 ? [K3: rat] :
% 5.31/5.59 ( A5
% 5.31/5.59 = ( times_times_rat @ B4 @ K3 ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % dvd_def
% 5.31/5.59 thf(fact_5275_dvd__def,axiom,
% 5.31/5.59 ( dvd_dvd_nat
% 5.31/5.59 = ( ^ [B4: nat,A5: nat] :
% 5.31/5.59 ? [K3: nat] :
% 5.31/5.59 ( A5
% 5.31/5.59 = ( times_times_nat @ B4 @ K3 ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % dvd_def
% 5.31/5.59 thf(fact_5276_dvd__def,axiom,
% 5.31/5.59 ( dvd_dvd_int
% 5.31/5.59 = ( ^ [B4: int,A5: int] :
% 5.31/5.59 ? [K3: int] :
% 5.31/5.59 ( A5
% 5.31/5.59 = ( times_times_int @ B4 @ K3 ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % dvd_def
% 5.31/5.59 thf(fact_5277_dvd__mult,axiom,
% 5.31/5.59 ! [A: real,C2: real,B: real] :
% 5.31/5.59 ( ( dvd_dvd_real @ A @ C2 )
% 5.31/5.59 => ( dvd_dvd_real @ A @ ( times_times_real @ B @ C2 ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % dvd_mult
% 5.31/5.59 thf(fact_5278_dvd__mult,axiom,
% 5.31/5.59 ! [A: rat,C2: rat,B: rat] :
% 5.31/5.59 ( ( dvd_dvd_rat @ A @ C2 )
% 5.31/5.59 => ( dvd_dvd_rat @ A @ ( times_times_rat @ B @ C2 ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % dvd_mult
% 5.31/5.59 thf(fact_5279_dvd__mult,axiom,
% 5.31/5.59 ! [A: nat,C2: nat,B: nat] :
% 5.31/5.59 ( ( dvd_dvd_nat @ A @ C2 )
% 5.31/5.59 => ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ C2 ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % dvd_mult
% 5.31/5.59 thf(fact_5280_dvd__mult,axiom,
% 5.31/5.59 ! [A: int,C2: int,B: int] :
% 5.31/5.59 ( ( dvd_dvd_int @ A @ C2 )
% 5.31/5.59 => ( dvd_dvd_int @ A @ ( times_times_int @ B @ C2 ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % dvd_mult
% 5.31/5.59 thf(fact_5281_dvd__mult2,axiom,
% 5.31/5.59 ! [A: real,B: real,C2: real] :
% 5.31/5.59 ( ( dvd_dvd_real @ A @ B )
% 5.31/5.59 => ( dvd_dvd_real @ A @ ( times_times_real @ B @ C2 ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % dvd_mult2
% 5.31/5.59 thf(fact_5282_dvd__mult2,axiom,
% 5.31/5.59 ! [A: rat,B: rat,C2: rat] :
% 5.31/5.59 ( ( dvd_dvd_rat @ A @ B )
% 5.31/5.59 => ( dvd_dvd_rat @ A @ ( times_times_rat @ B @ C2 ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % dvd_mult2
% 5.31/5.59 thf(fact_5283_dvd__mult2,axiom,
% 5.31/5.59 ! [A: nat,B: nat,C2: nat] :
% 5.31/5.59 ( ( dvd_dvd_nat @ A @ B )
% 5.31/5.59 => ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ C2 ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % dvd_mult2
% 5.31/5.59 thf(fact_5284_dvd__mult2,axiom,
% 5.31/5.59 ! [A: int,B: int,C2: int] :
% 5.31/5.59 ( ( dvd_dvd_int @ A @ B )
% 5.31/5.59 => ( dvd_dvd_int @ A @ ( times_times_int @ B @ C2 ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % dvd_mult2
% 5.31/5.59 thf(fact_5285_dvd__mult__left,axiom,
% 5.31/5.59 ! [A: real,B: real,C2: real] :
% 5.31/5.59 ( ( dvd_dvd_real @ ( times_times_real @ A @ B ) @ C2 )
% 5.31/5.59 => ( dvd_dvd_real @ A @ C2 ) ) ).
% 5.31/5.59
% 5.31/5.59 % dvd_mult_left
% 5.31/5.59 thf(fact_5286_dvd__mult__left,axiom,
% 5.31/5.59 ! [A: rat,B: rat,C2: rat] :
% 5.31/5.59 ( ( dvd_dvd_rat @ ( times_times_rat @ A @ B ) @ C2 )
% 5.31/5.59 => ( dvd_dvd_rat @ A @ C2 ) ) ).
% 5.31/5.59
% 5.31/5.59 % dvd_mult_left
% 5.31/5.59 thf(fact_5287_dvd__mult__left,axiom,
% 5.31/5.59 ! [A: nat,B: nat,C2: nat] :
% 5.31/5.59 ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ C2 )
% 5.31/5.59 => ( dvd_dvd_nat @ A @ C2 ) ) ).
% 5.31/5.59
% 5.31/5.59 % dvd_mult_left
% 5.31/5.59 thf(fact_5288_dvd__mult__left,axiom,
% 5.31/5.59 ! [A: int,B: int,C2: int] :
% 5.31/5.59 ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ C2 )
% 5.31/5.59 => ( dvd_dvd_int @ A @ C2 ) ) ).
% 5.31/5.59
% 5.31/5.59 % dvd_mult_left
% 5.31/5.59 thf(fact_5289_dvd__triv__left,axiom,
% 5.31/5.59 ! [A: real,B: real] : ( dvd_dvd_real @ A @ ( times_times_real @ A @ B ) ) ).
% 5.31/5.59
% 5.31/5.59 % dvd_triv_left
% 5.31/5.59 thf(fact_5290_dvd__triv__left,axiom,
% 5.31/5.59 ! [A: rat,B: rat] : ( dvd_dvd_rat @ A @ ( times_times_rat @ A @ B ) ) ).
% 5.31/5.59
% 5.31/5.59 % dvd_triv_left
% 5.31/5.59 thf(fact_5291_dvd__triv__left,axiom,
% 5.31/5.59 ! [A: nat,B: nat] : ( dvd_dvd_nat @ A @ ( times_times_nat @ A @ B ) ) ).
% 5.31/5.59
% 5.31/5.59 % dvd_triv_left
% 5.31/5.59 thf(fact_5292_dvd__triv__left,axiom,
% 5.31/5.59 ! [A: int,B: int] : ( dvd_dvd_int @ A @ ( times_times_int @ A @ B ) ) ).
% 5.31/5.59
% 5.31/5.59 % dvd_triv_left
% 5.31/5.59 thf(fact_5293_mult__dvd__mono,axiom,
% 5.31/5.59 ! [A: real,B: real,C2: real,D: real] :
% 5.31/5.59 ( ( dvd_dvd_real @ A @ B )
% 5.31/5.59 => ( ( dvd_dvd_real @ C2 @ D )
% 5.31/5.59 => ( dvd_dvd_real @ ( times_times_real @ A @ C2 ) @ ( times_times_real @ B @ D ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % mult_dvd_mono
% 5.31/5.59 thf(fact_5294_mult__dvd__mono,axiom,
% 5.31/5.59 ! [A: rat,B: rat,C2: rat,D: rat] :
% 5.31/5.59 ( ( dvd_dvd_rat @ A @ B )
% 5.31/5.59 => ( ( dvd_dvd_rat @ C2 @ D )
% 5.31/5.59 => ( dvd_dvd_rat @ ( times_times_rat @ A @ C2 ) @ ( times_times_rat @ B @ D ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % mult_dvd_mono
% 5.31/5.59 thf(fact_5295_mult__dvd__mono,axiom,
% 5.31/5.59 ! [A: nat,B: nat,C2: nat,D: nat] :
% 5.31/5.59 ( ( dvd_dvd_nat @ A @ B )
% 5.31/5.59 => ( ( dvd_dvd_nat @ C2 @ D )
% 5.31/5.59 => ( dvd_dvd_nat @ ( times_times_nat @ A @ C2 ) @ ( times_times_nat @ B @ D ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % mult_dvd_mono
% 5.31/5.59 thf(fact_5296_mult__dvd__mono,axiom,
% 5.31/5.59 ! [A: int,B: int,C2: int,D: int] :
% 5.31/5.59 ( ( dvd_dvd_int @ A @ B )
% 5.31/5.59 => ( ( dvd_dvd_int @ C2 @ D )
% 5.31/5.59 => ( dvd_dvd_int @ ( times_times_int @ A @ C2 ) @ ( times_times_int @ B @ D ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % mult_dvd_mono
% 5.31/5.59 thf(fact_5297_dvd__mult__right,axiom,
% 5.31/5.59 ! [A: real,B: real,C2: real] :
% 5.31/5.59 ( ( dvd_dvd_real @ ( times_times_real @ A @ B ) @ C2 )
% 5.31/5.59 => ( dvd_dvd_real @ B @ C2 ) ) ).
% 5.31/5.59
% 5.31/5.59 % dvd_mult_right
% 5.31/5.59 thf(fact_5298_dvd__mult__right,axiom,
% 5.31/5.59 ! [A: rat,B: rat,C2: rat] :
% 5.31/5.59 ( ( dvd_dvd_rat @ ( times_times_rat @ A @ B ) @ C2 )
% 5.31/5.59 => ( dvd_dvd_rat @ B @ C2 ) ) ).
% 5.31/5.59
% 5.31/5.59 % dvd_mult_right
% 5.31/5.59 thf(fact_5299_dvd__mult__right,axiom,
% 5.31/5.59 ! [A: nat,B: nat,C2: nat] :
% 5.31/5.59 ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ C2 )
% 5.31/5.59 => ( dvd_dvd_nat @ B @ C2 ) ) ).
% 5.31/5.59
% 5.31/5.59 % dvd_mult_right
% 5.31/5.59 thf(fact_5300_dvd__mult__right,axiom,
% 5.31/5.59 ! [A: int,B: int,C2: int] :
% 5.31/5.59 ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ C2 )
% 5.31/5.59 => ( dvd_dvd_int @ B @ C2 ) ) ).
% 5.31/5.59
% 5.31/5.59 % dvd_mult_right
% 5.31/5.59 thf(fact_5301_dvd__triv__right,axiom,
% 5.31/5.59 ! [A: real,B: real] : ( dvd_dvd_real @ A @ ( times_times_real @ B @ A ) ) ).
% 5.31/5.59
% 5.31/5.59 % dvd_triv_right
% 5.31/5.59 thf(fact_5302_dvd__triv__right,axiom,
% 5.31/5.59 ! [A: rat,B: rat] : ( dvd_dvd_rat @ A @ ( times_times_rat @ B @ A ) ) ).
% 5.31/5.59
% 5.31/5.59 % dvd_triv_right
% 5.31/5.59 thf(fact_5303_dvd__triv__right,axiom,
% 5.31/5.59 ! [A: nat,B: nat] : ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ A ) ) ).
% 5.31/5.59
% 5.31/5.59 % dvd_triv_right
% 5.31/5.59 thf(fact_5304_dvd__triv__right,axiom,
% 5.31/5.59 ! [A: int,B: int] : ( dvd_dvd_int @ A @ ( times_times_int @ B @ A ) ) ).
% 5.31/5.59
% 5.31/5.59 % dvd_triv_right
% 5.31/5.59 thf(fact_5305_dvd__add__right__iff,axiom,
% 5.31/5.59 ! [A: real,B: real,C2: real] :
% 5.31/5.59 ( ( dvd_dvd_real @ A @ B )
% 5.31/5.59 => ( ( dvd_dvd_real @ A @ ( plus_plus_real @ B @ C2 ) )
% 5.31/5.59 = ( dvd_dvd_real @ A @ C2 ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % dvd_add_right_iff
% 5.31/5.59 thf(fact_5306_dvd__add__right__iff,axiom,
% 5.31/5.59 ! [A: rat,B: rat,C2: rat] :
% 5.31/5.59 ( ( dvd_dvd_rat @ A @ B )
% 5.31/5.59 => ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ B @ C2 ) )
% 5.31/5.59 = ( dvd_dvd_rat @ A @ C2 ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % dvd_add_right_iff
% 5.31/5.59 thf(fact_5307_dvd__add__right__iff,axiom,
% 5.31/5.59 ! [A: nat,B: nat,C2: nat] :
% 5.31/5.59 ( ( dvd_dvd_nat @ A @ B )
% 5.31/5.59 => ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ C2 ) )
% 5.31/5.59 = ( dvd_dvd_nat @ A @ C2 ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % dvd_add_right_iff
% 5.31/5.59 thf(fact_5308_dvd__add__right__iff,axiom,
% 5.31/5.59 ! [A: int,B: int,C2: int] :
% 5.31/5.59 ( ( dvd_dvd_int @ A @ B )
% 5.31/5.59 => ( ( dvd_dvd_int @ A @ ( plus_plus_int @ B @ C2 ) )
% 5.31/5.59 = ( dvd_dvd_int @ A @ C2 ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % dvd_add_right_iff
% 5.31/5.59 thf(fact_5309_dvd__add__left__iff,axiom,
% 5.31/5.59 ! [A: real,C2: real,B: real] :
% 5.31/5.59 ( ( dvd_dvd_real @ A @ C2 )
% 5.31/5.59 => ( ( dvd_dvd_real @ A @ ( plus_plus_real @ B @ C2 ) )
% 5.31/5.59 = ( dvd_dvd_real @ A @ B ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % dvd_add_left_iff
% 5.31/5.59 thf(fact_5310_dvd__add__left__iff,axiom,
% 5.31/5.59 ! [A: rat,C2: rat,B: rat] :
% 5.31/5.59 ( ( dvd_dvd_rat @ A @ C2 )
% 5.31/5.59 => ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ B @ C2 ) )
% 5.31/5.59 = ( dvd_dvd_rat @ A @ B ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % dvd_add_left_iff
% 5.31/5.59 thf(fact_5311_dvd__add__left__iff,axiom,
% 5.31/5.59 ! [A: nat,C2: nat,B: nat] :
% 5.31/5.59 ( ( dvd_dvd_nat @ A @ C2 )
% 5.31/5.59 => ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ C2 ) )
% 5.31/5.59 = ( dvd_dvd_nat @ A @ B ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % dvd_add_left_iff
% 5.31/5.59 thf(fact_5312_dvd__add__left__iff,axiom,
% 5.31/5.59 ! [A: int,C2: int,B: int] :
% 5.31/5.59 ( ( dvd_dvd_int @ A @ C2 )
% 5.31/5.59 => ( ( dvd_dvd_int @ A @ ( plus_plus_int @ B @ C2 ) )
% 5.31/5.59 = ( dvd_dvd_int @ A @ B ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % dvd_add_left_iff
% 5.31/5.59 thf(fact_5313_dvd__add,axiom,
% 5.31/5.59 ! [A: real,B: real,C2: real] :
% 5.31/5.59 ( ( dvd_dvd_real @ A @ B )
% 5.31/5.59 => ( ( dvd_dvd_real @ A @ C2 )
% 5.31/5.59 => ( dvd_dvd_real @ A @ ( plus_plus_real @ B @ C2 ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % dvd_add
% 5.31/5.59 thf(fact_5314_dvd__add,axiom,
% 5.31/5.59 ! [A: rat,B: rat,C2: rat] :
% 5.31/5.59 ( ( dvd_dvd_rat @ A @ B )
% 5.31/5.59 => ( ( dvd_dvd_rat @ A @ C2 )
% 5.31/5.59 => ( dvd_dvd_rat @ A @ ( plus_plus_rat @ B @ C2 ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % dvd_add
% 5.31/5.59 thf(fact_5315_dvd__add,axiom,
% 5.31/5.59 ! [A: nat,B: nat,C2: nat] :
% 5.31/5.59 ( ( dvd_dvd_nat @ A @ B )
% 5.31/5.59 => ( ( dvd_dvd_nat @ A @ C2 )
% 5.31/5.59 => ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ C2 ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % dvd_add
% 5.31/5.59 thf(fact_5316_dvd__add,axiom,
% 5.31/5.59 ! [A: int,B: int,C2: int] :
% 5.31/5.59 ( ( dvd_dvd_int @ A @ B )
% 5.31/5.59 => ( ( dvd_dvd_int @ A @ C2 )
% 5.31/5.59 => ( dvd_dvd_int @ A @ ( plus_plus_int @ B @ C2 ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % dvd_add
% 5.31/5.59 thf(fact_5317_dvd__unit__imp__unit,axiom,
% 5.31/5.59 ! [A: code_integer,B: code_integer] :
% 5.31/5.59 ( ( dvd_dvd_Code_integer @ A @ B )
% 5.31/5.59 => ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.31/5.59 => ( dvd_dvd_Code_integer @ A @ one_one_Code_integer ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % dvd_unit_imp_unit
% 5.31/5.59 thf(fact_5318_dvd__unit__imp__unit,axiom,
% 5.31/5.59 ! [A: nat,B: nat] :
% 5.31/5.59 ( ( dvd_dvd_nat @ A @ B )
% 5.31/5.59 => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.31/5.59 => ( dvd_dvd_nat @ A @ one_one_nat ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % dvd_unit_imp_unit
% 5.31/5.59 thf(fact_5319_dvd__unit__imp__unit,axiom,
% 5.31/5.59 ! [A: int,B: int] :
% 5.31/5.59 ( ( dvd_dvd_int @ A @ B )
% 5.31/5.59 => ( ( dvd_dvd_int @ B @ one_one_int )
% 5.31/5.59 => ( dvd_dvd_int @ A @ one_one_int ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % dvd_unit_imp_unit
% 5.31/5.59 thf(fact_5320_unit__imp__dvd,axiom,
% 5.31/5.59 ! [B: code_integer,A: code_integer] :
% 5.31/5.59 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.31/5.59 => ( dvd_dvd_Code_integer @ B @ A ) ) ).
% 5.31/5.59
% 5.31/5.59 % unit_imp_dvd
% 5.31/5.59 thf(fact_5321_unit__imp__dvd,axiom,
% 5.31/5.59 ! [B: nat,A: nat] :
% 5.31/5.59 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.31/5.59 => ( dvd_dvd_nat @ B @ A ) ) ).
% 5.31/5.59
% 5.31/5.59 % unit_imp_dvd
% 5.31/5.59 thf(fact_5322_unit__imp__dvd,axiom,
% 5.31/5.59 ! [B: int,A: int] :
% 5.31/5.59 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.31/5.59 => ( dvd_dvd_int @ B @ A ) ) ).
% 5.31/5.59
% 5.31/5.59 % unit_imp_dvd
% 5.31/5.59 thf(fact_5323_one__dvd,axiom,
% 5.31/5.59 ! [A: code_integer] : ( dvd_dvd_Code_integer @ one_one_Code_integer @ A ) ).
% 5.31/5.59
% 5.31/5.59 % one_dvd
% 5.31/5.59 thf(fact_5324_one__dvd,axiom,
% 5.31/5.59 ! [A: complex] : ( dvd_dvd_complex @ one_one_complex @ A ) ).
% 5.31/5.59
% 5.31/5.59 % one_dvd
% 5.31/5.59 thf(fact_5325_one__dvd,axiom,
% 5.31/5.59 ! [A: real] : ( dvd_dvd_real @ one_one_real @ A ) ).
% 5.31/5.59
% 5.31/5.59 % one_dvd
% 5.31/5.59 thf(fact_5326_one__dvd,axiom,
% 5.31/5.59 ! [A: nat] : ( dvd_dvd_nat @ one_one_nat @ A ) ).
% 5.31/5.59
% 5.31/5.59 % one_dvd
% 5.31/5.59 thf(fact_5327_one__dvd,axiom,
% 5.31/5.59 ! [A: int] : ( dvd_dvd_int @ one_one_int @ A ) ).
% 5.31/5.59
% 5.31/5.59 % one_dvd
% 5.31/5.59 thf(fact_5328_dvd__diff,axiom,
% 5.31/5.59 ! [X: rat,Y: rat,Z3: rat] :
% 5.31/5.59 ( ( dvd_dvd_rat @ X @ Y )
% 5.31/5.59 => ( ( dvd_dvd_rat @ X @ Z3 )
% 5.31/5.59 => ( dvd_dvd_rat @ X @ ( minus_minus_rat @ Y @ Z3 ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % dvd_diff
% 5.31/5.59 thf(fact_5329_dvd__diff,axiom,
% 5.31/5.59 ! [X: int,Y: int,Z3: int] :
% 5.31/5.59 ( ( dvd_dvd_int @ X @ Y )
% 5.31/5.59 => ( ( dvd_dvd_int @ X @ Z3 )
% 5.31/5.59 => ( dvd_dvd_int @ X @ ( minus_minus_int @ Y @ Z3 ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % dvd_diff
% 5.31/5.59 thf(fact_5330_div__div__div__same,axiom,
% 5.31/5.59 ! [D: nat,B: nat,A: nat] :
% 5.31/5.59 ( ( dvd_dvd_nat @ D @ B )
% 5.31/5.59 => ( ( dvd_dvd_nat @ B @ A )
% 5.31/5.59 => ( ( divide_divide_nat @ ( divide_divide_nat @ A @ D ) @ ( divide_divide_nat @ B @ D ) )
% 5.31/5.59 = ( divide_divide_nat @ A @ B ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % div_div_div_same
% 5.31/5.59 thf(fact_5331_div__div__div__same,axiom,
% 5.31/5.59 ! [D: int,B: int,A: int] :
% 5.31/5.59 ( ( dvd_dvd_int @ D @ B )
% 5.31/5.59 => ( ( dvd_dvd_int @ B @ A )
% 5.31/5.59 => ( ( divide_divide_int @ ( divide_divide_int @ A @ D ) @ ( divide_divide_int @ B @ D ) )
% 5.31/5.59 = ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % div_div_div_same
% 5.31/5.59 thf(fact_5332_dvd__div__eq__cancel,axiom,
% 5.31/5.59 ! [A: complex,C2: complex,B: complex] :
% 5.31/5.59 ( ( ( divide1717551699836669952omplex @ A @ C2 )
% 5.31/5.59 = ( divide1717551699836669952omplex @ B @ C2 ) )
% 5.31/5.59 => ( ( dvd_dvd_complex @ C2 @ A )
% 5.31/5.59 => ( ( dvd_dvd_complex @ C2 @ B )
% 5.31/5.59 => ( A = B ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % dvd_div_eq_cancel
% 5.31/5.59 thf(fact_5333_dvd__div__eq__cancel,axiom,
% 5.31/5.59 ! [A: real,C2: real,B: real] :
% 5.31/5.59 ( ( ( divide_divide_real @ A @ C2 )
% 5.31/5.59 = ( divide_divide_real @ B @ C2 ) )
% 5.31/5.59 => ( ( dvd_dvd_real @ C2 @ A )
% 5.31/5.59 => ( ( dvd_dvd_real @ C2 @ B )
% 5.31/5.59 => ( A = B ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % dvd_div_eq_cancel
% 5.31/5.59 thf(fact_5334_dvd__div__eq__cancel,axiom,
% 5.31/5.59 ! [A: rat,C2: rat,B: rat] :
% 5.31/5.59 ( ( ( divide_divide_rat @ A @ C2 )
% 5.31/5.59 = ( divide_divide_rat @ B @ C2 ) )
% 5.31/5.59 => ( ( dvd_dvd_rat @ C2 @ A )
% 5.31/5.59 => ( ( dvd_dvd_rat @ C2 @ B )
% 5.31/5.59 => ( A = B ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % dvd_div_eq_cancel
% 5.31/5.59 thf(fact_5335_dvd__div__eq__cancel,axiom,
% 5.31/5.59 ! [A: nat,C2: nat,B: nat] :
% 5.31/5.59 ( ( ( divide_divide_nat @ A @ C2 )
% 5.31/5.59 = ( divide_divide_nat @ B @ C2 ) )
% 5.31/5.59 => ( ( dvd_dvd_nat @ C2 @ A )
% 5.31/5.59 => ( ( dvd_dvd_nat @ C2 @ B )
% 5.31/5.59 => ( A = B ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % dvd_div_eq_cancel
% 5.31/5.59 thf(fact_5336_dvd__div__eq__cancel,axiom,
% 5.31/5.59 ! [A: int,C2: int,B: int] :
% 5.31/5.59 ( ( ( divide_divide_int @ A @ C2 )
% 5.31/5.59 = ( divide_divide_int @ B @ C2 ) )
% 5.31/5.59 => ( ( dvd_dvd_int @ C2 @ A )
% 5.31/5.59 => ( ( dvd_dvd_int @ C2 @ B )
% 5.31/5.59 => ( A = B ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % dvd_div_eq_cancel
% 5.31/5.59 thf(fact_5337_dvd__div__eq__iff,axiom,
% 5.31/5.59 ! [C2: complex,A: complex,B: complex] :
% 5.31/5.59 ( ( dvd_dvd_complex @ C2 @ A )
% 5.31/5.59 => ( ( dvd_dvd_complex @ C2 @ B )
% 5.31/5.59 => ( ( ( divide1717551699836669952omplex @ A @ C2 )
% 5.31/5.59 = ( divide1717551699836669952omplex @ B @ C2 ) )
% 5.31/5.59 = ( A = B ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % dvd_div_eq_iff
% 5.31/5.59 thf(fact_5338_dvd__div__eq__iff,axiom,
% 5.31/5.59 ! [C2: real,A: real,B: real] :
% 5.31/5.59 ( ( dvd_dvd_real @ C2 @ A )
% 5.31/5.59 => ( ( dvd_dvd_real @ C2 @ B )
% 5.31/5.59 => ( ( ( divide_divide_real @ A @ C2 )
% 5.31/5.59 = ( divide_divide_real @ B @ C2 ) )
% 5.31/5.59 = ( A = B ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % dvd_div_eq_iff
% 5.31/5.59 thf(fact_5339_dvd__div__eq__iff,axiom,
% 5.31/5.59 ! [C2: rat,A: rat,B: rat] :
% 5.31/5.59 ( ( dvd_dvd_rat @ C2 @ A )
% 5.31/5.59 => ( ( dvd_dvd_rat @ C2 @ B )
% 5.31/5.59 => ( ( ( divide_divide_rat @ A @ C2 )
% 5.31/5.59 = ( divide_divide_rat @ B @ C2 ) )
% 5.31/5.59 = ( A = B ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % dvd_div_eq_iff
% 5.31/5.59 thf(fact_5340_dvd__div__eq__iff,axiom,
% 5.31/5.59 ! [C2: nat,A: nat,B: nat] :
% 5.31/5.59 ( ( dvd_dvd_nat @ C2 @ A )
% 5.31/5.59 => ( ( dvd_dvd_nat @ C2 @ B )
% 5.31/5.59 => ( ( ( divide_divide_nat @ A @ C2 )
% 5.31/5.59 = ( divide_divide_nat @ B @ C2 ) )
% 5.31/5.59 = ( A = B ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % dvd_div_eq_iff
% 5.31/5.59 thf(fact_5341_dvd__div__eq__iff,axiom,
% 5.31/5.59 ! [C2: int,A: int,B: int] :
% 5.31/5.59 ( ( dvd_dvd_int @ C2 @ A )
% 5.31/5.59 => ( ( dvd_dvd_int @ C2 @ B )
% 5.31/5.59 => ( ( ( divide_divide_int @ A @ C2 )
% 5.31/5.59 = ( divide_divide_int @ B @ C2 ) )
% 5.31/5.59 = ( A = B ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % dvd_div_eq_iff
% 5.31/5.59 thf(fact_5342_gcd__nat_Oextremum,axiom,
% 5.31/5.59 ! [A: nat] : ( dvd_dvd_nat @ A @ zero_zero_nat ) ).
% 5.31/5.59
% 5.31/5.59 % gcd_nat.extremum
% 5.31/5.59 thf(fact_5343_gcd__nat_Oextremum__strict,axiom,
% 5.31/5.59 ! [A: nat] :
% 5.31/5.59 ~ ( ( dvd_dvd_nat @ zero_zero_nat @ A )
% 5.31/5.59 & ( zero_zero_nat != A ) ) ).
% 5.31/5.59
% 5.31/5.59 % gcd_nat.extremum_strict
% 5.31/5.59 thf(fact_5344_gcd__nat_Oextremum__unique,axiom,
% 5.31/5.59 ! [A: nat] :
% 5.31/5.59 ( ( dvd_dvd_nat @ zero_zero_nat @ A )
% 5.31/5.59 = ( A = zero_zero_nat ) ) ).
% 5.31/5.59
% 5.31/5.59 % gcd_nat.extremum_unique
% 5.31/5.59 thf(fact_5345_gcd__nat_Onot__eq__extremum,axiom,
% 5.31/5.59 ! [A: nat] :
% 5.31/5.59 ( ( A != zero_zero_nat )
% 5.31/5.59 = ( ( dvd_dvd_nat @ A @ zero_zero_nat )
% 5.31/5.59 & ( A != zero_zero_nat ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % gcd_nat.not_eq_extremum
% 5.31/5.59 thf(fact_5346_gcd__nat_Oextremum__uniqueI,axiom,
% 5.31/5.59 ! [A: nat] :
% 5.31/5.59 ( ( dvd_dvd_nat @ zero_zero_nat @ A )
% 5.31/5.59 => ( A = zero_zero_nat ) ) ).
% 5.31/5.59
% 5.31/5.59 % gcd_nat.extremum_uniqueI
% 5.31/5.59 thf(fact_5347_dvd__mod__imp__dvd,axiom,
% 5.31/5.59 ! [C2: nat,A: nat,B: nat] :
% 5.31/5.59 ( ( dvd_dvd_nat @ C2 @ ( modulo_modulo_nat @ A @ B ) )
% 5.31/5.59 => ( ( dvd_dvd_nat @ C2 @ B )
% 5.31/5.59 => ( dvd_dvd_nat @ C2 @ A ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % dvd_mod_imp_dvd
% 5.31/5.59 thf(fact_5348_dvd__mod__imp__dvd,axiom,
% 5.31/5.59 ! [C2: int,A: int,B: int] :
% 5.31/5.59 ( ( dvd_dvd_int @ C2 @ ( modulo_modulo_int @ A @ B ) )
% 5.31/5.59 => ( ( dvd_dvd_int @ C2 @ B )
% 5.31/5.59 => ( dvd_dvd_int @ C2 @ A ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % dvd_mod_imp_dvd
% 5.31/5.59 thf(fact_5349_dvd__mod__imp__dvd,axiom,
% 5.31/5.59 ! [C2: code_natural,A: code_natural,B: code_natural] :
% 5.31/5.59 ( ( dvd_dvd_Code_natural @ C2 @ ( modulo8411746178871703098atural @ A @ B ) )
% 5.31/5.59 => ( ( dvd_dvd_Code_natural @ C2 @ B )
% 5.31/5.59 => ( dvd_dvd_Code_natural @ C2 @ A ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % dvd_mod_imp_dvd
% 5.31/5.59 thf(fact_5350_dvd__mod__iff,axiom,
% 5.31/5.59 ! [C2: nat,B: nat,A: nat] :
% 5.31/5.59 ( ( dvd_dvd_nat @ C2 @ B )
% 5.31/5.59 => ( ( dvd_dvd_nat @ C2 @ ( modulo_modulo_nat @ A @ B ) )
% 5.31/5.59 = ( dvd_dvd_nat @ C2 @ A ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % dvd_mod_iff
% 5.31/5.59 thf(fact_5351_dvd__mod__iff,axiom,
% 5.31/5.59 ! [C2: int,B: int,A: int] :
% 5.31/5.59 ( ( dvd_dvd_int @ C2 @ B )
% 5.31/5.59 => ( ( dvd_dvd_int @ C2 @ ( modulo_modulo_int @ A @ B ) )
% 5.31/5.59 = ( dvd_dvd_int @ C2 @ A ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % dvd_mod_iff
% 5.31/5.59 thf(fact_5352_dvd__mod__iff,axiom,
% 5.31/5.59 ! [C2: code_natural,B: code_natural,A: code_natural] :
% 5.31/5.59 ( ( dvd_dvd_Code_natural @ C2 @ B )
% 5.31/5.59 => ( ( dvd_dvd_Code_natural @ C2 @ ( modulo8411746178871703098atural @ A @ B ) )
% 5.31/5.59 = ( dvd_dvd_Code_natural @ C2 @ A ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % dvd_mod_iff
% 5.31/5.59 thf(fact_5353_sum__nonneg,axiom,
% 5.31/5.59 ! [A4: set_complex,F2: complex > real] :
% 5.31/5.59 ( ! [X3: complex] :
% 5.31/5.59 ( ( member_complex @ X3 @ A4 )
% 5.31/5.59 => ( ord_less_eq_real @ zero_zero_real @ ( F2 @ X3 ) ) )
% 5.31/5.59 => ( ord_less_eq_real @ zero_zero_real @ ( groups5808333547571424918x_real @ F2 @ A4 ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum_nonneg
% 5.31/5.59 thf(fact_5354_sum__nonneg,axiom,
% 5.31/5.59 ! [A4: set_real,F2: real > real] :
% 5.31/5.59 ( ! [X3: real] :
% 5.31/5.59 ( ( member_real @ X3 @ A4 )
% 5.31/5.59 => ( ord_less_eq_real @ zero_zero_real @ ( F2 @ X3 ) ) )
% 5.31/5.59 => ( ord_less_eq_real @ zero_zero_real @ ( groups8097168146408367636l_real @ F2 @ A4 ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum_nonneg
% 5.31/5.59 thf(fact_5355_sum__nonneg,axiom,
% 5.31/5.59 ! [A4: set_int,F2: int > real] :
% 5.31/5.59 ( ! [X3: int] :
% 5.31/5.59 ( ( member_int @ X3 @ A4 )
% 5.31/5.59 => ( ord_less_eq_real @ zero_zero_real @ ( F2 @ X3 ) ) )
% 5.31/5.59 => ( ord_less_eq_real @ zero_zero_real @ ( groups8778361861064173332t_real @ F2 @ A4 ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum_nonneg
% 5.31/5.59 thf(fact_5356_sum__nonneg,axiom,
% 5.31/5.59 ! [A4: set_complex,F2: complex > rat] :
% 5.31/5.59 ( ! [X3: complex] :
% 5.31/5.59 ( ( member_complex @ X3 @ A4 )
% 5.31/5.59 => ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ X3 ) ) )
% 5.31/5.59 => ( ord_less_eq_rat @ zero_zero_rat @ ( groups5058264527183730370ex_rat @ F2 @ A4 ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum_nonneg
% 5.31/5.59 thf(fact_5357_sum__nonneg,axiom,
% 5.31/5.59 ! [A4: set_real,F2: real > rat] :
% 5.31/5.59 ( ! [X3: real] :
% 5.31/5.59 ( ( member_real @ X3 @ A4 )
% 5.31/5.59 => ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ X3 ) ) )
% 5.31/5.59 => ( ord_less_eq_rat @ zero_zero_rat @ ( groups1300246762558778688al_rat @ F2 @ A4 ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum_nonneg
% 5.31/5.59 thf(fact_5358_sum__nonneg,axiom,
% 5.31/5.59 ! [A4: set_nat,F2: nat > rat] :
% 5.31/5.59 ( ! [X3: nat] :
% 5.31/5.59 ( ( member_nat @ X3 @ A4 )
% 5.31/5.59 => ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ X3 ) ) )
% 5.31/5.59 => ( ord_less_eq_rat @ zero_zero_rat @ ( groups2906978787729119204at_rat @ F2 @ A4 ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum_nonneg
% 5.31/5.59 thf(fact_5359_sum__nonneg,axiom,
% 5.31/5.59 ! [A4: set_int,F2: int > rat] :
% 5.31/5.59 ( ! [X3: int] :
% 5.31/5.59 ( ( member_int @ X3 @ A4 )
% 5.31/5.59 => ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ X3 ) ) )
% 5.31/5.59 => ( ord_less_eq_rat @ zero_zero_rat @ ( groups3906332499630173760nt_rat @ F2 @ A4 ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum_nonneg
% 5.31/5.59 thf(fact_5360_sum__nonneg,axiom,
% 5.31/5.59 ! [A4: set_complex,F2: complex > nat] :
% 5.31/5.59 ( ! [X3: complex] :
% 5.31/5.59 ( ( member_complex @ X3 @ A4 )
% 5.31/5.59 => ( ord_less_eq_nat @ zero_zero_nat @ ( F2 @ X3 ) ) )
% 5.31/5.59 => ( ord_less_eq_nat @ zero_zero_nat @ ( groups5693394587270226106ex_nat @ F2 @ A4 ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum_nonneg
% 5.31/5.59 thf(fact_5361_sum__nonneg,axiom,
% 5.31/5.59 ! [A4: set_real,F2: real > nat] :
% 5.31/5.59 ( ! [X3: real] :
% 5.31/5.59 ( ( member_real @ X3 @ A4 )
% 5.31/5.59 => ( ord_less_eq_nat @ zero_zero_nat @ ( F2 @ X3 ) ) )
% 5.31/5.59 => ( ord_less_eq_nat @ zero_zero_nat @ ( groups1935376822645274424al_nat @ F2 @ A4 ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum_nonneg
% 5.31/5.59 thf(fact_5362_sum__nonneg,axiom,
% 5.31/5.59 ! [A4: set_int,F2: int > nat] :
% 5.31/5.59 ( ! [X3: int] :
% 5.31/5.59 ( ( member_int @ X3 @ A4 )
% 5.31/5.59 => ( ord_less_eq_nat @ zero_zero_nat @ ( F2 @ X3 ) ) )
% 5.31/5.59 => ( ord_less_eq_nat @ zero_zero_nat @ ( groups4541462559716669496nt_nat @ F2 @ A4 ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum_nonneg
% 5.31/5.59 thf(fact_5363_sum__nonpos,axiom,
% 5.31/5.59 ! [A4: set_complex,F2: complex > real] :
% 5.31/5.59 ( ! [X3: complex] :
% 5.31/5.59 ( ( member_complex @ X3 @ A4 )
% 5.31/5.59 => ( ord_less_eq_real @ ( F2 @ X3 ) @ zero_zero_real ) )
% 5.31/5.59 => ( ord_less_eq_real @ ( groups5808333547571424918x_real @ F2 @ A4 ) @ zero_zero_real ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum_nonpos
% 5.31/5.59 thf(fact_5364_sum__nonpos,axiom,
% 5.31/5.59 ! [A4: set_real,F2: real > real] :
% 5.31/5.59 ( ! [X3: real] :
% 5.31/5.59 ( ( member_real @ X3 @ A4 )
% 5.31/5.59 => ( ord_less_eq_real @ ( F2 @ X3 ) @ zero_zero_real ) )
% 5.31/5.59 => ( ord_less_eq_real @ ( groups8097168146408367636l_real @ F2 @ A4 ) @ zero_zero_real ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum_nonpos
% 5.31/5.59 thf(fact_5365_sum__nonpos,axiom,
% 5.31/5.59 ! [A4: set_int,F2: int > real] :
% 5.31/5.59 ( ! [X3: int] :
% 5.31/5.59 ( ( member_int @ X3 @ A4 )
% 5.31/5.59 => ( ord_less_eq_real @ ( F2 @ X3 ) @ zero_zero_real ) )
% 5.31/5.59 => ( ord_less_eq_real @ ( groups8778361861064173332t_real @ F2 @ A4 ) @ zero_zero_real ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum_nonpos
% 5.31/5.59 thf(fact_5366_sum__nonpos,axiom,
% 5.31/5.59 ! [A4: set_complex,F2: complex > rat] :
% 5.31/5.59 ( ! [X3: complex] :
% 5.31/5.59 ( ( member_complex @ X3 @ A4 )
% 5.31/5.59 => ( ord_less_eq_rat @ ( F2 @ X3 ) @ zero_zero_rat ) )
% 5.31/5.59 => ( ord_less_eq_rat @ ( groups5058264527183730370ex_rat @ F2 @ A4 ) @ zero_zero_rat ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum_nonpos
% 5.31/5.59 thf(fact_5367_sum__nonpos,axiom,
% 5.31/5.59 ! [A4: set_real,F2: real > rat] :
% 5.31/5.59 ( ! [X3: real] :
% 5.31/5.59 ( ( member_real @ X3 @ A4 )
% 5.31/5.59 => ( ord_less_eq_rat @ ( F2 @ X3 ) @ zero_zero_rat ) )
% 5.31/5.59 => ( ord_less_eq_rat @ ( groups1300246762558778688al_rat @ F2 @ A4 ) @ zero_zero_rat ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum_nonpos
% 5.31/5.59 thf(fact_5368_sum__nonpos,axiom,
% 5.31/5.59 ! [A4: set_nat,F2: nat > rat] :
% 5.31/5.59 ( ! [X3: nat] :
% 5.31/5.59 ( ( member_nat @ X3 @ A4 )
% 5.31/5.59 => ( ord_less_eq_rat @ ( F2 @ X3 ) @ zero_zero_rat ) )
% 5.31/5.59 => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F2 @ A4 ) @ zero_zero_rat ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum_nonpos
% 5.31/5.59 thf(fact_5369_sum__nonpos,axiom,
% 5.31/5.59 ! [A4: set_int,F2: int > rat] :
% 5.31/5.59 ( ! [X3: int] :
% 5.31/5.59 ( ( member_int @ X3 @ A4 )
% 5.31/5.59 => ( ord_less_eq_rat @ ( F2 @ X3 ) @ zero_zero_rat ) )
% 5.31/5.59 => ( ord_less_eq_rat @ ( groups3906332499630173760nt_rat @ F2 @ A4 ) @ zero_zero_rat ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum_nonpos
% 5.31/5.59 thf(fact_5370_sum__nonpos,axiom,
% 5.31/5.59 ! [A4: set_complex,F2: complex > nat] :
% 5.31/5.59 ( ! [X3: complex] :
% 5.31/5.59 ( ( member_complex @ X3 @ A4 )
% 5.31/5.59 => ( ord_less_eq_nat @ ( F2 @ X3 ) @ zero_zero_nat ) )
% 5.31/5.59 => ( ord_less_eq_nat @ ( groups5693394587270226106ex_nat @ F2 @ A4 ) @ zero_zero_nat ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum_nonpos
% 5.31/5.59 thf(fact_5371_sum__nonpos,axiom,
% 5.31/5.59 ! [A4: set_real,F2: real > nat] :
% 5.31/5.59 ( ! [X3: real] :
% 5.31/5.59 ( ( member_real @ X3 @ A4 )
% 5.31/5.59 => ( ord_less_eq_nat @ ( F2 @ X3 ) @ zero_zero_nat ) )
% 5.31/5.59 => ( ord_less_eq_nat @ ( groups1935376822645274424al_nat @ F2 @ A4 ) @ zero_zero_nat ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum_nonpos
% 5.31/5.59 thf(fact_5372_sum__nonpos,axiom,
% 5.31/5.59 ! [A4: set_int,F2: int > nat] :
% 5.31/5.59 ( ! [X3: int] :
% 5.31/5.59 ( ( member_int @ X3 @ A4 )
% 5.31/5.59 => ( ord_less_eq_nat @ ( F2 @ X3 ) @ zero_zero_nat ) )
% 5.31/5.59 => ( ord_less_eq_nat @ ( groups4541462559716669496nt_nat @ F2 @ A4 ) @ zero_zero_nat ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum_nonpos
% 5.31/5.59 thf(fact_5373_dvd__diff__nat,axiom,
% 5.31/5.59 ! [K2: nat,M2: nat,N: nat] :
% 5.31/5.59 ( ( dvd_dvd_nat @ K2 @ M2 )
% 5.31/5.59 => ( ( dvd_dvd_nat @ K2 @ N )
% 5.31/5.59 => ( dvd_dvd_nat @ K2 @ ( minus_minus_nat @ M2 @ N ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % dvd_diff_nat
% 5.31/5.59 thf(fact_5374_sum__mono__inv,axiom,
% 5.31/5.59 ! [F2: real > rat,I5: set_real,G2: real > rat,I2: real] :
% 5.31/5.59 ( ( ( groups1300246762558778688al_rat @ F2 @ I5 )
% 5.31/5.59 = ( groups1300246762558778688al_rat @ G2 @ I5 ) )
% 5.31/5.59 => ( ! [I3: real] :
% 5.31/5.59 ( ( member_real @ I3 @ I5 )
% 5.31/5.59 => ( ord_less_eq_rat @ ( F2 @ I3 ) @ ( G2 @ I3 ) ) )
% 5.31/5.59 => ( ( member_real @ I2 @ I5 )
% 5.31/5.59 => ( ( finite_finite_real @ I5 )
% 5.31/5.59 => ( ( F2 @ I2 )
% 5.31/5.59 = ( G2 @ I2 ) ) ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum_mono_inv
% 5.31/5.59 thf(fact_5375_sum__mono__inv,axiom,
% 5.31/5.59 ! [F2: nat > rat,I5: set_nat,G2: nat > rat,I2: nat] :
% 5.31/5.59 ( ( ( groups2906978787729119204at_rat @ F2 @ I5 )
% 5.31/5.59 = ( groups2906978787729119204at_rat @ G2 @ I5 ) )
% 5.31/5.59 => ( ! [I3: nat] :
% 5.31/5.59 ( ( member_nat @ I3 @ I5 )
% 5.31/5.59 => ( ord_less_eq_rat @ ( F2 @ I3 ) @ ( G2 @ I3 ) ) )
% 5.31/5.59 => ( ( member_nat @ I2 @ I5 )
% 5.31/5.59 => ( ( finite_finite_nat @ I5 )
% 5.31/5.59 => ( ( F2 @ I2 )
% 5.31/5.59 = ( G2 @ I2 ) ) ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum_mono_inv
% 5.31/5.59 thf(fact_5376_sum__mono__inv,axiom,
% 5.31/5.59 ! [F2: int > rat,I5: set_int,G2: int > rat,I2: int] :
% 5.31/5.59 ( ( ( groups3906332499630173760nt_rat @ F2 @ I5 )
% 5.31/5.59 = ( groups3906332499630173760nt_rat @ G2 @ I5 ) )
% 5.31/5.59 => ( ! [I3: int] :
% 5.31/5.59 ( ( member_int @ I3 @ I5 )
% 5.31/5.59 => ( ord_less_eq_rat @ ( F2 @ I3 ) @ ( G2 @ I3 ) ) )
% 5.31/5.59 => ( ( member_int @ I2 @ I5 )
% 5.31/5.59 => ( ( finite_finite_int @ I5 )
% 5.31/5.59 => ( ( F2 @ I2 )
% 5.31/5.59 = ( G2 @ I2 ) ) ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum_mono_inv
% 5.31/5.59 thf(fact_5377_sum__mono__inv,axiom,
% 5.31/5.59 ! [F2: complex > rat,I5: set_complex,G2: complex > rat,I2: complex] :
% 5.31/5.59 ( ( ( groups5058264527183730370ex_rat @ F2 @ I5 )
% 5.31/5.59 = ( groups5058264527183730370ex_rat @ G2 @ I5 ) )
% 5.31/5.59 => ( ! [I3: complex] :
% 5.31/5.59 ( ( member_complex @ I3 @ I5 )
% 5.31/5.59 => ( ord_less_eq_rat @ ( F2 @ I3 ) @ ( G2 @ I3 ) ) )
% 5.31/5.59 => ( ( member_complex @ I2 @ I5 )
% 5.31/5.59 => ( ( finite3207457112153483333omplex @ I5 )
% 5.31/5.59 => ( ( F2 @ I2 )
% 5.31/5.59 = ( G2 @ I2 ) ) ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum_mono_inv
% 5.31/5.59 thf(fact_5378_sum__mono__inv,axiom,
% 5.31/5.59 ! [F2: real > nat,I5: set_real,G2: real > nat,I2: real] :
% 5.31/5.59 ( ( ( groups1935376822645274424al_nat @ F2 @ I5 )
% 5.31/5.59 = ( groups1935376822645274424al_nat @ G2 @ I5 ) )
% 5.31/5.59 => ( ! [I3: real] :
% 5.31/5.59 ( ( member_real @ I3 @ I5 )
% 5.31/5.59 => ( ord_less_eq_nat @ ( F2 @ I3 ) @ ( G2 @ I3 ) ) )
% 5.31/5.59 => ( ( member_real @ I2 @ I5 )
% 5.31/5.59 => ( ( finite_finite_real @ I5 )
% 5.31/5.59 => ( ( F2 @ I2 )
% 5.31/5.59 = ( G2 @ I2 ) ) ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum_mono_inv
% 5.31/5.59 thf(fact_5379_sum__mono__inv,axiom,
% 5.31/5.59 ! [F2: int > nat,I5: set_int,G2: int > nat,I2: int] :
% 5.31/5.59 ( ( ( groups4541462559716669496nt_nat @ F2 @ I5 )
% 5.31/5.59 = ( groups4541462559716669496nt_nat @ G2 @ I5 ) )
% 5.31/5.59 => ( ! [I3: int] :
% 5.31/5.59 ( ( member_int @ I3 @ I5 )
% 5.31/5.59 => ( ord_less_eq_nat @ ( F2 @ I3 ) @ ( G2 @ I3 ) ) )
% 5.31/5.59 => ( ( member_int @ I2 @ I5 )
% 5.31/5.59 => ( ( finite_finite_int @ I5 )
% 5.31/5.59 => ( ( F2 @ I2 )
% 5.31/5.59 = ( G2 @ I2 ) ) ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum_mono_inv
% 5.31/5.59 thf(fact_5380_sum__mono__inv,axiom,
% 5.31/5.59 ! [F2: complex > nat,I5: set_complex,G2: complex > nat,I2: complex] :
% 5.31/5.59 ( ( ( groups5693394587270226106ex_nat @ F2 @ I5 )
% 5.31/5.59 = ( groups5693394587270226106ex_nat @ G2 @ I5 ) )
% 5.31/5.59 => ( ! [I3: complex] :
% 5.31/5.59 ( ( member_complex @ I3 @ I5 )
% 5.31/5.59 => ( ord_less_eq_nat @ ( F2 @ I3 ) @ ( G2 @ I3 ) ) )
% 5.31/5.59 => ( ( member_complex @ I2 @ I5 )
% 5.31/5.59 => ( ( finite3207457112153483333omplex @ I5 )
% 5.31/5.59 => ( ( F2 @ I2 )
% 5.31/5.59 = ( G2 @ I2 ) ) ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum_mono_inv
% 5.31/5.59 thf(fact_5381_sum__mono__inv,axiom,
% 5.31/5.59 ! [F2: real > int,I5: set_real,G2: real > int,I2: real] :
% 5.31/5.59 ( ( ( groups1932886352136224148al_int @ F2 @ I5 )
% 5.31/5.59 = ( groups1932886352136224148al_int @ G2 @ I5 ) )
% 5.31/5.59 => ( ! [I3: real] :
% 5.31/5.59 ( ( member_real @ I3 @ I5 )
% 5.31/5.59 => ( ord_less_eq_int @ ( F2 @ I3 ) @ ( G2 @ I3 ) ) )
% 5.31/5.59 => ( ( member_real @ I2 @ I5 )
% 5.31/5.59 => ( ( finite_finite_real @ I5 )
% 5.31/5.59 => ( ( F2 @ I2 )
% 5.31/5.59 = ( G2 @ I2 ) ) ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum_mono_inv
% 5.31/5.59 thf(fact_5382_sum__mono__inv,axiom,
% 5.31/5.59 ! [F2: nat > int,I5: set_nat,G2: nat > int,I2: nat] :
% 5.31/5.59 ( ( ( groups3539618377306564664at_int @ F2 @ I5 )
% 5.31/5.59 = ( groups3539618377306564664at_int @ G2 @ I5 ) )
% 5.31/5.59 => ( ! [I3: nat] :
% 5.31/5.59 ( ( member_nat @ I3 @ I5 )
% 5.31/5.59 => ( ord_less_eq_int @ ( F2 @ I3 ) @ ( G2 @ I3 ) ) )
% 5.31/5.59 => ( ( member_nat @ I2 @ I5 )
% 5.31/5.59 => ( ( finite_finite_nat @ I5 )
% 5.31/5.59 => ( ( F2 @ I2 )
% 5.31/5.59 = ( G2 @ I2 ) ) ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum_mono_inv
% 5.31/5.59 thf(fact_5383_sum__mono__inv,axiom,
% 5.31/5.59 ! [F2: complex > int,I5: set_complex,G2: complex > int,I2: complex] :
% 5.31/5.59 ( ( ( groups5690904116761175830ex_int @ F2 @ I5 )
% 5.31/5.59 = ( groups5690904116761175830ex_int @ G2 @ I5 ) )
% 5.31/5.59 => ( ! [I3: complex] :
% 5.31/5.59 ( ( member_complex @ I3 @ I5 )
% 5.31/5.59 => ( ord_less_eq_int @ ( F2 @ I3 ) @ ( G2 @ I3 ) ) )
% 5.31/5.59 => ( ( member_complex @ I2 @ I5 )
% 5.31/5.59 => ( ( finite3207457112153483333omplex @ I5 )
% 5.31/5.59 => ( ( F2 @ I2 )
% 5.31/5.59 = ( G2 @ I2 ) ) ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum_mono_inv
% 5.31/5.59 thf(fact_5384_sum__cong__Suc,axiom,
% 5.31/5.59 ! [A4: set_nat,F2: nat > nat,G2: nat > nat] :
% 5.31/5.59 ( ~ ( member_nat @ zero_zero_nat @ A4 )
% 5.31/5.59 => ( ! [X3: nat] :
% 5.31/5.59 ( ( member_nat @ ( suc @ X3 ) @ A4 )
% 5.31/5.59 => ( ( F2 @ ( suc @ X3 ) )
% 5.31/5.59 = ( G2 @ ( suc @ X3 ) ) ) )
% 5.31/5.59 => ( ( groups3542108847815614940at_nat @ F2 @ A4 )
% 5.31/5.59 = ( groups3542108847815614940at_nat @ G2 @ A4 ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum_cong_Suc
% 5.31/5.59 thf(fact_5385_sum__cong__Suc,axiom,
% 5.31/5.59 ! [A4: set_nat,F2: nat > real,G2: nat > real] :
% 5.31/5.59 ( ~ ( member_nat @ zero_zero_nat @ A4 )
% 5.31/5.59 => ( ! [X3: nat] :
% 5.31/5.59 ( ( member_nat @ ( suc @ X3 ) @ A4 )
% 5.31/5.59 => ( ( F2 @ ( suc @ X3 ) )
% 5.31/5.59 = ( G2 @ ( suc @ X3 ) ) ) )
% 5.31/5.59 => ( ( groups6591440286371151544t_real @ F2 @ A4 )
% 5.31/5.59 = ( groups6591440286371151544t_real @ G2 @ A4 ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum_cong_Suc
% 5.31/5.59 thf(fact_5386_sum_Ointer__filter,axiom,
% 5.31/5.59 ! [A4: set_real,G2: real > complex,P2: real > $o] :
% 5.31/5.59 ( ( finite_finite_real @ A4 )
% 5.31/5.59 => ( ( groups5754745047067104278omplex @ G2
% 5.31/5.59 @ ( collect_real
% 5.31/5.59 @ ^ [X4: real] :
% 5.31/5.59 ( ( member_real @ X4 @ A4 )
% 5.31/5.59 & ( P2 @ X4 ) ) ) )
% 5.31/5.59 = ( groups5754745047067104278omplex
% 5.31/5.59 @ ^ [X4: real] : ( if_complex @ ( P2 @ X4 ) @ ( G2 @ X4 ) @ zero_zero_complex )
% 5.31/5.59 @ A4 ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum.inter_filter
% 5.31/5.59 thf(fact_5387_sum_Ointer__filter,axiom,
% 5.31/5.59 ! [A4: set_nat,G2: nat > complex,P2: nat > $o] :
% 5.31/5.59 ( ( finite_finite_nat @ A4 )
% 5.31/5.59 => ( ( groups2073611262835488442omplex @ G2
% 5.31/5.59 @ ( collect_nat
% 5.31/5.59 @ ^ [X4: nat] :
% 5.31/5.59 ( ( member_nat @ X4 @ A4 )
% 5.31/5.59 & ( P2 @ X4 ) ) ) )
% 5.31/5.59 = ( groups2073611262835488442omplex
% 5.31/5.59 @ ^ [X4: nat] : ( if_complex @ ( P2 @ X4 ) @ ( G2 @ X4 ) @ zero_zero_complex )
% 5.31/5.59 @ A4 ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum.inter_filter
% 5.31/5.59 thf(fact_5388_sum_Ointer__filter,axiom,
% 5.31/5.59 ! [A4: set_int,G2: int > complex,P2: int > $o] :
% 5.31/5.59 ( ( finite_finite_int @ A4 )
% 5.31/5.59 => ( ( groups3049146728041665814omplex @ G2
% 5.31/5.59 @ ( collect_int
% 5.31/5.59 @ ^ [X4: int] :
% 5.31/5.59 ( ( member_int @ X4 @ A4 )
% 5.31/5.59 & ( P2 @ X4 ) ) ) )
% 5.31/5.59 = ( groups3049146728041665814omplex
% 5.31/5.59 @ ^ [X4: int] : ( if_complex @ ( P2 @ X4 ) @ ( G2 @ X4 ) @ zero_zero_complex )
% 5.31/5.59 @ A4 ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum.inter_filter
% 5.31/5.59 thf(fact_5389_sum_Ointer__filter,axiom,
% 5.31/5.59 ! [A4: set_complex,G2: complex > complex,P2: complex > $o] :
% 5.31/5.59 ( ( finite3207457112153483333omplex @ A4 )
% 5.31/5.59 => ( ( groups7754918857620584856omplex @ G2
% 5.31/5.59 @ ( collect_complex
% 5.31/5.59 @ ^ [X4: complex] :
% 5.31/5.59 ( ( member_complex @ X4 @ A4 )
% 5.31/5.59 & ( P2 @ X4 ) ) ) )
% 5.31/5.59 = ( groups7754918857620584856omplex
% 5.31/5.59 @ ^ [X4: complex] : ( if_complex @ ( P2 @ X4 ) @ ( G2 @ X4 ) @ zero_zero_complex )
% 5.31/5.59 @ A4 ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum.inter_filter
% 5.31/5.59 thf(fact_5390_sum_Ointer__filter,axiom,
% 5.31/5.59 ! [A4: set_real,G2: real > real,P2: real > $o] :
% 5.31/5.59 ( ( finite_finite_real @ A4 )
% 5.31/5.59 => ( ( groups8097168146408367636l_real @ G2
% 5.31/5.59 @ ( collect_real
% 5.31/5.59 @ ^ [X4: real] :
% 5.31/5.59 ( ( member_real @ X4 @ A4 )
% 5.31/5.59 & ( P2 @ X4 ) ) ) )
% 5.31/5.59 = ( groups8097168146408367636l_real
% 5.31/5.59 @ ^ [X4: real] : ( if_real @ ( P2 @ X4 ) @ ( G2 @ X4 ) @ zero_zero_real )
% 5.31/5.59 @ A4 ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum.inter_filter
% 5.31/5.59 thf(fact_5391_sum_Ointer__filter,axiom,
% 5.31/5.59 ! [A4: set_int,G2: int > real,P2: int > $o] :
% 5.31/5.59 ( ( finite_finite_int @ A4 )
% 5.31/5.59 => ( ( groups8778361861064173332t_real @ G2
% 5.31/5.59 @ ( collect_int
% 5.31/5.59 @ ^ [X4: int] :
% 5.31/5.59 ( ( member_int @ X4 @ A4 )
% 5.31/5.59 & ( P2 @ X4 ) ) ) )
% 5.31/5.59 = ( groups8778361861064173332t_real
% 5.31/5.59 @ ^ [X4: int] : ( if_real @ ( P2 @ X4 ) @ ( G2 @ X4 ) @ zero_zero_real )
% 5.31/5.59 @ A4 ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum.inter_filter
% 5.31/5.59 thf(fact_5392_sum_Ointer__filter,axiom,
% 5.31/5.59 ! [A4: set_complex,G2: complex > real,P2: complex > $o] :
% 5.31/5.59 ( ( finite3207457112153483333omplex @ A4 )
% 5.31/5.59 => ( ( groups5808333547571424918x_real @ G2
% 5.31/5.59 @ ( collect_complex
% 5.31/5.59 @ ^ [X4: complex] :
% 5.31/5.59 ( ( member_complex @ X4 @ A4 )
% 5.31/5.59 & ( P2 @ X4 ) ) ) )
% 5.31/5.59 = ( groups5808333547571424918x_real
% 5.31/5.59 @ ^ [X4: complex] : ( if_real @ ( P2 @ X4 ) @ ( G2 @ X4 ) @ zero_zero_real )
% 5.31/5.59 @ A4 ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum.inter_filter
% 5.31/5.59 thf(fact_5393_sum_Ointer__filter,axiom,
% 5.31/5.59 ! [A4: set_real,G2: real > rat,P2: real > $o] :
% 5.31/5.59 ( ( finite_finite_real @ A4 )
% 5.31/5.59 => ( ( groups1300246762558778688al_rat @ G2
% 5.31/5.59 @ ( collect_real
% 5.31/5.59 @ ^ [X4: real] :
% 5.31/5.59 ( ( member_real @ X4 @ A4 )
% 5.31/5.59 & ( P2 @ X4 ) ) ) )
% 5.31/5.59 = ( groups1300246762558778688al_rat
% 5.31/5.59 @ ^ [X4: real] : ( if_rat @ ( P2 @ X4 ) @ ( G2 @ X4 ) @ zero_zero_rat )
% 5.31/5.59 @ A4 ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum.inter_filter
% 5.31/5.59 thf(fact_5394_sum_Ointer__filter,axiom,
% 5.31/5.59 ! [A4: set_nat,G2: nat > rat,P2: nat > $o] :
% 5.31/5.59 ( ( finite_finite_nat @ A4 )
% 5.31/5.59 => ( ( groups2906978787729119204at_rat @ G2
% 5.31/5.59 @ ( collect_nat
% 5.31/5.59 @ ^ [X4: nat] :
% 5.31/5.59 ( ( member_nat @ X4 @ A4 )
% 5.31/5.59 & ( P2 @ X4 ) ) ) )
% 5.31/5.59 = ( groups2906978787729119204at_rat
% 5.31/5.59 @ ^ [X4: nat] : ( if_rat @ ( P2 @ X4 ) @ ( G2 @ X4 ) @ zero_zero_rat )
% 5.31/5.59 @ A4 ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum.inter_filter
% 5.31/5.59 thf(fact_5395_sum_Ointer__filter,axiom,
% 5.31/5.59 ! [A4: set_int,G2: int > rat,P2: int > $o] :
% 5.31/5.59 ( ( finite_finite_int @ A4 )
% 5.31/5.59 => ( ( groups3906332499630173760nt_rat @ G2
% 5.31/5.59 @ ( collect_int
% 5.31/5.59 @ ^ [X4: int] :
% 5.31/5.59 ( ( member_int @ X4 @ A4 )
% 5.31/5.59 & ( P2 @ X4 ) ) ) )
% 5.31/5.59 = ( groups3906332499630173760nt_rat
% 5.31/5.59 @ ^ [X4: int] : ( if_rat @ ( P2 @ X4 ) @ ( G2 @ X4 ) @ zero_zero_rat )
% 5.31/5.59 @ A4 ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum.inter_filter
% 5.31/5.59 thf(fact_5396_subset__divisors__dvd,axiom,
% 5.31/5.59 ! [A: complex,B: complex] :
% 5.31/5.59 ( ( ord_le211207098394363844omplex
% 5.31/5.59 @ ( collect_complex
% 5.31/5.59 @ ^ [C3: complex] : ( dvd_dvd_complex @ C3 @ A ) )
% 5.31/5.59 @ ( collect_complex
% 5.31/5.59 @ ^ [C3: complex] : ( dvd_dvd_complex @ C3 @ B ) ) )
% 5.31/5.59 = ( dvd_dvd_complex @ A @ B ) ) ).
% 5.31/5.59
% 5.31/5.59 % subset_divisors_dvd
% 5.31/5.59 thf(fact_5397_subset__divisors__dvd,axiom,
% 5.31/5.59 ! [A: real,B: real] :
% 5.31/5.59 ( ( ord_less_eq_set_real
% 5.31/5.59 @ ( collect_real
% 5.31/5.59 @ ^ [C3: real] : ( dvd_dvd_real @ C3 @ A ) )
% 5.31/5.59 @ ( collect_real
% 5.31/5.59 @ ^ [C3: real] : ( dvd_dvd_real @ C3 @ B ) ) )
% 5.31/5.59 = ( dvd_dvd_real @ A @ B ) ) ).
% 5.31/5.59
% 5.31/5.59 % subset_divisors_dvd
% 5.31/5.59 thf(fact_5398_subset__divisors__dvd,axiom,
% 5.31/5.59 ! [A: int,B: int] :
% 5.31/5.59 ( ( ord_less_eq_set_int
% 5.31/5.59 @ ( collect_int
% 5.31/5.59 @ ^ [C3: int] : ( dvd_dvd_int @ C3 @ A ) )
% 5.31/5.59 @ ( collect_int
% 5.31/5.59 @ ^ [C3: int] : ( dvd_dvd_int @ C3 @ B ) ) )
% 5.31/5.59 = ( dvd_dvd_int @ A @ B ) ) ).
% 5.31/5.59
% 5.31/5.59 % subset_divisors_dvd
% 5.31/5.59 thf(fact_5399_subset__divisors__dvd,axiom,
% 5.31/5.59 ! [A: nat,B: nat] :
% 5.31/5.59 ( ( ord_less_eq_set_nat
% 5.31/5.59 @ ( collect_nat
% 5.31/5.59 @ ^ [C3: nat] : ( dvd_dvd_nat @ C3 @ A ) )
% 5.31/5.59 @ ( collect_nat
% 5.31/5.59 @ ^ [C3: nat] : ( dvd_dvd_nat @ C3 @ B ) ) )
% 5.31/5.59 = ( dvd_dvd_nat @ A @ B ) ) ).
% 5.31/5.59
% 5.31/5.59 % subset_divisors_dvd
% 5.31/5.59 thf(fact_5400_strict__subset__divisors__dvd,axiom,
% 5.31/5.59 ! [A: complex,B: complex] :
% 5.31/5.59 ( ( ord_less_set_complex
% 5.31/5.59 @ ( collect_complex
% 5.31/5.59 @ ^ [C3: complex] : ( dvd_dvd_complex @ C3 @ A ) )
% 5.31/5.59 @ ( collect_complex
% 5.31/5.59 @ ^ [C3: complex] : ( dvd_dvd_complex @ C3 @ B ) ) )
% 5.31/5.59 = ( ( dvd_dvd_complex @ A @ B )
% 5.31/5.59 & ~ ( dvd_dvd_complex @ B @ A ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % strict_subset_divisors_dvd
% 5.31/5.59 thf(fact_5401_strict__subset__divisors__dvd,axiom,
% 5.31/5.59 ! [A: real,B: real] :
% 5.31/5.59 ( ( ord_less_set_real
% 5.31/5.59 @ ( collect_real
% 5.31/5.59 @ ^ [C3: real] : ( dvd_dvd_real @ C3 @ A ) )
% 5.31/5.59 @ ( collect_real
% 5.31/5.59 @ ^ [C3: real] : ( dvd_dvd_real @ C3 @ B ) ) )
% 5.31/5.59 = ( ( dvd_dvd_real @ A @ B )
% 5.31/5.59 & ~ ( dvd_dvd_real @ B @ A ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % strict_subset_divisors_dvd
% 5.31/5.59 thf(fact_5402_strict__subset__divisors__dvd,axiom,
% 5.31/5.59 ! [A: nat,B: nat] :
% 5.31/5.59 ( ( ord_less_set_nat
% 5.31/5.59 @ ( collect_nat
% 5.31/5.59 @ ^ [C3: nat] : ( dvd_dvd_nat @ C3 @ A ) )
% 5.31/5.59 @ ( collect_nat
% 5.31/5.59 @ ^ [C3: nat] : ( dvd_dvd_nat @ C3 @ B ) ) )
% 5.31/5.59 = ( ( dvd_dvd_nat @ A @ B )
% 5.31/5.59 & ~ ( dvd_dvd_nat @ B @ A ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % strict_subset_divisors_dvd
% 5.31/5.59 thf(fact_5403_strict__subset__divisors__dvd,axiom,
% 5.31/5.59 ! [A: int,B: int] :
% 5.31/5.59 ( ( ord_less_set_int
% 5.31/5.59 @ ( collect_int
% 5.31/5.59 @ ^ [C3: int] : ( dvd_dvd_int @ C3 @ A ) )
% 5.31/5.59 @ ( collect_int
% 5.31/5.59 @ ^ [C3: int] : ( dvd_dvd_int @ C3 @ B ) ) )
% 5.31/5.59 = ( ( dvd_dvd_int @ A @ B )
% 5.31/5.59 & ~ ( dvd_dvd_int @ B @ A ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % strict_subset_divisors_dvd
% 5.31/5.59 thf(fact_5404_sum__le__included,axiom,
% 5.31/5.59 ! [S2: set_int,T: set_int,G2: int > real,I2: int > int,F2: int > real] :
% 5.31/5.59 ( ( finite_finite_int @ S2 )
% 5.31/5.59 => ( ( finite_finite_int @ T )
% 5.31/5.59 => ( ! [X3: int] :
% 5.31/5.59 ( ( member_int @ X3 @ T )
% 5.31/5.59 => ( ord_less_eq_real @ zero_zero_real @ ( G2 @ X3 ) ) )
% 5.31/5.59 => ( ! [X3: int] :
% 5.31/5.59 ( ( member_int @ X3 @ S2 )
% 5.31/5.59 => ? [Xa: int] :
% 5.31/5.59 ( ( member_int @ Xa @ T )
% 5.31/5.59 & ( ( I2 @ Xa )
% 5.31/5.59 = X3 )
% 5.31/5.59 & ( ord_less_eq_real @ ( F2 @ X3 ) @ ( G2 @ Xa ) ) ) )
% 5.31/5.59 => ( ord_less_eq_real @ ( groups8778361861064173332t_real @ F2 @ S2 ) @ ( groups8778361861064173332t_real @ G2 @ T ) ) ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum_le_included
% 5.31/5.59 thf(fact_5405_sum__le__included,axiom,
% 5.31/5.59 ! [S2: set_int,T: set_complex,G2: complex > real,I2: complex > int,F2: int > real] :
% 5.31/5.59 ( ( finite_finite_int @ S2 )
% 5.31/5.59 => ( ( finite3207457112153483333omplex @ T )
% 5.31/5.59 => ( ! [X3: complex] :
% 5.31/5.59 ( ( member_complex @ X3 @ T )
% 5.31/5.59 => ( ord_less_eq_real @ zero_zero_real @ ( G2 @ X3 ) ) )
% 5.31/5.59 => ( ! [X3: int] :
% 5.31/5.59 ( ( member_int @ X3 @ S2 )
% 5.31/5.59 => ? [Xa: complex] :
% 5.31/5.59 ( ( member_complex @ Xa @ T )
% 5.31/5.59 & ( ( I2 @ Xa )
% 5.31/5.59 = X3 )
% 5.31/5.59 & ( ord_less_eq_real @ ( F2 @ X3 ) @ ( G2 @ Xa ) ) ) )
% 5.31/5.59 => ( ord_less_eq_real @ ( groups8778361861064173332t_real @ F2 @ S2 ) @ ( groups5808333547571424918x_real @ G2 @ T ) ) ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum_le_included
% 5.31/5.59 thf(fact_5406_sum__le__included,axiom,
% 5.31/5.59 ! [S2: set_complex,T: set_int,G2: int > real,I2: int > complex,F2: complex > real] :
% 5.31/5.59 ( ( finite3207457112153483333omplex @ S2 )
% 5.31/5.59 => ( ( finite_finite_int @ T )
% 5.31/5.59 => ( ! [X3: int] :
% 5.31/5.59 ( ( member_int @ X3 @ T )
% 5.31/5.59 => ( ord_less_eq_real @ zero_zero_real @ ( G2 @ X3 ) ) )
% 5.31/5.59 => ( ! [X3: complex] :
% 5.31/5.59 ( ( member_complex @ X3 @ S2 )
% 5.31/5.59 => ? [Xa: int] :
% 5.31/5.59 ( ( member_int @ Xa @ T )
% 5.31/5.59 & ( ( I2 @ Xa )
% 5.31/5.59 = X3 )
% 5.31/5.59 & ( ord_less_eq_real @ ( F2 @ X3 ) @ ( G2 @ Xa ) ) ) )
% 5.31/5.59 => ( ord_less_eq_real @ ( groups5808333547571424918x_real @ F2 @ S2 ) @ ( groups8778361861064173332t_real @ G2 @ T ) ) ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum_le_included
% 5.31/5.59 thf(fact_5407_sum__le__included,axiom,
% 5.31/5.59 ! [S2: set_complex,T: set_complex,G2: complex > real,I2: complex > complex,F2: complex > real] :
% 5.31/5.59 ( ( finite3207457112153483333omplex @ S2 )
% 5.31/5.59 => ( ( finite3207457112153483333omplex @ T )
% 5.31/5.59 => ( ! [X3: complex] :
% 5.31/5.59 ( ( member_complex @ X3 @ T )
% 5.31/5.59 => ( ord_less_eq_real @ zero_zero_real @ ( G2 @ X3 ) ) )
% 5.31/5.59 => ( ! [X3: complex] :
% 5.31/5.59 ( ( member_complex @ X3 @ S2 )
% 5.31/5.59 => ? [Xa: complex] :
% 5.31/5.59 ( ( member_complex @ Xa @ T )
% 5.31/5.59 & ( ( I2 @ Xa )
% 5.31/5.59 = X3 )
% 5.31/5.59 & ( ord_less_eq_real @ ( F2 @ X3 ) @ ( G2 @ Xa ) ) ) )
% 5.31/5.59 => ( ord_less_eq_real @ ( groups5808333547571424918x_real @ F2 @ S2 ) @ ( groups5808333547571424918x_real @ G2 @ T ) ) ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum_le_included
% 5.31/5.59 thf(fact_5408_sum__le__included,axiom,
% 5.31/5.59 ! [S2: set_nat,T: set_nat,G2: nat > rat,I2: nat > nat,F2: nat > rat] :
% 5.31/5.59 ( ( finite_finite_nat @ S2 )
% 5.31/5.59 => ( ( finite_finite_nat @ T )
% 5.31/5.59 => ( ! [X3: nat] :
% 5.31/5.59 ( ( member_nat @ X3 @ T )
% 5.31/5.59 => ( ord_less_eq_rat @ zero_zero_rat @ ( G2 @ X3 ) ) )
% 5.31/5.59 => ( ! [X3: nat] :
% 5.31/5.59 ( ( member_nat @ X3 @ S2 )
% 5.31/5.59 => ? [Xa: nat] :
% 5.31/5.59 ( ( member_nat @ Xa @ T )
% 5.31/5.59 & ( ( I2 @ Xa )
% 5.31/5.59 = X3 )
% 5.31/5.59 & ( ord_less_eq_rat @ ( F2 @ X3 ) @ ( G2 @ Xa ) ) ) )
% 5.31/5.59 => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F2 @ S2 ) @ ( groups2906978787729119204at_rat @ G2 @ T ) ) ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum_le_included
% 5.31/5.59 thf(fact_5409_sum__le__included,axiom,
% 5.31/5.59 ! [S2: set_nat,T: set_int,G2: int > rat,I2: int > nat,F2: nat > rat] :
% 5.31/5.59 ( ( finite_finite_nat @ S2 )
% 5.31/5.59 => ( ( finite_finite_int @ T )
% 5.31/5.59 => ( ! [X3: int] :
% 5.31/5.59 ( ( member_int @ X3 @ T )
% 5.31/5.59 => ( ord_less_eq_rat @ zero_zero_rat @ ( G2 @ X3 ) ) )
% 5.31/5.59 => ( ! [X3: nat] :
% 5.31/5.59 ( ( member_nat @ X3 @ S2 )
% 5.31/5.59 => ? [Xa: int] :
% 5.31/5.59 ( ( member_int @ Xa @ T )
% 5.31/5.59 & ( ( I2 @ Xa )
% 5.31/5.59 = X3 )
% 5.31/5.59 & ( ord_less_eq_rat @ ( F2 @ X3 ) @ ( G2 @ Xa ) ) ) )
% 5.31/5.59 => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F2 @ S2 ) @ ( groups3906332499630173760nt_rat @ G2 @ T ) ) ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum_le_included
% 5.31/5.59 thf(fact_5410_sum__le__included,axiom,
% 5.31/5.59 ! [S2: set_nat,T: set_complex,G2: complex > rat,I2: complex > nat,F2: nat > rat] :
% 5.31/5.59 ( ( finite_finite_nat @ S2 )
% 5.31/5.59 => ( ( finite3207457112153483333omplex @ T )
% 5.31/5.59 => ( ! [X3: complex] :
% 5.31/5.59 ( ( member_complex @ X3 @ T )
% 5.31/5.59 => ( ord_less_eq_rat @ zero_zero_rat @ ( G2 @ X3 ) ) )
% 5.31/5.59 => ( ! [X3: nat] :
% 5.31/5.59 ( ( member_nat @ X3 @ S2 )
% 5.31/5.59 => ? [Xa: complex] :
% 5.31/5.59 ( ( member_complex @ Xa @ T )
% 5.31/5.59 & ( ( I2 @ Xa )
% 5.31/5.59 = X3 )
% 5.31/5.59 & ( ord_less_eq_rat @ ( F2 @ X3 ) @ ( G2 @ Xa ) ) ) )
% 5.31/5.59 => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F2 @ S2 ) @ ( groups5058264527183730370ex_rat @ G2 @ T ) ) ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum_le_included
% 5.31/5.59 thf(fact_5411_sum__le__included,axiom,
% 5.31/5.59 ! [S2: set_int,T: set_nat,G2: nat > rat,I2: nat > int,F2: int > rat] :
% 5.31/5.59 ( ( finite_finite_int @ S2 )
% 5.31/5.59 => ( ( finite_finite_nat @ T )
% 5.31/5.59 => ( ! [X3: nat] :
% 5.31/5.59 ( ( member_nat @ X3 @ T )
% 5.31/5.59 => ( ord_less_eq_rat @ zero_zero_rat @ ( G2 @ X3 ) ) )
% 5.31/5.59 => ( ! [X3: int] :
% 5.31/5.59 ( ( member_int @ X3 @ S2 )
% 5.31/5.59 => ? [Xa: nat] :
% 5.31/5.59 ( ( member_nat @ Xa @ T )
% 5.31/5.59 & ( ( I2 @ Xa )
% 5.31/5.59 = X3 )
% 5.31/5.59 & ( ord_less_eq_rat @ ( F2 @ X3 ) @ ( G2 @ Xa ) ) ) )
% 5.31/5.59 => ( ord_less_eq_rat @ ( groups3906332499630173760nt_rat @ F2 @ S2 ) @ ( groups2906978787729119204at_rat @ G2 @ T ) ) ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum_le_included
% 5.31/5.59 thf(fact_5412_sum__le__included,axiom,
% 5.31/5.59 ! [S2: set_int,T: set_int,G2: int > rat,I2: int > int,F2: int > rat] :
% 5.31/5.59 ( ( finite_finite_int @ S2 )
% 5.31/5.59 => ( ( finite_finite_int @ T )
% 5.31/5.59 => ( ! [X3: int] :
% 5.31/5.59 ( ( member_int @ X3 @ T )
% 5.31/5.59 => ( ord_less_eq_rat @ zero_zero_rat @ ( G2 @ X3 ) ) )
% 5.31/5.59 => ( ! [X3: int] :
% 5.31/5.59 ( ( member_int @ X3 @ S2 )
% 5.31/5.59 => ? [Xa: int] :
% 5.31/5.59 ( ( member_int @ Xa @ T )
% 5.31/5.59 & ( ( I2 @ Xa )
% 5.31/5.59 = X3 )
% 5.31/5.59 & ( ord_less_eq_rat @ ( F2 @ X3 ) @ ( G2 @ Xa ) ) ) )
% 5.31/5.59 => ( ord_less_eq_rat @ ( groups3906332499630173760nt_rat @ F2 @ S2 ) @ ( groups3906332499630173760nt_rat @ G2 @ T ) ) ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum_le_included
% 5.31/5.59 thf(fact_5413_sum__le__included,axiom,
% 5.31/5.59 ! [S2: set_int,T: set_complex,G2: complex > rat,I2: complex > int,F2: int > rat] :
% 5.31/5.59 ( ( finite_finite_int @ S2 )
% 5.31/5.59 => ( ( finite3207457112153483333omplex @ T )
% 5.31/5.59 => ( ! [X3: complex] :
% 5.31/5.59 ( ( member_complex @ X3 @ T )
% 5.31/5.59 => ( ord_less_eq_rat @ zero_zero_rat @ ( G2 @ X3 ) ) )
% 5.31/5.59 => ( ! [X3: int] :
% 5.31/5.59 ( ( member_int @ X3 @ S2 )
% 5.31/5.59 => ? [Xa: complex] :
% 5.31/5.59 ( ( member_complex @ Xa @ T )
% 5.31/5.59 & ( ( I2 @ Xa )
% 5.31/5.59 = X3 )
% 5.31/5.59 & ( ord_less_eq_rat @ ( F2 @ X3 ) @ ( G2 @ Xa ) ) ) )
% 5.31/5.59 => ( ord_less_eq_rat @ ( groups3906332499630173760nt_rat @ F2 @ S2 ) @ ( groups5058264527183730370ex_rat @ G2 @ T ) ) ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum_le_included
% 5.31/5.59 thf(fact_5414_sum__nonneg__eq__0__iff,axiom,
% 5.31/5.59 ! [A4: set_real,F2: real > real] :
% 5.31/5.59 ( ( finite_finite_real @ A4 )
% 5.31/5.59 => ( ! [X3: real] :
% 5.31/5.59 ( ( member_real @ X3 @ A4 )
% 5.31/5.59 => ( ord_less_eq_real @ zero_zero_real @ ( F2 @ X3 ) ) )
% 5.31/5.59 => ( ( ( groups8097168146408367636l_real @ F2 @ A4 )
% 5.31/5.59 = zero_zero_real )
% 5.31/5.59 = ( ! [X4: real] :
% 5.31/5.59 ( ( member_real @ X4 @ A4 )
% 5.31/5.59 => ( ( F2 @ X4 )
% 5.31/5.59 = zero_zero_real ) ) ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum_nonneg_eq_0_iff
% 5.31/5.59 thf(fact_5415_sum__nonneg__eq__0__iff,axiom,
% 5.31/5.59 ! [A4: set_int,F2: int > real] :
% 5.31/5.59 ( ( finite_finite_int @ A4 )
% 5.31/5.59 => ( ! [X3: int] :
% 5.31/5.59 ( ( member_int @ X3 @ A4 )
% 5.31/5.59 => ( ord_less_eq_real @ zero_zero_real @ ( F2 @ X3 ) ) )
% 5.31/5.59 => ( ( ( groups8778361861064173332t_real @ F2 @ A4 )
% 5.31/5.59 = zero_zero_real )
% 5.31/5.59 = ( ! [X4: int] :
% 5.31/5.59 ( ( member_int @ X4 @ A4 )
% 5.31/5.59 => ( ( F2 @ X4 )
% 5.31/5.59 = zero_zero_real ) ) ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum_nonneg_eq_0_iff
% 5.31/5.59 thf(fact_5416_sum__nonneg__eq__0__iff,axiom,
% 5.31/5.59 ! [A4: set_complex,F2: complex > real] :
% 5.31/5.59 ( ( finite3207457112153483333omplex @ A4 )
% 5.31/5.59 => ( ! [X3: complex] :
% 5.31/5.59 ( ( member_complex @ X3 @ A4 )
% 5.31/5.59 => ( ord_less_eq_real @ zero_zero_real @ ( F2 @ X3 ) ) )
% 5.31/5.59 => ( ( ( groups5808333547571424918x_real @ F2 @ A4 )
% 5.31/5.59 = zero_zero_real )
% 5.31/5.59 = ( ! [X4: complex] :
% 5.31/5.59 ( ( member_complex @ X4 @ A4 )
% 5.31/5.59 => ( ( F2 @ X4 )
% 5.31/5.59 = zero_zero_real ) ) ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum_nonneg_eq_0_iff
% 5.31/5.59 thf(fact_5417_sum__nonneg__eq__0__iff,axiom,
% 5.31/5.59 ! [A4: set_real,F2: real > rat] :
% 5.31/5.59 ( ( finite_finite_real @ A4 )
% 5.31/5.59 => ( ! [X3: real] :
% 5.31/5.59 ( ( member_real @ X3 @ A4 )
% 5.31/5.59 => ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ X3 ) ) )
% 5.31/5.59 => ( ( ( groups1300246762558778688al_rat @ F2 @ A4 )
% 5.31/5.59 = zero_zero_rat )
% 5.31/5.59 = ( ! [X4: real] :
% 5.31/5.59 ( ( member_real @ X4 @ A4 )
% 5.31/5.59 => ( ( F2 @ X4 )
% 5.31/5.59 = zero_zero_rat ) ) ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum_nonneg_eq_0_iff
% 5.31/5.59 thf(fact_5418_sum__nonneg__eq__0__iff,axiom,
% 5.31/5.59 ! [A4: set_nat,F2: nat > rat] :
% 5.31/5.59 ( ( finite_finite_nat @ A4 )
% 5.31/5.59 => ( ! [X3: nat] :
% 5.31/5.59 ( ( member_nat @ X3 @ A4 )
% 5.31/5.59 => ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ X3 ) ) )
% 5.31/5.59 => ( ( ( groups2906978787729119204at_rat @ F2 @ A4 )
% 5.31/5.59 = zero_zero_rat )
% 5.31/5.59 = ( ! [X4: nat] :
% 5.31/5.59 ( ( member_nat @ X4 @ A4 )
% 5.31/5.59 => ( ( F2 @ X4 )
% 5.31/5.59 = zero_zero_rat ) ) ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum_nonneg_eq_0_iff
% 5.31/5.59 thf(fact_5419_sum__nonneg__eq__0__iff,axiom,
% 5.31/5.59 ! [A4: set_int,F2: int > rat] :
% 5.31/5.59 ( ( finite_finite_int @ A4 )
% 5.31/5.59 => ( ! [X3: int] :
% 5.31/5.59 ( ( member_int @ X3 @ A4 )
% 5.31/5.59 => ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ X3 ) ) )
% 5.31/5.59 => ( ( ( groups3906332499630173760nt_rat @ F2 @ A4 )
% 5.31/5.59 = zero_zero_rat )
% 5.31/5.59 = ( ! [X4: int] :
% 5.31/5.59 ( ( member_int @ X4 @ A4 )
% 5.31/5.59 => ( ( F2 @ X4 )
% 5.31/5.59 = zero_zero_rat ) ) ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum_nonneg_eq_0_iff
% 5.31/5.59 thf(fact_5420_sum__nonneg__eq__0__iff,axiom,
% 5.31/5.59 ! [A4: set_complex,F2: complex > rat] :
% 5.31/5.59 ( ( finite3207457112153483333omplex @ A4 )
% 5.31/5.59 => ( ! [X3: complex] :
% 5.31/5.59 ( ( member_complex @ X3 @ A4 )
% 5.31/5.59 => ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ X3 ) ) )
% 5.31/5.59 => ( ( ( groups5058264527183730370ex_rat @ F2 @ A4 )
% 5.31/5.59 = zero_zero_rat )
% 5.31/5.59 = ( ! [X4: complex] :
% 5.31/5.59 ( ( member_complex @ X4 @ A4 )
% 5.31/5.59 => ( ( F2 @ X4 )
% 5.31/5.59 = zero_zero_rat ) ) ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum_nonneg_eq_0_iff
% 5.31/5.59 thf(fact_5421_sum__nonneg__eq__0__iff,axiom,
% 5.31/5.59 ! [A4: set_real,F2: real > nat] :
% 5.31/5.59 ( ( finite_finite_real @ A4 )
% 5.31/5.59 => ( ! [X3: real] :
% 5.31/5.59 ( ( member_real @ X3 @ A4 )
% 5.31/5.59 => ( ord_less_eq_nat @ zero_zero_nat @ ( F2 @ X3 ) ) )
% 5.31/5.59 => ( ( ( groups1935376822645274424al_nat @ F2 @ A4 )
% 5.31/5.59 = zero_zero_nat )
% 5.31/5.59 = ( ! [X4: real] :
% 5.31/5.59 ( ( member_real @ X4 @ A4 )
% 5.31/5.59 => ( ( F2 @ X4 )
% 5.31/5.59 = zero_zero_nat ) ) ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum_nonneg_eq_0_iff
% 5.31/5.59 thf(fact_5422_sum__nonneg__eq__0__iff,axiom,
% 5.31/5.59 ! [A4: set_int,F2: int > nat] :
% 5.31/5.59 ( ( finite_finite_int @ A4 )
% 5.31/5.59 => ( ! [X3: int] :
% 5.31/5.59 ( ( member_int @ X3 @ A4 )
% 5.31/5.59 => ( ord_less_eq_nat @ zero_zero_nat @ ( F2 @ X3 ) ) )
% 5.31/5.59 => ( ( ( groups4541462559716669496nt_nat @ F2 @ A4 )
% 5.31/5.59 = zero_zero_nat )
% 5.31/5.59 = ( ! [X4: int] :
% 5.31/5.59 ( ( member_int @ X4 @ A4 )
% 5.31/5.59 => ( ( F2 @ X4 )
% 5.31/5.59 = zero_zero_nat ) ) ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum_nonneg_eq_0_iff
% 5.31/5.59 thf(fact_5423_sum__nonneg__eq__0__iff,axiom,
% 5.31/5.59 ! [A4: set_complex,F2: complex > nat] :
% 5.31/5.59 ( ( finite3207457112153483333omplex @ A4 )
% 5.31/5.59 => ( ! [X3: complex] :
% 5.31/5.59 ( ( member_complex @ X3 @ A4 )
% 5.31/5.59 => ( ord_less_eq_nat @ zero_zero_nat @ ( F2 @ X3 ) ) )
% 5.31/5.59 => ( ( ( groups5693394587270226106ex_nat @ F2 @ A4 )
% 5.31/5.59 = zero_zero_nat )
% 5.31/5.59 = ( ! [X4: complex] :
% 5.31/5.59 ( ( member_complex @ X4 @ A4 )
% 5.31/5.59 => ( ( F2 @ X4 )
% 5.31/5.59 = zero_zero_nat ) ) ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum_nonneg_eq_0_iff
% 5.31/5.59 thf(fact_5424_sum__strict__mono__ex1,axiom,
% 5.31/5.59 ! [A4: set_int,F2: int > real,G2: int > real] :
% 5.31/5.59 ( ( finite_finite_int @ A4 )
% 5.31/5.59 => ( ! [X3: int] :
% 5.31/5.59 ( ( member_int @ X3 @ A4 )
% 5.31/5.59 => ( ord_less_eq_real @ ( F2 @ X3 ) @ ( G2 @ X3 ) ) )
% 5.31/5.59 => ( ? [X5: int] :
% 5.31/5.59 ( ( member_int @ X5 @ A4 )
% 5.31/5.59 & ( ord_less_real @ ( F2 @ X5 ) @ ( G2 @ X5 ) ) )
% 5.31/5.59 => ( ord_less_real @ ( groups8778361861064173332t_real @ F2 @ A4 ) @ ( groups8778361861064173332t_real @ G2 @ A4 ) ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum_strict_mono_ex1
% 5.31/5.59 thf(fact_5425_sum__strict__mono__ex1,axiom,
% 5.31/5.59 ! [A4: set_complex,F2: complex > real,G2: complex > real] :
% 5.31/5.59 ( ( finite3207457112153483333omplex @ A4 )
% 5.31/5.59 => ( ! [X3: complex] :
% 5.31/5.59 ( ( member_complex @ X3 @ A4 )
% 5.31/5.59 => ( ord_less_eq_real @ ( F2 @ X3 ) @ ( G2 @ X3 ) ) )
% 5.31/5.59 => ( ? [X5: complex] :
% 5.31/5.59 ( ( member_complex @ X5 @ A4 )
% 5.31/5.59 & ( ord_less_real @ ( F2 @ X5 ) @ ( G2 @ X5 ) ) )
% 5.31/5.59 => ( ord_less_real @ ( groups5808333547571424918x_real @ F2 @ A4 ) @ ( groups5808333547571424918x_real @ G2 @ A4 ) ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum_strict_mono_ex1
% 5.31/5.59 thf(fact_5426_sum__strict__mono__ex1,axiom,
% 5.31/5.59 ! [A4: set_nat,F2: nat > rat,G2: nat > rat] :
% 5.31/5.59 ( ( finite_finite_nat @ A4 )
% 5.31/5.59 => ( ! [X3: nat] :
% 5.31/5.59 ( ( member_nat @ X3 @ A4 )
% 5.31/5.59 => ( ord_less_eq_rat @ ( F2 @ X3 ) @ ( G2 @ X3 ) ) )
% 5.31/5.59 => ( ? [X5: nat] :
% 5.31/5.59 ( ( member_nat @ X5 @ A4 )
% 5.31/5.59 & ( ord_less_rat @ ( F2 @ X5 ) @ ( G2 @ X5 ) ) )
% 5.31/5.59 => ( ord_less_rat @ ( groups2906978787729119204at_rat @ F2 @ A4 ) @ ( groups2906978787729119204at_rat @ G2 @ A4 ) ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum_strict_mono_ex1
% 5.31/5.59 thf(fact_5427_sum__strict__mono__ex1,axiom,
% 5.31/5.59 ! [A4: set_int,F2: int > rat,G2: int > rat] :
% 5.31/5.59 ( ( finite_finite_int @ A4 )
% 5.31/5.59 => ( ! [X3: int] :
% 5.31/5.59 ( ( member_int @ X3 @ A4 )
% 5.31/5.59 => ( ord_less_eq_rat @ ( F2 @ X3 ) @ ( G2 @ X3 ) ) )
% 5.31/5.59 => ( ? [X5: int] :
% 5.31/5.59 ( ( member_int @ X5 @ A4 )
% 5.31/5.59 & ( ord_less_rat @ ( F2 @ X5 ) @ ( G2 @ X5 ) ) )
% 5.31/5.59 => ( ord_less_rat @ ( groups3906332499630173760nt_rat @ F2 @ A4 ) @ ( groups3906332499630173760nt_rat @ G2 @ A4 ) ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum_strict_mono_ex1
% 5.31/5.59 thf(fact_5428_sum__strict__mono__ex1,axiom,
% 5.31/5.59 ! [A4: set_complex,F2: complex > rat,G2: complex > rat] :
% 5.31/5.59 ( ( finite3207457112153483333omplex @ A4 )
% 5.31/5.59 => ( ! [X3: complex] :
% 5.31/5.59 ( ( member_complex @ X3 @ A4 )
% 5.31/5.59 => ( ord_less_eq_rat @ ( F2 @ X3 ) @ ( G2 @ X3 ) ) )
% 5.31/5.59 => ( ? [X5: complex] :
% 5.31/5.59 ( ( member_complex @ X5 @ A4 )
% 5.31/5.59 & ( ord_less_rat @ ( F2 @ X5 ) @ ( G2 @ X5 ) ) )
% 5.31/5.59 => ( ord_less_rat @ ( groups5058264527183730370ex_rat @ F2 @ A4 ) @ ( groups5058264527183730370ex_rat @ G2 @ A4 ) ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum_strict_mono_ex1
% 5.31/5.59 thf(fact_5429_sum__strict__mono__ex1,axiom,
% 5.31/5.59 ! [A4: set_int,F2: int > nat,G2: int > nat] :
% 5.31/5.59 ( ( finite_finite_int @ A4 )
% 5.31/5.59 => ( ! [X3: int] :
% 5.31/5.59 ( ( member_int @ X3 @ A4 )
% 5.31/5.59 => ( ord_less_eq_nat @ ( F2 @ X3 ) @ ( G2 @ X3 ) ) )
% 5.31/5.59 => ( ? [X5: int] :
% 5.31/5.59 ( ( member_int @ X5 @ A4 )
% 5.31/5.59 & ( ord_less_nat @ ( F2 @ X5 ) @ ( G2 @ X5 ) ) )
% 5.31/5.59 => ( ord_less_nat @ ( groups4541462559716669496nt_nat @ F2 @ A4 ) @ ( groups4541462559716669496nt_nat @ G2 @ A4 ) ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum_strict_mono_ex1
% 5.31/5.59 thf(fact_5430_sum__strict__mono__ex1,axiom,
% 5.31/5.59 ! [A4: set_complex,F2: complex > nat,G2: complex > nat] :
% 5.31/5.59 ( ( finite3207457112153483333omplex @ A4 )
% 5.31/5.59 => ( ! [X3: complex] :
% 5.31/5.59 ( ( member_complex @ X3 @ A4 )
% 5.31/5.59 => ( ord_less_eq_nat @ ( F2 @ X3 ) @ ( G2 @ X3 ) ) )
% 5.31/5.59 => ( ? [X5: complex] :
% 5.31/5.59 ( ( member_complex @ X5 @ A4 )
% 5.31/5.59 & ( ord_less_nat @ ( F2 @ X5 ) @ ( G2 @ X5 ) ) )
% 5.31/5.59 => ( ord_less_nat @ ( groups5693394587270226106ex_nat @ F2 @ A4 ) @ ( groups5693394587270226106ex_nat @ G2 @ A4 ) ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum_strict_mono_ex1
% 5.31/5.59 thf(fact_5431_sum__strict__mono__ex1,axiom,
% 5.31/5.59 ! [A4: set_nat,F2: nat > int,G2: nat > int] :
% 5.31/5.59 ( ( finite_finite_nat @ A4 )
% 5.31/5.59 => ( ! [X3: nat] :
% 5.31/5.59 ( ( member_nat @ X3 @ A4 )
% 5.31/5.59 => ( ord_less_eq_int @ ( F2 @ X3 ) @ ( G2 @ X3 ) ) )
% 5.31/5.59 => ( ? [X5: nat] :
% 5.31/5.59 ( ( member_nat @ X5 @ A4 )
% 5.31/5.59 & ( ord_less_int @ ( F2 @ X5 ) @ ( G2 @ X5 ) ) )
% 5.31/5.59 => ( ord_less_int @ ( groups3539618377306564664at_int @ F2 @ A4 ) @ ( groups3539618377306564664at_int @ G2 @ A4 ) ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum_strict_mono_ex1
% 5.31/5.59 thf(fact_5432_sum__strict__mono__ex1,axiom,
% 5.31/5.59 ! [A4: set_complex,F2: complex > int,G2: complex > int] :
% 5.31/5.59 ( ( finite3207457112153483333omplex @ A4 )
% 5.31/5.59 => ( ! [X3: complex] :
% 5.31/5.59 ( ( member_complex @ X3 @ A4 )
% 5.31/5.59 => ( ord_less_eq_int @ ( F2 @ X3 ) @ ( G2 @ X3 ) ) )
% 5.31/5.59 => ( ? [X5: complex] :
% 5.31/5.59 ( ( member_complex @ X5 @ A4 )
% 5.31/5.59 & ( ord_less_int @ ( F2 @ X5 ) @ ( G2 @ X5 ) ) )
% 5.31/5.59 => ( ord_less_int @ ( groups5690904116761175830ex_int @ F2 @ A4 ) @ ( groups5690904116761175830ex_int @ G2 @ A4 ) ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum_strict_mono_ex1
% 5.31/5.59 thf(fact_5433_sum__strict__mono__ex1,axiom,
% 5.31/5.59 ! [A4: set_nat,F2: nat > nat,G2: nat > nat] :
% 5.31/5.59 ( ( finite_finite_nat @ A4 )
% 5.31/5.59 => ( ! [X3: nat] :
% 5.31/5.59 ( ( member_nat @ X3 @ A4 )
% 5.31/5.59 => ( ord_less_eq_nat @ ( F2 @ X3 ) @ ( G2 @ X3 ) ) )
% 5.31/5.59 => ( ? [X5: nat] :
% 5.31/5.59 ( ( member_nat @ X5 @ A4 )
% 5.31/5.59 & ( ord_less_nat @ ( F2 @ X5 ) @ ( G2 @ X5 ) ) )
% 5.31/5.59 => ( ord_less_nat @ ( groups3542108847815614940at_nat @ F2 @ A4 ) @ ( groups3542108847815614940at_nat @ G2 @ A4 ) ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum_strict_mono_ex1
% 5.31/5.59 thf(fact_5434_sum_Orelated,axiom,
% 5.31/5.59 ! [R2: complex > complex > $o,S3: set_nat,H: nat > complex,G2: nat > complex] :
% 5.31/5.59 ( ( R2 @ zero_zero_complex @ zero_zero_complex )
% 5.31/5.59 => ( ! [X15: complex,Y15: complex,X23: complex,Y23: complex] :
% 5.31/5.59 ( ( ( R2 @ X15 @ X23 )
% 5.31/5.59 & ( R2 @ Y15 @ Y23 ) )
% 5.31/5.59 => ( R2 @ ( plus_plus_complex @ X15 @ Y15 ) @ ( plus_plus_complex @ X23 @ Y23 ) ) )
% 5.31/5.59 => ( ( finite_finite_nat @ S3 )
% 5.31/5.59 => ( ! [X3: nat] :
% 5.31/5.59 ( ( member_nat @ X3 @ S3 )
% 5.31/5.59 => ( R2 @ ( H @ X3 ) @ ( G2 @ X3 ) ) )
% 5.31/5.59 => ( R2 @ ( groups2073611262835488442omplex @ H @ S3 ) @ ( groups2073611262835488442omplex @ G2 @ S3 ) ) ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum.related
% 5.31/5.59 thf(fact_5435_sum_Orelated,axiom,
% 5.31/5.59 ! [R2: complex > complex > $o,S3: set_int,H: int > complex,G2: int > complex] :
% 5.31/5.59 ( ( R2 @ zero_zero_complex @ zero_zero_complex )
% 5.31/5.59 => ( ! [X15: complex,Y15: complex,X23: complex,Y23: complex] :
% 5.31/5.59 ( ( ( R2 @ X15 @ X23 )
% 5.31/5.59 & ( R2 @ Y15 @ Y23 ) )
% 5.31/5.59 => ( R2 @ ( plus_plus_complex @ X15 @ Y15 ) @ ( plus_plus_complex @ X23 @ Y23 ) ) )
% 5.31/5.59 => ( ( finite_finite_int @ S3 )
% 5.31/5.59 => ( ! [X3: int] :
% 5.31/5.59 ( ( member_int @ X3 @ S3 )
% 5.31/5.59 => ( R2 @ ( H @ X3 ) @ ( G2 @ X3 ) ) )
% 5.31/5.59 => ( R2 @ ( groups3049146728041665814omplex @ H @ S3 ) @ ( groups3049146728041665814omplex @ G2 @ S3 ) ) ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum.related
% 5.31/5.59 thf(fact_5436_sum_Orelated,axiom,
% 5.31/5.59 ! [R2: complex > complex > $o,S3: set_complex,H: complex > complex,G2: complex > complex] :
% 5.31/5.59 ( ( R2 @ zero_zero_complex @ zero_zero_complex )
% 5.31/5.59 => ( ! [X15: complex,Y15: complex,X23: complex,Y23: complex] :
% 5.31/5.59 ( ( ( R2 @ X15 @ X23 )
% 5.31/5.59 & ( R2 @ Y15 @ Y23 ) )
% 5.31/5.59 => ( R2 @ ( plus_plus_complex @ X15 @ Y15 ) @ ( plus_plus_complex @ X23 @ Y23 ) ) )
% 5.31/5.59 => ( ( finite3207457112153483333omplex @ S3 )
% 5.31/5.59 => ( ! [X3: complex] :
% 5.31/5.59 ( ( member_complex @ X3 @ S3 )
% 5.31/5.59 => ( R2 @ ( H @ X3 ) @ ( G2 @ X3 ) ) )
% 5.31/5.59 => ( R2 @ ( groups7754918857620584856omplex @ H @ S3 ) @ ( groups7754918857620584856omplex @ G2 @ S3 ) ) ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum.related
% 5.31/5.59 thf(fact_5437_sum_Orelated,axiom,
% 5.31/5.59 ! [R2: real > real > $o,S3: set_int,H: int > real,G2: int > real] :
% 5.31/5.59 ( ( R2 @ zero_zero_real @ zero_zero_real )
% 5.31/5.59 => ( ! [X15: real,Y15: real,X23: real,Y23: real] :
% 5.31/5.59 ( ( ( R2 @ X15 @ X23 )
% 5.31/5.59 & ( R2 @ Y15 @ Y23 ) )
% 5.31/5.59 => ( R2 @ ( plus_plus_real @ X15 @ Y15 ) @ ( plus_plus_real @ X23 @ Y23 ) ) )
% 5.31/5.59 => ( ( finite_finite_int @ S3 )
% 5.31/5.59 => ( ! [X3: int] :
% 5.31/5.59 ( ( member_int @ X3 @ S3 )
% 5.31/5.59 => ( R2 @ ( H @ X3 ) @ ( G2 @ X3 ) ) )
% 5.31/5.59 => ( R2 @ ( groups8778361861064173332t_real @ H @ S3 ) @ ( groups8778361861064173332t_real @ G2 @ S3 ) ) ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum.related
% 5.31/5.59 thf(fact_5438_sum_Orelated,axiom,
% 5.31/5.59 ! [R2: real > real > $o,S3: set_complex,H: complex > real,G2: complex > real] :
% 5.31/5.59 ( ( R2 @ zero_zero_real @ zero_zero_real )
% 5.31/5.59 => ( ! [X15: real,Y15: real,X23: real,Y23: real] :
% 5.31/5.59 ( ( ( R2 @ X15 @ X23 )
% 5.31/5.59 & ( R2 @ Y15 @ Y23 ) )
% 5.31/5.59 => ( R2 @ ( plus_plus_real @ X15 @ Y15 ) @ ( plus_plus_real @ X23 @ Y23 ) ) )
% 5.31/5.59 => ( ( finite3207457112153483333omplex @ S3 )
% 5.31/5.59 => ( ! [X3: complex] :
% 5.31/5.59 ( ( member_complex @ X3 @ S3 )
% 5.31/5.59 => ( R2 @ ( H @ X3 ) @ ( G2 @ X3 ) ) )
% 5.31/5.59 => ( R2 @ ( groups5808333547571424918x_real @ H @ S3 ) @ ( groups5808333547571424918x_real @ G2 @ S3 ) ) ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum.related
% 5.31/5.59 thf(fact_5439_sum_Orelated,axiom,
% 5.31/5.59 ! [R2: rat > rat > $o,S3: set_nat,H: nat > rat,G2: nat > rat] :
% 5.31/5.59 ( ( R2 @ zero_zero_rat @ zero_zero_rat )
% 5.31/5.59 => ( ! [X15: rat,Y15: rat,X23: rat,Y23: rat] :
% 5.31/5.59 ( ( ( R2 @ X15 @ X23 )
% 5.31/5.59 & ( R2 @ Y15 @ Y23 ) )
% 5.31/5.59 => ( R2 @ ( plus_plus_rat @ X15 @ Y15 ) @ ( plus_plus_rat @ X23 @ Y23 ) ) )
% 5.31/5.59 => ( ( finite_finite_nat @ S3 )
% 5.31/5.59 => ( ! [X3: nat] :
% 5.31/5.59 ( ( member_nat @ X3 @ S3 )
% 5.31/5.59 => ( R2 @ ( H @ X3 ) @ ( G2 @ X3 ) ) )
% 5.31/5.59 => ( R2 @ ( groups2906978787729119204at_rat @ H @ S3 ) @ ( groups2906978787729119204at_rat @ G2 @ S3 ) ) ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum.related
% 5.31/5.59 thf(fact_5440_sum_Orelated,axiom,
% 5.31/5.59 ! [R2: rat > rat > $o,S3: set_int,H: int > rat,G2: int > rat] :
% 5.31/5.59 ( ( R2 @ zero_zero_rat @ zero_zero_rat )
% 5.31/5.59 => ( ! [X15: rat,Y15: rat,X23: rat,Y23: rat] :
% 5.31/5.59 ( ( ( R2 @ X15 @ X23 )
% 5.31/5.59 & ( R2 @ Y15 @ Y23 ) )
% 5.31/5.59 => ( R2 @ ( plus_plus_rat @ X15 @ Y15 ) @ ( plus_plus_rat @ X23 @ Y23 ) ) )
% 5.31/5.59 => ( ( finite_finite_int @ S3 )
% 5.31/5.59 => ( ! [X3: int] :
% 5.31/5.59 ( ( member_int @ X3 @ S3 )
% 5.31/5.59 => ( R2 @ ( H @ X3 ) @ ( G2 @ X3 ) ) )
% 5.31/5.59 => ( R2 @ ( groups3906332499630173760nt_rat @ H @ S3 ) @ ( groups3906332499630173760nt_rat @ G2 @ S3 ) ) ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum.related
% 5.31/5.59 thf(fact_5441_sum_Orelated,axiom,
% 5.31/5.59 ! [R2: rat > rat > $o,S3: set_complex,H: complex > rat,G2: complex > rat] :
% 5.31/5.59 ( ( R2 @ zero_zero_rat @ zero_zero_rat )
% 5.31/5.59 => ( ! [X15: rat,Y15: rat,X23: rat,Y23: rat] :
% 5.31/5.59 ( ( ( R2 @ X15 @ X23 )
% 5.31/5.59 & ( R2 @ Y15 @ Y23 ) )
% 5.31/5.59 => ( R2 @ ( plus_plus_rat @ X15 @ Y15 ) @ ( plus_plus_rat @ X23 @ Y23 ) ) )
% 5.31/5.59 => ( ( finite3207457112153483333omplex @ S3 )
% 5.31/5.59 => ( ! [X3: complex] :
% 5.31/5.59 ( ( member_complex @ X3 @ S3 )
% 5.31/5.59 => ( R2 @ ( H @ X3 ) @ ( G2 @ X3 ) ) )
% 5.31/5.59 => ( R2 @ ( groups5058264527183730370ex_rat @ H @ S3 ) @ ( groups5058264527183730370ex_rat @ G2 @ S3 ) ) ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum.related
% 5.31/5.59 thf(fact_5442_sum_Orelated,axiom,
% 5.31/5.59 ! [R2: nat > nat > $o,S3: set_int,H: int > nat,G2: int > nat] :
% 5.31/5.59 ( ( R2 @ zero_zero_nat @ zero_zero_nat )
% 5.31/5.59 => ( ! [X15: nat,Y15: nat,X23: nat,Y23: nat] :
% 5.31/5.59 ( ( ( R2 @ X15 @ X23 )
% 5.31/5.59 & ( R2 @ Y15 @ Y23 ) )
% 5.31/5.59 => ( R2 @ ( plus_plus_nat @ X15 @ Y15 ) @ ( plus_plus_nat @ X23 @ Y23 ) ) )
% 5.31/5.59 => ( ( finite_finite_int @ S3 )
% 5.31/5.59 => ( ! [X3: int] :
% 5.31/5.59 ( ( member_int @ X3 @ S3 )
% 5.31/5.59 => ( R2 @ ( H @ X3 ) @ ( G2 @ X3 ) ) )
% 5.31/5.59 => ( R2 @ ( groups4541462559716669496nt_nat @ H @ S3 ) @ ( groups4541462559716669496nt_nat @ G2 @ S3 ) ) ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum.related
% 5.31/5.59 thf(fact_5443_sum_Orelated,axiom,
% 5.31/5.59 ! [R2: nat > nat > $o,S3: set_complex,H: complex > nat,G2: complex > nat] :
% 5.31/5.59 ( ( R2 @ zero_zero_nat @ zero_zero_nat )
% 5.31/5.59 => ( ! [X15: nat,Y15: nat,X23: nat,Y23: nat] :
% 5.31/5.59 ( ( ( R2 @ X15 @ X23 )
% 5.31/5.59 & ( R2 @ Y15 @ Y23 ) )
% 5.31/5.59 => ( R2 @ ( plus_plus_nat @ X15 @ Y15 ) @ ( plus_plus_nat @ X23 @ Y23 ) ) )
% 5.31/5.59 => ( ( finite3207457112153483333omplex @ S3 )
% 5.31/5.59 => ( ! [X3: complex] :
% 5.31/5.59 ( ( member_complex @ X3 @ S3 )
% 5.31/5.59 => ( R2 @ ( H @ X3 ) @ ( G2 @ X3 ) ) )
% 5.31/5.59 => ( R2 @ ( groups5693394587270226106ex_nat @ H @ S3 ) @ ( groups5693394587270226106ex_nat @ G2 @ S3 ) ) ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum.related
% 5.31/5.59 thf(fact_5444_sum_Oreindex__bij__witness__not__neutral,axiom,
% 5.31/5.59 ! [S5: set_real,T4: set_real,S3: set_real,I2: real > real,J2: real > real,T5: set_real,G2: real > complex,H: real > complex] :
% 5.31/5.59 ( ( finite_finite_real @ S5 )
% 5.31/5.59 => ( ( finite_finite_real @ T4 )
% 5.31/5.59 => ( ! [A3: real] :
% 5.31/5.59 ( ( member_real @ A3 @ ( minus_minus_set_real @ S3 @ S5 ) )
% 5.31/5.59 => ( ( I2 @ ( J2 @ A3 ) )
% 5.31/5.59 = A3 ) )
% 5.31/5.59 => ( ! [A3: real] :
% 5.31/5.59 ( ( member_real @ A3 @ ( minus_minus_set_real @ S3 @ S5 ) )
% 5.31/5.59 => ( member_real @ ( J2 @ A3 ) @ ( minus_minus_set_real @ T5 @ T4 ) ) )
% 5.31/5.59 => ( ! [B3: real] :
% 5.31/5.59 ( ( member_real @ B3 @ ( minus_minus_set_real @ T5 @ T4 ) )
% 5.31/5.59 => ( ( J2 @ ( I2 @ B3 ) )
% 5.31/5.59 = B3 ) )
% 5.31/5.59 => ( ! [B3: real] :
% 5.31/5.59 ( ( member_real @ B3 @ ( minus_minus_set_real @ T5 @ T4 ) )
% 5.31/5.59 => ( member_real @ ( I2 @ B3 ) @ ( minus_minus_set_real @ S3 @ S5 ) ) )
% 5.31/5.59 => ( ! [A3: real] :
% 5.31/5.59 ( ( member_real @ A3 @ S5 )
% 5.31/5.59 => ( ( G2 @ A3 )
% 5.31/5.59 = zero_zero_complex ) )
% 5.31/5.59 => ( ! [B3: real] :
% 5.31/5.59 ( ( member_real @ B3 @ T4 )
% 5.31/5.59 => ( ( H @ B3 )
% 5.31/5.59 = zero_zero_complex ) )
% 5.31/5.59 => ( ! [A3: real] :
% 5.31/5.59 ( ( member_real @ A3 @ S3 )
% 5.31/5.59 => ( ( H @ ( J2 @ A3 ) )
% 5.31/5.59 = ( G2 @ A3 ) ) )
% 5.31/5.59 => ( ( groups5754745047067104278omplex @ G2 @ S3 )
% 5.31/5.59 = ( groups5754745047067104278omplex @ H @ T5 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum.reindex_bij_witness_not_neutral
% 5.31/5.59 thf(fact_5445_sum_Oreindex__bij__witness__not__neutral,axiom,
% 5.31/5.59 ! [S5: set_real,T4: set_int,S3: set_real,I2: int > real,J2: real > int,T5: set_int,G2: real > complex,H: int > complex] :
% 5.31/5.59 ( ( finite_finite_real @ S5 )
% 5.31/5.59 => ( ( finite_finite_int @ T4 )
% 5.31/5.59 => ( ! [A3: real] :
% 5.31/5.59 ( ( member_real @ A3 @ ( minus_minus_set_real @ S3 @ S5 ) )
% 5.31/5.59 => ( ( I2 @ ( J2 @ A3 ) )
% 5.31/5.59 = A3 ) )
% 5.31/5.59 => ( ! [A3: real] :
% 5.31/5.59 ( ( member_real @ A3 @ ( minus_minus_set_real @ S3 @ S5 ) )
% 5.31/5.59 => ( member_int @ ( J2 @ A3 ) @ ( minus_minus_set_int @ T5 @ T4 ) ) )
% 5.31/5.59 => ( ! [B3: int] :
% 5.31/5.59 ( ( member_int @ B3 @ ( minus_minus_set_int @ T5 @ T4 ) )
% 5.31/5.59 => ( ( J2 @ ( I2 @ B3 ) )
% 5.31/5.59 = B3 ) )
% 5.31/5.59 => ( ! [B3: int] :
% 5.31/5.59 ( ( member_int @ B3 @ ( minus_minus_set_int @ T5 @ T4 ) )
% 5.31/5.59 => ( member_real @ ( I2 @ B3 ) @ ( minus_minus_set_real @ S3 @ S5 ) ) )
% 5.31/5.59 => ( ! [A3: real] :
% 5.31/5.59 ( ( member_real @ A3 @ S5 )
% 5.31/5.59 => ( ( G2 @ A3 )
% 5.31/5.59 = zero_zero_complex ) )
% 5.31/5.59 => ( ! [B3: int] :
% 5.31/5.59 ( ( member_int @ B3 @ T4 )
% 5.31/5.59 => ( ( H @ B3 )
% 5.31/5.59 = zero_zero_complex ) )
% 5.31/5.59 => ( ! [A3: real] :
% 5.31/5.59 ( ( member_real @ A3 @ S3 )
% 5.31/5.59 => ( ( H @ ( J2 @ A3 ) )
% 5.31/5.59 = ( G2 @ A3 ) ) )
% 5.31/5.59 => ( ( groups5754745047067104278omplex @ G2 @ S3 )
% 5.31/5.59 = ( groups3049146728041665814omplex @ H @ T5 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum.reindex_bij_witness_not_neutral
% 5.31/5.59 thf(fact_5446_sum_Oreindex__bij__witness__not__neutral,axiom,
% 5.31/5.59 ! [S5: set_real,T4: set_complex,S3: set_real,I2: complex > real,J2: real > complex,T5: set_complex,G2: real > complex,H: complex > complex] :
% 5.31/5.59 ( ( finite_finite_real @ S5 )
% 5.31/5.59 => ( ( finite3207457112153483333omplex @ T4 )
% 5.31/5.59 => ( ! [A3: real] :
% 5.31/5.59 ( ( member_real @ A3 @ ( minus_minus_set_real @ S3 @ S5 ) )
% 5.31/5.59 => ( ( I2 @ ( J2 @ A3 ) )
% 5.31/5.59 = A3 ) )
% 5.31/5.59 => ( ! [A3: real] :
% 5.31/5.59 ( ( member_real @ A3 @ ( minus_minus_set_real @ S3 @ S5 ) )
% 5.31/5.59 => ( member_complex @ ( J2 @ A3 ) @ ( minus_811609699411566653omplex @ T5 @ T4 ) ) )
% 5.31/5.59 => ( ! [B3: complex] :
% 5.31/5.59 ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ T5 @ T4 ) )
% 5.31/5.59 => ( ( J2 @ ( I2 @ B3 ) )
% 5.31/5.59 = B3 ) )
% 5.31/5.59 => ( ! [B3: complex] :
% 5.31/5.59 ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ T5 @ T4 ) )
% 5.31/5.59 => ( member_real @ ( I2 @ B3 ) @ ( minus_minus_set_real @ S3 @ S5 ) ) )
% 5.31/5.59 => ( ! [A3: real] :
% 5.31/5.59 ( ( member_real @ A3 @ S5 )
% 5.31/5.59 => ( ( G2 @ A3 )
% 5.31/5.59 = zero_zero_complex ) )
% 5.31/5.59 => ( ! [B3: complex] :
% 5.31/5.59 ( ( member_complex @ B3 @ T4 )
% 5.31/5.59 => ( ( H @ B3 )
% 5.31/5.59 = zero_zero_complex ) )
% 5.31/5.59 => ( ! [A3: real] :
% 5.31/5.59 ( ( member_real @ A3 @ S3 )
% 5.31/5.59 => ( ( H @ ( J2 @ A3 ) )
% 5.31/5.59 = ( G2 @ A3 ) ) )
% 5.31/5.59 => ( ( groups5754745047067104278omplex @ G2 @ S3 )
% 5.31/5.59 = ( groups7754918857620584856omplex @ H @ T5 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum.reindex_bij_witness_not_neutral
% 5.31/5.59 thf(fact_5447_sum_Oreindex__bij__witness__not__neutral,axiom,
% 5.31/5.59 ! [S5: set_int,T4: set_real,S3: set_int,I2: real > int,J2: int > real,T5: set_real,G2: int > complex,H: real > complex] :
% 5.31/5.59 ( ( finite_finite_int @ S5 )
% 5.31/5.59 => ( ( finite_finite_real @ T4 )
% 5.31/5.59 => ( ! [A3: int] :
% 5.31/5.59 ( ( member_int @ A3 @ ( minus_minus_set_int @ S3 @ S5 ) )
% 5.31/5.59 => ( ( I2 @ ( J2 @ A3 ) )
% 5.31/5.59 = A3 ) )
% 5.31/5.59 => ( ! [A3: int] :
% 5.31/5.59 ( ( member_int @ A3 @ ( minus_minus_set_int @ S3 @ S5 ) )
% 5.31/5.59 => ( member_real @ ( J2 @ A3 ) @ ( minus_minus_set_real @ T5 @ T4 ) ) )
% 5.31/5.59 => ( ! [B3: real] :
% 5.31/5.59 ( ( member_real @ B3 @ ( minus_minus_set_real @ T5 @ T4 ) )
% 5.31/5.59 => ( ( J2 @ ( I2 @ B3 ) )
% 5.31/5.59 = B3 ) )
% 5.31/5.59 => ( ! [B3: real] :
% 5.31/5.59 ( ( member_real @ B3 @ ( minus_minus_set_real @ T5 @ T4 ) )
% 5.31/5.59 => ( member_int @ ( I2 @ B3 ) @ ( minus_minus_set_int @ S3 @ S5 ) ) )
% 5.31/5.59 => ( ! [A3: int] :
% 5.31/5.59 ( ( member_int @ A3 @ S5 )
% 5.31/5.59 => ( ( G2 @ A3 )
% 5.31/5.59 = zero_zero_complex ) )
% 5.31/5.59 => ( ! [B3: real] :
% 5.31/5.59 ( ( member_real @ B3 @ T4 )
% 5.31/5.59 => ( ( H @ B3 )
% 5.31/5.59 = zero_zero_complex ) )
% 5.31/5.59 => ( ! [A3: int] :
% 5.31/5.59 ( ( member_int @ A3 @ S3 )
% 5.31/5.59 => ( ( H @ ( J2 @ A3 ) )
% 5.31/5.59 = ( G2 @ A3 ) ) )
% 5.31/5.59 => ( ( groups3049146728041665814omplex @ G2 @ S3 )
% 5.31/5.59 = ( groups5754745047067104278omplex @ H @ T5 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum.reindex_bij_witness_not_neutral
% 5.31/5.59 thf(fact_5448_sum_Oreindex__bij__witness__not__neutral,axiom,
% 5.31/5.59 ! [S5: set_int,T4: set_int,S3: set_int,I2: int > int,J2: int > int,T5: set_int,G2: int > complex,H: int > complex] :
% 5.31/5.59 ( ( finite_finite_int @ S5 )
% 5.31/5.59 => ( ( finite_finite_int @ T4 )
% 5.31/5.59 => ( ! [A3: int] :
% 5.31/5.59 ( ( member_int @ A3 @ ( minus_minus_set_int @ S3 @ S5 ) )
% 5.31/5.59 => ( ( I2 @ ( J2 @ A3 ) )
% 5.31/5.59 = A3 ) )
% 5.31/5.59 => ( ! [A3: int] :
% 5.31/5.59 ( ( member_int @ A3 @ ( minus_minus_set_int @ S3 @ S5 ) )
% 5.31/5.59 => ( member_int @ ( J2 @ A3 ) @ ( minus_minus_set_int @ T5 @ T4 ) ) )
% 5.31/5.59 => ( ! [B3: int] :
% 5.31/5.59 ( ( member_int @ B3 @ ( minus_minus_set_int @ T5 @ T4 ) )
% 5.31/5.59 => ( ( J2 @ ( I2 @ B3 ) )
% 5.31/5.59 = B3 ) )
% 5.31/5.59 => ( ! [B3: int] :
% 5.31/5.59 ( ( member_int @ B3 @ ( minus_minus_set_int @ T5 @ T4 ) )
% 5.31/5.59 => ( member_int @ ( I2 @ B3 ) @ ( minus_minus_set_int @ S3 @ S5 ) ) )
% 5.31/5.59 => ( ! [A3: int] :
% 5.31/5.59 ( ( member_int @ A3 @ S5 )
% 5.31/5.59 => ( ( G2 @ A3 )
% 5.31/5.59 = zero_zero_complex ) )
% 5.31/5.59 => ( ! [B3: int] :
% 5.31/5.59 ( ( member_int @ B3 @ T4 )
% 5.31/5.59 => ( ( H @ B3 )
% 5.31/5.59 = zero_zero_complex ) )
% 5.31/5.59 => ( ! [A3: int] :
% 5.31/5.59 ( ( member_int @ A3 @ S3 )
% 5.31/5.59 => ( ( H @ ( J2 @ A3 ) )
% 5.31/5.59 = ( G2 @ A3 ) ) )
% 5.31/5.59 => ( ( groups3049146728041665814omplex @ G2 @ S3 )
% 5.31/5.59 = ( groups3049146728041665814omplex @ H @ T5 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum.reindex_bij_witness_not_neutral
% 5.31/5.59 thf(fact_5449_sum_Oreindex__bij__witness__not__neutral,axiom,
% 5.31/5.59 ! [S5: set_int,T4: set_complex,S3: set_int,I2: complex > int,J2: int > complex,T5: set_complex,G2: int > complex,H: complex > complex] :
% 5.31/5.59 ( ( finite_finite_int @ S5 )
% 5.31/5.59 => ( ( finite3207457112153483333omplex @ T4 )
% 5.31/5.59 => ( ! [A3: int] :
% 5.31/5.59 ( ( member_int @ A3 @ ( minus_minus_set_int @ S3 @ S5 ) )
% 5.31/5.59 => ( ( I2 @ ( J2 @ A3 ) )
% 5.31/5.59 = A3 ) )
% 5.31/5.59 => ( ! [A3: int] :
% 5.31/5.59 ( ( member_int @ A3 @ ( minus_minus_set_int @ S3 @ S5 ) )
% 5.31/5.59 => ( member_complex @ ( J2 @ A3 ) @ ( minus_811609699411566653omplex @ T5 @ T4 ) ) )
% 5.31/5.59 => ( ! [B3: complex] :
% 5.31/5.59 ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ T5 @ T4 ) )
% 5.31/5.59 => ( ( J2 @ ( I2 @ B3 ) )
% 5.31/5.59 = B3 ) )
% 5.31/5.59 => ( ! [B3: complex] :
% 5.31/5.59 ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ T5 @ T4 ) )
% 5.31/5.59 => ( member_int @ ( I2 @ B3 ) @ ( minus_minus_set_int @ S3 @ S5 ) ) )
% 5.31/5.59 => ( ! [A3: int] :
% 5.31/5.59 ( ( member_int @ A3 @ S5 )
% 5.31/5.59 => ( ( G2 @ A3 )
% 5.31/5.59 = zero_zero_complex ) )
% 5.31/5.59 => ( ! [B3: complex] :
% 5.31/5.59 ( ( member_complex @ B3 @ T4 )
% 5.31/5.59 => ( ( H @ B3 )
% 5.31/5.59 = zero_zero_complex ) )
% 5.31/5.59 => ( ! [A3: int] :
% 5.31/5.59 ( ( member_int @ A3 @ S3 )
% 5.31/5.59 => ( ( H @ ( J2 @ A3 ) )
% 5.31/5.59 = ( G2 @ A3 ) ) )
% 5.31/5.59 => ( ( groups3049146728041665814omplex @ G2 @ S3 )
% 5.31/5.59 = ( groups7754918857620584856omplex @ H @ T5 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum.reindex_bij_witness_not_neutral
% 5.31/5.59 thf(fact_5450_sum_Oreindex__bij__witness__not__neutral,axiom,
% 5.31/5.59 ! [S5: set_complex,T4: set_real,S3: set_complex,I2: real > complex,J2: complex > real,T5: set_real,G2: complex > complex,H: real > complex] :
% 5.31/5.59 ( ( finite3207457112153483333omplex @ S5 )
% 5.31/5.59 => ( ( finite_finite_real @ T4 )
% 5.31/5.59 => ( ! [A3: complex] :
% 5.31/5.59 ( ( member_complex @ A3 @ ( minus_811609699411566653omplex @ S3 @ S5 ) )
% 5.31/5.59 => ( ( I2 @ ( J2 @ A3 ) )
% 5.31/5.59 = A3 ) )
% 5.31/5.59 => ( ! [A3: complex] :
% 5.31/5.59 ( ( member_complex @ A3 @ ( minus_811609699411566653omplex @ S3 @ S5 ) )
% 5.31/5.59 => ( member_real @ ( J2 @ A3 ) @ ( minus_minus_set_real @ T5 @ T4 ) ) )
% 5.31/5.59 => ( ! [B3: real] :
% 5.31/5.59 ( ( member_real @ B3 @ ( minus_minus_set_real @ T5 @ T4 ) )
% 5.31/5.59 => ( ( J2 @ ( I2 @ B3 ) )
% 5.31/5.59 = B3 ) )
% 5.31/5.59 => ( ! [B3: real] :
% 5.31/5.59 ( ( member_real @ B3 @ ( minus_minus_set_real @ T5 @ T4 ) )
% 5.31/5.59 => ( member_complex @ ( I2 @ B3 ) @ ( minus_811609699411566653omplex @ S3 @ S5 ) ) )
% 5.31/5.59 => ( ! [A3: complex] :
% 5.31/5.59 ( ( member_complex @ A3 @ S5 )
% 5.31/5.59 => ( ( G2 @ A3 )
% 5.31/5.59 = zero_zero_complex ) )
% 5.31/5.59 => ( ! [B3: real] :
% 5.31/5.59 ( ( member_real @ B3 @ T4 )
% 5.31/5.59 => ( ( H @ B3 )
% 5.31/5.59 = zero_zero_complex ) )
% 5.31/5.59 => ( ! [A3: complex] :
% 5.31/5.59 ( ( member_complex @ A3 @ S3 )
% 5.31/5.59 => ( ( H @ ( J2 @ A3 ) )
% 5.31/5.59 = ( G2 @ A3 ) ) )
% 5.31/5.59 => ( ( groups7754918857620584856omplex @ G2 @ S3 )
% 5.31/5.59 = ( groups5754745047067104278omplex @ H @ T5 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum.reindex_bij_witness_not_neutral
% 5.31/5.59 thf(fact_5451_sum_Oreindex__bij__witness__not__neutral,axiom,
% 5.31/5.59 ! [S5: set_complex,T4: set_int,S3: set_complex,I2: int > complex,J2: complex > int,T5: set_int,G2: complex > complex,H: int > complex] :
% 5.31/5.59 ( ( finite3207457112153483333omplex @ S5 )
% 5.31/5.59 => ( ( finite_finite_int @ T4 )
% 5.31/5.59 => ( ! [A3: complex] :
% 5.31/5.59 ( ( member_complex @ A3 @ ( minus_811609699411566653omplex @ S3 @ S5 ) )
% 5.31/5.59 => ( ( I2 @ ( J2 @ A3 ) )
% 5.31/5.59 = A3 ) )
% 5.31/5.59 => ( ! [A3: complex] :
% 5.31/5.59 ( ( member_complex @ A3 @ ( minus_811609699411566653omplex @ S3 @ S5 ) )
% 5.31/5.59 => ( member_int @ ( J2 @ A3 ) @ ( minus_minus_set_int @ T5 @ T4 ) ) )
% 5.31/5.59 => ( ! [B3: int] :
% 5.31/5.59 ( ( member_int @ B3 @ ( minus_minus_set_int @ T5 @ T4 ) )
% 5.31/5.59 => ( ( J2 @ ( I2 @ B3 ) )
% 5.31/5.59 = B3 ) )
% 5.31/5.59 => ( ! [B3: int] :
% 5.31/5.59 ( ( member_int @ B3 @ ( minus_minus_set_int @ T5 @ T4 ) )
% 5.31/5.59 => ( member_complex @ ( I2 @ B3 ) @ ( minus_811609699411566653omplex @ S3 @ S5 ) ) )
% 5.31/5.59 => ( ! [A3: complex] :
% 5.31/5.59 ( ( member_complex @ A3 @ S5 )
% 5.31/5.59 => ( ( G2 @ A3 )
% 5.31/5.59 = zero_zero_complex ) )
% 5.31/5.59 => ( ! [B3: int] :
% 5.31/5.59 ( ( member_int @ B3 @ T4 )
% 5.31/5.59 => ( ( H @ B3 )
% 5.31/5.59 = zero_zero_complex ) )
% 5.31/5.59 => ( ! [A3: complex] :
% 5.31/5.59 ( ( member_complex @ A3 @ S3 )
% 5.31/5.59 => ( ( H @ ( J2 @ A3 ) )
% 5.31/5.59 = ( G2 @ A3 ) ) )
% 5.31/5.59 => ( ( groups7754918857620584856omplex @ G2 @ S3 )
% 5.31/5.59 = ( groups3049146728041665814omplex @ H @ T5 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum.reindex_bij_witness_not_neutral
% 5.31/5.59 thf(fact_5452_sum_Oreindex__bij__witness__not__neutral,axiom,
% 5.31/5.59 ! [S5: set_complex,T4: set_complex,S3: set_complex,I2: complex > complex,J2: complex > complex,T5: set_complex,G2: complex > complex,H: complex > complex] :
% 5.31/5.59 ( ( finite3207457112153483333omplex @ S5 )
% 5.31/5.59 => ( ( finite3207457112153483333omplex @ T4 )
% 5.31/5.59 => ( ! [A3: complex] :
% 5.31/5.59 ( ( member_complex @ A3 @ ( minus_811609699411566653omplex @ S3 @ S5 ) )
% 5.31/5.59 => ( ( I2 @ ( J2 @ A3 ) )
% 5.31/5.59 = A3 ) )
% 5.31/5.59 => ( ! [A3: complex] :
% 5.31/5.59 ( ( member_complex @ A3 @ ( minus_811609699411566653omplex @ S3 @ S5 ) )
% 5.31/5.59 => ( member_complex @ ( J2 @ A3 ) @ ( minus_811609699411566653omplex @ T5 @ T4 ) ) )
% 5.31/5.59 => ( ! [B3: complex] :
% 5.31/5.59 ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ T5 @ T4 ) )
% 5.31/5.59 => ( ( J2 @ ( I2 @ B3 ) )
% 5.31/5.59 = B3 ) )
% 5.31/5.59 => ( ! [B3: complex] :
% 5.31/5.59 ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ T5 @ T4 ) )
% 5.31/5.59 => ( member_complex @ ( I2 @ B3 ) @ ( minus_811609699411566653omplex @ S3 @ S5 ) ) )
% 5.31/5.59 => ( ! [A3: complex] :
% 5.31/5.59 ( ( member_complex @ A3 @ S5 )
% 5.31/5.59 => ( ( G2 @ A3 )
% 5.31/5.59 = zero_zero_complex ) )
% 5.31/5.59 => ( ! [B3: complex] :
% 5.31/5.59 ( ( member_complex @ B3 @ T4 )
% 5.31/5.59 => ( ( H @ B3 )
% 5.31/5.59 = zero_zero_complex ) )
% 5.31/5.59 => ( ! [A3: complex] :
% 5.31/5.59 ( ( member_complex @ A3 @ S3 )
% 5.31/5.59 => ( ( H @ ( J2 @ A3 ) )
% 5.31/5.59 = ( G2 @ A3 ) ) )
% 5.31/5.59 => ( ( groups7754918857620584856omplex @ G2 @ S3 )
% 5.31/5.59 = ( groups7754918857620584856omplex @ H @ T5 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.31/5.59
% 5.31/5.59 % sum.reindex_bij_witness_not_neutral
% 5.31/5.59 thf(fact_5453_sum_Oreindex__bij__witness__not__neutral,axiom,
% 5.31/5.59 ! [S5: set_real,T4: set_real,S3: set_real,I2: real > real,J2: real > real,T5: set_real,G2: real > real,H: real > real] :
% 5.31/5.59 ( ( finite_finite_real @ S5 )
% 5.31/5.59 => ( ( finite_finite_real @ T4 )
% 5.31/5.59 => ( ! [A3: real] :
% 5.31/5.59 ( ( member_real @ A3 @ ( minus_minus_set_real @ S3 @ S5 ) )
% 5.31/5.59 => ( ( I2 @ ( J2 @ A3 ) )
% 5.31/5.59 = A3 ) )
% 5.31/5.59 => ( ! [A3: real] :
% 5.31/5.59 ( ( member_real @ A3 @ ( minus_minus_set_real @ S3 @ S5 ) )
% 5.31/5.59 => ( member_real @ ( J2 @ A3 ) @ ( minus_minus_set_real @ T5 @ T4 ) ) )
% 5.31/5.59 => ( ! [B3: real] :
% 5.31/5.59 ( ( member_real @ B3 @ ( minus_minus_set_real @ T5 @ T4 ) )
% 5.31/5.59 => ( ( J2 @ ( I2 @ B3 ) )
% 5.31/5.59 = B3 ) )
% 5.31/5.59 => ( ! [B3: real] :
% 5.31/5.60 ( ( member_real @ B3 @ ( minus_minus_set_real @ T5 @ T4 ) )
% 5.31/5.60 => ( member_real @ ( I2 @ B3 ) @ ( minus_minus_set_real @ S3 @ S5 ) ) )
% 5.31/5.60 => ( ! [A3: real] :
% 5.31/5.60 ( ( member_real @ A3 @ S5 )
% 5.31/5.60 => ( ( G2 @ A3 )
% 5.31/5.60 = zero_zero_real ) )
% 5.31/5.60 => ( ! [B3: real] :
% 5.31/5.60 ( ( member_real @ B3 @ T4 )
% 5.31/5.60 => ( ( H @ B3 )
% 5.31/5.60 = zero_zero_real ) )
% 5.31/5.60 => ( ! [A3: real] :
% 5.31/5.60 ( ( member_real @ A3 @ S3 )
% 5.31/5.60 => ( ( H @ ( J2 @ A3 ) )
% 5.31/5.60 = ( G2 @ A3 ) ) )
% 5.31/5.60 => ( ( groups8097168146408367636l_real @ G2 @ S3 )
% 5.31/5.60 = ( groups8097168146408367636l_real @ H @ T5 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum.reindex_bij_witness_not_neutral
% 5.31/5.60 thf(fact_5454_not__is__unit__0,axiom,
% 5.31/5.60 ~ ( dvd_dvd_Code_integer @ zero_z3403309356797280102nteger @ one_one_Code_integer ) ).
% 5.31/5.60
% 5.31/5.60 % not_is_unit_0
% 5.31/5.60 thf(fact_5455_not__is__unit__0,axiom,
% 5.31/5.60 ~ ( dvd_dvd_nat @ zero_zero_nat @ one_one_nat ) ).
% 5.31/5.60
% 5.31/5.60 % not_is_unit_0
% 5.31/5.60 thf(fact_5456_not__is__unit__0,axiom,
% 5.31/5.60 ~ ( dvd_dvd_int @ zero_zero_int @ one_one_int ) ).
% 5.31/5.60
% 5.31/5.60 % not_is_unit_0
% 5.31/5.60 thf(fact_5457_dvd__div__eq__0__iff,axiom,
% 5.31/5.60 ! [B: complex,A: complex] :
% 5.31/5.60 ( ( dvd_dvd_complex @ B @ A )
% 5.31/5.60 => ( ( ( divide1717551699836669952omplex @ A @ B )
% 5.31/5.60 = zero_zero_complex )
% 5.31/5.60 = ( A = zero_zero_complex ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % dvd_div_eq_0_iff
% 5.31/5.60 thf(fact_5458_dvd__div__eq__0__iff,axiom,
% 5.31/5.60 ! [B: real,A: real] :
% 5.31/5.60 ( ( dvd_dvd_real @ B @ A )
% 5.31/5.60 => ( ( ( divide_divide_real @ A @ B )
% 5.31/5.60 = zero_zero_real )
% 5.31/5.60 = ( A = zero_zero_real ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % dvd_div_eq_0_iff
% 5.31/5.60 thf(fact_5459_dvd__div__eq__0__iff,axiom,
% 5.31/5.60 ! [B: rat,A: rat] :
% 5.31/5.60 ( ( dvd_dvd_rat @ B @ A )
% 5.31/5.60 => ( ( ( divide_divide_rat @ A @ B )
% 5.31/5.60 = zero_zero_rat )
% 5.31/5.60 = ( A = zero_zero_rat ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % dvd_div_eq_0_iff
% 5.31/5.60 thf(fact_5460_dvd__div__eq__0__iff,axiom,
% 5.31/5.60 ! [B: nat,A: nat] :
% 5.31/5.60 ( ( dvd_dvd_nat @ B @ A )
% 5.31/5.60 => ( ( ( divide_divide_nat @ A @ B )
% 5.31/5.60 = zero_zero_nat )
% 5.31/5.60 = ( A = zero_zero_nat ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % dvd_div_eq_0_iff
% 5.31/5.60 thf(fact_5461_dvd__div__eq__0__iff,axiom,
% 5.31/5.60 ! [B: int,A: int] :
% 5.31/5.60 ( ( dvd_dvd_int @ B @ A )
% 5.31/5.60 => ( ( ( divide_divide_int @ A @ B )
% 5.31/5.60 = zero_zero_int )
% 5.31/5.60 = ( A = zero_zero_int ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % dvd_div_eq_0_iff
% 5.31/5.60 thf(fact_5462_unit__mult__right__cancel,axiom,
% 5.31/5.60 ! [A: code_integer,B: code_integer,C2: code_integer] :
% 5.31/5.60 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.31/5.60 => ( ( ( times_3573771949741848930nteger @ B @ A )
% 5.31/5.60 = ( times_3573771949741848930nteger @ C2 @ A ) )
% 5.31/5.60 = ( B = C2 ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % unit_mult_right_cancel
% 5.31/5.60 thf(fact_5463_unit__mult__right__cancel,axiom,
% 5.31/5.60 ! [A: nat,B: nat,C2: nat] :
% 5.31/5.60 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.31/5.60 => ( ( ( times_times_nat @ B @ A )
% 5.31/5.60 = ( times_times_nat @ C2 @ A ) )
% 5.31/5.60 = ( B = C2 ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % unit_mult_right_cancel
% 5.31/5.60 thf(fact_5464_unit__mult__right__cancel,axiom,
% 5.31/5.60 ! [A: int,B: int,C2: int] :
% 5.31/5.60 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.31/5.60 => ( ( ( times_times_int @ B @ A )
% 5.31/5.60 = ( times_times_int @ C2 @ A ) )
% 5.31/5.60 = ( B = C2 ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % unit_mult_right_cancel
% 5.31/5.60 thf(fact_5465_unit__mult__left__cancel,axiom,
% 5.31/5.60 ! [A: code_integer,B: code_integer,C2: code_integer] :
% 5.31/5.60 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.31/5.60 => ( ( ( times_3573771949741848930nteger @ A @ B )
% 5.31/5.60 = ( times_3573771949741848930nteger @ A @ C2 ) )
% 5.31/5.60 = ( B = C2 ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % unit_mult_left_cancel
% 5.31/5.60 thf(fact_5466_unit__mult__left__cancel,axiom,
% 5.31/5.60 ! [A: nat,B: nat,C2: nat] :
% 5.31/5.60 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.31/5.60 => ( ( ( times_times_nat @ A @ B )
% 5.31/5.60 = ( times_times_nat @ A @ C2 ) )
% 5.31/5.60 = ( B = C2 ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % unit_mult_left_cancel
% 5.31/5.60 thf(fact_5467_unit__mult__left__cancel,axiom,
% 5.31/5.60 ! [A: int,B: int,C2: int] :
% 5.31/5.60 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.31/5.60 => ( ( ( times_times_int @ A @ B )
% 5.31/5.60 = ( times_times_int @ A @ C2 ) )
% 5.31/5.60 = ( B = C2 ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % unit_mult_left_cancel
% 5.31/5.60 thf(fact_5468_mult__unit__dvd__iff_H,axiom,
% 5.31/5.60 ! [A: code_integer,B: code_integer,C2: code_integer] :
% 5.31/5.60 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.31/5.60 => ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ C2 )
% 5.31/5.60 = ( dvd_dvd_Code_integer @ B @ C2 ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % mult_unit_dvd_iff'
% 5.31/5.60 thf(fact_5469_mult__unit__dvd__iff_H,axiom,
% 5.31/5.60 ! [A: nat,B: nat,C2: nat] :
% 5.31/5.60 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.31/5.60 => ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ C2 )
% 5.31/5.60 = ( dvd_dvd_nat @ B @ C2 ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % mult_unit_dvd_iff'
% 5.31/5.60 thf(fact_5470_mult__unit__dvd__iff_H,axiom,
% 5.31/5.60 ! [A: int,B: int,C2: int] :
% 5.31/5.60 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.31/5.60 => ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ C2 )
% 5.31/5.60 = ( dvd_dvd_int @ B @ C2 ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % mult_unit_dvd_iff'
% 5.31/5.60 thf(fact_5471_dvd__mult__unit__iff_H,axiom,
% 5.31/5.60 ! [B: code_integer,A: code_integer,C2: code_integer] :
% 5.31/5.60 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.31/5.60 => ( ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ B @ C2 ) )
% 5.31/5.60 = ( dvd_dvd_Code_integer @ A @ C2 ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % dvd_mult_unit_iff'
% 5.31/5.60 thf(fact_5472_dvd__mult__unit__iff_H,axiom,
% 5.31/5.60 ! [B: nat,A: nat,C2: nat] :
% 5.31/5.60 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.31/5.60 => ( ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ C2 ) )
% 5.31/5.60 = ( dvd_dvd_nat @ A @ C2 ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % dvd_mult_unit_iff'
% 5.31/5.60 thf(fact_5473_dvd__mult__unit__iff_H,axiom,
% 5.31/5.60 ! [B: int,A: int,C2: int] :
% 5.31/5.60 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.31/5.60 => ( ( dvd_dvd_int @ A @ ( times_times_int @ B @ C2 ) )
% 5.31/5.60 = ( dvd_dvd_int @ A @ C2 ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % dvd_mult_unit_iff'
% 5.31/5.60 thf(fact_5474_mult__unit__dvd__iff,axiom,
% 5.31/5.60 ! [B: code_integer,A: code_integer,C2: code_integer] :
% 5.31/5.60 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.31/5.60 => ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ C2 )
% 5.31/5.60 = ( dvd_dvd_Code_integer @ A @ C2 ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % mult_unit_dvd_iff
% 5.31/5.60 thf(fact_5475_mult__unit__dvd__iff,axiom,
% 5.31/5.60 ! [B: nat,A: nat,C2: nat] :
% 5.31/5.60 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.31/5.60 => ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ C2 )
% 5.31/5.60 = ( dvd_dvd_nat @ A @ C2 ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % mult_unit_dvd_iff
% 5.31/5.60 thf(fact_5476_mult__unit__dvd__iff,axiom,
% 5.31/5.60 ! [B: int,A: int,C2: int] :
% 5.31/5.60 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.31/5.60 => ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ C2 )
% 5.31/5.60 = ( dvd_dvd_int @ A @ C2 ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % mult_unit_dvd_iff
% 5.31/5.60 thf(fact_5477_dvd__mult__unit__iff,axiom,
% 5.31/5.60 ! [B: code_integer,A: code_integer,C2: code_integer] :
% 5.31/5.60 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.31/5.60 => ( ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ C2 @ B ) )
% 5.31/5.60 = ( dvd_dvd_Code_integer @ A @ C2 ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % dvd_mult_unit_iff
% 5.31/5.60 thf(fact_5478_dvd__mult__unit__iff,axiom,
% 5.31/5.60 ! [B: nat,A: nat,C2: nat] :
% 5.31/5.60 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.31/5.60 => ( ( dvd_dvd_nat @ A @ ( times_times_nat @ C2 @ B ) )
% 5.31/5.60 = ( dvd_dvd_nat @ A @ C2 ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % dvd_mult_unit_iff
% 5.31/5.60 thf(fact_5479_dvd__mult__unit__iff,axiom,
% 5.31/5.60 ! [B: int,A: int,C2: int] :
% 5.31/5.60 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.31/5.60 => ( ( dvd_dvd_int @ A @ ( times_times_int @ C2 @ B ) )
% 5.31/5.60 = ( dvd_dvd_int @ A @ C2 ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % dvd_mult_unit_iff
% 5.31/5.60 thf(fact_5480_is__unit__mult__iff,axiom,
% 5.31/5.60 ! [A: code_integer,B: code_integer] :
% 5.31/5.60 ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ one_one_Code_integer )
% 5.31/5.60 = ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.31/5.60 & ( dvd_dvd_Code_integer @ B @ one_one_Code_integer ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % is_unit_mult_iff
% 5.31/5.60 thf(fact_5481_is__unit__mult__iff,axiom,
% 5.31/5.60 ! [A: nat,B: nat] :
% 5.31/5.60 ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ one_one_nat )
% 5.31/5.60 = ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.31/5.60 & ( dvd_dvd_nat @ B @ one_one_nat ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % is_unit_mult_iff
% 5.31/5.60 thf(fact_5482_is__unit__mult__iff,axiom,
% 5.31/5.60 ! [A: int,B: int] :
% 5.31/5.60 ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ one_one_int )
% 5.31/5.60 = ( ( dvd_dvd_int @ A @ one_one_int )
% 5.31/5.60 & ( dvd_dvd_int @ B @ one_one_int ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % is_unit_mult_iff
% 5.31/5.60 thf(fact_5483_dvd__div__mult,axiom,
% 5.31/5.60 ! [C2: nat,B: nat,A: nat] :
% 5.31/5.60 ( ( dvd_dvd_nat @ C2 @ B )
% 5.31/5.60 => ( ( times_times_nat @ ( divide_divide_nat @ B @ C2 ) @ A )
% 5.31/5.60 = ( divide_divide_nat @ ( times_times_nat @ B @ A ) @ C2 ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % dvd_div_mult
% 5.31/5.60 thf(fact_5484_dvd__div__mult,axiom,
% 5.31/5.60 ! [C2: int,B: int,A: int] :
% 5.31/5.60 ( ( dvd_dvd_int @ C2 @ B )
% 5.31/5.60 => ( ( times_times_int @ ( divide_divide_int @ B @ C2 ) @ A )
% 5.31/5.60 = ( divide_divide_int @ ( times_times_int @ B @ A ) @ C2 ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % dvd_div_mult
% 5.31/5.60 thf(fact_5485_div__mult__swap,axiom,
% 5.31/5.60 ! [C2: nat,B: nat,A: nat] :
% 5.31/5.60 ( ( dvd_dvd_nat @ C2 @ B )
% 5.31/5.60 => ( ( times_times_nat @ A @ ( divide_divide_nat @ B @ C2 ) )
% 5.31/5.60 = ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ C2 ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % div_mult_swap
% 5.31/5.60 thf(fact_5486_div__mult__swap,axiom,
% 5.31/5.60 ! [C2: int,B: int,A: int] :
% 5.31/5.60 ( ( dvd_dvd_int @ C2 @ B )
% 5.31/5.60 => ( ( times_times_int @ A @ ( divide_divide_int @ B @ C2 ) )
% 5.31/5.60 = ( divide_divide_int @ ( times_times_int @ A @ B ) @ C2 ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % div_mult_swap
% 5.31/5.60 thf(fact_5487_div__div__eq__right,axiom,
% 5.31/5.60 ! [C2: nat,B: nat,A: nat] :
% 5.31/5.60 ( ( dvd_dvd_nat @ C2 @ B )
% 5.31/5.60 => ( ( dvd_dvd_nat @ B @ A )
% 5.31/5.60 => ( ( divide_divide_nat @ A @ ( divide_divide_nat @ B @ C2 ) )
% 5.31/5.60 = ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ C2 ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % div_div_eq_right
% 5.31/5.60 thf(fact_5488_div__div__eq__right,axiom,
% 5.31/5.60 ! [C2: int,B: int,A: int] :
% 5.31/5.60 ( ( dvd_dvd_int @ C2 @ B )
% 5.31/5.60 => ( ( dvd_dvd_int @ B @ A )
% 5.31/5.60 => ( ( divide_divide_int @ A @ ( divide_divide_int @ B @ C2 ) )
% 5.31/5.60 = ( times_times_int @ ( divide_divide_int @ A @ B ) @ C2 ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % div_div_eq_right
% 5.31/5.60 thf(fact_5489_dvd__div__mult2__eq,axiom,
% 5.31/5.60 ! [B: nat,C2: nat,A: nat] :
% 5.31/5.60 ( ( dvd_dvd_nat @ ( times_times_nat @ B @ C2 ) @ A )
% 5.31/5.60 => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ C2 ) )
% 5.31/5.60 = ( divide_divide_nat @ ( divide_divide_nat @ A @ B ) @ C2 ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % dvd_div_mult2_eq
% 5.31/5.60 thf(fact_5490_dvd__div__mult2__eq,axiom,
% 5.31/5.60 ! [B: int,C2: int,A: int] :
% 5.31/5.60 ( ( dvd_dvd_int @ ( times_times_int @ B @ C2 ) @ A )
% 5.31/5.60 => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C2 ) )
% 5.31/5.60 = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C2 ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % dvd_div_mult2_eq
% 5.31/5.60 thf(fact_5491_dvd__mult__imp__div,axiom,
% 5.31/5.60 ! [A: nat,C2: nat,B: nat] :
% 5.31/5.60 ( ( dvd_dvd_nat @ ( times_times_nat @ A @ C2 ) @ B )
% 5.31/5.60 => ( dvd_dvd_nat @ A @ ( divide_divide_nat @ B @ C2 ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % dvd_mult_imp_div
% 5.31/5.60 thf(fact_5492_dvd__mult__imp__div,axiom,
% 5.31/5.60 ! [A: int,C2: int,B: int] :
% 5.31/5.60 ( ( dvd_dvd_int @ ( times_times_int @ A @ C2 ) @ B )
% 5.31/5.60 => ( dvd_dvd_int @ A @ ( divide_divide_int @ B @ C2 ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % dvd_mult_imp_div
% 5.31/5.60 thf(fact_5493_div__mult__div__if__dvd,axiom,
% 5.31/5.60 ! [B: nat,A: nat,D: nat,C2: nat] :
% 5.31/5.60 ( ( dvd_dvd_nat @ B @ A )
% 5.31/5.60 => ( ( dvd_dvd_nat @ D @ C2 )
% 5.31/5.60 => ( ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ ( divide_divide_nat @ C2 @ D ) )
% 5.31/5.60 = ( divide_divide_nat @ ( times_times_nat @ A @ C2 ) @ ( times_times_nat @ B @ D ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % div_mult_div_if_dvd
% 5.31/5.60 thf(fact_5494_div__mult__div__if__dvd,axiom,
% 5.31/5.60 ! [B: int,A: int,D: int,C2: int] :
% 5.31/5.60 ( ( dvd_dvd_int @ B @ A )
% 5.31/5.60 => ( ( dvd_dvd_int @ D @ C2 )
% 5.31/5.60 => ( ( times_times_int @ ( divide_divide_int @ A @ B ) @ ( divide_divide_int @ C2 @ D ) )
% 5.31/5.60 = ( divide_divide_int @ ( times_times_int @ A @ C2 ) @ ( times_times_int @ B @ D ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % div_mult_div_if_dvd
% 5.31/5.60 thf(fact_5495_unit__div__cancel,axiom,
% 5.31/5.60 ! [A: code_integer,B: code_integer,C2: code_integer] :
% 5.31/5.60 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.31/5.60 => ( ( ( divide6298287555418463151nteger @ B @ A )
% 5.31/5.60 = ( divide6298287555418463151nteger @ C2 @ A ) )
% 5.31/5.60 = ( B = C2 ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % unit_div_cancel
% 5.31/5.60 thf(fact_5496_unit__div__cancel,axiom,
% 5.31/5.60 ! [A: nat,B: nat,C2: nat] :
% 5.31/5.60 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.31/5.60 => ( ( ( divide_divide_nat @ B @ A )
% 5.31/5.60 = ( divide_divide_nat @ C2 @ A ) )
% 5.31/5.60 = ( B = C2 ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % unit_div_cancel
% 5.31/5.60 thf(fact_5497_unit__div__cancel,axiom,
% 5.31/5.60 ! [A: int,B: int,C2: int] :
% 5.31/5.60 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.31/5.60 => ( ( ( divide_divide_int @ B @ A )
% 5.31/5.60 = ( divide_divide_int @ C2 @ A ) )
% 5.31/5.60 = ( B = C2 ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % unit_div_cancel
% 5.31/5.60 thf(fact_5498_div__unit__dvd__iff,axiom,
% 5.31/5.60 ! [B: code_integer,A: code_integer,C2: code_integer] :
% 5.31/5.60 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.31/5.60 => ( ( dvd_dvd_Code_integer @ ( divide6298287555418463151nteger @ A @ B ) @ C2 )
% 5.31/5.60 = ( dvd_dvd_Code_integer @ A @ C2 ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % div_unit_dvd_iff
% 5.31/5.60 thf(fact_5499_div__unit__dvd__iff,axiom,
% 5.31/5.60 ! [B: nat,A: nat,C2: nat] :
% 5.31/5.60 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.31/5.60 => ( ( dvd_dvd_nat @ ( divide_divide_nat @ A @ B ) @ C2 )
% 5.31/5.60 = ( dvd_dvd_nat @ A @ C2 ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % div_unit_dvd_iff
% 5.31/5.60 thf(fact_5500_div__unit__dvd__iff,axiom,
% 5.31/5.60 ! [B: int,A: int,C2: int] :
% 5.31/5.60 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.31/5.60 => ( ( dvd_dvd_int @ ( divide_divide_int @ A @ B ) @ C2 )
% 5.31/5.60 = ( dvd_dvd_int @ A @ C2 ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % div_unit_dvd_iff
% 5.31/5.60 thf(fact_5501_dvd__div__unit__iff,axiom,
% 5.31/5.60 ! [B: code_integer,A: code_integer,C2: code_integer] :
% 5.31/5.60 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.31/5.60 => ( ( dvd_dvd_Code_integer @ A @ ( divide6298287555418463151nteger @ C2 @ B ) )
% 5.31/5.60 = ( dvd_dvd_Code_integer @ A @ C2 ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % dvd_div_unit_iff
% 5.31/5.60 thf(fact_5502_dvd__div__unit__iff,axiom,
% 5.31/5.60 ! [B: nat,A: nat,C2: nat] :
% 5.31/5.60 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.31/5.60 => ( ( dvd_dvd_nat @ A @ ( divide_divide_nat @ C2 @ B ) )
% 5.31/5.60 = ( dvd_dvd_nat @ A @ C2 ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % dvd_div_unit_iff
% 5.31/5.60 thf(fact_5503_dvd__div__unit__iff,axiom,
% 5.31/5.60 ! [B: int,A: int,C2: int] :
% 5.31/5.60 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.31/5.60 => ( ( dvd_dvd_int @ A @ ( divide_divide_int @ C2 @ B ) )
% 5.31/5.60 = ( dvd_dvd_int @ A @ C2 ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % dvd_div_unit_iff
% 5.31/5.60 thf(fact_5504_mod__eq__0__iff__dvd,axiom,
% 5.31/5.60 ! [A: nat,B: nat] :
% 5.31/5.60 ( ( ( modulo_modulo_nat @ A @ B )
% 5.31/5.60 = zero_zero_nat )
% 5.31/5.60 = ( dvd_dvd_nat @ B @ A ) ) ).
% 5.31/5.60
% 5.31/5.60 % mod_eq_0_iff_dvd
% 5.31/5.60 thf(fact_5505_mod__eq__0__iff__dvd,axiom,
% 5.31/5.60 ! [A: int,B: int] :
% 5.31/5.60 ( ( ( modulo_modulo_int @ A @ B )
% 5.31/5.60 = zero_zero_int )
% 5.31/5.60 = ( dvd_dvd_int @ B @ A ) ) ).
% 5.31/5.60
% 5.31/5.60 % mod_eq_0_iff_dvd
% 5.31/5.60 thf(fact_5506_mod__eq__0__iff__dvd,axiom,
% 5.31/5.60 ! [A: code_natural,B: code_natural] :
% 5.31/5.60 ( ( ( modulo8411746178871703098atural @ A @ B )
% 5.31/5.60 = zero_z2226904508553997617atural )
% 5.31/5.60 = ( dvd_dvd_Code_natural @ B @ A ) ) ).
% 5.31/5.60
% 5.31/5.60 % mod_eq_0_iff_dvd
% 5.31/5.60 thf(fact_5507_dvd__eq__mod__eq__0,axiom,
% 5.31/5.60 ( dvd_dvd_nat
% 5.31/5.60 = ( ^ [A5: nat,B4: nat] :
% 5.31/5.60 ( ( modulo_modulo_nat @ B4 @ A5 )
% 5.31/5.60 = zero_zero_nat ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % dvd_eq_mod_eq_0
% 5.31/5.60 thf(fact_5508_dvd__eq__mod__eq__0,axiom,
% 5.31/5.60 ( dvd_dvd_int
% 5.31/5.60 = ( ^ [A5: int,B4: int] :
% 5.31/5.60 ( ( modulo_modulo_int @ B4 @ A5 )
% 5.31/5.60 = zero_zero_int ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % dvd_eq_mod_eq_0
% 5.31/5.60 thf(fact_5509_dvd__eq__mod__eq__0,axiom,
% 5.31/5.60 ( dvd_dvd_Code_natural
% 5.31/5.60 = ( ^ [A5: code_natural,B4: code_natural] :
% 5.31/5.60 ( ( modulo8411746178871703098atural @ B4 @ A5 )
% 5.31/5.60 = zero_z2226904508553997617atural ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % dvd_eq_mod_eq_0
% 5.31/5.60 thf(fact_5510_mod__0__imp__dvd,axiom,
% 5.31/5.60 ! [A: nat,B: nat] :
% 5.31/5.60 ( ( ( modulo_modulo_nat @ A @ B )
% 5.31/5.60 = zero_zero_nat )
% 5.31/5.60 => ( dvd_dvd_nat @ B @ A ) ) ).
% 5.31/5.60
% 5.31/5.60 % mod_0_imp_dvd
% 5.31/5.60 thf(fact_5511_mod__0__imp__dvd,axiom,
% 5.31/5.60 ! [A: int,B: int] :
% 5.31/5.60 ( ( ( modulo_modulo_int @ A @ B )
% 5.31/5.60 = zero_zero_int )
% 5.31/5.60 => ( dvd_dvd_int @ B @ A ) ) ).
% 5.31/5.60
% 5.31/5.60 % mod_0_imp_dvd
% 5.31/5.60 thf(fact_5512_mod__0__imp__dvd,axiom,
% 5.31/5.60 ! [A: code_natural,B: code_natural] :
% 5.31/5.60 ( ( ( modulo8411746178871703098atural @ A @ B )
% 5.31/5.60 = zero_z2226904508553997617atural )
% 5.31/5.60 => ( dvd_dvd_Code_natural @ B @ A ) ) ).
% 5.31/5.60
% 5.31/5.60 % mod_0_imp_dvd
% 5.31/5.60 thf(fact_5513_dvd__power__le,axiom,
% 5.31/5.60 ! [X: nat,Y: nat,N: nat,M2: nat] :
% 5.31/5.60 ( ( dvd_dvd_nat @ X @ Y )
% 5.31/5.60 => ( ( ord_less_eq_nat @ N @ M2 )
% 5.31/5.60 => ( dvd_dvd_nat @ ( power_power_nat @ X @ N ) @ ( power_power_nat @ Y @ M2 ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % dvd_power_le
% 5.31/5.60 thf(fact_5514_dvd__power__le,axiom,
% 5.31/5.60 ! [X: real,Y: real,N: nat,M2: nat] :
% 5.31/5.60 ( ( dvd_dvd_real @ X @ Y )
% 5.31/5.60 => ( ( ord_less_eq_nat @ N @ M2 )
% 5.31/5.60 => ( dvd_dvd_real @ ( power_power_real @ X @ N ) @ ( power_power_real @ Y @ M2 ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % dvd_power_le
% 5.31/5.60 thf(fact_5515_dvd__power__le,axiom,
% 5.31/5.60 ! [X: int,Y: int,N: nat,M2: nat] :
% 5.31/5.60 ( ( dvd_dvd_int @ X @ Y )
% 5.31/5.60 => ( ( ord_less_eq_nat @ N @ M2 )
% 5.31/5.60 => ( dvd_dvd_int @ ( power_power_int @ X @ N ) @ ( power_power_int @ Y @ M2 ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % dvd_power_le
% 5.31/5.60 thf(fact_5516_dvd__power__le,axiom,
% 5.31/5.60 ! [X: complex,Y: complex,N: nat,M2: nat] :
% 5.31/5.60 ( ( dvd_dvd_complex @ X @ Y )
% 5.31/5.60 => ( ( ord_less_eq_nat @ N @ M2 )
% 5.31/5.60 => ( dvd_dvd_complex @ ( power_power_complex @ X @ N ) @ ( power_power_complex @ Y @ M2 ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % dvd_power_le
% 5.31/5.60 thf(fact_5517_power__le__dvd,axiom,
% 5.31/5.60 ! [A: nat,N: nat,B: nat,M2: nat] :
% 5.31/5.60 ( ( dvd_dvd_nat @ ( power_power_nat @ A @ N ) @ B )
% 5.31/5.60 => ( ( ord_less_eq_nat @ M2 @ N )
% 5.31/5.60 => ( dvd_dvd_nat @ ( power_power_nat @ A @ M2 ) @ B ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % power_le_dvd
% 5.31/5.60 thf(fact_5518_power__le__dvd,axiom,
% 5.31/5.60 ! [A: real,N: nat,B: real,M2: nat] :
% 5.31/5.60 ( ( dvd_dvd_real @ ( power_power_real @ A @ N ) @ B )
% 5.31/5.60 => ( ( ord_less_eq_nat @ M2 @ N )
% 5.31/5.60 => ( dvd_dvd_real @ ( power_power_real @ A @ M2 ) @ B ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % power_le_dvd
% 5.31/5.60 thf(fact_5519_power__le__dvd,axiom,
% 5.31/5.60 ! [A: int,N: nat,B: int,M2: nat] :
% 5.31/5.60 ( ( dvd_dvd_int @ ( power_power_int @ A @ N ) @ B )
% 5.31/5.60 => ( ( ord_less_eq_nat @ M2 @ N )
% 5.31/5.60 => ( dvd_dvd_int @ ( power_power_int @ A @ M2 ) @ B ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % power_le_dvd
% 5.31/5.60 thf(fact_5520_power__le__dvd,axiom,
% 5.31/5.60 ! [A: complex,N: nat,B: complex,M2: nat] :
% 5.31/5.60 ( ( dvd_dvd_complex @ ( power_power_complex @ A @ N ) @ B )
% 5.31/5.60 => ( ( ord_less_eq_nat @ M2 @ N )
% 5.31/5.60 => ( dvd_dvd_complex @ ( power_power_complex @ A @ M2 ) @ B ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % power_le_dvd
% 5.31/5.60 thf(fact_5521_le__imp__power__dvd,axiom,
% 5.31/5.60 ! [M2: nat,N: nat,A: nat] :
% 5.31/5.60 ( ( ord_less_eq_nat @ M2 @ N )
% 5.31/5.60 => ( dvd_dvd_nat @ ( power_power_nat @ A @ M2 ) @ ( power_power_nat @ A @ N ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % le_imp_power_dvd
% 5.31/5.60 thf(fact_5522_le__imp__power__dvd,axiom,
% 5.31/5.60 ! [M2: nat,N: nat,A: real] :
% 5.31/5.60 ( ( ord_less_eq_nat @ M2 @ N )
% 5.31/5.60 => ( dvd_dvd_real @ ( power_power_real @ A @ M2 ) @ ( power_power_real @ A @ N ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % le_imp_power_dvd
% 5.31/5.60 thf(fact_5523_le__imp__power__dvd,axiom,
% 5.31/5.60 ! [M2: nat,N: nat,A: int] :
% 5.31/5.60 ( ( ord_less_eq_nat @ M2 @ N )
% 5.31/5.60 => ( dvd_dvd_int @ ( power_power_int @ A @ M2 ) @ ( power_power_int @ A @ N ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % le_imp_power_dvd
% 5.31/5.60 thf(fact_5524_le__imp__power__dvd,axiom,
% 5.31/5.60 ! [M2: nat,N: nat,A: complex] :
% 5.31/5.60 ( ( ord_less_eq_nat @ M2 @ N )
% 5.31/5.60 => ( dvd_dvd_complex @ ( power_power_complex @ A @ M2 ) @ ( power_power_complex @ A @ N ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % le_imp_power_dvd
% 5.31/5.60 thf(fact_5525_dvd__minus__mod,axiom,
% 5.31/5.60 ! [B: nat,A: nat] : ( dvd_dvd_nat @ B @ ( minus_minus_nat @ A @ ( modulo_modulo_nat @ A @ B ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % dvd_minus_mod
% 5.31/5.60 thf(fact_5526_dvd__minus__mod,axiom,
% 5.31/5.60 ! [B: int,A: int] : ( dvd_dvd_int @ B @ ( minus_minus_int @ A @ ( modulo_modulo_int @ A @ B ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % dvd_minus_mod
% 5.31/5.60 thf(fact_5527_dvd__minus__mod,axiom,
% 5.31/5.60 ! [B: code_natural,A: code_natural] : ( dvd_dvd_Code_natural @ B @ ( minus_7197305767214868737atural @ A @ ( modulo8411746178871703098atural @ A @ B ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % dvd_minus_mod
% 5.31/5.60 thf(fact_5528_dvd__pos__nat,axiom,
% 5.31/5.60 ! [N: nat,M2: nat] :
% 5.31/5.60 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.60 => ( ( dvd_dvd_nat @ M2 @ N )
% 5.31/5.60 => ( ord_less_nat @ zero_zero_nat @ M2 ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % dvd_pos_nat
% 5.31/5.60 thf(fact_5529_nat__dvd__not__less,axiom,
% 5.31/5.60 ! [M2: nat,N: nat] :
% 5.31/5.60 ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 5.31/5.60 => ( ( ord_less_nat @ M2 @ N )
% 5.31/5.60 => ~ ( dvd_dvd_nat @ N @ M2 ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % nat_dvd_not_less
% 5.31/5.60 thf(fact_5530_pochhammer__pos,axiom,
% 5.31/5.60 ! [X: real,N: nat] :
% 5.31/5.60 ( ( ord_less_real @ zero_zero_real @ X )
% 5.31/5.60 => ( ord_less_real @ zero_zero_real @ ( comm_s7457072308508201937r_real @ X @ N ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % pochhammer_pos
% 5.31/5.60 thf(fact_5531_pochhammer__pos,axiom,
% 5.31/5.60 ! [X: rat,N: nat] :
% 5.31/5.60 ( ( ord_less_rat @ zero_zero_rat @ X )
% 5.31/5.60 => ( ord_less_rat @ zero_zero_rat @ ( comm_s4028243227959126397er_rat @ X @ N ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % pochhammer_pos
% 5.31/5.60 thf(fact_5532_pochhammer__pos,axiom,
% 5.31/5.60 ! [X: nat,N: nat] :
% 5.31/5.60 ( ( ord_less_nat @ zero_zero_nat @ X )
% 5.31/5.60 => ( ord_less_nat @ zero_zero_nat @ ( comm_s4663373288045622133er_nat @ X @ N ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % pochhammer_pos
% 5.31/5.60 thf(fact_5533_pochhammer__pos,axiom,
% 5.31/5.60 ! [X: int,N: nat] :
% 5.31/5.60 ( ( ord_less_int @ zero_zero_int @ X )
% 5.31/5.60 => ( ord_less_int @ zero_zero_int @ ( comm_s4660882817536571857er_int @ X @ N ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % pochhammer_pos
% 5.31/5.60 thf(fact_5534_dvd__minus__self,axiom,
% 5.31/5.60 ! [M2: nat,N: nat] :
% 5.31/5.60 ( ( dvd_dvd_nat @ M2 @ ( minus_minus_nat @ N @ M2 ) )
% 5.31/5.60 = ( ( ord_less_nat @ N @ M2 )
% 5.31/5.60 | ( dvd_dvd_nat @ M2 @ N ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % dvd_minus_self
% 5.31/5.60 thf(fact_5535_sum__nonneg__0,axiom,
% 5.31/5.60 ! [S2: set_real,F2: real > real,I2: real] :
% 5.31/5.60 ( ( finite_finite_real @ S2 )
% 5.31/5.60 => ( ! [I3: real] :
% 5.31/5.60 ( ( member_real @ I3 @ S2 )
% 5.31/5.60 => ( ord_less_eq_real @ zero_zero_real @ ( F2 @ I3 ) ) )
% 5.31/5.60 => ( ( ( groups8097168146408367636l_real @ F2 @ S2 )
% 5.31/5.60 = zero_zero_real )
% 5.31/5.60 => ( ( member_real @ I2 @ S2 )
% 5.31/5.60 => ( ( F2 @ I2 )
% 5.31/5.60 = zero_zero_real ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum_nonneg_0
% 5.31/5.60 thf(fact_5536_sum__nonneg__0,axiom,
% 5.31/5.60 ! [S2: set_int,F2: int > real,I2: int] :
% 5.31/5.60 ( ( finite_finite_int @ S2 )
% 5.31/5.60 => ( ! [I3: int] :
% 5.31/5.60 ( ( member_int @ I3 @ S2 )
% 5.31/5.60 => ( ord_less_eq_real @ zero_zero_real @ ( F2 @ I3 ) ) )
% 5.31/5.60 => ( ( ( groups8778361861064173332t_real @ F2 @ S2 )
% 5.31/5.60 = zero_zero_real )
% 5.31/5.60 => ( ( member_int @ I2 @ S2 )
% 5.31/5.60 => ( ( F2 @ I2 )
% 5.31/5.60 = zero_zero_real ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum_nonneg_0
% 5.31/5.60 thf(fact_5537_sum__nonneg__0,axiom,
% 5.31/5.60 ! [S2: set_complex,F2: complex > real,I2: complex] :
% 5.31/5.60 ( ( finite3207457112153483333omplex @ S2 )
% 5.31/5.60 => ( ! [I3: complex] :
% 5.31/5.60 ( ( member_complex @ I3 @ S2 )
% 5.31/5.60 => ( ord_less_eq_real @ zero_zero_real @ ( F2 @ I3 ) ) )
% 5.31/5.60 => ( ( ( groups5808333547571424918x_real @ F2 @ S2 )
% 5.31/5.60 = zero_zero_real )
% 5.31/5.60 => ( ( member_complex @ I2 @ S2 )
% 5.31/5.60 => ( ( F2 @ I2 )
% 5.31/5.60 = zero_zero_real ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum_nonneg_0
% 5.31/5.60 thf(fact_5538_sum__nonneg__0,axiom,
% 5.31/5.60 ! [S2: set_real,F2: real > rat,I2: real] :
% 5.31/5.60 ( ( finite_finite_real @ S2 )
% 5.31/5.60 => ( ! [I3: real] :
% 5.31/5.60 ( ( member_real @ I3 @ S2 )
% 5.31/5.60 => ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ I3 ) ) )
% 5.31/5.60 => ( ( ( groups1300246762558778688al_rat @ F2 @ S2 )
% 5.31/5.60 = zero_zero_rat )
% 5.31/5.60 => ( ( member_real @ I2 @ S2 )
% 5.31/5.60 => ( ( F2 @ I2 )
% 5.31/5.60 = zero_zero_rat ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum_nonneg_0
% 5.31/5.60 thf(fact_5539_sum__nonneg__0,axiom,
% 5.31/5.60 ! [S2: set_nat,F2: nat > rat,I2: nat] :
% 5.31/5.60 ( ( finite_finite_nat @ S2 )
% 5.31/5.60 => ( ! [I3: nat] :
% 5.31/5.60 ( ( member_nat @ I3 @ S2 )
% 5.31/5.60 => ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ I3 ) ) )
% 5.31/5.60 => ( ( ( groups2906978787729119204at_rat @ F2 @ S2 )
% 5.31/5.60 = zero_zero_rat )
% 5.31/5.60 => ( ( member_nat @ I2 @ S2 )
% 5.31/5.60 => ( ( F2 @ I2 )
% 5.31/5.60 = zero_zero_rat ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum_nonneg_0
% 5.31/5.60 thf(fact_5540_sum__nonneg__0,axiom,
% 5.31/5.60 ! [S2: set_int,F2: int > rat,I2: int] :
% 5.31/5.60 ( ( finite_finite_int @ S2 )
% 5.31/5.60 => ( ! [I3: int] :
% 5.31/5.60 ( ( member_int @ I3 @ S2 )
% 5.31/5.60 => ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ I3 ) ) )
% 5.31/5.60 => ( ( ( groups3906332499630173760nt_rat @ F2 @ S2 )
% 5.31/5.60 = zero_zero_rat )
% 5.31/5.60 => ( ( member_int @ I2 @ S2 )
% 5.31/5.60 => ( ( F2 @ I2 )
% 5.31/5.60 = zero_zero_rat ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum_nonneg_0
% 5.31/5.60 thf(fact_5541_sum__nonneg__0,axiom,
% 5.31/5.60 ! [S2: set_complex,F2: complex > rat,I2: complex] :
% 5.31/5.60 ( ( finite3207457112153483333omplex @ S2 )
% 5.31/5.60 => ( ! [I3: complex] :
% 5.31/5.60 ( ( member_complex @ I3 @ S2 )
% 5.31/5.60 => ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ I3 ) ) )
% 5.31/5.60 => ( ( ( groups5058264527183730370ex_rat @ F2 @ S2 )
% 5.31/5.60 = zero_zero_rat )
% 5.31/5.60 => ( ( member_complex @ I2 @ S2 )
% 5.31/5.60 => ( ( F2 @ I2 )
% 5.31/5.60 = zero_zero_rat ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum_nonneg_0
% 5.31/5.60 thf(fact_5542_sum__nonneg__0,axiom,
% 5.31/5.60 ! [S2: set_real,F2: real > nat,I2: real] :
% 5.31/5.60 ( ( finite_finite_real @ S2 )
% 5.31/5.60 => ( ! [I3: real] :
% 5.31/5.60 ( ( member_real @ I3 @ S2 )
% 5.31/5.60 => ( ord_less_eq_nat @ zero_zero_nat @ ( F2 @ I3 ) ) )
% 5.31/5.60 => ( ( ( groups1935376822645274424al_nat @ F2 @ S2 )
% 5.31/5.60 = zero_zero_nat )
% 5.31/5.60 => ( ( member_real @ I2 @ S2 )
% 5.31/5.60 => ( ( F2 @ I2 )
% 5.31/5.60 = zero_zero_nat ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum_nonneg_0
% 5.31/5.60 thf(fact_5543_sum__nonneg__0,axiom,
% 5.31/5.60 ! [S2: set_int,F2: int > nat,I2: int] :
% 5.31/5.60 ( ( finite_finite_int @ S2 )
% 5.31/5.60 => ( ! [I3: int] :
% 5.31/5.60 ( ( member_int @ I3 @ S2 )
% 5.31/5.60 => ( ord_less_eq_nat @ zero_zero_nat @ ( F2 @ I3 ) ) )
% 5.31/5.60 => ( ( ( groups4541462559716669496nt_nat @ F2 @ S2 )
% 5.31/5.60 = zero_zero_nat )
% 5.31/5.60 => ( ( member_int @ I2 @ S2 )
% 5.31/5.60 => ( ( F2 @ I2 )
% 5.31/5.60 = zero_zero_nat ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum_nonneg_0
% 5.31/5.60 thf(fact_5544_sum__nonneg__0,axiom,
% 5.31/5.60 ! [S2: set_complex,F2: complex > nat,I2: complex] :
% 5.31/5.60 ( ( finite3207457112153483333omplex @ S2 )
% 5.31/5.60 => ( ! [I3: complex] :
% 5.31/5.60 ( ( member_complex @ I3 @ S2 )
% 5.31/5.60 => ( ord_less_eq_nat @ zero_zero_nat @ ( F2 @ I3 ) ) )
% 5.31/5.60 => ( ( ( groups5693394587270226106ex_nat @ F2 @ S2 )
% 5.31/5.60 = zero_zero_nat )
% 5.31/5.60 => ( ( member_complex @ I2 @ S2 )
% 5.31/5.60 => ( ( F2 @ I2 )
% 5.31/5.60 = zero_zero_nat ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum_nonneg_0
% 5.31/5.60 thf(fact_5545_sum__nonneg__leq__bound,axiom,
% 5.31/5.60 ! [S2: set_real,F2: real > real,B5: real,I2: real] :
% 5.31/5.60 ( ( finite_finite_real @ S2 )
% 5.31/5.60 => ( ! [I3: real] :
% 5.31/5.60 ( ( member_real @ I3 @ S2 )
% 5.31/5.60 => ( ord_less_eq_real @ zero_zero_real @ ( F2 @ I3 ) ) )
% 5.31/5.60 => ( ( ( groups8097168146408367636l_real @ F2 @ S2 )
% 5.31/5.60 = B5 )
% 5.31/5.60 => ( ( member_real @ I2 @ S2 )
% 5.31/5.60 => ( ord_less_eq_real @ ( F2 @ I2 ) @ B5 ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum_nonneg_leq_bound
% 5.31/5.60 thf(fact_5546_sum__nonneg__leq__bound,axiom,
% 5.31/5.60 ! [S2: set_int,F2: int > real,B5: real,I2: int] :
% 5.31/5.60 ( ( finite_finite_int @ S2 )
% 5.31/5.60 => ( ! [I3: int] :
% 5.31/5.60 ( ( member_int @ I3 @ S2 )
% 5.31/5.60 => ( ord_less_eq_real @ zero_zero_real @ ( F2 @ I3 ) ) )
% 5.31/5.60 => ( ( ( groups8778361861064173332t_real @ F2 @ S2 )
% 5.31/5.60 = B5 )
% 5.31/5.60 => ( ( member_int @ I2 @ S2 )
% 5.31/5.60 => ( ord_less_eq_real @ ( F2 @ I2 ) @ B5 ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum_nonneg_leq_bound
% 5.31/5.60 thf(fact_5547_sum__nonneg__leq__bound,axiom,
% 5.31/5.60 ! [S2: set_complex,F2: complex > real,B5: real,I2: complex] :
% 5.31/5.60 ( ( finite3207457112153483333omplex @ S2 )
% 5.31/5.60 => ( ! [I3: complex] :
% 5.31/5.60 ( ( member_complex @ I3 @ S2 )
% 5.31/5.60 => ( ord_less_eq_real @ zero_zero_real @ ( F2 @ I3 ) ) )
% 5.31/5.60 => ( ( ( groups5808333547571424918x_real @ F2 @ S2 )
% 5.31/5.60 = B5 )
% 5.31/5.60 => ( ( member_complex @ I2 @ S2 )
% 5.31/5.60 => ( ord_less_eq_real @ ( F2 @ I2 ) @ B5 ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum_nonneg_leq_bound
% 5.31/5.60 thf(fact_5548_sum__nonneg__leq__bound,axiom,
% 5.31/5.60 ! [S2: set_real,F2: real > rat,B5: rat,I2: real] :
% 5.31/5.60 ( ( finite_finite_real @ S2 )
% 5.31/5.60 => ( ! [I3: real] :
% 5.31/5.60 ( ( member_real @ I3 @ S2 )
% 5.31/5.60 => ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ I3 ) ) )
% 5.31/5.60 => ( ( ( groups1300246762558778688al_rat @ F2 @ S2 )
% 5.31/5.60 = B5 )
% 5.31/5.60 => ( ( member_real @ I2 @ S2 )
% 5.31/5.60 => ( ord_less_eq_rat @ ( F2 @ I2 ) @ B5 ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum_nonneg_leq_bound
% 5.31/5.60 thf(fact_5549_sum__nonneg__leq__bound,axiom,
% 5.31/5.60 ! [S2: set_nat,F2: nat > rat,B5: rat,I2: nat] :
% 5.31/5.60 ( ( finite_finite_nat @ S2 )
% 5.31/5.60 => ( ! [I3: nat] :
% 5.31/5.60 ( ( member_nat @ I3 @ S2 )
% 5.31/5.60 => ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ I3 ) ) )
% 5.31/5.60 => ( ( ( groups2906978787729119204at_rat @ F2 @ S2 )
% 5.31/5.60 = B5 )
% 5.31/5.60 => ( ( member_nat @ I2 @ S2 )
% 5.31/5.60 => ( ord_less_eq_rat @ ( F2 @ I2 ) @ B5 ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum_nonneg_leq_bound
% 5.31/5.60 thf(fact_5550_sum__nonneg__leq__bound,axiom,
% 5.31/5.60 ! [S2: set_int,F2: int > rat,B5: rat,I2: int] :
% 5.31/5.60 ( ( finite_finite_int @ S2 )
% 5.31/5.60 => ( ! [I3: int] :
% 5.31/5.60 ( ( member_int @ I3 @ S2 )
% 5.31/5.60 => ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ I3 ) ) )
% 5.31/5.60 => ( ( ( groups3906332499630173760nt_rat @ F2 @ S2 )
% 5.31/5.60 = B5 )
% 5.31/5.60 => ( ( member_int @ I2 @ S2 )
% 5.31/5.60 => ( ord_less_eq_rat @ ( F2 @ I2 ) @ B5 ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum_nonneg_leq_bound
% 5.31/5.60 thf(fact_5551_sum__nonneg__leq__bound,axiom,
% 5.31/5.60 ! [S2: set_complex,F2: complex > rat,B5: rat,I2: complex] :
% 5.31/5.60 ( ( finite3207457112153483333omplex @ S2 )
% 5.31/5.60 => ( ! [I3: complex] :
% 5.31/5.60 ( ( member_complex @ I3 @ S2 )
% 5.31/5.60 => ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ I3 ) ) )
% 5.31/5.60 => ( ( ( groups5058264527183730370ex_rat @ F2 @ S2 )
% 5.31/5.60 = B5 )
% 5.31/5.60 => ( ( member_complex @ I2 @ S2 )
% 5.31/5.60 => ( ord_less_eq_rat @ ( F2 @ I2 ) @ B5 ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum_nonneg_leq_bound
% 5.31/5.60 thf(fact_5552_sum__nonneg__leq__bound,axiom,
% 5.31/5.60 ! [S2: set_real,F2: real > nat,B5: nat,I2: real] :
% 5.31/5.60 ( ( finite_finite_real @ S2 )
% 5.31/5.60 => ( ! [I3: real] :
% 5.31/5.60 ( ( member_real @ I3 @ S2 )
% 5.31/5.60 => ( ord_less_eq_nat @ zero_zero_nat @ ( F2 @ I3 ) ) )
% 5.31/5.60 => ( ( ( groups1935376822645274424al_nat @ F2 @ S2 )
% 5.31/5.60 = B5 )
% 5.31/5.60 => ( ( member_real @ I2 @ S2 )
% 5.31/5.60 => ( ord_less_eq_nat @ ( F2 @ I2 ) @ B5 ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum_nonneg_leq_bound
% 5.31/5.60 thf(fact_5553_sum__nonneg__leq__bound,axiom,
% 5.31/5.60 ! [S2: set_int,F2: int > nat,B5: nat,I2: int] :
% 5.31/5.60 ( ( finite_finite_int @ S2 )
% 5.31/5.60 => ( ! [I3: int] :
% 5.31/5.60 ( ( member_int @ I3 @ S2 )
% 5.31/5.60 => ( ord_less_eq_nat @ zero_zero_nat @ ( F2 @ I3 ) ) )
% 5.31/5.60 => ( ( ( groups4541462559716669496nt_nat @ F2 @ S2 )
% 5.31/5.60 = B5 )
% 5.31/5.60 => ( ( member_int @ I2 @ S2 )
% 5.31/5.60 => ( ord_less_eq_nat @ ( F2 @ I2 ) @ B5 ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum_nonneg_leq_bound
% 5.31/5.60 thf(fact_5554_sum__nonneg__leq__bound,axiom,
% 5.31/5.60 ! [S2: set_complex,F2: complex > nat,B5: nat,I2: complex] :
% 5.31/5.60 ( ( finite3207457112153483333omplex @ S2 )
% 5.31/5.60 => ( ! [I3: complex] :
% 5.31/5.60 ( ( member_complex @ I3 @ S2 )
% 5.31/5.60 => ( ord_less_eq_nat @ zero_zero_nat @ ( F2 @ I3 ) ) )
% 5.31/5.60 => ( ( ( groups5693394587270226106ex_nat @ F2 @ S2 )
% 5.31/5.60 = B5 )
% 5.31/5.60 => ( ( member_complex @ I2 @ S2 )
% 5.31/5.60 => ( ord_less_eq_nat @ ( F2 @ I2 ) @ B5 ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum_nonneg_leq_bound
% 5.31/5.60 thf(fact_5555_less__eq__dvd__minus,axiom,
% 5.31/5.60 ! [M2: nat,N: nat] :
% 5.31/5.60 ( ( ord_less_eq_nat @ M2 @ N )
% 5.31/5.60 => ( ( dvd_dvd_nat @ M2 @ N )
% 5.31/5.60 = ( dvd_dvd_nat @ M2 @ ( minus_minus_nat @ N @ M2 ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % less_eq_dvd_minus
% 5.31/5.60 thf(fact_5556_dvd__diffD1,axiom,
% 5.31/5.60 ! [K2: nat,M2: nat,N: nat] :
% 5.31/5.60 ( ( dvd_dvd_nat @ K2 @ ( minus_minus_nat @ M2 @ N ) )
% 5.31/5.60 => ( ( dvd_dvd_nat @ K2 @ M2 )
% 5.31/5.60 => ( ( ord_less_eq_nat @ N @ M2 )
% 5.31/5.60 => ( dvd_dvd_nat @ K2 @ N ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % dvd_diffD1
% 5.31/5.60 thf(fact_5557_dvd__diffD,axiom,
% 5.31/5.60 ! [K2: nat,M2: nat,N: nat] :
% 5.31/5.60 ( ( dvd_dvd_nat @ K2 @ ( minus_minus_nat @ M2 @ N ) )
% 5.31/5.60 => ( ( dvd_dvd_nat @ K2 @ N )
% 5.31/5.60 => ( ( ord_less_eq_nat @ N @ M2 )
% 5.31/5.60 => ( dvd_dvd_nat @ K2 @ M2 ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % dvd_diffD
% 5.31/5.60 thf(fact_5558_pochhammer__eq__0__mono,axiom,
% 5.31/5.60 ! [A: complex,N: nat,M2: nat] :
% 5.31/5.60 ( ( ( comm_s2602460028002588243omplex @ A @ N )
% 5.31/5.60 = zero_zero_complex )
% 5.31/5.60 => ( ( ord_less_eq_nat @ N @ M2 )
% 5.31/5.60 => ( ( comm_s2602460028002588243omplex @ A @ M2 )
% 5.31/5.60 = zero_zero_complex ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % pochhammer_eq_0_mono
% 5.31/5.60 thf(fact_5559_pochhammer__eq__0__mono,axiom,
% 5.31/5.60 ! [A: real,N: nat,M2: nat] :
% 5.31/5.60 ( ( ( comm_s7457072308508201937r_real @ A @ N )
% 5.31/5.60 = zero_zero_real )
% 5.31/5.60 => ( ( ord_less_eq_nat @ N @ M2 )
% 5.31/5.60 => ( ( comm_s7457072308508201937r_real @ A @ M2 )
% 5.31/5.60 = zero_zero_real ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % pochhammer_eq_0_mono
% 5.31/5.60 thf(fact_5560_pochhammer__eq__0__mono,axiom,
% 5.31/5.60 ! [A: rat,N: nat,M2: nat] :
% 5.31/5.60 ( ( ( comm_s4028243227959126397er_rat @ A @ N )
% 5.31/5.60 = zero_zero_rat )
% 5.31/5.60 => ( ( ord_less_eq_nat @ N @ M2 )
% 5.31/5.60 => ( ( comm_s4028243227959126397er_rat @ A @ M2 )
% 5.31/5.60 = zero_zero_rat ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % pochhammer_eq_0_mono
% 5.31/5.60 thf(fact_5561_pochhammer__neq__0__mono,axiom,
% 5.31/5.60 ! [A: complex,M2: nat,N: nat] :
% 5.31/5.60 ( ( ( comm_s2602460028002588243omplex @ A @ M2 )
% 5.31/5.60 != zero_zero_complex )
% 5.31/5.60 => ( ( ord_less_eq_nat @ N @ M2 )
% 5.31/5.60 => ( ( comm_s2602460028002588243omplex @ A @ N )
% 5.31/5.60 != zero_zero_complex ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % pochhammer_neq_0_mono
% 5.31/5.60 thf(fact_5562_pochhammer__neq__0__mono,axiom,
% 5.31/5.60 ! [A: real,M2: nat,N: nat] :
% 5.31/5.60 ( ( ( comm_s7457072308508201937r_real @ A @ M2 )
% 5.31/5.60 != zero_zero_real )
% 5.31/5.60 => ( ( ord_less_eq_nat @ N @ M2 )
% 5.31/5.60 => ( ( comm_s7457072308508201937r_real @ A @ N )
% 5.31/5.60 != zero_zero_real ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % pochhammer_neq_0_mono
% 5.31/5.60 thf(fact_5563_pochhammer__neq__0__mono,axiom,
% 5.31/5.60 ! [A: rat,M2: nat,N: nat] :
% 5.31/5.60 ( ( ( comm_s4028243227959126397er_rat @ A @ M2 )
% 5.31/5.60 != zero_zero_rat )
% 5.31/5.60 => ( ( ord_less_eq_nat @ N @ M2 )
% 5.31/5.60 => ( ( comm_s4028243227959126397er_rat @ A @ N )
% 5.31/5.60 != zero_zero_rat ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % pochhammer_neq_0_mono
% 5.31/5.60 thf(fact_5564_bezout__add__nat,axiom,
% 5.31/5.60 ! [A: nat,B: nat] :
% 5.31/5.60 ? [D5: nat,X3: nat,Y3: nat] :
% 5.31/5.60 ( ( dvd_dvd_nat @ D5 @ A )
% 5.31/5.60 & ( dvd_dvd_nat @ D5 @ B )
% 5.31/5.60 & ( ( ( times_times_nat @ A @ X3 )
% 5.31/5.60 = ( plus_plus_nat @ ( times_times_nat @ B @ Y3 ) @ D5 ) )
% 5.31/5.60 | ( ( times_times_nat @ B @ X3 )
% 5.31/5.60 = ( plus_plus_nat @ ( times_times_nat @ A @ Y3 ) @ D5 ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % bezout_add_nat
% 5.31/5.60 thf(fact_5565_bezout__lemma__nat,axiom,
% 5.31/5.60 ! [D: nat,A: nat,B: nat,X: nat,Y: nat] :
% 5.31/5.60 ( ( dvd_dvd_nat @ D @ A )
% 5.31/5.60 => ( ( dvd_dvd_nat @ D @ B )
% 5.31/5.60 => ( ( ( ( times_times_nat @ A @ X )
% 5.31/5.60 = ( plus_plus_nat @ ( times_times_nat @ B @ Y ) @ D ) )
% 5.31/5.60 | ( ( times_times_nat @ B @ X )
% 5.31/5.60 = ( plus_plus_nat @ ( times_times_nat @ A @ Y ) @ D ) ) )
% 5.31/5.60 => ? [X3: nat,Y3: nat] :
% 5.31/5.60 ( ( dvd_dvd_nat @ D @ A )
% 5.31/5.60 & ( dvd_dvd_nat @ D @ ( plus_plus_nat @ A @ B ) )
% 5.31/5.60 & ( ( ( times_times_nat @ A @ X3 )
% 5.31/5.60 = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ Y3 ) @ D ) )
% 5.31/5.60 | ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ X3 )
% 5.31/5.60 = ( plus_plus_nat @ ( times_times_nat @ A @ Y3 ) @ D ) ) ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % bezout_lemma_nat
% 5.31/5.60 thf(fact_5566_bezout1__nat,axiom,
% 5.31/5.60 ! [A: nat,B: nat] :
% 5.31/5.60 ? [D5: nat,X3: nat,Y3: nat] :
% 5.31/5.60 ( ( dvd_dvd_nat @ D5 @ A )
% 5.31/5.60 & ( dvd_dvd_nat @ D5 @ B )
% 5.31/5.60 & ( ( ( minus_minus_nat @ ( times_times_nat @ A @ X3 ) @ ( times_times_nat @ B @ Y3 ) )
% 5.31/5.60 = D5 )
% 5.31/5.60 | ( ( minus_minus_nat @ ( times_times_nat @ B @ X3 ) @ ( times_times_nat @ A @ Y3 ) )
% 5.31/5.60 = D5 ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % bezout1_nat
% 5.31/5.60 thf(fact_5567_sum_Ointer__restrict,axiom,
% 5.31/5.60 ! [A4: set_real,G2: real > complex,B5: set_real] :
% 5.31/5.60 ( ( finite_finite_real @ A4 )
% 5.31/5.60 => ( ( groups5754745047067104278omplex @ G2 @ ( inf_inf_set_real @ A4 @ B5 ) )
% 5.31/5.60 = ( groups5754745047067104278omplex
% 5.31/5.60 @ ^ [X4: real] : ( if_complex @ ( member_real @ X4 @ B5 ) @ ( G2 @ X4 ) @ zero_zero_complex )
% 5.31/5.60 @ A4 ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum.inter_restrict
% 5.31/5.60 thf(fact_5568_sum_Ointer__restrict,axiom,
% 5.31/5.60 ! [A4: set_int,G2: int > complex,B5: set_int] :
% 5.31/5.60 ( ( finite_finite_int @ A4 )
% 5.31/5.60 => ( ( groups3049146728041665814omplex @ G2 @ ( inf_inf_set_int @ A4 @ B5 ) )
% 5.31/5.60 = ( groups3049146728041665814omplex
% 5.31/5.60 @ ^ [X4: int] : ( if_complex @ ( member_int @ X4 @ B5 ) @ ( G2 @ X4 ) @ zero_zero_complex )
% 5.31/5.60 @ A4 ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum.inter_restrict
% 5.31/5.60 thf(fact_5569_sum_Ointer__restrict,axiom,
% 5.31/5.60 ! [A4: set_complex,G2: complex > complex,B5: set_complex] :
% 5.31/5.60 ( ( finite3207457112153483333omplex @ A4 )
% 5.31/5.60 => ( ( groups7754918857620584856omplex @ G2 @ ( inf_inf_set_complex @ A4 @ B5 ) )
% 5.31/5.60 = ( groups7754918857620584856omplex
% 5.31/5.60 @ ^ [X4: complex] : ( if_complex @ ( member_complex @ X4 @ B5 ) @ ( G2 @ X4 ) @ zero_zero_complex )
% 5.31/5.60 @ A4 ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum.inter_restrict
% 5.31/5.60 thf(fact_5570_sum_Ointer__restrict,axiom,
% 5.31/5.60 ! [A4: set_real,G2: real > real,B5: set_real] :
% 5.31/5.60 ( ( finite_finite_real @ A4 )
% 5.31/5.60 => ( ( groups8097168146408367636l_real @ G2 @ ( inf_inf_set_real @ A4 @ B5 ) )
% 5.31/5.60 = ( groups8097168146408367636l_real
% 5.31/5.60 @ ^ [X4: real] : ( if_real @ ( member_real @ X4 @ B5 ) @ ( G2 @ X4 ) @ zero_zero_real )
% 5.31/5.60 @ A4 ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum.inter_restrict
% 5.31/5.60 thf(fact_5571_sum_Ointer__restrict,axiom,
% 5.31/5.60 ! [A4: set_int,G2: int > real,B5: set_int] :
% 5.31/5.60 ( ( finite_finite_int @ A4 )
% 5.31/5.60 => ( ( groups8778361861064173332t_real @ G2 @ ( inf_inf_set_int @ A4 @ B5 ) )
% 5.31/5.60 = ( groups8778361861064173332t_real
% 5.31/5.60 @ ^ [X4: int] : ( if_real @ ( member_int @ X4 @ B5 ) @ ( G2 @ X4 ) @ zero_zero_real )
% 5.31/5.60 @ A4 ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum.inter_restrict
% 5.31/5.60 thf(fact_5572_sum_Ointer__restrict,axiom,
% 5.31/5.60 ! [A4: set_complex,G2: complex > real,B5: set_complex] :
% 5.31/5.60 ( ( finite3207457112153483333omplex @ A4 )
% 5.31/5.60 => ( ( groups5808333547571424918x_real @ G2 @ ( inf_inf_set_complex @ A4 @ B5 ) )
% 5.31/5.60 = ( groups5808333547571424918x_real
% 5.31/5.60 @ ^ [X4: complex] : ( if_real @ ( member_complex @ X4 @ B5 ) @ ( G2 @ X4 ) @ zero_zero_real )
% 5.31/5.60 @ A4 ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum.inter_restrict
% 5.31/5.60 thf(fact_5573_sum_Ointer__restrict,axiom,
% 5.31/5.60 ! [A4: set_real,G2: real > rat,B5: set_real] :
% 5.31/5.60 ( ( finite_finite_real @ A4 )
% 5.31/5.60 => ( ( groups1300246762558778688al_rat @ G2 @ ( inf_inf_set_real @ A4 @ B5 ) )
% 5.31/5.60 = ( groups1300246762558778688al_rat
% 5.31/5.60 @ ^ [X4: real] : ( if_rat @ ( member_real @ X4 @ B5 ) @ ( G2 @ X4 ) @ zero_zero_rat )
% 5.31/5.60 @ A4 ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum.inter_restrict
% 5.31/5.60 thf(fact_5574_sum_Ointer__restrict,axiom,
% 5.31/5.60 ! [A4: set_int,G2: int > rat,B5: set_int] :
% 5.31/5.60 ( ( finite_finite_int @ A4 )
% 5.31/5.60 => ( ( groups3906332499630173760nt_rat @ G2 @ ( inf_inf_set_int @ A4 @ B5 ) )
% 5.31/5.60 = ( groups3906332499630173760nt_rat
% 5.31/5.60 @ ^ [X4: int] : ( if_rat @ ( member_int @ X4 @ B5 ) @ ( G2 @ X4 ) @ zero_zero_rat )
% 5.31/5.60 @ A4 ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum.inter_restrict
% 5.31/5.60 thf(fact_5575_sum_Ointer__restrict,axiom,
% 5.31/5.60 ! [A4: set_complex,G2: complex > rat,B5: set_complex] :
% 5.31/5.60 ( ( finite3207457112153483333omplex @ A4 )
% 5.31/5.60 => ( ( groups5058264527183730370ex_rat @ G2 @ ( inf_inf_set_complex @ A4 @ B5 ) )
% 5.31/5.60 = ( groups5058264527183730370ex_rat
% 5.31/5.60 @ ^ [X4: complex] : ( if_rat @ ( member_complex @ X4 @ B5 ) @ ( G2 @ X4 ) @ zero_zero_rat )
% 5.31/5.60 @ A4 ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum.inter_restrict
% 5.31/5.60 thf(fact_5576_sum_Ointer__restrict,axiom,
% 5.31/5.60 ! [A4: set_real,G2: real > nat,B5: set_real] :
% 5.31/5.60 ( ( finite_finite_real @ A4 )
% 5.31/5.60 => ( ( groups1935376822645274424al_nat @ G2 @ ( inf_inf_set_real @ A4 @ B5 ) )
% 5.31/5.60 = ( groups1935376822645274424al_nat
% 5.31/5.60 @ ^ [X4: real] : ( if_nat @ ( member_real @ X4 @ B5 ) @ ( G2 @ X4 ) @ zero_zero_nat )
% 5.31/5.60 @ A4 ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum.inter_restrict
% 5.31/5.60 thf(fact_5577_sum_Osetdiff__irrelevant,axiom,
% 5.31/5.60 ! [A4: set_real,G2: real > complex] :
% 5.31/5.60 ( ( finite_finite_real @ A4 )
% 5.31/5.60 => ( ( groups5754745047067104278omplex @ G2
% 5.31/5.60 @ ( minus_minus_set_real @ A4
% 5.31/5.60 @ ( collect_real
% 5.31/5.60 @ ^ [X4: real] :
% 5.31/5.60 ( ( G2 @ X4 )
% 5.31/5.60 = zero_zero_complex ) ) ) )
% 5.31/5.60 = ( groups5754745047067104278omplex @ G2 @ A4 ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum.setdiff_irrelevant
% 5.31/5.60 thf(fact_5578_sum_Osetdiff__irrelevant,axiom,
% 5.31/5.60 ! [A4: set_int,G2: int > complex] :
% 5.31/5.60 ( ( finite_finite_int @ A4 )
% 5.31/5.60 => ( ( groups3049146728041665814omplex @ G2
% 5.31/5.60 @ ( minus_minus_set_int @ A4
% 5.31/5.60 @ ( collect_int
% 5.31/5.60 @ ^ [X4: int] :
% 5.31/5.60 ( ( G2 @ X4 )
% 5.31/5.60 = zero_zero_complex ) ) ) )
% 5.31/5.60 = ( groups3049146728041665814omplex @ G2 @ A4 ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum.setdiff_irrelevant
% 5.31/5.60 thf(fact_5579_sum_Osetdiff__irrelevant,axiom,
% 5.31/5.60 ! [A4: set_complex,G2: complex > complex] :
% 5.31/5.60 ( ( finite3207457112153483333omplex @ A4 )
% 5.31/5.60 => ( ( groups7754918857620584856omplex @ G2
% 5.31/5.60 @ ( minus_811609699411566653omplex @ A4
% 5.31/5.60 @ ( collect_complex
% 5.31/5.60 @ ^ [X4: complex] :
% 5.31/5.60 ( ( G2 @ X4 )
% 5.31/5.60 = zero_zero_complex ) ) ) )
% 5.31/5.60 = ( groups7754918857620584856omplex @ G2 @ A4 ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum.setdiff_irrelevant
% 5.31/5.60 thf(fact_5580_sum_Osetdiff__irrelevant,axiom,
% 5.31/5.60 ! [A4: set_real,G2: real > real] :
% 5.31/5.60 ( ( finite_finite_real @ A4 )
% 5.31/5.60 => ( ( groups8097168146408367636l_real @ G2
% 5.31/5.60 @ ( minus_minus_set_real @ A4
% 5.31/5.60 @ ( collect_real
% 5.31/5.60 @ ^ [X4: real] :
% 5.31/5.60 ( ( G2 @ X4 )
% 5.31/5.60 = zero_zero_real ) ) ) )
% 5.31/5.60 = ( groups8097168146408367636l_real @ G2 @ A4 ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum.setdiff_irrelevant
% 5.31/5.60 thf(fact_5581_sum_Osetdiff__irrelevant,axiom,
% 5.31/5.60 ! [A4: set_int,G2: int > real] :
% 5.31/5.60 ( ( finite_finite_int @ A4 )
% 5.31/5.60 => ( ( groups8778361861064173332t_real @ G2
% 5.31/5.60 @ ( minus_minus_set_int @ A4
% 5.31/5.60 @ ( collect_int
% 5.31/5.60 @ ^ [X4: int] :
% 5.31/5.60 ( ( G2 @ X4 )
% 5.31/5.60 = zero_zero_real ) ) ) )
% 5.31/5.60 = ( groups8778361861064173332t_real @ G2 @ A4 ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum.setdiff_irrelevant
% 5.31/5.60 thf(fact_5582_sum_Osetdiff__irrelevant,axiom,
% 5.31/5.60 ! [A4: set_complex,G2: complex > real] :
% 5.31/5.60 ( ( finite3207457112153483333omplex @ A4 )
% 5.31/5.60 => ( ( groups5808333547571424918x_real @ G2
% 5.31/5.60 @ ( minus_811609699411566653omplex @ A4
% 5.31/5.60 @ ( collect_complex
% 5.31/5.60 @ ^ [X4: complex] :
% 5.31/5.60 ( ( G2 @ X4 )
% 5.31/5.60 = zero_zero_real ) ) ) )
% 5.31/5.60 = ( groups5808333547571424918x_real @ G2 @ A4 ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum.setdiff_irrelevant
% 5.31/5.60 thf(fact_5583_sum_Osetdiff__irrelevant,axiom,
% 5.31/5.60 ! [A4: set_real,G2: real > rat] :
% 5.31/5.60 ( ( finite_finite_real @ A4 )
% 5.31/5.60 => ( ( groups1300246762558778688al_rat @ G2
% 5.31/5.60 @ ( minus_minus_set_real @ A4
% 5.31/5.60 @ ( collect_real
% 5.31/5.60 @ ^ [X4: real] :
% 5.31/5.60 ( ( G2 @ X4 )
% 5.31/5.60 = zero_zero_rat ) ) ) )
% 5.31/5.60 = ( groups1300246762558778688al_rat @ G2 @ A4 ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum.setdiff_irrelevant
% 5.31/5.60 thf(fact_5584_sum_Osetdiff__irrelevant,axiom,
% 5.31/5.60 ! [A4: set_int,G2: int > rat] :
% 5.31/5.60 ( ( finite_finite_int @ A4 )
% 5.31/5.60 => ( ( groups3906332499630173760nt_rat @ G2
% 5.31/5.60 @ ( minus_minus_set_int @ A4
% 5.31/5.60 @ ( collect_int
% 5.31/5.60 @ ^ [X4: int] :
% 5.31/5.60 ( ( G2 @ X4 )
% 5.31/5.60 = zero_zero_rat ) ) ) )
% 5.31/5.60 = ( groups3906332499630173760nt_rat @ G2 @ A4 ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum.setdiff_irrelevant
% 5.31/5.60 thf(fact_5585_sum_Osetdiff__irrelevant,axiom,
% 5.31/5.60 ! [A4: set_complex,G2: complex > rat] :
% 5.31/5.60 ( ( finite3207457112153483333omplex @ A4 )
% 5.31/5.60 => ( ( groups5058264527183730370ex_rat @ G2
% 5.31/5.60 @ ( minus_811609699411566653omplex @ A4
% 5.31/5.60 @ ( collect_complex
% 5.31/5.60 @ ^ [X4: complex] :
% 5.31/5.60 ( ( G2 @ X4 )
% 5.31/5.60 = zero_zero_rat ) ) ) )
% 5.31/5.60 = ( groups5058264527183730370ex_rat @ G2 @ A4 ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum.setdiff_irrelevant
% 5.31/5.60 thf(fact_5586_sum_Osetdiff__irrelevant,axiom,
% 5.31/5.60 ! [A4: set_real,G2: real > nat] :
% 5.31/5.60 ( ( finite_finite_real @ A4 )
% 5.31/5.60 => ( ( groups1935376822645274424al_nat @ G2
% 5.31/5.60 @ ( minus_minus_set_real @ A4
% 5.31/5.60 @ ( collect_real
% 5.31/5.60 @ ^ [X4: real] :
% 5.31/5.60 ( ( G2 @ X4 )
% 5.31/5.60 = zero_zero_nat ) ) ) )
% 5.31/5.60 = ( groups1935376822645274424al_nat @ G2 @ A4 ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum.setdiff_irrelevant
% 5.31/5.60 thf(fact_5587_sum_Oshift__bounds__cl__Suc__ivl,axiom,
% 5.31/5.60 ! [G2: nat > nat,M2: nat,N: nat] :
% 5.31/5.60 ( ( groups3542108847815614940at_nat @ G2 @ ( set_or1269000886237332187st_nat @ ( suc @ M2 ) @ ( suc @ N ) ) )
% 5.31/5.60 = ( groups3542108847815614940at_nat
% 5.31/5.60 @ ^ [I: nat] : ( G2 @ ( suc @ I ) )
% 5.31/5.60 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum.shift_bounds_cl_Suc_ivl
% 5.31/5.60 thf(fact_5588_sum_Oshift__bounds__cl__Suc__ivl,axiom,
% 5.31/5.60 ! [G2: nat > real,M2: nat,N: nat] :
% 5.31/5.60 ( ( groups6591440286371151544t_real @ G2 @ ( set_or1269000886237332187st_nat @ ( suc @ M2 ) @ ( suc @ N ) ) )
% 5.31/5.60 = ( groups6591440286371151544t_real
% 5.31/5.60 @ ^ [I: nat] : ( G2 @ ( suc @ I ) )
% 5.31/5.60 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum.shift_bounds_cl_Suc_ivl
% 5.31/5.60 thf(fact_5589_sum_Oshift__bounds__cl__nat__ivl,axiom,
% 5.31/5.60 ! [G2: nat > nat,M2: nat,K2: nat,N: nat] :
% 5.31/5.60 ( ( groups3542108847815614940at_nat @ G2 @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ M2 @ K2 ) @ ( plus_plus_nat @ N @ K2 ) ) )
% 5.31/5.60 = ( groups3542108847815614940at_nat
% 5.31/5.60 @ ^ [I: nat] : ( G2 @ ( plus_plus_nat @ I @ K2 ) )
% 5.31/5.60 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum.shift_bounds_cl_nat_ivl
% 5.31/5.60 thf(fact_5590_sum_Oshift__bounds__cl__nat__ivl,axiom,
% 5.31/5.60 ! [G2: nat > real,M2: nat,K2: nat,N: nat] :
% 5.31/5.60 ( ( groups6591440286371151544t_real @ G2 @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ M2 @ K2 ) @ ( plus_plus_nat @ N @ K2 ) ) )
% 5.31/5.60 = ( groups6591440286371151544t_real
% 5.31/5.60 @ ^ [I: nat] : ( G2 @ ( plus_plus_nat @ I @ K2 ) )
% 5.31/5.60 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum.shift_bounds_cl_nat_ivl
% 5.31/5.60 thf(fact_5591_sum__pos2,axiom,
% 5.31/5.60 ! [I5: set_real,I2: real,F2: real > real] :
% 5.31/5.60 ( ( finite_finite_real @ I5 )
% 5.31/5.60 => ( ( member_real @ I2 @ I5 )
% 5.31/5.60 => ( ( ord_less_real @ zero_zero_real @ ( F2 @ I2 ) )
% 5.31/5.60 => ( ! [I3: real] :
% 5.31/5.60 ( ( member_real @ I3 @ I5 )
% 5.31/5.60 => ( ord_less_eq_real @ zero_zero_real @ ( F2 @ I3 ) ) )
% 5.31/5.60 => ( ord_less_real @ zero_zero_real @ ( groups8097168146408367636l_real @ F2 @ I5 ) ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum_pos2
% 5.31/5.60 thf(fact_5592_sum__pos2,axiom,
% 5.31/5.60 ! [I5: set_int,I2: int,F2: int > real] :
% 5.31/5.60 ( ( finite_finite_int @ I5 )
% 5.31/5.60 => ( ( member_int @ I2 @ I5 )
% 5.31/5.60 => ( ( ord_less_real @ zero_zero_real @ ( F2 @ I2 ) )
% 5.31/5.60 => ( ! [I3: int] :
% 5.31/5.60 ( ( member_int @ I3 @ I5 )
% 5.31/5.60 => ( ord_less_eq_real @ zero_zero_real @ ( F2 @ I3 ) ) )
% 5.31/5.60 => ( ord_less_real @ zero_zero_real @ ( groups8778361861064173332t_real @ F2 @ I5 ) ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum_pos2
% 5.31/5.60 thf(fact_5593_sum__pos2,axiom,
% 5.31/5.60 ! [I5: set_complex,I2: complex,F2: complex > real] :
% 5.31/5.60 ( ( finite3207457112153483333omplex @ I5 )
% 5.31/5.60 => ( ( member_complex @ I2 @ I5 )
% 5.31/5.60 => ( ( ord_less_real @ zero_zero_real @ ( F2 @ I2 ) )
% 5.31/5.60 => ( ! [I3: complex] :
% 5.31/5.60 ( ( member_complex @ I3 @ I5 )
% 5.31/5.60 => ( ord_less_eq_real @ zero_zero_real @ ( F2 @ I3 ) ) )
% 5.31/5.60 => ( ord_less_real @ zero_zero_real @ ( groups5808333547571424918x_real @ F2 @ I5 ) ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum_pos2
% 5.31/5.60 thf(fact_5594_sum__pos2,axiom,
% 5.31/5.60 ! [I5: set_real,I2: real,F2: real > rat] :
% 5.31/5.60 ( ( finite_finite_real @ I5 )
% 5.31/5.60 => ( ( member_real @ I2 @ I5 )
% 5.31/5.60 => ( ( ord_less_rat @ zero_zero_rat @ ( F2 @ I2 ) )
% 5.31/5.60 => ( ! [I3: real] :
% 5.31/5.60 ( ( member_real @ I3 @ I5 )
% 5.31/5.60 => ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ I3 ) ) )
% 5.31/5.60 => ( ord_less_rat @ zero_zero_rat @ ( groups1300246762558778688al_rat @ F2 @ I5 ) ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum_pos2
% 5.31/5.60 thf(fact_5595_sum__pos2,axiom,
% 5.31/5.60 ! [I5: set_nat,I2: nat,F2: nat > rat] :
% 5.31/5.60 ( ( finite_finite_nat @ I5 )
% 5.31/5.60 => ( ( member_nat @ I2 @ I5 )
% 5.31/5.60 => ( ( ord_less_rat @ zero_zero_rat @ ( F2 @ I2 ) )
% 5.31/5.60 => ( ! [I3: nat] :
% 5.31/5.60 ( ( member_nat @ I3 @ I5 )
% 5.31/5.60 => ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ I3 ) ) )
% 5.31/5.60 => ( ord_less_rat @ zero_zero_rat @ ( groups2906978787729119204at_rat @ F2 @ I5 ) ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum_pos2
% 5.31/5.60 thf(fact_5596_sum__pos2,axiom,
% 5.31/5.60 ! [I5: set_int,I2: int,F2: int > rat] :
% 5.31/5.60 ( ( finite_finite_int @ I5 )
% 5.31/5.60 => ( ( member_int @ I2 @ I5 )
% 5.31/5.60 => ( ( ord_less_rat @ zero_zero_rat @ ( F2 @ I2 ) )
% 5.31/5.60 => ( ! [I3: int] :
% 5.31/5.60 ( ( member_int @ I3 @ I5 )
% 5.31/5.60 => ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ I3 ) ) )
% 5.31/5.60 => ( ord_less_rat @ zero_zero_rat @ ( groups3906332499630173760nt_rat @ F2 @ I5 ) ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum_pos2
% 5.31/5.60 thf(fact_5597_sum__pos2,axiom,
% 5.31/5.60 ! [I5: set_complex,I2: complex,F2: complex > rat] :
% 5.31/5.60 ( ( finite3207457112153483333omplex @ I5 )
% 5.31/5.60 => ( ( member_complex @ I2 @ I5 )
% 5.31/5.60 => ( ( ord_less_rat @ zero_zero_rat @ ( F2 @ I2 ) )
% 5.31/5.60 => ( ! [I3: complex] :
% 5.31/5.60 ( ( member_complex @ I3 @ I5 )
% 5.31/5.60 => ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ I3 ) ) )
% 5.31/5.60 => ( ord_less_rat @ zero_zero_rat @ ( groups5058264527183730370ex_rat @ F2 @ I5 ) ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum_pos2
% 5.31/5.60 thf(fact_5598_sum__pos2,axiom,
% 5.31/5.60 ! [I5: set_real,I2: real,F2: real > nat] :
% 5.31/5.60 ( ( finite_finite_real @ I5 )
% 5.31/5.60 => ( ( member_real @ I2 @ I5 )
% 5.31/5.60 => ( ( ord_less_nat @ zero_zero_nat @ ( F2 @ I2 ) )
% 5.31/5.60 => ( ! [I3: real] :
% 5.31/5.60 ( ( member_real @ I3 @ I5 )
% 5.31/5.60 => ( ord_less_eq_nat @ zero_zero_nat @ ( F2 @ I3 ) ) )
% 5.31/5.60 => ( ord_less_nat @ zero_zero_nat @ ( groups1935376822645274424al_nat @ F2 @ I5 ) ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum_pos2
% 5.31/5.60 thf(fact_5599_sum__pos2,axiom,
% 5.31/5.60 ! [I5: set_int,I2: int,F2: int > nat] :
% 5.31/5.60 ( ( finite_finite_int @ I5 )
% 5.31/5.60 => ( ( member_int @ I2 @ I5 )
% 5.31/5.60 => ( ( ord_less_nat @ zero_zero_nat @ ( F2 @ I2 ) )
% 5.31/5.60 => ( ! [I3: int] :
% 5.31/5.60 ( ( member_int @ I3 @ I5 )
% 5.31/5.60 => ( ord_less_eq_nat @ zero_zero_nat @ ( F2 @ I3 ) ) )
% 5.31/5.60 => ( ord_less_nat @ zero_zero_nat @ ( groups4541462559716669496nt_nat @ F2 @ I5 ) ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum_pos2
% 5.31/5.60 thf(fact_5600_sum__pos2,axiom,
% 5.31/5.60 ! [I5: set_complex,I2: complex,F2: complex > nat] :
% 5.31/5.60 ( ( finite3207457112153483333omplex @ I5 )
% 5.31/5.60 => ( ( member_complex @ I2 @ I5 )
% 5.31/5.60 => ( ( ord_less_nat @ zero_zero_nat @ ( F2 @ I2 ) )
% 5.31/5.60 => ( ! [I3: complex] :
% 5.31/5.60 ( ( member_complex @ I3 @ I5 )
% 5.31/5.60 => ( ord_less_eq_nat @ zero_zero_nat @ ( F2 @ I3 ) ) )
% 5.31/5.60 => ( ord_less_nat @ zero_zero_nat @ ( groups5693394587270226106ex_nat @ F2 @ I5 ) ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum_pos2
% 5.31/5.60 thf(fact_5601_sum__pos,axiom,
% 5.31/5.60 ! [I5: set_complex,F2: complex > real] :
% 5.31/5.60 ( ( finite3207457112153483333omplex @ I5 )
% 5.31/5.60 => ( ( I5 != bot_bot_set_complex )
% 5.31/5.60 => ( ! [I3: complex] :
% 5.31/5.60 ( ( member_complex @ I3 @ I5 )
% 5.31/5.60 => ( ord_less_real @ zero_zero_real @ ( F2 @ I3 ) ) )
% 5.31/5.60 => ( ord_less_real @ zero_zero_real @ ( groups5808333547571424918x_real @ F2 @ I5 ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum_pos
% 5.31/5.60 thf(fact_5602_sum__pos,axiom,
% 5.31/5.60 ! [I5: set_int,F2: int > real] :
% 5.31/5.60 ( ( finite_finite_int @ I5 )
% 5.31/5.60 => ( ( I5 != bot_bot_set_int )
% 5.31/5.60 => ( ! [I3: int] :
% 5.31/5.60 ( ( member_int @ I3 @ I5 )
% 5.31/5.60 => ( ord_less_real @ zero_zero_real @ ( F2 @ I3 ) ) )
% 5.31/5.60 => ( ord_less_real @ zero_zero_real @ ( groups8778361861064173332t_real @ F2 @ I5 ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum_pos
% 5.31/5.60 thf(fact_5603_sum__pos,axiom,
% 5.31/5.60 ! [I5: set_real,F2: real > real] :
% 5.31/5.60 ( ( finite_finite_real @ I5 )
% 5.31/5.60 => ( ( I5 != bot_bot_set_real )
% 5.31/5.60 => ( ! [I3: real] :
% 5.31/5.60 ( ( member_real @ I3 @ I5 )
% 5.31/5.60 => ( ord_less_real @ zero_zero_real @ ( F2 @ I3 ) ) )
% 5.31/5.60 => ( ord_less_real @ zero_zero_real @ ( groups8097168146408367636l_real @ F2 @ I5 ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum_pos
% 5.31/5.60 thf(fact_5604_sum__pos,axiom,
% 5.31/5.60 ! [I5: set_complex,F2: complex > rat] :
% 5.31/5.60 ( ( finite3207457112153483333omplex @ I5 )
% 5.31/5.60 => ( ( I5 != bot_bot_set_complex )
% 5.31/5.60 => ( ! [I3: complex] :
% 5.31/5.60 ( ( member_complex @ I3 @ I5 )
% 5.31/5.60 => ( ord_less_rat @ zero_zero_rat @ ( F2 @ I3 ) ) )
% 5.31/5.60 => ( ord_less_rat @ zero_zero_rat @ ( groups5058264527183730370ex_rat @ F2 @ I5 ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum_pos
% 5.31/5.60 thf(fact_5605_sum__pos,axiom,
% 5.31/5.60 ! [I5: set_nat,F2: nat > rat] :
% 5.31/5.60 ( ( finite_finite_nat @ I5 )
% 5.31/5.60 => ( ( I5 != bot_bot_set_nat )
% 5.31/5.60 => ( ! [I3: nat] :
% 5.31/5.60 ( ( member_nat @ I3 @ I5 )
% 5.31/5.60 => ( ord_less_rat @ zero_zero_rat @ ( F2 @ I3 ) ) )
% 5.31/5.60 => ( ord_less_rat @ zero_zero_rat @ ( groups2906978787729119204at_rat @ F2 @ I5 ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum_pos
% 5.31/5.60 thf(fact_5606_sum__pos,axiom,
% 5.31/5.60 ! [I5: set_int,F2: int > rat] :
% 5.31/5.60 ( ( finite_finite_int @ I5 )
% 5.31/5.60 => ( ( I5 != bot_bot_set_int )
% 5.31/5.60 => ( ! [I3: int] :
% 5.31/5.60 ( ( member_int @ I3 @ I5 )
% 5.31/5.60 => ( ord_less_rat @ zero_zero_rat @ ( F2 @ I3 ) ) )
% 5.31/5.60 => ( ord_less_rat @ zero_zero_rat @ ( groups3906332499630173760nt_rat @ F2 @ I5 ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum_pos
% 5.31/5.60 thf(fact_5607_sum__pos,axiom,
% 5.31/5.60 ! [I5: set_real,F2: real > rat] :
% 5.31/5.60 ( ( finite_finite_real @ I5 )
% 5.31/5.60 => ( ( I5 != bot_bot_set_real )
% 5.31/5.60 => ( ! [I3: real] :
% 5.31/5.60 ( ( member_real @ I3 @ I5 )
% 5.31/5.60 => ( ord_less_rat @ zero_zero_rat @ ( F2 @ I3 ) ) )
% 5.31/5.60 => ( ord_less_rat @ zero_zero_rat @ ( groups1300246762558778688al_rat @ F2 @ I5 ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum_pos
% 5.31/5.60 thf(fact_5608_sum__pos,axiom,
% 5.31/5.60 ! [I5: set_complex,F2: complex > nat] :
% 5.31/5.60 ( ( finite3207457112153483333omplex @ I5 )
% 5.31/5.60 => ( ( I5 != bot_bot_set_complex )
% 5.31/5.60 => ( ! [I3: complex] :
% 5.31/5.60 ( ( member_complex @ I3 @ I5 )
% 5.31/5.60 => ( ord_less_nat @ zero_zero_nat @ ( F2 @ I3 ) ) )
% 5.31/5.60 => ( ord_less_nat @ zero_zero_nat @ ( groups5693394587270226106ex_nat @ F2 @ I5 ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum_pos
% 5.31/5.60 thf(fact_5609_sum__pos,axiom,
% 5.31/5.60 ! [I5: set_int,F2: int > nat] :
% 5.31/5.60 ( ( finite_finite_int @ I5 )
% 5.31/5.60 => ( ( I5 != bot_bot_set_int )
% 5.31/5.60 => ( ! [I3: int] :
% 5.31/5.60 ( ( member_int @ I3 @ I5 )
% 5.31/5.60 => ( ord_less_nat @ zero_zero_nat @ ( F2 @ I3 ) ) )
% 5.31/5.60 => ( ord_less_nat @ zero_zero_nat @ ( groups4541462559716669496nt_nat @ F2 @ I5 ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum_pos
% 5.31/5.60 thf(fact_5610_sum__pos,axiom,
% 5.31/5.60 ! [I5: set_real,F2: real > nat] :
% 5.31/5.60 ( ( finite_finite_real @ I5 )
% 5.31/5.60 => ( ( I5 != bot_bot_set_real )
% 5.31/5.60 => ( ! [I3: real] :
% 5.31/5.60 ( ( member_real @ I3 @ I5 )
% 5.31/5.60 => ( ord_less_nat @ zero_zero_nat @ ( F2 @ I3 ) ) )
% 5.31/5.60 => ( ord_less_nat @ zero_zero_nat @ ( groups1935376822645274424al_nat @ F2 @ I5 ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum_pos
% 5.31/5.60 thf(fact_5611_sum__bounded__below,axiom,
% 5.31/5.60 ! [A4: set_real,K5: real,F2: real > real] :
% 5.31/5.60 ( ! [I3: real] :
% 5.31/5.60 ( ( member_real @ I3 @ A4 )
% 5.31/5.60 => ( ord_less_eq_real @ K5 @ ( F2 @ I3 ) ) )
% 5.31/5.60 => ( ord_less_eq_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( finite_card_real @ A4 ) ) @ K5 ) @ ( groups8097168146408367636l_real @ F2 @ A4 ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum_bounded_below
% 5.31/5.60 thf(fact_5612_sum__bounded__below,axiom,
% 5.31/5.60 ! [A4: set_complex,K5: real,F2: complex > real] :
% 5.31/5.60 ( ! [I3: complex] :
% 5.31/5.60 ( ( member_complex @ I3 @ A4 )
% 5.31/5.60 => ( ord_less_eq_real @ K5 @ ( F2 @ I3 ) ) )
% 5.31/5.60 => ( ord_less_eq_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( finite_card_complex @ A4 ) ) @ K5 ) @ ( groups5808333547571424918x_real @ F2 @ A4 ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum_bounded_below
% 5.31/5.60 thf(fact_5613_sum__bounded__below,axiom,
% 5.31/5.60 ! [A4: set_int,K5: real,F2: int > real] :
% 5.31/5.60 ( ! [I3: int] :
% 5.31/5.60 ( ( member_int @ I3 @ A4 )
% 5.31/5.60 => ( ord_less_eq_real @ K5 @ ( F2 @ I3 ) ) )
% 5.31/5.60 => ( ord_less_eq_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( finite_card_int @ A4 ) ) @ K5 ) @ ( groups8778361861064173332t_real @ F2 @ A4 ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum_bounded_below
% 5.31/5.60 thf(fact_5614_sum__bounded__below,axiom,
% 5.31/5.60 ! [A4: set_real,K5: rat,F2: real > rat] :
% 5.31/5.60 ( ! [I3: real] :
% 5.31/5.60 ( ( member_real @ I3 @ A4 )
% 5.31/5.60 => ( ord_less_eq_rat @ K5 @ ( F2 @ I3 ) ) )
% 5.31/5.60 => ( ord_less_eq_rat @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( finite_card_real @ A4 ) ) @ K5 ) @ ( groups1300246762558778688al_rat @ F2 @ A4 ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum_bounded_below
% 5.31/5.60 thf(fact_5615_sum__bounded__below,axiom,
% 5.31/5.60 ! [A4: set_nat,K5: rat,F2: nat > rat] :
% 5.31/5.60 ( ! [I3: nat] :
% 5.31/5.60 ( ( member_nat @ I3 @ A4 )
% 5.31/5.60 => ( ord_less_eq_rat @ K5 @ ( F2 @ I3 ) ) )
% 5.31/5.60 => ( ord_less_eq_rat @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( finite_card_nat @ A4 ) ) @ K5 ) @ ( groups2906978787729119204at_rat @ F2 @ A4 ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum_bounded_below
% 5.31/5.60 thf(fact_5616_sum__bounded__below,axiom,
% 5.31/5.60 ! [A4: set_complex,K5: rat,F2: complex > rat] :
% 5.31/5.60 ( ! [I3: complex] :
% 5.31/5.60 ( ( member_complex @ I3 @ A4 )
% 5.31/5.60 => ( ord_less_eq_rat @ K5 @ ( F2 @ I3 ) ) )
% 5.31/5.60 => ( ord_less_eq_rat @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( finite_card_complex @ A4 ) ) @ K5 ) @ ( groups5058264527183730370ex_rat @ F2 @ A4 ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum_bounded_below
% 5.31/5.60 thf(fact_5617_sum__bounded__below,axiom,
% 5.31/5.60 ! [A4: set_int,K5: rat,F2: int > rat] :
% 5.31/5.60 ( ! [I3: int] :
% 5.31/5.60 ( ( member_int @ I3 @ A4 )
% 5.31/5.60 => ( ord_less_eq_rat @ K5 @ ( F2 @ I3 ) ) )
% 5.31/5.60 => ( ord_less_eq_rat @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( finite_card_int @ A4 ) ) @ K5 ) @ ( groups3906332499630173760nt_rat @ F2 @ A4 ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum_bounded_below
% 5.31/5.60 thf(fact_5618_sum__bounded__below,axiom,
% 5.31/5.60 ! [A4: set_real,K5: nat,F2: real > nat] :
% 5.31/5.60 ( ! [I3: real] :
% 5.31/5.60 ( ( member_real @ I3 @ A4 )
% 5.31/5.60 => ( ord_less_eq_nat @ K5 @ ( F2 @ I3 ) ) )
% 5.31/5.60 => ( ord_less_eq_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ ( finite_card_real @ A4 ) ) @ K5 ) @ ( groups1935376822645274424al_nat @ F2 @ A4 ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum_bounded_below
% 5.31/5.60 thf(fact_5619_sum__bounded__below,axiom,
% 5.31/5.60 ! [A4: set_complex,K5: nat,F2: complex > nat] :
% 5.31/5.60 ( ! [I3: complex] :
% 5.31/5.60 ( ( member_complex @ I3 @ A4 )
% 5.31/5.60 => ( ord_less_eq_nat @ K5 @ ( F2 @ I3 ) ) )
% 5.31/5.60 => ( ord_less_eq_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ ( finite_card_complex @ A4 ) ) @ K5 ) @ ( groups5693394587270226106ex_nat @ F2 @ A4 ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum_bounded_below
% 5.31/5.60 thf(fact_5620_sum__bounded__below,axiom,
% 5.31/5.60 ! [A4: set_int,K5: nat,F2: int > nat] :
% 5.31/5.60 ( ! [I3: int] :
% 5.31/5.60 ( ( member_int @ I3 @ A4 )
% 5.31/5.60 => ( ord_less_eq_nat @ K5 @ ( F2 @ I3 ) ) )
% 5.31/5.60 => ( ord_less_eq_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ ( finite_card_int @ A4 ) ) @ K5 ) @ ( groups4541462559716669496nt_nat @ F2 @ A4 ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum_bounded_below
% 5.31/5.60 thf(fact_5621_sum__bounded__above,axiom,
% 5.31/5.60 ! [A4: set_real,F2: real > real,K5: real] :
% 5.31/5.60 ( ! [I3: real] :
% 5.31/5.60 ( ( member_real @ I3 @ A4 )
% 5.31/5.60 => ( ord_less_eq_real @ ( F2 @ I3 ) @ K5 ) )
% 5.31/5.60 => ( ord_less_eq_real @ ( groups8097168146408367636l_real @ F2 @ A4 ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( finite_card_real @ A4 ) ) @ K5 ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum_bounded_above
% 5.31/5.60 thf(fact_5622_sum__bounded__above,axiom,
% 5.31/5.60 ! [A4: set_complex,F2: complex > real,K5: real] :
% 5.31/5.60 ( ! [I3: complex] :
% 5.31/5.60 ( ( member_complex @ I3 @ A4 )
% 5.31/5.60 => ( ord_less_eq_real @ ( F2 @ I3 ) @ K5 ) )
% 5.31/5.60 => ( ord_less_eq_real @ ( groups5808333547571424918x_real @ F2 @ A4 ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( finite_card_complex @ A4 ) ) @ K5 ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum_bounded_above
% 5.31/5.60 thf(fact_5623_sum__bounded__above,axiom,
% 5.31/5.60 ! [A4: set_int,F2: int > real,K5: real] :
% 5.31/5.60 ( ! [I3: int] :
% 5.31/5.60 ( ( member_int @ I3 @ A4 )
% 5.31/5.60 => ( ord_less_eq_real @ ( F2 @ I3 ) @ K5 ) )
% 5.31/5.60 => ( ord_less_eq_real @ ( groups8778361861064173332t_real @ F2 @ A4 ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( finite_card_int @ A4 ) ) @ K5 ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum_bounded_above
% 5.31/5.60 thf(fact_5624_sum__bounded__above,axiom,
% 5.31/5.60 ! [A4: set_real,F2: real > rat,K5: rat] :
% 5.31/5.60 ( ! [I3: real] :
% 5.31/5.60 ( ( member_real @ I3 @ A4 )
% 5.31/5.60 => ( ord_less_eq_rat @ ( F2 @ I3 ) @ K5 ) )
% 5.31/5.60 => ( ord_less_eq_rat @ ( groups1300246762558778688al_rat @ F2 @ A4 ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( finite_card_real @ A4 ) ) @ K5 ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum_bounded_above
% 5.31/5.60 thf(fact_5625_sum__bounded__above,axiom,
% 5.31/5.60 ! [A4: set_nat,F2: nat > rat,K5: rat] :
% 5.31/5.60 ( ! [I3: nat] :
% 5.31/5.60 ( ( member_nat @ I3 @ A4 )
% 5.31/5.60 => ( ord_less_eq_rat @ ( F2 @ I3 ) @ K5 ) )
% 5.31/5.60 => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F2 @ A4 ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( finite_card_nat @ A4 ) ) @ K5 ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum_bounded_above
% 5.31/5.60 thf(fact_5626_sum__bounded__above,axiom,
% 5.31/5.60 ! [A4: set_complex,F2: complex > rat,K5: rat] :
% 5.31/5.60 ( ! [I3: complex] :
% 5.31/5.60 ( ( member_complex @ I3 @ A4 )
% 5.31/5.60 => ( ord_less_eq_rat @ ( F2 @ I3 ) @ K5 ) )
% 5.31/5.60 => ( ord_less_eq_rat @ ( groups5058264527183730370ex_rat @ F2 @ A4 ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( finite_card_complex @ A4 ) ) @ K5 ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum_bounded_above
% 5.31/5.60 thf(fact_5627_sum__bounded__above,axiom,
% 5.31/5.60 ! [A4: set_int,F2: int > rat,K5: rat] :
% 5.31/5.60 ( ! [I3: int] :
% 5.31/5.60 ( ( member_int @ I3 @ A4 )
% 5.31/5.60 => ( ord_less_eq_rat @ ( F2 @ I3 ) @ K5 ) )
% 5.31/5.60 => ( ord_less_eq_rat @ ( groups3906332499630173760nt_rat @ F2 @ A4 ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( finite_card_int @ A4 ) ) @ K5 ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum_bounded_above
% 5.31/5.60 thf(fact_5628_sum__bounded__above,axiom,
% 5.31/5.60 ! [A4: set_real,F2: real > nat,K5: nat] :
% 5.31/5.60 ( ! [I3: real] :
% 5.31/5.60 ( ( member_real @ I3 @ A4 )
% 5.31/5.60 => ( ord_less_eq_nat @ ( F2 @ I3 ) @ K5 ) )
% 5.31/5.60 => ( ord_less_eq_nat @ ( groups1935376822645274424al_nat @ F2 @ A4 ) @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ ( finite_card_real @ A4 ) ) @ K5 ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum_bounded_above
% 5.31/5.60 thf(fact_5629_sum__bounded__above,axiom,
% 5.31/5.60 ! [A4: set_complex,F2: complex > nat,K5: nat] :
% 5.31/5.60 ( ! [I3: complex] :
% 5.31/5.60 ( ( member_complex @ I3 @ A4 )
% 5.31/5.60 => ( ord_less_eq_nat @ ( F2 @ I3 ) @ K5 ) )
% 5.31/5.60 => ( ord_less_eq_nat @ ( groups5693394587270226106ex_nat @ F2 @ A4 ) @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ ( finite_card_complex @ A4 ) ) @ K5 ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum_bounded_above
% 5.31/5.60 thf(fact_5630_sum__bounded__above,axiom,
% 5.31/5.60 ! [A4: set_int,F2: int > nat,K5: nat] :
% 5.31/5.60 ( ! [I3: int] :
% 5.31/5.60 ( ( member_int @ I3 @ A4 )
% 5.31/5.60 => ( ord_less_eq_nat @ ( F2 @ I3 ) @ K5 ) )
% 5.31/5.60 => ( ord_less_eq_nat @ ( groups4541462559716669496nt_nat @ F2 @ A4 ) @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ ( finite_card_int @ A4 ) ) @ K5 ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum_bounded_above
% 5.31/5.60 thf(fact_5631_sum_Omono__neutral__cong__right,axiom,
% 5.31/5.60 ! [T5: set_real,S3: set_real,G2: real > complex,H: real > complex] :
% 5.31/5.60 ( ( finite_finite_real @ T5 )
% 5.31/5.60 => ( ( ord_less_eq_set_real @ S3 @ T5 )
% 5.31/5.60 => ( ! [X3: real] :
% 5.31/5.60 ( ( member_real @ X3 @ ( minus_minus_set_real @ T5 @ S3 ) )
% 5.31/5.60 => ( ( G2 @ X3 )
% 5.31/5.60 = zero_zero_complex ) )
% 5.31/5.60 => ( ! [X3: real] :
% 5.31/5.60 ( ( member_real @ X3 @ S3 )
% 5.31/5.60 => ( ( G2 @ X3 )
% 5.31/5.60 = ( H @ X3 ) ) )
% 5.31/5.60 => ( ( groups5754745047067104278omplex @ G2 @ T5 )
% 5.31/5.60 = ( groups5754745047067104278omplex @ H @ S3 ) ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum.mono_neutral_cong_right
% 5.31/5.60 thf(fact_5632_sum_Omono__neutral__cong__right,axiom,
% 5.31/5.60 ! [T5: set_int,S3: set_int,G2: int > complex,H: int > complex] :
% 5.31/5.60 ( ( finite_finite_int @ T5 )
% 5.31/5.60 => ( ( ord_less_eq_set_int @ S3 @ T5 )
% 5.31/5.60 => ( ! [X3: int] :
% 5.31/5.60 ( ( member_int @ X3 @ ( minus_minus_set_int @ T5 @ S3 ) )
% 5.31/5.60 => ( ( G2 @ X3 )
% 5.31/5.60 = zero_zero_complex ) )
% 5.31/5.60 => ( ! [X3: int] :
% 5.31/5.60 ( ( member_int @ X3 @ S3 )
% 5.31/5.60 => ( ( G2 @ X3 )
% 5.31/5.60 = ( H @ X3 ) ) )
% 5.31/5.60 => ( ( groups3049146728041665814omplex @ G2 @ T5 )
% 5.31/5.60 = ( groups3049146728041665814omplex @ H @ S3 ) ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum.mono_neutral_cong_right
% 5.31/5.60 thf(fact_5633_sum_Omono__neutral__cong__right,axiom,
% 5.31/5.60 ! [T5: set_complex,S3: set_complex,G2: complex > complex,H: complex > complex] :
% 5.31/5.60 ( ( finite3207457112153483333omplex @ T5 )
% 5.31/5.60 => ( ( ord_le211207098394363844omplex @ S3 @ T5 )
% 5.31/5.60 => ( ! [X3: complex] :
% 5.31/5.60 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T5 @ S3 ) )
% 5.31/5.60 => ( ( G2 @ X3 )
% 5.31/5.60 = zero_zero_complex ) )
% 5.31/5.60 => ( ! [X3: complex] :
% 5.31/5.60 ( ( member_complex @ X3 @ S3 )
% 5.31/5.60 => ( ( G2 @ X3 )
% 5.31/5.60 = ( H @ X3 ) ) )
% 5.31/5.60 => ( ( groups7754918857620584856omplex @ G2 @ T5 )
% 5.31/5.60 = ( groups7754918857620584856omplex @ H @ S3 ) ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum.mono_neutral_cong_right
% 5.31/5.60 thf(fact_5634_sum_Omono__neutral__cong__right,axiom,
% 5.31/5.60 ! [T5: set_real,S3: set_real,G2: real > real,H: real > real] :
% 5.31/5.60 ( ( finite_finite_real @ T5 )
% 5.31/5.60 => ( ( ord_less_eq_set_real @ S3 @ T5 )
% 5.31/5.60 => ( ! [X3: real] :
% 5.31/5.60 ( ( member_real @ X3 @ ( minus_minus_set_real @ T5 @ S3 ) )
% 5.31/5.60 => ( ( G2 @ X3 )
% 5.31/5.60 = zero_zero_real ) )
% 5.31/5.60 => ( ! [X3: real] :
% 5.31/5.60 ( ( member_real @ X3 @ S3 )
% 5.31/5.60 => ( ( G2 @ X3 )
% 5.31/5.60 = ( H @ X3 ) ) )
% 5.31/5.60 => ( ( groups8097168146408367636l_real @ G2 @ T5 )
% 5.31/5.60 = ( groups8097168146408367636l_real @ H @ S3 ) ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum.mono_neutral_cong_right
% 5.31/5.60 thf(fact_5635_sum_Omono__neutral__cong__right,axiom,
% 5.31/5.60 ! [T5: set_int,S3: set_int,G2: int > real,H: int > real] :
% 5.31/5.60 ( ( finite_finite_int @ T5 )
% 5.31/5.60 => ( ( ord_less_eq_set_int @ S3 @ T5 )
% 5.31/5.60 => ( ! [X3: int] :
% 5.31/5.60 ( ( member_int @ X3 @ ( minus_minus_set_int @ T5 @ S3 ) )
% 5.31/5.60 => ( ( G2 @ X3 )
% 5.31/5.60 = zero_zero_real ) )
% 5.31/5.60 => ( ! [X3: int] :
% 5.31/5.60 ( ( member_int @ X3 @ S3 )
% 5.31/5.60 => ( ( G2 @ X3 )
% 5.31/5.60 = ( H @ X3 ) ) )
% 5.31/5.60 => ( ( groups8778361861064173332t_real @ G2 @ T5 )
% 5.31/5.60 = ( groups8778361861064173332t_real @ H @ S3 ) ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum.mono_neutral_cong_right
% 5.31/5.60 thf(fact_5636_sum_Omono__neutral__cong__right,axiom,
% 5.31/5.60 ! [T5: set_complex,S3: set_complex,G2: complex > real,H: complex > real] :
% 5.31/5.60 ( ( finite3207457112153483333omplex @ T5 )
% 5.31/5.60 => ( ( ord_le211207098394363844omplex @ S3 @ T5 )
% 5.31/5.60 => ( ! [X3: complex] :
% 5.31/5.60 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T5 @ S3 ) )
% 5.31/5.60 => ( ( G2 @ X3 )
% 5.31/5.60 = zero_zero_real ) )
% 5.31/5.60 => ( ! [X3: complex] :
% 5.31/5.60 ( ( member_complex @ X3 @ S3 )
% 5.31/5.60 => ( ( G2 @ X3 )
% 5.31/5.60 = ( H @ X3 ) ) )
% 5.31/5.60 => ( ( groups5808333547571424918x_real @ G2 @ T5 )
% 5.31/5.60 = ( groups5808333547571424918x_real @ H @ S3 ) ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum.mono_neutral_cong_right
% 5.31/5.60 thf(fact_5637_sum_Omono__neutral__cong__right,axiom,
% 5.31/5.60 ! [T5: set_real,S3: set_real,G2: real > rat,H: real > rat] :
% 5.31/5.60 ( ( finite_finite_real @ T5 )
% 5.31/5.60 => ( ( ord_less_eq_set_real @ S3 @ T5 )
% 5.31/5.60 => ( ! [X3: real] :
% 5.31/5.60 ( ( member_real @ X3 @ ( minus_minus_set_real @ T5 @ S3 ) )
% 5.31/5.60 => ( ( G2 @ X3 )
% 5.31/5.60 = zero_zero_rat ) )
% 5.31/5.60 => ( ! [X3: real] :
% 5.31/5.60 ( ( member_real @ X3 @ S3 )
% 5.31/5.60 => ( ( G2 @ X3 )
% 5.31/5.60 = ( H @ X3 ) ) )
% 5.31/5.60 => ( ( groups1300246762558778688al_rat @ G2 @ T5 )
% 5.31/5.60 = ( groups1300246762558778688al_rat @ H @ S3 ) ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum.mono_neutral_cong_right
% 5.31/5.60 thf(fact_5638_sum_Omono__neutral__cong__right,axiom,
% 5.31/5.60 ! [T5: set_int,S3: set_int,G2: int > rat,H: int > rat] :
% 5.31/5.60 ( ( finite_finite_int @ T5 )
% 5.31/5.60 => ( ( ord_less_eq_set_int @ S3 @ T5 )
% 5.31/5.60 => ( ! [X3: int] :
% 5.31/5.60 ( ( member_int @ X3 @ ( minus_minus_set_int @ T5 @ S3 ) )
% 5.31/5.60 => ( ( G2 @ X3 )
% 5.31/5.60 = zero_zero_rat ) )
% 5.31/5.60 => ( ! [X3: int] :
% 5.31/5.60 ( ( member_int @ X3 @ S3 )
% 5.31/5.60 => ( ( G2 @ X3 )
% 5.31/5.60 = ( H @ X3 ) ) )
% 5.31/5.60 => ( ( groups3906332499630173760nt_rat @ G2 @ T5 )
% 5.31/5.60 = ( groups3906332499630173760nt_rat @ H @ S3 ) ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum.mono_neutral_cong_right
% 5.31/5.60 thf(fact_5639_sum_Omono__neutral__cong__right,axiom,
% 5.31/5.60 ! [T5: set_complex,S3: set_complex,G2: complex > rat,H: complex > rat] :
% 5.31/5.60 ( ( finite3207457112153483333omplex @ T5 )
% 5.31/5.60 => ( ( ord_le211207098394363844omplex @ S3 @ T5 )
% 5.31/5.60 => ( ! [X3: complex] :
% 5.31/5.60 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T5 @ S3 ) )
% 5.31/5.60 => ( ( G2 @ X3 )
% 5.31/5.60 = zero_zero_rat ) )
% 5.31/5.60 => ( ! [X3: complex] :
% 5.31/5.60 ( ( member_complex @ X3 @ S3 )
% 5.31/5.60 => ( ( G2 @ X3 )
% 5.31/5.60 = ( H @ X3 ) ) )
% 5.31/5.60 => ( ( groups5058264527183730370ex_rat @ G2 @ T5 )
% 5.31/5.60 = ( groups5058264527183730370ex_rat @ H @ S3 ) ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum.mono_neutral_cong_right
% 5.31/5.60 thf(fact_5640_sum_Omono__neutral__cong__right,axiom,
% 5.31/5.60 ! [T5: set_real,S3: set_real,G2: real > nat,H: real > nat] :
% 5.31/5.60 ( ( finite_finite_real @ T5 )
% 5.31/5.60 => ( ( ord_less_eq_set_real @ S3 @ T5 )
% 5.31/5.60 => ( ! [X3: real] :
% 5.31/5.60 ( ( member_real @ X3 @ ( minus_minus_set_real @ T5 @ S3 ) )
% 5.31/5.60 => ( ( G2 @ X3 )
% 5.31/5.60 = zero_zero_nat ) )
% 5.31/5.60 => ( ! [X3: real] :
% 5.31/5.60 ( ( member_real @ X3 @ S3 )
% 5.31/5.60 => ( ( G2 @ X3 )
% 5.31/5.60 = ( H @ X3 ) ) )
% 5.31/5.60 => ( ( groups1935376822645274424al_nat @ G2 @ T5 )
% 5.31/5.60 = ( groups1935376822645274424al_nat @ H @ S3 ) ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum.mono_neutral_cong_right
% 5.31/5.60 thf(fact_5641_sum_Omono__neutral__cong__left,axiom,
% 5.31/5.60 ! [T5: set_real,S3: set_real,H: real > complex,G2: real > complex] :
% 5.31/5.60 ( ( finite_finite_real @ T5 )
% 5.31/5.60 => ( ( ord_less_eq_set_real @ S3 @ T5 )
% 5.31/5.60 => ( ! [X3: real] :
% 5.31/5.60 ( ( member_real @ X3 @ ( minus_minus_set_real @ T5 @ S3 ) )
% 5.31/5.60 => ( ( H @ X3 )
% 5.31/5.60 = zero_zero_complex ) )
% 5.31/5.60 => ( ! [X3: real] :
% 5.31/5.60 ( ( member_real @ X3 @ S3 )
% 5.31/5.60 => ( ( G2 @ X3 )
% 5.31/5.60 = ( H @ X3 ) ) )
% 5.31/5.60 => ( ( groups5754745047067104278omplex @ G2 @ S3 )
% 5.31/5.60 = ( groups5754745047067104278omplex @ H @ T5 ) ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum.mono_neutral_cong_left
% 5.31/5.60 thf(fact_5642_sum_Omono__neutral__cong__left,axiom,
% 5.31/5.60 ! [T5: set_int,S3: set_int,H: int > complex,G2: int > complex] :
% 5.31/5.60 ( ( finite_finite_int @ T5 )
% 5.31/5.60 => ( ( ord_less_eq_set_int @ S3 @ T5 )
% 5.31/5.60 => ( ! [X3: int] :
% 5.31/5.60 ( ( member_int @ X3 @ ( minus_minus_set_int @ T5 @ S3 ) )
% 5.31/5.60 => ( ( H @ X3 )
% 5.31/5.60 = zero_zero_complex ) )
% 5.31/5.60 => ( ! [X3: int] :
% 5.31/5.60 ( ( member_int @ X3 @ S3 )
% 5.31/5.60 => ( ( G2 @ X3 )
% 5.31/5.60 = ( H @ X3 ) ) )
% 5.31/5.60 => ( ( groups3049146728041665814omplex @ G2 @ S3 )
% 5.31/5.60 = ( groups3049146728041665814omplex @ H @ T5 ) ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum.mono_neutral_cong_left
% 5.31/5.60 thf(fact_5643_sum_Omono__neutral__cong__left,axiom,
% 5.31/5.60 ! [T5: set_complex,S3: set_complex,H: complex > complex,G2: complex > complex] :
% 5.31/5.60 ( ( finite3207457112153483333omplex @ T5 )
% 5.31/5.60 => ( ( ord_le211207098394363844omplex @ S3 @ T5 )
% 5.31/5.60 => ( ! [X3: complex] :
% 5.31/5.60 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T5 @ S3 ) )
% 5.31/5.60 => ( ( H @ X3 )
% 5.31/5.60 = zero_zero_complex ) )
% 5.31/5.60 => ( ! [X3: complex] :
% 5.31/5.60 ( ( member_complex @ X3 @ S3 )
% 5.31/5.60 => ( ( G2 @ X3 )
% 5.31/5.60 = ( H @ X3 ) ) )
% 5.31/5.60 => ( ( groups7754918857620584856omplex @ G2 @ S3 )
% 5.31/5.60 = ( groups7754918857620584856omplex @ H @ T5 ) ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum.mono_neutral_cong_left
% 5.31/5.60 thf(fact_5644_sum_Omono__neutral__cong__left,axiom,
% 5.31/5.60 ! [T5: set_real,S3: set_real,H: real > real,G2: real > real] :
% 5.31/5.60 ( ( finite_finite_real @ T5 )
% 5.31/5.60 => ( ( ord_less_eq_set_real @ S3 @ T5 )
% 5.31/5.60 => ( ! [X3: real] :
% 5.31/5.60 ( ( member_real @ X3 @ ( minus_minus_set_real @ T5 @ S3 ) )
% 5.31/5.60 => ( ( H @ X3 )
% 5.31/5.60 = zero_zero_real ) )
% 5.31/5.60 => ( ! [X3: real] :
% 5.31/5.60 ( ( member_real @ X3 @ S3 )
% 5.31/5.60 => ( ( G2 @ X3 )
% 5.31/5.60 = ( H @ X3 ) ) )
% 5.31/5.60 => ( ( groups8097168146408367636l_real @ G2 @ S3 )
% 5.31/5.60 = ( groups8097168146408367636l_real @ H @ T5 ) ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum.mono_neutral_cong_left
% 5.31/5.60 thf(fact_5645_sum_Omono__neutral__cong__left,axiom,
% 5.31/5.60 ! [T5: set_int,S3: set_int,H: int > real,G2: int > real] :
% 5.31/5.60 ( ( finite_finite_int @ T5 )
% 5.31/5.60 => ( ( ord_less_eq_set_int @ S3 @ T5 )
% 5.31/5.60 => ( ! [X3: int] :
% 5.31/5.60 ( ( member_int @ X3 @ ( minus_minus_set_int @ T5 @ S3 ) )
% 5.31/5.60 => ( ( H @ X3 )
% 5.31/5.60 = zero_zero_real ) )
% 5.31/5.60 => ( ! [X3: int] :
% 5.31/5.60 ( ( member_int @ X3 @ S3 )
% 5.31/5.60 => ( ( G2 @ X3 )
% 5.31/5.60 = ( H @ X3 ) ) )
% 5.31/5.60 => ( ( groups8778361861064173332t_real @ G2 @ S3 )
% 5.31/5.60 = ( groups8778361861064173332t_real @ H @ T5 ) ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum.mono_neutral_cong_left
% 5.31/5.60 thf(fact_5646_sum_Omono__neutral__cong__left,axiom,
% 5.31/5.60 ! [T5: set_complex,S3: set_complex,H: complex > real,G2: complex > real] :
% 5.31/5.60 ( ( finite3207457112153483333omplex @ T5 )
% 5.31/5.60 => ( ( ord_le211207098394363844omplex @ S3 @ T5 )
% 5.31/5.60 => ( ! [X3: complex] :
% 5.31/5.60 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T5 @ S3 ) )
% 5.31/5.60 => ( ( H @ X3 )
% 5.31/5.60 = zero_zero_real ) )
% 5.31/5.60 => ( ! [X3: complex] :
% 5.31/5.60 ( ( member_complex @ X3 @ S3 )
% 5.31/5.60 => ( ( G2 @ X3 )
% 5.31/5.60 = ( H @ X3 ) ) )
% 5.31/5.60 => ( ( groups5808333547571424918x_real @ G2 @ S3 )
% 5.31/5.60 = ( groups5808333547571424918x_real @ H @ T5 ) ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum.mono_neutral_cong_left
% 5.31/5.60 thf(fact_5647_sum_Omono__neutral__cong__left,axiom,
% 5.31/5.60 ! [T5: set_real,S3: set_real,H: real > rat,G2: real > rat] :
% 5.31/5.60 ( ( finite_finite_real @ T5 )
% 5.31/5.60 => ( ( ord_less_eq_set_real @ S3 @ T5 )
% 5.31/5.60 => ( ! [X3: real] :
% 5.31/5.60 ( ( member_real @ X3 @ ( minus_minus_set_real @ T5 @ S3 ) )
% 5.31/5.60 => ( ( H @ X3 )
% 5.31/5.60 = zero_zero_rat ) )
% 5.31/5.60 => ( ! [X3: real] :
% 5.31/5.60 ( ( member_real @ X3 @ S3 )
% 5.31/5.60 => ( ( G2 @ X3 )
% 5.31/5.60 = ( H @ X3 ) ) )
% 5.31/5.60 => ( ( groups1300246762558778688al_rat @ G2 @ S3 )
% 5.31/5.60 = ( groups1300246762558778688al_rat @ H @ T5 ) ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum.mono_neutral_cong_left
% 5.31/5.60 thf(fact_5648_sum_Omono__neutral__cong__left,axiom,
% 5.31/5.60 ! [T5: set_int,S3: set_int,H: int > rat,G2: int > rat] :
% 5.31/5.60 ( ( finite_finite_int @ T5 )
% 5.31/5.60 => ( ( ord_less_eq_set_int @ S3 @ T5 )
% 5.31/5.60 => ( ! [X3: int] :
% 5.31/5.60 ( ( member_int @ X3 @ ( minus_minus_set_int @ T5 @ S3 ) )
% 5.31/5.60 => ( ( H @ X3 )
% 5.31/5.60 = zero_zero_rat ) )
% 5.31/5.60 => ( ! [X3: int] :
% 5.31/5.60 ( ( member_int @ X3 @ S3 )
% 5.31/5.60 => ( ( G2 @ X3 )
% 5.31/5.60 = ( H @ X3 ) ) )
% 5.31/5.60 => ( ( groups3906332499630173760nt_rat @ G2 @ S3 )
% 5.31/5.60 = ( groups3906332499630173760nt_rat @ H @ T5 ) ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum.mono_neutral_cong_left
% 5.31/5.60 thf(fact_5649_sum_Omono__neutral__cong__left,axiom,
% 5.31/5.60 ! [T5: set_complex,S3: set_complex,H: complex > rat,G2: complex > rat] :
% 5.31/5.60 ( ( finite3207457112153483333omplex @ T5 )
% 5.31/5.60 => ( ( ord_le211207098394363844omplex @ S3 @ T5 )
% 5.31/5.60 => ( ! [X3: complex] :
% 5.31/5.60 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T5 @ S3 ) )
% 5.31/5.60 => ( ( H @ X3 )
% 5.31/5.60 = zero_zero_rat ) )
% 5.31/5.60 => ( ! [X3: complex] :
% 5.31/5.60 ( ( member_complex @ X3 @ S3 )
% 5.31/5.60 => ( ( G2 @ X3 )
% 5.31/5.60 = ( H @ X3 ) ) )
% 5.31/5.60 => ( ( groups5058264527183730370ex_rat @ G2 @ S3 )
% 5.31/5.60 = ( groups5058264527183730370ex_rat @ H @ T5 ) ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum.mono_neutral_cong_left
% 5.31/5.60 thf(fact_5650_sum_Omono__neutral__cong__left,axiom,
% 5.31/5.60 ! [T5: set_real,S3: set_real,H: real > nat,G2: real > nat] :
% 5.31/5.60 ( ( finite_finite_real @ T5 )
% 5.31/5.60 => ( ( ord_less_eq_set_real @ S3 @ T5 )
% 5.31/5.60 => ( ! [X3: real] :
% 5.31/5.60 ( ( member_real @ X3 @ ( minus_minus_set_real @ T5 @ S3 ) )
% 5.31/5.60 => ( ( H @ X3 )
% 5.31/5.60 = zero_zero_nat ) )
% 5.31/5.60 => ( ! [X3: real] :
% 5.31/5.60 ( ( member_real @ X3 @ S3 )
% 5.31/5.60 => ( ( G2 @ X3 )
% 5.31/5.60 = ( H @ X3 ) ) )
% 5.31/5.60 => ( ( groups1935376822645274424al_nat @ G2 @ S3 )
% 5.31/5.60 = ( groups1935376822645274424al_nat @ H @ T5 ) ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum.mono_neutral_cong_left
% 5.31/5.60 thf(fact_5651_sum_Omono__neutral__right,axiom,
% 5.31/5.60 ! [T5: set_int,S3: set_int,G2: int > complex] :
% 5.31/5.60 ( ( finite_finite_int @ T5 )
% 5.31/5.60 => ( ( ord_less_eq_set_int @ S3 @ T5 )
% 5.31/5.60 => ( ! [X3: int] :
% 5.31/5.60 ( ( member_int @ X3 @ ( minus_minus_set_int @ T5 @ S3 ) )
% 5.31/5.60 => ( ( G2 @ X3 )
% 5.31/5.60 = zero_zero_complex ) )
% 5.31/5.60 => ( ( groups3049146728041665814omplex @ G2 @ T5 )
% 5.31/5.60 = ( groups3049146728041665814omplex @ G2 @ S3 ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum.mono_neutral_right
% 5.31/5.60 thf(fact_5652_sum_Omono__neutral__right,axiom,
% 5.31/5.60 ! [T5: set_complex,S3: set_complex,G2: complex > complex] :
% 5.31/5.60 ( ( finite3207457112153483333omplex @ T5 )
% 5.31/5.60 => ( ( ord_le211207098394363844omplex @ S3 @ T5 )
% 5.31/5.60 => ( ! [X3: complex] :
% 5.31/5.60 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T5 @ S3 ) )
% 5.31/5.60 => ( ( G2 @ X3 )
% 5.31/5.60 = zero_zero_complex ) )
% 5.31/5.60 => ( ( groups7754918857620584856omplex @ G2 @ T5 )
% 5.31/5.60 = ( groups7754918857620584856omplex @ G2 @ S3 ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum.mono_neutral_right
% 5.31/5.60 thf(fact_5653_sum_Omono__neutral__right,axiom,
% 5.31/5.60 ! [T5: set_int,S3: set_int,G2: int > real] :
% 5.31/5.60 ( ( finite_finite_int @ T5 )
% 5.31/5.60 => ( ( ord_less_eq_set_int @ S3 @ T5 )
% 5.31/5.60 => ( ! [X3: int] :
% 5.31/5.60 ( ( member_int @ X3 @ ( minus_minus_set_int @ T5 @ S3 ) )
% 5.31/5.60 => ( ( G2 @ X3 )
% 5.31/5.60 = zero_zero_real ) )
% 5.31/5.60 => ( ( groups8778361861064173332t_real @ G2 @ T5 )
% 5.31/5.60 = ( groups8778361861064173332t_real @ G2 @ S3 ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum.mono_neutral_right
% 5.31/5.60 thf(fact_5654_sum_Omono__neutral__right,axiom,
% 5.31/5.60 ! [T5: set_complex,S3: set_complex,G2: complex > real] :
% 5.31/5.60 ( ( finite3207457112153483333omplex @ T5 )
% 5.31/5.60 => ( ( ord_le211207098394363844omplex @ S3 @ T5 )
% 5.31/5.60 => ( ! [X3: complex] :
% 5.31/5.60 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T5 @ S3 ) )
% 5.31/5.60 => ( ( G2 @ X3 )
% 5.31/5.60 = zero_zero_real ) )
% 5.31/5.60 => ( ( groups5808333547571424918x_real @ G2 @ T5 )
% 5.31/5.60 = ( groups5808333547571424918x_real @ G2 @ S3 ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum.mono_neutral_right
% 5.31/5.60 thf(fact_5655_sum_Omono__neutral__right,axiom,
% 5.31/5.60 ! [T5: set_int,S3: set_int,G2: int > rat] :
% 5.31/5.60 ( ( finite_finite_int @ T5 )
% 5.31/5.60 => ( ( ord_less_eq_set_int @ S3 @ T5 )
% 5.31/5.60 => ( ! [X3: int] :
% 5.31/5.60 ( ( member_int @ X3 @ ( minus_minus_set_int @ T5 @ S3 ) )
% 5.31/5.60 => ( ( G2 @ X3 )
% 5.31/5.60 = zero_zero_rat ) )
% 5.31/5.60 => ( ( groups3906332499630173760nt_rat @ G2 @ T5 )
% 5.31/5.60 = ( groups3906332499630173760nt_rat @ G2 @ S3 ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum.mono_neutral_right
% 5.31/5.60 thf(fact_5656_sum_Omono__neutral__right,axiom,
% 5.31/5.60 ! [T5: set_complex,S3: set_complex,G2: complex > rat] :
% 5.31/5.60 ( ( finite3207457112153483333omplex @ T5 )
% 5.31/5.60 => ( ( ord_le211207098394363844omplex @ S3 @ T5 )
% 5.31/5.60 => ( ! [X3: complex] :
% 5.31/5.60 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T5 @ S3 ) )
% 5.31/5.60 => ( ( G2 @ X3 )
% 5.31/5.60 = zero_zero_rat ) )
% 5.31/5.60 => ( ( groups5058264527183730370ex_rat @ G2 @ T5 )
% 5.31/5.60 = ( groups5058264527183730370ex_rat @ G2 @ S3 ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum.mono_neutral_right
% 5.31/5.60 thf(fact_5657_sum_Omono__neutral__right,axiom,
% 5.31/5.60 ! [T5: set_int,S3: set_int,G2: int > nat] :
% 5.31/5.60 ( ( finite_finite_int @ T5 )
% 5.31/5.60 => ( ( ord_less_eq_set_int @ S3 @ T5 )
% 5.31/5.60 => ( ! [X3: int] :
% 5.31/5.60 ( ( member_int @ X3 @ ( minus_minus_set_int @ T5 @ S3 ) )
% 5.31/5.60 => ( ( G2 @ X3 )
% 5.31/5.60 = zero_zero_nat ) )
% 5.31/5.60 => ( ( groups4541462559716669496nt_nat @ G2 @ T5 )
% 5.31/5.60 = ( groups4541462559716669496nt_nat @ G2 @ S3 ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum.mono_neutral_right
% 5.31/5.60 thf(fact_5658_sum_Omono__neutral__right,axiom,
% 5.31/5.60 ! [T5: set_complex,S3: set_complex,G2: complex > nat] :
% 5.31/5.60 ( ( finite3207457112153483333omplex @ T5 )
% 5.31/5.60 => ( ( ord_le211207098394363844omplex @ S3 @ T5 )
% 5.31/5.60 => ( ! [X3: complex] :
% 5.31/5.60 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T5 @ S3 ) )
% 5.31/5.60 => ( ( G2 @ X3 )
% 5.31/5.60 = zero_zero_nat ) )
% 5.31/5.60 => ( ( groups5693394587270226106ex_nat @ G2 @ T5 )
% 5.31/5.60 = ( groups5693394587270226106ex_nat @ G2 @ S3 ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum.mono_neutral_right
% 5.31/5.60 thf(fact_5659_sum_Omono__neutral__right,axiom,
% 5.31/5.60 ! [T5: set_complex,S3: set_complex,G2: complex > int] :
% 5.31/5.60 ( ( finite3207457112153483333omplex @ T5 )
% 5.31/5.60 => ( ( ord_le211207098394363844omplex @ S3 @ T5 )
% 5.31/5.60 => ( ! [X3: complex] :
% 5.31/5.60 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T5 @ S3 ) )
% 5.31/5.60 => ( ( G2 @ X3 )
% 5.31/5.60 = zero_zero_int ) )
% 5.31/5.60 => ( ( groups5690904116761175830ex_int @ G2 @ T5 )
% 5.31/5.60 = ( groups5690904116761175830ex_int @ G2 @ S3 ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum.mono_neutral_right
% 5.31/5.60 thf(fact_5660_sum_Omono__neutral__right,axiom,
% 5.31/5.60 ! [T5: set_nat,S3: set_nat,G2: nat > complex] :
% 5.31/5.60 ( ( finite_finite_nat @ T5 )
% 5.31/5.60 => ( ( ord_less_eq_set_nat @ S3 @ T5 )
% 5.31/5.60 => ( ! [X3: nat] :
% 5.31/5.60 ( ( member_nat @ X3 @ ( minus_minus_set_nat @ T5 @ S3 ) )
% 5.31/5.60 => ( ( G2 @ X3 )
% 5.31/5.60 = zero_zero_complex ) )
% 5.31/5.60 => ( ( groups2073611262835488442omplex @ G2 @ T5 )
% 5.31/5.60 = ( groups2073611262835488442omplex @ G2 @ S3 ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum.mono_neutral_right
% 5.31/5.60 thf(fact_5661_sum_Omono__neutral__left,axiom,
% 5.31/5.60 ! [T5: set_int,S3: set_int,G2: int > complex] :
% 5.31/5.60 ( ( finite_finite_int @ T5 )
% 5.31/5.60 => ( ( ord_less_eq_set_int @ S3 @ T5 )
% 5.31/5.60 => ( ! [X3: int] :
% 5.31/5.60 ( ( member_int @ X3 @ ( minus_minus_set_int @ T5 @ S3 ) )
% 5.31/5.60 => ( ( G2 @ X3 )
% 5.31/5.60 = zero_zero_complex ) )
% 5.31/5.60 => ( ( groups3049146728041665814omplex @ G2 @ S3 )
% 5.31/5.60 = ( groups3049146728041665814omplex @ G2 @ T5 ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum.mono_neutral_left
% 5.31/5.60 thf(fact_5662_sum_Omono__neutral__left,axiom,
% 5.31/5.60 ! [T5: set_complex,S3: set_complex,G2: complex > complex] :
% 5.31/5.60 ( ( finite3207457112153483333omplex @ T5 )
% 5.31/5.60 => ( ( ord_le211207098394363844omplex @ S3 @ T5 )
% 5.31/5.60 => ( ! [X3: complex] :
% 5.31/5.60 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T5 @ S3 ) )
% 5.31/5.60 => ( ( G2 @ X3 )
% 5.31/5.60 = zero_zero_complex ) )
% 5.31/5.60 => ( ( groups7754918857620584856omplex @ G2 @ S3 )
% 5.31/5.60 = ( groups7754918857620584856omplex @ G2 @ T5 ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum.mono_neutral_left
% 5.31/5.60 thf(fact_5663_sum_Omono__neutral__left,axiom,
% 5.31/5.60 ! [T5: set_int,S3: set_int,G2: int > real] :
% 5.31/5.60 ( ( finite_finite_int @ T5 )
% 5.31/5.60 => ( ( ord_less_eq_set_int @ S3 @ T5 )
% 5.31/5.60 => ( ! [X3: int] :
% 5.31/5.60 ( ( member_int @ X3 @ ( minus_minus_set_int @ T5 @ S3 ) )
% 5.31/5.60 => ( ( G2 @ X3 )
% 5.31/5.60 = zero_zero_real ) )
% 5.31/5.60 => ( ( groups8778361861064173332t_real @ G2 @ S3 )
% 5.31/5.60 = ( groups8778361861064173332t_real @ G2 @ T5 ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum.mono_neutral_left
% 5.31/5.60 thf(fact_5664_sum_Omono__neutral__left,axiom,
% 5.31/5.60 ! [T5: set_complex,S3: set_complex,G2: complex > real] :
% 5.31/5.60 ( ( finite3207457112153483333omplex @ T5 )
% 5.31/5.60 => ( ( ord_le211207098394363844omplex @ S3 @ T5 )
% 5.31/5.60 => ( ! [X3: complex] :
% 5.31/5.60 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T5 @ S3 ) )
% 5.31/5.60 => ( ( G2 @ X3 )
% 5.31/5.60 = zero_zero_real ) )
% 5.31/5.60 => ( ( groups5808333547571424918x_real @ G2 @ S3 )
% 5.31/5.60 = ( groups5808333547571424918x_real @ G2 @ T5 ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum.mono_neutral_left
% 5.31/5.60 thf(fact_5665_sum_Omono__neutral__left,axiom,
% 5.31/5.60 ! [T5: set_int,S3: set_int,G2: int > rat] :
% 5.31/5.60 ( ( finite_finite_int @ T5 )
% 5.31/5.60 => ( ( ord_less_eq_set_int @ S3 @ T5 )
% 5.31/5.60 => ( ! [X3: int] :
% 5.31/5.60 ( ( member_int @ X3 @ ( minus_minus_set_int @ T5 @ S3 ) )
% 5.31/5.60 => ( ( G2 @ X3 )
% 5.31/5.60 = zero_zero_rat ) )
% 5.31/5.60 => ( ( groups3906332499630173760nt_rat @ G2 @ S3 )
% 5.31/5.60 = ( groups3906332499630173760nt_rat @ G2 @ T5 ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum.mono_neutral_left
% 5.31/5.60 thf(fact_5666_sum_Omono__neutral__left,axiom,
% 5.31/5.60 ! [T5: set_complex,S3: set_complex,G2: complex > rat] :
% 5.31/5.60 ( ( finite3207457112153483333omplex @ T5 )
% 5.31/5.60 => ( ( ord_le211207098394363844omplex @ S3 @ T5 )
% 5.31/5.60 => ( ! [X3: complex] :
% 5.31/5.60 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T5 @ S3 ) )
% 5.31/5.60 => ( ( G2 @ X3 )
% 5.31/5.60 = zero_zero_rat ) )
% 5.31/5.60 => ( ( groups5058264527183730370ex_rat @ G2 @ S3 )
% 5.31/5.60 = ( groups5058264527183730370ex_rat @ G2 @ T5 ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum.mono_neutral_left
% 5.31/5.60 thf(fact_5667_sum_Omono__neutral__left,axiom,
% 5.31/5.60 ! [T5: set_int,S3: set_int,G2: int > nat] :
% 5.31/5.60 ( ( finite_finite_int @ T5 )
% 5.31/5.60 => ( ( ord_less_eq_set_int @ S3 @ T5 )
% 5.31/5.60 => ( ! [X3: int] :
% 5.31/5.60 ( ( member_int @ X3 @ ( minus_minus_set_int @ T5 @ S3 ) )
% 5.31/5.60 => ( ( G2 @ X3 )
% 5.31/5.60 = zero_zero_nat ) )
% 5.31/5.60 => ( ( groups4541462559716669496nt_nat @ G2 @ S3 )
% 5.31/5.60 = ( groups4541462559716669496nt_nat @ G2 @ T5 ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum.mono_neutral_left
% 5.31/5.60 thf(fact_5668_sum_Omono__neutral__left,axiom,
% 5.31/5.60 ! [T5: set_complex,S3: set_complex,G2: complex > nat] :
% 5.31/5.60 ( ( finite3207457112153483333omplex @ T5 )
% 5.31/5.60 => ( ( ord_le211207098394363844omplex @ S3 @ T5 )
% 5.31/5.60 => ( ! [X3: complex] :
% 5.31/5.60 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T5 @ S3 ) )
% 5.31/5.60 => ( ( G2 @ X3 )
% 5.31/5.60 = zero_zero_nat ) )
% 5.31/5.60 => ( ( groups5693394587270226106ex_nat @ G2 @ S3 )
% 5.31/5.60 = ( groups5693394587270226106ex_nat @ G2 @ T5 ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum.mono_neutral_left
% 5.31/5.60 thf(fact_5669_sum_Omono__neutral__left,axiom,
% 5.31/5.60 ! [T5: set_complex,S3: set_complex,G2: complex > int] :
% 5.31/5.60 ( ( finite3207457112153483333omplex @ T5 )
% 5.31/5.60 => ( ( ord_le211207098394363844omplex @ S3 @ T5 )
% 5.31/5.60 => ( ! [X3: complex] :
% 5.31/5.60 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T5 @ S3 ) )
% 5.31/5.60 => ( ( G2 @ X3 )
% 5.31/5.60 = zero_zero_int ) )
% 5.31/5.60 => ( ( groups5690904116761175830ex_int @ G2 @ S3 )
% 5.31/5.60 = ( groups5690904116761175830ex_int @ G2 @ T5 ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum.mono_neutral_left
% 5.31/5.60 thf(fact_5670_sum_Omono__neutral__left,axiom,
% 5.31/5.60 ! [T5: set_nat,S3: set_nat,G2: nat > complex] :
% 5.31/5.60 ( ( finite_finite_nat @ T5 )
% 5.31/5.60 => ( ( ord_less_eq_set_nat @ S3 @ T5 )
% 5.31/5.60 => ( ! [X3: nat] :
% 5.31/5.60 ( ( member_nat @ X3 @ ( minus_minus_set_nat @ T5 @ S3 ) )
% 5.31/5.60 => ( ( G2 @ X3 )
% 5.31/5.60 = zero_zero_complex ) )
% 5.31/5.60 => ( ( groups2073611262835488442omplex @ G2 @ S3 )
% 5.31/5.60 = ( groups2073611262835488442omplex @ G2 @ T5 ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum.mono_neutral_left
% 5.31/5.60 thf(fact_5671_sum_Osame__carrierI,axiom,
% 5.31/5.60 ! [C4: set_real,A4: set_real,B5: set_real,G2: real > complex,H: real > complex] :
% 5.31/5.60 ( ( finite_finite_real @ C4 )
% 5.31/5.60 => ( ( ord_less_eq_set_real @ A4 @ C4 )
% 5.31/5.60 => ( ( ord_less_eq_set_real @ B5 @ C4 )
% 5.31/5.60 => ( ! [A3: real] :
% 5.31/5.60 ( ( member_real @ A3 @ ( minus_minus_set_real @ C4 @ A4 ) )
% 5.31/5.60 => ( ( G2 @ A3 )
% 5.31/5.60 = zero_zero_complex ) )
% 5.31/5.60 => ( ! [B3: real] :
% 5.31/5.60 ( ( member_real @ B3 @ ( minus_minus_set_real @ C4 @ B5 ) )
% 5.31/5.60 => ( ( H @ B3 )
% 5.31/5.60 = zero_zero_complex ) )
% 5.31/5.60 => ( ( ( groups5754745047067104278omplex @ G2 @ C4 )
% 5.31/5.60 = ( groups5754745047067104278omplex @ H @ C4 ) )
% 5.31/5.60 => ( ( groups5754745047067104278omplex @ G2 @ A4 )
% 5.31/5.60 = ( groups5754745047067104278omplex @ H @ B5 ) ) ) ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum.same_carrierI
% 5.31/5.60 thf(fact_5672_sum_Osame__carrierI,axiom,
% 5.31/5.60 ! [C4: set_int,A4: set_int,B5: set_int,G2: int > complex,H: int > complex] :
% 5.31/5.60 ( ( finite_finite_int @ C4 )
% 5.31/5.60 => ( ( ord_less_eq_set_int @ A4 @ C4 )
% 5.31/5.60 => ( ( ord_less_eq_set_int @ B5 @ C4 )
% 5.31/5.60 => ( ! [A3: int] :
% 5.31/5.60 ( ( member_int @ A3 @ ( minus_minus_set_int @ C4 @ A4 ) )
% 5.31/5.60 => ( ( G2 @ A3 )
% 5.31/5.60 = zero_zero_complex ) )
% 5.31/5.60 => ( ! [B3: int] :
% 5.31/5.60 ( ( member_int @ B3 @ ( minus_minus_set_int @ C4 @ B5 ) )
% 5.31/5.60 => ( ( H @ B3 )
% 5.31/5.60 = zero_zero_complex ) )
% 5.31/5.60 => ( ( ( groups3049146728041665814omplex @ G2 @ C4 )
% 5.31/5.60 = ( groups3049146728041665814omplex @ H @ C4 ) )
% 5.31/5.60 => ( ( groups3049146728041665814omplex @ G2 @ A4 )
% 5.31/5.60 = ( groups3049146728041665814omplex @ H @ B5 ) ) ) ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum.same_carrierI
% 5.31/5.60 thf(fact_5673_sum_Osame__carrierI,axiom,
% 5.31/5.60 ! [C4: set_complex,A4: set_complex,B5: set_complex,G2: complex > complex,H: complex > complex] :
% 5.31/5.60 ( ( finite3207457112153483333omplex @ C4 )
% 5.31/5.60 => ( ( ord_le211207098394363844omplex @ A4 @ C4 )
% 5.31/5.60 => ( ( ord_le211207098394363844omplex @ B5 @ C4 )
% 5.31/5.60 => ( ! [A3: complex] :
% 5.31/5.60 ( ( member_complex @ A3 @ ( minus_811609699411566653omplex @ C4 @ A4 ) )
% 5.31/5.60 => ( ( G2 @ A3 )
% 5.31/5.60 = zero_zero_complex ) )
% 5.31/5.60 => ( ! [B3: complex] :
% 5.31/5.60 ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ C4 @ B5 ) )
% 5.31/5.60 => ( ( H @ B3 )
% 5.31/5.60 = zero_zero_complex ) )
% 5.31/5.60 => ( ( ( groups7754918857620584856omplex @ G2 @ C4 )
% 5.31/5.60 = ( groups7754918857620584856omplex @ H @ C4 ) )
% 5.31/5.60 => ( ( groups7754918857620584856omplex @ G2 @ A4 )
% 5.31/5.60 = ( groups7754918857620584856omplex @ H @ B5 ) ) ) ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum.same_carrierI
% 5.31/5.60 thf(fact_5674_sum_Osame__carrierI,axiom,
% 5.31/5.60 ! [C4: set_real,A4: set_real,B5: set_real,G2: real > real,H: real > real] :
% 5.31/5.60 ( ( finite_finite_real @ C4 )
% 5.31/5.60 => ( ( ord_less_eq_set_real @ A4 @ C4 )
% 5.31/5.60 => ( ( ord_less_eq_set_real @ B5 @ C4 )
% 5.31/5.60 => ( ! [A3: real] :
% 5.31/5.60 ( ( member_real @ A3 @ ( minus_minus_set_real @ C4 @ A4 ) )
% 5.31/5.60 => ( ( G2 @ A3 )
% 5.31/5.60 = zero_zero_real ) )
% 5.31/5.60 => ( ! [B3: real] :
% 5.31/5.60 ( ( member_real @ B3 @ ( minus_minus_set_real @ C4 @ B5 ) )
% 5.31/5.60 => ( ( H @ B3 )
% 5.31/5.60 = zero_zero_real ) )
% 5.31/5.60 => ( ( ( groups8097168146408367636l_real @ G2 @ C4 )
% 5.31/5.60 = ( groups8097168146408367636l_real @ H @ C4 ) )
% 5.31/5.60 => ( ( groups8097168146408367636l_real @ G2 @ A4 )
% 5.31/5.60 = ( groups8097168146408367636l_real @ H @ B5 ) ) ) ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum.same_carrierI
% 5.31/5.60 thf(fact_5675_sum_Osame__carrierI,axiom,
% 5.31/5.60 ! [C4: set_int,A4: set_int,B5: set_int,G2: int > real,H: int > real] :
% 5.31/5.60 ( ( finite_finite_int @ C4 )
% 5.31/5.60 => ( ( ord_less_eq_set_int @ A4 @ C4 )
% 5.31/5.60 => ( ( ord_less_eq_set_int @ B5 @ C4 )
% 5.31/5.60 => ( ! [A3: int] :
% 5.31/5.60 ( ( member_int @ A3 @ ( minus_minus_set_int @ C4 @ A4 ) )
% 5.31/5.60 => ( ( G2 @ A3 )
% 5.31/5.60 = zero_zero_real ) )
% 5.31/5.60 => ( ! [B3: int] :
% 5.31/5.60 ( ( member_int @ B3 @ ( minus_minus_set_int @ C4 @ B5 ) )
% 5.31/5.60 => ( ( H @ B3 )
% 5.31/5.60 = zero_zero_real ) )
% 5.31/5.60 => ( ( ( groups8778361861064173332t_real @ G2 @ C4 )
% 5.31/5.60 = ( groups8778361861064173332t_real @ H @ C4 ) )
% 5.31/5.60 => ( ( groups8778361861064173332t_real @ G2 @ A4 )
% 5.31/5.60 = ( groups8778361861064173332t_real @ H @ B5 ) ) ) ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum.same_carrierI
% 5.31/5.60 thf(fact_5676_sum_Osame__carrierI,axiom,
% 5.31/5.60 ! [C4: set_complex,A4: set_complex,B5: set_complex,G2: complex > real,H: complex > real] :
% 5.31/5.60 ( ( finite3207457112153483333omplex @ C4 )
% 5.31/5.60 => ( ( ord_le211207098394363844omplex @ A4 @ C4 )
% 5.31/5.60 => ( ( ord_le211207098394363844omplex @ B5 @ C4 )
% 5.31/5.60 => ( ! [A3: complex] :
% 5.31/5.60 ( ( member_complex @ A3 @ ( minus_811609699411566653omplex @ C4 @ A4 ) )
% 5.31/5.60 => ( ( G2 @ A3 )
% 5.31/5.60 = zero_zero_real ) )
% 5.31/5.60 => ( ! [B3: complex] :
% 5.31/5.60 ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ C4 @ B5 ) )
% 5.31/5.60 => ( ( H @ B3 )
% 5.31/5.60 = zero_zero_real ) )
% 5.31/5.60 => ( ( ( groups5808333547571424918x_real @ G2 @ C4 )
% 5.31/5.60 = ( groups5808333547571424918x_real @ H @ C4 ) )
% 5.31/5.60 => ( ( groups5808333547571424918x_real @ G2 @ A4 )
% 5.31/5.60 = ( groups5808333547571424918x_real @ H @ B5 ) ) ) ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum.same_carrierI
% 5.31/5.60 thf(fact_5677_sum_Osame__carrierI,axiom,
% 5.31/5.60 ! [C4: set_real,A4: set_real,B5: set_real,G2: real > rat,H: real > rat] :
% 5.31/5.60 ( ( finite_finite_real @ C4 )
% 5.31/5.60 => ( ( ord_less_eq_set_real @ A4 @ C4 )
% 5.31/5.60 => ( ( ord_less_eq_set_real @ B5 @ C4 )
% 5.31/5.60 => ( ! [A3: real] :
% 5.31/5.60 ( ( member_real @ A3 @ ( minus_minus_set_real @ C4 @ A4 ) )
% 5.31/5.60 => ( ( G2 @ A3 )
% 5.31/5.60 = zero_zero_rat ) )
% 5.31/5.60 => ( ! [B3: real] :
% 5.31/5.60 ( ( member_real @ B3 @ ( minus_minus_set_real @ C4 @ B5 ) )
% 5.31/5.60 => ( ( H @ B3 )
% 5.31/5.60 = zero_zero_rat ) )
% 5.31/5.60 => ( ( ( groups1300246762558778688al_rat @ G2 @ C4 )
% 5.31/5.60 = ( groups1300246762558778688al_rat @ H @ C4 ) )
% 5.31/5.60 => ( ( groups1300246762558778688al_rat @ G2 @ A4 )
% 5.31/5.60 = ( groups1300246762558778688al_rat @ H @ B5 ) ) ) ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum.same_carrierI
% 5.31/5.60 thf(fact_5678_sum_Osame__carrierI,axiom,
% 5.31/5.60 ! [C4: set_int,A4: set_int,B5: set_int,G2: int > rat,H: int > rat] :
% 5.31/5.60 ( ( finite_finite_int @ C4 )
% 5.31/5.60 => ( ( ord_less_eq_set_int @ A4 @ C4 )
% 5.31/5.60 => ( ( ord_less_eq_set_int @ B5 @ C4 )
% 5.31/5.60 => ( ! [A3: int] :
% 5.31/5.60 ( ( member_int @ A3 @ ( minus_minus_set_int @ C4 @ A4 ) )
% 5.31/5.60 => ( ( G2 @ A3 )
% 5.31/5.60 = zero_zero_rat ) )
% 5.31/5.60 => ( ! [B3: int] :
% 5.31/5.60 ( ( member_int @ B3 @ ( minus_minus_set_int @ C4 @ B5 ) )
% 5.31/5.60 => ( ( H @ B3 )
% 5.31/5.60 = zero_zero_rat ) )
% 5.31/5.60 => ( ( ( groups3906332499630173760nt_rat @ G2 @ C4 )
% 5.31/5.60 = ( groups3906332499630173760nt_rat @ H @ C4 ) )
% 5.31/5.60 => ( ( groups3906332499630173760nt_rat @ G2 @ A4 )
% 5.31/5.60 = ( groups3906332499630173760nt_rat @ H @ B5 ) ) ) ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum.same_carrierI
% 5.31/5.60 thf(fact_5679_sum_Osame__carrierI,axiom,
% 5.31/5.60 ! [C4: set_complex,A4: set_complex,B5: set_complex,G2: complex > rat,H: complex > rat] :
% 5.31/5.60 ( ( finite3207457112153483333omplex @ C4 )
% 5.31/5.60 => ( ( ord_le211207098394363844omplex @ A4 @ C4 )
% 5.31/5.60 => ( ( ord_le211207098394363844omplex @ B5 @ C4 )
% 5.31/5.60 => ( ! [A3: complex] :
% 5.31/5.60 ( ( member_complex @ A3 @ ( minus_811609699411566653omplex @ C4 @ A4 ) )
% 5.31/5.60 => ( ( G2 @ A3 )
% 5.31/5.60 = zero_zero_rat ) )
% 5.31/5.60 => ( ! [B3: complex] :
% 5.31/5.60 ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ C4 @ B5 ) )
% 5.31/5.60 => ( ( H @ B3 )
% 5.31/5.60 = zero_zero_rat ) )
% 5.31/5.60 => ( ( ( groups5058264527183730370ex_rat @ G2 @ C4 )
% 5.31/5.60 = ( groups5058264527183730370ex_rat @ H @ C4 ) )
% 5.31/5.60 => ( ( groups5058264527183730370ex_rat @ G2 @ A4 )
% 5.31/5.60 = ( groups5058264527183730370ex_rat @ H @ B5 ) ) ) ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum.same_carrierI
% 5.31/5.60 thf(fact_5680_sum_Osame__carrierI,axiom,
% 5.31/5.60 ! [C4: set_real,A4: set_real,B5: set_real,G2: real > nat,H: real > nat] :
% 5.31/5.60 ( ( finite_finite_real @ C4 )
% 5.31/5.60 => ( ( ord_less_eq_set_real @ A4 @ C4 )
% 5.31/5.60 => ( ( ord_less_eq_set_real @ B5 @ C4 )
% 5.31/5.60 => ( ! [A3: real] :
% 5.31/5.60 ( ( member_real @ A3 @ ( minus_minus_set_real @ C4 @ A4 ) )
% 5.31/5.60 => ( ( G2 @ A3 )
% 5.31/5.60 = zero_zero_nat ) )
% 5.31/5.60 => ( ! [B3: real] :
% 5.31/5.60 ( ( member_real @ B3 @ ( minus_minus_set_real @ C4 @ B5 ) )
% 5.31/5.60 => ( ( H @ B3 )
% 5.31/5.60 = zero_zero_nat ) )
% 5.31/5.60 => ( ( ( groups1935376822645274424al_nat @ G2 @ C4 )
% 5.31/5.60 = ( groups1935376822645274424al_nat @ H @ C4 ) )
% 5.31/5.60 => ( ( groups1935376822645274424al_nat @ G2 @ A4 )
% 5.31/5.60 = ( groups1935376822645274424al_nat @ H @ B5 ) ) ) ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum.same_carrierI
% 5.31/5.60 thf(fact_5681_sum_Osame__carrier,axiom,
% 5.31/5.60 ! [C4: set_real,A4: set_real,B5: set_real,G2: real > complex,H: real > complex] :
% 5.31/5.60 ( ( finite_finite_real @ C4 )
% 5.31/5.60 => ( ( ord_less_eq_set_real @ A4 @ C4 )
% 5.31/5.60 => ( ( ord_less_eq_set_real @ B5 @ C4 )
% 5.31/5.60 => ( ! [A3: real] :
% 5.31/5.60 ( ( member_real @ A3 @ ( minus_minus_set_real @ C4 @ A4 ) )
% 5.31/5.60 => ( ( G2 @ A3 )
% 5.31/5.60 = zero_zero_complex ) )
% 5.31/5.60 => ( ! [B3: real] :
% 5.31/5.60 ( ( member_real @ B3 @ ( minus_minus_set_real @ C4 @ B5 ) )
% 5.31/5.60 => ( ( H @ B3 )
% 5.31/5.60 = zero_zero_complex ) )
% 5.31/5.60 => ( ( ( groups5754745047067104278omplex @ G2 @ A4 )
% 5.31/5.60 = ( groups5754745047067104278omplex @ H @ B5 ) )
% 5.31/5.60 = ( ( groups5754745047067104278omplex @ G2 @ C4 )
% 5.31/5.60 = ( groups5754745047067104278omplex @ H @ C4 ) ) ) ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum.same_carrier
% 5.31/5.60 thf(fact_5682_sum_Osame__carrier,axiom,
% 5.31/5.60 ! [C4: set_int,A4: set_int,B5: set_int,G2: int > complex,H: int > complex] :
% 5.31/5.60 ( ( finite_finite_int @ C4 )
% 5.31/5.60 => ( ( ord_less_eq_set_int @ A4 @ C4 )
% 5.31/5.60 => ( ( ord_less_eq_set_int @ B5 @ C4 )
% 5.31/5.60 => ( ! [A3: int] :
% 5.31/5.60 ( ( member_int @ A3 @ ( minus_minus_set_int @ C4 @ A4 ) )
% 5.31/5.60 => ( ( G2 @ A3 )
% 5.31/5.60 = zero_zero_complex ) )
% 5.31/5.60 => ( ! [B3: int] :
% 5.31/5.60 ( ( member_int @ B3 @ ( minus_minus_set_int @ C4 @ B5 ) )
% 5.31/5.60 => ( ( H @ B3 )
% 5.31/5.60 = zero_zero_complex ) )
% 5.31/5.60 => ( ( ( groups3049146728041665814omplex @ G2 @ A4 )
% 5.31/5.60 = ( groups3049146728041665814omplex @ H @ B5 ) )
% 5.31/5.60 = ( ( groups3049146728041665814omplex @ G2 @ C4 )
% 5.31/5.60 = ( groups3049146728041665814omplex @ H @ C4 ) ) ) ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum.same_carrier
% 5.31/5.60 thf(fact_5683_sum_Osame__carrier,axiom,
% 5.31/5.60 ! [C4: set_complex,A4: set_complex,B5: set_complex,G2: complex > complex,H: complex > complex] :
% 5.31/5.60 ( ( finite3207457112153483333omplex @ C4 )
% 5.31/5.60 => ( ( ord_le211207098394363844omplex @ A4 @ C4 )
% 5.31/5.60 => ( ( ord_le211207098394363844omplex @ B5 @ C4 )
% 5.31/5.60 => ( ! [A3: complex] :
% 5.31/5.60 ( ( member_complex @ A3 @ ( minus_811609699411566653omplex @ C4 @ A4 ) )
% 5.31/5.60 => ( ( G2 @ A3 )
% 5.31/5.60 = zero_zero_complex ) )
% 5.31/5.60 => ( ! [B3: complex] :
% 5.31/5.60 ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ C4 @ B5 ) )
% 5.31/5.60 => ( ( H @ B3 )
% 5.31/5.60 = zero_zero_complex ) )
% 5.31/5.60 => ( ( ( groups7754918857620584856omplex @ G2 @ A4 )
% 5.31/5.60 = ( groups7754918857620584856omplex @ H @ B5 ) )
% 5.31/5.60 = ( ( groups7754918857620584856omplex @ G2 @ C4 )
% 5.31/5.60 = ( groups7754918857620584856omplex @ H @ C4 ) ) ) ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum.same_carrier
% 5.31/5.60 thf(fact_5684_sum_Osame__carrier,axiom,
% 5.31/5.60 ! [C4: set_real,A4: set_real,B5: set_real,G2: real > real,H: real > real] :
% 5.31/5.60 ( ( finite_finite_real @ C4 )
% 5.31/5.60 => ( ( ord_less_eq_set_real @ A4 @ C4 )
% 5.31/5.60 => ( ( ord_less_eq_set_real @ B5 @ C4 )
% 5.31/5.60 => ( ! [A3: real] :
% 5.31/5.60 ( ( member_real @ A3 @ ( minus_minus_set_real @ C4 @ A4 ) )
% 5.31/5.60 => ( ( G2 @ A3 )
% 5.31/5.60 = zero_zero_real ) )
% 5.31/5.60 => ( ! [B3: real] :
% 5.31/5.60 ( ( member_real @ B3 @ ( minus_minus_set_real @ C4 @ B5 ) )
% 5.31/5.60 => ( ( H @ B3 )
% 5.31/5.60 = zero_zero_real ) )
% 5.31/5.60 => ( ( ( groups8097168146408367636l_real @ G2 @ A4 )
% 5.31/5.60 = ( groups8097168146408367636l_real @ H @ B5 ) )
% 5.31/5.60 = ( ( groups8097168146408367636l_real @ G2 @ C4 )
% 5.31/5.60 = ( groups8097168146408367636l_real @ H @ C4 ) ) ) ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum.same_carrier
% 5.31/5.60 thf(fact_5685_sum_Osame__carrier,axiom,
% 5.31/5.60 ! [C4: set_int,A4: set_int,B5: set_int,G2: int > real,H: int > real] :
% 5.31/5.60 ( ( finite_finite_int @ C4 )
% 5.31/5.60 => ( ( ord_less_eq_set_int @ A4 @ C4 )
% 5.31/5.60 => ( ( ord_less_eq_set_int @ B5 @ C4 )
% 5.31/5.60 => ( ! [A3: int] :
% 5.31/5.60 ( ( member_int @ A3 @ ( minus_minus_set_int @ C4 @ A4 ) )
% 5.31/5.60 => ( ( G2 @ A3 )
% 5.31/5.60 = zero_zero_real ) )
% 5.31/5.60 => ( ! [B3: int] :
% 5.31/5.60 ( ( member_int @ B3 @ ( minus_minus_set_int @ C4 @ B5 ) )
% 5.31/5.60 => ( ( H @ B3 )
% 5.31/5.60 = zero_zero_real ) )
% 5.31/5.60 => ( ( ( groups8778361861064173332t_real @ G2 @ A4 )
% 5.31/5.60 = ( groups8778361861064173332t_real @ H @ B5 ) )
% 5.31/5.60 = ( ( groups8778361861064173332t_real @ G2 @ C4 )
% 5.31/5.60 = ( groups8778361861064173332t_real @ H @ C4 ) ) ) ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum.same_carrier
% 5.31/5.60 thf(fact_5686_sum_Osame__carrier,axiom,
% 5.31/5.60 ! [C4: set_complex,A4: set_complex,B5: set_complex,G2: complex > real,H: complex > real] :
% 5.31/5.60 ( ( finite3207457112153483333omplex @ C4 )
% 5.31/5.60 => ( ( ord_le211207098394363844omplex @ A4 @ C4 )
% 5.31/5.60 => ( ( ord_le211207098394363844omplex @ B5 @ C4 )
% 5.31/5.60 => ( ! [A3: complex] :
% 5.31/5.60 ( ( member_complex @ A3 @ ( minus_811609699411566653omplex @ C4 @ A4 ) )
% 5.31/5.60 => ( ( G2 @ A3 )
% 5.31/5.60 = zero_zero_real ) )
% 5.31/5.60 => ( ! [B3: complex] :
% 5.31/5.60 ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ C4 @ B5 ) )
% 5.31/5.60 => ( ( H @ B3 )
% 5.31/5.60 = zero_zero_real ) )
% 5.31/5.60 => ( ( ( groups5808333547571424918x_real @ G2 @ A4 )
% 5.31/5.60 = ( groups5808333547571424918x_real @ H @ B5 ) )
% 5.31/5.60 = ( ( groups5808333547571424918x_real @ G2 @ C4 )
% 5.31/5.60 = ( groups5808333547571424918x_real @ H @ C4 ) ) ) ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum.same_carrier
% 5.31/5.60 thf(fact_5687_sum_Osame__carrier,axiom,
% 5.31/5.60 ! [C4: set_real,A4: set_real,B5: set_real,G2: real > rat,H: real > rat] :
% 5.31/5.60 ( ( finite_finite_real @ C4 )
% 5.31/5.60 => ( ( ord_less_eq_set_real @ A4 @ C4 )
% 5.31/5.60 => ( ( ord_less_eq_set_real @ B5 @ C4 )
% 5.31/5.60 => ( ! [A3: real] :
% 5.31/5.60 ( ( member_real @ A3 @ ( minus_minus_set_real @ C4 @ A4 ) )
% 5.31/5.60 => ( ( G2 @ A3 )
% 5.31/5.60 = zero_zero_rat ) )
% 5.31/5.60 => ( ! [B3: real] :
% 5.31/5.60 ( ( member_real @ B3 @ ( minus_minus_set_real @ C4 @ B5 ) )
% 5.31/5.60 => ( ( H @ B3 )
% 5.31/5.60 = zero_zero_rat ) )
% 5.31/5.60 => ( ( ( groups1300246762558778688al_rat @ G2 @ A4 )
% 5.31/5.60 = ( groups1300246762558778688al_rat @ H @ B5 ) )
% 5.31/5.60 = ( ( groups1300246762558778688al_rat @ G2 @ C4 )
% 5.31/5.60 = ( groups1300246762558778688al_rat @ H @ C4 ) ) ) ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum.same_carrier
% 5.31/5.60 thf(fact_5688_sum_Osame__carrier,axiom,
% 5.31/5.60 ! [C4: set_int,A4: set_int,B5: set_int,G2: int > rat,H: int > rat] :
% 5.31/5.60 ( ( finite_finite_int @ C4 )
% 5.31/5.60 => ( ( ord_less_eq_set_int @ A4 @ C4 )
% 5.31/5.60 => ( ( ord_less_eq_set_int @ B5 @ C4 )
% 5.31/5.60 => ( ! [A3: int] :
% 5.31/5.60 ( ( member_int @ A3 @ ( minus_minus_set_int @ C4 @ A4 ) )
% 5.31/5.60 => ( ( G2 @ A3 )
% 5.31/5.60 = zero_zero_rat ) )
% 5.31/5.60 => ( ! [B3: int] :
% 5.31/5.60 ( ( member_int @ B3 @ ( minus_minus_set_int @ C4 @ B5 ) )
% 5.31/5.60 => ( ( H @ B3 )
% 5.31/5.60 = zero_zero_rat ) )
% 5.31/5.60 => ( ( ( groups3906332499630173760nt_rat @ G2 @ A4 )
% 5.31/5.60 = ( groups3906332499630173760nt_rat @ H @ B5 ) )
% 5.31/5.60 = ( ( groups3906332499630173760nt_rat @ G2 @ C4 )
% 5.31/5.60 = ( groups3906332499630173760nt_rat @ H @ C4 ) ) ) ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum.same_carrier
% 5.31/5.60 thf(fact_5689_sum_Osame__carrier,axiom,
% 5.31/5.60 ! [C4: set_complex,A4: set_complex,B5: set_complex,G2: complex > rat,H: complex > rat] :
% 5.31/5.60 ( ( finite3207457112153483333omplex @ C4 )
% 5.31/5.60 => ( ( ord_le211207098394363844omplex @ A4 @ C4 )
% 5.31/5.60 => ( ( ord_le211207098394363844omplex @ B5 @ C4 )
% 5.31/5.60 => ( ! [A3: complex] :
% 5.31/5.60 ( ( member_complex @ A3 @ ( minus_811609699411566653omplex @ C4 @ A4 ) )
% 5.31/5.60 => ( ( G2 @ A3 )
% 5.31/5.60 = zero_zero_rat ) )
% 5.31/5.60 => ( ! [B3: complex] :
% 5.31/5.60 ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ C4 @ B5 ) )
% 5.31/5.60 => ( ( H @ B3 )
% 5.31/5.60 = zero_zero_rat ) )
% 5.31/5.60 => ( ( ( groups5058264527183730370ex_rat @ G2 @ A4 )
% 5.31/5.60 = ( groups5058264527183730370ex_rat @ H @ B5 ) )
% 5.31/5.60 = ( ( groups5058264527183730370ex_rat @ G2 @ C4 )
% 5.31/5.60 = ( groups5058264527183730370ex_rat @ H @ C4 ) ) ) ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum.same_carrier
% 5.31/5.60 thf(fact_5690_sum_Osame__carrier,axiom,
% 5.31/5.60 ! [C4: set_real,A4: set_real,B5: set_real,G2: real > nat,H: real > nat] :
% 5.31/5.60 ( ( finite_finite_real @ C4 )
% 5.31/5.60 => ( ( ord_less_eq_set_real @ A4 @ C4 )
% 5.31/5.60 => ( ( ord_less_eq_set_real @ B5 @ C4 )
% 5.31/5.60 => ( ! [A3: real] :
% 5.31/5.60 ( ( member_real @ A3 @ ( minus_minus_set_real @ C4 @ A4 ) )
% 5.31/5.60 => ( ( G2 @ A3 )
% 5.31/5.60 = zero_zero_nat ) )
% 5.31/5.60 => ( ! [B3: real] :
% 5.31/5.60 ( ( member_real @ B3 @ ( minus_minus_set_real @ C4 @ B5 ) )
% 5.31/5.60 => ( ( H @ B3 )
% 5.31/5.60 = zero_zero_nat ) )
% 5.31/5.60 => ( ( ( groups1935376822645274424al_nat @ G2 @ A4 )
% 5.31/5.60 = ( groups1935376822645274424al_nat @ H @ B5 ) )
% 5.31/5.60 = ( ( groups1935376822645274424al_nat @ G2 @ C4 )
% 5.31/5.60 = ( groups1935376822645274424al_nat @ H @ C4 ) ) ) ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum.same_carrier
% 5.31/5.60 thf(fact_5691_sum_Omono__neutral__cong,axiom,
% 5.31/5.60 ! [T5: set_real,S3: set_real,H: real > complex,G2: real > complex] :
% 5.31/5.60 ( ( finite_finite_real @ T5 )
% 5.31/5.60 => ( ( finite_finite_real @ S3 )
% 5.31/5.60 => ( ! [I3: real] :
% 5.31/5.60 ( ( member_real @ I3 @ ( minus_minus_set_real @ T5 @ S3 ) )
% 5.31/5.60 => ( ( H @ I3 )
% 5.31/5.60 = zero_zero_complex ) )
% 5.31/5.60 => ( ! [I3: real] :
% 5.31/5.60 ( ( member_real @ I3 @ ( minus_minus_set_real @ S3 @ T5 ) )
% 5.31/5.60 => ( ( G2 @ I3 )
% 5.31/5.60 = zero_zero_complex ) )
% 5.31/5.60 => ( ! [X3: real] :
% 5.31/5.60 ( ( member_real @ X3 @ ( inf_inf_set_real @ S3 @ T5 ) )
% 5.31/5.60 => ( ( G2 @ X3 )
% 5.31/5.60 = ( H @ X3 ) ) )
% 5.31/5.60 => ( ( groups5754745047067104278omplex @ G2 @ S3 )
% 5.31/5.60 = ( groups5754745047067104278omplex @ H @ T5 ) ) ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum.mono_neutral_cong
% 5.31/5.60 thf(fact_5692_sum_Omono__neutral__cong,axiom,
% 5.31/5.60 ! [T5: set_int,S3: set_int,H: int > complex,G2: int > complex] :
% 5.31/5.60 ( ( finite_finite_int @ T5 )
% 5.31/5.60 => ( ( finite_finite_int @ S3 )
% 5.31/5.60 => ( ! [I3: int] :
% 5.31/5.60 ( ( member_int @ I3 @ ( minus_minus_set_int @ T5 @ S3 ) )
% 5.31/5.60 => ( ( H @ I3 )
% 5.31/5.60 = zero_zero_complex ) )
% 5.31/5.60 => ( ! [I3: int] :
% 5.31/5.60 ( ( member_int @ I3 @ ( minus_minus_set_int @ S3 @ T5 ) )
% 5.31/5.60 => ( ( G2 @ I3 )
% 5.31/5.60 = zero_zero_complex ) )
% 5.31/5.60 => ( ! [X3: int] :
% 5.31/5.60 ( ( member_int @ X3 @ ( inf_inf_set_int @ S3 @ T5 ) )
% 5.31/5.60 => ( ( G2 @ X3 )
% 5.31/5.60 = ( H @ X3 ) ) )
% 5.31/5.60 => ( ( groups3049146728041665814omplex @ G2 @ S3 )
% 5.31/5.60 = ( groups3049146728041665814omplex @ H @ T5 ) ) ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum.mono_neutral_cong
% 5.31/5.60 thf(fact_5693_sum_Omono__neutral__cong,axiom,
% 5.31/5.60 ! [T5: set_complex,S3: set_complex,H: complex > complex,G2: complex > complex] :
% 5.31/5.60 ( ( finite3207457112153483333omplex @ T5 )
% 5.31/5.60 => ( ( finite3207457112153483333omplex @ S3 )
% 5.31/5.60 => ( ! [I3: complex] :
% 5.31/5.60 ( ( member_complex @ I3 @ ( minus_811609699411566653omplex @ T5 @ S3 ) )
% 5.31/5.60 => ( ( H @ I3 )
% 5.31/5.60 = zero_zero_complex ) )
% 5.31/5.60 => ( ! [I3: complex] :
% 5.31/5.60 ( ( member_complex @ I3 @ ( minus_811609699411566653omplex @ S3 @ T5 ) )
% 5.31/5.60 => ( ( G2 @ I3 )
% 5.31/5.60 = zero_zero_complex ) )
% 5.31/5.60 => ( ! [X3: complex] :
% 5.31/5.60 ( ( member_complex @ X3 @ ( inf_inf_set_complex @ S3 @ T5 ) )
% 5.31/5.60 => ( ( G2 @ X3 )
% 5.31/5.60 = ( H @ X3 ) ) )
% 5.31/5.60 => ( ( groups7754918857620584856omplex @ G2 @ S3 )
% 5.31/5.60 = ( groups7754918857620584856omplex @ H @ T5 ) ) ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum.mono_neutral_cong
% 5.31/5.60 thf(fact_5694_sum_Omono__neutral__cong,axiom,
% 5.31/5.60 ! [T5: set_real,S3: set_real,H: real > real,G2: real > real] :
% 5.31/5.60 ( ( finite_finite_real @ T5 )
% 5.31/5.60 => ( ( finite_finite_real @ S3 )
% 5.31/5.60 => ( ! [I3: real] :
% 5.31/5.60 ( ( member_real @ I3 @ ( minus_minus_set_real @ T5 @ S3 ) )
% 5.31/5.60 => ( ( H @ I3 )
% 5.31/5.60 = zero_zero_real ) )
% 5.31/5.60 => ( ! [I3: real] :
% 5.31/5.60 ( ( member_real @ I3 @ ( minus_minus_set_real @ S3 @ T5 ) )
% 5.31/5.60 => ( ( G2 @ I3 )
% 5.31/5.60 = zero_zero_real ) )
% 5.31/5.60 => ( ! [X3: real] :
% 5.31/5.60 ( ( member_real @ X3 @ ( inf_inf_set_real @ S3 @ T5 ) )
% 5.31/5.60 => ( ( G2 @ X3 )
% 5.31/5.60 = ( H @ X3 ) ) )
% 5.31/5.60 => ( ( groups8097168146408367636l_real @ G2 @ S3 )
% 5.31/5.60 = ( groups8097168146408367636l_real @ H @ T5 ) ) ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum.mono_neutral_cong
% 5.31/5.60 thf(fact_5695_sum_Omono__neutral__cong,axiom,
% 5.31/5.60 ! [T5: set_int,S3: set_int,H: int > real,G2: int > real] :
% 5.31/5.60 ( ( finite_finite_int @ T5 )
% 5.31/5.60 => ( ( finite_finite_int @ S3 )
% 5.31/5.60 => ( ! [I3: int] :
% 5.31/5.60 ( ( member_int @ I3 @ ( minus_minus_set_int @ T5 @ S3 ) )
% 5.31/5.60 => ( ( H @ I3 )
% 5.31/5.60 = zero_zero_real ) )
% 5.31/5.60 => ( ! [I3: int] :
% 5.31/5.60 ( ( member_int @ I3 @ ( minus_minus_set_int @ S3 @ T5 ) )
% 5.31/5.60 => ( ( G2 @ I3 )
% 5.31/5.60 = zero_zero_real ) )
% 5.31/5.60 => ( ! [X3: int] :
% 5.31/5.60 ( ( member_int @ X3 @ ( inf_inf_set_int @ S3 @ T5 ) )
% 5.31/5.60 => ( ( G2 @ X3 )
% 5.31/5.60 = ( H @ X3 ) ) )
% 5.31/5.60 => ( ( groups8778361861064173332t_real @ G2 @ S3 )
% 5.31/5.60 = ( groups8778361861064173332t_real @ H @ T5 ) ) ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum.mono_neutral_cong
% 5.31/5.60 thf(fact_5696_sum_Omono__neutral__cong,axiom,
% 5.31/5.60 ! [T5: set_complex,S3: set_complex,H: complex > real,G2: complex > real] :
% 5.31/5.60 ( ( finite3207457112153483333omplex @ T5 )
% 5.31/5.60 => ( ( finite3207457112153483333omplex @ S3 )
% 5.31/5.60 => ( ! [I3: complex] :
% 5.31/5.60 ( ( member_complex @ I3 @ ( minus_811609699411566653omplex @ T5 @ S3 ) )
% 5.31/5.60 => ( ( H @ I3 )
% 5.31/5.60 = zero_zero_real ) )
% 5.31/5.60 => ( ! [I3: complex] :
% 5.31/5.60 ( ( member_complex @ I3 @ ( minus_811609699411566653omplex @ S3 @ T5 ) )
% 5.31/5.60 => ( ( G2 @ I3 )
% 5.31/5.60 = zero_zero_real ) )
% 5.31/5.60 => ( ! [X3: complex] :
% 5.31/5.60 ( ( member_complex @ X3 @ ( inf_inf_set_complex @ S3 @ T5 ) )
% 5.31/5.60 => ( ( G2 @ X3 )
% 5.31/5.60 = ( H @ X3 ) ) )
% 5.31/5.60 => ( ( groups5808333547571424918x_real @ G2 @ S3 )
% 5.31/5.60 = ( groups5808333547571424918x_real @ H @ T5 ) ) ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum.mono_neutral_cong
% 5.31/5.60 thf(fact_5697_sum_Omono__neutral__cong,axiom,
% 5.31/5.60 ! [T5: set_real,S3: set_real,H: real > rat,G2: real > rat] :
% 5.31/5.60 ( ( finite_finite_real @ T5 )
% 5.31/5.60 => ( ( finite_finite_real @ S3 )
% 5.31/5.60 => ( ! [I3: real] :
% 5.31/5.60 ( ( member_real @ I3 @ ( minus_minus_set_real @ T5 @ S3 ) )
% 5.31/5.60 => ( ( H @ I3 )
% 5.31/5.60 = zero_zero_rat ) )
% 5.31/5.60 => ( ! [I3: real] :
% 5.31/5.60 ( ( member_real @ I3 @ ( minus_minus_set_real @ S3 @ T5 ) )
% 5.31/5.60 => ( ( G2 @ I3 )
% 5.31/5.60 = zero_zero_rat ) )
% 5.31/5.60 => ( ! [X3: real] :
% 5.31/5.60 ( ( member_real @ X3 @ ( inf_inf_set_real @ S3 @ T5 ) )
% 5.31/5.60 => ( ( G2 @ X3 )
% 5.31/5.60 = ( H @ X3 ) ) )
% 5.31/5.60 => ( ( groups1300246762558778688al_rat @ G2 @ S3 )
% 5.31/5.60 = ( groups1300246762558778688al_rat @ H @ T5 ) ) ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum.mono_neutral_cong
% 5.31/5.60 thf(fact_5698_sum_Omono__neutral__cong,axiom,
% 5.31/5.60 ! [T5: set_int,S3: set_int,H: int > rat,G2: int > rat] :
% 5.31/5.60 ( ( finite_finite_int @ T5 )
% 5.31/5.60 => ( ( finite_finite_int @ S3 )
% 5.31/5.60 => ( ! [I3: int] :
% 5.31/5.60 ( ( member_int @ I3 @ ( minus_minus_set_int @ T5 @ S3 ) )
% 5.31/5.60 => ( ( H @ I3 )
% 5.31/5.60 = zero_zero_rat ) )
% 5.31/5.60 => ( ! [I3: int] :
% 5.31/5.60 ( ( member_int @ I3 @ ( minus_minus_set_int @ S3 @ T5 ) )
% 5.31/5.60 => ( ( G2 @ I3 )
% 5.31/5.60 = zero_zero_rat ) )
% 5.31/5.60 => ( ! [X3: int] :
% 5.31/5.60 ( ( member_int @ X3 @ ( inf_inf_set_int @ S3 @ T5 ) )
% 5.31/5.60 => ( ( G2 @ X3 )
% 5.31/5.60 = ( H @ X3 ) ) )
% 5.31/5.60 => ( ( groups3906332499630173760nt_rat @ G2 @ S3 )
% 5.31/5.60 = ( groups3906332499630173760nt_rat @ H @ T5 ) ) ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum.mono_neutral_cong
% 5.31/5.60 thf(fact_5699_sum_Omono__neutral__cong,axiom,
% 5.31/5.60 ! [T5: set_complex,S3: set_complex,H: complex > rat,G2: complex > rat] :
% 5.31/5.60 ( ( finite3207457112153483333omplex @ T5 )
% 5.31/5.60 => ( ( finite3207457112153483333omplex @ S3 )
% 5.31/5.60 => ( ! [I3: complex] :
% 5.31/5.60 ( ( member_complex @ I3 @ ( minus_811609699411566653omplex @ T5 @ S3 ) )
% 5.31/5.60 => ( ( H @ I3 )
% 5.31/5.60 = zero_zero_rat ) )
% 5.31/5.60 => ( ! [I3: complex] :
% 5.31/5.60 ( ( member_complex @ I3 @ ( minus_811609699411566653omplex @ S3 @ T5 ) )
% 5.31/5.60 => ( ( G2 @ I3 )
% 5.31/5.60 = zero_zero_rat ) )
% 5.31/5.60 => ( ! [X3: complex] :
% 5.31/5.60 ( ( member_complex @ X3 @ ( inf_inf_set_complex @ S3 @ T5 ) )
% 5.31/5.60 => ( ( G2 @ X3 )
% 5.31/5.60 = ( H @ X3 ) ) )
% 5.31/5.60 => ( ( groups5058264527183730370ex_rat @ G2 @ S3 )
% 5.31/5.60 = ( groups5058264527183730370ex_rat @ H @ T5 ) ) ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum.mono_neutral_cong
% 5.31/5.60 thf(fact_5700_sum_Omono__neutral__cong,axiom,
% 5.31/5.60 ! [T5: set_real,S3: set_real,H: real > nat,G2: real > nat] :
% 5.31/5.60 ( ( finite_finite_real @ T5 )
% 5.31/5.60 => ( ( finite_finite_real @ S3 )
% 5.31/5.60 => ( ! [I3: real] :
% 5.31/5.60 ( ( member_real @ I3 @ ( minus_minus_set_real @ T5 @ S3 ) )
% 5.31/5.60 => ( ( H @ I3 )
% 5.31/5.60 = zero_zero_nat ) )
% 5.31/5.60 => ( ! [I3: real] :
% 5.31/5.60 ( ( member_real @ I3 @ ( minus_minus_set_real @ S3 @ T5 ) )
% 5.31/5.60 => ( ( G2 @ I3 )
% 5.31/5.60 = zero_zero_nat ) )
% 5.31/5.60 => ( ! [X3: real] :
% 5.31/5.60 ( ( member_real @ X3 @ ( inf_inf_set_real @ S3 @ T5 ) )
% 5.31/5.60 => ( ( G2 @ X3 )
% 5.31/5.60 = ( H @ X3 ) ) )
% 5.31/5.60 => ( ( groups1935376822645274424al_nat @ G2 @ S3 )
% 5.31/5.60 = ( groups1935376822645274424al_nat @ H @ T5 ) ) ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum.mono_neutral_cong
% 5.31/5.60 thf(fact_5701_unity__coeff__ex,axiom,
% 5.31/5.60 ! [P2: complex > $o,L: complex] :
% 5.31/5.60 ( ( ? [X4: complex] : ( P2 @ ( times_times_complex @ L @ X4 ) ) )
% 5.31/5.60 = ( ? [X4: complex] :
% 5.31/5.60 ( ( dvd_dvd_complex @ L @ ( plus_plus_complex @ X4 @ zero_zero_complex ) )
% 5.31/5.60 & ( P2 @ X4 ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % unity_coeff_ex
% 5.31/5.60 thf(fact_5702_unity__coeff__ex,axiom,
% 5.31/5.60 ! [P2: real > $o,L: real] :
% 5.31/5.60 ( ( ? [X4: real] : ( P2 @ ( times_times_real @ L @ X4 ) ) )
% 5.31/5.60 = ( ? [X4: real] :
% 5.31/5.60 ( ( dvd_dvd_real @ L @ ( plus_plus_real @ X4 @ zero_zero_real ) )
% 5.31/5.60 & ( P2 @ X4 ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % unity_coeff_ex
% 5.31/5.60 thf(fact_5703_unity__coeff__ex,axiom,
% 5.31/5.60 ! [P2: rat > $o,L: rat] :
% 5.31/5.60 ( ( ? [X4: rat] : ( P2 @ ( times_times_rat @ L @ X4 ) ) )
% 5.31/5.60 = ( ? [X4: rat] :
% 5.31/5.60 ( ( dvd_dvd_rat @ L @ ( plus_plus_rat @ X4 @ zero_zero_rat ) )
% 5.31/5.60 & ( P2 @ X4 ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % unity_coeff_ex
% 5.31/5.60 thf(fact_5704_unity__coeff__ex,axiom,
% 5.31/5.60 ! [P2: nat > $o,L: nat] :
% 5.31/5.60 ( ( ? [X4: nat] : ( P2 @ ( times_times_nat @ L @ X4 ) ) )
% 5.31/5.60 = ( ? [X4: nat] :
% 5.31/5.60 ( ( dvd_dvd_nat @ L @ ( plus_plus_nat @ X4 @ zero_zero_nat ) )
% 5.31/5.60 & ( P2 @ X4 ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % unity_coeff_ex
% 5.31/5.60 thf(fact_5705_unity__coeff__ex,axiom,
% 5.31/5.60 ! [P2: int > $o,L: int] :
% 5.31/5.60 ( ( ? [X4: int] : ( P2 @ ( times_times_int @ L @ X4 ) ) )
% 5.31/5.60 = ( ? [X4: int] :
% 5.31/5.60 ( ( dvd_dvd_int @ L @ ( plus_plus_int @ X4 @ zero_zero_int ) )
% 5.31/5.60 & ( P2 @ X4 ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % unity_coeff_ex
% 5.31/5.60 thf(fact_5706_unit__dvdE,axiom,
% 5.31/5.60 ! [A: code_integer,B: code_integer] :
% 5.31/5.60 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.31/5.60 => ~ ( ( A != zero_z3403309356797280102nteger )
% 5.31/5.60 => ! [C: code_integer] :
% 5.31/5.60 ( B
% 5.31/5.60 != ( times_3573771949741848930nteger @ A @ C ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % unit_dvdE
% 5.31/5.60 thf(fact_5707_unit__dvdE,axiom,
% 5.31/5.60 ! [A: nat,B: nat] :
% 5.31/5.60 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.31/5.60 => ~ ( ( A != zero_zero_nat )
% 5.31/5.60 => ! [C: nat] :
% 5.31/5.60 ( B
% 5.31/5.60 != ( times_times_nat @ A @ C ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % unit_dvdE
% 5.31/5.60 thf(fact_5708_unit__dvdE,axiom,
% 5.31/5.60 ! [A: int,B: int] :
% 5.31/5.60 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.31/5.60 => ~ ( ( A != zero_zero_int )
% 5.31/5.60 => ! [C: int] :
% 5.31/5.60 ( B
% 5.31/5.60 != ( times_times_int @ A @ C ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % unit_dvdE
% 5.31/5.60 thf(fact_5709_dvd__div__div__eq__mult,axiom,
% 5.31/5.60 ! [A: nat,C2: nat,B: nat,D: nat] :
% 5.31/5.60 ( ( A != zero_zero_nat )
% 5.31/5.60 => ( ( C2 != zero_zero_nat )
% 5.31/5.60 => ( ( dvd_dvd_nat @ A @ B )
% 5.31/5.60 => ( ( dvd_dvd_nat @ C2 @ D )
% 5.31/5.60 => ( ( ( divide_divide_nat @ B @ A )
% 5.31/5.60 = ( divide_divide_nat @ D @ C2 ) )
% 5.31/5.60 = ( ( times_times_nat @ B @ C2 )
% 5.31/5.60 = ( times_times_nat @ A @ D ) ) ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % dvd_div_div_eq_mult
% 5.31/5.60 thf(fact_5710_dvd__div__div__eq__mult,axiom,
% 5.31/5.60 ! [A: int,C2: int,B: int,D: int] :
% 5.31/5.60 ( ( A != zero_zero_int )
% 5.31/5.60 => ( ( C2 != zero_zero_int )
% 5.31/5.60 => ( ( dvd_dvd_int @ A @ B )
% 5.31/5.60 => ( ( dvd_dvd_int @ C2 @ D )
% 5.31/5.60 => ( ( ( divide_divide_int @ B @ A )
% 5.31/5.60 = ( divide_divide_int @ D @ C2 ) )
% 5.31/5.60 = ( ( times_times_int @ B @ C2 )
% 5.31/5.60 = ( times_times_int @ A @ D ) ) ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % dvd_div_div_eq_mult
% 5.31/5.60 thf(fact_5711_dvd__div__iff__mult,axiom,
% 5.31/5.60 ! [C2: nat,B: nat,A: nat] :
% 5.31/5.60 ( ( C2 != zero_zero_nat )
% 5.31/5.60 => ( ( dvd_dvd_nat @ C2 @ B )
% 5.31/5.60 => ( ( dvd_dvd_nat @ A @ ( divide_divide_nat @ B @ C2 ) )
% 5.31/5.60 = ( dvd_dvd_nat @ ( times_times_nat @ A @ C2 ) @ B ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % dvd_div_iff_mult
% 5.31/5.60 thf(fact_5712_dvd__div__iff__mult,axiom,
% 5.31/5.60 ! [C2: int,B: int,A: int] :
% 5.31/5.60 ( ( C2 != zero_zero_int )
% 5.31/5.60 => ( ( dvd_dvd_int @ C2 @ B )
% 5.31/5.60 => ( ( dvd_dvd_int @ A @ ( divide_divide_int @ B @ C2 ) )
% 5.31/5.60 = ( dvd_dvd_int @ ( times_times_int @ A @ C2 ) @ B ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % dvd_div_iff_mult
% 5.31/5.60 thf(fact_5713_div__dvd__iff__mult,axiom,
% 5.31/5.60 ! [B: nat,A: nat,C2: nat] :
% 5.31/5.60 ( ( B != zero_zero_nat )
% 5.31/5.60 => ( ( dvd_dvd_nat @ B @ A )
% 5.31/5.60 => ( ( dvd_dvd_nat @ ( divide_divide_nat @ A @ B ) @ C2 )
% 5.31/5.60 = ( dvd_dvd_nat @ A @ ( times_times_nat @ C2 @ B ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % div_dvd_iff_mult
% 5.31/5.60 thf(fact_5714_div__dvd__iff__mult,axiom,
% 5.31/5.60 ! [B: int,A: int,C2: int] :
% 5.31/5.60 ( ( B != zero_zero_int )
% 5.31/5.60 => ( ( dvd_dvd_int @ B @ A )
% 5.31/5.60 => ( ( dvd_dvd_int @ ( divide_divide_int @ A @ B ) @ C2 )
% 5.31/5.60 = ( dvd_dvd_int @ A @ ( times_times_int @ C2 @ B ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % div_dvd_iff_mult
% 5.31/5.60 thf(fact_5715_dvd__div__eq__mult,axiom,
% 5.31/5.60 ! [A: nat,B: nat,C2: nat] :
% 5.31/5.60 ( ( A != zero_zero_nat )
% 5.31/5.60 => ( ( dvd_dvd_nat @ A @ B )
% 5.31/5.60 => ( ( ( divide_divide_nat @ B @ A )
% 5.31/5.60 = C2 )
% 5.31/5.60 = ( B
% 5.31/5.60 = ( times_times_nat @ C2 @ A ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % dvd_div_eq_mult
% 5.31/5.60 thf(fact_5716_dvd__div__eq__mult,axiom,
% 5.31/5.60 ! [A: int,B: int,C2: int] :
% 5.31/5.60 ( ( A != zero_zero_int )
% 5.31/5.60 => ( ( dvd_dvd_int @ A @ B )
% 5.31/5.60 => ( ( ( divide_divide_int @ B @ A )
% 5.31/5.60 = C2 )
% 5.31/5.60 = ( B
% 5.31/5.60 = ( times_times_int @ C2 @ A ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % dvd_div_eq_mult
% 5.31/5.60 thf(fact_5717_unit__div__eq__0__iff,axiom,
% 5.31/5.60 ! [B: code_integer,A: code_integer] :
% 5.31/5.60 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.31/5.60 => ( ( ( divide6298287555418463151nteger @ A @ B )
% 5.31/5.60 = zero_z3403309356797280102nteger )
% 5.31/5.60 = ( A = zero_z3403309356797280102nteger ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % unit_div_eq_0_iff
% 5.31/5.60 thf(fact_5718_unit__div__eq__0__iff,axiom,
% 5.31/5.60 ! [B: nat,A: nat] :
% 5.31/5.60 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.31/5.60 => ( ( ( divide_divide_nat @ A @ B )
% 5.31/5.60 = zero_zero_nat )
% 5.31/5.60 = ( A = zero_zero_nat ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % unit_div_eq_0_iff
% 5.31/5.60 thf(fact_5719_unit__div__eq__0__iff,axiom,
% 5.31/5.60 ! [B: int,A: int] :
% 5.31/5.60 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.31/5.60 => ( ( ( divide_divide_int @ A @ B )
% 5.31/5.60 = zero_zero_int )
% 5.31/5.60 = ( A = zero_zero_int ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % unit_div_eq_0_iff
% 5.31/5.60 thf(fact_5720_inf__period_I4_J,axiom,
% 5.31/5.60 ! [D: real,D3: real,T: real] :
% 5.31/5.60 ( ( dvd_dvd_real @ D @ D3 )
% 5.31/5.60 => ! [X5: real,K4: real] :
% 5.31/5.60 ( ( ~ ( dvd_dvd_real @ D @ ( plus_plus_real @ X5 @ T ) ) )
% 5.31/5.60 = ( ~ ( dvd_dvd_real @ D @ ( plus_plus_real @ ( minus_minus_real @ X5 @ ( times_times_real @ K4 @ D3 ) ) @ T ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % inf_period(4)
% 5.31/5.60 thf(fact_5721_inf__period_I4_J,axiom,
% 5.31/5.60 ! [D: rat,D3: rat,T: rat] :
% 5.31/5.60 ( ( dvd_dvd_rat @ D @ D3 )
% 5.31/5.60 => ! [X5: rat,K4: rat] :
% 5.31/5.60 ( ( ~ ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X5 @ T ) ) )
% 5.31/5.60 = ( ~ ( dvd_dvd_rat @ D @ ( plus_plus_rat @ ( minus_minus_rat @ X5 @ ( times_times_rat @ K4 @ D3 ) ) @ T ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % inf_period(4)
% 5.31/5.60 thf(fact_5722_inf__period_I4_J,axiom,
% 5.31/5.60 ! [D: int,D3: int,T: int] :
% 5.31/5.60 ( ( dvd_dvd_int @ D @ D3 )
% 5.31/5.60 => ! [X5: int,K4: int] :
% 5.31/5.60 ( ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ X5 @ T ) ) )
% 5.31/5.60 = ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ ( minus_minus_int @ X5 @ ( times_times_int @ K4 @ D3 ) ) @ T ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % inf_period(4)
% 5.31/5.60 thf(fact_5723_inf__period_I3_J,axiom,
% 5.31/5.60 ! [D: real,D3: real,T: real] :
% 5.31/5.60 ( ( dvd_dvd_real @ D @ D3 )
% 5.31/5.60 => ! [X5: real,K4: real] :
% 5.31/5.60 ( ( dvd_dvd_real @ D @ ( plus_plus_real @ X5 @ T ) )
% 5.31/5.60 = ( dvd_dvd_real @ D @ ( plus_plus_real @ ( minus_minus_real @ X5 @ ( times_times_real @ K4 @ D3 ) ) @ T ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % inf_period(3)
% 5.31/5.60 thf(fact_5724_inf__period_I3_J,axiom,
% 5.31/5.60 ! [D: rat,D3: rat,T: rat] :
% 5.31/5.60 ( ( dvd_dvd_rat @ D @ D3 )
% 5.31/5.60 => ! [X5: rat,K4: rat] :
% 5.31/5.60 ( ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X5 @ T ) )
% 5.31/5.60 = ( dvd_dvd_rat @ D @ ( plus_plus_rat @ ( minus_minus_rat @ X5 @ ( times_times_rat @ K4 @ D3 ) ) @ T ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % inf_period(3)
% 5.31/5.60 thf(fact_5725_inf__period_I3_J,axiom,
% 5.31/5.60 ! [D: int,D3: int,T: int] :
% 5.31/5.60 ( ( dvd_dvd_int @ D @ D3 )
% 5.31/5.60 => ! [X5: int,K4: int] :
% 5.31/5.60 ( ( dvd_dvd_int @ D @ ( plus_plus_int @ X5 @ T ) )
% 5.31/5.60 = ( dvd_dvd_int @ D @ ( plus_plus_int @ ( minus_minus_int @ X5 @ ( times_times_int @ K4 @ D3 ) ) @ T ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % inf_period(3)
% 5.31/5.60 thf(fact_5726_unit__eq__div1,axiom,
% 5.31/5.60 ! [B: code_integer,A: code_integer,C2: code_integer] :
% 5.31/5.60 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.31/5.60 => ( ( ( divide6298287555418463151nteger @ A @ B )
% 5.31/5.60 = C2 )
% 5.31/5.60 = ( A
% 5.31/5.60 = ( times_3573771949741848930nteger @ C2 @ B ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % unit_eq_div1
% 5.31/5.60 thf(fact_5727_unit__eq__div1,axiom,
% 5.31/5.60 ! [B: nat,A: nat,C2: nat] :
% 5.31/5.60 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.31/5.60 => ( ( ( divide_divide_nat @ A @ B )
% 5.31/5.60 = C2 )
% 5.31/5.60 = ( A
% 5.31/5.60 = ( times_times_nat @ C2 @ B ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % unit_eq_div1
% 5.31/5.60 thf(fact_5728_unit__eq__div1,axiom,
% 5.31/5.60 ! [B: int,A: int,C2: int] :
% 5.31/5.60 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.31/5.60 => ( ( ( divide_divide_int @ A @ B )
% 5.31/5.60 = C2 )
% 5.31/5.60 = ( A
% 5.31/5.60 = ( times_times_int @ C2 @ B ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % unit_eq_div1
% 5.31/5.60 thf(fact_5729_unit__eq__div2,axiom,
% 5.31/5.60 ! [B: code_integer,A: code_integer,C2: code_integer] :
% 5.31/5.60 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.31/5.60 => ( ( A
% 5.31/5.60 = ( divide6298287555418463151nteger @ C2 @ B ) )
% 5.31/5.60 = ( ( times_3573771949741848930nteger @ A @ B )
% 5.31/5.60 = C2 ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % unit_eq_div2
% 5.31/5.60 thf(fact_5730_unit__eq__div2,axiom,
% 5.31/5.60 ! [B: nat,A: nat,C2: nat] :
% 5.31/5.60 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.31/5.60 => ( ( A
% 5.31/5.60 = ( divide_divide_nat @ C2 @ B ) )
% 5.31/5.60 = ( ( times_times_nat @ A @ B )
% 5.31/5.60 = C2 ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % unit_eq_div2
% 5.31/5.60 thf(fact_5731_unit__eq__div2,axiom,
% 5.31/5.60 ! [B: int,A: int,C2: int] :
% 5.31/5.60 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.31/5.60 => ( ( A
% 5.31/5.60 = ( divide_divide_int @ C2 @ B ) )
% 5.31/5.60 = ( ( times_times_int @ A @ B )
% 5.31/5.60 = C2 ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % unit_eq_div2
% 5.31/5.60 thf(fact_5732_div__mult__unit2,axiom,
% 5.31/5.60 ! [C2: code_integer,B: code_integer,A: code_integer] :
% 5.31/5.60 ( ( dvd_dvd_Code_integer @ C2 @ one_one_Code_integer )
% 5.31/5.60 => ( ( dvd_dvd_Code_integer @ B @ A )
% 5.31/5.60 => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ B @ C2 ) )
% 5.31/5.60 = ( divide6298287555418463151nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C2 ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % div_mult_unit2
% 5.31/5.60 thf(fact_5733_div__mult__unit2,axiom,
% 5.31/5.60 ! [C2: nat,B: nat,A: nat] :
% 5.31/5.60 ( ( dvd_dvd_nat @ C2 @ one_one_nat )
% 5.31/5.60 => ( ( dvd_dvd_nat @ B @ A )
% 5.31/5.60 => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ C2 ) )
% 5.31/5.60 = ( divide_divide_nat @ ( divide_divide_nat @ A @ B ) @ C2 ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % div_mult_unit2
% 5.31/5.60 thf(fact_5734_div__mult__unit2,axiom,
% 5.31/5.60 ! [C2: int,B: int,A: int] :
% 5.31/5.60 ( ( dvd_dvd_int @ C2 @ one_one_int )
% 5.31/5.60 => ( ( dvd_dvd_int @ B @ A )
% 5.31/5.60 => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C2 ) )
% 5.31/5.60 = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C2 ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % div_mult_unit2
% 5.31/5.60 thf(fact_5735_unit__div__commute,axiom,
% 5.31/5.60 ! [B: code_integer,A: code_integer,C2: code_integer] :
% 5.31/5.60 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.31/5.60 => ( ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C2 )
% 5.31/5.60 = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ C2 ) @ B ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % unit_div_commute
% 5.31/5.60 thf(fact_5736_unit__div__commute,axiom,
% 5.31/5.60 ! [B: nat,A: nat,C2: nat] :
% 5.31/5.60 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.31/5.60 => ( ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ C2 )
% 5.31/5.60 = ( divide_divide_nat @ ( times_times_nat @ A @ C2 ) @ B ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % unit_div_commute
% 5.31/5.60 thf(fact_5737_unit__div__commute,axiom,
% 5.31/5.60 ! [B: int,A: int,C2: int] :
% 5.31/5.60 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.31/5.60 => ( ( times_times_int @ ( divide_divide_int @ A @ B ) @ C2 )
% 5.31/5.60 = ( divide_divide_int @ ( times_times_int @ A @ C2 ) @ B ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % unit_div_commute
% 5.31/5.60 thf(fact_5738_unit__div__mult__swap,axiom,
% 5.31/5.60 ! [C2: code_integer,A: code_integer,B: code_integer] :
% 5.31/5.60 ( ( dvd_dvd_Code_integer @ C2 @ one_one_Code_integer )
% 5.31/5.60 => ( ( times_3573771949741848930nteger @ A @ ( divide6298287555418463151nteger @ B @ C2 ) )
% 5.31/5.60 = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C2 ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % unit_div_mult_swap
% 5.31/5.60 thf(fact_5739_unit__div__mult__swap,axiom,
% 5.31/5.60 ! [C2: nat,A: nat,B: nat] :
% 5.31/5.60 ( ( dvd_dvd_nat @ C2 @ one_one_nat )
% 5.31/5.60 => ( ( times_times_nat @ A @ ( divide_divide_nat @ B @ C2 ) )
% 5.31/5.60 = ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ C2 ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % unit_div_mult_swap
% 5.31/5.60 thf(fact_5740_unit__div__mult__swap,axiom,
% 5.31/5.60 ! [C2: int,A: int,B: int] :
% 5.31/5.60 ( ( dvd_dvd_int @ C2 @ one_one_int )
% 5.31/5.60 => ( ( times_times_int @ A @ ( divide_divide_int @ B @ C2 ) )
% 5.31/5.60 = ( divide_divide_int @ ( times_times_int @ A @ B ) @ C2 ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % unit_div_mult_swap
% 5.31/5.60 thf(fact_5741_is__unit__div__mult2__eq,axiom,
% 5.31/5.60 ! [B: code_integer,C2: code_integer,A: code_integer] :
% 5.31/5.60 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.31/5.60 => ( ( dvd_dvd_Code_integer @ C2 @ one_one_Code_integer )
% 5.31/5.60 => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ B @ C2 ) )
% 5.31/5.60 = ( divide6298287555418463151nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C2 ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % is_unit_div_mult2_eq
% 5.31/5.60 thf(fact_5742_is__unit__div__mult2__eq,axiom,
% 5.31/5.60 ! [B: nat,C2: nat,A: nat] :
% 5.31/5.60 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.31/5.60 => ( ( dvd_dvd_nat @ C2 @ one_one_nat )
% 5.31/5.60 => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ C2 ) )
% 5.31/5.60 = ( divide_divide_nat @ ( divide_divide_nat @ A @ B ) @ C2 ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % is_unit_div_mult2_eq
% 5.31/5.60 thf(fact_5743_is__unit__div__mult2__eq,axiom,
% 5.31/5.60 ! [B: int,C2: int,A: int] :
% 5.31/5.60 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.31/5.60 => ( ( dvd_dvd_int @ C2 @ one_one_int )
% 5.31/5.60 => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C2 ) )
% 5.31/5.60 = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C2 ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % is_unit_div_mult2_eq
% 5.31/5.60 thf(fact_5744_is__unit__power__iff,axiom,
% 5.31/5.60 ! [A: code_integer,N: nat] :
% 5.31/5.60 ( ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ A @ N ) @ one_one_Code_integer )
% 5.31/5.60 = ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.31/5.60 | ( N = zero_zero_nat ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % is_unit_power_iff
% 5.31/5.60 thf(fact_5745_is__unit__power__iff,axiom,
% 5.31/5.60 ! [A: nat,N: nat] :
% 5.31/5.60 ( ( dvd_dvd_nat @ ( power_power_nat @ A @ N ) @ one_one_nat )
% 5.31/5.60 = ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.31/5.60 | ( N = zero_zero_nat ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % is_unit_power_iff
% 5.31/5.60 thf(fact_5746_is__unit__power__iff,axiom,
% 5.31/5.60 ! [A: int,N: nat] :
% 5.31/5.60 ( ( dvd_dvd_int @ ( power_power_int @ A @ N ) @ one_one_int )
% 5.31/5.60 = ( ( dvd_dvd_int @ A @ one_one_int )
% 5.31/5.60 | ( N = zero_zero_nat ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % is_unit_power_iff
% 5.31/5.60 thf(fact_5747_unit__imp__mod__eq__0,axiom,
% 5.31/5.60 ! [B: code_integer,A: code_integer] :
% 5.31/5.60 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.31/5.60 => ( ( modulo364778990260209775nteger @ A @ B )
% 5.31/5.60 = zero_z3403309356797280102nteger ) ) ).
% 5.31/5.60
% 5.31/5.60 % unit_imp_mod_eq_0
% 5.31/5.60 thf(fact_5748_unit__imp__mod__eq__0,axiom,
% 5.31/5.60 ! [B: nat,A: nat] :
% 5.31/5.60 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.31/5.60 => ( ( modulo_modulo_nat @ A @ B )
% 5.31/5.60 = zero_zero_nat ) ) ).
% 5.31/5.60
% 5.31/5.60 % unit_imp_mod_eq_0
% 5.31/5.60 thf(fact_5749_unit__imp__mod__eq__0,axiom,
% 5.31/5.60 ! [B: int,A: int] :
% 5.31/5.60 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.31/5.60 => ( ( modulo_modulo_int @ A @ B )
% 5.31/5.60 = zero_zero_int ) ) ).
% 5.31/5.60
% 5.31/5.60 % unit_imp_mod_eq_0
% 5.31/5.60 thf(fact_5750_unit__imp__mod__eq__0,axiom,
% 5.31/5.60 ! [B: code_natural,A: code_natural] :
% 5.31/5.60 ( ( dvd_dvd_Code_natural @ B @ one_one_Code_natural )
% 5.31/5.60 => ( ( modulo8411746178871703098atural @ A @ B )
% 5.31/5.60 = zero_z2226904508553997617atural ) ) ).
% 5.31/5.60
% 5.31/5.60 % unit_imp_mod_eq_0
% 5.31/5.60 thf(fact_5751_pochhammer__nonneg,axiom,
% 5.31/5.60 ! [X: real,N: nat] :
% 5.31/5.60 ( ( ord_less_real @ zero_zero_real @ X )
% 5.31/5.60 => ( ord_less_eq_real @ zero_zero_real @ ( comm_s7457072308508201937r_real @ X @ N ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % pochhammer_nonneg
% 5.31/5.60 thf(fact_5752_pochhammer__nonneg,axiom,
% 5.31/5.60 ! [X: rat,N: nat] :
% 5.31/5.60 ( ( ord_less_rat @ zero_zero_rat @ X )
% 5.31/5.60 => ( ord_less_eq_rat @ zero_zero_rat @ ( comm_s4028243227959126397er_rat @ X @ N ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % pochhammer_nonneg
% 5.31/5.60 thf(fact_5753_pochhammer__nonneg,axiom,
% 5.31/5.60 ! [X: nat,N: nat] :
% 5.31/5.60 ( ( ord_less_nat @ zero_zero_nat @ X )
% 5.31/5.60 => ( ord_less_eq_nat @ zero_zero_nat @ ( comm_s4663373288045622133er_nat @ X @ N ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % pochhammer_nonneg
% 5.31/5.60 thf(fact_5754_pochhammer__nonneg,axiom,
% 5.31/5.60 ! [X: int,N: nat] :
% 5.31/5.60 ( ( ord_less_int @ zero_zero_int @ X )
% 5.31/5.60 => ( ord_less_eq_int @ zero_zero_int @ ( comm_s4660882817536571857er_int @ X @ N ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % pochhammer_nonneg
% 5.31/5.60 thf(fact_5755_dvd__imp__le,axiom,
% 5.31/5.60 ! [K2: nat,N: nat] :
% 5.31/5.60 ( ( dvd_dvd_nat @ K2 @ N )
% 5.31/5.60 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.60 => ( ord_less_eq_nat @ K2 @ N ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % dvd_imp_le
% 5.31/5.60 thf(fact_5756_dvd__mult__cancel,axiom,
% 5.31/5.60 ! [K2: nat,M2: nat,N: nat] :
% 5.31/5.60 ( ( dvd_dvd_nat @ ( times_times_nat @ K2 @ M2 ) @ ( times_times_nat @ K2 @ N ) )
% 5.31/5.60 => ( ( ord_less_nat @ zero_zero_nat @ K2 )
% 5.31/5.60 => ( dvd_dvd_nat @ M2 @ N ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % dvd_mult_cancel
% 5.31/5.60 thf(fact_5757_nat__mult__dvd__cancel1,axiom,
% 5.31/5.60 ! [K2: nat,M2: nat,N: nat] :
% 5.31/5.60 ( ( ord_less_nat @ zero_zero_nat @ K2 )
% 5.31/5.60 => ( ( dvd_dvd_nat @ ( times_times_nat @ K2 @ M2 ) @ ( times_times_nat @ K2 @ N ) )
% 5.31/5.60 = ( dvd_dvd_nat @ M2 @ N ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % nat_mult_dvd_cancel1
% 5.31/5.60 thf(fact_5758_pochhammer__0__left,axiom,
% 5.31/5.60 ! [N: nat] :
% 5.31/5.60 ( ( ( N = zero_zero_nat )
% 5.31/5.60 => ( ( comm_s8582702949713902594nteger @ zero_z3403309356797280102nteger @ N )
% 5.31/5.60 = one_one_Code_integer ) )
% 5.31/5.60 & ( ( N != zero_zero_nat )
% 5.31/5.60 => ( ( comm_s8582702949713902594nteger @ zero_z3403309356797280102nteger @ N )
% 5.31/5.60 = zero_z3403309356797280102nteger ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % pochhammer_0_left
% 5.31/5.60 thf(fact_5759_pochhammer__0__left,axiom,
% 5.31/5.60 ! [N: nat] :
% 5.31/5.60 ( ( ( N = zero_zero_nat )
% 5.31/5.60 => ( ( comm_s2602460028002588243omplex @ zero_zero_complex @ N )
% 5.31/5.60 = one_one_complex ) )
% 5.31/5.60 & ( ( N != zero_zero_nat )
% 5.31/5.60 => ( ( comm_s2602460028002588243omplex @ zero_zero_complex @ N )
% 5.31/5.60 = zero_zero_complex ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % pochhammer_0_left
% 5.31/5.60 thf(fact_5760_pochhammer__0__left,axiom,
% 5.31/5.60 ! [N: nat] :
% 5.31/5.60 ( ( ( N = zero_zero_nat )
% 5.31/5.60 => ( ( comm_s7457072308508201937r_real @ zero_zero_real @ N )
% 5.31/5.60 = one_one_real ) )
% 5.31/5.60 & ( ( N != zero_zero_nat )
% 5.31/5.60 => ( ( comm_s7457072308508201937r_real @ zero_zero_real @ N )
% 5.31/5.60 = zero_zero_real ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % pochhammer_0_left
% 5.31/5.60 thf(fact_5761_pochhammer__0__left,axiom,
% 5.31/5.60 ! [N: nat] :
% 5.31/5.60 ( ( ( N = zero_zero_nat )
% 5.31/5.60 => ( ( comm_s4028243227959126397er_rat @ zero_zero_rat @ N )
% 5.31/5.60 = one_one_rat ) )
% 5.31/5.60 & ( ( N != zero_zero_nat )
% 5.31/5.60 => ( ( comm_s4028243227959126397er_rat @ zero_zero_rat @ N )
% 5.31/5.60 = zero_zero_rat ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % pochhammer_0_left
% 5.31/5.60 thf(fact_5762_pochhammer__0__left,axiom,
% 5.31/5.60 ! [N: nat] :
% 5.31/5.60 ( ( ( N = zero_zero_nat )
% 5.31/5.60 => ( ( comm_s4663373288045622133er_nat @ zero_zero_nat @ N )
% 5.31/5.60 = one_one_nat ) )
% 5.31/5.60 & ( ( N != zero_zero_nat )
% 5.31/5.60 => ( ( comm_s4663373288045622133er_nat @ zero_zero_nat @ N )
% 5.31/5.60 = zero_zero_nat ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % pochhammer_0_left
% 5.31/5.60 thf(fact_5763_pochhammer__0__left,axiom,
% 5.31/5.60 ! [N: nat] :
% 5.31/5.60 ( ( ( N = zero_zero_nat )
% 5.31/5.60 => ( ( comm_s4660882817536571857er_int @ zero_zero_int @ N )
% 5.31/5.60 = one_one_int ) )
% 5.31/5.60 & ( ( N != zero_zero_nat )
% 5.31/5.60 => ( ( comm_s4660882817536571857er_int @ zero_zero_int @ N )
% 5.31/5.60 = zero_zero_int ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % pochhammer_0_left
% 5.31/5.60 thf(fact_5764_bezout__add__strong__nat,axiom,
% 5.31/5.60 ! [A: nat,B: nat] :
% 5.31/5.60 ( ( A != zero_zero_nat )
% 5.31/5.60 => ? [D5: nat,X3: nat,Y3: nat] :
% 5.31/5.60 ( ( dvd_dvd_nat @ D5 @ A )
% 5.31/5.60 & ( dvd_dvd_nat @ D5 @ B )
% 5.31/5.60 & ( ( times_times_nat @ A @ X3 )
% 5.31/5.60 = ( plus_plus_nat @ ( times_times_nat @ B @ Y3 ) @ D5 ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % bezout_add_strong_nat
% 5.31/5.60 thf(fact_5765_mod__greater__zero__iff__not__dvd,axiom,
% 5.31/5.60 ! [M2: nat,N: nat] :
% 5.31/5.60 ( ( ord_less_nat @ zero_zero_nat @ ( modulo_modulo_nat @ M2 @ N ) )
% 5.31/5.60 = ( ~ ( dvd_dvd_nat @ N @ M2 ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % mod_greater_zero_iff_not_dvd
% 5.31/5.60 thf(fact_5766_mod__eq__dvd__iff__nat,axiom,
% 5.31/5.60 ! [N: nat,M2: nat,Q2: nat] :
% 5.31/5.60 ( ( ord_less_eq_nat @ N @ M2 )
% 5.31/5.60 => ( ( ( modulo_modulo_nat @ M2 @ Q2 )
% 5.31/5.60 = ( modulo_modulo_nat @ N @ Q2 ) )
% 5.31/5.60 = ( dvd_dvd_nat @ Q2 @ ( minus_minus_nat @ M2 @ N ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % mod_eq_dvd_iff_nat
% 5.31/5.60 thf(fact_5767_sum__power__add,axiom,
% 5.31/5.60 ! [X: complex,M2: nat,I5: set_nat] :
% 5.31/5.60 ( ( groups2073611262835488442omplex
% 5.31/5.60 @ ^ [I: nat] : ( power_power_complex @ X @ ( plus_plus_nat @ M2 @ I ) )
% 5.31/5.60 @ I5 )
% 5.31/5.60 = ( times_times_complex @ ( power_power_complex @ X @ M2 ) @ ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ I5 ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum_power_add
% 5.31/5.60 thf(fact_5768_sum__power__add,axiom,
% 5.31/5.60 ! [X: rat,M2: nat,I5: set_nat] :
% 5.31/5.60 ( ( groups2906978787729119204at_rat
% 5.31/5.60 @ ^ [I: nat] : ( power_power_rat @ X @ ( plus_plus_nat @ M2 @ I ) )
% 5.31/5.60 @ I5 )
% 5.31/5.60 = ( times_times_rat @ ( power_power_rat @ X @ M2 ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ I5 ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum_power_add
% 5.31/5.60 thf(fact_5769_sum__power__add,axiom,
% 5.31/5.60 ! [X: int,M2: nat,I5: set_nat] :
% 5.31/5.60 ( ( groups3539618377306564664at_int
% 5.31/5.60 @ ^ [I: nat] : ( power_power_int @ X @ ( plus_plus_nat @ M2 @ I ) )
% 5.31/5.60 @ I5 )
% 5.31/5.60 = ( times_times_int @ ( power_power_int @ X @ M2 ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X ) @ I5 ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum_power_add
% 5.31/5.60 thf(fact_5770_sum__power__add,axiom,
% 5.31/5.60 ! [X: real,M2: nat,I5: set_nat] :
% 5.31/5.60 ( ( groups6591440286371151544t_real
% 5.31/5.60 @ ^ [I: nat] : ( power_power_real @ X @ ( plus_plus_nat @ M2 @ I ) )
% 5.31/5.60 @ I5 )
% 5.31/5.60 = ( times_times_real @ ( power_power_real @ X @ M2 ) @ ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ I5 ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum_power_add
% 5.31/5.60 thf(fact_5771_sum__mono2,axiom,
% 5.31/5.60 ! [B5: set_real,A4: set_real,F2: real > real] :
% 5.31/5.60 ( ( finite_finite_real @ B5 )
% 5.31/5.60 => ( ( ord_less_eq_set_real @ A4 @ B5 )
% 5.31/5.60 => ( ! [B3: real] :
% 5.31/5.60 ( ( member_real @ B3 @ ( minus_minus_set_real @ B5 @ A4 ) )
% 5.31/5.60 => ( ord_less_eq_real @ zero_zero_real @ ( F2 @ B3 ) ) )
% 5.31/5.60 => ( ord_less_eq_real @ ( groups8097168146408367636l_real @ F2 @ A4 ) @ ( groups8097168146408367636l_real @ F2 @ B5 ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum_mono2
% 5.31/5.60 thf(fact_5772_sum__mono2,axiom,
% 5.31/5.60 ! [B5: set_int,A4: set_int,F2: int > real] :
% 5.31/5.60 ( ( finite_finite_int @ B5 )
% 5.31/5.60 => ( ( ord_less_eq_set_int @ A4 @ B5 )
% 5.31/5.60 => ( ! [B3: int] :
% 5.31/5.60 ( ( member_int @ B3 @ ( minus_minus_set_int @ B5 @ A4 ) )
% 5.31/5.60 => ( ord_less_eq_real @ zero_zero_real @ ( F2 @ B3 ) ) )
% 5.31/5.60 => ( ord_less_eq_real @ ( groups8778361861064173332t_real @ F2 @ A4 ) @ ( groups8778361861064173332t_real @ F2 @ B5 ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum_mono2
% 5.31/5.60 thf(fact_5773_sum__mono2,axiom,
% 5.31/5.60 ! [B5: set_complex,A4: set_complex,F2: complex > real] :
% 5.31/5.60 ( ( finite3207457112153483333omplex @ B5 )
% 5.31/5.60 => ( ( ord_le211207098394363844omplex @ A4 @ B5 )
% 5.31/5.60 => ( ! [B3: complex] :
% 5.31/5.60 ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ B5 @ A4 ) )
% 5.31/5.60 => ( ord_less_eq_real @ zero_zero_real @ ( F2 @ B3 ) ) )
% 5.31/5.60 => ( ord_less_eq_real @ ( groups5808333547571424918x_real @ F2 @ A4 ) @ ( groups5808333547571424918x_real @ F2 @ B5 ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum_mono2
% 5.31/5.60 thf(fact_5774_sum__mono2,axiom,
% 5.31/5.60 ! [B5: set_real,A4: set_real,F2: real > rat] :
% 5.31/5.60 ( ( finite_finite_real @ B5 )
% 5.31/5.60 => ( ( ord_less_eq_set_real @ A4 @ B5 )
% 5.31/5.60 => ( ! [B3: real] :
% 5.31/5.60 ( ( member_real @ B3 @ ( minus_minus_set_real @ B5 @ A4 ) )
% 5.31/5.60 => ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ B3 ) ) )
% 5.31/5.60 => ( ord_less_eq_rat @ ( groups1300246762558778688al_rat @ F2 @ A4 ) @ ( groups1300246762558778688al_rat @ F2 @ B5 ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum_mono2
% 5.31/5.60 thf(fact_5775_sum__mono2,axiom,
% 5.31/5.60 ! [B5: set_int,A4: set_int,F2: int > rat] :
% 5.31/5.60 ( ( finite_finite_int @ B5 )
% 5.31/5.60 => ( ( ord_less_eq_set_int @ A4 @ B5 )
% 5.31/5.60 => ( ! [B3: int] :
% 5.31/5.60 ( ( member_int @ B3 @ ( minus_minus_set_int @ B5 @ A4 ) )
% 5.31/5.60 => ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ B3 ) ) )
% 5.31/5.60 => ( ord_less_eq_rat @ ( groups3906332499630173760nt_rat @ F2 @ A4 ) @ ( groups3906332499630173760nt_rat @ F2 @ B5 ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum_mono2
% 5.31/5.60 thf(fact_5776_sum__mono2,axiom,
% 5.31/5.60 ! [B5: set_complex,A4: set_complex,F2: complex > rat] :
% 5.31/5.60 ( ( finite3207457112153483333omplex @ B5 )
% 5.31/5.60 => ( ( ord_le211207098394363844omplex @ A4 @ B5 )
% 5.31/5.60 => ( ! [B3: complex] :
% 5.31/5.60 ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ B5 @ A4 ) )
% 5.31/5.60 => ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ B3 ) ) )
% 5.31/5.60 => ( ord_less_eq_rat @ ( groups5058264527183730370ex_rat @ F2 @ A4 ) @ ( groups5058264527183730370ex_rat @ F2 @ B5 ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum_mono2
% 5.31/5.60 thf(fact_5777_sum__mono2,axiom,
% 5.31/5.60 ! [B5: set_real,A4: set_real,F2: real > nat] :
% 5.31/5.60 ( ( finite_finite_real @ B5 )
% 5.31/5.60 => ( ( ord_less_eq_set_real @ A4 @ B5 )
% 5.31/5.60 => ( ! [B3: real] :
% 5.31/5.60 ( ( member_real @ B3 @ ( minus_minus_set_real @ B5 @ A4 ) )
% 5.31/5.60 => ( ord_less_eq_nat @ zero_zero_nat @ ( F2 @ B3 ) ) )
% 5.31/5.60 => ( ord_less_eq_nat @ ( groups1935376822645274424al_nat @ F2 @ A4 ) @ ( groups1935376822645274424al_nat @ F2 @ B5 ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum_mono2
% 5.31/5.60 thf(fact_5778_sum__mono2,axiom,
% 5.31/5.60 ! [B5: set_int,A4: set_int,F2: int > nat] :
% 5.31/5.60 ( ( finite_finite_int @ B5 )
% 5.31/5.60 => ( ( ord_less_eq_set_int @ A4 @ B5 )
% 5.31/5.60 => ( ! [B3: int] :
% 5.31/5.60 ( ( member_int @ B3 @ ( minus_minus_set_int @ B5 @ A4 ) )
% 5.31/5.60 => ( ord_less_eq_nat @ zero_zero_nat @ ( F2 @ B3 ) ) )
% 5.31/5.60 => ( ord_less_eq_nat @ ( groups4541462559716669496nt_nat @ F2 @ A4 ) @ ( groups4541462559716669496nt_nat @ F2 @ B5 ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum_mono2
% 5.31/5.60 thf(fact_5779_sum__mono2,axiom,
% 5.31/5.60 ! [B5: set_complex,A4: set_complex,F2: complex > nat] :
% 5.31/5.60 ( ( finite3207457112153483333omplex @ B5 )
% 5.31/5.60 => ( ( ord_le211207098394363844omplex @ A4 @ B5 )
% 5.31/5.60 => ( ! [B3: complex] :
% 5.31/5.60 ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ B5 @ A4 ) )
% 5.31/5.60 => ( ord_less_eq_nat @ zero_zero_nat @ ( F2 @ B3 ) ) )
% 5.31/5.60 => ( ord_less_eq_nat @ ( groups5693394587270226106ex_nat @ F2 @ A4 ) @ ( groups5693394587270226106ex_nat @ F2 @ B5 ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum_mono2
% 5.31/5.60 thf(fact_5780_sum__mono2,axiom,
% 5.31/5.60 ! [B5: set_real,A4: set_real,F2: real > int] :
% 5.31/5.60 ( ( finite_finite_real @ B5 )
% 5.31/5.60 => ( ( ord_less_eq_set_real @ A4 @ B5 )
% 5.31/5.60 => ( ! [B3: real] :
% 5.31/5.60 ( ( member_real @ B3 @ ( minus_minus_set_real @ B5 @ A4 ) )
% 5.31/5.60 => ( ord_less_eq_int @ zero_zero_int @ ( F2 @ B3 ) ) )
% 5.31/5.60 => ( ord_less_eq_int @ ( groups1932886352136224148al_int @ F2 @ A4 ) @ ( groups1932886352136224148al_int @ F2 @ B5 ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum_mono2
% 5.31/5.60 thf(fact_5781_sum_Ounion__inter__neutral,axiom,
% 5.31/5.60 ! [A4: set_int,B5: set_int,G2: int > complex] :
% 5.31/5.60 ( ( finite_finite_int @ A4 )
% 5.31/5.60 => ( ( finite_finite_int @ B5 )
% 5.31/5.60 => ( ! [X3: int] :
% 5.31/5.60 ( ( member_int @ X3 @ ( inf_inf_set_int @ A4 @ B5 ) )
% 5.31/5.60 => ( ( G2 @ X3 )
% 5.31/5.60 = zero_zero_complex ) )
% 5.31/5.60 => ( ( groups3049146728041665814omplex @ G2 @ ( sup_sup_set_int @ A4 @ B5 ) )
% 5.31/5.60 = ( plus_plus_complex @ ( groups3049146728041665814omplex @ G2 @ A4 ) @ ( groups3049146728041665814omplex @ G2 @ B5 ) ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum.union_inter_neutral
% 5.31/5.60 thf(fact_5782_sum_Ounion__inter__neutral,axiom,
% 5.31/5.60 ! [A4: set_complex,B5: set_complex,G2: complex > complex] :
% 5.31/5.60 ( ( finite3207457112153483333omplex @ A4 )
% 5.31/5.60 => ( ( finite3207457112153483333omplex @ B5 )
% 5.31/5.60 => ( ! [X3: complex] :
% 5.31/5.60 ( ( member_complex @ X3 @ ( inf_inf_set_complex @ A4 @ B5 ) )
% 5.31/5.60 => ( ( G2 @ X3 )
% 5.31/5.60 = zero_zero_complex ) )
% 5.31/5.60 => ( ( groups7754918857620584856omplex @ G2 @ ( sup_sup_set_complex @ A4 @ B5 ) )
% 5.31/5.60 = ( plus_plus_complex @ ( groups7754918857620584856omplex @ G2 @ A4 ) @ ( groups7754918857620584856omplex @ G2 @ B5 ) ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum.union_inter_neutral
% 5.31/5.60 thf(fact_5783_sum_Ounion__inter__neutral,axiom,
% 5.31/5.60 ! [A4: set_int,B5: set_int,G2: int > real] :
% 5.31/5.60 ( ( finite_finite_int @ A4 )
% 5.31/5.60 => ( ( finite_finite_int @ B5 )
% 5.31/5.60 => ( ! [X3: int] :
% 5.31/5.60 ( ( member_int @ X3 @ ( inf_inf_set_int @ A4 @ B5 ) )
% 5.31/5.60 => ( ( G2 @ X3 )
% 5.31/5.60 = zero_zero_real ) )
% 5.31/5.60 => ( ( groups8778361861064173332t_real @ G2 @ ( sup_sup_set_int @ A4 @ B5 ) )
% 5.31/5.60 = ( plus_plus_real @ ( groups8778361861064173332t_real @ G2 @ A4 ) @ ( groups8778361861064173332t_real @ G2 @ B5 ) ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum.union_inter_neutral
% 5.31/5.60 thf(fact_5784_sum_Ounion__inter__neutral,axiom,
% 5.31/5.60 ! [A4: set_complex,B5: set_complex,G2: complex > real] :
% 5.31/5.60 ( ( finite3207457112153483333omplex @ A4 )
% 5.31/5.60 => ( ( finite3207457112153483333omplex @ B5 )
% 5.31/5.60 => ( ! [X3: complex] :
% 5.31/5.60 ( ( member_complex @ X3 @ ( inf_inf_set_complex @ A4 @ B5 ) )
% 5.31/5.60 => ( ( G2 @ X3 )
% 5.31/5.60 = zero_zero_real ) )
% 5.31/5.60 => ( ( groups5808333547571424918x_real @ G2 @ ( sup_sup_set_complex @ A4 @ B5 ) )
% 5.31/5.60 = ( plus_plus_real @ ( groups5808333547571424918x_real @ G2 @ A4 ) @ ( groups5808333547571424918x_real @ G2 @ B5 ) ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum.union_inter_neutral
% 5.31/5.60 thf(fact_5785_sum_Ounion__inter__neutral,axiom,
% 5.31/5.60 ! [A4: set_int,B5: set_int,G2: int > rat] :
% 5.31/5.60 ( ( finite_finite_int @ A4 )
% 5.31/5.60 => ( ( finite_finite_int @ B5 )
% 5.31/5.60 => ( ! [X3: int] :
% 5.31/5.60 ( ( member_int @ X3 @ ( inf_inf_set_int @ A4 @ B5 ) )
% 5.31/5.60 => ( ( G2 @ X3 )
% 5.31/5.60 = zero_zero_rat ) )
% 5.31/5.60 => ( ( groups3906332499630173760nt_rat @ G2 @ ( sup_sup_set_int @ A4 @ B5 ) )
% 5.31/5.60 = ( plus_plus_rat @ ( groups3906332499630173760nt_rat @ G2 @ A4 ) @ ( groups3906332499630173760nt_rat @ G2 @ B5 ) ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum.union_inter_neutral
% 5.31/5.60 thf(fact_5786_sum_Ounion__inter__neutral,axiom,
% 5.31/5.60 ! [A4: set_complex,B5: set_complex,G2: complex > rat] :
% 5.31/5.60 ( ( finite3207457112153483333omplex @ A4 )
% 5.31/5.60 => ( ( finite3207457112153483333omplex @ B5 )
% 5.31/5.60 => ( ! [X3: complex] :
% 5.31/5.60 ( ( member_complex @ X3 @ ( inf_inf_set_complex @ A4 @ B5 ) )
% 5.31/5.60 => ( ( G2 @ X3 )
% 5.31/5.60 = zero_zero_rat ) )
% 5.31/5.60 => ( ( groups5058264527183730370ex_rat @ G2 @ ( sup_sup_set_complex @ A4 @ B5 ) )
% 5.31/5.60 = ( plus_plus_rat @ ( groups5058264527183730370ex_rat @ G2 @ A4 ) @ ( groups5058264527183730370ex_rat @ G2 @ B5 ) ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum.union_inter_neutral
% 5.31/5.60 thf(fact_5787_sum_Ounion__inter__neutral,axiom,
% 5.31/5.60 ! [A4: set_int,B5: set_int,G2: int > nat] :
% 5.31/5.60 ( ( finite_finite_int @ A4 )
% 5.31/5.60 => ( ( finite_finite_int @ B5 )
% 5.31/5.60 => ( ! [X3: int] :
% 5.31/5.60 ( ( member_int @ X3 @ ( inf_inf_set_int @ A4 @ B5 ) )
% 5.31/5.60 => ( ( G2 @ X3 )
% 5.31/5.60 = zero_zero_nat ) )
% 5.31/5.60 => ( ( groups4541462559716669496nt_nat @ G2 @ ( sup_sup_set_int @ A4 @ B5 ) )
% 5.31/5.60 = ( plus_plus_nat @ ( groups4541462559716669496nt_nat @ G2 @ A4 ) @ ( groups4541462559716669496nt_nat @ G2 @ B5 ) ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum.union_inter_neutral
% 5.31/5.60 thf(fact_5788_sum_Ounion__inter__neutral,axiom,
% 5.31/5.60 ! [A4: set_complex,B5: set_complex,G2: complex > nat] :
% 5.31/5.60 ( ( finite3207457112153483333omplex @ A4 )
% 5.31/5.60 => ( ( finite3207457112153483333omplex @ B5 )
% 5.31/5.60 => ( ! [X3: complex] :
% 5.31/5.60 ( ( member_complex @ X3 @ ( inf_inf_set_complex @ A4 @ B5 ) )
% 5.31/5.60 => ( ( G2 @ X3 )
% 5.31/5.60 = zero_zero_nat ) )
% 5.31/5.60 => ( ( groups5693394587270226106ex_nat @ G2 @ ( sup_sup_set_complex @ A4 @ B5 ) )
% 5.31/5.60 = ( plus_plus_nat @ ( groups5693394587270226106ex_nat @ G2 @ A4 ) @ ( groups5693394587270226106ex_nat @ G2 @ B5 ) ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum.union_inter_neutral
% 5.31/5.60 thf(fact_5789_sum_Ounion__inter__neutral,axiom,
% 5.31/5.60 ! [A4: set_complex,B5: set_complex,G2: complex > int] :
% 5.31/5.60 ( ( finite3207457112153483333omplex @ A4 )
% 5.31/5.60 => ( ( finite3207457112153483333omplex @ B5 )
% 5.31/5.60 => ( ! [X3: complex] :
% 5.31/5.60 ( ( member_complex @ X3 @ ( inf_inf_set_complex @ A4 @ B5 ) )
% 5.31/5.60 => ( ( G2 @ X3 )
% 5.31/5.60 = zero_zero_int ) )
% 5.31/5.60 => ( ( groups5690904116761175830ex_int @ G2 @ ( sup_sup_set_complex @ A4 @ B5 ) )
% 5.31/5.60 = ( plus_plus_int @ ( groups5690904116761175830ex_int @ G2 @ A4 ) @ ( groups5690904116761175830ex_int @ G2 @ B5 ) ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum.union_inter_neutral
% 5.31/5.60 thf(fact_5790_sum_Ounion__inter__neutral,axiom,
% 5.31/5.60 ! [A4: set_nat,B5: set_nat,G2: nat > complex] :
% 5.31/5.60 ( ( finite_finite_nat @ A4 )
% 5.31/5.60 => ( ( finite_finite_nat @ B5 )
% 5.31/5.60 => ( ! [X3: nat] :
% 5.31/5.60 ( ( member_nat @ X3 @ ( inf_inf_set_nat @ A4 @ B5 ) )
% 5.31/5.60 => ( ( G2 @ X3 )
% 5.31/5.60 = zero_zero_complex ) )
% 5.31/5.60 => ( ( groups2073611262835488442omplex @ G2 @ ( sup_sup_set_nat @ A4 @ B5 ) )
% 5.31/5.60 = ( plus_plus_complex @ ( groups2073611262835488442omplex @ G2 @ A4 ) @ ( groups2073611262835488442omplex @ G2 @ B5 ) ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum.union_inter_neutral
% 5.31/5.60 thf(fact_5791_sum_OatLeastAtMost__rev,axiom,
% 5.31/5.60 ! [G2: nat > nat,N: nat,M2: nat] :
% 5.31/5.60 ( ( groups3542108847815614940at_nat @ G2 @ ( set_or1269000886237332187st_nat @ N @ M2 ) )
% 5.31/5.60 = ( groups3542108847815614940at_nat
% 5.31/5.60 @ ^ [I: nat] : ( G2 @ ( minus_minus_nat @ ( plus_plus_nat @ M2 @ N ) @ I ) )
% 5.31/5.60 @ ( set_or1269000886237332187st_nat @ N @ M2 ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum.atLeastAtMost_rev
% 5.31/5.60 thf(fact_5792_sum_OatLeastAtMost__rev,axiom,
% 5.31/5.60 ! [G2: nat > real,N: nat,M2: nat] :
% 5.31/5.60 ( ( groups6591440286371151544t_real @ G2 @ ( set_or1269000886237332187st_nat @ N @ M2 ) )
% 5.31/5.60 = ( groups6591440286371151544t_real
% 5.31/5.60 @ ^ [I: nat] : ( G2 @ ( minus_minus_nat @ ( plus_plus_nat @ M2 @ N ) @ I ) )
% 5.31/5.60 @ ( set_or1269000886237332187st_nat @ N @ M2 ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum.atLeastAtMost_rev
% 5.31/5.60 thf(fact_5793_finite__divisors__nat,axiom,
% 5.31/5.60 ! [M2: nat] :
% 5.31/5.60 ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 5.31/5.60 => ( finite_finite_nat
% 5.31/5.60 @ ( collect_nat
% 5.31/5.60 @ ^ [D2: nat] : ( dvd_dvd_nat @ D2 @ M2 ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % finite_divisors_nat
% 5.31/5.60 thf(fact_5794_powser__sums__zero,axiom,
% 5.31/5.60 ! [A: nat > complex] :
% 5.31/5.60 ( sums_complex
% 5.31/5.60 @ ^ [N4: nat] : ( times_times_complex @ ( A @ N4 ) @ ( power_power_complex @ zero_zero_complex @ N4 ) )
% 5.31/5.60 @ ( A @ zero_zero_nat ) ) ).
% 5.31/5.60
% 5.31/5.60 % powser_sums_zero
% 5.31/5.60 thf(fact_5795_powser__sums__zero,axiom,
% 5.31/5.60 ! [A: nat > real] :
% 5.31/5.60 ( sums_real
% 5.31/5.60 @ ^ [N4: nat] : ( times_times_real @ ( A @ N4 ) @ ( power_power_real @ zero_zero_real @ N4 ) )
% 5.31/5.60 @ ( A @ zero_zero_nat ) ) ).
% 5.31/5.60
% 5.31/5.60 % powser_sums_zero
% 5.31/5.60 thf(fact_5796_sum__shift__lb__Suc0__0,axiom,
% 5.31/5.60 ! [F2: nat > complex,K2: nat] :
% 5.31/5.60 ( ( ( F2 @ zero_zero_nat )
% 5.31/5.60 = zero_zero_complex )
% 5.31/5.60 => ( ( groups2073611262835488442omplex @ F2 @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ K2 ) )
% 5.31/5.60 = ( groups2073611262835488442omplex @ F2 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K2 ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum_shift_lb_Suc0_0
% 5.31/5.60 thf(fact_5797_sum__shift__lb__Suc0__0,axiom,
% 5.31/5.60 ! [F2: nat > rat,K2: nat] :
% 5.31/5.60 ( ( ( F2 @ zero_zero_nat )
% 5.31/5.60 = zero_zero_rat )
% 5.31/5.60 => ( ( groups2906978787729119204at_rat @ F2 @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ K2 ) )
% 5.31/5.60 = ( groups2906978787729119204at_rat @ F2 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K2 ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum_shift_lb_Suc0_0
% 5.31/5.60 thf(fact_5798_sum__shift__lb__Suc0__0,axiom,
% 5.31/5.60 ! [F2: nat > int,K2: nat] :
% 5.31/5.60 ( ( ( F2 @ zero_zero_nat )
% 5.31/5.60 = zero_zero_int )
% 5.31/5.60 => ( ( groups3539618377306564664at_int @ F2 @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ K2 ) )
% 5.31/5.60 = ( groups3539618377306564664at_int @ F2 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K2 ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum_shift_lb_Suc0_0
% 5.31/5.60 thf(fact_5799_sum__shift__lb__Suc0__0,axiom,
% 5.31/5.60 ! [F2: nat > nat,K2: nat] :
% 5.31/5.60 ( ( ( F2 @ zero_zero_nat )
% 5.31/5.60 = zero_zero_nat )
% 5.31/5.60 => ( ( groups3542108847815614940at_nat @ F2 @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ K2 ) )
% 5.31/5.60 = ( groups3542108847815614940at_nat @ F2 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K2 ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum_shift_lb_Suc0_0
% 5.31/5.60 thf(fact_5800_sum__shift__lb__Suc0__0,axiom,
% 5.31/5.60 ! [F2: nat > real,K2: nat] :
% 5.31/5.60 ( ( ( F2 @ zero_zero_nat )
% 5.31/5.60 = zero_zero_real )
% 5.31/5.60 => ( ( groups6591440286371151544t_real @ F2 @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ K2 ) )
% 5.31/5.60 = ( groups6591440286371151544t_real @ F2 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K2 ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum_shift_lb_Suc0_0
% 5.31/5.60 thf(fact_5801_sum_OatLeast0__atMost__Suc,axiom,
% 5.31/5.60 ! [G2: nat > rat,N: nat] :
% 5.31/5.60 ( ( groups2906978787729119204at_rat @ G2 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 5.31/5.60 = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G2 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) @ ( G2 @ ( suc @ N ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum.atLeast0_atMost_Suc
% 5.31/5.60 thf(fact_5802_sum_OatLeast0__atMost__Suc,axiom,
% 5.31/5.60 ! [G2: nat > int,N: nat] :
% 5.31/5.60 ( ( groups3539618377306564664at_int @ G2 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 5.31/5.60 = ( plus_plus_int @ ( groups3539618377306564664at_int @ G2 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) @ ( G2 @ ( suc @ N ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum.atLeast0_atMost_Suc
% 5.31/5.60 thf(fact_5803_sum_OatLeast0__atMost__Suc,axiom,
% 5.31/5.60 ! [G2: nat > nat,N: nat] :
% 5.31/5.60 ( ( groups3542108847815614940at_nat @ G2 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 5.31/5.60 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G2 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) @ ( G2 @ ( suc @ N ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum.atLeast0_atMost_Suc
% 5.31/5.60 thf(fact_5804_sum_OatLeast0__atMost__Suc,axiom,
% 5.31/5.60 ! [G2: nat > real,N: nat] :
% 5.31/5.60 ( ( groups6591440286371151544t_real @ G2 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 5.31/5.60 = ( plus_plus_real @ ( groups6591440286371151544t_real @ G2 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) @ ( G2 @ ( suc @ N ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum.atLeast0_atMost_Suc
% 5.31/5.60 thf(fact_5805_sum_OatLeast__Suc__atMost,axiom,
% 5.31/5.60 ! [M2: nat,N: nat,G2: nat > rat] :
% 5.31/5.60 ( ( ord_less_eq_nat @ M2 @ N )
% 5.31/5.60 => ( ( groups2906978787729119204at_rat @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ N ) )
% 5.31/5.60 = ( plus_plus_rat @ ( G2 @ M2 ) @ ( groups2906978787729119204at_rat @ G2 @ ( set_or1269000886237332187st_nat @ ( suc @ M2 ) @ N ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum.atLeast_Suc_atMost
% 5.31/5.60 thf(fact_5806_sum_OatLeast__Suc__atMost,axiom,
% 5.31/5.60 ! [M2: nat,N: nat,G2: nat > int] :
% 5.31/5.60 ( ( ord_less_eq_nat @ M2 @ N )
% 5.31/5.60 => ( ( groups3539618377306564664at_int @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ N ) )
% 5.31/5.60 = ( plus_plus_int @ ( G2 @ M2 ) @ ( groups3539618377306564664at_int @ G2 @ ( set_or1269000886237332187st_nat @ ( suc @ M2 ) @ N ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum.atLeast_Suc_atMost
% 5.31/5.60 thf(fact_5807_sum_OatLeast__Suc__atMost,axiom,
% 5.31/5.60 ! [M2: nat,N: nat,G2: nat > nat] :
% 5.31/5.60 ( ( ord_less_eq_nat @ M2 @ N )
% 5.31/5.60 => ( ( groups3542108847815614940at_nat @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ N ) )
% 5.31/5.60 = ( plus_plus_nat @ ( G2 @ M2 ) @ ( groups3542108847815614940at_nat @ G2 @ ( set_or1269000886237332187st_nat @ ( suc @ M2 ) @ N ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum.atLeast_Suc_atMost
% 5.31/5.60 thf(fact_5808_sum_OatLeast__Suc__atMost,axiom,
% 5.31/5.60 ! [M2: nat,N: nat,G2: nat > real] :
% 5.31/5.60 ( ( ord_less_eq_nat @ M2 @ N )
% 5.31/5.60 => ( ( groups6591440286371151544t_real @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ N ) )
% 5.31/5.60 = ( plus_plus_real @ ( G2 @ M2 ) @ ( groups6591440286371151544t_real @ G2 @ ( set_or1269000886237332187st_nat @ ( suc @ M2 ) @ N ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum.atLeast_Suc_atMost
% 5.31/5.60 thf(fact_5809_sum_Onat__ivl__Suc_H,axiom,
% 5.31/5.60 ! [M2: nat,N: nat,G2: nat > rat] :
% 5.31/5.60 ( ( ord_less_eq_nat @ M2 @ ( suc @ N ) )
% 5.31/5.60 => ( ( groups2906978787729119204at_rat @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N ) ) )
% 5.31/5.60 = ( plus_plus_rat @ ( G2 @ ( suc @ N ) ) @ ( groups2906978787729119204at_rat @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum.nat_ivl_Suc'
% 5.31/5.60 thf(fact_5810_sum_Onat__ivl__Suc_H,axiom,
% 5.31/5.60 ! [M2: nat,N: nat,G2: nat > int] :
% 5.31/5.60 ( ( ord_less_eq_nat @ M2 @ ( suc @ N ) )
% 5.31/5.60 => ( ( groups3539618377306564664at_int @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N ) ) )
% 5.31/5.60 = ( plus_plus_int @ ( G2 @ ( suc @ N ) ) @ ( groups3539618377306564664at_int @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum.nat_ivl_Suc'
% 5.31/5.60 thf(fact_5811_sum_Onat__ivl__Suc_H,axiom,
% 5.31/5.60 ! [M2: nat,N: nat,G2: nat > nat] :
% 5.31/5.60 ( ( ord_less_eq_nat @ M2 @ ( suc @ N ) )
% 5.31/5.60 => ( ( groups3542108847815614940at_nat @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N ) ) )
% 5.31/5.60 = ( plus_plus_nat @ ( G2 @ ( suc @ N ) ) @ ( groups3542108847815614940at_nat @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum.nat_ivl_Suc'
% 5.31/5.60 thf(fact_5812_sum_Onat__ivl__Suc_H,axiom,
% 5.31/5.60 ! [M2: nat,N: nat,G2: nat > real] :
% 5.31/5.60 ( ( ord_less_eq_nat @ M2 @ ( suc @ N ) )
% 5.31/5.60 => ( ( groups6591440286371151544t_real @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N ) ) )
% 5.31/5.60 = ( plus_plus_real @ ( G2 @ ( suc @ N ) ) @ ( groups6591440286371151544t_real @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum.nat_ivl_Suc'
% 5.31/5.60 thf(fact_5813_even__zero,axiom,
% 5.31/5.60 dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ zero_zero_nat ).
% 5.31/5.60
% 5.31/5.60 % even_zero
% 5.31/5.60 thf(fact_5814_even__zero,axiom,
% 5.31/5.60 dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ zero_zero_int ).
% 5.31/5.60
% 5.31/5.60 % even_zero
% 5.31/5.60 thf(fact_5815_is__unitE,axiom,
% 5.31/5.60 ! [A: code_integer,C2: code_integer] :
% 5.31/5.60 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.31/5.60 => ~ ( ( A != zero_z3403309356797280102nteger )
% 5.31/5.60 => ! [B3: code_integer] :
% 5.31/5.60 ( ( B3 != zero_z3403309356797280102nteger )
% 5.31/5.60 => ( ( dvd_dvd_Code_integer @ B3 @ one_one_Code_integer )
% 5.31/5.60 => ( ( ( divide6298287555418463151nteger @ one_one_Code_integer @ A )
% 5.31/5.60 = B3 )
% 5.31/5.60 => ( ( ( divide6298287555418463151nteger @ one_one_Code_integer @ B3 )
% 5.31/5.60 = A )
% 5.31/5.60 => ( ( ( times_3573771949741848930nteger @ A @ B3 )
% 5.31/5.60 = one_one_Code_integer )
% 5.31/5.60 => ( ( divide6298287555418463151nteger @ C2 @ A )
% 5.31/5.60 != ( times_3573771949741848930nteger @ C2 @ B3 ) ) ) ) ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % is_unitE
% 5.31/5.60 thf(fact_5816_is__unitE,axiom,
% 5.31/5.60 ! [A: nat,C2: nat] :
% 5.31/5.60 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.31/5.60 => ~ ( ( A != zero_zero_nat )
% 5.31/5.60 => ! [B3: nat] :
% 5.31/5.60 ( ( B3 != zero_zero_nat )
% 5.31/5.60 => ( ( dvd_dvd_nat @ B3 @ one_one_nat )
% 5.31/5.60 => ( ( ( divide_divide_nat @ one_one_nat @ A )
% 5.31/5.60 = B3 )
% 5.31/5.60 => ( ( ( divide_divide_nat @ one_one_nat @ B3 )
% 5.31/5.60 = A )
% 5.31/5.60 => ( ( ( times_times_nat @ A @ B3 )
% 5.31/5.60 = one_one_nat )
% 5.31/5.60 => ( ( divide_divide_nat @ C2 @ A )
% 5.31/5.60 != ( times_times_nat @ C2 @ B3 ) ) ) ) ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % is_unitE
% 5.31/5.60 thf(fact_5817_is__unitE,axiom,
% 5.31/5.60 ! [A: int,C2: int] :
% 5.31/5.60 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.31/5.60 => ~ ( ( A != zero_zero_int )
% 5.31/5.60 => ! [B3: int] :
% 5.31/5.60 ( ( B3 != zero_zero_int )
% 5.31/5.60 => ( ( dvd_dvd_int @ B3 @ one_one_int )
% 5.31/5.60 => ( ( ( divide_divide_int @ one_one_int @ A )
% 5.31/5.60 = B3 )
% 5.31/5.60 => ( ( ( divide_divide_int @ one_one_int @ B3 )
% 5.31/5.60 = A )
% 5.31/5.60 => ( ( ( times_times_int @ A @ B3 )
% 5.31/5.60 = one_one_int )
% 5.31/5.60 => ( ( divide_divide_int @ C2 @ A )
% 5.31/5.60 != ( times_times_int @ C2 @ B3 ) ) ) ) ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % is_unitE
% 5.31/5.60 thf(fact_5818_is__unit__div__mult__cancel__left,axiom,
% 5.31/5.60 ! [A: code_integer,B: code_integer] :
% 5.31/5.60 ( ( A != zero_z3403309356797280102nteger )
% 5.31/5.60 => ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.31/5.60 => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ A @ B ) )
% 5.31/5.60 = ( divide6298287555418463151nteger @ one_one_Code_integer @ B ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % is_unit_div_mult_cancel_left
% 5.31/5.60 thf(fact_5819_is__unit__div__mult__cancel__left,axiom,
% 5.31/5.60 ! [A: nat,B: nat] :
% 5.31/5.60 ( ( A != zero_zero_nat )
% 5.31/5.60 => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.31/5.60 => ( ( divide_divide_nat @ A @ ( times_times_nat @ A @ B ) )
% 5.31/5.60 = ( divide_divide_nat @ one_one_nat @ B ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % is_unit_div_mult_cancel_left
% 5.31/5.60 thf(fact_5820_is__unit__div__mult__cancel__left,axiom,
% 5.31/5.60 ! [A: int,B: int] :
% 5.31/5.60 ( ( A != zero_zero_int )
% 5.31/5.60 => ( ( dvd_dvd_int @ B @ one_one_int )
% 5.31/5.60 => ( ( divide_divide_int @ A @ ( times_times_int @ A @ B ) )
% 5.31/5.60 = ( divide_divide_int @ one_one_int @ B ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % is_unit_div_mult_cancel_left
% 5.31/5.60 thf(fact_5821_is__unit__div__mult__cancel__right,axiom,
% 5.31/5.60 ! [A: code_integer,B: code_integer] :
% 5.31/5.60 ( ( A != zero_z3403309356797280102nteger )
% 5.31/5.60 => ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.31/5.60 => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ B @ A ) )
% 5.31/5.60 = ( divide6298287555418463151nteger @ one_one_Code_integer @ B ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % is_unit_div_mult_cancel_right
% 5.31/5.60 thf(fact_5822_is__unit__div__mult__cancel__right,axiom,
% 5.31/5.60 ! [A: nat,B: nat] :
% 5.31/5.60 ( ( A != zero_zero_nat )
% 5.31/5.60 => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.31/5.60 => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ A ) )
% 5.31/5.60 = ( divide_divide_nat @ one_one_nat @ B ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % is_unit_div_mult_cancel_right
% 5.31/5.60 thf(fact_5823_is__unit__div__mult__cancel__right,axiom,
% 5.31/5.60 ! [A: int,B: int] :
% 5.31/5.60 ( ( A != zero_zero_int )
% 5.31/5.60 => ( ( dvd_dvd_int @ B @ one_one_int )
% 5.31/5.60 => ( ( divide_divide_int @ A @ ( times_times_int @ B @ A ) )
% 5.31/5.60 = ( divide_divide_int @ one_one_int @ B ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % is_unit_div_mult_cancel_right
% 5.31/5.60 thf(fact_5824_evenE,axiom,
% 5.31/5.60 ! [A: nat] :
% 5.31/5.60 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.31/5.60 => ~ ! [B3: nat] :
% 5.31/5.60 ( A
% 5.31/5.60 != ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B3 ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % evenE
% 5.31/5.60 thf(fact_5825_evenE,axiom,
% 5.31/5.60 ! [A: int] :
% 5.31/5.60 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.31/5.60 => ~ ! [B3: int] :
% 5.31/5.60 ( A
% 5.31/5.60 != ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B3 ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % evenE
% 5.31/5.60 thf(fact_5826_dvd__power__iff,axiom,
% 5.31/5.60 ! [X: code_integer,M2: nat,N: nat] :
% 5.31/5.60 ( ( X != zero_z3403309356797280102nteger )
% 5.31/5.60 => ( ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ X @ M2 ) @ ( power_8256067586552552935nteger @ X @ N ) )
% 5.31/5.60 = ( ( dvd_dvd_Code_integer @ X @ one_one_Code_integer )
% 5.31/5.60 | ( ord_less_eq_nat @ M2 @ N ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % dvd_power_iff
% 5.31/5.60 thf(fact_5827_dvd__power__iff,axiom,
% 5.31/5.60 ! [X: nat,M2: nat,N: nat] :
% 5.31/5.60 ( ( X != zero_zero_nat )
% 5.31/5.60 => ( ( dvd_dvd_nat @ ( power_power_nat @ X @ M2 ) @ ( power_power_nat @ X @ N ) )
% 5.31/5.60 = ( ( dvd_dvd_nat @ X @ one_one_nat )
% 5.31/5.60 | ( ord_less_eq_nat @ M2 @ N ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % dvd_power_iff
% 5.31/5.60 thf(fact_5828_dvd__power__iff,axiom,
% 5.31/5.60 ! [X: int,M2: nat,N: nat] :
% 5.31/5.60 ( ( X != zero_zero_int )
% 5.31/5.60 => ( ( dvd_dvd_int @ ( power_power_int @ X @ M2 ) @ ( power_power_int @ X @ N ) )
% 5.31/5.60 = ( ( dvd_dvd_int @ X @ one_one_int )
% 5.31/5.60 | ( ord_less_eq_nat @ M2 @ N ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % dvd_power_iff
% 5.31/5.60 thf(fact_5829_dvd__power,axiom,
% 5.31/5.60 ! [N: nat,X: code_integer] :
% 5.31/5.60 ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.60 | ( X = one_one_Code_integer ) )
% 5.31/5.60 => ( dvd_dvd_Code_integer @ X @ ( power_8256067586552552935nteger @ X @ N ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % dvd_power
% 5.31/5.60 thf(fact_5830_dvd__power,axiom,
% 5.31/5.60 ! [N: nat,X: nat] :
% 5.31/5.60 ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.60 | ( X = one_one_nat ) )
% 5.31/5.60 => ( dvd_dvd_nat @ X @ ( power_power_nat @ X @ N ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % dvd_power
% 5.31/5.60 thf(fact_5831_dvd__power,axiom,
% 5.31/5.60 ! [N: nat,X: real] :
% 5.31/5.60 ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.60 | ( X = one_one_real ) )
% 5.31/5.60 => ( dvd_dvd_real @ X @ ( power_power_real @ X @ N ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % dvd_power
% 5.31/5.60 thf(fact_5832_dvd__power,axiom,
% 5.31/5.60 ! [N: nat,X: int] :
% 5.31/5.60 ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.60 | ( X = one_one_int ) )
% 5.31/5.60 => ( dvd_dvd_int @ X @ ( power_power_int @ X @ N ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % dvd_power
% 5.31/5.60 thf(fact_5833_dvd__power,axiom,
% 5.31/5.60 ! [N: nat,X: complex] :
% 5.31/5.60 ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.60 | ( X = one_one_complex ) )
% 5.31/5.60 => ( dvd_dvd_complex @ X @ ( power_power_complex @ X @ N ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % dvd_power
% 5.31/5.60 thf(fact_5834_sum__strict__mono2,axiom,
% 5.31/5.60 ! [B5: set_real,A4: set_real,B: real,F2: real > real] :
% 5.31/5.60 ( ( finite_finite_real @ B5 )
% 5.31/5.60 => ( ( ord_less_eq_set_real @ A4 @ B5 )
% 5.31/5.60 => ( ( member_real @ B @ ( minus_minus_set_real @ B5 @ A4 ) )
% 5.31/5.60 => ( ( ord_less_real @ zero_zero_real @ ( F2 @ B ) )
% 5.31/5.60 => ( ! [X3: real] :
% 5.31/5.60 ( ( member_real @ X3 @ B5 )
% 5.31/5.60 => ( ord_less_eq_real @ zero_zero_real @ ( F2 @ X3 ) ) )
% 5.31/5.60 => ( ord_less_real @ ( groups8097168146408367636l_real @ F2 @ A4 ) @ ( groups8097168146408367636l_real @ F2 @ B5 ) ) ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum_strict_mono2
% 5.31/5.60 thf(fact_5835_sum__strict__mono2,axiom,
% 5.31/5.60 ! [B5: set_int,A4: set_int,B: int,F2: int > real] :
% 5.31/5.60 ( ( finite_finite_int @ B5 )
% 5.31/5.60 => ( ( ord_less_eq_set_int @ A4 @ B5 )
% 5.31/5.60 => ( ( member_int @ B @ ( minus_minus_set_int @ B5 @ A4 ) )
% 5.31/5.60 => ( ( ord_less_real @ zero_zero_real @ ( F2 @ B ) )
% 5.31/5.60 => ( ! [X3: int] :
% 5.31/5.60 ( ( member_int @ X3 @ B5 )
% 5.31/5.60 => ( ord_less_eq_real @ zero_zero_real @ ( F2 @ X3 ) ) )
% 5.31/5.60 => ( ord_less_real @ ( groups8778361861064173332t_real @ F2 @ A4 ) @ ( groups8778361861064173332t_real @ F2 @ B5 ) ) ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum_strict_mono2
% 5.31/5.60 thf(fact_5836_sum__strict__mono2,axiom,
% 5.31/5.60 ! [B5: set_complex,A4: set_complex,B: complex,F2: complex > real] :
% 5.31/5.60 ( ( finite3207457112153483333omplex @ B5 )
% 5.31/5.60 => ( ( ord_le211207098394363844omplex @ A4 @ B5 )
% 5.31/5.60 => ( ( member_complex @ B @ ( minus_811609699411566653omplex @ B5 @ A4 ) )
% 5.31/5.60 => ( ( ord_less_real @ zero_zero_real @ ( F2 @ B ) )
% 5.31/5.60 => ( ! [X3: complex] :
% 5.31/5.60 ( ( member_complex @ X3 @ B5 )
% 5.31/5.60 => ( ord_less_eq_real @ zero_zero_real @ ( F2 @ X3 ) ) )
% 5.31/5.60 => ( ord_less_real @ ( groups5808333547571424918x_real @ F2 @ A4 ) @ ( groups5808333547571424918x_real @ F2 @ B5 ) ) ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum_strict_mono2
% 5.31/5.60 thf(fact_5837_sum__strict__mono2,axiom,
% 5.31/5.60 ! [B5: set_real,A4: set_real,B: real,F2: real > rat] :
% 5.31/5.60 ( ( finite_finite_real @ B5 )
% 5.31/5.60 => ( ( ord_less_eq_set_real @ A4 @ B5 )
% 5.31/5.60 => ( ( member_real @ B @ ( minus_minus_set_real @ B5 @ A4 ) )
% 5.31/5.60 => ( ( ord_less_rat @ zero_zero_rat @ ( F2 @ B ) )
% 5.31/5.60 => ( ! [X3: real] :
% 5.31/5.60 ( ( member_real @ X3 @ B5 )
% 5.31/5.60 => ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ X3 ) ) )
% 5.31/5.60 => ( ord_less_rat @ ( groups1300246762558778688al_rat @ F2 @ A4 ) @ ( groups1300246762558778688al_rat @ F2 @ B5 ) ) ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum_strict_mono2
% 5.31/5.60 thf(fact_5838_sum__strict__mono2,axiom,
% 5.31/5.60 ! [B5: set_int,A4: set_int,B: int,F2: int > rat] :
% 5.31/5.60 ( ( finite_finite_int @ B5 )
% 5.31/5.60 => ( ( ord_less_eq_set_int @ A4 @ B5 )
% 5.31/5.60 => ( ( member_int @ B @ ( minus_minus_set_int @ B5 @ A4 ) )
% 5.31/5.60 => ( ( ord_less_rat @ zero_zero_rat @ ( F2 @ B ) )
% 5.31/5.60 => ( ! [X3: int] :
% 5.31/5.60 ( ( member_int @ X3 @ B5 )
% 5.31/5.60 => ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ X3 ) ) )
% 5.31/5.60 => ( ord_less_rat @ ( groups3906332499630173760nt_rat @ F2 @ A4 ) @ ( groups3906332499630173760nt_rat @ F2 @ B5 ) ) ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum_strict_mono2
% 5.31/5.60 thf(fact_5839_sum__strict__mono2,axiom,
% 5.31/5.60 ! [B5: set_complex,A4: set_complex,B: complex,F2: complex > rat] :
% 5.31/5.60 ( ( finite3207457112153483333omplex @ B5 )
% 5.31/5.60 => ( ( ord_le211207098394363844omplex @ A4 @ B5 )
% 5.31/5.60 => ( ( member_complex @ B @ ( minus_811609699411566653omplex @ B5 @ A4 ) )
% 5.31/5.60 => ( ( ord_less_rat @ zero_zero_rat @ ( F2 @ B ) )
% 5.31/5.60 => ( ! [X3: complex] :
% 5.31/5.60 ( ( member_complex @ X3 @ B5 )
% 5.31/5.60 => ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ X3 ) ) )
% 5.31/5.60 => ( ord_less_rat @ ( groups5058264527183730370ex_rat @ F2 @ A4 ) @ ( groups5058264527183730370ex_rat @ F2 @ B5 ) ) ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum_strict_mono2
% 5.31/5.60 thf(fact_5840_sum__strict__mono2,axiom,
% 5.31/5.60 ! [B5: set_real,A4: set_real,B: real,F2: real > nat] :
% 5.31/5.60 ( ( finite_finite_real @ B5 )
% 5.31/5.60 => ( ( ord_less_eq_set_real @ A4 @ B5 )
% 5.31/5.60 => ( ( member_real @ B @ ( minus_minus_set_real @ B5 @ A4 ) )
% 5.31/5.60 => ( ( ord_less_nat @ zero_zero_nat @ ( F2 @ B ) )
% 5.31/5.60 => ( ! [X3: real] :
% 5.31/5.60 ( ( member_real @ X3 @ B5 )
% 5.31/5.60 => ( ord_less_eq_nat @ zero_zero_nat @ ( F2 @ X3 ) ) )
% 5.31/5.60 => ( ord_less_nat @ ( groups1935376822645274424al_nat @ F2 @ A4 ) @ ( groups1935376822645274424al_nat @ F2 @ B5 ) ) ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum_strict_mono2
% 5.31/5.60 thf(fact_5841_sum__strict__mono2,axiom,
% 5.31/5.60 ! [B5: set_int,A4: set_int,B: int,F2: int > nat] :
% 5.31/5.60 ( ( finite_finite_int @ B5 )
% 5.31/5.60 => ( ( ord_less_eq_set_int @ A4 @ B5 )
% 5.31/5.60 => ( ( member_int @ B @ ( minus_minus_set_int @ B5 @ A4 ) )
% 5.31/5.60 => ( ( ord_less_nat @ zero_zero_nat @ ( F2 @ B ) )
% 5.31/5.60 => ( ! [X3: int] :
% 5.31/5.60 ( ( member_int @ X3 @ B5 )
% 5.31/5.60 => ( ord_less_eq_nat @ zero_zero_nat @ ( F2 @ X3 ) ) )
% 5.31/5.60 => ( ord_less_nat @ ( groups4541462559716669496nt_nat @ F2 @ A4 ) @ ( groups4541462559716669496nt_nat @ F2 @ B5 ) ) ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum_strict_mono2
% 5.31/5.60 thf(fact_5842_sum__strict__mono2,axiom,
% 5.31/5.60 ! [B5: set_complex,A4: set_complex,B: complex,F2: complex > nat] :
% 5.31/5.60 ( ( finite3207457112153483333omplex @ B5 )
% 5.31/5.60 => ( ( ord_le211207098394363844omplex @ A4 @ B5 )
% 5.31/5.60 => ( ( member_complex @ B @ ( minus_811609699411566653omplex @ B5 @ A4 ) )
% 5.31/5.60 => ( ( ord_less_nat @ zero_zero_nat @ ( F2 @ B ) )
% 5.31/5.60 => ( ! [X3: complex] :
% 5.31/5.60 ( ( member_complex @ X3 @ B5 )
% 5.31/5.60 => ( ord_less_eq_nat @ zero_zero_nat @ ( F2 @ X3 ) ) )
% 5.31/5.60 => ( ord_less_nat @ ( groups5693394587270226106ex_nat @ F2 @ A4 ) @ ( groups5693394587270226106ex_nat @ F2 @ B5 ) ) ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum_strict_mono2
% 5.31/5.60 thf(fact_5843_sum__strict__mono2,axiom,
% 5.31/5.60 ! [B5: set_real,A4: set_real,B: real,F2: real > int] :
% 5.31/5.60 ( ( finite_finite_real @ B5 )
% 5.31/5.60 => ( ( ord_less_eq_set_real @ A4 @ B5 )
% 5.31/5.60 => ( ( member_real @ B @ ( minus_minus_set_real @ B5 @ A4 ) )
% 5.31/5.60 => ( ( ord_less_int @ zero_zero_int @ ( F2 @ B ) )
% 5.31/5.60 => ( ! [X3: real] :
% 5.31/5.60 ( ( member_real @ X3 @ B5 )
% 5.31/5.60 => ( ord_less_eq_int @ zero_zero_int @ ( F2 @ X3 ) ) )
% 5.31/5.60 => ( ord_less_int @ ( groups1932886352136224148al_int @ F2 @ A4 ) @ ( groups1932886352136224148al_int @ F2 @ B5 ) ) ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum_strict_mono2
% 5.31/5.60 thf(fact_5844_member__le__sum,axiom,
% 5.31/5.60 ! [I2: complex,A4: set_complex,F2: complex > real] :
% 5.31/5.60 ( ( member_complex @ I2 @ A4 )
% 5.31/5.60 => ( ! [X3: complex] :
% 5.31/5.60 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ A4 @ ( insert_complex @ I2 @ bot_bot_set_complex ) ) )
% 5.31/5.60 => ( ord_less_eq_real @ zero_zero_real @ ( F2 @ X3 ) ) )
% 5.31/5.60 => ( ( finite3207457112153483333omplex @ A4 )
% 5.31/5.60 => ( ord_less_eq_real @ ( F2 @ I2 ) @ ( groups5808333547571424918x_real @ F2 @ A4 ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % member_le_sum
% 5.31/5.60 thf(fact_5845_member__le__sum,axiom,
% 5.31/5.60 ! [I2: int,A4: set_int,F2: int > real] :
% 5.31/5.60 ( ( member_int @ I2 @ A4 )
% 5.31/5.60 => ( ! [X3: int] :
% 5.31/5.60 ( ( member_int @ X3 @ ( minus_minus_set_int @ A4 @ ( insert_int @ I2 @ bot_bot_set_int ) ) )
% 5.31/5.60 => ( ord_less_eq_real @ zero_zero_real @ ( F2 @ X3 ) ) )
% 5.31/5.60 => ( ( finite_finite_int @ A4 )
% 5.31/5.60 => ( ord_less_eq_real @ ( F2 @ I2 ) @ ( groups8778361861064173332t_real @ F2 @ A4 ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % member_le_sum
% 5.31/5.60 thf(fact_5846_member__le__sum,axiom,
% 5.31/5.60 ! [I2: real,A4: set_real,F2: real > real] :
% 5.31/5.60 ( ( member_real @ I2 @ A4 )
% 5.31/5.60 => ( ! [X3: real] :
% 5.31/5.60 ( ( member_real @ X3 @ ( minus_minus_set_real @ A4 @ ( insert_real @ I2 @ bot_bot_set_real ) ) )
% 5.31/5.60 => ( ord_less_eq_real @ zero_zero_real @ ( F2 @ X3 ) ) )
% 5.31/5.60 => ( ( finite_finite_real @ A4 )
% 5.31/5.60 => ( ord_less_eq_real @ ( F2 @ I2 ) @ ( groups8097168146408367636l_real @ F2 @ A4 ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % member_le_sum
% 5.31/5.60 thf(fact_5847_member__le__sum,axiom,
% 5.31/5.60 ! [I2: complex,A4: set_complex,F2: complex > rat] :
% 5.31/5.60 ( ( member_complex @ I2 @ A4 )
% 5.31/5.60 => ( ! [X3: complex] :
% 5.31/5.60 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ A4 @ ( insert_complex @ I2 @ bot_bot_set_complex ) ) )
% 5.31/5.60 => ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ X3 ) ) )
% 5.31/5.60 => ( ( finite3207457112153483333omplex @ A4 )
% 5.31/5.60 => ( ord_less_eq_rat @ ( F2 @ I2 ) @ ( groups5058264527183730370ex_rat @ F2 @ A4 ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % member_le_sum
% 5.31/5.60 thf(fact_5848_member__le__sum,axiom,
% 5.31/5.60 ! [I2: int,A4: set_int,F2: int > rat] :
% 5.31/5.60 ( ( member_int @ I2 @ A4 )
% 5.31/5.60 => ( ! [X3: int] :
% 5.31/5.60 ( ( member_int @ X3 @ ( minus_minus_set_int @ A4 @ ( insert_int @ I2 @ bot_bot_set_int ) ) )
% 5.31/5.60 => ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ X3 ) ) )
% 5.31/5.60 => ( ( finite_finite_int @ A4 )
% 5.31/5.60 => ( ord_less_eq_rat @ ( F2 @ I2 ) @ ( groups3906332499630173760nt_rat @ F2 @ A4 ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % member_le_sum
% 5.31/5.60 thf(fact_5849_member__le__sum,axiom,
% 5.31/5.60 ! [I2: real,A4: set_real,F2: real > rat] :
% 5.31/5.60 ( ( member_real @ I2 @ A4 )
% 5.31/5.60 => ( ! [X3: real] :
% 5.31/5.60 ( ( member_real @ X3 @ ( minus_minus_set_real @ A4 @ ( insert_real @ I2 @ bot_bot_set_real ) ) )
% 5.31/5.60 => ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ X3 ) ) )
% 5.31/5.60 => ( ( finite_finite_real @ A4 )
% 5.31/5.60 => ( ord_less_eq_rat @ ( F2 @ I2 ) @ ( groups1300246762558778688al_rat @ F2 @ A4 ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % member_le_sum
% 5.31/5.60 thf(fact_5850_member__le__sum,axiom,
% 5.31/5.60 ! [I2: nat,A4: set_nat,F2: nat > rat] :
% 5.31/5.60 ( ( member_nat @ I2 @ A4 )
% 5.31/5.60 => ( ! [X3: nat] :
% 5.31/5.60 ( ( member_nat @ X3 @ ( minus_minus_set_nat @ A4 @ ( insert_nat @ I2 @ bot_bot_set_nat ) ) )
% 5.31/5.60 => ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ X3 ) ) )
% 5.31/5.60 => ( ( finite_finite_nat @ A4 )
% 5.31/5.60 => ( ord_less_eq_rat @ ( F2 @ I2 ) @ ( groups2906978787729119204at_rat @ F2 @ A4 ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % member_le_sum
% 5.31/5.60 thf(fact_5851_member__le__sum,axiom,
% 5.31/5.60 ! [I2: complex,A4: set_complex,F2: complex > nat] :
% 5.31/5.60 ( ( member_complex @ I2 @ A4 )
% 5.31/5.60 => ( ! [X3: complex] :
% 5.31/5.60 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ A4 @ ( insert_complex @ I2 @ bot_bot_set_complex ) ) )
% 5.31/5.60 => ( ord_less_eq_nat @ zero_zero_nat @ ( F2 @ X3 ) ) )
% 5.31/5.60 => ( ( finite3207457112153483333omplex @ A4 )
% 5.31/5.60 => ( ord_less_eq_nat @ ( F2 @ I2 ) @ ( groups5693394587270226106ex_nat @ F2 @ A4 ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % member_le_sum
% 5.31/5.60 thf(fact_5852_member__le__sum,axiom,
% 5.31/5.60 ! [I2: int,A4: set_int,F2: int > nat] :
% 5.31/5.60 ( ( member_int @ I2 @ A4 )
% 5.31/5.60 => ( ! [X3: int] :
% 5.31/5.60 ( ( member_int @ X3 @ ( minus_minus_set_int @ A4 @ ( insert_int @ I2 @ bot_bot_set_int ) ) )
% 5.31/5.60 => ( ord_less_eq_nat @ zero_zero_nat @ ( F2 @ X3 ) ) )
% 5.31/5.60 => ( ( finite_finite_int @ A4 )
% 5.31/5.60 => ( ord_less_eq_nat @ ( F2 @ I2 ) @ ( groups4541462559716669496nt_nat @ F2 @ A4 ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % member_le_sum
% 5.31/5.60 thf(fact_5853_member__le__sum,axiom,
% 5.31/5.60 ! [I2: real,A4: set_real,F2: real > nat] :
% 5.31/5.60 ( ( member_real @ I2 @ A4 )
% 5.31/5.60 => ( ! [X3: real] :
% 5.31/5.60 ( ( member_real @ X3 @ ( minus_minus_set_real @ A4 @ ( insert_real @ I2 @ bot_bot_set_real ) ) )
% 5.31/5.60 => ( ord_less_eq_nat @ zero_zero_nat @ ( F2 @ X3 ) ) )
% 5.31/5.60 => ( ( finite_finite_real @ A4 )
% 5.31/5.60 => ( ord_less_eq_nat @ ( F2 @ I2 ) @ ( groups1935376822645274424al_nat @ F2 @ A4 ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % member_le_sum
% 5.31/5.60 thf(fact_5854_div2__even__ext__nat,axiom,
% 5.31/5.60 ! [X: nat,Y: nat] :
% 5.31/5.60 ( ( ( divide_divide_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.31/5.60 = ( divide_divide_nat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.31/5.60 => ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ X )
% 5.31/5.60 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Y ) )
% 5.31/5.60 => ( X = Y ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % div2_even_ext_nat
% 5.31/5.60 thf(fact_5855_sum__bounded__above__strict,axiom,
% 5.31/5.60 ! [A4: set_real,F2: real > rat,K5: rat] :
% 5.31/5.60 ( ! [I3: real] :
% 5.31/5.60 ( ( member_real @ I3 @ A4 )
% 5.31/5.60 => ( ord_less_rat @ ( F2 @ I3 ) @ K5 ) )
% 5.31/5.60 => ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_real @ A4 ) )
% 5.31/5.60 => ( ord_less_rat @ ( groups1300246762558778688al_rat @ F2 @ A4 ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( finite_card_real @ A4 ) ) @ K5 ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum_bounded_above_strict
% 5.31/5.60 thf(fact_5856_sum__bounded__above__strict,axiom,
% 5.31/5.60 ! [A4: set_nat,F2: nat > rat,K5: rat] :
% 5.31/5.60 ( ! [I3: nat] :
% 5.31/5.60 ( ( member_nat @ I3 @ A4 )
% 5.31/5.60 => ( ord_less_rat @ ( F2 @ I3 ) @ K5 ) )
% 5.31/5.60 => ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_nat @ A4 ) )
% 5.31/5.60 => ( ord_less_rat @ ( groups2906978787729119204at_rat @ F2 @ A4 ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( finite_card_nat @ A4 ) ) @ K5 ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum_bounded_above_strict
% 5.31/5.60 thf(fact_5857_sum__bounded__above__strict,axiom,
% 5.31/5.60 ! [A4: set_complex,F2: complex > rat,K5: rat] :
% 5.31/5.60 ( ! [I3: complex] :
% 5.31/5.60 ( ( member_complex @ I3 @ A4 )
% 5.31/5.60 => ( ord_less_rat @ ( F2 @ I3 ) @ K5 ) )
% 5.31/5.60 => ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_complex @ A4 ) )
% 5.31/5.60 => ( ord_less_rat @ ( groups5058264527183730370ex_rat @ F2 @ A4 ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( finite_card_complex @ A4 ) ) @ K5 ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum_bounded_above_strict
% 5.31/5.60 thf(fact_5858_sum__bounded__above__strict,axiom,
% 5.31/5.60 ! [A4: set_int,F2: int > rat,K5: rat] :
% 5.31/5.60 ( ! [I3: int] :
% 5.31/5.60 ( ( member_int @ I3 @ A4 )
% 5.31/5.60 => ( ord_less_rat @ ( F2 @ I3 ) @ K5 ) )
% 5.31/5.60 => ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_int @ A4 ) )
% 5.31/5.60 => ( ord_less_rat @ ( groups3906332499630173760nt_rat @ F2 @ A4 ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( finite_card_int @ A4 ) ) @ K5 ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum_bounded_above_strict
% 5.31/5.60 thf(fact_5859_sum__bounded__above__strict,axiom,
% 5.31/5.60 ! [A4: set_real,F2: real > real,K5: real] :
% 5.31/5.60 ( ! [I3: real] :
% 5.31/5.60 ( ( member_real @ I3 @ A4 )
% 5.31/5.60 => ( ord_less_real @ ( F2 @ I3 ) @ K5 ) )
% 5.31/5.60 => ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_real @ A4 ) )
% 5.31/5.60 => ( ord_less_real @ ( groups8097168146408367636l_real @ F2 @ A4 ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( finite_card_real @ A4 ) ) @ K5 ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum_bounded_above_strict
% 5.31/5.60 thf(fact_5860_sum__bounded__above__strict,axiom,
% 5.31/5.60 ! [A4: set_complex,F2: complex > real,K5: real] :
% 5.31/5.60 ( ! [I3: complex] :
% 5.31/5.60 ( ( member_complex @ I3 @ A4 )
% 5.31/5.60 => ( ord_less_real @ ( F2 @ I3 ) @ K5 ) )
% 5.31/5.60 => ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_complex @ A4 ) )
% 5.31/5.60 => ( ord_less_real @ ( groups5808333547571424918x_real @ F2 @ A4 ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( finite_card_complex @ A4 ) ) @ K5 ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum_bounded_above_strict
% 5.31/5.60 thf(fact_5861_sum__bounded__above__strict,axiom,
% 5.31/5.60 ! [A4: set_int,F2: int > real,K5: real] :
% 5.31/5.60 ( ! [I3: int] :
% 5.31/5.60 ( ( member_int @ I3 @ A4 )
% 5.31/5.60 => ( ord_less_real @ ( F2 @ I3 ) @ K5 ) )
% 5.31/5.60 => ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_int @ A4 ) )
% 5.31/5.60 => ( ord_less_real @ ( groups8778361861064173332t_real @ F2 @ A4 ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( finite_card_int @ A4 ) ) @ K5 ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum_bounded_above_strict
% 5.31/5.60 thf(fact_5862_sum__bounded__above__strict,axiom,
% 5.31/5.60 ! [A4: set_real,F2: real > int,K5: int] :
% 5.31/5.60 ( ! [I3: real] :
% 5.31/5.60 ( ( member_real @ I3 @ A4 )
% 5.31/5.60 => ( ord_less_int @ ( F2 @ I3 ) @ K5 ) )
% 5.31/5.60 => ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_real @ A4 ) )
% 5.31/5.60 => ( ord_less_int @ ( groups1932886352136224148al_int @ F2 @ A4 ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ ( finite_card_real @ A4 ) ) @ K5 ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum_bounded_above_strict
% 5.31/5.60 thf(fact_5863_sum__bounded__above__strict,axiom,
% 5.31/5.60 ! [A4: set_nat,F2: nat > int,K5: int] :
% 5.31/5.60 ( ! [I3: nat] :
% 5.31/5.60 ( ( member_nat @ I3 @ A4 )
% 5.31/5.60 => ( ord_less_int @ ( F2 @ I3 ) @ K5 ) )
% 5.31/5.60 => ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_nat @ A4 ) )
% 5.31/5.60 => ( ord_less_int @ ( groups3539618377306564664at_int @ F2 @ A4 ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ ( finite_card_nat @ A4 ) ) @ K5 ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum_bounded_above_strict
% 5.31/5.60 thf(fact_5864_sum__bounded__above__strict,axiom,
% 5.31/5.60 ! [A4: set_complex,F2: complex > int,K5: int] :
% 5.31/5.60 ( ! [I3: complex] :
% 5.31/5.60 ( ( member_complex @ I3 @ A4 )
% 5.31/5.60 => ( ord_less_int @ ( F2 @ I3 ) @ K5 ) )
% 5.31/5.60 => ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_complex @ A4 ) )
% 5.31/5.60 => ( ord_less_int @ ( groups5690904116761175830ex_int @ F2 @ A4 ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ ( finite_card_complex @ A4 ) ) @ K5 ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum_bounded_above_strict
% 5.31/5.60 thf(fact_5865_sum__bounded__above__divide,axiom,
% 5.31/5.60 ! [A4: set_complex,F2: complex > real,K5: real] :
% 5.31/5.60 ( ! [I3: complex] :
% 5.31/5.60 ( ( member_complex @ I3 @ A4 )
% 5.31/5.60 => ( ord_less_eq_real @ ( F2 @ I3 ) @ ( divide_divide_real @ K5 @ ( semiri5074537144036343181t_real @ ( finite_card_complex @ A4 ) ) ) ) )
% 5.31/5.60 => ( ( finite3207457112153483333omplex @ A4 )
% 5.31/5.60 => ( ( A4 != bot_bot_set_complex )
% 5.31/5.60 => ( ord_less_eq_real @ ( groups5808333547571424918x_real @ F2 @ A4 ) @ K5 ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum_bounded_above_divide
% 5.31/5.60 thf(fact_5866_sum__bounded__above__divide,axiom,
% 5.31/5.60 ! [A4: set_int,F2: int > real,K5: real] :
% 5.31/5.60 ( ! [I3: int] :
% 5.31/5.60 ( ( member_int @ I3 @ A4 )
% 5.31/5.60 => ( ord_less_eq_real @ ( F2 @ I3 ) @ ( divide_divide_real @ K5 @ ( semiri5074537144036343181t_real @ ( finite_card_int @ A4 ) ) ) ) )
% 5.31/5.60 => ( ( finite_finite_int @ A4 )
% 5.31/5.60 => ( ( A4 != bot_bot_set_int )
% 5.31/5.60 => ( ord_less_eq_real @ ( groups8778361861064173332t_real @ F2 @ A4 ) @ K5 ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum_bounded_above_divide
% 5.31/5.60 thf(fact_5867_sum__bounded__above__divide,axiom,
% 5.31/5.60 ! [A4: set_real,F2: real > real,K5: real] :
% 5.31/5.60 ( ! [I3: real] :
% 5.31/5.60 ( ( member_real @ I3 @ A4 )
% 5.31/5.60 => ( ord_less_eq_real @ ( F2 @ I3 ) @ ( divide_divide_real @ K5 @ ( semiri5074537144036343181t_real @ ( finite_card_real @ A4 ) ) ) ) )
% 5.31/5.60 => ( ( finite_finite_real @ A4 )
% 5.31/5.60 => ( ( A4 != bot_bot_set_real )
% 5.31/5.60 => ( ord_less_eq_real @ ( groups8097168146408367636l_real @ F2 @ A4 ) @ K5 ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum_bounded_above_divide
% 5.31/5.60 thf(fact_5868_sum__bounded__above__divide,axiom,
% 5.31/5.60 ! [A4: set_complex,F2: complex > rat,K5: rat] :
% 5.31/5.60 ( ! [I3: complex] :
% 5.31/5.60 ( ( member_complex @ I3 @ A4 )
% 5.31/5.60 => ( ord_less_eq_rat @ ( F2 @ I3 ) @ ( divide_divide_rat @ K5 @ ( semiri681578069525770553at_rat @ ( finite_card_complex @ A4 ) ) ) ) )
% 5.31/5.60 => ( ( finite3207457112153483333omplex @ A4 )
% 5.31/5.60 => ( ( A4 != bot_bot_set_complex )
% 5.31/5.60 => ( ord_less_eq_rat @ ( groups5058264527183730370ex_rat @ F2 @ A4 ) @ K5 ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum_bounded_above_divide
% 5.31/5.60 thf(fact_5869_sum__bounded__above__divide,axiom,
% 5.31/5.60 ! [A4: set_nat,F2: nat > rat,K5: rat] :
% 5.31/5.60 ( ! [I3: nat] :
% 5.31/5.60 ( ( member_nat @ I3 @ A4 )
% 5.31/5.60 => ( ord_less_eq_rat @ ( F2 @ I3 ) @ ( divide_divide_rat @ K5 @ ( semiri681578069525770553at_rat @ ( finite_card_nat @ A4 ) ) ) ) )
% 5.31/5.60 => ( ( finite_finite_nat @ A4 )
% 5.31/5.60 => ( ( A4 != bot_bot_set_nat )
% 5.31/5.60 => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F2 @ A4 ) @ K5 ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum_bounded_above_divide
% 5.31/5.60 thf(fact_5870_sum__bounded__above__divide,axiom,
% 5.31/5.60 ! [A4: set_int,F2: int > rat,K5: rat] :
% 5.31/5.60 ( ! [I3: int] :
% 5.31/5.60 ( ( member_int @ I3 @ A4 )
% 5.31/5.60 => ( ord_less_eq_rat @ ( F2 @ I3 ) @ ( divide_divide_rat @ K5 @ ( semiri681578069525770553at_rat @ ( finite_card_int @ A4 ) ) ) ) )
% 5.31/5.60 => ( ( finite_finite_int @ A4 )
% 5.31/5.60 => ( ( A4 != bot_bot_set_int )
% 5.31/5.60 => ( ord_less_eq_rat @ ( groups3906332499630173760nt_rat @ F2 @ A4 ) @ K5 ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum_bounded_above_divide
% 5.31/5.60 thf(fact_5871_sum__bounded__above__divide,axiom,
% 5.31/5.60 ! [A4: set_real,F2: real > rat,K5: rat] :
% 5.31/5.60 ( ! [I3: real] :
% 5.31/5.60 ( ( member_real @ I3 @ A4 )
% 5.31/5.60 => ( ord_less_eq_rat @ ( F2 @ I3 ) @ ( divide_divide_rat @ K5 @ ( semiri681578069525770553at_rat @ ( finite_card_real @ A4 ) ) ) ) )
% 5.31/5.60 => ( ( finite_finite_real @ A4 )
% 5.31/5.60 => ( ( A4 != bot_bot_set_real )
% 5.31/5.60 => ( ord_less_eq_rat @ ( groups1300246762558778688al_rat @ F2 @ A4 ) @ K5 ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum_bounded_above_divide
% 5.31/5.60 thf(fact_5872_sum__bounded__above__divide,axiom,
% 5.31/5.60 ! [A4: set_nat,F2: nat > real,K5: real] :
% 5.31/5.60 ( ! [I3: nat] :
% 5.31/5.60 ( ( member_nat @ I3 @ A4 )
% 5.31/5.60 => ( ord_less_eq_real @ ( F2 @ I3 ) @ ( divide_divide_real @ K5 @ ( semiri5074537144036343181t_real @ ( finite_card_nat @ A4 ) ) ) ) )
% 5.31/5.60 => ( ( finite_finite_nat @ A4 )
% 5.31/5.60 => ( ( A4 != bot_bot_set_nat )
% 5.31/5.60 => ( ord_less_eq_real @ ( groups6591440286371151544t_real @ F2 @ A4 ) @ K5 ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum_bounded_above_divide
% 5.31/5.60 thf(fact_5873_sum__bounded__above__divide,axiom,
% 5.31/5.60 ! [A4: set_list_nat,F2: list_nat > real,K5: real] :
% 5.31/5.60 ( ! [I3: list_nat] :
% 5.31/5.60 ( ( member_list_nat @ I3 @ A4 )
% 5.31/5.60 => ( ord_less_eq_real @ ( F2 @ I3 ) @ ( divide_divide_real @ K5 @ ( semiri5074537144036343181t_real @ ( finite_card_list_nat @ A4 ) ) ) ) )
% 5.31/5.60 => ( ( finite8100373058378681591st_nat @ A4 )
% 5.31/5.60 => ( ( A4 != bot_bot_set_list_nat )
% 5.31/5.60 => ( ord_less_eq_real @ ( groups8399112307953289288t_real @ F2 @ A4 ) @ K5 ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum_bounded_above_divide
% 5.31/5.60 thf(fact_5874_sum__bounded__above__divide,axiom,
% 5.31/5.60 ! [A4: set_set_nat,F2: set_nat > real,K5: real] :
% 5.31/5.60 ( ! [I3: set_nat] :
% 5.31/5.60 ( ( member_set_nat @ I3 @ A4 )
% 5.31/5.60 => ( ord_less_eq_real @ ( F2 @ I3 ) @ ( divide_divide_real @ K5 @ ( semiri5074537144036343181t_real @ ( finite_card_set_nat @ A4 ) ) ) ) )
% 5.31/5.60 => ( ( finite1152437895449049373et_nat @ A4 )
% 5.31/5.60 => ( ( A4 != bot_bot_set_set_nat )
% 5.31/5.60 => ( ord_less_eq_real @ ( groups5107569545109728110t_real @ F2 @ A4 ) @ K5 ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum_bounded_above_divide
% 5.31/5.60 thf(fact_5875_pochhammer__rec,axiom,
% 5.31/5.60 ! [A: code_integer,N: nat] :
% 5.31/5.60 ( ( comm_s8582702949713902594nteger @ A @ ( suc @ N ) )
% 5.31/5.60 = ( times_3573771949741848930nteger @ A @ ( comm_s8582702949713902594nteger @ ( plus_p5714425477246183910nteger @ A @ one_one_Code_integer ) @ N ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % pochhammer_rec
% 5.31/5.60 thf(fact_5876_pochhammer__rec,axiom,
% 5.31/5.60 ! [A: complex,N: nat] :
% 5.31/5.60 ( ( comm_s2602460028002588243omplex @ A @ ( suc @ N ) )
% 5.31/5.60 = ( times_times_complex @ A @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ A @ one_one_complex ) @ N ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % pochhammer_rec
% 5.31/5.60 thf(fact_5877_pochhammer__rec,axiom,
% 5.31/5.60 ! [A: real,N: nat] :
% 5.31/5.60 ( ( comm_s7457072308508201937r_real @ A @ ( suc @ N ) )
% 5.31/5.60 = ( times_times_real @ A @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ A @ one_one_real ) @ N ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % pochhammer_rec
% 5.31/5.60 thf(fact_5878_pochhammer__rec,axiom,
% 5.31/5.60 ! [A: rat,N: nat] :
% 5.31/5.60 ( ( comm_s4028243227959126397er_rat @ A @ ( suc @ N ) )
% 5.31/5.60 = ( times_times_rat @ A @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ N ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % pochhammer_rec
% 5.31/5.60 thf(fact_5879_pochhammer__rec,axiom,
% 5.31/5.60 ! [A: nat,N: nat] :
% 5.31/5.60 ( ( comm_s4663373288045622133er_nat @ A @ ( suc @ N ) )
% 5.31/5.60 = ( times_times_nat @ A @ ( comm_s4663373288045622133er_nat @ ( plus_plus_nat @ A @ one_one_nat ) @ N ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % pochhammer_rec
% 5.31/5.60 thf(fact_5880_pochhammer__rec,axiom,
% 5.31/5.60 ! [A: int,N: nat] :
% 5.31/5.60 ( ( comm_s4660882817536571857er_int @ A @ ( suc @ N ) )
% 5.31/5.60 = ( times_times_int @ A @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ A @ one_one_int ) @ N ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % pochhammer_rec
% 5.31/5.60 thf(fact_5881_dvd__mult__cancel1,axiom,
% 5.31/5.60 ! [M2: nat,N: nat] :
% 5.31/5.60 ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 5.31/5.60 => ( ( dvd_dvd_nat @ ( times_times_nat @ M2 @ N ) @ M2 )
% 5.31/5.60 = ( N = one_one_nat ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % dvd_mult_cancel1
% 5.31/5.60 thf(fact_5882_dvd__mult__cancel2,axiom,
% 5.31/5.60 ! [M2: nat,N: nat] :
% 5.31/5.60 ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 5.31/5.60 => ( ( dvd_dvd_nat @ ( times_times_nat @ N @ M2 ) @ M2 )
% 5.31/5.60 = ( N = one_one_nat ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % dvd_mult_cancel2
% 5.31/5.60 thf(fact_5883_pochhammer__rec_H,axiom,
% 5.31/5.60 ! [Z3: rat,N: nat] :
% 5.31/5.60 ( ( comm_s4028243227959126397er_rat @ Z3 @ ( suc @ N ) )
% 5.31/5.60 = ( times_times_rat @ ( plus_plus_rat @ Z3 @ ( semiri681578069525770553at_rat @ N ) ) @ ( comm_s4028243227959126397er_rat @ Z3 @ N ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % pochhammer_rec'
% 5.31/5.60 thf(fact_5884_pochhammer__rec_H,axiom,
% 5.31/5.60 ! [Z3: real,N: nat] :
% 5.31/5.60 ( ( comm_s7457072308508201937r_real @ Z3 @ ( suc @ N ) )
% 5.31/5.60 = ( times_times_real @ ( plus_plus_real @ Z3 @ ( semiri5074537144036343181t_real @ N ) ) @ ( comm_s7457072308508201937r_real @ Z3 @ N ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % pochhammer_rec'
% 5.31/5.60 thf(fact_5885_pochhammer__rec_H,axiom,
% 5.31/5.60 ! [Z3: int,N: nat] :
% 5.31/5.60 ( ( comm_s4660882817536571857er_int @ Z3 @ ( suc @ N ) )
% 5.31/5.60 = ( times_times_int @ ( plus_plus_int @ Z3 @ ( semiri1314217659103216013at_int @ N ) ) @ ( comm_s4660882817536571857er_int @ Z3 @ N ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % pochhammer_rec'
% 5.31/5.60 thf(fact_5886_pochhammer__rec_H,axiom,
% 5.31/5.60 ! [Z3: nat,N: nat] :
% 5.31/5.60 ( ( comm_s4663373288045622133er_nat @ Z3 @ ( suc @ N ) )
% 5.31/5.60 = ( times_times_nat @ ( plus_plus_nat @ Z3 @ ( semiri1316708129612266289at_nat @ N ) ) @ ( comm_s4663373288045622133er_nat @ Z3 @ N ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % pochhammer_rec'
% 5.31/5.60 thf(fact_5887_pochhammer__Suc,axiom,
% 5.31/5.60 ! [A: rat,N: nat] :
% 5.31/5.60 ( ( comm_s4028243227959126397er_rat @ A @ ( suc @ N ) )
% 5.31/5.60 = ( times_times_rat @ ( comm_s4028243227959126397er_rat @ A @ N ) @ ( plus_plus_rat @ A @ ( semiri681578069525770553at_rat @ N ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % pochhammer_Suc
% 5.31/5.60 thf(fact_5888_pochhammer__Suc,axiom,
% 5.31/5.60 ! [A: real,N: nat] :
% 5.31/5.60 ( ( comm_s7457072308508201937r_real @ A @ ( suc @ N ) )
% 5.31/5.60 = ( times_times_real @ ( comm_s7457072308508201937r_real @ A @ N ) @ ( plus_plus_real @ A @ ( semiri5074537144036343181t_real @ N ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % pochhammer_Suc
% 5.31/5.60 thf(fact_5889_pochhammer__Suc,axiom,
% 5.31/5.60 ! [A: int,N: nat] :
% 5.31/5.60 ( ( comm_s4660882817536571857er_int @ A @ ( suc @ N ) )
% 5.31/5.60 = ( times_times_int @ ( comm_s4660882817536571857er_int @ A @ N ) @ ( plus_plus_int @ A @ ( semiri1314217659103216013at_int @ N ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % pochhammer_Suc
% 5.31/5.60 thf(fact_5890_pochhammer__Suc,axiom,
% 5.31/5.60 ! [A: nat,N: nat] :
% 5.31/5.60 ( ( comm_s4663373288045622133er_nat @ A @ ( suc @ N ) )
% 5.31/5.60 = ( times_times_nat @ ( comm_s4663373288045622133er_nat @ A @ N ) @ ( plus_plus_nat @ A @ ( semiri1316708129612266289at_nat @ N ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % pochhammer_Suc
% 5.31/5.60 thf(fact_5891_dvd__minus__add,axiom,
% 5.31/5.60 ! [Q2: nat,N: nat,R3: nat,M2: nat] :
% 5.31/5.60 ( ( ord_less_eq_nat @ Q2 @ N )
% 5.31/5.60 => ( ( ord_less_eq_nat @ Q2 @ ( times_times_nat @ R3 @ M2 ) )
% 5.31/5.60 => ( ( dvd_dvd_nat @ M2 @ ( minus_minus_nat @ N @ Q2 ) )
% 5.31/5.60 = ( dvd_dvd_nat @ M2 @ ( plus_plus_nat @ N @ ( minus_minus_nat @ ( times_times_nat @ R3 @ M2 ) @ Q2 ) ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % dvd_minus_add
% 5.31/5.60 thf(fact_5892_power__dvd__imp__le,axiom,
% 5.31/5.60 ! [I2: nat,M2: nat,N: nat] :
% 5.31/5.60 ( ( dvd_dvd_nat @ ( power_power_nat @ I2 @ M2 ) @ ( power_power_nat @ I2 @ N ) )
% 5.31/5.60 => ( ( ord_less_nat @ one_one_nat @ I2 )
% 5.31/5.60 => ( ord_less_eq_nat @ M2 @ N ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % power_dvd_imp_le
% 5.31/5.60 thf(fact_5893_pochhammer__product_H,axiom,
% 5.31/5.60 ! [Z3: rat,N: nat,M2: nat] :
% 5.31/5.60 ( ( comm_s4028243227959126397er_rat @ Z3 @ ( plus_plus_nat @ N @ M2 ) )
% 5.31/5.60 = ( times_times_rat @ ( comm_s4028243227959126397er_rat @ Z3 @ N ) @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ Z3 @ ( semiri681578069525770553at_rat @ N ) ) @ M2 ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % pochhammer_product'
% 5.31/5.60 thf(fact_5894_pochhammer__product_H,axiom,
% 5.31/5.60 ! [Z3: real,N: nat,M2: nat] :
% 5.31/5.60 ( ( comm_s7457072308508201937r_real @ Z3 @ ( plus_plus_nat @ N @ M2 ) )
% 5.31/5.60 = ( times_times_real @ ( comm_s7457072308508201937r_real @ Z3 @ N ) @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ Z3 @ ( semiri5074537144036343181t_real @ N ) ) @ M2 ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % pochhammer_product'
% 5.31/5.60 thf(fact_5895_pochhammer__product_H,axiom,
% 5.31/5.60 ! [Z3: int,N: nat,M2: nat] :
% 5.31/5.60 ( ( comm_s4660882817536571857er_int @ Z3 @ ( plus_plus_nat @ N @ M2 ) )
% 5.31/5.60 = ( times_times_int @ ( comm_s4660882817536571857er_int @ Z3 @ N ) @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ Z3 @ ( semiri1314217659103216013at_int @ N ) ) @ M2 ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % pochhammer_product'
% 5.31/5.60 thf(fact_5896_pochhammer__product_H,axiom,
% 5.31/5.60 ! [Z3: nat,N: nat,M2: nat] :
% 5.31/5.60 ( ( comm_s4663373288045622133er_nat @ Z3 @ ( plus_plus_nat @ N @ M2 ) )
% 5.31/5.60 = ( times_times_nat @ ( comm_s4663373288045622133er_nat @ Z3 @ N ) @ ( comm_s4663373288045622133er_nat @ ( plus_plus_nat @ Z3 @ ( semiri1316708129612266289at_nat @ N ) ) @ M2 ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % pochhammer_product'
% 5.31/5.60 thf(fact_5897_mod__nat__eqI,axiom,
% 5.31/5.60 ! [R3: nat,N: nat,M2: nat] :
% 5.31/5.60 ( ( ord_less_nat @ R3 @ N )
% 5.31/5.60 => ( ( ord_less_eq_nat @ R3 @ M2 )
% 5.31/5.60 => ( ( dvd_dvd_nat @ N @ ( minus_minus_nat @ M2 @ R3 ) )
% 5.31/5.60 => ( ( modulo_modulo_nat @ M2 @ N )
% 5.31/5.60 = R3 ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % mod_nat_eqI
% 5.31/5.60 thf(fact_5898_sum_OSuc__reindex__ivl,axiom,
% 5.31/5.60 ! [M2: nat,N: nat,G2: nat > rat] :
% 5.31/5.60 ( ( ord_less_eq_nat @ M2 @ N )
% 5.31/5.60 => ( ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) @ ( G2 @ ( suc @ N ) ) )
% 5.31/5.60 = ( plus_plus_rat @ ( G2 @ M2 )
% 5.31/5.60 @ ( groups2906978787729119204at_rat
% 5.31/5.60 @ ^ [I: nat] : ( G2 @ ( suc @ I ) )
% 5.31/5.60 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum.Suc_reindex_ivl
% 5.31/5.60 thf(fact_5899_sum_OSuc__reindex__ivl,axiom,
% 5.31/5.60 ! [M2: nat,N: nat,G2: nat > int] :
% 5.31/5.60 ( ( ord_less_eq_nat @ M2 @ N )
% 5.31/5.60 => ( ( plus_plus_int @ ( groups3539618377306564664at_int @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) @ ( G2 @ ( suc @ N ) ) )
% 5.31/5.60 = ( plus_plus_int @ ( G2 @ M2 )
% 5.31/5.60 @ ( groups3539618377306564664at_int
% 5.31/5.60 @ ^ [I: nat] : ( G2 @ ( suc @ I ) )
% 5.31/5.60 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum.Suc_reindex_ivl
% 5.31/5.60 thf(fact_5900_sum_OSuc__reindex__ivl,axiom,
% 5.31/5.60 ! [M2: nat,N: nat,G2: nat > nat] :
% 5.31/5.60 ( ( ord_less_eq_nat @ M2 @ N )
% 5.31/5.60 => ( ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) @ ( G2 @ ( suc @ N ) ) )
% 5.31/5.60 = ( plus_plus_nat @ ( G2 @ M2 )
% 5.31/5.60 @ ( groups3542108847815614940at_nat
% 5.31/5.60 @ ^ [I: nat] : ( G2 @ ( suc @ I ) )
% 5.31/5.60 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum.Suc_reindex_ivl
% 5.31/5.60 thf(fact_5901_sum_OSuc__reindex__ivl,axiom,
% 5.31/5.60 ! [M2: nat,N: nat,G2: nat > real] :
% 5.31/5.60 ( ( ord_less_eq_nat @ M2 @ N )
% 5.31/5.60 => ( ( plus_plus_real @ ( groups6591440286371151544t_real @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) @ ( G2 @ ( suc @ N ) ) )
% 5.31/5.60 = ( plus_plus_real @ ( G2 @ M2 )
% 5.31/5.60 @ ( groups6591440286371151544t_real
% 5.31/5.60 @ ^ [I: nat] : ( G2 @ ( suc @ I ) )
% 5.31/5.60 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum.Suc_reindex_ivl
% 5.31/5.60 thf(fact_5902_sum__Suc__diff,axiom,
% 5.31/5.60 ! [M2: nat,N: nat,F2: nat > rat] :
% 5.31/5.60 ( ( ord_less_eq_nat @ M2 @ ( suc @ N ) )
% 5.31/5.60 => ( ( groups2906978787729119204at_rat
% 5.31/5.60 @ ^ [I: nat] : ( minus_minus_rat @ ( F2 @ ( suc @ I ) ) @ ( F2 @ I ) )
% 5.31/5.60 @ ( set_or1269000886237332187st_nat @ M2 @ N ) )
% 5.31/5.60 = ( minus_minus_rat @ ( F2 @ ( suc @ N ) ) @ ( F2 @ M2 ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum_Suc_diff
% 5.31/5.60 thf(fact_5903_sum__Suc__diff,axiom,
% 5.31/5.60 ! [M2: nat,N: nat,F2: nat > int] :
% 5.31/5.60 ( ( ord_less_eq_nat @ M2 @ ( suc @ N ) )
% 5.31/5.60 => ( ( groups3539618377306564664at_int
% 5.31/5.60 @ ^ [I: nat] : ( minus_minus_int @ ( F2 @ ( suc @ I ) ) @ ( F2 @ I ) )
% 5.31/5.60 @ ( set_or1269000886237332187st_nat @ M2 @ N ) )
% 5.31/5.60 = ( minus_minus_int @ ( F2 @ ( suc @ N ) ) @ ( F2 @ M2 ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum_Suc_diff
% 5.31/5.60 thf(fact_5904_sum__Suc__diff,axiom,
% 5.31/5.60 ! [M2: nat,N: nat,F2: nat > real] :
% 5.31/5.60 ( ( ord_less_eq_nat @ M2 @ ( suc @ N ) )
% 5.31/5.60 => ( ( groups6591440286371151544t_real
% 5.31/5.60 @ ^ [I: nat] : ( minus_minus_real @ ( F2 @ ( suc @ I ) ) @ ( F2 @ I ) )
% 5.31/5.60 @ ( set_or1269000886237332187st_nat @ M2 @ N ) )
% 5.31/5.60 = ( minus_minus_real @ ( F2 @ ( suc @ N ) ) @ ( F2 @ M2 ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum_Suc_diff
% 5.31/5.60 thf(fact_5905_sum__norm__bound,axiom,
% 5.31/5.60 ! [S3: set_real,F2: real > complex,K5: real] :
% 5.31/5.60 ( ! [X3: real] :
% 5.31/5.60 ( ( member_real @ X3 @ S3 )
% 5.31/5.60 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F2 @ X3 ) ) @ K5 ) )
% 5.31/5.60 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups5754745047067104278omplex @ F2 @ S3 ) ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( finite_card_real @ S3 ) ) @ K5 ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum_norm_bound
% 5.31/5.60 thf(fact_5906_sum__norm__bound,axiom,
% 5.31/5.60 ! [S3: set_nat,F2: nat > complex,K5: real] :
% 5.31/5.60 ( ! [X3: nat] :
% 5.31/5.60 ( ( member_nat @ X3 @ S3 )
% 5.31/5.60 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F2 @ X3 ) ) @ K5 ) )
% 5.31/5.60 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups2073611262835488442omplex @ F2 @ S3 ) ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( finite_card_nat @ S3 ) ) @ K5 ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum_norm_bound
% 5.31/5.60 thf(fact_5907_sum__norm__bound,axiom,
% 5.31/5.60 ! [S3: set_complex,F2: complex > complex,K5: real] :
% 5.31/5.60 ( ! [X3: complex] :
% 5.31/5.60 ( ( member_complex @ X3 @ S3 )
% 5.31/5.60 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F2 @ X3 ) ) @ K5 ) )
% 5.31/5.60 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups7754918857620584856omplex @ F2 @ S3 ) ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( finite_card_complex @ S3 ) ) @ K5 ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum_norm_bound
% 5.31/5.60 thf(fact_5908_sum__norm__bound,axiom,
% 5.31/5.60 ! [S3: set_int,F2: int > complex,K5: real] :
% 5.31/5.60 ( ! [X3: int] :
% 5.31/5.60 ( ( member_int @ X3 @ S3 )
% 5.31/5.60 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F2 @ X3 ) ) @ K5 ) )
% 5.31/5.60 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups3049146728041665814omplex @ F2 @ S3 ) ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( finite_card_int @ S3 ) ) @ K5 ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum_norm_bound
% 5.31/5.60 thf(fact_5909_sum__norm__bound,axiom,
% 5.31/5.60 ! [S3: set_list_nat,F2: list_nat > complex,K5: real] :
% 5.31/5.60 ( ! [X3: list_nat] :
% 5.31/5.60 ( ( member_list_nat @ X3 @ S3 )
% 5.31/5.60 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F2 @ X3 ) ) @ K5 ) )
% 5.31/5.60 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups6529277132148336714omplex @ F2 @ S3 ) ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( finite_card_list_nat @ S3 ) ) @ K5 ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum_norm_bound
% 5.31/5.60 thf(fact_5910_sum__norm__bound,axiom,
% 5.31/5.60 ! [S3: set_set_nat,F2: set_nat > complex,K5: real] :
% 5.31/5.60 ( ! [X3: set_nat] :
% 5.31/5.60 ( ( member_set_nat @ X3 @ S3 )
% 5.31/5.60 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F2 @ X3 ) ) @ K5 ) )
% 5.31/5.60 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups8255218700646806128omplex @ F2 @ S3 ) ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( finite_card_set_nat @ S3 ) ) @ K5 ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum_norm_bound
% 5.31/5.60 thf(fact_5911_sum__norm__bound,axiom,
% 5.31/5.60 ! [S3: set_nat,F2: nat > real,K5: real] :
% 5.31/5.60 ( ! [X3: nat] :
% 5.31/5.60 ( ( member_nat @ X3 @ S3 )
% 5.31/5.60 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( F2 @ X3 ) ) @ K5 ) )
% 5.31/5.60 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( groups6591440286371151544t_real @ F2 @ S3 ) ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( finite_card_nat @ S3 ) ) @ K5 ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum_norm_bound
% 5.31/5.60 thf(fact_5912_sum_Oub__add__nat,axiom,
% 5.31/5.60 ! [M2: nat,N: nat,G2: nat > rat,P: nat] :
% 5.31/5.60 ( ( ord_less_eq_nat @ M2 @ ( plus_plus_nat @ N @ one_one_nat ) )
% 5.31/5.60 => ( ( groups2906978787729119204at_rat @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ ( plus_plus_nat @ N @ P ) ) )
% 5.31/5.60 = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) @ ( groups2906978787729119204at_rat @ G2 @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ ( plus_plus_nat @ N @ P ) ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum.ub_add_nat
% 5.31/5.60 thf(fact_5913_sum_Oub__add__nat,axiom,
% 5.31/5.60 ! [M2: nat,N: nat,G2: nat > int,P: nat] :
% 5.31/5.60 ( ( ord_less_eq_nat @ M2 @ ( plus_plus_nat @ N @ one_one_nat ) )
% 5.31/5.60 => ( ( groups3539618377306564664at_int @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ ( plus_plus_nat @ N @ P ) ) )
% 5.31/5.60 = ( plus_plus_int @ ( groups3539618377306564664at_int @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) @ ( groups3539618377306564664at_int @ G2 @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ ( plus_plus_nat @ N @ P ) ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum.ub_add_nat
% 5.31/5.60 thf(fact_5914_sum_Oub__add__nat,axiom,
% 5.31/5.60 ! [M2: nat,N: nat,G2: nat > nat,P: nat] :
% 5.31/5.60 ( ( ord_less_eq_nat @ M2 @ ( plus_plus_nat @ N @ one_one_nat ) )
% 5.31/5.60 => ( ( groups3542108847815614940at_nat @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ ( plus_plus_nat @ N @ P ) ) )
% 5.31/5.60 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) @ ( groups3542108847815614940at_nat @ G2 @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ ( plus_plus_nat @ N @ P ) ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum.ub_add_nat
% 5.31/5.60 thf(fact_5915_sum_Oub__add__nat,axiom,
% 5.31/5.60 ! [M2: nat,N: nat,G2: nat > real,P: nat] :
% 5.31/5.60 ( ( ord_less_eq_nat @ M2 @ ( plus_plus_nat @ N @ one_one_nat ) )
% 5.31/5.60 => ( ( groups6591440286371151544t_real @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ ( plus_plus_nat @ N @ P ) ) )
% 5.31/5.60 = ( plus_plus_real @ ( groups6591440286371151544t_real @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) @ ( groups6591440286371151544t_real @ G2 @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ ( plus_plus_nat @ N @ P ) ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum.ub_add_nat
% 5.31/5.60 thf(fact_5916_even__two__times__div__two,axiom,
% 5.31/5.60 ! [A: nat] :
% 5.31/5.60 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.31/5.60 => ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.31/5.60 = A ) ) ).
% 5.31/5.60
% 5.31/5.60 % even_two_times_div_two
% 5.31/5.60 thf(fact_5917_even__two__times__div__two,axiom,
% 5.31/5.60 ! [A: int] :
% 5.31/5.60 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.31/5.60 => ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) )
% 5.31/5.60 = A ) ) ).
% 5.31/5.60
% 5.31/5.60 % even_two_times_div_two
% 5.31/5.60 thf(fact_5918_even__iff__mod__2__eq__zero,axiom,
% 5.31/5.60 ! [A: nat] :
% 5.31/5.60 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.31/5.60 = ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.31/5.60 = zero_zero_nat ) ) ).
% 5.31/5.60
% 5.31/5.60 % even_iff_mod_2_eq_zero
% 5.31/5.60 thf(fact_5919_even__iff__mod__2__eq__zero,axiom,
% 5.31/5.60 ! [A: int] :
% 5.31/5.60 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.31/5.60 = ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.31/5.60 = zero_zero_int ) ) ).
% 5.31/5.60
% 5.31/5.60 % even_iff_mod_2_eq_zero
% 5.31/5.60 thf(fact_5920_even__iff__mod__2__eq__zero,axiom,
% 5.31/5.60 ! [A: code_natural] :
% 5.31/5.60 ( ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A )
% 5.31/5.60 = ( ( modulo8411746178871703098atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 5.31/5.60 = zero_z2226904508553997617atural ) ) ).
% 5.31/5.60
% 5.31/5.60 % even_iff_mod_2_eq_zero
% 5.31/5.60 thf(fact_5921_power__mono__odd,axiom,
% 5.31/5.60 ! [N: nat,A: real,B: real] :
% 5.31/5.60 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.31/5.60 => ( ( ord_less_eq_real @ A @ B )
% 5.31/5.60 => ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % power_mono_odd
% 5.31/5.60 thf(fact_5922_power__mono__odd,axiom,
% 5.31/5.60 ! [N: nat,A: rat,B: rat] :
% 5.31/5.60 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.31/5.60 => ( ( ord_less_eq_rat @ A @ B )
% 5.31/5.60 => ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % power_mono_odd
% 5.31/5.60 thf(fact_5923_power__mono__odd,axiom,
% 5.31/5.60 ! [N: nat,A: int,B: int] :
% 5.31/5.60 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.31/5.60 => ( ( ord_less_eq_int @ A @ B )
% 5.31/5.60 => ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % power_mono_odd
% 5.31/5.60 thf(fact_5924_odd__pos,axiom,
% 5.31/5.60 ! [N: nat] :
% 5.31/5.60 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.31/5.60 => ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 5.31/5.60
% 5.31/5.60 % odd_pos
% 5.31/5.60 thf(fact_5925_dvd__power__iff__le,axiom,
% 5.31/5.60 ! [K2: nat,M2: nat,N: nat] :
% 5.31/5.60 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K2 )
% 5.31/5.60 => ( ( dvd_dvd_nat @ ( power_power_nat @ K2 @ M2 ) @ ( power_power_nat @ K2 @ N ) )
% 5.31/5.60 = ( ord_less_eq_nat @ M2 @ N ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % dvd_power_iff_le
% 5.31/5.60 thf(fact_5926_even__unset__bit__iff,axiom,
% 5.31/5.60 ! [M2: nat,A: nat] :
% 5.31/5.60 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se4205575877204974255it_nat @ M2 @ A ) )
% 5.31/5.60 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.31/5.60 | ( M2 = zero_zero_nat ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % even_unset_bit_iff
% 5.31/5.60 thf(fact_5927_even__unset__bit__iff,axiom,
% 5.31/5.60 ! [M2: nat,A: int] :
% 5.31/5.60 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se4203085406695923979it_int @ M2 @ A ) )
% 5.31/5.60 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.31/5.60 | ( M2 = zero_zero_nat ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % even_unset_bit_iff
% 5.31/5.60 thf(fact_5928_set__encode__def,axiom,
% 5.31/5.60 ( nat_set_encode
% 5.31/5.60 = ( groups3542108847815614940at_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % set_encode_def
% 5.31/5.60 thf(fact_5929_even__set__bit__iff,axiom,
% 5.31/5.60 ! [M2: nat,A: nat] :
% 5.31/5.60 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se7882103937844011126it_nat @ M2 @ A ) )
% 5.31/5.60 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.31/5.60 & ( M2 != zero_zero_nat ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % even_set_bit_iff
% 5.31/5.60 thf(fact_5930_even__set__bit__iff,axiom,
% 5.31/5.60 ! [M2: nat,A: int] :
% 5.31/5.60 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se7879613467334960850it_int @ M2 @ A ) )
% 5.31/5.60 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.31/5.60 & ( M2 != zero_zero_nat ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % even_set_bit_iff
% 5.31/5.60 thf(fact_5931_even__flip__bit__iff,axiom,
% 5.31/5.60 ! [M2: nat,A: nat] :
% 5.31/5.60 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se2161824704523386999it_nat @ M2 @ A ) )
% 5.31/5.60 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.31/5.60 != ( M2 = zero_zero_nat ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % even_flip_bit_iff
% 5.31/5.60 thf(fact_5932_even__flip__bit__iff,axiom,
% 5.31/5.60 ! [M2: nat,A: int] :
% 5.31/5.60 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se2159334234014336723it_int @ M2 @ A ) )
% 5.31/5.60 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.31/5.60 != ( M2 = zero_zero_nat ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % even_flip_bit_iff
% 5.31/5.60 thf(fact_5933_pochhammer__product,axiom,
% 5.31/5.60 ! [M2: nat,N: nat,Z3: rat] :
% 5.31/5.60 ( ( ord_less_eq_nat @ M2 @ N )
% 5.31/5.60 => ( ( comm_s4028243227959126397er_rat @ Z3 @ N )
% 5.31/5.60 = ( times_times_rat @ ( comm_s4028243227959126397er_rat @ Z3 @ M2 ) @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ Z3 @ ( semiri681578069525770553at_rat @ M2 ) ) @ ( minus_minus_nat @ N @ M2 ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % pochhammer_product
% 5.31/5.60 thf(fact_5934_pochhammer__product,axiom,
% 5.31/5.60 ! [M2: nat,N: nat,Z3: real] :
% 5.31/5.60 ( ( ord_less_eq_nat @ M2 @ N )
% 5.31/5.60 => ( ( comm_s7457072308508201937r_real @ Z3 @ N )
% 5.31/5.60 = ( times_times_real @ ( comm_s7457072308508201937r_real @ Z3 @ M2 ) @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ Z3 @ ( semiri5074537144036343181t_real @ M2 ) ) @ ( minus_minus_nat @ N @ M2 ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % pochhammer_product
% 5.31/5.60 thf(fact_5935_pochhammer__product,axiom,
% 5.31/5.60 ! [M2: nat,N: nat,Z3: int] :
% 5.31/5.60 ( ( ord_less_eq_nat @ M2 @ N )
% 5.31/5.60 => ( ( comm_s4660882817536571857er_int @ Z3 @ N )
% 5.31/5.60 = ( times_times_int @ ( comm_s4660882817536571857er_int @ Z3 @ M2 ) @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ Z3 @ ( semiri1314217659103216013at_int @ M2 ) ) @ ( minus_minus_nat @ N @ M2 ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % pochhammer_product
% 5.31/5.60 thf(fact_5936_pochhammer__product,axiom,
% 5.31/5.60 ! [M2: nat,N: nat,Z3: nat] :
% 5.31/5.60 ( ( ord_less_eq_nat @ M2 @ N )
% 5.31/5.60 => ( ( comm_s4663373288045622133er_nat @ Z3 @ N )
% 5.31/5.60 = ( times_times_nat @ ( comm_s4663373288045622133er_nat @ Z3 @ M2 ) @ ( comm_s4663373288045622133er_nat @ ( plus_plus_nat @ Z3 @ ( semiri1316708129612266289at_nat @ M2 ) ) @ ( minus_minus_nat @ N @ M2 ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % pochhammer_product
% 5.31/5.60 thf(fact_5937_oddE,axiom,
% 5.31/5.60 ! [A: code_integer] :
% 5.31/5.60 ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.31/5.60 => ~ ! [B3: code_integer] :
% 5.31/5.60 ( A
% 5.31/5.60 != ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B3 ) @ one_one_Code_integer ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % oddE
% 5.31/5.60 thf(fact_5938_oddE,axiom,
% 5.31/5.60 ! [A: nat] :
% 5.31/5.60 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.31/5.60 => ~ ! [B3: nat] :
% 5.31/5.60 ( A
% 5.31/5.60 != ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B3 ) @ one_one_nat ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % oddE
% 5.31/5.60 thf(fact_5939_oddE,axiom,
% 5.31/5.60 ! [A: int] :
% 5.31/5.60 ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.31/5.60 => ~ ! [B3: int] :
% 5.31/5.60 ( A
% 5.31/5.60 != ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B3 ) @ one_one_int ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % oddE
% 5.31/5.60 thf(fact_5940_mod2__eq__if,axiom,
% 5.31/5.60 ! [A: code_integer] :
% 5.31/5.60 ( ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.31/5.60 => ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.31/5.60 = zero_z3403309356797280102nteger ) )
% 5.31/5.60 & ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.31/5.60 => ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.31/5.60 = one_one_Code_integer ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % mod2_eq_if
% 5.31/5.60 thf(fact_5941_mod2__eq__if,axiom,
% 5.31/5.60 ! [A: nat] :
% 5.31/5.60 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.31/5.60 => ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.31/5.60 = zero_zero_nat ) )
% 5.31/5.60 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.31/5.60 => ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.31/5.60 = one_one_nat ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % mod2_eq_if
% 5.31/5.60 thf(fact_5942_mod2__eq__if,axiom,
% 5.31/5.60 ! [A: int] :
% 5.31/5.60 ( ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.31/5.60 => ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.31/5.60 = zero_zero_int ) )
% 5.31/5.60 & ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.31/5.60 => ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.31/5.60 = one_one_int ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % mod2_eq_if
% 5.31/5.60 thf(fact_5943_mod2__eq__if,axiom,
% 5.31/5.60 ! [A: code_natural] :
% 5.31/5.60 ( ( ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A )
% 5.31/5.60 => ( ( modulo8411746178871703098atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 5.31/5.60 = zero_z2226904508553997617atural ) )
% 5.31/5.60 & ( ~ ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A )
% 5.31/5.60 => ( ( modulo8411746178871703098atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 5.31/5.60 = one_one_Code_natural ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % mod2_eq_if
% 5.31/5.60 thf(fact_5944_parity__cases,axiom,
% 5.31/5.60 ! [A: code_integer] :
% 5.31/5.60 ( ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.31/5.60 => ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.31/5.60 != zero_z3403309356797280102nteger ) )
% 5.31/5.60 => ~ ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.31/5.60 => ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.31/5.60 != one_one_Code_integer ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % parity_cases
% 5.31/5.60 thf(fact_5945_parity__cases,axiom,
% 5.31/5.60 ! [A: nat] :
% 5.31/5.60 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.31/5.60 => ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.31/5.60 != zero_zero_nat ) )
% 5.31/5.60 => ~ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.31/5.60 => ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.31/5.60 != one_one_nat ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % parity_cases
% 5.31/5.60 thf(fact_5946_parity__cases,axiom,
% 5.31/5.60 ! [A: int] :
% 5.31/5.60 ( ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.31/5.60 => ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.31/5.60 != zero_zero_int ) )
% 5.31/5.60 => ~ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.31/5.60 => ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.31/5.60 != one_one_int ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % parity_cases
% 5.31/5.60 thf(fact_5947_parity__cases,axiom,
% 5.31/5.60 ! [A: code_natural] :
% 5.31/5.60 ( ( ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A )
% 5.31/5.60 => ( ( modulo8411746178871703098atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 5.31/5.60 != zero_z2226904508553997617atural ) )
% 5.31/5.60 => ~ ( ~ ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A )
% 5.31/5.60 => ( ( modulo8411746178871703098atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 5.31/5.60 != one_one_Code_natural ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % parity_cases
% 5.31/5.60 thf(fact_5948_zero__le__even__power,axiom,
% 5.31/5.60 ! [N: nat,A: real] :
% 5.31/5.60 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.31/5.60 => ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ N ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % zero_le_even_power
% 5.31/5.60 thf(fact_5949_zero__le__even__power,axiom,
% 5.31/5.60 ! [N: nat,A: rat] :
% 5.31/5.60 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.31/5.60 => ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ N ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % zero_le_even_power
% 5.31/5.60 thf(fact_5950_zero__le__even__power,axiom,
% 5.31/5.60 ! [N: nat,A: int] :
% 5.31/5.60 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.31/5.60 => ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ N ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % zero_le_even_power
% 5.31/5.60 thf(fact_5951_zero__le__odd__power,axiom,
% 5.31/5.60 ! [N: nat,A: real] :
% 5.31/5.60 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.31/5.60 => ( ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ N ) )
% 5.31/5.60 = ( ord_less_eq_real @ zero_zero_real @ A ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % zero_le_odd_power
% 5.31/5.60 thf(fact_5952_zero__le__odd__power,axiom,
% 5.31/5.60 ! [N: nat,A: rat] :
% 5.31/5.60 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.31/5.60 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ N ) )
% 5.31/5.60 = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % zero_le_odd_power
% 5.31/5.60 thf(fact_5953_zero__le__odd__power,axiom,
% 5.31/5.60 ! [N: nat,A: int] :
% 5.31/5.60 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.31/5.60 => ( ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ N ) )
% 5.31/5.60 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % zero_le_odd_power
% 5.31/5.60 thf(fact_5954_zero__le__power__eq,axiom,
% 5.31/5.60 ! [A: real,N: nat] :
% 5.31/5.60 ( ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ N ) )
% 5.31/5.60 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.31/5.60 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.31/5.60 & ( ord_less_eq_real @ zero_zero_real @ A ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % zero_le_power_eq
% 5.31/5.60 thf(fact_5955_zero__le__power__eq,axiom,
% 5.31/5.60 ! [A: rat,N: nat] :
% 5.31/5.60 ( ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ N ) )
% 5.31/5.60 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.31/5.60 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.31/5.60 & ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % zero_le_power_eq
% 5.31/5.60 thf(fact_5956_zero__le__power__eq,axiom,
% 5.31/5.60 ! [A: int,N: nat] :
% 5.31/5.60 ( ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ N ) )
% 5.31/5.60 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.31/5.60 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.31/5.60 & ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % zero_le_power_eq
% 5.31/5.60 thf(fact_5957_sum__natinterval__diff,axiom,
% 5.31/5.60 ! [M2: nat,N: nat,F2: nat > complex] :
% 5.31/5.60 ( ( ( ord_less_eq_nat @ M2 @ N )
% 5.31/5.60 => ( ( groups2073611262835488442omplex
% 5.31/5.60 @ ^ [K3: nat] : ( minus_minus_complex @ ( F2 @ K3 ) @ ( F2 @ ( plus_plus_nat @ K3 @ one_one_nat ) ) )
% 5.31/5.60 @ ( set_or1269000886237332187st_nat @ M2 @ N ) )
% 5.31/5.60 = ( minus_minus_complex @ ( F2 @ M2 ) @ ( F2 @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ) )
% 5.31/5.60 & ( ~ ( ord_less_eq_nat @ M2 @ N )
% 5.31/5.60 => ( ( groups2073611262835488442omplex
% 5.31/5.60 @ ^ [K3: nat] : ( minus_minus_complex @ ( F2 @ K3 ) @ ( F2 @ ( plus_plus_nat @ K3 @ one_one_nat ) ) )
% 5.31/5.60 @ ( set_or1269000886237332187st_nat @ M2 @ N ) )
% 5.31/5.60 = zero_zero_complex ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum_natinterval_diff
% 5.31/5.60 thf(fact_5958_sum__natinterval__diff,axiom,
% 5.31/5.60 ! [M2: nat,N: nat,F2: nat > rat] :
% 5.31/5.60 ( ( ( ord_less_eq_nat @ M2 @ N )
% 5.31/5.60 => ( ( groups2906978787729119204at_rat
% 5.31/5.60 @ ^ [K3: nat] : ( minus_minus_rat @ ( F2 @ K3 ) @ ( F2 @ ( plus_plus_nat @ K3 @ one_one_nat ) ) )
% 5.31/5.60 @ ( set_or1269000886237332187st_nat @ M2 @ N ) )
% 5.31/5.60 = ( minus_minus_rat @ ( F2 @ M2 ) @ ( F2 @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ) )
% 5.31/5.60 & ( ~ ( ord_less_eq_nat @ M2 @ N )
% 5.31/5.60 => ( ( groups2906978787729119204at_rat
% 5.31/5.60 @ ^ [K3: nat] : ( minus_minus_rat @ ( F2 @ K3 ) @ ( F2 @ ( plus_plus_nat @ K3 @ one_one_nat ) ) )
% 5.31/5.60 @ ( set_or1269000886237332187st_nat @ M2 @ N ) )
% 5.31/5.60 = zero_zero_rat ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum_natinterval_diff
% 5.31/5.60 thf(fact_5959_sum__natinterval__diff,axiom,
% 5.31/5.60 ! [M2: nat,N: nat,F2: nat > int] :
% 5.31/5.60 ( ( ( ord_less_eq_nat @ M2 @ N )
% 5.31/5.60 => ( ( groups3539618377306564664at_int
% 5.31/5.60 @ ^ [K3: nat] : ( minus_minus_int @ ( F2 @ K3 ) @ ( F2 @ ( plus_plus_nat @ K3 @ one_one_nat ) ) )
% 5.31/5.60 @ ( set_or1269000886237332187st_nat @ M2 @ N ) )
% 5.31/5.60 = ( minus_minus_int @ ( F2 @ M2 ) @ ( F2 @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ) )
% 5.31/5.60 & ( ~ ( ord_less_eq_nat @ M2 @ N )
% 5.31/5.60 => ( ( groups3539618377306564664at_int
% 5.31/5.60 @ ^ [K3: nat] : ( minus_minus_int @ ( F2 @ K3 ) @ ( F2 @ ( plus_plus_nat @ K3 @ one_one_nat ) ) )
% 5.31/5.60 @ ( set_or1269000886237332187st_nat @ M2 @ N ) )
% 5.31/5.60 = zero_zero_int ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum_natinterval_diff
% 5.31/5.60 thf(fact_5960_sum__natinterval__diff,axiom,
% 5.31/5.60 ! [M2: nat,N: nat,F2: nat > real] :
% 5.31/5.60 ( ( ( ord_less_eq_nat @ M2 @ N )
% 5.31/5.60 => ( ( groups6591440286371151544t_real
% 5.31/5.60 @ ^ [K3: nat] : ( minus_minus_real @ ( F2 @ K3 ) @ ( F2 @ ( plus_plus_nat @ K3 @ one_one_nat ) ) )
% 5.31/5.60 @ ( set_or1269000886237332187st_nat @ M2 @ N ) )
% 5.31/5.60 = ( minus_minus_real @ ( F2 @ M2 ) @ ( F2 @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ) )
% 5.31/5.60 & ( ~ ( ord_less_eq_nat @ M2 @ N )
% 5.31/5.60 => ( ( groups6591440286371151544t_real
% 5.31/5.60 @ ^ [K3: nat] : ( minus_minus_real @ ( F2 @ K3 ) @ ( F2 @ ( plus_plus_nat @ K3 @ one_one_nat ) ) )
% 5.31/5.60 @ ( set_or1269000886237332187st_nat @ M2 @ N ) )
% 5.31/5.60 = zero_zero_real ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum_natinterval_diff
% 5.31/5.60 thf(fact_5961_sum__telescope_H_H,axiom,
% 5.31/5.60 ! [M2: nat,N: nat,F2: nat > rat] :
% 5.31/5.60 ( ( ord_less_eq_nat @ M2 @ N )
% 5.31/5.60 => ( ( groups2906978787729119204at_rat
% 5.31/5.60 @ ^ [K3: nat] : ( minus_minus_rat @ ( F2 @ K3 ) @ ( F2 @ ( minus_minus_nat @ K3 @ one_one_nat ) ) )
% 5.31/5.60 @ ( set_or1269000886237332187st_nat @ ( suc @ M2 ) @ N ) )
% 5.31/5.60 = ( minus_minus_rat @ ( F2 @ N ) @ ( F2 @ M2 ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum_telescope''
% 5.31/5.60 thf(fact_5962_sum__telescope_H_H,axiom,
% 5.31/5.60 ! [M2: nat,N: nat,F2: nat > int] :
% 5.31/5.60 ( ( ord_less_eq_nat @ M2 @ N )
% 5.31/5.60 => ( ( groups3539618377306564664at_int
% 5.31/5.60 @ ^ [K3: nat] : ( minus_minus_int @ ( F2 @ K3 ) @ ( F2 @ ( minus_minus_nat @ K3 @ one_one_nat ) ) )
% 5.31/5.60 @ ( set_or1269000886237332187st_nat @ ( suc @ M2 ) @ N ) )
% 5.31/5.60 = ( minus_minus_int @ ( F2 @ N ) @ ( F2 @ M2 ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum_telescope''
% 5.31/5.60 thf(fact_5963_sum__telescope_H_H,axiom,
% 5.31/5.60 ! [M2: nat,N: nat,F2: nat > real] :
% 5.31/5.60 ( ( ord_less_eq_nat @ M2 @ N )
% 5.31/5.60 => ( ( groups6591440286371151544t_real
% 5.31/5.60 @ ^ [K3: nat] : ( minus_minus_real @ ( F2 @ K3 ) @ ( F2 @ ( minus_minus_nat @ K3 @ one_one_nat ) ) )
% 5.31/5.60 @ ( set_or1269000886237332187st_nat @ ( suc @ M2 ) @ N ) )
% 5.31/5.60 = ( minus_minus_real @ ( F2 @ N ) @ ( F2 @ M2 ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum_telescope''
% 5.31/5.60 thf(fact_5964_even__set__encode__iff,axiom,
% 5.31/5.60 ! [A4: set_nat] :
% 5.31/5.60 ( ( finite_finite_nat @ A4 )
% 5.31/5.60 => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( nat_set_encode @ A4 ) )
% 5.31/5.60 = ( ~ ( member_nat @ zero_zero_nat @ A4 ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % even_set_encode_iff
% 5.31/5.60 thf(fact_5965_zero__less__power__eq,axiom,
% 5.31/5.60 ! [A: real,N: nat] :
% 5.31/5.60 ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ A @ N ) )
% 5.31/5.60 = ( ( N = zero_zero_nat )
% 5.31/5.60 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.31/5.60 & ( A != zero_zero_real ) )
% 5.31/5.60 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.31/5.60 & ( ord_less_real @ zero_zero_real @ A ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % zero_less_power_eq
% 5.31/5.60 thf(fact_5966_zero__less__power__eq,axiom,
% 5.31/5.60 ! [A: rat,N: nat] :
% 5.31/5.60 ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ A @ N ) )
% 5.31/5.60 = ( ( N = zero_zero_nat )
% 5.31/5.60 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.31/5.60 & ( A != zero_zero_rat ) )
% 5.31/5.60 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.31/5.60 & ( ord_less_rat @ zero_zero_rat @ A ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % zero_less_power_eq
% 5.31/5.60 thf(fact_5967_zero__less__power__eq,axiom,
% 5.31/5.60 ! [A: int,N: nat] :
% 5.31/5.60 ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ A @ N ) )
% 5.31/5.60 = ( ( N = zero_zero_nat )
% 5.31/5.60 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.31/5.60 & ( A != zero_zero_int ) )
% 5.31/5.60 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.31/5.60 & ( ord_less_int @ zero_zero_int @ A ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % zero_less_power_eq
% 5.31/5.60 thf(fact_5968_sum__gp__multiplied,axiom,
% 5.31/5.60 ! [M2: nat,N: nat,X: code_integer] :
% 5.31/5.60 ( ( ord_less_eq_nat @ M2 @ N )
% 5.31/5.60 => ( ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ one_one_Code_integer @ X ) @ ( groups7501900531339628137nteger @ ( power_8256067586552552935nteger @ X ) @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) )
% 5.31/5.60 = ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ X @ M2 ) @ ( power_8256067586552552935nteger @ X @ ( suc @ N ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum_gp_multiplied
% 5.31/5.60 thf(fact_5969_sum__gp__multiplied,axiom,
% 5.31/5.60 ! [M2: nat,N: nat,X: complex] :
% 5.31/5.60 ( ( ord_less_eq_nat @ M2 @ N )
% 5.31/5.60 => ( ( times_times_complex @ ( minus_minus_complex @ one_one_complex @ X ) @ ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) )
% 5.31/5.60 = ( minus_minus_complex @ ( power_power_complex @ X @ M2 ) @ ( power_power_complex @ X @ ( suc @ N ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum_gp_multiplied
% 5.31/5.60 thf(fact_5970_sum__gp__multiplied,axiom,
% 5.31/5.60 ! [M2: nat,N: nat,X: rat] :
% 5.31/5.60 ( ( ord_less_eq_nat @ M2 @ N )
% 5.31/5.60 => ( ( times_times_rat @ ( minus_minus_rat @ one_one_rat @ X ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) )
% 5.31/5.60 = ( minus_minus_rat @ ( power_power_rat @ X @ M2 ) @ ( power_power_rat @ X @ ( suc @ N ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum_gp_multiplied
% 5.31/5.60 thf(fact_5971_sum__gp__multiplied,axiom,
% 5.31/5.60 ! [M2: nat,N: nat,X: int] :
% 5.31/5.60 ( ( ord_less_eq_nat @ M2 @ N )
% 5.31/5.60 => ( ( times_times_int @ ( minus_minus_int @ one_one_int @ X ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X ) @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) )
% 5.31/5.60 = ( minus_minus_int @ ( power_power_int @ X @ M2 ) @ ( power_power_int @ X @ ( suc @ N ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum_gp_multiplied
% 5.31/5.60 thf(fact_5972_sum__gp__multiplied,axiom,
% 5.31/5.60 ! [M2: nat,N: nat,X: real] :
% 5.31/5.60 ( ( ord_less_eq_nat @ M2 @ N )
% 5.31/5.60 => ( ( times_times_real @ ( minus_minus_real @ one_one_real @ X ) @ ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) )
% 5.31/5.60 = ( minus_minus_real @ ( power_power_real @ X @ M2 ) @ ( power_power_real @ X @ ( suc @ N ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum_gp_multiplied
% 5.31/5.60 thf(fact_5973_sum_Oin__pairs,axiom,
% 5.31/5.60 ! [G2: nat > rat,M2: nat,N: nat] :
% 5.31/5.60 ( ( groups2906978787729119204at_rat @ G2 @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 5.31/5.60 = ( groups2906978787729119204at_rat
% 5.31/5.60 @ ^ [I: nat] : ( plus_plus_rat @ ( G2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I ) ) @ ( G2 @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I ) ) ) )
% 5.31/5.60 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum.in_pairs
% 5.31/5.60 thf(fact_5974_sum_Oin__pairs,axiom,
% 5.31/5.60 ! [G2: nat > int,M2: nat,N: nat] :
% 5.31/5.60 ( ( groups3539618377306564664at_int @ G2 @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 5.31/5.60 = ( groups3539618377306564664at_int
% 5.31/5.60 @ ^ [I: nat] : ( plus_plus_int @ ( G2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I ) ) @ ( G2 @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I ) ) ) )
% 5.31/5.60 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum.in_pairs
% 5.31/5.60 thf(fact_5975_sum_Oin__pairs,axiom,
% 5.31/5.60 ! [G2: nat > nat,M2: nat,N: nat] :
% 5.31/5.60 ( ( groups3542108847815614940at_nat @ G2 @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 5.31/5.60 = ( groups3542108847815614940at_nat
% 5.31/5.60 @ ^ [I: nat] : ( plus_plus_nat @ ( G2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I ) ) @ ( G2 @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I ) ) ) )
% 5.31/5.60 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum.in_pairs
% 5.31/5.60 thf(fact_5976_sum_Oin__pairs,axiom,
% 5.31/5.60 ! [G2: nat > real,M2: nat,N: nat] :
% 5.31/5.60 ( ( groups6591440286371151544t_real @ G2 @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 5.31/5.60 = ( groups6591440286371151544t_real
% 5.31/5.60 @ ^ [I: nat] : ( plus_plus_real @ ( G2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I ) ) @ ( G2 @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I ) ) ) )
% 5.31/5.60 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % sum.in_pairs
% 5.31/5.60 thf(fact_5977_even__mask__div__iff_H,axiom,
% 5.31/5.60 ! [M2: nat,N: nat] :
% 5.31/5.60 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M2 ) @ one_one_Code_integer ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) )
% 5.31/5.60 = ( ord_less_eq_nat @ M2 @ N ) ) ).
% 5.31/5.60
% 5.31/5.60 % even_mask_div_iff'
% 5.31/5.60 thf(fact_5978_even__mask__div__iff_H,axiom,
% 5.31/5.60 ! [M2: nat,N: nat] :
% 5.31/5.60 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) @ one_one_nat ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.31/5.60 = ( ord_less_eq_nat @ M2 @ N ) ) ).
% 5.31/5.60
% 5.31/5.60 % even_mask_div_iff'
% 5.31/5.60 thf(fact_5979_even__mask__div__iff_H,axiom,
% 5.31/5.60 ! [M2: nat,N: nat] :
% 5.31/5.60 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M2 ) @ one_one_int ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) )
% 5.31/5.60 = ( ord_less_eq_nat @ M2 @ N ) ) ).
% 5.31/5.60
% 5.31/5.60 % even_mask_div_iff'
% 5.31/5.60 thf(fact_5980_power__le__zero__eq,axiom,
% 5.31/5.60 ! [A: real,N: nat] :
% 5.31/5.60 ( ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ zero_zero_real )
% 5.31/5.60 = ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.60 & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.31/5.60 & ( ord_less_eq_real @ A @ zero_zero_real ) )
% 5.31/5.60 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.31/5.60 & ( A = zero_zero_real ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % power_le_zero_eq
% 5.31/5.60 thf(fact_5981_power__le__zero__eq,axiom,
% 5.31/5.60 ! [A: rat,N: nat] :
% 5.31/5.60 ( ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ zero_zero_rat )
% 5.31/5.60 = ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.60 & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.31/5.60 & ( ord_less_eq_rat @ A @ zero_zero_rat ) )
% 5.31/5.60 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.31/5.60 & ( A = zero_zero_rat ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % power_le_zero_eq
% 5.31/5.60 thf(fact_5982_power__le__zero__eq,axiom,
% 5.31/5.60 ! [A: int,N: nat] :
% 5.31/5.60 ( ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ zero_zero_int )
% 5.31/5.60 = ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.60 & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.31/5.60 & ( ord_less_eq_int @ A @ zero_zero_int ) )
% 5.31/5.60 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.31/5.60 & ( A = zero_zero_int ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % power_le_zero_eq
% 5.31/5.60 thf(fact_5983_mask__eq__sum__exp__nat,axiom,
% 5.31/5.60 ! [N: nat] :
% 5.31/5.60 ( ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ ( suc @ zero_zero_nat ) )
% 5.31/5.60 = ( groups3542108847815614940at_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.31/5.60 @ ( collect_nat
% 5.31/5.60 @ ^ [Q5: nat] : ( ord_less_nat @ Q5 @ N ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % mask_eq_sum_exp_nat
% 5.31/5.60 thf(fact_5984_gauss__sum__nat,axiom,
% 5.31/5.60 ! [N: nat] :
% 5.31/5.60 ( ( groups3542108847815614940at_nat
% 5.31/5.60 @ ^ [X4: nat] : X4
% 5.31/5.60 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 5.31/5.60 = ( divide_divide_nat @ ( times_times_nat @ N @ ( suc @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % gauss_sum_nat
% 5.31/5.60 thf(fact_5985_even__mod__4__div__2,axiom,
% 5.31/5.60 ! [N: nat] :
% 5.31/5.60 ( ( ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.31/5.60 = ( suc @ zero_zero_nat ) )
% 5.31/5.60 => ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % even_mod_4_div_2
% 5.31/5.60 thf(fact_5986_even__mask__div__iff,axiom,
% 5.31/5.60 ! [M2: nat,N: nat] :
% 5.31/5.60 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M2 ) @ one_one_Code_integer ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) )
% 5.31/5.60 = ( ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N )
% 5.31/5.60 = zero_z3403309356797280102nteger )
% 5.31/5.60 | ( ord_less_eq_nat @ M2 @ N ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % even_mask_div_iff
% 5.31/5.60 thf(fact_5987_even__mask__div__iff,axiom,
% 5.31/5.60 ! [M2: nat,N: nat] :
% 5.31/5.60 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) @ one_one_nat ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.31/5.60 = ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.31/5.60 = zero_zero_nat )
% 5.31/5.60 | ( ord_less_eq_nat @ M2 @ N ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % even_mask_div_iff
% 5.31/5.60 thf(fact_5988_even__mask__div__iff,axiom,
% 5.31/5.60 ! [M2: nat,N: nat] :
% 5.31/5.60 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M2 ) @ one_one_int ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) )
% 5.31/5.60 = ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 5.31/5.60 = zero_zero_int )
% 5.31/5.60 | ( ord_less_eq_nat @ M2 @ N ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % even_mask_div_iff
% 5.31/5.60 thf(fact_5989_double__gauss__sum,axiom,
% 5.31/5.60 ! [N: nat] :
% 5.31/5.60 ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( groups7501900531339628137nteger @ semiri4939895301339042750nteger @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 5.31/5.60 = ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ N ) @ ( plus_p5714425477246183910nteger @ ( semiri4939895301339042750nteger @ N ) @ one_one_Code_integer ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % double_gauss_sum
% 5.31/5.60 thf(fact_5990_double__gauss__sum,axiom,
% 5.31/5.60 ! [N: nat] :
% 5.31/5.60 ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( groups2906978787729119204at_rat @ semiri681578069525770553at_rat @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 5.31/5.60 = ( times_times_rat @ ( semiri681578069525770553at_rat @ N ) @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ N ) @ one_one_rat ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % double_gauss_sum
% 5.31/5.60 thf(fact_5991_double__gauss__sum,axiom,
% 5.31/5.60 ! [N: nat] :
% 5.31/5.60 ( ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ ( bit0 @ one ) ) @ ( groups7108830773950497114d_enat @ semiri4216267220026989637d_enat @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 5.31/5.60 = ( times_7803423173614009249d_enat @ ( semiri4216267220026989637d_enat @ N ) @ ( plus_p3455044024723400733d_enat @ ( semiri4216267220026989637d_enat @ N ) @ one_on7984719198319812577d_enat ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % double_gauss_sum
% 5.31/5.60 thf(fact_5992_double__gauss__sum,axiom,
% 5.31/5.60 ! [N: nat] :
% 5.31/5.60 ( ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( groups2073611262835488442omplex @ semiri8010041392384452111omplex @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 5.31/5.60 = ( times_times_complex @ ( semiri8010041392384452111omplex @ N ) @ ( plus_plus_complex @ ( semiri8010041392384452111omplex @ N ) @ one_one_complex ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % double_gauss_sum
% 5.31/5.60 thf(fact_5993_double__gauss__sum,axiom,
% 5.31/5.60 ! [N: nat] :
% 5.31/5.60 ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( groups3539618377306564664at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 5.31/5.60 = ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % double_gauss_sum
% 5.31/5.60 thf(fact_5994_double__gauss__sum,axiom,
% 5.31/5.60 ! [N: nat] :
% 5.31/5.60 ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( groups3542108847815614940at_nat @ semiri1316708129612266289at_nat @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 5.31/5.60 = ( times_times_nat @ ( semiri1316708129612266289at_nat @ N ) @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N ) @ one_one_nat ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % double_gauss_sum
% 5.31/5.60 thf(fact_5995_double__gauss__sum,axiom,
% 5.31/5.60 ! [N: nat] :
% 5.31/5.60 ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( groups6591440286371151544t_real @ semiri5074537144036343181t_real @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 5.31/5.60 = ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ N ) @ one_one_real ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % double_gauss_sum
% 5.31/5.60 thf(fact_5996_double__arith__series,axiom,
% 5.31/5.60 ! [A: code_integer,D: code_integer,N: nat] :
% 5.31/5.60 ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) )
% 5.31/5.60 @ ( groups7501900531339628137nteger
% 5.31/5.60 @ ^ [I: nat] : ( plus_p5714425477246183910nteger @ A @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ I ) @ D ) )
% 5.31/5.60 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 5.31/5.60 = ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ ( semiri4939895301339042750nteger @ N ) @ one_one_Code_integer ) @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ N ) @ D ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % double_arith_series
% 5.31/5.60 thf(fact_5997_double__arith__series,axiom,
% 5.31/5.60 ! [A: rat,D: rat,N: nat] :
% 5.31/5.60 ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) )
% 5.31/5.60 @ ( groups2906978787729119204at_rat
% 5.31/5.60 @ ^ [I: nat] : ( plus_plus_rat @ A @ ( times_times_rat @ ( semiri681578069525770553at_rat @ I ) @ D ) )
% 5.31/5.60 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 5.31/5.60 = ( 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 ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % double_arith_series
% 5.31/5.60 thf(fact_5998_double__arith__series,axiom,
% 5.31/5.60 ! [A: extended_enat,D: extended_enat,N: nat] :
% 5.31/5.60 ( ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ ( bit0 @ one ) )
% 5.31/5.60 @ ( groups7108830773950497114d_enat
% 5.31/5.60 @ ^ [I: nat] : ( plus_p3455044024723400733d_enat @ A @ ( times_7803423173614009249d_enat @ ( semiri4216267220026989637d_enat @ I ) @ D ) )
% 5.31/5.60 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 5.31/5.60 = ( times_7803423173614009249d_enat @ ( plus_p3455044024723400733d_enat @ ( semiri4216267220026989637d_enat @ N ) @ one_on7984719198319812577d_enat ) @ ( plus_p3455044024723400733d_enat @ ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ ( bit0 @ one ) ) @ A ) @ ( times_7803423173614009249d_enat @ ( semiri4216267220026989637d_enat @ N ) @ D ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % double_arith_series
% 5.31/5.60 thf(fact_5999_double__arith__series,axiom,
% 5.31/5.60 ! [A: complex,D: complex,N: nat] :
% 5.31/5.60 ( ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) )
% 5.31/5.60 @ ( groups2073611262835488442omplex
% 5.31/5.60 @ ^ [I: nat] : ( plus_plus_complex @ A @ ( times_times_complex @ ( semiri8010041392384452111omplex @ I ) @ D ) )
% 5.31/5.60 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 5.31/5.60 = ( 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 ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % double_arith_series
% 5.31/5.60 thf(fact_6000_double__arith__series,axiom,
% 5.31/5.60 ! [A: int,D: int,N: nat] :
% 5.31/5.60 ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) )
% 5.31/5.60 @ ( groups3539618377306564664at_int
% 5.31/5.60 @ ^ [I: nat] : ( plus_plus_int @ A @ ( times_times_int @ ( semiri1314217659103216013at_int @ I ) @ D ) )
% 5.31/5.60 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 5.31/5.60 = ( 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 ) ) ) ) ).
% 5.31/5.60
% 5.31/5.60 % double_arith_series
% 5.31/5.60 thf(fact_6001_double__arith__series,axiom,
% 5.31/5.60 ! [A: nat,D: nat,N: nat] :
% 5.31/5.60 ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
% 5.31/5.60 @ ( groups3542108847815614940at_nat
% 5.31/5.60 @ ^ [I: nat] : ( plus_plus_nat @ A @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ I ) @ D ) )
% 5.31/5.61 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 5.31/5.61 = ( 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 ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % double_arith_series
% 5.31/5.61 thf(fact_6002_double__arith__series,axiom,
% 5.31/5.61 ! [A: real,D: real,N: nat] :
% 5.31/5.61 ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) )
% 5.31/5.61 @ ( groups6591440286371151544t_real
% 5.31/5.61 @ ^ [I: nat] : ( plus_plus_real @ A @ ( times_times_real @ ( semiri5074537144036343181t_real @ I ) @ D ) )
% 5.31/5.61 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 5.31/5.61 = ( 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 ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % double_arith_series
% 5.31/5.61 thf(fact_6003_arith__series__nat,axiom,
% 5.31/5.61 ! [A: nat,D: nat,N: nat] :
% 5.31/5.61 ( ( groups3542108847815614940at_nat
% 5.31/5.61 @ ^ [I: nat] : ( plus_plus_nat @ A @ ( times_times_nat @ I @ D ) )
% 5.31/5.61 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 5.31/5.61 = ( 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 ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % arith_series_nat
% 5.31/5.61 thf(fact_6004_Sum__Icc__nat,axiom,
% 5.31/5.61 ! [M2: nat,N: nat] :
% 5.31/5.61 ( ( groups3542108847815614940at_nat
% 5.31/5.61 @ ^ [X4: nat] : X4
% 5.31/5.61 @ ( set_or1269000886237332187st_nat @ M2 @ N ) )
% 5.31/5.61 = ( divide_divide_nat @ ( minus_minus_nat @ ( times_times_nat @ N @ ( plus_plus_nat @ N @ one_one_nat ) ) @ ( times_times_nat @ M2 @ ( minus_minus_nat @ M2 @ one_one_nat ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % Sum_Icc_nat
% 5.31/5.61 thf(fact_6005_Bernoulli__inequality__even,axiom,
% 5.31/5.61 ! [N: nat,X: real] :
% 5.31/5.61 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.31/5.61 => ( 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 ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % Bernoulli_inequality_even
% 5.31/5.61 thf(fact_6006_gauss__sum,axiom,
% 5.31/5.61 ! [N: nat] :
% 5.31/5.61 ( ( groups7501900531339628137nteger @ semiri4939895301339042750nteger @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 5.31/5.61 = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ N ) @ ( plus_p5714425477246183910nteger @ ( semiri4939895301339042750nteger @ N ) @ one_one_Code_integer ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % gauss_sum
% 5.31/5.61 thf(fact_6007_gauss__sum,axiom,
% 5.31/5.61 ! [N: nat] :
% 5.31/5.61 ( ( groups3539618377306564664at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 5.31/5.61 = ( divide_divide_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % gauss_sum
% 5.31/5.61 thf(fact_6008_gauss__sum,axiom,
% 5.31/5.61 ! [N: nat] :
% 5.31/5.61 ( ( groups3542108847815614940at_nat @ semiri1316708129612266289at_nat @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 5.31/5.61 = ( divide_divide_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ N ) @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N ) @ one_one_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % gauss_sum
% 5.31/5.61 thf(fact_6009_arith__series,axiom,
% 5.31/5.61 ! [A: code_integer,D: code_integer,N: nat] :
% 5.31/5.61 ( ( groups7501900531339628137nteger
% 5.31/5.61 @ ^ [I: nat] : ( plus_p5714425477246183910nteger @ A @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ I ) @ D ) )
% 5.31/5.61 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 5.31/5.61 = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ ( semiri4939895301339042750nteger @ N ) @ one_one_Code_integer ) @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ N ) @ D ) ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % arith_series
% 5.31/5.61 thf(fact_6010_arith__series,axiom,
% 5.31/5.61 ! [A: int,D: int,N: nat] :
% 5.31/5.61 ( ( groups3539618377306564664at_int
% 5.31/5.61 @ ^ [I: nat] : ( plus_plus_int @ A @ ( times_times_int @ ( semiri1314217659103216013at_int @ I ) @ D ) )
% 5.31/5.61 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 5.31/5.61 = ( 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 ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % arith_series
% 5.31/5.61 thf(fact_6011_arith__series,axiom,
% 5.31/5.61 ! [A: nat,D: nat,N: nat] :
% 5.31/5.61 ( ( groups3542108847815614940at_nat
% 5.31/5.61 @ ^ [I: nat] : ( plus_plus_nat @ A @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ I ) @ D ) )
% 5.31/5.61 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 5.31/5.61 = ( 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 ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % arith_series
% 5.31/5.61 thf(fact_6012_double__gauss__sum__from__Suc__0,axiom,
% 5.31/5.61 ! [N: nat] :
% 5.31/5.61 ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( groups7501900531339628137nteger @ semiri4939895301339042750nteger @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) ) )
% 5.31/5.61 = ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ N ) @ ( plus_p5714425477246183910nteger @ ( semiri4939895301339042750nteger @ N ) @ one_one_Code_integer ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % double_gauss_sum_from_Suc_0
% 5.31/5.61 thf(fact_6013_double__gauss__sum__from__Suc__0,axiom,
% 5.31/5.61 ! [N: nat] :
% 5.31/5.61 ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( groups2906978787729119204at_rat @ semiri681578069525770553at_rat @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) ) )
% 5.31/5.61 = ( times_times_rat @ ( semiri681578069525770553at_rat @ N ) @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ N ) @ one_one_rat ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % double_gauss_sum_from_Suc_0
% 5.31/5.61 thf(fact_6014_double__gauss__sum__from__Suc__0,axiom,
% 5.31/5.61 ! [N: nat] :
% 5.31/5.61 ( ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ ( bit0 @ one ) ) @ ( groups7108830773950497114d_enat @ semiri4216267220026989637d_enat @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) ) )
% 5.31/5.61 = ( times_7803423173614009249d_enat @ ( semiri4216267220026989637d_enat @ N ) @ ( plus_p3455044024723400733d_enat @ ( semiri4216267220026989637d_enat @ N ) @ one_on7984719198319812577d_enat ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % double_gauss_sum_from_Suc_0
% 5.31/5.61 thf(fact_6015_double__gauss__sum__from__Suc__0,axiom,
% 5.31/5.61 ! [N: nat] :
% 5.31/5.61 ( ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( groups2073611262835488442omplex @ semiri8010041392384452111omplex @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) ) )
% 5.31/5.61 = ( times_times_complex @ ( semiri8010041392384452111omplex @ N ) @ ( plus_plus_complex @ ( semiri8010041392384452111omplex @ N ) @ one_one_complex ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % double_gauss_sum_from_Suc_0
% 5.31/5.61 thf(fact_6016_double__gauss__sum__from__Suc__0,axiom,
% 5.31/5.61 ! [N: nat] :
% 5.31/5.61 ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( groups3539618377306564664at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) ) )
% 5.31/5.61 = ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % double_gauss_sum_from_Suc_0
% 5.31/5.61 thf(fact_6017_double__gauss__sum__from__Suc__0,axiom,
% 5.31/5.61 ! [N: nat] :
% 5.31/5.61 ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( groups3542108847815614940at_nat @ semiri1316708129612266289at_nat @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) ) )
% 5.31/5.61 = ( times_times_nat @ ( semiri1316708129612266289at_nat @ N ) @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N ) @ one_one_nat ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % double_gauss_sum_from_Suc_0
% 5.31/5.61 thf(fact_6018_double__gauss__sum__from__Suc__0,axiom,
% 5.31/5.61 ! [N: nat] :
% 5.31/5.61 ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( groups6591440286371151544t_real @ semiri5074537144036343181t_real @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) ) )
% 5.31/5.61 = ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ N ) @ one_one_real ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % double_gauss_sum_from_Suc_0
% 5.31/5.61 thf(fact_6019_even__mult__exp__div__exp__iff,axiom,
% 5.31/5.61 ! [A: nat,M2: nat,N: nat] :
% 5.31/5.61 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( times_times_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.31/5.61 = ( ( ord_less_nat @ N @ M2 )
% 5.31/5.61 | ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.31/5.61 = zero_zero_nat )
% 5.31/5.61 | ( ( ord_less_eq_nat @ M2 @ N )
% 5.31/5.61 & ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M2 ) ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % even_mult_exp_div_exp_iff
% 5.31/5.61 thf(fact_6020_even__mult__exp__div__exp__iff,axiom,
% 5.31/5.61 ! [A: int,M2: nat,N: nat] :
% 5.31/5.61 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ ( times_times_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M2 ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) )
% 5.31/5.61 = ( ( ord_less_nat @ N @ M2 )
% 5.31/5.61 | ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 5.31/5.61 = zero_zero_int )
% 5.31/5.61 | ( ( ord_less_eq_nat @ M2 @ N )
% 5.31/5.61 & ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M2 ) ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % even_mult_exp_div_exp_iff
% 5.31/5.61 thf(fact_6021_sum__gp__offset,axiom,
% 5.31/5.61 ! [X: complex,M2: nat,N: nat] :
% 5.31/5.61 ( ( ( X = one_one_complex )
% 5.31/5.61 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_or1269000886237332187st_nat @ M2 @ ( plus_plus_nat @ M2 @ N ) ) )
% 5.31/5.61 = ( plus_plus_complex @ ( semiri8010041392384452111omplex @ N ) @ one_one_complex ) ) )
% 5.31/5.61 & ( ( X != one_one_complex )
% 5.31/5.61 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_or1269000886237332187st_nat @ M2 @ ( plus_plus_nat @ M2 @ N ) ) )
% 5.31/5.61 = ( divide1717551699836669952omplex @ ( times_times_complex @ ( power_power_complex @ X @ M2 ) @ ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ X @ ( suc @ N ) ) ) ) @ ( minus_minus_complex @ one_one_complex @ X ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % sum_gp_offset
% 5.31/5.61 thf(fact_6022_sum__gp__offset,axiom,
% 5.31/5.61 ! [X: rat,M2: nat,N: nat] :
% 5.31/5.61 ( ( ( X = one_one_rat )
% 5.31/5.61 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_or1269000886237332187st_nat @ M2 @ ( plus_plus_nat @ M2 @ N ) ) )
% 5.31/5.61 = ( plus_plus_rat @ ( semiri681578069525770553at_rat @ N ) @ one_one_rat ) ) )
% 5.31/5.61 & ( ( X != one_one_rat )
% 5.31/5.61 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_or1269000886237332187st_nat @ M2 @ ( plus_plus_nat @ M2 @ N ) ) )
% 5.31/5.61 = ( divide_divide_rat @ ( times_times_rat @ ( power_power_rat @ X @ M2 ) @ ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X @ ( suc @ N ) ) ) ) @ ( minus_minus_rat @ one_one_rat @ X ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % sum_gp_offset
% 5.31/5.61 thf(fact_6023_sum__gp__offset,axiom,
% 5.31/5.61 ! [X: real,M2: nat,N: nat] :
% 5.31/5.61 ( ( ( X = one_one_real )
% 5.31/5.61 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_or1269000886237332187st_nat @ M2 @ ( plus_plus_nat @ M2 @ N ) ) )
% 5.31/5.61 = ( plus_plus_real @ ( semiri5074537144036343181t_real @ N ) @ one_one_real ) ) )
% 5.31/5.61 & ( ( X != one_one_real )
% 5.31/5.61 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_or1269000886237332187st_nat @ M2 @ ( plus_plus_nat @ M2 @ N ) ) )
% 5.31/5.61 = ( divide_divide_real @ ( times_times_real @ ( power_power_real @ X @ M2 ) @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X @ ( suc @ N ) ) ) ) @ ( minus_minus_real @ one_one_real @ X ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % sum_gp_offset
% 5.31/5.61 thf(fact_6024_vebt__buildup_Osimps_I3_J,axiom,
% 5.31/5.61 ! [Va3: nat] :
% 5.31/5.61 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va3 ) ) )
% 5.31/5.61 => ( ( vEBT_vebt_buildup @ ( suc @ ( suc @ Va3 ) ) )
% 5.31/5.61 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ Va3 ) ) @ ( replicate_VEBT_VEBT @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_buildup @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_buildup @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 5.31/5.61 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va3 ) ) )
% 5.31/5.61 => ( ( vEBT_vebt_buildup @ ( suc @ ( suc @ Va3 ) ) )
% 5.31/5.61 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ Va3 ) ) @ ( replicate_VEBT_VEBT @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_buildup @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_buildup @ ( suc @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % vebt_buildup.simps(3)
% 5.31/5.61 thf(fact_6025_gauss__sum__from__Suc__0,axiom,
% 5.31/5.61 ! [N: nat] :
% 5.31/5.61 ( ( groups7501900531339628137nteger @ semiri4939895301339042750nteger @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) )
% 5.31/5.61 = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ N ) @ ( plus_p5714425477246183910nteger @ ( semiri4939895301339042750nteger @ N ) @ one_one_Code_integer ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % gauss_sum_from_Suc_0
% 5.31/5.61 thf(fact_6026_gauss__sum__from__Suc__0,axiom,
% 5.31/5.61 ! [N: nat] :
% 5.31/5.61 ( ( groups3539618377306564664at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) )
% 5.31/5.61 = ( divide_divide_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % gauss_sum_from_Suc_0
% 5.31/5.61 thf(fact_6027_gauss__sum__from__Suc__0,axiom,
% 5.31/5.61 ! [N: nat] :
% 5.31/5.61 ( ( groups3542108847815614940at_nat @ semiri1316708129612266289at_nat @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) )
% 5.31/5.61 = ( divide_divide_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ N ) @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N ) @ one_one_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % gauss_sum_from_Suc_0
% 5.31/5.61 thf(fact_6028_power__half__series,axiom,
% 5.31/5.61 ( sums_real
% 5.31/5.61 @ ^ [N4: nat] : ( power_power_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( suc @ N4 ) )
% 5.31/5.61 @ one_one_real ) ).
% 5.31/5.61
% 5.31/5.61 % power_half_series
% 5.31/5.61 thf(fact_6029_sums__zero,axiom,
% 5.31/5.61 ( sums_complex
% 5.31/5.61 @ ^ [N4: nat] : zero_zero_complex
% 5.31/5.61 @ zero_zero_complex ) ).
% 5.31/5.61
% 5.31/5.61 % sums_zero
% 5.31/5.61 thf(fact_6030_sums__zero,axiom,
% 5.31/5.61 ( sums_real
% 5.31/5.61 @ ^ [N4: nat] : zero_zero_real
% 5.31/5.61 @ zero_zero_real ) ).
% 5.31/5.61
% 5.31/5.61 % sums_zero
% 5.31/5.61 thf(fact_6031_sums__zero,axiom,
% 5.31/5.61 ( sums_nat
% 5.31/5.61 @ ^ [N4: nat] : zero_zero_nat
% 5.31/5.61 @ zero_zero_nat ) ).
% 5.31/5.61
% 5.31/5.61 % sums_zero
% 5.31/5.61 thf(fact_6032_sums__zero,axiom,
% 5.31/5.61 ( sums_int
% 5.31/5.61 @ ^ [N4: nat] : zero_zero_int
% 5.31/5.61 @ zero_zero_int ) ).
% 5.31/5.61
% 5.31/5.61 % sums_zero
% 5.31/5.61 thf(fact_6033_powser__sums__if,axiom,
% 5.31/5.61 ! [M2: nat,Z3: complex] :
% 5.31/5.61 ( sums_complex
% 5.31/5.61 @ ^ [N4: nat] : ( times_times_complex @ ( if_complex @ ( N4 = M2 ) @ one_one_complex @ zero_zero_complex ) @ ( power_power_complex @ Z3 @ N4 ) )
% 5.31/5.61 @ ( power_power_complex @ Z3 @ M2 ) ) ).
% 5.31/5.61
% 5.31/5.61 % powser_sums_if
% 5.31/5.61 thf(fact_6034_powser__sums__if,axiom,
% 5.31/5.61 ! [M2: nat,Z3: real] :
% 5.31/5.61 ( sums_real
% 5.31/5.61 @ ^ [N4: nat] : ( times_times_real @ ( if_real @ ( N4 = M2 ) @ one_one_real @ zero_zero_real ) @ ( power_power_real @ Z3 @ N4 ) )
% 5.31/5.61 @ ( power_power_real @ Z3 @ M2 ) ) ).
% 5.31/5.61
% 5.31/5.61 % powser_sums_if
% 5.31/5.61 thf(fact_6035_powser__sums__if,axiom,
% 5.31/5.61 ! [M2: nat,Z3: int] :
% 5.31/5.61 ( sums_int
% 5.31/5.61 @ ^ [N4: nat] : ( times_times_int @ ( if_int @ ( N4 = M2 ) @ one_one_int @ zero_zero_int ) @ ( power_power_int @ Z3 @ N4 ) )
% 5.31/5.61 @ ( power_power_int @ Z3 @ M2 ) ) ).
% 5.31/5.61
% 5.31/5.61 % powser_sums_if
% 5.31/5.61 thf(fact_6036_sums__If__finite__set,axiom,
% 5.31/5.61 ! [A4: set_nat,F2: nat > complex] :
% 5.31/5.61 ( ( finite_finite_nat @ A4 )
% 5.31/5.61 => ( sums_complex
% 5.31/5.61 @ ^ [R: nat] : ( if_complex @ ( member_nat @ R @ A4 ) @ ( F2 @ R ) @ zero_zero_complex )
% 5.31/5.61 @ ( groups2073611262835488442omplex @ F2 @ A4 ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % sums_If_finite_set
% 5.31/5.61 thf(fact_6037_sums__If__finite__set,axiom,
% 5.31/5.61 ! [A4: set_nat,F2: nat > int] :
% 5.31/5.61 ( ( finite_finite_nat @ A4 )
% 5.31/5.61 => ( sums_int
% 5.31/5.61 @ ^ [R: nat] : ( if_int @ ( member_nat @ R @ A4 ) @ ( F2 @ R ) @ zero_zero_int )
% 5.31/5.61 @ ( groups3539618377306564664at_int @ F2 @ A4 ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % sums_If_finite_set
% 5.31/5.61 thf(fact_6038_sums__If__finite__set,axiom,
% 5.31/5.61 ! [A4: set_nat,F2: nat > nat] :
% 5.31/5.61 ( ( finite_finite_nat @ A4 )
% 5.31/5.61 => ( sums_nat
% 5.31/5.61 @ ^ [R: nat] : ( if_nat @ ( member_nat @ R @ A4 ) @ ( F2 @ R ) @ zero_zero_nat )
% 5.31/5.61 @ ( groups3542108847815614940at_nat @ F2 @ A4 ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % sums_If_finite_set
% 5.31/5.61 thf(fact_6039_sums__If__finite__set,axiom,
% 5.31/5.61 ! [A4: set_nat,F2: nat > real] :
% 5.31/5.61 ( ( finite_finite_nat @ A4 )
% 5.31/5.61 => ( sums_real
% 5.31/5.61 @ ^ [R: nat] : ( if_real @ ( member_nat @ R @ A4 ) @ ( F2 @ R ) @ zero_zero_real )
% 5.31/5.61 @ ( groups6591440286371151544t_real @ F2 @ A4 ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % sums_If_finite_set
% 5.31/5.61 thf(fact_6040_sums__If__finite,axiom,
% 5.31/5.61 ! [P2: nat > $o,F2: nat > complex] :
% 5.31/5.61 ( ( finite_finite_nat @ ( collect_nat @ P2 ) )
% 5.31/5.61 => ( sums_complex
% 5.31/5.61 @ ^ [R: nat] : ( if_complex @ ( P2 @ R ) @ ( F2 @ R ) @ zero_zero_complex )
% 5.31/5.61 @ ( groups2073611262835488442omplex @ F2 @ ( collect_nat @ P2 ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % sums_If_finite
% 5.31/5.61 thf(fact_6041_sums__If__finite,axiom,
% 5.31/5.61 ! [P2: nat > $o,F2: nat > int] :
% 5.31/5.61 ( ( finite_finite_nat @ ( collect_nat @ P2 ) )
% 5.31/5.61 => ( sums_int
% 5.31/5.61 @ ^ [R: nat] : ( if_int @ ( P2 @ R ) @ ( F2 @ R ) @ zero_zero_int )
% 5.31/5.61 @ ( groups3539618377306564664at_int @ F2 @ ( collect_nat @ P2 ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % sums_If_finite
% 5.31/5.61 thf(fact_6042_sums__If__finite,axiom,
% 5.31/5.61 ! [P2: nat > $o,F2: nat > nat] :
% 5.31/5.61 ( ( finite_finite_nat @ ( collect_nat @ P2 ) )
% 5.31/5.61 => ( sums_nat
% 5.31/5.61 @ ^ [R: nat] : ( if_nat @ ( P2 @ R ) @ ( F2 @ R ) @ zero_zero_nat )
% 5.31/5.61 @ ( groups3542108847815614940at_nat @ F2 @ ( collect_nat @ P2 ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % sums_If_finite
% 5.31/5.61 thf(fact_6043_sums__If__finite,axiom,
% 5.31/5.61 ! [P2: nat > $o,F2: nat > real] :
% 5.31/5.61 ( ( finite_finite_nat @ ( collect_nat @ P2 ) )
% 5.31/5.61 => ( sums_real
% 5.31/5.61 @ ^ [R: nat] : ( if_real @ ( P2 @ R ) @ ( F2 @ R ) @ zero_zero_real )
% 5.31/5.61 @ ( groups6591440286371151544t_real @ F2 @ ( collect_nat @ P2 ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % sums_If_finite
% 5.31/5.61 thf(fact_6044_sums__finite,axiom,
% 5.31/5.61 ! [N6: set_nat,F2: nat > complex] :
% 5.31/5.61 ( ( finite_finite_nat @ N6 )
% 5.31/5.61 => ( ! [N3: nat] :
% 5.31/5.61 ( ~ ( member_nat @ N3 @ N6 )
% 5.31/5.61 => ( ( F2 @ N3 )
% 5.31/5.61 = zero_zero_complex ) )
% 5.31/5.61 => ( sums_complex @ F2 @ ( groups2073611262835488442omplex @ F2 @ N6 ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % sums_finite
% 5.31/5.61 thf(fact_6045_sums__finite,axiom,
% 5.31/5.61 ! [N6: set_nat,F2: nat > int] :
% 5.31/5.61 ( ( finite_finite_nat @ N6 )
% 5.31/5.61 => ( ! [N3: nat] :
% 5.31/5.61 ( ~ ( member_nat @ N3 @ N6 )
% 5.31/5.61 => ( ( F2 @ N3 )
% 5.31/5.61 = zero_zero_int ) )
% 5.31/5.61 => ( sums_int @ F2 @ ( groups3539618377306564664at_int @ F2 @ N6 ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % sums_finite
% 5.31/5.61 thf(fact_6046_sums__finite,axiom,
% 5.31/5.61 ! [N6: set_nat,F2: nat > nat] :
% 5.31/5.61 ( ( finite_finite_nat @ N6 )
% 5.31/5.61 => ( ! [N3: nat] :
% 5.31/5.61 ( ~ ( member_nat @ N3 @ N6 )
% 5.31/5.61 => ( ( F2 @ N3 )
% 5.31/5.61 = zero_zero_nat ) )
% 5.31/5.61 => ( sums_nat @ F2 @ ( groups3542108847815614940at_nat @ F2 @ N6 ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % sums_finite
% 5.31/5.61 thf(fact_6047_sums__finite,axiom,
% 5.31/5.61 ! [N6: set_nat,F2: nat > real] :
% 5.31/5.61 ( ( finite_finite_nat @ N6 )
% 5.31/5.61 => ( ! [N3: nat] :
% 5.31/5.61 ( ~ ( member_nat @ N3 @ N6 )
% 5.31/5.61 => ( ( F2 @ N3 )
% 5.31/5.61 = zero_zero_real ) )
% 5.31/5.61 => ( sums_real @ F2 @ ( groups6591440286371151544t_real @ F2 @ N6 ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % sums_finite
% 5.31/5.61 thf(fact_6048_sums__zero__iff__shift,axiom,
% 5.31/5.61 ! [N: nat,F2: nat > complex,S2: complex] :
% 5.31/5.61 ( ! [I3: nat] :
% 5.31/5.61 ( ( ord_less_nat @ I3 @ N )
% 5.31/5.61 => ( ( F2 @ I3 )
% 5.31/5.61 = zero_zero_complex ) )
% 5.31/5.61 => ( ( sums_complex
% 5.31/5.61 @ ^ [I: nat] : ( F2 @ ( plus_plus_nat @ I @ N ) )
% 5.31/5.61 @ S2 )
% 5.31/5.61 = ( sums_complex @ F2 @ S2 ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % sums_zero_iff_shift
% 5.31/5.61 thf(fact_6049_sums__zero__iff__shift,axiom,
% 5.31/5.61 ! [N: nat,F2: nat > real,S2: real] :
% 5.31/5.61 ( ! [I3: nat] :
% 5.31/5.61 ( ( ord_less_nat @ I3 @ N )
% 5.31/5.61 => ( ( F2 @ I3 )
% 5.31/5.61 = zero_zero_real ) )
% 5.31/5.61 => ( ( sums_real
% 5.31/5.61 @ ^ [I: nat] : ( F2 @ ( plus_plus_nat @ I @ N ) )
% 5.31/5.61 @ S2 )
% 5.31/5.61 = ( sums_real @ F2 @ S2 ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % sums_zero_iff_shift
% 5.31/5.61 thf(fact_6050_zdvd__mono,axiom,
% 5.31/5.61 ! [K2: int,M2: int,T: int] :
% 5.31/5.61 ( ( K2 != zero_zero_int )
% 5.31/5.61 => ( ( dvd_dvd_int @ M2 @ T )
% 5.31/5.61 = ( dvd_dvd_int @ ( times_times_int @ K2 @ M2 ) @ ( times_times_int @ K2 @ T ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % zdvd_mono
% 5.31/5.61 thf(fact_6051_zdvd__mult__cancel,axiom,
% 5.31/5.61 ! [K2: int,M2: int,N: int] :
% 5.31/5.61 ( ( dvd_dvd_int @ ( times_times_int @ K2 @ M2 ) @ ( times_times_int @ K2 @ N ) )
% 5.31/5.61 => ( ( K2 != zero_zero_int )
% 5.31/5.61 => ( dvd_dvd_int @ M2 @ N ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % zdvd_mult_cancel
% 5.31/5.61 thf(fact_6052_zdvd__period,axiom,
% 5.31/5.61 ! [A: int,D: int,X: int,T: int,C2: int] :
% 5.31/5.61 ( ( dvd_dvd_int @ A @ D )
% 5.31/5.61 => ( ( dvd_dvd_int @ A @ ( plus_plus_int @ X @ T ) )
% 5.31/5.61 = ( dvd_dvd_int @ A @ ( plus_plus_int @ ( plus_plus_int @ X @ ( times_times_int @ C2 @ D ) ) @ T ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % zdvd_period
% 5.31/5.61 thf(fact_6053_zdvd__reduce,axiom,
% 5.31/5.61 ! [K2: int,N: int,M2: int] :
% 5.31/5.61 ( ( dvd_dvd_int @ K2 @ ( plus_plus_int @ N @ ( times_times_int @ K2 @ M2 ) ) )
% 5.31/5.61 = ( dvd_dvd_int @ K2 @ N ) ) ).
% 5.31/5.61
% 5.31/5.61 % zdvd_reduce
% 5.31/5.61 thf(fact_6054_sum__subtractf__nat,axiom,
% 5.31/5.61 ! [A4: set_complex,G2: complex > nat,F2: complex > nat] :
% 5.31/5.61 ( ! [X3: complex] :
% 5.31/5.61 ( ( member_complex @ X3 @ A4 )
% 5.31/5.61 => ( ord_less_eq_nat @ ( G2 @ X3 ) @ ( F2 @ X3 ) ) )
% 5.31/5.61 => ( ( groups5693394587270226106ex_nat
% 5.31/5.61 @ ^ [X4: complex] : ( minus_minus_nat @ ( F2 @ X4 ) @ ( G2 @ X4 ) )
% 5.31/5.61 @ A4 )
% 5.31/5.61 = ( minus_minus_nat @ ( groups5693394587270226106ex_nat @ F2 @ A4 ) @ ( groups5693394587270226106ex_nat @ G2 @ A4 ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % sum_subtractf_nat
% 5.31/5.61 thf(fact_6055_sum__subtractf__nat,axiom,
% 5.31/5.61 ! [A4: set_real,G2: real > nat,F2: real > nat] :
% 5.31/5.61 ( ! [X3: real] :
% 5.31/5.61 ( ( member_real @ X3 @ A4 )
% 5.31/5.61 => ( ord_less_eq_nat @ ( G2 @ X3 ) @ ( F2 @ X3 ) ) )
% 5.31/5.61 => ( ( groups1935376822645274424al_nat
% 5.31/5.61 @ ^ [X4: real] : ( minus_minus_nat @ ( F2 @ X4 ) @ ( G2 @ X4 ) )
% 5.31/5.61 @ A4 )
% 5.31/5.61 = ( minus_minus_nat @ ( groups1935376822645274424al_nat @ F2 @ A4 ) @ ( groups1935376822645274424al_nat @ G2 @ A4 ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % sum_subtractf_nat
% 5.31/5.61 thf(fact_6056_sum__subtractf__nat,axiom,
% 5.31/5.61 ! [A4: set_set_nat,G2: set_nat > nat,F2: set_nat > nat] :
% 5.31/5.61 ( ! [X3: set_nat] :
% 5.31/5.61 ( ( member_set_nat @ X3 @ A4 )
% 5.31/5.61 => ( ord_less_eq_nat @ ( G2 @ X3 ) @ ( F2 @ X3 ) ) )
% 5.31/5.61 => ( ( groups8294997508430121362at_nat
% 5.31/5.61 @ ^ [X4: set_nat] : ( minus_minus_nat @ ( F2 @ X4 ) @ ( G2 @ X4 ) )
% 5.31/5.61 @ A4 )
% 5.31/5.61 = ( minus_minus_nat @ ( groups8294997508430121362at_nat @ F2 @ A4 ) @ ( groups8294997508430121362at_nat @ G2 @ A4 ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % sum_subtractf_nat
% 5.31/5.61 thf(fact_6057_sum__subtractf__nat,axiom,
% 5.31/5.61 ! [A4: set_int,G2: int > nat,F2: int > nat] :
% 5.31/5.61 ( ! [X3: int] :
% 5.31/5.61 ( ( member_int @ X3 @ A4 )
% 5.31/5.61 => ( ord_less_eq_nat @ ( G2 @ X3 ) @ ( F2 @ X3 ) ) )
% 5.31/5.61 => ( ( groups4541462559716669496nt_nat
% 5.31/5.61 @ ^ [X4: int] : ( minus_minus_nat @ ( F2 @ X4 ) @ ( G2 @ X4 ) )
% 5.31/5.61 @ A4 )
% 5.31/5.61 = ( minus_minus_nat @ ( groups4541462559716669496nt_nat @ F2 @ A4 ) @ ( groups4541462559716669496nt_nat @ G2 @ A4 ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % sum_subtractf_nat
% 5.31/5.61 thf(fact_6058_sum__subtractf__nat,axiom,
% 5.31/5.61 ! [A4: set_nat,G2: nat > nat,F2: nat > nat] :
% 5.31/5.61 ( ! [X3: nat] :
% 5.31/5.61 ( ( member_nat @ X3 @ A4 )
% 5.31/5.61 => ( ord_less_eq_nat @ ( G2 @ X3 ) @ ( F2 @ X3 ) ) )
% 5.31/5.61 => ( ( groups3542108847815614940at_nat
% 5.31/5.61 @ ^ [X4: nat] : ( minus_minus_nat @ ( F2 @ X4 ) @ ( G2 @ X4 ) )
% 5.31/5.61 @ A4 )
% 5.31/5.61 = ( minus_minus_nat @ ( groups3542108847815614940at_nat @ F2 @ A4 ) @ ( groups3542108847815614940at_nat @ G2 @ A4 ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % sum_subtractf_nat
% 5.31/5.61 thf(fact_6059_sum__eq__Suc0__iff,axiom,
% 5.31/5.61 ! [A4: set_int,F2: int > nat] :
% 5.31/5.61 ( ( finite_finite_int @ A4 )
% 5.31/5.61 => ( ( ( groups4541462559716669496nt_nat @ F2 @ A4 )
% 5.31/5.61 = ( suc @ zero_zero_nat ) )
% 5.31/5.61 = ( ? [X4: int] :
% 5.31/5.61 ( ( member_int @ X4 @ A4 )
% 5.31/5.61 & ( ( F2 @ X4 )
% 5.31/5.61 = ( suc @ zero_zero_nat ) )
% 5.31/5.61 & ! [Y4: int] :
% 5.31/5.61 ( ( member_int @ Y4 @ A4 )
% 5.31/5.61 => ( ( X4 != Y4 )
% 5.31/5.61 => ( ( F2 @ Y4 )
% 5.31/5.61 = zero_zero_nat ) ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % sum_eq_Suc0_iff
% 5.31/5.61 thf(fact_6060_sum__eq__Suc0__iff,axiom,
% 5.31/5.61 ! [A4: set_complex,F2: complex > nat] :
% 5.31/5.61 ( ( finite3207457112153483333omplex @ A4 )
% 5.31/5.61 => ( ( ( groups5693394587270226106ex_nat @ F2 @ A4 )
% 5.31/5.61 = ( suc @ zero_zero_nat ) )
% 5.31/5.61 = ( ? [X4: complex] :
% 5.31/5.61 ( ( member_complex @ X4 @ A4 )
% 5.31/5.61 & ( ( F2 @ X4 )
% 5.31/5.61 = ( suc @ zero_zero_nat ) )
% 5.31/5.61 & ! [Y4: complex] :
% 5.31/5.61 ( ( member_complex @ Y4 @ A4 )
% 5.31/5.61 => ( ( X4 != Y4 )
% 5.31/5.61 => ( ( F2 @ Y4 )
% 5.31/5.61 = zero_zero_nat ) ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % sum_eq_Suc0_iff
% 5.31/5.61 thf(fact_6061_sum__eq__Suc0__iff,axiom,
% 5.31/5.61 ! [A4: set_nat,F2: nat > nat] :
% 5.31/5.61 ( ( finite_finite_nat @ A4 )
% 5.31/5.61 => ( ( ( groups3542108847815614940at_nat @ F2 @ A4 )
% 5.31/5.61 = ( suc @ zero_zero_nat ) )
% 5.31/5.61 = ( ? [X4: nat] :
% 5.31/5.61 ( ( member_nat @ X4 @ A4 )
% 5.31/5.61 & ( ( F2 @ X4 )
% 5.31/5.61 = ( suc @ zero_zero_nat ) )
% 5.31/5.61 & ! [Y4: nat] :
% 5.31/5.61 ( ( member_nat @ Y4 @ A4 )
% 5.31/5.61 => ( ( X4 != Y4 )
% 5.31/5.61 => ( ( F2 @ Y4 )
% 5.31/5.61 = zero_zero_nat ) ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % sum_eq_Suc0_iff
% 5.31/5.61 thf(fact_6062_sum__SucD,axiom,
% 5.31/5.61 ! [F2: nat > nat,A4: set_nat,N: nat] :
% 5.31/5.61 ( ( ( groups3542108847815614940at_nat @ F2 @ A4 )
% 5.31/5.61 = ( suc @ N ) )
% 5.31/5.61 => ? [X3: nat] :
% 5.31/5.61 ( ( member_nat @ X3 @ A4 )
% 5.31/5.61 & ( ord_less_nat @ zero_zero_nat @ ( F2 @ X3 ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % sum_SucD
% 5.31/5.61 thf(fact_6063_sum__eq__1__iff,axiom,
% 5.31/5.61 ! [A4: set_int,F2: int > nat] :
% 5.31/5.61 ( ( finite_finite_int @ A4 )
% 5.31/5.61 => ( ( ( groups4541462559716669496nt_nat @ F2 @ A4 )
% 5.31/5.61 = one_one_nat )
% 5.31/5.61 = ( ? [X4: int] :
% 5.31/5.61 ( ( member_int @ X4 @ A4 )
% 5.31/5.61 & ( ( F2 @ X4 )
% 5.31/5.61 = one_one_nat )
% 5.31/5.61 & ! [Y4: int] :
% 5.31/5.61 ( ( member_int @ Y4 @ A4 )
% 5.31/5.61 => ( ( X4 != Y4 )
% 5.31/5.61 => ( ( F2 @ Y4 )
% 5.31/5.61 = zero_zero_nat ) ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % sum_eq_1_iff
% 5.31/5.61 thf(fact_6064_sum__eq__1__iff,axiom,
% 5.31/5.61 ! [A4: set_complex,F2: complex > nat] :
% 5.31/5.61 ( ( finite3207457112153483333omplex @ A4 )
% 5.31/5.61 => ( ( ( groups5693394587270226106ex_nat @ F2 @ A4 )
% 5.31/5.61 = one_one_nat )
% 5.31/5.61 = ( ? [X4: complex] :
% 5.31/5.61 ( ( member_complex @ X4 @ A4 )
% 5.31/5.61 & ( ( F2 @ X4 )
% 5.31/5.61 = one_one_nat )
% 5.31/5.61 & ! [Y4: complex] :
% 5.31/5.61 ( ( member_complex @ Y4 @ A4 )
% 5.31/5.61 => ( ( X4 != Y4 )
% 5.31/5.61 => ( ( F2 @ Y4 )
% 5.31/5.61 = zero_zero_nat ) ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % sum_eq_1_iff
% 5.31/5.61 thf(fact_6065_sum__eq__1__iff,axiom,
% 5.31/5.61 ! [A4: set_nat,F2: nat > nat] :
% 5.31/5.61 ( ( finite_finite_nat @ A4 )
% 5.31/5.61 => ( ( ( groups3542108847815614940at_nat @ F2 @ A4 )
% 5.31/5.61 = one_one_nat )
% 5.31/5.61 = ( ? [X4: nat] :
% 5.31/5.61 ( ( member_nat @ X4 @ A4 )
% 5.31/5.61 & ( ( F2 @ X4 )
% 5.31/5.61 = one_one_nat )
% 5.31/5.61 & ! [Y4: nat] :
% 5.31/5.61 ( ( member_nat @ Y4 @ A4 )
% 5.31/5.61 => ( ( X4 != Y4 )
% 5.31/5.61 => ( ( F2 @ Y4 )
% 5.31/5.61 = zero_zero_nat ) ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % sum_eq_1_iff
% 5.31/5.61 thf(fact_6066_sum__Suc,axiom,
% 5.31/5.61 ! [F2: complex > nat,A4: set_complex] :
% 5.31/5.61 ( ( groups5693394587270226106ex_nat
% 5.31/5.61 @ ^ [X4: complex] : ( suc @ ( F2 @ X4 ) )
% 5.31/5.61 @ A4 )
% 5.31/5.61 = ( plus_plus_nat @ ( groups5693394587270226106ex_nat @ F2 @ A4 ) @ ( finite_card_complex @ A4 ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % sum_Suc
% 5.31/5.61 thf(fact_6067_sum__Suc,axiom,
% 5.31/5.61 ! [F2: int > nat,A4: set_int] :
% 5.31/5.61 ( ( groups4541462559716669496nt_nat
% 5.31/5.61 @ ^ [X4: int] : ( suc @ ( F2 @ X4 ) )
% 5.31/5.61 @ A4 )
% 5.31/5.61 = ( plus_plus_nat @ ( groups4541462559716669496nt_nat @ F2 @ A4 ) @ ( finite_card_int @ A4 ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % sum_Suc
% 5.31/5.61 thf(fact_6068_sum__Suc,axiom,
% 5.31/5.61 ! [F2: list_nat > nat,A4: set_list_nat] :
% 5.31/5.61 ( ( groups4396056296759096172at_nat
% 5.31/5.61 @ ^ [X4: list_nat] : ( suc @ ( F2 @ X4 ) )
% 5.31/5.61 @ A4 )
% 5.31/5.61 = ( plus_plus_nat @ ( groups4396056296759096172at_nat @ F2 @ A4 ) @ ( finite_card_list_nat @ A4 ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % sum_Suc
% 5.31/5.61 thf(fact_6069_sum__Suc,axiom,
% 5.31/5.61 ! [F2: set_nat > nat,A4: set_set_nat] :
% 5.31/5.61 ( ( groups8294997508430121362at_nat
% 5.31/5.61 @ ^ [X4: set_nat] : ( suc @ ( F2 @ X4 ) )
% 5.31/5.61 @ A4 )
% 5.31/5.61 = ( plus_plus_nat @ ( groups8294997508430121362at_nat @ F2 @ A4 ) @ ( finite_card_set_nat @ A4 ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % sum_Suc
% 5.31/5.61 thf(fact_6070_sum__Suc,axiom,
% 5.31/5.61 ! [F2: nat > nat,A4: set_nat] :
% 5.31/5.61 ( ( groups3542108847815614940at_nat
% 5.31/5.61 @ ^ [X4: nat] : ( suc @ ( F2 @ X4 ) )
% 5.31/5.61 @ A4 )
% 5.31/5.61 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ F2 @ A4 ) @ ( finite_card_nat @ A4 ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % sum_Suc
% 5.31/5.61 thf(fact_6071_sum__multicount,axiom,
% 5.31/5.61 ! [S3: set_real,T5: set_real,R2: real > real > $o,K2: nat] :
% 5.31/5.61 ( ( finite_finite_real @ S3 )
% 5.31/5.61 => ( ( finite_finite_real @ T5 )
% 5.31/5.61 => ( ! [X3: real] :
% 5.31/5.61 ( ( member_real @ X3 @ T5 )
% 5.31/5.61 => ( ( finite_card_real
% 5.31/5.61 @ ( collect_real
% 5.31/5.61 @ ^ [I: real] :
% 5.31/5.61 ( ( member_real @ I @ S3 )
% 5.31/5.61 & ( R2 @ I @ X3 ) ) ) )
% 5.31/5.61 = K2 ) )
% 5.31/5.61 => ( ( groups1935376822645274424al_nat
% 5.31/5.61 @ ^ [I: real] :
% 5.31/5.61 ( finite_card_real
% 5.31/5.61 @ ( collect_real
% 5.31/5.61 @ ^ [J: real] :
% 5.31/5.61 ( ( member_real @ J @ T5 )
% 5.31/5.61 & ( R2 @ I @ J ) ) ) )
% 5.31/5.61 @ S3 )
% 5.31/5.61 = ( times_times_nat @ K2 @ ( finite_card_real @ T5 ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % sum_multicount
% 5.31/5.61 thf(fact_6072_sum__multicount,axiom,
% 5.31/5.61 ! [S3: set_real,T5: set_nat,R2: real > nat > $o,K2: nat] :
% 5.31/5.61 ( ( finite_finite_real @ S3 )
% 5.31/5.61 => ( ( finite_finite_nat @ T5 )
% 5.31/5.61 => ( ! [X3: nat] :
% 5.31/5.61 ( ( member_nat @ X3 @ T5 )
% 5.31/5.61 => ( ( finite_card_real
% 5.31/5.61 @ ( collect_real
% 5.31/5.61 @ ^ [I: real] :
% 5.31/5.61 ( ( member_real @ I @ S3 )
% 5.31/5.61 & ( R2 @ I @ X3 ) ) ) )
% 5.31/5.61 = K2 ) )
% 5.31/5.61 => ( ( groups1935376822645274424al_nat
% 5.31/5.61 @ ^ [I: real] :
% 5.31/5.61 ( finite_card_nat
% 5.31/5.61 @ ( collect_nat
% 5.31/5.61 @ ^ [J: nat] :
% 5.31/5.61 ( ( member_nat @ J @ T5 )
% 5.31/5.61 & ( R2 @ I @ J ) ) ) )
% 5.31/5.61 @ S3 )
% 5.31/5.61 = ( times_times_nat @ K2 @ ( finite_card_nat @ T5 ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % sum_multicount
% 5.31/5.61 thf(fact_6073_sum__multicount,axiom,
% 5.31/5.61 ! [S3: set_real,T5: set_int,R2: real > int > $o,K2: nat] :
% 5.31/5.61 ( ( finite_finite_real @ S3 )
% 5.31/5.61 => ( ( finite_finite_int @ T5 )
% 5.31/5.61 => ( ! [X3: int] :
% 5.31/5.61 ( ( member_int @ X3 @ T5 )
% 5.31/5.61 => ( ( finite_card_real
% 5.31/5.61 @ ( collect_real
% 5.31/5.61 @ ^ [I: real] :
% 5.31/5.61 ( ( member_real @ I @ S3 )
% 5.31/5.61 & ( R2 @ I @ X3 ) ) ) )
% 5.31/5.61 = K2 ) )
% 5.31/5.61 => ( ( groups1935376822645274424al_nat
% 5.31/5.61 @ ^ [I: real] :
% 5.31/5.61 ( finite_card_int
% 5.31/5.61 @ ( collect_int
% 5.31/5.61 @ ^ [J: int] :
% 5.31/5.61 ( ( member_int @ J @ T5 )
% 5.31/5.61 & ( R2 @ I @ J ) ) ) )
% 5.31/5.61 @ S3 )
% 5.31/5.61 = ( times_times_nat @ K2 @ ( finite_card_int @ T5 ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % sum_multicount
% 5.31/5.61 thf(fact_6074_sum__multicount,axiom,
% 5.31/5.61 ! [S3: set_real,T5: set_complex,R2: real > complex > $o,K2: nat] :
% 5.31/5.61 ( ( finite_finite_real @ S3 )
% 5.31/5.61 => ( ( finite3207457112153483333omplex @ T5 )
% 5.31/5.61 => ( ! [X3: complex] :
% 5.31/5.61 ( ( member_complex @ X3 @ T5 )
% 5.31/5.61 => ( ( finite_card_real
% 5.31/5.61 @ ( collect_real
% 5.31/5.61 @ ^ [I: real] :
% 5.31/5.61 ( ( member_real @ I @ S3 )
% 5.31/5.61 & ( R2 @ I @ X3 ) ) ) )
% 5.31/5.61 = K2 ) )
% 5.31/5.61 => ( ( groups1935376822645274424al_nat
% 5.31/5.61 @ ^ [I: real] :
% 5.31/5.61 ( finite_card_complex
% 5.31/5.61 @ ( collect_complex
% 5.31/5.61 @ ^ [J: complex] :
% 5.31/5.61 ( ( member_complex @ J @ T5 )
% 5.31/5.61 & ( R2 @ I @ J ) ) ) )
% 5.31/5.61 @ S3 )
% 5.31/5.61 = ( times_times_nat @ K2 @ ( finite_card_complex @ T5 ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % sum_multicount
% 5.31/5.61 thf(fact_6075_sum__multicount,axiom,
% 5.31/5.61 ! [S3: set_int,T5: set_real,R2: int > real > $o,K2: nat] :
% 5.31/5.61 ( ( finite_finite_int @ S3 )
% 5.31/5.61 => ( ( finite_finite_real @ T5 )
% 5.31/5.61 => ( ! [X3: real] :
% 5.31/5.61 ( ( member_real @ X3 @ T5 )
% 5.31/5.61 => ( ( finite_card_int
% 5.31/5.61 @ ( collect_int
% 5.31/5.61 @ ^ [I: int] :
% 5.31/5.61 ( ( member_int @ I @ S3 )
% 5.31/5.61 & ( R2 @ I @ X3 ) ) ) )
% 5.31/5.61 = K2 ) )
% 5.31/5.61 => ( ( groups4541462559716669496nt_nat
% 5.31/5.61 @ ^ [I: int] :
% 5.31/5.61 ( finite_card_real
% 5.31/5.61 @ ( collect_real
% 5.31/5.61 @ ^ [J: real] :
% 5.31/5.61 ( ( member_real @ J @ T5 )
% 5.31/5.61 & ( R2 @ I @ J ) ) ) )
% 5.31/5.61 @ S3 )
% 5.31/5.61 = ( times_times_nat @ K2 @ ( finite_card_real @ T5 ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % sum_multicount
% 5.31/5.61 thf(fact_6076_sum__multicount,axiom,
% 5.31/5.61 ! [S3: set_int,T5: set_nat,R2: int > nat > $o,K2: nat] :
% 5.31/5.61 ( ( finite_finite_int @ S3 )
% 5.31/5.61 => ( ( finite_finite_nat @ T5 )
% 5.31/5.61 => ( ! [X3: nat] :
% 5.31/5.61 ( ( member_nat @ X3 @ T5 )
% 5.31/5.61 => ( ( finite_card_int
% 5.31/5.61 @ ( collect_int
% 5.31/5.61 @ ^ [I: int] :
% 5.31/5.61 ( ( member_int @ I @ S3 )
% 5.31/5.61 & ( R2 @ I @ X3 ) ) ) )
% 5.31/5.61 = K2 ) )
% 5.31/5.61 => ( ( groups4541462559716669496nt_nat
% 5.31/5.61 @ ^ [I: int] :
% 5.31/5.61 ( finite_card_nat
% 5.31/5.61 @ ( collect_nat
% 5.31/5.61 @ ^ [J: nat] :
% 5.31/5.61 ( ( member_nat @ J @ T5 )
% 5.31/5.61 & ( R2 @ I @ J ) ) ) )
% 5.31/5.61 @ S3 )
% 5.31/5.61 = ( times_times_nat @ K2 @ ( finite_card_nat @ T5 ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % sum_multicount
% 5.31/5.61 thf(fact_6077_sum__multicount,axiom,
% 5.31/5.61 ! [S3: set_int,T5: set_int,R2: int > int > $o,K2: nat] :
% 5.31/5.61 ( ( finite_finite_int @ S3 )
% 5.31/5.61 => ( ( finite_finite_int @ T5 )
% 5.31/5.61 => ( ! [X3: int] :
% 5.31/5.61 ( ( member_int @ X3 @ T5 )
% 5.31/5.61 => ( ( finite_card_int
% 5.31/5.61 @ ( collect_int
% 5.31/5.61 @ ^ [I: int] :
% 5.31/5.61 ( ( member_int @ I @ S3 )
% 5.31/5.61 & ( R2 @ I @ X3 ) ) ) )
% 5.31/5.61 = K2 ) )
% 5.31/5.61 => ( ( groups4541462559716669496nt_nat
% 5.31/5.61 @ ^ [I: int] :
% 5.31/5.61 ( finite_card_int
% 5.31/5.61 @ ( collect_int
% 5.31/5.61 @ ^ [J: int] :
% 5.31/5.61 ( ( member_int @ J @ T5 )
% 5.31/5.61 & ( R2 @ I @ J ) ) ) )
% 5.31/5.61 @ S3 )
% 5.31/5.61 = ( times_times_nat @ K2 @ ( finite_card_int @ T5 ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % sum_multicount
% 5.31/5.61 thf(fact_6078_sum__multicount,axiom,
% 5.31/5.61 ! [S3: set_int,T5: set_complex,R2: int > complex > $o,K2: nat] :
% 5.31/5.61 ( ( finite_finite_int @ S3 )
% 5.31/5.61 => ( ( finite3207457112153483333omplex @ T5 )
% 5.31/5.61 => ( ! [X3: complex] :
% 5.31/5.61 ( ( member_complex @ X3 @ T5 )
% 5.31/5.61 => ( ( finite_card_int
% 5.31/5.61 @ ( collect_int
% 5.31/5.61 @ ^ [I: int] :
% 5.31/5.61 ( ( member_int @ I @ S3 )
% 5.31/5.61 & ( R2 @ I @ X3 ) ) ) )
% 5.31/5.61 = K2 ) )
% 5.31/5.61 => ( ( groups4541462559716669496nt_nat
% 5.31/5.61 @ ^ [I: int] :
% 5.31/5.61 ( finite_card_complex
% 5.31/5.61 @ ( collect_complex
% 5.31/5.61 @ ^ [J: complex] :
% 5.31/5.61 ( ( member_complex @ J @ T5 )
% 5.31/5.61 & ( R2 @ I @ J ) ) ) )
% 5.31/5.61 @ S3 )
% 5.31/5.61 = ( times_times_nat @ K2 @ ( finite_card_complex @ T5 ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % sum_multicount
% 5.31/5.61 thf(fact_6079_sum__multicount,axiom,
% 5.31/5.61 ! [S3: set_complex,T5: set_real,R2: complex > real > $o,K2: nat] :
% 5.31/5.61 ( ( finite3207457112153483333omplex @ S3 )
% 5.31/5.61 => ( ( finite_finite_real @ T5 )
% 5.31/5.61 => ( ! [X3: real] :
% 5.31/5.61 ( ( member_real @ X3 @ T5 )
% 5.31/5.61 => ( ( finite_card_complex
% 5.31/5.61 @ ( collect_complex
% 5.31/5.61 @ ^ [I: complex] :
% 5.31/5.61 ( ( member_complex @ I @ S3 )
% 5.31/5.61 & ( R2 @ I @ X3 ) ) ) )
% 5.31/5.61 = K2 ) )
% 5.31/5.61 => ( ( groups5693394587270226106ex_nat
% 5.31/5.61 @ ^ [I: complex] :
% 5.31/5.61 ( finite_card_real
% 5.31/5.61 @ ( collect_real
% 5.31/5.61 @ ^ [J: real] :
% 5.31/5.61 ( ( member_real @ J @ T5 )
% 5.31/5.61 & ( R2 @ I @ J ) ) ) )
% 5.31/5.61 @ S3 )
% 5.31/5.61 = ( times_times_nat @ K2 @ ( finite_card_real @ T5 ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % sum_multicount
% 5.31/5.61 thf(fact_6080_sum__multicount,axiom,
% 5.31/5.61 ! [S3: set_complex,T5: set_nat,R2: complex > nat > $o,K2: nat] :
% 5.31/5.61 ( ( finite3207457112153483333omplex @ S3 )
% 5.31/5.61 => ( ( finite_finite_nat @ T5 )
% 5.31/5.61 => ( ! [X3: nat] :
% 5.31/5.61 ( ( member_nat @ X3 @ T5 )
% 5.31/5.61 => ( ( finite_card_complex
% 5.31/5.61 @ ( collect_complex
% 5.31/5.61 @ ^ [I: complex] :
% 5.31/5.61 ( ( member_complex @ I @ S3 )
% 5.31/5.61 & ( R2 @ I @ X3 ) ) ) )
% 5.31/5.61 = K2 ) )
% 5.31/5.61 => ( ( groups5693394587270226106ex_nat
% 5.31/5.61 @ ^ [I: complex] :
% 5.31/5.61 ( finite_card_nat
% 5.31/5.61 @ ( collect_nat
% 5.31/5.61 @ ^ [J: nat] :
% 5.31/5.61 ( ( member_nat @ J @ T5 )
% 5.31/5.61 & ( R2 @ I @ J ) ) ) )
% 5.31/5.61 @ S3 )
% 5.31/5.61 = ( times_times_nat @ K2 @ ( finite_card_nat @ T5 ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % sum_multicount
% 5.31/5.61 thf(fact_6081_mod__int__pos__iff,axiom,
% 5.31/5.61 ! [K2: int,L: int] :
% 5.31/5.61 ( ( ord_less_eq_int @ zero_zero_int @ ( modulo_modulo_int @ K2 @ L ) )
% 5.31/5.61 = ( ( dvd_dvd_int @ L @ K2 )
% 5.31/5.61 | ( ( L = zero_zero_int )
% 5.31/5.61 & ( ord_less_eq_int @ zero_zero_int @ K2 ) )
% 5.31/5.61 | ( ord_less_int @ zero_zero_int @ L ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % mod_int_pos_iff
% 5.31/5.61 thf(fact_6082_sum__count__set,axiom,
% 5.31/5.61 ! [Xs2: list_complex,X8: set_complex] :
% 5.31/5.61 ( ( ord_le211207098394363844omplex @ ( set_complex2 @ Xs2 ) @ X8 )
% 5.31/5.61 => ( ( finite3207457112153483333omplex @ X8 )
% 5.31/5.61 => ( ( groups5693394587270226106ex_nat @ ( count_list_complex @ Xs2 ) @ X8 )
% 5.31/5.61 = ( size_s3451745648224563538omplex @ Xs2 ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % sum_count_set
% 5.31/5.61 thf(fact_6083_sum__count__set,axiom,
% 5.31/5.61 ! [Xs2: list_VEBT_VEBT,X8: set_VEBT_VEBT] :
% 5.31/5.61 ( ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ Xs2 ) @ X8 )
% 5.31/5.61 => ( ( finite5795047828879050333T_VEBT @ X8 )
% 5.31/5.61 => ( ( groups771621172384141258BT_nat @ ( count_list_VEBT_VEBT @ Xs2 ) @ X8 )
% 5.31/5.61 = ( size_s6755466524823107622T_VEBT @ Xs2 ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % sum_count_set
% 5.31/5.61 thf(fact_6084_sum__count__set,axiom,
% 5.31/5.61 ! [Xs2: list_o,X8: set_o] :
% 5.31/5.61 ( ( ord_less_eq_set_o @ ( set_o2 @ Xs2 ) @ X8 )
% 5.31/5.61 => ( ( finite_finite_o @ X8 )
% 5.31/5.61 => ( ( groups8507830703676809646_o_nat @ ( count_list_o @ Xs2 ) @ X8 )
% 5.31/5.61 = ( size_size_list_o @ Xs2 ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % sum_count_set
% 5.31/5.61 thf(fact_6085_sum__count__set,axiom,
% 5.31/5.61 ! [Xs2: list_int,X8: set_int] :
% 5.31/5.61 ( ( ord_less_eq_set_int @ ( set_int2 @ Xs2 ) @ X8 )
% 5.31/5.61 => ( ( finite_finite_int @ X8 )
% 5.31/5.61 => ( ( groups4541462559716669496nt_nat @ ( count_list_int @ Xs2 ) @ X8 )
% 5.31/5.61 = ( size_size_list_int @ Xs2 ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % sum_count_set
% 5.31/5.61 thf(fact_6086_sum__count__set,axiom,
% 5.31/5.61 ! [Xs2: list_nat,X8: set_nat] :
% 5.31/5.61 ( ( ord_less_eq_set_nat @ ( set_nat2 @ Xs2 ) @ X8 )
% 5.31/5.61 => ( ( finite_finite_nat @ X8 )
% 5.31/5.61 => ( ( groups3542108847815614940at_nat @ ( count_list_nat @ Xs2 ) @ X8 )
% 5.31/5.61 = ( size_size_list_nat @ Xs2 ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % sum_count_set
% 5.31/5.61 thf(fact_6087_sums__le,axiom,
% 5.31/5.61 ! [F2: nat > real,G2: nat > real,S2: real,T: real] :
% 5.31/5.61 ( ! [N3: nat] : ( ord_less_eq_real @ ( F2 @ N3 ) @ ( G2 @ N3 ) )
% 5.31/5.61 => ( ( sums_real @ F2 @ S2 )
% 5.31/5.61 => ( ( sums_real @ G2 @ T )
% 5.31/5.61 => ( ord_less_eq_real @ S2 @ T ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % sums_le
% 5.31/5.61 thf(fact_6088_sums__le,axiom,
% 5.31/5.61 ! [F2: nat > nat,G2: nat > nat,S2: nat,T: nat] :
% 5.31/5.61 ( ! [N3: nat] : ( ord_less_eq_nat @ ( F2 @ N3 ) @ ( G2 @ N3 ) )
% 5.31/5.61 => ( ( sums_nat @ F2 @ S2 )
% 5.31/5.61 => ( ( sums_nat @ G2 @ T )
% 5.31/5.61 => ( ord_less_eq_nat @ S2 @ T ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % sums_le
% 5.31/5.61 thf(fact_6089_sums__le,axiom,
% 5.31/5.61 ! [F2: nat > int,G2: nat > int,S2: int,T: int] :
% 5.31/5.61 ( ! [N3: nat] : ( ord_less_eq_int @ ( F2 @ N3 ) @ ( G2 @ N3 ) )
% 5.31/5.61 => ( ( sums_int @ F2 @ S2 )
% 5.31/5.61 => ( ( sums_int @ G2 @ T )
% 5.31/5.61 => ( ord_less_eq_int @ S2 @ T ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % sums_le
% 5.31/5.61 thf(fact_6090_sums__0,axiom,
% 5.31/5.61 ! [F2: nat > complex] :
% 5.31/5.61 ( ! [N3: nat] :
% 5.31/5.61 ( ( F2 @ N3 )
% 5.31/5.61 = zero_zero_complex )
% 5.31/5.61 => ( sums_complex @ F2 @ zero_zero_complex ) ) ).
% 5.31/5.61
% 5.31/5.61 % sums_0
% 5.31/5.61 thf(fact_6091_sums__0,axiom,
% 5.31/5.61 ! [F2: nat > real] :
% 5.31/5.61 ( ! [N3: nat] :
% 5.31/5.61 ( ( F2 @ N3 )
% 5.31/5.61 = zero_zero_real )
% 5.31/5.61 => ( sums_real @ F2 @ zero_zero_real ) ) ).
% 5.31/5.61
% 5.31/5.61 % sums_0
% 5.31/5.61 thf(fact_6092_sums__0,axiom,
% 5.31/5.61 ! [F2: nat > nat] :
% 5.31/5.61 ( ! [N3: nat] :
% 5.31/5.61 ( ( F2 @ N3 )
% 5.31/5.61 = zero_zero_nat )
% 5.31/5.61 => ( sums_nat @ F2 @ zero_zero_nat ) ) ).
% 5.31/5.61
% 5.31/5.61 % sums_0
% 5.31/5.61 thf(fact_6093_sums__0,axiom,
% 5.31/5.61 ! [F2: nat > int] :
% 5.31/5.61 ( ! [N3: nat] :
% 5.31/5.61 ( ( F2 @ N3 )
% 5.31/5.61 = zero_zero_int )
% 5.31/5.61 => ( sums_int @ F2 @ zero_zero_int ) ) ).
% 5.31/5.61
% 5.31/5.61 % sums_0
% 5.31/5.61 thf(fact_6094_sums__single,axiom,
% 5.31/5.61 ! [I2: nat,F2: nat > complex] :
% 5.31/5.61 ( sums_complex
% 5.31/5.61 @ ^ [R: nat] : ( if_complex @ ( R = I2 ) @ ( F2 @ R ) @ zero_zero_complex )
% 5.31/5.61 @ ( F2 @ I2 ) ) ).
% 5.31/5.61
% 5.31/5.61 % sums_single
% 5.31/5.61 thf(fact_6095_sums__single,axiom,
% 5.31/5.61 ! [I2: nat,F2: nat > real] :
% 5.31/5.61 ( sums_real
% 5.31/5.61 @ ^ [R: nat] : ( if_real @ ( R = I2 ) @ ( F2 @ R ) @ zero_zero_real )
% 5.31/5.61 @ ( F2 @ I2 ) ) ).
% 5.31/5.61
% 5.31/5.61 % sums_single
% 5.31/5.61 thf(fact_6096_sums__single,axiom,
% 5.31/5.61 ! [I2: nat,F2: nat > nat] :
% 5.31/5.61 ( sums_nat
% 5.31/5.61 @ ^ [R: nat] : ( if_nat @ ( R = I2 ) @ ( F2 @ R ) @ zero_zero_nat )
% 5.31/5.61 @ ( F2 @ I2 ) ) ).
% 5.31/5.61
% 5.31/5.61 % sums_single
% 5.31/5.61 thf(fact_6097_sums__single,axiom,
% 5.31/5.61 ! [I2: nat,F2: nat > int] :
% 5.31/5.61 ( sums_int
% 5.31/5.61 @ ^ [R: nat] : ( if_int @ ( R = I2 ) @ ( F2 @ R ) @ zero_zero_int )
% 5.31/5.61 @ ( F2 @ I2 ) ) ).
% 5.31/5.61
% 5.31/5.61 % sums_single
% 5.31/5.61 thf(fact_6098_sums__mult2,axiom,
% 5.31/5.61 ! [F2: nat > real,A: real,C2: real] :
% 5.31/5.61 ( ( sums_real @ F2 @ A )
% 5.31/5.61 => ( sums_real
% 5.31/5.61 @ ^ [N4: nat] : ( times_times_real @ ( F2 @ N4 ) @ C2 )
% 5.31/5.61 @ ( times_times_real @ A @ C2 ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % sums_mult2
% 5.31/5.61 thf(fact_6099_sums__mult,axiom,
% 5.31/5.61 ! [F2: nat > real,A: real,C2: real] :
% 5.31/5.61 ( ( sums_real @ F2 @ A )
% 5.31/5.61 => ( sums_real
% 5.31/5.61 @ ^ [N4: nat] : ( times_times_real @ C2 @ ( F2 @ N4 ) )
% 5.31/5.61 @ ( times_times_real @ C2 @ A ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % sums_mult
% 5.31/5.61 thf(fact_6100_Sum__Icc__int,axiom,
% 5.31/5.61 ! [M2: int,N: int] :
% 5.31/5.61 ( ( ord_less_eq_int @ M2 @ N )
% 5.31/5.61 => ( ( groups4538972089207619220nt_int
% 5.31/5.61 @ ^ [X4: int] : X4
% 5.31/5.61 @ ( set_or1266510415728281911st_int @ M2 @ N ) )
% 5.31/5.61 = ( divide_divide_int @ ( minus_minus_int @ ( times_times_int @ N @ ( plus_plus_int @ N @ one_one_int ) ) @ ( times_times_int @ M2 @ ( minus_minus_int @ M2 @ one_one_int ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % Sum_Icc_int
% 5.31/5.61 thf(fact_6101_sums__mult__iff,axiom,
% 5.31/5.61 ! [C2: complex,F2: nat > complex,D: complex] :
% 5.31/5.61 ( ( C2 != zero_zero_complex )
% 5.31/5.61 => ( ( sums_complex
% 5.31/5.61 @ ^ [N4: nat] : ( times_times_complex @ C2 @ ( F2 @ N4 ) )
% 5.31/5.61 @ ( times_times_complex @ C2 @ D ) )
% 5.31/5.61 = ( sums_complex @ F2 @ D ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % sums_mult_iff
% 5.31/5.61 thf(fact_6102_sums__mult__iff,axiom,
% 5.31/5.61 ! [C2: real,F2: nat > real,D: real] :
% 5.31/5.61 ( ( C2 != zero_zero_real )
% 5.31/5.61 => ( ( sums_real
% 5.31/5.61 @ ^ [N4: nat] : ( times_times_real @ C2 @ ( F2 @ N4 ) )
% 5.31/5.61 @ ( times_times_real @ C2 @ D ) )
% 5.31/5.61 = ( sums_real @ F2 @ D ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % sums_mult_iff
% 5.31/5.61 thf(fact_6103_sums__mult2__iff,axiom,
% 5.31/5.61 ! [C2: complex,F2: nat > complex,D: complex] :
% 5.31/5.61 ( ( C2 != zero_zero_complex )
% 5.31/5.61 => ( ( sums_complex
% 5.31/5.61 @ ^ [N4: nat] : ( times_times_complex @ ( F2 @ N4 ) @ C2 )
% 5.31/5.61 @ ( times_times_complex @ D @ C2 ) )
% 5.31/5.61 = ( sums_complex @ F2 @ D ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % sums_mult2_iff
% 5.31/5.61 thf(fact_6104_sums__mult2__iff,axiom,
% 5.31/5.61 ! [C2: real,F2: nat > real,D: real] :
% 5.31/5.61 ( ( C2 != zero_zero_real )
% 5.31/5.61 => ( ( sums_real
% 5.31/5.61 @ ^ [N4: nat] : ( times_times_real @ ( F2 @ N4 ) @ C2 )
% 5.31/5.61 @ ( times_times_real @ D @ C2 ) )
% 5.31/5.61 = ( sums_real @ F2 @ D ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % sums_mult2_iff
% 5.31/5.61 thf(fact_6105_sums__mult__D,axiom,
% 5.31/5.61 ! [C2: complex,F2: nat > complex,A: complex] :
% 5.31/5.61 ( ( sums_complex
% 5.31/5.61 @ ^ [N4: nat] : ( times_times_complex @ C2 @ ( F2 @ N4 ) )
% 5.31/5.61 @ A )
% 5.31/5.61 => ( ( C2 != zero_zero_complex )
% 5.31/5.61 => ( sums_complex @ F2 @ ( divide1717551699836669952omplex @ A @ C2 ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % sums_mult_D
% 5.31/5.61 thf(fact_6106_sums__mult__D,axiom,
% 5.31/5.61 ! [C2: real,F2: nat > real,A: real] :
% 5.31/5.61 ( ( sums_real
% 5.31/5.61 @ ^ [N4: nat] : ( times_times_real @ C2 @ ( F2 @ N4 ) )
% 5.31/5.61 @ A )
% 5.31/5.61 => ( ( C2 != zero_zero_real )
% 5.31/5.61 => ( sums_real @ F2 @ ( divide_divide_real @ A @ C2 ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % sums_mult_D
% 5.31/5.61 thf(fact_6107_sums__Suc__imp,axiom,
% 5.31/5.61 ! [F2: nat > complex,S2: complex] :
% 5.31/5.61 ( ( ( F2 @ zero_zero_nat )
% 5.31/5.61 = zero_zero_complex )
% 5.31/5.61 => ( ( sums_complex
% 5.31/5.61 @ ^ [N4: nat] : ( F2 @ ( suc @ N4 ) )
% 5.31/5.61 @ S2 )
% 5.31/5.61 => ( sums_complex @ F2 @ S2 ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % sums_Suc_imp
% 5.31/5.61 thf(fact_6108_sums__Suc__imp,axiom,
% 5.31/5.61 ! [F2: nat > real,S2: real] :
% 5.31/5.61 ( ( ( F2 @ zero_zero_nat )
% 5.31/5.61 = zero_zero_real )
% 5.31/5.61 => ( ( sums_real
% 5.31/5.61 @ ^ [N4: nat] : ( F2 @ ( suc @ N4 ) )
% 5.31/5.61 @ S2 )
% 5.31/5.61 => ( sums_real @ F2 @ S2 ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % sums_Suc_imp
% 5.31/5.61 thf(fact_6109_sums__Suc__iff,axiom,
% 5.31/5.61 ! [F2: nat > real,S2: real] :
% 5.31/5.61 ( ( sums_real
% 5.31/5.61 @ ^ [N4: nat] : ( F2 @ ( suc @ N4 ) )
% 5.31/5.61 @ S2 )
% 5.31/5.61 = ( sums_real @ F2 @ ( plus_plus_real @ S2 @ ( F2 @ zero_zero_nat ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % sums_Suc_iff
% 5.31/5.61 thf(fact_6110_sums__Suc,axiom,
% 5.31/5.61 ! [F2: nat > real,L: real] :
% 5.31/5.61 ( ( sums_real
% 5.31/5.61 @ ^ [N4: nat] : ( F2 @ ( suc @ N4 ) )
% 5.31/5.61 @ L )
% 5.31/5.61 => ( sums_real @ F2 @ ( plus_plus_real @ L @ ( F2 @ zero_zero_nat ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % sums_Suc
% 5.31/5.61 thf(fact_6111_sums__Suc,axiom,
% 5.31/5.61 ! [F2: nat > nat,L: nat] :
% 5.31/5.61 ( ( sums_nat
% 5.31/5.61 @ ^ [N4: nat] : ( F2 @ ( suc @ N4 ) )
% 5.31/5.61 @ L )
% 5.31/5.61 => ( sums_nat @ F2 @ ( plus_plus_nat @ L @ ( F2 @ zero_zero_nat ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % sums_Suc
% 5.31/5.61 thf(fact_6112_sums__Suc,axiom,
% 5.31/5.61 ! [F2: nat > int,L: int] :
% 5.31/5.61 ( ( sums_int
% 5.31/5.61 @ ^ [N4: nat] : ( F2 @ ( suc @ N4 ) )
% 5.31/5.61 @ L )
% 5.31/5.61 => ( sums_int @ F2 @ ( plus_plus_int @ L @ ( F2 @ zero_zero_nat ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % sums_Suc
% 5.31/5.61 thf(fact_6113_pochhammer__times__pochhammer__half,axiom,
% 5.31/5.61 ! [Z3: complex,N: nat] :
% 5.31/5.61 ( ( times_times_complex @ ( comm_s2602460028002588243omplex @ Z3 @ ( suc @ N ) ) @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ Z3 @ ( divide1717551699836669952omplex @ one_one_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) @ ( suc @ N ) ) )
% 5.31/5.61 = ( groups6464643781859351333omplex
% 5.31/5.61 @ ^ [K3: nat] : ( plus_plus_complex @ Z3 @ ( divide1717551699836669952omplex @ ( semiri8010041392384452111omplex @ K3 ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) )
% 5.31/5.61 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % pochhammer_times_pochhammer_half
% 5.31/5.61 thf(fact_6114_pochhammer__times__pochhammer__half,axiom,
% 5.31/5.61 ! [Z3: rat,N: nat] :
% 5.31/5.61 ( ( times_times_rat @ ( comm_s4028243227959126397er_rat @ Z3 @ ( suc @ N ) ) @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ Z3 @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) @ ( suc @ N ) ) )
% 5.31/5.61 = ( groups73079841787564623at_rat
% 5.31/5.61 @ ^ [K3: nat] : ( plus_plus_rat @ Z3 @ ( divide_divide_rat @ ( semiri681578069525770553at_rat @ K3 ) @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) )
% 5.31/5.61 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % pochhammer_times_pochhammer_half
% 5.31/5.61 thf(fact_6115_pochhammer__times__pochhammer__half,axiom,
% 5.31/5.61 ! [Z3: real,N: nat] :
% 5.31/5.61 ( ( times_times_real @ ( comm_s7457072308508201937r_real @ Z3 @ ( suc @ N ) ) @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ Z3 @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( suc @ N ) ) )
% 5.31/5.61 = ( groups129246275422532515t_real
% 5.31/5.61 @ ^ [K3: nat] : ( plus_plus_real @ Z3 @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ K3 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.31/5.61 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % pochhammer_times_pochhammer_half
% 5.31/5.61 thf(fact_6116_lemma__termdiff2,axiom,
% 5.31/5.61 ! [H: complex,Z3: complex,N: nat] :
% 5.31/5.61 ( ( H != zero_zero_complex )
% 5.31/5.61 => ( ( minus_minus_complex @ ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( power_power_complex @ ( plus_plus_complex @ Z3 @ H ) @ N ) @ ( power_power_complex @ Z3 @ N ) ) @ H ) @ ( times_times_complex @ ( semiri8010041392384452111omplex @ N ) @ ( power_power_complex @ Z3 @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) )
% 5.31/5.61 = ( times_times_complex @ H
% 5.31/5.61 @ ( groups2073611262835488442omplex
% 5.31/5.61 @ ^ [P5: nat] :
% 5.31/5.61 ( groups2073611262835488442omplex
% 5.31/5.61 @ ^ [Q5: nat] : ( times_times_complex @ ( power_power_complex @ ( plus_plus_complex @ Z3 @ H ) @ Q5 ) @ ( power_power_complex @ Z3 @ ( minus_minus_nat @ ( minus_minus_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Q5 ) ) )
% 5.31/5.61 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) @ P5 ) ) )
% 5.31/5.61 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % lemma_termdiff2
% 5.31/5.61 thf(fact_6117_lemma__termdiff2,axiom,
% 5.31/5.61 ! [H: rat,Z3: rat,N: nat] :
% 5.31/5.61 ( ( H != zero_zero_rat )
% 5.31/5.61 => ( ( minus_minus_rat @ ( divide_divide_rat @ ( minus_minus_rat @ ( power_power_rat @ ( plus_plus_rat @ Z3 @ H ) @ N ) @ ( power_power_rat @ Z3 @ N ) ) @ H ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ N ) @ ( power_power_rat @ Z3 @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) )
% 5.31/5.61 = ( times_times_rat @ H
% 5.31/5.61 @ ( groups2906978787729119204at_rat
% 5.31/5.61 @ ^ [P5: nat] :
% 5.31/5.61 ( groups2906978787729119204at_rat
% 5.31/5.61 @ ^ [Q5: nat] : ( times_times_rat @ ( power_power_rat @ ( plus_plus_rat @ Z3 @ H ) @ Q5 ) @ ( power_power_rat @ Z3 @ ( minus_minus_nat @ ( minus_minus_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Q5 ) ) )
% 5.31/5.61 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) @ P5 ) ) )
% 5.31/5.61 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % lemma_termdiff2
% 5.31/5.61 thf(fact_6118_lemma__termdiff2,axiom,
% 5.31/5.61 ! [H: real,Z3: real,N: nat] :
% 5.31/5.61 ( ( H != zero_zero_real )
% 5.31/5.61 => ( ( minus_minus_real @ ( divide_divide_real @ ( minus_minus_real @ ( power_power_real @ ( plus_plus_real @ Z3 @ H ) @ N ) @ ( power_power_real @ Z3 @ N ) ) @ H ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ Z3 @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) )
% 5.31/5.61 = ( times_times_real @ H
% 5.31/5.61 @ ( groups6591440286371151544t_real
% 5.31/5.61 @ ^ [P5: nat] :
% 5.31/5.61 ( groups6591440286371151544t_real
% 5.31/5.61 @ ^ [Q5: nat] : ( times_times_real @ ( power_power_real @ ( plus_plus_real @ Z3 @ H ) @ Q5 ) @ ( power_power_real @ Z3 @ ( minus_minus_nat @ ( minus_minus_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Q5 ) ) )
% 5.31/5.61 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) @ P5 ) ) )
% 5.31/5.61 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % lemma_termdiff2
% 5.31/5.61 thf(fact_6119_pochhammer__code,axiom,
% 5.31/5.61 ( comm_s8582702949713902594nteger
% 5.31/5.61 = ( ^ [A5: code_integer,N4: nat] :
% 5.31/5.61 ( if_Code_integer @ ( N4 = zero_zero_nat ) @ one_one_Code_integer
% 5.31/5.61 @ ( set_fo1084959871951514735nteger
% 5.31/5.61 @ ^ [O: nat] : ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ A5 @ ( semiri4939895301339042750nteger @ O ) ) )
% 5.31/5.61 @ zero_zero_nat
% 5.31/5.61 @ ( minus_minus_nat @ N4 @ one_one_nat )
% 5.31/5.61 @ one_one_Code_integer ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % pochhammer_code
% 5.31/5.61 thf(fact_6120_pochhammer__code,axiom,
% 5.31/5.61 ( comm_s2602460028002588243omplex
% 5.31/5.61 = ( ^ [A5: complex,N4: nat] :
% 5.31/5.61 ( if_complex @ ( N4 = zero_zero_nat ) @ one_one_complex
% 5.31/5.61 @ ( set_fo1517530859248394432omplex
% 5.31/5.61 @ ^ [O: nat] : ( times_times_complex @ ( plus_plus_complex @ A5 @ ( semiri8010041392384452111omplex @ O ) ) )
% 5.31/5.61 @ zero_zero_nat
% 5.31/5.61 @ ( minus_minus_nat @ N4 @ one_one_nat )
% 5.31/5.61 @ one_one_complex ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % pochhammer_code
% 5.31/5.61 thf(fact_6121_pochhammer__code,axiom,
% 5.31/5.61 ( comm_s4028243227959126397er_rat
% 5.31/5.61 = ( ^ [A5: rat,N4: nat] :
% 5.31/5.61 ( if_rat @ ( N4 = zero_zero_nat ) @ one_one_rat
% 5.31/5.61 @ ( set_fo1949268297981939178at_rat
% 5.31/5.61 @ ^ [O: nat] : ( times_times_rat @ ( plus_plus_rat @ A5 @ ( semiri681578069525770553at_rat @ O ) ) )
% 5.31/5.61 @ zero_zero_nat
% 5.31/5.61 @ ( minus_minus_nat @ N4 @ one_one_nat )
% 5.31/5.61 @ one_one_rat ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % pochhammer_code
% 5.31/5.61 thf(fact_6122_pochhammer__code,axiom,
% 5.31/5.61 ( comm_s7457072308508201937r_real
% 5.31/5.61 = ( ^ [A5: real,N4: nat] :
% 5.31/5.61 ( if_real @ ( N4 = zero_zero_nat ) @ one_one_real
% 5.31/5.61 @ ( set_fo3111899725591712190t_real
% 5.31/5.61 @ ^ [O: nat] : ( times_times_real @ ( plus_plus_real @ A5 @ ( semiri5074537144036343181t_real @ O ) ) )
% 5.31/5.61 @ zero_zero_nat
% 5.31/5.61 @ ( minus_minus_nat @ N4 @ one_one_nat )
% 5.31/5.61 @ one_one_real ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % pochhammer_code
% 5.31/5.61 thf(fact_6123_pochhammer__code,axiom,
% 5.31/5.61 ( comm_s4660882817536571857er_int
% 5.31/5.61 = ( ^ [A5: int,N4: nat] :
% 5.31/5.61 ( if_int @ ( N4 = zero_zero_nat ) @ one_one_int
% 5.31/5.61 @ ( set_fo2581907887559384638at_int
% 5.31/5.61 @ ^ [O: nat] : ( times_times_int @ ( plus_plus_int @ A5 @ ( semiri1314217659103216013at_int @ O ) ) )
% 5.31/5.61 @ zero_zero_nat
% 5.31/5.61 @ ( minus_minus_nat @ N4 @ one_one_nat )
% 5.31/5.61 @ one_one_int ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % pochhammer_code
% 5.31/5.61 thf(fact_6124_pochhammer__code,axiom,
% 5.31/5.61 ( comm_s4663373288045622133er_nat
% 5.31/5.61 = ( ^ [A5: nat,N4: nat] :
% 5.31/5.61 ( if_nat @ ( N4 = zero_zero_nat ) @ one_one_nat
% 5.31/5.61 @ ( set_fo2584398358068434914at_nat
% 5.31/5.61 @ ^ [O: nat] : ( times_times_nat @ ( plus_plus_nat @ A5 @ ( semiri1316708129612266289at_nat @ O ) ) )
% 5.31/5.61 @ zero_zero_nat
% 5.31/5.61 @ ( minus_minus_nat @ N4 @ one_one_nat )
% 5.31/5.61 @ one_one_nat ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % pochhammer_code
% 5.31/5.61 thf(fact_6125_of__nat__code,axiom,
% 5.31/5.61 ( semiri4939895301339042750nteger
% 5.31/5.61 = ( ^ [N4: nat] :
% 5.31/5.61 ( semiri4055485073559036834nteger
% 5.31/5.61 @ ^ [I: code_integer] : ( plus_p5714425477246183910nteger @ I @ one_one_Code_integer )
% 5.31/5.61 @ N4
% 5.31/5.61 @ zero_z3403309356797280102nteger ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % of_nat_code
% 5.31/5.61 thf(fact_6126_of__nat__code,axiom,
% 5.31/5.61 ( semiri8010041392384452111omplex
% 5.31/5.61 = ( ^ [N4: nat] :
% 5.31/5.61 ( semiri2816024913162550771omplex
% 5.31/5.61 @ ^ [I: complex] : ( plus_plus_complex @ I @ one_one_complex )
% 5.31/5.61 @ N4
% 5.31/5.61 @ zero_zero_complex ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % of_nat_code
% 5.31/5.61 thf(fact_6127_of__nat__code,axiom,
% 5.31/5.61 ( semiri681578069525770553at_rat
% 5.31/5.61 = ( ^ [N4: nat] :
% 5.31/5.61 ( semiri7787848453975740701ux_rat
% 5.31/5.61 @ ^ [I: rat] : ( plus_plus_rat @ I @ one_one_rat )
% 5.31/5.61 @ N4
% 5.31/5.61 @ zero_zero_rat ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % of_nat_code
% 5.31/5.61 thf(fact_6128_of__nat__code,axiom,
% 5.31/5.61 ( semiri5074537144036343181t_real
% 5.31/5.61 = ( ^ [N4: nat] :
% 5.31/5.61 ( semiri7260567687927622513x_real
% 5.31/5.61 @ ^ [I: real] : ( plus_plus_real @ I @ one_one_real )
% 5.31/5.61 @ N4
% 5.31/5.61 @ zero_zero_real ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % of_nat_code
% 5.31/5.61 thf(fact_6129_of__nat__code,axiom,
% 5.31/5.61 ( semiri1314217659103216013at_int
% 5.31/5.61 = ( ^ [N4: nat] :
% 5.31/5.61 ( semiri8420488043553186161ux_int
% 5.31/5.61 @ ^ [I: int] : ( plus_plus_int @ I @ one_one_int )
% 5.31/5.61 @ N4
% 5.31/5.61 @ zero_zero_int ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % of_nat_code
% 5.31/5.61 thf(fact_6130_of__nat__code,axiom,
% 5.31/5.61 ( semiri1316708129612266289at_nat
% 5.31/5.61 = ( ^ [N4: nat] :
% 5.31/5.61 ( semiri8422978514062236437ux_nat
% 5.31/5.61 @ ^ [I: nat] : ( plus_plus_nat @ I @ one_one_nat )
% 5.31/5.61 @ N4
% 5.31/5.61 @ zero_zero_nat ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % of_nat_code
% 5.31/5.61 thf(fact_6131_central__binomial__lower__bound,axiom,
% 5.31/5.61 ! [N: nat] :
% 5.31/5.61 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.61 => ( 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 ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % central_binomial_lower_bound
% 5.31/5.61 thf(fact_6132_concat__bit__Suc,axiom,
% 5.31/5.61 ! [N: nat,K2: int,L: int] :
% 5.31/5.61 ( ( bit_concat_bit @ ( suc @ N ) @ K2 @ L )
% 5.31/5.61 = ( plus_plus_int @ ( modulo_modulo_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_concat_bit @ N @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ L ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % concat_bit_Suc
% 5.31/5.61 thf(fact_6133_dbl__simps_I3_J,axiom,
% 5.31/5.61 ( ( neg_nu8804712462038260780nteger @ one_one_Code_integer )
% 5.31/5.61 = ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % dbl_simps(3)
% 5.31/5.61 thf(fact_6134_dbl__simps_I3_J,axiom,
% 5.31/5.61 ( ( neg_nu7009210354673126013omplex @ one_one_complex )
% 5.31/5.61 = ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % dbl_simps(3)
% 5.31/5.61 thf(fact_6135_dbl__simps_I3_J,axiom,
% 5.31/5.61 ( ( neg_numeral_dbl_real @ one_one_real )
% 5.31/5.61 = ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % dbl_simps(3)
% 5.31/5.61 thf(fact_6136_dbl__simps_I3_J,axiom,
% 5.31/5.61 ( ( neg_numeral_dbl_int @ one_one_int )
% 5.31/5.61 = ( numeral_numeral_int @ ( bit0 @ one ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % dbl_simps(3)
% 5.31/5.61 thf(fact_6137_lessThan__eq__iff,axiom,
% 5.31/5.61 ! [X: nat,Y: nat] :
% 5.31/5.61 ( ( ( set_ord_lessThan_nat @ X )
% 5.31/5.61 = ( set_ord_lessThan_nat @ Y ) )
% 5.31/5.61 = ( X = Y ) ) ).
% 5.31/5.61
% 5.31/5.61 % lessThan_eq_iff
% 5.31/5.61 thf(fact_6138_lessThan__iff,axiom,
% 5.31/5.61 ! [I2: set_nat,K2: set_nat] :
% 5.31/5.61 ( ( member_set_nat @ I2 @ ( set_or890127255671739683et_nat @ K2 ) )
% 5.31/5.61 = ( ord_less_set_nat @ I2 @ K2 ) ) ).
% 5.31/5.61
% 5.31/5.61 % lessThan_iff
% 5.31/5.61 thf(fact_6139_lessThan__iff,axiom,
% 5.31/5.61 ! [I2: real,K2: real] :
% 5.31/5.61 ( ( member_real @ I2 @ ( set_or5984915006950818249n_real @ K2 ) )
% 5.31/5.61 = ( ord_less_real @ I2 @ K2 ) ) ).
% 5.31/5.61
% 5.31/5.61 % lessThan_iff
% 5.31/5.61 thf(fact_6140_lessThan__iff,axiom,
% 5.31/5.61 ! [I2: rat,K2: rat] :
% 5.31/5.61 ( ( member_rat @ I2 @ ( set_ord_lessThan_rat @ K2 ) )
% 5.31/5.61 = ( ord_less_rat @ I2 @ K2 ) ) ).
% 5.31/5.61
% 5.31/5.61 % lessThan_iff
% 5.31/5.61 thf(fact_6141_lessThan__iff,axiom,
% 5.31/5.61 ! [I2: num,K2: num] :
% 5.31/5.61 ( ( member_num @ I2 @ ( set_ord_lessThan_num @ K2 ) )
% 5.31/5.61 = ( ord_less_num @ I2 @ K2 ) ) ).
% 5.31/5.61
% 5.31/5.61 % lessThan_iff
% 5.31/5.61 thf(fact_6142_lessThan__iff,axiom,
% 5.31/5.61 ! [I2: int,K2: int] :
% 5.31/5.61 ( ( member_int @ I2 @ ( set_ord_lessThan_int @ K2 ) )
% 5.31/5.61 = ( ord_less_int @ I2 @ K2 ) ) ).
% 5.31/5.61
% 5.31/5.61 % lessThan_iff
% 5.31/5.61 thf(fact_6143_lessThan__iff,axiom,
% 5.31/5.61 ! [I2: nat,K2: nat] :
% 5.31/5.61 ( ( member_nat @ I2 @ ( set_ord_lessThan_nat @ K2 ) )
% 5.31/5.61 = ( ord_less_nat @ I2 @ K2 ) ) ).
% 5.31/5.61
% 5.31/5.61 % lessThan_iff
% 5.31/5.61 thf(fact_6144_finite__lessThan,axiom,
% 5.31/5.61 ! [K2: nat] : ( finite_finite_nat @ ( set_ord_lessThan_nat @ K2 ) ) ).
% 5.31/5.61
% 5.31/5.61 % finite_lessThan
% 5.31/5.61 thf(fact_6145_concat__bit__0,axiom,
% 5.31/5.61 ! [K2: int,L: int] :
% 5.31/5.61 ( ( bit_concat_bit @ zero_zero_nat @ K2 @ L )
% 5.31/5.61 = L ) ).
% 5.31/5.61
% 5.31/5.61 % concat_bit_0
% 5.31/5.61 thf(fact_6146_card__lessThan,axiom,
% 5.31/5.61 ! [U: nat] :
% 5.31/5.61 ( ( finite_card_nat @ ( set_ord_lessThan_nat @ U ) )
% 5.31/5.61 = U ) ).
% 5.31/5.61
% 5.31/5.61 % card_lessThan
% 5.31/5.61 thf(fact_6147_dbl__simps_I2_J,axiom,
% 5.31/5.61 ( ( neg_nu7009210354673126013omplex @ zero_zero_complex )
% 5.31/5.61 = zero_zero_complex ) ).
% 5.31/5.61
% 5.31/5.61 % dbl_simps(2)
% 5.31/5.61 thf(fact_6148_dbl__simps_I2_J,axiom,
% 5.31/5.61 ( ( neg_numeral_dbl_real @ zero_zero_real )
% 5.31/5.61 = zero_zero_real ) ).
% 5.31/5.61
% 5.31/5.61 % dbl_simps(2)
% 5.31/5.61 thf(fact_6149_dbl__simps_I2_J,axiom,
% 5.31/5.61 ( ( neg_numeral_dbl_rat @ zero_zero_rat )
% 5.31/5.61 = zero_zero_rat ) ).
% 5.31/5.61
% 5.31/5.61 % dbl_simps(2)
% 5.31/5.61 thf(fact_6150_dbl__simps_I2_J,axiom,
% 5.31/5.61 ( ( neg_numeral_dbl_int @ zero_zero_int )
% 5.31/5.61 = zero_zero_int ) ).
% 5.31/5.61
% 5.31/5.61 % dbl_simps(2)
% 5.31/5.61 thf(fact_6151_prod__zero__iff,axiom,
% 5.31/5.61 ! [A4: set_nat,F2: nat > complex] :
% 5.31/5.61 ( ( finite_finite_nat @ A4 )
% 5.31/5.61 => ( ( ( groups6464643781859351333omplex @ F2 @ A4 )
% 5.31/5.61 = zero_zero_complex )
% 5.31/5.61 = ( ? [X4: nat] :
% 5.31/5.61 ( ( member_nat @ X4 @ A4 )
% 5.31/5.61 & ( ( F2 @ X4 )
% 5.31/5.61 = zero_zero_complex ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod_zero_iff
% 5.31/5.61 thf(fact_6152_prod__zero__iff,axiom,
% 5.31/5.61 ! [A4: set_int,F2: int > complex] :
% 5.31/5.61 ( ( finite_finite_int @ A4 )
% 5.31/5.61 => ( ( ( groups7440179247065528705omplex @ F2 @ A4 )
% 5.31/5.61 = zero_zero_complex )
% 5.31/5.61 = ( ? [X4: int] :
% 5.31/5.61 ( ( member_int @ X4 @ A4 )
% 5.31/5.61 & ( ( F2 @ X4 )
% 5.31/5.61 = zero_zero_complex ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod_zero_iff
% 5.31/5.61 thf(fact_6153_prod__zero__iff,axiom,
% 5.31/5.61 ! [A4: set_complex,F2: complex > complex] :
% 5.31/5.61 ( ( finite3207457112153483333omplex @ A4 )
% 5.31/5.61 => ( ( ( groups3708469109370488835omplex @ F2 @ A4 )
% 5.31/5.61 = zero_zero_complex )
% 5.31/5.61 = ( ? [X4: complex] :
% 5.31/5.61 ( ( member_complex @ X4 @ A4 )
% 5.31/5.61 & ( ( F2 @ X4 )
% 5.31/5.61 = zero_zero_complex ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod_zero_iff
% 5.31/5.61 thf(fact_6154_prod__zero__iff,axiom,
% 5.31/5.61 ! [A4: set_nat,F2: nat > real] :
% 5.31/5.61 ( ( finite_finite_nat @ A4 )
% 5.31/5.61 => ( ( ( groups129246275422532515t_real @ F2 @ A4 )
% 5.31/5.61 = zero_zero_real )
% 5.31/5.61 = ( ? [X4: nat] :
% 5.31/5.61 ( ( member_nat @ X4 @ A4 )
% 5.31/5.61 & ( ( F2 @ X4 )
% 5.31/5.61 = zero_zero_real ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod_zero_iff
% 5.31/5.61 thf(fact_6155_prod__zero__iff,axiom,
% 5.31/5.61 ! [A4: set_int,F2: int > real] :
% 5.31/5.61 ( ( finite_finite_int @ A4 )
% 5.31/5.61 => ( ( ( groups2316167850115554303t_real @ F2 @ A4 )
% 5.31/5.61 = zero_zero_real )
% 5.31/5.61 = ( ? [X4: int] :
% 5.31/5.61 ( ( member_int @ X4 @ A4 )
% 5.31/5.61 & ( ( F2 @ X4 )
% 5.31/5.61 = zero_zero_real ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod_zero_iff
% 5.31/5.61 thf(fact_6156_prod__zero__iff,axiom,
% 5.31/5.61 ! [A4: set_complex,F2: complex > real] :
% 5.31/5.61 ( ( finite3207457112153483333omplex @ A4 )
% 5.31/5.61 => ( ( ( groups766887009212190081x_real @ F2 @ A4 )
% 5.31/5.61 = zero_zero_real )
% 5.31/5.61 = ( ? [X4: complex] :
% 5.31/5.61 ( ( member_complex @ X4 @ A4 )
% 5.31/5.61 & ( ( F2 @ X4 )
% 5.31/5.61 = zero_zero_real ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod_zero_iff
% 5.31/5.61 thf(fact_6157_prod__zero__iff,axiom,
% 5.31/5.61 ! [A4: set_nat,F2: nat > rat] :
% 5.31/5.61 ( ( finite_finite_nat @ A4 )
% 5.31/5.61 => ( ( ( groups73079841787564623at_rat @ F2 @ A4 )
% 5.31/5.61 = zero_zero_rat )
% 5.31/5.61 = ( ? [X4: nat] :
% 5.31/5.61 ( ( member_nat @ X4 @ A4 )
% 5.31/5.61 & ( ( F2 @ X4 )
% 5.31/5.61 = zero_zero_rat ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod_zero_iff
% 5.31/5.61 thf(fact_6158_prod__zero__iff,axiom,
% 5.31/5.61 ! [A4: set_int,F2: int > rat] :
% 5.31/5.61 ( ( finite_finite_int @ A4 )
% 5.31/5.61 => ( ( ( groups1072433553688619179nt_rat @ F2 @ A4 )
% 5.31/5.61 = zero_zero_rat )
% 5.31/5.61 = ( ? [X4: int] :
% 5.31/5.61 ( ( member_int @ X4 @ A4 )
% 5.31/5.61 & ( ( F2 @ X4 )
% 5.31/5.61 = zero_zero_rat ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod_zero_iff
% 5.31/5.61 thf(fact_6159_prod__zero__iff,axiom,
% 5.31/5.61 ! [A4: set_complex,F2: complex > rat] :
% 5.31/5.61 ( ( finite3207457112153483333omplex @ A4 )
% 5.31/5.61 => ( ( ( groups225925009352817453ex_rat @ F2 @ A4 )
% 5.31/5.61 = zero_zero_rat )
% 5.31/5.61 = ( ? [X4: complex] :
% 5.31/5.61 ( ( member_complex @ X4 @ A4 )
% 5.31/5.61 & ( ( F2 @ X4 )
% 5.31/5.61 = zero_zero_rat ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod_zero_iff
% 5.31/5.61 thf(fact_6160_prod__zero__iff,axiom,
% 5.31/5.61 ! [A4: set_int,F2: int > nat] :
% 5.31/5.61 ( ( finite_finite_int @ A4 )
% 5.31/5.61 => ( ( ( groups1707563613775114915nt_nat @ F2 @ A4 )
% 5.31/5.61 = zero_zero_nat )
% 5.31/5.61 = ( ? [X4: int] :
% 5.31/5.61 ( ( member_int @ X4 @ A4 )
% 5.31/5.61 & ( ( F2 @ X4 )
% 5.31/5.61 = zero_zero_nat ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod_zero_iff
% 5.31/5.61 thf(fact_6161_lessThan__subset__iff,axiom,
% 5.31/5.61 ! [X: rat,Y: rat] :
% 5.31/5.61 ( ( ord_less_eq_set_rat @ ( set_ord_lessThan_rat @ X ) @ ( set_ord_lessThan_rat @ Y ) )
% 5.31/5.61 = ( ord_less_eq_rat @ X @ Y ) ) ).
% 5.31/5.61
% 5.31/5.61 % lessThan_subset_iff
% 5.31/5.61 thf(fact_6162_lessThan__subset__iff,axiom,
% 5.31/5.61 ! [X: num,Y: num] :
% 5.31/5.61 ( ( ord_less_eq_set_num @ ( set_ord_lessThan_num @ X ) @ ( set_ord_lessThan_num @ Y ) )
% 5.31/5.61 = ( ord_less_eq_num @ X @ Y ) ) ).
% 5.31/5.61
% 5.31/5.61 % lessThan_subset_iff
% 5.31/5.61 thf(fact_6163_lessThan__subset__iff,axiom,
% 5.31/5.61 ! [X: int,Y: int] :
% 5.31/5.61 ( ( ord_less_eq_set_int @ ( set_ord_lessThan_int @ X ) @ ( set_ord_lessThan_int @ Y ) )
% 5.31/5.61 = ( ord_less_eq_int @ X @ Y ) ) ).
% 5.31/5.61
% 5.31/5.61 % lessThan_subset_iff
% 5.31/5.61 thf(fact_6164_lessThan__subset__iff,axiom,
% 5.31/5.61 ! [X: nat,Y: nat] :
% 5.31/5.61 ( ( ord_less_eq_set_nat @ ( set_ord_lessThan_nat @ X ) @ ( set_ord_lessThan_nat @ Y ) )
% 5.31/5.61 = ( ord_less_eq_nat @ X @ Y ) ) ).
% 5.31/5.61
% 5.31/5.61 % lessThan_subset_iff
% 5.31/5.61 thf(fact_6165_lessThan__0,axiom,
% 5.31/5.61 ( ( set_ord_lessThan_nat @ zero_zero_nat )
% 5.31/5.61 = bot_bot_set_nat ) ).
% 5.31/5.61
% 5.31/5.61 % lessThan_0
% 5.31/5.61 thf(fact_6166_dbl__simps_I5_J,axiom,
% 5.31/5.61 ! [K2: num] :
% 5.31/5.61 ( ( neg_nu7009210354673126013omplex @ ( numera6690914467698888265omplex @ K2 ) )
% 5.31/5.61 = ( numera6690914467698888265omplex @ ( bit0 @ K2 ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % dbl_simps(5)
% 5.31/5.61 thf(fact_6167_dbl__simps_I5_J,axiom,
% 5.31/5.61 ! [K2: num] :
% 5.31/5.61 ( ( neg_numeral_dbl_real @ ( numeral_numeral_real @ K2 ) )
% 5.31/5.61 = ( numeral_numeral_real @ ( bit0 @ K2 ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % dbl_simps(5)
% 5.31/5.61 thf(fact_6168_dbl__simps_I5_J,axiom,
% 5.31/5.61 ! [K2: num] :
% 5.31/5.61 ( ( neg_numeral_dbl_int @ ( numeral_numeral_int @ K2 ) )
% 5.31/5.61 = ( numeral_numeral_int @ ( bit0 @ K2 ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % dbl_simps(5)
% 5.31/5.61 thf(fact_6169_prod_Oinsert,axiom,
% 5.31/5.61 ! [A4: set_real,X: real,G2: real > real] :
% 5.31/5.61 ( ( finite_finite_real @ A4 )
% 5.31/5.61 => ( ~ ( member_real @ X @ A4 )
% 5.31/5.61 => ( ( groups1681761925125756287l_real @ G2 @ ( insert_real @ X @ A4 ) )
% 5.31/5.61 = ( times_times_real @ ( G2 @ X ) @ ( groups1681761925125756287l_real @ G2 @ A4 ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.insert
% 5.31/5.61 thf(fact_6170_prod_Oinsert,axiom,
% 5.31/5.61 ! [A4: set_nat,X: nat,G2: nat > real] :
% 5.31/5.61 ( ( finite_finite_nat @ A4 )
% 5.31/5.61 => ( ~ ( member_nat @ X @ A4 )
% 5.31/5.61 => ( ( groups129246275422532515t_real @ G2 @ ( insert_nat @ X @ A4 ) )
% 5.31/5.61 = ( times_times_real @ ( G2 @ X ) @ ( groups129246275422532515t_real @ G2 @ A4 ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.insert
% 5.31/5.61 thf(fact_6171_prod_Oinsert,axiom,
% 5.31/5.61 ! [A4: set_int,X: int,G2: int > real] :
% 5.31/5.61 ( ( finite_finite_int @ A4 )
% 5.31/5.61 => ( ~ ( member_int @ X @ A4 )
% 5.31/5.61 => ( ( groups2316167850115554303t_real @ G2 @ ( insert_int @ X @ A4 ) )
% 5.31/5.61 = ( times_times_real @ ( G2 @ X ) @ ( groups2316167850115554303t_real @ G2 @ A4 ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.insert
% 5.31/5.61 thf(fact_6172_prod_Oinsert,axiom,
% 5.31/5.61 ! [A4: set_complex,X: complex,G2: complex > real] :
% 5.31/5.61 ( ( finite3207457112153483333omplex @ A4 )
% 5.31/5.61 => ( ~ ( member_complex @ X @ A4 )
% 5.31/5.61 => ( ( groups766887009212190081x_real @ G2 @ ( insert_complex @ X @ A4 ) )
% 5.31/5.61 = ( times_times_real @ ( G2 @ X ) @ ( groups766887009212190081x_real @ G2 @ A4 ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.insert
% 5.31/5.61 thf(fact_6173_prod_Oinsert,axiom,
% 5.31/5.61 ! [A4: set_real,X: real,G2: real > rat] :
% 5.31/5.61 ( ( finite_finite_real @ A4 )
% 5.31/5.61 => ( ~ ( member_real @ X @ A4 )
% 5.31/5.61 => ( ( groups4061424788464935467al_rat @ G2 @ ( insert_real @ X @ A4 ) )
% 5.31/5.61 = ( times_times_rat @ ( G2 @ X ) @ ( groups4061424788464935467al_rat @ G2 @ A4 ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.insert
% 5.31/5.61 thf(fact_6174_prod_Oinsert,axiom,
% 5.31/5.61 ! [A4: set_nat,X: nat,G2: nat > rat] :
% 5.31/5.61 ( ( finite_finite_nat @ A4 )
% 5.31/5.61 => ( ~ ( member_nat @ X @ A4 )
% 5.31/5.61 => ( ( groups73079841787564623at_rat @ G2 @ ( insert_nat @ X @ A4 ) )
% 5.31/5.61 = ( times_times_rat @ ( G2 @ X ) @ ( groups73079841787564623at_rat @ G2 @ A4 ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.insert
% 5.31/5.61 thf(fact_6175_prod_Oinsert,axiom,
% 5.31/5.61 ! [A4: set_int,X: int,G2: int > rat] :
% 5.31/5.61 ( ( finite_finite_int @ A4 )
% 5.31/5.61 => ( ~ ( member_int @ X @ A4 )
% 5.31/5.61 => ( ( groups1072433553688619179nt_rat @ G2 @ ( insert_int @ X @ A4 ) )
% 5.31/5.61 = ( times_times_rat @ ( G2 @ X ) @ ( groups1072433553688619179nt_rat @ G2 @ A4 ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.insert
% 5.31/5.61 thf(fact_6176_prod_Oinsert,axiom,
% 5.31/5.61 ! [A4: set_complex,X: complex,G2: complex > rat] :
% 5.31/5.61 ( ( finite3207457112153483333omplex @ A4 )
% 5.31/5.61 => ( ~ ( member_complex @ X @ A4 )
% 5.31/5.61 => ( ( groups225925009352817453ex_rat @ G2 @ ( insert_complex @ X @ A4 ) )
% 5.31/5.61 = ( times_times_rat @ ( G2 @ X ) @ ( groups225925009352817453ex_rat @ G2 @ A4 ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.insert
% 5.31/5.61 thf(fact_6177_prod_Oinsert,axiom,
% 5.31/5.61 ! [A4: set_real,X: real,G2: real > nat] :
% 5.31/5.61 ( ( finite_finite_real @ A4 )
% 5.31/5.61 => ( ~ ( member_real @ X @ A4 )
% 5.31/5.61 => ( ( groups4696554848551431203al_nat @ G2 @ ( insert_real @ X @ A4 ) )
% 5.31/5.61 = ( times_times_nat @ ( G2 @ X ) @ ( groups4696554848551431203al_nat @ G2 @ A4 ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.insert
% 5.31/5.61 thf(fact_6178_prod_Oinsert,axiom,
% 5.31/5.61 ! [A4: set_int,X: int,G2: int > nat] :
% 5.31/5.61 ( ( finite_finite_int @ A4 )
% 5.31/5.61 => ( ~ ( member_int @ X @ A4 )
% 5.31/5.61 => ( ( groups1707563613775114915nt_nat @ G2 @ ( insert_int @ X @ A4 ) )
% 5.31/5.61 = ( times_times_nat @ ( G2 @ X ) @ ( groups1707563613775114915nt_nat @ G2 @ A4 ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.insert
% 5.31/5.61 thf(fact_6179_sum_OlessThan__Suc,axiom,
% 5.31/5.61 ! [G2: nat > rat,N: nat] :
% 5.31/5.61 ( ( groups2906978787729119204at_rat @ G2 @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 5.31/5.61 = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G2 @ ( set_ord_lessThan_nat @ N ) ) @ ( G2 @ N ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % sum.lessThan_Suc
% 5.31/5.61 thf(fact_6180_sum_OlessThan__Suc,axiom,
% 5.31/5.61 ! [G2: nat > int,N: nat] :
% 5.31/5.61 ( ( groups3539618377306564664at_int @ G2 @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 5.31/5.61 = ( plus_plus_int @ ( groups3539618377306564664at_int @ G2 @ ( set_ord_lessThan_nat @ N ) ) @ ( G2 @ N ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % sum.lessThan_Suc
% 5.31/5.61 thf(fact_6181_sum_OlessThan__Suc,axiom,
% 5.31/5.61 ! [G2: nat > nat,N: nat] :
% 5.31/5.61 ( ( groups3542108847815614940at_nat @ G2 @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 5.31/5.61 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G2 @ ( set_ord_lessThan_nat @ N ) ) @ ( G2 @ N ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % sum.lessThan_Suc
% 5.31/5.61 thf(fact_6182_sum_OlessThan__Suc,axiom,
% 5.31/5.61 ! [G2: nat > real,N: nat] :
% 5.31/5.61 ( ( groups6591440286371151544t_real @ G2 @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 5.31/5.61 = ( plus_plus_real @ ( groups6591440286371151544t_real @ G2 @ ( set_ord_lessThan_nat @ N ) ) @ ( G2 @ N ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % sum.lessThan_Suc
% 5.31/5.61 thf(fact_6183_single__Diff__lessThan,axiom,
% 5.31/5.61 ! [K2: int] :
% 5.31/5.61 ( ( minus_minus_set_int @ ( insert_int @ K2 @ bot_bot_set_int ) @ ( set_ord_lessThan_int @ K2 ) )
% 5.31/5.61 = ( insert_int @ K2 @ bot_bot_set_int ) ) ).
% 5.31/5.61
% 5.31/5.61 % single_Diff_lessThan
% 5.31/5.61 thf(fact_6184_single__Diff__lessThan,axiom,
% 5.31/5.61 ! [K2: real] :
% 5.31/5.61 ( ( minus_minus_set_real @ ( insert_real @ K2 @ bot_bot_set_real ) @ ( set_or5984915006950818249n_real @ K2 ) )
% 5.31/5.61 = ( insert_real @ K2 @ bot_bot_set_real ) ) ).
% 5.31/5.61
% 5.31/5.61 % single_Diff_lessThan
% 5.31/5.61 thf(fact_6185_single__Diff__lessThan,axiom,
% 5.31/5.61 ! [K2: nat] :
% 5.31/5.61 ( ( minus_minus_set_nat @ ( insert_nat @ K2 @ bot_bot_set_nat ) @ ( set_ord_lessThan_nat @ K2 ) )
% 5.31/5.61 = ( insert_nat @ K2 @ bot_bot_set_nat ) ) ).
% 5.31/5.61
% 5.31/5.61 % single_Diff_lessThan
% 5.31/5.61 thf(fact_6186_prod_OlessThan__Suc,axiom,
% 5.31/5.61 ! [G2: nat > real,N: nat] :
% 5.31/5.61 ( ( groups129246275422532515t_real @ G2 @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 5.31/5.61 = ( times_times_real @ ( groups129246275422532515t_real @ G2 @ ( set_ord_lessThan_nat @ N ) ) @ ( G2 @ N ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.lessThan_Suc
% 5.31/5.61 thf(fact_6187_prod_OlessThan__Suc,axiom,
% 5.31/5.61 ! [G2: nat > rat,N: nat] :
% 5.31/5.61 ( ( groups73079841787564623at_rat @ G2 @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 5.31/5.61 = ( times_times_rat @ ( groups73079841787564623at_rat @ G2 @ ( set_ord_lessThan_nat @ N ) ) @ ( G2 @ N ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.lessThan_Suc
% 5.31/5.61 thf(fact_6188_prod_OlessThan__Suc,axiom,
% 5.31/5.61 ! [G2: nat > int,N: nat] :
% 5.31/5.61 ( ( groups705719431365010083at_int @ G2 @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 5.31/5.61 = ( times_times_int @ ( groups705719431365010083at_int @ G2 @ ( set_ord_lessThan_nat @ N ) ) @ ( G2 @ N ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.lessThan_Suc
% 5.31/5.61 thf(fact_6189_prod_OlessThan__Suc,axiom,
% 5.31/5.61 ! [G2: nat > nat,N: nat] :
% 5.31/5.61 ( ( groups708209901874060359at_nat @ G2 @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 5.31/5.61 = ( times_times_nat @ ( groups708209901874060359at_nat @ G2 @ ( set_ord_lessThan_nat @ N ) ) @ ( G2 @ N ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.lessThan_Suc
% 5.31/5.61 thf(fact_6190_prod_Ocl__ivl__Suc,axiom,
% 5.31/5.61 ! [N: nat,M2: nat,G2: nat > code_integer] :
% 5.31/5.61 ( ( ( ord_less_nat @ ( suc @ N ) @ M2 )
% 5.31/5.61 => ( ( groups3455450783089532116nteger @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N ) ) )
% 5.31/5.61 = one_one_Code_integer ) )
% 5.31/5.61 & ( ~ ( ord_less_nat @ ( suc @ N ) @ M2 )
% 5.31/5.61 => ( ( groups3455450783089532116nteger @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N ) ) )
% 5.31/5.61 = ( times_3573771949741848930nteger @ ( groups3455450783089532116nteger @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) @ ( G2 @ ( suc @ N ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.cl_ivl_Suc
% 5.31/5.61 thf(fact_6191_prod_Ocl__ivl__Suc,axiom,
% 5.31/5.61 ! [N: nat,M2: nat,G2: nat > complex] :
% 5.31/5.61 ( ( ( ord_less_nat @ ( suc @ N ) @ M2 )
% 5.31/5.61 => ( ( groups6464643781859351333omplex @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N ) ) )
% 5.31/5.61 = one_one_complex ) )
% 5.31/5.61 & ( ~ ( ord_less_nat @ ( suc @ N ) @ M2 )
% 5.31/5.61 => ( ( groups6464643781859351333omplex @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N ) ) )
% 5.31/5.61 = ( times_times_complex @ ( groups6464643781859351333omplex @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) @ ( G2 @ ( suc @ N ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.cl_ivl_Suc
% 5.31/5.61 thf(fact_6192_prod_Ocl__ivl__Suc,axiom,
% 5.31/5.61 ! [N: nat,M2: nat,G2: nat > real] :
% 5.31/5.61 ( ( ( ord_less_nat @ ( suc @ N ) @ M2 )
% 5.31/5.61 => ( ( groups129246275422532515t_real @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N ) ) )
% 5.31/5.61 = one_one_real ) )
% 5.31/5.61 & ( ~ ( ord_less_nat @ ( suc @ N ) @ M2 )
% 5.31/5.61 => ( ( groups129246275422532515t_real @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N ) ) )
% 5.31/5.61 = ( times_times_real @ ( groups129246275422532515t_real @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) @ ( G2 @ ( suc @ N ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.cl_ivl_Suc
% 5.31/5.61 thf(fact_6193_prod_Ocl__ivl__Suc,axiom,
% 5.31/5.61 ! [N: nat,M2: nat,G2: nat > rat] :
% 5.31/5.61 ( ( ( ord_less_nat @ ( suc @ N ) @ M2 )
% 5.31/5.61 => ( ( groups73079841787564623at_rat @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N ) ) )
% 5.31/5.61 = one_one_rat ) )
% 5.31/5.61 & ( ~ ( ord_less_nat @ ( suc @ N ) @ M2 )
% 5.31/5.61 => ( ( groups73079841787564623at_rat @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N ) ) )
% 5.31/5.61 = ( times_times_rat @ ( groups73079841787564623at_rat @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) @ ( G2 @ ( suc @ N ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.cl_ivl_Suc
% 5.31/5.61 thf(fact_6194_prod_Ocl__ivl__Suc,axiom,
% 5.31/5.61 ! [N: nat,M2: nat,G2: nat > int] :
% 5.31/5.61 ( ( ( ord_less_nat @ ( suc @ N ) @ M2 )
% 5.31/5.61 => ( ( groups705719431365010083at_int @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N ) ) )
% 5.31/5.61 = one_one_int ) )
% 5.31/5.61 & ( ~ ( ord_less_nat @ ( suc @ N ) @ M2 )
% 5.31/5.61 => ( ( groups705719431365010083at_int @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N ) ) )
% 5.31/5.61 = ( times_times_int @ ( groups705719431365010083at_int @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) @ ( G2 @ ( suc @ N ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.cl_ivl_Suc
% 5.31/5.61 thf(fact_6195_prod_Ocl__ivl__Suc,axiom,
% 5.31/5.61 ! [N: nat,M2: nat,G2: nat > nat] :
% 5.31/5.61 ( ( ( ord_less_nat @ ( suc @ N ) @ M2 )
% 5.31/5.61 => ( ( groups708209901874060359at_nat @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N ) ) )
% 5.31/5.61 = one_one_nat ) )
% 5.31/5.61 & ( ~ ( ord_less_nat @ ( suc @ N ) @ M2 )
% 5.31/5.61 => ( ( groups708209901874060359at_nat @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N ) ) )
% 5.31/5.61 = ( times_times_nat @ ( groups708209901874060359at_nat @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) @ ( G2 @ ( suc @ N ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.cl_ivl_Suc
% 5.31/5.61 thf(fact_6196_prod_Onat__diff__reindex,axiom,
% 5.31/5.61 ! [G2: nat > int,N: nat] :
% 5.31/5.61 ( ( groups705719431365010083at_int
% 5.31/5.61 @ ^ [I: nat] : ( G2 @ ( minus_minus_nat @ N @ ( suc @ I ) ) )
% 5.31/5.61 @ ( set_ord_lessThan_nat @ N ) )
% 5.31/5.61 = ( groups705719431365010083at_int @ G2 @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.nat_diff_reindex
% 5.31/5.61 thf(fact_6197_prod_Onat__diff__reindex,axiom,
% 5.31/5.61 ! [G2: nat > nat,N: nat] :
% 5.31/5.61 ( ( groups708209901874060359at_nat
% 5.31/5.61 @ ^ [I: nat] : ( G2 @ ( minus_minus_nat @ N @ ( suc @ I ) ) )
% 5.31/5.61 @ ( set_ord_lessThan_nat @ N ) )
% 5.31/5.61 = ( groups708209901874060359at_nat @ G2 @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.nat_diff_reindex
% 5.31/5.61 thf(fact_6198_lessThan__non__empty,axiom,
% 5.31/5.61 ! [X: int] :
% 5.31/5.61 ( ( set_ord_lessThan_int @ X )
% 5.31/5.61 != bot_bot_set_int ) ).
% 5.31/5.61
% 5.31/5.61 % lessThan_non_empty
% 5.31/5.61 thf(fact_6199_lessThan__non__empty,axiom,
% 5.31/5.61 ! [X: real] :
% 5.31/5.61 ( ( set_or5984915006950818249n_real @ X )
% 5.31/5.61 != bot_bot_set_real ) ).
% 5.31/5.61
% 5.31/5.61 % lessThan_non_empty
% 5.31/5.61 thf(fact_6200_infinite__Iio,axiom,
% 5.31/5.61 ! [A: int] :
% 5.31/5.61 ~ ( finite_finite_int @ ( set_ord_lessThan_int @ A ) ) ).
% 5.31/5.61
% 5.31/5.61 % infinite_Iio
% 5.31/5.61 thf(fact_6201_prod_Odistrib,axiom,
% 5.31/5.61 ! [G2: nat > int,H: nat > int,A4: set_nat] :
% 5.31/5.61 ( ( groups705719431365010083at_int
% 5.31/5.61 @ ^ [X4: nat] : ( times_times_int @ ( G2 @ X4 ) @ ( H @ X4 ) )
% 5.31/5.61 @ A4 )
% 5.31/5.61 = ( times_times_int @ ( groups705719431365010083at_int @ G2 @ A4 ) @ ( groups705719431365010083at_int @ H @ A4 ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.distrib
% 5.31/5.61 thf(fact_6202_prod_Odistrib,axiom,
% 5.31/5.61 ! [G2: int > int,H: int > int,A4: set_int] :
% 5.31/5.61 ( ( groups1705073143266064639nt_int
% 5.31/5.61 @ ^ [X4: int] : ( times_times_int @ ( G2 @ X4 ) @ ( H @ X4 ) )
% 5.31/5.61 @ A4 )
% 5.31/5.61 = ( times_times_int @ ( groups1705073143266064639nt_int @ G2 @ A4 ) @ ( groups1705073143266064639nt_int @ H @ A4 ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.distrib
% 5.31/5.61 thf(fact_6203_prod_Odistrib,axiom,
% 5.31/5.61 ! [G2: nat > nat,H: nat > nat,A4: set_nat] :
% 5.31/5.61 ( ( groups708209901874060359at_nat
% 5.31/5.61 @ ^ [X4: nat] : ( times_times_nat @ ( G2 @ X4 ) @ ( H @ X4 ) )
% 5.31/5.61 @ A4 )
% 5.31/5.61 = ( times_times_nat @ ( groups708209901874060359at_nat @ G2 @ A4 ) @ ( groups708209901874060359at_nat @ H @ A4 ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.distrib
% 5.31/5.61 thf(fact_6204_lessThan__def,axiom,
% 5.31/5.61 ( set_or890127255671739683et_nat
% 5.31/5.61 = ( ^ [U2: set_nat] :
% 5.31/5.61 ( collect_set_nat
% 5.31/5.61 @ ^ [X4: set_nat] : ( ord_less_set_nat @ X4 @ U2 ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % lessThan_def
% 5.31/5.61 thf(fact_6205_lessThan__def,axiom,
% 5.31/5.61 ( set_or5984915006950818249n_real
% 5.31/5.61 = ( ^ [U2: real] :
% 5.31/5.61 ( collect_real
% 5.31/5.61 @ ^ [X4: real] : ( ord_less_real @ X4 @ U2 ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % lessThan_def
% 5.31/5.61 thf(fact_6206_lessThan__def,axiom,
% 5.31/5.61 ( set_ord_lessThan_rat
% 5.31/5.61 = ( ^ [U2: rat] :
% 5.31/5.61 ( collect_rat
% 5.31/5.61 @ ^ [X4: rat] : ( ord_less_rat @ X4 @ U2 ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % lessThan_def
% 5.31/5.61 thf(fact_6207_lessThan__def,axiom,
% 5.31/5.61 ( set_ord_lessThan_num
% 5.31/5.61 = ( ^ [U2: num] :
% 5.31/5.61 ( collect_num
% 5.31/5.61 @ ^ [X4: num] : ( ord_less_num @ X4 @ U2 ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % lessThan_def
% 5.31/5.61 thf(fact_6208_lessThan__def,axiom,
% 5.31/5.61 ( set_ord_lessThan_int
% 5.31/5.61 = ( ^ [U2: int] :
% 5.31/5.61 ( collect_int
% 5.31/5.61 @ ^ [X4: int] : ( ord_less_int @ X4 @ U2 ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % lessThan_def
% 5.31/5.61 thf(fact_6209_lessThan__def,axiom,
% 5.31/5.61 ( set_ord_lessThan_nat
% 5.31/5.61 = ( ^ [U2: nat] :
% 5.31/5.61 ( collect_nat
% 5.31/5.61 @ ^ [X4: nat] : ( ord_less_nat @ X4 @ U2 ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % lessThan_def
% 5.31/5.61 thf(fact_6210_prod_OlessThan__Suc__shift,axiom,
% 5.31/5.61 ! [G2: nat > real,N: nat] :
% 5.31/5.61 ( ( groups129246275422532515t_real @ G2 @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 5.31/5.61 = ( times_times_real @ ( G2 @ zero_zero_nat )
% 5.31/5.61 @ ( groups129246275422532515t_real
% 5.31/5.61 @ ^ [I: nat] : ( G2 @ ( suc @ I ) )
% 5.31/5.61 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.lessThan_Suc_shift
% 5.31/5.61 thf(fact_6211_prod_OlessThan__Suc__shift,axiom,
% 5.31/5.61 ! [G2: nat > rat,N: nat] :
% 5.31/5.61 ( ( groups73079841787564623at_rat @ G2 @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 5.31/5.61 = ( times_times_rat @ ( G2 @ zero_zero_nat )
% 5.31/5.61 @ ( groups73079841787564623at_rat
% 5.31/5.61 @ ^ [I: nat] : ( G2 @ ( suc @ I ) )
% 5.31/5.61 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.lessThan_Suc_shift
% 5.31/5.61 thf(fact_6212_prod_OlessThan__Suc__shift,axiom,
% 5.31/5.61 ! [G2: nat > int,N: nat] :
% 5.31/5.61 ( ( groups705719431365010083at_int @ G2 @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 5.31/5.61 = ( times_times_int @ ( G2 @ zero_zero_nat )
% 5.31/5.61 @ ( groups705719431365010083at_int
% 5.31/5.61 @ ^ [I: nat] : ( G2 @ ( suc @ I ) )
% 5.31/5.61 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.lessThan_Suc_shift
% 5.31/5.61 thf(fact_6213_prod_OlessThan__Suc__shift,axiom,
% 5.31/5.61 ! [G2: nat > nat,N: nat] :
% 5.31/5.61 ( ( groups708209901874060359at_nat @ G2 @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 5.31/5.61 = ( times_times_nat @ ( G2 @ zero_zero_nat )
% 5.31/5.61 @ ( groups708209901874060359at_nat
% 5.31/5.61 @ ^ [I: nat] : ( G2 @ ( suc @ I ) )
% 5.31/5.61 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.lessThan_Suc_shift
% 5.31/5.61 thf(fact_6214_prod_OatLeast1__atMost__eq,axiom,
% 5.31/5.61 ! [G2: nat > int,N: nat] :
% 5.31/5.61 ( ( groups705719431365010083at_int @ G2 @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) )
% 5.31/5.61 = ( groups705719431365010083at_int
% 5.31/5.61 @ ^ [K3: nat] : ( G2 @ ( suc @ K3 ) )
% 5.31/5.61 @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.atLeast1_atMost_eq
% 5.31/5.61 thf(fact_6215_prod_OatLeast1__atMost__eq,axiom,
% 5.31/5.61 ! [G2: nat > nat,N: nat] :
% 5.31/5.61 ( ( groups708209901874060359at_nat @ G2 @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) )
% 5.31/5.61 = ( groups708209901874060359at_nat
% 5.31/5.61 @ ^ [K3: nat] : ( G2 @ ( suc @ K3 ) )
% 5.31/5.61 @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.atLeast1_atMost_eq
% 5.31/5.61 thf(fact_6216_prod__mono,axiom,
% 5.31/5.61 ! [A4: set_complex,F2: complex > real,G2: complex > real] :
% 5.31/5.61 ( ! [I3: complex] :
% 5.31/5.61 ( ( member_complex @ I3 @ A4 )
% 5.31/5.61 => ( ( ord_less_eq_real @ zero_zero_real @ ( F2 @ I3 ) )
% 5.31/5.61 & ( ord_less_eq_real @ ( F2 @ I3 ) @ ( G2 @ I3 ) ) ) )
% 5.31/5.61 => ( ord_less_eq_real @ ( groups766887009212190081x_real @ F2 @ A4 ) @ ( groups766887009212190081x_real @ G2 @ A4 ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod_mono
% 5.31/5.61 thf(fact_6217_prod__mono,axiom,
% 5.31/5.61 ! [A4: set_real,F2: real > real,G2: real > real] :
% 5.31/5.61 ( ! [I3: real] :
% 5.31/5.61 ( ( member_real @ I3 @ A4 )
% 5.31/5.61 => ( ( ord_less_eq_real @ zero_zero_real @ ( F2 @ I3 ) )
% 5.31/5.61 & ( ord_less_eq_real @ ( F2 @ I3 ) @ ( G2 @ I3 ) ) ) )
% 5.31/5.61 => ( ord_less_eq_real @ ( groups1681761925125756287l_real @ F2 @ A4 ) @ ( groups1681761925125756287l_real @ G2 @ A4 ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod_mono
% 5.31/5.61 thf(fact_6218_prod__mono,axiom,
% 5.31/5.61 ! [A4: set_nat,F2: nat > real,G2: nat > real] :
% 5.31/5.61 ( ! [I3: nat] :
% 5.31/5.61 ( ( member_nat @ I3 @ A4 )
% 5.31/5.61 => ( ( ord_less_eq_real @ zero_zero_real @ ( F2 @ I3 ) )
% 5.31/5.61 & ( ord_less_eq_real @ ( F2 @ I3 ) @ ( G2 @ I3 ) ) ) )
% 5.31/5.61 => ( ord_less_eq_real @ ( groups129246275422532515t_real @ F2 @ A4 ) @ ( groups129246275422532515t_real @ G2 @ A4 ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod_mono
% 5.31/5.61 thf(fact_6219_prod__mono,axiom,
% 5.31/5.61 ! [A4: set_int,F2: int > real,G2: int > real] :
% 5.31/5.61 ( ! [I3: int] :
% 5.31/5.61 ( ( member_int @ I3 @ A4 )
% 5.31/5.61 => ( ( ord_less_eq_real @ zero_zero_real @ ( F2 @ I3 ) )
% 5.31/5.61 & ( ord_less_eq_real @ ( F2 @ I3 ) @ ( G2 @ I3 ) ) ) )
% 5.31/5.61 => ( ord_less_eq_real @ ( groups2316167850115554303t_real @ F2 @ A4 ) @ ( groups2316167850115554303t_real @ G2 @ A4 ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod_mono
% 5.31/5.61 thf(fact_6220_prod__mono,axiom,
% 5.31/5.61 ! [A4: set_complex,F2: complex > rat,G2: complex > rat] :
% 5.31/5.61 ( ! [I3: complex] :
% 5.31/5.61 ( ( member_complex @ I3 @ A4 )
% 5.31/5.61 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ I3 ) )
% 5.31/5.61 & ( ord_less_eq_rat @ ( F2 @ I3 ) @ ( G2 @ I3 ) ) ) )
% 5.31/5.61 => ( ord_less_eq_rat @ ( groups225925009352817453ex_rat @ F2 @ A4 ) @ ( groups225925009352817453ex_rat @ G2 @ A4 ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod_mono
% 5.31/5.61 thf(fact_6221_prod__mono,axiom,
% 5.31/5.61 ! [A4: set_real,F2: real > rat,G2: real > rat] :
% 5.31/5.61 ( ! [I3: real] :
% 5.31/5.61 ( ( member_real @ I3 @ A4 )
% 5.31/5.61 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ I3 ) )
% 5.31/5.61 & ( ord_less_eq_rat @ ( F2 @ I3 ) @ ( G2 @ I3 ) ) ) )
% 5.31/5.61 => ( ord_less_eq_rat @ ( groups4061424788464935467al_rat @ F2 @ A4 ) @ ( groups4061424788464935467al_rat @ G2 @ A4 ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod_mono
% 5.31/5.61 thf(fact_6222_prod__mono,axiom,
% 5.31/5.61 ! [A4: set_nat,F2: nat > rat,G2: nat > rat] :
% 5.31/5.61 ( ! [I3: nat] :
% 5.31/5.61 ( ( member_nat @ I3 @ A4 )
% 5.31/5.61 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ I3 ) )
% 5.31/5.61 & ( ord_less_eq_rat @ ( F2 @ I3 ) @ ( G2 @ I3 ) ) ) )
% 5.31/5.61 => ( ord_less_eq_rat @ ( groups73079841787564623at_rat @ F2 @ A4 ) @ ( groups73079841787564623at_rat @ G2 @ A4 ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod_mono
% 5.31/5.61 thf(fact_6223_prod__mono,axiom,
% 5.31/5.61 ! [A4: set_int,F2: int > rat,G2: int > rat] :
% 5.31/5.61 ( ! [I3: int] :
% 5.31/5.61 ( ( member_int @ I3 @ A4 )
% 5.31/5.61 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ I3 ) )
% 5.31/5.61 & ( ord_less_eq_rat @ ( F2 @ I3 ) @ ( G2 @ I3 ) ) ) )
% 5.31/5.61 => ( ord_less_eq_rat @ ( groups1072433553688619179nt_rat @ F2 @ A4 ) @ ( groups1072433553688619179nt_rat @ G2 @ A4 ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod_mono
% 5.31/5.61 thf(fact_6224_prod__mono,axiom,
% 5.31/5.61 ! [A4: set_complex,F2: complex > nat,G2: complex > nat] :
% 5.31/5.61 ( ! [I3: complex] :
% 5.31/5.61 ( ( member_complex @ I3 @ A4 )
% 5.31/5.61 => ( ( ord_less_eq_nat @ zero_zero_nat @ ( F2 @ I3 ) )
% 5.31/5.61 & ( ord_less_eq_nat @ ( F2 @ I3 ) @ ( G2 @ I3 ) ) ) )
% 5.31/5.61 => ( ord_less_eq_nat @ ( groups861055069439313189ex_nat @ F2 @ A4 ) @ ( groups861055069439313189ex_nat @ G2 @ A4 ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod_mono
% 5.31/5.61 thf(fact_6225_prod__mono,axiom,
% 5.31/5.61 ! [A4: set_real,F2: real > nat,G2: real > nat] :
% 5.31/5.61 ( ! [I3: real] :
% 5.31/5.61 ( ( member_real @ I3 @ A4 )
% 5.31/5.61 => ( ( ord_less_eq_nat @ zero_zero_nat @ ( F2 @ I3 ) )
% 5.31/5.61 & ( ord_less_eq_nat @ ( F2 @ I3 ) @ ( G2 @ I3 ) ) ) )
% 5.31/5.61 => ( ord_less_eq_nat @ ( groups4696554848551431203al_nat @ F2 @ A4 ) @ ( groups4696554848551431203al_nat @ G2 @ A4 ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod_mono
% 5.31/5.61 thf(fact_6226_prod__nonneg,axiom,
% 5.31/5.61 ! [A4: set_nat,F2: nat > int] :
% 5.31/5.61 ( ! [X3: nat] :
% 5.31/5.61 ( ( member_nat @ X3 @ A4 )
% 5.31/5.61 => ( ord_less_eq_int @ zero_zero_int @ ( F2 @ X3 ) ) )
% 5.31/5.61 => ( ord_less_eq_int @ zero_zero_int @ ( groups705719431365010083at_int @ F2 @ A4 ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod_nonneg
% 5.31/5.61 thf(fact_6227_prod__nonneg,axiom,
% 5.31/5.61 ! [A4: set_int,F2: int > int] :
% 5.31/5.61 ( ! [X3: int] :
% 5.31/5.61 ( ( member_int @ X3 @ A4 )
% 5.31/5.61 => ( ord_less_eq_int @ zero_zero_int @ ( F2 @ X3 ) ) )
% 5.31/5.61 => ( ord_less_eq_int @ zero_zero_int @ ( groups1705073143266064639nt_int @ F2 @ A4 ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod_nonneg
% 5.31/5.61 thf(fact_6228_prod__nonneg,axiom,
% 5.31/5.61 ! [A4: set_nat,F2: nat > nat] :
% 5.31/5.61 ( ! [X3: nat] :
% 5.31/5.61 ( ( member_nat @ X3 @ A4 )
% 5.31/5.61 => ( ord_less_eq_nat @ zero_zero_nat @ ( F2 @ X3 ) ) )
% 5.31/5.61 => ( ord_less_eq_nat @ zero_zero_nat @ ( groups708209901874060359at_nat @ F2 @ A4 ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod_nonneg
% 5.31/5.61 thf(fact_6229_prod__pos,axiom,
% 5.31/5.61 ! [A4: set_nat,F2: nat > int] :
% 5.31/5.61 ( ! [X3: nat] :
% 5.31/5.61 ( ( member_nat @ X3 @ A4 )
% 5.31/5.61 => ( ord_less_int @ zero_zero_int @ ( F2 @ X3 ) ) )
% 5.31/5.61 => ( ord_less_int @ zero_zero_int @ ( groups705719431365010083at_int @ F2 @ A4 ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod_pos
% 5.31/5.61 thf(fact_6230_prod__pos,axiom,
% 5.31/5.61 ! [A4: set_int,F2: int > int] :
% 5.31/5.61 ( ! [X3: int] :
% 5.31/5.61 ( ( member_int @ X3 @ A4 )
% 5.31/5.61 => ( ord_less_int @ zero_zero_int @ ( F2 @ X3 ) ) )
% 5.31/5.61 => ( ord_less_int @ zero_zero_int @ ( groups1705073143266064639nt_int @ F2 @ A4 ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod_pos
% 5.31/5.61 thf(fact_6231_prod__pos,axiom,
% 5.31/5.61 ! [A4: set_nat,F2: nat > nat] :
% 5.31/5.61 ( ! [X3: nat] :
% 5.31/5.61 ( ( member_nat @ X3 @ A4 )
% 5.31/5.61 => ( ord_less_nat @ zero_zero_nat @ ( F2 @ X3 ) ) )
% 5.31/5.61 => ( ord_less_nat @ zero_zero_nat @ ( groups708209901874060359at_nat @ F2 @ A4 ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod_pos
% 5.31/5.61 thf(fact_6232_prod__ge__1,axiom,
% 5.31/5.61 ! [A4: set_complex,F2: complex > code_integer] :
% 5.31/5.61 ( ! [X3: complex] :
% 5.31/5.61 ( ( member_complex @ X3 @ A4 )
% 5.31/5.61 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( F2 @ X3 ) ) )
% 5.31/5.61 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( groups8682486955453173170nteger @ F2 @ A4 ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod_ge_1
% 5.31/5.61 thf(fact_6233_prod__ge__1,axiom,
% 5.31/5.61 ! [A4: set_real,F2: real > code_integer] :
% 5.31/5.61 ( ! [X3: real] :
% 5.31/5.61 ( ( member_real @ X3 @ A4 )
% 5.31/5.61 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( F2 @ X3 ) ) )
% 5.31/5.61 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( groups6225526099057966256nteger @ F2 @ A4 ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod_ge_1
% 5.31/5.61 thf(fact_6234_prod__ge__1,axiom,
% 5.31/5.61 ! [A4: set_nat,F2: nat > code_integer] :
% 5.31/5.61 ( ! [X3: nat] :
% 5.31/5.61 ( ( member_nat @ X3 @ A4 )
% 5.31/5.61 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( F2 @ X3 ) ) )
% 5.31/5.61 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( groups3455450783089532116nteger @ F2 @ A4 ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod_ge_1
% 5.31/5.61 thf(fact_6235_prod__ge__1,axiom,
% 5.31/5.61 ! [A4: set_int,F2: int > code_integer] :
% 5.31/5.61 ( ! [X3: int] :
% 5.31/5.61 ( ( member_int @ X3 @ A4 )
% 5.31/5.61 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( F2 @ X3 ) ) )
% 5.31/5.61 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( groups3827104343326376752nteger @ F2 @ A4 ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod_ge_1
% 5.31/5.61 thf(fact_6236_prod__ge__1,axiom,
% 5.31/5.61 ! [A4: set_complex,F2: complex > real] :
% 5.31/5.61 ( ! [X3: complex] :
% 5.31/5.61 ( ( member_complex @ X3 @ A4 )
% 5.31/5.61 => ( ord_less_eq_real @ one_one_real @ ( F2 @ X3 ) ) )
% 5.31/5.61 => ( ord_less_eq_real @ one_one_real @ ( groups766887009212190081x_real @ F2 @ A4 ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod_ge_1
% 5.31/5.61 thf(fact_6237_prod__ge__1,axiom,
% 5.31/5.61 ! [A4: set_real,F2: real > real] :
% 5.31/5.61 ( ! [X3: real] :
% 5.31/5.61 ( ( member_real @ X3 @ A4 )
% 5.31/5.61 => ( ord_less_eq_real @ one_one_real @ ( F2 @ X3 ) ) )
% 5.31/5.61 => ( ord_less_eq_real @ one_one_real @ ( groups1681761925125756287l_real @ F2 @ A4 ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod_ge_1
% 5.31/5.61 thf(fact_6238_prod__ge__1,axiom,
% 5.31/5.61 ! [A4: set_nat,F2: nat > real] :
% 5.31/5.61 ( ! [X3: nat] :
% 5.31/5.61 ( ( member_nat @ X3 @ A4 )
% 5.31/5.61 => ( ord_less_eq_real @ one_one_real @ ( F2 @ X3 ) ) )
% 5.31/5.61 => ( ord_less_eq_real @ one_one_real @ ( groups129246275422532515t_real @ F2 @ A4 ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod_ge_1
% 5.31/5.61 thf(fact_6239_prod__ge__1,axiom,
% 5.31/5.61 ! [A4: set_int,F2: int > real] :
% 5.31/5.61 ( ! [X3: int] :
% 5.31/5.61 ( ( member_int @ X3 @ A4 )
% 5.31/5.61 => ( ord_less_eq_real @ one_one_real @ ( F2 @ X3 ) ) )
% 5.31/5.61 => ( ord_less_eq_real @ one_one_real @ ( groups2316167850115554303t_real @ F2 @ A4 ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod_ge_1
% 5.31/5.61 thf(fact_6240_prod__ge__1,axiom,
% 5.31/5.61 ! [A4: set_complex,F2: complex > rat] :
% 5.31/5.61 ( ! [X3: complex] :
% 5.31/5.61 ( ( member_complex @ X3 @ A4 )
% 5.31/5.61 => ( ord_less_eq_rat @ one_one_rat @ ( F2 @ X3 ) ) )
% 5.31/5.61 => ( ord_less_eq_rat @ one_one_rat @ ( groups225925009352817453ex_rat @ F2 @ A4 ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod_ge_1
% 5.31/5.61 thf(fact_6241_prod__ge__1,axiom,
% 5.31/5.61 ! [A4: set_real,F2: real > rat] :
% 5.31/5.61 ( ! [X3: real] :
% 5.31/5.61 ( ( member_real @ X3 @ A4 )
% 5.31/5.61 => ( ord_less_eq_rat @ one_one_rat @ ( F2 @ X3 ) ) )
% 5.31/5.61 => ( ord_less_eq_rat @ one_one_rat @ ( groups4061424788464935467al_rat @ F2 @ A4 ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod_ge_1
% 5.31/5.61 thf(fact_6242_prod__zero,axiom,
% 5.31/5.61 ! [A4: set_nat,F2: nat > complex] :
% 5.31/5.61 ( ( finite_finite_nat @ A4 )
% 5.31/5.61 => ( ? [X5: nat] :
% 5.31/5.61 ( ( member_nat @ X5 @ A4 )
% 5.31/5.61 & ( ( F2 @ X5 )
% 5.31/5.61 = zero_zero_complex ) )
% 5.31/5.61 => ( ( groups6464643781859351333omplex @ F2 @ A4 )
% 5.31/5.61 = zero_zero_complex ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod_zero
% 5.31/5.61 thf(fact_6243_prod__zero,axiom,
% 5.31/5.61 ! [A4: set_int,F2: int > complex] :
% 5.31/5.61 ( ( finite_finite_int @ A4 )
% 5.31/5.61 => ( ? [X5: int] :
% 5.31/5.61 ( ( member_int @ X5 @ A4 )
% 5.31/5.61 & ( ( F2 @ X5 )
% 5.31/5.61 = zero_zero_complex ) )
% 5.31/5.61 => ( ( groups7440179247065528705omplex @ F2 @ A4 )
% 5.31/5.61 = zero_zero_complex ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod_zero
% 5.31/5.61 thf(fact_6244_prod__zero,axiom,
% 5.31/5.61 ! [A4: set_complex,F2: complex > complex] :
% 5.31/5.61 ( ( finite3207457112153483333omplex @ A4 )
% 5.31/5.61 => ( ? [X5: complex] :
% 5.31/5.61 ( ( member_complex @ X5 @ A4 )
% 5.31/5.61 & ( ( F2 @ X5 )
% 5.31/5.61 = zero_zero_complex ) )
% 5.31/5.61 => ( ( groups3708469109370488835omplex @ F2 @ A4 )
% 5.31/5.61 = zero_zero_complex ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod_zero
% 5.31/5.61 thf(fact_6245_prod__zero,axiom,
% 5.31/5.61 ! [A4: set_nat,F2: nat > real] :
% 5.31/5.61 ( ( finite_finite_nat @ A4 )
% 5.31/5.61 => ( ? [X5: nat] :
% 5.31/5.61 ( ( member_nat @ X5 @ A4 )
% 5.31/5.61 & ( ( F2 @ X5 )
% 5.31/5.61 = zero_zero_real ) )
% 5.31/5.61 => ( ( groups129246275422532515t_real @ F2 @ A4 )
% 5.31/5.61 = zero_zero_real ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod_zero
% 5.31/5.61 thf(fact_6246_prod__zero,axiom,
% 5.31/5.61 ! [A4: set_int,F2: int > real] :
% 5.31/5.61 ( ( finite_finite_int @ A4 )
% 5.31/5.61 => ( ? [X5: int] :
% 5.31/5.61 ( ( member_int @ X5 @ A4 )
% 5.31/5.61 & ( ( F2 @ X5 )
% 5.31/5.61 = zero_zero_real ) )
% 5.31/5.61 => ( ( groups2316167850115554303t_real @ F2 @ A4 )
% 5.31/5.61 = zero_zero_real ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod_zero
% 5.31/5.61 thf(fact_6247_prod__zero,axiom,
% 5.31/5.61 ! [A4: set_complex,F2: complex > real] :
% 5.31/5.61 ( ( finite3207457112153483333omplex @ A4 )
% 5.31/5.61 => ( ? [X5: complex] :
% 5.31/5.61 ( ( member_complex @ X5 @ A4 )
% 5.31/5.61 & ( ( F2 @ X5 )
% 5.31/5.61 = zero_zero_real ) )
% 5.31/5.61 => ( ( groups766887009212190081x_real @ F2 @ A4 )
% 5.31/5.61 = zero_zero_real ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod_zero
% 5.31/5.61 thf(fact_6248_prod__zero,axiom,
% 5.31/5.61 ! [A4: set_nat,F2: nat > rat] :
% 5.31/5.61 ( ( finite_finite_nat @ A4 )
% 5.31/5.61 => ( ? [X5: nat] :
% 5.31/5.61 ( ( member_nat @ X5 @ A4 )
% 5.31/5.61 & ( ( F2 @ X5 )
% 5.31/5.61 = zero_zero_rat ) )
% 5.31/5.61 => ( ( groups73079841787564623at_rat @ F2 @ A4 )
% 5.31/5.61 = zero_zero_rat ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod_zero
% 5.31/5.61 thf(fact_6249_prod__zero,axiom,
% 5.31/5.61 ! [A4: set_int,F2: int > rat] :
% 5.31/5.61 ( ( finite_finite_int @ A4 )
% 5.31/5.61 => ( ? [X5: int] :
% 5.31/5.61 ( ( member_int @ X5 @ A4 )
% 5.31/5.61 & ( ( F2 @ X5 )
% 5.31/5.61 = zero_zero_rat ) )
% 5.31/5.61 => ( ( groups1072433553688619179nt_rat @ F2 @ A4 )
% 5.31/5.61 = zero_zero_rat ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod_zero
% 5.31/5.61 thf(fact_6250_prod__zero,axiom,
% 5.31/5.61 ! [A4: set_complex,F2: complex > rat] :
% 5.31/5.61 ( ( finite3207457112153483333omplex @ A4 )
% 5.31/5.61 => ( ? [X5: complex] :
% 5.31/5.61 ( ( member_complex @ X5 @ A4 )
% 5.31/5.61 & ( ( F2 @ X5 )
% 5.31/5.61 = zero_zero_rat ) )
% 5.31/5.61 => ( ( groups225925009352817453ex_rat @ F2 @ A4 )
% 5.31/5.61 = zero_zero_rat ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod_zero
% 5.31/5.61 thf(fact_6251_prod__zero,axiom,
% 5.31/5.61 ! [A4: set_int,F2: int > nat] :
% 5.31/5.61 ( ( finite_finite_int @ A4 )
% 5.31/5.61 => ( ? [X5: int] :
% 5.31/5.61 ( ( member_int @ X5 @ A4 )
% 5.31/5.61 & ( ( F2 @ X5 )
% 5.31/5.61 = zero_zero_nat ) )
% 5.31/5.61 => ( ( groups1707563613775114915nt_nat @ F2 @ A4 )
% 5.31/5.61 = zero_zero_nat ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod_zero
% 5.31/5.61 thf(fact_6252_prod__atLeastAtMost__code,axiom,
% 5.31/5.61 ! [F2: nat > code_integer,A: nat,B: nat] :
% 5.31/5.61 ( ( groups3455450783089532116nteger @ F2 @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 5.31/5.61 = ( set_fo1084959871951514735nteger
% 5.31/5.61 @ ^ [A5: nat] : ( times_3573771949741848930nteger @ ( F2 @ A5 ) )
% 5.31/5.61 @ A
% 5.31/5.61 @ B
% 5.31/5.61 @ one_one_Code_integer ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod_atLeastAtMost_code
% 5.31/5.61 thf(fact_6253_prod__atLeastAtMost__code,axiom,
% 5.31/5.61 ! [F2: nat > complex,A: nat,B: nat] :
% 5.31/5.61 ( ( groups6464643781859351333omplex @ F2 @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 5.31/5.61 = ( set_fo1517530859248394432omplex
% 5.31/5.61 @ ^ [A5: nat] : ( times_times_complex @ ( F2 @ A5 ) )
% 5.31/5.61 @ A
% 5.31/5.61 @ B
% 5.31/5.61 @ one_one_complex ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod_atLeastAtMost_code
% 5.31/5.61 thf(fact_6254_prod__atLeastAtMost__code,axiom,
% 5.31/5.61 ! [F2: nat > real,A: nat,B: nat] :
% 5.31/5.61 ( ( groups129246275422532515t_real @ F2 @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 5.31/5.61 = ( set_fo3111899725591712190t_real
% 5.31/5.61 @ ^ [A5: nat] : ( times_times_real @ ( F2 @ A5 ) )
% 5.31/5.61 @ A
% 5.31/5.61 @ B
% 5.31/5.61 @ one_one_real ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod_atLeastAtMost_code
% 5.31/5.61 thf(fact_6255_prod__atLeastAtMost__code,axiom,
% 5.31/5.61 ! [F2: nat > rat,A: nat,B: nat] :
% 5.31/5.61 ( ( groups73079841787564623at_rat @ F2 @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 5.31/5.61 = ( set_fo1949268297981939178at_rat
% 5.31/5.61 @ ^ [A5: nat] : ( times_times_rat @ ( F2 @ A5 ) )
% 5.31/5.61 @ A
% 5.31/5.61 @ B
% 5.31/5.61 @ one_one_rat ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod_atLeastAtMost_code
% 5.31/5.61 thf(fact_6256_prod__atLeastAtMost__code,axiom,
% 5.31/5.61 ! [F2: nat > int,A: nat,B: nat] :
% 5.31/5.61 ( ( groups705719431365010083at_int @ F2 @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 5.31/5.61 = ( set_fo2581907887559384638at_int
% 5.31/5.61 @ ^ [A5: nat] : ( times_times_int @ ( F2 @ A5 ) )
% 5.31/5.61 @ A
% 5.31/5.61 @ B
% 5.31/5.61 @ one_one_int ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod_atLeastAtMost_code
% 5.31/5.61 thf(fact_6257_prod__atLeastAtMost__code,axiom,
% 5.31/5.61 ! [F2: nat > nat,A: nat,B: nat] :
% 5.31/5.61 ( ( groups708209901874060359at_nat @ F2 @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 5.31/5.61 = ( set_fo2584398358068434914at_nat
% 5.31/5.61 @ ^ [A5: nat] : ( times_times_nat @ ( F2 @ A5 ) )
% 5.31/5.61 @ A
% 5.31/5.61 @ B
% 5.31/5.61 @ one_one_nat ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod_atLeastAtMost_code
% 5.31/5.61 thf(fact_6258_Iio__eq__empty__iff,axiom,
% 5.31/5.61 ! [N: nat] :
% 5.31/5.61 ( ( ( set_ord_lessThan_nat @ N )
% 5.31/5.61 = bot_bot_set_nat )
% 5.31/5.61 = ( N = bot_bot_nat ) ) ).
% 5.31/5.61
% 5.31/5.61 % Iio_eq_empty_iff
% 5.31/5.61 thf(fact_6259_lessThan__strict__subset__iff,axiom,
% 5.31/5.61 ! [M2: real,N: real] :
% 5.31/5.61 ( ( ord_less_set_real @ ( set_or5984915006950818249n_real @ M2 ) @ ( set_or5984915006950818249n_real @ N ) )
% 5.31/5.61 = ( ord_less_real @ M2 @ N ) ) ).
% 5.31/5.61
% 5.31/5.61 % lessThan_strict_subset_iff
% 5.31/5.61 thf(fact_6260_lessThan__strict__subset__iff,axiom,
% 5.31/5.61 ! [M2: rat,N: rat] :
% 5.31/5.61 ( ( ord_less_set_rat @ ( set_ord_lessThan_rat @ M2 ) @ ( set_ord_lessThan_rat @ N ) )
% 5.31/5.61 = ( ord_less_rat @ M2 @ N ) ) ).
% 5.31/5.61
% 5.31/5.61 % lessThan_strict_subset_iff
% 5.31/5.61 thf(fact_6261_lessThan__strict__subset__iff,axiom,
% 5.31/5.61 ! [M2: num,N: num] :
% 5.31/5.61 ( ( ord_less_set_num @ ( set_ord_lessThan_num @ M2 ) @ ( set_ord_lessThan_num @ N ) )
% 5.31/5.61 = ( ord_less_num @ M2 @ N ) ) ).
% 5.31/5.61
% 5.31/5.61 % lessThan_strict_subset_iff
% 5.31/5.61 thf(fact_6262_lessThan__strict__subset__iff,axiom,
% 5.31/5.61 ! [M2: int,N: int] :
% 5.31/5.61 ( ( ord_less_set_int @ ( set_ord_lessThan_int @ M2 ) @ ( set_ord_lessThan_int @ N ) )
% 5.31/5.61 = ( ord_less_int @ M2 @ N ) ) ).
% 5.31/5.61
% 5.31/5.61 % lessThan_strict_subset_iff
% 5.31/5.61 thf(fact_6263_lessThan__strict__subset__iff,axiom,
% 5.31/5.61 ! [M2: nat,N: nat] :
% 5.31/5.61 ( ( ord_less_set_nat @ ( set_ord_lessThan_nat @ M2 ) @ ( set_ord_lessThan_nat @ N ) )
% 5.31/5.61 = ( ord_less_nat @ M2 @ N ) ) ).
% 5.31/5.61
% 5.31/5.61 % lessThan_strict_subset_iff
% 5.31/5.61 thf(fact_6264_lessThan__Suc,axiom,
% 5.31/5.61 ! [K2: nat] :
% 5.31/5.61 ( ( set_ord_lessThan_nat @ ( suc @ K2 ) )
% 5.31/5.61 = ( insert_nat @ K2 @ ( set_ord_lessThan_nat @ K2 ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % lessThan_Suc
% 5.31/5.61 thf(fact_6265_lessThan__empty__iff,axiom,
% 5.31/5.61 ! [N: nat] :
% 5.31/5.61 ( ( ( set_ord_lessThan_nat @ N )
% 5.31/5.61 = bot_bot_set_nat )
% 5.31/5.61 = ( N = zero_zero_nat ) ) ).
% 5.31/5.61
% 5.31/5.61 % lessThan_empty_iff
% 5.31/5.61 thf(fact_6266_dbl__def,axiom,
% 5.31/5.61 ( neg_numeral_dbl_real
% 5.31/5.61 = ( ^ [X4: real] : ( plus_plus_real @ X4 @ X4 ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % dbl_def
% 5.31/5.61 thf(fact_6267_dbl__def,axiom,
% 5.31/5.61 ( neg_numeral_dbl_rat
% 5.31/5.61 = ( ^ [X4: rat] : ( plus_plus_rat @ X4 @ X4 ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % dbl_def
% 5.31/5.61 thf(fact_6268_dbl__def,axiom,
% 5.31/5.61 ( neg_numeral_dbl_int
% 5.31/5.61 = ( ^ [X4: int] : ( plus_plus_int @ X4 @ X4 ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % dbl_def
% 5.31/5.61 thf(fact_6269_prod_Oshift__bounds__cl__Suc__ivl,axiom,
% 5.31/5.61 ! [G2: nat > int,M2: nat,N: nat] :
% 5.31/5.61 ( ( groups705719431365010083at_int @ G2 @ ( set_or1269000886237332187st_nat @ ( suc @ M2 ) @ ( suc @ N ) ) )
% 5.31/5.61 = ( groups705719431365010083at_int
% 5.31/5.61 @ ^ [I: nat] : ( G2 @ ( suc @ I ) )
% 5.31/5.61 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.shift_bounds_cl_Suc_ivl
% 5.31/5.61 thf(fact_6270_prod_Oshift__bounds__cl__Suc__ivl,axiom,
% 5.31/5.61 ! [G2: nat > nat,M2: nat,N: nat] :
% 5.31/5.61 ( ( groups708209901874060359at_nat @ G2 @ ( set_or1269000886237332187st_nat @ ( suc @ M2 ) @ ( suc @ N ) ) )
% 5.31/5.61 = ( groups708209901874060359at_nat
% 5.31/5.61 @ ^ [I: nat] : ( G2 @ ( suc @ I ) )
% 5.31/5.61 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.shift_bounds_cl_Suc_ivl
% 5.31/5.61 thf(fact_6271_prod_Oshift__bounds__cl__nat__ivl,axiom,
% 5.31/5.61 ! [G2: nat > int,M2: nat,K2: nat,N: nat] :
% 5.31/5.61 ( ( groups705719431365010083at_int @ G2 @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ M2 @ K2 ) @ ( plus_plus_nat @ N @ K2 ) ) )
% 5.31/5.61 = ( groups705719431365010083at_int
% 5.31/5.61 @ ^ [I: nat] : ( G2 @ ( plus_plus_nat @ I @ K2 ) )
% 5.31/5.61 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.shift_bounds_cl_nat_ivl
% 5.31/5.61 thf(fact_6272_prod_Oshift__bounds__cl__nat__ivl,axiom,
% 5.31/5.61 ! [G2: nat > nat,M2: nat,K2: nat,N: nat] :
% 5.31/5.61 ( ( groups708209901874060359at_nat @ G2 @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ M2 @ K2 ) @ ( plus_plus_nat @ N @ K2 ) ) )
% 5.31/5.61 = ( groups708209901874060359at_nat
% 5.31/5.61 @ ^ [I: nat] : ( G2 @ ( plus_plus_nat @ I @ K2 ) )
% 5.31/5.61 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.shift_bounds_cl_nat_ivl
% 5.31/5.61 thf(fact_6273_prod__le__1,axiom,
% 5.31/5.61 ! [A4: set_complex,F2: complex > code_integer] :
% 5.31/5.61 ( ! [X3: complex] :
% 5.31/5.61 ( ( member_complex @ X3 @ A4 )
% 5.31/5.61 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F2 @ X3 ) )
% 5.31/5.61 & ( ord_le3102999989581377725nteger @ ( F2 @ X3 ) @ one_one_Code_integer ) ) )
% 5.31/5.61 => ( ord_le3102999989581377725nteger @ ( groups8682486955453173170nteger @ F2 @ A4 ) @ one_one_Code_integer ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod_le_1
% 5.31/5.61 thf(fact_6274_prod__le__1,axiom,
% 5.31/5.61 ! [A4: set_real,F2: real > code_integer] :
% 5.31/5.61 ( ! [X3: real] :
% 5.31/5.61 ( ( member_real @ X3 @ A4 )
% 5.31/5.61 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F2 @ X3 ) )
% 5.31/5.61 & ( ord_le3102999989581377725nteger @ ( F2 @ X3 ) @ one_one_Code_integer ) ) )
% 5.31/5.61 => ( ord_le3102999989581377725nteger @ ( groups6225526099057966256nteger @ F2 @ A4 ) @ one_one_Code_integer ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod_le_1
% 5.31/5.61 thf(fact_6275_prod__le__1,axiom,
% 5.31/5.61 ! [A4: set_nat,F2: nat > code_integer] :
% 5.31/5.61 ( ! [X3: nat] :
% 5.31/5.61 ( ( member_nat @ X3 @ A4 )
% 5.31/5.61 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F2 @ X3 ) )
% 5.31/5.61 & ( ord_le3102999989581377725nteger @ ( F2 @ X3 ) @ one_one_Code_integer ) ) )
% 5.31/5.61 => ( ord_le3102999989581377725nteger @ ( groups3455450783089532116nteger @ F2 @ A4 ) @ one_one_Code_integer ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod_le_1
% 5.31/5.61 thf(fact_6276_prod__le__1,axiom,
% 5.31/5.61 ! [A4: set_int,F2: int > code_integer] :
% 5.31/5.61 ( ! [X3: int] :
% 5.31/5.61 ( ( member_int @ X3 @ A4 )
% 5.31/5.61 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F2 @ X3 ) )
% 5.31/5.61 & ( ord_le3102999989581377725nteger @ ( F2 @ X3 ) @ one_one_Code_integer ) ) )
% 5.31/5.61 => ( ord_le3102999989581377725nteger @ ( groups3827104343326376752nteger @ F2 @ A4 ) @ one_one_Code_integer ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod_le_1
% 5.31/5.61 thf(fact_6277_prod__le__1,axiom,
% 5.31/5.61 ! [A4: set_complex,F2: complex > real] :
% 5.31/5.61 ( ! [X3: complex] :
% 5.31/5.61 ( ( member_complex @ X3 @ A4 )
% 5.31/5.61 => ( ( ord_less_eq_real @ zero_zero_real @ ( F2 @ X3 ) )
% 5.31/5.61 & ( ord_less_eq_real @ ( F2 @ X3 ) @ one_one_real ) ) )
% 5.31/5.61 => ( ord_less_eq_real @ ( groups766887009212190081x_real @ F2 @ A4 ) @ one_one_real ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod_le_1
% 5.31/5.61 thf(fact_6278_prod__le__1,axiom,
% 5.31/5.61 ! [A4: set_real,F2: real > real] :
% 5.31/5.61 ( ! [X3: real] :
% 5.31/5.61 ( ( member_real @ X3 @ A4 )
% 5.31/5.61 => ( ( ord_less_eq_real @ zero_zero_real @ ( F2 @ X3 ) )
% 5.31/5.61 & ( ord_less_eq_real @ ( F2 @ X3 ) @ one_one_real ) ) )
% 5.31/5.61 => ( ord_less_eq_real @ ( groups1681761925125756287l_real @ F2 @ A4 ) @ one_one_real ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod_le_1
% 5.31/5.61 thf(fact_6279_prod__le__1,axiom,
% 5.31/5.61 ! [A4: set_nat,F2: nat > real] :
% 5.31/5.61 ( ! [X3: nat] :
% 5.31/5.61 ( ( member_nat @ X3 @ A4 )
% 5.31/5.61 => ( ( ord_less_eq_real @ zero_zero_real @ ( F2 @ X3 ) )
% 5.31/5.61 & ( ord_less_eq_real @ ( F2 @ X3 ) @ one_one_real ) ) )
% 5.31/5.61 => ( ord_less_eq_real @ ( groups129246275422532515t_real @ F2 @ A4 ) @ one_one_real ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod_le_1
% 5.31/5.61 thf(fact_6280_prod__le__1,axiom,
% 5.31/5.61 ! [A4: set_int,F2: int > real] :
% 5.31/5.61 ( ! [X3: int] :
% 5.31/5.61 ( ( member_int @ X3 @ A4 )
% 5.31/5.61 => ( ( ord_less_eq_real @ zero_zero_real @ ( F2 @ X3 ) )
% 5.31/5.61 & ( ord_less_eq_real @ ( F2 @ X3 ) @ one_one_real ) ) )
% 5.31/5.61 => ( ord_less_eq_real @ ( groups2316167850115554303t_real @ F2 @ A4 ) @ one_one_real ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod_le_1
% 5.31/5.61 thf(fact_6281_prod__le__1,axiom,
% 5.31/5.61 ! [A4: set_complex,F2: complex > rat] :
% 5.31/5.61 ( ! [X3: complex] :
% 5.31/5.61 ( ( member_complex @ X3 @ A4 )
% 5.31/5.61 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ X3 ) )
% 5.31/5.61 & ( ord_less_eq_rat @ ( F2 @ X3 ) @ one_one_rat ) ) )
% 5.31/5.61 => ( ord_less_eq_rat @ ( groups225925009352817453ex_rat @ F2 @ A4 ) @ one_one_rat ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod_le_1
% 5.31/5.61 thf(fact_6282_prod__le__1,axiom,
% 5.31/5.61 ! [A4: set_real,F2: real > rat] :
% 5.31/5.61 ( ! [X3: real] :
% 5.31/5.61 ( ( member_real @ X3 @ A4 )
% 5.31/5.61 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ X3 ) )
% 5.31/5.61 & ( ord_less_eq_rat @ ( F2 @ X3 ) @ one_one_rat ) ) )
% 5.31/5.61 => ( ord_less_eq_rat @ ( groups4061424788464935467al_rat @ F2 @ A4 ) @ one_one_rat ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod_le_1
% 5.31/5.61 thf(fact_6283_prod_Orelated,axiom,
% 5.31/5.61 ! [R2: code_integer > code_integer > $o,S3: set_nat,H: nat > code_integer,G2: nat > code_integer] :
% 5.31/5.61 ( ( R2 @ one_one_Code_integer @ one_one_Code_integer )
% 5.31/5.61 => ( ! [X15: code_integer,Y15: code_integer,X23: code_integer,Y23: code_integer] :
% 5.31/5.61 ( ( ( R2 @ X15 @ X23 )
% 5.31/5.61 & ( R2 @ Y15 @ Y23 ) )
% 5.31/5.61 => ( R2 @ ( times_3573771949741848930nteger @ X15 @ Y15 ) @ ( times_3573771949741848930nteger @ X23 @ Y23 ) ) )
% 5.31/5.61 => ( ( finite_finite_nat @ S3 )
% 5.31/5.61 => ( ! [X3: nat] :
% 5.31/5.61 ( ( member_nat @ X3 @ S3 )
% 5.31/5.61 => ( R2 @ ( H @ X3 ) @ ( G2 @ X3 ) ) )
% 5.31/5.61 => ( R2 @ ( groups3455450783089532116nteger @ H @ S3 ) @ ( groups3455450783089532116nteger @ G2 @ S3 ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.related
% 5.31/5.61 thf(fact_6284_prod_Orelated,axiom,
% 5.31/5.61 ! [R2: code_integer > code_integer > $o,S3: set_int,H: int > code_integer,G2: int > code_integer] :
% 5.31/5.61 ( ( R2 @ one_one_Code_integer @ one_one_Code_integer )
% 5.31/5.61 => ( ! [X15: code_integer,Y15: code_integer,X23: code_integer,Y23: code_integer] :
% 5.31/5.61 ( ( ( R2 @ X15 @ X23 )
% 5.31/5.61 & ( R2 @ Y15 @ Y23 ) )
% 5.31/5.61 => ( R2 @ ( times_3573771949741848930nteger @ X15 @ Y15 ) @ ( times_3573771949741848930nteger @ X23 @ Y23 ) ) )
% 5.31/5.61 => ( ( finite_finite_int @ S3 )
% 5.31/5.61 => ( ! [X3: int] :
% 5.31/5.61 ( ( member_int @ X3 @ S3 )
% 5.31/5.61 => ( R2 @ ( H @ X3 ) @ ( G2 @ X3 ) ) )
% 5.31/5.61 => ( R2 @ ( groups3827104343326376752nteger @ H @ S3 ) @ ( groups3827104343326376752nteger @ G2 @ S3 ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.related
% 5.31/5.61 thf(fact_6285_prod_Orelated,axiom,
% 5.31/5.61 ! [R2: code_integer > code_integer > $o,S3: set_complex,H: complex > code_integer,G2: complex > code_integer] :
% 5.31/5.61 ( ( R2 @ one_one_Code_integer @ one_one_Code_integer )
% 5.31/5.61 => ( ! [X15: code_integer,Y15: code_integer,X23: code_integer,Y23: code_integer] :
% 5.31/5.61 ( ( ( R2 @ X15 @ X23 )
% 5.31/5.61 & ( R2 @ Y15 @ Y23 ) )
% 5.31/5.61 => ( R2 @ ( times_3573771949741848930nteger @ X15 @ Y15 ) @ ( times_3573771949741848930nteger @ X23 @ Y23 ) ) )
% 5.31/5.61 => ( ( finite3207457112153483333omplex @ S3 )
% 5.31/5.61 => ( ! [X3: complex] :
% 5.31/5.61 ( ( member_complex @ X3 @ S3 )
% 5.31/5.61 => ( R2 @ ( H @ X3 ) @ ( G2 @ X3 ) ) )
% 5.31/5.61 => ( R2 @ ( groups8682486955453173170nteger @ H @ S3 ) @ ( groups8682486955453173170nteger @ G2 @ S3 ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.related
% 5.31/5.61 thf(fact_6286_prod_Orelated,axiom,
% 5.31/5.61 ! [R2: complex > complex > $o,S3: set_nat,H: nat > complex,G2: nat > complex] :
% 5.31/5.61 ( ( R2 @ one_one_complex @ one_one_complex )
% 5.31/5.61 => ( ! [X15: complex,Y15: complex,X23: complex,Y23: complex] :
% 5.31/5.61 ( ( ( R2 @ X15 @ X23 )
% 5.31/5.61 & ( R2 @ Y15 @ Y23 ) )
% 5.31/5.61 => ( R2 @ ( times_times_complex @ X15 @ Y15 ) @ ( times_times_complex @ X23 @ Y23 ) ) )
% 5.31/5.61 => ( ( finite_finite_nat @ S3 )
% 5.31/5.61 => ( ! [X3: nat] :
% 5.31/5.61 ( ( member_nat @ X3 @ S3 )
% 5.31/5.61 => ( R2 @ ( H @ X3 ) @ ( G2 @ X3 ) ) )
% 5.31/5.61 => ( R2 @ ( groups6464643781859351333omplex @ H @ S3 ) @ ( groups6464643781859351333omplex @ G2 @ S3 ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.related
% 5.31/5.61 thf(fact_6287_prod_Orelated,axiom,
% 5.31/5.61 ! [R2: complex > complex > $o,S3: set_int,H: int > complex,G2: int > complex] :
% 5.31/5.61 ( ( R2 @ one_one_complex @ one_one_complex )
% 5.31/5.61 => ( ! [X15: complex,Y15: complex,X23: complex,Y23: complex] :
% 5.31/5.61 ( ( ( R2 @ X15 @ X23 )
% 5.31/5.61 & ( R2 @ Y15 @ Y23 ) )
% 5.31/5.61 => ( R2 @ ( times_times_complex @ X15 @ Y15 ) @ ( times_times_complex @ X23 @ Y23 ) ) )
% 5.31/5.61 => ( ( finite_finite_int @ S3 )
% 5.31/5.61 => ( ! [X3: int] :
% 5.31/5.61 ( ( member_int @ X3 @ S3 )
% 5.31/5.61 => ( R2 @ ( H @ X3 ) @ ( G2 @ X3 ) ) )
% 5.31/5.61 => ( R2 @ ( groups7440179247065528705omplex @ H @ S3 ) @ ( groups7440179247065528705omplex @ G2 @ S3 ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.related
% 5.31/5.61 thf(fact_6288_prod_Orelated,axiom,
% 5.31/5.61 ! [R2: complex > complex > $o,S3: set_complex,H: complex > complex,G2: complex > complex] :
% 5.31/5.61 ( ( R2 @ one_one_complex @ one_one_complex )
% 5.31/5.61 => ( ! [X15: complex,Y15: complex,X23: complex,Y23: complex] :
% 5.31/5.61 ( ( ( R2 @ X15 @ X23 )
% 5.31/5.61 & ( R2 @ Y15 @ Y23 ) )
% 5.31/5.61 => ( R2 @ ( times_times_complex @ X15 @ Y15 ) @ ( times_times_complex @ X23 @ Y23 ) ) )
% 5.31/5.61 => ( ( finite3207457112153483333omplex @ S3 )
% 5.31/5.61 => ( ! [X3: complex] :
% 5.31/5.61 ( ( member_complex @ X3 @ S3 )
% 5.31/5.61 => ( R2 @ ( H @ X3 ) @ ( G2 @ X3 ) ) )
% 5.31/5.61 => ( R2 @ ( groups3708469109370488835omplex @ H @ S3 ) @ ( groups3708469109370488835omplex @ G2 @ S3 ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.related
% 5.31/5.61 thf(fact_6289_prod_Orelated,axiom,
% 5.31/5.61 ! [R2: real > real > $o,S3: set_nat,H: nat > real,G2: nat > real] :
% 5.31/5.61 ( ( R2 @ one_one_real @ one_one_real )
% 5.31/5.61 => ( ! [X15: real,Y15: real,X23: real,Y23: real] :
% 5.31/5.61 ( ( ( R2 @ X15 @ X23 )
% 5.31/5.61 & ( R2 @ Y15 @ Y23 ) )
% 5.31/5.61 => ( R2 @ ( times_times_real @ X15 @ Y15 ) @ ( times_times_real @ X23 @ Y23 ) ) )
% 5.31/5.61 => ( ( finite_finite_nat @ S3 )
% 5.31/5.61 => ( ! [X3: nat] :
% 5.31/5.61 ( ( member_nat @ X3 @ S3 )
% 5.31/5.61 => ( R2 @ ( H @ X3 ) @ ( G2 @ X3 ) ) )
% 5.31/5.61 => ( R2 @ ( groups129246275422532515t_real @ H @ S3 ) @ ( groups129246275422532515t_real @ G2 @ S3 ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.related
% 5.31/5.61 thf(fact_6290_prod_Orelated,axiom,
% 5.31/5.61 ! [R2: real > real > $o,S3: set_int,H: int > real,G2: int > real] :
% 5.31/5.61 ( ( R2 @ one_one_real @ one_one_real )
% 5.31/5.61 => ( ! [X15: real,Y15: real,X23: real,Y23: real] :
% 5.31/5.61 ( ( ( R2 @ X15 @ X23 )
% 5.31/5.61 & ( R2 @ Y15 @ Y23 ) )
% 5.31/5.61 => ( R2 @ ( times_times_real @ X15 @ Y15 ) @ ( times_times_real @ X23 @ Y23 ) ) )
% 5.31/5.61 => ( ( finite_finite_int @ S3 )
% 5.31/5.61 => ( ! [X3: int] :
% 5.31/5.61 ( ( member_int @ X3 @ S3 )
% 5.31/5.61 => ( R2 @ ( H @ X3 ) @ ( G2 @ X3 ) ) )
% 5.31/5.61 => ( R2 @ ( groups2316167850115554303t_real @ H @ S3 ) @ ( groups2316167850115554303t_real @ G2 @ S3 ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.related
% 5.31/5.61 thf(fact_6291_prod_Orelated,axiom,
% 5.31/5.61 ! [R2: real > real > $o,S3: set_complex,H: complex > real,G2: complex > real] :
% 5.31/5.61 ( ( R2 @ one_one_real @ one_one_real )
% 5.31/5.61 => ( ! [X15: real,Y15: real,X23: real,Y23: real] :
% 5.31/5.61 ( ( ( R2 @ X15 @ X23 )
% 5.31/5.61 & ( R2 @ Y15 @ Y23 ) )
% 5.31/5.61 => ( R2 @ ( times_times_real @ X15 @ Y15 ) @ ( times_times_real @ X23 @ Y23 ) ) )
% 5.31/5.61 => ( ( finite3207457112153483333omplex @ S3 )
% 5.31/5.61 => ( ! [X3: complex] :
% 5.31/5.61 ( ( member_complex @ X3 @ S3 )
% 5.31/5.61 => ( R2 @ ( H @ X3 ) @ ( G2 @ X3 ) ) )
% 5.31/5.61 => ( R2 @ ( groups766887009212190081x_real @ H @ S3 ) @ ( groups766887009212190081x_real @ G2 @ S3 ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.related
% 5.31/5.61 thf(fact_6292_prod_Orelated,axiom,
% 5.31/5.61 ! [R2: rat > rat > $o,S3: set_nat,H: nat > rat,G2: nat > rat] :
% 5.31/5.61 ( ( R2 @ one_one_rat @ one_one_rat )
% 5.31/5.61 => ( ! [X15: rat,Y15: rat,X23: rat,Y23: rat] :
% 5.31/5.61 ( ( ( R2 @ X15 @ X23 )
% 5.31/5.61 & ( R2 @ Y15 @ Y23 ) )
% 5.31/5.61 => ( R2 @ ( times_times_rat @ X15 @ Y15 ) @ ( times_times_rat @ X23 @ Y23 ) ) )
% 5.31/5.61 => ( ( finite_finite_nat @ S3 )
% 5.31/5.61 => ( ! [X3: nat] :
% 5.31/5.61 ( ( member_nat @ X3 @ S3 )
% 5.31/5.61 => ( R2 @ ( H @ X3 ) @ ( G2 @ X3 ) ) )
% 5.31/5.61 => ( R2 @ ( groups73079841787564623at_rat @ H @ S3 ) @ ( groups73079841787564623at_rat @ G2 @ S3 ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.related
% 5.31/5.61 thf(fact_6293_prod_Oinsert__if,axiom,
% 5.31/5.61 ! [A4: set_real,X: real,G2: real > real] :
% 5.31/5.61 ( ( finite_finite_real @ A4 )
% 5.31/5.61 => ( ( ( member_real @ X @ A4 )
% 5.31/5.61 => ( ( groups1681761925125756287l_real @ G2 @ ( insert_real @ X @ A4 ) )
% 5.31/5.61 = ( groups1681761925125756287l_real @ G2 @ A4 ) ) )
% 5.31/5.61 & ( ~ ( member_real @ X @ A4 )
% 5.31/5.61 => ( ( groups1681761925125756287l_real @ G2 @ ( insert_real @ X @ A4 ) )
% 5.31/5.61 = ( times_times_real @ ( G2 @ X ) @ ( groups1681761925125756287l_real @ G2 @ A4 ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.insert_if
% 5.31/5.61 thf(fact_6294_prod_Oinsert__if,axiom,
% 5.31/5.61 ! [A4: set_nat,X: nat,G2: nat > real] :
% 5.31/5.61 ( ( finite_finite_nat @ A4 )
% 5.31/5.61 => ( ( ( member_nat @ X @ A4 )
% 5.31/5.61 => ( ( groups129246275422532515t_real @ G2 @ ( insert_nat @ X @ A4 ) )
% 5.31/5.61 = ( groups129246275422532515t_real @ G2 @ A4 ) ) )
% 5.31/5.61 & ( ~ ( member_nat @ X @ A4 )
% 5.31/5.61 => ( ( groups129246275422532515t_real @ G2 @ ( insert_nat @ X @ A4 ) )
% 5.31/5.61 = ( times_times_real @ ( G2 @ X ) @ ( groups129246275422532515t_real @ G2 @ A4 ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.insert_if
% 5.31/5.61 thf(fact_6295_prod_Oinsert__if,axiom,
% 5.31/5.61 ! [A4: set_int,X: int,G2: int > real] :
% 5.31/5.61 ( ( finite_finite_int @ A4 )
% 5.31/5.61 => ( ( ( member_int @ X @ A4 )
% 5.31/5.61 => ( ( groups2316167850115554303t_real @ G2 @ ( insert_int @ X @ A4 ) )
% 5.31/5.61 = ( groups2316167850115554303t_real @ G2 @ A4 ) ) )
% 5.31/5.61 & ( ~ ( member_int @ X @ A4 )
% 5.31/5.61 => ( ( groups2316167850115554303t_real @ G2 @ ( insert_int @ X @ A4 ) )
% 5.31/5.61 = ( times_times_real @ ( G2 @ X ) @ ( groups2316167850115554303t_real @ G2 @ A4 ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.insert_if
% 5.31/5.61 thf(fact_6296_prod_Oinsert__if,axiom,
% 5.31/5.61 ! [A4: set_complex,X: complex,G2: complex > real] :
% 5.31/5.61 ( ( finite3207457112153483333omplex @ A4 )
% 5.31/5.61 => ( ( ( member_complex @ X @ A4 )
% 5.31/5.61 => ( ( groups766887009212190081x_real @ G2 @ ( insert_complex @ X @ A4 ) )
% 5.31/5.61 = ( groups766887009212190081x_real @ G2 @ A4 ) ) )
% 5.31/5.61 & ( ~ ( member_complex @ X @ A4 )
% 5.31/5.61 => ( ( groups766887009212190081x_real @ G2 @ ( insert_complex @ X @ A4 ) )
% 5.31/5.61 = ( times_times_real @ ( G2 @ X ) @ ( groups766887009212190081x_real @ G2 @ A4 ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.insert_if
% 5.31/5.61 thf(fact_6297_prod_Oinsert__if,axiom,
% 5.31/5.61 ! [A4: set_real,X: real,G2: real > rat] :
% 5.31/5.61 ( ( finite_finite_real @ A4 )
% 5.31/5.61 => ( ( ( member_real @ X @ A4 )
% 5.31/5.61 => ( ( groups4061424788464935467al_rat @ G2 @ ( insert_real @ X @ A4 ) )
% 5.31/5.61 = ( groups4061424788464935467al_rat @ G2 @ A4 ) ) )
% 5.31/5.61 & ( ~ ( member_real @ X @ A4 )
% 5.31/5.61 => ( ( groups4061424788464935467al_rat @ G2 @ ( insert_real @ X @ A4 ) )
% 5.31/5.61 = ( times_times_rat @ ( G2 @ X ) @ ( groups4061424788464935467al_rat @ G2 @ A4 ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.insert_if
% 5.31/5.61 thf(fact_6298_prod_Oinsert__if,axiom,
% 5.31/5.61 ! [A4: set_nat,X: nat,G2: nat > rat] :
% 5.31/5.61 ( ( finite_finite_nat @ A4 )
% 5.31/5.61 => ( ( ( member_nat @ X @ A4 )
% 5.31/5.61 => ( ( groups73079841787564623at_rat @ G2 @ ( insert_nat @ X @ A4 ) )
% 5.31/5.61 = ( groups73079841787564623at_rat @ G2 @ A4 ) ) )
% 5.31/5.61 & ( ~ ( member_nat @ X @ A4 )
% 5.31/5.61 => ( ( groups73079841787564623at_rat @ G2 @ ( insert_nat @ X @ A4 ) )
% 5.31/5.61 = ( times_times_rat @ ( G2 @ X ) @ ( groups73079841787564623at_rat @ G2 @ A4 ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.insert_if
% 5.31/5.61 thf(fact_6299_prod_Oinsert__if,axiom,
% 5.31/5.61 ! [A4: set_int,X: int,G2: int > rat] :
% 5.31/5.61 ( ( finite_finite_int @ A4 )
% 5.31/5.61 => ( ( ( member_int @ X @ A4 )
% 5.31/5.61 => ( ( groups1072433553688619179nt_rat @ G2 @ ( insert_int @ X @ A4 ) )
% 5.31/5.61 = ( groups1072433553688619179nt_rat @ G2 @ A4 ) ) )
% 5.31/5.61 & ( ~ ( member_int @ X @ A4 )
% 5.31/5.61 => ( ( groups1072433553688619179nt_rat @ G2 @ ( insert_int @ X @ A4 ) )
% 5.31/5.61 = ( times_times_rat @ ( G2 @ X ) @ ( groups1072433553688619179nt_rat @ G2 @ A4 ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.insert_if
% 5.31/5.61 thf(fact_6300_prod_Oinsert__if,axiom,
% 5.31/5.61 ! [A4: set_complex,X: complex,G2: complex > rat] :
% 5.31/5.61 ( ( finite3207457112153483333omplex @ A4 )
% 5.31/5.61 => ( ( ( member_complex @ X @ A4 )
% 5.31/5.61 => ( ( groups225925009352817453ex_rat @ G2 @ ( insert_complex @ X @ A4 ) )
% 5.31/5.61 = ( groups225925009352817453ex_rat @ G2 @ A4 ) ) )
% 5.31/5.61 & ( ~ ( member_complex @ X @ A4 )
% 5.31/5.61 => ( ( groups225925009352817453ex_rat @ G2 @ ( insert_complex @ X @ A4 ) )
% 5.31/5.61 = ( times_times_rat @ ( G2 @ X ) @ ( groups225925009352817453ex_rat @ G2 @ A4 ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.insert_if
% 5.31/5.61 thf(fact_6301_prod_Oinsert__if,axiom,
% 5.31/5.61 ! [A4: set_real,X: real,G2: real > nat] :
% 5.31/5.61 ( ( finite_finite_real @ A4 )
% 5.31/5.61 => ( ( ( member_real @ X @ A4 )
% 5.31/5.61 => ( ( groups4696554848551431203al_nat @ G2 @ ( insert_real @ X @ A4 ) )
% 5.31/5.61 = ( groups4696554848551431203al_nat @ G2 @ A4 ) ) )
% 5.31/5.61 & ( ~ ( member_real @ X @ A4 )
% 5.31/5.61 => ( ( groups4696554848551431203al_nat @ G2 @ ( insert_real @ X @ A4 ) )
% 5.31/5.61 = ( times_times_nat @ ( G2 @ X ) @ ( groups4696554848551431203al_nat @ G2 @ A4 ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.insert_if
% 5.31/5.61 thf(fact_6302_prod_Oinsert__if,axiom,
% 5.31/5.61 ! [A4: set_int,X: int,G2: int > nat] :
% 5.31/5.61 ( ( finite_finite_int @ A4 )
% 5.31/5.61 => ( ( ( member_int @ X @ A4 )
% 5.31/5.61 => ( ( groups1707563613775114915nt_nat @ G2 @ ( insert_int @ X @ A4 ) )
% 5.31/5.61 = ( groups1707563613775114915nt_nat @ G2 @ A4 ) ) )
% 5.31/5.61 & ( ~ ( member_int @ X @ A4 )
% 5.31/5.61 => ( ( groups1707563613775114915nt_nat @ G2 @ ( insert_int @ X @ A4 ) )
% 5.31/5.61 = ( times_times_nat @ ( G2 @ X ) @ ( groups1707563613775114915nt_nat @ G2 @ A4 ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.insert_if
% 5.31/5.61 thf(fact_6303_ivl__disj__int__one_I4_J,axiom,
% 5.31/5.61 ! [L: nat,U: nat] :
% 5.31/5.61 ( ( inf_inf_set_nat @ ( set_ord_lessThan_nat @ L ) @ ( set_or1269000886237332187st_nat @ L @ U ) )
% 5.31/5.61 = bot_bot_set_nat ) ).
% 5.31/5.61
% 5.31/5.61 % ivl_disj_int_one(4)
% 5.31/5.61 thf(fact_6304_ivl__disj__int__one_I4_J,axiom,
% 5.31/5.61 ! [L: int,U: int] :
% 5.31/5.61 ( ( inf_inf_set_int @ ( set_ord_lessThan_int @ L ) @ ( set_or1266510415728281911st_int @ L @ U ) )
% 5.31/5.61 = bot_bot_set_int ) ).
% 5.31/5.61
% 5.31/5.61 % ivl_disj_int_one(4)
% 5.31/5.61 thf(fact_6305_ivl__disj__int__one_I4_J,axiom,
% 5.31/5.61 ! [L: real,U: real] :
% 5.31/5.61 ( ( inf_inf_set_real @ ( set_or5984915006950818249n_real @ L ) @ ( set_or1222579329274155063t_real @ L @ U ) )
% 5.31/5.61 = bot_bot_set_real ) ).
% 5.31/5.61
% 5.31/5.61 % ivl_disj_int_one(4)
% 5.31/5.61 thf(fact_6306_prod_OatLeastAtMost__rev,axiom,
% 5.31/5.61 ! [G2: nat > int,N: nat,M2: nat] :
% 5.31/5.61 ( ( groups705719431365010083at_int @ G2 @ ( set_or1269000886237332187st_nat @ N @ M2 ) )
% 5.31/5.61 = ( groups705719431365010083at_int
% 5.31/5.61 @ ^ [I: nat] : ( G2 @ ( minus_minus_nat @ ( plus_plus_nat @ M2 @ N ) @ I ) )
% 5.31/5.61 @ ( set_or1269000886237332187st_nat @ N @ M2 ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.atLeastAtMost_rev
% 5.31/5.61 thf(fact_6307_prod_OatLeastAtMost__rev,axiom,
% 5.31/5.61 ! [G2: nat > nat,N: nat,M2: nat] :
% 5.31/5.61 ( ( groups708209901874060359at_nat @ G2 @ ( set_or1269000886237332187st_nat @ N @ M2 ) )
% 5.31/5.61 = ( groups708209901874060359at_nat
% 5.31/5.61 @ ^ [I: nat] : ( G2 @ ( minus_minus_nat @ ( plus_plus_nat @ M2 @ N ) @ I ) )
% 5.31/5.61 @ ( set_or1269000886237332187st_nat @ N @ M2 ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.atLeastAtMost_rev
% 5.31/5.61 thf(fact_6308_sum_Onat__diff__reindex,axiom,
% 5.31/5.61 ! [G2: nat > nat,N: nat] :
% 5.31/5.61 ( ( groups3542108847815614940at_nat
% 5.31/5.61 @ ^ [I: nat] : ( G2 @ ( minus_minus_nat @ N @ ( suc @ I ) ) )
% 5.31/5.61 @ ( set_ord_lessThan_nat @ N ) )
% 5.31/5.61 = ( groups3542108847815614940at_nat @ G2 @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % sum.nat_diff_reindex
% 5.31/5.61 thf(fact_6309_sum_Onat__diff__reindex,axiom,
% 5.31/5.61 ! [G2: nat > real,N: nat] :
% 5.31/5.61 ( ( groups6591440286371151544t_real
% 5.31/5.61 @ ^ [I: nat] : ( G2 @ ( minus_minus_nat @ N @ ( suc @ I ) ) )
% 5.31/5.61 @ ( set_ord_lessThan_nat @ N ) )
% 5.31/5.61 = ( groups6591440286371151544t_real @ G2 @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % sum.nat_diff_reindex
% 5.31/5.61 thf(fact_6310_sum__diff__distrib,axiom,
% 5.31/5.61 ! [Q: nat > nat,P2: nat > nat,N: nat] :
% 5.31/5.61 ( ! [X3: nat] : ( ord_less_eq_nat @ ( Q @ X3 ) @ ( P2 @ X3 ) )
% 5.31/5.61 => ( ( minus_minus_nat @ ( groups3542108847815614940at_nat @ P2 @ ( set_ord_lessThan_nat @ N ) ) @ ( groups3542108847815614940at_nat @ Q @ ( set_ord_lessThan_nat @ N ) ) )
% 5.31/5.61 = ( groups3542108847815614940at_nat
% 5.31/5.61 @ ^ [X4: nat] : ( minus_minus_nat @ ( P2 @ X4 ) @ ( Q @ X4 ) )
% 5.31/5.61 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % sum_diff_distrib
% 5.31/5.61 thf(fact_6311_less__1__prod2,axiom,
% 5.31/5.61 ! [I5: set_real,I2: real,F2: real > code_integer] :
% 5.31/5.61 ( ( finite_finite_real @ I5 )
% 5.31/5.61 => ( ( member_real @ I2 @ I5 )
% 5.31/5.61 => ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( F2 @ I2 ) )
% 5.31/5.61 => ( ! [I3: real] :
% 5.31/5.61 ( ( member_real @ I3 @ I5 )
% 5.31/5.61 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( F2 @ I3 ) ) )
% 5.31/5.61 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( groups6225526099057966256nteger @ F2 @ I5 ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % less_1_prod2
% 5.31/5.61 thf(fact_6312_less__1__prod2,axiom,
% 5.31/5.61 ! [I5: set_nat,I2: nat,F2: nat > code_integer] :
% 5.31/5.61 ( ( finite_finite_nat @ I5 )
% 5.31/5.61 => ( ( member_nat @ I2 @ I5 )
% 5.31/5.61 => ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( F2 @ I2 ) )
% 5.31/5.61 => ( ! [I3: nat] :
% 5.31/5.61 ( ( member_nat @ I3 @ I5 )
% 5.31/5.61 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( F2 @ I3 ) ) )
% 5.31/5.61 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( groups3455450783089532116nteger @ F2 @ I5 ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % less_1_prod2
% 5.31/5.61 thf(fact_6313_less__1__prod2,axiom,
% 5.31/5.61 ! [I5: set_int,I2: int,F2: int > code_integer] :
% 5.31/5.61 ( ( finite_finite_int @ I5 )
% 5.31/5.61 => ( ( member_int @ I2 @ I5 )
% 5.31/5.61 => ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( F2 @ I2 ) )
% 5.31/5.61 => ( ! [I3: int] :
% 5.31/5.61 ( ( member_int @ I3 @ I5 )
% 5.31/5.61 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( F2 @ I3 ) ) )
% 5.31/5.61 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( groups3827104343326376752nteger @ F2 @ I5 ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % less_1_prod2
% 5.31/5.61 thf(fact_6314_less__1__prod2,axiom,
% 5.31/5.61 ! [I5: set_complex,I2: complex,F2: complex > code_integer] :
% 5.31/5.61 ( ( finite3207457112153483333omplex @ I5 )
% 5.31/5.61 => ( ( member_complex @ I2 @ I5 )
% 5.31/5.61 => ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( F2 @ I2 ) )
% 5.31/5.61 => ( ! [I3: complex] :
% 5.31/5.61 ( ( member_complex @ I3 @ I5 )
% 5.31/5.61 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( F2 @ I3 ) ) )
% 5.31/5.61 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( groups8682486955453173170nteger @ F2 @ I5 ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % less_1_prod2
% 5.31/5.61 thf(fact_6315_less__1__prod2,axiom,
% 5.31/5.61 ! [I5: set_real,I2: real,F2: real > real] :
% 5.31/5.61 ( ( finite_finite_real @ I5 )
% 5.31/5.61 => ( ( member_real @ I2 @ I5 )
% 5.31/5.61 => ( ( ord_less_real @ one_one_real @ ( F2 @ I2 ) )
% 5.31/5.61 => ( ! [I3: real] :
% 5.31/5.61 ( ( member_real @ I3 @ I5 )
% 5.31/5.61 => ( ord_less_eq_real @ one_one_real @ ( F2 @ I3 ) ) )
% 5.31/5.61 => ( ord_less_real @ one_one_real @ ( groups1681761925125756287l_real @ F2 @ I5 ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % less_1_prod2
% 5.31/5.61 thf(fact_6316_less__1__prod2,axiom,
% 5.31/5.61 ! [I5: set_nat,I2: nat,F2: nat > real] :
% 5.31/5.61 ( ( finite_finite_nat @ I5 )
% 5.31/5.61 => ( ( member_nat @ I2 @ I5 )
% 5.31/5.61 => ( ( ord_less_real @ one_one_real @ ( F2 @ I2 ) )
% 5.31/5.61 => ( ! [I3: nat] :
% 5.31/5.61 ( ( member_nat @ I3 @ I5 )
% 5.31/5.61 => ( ord_less_eq_real @ one_one_real @ ( F2 @ I3 ) ) )
% 5.31/5.61 => ( ord_less_real @ one_one_real @ ( groups129246275422532515t_real @ F2 @ I5 ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % less_1_prod2
% 5.31/5.61 thf(fact_6317_less__1__prod2,axiom,
% 5.31/5.61 ! [I5: set_int,I2: int,F2: int > real] :
% 5.31/5.61 ( ( finite_finite_int @ I5 )
% 5.31/5.61 => ( ( member_int @ I2 @ I5 )
% 5.31/5.61 => ( ( ord_less_real @ one_one_real @ ( F2 @ I2 ) )
% 5.31/5.61 => ( ! [I3: int] :
% 5.31/5.61 ( ( member_int @ I3 @ I5 )
% 5.31/5.61 => ( ord_less_eq_real @ one_one_real @ ( F2 @ I3 ) ) )
% 5.31/5.61 => ( ord_less_real @ one_one_real @ ( groups2316167850115554303t_real @ F2 @ I5 ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % less_1_prod2
% 5.31/5.61 thf(fact_6318_less__1__prod2,axiom,
% 5.31/5.61 ! [I5: set_complex,I2: complex,F2: complex > real] :
% 5.31/5.61 ( ( finite3207457112153483333omplex @ I5 )
% 5.31/5.61 => ( ( member_complex @ I2 @ I5 )
% 5.31/5.61 => ( ( ord_less_real @ one_one_real @ ( F2 @ I2 ) )
% 5.31/5.61 => ( ! [I3: complex] :
% 5.31/5.61 ( ( member_complex @ I3 @ I5 )
% 5.31/5.61 => ( ord_less_eq_real @ one_one_real @ ( F2 @ I3 ) ) )
% 5.31/5.61 => ( ord_less_real @ one_one_real @ ( groups766887009212190081x_real @ F2 @ I5 ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % less_1_prod2
% 5.31/5.61 thf(fact_6319_less__1__prod2,axiom,
% 5.31/5.61 ! [I5: set_real,I2: real,F2: real > rat] :
% 5.31/5.61 ( ( finite_finite_real @ I5 )
% 5.31/5.61 => ( ( member_real @ I2 @ I5 )
% 5.31/5.61 => ( ( ord_less_rat @ one_one_rat @ ( F2 @ I2 ) )
% 5.31/5.61 => ( ! [I3: real] :
% 5.31/5.61 ( ( member_real @ I3 @ I5 )
% 5.31/5.61 => ( ord_less_eq_rat @ one_one_rat @ ( F2 @ I3 ) ) )
% 5.31/5.61 => ( ord_less_rat @ one_one_rat @ ( groups4061424788464935467al_rat @ F2 @ I5 ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % less_1_prod2
% 5.31/5.61 thf(fact_6320_less__1__prod2,axiom,
% 5.31/5.61 ! [I5: set_nat,I2: nat,F2: nat > rat] :
% 5.31/5.61 ( ( finite_finite_nat @ I5 )
% 5.31/5.61 => ( ( member_nat @ I2 @ I5 )
% 5.31/5.61 => ( ( ord_less_rat @ one_one_rat @ ( F2 @ I2 ) )
% 5.31/5.61 => ( ! [I3: nat] :
% 5.31/5.61 ( ( member_nat @ I3 @ I5 )
% 5.31/5.61 => ( ord_less_eq_rat @ one_one_rat @ ( F2 @ I3 ) ) )
% 5.31/5.61 => ( ord_less_rat @ one_one_rat @ ( groups73079841787564623at_rat @ F2 @ I5 ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % less_1_prod2
% 5.31/5.61 thf(fact_6321_prod_Osubset__diff,axiom,
% 5.31/5.61 ! [B5: set_int,A4: set_int,G2: int > real] :
% 5.31/5.61 ( ( ord_less_eq_set_int @ B5 @ A4 )
% 5.31/5.61 => ( ( finite_finite_int @ A4 )
% 5.31/5.61 => ( ( groups2316167850115554303t_real @ G2 @ A4 )
% 5.31/5.61 = ( times_times_real @ ( groups2316167850115554303t_real @ G2 @ ( minus_minus_set_int @ A4 @ B5 ) ) @ ( groups2316167850115554303t_real @ G2 @ B5 ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.subset_diff
% 5.31/5.61 thf(fact_6322_prod_Osubset__diff,axiom,
% 5.31/5.61 ! [B5: set_complex,A4: set_complex,G2: complex > real] :
% 5.31/5.61 ( ( ord_le211207098394363844omplex @ B5 @ A4 )
% 5.31/5.61 => ( ( finite3207457112153483333omplex @ A4 )
% 5.31/5.61 => ( ( groups766887009212190081x_real @ G2 @ A4 )
% 5.31/5.61 = ( times_times_real @ ( groups766887009212190081x_real @ G2 @ ( minus_811609699411566653omplex @ A4 @ B5 ) ) @ ( groups766887009212190081x_real @ G2 @ B5 ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.subset_diff
% 5.31/5.61 thf(fact_6323_prod_Osubset__diff,axiom,
% 5.31/5.61 ! [B5: set_int,A4: set_int,G2: int > rat] :
% 5.31/5.61 ( ( ord_less_eq_set_int @ B5 @ A4 )
% 5.31/5.61 => ( ( finite_finite_int @ A4 )
% 5.31/5.61 => ( ( groups1072433553688619179nt_rat @ G2 @ A4 )
% 5.31/5.61 = ( times_times_rat @ ( groups1072433553688619179nt_rat @ G2 @ ( minus_minus_set_int @ A4 @ B5 ) ) @ ( groups1072433553688619179nt_rat @ G2 @ B5 ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.subset_diff
% 5.31/5.61 thf(fact_6324_prod_Osubset__diff,axiom,
% 5.31/5.61 ! [B5: set_complex,A4: set_complex,G2: complex > rat] :
% 5.31/5.61 ( ( ord_le211207098394363844omplex @ B5 @ A4 )
% 5.31/5.61 => ( ( finite3207457112153483333omplex @ A4 )
% 5.31/5.61 => ( ( groups225925009352817453ex_rat @ G2 @ A4 )
% 5.31/5.61 = ( times_times_rat @ ( groups225925009352817453ex_rat @ G2 @ ( minus_811609699411566653omplex @ A4 @ B5 ) ) @ ( groups225925009352817453ex_rat @ G2 @ B5 ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.subset_diff
% 5.31/5.61 thf(fact_6325_prod_Osubset__diff,axiom,
% 5.31/5.61 ! [B5: set_int,A4: set_int,G2: int > nat] :
% 5.31/5.61 ( ( ord_less_eq_set_int @ B5 @ A4 )
% 5.31/5.61 => ( ( finite_finite_int @ A4 )
% 5.31/5.61 => ( ( groups1707563613775114915nt_nat @ G2 @ A4 )
% 5.31/5.61 = ( times_times_nat @ ( groups1707563613775114915nt_nat @ G2 @ ( minus_minus_set_int @ A4 @ B5 ) ) @ ( groups1707563613775114915nt_nat @ G2 @ B5 ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.subset_diff
% 5.31/5.61 thf(fact_6326_prod_Osubset__diff,axiom,
% 5.31/5.61 ! [B5: set_complex,A4: set_complex,G2: complex > nat] :
% 5.31/5.61 ( ( ord_le211207098394363844omplex @ B5 @ A4 )
% 5.31/5.61 => ( ( finite3207457112153483333omplex @ A4 )
% 5.31/5.61 => ( ( groups861055069439313189ex_nat @ G2 @ A4 )
% 5.31/5.61 = ( times_times_nat @ ( groups861055069439313189ex_nat @ G2 @ ( minus_811609699411566653omplex @ A4 @ B5 ) ) @ ( groups861055069439313189ex_nat @ G2 @ B5 ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.subset_diff
% 5.31/5.61 thf(fact_6327_prod_Osubset__diff,axiom,
% 5.31/5.61 ! [B5: set_complex,A4: set_complex,G2: complex > int] :
% 5.31/5.61 ( ( ord_le211207098394363844omplex @ B5 @ A4 )
% 5.31/5.61 => ( ( finite3207457112153483333omplex @ A4 )
% 5.31/5.61 => ( ( groups858564598930262913ex_int @ G2 @ A4 )
% 5.31/5.61 = ( times_times_int @ ( groups858564598930262913ex_int @ G2 @ ( minus_811609699411566653omplex @ A4 @ B5 ) ) @ ( groups858564598930262913ex_int @ G2 @ B5 ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.subset_diff
% 5.31/5.61 thf(fact_6328_prod_Osubset__diff,axiom,
% 5.31/5.61 ! [B5: set_nat,A4: set_nat,G2: nat > real] :
% 5.31/5.61 ( ( ord_less_eq_set_nat @ B5 @ A4 )
% 5.31/5.61 => ( ( finite_finite_nat @ A4 )
% 5.31/5.61 => ( ( groups129246275422532515t_real @ G2 @ A4 )
% 5.31/5.61 = ( times_times_real @ ( groups129246275422532515t_real @ G2 @ ( minus_minus_set_nat @ A4 @ B5 ) ) @ ( groups129246275422532515t_real @ G2 @ B5 ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.subset_diff
% 5.31/5.61 thf(fact_6329_prod_Osubset__diff,axiom,
% 5.31/5.61 ! [B5: set_nat,A4: set_nat,G2: nat > rat] :
% 5.31/5.61 ( ( ord_less_eq_set_nat @ B5 @ A4 )
% 5.31/5.61 => ( ( finite_finite_nat @ A4 )
% 5.31/5.61 => ( ( groups73079841787564623at_rat @ G2 @ A4 )
% 5.31/5.61 = ( times_times_rat @ ( groups73079841787564623at_rat @ G2 @ ( minus_minus_set_nat @ A4 @ B5 ) ) @ ( groups73079841787564623at_rat @ G2 @ B5 ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.subset_diff
% 5.31/5.61 thf(fact_6330_prod_Osubset__diff,axiom,
% 5.31/5.61 ! [B5: set_nat,A4: set_nat,G2: nat > int] :
% 5.31/5.61 ( ( ord_less_eq_set_nat @ B5 @ A4 )
% 5.31/5.61 => ( ( finite_finite_nat @ A4 )
% 5.31/5.61 => ( ( groups705719431365010083at_int @ G2 @ A4 )
% 5.31/5.61 = ( times_times_int @ ( groups705719431365010083at_int @ G2 @ ( minus_minus_set_nat @ A4 @ B5 ) ) @ ( groups705719431365010083at_int @ G2 @ B5 ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.subset_diff
% 5.31/5.61 thf(fact_6331_prod_Ounion__inter,axiom,
% 5.31/5.61 ! [A4: set_int,B5: set_int,G2: int > real] :
% 5.31/5.61 ( ( finite_finite_int @ A4 )
% 5.31/5.61 => ( ( finite_finite_int @ B5 )
% 5.31/5.61 => ( ( times_times_real @ ( groups2316167850115554303t_real @ G2 @ ( sup_sup_set_int @ A4 @ B5 ) ) @ ( groups2316167850115554303t_real @ G2 @ ( inf_inf_set_int @ A4 @ B5 ) ) )
% 5.31/5.61 = ( times_times_real @ ( groups2316167850115554303t_real @ G2 @ A4 ) @ ( groups2316167850115554303t_real @ G2 @ B5 ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.union_inter
% 5.31/5.61 thf(fact_6332_prod_Ounion__inter,axiom,
% 5.31/5.61 ! [A4: set_complex,B5: set_complex,G2: complex > real] :
% 5.31/5.61 ( ( finite3207457112153483333omplex @ A4 )
% 5.31/5.61 => ( ( finite3207457112153483333omplex @ B5 )
% 5.31/5.61 => ( ( times_times_real @ ( groups766887009212190081x_real @ G2 @ ( sup_sup_set_complex @ A4 @ B5 ) ) @ ( groups766887009212190081x_real @ G2 @ ( inf_inf_set_complex @ A4 @ B5 ) ) )
% 5.31/5.61 = ( times_times_real @ ( groups766887009212190081x_real @ G2 @ A4 ) @ ( groups766887009212190081x_real @ G2 @ B5 ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.union_inter
% 5.31/5.61 thf(fact_6333_prod_Ounion__inter,axiom,
% 5.31/5.61 ! [A4: set_nat,B5: set_nat,G2: nat > real] :
% 5.31/5.61 ( ( finite_finite_nat @ A4 )
% 5.31/5.61 => ( ( finite_finite_nat @ B5 )
% 5.31/5.61 => ( ( times_times_real @ ( groups129246275422532515t_real @ G2 @ ( sup_sup_set_nat @ A4 @ B5 ) ) @ ( groups129246275422532515t_real @ G2 @ ( inf_inf_set_nat @ A4 @ B5 ) ) )
% 5.31/5.61 = ( times_times_real @ ( groups129246275422532515t_real @ G2 @ A4 ) @ ( groups129246275422532515t_real @ G2 @ B5 ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.union_inter
% 5.31/5.61 thf(fact_6334_prod_Ounion__inter,axiom,
% 5.31/5.61 ! [A4: set_int,B5: set_int,G2: int > rat] :
% 5.31/5.61 ( ( finite_finite_int @ A4 )
% 5.31/5.61 => ( ( finite_finite_int @ B5 )
% 5.31/5.61 => ( ( times_times_rat @ ( groups1072433553688619179nt_rat @ G2 @ ( sup_sup_set_int @ A4 @ B5 ) ) @ ( groups1072433553688619179nt_rat @ G2 @ ( inf_inf_set_int @ A4 @ B5 ) ) )
% 5.31/5.61 = ( times_times_rat @ ( groups1072433553688619179nt_rat @ G2 @ A4 ) @ ( groups1072433553688619179nt_rat @ G2 @ B5 ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.union_inter
% 5.31/5.61 thf(fact_6335_prod_Ounion__inter,axiom,
% 5.31/5.61 ! [A4: set_complex,B5: set_complex,G2: complex > rat] :
% 5.31/5.61 ( ( finite3207457112153483333omplex @ A4 )
% 5.31/5.61 => ( ( finite3207457112153483333omplex @ B5 )
% 5.31/5.61 => ( ( times_times_rat @ ( groups225925009352817453ex_rat @ G2 @ ( sup_sup_set_complex @ A4 @ B5 ) ) @ ( groups225925009352817453ex_rat @ G2 @ ( inf_inf_set_complex @ A4 @ B5 ) ) )
% 5.31/5.61 = ( times_times_rat @ ( groups225925009352817453ex_rat @ G2 @ A4 ) @ ( groups225925009352817453ex_rat @ G2 @ B5 ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.union_inter
% 5.31/5.61 thf(fact_6336_prod_Ounion__inter,axiom,
% 5.31/5.61 ! [A4: set_nat,B5: set_nat,G2: nat > rat] :
% 5.31/5.61 ( ( finite_finite_nat @ A4 )
% 5.31/5.61 => ( ( finite_finite_nat @ B5 )
% 5.31/5.61 => ( ( times_times_rat @ ( groups73079841787564623at_rat @ G2 @ ( sup_sup_set_nat @ A4 @ B5 ) ) @ ( groups73079841787564623at_rat @ G2 @ ( inf_inf_set_nat @ A4 @ B5 ) ) )
% 5.31/5.61 = ( times_times_rat @ ( groups73079841787564623at_rat @ G2 @ A4 ) @ ( groups73079841787564623at_rat @ G2 @ B5 ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.union_inter
% 5.31/5.61 thf(fact_6337_prod_Ounion__inter,axiom,
% 5.31/5.61 ! [A4: set_int,B5: set_int,G2: int > nat] :
% 5.31/5.61 ( ( finite_finite_int @ A4 )
% 5.31/5.61 => ( ( finite_finite_int @ B5 )
% 5.31/5.61 => ( ( times_times_nat @ ( groups1707563613775114915nt_nat @ G2 @ ( sup_sup_set_int @ A4 @ B5 ) ) @ ( groups1707563613775114915nt_nat @ G2 @ ( inf_inf_set_int @ A4 @ B5 ) ) )
% 5.31/5.61 = ( times_times_nat @ ( groups1707563613775114915nt_nat @ G2 @ A4 ) @ ( groups1707563613775114915nt_nat @ G2 @ B5 ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.union_inter
% 5.31/5.61 thf(fact_6338_prod_Ounion__inter,axiom,
% 5.31/5.61 ! [A4: set_complex,B5: set_complex,G2: complex > nat] :
% 5.31/5.61 ( ( finite3207457112153483333omplex @ A4 )
% 5.31/5.61 => ( ( finite3207457112153483333omplex @ B5 )
% 5.31/5.61 => ( ( times_times_nat @ ( groups861055069439313189ex_nat @ G2 @ ( sup_sup_set_complex @ A4 @ B5 ) ) @ ( groups861055069439313189ex_nat @ G2 @ ( inf_inf_set_complex @ A4 @ B5 ) ) )
% 5.31/5.61 = ( times_times_nat @ ( groups861055069439313189ex_nat @ G2 @ A4 ) @ ( groups861055069439313189ex_nat @ G2 @ B5 ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.union_inter
% 5.31/5.61 thf(fact_6339_prod_Ounion__inter,axiom,
% 5.31/5.61 ! [A4: set_complex,B5: set_complex,G2: complex > int] :
% 5.31/5.61 ( ( finite3207457112153483333omplex @ A4 )
% 5.31/5.61 => ( ( finite3207457112153483333omplex @ B5 )
% 5.31/5.61 => ( ( times_times_int @ ( groups858564598930262913ex_int @ G2 @ ( sup_sup_set_complex @ A4 @ B5 ) ) @ ( groups858564598930262913ex_int @ G2 @ ( inf_inf_set_complex @ A4 @ B5 ) ) )
% 5.31/5.61 = ( times_times_int @ ( groups858564598930262913ex_int @ G2 @ A4 ) @ ( groups858564598930262913ex_int @ G2 @ B5 ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.union_inter
% 5.31/5.61 thf(fact_6340_prod_Ounion__inter,axiom,
% 5.31/5.61 ! [A4: set_nat,B5: set_nat,G2: nat > int] :
% 5.31/5.61 ( ( finite_finite_nat @ A4 )
% 5.31/5.61 => ( ( finite_finite_nat @ B5 )
% 5.31/5.61 => ( ( times_times_int @ ( groups705719431365010083at_int @ G2 @ ( sup_sup_set_nat @ A4 @ B5 ) ) @ ( groups705719431365010083at_int @ G2 @ ( inf_inf_set_nat @ A4 @ B5 ) ) )
% 5.31/5.61 = ( times_times_int @ ( groups705719431365010083at_int @ G2 @ A4 ) @ ( groups705719431365010083at_int @ G2 @ B5 ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.union_inter
% 5.31/5.61 thf(fact_6341_prod_OInt__Diff,axiom,
% 5.31/5.61 ! [A4: set_int,G2: int > real,B5: set_int] :
% 5.31/5.61 ( ( finite_finite_int @ A4 )
% 5.31/5.61 => ( ( groups2316167850115554303t_real @ G2 @ A4 )
% 5.31/5.61 = ( times_times_real @ ( groups2316167850115554303t_real @ G2 @ ( inf_inf_set_int @ A4 @ B5 ) ) @ ( groups2316167850115554303t_real @ G2 @ ( minus_minus_set_int @ A4 @ B5 ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.Int_Diff
% 5.31/5.61 thf(fact_6342_prod_OInt__Diff,axiom,
% 5.31/5.61 ! [A4: set_complex,G2: complex > real,B5: set_complex] :
% 5.31/5.61 ( ( finite3207457112153483333omplex @ A4 )
% 5.31/5.61 => ( ( groups766887009212190081x_real @ G2 @ A4 )
% 5.31/5.61 = ( times_times_real @ ( groups766887009212190081x_real @ G2 @ ( inf_inf_set_complex @ A4 @ B5 ) ) @ ( groups766887009212190081x_real @ G2 @ ( minus_811609699411566653omplex @ A4 @ B5 ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.Int_Diff
% 5.31/5.61 thf(fact_6343_prod_OInt__Diff,axiom,
% 5.31/5.61 ! [A4: set_nat,G2: nat > real,B5: set_nat] :
% 5.31/5.61 ( ( finite_finite_nat @ A4 )
% 5.31/5.61 => ( ( groups129246275422532515t_real @ G2 @ A4 )
% 5.31/5.61 = ( times_times_real @ ( groups129246275422532515t_real @ G2 @ ( inf_inf_set_nat @ A4 @ B5 ) ) @ ( groups129246275422532515t_real @ G2 @ ( minus_minus_set_nat @ A4 @ B5 ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.Int_Diff
% 5.31/5.61 thf(fact_6344_prod_OInt__Diff,axiom,
% 5.31/5.61 ! [A4: set_int,G2: int > rat,B5: set_int] :
% 5.31/5.61 ( ( finite_finite_int @ A4 )
% 5.31/5.61 => ( ( groups1072433553688619179nt_rat @ G2 @ A4 )
% 5.31/5.61 = ( times_times_rat @ ( groups1072433553688619179nt_rat @ G2 @ ( inf_inf_set_int @ A4 @ B5 ) ) @ ( groups1072433553688619179nt_rat @ G2 @ ( minus_minus_set_int @ A4 @ B5 ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.Int_Diff
% 5.31/5.61 thf(fact_6345_prod_OInt__Diff,axiom,
% 5.31/5.61 ! [A4: set_complex,G2: complex > rat,B5: set_complex] :
% 5.31/5.61 ( ( finite3207457112153483333omplex @ A4 )
% 5.31/5.61 => ( ( groups225925009352817453ex_rat @ G2 @ A4 )
% 5.31/5.61 = ( times_times_rat @ ( groups225925009352817453ex_rat @ G2 @ ( inf_inf_set_complex @ A4 @ B5 ) ) @ ( groups225925009352817453ex_rat @ G2 @ ( minus_811609699411566653omplex @ A4 @ B5 ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.Int_Diff
% 5.31/5.61 thf(fact_6346_prod_OInt__Diff,axiom,
% 5.31/5.61 ! [A4: set_nat,G2: nat > rat,B5: set_nat] :
% 5.31/5.61 ( ( finite_finite_nat @ A4 )
% 5.31/5.61 => ( ( groups73079841787564623at_rat @ G2 @ A4 )
% 5.31/5.61 = ( times_times_rat @ ( groups73079841787564623at_rat @ G2 @ ( inf_inf_set_nat @ A4 @ B5 ) ) @ ( groups73079841787564623at_rat @ G2 @ ( minus_minus_set_nat @ A4 @ B5 ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.Int_Diff
% 5.31/5.61 thf(fact_6347_prod_OInt__Diff,axiom,
% 5.31/5.61 ! [A4: set_int,G2: int > nat,B5: set_int] :
% 5.31/5.61 ( ( finite_finite_int @ A4 )
% 5.31/5.61 => ( ( groups1707563613775114915nt_nat @ G2 @ A4 )
% 5.31/5.61 = ( times_times_nat @ ( groups1707563613775114915nt_nat @ G2 @ ( inf_inf_set_int @ A4 @ B5 ) ) @ ( groups1707563613775114915nt_nat @ G2 @ ( minus_minus_set_int @ A4 @ B5 ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.Int_Diff
% 5.31/5.61 thf(fact_6348_prod_OInt__Diff,axiom,
% 5.31/5.61 ! [A4: set_complex,G2: complex > nat,B5: set_complex] :
% 5.31/5.61 ( ( finite3207457112153483333omplex @ A4 )
% 5.31/5.61 => ( ( groups861055069439313189ex_nat @ G2 @ A4 )
% 5.31/5.61 = ( times_times_nat @ ( groups861055069439313189ex_nat @ G2 @ ( inf_inf_set_complex @ A4 @ B5 ) ) @ ( groups861055069439313189ex_nat @ G2 @ ( minus_811609699411566653omplex @ A4 @ B5 ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.Int_Diff
% 5.31/5.61 thf(fact_6349_prod_OInt__Diff,axiom,
% 5.31/5.61 ! [A4: set_complex,G2: complex > int,B5: set_complex] :
% 5.31/5.61 ( ( finite3207457112153483333omplex @ A4 )
% 5.31/5.61 => ( ( groups858564598930262913ex_int @ G2 @ A4 )
% 5.31/5.61 = ( times_times_int @ ( groups858564598930262913ex_int @ G2 @ ( inf_inf_set_complex @ A4 @ B5 ) ) @ ( groups858564598930262913ex_int @ G2 @ ( minus_811609699411566653omplex @ A4 @ B5 ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.Int_Diff
% 5.31/5.61 thf(fact_6350_prod_OInt__Diff,axiom,
% 5.31/5.61 ! [A4: set_nat,G2: nat > int,B5: set_nat] :
% 5.31/5.61 ( ( finite_finite_nat @ A4 )
% 5.31/5.61 => ( ( groups705719431365010083at_int @ G2 @ A4 )
% 5.31/5.61 = ( times_times_int @ ( groups705719431365010083at_int @ G2 @ ( inf_inf_set_nat @ A4 @ B5 ) ) @ ( groups705719431365010083at_int @ G2 @ ( minus_minus_set_nat @ A4 @ B5 ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.Int_Diff
% 5.31/5.61 thf(fact_6351_prod_OatLeast0__atMost__Suc,axiom,
% 5.31/5.61 ! [G2: nat > real,N: nat] :
% 5.31/5.61 ( ( groups129246275422532515t_real @ G2 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 5.31/5.61 = ( times_times_real @ ( groups129246275422532515t_real @ G2 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) @ ( G2 @ ( suc @ N ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.atLeast0_atMost_Suc
% 5.31/5.61 thf(fact_6352_prod_OatLeast0__atMost__Suc,axiom,
% 5.31/5.61 ! [G2: nat > rat,N: nat] :
% 5.31/5.61 ( ( groups73079841787564623at_rat @ G2 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 5.31/5.61 = ( times_times_rat @ ( groups73079841787564623at_rat @ G2 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) @ ( G2 @ ( suc @ N ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.atLeast0_atMost_Suc
% 5.31/5.61 thf(fact_6353_prod_OatLeast0__atMost__Suc,axiom,
% 5.31/5.61 ! [G2: nat > int,N: nat] :
% 5.31/5.61 ( ( groups705719431365010083at_int @ G2 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 5.31/5.61 = ( times_times_int @ ( groups705719431365010083at_int @ G2 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) @ ( G2 @ ( suc @ N ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.atLeast0_atMost_Suc
% 5.31/5.61 thf(fact_6354_prod_OatLeast0__atMost__Suc,axiom,
% 5.31/5.61 ! [G2: nat > nat,N: nat] :
% 5.31/5.61 ( ( groups708209901874060359at_nat @ G2 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 5.31/5.61 = ( times_times_nat @ ( groups708209901874060359at_nat @ G2 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) @ ( G2 @ ( suc @ N ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.atLeast0_atMost_Suc
% 5.31/5.61 thf(fact_6355_prod_OatLeast__Suc__atMost,axiom,
% 5.31/5.61 ! [M2: nat,N: nat,G2: nat > real] :
% 5.31/5.61 ( ( ord_less_eq_nat @ M2 @ N )
% 5.31/5.61 => ( ( groups129246275422532515t_real @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ N ) )
% 5.31/5.61 = ( times_times_real @ ( G2 @ M2 ) @ ( groups129246275422532515t_real @ G2 @ ( set_or1269000886237332187st_nat @ ( suc @ M2 ) @ N ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.atLeast_Suc_atMost
% 5.31/5.61 thf(fact_6356_prod_OatLeast__Suc__atMost,axiom,
% 5.31/5.61 ! [M2: nat,N: nat,G2: nat > rat] :
% 5.31/5.61 ( ( ord_less_eq_nat @ M2 @ N )
% 5.31/5.61 => ( ( groups73079841787564623at_rat @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ N ) )
% 5.31/5.61 = ( times_times_rat @ ( G2 @ M2 ) @ ( groups73079841787564623at_rat @ G2 @ ( set_or1269000886237332187st_nat @ ( suc @ M2 ) @ N ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.atLeast_Suc_atMost
% 5.31/5.61 thf(fact_6357_prod_OatLeast__Suc__atMost,axiom,
% 5.31/5.61 ! [M2: nat,N: nat,G2: nat > int] :
% 5.31/5.61 ( ( ord_less_eq_nat @ M2 @ N )
% 5.31/5.61 => ( ( groups705719431365010083at_int @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ N ) )
% 5.31/5.61 = ( times_times_int @ ( G2 @ M2 ) @ ( groups705719431365010083at_int @ G2 @ ( set_or1269000886237332187st_nat @ ( suc @ M2 ) @ N ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.atLeast_Suc_atMost
% 5.31/5.61 thf(fact_6358_prod_OatLeast__Suc__atMost,axiom,
% 5.31/5.61 ! [M2: nat,N: nat,G2: nat > nat] :
% 5.31/5.61 ( ( ord_less_eq_nat @ M2 @ N )
% 5.31/5.61 => ( ( groups708209901874060359at_nat @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ N ) )
% 5.31/5.61 = ( times_times_nat @ ( G2 @ M2 ) @ ( groups708209901874060359at_nat @ G2 @ ( set_or1269000886237332187st_nat @ ( suc @ M2 ) @ N ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.atLeast_Suc_atMost
% 5.31/5.61 thf(fact_6359_prod_Onat__ivl__Suc_H,axiom,
% 5.31/5.61 ! [M2: nat,N: nat,G2: nat > real] :
% 5.31/5.61 ( ( ord_less_eq_nat @ M2 @ ( suc @ N ) )
% 5.31/5.61 => ( ( groups129246275422532515t_real @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N ) ) )
% 5.31/5.61 = ( times_times_real @ ( G2 @ ( suc @ N ) ) @ ( groups129246275422532515t_real @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.nat_ivl_Suc'
% 5.31/5.61 thf(fact_6360_prod_Onat__ivl__Suc_H,axiom,
% 5.31/5.61 ! [M2: nat,N: nat,G2: nat > rat] :
% 5.31/5.61 ( ( ord_less_eq_nat @ M2 @ ( suc @ N ) )
% 5.31/5.61 => ( ( groups73079841787564623at_rat @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N ) ) )
% 5.31/5.61 = ( times_times_rat @ ( G2 @ ( suc @ N ) ) @ ( groups73079841787564623at_rat @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.nat_ivl_Suc'
% 5.31/5.61 thf(fact_6361_prod_Onat__ivl__Suc_H,axiom,
% 5.31/5.61 ! [M2: nat,N: nat,G2: nat > int] :
% 5.31/5.61 ( ( ord_less_eq_nat @ M2 @ ( suc @ N ) )
% 5.31/5.61 => ( ( groups705719431365010083at_int @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N ) ) )
% 5.31/5.61 = ( times_times_int @ ( G2 @ ( suc @ N ) ) @ ( groups705719431365010083at_int @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.nat_ivl_Suc'
% 5.31/5.61 thf(fact_6362_prod_Onat__ivl__Suc_H,axiom,
% 5.31/5.61 ! [M2: nat,N: nat,G2: nat > nat] :
% 5.31/5.61 ( ( ord_less_eq_nat @ M2 @ ( suc @ N ) )
% 5.31/5.61 => ( ( groups708209901874060359at_nat @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N ) ) )
% 5.31/5.61 = ( times_times_nat @ ( G2 @ ( suc @ N ) ) @ ( groups708209901874060359at_nat @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.nat_ivl_Suc'
% 5.31/5.61 thf(fact_6363_Iio__Int__singleton,axiom,
% 5.31/5.61 ! [X: real,K2: real] :
% 5.31/5.61 ( ( ( ord_less_real @ X @ K2 )
% 5.31/5.61 => ( ( inf_inf_set_real @ ( set_or5984915006950818249n_real @ K2 ) @ ( insert_real @ X @ bot_bot_set_real ) )
% 5.31/5.61 = ( insert_real @ X @ bot_bot_set_real ) ) )
% 5.31/5.61 & ( ~ ( ord_less_real @ X @ K2 )
% 5.31/5.61 => ( ( inf_inf_set_real @ ( set_or5984915006950818249n_real @ K2 ) @ ( insert_real @ X @ bot_bot_set_real ) )
% 5.31/5.61 = bot_bot_set_real ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % Iio_Int_singleton
% 5.31/5.61 thf(fact_6364_Iio__Int__singleton,axiom,
% 5.31/5.61 ! [X: rat,K2: rat] :
% 5.31/5.61 ( ( ( ord_less_rat @ X @ K2 )
% 5.31/5.61 => ( ( inf_inf_set_rat @ ( set_ord_lessThan_rat @ K2 ) @ ( insert_rat @ X @ bot_bot_set_rat ) )
% 5.31/5.61 = ( insert_rat @ X @ bot_bot_set_rat ) ) )
% 5.31/5.61 & ( ~ ( ord_less_rat @ X @ K2 )
% 5.31/5.61 => ( ( inf_inf_set_rat @ ( set_ord_lessThan_rat @ K2 ) @ ( insert_rat @ X @ bot_bot_set_rat ) )
% 5.31/5.61 = bot_bot_set_rat ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % Iio_Int_singleton
% 5.31/5.61 thf(fact_6365_Iio__Int__singleton,axiom,
% 5.31/5.61 ! [X: num,K2: num] :
% 5.31/5.61 ( ( ( ord_less_num @ X @ K2 )
% 5.31/5.61 => ( ( inf_inf_set_num @ ( set_ord_lessThan_num @ K2 ) @ ( insert_num @ X @ bot_bot_set_num ) )
% 5.31/5.61 = ( insert_num @ X @ bot_bot_set_num ) ) )
% 5.31/5.61 & ( ~ ( ord_less_num @ X @ K2 )
% 5.31/5.61 => ( ( inf_inf_set_num @ ( set_ord_lessThan_num @ K2 ) @ ( insert_num @ X @ bot_bot_set_num ) )
% 5.31/5.61 = bot_bot_set_num ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % Iio_Int_singleton
% 5.31/5.61 thf(fact_6366_Iio__Int__singleton,axiom,
% 5.31/5.61 ! [X: int,K2: int] :
% 5.31/5.61 ( ( ( ord_less_int @ X @ K2 )
% 5.31/5.61 => ( ( inf_inf_set_int @ ( set_ord_lessThan_int @ K2 ) @ ( insert_int @ X @ bot_bot_set_int ) )
% 5.31/5.61 = ( insert_int @ X @ bot_bot_set_int ) ) )
% 5.31/5.61 & ( ~ ( ord_less_int @ X @ K2 )
% 5.31/5.61 => ( ( inf_inf_set_int @ ( set_ord_lessThan_int @ K2 ) @ ( insert_int @ X @ bot_bot_set_int ) )
% 5.31/5.61 = bot_bot_set_int ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % Iio_Int_singleton
% 5.31/5.61 thf(fact_6367_Iio__Int__singleton,axiom,
% 5.31/5.61 ! [X: nat,K2: nat] :
% 5.31/5.61 ( ( ( ord_less_nat @ X @ K2 )
% 5.31/5.61 => ( ( inf_inf_set_nat @ ( set_ord_lessThan_nat @ K2 ) @ ( insert_nat @ X @ bot_bot_set_nat ) )
% 5.31/5.61 = ( insert_nat @ X @ bot_bot_set_nat ) ) )
% 5.31/5.61 & ( ~ ( ord_less_nat @ X @ K2 )
% 5.31/5.61 => ( ( inf_inf_set_nat @ ( set_ord_lessThan_nat @ K2 ) @ ( insert_nat @ X @ bot_bot_set_nat ) )
% 5.31/5.61 = bot_bot_set_nat ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % Iio_Int_singleton
% 5.31/5.61 thf(fact_6368_prod_OSuc__reindex__ivl,axiom,
% 5.31/5.61 ! [M2: nat,N: nat,G2: nat > real] :
% 5.31/5.61 ( ( ord_less_eq_nat @ M2 @ N )
% 5.31/5.61 => ( ( times_times_real @ ( groups129246275422532515t_real @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) @ ( G2 @ ( suc @ N ) ) )
% 5.31/5.61 = ( times_times_real @ ( G2 @ M2 )
% 5.31/5.61 @ ( groups129246275422532515t_real
% 5.31/5.61 @ ^ [I: nat] : ( G2 @ ( suc @ I ) )
% 5.31/5.61 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.Suc_reindex_ivl
% 5.31/5.61 thf(fact_6369_prod_OSuc__reindex__ivl,axiom,
% 5.31/5.61 ! [M2: nat,N: nat,G2: nat > rat] :
% 5.31/5.61 ( ( ord_less_eq_nat @ M2 @ N )
% 5.31/5.61 => ( ( times_times_rat @ ( groups73079841787564623at_rat @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) @ ( G2 @ ( suc @ N ) ) )
% 5.31/5.61 = ( times_times_rat @ ( G2 @ M2 )
% 5.31/5.61 @ ( groups73079841787564623at_rat
% 5.31/5.61 @ ^ [I: nat] : ( G2 @ ( suc @ I ) )
% 5.31/5.61 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.Suc_reindex_ivl
% 5.31/5.61 thf(fact_6370_prod_OSuc__reindex__ivl,axiom,
% 5.31/5.61 ! [M2: nat,N: nat,G2: nat > int] :
% 5.31/5.61 ( ( ord_less_eq_nat @ M2 @ N )
% 5.31/5.61 => ( ( times_times_int @ ( groups705719431365010083at_int @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) @ ( G2 @ ( suc @ N ) ) )
% 5.31/5.61 = ( times_times_int @ ( G2 @ M2 )
% 5.31/5.61 @ ( groups705719431365010083at_int
% 5.31/5.61 @ ^ [I: nat] : ( G2 @ ( suc @ I ) )
% 5.31/5.61 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.Suc_reindex_ivl
% 5.31/5.61 thf(fact_6371_prod_OSuc__reindex__ivl,axiom,
% 5.31/5.61 ! [M2: nat,N: nat,G2: nat > nat] :
% 5.31/5.61 ( ( ord_less_eq_nat @ M2 @ N )
% 5.31/5.61 => ( ( times_times_nat @ ( groups708209901874060359at_nat @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) @ ( G2 @ ( suc @ N ) ) )
% 5.31/5.61 = ( times_times_nat @ ( G2 @ M2 )
% 5.31/5.61 @ ( groups708209901874060359at_nat
% 5.31/5.61 @ ^ [I: nat] : ( G2 @ ( suc @ I ) )
% 5.31/5.61 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.Suc_reindex_ivl
% 5.31/5.61 thf(fact_6372_sum_OlessThan__Suc__shift,axiom,
% 5.31/5.61 ! [G2: nat > rat,N: nat] :
% 5.31/5.61 ( ( groups2906978787729119204at_rat @ G2 @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 5.31/5.61 = ( plus_plus_rat @ ( G2 @ zero_zero_nat )
% 5.31/5.61 @ ( groups2906978787729119204at_rat
% 5.31/5.61 @ ^ [I: nat] : ( G2 @ ( suc @ I ) )
% 5.31/5.61 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % sum.lessThan_Suc_shift
% 5.31/5.61 thf(fact_6373_sum_OlessThan__Suc__shift,axiom,
% 5.31/5.61 ! [G2: nat > int,N: nat] :
% 5.31/5.61 ( ( groups3539618377306564664at_int @ G2 @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 5.31/5.61 = ( plus_plus_int @ ( G2 @ zero_zero_nat )
% 5.31/5.61 @ ( groups3539618377306564664at_int
% 5.31/5.61 @ ^ [I: nat] : ( G2 @ ( suc @ I ) )
% 5.31/5.61 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % sum.lessThan_Suc_shift
% 5.31/5.61 thf(fact_6374_sum_OlessThan__Suc__shift,axiom,
% 5.31/5.61 ! [G2: nat > nat,N: nat] :
% 5.31/5.61 ( ( groups3542108847815614940at_nat @ G2 @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 5.31/5.61 = ( plus_plus_nat @ ( G2 @ zero_zero_nat )
% 5.31/5.61 @ ( groups3542108847815614940at_nat
% 5.31/5.61 @ ^ [I: nat] : ( G2 @ ( suc @ I ) )
% 5.31/5.61 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % sum.lessThan_Suc_shift
% 5.31/5.61 thf(fact_6375_sum_OlessThan__Suc__shift,axiom,
% 5.31/5.61 ! [G2: nat > real,N: nat] :
% 5.31/5.61 ( ( groups6591440286371151544t_real @ G2 @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 5.31/5.61 = ( plus_plus_real @ ( G2 @ zero_zero_nat )
% 5.31/5.61 @ ( groups6591440286371151544t_real
% 5.31/5.61 @ ^ [I: nat] : ( G2 @ ( suc @ I ) )
% 5.31/5.61 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % sum.lessThan_Suc_shift
% 5.31/5.61 thf(fact_6376_sum__lessThan__telescope_H,axiom,
% 5.31/5.61 ! [F2: nat > rat,M2: nat] :
% 5.31/5.61 ( ( groups2906978787729119204at_rat
% 5.31/5.61 @ ^ [N4: nat] : ( minus_minus_rat @ ( F2 @ N4 ) @ ( F2 @ ( suc @ N4 ) ) )
% 5.31/5.61 @ ( set_ord_lessThan_nat @ M2 ) )
% 5.31/5.61 = ( minus_minus_rat @ ( F2 @ zero_zero_nat ) @ ( F2 @ M2 ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % sum_lessThan_telescope'
% 5.31/5.61 thf(fact_6377_sum__lessThan__telescope_H,axiom,
% 5.31/5.61 ! [F2: nat > int,M2: nat] :
% 5.31/5.61 ( ( groups3539618377306564664at_int
% 5.31/5.61 @ ^ [N4: nat] : ( minus_minus_int @ ( F2 @ N4 ) @ ( F2 @ ( suc @ N4 ) ) )
% 5.31/5.61 @ ( set_ord_lessThan_nat @ M2 ) )
% 5.31/5.61 = ( minus_minus_int @ ( F2 @ zero_zero_nat ) @ ( F2 @ M2 ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % sum_lessThan_telescope'
% 5.31/5.61 thf(fact_6378_sum__lessThan__telescope_H,axiom,
% 5.31/5.61 ! [F2: nat > real,M2: nat] :
% 5.31/5.61 ( ( groups6591440286371151544t_real
% 5.31/5.61 @ ^ [N4: nat] : ( minus_minus_real @ ( F2 @ N4 ) @ ( F2 @ ( suc @ N4 ) ) )
% 5.31/5.61 @ ( set_ord_lessThan_nat @ M2 ) )
% 5.31/5.61 = ( minus_minus_real @ ( F2 @ zero_zero_nat ) @ ( F2 @ M2 ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % sum_lessThan_telescope'
% 5.31/5.61 thf(fact_6379_sum__lessThan__telescope,axiom,
% 5.31/5.61 ! [F2: nat > rat,M2: nat] :
% 5.31/5.61 ( ( groups2906978787729119204at_rat
% 5.31/5.61 @ ^ [N4: nat] : ( minus_minus_rat @ ( F2 @ ( suc @ N4 ) ) @ ( F2 @ N4 ) )
% 5.31/5.61 @ ( set_ord_lessThan_nat @ M2 ) )
% 5.31/5.61 = ( minus_minus_rat @ ( F2 @ M2 ) @ ( F2 @ zero_zero_nat ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % sum_lessThan_telescope
% 5.31/5.61 thf(fact_6380_sum__lessThan__telescope,axiom,
% 5.31/5.61 ! [F2: nat > int,M2: nat] :
% 5.31/5.61 ( ( groups3539618377306564664at_int
% 5.31/5.61 @ ^ [N4: nat] : ( minus_minus_int @ ( F2 @ ( suc @ N4 ) ) @ ( F2 @ N4 ) )
% 5.31/5.61 @ ( set_ord_lessThan_nat @ M2 ) )
% 5.31/5.61 = ( minus_minus_int @ ( F2 @ M2 ) @ ( F2 @ zero_zero_nat ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % sum_lessThan_telescope
% 5.31/5.61 thf(fact_6381_sum__lessThan__telescope,axiom,
% 5.31/5.61 ! [F2: nat > real,M2: nat] :
% 5.31/5.61 ( ( groups6591440286371151544t_real
% 5.31/5.61 @ ^ [N4: nat] : ( minus_minus_real @ ( F2 @ ( suc @ N4 ) ) @ ( F2 @ N4 ) )
% 5.31/5.61 @ ( set_ord_lessThan_nat @ M2 ) )
% 5.31/5.61 = ( minus_minus_real @ ( F2 @ M2 ) @ ( F2 @ zero_zero_nat ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % sum_lessThan_telescope
% 5.31/5.61 thf(fact_6382_sumr__diff__mult__const2,axiom,
% 5.31/5.61 ! [F2: nat > rat,N: nat,R3: rat] :
% 5.31/5.61 ( ( minus_minus_rat @ ( groups2906978787729119204at_rat @ F2 @ ( set_ord_lessThan_nat @ N ) ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ N ) @ R3 ) )
% 5.31/5.61 = ( groups2906978787729119204at_rat
% 5.31/5.61 @ ^ [I: nat] : ( minus_minus_rat @ ( F2 @ I ) @ R3 )
% 5.31/5.61 @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % sumr_diff_mult_const2
% 5.31/5.61 thf(fact_6383_sumr__diff__mult__const2,axiom,
% 5.31/5.61 ! [F2: nat > int,N: nat,R3: int] :
% 5.31/5.61 ( ( minus_minus_int @ ( groups3539618377306564664at_int @ F2 @ ( set_ord_lessThan_nat @ N ) ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ R3 ) )
% 5.31/5.61 = ( groups3539618377306564664at_int
% 5.31/5.61 @ ^ [I: nat] : ( minus_minus_int @ ( F2 @ I ) @ R3 )
% 5.31/5.61 @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % sumr_diff_mult_const2
% 5.31/5.61 thf(fact_6384_sumr__diff__mult__const2,axiom,
% 5.31/5.61 ! [F2: nat > real,N: nat,R3: real] :
% 5.31/5.61 ( ( minus_minus_real @ ( groups6591440286371151544t_real @ F2 @ ( set_ord_lessThan_nat @ N ) ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ R3 ) )
% 5.31/5.61 = ( groups6591440286371151544t_real
% 5.31/5.61 @ ^ [I: nat] : ( minus_minus_real @ ( F2 @ I ) @ R3 )
% 5.31/5.61 @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % sumr_diff_mult_const2
% 5.31/5.61 thf(fact_6385_sum_OatLeast1__atMost__eq,axiom,
% 5.31/5.61 ! [G2: nat > nat,N: nat] :
% 5.31/5.61 ( ( groups3542108847815614940at_nat @ G2 @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) )
% 5.31/5.61 = ( groups3542108847815614940at_nat
% 5.31/5.61 @ ^ [K3: nat] : ( G2 @ ( suc @ K3 ) )
% 5.31/5.61 @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % sum.atLeast1_atMost_eq
% 5.31/5.61 thf(fact_6386_sum_OatLeast1__atMost__eq,axiom,
% 5.31/5.61 ! [G2: nat > real,N: nat] :
% 5.31/5.61 ( ( groups6591440286371151544t_real @ G2 @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) )
% 5.31/5.61 = ( groups6591440286371151544t_real
% 5.31/5.61 @ ^ [K3: nat] : ( G2 @ ( suc @ K3 ) )
% 5.31/5.61 @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % sum.atLeast1_atMost_eq
% 5.31/5.61 thf(fact_6387_prod__mono__strict,axiom,
% 5.31/5.61 ! [A4: set_complex,F2: complex > real,G2: complex > real] :
% 5.31/5.61 ( ( finite3207457112153483333omplex @ A4 )
% 5.31/5.61 => ( ! [I3: complex] :
% 5.31/5.61 ( ( member_complex @ I3 @ A4 )
% 5.31/5.61 => ( ( ord_less_eq_real @ zero_zero_real @ ( F2 @ I3 ) )
% 5.31/5.61 & ( ord_less_real @ ( F2 @ I3 ) @ ( G2 @ I3 ) ) ) )
% 5.31/5.61 => ( ( A4 != bot_bot_set_complex )
% 5.31/5.61 => ( ord_less_real @ ( groups766887009212190081x_real @ F2 @ A4 ) @ ( groups766887009212190081x_real @ G2 @ A4 ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod_mono_strict
% 5.31/5.61 thf(fact_6388_prod__mono__strict,axiom,
% 5.31/5.61 ! [A4: set_nat,F2: nat > real,G2: nat > real] :
% 5.31/5.61 ( ( finite_finite_nat @ A4 )
% 5.31/5.61 => ( ! [I3: nat] :
% 5.31/5.61 ( ( member_nat @ I3 @ A4 )
% 5.31/5.61 => ( ( ord_less_eq_real @ zero_zero_real @ ( F2 @ I3 ) )
% 5.31/5.61 & ( ord_less_real @ ( F2 @ I3 ) @ ( G2 @ I3 ) ) ) )
% 5.31/5.61 => ( ( A4 != bot_bot_set_nat )
% 5.31/5.61 => ( ord_less_real @ ( groups129246275422532515t_real @ F2 @ A4 ) @ ( groups129246275422532515t_real @ G2 @ A4 ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod_mono_strict
% 5.31/5.61 thf(fact_6389_prod__mono__strict,axiom,
% 5.31/5.61 ! [A4: set_int,F2: int > real,G2: int > real] :
% 5.31/5.61 ( ( finite_finite_int @ A4 )
% 5.31/5.61 => ( ! [I3: int] :
% 5.31/5.61 ( ( member_int @ I3 @ A4 )
% 5.31/5.61 => ( ( ord_less_eq_real @ zero_zero_real @ ( F2 @ I3 ) )
% 5.31/5.61 & ( ord_less_real @ ( F2 @ I3 ) @ ( G2 @ I3 ) ) ) )
% 5.31/5.61 => ( ( A4 != bot_bot_set_int )
% 5.31/5.61 => ( ord_less_real @ ( groups2316167850115554303t_real @ F2 @ A4 ) @ ( groups2316167850115554303t_real @ G2 @ A4 ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod_mono_strict
% 5.31/5.61 thf(fact_6390_prod__mono__strict,axiom,
% 5.31/5.61 ! [A4: set_real,F2: real > real,G2: real > real] :
% 5.31/5.61 ( ( finite_finite_real @ A4 )
% 5.31/5.61 => ( ! [I3: real] :
% 5.31/5.61 ( ( member_real @ I3 @ A4 )
% 5.31/5.61 => ( ( ord_less_eq_real @ zero_zero_real @ ( F2 @ I3 ) )
% 5.31/5.61 & ( ord_less_real @ ( F2 @ I3 ) @ ( G2 @ I3 ) ) ) )
% 5.31/5.61 => ( ( A4 != bot_bot_set_real )
% 5.31/5.61 => ( ord_less_real @ ( groups1681761925125756287l_real @ F2 @ A4 ) @ ( groups1681761925125756287l_real @ G2 @ A4 ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod_mono_strict
% 5.31/5.61 thf(fact_6391_prod__mono__strict,axiom,
% 5.31/5.61 ! [A4: set_complex,F2: complex > rat,G2: complex > rat] :
% 5.31/5.61 ( ( finite3207457112153483333omplex @ A4 )
% 5.31/5.61 => ( ! [I3: complex] :
% 5.31/5.61 ( ( member_complex @ I3 @ A4 )
% 5.31/5.61 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ I3 ) )
% 5.31/5.61 & ( ord_less_rat @ ( F2 @ I3 ) @ ( G2 @ I3 ) ) ) )
% 5.31/5.61 => ( ( A4 != bot_bot_set_complex )
% 5.31/5.61 => ( ord_less_rat @ ( groups225925009352817453ex_rat @ F2 @ A4 ) @ ( groups225925009352817453ex_rat @ G2 @ A4 ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod_mono_strict
% 5.31/5.61 thf(fact_6392_prod__mono__strict,axiom,
% 5.31/5.61 ! [A4: set_nat,F2: nat > rat,G2: nat > rat] :
% 5.31/5.61 ( ( finite_finite_nat @ A4 )
% 5.31/5.61 => ( ! [I3: nat] :
% 5.31/5.61 ( ( member_nat @ I3 @ A4 )
% 5.31/5.61 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ I3 ) )
% 5.31/5.61 & ( ord_less_rat @ ( F2 @ I3 ) @ ( G2 @ I3 ) ) ) )
% 5.31/5.61 => ( ( A4 != bot_bot_set_nat )
% 5.31/5.61 => ( ord_less_rat @ ( groups73079841787564623at_rat @ F2 @ A4 ) @ ( groups73079841787564623at_rat @ G2 @ A4 ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod_mono_strict
% 5.31/5.61 thf(fact_6393_prod__mono__strict,axiom,
% 5.31/5.61 ! [A4: set_int,F2: int > rat,G2: int > rat] :
% 5.31/5.61 ( ( finite_finite_int @ A4 )
% 5.31/5.61 => ( ! [I3: int] :
% 5.31/5.61 ( ( member_int @ I3 @ A4 )
% 5.31/5.61 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ I3 ) )
% 5.31/5.61 & ( ord_less_rat @ ( F2 @ I3 ) @ ( G2 @ I3 ) ) ) )
% 5.31/5.61 => ( ( A4 != bot_bot_set_int )
% 5.31/5.61 => ( ord_less_rat @ ( groups1072433553688619179nt_rat @ F2 @ A4 ) @ ( groups1072433553688619179nt_rat @ G2 @ A4 ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod_mono_strict
% 5.31/5.61 thf(fact_6394_prod__mono__strict,axiom,
% 5.31/5.61 ! [A4: set_real,F2: real > rat,G2: real > rat] :
% 5.31/5.61 ( ( finite_finite_real @ A4 )
% 5.31/5.61 => ( ! [I3: real] :
% 5.31/5.61 ( ( member_real @ I3 @ A4 )
% 5.31/5.61 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ I3 ) )
% 5.31/5.61 & ( ord_less_rat @ ( F2 @ I3 ) @ ( G2 @ I3 ) ) ) )
% 5.31/5.61 => ( ( A4 != bot_bot_set_real )
% 5.31/5.61 => ( ord_less_rat @ ( groups4061424788464935467al_rat @ F2 @ A4 ) @ ( groups4061424788464935467al_rat @ G2 @ A4 ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod_mono_strict
% 5.31/5.61 thf(fact_6395_prod__mono__strict,axiom,
% 5.31/5.61 ! [A4: set_complex,F2: complex > nat,G2: complex > nat] :
% 5.31/5.61 ( ( finite3207457112153483333omplex @ A4 )
% 5.31/5.61 => ( ! [I3: complex] :
% 5.31/5.61 ( ( member_complex @ I3 @ A4 )
% 5.31/5.61 => ( ( ord_less_eq_nat @ zero_zero_nat @ ( F2 @ I3 ) )
% 5.31/5.61 & ( ord_less_nat @ ( F2 @ I3 ) @ ( G2 @ I3 ) ) ) )
% 5.31/5.61 => ( ( A4 != bot_bot_set_complex )
% 5.31/5.61 => ( ord_less_nat @ ( groups861055069439313189ex_nat @ F2 @ A4 ) @ ( groups861055069439313189ex_nat @ G2 @ A4 ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod_mono_strict
% 5.31/5.61 thf(fact_6396_prod__mono__strict,axiom,
% 5.31/5.61 ! [A4: set_int,F2: int > nat,G2: int > nat] :
% 5.31/5.61 ( ( finite_finite_int @ A4 )
% 5.31/5.61 => ( ! [I3: int] :
% 5.31/5.61 ( ( member_int @ I3 @ A4 )
% 5.31/5.61 => ( ( ord_less_eq_nat @ zero_zero_nat @ ( F2 @ I3 ) )
% 5.31/5.61 & ( ord_less_nat @ ( F2 @ I3 ) @ ( G2 @ I3 ) ) ) )
% 5.31/5.61 => ( ( A4 != bot_bot_set_int )
% 5.31/5.61 => ( ord_less_nat @ ( groups1707563613775114915nt_nat @ F2 @ A4 ) @ ( groups1707563613775114915nt_nat @ G2 @ A4 ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod_mono_strict
% 5.31/5.61 thf(fact_6397_prod_Oremove,axiom,
% 5.31/5.61 ! [A4: set_complex,X: complex,G2: complex > real] :
% 5.31/5.61 ( ( finite3207457112153483333omplex @ A4 )
% 5.31/5.61 => ( ( member_complex @ X @ A4 )
% 5.31/5.61 => ( ( groups766887009212190081x_real @ G2 @ A4 )
% 5.31/5.61 = ( times_times_real @ ( G2 @ X ) @ ( groups766887009212190081x_real @ G2 @ ( minus_811609699411566653omplex @ A4 @ ( insert_complex @ X @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.remove
% 5.31/5.61 thf(fact_6398_prod_Oremove,axiom,
% 5.31/5.61 ! [A4: set_int,X: int,G2: int > real] :
% 5.31/5.61 ( ( finite_finite_int @ A4 )
% 5.31/5.61 => ( ( member_int @ X @ A4 )
% 5.31/5.61 => ( ( groups2316167850115554303t_real @ G2 @ A4 )
% 5.31/5.61 = ( times_times_real @ ( G2 @ X ) @ ( groups2316167850115554303t_real @ G2 @ ( minus_minus_set_int @ A4 @ ( insert_int @ X @ bot_bot_set_int ) ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.remove
% 5.31/5.61 thf(fact_6399_prod_Oremove,axiom,
% 5.31/5.61 ! [A4: set_real,X: real,G2: real > real] :
% 5.31/5.61 ( ( finite_finite_real @ A4 )
% 5.31/5.61 => ( ( member_real @ X @ A4 )
% 5.31/5.61 => ( ( groups1681761925125756287l_real @ G2 @ A4 )
% 5.31/5.61 = ( times_times_real @ ( G2 @ X ) @ ( groups1681761925125756287l_real @ G2 @ ( minus_minus_set_real @ A4 @ ( insert_real @ X @ bot_bot_set_real ) ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.remove
% 5.31/5.61 thf(fact_6400_prod_Oremove,axiom,
% 5.31/5.61 ! [A4: set_nat,X: nat,G2: nat > real] :
% 5.31/5.61 ( ( finite_finite_nat @ A4 )
% 5.31/5.61 => ( ( member_nat @ X @ A4 )
% 5.31/5.61 => ( ( groups129246275422532515t_real @ G2 @ A4 )
% 5.31/5.61 = ( times_times_real @ ( G2 @ X ) @ ( groups129246275422532515t_real @ G2 @ ( minus_minus_set_nat @ A4 @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.remove
% 5.31/5.61 thf(fact_6401_prod_Oremove,axiom,
% 5.31/5.61 ! [A4: set_complex,X: complex,G2: complex > rat] :
% 5.31/5.61 ( ( finite3207457112153483333omplex @ A4 )
% 5.31/5.61 => ( ( member_complex @ X @ A4 )
% 5.31/5.61 => ( ( groups225925009352817453ex_rat @ G2 @ A4 )
% 5.31/5.61 = ( times_times_rat @ ( G2 @ X ) @ ( groups225925009352817453ex_rat @ G2 @ ( minus_811609699411566653omplex @ A4 @ ( insert_complex @ X @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.remove
% 5.31/5.61 thf(fact_6402_prod_Oremove,axiom,
% 5.31/5.61 ! [A4: set_int,X: int,G2: int > rat] :
% 5.31/5.61 ( ( finite_finite_int @ A4 )
% 5.31/5.61 => ( ( member_int @ X @ A4 )
% 5.31/5.61 => ( ( groups1072433553688619179nt_rat @ G2 @ A4 )
% 5.31/5.61 = ( times_times_rat @ ( G2 @ X ) @ ( groups1072433553688619179nt_rat @ G2 @ ( minus_minus_set_int @ A4 @ ( insert_int @ X @ bot_bot_set_int ) ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.remove
% 5.31/5.61 thf(fact_6403_prod_Oremove,axiom,
% 5.31/5.61 ! [A4: set_real,X: real,G2: real > rat] :
% 5.31/5.61 ( ( finite_finite_real @ A4 )
% 5.31/5.61 => ( ( member_real @ X @ A4 )
% 5.31/5.61 => ( ( groups4061424788464935467al_rat @ G2 @ A4 )
% 5.31/5.61 = ( times_times_rat @ ( G2 @ X ) @ ( groups4061424788464935467al_rat @ G2 @ ( minus_minus_set_real @ A4 @ ( insert_real @ X @ bot_bot_set_real ) ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.remove
% 5.31/5.61 thf(fact_6404_prod_Oremove,axiom,
% 5.31/5.61 ! [A4: set_nat,X: nat,G2: nat > rat] :
% 5.31/5.61 ( ( finite_finite_nat @ A4 )
% 5.31/5.61 => ( ( member_nat @ X @ A4 )
% 5.31/5.61 => ( ( groups73079841787564623at_rat @ G2 @ A4 )
% 5.31/5.61 = ( times_times_rat @ ( G2 @ X ) @ ( groups73079841787564623at_rat @ G2 @ ( minus_minus_set_nat @ A4 @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.remove
% 5.31/5.61 thf(fact_6405_prod_Oremove,axiom,
% 5.31/5.61 ! [A4: set_complex,X: complex,G2: complex > nat] :
% 5.31/5.61 ( ( finite3207457112153483333omplex @ A4 )
% 5.31/5.61 => ( ( member_complex @ X @ A4 )
% 5.31/5.61 => ( ( groups861055069439313189ex_nat @ G2 @ A4 )
% 5.31/5.61 = ( times_times_nat @ ( G2 @ X ) @ ( groups861055069439313189ex_nat @ G2 @ ( minus_811609699411566653omplex @ A4 @ ( insert_complex @ X @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.remove
% 5.31/5.61 thf(fact_6406_prod_Oremove,axiom,
% 5.31/5.61 ! [A4: set_int,X: int,G2: int > nat] :
% 5.31/5.61 ( ( finite_finite_int @ A4 )
% 5.31/5.61 => ( ( member_int @ X @ A4 )
% 5.31/5.61 => ( ( groups1707563613775114915nt_nat @ G2 @ A4 )
% 5.31/5.61 = ( times_times_nat @ ( G2 @ X ) @ ( groups1707563613775114915nt_nat @ G2 @ ( minus_minus_set_int @ A4 @ ( insert_int @ X @ bot_bot_set_int ) ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.remove
% 5.31/5.61 thf(fact_6407_prod_Oinsert__remove,axiom,
% 5.31/5.61 ! [A4: set_complex,G2: complex > real,X: complex] :
% 5.31/5.61 ( ( finite3207457112153483333omplex @ A4 )
% 5.31/5.61 => ( ( groups766887009212190081x_real @ G2 @ ( insert_complex @ X @ A4 ) )
% 5.31/5.61 = ( times_times_real @ ( G2 @ X ) @ ( groups766887009212190081x_real @ G2 @ ( minus_811609699411566653omplex @ A4 @ ( insert_complex @ X @ bot_bot_set_complex ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.insert_remove
% 5.31/5.61 thf(fact_6408_prod_Oinsert__remove,axiom,
% 5.31/5.61 ! [A4: set_int,G2: int > real,X: int] :
% 5.31/5.61 ( ( finite_finite_int @ A4 )
% 5.31/5.61 => ( ( groups2316167850115554303t_real @ G2 @ ( insert_int @ X @ A4 ) )
% 5.31/5.61 = ( times_times_real @ ( G2 @ X ) @ ( groups2316167850115554303t_real @ G2 @ ( minus_minus_set_int @ A4 @ ( insert_int @ X @ bot_bot_set_int ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.insert_remove
% 5.31/5.61 thf(fact_6409_prod_Oinsert__remove,axiom,
% 5.31/5.61 ! [A4: set_real,G2: real > real,X: real] :
% 5.31/5.61 ( ( finite_finite_real @ A4 )
% 5.31/5.61 => ( ( groups1681761925125756287l_real @ G2 @ ( insert_real @ X @ A4 ) )
% 5.31/5.61 = ( times_times_real @ ( G2 @ X ) @ ( groups1681761925125756287l_real @ G2 @ ( minus_minus_set_real @ A4 @ ( insert_real @ X @ bot_bot_set_real ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.insert_remove
% 5.31/5.61 thf(fact_6410_prod_Oinsert__remove,axiom,
% 5.31/5.61 ! [A4: set_nat,G2: nat > real,X: nat] :
% 5.31/5.61 ( ( finite_finite_nat @ A4 )
% 5.31/5.61 => ( ( groups129246275422532515t_real @ G2 @ ( insert_nat @ X @ A4 ) )
% 5.31/5.61 = ( times_times_real @ ( G2 @ X ) @ ( groups129246275422532515t_real @ G2 @ ( minus_minus_set_nat @ A4 @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.insert_remove
% 5.31/5.61 thf(fact_6411_prod_Oinsert__remove,axiom,
% 5.31/5.61 ! [A4: set_complex,G2: complex > rat,X: complex] :
% 5.31/5.61 ( ( finite3207457112153483333omplex @ A4 )
% 5.31/5.61 => ( ( groups225925009352817453ex_rat @ G2 @ ( insert_complex @ X @ A4 ) )
% 5.31/5.61 = ( times_times_rat @ ( G2 @ X ) @ ( groups225925009352817453ex_rat @ G2 @ ( minus_811609699411566653omplex @ A4 @ ( insert_complex @ X @ bot_bot_set_complex ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.insert_remove
% 5.31/5.61 thf(fact_6412_prod_Oinsert__remove,axiom,
% 5.31/5.61 ! [A4: set_int,G2: int > rat,X: int] :
% 5.31/5.61 ( ( finite_finite_int @ A4 )
% 5.31/5.61 => ( ( groups1072433553688619179nt_rat @ G2 @ ( insert_int @ X @ A4 ) )
% 5.31/5.61 = ( times_times_rat @ ( G2 @ X ) @ ( groups1072433553688619179nt_rat @ G2 @ ( minus_minus_set_int @ A4 @ ( insert_int @ X @ bot_bot_set_int ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.insert_remove
% 5.31/5.61 thf(fact_6413_prod_Oinsert__remove,axiom,
% 5.31/5.61 ! [A4: set_real,G2: real > rat,X: real] :
% 5.31/5.61 ( ( finite_finite_real @ A4 )
% 5.31/5.61 => ( ( groups4061424788464935467al_rat @ G2 @ ( insert_real @ X @ A4 ) )
% 5.31/5.61 = ( times_times_rat @ ( G2 @ X ) @ ( groups4061424788464935467al_rat @ G2 @ ( minus_minus_set_real @ A4 @ ( insert_real @ X @ bot_bot_set_real ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.insert_remove
% 5.31/5.61 thf(fact_6414_prod_Oinsert__remove,axiom,
% 5.31/5.61 ! [A4: set_nat,G2: nat > rat,X: nat] :
% 5.31/5.61 ( ( finite_finite_nat @ A4 )
% 5.31/5.61 => ( ( groups73079841787564623at_rat @ G2 @ ( insert_nat @ X @ A4 ) )
% 5.31/5.61 = ( times_times_rat @ ( G2 @ X ) @ ( groups73079841787564623at_rat @ G2 @ ( minus_minus_set_nat @ A4 @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.insert_remove
% 5.31/5.61 thf(fact_6415_prod_Oinsert__remove,axiom,
% 5.31/5.61 ! [A4: set_complex,G2: complex > nat,X: complex] :
% 5.31/5.61 ( ( finite3207457112153483333omplex @ A4 )
% 5.31/5.61 => ( ( groups861055069439313189ex_nat @ G2 @ ( insert_complex @ X @ A4 ) )
% 5.31/5.61 = ( times_times_nat @ ( G2 @ X ) @ ( groups861055069439313189ex_nat @ G2 @ ( minus_811609699411566653omplex @ A4 @ ( insert_complex @ X @ bot_bot_set_complex ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.insert_remove
% 5.31/5.61 thf(fact_6416_prod_Oinsert__remove,axiom,
% 5.31/5.61 ! [A4: set_int,G2: int > nat,X: int] :
% 5.31/5.61 ( ( finite_finite_int @ A4 )
% 5.31/5.61 => ( ( groups1707563613775114915nt_nat @ G2 @ ( insert_int @ X @ A4 ) )
% 5.31/5.61 = ( times_times_nat @ ( G2 @ X ) @ ( groups1707563613775114915nt_nat @ G2 @ ( minus_minus_set_int @ A4 @ ( insert_int @ X @ bot_bot_set_int ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.insert_remove
% 5.31/5.61 thf(fact_6417_prod_Ounion__inter__neutral,axiom,
% 5.31/5.61 ! [A4: set_int,B5: set_int,G2: int > code_integer] :
% 5.31/5.61 ( ( finite_finite_int @ A4 )
% 5.31/5.61 => ( ( finite_finite_int @ B5 )
% 5.31/5.61 => ( ! [X3: int] :
% 5.31/5.61 ( ( member_int @ X3 @ ( inf_inf_set_int @ A4 @ B5 ) )
% 5.31/5.61 => ( ( G2 @ X3 )
% 5.31/5.61 = one_one_Code_integer ) )
% 5.31/5.61 => ( ( groups3827104343326376752nteger @ G2 @ ( sup_sup_set_int @ A4 @ B5 ) )
% 5.31/5.61 = ( times_3573771949741848930nteger @ ( groups3827104343326376752nteger @ G2 @ A4 ) @ ( groups3827104343326376752nteger @ G2 @ B5 ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.union_inter_neutral
% 5.31/5.61 thf(fact_6418_prod_Ounion__inter__neutral,axiom,
% 5.31/5.61 ! [A4: set_complex,B5: set_complex,G2: complex > code_integer] :
% 5.31/5.61 ( ( finite3207457112153483333omplex @ A4 )
% 5.31/5.61 => ( ( finite3207457112153483333omplex @ B5 )
% 5.31/5.61 => ( ! [X3: complex] :
% 5.31/5.61 ( ( member_complex @ X3 @ ( inf_inf_set_complex @ A4 @ B5 ) )
% 5.31/5.61 => ( ( G2 @ X3 )
% 5.31/5.61 = one_one_Code_integer ) )
% 5.31/5.61 => ( ( groups8682486955453173170nteger @ G2 @ ( sup_sup_set_complex @ A4 @ B5 ) )
% 5.31/5.61 = ( times_3573771949741848930nteger @ ( groups8682486955453173170nteger @ G2 @ A4 ) @ ( groups8682486955453173170nteger @ G2 @ B5 ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.union_inter_neutral
% 5.31/5.61 thf(fact_6419_prod_Ounion__inter__neutral,axiom,
% 5.31/5.61 ! [A4: set_int,B5: set_int,G2: int > complex] :
% 5.31/5.61 ( ( finite_finite_int @ A4 )
% 5.31/5.61 => ( ( finite_finite_int @ B5 )
% 5.31/5.61 => ( ! [X3: int] :
% 5.31/5.61 ( ( member_int @ X3 @ ( inf_inf_set_int @ A4 @ B5 ) )
% 5.31/5.61 => ( ( G2 @ X3 )
% 5.31/5.61 = one_one_complex ) )
% 5.31/5.61 => ( ( groups7440179247065528705omplex @ G2 @ ( sup_sup_set_int @ A4 @ B5 ) )
% 5.31/5.61 = ( times_times_complex @ ( groups7440179247065528705omplex @ G2 @ A4 ) @ ( groups7440179247065528705omplex @ G2 @ B5 ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.union_inter_neutral
% 5.31/5.61 thf(fact_6420_prod_Ounion__inter__neutral,axiom,
% 5.31/5.61 ! [A4: set_complex,B5: set_complex,G2: complex > complex] :
% 5.31/5.61 ( ( finite3207457112153483333omplex @ A4 )
% 5.31/5.61 => ( ( finite3207457112153483333omplex @ B5 )
% 5.31/5.61 => ( ! [X3: complex] :
% 5.31/5.61 ( ( member_complex @ X3 @ ( inf_inf_set_complex @ A4 @ B5 ) )
% 5.31/5.61 => ( ( G2 @ X3 )
% 5.31/5.61 = one_one_complex ) )
% 5.31/5.61 => ( ( groups3708469109370488835omplex @ G2 @ ( sup_sup_set_complex @ A4 @ B5 ) )
% 5.31/5.61 = ( times_times_complex @ ( groups3708469109370488835omplex @ G2 @ A4 ) @ ( groups3708469109370488835omplex @ G2 @ B5 ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.union_inter_neutral
% 5.31/5.61 thf(fact_6421_prod_Ounion__inter__neutral,axiom,
% 5.31/5.61 ! [A4: set_nat,B5: set_nat,G2: nat > code_integer] :
% 5.31/5.61 ( ( finite_finite_nat @ A4 )
% 5.31/5.61 => ( ( finite_finite_nat @ B5 )
% 5.31/5.61 => ( ! [X3: nat] :
% 5.31/5.61 ( ( member_nat @ X3 @ ( inf_inf_set_nat @ A4 @ B5 ) )
% 5.31/5.61 => ( ( G2 @ X3 )
% 5.31/5.61 = one_one_Code_integer ) )
% 5.31/5.61 => ( ( groups3455450783089532116nteger @ G2 @ ( sup_sup_set_nat @ A4 @ B5 ) )
% 5.31/5.61 = ( times_3573771949741848930nteger @ ( groups3455450783089532116nteger @ G2 @ A4 ) @ ( groups3455450783089532116nteger @ G2 @ B5 ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.union_inter_neutral
% 5.31/5.61 thf(fact_6422_prod_Ounion__inter__neutral,axiom,
% 5.31/5.61 ! [A4: set_nat,B5: set_nat,G2: nat > complex] :
% 5.31/5.61 ( ( finite_finite_nat @ A4 )
% 5.31/5.61 => ( ( finite_finite_nat @ B5 )
% 5.31/5.61 => ( ! [X3: nat] :
% 5.31/5.61 ( ( member_nat @ X3 @ ( inf_inf_set_nat @ A4 @ B5 ) )
% 5.31/5.61 => ( ( G2 @ X3 )
% 5.31/5.61 = one_one_complex ) )
% 5.31/5.61 => ( ( groups6464643781859351333omplex @ G2 @ ( sup_sup_set_nat @ A4 @ B5 ) )
% 5.31/5.61 = ( times_times_complex @ ( groups6464643781859351333omplex @ G2 @ A4 ) @ ( groups6464643781859351333omplex @ G2 @ B5 ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.union_inter_neutral
% 5.31/5.61 thf(fact_6423_prod_Ounion__inter__neutral,axiom,
% 5.31/5.61 ! [A4: set_int,B5: set_int,G2: int > real] :
% 5.31/5.61 ( ( finite_finite_int @ A4 )
% 5.31/5.61 => ( ( finite_finite_int @ B5 )
% 5.31/5.61 => ( ! [X3: int] :
% 5.31/5.61 ( ( member_int @ X3 @ ( inf_inf_set_int @ A4 @ B5 ) )
% 5.31/5.61 => ( ( G2 @ X3 )
% 5.31/5.61 = one_one_real ) )
% 5.31/5.61 => ( ( groups2316167850115554303t_real @ G2 @ ( sup_sup_set_int @ A4 @ B5 ) )
% 5.31/5.61 = ( times_times_real @ ( groups2316167850115554303t_real @ G2 @ A4 ) @ ( groups2316167850115554303t_real @ G2 @ B5 ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.union_inter_neutral
% 5.31/5.61 thf(fact_6424_prod_Ounion__inter__neutral,axiom,
% 5.31/5.61 ! [A4: set_complex,B5: set_complex,G2: complex > real] :
% 5.31/5.61 ( ( finite3207457112153483333omplex @ A4 )
% 5.31/5.61 => ( ( finite3207457112153483333omplex @ B5 )
% 5.31/5.61 => ( ! [X3: complex] :
% 5.31/5.61 ( ( member_complex @ X3 @ ( inf_inf_set_complex @ A4 @ B5 ) )
% 5.31/5.61 => ( ( G2 @ X3 )
% 5.31/5.61 = one_one_real ) )
% 5.31/5.61 => ( ( groups766887009212190081x_real @ G2 @ ( sup_sup_set_complex @ A4 @ B5 ) )
% 5.31/5.61 = ( times_times_real @ ( groups766887009212190081x_real @ G2 @ A4 ) @ ( groups766887009212190081x_real @ G2 @ B5 ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.union_inter_neutral
% 5.31/5.61 thf(fact_6425_prod_Ounion__inter__neutral,axiom,
% 5.31/5.61 ! [A4: set_nat,B5: set_nat,G2: nat > real] :
% 5.31/5.61 ( ( finite_finite_nat @ A4 )
% 5.31/5.61 => ( ( finite_finite_nat @ B5 )
% 5.31/5.61 => ( ! [X3: nat] :
% 5.31/5.61 ( ( member_nat @ X3 @ ( inf_inf_set_nat @ A4 @ B5 ) )
% 5.31/5.61 => ( ( G2 @ X3 )
% 5.31/5.61 = one_one_real ) )
% 5.31/5.61 => ( ( groups129246275422532515t_real @ G2 @ ( sup_sup_set_nat @ A4 @ B5 ) )
% 5.31/5.61 = ( times_times_real @ ( groups129246275422532515t_real @ G2 @ A4 ) @ ( groups129246275422532515t_real @ G2 @ B5 ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.union_inter_neutral
% 5.31/5.61 thf(fact_6426_prod_Ounion__inter__neutral,axiom,
% 5.31/5.61 ! [A4: set_int,B5: set_int,G2: int > rat] :
% 5.31/5.61 ( ( finite_finite_int @ A4 )
% 5.31/5.61 => ( ( finite_finite_int @ B5 )
% 5.31/5.61 => ( ! [X3: int] :
% 5.31/5.61 ( ( member_int @ X3 @ ( inf_inf_set_int @ A4 @ B5 ) )
% 5.31/5.61 => ( ( G2 @ X3 )
% 5.31/5.61 = one_one_rat ) )
% 5.31/5.61 => ( ( groups1072433553688619179nt_rat @ G2 @ ( sup_sup_set_int @ A4 @ B5 ) )
% 5.31/5.61 = ( times_times_rat @ ( groups1072433553688619179nt_rat @ G2 @ A4 ) @ ( groups1072433553688619179nt_rat @ G2 @ B5 ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.union_inter_neutral
% 5.31/5.61 thf(fact_6427_prod_Ounion__disjoint,axiom,
% 5.31/5.61 ! [A4: set_complex,B5: set_complex,G2: complex > real] :
% 5.31/5.61 ( ( finite3207457112153483333omplex @ A4 )
% 5.31/5.61 => ( ( finite3207457112153483333omplex @ B5 )
% 5.31/5.61 => ( ( ( inf_inf_set_complex @ A4 @ B5 )
% 5.31/5.61 = bot_bot_set_complex )
% 5.31/5.61 => ( ( groups766887009212190081x_real @ G2 @ ( sup_sup_set_complex @ A4 @ B5 ) )
% 5.31/5.61 = ( times_times_real @ ( groups766887009212190081x_real @ G2 @ A4 ) @ ( groups766887009212190081x_real @ G2 @ B5 ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.union_disjoint
% 5.31/5.61 thf(fact_6428_prod_Ounion__disjoint,axiom,
% 5.31/5.61 ! [A4: set_nat,B5: set_nat,G2: nat > real] :
% 5.31/5.61 ( ( finite_finite_nat @ A4 )
% 5.31/5.61 => ( ( finite_finite_nat @ B5 )
% 5.31/5.61 => ( ( ( inf_inf_set_nat @ A4 @ B5 )
% 5.31/5.61 = bot_bot_set_nat )
% 5.31/5.61 => ( ( groups129246275422532515t_real @ G2 @ ( sup_sup_set_nat @ A4 @ B5 ) )
% 5.31/5.61 = ( times_times_real @ ( groups129246275422532515t_real @ G2 @ A4 ) @ ( groups129246275422532515t_real @ G2 @ B5 ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.union_disjoint
% 5.31/5.61 thf(fact_6429_prod_Ounion__disjoint,axiom,
% 5.31/5.61 ! [A4: set_int,B5: set_int,G2: int > real] :
% 5.31/5.61 ( ( finite_finite_int @ A4 )
% 5.31/5.61 => ( ( finite_finite_int @ B5 )
% 5.31/5.61 => ( ( ( inf_inf_set_int @ A4 @ B5 )
% 5.31/5.61 = bot_bot_set_int )
% 5.31/5.61 => ( ( groups2316167850115554303t_real @ G2 @ ( sup_sup_set_int @ A4 @ B5 ) )
% 5.31/5.61 = ( times_times_real @ ( groups2316167850115554303t_real @ G2 @ A4 ) @ ( groups2316167850115554303t_real @ G2 @ B5 ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.union_disjoint
% 5.31/5.61 thf(fact_6430_prod_Ounion__disjoint,axiom,
% 5.31/5.61 ! [A4: set_real,B5: set_real,G2: real > real] :
% 5.31/5.61 ( ( finite_finite_real @ A4 )
% 5.31/5.61 => ( ( finite_finite_real @ B5 )
% 5.31/5.61 => ( ( ( inf_inf_set_real @ A4 @ B5 )
% 5.31/5.61 = bot_bot_set_real )
% 5.31/5.61 => ( ( groups1681761925125756287l_real @ G2 @ ( sup_sup_set_real @ A4 @ B5 ) )
% 5.31/5.61 = ( times_times_real @ ( groups1681761925125756287l_real @ G2 @ A4 ) @ ( groups1681761925125756287l_real @ G2 @ B5 ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.union_disjoint
% 5.31/5.61 thf(fact_6431_prod_Ounion__disjoint,axiom,
% 5.31/5.61 ! [A4: set_complex,B5: set_complex,G2: complex > rat] :
% 5.31/5.61 ( ( finite3207457112153483333omplex @ A4 )
% 5.31/5.61 => ( ( finite3207457112153483333omplex @ B5 )
% 5.31/5.61 => ( ( ( inf_inf_set_complex @ A4 @ B5 )
% 5.31/5.61 = bot_bot_set_complex )
% 5.31/5.61 => ( ( groups225925009352817453ex_rat @ G2 @ ( sup_sup_set_complex @ A4 @ B5 ) )
% 5.31/5.61 = ( times_times_rat @ ( groups225925009352817453ex_rat @ G2 @ A4 ) @ ( groups225925009352817453ex_rat @ G2 @ B5 ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.union_disjoint
% 5.31/5.61 thf(fact_6432_prod_Ounion__disjoint,axiom,
% 5.31/5.61 ! [A4: set_nat,B5: set_nat,G2: nat > rat] :
% 5.31/5.61 ( ( finite_finite_nat @ A4 )
% 5.31/5.61 => ( ( finite_finite_nat @ B5 )
% 5.31/5.61 => ( ( ( inf_inf_set_nat @ A4 @ B5 )
% 5.31/5.61 = bot_bot_set_nat )
% 5.31/5.61 => ( ( groups73079841787564623at_rat @ G2 @ ( sup_sup_set_nat @ A4 @ B5 ) )
% 5.31/5.61 = ( times_times_rat @ ( groups73079841787564623at_rat @ G2 @ A4 ) @ ( groups73079841787564623at_rat @ G2 @ B5 ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.union_disjoint
% 5.31/5.61 thf(fact_6433_prod_Ounion__disjoint,axiom,
% 5.31/5.61 ! [A4: set_int,B5: set_int,G2: int > rat] :
% 5.31/5.61 ( ( finite_finite_int @ A4 )
% 5.31/5.61 => ( ( finite_finite_int @ B5 )
% 5.31/5.61 => ( ( ( inf_inf_set_int @ A4 @ B5 )
% 5.31/5.61 = bot_bot_set_int )
% 5.31/5.61 => ( ( groups1072433553688619179nt_rat @ G2 @ ( sup_sup_set_int @ A4 @ B5 ) )
% 5.31/5.61 = ( times_times_rat @ ( groups1072433553688619179nt_rat @ G2 @ A4 ) @ ( groups1072433553688619179nt_rat @ G2 @ B5 ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.union_disjoint
% 5.31/5.61 thf(fact_6434_prod_Ounion__disjoint,axiom,
% 5.31/5.61 ! [A4: set_real,B5: set_real,G2: real > rat] :
% 5.31/5.61 ( ( finite_finite_real @ A4 )
% 5.31/5.61 => ( ( finite_finite_real @ B5 )
% 5.31/5.61 => ( ( ( inf_inf_set_real @ A4 @ B5 )
% 5.31/5.61 = bot_bot_set_real )
% 5.31/5.61 => ( ( groups4061424788464935467al_rat @ G2 @ ( sup_sup_set_real @ A4 @ B5 ) )
% 5.31/5.61 = ( times_times_rat @ ( groups4061424788464935467al_rat @ G2 @ A4 ) @ ( groups4061424788464935467al_rat @ G2 @ B5 ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.union_disjoint
% 5.31/5.61 thf(fact_6435_prod_Ounion__disjoint,axiom,
% 5.31/5.61 ! [A4: set_complex,B5: set_complex,G2: complex > nat] :
% 5.31/5.61 ( ( finite3207457112153483333omplex @ A4 )
% 5.31/5.61 => ( ( finite3207457112153483333omplex @ B5 )
% 5.31/5.61 => ( ( ( inf_inf_set_complex @ A4 @ B5 )
% 5.31/5.61 = bot_bot_set_complex )
% 5.31/5.61 => ( ( groups861055069439313189ex_nat @ G2 @ ( sup_sup_set_complex @ A4 @ B5 ) )
% 5.31/5.61 = ( times_times_nat @ ( groups861055069439313189ex_nat @ G2 @ A4 ) @ ( groups861055069439313189ex_nat @ G2 @ B5 ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.union_disjoint
% 5.31/5.61 thf(fact_6436_prod_Ounion__disjoint,axiom,
% 5.31/5.61 ! [A4: set_int,B5: set_int,G2: int > nat] :
% 5.31/5.61 ( ( finite_finite_int @ A4 )
% 5.31/5.61 => ( ( finite_finite_int @ B5 )
% 5.31/5.61 => ( ( ( inf_inf_set_int @ A4 @ B5 )
% 5.31/5.61 = bot_bot_set_int )
% 5.31/5.61 => ( ( groups1707563613775114915nt_nat @ G2 @ ( sup_sup_set_int @ A4 @ B5 ) )
% 5.31/5.61 = ( times_times_nat @ ( groups1707563613775114915nt_nat @ G2 @ A4 ) @ ( groups1707563613775114915nt_nat @ G2 @ B5 ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.union_disjoint
% 5.31/5.61 thf(fact_6437_binomial__maximum_H,axiom,
% 5.31/5.61 ! [N: nat,K2: nat] : ( ord_less_eq_nat @ ( binomial @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ K2 ) @ ( binomial @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ N ) ) ).
% 5.31/5.61
% 5.31/5.61 % binomial_maximum'
% 5.31/5.61 thf(fact_6438_binomial__mono,axiom,
% 5.31/5.61 ! [K2: nat,K6: nat,N: nat] :
% 5.31/5.61 ( ( ord_less_eq_nat @ K2 @ K6 )
% 5.31/5.61 => ( ( ord_less_eq_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K6 ) @ N )
% 5.31/5.61 => ( ord_less_eq_nat @ ( binomial @ N @ K2 ) @ ( binomial @ N @ K6 ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % binomial_mono
% 5.31/5.61 thf(fact_6439_binomial__antimono,axiom,
% 5.31/5.61 ! [K2: nat,K6: nat,N: nat] :
% 5.31/5.61 ( ( ord_less_eq_nat @ K2 @ K6 )
% 5.31/5.61 => ( ( ord_less_eq_nat @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ K2 )
% 5.31/5.61 => ( ( ord_less_eq_nat @ K6 @ N )
% 5.31/5.61 => ( ord_less_eq_nat @ ( binomial @ N @ K6 ) @ ( binomial @ N @ K2 ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % binomial_antimono
% 5.31/5.61 thf(fact_6440_binomial__maximum,axiom,
% 5.31/5.61 ! [N: nat,K2: nat] : ( ord_less_eq_nat @ ( binomial @ N @ K2 ) @ ( binomial @ N @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % binomial_maximum
% 5.31/5.61 thf(fact_6441_prod_Ounion__diff2,axiom,
% 5.31/5.61 ! [A4: set_int,B5: set_int,G2: int > real] :
% 5.31/5.61 ( ( finite_finite_int @ A4 )
% 5.31/5.61 => ( ( finite_finite_int @ B5 )
% 5.31/5.61 => ( ( groups2316167850115554303t_real @ G2 @ ( sup_sup_set_int @ A4 @ B5 ) )
% 5.31/5.61 = ( times_times_real @ ( times_times_real @ ( groups2316167850115554303t_real @ G2 @ ( minus_minus_set_int @ A4 @ B5 ) ) @ ( groups2316167850115554303t_real @ G2 @ ( minus_minus_set_int @ B5 @ A4 ) ) ) @ ( groups2316167850115554303t_real @ G2 @ ( inf_inf_set_int @ A4 @ B5 ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.union_diff2
% 5.31/5.61 thf(fact_6442_prod_Ounion__diff2,axiom,
% 5.31/5.61 ! [A4: set_complex,B5: set_complex,G2: complex > real] :
% 5.31/5.61 ( ( finite3207457112153483333omplex @ A4 )
% 5.31/5.61 => ( ( finite3207457112153483333omplex @ B5 )
% 5.31/5.61 => ( ( groups766887009212190081x_real @ G2 @ ( sup_sup_set_complex @ A4 @ B5 ) )
% 5.31/5.61 = ( times_times_real @ ( times_times_real @ ( groups766887009212190081x_real @ G2 @ ( minus_811609699411566653omplex @ A4 @ B5 ) ) @ ( groups766887009212190081x_real @ G2 @ ( minus_811609699411566653omplex @ B5 @ A4 ) ) ) @ ( groups766887009212190081x_real @ G2 @ ( inf_inf_set_complex @ A4 @ B5 ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.union_diff2
% 5.31/5.61 thf(fact_6443_prod_Ounion__diff2,axiom,
% 5.31/5.61 ! [A4: set_nat,B5: set_nat,G2: nat > real] :
% 5.31/5.61 ( ( finite_finite_nat @ A4 )
% 5.31/5.61 => ( ( finite_finite_nat @ B5 )
% 5.31/5.61 => ( ( groups129246275422532515t_real @ G2 @ ( sup_sup_set_nat @ A4 @ B5 ) )
% 5.31/5.61 = ( times_times_real @ ( times_times_real @ ( groups129246275422532515t_real @ G2 @ ( minus_minus_set_nat @ A4 @ B5 ) ) @ ( groups129246275422532515t_real @ G2 @ ( minus_minus_set_nat @ B5 @ A4 ) ) ) @ ( groups129246275422532515t_real @ G2 @ ( inf_inf_set_nat @ A4 @ B5 ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.union_diff2
% 5.31/5.61 thf(fact_6444_prod_Ounion__diff2,axiom,
% 5.31/5.61 ! [A4: set_int,B5: set_int,G2: int > rat] :
% 5.31/5.61 ( ( finite_finite_int @ A4 )
% 5.31/5.61 => ( ( finite_finite_int @ B5 )
% 5.31/5.61 => ( ( groups1072433553688619179nt_rat @ G2 @ ( sup_sup_set_int @ A4 @ B5 ) )
% 5.31/5.61 = ( times_times_rat @ ( times_times_rat @ ( groups1072433553688619179nt_rat @ G2 @ ( minus_minus_set_int @ A4 @ B5 ) ) @ ( groups1072433553688619179nt_rat @ G2 @ ( minus_minus_set_int @ B5 @ A4 ) ) ) @ ( groups1072433553688619179nt_rat @ G2 @ ( inf_inf_set_int @ A4 @ B5 ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.union_diff2
% 5.31/5.61 thf(fact_6445_prod_Ounion__diff2,axiom,
% 5.31/5.61 ! [A4: set_complex,B5: set_complex,G2: complex > rat] :
% 5.31/5.61 ( ( finite3207457112153483333omplex @ A4 )
% 5.31/5.61 => ( ( finite3207457112153483333omplex @ B5 )
% 5.31/5.61 => ( ( groups225925009352817453ex_rat @ G2 @ ( sup_sup_set_complex @ A4 @ B5 ) )
% 5.31/5.61 = ( times_times_rat @ ( times_times_rat @ ( groups225925009352817453ex_rat @ G2 @ ( minus_811609699411566653omplex @ A4 @ B5 ) ) @ ( groups225925009352817453ex_rat @ G2 @ ( minus_811609699411566653omplex @ B5 @ A4 ) ) ) @ ( groups225925009352817453ex_rat @ G2 @ ( inf_inf_set_complex @ A4 @ B5 ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.union_diff2
% 5.31/5.61 thf(fact_6446_prod_Ounion__diff2,axiom,
% 5.31/5.61 ! [A4: set_nat,B5: set_nat,G2: nat > rat] :
% 5.31/5.61 ( ( finite_finite_nat @ A4 )
% 5.31/5.61 => ( ( finite_finite_nat @ B5 )
% 5.31/5.61 => ( ( groups73079841787564623at_rat @ G2 @ ( sup_sup_set_nat @ A4 @ B5 ) )
% 5.31/5.61 = ( times_times_rat @ ( times_times_rat @ ( groups73079841787564623at_rat @ G2 @ ( minus_minus_set_nat @ A4 @ B5 ) ) @ ( groups73079841787564623at_rat @ G2 @ ( minus_minus_set_nat @ B5 @ A4 ) ) ) @ ( groups73079841787564623at_rat @ G2 @ ( inf_inf_set_nat @ A4 @ B5 ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.union_diff2
% 5.31/5.61 thf(fact_6447_prod_Ounion__diff2,axiom,
% 5.31/5.61 ! [A4: set_int,B5: set_int,G2: int > nat] :
% 5.31/5.61 ( ( finite_finite_int @ A4 )
% 5.31/5.61 => ( ( finite_finite_int @ B5 )
% 5.31/5.61 => ( ( groups1707563613775114915nt_nat @ G2 @ ( sup_sup_set_int @ A4 @ B5 ) )
% 5.31/5.61 = ( times_times_nat @ ( times_times_nat @ ( groups1707563613775114915nt_nat @ G2 @ ( minus_minus_set_int @ A4 @ B5 ) ) @ ( groups1707563613775114915nt_nat @ G2 @ ( minus_minus_set_int @ B5 @ A4 ) ) ) @ ( groups1707563613775114915nt_nat @ G2 @ ( inf_inf_set_int @ A4 @ B5 ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.union_diff2
% 5.31/5.61 thf(fact_6448_prod_Ounion__diff2,axiom,
% 5.31/5.61 ! [A4: set_complex,B5: set_complex,G2: complex > nat] :
% 5.31/5.61 ( ( finite3207457112153483333omplex @ A4 )
% 5.31/5.61 => ( ( finite3207457112153483333omplex @ B5 )
% 5.31/5.61 => ( ( groups861055069439313189ex_nat @ G2 @ ( sup_sup_set_complex @ A4 @ B5 ) )
% 5.31/5.61 = ( times_times_nat @ ( times_times_nat @ ( groups861055069439313189ex_nat @ G2 @ ( minus_811609699411566653omplex @ A4 @ B5 ) ) @ ( groups861055069439313189ex_nat @ G2 @ ( minus_811609699411566653omplex @ B5 @ A4 ) ) ) @ ( groups861055069439313189ex_nat @ G2 @ ( inf_inf_set_complex @ A4 @ B5 ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.union_diff2
% 5.31/5.61 thf(fact_6449_prod_Ounion__diff2,axiom,
% 5.31/5.61 ! [A4: set_complex,B5: set_complex,G2: complex > int] :
% 5.31/5.61 ( ( finite3207457112153483333omplex @ A4 )
% 5.31/5.61 => ( ( finite3207457112153483333omplex @ B5 )
% 5.31/5.61 => ( ( groups858564598930262913ex_int @ G2 @ ( sup_sup_set_complex @ A4 @ B5 ) )
% 5.31/5.61 = ( times_times_int @ ( times_times_int @ ( groups858564598930262913ex_int @ G2 @ ( minus_811609699411566653omplex @ A4 @ B5 ) ) @ ( groups858564598930262913ex_int @ G2 @ ( minus_811609699411566653omplex @ B5 @ A4 ) ) ) @ ( groups858564598930262913ex_int @ G2 @ ( inf_inf_set_complex @ A4 @ B5 ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.union_diff2
% 5.31/5.61 thf(fact_6450_prod_Ounion__diff2,axiom,
% 5.31/5.61 ! [A4: set_nat,B5: set_nat,G2: nat > int] :
% 5.31/5.61 ( ( finite_finite_nat @ A4 )
% 5.31/5.61 => ( ( finite_finite_nat @ B5 )
% 5.31/5.61 => ( ( groups705719431365010083at_int @ G2 @ ( sup_sup_set_nat @ A4 @ B5 ) )
% 5.31/5.61 = ( times_times_int @ ( times_times_int @ ( groups705719431365010083at_int @ G2 @ ( minus_minus_set_nat @ A4 @ B5 ) ) @ ( groups705719431365010083at_int @ G2 @ ( minus_minus_set_nat @ B5 @ A4 ) ) ) @ ( groups705719431365010083at_int @ G2 @ ( inf_inf_set_nat @ A4 @ B5 ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.union_diff2
% 5.31/5.61 thf(fact_6451_prod_Oub__add__nat,axiom,
% 5.31/5.61 ! [M2: nat,N: nat,G2: nat > real,P: nat] :
% 5.31/5.61 ( ( ord_less_eq_nat @ M2 @ ( plus_plus_nat @ N @ one_one_nat ) )
% 5.31/5.61 => ( ( groups129246275422532515t_real @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ ( plus_plus_nat @ N @ P ) ) )
% 5.31/5.61 = ( times_times_real @ ( groups129246275422532515t_real @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) @ ( groups129246275422532515t_real @ G2 @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ ( plus_plus_nat @ N @ P ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.ub_add_nat
% 5.31/5.61 thf(fact_6452_prod_Oub__add__nat,axiom,
% 5.31/5.61 ! [M2: nat,N: nat,G2: nat > rat,P: nat] :
% 5.31/5.61 ( ( ord_less_eq_nat @ M2 @ ( plus_plus_nat @ N @ one_one_nat ) )
% 5.31/5.61 => ( ( groups73079841787564623at_rat @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ ( plus_plus_nat @ N @ P ) ) )
% 5.31/5.61 = ( times_times_rat @ ( groups73079841787564623at_rat @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) @ ( groups73079841787564623at_rat @ G2 @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ ( plus_plus_nat @ N @ P ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.ub_add_nat
% 5.31/5.61 thf(fact_6453_prod_Oub__add__nat,axiom,
% 5.31/5.61 ! [M2: nat,N: nat,G2: nat > int,P: nat] :
% 5.31/5.61 ( ( ord_less_eq_nat @ M2 @ ( plus_plus_nat @ N @ one_one_nat ) )
% 5.31/5.61 => ( ( groups705719431365010083at_int @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ ( plus_plus_nat @ N @ P ) ) )
% 5.31/5.61 = ( times_times_int @ ( groups705719431365010083at_int @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) @ ( groups705719431365010083at_int @ G2 @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ ( plus_plus_nat @ N @ P ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.ub_add_nat
% 5.31/5.61 thf(fact_6454_prod_Oub__add__nat,axiom,
% 5.31/5.61 ! [M2: nat,N: nat,G2: nat > nat,P: nat] :
% 5.31/5.61 ( ( ord_less_eq_nat @ M2 @ ( plus_plus_nat @ N @ one_one_nat ) )
% 5.31/5.61 => ( ( groups708209901874060359at_nat @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ ( plus_plus_nat @ N @ P ) ) )
% 5.31/5.61 = ( times_times_nat @ ( groups708209901874060359at_nat @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) @ ( groups708209901874060359at_nat @ G2 @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ ( plus_plus_nat @ N @ P ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.ub_add_nat
% 5.31/5.61 thf(fact_6455_fold__atLeastAtMost__nat_Osimps,axiom,
% 5.31/5.61 ( set_fo2584398358068434914at_nat
% 5.31/5.61 = ( ^ [F4: nat > nat > nat,A5: nat,B4: nat,Acc2: nat] : ( if_nat @ ( ord_less_nat @ B4 @ A5 ) @ Acc2 @ ( set_fo2584398358068434914at_nat @ F4 @ ( plus_plus_nat @ A5 @ one_one_nat ) @ B4 @ ( F4 @ A5 @ Acc2 ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % fold_atLeastAtMost_nat.simps
% 5.31/5.61 thf(fact_6456_fold__atLeastAtMost__nat_Oelims,axiom,
% 5.31/5.61 ! [X: nat > nat > nat,Xa2: nat,Xb: nat,Xc: nat,Y: nat] :
% 5.31/5.61 ( ( ( set_fo2584398358068434914at_nat @ X @ Xa2 @ Xb @ Xc )
% 5.31/5.61 = Y )
% 5.31/5.61 => ( ( ( ord_less_nat @ Xb @ Xa2 )
% 5.31/5.61 => ( Y = Xc ) )
% 5.31/5.61 & ( ~ ( ord_less_nat @ Xb @ Xa2 )
% 5.31/5.61 => ( Y
% 5.31/5.61 = ( set_fo2584398358068434914at_nat @ X @ ( plus_plus_nat @ Xa2 @ one_one_nat ) @ Xb @ ( X @ Xa2 @ Xc ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % fold_atLeastAtMost_nat.elims
% 5.31/5.61 thf(fact_6457_prod_Odelta__remove,axiom,
% 5.31/5.61 ! [S3: set_complex,A: complex,B: complex > real,C2: complex > real] :
% 5.31/5.61 ( ( finite3207457112153483333omplex @ S3 )
% 5.31/5.61 => ( ( ( member_complex @ A @ S3 )
% 5.31/5.61 => ( ( groups766887009212190081x_real
% 5.31/5.61 @ ^ [K3: complex] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ ( C2 @ K3 ) )
% 5.31/5.61 @ S3 )
% 5.31/5.61 = ( times_times_real @ ( B @ A ) @ ( groups766887009212190081x_real @ C2 @ ( minus_811609699411566653omplex @ S3 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) )
% 5.31/5.61 & ( ~ ( member_complex @ A @ S3 )
% 5.31/5.61 => ( ( groups766887009212190081x_real
% 5.31/5.61 @ ^ [K3: complex] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ ( C2 @ K3 ) )
% 5.31/5.61 @ S3 )
% 5.31/5.61 = ( groups766887009212190081x_real @ C2 @ ( minus_811609699411566653omplex @ S3 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.delta_remove
% 5.31/5.61 thf(fact_6458_prod_Odelta__remove,axiom,
% 5.31/5.61 ! [S3: set_int,A: int,B: int > real,C2: int > real] :
% 5.31/5.61 ( ( finite_finite_int @ S3 )
% 5.31/5.61 => ( ( ( member_int @ A @ S3 )
% 5.31/5.61 => ( ( groups2316167850115554303t_real
% 5.31/5.61 @ ^ [K3: int] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ ( C2 @ K3 ) )
% 5.31/5.61 @ S3 )
% 5.31/5.61 = ( times_times_real @ ( B @ A ) @ ( groups2316167850115554303t_real @ C2 @ ( minus_minus_set_int @ S3 @ ( insert_int @ A @ bot_bot_set_int ) ) ) ) ) )
% 5.31/5.61 & ( ~ ( member_int @ A @ S3 )
% 5.31/5.61 => ( ( groups2316167850115554303t_real
% 5.31/5.61 @ ^ [K3: int] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ ( C2 @ K3 ) )
% 5.31/5.61 @ S3 )
% 5.31/5.61 = ( groups2316167850115554303t_real @ C2 @ ( minus_minus_set_int @ S3 @ ( insert_int @ A @ bot_bot_set_int ) ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.delta_remove
% 5.31/5.61 thf(fact_6459_prod_Odelta__remove,axiom,
% 5.31/5.61 ! [S3: set_real,A: real,B: real > real,C2: real > real] :
% 5.31/5.61 ( ( finite_finite_real @ S3 )
% 5.31/5.61 => ( ( ( member_real @ A @ S3 )
% 5.31/5.61 => ( ( groups1681761925125756287l_real
% 5.31/5.61 @ ^ [K3: real] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ ( C2 @ K3 ) )
% 5.31/5.61 @ S3 )
% 5.31/5.61 = ( times_times_real @ ( B @ A ) @ ( groups1681761925125756287l_real @ C2 @ ( minus_minus_set_real @ S3 @ ( insert_real @ A @ bot_bot_set_real ) ) ) ) ) )
% 5.31/5.61 & ( ~ ( member_real @ A @ S3 )
% 5.31/5.61 => ( ( groups1681761925125756287l_real
% 5.31/5.61 @ ^ [K3: real] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ ( C2 @ K3 ) )
% 5.31/5.61 @ S3 )
% 5.31/5.61 = ( groups1681761925125756287l_real @ C2 @ ( minus_minus_set_real @ S3 @ ( insert_real @ A @ bot_bot_set_real ) ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.delta_remove
% 5.31/5.61 thf(fact_6460_prod_Odelta__remove,axiom,
% 5.31/5.61 ! [S3: set_nat,A: nat,B: nat > real,C2: nat > real] :
% 5.31/5.61 ( ( finite_finite_nat @ S3 )
% 5.31/5.61 => ( ( ( member_nat @ A @ S3 )
% 5.31/5.61 => ( ( groups129246275422532515t_real
% 5.31/5.61 @ ^ [K3: nat] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ ( C2 @ K3 ) )
% 5.31/5.61 @ S3 )
% 5.31/5.61 = ( times_times_real @ ( B @ A ) @ ( groups129246275422532515t_real @ C2 @ ( minus_minus_set_nat @ S3 @ ( insert_nat @ A @ bot_bot_set_nat ) ) ) ) ) )
% 5.31/5.61 & ( ~ ( member_nat @ A @ S3 )
% 5.31/5.61 => ( ( groups129246275422532515t_real
% 5.31/5.61 @ ^ [K3: nat] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ ( C2 @ K3 ) )
% 5.31/5.61 @ S3 )
% 5.31/5.61 = ( groups129246275422532515t_real @ C2 @ ( minus_minus_set_nat @ S3 @ ( insert_nat @ A @ bot_bot_set_nat ) ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.delta_remove
% 5.31/5.61 thf(fact_6461_prod_Odelta__remove,axiom,
% 5.31/5.61 ! [S3: set_complex,A: complex,B: complex > rat,C2: complex > rat] :
% 5.31/5.61 ( ( finite3207457112153483333omplex @ S3 )
% 5.31/5.61 => ( ( ( member_complex @ A @ S3 )
% 5.31/5.61 => ( ( groups225925009352817453ex_rat
% 5.31/5.61 @ ^ [K3: complex] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ ( C2 @ K3 ) )
% 5.31/5.61 @ S3 )
% 5.31/5.61 = ( times_times_rat @ ( B @ A ) @ ( groups225925009352817453ex_rat @ C2 @ ( minus_811609699411566653omplex @ S3 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) )
% 5.31/5.61 & ( ~ ( member_complex @ A @ S3 )
% 5.31/5.61 => ( ( groups225925009352817453ex_rat
% 5.31/5.61 @ ^ [K3: complex] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ ( C2 @ K3 ) )
% 5.31/5.61 @ S3 )
% 5.31/5.61 = ( groups225925009352817453ex_rat @ C2 @ ( minus_811609699411566653omplex @ S3 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.delta_remove
% 5.31/5.61 thf(fact_6462_prod_Odelta__remove,axiom,
% 5.31/5.61 ! [S3: set_int,A: int,B: int > rat,C2: int > rat] :
% 5.31/5.61 ( ( finite_finite_int @ S3 )
% 5.31/5.61 => ( ( ( member_int @ A @ S3 )
% 5.31/5.61 => ( ( groups1072433553688619179nt_rat
% 5.31/5.61 @ ^ [K3: int] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ ( C2 @ K3 ) )
% 5.31/5.61 @ S3 )
% 5.31/5.61 = ( times_times_rat @ ( B @ A ) @ ( groups1072433553688619179nt_rat @ C2 @ ( minus_minus_set_int @ S3 @ ( insert_int @ A @ bot_bot_set_int ) ) ) ) ) )
% 5.31/5.61 & ( ~ ( member_int @ A @ S3 )
% 5.31/5.61 => ( ( groups1072433553688619179nt_rat
% 5.31/5.61 @ ^ [K3: int] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ ( C2 @ K3 ) )
% 5.31/5.61 @ S3 )
% 5.31/5.61 = ( groups1072433553688619179nt_rat @ C2 @ ( minus_minus_set_int @ S3 @ ( insert_int @ A @ bot_bot_set_int ) ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.delta_remove
% 5.31/5.61 thf(fact_6463_prod_Odelta__remove,axiom,
% 5.31/5.61 ! [S3: set_real,A: real,B: real > rat,C2: real > rat] :
% 5.31/5.61 ( ( finite_finite_real @ S3 )
% 5.31/5.61 => ( ( ( member_real @ A @ S3 )
% 5.31/5.61 => ( ( groups4061424788464935467al_rat
% 5.31/5.61 @ ^ [K3: real] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ ( C2 @ K3 ) )
% 5.31/5.61 @ S3 )
% 5.31/5.61 = ( times_times_rat @ ( B @ A ) @ ( groups4061424788464935467al_rat @ C2 @ ( minus_minus_set_real @ S3 @ ( insert_real @ A @ bot_bot_set_real ) ) ) ) ) )
% 5.31/5.61 & ( ~ ( member_real @ A @ S3 )
% 5.31/5.61 => ( ( groups4061424788464935467al_rat
% 5.31/5.61 @ ^ [K3: real] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ ( C2 @ K3 ) )
% 5.31/5.61 @ S3 )
% 5.31/5.61 = ( groups4061424788464935467al_rat @ C2 @ ( minus_minus_set_real @ S3 @ ( insert_real @ A @ bot_bot_set_real ) ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.delta_remove
% 5.31/5.61 thf(fact_6464_prod_Odelta__remove,axiom,
% 5.31/5.61 ! [S3: set_nat,A: nat,B: nat > rat,C2: nat > rat] :
% 5.31/5.61 ( ( finite_finite_nat @ S3 )
% 5.31/5.61 => ( ( ( member_nat @ A @ S3 )
% 5.31/5.61 => ( ( groups73079841787564623at_rat
% 5.31/5.61 @ ^ [K3: nat] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ ( C2 @ K3 ) )
% 5.31/5.61 @ S3 )
% 5.31/5.61 = ( times_times_rat @ ( B @ A ) @ ( groups73079841787564623at_rat @ C2 @ ( minus_minus_set_nat @ S3 @ ( insert_nat @ A @ bot_bot_set_nat ) ) ) ) ) )
% 5.31/5.61 & ( ~ ( member_nat @ A @ S3 )
% 5.31/5.61 => ( ( groups73079841787564623at_rat
% 5.31/5.61 @ ^ [K3: nat] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ ( C2 @ K3 ) )
% 5.31/5.61 @ S3 )
% 5.31/5.61 = ( groups73079841787564623at_rat @ C2 @ ( minus_minus_set_nat @ S3 @ ( insert_nat @ A @ bot_bot_set_nat ) ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.delta_remove
% 5.31/5.61 thf(fact_6465_prod_Odelta__remove,axiom,
% 5.31/5.61 ! [S3: set_complex,A: complex,B: complex > nat,C2: complex > nat] :
% 5.31/5.61 ( ( finite3207457112153483333omplex @ S3 )
% 5.31/5.61 => ( ( ( member_complex @ A @ S3 )
% 5.31/5.61 => ( ( groups861055069439313189ex_nat
% 5.31/5.61 @ ^ [K3: complex] : ( if_nat @ ( K3 = A ) @ ( B @ K3 ) @ ( C2 @ K3 ) )
% 5.31/5.61 @ S3 )
% 5.31/5.61 = ( times_times_nat @ ( B @ A ) @ ( groups861055069439313189ex_nat @ C2 @ ( minus_811609699411566653omplex @ S3 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) )
% 5.31/5.61 & ( ~ ( member_complex @ A @ S3 )
% 5.31/5.61 => ( ( groups861055069439313189ex_nat
% 5.31/5.61 @ ^ [K3: complex] : ( if_nat @ ( K3 = A ) @ ( B @ K3 ) @ ( C2 @ K3 ) )
% 5.31/5.61 @ S3 )
% 5.31/5.61 = ( groups861055069439313189ex_nat @ C2 @ ( minus_811609699411566653omplex @ S3 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.delta_remove
% 5.31/5.61 thf(fact_6466_prod_Odelta__remove,axiom,
% 5.31/5.61 ! [S3: set_int,A: int,B: int > nat,C2: int > nat] :
% 5.31/5.61 ( ( finite_finite_int @ S3 )
% 5.31/5.61 => ( ( ( member_int @ A @ S3 )
% 5.31/5.61 => ( ( groups1707563613775114915nt_nat
% 5.31/5.61 @ ^ [K3: int] : ( if_nat @ ( K3 = A ) @ ( B @ K3 ) @ ( C2 @ K3 ) )
% 5.31/5.61 @ S3 )
% 5.31/5.61 = ( times_times_nat @ ( B @ A ) @ ( groups1707563613775114915nt_nat @ C2 @ ( minus_minus_set_int @ S3 @ ( insert_int @ A @ bot_bot_set_int ) ) ) ) ) )
% 5.31/5.61 & ( ~ ( member_int @ A @ S3 )
% 5.31/5.61 => ( ( groups1707563613775114915nt_nat
% 5.31/5.61 @ ^ [K3: int] : ( if_nat @ ( K3 = A ) @ ( B @ K3 ) @ ( C2 @ K3 ) )
% 5.31/5.61 @ S3 )
% 5.31/5.61 = ( groups1707563613775114915nt_nat @ C2 @ ( minus_minus_set_int @ S3 @ ( insert_int @ A @ bot_bot_set_int ) ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.delta_remove
% 5.31/5.61 thf(fact_6467_power__diff__1__eq,axiom,
% 5.31/5.61 ! [X: code_integer,N: nat] :
% 5.31/5.61 ( ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ X @ N ) @ one_one_Code_integer )
% 5.31/5.61 = ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ X @ one_one_Code_integer ) @ ( groups7501900531339628137nteger @ ( power_8256067586552552935nteger @ X ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % power_diff_1_eq
% 5.31/5.61 thf(fact_6468_power__diff__1__eq,axiom,
% 5.31/5.61 ! [X: complex,N: nat] :
% 5.31/5.61 ( ( minus_minus_complex @ ( power_power_complex @ X @ N ) @ one_one_complex )
% 5.31/5.61 = ( times_times_complex @ ( minus_minus_complex @ X @ one_one_complex ) @ ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % power_diff_1_eq
% 5.31/5.61 thf(fact_6469_power__diff__1__eq,axiom,
% 5.31/5.61 ! [X: rat,N: nat] :
% 5.31/5.61 ( ( minus_minus_rat @ ( power_power_rat @ X @ N ) @ one_one_rat )
% 5.31/5.61 = ( times_times_rat @ ( minus_minus_rat @ X @ one_one_rat ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % power_diff_1_eq
% 5.31/5.61 thf(fact_6470_power__diff__1__eq,axiom,
% 5.31/5.61 ! [X: int,N: nat] :
% 5.31/5.61 ( ( minus_minus_int @ ( power_power_int @ X @ N ) @ one_one_int )
% 5.31/5.61 = ( times_times_int @ ( minus_minus_int @ X @ one_one_int ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % power_diff_1_eq
% 5.31/5.61 thf(fact_6471_power__diff__1__eq,axiom,
% 5.31/5.61 ! [X: real,N: nat] :
% 5.31/5.61 ( ( minus_minus_real @ ( power_power_real @ X @ N ) @ one_one_real )
% 5.31/5.61 = ( times_times_real @ ( minus_minus_real @ X @ one_one_real ) @ ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % power_diff_1_eq
% 5.31/5.61 thf(fact_6472_one__diff__power__eq,axiom,
% 5.31/5.61 ! [X: code_integer,N: nat] :
% 5.31/5.61 ( ( minus_8373710615458151222nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ X @ N ) )
% 5.31/5.61 = ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ one_one_Code_integer @ X ) @ ( groups7501900531339628137nteger @ ( power_8256067586552552935nteger @ X ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % one_diff_power_eq
% 5.31/5.61 thf(fact_6473_one__diff__power__eq,axiom,
% 5.31/5.61 ! [X: complex,N: nat] :
% 5.31/5.61 ( ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ X @ N ) )
% 5.31/5.61 = ( times_times_complex @ ( minus_minus_complex @ one_one_complex @ X ) @ ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % one_diff_power_eq
% 5.31/5.61 thf(fact_6474_one__diff__power__eq,axiom,
% 5.31/5.61 ! [X: rat,N: nat] :
% 5.31/5.61 ( ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X @ N ) )
% 5.31/5.61 = ( times_times_rat @ ( minus_minus_rat @ one_one_rat @ X ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % one_diff_power_eq
% 5.31/5.61 thf(fact_6475_one__diff__power__eq,axiom,
% 5.31/5.61 ! [X: int,N: nat] :
% 5.31/5.61 ( ( minus_minus_int @ one_one_int @ ( power_power_int @ X @ N ) )
% 5.31/5.61 = ( times_times_int @ ( minus_minus_int @ one_one_int @ X ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % one_diff_power_eq
% 5.31/5.61 thf(fact_6476_one__diff__power__eq,axiom,
% 5.31/5.61 ! [X: real,N: nat] :
% 5.31/5.61 ( ( minus_minus_real @ one_one_real @ ( power_power_real @ X @ N ) )
% 5.31/5.61 = ( times_times_real @ ( minus_minus_real @ one_one_real @ X ) @ ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % one_diff_power_eq
% 5.31/5.61 thf(fact_6477_geometric__sum,axiom,
% 5.31/5.61 ! [X: complex,N: nat] :
% 5.31/5.61 ( ( X != one_one_complex )
% 5.31/5.61 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_ord_lessThan_nat @ N ) )
% 5.31/5.61 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( power_power_complex @ X @ N ) @ one_one_complex ) @ ( minus_minus_complex @ X @ one_one_complex ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % geometric_sum
% 5.31/5.61 thf(fact_6478_geometric__sum,axiom,
% 5.31/5.61 ! [X: rat,N: nat] :
% 5.31/5.61 ( ( X != one_one_rat )
% 5.31/5.61 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_ord_lessThan_nat @ N ) )
% 5.31/5.61 = ( divide_divide_rat @ ( minus_minus_rat @ ( power_power_rat @ X @ N ) @ one_one_rat ) @ ( minus_minus_rat @ X @ one_one_rat ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % geometric_sum
% 5.31/5.61 thf(fact_6479_geometric__sum,axiom,
% 5.31/5.61 ! [X: real,N: nat] :
% 5.31/5.61 ( ( X != one_one_real )
% 5.31/5.61 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_ord_lessThan_nat @ N ) )
% 5.31/5.61 = ( divide_divide_real @ ( minus_minus_real @ ( power_power_real @ X @ N ) @ one_one_real ) @ ( minus_minus_real @ X @ one_one_real ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % geometric_sum
% 5.31/5.61 thf(fact_6480_prod__mono2,axiom,
% 5.31/5.61 ! [B5: set_real,A4: set_real,F2: real > code_integer] :
% 5.31/5.61 ( ( finite_finite_real @ B5 )
% 5.31/5.61 => ( ( ord_less_eq_set_real @ A4 @ B5 )
% 5.31/5.61 => ( ! [B3: real] :
% 5.31/5.61 ( ( member_real @ B3 @ ( minus_minus_set_real @ B5 @ A4 ) )
% 5.31/5.61 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( F2 @ B3 ) ) )
% 5.31/5.61 => ( ! [A3: real] :
% 5.31/5.61 ( ( member_real @ A3 @ A4 )
% 5.31/5.61 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F2 @ A3 ) ) )
% 5.31/5.61 => ( ord_le3102999989581377725nteger @ ( groups6225526099057966256nteger @ F2 @ A4 ) @ ( groups6225526099057966256nteger @ F2 @ B5 ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod_mono2
% 5.31/5.61 thf(fact_6481_prod__mono2,axiom,
% 5.31/5.61 ! [B5: set_int,A4: set_int,F2: int > code_integer] :
% 5.31/5.61 ( ( finite_finite_int @ B5 )
% 5.31/5.61 => ( ( ord_less_eq_set_int @ A4 @ B5 )
% 5.31/5.61 => ( ! [B3: int] :
% 5.31/5.61 ( ( member_int @ B3 @ ( minus_minus_set_int @ B5 @ A4 ) )
% 5.31/5.61 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( F2 @ B3 ) ) )
% 5.31/5.61 => ( ! [A3: int] :
% 5.31/5.61 ( ( member_int @ A3 @ A4 )
% 5.31/5.61 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F2 @ A3 ) ) )
% 5.31/5.61 => ( ord_le3102999989581377725nteger @ ( groups3827104343326376752nteger @ F2 @ A4 ) @ ( groups3827104343326376752nteger @ F2 @ B5 ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod_mono2
% 5.31/5.61 thf(fact_6482_prod__mono2,axiom,
% 5.31/5.61 ! [B5: set_complex,A4: set_complex,F2: complex > code_integer] :
% 5.31/5.61 ( ( finite3207457112153483333omplex @ B5 )
% 5.31/5.61 => ( ( ord_le211207098394363844omplex @ A4 @ B5 )
% 5.31/5.61 => ( ! [B3: complex] :
% 5.31/5.61 ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ B5 @ A4 ) )
% 5.31/5.61 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( F2 @ B3 ) ) )
% 5.31/5.61 => ( ! [A3: complex] :
% 5.31/5.61 ( ( member_complex @ A3 @ A4 )
% 5.31/5.61 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F2 @ A3 ) ) )
% 5.31/5.61 => ( ord_le3102999989581377725nteger @ ( groups8682486955453173170nteger @ F2 @ A4 ) @ ( groups8682486955453173170nteger @ F2 @ B5 ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod_mono2
% 5.31/5.61 thf(fact_6483_prod__mono2,axiom,
% 5.31/5.61 ! [B5: set_real,A4: set_real,F2: real > real] :
% 5.31/5.61 ( ( finite_finite_real @ B5 )
% 5.31/5.61 => ( ( ord_less_eq_set_real @ A4 @ B5 )
% 5.31/5.61 => ( ! [B3: real] :
% 5.31/5.61 ( ( member_real @ B3 @ ( minus_minus_set_real @ B5 @ A4 ) )
% 5.31/5.61 => ( ord_less_eq_real @ one_one_real @ ( F2 @ B3 ) ) )
% 5.31/5.61 => ( ! [A3: real] :
% 5.31/5.61 ( ( member_real @ A3 @ A4 )
% 5.31/5.61 => ( ord_less_eq_real @ zero_zero_real @ ( F2 @ A3 ) ) )
% 5.31/5.61 => ( ord_less_eq_real @ ( groups1681761925125756287l_real @ F2 @ A4 ) @ ( groups1681761925125756287l_real @ F2 @ B5 ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod_mono2
% 5.31/5.61 thf(fact_6484_prod__mono2,axiom,
% 5.31/5.61 ! [B5: set_int,A4: set_int,F2: int > real] :
% 5.31/5.61 ( ( finite_finite_int @ B5 )
% 5.31/5.61 => ( ( ord_less_eq_set_int @ A4 @ B5 )
% 5.31/5.61 => ( ! [B3: int] :
% 5.31/5.61 ( ( member_int @ B3 @ ( minus_minus_set_int @ B5 @ A4 ) )
% 5.31/5.61 => ( ord_less_eq_real @ one_one_real @ ( F2 @ B3 ) ) )
% 5.31/5.61 => ( ! [A3: int] :
% 5.31/5.61 ( ( member_int @ A3 @ A4 )
% 5.31/5.61 => ( ord_less_eq_real @ zero_zero_real @ ( F2 @ A3 ) ) )
% 5.31/5.61 => ( ord_less_eq_real @ ( groups2316167850115554303t_real @ F2 @ A4 ) @ ( groups2316167850115554303t_real @ F2 @ B5 ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod_mono2
% 5.31/5.61 thf(fact_6485_prod__mono2,axiom,
% 5.31/5.61 ! [B5: set_complex,A4: set_complex,F2: complex > real] :
% 5.31/5.61 ( ( finite3207457112153483333omplex @ B5 )
% 5.31/5.61 => ( ( ord_le211207098394363844omplex @ A4 @ B5 )
% 5.31/5.61 => ( ! [B3: complex] :
% 5.31/5.61 ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ B5 @ A4 ) )
% 5.31/5.61 => ( ord_less_eq_real @ one_one_real @ ( F2 @ B3 ) ) )
% 5.31/5.61 => ( ! [A3: complex] :
% 5.31/5.61 ( ( member_complex @ A3 @ A4 )
% 5.31/5.61 => ( ord_less_eq_real @ zero_zero_real @ ( F2 @ A3 ) ) )
% 5.31/5.61 => ( ord_less_eq_real @ ( groups766887009212190081x_real @ F2 @ A4 ) @ ( groups766887009212190081x_real @ F2 @ B5 ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod_mono2
% 5.31/5.61 thf(fact_6486_prod__mono2,axiom,
% 5.31/5.61 ! [B5: set_real,A4: set_real,F2: real > rat] :
% 5.31/5.61 ( ( finite_finite_real @ B5 )
% 5.31/5.61 => ( ( ord_less_eq_set_real @ A4 @ B5 )
% 5.31/5.61 => ( ! [B3: real] :
% 5.31/5.61 ( ( member_real @ B3 @ ( minus_minus_set_real @ B5 @ A4 ) )
% 5.31/5.61 => ( ord_less_eq_rat @ one_one_rat @ ( F2 @ B3 ) ) )
% 5.31/5.61 => ( ! [A3: real] :
% 5.31/5.61 ( ( member_real @ A3 @ A4 )
% 5.31/5.61 => ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ A3 ) ) )
% 5.31/5.61 => ( ord_less_eq_rat @ ( groups4061424788464935467al_rat @ F2 @ A4 ) @ ( groups4061424788464935467al_rat @ F2 @ B5 ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod_mono2
% 5.31/5.61 thf(fact_6487_prod__mono2,axiom,
% 5.31/5.61 ! [B5: set_int,A4: set_int,F2: int > rat] :
% 5.31/5.61 ( ( finite_finite_int @ B5 )
% 5.31/5.61 => ( ( ord_less_eq_set_int @ A4 @ B5 )
% 5.31/5.61 => ( ! [B3: int] :
% 5.31/5.61 ( ( member_int @ B3 @ ( minus_minus_set_int @ B5 @ A4 ) )
% 5.31/5.61 => ( ord_less_eq_rat @ one_one_rat @ ( F2 @ B3 ) ) )
% 5.31/5.61 => ( ! [A3: int] :
% 5.31/5.61 ( ( member_int @ A3 @ A4 )
% 5.31/5.61 => ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ A3 ) ) )
% 5.31/5.61 => ( ord_less_eq_rat @ ( groups1072433553688619179nt_rat @ F2 @ A4 ) @ ( groups1072433553688619179nt_rat @ F2 @ B5 ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod_mono2
% 5.31/5.61 thf(fact_6488_prod__mono2,axiom,
% 5.31/5.61 ! [B5: set_complex,A4: set_complex,F2: complex > rat] :
% 5.31/5.61 ( ( finite3207457112153483333omplex @ B5 )
% 5.31/5.61 => ( ( ord_le211207098394363844omplex @ A4 @ B5 )
% 5.31/5.61 => ( ! [B3: complex] :
% 5.31/5.61 ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ B5 @ A4 ) )
% 5.31/5.61 => ( ord_less_eq_rat @ one_one_rat @ ( F2 @ B3 ) ) )
% 5.31/5.61 => ( ! [A3: complex] :
% 5.31/5.61 ( ( member_complex @ A3 @ A4 )
% 5.31/5.61 => ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ A3 ) ) )
% 5.31/5.61 => ( ord_less_eq_rat @ ( groups225925009352817453ex_rat @ F2 @ A4 ) @ ( groups225925009352817453ex_rat @ F2 @ B5 ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod_mono2
% 5.31/5.61 thf(fact_6489_prod__mono2,axiom,
% 5.31/5.61 ! [B5: set_real,A4: set_real,F2: real > int] :
% 5.31/5.61 ( ( finite_finite_real @ B5 )
% 5.31/5.61 => ( ( ord_less_eq_set_real @ A4 @ B5 )
% 5.31/5.61 => ( ! [B3: real] :
% 5.31/5.61 ( ( member_real @ B3 @ ( minus_minus_set_real @ B5 @ A4 ) )
% 5.31/5.61 => ( ord_less_eq_int @ one_one_int @ ( F2 @ B3 ) ) )
% 5.31/5.61 => ( ! [A3: real] :
% 5.31/5.61 ( ( member_real @ A3 @ A4 )
% 5.31/5.61 => ( ord_less_eq_int @ zero_zero_int @ ( F2 @ A3 ) ) )
% 5.31/5.61 => ( ord_less_eq_int @ ( groups4694064378042380927al_int @ F2 @ A4 ) @ ( groups4694064378042380927al_int @ F2 @ B5 ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod_mono2
% 5.31/5.61 thf(fact_6490_prod__le__power,axiom,
% 5.31/5.61 ! [A4: set_real,F2: real > code_integer,N: code_integer,K2: nat] :
% 5.31/5.61 ( ! [I3: real] :
% 5.31/5.61 ( ( member_real @ I3 @ A4 )
% 5.31/5.61 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F2 @ I3 ) )
% 5.31/5.61 & ( ord_le3102999989581377725nteger @ ( F2 @ I3 ) @ N ) ) )
% 5.31/5.61 => ( ( ord_less_eq_nat @ ( finite_card_real @ A4 ) @ K2 )
% 5.31/5.61 => ( ( ord_le3102999989581377725nteger @ one_one_Code_integer @ N )
% 5.31/5.61 => ( ord_le3102999989581377725nteger @ ( groups6225526099057966256nteger @ F2 @ A4 ) @ ( power_8256067586552552935nteger @ N @ K2 ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod_le_power
% 5.31/5.61 thf(fact_6491_prod__le__power,axiom,
% 5.31/5.61 ! [A4: set_nat,F2: nat > code_integer,N: code_integer,K2: nat] :
% 5.31/5.61 ( ! [I3: nat] :
% 5.31/5.61 ( ( member_nat @ I3 @ A4 )
% 5.31/5.61 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F2 @ I3 ) )
% 5.31/5.61 & ( ord_le3102999989581377725nteger @ ( F2 @ I3 ) @ N ) ) )
% 5.31/5.61 => ( ( ord_less_eq_nat @ ( finite_card_nat @ A4 ) @ K2 )
% 5.31/5.61 => ( ( ord_le3102999989581377725nteger @ one_one_Code_integer @ N )
% 5.31/5.61 => ( ord_le3102999989581377725nteger @ ( groups3455450783089532116nteger @ F2 @ A4 ) @ ( power_8256067586552552935nteger @ N @ K2 ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod_le_power
% 5.31/5.61 thf(fact_6492_prod__le__power,axiom,
% 5.31/5.61 ! [A4: set_complex,F2: complex > code_integer,N: code_integer,K2: nat] :
% 5.31/5.61 ( ! [I3: complex] :
% 5.31/5.61 ( ( member_complex @ I3 @ A4 )
% 5.31/5.61 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F2 @ I3 ) )
% 5.31/5.61 & ( ord_le3102999989581377725nteger @ ( F2 @ I3 ) @ N ) ) )
% 5.31/5.61 => ( ( ord_less_eq_nat @ ( finite_card_complex @ A4 ) @ K2 )
% 5.31/5.61 => ( ( ord_le3102999989581377725nteger @ one_one_Code_integer @ N )
% 5.31/5.61 => ( ord_le3102999989581377725nteger @ ( groups8682486955453173170nteger @ F2 @ A4 ) @ ( power_8256067586552552935nteger @ N @ K2 ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod_le_power
% 5.31/5.61 thf(fact_6493_prod__le__power,axiom,
% 5.31/5.61 ! [A4: set_int,F2: int > code_integer,N: code_integer,K2: nat] :
% 5.31/5.61 ( ! [I3: int] :
% 5.31/5.61 ( ( member_int @ I3 @ A4 )
% 5.31/5.61 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F2 @ I3 ) )
% 5.31/5.61 & ( ord_le3102999989581377725nteger @ ( F2 @ I3 ) @ N ) ) )
% 5.31/5.61 => ( ( ord_less_eq_nat @ ( finite_card_int @ A4 ) @ K2 )
% 5.31/5.61 => ( ( ord_le3102999989581377725nteger @ one_one_Code_integer @ N )
% 5.31/5.61 => ( ord_le3102999989581377725nteger @ ( groups3827104343326376752nteger @ F2 @ A4 ) @ ( power_8256067586552552935nteger @ N @ K2 ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod_le_power
% 5.31/5.61 thf(fact_6494_prod__le__power,axiom,
% 5.31/5.61 ! [A4: set_real,F2: real > real,N: real,K2: nat] :
% 5.31/5.61 ( ! [I3: real] :
% 5.31/5.61 ( ( member_real @ I3 @ A4 )
% 5.31/5.61 => ( ( ord_less_eq_real @ zero_zero_real @ ( F2 @ I3 ) )
% 5.31/5.61 & ( ord_less_eq_real @ ( F2 @ I3 ) @ N ) ) )
% 5.31/5.61 => ( ( ord_less_eq_nat @ ( finite_card_real @ A4 ) @ K2 )
% 5.31/5.61 => ( ( ord_less_eq_real @ one_one_real @ N )
% 5.31/5.61 => ( ord_less_eq_real @ ( groups1681761925125756287l_real @ F2 @ A4 ) @ ( power_power_real @ N @ K2 ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod_le_power
% 5.31/5.61 thf(fact_6495_prod__le__power,axiom,
% 5.31/5.61 ! [A4: set_nat,F2: nat > real,N: real,K2: nat] :
% 5.31/5.61 ( ! [I3: nat] :
% 5.31/5.61 ( ( member_nat @ I3 @ A4 )
% 5.31/5.61 => ( ( ord_less_eq_real @ zero_zero_real @ ( F2 @ I3 ) )
% 5.31/5.61 & ( ord_less_eq_real @ ( F2 @ I3 ) @ N ) ) )
% 5.31/5.61 => ( ( ord_less_eq_nat @ ( finite_card_nat @ A4 ) @ K2 )
% 5.31/5.61 => ( ( ord_less_eq_real @ one_one_real @ N )
% 5.31/5.61 => ( ord_less_eq_real @ ( groups129246275422532515t_real @ F2 @ A4 ) @ ( power_power_real @ N @ K2 ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod_le_power
% 5.31/5.61 thf(fact_6496_prod__le__power,axiom,
% 5.31/5.61 ! [A4: set_complex,F2: complex > real,N: real,K2: nat] :
% 5.31/5.61 ( ! [I3: complex] :
% 5.31/5.61 ( ( member_complex @ I3 @ A4 )
% 5.31/5.61 => ( ( ord_less_eq_real @ zero_zero_real @ ( F2 @ I3 ) )
% 5.31/5.61 & ( ord_less_eq_real @ ( F2 @ I3 ) @ N ) ) )
% 5.31/5.61 => ( ( ord_less_eq_nat @ ( finite_card_complex @ A4 ) @ K2 )
% 5.31/5.61 => ( ( ord_less_eq_real @ one_one_real @ N )
% 5.31/5.61 => ( ord_less_eq_real @ ( groups766887009212190081x_real @ F2 @ A4 ) @ ( power_power_real @ N @ K2 ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod_le_power
% 5.31/5.61 thf(fact_6497_prod__le__power,axiom,
% 5.31/5.61 ! [A4: set_int,F2: int > real,N: real,K2: nat] :
% 5.31/5.61 ( ! [I3: int] :
% 5.31/5.61 ( ( member_int @ I3 @ A4 )
% 5.31/5.61 => ( ( ord_less_eq_real @ zero_zero_real @ ( F2 @ I3 ) )
% 5.31/5.61 & ( ord_less_eq_real @ ( F2 @ I3 ) @ N ) ) )
% 5.31/5.61 => ( ( ord_less_eq_nat @ ( finite_card_int @ A4 ) @ K2 )
% 5.31/5.61 => ( ( ord_less_eq_real @ one_one_real @ N )
% 5.31/5.61 => ( ord_less_eq_real @ ( groups2316167850115554303t_real @ F2 @ A4 ) @ ( power_power_real @ N @ K2 ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod_le_power
% 5.31/5.61 thf(fact_6498_prod__le__power,axiom,
% 5.31/5.61 ! [A4: set_real,F2: real > rat,N: rat,K2: nat] :
% 5.31/5.61 ( ! [I3: real] :
% 5.31/5.61 ( ( member_real @ I3 @ A4 )
% 5.31/5.61 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ I3 ) )
% 5.31/5.61 & ( ord_less_eq_rat @ ( F2 @ I3 ) @ N ) ) )
% 5.31/5.61 => ( ( ord_less_eq_nat @ ( finite_card_real @ A4 ) @ K2 )
% 5.31/5.61 => ( ( ord_less_eq_rat @ one_one_rat @ N )
% 5.31/5.61 => ( ord_less_eq_rat @ ( groups4061424788464935467al_rat @ F2 @ A4 ) @ ( power_power_rat @ N @ K2 ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod_le_power
% 5.31/5.61 thf(fact_6499_prod__le__power,axiom,
% 5.31/5.61 ! [A4: set_nat,F2: nat > rat,N: rat,K2: nat] :
% 5.31/5.61 ( ! [I3: nat] :
% 5.31/5.61 ( ( member_nat @ I3 @ A4 )
% 5.31/5.61 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ I3 ) )
% 5.31/5.61 & ( ord_less_eq_rat @ ( F2 @ I3 ) @ N ) ) )
% 5.31/5.61 => ( ( ord_less_eq_nat @ ( finite_card_nat @ A4 ) @ K2 )
% 5.31/5.61 => ( ( ord_less_eq_rat @ one_one_rat @ N )
% 5.31/5.61 => ( ord_less_eq_rat @ ( groups73079841787564623at_rat @ F2 @ A4 ) @ ( power_power_rat @ N @ K2 ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod_le_power
% 5.31/5.61 thf(fact_6500_prod__Un,axiom,
% 5.31/5.61 ! [A4: set_int,B5: set_int,F2: int > complex] :
% 5.31/5.61 ( ( finite_finite_int @ A4 )
% 5.31/5.61 => ( ( finite_finite_int @ B5 )
% 5.31/5.61 => ( ! [X3: int] :
% 5.31/5.61 ( ( member_int @ X3 @ ( inf_inf_set_int @ A4 @ B5 ) )
% 5.31/5.61 => ( ( F2 @ X3 )
% 5.31/5.61 != zero_zero_complex ) )
% 5.31/5.61 => ( ( groups7440179247065528705omplex @ F2 @ ( sup_sup_set_int @ A4 @ B5 ) )
% 5.31/5.61 = ( divide1717551699836669952omplex @ ( times_times_complex @ ( groups7440179247065528705omplex @ F2 @ A4 ) @ ( groups7440179247065528705omplex @ F2 @ B5 ) ) @ ( groups7440179247065528705omplex @ F2 @ ( inf_inf_set_int @ A4 @ B5 ) ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod_Un
% 5.31/5.61 thf(fact_6501_prod__Un,axiom,
% 5.31/5.61 ! [A4: set_complex,B5: set_complex,F2: complex > complex] :
% 5.31/5.61 ( ( finite3207457112153483333omplex @ A4 )
% 5.31/5.61 => ( ( finite3207457112153483333omplex @ B5 )
% 5.31/5.61 => ( ! [X3: complex] :
% 5.31/5.61 ( ( member_complex @ X3 @ ( inf_inf_set_complex @ A4 @ B5 ) )
% 5.31/5.61 => ( ( F2 @ X3 )
% 5.31/5.61 != zero_zero_complex ) )
% 5.31/5.61 => ( ( groups3708469109370488835omplex @ F2 @ ( sup_sup_set_complex @ A4 @ B5 ) )
% 5.31/5.61 = ( divide1717551699836669952omplex @ ( times_times_complex @ ( groups3708469109370488835omplex @ F2 @ A4 ) @ ( groups3708469109370488835omplex @ F2 @ B5 ) ) @ ( groups3708469109370488835omplex @ F2 @ ( inf_inf_set_complex @ A4 @ B5 ) ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod_Un
% 5.31/5.61 thf(fact_6502_prod__Un,axiom,
% 5.31/5.61 ! [A4: set_nat,B5: set_nat,F2: nat > complex] :
% 5.31/5.61 ( ( finite_finite_nat @ A4 )
% 5.31/5.61 => ( ( finite_finite_nat @ B5 )
% 5.31/5.61 => ( ! [X3: nat] :
% 5.31/5.61 ( ( member_nat @ X3 @ ( inf_inf_set_nat @ A4 @ B5 ) )
% 5.31/5.61 => ( ( F2 @ X3 )
% 5.31/5.61 != zero_zero_complex ) )
% 5.31/5.61 => ( ( groups6464643781859351333omplex @ F2 @ ( sup_sup_set_nat @ A4 @ B5 ) )
% 5.31/5.61 = ( divide1717551699836669952omplex @ ( times_times_complex @ ( groups6464643781859351333omplex @ F2 @ A4 ) @ ( groups6464643781859351333omplex @ F2 @ B5 ) ) @ ( groups6464643781859351333omplex @ F2 @ ( inf_inf_set_nat @ A4 @ B5 ) ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod_Un
% 5.31/5.61 thf(fact_6503_prod__Un,axiom,
% 5.31/5.61 ! [A4: set_int,B5: set_int,F2: int > real] :
% 5.31/5.61 ( ( finite_finite_int @ A4 )
% 5.31/5.61 => ( ( finite_finite_int @ B5 )
% 5.31/5.61 => ( ! [X3: int] :
% 5.31/5.61 ( ( member_int @ X3 @ ( inf_inf_set_int @ A4 @ B5 ) )
% 5.31/5.61 => ( ( F2 @ X3 )
% 5.31/5.61 != zero_zero_real ) )
% 5.31/5.61 => ( ( groups2316167850115554303t_real @ F2 @ ( sup_sup_set_int @ A4 @ B5 ) )
% 5.31/5.61 = ( divide_divide_real @ ( times_times_real @ ( groups2316167850115554303t_real @ F2 @ A4 ) @ ( groups2316167850115554303t_real @ F2 @ B5 ) ) @ ( groups2316167850115554303t_real @ F2 @ ( inf_inf_set_int @ A4 @ B5 ) ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod_Un
% 5.31/5.61 thf(fact_6504_prod__Un,axiom,
% 5.31/5.61 ! [A4: set_complex,B5: set_complex,F2: complex > real] :
% 5.31/5.61 ( ( finite3207457112153483333omplex @ A4 )
% 5.31/5.61 => ( ( finite3207457112153483333omplex @ B5 )
% 5.31/5.61 => ( ! [X3: complex] :
% 5.31/5.61 ( ( member_complex @ X3 @ ( inf_inf_set_complex @ A4 @ B5 ) )
% 5.31/5.61 => ( ( F2 @ X3 )
% 5.31/5.61 != zero_zero_real ) )
% 5.31/5.61 => ( ( groups766887009212190081x_real @ F2 @ ( sup_sup_set_complex @ A4 @ B5 ) )
% 5.31/5.61 = ( divide_divide_real @ ( times_times_real @ ( groups766887009212190081x_real @ F2 @ A4 ) @ ( groups766887009212190081x_real @ F2 @ B5 ) ) @ ( groups766887009212190081x_real @ F2 @ ( inf_inf_set_complex @ A4 @ B5 ) ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod_Un
% 5.31/5.61 thf(fact_6505_prod__Un,axiom,
% 5.31/5.61 ! [A4: set_nat,B5: set_nat,F2: nat > real] :
% 5.31/5.61 ( ( finite_finite_nat @ A4 )
% 5.31/5.61 => ( ( finite_finite_nat @ B5 )
% 5.31/5.61 => ( ! [X3: nat] :
% 5.31/5.61 ( ( member_nat @ X3 @ ( inf_inf_set_nat @ A4 @ B5 ) )
% 5.31/5.61 => ( ( F2 @ X3 )
% 5.31/5.61 != zero_zero_real ) )
% 5.31/5.61 => ( ( groups129246275422532515t_real @ F2 @ ( sup_sup_set_nat @ A4 @ B5 ) )
% 5.31/5.61 = ( divide_divide_real @ ( times_times_real @ ( groups129246275422532515t_real @ F2 @ A4 ) @ ( groups129246275422532515t_real @ F2 @ B5 ) ) @ ( groups129246275422532515t_real @ F2 @ ( inf_inf_set_nat @ A4 @ B5 ) ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod_Un
% 5.31/5.61 thf(fact_6506_prod__Un,axiom,
% 5.31/5.61 ! [A4: set_int,B5: set_int,F2: int > rat] :
% 5.31/5.61 ( ( finite_finite_int @ A4 )
% 5.31/5.61 => ( ( finite_finite_int @ B5 )
% 5.31/5.61 => ( ! [X3: int] :
% 5.31/5.61 ( ( member_int @ X3 @ ( inf_inf_set_int @ A4 @ B5 ) )
% 5.31/5.61 => ( ( F2 @ X3 )
% 5.31/5.61 != zero_zero_rat ) )
% 5.31/5.61 => ( ( groups1072433553688619179nt_rat @ F2 @ ( sup_sup_set_int @ A4 @ B5 ) )
% 5.31/5.61 = ( divide_divide_rat @ ( times_times_rat @ ( groups1072433553688619179nt_rat @ F2 @ A4 ) @ ( groups1072433553688619179nt_rat @ F2 @ B5 ) ) @ ( groups1072433553688619179nt_rat @ F2 @ ( inf_inf_set_int @ A4 @ B5 ) ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod_Un
% 5.31/5.61 thf(fact_6507_prod__Un,axiom,
% 5.31/5.61 ! [A4: set_complex,B5: set_complex,F2: complex > rat] :
% 5.31/5.61 ( ( finite3207457112153483333omplex @ A4 )
% 5.31/5.61 => ( ( finite3207457112153483333omplex @ B5 )
% 5.31/5.61 => ( ! [X3: complex] :
% 5.31/5.61 ( ( member_complex @ X3 @ ( inf_inf_set_complex @ A4 @ B5 ) )
% 5.31/5.61 => ( ( F2 @ X3 )
% 5.31/5.61 != zero_zero_rat ) )
% 5.31/5.61 => ( ( groups225925009352817453ex_rat @ F2 @ ( sup_sup_set_complex @ A4 @ B5 ) )
% 5.31/5.61 = ( divide_divide_rat @ ( times_times_rat @ ( groups225925009352817453ex_rat @ F2 @ A4 ) @ ( groups225925009352817453ex_rat @ F2 @ B5 ) ) @ ( groups225925009352817453ex_rat @ F2 @ ( inf_inf_set_complex @ A4 @ B5 ) ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod_Un
% 5.31/5.61 thf(fact_6508_prod__Un,axiom,
% 5.31/5.61 ! [A4: set_nat,B5: set_nat,F2: nat > rat] :
% 5.31/5.61 ( ( finite_finite_nat @ A4 )
% 5.31/5.61 => ( ( finite_finite_nat @ B5 )
% 5.31/5.61 => ( ! [X3: nat] :
% 5.31/5.61 ( ( member_nat @ X3 @ ( inf_inf_set_nat @ A4 @ B5 ) )
% 5.31/5.61 => ( ( F2 @ X3 )
% 5.31/5.61 != zero_zero_rat ) )
% 5.31/5.61 => ( ( groups73079841787564623at_rat @ F2 @ ( sup_sup_set_nat @ A4 @ B5 ) )
% 5.31/5.61 = ( divide_divide_rat @ ( times_times_rat @ ( groups73079841787564623at_rat @ F2 @ A4 ) @ ( groups73079841787564623at_rat @ F2 @ B5 ) ) @ ( groups73079841787564623at_rat @ F2 @ ( inf_inf_set_nat @ A4 @ B5 ) ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod_Un
% 5.31/5.61 thf(fact_6509_prod__Un,axiom,
% 5.31/5.61 ! [A4: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat,F2: product_prod_nat_nat > complex] :
% 5.31/5.61 ( ( finite6177210948735845034at_nat @ A4 )
% 5.31/5.61 => ( ( finite6177210948735845034at_nat @ B5 )
% 5.31/5.61 => ( ! [X3: product_prod_nat_nat] :
% 5.31/5.61 ( ( member8440522571783428010at_nat @ X3 @ ( inf_in2572325071724192079at_nat @ A4 @ B5 ) )
% 5.31/5.61 => ( ( F2 @ X3 )
% 5.31/5.61 != zero_zero_complex ) )
% 5.31/5.61 => ( ( groups8110221916422527690omplex @ F2 @ ( sup_su6327502436637775413at_nat @ A4 @ B5 ) )
% 5.31/5.61 = ( divide1717551699836669952omplex @ ( times_times_complex @ ( groups8110221916422527690omplex @ F2 @ A4 ) @ ( groups8110221916422527690omplex @ F2 @ B5 ) ) @ ( groups8110221916422527690omplex @ F2 @ ( inf_in2572325071724192079at_nat @ A4 @ B5 ) ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod_Un
% 5.31/5.61 thf(fact_6510_prod__diff1,axiom,
% 5.31/5.61 ! [A4: set_complex,F2: complex > complex,A: complex] :
% 5.31/5.61 ( ( finite3207457112153483333omplex @ A4 )
% 5.31/5.61 => ( ( ( F2 @ A )
% 5.31/5.61 != zero_zero_complex )
% 5.31/5.61 => ( ( ( member_complex @ A @ A4 )
% 5.31/5.61 => ( ( groups3708469109370488835omplex @ F2 @ ( minus_811609699411566653omplex @ A4 @ ( insert_complex @ A @ bot_bot_set_complex ) ) )
% 5.31/5.61 = ( divide1717551699836669952omplex @ ( groups3708469109370488835omplex @ F2 @ A4 ) @ ( F2 @ A ) ) ) )
% 5.31/5.61 & ( ~ ( member_complex @ A @ A4 )
% 5.31/5.61 => ( ( groups3708469109370488835omplex @ F2 @ ( minus_811609699411566653omplex @ A4 @ ( insert_complex @ A @ bot_bot_set_complex ) ) )
% 5.31/5.61 = ( groups3708469109370488835omplex @ F2 @ A4 ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod_diff1
% 5.31/5.61 thf(fact_6511_prod__diff1,axiom,
% 5.31/5.61 ! [A4: set_int,F2: int > complex,A: int] :
% 5.31/5.61 ( ( finite_finite_int @ A4 )
% 5.31/5.61 => ( ( ( F2 @ A )
% 5.31/5.61 != zero_zero_complex )
% 5.31/5.61 => ( ( ( member_int @ A @ A4 )
% 5.31/5.61 => ( ( groups7440179247065528705omplex @ F2 @ ( minus_minus_set_int @ A4 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 5.31/5.61 = ( divide1717551699836669952omplex @ ( groups7440179247065528705omplex @ F2 @ A4 ) @ ( F2 @ A ) ) ) )
% 5.31/5.61 & ( ~ ( member_int @ A @ A4 )
% 5.31/5.61 => ( ( groups7440179247065528705omplex @ F2 @ ( minus_minus_set_int @ A4 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 5.31/5.61 = ( groups7440179247065528705omplex @ F2 @ A4 ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod_diff1
% 5.31/5.61 thf(fact_6512_prod__diff1,axiom,
% 5.31/5.61 ! [A4: set_real,F2: real > complex,A: real] :
% 5.31/5.61 ( ( finite_finite_real @ A4 )
% 5.31/5.61 => ( ( ( F2 @ A )
% 5.31/5.61 != zero_zero_complex )
% 5.31/5.61 => ( ( ( member_real @ A @ A4 )
% 5.31/5.61 => ( ( groups713298508707869441omplex @ F2 @ ( minus_minus_set_real @ A4 @ ( insert_real @ A @ bot_bot_set_real ) ) )
% 5.31/5.61 = ( divide1717551699836669952omplex @ ( groups713298508707869441omplex @ F2 @ A4 ) @ ( F2 @ A ) ) ) )
% 5.31/5.61 & ( ~ ( member_real @ A @ A4 )
% 5.31/5.61 => ( ( groups713298508707869441omplex @ F2 @ ( minus_minus_set_real @ A4 @ ( insert_real @ A @ bot_bot_set_real ) ) )
% 5.31/5.61 = ( groups713298508707869441omplex @ F2 @ A4 ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod_diff1
% 5.31/5.61 thf(fact_6513_prod__diff1,axiom,
% 5.31/5.61 ! [A4: set_nat,F2: nat > complex,A: nat] :
% 5.31/5.61 ( ( finite_finite_nat @ A4 )
% 5.31/5.61 => ( ( ( F2 @ A )
% 5.31/5.61 != zero_zero_complex )
% 5.31/5.61 => ( ( ( member_nat @ A @ A4 )
% 5.31/5.61 => ( ( groups6464643781859351333omplex @ F2 @ ( minus_minus_set_nat @ A4 @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 5.31/5.61 = ( divide1717551699836669952omplex @ ( groups6464643781859351333omplex @ F2 @ A4 ) @ ( F2 @ A ) ) ) )
% 5.31/5.61 & ( ~ ( member_nat @ A @ A4 )
% 5.31/5.61 => ( ( groups6464643781859351333omplex @ F2 @ ( minus_minus_set_nat @ A4 @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 5.31/5.61 = ( groups6464643781859351333omplex @ F2 @ A4 ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod_diff1
% 5.31/5.61 thf(fact_6514_prod__diff1,axiom,
% 5.31/5.61 ! [A4: set_complex,F2: complex > real,A: complex] :
% 5.31/5.61 ( ( finite3207457112153483333omplex @ A4 )
% 5.31/5.61 => ( ( ( F2 @ A )
% 5.31/5.61 != zero_zero_real )
% 5.31/5.61 => ( ( ( member_complex @ A @ A4 )
% 5.31/5.61 => ( ( groups766887009212190081x_real @ F2 @ ( minus_811609699411566653omplex @ A4 @ ( insert_complex @ A @ bot_bot_set_complex ) ) )
% 5.31/5.61 = ( divide_divide_real @ ( groups766887009212190081x_real @ F2 @ A4 ) @ ( F2 @ A ) ) ) )
% 5.31/5.61 & ( ~ ( member_complex @ A @ A4 )
% 5.31/5.61 => ( ( groups766887009212190081x_real @ F2 @ ( minus_811609699411566653omplex @ A4 @ ( insert_complex @ A @ bot_bot_set_complex ) ) )
% 5.31/5.61 = ( groups766887009212190081x_real @ F2 @ A4 ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod_diff1
% 5.31/5.61 thf(fact_6515_prod__diff1,axiom,
% 5.31/5.61 ! [A4: set_int,F2: int > real,A: int] :
% 5.31/5.61 ( ( finite_finite_int @ A4 )
% 5.31/5.61 => ( ( ( F2 @ A )
% 5.31/5.61 != zero_zero_real )
% 5.31/5.61 => ( ( ( member_int @ A @ A4 )
% 5.31/5.61 => ( ( groups2316167850115554303t_real @ F2 @ ( minus_minus_set_int @ A4 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 5.31/5.61 = ( divide_divide_real @ ( groups2316167850115554303t_real @ F2 @ A4 ) @ ( F2 @ A ) ) ) )
% 5.31/5.61 & ( ~ ( member_int @ A @ A4 )
% 5.31/5.61 => ( ( groups2316167850115554303t_real @ F2 @ ( minus_minus_set_int @ A4 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 5.31/5.61 = ( groups2316167850115554303t_real @ F2 @ A4 ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod_diff1
% 5.31/5.61 thf(fact_6516_prod__diff1,axiom,
% 5.31/5.61 ! [A4: set_real,F2: real > real,A: real] :
% 5.31/5.61 ( ( finite_finite_real @ A4 )
% 5.31/5.61 => ( ( ( F2 @ A )
% 5.31/5.61 != zero_zero_real )
% 5.31/5.61 => ( ( ( member_real @ A @ A4 )
% 5.31/5.61 => ( ( groups1681761925125756287l_real @ F2 @ ( minus_minus_set_real @ A4 @ ( insert_real @ A @ bot_bot_set_real ) ) )
% 5.31/5.61 = ( divide_divide_real @ ( groups1681761925125756287l_real @ F2 @ A4 ) @ ( F2 @ A ) ) ) )
% 5.31/5.61 & ( ~ ( member_real @ A @ A4 )
% 5.31/5.61 => ( ( groups1681761925125756287l_real @ F2 @ ( minus_minus_set_real @ A4 @ ( insert_real @ A @ bot_bot_set_real ) ) )
% 5.31/5.61 = ( groups1681761925125756287l_real @ F2 @ A4 ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod_diff1
% 5.31/5.61 thf(fact_6517_prod__diff1,axiom,
% 5.31/5.61 ! [A4: set_nat,F2: nat > real,A: nat] :
% 5.31/5.61 ( ( finite_finite_nat @ A4 )
% 5.31/5.61 => ( ( ( F2 @ A )
% 5.31/5.61 != zero_zero_real )
% 5.31/5.61 => ( ( ( member_nat @ A @ A4 )
% 5.31/5.61 => ( ( groups129246275422532515t_real @ F2 @ ( minus_minus_set_nat @ A4 @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 5.31/5.61 = ( divide_divide_real @ ( groups129246275422532515t_real @ F2 @ A4 ) @ ( F2 @ A ) ) ) )
% 5.31/5.61 & ( ~ ( member_nat @ A @ A4 )
% 5.31/5.61 => ( ( groups129246275422532515t_real @ F2 @ ( minus_minus_set_nat @ A4 @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 5.31/5.61 = ( groups129246275422532515t_real @ F2 @ A4 ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod_diff1
% 5.31/5.61 thf(fact_6518_prod__diff1,axiom,
% 5.31/5.61 ! [A4: set_complex,F2: complex > rat,A: complex] :
% 5.31/5.61 ( ( finite3207457112153483333omplex @ A4 )
% 5.31/5.61 => ( ( ( F2 @ A )
% 5.31/5.61 != zero_zero_rat )
% 5.31/5.61 => ( ( ( member_complex @ A @ A4 )
% 5.31/5.61 => ( ( groups225925009352817453ex_rat @ F2 @ ( minus_811609699411566653omplex @ A4 @ ( insert_complex @ A @ bot_bot_set_complex ) ) )
% 5.31/5.61 = ( divide_divide_rat @ ( groups225925009352817453ex_rat @ F2 @ A4 ) @ ( F2 @ A ) ) ) )
% 5.31/5.61 & ( ~ ( member_complex @ A @ A4 )
% 5.31/5.61 => ( ( groups225925009352817453ex_rat @ F2 @ ( minus_811609699411566653omplex @ A4 @ ( insert_complex @ A @ bot_bot_set_complex ) ) )
% 5.31/5.61 = ( groups225925009352817453ex_rat @ F2 @ A4 ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod_diff1
% 5.31/5.61 thf(fact_6519_prod__diff1,axiom,
% 5.31/5.61 ! [A4: set_int,F2: int > rat,A: int] :
% 5.31/5.61 ( ( finite_finite_int @ A4 )
% 5.31/5.61 => ( ( ( F2 @ A )
% 5.31/5.61 != zero_zero_rat )
% 5.31/5.61 => ( ( ( member_int @ A @ A4 )
% 5.31/5.61 => ( ( groups1072433553688619179nt_rat @ F2 @ ( minus_minus_set_int @ A4 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 5.31/5.61 = ( divide_divide_rat @ ( groups1072433553688619179nt_rat @ F2 @ A4 ) @ ( F2 @ A ) ) ) )
% 5.31/5.61 & ( ~ ( member_int @ A @ A4 )
% 5.31/5.61 => ( ( groups1072433553688619179nt_rat @ F2 @ ( minus_minus_set_int @ A4 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 5.31/5.61 = ( groups1072433553688619179nt_rat @ F2 @ A4 ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod_diff1
% 5.31/5.61 thf(fact_6520_binomial__less__binomial__Suc,axiom,
% 5.31/5.61 ! [K2: nat,N: nat] :
% 5.31/5.61 ( ( ord_less_nat @ K2 @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.31/5.61 => ( ord_less_nat @ ( binomial @ N @ K2 ) @ ( binomial @ N @ ( suc @ K2 ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % binomial_less_binomial_Suc
% 5.31/5.61 thf(fact_6521_binomial__strict__antimono,axiom,
% 5.31/5.61 ! [K2: nat,K6: nat,N: nat] :
% 5.31/5.61 ( ( ord_less_nat @ K2 @ K6 )
% 5.31/5.61 => ( ( ord_less_eq_nat @ N @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K2 ) )
% 5.31/5.61 => ( ( ord_less_eq_nat @ K6 @ N )
% 5.31/5.61 => ( ord_less_nat @ ( binomial @ N @ K6 ) @ ( binomial @ N @ K2 ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % binomial_strict_antimono
% 5.31/5.61 thf(fact_6522_binomial__strict__mono,axiom,
% 5.31/5.61 ! [K2: nat,K6: nat,N: nat] :
% 5.31/5.61 ( ( ord_less_nat @ K2 @ K6 )
% 5.31/5.61 => ( ( ord_less_eq_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K6 ) @ N )
% 5.31/5.61 => ( ord_less_nat @ ( binomial @ N @ K2 ) @ ( binomial @ N @ K6 ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % binomial_strict_mono
% 5.31/5.61 thf(fact_6523_central__binomial__odd,axiom,
% 5.31/5.61 ! [N: nat] :
% 5.31/5.61 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.31/5.61 => ( ( binomial @ N @ ( suc @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.31/5.61 = ( binomial @ N @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % central_binomial_odd
% 5.31/5.61 thf(fact_6524_prod__gen__delta,axiom,
% 5.31/5.61 ! [S3: set_real,A: real,B: real > complex,C2: complex] :
% 5.31/5.61 ( ( finite_finite_real @ S3 )
% 5.31/5.61 => ( ( ( member_real @ A @ S3 )
% 5.31/5.61 => ( ( groups713298508707869441omplex
% 5.31/5.61 @ ^ [K3: real] : ( if_complex @ ( K3 = A ) @ ( B @ K3 ) @ C2 )
% 5.31/5.61 @ S3 )
% 5.31/5.61 = ( times_times_complex @ ( B @ A ) @ ( power_power_complex @ C2 @ ( minus_minus_nat @ ( finite_card_real @ S3 ) @ one_one_nat ) ) ) ) )
% 5.31/5.61 & ( ~ ( member_real @ A @ S3 )
% 5.31/5.61 => ( ( groups713298508707869441omplex
% 5.31/5.61 @ ^ [K3: real] : ( if_complex @ ( K3 = A ) @ ( B @ K3 ) @ C2 )
% 5.31/5.61 @ S3 )
% 5.31/5.61 = ( power_power_complex @ C2 @ ( finite_card_real @ S3 ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod_gen_delta
% 5.31/5.61 thf(fact_6525_prod__gen__delta,axiom,
% 5.31/5.61 ! [S3: set_nat,A: nat,B: nat > complex,C2: complex] :
% 5.31/5.61 ( ( finite_finite_nat @ S3 )
% 5.31/5.61 => ( ( ( member_nat @ A @ S3 )
% 5.31/5.61 => ( ( groups6464643781859351333omplex
% 5.31/5.61 @ ^ [K3: nat] : ( if_complex @ ( K3 = A ) @ ( B @ K3 ) @ C2 )
% 5.31/5.61 @ S3 )
% 5.31/5.61 = ( times_times_complex @ ( B @ A ) @ ( power_power_complex @ C2 @ ( minus_minus_nat @ ( finite_card_nat @ S3 ) @ one_one_nat ) ) ) ) )
% 5.31/5.61 & ( ~ ( member_nat @ A @ S3 )
% 5.31/5.61 => ( ( groups6464643781859351333omplex
% 5.31/5.61 @ ^ [K3: nat] : ( if_complex @ ( K3 = A ) @ ( B @ K3 ) @ C2 )
% 5.31/5.61 @ S3 )
% 5.31/5.61 = ( power_power_complex @ C2 @ ( finite_card_nat @ S3 ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod_gen_delta
% 5.31/5.61 thf(fact_6526_prod__gen__delta,axiom,
% 5.31/5.61 ! [S3: set_int,A: int,B: int > complex,C2: complex] :
% 5.31/5.61 ( ( finite_finite_int @ S3 )
% 5.31/5.61 => ( ( ( member_int @ A @ S3 )
% 5.31/5.61 => ( ( groups7440179247065528705omplex
% 5.31/5.61 @ ^ [K3: int] : ( if_complex @ ( K3 = A ) @ ( B @ K3 ) @ C2 )
% 5.31/5.61 @ S3 )
% 5.31/5.61 = ( times_times_complex @ ( B @ A ) @ ( power_power_complex @ C2 @ ( minus_minus_nat @ ( finite_card_int @ S3 ) @ one_one_nat ) ) ) ) )
% 5.31/5.61 & ( ~ ( member_int @ A @ S3 )
% 5.31/5.61 => ( ( groups7440179247065528705omplex
% 5.31/5.61 @ ^ [K3: int] : ( if_complex @ ( K3 = A ) @ ( B @ K3 ) @ C2 )
% 5.31/5.61 @ S3 )
% 5.31/5.61 = ( power_power_complex @ C2 @ ( finite_card_int @ S3 ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod_gen_delta
% 5.31/5.61 thf(fact_6527_prod__gen__delta,axiom,
% 5.31/5.61 ! [S3: set_complex,A: complex,B: complex > complex,C2: complex] :
% 5.31/5.61 ( ( finite3207457112153483333omplex @ S3 )
% 5.31/5.61 => ( ( ( member_complex @ A @ S3 )
% 5.31/5.61 => ( ( groups3708469109370488835omplex
% 5.31/5.61 @ ^ [K3: complex] : ( if_complex @ ( K3 = A ) @ ( B @ K3 ) @ C2 )
% 5.31/5.61 @ S3 )
% 5.31/5.61 = ( times_times_complex @ ( B @ A ) @ ( power_power_complex @ C2 @ ( minus_minus_nat @ ( finite_card_complex @ S3 ) @ one_one_nat ) ) ) ) )
% 5.31/5.61 & ( ~ ( member_complex @ A @ S3 )
% 5.31/5.61 => ( ( groups3708469109370488835omplex
% 5.31/5.61 @ ^ [K3: complex] : ( if_complex @ ( K3 = A ) @ ( B @ K3 ) @ C2 )
% 5.31/5.61 @ S3 )
% 5.31/5.61 = ( power_power_complex @ C2 @ ( finite_card_complex @ S3 ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod_gen_delta
% 5.31/5.61 thf(fact_6528_prod__gen__delta,axiom,
% 5.31/5.61 ! [S3: set_real,A: real,B: real > real,C2: real] :
% 5.31/5.61 ( ( finite_finite_real @ S3 )
% 5.31/5.61 => ( ( ( member_real @ A @ S3 )
% 5.31/5.61 => ( ( groups1681761925125756287l_real
% 5.31/5.61 @ ^ [K3: real] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ C2 )
% 5.31/5.61 @ S3 )
% 5.31/5.61 = ( times_times_real @ ( B @ A ) @ ( power_power_real @ C2 @ ( minus_minus_nat @ ( finite_card_real @ S3 ) @ one_one_nat ) ) ) ) )
% 5.31/5.61 & ( ~ ( member_real @ A @ S3 )
% 5.31/5.61 => ( ( groups1681761925125756287l_real
% 5.31/5.61 @ ^ [K3: real] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ C2 )
% 5.31/5.61 @ S3 )
% 5.31/5.61 = ( power_power_real @ C2 @ ( finite_card_real @ S3 ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod_gen_delta
% 5.31/5.61 thf(fact_6529_prod__gen__delta,axiom,
% 5.31/5.61 ! [S3: set_nat,A: nat,B: nat > real,C2: real] :
% 5.31/5.61 ( ( finite_finite_nat @ S3 )
% 5.31/5.61 => ( ( ( member_nat @ A @ S3 )
% 5.31/5.61 => ( ( groups129246275422532515t_real
% 5.31/5.61 @ ^ [K3: nat] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ C2 )
% 5.31/5.61 @ S3 )
% 5.31/5.61 = ( times_times_real @ ( B @ A ) @ ( power_power_real @ C2 @ ( minus_minus_nat @ ( finite_card_nat @ S3 ) @ one_one_nat ) ) ) ) )
% 5.31/5.61 & ( ~ ( member_nat @ A @ S3 )
% 5.31/5.61 => ( ( groups129246275422532515t_real
% 5.31/5.61 @ ^ [K3: nat] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ C2 )
% 5.31/5.61 @ S3 )
% 5.31/5.61 = ( power_power_real @ C2 @ ( finite_card_nat @ S3 ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod_gen_delta
% 5.31/5.61 thf(fact_6530_prod__gen__delta,axiom,
% 5.31/5.61 ! [S3: set_int,A: int,B: int > real,C2: real] :
% 5.31/5.61 ( ( finite_finite_int @ S3 )
% 5.31/5.61 => ( ( ( member_int @ A @ S3 )
% 5.31/5.61 => ( ( groups2316167850115554303t_real
% 5.31/5.61 @ ^ [K3: int] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ C2 )
% 5.31/5.61 @ S3 )
% 5.31/5.61 = ( times_times_real @ ( B @ A ) @ ( power_power_real @ C2 @ ( minus_minus_nat @ ( finite_card_int @ S3 ) @ one_one_nat ) ) ) ) )
% 5.31/5.61 & ( ~ ( member_int @ A @ S3 )
% 5.31/5.61 => ( ( groups2316167850115554303t_real
% 5.31/5.61 @ ^ [K3: int] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ C2 )
% 5.31/5.61 @ S3 )
% 5.31/5.61 = ( power_power_real @ C2 @ ( finite_card_int @ S3 ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod_gen_delta
% 5.31/5.61 thf(fact_6531_prod__gen__delta,axiom,
% 5.31/5.61 ! [S3: set_complex,A: complex,B: complex > real,C2: real] :
% 5.31/5.61 ( ( finite3207457112153483333omplex @ S3 )
% 5.31/5.61 => ( ( ( member_complex @ A @ S3 )
% 5.31/5.61 => ( ( groups766887009212190081x_real
% 5.31/5.61 @ ^ [K3: complex] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ C2 )
% 5.31/5.61 @ S3 )
% 5.31/5.61 = ( times_times_real @ ( B @ A ) @ ( power_power_real @ C2 @ ( minus_minus_nat @ ( finite_card_complex @ S3 ) @ one_one_nat ) ) ) ) )
% 5.31/5.61 & ( ~ ( member_complex @ A @ S3 )
% 5.31/5.61 => ( ( groups766887009212190081x_real
% 5.31/5.61 @ ^ [K3: complex] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ C2 )
% 5.31/5.61 @ S3 )
% 5.31/5.61 = ( power_power_real @ C2 @ ( finite_card_complex @ S3 ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod_gen_delta
% 5.31/5.61 thf(fact_6532_prod__gen__delta,axiom,
% 5.31/5.61 ! [S3: set_real,A: real,B: real > rat,C2: rat] :
% 5.31/5.61 ( ( finite_finite_real @ S3 )
% 5.31/5.61 => ( ( ( member_real @ A @ S3 )
% 5.31/5.61 => ( ( groups4061424788464935467al_rat
% 5.31/5.61 @ ^ [K3: real] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ C2 )
% 5.31/5.61 @ S3 )
% 5.31/5.61 = ( times_times_rat @ ( B @ A ) @ ( power_power_rat @ C2 @ ( minus_minus_nat @ ( finite_card_real @ S3 ) @ one_one_nat ) ) ) ) )
% 5.31/5.61 & ( ~ ( member_real @ A @ S3 )
% 5.31/5.61 => ( ( groups4061424788464935467al_rat
% 5.31/5.61 @ ^ [K3: real] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ C2 )
% 5.31/5.61 @ S3 )
% 5.31/5.61 = ( power_power_rat @ C2 @ ( finite_card_real @ S3 ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod_gen_delta
% 5.31/5.61 thf(fact_6533_prod__gen__delta,axiom,
% 5.31/5.61 ! [S3: set_nat,A: nat,B: nat > rat,C2: rat] :
% 5.31/5.61 ( ( finite_finite_nat @ S3 )
% 5.31/5.61 => ( ( ( member_nat @ A @ S3 )
% 5.31/5.61 => ( ( groups73079841787564623at_rat
% 5.31/5.61 @ ^ [K3: nat] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ C2 )
% 5.31/5.61 @ S3 )
% 5.31/5.61 = ( times_times_rat @ ( B @ A ) @ ( power_power_rat @ C2 @ ( minus_minus_nat @ ( finite_card_nat @ S3 ) @ one_one_nat ) ) ) ) )
% 5.31/5.61 & ( ~ ( member_nat @ A @ S3 )
% 5.31/5.61 => ( ( groups73079841787564623at_rat
% 5.31/5.61 @ ^ [K3: nat] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ C2 )
% 5.31/5.61 @ S3 )
% 5.31/5.61 = ( power_power_rat @ C2 @ ( finite_card_nat @ S3 ) ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod_gen_delta
% 5.31/5.61 thf(fact_6534_pochhammer__Suc__prod,axiom,
% 5.31/5.61 ! [A: rat,N: nat] :
% 5.31/5.61 ( ( comm_s4028243227959126397er_rat @ A @ ( suc @ N ) )
% 5.31/5.61 = ( groups73079841787564623at_rat
% 5.31/5.61 @ ^ [I: nat] : ( plus_plus_rat @ A @ ( semiri681578069525770553at_rat @ I ) )
% 5.31/5.61 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % pochhammer_Suc_prod
% 5.31/5.61 thf(fact_6535_pochhammer__Suc__prod,axiom,
% 5.31/5.61 ! [A: real,N: nat] :
% 5.31/5.61 ( ( comm_s7457072308508201937r_real @ A @ ( suc @ N ) )
% 5.31/5.61 = ( groups129246275422532515t_real
% 5.31/5.61 @ ^ [I: nat] : ( plus_plus_real @ A @ ( semiri5074537144036343181t_real @ I ) )
% 5.31/5.61 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % pochhammer_Suc_prod
% 5.31/5.61 thf(fact_6536_pochhammer__Suc__prod,axiom,
% 5.31/5.61 ! [A: int,N: nat] :
% 5.31/5.61 ( ( comm_s4660882817536571857er_int @ A @ ( suc @ N ) )
% 5.31/5.61 = ( groups705719431365010083at_int
% 5.31/5.61 @ ^ [I: nat] : ( plus_plus_int @ A @ ( semiri1314217659103216013at_int @ I ) )
% 5.31/5.61 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % pochhammer_Suc_prod
% 5.31/5.61 thf(fact_6537_pochhammer__Suc__prod,axiom,
% 5.31/5.61 ! [A: nat,N: nat] :
% 5.31/5.61 ( ( comm_s4663373288045622133er_nat @ A @ ( suc @ N ) )
% 5.31/5.61 = ( groups708209901874060359at_nat
% 5.31/5.61 @ ^ [I: nat] : ( plus_plus_nat @ A @ ( semiri1316708129612266289at_nat @ I ) )
% 5.31/5.61 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % pochhammer_Suc_prod
% 5.31/5.61 thf(fact_6538_sum__gp__strict,axiom,
% 5.31/5.61 ! [X: complex,N: nat] :
% 5.31/5.61 ( ( ( X = one_one_complex )
% 5.31/5.61 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_ord_lessThan_nat @ N ) )
% 5.31/5.61 = ( semiri8010041392384452111omplex @ N ) ) )
% 5.31/5.61 & ( ( X != one_one_complex )
% 5.31/5.61 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_ord_lessThan_nat @ N ) )
% 5.31/5.61 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ X @ N ) ) @ ( minus_minus_complex @ one_one_complex @ X ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % sum_gp_strict
% 5.31/5.61 thf(fact_6539_sum__gp__strict,axiom,
% 5.31/5.61 ! [X: rat,N: nat] :
% 5.31/5.61 ( ( ( X = one_one_rat )
% 5.31/5.61 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_ord_lessThan_nat @ N ) )
% 5.31/5.61 = ( semiri681578069525770553at_rat @ N ) ) )
% 5.31/5.61 & ( ( X != one_one_rat )
% 5.31/5.61 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_ord_lessThan_nat @ N ) )
% 5.31/5.61 = ( divide_divide_rat @ ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X @ N ) ) @ ( minus_minus_rat @ one_one_rat @ X ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % sum_gp_strict
% 5.31/5.61 thf(fact_6540_sum__gp__strict,axiom,
% 5.31/5.61 ! [X: real,N: nat] :
% 5.31/5.61 ( ( ( X = one_one_real )
% 5.31/5.61 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_ord_lessThan_nat @ N ) )
% 5.31/5.61 = ( semiri5074537144036343181t_real @ N ) ) )
% 5.31/5.61 & ( ( X != one_one_real )
% 5.31/5.61 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_ord_lessThan_nat @ N ) )
% 5.31/5.61 = ( divide_divide_real @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X @ N ) ) @ ( minus_minus_real @ one_one_real @ X ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % sum_gp_strict
% 5.31/5.61 thf(fact_6541_lemma__termdiff1,axiom,
% 5.31/5.61 ! [Z3: complex,H: complex,M2: nat] :
% 5.31/5.61 ( ( groups2073611262835488442omplex
% 5.31/5.61 @ ^ [P5: nat] : ( minus_minus_complex @ ( times_times_complex @ ( power_power_complex @ ( plus_plus_complex @ Z3 @ H ) @ ( minus_minus_nat @ M2 @ P5 ) ) @ ( power_power_complex @ Z3 @ P5 ) ) @ ( power_power_complex @ Z3 @ M2 ) )
% 5.31/5.61 @ ( set_ord_lessThan_nat @ M2 ) )
% 5.31/5.61 = ( groups2073611262835488442omplex
% 5.31/5.61 @ ^ [P5: nat] : ( times_times_complex @ ( power_power_complex @ Z3 @ P5 ) @ ( minus_minus_complex @ ( power_power_complex @ ( plus_plus_complex @ Z3 @ H ) @ ( minus_minus_nat @ M2 @ P5 ) ) @ ( power_power_complex @ Z3 @ ( minus_minus_nat @ M2 @ P5 ) ) ) )
% 5.31/5.61 @ ( set_ord_lessThan_nat @ M2 ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % lemma_termdiff1
% 5.31/5.61 thf(fact_6542_lemma__termdiff1,axiom,
% 5.31/5.61 ! [Z3: rat,H: rat,M2: nat] :
% 5.31/5.61 ( ( groups2906978787729119204at_rat
% 5.31/5.61 @ ^ [P5: nat] : ( minus_minus_rat @ ( times_times_rat @ ( power_power_rat @ ( plus_plus_rat @ Z3 @ H ) @ ( minus_minus_nat @ M2 @ P5 ) ) @ ( power_power_rat @ Z3 @ P5 ) ) @ ( power_power_rat @ Z3 @ M2 ) )
% 5.31/5.61 @ ( set_ord_lessThan_nat @ M2 ) )
% 5.31/5.61 = ( groups2906978787729119204at_rat
% 5.31/5.61 @ ^ [P5: nat] : ( times_times_rat @ ( power_power_rat @ Z3 @ P5 ) @ ( minus_minus_rat @ ( power_power_rat @ ( plus_plus_rat @ Z3 @ H ) @ ( minus_minus_nat @ M2 @ P5 ) ) @ ( power_power_rat @ Z3 @ ( minus_minus_nat @ M2 @ P5 ) ) ) )
% 5.31/5.61 @ ( set_ord_lessThan_nat @ M2 ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % lemma_termdiff1
% 5.31/5.61 thf(fact_6543_lemma__termdiff1,axiom,
% 5.31/5.61 ! [Z3: int,H: int,M2: nat] :
% 5.31/5.61 ( ( groups3539618377306564664at_int
% 5.31/5.61 @ ^ [P5: nat] : ( minus_minus_int @ ( times_times_int @ ( power_power_int @ ( plus_plus_int @ Z3 @ H ) @ ( minus_minus_nat @ M2 @ P5 ) ) @ ( power_power_int @ Z3 @ P5 ) ) @ ( power_power_int @ Z3 @ M2 ) )
% 5.31/5.61 @ ( set_ord_lessThan_nat @ M2 ) )
% 5.31/5.61 = ( groups3539618377306564664at_int
% 5.31/5.61 @ ^ [P5: nat] : ( times_times_int @ ( power_power_int @ Z3 @ P5 ) @ ( minus_minus_int @ ( power_power_int @ ( plus_plus_int @ Z3 @ H ) @ ( minus_minus_nat @ M2 @ P5 ) ) @ ( power_power_int @ Z3 @ ( minus_minus_nat @ M2 @ P5 ) ) ) )
% 5.31/5.61 @ ( set_ord_lessThan_nat @ M2 ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % lemma_termdiff1
% 5.31/5.61 thf(fact_6544_lemma__termdiff1,axiom,
% 5.31/5.61 ! [Z3: real,H: real,M2: nat] :
% 5.31/5.61 ( ( groups6591440286371151544t_real
% 5.31/5.61 @ ^ [P5: nat] : ( minus_minus_real @ ( times_times_real @ ( power_power_real @ ( plus_plus_real @ Z3 @ H ) @ ( minus_minus_nat @ M2 @ P5 ) ) @ ( power_power_real @ Z3 @ P5 ) ) @ ( power_power_real @ Z3 @ M2 ) )
% 5.31/5.61 @ ( set_ord_lessThan_nat @ M2 ) )
% 5.31/5.61 = ( groups6591440286371151544t_real
% 5.31/5.61 @ ^ [P5: nat] : ( times_times_real @ ( power_power_real @ Z3 @ P5 ) @ ( minus_minus_real @ ( power_power_real @ ( plus_plus_real @ Z3 @ H ) @ ( minus_minus_nat @ M2 @ P5 ) ) @ ( power_power_real @ Z3 @ ( minus_minus_nat @ M2 @ P5 ) ) ) )
% 5.31/5.61 @ ( set_ord_lessThan_nat @ M2 ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % lemma_termdiff1
% 5.31/5.61 thf(fact_6545_diff__power__eq__sum,axiom,
% 5.31/5.61 ! [X: complex,N: nat,Y: complex] :
% 5.31/5.61 ( ( minus_minus_complex @ ( power_power_complex @ X @ ( suc @ N ) ) @ ( power_power_complex @ Y @ ( suc @ N ) ) )
% 5.31/5.61 = ( times_times_complex @ ( minus_minus_complex @ X @ Y )
% 5.31/5.61 @ ( groups2073611262835488442omplex
% 5.31/5.61 @ ^ [P5: nat] : ( times_times_complex @ ( power_power_complex @ X @ P5 ) @ ( power_power_complex @ Y @ ( minus_minus_nat @ N @ P5 ) ) )
% 5.31/5.61 @ ( set_ord_lessThan_nat @ ( suc @ N ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % diff_power_eq_sum
% 5.31/5.61 thf(fact_6546_diff__power__eq__sum,axiom,
% 5.31/5.61 ! [X: rat,N: nat,Y: rat] :
% 5.31/5.61 ( ( minus_minus_rat @ ( power_power_rat @ X @ ( suc @ N ) ) @ ( power_power_rat @ Y @ ( suc @ N ) ) )
% 5.31/5.61 = ( times_times_rat @ ( minus_minus_rat @ X @ Y )
% 5.31/5.61 @ ( groups2906978787729119204at_rat
% 5.31/5.61 @ ^ [P5: nat] : ( times_times_rat @ ( power_power_rat @ X @ P5 ) @ ( power_power_rat @ Y @ ( minus_minus_nat @ N @ P5 ) ) )
% 5.31/5.61 @ ( set_ord_lessThan_nat @ ( suc @ N ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % diff_power_eq_sum
% 5.31/5.61 thf(fact_6547_diff__power__eq__sum,axiom,
% 5.31/5.61 ! [X: int,N: nat,Y: int] :
% 5.31/5.61 ( ( minus_minus_int @ ( power_power_int @ X @ ( suc @ N ) ) @ ( power_power_int @ Y @ ( suc @ N ) ) )
% 5.31/5.61 = ( times_times_int @ ( minus_minus_int @ X @ Y )
% 5.31/5.61 @ ( groups3539618377306564664at_int
% 5.31/5.61 @ ^ [P5: nat] : ( times_times_int @ ( power_power_int @ X @ P5 ) @ ( power_power_int @ Y @ ( minus_minus_nat @ N @ P5 ) ) )
% 5.31/5.61 @ ( set_ord_lessThan_nat @ ( suc @ N ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % diff_power_eq_sum
% 5.31/5.61 thf(fact_6548_diff__power__eq__sum,axiom,
% 5.31/5.61 ! [X: real,N: nat,Y: real] :
% 5.31/5.61 ( ( minus_minus_real @ ( power_power_real @ X @ ( suc @ N ) ) @ ( power_power_real @ Y @ ( suc @ N ) ) )
% 5.31/5.61 = ( times_times_real @ ( minus_minus_real @ X @ Y )
% 5.31/5.61 @ ( groups6591440286371151544t_real
% 5.31/5.61 @ ^ [P5: nat] : ( times_times_real @ ( power_power_real @ X @ P5 ) @ ( power_power_real @ Y @ ( minus_minus_nat @ N @ P5 ) ) )
% 5.31/5.61 @ ( set_ord_lessThan_nat @ ( suc @ N ) ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % diff_power_eq_sum
% 5.31/5.61 thf(fact_6549_power__diff__sumr2,axiom,
% 5.31/5.61 ! [X: complex,N: nat,Y: complex] :
% 5.31/5.61 ( ( minus_minus_complex @ ( power_power_complex @ X @ N ) @ ( power_power_complex @ Y @ N ) )
% 5.31/5.61 = ( times_times_complex @ ( minus_minus_complex @ X @ Y )
% 5.31/5.61 @ ( groups2073611262835488442omplex
% 5.31/5.61 @ ^ [I: nat] : ( times_times_complex @ ( power_power_complex @ Y @ ( minus_minus_nat @ N @ ( suc @ I ) ) ) @ ( power_power_complex @ X @ I ) )
% 5.31/5.61 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % power_diff_sumr2
% 5.31/5.61 thf(fact_6550_power__diff__sumr2,axiom,
% 5.31/5.61 ! [X: rat,N: nat,Y: rat] :
% 5.31/5.61 ( ( minus_minus_rat @ ( power_power_rat @ X @ N ) @ ( power_power_rat @ Y @ N ) )
% 5.31/5.61 = ( times_times_rat @ ( minus_minus_rat @ X @ Y )
% 5.31/5.61 @ ( groups2906978787729119204at_rat
% 5.31/5.61 @ ^ [I: nat] : ( times_times_rat @ ( power_power_rat @ Y @ ( minus_minus_nat @ N @ ( suc @ I ) ) ) @ ( power_power_rat @ X @ I ) )
% 5.31/5.61 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % power_diff_sumr2
% 5.31/5.61 thf(fact_6551_power__diff__sumr2,axiom,
% 5.31/5.61 ! [X: int,N: nat,Y: int] :
% 5.31/5.61 ( ( minus_minus_int @ ( power_power_int @ X @ N ) @ ( power_power_int @ Y @ N ) )
% 5.31/5.61 = ( times_times_int @ ( minus_minus_int @ X @ Y )
% 5.31/5.61 @ ( groups3539618377306564664at_int
% 5.31/5.61 @ ^ [I: nat] : ( times_times_int @ ( power_power_int @ Y @ ( minus_minus_nat @ N @ ( suc @ I ) ) ) @ ( power_power_int @ X @ I ) )
% 5.31/5.61 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % power_diff_sumr2
% 5.31/5.61 thf(fact_6552_power__diff__sumr2,axiom,
% 5.31/5.61 ! [X: real,N: nat,Y: real] :
% 5.31/5.61 ( ( minus_minus_real @ ( power_power_real @ X @ N ) @ ( power_power_real @ Y @ N ) )
% 5.31/5.61 = ( times_times_real @ ( minus_minus_real @ X @ Y )
% 5.31/5.61 @ ( groups6591440286371151544t_real
% 5.31/5.61 @ ^ [I: nat] : ( times_times_real @ ( power_power_real @ Y @ ( minus_minus_nat @ N @ ( suc @ I ) ) ) @ ( power_power_real @ X @ I ) )
% 5.31/5.61 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % power_diff_sumr2
% 5.31/5.61 thf(fact_6553_real__sum__nat__ivl__bounded2,axiom,
% 5.31/5.61 ! [N: nat,F2: nat > rat,K5: rat,K2: nat] :
% 5.31/5.61 ( ! [P7: nat] :
% 5.31/5.61 ( ( ord_less_nat @ P7 @ N )
% 5.31/5.61 => ( ord_less_eq_rat @ ( F2 @ P7 ) @ K5 ) )
% 5.31/5.61 => ( ( ord_less_eq_rat @ zero_zero_rat @ K5 )
% 5.31/5.61 => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F2 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ K2 ) ) ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ N ) @ K5 ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % real_sum_nat_ivl_bounded2
% 5.31/5.61 thf(fact_6554_real__sum__nat__ivl__bounded2,axiom,
% 5.31/5.61 ! [N: nat,F2: nat > int,K5: int,K2: nat] :
% 5.31/5.61 ( ! [P7: nat] :
% 5.31/5.61 ( ( ord_less_nat @ P7 @ N )
% 5.31/5.61 => ( ord_less_eq_int @ ( F2 @ P7 ) @ K5 ) )
% 5.31/5.61 => ( ( ord_less_eq_int @ zero_zero_int @ K5 )
% 5.31/5.61 => ( ord_less_eq_int @ ( groups3539618377306564664at_int @ F2 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ K2 ) ) ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ K5 ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % real_sum_nat_ivl_bounded2
% 5.31/5.61 thf(fact_6555_real__sum__nat__ivl__bounded2,axiom,
% 5.31/5.61 ! [N: nat,F2: nat > nat,K5: nat,K2: nat] :
% 5.31/5.61 ( ! [P7: nat] :
% 5.31/5.61 ( ( ord_less_nat @ P7 @ N )
% 5.31/5.61 => ( ord_less_eq_nat @ ( F2 @ P7 ) @ K5 ) )
% 5.31/5.61 => ( ( ord_less_eq_nat @ zero_zero_nat @ K5 )
% 5.31/5.61 => ( ord_less_eq_nat @ ( groups3542108847815614940at_nat @ F2 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ K2 ) ) ) @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ N ) @ K5 ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % real_sum_nat_ivl_bounded2
% 5.31/5.61 thf(fact_6556_real__sum__nat__ivl__bounded2,axiom,
% 5.31/5.61 ! [N: nat,F2: nat > real,K5: real,K2: nat] :
% 5.31/5.61 ( ! [P7: nat] :
% 5.31/5.61 ( ( ord_less_nat @ P7 @ N )
% 5.31/5.61 => ( ord_less_eq_real @ ( F2 @ P7 ) @ K5 ) )
% 5.31/5.61 => ( ( ord_less_eq_real @ zero_zero_real @ K5 )
% 5.31/5.61 => ( ord_less_eq_real @ ( groups6591440286371151544t_real @ F2 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ K2 ) ) ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ K5 ) ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % real_sum_nat_ivl_bounded2
% 5.31/5.61 thf(fact_6557_prod_Oin__pairs,axiom,
% 5.31/5.61 ! [G2: nat > real,M2: nat,N: nat] :
% 5.31/5.61 ( ( groups129246275422532515t_real @ G2 @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 5.31/5.61 = ( groups129246275422532515t_real
% 5.31/5.61 @ ^ [I: nat] : ( times_times_real @ ( G2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I ) ) @ ( G2 @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I ) ) ) )
% 5.31/5.61 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) ) ).
% 5.31/5.61
% 5.31/5.61 % prod.in_pairs
% 5.31/5.62 thf(fact_6558_prod_Oin__pairs,axiom,
% 5.31/5.62 ! [G2: nat > rat,M2: nat,N: nat] :
% 5.31/5.62 ( ( groups73079841787564623at_rat @ G2 @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 5.31/5.62 = ( groups73079841787564623at_rat
% 5.31/5.62 @ ^ [I: nat] : ( times_times_rat @ ( G2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I ) ) @ ( G2 @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I ) ) ) )
% 5.31/5.62 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % prod.in_pairs
% 5.31/5.62 thf(fact_6559_prod_Oin__pairs,axiom,
% 5.31/5.62 ! [G2: nat > int,M2: nat,N: nat] :
% 5.31/5.62 ( ( groups705719431365010083at_int @ G2 @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 5.31/5.62 = ( groups705719431365010083at_int
% 5.31/5.62 @ ^ [I: nat] : ( times_times_int @ ( G2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I ) ) @ ( G2 @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I ) ) ) )
% 5.31/5.62 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % prod.in_pairs
% 5.31/5.62 thf(fact_6560_prod_Oin__pairs,axiom,
% 5.31/5.62 ! [G2: nat > nat,M2: nat,N: nat] :
% 5.31/5.62 ( ( groups708209901874060359at_nat @ G2 @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 5.31/5.62 = ( groups708209901874060359at_nat
% 5.31/5.62 @ ^ [I: nat] : ( times_times_nat @ ( G2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I ) ) @ ( G2 @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I ) ) ) )
% 5.31/5.62 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % prod.in_pairs
% 5.31/5.62 thf(fact_6561_sum__atLeastAtMost__code,axiom,
% 5.31/5.62 ! [F2: nat > complex,A: nat,B: nat] :
% 5.31/5.62 ( ( groups2073611262835488442omplex @ F2 @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 5.31/5.62 = ( set_fo1517530859248394432omplex
% 5.31/5.62 @ ^ [A5: nat] : ( plus_plus_complex @ ( F2 @ A5 ) )
% 5.31/5.62 @ A
% 5.31/5.62 @ B
% 5.31/5.62 @ zero_zero_complex ) ) ).
% 5.31/5.62
% 5.31/5.62 % sum_atLeastAtMost_code
% 5.31/5.62 thf(fact_6562_sum__atLeastAtMost__code,axiom,
% 5.31/5.62 ! [F2: nat > rat,A: nat,B: nat] :
% 5.31/5.62 ( ( groups2906978787729119204at_rat @ F2 @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 5.31/5.62 = ( set_fo1949268297981939178at_rat
% 5.31/5.62 @ ^ [A5: nat] : ( plus_plus_rat @ ( F2 @ A5 ) )
% 5.31/5.62 @ A
% 5.31/5.62 @ B
% 5.31/5.62 @ zero_zero_rat ) ) ).
% 5.31/5.62
% 5.31/5.62 % sum_atLeastAtMost_code
% 5.31/5.62 thf(fact_6563_sum__atLeastAtMost__code,axiom,
% 5.31/5.62 ! [F2: nat > int,A: nat,B: nat] :
% 5.31/5.62 ( ( groups3539618377306564664at_int @ F2 @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 5.31/5.62 = ( set_fo2581907887559384638at_int
% 5.31/5.62 @ ^ [A5: nat] : ( plus_plus_int @ ( F2 @ A5 ) )
% 5.31/5.62 @ A
% 5.31/5.62 @ B
% 5.31/5.62 @ zero_zero_int ) ) ).
% 5.31/5.62
% 5.31/5.62 % sum_atLeastAtMost_code
% 5.31/5.62 thf(fact_6564_sum__atLeastAtMost__code,axiom,
% 5.31/5.62 ! [F2: nat > nat,A: nat,B: nat] :
% 5.31/5.62 ( ( groups3542108847815614940at_nat @ F2 @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 5.31/5.62 = ( set_fo2584398358068434914at_nat
% 5.31/5.62 @ ^ [A5: nat] : ( plus_plus_nat @ ( F2 @ A5 ) )
% 5.31/5.62 @ A
% 5.31/5.62 @ B
% 5.31/5.62 @ zero_zero_nat ) ) ).
% 5.31/5.62
% 5.31/5.62 % sum_atLeastAtMost_code
% 5.31/5.62 thf(fact_6565_sum__atLeastAtMost__code,axiom,
% 5.31/5.62 ! [F2: nat > real,A: nat,B: nat] :
% 5.31/5.62 ( ( groups6591440286371151544t_real @ F2 @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 5.31/5.62 = ( set_fo3111899725591712190t_real
% 5.31/5.62 @ ^ [A5: nat] : ( plus_plus_real @ ( F2 @ A5 ) )
% 5.31/5.62 @ A
% 5.31/5.62 @ B
% 5.31/5.62 @ zero_zero_real ) ) ).
% 5.31/5.62
% 5.31/5.62 % sum_atLeastAtMost_code
% 5.31/5.62 thf(fact_6566_pochhammer__Suc__prod__rev,axiom,
% 5.31/5.62 ! [A: rat,N: nat] :
% 5.31/5.62 ( ( comm_s4028243227959126397er_rat @ A @ ( suc @ N ) )
% 5.31/5.62 = ( groups73079841787564623at_rat
% 5.31/5.62 @ ^ [I: nat] : ( plus_plus_rat @ A @ ( semiri681578069525770553at_rat @ ( minus_minus_nat @ N @ I ) ) )
% 5.31/5.62 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % pochhammer_Suc_prod_rev
% 5.31/5.62 thf(fact_6567_pochhammer__Suc__prod__rev,axiom,
% 5.31/5.62 ! [A: real,N: nat] :
% 5.31/5.62 ( ( comm_s7457072308508201937r_real @ A @ ( suc @ N ) )
% 5.31/5.62 = ( groups129246275422532515t_real
% 5.31/5.62 @ ^ [I: nat] : ( plus_plus_real @ A @ ( semiri5074537144036343181t_real @ ( minus_minus_nat @ N @ I ) ) )
% 5.31/5.62 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % pochhammer_Suc_prod_rev
% 5.31/5.62 thf(fact_6568_pochhammer__Suc__prod__rev,axiom,
% 5.31/5.62 ! [A: int,N: nat] :
% 5.31/5.62 ( ( comm_s4660882817536571857er_int @ A @ ( suc @ N ) )
% 5.31/5.62 = ( groups705719431365010083at_int
% 5.31/5.62 @ ^ [I: nat] : ( plus_plus_int @ A @ ( semiri1314217659103216013at_int @ ( minus_minus_nat @ N @ I ) ) )
% 5.31/5.62 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % pochhammer_Suc_prod_rev
% 5.31/5.62 thf(fact_6569_pochhammer__Suc__prod__rev,axiom,
% 5.31/5.62 ! [A: nat,N: nat] :
% 5.31/5.62 ( ( comm_s4663373288045622133er_nat @ A @ ( suc @ N ) )
% 5.31/5.62 = ( groups708209901874060359at_nat
% 5.31/5.62 @ ^ [I: nat] : ( plus_plus_nat @ A @ ( semiri1316708129612266289at_nat @ ( minus_minus_nat @ N @ I ) ) )
% 5.31/5.62 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % pochhammer_Suc_prod_rev
% 5.31/5.62 thf(fact_6570_one__diff__power__eq_H,axiom,
% 5.31/5.62 ! [X: code_integer,N: nat] :
% 5.31/5.62 ( ( minus_8373710615458151222nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ X @ N ) )
% 5.31/5.62 = ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ one_one_Code_integer @ X )
% 5.31/5.62 @ ( groups7501900531339628137nteger
% 5.31/5.62 @ ^ [I: nat] : ( power_8256067586552552935nteger @ X @ ( minus_minus_nat @ N @ ( suc @ I ) ) )
% 5.31/5.62 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % one_diff_power_eq'
% 5.31/5.62 thf(fact_6571_one__diff__power__eq_H,axiom,
% 5.31/5.62 ! [X: complex,N: nat] :
% 5.31/5.62 ( ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ X @ N ) )
% 5.31/5.62 = ( times_times_complex @ ( minus_minus_complex @ one_one_complex @ X )
% 5.31/5.62 @ ( groups2073611262835488442omplex
% 5.31/5.62 @ ^ [I: nat] : ( power_power_complex @ X @ ( minus_minus_nat @ N @ ( suc @ I ) ) )
% 5.31/5.62 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % one_diff_power_eq'
% 5.31/5.62 thf(fact_6572_one__diff__power__eq_H,axiom,
% 5.31/5.62 ! [X: rat,N: nat] :
% 5.31/5.62 ( ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X @ N ) )
% 5.31/5.62 = ( times_times_rat @ ( minus_minus_rat @ one_one_rat @ X )
% 5.31/5.62 @ ( groups2906978787729119204at_rat
% 5.31/5.62 @ ^ [I: nat] : ( power_power_rat @ X @ ( minus_minus_nat @ N @ ( suc @ I ) ) )
% 5.31/5.62 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % one_diff_power_eq'
% 5.31/5.62 thf(fact_6573_one__diff__power__eq_H,axiom,
% 5.31/5.62 ! [X: int,N: nat] :
% 5.31/5.62 ( ( minus_minus_int @ one_one_int @ ( power_power_int @ X @ N ) )
% 5.31/5.62 = ( times_times_int @ ( minus_minus_int @ one_one_int @ X )
% 5.31/5.62 @ ( groups3539618377306564664at_int
% 5.31/5.62 @ ^ [I: nat] : ( power_power_int @ X @ ( minus_minus_nat @ N @ ( suc @ I ) ) )
% 5.31/5.62 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % one_diff_power_eq'
% 5.31/5.62 thf(fact_6574_one__diff__power__eq_H,axiom,
% 5.31/5.62 ! [X: real,N: nat] :
% 5.31/5.62 ( ( minus_minus_real @ one_one_real @ ( power_power_real @ X @ N ) )
% 5.31/5.62 = ( times_times_real @ ( minus_minus_real @ one_one_real @ X )
% 5.31/5.62 @ ( groups6591440286371151544t_real
% 5.31/5.62 @ ^ [I: nat] : ( power_power_real @ X @ ( minus_minus_nat @ N @ ( suc @ I ) ) )
% 5.31/5.62 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % one_diff_power_eq'
% 5.31/5.62 thf(fact_6575_sum__split__even__odd,axiom,
% 5.31/5.62 ! [F2: nat > real,G2: nat > real,N: nat] :
% 5.31/5.62 ( ( groups6591440286371151544t_real
% 5.31/5.62 @ ^ [I: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I ) @ ( F2 @ I ) @ ( G2 @ I ) )
% 5.31/5.62 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.31/5.62 = ( plus_plus_real
% 5.31/5.62 @ ( groups6591440286371151544t_real
% 5.31/5.62 @ ^ [I: nat] : ( F2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I ) )
% 5.31/5.62 @ ( set_ord_lessThan_nat @ N ) )
% 5.31/5.62 @ ( groups6591440286371151544t_real
% 5.31/5.62 @ ^ [I: nat] : ( G2 @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I ) @ one_one_nat ) )
% 5.31/5.62 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % sum_split_even_odd
% 5.31/5.62 thf(fact_6576_zero__less__binomial__iff,axiom,
% 5.31/5.62 ! [N: nat,K2: nat] :
% 5.31/5.62 ( ( ord_less_nat @ zero_zero_nat @ ( binomial @ N @ K2 ) )
% 5.31/5.62 = ( ord_less_eq_nat @ K2 @ N ) ) ).
% 5.31/5.62
% 5.31/5.62 % zero_less_binomial_iff
% 5.31/5.62 thf(fact_6577_choose__two,axiom,
% 5.31/5.62 ! [N: nat] :
% 5.31/5.62 ( ( binomial @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.31/5.62 = ( divide_divide_nat @ ( times_times_nat @ N @ ( minus_minus_nat @ N @ one_one_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % choose_two
% 5.31/5.62 thf(fact_6578_binomial__n__0,axiom,
% 5.31/5.62 ! [N: nat] :
% 5.31/5.62 ( ( binomial @ N @ zero_zero_nat )
% 5.31/5.62 = one_one_nat ) ).
% 5.31/5.62
% 5.31/5.62 % binomial_n_0
% 5.31/5.62 thf(fact_6579_binomial__Suc__Suc,axiom,
% 5.31/5.62 ! [N: nat,K2: nat] :
% 5.31/5.62 ( ( binomial @ ( suc @ N ) @ ( suc @ K2 ) )
% 5.31/5.62 = ( plus_plus_nat @ ( binomial @ N @ K2 ) @ ( binomial @ N @ ( suc @ K2 ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % binomial_Suc_Suc
% 5.31/5.62 thf(fact_6580_binomial__eq__0__iff,axiom,
% 5.31/5.62 ! [N: nat,K2: nat] :
% 5.31/5.62 ( ( ( binomial @ N @ K2 )
% 5.31/5.62 = zero_zero_nat )
% 5.31/5.62 = ( ord_less_nat @ N @ K2 ) ) ).
% 5.31/5.62
% 5.31/5.62 % binomial_eq_0_iff
% 5.31/5.62 thf(fact_6581_binomial__1,axiom,
% 5.31/5.62 ! [N: nat] :
% 5.31/5.62 ( ( binomial @ N @ ( suc @ zero_zero_nat ) )
% 5.31/5.62 = N ) ).
% 5.31/5.62
% 5.31/5.62 % binomial_1
% 5.31/5.62 thf(fact_6582_binomial__0__Suc,axiom,
% 5.31/5.62 ! [K2: nat] :
% 5.31/5.62 ( ( binomial @ zero_zero_nat @ ( suc @ K2 ) )
% 5.31/5.62 = zero_zero_nat ) ).
% 5.31/5.62
% 5.31/5.62 % binomial_0_Suc
% 5.31/5.62 thf(fact_6583_binomial__Suc__n,axiom,
% 5.31/5.62 ! [N: nat] :
% 5.31/5.62 ( ( binomial @ ( suc @ N ) @ N )
% 5.31/5.62 = ( suc @ N ) ) ).
% 5.31/5.62
% 5.31/5.62 % binomial_Suc_n
% 5.31/5.62 thf(fact_6584_prod__pos__nat__iff,axiom,
% 5.31/5.62 ! [A4: set_int,F2: int > nat] :
% 5.31/5.62 ( ( finite_finite_int @ A4 )
% 5.31/5.62 => ( ( ord_less_nat @ zero_zero_nat @ ( groups1707563613775114915nt_nat @ F2 @ A4 ) )
% 5.31/5.62 = ( ! [X4: int] :
% 5.31/5.62 ( ( member_int @ X4 @ A4 )
% 5.31/5.62 => ( ord_less_nat @ zero_zero_nat @ ( F2 @ X4 ) ) ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % prod_pos_nat_iff
% 5.31/5.62 thf(fact_6585_prod__pos__nat__iff,axiom,
% 5.31/5.62 ! [A4: set_complex,F2: complex > nat] :
% 5.31/5.62 ( ( finite3207457112153483333omplex @ A4 )
% 5.31/5.62 => ( ( ord_less_nat @ zero_zero_nat @ ( groups861055069439313189ex_nat @ F2 @ A4 ) )
% 5.31/5.62 = ( ! [X4: complex] :
% 5.31/5.62 ( ( member_complex @ X4 @ A4 )
% 5.31/5.62 => ( ord_less_nat @ zero_zero_nat @ ( F2 @ X4 ) ) ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % prod_pos_nat_iff
% 5.31/5.62 thf(fact_6586_prod__pos__nat__iff,axiom,
% 5.31/5.62 ! [A4: set_nat,F2: nat > nat] :
% 5.31/5.62 ( ( finite_finite_nat @ A4 )
% 5.31/5.62 => ( ( ord_less_nat @ zero_zero_nat @ ( groups708209901874060359at_nat @ F2 @ A4 ) )
% 5.31/5.62 = ( ! [X4: nat] :
% 5.31/5.62 ( ( member_nat @ X4 @ A4 )
% 5.31/5.62 => ( ord_less_nat @ zero_zero_nat @ ( F2 @ X4 ) ) ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % prod_pos_nat_iff
% 5.31/5.62 thf(fact_6587_prod__int__eq,axiom,
% 5.31/5.62 ! [I2: nat,J2: nat] :
% 5.31/5.62 ( ( groups705719431365010083at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ I2 @ J2 ) )
% 5.31/5.62 = ( groups1705073143266064639nt_int
% 5.31/5.62 @ ^ [X4: int] : X4
% 5.31/5.62 @ ( set_or1266510415728281911st_int @ ( semiri1314217659103216013at_int @ I2 ) @ ( semiri1314217659103216013at_int @ J2 ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % prod_int_eq
% 5.31/5.62 thf(fact_6588_prod__int__plus__eq,axiom,
% 5.31/5.62 ! [I2: nat,J2: nat] :
% 5.31/5.62 ( ( groups705719431365010083at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ I2 @ ( plus_plus_nat @ I2 @ J2 ) ) )
% 5.31/5.62 = ( groups1705073143266064639nt_int
% 5.31/5.62 @ ^ [X4: int] : X4
% 5.31/5.62 @ ( set_or1266510415728281911st_int @ ( semiri1314217659103216013at_int @ I2 ) @ ( semiri1314217659103216013at_int @ ( plus_plus_nat @ I2 @ J2 ) ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % prod_int_plus_eq
% 5.31/5.62 thf(fact_6589_binomial__eq__0,axiom,
% 5.31/5.62 ! [N: nat,K2: nat] :
% 5.31/5.62 ( ( ord_less_nat @ N @ K2 )
% 5.31/5.62 => ( ( binomial @ N @ K2 )
% 5.31/5.62 = zero_zero_nat ) ) ).
% 5.31/5.62
% 5.31/5.62 % binomial_eq_0
% 5.31/5.62 thf(fact_6590_Suc__times__binomial,axiom,
% 5.31/5.62 ! [K2: nat,N: nat] :
% 5.31/5.62 ( ( times_times_nat @ ( suc @ K2 ) @ ( binomial @ ( suc @ N ) @ ( suc @ K2 ) ) )
% 5.31/5.62 = ( times_times_nat @ ( suc @ N ) @ ( binomial @ N @ K2 ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % Suc_times_binomial
% 5.31/5.62 thf(fact_6591_Suc__times__binomial__eq,axiom,
% 5.31/5.62 ! [N: nat,K2: nat] :
% 5.31/5.62 ( ( times_times_nat @ ( suc @ N ) @ ( binomial @ N @ K2 ) )
% 5.31/5.62 = ( times_times_nat @ ( binomial @ ( suc @ N ) @ ( suc @ K2 ) ) @ ( suc @ K2 ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % Suc_times_binomial_eq
% 5.31/5.62 thf(fact_6592_binomial__symmetric,axiom,
% 5.31/5.62 ! [K2: nat,N: nat] :
% 5.31/5.62 ( ( ord_less_eq_nat @ K2 @ N )
% 5.31/5.62 => ( ( binomial @ N @ K2 )
% 5.31/5.62 = ( binomial @ N @ ( minus_minus_nat @ N @ K2 ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % binomial_symmetric
% 5.31/5.62 thf(fact_6593_choose__mult__lemma,axiom,
% 5.31/5.62 ! [M2: nat,R3: nat,K2: nat] :
% 5.31/5.62 ( ( times_times_nat @ ( binomial @ ( plus_plus_nat @ ( plus_plus_nat @ M2 @ R3 ) @ K2 ) @ ( plus_plus_nat @ M2 @ K2 ) ) @ ( binomial @ ( plus_plus_nat @ M2 @ K2 ) @ K2 ) )
% 5.31/5.62 = ( times_times_nat @ ( binomial @ ( plus_plus_nat @ ( plus_plus_nat @ M2 @ R3 ) @ K2 ) @ K2 ) @ ( binomial @ ( plus_plus_nat @ M2 @ R3 ) @ M2 ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % choose_mult_lemma
% 5.31/5.62 thf(fact_6594_binomial__le__pow,axiom,
% 5.31/5.62 ! [R3: nat,N: nat] :
% 5.31/5.62 ( ( ord_less_eq_nat @ R3 @ N )
% 5.31/5.62 => ( ord_less_eq_nat @ ( binomial @ N @ R3 ) @ ( power_power_nat @ N @ R3 ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % binomial_le_pow
% 5.31/5.62 thf(fact_6595_zero__less__binomial,axiom,
% 5.31/5.62 ! [K2: nat,N: nat] :
% 5.31/5.62 ( ( ord_less_eq_nat @ K2 @ N )
% 5.31/5.62 => ( ord_less_nat @ zero_zero_nat @ ( binomial @ N @ K2 ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % zero_less_binomial
% 5.31/5.62 thf(fact_6596_Suc__times__binomial__add,axiom,
% 5.31/5.62 ! [A: nat,B: nat] :
% 5.31/5.62 ( ( times_times_nat @ ( suc @ A ) @ ( binomial @ ( suc @ ( plus_plus_nat @ A @ B ) ) @ ( suc @ A ) ) )
% 5.31/5.62 = ( times_times_nat @ ( suc @ B ) @ ( binomial @ ( suc @ ( plus_plus_nat @ A @ B ) ) @ A ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % Suc_times_binomial_add
% 5.31/5.62 thf(fact_6597_binomial__Suc__Suc__eq__times,axiom,
% 5.31/5.62 ! [N: nat,K2: nat] :
% 5.31/5.62 ( ( binomial @ ( suc @ N ) @ ( suc @ K2 ) )
% 5.31/5.62 = ( divide_divide_nat @ ( times_times_nat @ ( suc @ N ) @ ( binomial @ N @ K2 ) ) @ ( suc @ K2 ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % binomial_Suc_Suc_eq_times
% 5.31/5.62 thf(fact_6598_choose__mult,axiom,
% 5.31/5.62 ! [K2: nat,M2: nat,N: nat] :
% 5.31/5.62 ( ( ord_less_eq_nat @ K2 @ M2 )
% 5.31/5.62 => ( ( ord_less_eq_nat @ M2 @ N )
% 5.31/5.62 => ( ( times_times_nat @ ( binomial @ N @ M2 ) @ ( binomial @ M2 @ K2 ) )
% 5.31/5.62 = ( times_times_nat @ ( binomial @ N @ K2 ) @ ( binomial @ ( minus_minus_nat @ N @ K2 ) @ ( minus_minus_nat @ M2 @ K2 ) ) ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % choose_mult
% 5.31/5.62 thf(fact_6599_binomial__absorb__comp,axiom,
% 5.31/5.62 ! [N: nat,K2: nat] :
% 5.31/5.62 ( ( times_times_nat @ ( minus_minus_nat @ N @ K2 ) @ ( binomial @ N @ K2 ) )
% 5.31/5.62 = ( times_times_nat @ N @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ K2 ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % binomial_absorb_comp
% 5.31/5.62 thf(fact_6600_binomial__absorption,axiom,
% 5.31/5.62 ! [K2: nat,N: nat] :
% 5.31/5.62 ( ( times_times_nat @ ( suc @ K2 ) @ ( binomial @ N @ ( suc @ K2 ) ) )
% 5.31/5.62 = ( times_times_nat @ N @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ K2 ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % binomial_absorption
% 5.31/5.62 thf(fact_6601_sum__bounds__lt__plus1,axiom,
% 5.31/5.62 ! [F2: nat > nat,Mm: nat] :
% 5.31/5.62 ( ( groups3542108847815614940at_nat
% 5.31/5.62 @ ^ [K3: nat] : ( F2 @ ( suc @ K3 ) )
% 5.31/5.62 @ ( set_ord_lessThan_nat @ Mm ) )
% 5.31/5.62 = ( groups3542108847815614940at_nat @ F2 @ ( set_or1269000886237332187st_nat @ one_one_nat @ Mm ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % sum_bounds_lt_plus1
% 5.31/5.62 thf(fact_6602_sum__bounds__lt__plus1,axiom,
% 5.31/5.62 ! [F2: nat > real,Mm: nat] :
% 5.31/5.62 ( ( groups6591440286371151544t_real
% 5.31/5.62 @ ^ [K3: nat] : ( F2 @ ( suc @ K3 ) )
% 5.31/5.62 @ ( set_ord_lessThan_nat @ Mm ) )
% 5.31/5.62 = ( groups6591440286371151544t_real @ F2 @ ( set_or1269000886237332187st_nat @ one_one_nat @ Mm ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % sum_bounds_lt_plus1
% 5.31/5.62 thf(fact_6603_binomial__ge__n__over__k__pow__k,axiom,
% 5.31/5.62 ! [K2: nat,N: nat] :
% 5.31/5.62 ( ( ord_less_eq_nat @ K2 @ N )
% 5.31/5.62 => ( ord_less_eq_real @ ( power_power_real @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ N ) @ ( semiri5074537144036343181t_real @ K2 ) ) @ K2 ) @ ( semiri5074537144036343181t_real @ ( binomial @ N @ K2 ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % binomial_ge_n_over_k_pow_k
% 5.31/5.62 thf(fact_6604_binomial__ge__n__over__k__pow__k,axiom,
% 5.31/5.62 ! [K2: nat,N: nat] :
% 5.31/5.62 ( ( ord_less_eq_nat @ K2 @ N )
% 5.31/5.62 => ( ord_less_eq_rat @ ( power_power_rat @ ( divide_divide_rat @ ( semiri681578069525770553at_rat @ N ) @ ( semiri681578069525770553at_rat @ K2 ) ) @ K2 ) @ ( semiri681578069525770553at_rat @ ( binomial @ N @ K2 ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % binomial_ge_n_over_k_pow_k
% 5.31/5.62 thf(fact_6605_binomial__le__pow2,axiom,
% 5.31/5.62 ! [N: nat,K2: nat] : ( ord_less_eq_nat @ ( binomial @ N @ K2 ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.31/5.62
% 5.31/5.62 % binomial_le_pow2
% 5.31/5.62 thf(fact_6606_choose__reduce__nat,axiom,
% 5.31/5.62 ! [N: nat,K2: nat] :
% 5.31/5.62 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.62 => ( ( ord_less_nat @ zero_zero_nat @ K2 )
% 5.31/5.62 => ( ( binomial @ N @ K2 )
% 5.31/5.62 = ( plus_plus_nat @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ ( minus_minus_nat @ K2 @ one_one_nat ) ) @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ K2 ) ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % choose_reduce_nat
% 5.31/5.62 thf(fact_6607_times__binomial__minus1__eq,axiom,
% 5.31/5.62 ! [K2: nat,N: nat] :
% 5.31/5.62 ( ( ord_less_nat @ zero_zero_nat @ K2 )
% 5.31/5.62 => ( ( times_times_nat @ K2 @ ( binomial @ N @ K2 ) )
% 5.31/5.62 = ( times_times_nat @ N @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ ( minus_minus_nat @ K2 @ one_one_nat ) ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % times_binomial_minus1_eq
% 5.31/5.62 thf(fact_6608_binomial__addition__formula,axiom,
% 5.31/5.62 ! [N: nat,K2: nat] :
% 5.31/5.62 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.62 => ( ( binomial @ N @ ( suc @ K2 ) )
% 5.31/5.62 = ( plus_plus_nat @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ ( suc @ K2 ) ) @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ K2 ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % binomial_addition_formula
% 5.31/5.62 thf(fact_6609_choose__odd__sum,axiom,
% 5.31/5.62 ! [N: nat] :
% 5.31/5.62 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.62 => ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) )
% 5.31/5.62 @ ( groups2906978787729119204at_rat
% 5.31/5.62 @ ^ [I: nat] :
% 5.31/5.62 ( if_rat
% 5.31/5.62 @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I )
% 5.31/5.62 @ ( semiri681578069525770553at_rat @ ( binomial @ N @ I ) )
% 5.31/5.62 @ zero_zero_rat )
% 5.31/5.62 @ ( set_ord_atMost_nat @ N ) ) )
% 5.31/5.62 = ( power_power_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % choose_odd_sum
% 5.31/5.62 thf(fact_6610_choose__odd__sum,axiom,
% 5.31/5.62 ! [N: nat] :
% 5.31/5.62 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.62 => ( ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) )
% 5.31/5.62 @ ( groups2073611262835488442omplex
% 5.31/5.62 @ ^ [I: nat] :
% 5.31/5.62 ( if_complex
% 5.31/5.62 @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I )
% 5.31/5.62 @ ( semiri8010041392384452111omplex @ ( binomial @ N @ I ) )
% 5.31/5.62 @ zero_zero_complex )
% 5.31/5.62 @ ( set_ord_atMost_nat @ N ) ) )
% 5.31/5.62 = ( power_power_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % choose_odd_sum
% 5.31/5.62 thf(fact_6611_choose__odd__sum,axiom,
% 5.31/5.62 ! [N: nat] :
% 5.31/5.62 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.62 => ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) )
% 5.31/5.62 @ ( groups3539618377306564664at_int
% 5.31/5.62 @ ^ [I: nat] :
% 5.31/5.62 ( if_int
% 5.31/5.62 @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I )
% 5.31/5.62 @ ( semiri1314217659103216013at_int @ ( binomial @ N @ I ) )
% 5.31/5.62 @ zero_zero_int )
% 5.31/5.62 @ ( set_ord_atMost_nat @ N ) ) )
% 5.31/5.62 = ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % choose_odd_sum
% 5.31/5.62 thf(fact_6612_choose__odd__sum,axiom,
% 5.31/5.62 ! [N: nat] :
% 5.31/5.62 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.62 => ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) )
% 5.31/5.62 @ ( groups6591440286371151544t_real
% 5.31/5.62 @ ^ [I: nat] :
% 5.31/5.62 ( if_real
% 5.31/5.62 @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I )
% 5.31/5.62 @ ( semiri5074537144036343181t_real @ ( binomial @ N @ I ) )
% 5.31/5.62 @ zero_zero_real )
% 5.31/5.62 @ ( set_ord_atMost_nat @ N ) ) )
% 5.31/5.62 = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % choose_odd_sum
% 5.31/5.62 thf(fact_6613_choose__even__sum,axiom,
% 5.31/5.62 ! [N: nat] :
% 5.31/5.62 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.62 => ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) )
% 5.31/5.62 @ ( groups2906978787729119204at_rat
% 5.31/5.62 @ ^ [I: nat] : ( if_rat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I ) @ ( semiri681578069525770553at_rat @ ( binomial @ N @ I ) ) @ zero_zero_rat )
% 5.31/5.62 @ ( set_ord_atMost_nat @ N ) ) )
% 5.31/5.62 = ( power_power_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % choose_even_sum
% 5.31/5.62 thf(fact_6614_choose__even__sum,axiom,
% 5.31/5.62 ! [N: nat] :
% 5.31/5.62 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.62 => ( ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) )
% 5.31/5.62 @ ( groups2073611262835488442omplex
% 5.31/5.62 @ ^ [I: nat] : ( if_complex @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I ) @ ( semiri8010041392384452111omplex @ ( binomial @ N @ I ) ) @ zero_zero_complex )
% 5.31/5.62 @ ( set_ord_atMost_nat @ N ) ) )
% 5.31/5.62 = ( power_power_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % choose_even_sum
% 5.31/5.62 thf(fact_6615_choose__even__sum,axiom,
% 5.31/5.62 ! [N: nat] :
% 5.31/5.62 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.62 => ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) )
% 5.31/5.62 @ ( groups3539618377306564664at_int
% 5.31/5.62 @ ^ [I: nat] : ( if_int @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I ) @ ( semiri1314217659103216013at_int @ ( binomial @ N @ I ) ) @ zero_zero_int )
% 5.31/5.62 @ ( set_ord_atMost_nat @ N ) ) )
% 5.31/5.62 = ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % choose_even_sum
% 5.31/5.62 thf(fact_6616_choose__even__sum,axiom,
% 5.31/5.62 ! [N: nat] :
% 5.31/5.62 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.62 => ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) )
% 5.31/5.62 @ ( groups6591440286371151544t_real
% 5.31/5.62 @ ^ [I: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I ) @ ( semiri5074537144036343181t_real @ ( binomial @ N @ I ) ) @ zero_zero_real )
% 5.31/5.62 @ ( set_ord_atMost_nat @ N ) ) )
% 5.31/5.62 = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % choose_even_sum
% 5.31/5.62 thf(fact_6617_card__lists__distinct__length__eq,axiom,
% 5.31/5.62 ! [A4: set_list_nat,K2: nat] :
% 5.31/5.62 ( ( finite8100373058378681591st_nat @ A4 )
% 5.31/5.62 => ( ( ord_less_eq_nat @ K2 @ ( finite_card_list_nat @ A4 ) )
% 5.31/5.62 => ( ( finite7325466520557071688st_nat
% 5.31/5.62 @ ( collec5989764272469232197st_nat
% 5.31/5.62 @ ^ [Xs: list_list_nat] :
% 5.31/5.62 ( ( ( size_s3023201423986296836st_nat @ Xs )
% 5.31/5.62 = K2 )
% 5.31/5.62 & ( distinct_list_nat @ Xs )
% 5.31/5.62 & ( ord_le6045566169113846134st_nat @ ( set_list_nat2 @ Xs ) @ A4 ) ) ) )
% 5.31/5.62 = ( groups708209901874060359at_nat
% 5.31/5.62 @ ^ [X4: nat] : X4
% 5.31/5.62 @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ ( minus_minus_nat @ ( finite_card_list_nat @ A4 ) @ K2 ) @ one_one_nat ) @ ( finite_card_list_nat @ A4 ) ) ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % card_lists_distinct_length_eq
% 5.31/5.62 thf(fact_6618_card__lists__distinct__length__eq,axiom,
% 5.31/5.62 ! [A4: set_set_nat,K2: nat] :
% 5.31/5.62 ( ( finite1152437895449049373et_nat @ A4 )
% 5.31/5.62 => ( ( ord_less_eq_nat @ K2 @ ( finite_card_set_nat @ A4 ) )
% 5.31/5.62 => ( ( finite5631907774883551598et_nat
% 5.31/5.62 @ ( collect_list_set_nat
% 5.31/5.62 @ ^ [Xs: list_set_nat] :
% 5.31/5.62 ( ( ( size_s3254054031482475050et_nat @ Xs )
% 5.31/5.62 = K2 )
% 5.31/5.62 & ( distinct_set_nat @ Xs )
% 5.31/5.62 & ( ord_le6893508408891458716et_nat @ ( set_set_nat2 @ Xs ) @ A4 ) ) ) )
% 5.31/5.62 = ( groups708209901874060359at_nat
% 5.31/5.62 @ ^ [X4: nat] : X4
% 5.31/5.62 @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ ( minus_minus_nat @ ( finite_card_set_nat @ A4 ) @ K2 ) @ one_one_nat ) @ ( finite_card_set_nat @ A4 ) ) ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % card_lists_distinct_length_eq
% 5.31/5.62 thf(fact_6619_card__lists__distinct__length__eq,axiom,
% 5.31/5.62 ! [A4: set_complex,K2: nat] :
% 5.31/5.62 ( ( finite3207457112153483333omplex @ A4 )
% 5.31/5.62 => ( ( ord_less_eq_nat @ K2 @ ( finite_card_complex @ A4 ) )
% 5.31/5.62 => ( ( finite5120063068150530198omplex
% 5.31/5.62 @ ( collect_list_complex
% 5.31/5.62 @ ^ [Xs: list_complex] :
% 5.31/5.62 ( ( ( size_s3451745648224563538omplex @ Xs )
% 5.31/5.62 = K2 )
% 5.31/5.62 & ( distinct_complex @ Xs )
% 5.31/5.62 & ( ord_le211207098394363844omplex @ ( set_complex2 @ Xs ) @ A4 ) ) ) )
% 5.31/5.62 = ( groups708209901874060359at_nat
% 5.31/5.62 @ ^ [X4: nat] : X4
% 5.31/5.62 @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ ( minus_minus_nat @ ( finite_card_complex @ A4 ) @ K2 ) @ one_one_nat ) @ ( finite_card_complex @ A4 ) ) ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % card_lists_distinct_length_eq
% 5.31/5.62 thf(fact_6620_card__lists__distinct__length__eq,axiom,
% 5.31/5.62 ! [A4: set_VEBT_VEBT,K2: nat] :
% 5.31/5.62 ( ( finite5795047828879050333T_VEBT @ A4 )
% 5.31/5.62 => ( ( ord_less_eq_nat @ K2 @ ( finite7802652506058667612T_VEBT @ A4 ) )
% 5.31/5.62 => ( ( finite5915292604075114978T_VEBT
% 5.31/5.62 @ ( collec5608196760682091941T_VEBT
% 5.31/5.62 @ ^ [Xs: list_VEBT_VEBT] :
% 5.31/5.62 ( ( ( size_s6755466524823107622T_VEBT @ Xs )
% 5.31/5.62 = K2 )
% 5.31/5.62 & ( distinct_VEBT_VEBT @ Xs )
% 5.31/5.62 & ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ Xs ) @ A4 ) ) ) )
% 5.31/5.62 = ( groups708209901874060359at_nat
% 5.31/5.62 @ ^ [X4: nat] : X4
% 5.31/5.62 @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ ( minus_minus_nat @ ( finite7802652506058667612T_VEBT @ A4 ) @ K2 ) @ one_one_nat ) @ ( finite7802652506058667612T_VEBT @ A4 ) ) ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % card_lists_distinct_length_eq
% 5.31/5.62 thf(fact_6621_card__lists__distinct__length__eq,axiom,
% 5.31/5.62 ! [A4: set_o,K2: nat] :
% 5.31/5.62 ( ( finite_finite_o @ A4 )
% 5.31/5.62 => ( ( ord_less_eq_nat @ K2 @ ( finite_card_o @ A4 ) )
% 5.31/5.62 => ( ( finite_card_list_o
% 5.31/5.62 @ ( collect_list_o
% 5.31/5.62 @ ^ [Xs: list_o] :
% 5.31/5.62 ( ( ( size_size_list_o @ Xs )
% 5.31/5.62 = K2 )
% 5.31/5.62 & ( distinct_o @ Xs )
% 5.31/5.62 & ( ord_less_eq_set_o @ ( set_o2 @ Xs ) @ A4 ) ) ) )
% 5.31/5.62 = ( groups708209901874060359at_nat
% 5.31/5.62 @ ^ [X4: nat] : X4
% 5.31/5.62 @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ ( minus_minus_nat @ ( finite_card_o @ A4 ) @ K2 ) @ one_one_nat ) @ ( finite_card_o @ A4 ) ) ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % card_lists_distinct_length_eq
% 5.31/5.62 thf(fact_6622_card__lists__distinct__length__eq,axiom,
% 5.31/5.62 ! [A4: set_int,K2: nat] :
% 5.31/5.62 ( ( finite_finite_int @ A4 )
% 5.31/5.62 => ( ( ord_less_eq_nat @ K2 @ ( finite_card_int @ A4 ) )
% 5.31/5.62 => ( ( finite_card_list_int
% 5.31/5.62 @ ( collect_list_int
% 5.31/5.62 @ ^ [Xs: list_int] :
% 5.31/5.62 ( ( ( size_size_list_int @ Xs )
% 5.31/5.62 = K2 )
% 5.31/5.62 & ( distinct_int @ Xs )
% 5.31/5.62 & ( ord_less_eq_set_int @ ( set_int2 @ Xs ) @ A4 ) ) ) )
% 5.31/5.62 = ( groups708209901874060359at_nat
% 5.31/5.62 @ ^ [X4: nat] : X4
% 5.31/5.62 @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ ( minus_minus_nat @ ( finite_card_int @ A4 ) @ K2 ) @ one_one_nat ) @ ( finite_card_int @ A4 ) ) ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % card_lists_distinct_length_eq
% 5.31/5.62 thf(fact_6623_card__lists__distinct__length__eq,axiom,
% 5.31/5.62 ! [A4: set_nat,K2: nat] :
% 5.31/5.62 ( ( finite_finite_nat @ A4 )
% 5.31/5.62 => ( ( ord_less_eq_nat @ K2 @ ( finite_card_nat @ A4 ) )
% 5.31/5.62 => ( ( finite_card_list_nat
% 5.31/5.62 @ ( collect_list_nat
% 5.31/5.62 @ ^ [Xs: list_nat] :
% 5.31/5.62 ( ( ( size_size_list_nat @ Xs )
% 5.31/5.62 = K2 )
% 5.31/5.62 & ( distinct_nat @ Xs )
% 5.31/5.62 & ( ord_less_eq_set_nat @ ( set_nat2 @ Xs ) @ A4 ) ) ) )
% 5.31/5.62 = ( groups708209901874060359at_nat
% 5.31/5.62 @ ^ [X4: nat] : X4
% 5.31/5.62 @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ ( minus_minus_nat @ ( finite_card_nat @ A4 ) @ K2 ) @ one_one_nat ) @ ( finite_card_nat @ A4 ) ) ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % card_lists_distinct_length_eq
% 5.31/5.62 thf(fact_6624_gchoose__row__sum__weighted,axiom,
% 5.31/5.62 ! [R3: complex,M2: nat] :
% 5.31/5.62 ( ( groups2073611262835488442omplex
% 5.31/5.62 @ ^ [K3: nat] : ( times_times_complex @ ( gbinomial_complex @ R3 @ K3 ) @ ( minus_minus_complex @ ( divide1717551699836669952omplex @ R3 @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) @ ( semiri8010041392384452111omplex @ K3 ) ) )
% 5.31/5.62 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ M2 ) )
% 5.31/5.62 = ( times_times_complex @ ( divide1717551699836669952omplex @ ( semiri8010041392384452111omplex @ ( suc @ M2 ) ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) @ ( gbinomial_complex @ R3 @ ( suc @ M2 ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % gchoose_row_sum_weighted
% 5.31/5.62 thf(fact_6625_gchoose__row__sum__weighted,axiom,
% 5.31/5.62 ! [R3: rat,M2: nat] :
% 5.31/5.62 ( ( groups2906978787729119204at_rat
% 5.31/5.62 @ ^ [K3: nat] : ( times_times_rat @ ( gbinomial_rat @ R3 @ K3 ) @ ( minus_minus_rat @ ( divide_divide_rat @ R3 @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) @ ( semiri681578069525770553at_rat @ K3 ) ) )
% 5.31/5.62 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ M2 ) )
% 5.31/5.62 = ( times_times_rat @ ( divide_divide_rat @ ( semiri681578069525770553at_rat @ ( suc @ M2 ) ) @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) @ ( gbinomial_rat @ R3 @ ( suc @ M2 ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % gchoose_row_sum_weighted
% 5.31/5.62 thf(fact_6626_gchoose__row__sum__weighted,axiom,
% 5.31/5.62 ! [R3: real,M2: nat] :
% 5.31/5.62 ( ( groups6591440286371151544t_real
% 5.31/5.62 @ ^ [K3: nat] : ( times_times_real @ ( gbinomial_real @ R3 @ K3 ) @ ( minus_minus_real @ ( divide_divide_real @ R3 @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ K3 ) ) )
% 5.31/5.62 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ M2 ) )
% 5.31/5.62 = ( times_times_real @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ ( suc @ M2 ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( gbinomial_real @ R3 @ ( suc @ M2 ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % gchoose_row_sum_weighted
% 5.31/5.62 thf(fact_6627_vebt__buildup_Opelims,axiom,
% 5.31/5.62 ! [X: nat,Y: vEBT_VEBT] :
% 5.31/5.62 ( ( ( vEBT_vebt_buildup @ X )
% 5.31/5.62 = Y )
% 5.31/5.62 => ( ( accp_nat @ vEBT_v4011308405150292612up_rel @ X )
% 5.31/5.62 => ( ( ( X = zero_zero_nat )
% 5.31/5.62 => ( ( Y
% 5.31/5.62 = ( vEBT_Leaf @ $false @ $false ) )
% 5.31/5.62 => ~ ( accp_nat @ vEBT_v4011308405150292612up_rel @ zero_zero_nat ) ) )
% 5.31/5.62 => ( ( ( X
% 5.31/5.62 = ( suc @ zero_zero_nat ) )
% 5.31/5.62 => ( ( Y
% 5.31/5.62 = ( vEBT_Leaf @ $false @ $false ) )
% 5.31/5.62 => ~ ( accp_nat @ vEBT_v4011308405150292612up_rel @ ( suc @ zero_zero_nat ) ) ) )
% 5.31/5.62 => ~ ! [Va: nat] :
% 5.31/5.62 ( ( X
% 5.31/5.62 = ( suc @ ( suc @ Va ) ) )
% 5.31/5.62 => ( ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va ) ) )
% 5.31/5.62 => ( Y
% 5.31/5.62 = ( 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 ) ) ) ) ) ) )
% 5.31/5.62 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va ) ) )
% 5.31/5.62 => ( Y
% 5.31/5.62 = ( 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 ) ) ) ) ) ) ) ) )
% 5.31/5.62 => ~ ( accp_nat @ vEBT_v4011308405150292612up_rel @ ( suc @ ( suc @ Va ) ) ) ) ) ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % vebt_buildup.pelims
% 5.31/5.62 thf(fact_6628_flip__bit__0,axiom,
% 5.31/5.62 ! [A: nat] :
% 5.31/5.62 ( ( bit_se2161824704523386999it_nat @ zero_zero_nat @ A )
% 5.31/5.62 = ( 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 ) ) ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % flip_bit_0
% 5.31/5.62 thf(fact_6629_flip__bit__0,axiom,
% 5.31/5.62 ! [A: int] :
% 5.31/5.62 ( ( bit_se2159334234014336723it_int @ zero_zero_nat @ A )
% 5.31/5.62 = ( 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 ) ) ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % flip_bit_0
% 5.31/5.62 thf(fact_6630_flip__bit__0,axiom,
% 5.31/5.62 ! [A: code_integer] :
% 5.31/5.62 ( ( bit_se1345352211410354436nteger @ zero_zero_nat @ A )
% 5.31/5.62 = ( plus_p5714425477246183910nteger @ ( zero_n356916108424825756nteger @ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % flip_bit_0
% 5.31/5.62 thf(fact_6631_atMost__eq__iff,axiom,
% 5.31/5.62 ! [X: nat,Y: nat] :
% 5.31/5.62 ( ( ( set_ord_atMost_nat @ X )
% 5.31/5.62 = ( set_ord_atMost_nat @ Y ) )
% 5.31/5.62 = ( X = Y ) ) ).
% 5.31/5.62
% 5.31/5.62 % atMost_eq_iff
% 5.31/5.62 thf(fact_6632_atMost__iff,axiom,
% 5.31/5.62 ! [I2: real,K2: real] :
% 5.31/5.62 ( ( member_real @ I2 @ ( set_ord_atMost_real @ K2 ) )
% 5.31/5.62 = ( ord_less_eq_real @ I2 @ K2 ) ) ).
% 5.31/5.62
% 5.31/5.62 % atMost_iff
% 5.31/5.62 thf(fact_6633_atMost__iff,axiom,
% 5.31/5.62 ! [I2: set_nat,K2: set_nat] :
% 5.31/5.62 ( ( member_set_nat @ I2 @ ( set_or4236626031148496127et_nat @ K2 ) )
% 5.31/5.62 = ( ord_less_eq_set_nat @ I2 @ K2 ) ) ).
% 5.31/5.62
% 5.31/5.62 % atMost_iff
% 5.31/5.62 thf(fact_6634_atMost__iff,axiom,
% 5.31/5.62 ! [I2: rat,K2: rat] :
% 5.31/5.62 ( ( member_rat @ I2 @ ( set_ord_atMost_rat @ K2 ) )
% 5.31/5.62 = ( ord_less_eq_rat @ I2 @ K2 ) ) ).
% 5.31/5.62
% 5.31/5.62 % atMost_iff
% 5.31/5.62 thf(fact_6635_atMost__iff,axiom,
% 5.31/5.62 ! [I2: num,K2: num] :
% 5.31/5.62 ( ( member_num @ I2 @ ( set_ord_atMost_num @ K2 ) )
% 5.31/5.62 = ( ord_less_eq_num @ I2 @ K2 ) ) ).
% 5.31/5.62
% 5.31/5.62 % atMost_iff
% 5.31/5.62 thf(fact_6636_atMost__iff,axiom,
% 5.31/5.62 ! [I2: int,K2: int] :
% 5.31/5.62 ( ( member_int @ I2 @ ( set_ord_atMost_int @ K2 ) )
% 5.31/5.62 = ( ord_less_eq_int @ I2 @ K2 ) ) ).
% 5.31/5.62
% 5.31/5.62 % atMost_iff
% 5.31/5.62 thf(fact_6637_atMost__iff,axiom,
% 5.31/5.62 ! [I2: nat,K2: nat] :
% 5.31/5.62 ( ( member_nat @ I2 @ ( set_ord_atMost_nat @ K2 ) )
% 5.31/5.62 = ( ord_less_eq_nat @ I2 @ K2 ) ) ).
% 5.31/5.62
% 5.31/5.62 % atMost_iff
% 5.31/5.62 thf(fact_6638_of__bool__less__eq__iff,axiom,
% 5.31/5.62 ! [P2: $o,Q: $o] :
% 5.31/5.62 ( ( ord_less_eq_rat @ ( zero_n2052037380579107095ol_rat @ P2 ) @ ( zero_n2052037380579107095ol_rat @ Q ) )
% 5.31/5.62 = ( P2
% 5.31/5.62 => Q ) ) ).
% 5.31/5.62
% 5.31/5.62 % of_bool_less_eq_iff
% 5.31/5.62 thf(fact_6639_of__bool__less__eq__iff,axiom,
% 5.31/5.62 ! [P2: $o,Q: $o] :
% 5.31/5.62 ( ( ord_less_eq_nat @ ( zero_n2687167440665602831ol_nat @ P2 ) @ ( zero_n2687167440665602831ol_nat @ Q ) )
% 5.31/5.62 = ( P2
% 5.31/5.62 => Q ) ) ).
% 5.31/5.62
% 5.31/5.62 % of_bool_less_eq_iff
% 5.31/5.62 thf(fact_6640_of__bool__less__eq__iff,axiom,
% 5.31/5.62 ! [P2: $o,Q: $o] :
% 5.31/5.62 ( ( ord_less_eq_int @ ( zero_n2684676970156552555ol_int @ P2 ) @ ( zero_n2684676970156552555ol_int @ Q ) )
% 5.31/5.62 = ( P2
% 5.31/5.62 => Q ) ) ).
% 5.31/5.62
% 5.31/5.62 % of_bool_less_eq_iff
% 5.31/5.62 thf(fact_6641_of__bool__less__eq__iff,axiom,
% 5.31/5.62 ! [P2: $o,Q: $o] :
% 5.31/5.62 ( ( ord_le3102999989581377725nteger @ ( zero_n356916108424825756nteger @ P2 ) @ ( zero_n356916108424825756nteger @ Q ) )
% 5.31/5.62 = ( P2
% 5.31/5.62 => Q ) ) ).
% 5.31/5.62
% 5.31/5.62 % of_bool_less_eq_iff
% 5.31/5.62 thf(fact_6642_of__bool__eq_I1_J,axiom,
% 5.31/5.62 ( ( zero_n1201886186963655149omplex @ $false )
% 5.31/5.62 = zero_zero_complex ) ).
% 5.31/5.62
% 5.31/5.62 % of_bool_eq(1)
% 5.31/5.62 thf(fact_6643_of__bool__eq_I1_J,axiom,
% 5.31/5.62 ( ( zero_n3304061248610475627l_real @ $false )
% 5.31/5.62 = zero_zero_real ) ).
% 5.31/5.62
% 5.31/5.62 % of_bool_eq(1)
% 5.31/5.62 thf(fact_6644_of__bool__eq_I1_J,axiom,
% 5.31/5.62 ( ( zero_n2052037380579107095ol_rat @ $false )
% 5.31/5.62 = zero_zero_rat ) ).
% 5.31/5.62
% 5.31/5.62 % of_bool_eq(1)
% 5.31/5.62 thf(fact_6645_of__bool__eq_I1_J,axiom,
% 5.31/5.62 ( ( zero_n2687167440665602831ol_nat @ $false )
% 5.31/5.62 = zero_zero_nat ) ).
% 5.31/5.62
% 5.31/5.62 % of_bool_eq(1)
% 5.31/5.62 thf(fact_6646_of__bool__eq_I1_J,axiom,
% 5.31/5.62 ( ( zero_n2684676970156552555ol_int @ $false )
% 5.31/5.62 = zero_zero_int ) ).
% 5.31/5.62
% 5.31/5.62 % of_bool_eq(1)
% 5.31/5.62 thf(fact_6647_of__bool__eq_I1_J,axiom,
% 5.31/5.62 ( ( zero_n356916108424825756nteger @ $false )
% 5.31/5.62 = zero_z3403309356797280102nteger ) ).
% 5.31/5.62
% 5.31/5.62 % of_bool_eq(1)
% 5.31/5.62 thf(fact_6648_of__bool__eq__0__iff,axiom,
% 5.31/5.62 ! [P2: $o] :
% 5.31/5.62 ( ( ( zero_n1201886186963655149omplex @ P2 )
% 5.31/5.62 = zero_zero_complex )
% 5.31/5.62 = ~ P2 ) ).
% 5.31/5.62
% 5.31/5.62 % of_bool_eq_0_iff
% 5.31/5.62 thf(fact_6649_of__bool__eq__0__iff,axiom,
% 5.31/5.62 ! [P2: $o] :
% 5.31/5.62 ( ( ( zero_n3304061248610475627l_real @ P2 )
% 5.31/5.62 = zero_zero_real )
% 5.31/5.62 = ~ P2 ) ).
% 5.31/5.62
% 5.31/5.62 % of_bool_eq_0_iff
% 5.31/5.62 thf(fact_6650_of__bool__eq__0__iff,axiom,
% 5.31/5.62 ! [P2: $o] :
% 5.31/5.62 ( ( ( zero_n2052037380579107095ol_rat @ P2 )
% 5.31/5.62 = zero_zero_rat )
% 5.31/5.62 = ~ P2 ) ).
% 5.31/5.62
% 5.31/5.62 % of_bool_eq_0_iff
% 5.31/5.62 thf(fact_6651_of__bool__eq__0__iff,axiom,
% 5.31/5.62 ! [P2: $o] :
% 5.31/5.62 ( ( ( zero_n2687167440665602831ol_nat @ P2 )
% 5.31/5.62 = zero_zero_nat )
% 5.31/5.62 = ~ P2 ) ).
% 5.31/5.62
% 5.31/5.62 % of_bool_eq_0_iff
% 5.31/5.62 thf(fact_6652_of__bool__eq__0__iff,axiom,
% 5.31/5.62 ! [P2: $o] :
% 5.31/5.62 ( ( ( zero_n2684676970156552555ol_int @ P2 )
% 5.31/5.62 = zero_zero_int )
% 5.31/5.62 = ~ P2 ) ).
% 5.31/5.62
% 5.31/5.62 % of_bool_eq_0_iff
% 5.31/5.62 thf(fact_6653_of__bool__eq__0__iff,axiom,
% 5.31/5.62 ! [P2: $o] :
% 5.31/5.62 ( ( ( zero_n356916108424825756nteger @ P2 )
% 5.31/5.62 = zero_z3403309356797280102nteger )
% 5.31/5.62 = ~ P2 ) ).
% 5.31/5.62
% 5.31/5.62 % of_bool_eq_0_iff
% 5.31/5.62 thf(fact_6654_of__bool__less__iff,axiom,
% 5.31/5.62 ! [P2: $o,Q: $o] :
% 5.31/5.62 ( ( ord_less_real @ ( zero_n3304061248610475627l_real @ P2 ) @ ( zero_n3304061248610475627l_real @ Q ) )
% 5.31/5.62 = ( ~ P2
% 5.31/5.62 & Q ) ) ).
% 5.31/5.62
% 5.31/5.62 % of_bool_less_iff
% 5.31/5.62 thf(fact_6655_of__bool__less__iff,axiom,
% 5.31/5.62 ! [P2: $o,Q: $o] :
% 5.31/5.62 ( ( ord_less_rat @ ( zero_n2052037380579107095ol_rat @ P2 ) @ ( zero_n2052037380579107095ol_rat @ Q ) )
% 5.31/5.62 = ( ~ P2
% 5.31/5.62 & Q ) ) ).
% 5.31/5.62
% 5.31/5.62 % of_bool_less_iff
% 5.31/5.62 thf(fact_6656_of__bool__less__iff,axiom,
% 5.31/5.62 ! [P2: $o,Q: $o] :
% 5.31/5.62 ( ( ord_less_nat @ ( zero_n2687167440665602831ol_nat @ P2 ) @ ( zero_n2687167440665602831ol_nat @ Q ) )
% 5.31/5.62 = ( ~ P2
% 5.31/5.62 & Q ) ) ).
% 5.31/5.62
% 5.31/5.62 % of_bool_less_iff
% 5.31/5.62 thf(fact_6657_of__bool__less__iff,axiom,
% 5.31/5.62 ! [P2: $o,Q: $o] :
% 5.31/5.62 ( ( ord_less_int @ ( zero_n2684676970156552555ol_int @ P2 ) @ ( zero_n2684676970156552555ol_int @ Q ) )
% 5.31/5.62 = ( ~ P2
% 5.31/5.62 & Q ) ) ).
% 5.31/5.62
% 5.31/5.62 % of_bool_less_iff
% 5.31/5.62 thf(fact_6658_of__bool__less__iff,axiom,
% 5.31/5.62 ! [P2: $o,Q: $o] :
% 5.31/5.62 ( ( ord_le6747313008572928689nteger @ ( zero_n356916108424825756nteger @ P2 ) @ ( zero_n356916108424825756nteger @ Q ) )
% 5.31/5.62 = ( ~ P2
% 5.31/5.62 & Q ) ) ).
% 5.31/5.62
% 5.31/5.62 % of_bool_less_iff
% 5.31/5.62 thf(fact_6659_of__bool__eq__1__iff,axiom,
% 5.31/5.62 ! [P2: $o] :
% 5.31/5.62 ( ( ( zero_n1201886186963655149omplex @ P2 )
% 5.31/5.62 = one_one_complex )
% 5.31/5.62 = P2 ) ).
% 5.31/5.62
% 5.31/5.62 % of_bool_eq_1_iff
% 5.31/5.62 thf(fact_6660_of__bool__eq__1__iff,axiom,
% 5.31/5.62 ! [P2: $o] :
% 5.31/5.62 ( ( ( zero_n3304061248610475627l_real @ P2 )
% 5.31/5.62 = one_one_real )
% 5.31/5.62 = P2 ) ).
% 5.31/5.62
% 5.31/5.62 % of_bool_eq_1_iff
% 5.31/5.62 thf(fact_6661_of__bool__eq__1__iff,axiom,
% 5.31/5.62 ! [P2: $o] :
% 5.31/5.62 ( ( ( zero_n2687167440665602831ol_nat @ P2 )
% 5.31/5.62 = one_one_nat )
% 5.31/5.62 = P2 ) ).
% 5.31/5.62
% 5.31/5.62 % of_bool_eq_1_iff
% 5.31/5.62 thf(fact_6662_of__bool__eq__1__iff,axiom,
% 5.31/5.62 ! [P2: $o] :
% 5.31/5.62 ( ( ( zero_n2684676970156552555ol_int @ P2 )
% 5.31/5.62 = one_one_int )
% 5.31/5.62 = P2 ) ).
% 5.31/5.62
% 5.31/5.62 % of_bool_eq_1_iff
% 5.31/5.62 thf(fact_6663_of__bool__eq__1__iff,axiom,
% 5.31/5.62 ! [P2: $o] :
% 5.31/5.62 ( ( ( zero_n356916108424825756nteger @ P2 )
% 5.31/5.62 = one_one_Code_integer )
% 5.31/5.62 = P2 ) ).
% 5.31/5.62
% 5.31/5.62 % of_bool_eq_1_iff
% 5.31/5.62 thf(fact_6664_of__bool__eq_I2_J,axiom,
% 5.31/5.62 ( ( zero_n1201886186963655149omplex @ $true )
% 5.31/5.62 = one_one_complex ) ).
% 5.31/5.62
% 5.31/5.62 % of_bool_eq(2)
% 5.31/5.62 thf(fact_6665_of__bool__eq_I2_J,axiom,
% 5.31/5.62 ( ( zero_n3304061248610475627l_real @ $true )
% 5.31/5.62 = one_one_real ) ).
% 5.31/5.62
% 5.31/5.62 % of_bool_eq(2)
% 5.31/5.62 thf(fact_6666_of__bool__eq_I2_J,axiom,
% 5.31/5.62 ( ( zero_n2687167440665602831ol_nat @ $true )
% 5.31/5.62 = one_one_nat ) ).
% 5.31/5.62
% 5.31/5.62 % of_bool_eq(2)
% 5.31/5.62 thf(fact_6667_of__bool__eq_I2_J,axiom,
% 5.31/5.62 ( ( zero_n2684676970156552555ol_int @ $true )
% 5.31/5.62 = one_one_int ) ).
% 5.31/5.62
% 5.31/5.62 % of_bool_eq(2)
% 5.31/5.62 thf(fact_6668_of__bool__eq_I2_J,axiom,
% 5.31/5.62 ( ( zero_n356916108424825756nteger @ $true )
% 5.31/5.62 = one_one_Code_integer ) ).
% 5.31/5.62
% 5.31/5.62 % of_bool_eq(2)
% 5.31/5.62 thf(fact_6669_of__nat__of__bool,axiom,
% 5.31/5.62 ! [P2: $o] :
% 5.31/5.62 ( ( semiri5074537144036343181t_real @ ( zero_n2687167440665602831ol_nat @ P2 ) )
% 5.31/5.62 = ( zero_n3304061248610475627l_real @ P2 ) ) ).
% 5.31/5.62
% 5.31/5.62 % of_nat_of_bool
% 5.31/5.62 thf(fact_6670_of__nat__of__bool,axiom,
% 5.31/5.62 ! [P2: $o] :
% 5.31/5.62 ( ( semiri1316708129612266289at_nat @ ( zero_n2687167440665602831ol_nat @ P2 ) )
% 5.31/5.62 = ( zero_n2687167440665602831ol_nat @ P2 ) ) ).
% 5.31/5.62
% 5.31/5.62 % of_nat_of_bool
% 5.31/5.62 thf(fact_6671_of__nat__of__bool,axiom,
% 5.31/5.62 ! [P2: $o] :
% 5.31/5.62 ( ( semiri1314217659103216013at_int @ ( zero_n2687167440665602831ol_nat @ P2 ) )
% 5.31/5.62 = ( zero_n2684676970156552555ol_int @ P2 ) ) ).
% 5.31/5.62
% 5.31/5.62 % of_nat_of_bool
% 5.31/5.62 thf(fact_6672_of__nat__of__bool,axiom,
% 5.31/5.62 ! [P2: $o] :
% 5.31/5.62 ( ( semiri4939895301339042750nteger @ ( zero_n2687167440665602831ol_nat @ P2 ) )
% 5.31/5.62 = ( zero_n356916108424825756nteger @ P2 ) ) ).
% 5.31/5.62
% 5.31/5.62 % of_nat_of_bool
% 5.31/5.62 thf(fact_6673_of__bool__or__iff,axiom,
% 5.31/5.62 ! [P2: $o,Q: $o] :
% 5.31/5.62 ( ( zero_n2687167440665602831ol_nat
% 5.31/5.62 @ ( P2
% 5.31/5.62 | Q ) )
% 5.31/5.62 = ( ord_max_nat @ ( zero_n2687167440665602831ol_nat @ P2 ) @ ( zero_n2687167440665602831ol_nat @ Q ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % of_bool_or_iff
% 5.31/5.62 thf(fact_6674_of__bool__or__iff,axiom,
% 5.31/5.62 ! [P2: $o,Q: $o] :
% 5.31/5.62 ( ( zero_n2684676970156552555ol_int
% 5.31/5.62 @ ( P2
% 5.31/5.62 | Q ) )
% 5.31/5.62 = ( ord_max_int @ ( zero_n2684676970156552555ol_int @ P2 ) @ ( zero_n2684676970156552555ol_int @ Q ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % of_bool_or_iff
% 5.31/5.62 thf(fact_6675_of__bool__or__iff,axiom,
% 5.31/5.62 ! [P2: $o,Q: $o] :
% 5.31/5.62 ( ( zero_n356916108424825756nteger
% 5.31/5.62 @ ( P2
% 5.31/5.62 | Q ) )
% 5.31/5.62 = ( ord_max_Code_integer @ ( zero_n356916108424825756nteger @ P2 ) @ ( zero_n356916108424825756nteger @ Q ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % of_bool_or_iff
% 5.31/5.62 thf(fact_6676_finite__atMost,axiom,
% 5.31/5.62 ! [K2: nat] : ( finite_finite_nat @ ( set_ord_atMost_nat @ K2 ) ) ).
% 5.31/5.62
% 5.31/5.62 % finite_atMost
% 5.31/5.62 thf(fact_6677_zero__less__of__bool__iff,axiom,
% 5.31/5.62 ! [P2: $o] :
% 5.31/5.62 ( ( ord_less_real @ zero_zero_real @ ( zero_n3304061248610475627l_real @ P2 ) )
% 5.31/5.62 = P2 ) ).
% 5.31/5.62
% 5.31/5.62 % zero_less_of_bool_iff
% 5.31/5.62 thf(fact_6678_zero__less__of__bool__iff,axiom,
% 5.31/5.62 ! [P2: $o] :
% 5.31/5.62 ( ( ord_less_rat @ zero_zero_rat @ ( zero_n2052037380579107095ol_rat @ P2 ) )
% 5.31/5.62 = P2 ) ).
% 5.31/5.62
% 5.31/5.62 % zero_less_of_bool_iff
% 5.31/5.62 thf(fact_6679_zero__less__of__bool__iff,axiom,
% 5.31/5.62 ! [P2: $o] :
% 5.31/5.62 ( ( ord_less_nat @ zero_zero_nat @ ( zero_n2687167440665602831ol_nat @ P2 ) )
% 5.31/5.62 = P2 ) ).
% 5.31/5.62
% 5.31/5.62 % zero_less_of_bool_iff
% 5.31/5.62 thf(fact_6680_zero__less__of__bool__iff,axiom,
% 5.31/5.62 ! [P2: $o] :
% 5.31/5.62 ( ( ord_less_int @ zero_zero_int @ ( zero_n2684676970156552555ol_int @ P2 ) )
% 5.31/5.62 = P2 ) ).
% 5.31/5.62
% 5.31/5.62 % zero_less_of_bool_iff
% 5.31/5.62 thf(fact_6681_zero__less__of__bool__iff,axiom,
% 5.31/5.62 ! [P2: $o] :
% 5.31/5.62 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( zero_n356916108424825756nteger @ P2 ) )
% 5.31/5.62 = P2 ) ).
% 5.31/5.62
% 5.31/5.62 % zero_less_of_bool_iff
% 5.31/5.62 thf(fact_6682_atMost__subset__iff,axiom,
% 5.31/5.62 ! [X: set_nat,Y: set_nat] :
% 5.31/5.62 ( ( ord_le6893508408891458716et_nat @ ( set_or4236626031148496127et_nat @ X ) @ ( set_or4236626031148496127et_nat @ Y ) )
% 5.31/5.62 = ( ord_less_eq_set_nat @ X @ Y ) ) ).
% 5.31/5.62
% 5.31/5.62 % atMost_subset_iff
% 5.31/5.62 thf(fact_6683_atMost__subset__iff,axiom,
% 5.31/5.62 ! [X: rat,Y: rat] :
% 5.31/5.62 ( ( ord_less_eq_set_rat @ ( set_ord_atMost_rat @ X ) @ ( set_ord_atMost_rat @ Y ) )
% 5.31/5.62 = ( ord_less_eq_rat @ X @ Y ) ) ).
% 5.31/5.62
% 5.31/5.62 % atMost_subset_iff
% 5.31/5.62 thf(fact_6684_atMost__subset__iff,axiom,
% 5.31/5.62 ! [X: num,Y: num] :
% 5.31/5.62 ( ( ord_less_eq_set_num @ ( set_ord_atMost_num @ X ) @ ( set_ord_atMost_num @ Y ) )
% 5.31/5.62 = ( ord_less_eq_num @ X @ Y ) ) ).
% 5.31/5.62
% 5.31/5.62 % atMost_subset_iff
% 5.31/5.62 thf(fact_6685_atMost__subset__iff,axiom,
% 5.31/5.62 ! [X: int,Y: int] :
% 5.31/5.62 ( ( ord_less_eq_set_int @ ( set_ord_atMost_int @ X ) @ ( set_ord_atMost_int @ Y ) )
% 5.31/5.62 = ( ord_less_eq_int @ X @ Y ) ) ).
% 5.31/5.62
% 5.31/5.62 % atMost_subset_iff
% 5.31/5.62 thf(fact_6686_atMost__subset__iff,axiom,
% 5.31/5.62 ! [X: nat,Y: nat] :
% 5.31/5.62 ( ( ord_less_eq_set_nat @ ( set_ord_atMost_nat @ X ) @ ( set_ord_atMost_nat @ Y ) )
% 5.31/5.62 = ( ord_less_eq_nat @ X @ Y ) ) ).
% 5.31/5.62
% 5.31/5.62 % atMost_subset_iff
% 5.31/5.62 thf(fact_6687_of__bool__less__one__iff,axiom,
% 5.31/5.62 ! [P2: $o] :
% 5.31/5.62 ( ( ord_less_real @ ( zero_n3304061248610475627l_real @ P2 ) @ one_one_real )
% 5.31/5.62 = ~ P2 ) ).
% 5.31/5.62
% 5.31/5.62 % of_bool_less_one_iff
% 5.31/5.62 thf(fact_6688_of__bool__less__one__iff,axiom,
% 5.31/5.62 ! [P2: $o] :
% 5.31/5.62 ( ( ord_less_rat @ ( zero_n2052037380579107095ol_rat @ P2 ) @ one_one_rat )
% 5.31/5.62 = ~ P2 ) ).
% 5.31/5.62
% 5.31/5.62 % of_bool_less_one_iff
% 5.31/5.62 thf(fact_6689_of__bool__less__one__iff,axiom,
% 5.31/5.62 ! [P2: $o] :
% 5.31/5.62 ( ( ord_less_nat @ ( zero_n2687167440665602831ol_nat @ P2 ) @ one_one_nat )
% 5.31/5.62 = ~ P2 ) ).
% 5.31/5.62
% 5.31/5.62 % of_bool_less_one_iff
% 5.31/5.62 thf(fact_6690_of__bool__less__one__iff,axiom,
% 5.31/5.62 ! [P2: $o] :
% 5.31/5.62 ( ( ord_less_int @ ( zero_n2684676970156552555ol_int @ P2 ) @ one_one_int )
% 5.31/5.62 = ~ P2 ) ).
% 5.31/5.62
% 5.31/5.62 % of_bool_less_one_iff
% 5.31/5.62 thf(fact_6691_of__bool__less__one__iff,axiom,
% 5.31/5.62 ! [P2: $o] :
% 5.31/5.62 ( ( ord_le6747313008572928689nteger @ ( zero_n356916108424825756nteger @ P2 ) @ one_one_Code_integer )
% 5.31/5.62 = ~ P2 ) ).
% 5.31/5.62
% 5.31/5.62 % of_bool_less_one_iff
% 5.31/5.62 thf(fact_6692_of__bool__not__iff,axiom,
% 5.31/5.62 ! [P2: $o] :
% 5.31/5.62 ( ( zero_n1201886186963655149omplex @ ~ P2 )
% 5.31/5.62 = ( minus_minus_complex @ one_one_complex @ ( zero_n1201886186963655149omplex @ P2 ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % of_bool_not_iff
% 5.31/5.62 thf(fact_6693_of__bool__not__iff,axiom,
% 5.31/5.62 ! [P2: $o] :
% 5.31/5.62 ( ( zero_n3304061248610475627l_real @ ~ P2 )
% 5.31/5.62 = ( minus_minus_real @ one_one_real @ ( zero_n3304061248610475627l_real @ P2 ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % of_bool_not_iff
% 5.31/5.62 thf(fact_6694_of__bool__not__iff,axiom,
% 5.31/5.62 ! [P2: $o] :
% 5.31/5.62 ( ( zero_n2052037380579107095ol_rat @ ~ P2 )
% 5.31/5.62 = ( minus_minus_rat @ one_one_rat @ ( zero_n2052037380579107095ol_rat @ P2 ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % of_bool_not_iff
% 5.31/5.62 thf(fact_6695_of__bool__not__iff,axiom,
% 5.31/5.62 ! [P2: $o] :
% 5.31/5.62 ( ( zero_n2684676970156552555ol_int @ ~ P2 )
% 5.31/5.62 = ( minus_minus_int @ one_one_int @ ( zero_n2684676970156552555ol_int @ P2 ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % of_bool_not_iff
% 5.31/5.62 thf(fact_6696_of__bool__not__iff,axiom,
% 5.31/5.62 ! [P2: $o] :
% 5.31/5.62 ( ( zero_n356916108424825756nteger @ ~ P2 )
% 5.31/5.62 = ( minus_8373710615458151222nteger @ one_one_Code_integer @ ( zero_n356916108424825756nteger @ P2 ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % of_bool_not_iff
% 5.31/5.62 thf(fact_6697_Suc__0__mod__eq,axiom,
% 5.31/5.62 ! [N: nat] :
% 5.31/5.62 ( ( modulo_modulo_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.31/5.62 = ( zero_n2687167440665602831ol_nat
% 5.31/5.62 @ ( N
% 5.31/5.62 != ( suc @ zero_zero_nat ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % Suc_0_mod_eq
% 5.31/5.62 thf(fact_6698_gbinomial__0_I2_J,axiom,
% 5.31/5.62 ! [K2: nat] :
% 5.31/5.62 ( ( gbinomial_complex @ zero_zero_complex @ ( suc @ K2 ) )
% 5.31/5.62 = zero_zero_complex ) ).
% 5.31/5.62
% 5.31/5.62 % gbinomial_0(2)
% 5.31/5.62 thf(fact_6699_gbinomial__0_I2_J,axiom,
% 5.31/5.62 ! [K2: nat] :
% 5.31/5.62 ( ( gbinomial_real @ zero_zero_real @ ( suc @ K2 ) )
% 5.31/5.62 = zero_zero_real ) ).
% 5.31/5.62
% 5.31/5.62 % gbinomial_0(2)
% 5.31/5.62 thf(fact_6700_gbinomial__0_I2_J,axiom,
% 5.31/5.62 ! [K2: nat] :
% 5.31/5.62 ( ( gbinomial_rat @ zero_zero_rat @ ( suc @ K2 ) )
% 5.31/5.62 = zero_zero_rat ) ).
% 5.31/5.62
% 5.31/5.62 % gbinomial_0(2)
% 5.31/5.62 thf(fact_6701_gbinomial__0_I2_J,axiom,
% 5.31/5.62 ! [K2: nat] :
% 5.31/5.62 ( ( gbinomial_nat @ zero_zero_nat @ ( suc @ K2 ) )
% 5.31/5.62 = zero_zero_nat ) ).
% 5.31/5.62
% 5.31/5.62 % gbinomial_0(2)
% 5.31/5.62 thf(fact_6702_gbinomial__0_I2_J,axiom,
% 5.31/5.62 ! [K2: nat] :
% 5.31/5.62 ( ( gbinomial_int @ zero_zero_int @ ( suc @ K2 ) )
% 5.31/5.62 = zero_zero_int ) ).
% 5.31/5.62
% 5.31/5.62 % gbinomial_0(2)
% 5.31/5.62 thf(fact_6703_gbinomial__0_I1_J,axiom,
% 5.31/5.62 ! [A: code_integer] :
% 5.31/5.62 ( ( gbinom8545251970709558553nteger @ A @ zero_zero_nat )
% 5.31/5.62 = one_one_Code_integer ) ).
% 5.31/5.62
% 5.31/5.62 % gbinomial_0(1)
% 5.31/5.62 thf(fact_6704_gbinomial__0_I1_J,axiom,
% 5.31/5.62 ! [A: complex] :
% 5.31/5.62 ( ( gbinomial_complex @ A @ zero_zero_nat )
% 5.31/5.62 = one_one_complex ) ).
% 5.31/5.62
% 5.31/5.62 % gbinomial_0(1)
% 5.31/5.62 thf(fact_6705_gbinomial__0_I1_J,axiom,
% 5.31/5.62 ! [A: real] :
% 5.31/5.62 ( ( gbinomial_real @ A @ zero_zero_nat )
% 5.31/5.62 = one_one_real ) ).
% 5.31/5.62
% 5.31/5.62 % gbinomial_0(1)
% 5.31/5.62 thf(fact_6706_gbinomial__0_I1_J,axiom,
% 5.31/5.62 ! [A: nat] :
% 5.31/5.62 ( ( gbinomial_nat @ A @ zero_zero_nat )
% 5.31/5.62 = one_one_nat ) ).
% 5.31/5.62
% 5.31/5.62 % gbinomial_0(1)
% 5.31/5.62 thf(fact_6707_gbinomial__0_I1_J,axiom,
% 5.31/5.62 ! [A: int] :
% 5.31/5.62 ( ( gbinomial_int @ A @ zero_zero_nat )
% 5.31/5.62 = one_one_int ) ).
% 5.31/5.62
% 5.31/5.62 % gbinomial_0(1)
% 5.31/5.62 thf(fact_6708_card__atMost,axiom,
% 5.31/5.62 ! [U: nat] :
% 5.31/5.62 ( ( finite_card_nat @ ( set_ord_atMost_nat @ U ) )
% 5.31/5.62 = ( suc @ U ) ) ).
% 5.31/5.62
% 5.31/5.62 % card_atMost
% 5.31/5.62 thf(fact_6709_Icc__subset__Iic__iff,axiom,
% 5.31/5.62 ! [L: set_nat,H: set_nat,H3: set_nat] :
% 5.31/5.62 ( ( ord_le6893508408891458716et_nat @ ( set_or4548717258645045905et_nat @ L @ H ) @ ( set_or4236626031148496127et_nat @ H3 ) )
% 5.31/5.62 = ( ~ ( ord_less_eq_set_nat @ L @ H )
% 5.31/5.62 | ( ord_less_eq_set_nat @ H @ H3 ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % Icc_subset_Iic_iff
% 5.31/5.62 thf(fact_6710_Icc__subset__Iic__iff,axiom,
% 5.31/5.62 ! [L: rat,H: rat,H3: rat] :
% 5.31/5.62 ( ( ord_less_eq_set_rat @ ( set_or633870826150836451st_rat @ L @ H ) @ ( set_ord_atMost_rat @ H3 ) )
% 5.31/5.62 = ( ~ ( ord_less_eq_rat @ L @ H )
% 5.31/5.62 | ( ord_less_eq_rat @ H @ H3 ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % Icc_subset_Iic_iff
% 5.31/5.62 thf(fact_6711_Icc__subset__Iic__iff,axiom,
% 5.31/5.62 ! [L: num,H: num,H3: num] :
% 5.31/5.62 ( ( ord_less_eq_set_num @ ( set_or7049704709247886629st_num @ L @ H ) @ ( set_ord_atMost_num @ H3 ) )
% 5.31/5.62 = ( ~ ( ord_less_eq_num @ L @ H )
% 5.31/5.62 | ( ord_less_eq_num @ H @ H3 ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % Icc_subset_Iic_iff
% 5.31/5.62 thf(fact_6712_Icc__subset__Iic__iff,axiom,
% 5.31/5.62 ! [L: nat,H: nat,H3: nat] :
% 5.31/5.62 ( ( ord_less_eq_set_nat @ ( set_or1269000886237332187st_nat @ L @ H ) @ ( set_ord_atMost_nat @ H3 ) )
% 5.31/5.62 = ( ~ ( ord_less_eq_nat @ L @ H )
% 5.31/5.62 | ( ord_less_eq_nat @ H @ H3 ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % Icc_subset_Iic_iff
% 5.31/5.62 thf(fact_6713_Icc__subset__Iic__iff,axiom,
% 5.31/5.62 ! [L: int,H: int,H3: int] :
% 5.31/5.62 ( ( ord_less_eq_set_int @ ( set_or1266510415728281911st_int @ L @ H ) @ ( set_ord_atMost_int @ H3 ) )
% 5.31/5.62 = ( ~ ( ord_less_eq_int @ L @ H )
% 5.31/5.62 | ( ord_less_eq_int @ H @ H3 ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % Icc_subset_Iic_iff
% 5.31/5.62 thf(fact_6714_Icc__subset__Iic__iff,axiom,
% 5.31/5.62 ! [L: real,H: real,H3: real] :
% 5.31/5.62 ( ( ord_less_eq_set_real @ ( set_or1222579329274155063t_real @ L @ H ) @ ( set_ord_atMost_real @ H3 ) )
% 5.31/5.62 = ( ~ ( ord_less_eq_real @ L @ H )
% 5.31/5.62 | ( ord_less_eq_real @ H @ H3 ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % Icc_subset_Iic_iff
% 5.31/5.62 thf(fact_6715_sum_OatMost__Suc,axiom,
% 5.31/5.62 ! [G2: nat > rat,N: nat] :
% 5.31/5.62 ( ( groups2906978787729119204at_rat @ G2 @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 5.31/5.62 = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G2 @ ( set_ord_atMost_nat @ N ) ) @ ( G2 @ ( suc @ N ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % sum.atMost_Suc
% 5.31/5.62 thf(fact_6716_sum_OatMost__Suc,axiom,
% 5.31/5.62 ! [G2: nat > int,N: nat] :
% 5.31/5.62 ( ( groups3539618377306564664at_int @ G2 @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 5.31/5.62 = ( plus_plus_int @ ( groups3539618377306564664at_int @ G2 @ ( set_ord_atMost_nat @ N ) ) @ ( G2 @ ( suc @ N ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % sum.atMost_Suc
% 5.31/5.62 thf(fact_6717_sum_OatMost__Suc,axiom,
% 5.31/5.62 ! [G2: nat > nat,N: nat] :
% 5.31/5.62 ( ( groups3542108847815614940at_nat @ G2 @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 5.31/5.62 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G2 @ ( set_ord_atMost_nat @ N ) ) @ ( G2 @ ( suc @ N ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % sum.atMost_Suc
% 5.31/5.62 thf(fact_6718_sum_OatMost__Suc,axiom,
% 5.31/5.62 ! [G2: nat > real,N: nat] :
% 5.31/5.62 ( ( groups6591440286371151544t_real @ G2 @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 5.31/5.62 = ( plus_plus_real @ ( groups6591440286371151544t_real @ G2 @ ( set_ord_atMost_nat @ N ) ) @ ( G2 @ ( suc @ N ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % sum.atMost_Suc
% 5.31/5.62 thf(fact_6719_prod_OatMost__Suc,axiom,
% 5.31/5.62 ! [G2: nat > real,N: nat] :
% 5.31/5.62 ( ( groups129246275422532515t_real @ G2 @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 5.31/5.62 = ( times_times_real @ ( groups129246275422532515t_real @ G2 @ ( set_ord_atMost_nat @ N ) ) @ ( G2 @ ( suc @ N ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % prod.atMost_Suc
% 5.31/5.62 thf(fact_6720_prod_OatMost__Suc,axiom,
% 5.31/5.62 ! [G2: nat > rat,N: nat] :
% 5.31/5.62 ( ( groups73079841787564623at_rat @ G2 @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 5.31/5.62 = ( times_times_rat @ ( groups73079841787564623at_rat @ G2 @ ( set_ord_atMost_nat @ N ) ) @ ( G2 @ ( suc @ N ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % prod.atMost_Suc
% 5.31/5.62 thf(fact_6721_prod_OatMost__Suc,axiom,
% 5.31/5.62 ! [G2: nat > int,N: nat] :
% 5.31/5.62 ( ( groups705719431365010083at_int @ G2 @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 5.31/5.62 = ( times_times_int @ ( groups705719431365010083at_int @ G2 @ ( set_ord_atMost_nat @ N ) ) @ ( G2 @ ( suc @ N ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % prod.atMost_Suc
% 5.31/5.62 thf(fact_6722_prod_OatMost__Suc,axiom,
% 5.31/5.62 ! [G2: nat > nat,N: nat] :
% 5.31/5.62 ( ( groups708209901874060359at_nat @ G2 @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 5.31/5.62 = ( times_times_nat @ ( groups708209901874060359at_nat @ G2 @ ( set_ord_atMost_nat @ N ) ) @ ( G2 @ ( suc @ N ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % prod.atMost_Suc
% 5.31/5.62 thf(fact_6723_atMost__0,axiom,
% 5.31/5.62 ( ( set_ord_atMost_nat @ zero_zero_nat )
% 5.31/5.62 = ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ).
% 5.31/5.62
% 5.31/5.62 % atMost_0
% 5.31/5.62 thf(fact_6724_distinct__swap,axiom,
% 5.31/5.62 ! [I2: nat,Xs2: list_VEBT_VEBT,J2: nat] :
% 5.31/5.62 ( ( ord_less_nat @ I2 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 5.31/5.62 => ( ( ord_less_nat @ J2 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 5.31/5.62 => ( ( distinct_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs2 @ I2 @ ( nth_VEBT_VEBT @ Xs2 @ J2 ) ) @ J2 @ ( nth_VEBT_VEBT @ Xs2 @ I2 ) ) )
% 5.31/5.62 = ( distinct_VEBT_VEBT @ Xs2 ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % distinct_swap
% 5.31/5.62 thf(fact_6725_distinct__swap,axiom,
% 5.31/5.62 ! [I2: nat,Xs2: list_o,J2: nat] :
% 5.31/5.62 ( ( ord_less_nat @ I2 @ ( size_size_list_o @ Xs2 ) )
% 5.31/5.62 => ( ( ord_less_nat @ J2 @ ( size_size_list_o @ Xs2 ) )
% 5.31/5.62 => ( ( distinct_o @ ( list_update_o @ ( list_update_o @ Xs2 @ I2 @ ( nth_o @ Xs2 @ J2 ) ) @ J2 @ ( nth_o @ Xs2 @ I2 ) ) )
% 5.31/5.62 = ( distinct_o @ Xs2 ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % distinct_swap
% 5.31/5.62 thf(fact_6726_distinct__swap,axiom,
% 5.31/5.62 ! [I2: nat,Xs2: list_nat,J2: nat] :
% 5.31/5.62 ( ( ord_less_nat @ I2 @ ( size_size_list_nat @ Xs2 ) )
% 5.31/5.62 => ( ( ord_less_nat @ J2 @ ( size_size_list_nat @ Xs2 ) )
% 5.31/5.62 => ( ( distinct_nat @ ( list_update_nat @ ( list_update_nat @ Xs2 @ I2 @ ( nth_nat @ Xs2 @ J2 ) ) @ J2 @ ( nth_nat @ Xs2 @ I2 ) ) )
% 5.31/5.62 = ( distinct_nat @ Xs2 ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % distinct_swap
% 5.31/5.62 thf(fact_6727_distinct__swap,axiom,
% 5.31/5.62 ! [I2: nat,Xs2: list_int,J2: nat] :
% 5.31/5.62 ( ( ord_less_nat @ I2 @ ( size_size_list_int @ Xs2 ) )
% 5.31/5.62 => ( ( ord_less_nat @ J2 @ ( size_size_list_int @ Xs2 ) )
% 5.31/5.62 => ( ( distinct_int @ ( list_update_int @ ( list_update_int @ Xs2 @ I2 @ ( nth_int @ Xs2 @ J2 ) ) @ J2 @ ( nth_int @ Xs2 @ I2 ) ) )
% 5.31/5.62 = ( distinct_int @ Xs2 ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % distinct_swap
% 5.31/5.62 thf(fact_6728_sum__mult__of__bool__eq,axiom,
% 5.31/5.62 ! [A4: set_real,F2: real > real,P2: real > $o] :
% 5.31/5.62 ( ( finite_finite_real @ A4 )
% 5.31/5.62 => ( ( groups8097168146408367636l_real
% 5.31/5.62 @ ^ [X4: real] : ( times_times_real @ ( F2 @ X4 ) @ ( zero_n3304061248610475627l_real @ ( P2 @ X4 ) ) )
% 5.31/5.62 @ A4 )
% 5.31/5.62 = ( groups8097168146408367636l_real @ F2 @ ( inf_inf_set_real @ A4 @ ( collect_real @ P2 ) ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % sum_mult_of_bool_eq
% 5.31/5.62 thf(fact_6729_sum__mult__of__bool__eq,axiom,
% 5.31/5.62 ! [A4: set_int,F2: int > real,P2: int > $o] :
% 5.31/5.62 ( ( finite_finite_int @ A4 )
% 5.31/5.62 => ( ( groups8778361861064173332t_real
% 5.31/5.62 @ ^ [X4: int] : ( times_times_real @ ( F2 @ X4 ) @ ( zero_n3304061248610475627l_real @ ( P2 @ X4 ) ) )
% 5.31/5.62 @ A4 )
% 5.31/5.62 = ( groups8778361861064173332t_real @ F2 @ ( inf_inf_set_int @ A4 @ ( collect_int @ P2 ) ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % sum_mult_of_bool_eq
% 5.31/5.62 thf(fact_6730_sum__mult__of__bool__eq,axiom,
% 5.31/5.62 ! [A4: set_complex,F2: complex > real,P2: complex > $o] :
% 5.31/5.62 ( ( finite3207457112153483333omplex @ A4 )
% 5.31/5.62 => ( ( groups5808333547571424918x_real
% 5.31/5.62 @ ^ [X4: complex] : ( times_times_real @ ( F2 @ X4 ) @ ( zero_n3304061248610475627l_real @ ( P2 @ X4 ) ) )
% 5.31/5.62 @ A4 )
% 5.31/5.62 = ( groups5808333547571424918x_real @ F2 @ ( inf_inf_set_complex @ A4 @ ( collect_complex @ P2 ) ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % sum_mult_of_bool_eq
% 5.31/5.62 thf(fact_6731_sum__mult__of__bool__eq,axiom,
% 5.31/5.62 ! [A4: set_real,F2: real > rat,P2: real > $o] :
% 5.31/5.62 ( ( finite_finite_real @ A4 )
% 5.31/5.62 => ( ( groups1300246762558778688al_rat
% 5.31/5.62 @ ^ [X4: real] : ( times_times_rat @ ( F2 @ X4 ) @ ( zero_n2052037380579107095ol_rat @ ( P2 @ X4 ) ) )
% 5.31/5.62 @ A4 )
% 5.31/5.62 = ( groups1300246762558778688al_rat @ F2 @ ( inf_inf_set_real @ A4 @ ( collect_real @ P2 ) ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % sum_mult_of_bool_eq
% 5.31/5.62 thf(fact_6732_sum__mult__of__bool__eq,axiom,
% 5.31/5.62 ! [A4: set_int,F2: int > rat,P2: int > $o] :
% 5.31/5.62 ( ( finite_finite_int @ A4 )
% 5.31/5.62 => ( ( groups3906332499630173760nt_rat
% 5.31/5.62 @ ^ [X4: int] : ( times_times_rat @ ( F2 @ X4 ) @ ( zero_n2052037380579107095ol_rat @ ( P2 @ X4 ) ) )
% 5.31/5.62 @ A4 )
% 5.31/5.62 = ( groups3906332499630173760nt_rat @ F2 @ ( inf_inf_set_int @ A4 @ ( collect_int @ P2 ) ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % sum_mult_of_bool_eq
% 5.31/5.62 thf(fact_6733_sum__mult__of__bool__eq,axiom,
% 5.31/5.62 ! [A4: set_complex,F2: complex > rat,P2: complex > $o] :
% 5.31/5.62 ( ( finite3207457112153483333omplex @ A4 )
% 5.31/5.62 => ( ( groups5058264527183730370ex_rat
% 5.31/5.62 @ ^ [X4: complex] : ( times_times_rat @ ( F2 @ X4 ) @ ( zero_n2052037380579107095ol_rat @ ( P2 @ X4 ) ) )
% 5.31/5.62 @ A4 )
% 5.31/5.62 = ( groups5058264527183730370ex_rat @ F2 @ ( inf_inf_set_complex @ A4 @ ( collect_complex @ P2 ) ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % sum_mult_of_bool_eq
% 5.31/5.62 thf(fact_6734_sum__mult__of__bool__eq,axiom,
% 5.31/5.62 ! [A4: set_nat,F2: nat > rat,P2: nat > $o] :
% 5.31/5.62 ( ( finite_finite_nat @ A4 )
% 5.31/5.62 => ( ( groups2906978787729119204at_rat
% 5.31/5.62 @ ^ [X4: nat] : ( times_times_rat @ ( F2 @ X4 ) @ ( zero_n2052037380579107095ol_rat @ ( P2 @ X4 ) ) )
% 5.31/5.62 @ A4 )
% 5.31/5.62 = ( groups2906978787729119204at_rat @ F2 @ ( inf_inf_set_nat @ A4 @ ( collect_nat @ P2 ) ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % sum_mult_of_bool_eq
% 5.31/5.62 thf(fact_6735_sum__mult__of__bool__eq,axiom,
% 5.31/5.62 ! [A4: set_real,F2: real > nat,P2: real > $o] :
% 5.31/5.62 ( ( finite_finite_real @ A4 )
% 5.31/5.62 => ( ( groups1935376822645274424al_nat
% 5.31/5.62 @ ^ [X4: real] : ( times_times_nat @ ( F2 @ X4 ) @ ( zero_n2687167440665602831ol_nat @ ( P2 @ X4 ) ) )
% 5.31/5.62 @ A4 )
% 5.31/5.62 = ( groups1935376822645274424al_nat @ F2 @ ( inf_inf_set_real @ A4 @ ( collect_real @ P2 ) ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % sum_mult_of_bool_eq
% 5.31/5.62 thf(fact_6736_sum__mult__of__bool__eq,axiom,
% 5.31/5.62 ! [A4: set_int,F2: int > nat,P2: int > $o] :
% 5.31/5.62 ( ( finite_finite_int @ A4 )
% 5.31/5.62 => ( ( groups4541462559716669496nt_nat
% 5.31/5.62 @ ^ [X4: int] : ( times_times_nat @ ( F2 @ X4 ) @ ( zero_n2687167440665602831ol_nat @ ( P2 @ X4 ) ) )
% 5.31/5.62 @ A4 )
% 5.31/5.62 = ( groups4541462559716669496nt_nat @ F2 @ ( inf_inf_set_int @ A4 @ ( collect_int @ P2 ) ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % sum_mult_of_bool_eq
% 5.31/5.62 thf(fact_6737_sum__mult__of__bool__eq,axiom,
% 5.31/5.62 ! [A4: set_complex,F2: complex > nat,P2: complex > $o] :
% 5.31/5.62 ( ( finite3207457112153483333omplex @ A4 )
% 5.31/5.62 => ( ( groups5693394587270226106ex_nat
% 5.31/5.62 @ ^ [X4: complex] : ( times_times_nat @ ( F2 @ X4 ) @ ( zero_n2687167440665602831ol_nat @ ( P2 @ X4 ) ) )
% 5.31/5.62 @ A4 )
% 5.31/5.62 = ( groups5693394587270226106ex_nat @ F2 @ ( inf_inf_set_complex @ A4 @ ( collect_complex @ P2 ) ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % sum_mult_of_bool_eq
% 5.31/5.62 thf(fact_6738_sum__of__bool__mult__eq,axiom,
% 5.31/5.62 ! [A4: set_real,P2: real > $o,F2: real > real] :
% 5.31/5.62 ( ( finite_finite_real @ A4 )
% 5.31/5.62 => ( ( groups8097168146408367636l_real
% 5.31/5.62 @ ^ [X4: real] : ( times_times_real @ ( zero_n3304061248610475627l_real @ ( P2 @ X4 ) ) @ ( F2 @ X4 ) )
% 5.31/5.62 @ A4 )
% 5.31/5.62 = ( groups8097168146408367636l_real @ F2 @ ( inf_inf_set_real @ A4 @ ( collect_real @ P2 ) ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % sum_of_bool_mult_eq
% 5.31/5.62 thf(fact_6739_sum__of__bool__mult__eq,axiom,
% 5.31/5.62 ! [A4: set_int,P2: int > $o,F2: int > real] :
% 5.31/5.62 ( ( finite_finite_int @ A4 )
% 5.31/5.62 => ( ( groups8778361861064173332t_real
% 5.31/5.62 @ ^ [X4: int] : ( times_times_real @ ( zero_n3304061248610475627l_real @ ( P2 @ X4 ) ) @ ( F2 @ X4 ) )
% 5.31/5.62 @ A4 )
% 5.31/5.62 = ( groups8778361861064173332t_real @ F2 @ ( inf_inf_set_int @ A4 @ ( collect_int @ P2 ) ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % sum_of_bool_mult_eq
% 5.31/5.62 thf(fact_6740_sum__of__bool__mult__eq,axiom,
% 5.31/5.62 ! [A4: set_complex,P2: complex > $o,F2: complex > real] :
% 5.31/5.62 ( ( finite3207457112153483333omplex @ A4 )
% 5.31/5.62 => ( ( groups5808333547571424918x_real
% 5.31/5.62 @ ^ [X4: complex] : ( times_times_real @ ( zero_n3304061248610475627l_real @ ( P2 @ X4 ) ) @ ( F2 @ X4 ) )
% 5.31/5.62 @ A4 )
% 5.31/5.62 = ( groups5808333547571424918x_real @ F2 @ ( inf_inf_set_complex @ A4 @ ( collect_complex @ P2 ) ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % sum_of_bool_mult_eq
% 5.31/5.62 thf(fact_6741_sum__of__bool__mult__eq,axiom,
% 5.31/5.62 ! [A4: set_real,P2: real > $o,F2: real > rat] :
% 5.31/5.62 ( ( finite_finite_real @ A4 )
% 5.31/5.62 => ( ( groups1300246762558778688al_rat
% 5.31/5.62 @ ^ [X4: real] : ( times_times_rat @ ( zero_n2052037380579107095ol_rat @ ( P2 @ X4 ) ) @ ( F2 @ X4 ) )
% 5.31/5.62 @ A4 )
% 5.31/5.62 = ( groups1300246762558778688al_rat @ F2 @ ( inf_inf_set_real @ A4 @ ( collect_real @ P2 ) ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % sum_of_bool_mult_eq
% 5.31/5.62 thf(fact_6742_sum__of__bool__mult__eq,axiom,
% 5.31/5.62 ! [A4: set_int,P2: int > $o,F2: int > rat] :
% 5.31/5.62 ( ( finite_finite_int @ A4 )
% 5.31/5.62 => ( ( groups3906332499630173760nt_rat
% 5.31/5.62 @ ^ [X4: int] : ( times_times_rat @ ( zero_n2052037380579107095ol_rat @ ( P2 @ X4 ) ) @ ( F2 @ X4 ) )
% 5.31/5.62 @ A4 )
% 5.31/5.62 = ( groups3906332499630173760nt_rat @ F2 @ ( inf_inf_set_int @ A4 @ ( collect_int @ P2 ) ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % sum_of_bool_mult_eq
% 5.31/5.62 thf(fact_6743_sum__of__bool__mult__eq,axiom,
% 5.31/5.62 ! [A4: set_complex,P2: complex > $o,F2: complex > rat] :
% 5.31/5.62 ( ( finite3207457112153483333omplex @ A4 )
% 5.31/5.62 => ( ( groups5058264527183730370ex_rat
% 5.31/5.62 @ ^ [X4: complex] : ( times_times_rat @ ( zero_n2052037380579107095ol_rat @ ( P2 @ X4 ) ) @ ( F2 @ X4 ) )
% 5.31/5.62 @ A4 )
% 5.31/5.62 = ( groups5058264527183730370ex_rat @ F2 @ ( inf_inf_set_complex @ A4 @ ( collect_complex @ P2 ) ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % sum_of_bool_mult_eq
% 5.31/5.62 thf(fact_6744_sum__of__bool__mult__eq,axiom,
% 5.31/5.62 ! [A4: set_nat,P2: nat > $o,F2: nat > rat] :
% 5.31/5.62 ( ( finite_finite_nat @ A4 )
% 5.31/5.62 => ( ( groups2906978787729119204at_rat
% 5.31/5.62 @ ^ [X4: nat] : ( times_times_rat @ ( zero_n2052037380579107095ol_rat @ ( P2 @ X4 ) ) @ ( F2 @ X4 ) )
% 5.31/5.62 @ A4 )
% 5.31/5.62 = ( groups2906978787729119204at_rat @ F2 @ ( inf_inf_set_nat @ A4 @ ( collect_nat @ P2 ) ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % sum_of_bool_mult_eq
% 5.31/5.62 thf(fact_6745_sum__of__bool__mult__eq,axiom,
% 5.31/5.62 ! [A4: set_real,P2: real > $o,F2: real > nat] :
% 5.31/5.62 ( ( finite_finite_real @ A4 )
% 5.31/5.62 => ( ( groups1935376822645274424al_nat
% 5.31/5.62 @ ^ [X4: real] : ( times_times_nat @ ( zero_n2687167440665602831ol_nat @ ( P2 @ X4 ) ) @ ( F2 @ X4 ) )
% 5.31/5.62 @ A4 )
% 5.31/5.62 = ( groups1935376822645274424al_nat @ F2 @ ( inf_inf_set_real @ A4 @ ( collect_real @ P2 ) ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % sum_of_bool_mult_eq
% 5.31/5.62 thf(fact_6746_sum__of__bool__mult__eq,axiom,
% 5.31/5.62 ! [A4: set_int,P2: int > $o,F2: int > nat] :
% 5.31/5.62 ( ( finite_finite_int @ A4 )
% 5.31/5.62 => ( ( groups4541462559716669496nt_nat
% 5.31/5.62 @ ^ [X4: int] : ( times_times_nat @ ( zero_n2687167440665602831ol_nat @ ( P2 @ X4 ) ) @ ( F2 @ X4 ) )
% 5.31/5.62 @ A4 )
% 5.31/5.62 = ( groups4541462559716669496nt_nat @ F2 @ ( inf_inf_set_int @ A4 @ ( collect_int @ P2 ) ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % sum_of_bool_mult_eq
% 5.31/5.62 thf(fact_6747_sum__of__bool__mult__eq,axiom,
% 5.31/5.62 ! [A4: set_complex,P2: complex > $o,F2: complex > nat] :
% 5.31/5.62 ( ( finite3207457112153483333omplex @ A4 )
% 5.31/5.62 => ( ( groups5693394587270226106ex_nat
% 5.31/5.62 @ ^ [X4: complex] : ( times_times_nat @ ( zero_n2687167440665602831ol_nat @ ( P2 @ X4 ) ) @ ( F2 @ X4 ) )
% 5.31/5.62 @ A4 )
% 5.31/5.62 = ( groups5693394587270226106ex_nat @ F2 @ ( inf_inf_set_complex @ A4 @ ( collect_complex @ P2 ) ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % sum_of_bool_mult_eq
% 5.31/5.62 thf(fact_6748_of__bool__half__eq__0,axiom,
% 5.31/5.62 ! [B: $o] :
% 5.31/5.62 ( ( divide_divide_nat @ ( zero_n2687167440665602831ol_nat @ B ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.31/5.62 = zero_zero_nat ) ).
% 5.31/5.62
% 5.31/5.62 % of_bool_half_eq_0
% 5.31/5.62 thf(fact_6749_of__bool__half__eq__0,axiom,
% 5.31/5.62 ! [B: $o] :
% 5.31/5.62 ( ( divide_divide_int @ ( zero_n2684676970156552555ol_int @ B ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.31/5.62 = zero_zero_int ) ).
% 5.31/5.62
% 5.31/5.62 % of_bool_half_eq_0
% 5.31/5.62 thf(fact_6750_of__bool__half__eq__0,axiom,
% 5.31/5.62 ! [B: $o] :
% 5.31/5.62 ( ( divide6298287555418463151nteger @ ( zero_n356916108424825756nteger @ B ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.31/5.62 = zero_z3403309356797280102nteger ) ).
% 5.31/5.62
% 5.31/5.62 % of_bool_half_eq_0
% 5.31/5.62 thf(fact_6751_finite__lists__distinct__length__eq,axiom,
% 5.31/5.62 ! [A4: set_complex,N: nat] :
% 5.31/5.62 ( ( finite3207457112153483333omplex @ A4 )
% 5.31/5.62 => ( finite8712137658972009173omplex
% 5.31/5.62 @ ( collect_list_complex
% 5.31/5.62 @ ^ [Xs: list_complex] :
% 5.31/5.62 ( ( ( size_s3451745648224563538omplex @ Xs )
% 5.31/5.62 = N )
% 5.31/5.62 & ( distinct_complex @ Xs )
% 5.31/5.62 & ( ord_le211207098394363844omplex @ ( set_complex2 @ Xs ) @ A4 ) ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % finite_lists_distinct_length_eq
% 5.31/5.62 thf(fact_6752_finite__lists__distinct__length__eq,axiom,
% 5.31/5.62 ! [A4: set_VEBT_VEBT,N: nat] :
% 5.31/5.62 ( ( finite5795047828879050333T_VEBT @ A4 )
% 5.31/5.62 => ( finite3004134309566078307T_VEBT
% 5.31/5.62 @ ( collec5608196760682091941T_VEBT
% 5.31/5.62 @ ^ [Xs: list_VEBT_VEBT] :
% 5.31/5.62 ( ( ( size_s6755466524823107622T_VEBT @ Xs )
% 5.31/5.62 = N )
% 5.31/5.62 & ( distinct_VEBT_VEBT @ Xs )
% 5.31/5.62 & ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ Xs ) @ A4 ) ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % finite_lists_distinct_length_eq
% 5.31/5.62 thf(fact_6753_finite__lists__distinct__length__eq,axiom,
% 5.31/5.62 ! [A4: set_o,N: nat] :
% 5.31/5.62 ( ( finite_finite_o @ A4 )
% 5.31/5.62 => ( finite_finite_list_o
% 5.31/5.62 @ ( collect_list_o
% 5.31/5.62 @ ^ [Xs: list_o] :
% 5.31/5.62 ( ( ( size_size_list_o @ Xs )
% 5.31/5.62 = N )
% 5.31/5.62 & ( distinct_o @ Xs )
% 5.31/5.62 & ( ord_less_eq_set_o @ ( set_o2 @ Xs ) @ A4 ) ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % finite_lists_distinct_length_eq
% 5.31/5.62 thf(fact_6754_finite__lists__distinct__length__eq,axiom,
% 5.31/5.62 ! [A4: set_int,N: nat] :
% 5.31/5.62 ( ( finite_finite_int @ A4 )
% 5.31/5.62 => ( finite3922522038869484883st_int
% 5.31/5.62 @ ( collect_list_int
% 5.31/5.62 @ ^ [Xs: list_int] :
% 5.31/5.62 ( ( ( size_size_list_int @ Xs )
% 5.31/5.62 = N )
% 5.31/5.62 & ( distinct_int @ Xs )
% 5.31/5.62 & ( ord_less_eq_set_int @ ( set_int2 @ Xs ) @ A4 ) ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % finite_lists_distinct_length_eq
% 5.31/5.62 thf(fact_6755_finite__lists__distinct__length__eq,axiom,
% 5.31/5.62 ! [A4: set_nat,N: nat] :
% 5.31/5.62 ( ( finite_finite_nat @ A4 )
% 5.31/5.62 => ( finite8100373058378681591st_nat
% 5.31/5.62 @ ( collect_list_nat
% 5.31/5.62 @ ^ [Xs: list_nat] :
% 5.31/5.62 ( ( ( size_size_list_nat @ Xs )
% 5.31/5.62 = N )
% 5.31/5.62 & ( distinct_nat @ Xs )
% 5.31/5.62 & ( ord_less_eq_set_nat @ ( set_nat2 @ Xs ) @ A4 ) ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % finite_lists_distinct_length_eq
% 5.31/5.62 thf(fact_6756_one__div__2__pow__eq,axiom,
% 5.31/5.62 ! [N: nat] :
% 5.31/5.62 ( ( divide_divide_nat @ one_one_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.31/5.62 = ( zero_n2687167440665602831ol_nat @ ( N = zero_zero_nat ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % one_div_2_pow_eq
% 5.31/5.62 thf(fact_6757_one__div__2__pow__eq,axiom,
% 5.31/5.62 ! [N: nat] :
% 5.31/5.62 ( ( divide_divide_int @ one_one_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.31/5.62 = ( zero_n2684676970156552555ol_int @ ( N = zero_zero_nat ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % one_div_2_pow_eq
% 5.31/5.62 thf(fact_6758_one__div__2__pow__eq,axiom,
% 5.31/5.62 ! [N: nat] :
% 5.31/5.62 ( ( divide6298287555418463151nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 5.31/5.62 = ( zero_n356916108424825756nteger @ ( N = zero_zero_nat ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % one_div_2_pow_eq
% 5.31/5.62 thf(fact_6759_bits__1__div__exp,axiom,
% 5.31/5.62 ! [N: nat] :
% 5.31/5.62 ( ( divide_divide_nat @ one_one_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.31/5.62 = ( zero_n2687167440665602831ol_nat @ ( N = zero_zero_nat ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % bits_1_div_exp
% 5.31/5.62 thf(fact_6760_bits__1__div__exp,axiom,
% 5.31/5.62 ! [N: nat] :
% 5.31/5.62 ( ( divide_divide_int @ one_one_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.31/5.62 = ( zero_n2684676970156552555ol_int @ ( N = zero_zero_nat ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % bits_1_div_exp
% 5.31/5.62 thf(fact_6761_bits__1__div__exp,axiom,
% 5.31/5.62 ! [N: nat] :
% 5.31/5.62 ( ( divide6298287555418463151nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 5.31/5.62 = ( zero_n356916108424825756nteger @ ( N = zero_zero_nat ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % bits_1_div_exp
% 5.31/5.62 thf(fact_6762_one__mod__2__pow__eq,axiom,
% 5.31/5.62 ! [N: nat] :
% 5.31/5.62 ( ( modulo8411746178871703098atural @ one_one_Code_natural @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N ) )
% 5.31/5.62 = ( zero_n8403883297036319079atural @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % one_mod_2_pow_eq
% 5.31/5.62 thf(fact_6763_one__mod__2__pow__eq,axiom,
% 5.31/5.62 ! [N: nat] :
% 5.31/5.62 ( ( modulo_modulo_nat @ one_one_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.31/5.62 = ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % one_mod_2_pow_eq
% 5.31/5.62 thf(fact_6764_one__mod__2__pow__eq,axiom,
% 5.31/5.62 ! [N: nat] :
% 5.31/5.62 ( ( modulo_modulo_int @ one_one_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.31/5.62 = ( zero_n2684676970156552555ol_int @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % one_mod_2_pow_eq
% 5.31/5.62 thf(fact_6765_one__mod__2__pow__eq,axiom,
% 5.31/5.62 ! [N: nat] :
% 5.31/5.62 ( ( modulo364778990260209775nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 5.31/5.62 = ( zero_n356916108424825756nteger @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % one_mod_2_pow_eq
% 5.31/5.62 thf(fact_6766_of__bool__eq__iff,axiom,
% 5.31/5.62 ! [P: $o,Q2: $o] :
% 5.31/5.62 ( ( ( zero_n2687167440665602831ol_nat @ P )
% 5.31/5.62 = ( zero_n2687167440665602831ol_nat @ Q2 ) )
% 5.31/5.62 = ( P = Q2 ) ) ).
% 5.31/5.62
% 5.31/5.62 % of_bool_eq_iff
% 5.31/5.62 thf(fact_6767_of__bool__eq__iff,axiom,
% 5.31/5.62 ! [P: $o,Q2: $o] :
% 5.31/5.62 ( ( ( zero_n2684676970156552555ol_int @ P )
% 5.31/5.62 = ( zero_n2684676970156552555ol_int @ Q2 ) )
% 5.31/5.62 = ( P = Q2 ) ) ).
% 5.31/5.62
% 5.31/5.62 % of_bool_eq_iff
% 5.31/5.62 thf(fact_6768_of__bool__eq__iff,axiom,
% 5.31/5.62 ! [P: $o,Q2: $o] :
% 5.31/5.62 ( ( ( zero_n356916108424825756nteger @ P )
% 5.31/5.62 = ( zero_n356916108424825756nteger @ Q2 ) )
% 5.31/5.62 = ( P = Q2 ) ) ).
% 5.31/5.62
% 5.31/5.62 % of_bool_eq_iff
% 5.31/5.62 thf(fact_6769_of__bool__conj,axiom,
% 5.31/5.62 ! [P2: $o,Q: $o] :
% 5.31/5.62 ( ( zero_n3304061248610475627l_real
% 5.31/5.62 @ ( P2
% 5.31/5.62 & Q ) )
% 5.31/5.62 = ( times_times_real @ ( zero_n3304061248610475627l_real @ P2 ) @ ( zero_n3304061248610475627l_real @ Q ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % of_bool_conj
% 5.31/5.62 thf(fact_6770_of__bool__conj,axiom,
% 5.31/5.62 ! [P2: $o,Q: $o] :
% 5.31/5.62 ( ( zero_n2052037380579107095ol_rat
% 5.31/5.62 @ ( P2
% 5.31/5.62 & Q ) )
% 5.31/5.62 = ( times_times_rat @ ( zero_n2052037380579107095ol_rat @ P2 ) @ ( zero_n2052037380579107095ol_rat @ Q ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % of_bool_conj
% 5.31/5.62 thf(fact_6771_of__bool__conj,axiom,
% 5.31/5.62 ! [P2: $o,Q: $o] :
% 5.31/5.62 ( ( zero_n2687167440665602831ol_nat
% 5.31/5.62 @ ( P2
% 5.31/5.62 & Q ) )
% 5.31/5.62 = ( times_times_nat @ ( zero_n2687167440665602831ol_nat @ P2 ) @ ( zero_n2687167440665602831ol_nat @ Q ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % of_bool_conj
% 5.31/5.62 thf(fact_6772_of__bool__conj,axiom,
% 5.31/5.62 ! [P2: $o,Q: $o] :
% 5.31/5.62 ( ( zero_n2684676970156552555ol_int
% 5.31/5.62 @ ( P2
% 5.31/5.62 & Q ) )
% 5.31/5.62 = ( times_times_int @ ( zero_n2684676970156552555ol_int @ P2 ) @ ( zero_n2684676970156552555ol_int @ Q ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % of_bool_conj
% 5.31/5.62 thf(fact_6773_of__bool__conj,axiom,
% 5.31/5.62 ! [P2: $o,Q: $o] :
% 5.31/5.62 ( ( zero_n356916108424825756nteger
% 5.31/5.62 @ ( P2
% 5.31/5.62 & Q ) )
% 5.31/5.62 = ( times_3573771949741848930nteger @ ( zero_n356916108424825756nteger @ P2 ) @ ( zero_n356916108424825756nteger @ Q ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % of_bool_conj
% 5.31/5.62 thf(fact_6774_not__empty__eq__Iic__eq__empty,axiom,
% 5.31/5.62 ! [H: int] :
% 5.31/5.62 ( bot_bot_set_int
% 5.31/5.62 != ( set_ord_atMost_int @ H ) ) ).
% 5.31/5.62
% 5.31/5.62 % not_empty_eq_Iic_eq_empty
% 5.31/5.62 thf(fact_6775_not__empty__eq__Iic__eq__empty,axiom,
% 5.31/5.62 ! [H: real] :
% 5.31/5.62 ( bot_bot_set_real
% 5.31/5.62 != ( set_ord_atMost_real @ H ) ) ).
% 5.31/5.62
% 5.31/5.62 % not_empty_eq_Iic_eq_empty
% 5.31/5.62 thf(fact_6776_not__empty__eq__Iic__eq__empty,axiom,
% 5.31/5.62 ! [H: nat] :
% 5.31/5.62 ( bot_bot_set_nat
% 5.31/5.62 != ( set_ord_atMost_nat @ H ) ) ).
% 5.31/5.62
% 5.31/5.62 % not_empty_eq_Iic_eq_empty
% 5.31/5.62 thf(fact_6777_infinite__Iic,axiom,
% 5.31/5.62 ! [A: int] :
% 5.31/5.62 ~ ( finite_finite_int @ ( set_ord_atMost_int @ A ) ) ).
% 5.31/5.62
% 5.31/5.62 % infinite_Iic
% 5.31/5.62 thf(fact_6778_not__Iic__eq__Icc,axiom,
% 5.31/5.62 ! [H3: int,L: int,H: int] :
% 5.31/5.62 ( ( set_ord_atMost_int @ H3 )
% 5.31/5.62 != ( set_or1266510415728281911st_int @ L @ H ) ) ).
% 5.31/5.62
% 5.31/5.62 % not_Iic_eq_Icc
% 5.31/5.62 thf(fact_6779_not__Iic__eq__Icc,axiom,
% 5.31/5.62 ! [H3: real,L: real,H: real] :
% 5.31/5.62 ( ( set_ord_atMost_real @ H3 )
% 5.31/5.62 != ( set_or1222579329274155063t_real @ L @ H ) ) ).
% 5.31/5.62
% 5.31/5.62 % not_Iic_eq_Icc
% 5.31/5.62 thf(fact_6780_atMost__def,axiom,
% 5.31/5.62 ( set_ord_atMost_real
% 5.31/5.62 = ( ^ [U2: real] :
% 5.31/5.62 ( collect_real
% 5.31/5.62 @ ^ [X4: real] : ( ord_less_eq_real @ X4 @ U2 ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % atMost_def
% 5.31/5.62 thf(fact_6781_atMost__def,axiom,
% 5.31/5.62 ( set_or4236626031148496127et_nat
% 5.31/5.62 = ( ^ [U2: set_nat] :
% 5.31/5.62 ( collect_set_nat
% 5.31/5.62 @ ^ [X4: set_nat] : ( ord_less_eq_set_nat @ X4 @ U2 ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % atMost_def
% 5.31/5.62 thf(fact_6782_atMost__def,axiom,
% 5.31/5.62 ( set_ord_atMost_rat
% 5.31/5.62 = ( ^ [U2: rat] :
% 5.31/5.62 ( collect_rat
% 5.31/5.62 @ ^ [X4: rat] : ( ord_less_eq_rat @ X4 @ U2 ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % atMost_def
% 5.31/5.62 thf(fact_6783_atMost__def,axiom,
% 5.31/5.62 ( set_ord_atMost_num
% 5.31/5.62 = ( ^ [U2: num] :
% 5.31/5.62 ( collect_num
% 5.31/5.62 @ ^ [X4: num] : ( ord_less_eq_num @ X4 @ U2 ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % atMost_def
% 5.31/5.62 thf(fact_6784_atMost__def,axiom,
% 5.31/5.62 ( set_ord_atMost_int
% 5.31/5.62 = ( ^ [U2: int] :
% 5.31/5.62 ( collect_int
% 5.31/5.62 @ ^ [X4: int] : ( ord_less_eq_int @ X4 @ U2 ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % atMost_def
% 5.31/5.62 thf(fact_6785_atMost__def,axiom,
% 5.31/5.62 ( set_ord_atMost_nat
% 5.31/5.62 = ( ^ [U2: nat] :
% 5.31/5.62 ( collect_nat
% 5.31/5.62 @ ^ [X4: nat] : ( ord_less_eq_nat @ X4 @ U2 ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % atMost_def
% 5.31/5.62 thf(fact_6786_zero__less__eq__of__bool,axiom,
% 5.31/5.62 ! [P2: $o] : ( ord_less_eq_real @ zero_zero_real @ ( zero_n3304061248610475627l_real @ P2 ) ) ).
% 5.31/5.62
% 5.31/5.62 % zero_less_eq_of_bool
% 5.31/5.62 thf(fact_6787_zero__less__eq__of__bool,axiom,
% 5.31/5.62 ! [P2: $o] : ( ord_less_eq_rat @ zero_zero_rat @ ( zero_n2052037380579107095ol_rat @ P2 ) ) ).
% 5.31/5.62
% 5.31/5.62 % zero_less_eq_of_bool
% 5.31/5.62 thf(fact_6788_zero__less__eq__of__bool,axiom,
% 5.31/5.62 ! [P2: $o] : ( ord_less_eq_nat @ zero_zero_nat @ ( zero_n2687167440665602831ol_nat @ P2 ) ) ).
% 5.31/5.62
% 5.31/5.62 % zero_less_eq_of_bool
% 5.31/5.62 thf(fact_6789_zero__less__eq__of__bool,axiom,
% 5.31/5.62 ! [P2: $o] : ( ord_less_eq_int @ zero_zero_int @ ( zero_n2684676970156552555ol_int @ P2 ) ) ).
% 5.31/5.62
% 5.31/5.62 % zero_less_eq_of_bool
% 5.31/5.62 thf(fact_6790_zero__less__eq__of__bool,axiom,
% 5.31/5.62 ! [P2: $o] : ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( zero_n356916108424825756nteger @ P2 ) ) ).
% 5.31/5.62
% 5.31/5.62 % zero_less_eq_of_bool
% 5.31/5.62 thf(fact_6791_of__bool__less__eq__one,axiom,
% 5.31/5.62 ! [P2: $o] : ( ord_less_eq_real @ ( zero_n3304061248610475627l_real @ P2 ) @ one_one_real ) ).
% 5.31/5.62
% 5.31/5.62 % of_bool_less_eq_one
% 5.31/5.62 thf(fact_6792_of__bool__less__eq__one,axiom,
% 5.31/5.62 ! [P2: $o] : ( ord_less_eq_rat @ ( zero_n2052037380579107095ol_rat @ P2 ) @ one_one_rat ) ).
% 5.31/5.62
% 5.31/5.62 % of_bool_less_eq_one
% 5.31/5.62 thf(fact_6793_of__bool__less__eq__one,axiom,
% 5.31/5.62 ! [P2: $o] : ( ord_less_eq_nat @ ( zero_n2687167440665602831ol_nat @ P2 ) @ one_one_nat ) ).
% 5.31/5.62
% 5.31/5.62 % of_bool_less_eq_one
% 5.31/5.62 thf(fact_6794_of__bool__less__eq__one,axiom,
% 5.31/5.62 ! [P2: $o] : ( ord_less_eq_int @ ( zero_n2684676970156552555ol_int @ P2 ) @ one_one_int ) ).
% 5.31/5.62
% 5.31/5.62 % of_bool_less_eq_one
% 5.31/5.62 thf(fact_6795_of__bool__less__eq__one,axiom,
% 5.31/5.62 ! [P2: $o] : ( ord_le3102999989581377725nteger @ ( zero_n356916108424825756nteger @ P2 ) @ one_one_Code_integer ) ).
% 5.31/5.62
% 5.31/5.62 % of_bool_less_eq_one
% 5.31/5.62 thf(fact_6796_of__bool__def,axiom,
% 5.31/5.62 ( zero_n1201886186963655149omplex
% 5.31/5.62 = ( ^ [P5: $o] : ( if_complex @ P5 @ one_one_complex @ zero_zero_complex ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % of_bool_def
% 5.31/5.62 thf(fact_6797_of__bool__def,axiom,
% 5.31/5.62 ( zero_n3304061248610475627l_real
% 5.31/5.62 = ( ^ [P5: $o] : ( if_real @ P5 @ one_one_real @ zero_zero_real ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % of_bool_def
% 5.31/5.62 thf(fact_6798_of__bool__def,axiom,
% 5.31/5.62 ( zero_n2052037380579107095ol_rat
% 5.31/5.62 = ( ^ [P5: $o] : ( if_rat @ P5 @ one_one_rat @ zero_zero_rat ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % of_bool_def
% 5.31/5.62 thf(fact_6799_of__bool__def,axiom,
% 5.31/5.62 ( zero_n2687167440665602831ol_nat
% 5.31/5.62 = ( ^ [P5: $o] : ( if_nat @ P5 @ one_one_nat @ zero_zero_nat ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % of_bool_def
% 5.31/5.62 thf(fact_6800_of__bool__def,axiom,
% 5.31/5.62 ( zero_n2684676970156552555ol_int
% 5.31/5.62 = ( ^ [P5: $o] : ( if_int @ P5 @ one_one_int @ zero_zero_int ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % of_bool_def
% 5.31/5.62 thf(fact_6801_of__bool__def,axiom,
% 5.31/5.62 ( zero_n356916108424825756nteger
% 5.31/5.62 = ( ^ [P5: $o] : ( if_Code_integer @ P5 @ one_one_Code_integer @ zero_z3403309356797280102nteger ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % of_bool_def
% 5.31/5.62 thf(fact_6802_split__of__bool,axiom,
% 5.31/5.62 ! [P2: complex > $o,P: $o] :
% 5.31/5.62 ( ( P2 @ ( zero_n1201886186963655149omplex @ P ) )
% 5.31/5.62 = ( ( P
% 5.31/5.62 => ( P2 @ one_one_complex ) )
% 5.31/5.62 & ( ~ P
% 5.31/5.62 => ( P2 @ zero_zero_complex ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % split_of_bool
% 5.31/5.62 thf(fact_6803_split__of__bool,axiom,
% 5.31/5.62 ! [P2: real > $o,P: $o] :
% 5.31/5.62 ( ( P2 @ ( zero_n3304061248610475627l_real @ P ) )
% 5.31/5.62 = ( ( P
% 5.31/5.62 => ( P2 @ one_one_real ) )
% 5.31/5.62 & ( ~ P
% 5.31/5.62 => ( P2 @ zero_zero_real ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % split_of_bool
% 5.31/5.62 thf(fact_6804_split__of__bool,axiom,
% 5.31/5.62 ! [P2: rat > $o,P: $o] :
% 5.31/5.62 ( ( P2 @ ( zero_n2052037380579107095ol_rat @ P ) )
% 5.31/5.62 = ( ( P
% 5.31/5.62 => ( P2 @ one_one_rat ) )
% 5.31/5.62 & ( ~ P
% 5.31/5.62 => ( P2 @ zero_zero_rat ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % split_of_bool
% 5.31/5.62 thf(fact_6805_split__of__bool,axiom,
% 5.31/5.62 ! [P2: nat > $o,P: $o] :
% 5.31/5.62 ( ( P2 @ ( zero_n2687167440665602831ol_nat @ P ) )
% 5.31/5.62 = ( ( P
% 5.31/5.62 => ( P2 @ one_one_nat ) )
% 5.31/5.62 & ( ~ P
% 5.31/5.62 => ( P2 @ zero_zero_nat ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % split_of_bool
% 5.31/5.62 thf(fact_6806_split__of__bool,axiom,
% 5.31/5.62 ! [P2: int > $o,P: $o] :
% 5.31/5.62 ( ( P2 @ ( zero_n2684676970156552555ol_int @ P ) )
% 5.31/5.62 = ( ( P
% 5.31/5.62 => ( P2 @ one_one_int ) )
% 5.31/5.62 & ( ~ P
% 5.31/5.62 => ( P2 @ zero_zero_int ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % split_of_bool
% 5.31/5.62 thf(fact_6807_split__of__bool,axiom,
% 5.31/5.62 ! [P2: code_integer > $o,P: $o] :
% 5.31/5.62 ( ( P2 @ ( zero_n356916108424825756nteger @ P ) )
% 5.31/5.62 = ( ( P
% 5.31/5.62 => ( P2 @ one_one_Code_integer ) )
% 5.31/5.62 & ( ~ P
% 5.31/5.62 => ( P2 @ zero_z3403309356797280102nteger ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % split_of_bool
% 5.31/5.62 thf(fact_6808_split__of__bool__asm,axiom,
% 5.31/5.62 ! [P2: complex > $o,P: $o] :
% 5.31/5.62 ( ( P2 @ ( zero_n1201886186963655149omplex @ P ) )
% 5.31/5.62 = ( ~ ( ( P
% 5.31/5.62 & ~ ( P2 @ one_one_complex ) )
% 5.31/5.62 | ( ~ P
% 5.31/5.62 & ~ ( P2 @ zero_zero_complex ) ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % split_of_bool_asm
% 5.31/5.62 thf(fact_6809_split__of__bool__asm,axiom,
% 5.31/5.62 ! [P2: real > $o,P: $o] :
% 5.31/5.62 ( ( P2 @ ( zero_n3304061248610475627l_real @ P ) )
% 5.31/5.62 = ( ~ ( ( P
% 5.31/5.62 & ~ ( P2 @ one_one_real ) )
% 5.31/5.62 | ( ~ P
% 5.31/5.62 & ~ ( P2 @ zero_zero_real ) ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % split_of_bool_asm
% 5.31/5.62 thf(fact_6810_split__of__bool__asm,axiom,
% 5.31/5.62 ! [P2: rat > $o,P: $o] :
% 5.31/5.62 ( ( P2 @ ( zero_n2052037380579107095ol_rat @ P ) )
% 5.31/5.62 = ( ~ ( ( P
% 5.31/5.62 & ~ ( P2 @ one_one_rat ) )
% 5.31/5.62 | ( ~ P
% 5.31/5.62 & ~ ( P2 @ zero_zero_rat ) ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % split_of_bool_asm
% 5.31/5.62 thf(fact_6811_split__of__bool__asm,axiom,
% 5.31/5.62 ! [P2: nat > $o,P: $o] :
% 5.31/5.62 ( ( P2 @ ( zero_n2687167440665602831ol_nat @ P ) )
% 5.31/5.62 = ( ~ ( ( P
% 5.31/5.62 & ~ ( P2 @ one_one_nat ) )
% 5.31/5.62 | ( ~ P
% 5.31/5.62 & ~ ( P2 @ zero_zero_nat ) ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % split_of_bool_asm
% 5.31/5.62 thf(fact_6812_split__of__bool__asm,axiom,
% 5.31/5.62 ! [P2: int > $o,P: $o] :
% 5.31/5.62 ( ( P2 @ ( zero_n2684676970156552555ol_int @ P ) )
% 5.31/5.62 = ( ~ ( ( P
% 5.31/5.62 & ~ ( P2 @ one_one_int ) )
% 5.31/5.62 | ( ~ P
% 5.31/5.62 & ~ ( P2 @ zero_zero_int ) ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % split_of_bool_asm
% 5.31/5.62 thf(fact_6813_split__of__bool__asm,axiom,
% 5.31/5.62 ! [P2: code_integer > $o,P: $o] :
% 5.31/5.62 ( ( P2 @ ( zero_n356916108424825756nteger @ P ) )
% 5.31/5.62 = ( ~ ( ( P
% 5.31/5.62 & ~ ( P2 @ one_one_Code_integer ) )
% 5.31/5.62 | ( ~ P
% 5.31/5.62 & ~ ( P2 @ zero_z3403309356797280102nteger ) ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % split_of_bool_asm
% 5.31/5.62 thf(fact_6814_atMost__atLeast0,axiom,
% 5.31/5.62 ( set_ord_atMost_nat
% 5.31/5.62 = ( set_or1269000886237332187st_nat @ zero_zero_nat ) ) ).
% 5.31/5.62
% 5.31/5.62 % atMost_atLeast0
% 5.31/5.62 thf(fact_6815_lessThan__Suc__atMost,axiom,
% 5.31/5.62 ! [K2: nat] :
% 5.31/5.62 ( ( set_ord_lessThan_nat @ ( suc @ K2 ) )
% 5.31/5.62 = ( set_ord_atMost_nat @ K2 ) ) ).
% 5.31/5.62
% 5.31/5.62 % lessThan_Suc_atMost
% 5.31/5.62 thf(fact_6816_atMost__Suc,axiom,
% 5.31/5.62 ! [K2: nat] :
% 5.31/5.62 ( ( set_ord_atMost_nat @ ( suc @ K2 ) )
% 5.31/5.62 = ( insert_nat @ ( suc @ K2 ) @ ( set_ord_atMost_nat @ K2 ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % atMost_Suc
% 5.31/5.62 thf(fact_6817_not__Iic__le__Icc,axiom,
% 5.31/5.62 ! [H: int,L3: int,H3: int] :
% 5.31/5.62 ~ ( ord_less_eq_set_int @ ( set_ord_atMost_int @ H ) @ ( set_or1266510415728281911st_int @ L3 @ H3 ) ) ).
% 5.31/5.62
% 5.31/5.62 % not_Iic_le_Icc
% 5.31/5.62 thf(fact_6818_not__Iic__le__Icc,axiom,
% 5.31/5.62 ! [H: real,L3: real,H3: real] :
% 5.31/5.62 ~ ( ord_less_eq_set_real @ ( set_ord_atMost_real @ H ) @ ( set_or1222579329274155063t_real @ L3 @ H3 ) ) ).
% 5.31/5.62
% 5.31/5.62 % not_Iic_le_Icc
% 5.31/5.62 thf(fact_6819_nth__eq__iff__index__eq,axiom,
% 5.31/5.62 ! [Xs2: list_VEBT_VEBT,I2: nat,J2: nat] :
% 5.31/5.62 ( ( distinct_VEBT_VEBT @ Xs2 )
% 5.31/5.62 => ( ( ord_less_nat @ I2 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 5.31/5.62 => ( ( ord_less_nat @ J2 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 5.31/5.62 => ( ( ( nth_VEBT_VEBT @ Xs2 @ I2 )
% 5.31/5.62 = ( nth_VEBT_VEBT @ Xs2 @ J2 ) )
% 5.31/5.62 = ( I2 = J2 ) ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % nth_eq_iff_index_eq
% 5.31/5.62 thf(fact_6820_nth__eq__iff__index__eq,axiom,
% 5.31/5.62 ! [Xs2: list_o,I2: nat,J2: nat] :
% 5.31/5.62 ( ( distinct_o @ Xs2 )
% 5.31/5.62 => ( ( ord_less_nat @ I2 @ ( size_size_list_o @ Xs2 ) )
% 5.31/5.62 => ( ( ord_less_nat @ J2 @ ( size_size_list_o @ Xs2 ) )
% 5.31/5.62 => ( ( ( nth_o @ Xs2 @ I2 )
% 5.31/5.62 = ( nth_o @ Xs2 @ J2 ) )
% 5.31/5.62 = ( I2 = J2 ) ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % nth_eq_iff_index_eq
% 5.31/5.62 thf(fact_6821_nth__eq__iff__index__eq,axiom,
% 5.31/5.62 ! [Xs2: list_nat,I2: nat,J2: nat] :
% 5.31/5.62 ( ( distinct_nat @ Xs2 )
% 5.31/5.62 => ( ( ord_less_nat @ I2 @ ( size_size_list_nat @ Xs2 ) )
% 5.31/5.62 => ( ( ord_less_nat @ J2 @ ( size_size_list_nat @ Xs2 ) )
% 5.31/5.62 => ( ( ( nth_nat @ Xs2 @ I2 )
% 5.31/5.62 = ( nth_nat @ Xs2 @ J2 ) )
% 5.31/5.62 = ( I2 = J2 ) ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % nth_eq_iff_index_eq
% 5.31/5.62 thf(fact_6822_nth__eq__iff__index__eq,axiom,
% 5.31/5.62 ! [Xs2: list_int,I2: nat,J2: nat] :
% 5.31/5.62 ( ( distinct_int @ Xs2 )
% 5.31/5.62 => ( ( ord_less_nat @ I2 @ ( size_size_list_int @ Xs2 ) )
% 5.31/5.62 => ( ( ord_less_nat @ J2 @ ( size_size_list_int @ Xs2 ) )
% 5.31/5.62 => ( ( ( nth_int @ Xs2 @ I2 )
% 5.31/5.62 = ( nth_int @ Xs2 @ J2 ) )
% 5.31/5.62 = ( I2 = J2 ) ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % nth_eq_iff_index_eq
% 5.31/5.62 thf(fact_6823_distinct__conv__nth,axiom,
% 5.31/5.62 ( distinct_VEBT_VEBT
% 5.31/5.62 = ( ^ [Xs: list_VEBT_VEBT] :
% 5.31/5.62 ! [I: nat] :
% 5.31/5.62 ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 5.31/5.62 => ! [J: nat] :
% 5.31/5.62 ( ( ord_less_nat @ J @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 5.31/5.62 => ( ( I != J )
% 5.31/5.62 => ( ( nth_VEBT_VEBT @ Xs @ I )
% 5.31/5.62 != ( nth_VEBT_VEBT @ Xs @ J ) ) ) ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % distinct_conv_nth
% 5.31/5.62 thf(fact_6824_distinct__conv__nth,axiom,
% 5.31/5.62 ( distinct_o
% 5.31/5.62 = ( ^ [Xs: list_o] :
% 5.31/5.62 ! [I: nat] :
% 5.31/5.62 ( ( ord_less_nat @ I @ ( size_size_list_o @ Xs ) )
% 5.31/5.62 => ! [J: nat] :
% 5.31/5.62 ( ( ord_less_nat @ J @ ( size_size_list_o @ Xs ) )
% 5.31/5.62 => ( ( I != J )
% 5.31/5.62 => ( ( nth_o @ Xs @ I )
% 5.31/5.62 != ( nth_o @ Xs @ J ) ) ) ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % distinct_conv_nth
% 5.31/5.62 thf(fact_6825_distinct__conv__nth,axiom,
% 5.31/5.62 ( distinct_nat
% 5.31/5.62 = ( ^ [Xs: list_nat] :
% 5.31/5.62 ! [I: nat] :
% 5.31/5.62 ( ( ord_less_nat @ I @ ( size_size_list_nat @ Xs ) )
% 5.31/5.62 => ! [J: nat] :
% 5.31/5.62 ( ( ord_less_nat @ J @ ( size_size_list_nat @ Xs ) )
% 5.31/5.62 => ( ( I != J )
% 5.31/5.62 => ( ( nth_nat @ Xs @ I )
% 5.31/5.62 != ( nth_nat @ Xs @ J ) ) ) ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % distinct_conv_nth
% 5.31/5.62 thf(fact_6826_distinct__conv__nth,axiom,
% 5.31/5.62 ( distinct_int
% 5.31/5.62 = ( ^ [Xs: list_int] :
% 5.31/5.62 ! [I: nat] :
% 5.31/5.62 ( ( ord_less_nat @ I @ ( size_size_list_int @ Xs ) )
% 5.31/5.62 => ! [J: nat] :
% 5.31/5.62 ( ( ord_less_nat @ J @ ( size_size_list_int @ Xs ) )
% 5.31/5.62 => ( ( I != J )
% 5.31/5.62 => ( ( nth_int @ Xs @ I )
% 5.31/5.62 != ( nth_int @ Xs @ J ) ) ) ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % distinct_conv_nth
% 5.31/5.62 thf(fact_6827_card__distinct,axiom,
% 5.31/5.62 ! [Xs2: list_complex] :
% 5.31/5.62 ( ( ( finite_card_complex @ ( set_complex2 @ Xs2 ) )
% 5.31/5.62 = ( size_s3451745648224563538omplex @ Xs2 ) )
% 5.31/5.62 => ( distinct_complex @ Xs2 ) ) ).
% 5.31/5.62
% 5.31/5.62 % card_distinct
% 5.31/5.62 thf(fact_6828_card__distinct,axiom,
% 5.31/5.62 ! [Xs2: list_list_nat] :
% 5.31/5.62 ( ( ( finite_card_list_nat @ ( set_list_nat2 @ Xs2 ) )
% 5.31/5.62 = ( size_s3023201423986296836st_nat @ Xs2 ) )
% 5.31/5.62 => ( distinct_list_nat @ Xs2 ) ) ).
% 5.31/5.62
% 5.31/5.62 % card_distinct
% 5.31/5.62 thf(fact_6829_card__distinct,axiom,
% 5.31/5.62 ! [Xs2: list_set_nat] :
% 5.31/5.62 ( ( ( finite_card_set_nat @ ( set_set_nat2 @ Xs2 ) )
% 5.31/5.62 = ( size_s3254054031482475050et_nat @ Xs2 ) )
% 5.31/5.62 => ( distinct_set_nat @ Xs2 ) ) ).
% 5.31/5.62
% 5.31/5.62 % card_distinct
% 5.31/5.62 thf(fact_6830_card__distinct,axiom,
% 5.31/5.62 ! [Xs2: list_VEBT_VEBT] :
% 5.31/5.62 ( ( ( finite7802652506058667612T_VEBT @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 5.31/5.62 = ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 5.31/5.62 => ( distinct_VEBT_VEBT @ Xs2 ) ) ).
% 5.31/5.62
% 5.31/5.62 % card_distinct
% 5.31/5.62 thf(fact_6831_card__distinct,axiom,
% 5.31/5.62 ! [Xs2: list_o] :
% 5.31/5.62 ( ( ( finite_card_o @ ( set_o2 @ Xs2 ) )
% 5.31/5.62 = ( size_size_list_o @ Xs2 ) )
% 5.31/5.62 => ( distinct_o @ Xs2 ) ) ).
% 5.31/5.62
% 5.31/5.62 % card_distinct
% 5.31/5.62 thf(fact_6832_card__distinct,axiom,
% 5.31/5.62 ! [Xs2: list_nat] :
% 5.31/5.62 ( ( ( finite_card_nat @ ( set_nat2 @ Xs2 ) )
% 5.31/5.62 = ( size_size_list_nat @ Xs2 ) )
% 5.31/5.62 => ( distinct_nat @ Xs2 ) ) ).
% 5.31/5.62
% 5.31/5.62 % card_distinct
% 5.31/5.62 thf(fact_6833_card__distinct,axiom,
% 5.31/5.62 ! [Xs2: list_int] :
% 5.31/5.62 ( ( ( finite_card_int @ ( set_int2 @ Xs2 ) )
% 5.31/5.62 = ( size_size_list_int @ Xs2 ) )
% 5.31/5.62 => ( distinct_int @ Xs2 ) ) ).
% 5.31/5.62
% 5.31/5.62 % card_distinct
% 5.31/5.62 thf(fact_6834_distinct__card,axiom,
% 5.31/5.62 ! [Xs2: list_complex] :
% 5.31/5.62 ( ( distinct_complex @ Xs2 )
% 5.31/5.62 => ( ( finite_card_complex @ ( set_complex2 @ Xs2 ) )
% 5.31/5.62 = ( size_s3451745648224563538omplex @ Xs2 ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % distinct_card
% 5.31/5.62 thf(fact_6835_distinct__card,axiom,
% 5.31/5.62 ! [Xs2: list_list_nat] :
% 5.31/5.62 ( ( distinct_list_nat @ Xs2 )
% 5.31/5.62 => ( ( finite_card_list_nat @ ( set_list_nat2 @ Xs2 ) )
% 5.31/5.62 = ( size_s3023201423986296836st_nat @ Xs2 ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % distinct_card
% 5.31/5.62 thf(fact_6836_distinct__card,axiom,
% 5.31/5.62 ! [Xs2: list_set_nat] :
% 5.31/5.62 ( ( distinct_set_nat @ Xs2 )
% 5.31/5.62 => ( ( finite_card_set_nat @ ( set_set_nat2 @ Xs2 ) )
% 5.31/5.62 = ( size_s3254054031482475050et_nat @ Xs2 ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % distinct_card
% 5.31/5.62 thf(fact_6837_distinct__card,axiom,
% 5.31/5.62 ! [Xs2: list_VEBT_VEBT] :
% 5.31/5.62 ( ( distinct_VEBT_VEBT @ Xs2 )
% 5.31/5.62 => ( ( finite7802652506058667612T_VEBT @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 5.31/5.62 = ( size_s6755466524823107622T_VEBT @ Xs2 ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % distinct_card
% 5.31/5.62 thf(fact_6838_distinct__card,axiom,
% 5.31/5.62 ! [Xs2: list_o] :
% 5.31/5.62 ( ( distinct_o @ Xs2 )
% 5.31/5.62 => ( ( finite_card_o @ ( set_o2 @ Xs2 ) )
% 5.31/5.62 = ( size_size_list_o @ Xs2 ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % distinct_card
% 5.31/5.62 thf(fact_6839_distinct__card,axiom,
% 5.31/5.62 ! [Xs2: list_nat] :
% 5.31/5.62 ( ( distinct_nat @ Xs2 )
% 5.31/5.62 => ( ( finite_card_nat @ ( set_nat2 @ Xs2 ) )
% 5.31/5.62 = ( size_size_list_nat @ Xs2 ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % distinct_card
% 5.31/5.62 thf(fact_6840_distinct__card,axiom,
% 5.31/5.62 ! [Xs2: list_int] :
% 5.31/5.62 ( ( distinct_int @ Xs2 )
% 5.31/5.62 => ( ( finite_card_int @ ( set_int2 @ Xs2 ) )
% 5.31/5.62 = ( size_size_list_int @ Xs2 ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % distinct_card
% 5.31/5.62 thf(fact_6841_gbinomial__Suc__Suc,axiom,
% 5.31/5.62 ! [A: complex,K2: nat] :
% 5.31/5.62 ( ( gbinomial_complex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( suc @ K2 ) )
% 5.31/5.62 = ( plus_plus_complex @ ( gbinomial_complex @ A @ K2 ) @ ( gbinomial_complex @ A @ ( suc @ K2 ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % gbinomial_Suc_Suc
% 5.31/5.62 thf(fact_6842_gbinomial__Suc__Suc,axiom,
% 5.31/5.62 ! [A: real,K2: nat] :
% 5.31/5.62 ( ( gbinomial_real @ ( plus_plus_real @ A @ one_one_real ) @ ( suc @ K2 ) )
% 5.31/5.62 = ( plus_plus_real @ ( gbinomial_real @ A @ K2 ) @ ( gbinomial_real @ A @ ( suc @ K2 ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % gbinomial_Suc_Suc
% 5.31/5.62 thf(fact_6843_gbinomial__Suc__Suc,axiom,
% 5.31/5.62 ! [A: rat,K2: nat] :
% 5.31/5.62 ( ( gbinomial_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( suc @ K2 ) )
% 5.31/5.62 = ( plus_plus_rat @ ( gbinomial_rat @ A @ K2 ) @ ( gbinomial_rat @ A @ ( suc @ K2 ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % gbinomial_Suc_Suc
% 5.31/5.62 thf(fact_6844_gbinomial__of__nat__symmetric,axiom,
% 5.31/5.62 ! [K2: nat,N: nat] :
% 5.31/5.62 ( ( ord_less_eq_nat @ K2 @ N )
% 5.31/5.62 => ( ( gbinomial_real @ ( semiri5074537144036343181t_real @ N ) @ K2 )
% 5.31/5.62 = ( gbinomial_real @ ( semiri5074537144036343181t_real @ N ) @ ( minus_minus_nat @ N @ K2 ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % gbinomial_of_nat_symmetric
% 5.31/5.62 thf(fact_6845_Iic__subset__Iio__iff,axiom,
% 5.31/5.62 ! [A: real,B: real] :
% 5.31/5.62 ( ( ord_less_eq_set_real @ ( set_ord_atMost_real @ A ) @ ( set_or5984915006950818249n_real @ B ) )
% 5.31/5.62 = ( ord_less_real @ A @ B ) ) ).
% 5.31/5.62
% 5.31/5.62 % Iic_subset_Iio_iff
% 5.31/5.62 thf(fact_6846_Iic__subset__Iio__iff,axiom,
% 5.31/5.62 ! [A: rat,B: rat] :
% 5.31/5.62 ( ( ord_less_eq_set_rat @ ( set_ord_atMost_rat @ A ) @ ( set_ord_lessThan_rat @ B ) )
% 5.31/5.62 = ( ord_less_rat @ A @ B ) ) ).
% 5.31/5.62
% 5.31/5.62 % Iic_subset_Iio_iff
% 5.31/5.62 thf(fact_6847_Iic__subset__Iio__iff,axiom,
% 5.31/5.62 ! [A: num,B: num] :
% 5.31/5.62 ( ( ord_less_eq_set_num @ ( set_ord_atMost_num @ A ) @ ( set_ord_lessThan_num @ B ) )
% 5.31/5.62 = ( ord_less_num @ A @ B ) ) ).
% 5.31/5.62
% 5.31/5.62 % Iic_subset_Iio_iff
% 5.31/5.62 thf(fact_6848_Iic__subset__Iio__iff,axiom,
% 5.31/5.62 ! [A: int,B: int] :
% 5.31/5.62 ( ( ord_less_eq_set_int @ ( set_ord_atMost_int @ A ) @ ( set_ord_lessThan_int @ B ) )
% 5.31/5.62 = ( ord_less_int @ A @ B ) ) ).
% 5.31/5.62
% 5.31/5.62 % Iic_subset_Iio_iff
% 5.31/5.62 thf(fact_6849_Iic__subset__Iio__iff,axiom,
% 5.31/5.62 ! [A: nat,B: nat] :
% 5.31/5.62 ( ( ord_less_eq_set_nat @ ( set_ord_atMost_nat @ A ) @ ( set_ord_lessThan_nat @ B ) )
% 5.31/5.62 = ( ord_less_nat @ A @ B ) ) ).
% 5.31/5.62
% 5.31/5.62 % Iic_subset_Iio_iff
% 5.31/5.62 thf(fact_6850_sum__choose__upper,axiom,
% 5.31/5.62 ! [M2: nat,N: nat] :
% 5.31/5.62 ( ( groups3542108847815614940at_nat
% 5.31/5.62 @ ^ [K3: nat] : ( binomial @ K3 @ M2 )
% 5.31/5.62 @ ( set_ord_atMost_nat @ N ) )
% 5.31/5.62 = ( binomial @ ( suc @ N ) @ ( suc @ M2 ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % sum_choose_upper
% 5.31/5.62 thf(fact_6851_distinct__Ex1,axiom,
% 5.31/5.62 ! [Xs2: list_complex,X: complex] :
% 5.31/5.62 ( ( distinct_complex @ Xs2 )
% 5.31/5.62 => ( ( member_complex @ X @ ( set_complex2 @ Xs2 ) )
% 5.31/5.62 => ? [X3: nat] :
% 5.31/5.62 ( ( ord_less_nat @ X3 @ ( size_s3451745648224563538omplex @ Xs2 ) )
% 5.31/5.62 & ( ( nth_complex @ Xs2 @ X3 )
% 5.31/5.62 = X )
% 5.31/5.62 & ! [Y6: nat] :
% 5.31/5.62 ( ( ( ord_less_nat @ Y6 @ ( size_s3451745648224563538omplex @ Xs2 ) )
% 5.31/5.62 & ( ( nth_complex @ Xs2 @ Y6 )
% 5.31/5.62 = X ) )
% 5.31/5.62 => ( Y6 = X3 ) ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % distinct_Ex1
% 5.31/5.62 thf(fact_6852_distinct__Ex1,axiom,
% 5.31/5.62 ! [Xs2: list_real,X: real] :
% 5.31/5.62 ( ( distinct_real @ Xs2 )
% 5.31/5.62 => ( ( member_real @ X @ ( set_real2 @ Xs2 ) )
% 5.31/5.62 => ? [X3: nat] :
% 5.31/5.62 ( ( ord_less_nat @ X3 @ ( size_size_list_real @ Xs2 ) )
% 5.31/5.62 & ( ( nth_real @ Xs2 @ X3 )
% 5.31/5.62 = X )
% 5.31/5.62 & ! [Y6: nat] :
% 5.31/5.62 ( ( ( ord_less_nat @ Y6 @ ( size_size_list_real @ Xs2 ) )
% 5.31/5.62 & ( ( nth_real @ Xs2 @ Y6 )
% 5.31/5.62 = X ) )
% 5.31/5.62 => ( Y6 = X3 ) ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % distinct_Ex1
% 5.31/5.62 thf(fact_6853_distinct__Ex1,axiom,
% 5.31/5.62 ! [Xs2: list_set_nat,X: set_nat] :
% 5.31/5.62 ( ( distinct_set_nat @ Xs2 )
% 5.31/5.62 => ( ( member_set_nat @ X @ ( set_set_nat2 @ Xs2 ) )
% 5.31/5.62 => ? [X3: nat] :
% 5.31/5.62 ( ( ord_less_nat @ X3 @ ( size_s3254054031482475050et_nat @ Xs2 ) )
% 5.31/5.62 & ( ( nth_set_nat @ Xs2 @ X3 )
% 5.31/5.62 = X )
% 5.31/5.62 & ! [Y6: nat] :
% 5.31/5.62 ( ( ( ord_less_nat @ Y6 @ ( size_s3254054031482475050et_nat @ Xs2 ) )
% 5.31/5.62 & ( ( nth_set_nat @ Xs2 @ Y6 )
% 5.31/5.62 = X ) )
% 5.31/5.62 => ( Y6 = X3 ) ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % distinct_Ex1
% 5.31/5.62 thf(fact_6854_distinct__Ex1,axiom,
% 5.31/5.62 ! [Xs2: list_VEBT_VEBT,X: vEBT_VEBT] :
% 5.31/5.62 ( ( distinct_VEBT_VEBT @ Xs2 )
% 5.31/5.62 => ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 5.31/5.62 => ? [X3: nat] :
% 5.31/5.62 ( ( ord_less_nat @ X3 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 5.31/5.62 & ( ( nth_VEBT_VEBT @ Xs2 @ X3 )
% 5.31/5.62 = X )
% 5.31/5.62 & ! [Y6: nat] :
% 5.31/5.62 ( ( ( ord_less_nat @ Y6 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 5.31/5.62 & ( ( nth_VEBT_VEBT @ Xs2 @ Y6 )
% 5.31/5.62 = X ) )
% 5.31/5.62 => ( Y6 = X3 ) ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % distinct_Ex1
% 5.31/5.62 thf(fact_6855_distinct__Ex1,axiom,
% 5.31/5.62 ! [Xs2: list_o,X: $o] :
% 5.31/5.62 ( ( distinct_o @ Xs2 )
% 5.31/5.62 => ( ( member_o @ X @ ( set_o2 @ Xs2 ) )
% 5.31/5.62 => ? [X3: nat] :
% 5.31/5.62 ( ( ord_less_nat @ X3 @ ( size_size_list_o @ Xs2 ) )
% 5.31/5.62 & ( ( nth_o @ Xs2 @ X3 )
% 5.31/5.62 = X )
% 5.31/5.62 & ! [Y6: nat] :
% 5.31/5.62 ( ( ( ord_less_nat @ Y6 @ ( size_size_list_o @ Xs2 ) )
% 5.31/5.62 & ( ( nth_o @ Xs2 @ Y6 )
% 5.31/5.62 = X ) )
% 5.31/5.62 => ( Y6 = X3 ) ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % distinct_Ex1
% 5.31/5.62 thf(fact_6856_distinct__Ex1,axiom,
% 5.31/5.62 ! [Xs2: list_nat,X: nat] :
% 5.31/5.62 ( ( distinct_nat @ Xs2 )
% 5.31/5.62 => ( ( member_nat @ X @ ( set_nat2 @ Xs2 ) )
% 5.31/5.62 => ? [X3: nat] :
% 5.31/5.62 ( ( ord_less_nat @ X3 @ ( size_size_list_nat @ Xs2 ) )
% 5.31/5.62 & ( ( nth_nat @ Xs2 @ X3 )
% 5.31/5.62 = X )
% 5.31/5.62 & ! [Y6: nat] :
% 5.31/5.62 ( ( ( ord_less_nat @ Y6 @ ( size_size_list_nat @ Xs2 ) )
% 5.31/5.62 & ( ( nth_nat @ Xs2 @ Y6 )
% 5.31/5.62 = X ) )
% 5.31/5.62 => ( Y6 = X3 ) ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % distinct_Ex1
% 5.31/5.62 thf(fact_6857_distinct__Ex1,axiom,
% 5.31/5.62 ! [Xs2: list_int,X: int] :
% 5.31/5.62 ( ( distinct_int @ Xs2 )
% 5.31/5.62 => ( ( member_int @ X @ ( set_int2 @ Xs2 ) )
% 5.31/5.62 => ? [X3: nat] :
% 5.31/5.62 ( ( ord_less_nat @ X3 @ ( size_size_list_int @ Xs2 ) )
% 5.31/5.62 & ( ( nth_int @ Xs2 @ X3 )
% 5.31/5.62 = X )
% 5.31/5.62 & ! [Y6: nat] :
% 5.31/5.62 ( ( ( ord_less_nat @ Y6 @ ( size_size_list_int @ Xs2 ) )
% 5.31/5.62 & ( ( nth_int @ Xs2 @ Y6 )
% 5.31/5.62 = X ) )
% 5.31/5.62 => ( Y6 = X3 ) ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % distinct_Ex1
% 5.31/5.62 thf(fact_6858_gbinomial__partial__sum__poly__xpos,axiom,
% 5.31/5.62 ! [M2: nat,A: complex,X: complex,Y: complex] :
% 5.31/5.62 ( ( groups2073611262835488442omplex
% 5.31/5.62 @ ^ [K3: nat] : ( times_times_complex @ ( times_times_complex @ ( gbinomial_complex @ ( plus_plus_complex @ ( semiri8010041392384452111omplex @ M2 ) @ A ) @ K3 ) @ ( power_power_complex @ X @ K3 ) ) @ ( power_power_complex @ Y @ ( minus_minus_nat @ M2 @ K3 ) ) )
% 5.31/5.62 @ ( set_ord_atMost_nat @ M2 ) )
% 5.31/5.62 = ( groups2073611262835488442omplex
% 5.31/5.62 @ ^ [K3: nat] : ( times_times_complex @ ( times_times_complex @ ( gbinomial_complex @ ( minus_minus_complex @ ( plus_plus_complex @ ( semiri8010041392384452111omplex @ K3 ) @ A ) @ one_one_complex ) @ K3 ) @ ( power_power_complex @ X @ K3 ) ) @ ( power_power_complex @ ( plus_plus_complex @ X @ Y ) @ ( minus_minus_nat @ M2 @ K3 ) ) )
% 5.31/5.62 @ ( set_ord_atMost_nat @ M2 ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % gbinomial_partial_sum_poly_xpos
% 5.31/5.62 thf(fact_6859_gbinomial__partial__sum__poly__xpos,axiom,
% 5.31/5.62 ! [M2: nat,A: rat,X: rat,Y: rat] :
% 5.31/5.62 ( ( groups2906978787729119204at_rat
% 5.31/5.62 @ ^ [K3: nat] : ( times_times_rat @ ( times_times_rat @ ( gbinomial_rat @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ M2 ) @ A ) @ K3 ) @ ( power_power_rat @ X @ K3 ) ) @ ( power_power_rat @ Y @ ( minus_minus_nat @ M2 @ K3 ) ) )
% 5.31/5.62 @ ( set_ord_atMost_nat @ M2 ) )
% 5.31/5.62 = ( groups2906978787729119204at_rat
% 5.31/5.62 @ ^ [K3: nat] : ( times_times_rat @ ( times_times_rat @ ( gbinomial_rat @ ( minus_minus_rat @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ K3 ) @ A ) @ one_one_rat ) @ K3 ) @ ( power_power_rat @ X @ K3 ) ) @ ( power_power_rat @ ( plus_plus_rat @ X @ Y ) @ ( minus_minus_nat @ M2 @ K3 ) ) )
% 5.31/5.62 @ ( set_ord_atMost_nat @ M2 ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % gbinomial_partial_sum_poly_xpos
% 5.31/5.62 thf(fact_6860_gbinomial__partial__sum__poly__xpos,axiom,
% 5.31/5.62 ! [M2: nat,A: real,X: real,Y: real] :
% 5.31/5.62 ( ( groups6591440286371151544t_real
% 5.31/5.62 @ ^ [K3: nat] : ( times_times_real @ ( times_times_real @ ( gbinomial_real @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ M2 ) @ A ) @ K3 ) @ ( power_power_real @ X @ K3 ) ) @ ( power_power_real @ Y @ ( minus_minus_nat @ M2 @ K3 ) ) )
% 5.31/5.62 @ ( set_ord_atMost_nat @ M2 ) )
% 5.31/5.62 = ( groups6591440286371151544t_real
% 5.31/5.62 @ ^ [K3: nat] : ( times_times_real @ ( times_times_real @ ( gbinomial_real @ ( minus_minus_real @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ K3 ) @ A ) @ one_one_real ) @ K3 ) @ ( power_power_real @ X @ K3 ) ) @ ( power_power_real @ ( plus_plus_real @ X @ Y ) @ ( minus_minus_nat @ M2 @ K3 ) ) )
% 5.31/5.62 @ ( set_ord_atMost_nat @ M2 ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % gbinomial_partial_sum_poly_xpos
% 5.31/5.62 thf(fact_6861_gbinomial__addition__formula,axiom,
% 5.31/5.62 ! [A: complex,K2: nat] :
% 5.31/5.62 ( ( gbinomial_complex @ A @ ( suc @ K2 ) )
% 5.31/5.62 = ( plus_plus_complex @ ( gbinomial_complex @ ( minus_minus_complex @ A @ one_one_complex ) @ ( suc @ K2 ) ) @ ( gbinomial_complex @ ( minus_minus_complex @ A @ one_one_complex ) @ K2 ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % gbinomial_addition_formula
% 5.31/5.62 thf(fact_6862_gbinomial__addition__formula,axiom,
% 5.31/5.62 ! [A: real,K2: nat] :
% 5.31/5.62 ( ( gbinomial_real @ A @ ( suc @ K2 ) )
% 5.31/5.62 = ( plus_plus_real @ ( gbinomial_real @ ( minus_minus_real @ A @ one_one_real ) @ ( suc @ K2 ) ) @ ( gbinomial_real @ ( minus_minus_real @ A @ one_one_real ) @ K2 ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % gbinomial_addition_formula
% 5.31/5.62 thf(fact_6863_gbinomial__addition__formula,axiom,
% 5.31/5.62 ! [A: rat,K2: nat] :
% 5.31/5.62 ( ( gbinomial_rat @ A @ ( suc @ K2 ) )
% 5.31/5.62 = ( plus_plus_rat @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ ( suc @ K2 ) ) @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ K2 ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % gbinomial_addition_formula
% 5.31/5.62 thf(fact_6864_gbinomial__absorb__comp,axiom,
% 5.31/5.62 ! [A: complex,K2: nat] :
% 5.31/5.62 ( ( times_times_complex @ ( minus_minus_complex @ A @ ( semiri8010041392384452111omplex @ K2 ) ) @ ( gbinomial_complex @ A @ K2 ) )
% 5.31/5.62 = ( times_times_complex @ A @ ( gbinomial_complex @ ( minus_minus_complex @ A @ one_one_complex ) @ K2 ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % gbinomial_absorb_comp
% 5.31/5.62 thf(fact_6865_gbinomial__absorb__comp,axiom,
% 5.31/5.62 ! [A: rat,K2: nat] :
% 5.31/5.62 ( ( times_times_rat @ ( minus_minus_rat @ A @ ( semiri681578069525770553at_rat @ K2 ) ) @ ( gbinomial_rat @ A @ K2 ) )
% 5.31/5.62 = ( times_times_rat @ A @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ K2 ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % gbinomial_absorb_comp
% 5.31/5.62 thf(fact_6866_gbinomial__absorb__comp,axiom,
% 5.31/5.62 ! [A: real,K2: nat] :
% 5.31/5.62 ( ( times_times_real @ ( minus_minus_real @ A @ ( semiri5074537144036343181t_real @ K2 ) ) @ ( gbinomial_real @ A @ K2 ) )
% 5.31/5.62 = ( times_times_real @ A @ ( gbinomial_real @ ( minus_minus_real @ A @ one_one_real ) @ K2 ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % gbinomial_absorb_comp
% 5.31/5.62 thf(fact_6867_gbinomial__ge__n__over__k__pow__k,axiom,
% 5.31/5.62 ! [K2: nat,A: real] :
% 5.31/5.62 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ K2 ) @ A )
% 5.31/5.62 => ( ord_less_eq_real @ ( power_power_real @ ( divide_divide_real @ A @ ( semiri5074537144036343181t_real @ K2 ) ) @ K2 ) @ ( gbinomial_real @ A @ K2 ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % gbinomial_ge_n_over_k_pow_k
% 5.31/5.62 thf(fact_6868_gbinomial__ge__n__over__k__pow__k,axiom,
% 5.31/5.62 ! [K2: nat,A: rat] :
% 5.31/5.62 ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ K2 ) @ A )
% 5.31/5.62 => ( ord_less_eq_rat @ ( power_power_rat @ ( divide_divide_rat @ A @ ( semiri681578069525770553at_rat @ K2 ) ) @ K2 ) @ ( gbinomial_rat @ A @ K2 ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % gbinomial_ge_n_over_k_pow_k
% 5.31/5.62 thf(fact_6869_gbinomial__mult__1_H,axiom,
% 5.31/5.62 ! [A: rat,K2: nat] :
% 5.31/5.62 ( ( times_times_rat @ ( gbinomial_rat @ A @ K2 ) @ A )
% 5.31/5.62 = ( plus_plus_rat @ ( times_times_rat @ ( semiri681578069525770553at_rat @ K2 ) @ ( gbinomial_rat @ A @ K2 ) ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( suc @ K2 ) ) @ ( gbinomial_rat @ A @ ( suc @ K2 ) ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % gbinomial_mult_1'
% 5.31/5.62 thf(fact_6870_gbinomial__mult__1_H,axiom,
% 5.31/5.62 ! [A: real,K2: nat] :
% 5.31/5.62 ( ( times_times_real @ ( gbinomial_real @ A @ K2 ) @ A )
% 5.31/5.62 = ( plus_plus_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ K2 ) @ ( gbinomial_real @ A @ K2 ) ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ K2 ) ) @ ( gbinomial_real @ A @ ( suc @ K2 ) ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % gbinomial_mult_1'
% 5.31/5.62 thf(fact_6871_gbinomial__mult__1,axiom,
% 5.31/5.62 ! [A: rat,K2: nat] :
% 5.31/5.62 ( ( times_times_rat @ A @ ( gbinomial_rat @ A @ K2 ) )
% 5.31/5.62 = ( plus_plus_rat @ ( times_times_rat @ ( semiri681578069525770553at_rat @ K2 ) @ ( gbinomial_rat @ A @ K2 ) ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( suc @ K2 ) ) @ ( gbinomial_rat @ A @ ( suc @ K2 ) ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % gbinomial_mult_1
% 5.31/5.62 thf(fact_6872_gbinomial__mult__1,axiom,
% 5.31/5.62 ! [A: real,K2: nat] :
% 5.31/5.62 ( ( times_times_real @ A @ ( gbinomial_real @ A @ K2 ) )
% 5.31/5.62 = ( plus_plus_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ K2 ) @ ( gbinomial_real @ A @ K2 ) ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ K2 ) ) @ ( gbinomial_real @ A @ ( suc @ K2 ) ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % gbinomial_mult_1
% 5.31/5.62 thf(fact_6873_sum_OatMost__Suc__shift,axiom,
% 5.31/5.62 ! [G2: nat > rat,N: nat] :
% 5.31/5.62 ( ( groups2906978787729119204at_rat @ G2 @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 5.31/5.62 = ( plus_plus_rat @ ( G2 @ zero_zero_nat )
% 5.31/5.62 @ ( groups2906978787729119204at_rat
% 5.31/5.62 @ ^ [I: nat] : ( G2 @ ( suc @ I ) )
% 5.31/5.62 @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % sum.atMost_Suc_shift
% 5.31/5.62 thf(fact_6874_sum_OatMost__Suc__shift,axiom,
% 5.31/5.62 ! [G2: nat > int,N: nat] :
% 5.31/5.62 ( ( groups3539618377306564664at_int @ G2 @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 5.31/5.62 = ( plus_plus_int @ ( G2 @ zero_zero_nat )
% 5.31/5.62 @ ( groups3539618377306564664at_int
% 5.31/5.62 @ ^ [I: nat] : ( G2 @ ( suc @ I ) )
% 5.31/5.62 @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % sum.atMost_Suc_shift
% 5.31/5.62 thf(fact_6875_sum_OatMost__Suc__shift,axiom,
% 5.31/5.62 ! [G2: nat > nat,N: nat] :
% 5.31/5.62 ( ( groups3542108847815614940at_nat @ G2 @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 5.31/5.62 = ( plus_plus_nat @ ( G2 @ zero_zero_nat )
% 5.31/5.62 @ ( groups3542108847815614940at_nat
% 5.31/5.62 @ ^ [I: nat] : ( G2 @ ( suc @ I ) )
% 5.31/5.62 @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % sum.atMost_Suc_shift
% 5.31/5.62 thf(fact_6876_sum_OatMost__Suc__shift,axiom,
% 5.31/5.62 ! [G2: nat > real,N: nat] :
% 5.31/5.62 ( ( groups6591440286371151544t_real @ G2 @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 5.31/5.62 = ( plus_plus_real @ ( G2 @ zero_zero_nat )
% 5.31/5.62 @ ( groups6591440286371151544t_real
% 5.31/5.62 @ ^ [I: nat] : ( G2 @ ( suc @ I ) )
% 5.31/5.62 @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % sum.atMost_Suc_shift
% 5.31/5.62 thf(fact_6877_sum__telescope,axiom,
% 5.31/5.62 ! [F2: nat > rat,I2: nat] :
% 5.31/5.62 ( ( groups2906978787729119204at_rat
% 5.31/5.62 @ ^ [I: nat] : ( minus_minus_rat @ ( F2 @ I ) @ ( F2 @ ( suc @ I ) ) )
% 5.31/5.62 @ ( set_ord_atMost_nat @ I2 ) )
% 5.31/5.62 = ( minus_minus_rat @ ( F2 @ zero_zero_nat ) @ ( F2 @ ( suc @ I2 ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % sum_telescope
% 5.31/5.62 thf(fact_6878_sum__telescope,axiom,
% 5.31/5.62 ! [F2: nat > int,I2: nat] :
% 5.31/5.62 ( ( groups3539618377306564664at_int
% 5.31/5.62 @ ^ [I: nat] : ( minus_minus_int @ ( F2 @ I ) @ ( F2 @ ( suc @ I ) ) )
% 5.31/5.62 @ ( set_ord_atMost_nat @ I2 ) )
% 5.31/5.62 = ( minus_minus_int @ ( F2 @ zero_zero_nat ) @ ( F2 @ ( suc @ I2 ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % sum_telescope
% 5.31/5.62 thf(fact_6879_sum__telescope,axiom,
% 5.31/5.62 ! [F2: nat > real,I2: nat] :
% 5.31/5.62 ( ( groups6591440286371151544t_real
% 5.31/5.62 @ ^ [I: nat] : ( minus_minus_real @ ( F2 @ I ) @ ( F2 @ ( suc @ I ) ) )
% 5.31/5.62 @ ( set_ord_atMost_nat @ I2 ) )
% 5.31/5.62 = ( minus_minus_real @ ( F2 @ zero_zero_nat ) @ ( F2 @ ( suc @ I2 ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % sum_telescope
% 5.31/5.62 thf(fact_6880_polyfun__eq__coeffs,axiom,
% 5.31/5.62 ! [C2: nat > complex,N: nat,D: nat > complex] :
% 5.31/5.62 ( ( ! [X4: complex] :
% 5.31/5.62 ( ( groups2073611262835488442omplex
% 5.31/5.62 @ ^ [I: nat] : ( times_times_complex @ ( C2 @ I ) @ ( power_power_complex @ X4 @ I ) )
% 5.31/5.62 @ ( set_ord_atMost_nat @ N ) )
% 5.31/5.62 = ( groups2073611262835488442omplex
% 5.31/5.62 @ ^ [I: nat] : ( times_times_complex @ ( D @ I ) @ ( power_power_complex @ X4 @ I ) )
% 5.31/5.62 @ ( set_ord_atMost_nat @ N ) ) ) )
% 5.31/5.62 = ( ! [I: nat] :
% 5.31/5.62 ( ( ord_less_eq_nat @ I @ N )
% 5.31/5.62 => ( ( C2 @ I )
% 5.31/5.62 = ( D @ I ) ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % polyfun_eq_coeffs
% 5.31/5.62 thf(fact_6881_polyfun__eq__coeffs,axiom,
% 5.31/5.62 ! [C2: nat > real,N: nat,D: nat > real] :
% 5.31/5.62 ( ( ! [X4: real] :
% 5.31/5.62 ( ( groups6591440286371151544t_real
% 5.31/5.62 @ ^ [I: nat] : ( times_times_real @ ( C2 @ I ) @ ( power_power_real @ X4 @ I ) )
% 5.31/5.62 @ ( set_ord_atMost_nat @ N ) )
% 5.31/5.62 = ( groups6591440286371151544t_real
% 5.31/5.62 @ ^ [I: nat] : ( times_times_real @ ( D @ I ) @ ( power_power_real @ X4 @ I ) )
% 5.31/5.62 @ ( set_ord_atMost_nat @ N ) ) ) )
% 5.31/5.62 = ( ! [I: nat] :
% 5.31/5.62 ( ( ord_less_eq_nat @ I @ N )
% 5.31/5.62 => ( ( C2 @ I )
% 5.31/5.62 = ( D @ I ) ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % polyfun_eq_coeffs
% 5.31/5.62 thf(fact_6882_prod_OatMost__Suc__shift,axiom,
% 5.31/5.62 ! [G2: nat > real,N: nat] :
% 5.31/5.62 ( ( groups129246275422532515t_real @ G2 @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 5.31/5.62 = ( times_times_real @ ( G2 @ zero_zero_nat )
% 5.31/5.62 @ ( groups129246275422532515t_real
% 5.31/5.62 @ ^ [I: nat] : ( G2 @ ( suc @ I ) )
% 5.31/5.62 @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % prod.atMost_Suc_shift
% 5.31/5.62 thf(fact_6883_prod_OatMost__Suc__shift,axiom,
% 5.31/5.62 ! [G2: nat > rat,N: nat] :
% 5.31/5.62 ( ( groups73079841787564623at_rat @ G2 @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 5.31/5.62 = ( times_times_rat @ ( G2 @ zero_zero_nat )
% 5.31/5.62 @ ( groups73079841787564623at_rat
% 5.31/5.62 @ ^ [I: nat] : ( G2 @ ( suc @ I ) )
% 5.31/5.62 @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % prod.atMost_Suc_shift
% 5.31/5.62 thf(fact_6884_prod_OatMost__Suc__shift,axiom,
% 5.31/5.62 ! [G2: nat > int,N: nat] :
% 5.31/5.62 ( ( groups705719431365010083at_int @ G2 @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 5.31/5.62 = ( times_times_int @ ( G2 @ zero_zero_nat )
% 5.31/5.62 @ ( groups705719431365010083at_int
% 5.31/5.62 @ ^ [I: nat] : ( G2 @ ( suc @ I ) )
% 5.31/5.62 @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % prod.atMost_Suc_shift
% 5.31/5.62 thf(fact_6885_prod_OatMost__Suc__shift,axiom,
% 5.31/5.62 ! [G2: nat > nat,N: nat] :
% 5.31/5.62 ( ( groups708209901874060359at_nat @ G2 @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 5.31/5.62 = ( times_times_nat @ ( G2 @ zero_zero_nat )
% 5.31/5.62 @ ( groups708209901874060359at_nat
% 5.31/5.62 @ ^ [I: nat] : ( G2 @ ( suc @ I ) )
% 5.31/5.62 @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % prod.atMost_Suc_shift
% 5.31/5.62 thf(fact_6886_sum_Onested__swap_H,axiom,
% 5.31/5.62 ! [A: nat > nat > nat,N: nat] :
% 5.31/5.62 ( ( groups3542108847815614940at_nat
% 5.31/5.62 @ ^ [I: nat] : ( groups3542108847815614940at_nat @ ( A @ I ) @ ( set_ord_lessThan_nat @ I ) )
% 5.31/5.62 @ ( set_ord_atMost_nat @ N ) )
% 5.31/5.62 = ( groups3542108847815614940at_nat
% 5.31/5.62 @ ^ [J: nat] :
% 5.31/5.62 ( groups3542108847815614940at_nat
% 5.31/5.62 @ ^ [I: nat] : ( A @ I @ J )
% 5.31/5.62 @ ( set_or1269000886237332187st_nat @ ( suc @ J ) @ N ) )
% 5.31/5.62 @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % sum.nested_swap'
% 5.31/5.62 thf(fact_6887_sum_Onested__swap_H,axiom,
% 5.31/5.62 ! [A: nat > nat > real,N: nat] :
% 5.31/5.62 ( ( groups6591440286371151544t_real
% 5.31/5.62 @ ^ [I: nat] : ( groups6591440286371151544t_real @ ( A @ I ) @ ( set_ord_lessThan_nat @ I ) )
% 5.31/5.62 @ ( set_ord_atMost_nat @ N ) )
% 5.31/5.62 = ( groups6591440286371151544t_real
% 5.31/5.62 @ ^ [J: nat] :
% 5.31/5.62 ( groups6591440286371151544t_real
% 5.31/5.62 @ ^ [I: nat] : ( A @ I @ J )
% 5.31/5.62 @ ( set_or1269000886237332187st_nat @ ( suc @ J ) @ N ) )
% 5.31/5.62 @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % sum.nested_swap'
% 5.31/5.62 thf(fact_6888_ivl__disj__un__one_I4_J,axiom,
% 5.31/5.62 ! [L: rat,U: rat] :
% 5.31/5.62 ( ( ord_less_eq_rat @ L @ U )
% 5.31/5.62 => ( ( sup_sup_set_rat @ ( set_ord_lessThan_rat @ L ) @ ( set_or633870826150836451st_rat @ L @ U ) )
% 5.31/5.62 = ( set_ord_atMost_rat @ U ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % ivl_disj_un_one(4)
% 5.31/5.62 thf(fact_6889_ivl__disj__un__one_I4_J,axiom,
% 5.31/5.62 ! [L: num,U: num] :
% 5.31/5.62 ( ( ord_less_eq_num @ L @ U )
% 5.31/5.62 => ( ( sup_sup_set_num @ ( set_ord_lessThan_num @ L ) @ ( set_or7049704709247886629st_num @ L @ U ) )
% 5.31/5.62 = ( set_ord_atMost_num @ U ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % ivl_disj_un_one(4)
% 5.31/5.62 thf(fact_6890_ivl__disj__un__one_I4_J,axiom,
% 5.31/5.62 ! [L: nat,U: nat] :
% 5.31/5.62 ( ( ord_less_eq_nat @ L @ U )
% 5.31/5.62 => ( ( sup_sup_set_nat @ ( set_ord_lessThan_nat @ L ) @ ( set_or1269000886237332187st_nat @ L @ U ) )
% 5.31/5.62 = ( set_ord_atMost_nat @ U ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % ivl_disj_un_one(4)
% 5.31/5.62 thf(fact_6891_ivl__disj__un__one_I4_J,axiom,
% 5.31/5.62 ! [L: int,U: int] :
% 5.31/5.62 ( ( ord_less_eq_int @ L @ U )
% 5.31/5.62 => ( ( sup_sup_set_int @ ( set_ord_lessThan_int @ L ) @ ( set_or1266510415728281911st_int @ L @ U ) )
% 5.31/5.62 = ( set_ord_atMost_int @ U ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % ivl_disj_un_one(4)
% 5.31/5.62 thf(fact_6892_ivl__disj__un__one_I4_J,axiom,
% 5.31/5.62 ! [L: real,U: real] :
% 5.31/5.62 ( ( ord_less_eq_real @ L @ U )
% 5.31/5.62 => ( ( sup_sup_set_real @ ( set_or5984915006950818249n_real @ L ) @ ( set_or1222579329274155063t_real @ L @ U ) )
% 5.31/5.62 = ( set_ord_atMost_real @ U ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % ivl_disj_un_one(4)
% 5.31/5.62 thf(fact_6893_ivl__disj__un__singleton_I2_J,axiom,
% 5.31/5.62 ! [U: int] :
% 5.31/5.62 ( ( sup_sup_set_int @ ( set_ord_lessThan_int @ U ) @ ( insert_int @ U @ bot_bot_set_int ) )
% 5.31/5.62 = ( set_ord_atMost_int @ U ) ) ).
% 5.31/5.62
% 5.31/5.62 % ivl_disj_un_singleton(2)
% 5.31/5.62 thf(fact_6894_ivl__disj__un__singleton_I2_J,axiom,
% 5.31/5.62 ! [U: real] :
% 5.31/5.62 ( ( sup_sup_set_real @ ( set_or5984915006950818249n_real @ U ) @ ( insert_real @ U @ bot_bot_set_real ) )
% 5.31/5.62 = ( set_ord_atMost_real @ U ) ) ).
% 5.31/5.62
% 5.31/5.62 % ivl_disj_un_singleton(2)
% 5.31/5.62 thf(fact_6895_ivl__disj__un__singleton_I2_J,axiom,
% 5.31/5.62 ! [U: nat] :
% 5.31/5.62 ( ( sup_sup_set_nat @ ( set_ord_lessThan_nat @ U ) @ ( insert_nat @ U @ bot_bot_set_nat ) )
% 5.31/5.62 = ( set_ord_atMost_nat @ U ) ) ).
% 5.31/5.62
% 5.31/5.62 % ivl_disj_un_singleton(2)
% 5.31/5.62 thf(fact_6896_prod_Onested__swap_H,axiom,
% 5.31/5.62 ! [A: nat > nat > int,N: nat] :
% 5.31/5.62 ( ( groups705719431365010083at_int
% 5.31/5.62 @ ^ [I: nat] : ( groups705719431365010083at_int @ ( A @ I ) @ ( set_ord_lessThan_nat @ I ) )
% 5.31/5.62 @ ( set_ord_atMost_nat @ N ) )
% 5.31/5.62 = ( groups705719431365010083at_int
% 5.31/5.62 @ ^ [J: nat] :
% 5.31/5.62 ( groups705719431365010083at_int
% 5.31/5.62 @ ^ [I: nat] : ( A @ I @ J )
% 5.31/5.62 @ ( set_or1269000886237332187st_nat @ ( suc @ J ) @ N ) )
% 5.31/5.62 @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % prod.nested_swap'
% 5.31/5.62 thf(fact_6897_prod_Onested__swap_H,axiom,
% 5.31/5.62 ! [A: nat > nat > nat,N: nat] :
% 5.31/5.62 ( ( groups708209901874060359at_nat
% 5.31/5.62 @ ^ [I: nat] : ( groups708209901874060359at_nat @ ( A @ I ) @ ( set_ord_lessThan_nat @ I ) )
% 5.31/5.62 @ ( set_ord_atMost_nat @ N ) )
% 5.31/5.62 = ( groups708209901874060359at_nat
% 5.31/5.62 @ ^ [J: nat] :
% 5.31/5.62 ( groups708209901874060359at_nat
% 5.31/5.62 @ ^ [I: nat] : ( A @ I @ J )
% 5.31/5.62 @ ( set_or1269000886237332187st_nat @ ( suc @ J ) @ N ) )
% 5.31/5.62 @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % prod.nested_swap'
% 5.31/5.62 thf(fact_6898_sum__choose__lower,axiom,
% 5.31/5.62 ! [R3: nat,N: nat] :
% 5.31/5.62 ( ( groups3542108847815614940at_nat
% 5.31/5.62 @ ^ [K3: nat] : ( binomial @ ( plus_plus_nat @ R3 @ K3 ) @ K3 )
% 5.31/5.62 @ ( set_ord_atMost_nat @ N ) )
% 5.31/5.62 = ( binomial @ ( suc @ ( plus_plus_nat @ R3 @ N ) ) @ N ) ) ).
% 5.31/5.62
% 5.31/5.62 % sum_choose_lower
% 5.31/5.62 thf(fact_6899_Suc__times__gbinomial,axiom,
% 5.31/5.62 ! [K2: nat,A: complex] :
% 5.31/5.62 ( ( times_times_complex @ ( semiri8010041392384452111omplex @ ( suc @ K2 ) ) @ ( gbinomial_complex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( suc @ K2 ) ) )
% 5.31/5.62 = ( times_times_complex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( gbinomial_complex @ A @ K2 ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % Suc_times_gbinomial
% 5.31/5.62 thf(fact_6900_Suc__times__gbinomial,axiom,
% 5.31/5.62 ! [K2: nat,A: rat] :
% 5.31/5.62 ( ( times_times_rat @ ( semiri681578069525770553at_rat @ ( suc @ K2 ) ) @ ( gbinomial_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( suc @ K2 ) ) )
% 5.31/5.62 = ( times_times_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( gbinomial_rat @ A @ K2 ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % Suc_times_gbinomial
% 5.31/5.62 thf(fact_6901_Suc__times__gbinomial,axiom,
% 5.31/5.62 ! [K2: nat,A: real] :
% 5.31/5.62 ( ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ K2 ) ) @ ( gbinomial_real @ ( plus_plus_real @ A @ one_one_real ) @ ( suc @ K2 ) ) )
% 5.31/5.62 = ( times_times_real @ ( plus_plus_real @ A @ one_one_real ) @ ( gbinomial_real @ A @ K2 ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % Suc_times_gbinomial
% 5.31/5.62 thf(fact_6902_gbinomial__absorption,axiom,
% 5.31/5.62 ! [K2: nat,A: complex] :
% 5.31/5.62 ( ( times_times_complex @ ( semiri8010041392384452111omplex @ ( suc @ K2 ) ) @ ( gbinomial_complex @ A @ ( suc @ K2 ) ) )
% 5.31/5.62 = ( times_times_complex @ A @ ( gbinomial_complex @ ( minus_minus_complex @ A @ one_one_complex ) @ K2 ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % gbinomial_absorption
% 5.31/5.62 thf(fact_6903_gbinomial__absorption,axiom,
% 5.31/5.62 ! [K2: nat,A: rat] :
% 5.31/5.62 ( ( times_times_rat @ ( semiri681578069525770553at_rat @ ( suc @ K2 ) ) @ ( gbinomial_rat @ A @ ( suc @ K2 ) ) )
% 5.31/5.62 = ( times_times_rat @ A @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ K2 ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % gbinomial_absorption
% 5.31/5.62 thf(fact_6904_gbinomial__absorption,axiom,
% 5.31/5.62 ! [K2: nat,A: real] :
% 5.31/5.62 ( ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ K2 ) ) @ ( gbinomial_real @ A @ ( suc @ K2 ) ) )
% 5.31/5.62 = ( times_times_real @ A @ ( gbinomial_real @ ( minus_minus_real @ A @ one_one_real ) @ K2 ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % gbinomial_absorption
% 5.31/5.62 thf(fact_6905_gbinomial__trinomial__revision,axiom,
% 5.31/5.62 ! [K2: nat,M2: nat,A: rat] :
% 5.31/5.62 ( ( ord_less_eq_nat @ K2 @ M2 )
% 5.31/5.62 => ( ( times_times_rat @ ( gbinomial_rat @ A @ M2 ) @ ( gbinomial_rat @ ( semiri681578069525770553at_rat @ M2 ) @ K2 ) )
% 5.31/5.62 = ( times_times_rat @ ( gbinomial_rat @ A @ K2 ) @ ( gbinomial_rat @ ( minus_minus_rat @ A @ ( semiri681578069525770553at_rat @ K2 ) ) @ ( minus_minus_nat @ M2 @ K2 ) ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % gbinomial_trinomial_revision
% 5.31/5.62 thf(fact_6906_gbinomial__trinomial__revision,axiom,
% 5.31/5.62 ! [K2: nat,M2: nat,A: real] :
% 5.31/5.62 ( ( ord_less_eq_nat @ K2 @ M2 )
% 5.31/5.62 => ( ( times_times_real @ ( gbinomial_real @ A @ M2 ) @ ( gbinomial_real @ ( semiri5074537144036343181t_real @ M2 ) @ K2 ) )
% 5.31/5.62 = ( times_times_real @ ( gbinomial_real @ A @ K2 ) @ ( gbinomial_real @ ( minus_minus_real @ A @ ( semiri5074537144036343181t_real @ K2 ) ) @ ( minus_minus_nat @ M2 @ K2 ) ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % gbinomial_trinomial_revision
% 5.31/5.62 thf(fact_6907_zero__polynom__imp__zero__coeffs,axiom,
% 5.31/5.62 ! [C2: nat > complex,N: nat,K2: nat] :
% 5.31/5.62 ( ! [W: complex] :
% 5.31/5.62 ( ( groups2073611262835488442omplex
% 5.31/5.62 @ ^ [I: nat] : ( times_times_complex @ ( C2 @ I ) @ ( power_power_complex @ W @ I ) )
% 5.31/5.62 @ ( set_ord_atMost_nat @ N ) )
% 5.31/5.62 = zero_zero_complex )
% 5.31/5.62 => ( ( ord_less_eq_nat @ K2 @ N )
% 5.31/5.62 => ( ( C2 @ K2 )
% 5.31/5.62 = zero_zero_complex ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % zero_polynom_imp_zero_coeffs
% 5.31/5.62 thf(fact_6908_zero__polynom__imp__zero__coeffs,axiom,
% 5.31/5.62 ! [C2: nat > real,N: nat,K2: nat] :
% 5.31/5.62 ( ! [W: real] :
% 5.31/5.62 ( ( groups6591440286371151544t_real
% 5.31/5.62 @ ^ [I: nat] : ( times_times_real @ ( C2 @ I ) @ ( power_power_real @ W @ I ) )
% 5.31/5.62 @ ( set_ord_atMost_nat @ N ) )
% 5.31/5.62 = zero_zero_real )
% 5.31/5.62 => ( ( ord_less_eq_nat @ K2 @ N )
% 5.31/5.62 => ( ( C2 @ K2 )
% 5.31/5.62 = zero_zero_real ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % zero_polynom_imp_zero_coeffs
% 5.31/5.62 thf(fact_6909_polyfun__eq__0,axiom,
% 5.31/5.62 ! [C2: nat > complex,N: nat] :
% 5.31/5.62 ( ( ! [X4: complex] :
% 5.31/5.62 ( ( groups2073611262835488442omplex
% 5.31/5.62 @ ^ [I: nat] : ( times_times_complex @ ( C2 @ I ) @ ( power_power_complex @ X4 @ I ) )
% 5.31/5.62 @ ( set_ord_atMost_nat @ N ) )
% 5.31/5.62 = zero_zero_complex ) )
% 5.31/5.62 = ( ! [I: nat] :
% 5.31/5.62 ( ( ord_less_eq_nat @ I @ N )
% 5.31/5.62 => ( ( C2 @ I )
% 5.31/5.62 = zero_zero_complex ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % polyfun_eq_0
% 5.31/5.62 thf(fact_6910_polyfun__eq__0,axiom,
% 5.31/5.62 ! [C2: nat > real,N: nat] :
% 5.31/5.62 ( ( ! [X4: real] :
% 5.31/5.62 ( ( groups6591440286371151544t_real
% 5.31/5.62 @ ^ [I: nat] : ( times_times_real @ ( C2 @ I ) @ ( power_power_real @ X4 @ I ) )
% 5.31/5.62 @ ( set_ord_atMost_nat @ N ) )
% 5.31/5.62 = zero_zero_real ) )
% 5.31/5.62 = ( ! [I: nat] :
% 5.31/5.62 ( ( ord_less_eq_nat @ I @ N )
% 5.31/5.62 => ( ( C2 @ I )
% 5.31/5.62 = zero_zero_real ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % polyfun_eq_0
% 5.31/5.62 thf(fact_6911_sum_OatMost__shift,axiom,
% 5.31/5.62 ! [G2: nat > rat,N: nat] :
% 5.31/5.62 ( ( groups2906978787729119204at_rat @ G2 @ ( set_ord_atMost_nat @ N ) )
% 5.31/5.62 = ( plus_plus_rat @ ( G2 @ zero_zero_nat )
% 5.31/5.62 @ ( groups2906978787729119204at_rat
% 5.31/5.62 @ ^ [I: nat] : ( G2 @ ( suc @ I ) )
% 5.31/5.62 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % sum.atMost_shift
% 5.31/5.62 thf(fact_6912_sum_OatMost__shift,axiom,
% 5.31/5.62 ! [G2: nat > int,N: nat] :
% 5.31/5.62 ( ( groups3539618377306564664at_int @ G2 @ ( set_ord_atMost_nat @ N ) )
% 5.31/5.62 = ( plus_plus_int @ ( G2 @ zero_zero_nat )
% 5.31/5.62 @ ( groups3539618377306564664at_int
% 5.31/5.62 @ ^ [I: nat] : ( G2 @ ( suc @ I ) )
% 5.31/5.62 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % sum.atMost_shift
% 5.31/5.62 thf(fact_6913_sum_OatMost__shift,axiom,
% 5.31/5.62 ! [G2: nat > nat,N: nat] :
% 5.31/5.62 ( ( groups3542108847815614940at_nat @ G2 @ ( set_ord_atMost_nat @ N ) )
% 5.31/5.62 = ( plus_plus_nat @ ( G2 @ zero_zero_nat )
% 5.31/5.62 @ ( groups3542108847815614940at_nat
% 5.31/5.62 @ ^ [I: nat] : ( G2 @ ( suc @ I ) )
% 5.31/5.62 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % sum.atMost_shift
% 5.31/5.62 thf(fact_6914_sum_OatMost__shift,axiom,
% 5.31/5.62 ! [G2: nat > real,N: nat] :
% 5.31/5.62 ( ( groups6591440286371151544t_real @ G2 @ ( set_ord_atMost_nat @ N ) )
% 5.31/5.62 = ( plus_plus_real @ ( G2 @ zero_zero_nat )
% 5.31/5.62 @ ( groups6591440286371151544t_real
% 5.31/5.62 @ ^ [I: nat] : ( G2 @ ( suc @ I ) )
% 5.31/5.62 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % sum.atMost_shift
% 5.31/5.62 thf(fact_6915_sum__up__index__split,axiom,
% 5.31/5.62 ! [F2: nat > rat,M2: nat,N: nat] :
% 5.31/5.62 ( ( groups2906978787729119204at_rat @ F2 @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M2 @ N ) ) )
% 5.31/5.62 = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ F2 @ ( set_ord_atMost_nat @ M2 ) ) @ ( groups2906978787729119204at_rat @ F2 @ ( set_or1269000886237332187st_nat @ ( suc @ M2 ) @ ( plus_plus_nat @ M2 @ N ) ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % sum_up_index_split
% 5.31/5.62 thf(fact_6916_sum__up__index__split,axiom,
% 5.31/5.62 ! [F2: nat > int,M2: nat,N: nat] :
% 5.31/5.62 ( ( groups3539618377306564664at_int @ F2 @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M2 @ N ) ) )
% 5.31/5.62 = ( plus_plus_int @ ( groups3539618377306564664at_int @ F2 @ ( set_ord_atMost_nat @ M2 ) ) @ ( groups3539618377306564664at_int @ F2 @ ( set_or1269000886237332187st_nat @ ( suc @ M2 ) @ ( plus_plus_nat @ M2 @ N ) ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % sum_up_index_split
% 5.31/5.62 thf(fact_6917_sum__up__index__split,axiom,
% 5.31/5.62 ! [F2: nat > nat,M2: nat,N: nat] :
% 5.31/5.62 ( ( groups3542108847815614940at_nat @ F2 @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M2 @ N ) ) )
% 5.31/5.62 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ F2 @ ( set_ord_atMost_nat @ M2 ) ) @ ( groups3542108847815614940at_nat @ F2 @ ( set_or1269000886237332187st_nat @ ( suc @ M2 ) @ ( plus_plus_nat @ M2 @ N ) ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % sum_up_index_split
% 5.31/5.62 thf(fact_6918_sum__up__index__split,axiom,
% 5.31/5.62 ! [F2: nat > real,M2: nat,N: nat] :
% 5.31/5.62 ( ( groups6591440286371151544t_real @ F2 @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M2 @ N ) ) )
% 5.31/5.62 = ( plus_plus_real @ ( groups6591440286371151544t_real @ F2 @ ( set_ord_atMost_nat @ M2 ) ) @ ( groups6591440286371151544t_real @ F2 @ ( set_or1269000886237332187st_nat @ ( suc @ M2 ) @ ( plus_plus_nat @ M2 @ N ) ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % sum_up_index_split
% 5.31/5.62 thf(fact_6919_prod_OatMost__shift,axiom,
% 5.31/5.62 ! [G2: nat > real,N: nat] :
% 5.31/5.62 ( ( groups129246275422532515t_real @ G2 @ ( set_ord_atMost_nat @ N ) )
% 5.31/5.62 = ( times_times_real @ ( G2 @ zero_zero_nat )
% 5.31/5.62 @ ( groups129246275422532515t_real
% 5.31/5.62 @ ^ [I: nat] : ( G2 @ ( suc @ I ) )
% 5.31/5.62 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % prod.atMost_shift
% 5.31/5.62 thf(fact_6920_prod_OatMost__shift,axiom,
% 5.31/5.62 ! [G2: nat > rat,N: nat] :
% 5.31/5.62 ( ( groups73079841787564623at_rat @ G2 @ ( set_ord_atMost_nat @ N ) )
% 5.31/5.62 = ( times_times_rat @ ( G2 @ zero_zero_nat )
% 5.31/5.62 @ ( groups73079841787564623at_rat
% 5.31/5.62 @ ^ [I: nat] : ( G2 @ ( suc @ I ) )
% 5.31/5.62 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % prod.atMost_shift
% 5.31/5.62 thf(fact_6921_prod_OatMost__shift,axiom,
% 5.31/5.62 ! [G2: nat > int,N: nat] :
% 5.31/5.62 ( ( groups705719431365010083at_int @ G2 @ ( set_ord_atMost_nat @ N ) )
% 5.31/5.62 = ( times_times_int @ ( G2 @ zero_zero_nat )
% 5.31/5.62 @ ( groups705719431365010083at_int
% 5.31/5.62 @ ^ [I: nat] : ( G2 @ ( suc @ I ) )
% 5.31/5.62 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % prod.atMost_shift
% 5.31/5.62 thf(fact_6922_prod_OatMost__shift,axiom,
% 5.31/5.62 ! [G2: nat > nat,N: nat] :
% 5.31/5.62 ( ( groups708209901874060359at_nat @ G2 @ ( set_ord_atMost_nat @ N ) )
% 5.31/5.62 = ( times_times_nat @ ( G2 @ zero_zero_nat )
% 5.31/5.62 @ ( groups708209901874060359at_nat
% 5.31/5.62 @ ^ [I: nat] : ( G2 @ ( suc @ I ) )
% 5.31/5.62 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % prod.atMost_shift
% 5.31/5.62 thf(fact_6923_gbinomial__r__part__sum,axiom,
% 5.31/5.62 ! [M2: nat] :
% 5.31/5.62 ( ( groups2906978787729119204at_rat @ ( gbinomial_rat @ ( plus_plus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( semiri681578069525770553at_rat @ M2 ) ) @ one_one_rat ) ) @ ( set_ord_atMost_nat @ M2 ) )
% 5.31/5.62 = ( power_power_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % gbinomial_r_part_sum
% 5.31/5.62 thf(fact_6924_gbinomial__r__part__sum,axiom,
% 5.31/5.62 ! [M2: nat] :
% 5.31/5.62 ( ( groups2073611262835488442omplex @ ( gbinomial_complex @ ( plus_plus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( semiri8010041392384452111omplex @ M2 ) ) @ one_one_complex ) ) @ ( set_ord_atMost_nat @ M2 ) )
% 5.31/5.62 = ( power_power_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % gbinomial_r_part_sum
% 5.31/5.62 thf(fact_6925_gbinomial__r__part__sum,axiom,
% 5.31/5.62 ! [M2: nat] :
% 5.31/5.62 ( ( groups6591440286371151544t_real @ ( gbinomial_real @ ( plus_plus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M2 ) ) @ one_one_real ) ) @ ( set_ord_atMost_nat @ M2 ) )
% 5.31/5.62 = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % gbinomial_r_part_sum
% 5.31/5.62 thf(fact_6926_sum__choose__diagonal,axiom,
% 5.31/5.62 ! [M2: nat,N: nat] :
% 5.31/5.62 ( ( ord_less_eq_nat @ M2 @ N )
% 5.31/5.62 => ( ( groups3542108847815614940at_nat
% 5.31/5.62 @ ^ [K3: nat] : ( binomial @ ( minus_minus_nat @ N @ K3 ) @ ( minus_minus_nat @ M2 @ K3 ) )
% 5.31/5.62 @ ( set_ord_atMost_nat @ M2 ) )
% 5.31/5.62 = ( binomial @ ( suc @ N ) @ M2 ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % sum_choose_diagonal
% 5.31/5.62 thf(fact_6927_vandermonde,axiom,
% 5.31/5.62 ! [M2: nat,N: nat,R3: nat] :
% 5.31/5.62 ( ( groups3542108847815614940at_nat
% 5.31/5.62 @ ^ [K3: nat] : ( times_times_nat @ ( binomial @ M2 @ K3 ) @ ( binomial @ N @ ( minus_minus_nat @ R3 @ K3 ) ) )
% 5.31/5.62 @ ( set_ord_atMost_nat @ R3 ) )
% 5.31/5.62 = ( binomial @ ( plus_plus_nat @ M2 @ N ) @ R3 ) ) ).
% 5.31/5.62
% 5.31/5.62 % vandermonde
% 5.31/5.62 thf(fact_6928_bits__induct,axiom,
% 5.31/5.62 ! [P2: nat > $o,A: nat] :
% 5.31/5.62 ( ! [A3: nat] :
% 5.31/5.62 ( ( ( divide_divide_nat @ A3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.31/5.62 = A3 )
% 5.31/5.62 => ( P2 @ A3 ) )
% 5.31/5.62 => ( ! [A3: nat,B3: $o] :
% 5.31/5.62 ( ( P2 @ A3 )
% 5.31/5.62 => ( ( ( divide_divide_nat @ ( plus_plus_nat @ ( zero_n2687167440665602831ol_nat @ B3 ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.31/5.62 = A3 )
% 5.31/5.62 => ( P2 @ ( plus_plus_nat @ ( zero_n2687167440665602831ol_nat @ B3 ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A3 ) ) ) ) )
% 5.31/5.62 => ( P2 @ A ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % bits_induct
% 5.31/5.62 thf(fact_6929_bits__induct,axiom,
% 5.31/5.62 ! [P2: int > $o,A: int] :
% 5.31/5.62 ( ! [A3: int] :
% 5.31/5.62 ( ( ( divide_divide_int @ A3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.31/5.62 = A3 )
% 5.31/5.62 => ( P2 @ A3 ) )
% 5.31/5.62 => ( ! [A3: int,B3: $o] :
% 5.31/5.62 ( ( P2 @ A3 )
% 5.31/5.62 => ( ( ( divide_divide_int @ ( plus_plus_int @ ( zero_n2684676970156552555ol_int @ B3 ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A3 ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.31/5.62 = A3 )
% 5.31/5.62 => ( P2 @ ( plus_plus_int @ ( zero_n2684676970156552555ol_int @ B3 ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A3 ) ) ) ) )
% 5.31/5.62 => ( P2 @ A ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % bits_induct
% 5.31/5.62 thf(fact_6930_bits__induct,axiom,
% 5.31/5.62 ! [P2: code_integer > $o,A: code_integer] :
% 5.31/5.62 ( ! [A3: code_integer] :
% 5.31/5.62 ( ( ( divide6298287555418463151nteger @ A3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.31/5.62 = A3 )
% 5.31/5.62 => ( P2 @ A3 ) )
% 5.31/5.62 => ( ! [A3: code_integer,B3: $o] :
% 5.31/5.62 ( ( P2 @ A3 )
% 5.31/5.62 => ( ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ ( zero_n356916108424825756nteger @ B3 ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A3 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.31/5.62 = A3 )
% 5.31/5.62 => ( P2 @ ( plus_p5714425477246183910nteger @ ( zero_n356916108424825756nteger @ B3 ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A3 ) ) ) ) )
% 5.31/5.62 => ( P2 @ A ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % bits_induct
% 5.31/5.62 thf(fact_6931_gbinomial__partial__row__sum,axiom,
% 5.31/5.62 ! [A: complex,M2: nat] :
% 5.31/5.62 ( ( groups2073611262835488442omplex
% 5.31/5.62 @ ^ [K3: nat] : ( times_times_complex @ ( gbinomial_complex @ A @ K3 ) @ ( minus_minus_complex @ ( divide1717551699836669952omplex @ A @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) @ ( semiri8010041392384452111omplex @ K3 ) ) )
% 5.31/5.62 @ ( set_ord_atMost_nat @ M2 ) )
% 5.31/5.62 = ( times_times_complex @ ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( semiri8010041392384452111omplex @ M2 ) @ one_one_complex ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) @ ( gbinomial_complex @ A @ ( plus_plus_nat @ M2 @ one_one_nat ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % gbinomial_partial_row_sum
% 5.31/5.62 thf(fact_6932_gbinomial__partial__row__sum,axiom,
% 5.31/5.62 ! [A: rat,M2: nat] :
% 5.31/5.62 ( ( groups2906978787729119204at_rat
% 5.31/5.62 @ ^ [K3: nat] : ( times_times_rat @ ( gbinomial_rat @ A @ K3 ) @ ( minus_minus_rat @ ( divide_divide_rat @ A @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) @ ( semiri681578069525770553at_rat @ K3 ) ) )
% 5.31/5.62 @ ( set_ord_atMost_nat @ M2 ) )
% 5.31/5.62 = ( times_times_rat @ ( divide_divide_rat @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ M2 ) @ one_one_rat ) @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) @ ( gbinomial_rat @ A @ ( plus_plus_nat @ M2 @ one_one_nat ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % gbinomial_partial_row_sum
% 5.31/5.62 thf(fact_6933_gbinomial__partial__row__sum,axiom,
% 5.31/5.62 ! [A: real,M2: nat] :
% 5.31/5.62 ( ( groups6591440286371151544t_real
% 5.31/5.62 @ ^ [K3: nat] : ( times_times_real @ ( gbinomial_real @ A @ K3 ) @ ( minus_minus_real @ ( divide_divide_real @ A @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ K3 ) ) )
% 5.31/5.62 @ ( set_ord_atMost_nat @ M2 ) )
% 5.31/5.62 = ( times_times_real @ ( divide_divide_real @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ M2 ) @ one_one_real ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( gbinomial_real @ A @ ( plus_plus_nat @ M2 @ one_one_nat ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % gbinomial_partial_row_sum
% 5.31/5.62 thf(fact_6934_gbinomial__factors,axiom,
% 5.31/5.62 ! [A: complex,K2: nat] :
% 5.31/5.62 ( ( gbinomial_complex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( suc @ K2 ) )
% 5.31/5.62 = ( times_times_complex @ ( divide1717551699836669952omplex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( semiri8010041392384452111omplex @ ( suc @ K2 ) ) ) @ ( gbinomial_complex @ A @ K2 ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % gbinomial_factors
% 5.31/5.62 thf(fact_6935_gbinomial__factors,axiom,
% 5.31/5.62 ! [A: rat,K2: nat] :
% 5.31/5.62 ( ( gbinomial_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( suc @ K2 ) )
% 5.31/5.62 = ( times_times_rat @ ( divide_divide_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( semiri681578069525770553at_rat @ ( suc @ K2 ) ) ) @ ( gbinomial_rat @ A @ K2 ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % gbinomial_factors
% 5.31/5.62 thf(fact_6936_gbinomial__factors,axiom,
% 5.31/5.62 ! [A: real,K2: nat] :
% 5.31/5.62 ( ( gbinomial_real @ ( plus_plus_real @ A @ one_one_real ) @ ( suc @ K2 ) )
% 5.31/5.62 = ( times_times_real @ ( divide_divide_real @ ( plus_plus_real @ A @ one_one_real ) @ ( semiri5074537144036343181t_real @ ( suc @ K2 ) ) ) @ ( gbinomial_real @ A @ K2 ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % gbinomial_factors
% 5.31/5.62 thf(fact_6937_gbinomial__rec,axiom,
% 5.31/5.62 ! [A: complex,K2: nat] :
% 5.31/5.62 ( ( gbinomial_complex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( suc @ K2 ) )
% 5.31/5.62 = ( times_times_complex @ ( gbinomial_complex @ A @ K2 ) @ ( divide1717551699836669952omplex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( semiri8010041392384452111omplex @ ( suc @ K2 ) ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % gbinomial_rec
% 5.31/5.62 thf(fact_6938_gbinomial__rec,axiom,
% 5.31/5.62 ! [A: rat,K2: nat] :
% 5.31/5.62 ( ( gbinomial_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( suc @ K2 ) )
% 5.31/5.62 = ( times_times_rat @ ( gbinomial_rat @ A @ K2 ) @ ( divide_divide_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( semiri681578069525770553at_rat @ ( suc @ K2 ) ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % gbinomial_rec
% 5.31/5.62 thf(fact_6939_gbinomial__rec,axiom,
% 5.31/5.62 ! [A: real,K2: nat] :
% 5.31/5.62 ( ( gbinomial_real @ ( plus_plus_real @ A @ one_one_real ) @ ( suc @ K2 ) )
% 5.31/5.62 = ( times_times_real @ ( gbinomial_real @ A @ K2 ) @ ( divide_divide_real @ ( plus_plus_real @ A @ one_one_real ) @ ( semiri5074537144036343181t_real @ ( suc @ K2 ) ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % gbinomial_rec
% 5.31/5.62 thf(fact_6940_sum__gp__basic,axiom,
% 5.31/5.62 ! [X: code_integer,N: nat] :
% 5.31/5.62 ( ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ one_one_Code_integer @ X ) @ ( groups7501900531339628137nteger @ ( power_8256067586552552935nteger @ X ) @ ( set_ord_atMost_nat @ N ) ) )
% 5.31/5.62 = ( minus_8373710615458151222nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ X @ ( suc @ N ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % sum_gp_basic
% 5.31/5.62 thf(fact_6941_sum__gp__basic,axiom,
% 5.31/5.62 ! [X: complex,N: nat] :
% 5.31/5.62 ( ( times_times_complex @ ( minus_minus_complex @ one_one_complex @ X ) @ ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_ord_atMost_nat @ N ) ) )
% 5.31/5.62 = ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ X @ ( suc @ N ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % sum_gp_basic
% 5.31/5.62 thf(fact_6942_sum__gp__basic,axiom,
% 5.31/5.62 ! [X: rat,N: nat] :
% 5.31/5.62 ( ( times_times_rat @ ( minus_minus_rat @ one_one_rat @ X ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_ord_atMost_nat @ N ) ) )
% 5.31/5.62 = ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X @ ( suc @ N ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % sum_gp_basic
% 5.31/5.62 thf(fact_6943_sum__gp__basic,axiom,
% 5.31/5.62 ! [X: int,N: nat] :
% 5.31/5.62 ( ( times_times_int @ ( minus_minus_int @ one_one_int @ X ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X ) @ ( set_ord_atMost_nat @ N ) ) )
% 5.31/5.62 = ( minus_minus_int @ one_one_int @ ( power_power_int @ X @ ( suc @ N ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % sum_gp_basic
% 5.31/5.62 thf(fact_6944_sum__gp__basic,axiom,
% 5.31/5.62 ! [X: real,N: nat] :
% 5.31/5.62 ( ( times_times_real @ ( minus_minus_real @ one_one_real @ X ) @ ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_ord_atMost_nat @ N ) ) )
% 5.31/5.62 = ( minus_minus_real @ one_one_real @ ( power_power_real @ X @ ( suc @ N ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % sum_gp_basic
% 5.31/5.62 thf(fact_6945_polyfun__finite__roots,axiom,
% 5.31/5.62 ! [C2: nat > complex,N: nat] :
% 5.31/5.62 ( ( finite3207457112153483333omplex
% 5.31/5.62 @ ( collect_complex
% 5.31/5.62 @ ^ [X4: complex] :
% 5.31/5.62 ( ( groups2073611262835488442omplex
% 5.31/5.62 @ ^ [I: nat] : ( times_times_complex @ ( C2 @ I ) @ ( power_power_complex @ X4 @ I ) )
% 5.31/5.62 @ ( set_ord_atMost_nat @ N ) )
% 5.31/5.62 = zero_zero_complex ) ) )
% 5.31/5.62 = ( ? [I: nat] :
% 5.31/5.62 ( ( ord_less_eq_nat @ I @ N )
% 5.31/5.62 & ( ( C2 @ I )
% 5.31/5.62 != zero_zero_complex ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % polyfun_finite_roots
% 5.31/5.62 thf(fact_6946_polyfun__finite__roots,axiom,
% 5.31/5.62 ! [C2: nat > real,N: nat] :
% 5.31/5.62 ( ( finite_finite_real
% 5.31/5.62 @ ( collect_real
% 5.31/5.62 @ ^ [X4: real] :
% 5.31/5.62 ( ( groups6591440286371151544t_real
% 5.31/5.62 @ ^ [I: nat] : ( times_times_real @ ( C2 @ I ) @ ( power_power_real @ X4 @ I ) )
% 5.31/5.62 @ ( set_ord_atMost_nat @ N ) )
% 5.31/5.62 = zero_zero_real ) ) )
% 5.31/5.62 = ( ? [I: nat] :
% 5.31/5.62 ( ( ord_less_eq_nat @ I @ N )
% 5.31/5.62 & ( ( C2 @ I )
% 5.31/5.62 != zero_zero_real ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % polyfun_finite_roots
% 5.31/5.62 thf(fact_6947_polyfun__roots__finite,axiom,
% 5.31/5.62 ! [C2: nat > complex,K2: nat,N: nat] :
% 5.31/5.62 ( ( ( C2 @ K2 )
% 5.31/5.62 != zero_zero_complex )
% 5.31/5.62 => ( ( ord_less_eq_nat @ K2 @ N )
% 5.31/5.62 => ( finite3207457112153483333omplex
% 5.31/5.62 @ ( collect_complex
% 5.31/5.62 @ ^ [Z4: complex] :
% 5.31/5.62 ( ( groups2073611262835488442omplex
% 5.31/5.62 @ ^ [I: nat] : ( times_times_complex @ ( C2 @ I ) @ ( power_power_complex @ Z4 @ I ) )
% 5.31/5.62 @ ( set_ord_atMost_nat @ N ) )
% 5.31/5.62 = zero_zero_complex ) ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % polyfun_roots_finite
% 5.31/5.62 thf(fact_6948_polyfun__roots__finite,axiom,
% 5.31/5.62 ! [C2: nat > real,K2: nat,N: nat] :
% 5.31/5.62 ( ( ( C2 @ K2 )
% 5.31/5.62 != zero_zero_real )
% 5.31/5.62 => ( ( ord_less_eq_nat @ K2 @ N )
% 5.31/5.62 => ( finite_finite_real
% 5.31/5.62 @ ( collect_real
% 5.31/5.62 @ ^ [Z4: real] :
% 5.31/5.62 ( ( groups6591440286371151544t_real
% 5.31/5.62 @ ^ [I: nat] : ( times_times_real @ ( C2 @ I ) @ ( power_power_real @ Z4 @ I ) )
% 5.31/5.62 @ ( set_ord_atMost_nat @ N ) )
% 5.31/5.62 = zero_zero_real ) ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % polyfun_roots_finite
% 5.31/5.62 thf(fact_6949_polyfun__roots__card,axiom,
% 5.31/5.62 ! [C2: nat > complex,K2: nat,N: nat] :
% 5.31/5.62 ( ( ( C2 @ K2 )
% 5.31/5.62 != zero_zero_complex )
% 5.31/5.62 => ( ( ord_less_eq_nat @ K2 @ N )
% 5.31/5.62 => ( ord_less_eq_nat
% 5.31/5.62 @ ( finite_card_complex
% 5.31/5.62 @ ( collect_complex
% 5.31/5.62 @ ^ [Z4: complex] :
% 5.31/5.62 ( ( groups2073611262835488442omplex
% 5.31/5.62 @ ^ [I: nat] : ( times_times_complex @ ( C2 @ I ) @ ( power_power_complex @ Z4 @ I ) )
% 5.31/5.62 @ ( set_ord_atMost_nat @ N ) )
% 5.31/5.62 = zero_zero_complex ) ) )
% 5.31/5.62 @ N ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % polyfun_roots_card
% 5.31/5.62 thf(fact_6950_polyfun__roots__card,axiom,
% 5.31/5.62 ! [C2: nat > real,K2: nat,N: nat] :
% 5.31/5.62 ( ( ( C2 @ K2 )
% 5.31/5.62 != zero_zero_real )
% 5.31/5.62 => ( ( ord_less_eq_nat @ K2 @ N )
% 5.31/5.62 => ( ord_less_eq_nat
% 5.31/5.62 @ ( finite_card_real
% 5.31/5.62 @ ( collect_real
% 5.31/5.62 @ ^ [Z4: real] :
% 5.31/5.62 ( ( groups6591440286371151544t_real
% 5.31/5.62 @ ^ [I: nat] : ( times_times_real @ ( C2 @ I ) @ ( power_power_real @ Z4 @ I ) )
% 5.31/5.62 @ ( set_ord_atMost_nat @ N ) )
% 5.31/5.62 = zero_zero_real ) ) )
% 5.31/5.62 @ N ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % polyfun_roots_card
% 5.31/5.62 thf(fact_6951_polyfun__linear__factor__root,axiom,
% 5.31/5.62 ! [C2: nat > complex,A: complex,N: nat] :
% 5.31/5.62 ( ( ( groups2073611262835488442omplex
% 5.31/5.62 @ ^ [I: nat] : ( times_times_complex @ ( C2 @ I ) @ ( power_power_complex @ A @ I ) )
% 5.31/5.62 @ ( set_ord_atMost_nat @ N ) )
% 5.31/5.62 = zero_zero_complex )
% 5.31/5.62 => ~ ! [B3: nat > complex] :
% 5.31/5.62 ~ ! [Z5: complex] :
% 5.31/5.62 ( ( groups2073611262835488442omplex
% 5.31/5.62 @ ^ [I: nat] : ( times_times_complex @ ( C2 @ I ) @ ( power_power_complex @ Z5 @ I ) )
% 5.31/5.62 @ ( set_ord_atMost_nat @ N ) )
% 5.31/5.62 = ( times_times_complex @ ( minus_minus_complex @ Z5 @ A )
% 5.31/5.62 @ ( groups2073611262835488442omplex
% 5.31/5.62 @ ^ [I: nat] : ( times_times_complex @ ( B3 @ I ) @ ( power_power_complex @ Z5 @ I ) )
% 5.31/5.62 @ ( set_ord_lessThan_nat @ N ) ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % polyfun_linear_factor_root
% 5.31/5.62 thf(fact_6952_polyfun__linear__factor__root,axiom,
% 5.31/5.62 ! [C2: nat > rat,A: rat,N: nat] :
% 5.31/5.62 ( ( ( groups2906978787729119204at_rat
% 5.31/5.62 @ ^ [I: nat] : ( times_times_rat @ ( C2 @ I ) @ ( power_power_rat @ A @ I ) )
% 5.31/5.62 @ ( set_ord_atMost_nat @ N ) )
% 5.31/5.62 = zero_zero_rat )
% 5.31/5.62 => ~ ! [B3: nat > rat] :
% 5.31/5.62 ~ ! [Z5: rat] :
% 5.31/5.62 ( ( groups2906978787729119204at_rat
% 5.31/5.62 @ ^ [I: nat] : ( times_times_rat @ ( C2 @ I ) @ ( power_power_rat @ Z5 @ I ) )
% 5.31/5.62 @ ( set_ord_atMost_nat @ N ) )
% 5.31/5.62 = ( times_times_rat @ ( minus_minus_rat @ Z5 @ A )
% 5.31/5.62 @ ( groups2906978787729119204at_rat
% 5.31/5.62 @ ^ [I: nat] : ( times_times_rat @ ( B3 @ I ) @ ( power_power_rat @ Z5 @ I ) )
% 5.31/5.62 @ ( set_ord_lessThan_nat @ N ) ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % polyfun_linear_factor_root
% 5.31/5.62 thf(fact_6953_polyfun__linear__factor__root,axiom,
% 5.31/5.62 ! [C2: nat > int,A: int,N: nat] :
% 5.31/5.62 ( ( ( groups3539618377306564664at_int
% 5.31/5.62 @ ^ [I: nat] : ( times_times_int @ ( C2 @ I ) @ ( power_power_int @ A @ I ) )
% 5.31/5.62 @ ( set_ord_atMost_nat @ N ) )
% 5.31/5.62 = zero_zero_int )
% 5.31/5.62 => ~ ! [B3: nat > int] :
% 5.31/5.62 ~ ! [Z5: int] :
% 5.31/5.62 ( ( groups3539618377306564664at_int
% 5.31/5.62 @ ^ [I: nat] : ( times_times_int @ ( C2 @ I ) @ ( power_power_int @ Z5 @ I ) )
% 5.31/5.62 @ ( set_ord_atMost_nat @ N ) )
% 5.31/5.62 = ( times_times_int @ ( minus_minus_int @ Z5 @ A )
% 5.31/5.62 @ ( groups3539618377306564664at_int
% 5.31/5.62 @ ^ [I: nat] : ( times_times_int @ ( B3 @ I ) @ ( power_power_int @ Z5 @ I ) )
% 5.31/5.62 @ ( set_ord_lessThan_nat @ N ) ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % polyfun_linear_factor_root
% 5.31/5.62 thf(fact_6954_polyfun__linear__factor__root,axiom,
% 5.31/5.62 ! [C2: nat > real,A: real,N: nat] :
% 5.31/5.62 ( ( ( groups6591440286371151544t_real
% 5.31/5.62 @ ^ [I: nat] : ( times_times_real @ ( C2 @ I ) @ ( power_power_real @ A @ I ) )
% 5.31/5.62 @ ( set_ord_atMost_nat @ N ) )
% 5.31/5.62 = zero_zero_real )
% 5.31/5.62 => ~ ! [B3: nat > real] :
% 5.31/5.62 ~ ! [Z5: real] :
% 5.31/5.62 ( ( groups6591440286371151544t_real
% 5.31/5.62 @ ^ [I: nat] : ( times_times_real @ ( C2 @ I ) @ ( power_power_real @ Z5 @ I ) )
% 5.31/5.62 @ ( set_ord_atMost_nat @ N ) )
% 5.31/5.62 = ( times_times_real @ ( minus_minus_real @ Z5 @ A )
% 5.31/5.62 @ ( groups6591440286371151544t_real
% 5.31/5.62 @ ^ [I: nat] : ( times_times_real @ ( B3 @ I ) @ ( power_power_real @ Z5 @ I ) )
% 5.31/5.62 @ ( set_ord_lessThan_nat @ N ) ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % polyfun_linear_factor_root
% 5.31/5.62 thf(fact_6955_polyfun__linear__factor,axiom,
% 5.31/5.62 ! [C2: nat > complex,N: nat,A: complex] :
% 5.31/5.62 ? [B3: nat > complex] :
% 5.31/5.62 ! [Z5: complex] :
% 5.31/5.62 ( ( groups2073611262835488442omplex
% 5.31/5.62 @ ^ [I: nat] : ( times_times_complex @ ( C2 @ I ) @ ( power_power_complex @ Z5 @ I ) )
% 5.31/5.62 @ ( set_ord_atMost_nat @ N ) )
% 5.31/5.62 = ( plus_plus_complex
% 5.31/5.62 @ ( times_times_complex @ ( minus_minus_complex @ Z5 @ A )
% 5.31/5.62 @ ( groups2073611262835488442omplex
% 5.31/5.62 @ ^ [I: nat] : ( times_times_complex @ ( B3 @ I ) @ ( power_power_complex @ Z5 @ I ) )
% 5.31/5.62 @ ( set_ord_lessThan_nat @ N ) ) )
% 5.31/5.62 @ ( groups2073611262835488442omplex
% 5.31/5.62 @ ^ [I: nat] : ( times_times_complex @ ( C2 @ I ) @ ( power_power_complex @ A @ I ) )
% 5.31/5.62 @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % polyfun_linear_factor
% 5.31/5.62 thf(fact_6956_polyfun__linear__factor,axiom,
% 5.31/5.62 ! [C2: nat > rat,N: nat,A: rat] :
% 5.31/5.62 ? [B3: nat > rat] :
% 5.31/5.62 ! [Z5: rat] :
% 5.31/5.62 ( ( groups2906978787729119204at_rat
% 5.31/5.62 @ ^ [I: nat] : ( times_times_rat @ ( C2 @ I ) @ ( power_power_rat @ Z5 @ I ) )
% 5.31/5.62 @ ( set_ord_atMost_nat @ N ) )
% 5.31/5.62 = ( plus_plus_rat
% 5.31/5.62 @ ( times_times_rat @ ( minus_minus_rat @ Z5 @ A )
% 5.31/5.62 @ ( groups2906978787729119204at_rat
% 5.31/5.62 @ ^ [I: nat] : ( times_times_rat @ ( B3 @ I ) @ ( power_power_rat @ Z5 @ I ) )
% 5.31/5.62 @ ( set_ord_lessThan_nat @ N ) ) )
% 5.31/5.62 @ ( groups2906978787729119204at_rat
% 5.31/5.62 @ ^ [I: nat] : ( times_times_rat @ ( C2 @ I ) @ ( power_power_rat @ A @ I ) )
% 5.31/5.62 @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % polyfun_linear_factor
% 5.31/5.62 thf(fact_6957_polyfun__linear__factor,axiom,
% 5.31/5.62 ! [C2: nat > int,N: nat,A: int] :
% 5.31/5.62 ? [B3: nat > int] :
% 5.31/5.62 ! [Z5: int] :
% 5.31/5.62 ( ( groups3539618377306564664at_int
% 5.31/5.62 @ ^ [I: nat] : ( times_times_int @ ( C2 @ I ) @ ( power_power_int @ Z5 @ I ) )
% 5.31/5.62 @ ( set_ord_atMost_nat @ N ) )
% 5.31/5.62 = ( plus_plus_int
% 5.31/5.62 @ ( times_times_int @ ( minus_minus_int @ Z5 @ A )
% 5.31/5.62 @ ( groups3539618377306564664at_int
% 5.31/5.62 @ ^ [I: nat] : ( times_times_int @ ( B3 @ I ) @ ( power_power_int @ Z5 @ I ) )
% 5.31/5.62 @ ( set_ord_lessThan_nat @ N ) ) )
% 5.31/5.62 @ ( groups3539618377306564664at_int
% 5.31/5.62 @ ^ [I: nat] : ( times_times_int @ ( C2 @ I ) @ ( power_power_int @ A @ I ) )
% 5.31/5.62 @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % polyfun_linear_factor
% 5.31/5.62 thf(fact_6958_polyfun__linear__factor,axiom,
% 5.31/5.62 ! [C2: nat > real,N: nat,A: real] :
% 5.31/5.62 ? [B3: nat > real] :
% 5.31/5.62 ! [Z5: real] :
% 5.31/5.62 ( ( groups6591440286371151544t_real
% 5.31/5.62 @ ^ [I: nat] : ( times_times_real @ ( C2 @ I ) @ ( power_power_real @ Z5 @ I ) )
% 5.31/5.62 @ ( set_ord_atMost_nat @ N ) )
% 5.31/5.62 = ( plus_plus_real
% 5.31/5.62 @ ( times_times_real @ ( minus_minus_real @ Z5 @ A )
% 5.31/5.62 @ ( groups6591440286371151544t_real
% 5.31/5.62 @ ^ [I: nat] : ( times_times_real @ ( B3 @ I ) @ ( power_power_real @ Z5 @ I ) )
% 5.31/5.62 @ ( set_ord_lessThan_nat @ N ) ) )
% 5.31/5.62 @ ( groups6591440286371151544t_real
% 5.31/5.62 @ ^ [I: nat] : ( times_times_real @ ( C2 @ I ) @ ( power_power_real @ A @ I ) )
% 5.31/5.62 @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % polyfun_linear_factor
% 5.31/5.62 thf(fact_6959_sum__power__shift,axiom,
% 5.31/5.62 ! [M2: nat,N: nat,X: complex] :
% 5.31/5.62 ( ( ord_less_eq_nat @ M2 @ N )
% 5.31/5.62 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_or1269000886237332187st_nat @ M2 @ N ) )
% 5.31/5.62 = ( times_times_complex @ ( power_power_complex @ X @ M2 ) @ ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_ord_atMost_nat @ ( minus_minus_nat @ N @ M2 ) ) ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % sum_power_shift
% 5.31/5.62 thf(fact_6960_sum__power__shift,axiom,
% 5.31/5.62 ! [M2: nat,N: nat,X: rat] :
% 5.31/5.62 ( ( ord_less_eq_nat @ M2 @ N )
% 5.31/5.62 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_or1269000886237332187st_nat @ M2 @ N ) )
% 5.31/5.62 = ( times_times_rat @ ( power_power_rat @ X @ M2 ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_ord_atMost_nat @ ( minus_minus_nat @ N @ M2 ) ) ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % sum_power_shift
% 5.31/5.62 thf(fact_6961_sum__power__shift,axiom,
% 5.31/5.62 ! [M2: nat,N: nat,X: int] :
% 5.31/5.62 ( ( ord_less_eq_nat @ M2 @ N )
% 5.31/5.62 => ( ( groups3539618377306564664at_int @ ( power_power_int @ X ) @ ( set_or1269000886237332187st_nat @ M2 @ N ) )
% 5.31/5.62 = ( times_times_int @ ( power_power_int @ X @ M2 ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X ) @ ( set_ord_atMost_nat @ ( minus_minus_nat @ N @ M2 ) ) ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % sum_power_shift
% 5.31/5.62 thf(fact_6962_sum__power__shift,axiom,
% 5.31/5.62 ! [M2: nat,N: nat,X: real] :
% 5.31/5.62 ( ( ord_less_eq_nat @ M2 @ N )
% 5.31/5.62 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_or1269000886237332187st_nat @ M2 @ N ) )
% 5.31/5.62 = ( times_times_real @ ( power_power_real @ X @ M2 ) @ ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_ord_atMost_nat @ ( minus_minus_nat @ N @ M2 ) ) ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % sum_power_shift
% 5.31/5.62 thf(fact_6963_binomial,axiom,
% 5.31/5.62 ! [A: nat,B: nat,N: nat] :
% 5.31/5.62 ( ( power_power_nat @ ( plus_plus_nat @ A @ B ) @ N )
% 5.31/5.62 = ( groups3542108847815614940at_nat
% 5.31/5.62 @ ^ [K3: nat] : ( times_times_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ ( binomial @ N @ K3 ) ) @ ( power_power_nat @ A @ K3 ) ) @ ( power_power_nat @ B @ ( minus_minus_nat @ N @ K3 ) ) )
% 5.31/5.62 @ ( set_ord_atMost_nat @ N ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % binomial
% 5.31/5.62 thf(fact_6964_atLeast1__atMost__eq__remove0,axiom,
% 5.31/5.62 ! [N: nat] :
% 5.31/5.62 ( ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.31/5.62 = ( minus_minus_set_nat @ ( set_ord_atMost_nat @ N ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % atLeast1_atMost_eq_remove0
% 5.31/5.62 thf(fact_6965_exp__mod__exp,axiom,
% 5.31/5.62 ! [M2: nat,N: nat] :
% 5.31/5.62 ( ( modulo8411746178871703098atural @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ M2 ) @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N ) )
% 5.31/5.62 = ( times_2397367101498566445atural @ ( zero_n8403883297036319079atural @ ( ord_less_nat @ M2 @ N ) ) @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ M2 ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % exp_mod_exp
% 5.31/5.62 thf(fact_6966_exp__mod__exp,axiom,
% 5.31/5.62 ! [M2: nat,N: nat] :
% 5.31/5.62 ( ( modulo_modulo_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.31/5.62 = ( times_times_nat @ ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ M2 @ N ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % exp_mod_exp
% 5.31/5.62 thf(fact_6967_exp__mod__exp,axiom,
% 5.31/5.62 ! [M2: nat,N: nat] :
% 5.31/5.62 ( ( modulo_modulo_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M2 ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.31/5.62 = ( times_times_int @ ( zero_n2684676970156552555ol_int @ ( ord_less_nat @ M2 @ N ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M2 ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % exp_mod_exp
% 5.31/5.62 thf(fact_6968_exp__mod__exp,axiom,
% 5.31/5.62 ! [M2: nat,N: nat] :
% 5.31/5.62 ( ( modulo364778990260209775nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M2 ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 5.31/5.62 = ( times_3573771949741848930nteger @ ( zero_n356916108424825756nteger @ ( ord_less_nat @ M2 @ N ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M2 ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % exp_mod_exp
% 5.31/5.62 thf(fact_6969_gbinomial__reduce__nat,axiom,
% 5.31/5.62 ! [K2: nat,A: complex] :
% 5.31/5.62 ( ( ord_less_nat @ zero_zero_nat @ K2 )
% 5.31/5.62 => ( ( gbinomial_complex @ A @ K2 )
% 5.31/5.62 = ( plus_plus_complex @ ( gbinomial_complex @ ( minus_minus_complex @ A @ one_one_complex ) @ ( minus_minus_nat @ K2 @ one_one_nat ) ) @ ( gbinomial_complex @ ( minus_minus_complex @ A @ one_one_complex ) @ K2 ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % gbinomial_reduce_nat
% 5.31/5.62 thf(fact_6970_gbinomial__reduce__nat,axiom,
% 5.31/5.62 ! [K2: nat,A: real] :
% 5.31/5.62 ( ( ord_less_nat @ zero_zero_nat @ K2 )
% 5.31/5.62 => ( ( gbinomial_real @ A @ K2 )
% 5.31/5.62 = ( plus_plus_real @ ( gbinomial_real @ ( minus_minus_real @ A @ one_one_real ) @ ( minus_minus_nat @ K2 @ one_one_nat ) ) @ ( gbinomial_real @ ( minus_minus_real @ A @ one_one_real ) @ K2 ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % gbinomial_reduce_nat
% 5.31/5.62 thf(fact_6971_gbinomial__reduce__nat,axiom,
% 5.31/5.62 ! [K2: nat,A: rat] :
% 5.31/5.62 ( ( ord_less_nat @ zero_zero_nat @ K2 )
% 5.31/5.62 => ( ( gbinomial_rat @ A @ K2 )
% 5.31/5.62 = ( plus_plus_rat @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ ( minus_minus_nat @ K2 @ one_one_nat ) ) @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ K2 ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % gbinomial_reduce_nat
% 5.31/5.62 thf(fact_6972_sum_Oin__pairs__0,axiom,
% 5.31/5.62 ! [G2: nat > rat,N: nat] :
% 5.31/5.62 ( ( groups2906978787729119204at_rat @ G2 @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 5.31/5.62 = ( groups2906978787729119204at_rat
% 5.31/5.62 @ ^ [I: nat] : ( plus_plus_rat @ ( G2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I ) ) @ ( G2 @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I ) ) ) )
% 5.31/5.62 @ ( set_ord_atMost_nat @ N ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % sum.in_pairs_0
% 5.31/5.62 thf(fact_6973_sum_Oin__pairs__0,axiom,
% 5.31/5.62 ! [G2: nat > int,N: nat] :
% 5.31/5.62 ( ( groups3539618377306564664at_int @ G2 @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 5.31/5.62 = ( groups3539618377306564664at_int
% 5.31/5.62 @ ^ [I: nat] : ( plus_plus_int @ ( G2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I ) ) @ ( G2 @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I ) ) ) )
% 5.31/5.62 @ ( set_ord_atMost_nat @ N ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % sum.in_pairs_0
% 5.31/5.62 thf(fact_6974_sum_Oin__pairs__0,axiom,
% 5.31/5.62 ! [G2: nat > nat,N: nat] :
% 5.31/5.62 ( ( groups3542108847815614940at_nat @ G2 @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 5.31/5.62 = ( groups3542108847815614940at_nat
% 5.31/5.62 @ ^ [I: nat] : ( plus_plus_nat @ ( G2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I ) ) @ ( G2 @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I ) ) ) )
% 5.31/5.62 @ ( set_ord_atMost_nat @ N ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % sum.in_pairs_0
% 5.31/5.62 thf(fact_6975_sum_Oin__pairs__0,axiom,
% 5.31/5.62 ! [G2: nat > real,N: nat] :
% 5.31/5.62 ( ( groups6591440286371151544t_real @ G2 @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 5.31/5.62 = ( groups6591440286371151544t_real
% 5.31/5.62 @ ^ [I: nat] : ( plus_plus_real @ ( G2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I ) ) @ ( G2 @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I ) ) ) )
% 5.31/5.62 @ ( set_ord_atMost_nat @ N ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % sum.in_pairs_0
% 5.31/5.62 thf(fact_6976_polyfun__rootbound,axiom,
% 5.31/5.62 ! [C2: nat > complex,K2: nat,N: nat] :
% 5.31/5.62 ( ( ( C2 @ K2 )
% 5.31/5.62 != zero_zero_complex )
% 5.31/5.62 => ( ( ord_less_eq_nat @ K2 @ N )
% 5.31/5.62 => ( ( finite3207457112153483333omplex
% 5.31/5.62 @ ( collect_complex
% 5.31/5.62 @ ^ [Z4: complex] :
% 5.31/5.62 ( ( groups2073611262835488442omplex
% 5.31/5.62 @ ^ [I: nat] : ( times_times_complex @ ( C2 @ I ) @ ( power_power_complex @ Z4 @ I ) )
% 5.31/5.62 @ ( set_ord_atMost_nat @ N ) )
% 5.31/5.62 = zero_zero_complex ) ) )
% 5.31/5.62 & ( ord_less_eq_nat
% 5.31/5.62 @ ( finite_card_complex
% 5.31/5.62 @ ( collect_complex
% 5.31/5.62 @ ^ [Z4: complex] :
% 5.31/5.62 ( ( groups2073611262835488442omplex
% 5.31/5.62 @ ^ [I: nat] : ( times_times_complex @ ( C2 @ I ) @ ( power_power_complex @ Z4 @ I ) )
% 5.31/5.62 @ ( set_ord_atMost_nat @ N ) )
% 5.31/5.62 = zero_zero_complex ) ) )
% 5.31/5.62 @ N ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % polyfun_rootbound
% 5.31/5.62 thf(fact_6977_polyfun__rootbound,axiom,
% 5.31/5.62 ! [C2: nat > real,K2: nat,N: nat] :
% 5.31/5.62 ( ( ( C2 @ K2 )
% 5.31/5.62 != zero_zero_real )
% 5.31/5.62 => ( ( ord_less_eq_nat @ K2 @ N )
% 5.31/5.62 => ( ( finite_finite_real
% 5.31/5.62 @ ( collect_real
% 5.31/5.62 @ ^ [Z4: real] :
% 5.31/5.62 ( ( groups6591440286371151544t_real
% 5.31/5.62 @ ^ [I: nat] : ( times_times_real @ ( C2 @ I ) @ ( power_power_real @ Z4 @ I ) )
% 5.31/5.62 @ ( set_ord_atMost_nat @ N ) )
% 5.31/5.62 = zero_zero_real ) ) )
% 5.31/5.62 & ( ord_less_eq_nat
% 5.31/5.62 @ ( finite_card_real
% 5.31/5.62 @ ( collect_real
% 5.31/5.62 @ ^ [Z4: real] :
% 5.31/5.62 ( ( groups6591440286371151544t_real
% 5.31/5.62 @ ^ [I: nat] : ( times_times_real @ ( C2 @ I ) @ ( power_power_real @ Z4 @ I ) )
% 5.31/5.62 @ ( set_ord_atMost_nat @ N ) )
% 5.31/5.62 = zero_zero_real ) ) )
% 5.31/5.62 @ N ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % polyfun_rootbound
% 5.31/5.62 thf(fact_6978_polynomial__product,axiom,
% 5.31/5.62 ! [M2: nat,A: nat > complex,N: nat,B: nat > complex,X: complex] :
% 5.31/5.62 ( ! [I3: nat] :
% 5.31/5.62 ( ( ord_less_nat @ M2 @ I3 )
% 5.31/5.62 => ( ( A @ I3 )
% 5.31/5.62 = zero_zero_complex ) )
% 5.31/5.62 => ( ! [J3: nat] :
% 5.31/5.62 ( ( ord_less_nat @ N @ J3 )
% 5.31/5.62 => ( ( B @ J3 )
% 5.31/5.62 = zero_zero_complex ) )
% 5.31/5.62 => ( ( times_times_complex
% 5.31/5.62 @ ( groups2073611262835488442omplex
% 5.31/5.62 @ ^ [I: nat] : ( times_times_complex @ ( A @ I ) @ ( power_power_complex @ X @ I ) )
% 5.31/5.62 @ ( set_ord_atMost_nat @ M2 ) )
% 5.31/5.62 @ ( groups2073611262835488442omplex
% 5.31/5.62 @ ^ [J: nat] : ( times_times_complex @ ( B @ J ) @ ( power_power_complex @ X @ J ) )
% 5.31/5.62 @ ( set_ord_atMost_nat @ N ) ) )
% 5.31/5.62 = ( groups2073611262835488442omplex
% 5.31/5.62 @ ^ [R: nat] :
% 5.31/5.62 ( times_times_complex
% 5.31/5.62 @ ( groups2073611262835488442omplex
% 5.31/5.62 @ ^ [K3: nat] : ( times_times_complex @ ( A @ K3 ) @ ( B @ ( minus_minus_nat @ R @ K3 ) ) )
% 5.31/5.62 @ ( set_ord_atMost_nat @ R ) )
% 5.31/5.62 @ ( power_power_complex @ X @ R ) )
% 5.31/5.62 @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M2 @ N ) ) ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % polynomial_product
% 5.31/5.62 thf(fact_6979_polynomial__product,axiom,
% 5.31/5.62 ! [M2: nat,A: nat > rat,N: nat,B: nat > rat,X: rat] :
% 5.31/5.62 ( ! [I3: nat] :
% 5.31/5.62 ( ( ord_less_nat @ M2 @ I3 )
% 5.31/5.62 => ( ( A @ I3 )
% 5.31/5.62 = zero_zero_rat ) )
% 5.31/5.62 => ( ! [J3: nat] :
% 5.31/5.62 ( ( ord_less_nat @ N @ J3 )
% 5.31/5.62 => ( ( B @ J3 )
% 5.31/5.62 = zero_zero_rat ) )
% 5.31/5.62 => ( ( times_times_rat
% 5.31/5.62 @ ( groups2906978787729119204at_rat
% 5.31/5.62 @ ^ [I: nat] : ( times_times_rat @ ( A @ I ) @ ( power_power_rat @ X @ I ) )
% 5.31/5.62 @ ( set_ord_atMost_nat @ M2 ) )
% 5.31/5.62 @ ( groups2906978787729119204at_rat
% 5.31/5.62 @ ^ [J: nat] : ( times_times_rat @ ( B @ J ) @ ( power_power_rat @ X @ J ) )
% 5.31/5.62 @ ( set_ord_atMost_nat @ N ) ) )
% 5.31/5.62 = ( groups2906978787729119204at_rat
% 5.31/5.62 @ ^ [R: nat] :
% 5.31/5.62 ( times_times_rat
% 5.31/5.62 @ ( groups2906978787729119204at_rat
% 5.31/5.62 @ ^ [K3: nat] : ( times_times_rat @ ( A @ K3 ) @ ( B @ ( minus_minus_nat @ R @ K3 ) ) )
% 5.31/5.62 @ ( set_ord_atMost_nat @ R ) )
% 5.31/5.62 @ ( power_power_rat @ X @ R ) )
% 5.31/5.62 @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M2 @ N ) ) ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % polynomial_product
% 5.31/5.62 thf(fact_6980_polynomial__product,axiom,
% 5.31/5.62 ! [M2: nat,A: nat > int,N: nat,B: nat > int,X: int] :
% 5.31/5.62 ( ! [I3: nat] :
% 5.31/5.62 ( ( ord_less_nat @ M2 @ I3 )
% 5.31/5.62 => ( ( A @ I3 )
% 5.31/5.62 = zero_zero_int ) )
% 5.31/5.62 => ( ! [J3: nat] :
% 5.31/5.62 ( ( ord_less_nat @ N @ J3 )
% 5.31/5.62 => ( ( B @ J3 )
% 5.31/5.62 = zero_zero_int ) )
% 5.31/5.62 => ( ( times_times_int
% 5.31/5.62 @ ( groups3539618377306564664at_int
% 5.31/5.62 @ ^ [I: nat] : ( times_times_int @ ( A @ I ) @ ( power_power_int @ X @ I ) )
% 5.31/5.62 @ ( set_ord_atMost_nat @ M2 ) )
% 5.31/5.62 @ ( groups3539618377306564664at_int
% 5.31/5.62 @ ^ [J: nat] : ( times_times_int @ ( B @ J ) @ ( power_power_int @ X @ J ) )
% 5.31/5.62 @ ( set_ord_atMost_nat @ N ) ) )
% 5.31/5.62 = ( groups3539618377306564664at_int
% 5.31/5.62 @ ^ [R: nat] :
% 5.31/5.62 ( times_times_int
% 5.31/5.62 @ ( groups3539618377306564664at_int
% 5.31/5.62 @ ^ [K3: nat] : ( times_times_int @ ( A @ K3 ) @ ( B @ ( minus_minus_nat @ R @ K3 ) ) )
% 5.31/5.62 @ ( set_ord_atMost_nat @ R ) )
% 5.31/5.62 @ ( power_power_int @ X @ R ) )
% 5.31/5.62 @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M2 @ N ) ) ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % polynomial_product
% 5.31/5.62 thf(fact_6981_polynomial__product,axiom,
% 5.31/5.62 ! [M2: nat,A: nat > real,N: nat,B: nat > real,X: real] :
% 5.31/5.62 ( ! [I3: nat] :
% 5.31/5.62 ( ( ord_less_nat @ M2 @ I3 )
% 5.31/5.62 => ( ( A @ I3 )
% 5.31/5.62 = zero_zero_real ) )
% 5.31/5.62 => ( ! [J3: nat] :
% 5.31/5.62 ( ( ord_less_nat @ N @ J3 )
% 5.31/5.62 => ( ( B @ J3 )
% 5.31/5.62 = zero_zero_real ) )
% 5.31/5.62 => ( ( times_times_real
% 5.31/5.62 @ ( groups6591440286371151544t_real
% 5.31/5.62 @ ^ [I: nat] : ( times_times_real @ ( A @ I ) @ ( power_power_real @ X @ I ) )
% 5.31/5.62 @ ( set_ord_atMost_nat @ M2 ) )
% 5.31/5.62 @ ( groups6591440286371151544t_real
% 5.31/5.62 @ ^ [J: nat] : ( times_times_real @ ( B @ J ) @ ( power_power_real @ X @ J ) )
% 5.31/5.62 @ ( set_ord_atMost_nat @ N ) ) )
% 5.31/5.62 = ( groups6591440286371151544t_real
% 5.31/5.62 @ ^ [R: nat] :
% 5.31/5.62 ( times_times_real
% 5.31/5.62 @ ( groups6591440286371151544t_real
% 5.31/5.62 @ ^ [K3: nat] : ( times_times_real @ ( A @ K3 ) @ ( B @ ( minus_minus_nat @ R @ K3 ) ) )
% 5.31/5.62 @ ( set_ord_atMost_nat @ R ) )
% 5.31/5.62 @ ( power_power_real @ X @ R ) )
% 5.31/5.62 @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M2 @ N ) ) ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % polynomial_product
% 5.31/5.62 thf(fact_6982_prod_Oin__pairs__0,axiom,
% 5.31/5.62 ! [G2: nat > real,N: nat] :
% 5.31/5.62 ( ( groups129246275422532515t_real @ G2 @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 5.31/5.62 = ( groups129246275422532515t_real
% 5.31/5.62 @ ^ [I: nat] : ( times_times_real @ ( G2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I ) ) @ ( G2 @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I ) ) ) )
% 5.31/5.62 @ ( set_ord_atMost_nat @ N ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % prod.in_pairs_0
% 5.31/5.62 thf(fact_6983_prod_Oin__pairs__0,axiom,
% 5.31/5.62 ! [G2: nat > rat,N: nat] :
% 5.31/5.62 ( ( groups73079841787564623at_rat @ G2 @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 5.31/5.62 = ( groups73079841787564623at_rat
% 5.31/5.62 @ ^ [I: nat] : ( times_times_rat @ ( G2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I ) ) @ ( G2 @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I ) ) ) )
% 5.31/5.62 @ ( set_ord_atMost_nat @ N ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % prod.in_pairs_0
% 5.31/5.62 thf(fact_6984_prod_Oin__pairs__0,axiom,
% 5.31/5.62 ! [G2: nat > int,N: nat] :
% 5.31/5.62 ( ( groups705719431365010083at_int @ G2 @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 5.31/5.62 = ( groups705719431365010083at_int
% 5.31/5.62 @ ^ [I: nat] : ( times_times_int @ ( G2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I ) ) @ ( G2 @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I ) ) ) )
% 5.31/5.62 @ ( set_ord_atMost_nat @ N ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % prod.in_pairs_0
% 5.31/5.62 thf(fact_6985_prod_Oin__pairs__0,axiom,
% 5.31/5.62 ! [G2: nat > nat,N: nat] :
% 5.31/5.62 ( ( groups708209901874060359at_nat @ G2 @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 5.31/5.62 = ( groups708209901874060359at_nat
% 5.31/5.62 @ ^ [I: nat] : ( times_times_nat @ ( G2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I ) ) @ ( G2 @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I ) ) ) )
% 5.31/5.62 @ ( set_ord_atMost_nat @ N ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % prod.in_pairs_0
% 5.31/5.62 thf(fact_6986_polyfun__eq__const,axiom,
% 5.31/5.62 ! [C2: nat > complex,N: nat,K2: complex] :
% 5.31/5.62 ( ( ! [X4: complex] :
% 5.31/5.62 ( ( groups2073611262835488442omplex
% 5.31/5.62 @ ^ [I: nat] : ( times_times_complex @ ( C2 @ I ) @ ( power_power_complex @ X4 @ I ) )
% 5.31/5.62 @ ( set_ord_atMost_nat @ N ) )
% 5.31/5.62 = K2 ) )
% 5.31/5.62 = ( ( ( C2 @ zero_zero_nat )
% 5.31/5.62 = K2 )
% 5.31/5.62 & ! [X4: nat] :
% 5.31/5.62 ( ( member_nat @ X4 @ ( set_or1269000886237332187st_nat @ one_one_nat @ N ) )
% 5.31/5.62 => ( ( C2 @ X4 )
% 5.31/5.62 = zero_zero_complex ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % polyfun_eq_const
% 5.31/5.62 thf(fact_6987_polyfun__eq__const,axiom,
% 5.31/5.62 ! [C2: nat > real,N: nat,K2: real] :
% 5.31/5.62 ( ( ! [X4: real] :
% 5.31/5.62 ( ( groups6591440286371151544t_real
% 5.31/5.62 @ ^ [I: nat] : ( times_times_real @ ( C2 @ I ) @ ( power_power_real @ X4 @ I ) )
% 5.31/5.62 @ ( set_ord_atMost_nat @ N ) )
% 5.31/5.62 = K2 ) )
% 5.31/5.62 = ( ( ( C2 @ zero_zero_nat )
% 5.31/5.62 = K2 )
% 5.31/5.62 & ! [X4: nat] :
% 5.31/5.62 ( ( member_nat @ X4 @ ( set_or1269000886237332187st_nat @ one_one_nat @ N ) )
% 5.31/5.62 => ( ( C2 @ X4 )
% 5.31/5.62 = zero_zero_real ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % polyfun_eq_const
% 5.31/5.62 thf(fact_6988_binomial__ring,axiom,
% 5.31/5.62 ! [A: complex,B: complex,N: nat] :
% 5.31/5.62 ( ( power_power_complex @ ( plus_plus_complex @ A @ B ) @ N )
% 5.31/5.62 = ( groups2073611262835488442omplex
% 5.31/5.62 @ ^ [K3: nat] : ( times_times_complex @ ( times_times_complex @ ( semiri8010041392384452111omplex @ ( binomial @ N @ K3 ) ) @ ( power_power_complex @ A @ K3 ) ) @ ( power_power_complex @ B @ ( minus_minus_nat @ N @ K3 ) ) )
% 5.31/5.62 @ ( set_ord_atMost_nat @ N ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % binomial_ring
% 5.31/5.62 thf(fact_6989_binomial__ring,axiom,
% 5.31/5.62 ! [A: rat,B: rat,N: nat] :
% 5.31/5.62 ( ( power_power_rat @ ( plus_plus_rat @ A @ B ) @ N )
% 5.31/5.62 = ( groups2906978787729119204at_rat
% 5.31/5.62 @ ^ [K3: nat] : ( times_times_rat @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( binomial @ N @ K3 ) ) @ ( power_power_rat @ A @ K3 ) ) @ ( power_power_rat @ B @ ( minus_minus_nat @ N @ K3 ) ) )
% 5.31/5.62 @ ( set_ord_atMost_nat @ N ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % binomial_ring
% 5.31/5.62 thf(fact_6990_binomial__ring,axiom,
% 5.31/5.62 ! [A: int,B: int,N: nat] :
% 5.31/5.62 ( ( power_power_int @ ( plus_plus_int @ A @ B ) @ N )
% 5.31/5.62 = ( groups3539618377306564664at_int
% 5.31/5.62 @ ^ [K3: nat] : ( times_times_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ ( binomial @ N @ K3 ) ) @ ( power_power_int @ A @ K3 ) ) @ ( power_power_int @ B @ ( minus_minus_nat @ N @ K3 ) ) )
% 5.31/5.62 @ ( set_ord_atMost_nat @ N ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % binomial_ring
% 5.31/5.62 thf(fact_6991_binomial__ring,axiom,
% 5.31/5.62 ! [A: nat,B: nat,N: nat] :
% 5.31/5.62 ( ( power_power_nat @ ( plus_plus_nat @ A @ B ) @ N )
% 5.31/5.62 = ( groups3542108847815614940at_nat
% 5.31/5.62 @ ^ [K3: nat] : ( times_times_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ ( binomial @ N @ K3 ) ) @ ( power_power_nat @ A @ K3 ) ) @ ( power_power_nat @ B @ ( minus_minus_nat @ N @ K3 ) ) )
% 5.31/5.62 @ ( set_ord_atMost_nat @ N ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % binomial_ring
% 5.31/5.62 thf(fact_6992_binomial__ring,axiom,
% 5.31/5.62 ! [A: real,B: real,N: nat] :
% 5.31/5.62 ( ( power_power_real @ ( plus_plus_real @ A @ B ) @ N )
% 5.31/5.62 = ( groups6591440286371151544t_real
% 5.31/5.62 @ ^ [K3: nat] : ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( binomial @ N @ K3 ) ) @ ( power_power_real @ A @ K3 ) ) @ ( power_power_real @ B @ ( minus_minus_nat @ N @ K3 ) ) )
% 5.31/5.62 @ ( set_ord_atMost_nat @ N ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % binomial_ring
% 5.31/5.62 thf(fact_6993_pochhammer__binomial__sum,axiom,
% 5.31/5.62 ! [A: rat,B: rat,N: nat] :
% 5.31/5.62 ( ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ A @ B ) @ N )
% 5.31/5.62 = ( groups2906978787729119204at_rat
% 5.31/5.62 @ ^ [K3: nat] : ( times_times_rat @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( binomial @ N @ K3 ) ) @ ( comm_s4028243227959126397er_rat @ A @ K3 ) ) @ ( comm_s4028243227959126397er_rat @ B @ ( minus_minus_nat @ N @ K3 ) ) )
% 5.31/5.62 @ ( set_ord_atMost_nat @ N ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % pochhammer_binomial_sum
% 5.31/5.62 thf(fact_6994_pochhammer__binomial__sum,axiom,
% 5.31/5.62 ! [A: int,B: int,N: nat] :
% 5.31/5.62 ( ( comm_s4660882817536571857er_int @ ( plus_plus_int @ A @ B ) @ N )
% 5.31/5.62 = ( groups3539618377306564664at_int
% 5.31/5.62 @ ^ [K3: nat] : ( times_times_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ ( binomial @ N @ K3 ) ) @ ( comm_s4660882817536571857er_int @ A @ K3 ) ) @ ( comm_s4660882817536571857er_int @ B @ ( minus_minus_nat @ N @ K3 ) ) )
% 5.31/5.62 @ ( set_ord_atMost_nat @ N ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % pochhammer_binomial_sum
% 5.31/5.62 thf(fact_6995_pochhammer__binomial__sum,axiom,
% 5.31/5.62 ! [A: real,B: real,N: nat] :
% 5.31/5.62 ( ( comm_s7457072308508201937r_real @ ( plus_plus_real @ A @ B ) @ N )
% 5.31/5.62 = ( groups6591440286371151544t_real
% 5.31/5.62 @ ^ [K3: nat] : ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( binomial @ N @ K3 ) ) @ ( comm_s7457072308508201937r_real @ A @ K3 ) ) @ ( comm_s7457072308508201937r_real @ B @ ( minus_minus_nat @ N @ K3 ) ) )
% 5.31/5.62 @ ( set_ord_atMost_nat @ N ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % pochhammer_binomial_sum
% 5.31/5.62 thf(fact_6996_polynomial__product__nat,axiom,
% 5.31/5.62 ! [M2: nat,A: nat > nat,N: nat,B: nat > nat,X: nat] :
% 5.31/5.62 ( ! [I3: nat] :
% 5.31/5.62 ( ( ord_less_nat @ M2 @ I3 )
% 5.31/5.62 => ( ( A @ I3 )
% 5.31/5.62 = zero_zero_nat ) )
% 5.31/5.62 => ( ! [J3: nat] :
% 5.31/5.62 ( ( ord_less_nat @ N @ J3 )
% 5.31/5.62 => ( ( B @ J3 )
% 5.31/5.62 = zero_zero_nat ) )
% 5.31/5.62 => ( ( times_times_nat
% 5.31/5.62 @ ( groups3542108847815614940at_nat
% 5.31/5.62 @ ^ [I: nat] : ( times_times_nat @ ( A @ I ) @ ( power_power_nat @ X @ I ) )
% 5.31/5.62 @ ( set_ord_atMost_nat @ M2 ) )
% 5.31/5.62 @ ( groups3542108847815614940at_nat
% 5.31/5.62 @ ^ [J: nat] : ( times_times_nat @ ( B @ J ) @ ( power_power_nat @ X @ J ) )
% 5.31/5.62 @ ( set_ord_atMost_nat @ N ) ) )
% 5.31/5.62 = ( groups3542108847815614940at_nat
% 5.31/5.62 @ ^ [R: nat] :
% 5.31/5.62 ( times_times_nat
% 5.31/5.62 @ ( groups3542108847815614940at_nat
% 5.31/5.62 @ ^ [K3: nat] : ( times_times_nat @ ( A @ K3 ) @ ( B @ ( minus_minus_nat @ R @ K3 ) ) )
% 5.31/5.62 @ ( set_ord_atMost_nat @ R ) )
% 5.31/5.62 @ ( power_power_nat @ X @ R ) )
% 5.31/5.62 @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M2 @ N ) ) ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % polynomial_product_nat
% 5.31/5.62 thf(fact_6997_choose__square__sum,axiom,
% 5.31/5.62 ! [N: nat] :
% 5.31/5.62 ( ( groups3542108847815614940at_nat
% 5.31/5.62 @ ^ [K3: nat] : ( power_power_nat @ ( binomial @ N @ K3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.31/5.62 @ ( set_ord_atMost_nat @ N ) )
% 5.31/5.62 = ( binomial @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ N ) ) ).
% 5.31/5.62
% 5.31/5.62 % choose_square_sum
% 5.31/5.62 thf(fact_6998_set__update__distinct,axiom,
% 5.31/5.62 ! [Xs2: list_VEBT_VEBT,N: nat,X: vEBT_VEBT] :
% 5.31/5.62 ( ( distinct_VEBT_VEBT @ Xs2 )
% 5.31/5.62 => ( ( ord_less_nat @ N @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 5.31/5.62 => ( ( set_VEBT_VEBT2 @ ( list_u1324408373059187874T_VEBT @ Xs2 @ N @ X ) )
% 5.31/5.62 = ( insert_VEBT_VEBT @ X @ ( minus_5127226145743854075T_VEBT @ ( set_VEBT_VEBT2 @ Xs2 ) @ ( insert_VEBT_VEBT @ ( nth_VEBT_VEBT @ Xs2 @ N ) @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % set_update_distinct
% 5.31/5.62 thf(fact_6999_set__update__distinct,axiom,
% 5.31/5.62 ! [Xs2: list_o,N: nat,X: $o] :
% 5.31/5.62 ( ( distinct_o @ Xs2 )
% 5.31/5.62 => ( ( ord_less_nat @ N @ ( size_size_list_o @ Xs2 ) )
% 5.31/5.62 => ( ( set_o2 @ ( list_update_o @ Xs2 @ N @ X ) )
% 5.31/5.62 = ( insert_o @ X @ ( minus_minus_set_o @ ( set_o2 @ Xs2 ) @ ( insert_o @ ( nth_o @ Xs2 @ N ) @ bot_bot_set_o ) ) ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % set_update_distinct
% 5.31/5.62 thf(fact_7000_set__update__distinct,axiom,
% 5.31/5.62 ! [Xs2: list_int,N: nat,X: int] :
% 5.31/5.62 ( ( distinct_int @ Xs2 )
% 5.31/5.62 => ( ( ord_less_nat @ N @ ( size_size_list_int @ Xs2 ) )
% 5.31/5.62 => ( ( set_int2 @ ( list_update_int @ Xs2 @ N @ X ) )
% 5.31/5.62 = ( insert_int @ X @ ( minus_minus_set_int @ ( set_int2 @ Xs2 ) @ ( insert_int @ ( nth_int @ Xs2 @ N ) @ bot_bot_set_int ) ) ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % set_update_distinct
% 5.31/5.62 thf(fact_7001_set__update__distinct,axiom,
% 5.31/5.62 ! [Xs2: list_real,N: nat,X: real] :
% 5.31/5.62 ( ( distinct_real @ Xs2 )
% 5.31/5.62 => ( ( ord_less_nat @ N @ ( size_size_list_real @ Xs2 ) )
% 5.31/5.62 => ( ( set_real2 @ ( list_update_real @ Xs2 @ N @ X ) )
% 5.31/5.62 = ( insert_real @ X @ ( minus_minus_set_real @ ( set_real2 @ Xs2 ) @ ( insert_real @ ( nth_real @ Xs2 @ N ) @ bot_bot_set_real ) ) ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % set_update_distinct
% 5.31/5.62 thf(fact_7002_set__update__distinct,axiom,
% 5.31/5.62 ! [Xs2: list_P6011104703257516679at_nat,N: nat,X: product_prod_nat_nat] :
% 5.31/5.62 ( ( distin6923225563576452346at_nat @ Xs2 )
% 5.31/5.62 => ( ( ord_less_nat @ N @ ( size_s5460976970255530739at_nat @ Xs2 ) )
% 5.31/5.62 => ( ( set_Pr5648618587558075414at_nat @ ( list_u6180841689913720943at_nat @ Xs2 @ N @ X ) )
% 5.31/5.62 = ( insert8211810215607154385at_nat @ X @ ( minus_1356011639430497352at_nat @ ( set_Pr5648618587558075414at_nat @ Xs2 ) @ ( insert8211810215607154385at_nat @ ( nth_Pr7617993195940197384at_nat @ Xs2 @ N ) @ bot_bo2099793752762293965at_nat ) ) ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % set_update_distinct
% 5.31/5.62 thf(fact_7003_set__update__distinct,axiom,
% 5.31/5.62 ! [Xs2: list_nat,N: nat,X: nat] :
% 5.31/5.62 ( ( distinct_nat @ Xs2 )
% 5.31/5.62 => ( ( ord_less_nat @ N @ ( size_size_list_nat @ Xs2 ) )
% 5.31/5.62 => ( ( set_nat2 @ ( list_update_nat @ Xs2 @ N @ X ) )
% 5.31/5.62 = ( insert_nat @ X @ ( minus_minus_set_nat @ ( set_nat2 @ Xs2 ) @ ( insert_nat @ ( nth_nat @ Xs2 @ N ) @ bot_bot_set_nat ) ) ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % set_update_distinct
% 5.31/5.62 thf(fact_7004_sum_Ozero__middle,axiom,
% 5.31/5.62 ! [P: nat,K2: nat,G2: nat > complex,H: nat > complex] :
% 5.31/5.62 ( ( ord_less_eq_nat @ one_one_nat @ P )
% 5.31/5.62 => ( ( ord_less_eq_nat @ K2 @ P )
% 5.31/5.62 => ( ( groups2073611262835488442omplex
% 5.31/5.62 @ ^ [J: nat] : ( if_complex @ ( ord_less_nat @ J @ K2 ) @ ( G2 @ J ) @ ( if_complex @ ( J = K2 ) @ zero_zero_complex @ ( H @ ( minus_minus_nat @ J @ ( suc @ zero_zero_nat ) ) ) ) )
% 5.31/5.62 @ ( set_ord_atMost_nat @ P ) )
% 5.31/5.62 = ( groups2073611262835488442omplex
% 5.31/5.62 @ ^ [J: nat] : ( if_complex @ ( ord_less_nat @ J @ K2 ) @ ( G2 @ J ) @ ( H @ J ) )
% 5.31/5.62 @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % sum.zero_middle
% 5.31/5.62 thf(fact_7005_sum_Ozero__middle,axiom,
% 5.31/5.62 ! [P: nat,K2: nat,G2: nat > rat,H: nat > rat] :
% 5.31/5.62 ( ( ord_less_eq_nat @ one_one_nat @ P )
% 5.31/5.62 => ( ( ord_less_eq_nat @ K2 @ P )
% 5.31/5.62 => ( ( groups2906978787729119204at_rat
% 5.31/5.62 @ ^ [J: nat] : ( if_rat @ ( ord_less_nat @ J @ K2 ) @ ( G2 @ J ) @ ( if_rat @ ( J = K2 ) @ zero_zero_rat @ ( H @ ( minus_minus_nat @ J @ ( suc @ zero_zero_nat ) ) ) ) )
% 5.31/5.62 @ ( set_ord_atMost_nat @ P ) )
% 5.31/5.62 = ( groups2906978787729119204at_rat
% 5.31/5.62 @ ^ [J: nat] : ( if_rat @ ( ord_less_nat @ J @ K2 ) @ ( G2 @ J ) @ ( H @ J ) )
% 5.31/5.62 @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % sum.zero_middle
% 5.31/5.62 thf(fact_7006_sum_Ozero__middle,axiom,
% 5.31/5.62 ! [P: nat,K2: nat,G2: nat > int,H: nat > int] :
% 5.31/5.62 ( ( ord_less_eq_nat @ one_one_nat @ P )
% 5.31/5.62 => ( ( ord_less_eq_nat @ K2 @ P )
% 5.31/5.62 => ( ( groups3539618377306564664at_int
% 5.31/5.62 @ ^ [J: nat] : ( if_int @ ( ord_less_nat @ J @ K2 ) @ ( G2 @ J ) @ ( if_int @ ( J = K2 ) @ zero_zero_int @ ( H @ ( minus_minus_nat @ J @ ( suc @ zero_zero_nat ) ) ) ) )
% 5.31/5.62 @ ( set_ord_atMost_nat @ P ) )
% 5.31/5.62 = ( groups3539618377306564664at_int
% 5.31/5.62 @ ^ [J: nat] : ( if_int @ ( ord_less_nat @ J @ K2 ) @ ( G2 @ J ) @ ( H @ J ) )
% 5.31/5.62 @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % sum.zero_middle
% 5.31/5.62 thf(fact_7007_sum_Ozero__middle,axiom,
% 5.31/5.62 ! [P: nat,K2: nat,G2: nat > nat,H: nat > nat] :
% 5.31/5.62 ( ( ord_less_eq_nat @ one_one_nat @ P )
% 5.31/5.62 => ( ( ord_less_eq_nat @ K2 @ P )
% 5.31/5.62 => ( ( groups3542108847815614940at_nat
% 5.31/5.62 @ ^ [J: nat] : ( if_nat @ ( ord_less_nat @ J @ K2 ) @ ( G2 @ J ) @ ( if_nat @ ( J = K2 ) @ zero_zero_nat @ ( H @ ( minus_minus_nat @ J @ ( suc @ zero_zero_nat ) ) ) ) )
% 5.31/5.62 @ ( set_ord_atMost_nat @ P ) )
% 5.31/5.62 = ( groups3542108847815614940at_nat
% 5.31/5.62 @ ^ [J: nat] : ( if_nat @ ( ord_less_nat @ J @ K2 ) @ ( G2 @ J ) @ ( H @ J ) )
% 5.31/5.62 @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % sum.zero_middle
% 5.31/5.62 thf(fact_7008_sum_Ozero__middle,axiom,
% 5.31/5.62 ! [P: nat,K2: nat,G2: nat > real,H: nat > real] :
% 5.31/5.62 ( ( ord_less_eq_nat @ one_one_nat @ P )
% 5.31/5.62 => ( ( ord_less_eq_nat @ K2 @ P )
% 5.31/5.62 => ( ( groups6591440286371151544t_real
% 5.31/5.62 @ ^ [J: nat] : ( if_real @ ( ord_less_nat @ J @ K2 ) @ ( G2 @ J ) @ ( if_real @ ( J = K2 ) @ zero_zero_real @ ( H @ ( minus_minus_nat @ J @ ( suc @ zero_zero_nat ) ) ) ) )
% 5.31/5.62 @ ( set_ord_atMost_nat @ P ) )
% 5.31/5.62 = ( groups6591440286371151544t_real
% 5.31/5.62 @ ^ [J: nat] : ( if_real @ ( ord_less_nat @ J @ K2 ) @ ( G2 @ J ) @ ( H @ J ) )
% 5.31/5.62 @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % sum.zero_middle
% 5.31/5.62 thf(fact_7009_prod_Ozero__middle,axiom,
% 5.31/5.62 ! [P: nat,K2: nat,G2: nat > code_integer,H: nat > code_integer] :
% 5.31/5.62 ( ( ord_less_eq_nat @ one_one_nat @ P )
% 5.31/5.62 => ( ( ord_less_eq_nat @ K2 @ P )
% 5.31/5.62 => ( ( groups3455450783089532116nteger
% 5.31/5.62 @ ^ [J: nat] : ( if_Code_integer @ ( ord_less_nat @ J @ K2 ) @ ( G2 @ J ) @ ( if_Code_integer @ ( J = K2 ) @ one_one_Code_integer @ ( H @ ( minus_minus_nat @ J @ ( suc @ zero_zero_nat ) ) ) ) )
% 5.31/5.62 @ ( set_ord_atMost_nat @ P ) )
% 5.31/5.62 = ( groups3455450783089532116nteger
% 5.31/5.62 @ ^ [J: nat] : ( if_Code_integer @ ( ord_less_nat @ J @ K2 ) @ ( G2 @ J ) @ ( H @ J ) )
% 5.31/5.62 @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % prod.zero_middle
% 5.31/5.62 thf(fact_7010_prod_Ozero__middle,axiom,
% 5.31/5.62 ! [P: nat,K2: nat,G2: nat > complex,H: nat > complex] :
% 5.31/5.62 ( ( ord_less_eq_nat @ one_one_nat @ P )
% 5.31/5.62 => ( ( ord_less_eq_nat @ K2 @ P )
% 5.31/5.62 => ( ( groups6464643781859351333omplex
% 5.31/5.62 @ ^ [J: nat] : ( if_complex @ ( ord_less_nat @ J @ K2 ) @ ( G2 @ J ) @ ( if_complex @ ( J = K2 ) @ one_one_complex @ ( H @ ( minus_minus_nat @ J @ ( suc @ zero_zero_nat ) ) ) ) )
% 5.31/5.62 @ ( set_ord_atMost_nat @ P ) )
% 5.31/5.62 = ( groups6464643781859351333omplex
% 5.31/5.62 @ ^ [J: nat] : ( if_complex @ ( ord_less_nat @ J @ K2 ) @ ( G2 @ J ) @ ( H @ J ) )
% 5.31/5.62 @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % prod.zero_middle
% 5.31/5.62 thf(fact_7011_prod_Ozero__middle,axiom,
% 5.31/5.62 ! [P: nat,K2: nat,G2: nat > real,H: nat > real] :
% 5.31/5.62 ( ( ord_less_eq_nat @ one_one_nat @ P )
% 5.31/5.62 => ( ( ord_less_eq_nat @ K2 @ P )
% 5.31/5.62 => ( ( groups129246275422532515t_real
% 5.31/5.62 @ ^ [J: nat] : ( if_real @ ( ord_less_nat @ J @ K2 ) @ ( G2 @ J ) @ ( if_real @ ( J = K2 ) @ one_one_real @ ( H @ ( minus_minus_nat @ J @ ( suc @ zero_zero_nat ) ) ) ) )
% 5.31/5.62 @ ( set_ord_atMost_nat @ P ) )
% 5.31/5.62 = ( groups129246275422532515t_real
% 5.31/5.62 @ ^ [J: nat] : ( if_real @ ( ord_less_nat @ J @ K2 ) @ ( G2 @ J ) @ ( H @ J ) )
% 5.31/5.62 @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % prod.zero_middle
% 5.31/5.62 thf(fact_7012_prod_Ozero__middle,axiom,
% 5.31/5.62 ! [P: nat,K2: nat,G2: nat > int,H: nat > int] :
% 5.31/5.62 ( ( ord_less_eq_nat @ one_one_nat @ P )
% 5.31/5.62 => ( ( ord_less_eq_nat @ K2 @ P )
% 5.31/5.62 => ( ( groups705719431365010083at_int
% 5.31/5.62 @ ^ [J: nat] : ( if_int @ ( ord_less_nat @ J @ K2 ) @ ( G2 @ J ) @ ( if_int @ ( J = K2 ) @ one_one_int @ ( H @ ( minus_minus_nat @ J @ ( suc @ zero_zero_nat ) ) ) ) )
% 5.31/5.62 @ ( set_ord_atMost_nat @ P ) )
% 5.31/5.62 = ( groups705719431365010083at_int
% 5.31/5.62 @ ^ [J: nat] : ( if_int @ ( ord_less_nat @ J @ K2 ) @ ( G2 @ J ) @ ( H @ J ) )
% 5.31/5.62 @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % prod.zero_middle
% 5.31/5.62 thf(fact_7013_prod_Ozero__middle,axiom,
% 5.31/5.62 ! [P: nat,K2: nat,G2: nat > nat,H: nat > nat] :
% 5.31/5.62 ( ( ord_less_eq_nat @ one_one_nat @ P )
% 5.31/5.62 => ( ( ord_less_eq_nat @ K2 @ P )
% 5.31/5.62 => ( ( groups708209901874060359at_nat
% 5.31/5.62 @ ^ [J: nat] : ( if_nat @ ( ord_less_nat @ J @ K2 ) @ ( G2 @ J ) @ ( if_nat @ ( J = K2 ) @ one_one_nat @ ( H @ ( minus_minus_nat @ J @ ( suc @ zero_zero_nat ) ) ) ) )
% 5.31/5.62 @ ( set_ord_atMost_nat @ P ) )
% 5.31/5.62 = ( groups708209901874060359at_nat
% 5.31/5.62 @ ^ [J: nat] : ( if_nat @ ( ord_less_nat @ J @ K2 ) @ ( G2 @ J ) @ ( H @ J ) )
% 5.31/5.62 @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % prod.zero_middle
% 5.31/5.62 thf(fact_7014_gbinomial__sum__up__index,axiom,
% 5.31/5.62 ! [K2: nat,N: nat] :
% 5.31/5.62 ( ( groups2073611262835488442omplex
% 5.31/5.62 @ ^ [J: nat] : ( gbinomial_complex @ ( semiri8010041392384452111omplex @ J ) @ K2 )
% 5.31/5.62 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 5.31/5.62 = ( gbinomial_complex @ ( plus_plus_complex @ ( semiri8010041392384452111omplex @ N ) @ one_one_complex ) @ ( plus_plus_nat @ K2 @ one_one_nat ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % gbinomial_sum_up_index
% 5.31/5.62 thf(fact_7015_gbinomial__sum__up__index,axiom,
% 5.31/5.62 ! [K2: nat,N: nat] :
% 5.31/5.62 ( ( groups2906978787729119204at_rat
% 5.31/5.62 @ ^ [J: nat] : ( gbinomial_rat @ ( semiri681578069525770553at_rat @ J ) @ K2 )
% 5.31/5.62 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 5.31/5.62 = ( gbinomial_rat @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ N ) @ one_one_rat ) @ ( plus_plus_nat @ K2 @ one_one_nat ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % gbinomial_sum_up_index
% 5.31/5.62 thf(fact_7016_gbinomial__sum__up__index,axiom,
% 5.31/5.62 ! [K2: nat,N: nat] :
% 5.31/5.62 ( ( groups6591440286371151544t_real
% 5.31/5.62 @ ^ [J: nat] : ( gbinomial_real @ ( semiri5074537144036343181t_real @ J ) @ K2 )
% 5.31/5.62 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 5.31/5.62 = ( gbinomial_real @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ N ) @ one_one_real ) @ ( plus_plus_nat @ K2 @ one_one_nat ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % gbinomial_sum_up_index
% 5.31/5.62 thf(fact_7017_exp__div__exp__eq,axiom,
% 5.31/5.62 ! [M2: nat,N: nat] :
% 5.31/5.62 ( ( divide_divide_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.31/5.62 = ( times_times_nat
% 5.31/5.62 @ ( zero_n2687167440665602831ol_nat
% 5.31/5.62 @ ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 )
% 5.31/5.62 != zero_zero_nat )
% 5.31/5.62 & ( ord_less_eq_nat @ N @ M2 ) ) )
% 5.31/5.62 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ M2 @ N ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % exp_div_exp_eq
% 5.31/5.62 thf(fact_7018_exp__div__exp__eq,axiom,
% 5.31/5.62 ! [M2: nat,N: nat] :
% 5.31/5.62 ( ( divide_divide_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M2 ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.31/5.62 = ( times_times_int
% 5.31/5.62 @ ( zero_n2684676970156552555ol_int
% 5.31/5.62 @ ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M2 )
% 5.31/5.62 != zero_zero_int )
% 5.31/5.62 & ( ord_less_eq_nat @ N @ M2 ) ) )
% 5.31/5.62 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_nat @ M2 @ N ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % exp_div_exp_eq
% 5.31/5.62 thf(fact_7019_exp__div__exp__eq,axiom,
% 5.31/5.62 ! [M2: nat,N: nat] :
% 5.31/5.62 ( ( divide6298287555418463151nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M2 ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 5.31/5.62 = ( times_3573771949741848930nteger
% 5.31/5.62 @ ( zero_n356916108424825756nteger
% 5.31/5.62 @ ( ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M2 )
% 5.31/5.62 != zero_z3403309356797280102nteger )
% 5.31/5.62 & ( ord_less_eq_nat @ N @ M2 ) ) )
% 5.31/5.62 @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_minus_nat @ M2 @ N ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % exp_div_exp_eq
% 5.31/5.62 thf(fact_7020_gbinomial__absorption_H,axiom,
% 5.31/5.62 ! [K2: nat,A: complex] :
% 5.31/5.62 ( ( ord_less_nat @ zero_zero_nat @ K2 )
% 5.31/5.62 => ( ( gbinomial_complex @ A @ K2 )
% 5.31/5.62 = ( times_times_complex @ ( divide1717551699836669952omplex @ A @ ( semiri8010041392384452111omplex @ K2 ) ) @ ( gbinomial_complex @ ( minus_minus_complex @ A @ one_one_complex ) @ ( minus_minus_nat @ K2 @ one_one_nat ) ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % gbinomial_absorption'
% 5.31/5.62 thf(fact_7021_gbinomial__absorption_H,axiom,
% 5.31/5.62 ! [K2: nat,A: rat] :
% 5.31/5.62 ( ( ord_less_nat @ zero_zero_nat @ K2 )
% 5.31/5.62 => ( ( gbinomial_rat @ A @ K2 )
% 5.31/5.62 = ( times_times_rat @ ( divide_divide_rat @ A @ ( semiri681578069525770553at_rat @ K2 ) ) @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ ( minus_minus_nat @ K2 @ one_one_nat ) ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % gbinomial_absorption'
% 5.31/5.62 thf(fact_7022_gbinomial__absorption_H,axiom,
% 5.31/5.62 ! [K2: nat,A: real] :
% 5.31/5.62 ( ( ord_less_nat @ zero_zero_nat @ K2 )
% 5.31/5.62 => ( ( gbinomial_real @ A @ K2 )
% 5.31/5.62 = ( times_times_real @ ( divide_divide_real @ A @ ( semiri5074537144036343181t_real @ K2 ) ) @ ( gbinomial_real @ ( minus_minus_real @ A @ one_one_real ) @ ( minus_minus_nat @ K2 @ one_one_nat ) ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % gbinomial_absorption'
% 5.31/5.62 thf(fact_7023_sum__gp0,axiom,
% 5.31/5.62 ! [X: complex,N: nat] :
% 5.31/5.62 ( ( ( X = one_one_complex )
% 5.31/5.62 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_ord_atMost_nat @ N ) )
% 5.31/5.62 = ( semiri8010041392384452111omplex @ ( plus_plus_nat @ N @ one_one_nat ) ) ) )
% 5.31/5.62 & ( ( X != one_one_complex )
% 5.31/5.62 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_ord_atMost_nat @ N ) )
% 5.31/5.62 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ X @ ( suc @ N ) ) ) @ ( minus_minus_complex @ one_one_complex @ X ) ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % sum_gp0
% 5.31/5.62 thf(fact_7024_sum__gp0,axiom,
% 5.31/5.62 ! [X: rat,N: nat] :
% 5.31/5.62 ( ( ( X = one_one_rat )
% 5.31/5.62 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_ord_atMost_nat @ N ) )
% 5.31/5.62 = ( semiri681578069525770553at_rat @ ( plus_plus_nat @ N @ one_one_nat ) ) ) )
% 5.31/5.62 & ( ( X != one_one_rat )
% 5.31/5.62 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_ord_atMost_nat @ N ) )
% 5.31/5.62 = ( divide_divide_rat @ ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X @ ( suc @ N ) ) ) @ ( minus_minus_rat @ one_one_rat @ X ) ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % sum_gp0
% 5.31/5.62 thf(fact_7025_sum__gp0,axiom,
% 5.31/5.62 ! [X: real,N: nat] :
% 5.31/5.62 ( ( ( X = one_one_real )
% 5.31/5.62 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_ord_atMost_nat @ N ) )
% 5.31/5.62 = ( semiri5074537144036343181t_real @ ( plus_plus_nat @ N @ one_one_nat ) ) ) )
% 5.31/5.62 & ( ( X != one_one_real )
% 5.31/5.62 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_ord_atMost_nat @ N ) )
% 5.31/5.62 = ( divide_divide_real @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X @ ( suc @ N ) ) ) @ ( minus_minus_real @ one_one_real @ X ) ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % sum_gp0
% 5.31/5.62 thf(fact_7026_polyfun__diff__alt,axiom,
% 5.31/5.62 ! [N: nat,A: nat > complex,X: complex,Y: complex] :
% 5.31/5.62 ( ( ord_less_eq_nat @ one_one_nat @ N )
% 5.31/5.62 => ( ( minus_minus_complex
% 5.31/5.62 @ ( groups2073611262835488442omplex
% 5.31/5.62 @ ^ [I: nat] : ( times_times_complex @ ( A @ I ) @ ( power_power_complex @ X @ I ) )
% 5.31/5.62 @ ( set_ord_atMost_nat @ N ) )
% 5.31/5.62 @ ( groups2073611262835488442omplex
% 5.31/5.62 @ ^ [I: nat] : ( times_times_complex @ ( A @ I ) @ ( power_power_complex @ Y @ I ) )
% 5.31/5.62 @ ( set_ord_atMost_nat @ N ) ) )
% 5.31/5.62 = ( times_times_complex @ ( minus_minus_complex @ X @ Y )
% 5.31/5.62 @ ( groups2073611262835488442omplex
% 5.31/5.62 @ ^ [J: nat] :
% 5.31/5.62 ( groups2073611262835488442omplex
% 5.31/5.62 @ ^ [K3: nat] : ( times_times_complex @ ( times_times_complex @ ( A @ ( plus_plus_nat @ ( plus_plus_nat @ J @ K3 ) @ one_one_nat ) ) @ ( power_power_complex @ Y @ K3 ) ) @ ( power_power_complex @ X @ J ) )
% 5.31/5.62 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ J ) ) )
% 5.31/5.62 @ ( set_ord_lessThan_nat @ N ) ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % polyfun_diff_alt
% 5.31/5.62 thf(fact_7027_polyfun__diff__alt,axiom,
% 5.31/5.62 ! [N: nat,A: nat > rat,X: rat,Y: rat] :
% 5.31/5.62 ( ( ord_less_eq_nat @ one_one_nat @ N )
% 5.31/5.62 => ( ( minus_minus_rat
% 5.31/5.62 @ ( groups2906978787729119204at_rat
% 5.31/5.62 @ ^ [I: nat] : ( times_times_rat @ ( A @ I ) @ ( power_power_rat @ X @ I ) )
% 5.31/5.62 @ ( set_ord_atMost_nat @ N ) )
% 5.31/5.62 @ ( groups2906978787729119204at_rat
% 5.31/5.62 @ ^ [I: nat] : ( times_times_rat @ ( A @ I ) @ ( power_power_rat @ Y @ I ) )
% 5.31/5.62 @ ( set_ord_atMost_nat @ N ) ) )
% 5.31/5.62 = ( times_times_rat @ ( minus_minus_rat @ X @ Y )
% 5.31/5.62 @ ( groups2906978787729119204at_rat
% 5.31/5.62 @ ^ [J: nat] :
% 5.31/5.62 ( groups2906978787729119204at_rat
% 5.31/5.62 @ ^ [K3: nat] : ( times_times_rat @ ( times_times_rat @ ( A @ ( plus_plus_nat @ ( plus_plus_nat @ J @ K3 ) @ one_one_nat ) ) @ ( power_power_rat @ Y @ K3 ) ) @ ( power_power_rat @ X @ J ) )
% 5.31/5.62 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ J ) ) )
% 5.31/5.62 @ ( set_ord_lessThan_nat @ N ) ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % polyfun_diff_alt
% 5.31/5.62 thf(fact_7028_polyfun__diff__alt,axiom,
% 5.31/5.62 ! [N: nat,A: nat > int,X: int,Y: int] :
% 5.31/5.62 ( ( ord_less_eq_nat @ one_one_nat @ N )
% 5.31/5.62 => ( ( minus_minus_int
% 5.31/5.62 @ ( groups3539618377306564664at_int
% 5.31/5.62 @ ^ [I: nat] : ( times_times_int @ ( A @ I ) @ ( power_power_int @ X @ I ) )
% 5.31/5.62 @ ( set_ord_atMost_nat @ N ) )
% 5.31/5.62 @ ( groups3539618377306564664at_int
% 5.31/5.62 @ ^ [I: nat] : ( times_times_int @ ( A @ I ) @ ( power_power_int @ Y @ I ) )
% 5.31/5.62 @ ( set_ord_atMost_nat @ N ) ) )
% 5.31/5.62 = ( times_times_int @ ( minus_minus_int @ X @ Y )
% 5.31/5.62 @ ( groups3539618377306564664at_int
% 5.31/5.62 @ ^ [J: nat] :
% 5.31/5.62 ( groups3539618377306564664at_int
% 5.31/5.62 @ ^ [K3: nat] : ( times_times_int @ ( times_times_int @ ( A @ ( plus_plus_nat @ ( plus_plus_nat @ J @ K3 ) @ one_one_nat ) ) @ ( power_power_int @ Y @ K3 ) ) @ ( power_power_int @ X @ J ) )
% 5.31/5.62 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ J ) ) )
% 5.31/5.62 @ ( set_ord_lessThan_nat @ N ) ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % polyfun_diff_alt
% 5.31/5.62 thf(fact_7029_polyfun__diff__alt,axiom,
% 5.31/5.62 ! [N: nat,A: nat > real,X: real,Y: real] :
% 5.31/5.62 ( ( ord_less_eq_nat @ one_one_nat @ N )
% 5.31/5.62 => ( ( minus_minus_real
% 5.31/5.62 @ ( groups6591440286371151544t_real
% 5.31/5.62 @ ^ [I: nat] : ( times_times_real @ ( A @ I ) @ ( power_power_real @ X @ I ) )
% 5.31/5.62 @ ( set_ord_atMost_nat @ N ) )
% 5.31/5.62 @ ( groups6591440286371151544t_real
% 5.31/5.62 @ ^ [I: nat] : ( times_times_real @ ( A @ I ) @ ( power_power_real @ Y @ I ) )
% 5.31/5.62 @ ( set_ord_atMost_nat @ N ) ) )
% 5.31/5.62 = ( times_times_real @ ( minus_minus_real @ X @ Y )
% 5.31/5.62 @ ( groups6591440286371151544t_real
% 5.31/5.62 @ ^ [J: nat] :
% 5.31/5.62 ( groups6591440286371151544t_real
% 5.31/5.62 @ ^ [K3: nat] : ( times_times_real @ ( times_times_real @ ( A @ ( plus_plus_nat @ ( plus_plus_nat @ J @ K3 ) @ one_one_nat ) ) @ ( power_power_real @ Y @ K3 ) ) @ ( power_power_real @ X @ J ) )
% 5.31/5.62 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ J ) ) )
% 5.31/5.62 @ ( set_ord_lessThan_nat @ N ) ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % polyfun_diff_alt
% 5.31/5.62 thf(fact_7030_binomial__r__part__sum,axiom,
% 5.31/5.62 ! [M2: nat] :
% 5.31/5.62 ( ( groups3542108847815614940at_nat @ ( binomial @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) @ one_one_nat ) ) @ ( set_ord_atMost_nat @ M2 ) )
% 5.31/5.62 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % binomial_r_part_sum
% 5.31/5.62 thf(fact_7031_choose__linear__sum,axiom,
% 5.31/5.62 ! [N: nat] :
% 5.31/5.62 ( ( groups3542108847815614940at_nat
% 5.31/5.62 @ ^ [I: nat] : ( times_times_nat @ I @ ( binomial @ N @ I ) )
% 5.31/5.62 @ ( set_ord_atMost_nat @ N ) )
% 5.31/5.62 = ( times_times_nat @ N @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % choose_linear_sum
% 5.31/5.62 thf(fact_7032_card__lists__length__le,axiom,
% 5.31/5.62 ! [A4: set_list_nat,N: nat] :
% 5.31/5.62 ( ( finite8100373058378681591st_nat @ A4 )
% 5.31/5.62 => ( ( finite7325466520557071688st_nat
% 5.31/5.62 @ ( collec5989764272469232197st_nat
% 5.31/5.62 @ ^ [Xs: list_list_nat] :
% 5.31/5.62 ( ( ord_le6045566169113846134st_nat @ ( set_list_nat2 @ Xs ) @ A4 )
% 5.31/5.62 & ( ord_less_eq_nat @ ( size_s3023201423986296836st_nat @ Xs ) @ N ) ) ) )
% 5.31/5.62 = ( groups3542108847815614940at_nat @ ( power_power_nat @ ( finite_card_list_nat @ A4 ) ) @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % card_lists_length_le
% 5.31/5.62 thf(fact_7033_card__lists__length__le,axiom,
% 5.31/5.62 ! [A4: set_set_nat,N: nat] :
% 5.31/5.62 ( ( finite1152437895449049373et_nat @ A4 )
% 5.31/5.62 => ( ( finite5631907774883551598et_nat
% 5.31/5.62 @ ( collect_list_set_nat
% 5.31/5.62 @ ^ [Xs: list_set_nat] :
% 5.31/5.62 ( ( ord_le6893508408891458716et_nat @ ( set_set_nat2 @ Xs ) @ A4 )
% 5.31/5.62 & ( ord_less_eq_nat @ ( size_s3254054031482475050et_nat @ Xs ) @ N ) ) ) )
% 5.31/5.62 = ( groups3542108847815614940at_nat @ ( power_power_nat @ ( finite_card_set_nat @ A4 ) ) @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % card_lists_length_le
% 5.31/5.62 thf(fact_7034_card__lists__length__le,axiom,
% 5.31/5.62 ! [A4: set_complex,N: nat] :
% 5.31/5.62 ( ( finite3207457112153483333omplex @ A4 )
% 5.31/5.62 => ( ( finite5120063068150530198omplex
% 5.31/5.62 @ ( collect_list_complex
% 5.31/5.62 @ ^ [Xs: list_complex] :
% 5.31/5.62 ( ( ord_le211207098394363844omplex @ ( set_complex2 @ Xs ) @ A4 )
% 5.31/5.62 & ( ord_less_eq_nat @ ( size_s3451745648224563538omplex @ Xs ) @ N ) ) ) )
% 5.31/5.62 = ( groups3542108847815614940at_nat @ ( power_power_nat @ ( finite_card_complex @ A4 ) ) @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % card_lists_length_le
% 5.31/5.62 thf(fact_7035_card__lists__length__le,axiom,
% 5.31/5.62 ! [A4: set_VEBT_VEBT,N: nat] :
% 5.31/5.62 ( ( finite5795047828879050333T_VEBT @ A4 )
% 5.31/5.62 => ( ( finite5915292604075114978T_VEBT
% 5.31/5.62 @ ( collec5608196760682091941T_VEBT
% 5.31/5.62 @ ^ [Xs: list_VEBT_VEBT] :
% 5.31/5.62 ( ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ Xs ) @ A4 )
% 5.31/5.62 & ( ord_less_eq_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ N ) ) ) )
% 5.31/5.62 = ( groups3542108847815614940at_nat @ ( power_power_nat @ ( finite7802652506058667612T_VEBT @ A4 ) ) @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % card_lists_length_le
% 5.31/5.62 thf(fact_7036_card__lists__length__le,axiom,
% 5.31/5.62 ! [A4: set_o,N: nat] :
% 5.31/5.62 ( ( finite_finite_o @ A4 )
% 5.31/5.62 => ( ( finite_card_list_o
% 5.31/5.62 @ ( collect_list_o
% 5.31/5.62 @ ^ [Xs: list_o] :
% 5.31/5.62 ( ( ord_less_eq_set_o @ ( set_o2 @ Xs ) @ A4 )
% 5.31/5.62 & ( ord_less_eq_nat @ ( size_size_list_o @ Xs ) @ N ) ) ) )
% 5.31/5.62 = ( groups3542108847815614940at_nat @ ( power_power_nat @ ( finite_card_o @ A4 ) ) @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % card_lists_length_le
% 5.31/5.62 thf(fact_7037_card__lists__length__le,axiom,
% 5.31/5.62 ! [A4: set_int,N: nat] :
% 5.31/5.62 ( ( finite_finite_int @ A4 )
% 5.31/5.62 => ( ( finite_card_list_int
% 5.31/5.62 @ ( collect_list_int
% 5.31/5.62 @ ^ [Xs: list_int] :
% 5.31/5.62 ( ( ord_less_eq_set_int @ ( set_int2 @ Xs ) @ A4 )
% 5.31/5.62 & ( ord_less_eq_nat @ ( size_size_list_int @ Xs ) @ N ) ) ) )
% 5.31/5.62 = ( groups3542108847815614940at_nat @ ( power_power_nat @ ( finite_card_int @ A4 ) ) @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % card_lists_length_le
% 5.31/5.62 thf(fact_7038_card__lists__length__le,axiom,
% 5.31/5.62 ! [A4: set_nat,N: nat] :
% 5.31/5.62 ( ( finite_finite_nat @ A4 )
% 5.31/5.62 => ( ( finite_card_list_nat
% 5.31/5.62 @ ( collect_list_nat
% 5.31/5.62 @ ^ [Xs: list_nat] :
% 5.31/5.62 ( ( ord_less_eq_set_nat @ ( set_nat2 @ Xs ) @ A4 )
% 5.31/5.62 & ( ord_less_eq_nat @ ( size_size_list_nat @ Xs ) @ N ) ) ) )
% 5.31/5.62 = ( groups3542108847815614940at_nat @ ( power_power_nat @ ( finite_card_nat @ A4 ) ) @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % card_lists_length_le
% 5.31/5.62 thf(fact_7039_polyfun__extremal__lemma,axiom,
% 5.31/5.62 ! [E: real,C2: nat > complex,N: nat] :
% 5.31/5.62 ( ( ord_less_real @ zero_zero_real @ E )
% 5.31/5.62 => ? [M8: real] :
% 5.31/5.62 ! [Z5: complex] :
% 5.31/5.62 ( ( ord_less_eq_real @ M8 @ ( real_V1022390504157884413omplex @ Z5 ) )
% 5.31/5.62 => ( ord_less_eq_real
% 5.31/5.62 @ ( real_V1022390504157884413omplex
% 5.31/5.62 @ ( groups2073611262835488442omplex
% 5.31/5.62 @ ^ [I: nat] : ( times_times_complex @ ( C2 @ I ) @ ( power_power_complex @ Z5 @ I ) )
% 5.31/5.62 @ ( set_ord_atMost_nat @ N ) ) )
% 5.31/5.62 @ ( times_times_real @ E @ ( power_power_real @ ( real_V1022390504157884413omplex @ Z5 ) @ ( suc @ N ) ) ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % polyfun_extremal_lemma
% 5.31/5.62 thf(fact_7040_polyfun__extremal__lemma,axiom,
% 5.31/5.62 ! [E: real,C2: nat > real,N: nat] :
% 5.31/5.62 ( ( ord_less_real @ zero_zero_real @ E )
% 5.31/5.62 => ? [M8: real] :
% 5.31/5.62 ! [Z5: real] :
% 5.31/5.62 ( ( ord_less_eq_real @ M8 @ ( real_V7735802525324610683m_real @ Z5 ) )
% 5.31/5.62 => ( ord_less_eq_real
% 5.31/5.62 @ ( real_V7735802525324610683m_real
% 5.31/5.62 @ ( groups6591440286371151544t_real
% 5.31/5.62 @ ^ [I: nat] : ( times_times_real @ ( C2 @ I ) @ ( power_power_real @ Z5 @ I ) )
% 5.31/5.62 @ ( set_ord_atMost_nat @ N ) ) )
% 5.31/5.62 @ ( times_times_real @ E @ ( power_power_real @ ( real_V7735802525324610683m_real @ Z5 ) @ ( suc @ N ) ) ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % polyfun_extremal_lemma
% 5.31/5.62 thf(fact_7041_polyfun__diff,axiom,
% 5.31/5.62 ! [N: nat,A: nat > complex,X: complex,Y: complex] :
% 5.31/5.62 ( ( ord_less_eq_nat @ one_one_nat @ N )
% 5.31/5.62 => ( ( minus_minus_complex
% 5.31/5.62 @ ( groups2073611262835488442omplex
% 5.31/5.62 @ ^ [I: nat] : ( times_times_complex @ ( A @ I ) @ ( power_power_complex @ X @ I ) )
% 5.31/5.62 @ ( set_ord_atMost_nat @ N ) )
% 5.31/5.62 @ ( groups2073611262835488442omplex
% 5.31/5.62 @ ^ [I: nat] : ( times_times_complex @ ( A @ I ) @ ( power_power_complex @ Y @ I ) )
% 5.31/5.62 @ ( set_ord_atMost_nat @ N ) ) )
% 5.31/5.62 = ( times_times_complex @ ( minus_minus_complex @ X @ Y )
% 5.31/5.62 @ ( groups2073611262835488442omplex
% 5.31/5.62 @ ^ [J: nat] :
% 5.31/5.62 ( times_times_complex
% 5.31/5.62 @ ( groups2073611262835488442omplex
% 5.31/5.62 @ ^ [I: nat] : ( times_times_complex @ ( A @ I ) @ ( power_power_complex @ Y @ ( minus_minus_nat @ ( minus_minus_nat @ I @ J ) @ one_one_nat ) ) )
% 5.31/5.62 @ ( set_or1269000886237332187st_nat @ ( suc @ J ) @ N ) )
% 5.31/5.62 @ ( power_power_complex @ X @ J ) )
% 5.31/5.62 @ ( set_ord_lessThan_nat @ N ) ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % polyfun_diff
% 5.31/5.62 thf(fact_7042_polyfun__diff,axiom,
% 5.31/5.62 ! [N: nat,A: nat > rat,X: rat,Y: rat] :
% 5.31/5.62 ( ( ord_less_eq_nat @ one_one_nat @ N )
% 5.31/5.62 => ( ( minus_minus_rat
% 5.31/5.62 @ ( groups2906978787729119204at_rat
% 5.31/5.62 @ ^ [I: nat] : ( times_times_rat @ ( A @ I ) @ ( power_power_rat @ X @ I ) )
% 5.31/5.62 @ ( set_ord_atMost_nat @ N ) )
% 5.31/5.62 @ ( groups2906978787729119204at_rat
% 5.31/5.62 @ ^ [I: nat] : ( times_times_rat @ ( A @ I ) @ ( power_power_rat @ Y @ I ) )
% 5.31/5.62 @ ( set_ord_atMost_nat @ N ) ) )
% 5.31/5.62 = ( times_times_rat @ ( minus_minus_rat @ X @ Y )
% 5.31/5.62 @ ( groups2906978787729119204at_rat
% 5.31/5.62 @ ^ [J: nat] :
% 5.31/5.62 ( times_times_rat
% 5.31/5.62 @ ( groups2906978787729119204at_rat
% 5.31/5.62 @ ^ [I: nat] : ( times_times_rat @ ( A @ I ) @ ( power_power_rat @ Y @ ( minus_minus_nat @ ( minus_minus_nat @ I @ J ) @ one_one_nat ) ) )
% 5.31/5.62 @ ( set_or1269000886237332187st_nat @ ( suc @ J ) @ N ) )
% 5.31/5.62 @ ( power_power_rat @ X @ J ) )
% 5.31/5.62 @ ( set_ord_lessThan_nat @ N ) ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % polyfun_diff
% 5.31/5.62 thf(fact_7043_polyfun__diff,axiom,
% 5.31/5.62 ! [N: nat,A: nat > int,X: int,Y: int] :
% 5.31/5.62 ( ( ord_less_eq_nat @ one_one_nat @ N )
% 5.31/5.62 => ( ( minus_minus_int
% 5.31/5.62 @ ( groups3539618377306564664at_int
% 5.31/5.62 @ ^ [I: nat] : ( times_times_int @ ( A @ I ) @ ( power_power_int @ X @ I ) )
% 5.31/5.62 @ ( set_ord_atMost_nat @ N ) )
% 5.31/5.62 @ ( groups3539618377306564664at_int
% 5.31/5.62 @ ^ [I: nat] : ( times_times_int @ ( A @ I ) @ ( power_power_int @ Y @ I ) )
% 5.31/5.62 @ ( set_ord_atMost_nat @ N ) ) )
% 5.31/5.62 = ( times_times_int @ ( minus_minus_int @ X @ Y )
% 5.31/5.62 @ ( groups3539618377306564664at_int
% 5.31/5.62 @ ^ [J: nat] :
% 5.31/5.62 ( times_times_int
% 5.31/5.62 @ ( groups3539618377306564664at_int
% 5.31/5.62 @ ^ [I: nat] : ( times_times_int @ ( A @ I ) @ ( power_power_int @ Y @ ( minus_minus_nat @ ( minus_minus_nat @ I @ J ) @ one_one_nat ) ) )
% 5.31/5.62 @ ( set_or1269000886237332187st_nat @ ( suc @ J ) @ N ) )
% 5.31/5.62 @ ( power_power_int @ X @ J ) )
% 5.31/5.62 @ ( set_ord_lessThan_nat @ N ) ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % polyfun_diff
% 5.31/5.62 thf(fact_7044_polyfun__diff,axiom,
% 5.31/5.62 ! [N: nat,A: nat > real,X: real,Y: real] :
% 5.31/5.62 ( ( ord_less_eq_nat @ one_one_nat @ N )
% 5.31/5.62 => ( ( minus_minus_real
% 5.31/5.62 @ ( groups6591440286371151544t_real
% 5.31/5.62 @ ^ [I: nat] : ( times_times_real @ ( A @ I ) @ ( power_power_real @ X @ I ) )
% 5.31/5.62 @ ( set_ord_atMost_nat @ N ) )
% 5.31/5.62 @ ( groups6591440286371151544t_real
% 5.31/5.62 @ ^ [I: nat] : ( times_times_real @ ( A @ I ) @ ( power_power_real @ Y @ I ) )
% 5.31/5.62 @ ( set_ord_atMost_nat @ N ) ) )
% 5.31/5.62 = ( times_times_real @ ( minus_minus_real @ X @ Y )
% 5.31/5.62 @ ( groups6591440286371151544t_real
% 5.31/5.62 @ ^ [J: nat] :
% 5.31/5.62 ( times_times_real
% 5.31/5.62 @ ( groups6591440286371151544t_real
% 5.31/5.62 @ ^ [I: nat] : ( times_times_real @ ( A @ I ) @ ( power_power_real @ Y @ ( minus_minus_nat @ ( minus_minus_nat @ I @ J ) @ one_one_nat ) ) )
% 5.31/5.62 @ ( set_or1269000886237332187st_nat @ ( suc @ J ) @ N ) )
% 5.31/5.62 @ ( power_power_real @ X @ J ) )
% 5.31/5.62 @ ( set_ord_lessThan_nat @ N ) ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % polyfun_diff
% 5.31/5.62 thf(fact_7045_card__lists__distinct__length__eq_H,axiom,
% 5.31/5.62 ! [K2: nat,A4: set_complex] :
% 5.31/5.62 ( ( ord_less_nat @ K2 @ ( finite_card_complex @ A4 ) )
% 5.31/5.62 => ( ( finite5120063068150530198omplex
% 5.31/5.62 @ ( collect_list_complex
% 5.31/5.62 @ ^ [Xs: list_complex] :
% 5.31/5.62 ( ( ( size_s3451745648224563538omplex @ Xs )
% 5.31/5.62 = K2 )
% 5.31/5.62 & ( distinct_complex @ Xs )
% 5.31/5.62 & ( ord_le211207098394363844omplex @ ( set_complex2 @ Xs ) @ A4 ) ) ) )
% 5.31/5.62 = ( groups708209901874060359at_nat
% 5.31/5.62 @ ^ [X4: nat] : X4
% 5.31/5.62 @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ ( minus_minus_nat @ ( finite_card_complex @ A4 ) @ K2 ) @ one_one_nat ) @ ( finite_card_complex @ A4 ) ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % card_lists_distinct_length_eq'
% 5.31/5.62 thf(fact_7046_card__lists__distinct__length__eq_H,axiom,
% 5.31/5.62 ! [K2: nat,A4: set_list_nat] :
% 5.31/5.62 ( ( ord_less_nat @ K2 @ ( finite_card_list_nat @ A4 ) )
% 5.31/5.62 => ( ( finite7325466520557071688st_nat
% 5.31/5.62 @ ( collec5989764272469232197st_nat
% 5.31/5.62 @ ^ [Xs: list_list_nat] :
% 5.31/5.62 ( ( ( size_s3023201423986296836st_nat @ Xs )
% 5.31/5.62 = K2 )
% 5.31/5.62 & ( distinct_list_nat @ Xs )
% 5.31/5.62 & ( ord_le6045566169113846134st_nat @ ( set_list_nat2 @ Xs ) @ A4 ) ) ) )
% 5.31/5.62 = ( groups708209901874060359at_nat
% 5.31/5.62 @ ^ [X4: nat] : X4
% 5.31/5.62 @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ ( minus_minus_nat @ ( finite_card_list_nat @ A4 ) @ K2 ) @ one_one_nat ) @ ( finite_card_list_nat @ A4 ) ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % card_lists_distinct_length_eq'
% 5.31/5.62 thf(fact_7047_card__lists__distinct__length__eq_H,axiom,
% 5.31/5.62 ! [K2: nat,A4: set_set_nat] :
% 5.31/5.62 ( ( ord_less_nat @ K2 @ ( finite_card_set_nat @ A4 ) )
% 5.31/5.62 => ( ( finite5631907774883551598et_nat
% 5.31/5.62 @ ( collect_list_set_nat
% 5.31/5.62 @ ^ [Xs: list_set_nat] :
% 5.31/5.62 ( ( ( size_s3254054031482475050et_nat @ Xs )
% 5.31/5.62 = K2 )
% 5.31/5.62 & ( distinct_set_nat @ Xs )
% 5.31/5.62 & ( ord_le6893508408891458716et_nat @ ( set_set_nat2 @ Xs ) @ A4 ) ) ) )
% 5.31/5.62 = ( groups708209901874060359at_nat
% 5.31/5.62 @ ^ [X4: nat] : X4
% 5.31/5.62 @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ ( minus_minus_nat @ ( finite_card_set_nat @ A4 ) @ K2 ) @ one_one_nat ) @ ( finite_card_set_nat @ A4 ) ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % card_lists_distinct_length_eq'
% 5.31/5.62 thf(fact_7048_card__lists__distinct__length__eq_H,axiom,
% 5.31/5.62 ! [K2: nat,A4: set_VEBT_VEBT] :
% 5.31/5.62 ( ( ord_less_nat @ K2 @ ( finite7802652506058667612T_VEBT @ A4 ) )
% 5.31/5.62 => ( ( finite5915292604075114978T_VEBT
% 5.31/5.62 @ ( collec5608196760682091941T_VEBT
% 5.31/5.62 @ ^ [Xs: list_VEBT_VEBT] :
% 5.31/5.62 ( ( ( size_s6755466524823107622T_VEBT @ Xs )
% 5.31/5.62 = K2 )
% 5.31/5.62 & ( distinct_VEBT_VEBT @ Xs )
% 5.31/5.62 & ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ Xs ) @ A4 ) ) ) )
% 5.31/5.62 = ( groups708209901874060359at_nat
% 5.31/5.62 @ ^ [X4: nat] : X4
% 5.31/5.62 @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ ( minus_minus_nat @ ( finite7802652506058667612T_VEBT @ A4 ) @ K2 ) @ one_one_nat ) @ ( finite7802652506058667612T_VEBT @ A4 ) ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % card_lists_distinct_length_eq'
% 5.31/5.62 thf(fact_7049_card__lists__distinct__length__eq_H,axiom,
% 5.31/5.62 ! [K2: nat,A4: set_o] :
% 5.31/5.62 ( ( ord_less_nat @ K2 @ ( finite_card_o @ A4 ) )
% 5.31/5.62 => ( ( finite_card_list_o
% 5.31/5.62 @ ( collect_list_o
% 5.31/5.62 @ ^ [Xs: list_o] :
% 5.31/5.62 ( ( ( size_size_list_o @ Xs )
% 5.31/5.62 = K2 )
% 5.31/5.62 & ( distinct_o @ Xs )
% 5.31/5.62 & ( ord_less_eq_set_o @ ( set_o2 @ Xs ) @ A4 ) ) ) )
% 5.31/5.62 = ( groups708209901874060359at_nat
% 5.31/5.62 @ ^ [X4: nat] : X4
% 5.31/5.62 @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ ( minus_minus_nat @ ( finite_card_o @ A4 ) @ K2 ) @ one_one_nat ) @ ( finite_card_o @ A4 ) ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % card_lists_distinct_length_eq'
% 5.31/5.62 thf(fact_7050_card__lists__distinct__length__eq_H,axiom,
% 5.31/5.62 ! [K2: nat,A4: set_int] :
% 5.31/5.62 ( ( ord_less_nat @ K2 @ ( finite_card_int @ A4 ) )
% 5.31/5.62 => ( ( finite_card_list_int
% 5.31/5.62 @ ( collect_list_int
% 5.31/5.62 @ ^ [Xs: list_int] :
% 5.31/5.62 ( ( ( size_size_list_int @ Xs )
% 5.31/5.62 = K2 )
% 5.31/5.62 & ( distinct_int @ Xs )
% 5.31/5.62 & ( ord_less_eq_set_int @ ( set_int2 @ Xs ) @ A4 ) ) ) )
% 5.31/5.62 = ( groups708209901874060359at_nat
% 5.31/5.62 @ ^ [X4: nat] : X4
% 5.31/5.62 @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ ( minus_minus_nat @ ( finite_card_int @ A4 ) @ K2 ) @ one_one_nat ) @ ( finite_card_int @ A4 ) ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % card_lists_distinct_length_eq'
% 5.31/5.62 thf(fact_7051_card__lists__distinct__length__eq_H,axiom,
% 5.31/5.62 ! [K2: nat,A4: set_nat] :
% 5.31/5.62 ( ( ord_less_nat @ K2 @ ( finite_card_nat @ A4 ) )
% 5.31/5.62 => ( ( finite_card_list_nat
% 5.31/5.62 @ ( collect_list_nat
% 5.31/5.62 @ ^ [Xs: list_nat] :
% 5.31/5.62 ( ( ( size_size_list_nat @ Xs )
% 5.31/5.62 = K2 )
% 5.31/5.62 & ( distinct_nat @ Xs )
% 5.31/5.62 & ( ord_less_eq_set_nat @ ( set_nat2 @ Xs ) @ A4 ) ) ) )
% 5.31/5.62 = ( groups708209901874060359at_nat
% 5.31/5.62 @ ^ [X4: nat] : X4
% 5.31/5.62 @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ ( minus_minus_nat @ ( finite_card_nat @ A4 ) @ K2 ) @ one_one_nat ) @ ( finite_card_nat @ A4 ) ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % card_lists_distinct_length_eq'
% 5.31/5.62 thf(fact_7052_Divides_Oadjust__div__eq,axiom,
% 5.31/5.62 ! [Q2: int,R3: int] :
% 5.31/5.62 ( ( adjust_div @ ( product_Pair_int_int @ Q2 @ R3 ) )
% 5.31/5.62 = ( plus_plus_int @ Q2 @ ( zero_n2684676970156552555ol_int @ ( R3 != zero_zero_int ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % Divides.adjust_div_eq
% 5.31/5.62 thf(fact_7053_list__decode_Opinduct,axiom,
% 5.31/5.62 ! [A0: nat,P2: nat > $o] :
% 5.31/5.62 ( ( accp_nat @ nat_list_decode_rel @ A0 )
% 5.31/5.62 => ( ( ( accp_nat @ nat_list_decode_rel @ zero_zero_nat )
% 5.31/5.62 => ( P2 @ zero_zero_nat ) )
% 5.31/5.62 => ( ! [N3: nat] :
% 5.31/5.62 ( ( accp_nat @ nat_list_decode_rel @ ( suc @ N3 ) )
% 5.31/5.62 => ( ! [X5: nat,Y6: nat] :
% 5.31/5.62 ( ( ( product_Pair_nat_nat @ X5 @ Y6 )
% 5.31/5.62 = ( nat_prod_decode @ N3 ) )
% 5.31/5.62 => ( P2 @ Y6 ) )
% 5.31/5.62 => ( P2 @ ( suc @ N3 ) ) ) )
% 5.31/5.62 => ( P2 @ A0 ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % list_decode.pinduct
% 5.31/5.62 thf(fact_7054_gbinomial__code,axiom,
% 5.31/5.62 ( gbinomial_complex
% 5.31/5.62 = ( ^ [A5: complex,K3: nat] :
% 5.31/5.62 ( if_complex @ ( K3 = zero_zero_nat ) @ one_one_complex
% 5.31/5.62 @ ( divide1717551699836669952omplex
% 5.31/5.62 @ ( set_fo1517530859248394432omplex
% 5.31/5.62 @ ^ [L2: nat] : ( times_times_complex @ ( minus_minus_complex @ A5 @ ( semiri8010041392384452111omplex @ L2 ) ) )
% 5.31/5.62 @ zero_zero_nat
% 5.31/5.62 @ ( minus_minus_nat @ K3 @ one_one_nat )
% 5.31/5.62 @ one_one_complex )
% 5.31/5.62 @ ( semiri5044797733671781792omplex @ K3 ) ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % gbinomial_code
% 5.31/5.62 thf(fact_7055_gbinomial__code,axiom,
% 5.31/5.62 ( gbinomial_rat
% 5.31/5.62 = ( ^ [A5: rat,K3: nat] :
% 5.31/5.62 ( if_rat @ ( K3 = zero_zero_nat ) @ one_one_rat
% 5.31/5.62 @ ( divide_divide_rat
% 5.31/5.62 @ ( set_fo1949268297981939178at_rat
% 5.31/5.62 @ ^ [L2: nat] : ( times_times_rat @ ( minus_minus_rat @ A5 @ ( semiri681578069525770553at_rat @ L2 ) ) )
% 5.31/5.62 @ zero_zero_nat
% 5.31/5.62 @ ( minus_minus_nat @ K3 @ one_one_nat )
% 5.31/5.62 @ one_one_rat )
% 5.31/5.62 @ ( semiri773545260158071498ct_rat @ K3 ) ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % gbinomial_code
% 5.31/5.62 thf(fact_7056_gbinomial__code,axiom,
% 5.31/5.62 ( gbinomial_real
% 5.31/5.62 = ( ^ [A5: real,K3: nat] :
% 5.31/5.62 ( if_real @ ( K3 = zero_zero_nat ) @ one_one_real
% 5.31/5.62 @ ( divide_divide_real
% 5.31/5.62 @ ( set_fo3111899725591712190t_real
% 5.31/5.62 @ ^ [L2: nat] : ( times_times_real @ ( minus_minus_real @ A5 @ ( semiri5074537144036343181t_real @ L2 ) ) )
% 5.31/5.62 @ zero_zero_nat
% 5.31/5.62 @ ( minus_minus_nat @ K3 @ one_one_nat )
% 5.31/5.62 @ one_one_real )
% 5.31/5.62 @ ( semiri2265585572941072030t_real @ K3 ) ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % gbinomial_code
% 5.31/5.62 thf(fact_7057_choose__alternating__sum,axiom,
% 5.31/5.62 ! [N: nat] :
% 5.31/5.62 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.62 => ( ( groups2073611262835488442omplex
% 5.31/5.62 @ ^ [I: nat] : ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ I ) @ ( semiri8010041392384452111omplex @ ( binomial @ N @ I ) ) )
% 5.31/5.62 @ ( set_ord_atMost_nat @ N ) )
% 5.31/5.62 = zero_zero_complex ) ) ).
% 5.31/5.62
% 5.31/5.62 % choose_alternating_sum
% 5.31/5.62 thf(fact_7058_choose__alternating__sum,axiom,
% 5.31/5.62 ! [N: nat] :
% 5.31/5.62 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.62 => ( ( groups7501900531339628137nteger
% 5.31/5.62 @ ^ [I: nat] : ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ I ) @ ( semiri4939895301339042750nteger @ ( binomial @ N @ I ) ) )
% 5.31/5.62 @ ( set_ord_atMost_nat @ N ) )
% 5.31/5.62 = zero_z3403309356797280102nteger ) ) ).
% 5.31/5.62
% 5.31/5.62 % choose_alternating_sum
% 5.31/5.62 thf(fact_7059_choose__alternating__sum,axiom,
% 5.31/5.62 ! [N: nat] :
% 5.31/5.62 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.62 => ( ( groups2906978787729119204at_rat
% 5.31/5.62 @ ^ [I: nat] : ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ I ) @ ( semiri681578069525770553at_rat @ ( binomial @ N @ I ) ) )
% 5.31/5.62 @ ( set_ord_atMost_nat @ N ) )
% 5.31/5.62 = zero_zero_rat ) ) ).
% 5.31/5.62
% 5.31/5.62 % choose_alternating_sum
% 5.31/5.62 thf(fact_7060_choose__alternating__sum,axiom,
% 5.31/5.62 ! [N: nat] :
% 5.31/5.62 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.62 => ( ( groups3539618377306564664at_int
% 5.31/5.62 @ ^ [I: nat] : ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ I ) @ ( semiri1314217659103216013at_int @ ( binomial @ N @ I ) ) )
% 5.31/5.62 @ ( set_ord_atMost_nat @ N ) )
% 5.31/5.62 = zero_zero_int ) ) ).
% 5.31/5.62
% 5.31/5.62 % choose_alternating_sum
% 5.31/5.62 thf(fact_7061_choose__alternating__sum,axiom,
% 5.31/5.62 ! [N: nat] :
% 5.31/5.62 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.62 => ( ( groups6591440286371151544t_real
% 5.31/5.62 @ ^ [I: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I ) @ ( semiri5074537144036343181t_real @ ( binomial @ N @ I ) ) )
% 5.31/5.62 @ ( set_ord_atMost_nat @ N ) )
% 5.31/5.62 = zero_zero_real ) ) ).
% 5.31/5.62
% 5.31/5.62 % choose_alternating_sum
% 5.31/5.62 thf(fact_7062_signed__take__bit__Suc,axiom,
% 5.31/5.62 ! [N: nat,A: int] :
% 5.31/5.62 ( ( bit_ri631733984087533419it_int @ ( suc @ N ) @ A )
% 5.31/5.62 = ( 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 ) ) ) ) ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % signed_take_bit_Suc
% 5.31/5.62 thf(fact_7063_set__decode__0,axiom,
% 5.31/5.62 ! [X: nat] :
% 5.31/5.62 ( ( member_nat @ zero_zero_nat @ ( nat_set_decode @ X ) )
% 5.31/5.62 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ X ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % set_decode_0
% 5.31/5.62 thf(fact_7064_add_Oinverse__inverse,axiom,
% 5.31/5.62 ! [A: int] :
% 5.31/5.62 ( ( uminus_uminus_int @ ( uminus_uminus_int @ A ) )
% 5.31/5.62 = A ) ).
% 5.31/5.62
% 5.31/5.62 % add.inverse_inverse
% 5.31/5.62 thf(fact_7065_add_Oinverse__inverse,axiom,
% 5.31/5.62 ! [A: real] :
% 5.31/5.62 ( ( uminus_uminus_real @ ( uminus_uminus_real @ A ) )
% 5.31/5.62 = A ) ).
% 5.31/5.62
% 5.31/5.62 % add.inverse_inverse
% 5.31/5.62 thf(fact_7066_add_Oinverse__inverse,axiom,
% 5.31/5.62 ! [A: complex] :
% 5.31/5.62 ( ( uminus1482373934393186551omplex @ ( uminus1482373934393186551omplex @ A ) )
% 5.31/5.62 = A ) ).
% 5.31/5.62
% 5.31/5.62 % add.inverse_inverse
% 5.31/5.62 thf(fact_7067_add_Oinverse__inverse,axiom,
% 5.31/5.62 ! [A: code_integer] :
% 5.31/5.62 ( ( uminus1351360451143612070nteger @ ( uminus1351360451143612070nteger @ A ) )
% 5.31/5.62 = A ) ).
% 5.31/5.62
% 5.31/5.62 % add.inverse_inverse
% 5.31/5.62 thf(fact_7068_add_Oinverse__inverse,axiom,
% 5.31/5.62 ! [A: rat] :
% 5.31/5.62 ( ( uminus_uminus_rat @ ( uminus_uminus_rat @ A ) )
% 5.31/5.62 = A ) ).
% 5.31/5.62
% 5.31/5.62 % add.inverse_inverse
% 5.31/5.62 thf(fact_7069_neg__equal__iff__equal,axiom,
% 5.31/5.62 ! [A: int,B: int] :
% 5.31/5.62 ( ( ( uminus_uminus_int @ A )
% 5.31/5.62 = ( uminus_uminus_int @ B ) )
% 5.31/5.62 = ( A = B ) ) ).
% 5.31/5.62
% 5.31/5.62 % neg_equal_iff_equal
% 5.31/5.62 thf(fact_7070_neg__equal__iff__equal,axiom,
% 5.31/5.62 ! [A: real,B: real] :
% 5.31/5.62 ( ( ( uminus_uminus_real @ A )
% 5.31/5.62 = ( uminus_uminus_real @ B ) )
% 5.31/5.62 = ( A = B ) ) ).
% 5.31/5.62
% 5.31/5.62 % neg_equal_iff_equal
% 5.31/5.62 thf(fact_7071_neg__equal__iff__equal,axiom,
% 5.31/5.62 ! [A: complex,B: complex] :
% 5.31/5.62 ( ( ( uminus1482373934393186551omplex @ A )
% 5.31/5.62 = ( uminus1482373934393186551omplex @ B ) )
% 5.31/5.62 = ( A = B ) ) ).
% 5.31/5.62
% 5.31/5.62 % neg_equal_iff_equal
% 5.31/5.62 thf(fact_7072_neg__equal__iff__equal,axiom,
% 5.31/5.62 ! [A: code_integer,B: code_integer] :
% 5.31/5.62 ( ( ( uminus1351360451143612070nteger @ A )
% 5.31/5.62 = ( uminus1351360451143612070nteger @ B ) )
% 5.31/5.62 = ( A = B ) ) ).
% 5.31/5.62
% 5.31/5.62 % neg_equal_iff_equal
% 5.31/5.62 thf(fact_7073_neg__equal__iff__equal,axiom,
% 5.31/5.62 ! [A: rat,B: rat] :
% 5.31/5.62 ( ( ( uminus_uminus_rat @ A )
% 5.31/5.62 = ( uminus_uminus_rat @ B ) )
% 5.31/5.62 = ( A = B ) ) ).
% 5.31/5.62
% 5.31/5.62 % neg_equal_iff_equal
% 5.31/5.62 thf(fact_7074_of__nat__id,axiom,
% 5.31/5.62 ( semiri1316708129612266289at_nat
% 5.31/5.62 = ( ^ [N4: nat] : N4 ) ) ).
% 5.31/5.62
% 5.31/5.62 % of_nat_id
% 5.31/5.62 thf(fact_7075_compl__le__compl__iff,axiom,
% 5.31/5.62 ! [X: set_nat,Y: set_nat] :
% 5.31/5.62 ( ( ord_less_eq_set_nat @ ( uminus5710092332889474511et_nat @ X ) @ ( uminus5710092332889474511et_nat @ Y ) )
% 5.31/5.62 = ( ord_less_eq_set_nat @ Y @ X ) ) ).
% 5.31/5.62
% 5.31/5.62 % compl_le_compl_iff
% 5.31/5.62 thf(fact_7076_neg__le__iff__le,axiom,
% 5.31/5.62 ! [B: real,A: real] :
% 5.31/5.62 ( ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) )
% 5.31/5.62 = ( ord_less_eq_real @ A @ B ) ) ).
% 5.31/5.62
% 5.31/5.62 % neg_le_iff_le
% 5.31/5.62 thf(fact_7077_neg__le__iff__le,axiom,
% 5.31/5.62 ! [B: code_integer,A: code_integer] :
% 5.31/5.62 ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) )
% 5.31/5.62 = ( ord_le3102999989581377725nteger @ A @ B ) ) ).
% 5.31/5.62
% 5.31/5.62 % neg_le_iff_le
% 5.31/5.62 thf(fact_7078_neg__le__iff__le,axiom,
% 5.31/5.62 ! [B: rat,A: rat] :
% 5.31/5.62 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) )
% 5.31/5.62 = ( ord_less_eq_rat @ A @ B ) ) ).
% 5.31/5.62
% 5.31/5.62 % neg_le_iff_le
% 5.31/5.62 thf(fact_7079_neg__le__iff__le,axiom,
% 5.31/5.62 ! [B: int,A: int] :
% 5.31/5.62 ( ( ord_less_eq_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) )
% 5.31/5.62 = ( ord_less_eq_int @ A @ B ) ) ).
% 5.31/5.62
% 5.31/5.62 % neg_le_iff_le
% 5.31/5.62 thf(fact_7080_neg__equal__zero,axiom,
% 5.31/5.62 ! [A: int] :
% 5.31/5.62 ( ( ( uminus_uminus_int @ A )
% 5.31/5.62 = A )
% 5.31/5.62 = ( A = zero_zero_int ) ) ).
% 5.31/5.62
% 5.31/5.62 % neg_equal_zero
% 5.31/5.62 thf(fact_7081_neg__equal__zero,axiom,
% 5.31/5.62 ! [A: real] :
% 5.31/5.62 ( ( ( uminus_uminus_real @ A )
% 5.31/5.62 = A )
% 5.31/5.62 = ( A = zero_zero_real ) ) ).
% 5.31/5.62
% 5.31/5.62 % neg_equal_zero
% 5.31/5.62 thf(fact_7082_neg__equal__zero,axiom,
% 5.31/5.62 ! [A: code_integer] :
% 5.31/5.62 ( ( ( uminus1351360451143612070nteger @ A )
% 5.31/5.62 = A )
% 5.31/5.62 = ( A = zero_z3403309356797280102nteger ) ) ).
% 5.31/5.62
% 5.31/5.62 % neg_equal_zero
% 5.31/5.62 thf(fact_7083_neg__equal__zero,axiom,
% 5.31/5.62 ! [A: rat] :
% 5.31/5.62 ( ( ( uminus_uminus_rat @ A )
% 5.31/5.62 = A )
% 5.31/5.62 = ( A = zero_zero_rat ) ) ).
% 5.31/5.62
% 5.31/5.62 % neg_equal_zero
% 5.31/5.62 thf(fact_7084_equal__neg__zero,axiom,
% 5.31/5.62 ! [A: int] :
% 5.31/5.62 ( ( A
% 5.31/5.62 = ( uminus_uminus_int @ A ) )
% 5.31/5.62 = ( A = zero_zero_int ) ) ).
% 5.31/5.62
% 5.31/5.62 % equal_neg_zero
% 5.31/5.62 thf(fact_7085_equal__neg__zero,axiom,
% 5.31/5.62 ! [A: real] :
% 5.31/5.62 ( ( A
% 5.31/5.62 = ( uminus_uminus_real @ A ) )
% 5.31/5.62 = ( A = zero_zero_real ) ) ).
% 5.31/5.62
% 5.31/5.62 % equal_neg_zero
% 5.31/5.62 thf(fact_7086_equal__neg__zero,axiom,
% 5.31/5.62 ! [A: code_integer] :
% 5.31/5.62 ( ( A
% 5.31/5.62 = ( uminus1351360451143612070nteger @ A ) )
% 5.31/5.62 = ( A = zero_z3403309356797280102nteger ) ) ).
% 5.31/5.62
% 5.31/5.62 % equal_neg_zero
% 5.31/5.62 thf(fact_7087_equal__neg__zero,axiom,
% 5.31/5.62 ! [A: rat] :
% 5.31/5.62 ( ( A
% 5.31/5.62 = ( uminus_uminus_rat @ A ) )
% 5.31/5.62 = ( A = zero_zero_rat ) ) ).
% 5.31/5.62
% 5.31/5.62 % equal_neg_zero
% 5.31/5.62 thf(fact_7088_neg__equal__0__iff__equal,axiom,
% 5.31/5.62 ! [A: int] :
% 5.31/5.62 ( ( ( uminus_uminus_int @ A )
% 5.31/5.62 = zero_zero_int )
% 5.31/5.62 = ( A = zero_zero_int ) ) ).
% 5.31/5.62
% 5.31/5.62 % neg_equal_0_iff_equal
% 5.31/5.62 thf(fact_7089_neg__equal__0__iff__equal,axiom,
% 5.31/5.62 ! [A: real] :
% 5.31/5.62 ( ( ( uminus_uminus_real @ A )
% 5.31/5.62 = zero_zero_real )
% 5.31/5.62 = ( A = zero_zero_real ) ) ).
% 5.31/5.62
% 5.31/5.62 % neg_equal_0_iff_equal
% 5.31/5.62 thf(fact_7090_neg__equal__0__iff__equal,axiom,
% 5.31/5.62 ! [A: complex] :
% 5.31/5.62 ( ( ( uminus1482373934393186551omplex @ A )
% 5.31/5.62 = zero_zero_complex )
% 5.31/5.62 = ( A = zero_zero_complex ) ) ).
% 5.31/5.62
% 5.31/5.62 % neg_equal_0_iff_equal
% 5.31/5.62 thf(fact_7091_neg__equal__0__iff__equal,axiom,
% 5.31/5.62 ! [A: code_integer] :
% 5.31/5.62 ( ( ( uminus1351360451143612070nteger @ A )
% 5.31/5.62 = zero_z3403309356797280102nteger )
% 5.31/5.62 = ( A = zero_z3403309356797280102nteger ) ) ).
% 5.31/5.62
% 5.31/5.62 % neg_equal_0_iff_equal
% 5.31/5.62 thf(fact_7092_neg__equal__0__iff__equal,axiom,
% 5.31/5.62 ! [A: rat] :
% 5.31/5.62 ( ( ( uminus_uminus_rat @ A )
% 5.31/5.62 = zero_zero_rat )
% 5.31/5.62 = ( A = zero_zero_rat ) ) ).
% 5.31/5.62
% 5.31/5.62 % neg_equal_0_iff_equal
% 5.31/5.62 thf(fact_7093_neg__0__equal__iff__equal,axiom,
% 5.31/5.62 ! [A: int] :
% 5.31/5.62 ( ( zero_zero_int
% 5.31/5.62 = ( uminus_uminus_int @ A ) )
% 5.31/5.62 = ( zero_zero_int = A ) ) ).
% 5.31/5.62
% 5.31/5.62 % neg_0_equal_iff_equal
% 5.31/5.62 thf(fact_7094_neg__0__equal__iff__equal,axiom,
% 5.31/5.62 ! [A: real] :
% 5.31/5.62 ( ( zero_zero_real
% 5.31/5.62 = ( uminus_uminus_real @ A ) )
% 5.31/5.62 = ( zero_zero_real = A ) ) ).
% 5.31/5.62
% 5.31/5.62 % neg_0_equal_iff_equal
% 5.31/5.62 thf(fact_7095_neg__0__equal__iff__equal,axiom,
% 5.31/5.62 ! [A: complex] :
% 5.31/5.62 ( ( zero_zero_complex
% 5.31/5.62 = ( uminus1482373934393186551omplex @ A ) )
% 5.31/5.62 = ( zero_zero_complex = A ) ) ).
% 5.31/5.62
% 5.31/5.62 % neg_0_equal_iff_equal
% 5.31/5.62 thf(fact_7096_neg__0__equal__iff__equal,axiom,
% 5.31/5.62 ! [A: code_integer] :
% 5.31/5.62 ( ( zero_z3403309356797280102nteger
% 5.31/5.62 = ( uminus1351360451143612070nteger @ A ) )
% 5.31/5.62 = ( zero_z3403309356797280102nteger = A ) ) ).
% 5.31/5.62
% 5.31/5.62 % neg_0_equal_iff_equal
% 5.31/5.62 thf(fact_7097_neg__0__equal__iff__equal,axiom,
% 5.31/5.62 ! [A: rat] :
% 5.31/5.62 ( ( zero_zero_rat
% 5.31/5.62 = ( uminus_uminus_rat @ A ) )
% 5.31/5.62 = ( zero_zero_rat = A ) ) ).
% 5.31/5.62
% 5.31/5.62 % neg_0_equal_iff_equal
% 5.31/5.62 thf(fact_7098_add_Oinverse__neutral,axiom,
% 5.31/5.62 ( ( uminus_uminus_int @ zero_zero_int )
% 5.31/5.62 = zero_zero_int ) ).
% 5.31/5.62
% 5.31/5.62 % add.inverse_neutral
% 5.31/5.62 thf(fact_7099_add_Oinverse__neutral,axiom,
% 5.31/5.62 ( ( uminus_uminus_real @ zero_zero_real )
% 5.31/5.62 = zero_zero_real ) ).
% 5.31/5.62
% 5.31/5.62 % add.inverse_neutral
% 5.31/5.62 thf(fact_7100_add_Oinverse__neutral,axiom,
% 5.31/5.62 ( ( uminus1482373934393186551omplex @ zero_zero_complex )
% 5.31/5.62 = zero_zero_complex ) ).
% 5.31/5.62
% 5.31/5.62 % add.inverse_neutral
% 5.31/5.62 thf(fact_7101_add_Oinverse__neutral,axiom,
% 5.31/5.62 ( ( uminus1351360451143612070nteger @ zero_z3403309356797280102nteger )
% 5.31/5.62 = zero_z3403309356797280102nteger ) ).
% 5.31/5.62
% 5.31/5.62 % add.inverse_neutral
% 5.31/5.62 thf(fact_7102_add_Oinverse__neutral,axiom,
% 5.31/5.62 ( ( uminus_uminus_rat @ zero_zero_rat )
% 5.31/5.62 = zero_zero_rat ) ).
% 5.31/5.62
% 5.31/5.62 % add.inverse_neutral
% 5.31/5.62 thf(fact_7103_neg__less__iff__less,axiom,
% 5.31/5.62 ! [B: int,A: int] :
% 5.31/5.62 ( ( ord_less_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) )
% 5.31/5.62 = ( ord_less_int @ A @ B ) ) ).
% 5.31/5.62
% 5.31/5.62 % neg_less_iff_less
% 5.31/5.62 thf(fact_7104_neg__less__iff__less,axiom,
% 5.31/5.62 ! [B: real,A: real] :
% 5.31/5.62 ( ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) )
% 5.31/5.62 = ( ord_less_real @ A @ B ) ) ).
% 5.31/5.62
% 5.31/5.62 % neg_less_iff_less
% 5.31/5.62 thf(fact_7105_neg__less__iff__less,axiom,
% 5.31/5.62 ! [B: code_integer,A: code_integer] :
% 5.31/5.62 ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) )
% 5.31/5.62 = ( ord_le6747313008572928689nteger @ A @ B ) ) ).
% 5.31/5.62
% 5.31/5.62 % neg_less_iff_less
% 5.31/5.62 thf(fact_7106_neg__less__iff__less,axiom,
% 5.31/5.62 ! [B: rat,A: rat] :
% 5.31/5.62 ( ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) )
% 5.31/5.62 = ( ord_less_rat @ A @ B ) ) ).
% 5.31/5.62
% 5.31/5.62 % neg_less_iff_less
% 5.31/5.62 thf(fact_7107_neg__numeral__eq__iff,axiom,
% 5.31/5.62 ! [M2: num,N: num] :
% 5.31/5.62 ( ( ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) )
% 5.31/5.62 = ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.31/5.62 = ( M2 = N ) ) ).
% 5.31/5.62
% 5.31/5.62 % neg_numeral_eq_iff
% 5.31/5.62 thf(fact_7108_neg__numeral__eq__iff,axiom,
% 5.31/5.62 ! [M2: num,N: num] :
% 5.31/5.62 ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ M2 ) )
% 5.31/5.62 = ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 5.31/5.62 = ( M2 = N ) ) ).
% 5.31/5.62
% 5.31/5.62 % neg_numeral_eq_iff
% 5.31/5.62 thf(fact_7109_neg__numeral__eq__iff,axiom,
% 5.31/5.62 ! [M2: num,N: num] :
% 5.31/5.62 ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M2 ) )
% 5.31/5.62 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 5.31/5.62 = ( M2 = N ) ) ).
% 5.31/5.62
% 5.31/5.62 % neg_numeral_eq_iff
% 5.31/5.62 thf(fact_7110_neg__numeral__eq__iff,axiom,
% 5.31/5.62 ! [M2: num,N: num] :
% 5.31/5.62 ( ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M2 ) )
% 5.31/5.62 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 5.31/5.62 = ( M2 = N ) ) ).
% 5.31/5.62
% 5.31/5.62 % neg_numeral_eq_iff
% 5.31/5.62 thf(fact_7111_neg__numeral__eq__iff,axiom,
% 5.31/5.62 ! [M2: num,N: num] :
% 5.31/5.62 ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ M2 ) )
% 5.31/5.62 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 5.31/5.62 = ( M2 = N ) ) ).
% 5.31/5.62
% 5.31/5.62 % neg_numeral_eq_iff
% 5.31/5.62 thf(fact_7112_mult__minus__right,axiom,
% 5.31/5.62 ! [A: int,B: int] :
% 5.31/5.62 ( ( times_times_int @ A @ ( uminus_uminus_int @ B ) )
% 5.31/5.62 = ( uminus_uminus_int @ ( times_times_int @ A @ B ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % mult_minus_right
% 5.31/5.62 thf(fact_7113_mult__minus__right,axiom,
% 5.31/5.62 ! [A: real,B: real] :
% 5.31/5.62 ( ( times_times_real @ A @ ( uminus_uminus_real @ B ) )
% 5.31/5.62 = ( uminus_uminus_real @ ( times_times_real @ A @ B ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % mult_minus_right
% 5.31/5.62 thf(fact_7114_mult__minus__right,axiom,
% 5.31/5.62 ! [A: complex,B: complex] :
% 5.31/5.62 ( ( times_times_complex @ A @ ( uminus1482373934393186551omplex @ B ) )
% 5.31/5.62 = ( uminus1482373934393186551omplex @ ( times_times_complex @ A @ B ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % mult_minus_right
% 5.31/5.62 thf(fact_7115_mult__minus__right,axiom,
% 5.31/5.62 ! [A: code_integer,B: code_integer] :
% 5.31/5.62 ( ( times_3573771949741848930nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 5.31/5.62 = ( uminus1351360451143612070nteger @ ( times_3573771949741848930nteger @ A @ B ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % mult_minus_right
% 5.31/5.62 thf(fact_7116_mult__minus__right,axiom,
% 5.31/5.62 ! [A: rat,B: rat] :
% 5.31/5.62 ( ( times_times_rat @ A @ ( uminus_uminus_rat @ B ) )
% 5.31/5.62 = ( uminus_uminus_rat @ ( times_times_rat @ A @ B ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % mult_minus_right
% 5.31/5.62 thf(fact_7117_minus__mult__minus,axiom,
% 5.31/5.62 ! [A: int,B: int] :
% 5.31/5.62 ( ( times_times_int @ ( uminus_uminus_int @ A ) @ ( uminus_uminus_int @ B ) )
% 5.31/5.62 = ( times_times_int @ A @ B ) ) ).
% 5.31/5.62
% 5.31/5.62 % minus_mult_minus
% 5.31/5.62 thf(fact_7118_minus__mult__minus,axiom,
% 5.31/5.62 ! [A: real,B: real] :
% 5.31/5.62 ( ( times_times_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B ) )
% 5.31/5.62 = ( times_times_real @ A @ B ) ) ).
% 5.31/5.62
% 5.31/5.62 % minus_mult_minus
% 5.31/5.62 thf(fact_7119_minus__mult__minus,axiom,
% 5.31/5.62 ! [A: complex,B: complex] :
% 5.31/5.62 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ A ) @ ( uminus1482373934393186551omplex @ B ) )
% 5.31/5.62 = ( times_times_complex @ A @ B ) ) ).
% 5.31/5.62
% 5.31/5.62 % minus_mult_minus
% 5.31/5.62 thf(fact_7120_minus__mult__minus,axiom,
% 5.31/5.62 ! [A: code_integer,B: code_integer] :
% 5.31/5.62 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ A ) @ ( uminus1351360451143612070nteger @ B ) )
% 5.31/5.62 = ( times_3573771949741848930nteger @ A @ B ) ) ).
% 5.31/5.62
% 5.31/5.62 % minus_mult_minus
% 5.31/5.62 thf(fact_7121_minus__mult__minus,axiom,
% 5.31/5.62 ! [A: rat,B: rat] :
% 5.31/5.62 ( ( times_times_rat @ ( uminus_uminus_rat @ A ) @ ( uminus_uminus_rat @ B ) )
% 5.31/5.62 = ( times_times_rat @ A @ B ) ) ).
% 5.31/5.62
% 5.31/5.62 % minus_mult_minus
% 5.31/5.62 thf(fact_7122_mult__minus__left,axiom,
% 5.31/5.62 ! [A: int,B: int] :
% 5.31/5.62 ( ( times_times_int @ ( uminus_uminus_int @ A ) @ B )
% 5.31/5.62 = ( uminus_uminus_int @ ( times_times_int @ A @ B ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % mult_minus_left
% 5.31/5.62 thf(fact_7123_mult__minus__left,axiom,
% 5.31/5.62 ! [A: real,B: real] :
% 5.31/5.62 ( ( times_times_real @ ( uminus_uminus_real @ A ) @ B )
% 5.31/5.62 = ( uminus_uminus_real @ ( times_times_real @ A @ B ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % mult_minus_left
% 5.31/5.62 thf(fact_7124_mult__minus__left,axiom,
% 5.31/5.62 ! [A: complex,B: complex] :
% 5.31/5.62 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ A ) @ B )
% 5.31/5.62 = ( uminus1482373934393186551omplex @ ( times_times_complex @ A @ B ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % mult_minus_left
% 5.31/5.62 thf(fact_7125_mult__minus__left,axiom,
% 5.31/5.62 ! [A: code_integer,B: code_integer] :
% 5.31/5.62 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 5.31/5.62 = ( uminus1351360451143612070nteger @ ( times_3573771949741848930nteger @ A @ B ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % mult_minus_left
% 5.31/5.62 thf(fact_7126_mult__minus__left,axiom,
% 5.31/5.62 ! [A: rat,B: rat] :
% 5.31/5.62 ( ( times_times_rat @ ( uminus_uminus_rat @ A ) @ B )
% 5.31/5.62 = ( uminus_uminus_rat @ ( times_times_rat @ A @ B ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % mult_minus_left
% 5.31/5.62 thf(fact_7127_add__minus__cancel,axiom,
% 5.31/5.62 ! [A: int,B: int] :
% 5.31/5.62 ( ( plus_plus_int @ A @ ( plus_plus_int @ ( uminus_uminus_int @ A ) @ B ) )
% 5.31/5.62 = B ) ).
% 5.31/5.62
% 5.31/5.62 % add_minus_cancel
% 5.31/5.62 thf(fact_7128_add__minus__cancel,axiom,
% 5.31/5.62 ! [A: real,B: real] :
% 5.31/5.62 ( ( plus_plus_real @ A @ ( plus_plus_real @ ( uminus_uminus_real @ A ) @ B ) )
% 5.31/5.62 = B ) ).
% 5.31/5.62
% 5.31/5.62 % add_minus_cancel
% 5.31/5.62 thf(fact_7129_add__minus__cancel,axiom,
% 5.31/5.62 ! [A: complex,B: complex] :
% 5.31/5.62 ( ( plus_plus_complex @ A @ ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ B ) )
% 5.31/5.62 = B ) ).
% 5.31/5.62
% 5.31/5.62 % add_minus_cancel
% 5.31/5.62 thf(fact_7130_add__minus__cancel,axiom,
% 5.31/5.62 ! [A: code_integer,B: code_integer] :
% 5.31/5.62 ( ( plus_p5714425477246183910nteger @ A @ ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) )
% 5.31/5.62 = B ) ).
% 5.31/5.62
% 5.31/5.62 % add_minus_cancel
% 5.31/5.62 thf(fact_7131_add__minus__cancel,axiom,
% 5.31/5.62 ! [A: rat,B: rat] :
% 5.31/5.62 ( ( plus_plus_rat @ A @ ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ B ) )
% 5.31/5.62 = B ) ).
% 5.31/5.62
% 5.31/5.62 % add_minus_cancel
% 5.31/5.62 thf(fact_7132_minus__add__cancel,axiom,
% 5.31/5.62 ! [A: int,B: int] :
% 5.31/5.62 ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ ( plus_plus_int @ A @ B ) )
% 5.31/5.62 = B ) ).
% 5.31/5.62
% 5.31/5.62 % minus_add_cancel
% 5.31/5.62 thf(fact_7133_minus__add__cancel,axiom,
% 5.31/5.62 ! [A: real,B: real] :
% 5.31/5.62 ( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ ( plus_plus_real @ A @ B ) )
% 5.31/5.62 = B ) ).
% 5.31/5.62
% 5.31/5.62 % minus_add_cancel
% 5.31/5.62 thf(fact_7134_minus__add__cancel,axiom,
% 5.31/5.62 ! [A: complex,B: complex] :
% 5.31/5.62 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ ( plus_plus_complex @ A @ B ) )
% 5.31/5.62 = B ) ).
% 5.31/5.62
% 5.31/5.62 % minus_add_cancel
% 5.31/5.62 thf(fact_7135_minus__add__cancel,axiom,
% 5.31/5.62 ! [A: code_integer,B: code_integer] :
% 5.31/5.62 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 5.31/5.62 = B ) ).
% 5.31/5.62
% 5.31/5.62 % minus_add_cancel
% 5.31/5.62 thf(fact_7136_minus__add__cancel,axiom,
% 5.31/5.62 ! [A: rat,B: rat] :
% 5.31/5.62 ( ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ ( plus_plus_rat @ A @ B ) )
% 5.31/5.62 = B ) ).
% 5.31/5.62
% 5.31/5.62 % minus_add_cancel
% 5.31/5.62 thf(fact_7137_minus__add__distrib,axiom,
% 5.31/5.62 ! [A: int,B: int] :
% 5.31/5.62 ( ( uminus_uminus_int @ ( plus_plus_int @ A @ B ) )
% 5.31/5.62 = ( plus_plus_int @ ( uminus_uminus_int @ A ) @ ( uminus_uminus_int @ B ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % minus_add_distrib
% 5.31/5.62 thf(fact_7138_minus__add__distrib,axiom,
% 5.31/5.62 ! [A: real,B: real] :
% 5.31/5.62 ( ( uminus_uminus_real @ ( plus_plus_real @ A @ B ) )
% 5.31/5.62 = ( plus_plus_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % minus_add_distrib
% 5.31/5.62 thf(fact_7139_minus__add__distrib,axiom,
% 5.31/5.62 ! [A: complex,B: complex] :
% 5.31/5.62 ( ( uminus1482373934393186551omplex @ ( plus_plus_complex @ A @ B ) )
% 5.31/5.62 = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ ( uminus1482373934393186551omplex @ B ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % minus_add_distrib
% 5.31/5.62 thf(fact_7140_minus__add__distrib,axiom,
% 5.31/5.62 ! [A: code_integer,B: code_integer] :
% 5.31/5.62 ( ( uminus1351360451143612070nteger @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 5.31/5.62 = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ ( uminus1351360451143612070nteger @ B ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % minus_add_distrib
% 5.31/5.62 thf(fact_7141_minus__add__distrib,axiom,
% 5.31/5.62 ! [A: rat,B: rat] :
% 5.31/5.62 ( ( uminus_uminus_rat @ ( plus_plus_rat @ A @ B ) )
% 5.31/5.62 = ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ ( uminus_uminus_rat @ B ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % minus_add_distrib
% 5.31/5.62 thf(fact_7142_minus__diff__eq,axiom,
% 5.31/5.62 ! [A: int,B: int] :
% 5.31/5.62 ( ( uminus_uminus_int @ ( minus_minus_int @ A @ B ) )
% 5.31/5.62 = ( minus_minus_int @ B @ A ) ) ).
% 5.31/5.62
% 5.31/5.62 % minus_diff_eq
% 5.31/5.62 thf(fact_7143_minus__diff__eq,axiom,
% 5.31/5.62 ! [A: real,B: real] :
% 5.31/5.62 ( ( uminus_uminus_real @ ( minus_minus_real @ A @ B ) )
% 5.31/5.62 = ( minus_minus_real @ B @ A ) ) ).
% 5.31/5.62
% 5.31/5.62 % minus_diff_eq
% 5.31/5.62 thf(fact_7144_minus__diff__eq,axiom,
% 5.31/5.62 ! [A: complex,B: complex] :
% 5.31/5.62 ( ( uminus1482373934393186551omplex @ ( minus_minus_complex @ A @ B ) )
% 5.31/5.62 = ( minus_minus_complex @ B @ A ) ) ).
% 5.31/5.62
% 5.31/5.62 % minus_diff_eq
% 5.31/5.62 thf(fact_7145_minus__diff__eq,axiom,
% 5.31/5.62 ! [A: code_integer,B: code_integer] :
% 5.31/5.62 ( ( uminus1351360451143612070nteger @ ( minus_8373710615458151222nteger @ A @ B ) )
% 5.31/5.62 = ( minus_8373710615458151222nteger @ B @ A ) ) ).
% 5.31/5.62
% 5.31/5.62 % minus_diff_eq
% 5.31/5.62 thf(fact_7146_minus__diff__eq,axiom,
% 5.31/5.62 ! [A: rat,B: rat] :
% 5.31/5.62 ( ( uminus_uminus_rat @ ( minus_minus_rat @ A @ B ) )
% 5.31/5.62 = ( minus_minus_rat @ B @ A ) ) ).
% 5.31/5.62
% 5.31/5.62 % minus_diff_eq
% 5.31/5.62 thf(fact_7147_dvd__minus__iff,axiom,
% 5.31/5.62 ! [X: int,Y: int] :
% 5.31/5.62 ( ( dvd_dvd_int @ X @ ( uminus_uminus_int @ Y ) )
% 5.31/5.62 = ( dvd_dvd_int @ X @ Y ) ) ).
% 5.31/5.62
% 5.31/5.62 % dvd_minus_iff
% 5.31/5.62 thf(fact_7148_dvd__minus__iff,axiom,
% 5.31/5.62 ! [X: real,Y: real] :
% 5.31/5.62 ( ( dvd_dvd_real @ X @ ( uminus_uminus_real @ Y ) )
% 5.31/5.62 = ( dvd_dvd_real @ X @ Y ) ) ).
% 5.31/5.62
% 5.31/5.62 % dvd_minus_iff
% 5.31/5.62 thf(fact_7149_dvd__minus__iff,axiom,
% 5.31/5.62 ! [X: complex,Y: complex] :
% 5.31/5.62 ( ( dvd_dvd_complex @ X @ ( uminus1482373934393186551omplex @ Y ) )
% 5.31/5.62 = ( dvd_dvd_complex @ X @ Y ) ) ).
% 5.31/5.62
% 5.31/5.62 % dvd_minus_iff
% 5.31/5.62 thf(fact_7150_dvd__minus__iff,axiom,
% 5.31/5.62 ! [X: code_integer,Y: code_integer] :
% 5.31/5.62 ( ( dvd_dvd_Code_integer @ X @ ( uminus1351360451143612070nteger @ Y ) )
% 5.31/5.62 = ( dvd_dvd_Code_integer @ X @ Y ) ) ).
% 5.31/5.62
% 5.31/5.62 % dvd_minus_iff
% 5.31/5.62 thf(fact_7151_dvd__minus__iff,axiom,
% 5.31/5.62 ! [X: rat,Y: rat] :
% 5.31/5.62 ( ( dvd_dvd_rat @ X @ ( uminus_uminus_rat @ Y ) )
% 5.31/5.62 = ( dvd_dvd_rat @ X @ Y ) ) ).
% 5.31/5.62
% 5.31/5.62 % dvd_minus_iff
% 5.31/5.62 thf(fact_7152_minus__dvd__iff,axiom,
% 5.31/5.62 ! [X: int,Y: int] :
% 5.31/5.62 ( ( dvd_dvd_int @ ( uminus_uminus_int @ X ) @ Y )
% 5.31/5.62 = ( dvd_dvd_int @ X @ Y ) ) ).
% 5.31/5.62
% 5.31/5.62 % minus_dvd_iff
% 5.31/5.62 thf(fact_7153_minus__dvd__iff,axiom,
% 5.31/5.62 ! [X: real,Y: real] :
% 5.31/5.62 ( ( dvd_dvd_real @ ( uminus_uminus_real @ X ) @ Y )
% 5.31/5.62 = ( dvd_dvd_real @ X @ Y ) ) ).
% 5.31/5.62
% 5.31/5.62 % minus_dvd_iff
% 5.31/5.62 thf(fact_7154_minus__dvd__iff,axiom,
% 5.31/5.62 ! [X: complex,Y: complex] :
% 5.31/5.62 ( ( dvd_dvd_complex @ ( uminus1482373934393186551omplex @ X ) @ Y )
% 5.31/5.62 = ( dvd_dvd_complex @ X @ Y ) ) ).
% 5.31/5.62
% 5.31/5.62 % minus_dvd_iff
% 5.31/5.62 thf(fact_7155_minus__dvd__iff,axiom,
% 5.31/5.62 ! [X: code_integer,Y: code_integer] :
% 5.31/5.62 ( ( dvd_dvd_Code_integer @ ( uminus1351360451143612070nteger @ X ) @ Y )
% 5.31/5.62 = ( dvd_dvd_Code_integer @ X @ Y ) ) ).
% 5.31/5.62
% 5.31/5.62 % minus_dvd_iff
% 5.31/5.62 thf(fact_7156_minus__dvd__iff,axiom,
% 5.31/5.62 ! [X: rat,Y: rat] :
% 5.31/5.62 ( ( dvd_dvd_rat @ ( uminus_uminus_rat @ X ) @ Y )
% 5.31/5.62 = ( dvd_dvd_rat @ X @ Y ) ) ).
% 5.31/5.62
% 5.31/5.62 % minus_dvd_iff
% 5.31/5.62 thf(fact_7157_negative__eq__positive,axiom,
% 5.31/5.62 ! [N: nat,M2: nat] :
% 5.31/5.62 ( ( ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) )
% 5.31/5.62 = ( semiri1314217659103216013at_int @ M2 ) )
% 5.31/5.62 = ( ( N = zero_zero_nat )
% 5.31/5.62 & ( M2 = zero_zero_nat ) ) ) ).
% 5.31/5.62
% 5.31/5.62 % negative_eq_positive
% 5.31/5.62 thf(fact_7158_signed__take__bit__of__0,axiom,
% 5.31/5.62 ! [N: nat] :
% 5.31/5.62 ( ( bit_ri631733984087533419it_int @ N @ zero_zero_int )
% 5.31/5.62 = zero_zero_int ) ).
% 5.31/5.62
% 5.31/5.62 % signed_take_bit_of_0
% 5.31/5.62 thf(fact_7159_set__decode__inverse,axiom,
% 5.31/5.62 ! [N: nat] :
% 5.31/5.62 ( ( nat_set_encode @ ( nat_set_decode @ N ) )
% 5.31/5.62 = N ) ).
% 5.31/5.62
% 5.31/5.62 % set_decode_inverse
% 5.31/5.62 thf(fact_7160_neg__less__eq__nonneg,axiom,
% 5.31/5.62 ! [A: real] :
% 5.31/5.62 ( ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ A )
% 5.31/5.62 = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 5.31/5.62
% 5.31/5.62 % neg_less_eq_nonneg
% 5.31/5.62 thf(fact_7161_neg__less__eq__nonneg,axiom,
% 5.31/5.62 ! [A: code_integer] :
% 5.31/5.62 ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ A )
% 5.31/5.62 = ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 5.31/5.62
% 5.31/5.62 % neg_less_eq_nonneg
% 5.31/5.62 thf(fact_7162_neg__less__eq__nonneg,axiom,
% 5.31/5.62 ! [A: rat] :
% 5.31/5.62 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ A )
% 5.31/5.62 = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 5.31/5.62
% 5.31/5.62 % neg_less_eq_nonneg
% 5.31/5.62 thf(fact_7163_neg__less__eq__nonneg,axiom,
% 5.31/5.62 ! [A: int] :
% 5.31/5.62 ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ A )
% 5.31/5.62 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 5.31/5.62
% 5.31/5.62 % neg_less_eq_nonneg
% 5.31/5.62 thf(fact_7164_less__eq__neg__nonpos,axiom,
% 5.31/5.62 ! [A: real] :
% 5.31/5.62 ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ A ) )
% 5.31/5.62 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 5.31/5.62
% 5.31/5.62 % less_eq_neg_nonpos
% 5.31/5.62 thf(fact_7165_less__eq__neg__nonpos,axiom,
% 5.31/5.62 ! [A: code_integer] :
% 5.31/5.62 ( ( ord_le3102999989581377725nteger @ A @ ( uminus1351360451143612070nteger @ A ) )
% 5.31/5.62 = ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 5.31/5.62
% 5.31/5.62 % less_eq_neg_nonpos
% 5.31/5.62 thf(fact_7166_less__eq__neg__nonpos,axiom,
% 5.31/5.62 ! [A: rat] :
% 5.31/5.62 ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ A ) )
% 5.31/5.62 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 5.31/5.62
% 5.31/5.62 % less_eq_neg_nonpos
% 5.31/5.62 thf(fact_7167_less__eq__neg__nonpos,axiom,
% 5.31/5.62 ! [A: int] :
% 5.31/5.62 ( ( ord_less_eq_int @ A @ ( uminus_uminus_int @ A ) )
% 5.31/5.62 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 5.31/5.62
% 5.31/5.62 % less_eq_neg_nonpos
% 5.31/5.62 thf(fact_7168_neg__le__0__iff__le,axiom,
% 5.31/5.62 ! [A: real] :
% 5.31/5.62 ( ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ zero_zero_real )
% 5.31/5.62 = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 5.31/5.62
% 5.31/5.62 % neg_le_0_iff_le
% 5.31/5.62 thf(fact_7169_neg__le__0__iff__le,axiom,
% 5.31/5.62 ! [A: code_integer] :
% 5.31/5.62 ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ zero_z3403309356797280102nteger )
% 5.31/5.62 = ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 5.31/5.62
% 5.31/5.62 % neg_le_0_iff_le
% 5.31/5.62 thf(fact_7170_neg__le__0__iff__le,axiom,
% 5.31/5.62 ! [A: rat] :
% 5.31/5.62 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ zero_zero_rat )
% 5.31/5.62 = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 5.31/5.62
% 5.31/5.62 % neg_le_0_iff_le
% 5.31/5.62 thf(fact_7171_neg__le__0__iff__le,axiom,
% 5.31/5.62 ! [A: int] :
% 5.31/5.62 ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ zero_zero_int )
% 5.31/5.62 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 5.31/5.62
% 5.31/5.62 % neg_le_0_iff_le
% 5.31/5.62 thf(fact_7172_neg__0__le__iff__le,axiom,
% 5.31/5.62 ! [A: real] :
% 5.31/5.62 ( ( ord_less_eq_real @ zero_zero_real @ ( uminus_uminus_real @ A ) )
% 5.31/5.62 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 5.31/5.62
% 5.31/5.62 % neg_0_le_iff_le
% 5.31/5.62 thf(fact_7173_neg__0__le__iff__le,axiom,
% 5.31/5.62 ! [A: code_integer] :
% 5.31/5.62 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ A ) )
% 5.31/5.62 = ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 5.31/5.62
% 5.31/5.62 % neg_0_le_iff_le
% 5.31/5.62 thf(fact_7174_neg__0__le__iff__le,axiom,
% 5.31/5.62 ! [A: rat] :
% 5.31/5.62 ( ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ A ) )
% 5.31/5.62 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 5.31/5.62
% 5.31/5.62 % neg_0_le_iff_le
% 5.31/5.62 thf(fact_7175_neg__0__le__iff__le,axiom,
% 5.31/5.62 ! [A: int] :
% 5.31/5.62 ( ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ A ) )
% 5.31/5.62 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 5.31/5.62
% 5.31/5.62 % neg_0_le_iff_le
% 5.31/5.62 thf(fact_7176_less__neg__neg,axiom,
% 5.31/5.62 ! [A: int] :
% 5.31/5.62 ( ( ord_less_int @ A @ ( uminus_uminus_int @ A ) )
% 5.31/5.62 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 5.31/5.62
% 5.31/5.62 % less_neg_neg
% 5.31/5.62 thf(fact_7177_less__neg__neg,axiom,
% 5.31/5.62 ! [A: real] :
% 5.31/5.62 ( ( ord_less_real @ A @ ( uminus_uminus_real @ A ) )
% 5.31/5.62 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 5.31/5.62
% 5.31/5.62 % less_neg_neg
% 5.31/5.62 thf(fact_7178_less__neg__neg,axiom,
% 5.31/5.62 ! [A: code_integer] :
% 5.31/5.62 ( ( ord_le6747313008572928689nteger @ A @ ( uminus1351360451143612070nteger @ A ) )
% 5.31/5.62 = ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 5.31/5.62
% 5.31/5.62 % less_neg_neg
% 5.31/5.62 thf(fact_7179_less__neg__neg,axiom,
% 5.31/5.62 ! [A: rat] :
% 5.31/5.62 ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ A ) )
% 5.31/5.62 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 5.31/5.62
% 5.31/5.62 % less_neg_neg
% 5.31/5.62 thf(fact_7180_neg__less__pos,axiom,
% 5.31/5.62 ! [A: int] :
% 5.31/5.62 ( ( ord_less_int @ ( uminus_uminus_int @ A ) @ A )
% 5.31/5.62 = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 5.31/5.62
% 5.31/5.62 % neg_less_pos
% 5.31/5.62 thf(fact_7181_neg__less__pos,axiom,
% 5.31/5.62 ! [A: real] :
% 5.31/5.62 ( ( ord_less_real @ ( uminus_uminus_real @ A ) @ A )
% 5.31/5.62 = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 5.31/5.62
% 5.31/5.62 % neg_less_pos
% 5.31/5.62 thf(fact_7182_neg__less__pos,axiom,
% 5.31/5.62 ! [A: code_integer] :
% 5.31/5.62 ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ A ) @ A )
% 5.31/5.62 = ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 5.31/5.62
% 5.31/5.62 % neg_less_pos
% 5.31/5.62 thf(fact_7183_neg__less__pos,axiom,
% 5.31/5.62 ! [A: rat] :
% 5.31/5.62 ( ( ord_less_rat @ ( uminus_uminus_rat @ A ) @ A )
% 5.31/5.62 = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 5.31/5.62
% 5.31/5.62 % neg_less_pos
% 5.31/5.62 thf(fact_7184_neg__0__less__iff__less,axiom,
% 5.31/5.62 ! [A: int] :
% 5.31/5.62 ( ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ A ) )
% 5.31/5.62 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 5.31/5.62
% 5.31/5.62 % neg_0_less_iff_less
% 5.31/5.62 thf(fact_7185_neg__0__less__iff__less,axiom,
% 5.31/5.62 ! [A: real] :
% 5.31/5.62 ( ( ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ A ) )
% 5.31/5.62 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 5.31/5.62
% 5.31/5.62 % neg_0_less_iff_less
% 5.31/5.62 thf(fact_7186_neg__0__less__iff__less,axiom,
% 5.31/5.62 ! [A: code_integer] :
% 5.31/5.62 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ A ) )
% 5.31/5.62 = ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 5.31/5.62
% 5.31/5.62 % neg_0_less_iff_less
% 5.31/5.62 thf(fact_7187_neg__0__less__iff__less,axiom,
% 5.31/5.62 ! [A: rat] :
% 5.31/5.62 ( ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ A ) )
% 5.31/5.62 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 5.31/5.62
% 5.31/5.62 % neg_0_less_iff_less
% 5.31/5.62 thf(fact_7188_neg__less__0__iff__less,axiom,
% 5.31/5.63 ! [A: int] :
% 5.31/5.63 ( ( ord_less_int @ ( uminus_uminus_int @ A ) @ zero_zero_int )
% 5.31/5.63 = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 5.31/5.63
% 5.31/5.63 % neg_less_0_iff_less
% 5.31/5.63 thf(fact_7189_neg__less__0__iff__less,axiom,
% 5.31/5.63 ! [A: real] :
% 5.31/5.63 ( ( ord_less_real @ ( uminus_uminus_real @ A ) @ zero_zero_real )
% 5.31/5.63 = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 5.31/5.63
% 5.31/5.63 % neg_less_0_iff_less
% 5.31/5.63 thf(fact_7190_neg__less__0__iff__less,axiom,
% 5.31/5.63 ! [A: code_integer] :
% 5.31/5.63 ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ A ) @ zero_z3403309356797280102nteger )
% 5.31/5.63 = ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 5.31/5.63
% 5.31/5.63 % neg_less_0_iff_less
% 5.31/5.63 thf(fact_7191_neg__less__0__iff__less,axiom,
% 5.31/5.63 ! [A: rat] :
% 5.31/5.63 ( ( ord_less_rat @ ( uminus_uminus_rat @ A ) @ zero_zero_rat )
% 5.31/5.63 = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 5.31/5.63
% 5.31/5.63 % neg_less_0_iff_less
% 5.31/5.63 thf(fact_7192_add_Oright__inverse,axiom,
% 5.31/5.63 ! [A: int] :
% 5.31/5.63 ( ( plus_plus_int @ A @ ( uminus_uminus_int @ A ) )
% 5.31/5.63 = zero_zero_int ) ).
% 5.31/5.63
% 5.31/5.63 % add.right_inverse
% 5.31/5.63 thf(fact_7193_add_Oright__inverse,axiom,
% 5.31/5.63 ! [A: real] :
% 5.31/5.63 ( ( plus_plus_real @ A @ ( uminus_uminus_real @ A ) )
% 5.31/5.63 = zero_zero_real ) ).
% 5.31/5.63
% 5.31/5.63 % add.right_inverse
% 5.31/5.63 thf(fact_7194_add_Oright__inverse,axiom,
% 5.31/5.63 ! [A: complex] :
% 5.31/5.63 ( ( plus_plus_complex @ A @ ( uminus1482373934393186551omplex @ A ) )
% 5.31/5.63 = zero_zero_complex ) ).
% 5.31/5.63
% 5.31/5.63 % add.right_inverse
% 5.31/5.63 thf(fact_7195_add_Oright__inverse,axiom,
% 5.31/5.63 ! [A: code_integer] :
% 5.31/5.63 ( ( plus_p5714425477246183910nteger @ A @ ( uminus1351360451143612070nteger @ A ) )
% 5.31/5.63 = zero_z3403309356797280102nteger ) ).
% 5.31/5.63
% 5.31/5.63 % add.right_inverse
% 5.31/5.63 thf(fact_7196_add_Oright__inverse,axiom,
% 5.31/5.63 ! [A: rat] :
% 5.31/5.63 ( ( plus_plus_rat @ A @ ( uminus_uminus_rat @ A ) )
% 5.31/5.63 = zero_zero_rat ) ).
% 5.31/5.63
% 5.31/5.63 % add.right_inverse
% 5.31/5.63 thf(fact_7197_ab__left__minus,axiom,
% 5.31/5.63 ! [A: int] :
% 5.31/5.63 ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ A )
% 5.31/5.63 = zero_zero_int ) ).
% 5.31/5.63
% 5.31/5.63 % ab_left_minus
% 5.31/5.63 thf(fact_7198_ab__left__minus,axiom,
% 5.31/5.63 ! [A: real] :
% 5.31/5.63 ( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ A )
% 5.31/5.63 = zero_zero_real ) ).
% 5.31/5.63
% 5.31/5.63 % ab_left_minus
% 5.31/5.63 thf(fact_7199_ab__left__minus,axiom,
% 5.31/5.63 ! [A: complex] :
% 5.31/5.63 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ A )
% 5.31/5.63 = zero_zero_complex ) ).
% 5.31/5.63
% 5.31/5.63 % ab_left_minus
% 5.31/5.63 thf(fact_7200_ab__left__minus,axiom,
% 5.31/5.63 ! [A: code_integer] :
% 5.31/5.63 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ A )
% 5.31/5.63 = zero_z3403309356797280102nteger ) ).
% 5.31/5.63
% 5.31/5.63 % ab_left_minus
% 5.31/5.63 thf(fact_7201_ab__left__minus,axiom,
% 5.31/5.63 ! [A: rat] :
% 5.31/5.63 ( ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ A )
% 5.31/5.63 = zero_zero_rat ) ).
% 5.31/5.63
% 5.31/5.63 % ab_left_minus
% 5.31/5.63 thf(fact_7202_verit__minus__simplify_I3_J,axiom,
% 5.31/5.63 ! [B: int] :
% 5.31/5.63 ( ( minus_minus_int @ zero_zero_int @ B )
% 5.31/5.63 = ( uminus_uminus_int @ B ) ) ).
% 5.31/5.63
% 5.31/5.63 % verit_minus_simplify(3)
% 5.31/5.63 thf(fact_7203_verit__minus__simplify_I3_J,axiom,
% 5.31/5.63 ! [B: real] :
% 5.31/5.63 ( ( minus_minus_real @ zero_zero_real @ B )
% 5.31/5.63 = ( uminus_uminus_real @ B ) ) ).
% 5.31/5.63
% 5.31/5.63 % verit_minus_simplify(3)
% 5.31/5.63 thf(fact_7204_verit__minus__simplify_I3_J,axiom,
% 5.31/5.63 ! [B: complex] :
% 5.31/5.63 ( ( minus_minus_complex @ zero_zero_complex @ B )
% 5.31/5.63 = ( uminus1482373934393186551omplex @ B ) ) ).
% 5.31/5.63
% 5.31/5.63 % verit_minus_simplify(3)
% 5.31/5.63 thf(fact_7205_verit__minus__simplify_I3_J,axiom,
% 5.31/5.63 ! [B: code_integer] :
% 5.31/5.63 ( ( minus_8373710615458151222nteger @ zero_z3403309356797280102nteger @ B )
% 5.31/5.63 = ( uminus1351360451143612070nteger @ B ) ) ).
% 5.31/5.63
% 5.31/5.63 % verit_minus_simplify(3)
% 5.31/5.63 thf(fact_7206_verit__minus__simplify_I3_J,axiom,
% 5.31/5.63 ! [B: rat] :
% 5.31/5.63 ( ( minus_minus_rat @ zero_zero_rat @ B )
% 5.31/5.63 = ( uminus_uminus_rat @ B ) ) ).
% 5.31/5.63
% 5.31/5.63 % verit_minus_simplify(3)
% 5.31/5.63 thf(fact_7207_diff__0,axiom,
% 5.31/5.63 ! [A: int] :
% 5.31/5.63 ( ( minus_minus_int @ zero_zero_int @ A )
% 5.31/5.63 = ( uminus_uminus_int @ A ) ) ).
% 5.31/5.63
% 5.31/5.63 % diff_0
% 5.31/5.63 thf(fact_7208_diff__0,axiom,
% 5.31/5.63 ! [A: real] :
% 5.31/5.63 ( ( minus_minus_real @ zero_zero_real @ A )
% 5.31/5.63 = ( uminus_uminus_real @ A ) ) ).
% 5.31/5.63
% 5.31/5.63 % diff_0
% 5.31/5.63 thf(fact_7209_diff__0,axiom,
% 5.31/5.63 ! [A: complex] :
% 5.31/5.63 ( ( minus_minus_complex @ zero_zero_complex @ A )
% 5.31/5.63 = ( uminus1482373934393186551omplex @ A ) ) ).
% 5.31/5.63
% 5.31/5.63 % diff_0
% 5.31/5.63 thf(fact_7210_diff__0,axiom,
% 5.31/5.63 ! [A: code_integer] :
% 5.31/5.63 ( ( minus_8373710615458151222nteger @ zero_z3403309356797280102nteger @ A )
% 5.31/5.63 = ( uminus1351360451143612070nteger @ A ) ) ).
% 5.31/5.63
% 5.31/5.63 % diff_0
% 5.31/5.63 thf(fact_7211_diff__0,axiom,
% 5.31/5.63 ! [A: rat] :
% 5.31/5.63 ( ( minus_minus_rat @ zero_zero_rat @ A )
% 5.31/5.63 = ( uminus_uminus_rat @ A ) ) ).
% 5.31/5.63
% 5.31/5.63 % diff_0
% 5.31/5.63 thf(fact_7212_add__neg__numeral__simps_I3_J,axiom,
% 5.31/5.63 ! [M2: num,N: num] :
% 5.31/5.63 ( ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.31/5.63 = ( uminus_uminus_int @ ( plus_plus_int @ ( numeral_numeral_int @ M2 ) @ ( numeral_numeral_int @ N ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % add_neg_numeral_simps(3)
% 5.31/5.63 thf(fact_7213_add__neg__numeral__simps_I3_J,axiom,
% 5.31/5.63 ! [M2: num,N: num] :
% 5.31/5.63 ( ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M2 ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 5.31/5.63 = ( uminus_uminus_real @ ( plus_plus_real @ ( numeral_numeral_real @ M2 ) @ ( numeral_numeral_real @ N ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % add_neg_numeral_simps(3)
% 5.31/5.63 thf(fact_7214_add__neg__numeral__simps_I3_J,axiom,
% 5.31/5.63 ! [M2: num,N: num] :
% 5.31/5.63 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M2 ) ) @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 5.31/5.63 = ( uminus1482373934393186551omplex @ ( plus_plus_complex @ ( numera6690914467698888265omplex @ M2 ) @ ( numera6690914467698888265omplex @ N ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % add_neg_numeral_simps(3)
% 5.31/5.63 thf(fact_7215_add__neg__numeral__simps_I3_J,axiom,
% 5.31/5.63 ! [M2: num,N: num] :
% 5.31/5.63 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M2 ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 5.31/5.63 = ( uminus1351360451143612070nteger @ ( plus_p5714425477246183910nteger @ ( numera6620942414471956472nteger @ M2 ) @ ( numera6620942414471956472nteger @ N ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % add_neg_numeral_simps(3)
% 5.31/5.63 thf(fact_7216_add__neg__numeral__simps_I3_J,axiom,
% 5.31/5.63 ! [M2: num,N: num] :
% 5.31/5.63 ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M2 ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 5.31/5.63 = ( uminus_uminus_rat @ ( plus_plus_rat @ ( numeral_numeral_rat @ M2 ) @ ( numeral_numeral_rat @ N ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % add_neg_numeral_simps(3)
% 5.31/5.63 thf(fact_7217_mult__minus1__right,axiom,
% 5.31/5.63 ! [Z3: int] :
% 5.31/5.63 ( ( times_times_int @ Z3 @ ( uminus_uminus_int @ one_one_int ) )
% 5.31/5.63 = ( uminus_uminus_int @ Z3 ) ) ).
% 5.31/5.63
% 5.31/5.63 % mult_minus1_right
% 5.31/5.63 thf(fact_7218_mult__minus1__right,axiom,
% 5.31/5.63 ! [Z3: real] :
% 5.31/5.63 ( ( times_times_real @ Z3 @ ( uminus_uminus_real @ one_one_real ) )
% 5.31/5.63 = ( uminus_uminus_real @ Z3 ) ) ).
% 5.31/5.63
% 5.31/5.63 % mult_minus1_right
% 5.31/5.63 thf(fact_7219_mult__minus1__right,axiom,
% 5.31/5.63 ! [Z3: complex] :
% 5.31/5.63 ( ( times_times_complex @ Z3 @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.31/5.63 = ( uminus1482373934393186551omplex @ Z3 ) ) ).
% 5.31/5.63
% 5.31/5.63 % mult_minus1_right
% 5.31/5.63 thf(fact_7220_mult__minus1__right,axiom,
% 5.31/5.63 ! [Z3: code_integer] :
% 5.31/5.63 ( ( times_3573771949741848930nteger @ Z3 @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.31/5.63 = ( uminus1351360451143612070nteger @ Z3 ) ) ).
% 5.31/5.63
% 5.31/5.63 % mult_minus1_right
% 5.31/5.63 thf(fact_7221_mult__minus1__right,axiom,
% 5.31/5.63 ! [Z3: rat] :
% 5.31/5.63 ( ( times_times_rat @ Z3 @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.31/5.63 = ( uminus_uminus_rat @ Z3 ) ) ).
% 5.31/5.63
% 5.31/5.63 % mult_minus1_right
% 5.31/5.63 thf(fact_7222_mult__minus1,axiom,
% 5.31/5.63 ! [Z3: int] :
% 5.31/5.63 ( ( times_times_int @ ( uminus_uminus_int @ one_one_int ) @ Z3 )
% 5.31/5.63 = ( uminus_uminus_int @ Z3 ) ) ).
% 5.31/5.63
% 5.31/5.63 % mult_minus1
% 5.31/5.63 thf(fact_7223_mult__minus1,axiom,
% 5.31/5.63 ! [Z3: real] :
% 5.31/5.63 ( ( times_times_real @ ( uminus_uminus_real @ one_one_real ) @ Z3 )
% 5.31/5.63 = ( uminus_uminus_real @ Z3 ) ) ).
% 5.31/5.63
% 5.31/5.63 % mult_minus1
% 5.31/5.63 thf(fact_7224_mult__minus1,axiom,
% 5.31/5.63 ! [Z3: complex] :
% 5.31/5.63 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ Z3 )
% 5.31/5.63 = ( uminus1482373934393186551omplex @ Z3 ) ) ).
% 5.31/5.63
% 5.31/5.63 % mult_minus1
% 5.31/5.63 thf(fact_7225_mult__minus1,axiom,
% 5.31/5.63 ! [Z3: code_integer] :
% 5.31/5.63 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ Z3 )
% 5.31/5.63 = ( uminus1351360451143612070nteger @ Z3 ) ) ).
% 5.31/5.63
% 5.31/5.63 % mult_minus1
% 5.31/5.63 thf(fact_7226_mult__minus1,axiom,
% 5.31/5.63 ! [Z3: rat] :
% 5.31/5.63 ( ( times_times_rat @ ( uminus_uminus_rat @ one_one_rat ) @ Z3 )
% 5.31/5.63 = ( uminus_uminus_rat @ Z3 ) ) ).
% 5.31/5.63
% 5.31/5.63 % mult_minus1
% 5.31/5.63 thf(fact_7227_diff__minus__eq__add,axiom,
% 5.31/5.63 ! [A: int,B: int] :
% 5.31/5.63 ( ( minus_minus_int @ A @ ( uminus_uminus_int @ B ) )
% 5.31/5.63 = ( plus_plus_int @ A @ B ) ) ).
% 5.31/5.63
% 5.31/5.63 % diff_minus_eq_add
% 5.31/5.63 thf(fact_7228_diff__minus__eq__add,axiom,
% 5.31/5.63 ! [A: real,B: real] :
% 5.31/5.63 ( ( minus_minus_real @ A @ ( uminus_uminus_real @ B ) )
% 5.31/5.63 = ( plus_plus_real @ A @ B ) ) ).
% 5.31/5.63
% 5.31/5.63 % diff_minus_eq_add
% 5.31/5.63 thf(fact_7229_diff__minus__eq__add,axiom,
% 5.31/5.63 ! [A: complex,B: complex] :
% 5.31/5.63 ( ( minus_minus_complex @ A @ ( uminus1482373934393186551omplex @ B ) )
% 5.31/5.63 = ( plus_plus_complex @ A @ B ) ) ).
% 5.31/5.63
% 5.31/5.63 % diff_minus_eq_add
% 5.31/5.63 thf(fact_7230_diff__minus__eq__add,axiom,
% 5.31/5.63 ! [A: code_integer,B: code_integer] :
% 5.31/5.63 ( ( minus_8373710615458151222nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 5.31/5.63 = ( plus_p5714425477246183910nteger @ A @ B ) ) ).
% 5.31/5.63
% 5.31/5.63 % diff_minus_eq_add
% 5.31/5.63 thf(fact_7231_diff__minus__eq__add,axiom,
% 5.31/5.63 ! [A: rat,B: rat] :
% 5.31/5.63 ( ( minus_minus_rat @ A @ ( uminus_uminus_rat @ B ) )
% 5.31/5.63 = ( plus_plus_rat @ A @ B ) ) ).
% 5.31/5.63
% 5.31/5.63 % diff_minus_eq_add
% 5.31/5.63 thf(fact_7232_uminus__add__conv__diff,axiom,
% 5.31/5.63 ! [A: int,B: int] :
% 5.31/5.63 ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ B )
% 5.31/5.63 = ( minus_minus_int @ B @ A ) ) ).
% 5.31/5.63
% 5.31/5.63 % uminus_add_conv_diff
% 5.31/5.63 thf(fact_7233_uminus__add__conv__diff,axiom,
% 5.31/5.63 ! [A: real,B: real] :
% 5.31/5.63 ( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ B )
% 5.31/5.63 = ( minus_minus_real @ B @ A ) ) ).
% 5.31/5.63
% 5.31/5.63 % uminus_add_conv_diff
% 5.31/5.63 thf(fact_7234_uminus__add__conv__diff,axiom,
% 5.31/5.63 ! [A: complex,B: complex] :
% 5.31/5.63 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ B )
% 5.31/5.63 = ( minus_minus_complex @ B @ A ) ) ).
% 5.31/5.63
% 5.31/5.63 % uminus_add_conv_diff
% 5.31/5.63 thf(fact_7235_uminus__add__conv__diff,axiom,
% 5.31/5.63 ! [A: code_integer,B: code_integer] :
% 5.31/5.63 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 5.31/5.63 = ( minus_8373710615458151222nteger @ B @ A ) ) ).
% 5.31/5.63
% 5.31/5.63 % uminus_add_conv_diff
% 5.31/5.63 thf(fact_7236_uminus__add__conv__diff,axiom,
% 5.31/5.63 ! [A: rat,B: rat] :
% 5.31/5.63 ( ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ B )
% 5.31/5.63 = ( minus_minus_rat @ B @ A ) ) ).
% 5.31/5.63
% 5.31/5.63 % uminus_add_conv_diff
% 5.31/5.63 thf(fact_7237_fact__0,axiom,
% 5.31/5.63 ( ( semiri3624122377584611663nteger @ zero_zero_nat )
% 5.31/5.63 = one_one_Code_integer ) ).
% 5.31/5.63
% 5.31/5.63 % fact_0
% 5.31/5.63 thf(fact_7238_fact__0,axiom,
% 5.31/5.63 ( ( semiri5044797733671781792omplex @ zero_zero_nat )
% 5.31/5.63 = one_one_complex ) ).
% 5.31/5.63
% 5.31/5.63 % fact_0
% 5.31/5.63 thf(fact_7239_fact__0,axiom,
% 5.31/5.63 ( ( semiri1406184849735516958ct_int @ zero_zero_nat )
% 5.31/5.63 = one_one_int ) ).
% 5.31/5.63
% 5.31/5.63 % fact_0
% 5.31/5.63 thf(fact_7240_fact__0,axiom,
% 5.31/5.63 ( ( semiri1408675320244567234ct_nat @ zero_zero_nat )
% 5.31/5.63 = one_one_nat ) ).
% 5.31/5.63
% 5.31/5.63 % fact_0
% 5.31/5.63 thf(fact_7241_fact__0,axiom,
% 5.31/5.63 ( ( semiri2265585572941072030t_real @ zero_zero_nat )
% 5.31/5.63 = one_one_real ) ).
% 5.31/5.63
% 5.31/5.63 % fact_0
% 5.31/5.63 thf(fact_7242_negative__zless,axiom,
% 5.31/5.63 ! [N: nat,M2: nat] : ( ord_less_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N ) ) ) @ ( semiri1314217659103216013at_int @ M2 ) ) ).
% 5.31/5.63
% 5.31/5.63 % negative_zless
% 5.31/5.63 thf(fact_7243_signed__take__bit__Suc__1,axiom,
% 5.31/5.63 ! [N: nat] :
% 5.31/5.63 ( ( bit_ri6519982836138164636nteger @ ( suc @ N ) @ one_one_Code_integer )
% 5.31/5.63 = one_one_Code_integer ) ).
% 5.31/5.63
% 5.31/5.63 % signed_take_bit_Suc_1
% 5.31/5.63 thf(fact_7244_signed__take__bit__Suc__1,axiom,
% 5.31/5.63 ! [N: nat] :
% 5.31/5.63 ( ( bit_ri631733984087533419it_int @ ( suc @ N ) @ one_one_int )
% 5.31/5.63 = one_one_int ) ).
% 5.31/5.63
% 5.31/5.63 % signed_take_bit_Suc_1
% 5.31/5.63 thf(fact_7245_dbl__simps_I1_J,axiom,
% 5.31/5.63 ! [K2: num] :
% 5.31/5.63 ( ( neg_numeral_dbl_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K2 ) ) )
% 5.31/5.63 = ( uminus_uminus_int @ ( neg_numeral_dbl_int @ ( numeral_numeral_int @ K2 ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % dbl_simps(1)
% 5.31/5.63 thf(fact_7246_dbl__simps_I1_J,axiom,
% 5.31/5.63 ! [K2: num] :
% 5.31/5.63 ( ( neg_numeral_dbl_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ K2 ) ) )
% 5.31/5.63 = ( uminus_uminus_real @ ( neg_numeral_dbl_real @ ( numeral_numeral_real @ K2 ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % dbl_simps(1)
% 5.31/5.63 thf(fact_7247_dbl__simps_I1_J,axiom,
% 5.31/5.63 ! [K2: num] :
% 5.31/5.63 ( ( neg_nu7009210354673126013omplex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ K2 ) ) )
% 5.31/5.63 = ( uminus1482373934393186551omplex @ ( neg_nu7009210354673126013omplex @ ( numera6690914467698888265omplex @ K2 ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % dbl_simps(1)
% 5.31/5.63 thf(fact_7248_dbl__simps_I1_J,axiom,
% 5.31/5.63 ! [K2: num] :
% 5.31/5.63 ( ( neg_nu8804712462038260780nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ K2 ) ) )
% 5.31/5.63 = ( uminus1351360451143612070nteger @ ( neg_nu8804712462038260780nteger @ ( numera6620942414471956472nteger @ K2 ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % dbl_simps(1)
% 5.31/5.63 thf(fact_7249_dbl__simps_I1_J,axiom,
% 5.31/5.63 ! [K2: num] :
% 5.31/5.63 ( ( neg_numeral_dbl_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ K2 ) ) )
% 5.31/5.63 = ( uminus_uminus_rat @ ( neg_numeral_dbl_rat @ ( numeral_numeral_rat @ K2 ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % dbl_simps(1)
% 5.31/5.63 thf(fact_7250_dbl__inc__simps_I4_J,axiom,
% 5.31/5.63 ( ( neg_nu5851722552734809277nc_int @ ( uminus_uminus_int @ one_one_int ) )
% 5.31/5.63 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.31/5.63
% 5.31/5.63 % dbl_inc_simps(4)
% 5.31/5.63 thf(fact_7251_dbl__inc__simps_I4_J,axiom,
% 5.31/5.63 ( ( neg_nu8295874005876285629c_real @ ( uminus_uminus_real @ one_one_real ) )
% 5.31/5.63 = ( uminus_uminus_real @ one_one_real ) ) ).
% 5.31/5.63
% 5.31/5.63 % dbl_inc_simps(4)
% 5.31/5.63 thf(fact_7252_dbl__inc__simps_I4_J,axiom,
% 5.31/5.63 ( ( neg_nu8557863876264182079omplex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.31/5.63 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.31/5.63
% 5.31/5.63 % dbl_inc_simps(4)
% 5.31/5.63 thf(fact_7253_dbl__inc__simps_I4_J,axiom,
% 5.31/5.63 ( ( neg_nu5831290666863070958nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.31/5.63 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.31/5.63
% 5.31/5.63 % dbl_inc_simps(4)
% 5.31/5.63 thf(fact_7254_dbl__inc__simps_I4_J,axiom,
% 5.31/5.63 ( ( neg_nu5219082963157363817nc_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.31/5.63 = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.31/5.63
% 5.31/5.63 % dbl_inc_simps(4)
% 5.31/5.63 thf(fact_7255_set__decode__zero,axiom,
% 5.31/5.63 ( ( nat_set_decode @ zero_zero_nat )
% 5.31/5.63 = bot_bot_set_nat ) ).
% 5.31/5.63
% 5.31/5.63 % set_decode_zero
% 5.31/5.63 thf(fact_7256_set__encode__inverse,axiom,
% 5.31/5.63 ! [A4: set_nat] :
% 5.31/5.63 ( ( finite_finite_nat @ A4 )
% 5.31/5.63 => ( ( nat_set_decode @ ( nat_set_encode @ A4 ) )
% 5.31/5.63 = A4 ) ) ).
% 5.31/5.63
% 5.31/5.63 % set_encode_inverse
% 5.31/5.63 thf(fact_7257_add__neg__numeral__special_I7_J,axiom,
% 5.31/5.63 ( ( plus_plus_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) )
% 5.31/5.63 = zero_zero_int ) ).
% 5.31/5.63
% 5.31/5.63 % add_neg_numeral_special(7)
% 5.31/5.63 thf(fact_7258_add__neg__numeral__special_I7_J,axiom,
% 5.31/5.63 ( ( plus_plus_real @ one_one_real @ ( uminus_uminus_real @ one_one_real ) )
% 5.31/5.63 = zero_zero_real ) ).
% 5.31/5.63
% 5.31/5.63 % add_neg_numeral_special(7)
% 5.31/5.63 thf(fact_7259_add__neg__numeral__special_I7_J,axiom,
% 5.31/5.63 ( ( plus_plus_complex @ one_one_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.31/5.63 = zero_zero_complex ) ).
% 5.31/5.63
% 5.31/5.63 % add_neg_numeral_special(7)
% 5.31/5.63 thf(fact_7260_add__neg__numeral__special_I7_J,axiom,
% 5.31/5.63 ( ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.31/5.63 = zero_z3403309356797280102nteger ) ).
% 5.31/5.63
% 5.31/5.63 % add_neg_numeral_special(7)
% 5.31/5.63 thf(fact_7261_add__neg__numeral__special_I7_J,axiom,
% 5.31/5.63 ( ( plus_plus_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.31/5.63 = zero_zero_rat ) ).
% 5.31/5.63
% 5.31/5.63 % add_neg_numeral_special(7)
% 5.31/5.63 thf(fact_7262_add__neg__numeral__special_I8_J,axiom,
% 5.31/5.63 ( ( plus_plus_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int )
% 5.31/5.63 = zero_zero_int ) ).
% 5.31/5.63
% 5.31/5.63 % add_neg_numeral_special(8)
% 5.31/5.63 thf(fact_7263_add__neg__numeral__special_I8_J,axiom,
% 5.31/5.63 ( ( plus_plus_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real )
% 5.31/5.63 = zero_zero_real ) ).
% 5.31/5.63
% 5.31/5.63 % add_neg_numeral_special(8)
% 5.31/5.63 thf(fact_7264_add__neg__numeral__special_I8_J,axiom,
% 5.31/5.63 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ one_one_complex )
% 5.31/5.63 = zero_zero_complex ) ).
% 5.31/5.63
% 5.31/5.63 % add_neg_numeral_special(8)
% 5.31/5.63 thf(fact_7265_add__neg__numeral__special_I8_J,axiom,
% 5.31/5.63 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer )
% 5.31/5.63 = zero_z3403309356797280102nteger ) ).
% 5.31/5.63
% 5.31/5.63 % add_neg_numeral_special(8)
% 5.31/5.63 thf(fact_7266_add__neg__numeral__special_I8_J,axiom,
% 5.31/5.63 ( ( plus_plus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat )
% 5.31/5.63 = zero_zero_rat ) ).
% 5.31/5.63
% 5.31/5.63 % add_neg_numeral_special(8)
% 5.31/5.63 thf(fact_7267_diff__numeral__special_I12_J,axiom,
% 5.31/5.63 ( ( minus_minus_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ one_one_int ) )
% 5.31/5.63 = zero_zero_int ) ).
% 5.31/5.63
% 5.31/5.63 % diff_numeral_special(12)
% 5.31/5.63 thf(fact_7268_diff__numeral__special_I12_J,axiom,
% 5.31/5.63 ( ( minus_minus_real @ ( uminus_uminus_real @ one_one_real ) @ ( uminus_uminus_real @ one_one_real ) )
% 5.31/5.63 = zero_zero_real ) ).
% 5.31/5.63
% 5.31/5.63 % diff_numeral_special(12)
% 5.31/5.63 thf(fact_7269_diff__numeral__special_I12_J,axiom,
% 5.31/5.63 ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.31/5.63 = zero_zero_complex ) ).
% 5.31/5.63
% 5.31/5.63 % diff_numeral_special(12)
% 5.31/5.63 thf(fact_7270_diff__numeral__special_I12_J,axiom,
% 5.31/5.63 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.31/5.63 = zero_z3403309356797280102nteger ) ).
% 5.31/5.63
% 5.31/5.63 % diff_numeral_special(12)
% 5.31/5.63 thf(fact_7271_diff__numeral__special_I12_J,axiom,
% 5.31/5.63 ( ( minus_minus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.31/5.63 = zero_zero_rat ) ).
% 5.31/5.63
% 5.31/5.63 % diff_numeral_special(12)
% 5.31/5.63 thf(fact_7272_neg__one__eq__numeral__iff,axiom,
% 5.31/5.63 ! [N: num] :
% 5.31/5.63 ( ( ( uminus_uminus_int @ one_one_int )
% 5.31/5.63 = ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.31/5.63 = ( N = one ) ) ).
% 5.31/5.63
% 5.31/5.63 % neg_one_eq_numeral_iff
% 5.31/5.63 thf(fact_7273_neg__one__eq__numeral__iff,axiom,
% 5.31/5.63 ! [N: num] :
% 5.31/5.63 ( ( ( uminus_uminus_real @ one_one_real )
% 5.31/5.63 = ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 5.31/5.63 = ( N = one ) ) ).
% 5.31/5.63
% 5.31/5.63 % neg_one_eq_numeral_iff
% 5.31/5.63 thf(fact_7274_neg__one__eq__numeral__iff,axiom,
% 5.31/5.63 ! [N: num] :
% 5.31/5.63 ( ( ( uminus1482373934393186551omplex @ one_one_complex )
% 5.31/5.63 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 5.31/5.63 = ( N = one ) ) ).
% 5.31/5.63
% 5.31/5.63 % neg_one_eq_numeral_iff
% 5.31/5.63 thf(fact_7275_neg__one__eq__numeral__iff,axiom,
% 5.31/5.63 ! [N: num] :
% 5.31/5.63 ( ( ( uminus1351360451143612070nteger @ one_one_Code_integer )
% 5.31/5.63 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 5.31/5.63 = ( N = one ) ) ).
% 5.31/5.63
% 5.31/5.63 % neg_one_eq_numeral_iff
% 5.31/5.63 thf(fact_7276_neg__one__eq__numeral__iff,axiom,
% 5.31/5.63 ! [N: num] :
% 5.31/5.63 ( ( ( uminus_uminus_rat @ one_one_rat )
% 5.31/5.63 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 5.31/5.63 = ( N = one ) ) ).
% 5.31/5.63
% 5.31/5.63 % neg_one_eq_numeral_iff
% 5.31/5.63 thf(fact_7277_numeral__eq__neg__one__iff,axiom,
% 5.31/5.63 ! [N: num] :
% 5.31/5.63 ( ( ( uminus_uminus_int @ ( numeral_numeral_int @ N ) )
% 5.31/5.63 = ( uminus_uminus_int @ one_one_int ) )
% 5.31/5.63 = ( N = one ) ) ).
% 5.31/5.63
% 5.31/5.63 % numeral_eq_neg_one_iff
% 5.31/5.63 thf(fact_7278_numeral__eq__neg__one__iff,axiom,
% 5.31/5.63 ! [N: num] :
% 5.31/5.63 ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ N ) )
% 5.31/5.63 = ( uminus_uminus_real @ one_one_real ) )
% 5.31/5.63 = ( N = one ) ) ).
% 5.31/5.63
% 5.31/5.63 % numeral_eq_neg_one_iff
% 5.31/5.63 thf(fact_7279_numeral__eq__neg__one__iff,axiom,
% 5.31/5.63 ! [N: num] :
% 5.31/5.63 ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) )
% 5.31/5.63 = ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.31/5.63 = ( N = one ) ) ).
% 5.31/5.63
% 5.31/5.63 % numeral_eq_neg_one_iff
% 5.31/5.63 thf(fact_7280_numeral__eq__neg__one__iff,axiom,
% 5.31/5.63 ! [N: num] :
% 5.31/5.63 ( ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) )
% 5.31/5.63 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.31/5.63 = ( N = one ) ) ).
% 5.31/5.63
% 5.31/5.63 % numeral_eq_neg_one_iff
% 5.31/5.63 thf(fact_7281_numeral__eq__neg__one__iff,axiom,
% 5.31/5.63 ! [N: num] :
% 5.31/5.63 ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) )
% 5.31/5.63 = ( uminus_uminus_rat @ one_one_rat ) )
% 5.31/5.63 = ( N = one ) ) ).
% 5.31/5.63
% 5.31/5.63 % numeral_eq_neg_one_iff
% 5.31/5.63 thf(fact_7282_left__minus__one__mult__self,axiom,
% 5.31/5.63 ! [N: nat,A: int] :
% 5.31/5.63 ( ( 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 ) )
% 5.31/5.63 = A ) ).
% 5.31/5.63
% 5.31/5.63 % left_minus_one_mult_self
% 5.31/5.63 thf(fact_7283_left__minus__one__mult__self,axiom,
% 5.31/5.63 ! [N: nat,A: real] :
% 5.31/5.63 ( ( 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 ) )
% 5.31/5.63 = A ) ).
% 5.31/5.63
% 5.31/5.63 % left_minus_one_mult_self
% 5.31/5.63 thf(fact_7284_left__minus__one__mult__self,axiom,
% 5.31/5.63 ! [N: nat,A: complex] :
% 5.31/5.63 ( ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) @ ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) @ A ) )
% 5.31/5.63 = A ) ).
% 5.31/5.63
% 5.31/5.63 % left_minus_one_mult_self
% 5.31/5.63 thf(fact_7285_left__minus__one__mult__self,axiom,
% 5.31/5.63 ! [N: nat,A: code_integer] :
% 5.31/5.63 ( ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N ) @ ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N ) @ A ) )
% 5.31/5.63 = A ) ).
% 5.31/5.63
% 5.31/5.63 % left_minus_one_mult_self
% 5.31/5.63 thf(fact_7286_left__minus__one__mult__self,axiom,
% 5.31/5.63 ! [N: nat,A: rat] :
% 5.31/5.63 ( ( 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 ) )
% 5.31/5.63 = A ) ).
% 5.31/5.63
% 5.31/5.63 % left_minus_one_mult_self
% 5.31/5.63 thf(fact_7287_minus__one__mult__self,axiom,
% 5.31/5.63 ! [N: nat] :
% 5.31/5.63 ( ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N ) @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N ) )
% 5.31/5.63 = one_one_int ) ).
% 5.31/5.63
% 5.31/5.63 % minus_one_mult_self
% 5.31/5.63 thf(fact_7288_minus__one__mult__self,axiom,
% 5.31/5.63 ! [N: nat] :
% 5.31/5.63 ( ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) )
% 5.31/5.63 = one_one_real ) ).
% 5.31/5.63
% 5.31/5.63 % minus_one_mult_self
% 5.31/5.63 thf(fact_7289_minus__one__mult__self,axiom,
% 5.31/5.63 ! [N: nat] :
% 5.31/5.63 ( ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) )
% 5.31/5.63 = one_one_complex ) ).
% 5.31/5.63
% 5.31/5.63 % minus_one_mult_self
% 5.31/5.63 thf(fact_7290_minus__one__mult__self,axiom,
% 5.31/5.63 ! [N: nat] :
% 5.31/5.63 ( ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N ) @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N ) )
% 5.31/5.63 = one_one_Code_integer ) ).
% 5.31/5.63
% 5.31/5.63 % minus_one_mult_self
% 5.31/5.63 thf(fact_7291_minus__one__mult__self,axiom,
% 5.31/5.63 ! [N: nat] :
% 5.31/5.63 ( ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N ) @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N ) )
% 5.31/5.63 = one_one_rat ) ).
% 5.31/5.63
% 5.31/5.63 % minus_one_mult_self
% 5.31/5.63 thf(fact_7292_mod__minus1__right,axiom,
% 5.31/5.63 ! [A: int] :
% 5.31/5.63 ( ( modulo_modulo_int @ A @ ( uminus_uminus_int @ one_one_int ) )
% 5.31/5.63 = zero_zero_int ) ).
% 5.31/5.63
% 5.31/5.63 % mod_minus1_right
% 5.31/5.63 thf(fact_7293_mod__minus1__right,axiom,
% 5.31/5.63 ! [A: code_integer] :
% 5.31/5.63 ( ( modulo364778990260209775nteger @ A @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.31/5.63 = zero_z3403309356797280102nteger ) ).
% 5.31/5.63
% 5.31/5.63 % mod_minus1_right
% 5.31/5.63 thf(fact_7294_max__number__of_I2_J,axiom,
% 5.31/5.63 ! [U: num,V2: num] :
% 5.31/5.63 ( ( ( ord_less_eq_real @ ( numeral_numeral_real @ U ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V2 ) ) )
% 5.31/5.63 => ( ( ord_max_real @ ( numeral_numeral_real @ U ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V2 ) ) )
% 5.31/5.63 = ( uminus_uminus_real @ ( numeral_numeral_real @ V2 ) ) ) )
% 5.31/5.63 & ( ~ ( ord_less_eq_real @ ( numeral_numeral_real @ U ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V2 ) ) )
% 5.31/5.63 => ( ( ord_max_real @ ( numeral_numeral_real @ U ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V2 ) ) )
% 5.31/5.63 = ( numeral_numeral_real @ U ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % max_number_of(2)
% 5.31/5.63 thf(fact_7295_max__number__of_I2_J,axiom,
% 5.31/5.63 ! [U: num,V2: num] :
% 5.31/5.63 ( ( ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ U ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V2 ) ) )
% 5.31/5.63 => ( ( ord_max_Code_integer @ ( numera6620942414471956472nteger @ U ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V2 ) ) )
% 5.31/5.63 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V2 ) ) ) )
% 5.31/5.63 & ( ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ U ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V2 ) ) )
% 5.31/5.63 => ( ( ord_max_Code_integer @ ( numera6620942414471956472nteger @ U ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V2 ) ) )
% 5.31/5.63 = ( numera6620942414471956472nteger @ U ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % max_number_of(2)
% 5.31/5.63 thf(fact_7296_max__number__of_I2_J,axiom,
% 5.31/5.63 ! [U: num,V2: num] :
% 5.31/5.63 ( ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ U ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V2 ) ) )
% 5.31/5.63 => ( ( ord_max_rat @ ( numeral_numeral_rat @ U ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V2 ) ) )
% 5.31/5.63 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ V2 ) ) ) )
% 5.31/5.63 & ( ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ U ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V2 ) ) )
% 5.31/5.63 => ( ( ord_max_rat @ ( numeral_numeral_rat @ U ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V2 ) ) )
% 5.31/5.63 = ( numeral_numeral_rat @ U ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % max_number_of(2)
% 5.31/5.63 thf(fact_7297_max__number__of_I2_J,axiom,
% 5.31/5.63 ! [U: num,V2: num] :
% 5.31/5.63 ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ U ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V2 ) ) )
% 5.31/5.63 => ( ( ord_max_int @ ( numeral_numeral_int @ U ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V2 ) ) )
% 5.31/5.63 = ( uminus_uminus_int @ ( numeral_numeral_int @ V2 ) ) ) )
% 5.31/5.63 & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ U ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V2 ) ) )
% 5.31/5.63 => ( ( ord_max_int @ ( numeral_numeral_int @ U ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V2 ) ) )
% 5.31/5.63 = ( numeral_numeral_int @ U ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % max_number_of(2)
% 5.31/5.63 thf(fact_7298_max__number__of_I3_J,axiom,
% 5.31/5.63 ! [U: num,V2: num] :
% 5.31/5.63 ( ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( numeral_numeral_real @ V2 ) )
% 5.31/5.63 => ( ( ord_max_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( numeral_numeral_real @ V2 ) )
% 5.31/5.63 = ( numeral_numeral_real @ V2 ) ) )
% 5.31/5.63 & ( ~ ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( numeral_numeral_real @ V2 ) )
% 5.31/5.63 => ( ( ord_max_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( numeral_numeral_real @ V2 ) )
% 5.31/5.63 = ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % max_number_of(3)
% 5.31/5.63 thf(fact_7299_max__number__of_I3_J,axiom,
% 5.31/5.63 ! [U: num,V2: num] :
% 5.31/5.63 ( ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( numera6620942414471956472nteger @ V2 ) )
% 5.31/5.63 => ( ( ord_max_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( numera6620942414471956472nteger @ V2 ) )
% 5.31/5.63 = ( numera6620942414471956472nteger @ V2 ) ) )
% 5.31/5.63 & ( ~ ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( numera6620942414471956472nteger @ V2 ) )
% 5.31/5.63 => ( ( ord_max_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( numera6620942414471956472nteger @ V2 ) )
% 5.31/5.63 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % max_number_of(3)
% 5.31/5.63 thf(fact_7300_max__number__of_I3_J,axiom,
% 5.31/5.63 ! [U: num,V2: num] :
% 5.31/5.63 ( ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( numeral_numeral_rat @ V2 ) )
% 5.31/5.63 => ( ( ord_max_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( numeral_numeral_rat @ V2 ) )
% 5.31/5.63 = ( numeral_numeral_rat @ V2 ) ) )
% 5.31/5.63 & ( ~ ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( numeral_numeral_rat @ V2 ) )
% 5.31/5.63 => ( ( ord_max_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( numeral_numeral_rat @ V2 ) )
% 5.31/5.63 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % max_number_of(3)
% 5.31/5.63 thf(fact_7301_max__number__of_I3_J,axiom,
% 5.31/5.63 ! [U: num,V2: num] :
% 5.31/5.63 ( ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( numeral_numeral_int @ V2 ) )
% 5.31/5.63 => ( ( ord_max_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( numeral_numeral_int @ V2 ) )
% 5.31/5.63 = ( numeral_numeral_int @ V2 ) ) )
% 5.31/5.63 & ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( numeral_numeral_int @ V2 ) )
% 5.31/5.63 => ( ( ord_max_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( numeral_numeral_int @ V2 ) )
% 5.31/5.63 = ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % max_number_of(3)
% 5.31/5.63 thf(fact_7302_max__number__of_I4_J,axiom,
% 5.31/5.63 ! [U: num,V2: num] :
% 5.31/5.63 ( ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V2 ) ) )
% 5.31/5.63 => ( ( ord_max_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V2 ) ) )
% 5.31/5.63 = ( uminus_uminus_real @ ( numeral_numeral_real @ V2 ) ) ) )
% 5.31/5.63 & ( ~ ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V2 ) ) )
% 5.31/5.63 => ( ( ord_max_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V2 ) ) )
% 5.31/5.63 = ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % max_number_of(4)
% 5.31/5.63 thf(fact_7303_max__number__of_I4_J,axiom,
% 5.31/5.63 ! [U: num,V2: num] :
% 5.31/5.63 ( ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V2 ) ) )
% 5.31/5.63 => ( ( ord_max_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V2 ) ) )
% 5.31/5.63 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V2 ) ) ) )
% 5.31/5.63 & ( ~ ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V2 ) ) )
% 5.31/5.63 => ( ( ord_max_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V2 ) ) )
% 5.31/5.63 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % max_number_of(4)
% 5.31/5.63 thf(fact_7304_max__number__of_I4_J,axiom,
% 5.31/5.63 ! [U: num,V2: num] :
% 5.31/5.63 ( ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V2 ) ) )
% 5.31/5.63 => ( ( ord_max_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V2 ) ) )
% 5.31/5.63 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ V2 ) ) ) )
% 5.31/5.63 & ( ~ ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V2 ) ) )
% 5.31/5.63 => ( ( ord_max_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V2 ) ) )
% 5.31/5.63 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % max_number_of(4)
% 5.31/5.63 thf(fact_7305_max__number__of_I4_J,axiom,
% 5.31/5.63 ! [U: num,V2: num] :
% 5.31/5.63 ( ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V2 ) ) )
% 5.31/5.63 => ( ( ord_max_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V2 ) ) )
% 5.31/5.63 = ( uminus_uminus_int @ ( numeral_numeral_int @ V2 ) ) ) )
% 5.31/5.63 & ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V2 ) ) )
% 5.31/5.63 => ( ( ord_max_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V2 ) ) )
% 5.31/5.63 = ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % max_number_of(4)
% 5.31/5.63 thf(fact_7306_fact__Suc__0,axiom,
% 5.31/5.63 ( ( semiri3624122377584611663nteger @ ( suc @ zero_zero_nat ) )
% 5.31/5.63 = one_one_Code_integer ) ).
% 5.31/5.63
% 5.31/5.63 % fact_Suc_0
% 5.31/5.63 thf(fact_7307_fact__Suc__0,axiom,
% 5.31/5.63 ( ( semiri5044797733671781792omplex @ ( suc @ zero_zero_nat ) )
% 5.31/5.63 = one_one_complex ) ).
% 5.31/5.63
% 5.31/5.63 % fact_Suc_0
% 5.31/5.63 thf(fact_7308_fact__Suc__0,axiom,
% 5.31/5.63 ( ( semiri1406184849735516958ct_int @ ( suc @ zero_zero_nat ) )
% 5.31/5.63 = one_one_int ) ).
% 5.31/5.63
% 5.31/5.63 % fact_Suc_0
% 5.31/5.63 thf(fact_7309_fact__Suc__0,axiom,
% 5.31/5.63 ( ( semiri1408675320244567234ct_nat @ ( suc @ zero_zero_nat ) )
% 5.31/5.63 = one_one_nat ) ).
% 5.31/5.63
% 5.31/5.63 % fact_Suc_0
% 5.31/5.63 thf(fact_7310_fact__Suc__0,axiom,
% 5.31/5.63 ( ( semiri2265585572941072030t_real @ ( suc @ zero_zero_nat ) )
% 5.31/5.63 = one_one_real ) ).
% 5.31/5.63
% 5.31/5.63 % fact_Suc_0
% 5.31/5.63 thf(fact_7311_fact__Suc,axiom,
% 5.31/5.63 ! [N: nat] :
% 5.31/5.63 ( ( semiri773545260158071498ct_rat @ ( suc @ N ) )
% 5.31/5.63 = ( times_times_rat @ ( semiri681578069525770553at_rat @ ( suc @ N ) ) @ ( semiri773545260158071498ct_rat @ N ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % fact_Suc
% 5.31/5.63 thf(fact_7312_fact__Suc,axiom,
% 5.31/5.63 ! [N: nat] :
% 5.31/5.63 ( ( semiri1406184849735516958ct_int @ ( suc @ N ) )
% 5.31/5.63 = ( times_times_int @ ( semiri1314217659103216013at_int @ ( suc @ N ) ) @ ( semiri1406184849735516958ct_int @ N ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % fact_Suc
% 5.31/5.63 thf(fact_7313_fact__Suc,axiom,
% 5.31/5.63 ! [N: nat] :
% 5.31/5.63 ( ( semiri1408675320244567234ct_nat @ ( suc @ N ) )
% 5.31/5.63 = ( times_times_nat @ ( semiri1316708129612266289at_nat @ ( suc @ N ) ) @ ( semiri1408675320244567234ct_nat @ N ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % fact_Suc
% 5.31/5.63 thf(fact_7314_fact__Suc,axiom,
% 5.31/5.63 ! [N: nat] :
% 5.31/5.63 ( ( semiri2265585572941072030t_real @ ( suc @ N ) )
% 5.31/5.63 = ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) @ ( semiri2265585572941072030t_real @ N ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % fact_Suc
% 5.31/5.63 thf(fact_7315_diff__numeral__simps_I3_J,axiom,
% 5.31/5.63 ! [M2: num,N: num] :
% 5.31/5.63 ( ( minus_minus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ ( numeral_numeral_int @ N ) )
% 5.31/5.63 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( plus_plus_num @ M2 @ N ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % diff_numeral_simps(3)
% 5.31/5.63 thf(fact_7316_diff__numeral__simps_I3_J,axiom,
% 5.31/5.63 ! [M2: num,N: num] :
% 5.31/5.63 ( ( minus_minus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M2 ) ) @ ( numeral_numeral_real @ N ) )
% 5.31/5.63 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( plus_plus_num @ M2 @ N ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % diff_numeral_simps(3)
% 5.31/5.63 thf(fact_7317_diff__numeral__simps_I3_J,axiom,
% 5.31/5.63 ! [M2: num,N: num] :
% 5.31/5.63 ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M2 ) ) @ ( numera6690914467698888265omplex @ N ) )
% 5.31/5.63 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( plus_plus_num @ M2 @ N ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % diff_numeral_simps(3)
% 5.31/5.63 thf(fact_7318_diff__numeral__simps_I3_J,axiom,
% 5.31/5.63 ! [M2: num,N: num] :
% 5.31/5.63 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M2 ) ) @ ( numera6620942414471956472nteger @ N ) )
% 5.31/5.63 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( plus_plus_num @ M2 @ N ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % diff_numeral_simps(3)
% 5.31/5.63 thf(fact_7319_diff__numeral__simps_I3_J,axiom,
% 5.31/5.63 ! [M2: num,N: num] :
% 5.31/5.63 ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M2 ) ) @ ( numeral_numeral_rat @ N ) )
% 5.31/5.63 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( plus_plus_num @ M2 @ N ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % diff_numeral_simps(3)
% 5.31/5.63 thf(fact_7320_diff__numeral__simps_I2_J,axiom,
% 5.31/5.63 ! [M2: num,N: num] :
% 5.31/5.63 ( ( minus_minus_int @ ( numeral_numeral_int @ M2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.31/5.63 = ( numeral_numeral_int @ ( plus_plus_num @ M2 @ N ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % diff_numeral_simps(2)
% 5.31/5.63 thf(fact_7321_diff__numeral__simps_I2_J,axiom,
% 5.31/5.63 ! [M2: num,N: num] :
% 5.31/5.63 ( ( minus_minus_real @ ( numeral_numeral_real @ M2 ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 5.31/5.63 = ( numeral_numeral_real @ ( plus_plus_num @ M2 @ N ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % diff_numeral_simps(2)
% 5.31/5.63 thf(fact_7322_diff__numeral__simps_I2_J,axiom,
% 5.31/5.63 ! [M2: num,N: num] :
% 5.31/5.63 ( ( minus_minus_complex @ ( numera6690914467698888265omplex @ M2 ) @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 5.31/5.63 = ( numera6690914467698888265omplex @ ( plus_plus_num @ M2 @ N ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % diff_numeral_simps(2)
% 5.31/5.63 thf(fact_7323_diff__numeral__simps_I2_J,axiom,
% 5.31/5.63 ! [M2: num,N: num] :
% 5.31/5.63 ( ( minus_8373710615458151222nteger @ ( numera6620942414471956472nteger @ M2 ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 5.31/5.63 = ( numera6620942414471956472nteger @ ( plus_plus_num @ M2 @ N ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % diff_numeral_simps(2)
% 5.31/5.63 thf(fact_7324_diff__numeral__simps_I2_J,axiom,
% 5.31/5.63 ! [M2: num,N: num] :
% 5.31/5.63 ( ( minus_minus_rat @ ( numeral_numeral_rat @ M2 ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 5.31/5.63 = ( numeral_numeral_rat @ ( plus_plus_num @ M2 @ N ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % diff_numeral_simps(2)
% 5.31/5.63 thf(fact_7325_mult__neg__numeral__simps_I3_J,axiom,
% 5.31/5.63 ! [M2: num,N: num] :
% 5.31/5.63 ( ( times_times_int @ ( numeral_numeral_int @ M2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.31/5.63 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( times_times_num @ M2 @ N ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % mult_neg_numeral_simps(3)
% 5.31/5.63 thf(fact_7326_mult__neg__numeral__simps_I3_J,axiom,
% 5.31/5.63 ! [M2: num,N: num] :
% 5.31/5.63 ( ( times_times_real @ ( numeral_numeral_real @ M2 ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 5.31/5.63 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( times_times_num @ M2 @ N ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % mult_neg_numeral_simps(3)
% 5.31/5.63 thf(fact_7327_mult__neg__numeral__simps_I3_J,axiom,
% 5.31/5.63 ! [M2: num,N: num] :
% 5.31/5.63 ( ( times_times_complex @ ( numera6690914467698888265omplex @ M2 ) @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 5.31/5.63 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( times_times_num @ M2 @ N ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % mult_neg_numeral_simps(3)
% 5.31/5.63 thf(fact_7328_mult__neg__numeral__simps_I3_J,axiom,
% 5.31/5.63 ! [M2: num,N: num] :
% 5.31/5.63 ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ M2 ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 5.31/5.63 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ M2 @ N ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % mult_neg_numeral_simps(3)
% 5.31/5.63 thf(fact_7329_mult__neg__numeral__simps_I3_J,axiom,
% 5.31/5.63 ! [M2: num,N: num] :
% 5.31/5.63 ( ( times_times_rat @ ( numeral_numeral_rat @ M2 ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 5.31/5.63 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( times_times_num @ M2 @ N ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % mult_neg_numeral_simps(3)
% 5.31/5.63 thf(fact_7330_mult__neg__numeral__simps_I2_J,axiom,
% 5.31/5.63 ! [M2: num,N: num] :
% 5.31/5.63 ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ ( numeral_numeral_int @ N ) )
% 5.31/5.63 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( times_times_num @ M2 @ N ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % mult_neg_numeral_simps(2)
% 5.31/5.63 thf(fact_7331_mult__neg__numeral__simps_I2_J,axiom,
% 5.31/5.63 ! [M2: num,N: num] :
% 5.31/5.63 ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M2 ) ) @ ( numeral_numeral_real @ N ) )
% 5.31/5.63 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( times_times_num @ M2 @ N ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % mult_neg_numeral_simps(2)
% 5.31/5.63 thf(fact_7332_mult__neg__numeral__simps_I2_J,axiom,
% 5.31/5.63 ! [M2: num,N: num] :
% 5.31/5.63 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M2 ) ) @ ( numera6690914467698888265omplex @ N ) )
% 5.31/5.63 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( times_times_num @ M2 @ N ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % mult_neg_numeral_simps(2)
% 5.31/5.63 thf(fact_7333_mult__neg__numeral__simps_I2_J,axiom,
% 5.31/5.63 ! [M2: num,N: num] :
% 5.31/5.63 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M2 ) ) @ ( numera6620942414471956472nteger @ N ) )
% 5.31/5.63 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ M2 @ N ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % mult_neg_numeral_simps(2)
% 5.31/5.63 thf(fact_7334_mult__neg__numeral__simps_I2_J,axiom,
% 5.31/5.63 ! [M2: num,N: num] :
% 5.31/5.63 ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M2 ) ) @ ( numeral_numeral_rat @ N ) )
% 5.31/5.63 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( times_times_num @ M2 @ N ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % mult_neg_numeral_simps(2)
% 5.31/5.63 thf(fact_7335_mult__neg__numeral__simps_I1_J,axiom,
% 5.31/5.63 ! [M2: num,N: num] :
% 5.31/5.63 ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.31/5.63 = ( numeral_numeral_int @ ( times_times_num @ M2 @ N ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % mult_neg_numeral_simps(1)
% 5.31/5.63 thf(fact_7336_mult__neg__numeral__simps_I1_J,axiom,
% 5.31/5.63 ! [M2: num,N: num] :
% 5.31/5.63 ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M2 ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 5.31/5.63 = ( numeral_numeral_real @ ( times_times_num @ M2 @ N ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % mult_neg_numeral_simps(1)
% 5.31/5.63 thf(fact_7337_mult__neg__numeral__simps_I1_J,axiom,
% 5.31/5.63 ! [M2: num,N: num] :
% 5.31/5.63 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M2 ) ) @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 5.31/5.63 = ( numera6690914467698888265omplex @ ( times_times_num @ M2 @ N ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % mult_neg_numeral_simps(1)
% 5.31/5.63 thf(fact_7338_mult__neg__numeral__simps_I1_J,axiom,
% 5.31/5.63 ! [M2: num,N: num] :
% 5.31/5.63 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M2 ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 5.31/5.63 = ( numera6620942414471956472nteger @ ( times_times_num @ M2 @ N ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % mult_neg_numeral_simps(1)
% 5.31/5.63 thf(fact_7339_mult__neg__numeral__simps_I1_J,axiom,
% 5.31/5.63 ! [M2: num,N: num] :
% 5.31/5.63 ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M2 ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 5.31/5.63 = ( numeral_numeral_rat @ ( times_times_num @ M2 @ N ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % mult_neg_numeral_simps(1)
% 5.31/5.63 thf(fact_7340_semiring__norm_I172_J,axiom,
% 5.31/5.63 ! [V2: num,W2: num,Y: int] :
% 5.31/5.63 ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V2 ) ) @ ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W2 ) ) @ Y ) )
% 5.31/5.63 = ( times_times_int @ ( numeral_numeral_int @ ( times_times_num @ V2 @ W2 ) ) @ Y ) ) ).
% 5.31/5.63
% 5.31/5.63 % semiring_norm(172)
% 5.31/5.63 thf(fact_7341_semiring__norm_I172_J,axiom,
% 5.31/5.63 ! [V2: num,W2: num,Y: real] :
% 5.31/5.63 ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V2 ) ) @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) @ Y ) )
% 5.31/5.63 = ( times_times_real @ ( numeral_numeral_real @ ( times_times_num @ V2 @ W2 ) ) @ Y ) ) ).
% 5.31/5.63
% 5.31/5.63 % semiring_norm(172)
% 5.31/5.63 thf(fact_7342_semiring__norm_I172_J,axiom,
% 5.31/5.63 ! [V2: num,W2: num,Y: complex] :
% 5.31/5.63 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ V2 ) ) @ ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W2 ) ) @ Y ) )
% 5.31/5.63 = ( times_times_complex @ ( numera6690914467698888265omplex @ ( times_times_num @ V2 @ W2 ) ) @ Y ) ) ).
% 5.31/5.63
% 5.31/5.63 % semiring_norm(172)
% 5.31/5.63 thf(fact_7343_semiring__norm_I172_J,axiom,
% 5.31/5.63 ! [V2: num,W2: num,Y: code_integer] :
% 5.31/5.63 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V2 ) ) @ ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ W2 ) ) @ Y ) )
% 5.31/5.63 = ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ V2 @ W2 ) ) @ Y ) ) ).
% 5.31/5.63
% 5.31/5.63 % semiring_norm(172)
% 5.31/5.63 thf(fact_7344_semiring__norm_I172_J,axiom,
% 5.31/5.63 ! [V2: num,W2: num,Y: rat] :
% 5.31/5.63 ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V2 ) ) @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ Y ) )
% 5.31/5.63 = ( times_times_rat @ ( numeral_numeral_rat @ ( times_times_num @ V2 @ W2 ) ) @ Y ) ) ).
% 5.31/5.63
% 5.31/5.63 % semiring_norm(172)
% 5.31/5.63 thf(fact_7345_semiring__norm_I171_J,axiom,
% 5.31/5.63 ! [V2: num,W2: num,Y: int] :
% 5.31/5.63 ( ( times_times_int @ ( numeral_numeral_int @ V2 ) @ ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W2 ) ) @ Y ) )
% 5.31/5.63 = ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( times_times_num @ V2 @ W2 ) ) ) @ Y ) ) ).
% 5.31/5.63
% 5.31/5.63 % semiring_norm(171)
% 5.31/5.63 thf(fact_7346_semiring__norm_I171_J,axiom,
% 5.31/5.63 ! [V2: num,W2: num,Y: real] :
% 5.31/5.63 ( ( times_times_real @ ( numeral_numeral_real @ V2 ) @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) @ Y ) )
% 5.31/5.63 = ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ ( times_times_num @ V2 @ W2 ) ) ) @ Y ) ) ).
% 5.31/5.63
% 5.31/5.63 % semiring_norm(171)
% 5.31/5.63 thf(fact_7347_semiring__norm_I171_J,axiom,
% 5.31/5.63 ! [V2: num,W2: num,Y: complex] :
% 5.31/5.63 ( ( times_times_complex @ ( numera6690914467698888265omplex @ V2 ) @ ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W2 ) ) @ Y ) )
% 5.31/5.63 = ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( times_times_num @ V2 @ W2 ) ) ) @ Y ) ) ).
% 5.31/5.63
% 5.31/5.63 % semiring_norm(171)
% 5.31/5.63 thf(fact_7348_semiring__norm_I171_J,axiom,
% 5.31/5.63 ! [V2: num,W2: num,Y: code_integer] :
% 5.31/5.63 ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ V2 ) @ ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ W2 ) ) @ Y ) )
% 5.31/5.63 = ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ V2 @ W2 ) ) ) @ Y ) ) ).
% 5.31/5.63
% 5.31/5.63 % semiring_norm(171)
% 5.31/5.63 thf(fact_7349_semiring__norm_I171_J,axiom,
% 5.31/5.63 ! [V2: num,W2: num,Y: rat] :
% 5.31/5.63 ( ( times_times_rat @ ( numeral_numeral_rat @ V2 ) @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ Y ) )
% 5.31/5.63 = ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( times_times_num @ V2 @ W2 ) ) ) @ Y ) ) ).
% 5.31/5.63
% 5.31/5.63 % semiring_norm(171)
% 5.31/5.63 thf(fact_7350_semiring__norm_I170_J,axiom,
% 5.31/5.63 ! [V2: num,W2: num,Y: int] :
% 5.31/5.63 ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V2 ) ) @ ( times_times_int @ ( numeral_numeral_int @ W2 ) @ Y ) )
% 5.31/5.63 = ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( times_times_num @ V2 @ W2 ) ) ) @ Y ) ) ).
% 5.31/5.63
% 5.31/5.63 % semiring_norm(170)
% 5.31/5.63 thf(fact_7351_semiring__norm_I170_J,axiom,
% 5.31/5.63 ! [V2: num,W2: num,Y: real] :
% 5.31/5.63 ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V2 ) ) @ ( times_times_real @ ( numeral_numeral_real @ W2 ) @ Y ) )
% 5.31/5.63 = ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ ( times_times_num @ V2 @ W2 ) ) ) @ Y ) ) ).
% 5.31/5.63
% 5.31/5.63 % semiring_norm(170)
% 5.31/5.63 thf(fact_7352_semiring__norm_I170_J,axiom,
% 5.31/5.63 ! [V2: num,W2: num,Y: complex] :
% 5.31/5.63 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ V2 ) ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ W2 ) @ Y ) )
% 5.31/5.63 = ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( times_times_num @ V2 @ W2 ) ) ) @ Y ) ) ).
% 5.31/5.63
% 5.31/5.63 % semiring_norm(170)
% 5.31/5.63 thf(fact_7353_semiring__norm_I170_J,axiom,
% 5.31/5.63 ! [V2: num,W2: num,Y: code_integer] :
% 5.31/5.63 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V2 ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ W2 ) @ Y ) )
% 5.31/5.63 = ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ V2 @ W2 ) ) ) @ Y ) ) ).
% 5.31/5.63
% 5.31/5.63 % semiring_norm(170)
% 5.31/5.63 thf(fact_7354_semiring__norm_I170_J,axiom,
% 5.31/5.63 ! [V2: num,W2: num,Y: rat] :
% 5.31/5.63 ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V2 ) ) @ ( times_times_rat @ ( numeral_numeral_rat @ W2 ) @ Y ) )
% 5.31/5.63 = ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( times_times_num @ V2 @ W2 ) ) ) @ Y ) ) ).
% 5.31/5.63
% 5.31/5.63 % semiring_norm(170)
% 5.31/5.63 thf(fact_7355_neg__numeral__le__iff,axiom,
% 5.31/5.63 ! [M2: num,N: num] :
% 5.31/5.63 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M2 ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 5.31/5.63 = ( ord_less_eq_num @ N @ M2 ) ) ).
% 5.31/5.63
% 5.31/5.63 % neg_numeral_le_iff
% 5.31/5.63 thf(fact_7356_neg__numeral__le__iff,axiom,
% 5.31/5.63 ! [M2: num,N: num] :
% 5.31/5.63 ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M2 ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 5.31/5.63 = ( ord_less_eq_num @ N @ M2 ) ) ).
% 5.31/5.63
% 5.31/5.63 % neg_numeral_le_iff
% 5.31/5.63 thf(fact_7357_neg__numeral__le__iff,axiom,
% 5.31/5.63 ! [M2: num,N: num] :
% 5.31/5.63 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M2 ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 5.31/5.63 = ( ord_less_eq_num @ N @ M2 ) ) ).
% 5.31/5.63
% 5.31/5.63 % neg_numeral_le_iff
% 5.31/5.63 thf(fact_7358_neg__numeral__le__iff,axiom,
% 5.31/5.63 ! [M2: num,N: num] :
% 5.31/5.63 ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.31/5.63 = ( ord_less_eq_num @ N @ M2 ) ) ).
% 5.31/5.63
% 5.31/5.63 % neg_numeral_le_iff
% 5.31/5.63 thf(fact_7359_neg__numeral__less__iff,axiom,
% 5.31/5.63 ! [M2: num,N: num] :
% 5.31/5.63 ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.31/5.63 = ( ord_less_num @ N @ M2 ) ) ).
% 5.31/5.63
% 5.31/5.63 % neg_numeral_less_iff
% 5.31/5.63 thf(fact_7360_neg__numeral__less__iff,axiom,
% 5.31/5.63 ! [M2: num,N: num] :
% 5.31/5.63 ( ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M2 ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 5.31/5.63 = ( ord_less_num @ N @ M2 ) ) ).
% 5.31/5.63
% 5.31/5.63 % neg_numeral_less_iff
% 5.31/5.63 thf(fact_7361_neg__numeral__less__iff,axiom,
% 5.31/5.63 ! [M2: num,N: num] :
% 5.31/5.63 ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M2 ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 5.31/5.63 = ( ord_less_num @ N @ M2 ) ) ).
% 5.31/5.63
% 5.31/5.63 % neg_numeral_less_iff
% 5.31/5.63 thf(fact_7362_neg__numeral__less__iff,axiom,
% 5.31/5.63 ! [M2: num,N: num] :
% 5.31/5.63 ( ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M2 ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 5.31/5.63 = ( ord_less_num @ N @ M2 ) ) ).
% 5.31/5.63
% 5.31/5.63 % neg_numeral_less_iff
% 5.31/5.63 thf(fact_7363_dbl__dec__simps_I2_J,axiom,
% 5.31/5.63 ( ( neg_nu3811975205180677377ec_int @ zero_zero_int )
% 5.31/5.63 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.31/5.63
% 5.31/5.63 % dbl_dec_simps(2)
% 5.31/5.63 thf(fact_7364_dbl__dec__simps_I2_J,axiom,
% 5.31/5.63 ( ( neg_nu6075765906172075777c_real @ zero_zero_real )
% 5.31/5.63 = ( uminus_uminus_real @ one_one_real ) ) ).
% 5.31/5.63
% 5.31/5.63 % dbl_dec_simps(2)
% 5.31/5.63 thf(fact_7365_dbl__dec__simps_I2_J,axiom,
% 5.31/5.63 ( ( neg_nu6511756317524482435omplex @ zero_zero_complex )
% 5.31/5.63 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.31/5.63
% 5.31/5.63 % dbl_dec_simps(2)
% 5.31/5.63 thf(fact_7366_dbl__dec__simps_I2_J,axiom,
% 5.31/5.63 ( ( neg_nu7757733837767384882nteger @ zero_z3403309356797280102nteger )
% 5.31/5.63 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.31/5.63
% 5.31/5.63 % dbl_dec_simps(2)
% 5.31/5.63 thf(fact_7367_dbl__dec__simps_I2_J,axiom,
% 5.31/5.63 ( ( neg_nu3179335615603231917ec_rat @ zero_zero_rat )
% 5.31/5.63 = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.31/5.63
% 5.31/5.63 % dbl_dec_simps(2)
% 5.31/5.63 thf(fact_7368_not__neg__one__le__neg__numeral__iff,axiom,
% 5.31/5.63 ! [M2: num] :
% 5.31/5.63 ( ( ~ ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ M2 ) ) ) )
% 5.31/5.63 = ( M2 != one ) ) ).
% 5.31/5.63
% 5.31/5.63 % not_neg_one_le_neg_numeral_iff
% 5.31/5.63 thf(fact_7369_not__neg__one__le__neg__numeral__iff,axiom,
% 5.31/5.63 ! [M2: num] :
% 5.31/5.63 ( ( ~ ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M2 ) ) ) )
% 5.31/5.63 = ( M2 != one ) ) ).
% 5.31/5.63
% 5.31/5.63 % not_neg_one_le_neg_numeral_iff
% 5.31/5.63 thf(fact_7370_not__neg__one__le__neg__numeral__iff,axiom,
% 5.31/5.63 ! [M2: num] :
% 5.31/5.63 ( ( ~ ( ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M2 ) ) ) )
% 5.31/5.63 = ( M2 != one ) ) ).
% 5.31/5.63
% 5.31/5.63 % not_neg_one_le_neg_numeral_iff
% 5.31/5.63 thf(fact_7371_not__neg__one__le__neg__numeral__iff,axiom,
% 5.31/5.63 ! [M2: num] :
% 5.31/5.63 ( ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) ) )
% 5.31/5.63 = ( M2 != one ) ) ).
% 5.31/5.63
% 5.31/5.63 % not_neg_one_le_neg_numeral_iff
% 5.31/5.63 thf(fact_7372_divide__le__eq__numeral1_I2_J,axiom,
% 5.31/5.63 ! [B: real,W2: num,A: real] :
% 5.31/5.63 ( ( ord_less_eq_real @ ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) ) @ A )
% 5.31/5.63 = ( ord_less_eq_real @ ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) ) @ B ) ) ).
% 5.31/5.63
% 5.31/5.63 % divide_le_eq_numeral1(2)
% 5.31/5.63 thf(fact_7373_divide__le__eq__numeral1_I2_J,axiom,
% 5.31/5.63 ! [B: rat,W2: num,A: rat] :
% 5.31/5.63 ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) ) @ A )
% 5.31/5.63 = ( ord_less_eq_rat @ ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) ) @ B ) ) ).
% 5.31/5.63
% 5.31/5.63 % divide_le_eq_numeral1(2)
% 5.31/5.63 thf(fact_7374_le__divide__eq__numeral1_I2_J,axiom,
% 5.31/5.63 ! [A: real,B: real,W2: num] :
% 5.31/5.63 ( ( ord_less_eq_real @ A @ ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) ) )
% 5.31/5.63 = ( ord_less_eq_real @ B @ ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % le_divide_eq_numeral1(2)
% 5.31/5.63 thf(fact_7375_le__divide__eq__numeral1_I2_J,axiom,
% 5.31/5.63 ! [A: rat,B: rat,W2: num] :
% 5.31/5.63 ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) ) )
% 5.31/5.63 = ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % le_divide_eq_numeral1(2)
% 5.31/5.63 thf(fact_7376_divide__eq__eq__numeral1_I2_J,axiom,
% 5.31/5.63 ! [B: real,W2: num,A: real] :
% 5.31/5.63 ( ( ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) )
% 5.31/5.63 = A )
% 5.31/5.63 = ( ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) )
% 5.31/5.63 != zero_zero_real )
% 5.31/5.63 => ( B
% 5.31/5.63 = ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) ) ) )
% 5.31/5.63 & ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) )
% 5.31/5.63 = zero_zero_real )
% 5.31/5.63 => ( A = zero_zero_real ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % divide_eq_eq_numeral1(2)
% 5.31/5.63 thf(fact_7377_divide__eq__eq__numeral1_I2_J,axiom,
% 5.31/5.63 ! [B: complex,W2: num,A: complex] :
% 5.31/5.63 ( ( ( divide1717551699836669952omplex @ B @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W2 ) ) )
% 5.31/5.63 = A )
% 5.31/5.63 = ( ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W2 ) )
% 5.31/5.63 != zero_zero_complex )
% 5.31/5.63 => ( B
% 5.31/5.63 = ( times_times_complex @ A @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W2 ) ) ) ) )
% 5.31/5.63 & ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W2 ) )
% 5.31/5.63 = zero_zero_complex )
% 5.31/5.63 => ( A = zero_zero_complex ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % divide_eq_eq_numeral1(2)
% 5.31/5.63 thf(fact_7378_divide__eq__eq__numeral1_I2_J,axiom,
% 5.31/5.63 ! [B: rat,W2: num,A: rat] :
% 5.31/5.63 ( ( ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) )
% 5.31/5.63 = A )
% 5.31/5.63 = ( ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) )
% 5.31/5.63 != zero_zero_rat )
% 5.31/5.63 => ( B
% 5.31/5.63 = ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) ) ) )
% 5.31/5.63 & ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) )
% 5.31/5.63 = zero_zero_rat )
% 5.31/5.63 => ( A = zero_zero_rat ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % divide_eq_eq_numeral1(2)
% 5.31/5.63 thf(fact_7379_eq__divide__eq__numeral1_I2_J,axiom,
% 5.31/5.63 ! [A: real,B: real,W2: num] :
% 5.31/5.63 ( ( A
% 5.31/5.63 = ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) ) )
% 5.31/5.63 = ( ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) )
% 5.31/5.63 != zero_zero_real )
% 5.31/5.63 => ( ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) )
% 5.31/5.63 = B ) )
% 5.31/5.63 & ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) )
% 5.31/5.63 = zero_zero_real )
% 5.31/5.63 => ( A = zero_zero_real ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % eq_divide_eq_numeral1(2)
% 5.31/5.63 thf(fact_7380_eq__divide__eq__numeral1_I2_J,axiom,
% 5.31/5.63 ! [A: complex,B: complex,W2: num] :
% 5.31/5.63 ( ( A
% 5.31/5.63 = ( divide1717551699836669952omplex @ B @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W2 ) ) ) )
% 5.31/5.63 = ( ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W2 ) )
% 5.31/5.63 != zero_zero_complex )
% 5.31/5.63 => ( ( times_times_complex @ A @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W2 ) ) )
% 5.31/5.63 = B ) )
% 5.31/5.63 & ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W2 ) )
% 5.31/5.63 = zero_zero_complex )
% 5.31/5.63 => ( A = zero_zero_complex ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % eq_divide_eq_numeral1(2)
% 5.31/5.63 thf(fact_7381_eq__divide__eq__numeral1_I2_J,axiom,
% 5.31/5.63 ! [A: rat,B: rat,W2: num] :
% 5.31/5.63 ( ( A
% 5.31/5.63 = ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) ) )
% 5.31/5.63 = ( ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) )
% 5.31/5.63 != zero_zero_rat )
% 5.31/5.63 => ( ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) )
% 5.31/5.63 = B ) )
% 5.31/5.63 & ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) )
% 5.31/5.63 = zero_zero_rat )
% 5.31/5.63 => ( A = zero_zero_rat ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % eq_divide_eq_numeral1(2)
% 5.31/5.63 thf(fact_7382_neg__numeral__less__neg__one__iff,axiom,
% 5.31/5.63 ! [M2: num] :
% 5.31/5.63 ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ ( uminus_uminus_int @ one_one_int ) )
% 5.31/5.63 = ( M2 != one ) ) ).
% 5.31/5.63
% 5.31/5.63 % neg_numeral_less_neg_one_iff
% 5.31/5.63 thf(fact_7383_neg__numeral__less__neg__one__iff,axiom,
% 5.31/5.63 ! [M2: num] :
% 5.31/5.63 ( ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M2 ) ) @ ( uminus_uminus_real @ one_one_real ) )
% 5.31/5.63 = ( M2 != one ) ) ).
% 5.31/5.63
% 5.31/5.63 % neg_numeral_less_neg_one_iff
% 5.31/5.63 thf(fact_7384_neg__numeral__less__neg__one__iff,axiom,
% 5.31/5.63 ! [M2: num] :
% 5.31/5.63 ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M2 ) ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.31/5.63 = ( M2 != one ) ) ).
% 5.31/5.63
% 5.31/5.63 % neg_numeral_less_neg_one_iff
% 5.31/5.63 thf(fact_7385_neg__numeral__less__neg__one__iff,axiom,
% 5.31/5.63 ! [M2: num] :
% 5.31/5.63 ( ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M2 ) ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.31/5.63 = ( M2 != one ) ) ).
% 5.31/5.63
% 5.31/5.63 % neg_numeral_less_neg_one_iff
% 5.31/5.63 thf(fact_7386_less__divide__eq__numeral1_I2_J,axiom,
% 5.31/5.63 ! [A: real,B: real,W2: num] :
% 5.31/5.63 ( ( ord_less_real @ A @ ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) ) )
% 5.31/5.63 = ( ord_less_real @ B @ ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % less_divide_eq_numeral1(2)
% 5.31/5.63 thf(fact_7387_less__divide__eq__numeral1_I2_J,axiom,
% 5.31/5.63 ! [A: rat,B: rat,W2: num] :
% 5.31/5.63 ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) ) )
% 5.31/5.63 = ( ord_less_rat @ B @ ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % less_divide_eq_numeral1(2)
% 5.31/5.63 thf(fact_7388_divide__less__eq__numeral1_I2_J,axiom,
% 5.31/5.63 ! [B: real,W2: num,A: real] :
% 5.31/5.63 ( ( ord_less_real @ ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) ) @ A )
% 5.31/5.63 = ( ord_less_real @ ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) ) @ B ) ) ).
% 5.31/5.63
% 5.31/5.63 % divide_less_eq_numeral1(2)
% 5.31/5.63 thf(fact_7389_divide__less__eq__numeral1_I2_J,axiom,
% 5.31/5.63 ! [B: rat,W2: num,A: rat] :
% 5.31/5.63 ( ( ord_less_rat @ ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) ) @ A )
% 5.31/5.63 = ( ord_less_rat @ ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) ) @ B ) ) ).
% 5.31/5.63
% 5.31/5.63 % divide_less_eq_numeral1(2)
% 5.31/5.63 thf(fact_7390_dbl__dec__simps_I1_J,axiom,
% 5.31/5.63 ! [K2: num] :
% 5.31/5.63 ( ( neg_nu3811975205180677377ec_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K2 ) ) )
% 5.31/5.63 = ( uminus_uminus_int @ ( neg_nu5851722552734809277nc_int @ ( numeral_numeral_int @ K2 ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % dbl_dec_simps(1)
% 5.31/5.63 thf(fact_7391_dbl__dec__simps_I1_J,axiom,
% 5.31/5.63 ! [K2: num] :
% 5.31/5.63 ( ( neg_nu6075765906172075777c_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ K2 ) ) )
% 5.31/5.63 = ( uminus_uminus_real @ ( neg_nu8295874005876285629c_real @ ( numeral_numeral_real @ K2 ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % dbl_dec_simps(1)
% 5.31/5.63 thf(fact_7392_dbl__dec__simps_I1_J,axiom,
% 5.31/5.63 ! [K2: num] :
% 5.31/5.63 ( ( neg_nu6511756317524482435omplex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ K2 ) ) )
% 5.31/5.63 = ( uminus1482373934393186551omplex @ ( neg_nu8557863876264182079omplex @ ( numera6690914467698888265omplex @ K2 ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % dbl_dec_simps(1)
% 5.31/5.63 thf(fact_7393_dbl__dec__simps_I1_J,axiom,
% 5.31/5.63 ! [K2: num] :
% 5.31/5.63 ( ( neg_nu7757733837767384882nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ K2 ) ) )
% 5.31/5.63 = ( uminus1351360451143612070nteger @ ( neg_nu5831290666863070958nteger @ ( numera6620942414471956472nteger @ K2 ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % dbl_dec_simps(1)
% 5.31/5.63 thf(fact_7394_dbl__dec__simps_I1_J,axiom,
% 5.31/5.63 ! [K2: num] :
% 5.31/5.63 ( ( neg_nu3179335615603231917ec_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ K2 ) ) )
% 5.31/5.63 = ( uminus_uminus_rat @ ( neg_nu5219082963157363817nc_rat @ ( numeral_numeral_rat @ K2 ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % dbl_dec_simps(1)
% 5.31/5.63 thf(fact_7395_dbl__inc__simps_I1_J,axiom,
% 5.31/5.63 ! [K2: num] :
% 5.31/5.63 ( ( neg_nu5851722552734809277nc_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K2 ) ) )
% 5.31/5.63 = ( uminus_uminus_int @ ( neg_nu3811975205180677377ec_int @ ( numeral_numeral_int @ K2 ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % dbl_inc_simps(1)
% 5.31/5.63 thf(fact_7396_dbl__inc__simps_I1_J,axiom,
% 5.31/5.63 ! [K2: num] :
% 5.31/5.63 ( ( neg_nu8295874005876285629c_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ K2 ) ) )
% 5.31/5.63 = ( uminus_uminus_real @ ( neg_nu6075765906172075777c_real @ ( numeral_numeral_real @ K2 ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % dbl_inc_simps(1)
% 5.31/5.63 thf(fact_7397_dbl__inc__simps_I1_J,axiom,
% 5.31/5.63 ! [K2: num] :
% 5.31/5.63 ( ( neg_nu8557863876264182079omplex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ K2 ) ) )
% 5.31/5.63 = ( uminus1482373934393186551omplex @ ( neg_nu6511756317524482435omplex @ ( numera6690914467698888265omplex @ K2 ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % dbl_inc_simps(1)
% 5.31/5.63 thf(fact_7398_dbl__inc__simps_I1_J,axiom,
% 5.31/5.63 ! [K2: num] :
% 5.31/5.63 ( ( neg_nu5831290666863070958nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ K2 ) ) )
% 5.31/5.63 = ( uminus1351360451143612070nteger @ ( neg_nu7757733837767384882nteger @ ( numera6620942414471956472nteger @ K2 ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % dbl_inc_simps(1)
% 5.31/5.63 thf(fact_7399_dbl__inc__simps_I1_J,axiom,
% 5.31/5.63 ! [K2: num] :
% 5.31/5.63 ( ( neg_nu5219082963157363817nc_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ K2 ) ) )
% 5.31/5.63 = ( uminus_uminus_rat @ ( neg_nu3179335615603231917ec_rat @ ( numeral_numeral_rat @ K2 ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % dbl_inc_simps(1)
% 5.31/5.63 thf(fact_7400_signed__take__bit__Suc__minus__bit0,axiom,
% 5.31/5.63 ! [N: nat,K2: num] :
% 5.31/5.63 ( ( bit_ri631733984087533419it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K2 ) ) ) )
% 5.31/5.63 = ( times_times_int @ ( bit_ri631733984087533419it_int @ N @ ( uminus_uminus_int @ ( numeral_numeral_int @ K2 ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % signed_take_bit_Suc_minus_bit0
% 5.31/5.63 thf(fact_7401_signed__take__bit__Suc__bit0,axiom,
% 5.31/5.63 ! [N: nat,K2: num] :
% 5.31/5.63 ( ( bit_ri631733984087533419it_int @ ( suc @ N ) @ ( numeral_numeral_int @ ( bit0 @ K2 ) ) )
% 5.31/5.63 = ( times_times_int @ ( bit_ri631733984087533419it_int @ N @ ( numeral_numeral_int @ K2 ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % signed_take_bit_Suc_bit0
% 5.31/5.63 thf(fact_7402_add__neg__numeral__special_I9_J,axiom,
% 5.31/5.63 ( ( plus_plus_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ one_one_int ) )
% 5.31/5.63 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % add_neg_numeral_special(9)
% 5.31/5.63 thf(fact_7403_add__neg__numeral__special_I9_J,axiom,
% 5.31/5.63 ( ( plus_plus_real @ ( uminus_uminus_real @ one_one_real ) @ ( uminus_uminus_real @ one_one_real ) )
% 5.31/5.63 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % add_neg_numeral_special(9)
% 5.31/5.63 thf(fact_7404_add__neg__numeral__special_I9_J,axiom,
% 5.31/5.63 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.31/5.63 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % add_neg_numeral_special(9)
% 5.31/5.63 thf(fact_7405_add__neg__numeral__special_I9_J,axiom,
% 5.31/5.63 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.31/5.63 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % add_neg_numeral_special(9)
% 5.31/5.63 thf(fact_7406_add__neg__numeral__special_I9_J,axiom,
% 5.31/5.63 ( ( plus_plus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.31/5.63 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % add_neg_numeral_special(9)
% 5.31/5.63 thf(fact_7407_diff__numeral__special_I11_J,axiom,
% 5.31/5.63 ( ( minus_minus_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) )
% 5.31/5.63 = ( numeral_numeral_int @ ( bit0 @ one ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % diff_numeral_special(11)
% 5.31/5.63 thf(fact_7408_diff__numeral__special_I11_J,axiom,
% 5.31/5.63 ( ( minus_minus_real @ one_one_real @ ( uminus_uminus_real @ one_one_real ) )
% 5.31/5.63 = ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % diff_numeral_special(11)
% 5.31/5.63 thf(fact_7409_diff__numeral__special_I11_J,axiom,
% 5.31/5.63 ( ( minus_minus_complex @ one_one_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.31/5.63 = ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % diff_numeral_special(11)
% 5.31/5.63 thf(fact_7410_diff__numeral__special_I11_J,axiom,
% 5.31/5.63 ( ( minus_8373710615458151222nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.31/5.63 = ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % diff_numeral_special(11)
% 5.31/5.63 thf(fact_7411_diff__numeral__special_I11_J,axiom,
% 5.31/5.63 ( ( minus_minus_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.31/5.63 = ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % diff_numeral_special(11)
% 5.31/5.63 thf(fact_7412_diff__numeral__special_I10_J,axiom,
% 5.31/5.63 ( ( minus_minus_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int )
% 5.31/5.63 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % diff_numeral_special(10)
% 5.31/5.63 thf(fact_7413_diff__numeral__special_I10_J,axiom,
% 5.31/5.63 ( ( minus_minus_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real )
% 5.31/5.63 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % diff_numeral_special(10)
% 5.31/5.63 thf(fact_7414_diff__numeral__special_I10_J,axiom,
% 5.31/5.63 ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ one_one_complex )
% 5.31/5.63 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % diff_numeral_special(10)
% 5.31/5.63 thf(fact_7415_diff__numeral__special_I10_J,axiom,
% 5.31/5.63 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer )
% 5.31/5.63 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % diff_numeral_special(10)
% 5.31/5.63 thf(fact_7416_diff__numeral__special_I10_J,axiom,
% 5.31/5.63 ( ( minus_minus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat )
% 5.31/5.63 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % diff_numeral_special(10)
% 5.31/5.63 thf(fact_7417_Power_Oring__1__class_Opower__minus__even,axiom,
% 5.31/5.63 ! [A: int,N: nat] :
% 5.31/5.63 ( ( power_power_int @ ( uminus_uminus_int @ A ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.31/5.63 = ( power_power_int @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % Power.ring_1_class.power_minus_even
% 5.31/5.63 thf(fact_7418_Power_Oring__1__class_Opower__minus__even,axiom,
% 5.31/5.63 ! [A: real,N: nat] :
% 5.31/5.63 ( ( power_power_real @ ( uminus_uminus_real @ A ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.31/5.63 = ( power_power_real @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % Power.ring_1_class.power_minus_even
% 5.31/5.63 thf(fact_7419_Power_Oring__1__class_Opower__minus__even,axiom,
% 5.31/5.63 ! [A: complex,N: nat] :
% 5.31/5.63 ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.31/5.63 = ( power_power_complex @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % Power.ring_1_class.power_minus_even
% 5.31/5.63 thf(fact_7420_Power_Oring__1__class_Opower__minus__even,axiom,
% 5.31/5.63 ! [A: code_integer,N: nat] :
% 5.31/5.63 ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.31/5.63 = ( power_8256067586552552935nteger @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % Power.ring_1_class.power_minus_even
% 5.31/5.63 thf(fact_7421_Power_Oring__1__class_Opower__minus__even,axiom,
% 5.31/5.63 ! [A: rat,N: nat] :
% 5.31/5.63 ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.31/5.63 = ( power_power_rat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % Power.ring_1_class.power_minus_even
% 5.31/5.63 thf(fact_7422_diff__numeral__special_I4_J,axiom,
% 5.31/5.63 ! [M2: num] :
% 5.31/5.63 ( ( minus_minus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ one_one_int )
% 5.31/5.63 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( plus_plus_num @ M2 @ one ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % diff_numeral_special(4)
% 5.31/5.63 thf(fact_7423_diff__numeral__special_I4_J,axiom,
% 5.31/5.63 ! [M2: num] :
% 5.31/5.63 ( ( minus_minus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M2 ) ) @ one_one_real )
% 5.31/5.63 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( plus_plus_num @ M2 @ one ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % diff_numeral_special(4)
% 5.31/5.63 thf(fact_7424_diff__numeral__special_I4_J,axiom,
% 5.31/5.63 ! [M2: num] :
% 5.31/5.63 ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M2 ) ) @ one_one_complex )
% 5.31/5.63 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( plus_plus_num @ M2 @ one ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % diff_numeral_special(4)
% 5.31/5.63 thf(fact_7425_diff__numeral__special_I4_J,axiom,
% 5.31/5.63 ! [M2: num] :
% 5.31/5.63 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M2 ) ) @ one_one_Code_integer )
% 5.31/5.63 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( plus_plus_num @ M2 @ one ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % diff_numeral_special(4)
% 5.31/5.63 thf(fact_7426_diff__numeral__special_I4_J,axiom,
% 5.31/5.63 ! [M2: num] :
% 5.31/5.63 ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M2 ) ) @ one_one_rat )
% 5.31/5.63 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( plus_plus_num @ M2 @ one ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % diff_numeral_special(4)
% 5.31/5.63 thf(fact_7427_diff__numeral__special_I3_J,axiom,
% 5.31/5.63 ! [N: num] :
% 5.31/5.63 ( ( minus_minus_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.31/5.63 = ( numeral_numeral_int @ ( plus_plus_num @ one @ N ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % diff_numeral_special(3)
% 5.31/5.63 thf(fact_7428_diff__numeral__special_I3_J,axiom,
% 5.31/5.63 ! [N: num] :
% 5.31/5.63 ( ( minus_minus_real @ one_one_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 5.31/5.63 = ( numeral_numeral_real @ ( plus_plus_num @ one @ N ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % diff_numeral_special(3)
% 5.31/5.63 thf(fact_7429_diff__numeral__special_I3_J,axiom,
% 5.31/5.63 ! [N: num] :
% 5.31/5.63 ( ( minus_minus_complex @ one_one_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 5.31/5.63 = ( numera6690914467698888265omplex @ ( plus_plus_num @ one @ N ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % diff_numeral_special(3)
% 5.31/5.63 thf(fact_7430_diff__numeral__special_I3_J,axiom,
% 5.31/5.63 ! [N: num] :
% 5.31/5.63 ( ( minus_8373710615458151222nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 5.31/5.63 = ( numera6620942414471956472nteger @ ( plus_plus_num @ one @ N ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % diff_numeral_special(3)
% 5.31/5.63 thf(fact_7431_diff__numeral__special_I3_J,axiom,
% 5.31/5.63 ! [N: num] :
% 5.31/5.63 ( ( minus_minus_rat @ one_one_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 5.31/5.63 = ( numeral_numeral_rat @ ( plus_plus_num @ one @ N ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % diff_numeral_special(3)
% 5.31/5.63 thf(fact_7432_set__decode__Suc,axiom,
% 5.31/5.63 ! [N: nat,X: nat] :
% 5.31/5.63 ( ( member_nat @ ( suc @ N ) @ ( nat_set_decode @ X ) )
% 5.31/5.63 = ( member_nat @ N @ ( nat_set_decode @ ( divide_divide_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % set_decode_Suc
% 5.31/5.63 thf(fact_7433_dbl__simps_I4_J,axiom,
% 5.31/5.63 ( ( neg_numeral_dbl_int @ ( uminus_uminus_int @ one_one_int ) )
% 5.31/5.63 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % dbl_simps(4)
% 5.31/5.63 thf(fact_7434_dbl__simps_I4_J,axiom,
% 5.31/5.63 ( ( neg_numeral_dbl_real @ ( uminus_uminus_real @ one_one_real ) )
% 5.31/5.63 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % dbl_simps(4)
% 5.31/5.63 thf(fact_7435_dbl__simps_I4_J,axiom,
% 5.31/5.63 ( ( neg_nu7009210354673126013omplex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.31/5.63 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % dbl_simps(4)
% 5.31/5.63 thf(fact_7436_dbl__simps_I4_J,axiom,
% 5.31/5.63 ( ( neg_nu8804712462038260780nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.31/5.63 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % dbl_simps(4)
% 5.31/5.63 thf(fact_7437_dbl__simps_I4_J,axiom,
% 5.31/5.63 ( ( neg_numeral_dbl_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.31/5.63 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % dbl_simps(4)
% 5.31/5.63 thf(fact_7438_power__minus1__even,axiom,
% 5.31/5.63 ! [N: nat] :
% 5.31/5.63 ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.31/5.63 = one_one_int ) ).
% 5.31/5.63
% 5.31/5.63 % power_minus1_even
% 5.31/5.63 thf(fact_7439_power__minus1__even,axiom,
% 5.31/5.63 ! [N: nat] :
% 5.31/5.63 ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.31/5.63 = one_one_real ) ).
% 5.31/5.63
% 5.31/5.63 % power_minus1_even
% 5.31/5.63 thf(fact_7440_power__minus1__even,axiom,
% 5.31/5.63 ! [N: nat] :
% 5.31/5.63 ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.31/5.63 = one_one_complex ) ).
% 5.31/5.63
% 5.31/5.63 % power_minus1_even
% 5.31/5.63 thf(fact_7441_power__minus1__even,axiom,
% 5.31/5.63 ! [N: nat] :
% 5.31/5.63 ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.31/5.63 = one_one_Code_integer ) ).
% 5.31/5.63
% 5.31/5.63 % power_minus1_even
% 5.31/5.63 thf(fact_7442_power__minus1__even,axiom,
% 5.31/5.63 ! [N: nat] :
% 5.31/5.63 ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.31/5.63 = one_one_rat ) ).
% 5.31/5.63
% 5.31/5.63 % power_minus1_even
% 5.31/5.63 thf(fact_7443_signed__take__bit__0,axiom,
% 5.31/5.63 ! [A: code_integer] :
% 5.31/5.63 ( ( bit_ri6519982836138164636nteger @ zero_zero_nat @ A )
% 5.31/5.63 = ( uminus1351360451143612070nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % signed_take_bit_0
% 5.31/5.63 thf(fact_7444_signed__take__bit__0,axiom,
% 5.31/5.63 ! [A: int] :
% 5.31/5.63 ( ( bit_ri631733984087533419it_int @ zero_zero_nat @ A )
% 5.31/5.63 = ( uminus_uminus_int @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % signed_take_bit_0
% 5.31/5.63 thf(fact_7445_equation__minus__iff,axiom,
% 5.31/5.63 ! [A: int,B: int] :
% 5.31/5.63 ( ( A
% 5.31/5.63 = ( uminus_uminus_int @ B ) )
% 5.31/5.63 = ( B
% 5.31/5.63 = ( uminus_uminus_int @ A ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % equation_minus_iff
% 5.31/5.63 thf(fact_7446_equation__minus__iff,axiom,
% 5.31/5.63 ! [A: real,B: real] :
% 5.31/5.63 ( ( A
% 5.31/5.63 = ( uminus_uminus_real @ B ) )
% 5.31/5.63 = ( B
% 5.31/5.63 = ( uminus_uminus_real @ A ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % equation_minus_iff
% 5.31/5.63 thf(fact_7447_equation__minus__iff,axiom,
% 5.31/5.63 ! [A: complex,B: complex] :
% 5.31/5.63 ( ( A
% 5.31/5.63 = ( uminus1482373934393186551omplex @ B ) )
% 5.31/5.63 = ( B
% 5.31/5.63 = ( uminus1482373934393186551omplex @ A ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % equation_minus_iff
% 5.31/5.63 thf(fact_7448_equation__minus__iff,axiom,
% 5.31/5.63 ! [A: code_integer,B: code_integer] :
% 5.31/5.63 ( ( A
% 5.31/5.63 = ( uminus1351360451143612070nteger @ B ) )
% 5.31/5.63 = ( B
% 5.31/5.63 = ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % equation_minus_iff
% 5.31/5.63 thf(fact_7449_equation__minus__iff,axiom,
% 5.31/5.63 ! [A: rat,B: rat] :
% 5.31/5.63 ( ( A
% 5.31/5.63 = ( uminus_uminus_rat @ B ) )
% 5.31/5.63 = ( B
% 5.31/5.63 = ( uminus_uminus_rat @ A ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % equation_minus_iff
% 5.31/5.63 thf(fact_7450_minus__equation__iff,axiom,
% 5.31/5.63 ! [A: int,B: int] :
% 5.31/5.63 ( ( ( uminus_uminus_int @ A )
% 5.31/5.63 = B )
% 5.31/5.63 = ( ( uminus_uminus_int @ B )
% 5.31/5.63 = A ) ) ).
% 5.31/5.63
% 5.31/5.63 % minus_equation_iff
% 5.31/5.63 thf(fact_7451_minus__equation__iff,axiom,
% 5.31/5.63 ! [A: real,B: real] :
% 5.31/5.63 ( ( ( uminus_uminus_real @ A )
% 5.31/5.63 = B )
% 5.31/5.63 = ( ( uminus_uminus_real @ B )
% 5.31/5.63 = A ) ) ).
% 5.31/5.63
% 5.31/5.63 % minus_equation_iff
% 5.31/5.63 thf(fact_7452_minus__equation__iff,axiom,
% 5.31/5.63 ! [A: complex,B: complex] :
% 5.31/5.63 ( ( ( uminus1482373934393186551omplex @ A )
% 5.31/5.63 = B )
% 5.31/5.63 = ( ( uminus1482373934393186551omplex @ B )
% 5.31/5.63 = A ) ) ).
% 5.31/5.63
% 5.31/5.63 % minus_equation_iff
% 5.31/5.63 thf(fact_7453_minus__equation__iff,axiom,
% 5.31/5.63 ! [A: code_integer,B: code_integer] :
% 5.31/5.63 ( ( ( uminus1351360451143612070nteger @ A )
% 5.31/5.63 = B )
% 5.31/5.63 = ( ( uminus1351360451143612070nteger @ B )
% 5.31/5.63 = A ) ) ).
% 5.31/5.63
% 5.31/5.63 % minus_equation_iff
% 5.31/5.63 thf(fact_7454_minus__equation__iff,axiom,
% 5.31/5.63 ! [A: rat,B: rat] :
% 5.31/5.63 ( ( ( uminus_uminus_rat @ A )
% 5.31/5.63 = B )
% 5.31/5.63 = ( ( uminus_uminus_rat @ B )
% 5.31/5.63 = A ) ) ).
% 5.31/5.63
% 5.31/5.63 % minus_equation_iff
% 5.31/5.63 thf(fact_7455_fact__mono__nat,axiom,
% 5.31/5.63 ! [M2: nat,N: nat] :
% 5.31/5.63 ( ( ord_less_eq_nat @ M2 @ N )
% 5.31/5.63 => ( ord_less_eq_nat @ ( semiri1408675320244567234ct_nat @ M2 ) @ ( semiri1408675320244567234ct_nat @ N ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % fact_mono_nat
% 5.31/5.63 thf(fact_7456_fact__ge__self,axiom,
% 5.31/5.63 ! [N: nat] : ( ord_less_eq_nat @ N @ ( semiri1408675320244567234ct_nat @ N ) ) ).
% 5.31/5.63
% 5.31/5.63 % fact_ge_self
% 5.31/5.63 thf(fact_7457_fact__nonzero,axiom,
% 5.31/5.63 ! [N: nat] :
% 5.31/5.63 ( ( semiri5044797733671781792omplex @ N )
% 5.31/5.63 != zero_zero_complex ) ).
% 5.31/5.63
% 5.31/5.63 % fact_nonzero
% 5.31/5.63 thf(fact_7458_fact__nonzero,axiom,
% 5.31/5.63 ! [N: nat] :
% 5.31/5.63 ( ( semiri773545260158071498ct_rat @ N )
% 5.31/5.63 != zero_zero_rat ) ).
% 5.31/5.63
% 5.31/5.63 % fact_nonzero
% 5.31/5.63 thf(fact_7459_fact__nonzero,axiom,
% 5.31/5.63 ! [N: nat] :
% 5.31/5.63 ( ( semiri1406184849735516958ct_int @ N )
% 5.31/5.63 != zero_zero_int ) ).
% 5.31/5.63
% 5.31/5.63 % fact_nonzero
% 5.31/5.63 thf(fact_7460_fact__nonzero,axiom,
% 5.31/5.63 ! [N: nat] :
% 5.31/5.63 ( ( semiri1408675320244567234ct_nat @ N )
% 5.31/5.63 != zero_zero_nat ) ).
% 5.31/5.63
% 5.31/5.63 % fact_nonzero
% 5.31/5.63 thf(fact_7461_fact__nonzero,axiom,
% 5.31/5.63 ! [N: nat] :
% 5.31/5.63 ( ( semiri2265585572941072030t_real @ N )
% 5.31/5.63 != zero_zero_real ) ).
% 5.31/5.63
% 5.31/5.63 % fact_nonzero
% 5.31/5.63 thf(fact_7462_compl__le__swap2,axiom,
% 5.31/5.63 ! [Y: set_nat,X: set_nat] :
% 5.31/5.63 ( ( ord_less_eq_set_nat @ ( uminus5710092332889474511et_nat @ Y ) @ X )
% 5.31/5.63 => ( ord_less_eq_set_nat @ ( uminus5710092332889474511et_nat @ X ) @ Y ) ) ).
% 5.31/5.63
% 5.31/5.63 % compl_le_swap2
% 5.31/5.63 thf(fact_7463_compl__le__swap1,axiom,
% 5.31/5.63 ! [Y: set_nat,X: set_nat] :
% 5.31/5.63 ( ( ord_less_eq_set_nat @ Y @ ( uminus5710092332889474511et_nat @ X ) )
% 5.31/5.63 => ( ord_less_eq_set_nat @ X @ ( uminus5710092332889474511et_nat @ Y ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % compl_le_swap1
% 5.31/5.63 thf(fact_7464_compl__mono,axiom,
% 5.31/5.63 ! [X: set_nat,Y: set_nat] :
% 5.31/5.63 ( ( ord_less_eq_set_nat @ X @ Y )
% 5.31/5.63 => ( ord_less_eq_set_nat @ ( uminus5710092332889474511et_nat @ Y ) @ ( uminus5710092332889474511et_nat @ X ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % compl_mono
% 5.31/5.63 thf(fact_7465_le__imp__neg__le,axiom,
% 5.31/5.63 ! [A: real,B: real] :
% 5.31/5.63 ( ( ord_less_eq_real @ A @ B )
% 5.31/5.63 => ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % le_imp_neg_le
% 5.31/5.63 thf(fact_7466_le__imp__neg__le,axiom,
% 5.31/5.63 ! [A: code_integer,B: code_integer] :
% 5.31/5.63 ( ( ord_le3102999989581377725nteger @ A @ B )
% 5.31/5.63 => ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % le_imp_neg_le
% 5.31/5.63 thf(fact_7467_le__imp__neg__le,axiom,
% 5.31/5.63 ! [A: rat,B: rat] :
% 5.31/5.63 ( ( ord_less_eq_rat @ A @ B )
% 5.31/5.63 => ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % le_imp_neg_le
% 5.31/5.63 thf(fact_7468_le__imp__neg__le,axiom,
% 5.31/5.63 ! [A: int,B: int] :
% 5.31/5.63 ( ( ord_less_eq_int @ A @ B )
% 5.31/5.63 => ( ord_less_eq_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % le_imp_neg_le
% 5.31/5.63 thf(fact_7469_minus__le__iff,axiom,
% 5.31/5.63 ! [A: real,B: real] :
% 5.31/5.63 ( ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ B )
% 5.31/5.63 = ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ A ) ) ).
% 5.31/5.63
% 5.31/5.63 % minus_le_iff
% 5.31/5.63 thf(fact_7470_minus__le__iff,axiom,
% 5.31/5.63 ! [A: code_integer,B: code_integer] :
% 5.31/5.63 ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 5.31/5.63 = ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ B ) @ A ) ) ).
% 5.31/5.63
% 5.31/5.63 % minus_le_iff
% 5.31/5.63 thf(fact_7471_minus__le__iff,axiom,
% 5.31/5.63 ! [A: rat,B: rat] :
% 5.31/5.63 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ B )
% 5.31/5.63 = ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ A ) ) ).
% 5.31/5.63
% 5.31/5.63 % minus_le_iff
% 5.31/5.63 thf(fact_7472_minus__le__iff,axiom,
% 5.31/5.63 ! [A: int,B: int] :
% 5.31/5.63 ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B )
% 5.31/5.63 = ( ord_less_eq_int @ ( uminus_uminus_int @ B ) @ A ) ) ).
% 5.31/5.63
% 5.31/5.63 % minus_le_iff
% 5.31/5.63 thf(fact_7473_le__minus__iff,axiom,
% 5.31/5.63 ! [A: real,B: real] :
% 5.31/5.63 ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ B ) )
% 5.31/5.63 = ( ord_less_eq_real @ B @ ( uminus_uminus_real @ A ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % le_minus_iff
% 5.31/5.63 thf(fact_7474_le__minus__iff,axiom,
% 5.31/5.63 ! [A: code_integer,B: code_integer] :
% 5.31/5.63 ( ( ord_le3102999989581377725nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 5.31/5.63 = ( ord_le3102999989581377725nteger @ B @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % le_minus_iff
% 5.31/5.63 thf(fact_7475_le__minus__iff,axiom,
% 5.31/5.63 ! [A: rat,B: rat] :
% 5.31/5.63 ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ B ) )
% 5.31/5.63 = ( ord_less_eq_rat @ B @ ( uminus_uminus_rat @ A ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % le_minus_iff
% 5.31/5.63 thf(fact_7476_le__minus__iff,axiom,
% 5.31/5.63 ! [A: int,B: int] :
% 5.31/5.63 ( ( ord_less_eq_int @ A @ ( uminus_uminus_int @ B ) )
% 5.31/5.63 = ( ord_less_eq_int @ B @ ( uminus_uminus_int @ A ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % le_minus_iff
% 5.31/5.63 thf(fact_7477_less__minus__iff,axiom,
% 5.31/5.63 ! [A: int,B: int] :
% 5.31/5.63 ( ( ord_less_int @ A @ ( uminus_uminus_int @ B ) )
% 5.31/5.63 = ( ord_less_int @ B @ ( uminus_uminus_int @ A ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % less_minus_iff
% 5.31/5.63 thf(fact_7478_less__minus__iff,axiom,
% 5.31/5.63 ! [A: real,B: real] :
% 5.31/5.63 ( ( ord_less_real @ A @ ( uminus_uminus_real @ B ) )
% 5.31/5.63 = ( ord_less_real @ B @ ( uminus_uminus_real @ A ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % less_minus_iff
% 5.31/5.63 thf(fact_7479_less__minus__iff,axiom,
% 5.31/5.63 ! [A: code_integer,B: code_integer] :
% 5.31/5.63 ( ( ord_le6747313008572928689nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 5.31/5.63 = ( ord_le6747313008572928689nteger @ B @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % less_minus_iff
% 5.31/5.63 thf(fact_7480_less__minus__iff,axiom,
% 5.31/5.63 ! [A: rat,B: rat] :
% 5.31/5.63 ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ B ) )
% 5.31/5.63 = ( ord_less_rat @ B @ ( uminus_uminus_rat @ A ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % less_minus_iff
% 5.31/5.63 thf(fact_7481_minus__less__iff,axiom,
% 5.31/5.63 ! [A: int,B: int] :
% 5.31/5.63 ( ( ord_less_int @ ( uminus_uminus_int @ A ) @ B )
% 5.31/5.63 = ( ord_less_int @ ( uminus_uminus_int @ B ) @ A ) ) ).
% 5.31/5.63
% 5.31/5.63 % minus_less_iff
% 5.31/5.63 thf(fact_7482_minus__less__iff,axiom,
% 5.31/5.63 ! [A: real,B: real] :
% 5.31/5.63 ( ( ord_less_real @ ( uminus_uminus_real @ A ) @ B )
% 5.31/5.63 = ( ord_less_real @ ( uminus_uminus_real @ B ) @ A ) ) ).
% 5.31/5.63
% 5.31/5.63 % minus_less_iff
% 5.31/5.63 thf(fact_7483_minus__less__iff,axiom,
% 5.31/5.63 ! [A: code_integer,B: code_integer] :
% 5.31/5.63 ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 5.31/5.63 = ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ B ) @ A ) ) ).
% 5.31/5.63
% 5.31/5.63 % minus_less_iff
% 5.31/5.63 thf(fact_7484_minus__less__iff,axiom,
% 5.31/5.63 ! [A: rat,B: rat] :
% 5.31/5.63 ( ( ord_less_rat @ ( uminus_uminus_rat @ A ) @ B )
% 5.31/5.63 = ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ A ) ) ).
% 5.31/5.63
% 5.31/5.63 % minus_less_iff
% 5.31/5.63 thf(fact_7485_neg__numeral__neq__numeral,axiom,
% 5.31/5.63 ! [M2: num,N: num] :
% 5.31/5.63 ( ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) )
% 5.31/5.63 != ( numeral_numeral_int @ N ) ) ).
% 5.31/5.63
% 5.31/5.63 % neg_numeral_neq_numeral
% 5.31/5.63 thf(fact_7486_neg__numeral__neq__numeral,axiom,
% 5.31/5.63 ! [M2: num,N: num] :
% 5.31/5.63 ( ( uminus_uminus_real @ ( numeral_numeral_real @ M2 ) )
% 5.31/5.63 != ( numeral_numeral_real @ N ) ) ).
% 5.31/5.63
% 5.31/5.63 % neg_numeral_neq_numeral
% 5.31/5.63 thf(fact_7487_neg__numeral__neq__numeral,axiom,
% 5.31/5.63 ! [M2: num,N: num] :
% 5.31/5.63 ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M2 ) )
% 5.31/5.63 != ( numera6690914467698888265omplex @ N ) ) ).
% 5.31/5.63
% 5.31/5.63 % neg_numeral_neq_numeral
% 5.31/5.63 thf(fact_7488_neg__numeral__neq__numeral,axiom,
% 5.31/5.63 ! [M2: num,N: num] :
% 5.31/5.63 ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M2 ) )
% 5.31/5.63 != ( numera6620942414471956472nteger @ N ) ) ).
% 5.31/5.63
% 5.31/5.63 % neg_numeral_neq_numeral
% 5.31/5.63 thf(fact_7489_neg__numeral__neq__numeral,axiom,
% 5.31/5.63 ! [M2: num,N: num] :
% 5.31/5.63 ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ M2 ) )
% 5.31/5.63 != ( numeral_numeral_rat @ N ) ) ).
% 5.31/5.63
% 5.31/5.63 % neg_numeral_neq_numeral
% 5.31/5.63 thf(fact_7490_numeral__neq__neg__numeral,axiom,
% 5.31/5.63 ! [M2: num,N: num] :
% 5.31/5.63 ( ( numeral_numeral_int @ M2 )
% 5.31/5.63 != ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % numeral_neq_neg_numeral
% 5.31/5.63 thf(fact_7491_numeral__neq__neg__numeral,axiom,
% 5.31/5.63 ! [M2: num,N: num] :
% 5.31/5.63 ( ( numeral_numeral_real @ M2 )
% 5.31/5.63 != ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % numeral_neq_neg_numeral
% 5.31/5.63 thf(fact_7492_numeral__neq__neg__numeral,axiom,
% 5.31/5.63 ! [M2: num,N: num] :
% 5.31/5.63 ( ( numera6690914467698888265omplex @ M2 )
% 5.31/5.63 != ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % numeral_neq_neg_numeral
% 5.31/5.63 thf(fact_7493_numeral__neq__neg__numeral,axiom,
% 5.31/5.63 ! [M2: num,N: num] :
% 5.31/5.63 ( ( numera6620942414471956472nteger @ M2 )
% 5.31/5.63 != ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % numeral_neq_neg_numeral
% 5.31/5.63 thf(fact_7494_numeral__neq__neg__numeral,axiom,
% 5.31/5.63 ! [M2: num,N: num] :
% 5.31/5.63 ( ( numeral_numeral_rat @ M2 )
% 5.31/5.63 != ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % numeral_neq_neg_numeral
% 5.31/5.63 thf(fact_7495_minus__mult__commute,axiom,
% 5.31/5.63 ! [A: int,B: int] :
% 5.31/5.63 ( ( times_times_int @ ( uminus_uminus_int @ A ) @ B )
% 5.31/5.63 = ( times_times_int @ A @ ( uminus_uminus_int @ B ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % minus_mult_commute
% 5.31/5.63 thf(fact_7496_minus__mult__commute,axiom,
% 5.31/5.63 ! [A: real,B: real] :
% 5.31/5.63 ( ( times_times_real @ ( uminus_uminus_real @ A ) @ B )
% 5.31/5.63 = ( times_times_real @ A @ ( uminus_uminus_real @ B ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % minus_mult_commute
% 5.31/5.63 thf(fact_7497_minus__mult__commute,axiom,
% 5.31/5.63 ! [A: complex,B: complex] :
% 5.31/5.63 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ A ) @ B )
% 5.31/5.63 = ( times_times_complex @ A @ ( uminus1482373934393186551omplex @ B ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % minus_mult_commute
% 5.31/5.63 thf(fact_7498_minus__mult__commute,axiom,
% 5.31/5.63 ! [A: code_integer,B: code_integer] :
% 5.31/5.63 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 5.31/5.63 = ( times_3573771949741848930nteger @ A @ ( uminus1351360451143612070nteger @ B ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % minus_mult_commute
% 5.31/5.63 thf(fact_7499_minus__mult__commute,axiom,
% 5.31/5.63 ! [A: rat,B: rat] :
% 5.31/5.63 ( ( times_times_rat @ ( uminus_uminus_rat @ A ) @ B )
% 5.31/5.63 = ( times_times_rat @ A @ ( uminus_uminus_rat @ B ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % minus_mult_commute
% 5.31/5.63 thf(fact_7500_square__eq__iff,axiom,
% 5.31/5.63 ! [A: int,B: int] :
% 5.31/5.63 ( ( ( times_times_int @ A @ A )
% 5.31/5.63 = ( times_times_int @ B @ B ) )
% 5.31/5.63 = ( ( A = B )
% 5.31/5.63 | ( A
% 5.31/5.63 = ( uminus_uminus_int @ B ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % square_eq_iff
% 5.31/5.63 thf(fact_7501_square__eq__iff,axiom,
% 5.31/5.63 ! [A: real,B: real] :
% 5.31/5.63 ( ( ( times_times_real @ A @ A )
% 5.31/5.63 = ( times_times_real @ B @ B ) )
% 5.31/5.63 = ( ( A = B )
% 5.31/5.63 | ( A
% 5.31/5.63 = ( uminus_uminus_real @ B ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % square_eq_iff
% 5.31/5.63 thf(fact_7502_square__eq__iff,axiom,
% 5.31/5.63 ! [A: complex,B: complex] :
% 5.31/5.63 ( ( ( times_times_complex @ A @ A )
% 5.31/5.63 = ( times_times_complex @ B @ B ) )
% 5.31/5.63 = ( ( A = B )
% 5.31/5.63 | ( A
% 5.31/5.63 = ( uminus1482373934393186551omplex @ B ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % square_eq_iff
% 5.31/5.63 thf(fact_7503_square__eq__iff,axiom,
% 5.31/5.63 ! [A: code_integer,B: code_integer] :
% 5.31/5.63 ( ( ( times_3573771949741848930nteger @ A @ A )
% 5.31/5.63 = ( times_3573771949741848930nteger @ B @ B ) )
% 5.31/5.63 = ( ( A = B )
% 5.31/5.63 | ( A
% 5.31/5.63 = ( uminus1351360451143612070nteger @ B ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % square_eq_iff
% 5.31/5.63 thf(fact_7504_square__eq__iff,axiom,
% 5.31/5.63 ! [A: rat,B: rat] :
% 5.31/5.63 ( ( ( times_times_rat @ A @ A )
% 5.31/5.63 = ( times_times_rat @ B @ B ) )
% 5.31/5.63 = ( ( A = B )
% 5.31/5.63 | ( A
% 5.31/5.63 = ( uminus_uminus_rat @ B ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % square_eq_iff
% 5.31/5.63 thf(fact_7505_is__num__normalize_I8_J,axiom,
% 5.31/5.63 ! [A: int,B: int] :
% 5.31/5.63 ( ( uminus_uminus_int @ ( plus_plus_int @ A @ B ) )
% 5.31/5.63 = ( plus_plus_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % is_num_normalize(8)
% 5.31/5.63 thf(fact_7506_is__num__normalize_I8_J,axiom,
% 5.31/5.63 ! [A: real,B: real] :
% 5.31/5.63 ( ( uminus_uminus_real @ ( plus_plus_real @ A @ B ) )
% 5.31/5.63 = ( plus_plus_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % is_num_normalize(8)
% 5.31/5.63 thf(fact_7507_is__num__normalize_I8_J,axiom,
% 5.31/5.63 ! [A: complex,B: complex] :
% 5.31/5.63 ( ( uminus1482373934393186551omplex @ ( plus_plus_complex @ A @ B ) )
% 5.31/5.63 = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ B ) @ ( uminus1482373934393186551omplex @ A ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % is_num_normalize(8)
% 5.31/5.63 thf(fact_7508_is__num__normalize_I8_J,axiom,
% 5.31/5.63 ! [A: code_integer,B: code_integer] :
% 5.31/5.63 ( ( uminus1351360451143612070nteger @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 5.31/5.63 = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % is_num_normalize(8)
% 5.31/5.63 thf(fact_7509_is__num__normalize_I8_J,axiom,
% 5.31/5.63 ! [A: rat,B: rat] :
% 5.31/5.63 ( ( uminus_uminus_rat @ ( plus_plus_rat @ A @ B ) )
% 5.31/5.63 = ( plus_plus_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % is_num_normalize(8)
% 5.31/5.63 thf(fact_7510_group__cancel_Oneg1,axiom,
% 5.31/5.63 ! [A4: int,K2: int,A: int] :
% 5.31/5.63 ( ( A4
% 5.31/5.63 = ( plus_plus_int @ K2 @ A ) )
% 5.31/5.63 => ( ( uminus_uminus_int @ A4 )
% 5.31/5.63 = ( plus_plus_int @ ( uminus_uminus_int @ K2 ) @ ( uminus_uminus_int @ A ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % group_cancel.neg1
% 5.31/5.63 thf(fact_7511_group__cancel_Oneg1,axiom,
% 5.31/5.63 ! [A4: real,K2: real,A: real] :
% 5.31/5.63 ( ( A4
% 5.31/5.63 = ( plus_plus_real @ K2 @ A ) )
% 5.31/5.63 => ( ( uminus_uminus_real @ A4 )
% 5.31/5.63 = ( plus_plus_real @ ( uminus_uminus_real @ K2 ) @ ( uminus_uminus_real @ A ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % group_cancel.neg1
% 5.31/5.63 thf(fact_7512_group__cancel_Oneg1,axiom,
% 5.31/5.63 ! [A4: complex,K2: complex,A: complex] :
% 5.31/5.63 ( ( A4
% 5.31/5.63 = ( plus_plus_complex @ K2 @ A ) )
% 5.31/5.63 => ( ( uminus1482373934393186551omplex @ A4 )
% 5.31/5.63 = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ K2 ) @ ( uminus1482373934393186551omplex @ A ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % group_cancel.neg1
% 5.31/5.63 thf(fact_7513_group__cancel_Oneg1,axiom,
% 5.31/5.63 ! [A4: code_integer,K2: code_integer,A: code_integer] :
% 5.31/5.63 ( ( A4
% 5.31/5.63 = ( plus_p5714425477246183910nteger @ K2 @ A ) )
% 5.31/5.63 => ( ( uminus1351360451143612070nteger @ A4 )
% 5.31/5.63 = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ K2 ) @ ( uminus1351360451143612070nteger @ A ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % group_cancel.neg1
% 5.31/5.63 thf(fact_7514_group__cancel_Oneg1,axiom,
% 5.31/5.63 ! [A4: rat,K2: rat,A: rat] :
% 5.31/5.63 ( ( A4
% 5.31/5.63 = ( plus_plus_rat @ K2 @ A ) )
% 5.31/5.63 => ( ( uminus_uminus_rat @ A4 )
% 5.31/5.63 = ( plus_plus_rat @ ( uminus_uminus_rat @ K2 ) @ ( uminus_uminus_rat @ A ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % group_cancel.neg1
% 5.31/5.63 thf(fact_7515_add_Oinverse__distrib__swap,axiom,
% 5.31/5.63 ! [A: int,B: int] :
% 5.31/5.63 ( ( uminus_uminus_int @ ( plus_plus_int @ A @ B ) )
% 5.31/5.63 = ( plus_plus_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % add.inverse_distrib_swap
% 5.31/5.63 thf(fact_7516_add_Oinverse__distrib__swap,axiom,
% 5.31/5.63 ! [A: real,B: real] :
% 5.31/5.63 ( ( uminus_uminus_real @ ( plus_plus_real @ A @ B ) )
% 5.31/5.63 = ( plus_plus_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % add.inverse_distrib_swap
% 5.31/5.63 thf(fact_7517_add_Oinverse__distrib__swap,axiom,
% 5.31/5.63 ! [A: complex,B: complex] :
% 5.31/5.63 ( ( uminus1482373934393186551omplex @ ( plus_plus_complex @ A @ B ) )
% 5.31/5.63 = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ B ) @ ( uminus1482373934393186551omplex @ A ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % add.inverse_distrib_swap
% 5.31/5.63 thf(fact_7518_add_Oinverse__distrib__swap,axiom,
% 5.31/5.63 ! [A: code_integer,B: code_integer] :
% 5.31/5.63 ( ( uminus1351360451143612070nteger @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 5.31/5.63 = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % add.inverse_distrib_swap
% 5.31/5.63 thf(fact_7519_add_Oinverse__distrib__swap,axiom,
% 5.31/5.63 ! [A: rat,B: rat] :
% 5.31/5.63 ( ( uminus_uminus_rat @ ( plus_plus_rat @ A @ B ) )
% 5.31/5.63 = ( plus_plus_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % add.inverse_distrib_swap
% 5.31/5.63 thf(fact_7520_one__neq__neg__one,axiom,
% 5.31/5.63 ( one_one_int
% 5.31/5.63 != ( uminus_uminus_int @ one_one_int ) ) ).
% 5.31/5.63
% 5.31/5.63 % one_neq_neg_one
% 5.31/5.63 thf(fact_7521_one__neq__neg__one,axiom,
% 5.31/5.63 ( one_one_real
% 5.31/5.63 != ( uminus_uminus_real @ one_one_real ) ) ).
% 5.31/5.63
% 5.31/5.63 % one_neq_neg_one
% 5.31/5.63 thf(fact_7522_one__neq__neg__one,axiom,
% 5.31/5.63 ( one_one_complex
% 5.31/5.63 != ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.31/5.63
% 5.31/5.63 % one_neq_neg_one
% 5.31/5.63 thf(fact_7523_one__neq__neg__one,axiom,
% 5.31/5.63 ( one_one_Code_integer
% 5.31/5.63 != ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.31/5.63
% 5.31/5.63 % one_neq_neg_one
% 5.31/5.63 thf(fact_7524_one__neq__neg__one,axiom,
% 5.31/5.63 ( one_one_rat
% 5.31/5.63 != ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.31/5.63
% 5.31/5.63 % one_neq_neg_one
% 5.31/5.63 thf(fact_7525_minus__diff__commute,axiom,
% 5.31/5.63 ! [B: int,A: int] :
% 5.31/5.63 ( ( minus_minus_int @ ( uminus_uminus_int @ B ) @ A )
% 5.31/5.63 = ( minus_minus_int @ ( uminus_uminus_int @ A ) @ B ) ) ).
% 5.31/5.63
% 5.31/5.63 % minus_diff_commute
% 5.31/5.63 thf(fact_7526_minus__diff__commute,axiom,
% 5.31/5.63 ! [B: real,A: real] :
% 5.31/5.63 ( ( minus_minus_real @ ( uminus_uminus_real @ B ) @ A )
% 5.31/5.63 = ( minus_minus_real @ ( uminus_uminus_real @ A ) @ B ) ) ).
% 5.31/5.63
% 5.31/5.63 % minus_diff_commute
% 5.31/5.63 thf(fact_7527_minus__diff__commute,axiom,
% 5.31/5.63 ! [B: complex,A: complex] :
% 5.31/5.63 ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ B ) @ A )
% 5.31/5.63 = ( minus_minus_complex @ ( uminus1482373934393186551omplex @ A ) @ B ) ) ).
% 5.31/5.63
% 5.31/5.63 % minus_diff_commute
% 5.31/5.63 thf(fact_7528_minus__diff__commute,axiom,
% 5.31/5.63 ! [B: code_integer,A: code_integer] :
% 5.31/5.63 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ B ) @ A )
% 5.31/5.63 = ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ).
% 5.31/5.63
% 5.31/5.63 % minus_diff_commute
% 5.31/5.63 thf(fact_7529_minus__diff__commute,axiom,
% 5.31/5.63 ! [B: rat,A: rat] :
% 5.31/5.63 ( ( minus_minus_rat @ ( uminus_uminus_rat @ B ) @ A )
% 5.31/5.63 = ( minus_minus_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ).
% 5.31/5.63
% 5.31/5.63 % minus_diff_commute
% 5.31/5.63 thf(fact_7530_signed__take__bit__mult,axiom,
% 5.31/5.63 ! [N: nat,K2: int,L: int] :
% 5.31/5.63 ( ( bit_ri631733984087533419it_int @ N @ ( times_times_int @ ( bit_ri631733984087533419it_int @ N @ K2 ) @ ( bit_ri631733984087533419it_int @ N @ L ) ) )
% 5.31/5.63 = ( bit_ri631733984087533419it_int @ N @ ( times_times_int @ K2 @ L ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % signed_take_bit_mult
% 5.31/5.63 thf(fact_7531_fact__less__mono__nat,axiom,
% 5.31/5.63 ! [M2: nat,N: nat] :
% 5.31/5.63 ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 5.31/5.63 => ( ( ord_less_nat @ M2 @ N )
% 5.31/5.63 => ( ord_less_nat @ ( semiri1408675320244567234ct_nat @ M2 ) @ ( semiri1408675320244567234ct_nat @ N ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % fact_less_mono_nat
% 5.31/5.63 thf(fact_7532_fact__ge__zero,axiom,
% 5.31/5.63 ! [N: nat] : ( ord_less_eq_rat @ zero_zero_rat @ ( semiri773545260158071498ct_rat @ N ) ) ).
% 5.31/5.63
% 5.31/5.63 % fact_ge_zero
% 5.31/5.63 thf(fact_7533_fact__ge__zero,axiom,
% 5.31/5.63 ! [N: nat] : ( ord_less_eq_int @ zero_zero_int @ ( semiri1406184849735516958ct_int @ N ) ) ).
% 5.31/5.63
% 5.31/5.63 % fact_ge_zero
% 5.31/5.63 thf(fact_7534_fact__ge__zero,axiom,
% 5.31/5.63 ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( semiri1408675320244567234ct_nat @ N ) ) ).
% 5.31/5.63
% 5.31/5.63 % fact_ge_zero
% 5.31/5.63 thf(fact_7535_fact__ge__zero,axiom,
% 5.31/5.63 ! [N: nat] : ( ord_less_eq_real @ zero_zero_real @ ( semiri2265585572941072030t_real @ N ) ) ).
% 5.31/5.63
% 5.31/5.63 % fact_ge_zero
% 5.31/5.63 thf(fact_7536_fact__not__neg,axiom,
% 5.31/5.63 ! [N: nat] :
% 5.31/5.63 ~ ( ord_less_rat @ ( semiri773545260158071498ct_rat @ N ) @ zero_zero_rat ) ).
% 5.31/5.63
% 5.31/5.63 % fact_not_neg
% 5.31/5.63 thf(fact_7537_fact__not__neg,axiom,
% 5.31/5.63 ! [N: nat] :
% 5.31/5.63 ~ ( ord_less_int @ ( semiri1406184849735516958ct_int @ N ) @ zero_zero_int ) ).
% 5.31/5.63
% 5.31/5.63 % fact_not_neg
% 5.31/5.63 thf(fact_7538_fact__not__neg,axiom,
% 5.31/5.63 ! [N: nat] :
% 5.31/5.63 ~ ( ord_less_nat @ ( semiri1408675320244567234ct_nat @ N ) @ zero_zero_nat ) ).
% 5.31/5.63
% 5.31/5.63 % fact_not_neg
% 5.31/5.63 thf(fact_7539_fact__not__neg,axiom,
% 5.31/5.63 ! [N: nat] :
% 5.31/5.63 ~ ( ord_less_real @ ( semiri2265585572941072030t_real @ N ) @ zero_zero_real ) ).
% 5.31/5.63
% 5.31/5.63 % fact_not_neg
% 5.31/5.63 thf(fact_7540_fact__gt__zero,axiom,
% 5.31/5.63 ! [N: nat] : ( ord_less_rat @ zero_zero_rat @ ( semiri773545260158071498ct_rat @ N ) ) ).
% 5.31/5.63
% 5.31/5.63 % fact_gt_zero
% 5.31/5.63 thf(fact_7541_fact__gt__zero,axiom,
% 5.31/5.63 ! [N: nat] : ( ord_less_int @ zero_zero_int @ ( semiri1406184849735516958ct_int @ N ) ) ).
% 5.31/5.63
% 5.31/5.63 % fact_gt_zero
% 5.31/5.63 thf(fact_7542_fact__gt__zero,axiom,
% 5.31/5.63 ! [N: nat] : ( ord_less_nat @ zero_zero_nat @ ( semiri1408675320244567234ct_nat @ N ) ) ).
% 5.31/5.63
% 5.31/5.63 % fact_gt_zero
% 5.31/5.63 thf(fact_7543_fact__gt__zero,axiom,
% 5.31/5.63 ! [N: nat] : ( ord_less_real @ zero_zero_real @ ( semiri2265585572941072030t_real @ N ) ) ).
% 5.31/5.63
% 5.31/5.63 % fact_gt_zero
% 5.31/5.63 thf(fact_7544_finite__set__decode,axiom,
% 5.31/5.63 ! [N: nat] : ( finite_finite_nat @ ( nat_set_decode @ N ) ) ).
% 5.31/5.63
% 5.31/5.63 % finite_set_decode
% 5.31/5.63 thf(fact_7545_fact__ge__1,axiom,
% 5.31/5.63 ! [N: nat] : ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( semiri3624122377584611663nteger @ N ) ) ).
% 5.31/5.63
% 5.31/5.63 % fact_ge_1
% 5.31/5.63 thf(fact_7546_fact__ge__1,axiom,
% 5.31/5.63 ! [N: nat] : ( ord_less_eq_rat @ one_one_rat @ ( semiri773545260158071498ct_rat @ N ) ) ).
% 5.31/5.63
% 5.31/5.63 % fact_ge_1
% 5.31/5.63 thf(fact_7547_fact__ge__1,axiom,
% 5.31/5.63 ! [N: nat] : ( ord_less_eq_int @ one_one_int @ ( semiri1406184849735516958ct_int @ N ) ) ).
% 5.31/5.63
% 5.31/5.63 % fact_ge_1
% 5.31/5.63 thf(fact_7548_fact__ge__1,axiom,
% 5.31/5.63 ! [N: nat] : ( ord_less_eq_nat @ one_one_nat @ ( semiri1408675320244567234ct_nat @ N ) ) ).
% 5.31/5.63
% 5.31/5.63 % fact_ge_1
% 5.31/5.63 thf(fact_7549_fact__ge__1,axiom,
% 5.31/5.63 ! [N: nat] : ( ord_less_eq_real @ one_one_real @ ( semiri2265585572941072030t_real @ N ) ) ).
% 5.31/5.63
% 5.31/5.63 % fact_ge_1
% 5.31/5.63 thf(fact_7550_neg__numeral__le__numeral,axiom,
% 5.31/5.63 ! [M2: num,N: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M2 ) ) @ ( numeral_numeral_real @ N ) ) ).
% 5.31/5.63
% 5.31/5.63 % neg_numeral_le_numeral
% 5.31/5.63 thf(fact_7551_neg__numeral__le__numeral,axiom,
% 5.31/5.63 ! [M2: num,N: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M2 ) ) @ ( numera6620942414471956472nteger @ N ) ) ).
% 5.31/5.63
% 5.31/5.63 % neg_numeral_le_numeral
% 5.31/5.63 thf(fact_7552_neg__numeral__le__numeral,axiom,
% 5.31/5.63 ! [M2: num,N: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M2 ) ) @ ( numeral_numeral_rat @ N ) ) ).
% 5.31/5.63
% 5.31/5.63 % neg_numeral_le_numeral
% 5.31/5.63 thf(fact_7553_neg__numeral__le__numeral,axiom,
% 5.31/5.63 ! [M2: num,N: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ ( numeral_numeral_int @ N ) ) ).
% 5.31/5.63
% 5.31/5.63 % neg_numeral_le_numeral
% 5.31/5.63 thf(fact_7554_not__numeral__le__neg__numeral,axiom,
% 5.31/5.63 ! [M2: num,N: num] :
% 5.31/5.63 ~ ( ord_less_eq_real @ ( numeral_numeral_real @ M2 ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % not_numeral_le_neg_numeral
% 5.31/5.63 thf(fact_7555_not__numeral__le__neg__numeral,axiom,
% 5.31/5.63 ! [M2: num,N: num] :
% 5.31/5.63 ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ M2 ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % not_numeral_le_neg_numeral
% 5.31/5.63 thf(fact_7556_not__numeral__le__neg__numeral,axiom,
% 5.31/5.63 ! [M2: num,N: num] :
% 5.31/5.63 ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ M2 ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % not_numeral_le_neg_numeral
% 5.31/5.63 thf(fact_7557_not__numeral__le__neg__numeral,axiom,
% 5.31/5.63 ! [M2: num,N: num] :
% 5.31/5.63 ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % not_numeral_le_neg_numeral
% 5.31/5.63 thf(fact_7558_zero__neq__neg__numeral,axiom,
% 5.31/5.63 ! [N: num] :
% 5.31/5.63 ( zero_zero_int
% 5.31/5.63 != ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % zero_neq_neg_numeral
% 5.31/5.63 thf(fact_7559_zero__neq__neg__numeral,axiom,
% 5.31/5.63 ! [N: num] :
% 5.31/5.63 ( zero_zero_real
% 5.31/5.63 != ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % zero_neq_neg_numeral
% 5.31/5.63 thf(fact_7560_zero__neq__neg__numeral,axiom,
% 5.31/5.63 ! [N: num] :
% 5.31/5.63 ( zero_zero_complex
% 5.31/5.63 != ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % zero_neq_neg_numeral
% 5.31/5.63 thf(fact_7561_zero__neq__neg__numeral,axiom,
% 5.31/5.63 ! [N: num] :
% 5.31/5.63 ( zero_z3403309356797280102nteger
% 5.31/5.63 != ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % zero_neq_neg_numeral
% 5.31/5.63 thf(fact_7562_zero__neq__neg__numeral,axiom,
% 5.31/5.63 ! [N: num] :
% 5.31/5.63 ( zero_zero_rat
% 5.31/5.63 != ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % zero_neq_neg_numeral
% 5.31/5.63 thf(fact_7563_not__numeral__less__neg__numeral,axiom,
% 5.31/5.63 ! [M2: num,N: num] :
% 5.31/5.63 ~ ( ord_less_int @ ( numeral_numeral_int @ M2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % not_numeral_less_neg_numeral
% 5.31/5.63 thf(fact_7564_not__numeral__less__neg__numeral,axiom,
% 5.31/5.63 ! [M2: num,N: num] :
% 5.31/5.63 ~ ( ord_less_real @ ( numeral_numeral_real @ M2 ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % not_numeral_less_neg_numeral
% 5.31/5.63 thf(fact_7565_not__numeral__less__neg__numeral,axiom,
% 5.31/5.63 ! [M2: num,N: num] :
% 5.31/5.63 ~ ( ord_le6747313008572928689nteger @ ( numera6620942414471956472nteger @ M2 ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % not_numeral_less_neg_numeral
% 5.31/5.63 thf(fact_7566_not__numeral__less__neg__numeral,axiom,
% 5.31/5.63 ! [M2: num,N: num] :
% 5.31/5.63 ~ ( ord_less_rat @ ( numeral_numeral_rat @ M2 ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % not_numeral_less_neg_numeral
% 5.31/5.63 thf(fact_7567_neg__numeral__less__numeral,axiom,
% 5.31/5.63 ! [M2: num,N: num] : ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ ( numeral_numeral_int @ N ) ) ).
% 5.31/5.63
% 5.31/5.63 % neg_numeral_less_numeral
% 5.31/5.63 thf(fact_7568_neg__numeral__less__numeral,axiom,
% 5.31/5.63 ! [M2: num,N: num] : ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M2 ) ) @ ( numeral_numeral_real @ N ) ) ).
% 5.31/5.63
% 5.31/5.63 % neg_numeral_less_numeral
% 5.31/5.63 thf(fact_7569_neg__numeral__less__numeral,axiom,
% 5.31/5.63 ! [M2: num,N: num] : ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M2 ) ) @ ( numera6620942414471956472nteger @ N ) ) ).
% 5.31/5.63
% 5.31/5.63 % neg_numeral_less_numeral
% 5.31/5.63 thf(fact_7570_neg__numeral__less__numeral,axiom,
% 5.31/5.63 ! [M2: num,N: num] : ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M2 ) ) @ ( numeral_numeral_rat @ N ) ) ).
% 5.31/5.63
% 5.31/5.63 % neg_numeral_less_numeral
% 5.31/5.63 thf(fact_7571_le__minus__one__simps_I4_J,axiom,
% 5.31/5.63 ~ ( ord_less_eq_real @ one_one_real @ ( uminus_uminus_real @ one_one_real ) ) ).
% 5.31/5.63
% 5.31/5.63 % le_minus_one_simps(4)
% 5.31/5.63 thf(fact_7572_le__minus__one__simps_I4_J,axiom,
% 5.31/5.63 ~ ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.31/5.63
% 5.31/5.63 % le_minus_one_simps(4)
% 5.31/5.63 thf(fact_7573_le__minus__one__simps_I4_J,axiom,
% 5.31/5.63 ~ ( ord_less_eq_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.31/5.63
% 5.31/5.63 % le_minus_one_simps(4)
% 5.31/5.63 thf(fact_7574_le__minus__one__simps_I4_J,axiom,
% 5.31/5.63 ~ ( ord_less_eq_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 5.31/5.63
% 5.31/5.63 % le_minus_one_simps(4)
% 5.31/5.63 thf(fact_7575_le__minus__one__simps_I2_J,axiom,
% 5.31/5.63 ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ).
% 5.31/5.63
% 5.31/5.63 % le_minus_one_simps(2)
% 5.31/5.63 thf(fact_7576_le__minus__one__simps_I2_J,axiom,
% 5.31/5.63 ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer ).
% 5.31/5.63
% 5.31/5.63 % le_minus_one_simps(2)
% 5.31/5.63 thf(fact_7577_le__minus__one__simps_I2_J,axiom,
% 5.31/5.63 ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat ).
% 5.31/5.63
% 5.31/5.63 % le_minus_one_simps(2)
% 5.31/5.63 thf(fact_7578_le__minus__one__simps_I2_J,axiom,
% 5.31/5.63 ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int ).
% 5.31/5.63
% 5.31/5.63 % le_minus_one_simps(2)
% 5.31/5.63 thf(fact_7579_add__eq__0__iff,axiom,
% 5.31/5.63 ! [A: int,B: int] :
% 5.31/5.63 ( ( ( plus_plus_int @ A @ B )
% 5.31/5.63 = zero_zero_int )
% 5.31/5.63 = ( B
% 5.31/5.63 = ( uminus_uminus_int @ A ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % add_eq_0_iff
% 5.31/5.63 thf(fact_7580_add__eq__0__iff,axiom,
% 5.31/5.63 ! [A: real,B: real] :
% 5.31/5.63 ( ( ( plus_plus_real @ A @ B )
% 5.31/5.63 = zero_zero_real )
% 5.31/5.63 = ( B
% 5.31/5.63 = ( uminus_uminus_real @ A ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % add_eq_0_iff
% 5.31/5.63 thf(fact_7581_add__eq__0__iff,axiom,
% 5.31/5.63 ! [A: complex,B: complex] :
% 5.31/5.63 ( ( ( plus_plus_complex @ A @ B )
% 5.31/5.63 = zero_zero_complex )
% 5.31/5.63 = ( B
% 5.31/5.63 = ( uminus1482373934393186551omplex @ A ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % add_eq_0_iff
% 5.31/5.63 thf(fact_7582_add__eq__0__iff,axiom,
% 5.31/5.63 ! [A: code_integer,B: code_integer] :
% 5.31/5.63 ( ( ( plus_p5714425477246183910nteger @ A @ B )
% 5.31/5.63 = zero_z3403309356797280102nteger )
% 5.31/5.63 = ( B
% 5.31/5.63 = ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % add_eq_0_iff
% 5.31/5.63 thf(fact_7583_add__eq__0__iff,axiom,
% 5.31/5.63 ! [A: rat,B: rat] :
% 5.31/5.63 ( ( ( plus_plus_rat @ A @ B )
% 5.31/5.63 = zero_zero_rat )
% 5.31/5.63 = ( B
% 5.31/5.63 = ( uminus_uminus_rat @ A ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % add_eq_0_iff
% 5.31/5.63 thf(fact_7584_ab__group__add__class_Oab__left__minus,axiom,
% 5.31/5.63 ! [A: int] :
% 5.31/5.63 ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ A )
% 5.31/5.63 = zero_zero_int ) ).
% 5.31/5.63
% 5.31/5.63 % ab_group_add_class.ab_left_minus
% 5.31/5.63 thf(fact_7585_ab__group__add__class_Oab__left__minus,axiom,
% 5.31/5.63 ! [A: real] :
% 5.31/5.63 ( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ A )
% 5.31/5.63 = zero_zero_real ) ).
% 5.31/5.63
% 5.31/5.63 % ab_group_add_class.ab_left_minus
% 5.31/5.63 thf(fact_7586_ab__group__add__class_Oab__left__minus,axiom,
% 5.31/5.63 ! [A: complex] :
% 5.31/5.63 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ A )
% 5.31/5.63 = zero_zero_complex ) ).
% 5.31/5.63
% 5.31/5.63 % ab_group_add_class.ab_left_minus
% 5.31/5.63 thf(fact_7587_ab__group__add__class_Oab__left__minus,axiom,
% 5.31/5.63 ! [A: code_integer] :
% 5.31/5.63 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ A )
% 5.31/5.63 = zero_z3403309356797280102nteger ) ).
% 5.31/5.63
% 5.31/5.63 % ab_group_add_class.ab_left_minus
% 5.31/5.63 thf(fact_7588_ab__group__add__class_Oab__left__minus,axiom,
% 5.31/5.63 ! [A: rat] :
% 5.31/5.63 ( ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ A )
% 5.31/5.63 = zero_zero_rat ) ).
% 5.31/5.63
% 5.31/5.63 % ab_group_add_class.ab_left_minus
% 5.31/5.63 thf(fact_7589_add_Oinverse__unique,axiom,
% 5.31/5.63 ! [A: int,B: int] :
% 5.31/5.63 ( ( ( plus_plus_int @ A @ B )
% 5.31/5.63 = zero_zero_int )
% 5.31/5.63 => ( ( uminus_uminus_int @ A )
% 5.31/5.63 = B ) ) ).
% 5.31/5.63
% 5.31/5.63 % add.inverse_unique
% 5.31/5.63 thf(fact_7590_add_Oinverse__unique,axiom,
% 5.31/5.63 ! [A: real,B: real] :
% 5.31/5.63 ( ( ( plus_plus_real @ A @ B )
% 5.31/5.63 = zero_zero_real )
% 5.31/5.63 => ( ( uminus_uminus_real @ A )
% 5.31/5.63 = B ) ) ).
% 5.31/5.63
% 5.31/5.63 % add.inverse_unique
% 5.31/5.63 thf(fact_7591_add_Oinverse__unique,axiom,
% 5.31/5.63 ! [A: complex,B: complex] :
% 5.31/5.63 ( ( ( plus_plus_complex @ A @ B )
% 5.31/5.63 = zero_zero_complex )
% 5.31/5.63 => ( ( uminus1482373934393186551omplex @ A )
% 5.31/5.63 = B ) ) ).
% 5.31/5.63
% 5.31/5.63 % add.inverse_unique
% 5.31/5.63 thf(fact_7592_add_Oinverse__unique,axiom,
% 5.31/5.63 ! [A: code_integer,B: code_integer] :
% 5.31/5.63 ( ( ( plus_p5714425477246183910nteger @ A @ B )
% 5.31/5.63 = zero_z3403309356797280102nteger )
% 5.31/5.63 => ( ( uminus1351360451143612070nteger @ A )
% 5.31/5.63 = B ) ) ).
% 5.31/5.63
% 5.31/5.63 % add.inverse_unique
% 5.31/5.63 thf(fact_7593_add_Oinverse__unique,axiom,
% 5.31/5.63 ! [A: rat,B: rat] :
% 5.31/5.63 ( ( ( plus_plus_rat @ A @ B )
% 5.31/5.63 = zero_zero_rat )
% 5.31/5.63 => ( ( uminus_uminus_rat @ A )
% 5.31/5.63 = B ) ) ).
% 5.31/5.63
% 5.31/5.63 % add.inverse_unique
% 5.31/5.63 thf(fact_7594_eq__neg__iff__add__eq__0,axiom,
% 5.31/5.63 ! [A: int,B: int] :
% 5.31/5.63 ( ( A
% 5.31/5.63 = ( uminus_uminus_int @ B ) )
% 5.31/5.63 = ( ( plus_plus_int @ A @ B )
% 5.31/5.63 = zero_zero_int ) ) ).
% 5.31/5.63
% 5.31/5.63 % eq_neg_iff_add_eq_0
% 5.31/5.63 thf(fact_7595_eq__neg__iff__add__eq__0,axiom,
% 5.31/5.63 ! [A: real,B: real] :
% 5.31/5.63 ( ( A
% 5.31/5.63 = ( uminus_uminus_real @ B ) )
% 5.31/5.63 = ( ( plus_plus_real @ A @ B )
% 5.31/5.63 = zero_zero_real ) ) ).
% 5.31/5.63
% 5.31/5.63 % eq_neg_iff_add_eq_0
% 5.31/5.63 thf(fact_7596_eq__neg__iff__add__eq__0,axiom,
% 5.31/5.63 ! [A: complex,B: complex] :
% 5.31/5.63 ( ( A
% 5.31/5.63 = ( uminus1482373934393186551omplex @ B ) )
% 5.31/5.63 = ( ( plus_plus_complex @ A @ B )
% 5.31/5.63 = zero_zero_complex ) ) ).
% 5.31/5.63
% 5.31/5.63 % eq_neg_iff_add_eq_0
% 5.31/5.63 thf(fact_7597_eq__neg__iff__add__eq__0,axiom,
% 5.31/5.63 ! [A: code_integer,B: code_integer] :
% 5.31/5.63 ( ( A
% 5.31/5.63 = ( uminus1351360451143612070nteger @ B ) )
% 5.31/5.63 = ( ( plus_p5714425477246183910nteger @ A @ B )
% 5.31/5.63 = zero_z3403309356797280102nteger ) ) ).
% 5.31/5.63
% 5.31/5.63 % eq_neg_iff_add_eq_0
% 5.31/5.63 thf(fact_7598_eq__neg__iff__add__eq__0,axiom,
% 5.31/5.63 ! [A: rat,B: rat] :
% 5.31/5.63 ( ( A
% 5.31/5.63 = ( uminus_uminus_rat @ B ) )
% 5.31/5.63 = ( ( plus_plus_rat @ A @ B )
% 5.31/5.63 = zero_zero_rat ) ) ).
% 5.31/5.63
% 5.31/5.63 % eq_neg_iff_add_eq_0
% 5.31/5.63 thf(fact_7599_neg__eq__iff__add__eq__0,axiom,
% 5.31/5.63 ! [A: int,B: int] :
% 5.31/5.63 ( ( ( uminus_uminus_int @ A )
% 5.31/5.63 = B )
% 5.31/5.63 = ( ( plus_plus_int @ A @ B )
% 5.31/5.63 = zero_zero_int ) ) ).
% 5.31/5.63
% 5.31/5.63 % neg_eq_iff_add_eq_0
% 5.31/5.63 thf(fact_7600_neg__eq__iff__add__eq__0,axiom,
% 5.31/5.63 ! [A: real,B: real] :
% 5.31/5.63 ( ( ( uminus_uminus_real @ A )
% 5.31/5.63 = B )
% 5.31/5.63 = ( ( plus_plus_real @ A @ B )
% 5.31/5.63 = zero_zero_real ) ) ).
% 5.31/5.63
% 5.31/5.63 % neg_eq_iff_add_eq_0
% 5.31/5.63 thf(fact_7601_neg__eq__iff__add__eq__0,axiom,
% 5.31/5.63 ! [A: complex,B: complex] :
% 5.31/5.63 ( ( ( uminus1482373934393186551omplex @ A )
% 5.31/5.63 = B )
% 5.31/5.63 = ( ( plus_plus_complex @ A @ B )
% 5.31/5.63 = zero_zero_complex ) ) ).
% 5.31/5.63
% 5.31/5.63 % neg_eq_iff_add_eq_0
% 5.31/5.63 thf(fact_7602_neg__eq__iff__add__eq__0,axiom,
% 5.31/5.63 ! [A: code_integer,B: code_integer] :
% 5.31/5.63 ( ( ( uminus1351360451143612070nteger @ A )
% 5.31/5.63 = B )
% 5.31/5.63 = ( ( plus_p5714425477246183910nteger @ A @ B )
% 5.31/5.63 = zero_z3403309356797280102nteger ) ) ).
% 5.31/5.63
% 5.31/5.63 % neg_eq_iff_add_eq_0
% 5.31/5.63 thf(fact_7603_neg__eq__iff__add__eq__0,axiom,
% 5.31/5.63 ! [A: rat,B: rat] :
% 5.31/5.63 ( ( ( uminus_uminus_rat @ A )
% 5.31/5.63 = B )
% 5.31/5.63 = ( ( plus_plus_rat @ A @ B )
% 5.31/5.63 = zero_zero_rat ) ) ).
% 5.31/5.63
% 5.31/5.63 % neg_eq_iff_add_eq_0
% 5.31/5.63 thf(fact_7604_zero__neq__neg__one,axiom,
% 5.31/5.63 ( zero_zero_int
% 5.31/5.63 != ( uminus_uminus_int @ one_one_int ) ) ).
% 5.31/5.63
% 5.31/5.63 % zero_neq_neg_one
% 5.31/5.63 thf(fact_7605_zero__neq__neg__one,axiom,
% 5.31/5.63 ( zero_zero_real
% 5.31/5.63 != ( uminus_uminus_real @ one_one_real ) ) ).
% 5.31/5.63
% 5.31/5.63 % zero_neq_neg_one
% 5.31/5.63 thf(fact_7606_zero__neq__neg__one,axiom,
% 5.31/5.63 ( zero_zero_complex
% 5.31/5.63 != ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.31/5.63
% 5.31/5.63 % zero_neq_neg_one
% 5.31/5.63 thf(fact_7607_zero__neq__neg__one,axiom,
% 5.31/5.63 ( zero_z3403309356797280102nteger
% 5.31/5.63 != ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.31/5.63
% 5.31/5.63 % zero_neq_neg_one
% 5.31/5.63 thf(fact_7608_zero__neq__neg__one,axiom,
% 5.31/5.63 ( zero_zero_rat
% 5.31/5.63 != ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.31/5.63
% 5.31/5.63 % zero_neq_neg_one
% 5.31/5.63 thf(fact_7609_less__minus__one__simps_I4_J,axiom,
% 5.31/5.63 ~ ( ord_less_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 5.31/5.63
% 5.31/5.63 % less_minus_one_simps(4)
% 5.31/5.63 thf(fact_7610_less__minus__one__simps_I4_J,axiom,
% 5.31/5.63 ~ ( ord_less_real @ one_one_real @ ( uminus_uminus_real @ one_one_real ) ) ).
% 5.31/5.63
% 5.31/5.63 % less_minus_one_simps(4)
% 5.31/5.63 thf(fact_7611_less__minus__one__simps_I4_J,axiom,
% 5.31/5.63 ~ ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.31/5.63
% 5.31/5.63 % less_minus_one_simps(4)
% 5.31/5.63 thf(fact_7612_less__minus__one__simps_I4_J,axiom,
% 5.31/5.63 ~ ( ord_less_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.31/5.63
% 5.31/5.63 % less_minus_one_simps(4)
% 5.31/5.63 thf(fact_7613_less__minus__one__simps_I2_J,axiom,
% 5.31/5.63 ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int ).
% 5.31/5.63
% 5.31/5.63 % less_minus_one_simps(2)
% 5.31/5.63 thf(fact_7614_less__minus__one__simps_I2_J,axiom,
% 5.31/5.63 ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ).
% 5.31/5.63
% 5.31/5.63 % less_minus_one_simps(2)
% 5.31/5.63 thf(fact_7615_less__minus__one__simps_I2_J,axiom,
% 5.31/5.63 ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer ).
% 5.31/5.63
% 5.31/5.63 % less_minus_one_simps(2)
% 5.31/5.63 thf(fact_7616_less__minus__one__simps_I2_J,axiom,
% 5.31/5.63 ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat ).
% 5.31/5.63
% 5.31/5.63 % less_minus_one_simps(2)
% 5.31/5.63 thf(fact_7617_numeral__times__minus__swap,axiom,
% 5.31/5.63 ! [W2: num,X: int] :
% 5.31/5.63 ( ( times_times_int @ ( numeral_numeral_int @ W2 ) @ ( uminus_uminus_int @ X ) )
% 5.31/5.63 = ( times_times_int @ X @ ( uminus_uminus_int @ ( numeral_numeral_int @ W2 ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % numeral_times_minus_swap
% 5.31/5.63 thf(fact_7618_numeral__times__minus__swap,axiom,
% 5.31/5.63 ! [W2: num,X: real] :
% 5.31/5.63 ( ( times_times_real @ ( numeral_numeral_real @ W2 ) @ ( uminus_uminus_real @ X ) )
% 5.31/5.63 = ( times_times_real @ X @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % numeral_times_minus_swap
% 5.31/5.63 thf(fact_7619_numeral__times__minus__swap,axiom,
% 5.31/5.63 ! [W2: num,X: complex] :
% 5.31/5.63 ( ( times_times_complex @ ( numera6690914467698888265omplex @ W2 ) @ ( uminus1482373934393186551omplex @ X ) )
% 5.31/5.63 = ( times_times_complex @ X @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W2 ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % numeral_times_minus_swap
% 5.31/5.63 thf(fact_7620_numeral__times__minus__swap,axiom,
% 5.31/5.63 ! [W2: num,X: code_integer] :
% 5.31/5.63 ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ W2 ) @ ( uminus1351360451143612070nteger @ X ) )
% 5.31/5.63 = ( times_3573771949741848930nteger @ X @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ W2 ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % numeral_times_minus_swap
% 5.31/5.63 thf(fact_7621_numeral__times__minus__swap,axiom,
% 5.31/5.63 ! [W2: num,X: rat] :
% 5.31/5.63 ( ( times_times_rat @ ( numeral_numeral_rat @ W2 ) @ ( uminus_uminus_rat @ X ) )
% 5.31/5.63 = ( times_times_rat @ X @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % numeral_times_minus_swap
% 5.31/5.63 thf(fact_7622_nonzero__minus__divide__divide,axiom,
% 5.31/5.63 ! [B: real,A: real] :
% 5.31/5.63 ( ( B != zero_zero_real )
% 5.31/5.63 => ( ( divide_divide_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B ) )
% 5.31/5.63 = ( divide_divide_real @ A @ B ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % nonzero_minus_divide_divide
% 5.31/5.63 thf(fact_7623_nonzero__minus__divide__divide,axiom,
% 5.31/5.63 ! [B: complex,A: complex] :
% 5.31/5.63 ( ( B != zero_zero_complex )
% 5.31/5.63 => ( ( divide1717551699836669952omplex @ ( uminus1482373934393186551omplex @ A ) @ ( uminus1482373934393186551omplex @ B ) )
% 5.31/5.63 = ( divide1717551699836669952omplex @ A @ B ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % nonzero_minus_divide_divide
% 5.31/5.63 thf(fact_7624_nonzero__minus__divide__divide,axiom,
% 5.31/5.63 ! [B: rat,A: rat] :
% 5.31/5.63 ( ( B != zero_zero_rat )
% 5.31/5.63 => ( ( divide_divide_rat @ ( uminus_uminus_rat @ A ) @ ( uminus_uminus_rat @ B ) )
% 5.31/5.63 = ( divide_divide_rat @ A @ B ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % nonzero_minus_divide_divide
% 5.31/5.63 thf(fact_7625_nonzero__minus__divide__right,axiom,
% 5.31/5.63 ! [B: real,A: real] :
% 5.31/5.63 ( ( B != zero_zero_real )
% 5.31/5.63 => ( ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) )
% 5.31/5.63 = ( divide_divide_real @ A @ ( uminus_uminus_real @ B ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % nonzero_minus_divide_right
% 5.31/5.63 thf(fact_7626_nonzero__minus__divide__right,axiom,
% 5.31/5.63 ! [B: complex,A: complex] :
% 5.31/5.63 ( ( B != zero_zero_complex )
% 5.31/5.63 => ( ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 5.31/5.63 = ( divide1717551699836669952omplex @ A @ ( uminus1482373934393186551omplex @ B ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % nonzero_minus_divide_right
% 5.31/5.63 thf(fact_7627_nonzero__minus__divide__right,axiom,
% 5.31/5.63 ! [B: rat,A: rat] :
% 5.31/5.63 ( ( B != zero_zero_rat )
% 5.31/5.63 => ( ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) )
% 5.31/5.63 = ( divide_divide_rat @ A @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % nonzero_minus_divide_right
% 5.31/5.63 thf(fact_7628_one__neq__neg__numeral,axiom,
% 5.31/5.63 ! [N: num] :
% 5.31/5.63 ( one_one_int
% 5.31/5.63 != ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % one_neq_neg_numeral
% 5.31/5.63 thf(fact_7629_one__neq__neg__numeral,axiom,
% 5.31/5.63 ! [N: num] :
% 5.31/5.63 ( one_one_real
% 5.31/5.63 != ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % one_neq_neg_numeral
% 5.31/5.63 thf(fact_7630_one__neq__neg__numeral,axiom,
% 5.31/5.63 ! [N: num] :
% 5.31/5.63 ( one_one_complex
% 5.31/5.63 != ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % one_neq_neg_numeral
% 5.31/5.63 thf(fact_7631_one__neq__neg__numeral,axiom,
% 5.31/5.63 ! [N: num] :
% 5.31/5.63 ( one_one_Code_integer
% 5.31/5.63 != ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % one_neq_neg_numeral
% 5.31/5.63 thf(fact_7632_one__neq__neg__numeral,axiom,
% 5.31/5.63 ! [N: num] :
% 5.31/5.63 ( one_one_rat
% 5.31/5.63 != ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % one_neq_neg_numeral
% 5.31/5.63 thf(fact_7633_numeral__neq__neg__one,axiom,
% 5.31/5.63 ! [N: num] :
% 5.31/5.63 ( ( numeral_numeral_int @ N )
% 5.31/5.63 != ( uminus_uminus_int @ one_one_int ) ) ).
% 5.31/5.63
% 5.31/5.63 % numeral_neq_neg_one
% 5.31/5.63 thf(fact_7634_numeral__neq__neg__one,axiom,
% 5.31/5.63 ! [N: num] :
% 5.31/5.63 ( ( numeral_numeral_real @ N )
% 5.31/5.63 != ( uminus_uminus_real @ one_one_real ) ) ).
% 5.31/5.63
% 5.31/5.63 % numeral_neq_neg_one
% 5.31/5.63 thf(fact_7635_numeral__neq__neg__one,axiom,
% 5.31/5.63 ! [N: num] :
% 5.31/5.63 ( ( numera6690914467698888265omplex @ N )
% 5.31/5.63 != ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.31/5.63
% 5.31/5.63 % numeral_neq_neg_one
% 5.31/5.63 thf(fact_7636_numeral__neq__neg__one,axiom,
% 5.31/5.63 ! [N: num] :
% 5.31/5.63 ( ( numera6620942414471956472nteger @ N )
% 5.31/5.63 != ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.31/5.63
% 5.31/5.63 % numeral_neq_neg_one
% 5.31/5.63 thf(fact_7637_numeral__neq__neg__one,axiom,
% 5.31/5.63 ! [N: num] :
% 5.31/5.63 ( ( numeral_numeral_rat @ N )
% 5.31/5.63 != ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.31/5.63
% 5.31/5.63 % numeral_neq_neg_one
% 5.31/5.63 thf(fact_7638_square__eq__1__iff,axiom,
% 5.31/5.63 ! [X: int] :
% 5.31/5.63 ( ( ( times_times_int @ X @ X )
% 5.31/5.63 = one_one_int )
% 5.31/5.63 = ( ( X = one_one_int )
% 5.31/5.63 | ( X
% 5.31/5.63 = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % square_eq_1_iff
% 5.31/5.63 thf(fact_7639_square__eq__1__iff,axiom,
% 5.31/5.63 ! [X: real] :
% 5.31/5.63 ( ( ( times_times_real @ X @ X )
% 5.31/5.63 = one_one_real )
% 5.31/5.63 = ( ( X = one_one_real )
% 5.31/5.63 | ( X
% 5.31/5.63 = ( uminus_uminus_real @ one_one_real ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % square_eq_1_iff
% 5.31/5.63 thf(fact_7640_square__eq__1__iff,axiom,
% 5.31/5.63 ! [X: complex] :
% 5.31/5.63 ( ( ( times_times_complex @ X @ X )
% 5.31/5.63 = one_one_complex )
% 5.31/5.63 = ( ( X = one_one_complex )
% 5.31/5.63 | ( X
% 5.31/5.63 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % square_eq_1_iff
% 5.31/5.63 thf(fact_7641_square__eq__1__iff,axiom,
% 5.31/5.63 ! [X: code_integer] :
% 5.31/5.63 ( ( ( times_3573771949741848930nteger @ X @ X )
% 5.31/5.63 = one_one_Code_integer )
% 5.31/5.63 = ( ( X = one_one_Code_integer )
% 5.31/5.63 | ( X
% 5.31/5.63 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % square_eq_1_iff
% 5.31/5.63 thf(fact_7642_square__eq__1__iff,axiom,
% 5.31/5.63 ! [X: rat] :
% 5.31/5.63 ( ( ( times_times_rat @ X @ X )
% 5.31/5.63 = one_one_rat )
% 5.31/5.63 = ( ( X = one_one_rat )
% 5.31/5.63 | ( X
% 5.31/5.63 = ( uminus_uminus_rat @ one_one_rat ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % square_eq_1_iff
% 5.31/5.63 thf(fact_7643_fact__mono,axiom,
% 5.31/5.63 ! [M2: nat,N: nat] :
% 5.31/5.63 ( ( ord_less_eq_nat @ M2 @ N )
% 5.31/5.63 => ( ord_less_eq_rat @ ( semiri773545260158071498ct_rat @ M2 ) @ ( semiri773545260158071498ct_rat @ N ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % fact_mono
% 5.31/5.63 thf(fact_7644_fact__mono,axiom,
% 5.31/5.63 ! [M2: nat,N: nat] :
% 5.31/5.63 ( ( ord_less_eq_nat @ M2 @ N )
% 5.31/5.63 => ( ord_less_eq_int @ ( semiri1406184849735516958ct_int @ M2 ) @ ( semiri1406184849735516958ct_int @ N ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % fact_mono
% 5.31/5.63 thf(fact_7645_fact__mono,axiom,
% 5.31/5.63 ! [M2: nat,N: nat] :
% 5.31/5.63 ( ( ord_less_eq_nat @ M2 @ N )
% 5.31/5.63 => ( ord_less_eq_nat @ ( semiri1408675320244567234ct_nat @ M2 ) @ ( semiri1408675320244567234ct_nat @ N ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % fact_mono
% 5.31/5.63 thf(fact_7646_fact__mono,axiom,
% 5.31/5.63 ! [M2: nat,N: nat] :
% 5.31/5.63 ( ( ord_less_eq_nat @ M2 @ N )
% 5.31/5.63 => ( ord_less_eq_real @ ( semiri2265585572941072030t_real @ M2 ) @ ( semiri2265585572941072030t_real @ N ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % fact_mono
% 5.31/5.63 thf(fact_7647_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 5.31/5.63 ( minus_minus_int
% 5.31/5.63 = ( ^ [A5: int,B4: int] : ( plus_plus_int @ A5 @ ( uminus_uminus_int @ B4 ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % ab_group_add_class.ab_diff_conv_add_uminus
% 5.31/5.63 thf(fact_7648_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 5.31/5.63 ( minus_minus_real
% 5.31/5.63 = ( ^ [A5: real,B4: real] : ( plus_plus_real @ A5 @ ( uminus_uminus_real @ B4 ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % ab_group_add_class.ab_diff_conv_add_uminus
% 5.31/5.63 thf(fact_7649_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 5.31/5.63 ( minus_minus_complex
% 5.31/5.63 = ( ^ [A5: complex,B4: complex] : ( plus_plus_complex @ A5 @ ( uminus1482373934393186551omplex @ B4 ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % ab_group_add_class.ab_diff_conv_add_uminus
% 5.31/5.63 thf(fact_7650_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 5.31/5.63 ( minus_8373710615458151222nteger
% 5.31/5.63 = ( ^ [A5: code_integer,B4: code_integer] : ( plus_p5714425477246183910nteger @ A5 @ ( uminus1351360451143612070nteger @ B4 ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % ab_group_add_class.ab_diff_conv_add_uminus
% 5.31/5.63 thf(fact_7651_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 5.31/5.63 ( minus_minus_rat
% 5.31/5.63 = ( ^ [A5: rat,B4: rat] : ( plus_plus_rat @ A5 @ ( uminus_uminus_rat @ B4 ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % ab_group_add_class.ab_diff_conv_add_uminus
% 5.31/5.63 thf(fact_7652_diff__conv__add__uminus,axiom,
% 5.31/5.63 ( minus_minus_int
% 5.31/5.63 = ( ^ [A5: int,B4: int] : ( plus_plus_int @ A5 @ ( uminus_uminus_int @ B4 ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % diff_conv_add_uminus
% 5.31/5.63 thf(fact_7653_diff__conv__add__uminus,axiom,
% 5.31/5.63 ( minus_minus_real
% 5.31/5.63 = ( ^ [A5: real,B4: real] : ( plus_plus_real @ A5 @ ( uminus_uminus_real @ B4 ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % diff_conv_add_uminus
% 5.31/5.63 thf(fact_7654_diff__conv__add__uminus,axiom,
% 5.31/5.63 ( minus_minus_complex
% 5.31/5.63 = ( ^ [A5: complex,B4: complex] : ( plus_plus_complex @ A5 @ ( uminus1482373934393186551omplex @ B4 ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % diff_conv_add_uminus
% 5.31/5.63 thf(fact_7655_diff__conv__add__uminus,axiom,
% 5.31/5.63 ( minus_8373710615458151222nteger
% 5.31/5.63 = ( ^ [A5: code_integer,B4: code_integer] : ( plus_p5714425477246183910nteger @ A5 @ ( uminus1351360451143612070nteger @ B4 ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % diff_conv_add_uminus
% 5.31/5.63 thf(fact_7656_diff__conv__add__uminus,axiom,
% 5.31/5.63 ( minus_minus_rat
% 5.31/5.63 = ( ^ [A5: rat,B4: rat] : ( plus_plus_rat @ A5 @ ( uminus_uminus_rat @ B4 ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % diff_conv_add_uminus
% 5.31/5.63 thf(fact_7657_group__cancel_Osub2,axiom,
% 5.31/5.63 ! [B5: int,K2: int,B: int,A: int] :
% 5.31/5.63 ( ( B5
% 5.31/5.63 = ( plus_plus_int @ K2 @ B ) )
% 5.31/5.63 => ( ( minus_minus_int @ A @ B5 )
% 5.31/5.63 = ( plus_plus_int @ ( uminus_uminus_int @ K2 ) @ ( minus_minus_int @ A @ B ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % group_cancel.sub2
% 5.31/5.63 thf(fact_7658_group__cancel_Osub2,axiom,
% 5.31/5.63 ! [B5: real,K2: real,B: real,A: real] :
% 5.31/5.63 ( ( B5
% 5.31/5.63 = ( plus_plus_real @ K2 @ B ) )
% 5.31/5.63 => ( ( minus_minus_real @ A @ B5 )
% 5.31/5.63 = ( plus_plus_real @ ( uminus_uminus_real @ K2 ) @ ( minus_minus_real @ A @ B ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % group_cancel.sub2
% 5.31/5.63 thf(fact_7659_group__cancel_Osub2,axiom,
% 5.31/5.63 ! [B5: complex,K2: complex,B: complex,A: complex] :
% 5.31/5.63 ( ( B5
% 5.31/5.63 = ( plus_plus_complex @ K2 @ B ) )
% 5.31/5.63 => ( ( minus_minus_complex @ A @ B5 )
% 5.31/5.63 = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ K2 ) @ ( minus_minus_complex @ A @ B ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % group_cancel.sub2
% 5.31/5.63 thf(fact_7660_group__cancel_Osub2,axiom,
% 5.31/5.63 ! [B5: code_integer,K2: code_integer,B: code_integer,A: code_integer] :
% 5.31/5.63 ( ( B5
% 5.31/5.63 = ( plus_p5714425477246183910nteger @ K2 @ B ) )
% 5.31/5.63 => ( ( minus_8373710615458151222nteger @ A @ B5 )
% 5.31/5.63 = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ K2 ) @ ( minus_8373710615458151222nteger @ A @ B ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % group_cancel.sub2
% 5.31/5.63 thf(fact_7661_group__cancel_Osub2,axiom,
% 5.31/5.63 ! [B5: rat,K2: rat,B: rat,A: rat] :
% 5.31/5.63 ( ( B5
% 5.31/5.63 = ( plus_plus_rat @ K2 @ B ) )
% 5.31/5.63 => ( ( minus_minus_rat @ A @ B5 )
% 5.31/5.63 = ( plus_plus_rat @ ( uminus_uminus_rat @ K2 ) @ ( minus_minus_rat @ A @ B ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % group_cancel.sub2
% 5.31/5.63 thf(fact_7662_dvd__neg__div,axiom,
% 5.31/5.63 ! [B: int,A: int] :
% 5.31/5.63 ( ( dvd_dvd_int @ B @ A )
% 5.31/5.63 => ( ( divide_divide_int @ ( uminus_uminus_int @ A ) @ B )
% 5.31/5.63 = ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % dvd_neg_div
% 5.31/5.63 thf(fact_7663_dvd__neg__div,axiom,
% 5.31/5.63 ! [B: real,A: real] :
% 5.31/5.63 ( ( dvd_dvd_real @ B @ A )
% 5.31/5.63 => ( ( divide_divide_real @ ( uminus_uminus_real @ A ) @ B )
% 5.31/5.63 = ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % dvd_neg_div
% 5.31/5.63 thf(fact_7664_dvd__neg__div,axiom,
% 5.31/5.63 ! [B: complex,A: complex] :
% 5.31/5.63 ( ( dvd_dvd_complex @ B @ A )
% 5.31/5.63 => ( ( divide1717551699836669952omplex @ ( uminus1482373934393186551omplex @ A ) @ B )
% 5.31/5.63 = ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % dvd_neg_div
% 5.31/5.63 thf(fact_7665_dvd__neg__div,axiom,
% 5.31/5.63 ! [B: code_integer,A: code_integer] :
% 5.31/5.63 ( ( dvd_dvd_Code_integer @ B @ A )
% 5.31/5.63 => ( ( divide6298287555418463151nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 5.31/5.63 = ( uminus1351360451143612070nteger @ ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % dvd_neg_div
% 5.31/5.63 thf(fact_7666_dvd__neg__div,axiom,
% 5.31/5.63 ! [B: rat,A: rat] :
% 5.31/5.63 ( ( dvd_dvd_rat @ B @ A )
% 5.31/5.63 => ( ( divide_divide_rat @ ( uminus_uminus_rat @ A ) @ B )
% 5.31/5.63 = ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % dvd_neg_div
% 5.31/5.63 thf(fact_7667_dvd__div__neg,axiom,
% 5.31/5.63 ! [B: int,A: int] :
% 5.31/5.63 ( ( dvd_dvd_int @ B @ A )
% 5.31/5.63 => ( ( divide_divide_int @ A @ ( uminus_uminus_int @ B ) )
% 5.31/5.63 = ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % dvd_div_neg
% 5.31/5.63 thf(fact_7668_dvd__div__neg,axiom,
% 5.31/5.63 ! [B: real,A: real] :
% 5.31/5.63 ( ( dvd_dvd_real @ B @ A )
% 5.31/5.63 => ( ( divide_divide_real @ A @ ( uminus_uminus_real @ B ) )
% 5.31/5.63 = ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % dvd_div_neg
% 5.31/5.63 thf(fact_7669_dvd__div__neg,axiom,
% 5.31/5.63 ! [B: complex,A: complex] :
% 5.31/5.63 ( ( dvd_dvd_complex @ B @ A )
% 5.31/5.63 => ( ( divide1717551699836669952omplex @ A @ ( uminus1482373934393186551omplex @ B ) )
% 5.31/5.63 = ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % dvd_div_neg
% 5.31/5.63 thf(fact_7670_dvd__div__neg,axiom,
% 5.31/5.63 ! [B: code_integer,A: code_integer] :
% 5.31/5.63 ( ( dvd_dvd_Code_integer @ B @ A )
% 5.31/5.63 => ( ( divide6298287555418463151nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 5.31/5.63 = ( uminus1351360451143612070nteger @ ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % dvd_div_neg
% 5.31/5.63 thf(fact_7671_dvd__div__neg,axiom,
% 5.31/5.63 ! [B: rat,A: rat] :
% 5.31/5.63 ( ( dvd_dvd_rat @ B @ A )
% 5.31/5.63 => ( ( divide_divide_rat @ A @ ( uminus_uminus_rat @ B ) )
% 5.31/5.63 = ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % dvd_div_neg
% 5.31/5.63 thf(fact_7672_fact__dvd,axiom,
% 5.31/5.63 ! [N: nat,M2: nat] :
% 5.31/5.63 ( ( ord_less_eq_nat @ N @ M2 )
% 5.31/5.63 => ( dvd_dvd_int @ ( semiri1406184849735516958ct_int @ N ) @ ( semiri1406184849735516958ct_int @ M2 ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % fact_dvd
% 5.31/5.63 thf(fact_7673_fact__dvd,axiom,
% 5.31/5.63 ! [N: nat,M2: nat] :
% 5.31/5.63 ( ( ord_less_eq_nat @ N @ M2 )
% 5.31/5.63 => ( dvd_dvd_nat @ ( semiri1408675320244567234ct_nat @ N ) @ ( semiri1408675320244567234ct_nat @ M2 ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % fact_dvd
% 5.31/5.63 thf(fact_7674_fact__dvd,axiom,
% 5.31/5.63 ! [N: nat,M2: nat] :
% 5.31/5.63 ( ( ord_less_eq_nat @ N @ M2 )
% 5.31/5.63 => ( dvd_dvd_real @ ( semiri2265585572941072030t_real @ N ) @ ( semiri2265585572941072030t_real @ M2 ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % fact_dvd
% 5.31/5.63 thf(fact_7675_real__minus__mult__self__le,axiom,
% 5.31/5.63 ! [U: real,X: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( times_times_real @ U @ U ) ) @ ( times_times_real @ X @ X ) ) ).
% 5.31/5.63
% 5.31/5.63 % real_minus_mult_self_le
% 5.31/5.63 thf(fact_7676_int__of__nat__induct,axiom,
% 5.31/5.63 ! [P2: int > $o,Z3: int] :
% 5.31/5.63 ( ! [N3: nat] : ( P2 @ ( semiri1314217659103216013at_int @ N3 ) )
% 5.31/5.63 => ( ! [N3: nat] : ( P2 @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N3 ) ) ) )
% 5.31/5.63 => ( P2 @ Z3 ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % int_of_nat_induct
% 5.31/5.63 thf(fact_7677_int__cases,axiom,
% 5.31/5.63 ! [Z3: int] :
% 5.31/5.63 ( ! [N3: nat] :
% 5.31/5.63 ( Z3
% 5.31/5.63 != ( semiri1314217659103216013at_int @ N3 ) )
% 5.31/5.63 => ~ ! [N3: nat] :
% 5.31/5.63 ( Z3
% 5.31/5.63 != ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N3 ) ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % int_cases
% 5.31/5.63 thf(fact_7678_zmult__eq__1__iff,axiom,
% 5.31/5.63 ! [M2: int,N: int] :
% 5.31/5.63 ( ( ( times_times_int @ M2 @ N )
% 5.31/5.63 = one_one_int )
% 5.31/5.63 = ( ( ( M2 = one_one_int )
% 5.31/5.63 & ( N = one_one_int ) )
% 5.31/5.63 | ( ( M2
% 5.31/5.63 = ( uminus_uminus_int @ one_one_int ) )
% 5.31/5.63 & ( N
% 5.31/5.63 = ( uminus_uminus_int @ one_one_int ) ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % zmult_eq_1_iff
% 5.31/5.63 thf(fact_7679_pos__zmult__eq__1__iff__lemma,axiom,
% 5.31/5.63 ! [M2: int,N: int] :
% 5.31/5.63 ( ( ( times_times_int @ M2 @ N )
% 5.31/5.63 = one_one_int )
% 5.31/5.63 => ( ( M2 = one_one_int )
% 5.31/5.63 | ( M2
% 5.31/5.63 = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % pos_zmult_eq_1_iff_lemma
% 5.31/5.63 thf(fact_7680_zmod__zminus1__not__zero,axiom,
% 5.31/5.63 ! [K2: int,L: int] :
% 5.31/5.63 ( ( ( modulo_modulo_int @ ( uminus_uminus_int @ K2 ) @ L )
% 5.31/5.63 != zero_zero_int )
% 5.31/5.63 => ( ( modulo_modulo_int @ K2 @ L )
% 5.31/5.63 != zero_zero_int ) ) ).
% 5.31/5.63
% 5.31/5.63 % zmod_zminus1_not_zero
% 5.31/5.63 thf(fact_7681_zmod__zminus2__not__zero,axiom,
% 5.31/5.63 ! [K2: int,L: int] :
% 5.31/5.63 ( ( ( modulo_modulo_int @ K2 @ ( uminus_uminus_int @ L ) )
% 5.31/5.63 != zero_zero_int )
% 5.31/5.63 => ( ( modulo_modulo_int @ K2 @ L )
% 5.31/5.63 != zero_zero_int ) ) ).
% 5.31/5.63
% 5.31/5.63 % zmod_zminus2_not_zero
% 5.31/5.63 thf(fact_7682_pochhammer__same,axiom,
% 5.31/5.63 ! [N: nat] :
% 5.31/5.63 ( ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ N ) ) @ N )
% 5.31/5.63 = ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) @ ( semiri5044797733671781792omplex @ N ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % pochhammer_same
% 5.31/5.63 thf(fact_7683_pochhammer__same,axiom,
% 5.31/5.63 ! [N: nat] :
% 5.31/5.63 ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ ( semiri4939895301339042750nteger @ N ) ) @ N )
% 5.31/5.63 = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N ) @ ( semiri3624122377584611663nteger @ N ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % pochhammer_same
% 5.31/5.63 thf(fact_7684_pochhammer__same,axiom,
% 5.31/5.63 ! [N: nat] :
% 5.31/5.63 ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ N ) ) @ N )
% 5.31/5.63 = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N ) @ ( semiri773545260158071498ct_rat @ N ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % pochhammer_same
% 5.31/5.63 thf(fact_7685_pochhammer__same,axiom,
% 5.31/5.63 ! [N: nat] :
% 5.31/5.63 ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) @ N )
% 5.31/5.63 = ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N ) @ ( semiri1406184849735516958ct_int @ N ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % pochhammer_same
% 5.31/5.63 thf(fact_7686_pochhammer__same,axiom,
% 5.31/5.63 ! [N: nat] :
% 5.31/5.63 ( ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N ) ) @ N )
% 5.31/5.63 = ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) @ ( semiri2265585572941072030t_real @ N ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % pochhammer_same
% 5.31/5.63 thf(fact_7687_fact__ge__Suc__0__nat,axiom,
% 5.31/5.63 ! [N: nat] : ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( semiri1408675320244567234ct_nat @ N ) ) ).
% 5.31/5.63
% 5.31/5.63 % fact_ge_Suc_0_nat
% 5.31/5.63 thf(fact_7688_dvd__fact,axiom,
% 5.31/5.63 ! [M2: nat,N: nat] :
% 5.31/5.63 ( ( ord_less_eq_nat @ one_one_nat @ M2 )
% 5.31/5.63 => ( ( ord_less_eq_nat @ M2 @ N )
% 5.31/5.63 => ( dvd_dvd_nat @ M2 @ ( semiri1408675320244567234ct_nat @ N ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % dvd_fact
% 5.31/5.63 thf(fact_7689_not__zero__le__neg__numeral,axiom,
% 5.31/5.63 ! [N: num] :
% 5.31/5.63 ~ ( ord_less_eq_real @ zero_zero_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % not_zero_le_neg_numeral
% 5.31/5.63 thf(fact_7690_not__zero__le__neg__numeral,axiom,
% 5.31/5.63 ! [N: num] :
% 5.31/5.63 ~ ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % not_zero_le_neg_numeral
% 5.31/5.63 thf(fact_7691_not__zero__le__neg__numeral,axiom,
% 5.31/5.63 ! [N: num] :
% 5.31/5.63 ~ ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % not_zero_le_neg_numeral
% 5.31/5.63 thf(fact_7692_not__zero__le__neg__numeral,axiom,
% 5.31/5.63 ! [N: num] :
% 5.31/5.63 ~ ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % not_zero_le_neg_numeral
% 5.31/5.63 thf(fact_7693_neg__numeral__le__zero,axiom,
% 5.31/5.63 ! [N: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) @ zero_zero_real ) ).
% 5.31/5.63
% 5.31/5.63 % neg_numeral_le_zero
% 5.31/5.63 thf(fact_7694_neg__numeral__le__zero,axiom,
% 5.31/5.63 ! [N: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) @ zero_z3403309356797280102nteger ) ).
% 5.31/5.63
% 5.31/5.63 % neg_numeral_le_zero
% 5.31/5.63 thf(fact_7695_neg__numeral__le__zero,axiom,
% 5.31/5.63 ! [N: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) @ zero_zero_rat ) ).
% 5.31/5.63
% 5.31/5.63 % neg_numeral_le_zero
% 5.31/5.63 thf(fact_7696_neg__numeral__le__zero,axiom,
% 5.31/5.63 ! [N: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) @ zero_zero_int ) ).
% 5.31/5.63
% 5.31/5.63 % neg_numeral_le_zero
% 5.31/5.63 thf(fact_7697_not__zero__less__neg__numeral,axiom,
% 5.31/5.63 ! [N: num] :
% 5.31/5.63 ~ ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % not_zero_less_neg_numeral
% 5.31/5.63 thf(fact_7698_not__zero__less__neg__numeral,axiom,
% 5.31/5.63 ! [N: num] :
% 5.31/5.63 ~ ( ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % not_zero_less_neg_numeral
% 5.31/5.63 thf(fact_7699_not__zero__less__neg__numeral,axiom,
% 5.31/5.63 ! [N: num] :
% 5.31/5.63 ~ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % not_zero_less_neg_numeral
% 5.31/5.63 thf(fact_7700_not__zero__less__neg__numeral,axiom,
% 5.31/5.63 ! [N: num] :
% 5.31/5.63 ~ ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % not_zero_less_neg_numeral
% 5.31/5.63 thf(fact_7701_neg__numeral__less__zero,axiom,
% 5.31/5.63 ! [N: num] : ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) @ zero_zero_int ) ).
% 5.31/5.63
% 5.31/5.63 % neg_numeral_less_zero
% 5.31/5.63 thf(fact_7702_neg__numeral__less__zero,axiom,
% 5.31/5.63 ! [N: num] : ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) @ zero_zero_real ) ).
% 5.31/5.63
% 5.31/5.63 % neg_numeral_less_zero
% 5.31/5.63 thf(fact_7703_neg__numeral__less__zero,axiom,
% 5.31/5.63 ! [N: num] : ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) @ zero_z3403309356797280102nteger ) ).
% 5.31/5.63
% 5.31/5.63 % neg_numeral_less_zero
% 5.31/5.63 thf(fact_7704_neg__numeral__less__zero,axiom,
% 5.31/5.63 ! [N: num] : ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) @ zero_zero_rat ) ).
% 5.31/5.63
% 5.31/5.63 % neg_numeral_less_zero
% 5.31/5.63 thf(fact_7705_le__minus__one__simps_I1_J,axiom,
% 5.31/5.63 ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ zero_zero_real ).
% 5.31/5.63
% 5.31/5.63 % le_minus_one_simps(1)
% 5.31/5.63 thf(fact_7706_le__minus__one__simps_I1_J,axiom,
% 5.31/5.63 ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ zero_z3403309356797280102nteger ).
% 5.31/5.63
% 5.31/5.63 % le_minus_one_simps(1)
% 5.31/5.63 thf(fact_7707_le__minus__one__simps_I1_J,axiom,
% 5.31/5.63 ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ zero_zero_rat ).
% 5.31/5.63
% 5.31/5.63 % le_minus_one_simps(1)
% 5.31/5.63 thf(fact_7708_le__minus__one__simps_I1_J,axiom,
% 5.31/5.63 ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ zero_zero_int ).
% 5.31/5.63
% 5.31/5.63 % le_minus_one_simps(1)
% 5.31/5.63 thf(fact_7709_le__minus__one__simps_I3_J,axiom,
% 5.31/5.63 ~ ( ord_less_eq_real @ zero_zero_real @ ( uminus_uminus_real @ one_one_real ) ) ).
% 5.31/5.63
% 5.31/5.63 % le_minus_one_simps(3)
% 5.31/5.63 thf(fact_7710_le__minus__one__simps_I3_J,axiom,
% 5.31/5.63 ~ ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.31/5.63
% 5.31/5.63 % le_minus_one_simps(3)
% 5.31/5.63 thf(fact_7711_le__minus__one__simps_I3_J,axiom,
% 5.31/5.63 ~ ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.31/5.63
% 5.31/5.63 % le_minus_one_simps(3)
% 5.31/5.63 thf(fact_7712_le__minus__one__simps_I3_J,axiom,
% 5.31/5.63 ~ ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 5.31/5.63
% 5.31/5.63 % le_minus_one_simps(3)
% 5.31/5.63 thf(fact_7713_less__minus__one__simps_I1_J,axiom,
% 5.31/5.63 ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ zero_zero_int ).
% 5.31/5.63
% 5.31/5.63 % less_minus_one_simps(1)
% 5.31/5.63 thf(fact_7714_less__minus__one__simps_I1_J,axiom,
% 5.31/5.63 ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ zero_zero_real ).
% 5.31/5.63
% 5.31/5.63 % less_minus_one_simps(1)
% 5.31/5.63 thf(fact_7715_less__minus__one__simps_I1_J,axiom,
% 5.31/5.63 ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ zero_z3403309356797280102nteger ).
% 5.31/5.63
% 5.31/5.63 % less_minus_one_simps(1)
% 5.31/5.63 thf(fact_7716_less__minus__one__simps_I1_J,axiom,
% 5.31/5.63 ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ zero_zero_rat ).
% 5.31/5.63
% 5.31/5.63 % less_minus_one_simps(1)
% 5.31/5.63 thf(fact_7717_less__minus__one__simps_I3_J,axiom,
% 5.31/5.63 ~ ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 5.31/5.63
% 5.31/5.63 % less_minus_one_simps(3)
% 5.31/5.63 thf(fact_7718_less__minus__one__simps_I3_J,axiom,
% 5.31/5.63 ~ ( ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ one_one_real ) ) ).
% 5.31/5.63
% 5.31/5.63 % less_minus_one_simps(3)
% 5.31/5.63 thf(fact_7719_less__minus__one__simps_I3_J,axiom,
% 5.31/5.63 ~ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.31/5.63
% 5.31/5.63 % less_minus_one_simps(3)
% 5.31/5.63 thf(fact_7720_less__minus__one__simps_I3_J,axiom,
% 5.31/5.63 ~ ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.31/5.63
% 5.31/5.63 % less_minus_one_simps(3)
% 5.31/5.63 thf(fact_7721_not__one__le__neg__numeral,axiom,
% 5.31/5.63 ! [M2: num] :
% 5.31/5.63 ~ ( ord_less_eq_real @ one_one_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M2 ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % not_one_le_neg_numeral
% 5.31/5.63 thf(fact_7722_not__one__le__neg__numeral,axiom,
% 5.31/5.63 ! [M2: num] :
% 5.31/5.63 ~ ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M2 ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % not_one_le_neg_numeral
% 5.31/5.63 thf(fact_7723_not__one__le__neg__numeral,axiom,
% 5.31/5.63 ! [M2: num] :
% 5.31/5.63 ~ ( ord_less_eq_rat @ one_one_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M2 ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % not_one_le_neg_numeral
% 5.31/5.63 thf(fact_7724_not__one__le__neg__numeral,axiom,
% 5.31/5.63 ! [M2: num] :
% 5.31/5.63 ~ ( ord_less_eq_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % not_one_le_neg_numeral
% 5.31/5.63 thf(fact_7725_not__numeral__le__neg__one,axiom,
% 5.31/5.63 ! [M2: num] :
% 5.31/5.63 ~ ( ord_less_eq_real @ ( numeral_numeral_real @ M2 ) @ ( uminus_uminus_real @ one_one_real ) ) ).
% 5.31/5.63
% 5.31/5.63 % not_numeral_le_neg_one
% 5.31/5.63 thf(fact_7726_not__numeral__le__neg__one,axiom,
% 5.31/5.63 ! [M2: num] :
% 5.31/5.63 ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ M2 ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.31/5.63
% 5.31/5.63 % not_numeral_le_neg_one
% 5.31/5.63 thf(fact_7727_not__numeral__le__neg__one,axiom,
% 5.31/5.63 ! [M2: num] :
% 5.31/5.63 ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ M2 ) @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.31/5.63
% 5.31/5.63 % not_numeral_le_neg_one
% 5.31/5.63 thf(fact_7728_not__numeral__le__neg__one,axiom,
% 5.31/5.63 ! [M2: num] :
% 5.31/5.63 ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M2 ) @ ( uminus_uminus_int @ one_one_int ) ) ).
% 5.31/5.63
% 5.31/5.63 % not_numeral_le_neg_one
% 5.31/5.63 thf(fact_7729_neg__numeral__le__neg__one,axiom,
% 5.31/5.63 ! [M2: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M2 ) ) @ ( uminus_uminus_real @ one_one_real ) ) ).
% 5.31/5.63
% 5.31/5.63 % neg_numeral_le_neg_one
% 5.31/5.63 thf(fact_7730_neg__numeral__le__neg__one,axiom,
% 5.31/5.63 ! [M2: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M2 ) ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.31/5.63
% 5.31/5.63 % neg_numeral_le_neg_one
% 5.31/5.63 thf(fact_7731_neg__numeral__le__neg__one,axiom,
% 5.31/5.63 ! [M2: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M2 ) ) @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.31/5.63
% 5.31/5.63 % neg_numeral_le_neg_one
% 5.31/5.63 thf(fact_7732_neg__numeral__le__neg__one,axiom,
% 5.31/5.63 ! [M2: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ ( uminus_uminus_int @ one_one_int ) ) ).
% 5.31/5.63
% 5.31/5.63 % neg_numeral_le_neg_one
% 5.31/5.63 thf(fact_7733_neg__one__le__numeral,axiom,
% 5.31/5.63 ! [M2: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ ( numeral_numeral_real @ M2 ) ) ).
% 5.31/5.63
% 5.31/5.63 % neg_one_le_numeral
% 5.31/5.63 thf(fact_7734_neg__one__le__numeral,axiom,
% 5.31/5.63 ! [M2: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ M2 ) ) ).
% 5.31/5.63
% 5.31/5.63 % neg_one_le_numeral
% 5.31/5.63 thf(fact_7735_neg__one__le__numeral,axiom,
% 5.31/5.63 ! [M2: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( numeral_numeral_rat @ M2 ) ) ).
% 5.31/5.63
% 5.31/5.63 % neg_one_le_numeral
% 5.31/5.63 thf(fact_7736_neg__one__le__numeral,axiom,
% 5.31/5.63 ! [M2: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ M2 ) ) ).
% 5.31/5.63
% 5.31/5.63 % neg_one_le_numeral
% 5.31/5.63 thf(fact_7737_neg__numeral__le__one,axiom,
% 5.31/5.63 ! [M2: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M2 ) ) @ one_one_real ) ).
% 5.31/5.63
% 5.31/5.63 % neg_numeral_le_one
% 5.31/5.63 thf(fact_7738_neg__numeral__le__one,axiom,
% 5.31/5.63 ! [M2: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M2 ) ) @ one_one_Code_integer ) ).
% 5.31/5.63
% 5.31/5.63 % neg_numeral_le_one
% 5.31/5.63 thf(fact_7739_neg__numeral__le__one,axiom,
% 5.31/5.63 ! [M2: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M2 ) ) @ one_one_rat ) ).
% 5.31/5.63
% 5.31/5.63 % neg_numeral_le_one
% 5.31/5.63 thf(fact_7740_neg__numeral__le__one,axiom,
% 5.31/5.63 ! [M2: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ one_one_int ) ).
% 5.31/5.63
% 5.31/5.63 % neg_numeral_le_one
% 5.31/5.63 thf(fact_7741_gbinomial__pochhammer,axiom,
% 5.31/5.63 ( gbinomial_complex
% 5.31/5.63 = ( ^ [A5: complex,K3: nat] : ( divide1717551699836669952omplex @ ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ K3 ) @ ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ A5 ) @ K3 ) ) @ ( semiri5044797733671781792omplex @ K3 ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % gbinomial_pochhammer
% 5.31/5.63 thf(fact_7742_gbinomial__pochhammer,axiom,
% 5.31/5.63 ( gbinomial_rat
% 5.31/5.63 = ( ^ [A5: rat,K3: nat] : ( divide_divide_rat @ ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ K3 ) @ ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ A5 ) @ K3 ) ) @ ( semiri773545260158071498ct_rat @ K3 ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % gbinomial_pochhammer
% 5.31/5.63 thf(fact_7743_gbinomial__pochhammer,axiom,
% 5.31/5.63 ( gbinomial_real
% 5.31/5.63 = ( ^ [A5: real,K3: nat] : ( divide_divide_real @ ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K3 ) @ ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ A5 ) @ K3 ) ) @ ( semiri2265585572941072030t_real @ K3 ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % gbinomial_pochhammer
% 5.31/5.63 thf(fact_7744_neg__numeral__less__one,axiom,
% 5.31/5.63 ! [M2: num] : ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ one_one_int ) ).
% 5.31/5.63
% 5.31/5.63 % neg_numeral_less_one
% 5.31/5.63 thf(fact_7745_neg__numeral__less__one,axiom,
% 5.31/5.63 ! [M2: num] : ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M2 ) ) @ one_one_real ) ).
% 5.31/5.63
% 5.31/5.63 % neg_numeral_less_one
% 5.31/5.63 thf(fact_7746_neg__numeral__less__one,axiom,
% 5.31/5.63 ! [M2: num] : ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M2 ) ) @ one_one_Code_integer ) ).
% 5.31/5.63
% 5.31/5.63 % neg_numeral_less_one
% 5.31/5.63 thf(fact_7747_neg__numeral__less__one,axiom,
% 5.31/5.63 ! [M2: num] : ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M2 ) ) @ one_one_rat ) ).
% 5.31/5.63
% 5.31/5.63 % neg_numeral_less_one
% 5.31/5.63 thf(fact_7748_neg__one__less__numeral,axiom,
% 5.31/5.63 ! [M2: num] : ( ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ M2 ) ) ).
% 5.31/5.63
% 5.31/5.63 % neg_one_less_numeral
% 5.31/5.63 thf(fact_7749_neg__one__less__numeral,axiom,
% 5.31/5.63 ! [M2: num] : ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ ( numeral_numeral_real @ M2 ) ) ).
% 5.31/5.63
% 5.31/5.63 % neg_one_less_numeral
% 5.31/5.63 thf(fact_7750_neg__one__less__numeral,axiom,
% 5.31/5.63 ! [M2: num] : ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ M2 ) ) ).
% 5.31/5.63
% 5.31/5.63 % neg_one_less_numeral
% 5.31/5.63 thf(fact_7751_neg__one__less__numeral,axiom,
% 5.31/5.63 ! [M2: num] : ( ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( numeral_numeral_rat @ M2 ) ) ).
% 5.31/5.63
% 5.31/5.63 % neg_one_less_numeral
% 5.31/5.63 thf(fact_7752_not__numeral__less__neg__one,axiom,
% 5.31/5.63 ! [M2: num] :
% 5.31/5.63 ~ ( ord_less_int @ ( numeral_numeral_int @ M2 ) @ ( uminus_uminus_int @ one_one_int ) ) ).
% 5.31/5.63
% 5.31/5.63 % not_numeral_less_neg_one
% 5.31/5.63 thf(fact_7753_not__numeral__less__neg__one,axiom,
% 5.31/5.63 ! [M2: num] :
% 5.31/5.63 ~ ( ord_less_real @ ( numeral_numeral_real @ M2 ) @ ( uminus_uminus_real @ one_one_real ) ) ).
% 5.31/5.63
% 5.31/5.63 % not_numeral_less_neg_one
% 5.31/5.63 thf(fact_7754_not__numeral__less__neg__one,axiom,
% 5.31/5.63 ! [M2: num] :
% 5.31/5.63 ~ ( ord_le6747313008572928689nteger @ ( numera6620942414471956472nteger @ M2 ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.31/5.63
% 5.31/5.63 % not_numeral_less_neg_one
% 5.31/5.63 thf(fact_7755_not__numeral__less__neg__one,axiom,
% 5.31/5.63 ! [M2: num] :
% 5.31/5.63 ~ ( ord_less_rat @ ( numeral_numeral_rat @ M2 ) @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.31/5.63
% 5.31/5.63 % not_numeral_less_neg_one
% 5.31/5.63 thf(fact_7756_not__one__less__neg__numeral,axiom,
% 5.31/5.63 ! [M2: num] :
% 5.31/5.63 ~ ( ord_less_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % not_one_less_neg_numeral
% 5.31/5.63 thf(fact_7757_not__one__less__neg__numeral,axiom,
% 5.31/5.63 ! [M2: num] :
% 5.31/5.63 ~ ( ord_less_real @ one_one_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M2 ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % not_one_less_neg_numeral
% 5.31/5.63 thf(fact_7758_not__one__less__neg__numeral,axiom,
% 5.31/5.63 ! [M2: num] :
% 5.31/5.63 ~ ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M2 ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % not_one_less_neg_numeral
% 5.31/5.63 thf(fact_7759_not__one__less__neg__numeral,axiom,
% 5.31/5.63 ! [M2: num] :
% 5.31/5.63 ~ ( ord_less_rat @ one_one_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M2 ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % not_one_less_neg_numeral
% 5.31/5.63 thf(fact_7760_not__neg__one__less__neg__numeral,axiom,
% 5.31/5.63 ! [M2: num] :
% 5.31/5.63 ~ ( ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % not_neg_one_less_neg_numeral
% 5.31/5.63 thf(fact_7761_not__neg__one__less__neg__numeral,axiom,
% 5.31/5.63 ! [M2: num] :
% 5.31/5.63 ~ ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ M2 ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % not_neg_one_less_neg_numeral
% 5.31/5.63 thf(fact_7762_not__neg__one__less__neg__numeral,axiom,
% 5.31/5.63 ! [M2: num] :
% 5.31/5.63 ~ ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M2 ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % not_neg_one_less_neg_numeral
% 5.31/5.63 thf(fact_7763_not__neg__one__less__neg__numeral,axiom,
% 5.31/5.63 ! [M2: num] :
% 5.31/5.63 ~ ( ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M2 ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % not_neg_one_less_neg_numeral
% 5.31/5.63 thf(fact_7764_eq__minus__divide__eq,axiom,
% 5.31/5.63 ! [A: real,B: real,C2: real] :
% 5.31/5.63 ( ( A
% 5.31/5.63 = ( uminus_uminus_real @ ( divide_divide_real @ B @ C2 ) ) )
% 5.31/5.63 = ( ( ( C2 != zero_zero_real )
% 5.31/5.63 => ( ( times_times_real @ A @ C2 )
% 5.31/5.63 = ( uminus_uminus_real @ B ) ) )
% 5.31/5.63 & ( ( C2 = zero_zero_real )
% 5.31/5.63 => ( A = zero_zero_real ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % eq_minus_divide_eq
% 5.31/5.63 thf(fact_7765_eq__minus__divide__eq,axiom,
% 5.31/5.63 ! [A: complex,B: complex,C2: complex] :
% 5.31/5.63 ( ( A
% 5.31/5.63 = ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ B @ C2 ) ) )
% 5.31/5.63 = ( ( ( C2 != zero_zero_complex )
% 5.31/5.63 => ( ( times_times_complex @ A @ C2 )
% 5.31/5.63 = ( uminus1482373934393186551omplex @ B ) ) )
% 5.31/5.63 & ( ( C2 = zero_zero_complex )
% 5.31/5.63 => ( A = zero_zero_complex ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % eq_minus_divide_eq
% 5.31/5.63 thf(fact_7766_eq__minus__divide__eq,axiom,
% 5.31/5.63 ! [A: rat,B: rat,C2: rat] :
% 5.31/5.63 ( ( A
% 5.31/5.63 = ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C2 ) ) )
% 5.31/5.63 = ( ( ( C2 != zero_zero_rat )
% 5.31/5.63 => ( ( times_times_rat @ A @ C2 )
% 5.31/5.63 = ( uminus_uminus_rat @ B ) ) )
% 5.31/5.63 & ( ( C2 = zero_zero_rat )
% 5.31/5.63 => ( A = zero_zero_rat ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % eq_minus_divide_eq
% 5.31/5.63 thf(fact_7767_minus__divide__eq__eq,axiom,
% 5.31/5.63 ! [B: real,C2: real,A: real] :
% 5.31/5.63 ( ( ( uminus_uminus_real @ ( divide_divide_real @ B @ C2 ) )
% 5.31/5.63 = A )
% 5.31/5.63 = ( ( ( C2 != zero_zero_real )
% 5.31/5.63 => ( ( uminus_uminus_real @ B )
% 5.31/5.63 = ( times_times_real @ A @ C2 ) ) )
% 5.31/5.63 & ( ( C2 = zero_zero_real )
% 5.31/5.63 => ( A = zero_zero_real ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % minus_divide_eq_eq
% 5.31/5.63 thf(fact_7768_minus__divide__eq__eq,axiom,
% 5.31/5.63 ! [B: complex,C2: complex,A: complex] :
% 5.31/5.63 ( ( ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ B @ C2 ) )
% 5.31/5.63 = A )
% 5.31/5.63 = ( ( ( C2 != zero_zero_complex )
% 5.31/5.63 => ( ( uminus1482373934393186551omplex @ B )
% 5.31/5.63 = ( times_times_complex @ A @ C2 ) ) )
% 5.31/5.63 & ( ( C2 = zero_zero_complex )
% 5.31/5.63 => ( A = zero_zero_complex ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % minus_divide_eq_eq
% 5.31/5.63 thf(fact_7769_minus__divide__eq__eq,axiom,
% 5.31/5.63 ! [B: rat,C2: rat,A: rat] :
% 5.31/5.63 ( ( ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C2 ) )
% 5.31/5.63 = A )
% 5.31/5.63 = ( ( ( C2 != zero_zero_rat )
% 5.31/5.63 => ( ( uminus_uminus_rat @ B )
% 5.31/5.63 = ( times_times_rat @ A @ C2 ) ) )
% 5.31/5.63 & ( ( C2 = zero_zero_rat )
% 5.31/5.63 => ( A = zero_zero_rat ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % minus_divide_eq_eq
% 5.31/5.63 thf(fact_7770_nonzero__neg__divide__eq__eq,axiom,
% 5.31/5.63 ! [B: real,A: real,C2: real] :
% 5.31/5.63 ( ( B != zero_zero_real )
% 5.31/5.63 => ( ( ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) )
% 5.31/5.63 = C2 )
% 5.31/5.63 = ( ( uminus_uminus_real @ A )
% 5.31/5.63 = ( times_times_real @ C2 @ B ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % nonzero_neg_divide_eq_eq
% 5.31/5.63 thf(fact_7771_nonzero__neg__divide__eq__eq,axiom,
% 5.31/5.63 ! [B: complex,A: complex,C2: complex] :
% 5.31/5.63 ( ( B != zero_zero_complex )
% 5.31/5.63 => ( ( ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 5.31/5.63 = C2 )
% 5.31/5.63 = ( ( uminus1482373934393186551omplex @ A )
% 5.31/5.63 = ( times_times_complex @ C2 @ B ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % nonzero_neg_divide_eq_eq
% 5.31/5.63 thf(fact_7772_nonzero__neg__divide__eq__eq,axiom,
% 5.31/5.63 ! [B: rat,A: rat,C2: rat] :
% 5.31/5.63 ( ( B != zero_zero_rat )
% 5.31/5.63 => ( ( ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) )
% 5.31/5.63 = C2 )
% 5.31/5.63 = ( ( uminus_uminus_rat @ A )
% 5.31/5.63 = ( times_times_rat @ C2 @ B ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % nonzero_neg_divide_eq_eq
% 5.31/5.63 thf(fact_7773_nonzero__neg__divide__eq__eq2,axiom,
% 5.31/5.63 ! [B: real,C2: real,A: real] :
% 5.31/5.63 ( ( B != zero_zero_real )
% 5.31/5.63 => ( ( C2
% 5.31/5.63 = ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) ) )
% 5.31/5.63 = ( ( times_times_real @ C2 @ B )
% 5.31/5.63 = ( uminus_uminus_real @ A ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % nonzero_neg_divide_eq_eq2
% 5.31/5.63 thf(fact_7774_nonzero__neg__divide__eq__eq2,axiom,
% 5.31/5.63 ! [B: complex,C2: complex,A: complex] :
% 5.31/5.63 ( ( B != zero_zero_complex )
% 5.31/5.63 => ( ( C2
% 5.31/5.63 = ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 5.31/5.63 = ( ( times_times_complex @ C2 @ B )
% 5.31/5.63 = ( uminus1482373934393186551omplex @ A ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % nonzero_neg_divide_eq_eq2
% 5.31/5.63 thf(fact_7775_nonzero__neg__divide__eq__eq2,axiom,
% 5.31/5.63 ! [B: rat,C2: rat,A: rat] :
% 5.31/5.63 ( ( B != zero_zero_rat )
% 5.31/5.63 => ( ( C2
% 5.31/5.63 = ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) ) )
% 5.31/5.63 = ( ( times_times_rat @ C2 @ B )
% 5.31/5.63 = ( uminus_uminus_rat @ A ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % nonzero_neg_divide_eq_eq2
% 5.31/5.63 thf(fact_7776_mult__1s__ring__1_I1_J,axiom,
% 5.31/5.63 ! [B: int] :
% 5.31/5.63 ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ one ) ) @ B )
% 5.31/5.63 = ( uminus_uminus_int @ B ) ) ).
% 5.31/5.63
% 5.31/5.63 % mult_1s_ring_1(1)
% 5.31/5.63 thf(fact_7777_mult__1s__ring__1_I1_J,axiom,
% 5.31/5.63 ! [B: real] :
% 5.31/5.63 ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ one ) ) @ B )
% 5.31/5.63 = ( uminus_uminus_real @ B ) ) ).
% 5.31/5.63
% 5.31/5.63 % mult_1s_ring_1(1)
% 5.31/5.63 thf(fact_7778_mult__1s__ring__1_I1_J,axiom,
% 5.31/5.63 ! [B: complex] :
% 5.31/5.63 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ one ) ) @ B )
% 5.31/5.63 = ( uminus1482373934393186551omplex @ B ) ) ).
% 5.31/5.63
% 5.31/5.63 % mult_1s_ring_1(1)
% 5.31/5.63 thf(fact_7779_mult__1s__ring__1_I1_J,axiom,
% 5.31/5.63 ! [B: code_integer] :
% 5.31/5.63 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ one ) ) @ B )
% 5.31/5.63 = ( uminus1351360451143612070nteger @ B ) ) ).
% 5.31/5.63
% 5.31/5.63 % mult_1s_ring_1(1)
% 5.31/5.63 thf(fact_7780_mult__1s__ring__1_I1_J,axiom,
% 5.31/5.63 ! [B: rat] :
% 5.31/5.63 ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ one ) ) @ B )
% 5.31/5.63 = ( uminus_uminus_rat @ B ) ) ).
% 5.31/5.63
% 5.31/5.63 % mult_1s_ring_1(1)
% 5.31/5.63 thf(fact_7781_mult__1s__ring__1_I2_J,axiom,
% 5.31/5.63 ! [B: int] :
% 5.31/5.63 ( ( times_times_int @ B @ ( uminus_uminus_int @ ( numeral_numeral_int @ one ) ) )
% 5.31/5.63 = ( uminus_uminus_int @ B ) ) ).
% 5.31/5.63
% 5.31/5.63 % mult_1s_ring_1(2)
% 5.31/5.63 thf(fact_7782_mult__1s__ring__1_I2_J,axiom,
% 5.31/5.63 ! [B: real] :
% 5.31/5.63 ( ( times_times_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ one ) ) )
% 5.31/5.63 = ( uminus_uminus_real @ B ) ) ).
% 5.31/5.63
% 5.31/5.63 % mult_1s_ring_1(2)
% 5.31/5.63 thf(fact_7783_mult__1s__ring__1_I2_J,axiom,
% 5.31/5.63 ! [B: complex] :
% 5.31/5.63 ( ( times_times_complex @ B @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ one ) ) )
% 5.31/5.63 = ( uminus1482373934393186551omplex @ B ) ) ).
% 5.31/5.63
% 5.31/5.63 % mult_1s_ring_1(2)
% 5.31/5.63 thf(fact_7784_mult__1s__ring__1_I2_J,axiom,
% 5.31/5.63 ! [B: code_integer] :
% 5.31/5.63 ( ( times_3573771949741848930nteger @ B @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ one ) ) )
% 5.31/5.63 = ( uminus1351360451143612070nteger @ B ) ) ).
% 5.31/5.63
% 5.31/5.63 % mult_1s_ring_1(2)
% 5.31/5.63 thf(fact_7785_mult__1s__ring__1_I2_J,axiom,
% 5.31/5.63 ! [B: rat] :
% 5.31/5.63 ( ( times_times_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ one ) ) )
% 5.31/5.63 = ( uminus_uminus_rat @ B ) ) ).
% 5.31/5.63
% 5.31/5.63 % mult_1s_ring_1(2)
% 5.31/5.63 thf(fact_7786_divide__eq__minus__1__iff,axiom,
% 5.31/5.63 ! [A: real,B: real] :
% 5.31/5.63 ( ( ( divide_divide_real @ A @ B )
% 5.31/5.63 = ( uminus_uminus_real @ one_one_real ) )
% 5.31/5.63 = ( ( B != zero_zero_real )
% 5.31/5.63 & ( A
% 5.31/5.63 = ( uminus_uminus_real @ B ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % divide_eq_minus_1_iff
% 5.31/5.63 thf(fact_7787_divide__eq__minus__1__iff,axiom,
% 5.31/5.63 ! [A: complex,B: complex] :
% 5.31/5.63 ( ( ( divide1717551699836669952omplex @ A @ B )
% 5.31/5.63 = ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.31/5.63 = ( ( B != zero_zero_complex )
% 5.31/5.63 & ( A
% 5.31/5.63 = ( uminus1482373934393186551omplex @ B ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % divide_eq_minus_1_iff
% 5.31/5.63 thf(fact_7788_divide__eq__minus__1__iff,axiom,
% 5.31/5.63 ! [A: rat,B: rat] :
% 5.31/5.63 ( ( ( divide_divide_rat @ A @ B )
% 5.31/5.63 = ( uminus_uminus_rat @ one_one_rat ) )
% 5.31/5.63 = ( ( B != zero_zero_rat )
% 5.31/5.63 & ( A
% 5.31/5.63 = ( uminus_uminus_rat @ B ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % divide_eq_minus_1_iff
% 5.31/5.63 thf(fact_7789_uminus__numeral__One,axiom,
% 5.31/5.63 ( ( uminus_uminus_int @ ( numeral_numeral_int @ one ) )
% 5.31/5.63 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.31/5.63
% 5.31/5.63 % uminus_numeral_One
% 5.31/5.63 thf(fact_7790_uminus__numeral__One,axiom,
% 5.31/5.63 ( ( uminus_uminus_real @ ( numeral_numeral_real @ one ) )
% 5.31/5.63 = ( uminus_uminus_real @ one_one_real ) ) ).
% 5.31/5.63
% 5.31/5.63 % uminus_numeral_One
% 5.31/5.63 thf(fact_7791_uminus__numeral__One,axiom,
% 5.31/5.63 ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ one ) )
% 5.31/5.63 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.31/5.63
% 5.31/5.63 % uminus_numeral_One
% 5.31/5.63 thf(fact_7792_uminus__numeral__One,axiom,
% 5.31/5.63 ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ one ) )
% 5.31/5.63 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.31/5.63
% 5.31/5.63 % uminus_numeral_One
% 5.31/5.63 thf(fact_7793_uminus__numeral__One,axiom,
% 5.31/5.63 ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ one ) )
% 5.31/5.63 = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.31/5.63
% 5.31/5.63 % uminus_numeral_One
% 5.31/5.63 thf(fact_7794_fact__less__mono,axiom,
% 5.31/5.63 ! [M2: nat,N: nat] :
% 5.31/5.63 ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 5.31/5.63 => ( ( ord_less_nat @ M2 @ N )
% 5.31/5.63 => ( ord_less_rat @ ( semiri773545260158071498ct_rat @ M2 ) @ ( semiri773545260158071498ct_rat @ N ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % fact_less_mono
% 5.31/5.63 thf(fact_7795_fact__less__mono,axiom,
% 5.31/5.63 ! [M2: nat,N: nat] :
% 5.31/5.63 ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 5.31/5.63 => ( ( ord_less_nat @ M2 @ N )
% 5.31/5.63 => ( ord_less_int @ ( semiri1406184849735516958ct_int @ M2 ) @ ( semiri1406184849735516958ct_int @ N ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % fact_less_mono
% 5.31/5.63 thf(fact_7796_fact__less__mono,axiom,
% 5.31/5.63 ! [M2: nat,N: nat] :
% 5.31/5.63 ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 5.31/5.63 => ( ( ord_less_nat @ M2 @ N )
% 5.31/5.63 => ( ord_less_nat @ ( semiri1408675320244567234ct_nat @ M2 ) @ ( semiri1408675320244567234ct_nat @ N ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % fact_less_mono
% 5.31/5.63 thf(fact_7797_fact__less__mono,axiom,
% 5.31/5.63 ! [M2: nat,N: nat] :
% 5.31/5.63 ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 5.31/5.63 => ( ( ord_less_nat @ M2 @ N )
% 5.31/5.63 => ( ord_less_real @ ( semiri2265585572941072030t_real @ M2 ) @ ( semiri2265585572941072030t_real @ N ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % fact_less_mono
% 5.31/5.63 thf(fact_7798_power__minus,axiom,
% 5.31/5.63 ! [A: int,N: nat] :
% 5.31/5.63 ( ( power_power_int @ ( uminus_uminus_int @ A ) @ N )
% 5.31/5.63 = ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N ) @ ( power_power_int @ A @ N ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % power_minus
% 5.31/5.63 thf(fact_7799_power__minus,axiom,
% 5.31/5.63 ! [A: real,N: nat] :
% 5.31/5.63 ( ( power_power_real @ ( uminus_uminus_real @ A ) @ N )
% 5.31/5.63 = ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) @ ( power_power_real @ A @ N ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % power_minus
% 5.31/5.63 thf(fact_7800_power__minus,axiom,
% 5.31/5.63 ! [A: complex,N: nat] :
% 5.31/5.63 ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N )
% 5.31/5.63 = ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) @ ( power_power_complex @ A @ N ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % power_minus
% 5.31/5.63 thf(fact_7801_power__minus,axiom,
% 5.31/5.63 ! [A: code_integer,N: nat] :
% 5.31/5.63 ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N )
% 5.31/5.63 = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N ) @ ( power_8256067586552552935nteger @ A @ N ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % power_minus
% 5.31/5.63 thf(fact_7802_power__minus,axiom,
% 5.31/5.63 ! [A: rat,N: nat] :
% 5.31/5.63 ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N )
% 5.31/5.63 = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N ) @ ( power_power_rat @ A @ N ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % power_minus
% 5.31/5.63 thf(fact_7803_inf__shunt,axiom,
% 5.31/5.63 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] :
% 5.31/5.63 ( ( ( inf_in2572325071724192079at_nat @ X @ Y )
% 5.31/5.63 = bot_bo2099793752762293965at_nat )
% 5.31/5.63 = ( ord_le3146513528884898305at_nat @ X @ ( uminus6524753893492686040at_nat @ Y ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % inf_shunt
% 5.31/5.63 thf(fact_7804_inf__shunt,axiom,
% 5.31/5.63 ! [X: set_int,Y: set_int] :
% 5.31/5.63 ( ( ( inf_inf_set_int @ X @ Y )
% 5.31/5.63 = bot_bot_set_int )
% 5.31/5.63 = ( ord_less_eq_set_int @ X @ ( uminus1532241313380277803et_int @ Y ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % inf_shunt
% 5.31/5.63 thf(fact_7805_inf__shunt,axiom,
% 5.31/5.63 ! [X: set_real,Y: set_real] :
% 5.31/5.63 ( ( ( inf_inf_set_real @ X @ Y )
% 5.31/5.63 = bot_bot_set_real )
% 5.31/5.63 = ( ord_less_eq_set_real @ X @ ( uminus612125837232591019t_real @ Y ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % inf_shunt
% 5.31/5.63 thf(fact_7806_inf__shunt,axiom,
% 5.31/5.63 ! [X: set_nat,Y: set_nat] :
% 5.31/5.63 ( ( ( inf_inf_set_nat @ X @ Y )
% 5.31/5.63 = bot_bot_set_nat )
% 5.31/5.63 = ( ord_less_eq_set_nat @ X @ ( uminus5710092332889474511et_nat @ Y ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % inf_shunt
% 5.31/5.63 thf(fact_7807_fact__fact__dvd__fact,axiom,
% 5.31/5.63 ! [K2: nat,N: nat] : ( dvd_dvd_rat @ ( times_times_rat @ ( semiri773545260158071498ct_rat @ K2 ) @ ( semiri773545260158071498ct_rat @ N ) ) @ ( semiri773545260158071498ct_rat @ ( plus_plus_nat @ K2 @ N ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % fact_fact_dvd_fact
% 5.31/5.63 thf(fact_7808_fact__fact__dvd__fact,axiom,
% 5.31/5.63 ! [K2: nat,N: nat] : ( dvd_dvd_int @ ( times_times_int @ ( semiri1406184849735516958ct_int @ K2 ) @ ( semiri1406184849735516958ct_int @ N ) ) @ ( semiri1406184849735516958ct_int @ ( plus_plus_nat @ K2 @ N ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % fact_fact_dvd_fact
% 5.31/5.63 thf(fact_7809_fact__fact__dvd__fact,axiom,
% 5.31/5.63 ! [K2: nat,N: nat] : ( dvd_dvd_nat @ ( times_times_nat @ ( semiri1408675320244567234ct_nat @ K2 ) @ ( semiri1408675320244567234ct_nat @ N ) ) @ ( semiri1408675320244567234ct_nat @ ( plus_plus_nat @ K2 @ N ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % fact_fact_dvd_fact
% 5.31/5.63 thf(fact_7810_fact__fact__dvd__fact,axiom,
% 5.31/5.63 ! [K2: nat,N: nat] : ( dvd_dvd_real @ ( times_times_real @ ( semiri2265585572941072030t_real @ K2 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( semiri2265585572941072030t_real @ ( plus_plus_nat @ K2 @ N ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % fact_fact_dvd_fact
% 5.31/5.63 thf(fact_7811_fact__mod,axiom,
% 5.31/5.63 ! [M2: nat,N: nat] :
% 5.31/5.63 ( ( ord_less_eq_nat @ M2 @ N )
% 5.31/5.63 => ( ( modulo_modulo_int @ ( semiri1406184849735516958ct_int @ N ) @ ( semiri1406184849735516958ct_int @ M2 ) )
% 5.31/5.63 = zero_zero_int ) ) ).
% 5.31/5.63
% 5.31/5.63 % fact_mod
% 5.31/5.63 thf(fact_7812_fact__mod,axiom,
% 5.31/5.63 ! [M2: nat,N: nat] :
% 5.31/5.63 ( ( ord_less_eq_nat @ M2 @ N )
% 5.31/5.63 => ( ( modulo8411746178871703098atural @ ( semiri2447717529341329178atural @ N ) @ ( semiri2447717529341329178atural @ M2 ) )
% 5.31/5.63 = zero_z2226904508553997617atural ) ) ).
% 5.31/5.63
% 5.31/5.63 % fact_mod
% 5.31/5.63 thf(fact_7813_fact__mod,axiom,
% 5.31/5.63 ! [M2: nat,N: nat] :
% 5.31/5.63 ( ( ord_less_eq_nat @ M2 @ N )
% 5.31/5.63 => ( ( modulo_modulo_nat @ ( semiri1408675320244567234ct_nat @ N ) @ ( semiri1408675320244567234ct_nat @ M2 ) )
% 5.31/5.63 = zero_zero_nat ) ) ).
% 5.31/5.63
% 5.31/5.63 % fact_mod
% 5.31/5.63 thf(fact_7814_sup__neg__inf,axiom,
% 5.31/5.63 ! [P: set_Pr1261947904930325089at_nat,Q2: set_Pr1261947904930325089at_nat,R3: set_Pr1261947904930325089at_nat] :
% 5.31/5.63 ( ( ord_le3146513528884898305at_nat @ P @ ( sup_su6327502436637775413at_nat @ Q2 @ R3 ) )
% 5.31/5.63 = ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ P @ ( uminus6524753893492686040at_nat @ Q2 ) ) @ R3 ) ) ).
% 5.31/5.63
% 5.31/5.63 % sup_neg_inf
% 5.31/5.63 thf(fact_7815_sup__neg__inf,axiom,
% 5.31/5.63 ! [P: set_nat,Q2: set_nat,R3: set_nat] :
% 5.31/5.63 ( ( ord_less_eq_set_nat @ P @ ( sup_sup_set_nat @ Q2 @ R3 ) )
% 5.31/5.63 = ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ P @ ( uminus5710092332889474511et_nat @ Q2 ) ) @ R3 ) ) ).
% 5.31/5.63
% 5.31/5.63 % sup_neg_inf
% 5.31/5.63 thf(fact_7816_shunt2,axiom,
% 5.31/5.63 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,Z3: set_Pr1261947904930325089at_nat] :
% 5.31/5.63 ( ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ X @ ( uminus6524753893492686040at_nat @ Y ) ) @ Z3 )
% 5.31/5.63 = ( ord_le3146513528884898305at_nat @ X @ ( sup_su6327502436637775413at_nat @ Y @ Z3 ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % shunt2
% 5.31/5.63 thf(fact_7817_shunt2,axiom,
% 5.31/5.63 ! [X: set_nat,Y: set_nat,Z3: set_nat] :
% 5.31/5.63 ( ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ X @ ( uminus5710092332889474511et_nat @ Y ) ) @ Z3 )
% 5.31/5.63 = ( ord_less_eq_set_nat @ X @ ( sup_sup_set_nat @ Y @ Z3 ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % shunt2
% 5.31/5.63 thf(fact_7818_shunt1,axiom,
% 5.31/5.63 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,Z3: set_Pr1261947904930325089at_nat] :
% 5.31/5.63 ( ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ X @ Y ) @ Z3 )
% 5.31/5.63 = ( ord_le3146513528884898305at_nat @ X @ ( sup_su6327502436637775413at_nat @ ( uminus6524753893492686040at_nat @ Y ) @ Z3 ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % shunt1
% 5.31/5.63 thf(fact_7819_shunt1,axiom,
% 5.31/5.63 ! [X: set_nat,Y: set_nat,Z3: set_nat] :
% 5.31/5.63 ( ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ X @ Y ) @ Z3 )
% 5.31/5.63 = ( ord_less_eq_set_nat @ X @ ( sup_sup_set_nat @ ( uminus5710092332889474511et_nat @ Y ) @ Z3 ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % shunt1
% 5.31/5.63 thf(fact_7820_fact__le__power,axiom,
% 5.31/5.63 ! [N: nat] : ( ord_less_eq_rat @ ( semiri773545260158071498ct_rat @ N ) @ ( semiri681578069525770553at_rat @ ( power_power_nat @ N @ N ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % fact_le_power
% 5.31/5.63 thf(fact_7821_fact__le__power,axiom,
% 5.31/5.63 ! [N: nat] : ( ord_less_eq_int @ ( semiri1406184849735516958ct_int @ N ) @ ( semiri1314217659103216013at_int @ ( power_power_nat @ N @ N ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % fact_le_power
% 5.31/5.63 thf(fact_7822_fact__le__power,axiom,
% 5.31/5.63 ! [N: nat] : ( ord_less_eq_nat @ ( semiri1408675320244567234ct_nat @ N ) @ ( semiri1316708129612266289at_nat @ ( power_power_nat @ N @ N ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % fact_le_power
% 5.31/5.63 thf(fact_7823_fact__le__power,axiom,
% 5.31/5.63 ! [N: nat] : ( ord_less_eq_real @ ( semiri2265585572941072030t_real @ N ) @ ( semiri5074537144036343181t_real @ ( power_power_nat @ N @ N ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % fact_le_power
% 5.31/5.63 thf(fact_7824_int__cases4,axiom,
% 5.31/5.63 ! [M2: int] :
% 5.31/5.63 ( ! [N3: nat] :
% 5.31/5.63 ( M2
% 5.31/5.63 != ( semiri1314217659103216013at_int @ N3 ) )
% 5.31/5.63 => ~ ! [N3: nat] :
% 5.31/5.63 ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 5.31/5.63 => ( M2
% 5.31/5.63 != ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N3 ) ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % int_cases4
% 5.31/5.63 thf(fact_7825_int__zle__neg,axiom,
% 5.31/5.63 ! [N: nat,M2: nat] :
% 5.31/5.63 ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ N ) @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ M2 ) ) )
% 5.31/5.63 = ( ( N = zero_zero_nat )
% 5.31/5.63 & ( M2 = zero_zero_nat ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % int_zle_neg
% 5.31/5.63 thf(fact_7826_zmod__zminus1__eq__if,axiom,
% 5.31/5.63 ! [A: int,B: int] :
% 5.31/5.63 ( ( ( ( modulo_modulo_int @ A @ B )
% 5.31/5.63 = zero_zero_int )
% 5.31/5.63 => ( ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ B )
% 5.31/5.63 = zero_zero_int ) )
% 5.31/5.63 & ( ( ( modulo_modulo_int @ A @ B )
% 5.31/5.63 != zero_zero_int )
% 5.31/5.63 => ( ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ B )
% 5.31/5.63 = ( minus_minus_int @ B @ ( modulo_modulo_int @ A @ B ) ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % zmod_zminus1_eq_if
% 5.31/5.63 thf(fact_7827_zmod__zminus2__eq__if,axiom,
% 5.31/5.63 ! [A: int,B: int] :
% 5.31/5.63 ( ( ( ( modulo_modulo_int @ A @ B )
% 5.31/5.63 = zero_zero_int )
% 5.31/5.63 => ( ( modulo_modulo_int @ A @ ( uminus_uminus_int @ B ) )
% 5.31/5.63 = zero_zero_int ) )
% 5.31/5.63 & ( ( ( modulo_modulo_int @ A @ B )
% 5.31/5.63 != zero_zero_int )
% 5.31/5.63 => ( ( modulo_modulo_int @ A @ ( uminus_uminus_int @ B ) )
% 5.31/5.63 = ( minus_minus_int @ ( modulo_modulo_int @ A @ B ) @ B ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % zmod_zminus2_eq_if
% 5.31/5.63 thf(fact_7828_fact__div__fact__le__pow,axiom,
% 5.31/5.63 ! [R3: nat,N: nat] :
% 5.31/5.63 ( ( ord_less_eq_nat @ R3 @ N )
% 5.31/5.63 => ( ord_less_eq_nat @ ( divide_divide_nat @ ( semiri1408675320244567234ct_nat @ N ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N @ R3 ) ) ) @ ( power_power_nat @ N @ R3 ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % fact_div_fact_le_pow
% 5.31/5.63 thf(fact_7829_binomial__fact__lemma,axiom,
% 5.31/5.63 ! [K2: nat,N: nat] :
% 5.31/5.63 ( ( ord_less_eq_nat @ K2 @ N )
% 5.31/5.63 => ( ( times_times_nat @ ( times_times_nat @ ( semiri1408675320244567234ct_nat @ K2 ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N @ K2 ) ) ) @ ( binomial @ N @ K2 ) )
% 5.31/5.63 = ( semiri1408675320244567234ct_nat @ N ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % binomial_fact_lemma
% 5.31/5.63 thf(fact_7830_subset__decode__imp__le,axiom,
% 5.31/5.63 ! [M2: nat,N: nat] :
% 5.31/5.63 ( ( ord_less_eq_set_nat @ ( nat_set_decode @ M2 ) @ ( nat_set_decode @ N ) )
% 5.31/5.63 => ( ord_less_eq_nat @ M2 @ N ) ) ).
% 5.31/5.63
% 5.31/5.63 % subset_decode_imp_le
% 5.31/5.63 thf(fact_7831_less__minus__divide__eq,axiom,
% 5.31/5.63 ! [A: real,B: real,C2: real] :
% 5.31/5.63 ( ( ord_less_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C2 ) ) )
% 5.31/5.63 = ( ( ( ord_less_real @ zero_zero_real @ C2 )
% 5.31/5.63 => ( ord_less_real @ ( times_times_real @ A @ C2 ) @ ( uminus_uminus_real @ B ) ) )
% 5.31/5.63 & ( ~ ( ord_less_real @ zero_zero_real @ C2 )
% 5.31/5.63 => ( ( ( ord_less_real @ C2 @ zero_zero_real )
% 5.31/5.63 => ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C2 ) ) )
% 5.31/5.63 & ( ~ ( ord_less_real @ C2 @ zero_zero_real )
% 5.31/5.63 => ( ord_less_real @ A @ zero_zero_real ) ) ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % less_minus_divide_eq
% 5.31/5.63 thf(fact_7832_less__minus__divide__eq,axiom,
% 5.31/5.63 ! [A: rat,B: rat,C2: rat] :
% 5.31/5.63 ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C2 ) ) )
% 5.31/5.63 = ( ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 5.31/5.63 => ( ord_less_rat @ ( times_times_rat @ A @ C2 ) @ ( uminus_uminus_rat @ B ) ) )
% 5.31/5.63 & ( ~ ( ord_less_rat @ zero_zero_rat @ C2 )
% 5.31/5.63 => ( ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 5.31/5.63 => ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C2 ) ) )
% 5.31/5.63 & ( ~ ( ord_less_rat @ C2 @ zero_zero_rat )
% 5.31/5.63 => ( ord_less_rat @ A @ zero_zero_rat ) ) ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % less_minus_divide_eq
% 5.31/5.63 thf(fact_7833_minus__divide__less__eq,axiom,
% 5.31/5.63 ! [B: real,C2: real,A: real] :
% 5.31/5.63 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C2 ) ) @ A )
% 5.31/5.63 = ( ( ( ord_less_real @ zero_zero_real @ C2 )
% 5.31/5.63 => ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C2 ) ) )
% 5.31/5.63 & ( ~ ( ord_less_real @ zero_zero_real @ C2 )
% 5.31/5.63 => ( ( ( ord_less_real @ C2 @ zero_zero_real )
% 5.31/5.63 => ( ord_less_real @ ( times_times_real @ A @ C2 ) @ ( uminus_uminus_real @ B ) ) )
% 5.31/5.63 & ( ~ ( ord_less_real @ C2 @ zero_zero_real )
% 5.31/5.63 => ( ord_less_real @ zero_zero_real @ A ) ) ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % minus_divide_less_eq
% 5.31/5.63 thf(fact_7834_minus__divide__less__eq,axiom,
% 5.31/5.63 ! [B: rat,C2: rat,A: rat] :
% 5.31/5.63 ( ( ord_less_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C2 ) ) @ A )
% 5.31/5.63 = ( ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 5.31/5.63 => ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C2 ) ) )
% 5.31/5.63 & ( ~ ( ord_less_rat @ zero_zero_rat @ C2 )
% 5.31/5.63 => ( ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 5.31/5.63 => ( ord_less_rat @ ( times_times_rat @ A @ C2 ) @ ( uminus_uminus_rat @ B ) ) )
% 5.31/5.63 & ( ~ ( ord_less_rat @ C2 @ zero_zero_rat )
% 5.31/5.63 => ( ord_less_rat @ zero_zero_rat @ A ) ) ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % minus_divide_less_eq
% 5.31/5.63 thf(fact_7835_neg__less__minus__divide__eq,axiom,
% 5.31/5.63 ! [C2: real,A: real,B: real] :
% 5.31/5.63 ( ( ord_less_real @ C2 @ zero_zero_real )
% 5.31/5.63 => ( ( ord_less_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C2 ) ) )
% 5.31/5.63 = ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C2 ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % neg_less_minus_divide_eq
% 5.31/5.63 thf(fact_7836_neg__less__minus__divide__eq,axiom,
% 5.31/5.63 ! [C2: rat,A: rat,B: rat] :
% 5.31/5.63 ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 5.31/5.63 => ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C2 ) ) )
% 5.31/5.63 = ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C2 ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % neg_less_minus_divide_eq
% 5.31/5.63 thf(fact_7837_neg__minus__divide__less__eq,axiom,
% 5.31/5.63 ! [C2: real,B: real,A: real] :
% 5.31/5.63 ( ( ord_less_real @ C2 @ zero_zero_real )
% 5.31/5.63 => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C2 ) ) @ A )
% 5.31/5.63 = ( ord_less_real @ ( times_times_real @ A @ C2 ) @ ( uminus_uminus_real @ B ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % neg_minus_divide_less_eq
% 5.31/5.63 thf(fact_7838_neg__minus__divide__less__eq,axiom,
% 5.31/5.63 ! [C2: rat,B: rat,A: rat] :
% 5.31/5.63 ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 5.31/5.63 => ( ( ord_less_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C2 ) ) @ A )
% 5.31/5.63 = ( ord_less_rat @ ( times_times_rat @ A @ C2 ) @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % neg_minus_divide_less_eq
% 5.31/5.63 thf(fact_7839_pos__less__minus__divide__eq,axiom,
% 5.31/5.63 ! [C2: real,A: real,B: real] :
% 5.31/5.63 ( ( ord_less_real @ zero_zero_real @ C2 )
% 5.31/5.63 => ( ( ord_less_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C2 ) ) )
% 5.31/5.63 = ( ord_less_real @ ( times_times_real @ A @ C2 ) @ ( uminus_uminus_real @ B ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % pos_less_minus_divide_eq
% 5.31/5.63 thf(fact_7840_pos__less__minus__divide__eq,axiom,
% 5.31/5.63 ! [C2: rat,A: rat,B: rat] :
% 5.31/5.63 ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 5.31/5.63 => ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C2 ) ) )
% 5.31/5.63 = ( ord_less_rat @ ( times_times_rat @ A @ C2 ) @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % pos_less_minus_divide_eq
% 5.31/5.63 thf(fact_7841_pos__minus__divide__less__eq,axiom,
% 5.31/5.63 ! [C2: real,B: real,A: real] :
% 5.31/5.63 ( ( ord_less_real @ zero_zero_real @ C2 )
% 5.31/5.63 => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C2 ) ) @ A )
% 5.31/5.63 = ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C2 ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % pos_minus_divide_less_eq
% 5.31/5.63 thf(fact_7842_pos__minus__divide__less__eq,axiom,
% 5.31/5.63 ! [C2: rat,B: rat,A: rat] :
% 5.31/5.63 ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 5.31/5.63 => ( ( ord_less_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C2 ) ) @ A )
% 5.31/5.63 = ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C2 ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % pos_minus_divide_less_eq
% 5.31/5.63 thf(fact_7843_eq__divide__eq__numeral_I2_J,axiom,
% 5.31/5.63 ! [W2: num,B: real,C2: real] :
% 5.31/5.63 ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) )
% 5.31/5.63 = ( divide_divide_real @ B @ C2 ) )
% 5.31/5.63 = ( ( ( C2 != zero_zero_real )
% 5.31/5.63 => ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) @ C2 )
% 5.31/5.63 = B ) )
% 5.31/5.63 & ( ( C2 = zero_zero_real )
% 5.31/5.63 => ( ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) )
% 5.31/5.63 = zero_zero_real ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % eq_divide_eq_numeral(2)
% 5.31/5.63 thf(fact_7844_eq__divide__eq__numeral_I2_J,axiom,
% 5.31/5.63 ! [W2: num,B: complex,C2: complex] :
% 5.31/5.63 ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W2 ) )
% 5.31/5.63 = ( divide1717551699836669952omplex @ B @ C2 ) )
% 5.31/5.63 = ( ( ( C2 != zero_zero_complex )
% 5.31/5.63 => ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W2 ) ) @ C2 )
% 5.31/5.63 = B ) )
% 5.31/5.63 & ( ( C2 = zero_zero_complex )
% 5.31/5.63 => ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W2 ) )
% 5.31/5.63 = zero_zero_complex ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % eq_divide_eq_numeral(2)
% 5.31/5.63 thf(fact_7845_eq__divide__eq__numeral_I2_J,axiom,
% 5.31/5.63 ! [W2: num,B: rat,C2: rat] :
% 5.31/5.63 ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) )
% 5.31/5.63 = ( divide_divide_rat @ B @ C2 ) )
% 5.31/5.63 = ( ( ( C2 != zero_zero_rat )
% 5.31/5.63 => ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ C2 )
% 5.31/5.63 = B ) )
% 5.31/5.63 & ( ( C2 = zero_zero_rat )
% 5.31/5.63 => ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) )
% 5.31/5.63 = zero_zero_rat ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % eq_divide_eq_numeral(2)
% 5.31/5.63 thf(fact_7846_divide__eq__eq__numeral_I2_J,axiom,
% 5.31/5.63 ! [B: real,C2: real,W2: num] :
% 5.31/5.63 ( ( ( divide_divide_real @ B @ C2 )
% 5.31/5.63 = ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) )
% 5.31/5.63 = ( ( ( C2 != zero_zero_real )
% 5.31/5.63 => ( B
% 5.31/5.63 = ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) @ C2 ) ) )
% 5.31/5.63 & ( ( C2 = zero_zero_real )
% 5.31/5.63 => ( ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) )
% 5.31/5.63 = zero_zero_real ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % divide_eq_eq_numeral(2)
% 5.31/5.63 thf(fact_7847_divide__eq__eq__numeral_I2_J,axiom,
% 5.31/5.63 ! [B: complex,C2: complex,W2: num] :
% 5.31/5.63 ( ( ( divide1717551699836669952omplex @ B @ C2 )
% 5.31/5.63 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W2 ) ) )
% 5.31/5.63 = ( ( ( C2 != zero_zero_complex )
% 5.31/5.63 => ( B
% 5.31/5.63 = ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W2 ) ) @ C2 ) ) )
% 5.31/5.63 & ( ( C2 = zero_zero_complex )
% 5.31/5.63 => ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W2 ) )
% 5.31/5.63 = zero_zero_complex ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % divide_eq_eq_numeral(2)
% 5.31/5.63 thf(fact_7848_divide__eq__eq__numeral_I2_J,axiom,
% 5.31/5.63 ! [B: rat,C2: rat,W2: num] :
% 5.31/5.63 ( ( ( divide_divide_rat @ B @ C2 )
% 5.31/5.63 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) )
% 5.31/5.63 = ( ( ( C2 != zero_zero_rat )
% 5.31/5.63 => ( B
% 5.31/5.63 = ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ C2 ) ) )
% 5.31/5.63 & ( ( C2 = zero_zero_rat )
% 5.31/5.63 => ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) )
% 5.31/5.63 = zero_zero_rat ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % divide_eq_eq_numeral(2)
% 5.31/5.63 thf(fact_7849_add__divide__eq__if__simps_I3_J,axiom,
% 5.31/5.63 ! [Z3: real,A: real,B: real] :
% 5.31/5.63 ( ( ( Z3 = zero_zero_real )
% 5.31/5.63 => ( ( plus_plus_real @ ( uminus_uminus_real @ ( divide_divide_real @ A @ Z3 ) ) @ B )
% 5.31/5.63 = B ) )
% 5.31/5.63 & ( ( Z3 != zero_zero_real )
% 5.31/5.63 => ( ( plus_plus_real @ ( uminus_uminus_real @ ( divide_divide_real @ A @ Z3 ) ) @ B )
% 5.31/5.63 = ( divide_divide_real @ ( plus_plus_real @ ( uminus_uminus_real @ A ) @ ( times_times_real @ B @ Z3 ) ) @ Z3 ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % add_divide_eq_if_simps(3)
% 5.31/5.63 thf(fact_7850_add__divide__eq__if__simps_I3_J,axiom,
% 5.31/5.63 ! [Z3: complex,A: complex,B: complex] :
% 5.31/5.63 ( ( ( Z3 = zero_zero_complex )
% 5.31/5.63 => ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ Z3 ) ) @ B )
% 5.31/5.63 = B ) )
% 5.31/5.63 & ( ( Z3 != zero_zero_complex )
% 5.31/5.63 => ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ Z3 ) ) @ B )
% 5.31/5.63 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ ( times_times_complex @ B @ Z3 ) ) @ Z3 ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % add_divide_eq_if_simps(3)
% 5.31/5.63 thf(fact_7851_add__divide__eq__if__simps_I3_J,axiom,
% 5.31/5.63 ! [Z3: rat,A: rat,B: rat] :
% 5.31/5.63 ( ( ( Z3 = zero_zero_rat )
% 5.31/5.63 => ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ A @ Z3 ) ) @ B )
% 5.31/5.63 = B ) )
% 5.31/5.63 & ( ( Z3 != zero_zero_rat )
% 5.31/5.63 => ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ A @ Z3 ) ) @ B )
% 5.31/5.63 = ( divide_divide_rat @ ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ ( times_times_rat @ B @ Z3 ) ) @ Z3 ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % add_divide_eq_if_simps(3)
% 5.31/5.63 thf(fact_7852_minus__divide__add__eq__iff,axiom,
% 5.31/5.63 ! [Z3: real,X: real,Y: real] :
% 5.31/5.63 ( ( Z3 != zero_zero_real )
% 5.31/5.63 => ( ( plus_plus_real @ ( uminus_uminus_real @ ( divide_divide_real @ X @ Z3 ) ) @ Y )
% 5.31/5.63 = ( divide_divide_real @ ( plus_plus_real @ ( uminus_uminus_real @ X ) @ ( times_times_real @ Y @ Z3 ) ) @ Z3 ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % minus_divide_add_eq_iff
% 5.31/5.63 thf(fact_7853_minus__divide__add__eq__iff,axiom,
% 5.31/5.63 ! [Z3: complex,X: complex,Y: complex] :
% 5.31/5.63 ( ( Z3 != zero_zero_complex )
% 5.31/5.63 => ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ X @ Z3 ) ) @ Y )
% 5.31/5.63 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( uminus1482373934393186551omplex @ X ) @ ( times_times_complex @ Y @ Z3 ) ) @ Z3 ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % minus_divide_add_eq_iff
% 5.31/5.63 thf(fact_7854_minus__divide__add__eq__iff,axiom,
% 5.31/5.63 ! [Z3: rat,X: rat,Y: rat] :
% 5.31/5.63 ( ( Z3 != zero_zero_rat )
% 5.31/5.63 => ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ X @ Z3 ) ) @ Y )
% 5.31/5.63 = ( divide_divide_rat @ ( plus_plus_rat @ ( uminus_uminus_rat @ X ) @ ( times_times_rat @ Y @ Z3 ) ) @ Z3 ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % minus_divide_add_eq_iff
% 5.31/5.63 thf(fact_7855_signed__take__bit__int__greater__eq,axiom,
% 5.31/5.63 ! [K2: int,N: nat] :
% 5.31/5.63 ( ( ord_less_int @ K2 @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) )
% 5.31/5.63 => ( ord_less_eq_int @ ( plus_plus_int @ K2 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ N ) ) ) @ ( bit_ri631733984087533419it_int @ N @ K2 ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % signed_take_bit_int_greater_eq
% 5.31/5.63 thf(fact_7856_add__divide__eq__if__simps_I6_J,axiom,
% 5.31/5.63 ! [Z3: real,A: real,B: real] :
% 5.31/5.63 ( ( ( Z3 = zero_zero_real )
% 5.31/5.63 => ( ( minus_minus_real @ ( uminus_uminus_real @ ( divide_divide_real @ A @ Z3 ) ) @ B )
% 5.31/5.63 = ( uminus_uminus_real @ B ) ) )
% 5.31/5.63 & ( ( Z3 != zero_zero_real )
% 5.31/5.63 => ( ( minus_minus_real @ ( uminus_uminus_real @ ( divide_divide_real @ A @ Z3 ) ) @ B )
% 5.31/5.63 = ( divide_divide_real @ ( minus_minus_real @ ( uminus_uminus_real @ A ) @ ( times_times_real @ B @ Z3 ) ) @ Z3 ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % add_divide_eq_if_simps(6)
% 5.31/5.63 thf(fact_7857_add__divide__eq__if__simps_I6_J,axiom,
% 5.31/5.63 ! [Z3: complex,A: complex,B: complex] :
% 5.31/5.63 ( ( ( Z3 = zero_zero_complex )
% 5.31/5.63 => ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ Z3 ) ) @ B )
% 5.31/5.63 = ( uminus1482373934393186551omplex @ B ) ) )
% 5.31/5.63 & ( ( Z3 != zero_zero_complex )
% 5.31/5.63 => ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ Z3 ) ) @ B )
% 5.31/5.63 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( uminus1482373934393186551omplex @ A ) @ ( times_times_complex @ B @ Z3 ) ) @ Z3 ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % add_divide_eq_if_simps(6)
% 5.31/5.63 thf(fact_7858_add__divide__eq__if__simps_I6_J,axiom,
% 5.31/5.63 ! [Z3: rat,A: rat,B: rat] :
% 5.31/5.63 ( ( ( Z3 = zero_zero_rat )
% 5.31/5.63 => ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ A @ Z3 ) ) @ B )
% 5.31/5.63 = ( uminus_uminus_rat @ B ) ) )
% 5.31/5.63 & ( ( Z3 != zero_zero_rat )
% 5.31/5.63 => ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ A @ Z3 ) ) @ B )
% 5.31/5.63 = ( divide_divide_rat @ ( minus_minus_rat @ ( uminus_uminus_rat @ A ) @ ( times_times_rat @ B @ Z3 ) ) @ Z3 ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % add_divide_eq_if_simps(6)
% 5.31/5.63 thf(fact_7859_add__divide__eq__if__simps_I5_J,axiom,
% 5.31/5.63 ! [Z3: real,A: real,B: real] :
% 5.31/5.63 ( ( ( Z3 = zero_zero_real )
% 5.31/5.63 => ( ( minus_minus_real @ ( divide_divide_real @ A @ Z3 ) @ B )
% 5.31/5.63 = ( uminus_uminus_real @ B ) ) )
% 5.31/5.63 & ( ( Z3 != zero_zero_real )
% 5.31/5.63 => ( ( minus_minus_real @ ( divide_divide_real @ A @ Z3 ) @ B )
% 5.31/5.63 = ( divide_divide_real @ ( minus_minus_real @ A @ ( times_times_real @ B @ Z3 ) ) @ Z3 ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % add_divide_eq_if_simps(5)
% 5.31/5.63 thf(fact_7860_add__divide__eq__if__simps_I5_J,axiom,
% 5.31/5.63 ! [Z3: complex,A: complex,B: complex] :
% 5.31/5.63 ( ( ( Z3 = zero_zero_complex )
% 5.31/5.63 => ( ( minus_minus_complex @ ( divide1717551699836669952omplex @ A @ Z3 ) @ B )
% 5.31/5.63 = ( uminus1482373934393186551omplex @ B ) ) )
% 5.31/5.63 & ( ( Z3 != zero_zero_complex )
% 5.31/5.63 => ( ( minus_minus_complex @ ( divide1717551699836669952omplex @ A @ Z3 ) @ B )
% 5.31/5.63 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ A @ ( times_times_complex @ B @ Z3 ) ) @ Z3 ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % add_divide_eq_if_simps(5)
% 5.31/5.63 thf(fact_7861_add__divide__eq__if__simps_I5_J,axiom,
% 5.31/5.63 ! [Z3: rat,A: rat,B: rat] :
% 5.31/5.63 ( ( ( Z3 = zero_zero_rat )
% 5.31/5.63 => ( ( minus_minus_rat @ ( divide_divide_rat @ A @ Z3 ) @ B )
% 5.31/5.63 = ( uminus_uminus_rat @ B ) ) )
% 5.31/5.63 & ( ( Z3 != zero_zero_rat )
% 5.31/5.63 => ( ( minus_minus_rat @ ( divide_divide_rat @ A @ Z3 ) @ B )
% 5.31/5.63 = ( divide_divide_rat @ ( minus_minus_rat @ A @ ( times_times_rat @ B @ Z3 ) ) @ Z3 ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % add_divide_eq_if_simps(5)
% 5.31/5.63 thf(fact_7862_minus__divide__diff__eq__iff,axiom,
% 5.31/5.63 ! [Z3: real,X: real,Y: real] :
% 5.31/5.63 ( ( Z3 != zero_zero_real )
% 5.31/5.63 => ( ( minus_minus_real @ ( uminus_uminus_real @ ( divide_divide_real @ X @ Z3 ) ) @ Y )
% 5.31/5.63 = ( divide_divide_real @ ( minus_minus_real @ ( uminus_uminus_real @ X ) @ ( times_times_real @ Y @ Z3 ) ) @ Z3 ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % minus_divide_diff_eq_iff
% 5.31/5.63 thf(fact_7863_minus__divide__diff__eq__iff,axiom,
% 5.31/5.63 ! [Z3: complex,X: complex,Y: complex] :
% 5.31/5.63 ( ( Z3 != zero_zero_complex )
% 5.31/5.63 => ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ X @ Z3 ) ) @ Y )
% 5.31/5.63 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( uminus1482373934393186551omplex @ X ) @ ( times_times_complex @ Y @ Z3 ) ) @ Z3 ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % minus_divide_diff_eq_iff
% 5.31/5.63 thf(fact_7864_minus__divide__diff__eq__iff,axiom,
% 5.31/5.63 ! [Z3: rat,X: rat,Y: rat] :
% 5.31/5.63 ( ( Z3 != zero_zero_rat )
% 5.31/5.63 => ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ X @ Z3 ) ) @ Y )
% 5.31/5.63 = ( divide_divide_rat @ ( minus_minus_rat @ ( uminus_uminus_rat @ X ) @ ( times_times_rat @ Y @ Z3 ) ) @ Z3 ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % minus_divide_diff_eq_iff
% 5.31/5.63 thf(fact_7865_choose__dvd,axiom,
% 5.31/5.63 ! [K2: nat,N: nat] :
% 5.31/5.63 ( ( ord_less_eq_nat @ K2 @ N )
% 5.31/5.63 => ( dvd_dvd_rat @ ( times_times_rat @ ( semiri773545260158071498ct_rat @ K2 ) @ ( semiri773545260158071498ct_rat @ ( minus_minus_nat @ N @ K2 ) ) ) @ ( semiri773545260158071498ct_rat @ N ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % choose_dvd
% 5.31/5.63 thf(fact_7866_choose__dvd,axiom,
% 5.31/5.63 ! [K2: nat,N: nat] :
% 5.31/5.63 ( ( ord_less_eq_nat @ K2 @ N )
% 5.31/5.63 => ( dvd_dvd_int @ ( times_times_int @ ( semiri1406184849735516958ct_int @ K2 ) @ ( semiri1406184849735516958ct_int @ ( minus_minus_nat @ N @ K2 ) ) ) @ ( semiri1406184849735516958ct_int @ N ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % choose_dvd
% 5.31/5.63 thf(fact_7867_choose__dvd,axiom,
% 5.31/5.63 ! [K2: nat,N: nat] :
% 5.31/5.63 ( ( ord_less_eq_nat @ K2 @ N )
% 5.31/5.63 => ( dvd_dvd_nat @ ( times_times_nat @ ( semiri1408675320244567234ct_nat @ K2 ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N @ K2 ) ) ) @ ( semiri1408675320244567234ct_nat @ N ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % choose_dvd
% 5.31/5.63 thf(fact_7868_choose__dvd,axiom,
% 5.31/5.63 ! [K2: nat,N: nat] :
% 5.31/5.63 ( ( ord_less_eq_nat @ K2 @ N )
% 5.31/5.63 => ( dvd_dvd_real @ ( times_times_real @ ( semiri2265585572941072030t_real @ K2 ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N @ K2 ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % choose_dvd
% 5.31/5.63 thf(fact_7869_int__cases3,axiom,
% 5.31/5.63 ! [K2: int] :
% 5.31/5.63 ( ( K2 != zero_zero_int )
% 5.31/5.63 => ( ! [N3: nat] :
% 5.31/5.63 ( ( K2
% 5.31/5.63 = ( semiri1314217659103216013at_int @ N3 ) )
% 5.31/5.63 => ~ ( ord_less_nat @ zero_zero_nat @ N3 ) )
% 5.31/5.63 => ~ ! [N3: nat] :
% 5.31/5.63 ( ( K2
% 5.31/5.63 = ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N3 ) ) )
% 5.31/5.63 => ~ ( ord_less_nat @ zero_zero_nat @ N3 ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % int_cases3
% 5.31/5.63 thf(fact_7870_pochhammer__of__nat__eq__0__lemma,axiom,
% 5.31/5.63 ! [N: nat,K2: nat] :
% 5.31/5.63 ( ( ord_less_nat @ N @ K2 )
% 5.31/5.63 => ( ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ N ) ) @ K2 )
% 5.31/5.63 = zero_zero_complex ) ) ).
% 5.31/5.63
% 5.31/5.63 % pochhammer_of_nat_eq_0_lemma
% 5.31/5.63 thf(fact_7871_pochhammer__of__nat__eq__0__lemma,axiom,
% 5.31/5.63 ! [N: nat,K2: nat] :
% 5.31/5.63 ( ( ord_less_nat @ N @ K2 )
% 5.31/5.63 => ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ ( semiri4939895301339042750nteger @ N ) ) @ K2 )
% 5.31/5.63 = zero_z3403309356797280102nteger ) ) ).
% 5.31/5.63
% 5.31/5.63 % pochhammer_of_nat_eq_0_lemma
% 5.31/5.63 thf(fact_7872_pochhammer__of__nat__eq__0__lemma,axiom,
% 5.31/5.63 ! [N: nat,K2: nat] :
% 5.31/5.63 ( ( ord_less_nat @ N @ K2 )
% 5.31/5.63 => ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ N ) ) @ K2 )
% 5.31/5.63 = zero_zero_rat ) ) ).
% 5.31/5.63
% 5.31/5.63 % pochhammer_of_nat_eq_0_lemma
% 5.31/5.63 thf(fact_7873_pochhammer__of__nat__eq__0__lemma,axiom,
% 5.31/5.63 ! [N: nat,K2: nat] :
% 5.31/5.63 ( ( ord_less_nat @ N @ K2 )
% 5.31/5.63 => ( ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N ) ) @ K2 )
% 5.31/5.63 = zero_zero_real ) ) ).
% 5.31/5.63
% 5.31/5.63 % pochhammer_of_nat_eq_0_lemma
% 5.31/5.63 thf(fact_7874_pochhammer__of__nat__eq__0__lemma,axiom,
% 5.31/5.63 ! [N: nat,K2: nat] :
% 5.31/5.63 ( ( ord_less_nat @ N @ K2 )
% 5.31/5.63 => ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) @ K2 )
% 5.31/5.63 = zero_zero_int ) ) ).
% 5.31/5.63
% 5.31/5.63 % pochhammer_of_nat_eq_0_lemma
% 5.31/5.63 thf(fact_7875_pochhammer__of__nat__eq__0__iff,axiom,
% 5.31/5.63 ! [N: nat,K2: nat] :
% 5.31/5.63 ( ( ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ N ) ) @ K2 )
% 5.31/5.63 = zero_zero_complex )
% 5.31/5.63 = ( ord_less_nat @ N @ K2 ) ) ).
% 5.31/5.63
% 5.31/5.63 % pochhammer_of_nat_eq_0_iff
% 5.31/5.63 thf(fact_7876_pochhammer__of__nat__eq__0__iff,axiom,
% 5.31/5.63 ! [N: nat,K2: nat] :
% 5.31/5.63 ( ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ ( semiri4939895301339042750nteger @ N ) ) @ K2 )
% 5.31/5.63 = zero_z3403309356797280102nteger )
% 5.31/5.63 = ( ord_less_nat @ N @ K2 ) ) ).
% 5.31/5.63
% 5.31/5.63 % pochhammer_of_nat_eq_0_iff
% 5.31/5.63 thf(fact_7877_pochhammer__of__nat__eq__0__iff,axiom,
% 5.31/5.63 ! [N: nat,K2: nat] :
% 5.31/5.63 ( ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ N ) ) @ K2 )
% 5.31/5.63 = zero_zero_rat )
% 5.31/5.63 = ( ord_less_nat @ N @ K2 ) ) ).
% 5.31/5.63
% 5.31/5.63 % pochhammer_of_nat_eq_0_iff
% 5.31/5.63 thf(fact_7878_pochhammer__of__nat__eq__0__iff,axiom,
% 5.31/5.63 ! [N: nat,K2: nat] :
% 5.31/5.63 ( ( ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N ) ) @ K2 )
% 5.31/5.63 = zero_zero_real )
% 5.31/5.63 = ( ord_less_nat @ N @ K2 ) ) ).
% 5.31/5.63
% 5.31/5.63 % pochhammer_of_nat_eq_0_iff
% 5.31/5.63 thf(fact_7879_pochhammer__of__nat__eq__0__iff,axiom,
% 5.31/5.63 ! [N: nat,K2: nat] :
% 5.31/5.63 ( ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) @ K2 )
% 5.31/5.63 = zero_zero_int )
% 5.31/5.63 = ( ord_less_nat @ N @ K2 ) ) ).
% 5.31/5.63
% 5.31/5.63 % pochhammer_of_nat_eq_0_iff
% 5.31/5.63 thf(fact_7880_pochhammer__eq__0__iff,axiom,
% 5.31/5.63 ! [A: complex,N: nat] :
% 5.31/5.63 ( ( ( comm_s2602460028002588243omplex @ A @ N )
% 5.31/5.63 = zero_zero_complex )
% 5.31/5.63 = ( ? [K3: nat] :
% 5.31/5.63 ( ( ord_less_nat @ K3 @ N )
% 5.31/5.63 & ( A
% 5.31/5.63 = ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ K3 ) ) ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % pochhammer_eq_0_iff
% 5.31/5.63 thf(fact_7881_pochhammer__eq__0__iff,axiom,
% 5.31/5.63 ! [A: rat,N: nat] :
% 5.31/5.63 ( ( ( comm_s4028243227959126397er_rat @ A @ N )
% 5.31/5.63 = zero_zero_rat )
% 5.31/5.63 = ( ? [K3: nat] :
% 5.31/5.63 ( ( ord_less_nat @ K3 @ N )
% 5.31/5.63 & ( A
% 5.31/5.63 = ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ K3 ) ) ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % pochhammer_eq_0_iff
% 5.31/5.63 thf(fact_7882_pochhammer__eq__0__iff,axiom,
% 5.31/5.63 ! [A: real,N: nat] :
% 5.31/5.63 ( ( ( comm_s7457072308508201937r_real @ A @ N )
% 5.31/5.63 = zero_zero_real )
% 5.31/5.63 = ( ? [K3: nat] :
% 5.31/5.63 ( ( ord_less_nat @ K3 @ N )
% 5.31/5.63 & ( A
% 5.31/5.63 = ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ K3 ) ) ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % pochhammer_eq_0_iff
% 5.31/5.63 thf(fact_7883_pochhammer__of__nat__eq__0__lemma_H,axiom,
% 5.31/5.63 ! [K2: nat,N: nat] :
% 5.31/5.63 ( ( ord_less_eq_nat @ K2 @ N )
% 5.31/5.63 => ( ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ N ) ) @ K2 )
% 5.31/5.63 != zero_zero_complex ) ) ).
% 5.31/5.63
% 5.31/5.63 % pochhammer_of_nat_eq_0_lemma'
% 5.31/5.63 thf(fact_7884_pochhammer__of__nat__eq__0__lemma_H,axiom,
% 5.31/5.63 ! [K2: nat,N: nat] :
% 5.31/5.63 ( ( ord_less_eq_nat @ K2 @ N )
% 5.31/5.63 => ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ ( semiri4939895301339042750nteger @ N ) ) @ K2 )
% 5.31/5.63 != zero_z3403309356797280102nteger ) ) ).
% 5.31/5.63
% 5.31/5.63 % pochhammer_of_nat_eq_0_lemma'
% 5.31/5.63 thf(fact_7885_pochhammer__of__nat__eq__0__lemma_H,axiom,
% 5.31/5.63 ! [K2: nat,N: nat] :
% 5.31/5.63 ( ( ord_less_eq_nat @ K2 @ N )
% 5.31/5.63 => ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ N ) ) @ K2 )
% 5.31/5.63 != zero_zero_rat ) ) ).
% 5.31/5.63
% 5.31/5.63 % pochhammer_of_nat_eq_0_lemma'
% 5.31/5.63 thf(fact_7886_pochhammer__of__nat__eq__0__lemma_H,axiom,
% 5.31/5.63 ! [K2: nat,N: nat] :
% 5.31/5.63 ( ( ord_less_eq_nat @ K2 @ N )
% 5.31/5.63 => ( ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N ) ) @ K2 )
% 5.31/5.63 != zero_zero_real ) ) ).
% 5.31/5.63
% 5.31/5.63 % pochhammer_of_nat_eq_0_lemma'
% 5.31/5.63 thf(fact_7887_pochhammer__of__nat__eq__0__lemma_H,axiom,
% 5.31/5.63 ! [K2: nat,N: nat] :
% 5.31/5.63 ( ( ord_less_eq_nat @ K2 @ N )
% 5.31/5.63 => ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) @ K2 )
% 5.31/5.63 != zero_zero_int ) ) ).
% 5.31/5.63
% 5.31/5.63 % pochhammer_of_nat_eq_0_lemma'
% 5.31/5.63 thf(fact_7888_not__zle__0__negative,axiom,
% 5.31/5.63 ! [N: nat] :
% 5.31/5.63 ~ ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % not_zle_0_negative
% 5.31/5.63 thf(fact_7889_negD,axiom,
% 5.31/5.63 ! [X: int] :
% 5.31/5.63 ( ( ord_less_int @ X @ zero_zero_int )
% 5.31/5.63 => ? [N3: nat] :
% 5.31/5.63 ( X
% 5.31/5.63 = ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N3 ) ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % negD
% 5.31/5.63 thf(fact_7890_negative__zless__0,axiom,
% 5.31/5.63 ! [N: nat] : ( ord_less_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N ) ) ) @ zero_zero_int ) ).
% 5.31/5.63
% 5.31/5.63 % negative_zless_0
% 5.31/5.63 thf(fact_7891_div__eq__minus1,axiom,
% 5.31/5.63 ! [B: int] :
% 5.31/5.63 ( ( ord_less_int @ zero_zero_int @ B )
% 5.31/5.63 => ( ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ B )
% 5.31/5.63 = ( uminus_uminus_int @ one_one_int ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % div_eq_minus1
% 5.31/5.63 thf(fact_7892_prod_OIf__cases,axiom,
% 5.31/5.63 ! [A4: set_real,P2: real > $o,H: real > real,G2: real > real] :
% 5.31/5.63 ( ( finite_finite_real @ A4 )
% 5.31/5.63 => ( ( groups1681761925125756287l_real
% 5.31/5.63 @ ^ [X4: real] : ( if_real @ ( P2 @ X4 ) @ ( H @ X4 ) @ ( G2 @ X4 ) )
% 5.31/5.63 @ A4 )
% 5.31/5.63 = ( times_times_real @ ( groups1681761925125756287l_real @ H @ ( inf_inf_set_real @ A4 @ ( collect_real @ P2 ) ) ) @ ( groups1681761925125756287l_real @ G2 @ ( inf_inf_set_real @ A4 @ ( uminus612125837232591019t_real @ ( collect_real @ P2 ) ) ) ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % prod.If_cases
% 5.31/5.63 thf(fact_7893_prod_OIf__cases,axiom,
% 5.31/5.63 ! [A4: set_int,P2: int > $o,H: int > real,G2: int > real] :
% 5.31/5.63 ( ( finite_finite_int @ A4 )
% 5.31/5.63 => ( ( groups2316167850115554303t_real
% 5.31/5.63 @ ^ [X4: int] : ( if_real @ ( P2 @ X4 ) @ ( H @ X4 ) @ ( G2 @ X4 ) )
% 5.31/5.63 @ A4 )
% 5.31/5.63 = ( times_times_real @ ( groups2316167850115554303t_real @ H @ ( inf_inf_set_int @ A4 @ ( collect_int @ P2 ) ) ) @ ( groups2316167850115554303t_real @ G2 @ ( inf_inf_set_int @ A4 @ ( uminus1532241313380277803et_int @ ( collect_int @ P2 ) ) ) ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % prod.If_cases
% 5.31/5.63 thf(fact_7894_prod_OIf__cases,axiom,
% 5.31/5.63 ! [A4: set_complex,P2: complex > $o,H: complex > real,G2: complex > real] :
% 5.31/5.63 ( ( finite3207457112153483333omplex @ A4 )
% 5.31/5.63 => ( ( groups766887009212190081x_real
% 5.31/5.63 @ ^ [X4: complex] : ( if_real @ ( P2 @ X4 ) @ ( H @ X4 ) @ ( G2 @ X4 ) )
% 5.31/5.63 @ A4 )
% 5.31/5.63 = ( times_times_real @ ( groups766887009212190081x_real @ H @ ( inf_inf_set_complex @ A4 @ ( collect_complex @ P2 ) ) ) @ ( groups766887009212190081x_real @ G2 @ ( inf_inf_set_complex @ A4 @ ( uminus8566677241136511917omplex @ ( collect_complex @ P2 ) ) ) ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % prod.If_cases
% 5.31/5.63 thf(fact_7895_prod_OIf__cases,axiom,
% 5.31/5.63 ! [A4: set_nat,P2: nat > $o,H: nat > real,G2: nat > real] :
% 5.31/5.63 ( ( finite_finite_nat @ A4 )
% 5.31/5.63 => ( ( groups129246275422532515t_real
% 5.31/5.63 @ ^ [X4: nat] : ( if_real @ ( P2 @ X4 ) @ ( H @ X4 ) @ ( G2 @ X4 ) )
% 5.31/5.63 @ A4 )
% 5.31/5.63 = ( times_times_real @ ( groups129246275422532515t_real @ H @ ( inf_inf_set_nat @ A4 @ ( collect_nat @ P2 ) ) ) @ ( groups129246275422532515t_real @ G2 @ ( inf_inf_set_nat @ A4 @ ( uminus5710092332889474511et_nat @ ( collect_nat @ P2 ) ) ) ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % prod.If_cases
% 5.31/5.63 thf(fact_7896_prod_OIf__cases,axiom,
% 5.31/5.63 ! [A4: set_real,P2: real > $o,H: real > rat,G2: real > rat] :
% 5.31/5.63 ( ( finite_finite_real @ A4 )
% 5.31/5.63 => ( ( groups4061424788464935467al_rat
% 5.31/5.63 @ ^ [X4: real] : ( if_rat @ ( P2 @ X4 ) @ ( H @ X4 ) @ ( G2 @ X4 ) )
% 5.31/5.63 @ A4 )
% 5.31/5.63 = ( times_times_rat @ ( groups4061424788464935467al_rat @ H @ ( inf_inf_set_real @ A4 @ ( collect_real @ P2 ) ) ) @ ( groups4061424788464935467al_rat @ G2 @ ( inf_inf_set_real @ A4 @ ( uminus612125837232591019t_real @ ( collect_real @ P2 ) ) ) ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % prod.If_cases
% 5.31/5.63 thf(fact_7897_prod_OIf__cases,axiom,
% 5.31/5.63 ! [A4: set_int,P2: int > $o,H: int > rat,G2: int > rat] :
% 5.31/5.63 ( ( finite_finite_int @ A4 )
% 5.31/5.63 => ( ( groups1072433553688619179nt_rat
% 5.31/5.63 @ ^ [X4: int] : ( if_rat @ ( P2 @ X4 ) @ ( H @ X4 ) @ ( G2 @ X4 ) )
% 5.31/5.63 @ A4 )
% 5.31/5.63 = ( times_times_rat @ ( groups1072433553688619179nt_rat @ H @ ( inf_inf_set_int @ A4 @ ( collect_int @ P2 ) ) ) @ ( groups1072433553688619179nt_rat @ G2 @ ( inf_inf_set_int @ A4 @ ( uminus1532241313380277803et_int @ ( collect_int @ P2 ) ) ) ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % prod.If_cases
% 5.31/5.63 thf(fact_7898_prod_OIf__cases,axiom,
% 5.31/5.63 ! [A4: set_complex,P2: complex > $o,H: complex > rat,G2: complex > rat] :
% 5.31/5.63 ( ( finite3207457112153483333omplex @ A4 )
% 5.31/5.63 => ( ( groups225925009352817453ex_rat
% 5.31/5.63 @ ^ [X4: complex] : ( if_rat @ ( P2 @ X4 ) @ ( H @ X4 ) @ ( G2 @ X4 ) )
% 5.31/5.63 @ A4 )
% 5.31/5.63 = ( times_times_rat @ ( groups225925009352817453ex_rat @ H @ ( inf_inf_set_complex @ A4 @ ( collect_complex @ P2 ) ) ) @ ( groups225925009352817453ex_rat @ G2 @ ( inf_inf_set_complex @ A4 @ ( uminus8566677241136511917omplex @ ( collect_complex @ P2 ) ) ) ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % prod.If_cases
% 5.31/5.63 thf(fact_7899_prod_OIf__cases,axiom,
% 5.31/5.63 ! [A4: set_nat,P2: nat > $o,H: nat > rat,G2: nat > rat] :
% 5.31/5.63 ( ( finite_finite_nat @ A4 )
% 5.31/5.63 => ( ( groups73079841787564623at_rat
% 5.31/5.63 @ ^ [X4: nat] : ( if_rat @ ( P2 @ X4 ) @ ( H @ X4 ) @ ( G2 @ X4 ) )
% 5.31/5.63 @ A4 )
% 5.31/5.63 = ( times_times_rat @ ( groups73079841787564623at_rat @ H @ ( inf_inf_set_nat @ A4 @ ( collect_nat @ P2 ) ) ) @ ( groups73079841787564623at_rat @ G2 @ ( inf_inf_set_nat @ A4 @ ( uminus5710092332889474511et_nat @ ( collect_nat @ P2 ) ) ) ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % prod.If_cases
% 5.31/5.63 thf(fact_7900_prod_OIf__cases,axiom,
% 5.31/5.63 ! [A4: set_real,P2: real > $o,H: real > nat,G2: real > nat] :
% 5.31/5.63 ( ( finite_finite_real @ A4 )
% 5.31/5.63 => ( ( groups4696554848551431203al_nat
% 5.31/5.63 @ ^ [X4: real] : ( if_nat @ ( P2 @ X4 ) @ ( H @ X4 ) @ ( G2 @ X4 ) )
% 5.31/5.63 @ A4 )
% 5.31/5.63 = ( times_times_nat @ ( groups4696554848551431203al_nat @ H @ ( inf_inf_set_real @ A4 @ ( collect_real @ P2 ) ) ) @ ( groups4696554848551431203al_nat @ G2 @ ( inf_inf_set_real @ A4 @ ( uminus612125837232591019t_real @ ( collect_real @ P2 ) ) ) ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % prod.If_cases
% 5.31/5.63 thf(fact_7901_prod_OIf__cases,axiom,
% 5.31/5.63 ! [A4: set_int,P2: int > $o,H: int > nat,G2: int > nat] :
% 5.31/5.63 ( ( finite_finite_int @ A4 )
% 5.31/5.63 => ( ( groups1707563613775114915nt_nat
% 5.31/5.63 @ ^ [X4: int] : ( if_nat @ ( P2 @ X4 ) @ ( H @ X4 ) @ ( G2 @ X4 ) )
% 5.31/5.63 @ A4 )
% 5.31/5.63 = ( times_times_nat @ ( groups1707563613775114915nt_nat @ H @ ( inf_inf_set_int @ A4 @ ( collect_int @ P2 ) ) ) @ ( groups1707563613775114915nt_nat @ G2 @ ( inf_inf_set_int @ A4 @ ( uminus1532241313380277803et_int @ ( collect_int @ P2 ) ) ) ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % prod.If_cases
% 5.31/5.63 thf(fact_7902_binomial__altdef__nat,axiom,
% 5.31/5.63 ! [K2: nat,N: nat] :
% 5.31/5.63 ( ( ord_less_eq_nat @ K2 @ N )
% 5.31/5.63 => ( ( binomial @ N @ K2 )
% 5.31/5.63 = ( divide_divide_nat @ ( semiri1408675320244567234ct_nat @ N ) @ ( times_times_nat @ ( semiri1408675320244567234ct_nat @ K2 ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N @ K2 ) ) ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % binomial_altdef_nat
% 5.31/5.63 thf(fact_7903_le__minus__divide__eq,axiom,
% 5.31/5.63 ! [A: real,B: real,C2: real] :
% 5.31/5.63 ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C2 ) ) )
% 5.31/5.63 = ( ( ( ord_less_real @ zero_zero_real @ C2 )
% 5.31/5.63 => ( ord_less_eq_real @ ( times_times_real @ A @ C2 ) @ ( uminus_uminus_real @ B ) ) )
% 5.31/5.63 & ( ~ ( ord_less_real @ zero_zero_real @ C2 )
% 5.31/5.63 => ( ( ( ord_less_real @ C2 @ zero_zero_real )
% 5.31/5.63 => ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C2 ) ) )
% 5.31/5.63 & ( ~ ( ord_less_real @ C2 @ zero_zero_real )
% 5.31/5.63 => ( ord_less_eq_real @ A @ zero_zero_real ) ) ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % le_minus_divide_eq
% 5.31/5.63 thf(fact_7904_le__minus__divide__eq,axiom,
% 5.31/5.63 ! [A: rat,B: rat,C2: rat] :
% 5.31/5.63 ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C2 ) ) )
% 5.31/5.63 = ( ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 5.31/5.63 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C2 ) @ ( uminus_uminus_rat @ B ) ) )
% 5.31/5.63 & ( ~ ( ord_less_rat @ zero_zero_rat @ C2 )
% 5.31/5.63 => ( ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 5.31/5.63 => ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C2 ) ) )
% 5.31/5.63 & ( ~ ( ord_less_rat @ C2 @ zero_zero_rat )
% 5.31/5.63 => ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % le_minus_divide_eq
% 5.31/5.63 thf(fact_7905_minus__divide__le__eq,axiom,
% 5.31/5.63 ! [B: real,C2: real,A: real] :
% 5.31/5.63 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C2 ) ) @ A )
% 5.31/5.63 = ( ( ( ord_less_real @ zero_zero_real @ C2 )
% 5.31/5.63 => ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C2 ) ) )
% 5.31/5.63 & ( ~ ( ord_less_real @ zero_zero_real @ C2 )
% 5.31/5.63 => ( ( ( ord_less_real @ C2 @ zero_zero_real )
% 5.31/5.63 => ( ord_less_eq_real @ ( times_times_real @ A @ C2 ) @ ( uminus_uminus_real @ B ) ) )
% 5.31/5.63 & ( ~ ( ord_less_real @ C2 @ zero_zero_real )
% 5.31/5.63 => ( ord_less_eq_real @ zero_zero_real @ A ) ) ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % minus_divide_le_eq
% 5.31/5.63 thf(fact_7906_minus__divide__le__eq,axiom,
% 5.31/5.63 ! [B: rat,C2: rat,A: rat] :
% 5.31/5.63 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C2 ) ) @ A )
% 5.31/5.63 = ( ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 5.31/5.63 => ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C2 ) ) )
% 5.31/5.63 & ( ~ ( ord_less_rat @ zero_zero_rat @ C2 )
% 5.31/5.63 => ( ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 5.31/5.63 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C2 ) @ ( uminus_uminus_rat @ B ) ) )
% 5.31/5.63 & ( ~ ( ord_less_rat @ C2 @ zero_zero_rat )
% 5.31/5.63 => ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % minus_divide_le_eq
% 5.31/5.63 thf(fact_7907_neg__le__minus__divide__eq,axiom,
% 5.31/5.63 ! [C2: real,A: real,B: real] :
% 5.31/5.63 ( ( ord_less_real @ C2 @ zero_zero_real )
% 5.31/5.63 => ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C2 ) ) )
% 5.31/5.63 = ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C2 ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % neg_le_minus_divide_eq
% 5.31/5.63 thf(fact_7908_neg__le__minus__divide__eq,axiom,
% 5.31/5.63 ! [C2: rat,A: rat,B: rat] :
% 5.31/5.63 ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 5.31/5.63 => ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C2 ) ) )
% 5.31/5.63 = ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C2 ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % neg_le_minus_divide_eq
% 5.31/5.63 thf(fact_7909_neg__minus__divide__le__eq,axiom,
% 5.31/5.63 ! [C2: real,B: real,A: real] :
% 5.31/5.63 ( ( ord_less_real @ C2 @ zero_zero_real )
% 5.31/5.63 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C2 ) ) @ A )
% 5.31/5.63 = ( ord_less_eq_real @ ( times_times_real @ A @ C2 ) @ ( uminus_uminus_real @ B ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % neg_minus_divide_le_eq
% 5.31/5.63 thf(fact_7910_neg__minus__divide__le__eq,axiom,
% 5.31/5.63 ! [C2: rat,B: rat,A: rat] :
% 5.31/5.63 ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 5.31/5.63 => ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C2 ) ) @ A )
% 5.31/5.63 = ( ord_less_eq_rat @ ( times_times_rat @ A @ C2 ) @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % neg_minus_divide_le_eq
% 5.31/5.63 thf(fact_7911_pos__le__minus__divide__eq,axiom,
% 5.31/5.63 ! [C2: real,A: real,B: real] :
% 5.31/5.63 ( ( ord_less_real @ zero_zero_real @ C2 )
% 5.31/5.63 => ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C2 ) ) )
% 5.31/5.63 = ( ord_less_eq_real @ ( times_times_real @ A @ C2 ) @ ( uminus_uminus_real @ B ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % pos_le_minus_divide_eq
% 5.31/5.63 thf(fact_7912_pos__le__minus__divide__eq,axiom,
% 5.31/5.63 ! [C2: rat,A: rat,B: rat] :
% 5.31/5.63 ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 5.31/5.63 => ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C2 ) ) )
% 5.31/5.63 = ( ord_less_eq_rat @ ( times_times_rat @ A @ C2 ) @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % pos_le_minus_divide_eq
% 5.31/5.63 thf(fact_7913_pos__minus__divide__le__eq,axiom,
% 5.31/5.63 ! [C2: real,B: real,A: real] :
% 5.31/5.63 ( ( ord_less_real @ zero_zero_real @ C2 )
% 5.31/5.63 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C2 ) ) @ A )
% 5.31/5.63 = ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C2 ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % pos_minus_divide_le_eq
% 5.31/5.63 thf(fact_7914_pos__minus__divide__le__eq,axiom,
% 5.31/5.63 ! [C2: rat,B: rat,A: rat] :
% 5.31/5.63 ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 5.31/5.63 => ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C2 ) ) @ A )
% 5.31/5.63 = ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C2 ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % pos_minus_divide_le_eq
% 5.31/5.63 thf(fact_7915_divide__less__eq__numeral_I2_J,axiom,
% 5.31/5.63 ! [B: real,C2: real,W2: num] :
% 5.31/5.63 ( ( ord_less_real @ ( divide_divide_real @ B @ C2 ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) )
% 5.31/5.63 = ( ( ( ord_less_real @ zero_zero_real @ C2 )
% 5.31/5.63 => ( ord_less_real @ B @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) @ C2 ) ) )
% 5.31/5.63 & ( ~ ( ord_less_real @ zero_zero_real @ C2 )
% 5.31/5.63 => ( ( ( ord_less_real @ C2 @ zero_zero_real )
% 5.31/5.63 => ( ord_less_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) @ C2 ) @ B ) )
% 5.31/5.63 & ( ~ ( ord_less_real @ C2 @ zero_zero_real )
% 5.31/5.63 => ( ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) ) ) ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % divide_less_eq_numeral(2)
% 5.31/5.63 thf(fact_7916_divide__less__eq__numeral_I2_J,axiom,
% 5.31/5.63 ! [B: rat,C2: rat,W2: num] :
% 5.31/5.63 ( ( ord_less_rat @ ( divide_divide_rat @ B @ C2 ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) )
% 5.31/5.63 = ( ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 5.31/5.63 => ( ord_less_rat @ B @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ C2 ) ) )
% 5.31/5.63 & ( ~ ( ord_less_rat @ zero_zero_rat @ C2 )
% 5.31/5.63 => ( ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 5.31/5.63 => ( ord_less_rat @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ C2 ) @ B ) )
% 5.31/5.63 & ( ~ ( ord_less_rat @ C2 @ zero_zero_rat )
% 5.31/5.63 => ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) ) ) ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % divide_less_eq_numeral(2)
% 5.31/5.63 thf(fact_7917_less__divide__eq__numeral_I2_J,axiom,
% 5.31/5.63 ! [W2: num,B: real,C2: real] :
% 5.31/5.63 ( ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) @ ( divide_divide_real @ B @ C2 ) )
% 5.31/5.63 = ( ( ( ord_less_real @ zero_zero_real @ C2 )
% 5.31/5.63 => ( ord_less_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) @ C2 ) @ B ) )
% 5.31/5.63 & ( ~ ( ord_less_real @ zero_zero_real @ C2 )
% 5.31/5.63 => ( ( ( ord_less_real @ C2 @ zero_zero_real )
% 5.31/5.63 => ( ord_less_real @ B @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) @ C2 ) ) )
% 5.31/5.63 & ( ~ ( ord_less_real @ C2 @ zero_zero_real )
% 5.31/5.63 => ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) @ zero_zero_real ) ) ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % less_divide_eq_numeral(2)
% 5.31/5.63 thf(fact_7918_less__divide__eq__numeral_I2_J,axiom,
% 5.31/5.63 ! [W2: num,B: rat,C2: rat] :
% 5.31/5.63 ( ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ ( divide_divide_rat @ B @ C2 ) )
% 5.31/5.63 = ( ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 5.31/5.63 => ( ord_less_rat @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ C2 ) @ B ) )
% 5.31/5.63 & ( ~ ( ord_less_rat @ zero_zero_rat @ C2 )
% 5.31/5.63 => ( ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 5.31/5.63 => ( ord_less_rat @ B @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ C2 ) ) )
% 5.31/5.63 & ( ~ ( ord_less_rat @ C2 @ zero_zero_rat )
% 5.31/5.63 => ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ zero_zero_rat ) ) ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % less_divide_eq_numeral(2)
% 5.31/5.63 thf(fact_7919_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 5.31/5.63 ! [K2: nat,N: nat] :
% 5.31/5.63 ( ( ord_less_eq_nat @ K2 @ N )
% 5.31/5.63 => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( plus_plus_nat @ N @ K2 ) )
% 5.31/5.63 = ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( minus_minus_nat @ N @ K2 ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % neg_one_power_add_eq_neg_one_power_diff
% 5.31/5.63 thf(fact_7920_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 5.31/5.63 ! [K2: nat,N: nat] :
% 5.31/5.63 ( ( ord_less_eq_nat @ K2 @ N )
% 5.31/5.63 => ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( plus_plus_nat @ N @ K2 ) )
% 5.31/5.63 = ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( minus_minus_nat @ N @ K2 ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % neg_one_power_add_eq_neg_one_power_diff
% 5.31/5.63 thf(fact_7921_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 5.31/5.63 ! [K2: nat,N: nat] :
% 5.31/5.63 ( ( ord_less_eq_nat @ K2 @ N )
% 5.31/5.63 => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( plus_plus_nat @ N @ K2 ) )
% 5.31/5.63 = ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( minus_minus_nat @ N @ K2 ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % neg_one_power_add_eq_neg_one_power_diff
% 5.31/5.63 thf(fact_7922_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 5.31/5.63 ! [K2: nat,N: nat] :
% 5.31/5.63 ( ( ord_less_eq_nat @ K2 @ N )
% 5.31/5.63 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( plus_plus_nat @ N @ K2 ) )
% 5.31/5.63 = ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( minus_minus_nat @ N @ K2 ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % neg_one_power_add_eq_neg_one_power_diff
% 5.31/5.63 thf(fact_7923_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 5.31/5.63 ! [K2: nat,N: nat] :
% 5.31/5.63 ( ( ord_less_eq_nat @ K2 @ N )
% 5.31/5.63 => ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( plus_plus_nat @ N @ K2 ) )
% 5.31/5.63 = ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( minus_minus_nat @ N @ K2 ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % neg_one_power_add_eq_neg_one_power_diff
% 5.31/5.63 thf(fact_7924_neg__int__cases,axiom,
% 5.31/5.63 ! [K2: int] :
% 5.31/5.63 ( ( ord_less_int @ K2 @ zero_zero_int )
% 5.31/5.63 => ~ ! [N3: nat] :
% 5.31/5.63 ( ( K2
% 5.31/5.63 = ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N3 ) ) )
% 5.31/5.63 => ~ ( ord_less_nat @ zero_zero_nat @ N3 ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % neg_int_cases
% 5.31/5.63 thf(fact_7925_minus__mod__int__eq,axiom,
% 5.31/5.63 ! [L: int,K2: int] :
% 5.31/5.63 ( ( ord_less_eq_int @ zero_zero_int @ L )
% 5.31/5.63 => ( ( modulo_modulo_int @ ( uminus_uminus_int @ K2 ) @ L )
% 5.31/5.63 = ( minus_minus_int @ ( minus_minus_int @ L @ one_one_int ) @ ( modulo_modulo_int @ ( minus_minus_int @ K2 @ one_one_int ) @ L ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % minus_mod_int_eq
% 5.31/5.63 thf(fact_7926_zmod__minus1,axiom,
% 5.31/5.63 ! [B: int] :
% 5.31/5.63 ( ( ord_less_int @ zero_zero_int @ B )
% 5.31/5.63 => ( ( modulo_modulo_int @ ( uminus_uminus_int @ one_one_int ) @ B )
% 5.31/5.63 = ( minus_minus_int @ B @ one_one_int ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % zmod_minus1
% 5.31/5.63 thf(fact_7927_zdiv__zminus1__eq__if,axiom,
% 5.31/5.63 ! [B: int,A: int] :
% 5.31/5.63 ( ( B != zero_zero_int )
% 5.31/5.63 => ( ( ( ( modulo_modulo_int @ A @ B )
% 5.31/5.63 = zero_zero_int )
% 5.31/5.63 => ( ( divide_divide_int @ ( uminus_uminus_int @ A ) @ B )
% 5.31/5.63 = ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) ) )
% 5.31/5.63 & ( ( ( modulo_modulo_int @ A @ B )
% 5.31/5.63 != zero_zero_int )
% 5.31/5.63 => ( ( divide_divide_int @ ( uminus_uminus_int @ A ) @ B )
% 5.31/5.63 = ( minus_minus_int @ ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) @ one_one_int ) ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % zdiv_zminus1_eq_if
% 5.31/5.63 thf(fact_7928_zdiv__zminus2__eq__if,axiom,
% 5.31/5.63 ! [B: int,A: int] :
% 5.31/5.63 ( ( B != zero_zero_int )
% 5.31/5.63 => ( ( ( ( modulo_modulo_int @ A @ B )
% 5.31/5.63 = zero_zero_int )
% 5.31/5.63 => ( ( divide_divide_int @ A @ ( uminus_uminus_int @ B ) )
% 5.31/5.63 = ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) ) )
% 5.31/5.63 & ( ( ( modulo_modulo_int @ A @ B )
% 5.31/5.63 != zero_zero_int )
% 5.31/5.63 => ( ( divide_divide_int @ A @ ( uminus_uminus_int @ B ) )
% 5.31/5.63 = ( minus_minus_int @ ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) @ one_one_int ) ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % zdiv_zminus2_eq_if
% 5.31/5.63 thf(fact_7929_fact__eq__fact__times,axiom,
% 5.31/5.63 ! [N: nat,M2: nat] :
% 5.31/5.63 ( ( ord_less_eq_nat @ N @ M2 )
% 5.31/5.63 => ( ( semiri1408675320244567234ct_nat @ M2 )
% 5.31/5.63 = ( times_times_nat @ ( semiri1408675320244567234ct_nat @ N )
% 5.31/5.63 @ ( groups708209901874060359at_nat
% 5.31/5.63 @ ^ [X4: nat] : X4
% 5.31/5.63 @ ( set_or1269000886237332187st_nat @ ( suc @ N ) @ M2 ) ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % fact_eq_fact_times
% 5.31/5.63 thf(fact_7930_signed__take__bit__rec,axiom,
% 5.31/5.63 ( bit_ri6519982836138164636nteger
% 5.31/5.63 = ( ^ [N4: nat,A5: code_integer] : ( if_Code_integer @ ( N4 = zero_zero_nat ) @ ( uminus1351360451143612070nteger @ ( modulo364778990260209775nteger @ A5 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) @ ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A5 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_ri6519982836138164636nteger @ ( minus_minus_nat @ N4 @ one_one_nat ) @ ( divide6298287555418463151nteger @ A5 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % signed_take_bit_rec
% 5.31/5.63 thf(fact_7931_signed__take__bit__rec,axiom,
% 5.31/5.63 ( bit_ri631733984087533419it_int
% 5.31/5.63 = ( ^ [N4: nat,A5: int] : ( if_int @ ( N4 = zero_zero_nat ) @ ( uminus_uminus_int @ ( modulo_modulo_int @ A5 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ ( plus_plus_int @ ( modulo_modulo_int @ A5 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_ri631733984087533419it_int @ ( minus_minus_nat @ N4 @ one_one_nat ) @ ( divide_divide_int @ A5 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % signed_take_bit_rec
% 5.31/5.63 thf(fact_7932_square__fact__le__2__fact,axiom,
% 5.31/5.63 ! [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 ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % square_fact_le_2_fact
% 5.31/5.63 thf(fact_7933_zminus1__lemma,axiom,
% 5.31/5.63 ! [A: int,B: int,Q2: int,R3: int] :
% 5.31/5.63 ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q2 @ R3 ) )
% 5.31/5.63 => ( ( B != zero_zero_int )
% 5.31/5.63 => ( eucl_rel_int @ ( uminus_uminus_int @ A ) @ B @ ( product_Pair_int_int @ ( if_int @ ( R3 = zero_zero_int ) @ ( uminus_uminus_int @ Q2 ) @ ( minus_minus_int @ ( uminus_uminus_int @ Q2 ) @ one_one_int ) ) @ ( if_int @ ( R3 = zero_zero_int ) @ zero_zero_int @ ( minus_minus_int @ B @ R3 ) ) ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % zminus1_lemma
% 5.31/5.63 thf(fact_7934_divide__le__eq__numeral_I2_J,axiom,
% 5.31/5.63 ! [B: real,C2: real,W2: num] :
% 5.31/5.63 ( ( ord_less_eq_real @ ( divide_divide_real @ B @ C2 ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) )
% 5.31/5.63 = ( ( ( ord_less_real @ zero_zero_real @ C2 )
% 5.31/5.63 => ( ord_less_eq_real @ B @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) @ C2 ) ) )
% 5.31/5.63 & ( ~ ( ord_less_real @ zero_zero_real @ C2 )
% 5.31/5.63 => ( ( ( ord_less_real @ C2 @ zero_zero_real )
% 5.31/5.63 => ( ord_less_eq_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) @ C2 ) @ B ) )
% 5.31/5.63 & ( ~ ( ord_less_real @ C2 @ zero_zero_real )
% 5.31/5.63 => ( ord_less_eq_real @ zero_zero_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) ) ) ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % divide_le_eq_numeral(2)
% 5.31/5.63 thf(fact_7935_divide__le__eq__numeral_I2_J,axiom,
% 5.31/5.63 ! [B: rat,C2: rat,W2: num] :
% 5.31/5.63 ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C2 ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) )
% 5.31/5.63 = ( ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 5.31/5.63 => ( ord_less_eq_rat @ B @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ C2 ) ) )
% 5.31/5.63 & ( ~ ( ord_less_rat @ zero_zero_rat @ C2 )
% 5.31/5.63 => ( ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 5.31/5.63 => ( ord_less_eq_rat @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ C2 ) @ B ) )
% 5.31/5.63 & ( ~ ( ord_less_rat @ C2 @ zero_zero_rat )
% 5.31/5.63 => ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) ) ) ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % divide_le_eq_numeral(2)
% 5.31/5.63 thf(fact_7936_le__divide__eq__numeral_I2_J,axiom,
% 5.31/5.63 ! [W2: num,B: real,C2: real] :
% 5.31/5.63 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) @ ( divide_divide_real @ B @ C2 ) )
% 5.31/5.63 = ( ( ( ord_less_real @ zero_zero_real @ C2 )
% 5.31/5.63 => ( ord_less_eq_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) @ C2 ) @ B ) )
% 5.31/5.63 & ( ~ ( ord_less_real @ zero_zero_real @ C2 )
% 5.31/5.63 => ( ( ( ord_less_real @ C2 @ zero_zero_real )
% 5.31/5.63 => ( ord_less_eq_real @ B @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) @ C2 ) ) )
% 5.31/5.63 & ( ~ ( ord_less_real @ C2 @ zero_zero_real )
% 5.31/5.63 => ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) @ zero_zero_real ) ) ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % le_divide_eq_numeral(2)
% 5.31/5.63 thf(fact_7937_le__divide__eq__numeral_I2_J,axiom,
% 5.31/5.63 ! [W2: num,B: rat,C2: rat] :
% 5.31/5.63 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ ( divide_divide_rat @ B @ C2 ) )
% 5.31/5.63 = ( ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 5.31/5.63 => ( ord_less_eq_rat @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ C2 ) @ B ) )
% 5.31/5.63 & ( ~ ( ord_less_rat @ zero_zero_rat @ C2 )
% 5.31/5.63 => ( ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 5.31/5.63 => ( ord_less_eq_rat @ B @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ C2 ) ) )
% 5.31/5.63 & ( ~ ( ord_less_rat @ C2 @ zero_zero_rat )
% 5.31/5.63 => ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ zero_zero_rat ) ) ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % le_divide_eq_numeral(2)
% 5.31/5.63 thf(fact_7938_square__le__1,axiom,
% 5.31/5.63 ! [X: real] :
% 5.31/5.63 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 5.31/5.63 => ( ( ord_less_eq_real @ X @ one_one_real )
% 5.31/5.63 => ( ord_less_eq_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % square_le_1
% 5.31/5.63 thf(fact_7939_square__le__1,axiom,
% 5.31/5.63 ! [X: code_integer] :
% 5.31/5.63 ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ X )
% 5.31/5.63 => ( ( ord_le3102999989581377725nteger @ X @ one_one_Code_integer )
% 5.31/5.63 => ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_Code_integer ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % square_le_1
% 5.31/5.63 thf(fact_7940_square__le__1,axiom,
% 5.31/5.63 ! [X: rat] :
% 5.31/5.63 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ X )
% 5.31/5.63 => ( ( ord_less_eq_rat @ X @ one_one_rat )
% 5.31/5.63 => ( ord_less_eq_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_rat ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % square_le_1
% 5.31/5.63 thf(fact_7941_square__le__1,axiom,
% 5.31/5.63 ! [X: int] :
% 5.31/5.63 ( ( ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ X )
% 5.31/5.63 => ( ( ord_less_eq_int @ X @ one_one_int )
% 5.31/5.63 => ( ord_less_eq_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_int ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % square_le_1
% 5.31/5.63 thf(fact_7942_minus__power__mult__self,axiom,
% 5.31/5.63 ! [A: int,N: nat] :
% 5.31/5.63 ( ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ A ) @ N ) @ ( power_power_int @ ( uminus_uminus_int @ A ) @ N ) )
% 5.31/5.63 = ( power_power_int @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % minus_power_mult_self
% 5.31/5.63 thf(fact_7943_minus__power__mult__self,axiom,
% 5.31/5.63 ! [A: real,N: nat] :
% 5.31/5.63 ( ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ A ) @ N ) @ ( power_power_real @ ( uminus_uminus_real @ A ) @ N ) )
% 5.31/5.63 = ( power_power_real @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % minus_power_mult_self
% 5.31/5.63 thf(fact_7944_minus__power__mult__self,axiom,
% 5.31/5.63 ! [A: complex,N: nat] :
% 5.31/5.63 ( ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N ) @ ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N ) )
% 5.31/5.63 = ( power_power_complex @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % minus_power_mult_self
% 5.31/5.63 thf(fact_7945_minus__power__mult__self,axiom,
% 5.31/5.63 ! [A: code_integer,N: nat] :
% 5.31/5.63 ( ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N ) @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N ) )
% 5.31/5.63 = ( power_8256067586552552935nteger @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % minus_power_mult_self
% 5.31/5.63 thf(fact_7946_minus__power__mult__self,axiom,
% 5.31/5.63 ! [A: rat,N: nat] :
% 5.31/5.63 ( ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N ) @ ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N ) )
% 5.31/5.63 = ( power_power_rat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % minus_power_mult_self
% 5.31/5.63 thf(fact_7947_fact__num__eq__if,axiom,
% 5.31/5.63 ( semiri3624122377584611663nteger
% 5.31/5.63 = ( ^ [M6: nat] : ( if_Code_integer @ ( M6 = zero_zero_nat ) @ one_one_Code_integer @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ M6 ) @ ( semiri3624122377584611663nteger @ ( minus_minus_nat @ M6 @ one_one_nat ) ) ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % fact_num_eq_if
% 5.31/5.63 thf(fact_7948_fact__num__eq__if,axiom,
% 5.31/5.63 ( semiri5044797733671781792omplex
% 5.31/5.63 = ( ^ [M6: nat] : ( if_complex @ ( M6 = zero_zero_nat ) @ one_one_complex @ ( times_times_complex @ ( semiri8010041392384452111omplex @ M6 ) @ ( semiri5044797733671781792omplex @ ( minus_minus_nat @ M6 @ one_one_nat ) ) ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % fact_num_eq_if
% 5.31/5.63 thf(fact_7949_fact__num__eq__if,axiom,
% 5.31/5.63 ( semiri773545260158071498ct_rat
% 5.31/5.63 = ( ^ [M6: nat] : ( if_rat @ ( M6 = zero_zero_nat ) @ one_one_rat @ ( times_times_rat @ ( semiri681578069525770553at_rat @ M6 ) @ ( semiri773545260158071498ct_rat @ ( minus_minus_nat @ M6 @ one_one_nat ) ) ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % fact_num_eq_if
% 5.31/5.63 thf(fact_7950_fact__num__eq__if,axiom,
% 5.31/5.63 ( semiri1406184849735516958ct_int
% 5.31/5.63 = ( ^ [M6: nat] : ( if_int @ ( M6 = zero_zero_nat ) @ one_one_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ M6 ) @ ( semiri1406184849735516958ct_int @ ( minus_minus_nat @ M6 @ one_one_nat ) ) ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % fact_num_eq_if
% 5.31/5.63 thf(fact_7951_fact__num__eq__if,axiom,
% 5.31/5.63 ( semiri1408675320244567234ct_nat
% 5.31/5.63 = ( ^ [M6: nat] : ( if_nat @ ( M6 = zero_zero_nat ) @ one_one_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ M6 ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ M6 @ one_one_nat ) ) ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % fact_num_eq_if
% 5.31/5.63 thf(fact_7952_fact__num__eq__if,axiom,
% 5.31/5.63 ( semiri2265585572941072030t_real
% 5.31/5.63 = ( ^ [M6: nat] : ( if_real @ ( M6 = zero_zero_nat ) @ one_one_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ M6 ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ M6 @ one_one_nat ) ) ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % fact_num_eq_if
% 5.31/5.63 thf(fact_7953_fact__code,axiom,
% 5.31/5.63 ( semiri1406184849735516958ct_int
% 5.31/5.63 = ( ^ [N4: nat] : ( semiri1314217659103216013at_int @ ( set_fo2584398358068434914at_nat @ times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 @ one_one_nat ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % fact_code
% 5.31/5.63 thf(fact_7954_fact__code,axiom,
% 5.31/5.63 ( semiri1408675320244567234ct_nat
% 5.31/5.63 = ( ^ [N4: nat] : ( semiri1316708129612266289at_nat @ ( set_fo2584398358068434914at_nat @ times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 @ one_one_nat ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % fact_code
% 5.31/5.63 thf(fact_7955_fact__code,axiom,
% 5.31/5.63 ( semiri2265585572941072030t_real
% 5.31/5.63 = ( ^ [N4: nat] : ( semiri5074537144036343181t_real @ ( set_fo2584398358068434914at_nat @ times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 @ one_one_nat ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % fact_code
% 5.31/5.63 thf(fact_7956_fact__reduce,axiom,
% 5.31/5.63 ! [N: nat] :
% 5.31/5.63 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.63 => ( ( semiri773545260158071498ct_rat @ N )
% 5.31/5.63 = ( times_times_rat @ ( semiri681578069525770553at_rat @ N ) @ ( semiri773545260158071498ct_rat @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % fact_reduce
% 5.31/5.63 thf(fact_7957_fact__reduce,axiom,
% 5.31/5.63 ! [N: nat] :
% 5.31/5.63 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.63 => ( ( semiri1406184849735516958ct_int @ N )
% 5.31/5.63 = ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ ( semiri1406184849735516958ct_int @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % fact_reduce
% 5.31/5.63 thf(fact_7958_fact__reduce,axiom,
% 5.31/5.63 ! [N: nat] :
% 5.31/5.63 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.63 => ( ( semiri1408675320244567234ct_nat @ N )
% 5.31/5.63 = ( times_times_nat @ ( semiri1316708129612266289at_nat @ N ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % fact_reduce
% 5.31/5.63 thf(fact_7959_fact__reduce,axiom,
% 5.31/5.63 ! [N: nat] :
% 5.31/5.63 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.63 => ( ( semiri2265585572941072030t_real @ N )
% 5.31/5.63 = ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % fact_reduce
% 5.31/5.63 thf(fact_7960_pochhammer__absorb__comp,axiom,
% 5.31/5.63 ! [R3: complex,K2: nat] :
% 5.31/5.63 ( ( times_times_complex @ ( minus_minus_complex @ R3 @ ( semiri8010041392384452111omplex @ K2 ) ) @ ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ R3 ) @ K2 ) )
% 5.31/5.63 = ( times_times_complex @ R3 @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ ( uminus1482373934393186551omplex @ R3 ) @ one_one_complex ) @ K2 ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % pochhammer_absorb_comp
% 5.31/5.63 thf(fact_7961_pochhammer__absorb__comp,axiom,
% 5.31/5.63 ! [R3: code_integer,K2: nat] :
% 5.31/5.63 ( ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ R3 @ ( semiri4939895301339042750nteger @ K2 ) ) @ ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ R3 ) @ K2 ) )
% 5.31/5.63 = ( times_3573771949741848930nteger @ R3 @ ( comm_s8582702949713902594nteger @ ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ R3 ) @ one_one_Code_integer ) @ K2 ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % pochhammer_absorb_comp
% 5.31/5.63 thf(fact_7962_pochhammer__absorb__comp,axiom,
% 5.31/5.63 ! [R3: rat,K2: nat] :
% 5.31/5.63 ( ( times_times_rat @ ( minus_minus_rat @ R3 @ ( semiri681578069525770553at_rat @ K2 ) ) @ ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ R3 ) @ K2 ) )
% 5.31/5.63 = ( times_times_rat @ R3 @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ ( uminus_uminus_rat @ R3 ) @ one_one_rat ) @ K2 ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % pochhammer_absorb_comp
% 5.31/5.63 thf(fact_7963_pochhammer__absorb__comp,axiom,
% 5.31/5.63 ! [R3: real,K2: nat] :
% 5.31/5.63 ( ( times_times_real @ ( minus_minus_real @ R3 @ ( semiri5074537144036343181t_real @ K2 ) ) @ ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ R3 ) @ K2 ) )
% 5.31/5.63 = ( times_times_real @ R3 @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ ( uminus_uminus_real @ R3 ) @ one_one_real ) @ K2 ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % pochhammer_absorb_comp
% 5.31/5.63 thf(fact_7964_pochhammer__absorb__comp,axiom,
% 5.31/5.63 ! [R3: int,K2: nat] :
% 5.31/5.63 ( ( times_times_int @ ( minus_minus_int @ R3 @ ( semiri1314217659103216013at_int @ K2 ) ) @ ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ R3 ) @ K2 ) )
% 5.31/5.63 = ( times_times_int @ R3 @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ ( uminus_uminus_int @ R3 ) @ one_one_int ) @ K2 ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % pochhammer_absorb_comp
% 5.31/5.63 thf(fact_7965_gbinomial__index__swap,axiom,
% 5.31/5.63 ! [K2: nat,N: nat] :
% 5.31/5.63 ( ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ K2 ) @ ( gbinomial_complex @ ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ N ) ) @ one_one_complex ) @ K2 ) )
% 5.31/5.63 = ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) @ ( gbinomial_complex @ ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ K2 ) ) @ one_one_complex ) @ N ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % gbinomial_index_swap
% 5.31/5.63 thf(fact_7966_gbinomial__index__swap,axiom,
% 5.31/5.63 ! [K2: nat,N: nat] :
% 5.31/5.63 ( ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ K2 ) @ ( gbinomial_rat @ ( minus_minus_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ N ) ) @ one_one_rat ) @ K2 ) )
% 5.31/5.63 = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N ) @ ( gbinomial_rat @ ( minus_minus_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ K2 ) ) @ one_one_rat ) @ N ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % gbinomial_index_swap
% 5.31/5.63 thf(fact_7967_gbinomial__index__swap,axiom,
% 5.31/5.63 ! [K2: nat,N: nat] :
% 5.31/5.63 ( ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K2 ) @ ( gbinomial_real @ ( minus_minus_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N ) ) @ one_one_real ) @ K2 ) )
% 5.31/5.63 = ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) @ ( gbinomial_real @ ( minus_minus_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ K2 ) ) @ one_one_real ) @ N ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % gbinomial_index_swap
% 5.31/5.63 thf(fact_7968_gbinomial__negated__upper,axiom,
% 5.31/5.63 ( gbinomial_complex
% 5.31/5.63 = ( ^ [A5: complex,K3: nat] : ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ K3 ) @ ( gbinomial_complex @ ( minus_minus_complex @ ( minus_minus_complex @ ( semiri8010041392384452111omplex @ K3 ) @ A5 ) @ one_one_complex ) @ K3 ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % gbinomial_negated_upper
% 5.31/5.63 thf(fact_7969_gbinomial__negated__upper,axiom,
% 5.31/5.63 ( gbinomial_rat
% 5.31/5.63 = ( ^ [A5: rat,K3: nat] : ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ K3 ) @ ( gbinomial_rat @ ( minus_minus_rat @ ( minus_minus_rat @ ( semiri681578069525770553at_rat @ K3 ) @ A5 ) @ one_one_rat ) @ K3 ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % gbinomial_negated_upper
% 5.31/5.63 thf(fact_7970_gbinomial__negated__upper,axiom,
% 5.31/5.63 ( gbinomial_real
% 5.31/5.63 = ( ^ [A5: real,K3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K3 ) @ ( gbinomial_real @ ( minus_minus_real @ ( minus_minus_real @ ( semiri5074537144036343181t_real @ K3 ) @ A5 ) @ one_one_real ) @ K3 ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % gbinomial_negated_upper
% 5.31/5.63 thf(fact_7971_binomial__fact,axiom,
% 5.31/5.63 ! [K2: nat,N: nat] :
% 5.31/5.63 ( ( ord_less_eq_nat @ K2 @ N )
% 5.31/5.63 => ( ( semiri8010041392384452111omplex @ ( binomial @ N @ K2 ) )
% 5.31/5.63 = ( divide1717551699836669952omplex @ ( semiri5044797733671781792omplex @ N ) @ ( times_times_complex @ ( semiri5044797733671781792omplex @ K2 ) @ ( semiri5044797733671781792omplex @ ( minus_minus_nat @ N @ K2 ) ) ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % binomial_fact
% 5.31/5.63 thf(fact_7972_binomial__fact,axiom,
% 5.31/5.63 ! [K2: nat,N: nat] :
% 5.31/5.63 ( ( ord_less_eq_nat @ K2 @ N )
% 5.31/5.63 => ( ( semiri681578069525770553at_rat @ ( binomial @ N @ K2 ) )
% 5.31/5.63 = ( divide_divide_rat @ ( semiri773545260158071498ct_rat @ N ) @ ( times_times_rat @ ( semiri773545260158071498ct_rat @ K2 ) @ ( semiri773545260158071498ct_rat @ ( minus_minus_nat @ N @ K2 ) ) ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % binomial_fact
% 5.31/5.63 thf(fact_7973_binomial__fact,axiom,
% 5.31/5.63 ! [K2: nat,N: nat] :
% 5.31/5.63 ( ( ord_less_eq_nat @ K2 @ N )
% 5.31/5.63 => ( ( semiri5074537144036343181t_real @ ( binomial @ N @ K2 ) )
% 5.31/5.63 = ( divide_divide_real @ ( semiri2265585572941072030t_real @ N ) @ ( times_times_real @ ( semiri2265585572941072030t_real @ K2 ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N @ K2 ) ) ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % binomial_fact
% 5.31/5.63 thf(fact_7974_fact__binomial,axiom,
% 5.31/5.63 ! [K2: nat,N: nat] :
% 5.31/5.63 ( ( ord_less_eq_nat @ K2 @ N )
% 5.31/5.63 => ( ( times_times_complex @ ( semiri5044797733671781792omplex @ K2 ) @ ( semiri8010041392384452111omplex @ ( binomial @ N @ K2 ) ) )
% 5.31/5.63 = ( divide1717551699836669952omplex @ ( semiri5044797733671781792omplex @ N ) @ ( semiri5044797733671781792omplex @ ( minus_minus_nat @ N @ K2 ) ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % fact_binomial
% 5.31/5.63 thf(fact_7975_fact__binomial,axiom,
% 5.31/5.63 ! [K2: nat,N: nat] :
% 5.31/5.63 ( ( ord_less_eq_nat @ K2 @ N )
% 5.31/5.63 => ( ( times_times_rat @ ( semiri773545260158071498ct_rat @ K2 ) @ ( semiri681578069525770553at_rat @ ( binomial @ N @ K2 ) ) )
% 5.31/5.63 = ( divide_divide_rat @ ( semiri773545260158071498ct_rat @ N ) @ ( semiri773545260158071498ct_rat @ ( minus_minus_nat @ N @ K2 ) ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % fact_binomial
% 5.31/5.63 thf(fact_7976_fact__binomial,axiom,
% 5.31/5.63 ! [K2: nat,N: nat] :
% 5.31/5.63 ( ( ord_less_eq_nat @ K2 @ N )
% 5.31/5.63 => ( ( times_times_real @ ( semiri2265585572941072030t_real @ K2 ) @ ( semiri5074537144036343181t_real @ ( binomial @ N @ K2 ) ) )
% 5.31/5.63 = ( divide_divide_real @ ( semiri2265585572941072030t_real @ N ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N @ K2 ) ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % fact_binomial
% 5.31/5.63 thf(fact_7977_Bernoulli__inequality,axiom,
% 5.31/5.63 ! [X: real,N: nat] :
% 5.31/5.63 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 5.31/5.63 => ( 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 ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % Bernoulli_inequality
% 5.31/5.63 thf(fact_7978_fact__div__fact,axiom,
% 5.31/5.63 ! [N: nat,M2: nat] :
% 5.31/5.63 ( ( ord_less_eq_nat @ N @ M2 )
% 5.31/5.63 => ( ( divide_divide_nat @ ( semiri1408675320244567234ct_nat @ M2 ) @ ( semiri1408675320244567234ct_nat @ N ) )
% 5.31/5.63 = ( groups708209901874060359at_nat
% 5.31/5.63 @ ^ [X4: nat] : X4
% 5.31/5.63 @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ M2 ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % fact_div_fact
% 5.31/5.63 thf(fact_7979_power__minus1__odd,axiom,
% 5.31/5.63 ! [N: nat] :
% 5.31/5.63 ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.31/5.63 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.31/5.63
% 5.31/5.63 % power_minus1_odd
% 5.31/5.63 thf(fact_7980_power__minus1__odd,axiom,
% 5.31/5.63 ! [N: nat] :
% 5.31/5.63 ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.31/5.63 = ( uminus_uminus_real @ one_one_real ) ) ).
% 5.31/5.63
% 5.31/5.63 % power_minus1_odd
% 5.31/5.63 thf(fact_7981_power__minus1__odd,axiom,
% 5.31/5.63 ! [N: nat] :
% 5.31/5.63 ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.31/5.63 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.31/5.63
% 5.31/5.63 % power_minus1_odd
% 5.31/5.63 thf(fact_7982_power__minus1__odd,axiom,
% 5.31/5.63 ! [N: nat] :
% 5.31/5.63 ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.31/5.63 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.31/5.63
% 5.31/5.63 % power_minus1_odd
% 5.31/5.63 thf(fact_7983_power__minus1__odd,axiom,
% 5.31/5.63 ! [N: nat] :
% 5.31/5.63 ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.31/5.63 = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.31/5.63
% 5.31/5.63 % power_minus1_odd
% 5.31/5.63 thf(fact_7984_gbinomial__minus,axiom,
% 5.31/5.63 ! [A: complex,K2: nat] :
% 5.31/5.63 ( ( gbinomial_complex @ ( uminus1482373934393186551omplex @ A ) @ K2 )
% 5.31/5.63 = ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ K2 ) @ ( gbinomial_complex @ ( minus_minus_complex @ ( plus_plus_complex @ A @ ( semiri8010041392384452111omplex @ K2 ) ) @ one_one_complex ) @ K2 ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % gbinomial_minus
% 5.31/5.63 thf(fact_7985_gbinomial__minus,axiom,
% 5.31/5.63 ! [A: rat,K2: nat] :
% 5.31/5.63 ( ( gbinomial_rat @ ( uminus_uminus_rat @ A ) @ K2 )
% 5.31/5.63 = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ K2 ) @ ( gbinomial_rat @ ( minus_minus_rat @ ( plus_plus_rat @ A @ ( semiri681578069525770553at_rat @ K2 ) ) @ one_one_rat ) @ K2 ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % gbinomial_minus
% 5.31/5.63 thf(fact_7986_gbinomial__minus,axiom,
% 5.31/5.63 ! [A: real,K2: nat] :
% 5.31/5.63 ( ( gbinomial_real @ ( uminus_uminus_real @ A ) @ K2 )
% 5.31/5.63 = ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K2 ) @ ( gbinomial_real @ ( minus_minus_real @ ( plus_plus_real @ A @ ( semiri5074537144036343181t_real @ K2 ) ) @ one_one_real ) @ K2 ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % gbinomial_minus
% 5.31/5.63 thf(fact_7987_signed__take__bit__int__less__eq,axiom,
% 5.31/5.63 ! [N: nat,K2: int] :
% 5.31/5.63 ( ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ K2 )
% 5.31/5.63 => ( ord_less_eq_int @ ( bit_ri631733984087533419it_int @ N @ K2 ) @ ( minus_minus_int @ K2 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ N ) ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % signed_take_bit_int_less_eq
% 5.31/5.63 thf(fact_7988_pochhammer__minus_H,axiom,
% 5.31/5.63 ! [B: complex,K2: nat] :
% 5.31/5.63 ( ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ ( minus_minus_complex @ B @ ( semiri8010041392384452111omplex @ K2 ) ) @ one_one_complex ) @ K2 )
% 5.31/5.63 = ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ K2 ) @ ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ B ) @ K2 ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % pochhammer_minus'
% 5.31/5.63 thf(fact_7989_pochhammer__minus_H,axiom,
% 5.31/5.63 ! [B: code_integer,K2: nat] :
% 5.31/5.63 ( ( comm_s8582702949713902594nteger @ ( plus_p5714425477246183910nteger @ ( minus_8373710615458151222nteger @ B @ ( semiri4939895301339042750nteger @ K2 ) ) @ one_one_Code_integer ) @ K2 )
% 5.31/5.63 = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ K2 ) @ ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ B ) @ K2 ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % pochhammer_minus'
% 5.31/5.63 thf(fact_7990_pochhammer__minus_H,axiom,
% 5.31/5.63 ! [B: rat,K2: nat] :
% 5.31/5.63 ( ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ ( minus_minus_rat @ B @ ( semiri681578069525770553at_rat @ K2 ) ) @ one_one_rat ) @ K2 )
% 5.31/5.63 = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ K2 ) @ ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ B ) @ K2 ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % pochhammer_minus'
% 5.31/5.63 thf(fact_7991_pochhammer__minus_H,axiom,
% 5.31/5.63 ! [B: real,K2: nat] :
% 5.31/5.63 ( ( comm_s7457072308508201937r_real @ ( plus_plus_real @ ( minus_minus_real @ B @ ( semiri5074537144036343181t_real @ K2 ) ) @ one_one_real ) @ K2 )
% 5.31/5.63 = ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K2 ) @ ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ B ) @ K2 ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % pochhammer_minus'
% 5.31/5.63 thf(fact_7992_pochhammer__minus_H,axiom,
% 5.31/5.63 ! [B: int,K2: nat] :
% 5.31/5.63 ( ( comm_s4660882817536571857er_int @ ( plus_plus_int @ ( minus_minus_int @ B @ ( semiri1314217659103216013at_int @ K2 ) ) @ one_one_int ) @ K2 )
% 5.31/5.63 = ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ K2 ) @ ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ B ) @ K2 ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % pochhammer_minus'
% 5.31/5.63 thf(fact_7993_pochhammer__minus,axiom,
% 5.31/5.63 ! [B: complex,K2: nat] :
% 5.31/5.63 ( ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ B ) @ K2 )
% 5.31/5.63 = ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ K2 ) @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ ( minus_minus_complex @ B @ ( semiri8010041392384452111omplex @ K2 ) ) @ one_one_complex ) @ K2 ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % pochhammer_minus
% 5.31/5.63 thf(fact_7994_pochhammer__minus,axiom,
% 5.31/5.63 ! [B: code_integer,K2: nat] :
% 5.31/5.63 ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ B ) @ K2 )
% 5.31/5.63 = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ K2 ) @ ( comm_s8582702949713902594nteger @ ( plus_p5714425477246183910nteger @ ( minus_8373710615458151222nteger @ B @ ( semiri4939895301339042750nteger @ K2 ) ) @ one_one_Code_integer ) @ K2 ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % pochhammer_minus
% 5.31/5.63 thf(fact_7995_pochhammer__minus,axiom,
% 5.31/5.63 ! [B: rat,K2: nat] :
% 5.31/5.63 ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ B ) @ K2 )
% 5.31/5.63 = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ K2 ) @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ ( minus_minus_rat @ B @ ( semiri681578069525770553at_rat @ K2 ) ) @ one_one_rat ) @ K2 ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % pochhammer_minus
% 5.31/5.63 thf(fact_7996_pochhammer__minus,axiom,
% 5.31/5.63 ! [B: real,K2: nat] :
% 5.31/5.63 ( ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ B ) @ K2 )
% 5.31/5.63 = ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K2 ) @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ ( minus_minus_real @ B @ ( semiri5074537144036343181t_real @ K2 ) ) @ one_one_real ) @ K2 ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % pochhammer_minus
% 5.31/5.63 thf(fact_7997_pochhammer__minus,axiom,
% 5.31/5.63 ! [B: int,K2: nat] :
% 5.31/5.63 ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ B ) @ K2 )
% 5.31/5.63 = ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ K2 ) @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ ( minus_minus_int @ B @ ( semiri1314217659103216013at_int @ K2 ) ) @ one_one_int ) @ K2 ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % pochhammer_minus
% 5.31/5.63 thf(fact_7998_int__bit__induct,axiom,
% 5.31/5.63 ! [P2: int > $o,K2: int] :
% 5.31/5.63 ( ( P2 @ zero_zero_int )
% 5.31/5.63 => ( ( P2 @ ( uminus_uminus_int @ one_one_int ) )
% 5.31/5.63 => ( ! [K: int] :
% 5.31/5.63 ( ( P2 @ K )
% 5.31/5.63 => ( ( K != zero_zero_int )
% 5.31/5.63 => ( P2 @ ( times_times_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) )
% 5.31/5.63 => ( ! [K: int] :
% 5.31/5.63 ( ( P2 @ K )
% 5.31/5.63 => ( ( K
% 5.31/5.63 != ( uminus_uminus_int @ one_one_int ) )
% 5.31/5.63 => ( P2 @ ( plus_plus_int @ one_one_int @ ( times_times_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) )
% 5.31/5.63 => ( P2 @ K2 ) ) ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % int_bit_induct
% 5.31/5.63 thf(fact_7999_gbinomial__sum__lower__neg,axiom,
% 5.31/5.63 ! [A: complex,M2: nat] :
% 5.31/5.63 ( ( groups2073611262835488442omplex
% 5.31/5.63 @ ^ [K3: nat] : ( times_times_complex @ ( gbinomial_complex @ A @ K3 ) @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ K3 ) )
% 5.31/5.63 @ ( set_ord_atMost_nat @ M2 ) )
% 5.31/5.63 = ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ M2 ) @ ( gbinomial_complex @ ( minus_minus_complex @ A @ one_one_complex ) @ M2 ) ) ) ).
% 5.31/5.63
% 5.31/5.63 % gbinomial_sum_lower_neg
% 5.31/5.63 thf(fact_8000_gbinomial__sum__lower__neg,axiom,
% 5.31/5.63 ! [A: rat,M2: nat] :
% 5.31/5.63 ( ( groups2906978787729119204at_rat
% 5.31/5.63 @ ^ [K3: nat] : ( times_times_rat @ ( gbinomial_rat @ A @ K3 ) @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ K3 ) )
% 5.31/5.64 @ ( set_ord_atMost_nat @ M2 ) )
% 5.31/5.64 = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ M2 ) @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ M2 ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % gbinomial_sum_lower_neg
% 5.31/5.64 thf(fact_8001_gbinomial__sum__lower__neg,axiom,
% 5.31/5.64 ! [A: real,M2: nat] :
% 5.31/5.64 ( ( groups6591440286371151544t_real
% 5.31/5.64 @ ^ [K3: nat] : ( times_times_real @ ( gbinomial_real @ A @ K3 ) @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K3 ) )
% 5.31/5.64 @ ( set_ord_atMost_nat @ M2 ) )
% 5.31/5.64 = ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ M2 ) @ ( gbinomial_real @ ( minus_minus_real @ A @ one_one_real ) @ M2 ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % gbinomial_sum_lower_neg
% 5.31/5.64 thf(fact_8002_gbinomial__Suc,axiom,
% 5.31/5.64 ! [A: complex,K2: nat] :
% 5.31/5.64 ( ( gbinomial_complex @ A @ ( suc @ K2 ) )
% 5.31/5.64 = ( divide1717551699836669952omplex
% 5.31/5.64 @ ( groups6464643781859351333omplex
% 5.31/5.64 @ ^ [I: nat] : ( minus_minus_complex @ A @ ( semiri8010041392384452111omplex @ I ) )
% 5.31/5.64 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K2 ) )
% 5.31/5.64 @ ( semiri5044797733671781792omplex @ ( suc @ K2 ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % gbinomial_Suc
% 5.31/5.64 thf(fact_8003_gbinomial__Suc,axiom,
% 5.31/5.64 ! [A: rat,K2: nat] :
% 5.31/5.64 ( ( gbinomial_rat @ A @ ( suc @ K2 ) )
% 5.31/5.64 = ( divide_divide_rat
% 5.31/5.64 @ ( groups73079841787564623at_rat
% 5.31/5.64 @ ^ [I: nat] : ( minus_minus_rat @ A @ ( semiri681578069525770553at_rat @ I ) )
% 5.31/5.64 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K2 ) )
% 5.31/5.64 @ ( semiri773545260158071498ct_rat @ ( suc @ K2 ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % gbinomial_Suc
% 5.31/5.64 thf(fact_8004_gbinomial__Suc,axiom,
% 5.31/5.64 ! [A: real,K2: nat] :
% 5.31/5.64 ( ( gbinomial_real @ A @ ( suc @ K2 ) )
% 5.31/5.64 = ( divide_divide_real
% 5.31/5.64 @ ( groups129246275422532515t_real
% 5.31/5.64 @ ^ [I: nat] : ( minus_minus_real @ A @ ( semiri5074537144036343181t_real @ I ) )
% 5.31/5.64 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K2 ) )
% 5.31/5.64 @ ( semiri2265585572941072030t_real @ ( suc @ K2 ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % gbinomial_Suc
% 5.31/5.64 thf(fact_8005_gbinomial__Suc,axiom,
% 5.31/5.64 ! [A: int,K2: nat] :
% 5.31/5.64 ( ( gbinomial_int @ A @ ( suc @ K2 ) )
% 5.31/5.64 = ( divide_divide_int
% 5.31/5.64 @ ( groups705719431365010083at_int
% 5.31/5.64 @ ^ [I: nat] : ( minus_minus_int @ A @ ( semiri1314217659103216013at_int @ I ) )
% 5.31/5.64 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K2 ) )
% 5.31/5.64 @ ( semiri1406184849735516958ct_int @ ( suc @ K2 ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % gbinomial_Suc
% 5.31/5.64 thf(fact_8006_gbinomial__Suc,axiom,
% 5.31/5.64 ! [A: nat,K2: nat] :
% 5.31/5.64 ( ( gbinomial_nat @ A @ ( suc @ K2 ) )
% 5.31/5.64 = ( divide_divide_nat
% 5.31/5.64 @ ( groups708209901874060359at_nat
% 5.31/5.64 @ ^ [I: nat] : ( minus_minus_nat @ A @ ( semiri1316708129612266289at_nat @ I ) )
% 5.31/5.64 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K2 ) )
% 5.31/5.64 @ ( semiri1408675320244567234ct_nat @ ( suc @ K2 ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % gbinomial_Suc
% 5.31/5.64 thf(fact_8007_gbinomial__partial__sum__poly,axiom,
% 5.31/5.64 ! [M2: nat,A: complex,X: complex,Y: complex] :
% 5.31/5.64 ( ( groups2073611262835488442omplex
% 5.31/5.64 @ ^ [K3: nat] : ( times_times_complex @ ( times_times_complex @ ( gbinomial_complex @ ( plus_plus_complex @ ( semiri8010041392384452111omplex @ M2 ) @ A ) @ K3 ) @ ( power_power_complex @ X @ K3 ) ) @ ( power_power_complex @ Y @ ( minus_minus_nat @ M2 @ K3 ) ) )
% 5.31/5.64 @ ( set_ord_atMost_nat @ M2 ) )
% 5.31/5.64 = ( groups2073611262835488442omplex
% 5.31/5.64 @ ^ [K3: nat] : ( times_times_complex @ ( times_times_complex @ ( gbinomial_complex @ ( uminus1482373934393186551omplex @ A ) @ K3 ) @ ( power_power_complex @ ( uminus1482373934393186551omplex @ X ) @ K3 ) ) @ ( power_power_complex @ ( plus_plus_complex @ X @ Y ) @ ( minus_minus_nat @ M2 @ K3 ) ) )
% 5.31/5.64 @ ( set_ord_atMost_nat @ M2 ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % gbinomial_partial_sum_poly
% 5.31/5.64 thf(fact_8008_gbinomial__partial__sum__poly,axiom,
% 5.31/5.64 ! [M2: nat,A: rat,X: rat,Y: rat] :
% 5.31/5.64 ( ( groups2906978787729119204at_rat
% 5.31/5.64 @ ^ [K3: nat] : ( times_times_rat @ ( times_times_rat @ ( gbinomial_rat @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ M2 ) @ A ) @ K3 ) @ ( power_power_rat @ X @ K3 ) ) @ ( power_power_rat @ Y @ ( minus_minus_nat @ M2 @ K3 ) ) )
% 5.31/5.64 @ ( set_ord_atMost_nat @ M2 ) )
% 5.31/5.64 = ( groups2906978787729119204at_rat
% 5.31/5.64 @ ^ [K3: nat] : ( times_times_rat @ ( times_times_rat @ ( gbinomial_rat @ ( uminus_uminus_rat @ A ) @ K3 ) @ ( power_power_rat @ ( uminus_uminus_rat @ X ) @ K3 ) ) @ ( power_power_rat @ ( plus_plus_rat @ X @ Y ) @ ( minus_minus_nat @ M2 @ K3 ) ) )
% 5.31/5.64 @ ( set_ord_atMost_nat @ M2 ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % gbinomial_partial_sum_poly
% 5.31/5.64 thf(fact_8009_gbinomial__partial__sum__poly,axiom,
% 5.31/5.64 ! [M2: nat,A: real,X: real,Y: real] :
% 5.31/5.64 ( ( groups6591440286371151544t_real
% 5.31/5.64 @ ^ [K3: nat] : ( times_times_real @ ( times_times_real @ ( gbinomial_real @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ M2 ) @ A ) @ K3 ) @ ( power_power_real @ X @ K3 ) ) @ ( power_power_real @ Y @ ( minus_minus_nat @ M2 @ K3 ) ) )
% 5.31/5.64 @ ( set_ord_atMost_nat @ M2 ) )
% 5.31/5.64 = ( groups6591440286371151544t_real
% 5.31/5.64 @ ^ [K3: nat] : ( times_times_real @ ( times_times_real @ ( gbinomial_real @ ( uminus_uminus_real @ A ) @ K3 ) @ ( power_power_real @ ( uminus_uminus_real @ X ) @ K3 ) ) @ ( power_power_real @ ( plus_plus_real @ X @ Y ) @ ( minus_minus_nat @ M2 @ K3 ) ) )
% 5.31/5.64 @ ( set_ord_atMost_nat @ M2 ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % gbinomial_partial_sum_poly
% 5.31/5.64 thf(fact_8010_root__polyfun,axiom,
% 5.31/5.64 ! [N: nat,Z3: int,A: int] :
% 5.31/5.64 ( ( ord_less_eq_nat @ one_one_nat @ N )
% 5.31/5.64 => ( ( ( power_power_int @ Z3 @ N )
% 5.31/5.64 = A )
% 5.31/5.64 = ( ( groups3539618377306564664at_int
% 5.31/5.64 @ ^ [I: nat] : ( times_times_int @ ( if_int @ ( I = zero_zero_nat ) @ ( uminus_uminus_int @ A ) @ ( if_int @ ( I = N ) @ one_one_int @ zero_zero_int ) ) @ ( power_power_int @ Z3 @ I ) )
% 5.31/5.64 @ ( set_ord_atMost_nat @ N ) )
% 5.31/5.64 = zero_zero_int ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % root_polyfun
% 5.31/5.64 thf(fact_8011_root__polyfun,axiom,
% 5.31/5.64 ! [N: nat,Z3: complex,A: complex] :
% 5.31/5.64 ( ( ord_less_eq_nat @ one_one_nat @ N )
% 5.31/5.64 => ( ( ( power_power_complex @ Z3 @ N )
% 5.31/5.64 = A )
% 5.31/5.64 = ( ( groups2073611262835488442omplex
% 5.31/5.64 @ ^ [I: nat] : ( times_times_complex @ ( if_complex @ ( I = zero_zero_nat ) @ ( uminus1482373934393186551omplex @ A ) @ ( if_complex @ ( I = N ) @ one_one_complex @ zero_zero_complex ) ) @ ( power_power_complex @ Z3 @ I ) )
% 5.31/5.64 @ ( set_ord_atMost_nat @ N ) )
% 5.31/5.64 = zero_zero_complex ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % root_polyfun
% 5.31/5.64 thf(fact_8012_root__polyfun,axiom,
% 5.31/5.64 ! [N: nat,Z3: code_integer,A: code_integer] :
% 5.31/5.64 ( ( ord_less_eq_nat @ one_one_nat @ N )
% 5.31/5.64 => ( ( ( power_8256067586552552935nteger @ Z3 @ N )
% 5.31/5.64 = A )
% 5.31/5.64 = ( ( groups7501900531339628137nteger
% 5.31/5.64 @ ^ [I: nat] : ( times_3573771949741848930nteger @ ( if_Code_integer @ ( I = zero_zero_nat ) @ ( uminus1351360451143612070nteger @ A ) @ ( if_Code_integer @ ( I = N ) @ one_one_Code_integer @ zero_z3403309356797280102nteger ) ) @ ( power_8256067586552552935nteger @ Z3 @ I ) )
% 5.31/5.64 @ ( set_ord_atMost_nat @ N ) )
% 5.31/5.64 = zero_z3403309356797280102nteger ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % root_polyfun
% 5.31/5.64 thf(fact_8013_root__polyfun,axiom,
% 5.31/5.64 ! [N: nat,Z3: rat,A: rat] :
% 5.31/5.64 ( ( ord_less_eq_nat @ one_one_nat @ N )
% 5.31/5.64 => ( ( ( power_power_rat @ Z3 @ N )
% 5.31/5.64 = A )
% 5.31/5.64 = ( ( groups2906978787729119204at_rat
% 5.31/5.64 @ ^ [I: nat] : ( times_times_rat @ ( if_rat @ ( I = zero_zero_nat ) @ ( uminus_uminus_rat @ A ) @ ( if_rat @ ( I = N ) @ one_one_rat @ zero_zero_rat ) ) @ ( power_power_rat @ Z3 @ I ) )
% 5.31/5.64 @ ( set_ord_atMost_nat @ N ) )
% 5.31/5.64 = zero_zero_rat ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % root_polyfun
% 5.31/5.64 thf(fact_8014_root__polyfun,axiom,
% 5.31/5.64 ! [N: nat,Z3: real,A: real] :
% 5.31/5.64 ( ( ord_less_eq_nat @ one_one_nat @ N )
% 5.31/5.64 => ( ( ( power_power_real @ Z3 @ N )
% 5.31/5.64 = A )
% 5.31/5.64 = ( ( groups6591440286371151544t_real
% 5.31/5.64 @ ^ [I: nat] : ( times_times_real @ ( if_real @ ( I = zero_zero_nat ) @ ( uminus_uminus_real @ A ) @ ( if_real @ ( I = N ) @ one_one_real @ zero_zero_real ) ) @ ( power_power_real @ Z3 @ I ) )
% 5.31/5.64 @ ( set_ord_atMost_nat @ N ) )
% 5.31/5.64 = zero_zero_real ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % root_polyfun
% 5.31/5.64 thf(fact_8015_set__decode__plus__power__2,axiom,
% 5.31/5.64 ! [N: nat,Z3: nat] :
% 5.31/5.64 ( ~ ( member_nat @ N @ ( nat_set_decode @ Z3 ) )
% 5.31/5.64 => ( ( nat_set_decode @ ( plus_plus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ Z3 ) )
% 5.31/5.64 = ( insert_nat @ N @ ( nat_set_decode @ Z3 ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % set_decode_plus_power_2
% 5.31/5.64 thf(fact_8016_choose__alternating__linear__sum,axiom,
% 5.31/5.64 ! [N: nat] :
% 5.31/5.64 ( ( N != one_one_nat )
% 5.31/5.64 => ( ( groups2073611262835488442omplex
% 5.31/5.64 @ ^ [I: nat] : ( times_times_complex @ ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ I ) @ ( semiri8010041392384452111omplex @ I ) ) @ ( semiri8010041392384452111omplex @ ( binomial @ N @ I ) ) )
% 5.31/5.64 @ ( set_ord_atMost_nat @ N ) )
% 5.31/5.64 = zero_zero_complex ) ) ).
% 5.31/5.64
% 5.31/5.64 % choose_alternating_linear_sum
% 5.31/5.64 thf(fact_8017_choose__alternating__linear__sum,axiom,
% 5.31/5.64 ! [N: nat] :
% 5.31/5.64 ( ( N != one_one_nat )
% 5.31/5.64 => ( ( groups7501900531339628137nteger
% 5.31/5.64 @ ^ [I: nat] : ( times_3573771949741848930nteger @ ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ I ) @ ( semiri4939895301339042750nteger @ I ) ) @ ( semiri4939895301339042750nteger @ ( binomial @ N @ I ) ) )
% 5.31/5.64 @ ( set_ord_atMost_nat @ N ) )
% 5.31/5.64 = zero_z3403309356797280102nteger ) ) ).
% 5.31/5.64
% 5.31/5.64 % choose_alternating_linear_sum
% 5.31/5.64 thf(fact_8018_choose__alternating__linear__sum,axiom,
% 5.31/5.64 ! [N: nat] :
% 5.31/5.64 ( ( N != one_one_nat )
% 5.31/5.64 => ( ( groups2906978787729119204at_rat
% 5.31/5.64 @ ^ [I: nat] : ( times_times_rat @ ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ I ) @ ( semiri681578069525770553at_rat @ I ) ) @ ( semiri681578069525770553at_rat @ ( binomial @ N @ I ) ) )
% 5.31/5.64 @ ( set_ord_atMost_nat @ N ) )
% 5.31/5.64 = zero_zero_rat ) ) ).
% 5.31/5.64
% 5.31/5.64 % choose_alternating_linear_sum
% 5.31/5.64 thf(fact_8019_choose__alternating__linear__sum,axiom,
% 5.31/5.64 ! [N: nat] :
% 5.31/5.64 ( ( N != one_one_nat )
% 5.31/5.64 => ( ( groups3539618377306564664at_int
% 5.31/5.64 @ ^ [I: nat] : ( times_times_int @ ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ I ) @ ( semiri1314217659103216013at_int @ I ) ) @ ( semiri1314217659103216013at_int @ ( binomial @ N @ I ) ) )
% 5.31/5.64 @ ( set_ord_atMost_nat @ N ) )
% 5.31/5.64 = zero_zero_int ) ) ).
% 5.31/5.64
% 5.31/5.64 % choose_alternating_linear_sum
% 5.31/5.64 thf(fact_8020_choose__alternating__linear__sum,axiom,
% 5.31/5.64 ! [N: nat] :
% 5.31/5.64 ( ( N != one_one_nat )
% 5.31/5.64 => ( ( groups6591440286371151544t_real
% 5.31/5.64 @ ^ [I: nat] : ( times_times_real @ ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I ) @ ( semiri5074537144036343181t_real @ I ) ) @ ( semiri5074537144036343181t_real @ ( binomial @ N @ I ) ) )
% 5.31/5.64 @ ( set_ord_atMost_nat @ N ) )
% 5.31/5.64 = zero_zero_real ) ) ).
% 5.31/5.64
% 5.31/5.64 % choose_alternating_linear_sum
% 5.31/5.64 thf(fact_8021_set__decode__def,axiom,
% 5.31/5.64 ( nat_set_decode
% 5.31/5.64 = ( ^ [X4: nat] :
% 5.31/5.64 ( collect_nat
% 5.31/5.64 @ ^ [N4: nat] :
% 5.31/5.64 ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ X4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) ) ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % set_decode_def
% 5.31/5.64 thf(fact_8022_fact__double,axiom,
% 5.31/5.64 ! [N: nat] :
% 5.31/5.64 ( ( semiri5044797733671781792omplex @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.31/5.64 = ( times_times_complex @ ( times_times_complex @ ( power_power_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) @ ( comm_s2602460028002588243omplex @ ( divide1717551699836669952omplex @ one_one_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) @ N ) ) @ ( semiri5044797733671781792omplex @ N ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % fact_double
% 5.31/5.64 thf(fact_8023_fact__double,axiom,
% 5.31/5.64 ! [N: nat] :
% 5.31/5.64 ( ( semiri773545260158071498ct_rat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.31/5.64 = ( times_times_rat @ ( times_times_rat @ ( power_power_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) @ ( comm_s4028243227959126397er_rat @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) @ N ) ) @ ( semiri773545260158071498ct_rat @ N ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % fact_double
% 5.31/5.64 thf(fact_8024_fact__double,axiom,
% 5.31/5.64 ! [N: nat] :
% 5.31/5.64 ( ( semiri2265585572941072030t_real @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.31/5.64 = ( times_times_real @ ( times_times_real @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) @ ( comm_s7457072308508201937r_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ N ) ) @ ( semiri2265585572941072030t_real @ N ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % fact_double
% 5.31/5.64 thf(fact_8025_binomial__code,axiom,
% 5.31/5.64 ( binomial
% 5.31/5.64 = ( ^ [N4: nat,K3: nat] : ( if_nat @ ( ord_less_nat @ N4 @ K3 ) @ zero_zero_nat @ ( if_nat @ ( ord_less_nat @ N4 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K3 ) ) @ ( binomial @ N4 @ ( minus_minus_nat @ N4 @ K3 ) ) @ ( divide_divide_nat @ ( set_fo2584398358068434914at_nat @ times_times_nat @ ( plus_plus_nat @ ( minus_minus_nat @ N4 @ K3 ) @ one_one_nat ) @ N4 @ one_one_nat ) @ ( semiri1408675320244567234ct_nat @ K3 ) ) ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % binomial_code
% 5.31/5.64 thf(fact_8026_Maclaurin__lemma,axiom,
% 5.31/5.64 ! [H: real,F2: real > real,J2: nat > real,N: nat] :
% 5.31/5.64 ( ( ord_less_real @ zero_zero_real @ H )
% 5.31/5.64 => ? [B8: real] :
% 5.31/5.64 ( ( F2 @ H )
% 5.31/5.64 = ( plus_plus_real
% 5.31/5.64 @ ( groups6591440286371151544t_real
% 5.31/5.64 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( J2 @ M6 ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ H @ M6 ) )
% 5.31/5.64 @ ( set_ord_lessThan_nat @ N ) )
% 5.31/5.64 @ ( times_times_real @ B8 @ ( divide_divide_real @ ( power_power_real @ H @ N ) @ ( semiri2265585572941072030t_real @ N ) ) ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % Maclaurin_lemma
% 5.31/5.64 thf(fact_8027_Maclaurin__zero,axiom,
% 5.31/5.64 ! [X: real,N: nat,Diff: nat > complex > real] :
% 5.31/5.64 ( ( X = zero_zero_real )
% 5.31/5.64 => ( ( N != zero_zero_nat )
% 5.31/5.64 => ( ( groups6591440286371151544t_real
% 5.31/5.64 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_complex ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ X @ M6 ) )
% 5.31/5.64 @ ( set_ord_lessThan_nat @ N ) )
% 5.31/5.64 = ( Diff @ zero_zero_nat @ zero_zero_complex ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % Maclaurin_zero
% 5.31/5.64 thf(fact_8028_Maclaurin__zero,axiom,
% 5.31/5.64 ! [X: real,N: nat,Diff: nat > real > real] :
% 5.31/5.64 ( ( X = zero_zero_real )
% 5.31/5.64 => ( ( N != zero_zero_nat )
% 5.31/5.64 => ( ( groups6591440286371151544t_real
% 5.31/5.64 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ X @ M6 ) )
% 5.31/5.64 @ ( set_ord_lessThan_nat @ N ) )
% 5.31/5.64 = ( Diff @ zero_zero_nat @ zero_zero_real ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % Maclaurin_zero
% 5.31/5.64 thf(fact_8029_Maclaurin__zero,axiom,
% 5.31/5.64 ! [X: real,N: nat,Diff: nat > rat > real] :
% 5.31/5.64 ( ( X = zero_zero_real )
% 5.31/5.64 => ( ( N != zero_zero_nat )
% 5.31/5.64 => ( ( groups6591440286371151544t_real
% 5.31/5.64 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_rat ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ X @ M6 ) )
% 5.31/5.64 @ ( set_ord_lessThan_nat @ N ) )
% 5.31/5.64 = ( Diff @ zero_zero_nat @ zero_zero_rat ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % Maclaurin_zero
% 5.31/5.64 thf(fact_8030_Maclaurin__zero,axiom,
% 5.31/5.64 ! [X: real,N: nat,Diff: nat > nat > real] :
% 5.31/5.64 ( ( X = zero_zero_real )
% 5.31/5.64 => ( ( N != zero_zero_nat )
% 5.31/5.64 => ( ( groups6591440286371151544t_real
% 5.31/5.64 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_nat ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ X @ M6 ) )
% 5.31/5.64 @ ( set_ord_lessThan_nat @ N ) )
% 5.31/5.64 = ( Diff @ zero_zero_nat @ zero_zero_nat ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % Maclaurin_zero
% 5.31/5.64 thf(fact_8031_Maclaurin__zero,axiom,
% 5.31/5.64 ! [X: real,N: nat,Diff: nat > int > real] :
% 5.31/5.64 ( ( X = zero_zero_real )
% 5.31/5.64 => ( ( N != zero_zero_nat )
% 5.31/5.64 => ( ( groups6591440286371151544t_real
% 5.31/5.64 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_int ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ X @ M6 ) )
% 5.31/5.64 @ ( set_ord_lessThan_nat @ N ) )
% 5.31/5.64 = ( Diff @ zero_zero_nat @ zero_zero_int ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % Maclaurin_zero
% 5.31/5.64 thf(fact_8032_sin__coeff__def,axiom,
% 5.31/5.64 ( sin_coeff
% 5.31/5.64 = ( ^ [N4: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) @ zero_zero_real @ ( divide_divide_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( divide_divide_nat @ ( minus_minus_nat @ N4 @ ( suc @ zero_zero_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( semiri2265585572941072030t_real @ N4 ) ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % sin_coeff_def
% 5.31/5.64 thf(fact_8033_fact__diff__Suc,axiom,
% 5.31/5.64 ! [N: nat,M2: nat] :
% 5.31/5.64 ( ( ord_less_nat @ N @ ( suc @ M2 ) )
% 5.31/5.64 => ( ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ ( suc @ M2 ) @ N ) )
% 5.31/5.64 = ( times_times_nat @ ( minus_minus_nat @ ( suc @ M2 ) @ N ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ M2 @ N ) ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % fact_diff_Suc
% 5.31/5.64 thf(fact_8034_sin__paired,axiom,
% 5.31/5.64 ! [X: real] :
% 5.31/5.64 ( sums_real
% 5.31/5.64 @ ^ [N4: nat] : ( times_times_real @ ( divide_divide_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N4 ) @ ( semiri2265585572941072030t_real @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) @ one_one_nat ) ) ) @ ( power_power_real @ X @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) @ one_one_nat ) ) )
% 5.31/5.64 @ ( sin_real @ X ) ) ).
% 5.31/5.64
% 5.31/5.64 % sin_paired
% 5.31/5.64 thf(fact_8035_and__int_Osimps,axiom,
% 5.31/5.64 ( bit_se725231765392027082nd_int
% 5.31/5.64 = ( ^ [K3: int,L2: int] :
% 5.31/5.64 ( if_int
% 5.31/5.64 @ ( ( member_int @ K3 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 5.31/5.64 & ( member_int @ L2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 5.31/5.64 @ ( uminus_uminus_int
% 5.31/5.64 @ ( zero_n2684676970156552555ol_int
% 5.31/5.64 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K3 )
% 5.31/5.64 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L2 ) ) ) )
% 5.31/5.64 @ ( plus_plus_int
% 5.31/5.64 @ ( zero_n2684676970156552555ol_int
% 5.31/5.64 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K3 )
% 5.31/5.64 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L2 ) ) )
% 5.31/5.64 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % and_int.simps
% 5.31/5.64 thf(fact_8036_sin__zero,axiom,
% 5.31/5.64 ( ( sin_complex @ zero_zero_complex )
% 5.31/5.64 = zero_zero_complex ) ).
% 5.31/5.64
% 5.31/5.64 % sin_zero
% 5.31/5.64 thf(fact_8037_sin__zero,axiom,
% 5.31/5.64 ( ( sin_real @ zero_zero_real )
% 5.31/5.64 = zero_zero_real ) ).
% 5.31/5.64
% 5.31/5.64 % sin_zero
% 5.31/5.64 thf(fact_8038_bit_Oconj__zero__right,axiom,
% 5.31/5.64 ! [X: int] :
% 5.31/5.64 ( ( bit_se725231765392027082nd_int @ X @ zero_zero_int )
% 5.31/5.64 = zero_zero_int ) ).
% 5.31/5.64
% 5.31/5.64 % bit.conj_zero_right
% 5.31/5.64 thf(fact_8039_bit_Oconj__zero__left,axiom,
% 5.31/5.64 ! [X: int] :
% 5.31/5.64 ( ( bit_se725231765392027082nd_int @ zero_zero_int @ X )
% 5.31/5.64 = zero_zero_int ) ).
% 5.31/5.64
% 5.31/5.64 % bit.conj_zero_left
% 5.31/5.64 thf(fact_8040_zero__and__eq,axiom,
% 5.31/5.64 ! [A: int] :
% 5.31/5.64 ( ( bit_se725231765392027082nd_int @ zero_zero_int @ A )
% 5.31/5.64 = zero_zero_int ) ).
% 5.31/5.64
% 5.31/5.64 % zero_and_eq
% 5.31/5.64 thf(fact_8041_zero__and__eq,axiom,
% 5.31/5.64 ! [A: nat] :
% 5.31/5.64 ( ( bit_se727722235901077358nd_nat @ zero_zero_nat @ A )
% 5.31/5.64 = zero_zero_nat ) ).
% 5.31/5.64
% 5.31/5.64 % zero_and_eq
% 5.31/5.64 thf(fact_8042_and__zero__eq,axiom,
% 5.31/5.64 ! [A: int] :
% 5.31/5.64 ( ( bit_se725231765392027082nd_int @ A @ zero_zero_int )
% 5.31/5.64 = zero_zero_int ) ).
% 5.31/5.64
% 5.31/5.64 % and_zero_eq
% 5.31/5.64 thf(fact_8043_and__zero__eq,axiom,
% 5.31/5.64 ! [A: nat] :
% 5.31/5.64 ( ( bit_se727722235901077358nd_nat @ A @ zero_zero_nat )
% 5.31/5.64 = zero_zero_nat ) ).
% 5.31/5.64
% 5.31/5.64 % and_zero_eq
% 5.31/5.64 thf(fact_8044_sin__coeff__0,axiom,
% 5.31/5.64 ( ( sin_coeff @ zero_zero_nat )
% 5.31/5.64 = zero_zero_real ) ).
% 5.31/5.64
% 5.31/5.64 % sin_coeff_0
% 5.31/5.64 thf(fact_8045_and__numerals_I5_J,axiom,
% 5.31/5.64 ! [X: num] :
% 5.31/5.64 ( ( bit_se3949692690581998587nteger @ ( numera6620942414471956472nteger @ ( bit0 @ X ) ) @ one_one_Code_integer )
% 5.31/5.64 = zero_z3403309356797280102nteger ) ).
% 5.31/5.64
% 5.31/5.64 % and_numerals(5)
% 5.31/5.64 thf(fact_8046_and__numerals_I5_J,axiom,
% 5.31/5.64 ! [X: num] :
% 5.31/5.64 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ X ) ) @ one_one_int )
% 5.31/5.64 = zero_zero_int ) ).
% 5.31/5.64
% 5.31/5.64 % and_numerals(5)
% 5.31/5.64 thf(fact_8047_and__numerals_I5_J,axiom,
% 5.31/5.64 ! [X: num] :
% 5.31/5.64 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit0 @ X ) ) @ one_one_nat )
% 5.31/5.64 = zero_zero_nat ) ).
% 5.31/5.64
% 5.31/5.64 % and_numerals(5)
% 5.31/5.64 thf(fact_8048_and__numerals_I1_J,axiom,
% 5.31/5.64 ! [Y: num] :
% 5.31/5.64 ( ( bit_se3949692690581998587nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ Y ) ) )
% 5.31/5.64 = zero_z3403309356797280102nteger ) ).
% 5.31/5.64
% 5.31/5.64 % and_numerals(1)
% 5.31/5.64 thf(fact_8049_and__numerals_I1_J,axiom,
% 5.31/5.64 ! [Y: num] :
% 5.31/5.64 ( ( bit_se725231765392027082nd_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ Y ) ) )
% 5.31/5.64 = zero_zero_int ) ).
% 5.31/5.64
% 5.31/5.64 % and_numerals(1)
% 5.31/5.64 thf(fact_8050_and__numerals_I1_J,axiom,
% 5.31/5.64 ! [Y: num] :
% 5.31/5.64 ( ( bit_se727722235901077358nd_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 5.31/5.64 = zero_zero_nat ) ).
% 5.31/5.64
% 5.31/5.64 % and_numerals(1)
% 5.31/5.64 thf(fact_8051_and__numerals_I3_J,axiom,
% 5.31/5.64 ! [X: num,Y: num] :
% 5.31/5.64 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ X ) ) @ ( numeral_numeral_int @ ( bit0 @ Y ) ) )
% 5.31/5.64 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ X ) @ ( numeral_numeral_int @ Y ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % and_numerals(3)
% 5.31/5.64 thf(fact_8052_and__numerals_I3_J,axiom,
% 5.31/5.64 ! [X: num,Y: num] :
% 5.31/5.64 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit0 @ X ) ) @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 5.31/5.64 = ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ X ) @ ( numeral_numeral_nat @ Y ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % and_numerals(3)
% 5.31/5.64 thf(fact_8053_and__int__rec,axiom,
% 5.31/5.64 ( bit_se725231765392027082nd_int
% 5.31/5.64 = ( ^ [K3: int,L2: int] :
% 5.31/5.64 ( plus_plus_int
% 5.31/5.64 @ ( zero_n2684676970156552555ol_int
% 5.31/5.64 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K3 )
% 5.31/5.64 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L2 ) ) )
% 5.31/5.64 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % and_int_rec
% 5.31/5.64 thf(fact_8054_and__int__unfold,axiom,
% 5.31/5.64 ( bit_se725231765392027082nd_int
% 5.31/5.64 = ( ^ [K3: int,L2: int] :
% 5.31/5.64 ( if_int
% 5.31/5.64 @ ( ( K3 = zero_zero_int )
% 5.31/5.64 | ( L2 = zero_zero_int ) )
% 5.31/5.64 @ zero_zero_int
% 5.31/5.64 @ ( if_int
% 5.31/5.64 @ ( K3
% 5.31/5.64 = ( uminus_uminus_int @ one_one_int ) )
% 5.31/5.64 @ L2
% 5.31/5.64 @ ( if_int
% 5.31/5.64 @ ( L2
% 5.31/5.64 = ( uminus_uminus_int @ one_one_int ) )
% 5.31/5.64 @ K3
% 5.31/5.64 @ ( plus_plus_int @ ( times_times_int @ ( modulo_modulo_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( modulo_modulo_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % and_int_unfold
% 5.31/5.64 thf(fact_8055_and__int_Oelims,axiom,
% 5.31/5.64 ! [X: int,Xa2: int,Y: int] :
% 5.31/5.64 ( ( ( bit_se725231765392027082nd_int @ X @ Xa2 )
% 5.31/5.64 = Y )
% 5.31/5.64 => ( ( ( ( member_int @ X @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 5.31/5.64 & ( member_int @ Xa2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 5.31/5.64 => ( Y
% 5.31/5.64 = ( uminus_uminus_int
% 5.31/5.64 @ ( zero_n2684676970156552555ol_int
% 5.31/5.64 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X )
% 5.31/5.64 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa2 ) ) ) ) ) )
% 5.31/5.64 & ( ~ ( ( member_int @ X @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 5.31/5.64 & ( member_int @ Xa2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 5.31/5.64 => ( Y
% 5.31/5.64 = ( plus_plus_int
% 5.31/5.64 @ ( zero_n2684676970156552555ol_int
% 5.31/5.64 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X )
% 5.31/5.64 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa2 ) ) )
% 5.31/5.64 @ ( 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 ) ) ) ) ) ) ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % and_int.elims
% 5.31/5.64 thf(fact_8056_Maclaurin__sin__expansion3,axiom,
% 5.31/5.64 ! [N: nat,X: real] :
% 5.31/5.64 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.64 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.31/5.64 => ? [T6: real] :
% 5.31/5.64 ( ( ord_less_real @ zero_zero_real @ T6 )
% 5.31/5.64 & ( ord_less_real @ T6 @ X )
% 5.31/5.64 & ( ( sin_real @ X )
% 5.31/5.64 = ( plus_plus_real
% 5.31/5.64 @ ( groups6591440286371151544t_real
% 5.31/5.64 @ ^ [M6: nat] : ( times_times_real @ ( sin_coeff @ M6 ) @ ( power_power_real @ X @ M6 ) )
% 5.31/5.64 @ ( set_ord_lessThan_nat @ N ) )
% 5.31/5.64 @ ( 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 ) ) ) ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % Maclaurin_sin_expansion3
% 5.31/5.64 thf(fact_8057_Maclaurin__sin__expansion4,axiom,
% 5.31/5.64 ! [X: real,N: nat] :
% 5.31/5.64 ( ( ord_less_real @ zero_zero_real @ X )
% 5.31/5.64 => ? [T6: real] :
% 5.31/5.64 ( ( ord_less_real @ zero_zero_real @ T6 )
% 5.31/5.64 & ( ord_less_eq_real @ T6 @ X )
% 5.31/5.64 & ( ( sin_real @ X )
% 5.31/5.64 = ( plus_plus_real
% 5.31/5.64 @ ( groups6591440286371151544t_real
% 5.31/5.64 @ ^ [M6: nat] : ( times_times_real @ ( sin_coeff @ M6 ) @ ( power_power_real @ X @ M6 ) )
% 5.31/5.64 @ ( set_ord_lessThan_nat @ N ) )
% 5.31/5.64 @ ( 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 ) ) ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % Maclaurin_sin_expansion4
% 5.31/5.64 thf(fact_8058_sumr__cos__zero__one,axiom,
% 5.31/5.64 ! [N: nat] :
% 5.31/5.64 ( ( groups6591440286371151544t_real
% 5.31/5.64 @ ^ [M6: nat] : ( times_times_real @ ( cos_coeff @ M6 ) @ ( power_power_real @ zero_zero_real @ M6 ) )
% 5.31/5.64 @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 5.31/5.64 = one_one_real ) ).
% 5.31/5.64
% 5.31/5.64 % sumr_cos_zero_one
% 5.31/5.64 thf(fact_8059_sin__cos__npi,axiom,
% 5.31/5.64 ! [N: nat] :
% 5.31/5.64 ( ( 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 ) ) ) )
% 5.31/5.64 = ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) ) ).
% 5.31/5.64
% 5.31/5.64 % sin_cos_npi
% 5.31/5.64 thf(fact_8060_Maclaurin__sin__expansion,axiom,
% 5.31/5.64 ! [X: real,N: nat] :
% 5.31/5.64 ? [T6: real] :
% 5.31/5.64 ( ( sin_real @ X )
% 5.31/5.64 = ( plus_plus_real
% 5.31/5.64 @ ( groups6591440286371151544t_real
% 5.31/5.64 @ ^ [M6: nat] : ( times_times_real @ ( sin_coeff @ M6 ) @ ( power_power_real @ X @ M6 ) )
% 5.31/5.64 @ ( set_ord_lessThan_nat @ N ) )
% 5.31/5.64 @ ( 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 ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % Maclaurin_sin_expansion
% 5.31/5.64 thf(fact_8061_signed__take__bit__Suc__minus__bit1,axiom,
% 5.31/5.64 ! [N: nat,K2: num] :
% 5.31/5.64 ( ( bit_ri631733984087533419it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K2 ) ) ) )
% 5.31/5.64 = ( plus_plus_int @ ( times_times_int @ ( bit_ri631733984087533419it_int @ N @ ( minus_minus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K2 ) ) @ one_one_int ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 5.31/5.64
% 5.31/5.64 % signed_take_bit_Suc_minus_bit1
% 5.31/5.64 thf(fact_8062_semiring__norm_I15_J,axiom,
% 5.31/5.64 ! [M2: num,N: num] :
% 5.31/5.64 ( ( times_times_num @ ( bit1 @ M2 ) @ ( bit0 @ N ) )
% 5.31/5.64 = ( bit0 @ ( times_times_num @ ( bit1 @ M2 ) @ N ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % semiring_norm(15)
% 5.31/5.64 thf(fact_8063_semiring__norm_I14_J,axiom,
% 5.31/5.64 ! [M2: num,N: num] :
% 5.31/5.64 ( ( times_times_num @ ( bit0 @ M2 ) @ ( bit1 @ N ) )
% 5.31/5.64 = ( bit0 @ ( times_times_num @ M2 @ ( bit1 @ N ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % semiring_norm(14)
% 5.31/5.64 thf(fact_8064_cos__coeff__0,axiom,
% 5.31/5.64 ( ( cos_coeff @ zero_zero_nat )
% 5.31/5.64 = one_one_real ) ).
% 5.31/5.64
% 5.31/5.64 % cos_coeff_0
% 5.31/5.64 thf(fact_8065_dbl__inc__simps_I5_J,axiom,
% 5.31/5.64 ! [K2: num] :
% 5.31/5.64 ( ( neg_nu8557863876264182079omplex @ ( numera6690914467698888265omplex @ K2 ) )
% 5.31/5.64 = ( numera6690914467698888265omplex @ ( bit1 @ K2 ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % dbl_inc_simps(5)
% 5.31/5.64 thf(fact_8066_dbl__inc__simps_I5_J,axiom,
% 5.31/5.64 ! [K2: num] :
% 5.31/5.64 ( ( neg_nu8295874005876285629c_real @ ( numeral_numeral_real @ K2 ) )
% 5.31/5.64 = ( numeral_numeral_real @ ( bit1 @ K2 ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % dbl_inc_simps(5)
% 5.31/5.64 thf(fact_8067_dbl__inc__simps_I5_J,axiom,
% 5.31/5.64 ! [K2: num] :
% 5.31/5.64 ( ( neg_nu5851722552734809277nc_int @ ( numeral_numeral_int @ K2 ) )
% 5.31/5.64 = ( numeral_numeral_int @ ( bit1 @ K2 ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % dbl_inc_simps(5)
% 5.31/5.64 thf(fact_8068_and__nat__numerals_I1_J,axiom,
% 5.31/5.64 ! [Y: num] :
% 5.31/5.64 ( ( bit_se727722235901077358nd_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 5.31/5.64 = zero_zero_nat ) ).
% 5.31/5.64
% 5.31/5.64 % and_nat_numerals(1)
% 5.31/5.64 thf(fact_8069_and__nat__numerals_I3_J,axiom,
% 5.31/5.64 ! [X: num] :
% 5.31/5.64 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit0 @ X ) ) @ ( suc @ zero_zero_nat ) )
% 5.31/5.64 = zero_zero_nat ) ).
% 5.31/5.64
% 5.31/5.64 % and_nat_numerals(3)
% 5.31/5.64 thf(fact_8070_zdiv__numeral__Bit1,axiom,
% 5.31/5.64 ! [V2: num,W2: num] :
% 5.31/5.64 ( ( divide_divide_int @ ( numeral_numeral_int @ ( bit1 @ V2 ) ) @ ( numeral_numeral_int @ ( bit0 @ W2 ) ) )
% 5.31/5.64 = ( divide_divide_int @ ( numeral_numeral_int @ V2 ) @ ( numeral_numeral_int @ W2 ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % zdiv_numeral_Bit1
% 5.31/5.64 thf(fact_8071_semiring__norm_I16_J,axiom,
% 5.31/5.64 ! [M2: num,N: num] :
% 5.31/5.64 ( ( times_times_num @ ( bit1 @ M2 ) @ ( bit1 @ N ) )
% 5.31/5.64 = ( bit1 @ ( plus_plus_num @ ( plus_plus_num @ M2 @ N ) @ ( bit0 @ ( times_times_num @ M2 @ N ) ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % semiring_norm(16)
% 5.31/5.64 thf(fact_8072_and__nat__numerals_I4_J,axiom,
% 5.31/5.64 ! [X: num] :
% 5.31/5.64 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ ( suc @ zero_zero_nat ) )
% 5.31/5.64 = one_one_nat ) ).
% 5.31/5.64
% 5.31/5.64 % and_nat_numerals(4)
% 5.31/5.64 thf(fact_8073_and__nat__numerals_I2_J,axiom,
% 5.31/5.64 ! [Y: num] :
% 5.31/5.64 ( ( bit_se727722235901077358nd_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 5.31/5.64 = one_one_nat ) ).
% 5.31/5.64
% 5.31/5.64 % and_nat_numerals(2)
% 5.31/5.64 thf(fact_8074_sin__npi2,axiom,
% 5.31/5.64 ! [N: nat] :
% 5.31/5.64 ( ( sin_real @ ( times_times_real @ pi @ ( semiri5074537144036343181t_real @ N ) ) )
% 5.31/5.64 = zero_zero_real ) ).
% 5.31/5.64
% 5.31/5.64 % sin_npi2
% 5.31/5.64 thf(fact_8075_sin__npi,axiom,
% 5.31/5.64 ! [N: nat] :
% 5.31/5.64 ( ( sin_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ pi ) )
% 5.31/5.64 = zero_zero_real ) ).
% 5.31/5.64
% 5.31/5.64 % sin_npi
% 5.31/5.64 thf(fact_8076_dbl__inc__simps_I3_J,axiom,
% 5.31/5.64 ( ( neg_nu5831290666863070958nteger @ one_one_Code_integer )
% 5.31/5.64 = ( numera6620942414471956472nteger @ ( bit1 @ one ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % dbl_inc_simps(3)
% 5.31/5.64 thf(fact_8077_dbl__inc__simps_I3_J,axiom,
% 5.31/5.64 ( ( neg_nu8557863876264182079omplex @ one_one_complex )
% 5.31/5.64 = ( numera6690914467698888265omplex @ ( bit1 @ one ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % dbl_inc_simps(3)
% 5.31/5.64 thf(fact_8078_dbl__inc__simps_I3_J,axiom,
% 5.31/5.64 ( ( neg_nu8295874005876285629c_real @ one_one_real )
% 5.31/5.64 = ( numeral_numeral_real @ ( bit1 @ one ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % dbl_inc_simps(3)
% 5.31/5.64 thf(fact_8079_dbl__inc__simps_I3_J,axiom,
% 5.31/5.64 ( ( neg_nu5851722552734809277nc_int @ one_one_int )
% 5.31/5.64 = ( numeral_numeral_int @ ( bit1 @ one ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % dbl_inc_simps(3)
% 5.31/5.64 thf(fact_8080_and__numerals_I4_J,axiom,
% 5.31/5.64 ! [X: num,Y: num] :
% 5.31/5.64 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ X ) ) @ ( numeral_numeral_int @ ( bit1 @ Y ) ) )
% 5.31/5.64 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ X ) @ ( numeral_numeral_int @ Y ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % and_numerals(4)
% 5.31/5.64 thf(fact_8081_and__numerals_I4_J,axiom,
% 5.31/5.64 ! [X: num,Y: num] :
% 5.31/5.64 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit0 @ X ) ) @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 5.31/5.64 = ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ X ) @ ( numeral_numeral_nat @ Y ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % and_numerals(4)
% 5.31/5.64 thf(fact_8082_and__numerals_I6_J,axiom,
% 5.31/5.64 ! [X: num,Y: num] :
% 5.31/5.64 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ X ) ) @ ( numeral_numeral_int @ ( bit0 @ Y ) ) )
% 5.31/5.64 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ X ) @ ( numeral_numeral_int @ Y ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % and_numerals(6)
% 5.31/5.64 thf(fact_8083_and__numerals_I6_J,axiom,
% 5.31/5.64 ! [X: num,Y: num] :
% 5.31/5.64 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 5.31/5.64 = ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ X ) @ ( numeral_numeral_nat @ Y ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % and_numerals(6)
% 5.31/5.64 thf(fact_8084_Suc__0__and__eq,axiom,
% 5.31/5.64 ! [N: nat] :
% 5.31/5.64 ( ( bit_se727722235901077358nd_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.31/5.64 = ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % Suc_0_and_eq
% 5.31/5.64 thf(fact_8085_and__Suc__0__eq,axiom,
% 5.31/5.64 ! [N: nat] :
% 5.31/5.64 ( ( bit_se727722235901077358nd_nat @ N @ ( suc @ zero_zero_nat ) )
% 5.31/5.64 = ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % and_Suc_0_eq
% 5.31/5.64 thf(fact_8086_div__Suc__eq__div__add3,axiom,
% 5.31/5.64 ! [M2: nat,N: nat] :
% 5.31/5.64 ( ( divide_divide_nat @ M2 @ ( suc @ ( suc @ ( suc @ N ) ) ) )
% 5.31/5.64 = ( divide_divide_nat @ M2 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ N ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % div_Suc_eq_div_add3
% 5.31/5.64 thf(fact_8087_Suc__div__eq__add3__div__numeral,axiom,
% 5.31/5.64 ! [M2: nat,V2: num] :
% 5.31/5.64 ( ( divide_divide_nat @ ( suc @ ( suc @ ( suc @ M2 ) ) ) @ ( numeral_numeral_nat @ V2 ) )
% 5.31/5.64 = ( divide_divide_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ M2 ) @ ( numeral_numeral_nat @ V2 ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % Suc_div_eq_add3_div_numeral
% 5.31/5.64 thf(fact_8088_mod__Suc__eq__mod__add3,axiom,
% 5.31/5.64 ! [M2: nat,N: nat] :
% 5.31/5.64 ( ( modulo_modulo_nat @ M2 @ ( suc @ ( suc @ ( suc @ N ) ) ) )
% 5.31/5.64 = ( modulo_modulo_nat @ M2 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ N ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % mod_Suc_eq_mod_add3
% 5.31/5.64 thf(fact_8089_Suc__mod__eq__add3__mod__numeral,axiom,
% 5.31/5.64 ! [M2: nat,V2: num] :
% 5.31/5.64 ( ( modulo_modulo_nat @ ( suc @ ( suc @ ( suc @ M2 ) ) ) @ ( numeral_numeral_nat @ V2 ) )
% 5.31/5.64 = ( modulo_modulo_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ M2 ) @ ( numeral_numeral_nat @ V2 ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % Suc_mod_eq_add3_mod_numeral
% 5.31/5.64 thf(fact_8090_dbl__dec__simps_I4_J,axiom,
% 5.31/5.64 ( ( neg_nu3811975205180677377ec_int @ ( uminus_uminus_int @ one_one_int ) )
% 5.31/5.64 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ one ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % dbl_dec_simps(4)
% 5.31/5.64 thf(fact_8091_dbl__dec__simps_I4_J,axiom,
% 5.31/5.64 ( ( neg_nu6075765906172075777c_real @ ( uminus_uminus_real @ one_one_real ) )
% 5.31/5.64 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % dbl_dec_simps(4)
% 5.31/5.64 thf(fact_8092_dbl__dec__simps_I4_J,axiom,
% 5.31/5.64 ( ( neg_nu6511756317524482435omplex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.31/5.64 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( bit1 @ one ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % dbl_dec_simps(4)
% 5.31/5.64 thf(fact_8093_dbl__dec__simps_I4_J,axiom,
% 5.31/5.64 ( ( neg_nu7757733837767384882nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.31/5.64 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit1 @ one ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % dbl_dec_simps(4)
% 5.31/5.64 thf(fact_8094_dbl__dec__simps_I4_J,axiom,
% 5.31/5.64 ( ( neg_nu3179335615603231917ec_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.31/5.64 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( bit1 @ one ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % dbl_dec_simps(4)
% 5.31/5.64 thf(fact_8095_sin__two__pi,axiom,
% 5.31/5.64 ( ( sin_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 5.31/5.64 = zero_zero_real ) ).
% 5.31/5.64
% 5.31/5.64 % sin_two_pi
% 5.31/5.64 thf(fact_8096_sin__2pi__minus,axiom,
% 5.31/5.64 ! [X: real] :
% 5.31/5.64 ( ( sin_real @ ( minus_minus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ X ) )
% 5.31/5.64 = ( uminus_uminus_real @ ( sin_real @ X ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % sin_2pi_minus
% 5.31/5.64 thf(fact_8097_sin__periodic,axiom,
% 5.31/5.64 ! [X: real] :
% 5.31/5.64 ( ( sin_real @ ( plus_plus_real @ X @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 5.31/5.64 = ( sin_real @ X ) ) ).
% 5.31/5.64
% 5.31/5.64 % sin_periodic
% 5.31/5.64 thf(fact_8098_and__numerals_I7_J,axiom,
% 5.31/5.64 ! [X: num,Y: num] :
% 5.31/5.64 ( ( bit_se3949692690581998587nteger @ ( numera6620942414471956472nteger @ ( bit1 @ X ) ) @ ( numera6620942414471956472nteger @ ( bit1 @ Y ) ) )
% 5.31/5.64 = ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se3949692690581998587nteger @ ( numera6620942414471956472nteger @ X ) @ ( numera6620942414471956472nteger @ Y ) ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % and_numerals(7)
% 5.31/5.64 thf(fact_8099_and__numerals_I7_J,axiom,
% 5.31/5.64 ! [X: num,Y: num] :
% 5.31/5.64 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ X ) ) @ ( numeral_numeral_int @ ( bit1 @ Y ) ) )
% 5.31/5.64 = ( 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 ) ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % and_numerals(7)
% 5.31/5.64 thf(fact_8100_and__numerals_I7_J,axiom,
% 5.31/5.64 ! [X: num,Y: num] :
% 5.31/5.64 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 5.31/5.64 = ( 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 ) ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % and_numerals(7)
% 5.31/5.64 thf(fact_8101_zmod__numeral__Bit1,axiom,
% 5.31/5.64 ! [V2: num,W2: num] :
% 5.31/5.64 ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ V2 ) ) @ ( numeral_numeral_int @ ( bit0 @ W2 ) ) )
% 5.31/5.64 = ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( modulo_modulo_int @ ( numeral_numeral_int @ V2 ) @ ( numeral_numeral_int @ W2 ) ) ) @ one_one_int ) ) ).
% 5.31/5.64
% 5.31/5.64 % zmod_numeral_Bit1
% 5.31/5.64 thf(fact_8102_sin__2npi,axiom,
% 5.31/5.64 ! [N: nat] :
% 5.31/5.64 ( ( sin_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) )
% 5.31/5.64 = zero_zero_real ) ).
% 5.31/5.64
% 5.31/5.64 % sin_2npi
% 5.31/5.64 thf(fact_8103_signed__take__bit__Suc__bit1,axiom,
% 5.31/5.64 ! [N: nat,K2: num] :
% 5.31/5.64 ( ( bit_ri631733984087533419it_int @ ( suc @ N ) @ ( numeral_numeral_int @ ( bit1 @ K2 ) ) )
% 5.31/5.64 = ( plus_plus_int @ ( times_times_int @ ( bit_ri631733984087533419it_int @ N @ ( numeral_numeral_int @ K2 ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 5.31/5.64
% 5.31/5.64 % signed_take_bit_Suc_bit1
% 5.31/5.64 thf(fact_8104_sin__3over2__pi,axiom,
% 5.31/5.64 ( ( sin_real @ ( times_times_real @ ( divide_divide_real @ ( numeral_numeral_real @ ( bit1 @ one ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ pi ) )
% 5.31/5.64 = ( uminus_uminus_real @ one_one_real ) ) ).
% 5.31/5.64
% 5.31/5.64 % sin_3over2_pi
% 5.31/5.64 thf(fact_8105_num_Oexhaust,axiom,
% 5.31/5.64 ! [Y: num] :
% 5.31/5.64 ( ( Y != one )
% 5.31/5.64 => ( ! [X23: num] :
% 5.31/5.64 ( Y
% 5.31/5.64 != ( bit0 @ X23 ) )
% 5.31/5.64 => ~ ! [X32: num] :
% 5.31/5.64 ( Y
% 5.31/5.64 != ( bit1 @ X32 ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % num.exhaust
% 5.31/5.64 thf(fact_8106_numeral__Bit1,axiom,
% 5.31/5.64 ! [N: num] :
% 5.31/5.64 ( ( numera6620942414471956472nteger @ ( bit1 @ N ) )
% 5.31/5.64 = ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ ( numera6620942414471956472nteger @ N ) @ ( numera6620942414471956472nteger @ N ) ) @ one_one_Code_integer ) ) ).
% 5.31/5.64
% 5.31/5.64 % numeral_Bit1
% 5.31/5.64 thf(fact_8107_numeral__Bit1,axiom,
% 5.31/5.64 ! [N: num] :
% 5.31/5.64 ( ( numeral_numeral_rat @ ( bit1 @ N ) )
% 5.31/5.64 = ( plus_plus_rat @ ( plus_plus_rat @ ( numeral_numeral_rat @ N ) @ ( numeral_numeral_rat @ N ) ) @ one_one_rat ) ) ).
% 5.31/5.64
% 5.31/5.64 % numeral_Bit1
% 5.31/5.64 thf(fact_8108_numeral__Bit1,axiom,
% 5.31/5.64 ! [N: num] :
% 5.31/5.64 ( ( numera1916890842035813515d_enat @ ( bit1 @ N ) )
% 5.31/5.64 = ( plus_p3455044024723400733d_enat @ ( plus_p3455044024723400733d_enat @ ( numera1916890842035813515d_enat @ N ) @ ( numera1916890842035813515d_enat @ N ) ) @ one_on7984719198319812577d_enat ) ) ).
% 5.31/5.64
% 5.31/5.64 % numeral_Bit1
% 5.31/5.64 thf(fact_8109_numeral__Bit1,axiom,
% 5.31/5.64 ! [N: num] :
% 5.31/5.64 ( ( numera6690914467698888265omplex @ ( bit1 @ N ) )
% 5.31/5.64 = ( plus_plus_complex @ ( plus_plus_complex @ ( numera6690914467698888265omplex @ N ) @ ( numera6690914467698888265omplex @ N ) ) @ one_one_complex ) ) ).
% 5.31/5.64
% 5.31/5.64 % numeral_Bit1
% 5.31/5.64 thf(fact_8110_numeral__Bit1,axiom,
% 5.31/5.64 ! [N: num] :
% 5.31/5.64 ( ( numeral_numeral_real @ ( bit1 @ N ) )
% 5.31/5.64 = ( plus_plus_real @ ( plus_plus_real @ ( numeral_numeral_real @ N ) @ ( numeral_numeral_real @ N ) ) @ one_one_real ) ) ).
% 5.31/5.64
% 5.31/5.64 % numeral_Bit1
% 5.31/5.64 thf(fact_8111_numeral__Bit1,axiom,
% 5.31/5.64 ! [N: num] :
% 5.31/5.64 ( ( numeral_numeral_nat @ ( bit1 @ N ) )
% 5.31/5.64 = ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ N ) ) @ one_one_nat ) ) ).
% 5.31/5.64
% 5.31/5.64 % numeral_Bit1
% 5.31/5.64 thf(fact_8112_numeral__Bit1,axiom,
% 5.31/5.64 ! [N: num] :
% 5.31/5.64 ( ( numeral_numeral_int @ ( bit1 @ N ) )
% 5.31/5.64 = ( plus_plus_int @ ( plus_plus_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ N ) ) @ one_one_int ) ) ).
% 5.31/5.64
% 5.31/5.64 % numeral_Bit1
% 5.31/5.64 thf(fact_8113_eval__nat__numeral_I3_J,axiom,
% 5.31/5.64 ! [N: num] :
% 5.31/5.64 ( ( numeral_numeral_nat @ ( bit1 @ N ) )
% 5.31/5.64 = ( suc @ ( numeral_numeral_nat @ ( bit0 @ N ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % eval_nat_numeral(3)
% 5.31/5.64 thf(fact_8114_cong__exp__iff__simps_I13_J,axiom,
% 5.31/5.64 ! [M2: num,Q2: num,N: num] :
% 5.31/5.64 ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ M2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 5.31/5.64 = ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) )
% 5.31/5.64 = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ M2 ) @ ( numeral_numeral_nat @ Q2 ) )
% 5.31/5.64 = ( modulo_modulo_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ Q2 ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % cong_exp_iff_simps(13)
% 5.31/5.64 thf(fact_8115_cong__exp__iff__simps_I13_J,axiom,
% 5.31/5.64 ! [M2: num,Q2: num,N: num] :
% 5.31/5.64 ( ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ M2 ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 5.31/5.64 = ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) ) )
% 5.31/5.64 = ( ( modulo_modulo_int @ ( numeral_numeral_int @ M2 ) @ ( numeral_numeral_int @ Q2 ) )
% 5.31/5.64 = ( modulo_modulo_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ Q2 ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % cong_exp_iff_simps(13)
% 5.31/5.64 thf(fact_8116_cong__exp__iff__simps_I12_J,axiom,
% 5.31/5.64 ! [M2: num,Q2: num,N: num] :
% 5.31/5.64 ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ M2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 5.31/5.64 != ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % cong_exp_iff_simps(12)
% 5.31/5.64 thf(fact_8117_cong__exp__iff__simps_I12_J,axiom,
% 5.31/5.64 ! [M2: num,Q2: num,N: num] :
% 5.31/5.64 ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ M2 ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 5.31/5.64 != ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % cong_exp_iff_simps(12)
% 5.31/5.64 thf(fact_8118_cong__exp__iff__simps_I10_J,axiom,
% 5.31/5.64 ! [M2: num,Q2: num,N: num] :
% 5.31/5.64 ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ M2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 5.31/5.64 != ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % cong_exp_iff_simps(10)
% 5.31/5.64 thf(fact_8119_cong__exp__iff__simps_I10_J,axiom,
% 5.31/5.64 ! [M2: num,Q2: num,N: num] :
% 5.31/5.64 ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ M2 ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 5.31/5.64 != ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % cong_exp_iff_simps(10)
% 5.31/5.64 thf(fact_8120_numeral__code_I3_J,axiom,
% 5.31/5.64 ! [N: num] :
% 5.31/5.64 ( ( numera6620942414471956472nteger @ ( bit1 @ N ) )
% 5.31/5.64 = ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ ( numera6620942414471956472nteger @ N ) @ ( numera6620942414471956472nteger @ N ) ) @ one_one_Code_integer ) ) ).
% 5.31/5.64
% 5.31/5.64 % numeral_code(3)
% 5.31/5.64 thf(fact_8121_numeral__code_I3_J,axiom,
% 5.31/5.64 ! [N: num] :
% 5.31/5.64 ( ( numeral_numeral_rat @ ( bit1 @ N ) )
% 5.31/5.64 = ( plus_plus_rat @ ( plus_plus_rat @ ( numeral_numeral_rat @ N ) @ ( numeral_numeral_rat @ N ) ) @ one_one_rat ) ) ).
% 5.31/5.64
% 5.31/5.64 % numeral_code(3)
% 5.31/5.64 thf(fact_8122_numeral__code_I3_J,axiom,
% 5.31/5.64 ! [N: num] :
% 5.31/5.64 ( ( numera1916890842035813515d_enat @ ( bit1 @ N ) )
% 5.31/5.64 = ( plus_p3455044024723400733d_enat @ ( plus_p3455044024723400733d_enat @ ( numera1916890842035813515d_enat @ N ) @ ( numera1916890842035813515d_enat @ N ) ) @ one_on7984719198319812577d_enat ) ) ).
% 5.31/5.64
% 5.31/5.64 % numeral_code(3)
% 5.31/5.64 thf(fact_8123_numeral__code_I3_J,axiom,
% 5.31/5.64 ! [N: num] :
% 5.31/5.64 ( ( numera6690914467698888265omplex @ ( bit1 @ N ) )
% 5.31/5.64 = ( plus_plus_complex @ ( plus_plus_complex @ ( numera6690914467698888265omplex @ N ) @ ( numera6690914467698888265omplex @ N ) ) @ one_one_complex ) ) ).
% 5.31/5.64
% 5.31/5.64 % numeral_code(3)
% 5.31/5.64 thf(fact_8124_numeral__code_I3_J,axiom,
% 5.31/5.64 ! [N: num] :
% 5.31/5.64 ( ( numeral_numeral_real @ ( bit1 @ N ) )
% 5.31/5.64 = ( plus_plus_real @ ( plus_plus_real @ ( numeral_numeral_real @ N ) @ ( numeral_numeral_real @ N ) ) @ one_one_real ) ) ).
% 5.31/5.64
% 5.31/5.64 % numeral_code(3)
% 5.31/5.64 thf(fact_8125_numeral__code_I3_J,axiom,
% 5.31/5.64 ! [N: num] :
% 5.31/5.64 ( ( numeral_numeral_nat @ ( bit1 @ N ) )
% 5.31/5.64 = ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ N ) ) @ one_one_nat ) ) ).
% 5.31/5.64
% 5.31/5.64 % numeral_code(3)
% 5.31/5.64 thf(fact_8126_numeral__code_I3_J,axiom,
% 5.31/5.64 ! [N: num] :
% 5.31/5.64 ( ( numeral_numeral_int @ ( bit1 @ N ) )
% 5.31/5.64 = ( plus_plus_int @ ( plus_plus_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ N ) ) @ one_one_int ) ) ).
% 5.31/5.64
% 5.31/5.64 % numeral_code(3)
% 5.31/5.64 thf(fact_8127_power__numeral__odd,axiom,
% 5.31/5.64 ! [Z3: complex,W2: num] :
% 5.31/5.64 ( ( power_power_complex @ Z3 @ ( numeral_numeral_nat @ ( bit1 @ W2 ) ) )
% 5.31/5.64 = ( times_times_complex @ ( times_times_complex @ Z3 @ ( power_power_complex @ Z3 @ ( numeral_numeral_nat @ W2 ) ) ) @ ( power_power_complex @ Z3 @ ( numeral_numeral_nat @ W2 ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % power_numeral_odd
% 5.31/5.64 thf(fact_8128_power__numeral__odd,axiom,
% 5.31/5.64 ! [Z3: real,W2: num] :
% 5.31/5.64 ( ( power_power_real @ Z3 @ ( numeral_numeral_nat @ ( bit1 @ W2 ) ) )
% 5.31/5.64 = ( times_times_real @ ( times_times_real @ Z3 @ ( power_power_real @ Z3 @ ( numeral_numeral_nat @ W2 ) ) ) @ ( power_power_real @ Z3 @ ( numeral_numeral_nat @ W2 ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % power_numeral_odd
% 5.31/5.64 thf(fact_8129_power__numeral__odd,axiom,
% 5.31/5.64 ! [Z3: rat,W2: num] :
% 5.31/5.64 ( ( power_power_rat @ Z3 @ ( numeral_numeral_nat @ ( bit1 @ W2 ) ) )
% 5.31/5.64 = ( times_times_rat @ ( times_times_rat @ Z3 @ ( power_power_rat @ Z3 @ ( numeral_numeral_nat @ W2 ) ) ) @ ( power_power_rat @ Z3 @ ( numeral_numeral_nat @ W2 ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % power_numeral_odd
% 5.31/5.64 thf(fact_8130_power__numeral__odd,axiom,
% 5.31/5.64 ! [Z3: nat,W2: num] :
% 5.31/5.64 ( ( power_power_nat @ Z3 @ ( numeral_numeral_nat @ ( bit1 @ W2 ) ) )
% 5.31/5.64 = ( times_times_nat @ ( times_times_nat @ Z3 @ ( power_power_nat @ Z3 @ ( numeral_numeral_nat @ W2 ) ) ) @ ( power_power_nat @ Z3 @ ( numeral_numeral_nat @ W2 ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % power_numeral_odd
% 5.31/5.64 thf(fact_8131_power__numeral__odd,axiom,
% 5.31/5.64 ! [Z3: int,W2: num] :
% 5.31/5.64 ( ( power_power_int @ Z3 @ ( numeral_numeral_nat @ ( bit1 @ W2 ) ) )
% 5.31/5.64 = ( times_times_int @ ( times_times_int @ Z3 @ ( power_power_int @ Z3 @ ( numeral_numeral_nat @ W2 ) ) ) @ ( power_power_int @ Z3 @ ( numeral_numeral_nat @ W2 ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % power_numeral_odd
% 5.31/5.64 thf(fact_8132_cong__exp__iff__simps_I3_J,axiom,
% 5.31/5.64 ! [N: num,Q2: num] :
% 5.31/5.64 ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 5.31/5.64 != zero_zero_nat ) ).
% 5.31/5.64
% 5.31/5.64 % cong_exp_iff_simps(3)
% 5.31/5.64 thf(fact_8133_cong__exp__iff__simps_I3_J,axiom,
% 5.31/5.64 ! [N: num,Q2: num] :
% 5.31/5.64 ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 5.31/5.64 != zero_zero_int ) ).
% 5.31/5.64
% 5.31/5.64 % cong_exp_iff_simps(3)
% 5.31/5.64 thf(fact_8134_power3__eq__cube,axiom,
% 5.31/5.64 ! [A: complex] :
% 5.31/5.64 ( ( power_power_complex @ A @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 5.31/5.64 = ( times_times_complex @ ( times_times_complex @ A @ A ) @ A ) ) ).
% 5.31/5.64
% 5.31/5.64 % power3_eq_cube
% 5.31/5.64 thf(fact_8135_power3__eq__cube,axiom,
% 5.31/5.64 ! [A: real] :
% 5.31/5.64 ( ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 5.31/5.64 = ( times_times_real @ ( times_times_real @ A @ A ) @ A ) ) ).
% 5.31/5.64
% 5.31/5.64 % power3_eq_cube
% 5.31/5.64 thf(fact_8136_power3__eq__cube,axiom,
% 5.31/5.64 ! [A: rat] :
% 5.31/5.64 ( ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 5.31/5.64 = ( times_times_rat @ ( times_times_rat @ A @ A ) @ A ) ) ).
% 5.31/5.64
% 5.31/5.64 % power3_eq_cube
% 5.31/5.64 thf(fact_8137_power3__eq__cube,axiom,
% 5.31/5.64 ! [A: nat] :
% 5.31/5.64 ( ( power_power_nat @ A @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 5.31/5.64 = ( times_times_nat @ ( times_times_nat @ A @ A ) @ A ) ) ).
% 5.31/5.64
% 5.31/5.64 % power3_eq_cube
% 5.31/5.64 thf(fact_8138_power3__eq__cube,axiom,
% 5.31/5.64 ! [A: int] :
% 5.31/5.64 ( ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 5.31/5.64 = ( times_times_int @ ( times_times_int @ A @ A ) @ A ) ) ).
% 5.31/5.64
% 5.31/5.64 % power3_eq_cube
% 5.31/5.64 thf(fact_8139_numeral__3__eq__3,axiom,
% 5.31/5.64 ( ( numeral_numeral_nat @ ( bit1 @ one ) )
% 5.31/5.64 = ( suc @ ( suc @ ( suc @ zero_zero_nat ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % numeral_3_eq_3
% 5.31/5.64 thf(fact_8140_Suc3__eq__add__3,axiom,
% 5.31/5.64 ! [N: nat] :
% 5.31/5.64 ( ( suc @ ( suc @ ( suc @ N ) ) )
% 5.31/5.64 = ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ N ) ) ).
% 5.31/5.64
% 5.31/5.64 % Suc3_eq_add_3
% 5.31/5.64 thf(fact_8141_num_Osize_I6_J,axiom,
% 5.31/5.64 ! [X33: num] :
% 5.31/5.64 ( ( size_size_num @ ( bit1 @ X33 ) )
% 5.31/5.64 = ( plus_plus_nat @ ( size_size_num @ X33 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % num.size(6)
% 5.31/5.64 thf(fact_8142_cong__exp__iff__simps_I7_J,axiom,
% 5.31/5.64 ! [Q2: num,N: num] :
% 5.31/5.64 ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ one ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 5.31/5.64 = ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) )
% 5.31/5.64 = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ Q2 ) )
% 5.31/5.64 = zero_zero_nat ) ) ).
% 5.31/5.64
% 5.31/5.64 % cong_exp_iff_simps(7)
% 5.31/5.64 thf(fact_8143_cong__exp__iff__simps_I7_J,axiom,
% 5.31/5.64 ! [Q2: num,N: num] :
% 5.31/5.64 ( ( ( modulo_modulo_int @ ( numeral_numeral_int @ one ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 5.31/5.64 = ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) ) )
% 5.31/5.64 = ( ( modulo_modulo_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ Q2 ) )
% 5.31/5.64 = zero_zero_int ) ) ).
% 5.31/5.64
% 5.31/5.64 % cong_exp_iff_simps(7)
% 5.31/5.64 thf(fact_8144_cong__exp__iff__simps_I11_J,axiom,
% 5.31/5.64 ! [M2: num,Q2: num] :
% 5.31/5.64 ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ M2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 5.31/5.64 = ( modulo_modulo_nat @ ( numeral_numeral_nat @ one ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) )
% 5.31/5.64 = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ M2 ) @ ( numeral_numeral_nat @ Q2 ) )
% 5.31/5.64 = zero_zero_nat ) ) ).
% 5.31/5.64
% 5.31/5.64 % cong_exp_iff_simps(11)
% 5.31/5.64 thf(fact_8145_cong__exp__iff__simps_I11_J,axiom,
% 5.31/5.64 ! [M2: num,Q2: num] :
% 5.31/5.64 ( ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ M2 ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 5.31/5.64 = ( modulo_modulo_int @ ( numeral_numeral_int @ one ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) ) )
% 5.31/5.64 = ( ( modulo_modulo_int @ ( numeral_numeral_int @ M2 ) @ ( numeral_numeral_int @ Q2 ) )
% 5.31/5.64 = zero_zero_int ) ) ).
% 5.31/5.64
% 5.31/5.64 % cong_exp_iff_simps(11)
% 5.31/5.64 thf(fact_8146_Suc__div__eq__add3__div,axiom,
% 5.31/5.64 ! [M2: nat,N: nat] :
% 5.31/5.64 ( ( divide_divide_nat @ ( suc @ ( suc @ ( suc @ M2 ) ) ) @ N )
% 5.31/5.64 = ( divide_divide_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ M2 ) @ N ) ) ).
% 5.31/5.64
% 5.31/5.64 % Suc_div_eq_add3_div
% 5.31/5.64 thf(fact_8147_card__3__iff,axiom,
% 5.31/5.64 ! [S3: set_complex] :
% 5.31/5.64 ( ( ( finite_card_complex @ S3 )
% 5.31/5.64 = ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 5.31/5.64 = ( ? [X4: complex,Y4: complex,Z4: complex] :
% 5.31/5.64 ( ( S3
% 5.31/5.64 = ( insert_complex @ X4 @ ( insert_complex @ Y4 @ ( insert_complex @ Z4 @ bot_bot_set_complex ) ) ) )
% 5.31/5.64 & ( X4 != Y4 )
% 5.31/5.64 & ( Y4 != Z4 )
% 5.31/5.64 & ( X4 != Z4 ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % card_3_iff
% 5.31/5.64 thf(fact_8148_card__3__iff,axiom,
% 5.31/5.64 ! [S3: set_list_nat] :
% 5.31/5.64 ( ( ( finite_card_list_nat @ S3 )
% 5.31/5.64 = ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 5.31/5.64 = ( ? [X4: list_nat,Y4: list_nat,Z4: list_nat] :
% 5.31/5.64 ( ( S3
% 5.31/5.64 = ( insert_list_nat @ X4 @ ( insert_list_nat @ Y4 @ ( insert_list_nat @ Z4 @ bot_bot_set_list_nat ) ) ) )
% 5.31/5.64 & ( X4 != Y4 )
% 5.31/5.64 & ( Y4 != Z4 )
% 5.31/5.64 & ( X4 != Z4 ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % card_3_iff
% 5.31/5.64 thf(fact_8149_card__3__iff,axiom,
% 5.31/5.64 ! [S3: set_set_nat] :
% 5.31/5.64 ( ( ( finite_card_set_nat @ S3 )
% 5.31/5.64 = ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 5.31/5.64 = ( ? [X4: set_nat,Y4: set_nat,Z4: set_nat] :
% 5.31/5.64 ( ( S3
% 5.31/5.64 = ( insert_set_nat @ X4 @ ( insert_set_nat @ Y4 @ ( insert_set_nat @ Z4 @ bot_bot_set_set_nat ) ) ) )
% 5.31/5.64 & ( X4 != Y4 )
% 5.31/5.64 & ( Y4 != Z4 )
% 5.31/5.64 & ( X4 != Z4 ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % card_3_iff
% 5.31/5.64 thf(fact_8150_card__3__iff,axiom,
% 5.31/5.64 ! [S3: set_nat] :
% 5.31/5.64 ( ( ( finite_card_nat @ S3 )
% 5.31/5.64 = ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 5.31/5.64 = ( ? [X4: nat,Y4: nat,Z4: nat] :
% 5.31/5.64 ( ( S3
% 5.31/5.64 = ( insert_nat @ X4 @ ( insert_nat @ Y4 @ ( insert_nat @ Z4 @ bot_bot_set_nat ) ) ) )
% 5.31/5.64 & ( X4 != Y4 )
% 5.31/5.64 & ( Y4 != Z4 )
% 5.31/5.64 & ( X4 != Z4 ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % card_3_iff
% 5.31/5.64 thf(fact_8151_card__3__iff,axiom,
% 5.31/5.64 ! [S3: set_int] :
% 5.31/5.64 ( ( ( finite_card_int @ S3 )
% 5.31/5.64 = ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 5.31/5.64 = ( ? [X4: int,Y4: int,Z4: int] :
% 5.31/5.64 ( ( S3
% 5.31/5.64 = ( insert_int @ X4 @ ( insert_int @ Y4 @ ( insert_int @ Z4 @ bot_bot_set_int ) ) ) )
% 5.31/5.64 & ( X4 != Y4 )
% 5.31/5.64 & ( Y4 != Z4 )
% 5.31/5.64 & ( X4 != Z4 ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % card_3_iff
% 5.31/5.64 thf(fact_8152_card__3__iff,axiom,
% 5.31/5.64 ! [S3: set_real] :
% 5.31/5.64 ( ( ( finite_card_real @ S3 )
% 5.31/5.64 = ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 5.31/5.64 = ( ? [X4: real,Y4: real,Z4: real] :
% 5.31/5.64 ( ( S3
% 5.31/5.64 = ( insert_real @ X4 @ ( insert_real @ Y4 @ ( insert_real @ Z4 @ bot_bot_set_real ) ) ) )
% 5.31/5.64 & ( X4 != Y4 )
% 5.31/5.64 & ( Y4 != Z4 )
% 5.31/5.64 & ( X4 != Z4 ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % card_3_iff
% 5.31/5.64 thf(fact_8153_Suc__mod__eq__add3__mod,axiom,
% 5.31/5.64 ! [M2: nat,N: nat] :
% 5.31/5.64 ( ( modulo_modulo_nat @ ( suc @ ( suc @ ( suc @ M2 ) ) ) @ N )
% 5.31/5.64 = ( modulo_modulo_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ M2 ) @ N ) ) ).
% 5.31/5.64
% 5.31/5.64 % Suc_mod_eq_add3_mod
% 5.31/5.64 thf(fact_8154_mod__exhaust__less__4,axiom,
% 5.31/5.64 ! [M2: nat] :
% 5.31/5.64 ( ( ( modulo_modulo_nat @ M2 @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.31/5.64 = zero_zero_nat )
% 5.31/5.64 | ( ( modulo_modulo_nat @ M2 @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.31/5.64 = one_one_nat )
% 5.31/5.64 | ( ( modulo_modulo_nat @ M2 @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.31/5.64 = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.31/5.64 | ( ( modulo_modulo_nat @ M2 @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.31/5.64 = ( numeral_numeral_nat @ ( bit1 @ one ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % mod_exhaust_less_4
% 5.31/5.64 thf(fact_8155_m2pi__less__pi,axiom,
% 5.31/5.64 ord_less_real @ ( uminus_uminus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) @ pi ).
% 5.31/5.64
% 5.31/5.64 % m2pi_less_pi
% 5.31/5.64 thf(fact_8156_sin__pi__divide__n__ge__0,axiom,
% 5.31/5.64 ! [N: nat] :
% 5.31/5.64 ( ( N != zero_zero_nat )
% 5.31/5.64 => ( ord_less_eq_real @ zero_zero_real @ ( sin_real @ ( divide_divide_real @ pi @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % sin_pi_divide_n_ge_0
% 5.31/5.64 thf(fact_8157_sin__coeff__Suc,axiom,
% 5.31/5.64 ! [N: nat] :
% 5.31/5.64 ( ( sin_coeff @ ( suc @ N ) )
% 5.31/5.64 = ( divide_divide_real @ ( cos_coeff @ N ) @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % sin_coeff_Suc
% 5.31/5.64 thf(fact_8158_sin__lt__zero,axiom,
% 5.31/5.64 ! [X: real] :
% 5.31/5.64 ( ( ord_less_real @ pi @ X )
% 5.31/5.64 => ( ( ord_less_real @ X @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 5.31/5.64 => ( ord_less_real @ ( sin_real @ X ) @ zero_zero_real ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % sin_lt_zero
% 5.31/5.64 thf(fact_8159_and__nat__unfold,axiom,
% 5.31/5.64 ( bit_se727722235901077358nd_nat
% 5.31/5.64 = ( ^ [M6: nat,N4: nat] :
% 5.31/5.64 ( if_nat
% 5.31/5.64 @ ( ( M6 = zero_zero_nat )
% 5.31/5.64 | ( N4 = zero_zero_nat ) )
% 5.31/5.64 @ zero_zero_nat
% 5.31/5.64 @ ( plus_plus_nat @ ( times_times_nat @ ( modulo_modulo_nat @ M6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( modulo_modulo_nat @ N4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( divide_divide_nat @ M6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % and_nat_unfold
% 5.31/5.64 thf(fact_8160_and__nat__rec,axiom,
% 5.31/5.64 ( bit_se727722235901077358nd_nat
% 5.31/5.64 = ( ^ [M6: nat,N4: nat] :
% 5.31/5.64 ( plus_plus_nat
% 5.31/5.64 @ ( zero_n2687167440665602831ol_nat
% 5.31/5.64 @ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M6 )
% 5.31/5.64 & ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) ) )
% 5.31/5.64 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( divide_divide_nat @ M6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % and_nat_rec
% 5.31/5.64 thf(fact_8161_sin__le__zero,axiom,
% 5.31/5.64 ! [X: real] :
% 5.31/5.64 ( ( ord_less_eq_real @ pi @ X )
% 5.31/5.64 => ( ( ord_less_real @ X @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 5.31/5.64 => ( ord_less_eq_real @ ( sin_real @ X ) @ zero_zero_real ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % sin_le_zero
% 5.31/5.64 thf(fact_8162_cos__coeff__Suc,axiom,
% 5.31/5.64 ! [N: nat] :
% 5.31/5.64 ( ( cos_coeff @ ( suc @ N ) )
% 5.31/5.64 = ( divide_divide_real @ ( uminus_uminus_real @ ( sin_coeff @ N ) ) @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % cos_coeff_Suc
% 5.31/5.64 thf(fact_8163_odd__mod__4__div__2,axiom,
% 5.31/5.64 ! [N: nat] :
% 5.31/5.64 ( ( ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.31/5.64 = ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 5.31/5.64 => ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % odd_mod_4_div_2
% 5.31/5.64 thf(fact_8164_sin__pi__divide__n__gt__0,axiom,
% 5.31/5.64 ! [N: nat] :
% 5.31/5.64 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.31/5.64 => ( ord_less_real @ zero_zero_real @ ( sin_real @ ( divide_divide_real @ pi @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % sin_pi_divide_n_gt_0
% 5.31/5.64 thf(fact_8165_sin__zero__lemma,axiom,
% 5.31/5.64 ! [X: real] :
% 5.31/5.64 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.31/5.64 => ( ( ( sin_real @ X )
% 5.31/5.64 = zero_zero_real )
% 5.31/5.64 => ? [N3: nat] :
% 5.31/5.64 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 )
% 5.31/5.64 & ( X
% 5.31/5.64 = ( times_times_real @ ( semiri5074537144036343181t_real @ N3 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % sin_zero_lemma
% 5.31/5.64 thf(fact_8166_sin__zero__iff,axiom,
% 5.31/5.64 ! [X: real] :
% 5.31/5.64 ( ( ( sin_real @ X )
% 5.31/5.64 = zero_zero_real )
% 5.31/5.64 = ( ? [N4: nat] :
% 5.31/5.64 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 )
% 5.31/5.64 & ( X
% 5.31/5.64 = ( times_times_real @ ( semiri5074537144036343181t_real @ N4 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) )
% 5.31/5.64 | ? [N4: nat] :
% 5.31/5.64 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 )
% 5.31/5.64 & ( X
% 5.31/5.64 = ( uminus_uminus_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N4 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % sin_zero_iff
% 5.31/5.64 thf(fact_8167_Maclaurin__minus__cos__expansion,axiom,
% 5.31/5.64 ! [N: nat,X: real] :
% 5.31/5.64 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.64 => ( ( ord_less_real @ X @ zero_zero_real )
% 5.31/5.64 => ? [T6: real] :
% 5.31/5.64 ( ( ord_less_real @ X @ T6 )
% 5.31/5.64 & ( ord_less_real @ T6 @ zero_zero_real )
% 5.31/5.64 & ( ( cos_real @ X )
% 5.31/5.64 = ( plus_plus_real
% 5.31/5.64 @ ( groups6591440286371151544t_real
% 5.31/5.64 @ ^ [M6: nat] : ( times_times_real @ ( cos_coeff @ M6 ) @ ( power_power_real @ X @ M6 ) )
% 5.31/5.64 @ ( set_ord_lessThan_nat @ N ) )
% 5.31/5.64 @ ( 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 ) ) ) ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % Maclaurin_minus_cos_expansion
% 5.31/5.64 thf(fact_8168_Maclaurin__cos__expansion2,axiom,
% 5.31/5.64 ! [X: real,N: nat] :
% 5.31/5.64 ( ( ord_less_real @ zero_zero_real @ X )
% 5.31/5.64 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.64 => ? [T6: real] :
% 5.31/5.64 ( ( ord_less_real @ zero_zero_real @ T6 )
% 5.31/5.64 & ( ord_less_real @ T6 @ X )
% 5.31/5.64 & ( ( cos_real @ X )
% 5.31/5.64 = ( plus_plus_real
% 5.31/5.64 @ ( groups6591440286371151544t_real
% 5.31/5.64 @ ^ [M6: nat] : ( times_times_real @ ( cos_coeff @ M6 ) @ ( power_power_real @ X @ M6 ) )
% 5.31/5.64 @ ( set_ord_lessThan_nat @ N ) )
% 5.31/5.64 @ ( 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 ) ) ) ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % Maclaurin_cos_expansion2
% 5.31/5.64 thf(fact_8169_Maclaurin__sin__expansion2,axiom,
% 5.31/5.64 ! [X: real,N: nat] :
% 5.31/5.64 ? [T6: real] :
% 5.31/5.64 ( ( ord_less_eq_real @ ( abs_abs_real @ T6 ) @ ( abs_abs_real @ X ) )
% 5.31/5.64 & ( ( sin_real @ X )
% 5.31/5.64 = ( plus_plus_real
% 5.31/5.64 @ ( groups6591440286371151544t_real
% 5.31/5.64 @ ^ [M6: nat] : ( times_times_real @ ( sin_coeff @ M6 ) @ ( power_power_real @ X @ M6 ) )
% 5.31/5.64 @ ( set_ord_lessThan_nat @ N ) )
% 5.31/5.64 @ ( 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 ) ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % Maclaurin_sin_expansion2
% 5.31/5.64 thf(fact_8170_signed__take__bit__numeral__minus__bit1,axiom,
% 5.31/5.64 ! [L: num,K2: num] :
% 5.31/5.64 ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K2 ) ) ) )
% 5.31/5.64 = ( plus_plus_int @ ( times_times_int @ ( bit_ri631733984087533419it_int @ ( pred_numeral @ L ) @ ( minus_minus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K2 ) ) @ one_one_int ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 5.31/5.64
% 5.31/5.64 % signed_take_bit_numeral_minus_bit1
% 5.31/5.64 thf(fact_8171_divmod__algorithm__code_I8_J,axiom,
% 5.31/5.64 ! [M2: num,N: num] :
% 5.31/5.64 ( ( ( ord_less_num @ M2 @ N )
% 5.31/5.64 => ( ( unique5055182867167087721od_nat @ ( bit1 @ M2 ) @ ( bit1 @ N ) )
% 5.31/5.64 = ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit1 @ M2 ) ) ) ) )
% 5.31/5.64 & ( ~ ( ord_less_num @ M2 @ N )
% 5.31/5.64 => ( ( unique5055182867167087721od_nat @ ( bit1 @ M2 ) @ ( bit1 @ N ) )
% 5.31/5.64 = ( unique5026877609467782581ep_nat @ ( bit1 @ N ) @ ( unique5055182867167087721od_nat @ ( bit1 @ M2 ) @ ( bit0 @ ( bit1 @ N ) ) ) ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % divmod_algorithm_code(8)
% 5.31/5.64 thf(fact_8172_divmod__algorithm__code_I8_J,axiom,
% 5.31/5.64 ! [M2: num,N: num] :
% 5.31/5.64 ( ( ( ord_less_num @ M2 @ N )
% 5.31/5.64 => ( ( unique5052692396658037445od_int @ ( bit1 @ M2 ) @ ( bit1 @ N ) )
% 5.31/5.64 = ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ ( bit1 @ M2 ) ) ) ) )
% 5.31/5.64 & ( ~ ( ord_less_num @ M2 @ N )
% 5.31/5.64 => ( ( unique5052692396658037445od_int @ ( bit1 @ M2 ) @ ( bit1 @ N ) )
% 5.31/5.64 = ( unique5024387138958732305ep_int @ ( bit1 @ N ) @ ( unique5052692396658037445od_int @ ( bit1 @ M2 ) @ ( bit0 @ ( bit1 @ N ) ) ) ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % divmod_algorithm_code(8)
% 5.31/5.64 thf(fact_8173_divmod__algorithm__code_I8_J,axiom,
% 5.31/5.64 ! [M2: num,N: num] :
% 5.31/5.64 ( ( ( ord_less_num @ M2 @ N )
% 5.31/5.64 => ( ( unique3479559517661332726nteger @ ( bit1 @ M2 ) @ ( bit1 @ N ) )
% 5.31/5.64 = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ ( bit1 @ M2 ) ) ) ) )
% 5.31/5.64 & ( ~ ( ord_less_num @ M2 @ N )
% 5.31/5.64 => ( ( unique3479559517661332726nteger @ ( bit1 @ M2 ) @ ( bit1 @ N ) )
% 5.31/5.64 = ( unique4921790084139445826nteger @ ( bit1 @ N ) @ ( unique3479559517661332726nteger @ ( bit1 @ M2 ) @ ( bit0 @ ( bit1 @ N ) ) ) ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % divmod_algorithm_code(8)
% 5.31/5.64 thf(fact_8174_divmod__algorithm__code_I7_J,axiom,
% 5.31/5.64 ! [M2: num,N: num] :
% 5.31/5.64 ( ( ( ord_less_eq_num @ M2 @ N )
% 5.31/5.64 => ( ( unique5055182867167087721od_nat @ ( bit0 @ M2 ) @ ( bit1 @ N ) )
% 5.31/5.64 = ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ M2 ) ) ) ) )
% 5.31/5.64 & ( ~ ( ord_less_eq_num @ M2 @ N )
% 5.31/5.64 => ( ( unique5055182867167087721od_nat @ ( bit0 @ M2 ) @ ( bit1 @ N ) )
% 5.31/5.64 = ( unique5026877609467782581ep_nat @ ( bit1 @ N ) @ ( unique5055182867167087721od_nat @ ( bit0 @ M2 ) @ ( bit0 @ ( bit1 @ N ) ) ) ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % divmod_algorithm_code(7)
% 5.31/5.64 thf(fact_8175_divmod__algorithm__code_I7_J,axiom,
% 5.31/5.64 ! [M2: num,N: num] :
% 5.31/5.64 ( ( ( ord_less_eq_num @ M2 @ N )
% 5.31/5.64 => ( ( unique5052692396658037445od_int @ ( bit0 @ M2 ) @ ( bit1 @ N ) )
% 5.31/5.64 = ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ ( bit0 @ M2 ) ) ) ) )
% 5.31/5.64 & ( ~ ( ord_less_eq_num @ M2 @ N )
% 5.31/5.64 => ( ( unique5052692396658037445od_int @ ( bit0 @ M2 ) @ ( bit1 @ N ) )
% 5.31/5.64 = ( unique5024387138958732305ep_int @ ( bit1 @ N ) @ ( unique5052692396658037445od_int @ ( bit0 @ M2 ) @ ( bit0 @ ( bit1 @ N ) ) ) ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % divmod_algorithm_code(7)
% 5.31/5.64 thf(fact_8176_divmod__algorithm__code_I7_J,axiom,
% 5.31/5.64 ! [M2: num,N: num] :
% 5.31/5.64 ( ( ( ord_less_eq_num @ M2 @ N )
% 5.31/5.64 => ( ( unique3479559517661332726nteger @ ( bit0 @ M2 ) @ ( bit1 @ N ) )
% 5.31/5.64 = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ ( bit0 @ M2 ) ) ) ) )
% 5.31/5.64 & ( ~ ( ord_less_eq_num @ M2 @ N )
% 5.31/5.64 => ( ( unique3479559517661332726nteger @ ( bit0 @ M2 ) @ ( bit1 @ N ) )
% 5.31/5.64 = ( unique4921790084139445826nteger @ ( bit1 @ N ) @ ( unique3479559517661332726nteger @ ( bit0 @ M2 ) @ ( bit0 @ ( bit1 @ N ) ) ) ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % divmod_algorithm_code(7)
% 5.31/5.64 thf(fact_8177_abs__idempotent,axiom,
% 5.31/5.64 ! [A: real] :
% 5.31/5.64 ( ( abs_abs_real @ ( abs_abs_real @ A ) )
% 5.31/5.64 = ( abs_abs_real @ A ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_idempotent
% 5.31/5.64 thf(fact_8178_abs__idempotent,axiom,
% 5.31/5.64 ! [A: int] :
% 5.31/5.64 ( ( abs_abs_int @ ( abs_abs_int @ A ) )
% 5.31/5.64 = ( abs_abs_int @ A ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_idempotent
% 5.31/5.64 thf(fact_8179_abs__idempotent,axiom,
% 5.31/5.64 ! [A: code_integer] :
% 5.31/5.64 ( ( abs_abs_Code_integer @ ( abs_abs_Code_integer @ A ) )
% 5.31/5.64 = ( abs_abs_Code_integer @ A ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_idempotent
% 5.31/5.64 thf(fact_8180_abs__idempotent,axiom,
% 5.31/5.64 ! [A: rat] :
% 5.31/5.64 ( ( abs_abs_rat @ ( abs_abs_rat @ A ) )
% 5.31/5.64 = ( abs_abs_rat @ A ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_idempotent
% 5.31/5.64 thf(fact_8181_abs__abs,axiom,
% 5.31/5.64 ! [A: real] :
% 5.31/5.64 ( ( abs_abs_real @ ( abs_abs_real @ A ) )
% 5.31/5.64 = ( abs_abs_real @ A ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_abs
% 5.31/5.64 thf(fact_8182_abs__abs,axiom,
% 5.31/5.64 ! [A: int] :
% 5.31/5.64 ( ( abs_abs_int @ ( abs_abs_int @ A ) )
% 5.31/5.64 = ( abs_abs_int @ A ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_abs
% 5.31/5.64 thf(fact_8183_abs__abs,axiom,
% 5.31/5.64 ! [A: code_integer] :
% 5.31/5.64 ( ( abs_abs_Code_integer @ ( abs_abs_Code_integer @ A ) )
% 5.31/5.64 = ( abs_abs_Code_integer @ A ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_abs
% 5.31/5.64 thf(fact_8184_abs__abs,axiom,
% 5.31/5.64 ! [A: rat] :
% 5.31/5.64 ( ( abs_abs_rat @ ( abs_abs_rat @ A ) )
% 5.31/5.64 = ( abs_abs_rat @ A ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_abs
% 5.31/5.64 thf(fact_8185_abs__0,axiom,
% 5.31/5.64 ( ( abs_abs_Code_integer @ zero_z3403309356797280102nteger )
% 5.31/5.64 = zero_z3403309356797280102nteger ) ).
% 5.31/5.64
% 5.31/5.64 % abs_0
% 5.31/5.64 thf(fact_8186_abs__0,axiom,
% 5.31/5.64 ( ( abs_abs_complex @ zero_zero_complex )
% 5.31/5.64 = zero_zero_complex ) ).
% 5.31/5.64
% 5.31/5.64 % abs_0
% 5.31/5.64 thf(fact_8187_abs__0,axiom,
% 5.31/5.64 ( ( abs_abs_real @ zero_zero_real )
% 5.31/5.64 = zero_zero_real ) ).
% 5.31/5.64
% 5.31/5.64 % abs_0
% 5.31/5.64 thf(fact_8188_abs__0,axiom,
% 5.31/5.64 ( ( abs_abs_rat @ zero_zero_rat )
% 5.31/5.64 = zero_zero_rat ) ).
% 5.31/5.64
% 5.31/5.64 % abs_0
% 5.31/5.64 thf(fact_8189_abs__0,axiom,
% 5.31/5.64 ( ( abs_abs_int @ zero_zero_int )
% 5.31/5.64 = zero_zero_int ) ).
% 5.31/5.64
% 5.31/5.64 % abs_0
% 5.31/5.64 thf(fact_8190_abs__0__eq,axiom,
% 5.31/5.64 ! [A: code_integer] :
% 5.31/5.64 ( ( zero_z3403309356797280102nteger
% 5.31/5.64 = ( abs_abs_Code_integer @ A ) )
% 5.31/5.64 = ( A = zero_z3403309356797280102nteger ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_0_eq
% 5.31/5.64 thf(fact_8191_abs__0__eq,axiom,
% 5.31/5.64 ! [A: real] :
% 5.31/5.64 ( ( zero_zero_real
% 5.31/5.64 = ( abs_abs_real @ A ) )
% 5.31/5.64 = ( A = zero_zero_real ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_0_eq
% 5.31/5.64 thf(fact_8192_abs__0__eq,axiom,
% 5.31/5.64 ! [A: rat] :
% 5.31/5.64 ( ( zero_zero_rat
% 5.31/5.64 = ( abs_abs_rat @ A ) )
% 5.31/5.64 = ( A = zero_zero_rat ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_0_eq
% 5.31/5.64 thf(fact_8193_abs__0__eq,axiom,
% 5.31/5.64 ! [A: int] :
% 5.31/5.64 ( ( zero_zero_int
% 5.31/5.64 = ( abs_abs_int @ A ) )
% 5.31/5.64 = ( A = zero_zero_int ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_0_eq
% 5.31/5.64 thf(fact_8194_abs__eq__0,axiom,
% 5.31/5.64 ! [A: code_integer] :
% 5.31/5.64 ( ( ( abs_abs_Code_integer @ A )
% 5.31/5.64 = zero_z3403309356797280102nteger )
% 5.31/5.64 = ( A = zero_z3403309356797280102nteger ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_eq_0
% 5.31/5.64 thf(fact_8195_abs__eq__0,axiom,
% 5.31/5.64 ! [A: real] :
% 5.31/5.64 ( ( ( abs_abs_real @ A )
% 5.31/5.64 = zero_zero_real )
% 5.31/5.64 = ( A = zero_zero_real ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_eq_0
% 5.31/5.64 thf(fact_8196_abs__eq__0,axiom,
% 5.31/5.64 ! [A: rat] :
% 5.31/5.64 ( ( ( abs_abs_rat @ A )
% 5.31/5.64 = zero_zero_rat )
% 5.31/5.64 = ( A = zero_zero_rat ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_eq_0
% 5.31/5.64 thf(fact_8197_abs__eq__0,axiom,
% 5.31/5.64 ! [A: int] :
% 5.31/5.64 ( ( ( abs_abs_int @ A )
% 5.31/5.64 = zero_zero_int )
% 5.31/5.64 = ( A = zero_zero_int ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_eq_0
% 5.31/5.64 thf(fact_8198_abs__zero,axiom,
% 5.31/5.64 ( ( abs_abs_Code_integer @ zero_z3403309356797280102nteger )
% 5.31/5.64 = zero_z3403309356797280102nteger ) ).
% 5.31/5.64
% 5.31/5.64 % abs_zero
% 5.31/5.64 thf(fact_8199_abs__zero,axiom,
% 5.31/5.64 ( ( abs_abs_real @ zero_zero_real )
% 5.31/5.64 = zero_zero_real ) ).
% 5.31/5.64
% 5.31/5.64 % abs_zero
% 5.31/5.64 thf(fact_8200_abs__zero,axiom,
% 5.31/5.64 ( ( abs_abs_rat @ zero_zero_rat )
% 5.31/5.64 = zero_zero_rat ) ).
% 5.31/5.64
% 5.31/5.64 % abs_zero
% 5.31/5.64 thf(fact_8201_abs__zero,axiom,
% 5.31/5.64 ( ( abs_abs_int @ zero_zero_int )
% 5.31/5.64 = zero_zero_int ) ).
% 5.31/5.64
% 5.31/5.64 % abs_zero
% 5.31/5.64 thf(fact_8202_abs__numeral,axiom,
% 5.31/5.64 ! [N: num] :
% 5.31/5.64 ( ( abs_abs_Code_integer @ ( numera6620942414471956472nteger @ N ) )
% 5.31/5.64 = ( numera6620942414471956472nteger @ N ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_numeral
% 5.31/5.64 thf(fact_8203_abs__numeral,axiom,
% 5.31/5.64 ! [N: num] :
% 5.31/5.64 ( ( abs_abs_rat @ ( numeral_numeral_rat @ N ) )
% 5.31/5.64 = ( numeral_numeral_rat @ N ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_numeral
% 5.31/5.64 thf(fact_8204_abs__numeral,axiom,
% 5.31/5.64 ! [N: num] :
% 5.31/5.64 ( ( abs_abs_real @ ( numeral_numeral_real @ N ) )
% 5.31/5.64 = ( numeral_numeral_real @ N ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_numeral
% 5.31/5.64 thf(fact_8205_abs__numeral,axiom,
% 5.31/5.64 ! [N: num] :
% 5.31/5.64 ( ( abs_abs_int @ ( numeral_numeral_int @ N ) )
% 5.31/5.64 = ( numeral_numeral_int @ N ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_numeral
% 5.31/5.64 thf(fact_8206_abs__mult__self__eq,axiom,
% 5.31/5.64 ! [A: code_integer] :
% 5.31/5.64 ( ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ A ) )
% 5.31/5.64 = ( times_3573771949741848930nteger @ A @ A ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_mult_self_eq
% 5.31/5.64 thf(fact_8207_abs__mult__self__eq,axiom,
% 5.31/5.64 ! [A: real] :
% 5.31/5.64 ( ( times_times_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ A ) )
% 5.31/5.64 = ( times_times_real @ A @ A ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_mult_self_eq
% 5.31/5.64 thf(fact_8208_abs__mult__self__eq,axiom,
% 5.31/5.64 ! [A: rat] :
% 5.31/5.64 ( ( times_times_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ A ) )
% 5.31/5.64 = ( times_times_rat @ A @ A ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_mult_self_eq
% 5.31/5.64 thf(fact_8209_abs__mult__self__eq,axiom,
% 5.31/5.64 ! [A: int] :
% 5.31/5.64 ( ( times_times_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ A ) )
% 5.31/5.64 = ( times_times_int @ A @ A ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_mult_self_eq
% 5.31/5.64 thf(fact_8210_abs__add__abs,axiom,
% 5.31/5.64 ! [A: code_integer,B: code_integer] :
% 5.31/5.64 ( ( abs_abs_Code_integer @ ( plus_p5714425477246183910nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) )
% 5.31/5.64 = ( plus_p5714425477246183910nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_add_abs
% 5.31/5.64 thf(fact_8211_abs__add__abs,axiom,
% 5.31/5.64 ! [A: real,B: real] :
% 5.31/5.64 ( ( abs_abs_real @ ( plus_plus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) )
% 5.31/5.64 = ( plus_plus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_add_abs
% 5.31/5.64 thf(fact_8212_abs__add__abs,axiom,
% 5.31/5.64 ! [A: rat,B: rat] :
% 5.31/5.64 ( ( abs_abs_rat @ ( plus_plus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) )
% 5.31/5.64 = ( plus_plus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_add_abs
% 5.31/5.64 thf(fact_8213_abs__add__abs,axiom,
% 5.31/5.64 ! [A: int,B: int] :
% 5.31/5.64 ( ( abs_abs_int @ ( plus_plus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) )
% 5.31/5.64 = ( plus_plus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_add_abs
% 5.31/5.64 thf(fact_8214_abs__1,axiom,
% 5.31/5.64 ( ( abs_abs_rat @ one_one_rat )
% 5.31/5.64 = one_one_rat ) ).
% 5.31/5.64
% 5.31/5.64 % abs_1
% 5.31/5.64 thf(fact_8215_abs__1,axiom,
% 5.31/5.64 ( ( abs_abs_Code_integer @ one_one_Code_integer )
% 5.31/5.64 = one_one_Code_integer ) ).
% 5.31/5.64
% 5.31/5.64 % abs_1
% 5.31/5.64 thf(fact_8216_abs__1,axiom,
% 5.31/5.64 ( ( abs_abs_complex @ one_one_complex )
% 5.31/5.64 = one_one_complex ) ).
% 5.31/5.64
% 5.31/5.64 % abs_1
% 5.31/5.64 thf(fact_8217_abs__1,axiom,
% 5.31/5.64 ( ( abs_abs_real @ one_one_real )
% 5.31/5.64 = one_one_real ) ).
% 5.31/5.64
% 5.31/5.64 % abs_1
% 5.31/5.64 thf(fact_8218_abs__1,axiom,
% 5.31/5.64 ( ( abs_abs_int @ one_one_int )
% 5.31/5.64 = one_one_int ) ).
% 5.31/5.64
% 5.31/5.64 % abs_1
% 5.31/5.64 thf(fact_8219_abs__minus__cancel,axiom,
% 5.31/5.64 ! [A: int] :
% 5.31/5.64 ( ( abs_abs_int @ ( uminus_uminus_int @ A ) )
% 5.31/5.64 = ( abs_abs_int @ A ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_minus_cancel
% 5.31/5.64 thf(fact_8220_abs__minus__cancel,axiom,
% 5.31/5.64 ! [A: real] :
% 5.31/5.64 ( ( abs_abs_real @ ( uminus_uminus_real @ A ) )
% 5.31/5.64 = ( abs_abs_real @ A ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_minus_cancel
% 5.31/5.64 thf(fact_8221_abs__minus__cancel,axiom,
% 5.31/5.64 ! [A: code_integer] :
% 5.31/5.64 ( ( abs_abs_Code_integer @ ( uminus1351360451143612070nteger @ A ) )
% 5.31/5.64 = ( abs_abs_Code_integer @ A ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_minus_cancel
% 5.31/5.64 thf(fact_8222_abs__minus__cancel,axiom,
% 5.31/5.64 ! [A: rat] :
% 5.31/5.64 ( ( abs_abs_rat @ ( uminus_uminus_rat @ A ) )
% 5.31/5.64 = ( abs_abs_rat @ A ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_minus_cancel
% 5.31/5.64 thf(fact_8223_abs__minus,axiom,
% 5.31/5.64 ! [A: int] :
% 5.31/5.64 ( ( abs_abs_int @ ( uminus_uminus_int @ A ) )
% 5.31/5.64 = ( abs_abs_int @ A ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_minus
% 5.31/5.64 thf(fact_8224_abs__minus,axiom,
% 5.31/5.64 ! [A: real] :
% 5.31/5.64 ( ( abs_abs_real @ ( uminus_uminus_real @ A ) )
% 5.31/5.64 = ( abs_abs_real @ A ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_minus
% 5.31/5.64 thf(fact_8225_abs__minus,axiom,
% 5.31/5.64 ! [A: complex] :
% 5.31/5.64 ( ( abs_abs_complex @ ( uminus1482373934393186551omplex @ A ) )
% 5.31/5.64 = ( abs_abs_complex @ A ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_minus
% 5.31/5.64 thf(fact_8226_abs__minus,axiom,
% 5.31/5.64 ! [A: code_integer] :
% 5.31/5.64 ( ( abs_abs_Code_integer @ ( uminus1351360451143612070nteger @ A ) )
% 5.31/5.64 = ( abs_abs_Code_integer @ A ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_minus
% 5.31/5.64 thf(fact_8227_abs__minus,axiom,
% 5.31/5.64 ! [A: rat] :
% 5.31/5.64 ( ( abs_abs_rat @ ( uminus_uminus_rat @ A ) )
% 5.31/5.64 = ( abs_abs_rat @ A ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_minus
% 5.31/5.64 thf(fact_8228_dvd__abs__iff,axiom,
% 5.31/5.64 ! [M2: real,K2: real] :
% 5.31/5.64 ( ( dvd_dvd_real @ M2 @ ( abs_abs_real @ K2 ) )
% 5.31/5.64 = ( dvd_dvd_real @ M2 @ K2 ) ) ).
% 5.31/5.64
% 5.31/5.64 % dvd_abs_iff
% 5.31/5.64 thf(fact_8229_dvd__abs__iff,axiom,
% 5.31/5.64 ! [M2: int,K2: int] :
% 5.31/5.64 ( ( dvd_dvd_int @ M2 @ ( abs_abs_int @ K2 ) )
% 5.31/5.64 = ( dvd_dvd_int @ M2 @ K2 ) ) ).
% 5.31/5.64
% 5.31/5.64 % dvd_abs_iff
% 5.31/5.64 thf(fact_8230_dvd__abs__iff,axiom,
% 5.31/5.64 ! [M2: code_integer,K2: code_integer] :
% 5.31/5.64 ( ( dvd_dvd_Code_integer @ M2 @ ( abs_abs_Code_integer @ K2 ) )
% 5.31/5.64 = ( dvd_dvd_Code_integer @ M2 @ K2 ) ) ).
% 5.31/5.64
% 5.31/5.64 % dvd_abs_iff
% 5.31/5.64 thf(fact_8231_dvd__abs__iff,axiom,
% 5.31/5.64 ! [M2: rat,K2: rat] :
% 5.31/5.64 ( ( dvd_dvd_rat @ M2 @ ( abs_abs_rat @ K2 ) )
% 5.31/5.64 = ( dvd_dvd_rat @ M2 @ K2 ) ) ).
% 5.31/5.64
% 5.31/5.64 % dvd_abs_iff
% 5.31/5.64 thf(fact_8232_abs__dvd__iff,axiom,
% 5.31/5.64 ! [M2: real,K2: real] :
% 5.31/5.64 ( ( dvd_dvd_real @ ( abs_abs_real @ M2 ) @ K2 )
% 5.31/5.64 = ( dvd_dvd_real @ M2 @ K2 ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_dvd_iff
% 5.31/5.64 thf(fact_8233_abs__dvd__iff,axiom,
% 5.31/5.64 ! [M2: int,K2: int] :
% 5.31/5.64 ( ( dvd_dvd_int @ ( abs_abs_int @ M2 ) @ K2 )
% 5.31/5.64 = ( dvd_dvd_int @ M2 @ K2 ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_dvd_iff
% 5.31/5.64 thf(fact_8234_abs__dvd__iff,axiom,
% 5.31/5.64 ! [M2: code_integer,K2: code_integer] :
% 5.31/5.64 ( ( dvd_dvd_Code_integer @ ( abs_abs_Code_integer @ M2 ) @ K2 )
% 5.31/5.64 = ( dvd_dvd_Code_integer @ M2 @ K2 ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_dvd_iff
% 5.31/5.64 thf(fact_8235_abs__dvd__iff,axiom,
% 5.31/5.64 ! [M2: rat,K2: rat] :
% 5.31/5.64 ( ( dvd_dvd_rat @ ( abs_abs_rat @ M2 ) @ K2 )
% 5.31/5.64 = ( dvd_dvd_rat @ M2 @ K2 ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_dvd_iff
% 5.31/5.64 thf(fact_8236_abs__of__nat,axiom,
% 5.31/5.64 ! [N: nat] :
% 5.31/5.64 ( ( abs_abs_Code_integer @ ( semiri4939895301339042750nteger @ N ) )
% 5.31/5.64 = ( semiri4939895301339042750nteger @ N ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_of_nat
% 5.31/5.64 thf(fact_8237_abs__of__nat,axiom,
% 5.31/5.64 ! [N: nat] :
% 5.31/5.64 ( ( abs_abs_rat @ ( semiri681578069525770553at_rat @ N ) )
% 5.31/5.64 = ( semiri681578069525770553at_rat @ N ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_of_nat
% 5.31/5.64 thf(fact_8238_abs__of__nat,axiom,
% 5.31/5.64 ! [N: nat] :
% 5.31/5.64 ( ( abs_abs_real @ ( semiri5074537144036343181t_real @ N ) )
% 5.31/5.64 = ( semiri5074537144036343181t_real @ N ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_of_nat
% 5.31/5.64 thf(fact_8239_abs__of__nat,axiom,
% 5.31/5.64 ! [N: nat] :
% 5.31/5.64 ( ( abs_abs_int @ ( semiri1314217659103216013at_int @ N ) )
% 5.31/5.64 = ( semiri1314217659103216013at_int @ N ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_of_nat
% 5.31/5.64 thf(fact_8240_abs__bool__eq,axiom,
% 5.31/5.64 ! [P2: $o] :
% 5.31/5.64 ( ( abs_abs_real @ ( zero_n3304061248610475627l_real @ P2 ) )
% 5.31/5.64 = ( zero_n3304061248610475627l_real @ P2 ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_bool_eq
% 5.31/5.64 thf(fact_8241_abs__bool__eq,axiom,
% 5.31/5.64 ! [P2: $o] :
% 5.31/5.64 ( ( abs_abs_rat @ ( zero_n2052037380579107095ol_rat @ P2 ) )
% 5.31/5.64 = ( zero_n2052037380579107095ol_rat @ P2 ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_bool_eq
% 5.31/5.64 thf(fact_8242_abs__bool__eq,axiom,
% 5.31/5.64 ! [P2: $o] :
% 5.31/5.64 ( ( abs_abs_int @ ( zero_n2684676970156552555ol_int @ P2 ) )
% 5.31/5.64 = ( zero_n2684676970156552555ol_int @ P2 ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_bool_eq
% 5.31/5.64 thf(fact_8243_abs__bool__eq,axiom,
% 5.31/5.64 ! [P2: $o] :
% 5.31/5.64 ( ( abs_abs_Code_integer @ ( zero_n356916108424825756nteger @ P2 ) )
% 5.31/5.64 = ( zero_n356916108424825756nteger @ P2 ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_bool_eq
% 5.31/5.64 thf(fact_8244_abs__of__nonneg,axiom,
% 5.31/5.64 ! [A: code_integer] :
% 5.31/5.64 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 5.31/5.64 => ( ( abs_abs_Code_integer @ A )
% 5.31/5.64 = A ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_of_nonneg
% 5.31/5.64 thf(fact_8245_abs__of__nonneg,axiom,
% 5.31/5.64 ! [A: real] :
% 5.31/5.64 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.31/5.64 => ( ( abs_abs_real @ A )
% 5.31/5.64 = A ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_of_nonneg
% 5.31/5.64 thf(fact_8246_abs__of__nonneg,axiom,
% 5.31/5.64 ! [A: rat] :
% 5.31/5.64 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.31/5.64 => ( ( abs_abs_rat @ A )
% 5.31/5.64 = A ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_of_nonneg
% 5.31/5.64 thf(fact_8247_abs__of__nonneg,axiom,
% 5.31/5.64 ! [A: int] :
% 5.31/5.64 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.31/5.64 => ( ( abs_abs_int @ A )
% 5.31/5.64 = A ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_of_nonneg
% 5.31/5.64 thf(fact_8248_abs__le__self__iff,axiom,
% 5.31/5.64 ! [A: code_integer] :
% 5.31/5.64 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ A )
% 5.31/5.64 = ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_le_self_iff
% 5.31/5.64 thf(fact_8249_abs__le__self__iff,axiom,
% 5.31/5.64 ! [A: real] :
% 5.31/5.64 ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ A )
% 5.31/5.64 = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_le_self_iff
% 5.31/5.64 thf(fact_8250_abs__le__self__iff,axiom,
% 5.31/5.64 ! [A: rat] :
% 5.31/5.64 ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ A )
% 5.31/5.64 = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_le_self_iff
% 5.31/5.64 thf(fact_8251_abs__le__self__iff,axiom,
% 5.31/5.64 ! [A: int] :
% 5.31/5.64 ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ A )
% 5.31/5.64 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_le_self_iff
% 5.31/5.64 thf(fact_8252_abs__le__zero__iff,axiom,
% 5.31/5.64 ! [A: code_integer] :
% 5.31/5.64 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ zero_z3403309356797280102nteger )
% 5.31/5.64 = ( A = zero_z3403309356797280102nteger ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_le_zero_iff
% 5.31/5.64 thf(fact_8253_abs__le__zero__iff,axiom,
% 5.31/5.64 ! [A: real] :
% 5.31/5.64 ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ zero_zero_real )
% 5.31/5.64 = ( A = zero_zero_real ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_le_zero_iff
% 5.31/5.64 thf(fact_8254_abs__le__zero__iff,axiom,
% 5.31/5.64 ! [A: rat] :
% 5.31/5.64 ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ zero_zero_rat )
% 5.31/5.64 = ( A = zero_zero_rat ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_le_zero_iff
% 5.31/5.64 thf(fact_8255_abs__le__zero__iff,axiom,
% 5.31/5.64 ! [A: int] :
% 5.31/5.64 ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ zero_zero_int )
% 5.31/5.64 = ( A = zero_zero_int ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_le_zero_iff
% 5.31/5.64 thf(fact_8256_zero__less__abs__iff,axiom,
% 5.31/5.64 ! [A: code_integer] :
% 5.31/5.64 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( abs_abs_Code_integer @ A ) )
% 5.31/5.64 = ( A != zero_z3403309356797280102nteger ) ) ).
% 5.31/5.64
% 5.31/5.64 % zero_less_abs_iff
% 5.31/5.64 thf(fact_8257_zero__less__abs__iff,axiom,
% 5.31/5.64 ! [A: real] :
% 5.31/5.64 ( ( ord_less_real @ zero_zero_real @ ( abs_abs_real @ A ) )
% 5.31/5.64 = ( A != zero_zero_real ) ) ).
% 5.31/5.64
% 5.31/5.64 % zero_less_abs_iff
% 5.31/5.64 thf(fact_8258_zero__less__abs__iff,axiom,
% 5.31/5.64 ! [A: rat] :
% 5.31/5.64 ( ( ord_less_rat @ zero_zero_rat @ ( abs_abs_rat @ A ) )
% 5.31/5.64 = ( A != zero_zero_rat ) ) ).
% 5.31/5.64
% 5.31/5.64 % zero_less_abs_iff
% 5.31/5.64 thf(fact_8259_zero__less__abs__iff,axiom,
% 5.31/5.64 ! [A: int] :
% 5.31/5.64 ( ( ord_less_int @ zero_zero_int @ ( abs_abs_int @ A ) )
% 5.31/5.64 = ( A != zero_zero_int ) ) ).
% 5.31/5.64
% 5.31/5.64 % zero_less_abs_iff
% 5.31/5.64 thf(fact_8260_abs__neg__numeral,axiom,
% 5.31/5.64 ! [N: num] :
% 5.31/5.64 ( ( abs_abs_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.31/5.64 = ( numeral_numeral_int @ N ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_neg_numeral
% 5.31/5.64 thf(fact_8261_abs__neg__numeral,axiom,
% 5.31/5.64 ! [N: num] :
% 5.31/5.64 ( ( abs_abs_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 5.31/5.64 = ( numeral_numeral_real @ N ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_neg_numeral
% 5.31/5.64 thf(fact_8262_abs__neg__numeral,axiom,
% 5.31/5.64 ! [N: num] :
% 5.31/5.64 ( ( abs_abs_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 5.31/5.64 = ( numera6620942414471956472nteger @ N ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_neg_numeral
% 5.31/5.64 thf(fact_8263_abs__neg__numeral,axiom,
% 5.31/5.64 ! [N: num] :
% 5.31/5.64 ( ( abs_abs_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 5.31/5.64 = ( numeral_numeral_rat @ N ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_neg_numeral
% 5.31/5.64 thf(fact_8264_abs__neg__one,axiom,
% 5.31/5.64 ( ( abs_abs_int @ ( uminus_uminus_int @ one_one_int ) )
% 5.31/5.64 = one_one_int ) ).
% 5.31/5.64
% 5.31/5.64 % abs_neg_one
% 5.31/5.64 thf(fact_8265_abs__neg__one,axiom,
% 5.31/5.64 ( ( abs_abs_real @ ( uminus_uminus_real @ one_one_real ) )
% 5.31/5.64 = one_one_real ) ).
% 5.31/5.64
% 5.31/5.64 % abs_neg_one
% 5.31/5.64 thf(fact_8266_abs__neg__one,axiom,
% 5.31/5.64 ( ( abs_abs_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.31/5.64 = one_one_Code_integer ) ).
% 5.31/5.64
% 5.31/5.64 % abs_neg_one
% 5.31/5.64 thf(fact_8267_abs__neg__one,axiom,
% 5.31/5.64 ( ( abs_abs_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.31/5.64 = one_one_rat ) ).
% 5.31/5.64
% 5.31/5.64 % abs_neg_one
% 5.31/5.64 thf(fact_8268_cos__zero,axiom,
% 5.31/5.64 ( ( cos_complex @ zero_zero_complex )
% 5.31/5.64 = one_one_complex ) ).
% 5.31/5.64
% 5.31/5.64 % cos_zero
% 5.31/5.64 thf(fact_8269_cos__zero,axiom,
% 5.31/5.64 ( ( cos_real @ zero_zero_real )
% 5.31/5.64 = one_one_real ) ).
% 5.31/5.64
% 5.31/5.64 % cos_zero
% 5.31/5.64 thf(fact_8270_pred__numeral__simps_I1_J,axiom,
% 5.31/5.64 ( ( pred_numeral @ one )
% 5.31/5.64 = zero_zero_nat ) ).
% 5.31/5.64
% 5.31/5.64 % pred_numeral_simps(1)
% 5.31/5.64 thf(fact_8271_eq__numeral__Suc,axiom,
% 5.31/5.64 ! [K2: num,N: nat] :
% 5.31/5.64 ( ( ( numeral_numeral_nat @ K2 )
% 5.31/5.64 = ( suc @ N ) )
% 5.31/5.64 = ( ( pred_numeral @ K2 )
% 5.31/5.64 = N ) ) ).
% 5.31/5.64
% 5.31/5.64 % eq_numeral_Suc
% 5.31/5.64 thf(fact_8272_Suc__eq__numeral,axiom,
% 5.31/5.64 ! [N: nat,K2: num] :
% 5.31/5.64 ( ( ( suc @ N )
% 5.31/5.64 = ( numeral_numeral_nat @ K2 ) )
% 5.31/5.64 = ( N
% 5.31/5.64 = ( pred_numeral @ K2 ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % Suc_eq_numeral
% 5.31/5.64 thf(fact_8273_sum__abs,axiom,
% 5.31/5.64 ! [F2: int > int,A4: set_int] :
% 5.31/5.64 ( ord_less_eq_int @ ( abs_abs_int @ ( groups4538972089207619220nt_int @ F2 @ A4 ) )
% 5.31/5.64 @ ( groups4538972089207619220nt_int
% 5.31/5.64 @ ^ [I: int] : ( abs_abs_int @ ( F2 @ I ) )
% 5.31/5.64 @ A4 ) ) ).
% 5.31/5.64
% 5.31/5.64 % sum_abs
% 5.31/5.64 thf(fact_8274_sum__abs,axiom,
% 5.31/5.64 ! [F2: nat > real,A4: set_nat] :
% 5.31/5.64 ( ord_less_eq_real @ ( abs_abs_real @ ( groups6591440286371151544t_real @ F2 @ A4 ) )
% 5.31/5.64 @ ( groups6591440286371151544t_real
% 5.31/5.64 @ ^ [I: nat] : ( abs_abs_real @ ( F2 @ I ) )
% 5.31/5.64 @ A4 ) ) ).
% 5.31/5.64
% 5.31/5.64 % sum_abs
% 5.31/5.64 thf(fact_8275_divide__le__0__abs__iff,axiom,
% 5.31/5.64 ! [A: real,B: real] :
% 5.31/5.64 ( ( ord_less_eq_real @ ( divide_divide_real @ A @ ( abs_abs_real @ B ) ) @ zero_zero_real )
% 5.31/5.64 = ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.31/5.64 | ( B = zero_zero_real ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % divide_le_0_abs_iff
% 5.31/5.64 thf(fact_8276_divide__le__0__abs__iff,axiom,
% 5.31/5.64 ! [A: rat,B: rat] :
% 5.31/5.64 ( ( ord_less_eq_rat @ ( divide_divide_rat @ A @ ( abs_abs_rat @ B ) ) @ zero_zero_rat )
% 5.31/5.64 = ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.31/5.64 | ( B = zero_zero_rat ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % divide_le_0_abs_iff
% 5.31/5.64 thf(fact_8277_zero__le__divide__abs__iff,axiom,
% 5.31/5.64 ! [A: real,B: real] :
% 5.31/5.64 ( ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ A @ ( abs_abs_real @ B ) ) )
% 5.31/5.64 = ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.31/5.64 | ( B = zero_zero_real ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % zero_le_divide_abs_iff
% 5.31/5.64 thf(fact_8278_zero__le__divide__abs__iff,axiom,
% 5.31/5.64 ! [A: rat,B: rat] :
% 5.31/5.64 ( ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ ( abs_abs_rat @ B ) ) )
% 5.31/5.64 = ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.31/5.64 | ( B = zero_zero_rat ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % zero_le_divide_abs_iff
% 5.31/5.64 thf(fact_8279_abs__of__nonpos,axiom,
% 5.31/5.64 ! [A: real] :
% 5.31/5.64 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.31/5.64 => ( ( abs_abs_real @ A )
% 5.31/5.64 = ( uminus_uminus_real @ A ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_of_nonpos
% 5.31/5.64 thf(fact_8280_abs__of__nonpos,axiom,
% 5.31/5.64 ! [A: code_integer] :
% 5.31/5.64 ( ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger )
% 5.31/5.64 => ( ( abs_abs_Code_integer @ A )
% 5.31/5.64 = ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_of_nonpos
% 5.31/5.64 thf(fact_8281_abs__of__nonpos,axiom,
% 5.31/5.64 ! [A: rat] :
% 5.31/5.64 ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.31/5.64 => ( ( abs_abs_rat @ A )
% 5.31/5.64 = ( uminus_uminus_rat @ A ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_of_nonpos
% 5.31/5.64 thf(fact_8282_abs__of__nonpos,axiom,
% 5.31/5.64 ! [A: int] :
% 5.31/5.64 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.31/5.64 => ( ( abs_abs_int @ A )
% 5.31/5.64 = ( uminus_uminus_int @ A ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_of_nonpos
% 5.31/5.64 thf(fact_8283_less__Suc__numeral,axiom,
% 5.31/5.64 ! [N: nat,K2: num] :
% 5.31/5.64 ( ( ord_less_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ K2 ) )
% 5.31/5.64 = ( ord_less_nat @ N @ ( pred_numeral @ K2 ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % less_Suc_numeral
% 5.31/5.64 thf(fact_8284_less__numeral__Suc,axiom,
% 5.31/5.64 ! [K2: num,N: nat] :
% 5.31/5.64 ( ( ord_less_nat @ ( numeral_numeral_nat @ K2 ) @ ( suc @ N ) )
% 5.31/5.64 = ( ord_less_nat @ ( pred_numeral @ K2 ) @ N ) ) ).
% 5.31/5.64
% 5.31/5.64 % less_numeral_Suc
% 5.31/5.64 thf(fact_8285_pred__numeral__simps_I3_J,axiom,
% 5.31/5.64 ! [K2: num] :
% 5.31/5.64 ( ( pred_numeral @ ( bit1 @ K2 ) )
% 5.31/5.64 = ( numeral_numeral_nat @ ( bit0 @ K2 ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % pred_numeral_simps(3)
% 5.31/5.64 thf(fact_8286_le__numeral__Suc,axiom,
% 5.31/5.64 ! [K2: num,N: nat] :
% 5.31/5.64 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ K2 ) @ ( suc @ N ) )
% 5.31/5.64 = ( ord_less_eq_nat @ ( pred_numeral @ K2 ) @ N ) ) ).
% 5.31/5.64
% 5.31/5.64 % le_numeral_Suc
% 5.31/5.64 thf(fact_8287_le__Suc__numeral,axiom,
% 5.31/5.64 ! [N: nat,K2: num] :
% 5.31/5.64 ( ( ord_less_eq_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ K2 ) )
% 5.31/5.64 = ( ord_less_eq_nat @ N @ ( pred_numeral @ K2 ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % le_Suc_numeral
% 5.31/5.64 thf(fact_8288_diff__numeral__Suc,axiom,
% 5.31/5.64 ! [K2: num,N: nat] :
% 5.31/5.64 ( ( minus_minus_nat @ ( numeral_numeral_nat @ K2 ) @ ( suc @ N ) )
% 5.31/5.64 = ( minus_minus_nat @ ( pred_numeral @ K2 ) @ N ) ) ).
% 5.31/5.64
% 5.31/5.64 % diff_numeral_Suc
% 5.31/5.64 thf(fact_8289_diff__Suc__numeral,axiom,
% 5.31/5.64 ! [N: nat,K2: num] :
% 5.31/5.64 ( ( minus_minus_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ K2 ) )
% 5.31/5.64 = ( minus_minus_nat @ N @ ( pred_numeral @ K2 ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % diff_Suc_numeral
% 5.31/5.64 thf(fact_8290_max__Suc__numeral,axiom,
% 5.31/5.64 ! [N: nat,K2: num] :
% 5.31/5.64 ( ( ord_max_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ K2 ) )
% 5.31/5.64 = ( suc @ ( ord_max_nat @ N @ ( pred_numeral @ K2 ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % max_Suc_numeral
% 5.31/5.64 thf(fact_8291_max__numeral__Suc,axiom,
% 5.31/5.64 ! [K2: num,N: nat] :
% 5.31/5.64 ( ( ord_max_nat @ ( numeral_numeral_nat @ K2 ) @ ( suc @ N ) )
% 5.31/5.64 = ( suc @ ( ord_max_nat @ ( pred_numeral @ K2 ) @ N ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % max_numeral_Suc
% 5.31/5.64 thf(fact_8292_sum__abs__ge__zero,axiom,
% 5.31/5.64 ! [F2: int > int,A4: set_int] :
% 5.31/5.64 ( ord_less_eq_int @ zero_zero_int
% 5.31/5.64 @ ( groups4538972089207619220nt_int
% 5.31/5.64 @ ^ [I: int] : ( abs_abs_int @ ( F2 @ I ) )
% 5.31/5.64 @ A4 ) ) ).
% 5.31/5.64
% 5.31/5.64 % sum_abs_ge_zero
% 5.31/5.64 thf(fact_8293_sum__abs__ge__zero,axiom,
% 5.31/5.64 ! [F2: nat > real,A4: set_nat] :
% 5.31/5.64 ( ord_less_eq_real @ zero_zero_real
% 5.31/5.64 @ ( groups6591440286371151544t_real
% 5.31/5.64 @ ^ [I: nat] : ( abs_abs_real @ ( F2 @ I ) )
% 5.31/5.64 @ A4 ) ) ).
% 5.31/5.64
% 5.31/5.64 % sum_abs_ge_zero
% 5.31/5.64 thf(fact_8294_minus__numeral__div__numeral,axiom,
% 5.31/5.64 ! [M2: num,N: num] :
% 5.31/5.64 ( ( divide_divide_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ ( numeral_numeral_int @ N ) )
% 5.31/5.64 = ( uminus_uminus_int @ ( adjust_div @ ( unique5052692396658037445od_int @ M2 @ N ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % minus_numeral_div_numeral
% 5.31/5.64 thf(fact_8295_numeral__div__minus__numeral,axiom,
% 5.31/5.64 ! [M2: num,N: num] :
% 5.31/5.64 ( ( divide_divide_int @ ( numeral_numeral_int @ M2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.31/5.64 = ( uminus_uminus_int @ ( adjust_div @ ( unique5052692396658037445od_int @ M2 @ N ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % numeral_div_minus_numeral
% 5.31/5.64 thf(fact_8296_zero__less__power__abs__iff,axiom,
% 5.31/5.64 ! [A: code_integer,N: nat] :
% 5.31/5.64 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( power_8256067586552552935nteger @ ( abs_abs_Code_integer @ A ) @ N ) )
% 5.31/5.64 = ( ( A != zero_z3403309356797280102nteger )
% 5.31/5.64 | ( N = zero_zero_nat ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % zero_less_power_abs_iff
% 5.31/5.64 thf(fact_8297_zero__less__power__abs__iff,axiom,
% 5.31/5.64 ! [A: real,N: nat] :
% 5.31/5.64 ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ ( abs_abs_real @ A ) @ N ) )
% 5.31/5.64 = ( ( A != zero_zero_real )
% 5.31/5.64 | ( N = zero_zero_nat ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % zero_less_power_abs_iff
% 5.31/5.64 thf(fact_8298_zero__less__power__abs__iff,axiom,
% 5.31/5.64 ! [A: rat,N: nat] :
% 5.31/5.64 ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ ( abs_abs_rat @ A ) @ N ) )
% 5.31/5.64 = ( ( A != zero_zero_rat )
% 5.31/5.64 | ( N = zero_zero_nat ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % zero_less_power_abs_iff
% 5.31/5.64 thf(fact_8299_zero__less__power__abs__iff,axiom,
% 5.31/5.64 ! [A: int,N: nat] :
% 5.31/5.64 ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ ( abs_abs_int @ A ) @ N ) )
% 5.31/5.64 = ( ( A != zero_zero_int )
% 5.31/5.64 | ( N = zero_zero_nat ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % zero_less_power_abs_iff
% 5.31/5.64 thf(fact_8300_sin__cos__squared__add3,axiom,
% 5.31/5.64 ! [X: complex] :
% 5.31/5.64 ( ( plus_plus_complex @ ( times_times_complex @ ( cos_complex @ X ) @ ( cos_complex @ X ) ) @ ( times_times_complex @ ( sin_complex @ X ) @ ( sin_complex @ X ) ) )
% 5.31/5.64 = one_one_complex ) ).
% 5.31/5.64
% 5.31/5.64 % sin_cos_squared_add3
% 5.31/5.64 thf(fact_8301_sin__cos__squared__add3,axiom,
% 5.31/5.64 ! [X: real] :
% 5.31/5.64 ( ( plus_plus_real @ ( times_times_real @ ( cos_real @ X ) @ ( cos_real @ X ) ) @ ( times_times_real @ ( sin_real @ X ) @ ( sin_real @ X ) ) )
% 5.31/5.64 = one_one_real ) ).
% 5.31/5.64
% 5.31/5.64 % sin_cos_squared_add3
% 5.31/5.64 thf(fact_8302_dvd__numeral__simp,axiom,
% 5.31/5.64 ! [M2: num,N: num] :
% 5.31/5.64 ( ( dvd_dvd_int @ ( numeral_numeral_int @ M2 ) @ ( numeral_numeral_int @ N ) )
% 5.31/5.64 = ( unique6319869463603278526ux_int @ ( unique5052692396658037445od_int @ N @ M2 ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % dvd_numeral_simp
% 5.31/5.64 thf(fact_8303_dvd__numeral__simp,axiom,
% 5.31/5.64 ! [M2: num,N: num] :
% 5.31/5.64 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ M2 ) @ ( numeral_numeral_nat @ N ) )
% 5.31/5.64 = ( unique6322359934112328802ux_nat @ ( unique5055182867167087721od_nat @ N @ M2 ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % dvd_numeral_simp
% 5.31/5.64 thf(fact_8304_divmod__algorithm__code_I2_J,axiom,
% 5.31/5.64 ! [M2: num] :
% 5.31/5.64 ( ( unique3479559517661332726nteger @ M2 @ one )
% 5.31/5.64 = ( produc1086072967326762835nteger @ ( numera6620942414471956472nteger @ M2 ) @ zero_z3403309356797280102nteger ) ) ).
% 5.31/5.64
% 5.31/5.64 % divmod_algorithm_code(2)
% 5.31/5.64 thf(fact_8305_divmod__algorithm__code_I2_J,axiom,
% 5.31/5.64 ! [M2: num] :
% 5.31/5.64 ( ( unique5052692396658037445od_int @ M2 @ one )
% 5.31/5.64 = ( product_Pair_int_int @ ( numeral_numeral_int @ M2 ) @ zero_zero_int ) ) ).
% 5.31/5.64
% 5.31/5.64 % divmod_algorithm_code(2)
% 5.31/5.64 thf(fact_8306_divmod__algorithm__code_I2_J,axiom,
% 5.31/5.64 ! [M2: num] :
% 5.31/5.64 ( ( unique5055182867167087721od_nat @ M2 @ one )
% 5.31/5.64 = ( product_Pair_nat_nat @ ( numeral_numeral_nat @ M2 ) @ zero_zero_nat ) ) ).
% 5.31/5.64
% 5.31/5.64 % divmod_algorithm_code(2)
% 5.31/5.64 thf(fact_8307_divmod__algorithm__code_I3_J,axiom,
% 5.31/5.64 ! [N: num] :
% 5.31/5.64 ( ( unique3479559517661332726nteger @ one @ ( bit0 @ N ) )
% 5.31/5.64 = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ one ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % divmod_algorithm_code(3)
% 5.31/5.64 thf(fact_8308_divmod__algorithm__code_I3_J,axiom,
% 5.31/5.64 ! [N: num] :
% 5.31/5.64 ( ( unique5052692396658037445od_int @ one @ ( bit0 @ N ) )
% 5.31/5.64 = ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ one ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % divmod_algorithm_code(3)
% 5.31/5.64 thf(fact_8309_divmod__algorithm__code_I3_J,axiom,
% 5.31/5.64 ! [N: num] :
% 5.31/5.64 ( ( unique5055182867167087721od_nat @ one @ ( bit0 @ N ) )
% 5.31/5.64 = ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ one ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % divmod_algorithm_code(3)
% 5.31/5.64 thf(fact_8310_divmod__algorithm__code_I4_J,axiom,
% 5.31/5.64 ! [N: num] :
% 5.31/5.64 ( ( unique3479559517661332726nteger @ one @ ( bit1 @ N ) )
% 5.31/5.64 = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ one ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % divmod_algorithm_code(4)
% 5.31/5.64 thf(fact_8311_divmod__algorithm__code_I4_J,axiom,
% 5.31/5.64 ! [N: num] :
% 5.31/5.64 ( ( unique5052692396658037445od_int @ one @ ( bit1 @ N ) )
% 5.31/5.64 = ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ one ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % divmod_algorithm_code(4)
% 5.31/5.64 thf(fact_8312_divmod__algorithm__code_I4_J,axiom,
% 5.31/5.64 ! [N: num] :
% 5.31/5.64 ( ( unique5055182867167087721od_nat @ one @ ( bit1 @ N ) )
% 5.31/5.64 = ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ one ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % divmod_algorithm_code(4)
% 5.31/5.64 thf(fact_8313_one__div__minus__numeral,axiom,
% 5.31/5.64 ! [N: num] :
% 5.31/5.64 ( ( divide_divide_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.31/5.64 = ( uminus_uminus_int @ ( adjust_div @ ( unique5052692396658037445od_int @ one @ N ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % one_div_minus_numeral
% 5.31/5.64 thf(fact_8314_minus__one__div__numeral,axiom,
% 5.31/5.64 ! [N: num] :
% 5.31/5.64 ( ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ N ) )
% 5.31/5.64 = ( uminus_uminus_int @ ( adjust_div @ ( unique5052692396658037445od_int @ one @ N ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % minus_one_div_numeral
% 5.31/5.64 thf(fact_8315_cos__two__pi,axiom,
% 5.31/5.64 ( ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 5.31/5.64 = one_one_real ) ).
% 5.31/5.64
% 5.31/5.64 % cos_two_pi
% 5.31/5.64 thf(fact_8316_cos__periodic,axiom,
% 5.31/5.64 ! [X: real] :
% 5.31/5.64 ( ( cos_real @ ( plus_plus_real @ X @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 5.31/5.64 = ( cos_real @ X ) ) ).
% 5.31/5.64
% 5.31/5.64 % cos_periodic
% 5.31/5.64 thf(fact_8317_cos__2pi__minus,axiom,
% 5.31/5.64 ! [X: real] :
% 5.31/5.64 ( ( cos_real @ ( minus_minus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ X ) )
% 5.31/5.64 = ( cos_real @ X ) ) ).
% 5.31/5.64
% 5.31/5.64 % cos_2pi_minus
% 5.31/5.64 thf(fact_8318_signed__take__bit__numeral__bit0,axiom,
% 5.31/5.64 ! [L: num,K2: num] :
% 5.31/5.64 ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ L ) @ ( numeral_numeral_int @ ( bit0 @ K2 ) ) )
% 5.31/5.64 = ( times_times_int @ ( bit_ri631733984087533419it_int @ ( pred_numeral @ L ) @ ( numeral_numeral_int @ K2 ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % signed_take_bit_numeral_bit0
% 5.31/5.64 thf(fact_8319_cos__npi,axiom,
% 5.31/5.64 ! [N: nat] :
% 5.31/5.64 ( ( cos_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ pi ) )
% 5.31/5.64 = ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) ) ).
% 5.31/5.64
% 5.31/5.64 % cos_npi
% 5.31/5.64 thf(fact_8320_cos__npi2,axiom,
% 5.31/5.64 ! [N: nat] :
% 5.31/5.64 ( ( cos_real @ ( times_times_real @ pi @ ( semiri5074537144036343181t_real @ N ) ) )
% 5.31/5.64 = ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) ) ).
% 5.31/5.64
% 5.31/5.64 % cos_npi2
% 5.31/5.64 thf(fact_8321_cos__2npi,axiom,
% 5.31/5.64 ! [N: nat] :
% 5.31/5.64 ( ( cos_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) )
% 5.31/5.64 = one_one_real ) ).
% 5.31/5.64
% 5.31/5.64 % cos_2npi
% 5.31/5.64 thf(fact_8322_signed__take__bit__numeral__minus__bit0,axiom,
% 5.31/5.64 ! [L: num,K2: num] :
% 5.31/5.64 ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K2 ) ) ) )
% 5.31/5.64 = ( times_times_int @ ( bit_ri631733984087533419it_int @ ( pred_numeral @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ K2 ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % signed_take_bit_numeral_minus_bit0
% 5.31/5.64 thf(fact_8323_cos__3over2__pi,axiom,
% 5.31/5.64 ( ( cos_real @ ( times_times_real @ ( divide_divide_real @ ( numeral_numeral_real @ ( bit1 @ one ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ pi ) )
% 5.31/5.64 = zero_zero_real ) ).
% 5.31/5.64
% 5.31/5.64 % cos_3over2_pi
% 5.31/5.64 thf(fact_8324_signed__take__bit__numeral__bit1,axiom,
% 5.31/5.64 ! [L: num,K2: num] :
% 5.31/5.64 ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ L ) @ ( numeral_numeral_int @ ( bit1 @ K2 ) ) )
% 5.31/5.64 = ( plus_plus_int @ ( times_times_int @ ( bit_ri631733984087533419it_int @ ( pred_numeral @ L ) @ ( numeral_numeral_int @ K2 ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 5.31/5.64
% 5.31/5.64 % signed_take_bit_numeral_bit1
% 5.31/5.64 thf(fact_8325_cos__pi__eq__zero,axiom,
% 5.31/5.64 ! [M2: nat] :
% 5.31/5.64 ( ( cos_real @ ( divide_divide_real @ ( times_times_real @ pi @ ( semiri5074537144036343181t_real @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.31/5.64 = zero_zero_real ) ).
% 5.31/5.64
% 5.31/5.64 % cos_pi_eq_zero
% 5.31/5.64 thf(fact_8326_abs__ge__self,axiom,
% 5.31/5.64 ! [A: real] : ( ord_less_eq_real @ A @ ( abs_abs_real @ A ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_ge_self
% 5.31/5.64 thf(fact_8327_abs__ge__self,axiom,
% 5.31/5.64 ! [A: code_integer] : ( ord_le3102999989581377725nteger @ A @ ( abs_abs_Code_integer @ A ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_ge_self
% 5.31/5.64 thf(fact_8328_abs__ge__self,axiom,
% 5.31/5.64 ! [A: rat] : ( ord_less_eq_rat @ A @ ( abs_abs_rat @ A ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_ge_self
% 5.31/5.64 thf(fact_8329_abs__ge__self,axiom,
% 5.31/5.64 ! [A: int] : ( ord_less_eq_int @ A @ ( abs_abs_int @ A ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_ge_self
% 5.31/5.64 thf(fact_8330_abs__le__D1,axiom,
% 5.31/5.64 ! [A: real,B: real] :
% 5.31/5.64 ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ B )
% 5.31/5.64 => ( ord_less_eq_real @ A @ B ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_le_D1
% 5.31/5.64 thf(fact_8331_abs__le__D1,axiom,
% 5.31/5.64 ! [A: code_integer,B: code_integer] :
% 5.31/5.64 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ B )
% 5.31/5.64 => ( ord_le3102999989581377725nteger @ A @ B ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_le_D1
% 5.31/5.64 thf(fact_8332_abs__le__D1,axiom,
% 5.31/5.64 ! [A: rat,B: rat] :
% 5.31/5.64 ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ B )
% 5.31/5.64 => ( ord_less_eq_rat @ A @ B ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_le_D1
% 5.31/5.64 thf(fact_8333_abs__le__D1,axiom,
% 5.31/5.64 ! [A: int,B: int] :
% 5.31/5.64 ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B )
% 5.31/5.64 => ( ord_less_eq_int @ A @ B ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_le_D1
% 5.31/5.64 thf(fact_8334_abs__eq__0__iff,axiom,
% 5.31/5.64 ! [A: code_integer] :
% 5.31/5.64 ( ( ( abs_abs_Code_integer @ A )
% 5.31/5.64 = zero_z3403309356797280102nteger )
% 5.31/5.64 = ( A = zero_z3403309356797280102nteger ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_eq_0_iff
% 5.31/5.64 thf(fact_8335_abs__eq__0__iff,axiom,
% 5.31/5.64 ! [A: complex] :
% 5.31/5.64 ( ( ( abs_abs_complex @ A )
% 5.31/5.64 = zero_zero_complex )
% 5.31/5.64 = ( A = zero_zero_complex ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_eq_0_iff
% 5.31/5.64 thf(fact_8336_abs__eq__0__iff,axiom,
% 5.31/5.64 ! [A: real] :
% 5.31/5.64 ( ( ( abs_abs_real @ A )
% 5.31/5.64 = zero_zero_real )
% 5.31/5.64 = ( A = zero_zero_real ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_eq_0_iff
% 5.31/5.64 thf(fact_8337_abs__eq__0__iff,axiom,
% 5.31/5.64 ! [A: rat] :
% 5.31/5.64 ( ( ( abs_abs_rat @ A )
% 5.31/5.64 = zero_zero_rat )
% 5.31/5.64 = ( A = zero_zero_rat ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_eq_0_iff
% 5.31/5.64 thf(fact_8338_abs__eq__0__iff,axiom,
% 5.31/5.64 ! [A: int] :
% 5.31/5.64 ( ( ( abs_abs_int @ A )
% 5.31/5.64 = zero_zero_int )
% 5.31/5.64 = ( A = zero_zero_int ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_eq_0_iff
% 5.31/5.64 thf(fact_8339_abs__mult,axiom,
% 5.31/5.64 ! [A: code_integer,B: code_integer] :
% 5.31/5.64 ( ( abs_abs_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) )
% 5.31/5.64 = ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_mult
% 5.31/5.64 thf(fact_8340_abs__mult,axiom,
% 5.31/5.64 ! [A: real,B: real] :
% 5.31/5.64 ( ( abs_abs_real @ ( times_times_real @ A @ B ) )
% 5.31/5.64 = ( times_times_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_mult
% 5.31/5.64 thf(fact_8341_abs__mult,axiom,
% 5.31/5.64 ! [A: rat,B: rat] :
% 5.31/5.64 ( ( abs_abs_rat @ ( times_times_rat @ A @ B ) )
% 5.31/5.64 = ( times_times_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_mult
% 5.31/5.64 thf(fact_8342_abs__mult,axiom,
% 5.31/5.64 ! [A: int,B: int] :
% 5.31/5.64 ( ( abs_abs_int @ ( times_times_int @ A @ B ) )
% 5.31/5.64 = ( times_times_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_mult
% 5.31/5.64 thf(fact_8343_abs__one,axiom,
% 5.31/5.64 ( ( abs_abs_rat @ one_one_rat )
% 5.31/5.64 = one_one_rat ) ).
% 5.31/5.64
% 5.31/5.64 % abs_one
% 5.31/5.64 thf(fact_8344_abs__one,axiom,
% 5.31/5.64 ( ( abs_abs_Code_integer @ one_one_Code_integer )
% 5.31/5.64 = one_one_Code_integer ) ).
% 5.31/5.64
% 5.31/5.64 % abs_one
% 5.31/5.64 thf(fact_8345_abs__one,axiom,
% 5.31/5.64 ( ( abs_abs_real @ one_one_real )
% 5.31/5.64 = one_one_real ) ).
% 5.31/5.64
% 5.31/5.64 % abs_one
% 5.31/5.64 thf(fact_8346_abs__one,axiom,
% 5.31/5.64 ( ( abs_abs_int @ one_one_int )
% 5.31/5.64 = one_one_int ) ).
% 5.31/5.64
% 5.31/5.64 % abs_one
% 5.31/5.64 thf(fact_8347_abs__minus__commute,axiom,
% 5.31/5.64 ! [A: real,B: real] :
% 5.31/5.64 ( ( abs_abs_real @ ( minus_minus_real @ A @ B ) )
% 5.31/5.64 = ( abs_abs_real @ ( minus_minus_real @ B @ A ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_minus_commute
% 5.31/5.64 thf(fact_8348_abs__minus__commute,axiom,
% 5.31/5.64 ! [A: code_integer,B: code_integer] :
% 5.31/5.64 ( ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ A @ B ) )
% 5.31/5.64 = ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ B @ A ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_minus_commute
% 5.31/5.64 thf(fact_8349_abs__minus__commute,axiom,
% 5.31/5.64 ! [A: rat,B: rat] :
% 5.31/5.64 ( ( abs_abs_rat @ ( minus_minus_rat @ A @ B ) )
% 5.31/5.64 = ( abs_abs_rat @ ( minus_minus_rat @ B @ A ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_minus_commute
% 5.31/5.64 thf(fact_8350_abs__minus__commute,axiom,
% 5.31/5.64 ! [A: int,B: int] :
% 5.31/5.64 ( ( abs_abs_int @ ( minus_minus_int @ A @ B ) )
% 5.31/5.64 = ( abs_abs_int @ ( minus_minus_int @ B @ A ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_minus_commute
% 5.31/5.64 thf(fact_8351_abs__eq__iff,axiom,
% 5.31/5.64 ! [X: int,Y: int] :
% 5.31/5.64 ( ( ( abs_abs_int @ X )
% 5.31/5.64 = ( abs_abs_int @ Y ) )
% 5.31/5.64 = ( ( X = Y )
% 5.31/5.64 | ( X
% 5.31/5.64 = ( uminus_uminus_int @ Y ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_eq_iff
% 5.31/5.64 thf(fact_8352_abs__eq__iff,axiom,
% 5.31/5.64 ! [X: real,Y: real] :
% 5.31/5.64 ( ( ( abs_abs_real @ X )
% 5.31/5.64 = ( abs_abs_real @ Y ) )
% 5.31/5.64 = ( ( X = Y )
% 5.31/5.64 | ( X
% 5.31/5.64 = ( uminus_uminus_real @ Y ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_eq_iff
% 5.31/5.64 thf(fact_8353_abs__eq__iff,axiom,
% 5.31/5.64 ! [X: code_integer,Y: code_integer] :
% 5.31/5.64 ( ( ( abs_abs_Code_integer @ X )
% 5.31/5.64 = ( abs_abs_Code_integer @ Y ) )
% 5.31/5.64 = ( ( X = Y )
% 5.31/5.64 | ( X
% 5.31/5.64 = ( uminus1351360451143612070nteger @ Y ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_eq_iff
% 5.31/5.64 thf(fact_8354_abs__eq__iff,axiom,
% 5.31/5.64 ! [X: rat,Y: rat] :
% 5.31/5.64 ( ( ( abs_abs_rat @ X )
% 5.31/5.64 = ( abs_abs_rat @ Y ) )
% 5.31/5.64 = ( ( X = Y )
% 5.31/5.64 | ( X
% 5.31/5.64 = ( uminus_uminus_rat @ Y ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_eq_iff
% 5.31/5.64 thf(fact_8355_dvd__if__abs__eq,axiom,
% 5.31/5.64 ! [L: real,K2: real] :
% 5.31/5.64 ( ( ( abs_abs_real @ L )
% 5.31/5.64 = ( abs_abs_real @ K2 ) )
% 5.31/5.64 => ( dvd_dvd_real @ L @ K2 ) ) ).
% 5.31/5.64
% 5.31/5.64 % dvd_if_abs_eq
% 5.31/5.64 thf(fact_8356_dvd__if__abs__eq,axiom,
% 5.31/5.64 ! [L: int,K2: int] :
% 5.31/5.64 ( ( ( abs_abs_int @ L )
% 5.31/5.64 = ( abs_abs_int @ K2 ) )
% 5.31/5.64 => ( dvd_dvd_int @ L @ K2 ) ) ).
% 5.31/5.64
% 5.31/5.64 % dvd_if_abs_eq
% 5.31/5.64 thf(fact_8357_dvd__if__abs__eq,axiom,
% 5.31/5.64 ! [L: code_integer,K2: code_integer] :
% 5.31/5.64 ( ( ( abs_abs_Code_integer @ L )
% 5.31/5.64 = ( abs_abs_Code_integer @ K2 ) )
% 5.31/5.64 => ( dvd_dvd_Code_integer @ L @ K2 ) ) ).
% 5.31/5.64
% 5.31/5.64 % dvd_if_abs_eq
% 5.31/5.64 thf(fact_8358_dvd__if__abs__eq,axiom,
% 5.31/5.64 ! [L: rat,K2: rat] :
% 5.31/5.64 ( ( ( abs_abs_rat @ L )
% 5.31/5.64 = ( abs_abs_rat @ K2 ) )
% 5.31/5.64 => ( dvd_dvd_rat @ L @ K2 ) ) ).
% 5.31/5.64
% 5.31/5.64 % dvd_if_abs_eq
% 5.31/5.64 thf(fact_8359_abs__ge__zero,axiom,
% 5.31/5.64 ! [A: code_integer] : ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( abs_abs_Code_integer @ A ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_ge_zero
% 5.31/5.64 thf(fact_8360_abs__ge__zero,axiom,
% 5.31/5.64 ! [A: real] : ( ord_less_eq_real @ zero_zero_real @ ( abs_abs_real @ A ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_ge_zero
% 5.31/5.64 thf(fact_8361_abs__ge__zero,axiom,
% 5.31/5.64 ! [A: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( abs_abs_rat @ A ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_ge_zero
% 5.31/5.64 thf(fact_8362_abs__ge__zero,axiom,
% 5.31/5.64 ! [A: int] : ( ord_less_eq_int @ zero_zero_int @ ( abs_abs_int @ A ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_ge_zero
% 5.31/5.64 thf(fact_8363_abs__not__less__zero,axiom,
% 5.31/5.64 ! [A: code_integer] :
% 5.31/5.64 ~ ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ A ) @ zero_z3403309356797280102nteger ) ).
% 5.31/5.64
% 5.31/5.64 % abs_not_less_zero
% 5.31/5.64 thf(fact_8364_abs__not__less__zero,axiom,
% 5.31/5.64 ! [A: real] :
% 5.31/5.64 ~ ( ord_less_real @ ( abs_abs_real @ A ) @ zero_zero_real ) ).
% 5.31/5.64
% 5.31/5.64 % abs_not_less_zero
% 5.31/5.64 thf(fact_8365_abs__not__less__zero,axiom,
% 5.31/5.64 ! [A: rat] :
% 5.31/5.64 ~ ( ord_less_rat @ ( abs_abs_rat @ A ) @ zero_zero_rat ) ).
% 5.31/5.64
% 5.31/5.64 % abs_not_less_zero
% 5.31/5.64 thf(fact_8366_abs__not__less__zero,axiom,
% 5.31/5.64 ! [A: int] :
% 5.31/5.64 ~ ( ord_less_int @ ( abs_abs_int @ A ) @ zero_zero_int ) ).
% 5.31/5.64
% 5.31/5.64 % abs_not_less_zero
% 5.31/5.64 thf(fact_8367_abs__of__pos,axiom,
% 5.31/5.64 ! [A: code_integer] :
% 5.31/5.64 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 5.31/5.64 => ( ( abs_abs_Code_integer @ A )
% 5.31/5.64 = A ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_of_pos
% 5.31/5.64 thf(fact_8368_abs__of__pos,axiom,
% 5.31/5.64 ! [A: real] :
% 5.31/5.64 ( ( ord_less_real @ zero_zero_real @ A )
% 5.31/5.64 => ( ( abs_abs_real @ A )
% 5.31/5.64 = A ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_of_pos
% 5.31/5.64 thf(fact_8369_abs__of__pos,axiom,
% 5.31/5.64 ! [A: rat] :
% 5.31/5.64 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.31/5.64 => ( ( abs_abs_rat @ A )
% 5.31/5.64 = A ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_of_pos
% 5.31/5.64 thf(fact_8370_abs__of__pos,axiom,
% 5.31/5.64 ! [A: int] :
% 5.31/5.64 ( ( ord_less_int @ zero_zero_int @ A )
% 5.31/5.64 => ( ( abs_abs_int @ A )
% 5.31/5.64 = A ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_of_pos
% 5.31/5.64 thf(fact_8371_abs__triangle__ineq,axiom,
% 5.31/5.64 ! [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 ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_triangle_ineq
% 5.31/5.64 thf(fact_8372_abs__triangle__ineq,axiom,
% 5.31/5.64 ! [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 ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_triangle_ineq
% 5.31/5.64 thf(fact_8373_abs__triangle__ineq,axiom,
% 5.31/5.64 ! [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 ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_triangle_ineq
% 5.31/5.64 thf(fact_8374_abs__triangle__ineq,axiom,
% 5.31/5.64 ! [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 ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_triangle_ineq
% 5.31/5.64 thf(fact_8375_abs__mult__less,axiom,
% 5.31/5.64 ! [A: code_integer,C2: code_integer,B: code_integer,D: code_integer] :
% 5.31/5.64 ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ A ) @ C2 )
% 5.31/5.64 => ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ B ) @ D )
% 5.31/5.64 => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) @ ( times_3573771949741848930nteger @ C2 @ D ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_mult_less
% 5.31/5.64 thf(fact_8376_abs__mult__less,axiom,
% 5.31/5.64 ! [A: real,C2: real,B: real,D: real] :
% 5.31/5.64 ( ( ord_less_real @ ( abs_abs_real @ A ) @ C2 )
% 5.31/5.64 => ( ( ord_less_real @ ( abs_abs_real @ B ) @ D )
% 5.31/5.64 => ( ord_less_real @ ( times_times_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) @ ( times_times_real @ C2 @ D ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_mult_less
% 5.31/5.64 thf(fact_8377_abs__mult__less,axiom,
% 5.31/5.64 ! [A: rat,C2: rat,B: rat,D: rat] :
% 5.31/5.64 ( ( ord_less_rat @ ( abs_abs_rat @ A ) @ C2 )
% 5.31/5.64 => ( ( ord_less_rat @ ( abs_abs_rat @ B ) @ D )
% 5.31/5.64 => ( ord_less_rat @ ( times_times_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) @ ( times_times_rat @ C2 @ D ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_mult_less
% 5.31/5.64 thf(fact_8378_abs__mult__less,axiom,
% 5.31/5.64 ! [A: int,C2: int,B: int,D: int] :
% 5.31/5.64 ( ( ord_less_int @ ( abs_abs_int @ A ) @ C2 )
% 5.31/5.64 => ( ( ord_less_int @ ( abs_abs_int @ B ) @ D )
% 5.31/5.64 => ( ord_less_int @ ( times_times_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) @ ( times_times_int @ C2 @ D ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_mult_less
% 5.31/5.64 thf(fact_8379_abs__triangle__ineq2__sym,axiom,
% 5.31/5.64 ! [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 ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_triangle_ineq2_sym
% 5.31/5.64 thf(fact_8380_abs__triangle__ineq2__sym,axiom,
% 5.31/5.64 ! [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 ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_triangle_ineq2_sym
% 5.31/5.64 thf(fact_8381_abs__triangle__ineq2__sym,axiom,
% 5.31/5.64 ! [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 ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_triangle_ineq2_sym
% 5.31/5.64 thf(fact_8382_abs__triangle__ineq2__sym,axiom,
% 5.31/5.64 ! [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 ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_triangle_ineq2_sym
% 5.31/5.64 thf(fact_8383_abs__triangle__ineq3,axiom,
% 5.31/5.64 ! [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 ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_triangle_ineq3
% 5.31/5.64 thf(fact_8384_abs__triangle__ineq3,axiom,
% 5.31/5.64 ! [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 ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_triangle_ineq3
% 5.31/5.64 thf(fact_8385_abs__triangle__ineq3,axiom,
% 5.31/5.64 ! [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 ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_triangle_ineq3
% 5.31/5.64 thf(fact_8386_abs__triangle__ineq3,axiom,
% 5.31/5.64 ! [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 ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_triangle_ineq3
% 5.31/5.64 thf(fact_8387_abs__triangle__ineq2,axiom,
% 5.31/5.64 ! [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 ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_triangle_ineq2
% 5.31/5.64 thf(fact_8388_abs__triangle__ineq2,axiom,
% 5.31/5.64 ! [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 ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_triangle_ineq2
% 5.31/5.64 thf(fact_8389_abs__triangle__ineq2,axiom,
% 5.31/5.64 ! [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 ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_triangle_ineq2
% 5.31/5.64 thf(fact_8390_abs__triangle__ineq2,axiom,
% 5.31/5.64 ! [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 ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_triangle_ineq2
% 5.31/5.64 thf(fact_8391_nonzero__abs__divide,axiom,
% 5.31/5.64 ! [B: real,A: real] :
% 5.31/5.64 ( ( B != zero_zero_real )
% 5.31/5.64 => ( ( abs_abs_real @ ( divide_divide_real @ A @ B ) )
% 5.31/5.64 = ( divide_divide_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % nonzero_abs_divide
% 5.31/5.64 thf(fact_8392_nonzero__abs__divide,axiom,
% 5.31/5.64 ! [B: rat,A: rat] :
% 5.31/5.64 ( ( B != zero_zero_rat )
% 5.31/5.64 => ( ( abs_abs_rat @ ( divide_divide_rat @ A @ B ) )
% 5.31/5.64 = ( divide_divide_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % nonzero_abs_divide
% 5.31/5.64 thf(fact_8393_abs__leI,axiom,
% 5.31/5.64 ! [A: real,B: real] :
% 5.31/5.64 ( ( ord_less_eq_real @ A @ B )
% 5.31/5.64 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ B )
% 5.31/5.64 => ( ord_less_eq_real @ ( abs_abs_real @ A ) @ B ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_leI
% 5.31/5.64 thf(fact_8394_abs__leI,axiom,
% 5.31/5.64 ! [A: code_integer,B: code_integer] :
% 5.31/5.64 ( ( ord_le3102999989581377725nteger @ A @ B )
% 5.31/5.64 => ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 5.31/5.64 => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ B ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_leI
% 5.31/5.64 thf(fact_8395_abs__leI,axiom,
% 5.31/5.64 ! [A: rat,B: rat] :
% 5.31/5.64 ( ( ord_less_eq_rat @ A @ B )
% 5.31/5.64 => ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ B )
% 5.31/5.64 => ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ B ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_leI
% 5.31/5.64 thf(fact_8396_abs__leI,axiom,
% 5.31/5.64 ! [A: int,B: int] :
% 5.31/5.64 ( ( ord_less_eq_int @ A @ B )
% 5.31/5.64 => ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B )
% 5.31/5.64 => ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_leI
% 5.31/5.64 thf(fact_8397_abs__le__D2,axiom,
% 5.31/5.64 ! [A: real,B: real] :
% 5.31/5.64 ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ B )
% 5.31/5.64 => ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ B ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_le_D2
% 5.31/5.64 thf(fact_8398_abs__le__D2,axiom,
% 5.31/5.64 ! [A: code_integer,B: code_integer] :
% 5.31/5.64 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ B )
% 5.31/5.64 => ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_le_D2
% 5.31/5.64 thf(fact_8399_abs__le__D2,axiom,
% 5.31/5.64 ! [A: rat,B: rat] :
% 5.31/5.64 ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ B )
% 5.31/5.64 => ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_le_D2
% 5.31/5.64 thf(fact_8400_abs__le__D2,axiom,
% 5.31/5.64 ! [A: int,B: int] :
% 5.31/5.64 ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B )
% 5.31/5.64 => ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_le_D2
% 5.31/5.64 thf(fact_8401_abs__le__iff,axiom,
% 5.31/5.64 ! [A: real,B: real] :
% 5.31/5.64 ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ B )
% 5.31/5.64 = ( ( ord_less_eq_real @ A @ B )
% 5.31/5.64 & ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ B ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_le_iff
% 5.31/5.64 thf(fact_8402_abs__le__iff,axiom,
% 5.31/5.64 ! [A: code_integer,B: code_integer] :
% 5.31/5.64 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ B )
% 5.31/5.64 = ( ( ord_le3102999989581377725nteger @ A @ B )
% 5.31/5.64 & ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_le_iff
% 5.31/5.64 thf(fact_8403_abs__le__iff,axiom,
% 5.31/5.64 ! [A: rat,B: rat] :
% 5.31/5.64 ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ B )
% 5.31/5.64 = ( ( ord_less_eq_rat @ A @ B )
% 5.31/5.64 & ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_le_iff
% 5.31/5.64 thf(fact_8404_abs__le__iff,axiom,
% 5.31/5.64 ! [A: int,B: int] :
% 5.31/5.64 ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B )
% 5.31/5.64 = ( ( ord_less_eq_int @ A @ B )
% 5.31/5.64 & ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_le_iff
% 5.31/5.64 thf(fact_8405_abs__ge__minus__self,axiom,
% 5.31/5.64 ! [A: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ ( abs_abs_real @ A ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_ge_minus_self
% 5.31/5.64 thf(fact_8406_abs__ge__minus__self,axiom,
% 5.31/5.64 ! [A: code_integer] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ ( abs_abs_Code_integer @ A ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_ge_minus_self
% 5.31/5.64 thf(fact_8407_abs__ge__minus__self,axiom,
% 5.31/5.64 ! [A: rat] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ ( abs_abs_rat @ A ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_ge_minus_self
% 5.31/5.64 thf(fact_8408_abs__ge__minus__self,axiom,
% 5.31/5.64 ! [A: int] : ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ ( abs_abs_int @ A ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_ge_minus_self
% 5.31/5.64 thf(fact_8409_abs__less__iff,axiom,
% 5.31/5.64 ! [A: int,B: int] :
% 5.31/5.64 ( ( ord_less_int @ ( abs_abs_int @ A ) @ B )
% 5.31/5.64 = ( ( ord_less_int @ A @ B )
% 5.31/5.64 & ( ord_less_int @ ( uminus_uminus_int @ A ) @ B ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_less_iff
% 5.31/5.64 thf(fact_8410_abs__less__iff,axiom,
% 5.31/5.64 ! [A: real,B: real] :
% 5.31/5.64 ( ( ord_less_real @ ( abs_abs_real @ A ) @ B )
% 5.31/5.64 = ( ( ord_less_real @ A @ B )
% 5.31/5.64 & ( ord_less_real @ ( uminus_uminus_real @ A ) @ B ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_less_iff
% 5.31/5.64 thf(fact_8411_abs__less__iff,axiom,
% 5.31/5.64 ! [A: code_integer,B: code_integer] :
% 5.31/5.64 ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ A ) @ B )
% 5.31/5.64 = ( ( ord_le6747313008572928689nteger @ A @ B )
% 5.31/5.64 & ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_less_iff
% 5.31/5.64 thf(fact_8412_abs__less__iff,axiom,
% 5.31/5.64 ! [A: rat,B: rat] :
% 5.31/5.64 ( ( ord_less_rat @ ( abs_abs_rat @ A ) @ B )
% 5.31/5.64 = ( ( ord_less_rat @ A @ B )
% 5.31/5.64 & ( ord_less_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_less_iff
% 5.31/5.64 thf(fact_8413_polar__Ex,axiom,
% 5.31/5.64 ! [X: real,Y: real] :
% 5.31/5.64 ? [R4: real,A3: real] :
% 5.31/5.64 ( ( X
% 5.31/5.64 = ( times_times_real @ R4 @ ( cos_real @ A3 ) ) )
% 5.31/5.64 & ( Y
% 5.31/5.64 = ( times_times_real @ R4 @ ( sin_real @ A3 ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % polar_Ex
% 5.31/5.64 thf(fact_8414_numeral__eq__Suc,axiom,
% 5.31/5.64 ( numeral_numeral_nat
% 5.31/5.64 = ( ^ [K3: num] : ( suc @ ( pred_numeral @ K3 ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % numeral_eq_Suc
% 5.31/5.64 thf(fact_8415_sin__cos__le1,axiom,
% 5.31/5.64 ! [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 ) ).
% 5.31/5.64
% 5.31/5.64 % sin_cos_le1
% 5.31/5.64 thf(fact_8416_dense__eq0__I,axiom,
% 5.31/5.64 ! [X: real] :
% 5.31/5.64 ( ! [E2: real] :
% 5.31/5.64 ( ( ord_less_real @ zero_zero_real @ E2 )
% 5.31/5.64 => ( ord_less_eq_real @ ( abs_abs_real @ X ) @ E2 ) )
% 5.31/5.64 => ( X = zero_zero_real ) ) ).
% 5.31/5.64
% 5.31/5.64 % dense_eq0_I
% 5.31/5.64 thf(fact_8417_dense__eq0__I,axiom,
% 5.31/5.64 ! [X: rat] :
% 5.31/5.64 ( ! [E2: rat] :
% 5.31/5.64 ( ( ord_less_rat @ zero_zero_rat @ E2 )
% 5.31/5.64 => ( ord_less_eq_rat @ ( abs_abs_rat @ X ) @ E2 ) )
% 5.31/5.64 => ( X = zero_zero_rat ) ) ).
% 5.31/5.64
% 5.31/5.64 % dense_eq0_I
% 5.31/5.64 thf(fact_8418_abs__mult__pos,axiom,
% 5.31/5.64 ! [X: code_integer,Y: code_integer] :
% 5.31/5.64 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ X )
% 5.31/5.64 => ( ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ Y ) @ X )
% 5.31/5.64 = ( abs_abs_Code_integer @ ( times_3573771949741848930nteger @ Y @ X ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_mult_pos
% 5.31/5.64 thf(fact_8419_abs__mult__pos,axiom,
% 5.31/5.64 ! [X: real,Y: real] :
% 5.31/5.64 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.31/5.64 => ( ( times_times_real @ ( abs_abs_real @ Y ) @ X )
% 5.31/5.64 = ( abs_abs_real @ ( times_times_real @ Y @ X ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_mult_pos
% 5.31/5.64 thf(fact_8420_abs__mult__pos,axiom,
% 5.31/5.64 ! [X: rat,Y: rat] :
% 5.31/5.64 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 5.31/5.64 => ( ( times_times_rat @ ( abs_abs_rat @ Y ) @ X )
% 5.31/5.64 = ( abs_abs_rat @ ( times_times_rat @ Y @ X ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_mult_pos
% 5.31/5.64 thf(fact_8421_abs__mult__pos,axiom,
% 5.31/5.64 ! [X: int,Y: int] :
% 5.31/5.64 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.31/5.64 => ( ( times_times_int @ ( abs_abs_int @ Y ) @ X )
% 5.31/5.64 = ( abs_abs_int @ ( times_times_int @ Y @ X ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_mult_pos
% 5.31/5.64 thf(fact_8422_abs__eq__mult,axiom,
% 5.31/5.64 ! [A: code_integer,B: code_integer] :
% 5.31/5.64 ( ( ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 5.31/5.64 | ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger ) )
% 5.31/5.64 & ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B )
% 5.31/5.64 | ( ord_le3102999989581377725nteger @ B @ zero_z3403309356797280102nteger ) ) )
% 5.31/5.64 => ( ( abs_abs_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) )
% 5.31/5.64 = ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_eq_mult
% 5.31/5.64 thf(fact_8423_abs__eq__mult,axiom,
% 5.31/5.64 ! [A: real,B: real] :
% 5.31/5.64 ( ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.31/5.64 | ( ord_less_eq_real @ A @ zero_zero_real ) )
% 5.31/5.64 & ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.31/5.64 | ( ord_less_eq_real @ B @ zero_zero_real ) ) )
% 5.31/5.64 => ( ( abs_abs_real @ ( times_times_real @ A @ B ) )
% 5.31/5.64 = ( times_times_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_eq_mult
% 5.31/5.64 thf(fact_8424_abs__eq__mult,axiom,
% 5.31/5.64 ! [A: rat,B: rat] :
% 5.31/5.64 ( ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.31/5.64 | ( ord_less_eq_rat @ A @ zero_zero_rat ) )
% 5.31/5.64 & ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.31/5.64 | ( ord_less_eq_rat @ B @ zero_zero_rat ) ) )
% 5.31/5.64 => ( ( abs_abs_rat @ ( times_times_rat @ A @ B ) )
% 5.31/5.64 = ( times_times_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_eq_mult
% 5.31/5.64 thf(fact_8425_abs__eq__mult,axiom,
% 5.31/5.64 ! [A: int,B: int] :
% 5.31/5.64 ( ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.31/5.64 | ( ord_less_eq_int @ A @ zero_zero_int ) )
% 5.31/5.64 & ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.31/5.64 | ( ord_less_eq_int @ B @ zero_zero_int ) ) )
% 5.31/5.64 => ( ( abs_abs_int @ ( times_times_int @ A @ B ) )
% 5.31/5.64 = ( times_times_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_eq_mult
% 5.31/5.64 thf(fact_8426_cos__one__sin__zero,axiom,
% 5.31/5.64 ! [X: complex] :
% 5.31/5.64 ( ( ( cos_complex @ X )
% 5.31/5.64 = one_one_complex )
% 5.31/5.64 => ( ( sin_complex @ X )
% 5.31/5.64 = zero_zero_complex ) ) ).
% 5.31/5.64
% 5.31/5.64 % cos_one_sin_zero
% 5.31/5.64 thf(fact_8427_cos__one__sin__zero,axiom,
% 5.31/5.64 ! [X: real] :
% 5.31/5.64 ( ( ( cos_real @ X )
% 5.31/5.64 = one_one_real )
% 5.31/5.64 => ( ( sin_real @ X )
% 5.31/5.64 = zero_zero_real ) ) ).
% 5.31/5.64
% 5.31/5.64 % cos_one_sin_zero
% 5.31/5.64 thf(fact_8428_abs__minus__le__zero,axiom,
% 5.31/5.64 ! [A: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( abs_abs_real @ A ) ) @ zero_zero_real ) ).
% 5.31/5.64
% 5.31/5.64 % abs_minus_le_zero
% 5.31/5.64 thf(fact_8429_abs__minus__le__zero,axiom,
% 5.31/5.64 ! [A: code_integer] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( abs_abs_Code_integer @ A ) ) @ zero_z3403309356797280102nteger ) ).
% 5.31/5.64
% 5.31/5.64 % abs_minus_le_zero
% 5.31/5.64 thf(fact_8430_abs__minus__le__zero,axiom,
% 5.31/5.64 ! [A: rat] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( abs_abs_rat @ A ) ) @ zero_zero_rat ) ).
% 5.31/5.64
% 5.31/5.64 % abs_minus_le_zero
% 5.31/5.64 thf(fact_8431_abs__minus__le__zero,axiom,
% 5.31/5.64 ! [A: int] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( abs_abs_int @ A ) ) @ zero_zero_int ) ).
% 5.31/5.64
% 5.31/5.64 % abs_minus_le_zero
% 5.31/5.64 thf(fact_8432_eq__abs__iff_H,axiom,
% 5.31/5.64 ! [A: real,B: real] :
% 5.31/5.64 ( ( A
% 5.31/5.64 = ( abs_abs_real @ B ) )
% 5.31/5.64 = ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.31/5.64 & ( ( B = A )
% 5.31/5.64 | ( B
% 5.31/5.64 = ( uminus_uminus_real @ A ) ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % eq_abs_iff'
% 5.31/5.64 thf(fact_8433_eq__abs__iff_H,axiom,
% 5.31/5.64 ! [A: code_integer,B: code_integer] :
% 5.31/5.64 ( ( A
% 5.31/5.64 = ( abs_abs_Code_integer @ B ) )
% 5.31/5.64 = ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 5.31/5.64 & ( ( B = A )
% 5.31/5.64 | ( B
% 5.31/5.64 = ( uminus1351360451143612070nteger @ A ) ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % eq_abs_iff'
% 5.31/5.64 thf(fact_8434_eq__abs__iff_H,axiom,
% 5.31/5.64 ! [A: rat,B: rat] :
% 5.31/5.64 ( ( A
% 5.31/5.64 = ( abs_abs_rat @ B ) )
% 5.31/5.64 = ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.31/5.64 & ( ( B = A )
% 5.31/5.64 | ( B
% 5.31/5.64 = ( uminus_uminus_rat @ A ) ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % eq_abs_iff'
% 5.31/5.64 thf(fact_8435_eq__abs__iff_H,axiom,
% 5.31/5.64 ! [A: int,B: int] :
% 5.31/5.64 ( ( A
% 5.31/5.64 = ( abs_abs_int @ B ) )
% 5.31/5.64 = ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.31/5.64 & ( ( B = A )
% 5.31/5.64 | ( B
% 5.31/5.64 = ( uminus_uminus_int @ A ) ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % eq_abs_iff'
% 5.31/5.64 thf(fact_8436_abs__eq__iff_H,axiom,
% 5.31/5.64 ! [A: real,B: real] :
% 5.31/5.64 ( ( ( abs_abs_real @ A )
% 5.31/5.64 = B )
% 5.31/5.64 = ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.31/5.64 & ( ( A = B )
% 5.31/5.64 | ( A
% 5.31/5.64 = ( uminus_uminus_real @ B ) ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_eq_iff'
% 5.31/5.64 thf(fact_8437_abs__eq__iff_H,axiom,
% 5.31/5.64 ! [A: code_integer,B: code_integer] :
% 5.31/5.64 ( ( ( abs_abs_Code_integer @ A )
% 5.31/5.64 = B )
% 5.31/5.64 = ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B )
% 5.31/5.64 & ( ( A = B )
% 5.31/5.64 | ( A
% 5.31/5.64 = ( uminus1351360451143612070nteger @ B ) ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_eq_iff'
% 5.31/5.64 thf(fact_8438_abs__eq__iff_H,axiom,
% 5.31/5.64 ! [A: rat,B: rat] :
% 5.31/5.64 ( ( ( abs_abs_rat @ A )
% 5.31/5.64 = B )
% 5.31/5.64 = ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.31/5.64 & ( ( A = B )
% 5.31/5.64 | ( A
% 5.31/5.64 = ( uminus_uminus_rat @ B ) ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_eq_iff'
% 5.31/5.64 thf(fact_8439_abs__eq__iff_H,axiom,
% 5.31/5.64 ! [A: int,B: int] :
% 5.31/5.64 ( ( ( abs_abs_int @ A )
% 5.31/5.64 = B )
% 5.31/5.64 = ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.31/5.64 & ( ( A = B )
% 5.31/5.64 | ( A
% 5.31/5.64 = ( uminus_uminus_int @ B ) ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_eq_iff'
% 5.31/5.64 thf(fact_8440_abs__div__pos,axiom,
% 5.31/5.64 ! [Y: real,X: real] :
% 5.31/5.64 ( ( ord_less_real @ zero_zero_real @ Y )
% 5.31/5.64 => ( ( divide_divide_real @ ( abs_abs_real @ X ) @ Y )
% 5.31/5.64 = ( abs_abs_real @ ( divide_divide_real @ X @ Y ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_div_pos
% 5.31/5.64 thf(fact_8441_abs__div__pos,axiom,
% 5.31/5.64 ! [Y: rat,X: rat] :
% 5.31/5.64 ( ( ord_less_rat @ zero_zero_rat @ Y )
% 5.31/5.64 => ( ( divide_divide_rat @ ( abs_abs_rat @ X ) @ Y )
% 5.31/5.64 = ( abs_abs_rat @ ( divide_divide_rat @ X @ Y ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_div_pos
% 5.31/5.64 thf(fact_8442_zero__le__power__abs,axiom,
% 5.31/5.64 ! [A: code_integer,N: nat] : ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( power_8256067586552552935nteger @ ( abs_abs_Code_integer @ A ) @ N ) ) ).
% 5.31/5.64
% 5.31/5.64 % zero_le_power_abs
% 5.31/5.64 thf(fact_8443_zero__le__power__abs,axiom,
% 5.31/5.64 ! [A: real,N: nat] : ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ ( abs_abs_real @ A ) @ N ) ) ).
% 5.31/5.64
% 5.31/5.64 % zero_le_power_abs
% 5.31/5.64 thf(fact_8444_zero__le__power__abs,axiom,
% 5.31/5.64 ! [A: rat,N: nat] : ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ ( abs_abs_rat @ A ) @ N ) ) ).
% 5.31/5.64
% 5.31/5.64 % zero_le_power_abs
% 5.31/5.64 thf(fact_8445_zero__le__power__abs,axiom,
% 5.31/5.64 ! [A: int,N: nat] : ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ ( abs_abs_int @ A ) @ N ) ) ).
% 5.31/5.64
% 5.31/5.64 % zero_le_power_abs
% 5.31/5.64 thf(fact_8446_abs__if__raw,axiom,
% 5.31/5.64 ( abs_abs_int
% 5.31/5.64 = ( ^ [A5: int] : ( if_int @ ( ord_less_int @ A5 @ zero_zero_int ) @ ( uminus_uminus_int @ A5 ) @ A5 ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_if_raw
% 5.31/5.64 thf(fact_8447_abs__if__raw,axiom,
% 5.31/5.64 ( abs_abs_real
% 5.31/5.64 = ( ^ [A5: real] : ( if_real @ ( ord_less_real @ A5 @ zero_zero_real ) @ ( uminus_uminus_real @ A5 ) @ A5 ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_if_raw
% 5.31/5.64 thf(fact_8448_abs__if__raw,axiom,
% 5.31/5.64 ( abs_abs_Code_integer
% 5.31/5.64 = ( ^ [A5: code_integer] : ( if_Code_integer @ ( ord_le6747313008572928689nteger @ A5 @ zero_z3403309356797280102nteger ) @ ( uminus1351360451143612070nteger @ A5 ) @ A5 ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_if_raw
% 5.31/5.64 thf(fact_8449_abs__if__raw,axiom,
% 5.31/5.64 ( abs_abs_rat
% 5.31/5.64 = ( ^ [A5: rat] : ( if_rat @ ( ord_less_rat @ A5 @ zero_zero_rat ) @ ( uminus_uminus_rat @ A5 ) @ A5 ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_if_raw
% 5.31/5.64 thf(fact_8450_abs__if,axiom,
% 5.31/5.64 ( abs_abs_int
% 5.31/5.64 = ( ^ [A5: int] : ( if_int @ ( ord_less_int @ A5 @ zero_zero_int ) @ ( uminus_uminus_int @ A5 ) @ A5 ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_if
% 5.31/5.64 thf(fact_8451_abs__if,axiom,
% 5.31/5.64 ( abs_abs_real
% 5.31/5.64 = ( ^ [A5: real] : ( if_real @ ( ord_less_real @ A5 @ zero_zero_real ) @ ( uminus_uminus_real @ A5 ) @ A5 ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_if
% 5.31/5.64 thf(fact_8452_abs__if,axiom,
% 5.31/5.64 ( abs_abs_Code_integer
% 5.31/5.64 = ( ^ [A5: code_integer] : ( if_Code_integer @ ( ord_le6747313008572928689nteger @ A5 @ zero_z3403309356797280102nteger ) @ ( uminus1351360451143612070nteger @ A5 ) @ A5 ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_if
% 5.31/5.64 thf(fact_8453_abs__if,axiom,
% 5.31/5.64 ( abs_abs_rat
% 5.31/5.64 = ( ^ [A5: rat] : ( if_rat @ ( ord_less_rat @ A5 @ zero_zero_rat ) @ ( uminus_uminus_rat @ A5 ) @ A5 ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_if
% 5.31/5.64 thf(fact_8454_abs__of__neg,axiom,
% 5.31/5.64 ! [A: int] :
% 5.31/5.64 ( ( ord_less_int @ A @ zero_zero_int )
% 5.31/5.64 => ( ( abs_abs_int @ A )
% 5.31/5.64 = ( uminus_uminus_int @ A ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_of_neg
% 5.31/5.64 thf(fact_8455_abs__of__neg,axiom,
% 5.31/5.64 ! [A: real] :
% 5.31/5.64 ( ( ord_less_real @ A @ zero_zero_real )
% 5.31/5.64 => ( ( abs_abs_real @ A )
% 5.31/5.64 = ( uminus_uminus_real @ A ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_of_neg
% 5.31/5.64 thf(fact_8456_abs__of__neg,axiom,
% 5.31/5.64 ! [A: code_integer] :
% 5.31/5.64 ( ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger )
% 5.31/5.64 => ( ( abs_abs_Code_integer @ A )
% 5.31/5.64 = ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_of_neg
% 5.31/5.64 thf(fact_8457_abs__of__neg,axiom,
% 5.31/5.64 ! [A: rat] :
% 5.31/5.64 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.31/5.64 => ( ( abs_abs_rat @ A )
% 5.31/5.64 = ( uminus_uminus_rat @ A ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_of_neg
% 5.31/5.64 thf(fact_8458_sin__add,axiom,
% 5.31/5.64 ! [X: real,Y: real] :
% 5.31/5.64 ( ( sin_real @ ( plus_plus_real @ X @ Y ) )
% 5.31/5.64 = ( plus_plus_real @ ( times_times_real @ ( sin_real @ X ) @ ( cos_real @ Y ) ) @ ( times_times_real @ ( cos_real @ X ) @ ( sin_real @ Y ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % sin_add
% 5.31/5.64 thf(fact_8459_abs__diff__le__iff,axiom,
% 5.31/5.64 ! [X: code_integer,A: code_integer,R3: code_integer] :
% 5.31/5.64 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ X @ A ) ) @ R3 )
% 5.31/5.64 = ( ( ord_le3102999989581377725nteger @ ( minus_8373710615458151222nteger @ A @ R3 ) @ X )
% 5.31/5.64 & ( ord_le3102999989581377725nteger @ X @ ( plus_p5714425477246183910nteger @ A @ R3 ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_diff_le_iff
% 5.31/5.64 thf(fact_8460_abs__diff__le__iff,axiom,
% 5.31/5.64 ! [X: real,A: real,R3: real] :
% 5.31/5.64 ( ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ X @ A ) ) @ R3 )
% 5.31/5.64 = ( ( ord_less_eq_real @ ( minus_minus_real @ A @ R3 ) @ X )
% 5.31/5.64 & ( ord_less_eq_real @ X @ ( plus_plus_real @ A @ R3 ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_diff_le_iff
% 5.31/5.64 thf(fact_8461_abs__diff__le__iff,axiom,
% 5.31/5.64 ! [X: rat,A: rat,R3: rat] :
% 5.31/5.64 ( ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ X @ A ) ) @ R3 )
% 5.31/5.64 = ( ( ord_less_eq_rat @ ( minus_minus_rat @ A @ R3 ) @ X )
% 5.31/5.64 & ( ord_less_eq_rat @ X @ ( plus_plus_rat @ A @ R3 ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_diff_le_iff
% 5.31/5.64 thf(fact_8462_abs__diff__le__iff,axiom,
% 5.31/5.64 ! [X: int,A: int,R3: int] :
% 5.31/5.64 ( ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ X @ A ) ) @ R3 )
% 5.31/5.64 = ( ( ord_less_eq_int @ ( minus_minus_int @ A @ R3 ) @ X )
% 5.31/5.64 & ( ord_less_eq_int @ X @ ( plus_plus_int @ A @ R3 ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_diff_le_iff
% 5.31/5.64 thf(fact_8463_abs__diff__triangle__ineq,axiom,
% 5.31/5.64 ! [A: code_integer,B: code_integer,C2: code_integer,D: code_integer] : ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ ( plus_p5714425477246183910nteger @ C2 @ D ) ) ) @ ( plus_p5714425477246183910nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ A @ C2 ) ) @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ B @ D ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_diff_triangle_ineq
% 5.31/5.64 thf(fact_8464_abs__diff__triangle__ineq,axiom,
% 5.31/5.64 ! [A: real,B: real,C2: real,D: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ C2 @ D ) ) ) @ ( plus_plus_real @ ( abs_abs_real @ ( minus_minus_real @ A @ C2 ) ) @ ( abs_abs_real @ ( minus_minus_real @ B @ D ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_diff_triangle_ineq
% 5.31/5.64 thf(fact_8465_abs__diff__triangle__ineq,axiom,
% 5.31/5.64 ! [A: rat,B: rat,C2: rat,D: rat] : ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ ( plus_plus_rat @ C2 @ D ) ) ) @ ( plus_plus_rat @ ( abs_abs_rat @ ( minus_minus_rat @ A @ C2 ) ) @ ( abs_abs_rat @ ( minus_minus_rat @ B @ D ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_diff_triangle_ineq
% 5.31/5.64 thf(fact_8466_abs__diff__triangle__ineq,axiom,
% 5.31/5.64 ! [A: int,B: int,C2: int,D: int] : ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ ( plus_plus_int @ C2 @ D ) ) ) @ ( plus_plus_int @ ( abs_abs_int @ ( minus_minus_int @ A @ C2 ) ) @ ( abs_abs_int @ ( minus_minus_int @ B @ D ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_diff_triangle_ineq
% 5.31/5.64 thf(fact_8467_abs__triangle__ineq4,axiom,
% 5.31/5.64 ! [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 ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_triangle_ineq4
% 5.31/5.64 thf(fact_8468_abs__triangle__ineq4,axiom,
% 5.31/5.64 ! [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 ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_triangle_ineq4
% 5.31/5.64 thf(fact_8469_abs__triangle__ineq4,axiom,
% 5.31/5.64 ! [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 ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_triangle_ineq4
% 5.31/5.64 thf(fact_8470_abs__triangle__ineq4,axiom,
% 5.31/5.64 ! [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 ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_triangle_ineq4
% 5.31/5.64 thf(fact_8471_sin__diff,axiom,
% 5.31/5.64 ! [X: real,Y: real] :
% 5.31/5.64 ( ( sin_real @ ( minus_minus_real @ X @ Y ) )
% 5.31/5.64 = ( minus_minus_real @ ( times_times_real @ ( sin_real @ X ) @ ( cos_real @ Y ) ) @ ( times_times_real @ ( cos_real @ X ) @ ( sin_real @ Y ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % sin_diff
% 5.31/5.64 thf(fact_8472_abs__diff__less__iff,axiom,
% 5.31/5.64 ! [X: code_integer,A: code_integer,R3: code_integer] :
% 5.31/5.64 ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ X @ A ) ) @ R3 )
% 5.31/5.64 = ( ( ord_le6747313008572928689nteger @ ( minus_8373710615458151222nteger @ A @ R3 ) @ X )
% 5.31/5.64 & ( ord_le6747313008572928689nteger @ X @ ( plus_p5714425477246183910nteger @ A @ R3 ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_diff_less_iff
% 5.31/5.64 thf(fact_8473_abs__diff__less__iff,axiom,
% 5.31/5.64 ! [X: real,A: real,R3: real] :
% 5.31/5.64 ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X @ A ) ) @ R3 )
% 5.31/5.64 = ( ( ord_less_real @ ( minus_minus_real @ A @ R3 ) @ X )
% 5.31/5.64 & ( ord_less_real @ X @ ( plus_plus_real @ A @ R3 ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_diff_less_iff
% 5.31/5.64 thf(fact_8474_abs__diff__less__iff,axiom,
% 5.31/5.64 ! [X: rat,A: rat,R3: rat] :
% 5.31/5.64 ( ( ord_less_rat @ ( abs_abs_rat @ ( minus_minus_rat @ X @ A ) ) @ R3 )
% 5.31/5.64 = ( ( ord_less_rat @ ( minus_minus_rat @ A @ R3 ) @ X )
% 5.31/5.64 & ( ord_less_rat @ X @ ( plus_plus_rat @ A @ R3 ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_diff_less_iff
% 5.31/5.64 thf(fact_8475_abs__diff__less__iff,axiom,
% 5.31/5.64 ! [X: int,A: int,R3: int] :
% 5.31/5.64 ( ( ord_less_int @ ( abs_abs_int @ ( minus_minus_int @ X @ A ) ) @ R3 )
% 5.31/5.64 = ( ( ord_less_int @ ( minus_minus_int @ A @ R3 ) @ X )
% 5.31/5.64 & ( ord_less_int @ X @ ( plus_plus_int @ A @ R3 ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_diff_less_iff
% 5.31/5.64 thf(fact_8476_pred__numeral__def,axiom,
% 5.31/5.64 ( pred_numeral
% 5.31/5.64 = ( ^ [K3: num] : ( minus_minus_nat @ ( numeral_numeral_nat @ K3 ) @ one_one_nat ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % pred_numeral_def
% 5.31/5.64 thf(fact_8477_lessThan__nat__numeral,axiom,
% 5.31/5.64 ! [K2: num] :
% 5.31/5.64 ( ( set_ord_lessThan_nat @ ( numeral_numeral_nat @ K2 ) )
% 5.31/5.64 = ( insert_nat @ ( pred_numeral @ K2 ) @ ( set_ord_lessThan_nat @ ( pred_numeral @ K2 ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % lessThan_nat_numeral
% 5.31/5.64 thf(fact_8478_atMost__nat__numeral,axiom,
% 5.31/5.64 ! [K2: num] :
% 5.31/5.64 ( ( set_ord_atMost_nat @ ( numeral_numeral_nat @ K2 ) )
% 5.31/5.64 = ( insert_nat @ ( numeral_numeral_nat @ K2 ) @ ( set_ord_atMost_nat @ ( pred_numeral @ K2 ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % atMost_nat_numeral
% 5.31/5.64 thf(fact_8479_cos__add,axiom,
% 5.31/5.64 ! [X: real,Y: real] :
% 5.31/5.64 ( ( cos_real @ ( plus_plus_real @ X @ Y ) )
% 5.31/5.64 = ( minus_minus_real @ ( times_times_real @ ( cos_real @ X ) @ ( cos_real @ Y ) ) @ ( times_times_real @ ( sin_real @ X ) @ ( sin_real @ Y ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % cos_add
% 5.31/5.64 thf(fact_8480_cos__diff,axiom,
% 5.31/5.64 ! [X: real,Y: real] :
% 5.31/5.64 ( ( cos_real @ ( minus_minus_real @ X @ Y ) )
% 5.31/5.64 = ( plus_plus_real @ ( times_times_real @ ( cos_real @ X ) @ ( cos_real @ Y ) ) @ ( times_times_real @ ( sin_real @ X ) @ ( sin_real @ Y ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % cos_diff
% 5.31/5.64 thf(fact_8481_abs__add__one__gt__zero,axiom,
% 5.31/5.64 ! [X: code_integer] : ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( abs_abs_Code_integer @ X ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_add_one_gt_zero
% 5.31/5.64 thf(fact_8482_abs__add__one__gt__zero,axiom,
% 5.31/5.64 ! [X: real] : ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ one_one_real @ ( abs_abs_real @ X ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_add_one_gt_zero
% 5.31/5.64 thf(fact_8483_abs__add__one__gt__zero,axiom,
% 5.31/5.64 ! [X: rat] : ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ one_one_rat @ ( abs_abs_rat @ X ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_add_one_gt_zero
% 5.31/5.64 thf(fact_8484_abs__add__one__gt__zero,axiom,
% 5.31/5.64 ! [X: int] : ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ ( abs_abs_int @ X ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_add_one_gt_zero
% 5.31/5.64 thf(fact_8485_sin__zero__norm__cos__one,axiom,
% 5.31/5.64 ! [X: real] :
% 5.31/5.64 ( ( ( sin_real @ X )
% 5.31/5.64 = zero_zero_real )
% 5.31/5.64 => ( ( real_V7735802525324610683m_real @ ( cos_real @ X ) )
% 5.31/5.64 = one_one_real ) ) ).
% 5.31/5.64
% 5.31/5.64 % sin_zero_norm_cos_one
% 5.31/5.64 thf(fact_8486_sin__zero__norm__cos__one,axiom,
% 5.31/5.64 ! [X: complex] :
% 5.31/5.64 ( ( ( sin_complex @ X )
% 5.31/5.64 = zero_zero_complex )
% 5.31/5.64 => ( ( real_V1022390504157884413omplex @ ( cos_complex @ X ) )
% 5.31/5.64 = one_one_real ) ) ).
% 5.31/5.64
% 5.31/5.64 % sin_zero_norm_cos_one
% 5.31/5.64 thf(fact_8487_fact__numeral,axiom,
% 5.31/5.64 ! [K2: num] :
% 5.31/5.64 ( ( semiri773545260158071498ct_rat @ ( numeral_numeral_nat @ K2 ) )
% 5.31/5.64 = ( times_times_rat @ ( numeral_numeral_rat @ K2 ) @ ( semiri773545260158071498ct_rat @ ( pred_numeral @ K2 ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % fact_numeral
% 5.31/5.64 thf(fact_8488_fact__numeral,axiom,
% 5.31/5.64 ! [K2: num] :
% 5.31/5.64 ( ( semiri4449623510593786356d_enat @ ( numeral_numeral_nat @ K2 ) )
% 5.31/5.64 = ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ K2 ) @ ( semiri4449623510593786356d_enat @ ( pred_numeral @ K2 ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % fact_numeral
% 5.31/5.64 thf(fact_8489_fact__numeral,axiom,
% 5.31/5.64 ! [K2: num] :
% 5.31/5.64 ( ( semiri5044797733671781792omplex @ ( numeral_numeral_nat @ K2 ) )
% 5.31/5.64 = ( times_times_complex @ ( numera6690914467698888265omplex @ K2 ) @ ( semiri5044797733671781792omplex @ ( pred_numeral @ K2 ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % fact_numeral
% 5.31/5.64 thf(fact_8490_fact__numeral,axiom,
% 5.31/5.64 ! [K2: num] :
% 5.31/5.64 ( ( semiri1406184849735516958ct_int @ ( numeral_numeral_nat @ K2 ) )
% 5.31/5.64 = ( times_times_int @ ( numeral_numeral_int @ K2 ) @ ( semiri1406184849735516958ct_int @ ( pred_numeral @ K2 ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % fact_numeral
% 5.31/5.64 thf(fact_8491_fact__numeral,axiom,
% 5.31/5.64 ! [K2: num] :
% 5.31/5.64 ( ( semiri1408675320244567234ct_nat @ ( numeral_numeral_nat @ K2 ) )
% 5.31/5.64 = ( times_times_nat @ ( numeral_numeral_nat @ K2 ) @ ( semiri1408675320244567234ct_nat @ ( pred_numeral @ K2 ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % fact_numeral
% 5.31/5.64 thf(fact_8492_fact__numeral,axiom,
% 5.31/5.64 ! [K2: num] :
% 5.31/5.64 ( ( semiri2265585572941072030t_real @ ( numeral_numeral_nat @ K2 ) )
% 5.31/5.64 = ( times_times_real @ ( numeral_numeral_real @ K2 ) @ ( semiri2265585572941072030t_real @ ( pred_numeral @ K2 ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % fact_numeral
% 5.31/5.64 thf(fact_8493_sin__double,axiom,
% 5.31/5.64 ! [X: complex] :
% 5.31/5.64 ( ( sin_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X ) )
% 5.31/5.64 = ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( sin_complex @ X ) ) @ ( cos_complex @ X ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % sin_double
% 5.31/5.64 thf(fact_8494_sin__double,axiom,
% 5.31/5.64 ! [X: real] :
% 5.31/5.64 ( ( sin_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) )
% 5.31/5.64 = ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( sin_real @ X ) ) @ ( cos_real @ X ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % sin_double
% 5.31/5.64 thf(fact_8495_abs__le__square__iff,axiom,
% 5.31/5.64 ! [X: code_integer,Y: code_integer] :
% 5.31/5.64 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ X ) @ ( abs_abs_Code_integer @ Y ) )
% 5.31/5.64 = ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_8256067586552552935nteger @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_le_square_iff
% 5.31/5.64 thf(fact_8496_abs__le__square__iff,axiom,
% 5.31/5.64 ! [X: real,Y: real] :
% 5.31/5.64 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ ( abs_abs_real @ Y ) )
% 5.31/5.64 = ( ord_less_eq_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_le_square_iff
% 5.31/5.64 thf(fact_8497_abs__le__square__iff,axiom,
% 5.31/5.64 ! [X: rat,Y: rat] :
% 5.31/5.64 ( ( ord_less_eq_rat @ ( abs_abs_rat @ X ) @ ( abs_abs_rat @ Y ) )
% 5.31/5.64 = ( ord_less_eq_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_le_square_iff
% 5.31/5.64 thf(fact_8498_abs__le__square__iff,axiom,
% 5.31/5.64 ! [X: int,Y: int] :
% 5.31/5.64 ( ( ord_less_eq_int @ ( abs_abs_int @ X ) @ ( abs_abs_int @ Y ) )
% 5.31/5.64 = ( ord_less_eq_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_le_square_iff
% 5.31/5.64 thf(fact_8499_divmod__int__def,axiom,
% 5.31/5.64 ( unique5052692396658037445od_int
% 5.31/5.64 = ( ^ [M6: num,N4: num] : ( product_Pair_int_int @ ( divide_divide_int @ ( numeral_numeral_int @ M6 ) @ ( numeral_numeral_int @ N4 ) ) @ ( modulo_modulo_int @ ( numeral_numeral_int @ M6 ) @ ( numeral_numeral_int @ N4 ) ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % divmod_int_def
% 5.31/5.64 thf(fact_8500_abs__sqrt__wlog,axiom,
% 5.31/5.64 ! [P2: code_integer > code_integer > $o,X: code_integer] :
% 5.31/5.64 ( ! [X3: code_integer] :
% 5.31/5.64 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ X3 )
% 5.31/5.64 => ( P2 @ X3 @ ( power_8256067586552552935nteger @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.31/5.64 => ( P2 @ ( abs_abs_Code_integer @ X ) @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_sqrt_wlog
% 5.31/5.64 thf(fact_8501_abs__sqrt__wlog,axiom,
% 5.31/5.64 ! [P2: real > real > $o,X: real] :
% 5.31/5.64 ( ! [X3: real] :
% 5.31/5.64 ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 5.31/5.64 => ( P2 @ X3 @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.31/5.64 => ( P2 @ ( abs_abs_real @ X ) @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_sqrt_wlog
% 5.31/5.64 thf(fact_8502_abs__sqrt__wlog,axiom,
% 5.31/5.64 ! [P2: rat > rat > $o,X: rat] :
% 5.31/5.64 ( ! [X3: rat] :
% 5.31/5.64 ( ( ord_less_eq_rat @ zero_zero_rat @ X3 )
% 5.31/5.64 => ( P2 @ X3 @ ( power_power_rat @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.31/5.64 => ( P2 @ ( abs_abs_rat @ X ) @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_sqrt_wlog
% 5.31/5.64 thf(fact_8503_abs__sqrt__wlog,axiom,
% 5.31/5.64 ! [P2: int > int > $o,X: int] :
% 5.31/5.64 ( ! [X3: int] :
% 5.31/5.64 ( ( ord_less_eq_int @ zero_zero_int @ X3 )
% 5.31/5.64 => ( P2 @ X3 @ ( power_power_int @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.31/5.64 => ( P2 @ ( abs_abs_int @ X ) @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_sqrt_wlog
% 5.31/5.64 thf(fact_8504_power2__le__iff__abs__le,axiom,
% 5.31/5.64 ! [Y: code_integer,X: code_integer] :
% 5.31/5.64 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ Y )
% 5.31/5.64 => ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_8256067586552552935nteger @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.31/5.64 = ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ X ) @ Y ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % power2_le_iff_abs_le
% 5.31/5.64 thf(fact_8505_power2__le__iff__abs__le,axiom,
% 5.31/5.64 ! [Y: real,X: real] :
% 5.31/5.64 ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.31/5.64 => ( ( ord_less_eq_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.31/5.64 = ( ord_less_eq_real @ ( abs_abs_real @ X ) @ Y ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % power2_le_iff_abs_le
% 5.31/5.64 thf(fact_8506_power2__le__iff__abs__le,axiom,
% 5.31/5.64 ! [Y: rat,X: rat] :
% 5.31/5.64 ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 5.31/5.64 => ( ( ord_less_eq_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.31/5.64 = ( ord_less_eq_rat @ ( abs_abs_rat @ X ) @ Y ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % power2_le_iff_abs_le
% 5.31/5.64 thf(fact_8507_power2__le__iff__abs__le,axiom,
% 5.31/5.64 ! [Y: int,X: int] :
% 5.31/5.64 ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.31/5.64 => ( ( ord_less_eq_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.31/5.64 = ( ord_less_eq_int @ ( abs_abs_int @ X ) @ Y ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % power2_le_iff_abs_le
% 5.31/5.64 thf(fact_8508_abs__square__le__1,axiom,
% 5.31/5.64 ! [X: code_integer] :
% 5.31/5.64 ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_Code_integer )
% 5.31/5.64 = ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ X ) @ one_one_Code_integer ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_square_le_1
% 5.31/5.64 thf(fact_8509_abs__square__le__1,axiom,
% 5.31/5.64 ! [X: real] :
% 5.31/5.64 ( ( ord_less_eq_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real )
% 5.31/5.64 = ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_square_le_1
% 5.31/5.64 thf(fact_8510_abs__square__le__1,axiom,
% 5.31/5.64 ! [X: rat] :
% 5.31/5.64 ( ( ord_less_eq_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_rat )
% 5.31/5.64 = ( ord_less_eq_rat @ ( abs_abs_rat @ X ) @ one_one_rat ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_square_le_1
% 5.31/5.64 thf(fact_8511_abs__square__le__1,axiom,
% 5.31/5.64 ! [X: int] :
% 5.31/5.64 ( ( ord_less_eq_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_int )
% 5.31/5.64 = ( ord_less_eq_int @ ( abs_abs_int @ X ) @ one_one_int ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_square_le_1
% 5.31/5.64 thf(fact_8512_divmod__def,axiom,
% 5.31/5.64 ( unique3479559517661332726nteger
% 5.31/5.64 = ( ^ [M6: num,N4: num] : ( produc1086072967326762835nteger @ ( divide6298287555418463151nteger @ ( numera6620942414471956472nteger @ M6 ) @ ( numera6620942414471956472nteger @ N4 ) ) @ ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ M6 ) @ ( numera6620942414471956472nteger @ N4 ) ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % divmod_def
% 5.31/5.64 thf(fact_8513_divmod__def,axiom,
% 5.31/5.64 ( unique5052692396658037445od_int
% 5.31/5.64 = ( ^ [M6: num,N4: num] : ( product_Pair_int_int @ ( divide_divide_int @ ( numeral_numeral_int @ M6 ) @ ( numeral_numeral_int @ N4 ) ) @ ( modulo_modulo_int @ ( numeral_numeral_int @ M6 ) @ ( numeral_numeral_int @ N4 ) ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % divmod_def
% 5.31/5.64 thf(fact_8514_divmod__def,axiom,
% 5.31/5.64 ( unique5055182867167087721od_nat
% 5.31/5.64 = ( ^ [M6: num,N4: num] : ( product_Pair_nat_nat @ ( divide_divide_nat @ ( numeral_numeral_nat @ M6 ) @ ( numeral_numeral_nat @ N4 ) ) @ ( modulo_modulo_nat @ ( numeral_numeral_nat @ M6 ) @ ( numeral_numeral_nat @ N4 ) ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % divmod_def
% 5.31/5.64 thf(fact_8515_divmod_H__nat__def,axiom,
% 5.31/5.64 ( unique5055182867167087721od_nat
% 5.31/5.64 = ( ^ [M6: num,N4: num] : ( product_Pair_nat_nat @ ( divide_divide_nat @ ( numeral_numeral_nat @ M6 ) @ ( numeral_numeral_nat @ N4 ) ) @ ( modulo_modulo_nat @ ( numeral_numeral_nat @ M6 ) @ ( numeral_numeral_nat @ N4 ) ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % divmod'_nat_def
% 5.31/5.64 thf(fact_8516_power__mono__even,axiom,
% 5.31/5.64 ! [N: nat,A: code_integer,B: code_integer] :
% 5.31/5.64 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.31/5.64 => ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) )
% 5.31/5.64 => ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ A @ N ) @ ( power_8256067586552552935nteger @ B @ N ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % power_mono_even
% 5.31/5.64 thf(fact_8517_power__mono__even,axiom,
% 5.31/5.64 ! [N: nat,A: real,B: real] :
% 5.31/5.64 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.31/5.64 => ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) )
% 5.31/5.64 => ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % power_mono_even
% 5.31/5.64 thf(fact_8518_power__mono__even,axiom,
% 5.31/5.64 ! [N: nat,A: rat,B: rat] :
% 5.31/5.64 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.31/5.64 => ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) )
% 5.31/5.64 => ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % power_mono_even
% 5.31/5.64 thf(fact_8519_power__mono__even,axiom,
% 5.31/5.64 ! [N: nat,A: int,B: int] :
% 5.31/5.64 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.31/5.64 => ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) )
% 5.31/5.64 => ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % power_mono_even
% 5.31/5.64 thf(fact_8520_convex__sum__bound__le,axiom,
% 5.31/5.64 ! [I5: set_complex,X: complex > code_integer,A: complex > code_integer,B: code_integer,Delta: code_integer] :
% 5.31/5.64 ( ! [I3: complex] :
% 5.31/5.64 ( ( member_complex @ I3 @ I5 )
% 5.31/5.64 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( X @ I3 ) ) )
% 5.31/5.64 => ( ( ( groups6621422865394947399nteger @ X @ I5 )
% 5.31/5.64 = one_one_Code_integer )
% 5.31/5.64 => ( ! [I3: complex] :
% 5.31/5.64 ( ( member_complex @ I3 @ I5 )
% 5.31/5.64 => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( A @ I3 ) @ B ) ) @ Delta ) )
% 5.31/5.64 => ( ord_le3102999989581377725nteger
% 5.31/5.64 @ ( abs_abs_Code_integer
% 5.31/5.64 @ ( minus_8373710615458151222nteger
% 5.31/5.64 @ ( groups6621422865394947399nteger
% 5.31/5.64 @ ^ [I: complex] : ( times_3573771949741848930nteger @ ( A @ I ) @ ( X @ I ) )
% 5.31/5.64 @ I5 )
% 5.31/5.64 @ B ) )
% 5.31/5.64 @ Delta ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % convex_sum_bound_le
% 5.31/5.64 thf(fact_8521_convex__sum__bound__le,axiom,
% 5.31/5.64 ! [I5: set_real,X: real > code_integer,A: real > code_integer,B: code_integer,Delta: code_integer] :
% 5.31/5.64 ( ! [I3: real] :
% 5.31/5.64 ( ( member_real @ I3 @ I5 )
% 5.31/5.64 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( X @ I3 ) ) )
% 5.31/5.64 => ( ( ( groups7713935264441627589nteger @ X @ I5 )
% 5.31/5.64 = one_one_Code_integer )
% 5.31/5.64 => ( ! [I3: real] :
% 5.31/5.64 ( ( member_real @ I3 @ I5 )
% 5.31/5.64 => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( A @ I3 ) @ B ) ) @ Delta ) )
% 5.31/5.64 => ( ord_le3102999989581377725nteger
% 5.31/5.64 @ ( abs_abs_Code_integer
% 5.31/5.64 @ ( minus_8373710615458151222nteger
% 5.31/5.64 @ ( groups7713935264441627589nteger
% 5.31/5.64 @ ^ [I: real] : ( times_3573771949741848930nteger @ ( A @ I ) @ ( X @ I ) )
% 5.31/5.64 @ I5 )
% 5.31/5.64 @ B ) )
% 5.31/5.64 @ Delta ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % convex_sum_bound_le
% 5.31/5.64 thf(fact_8522_convex__sum__bound__le,axiom,
% 5.31/5.64 ! [I5: set_nat,X: nat > code_integer,A: nat > code_integer,B: code_integer,Delta: code_integer] :
% 5.31/5.64 ( ! [I3: nat] :
% 5.31/5.64 ( ( member_nat @ I3 @ I5 )
% 5.31/5.64 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( X @ I3 ) ) )
% 5.31/5.64 => ( ( ( groups7501900531339628137nteger @ X @ I5 )
% 5.31/5.64 = one_one_Code_integer )
% 5.31/5.64 => ( ! [I3: nat] :
% 5.31/5.64 ( ( member_nat @ I3 @ I5 )
% 5.31/5.64 => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( A @ I3 ) @ B ) ) @ Delta ) )
% 5.31/5.64 => ( ord_le3102999989581377725nteger
% 5.31/5.64 @ ( abs_abs_Code_integer
% 5.31/5.64 @ ( minus_8373710615458151222nteger
% 5.31/5.64 @ ( groups7501900531339628137nteger
% 5.31/5.64 @ ^ [I: nat] : ( times_3573771949741848930nteger @ ( A @ I ) @ ( X @ I ) )
% 5.31/5.64 @ I5 )
% 5.31/5.64 @ B ) )
% 5.31/5.64 @ Delta ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % convex_sum_bound_le
% 5.31/5.64 thf(fact_8523_convex__sum__bound__le,axiom,
% 5.31/5.64 ! [I5: set_int,X: int > code_integer,A: int > code_integer,B: code_integer,Delta: code_integer] :
% 5.31/5.64 ( ! [I3: int] :
% 5.31/5.64 ( ( member_int @ I3 @ I5 )
% 5.31/5.64 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( X @ I3 ) ) )
% 5.31/5.64 => ( ( ( groups7873554091576472773nteger @ X @ I5 )
% 5.31/5.64 = one_one_Code_integer )
% 5.31/5.64 => ( ! [I3: int] :
% 5.31/5.64 ( ( member_int @ I3 @ I5 )
% 5.31/5.64 => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( A @ I3 ) @ B ) ) @ Delta ) )
% 5.31/5.64 => ( ord_le3102999989581377725nteger
% 5.31/5.64 @ ( abs_abs_Code_integer
% 5.31/5.64 @ ( minus_8373710615458151222nteger
% 5.31/5.64 @ ( groups7873554091576472773nteger
% 5.31/5.64 @ ^ [I: int] : ( times_3573771949741848930nteger @ ( A @ I ) @ ( X @ I ) )
% 5.31/5.64 @ I5 )
% 5.31/5.64 @ B ) )
% 5.31/5.64 @ Delta ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % convex_sum_bound_le
% 5.31/5.64 thf(fact_8524_convex__sum__bound__le,axiom,
% 5.31/5.64 ! [I5: set_complex,X: complex > real,A: complex > real,B: real,Delta: real] :
% 5.31/5.64 ( ! [I3: complex] :
% 5.31/5.64 ( ( member_complex @ I3 @ I5 )
% 5.31/5.64 => ( ord_less_eq_real @ zero_zero_real @ ( X @ I3 ) ) )
% 5.31/5.64 => ( ( ( groups5808333547571424918x_real @ X @ I5 )
% 5.31/5.64 = one_one_real )
% 5.31/5.64 => ( ! [I3: complex] :
% 5.31/5.64 ( ( member_complex @ I3 @ I5 )
% 5.31/5.64 => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( A @ I3 ) @ B ) ) @ Delta ) )
% 5.31/5.64 => ( ord_less_eq_real
% 5.31/5.64 @ ( abs_abs_real
% 5.31/5.64 @ ( minus_minus_real
% 5.31/5.64 @ ( groups5808333547571424918x_real
% 5.31/5.64 @ ^ [I: complex] : ( times_times_real @ ( A @ I ) @ ( X @ I ) )
% 5.31/5.64 @ I5 )
% 5.31/5.64 @ B ) )
% 5.31/5.64 @ Delta ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % convex_sum_bound_le
% 5.31/5.64 thf(fact_8525_convex__sum__bound__le,axiom,
% 5.31/5.64 ! [I5: set_real,X: real > real,A: real > real,B: real,Delta: real] :
% 5.31/5.64 ( ! [I3: real] :
% 5.31/5.64 ( ( member_real @ I3 @ I5 )
% 5.31/5.64 => ( ord_less_eq_real @ zero_zero_real @ ( X @ I3 ) ) )
% 5.31/5.64 => ( ( ( groups8097168146408367636l_real @ X @ I5 )
% 5.31/5.64 = one_one_real )
% 5.31/5.64 => ( ! [I3: real] :
% 5.31/5.64 ( ( member_real @ I3 @ I5 )
% 5.31/5.64 => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( A @ I3 ) @ B ) ) @ Delta ) )
% 5.31/5.64 => ( ord_less_eq_real
% 5.31/5.64 @ ( abs_abs_real
% 5.31/5.64 @ ( minus_minus_real
% 5.31/5.64 @ ( groups8097168146408367636l_real
% 5.31/5.64 @ ^ [I: real] : ( times_times_real @ ( A @ I ) @ ( X @ I ) )
% 5.31/5.64 @ I5 )
% 5.31/5.64 @ B ) )
% 5.31/5.64 @ Delta ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % convex_sum_bound_le
% 5.31/5.64 thf(fact_8526_convex__sum__bound__le,axiom,
% 5.31/5.64 ! [I5: set_int,X: int > real,A: int > real,B: real,Delta: real] :
% 5.31/5.64 ( ! [I3: int] :
% 5.31/5.64 ( ( member_int @ I3 @ I5 )
% 5.31/5.64 => ( ord_less_eq_real @ zero_zero_real @ ( X @ I3 ) ) )
% 5.31/5.64 => ( ( ( groups8778361861064173332t_real @ X @ I5 )
% 5.31/5.64 = one_one_real )
% 5.31/5.64 => ( ! [I3: int] :
% 5.31/5.64 ( ( member_int @ I3 @ I5 )
% 5.31/5.64 => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( A @ I3 ) @ B ) ) @ Delta ) )
% 5.31/5.64 => ( ord_less_eq_real
% 5.31/5.64 @ ( abs_abs_real
% 5.31/5.64 @ ( minus_minus_real
% 5.31/5.64 @ ( groups8778361861064173332t_real
% 5.31/5.64 @ ^ [I: int] : ( times_times_real @ ( A @ I ) @ ( X @ I ) )
% 5.31/5.64 @ I5 )
% 5.31/5.64 @ B ) )
% 5.31/5.64 @ Delta ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % convex_sum_bound_le
% 5.31/5.64 thf(fact_8527_convex__sum__bound__le,axiom,
% 5.31/5.64 ! [I5: set_complex,X: complex > rat,A: complex > rat,B: rat,Delta: rat] :
% 5.31/5.64 ( ! [I3: complex] :
% 5.31/5.64 ( ( member_complex @ I3 @ I5 )
% 5.31/5.64 => ( ord_less_eq_rat @ zero_zero_rat @ ( X @ I3 ) ) )
% 5.31/5.64 => ( ( ( groups5058264527183730370ex_rat @ X @ I5 )
% 5.31/5.64 = one_one_rat )
% 5.31/5.64 => ( ! [I3: complex] :
% 5.31/5.64 ( ( member_complex @ I3 @ I5 )
% 5.31/5.64 => ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( A @ I3 ) @ B ) ) @ Delta ) )
% 5.31/5.64 => ( ord_less_eq_rat
% 5.31/5.64 @ ( abs_abs_rat
% 5.31/5.64 @ ( minus_minus_rat
% 5.31/5.64 @ ( groups5058264527183730370ex_rat
% 5.31/5.64 @ ^ [I: complex] : ( times_times_rat @ ( A @ I ) @ ( X @ I ) )
% 5.31/5.64 @ I5 )
% 5.31/5.64 @ B ) )
% 5.31/5.64 @ Delta ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % convex_sum_bound_le
% 5.31/5.64 thf(fact_8528_convex__sum__bound__le,axiom,
% 5.31/5.64 ! [I5: set_real,X: real > rat,A: real > rat,B: rat,Delta: rat] :
% 5.31/5.64 ( ! [I3: real] :
% 5.31/5.64 ( ( member_real @ I3 @ I5 )
% 5.31/5.64 => ( ord_less_eq_rat @ zero_zero_rat @ ( X @ I3 ) ) )
% 5.31/5.64 => ( ( ( groups1300246762558778688al_rat @ X @ I5 )
% 5.31/5.64 = one_one_rat )
% 5.31/5.64 => ( ! [I3: real] :
% 5.31/5.64 ( ( member_real @ I3 @ I5 )
% 5.31/5.64 => ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( A @ I3 ) @ B ) ) @ Delta ) )
% 5.31/5.64 => ( ord_less_eq_rat
% 5.31/5.64 @ ( abs_abs_rat
% 5.31/5.64 @ ( minus_minus_rat
% 5.31/5.64 @ ( groups1300246762558778688al_rat
% 5.31/5.64 @ ^ [I: real] : ( times_times_rat @ ( A @ I ) @ ( X @ I ) )
% 5.31/5.64 @ I5 )
% 5.31/5.64 @ B ) )
% 5.31/5.64 @ Delta ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % convex_sum_bound_le
% 5.31/5.64 thf(fact_8529_convex__sum__bound__le,axiom,
% 5.31/5.64 ! [I5: set_nat,X: nat > rat,A: nat > rat,B: rat,Delta: rat] :
% 5.31/5.64 ( ! [I3: nat] :
% 5.31/5.64 ( ( member_nat @ I3 @ I5 )
% 5.31/5.64 => ( ord_less_eq_rat @ zero_zero_rat @ ( X @ I3 ) ) )
% 5.31/5.64 => ( ( ( groups2906978787729119204at_rat @ X @ I5 )
% 5.31/5.64 = one_one_rat )
% 5.31/5.64 => ( ! [I3: nat] :
% 5.31/5.64 ( ( member_nat @ I3 @ I5 )
% 5.31/5.64 => ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( A @ I3 ) @ B ) ) @ Delta ) )
% 5.31/5.64 => ( ord_less_eq_rat
% 5.31/5.64 @ ( abs_abs_rat
% 5.31/5.64 @ ( minus_minus_rat
% 5.31/5.64 @ ( groups2906978787729119204at_rat
% 5.31/5.64 @ ^ [I: nat] : ( times_times_rat @ ( A @ I ) @ ( X @ I ) )
% 5.31/5.64 @ I5 )
% 5.31/5.64 @ B ) )
% 5.31/5.64 @ Delta ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % convex_sum_bound_le
% 5.31/5.64 thf(fact_8530_cos__plus__cos,axiom,
% 5.31/5.64 ! [W2: complex,Z3: complex] :
% 5.31/5.64 ( ( plus_plus_complex @ ( cos_complex @ W2 ) @ ( cos_complex @ Z3 ) )
% 5.31/5.64 = ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( cos_complex @ ( divide1717551699836669952omplex @ ( plus_plus_complex @ W2 @ Z3 ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ) @ ( cos_complex @ ( divide1717551699836669952omplex @ ( minus_minus_complex @ W2 @ Z3 ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % cos_plus_cos
% 5.31/5.64 thf(fact_8531_cos__plus__cos,axiom,
% 5.31/5.64 ! [W2: real,Z3: real] :
% 5.31/5.64 ( ( plus_plus_real @ ( cos_real @ W2 ) @ ( cos_real @ Z3 ) )
% 5.31/5.64 = ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( cos_real @ ( divide_divide_real @ ( plus_plus_real @ W2 @ Z3 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) @ ( cos_real @ ( divide_divide_real @ ( minus_minus_real @ W2 @ Z3 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % cos_plus_cos
% 5.31/5.64 thf(fact_8532_cos__times__cos,axiom,
% 5.31/5.64 ! [W2: complex,Z3: complex] :
% 5.31/5.64 ( ( times_times_complex @ ( cos_complex @ W2 ) @ ( cos_complex @ Z3 ) )
% 5.31/5.64 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( cos_complex @ ( minus_minus_complex @ W2 @ Z3 ) ) @ ( cos_complex @ ( plus_plus_complex @ W2 @ Z3 ) ) ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % cos_times_cos
% 5.31/5.64 thf(fact_8533_cos__times__cos,axiom,
% 5.31/5.64 ! [W2: real,Z3: real] :
% 5.31/5.64 ( ( times_times_real @ ( cos_real @ W2 ) @ ( cos_real @ Z3 ) )
% 5.31/5.64 = ( divide_divide_real @ ( plus_plus_real @ ( cos_real @ ( minus_minus_real @ W2 @ Z3 ) ) @ ( cos_real @ ( plus_plus_real @ W2 @ Z3 ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % cos_times_cos
% 5.31/5.64 thf(fact_8534_cos__double__less__one,axiom,
% 5.31/5.64 ! [X: real] :
% 5.31/5.64 ( ( ord_less_real @ zero_zero_real @ X )
% 5.31/5.64 => ( ( ord_less_real @ X @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.31/5.64 => ( ord_less_real @ ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) ) @ one_one_real ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % cos_double_less_one
% 5.31/5.64 thf(fact_8535_cos__double__cos,axiom,
% 5.31/5.64 ! [W2: complex] :
% 5.31/5.64 ( ( cos_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ W2 ) )
% 5.31/5.64 = ( minus_minus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( power_power_complex @ ( cos_complex @ W2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ one_one_complex ) ) ).
% 5.31/5.64
% 5.31/5.64 % cos_double_cos
% 5.31/5.64 thf(fact_8536_cos__double__cos,axiom,
% 5.31/5.64 ! [W2: real] :
% 5.31/5.64 ( ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ W2 ) )
% 5.31/5.64 = ( minus_minus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( power_power_real @ ( cos_real @ W2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ one_one_real ) ) ).
% 5.31/5.64
% 5.31/5.64 % cos_double_cos
% 5.31/5.64 thf(fact_8537_cos__treble__cos,axiom,
% 5.31/5.64 ! [X: complex] :
% 5.31/5.64 ( ( cos_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit1 @ one ) ) @ X ) )
% 5.31/5.64 = ( minus_minus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ ( bit0 @ one ) ) ) @ ( power_power_complex @ ( cos_complex @ X ) @ ( numeral_numeral_nat @ ( bit1 @ one ) ) ) ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit1 @ one ) ) @ ( cos_complex @ X ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % cos_treble_cos
% 5.31/5.64 thf(fact_8538_cos__treble__cos,axiom,
% 5.31/5.64 ! [X: real] :
% 5.31/5.64 ( ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit1 @ one ) ) @ X ) )
% 5.31/5.64 = ( minus_minus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( cos_real @ X ) @ ( numeral_numeral_nat @ ( bit1 @ one ) ) ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit1 @ one ) ) @ ( cos_real @ X ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % cos_treble_cos
% 5.31/5.64 thf(fact_8539_cos__diff__cos,axiom,
% 5.31/5.64 ! [W2: complex,Z3: complex] :
% 5.31/5.64 ( ( minus_minus_complex @ ( cos_complex @ W2 ) @ ( cos_complex @ Z3 ) )
% 5.31/5.64 = ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( sin_complex @ ( divide1717551699836669952omplex @ ( plus_plus_complex @ W2 @ Z3 ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ) @ ( sin_complex @ ( divide1717551699836669952omplex @ ( minus_minus_complex @ Z3 @ W2 ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % cos_diff_cos
% 5.31/5.64 thf(fact_8540_cos__diff__cos,axiom,
% 5.31/5.64 ! [W2: real,Z3: real] :
% 5.31/5.64 ( ( minus_minus_real @ ( cos_real @ W2 ) @ ( cos_real @ Z3 ) )
% 5.31/5.64 = ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( sin_real @ ( divide_divide_real @ ( plus_plus_real @ W2 @ Z3 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) @ ( sin_real @ ( divide_divide_real @ ( minus_minus_real @ Z3 @ W2 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % cos_diff_cos
% 5.31/5.64 thf(fact_8541_sin__diff__sin,axiom,
% 5.31/5.64 ! [W2: complex,Z3: complex] :
% 5.31/5.64 ( ( minus_minus_complex @ ( sin_complex @ W2 ) @ ( sin_complex @ Z3 ) )
% 5.31/5.64 = ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( sin_complex @ ( divide1717551699836669952omplex @ ( minus_minus_complex @ W2 @ Z3 ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ) @ ( cos_complex @ ( divide1717551699836669952omplex @ ( plus_plus_complex @ W2 @ Z3 ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % sin_diff_sin
% 5.31/5.64 thf(fact_8542_sin__diff__sin,axiom,
% 5.31/5.64 ! [W2: real,Z3: real] :
% 5.31/5.64 ( ( minus_minus_real @ ( sin_real @ W2 ) @ ( sin_real @ Z3 ) )
% 5.31/5.64 = ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( sin_real @ ( divide_divide_real @ ( minus_minus_real @ W2 @ Z3 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) @ ( cos_real @ ( divide_divide_real @ ( plus_plus_real @ W2 @ Z3 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % sin_diff_sin
% 5.31/5.64 thf(fact_8543_sin__plus__sin,axiom,
% 5.31/5.64 ! [W2: complex,Z3: complex] :
% 5.31/5.64 ( ( plus_plus_complex @ ( sin_complex @ W2 ) @ ( sin_complex @ Z3 ) )
% 5.31/5.64 = ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( sin_complex @ ( divide1717551699836669952omplex @ ( plus_plus_complex @ W2 @ Z3 ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ) @ ( cos_complex @ ( divide1717551699836669952omplex @ ( minus_minus_complex @ W2 @ Z3 ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % sin_plus_sin
% 5.31/5.64 thf(fact_8544_sin__plus__sin,axiom,
% 5.31/5.64 ! [W2: real,Z3: real] :
% 5.31/5.64 ( ( plus_plus_real @ ( sin_real @ W2 ) @ ( sin_real @ Z3 ) )
% 5.31/5.64 = ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( sin_real @ ( divide_divide_real @ ( plus_plus_real @ W2 @ Z3 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) @ ( cos_real @ ( divide_divide_real @ ( minus_minus_real @ W2 @ Z3 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % sin_plus_sin
% 5.31/5.64 thf(fact_8545_cos__times__sin,axiom,
% 5.31/5.64 ! [W2: complex,Z3: complex] :
% 5.31/5.64 ( ( times_times_complex @ ( cos_complex @ W2 ) @ ( sin_complex @ Z3 ) )
% 5.31/5.64 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( sin_complex @ ( plus_plus_complex @ W2 @ Z3 ) ) @ ( sin_complex @ ( minus_minus_complex @ W2 @ Z3 ) ) ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % cos_times_sin
% 5.31/5.64 thf(fact_8546_cos__times__sin,axiom,
% 5.31/5.64 ! [W2: real,Z3: real] :
% 5.31/5.64 ( ( times_times_real @ ( cos_real @ W2 ) @ ( sin_real @ Z3 ) )
% 5.31/5.64 = ( divide_divide_real @ ( minus_minus_real @ ( sin_real @ ( plus_plus_real @ W2 @ Z3 ) ) @ ( sin_real @ ( minus_minus_real @ W2 @ Z3 ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % cos_times_sin
% 5.31/5.64 thf(fact_8547_sin__times__cos,axiom,
% 5.31/5.64 ! [W2: complex,Z3: complex] :
% 5.31/5.64 ( ( times_times_complex @ ( sin_complex @ W2 ) @ ( cos_complex @ Z3 ) )
% 5.31/5.64 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( sin_complex @ ( plus_plus_complex @ W2 @ Z3 ) ) @ ( sin_complex @ ( minus_minus_complex @ W2 @ Z3 ) ) ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % sin_times_cos
% 5.31/5.64 thf(fact_8548_sin__times__cos,axiom,
% 5.31/5.64 ! [W2: real,Z3: real] :
% 5.31/5.64 ( ( times_times_real @ ( sin_real @ W2 ) @ ( cos_real @ Z3 ) )
% 5.31/5.64 = ( divide_divide_real @ ( plus_plus_real @ ( sin_real @ ( plus_plus_real @ W2 @ Z3 ) ) @ ( sin_real @ ( minus_minus_real @ W2 @ Z3 ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % sin_times_cos
% 5.31/5.64 thf(fact_8549_sin__times__sin,axiom,
% 5.31/5.64 ! [W2: complex,Z3: complex] :
% 5.31/5.64 ( ( times_times_complex @ ( sin_complex @ W2 ) @ ( sin_complex @ Z3 ) )
% 5.31/5.64 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( cos_complex @ ( minus_minus_complex @ W2 @ Z3 ) ) @ ( cos_complex @ ( plus_plus_complex @ W2 @ Z3 ) ) ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % sin_times_sin
% 5.31/5.64 thf(fact_8550_sin__times__sin,axiom,
% 5.31/5.64 ! [W2: real,Z3: real] :
% 5.31/5.64 ( ( times_times_real @ ( sin_real @ W2 ) @ ( sin_real @ Z3 ) )
% 5.31/5.64 = ( divide_divide_real @ ( minus_minus_real @ ( cos_real @ ( minus_minus_real @ W2 @ Z3 ) ) @ ( cos_real @ ( plus_plus_real @ W2 @ Z3 ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % sin_times_sin
% 5.31/5.64 thf(fact_8551_Maclaurin__cos__expansion,axiom,
% 5.31/5.64 ! [X: real,N: nat] :
% 5.31/5.64 ? [T6: real] :
% 5.31/5.64 ( ( ord_less_eq_real @ ( abs_abs_real @ T6 ) @ ( abs_abs_real @ X ) )
% 5.31/5.64 & ( ( cos_real @ X )
% 5.31/5.64 = ( plus_plus_real
% 5.31/5.64 @ ( groups6591440286371151544t_real
% 5.31/5.64 @ ^ [M6: nat] : ( times_times_real @ ( cos_coeff @ M6 ) @ ( power_power_real @ X @ M6 ) )
% 5.31/5.64 @ ( set_ord_lessThan_nat @ N ) )
% 5.31/5.64 @ ( 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 ) ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % Maclaurin_cos_expansion
% 5.31/5.64 thf(fact_8552_cos__one__2pi,axiom,
% 5.31/5.64 ! [X: real] :
% 5.31/5.64 ( ( ( cos_real @ X )
% 5.31/5.64 = one_one_real )
% 5.31/5.64 = ( ? [X4: nat] :
% 5.31/5.64 ( X
% 5.31/5.64 = ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ X4 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ pi ) )
% 5.31/5.64 | ? [X4: nat] :
% 5.31/5.64 ( X
% 5.31/5.64 = ( uminus_uminus_real @ ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ X4 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ pi ) ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % cos_one_2pi
% 5.31/5.64 thf(fact_8553_sin__expansion__lemma,axiom,
% 5.31/5.64 ! [X: real,M2: nat] :
% 5.31/5.64 ( ( sin_real @ ( plus_plus_real @ X @ ( divide_divide_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ M2 ) ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 5.31/5.64 = ( cos_real @ ( plus_plus_real @ X @ ( divide_divide_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ M2 ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % sin_expansion_lemma
% 5.31/5.64 thf(fact_8554_cos__zero__lemma,axiom,
% 5.31/5.64 ! [X: real] :
% 5.31/5.64 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.31/5.64 => ( ( ( cos_real @ X )
% 5.31/5.64 = zero_zero_real )
% 5.31/5.64 => ? [N3: nat] :
% 5.31/5.64 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 )
% 5.31/5.64 & ( X
% 5.31/5.64 = ( times_times_real @ ( semiri5074537144036343181t_real @ N3 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % cos_zero_lemma
% 5.31/5.64 thf(fact_8555_cos__zero__iff,axiom,
% 5.31/5.64 ! [X: real] :
% 5.31/5.64 ( ( ( cos_real @ X )
% 5.31/5.64 = zero_zero_real )
% 5.31/5.64 = ( ? [N4: nat] :
% 5.31/5.64 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 )
% 5.31/5.64 & ( X
% 5.31/5.64 = ( times_times_real @ ( semiri5074537144036343181t_real @ N4 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) )
% 5.31/5.64 | ? [N4: nat] :
% 5.31/5.64 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 )
% 5.31/5.64 & ( X
% 5.31/5.64 = ( uminus_uminus_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N4 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % cos_zero_iff
% 5.31/5.64 thf(fact_8556_cos__expansion__lemma,axiom,
% 5.31/5.64 ! [X: real,M2: nat] :
% 5.31/5.64 ( ( cos_real @ ( plus_plus_real @ X @ ( divide_divide_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ M2 ) ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 5.31/5.64 = ( uminus_uminus_real @ ( sin_real @ ( plus_plus_real @ X @ ( divide_divide_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ M2 ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % cos_expansion_lemma
% 5.31/5.64 thf(fact_8557_cos__paired,axiom,
% 5.31/5.64 ! [X: real] :
% 5.31/5.64 ( sums_real
% 5.31/5.64 @ ^ [N4: nat] : ( times_times_real @ ( divide_divide_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N4 ) @ ( semiri2265585572941072030t_real @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) ) ) @ ( power_power_real @ X @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) ) )
% 5.31/5.64 @ ( cos_real @ X ) ) ).
% 5.31/5.64
% 5.31/5.64 % cos_paired
% 5.31/5.64 thf(fact_8558_sincos__total__2pi__le,axiom,
% 5.31/5.64 ! [X: real,Y: real] :
% 5.31/5.64 ( ( ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.31/5.64 = one_one_real )
% 5.31/5.64 => ? [T6: real] :
% 5.31/5.64 ( ( ord_less_eq_real @ zero_zero_real @ T6 )
% 5.31/5.64 & ( ord_less_eq_real @ T6 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 5.31/5.64 & ( X
% 5.31/5.64 = ( cos_real @ T6 ) )
% 5.31/5.64 & ( Y
% 5.31/5.64 = ( sin_real @ T6 ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % sincos_total_2pi_le
% 5.31/5.64 thf(fact_8559_sincos__total__2pi,axiom,
% 5.31/5.64 ! [X: real,Y: real] :
% 5.31/5.64 ( ( ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.31/5.64 = one_one_real )
% 5.31/5.64 => ~ ! [T6: real] :
% 5.31/5.64 ( ( ord_less_eq_real @ zero_zero_real @ T6 )
% 5.31/5.64 => ( ( ord_less_real @ T6 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 5.31/5.64 => ( ( X
% 5.31/5.64 = ( cos_real @ T6 ) )
% 5.31/5.64 => ( Y
% 5.31/5.64 != ( sin_real @ T6 ) ) ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % sincos_total_2pi
% 5.31/5.64 thf(fact_8560_monoseq__arctan__series,axiom,
% 5.31/5.64 ! [X: real] :
% 5.31/5.64 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 5.31/5.64 => ( topolo6980174941875973593q_real
% 5.31/5.64 @ ^ [N4: nat] : ( times_times_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( times_times_nat @ N4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) @ ( power_power_real @ X @ ( plus_plus_nat @ ( times_times_nat @ N4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % monoseq_arctan_series
% 5.31/5.64 thf(fact_8561_summable__arctan__series,axiom,
% 5.31/5.64 ! [X: real] :
% 5.31/5.64 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 5.31/5.64 => ( summable_real
% 5.31/5.64 @ ^ [K3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K3 ) @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( times_times_nat @ K3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) @ ( power_power_real @ X @ ( plus_plus_nat @ ( times_times_nat @ K3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % summable_arctan_series
% 5.31/5.64 thf(fact_8562_abs__ln__one__plus__x__minus__x__bound__nonpos,axiom,
% 5.31/5.64 ! [X: real] :
% 5.31/5.64 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 5.31/5.64 => ( ( ord_less_eq_real @ X @ zero_zero_real )
% 5.31/5.64 => ( 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 ) ) ) ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_ln_one_plus_x_minus_x_bound_nonpos
% 5.31/5.64 thf(fact_8563_pi__series,axiom,
% 5.31/5.64 ( ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.31/5.64 = ( suminf_real
% 5.31/5.64 @ ^ [K3: nat] : ( divide_divide_real @ ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K3 ) @ one_one_real ) @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( times_times_nat @ K3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % pi_series
% 5.31/5.64 thf(fact_8564_and__int_Opsimps,axiom,
% 5.31/5.64 ! [K2: int,L: int] :
% 5.31/5.64 ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ K2 @ L ) )
% 5.31/5.64 => ( ( ( ( member_int @ K2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 5.31/5.64 & ( member_int @ L @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 5.31/5.64 => ( ( bit_se725231765392027082nd_int @ K2 @ L )
% 5.31/5.64 = ( uminus_uminus_int
% 5.31/5.64 @ ( zero_n2684676970156552555ol_int
% 5.31/5.64 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K2 )
% 5.31/5.64 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L ) ) ) ) ) )
% 5.31/5.64 & ( ~ ( ( member_int @ K2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 5.31/5.64 & ( member_int @ L @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 5.31/5.64 => ( ( bit_se725231765392027082nd_int @ K2 @ L )
% 5.31/5.64 = ( plus_plus_int
% 5.31/5.64 @ ( zero_n2684676970156552555ol_int
% 5.31/5.64 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K2 )
% 5.31/5.64 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L ) ) )
% 5.31/5.64 @ ( 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 ) ) ) ) ) ) ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % and_int.psimps
% 5.31/5.64 thf(fact_8565_tan__npi,axiom,
% 5.31/5.64 ! [N: nat] :
% 5.31/5.64 ( ( tan_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ pi ) )
% 5.31/5.64 = zero_zero_real ) ).
% 5.31/5.64
% 5.31/5.64 % tan_npi
% 5.31/5.64 thf(fact_8566_tan__periodic__n,axiom,
% 5.31/5.64 ! [X: real,N: num] :
% 5.31/5.64 ( ( tan_real @ ( plus_plus_real @ X @ ( times_times_real @ ( numeral_numeral_real @ N ) @ pi ) ) )
% 5.31/5.64 = ( tan_real @ X ) ) ).
% 5.31/5.64
% 5.31/5.64 % tan_periodic_n
% 5.31/5.64 thf(fact_8567_tan__periodic__nat,axiom,
% 5.31/5.64 ! [X: real,N: nat] :
% 5.31/5.64 ( ( tan_real @ ( plus_plus_real @ X @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ pi ) ) )
% 5.31/5.64 = ( tan_real @ X ) ) ).
% 5.31/5.64
% 5.31/5.64 % tan_periodic_nat
% 5.31/5.64 thf(fact_8568_tan__periodic,axiom,
% 5.31/5.64 ! [X: real] :
% 5.31/5.64 ( ( tan_real @ ( plus_plus_real @ X @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 5.31/5.64 = ( tan_real @ X ) ) ).
% 5.31/5.64
% 5.31/5.64 % tan_periodic
% 5.31/5.64 thf(fact_8569_abs__zmult__eq__1,axiom,
% 5.31/5.64 ! [M2: int,N: int] :
% 5.31/5.64 ( ( ( abs_abs_int @ ( times_times_int @ M2 @ N ) )
% 5.31/5.64 = one_one_int )
% 5.31/5.64 => ( ( abs_abs_int @ M2 )
% 5.31/5.64 = one_one_int ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_zmult_eq_1
% 5.31/5.64 thf(fact_8570_abs__div,axiom,
% 5.31/5.64 ! [Y: int,X: int] :
% 5.31/5.64 ( ( dvd_dvd_int @ Y @ X )
% 5.31/5.64 => ( ( abs_abs_int @ ( divide_divide_int @ X @ Y ) )
% 5.31/5.64 = ( divide_divide_int @ ( abs_abs_int @ X ) @ ( abs_abs_int @ Y ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_div
% 5.31/5.64 thf(fact_8571_summable__rabs__comparison__test,axiom,
% 5.31/5.64 ! [F2: nat > real,G2: nat > real] :
% 5.31/5.64 ( ? [N7: nat] :
% 5.31/5.64 ! [N3: nat] :
% 5.31/5.64 ( ( ord_less_eq_nat @ N7 @ N3 )
% 5.31/5.64 => ( ord_less_eq_real @ ( abs_abs_real @ ( F2 @ N3 ) ) @ ( G2 @ N3 ) ) )
% 5.31/5.64 => ( ( summable_real @ G2 )
% 5.31/5.64 => ( summable_real
% 5.31/5.64 @ ^ [N4: nat] : ( abs_abs_real @ ( F2 @ N4 ) ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % summable_rabs_comparison_test
% 5.31/5.64 thf(fact_8572_ln__mult,axiom,
% 5.31/5.64 ! [X: real,Y: real] :
% 5.31/5.64 ( ( ord_less_real @ zero_zero_real @ X )
% 5.31/5.64 => ( ( ord_less_real @ zero_zero_real @ Y )
% 5.31/5.64 => ( ( ln_ln_real @ ( times_times_real @ X @ Y ) )
% 5.31/5.64 = ( plus_plus_real @ ( ln_ln_real @ X ) @ ( ln_ln_real @ Y ) ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % ln_mult
% 5.31/5.64 thf(fact_8573_zdvd__mult__cancel1,axiom,
% 5.31/5.64 ! [M2: int,N: int] :
% 5.31/5.64 ( ( M2 != zero_zero_int )
% 5.31/5.64 => ( ( dvd_dvd_int @ ( times_times_int @ M2 @ N ) @ M2 )
% 5.31/5.64 = ( ( abs_abs_int @ N )
% 5.31/5.64 = one_one_int ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % zdvd_mult_cancel1
% 5.31/5.64 thf(fact_8574_sum__pos__lt__pair,axiom,
% 5.31/5.64 ! [F2: nat > real,K2: nat] :
% 5.31/5.64 ( ( summable_real @ F2 )
% 5.31/5.64 => ( ! [D5: nat] : ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( F2 @ ( plus_plus_nat @ K2 @ ( times_times_nat @ ( suc @ ( suc @ zero_zero_nat ) ) @ D5 ) ) ) @ ( F2 @ ( plus_plus_nat @ K2 @ ( plus_plus_nat @ ( times_times_nat @ ( suc @ ( suc @ zero_zero_nat ) ) @ D5 ) @ one_one_nat ) ) ) ) )
% 5.31/5.64 => ( ord_less_real @ ( groups6591440286371151544t_real @ F2 @ ( set_ord_lessThan_nat @ K2 ) ) @ ( suminf_real @ F2 ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % sum_pos_lt_pair
% 5.31/5.64 thf(fact_8575_ln__realpow,axiom,
% 5.31/5.64 ! [X: real,N: nat] :
% 5.31/5.64 ( ( ord_less_real @ zero_zero_real @ X )
% 5.31/5.64 => ( ( ln_ln_real @ ( power_power_real @ X @ N ) )
% 5.31/5.64 = ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( ln_ln_real @ X ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % ln_realpow
% 5.31/5.64 thf(fact_8576_summable__power__series,axiom,
% 5.31/5.64 ! [F2: nat > real,Z3: real] :
% 5.31/5.64 ( ! [I3: nat] : ( ord_less_eq_real @ ( F2 @ I3 ) @ one_one_real )
% 5.31/5.64 => ( ! [I3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F2 @ I3 ) )
% 5.31/5.64 => ( ( ord_less_eq_real @ zero_zero_real @ Z3 )
% 5.31/5.64 => ( ( ord_less_real @ Z3 @ one_one_real )
% 5.31/5.64 => ( summable_real
% 5.31/5.64 @ ^ [I: nat] : ( times_times_real @ ( F2 @ I ) @ ( power_power_real @ Z3 @ I ) ) ) ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % summable_power_series
% 5.31/5.64 thf(fact_8577_nat__intermed__int__val,axiom,
% 5.31/5.64 ! [M2: nat,N: nat,F2: nat > int,K2: int] :
% 5.31/5.64 ( ! [I3: nat] :
% 5.31/5.64 ( ( ( ord_less_eq_nat @ M2 @ I3 )
% 5.31/5.64 & ( ord_less_nat @ I3 @ N ) )
% 5.31/5.64 => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( F2 @ ( suc @ I3 ) ) @ ( F2 @ I3 ) ) ) @ one_one_int ) )
% 5.31/5.64 => ( ( ord_less_eq_nat @ M2 @ N )
% 5.31/5.64 => ( ( ord_less_eq_int @ ( F2 @ M2 ) @ K2 )
% 5.31/5.64 => ( ( ord_less_eq_int @ K2 @ ( F2 @ N ) )
% 5.31/5.64 => ? [I3: nat] :
% 5.31/5.64 ( ( ord_less_eq_nat @ M2 @ I3 )
% 5.31/5.64 & ( ord_less_eq_nat @ I3 @ N )
% 5.31/5.64 & ( ( F2 @ I3 )
% 5.31/5.64 = K2 ) ) ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % nat_intermed_int_val
% 5.31/5.64 thf(fact_8578_incr__lemma,axiom,
% 5.31/5.64 ! [D: int,Z3: int,X: int] :
% 5.31/5.64 ( ( ord_less_int @ zero_zero_int @ D )
% 5.31/5.64 => ( ord_less_int @ Z3 @ ( plus_plus_int @ X @ ( times_times_int @ ( plus_plus_int @ ( abs_abs_int @ ( minus_minus_int @ X @ Z3 ) ) @ one_one_int ) @ D ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % incr_lemma
% 5.31/5.64 thf(fact_8579_decr__lemma,axiom,
% 5.31/5.64 ! [D: int,X: int,Z3: int] :
% 5.31/5.64 ( ( ord_less_int @ zero_zero_int @ D )
% 5.31/5.64 => ( ord_less_int @ ( minus_minus_int @ X @ ( times_times_int @ ( plus_plus_int @ ( abs_abs_int @ ( minus_minus_int @ X @ Z3 ) ) @ one_one_int ) @ D ) ) @ Z3 ) ) ).
% 5.31/5.64
% 5.31/5.64 % decr_lemma
% 5.31/5.64 thf(fact_8580_ln__series,axiom,
% 5.31/5.64 ! [X: real] :
% 5.31/5.64 ( ( ord_less_real @ zero_zero_real @ X )
% 5.31/5.64 => ( ( ord_less_real @ X @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.31/5.64 => ( ( ln_ln_real @ X )
% 5.31/5.64 = ( suminf_real
% 5.31/5.64 @ ^ [N4: nat] : ( times_times_real @ ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N4 ) @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ N4 @ one_one_nat ) ) ) ) @ ( power_power_real @ ( minus_minus_real @ X @ one_one_real ) @ ( suc @ N4 ) ) ) ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % ln_series
% 5.31/5.64 thf(fact_8581_nat__ivt__aux,axiom,
% 5.31/5.64 ! [N: nat,F2: nat > int,K2: int] :
% 5.31/5.64 ( ! [I3: nat] :
% 5.31/5.64 ( ( ord_less_nat @ I3 @ N )
% 5.31/5.64 => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( F2 @ ( suc @ I3 ) ) @ ( F2 @ I3 ) ) ) @ one_one_int ) )
% 5.31/5.64 => ( ( ord_less_eq_int @ ( F2 @ zero_zero_nat ) @ K2 )
% 5.31/5.64 => ( ( ord_less_eq_int @ K2 @ ( F2 @ N ) )
% 5.31/5.64 => ? [I3: nat] :
% 5.31/5.64 ( ( ord_less_eq_nat @ I3 @ N )
% 5.31/5.64 & ( ( F2 @ I3 )
% 5.31/5.64 = K2 ) ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % nat_ivt_aux
% 5.31/5.64 thf(fact_8582_nat0__intermed__int__val,axiom,
% 5.31/5.64 ! [N: nat,F2: nat > int,K2: int] :
% 5.31/5.64 ( ! [I3: nat] :
% 5.31/5.64 ( ( ord_less_nat @ I3 @ N )
% 5.31/5.64 => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( F2 @ ( plus_plus_nat @ I3 @ one_one_nat ) ) @ ( F2 @ I3 ) ) ) @ one_one_int ) )
% 5.31/5.64 => ( ( ord_less_eq_int @ ( F2 @ zero_zero_nat ) @ K2 )
% 5.31/5.64 => ( ( ord_less_eq_int @ K2 @ ( F2 @ N ) )
% 5.31/5.64 => ? [I3: nat] :
% 5.31/5.64 ( ( ord_less_eq_nat @ I3 @ N )
% 5.31/5.64 & ( ( F2 @ I3 )
% 5.31/5.64 = K2 ) ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % nat0_intermed_int_val
% 5.31/5.64 thf(fact_8583_ln__one__minus__pos__lower__bound,axiom,
% 5.31/5.64 ! [X: real] :
% 5.31/5.64 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.31/5.64 => ( ( ord_less_eq_real @ X @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.31/5.64 => ( 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 ) ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % ln_one_minus_pos_lower_bound
% 5.31/5.64 thf(fact_8584_abs__ln__one__plus__x__minus__x__bound,axiom,
% 5.31/5.64 ! [X: real] :
% 5.31/5.64 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.31/5.64 => ( 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 ) ) ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % abs_ln_one_plus_x_minus_x_bound
% 5.31/5.64 thf(fact_8585_and__int_Opelims,axiom,
% 5.31/5.64 ! [X: int,Xa2: int,Y: int] :
% 5.31/5.64 ( ( ( bit_se725231765392027082nd_int @ X @ Xa2 )
% 5.31/5.64 = Y )
% 5.31/5.64 => ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ X @ Xa2 ) )
% 5.31/5.64 => ~ ( ( ( ( ( member_int @ X @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 5.31/5.64 & ( member_int @ Xa2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 5.31/5.64 => ( Y
% 5.31/5.64 = ( uminus_uminus_int
% 5.31/5.64 @ ( zero_n2684676970156552555ol_int
% 5.31/5.64 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X )
% 5.31/5.64 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa2 ) ) ) ) ) )
% 5.31/5.64 & ( ~ ( ( member_int @ X @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 5.31/5.64 & ( member_int @ Xa2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 5.31/5.64 => ( Y
% 5.31/5.64 = ( plus_plus_int
% 5.31/5.64 @ ( zero_n2684676970156552555ol_int
% 5.31/5.64 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X )
% 5.31/5.64 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa2 ) ) )
% 5.31/5.64 @ ( 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 ) ) ) ) ) ) ) ) )
% 5.31/5.64 => ~ ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ X @ Xa2 ) ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % and_int.pelims
% 5.31/5.64 thf(fact_8586_arctan__series,axiom,
% 5.31/5.64 ! [X: real] :
% 5.31/5.64 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 5.31/5.64 => ( ( arctan @ X )
% 5.31/5.64 = ( suminf_real
% 5.31/5.64 @ ^ [K3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K3 ) @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( times_times_nat @ K3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) @ ( power_power_real @ X @ ( plus_plus_nat @ ( times_times_nat @ K3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % arctan_series
% 5.31/5.64 thf(fact_8587_Maclaurin__exp__lt,axiom,
% 5.31/5.64 ! [X: real,N: nat] :
% 5.31/5.64 ( ( X != zero_zero_real )
% 5.31/5.64 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.64 => ? [T6: real] :
% 5.31/5.64 ( ( ord_less_real @ zero_zero_real @ ( abs_abs_real @ T6 ) )
% 5.31/5.64 & ( ord_less_real @ ( abs_abs_real @ T6 ) @ ( abs_abs_real @ X ) )
% 5.31/5.64 & ( ( exp_real @ X )
% 5.31/5.64 = ( plus_plus_real
% 5.31/5.64 @ ( groups6591440286371151544t_real
% 5.31/5.64 @ ^ [M6: nat] : ( divide_divide_real @ ( power_power_real @ X @ M6 ) @ ( semiri2265585572941072030t_real @ M6 ) )
% 5.31/5.64 @ ( set_ord_lessThan_nat @ N ) )
% 5.31/5.64 @ ( times_times_real @ ( divide_divide_real @ ( exp_real @ T6 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % Maclaurin_exp_lt
% 5.31/5.64 thf(fact_8588_arctan__double,axiom,
% 5.31/5.64 ! [X: real] :
% 5.31/5.64 ( ( ord_less_real @ ( abs_abs_real @ X ) @ one_one_real )
% 5.31/5.64 => ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( arctan @ X ) )
% 5.31/5.64 = ( 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 ) ) ) ) ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % arctan_double
% 5.31/5.64 thf(fact_8589_real__exp__bound__lemma,axiom,
% 5.31/5.64 ! [X: real] :
% 5.31/5.64 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.31/5.64 => ( ( ord_less_eq_real @ X @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.31/5.64 => ( ord_less_eq_real @ ( exp_real @ X ) @ ( plus_plus_real @ one_one_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % real_exp_bound_lemma
% 5.31/5.64 thf(fact_8590_exp__ge__one__plus__x__over__n__power__n,axiom,
% 5.31/5.64 ! [N: nat,X: real] :
% 5.31/5.64 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N ) ) @ X )
% 5.31/5.64 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.64 => ( ord_less_eq_real @ ( power_power_real @ ( plus_plus_real @ one_one_real @ ( divide_divide_real @ X @ ( semiri5074537144036343181t_real @ N ) ) ) @ N ) @ ( exp_real @ X ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % exp_ge_one_plus_x_over_n_power_n
% 5.31/5.64 thf(fact_8591_exp__ge__one__minus__x__over__n__power__n,axiom,
% 5.31/5.64 ! [X: real,N: nat] :
% 5.31/5.64 ( ( ord_less_eq_real @ X @ ( semiri5074537144036343181t_real @ N ) )
% 5.31/5.64 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.64 => ( 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 ) ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % exp_ge_one_minus_x_over_n_power_n
% 5.31/5.64 thf(fact_8592_arctan__add,axiom,
% 5.31/5.64 ! [X: real,Y: real] :
% 5.31/5.64 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 5.31/5.64 => ( ( ord_less_real @ ( abs_abs_real @ Y ) @ one_one_real )
% 5.31/5.64 => ( ( plus_plus_real @ ( arctan @ X ) @ ( arctan @ Y ) )
% 5.31/5.64 = ( arctan @ ( divide_divide_real @ ( plus_plus_real @ X @ Y ) @ ( minus_minus_real @ one_one_real @ ( times_times_real @ X @ Y ) ) ) ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % arctan_add
% 5.31/5.64 thf(fact_8593_Maclaurin__exp__le,axiom,
% 5.31/5.64 ! [X: real,N: nat] :
% 5.31/5.64 ? [T6: real] :
% 5.31/5.64 ( ( ord_less_eq_real @ ( abs_abs_real @ T6 ) @ ( abs_abs_real @ X ) )
% 5.31/5.64 & ( ( exp_real @ X )
% 5.31/5.64 = ( plus_plus_real
% 5.31/5.64 @ ( groups6591440286371151544t_real
% 5.31/5.64 @ ^ [M6: nat] : ( divide_divide_real @ ( power_power_real @ X @ M6 ) @ ( semiri2265585572941072030t_real @ M6 ) )
% 5.31/5.64 @ ( set_ord_lessThan_nat @ N ) )
% 5.31/5.64 @ ( times_times_real @ ( divide_divide_real @ ( exp_real @ T6 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % Maclaurin_exp_le
% 5.31/5.64 thf(fact_8594_machin__Euler,axiom,
% 5.31/5.64 ( ( 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 ) ) ) ) ) ) ) ) ) ) )
% 5.31/5.64 = ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % machin_Euler
% 5.31/5.64 thf(fact_8595_machin,axiom,
% 5.31/5.64 ( ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.31/5.64 = ( 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 ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % machin
% 5.31/5.64 thf(fact_8596_tanh__real__altdef,axiom,
% 5.31/5.64 ( tanh_real
% 5.31/5.64 = ( ^ [X4: real] : ( divide_divide_real @ ( minus_minus_real @ one_one_real @ ( exp_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X4 ) ) ) @ ( plus_plus_real @ one_one_real @ ( exp_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X4 ) ) ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % tanh_real_altdef
% 5.31/5.64 thf(fact_8597_Maclaurin__sin__bound,axiom,
% 5.31/5.64 ! [X: real,N: nat] :
% 5.31/5.64 ( ord_less_eq_real
% 5.31/5.64 @ ( abs_abs_real
% 5.31/5.64 @ ( minus_minus_real @ ( sin_real @ X )
% 5.31/5.64 @ ( groups6591440286371151544t_real
% 5.31/5.64 @ ^ [M6: nat] : ( times_times_real @ ( sin_coeff @ M6 ) @ ( power_power_real @ X @ M6 ) )
% 5.31/5.64 @ ( set_ord_lessThan_nat @ N ) ) ) )
% 5.31/5.64 @ ( times_times_real @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ ( abs_abs_real @ X ) @ N ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % Maclaurin_sin_bound
% 5.31/5.64 thf(fact_8598_divmod__BitM__2__eq,axiom,
% 5.31/5.64 ! [M2: num] :
% 5.31/5.64 ( ( unique5052692396658037445od_int @ ( bitM @ M2 ) @ ( bit0 @ one ) )
% 5.31/5.64 = ( product_Pair_int_int @ ( minus_minus_int @ ( numeral_numeral_int @ M2 ) @ one_one_int ) @ one_one_int ) ) ).
% 5.31/5.64
% 5.31/5.64 % divmod_BitM_2_eq
% 5.31/5.64 thf(fact_8599_pred__numeral__simps_I2_J,axiom,
% 5.31/5.64 ! [K2: num] :
% 5.31/5.64 ( ( pred_numeral @ ( bit0 @ K2 ) )
% 5.31/5.64 = ( numeral_numeral_nat @ ( bitM @ K2 ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % pred_numeral_simps(2)
% 5.31/5.64 thf(fact_8600_sin__npi__int,axiom,
% 5.31/5.64 ! [N: int] :
% 5.31/5.64 ( ( sin_real @ ( times_times_real @ pi @ ( ring_1_of_int_real @ N ) ) )
% 5.31/5.64 = zero_zero_real ) ).
% 5.31/5.64
% 5.31/5.64 % sin_npi_int
% 5.31/5.64 thf(fact_8601_tan__periodic__int,axiom,
% 5.31/5.64 ! [X: real,I2: int] :
% 5.31/5.64 ( ( tan_real @ ( plus_plus_real @ X @ ( times_times_real @ ( ring_1_of_int_real @ I2 ) @ pi ) ) )
% 5.31/5.64 = ( tan_real @ X ) ) ).
% 5.31/5.64
% 5.31/5.64 % tan_periodic_int
% 5.31/5.64 thf(fact_8602_sin__int__2pin,axiom,
% 5.31/5.64 ! [N: int] :
% 5.31/5.64 ( ( sin_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ ( ring_1_of_int_real @ N ) ) )
% 5.31/5.64 = zero_zero_real ) ).
% 5.31/5.64
% 5.31/5.64 % sin_int_2pin
% 5.31/5.64 thf(fact_8603_cos__int__2pin,axiom,
% 5.31/5.64 ! [N: int] :
% 5.31/5.64 ( ( cos_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ ( ring_1_of_int_real @ N ) ) )
% 5.31/5.64 = one_one_real ) ).
% 5.31/5.64
% 5.31/5.64 % cos_int_2pin
% 5.31/5.64 thf(fact_8604_cos__npi__int,axiom,
% 5.31/5.64 ! [N: int] :
% 5.31/5.64 ( ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 5.31/5.64 => ( ( cos_real @ ( times_times_real @ pi @ ( ring_1_of_int_real @ N ) ) )
% 5.31/5.64 = one_one_real ) )
% 5.31/5.64 & ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 5.31/5.64 => ( ( cos_real @ ( times_times_real @ pi @ ( ring_1_of_int_real @ N ) ) )
% 5.31/5.64 = ( uminus_uminus_real @ one_one_real ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % cos_npi_int
% 5.31/5.64 thf(fact_8605_real__scaleR__def,axiom,
% 5.31/5.64 real_V1485227260804924795R_real = times_times_real ).
% 5.31/5.64
% 5.31/5.64 % real_scaleR_def
% 5.31/5.64 thf(fact_8606_divide__real__def,axiom,
% 5.31/5.64 ( divide_divide_real
% 5.31/5.64 = ( ^ [X4: real,Y4: real] : ( times_times_real @ X4 @ ( inverse_inverse_real @ Y4 ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % divide_real_def
% 5.31/5.64 thf(fact_8607_eval__nat__numeral_I2_J,axiom,
% 5.31/5.64 ! [N: num] :
% 5.31/5.64 ( ( numeral_numeral_nat @ ( bit0 @ N ) )
% 5.31/5.64 = ( suc @ ( numeral_numeral_nat @ ( bitM @ N ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % eval_nat_numeral(2)
% 5.31/5.64 thf(fact_8608_BitM__plus__one,axiom,
% 5.31/5.64 ! [N: num] :
% 5.31/5.64 ( ( plus_plus_num @ ( bitM @ N ) @ one )
% 5.31/5.64 = ( bit0 @ N ) ) ).
% 5.31/5.64
% 5.31/5.64 % BitM_plus_one
% 5.31/5.64 thf(fact_8609_one__plus__BitM,axiom,
% 5.31/5.64 ! [N: num] :
% 5.31/5.64 ( ( plus_plus_num @ one @ ( bitM @ N ) )
% 5.31/5.64 = ( bit0 @ N ) ) ).
% 5.31/5.64
% 5.31/5.64 % one_plus_BitM
% 5.31/5.64 thf(fact_8610_forall__pos__mono__1,axiom,
% 5.31/5.64 ! [P2: real > $o,E: real] :
% 5.31/5.64 ( ! [D5: real,E2: real] :
% 5.31/5.64 ( ( ord_less_real @ D5 @ E2 )
% 5.31/5.64 => ( ( P2 @ D5 )
% 5.31/5.64 => ( P2 @ E2 ) ) )
% 5.31/5.64 => ( ! [N3: nat] : ( P2 @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N3 ) ) ) )
% 5.31/5.64 => ( ( ord_less_real @ zero_zero_real @ E )
% 5.31/5.64 => ( P2 @ E ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % forall_pos_mono_1
% 5.31/5.64 thf(fact_8611_forall__pos__mono,axiom,
% 5.31/5.64 ! [P2: real > $o,E: real] :
% 5.31/5.64 ( ! [D5: real,E2: real] :
% 5.31/5.64 ( ( ord_less_real @ D5 @ E2 )
% 5.31/5.64 => ( ( P2 @ D5 )
% 5.31/5.64 => ( P2 @ E2 ) ) )
% 5.31/5.64 => ( ! [N3: nat] :
% 5.31/5.64 ( ( N3 != zero_zero_nat )
% 5.31/5.64 => ( P2 @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ N3 ) ) ) )
% 5.31/5.64 => ( ( ord_less_real @ zero_zero_real @ E )
% 5.31/5.64 => ( P2 @ E ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % forall_pos_mono
% 5.31/5.64 thf(fact_8612_real__arch__inverse,axiom,
% 5.31/5.64 ! [E: real] :
% 5.31/5.64 ( ( ord_less_real @ zero_zero_real @ E )
% 5.31/5.64 = ( ? [N4: nat] :
% 5.31/5.64 ( ( N4 != zero_zero_nat )
% 5.31/5.64 & ( ord_less_real @ zero_zero_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ N4 ) ) )
% 5.31/5.64 & ( ord_less_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ N4 ) ) @ E ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % real_arch_inverse
% 5.31/5.64 thf(fact_8613_sin__zero__iff__int2,axiom,
% 5.31/5.64 ! [X: real] :
% 5.31/5.64 ( ( ( sin_real @ X )
% 5.31/5.64 = zero_zero_real )
% 5.31/5.64 = ( ? [I: int] :
% 5.31/5.64 ( X
% 5.31/5.64 = ( times_times_real @ ( ring_1_of_int_real @ I ) @ pi ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % sin_zero_iff_int2
% 5.31/5.64 thf(fact_8614_cos__one__2pi__int,axiom,
% 5.31/5.64 ! [X: real] :
% 5.31/5.64 ( ( ( cos_real @ X )
% 5.31/5.64 = one_one_real )
% 5.31/5.64 = ( ? [X4: int] :
% 5.31/5.64 ( X
% 5.31/5.64 = ( times_times_real @ ( times_times_real @ ( ring_1_of_int_real @ X4 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ pi ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % cos_one_2pi_int
% 5.31/5.64 thf(fact_8615_cos__zero__iff__int,axiom,
% 5.31/5.64 ! [X: real] :
% 5.31/5.64 ( ( ( cos_real @ X )
% 5.31/5.64 = zero_zero_real )
% 5.31/5.64 = ( ? [I: int] :
% 5.31/5.64 ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ I )
% 5.31/5.64 & ( X
% 5.31/5.64 = ( times_times_real @ ( ring_1_of_int_real @ I ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % cos_zero_iff_int
% 5.31/5.64 thf(fact_8616_sin__zero__iff__int,axiom,
% 5.31/5.64 ! [X: real] :
% 5.31/5.64 ( ( ( sin_real @ X )
% 5.31/5.64 = zero_zero_real )
% 5.31/5.64 = ( ? [I: int] :
% 5.31/5.64 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ I )
% 5.31/5.64 & ( X
% 5.31/5.64 = ( times_times_real @ ( ring_1_of_int_real @ I ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % sin_zero_iff_int
% 5.31/5.64 thf(fact_8617_complex__unimodular__polar,axiom,
% 5.31/5.64 ! [Z3: complex] :
% 5.31/5.64 ( ( ( real_V1022390504157884413omplex @ Z3 )
% 5.31/5.64 = one_one_real )
% 5.31/5.64 => ~ ! [T6: real] :
% 5.31/5.64 ( ( ord_less_eq_real @ zero_zero_real @ T6 )
% 5.31/5.64 => ( ( ord_less_real @ T6 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 5.31/5.64 => ( Z3
% 5.31/5.64 != ( complex2 @ ( cos_real @ T6 ) @ ( sin_real @ T6 ) ) ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % complex_unimodular_polar
% 5.31/5.64 thf(fact_8618_arccos__cos__eq__abs__2pi,axiom,
% 5.31/5.64 ! [Theta: real] :
% 5.31/5.64 ~ ! [K: int] :
% 5.31/5.64 ( ( arccos @ ( cos_real @ Theta ) )
% 5.31/5.64 != ( abs_abs_real @ ( minus_minus_real @ Theta @ ( times_times_real @ ( ring_1_of_int_real @ K ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % arccos_cos_eq_abs_2pi
% 5.31/5.64 thf(fact_8619_log__base__10__eq1,axiom,
% 5.31/5.64 ! [X: real] :
% 5.31/5.64 ( ( ord_less_real @ zero_zero_real @ X )
% 5.31/5.64 => ( ( log2 @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ X )
% 5.31/5.64 = ( 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 ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % log_base_10_eq1
% 5.31/5.64 thf(fact_8620_complex__scaleR,axiom,
% 5.31/5.64 ! [R3: real,A: real,B: real] :
% 5.31/5.64 ( ( real_V2046097035970521341omplex @ R3 @ ( complex2 @ A @ B ) )
% 5.31/5.64 = ( complex2 @ ( times_times_real @ R3 @ A ) @ ( times_times_real @ R3 @ B ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % complex_scaleR
% 5.31/5.64 thf(fact_8621_complex__mult,axiom,
% 5.31/5.64 ! [A: real,B: real,C2: real,D: real] :
% 5.31/5.64 ( ( times_times_complex @ ( complex2 @ A @ B ) @ ( complex2 @ C2 @ D ) )
% 5.31/5.64 = ( complex2 @ ( minus_minus_real @ ( times_times_real @ A @ C2 ) @ ( times_times_real @ B @ D ) ) @ ( plus_plus_real @ ( times_times_real @ A @ D ) @ ( times_times_real @ B @ C2 ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % complex_mult
% 5.31/5.64 thf(fact_8622_log__mult,axiom,
% 5.31/5.64 ! [A: real,X: real,Y: real] :
% 5.31/5.64 ( ( ord_less_real @ zero_zero_real @ A )
% 5.31/5.64 => ( ( A != one_one_real )
% 5.31/5.64 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.31/5.64 => ( ( ord_less_real @ zero_zero_real @ Y )
% 5.31/5.64 => ( ( log2 @ A @ ( times_times_real @ X @ Y ) )
% 5.31/5.64 = ( plus_plus_real @ ( log2 @ A @ X ) @ ( log2 @ A @ Y ) ) ) ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % log_mult
% 5.31/5.64 thf(fact_8623_log__nat__power,axiom,
% 5.31/5.64 ! [X: real,B: real,N: nat] :
% 5.31/5.64 ( ( ord_less_real @ zero_zero_real @ X )
% 5.31/5.64 => ( ( log2 @ B @ ( power_power_real @ X @ N ) )
% 5.31/5.64 = ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( log2 @ B @ X ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % log_nat_power
% 5.31/5.64 thf(fact_8624_log__of__power__less,axiom,
% 5.31/5.64 ! [M2: nat,B: real,N: nat] :
% 5.31/5.64 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ M2 ) @ ( power_power_real @ B @ N ) )
% 5.31/5.64 => ( ( ord_less_real @ one_one_real @ B )
% 5.31/5.64 => ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 5.31/5.64 => ( ord_less_real @ ( log2 @ B @ ( semiri5074537144036343181t_real @ M2 ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % log_of_power_less
% 5.31/5.64 thf(fact_8625_log__eq__div__ln__mult__log,axiom,
% 5.31/5.64 ! [A: real,B: real,X: real] :
% 5.31/5.64 ( ( ord_less_real @ zero_zero_real @ A )
% 5.31/5.64 => ( ( A != one_one_real )
% 5.31/5.64 => ( ( ord_less_real @ zero_zero_real @ B )
% 5.31/5.64 => ( ( B != one_one_real )
% 5.31/5.64 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.31/5.64 => ( ( log2 @ A @ X )
% 5.31/5.64 = ( times_times_real @ ( divide_divide_real @ ( ln_ln_real @ B ) @ ( ln_ln_real @ A ) ) @ ( log2 @ B @ X ) ) ) ) ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % log_eq_div_ln_mult_log
% 5.31/5.64 thf(fact_8626_log__of__power__le,axiom,
% 5.31/5.64 ! [M2: nat,B: real,N: nat] :
% 5.31/5.64 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ M2 ) @ ( power_power_real @ B @ N ) )
% 5.31/5.64 => ( ( ord_less_real @ one_one_real @ B )
% 5.31/5.64 => ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 5.31/5.64 => ( ord_less_eq_real @ ( log2 @ B @ ( semiri5074537144036343181t_real @ M2 ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % log_of_power_le
% 5.31/5.64 thf(fact_8627_le__log2__of__power,axiom,
% 5.31/5.64 ! [N: nat,M2: nat] :
% 5.31/5.64 ( ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ M2 )
% 5.31/5.64 => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ N ) @ ( log2 @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M2 ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % le_log2_of_power
% 5.31/5.64 thf(fact_8628_divmod__step__nat__def,axiom,
% 5.31/5.64 ( unique5026877609467782581ep_nat
% 5.31/5.64 = ( ^ [L2: num] :
% 5.31/5.64 ( produc2626176000494625587at_nat
% 5.31/5.64 @ ^ [Q5: nat,R: nat] : ( if_Pro6206227464963214023at_nat @ ( ord_less_eq_nat @ ( numeral_numeral_nat @ L2 ) @ R ) @ ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q5 ) @ one_one_nat ) @ ( minus_minus_nat @ R @ ( numeral_numeral_nat @ L2 ) ) ) @ ( product_Pair_nat_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q5 ) @ R ) ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % divmod_step_nat_def
% 5.31/5.64 thf(fact_8629_log2__of__power__less,axiom,
% 5.31/5.64 ! [M2: nat,N: nat] :
% 5.31/5.64 ( ( ord_less_nat @ M2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.31/5.64 => ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 5.31/5.64 => ( ord_less_real @ ( log2 @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M2 ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % log2_of_power_less
% 5.31/5.64 thf(fact_8630_divmod__step__int__def,axiom,
% 5.31/5.64 ( unique5024387138958732305ep_int
% 5.31/5.64 = ( ^ [L2: num] :
% 5.31/5.64 ( produc4245557441103728435nt_int
% 5.31/5.64 @ ^ [Q5: int,R: int] : ( if_Pro3027730157355071871nt_int @ ( ord_less_eq_int @ ( numeral_numeral_int @ L2 ) @ R ) @ ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q5 ) @ one_one_int ) @ ( minus_minus_int @ R @ ( numeral_numeral_int @ L2 ) ) ) @ ( product_Pair_int_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q5 ) @ R ) ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % divmod_step_int_def
% 5.31/5.64 thf(fact_8631_log2__of__power__le,axiom,
% 5.31/5.64 ! [M2: nat,N: nat] :
% 5.31/5.64 ( ( ord_less_eq_nat @ M2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.31/5.64 => ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 5.31/5.64 => ( ord_less_eq_real @ ( log2 @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M2 ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % log2_of_power_le
% 5.31/5.64 thf(fact_8632_log__base__10__eq2,axiom,
% 5.31/5.64 ! [X: real] :
% 5.31/5.64 ( ( ord_less_real @ zero_zero_real @ X )
% 5.31/5.64 => ( ( log2 @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ X )
% 5.31/5.64 = ( times_times_real @ ( log2 @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ ( exp_real @ one_one_real ) ) @ ( ln_ln_real @ X ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % log_base_10_eq2
% 5.31/5.64 thf(fact_8633_ceiling__log__nat__eq__powr__iff,axiom,
% 5.31/5.64 ! [B: nat,K2: nat,N: nat] :
% 5.31/5.64 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 5.31/5.64 => ( ( ord_less_nat @ zero_zero_nat @ K2 )
% 5.31/5.64 => ( ( ( archim7802044766580827645g_real @ ( log2 @ ( semiri5074537144036343181t_real @ B ) @ ( semiri5074537144036343181t_real @ K2 ) ) )
% 5.31/5.64 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) )
% 5.31/5.64 = ( ( ord_less_nat @ ( power_power_nat @ B @ N ) @ K2 )
% 5.31/5.64 & ( ord_less_eq_nat @ K2 @ ( power_power_nat @ B @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % ceiling_log_nat_eq_powr_iff
% 5.31/5.64 thf(fact_8634_ceiling__log__nat__eq__if,axiom,
% 5.31/5.64 ! [B: nat,N: nat,K2: nat] :
% 5.31/5.64 ( ( ord_less_nat @ ( power_power_nat @ B @ N ) @ K2 )
% 5.31/5.64 => ( ( ord_less_eq_nat @ K2 @ ( power_power_nat @ B @ ( plus_plus_nat @ N @ one_one_nat ) ) )
% 5.31/5.64 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 5.31/5.64 => ( ( archim7802044766580827645g_real @ ( log2 @ ( semiri5074537144036343181t_real @ B ) @ ( semiri5074537144036343181t_real @ K2 ) ) )
% 5.31/5.64 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % ceiling_log_nat_eq_if
% 5.31/5.64 thf(fact_8635_ceiling__log2__div2,axiom,
% 5.31/5.64 ! [N: nat] :
% 5.31/5.64 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.31/5.64 => ( ( archim7802044766580827645g_real @ ( log2 @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N ) ) )
% 5.31/5.64 = ( plus_plus_int @ ( archim7802044766580827645g_real @ ( log2 @ ( 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 ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % ceiling_log2_div2
% 5.31/5.64 thf(fact_8636_divmod__nat__if,axiom,
% 5.31/5.64 ( divmod_nat
% 5.31/5.64 = ( ^ [M6: nat,N4: nat] :
% 5.31/5.64 ( if_Pro6206227464963214023at_nat
% 5.31/5.64 @ ( ( N4 = zero_zero_nat )
% 5.31/5.64 | ( ord_less_nat @ M6 @ N4 ) )
% 5.31/5.64 @ ( product_Pair_nat_nat @ zero_zero_nat @ M6 )
% 5.31/5.64 @ ( produc2626176000494625587at_nat
% 5.31/5.64 @ ^ [Q5: nat] : ( product_Pair_nat_nat @ ( suc @ Q5 ) )
% 5.31/5.64 @ ( divmod_nat @ ( minus_minus_nat @ M6 @ N4 ) @ N4 ) ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % divmod_nat_if
% 5.31/5.64 thf(fact_8637_floor__log__nat__eq__powr__iff,axiom,
% 5.31/5.64 ! [B: nat,K2: nat,N: nat] :
% 5.31/5.64 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 5.31/5.64 => ( ( ord_less_nat @ zero_zero_nat @ K2 )
% 5.31/5.64 => ( ( ( archim6058952711729229775r_real @ ( log2 @ ( semiri5074537144036343181t_real @ B ) @ ( semiri5074537144036343181t_real @ K2 ) ) )
% 5.31/5.64 = ( semiri1314217659103216013at_int @ N ) )
% 5.31/5.64 = ( ( ord_less_eq_nat @ ( power_power_nat @ B @ N ) @ K2 )
% 5.31/5.64 & ( ord_less_nat @ K2 @ ( power_power_nat @ B @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % floor_log_nat_eq_powr_iff
% 5.31/5.64 thf(fact_8638_divide__complex__def,axiom,
% 5.31/5.64 ( divide1717551699836669952omplex
% 5.31/5.64 = ( ^ [X4: complex,Y4: complex] : ( times_times_complex @ X4 @ ( invers8013647133539491842omplex @ Y4 ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % divide_complex_def
% 5.31/5.64 thf(fact_8639_prod__encode__def,axiom,
% 5.31/5.64 ( nat_prod_encode
% 5.31/5.64 = ( produc6842872674320459806at_nat
% 5.31/5.64 @ ^ [M6: nat,N4: nat] : ( plus_plus_nat @ ( nat_triangle @ ( plus_plus_nat @ M6 @ N4 ) ) @ M6 ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % prod_encode_def
% 5.31/5.64 thf(fact_8640_Divides_Oadjust__div__def,axiom,
% 5.31/5.64 ( adjust_div
% 5.31/5.64 = ( produc8211389475949308722nt_int
% 5.31/5.64 @ ^ [Q5: int,R: int] : ( plus_plus_int @ Q5 @ ( zero_n2684676970156552555ol_int @ ( R != zero_zero_int ) ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % Divides.adjust_div_def
% 5.31/5.64 thf(fact_8641_divmod__nat__def,axiom,
% 5.31/5.64 ( divmod_nat
% 5.31/5.64 = ( ^ [M6: nat,N4: nat] : ( product_Pair_nat_nat @ ( divide_divide_nat @ M6 @ N4 ) @ ( modulo_modulo_nat @ M6 @ N4 ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % divmod_nat_def
% 5.31/5.64 thf(fact_8642_floor__log2__div2,axiom,
% 5.31/5.64 ! [N: nat] :
% 5.31/5.64 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.31/5.64 => ( ( archim6058952711729229775r_real @ ( log2 @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N ) ) )
% 5.31/5.64 = ( plus_plus_int @ ( archim6058952711729229775r_real @ ( log2 @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ one_one_int ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % floor_log2_div2
% 5.31/5.64 thf(fact_8643_floor__log__nat__eq__if,axiom,
% 5.31/5.64 ! [B: nat,N: nat,K2: nat] :
% 5.31/5.64 ( ( ord_less_eq_nat @ ( power_power_nat @ B @ N ) @ K2 )
% 5.31/5.64 => ( ( ord_less_nat @ K2 @ ( power_power_nat @ B @ ( plus_plus_nat @ N @ one_one_nat ) ) )
% 5.31/5.64 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 5.31/5.64 => ( ( archim6058952711729229775r_real @ ( log2 @ ( semiri5074537144036343181t_real @ B ) @ ( semiri5074537144036343181t_real @ K2 ) ) )
% 5.31/5.64 = ( semiri1314217659103216013at_int @ N ) ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % floor_log_nat_eq_if
% 5.31/5.64 thf(fact_8644_cot__periodic,axiom,
% 5.31/5.64 ! [X: real] :
% 5.31/5.64 ( ( cot_real @ ( plus_plus_real @ X @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 5.31/5.64 = ( cot_real @ X ) ) ).
% 5.31/5.64
% 5.31/5.64 % cot_periodic
% 5.31/5.64 thf(fact_8645_modulo__int__unfold,axiom,
% 5.31/5.64 ! [L: int,K2: int,N: nat,M2: nat] :
% 5.31/5.64 ( ( ( ( ( sgn_sgn_int @ L )
% 5.31/5.64 = zero_zero_int )
% 5.31/5.64 | ( ( sgn_sgn_int @ K2 )
% 5.31/5.64 = zero_zero_int )
% 5.31/5.64 | ( N = zero_zero_nat ) )
% 5.31/5.64 => ( ( modulo_modulo_int @ ( times_times_int @ ( sgn_sgn_int @ K2 ) @ ( semiri1314217659103216013at_int @ M2 ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 5.31/5.64 = ( times_times_int @ ( sgn_sgn_int @ K2 ) @ ( semiri1314217659103216013at_int @ M2 ) ) ) )
% 5.31/5.64 & ( ~ ( ( ( sgn_sgn_int @ L )
% 5.31/5.64 = zero_zero_int )
% 5.31/5.64 | ( ( sgn_sgn_int @ K2 )
% 5.31/5.64 = zero_zero_int )
% 5.31/5.64 | ( N = zero_zero_nat ) )
% 5.31/5.64 => ( ( ( ( sgn_sgn_int @ K2 )
% 5.31/5.64 = ( sgn_sgn_int @ L ) )
% 5.31/5.64 => ( ( modulo_modulo_int @ ( times_times_int @ ( sgn_sgn_int @ K2 ) @ ( semiri1314217659103216013at_int @ M2 ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 5.31/5.64 = ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ M2 @ N ) ) ) ) )
% 5.31/5.64 & ( ( ( sgn_sgn_int @ K2 )
% 5.31/5.64 != ( sgn_sgn_int @ L ) )
% 5.31/5.64 => ( ( modulo_modulo_int @ ( times_times_int @ ( sgn_sgn_int @ K2 ) @ ( semiri1314217659103216013at_int @ M2 ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 5.31/5.64 = ( times_times_int @ ( sgn_sgn_int @ L )
% 5.31/5.64 @ ( minus_minus_int
% 5.31/5.64 @ ( semiri1314217659103216013at_int
% 5.31/5.64 @ ( times_times_nat @ N
% 5.31/5.64 @ ( zero_n2687167440665602831ol_nat
% 5.31/5.64 @ ~ ( dvd_dvd_nat @ N @ M2 ) ) ) )
% 5.31/5.64 @ ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ M2 @ N ) ) ) ) ) ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % modulo_int_unfold
% 5.31/5.64 thf(fact_8646_dvd__mult__sgn__iff,axiom,
% 5.31/5.64 ! [L: int,K2: int,R3: int] :
% 5.31/5.64 ( ( dvd_dvd_int @ L @ ( times_times_int @ K2 @ ( sgn_sgn_int @ R3 ) ) )
% 5.31/5.64 = ( ( dvd_dvd_int @ L @ K2 )
% 5.31/5.64 | ( R3 = zero_zero_int ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % dvd_mult_sgn_iff
% 5.31/5.64 thf(fact_8647_dvd__sgn__mult__iff,axiom,
% 5.31/5.64 ! [L: int,R3: int,K2: int] :
% 5.31/5.64 ( ( dvd_dvd_int @ L @ ( times_times_int @ ( sgn_sgn_int @ R3 ) @ K2 ) )
% 5.31/5.64 = ( ( dvd_dvd_int @ L @ K2 )
% 5.31/5.64 | ( R3 = zero_zero_int ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % dvd_sgn_mult_iff
% 5.31/5.64 thf(fact_8648_mult__sgn__dvd__iff,axiom,
% 5.31/5.64 ! [L: int,R3: int,K2: int] :
% 5.31/5.64 ( ( dvd_dvd_int @ ( times_times_int @ L @ ( sgn_sgn_int @ R3 ) ) @ K2 )
% 5.31/5.64 = ( ( dvd_dvd_int @ L @ K2 )
% 5.31/5.64 & ( ( R3 = zero_zero_int )
% 5.31/5.64 => ( K2 = zero_zero_int ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % mult_sgn_dvd_iff
% 5.31/5.64 thf(fact_8649_sgn__mult__dvd__iff,axiom,
% 5.31/5.64 ! [R3: int,L: int,K2: int] :
% 5.31/5.64 ( ( dvd_dvd_int @ ( times_times_int @ ( sgn_sgn_int @ R3 ) @ L ) @ K2 )
% 5.31/5.64 = ( ( dvd_dvd_int @ L @ K2 )
% 5.31/5.64 & ( ( R3 = zero_zero_int )
% 5.31/5.64 => ( K2 = zero_zero_int ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % sgn_mult_dvd_iff
% 5.31/5.64 thf(fact_8650_cot__npi,axiom,
% 5.31/5.64 ! [N: nat] :
% 5.31/5.64 ( ( cot_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ pi ) )
% 5.31/5.64 = zero_zero_real ) ).
% 5.31/5.64
% 5.31/5.64 % cot_npi
% 5.31/5.64 thf(fact_8651_int__sgnE,axiom,
% 5.31/5.64 ! [K2: int] :
% 5.31/5.64 ~ ! [N3: nat,L4: int] :
% 5.31/5.64 ( K2
% 5.31/5.64 != ( times_times_int @ ( sgn_sgn_int @ L4 ) @ ( semiri1314217659103216013at_int @ N3 ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % int_sgnE
% 5.31/5.64 thf(fact_8652_div__eq__sgn__abs,axiom,
% 5.31/5.64 ! [K2: int,L: int] :
% 5.31/5.64 ( ( ( sgn_sgn_int @ K2 )
% 5.31/5.64 = ( sgn_sgn_int @ L ) )
% 5.31/5.64 => ( ( divide_divide_int @ K2 @ L )
% 5.31/5.64 = ( divide_divide_int @ ( abs_abs_int @ K2 ) @ ( abs_abs_int @ L ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % div_eq_sgn_abs
% 5.31/5.64 thf(fact_8653_div__sgn__abs__cancel,axiom,
% 5.31/5.64 ! [V2: int,K2: int,L: int] :
% 5.31/5.64 ( ( V2 != zero_zero_int )
% 5.31/5.64 => ( ( divide_divide_int @ ( times_times_int @ ( sgn_sgn_int @ V2 ) @ ( abs_abs_int @ K2 ) ) @ ( times_times_int @ ( sgn_sgn_int @ V2 ) @ ( abs_abs_int @ L ) ) )
% 5.31/5.64 = ( divide_divide_int @ ( abs_abs_int @ K2 ) @ ( abs_abs_int @ L ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % div_sgn_abs_cancel
% 5.31/5.64 thf(fact_8654_div__dvd__sgn__abs,axiom,
% 5.31/5.64 ! [L: int,K2: int] :
% 5.31/5.64 ( ( dvd_dvd_int @ L @ K2 )
% 5.31/5.64 => ( ( divide_divide_int @ K2 @ L )
% 5.31/5.64 = ( times_times_int @ ( times_times_int @ ( sgn_sgn_int @ K2 ) @ ( sgn_sgn_int @ L ) ) @ ( divide_divide_int @ ( abs_abs_int @ K2 ) @ ( abs_abs_int @ L ) ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % div_dvd_sgn_abs
% 5.31/5.64 thf(fact_8655_eucl__rel__int__remainderI,axiom,
% 5.31/5.64 ! [R3: int,L: int,K2: int,Q2: int] :
% 5.31/5.64 ( ( ( sgn_sgn_int @ R3 )
% 5.31/5.64 = ( sgn_sgn_int @ L ) )
% 5.31/5.64 => ( ( ord_less_int @ ( abs_abs_int @ R3 ) @ ( abs_abs_int @ L ) )
% 5.31/5.64 => ( ( K2
% 5.31/5.64 = ( plus_plus_int @ ( times_times_int @ Q2 @ L ) @ R3 ) )
% 5.31/5.64 => ( eucl_rel_int @ K2 @ L @ ( product_Pair_int_int @ Q2 @ R3 ) ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % eucl_rel_int_remainderI
% 5.31/5.64 thf(fact_8656_eucl__rel__int_Osimps,axiom,
% 5.31/5.64 ( eucl_rel_int
% 5.31/5.64 = ( ^ [A13: int,A24: int,A32: product_prod_int_int] :
% 5.31/5.64 ( ? [K3: int] :
% 5.31/5.64 ( ( A13 = K3 )
% 5.31/5.64 & ( A24 = zero_zero_int )
% 5.31/5.64 & ( A32
% 5.31/5.64 = ( product_Pair_int_int @ zero_zero_int @ K3 ) ) )
% 5.31/5.64 | ? [L2: int,K3: int,Q5: int] :
% 5.31/5.64 ( ( A13 = K3 )
% 5.31/5.64 & ( A24 = L2 )
% 5.31/5.64 & ( A32
% 5.31/5.64 = ( product_Pair_int_int @ Q5 @ zero_zero_int ) )
% 5.31/5.64 & ( L2 != zero_zero_int )
% 5.31/5.64 & ( K3
% 5.31/5.64 = ( times_times_int @ Q5 @ L2 ) ) )
% 5.31/5.64 | ? [R: int,L2: int,K3: int,Q5: int] :
% 5.31/5.64 ( ( A13 = K3 )
% 5.31/5.64 & ( A24 = L2 )
% 5.31/5.64 & ( A32
% 5.31/5.64 = ( product_Pair_int_int @ Q5 @ R ) )
% 5.31/5.64 & ( ( sgn_sgn_int @ R )
% 5.31/5.64 = ( sgn_sgn_int @ L2 ) )
% 5.31/5.64 & ( ord_less_int @ ( abs_abs_int @ R ) @ ( abs_abs_int @ L2 ) )
% 5.31/5.64 & ( K3
% 5.31/5.64 = ( plus_plus_int @ ( times_times_int @ Q5 @ L2 ) @ R ) ) ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % eucl_rel_int.simps
% 5.31/5.64 thf(fact_8657_eucl__rel__int_Ocases,axiom,
% 5.31/5.64 ! [A12: int,A23: int,A33: product_prod_int_int] :
% 5.31/5.64 ( ( eucl_rel_int @ A12 @ A23 @ A33 )
% 5.31/5.64 => ( ( ( A23 = zero_zero_int )
% 5.31/5.64 => ( A33
% 5.31/5.64 != ( product_Pair_int_int @ zero_zero_int @ A12 ) ) )
% 5.31/5.64 => ( ! [Q3: int] :
% 5.31/5.64 ( ( A33
% 5.31/5.64 = ( product_Pair_int_int @ Q3 @ zero_zero_int ) )
% 5.31/5.64 => ( ( A23 != zero_zero_int )
% 5.31/5.64 => ( A12
% 5.31/5.64 != ( times_times_int @ Q3 @ A23 ) ) ) )
% 5.31/5.64 => ~ ! [R4: int,Q3: int] :
% 5.31/5.64 ( ( A33
% 5.31/5.64 = ( product_Pair_int_int @ Q3 @ R4 ) )
% 5.31/5.64 => ( ( ( sgn_sgn_int @ R4 )
% 5.31/5.64 = ( sgn_sgn_int @ A23 ) )
% 5.31/5.64 => ( ( ord_less_int @ ( abs_abs_int @ R4 ) @ ( abs_abs_int @ A23 ) )
% 5.31/5.64 => ( A12
% 5.31/5.64 != ( plus_plus_int @ ( times_times_int @ Q3 @ A23 ) @ R4 ) ) ) ) ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % eucl_rel_int.cases
% 5.31/5.64 thf(fact_8658_div__noneq__sgn__abs,axiom,
% 5.31/5.64 ! [L: int,K2: int] :
% 5.31/5.64 ( ( L != zero_zero_int )
% 5.31/5.64 => ( ( ( sgn_sgn_int @ K2 )
% 5.31/5.64 != ( sgn_sgn_int @ L ) )
% 5.31/5.64 => ( ( divide_divide_int @ K2 @ L )
% 5.31/5.64 = ( minus_minus_int @ ( uminus_uminus_int @ ( divide_divide_int @ ( abs_abs_int @ K2 ) @ ( abs_abs_int @ L ) ) )
% 5.31/5.64 @ ( zero_n2684676970156552555ol_int
% 5.31/5.64 @ ~ ( dvd_dvd_int @ L @ K2 ) ) ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % div_noneq_sgn_abs
% 5.31/5.64 thf(fact_8659_divide__int__unfold,axiom,
% 5.31/5.64 ! [L: int,K2: int,N: nat,M2: nat] :
% 5.31/5.64 ( ( ( ( ( sgn_sgn_int @ L )
% 5.31/5.64 = zero_zero_int )
% 5.31/5.64 | ( ( sgn_sgn_int @ K2 )
% 5.31/5.64 = zero_zero_int )
% 5.31/5.64 | ( N = zero_zero_nat ) )
% 5.31/5.64 => ( ( divide_divide_int @ ( times_times_int @ ( sgn_sgn_int @ K2 ) @ ( semiri1314217659103216013at_int @ M2 ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 5.31/5.64 = zero_zero_int ) )
% 5.31/5.64 & ( ~ ( ( ( sgn_sgn_int @ L )
% 5.31/5.64 = zero_zero_int )
% 5.31/5.64 | ( ( sgn_sgn_int @ K2 )
% 5.31/5.64 = zero_zero_int )
% 5.31/5.64 | ( N = zero_zero_nat ) )
% 5.31/5.64 => ( ( ( ( sgn_sgn_int @ K2 )
% 5.31/5.64 = ( sgn_sgn_int @ L ) )
% 5.31/5.64 => ( ( divide_divide_int @ ( times_times_int @ ( sgn_sgn_int @ K2 ) @ ( semiri1314217659103216013at_int @ M2 ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 5.31/5.64 = ( semiri1314217659103216013at_int @ ( divide_divide_nat @ M2 @ N ) ) ) )
% 5.31/5.64 & ( ( ( sgn_sgn_int @ K2 )
% 5.31/5.64 != ( sgn_sgn_int @ L ) )
% 5.31/5.64 => ( ( divide_divide_int @ ( times_times_int @ ( sgn_sgn_int @ K2 ) @ ( semiri1314217659103216013at_int @ M2 ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 5.31/5.64 = ( uminus_uminus_int
% 5.31/5.64 @ ( semiri1314217659103216013at_int
% 5.31/5.64 @ ( plus_plus_nat @ ( divide_divide_nat @ M2 @ N )
% 5.31/5.64 @ ( zero_n2687167440665602831ol_nat
% 5.31/5.64 @ ~ ( dvd_dvd_nat @ N @ M2 ) ) ) ) ) ) ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % divide_int_unfold
% 5.31/5.64 thf(fact_8660_natLess__def,axiom,
% 5.31/5.64 ( bNF_Ca8459412986667044542atLess
% 5.31/5.64 = ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ ord_less_nat ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % natLess_def
% 5.31/5.64 thf(fact_8661_modulo__int__def,axiom,
% 5.31/5.64 ( modulo_modulo_int
% 5.31/5.64 = ( ^ [K3: int,L2: int] :
% 5.31/5.64 ( if_int @ ( L2 = zero_zero_int ) @ K3
% 5.31/5.64 @ ( if_int
% 5.31/5.64 @ ( ( sgn_sgn_int @ K3 )
% 5.31/5.64 = ( sgn_sgn_int @ L2 ) )
% 5.31/5.64 @ ( times_times_int @ ( sgn_sgn_int @ L2 ) @ ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ ( nat2 @ ( abs_abs_int @ K3 ) ) @ ( nat2 @ ( abs_abs_int @ L2 ) ) ) ) )
% 5.31/5.64 @ ( times_times_int @ ( sgn_sgn_int @ L2 )
% 5.31/5.64 @ ( minus_minus_int
% 5.31/5.64 @ ( times_times_int @ ( abs_abs_int @ L2 )
% 5.31/5.64 @ ( zero_n2684676970156552555ol_int
% 5.31/5.64 @ ~ ( dvd_dvd_int @ L2 @ K3 ) ) )
% 5.31/5.64 @ ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ ( nat2 @ ( abs_abs_int @ K3 ) ) @ ( nat2 @ ( abs_abs_int @ L2 ) ) ) ) ) ) ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % modulo_int_def
% 5.31/5.64 thf(fact_8662_num_Osize__gen_I3_J,axiom,
% 5.31/5.64 ! [X33: num] :
% 5.31/5.64 ( ( size_num @ ( bit1 @ X33 ) )
% 5.31/5.64 = ( plus_plus_nat @ ( size_num @ X33 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % num.size_gen(3)
% 5.31/5.64 thf(fact_8663_mask__nat__positive__iff,axiom,
% 5.31/5.64 ! [N: nat] :
% 5.31/5.64 ( ( ord_less_nat @ zero_zero_nat @ ( bit_se2002935070580805687sk_nat @ N ) )
% 5.31/5.64 = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 5.31/5.64
% 5.31/5.64 % mask_nat_positive_iff
% 5.31/5.64 thf(fact_8664_nat__1,axiom,
% 5.31/5.64 ( ( nat2 @ one_one_int )
% 5.31/5.64 = ( suc @ zero_zero_nat ) ) ).
% 5.31/5.64
% 5.31/5.64 % nat_1
% 5.31/5.64 thf(fact_8665_nat__0__iff,axiom,
% 5.31/5.64 ! [I2: int] :
% 5.31/5.64 ( ( ( nat2 @ I2 )
% 5.31/5.64 = zero_zero_nat )
% 5.31/5.64 = ( ord_less_eq_int @ I2 @ zero_zero_int ) ) ).
% 5.31/5.64
% 5.31/5.64 % nat_0_iff
% 5.31/5.64 thf(fact_8666_nat__le__0,axiom,
% 5.31/5.64 ! [Z3: int] :
% 5.31/5.64 ( ( ord_less_eq_int @ Z3 @ zero_zero_int )
% 5.31/5.64 => ( ( nat2 @ Z3 )
% 5.31/5.64 = zero_zero_nat ) ) ).
% 5.31/5.64
% 5.31/5.64 % nat_le_0
% 5.31/5.64 thf(fact_8667_nat__neg__numeral,axiom,
% 5.31/5.64 ! [K2: num] :
% 5.31/5.64 ( ( nat2 @ ( uminus_uminus_int @ ( numeral_numeral_int @ K2 ) ) )
% 5.31/5.64 = zero_zero_nat ) ).
% 5.31/5.64
% 5.31/5.64 % nat_neg_numeral
% 5.31/5.64 thf(fact_8668_nat__zminus__int,axiom,
% 5.31/5.64 ! [N: nat] :
% 5.31/5.64 ( ( nat2 @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) )
% 5.31/5.64 = zero_zero_nat ) ).
% 5.31/5.64
% 5.31/5.64 % nat_zminus_int
% 5.31/5.64 thf(fact_8669_take__bit__of__Suc__0,axiom,
% 5.31/5.64 ! [N: nat] :
% 5.31/5.64 ( ( bit_se2925701944663578781it_nat @ N @ ( suc @ zero_zero_nat ) )
% 5.31/5.64 = ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % take_bit_of_Suc_0
% 5.31/5.64 thf(fact_8670_zero__less__nat__eq,axiom,
% 5.31/5.64 ! [Z3: int] :
% 5.31/5.64 ( ( ord_less_nat @ zero_zero_nat @ ( nat2 @ Z3 ) )
% 5.31/5.64 = ( ord_less_int @ zero_zero_int @ Z3 ) ) ).
% 5.31/5.64
% 5.31/5.64 % zero_less_nat_eq
% 5.31/5.64 thf(fact_8671_card__atLeastAtMost__int,axiom,
% 5.31/5.64 ! [L: int,U: int] :
% 5.31/5.64 ( ( finite_card_int @ ( set_or1266510415728281911st_int @ L @ U ) )
% 5.31/5.64 = ( nat2 @ ( plus_plus_int @ ( minus_minus_int @ U @ L ) @ one_one_int ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % card_atLeastAtMost_int
% 5.31/5.64 thf(fact_8672_nat__ceiling__le__eq,axiom,
% 5.31/5.64 ! [X: real,A: nat] :
% 5.31/5.64 ( ( ord_less_eq_nat @ ( nat2 @ ( archim7802044766580827645g_real @ X ) ) @ A )
% 5.31/5.64 = ( ord_less_eq_real @ X @ ( semiri5074537144036343181t_real @ A ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % nat_ceiling_le_eq
% 5.31/5.64 thf(fact_8673_one__less__nat__eq,axiom,
% 5.31/5.64 ! [Z3: int] :
% 5.31/5.64 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ ( nat2 @ Z3 ) )
% 5.31/5.64 = ( ord_less_int @ one_one_int @ Z3 ) ) ).
% 5.31/5.64
% 5.31/5.64 % one_less_nat_eq
% 5.31/5.64 thf(fact_8674_numeral__power__le__nat__cancel__iff,axiom,
% 5.31/5.64 ! [X: num,N: nat,A: int] :
% 5.31/5.64 ( ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N ) @ ( nat2 @ A ) )
% 5.31/5.64 = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) @ A ) ) ).
% 5.31/5.64
% 5.31/5.64 % numeral_power_le_nat_cancel_iff
% 5.31/5.64 thf(fact_8675_nat__le__numeral__power__cancel__iff,axiom,
% 5.31/5.64 ! [A: int,X: num,N: nat] :
% 5.31/5.64 ( ( ord_less_eq_nat @ ( nat2 @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N ) )
% 5.31/5.64 = ( ord_less_eq_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % nat_le_numeral_power_cancel_iff
% 5.31/5.64 thf(fact_8676_take__bit__tightened__less__eq__nat,axiom,
% 5.31/5.64 ! [M2: nat,N: nat,Q2: nat] :
% 5.31/5.64 ( ( ord_less_eq_nat @ M2 @ N )
% 5.31/5.64 => ( ord_less_eq_nat @ ( bit_se2925701944663578781it_nat @ M2 @ Q2 ) @ ( bit_se2925701944663578781it_nat @ N @ Q2 ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % take_bit_tightened_less_eq_nat
% 5.31/5.64 thf(fact_8677_take__bit__nat__less__eq__self,axiom,
% 5.31/5.64 ! [N: nat,M2: nat] : ( ord_less_eq_nat @ ( bit_se2925701944663578781it_nat @ N @ M2 ) @ M2 ) ).
% 5.31/5.64
% 5.31/5.64 % take_bit_nat_less_eq_self
% 5.31/5.64 thf(fact_8678_take__bit__mult,axiom,
% 5.31/5.64 ! [N: nat,K2: int,L: int] :
% 5.31/5.64 ( ( bit_se2923211474154528505it_int @ N @ ( times_times_int @ ( bit_se2923211474154528505it_int @ N @ K2 ) @ ( bit_se2923211474154528505it_int @ N @ L ) ) )
% 5.31/5.64 = ( bit_se2923211474154528505it_int @ N @ ( times_times_int @ K2 @ L ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % take_bit_mult
% 5.31/5.64 thf(fact_8679_less__eq__mask,axiom,
% 5.31/5.64 ! [N: nat] : ( ord_less_eq_nat @ N @ ( bit_se2002935070580805687sk_nat @ N ) ) ).
% 5.31/5.64
% 5.31/5.64 % less_eq_mask
% 5.31/5.64 thf(fact_8680_nat__zero__as__int,axiom,
% 5.31/5.64 ( zero_zero_nat
% 5.31/5.64 = ( nat2 @ zero_zero_int ) ) ).
% 5.31/5.64
% 5.31/5.64 % nat_zero_as_int
% 5.31/5.64 thf(fact_8681_take__bit__tightened__less__eq__int,axiom,
% 5.31/5.64 ! [M2: nat,N: nat,K2: int] :
% 5.31/5.64 ( ( ord_less_eq_nat @ M2 @ N )
% 5.31/5.64 => ( ord_less_eq_int @ ( bit_se2923211474154528505it_int @ M2 @ K2 ) @ ( bit_se2923211474154528505it_int @ N @ K2 ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % take_bit_tightened_less_eq_int
% 5.31/5.64 thf(fact_8682_nat__mono,axiom,
% 5.31/5.64 ! [X: int,Y: int] :
% 5.31/5.64 ( ( ord_less_eq_int @ X @ Y )
% 5.31/5.64 => ( ord_less_eq_nat @ ( nat2 @ X ) @ ( nat2 @ Y ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % nat_mono
% 5.31/5.64 thf(fact_8683_nat__le__iff,axiom,
% 5.31/5.64 ! [X: int,N: nat] :
% 5.31/5.64 ( ( ord_less_eq_nat @ ( nat2 @ X ) @ N )
% 5.31/5.64 = ( ord_less_eq_int @ X @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % nat_le_iff
% 5.31/5.64 thf(fact_8684_nat__abs__mult__distrib,axiom,
% 5.31/5.64 ! [W2: int,Z3: int] :
% 5.31/5.64 ( ( nat2 @ ( abs_abs_int @ ( times_times_int @ W2 @ Z3 ) ) )
% 5.31/5.64 = ( times_times_nat @ ( nat2 @ ( abs_abs_int @ W2 ) ) @ ( nat2 @ ( abs_abs_int @ Z3 ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % nat_abs_mult_distrib
% 5.31/5.64 thf(fact_8685_nat__times__as__int,axiom,
% 5.31/5.64 ( times_times_nat
% 5.31/5.64 = ( ^ [A5: nat,B4: nat] : ( nat2 @ ( times_times_int @ ( semiri1314217659103216013at_int @ A5 ) @ ( semiri1314217659103216013at_int @ B4 ) ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % nat_times_as_int
% 5.31/5.64 thf(fact_8686_less__mask,axiom,
% 5.31/5.64 ! [N: nat] :
% 5.31/5.64 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.31/5.64 => ( ord_less_nat @ N @ ( bit_se2002935070580805687sk_nat @ N ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % less_mask
% 5.31/5.64 thf(fact_8687_nat__le__eq__zle,axiom,
% 5.31/5.64 ! [W2: int,Z3: int] :
% 5.31/5.64 ( ( ( ord_less_int @ zero_zero_int @ W2 )
% 5.31/5.64 | ( ord_less_eq_int @ zero_zero_int @ Z3 ) )
% 5.31/5.64 => ( ( ord_less_eq_nat @ ( nat2 @ W2 ) @ ( nat2 @ Z3 ) )
% 5.31/5.64 = ( ord_less_eq_int @ W2 @ Z3 ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % nat_le_eq_zle
% 5.31/5.64 thf(fact_8688_nat__eq__iff2,axiom,
% 5.31/5.64 ! [M2: nat,W2: int] :
% 5.31/5.64 ( ( M2
% 5.31/5.64 = ( nat2 @ W2 ) )
% 5.31/5.64 = ( ( ( ord_less_eq_int @ zero_zero_int @ W2 )
% 5.31/5.64 => ( W2
% 5.31/5.64 = ( semiri1314217659103216013at_int @ M2 ) ) )
% 5.31/5.64 & ( ~ ( ord_less_eq_int @ zero_zero_int @ W2 )
% 5.31/5.64 => ( M2 = zero_zero_nat ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % nat_eq_iff2
% 5.31/5.64 thf(fact_8689_nat__eq__iff,axiom,
% 5.31/5.64 ! [W2: int,M2: nat] :
% 5.31/5.64 ( ( ( nat2 @ W2 )
% 5.31/5.64 = M2 )
% 5.31/5.64 = ( ( ( ord_less_eq_int @ zero_zero_int @ W2 )
% 5.31/5.64 => ( W2
% 5.31/5.64 = ( semiri1314217659103216013at_int @ M2 ) ) )
% 5.31/5.64 & ( ~ ( ord_less_eq_int @ zero_zero_int @ W2 )
% 5.31/5.64 => ( M2 = zero_zero_nat ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % nat_eq_iff
% 5.31/5.64 thf(fact_8690_split__nat,axiom,
% 5.31/5.64 ! [P2: nat > $o,I2: int] :
% 5.31/5.64 ( ( P2 @ ( nat2 @ I2 ) )
% 5.31/5.64 = ( ! [N4: nat] :
% 5.31/5.64 ( ( I2
% 5.31/5.64 = ( semiri1314217659103216013at_int @ N4 ) )
% 5.31/5.64 => ( P2 @ N4 ) )
% 5.31/5.64 & ( ( ord_less_int @ I2 @ zero_zero_int )
% 5.31/5.64 => ( P2 @ zero_zero_nat ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % split_nat
% 5.31/5.64 thf(fact_8691_le__nat__iff,axiom,
% 5.31/5.64 ! [K2: int,N: nat] :
% 5.31/5.64 ( ( ord_less_eq_int @ zero_zero_int @ K2 )
% 5.31/5.64 => ( ( ord_less_eq_nat @ N @ ( nat2 @ K2 ) )
% 5.31/5.64 = ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ N ) @ K2 ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % le_nat_iff
% 5.31/5.64 thf(fact_8692_nat__mult__distrib,axiom,
% 5.31/5.64 ! [Z3: int,Z6: int] :
% 5.31/5.64 ( ( ord_less_eq_int @ zero_zero_int @ Z3 )
% 5.31/5.64 => ( ( nat2 @ ( times_times_int @ Z3 @ Z6 ) )
% 5.31/5.64 = ( times_times_nat @ ( nat2 @ Z3 ) @ ( nat2 @ Z6 ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % nat_mult_distrib
% 5.31/5.64 thf(fact_8693_Suc__as__int,axiom,
% 5.31/5.64 ( suc
% 5.31/5.64 = ( ^ [A5: nat] : ( nat2 @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ A5 ) @ one_one_int ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % Suc_as_int
% 5.31/5.64 thf(fact_8694_nat__abs__triangle__ineq,axiom,
% 5.31/5.64 ! [K2: int,L: int] : ( ord_less_eq_nat @ ( nat2 @ ( abs_abs_int @ ( plus_plus_int @ K2 @ L ) ) ) @ ( plus_plus_nat @ ( nat2 @ ( abs_abs_int @ K2 ) ) @ ( nat2 @ ( abs_abs_int @ L ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % nat_abs_triangle_ineq
% 5.31/5.64 thf(fact_8695_nat__floor__neg,axiom,
% 5.31/5.64 ! [X: real] :
% 5.31/5.64 ( ( ord_less_eq_real @ X @ zero_zero_real )
% 5.31/5.64 => ( ( nat2 @ ( archim6058952711729229775r_real @ X ) )
% 5.31/5.64 = zero_zero_nat ) ) ).
% 5.31/5.64
% 5.31/5.64 % nat_floor_neg
% 5.31/5.64 thf(fact_8696_div__abs__eq__div__nat,axiom,
% 5.31/5.64 ! [K2: int,L: int] :
% 5.31/5.64 ( ( divide_divide_int @ ( abs_abs_int @ K2 ) @ ( abs_abs_int @ L ) )
% 5.31/5.64 = ( semiri1314217659103216013at_int @ ( divide_divide_nat @ ( nat2 @ ( abs_abs_int @ K2 ) ) @ ( nat2 @ ( abs_abs_int @ L ) ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % div_abs_eq_div_nat
% 5.31/5.64 thf(fact_8697_floor__eq3,axiom,
% 5.31/5.64 ! [N: nat,X: real] :
% 5.31/5.64 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ N ) @ X )
% 5.31/5.64 => ( ( ord_less_real @ X @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) )
% 5.31/5.64 => ( ( nat2 @ ( archim6058952711729229775r_real @ X ) )
% 5.31/5.64 = N ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % floor_eq3
% 5.31/5.64 thf(fact_8698_le__nat__floor,axiom,
% 5.31/5.64 ! [X: nat,A: real] :
% 5.31/5.64 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ X ) @ A )
% 5.31/5.64 => ( ord_less_eq_nat @ X @ ( nat2 @ ( archim6058952711729229775r_real @ A ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % le_nat_floor
% 5.31/5.64 thf(fact_8699_mod__abs__eq__div__nat,axiom,
% 5.31/5.64 ! [K2: int,L: int] :
% 5.31/5.64 ( ( modulo_modulo_int @ ( abs_abs_int @ K2 ) @ ( abs_abs_int @ L ) )
% 5.31/5.64 = ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ ( nat2 @ ( abs_abs_int @ K2 ) ) @ ( nat2 @ ( abs_abs_int @ L ) ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % mod_abs_eq_div_nat
% 5.31/5.64 thf(fact_8700_nat__2,axiom,
% 5.31/5.64 ( ( nat2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.31/5.64 = ( suc @ ( suc @ zero_zero_nat ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % nat_2
% 5.31/5.64 thf(fact_8701_sgn__power__injE,axiom,
% 5.31/5.64 ! [A: real,N: nat,X: real,B: real] :
% 5.31/5.64 ( ( ( times_times_real @ ( sgn_sgn_real @ A ) @ ( power_power_real @ ( abs_abs_real @ A ) @ N ) )
% 5.31/5.64 = X )
% 5.31/5.64 => ( ( X
% 5.31/5.64 = ( times_times_real @ ( sgn_sgn_real @ B ) @ ( power_power_real @ ( abs_abs_real @ B ) @ N ) ) )
% 5.31/5.64 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.64 => ( A = B ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % sgn_power_injE
% 5.31/5.64 thf(fact_8702_Suc__nat__eq__nat__zadd1,axiom,
% 5.31/5.64 ! [Z3: int] :
% 5.31/5.64 ( ( ord_less_eq_int @ zero_zero_int @ Z3 )
% 5.31/5.64 => ( ( suc @ ( nat2 @ Z3 ) )
% 5.31/5.64 = ( nat2 @ ( plus_plus_int @ one_one_int @ Z3 ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % Suc_nat_eq_nat_zadd1
% 5.31/5.64 thf(fact_8703_nat__mult__distrib__neg,axiom,
% 5.31/5.64 ! [Z3: int,Z6: int] :
% 5.31/5.64 ( ( ord_less_eq_int @ Z3 @ zero_zero_int )
% 5.31/5.64 => ( ( nat2 @ ( times_times_int @ Z3 @ Z6 ) )
% 5.31/5.64 = ( times_times_nat @ ( nat2 @ ( uminus_uminus_int @ Z3 ) ) @ ( nat2 @ ( uminus_uminus_int @ Z6 ) ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % nat_mult_distrib_neg
% 5.31/5.64 thf(fact_8704_nat__abs__int__diff,axiom,
% 5.31/5.64 ! [A: nat,B: nat] :
% 5.31/5.64 ( ( ( ord_less_eq_nat @ A @ B )
% 5.31/5.64 => ( ( nat2 @ ( abs_abs_int @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) )
% 5.31/5.64 = ( minus_minus_nat @ B @ A ) ) )
% 5.31/5.64 & ( ~ ( ord_less_eq_nat @ A @ B )
% 5.31/5.64 => ( ( nat2 @ ( abs_abs_int @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) )
% 5.31/5.64 = ( minus_minus_nat @ A @ B ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % nat_abs_int_diff
% 5.31/5.64 thf(fact_8705_floor__eq4,axiom,
% 5.31/5.64 ! [N: nat,X: real] :
% 5.31/5.64 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ N ) @ X )
% 5.31/5.64 => ( ( ord_less_real @ X @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) )
% 5.31/5.64 => ( ( nat2 @ ( archim6058952711729229775r_real @ X ) )
% 5.31/5.64 = N ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % floor_eq4
% 5.31/5.64 thf(fact_8706_num_Osize__gen_I1_J,axiom,
% 5.31/5.64 ( ( size_num @ one )
% 5.31/5.64 = zero_zero_nat ) ).
% 5.31/5.64
% 5.31/5.64 % num.size_gen(1)
% 5.31/5.64 thf(fact_8707_diff__nat__eq__if,axiom,
% 5.31/5.64 ! [Z6: int,Z3: int] :
% 5.31/5.64 ( ( ( ord_less_int @ Z6 @ zero_zero_int )
% 5.31/5.64 => ( ( minus_minus_nat @ ( nat2 @ Z3 ) @ ( nat2 @ Z6 ) )
% 5.31/5.64 = ( nat2 @ Z3 ) ) )
% 5.31/5.64 & ( ~ ( ord_less_int @ Z6 @ zero_zero_int )
% 5.31/5.64 => ( ( minus_minus_nat @ ( nat2 @ Z3 ) @ ( nat2 @ Z6 ) )
% 5.31/5.64 = ( if_nat @ ( ord_less_int @ ( minus_minus_int @ Z3 @ Z6 ) @ zero_zero_int ) @ zero_zero_nat @ ( nat2 @ ( minus_minus_int @ Z3 @ Z6 ) ) ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % diff_nat_eq_if
% 5.31/5.64 thf(fact_8708_take__bit__nat__less__self__iff,axiom,
% 5.31/5.64 ! [N: nat,M2: nat] :
% 5.31/5.64 ( ( ord_less_nat @ ( bit_se2925701944663578781it_nat @ N @ M2 ) @ M2 )
% 5.31/5.64 = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ M2 ) ) ).
% 5.31/5.64
% 5.31/5.64 % take_bit_nat_less_self_iff
% 5.31/5.64 thf(fact_8709_Suc__mask__eq__exp,axiom,
% 5.31/5.64 ! [N: nat] :
% 5.31/5.64 ( ( suc @ ( bit_se2002935070580805687sk_nat @ N ) )
% 5.31/5.64 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.31/5.64
% 5.31/5.64 % Suc_mask_eq_exp
% 5.31/5.64 thf(fact_8710_take__bit__Suc__minus__bit0,axiom,
% 5.31/5.64 ! [N: nat,K2: num] :
% 5.31/5.64 ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K2 ) ) ) )
% 5.31/5.64 = ( times_times_int @ ( bit_se2923211474154528505it_int @ N @ ( uminus_uminus_int @ ( numeral_numeral_int @ K2 ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % take_bit_Suc_minus_bit0
% 5.31/5.64 thf(fact_8711_nat__dvd__iff,axiom,
% 5.31/5.64 ! [Z3: int,M2: nat] :
% 5.31/5.64 ( ( dvd_dvd_nat @ ( nat2 @ Z3 ) @ M2 )
% 5.31/5.64 = ( ( ( ord_less_eq_int @ zero_zero_int @ Z3 )
% 5.31/5.64 => ( dvd_dvd_int @ Z3 @ ( semiri1314217659103216013at_int @ M2 ) ) )
% 5.31/5.64 & ( ~ ( ord_less_eq_int @ zero_zero_int @ Z3 )
% 5.31/5.64 => ( M2 = zero_zero_nat ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % nat_dvd_iff
% 5.31/5.64 thf(fact_8712_take__bit__numeral__minus__bit0,axiom,
% 5.31/5.64 ! [L: num,K2: num] :
% 5.31/5.64 ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K2 ) ) ) )
% 5.31/5.64 = ( times_times_int @ ( bit_se2923211474154528505it_int @ ( pred_numeral @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ K2 ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % take_bit_numeral_minus_bit0
% 5.31/5.64 thf(fact_8713_take__bit__int__less__eq,axiom,
% 5.31/5.64 ! [N: nat,K2: int] :
% 5.31/5.64 ( ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ K2 )
% 5.31/5.64 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.64 => ( ord_less_eq_int @ ( bit_se2923211474154528505it_int @ N @ K2 ) @ ( minus_minus_int @ K2 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % take_bit_int_less_eq
% 5.31/5.64 thf(fact_8714_signed__take__bit__eq__take__bit__shift,axiom,
% 5.31/5.64 ( bit_ri631733984087533419it_int
% 5.31/5.64 = ( ^ [N4: nat,K3: int] : ( minus_minus_int @ ( bit_se2923211474154528505it_int @ ( suc @ N4 ) @ ( plus_plus_int @ K3 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N4 ) ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N4 ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % signed_take_bit_eq_take_bit_shift
% 5.31/5.64 thf(fact_8715_arctan__inverse,axiom,
% 5.31/5.64 ! [X: real] :
% 5.31/5.64 ( ( X != zero_zero_real )
% 5.31/5.64 => ( ( arctan @ ( divide_divide_real @ one_one_real @ X ) )
% 5.31/5.64 = ( minus_minus_real @ ( divide_divide_real @ ( times_times_real @ ( sgn_sgn_real @ X ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( arctan @ X ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % arctan_inverse
% 5.31/5.64 thf(fact_8716_num_Osize__gen_I2_J,axiom,
% 5.31/5.64 ! [X2: num] :
% 5.31/5.64 ( ( size_num @ ( bit0 @ X2 ) )
% 5.31/5.64 = ( plus_plus_nat @ ( size_num @ X2 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % num.size_gen(2)
% 5.31/5.64 thf(fact_8717_take__bit__numeral__minus__bit1,axiom,
% 5.31/5.64 ! [L: num,K2: num] :
% 5.31/5.64 ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K2 ) ) ) )
% 5.31/5.64 = ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ ( pred_numeral @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ K2 ) ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 5.31/5.64
% 5.31/5.64 % take_bit_numeral_minus_bit1
% 5.31/5.64 thf(fact_8718_take__bit__Suc__minus__bit1,axiom,
% 5.31/5.64 ! [N: nat,K2: num] :
% 5.31/5.64 ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K2 ) ) ) )
% 5.31/5.64 = ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ N @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ K2 ) ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 5.31/5.64
% 5.31/5.64 % take_bit_Suc_minus_bit1
% 5.31/5.64 thf(fact_8719_or__int__unfold,axiom,
% 5.31/5.64 ( bit_se1409905431419307370or_int
% 5.31/5.64 = ( ^ [K3: int,L2: int] :
% 5.31/5.64 ( if_int
% 5.31/5.64 @ ( ( K3
% 5.31/5.64 = ( uminus_uminus_int @ one_one_int ) )
% 5.31/5.64 | ( L2
% 5.31/5.64 = ( uminus_uminus_int @ one_one_int ) ) )
% 5.31/5.64 @ ( uminus_uminus_int @ one_one_int )
% 5.31/5.64 @ ( if_int @ ( K3 = zero_zero_int ) @ L2 @ ( if_int @ ( L2 = zero_zero_int ) @ K3 @ ( plus_plus_int @ ( ord_max_int @ ( modulo_modulo_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( modulo_modulo_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % or_int_unfold
% 5.31/5.64 thf(fact_8720_arctan__half,axiom,
% 5.31/5.64 ( arctan
% 5.31/5.64 = ( ^ [X4: real] : ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( arctan @ ( divide_divide_real @ X4 @ ( plus_plus_real @ one_one_real @ ( sqrt @ ( plus_plus_real @ one_one_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % arctan_half
% 5.31/5.64 thf(fact_8721_real__sqrt__mult__self,axiom,
% 5.31/5.64 ! [A: real] :
% 5.31/5.64 ( ( times_times_real @ ( sqrt @ A ) @ ( sqrt @ A ) )
% 5.31/5.64 = ( abs_abs_real @ A ) ) ).
% 5.31/5.64
% 5.31/5.64 % real_sqrt_mult_self
% 5.31/5.64 thf(fact_8722_real__sqrt__abs2,axiom,
% 5.31/5.64 ! [X: real] :
% 5.31/5.64 ( ( sqrt @ ( times_times_real @ X @ X ) )
% 5.31/5.64 = ( abs_abs_real @ X ) ) ).
% 5.31/5.64
% 5.31/5.64 % real_sqrt_abs2
% 5.31/5.64 thf(fact_8723_pred__numeral__inc,axiom,
% 5.31/5.64 ! [K2: num] :
% 5.31/5.64 ( ( pred_numeral @ ( inc @ K2 ) )
% 5.31/5.64 = ( numeral_numeral_nat @ K2 ) ) ).
% 5.31/5.64
% 5.31/5.64 % pred_numeral_inc
% 5.31/5.64 thf(fact_8724_real__sqrt__sum__squares__mult__squared__eq,axiom,
% 5.31/5.64 ! [X: real,Y: real,Xa2: real,Ya: real] :
% 5.31/5.64 ( ( 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 ) ) )
% 5.31/5.64 = ( 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 ) ) ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % real_sqrt_sum_squares_mult_squared_eq
% 5.31/5.64 thf(fact_8725_real__sqrt__mult,axiom,
% 5.31/5.64 ! [X: real,Y: real] :
% 5.31/5.64 ( ( sqrt @ ( times_times_real @ X @ Y ) )
% 5.31/5.64 = ( times_times_real @ ( sqrt @ X ) @ ( sqrt @ Y ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % real_sqrt_mult
% 5.31/5.64 thf(fact_8726_num__induct,axiom,
% 5.31/5.64 ! [P2: num > $o,X: num] :
% 5.31/5.64 ( ( P2 @ one )
% 5.31/5.64 => ( ! [X3: num] :
% 5.31/5.64 ( ( P2 @ X3 )
% 5.31/5.64 => ( P2 @ ( inc @ X3 ) ) )
% 5.31/5.64 => ( P2 @ X ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % num_induct
% 5.31/5.64 thf(fact_8727_add__inc,axiom,
% 5.31/5.64 ! [X: num,Y: num] :
% 5.31/5.64 ( ( plus_plus_num @ X @ ( inc @ Y ) )
% 5.31/5.64 = ( inc @ ( plus_plus_num @ X @ Y ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % add_inc
% 5.31/5.64 thf(fact_8728_inc_Osimps_I1_J,axiom,
% 5.31/5.64 ( ( inc @ one )
% 5.31/5.64 = ( bit0 @ one ) ) ).
% 5.31/5.64
% 5.31/5.64 % inc.simps(1)
% 5.31/5.64 thf(fact_8729_inc_Osimps_I2_J,axiom,
% 5.31/5.64 ! [X: num] :
% 5.31/5.64 ( ( inc @ ( bit0 @ X ) )
% 5.31/5.64 = ( bit1 @ X ) ) ).
% 5.31/5.64
% 5.31/5.64 % inc.simps(2)
% 5.31/5.64 thf(fact_8730_inc_Osimps_I3_J,axiom,
% 5.31/5.64 ! [X: num] :
% 5.31/5.64 ( ( inc @ ( bit1 @ X ) )
% 5.31/5.64 = ( bit0 @ ( inc @ X ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % inc.simps(3)
% 5.31/5.64 thf(fact_8731_add__One,axiom,
% 5.31/5.64 ! [X: num] :
% 5.31/5.64 ( ( plus_plus_num @ X @ one )
% 5.31/5.64 = ( inc @ X ) ) ).
% 5.31/5.64
% 5.31/5.64 % add_One
% 5.31/5.64 thf(fact_8732_le__real__sqrt__sumsq,axiom,
% 5.31/5.64 ! [X: real,Y: real] : ( ord_less_eq_real @ X @ ( sqrt @ ( plus_plus_real @ ( times_times_real @ X @ X ) @ ( times_times_real @ Y @ Y ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % le_real_sqrt_sumsq
% 5.31/5.64 thf(fact_8733_inc__BitM__eq,axiom,
% 5.31/5.64 ! [N: num] :
% 5.31/5.64 ( ( inc @ ( bitM @ N ) )
% 5.31/5.64 = ( bit0 @ N ) ) ).
% 5.31/5.64
% 5.31/5.64 % inc_BitM_eq
% 5.31/5.64 thf(fact_8734_BitM__inc__eq,axiom,
% 5.31/5.64 ! [N: num] :
% 5.31/5.64 ( ( bitM @ ( inc @ N ) )
% 5.31/5.64 = ( bit1 @ N ) ) ).
% 5.31/5.64
% 5.31/5.64 % BitM_inc_eq
% 5.31/5.64 thf(fact_8735_mult__inc,axiom,
% 5.31/5.64 ! [X: num,Y: num] :
% 5.31/5.64 ( ( times_times_num @ X @ ( inc @ Y ) )
% 5.31/5.64 = ( plus_plus_num @ ( times_times_num @ X @ Y ) @ X ) ) ).
% 5.31/5.64
% 5.31/5.64 % mult_inc
% 5.31/5.64 thf(fact_8736_real__sqrt__sum__squares__mult__ge__zero,axiom,
% 5.31/5.64 ! [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 ) ) ) ) ) ) ) ).
% 5.31/5.64
% 5.31/5.64 % real_sqrt_sum_squares_mult_ge_zero
% 5.31/5.64 thf(fact_8737_arith__geo__mean__sqrt,axiom,
% 5.31/5.64 ! [X: real,Y: real] :
% 5.31/5.64 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.31/5.65 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.31/5.65 => ( ord_less_eq_real @ ( sqrt @ ( times_times_real @ X @ Y ) ) @ ( divide_divide_real @ ( plus_plus_real @ X @ Y ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % arith_geo_mean_sqrt
% 5.31/5.65 thf(fact_8738_or__int__rec,axiom,
% 5.31/5.65 ( bit_se1409905431419307370or_int
% 5.31/5.65 = ( ^ [K3: int,L2: int] :
% 5.31/5.65 ( plus_plus_int
% 5.31/5.65 @ ( zero_n2684676970156552555ol_int
% 5.31/5.65 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K3 )
% 5.31/5.65 | ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L2 ) ) )
% 5.31/5.65 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % or_int_rec
% 5.31/5.65 thf(fact_8739_signed__take__bit__eq__take__bit__minus,axiom,
% 5.31/5.65 ( bit_ri631733984087533419it_int
% 5.31/5.65 = ( ^ [N4: nat,K3: int] : ( minus_minus_int @ ( bit_se2923211474154528505it_int @ ( suc @ N4 ) @ K3 ) @ ( times_times_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ N4 ) ) @ ( zero_n2684676970156552555ol_int @ ( bit_se1146084159140164899it_int @ K3 @ N4 ) ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % signed_take_bit_eq_take_bit_minus
% 5.31/5.65 thf(fact_8740_cis__2pi,axiom,
% 5.31/5.65 ( ( cis @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 5.31/5.65 = one_one_complex ) ).
% 5.31/5.65
% 5.31/5.65 % cis_2pi
% 5.31/5.65 thf(fact_8741_take__bit__Suc__from__most,axiom,
% 5.31/5.65 ! [N: nat,K2: int] :
% 5.31/5.65 ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ K2 )
% 5.31/5.65 = ( plus_plus_int @ ( times_times_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ ( zero_n2684676970156552555ol_int @ ( bit_se1146084159140164899it_int @ K2 @ N ) ) ) @ ( bit_se2923211474154528505it_int @ N @ K2 ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % take_bit_Suc_from_most
% 5.31/5.65 thf(fact_8742_pi__def,axiom,
% 5.31/5.65 ( pi
% 5.31/5.65 = ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) )
% 5.31/5.65 @ ( the_real
% 5.31/5.65 @ ^ [X4: real] :
% 5.31/5.65 ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.31/5.65 & ( ord_less_eq_real @ X4 @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.31/5.65 & ( ( cos_real @ X4 )
% 5.31/5.65 = zero_zero_real ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % pi_def
% 5.31/5.65 thf(fact_8743_or__nat__numerals_I4_J,axiom,
% 5.31/5.65 ! [X: num] :
% 5.31/5.65 ( ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ ( suc @ zero_zero_nat ) )
% 5.31/5.65 = ( numeral_numeral_nat @ ( bit1 @ X ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % or_nat_numerals(4)
% 5.31/5.65 thf(fact_8744_or__nat__numerals_I2_J,axiom,
% 5.31/5.65 ! [Y: num] :
% 5.31/5.65 ( ( bit_se1412395901928357646or_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 5.31/5.65 = ( numeral_numeral_nat @ ( bit1 @ Y ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % or_nat_numerals(2)
% 5.31/5.65 thf(fact_8745_or__nat__numerals_I1_J,axiom,
% 5.31/5.65 ! [Y: num] :
% 5.31/5.65 ( ( bit_se1412395901928357646or_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 5.31/5.65 = ( numeral_numeral_nat @ ( bit1 @ Y ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % or_nat_numerals(1)
% 5.31/5.65 thf(fact_8746_or__nat__numerals_I3_J,axiom,
% 5.31/5.65 ! [X: num] :
% 5.31/5.65 ( ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ ( bit0 @ X ) ) @ ( suc @ zero_zero_nat ) )
% 5.31/5.65 = ( numeral_numeral_nat @ ( bit1 @ X ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % or_nat_numerals(3)
% 5.31/5.65 thf(fact_8747_bit__minus__numeral__Bit0__Suc__iff,axiom,
% 5.31/5.65 ! [W2: num,N: nat] :
% 5.31/5.65 ( ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ W2 ) ) ) @ ( suc @ N ) )
% 5.31/5.65 = ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W2 ) ) @ N ) ) ).
% 5.31/5.65
% 5.31/5.65 % bit_minus_numeral_Bit0_Suc_iff
% 5.31/5.65 thf(fact_8748_bit__minus__numeral__Bit1__Suc__iff,axiom,
% 5.31/5.65 ! [W2: num,N: nat] :
% 5.31/5.65 ( ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ W2 ) ) ) @ ( suc @ N ) )
% 5.31/5.65 = ( ~ ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ W2 ) @ N ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % bit_minus_numeral_Bit1_Suc_iff
% 5.31/5.65 thf(fact_8749_cis__mult,axiom,
% 5.31/5.65 ! [A: real,B: real] :
% 5.31/5.65 ( ( times_times_complex @ ( cis @ A ) @ ( cis @ B ) )
% 5.31/5.65 = ( cis @ ( plus_plus_real @ A @ B ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % cis_mult
% 5.31/5.65 thf(fact_8750_DeMoivre,axiom,
% 5.31/5.65 ! [A: real,N: nat] :
% 5.31/5.65 ( ( power_power_complex @ ( cis @ A ) @ N )
% 5.31/5.65 = ( cis @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ A ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % DeMoivre
% 5.31/5.65 thf(fact_8751_bit__concat__bit__iff,axiom,
% 5.31/5.65 ! [M2: nat,K2: int,L: int,N: nat] :
% 5.31/5.65 ( ( bit_se1146084159140164899it_int @ ( bit_concat_bit @ M2 @ K2 @ L ) @ N )
% 5.31/5.65 = ( ( ( ord_less_nat @ N @ M2 )
% 5.31/5.65 & ( bit_se1146084159140164899it_int @ K2 @ N ) )
% 5.31/5.65 | ( ( ord_less_eq_nat @ M2 @ N )
% 5.31/5.65 & ( bit_se1146084159140164899it_int @ L @ ( minus_minus_nat @ N @ M2 ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % bit_concat_bit_iff
% 5.31/5.65 thf(fact_8752_int__bit__bound,axiom,
% 5.31/5.65 ! [K2: int] :
% 5.31/5.65 ~ ! [N3: nat] :
% 5.31/5.65 ( ! [M3: nat] :
% 5.31/5.65 ( ( ord_less_eq_nat @ N3 @ M3 )
% 5.31/5.65 => ( ( bit_se1146084159140164899it_int @ K2 @ M3 )
% 5.31/5.65 = ( bit_se1146084159140164899it_int @ K2 @ N3 ) ) )
% 5.31/5.65 => ~ ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 5.31/5.65 => ( ( bit_se1146084159140164899it_int @ K2 @ ( minus_minus_nat @ N3 @ one_one_nat ) )
% 5.31/5.65 = ( ~ ( bit_se1146084159140164899it_int @ K2 @ N3 ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % int_bit_bound
% 5.31/5.65 thf(fact_8753_set__bit__eq,axiom,
% 5.31/5.65 ( bit_se7879613467334960850it_int
% 5.31/5.65 = ( ^ [N4: nat,K3: int] :
% 5.31/5.65 ( plus_plus_int @ K3
% 5.31/5.65 @ ( times_times_int
% 5.31/5.65 @ ( zero_n2684676970156552555ol_int
% 5.31/5.65 @ ~ ( bit_se1146084159140164899it_int @ K3 @ N4 ) )
% 5.31/5.65 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N4 ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % set_bit_eq
% 5.31/5.65 thf(fact_8754_unset__bit__eq,axiom,
% 5.31/5.65 ( bit_se4203085406695923979it_int
% 5.31/5.65 = ( ^ [N4: nat,K3: int] : ( minus_minus_int @ K3 @ ( times_times_int @ ( zero_n2684676970156552555ol_int @ ( bit_se1146084159140164899it_int @ K3 @ N4 ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N4 ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % unset_bit_eq
% 5.31/5.65 thf(fact_8755_or__Suc__0__eq,axiom,
% 5.31/5.65 ! [N: nat] :
% 5.31/5.65 ( ( bit_se1412395901928357646or_nat @ N @ ( suc @ zero_zero_nat ) )
% 5.31/5.65 = ( plus_plus_nat @ N @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % or_Suc_0_eq
% 5.31/5.65 thf(fact_8756_Suc__0__or__eq,axiom,
% 5.31/5.65 ! [N: nat] :
% 5.31/5.65 ( ( bit_se1412395901928357646or_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.31/5.65 = ( plus_plus_nat @ N @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % Suc_0_or_eq
% 5.31/5.65 thf(fact_8757_or__nat__rec,axiom,
% 5.31/5.65 ( bit_se1412395901928357646or_nat
% 5.31/5.65 = ( ^ [M6: nat,N4: nat] :
% 5.31/5.65 ( plus_plus_nat
% 5.31/5.65 @ ( zero_n2687167440665602831ol_nat
% 5.31/5.65 @ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M6 )
% 5.31/5.65 | ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) ) )
% 5.31/5.65 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se1412395901928357646or_nat @ ( divide_divide_nat @ M6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % or_nat_rec
% 5.31/5.65 thf(fact_8758_or__nat__unfold,axiom,
% 5.31/5.65 ( bit_se1412395901928357646or_nat
% 5.31/5.65 = ( ^ [M6: nat,N4: nat] : ( if_nat @ ( M6 = zero_zero_nat ) @ N4 @ ( if_nat @ ( N4 = zero_zero_nat ) @ M6 @ ( plus_plus_nat @ ( ord_max_nat @ ( modulo_modulo_nat @ M6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( modulo_modulo_nat @ N4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se1412395901928357646or_nat @ ( divide_divide_nat @ M6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % or_nat_unfold
% 5.31/5.65 thf(fact_8759_bij__betw__roots__unity,axiom,
% 5.31/5.65 ! [N: nat] :
% 5.31/5.65 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.65 => ( bij_betw_nat_complex
% 5.31/5.65 @ ^ [K3: nat] : ( cis @ ( divide_divide_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ ( semiri5074537144036343181t_real @ K3 ) ) @ ( semiri5074537144036343181t_real @ N ) ) )
% 5.31/5.65 @ ( set_ord_lessThan_nat @ N )
% 5.31/5.65 @ ( collect_complex
% 5.31/5.65 @ ^ [Z4: complex] :
% 5.31/5.65 ( ( power_power_complex @ Z4 @ N )
% 5.31/5.65 = one_one_complex ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % bij_betw_roots_unity
% 5.31/5.65 thf(fact_8760_cis__multiple__2pi,axiom,
% 5.31/5.65 ! [N: real] :
% 5.31/5.65 ( ( member_real @ N @ ring_1_Ints_real )
% 5.31/5.65 => ( ( cis @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ N ) )
% 5.31/5.65 = one_one_complex ) ) ).
% 5.31/5.65
% 5.31/5.65 % cis_multiple_2pi
% 5.31/5.65 thf(fact_8761_not__bit__Suc__0__Suc,axiom,
% 5.31/5.65 ! [N: nat] :
% 5.31/5.65 ~ ( bit_se1148574629649215175it_nat @ ( suc @ zero_zero_nat ) @ ( suc @ N ) ) ).
% 5.31/5.65
% 5.31/5.65 % not_bit_Suc_0_Suc
% 5.31/5.65 thf(fact_8762_bit__Suc__0__iff,axiom,
% 5.31/5.65 ! [N: nat] :
% 5.31/5.65 ( ( bit_se1148574629649215175it_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.31/5.65 = ( N = zero_zero_nat ) ) ).
% 5.31/5.65
% 5.31/5.65 % bit_Suc_0_iff
% 5.31/5.65 thf(fact_8763_not__bit__Suc__0__numeral,axiom,
% 5.31/5.65 ! [N: num] :
% 5.31/5.65 ~ ( bit_se1148574629649215175it_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ N ) ) ).
% 5.31/5.65
% 5.31/5.65 % not_bit_Suc_0_numeral
% 5.31/5.65 thf(fact_8764_sin__times__pi__eq__0,axiom,
% 5.31/5.65 ! [X: real] :
% 5.31/5.65 ( ( ( sin_real @ ( times_times_real @ X @ pi ) )
% 5.31/5.65 = zero_zero_real )
% 5.31/5.65 = ( member_real @ X @ ring_1_Ints_real ) ) ).
% 5.31/5.65
% 5.31/5.65 % sin_times_pi_eq_0
% 5.31/5.65 thf(fact_8765_sin__integer__2pi,axiom,
% 5.31/5.65 ! [N: real] :
% 5.31/5.65 ( ( member_real @ N @ ring_1_Ints_real )
% 5.31/5.65 => ( ( sin_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ N ) )
% 5.31/5.65 = zero_zero_real ) ) ).
% 5.31/5.65
% 5.31/5.65 % sin_integer_2pi
% 5.31/5.65 thf(fact_8766_cos__integer__2pi,axiom,
% 5.31/5.65 ! [N: real] :
% 5.31/5.65 ( ( member_real @ N @ ring_1_Ints_real )
% 5.31/5.65 => ( ( cos_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ N ) )
% 5.31/5.65 = one_one_real ) ) ).
% 5.31/5.65
% 5.31/5.65 % cos_integer_2pi
% 5.31/5.65 thf(fact_8767_i__even__power,axiom,
% 5.31/5.65 ! [N: nat] :
% 5.31/5.65 ( ( power_power_complex @ imaginary_unit @ ( times_times_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.31/5.65 = ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) ) ).
% 5.31/5.65
% 5.31/5.65 % i_even_power
% 5.31/5.65 thf(fact_8768_Suc__0__xor__eq,axiom,
% 5.31/5.65 ! [N: nat] :
% 5.31/5.65 ( ( bit_se6528837805403552850or_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.31/5.65 = ( minus_minus_nat @ ( plus_plus_nat @ N @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.31/5.65 @ ( zero_n2687167440665602831ol_nat
% 5.31/5.65 @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % Suc_0_xor_eq
% 5.31/5.65 thf(fact_8769_xor__Suc__0__eq,axiom,
% 5.31/5.65 ! [N: nat] :
% 5.31/5.65 ( ( bit_se6528837805403552850or_nat @ N @ ( suc @ zero_zero_nat ) )
% 5.31/5.65 = ( minus_minus_nat @ ( plus_plus_nat @ N @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.31/5.65 @ ( zero_n2687167440665602831ol_nat
% 5.31/5.65 @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % xor_Suc_0_eq
% 5.31/5.65 thf(fact_8770_horner__sum__of__bool__2__less,axiom,
% 5.31/5.65 ! [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 ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % horner_sum_of_bool_2_less
% 5.31/5.65 thf(fact_8771_complex__i__mult__minus,axiom,
% 5.31/5.65 ! [X: complex] :
% 5.31/5.65 ( ( times_times_complex @ imaginary_unit @ ( times_times_complex @ imaginary_unit @ X ) )
% 5.31/5.65 = ( uminus1482373934393186551omplex @ X ) ) ).
% 5.31/5.65
% 5.31/5.65 % complex_i_mult_minus
% 5.31/5.65 thf(fact_8772_divide__numeral__i,axiom,
% 5.31/5.65 ! [Z3: complex,N: num] :
% 5.31/5.65 ( ( divide1717551699836669952omplex @ Z3 @ ( times_times_complex @ ( numera6690914467698888265omplex @ N ) @ imaginary_unit ) )
% 5.31/5.65 = ( divide1717551699836669952omplex @ ( uminus1482373934393186551omplex @ ( times_times_complex @ imaginary_unit @ Z3 ) ) @ ( numera6690914467698888265omplex @ N ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % divide_numeral_i
% 5.31/5.65 thf(fact_8773_divide__i,axiom,
% 5.31/5.65 ! [X: complex] :
% 5.31/5.65 ( ( divide1717551699836669952omplex @ X @ imaginary_unit )
% 5.31/5.65 = ( times_times_complex @ ( uminus1482373934393186551omplex @ imaginary_unit ) @ X ) ) ).
% 5.31/5.65
% 5.31/5.65 % divide_i
% 5.31/5.65 thf(fact_8774_i__squared,axiom,
% 5.31/5.65 ( ( times_times_complex @ imaginary_unit @ imaginary_unit )
% 5.31/5.65 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.31/5.65
% 5.31/5.65 % i_squared
% 5.31/5.65 thf(fact_8775_xor__nat__numerals_I1_J,axiom,
% 5.31/5.65 ! [Y: num] :
% 5.31/5.65 ( ( bit_se6528837805403552850or_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 5.31/5.65 = ( numeral_numeral_nat @ ( bit1 @ Y ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % xor_nat_numerals(1)
% 5.31/5.65 thf(fact_8776_xor__nat__numerals_I2_J,axiom,
% 5.31/5.65 ! [Y: num] :
% 5.31/5.65 ( ( bit_se6528837805403552850or_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 5.31/5.65 = ( numeral_numeral_nat @ ( bit0 @ Y ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % xor_nat_numerals(2)
% 5.31/5.65 thf(fact_8777_xor__nat__numerals_I3_J,axiom,
% 5.31/5.65 ! [X: num] :
% 5.31/5.65 ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit0 @ X ) ) @ ( suc @ zero_zero_nat ) )
% 5.31/5.65 = ( numeral_numeral_nat @ ( bit1 @ X ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % xor_nat_numerals(3)
% 5.31/5.65 thf(fact_8778_xor__nat__numerals_I4_J,axiom,
% 5.31/5.65 ! [X: num] :
% 5.31/5.65 ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ ( suc @ zero_zero_nat ) )
% 5.31/5.65 = ( numeral_numeral_nat @ ( bit0 @ X ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % xor_nat_numerals(4)
% 5.31/5.65 thf(fact_8779_i__times__eq__iff,axiom,
% 5.31/5.65 ! [W2: complex,Z3: complex] :
% 5.31/5.65 ( ( ( times_times_complex @ imaginary_unit @ W2 )
% 5.31/5.65 = Z3 )
% 5.31/5.65 = ( W2
% 5.31/5.65 = ( uminus1482373934393186551omplex @ ( times_times_complex @ imaginary_unit @ Z3 ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % i_times_eq_iff
% 5.31/5.65 thf(fact_8780_i__mult__Complex,axiom,
% 5.31/5.65 ! [A: real,B: real] :
% 5.31/5.65 ( ( times_times_complex @ imaginary_unit @ ( complex2 @ A @ B ) )
% 5.31/5.65 = ( complex2 @ ( uminus_uminus_real @ B ) @ A ) ) ).
% 5.31/5.65
% 5.31/5.65 % i_mult_Complex
% 5.31/5.65 thf(fact_8781_Complex__mult__i,axiom,
% 5.31/5.65 ! [A: real,B: real] :
% 5.31/5.65 ( ( times_times_complex @ ( complex2 @ A @ B ) @ imaginary_unit )
% 5.31/5.65 = ( complex2 @ ( uminus_uminus_real @ B ) @ A ) ) ).
% 5.31/5.65
% 5.31/5.65 % Complex_mult_i
% 5.31/5.65 thf(fact_8782_xor__nat__unfold,axiom,
% 5.31/5.65 ( bit_se6528837805403552850or_nat
% 5.31/5.65 = ( ^ [M6: nat,N4: nat] : ( if_nat @ ( M6 = zero_zero_nat ) @ N4 @ ( if_nat @ ( N4 = zero_zero_nat ) @ M6 @ ( plus_plus_nat @ ( modulo_modulo_nat @ ( plus_plus_nat @ ( modulo_modulo_nat @ M6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( modulo_modulo_nat @ N4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se6528837805403552850or_nat @ ( divide_divide_nat @ M6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % xor_nat_unfold
% 5.31/5.65 thf(fact_8783_xor__nat__rec,axiom,
% 5.31/5.65 ( bit_se6528837805403552850or_nat
% 5.31/5.65 = ( ^ [M6: nat,N4: nat] :
% 5.31/5.65 ( plus_plus_nat
% 5.31/5.65 @ ( zero_n2687167440665602831ol_nat
% 5.31/5.65 @ ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M6 ) )
% 5.31/5.65 != ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) ) ) )
% 5.31/5.65 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se6528837805403552850or_nat @ ( divide_divide_nat @ M6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % xor_nat_rec
% 5.31/5.65 thf(fact_8784_Sum__Ico__nat,axiom,
% 5.31/5.65 ! [M2: nat,N: nat] :
% 5.31/5.65 ( ( groups3542108847815614940at_nat
% 5.31/5.65 @ ^ [X4: nat] : X4
% 5.31/5.65 @ ( set_or4665077453230672383an_nat @ M2 @ N ) )
% 5.31/5.65 = ( divide_divide_nat @ ( minus_minus_nat @ ( times_times_nat @ N @ ( minus_minus_nat @ N @ one_one_nat ) ) @ ( times_times_nat @ M2 @ ( minus_minus_nat @ M2 @ one_one_nat ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % Sum_Ico_nat
% 5.31/5.65 thf(fact_8785_Least__eq__0,axiom,
% 5.31/5.65 ! [P2: nat > $o] :
% 5.31/5.65 ( ( P2 @ zero_zero_nat )
% 5.31/5.65 => ( ( ord_Least_nat @ P2 )
% 5.31/5.65 = zero_zero_nat ) ) ).
% 5.31/5.65
% 5.31/5.65 % Least_eq_0
% 5.31/5.65 thf(fact_8786_finite__atLeastLessThan,axiom,
% 5.31/5.65 ! [L: nat,U: nat] : ( finite_finite_nat @ ( set_or4665077453230672383an_nat @ L @ U ) ) ).
% 5.31/5.65
% 5.31/5.65 % finite_atLeastLessThan
% 5.31/5.65 thf(fact_8787_card__atLeastLessThan,axiom,
% 5.31/5.65 ! [L: nat,U: nat] :
% 5.31/5.65 ( ( finite_card_nat @ ( set_or4665077453230672383an_nat @ L @ U ) )
% 5.31/5.65 = ( minus_minus_nat @ U @ L ) ) ).
% 5.31/5.65
% 5.31/5.65 % card_atLeastLessThan
% 5.31/5.65 thf(fact_8788_atLeastLessThan__singleton,axiom,
% 5.31/5.65 ! [M2: nat] :
% 5.31/5.65 ( ( set_or4665077453230672383an_nat @ M2 @ ( suc @ M2 ) )
% 5.31/5.65 = ( insert_nat @ M2 @ bot_bot_set_nat ) ) ).
% 5.31/5.65
% 5.31/5.65 % atLeastLessThan_singleton
% 5.31/5.65 thf(fact_8789_all__nat__less__eq,axiom,
% 5.31/5.65 ! [N: nat,P2: nat > $o] :
% 5.31/5.65 ( ( ! [M6: nat] :
% 5.31/5.65 ( ( ord_less_nat @ M6 @ N )
% 5.31/5.65 => ( P2 @ M6 ) ) )
% 5.31/5.65 = ( ! [X4: nat] :
% 5.31/5.65 ( ( member_nat @ X4 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) )
% 5.31/5.65 => ( P2 @ X4 ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % all_nat_less_eq
% 5.31/5.65 thf(fact_8790_ex__nat__less__eq,axiom,
% 5.31/5.65 ! [N: nat,P2: nat > $o] :
% 5.31/5.65 ( ( ? [M6: nat] :
% 5.31/5.65 ( ( ord_less_nat @ M6 @ N )
% 5.31/5.65 & ( P2 @ M6 ) ) )
% 5.31/5.65 = ( ? [X4: nat] :
% 5.31/5.65 ( ( member_nat @ X4 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) )
% 5.31/5.65 & ( P2 @ X4 ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % ex_nat_less_eq
% 5.31/5.65 thf(fact_8791_atLeastLessThanSuc__atLeastAtMost,axiom,
% 5.31/5.65 ! [L: nat,U: nat] :
% 5.31/5.65 ( ( set_or4665077453230672383an_nat @ L @ ( suc @ U ) )
% 5.31/5.65 = ( set_or1269000886237332187st_nat @ L @ U ) ) ).
% 5.31/5.65
% 5.31/5.65 % atLeastLessThanSuc_atLeastAtMost
% 5.31/5.65 thf(fact_8792_lessThan__atLeast0,axiom,
% 5.31/5.65 ( set_ord_lessThan_nat
% 5.31/5.65 = ( set_or4665077453230672383an_nat @ zero_zero_nat ) ) ).
% 5.31/5.65
% 5.31/5.65 % lessThan_atLeast0
% 5.31/5.65 thf(fact_8793_atLeastLessThan0,axiom,
% 5.31/5.65 ! [M2: nat] :
% 5.31/5.65 ( ( set_or4665077453230672383an_nat @ M2 @ zero_zero_nat )
% 5.31/5.65 = bot_bot_set_nat ) ).
% 5.31/5.65
% 5.31/5.65 % atLeastLessThan0
% 5.31/5.65 thf(fact_8794_Least__Suc2,axiom,
% 5.31/5.65 ! [P2: nat > $o,N: nat,Q: nat > $o,M2: nat] :
% 5.31/5.65 ( ( P2 @ N )
% 5.31/5.65 => ( ( Q @ M2 )
% 5.31/5.65 => ( ~ ( P2 @ zero_zero_nat )
% 5.31/5.65 => ( ! [K: nat] :
% 5.31/5.65 ( ( P2 @ ( suc @ K ) )
% 5.31/5.65 = ( Q @ K ) )
% 5.31/5.65 => ( ( ord_Least_nat @ P2 )
% 5.31/5.65 = ( suc @ ( ord_Least_nat @ Q ) ) ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % Least_Suc2
% 5.31/5.65 thf(fact_8795_Least__Suc,axiom,
% 5.31/5.65 ! [P2: nat > $o,N: nat] :
% 5.31/5.65 ( ( P2 @ N )
% 5.31/5.65 => ( ~ ( P2 @ zero_zero_nat )
% 5.31/5.65 => ( ( ord_Least_nat @ P2 )
% 5.31/5.65 = ( suc
% 5.31/5.65 @ ( ord_Least_nat
% 5.31/5.65 @ ^ [M6: nat] : ( P2 @ ( suc @ M6 ) ) ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % Least_Suc
% 5.31/5.65 thf(fact_8796_atLeast0__lessThan__Suc,axiom,
% 5.31/5.65 ! [N: nat] :
% 5.31/5.65 ( ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( suc @ N ) )
% 5.31/5.65 = ( insert_nat @ N @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % atLeast0_lessThan_Suc
% 5.31/5.65 thf(fact_8797_subset__eq__atLeast0__lessThan__finite,axiom,
% 5.31/5.65 ! [N6: set_nat,N: nat] :
% 5.31/5.65 ( ( ord_less_eq_set_nat @ N6 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) )
% 5.31/5.65 => ( finite_finite_nat @ N6 ) ) ).
% 5.31/5.65
% 5.31/5.65 % subset_eq_atLeast0_lessThan_finite
% 5.31/5.65 thf(fact_8798_subset__card__intvl__is__intvl,axiom,
% 5.31/5.65 ! [A4: set_nat,K2: nat] :
% 5.31/5.65 ( ( ord_less_eq_set_nat @ A4 @ ( set_or4665077453230672383an_nat @ K2 @ ( plus_plus_nat @ K2 @ ( finite_card_nat @ A4 ) ) ) )
% 5.31/5.65 => ( A4
% 5.31/5.65 = ( set_or4665077453230672383an_nat @ K2 @ ( plus_plus_nat @ K2 @ ( finite_card_nat @ A4 ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % subset_card_intvl_is_intvl
% 5.31/5.65 thf(fact_8799_atLeastLessThan__add__Un,axiom,
% 5.31/5.65 ! [I2: nat,J2: nat,K2: nat] :
% 5.31/5.65 ( ( ord_less_eq_nat @ I2 @ J2 )
% 5.31/5.65 => ( ( set_or4665077453230672383an_nat @ I2 @ ( plus_plus_nat @ J2 @ K2 ) )
% 5.31/5.65 = ( sup_sup_set_nat @ ( set_or4665077453230672383an_nat @ I2 @ J2 ) @ ( set_or4665077453230672383an_nat @ J2 @ ( plus_plus_nat @ J2 @ K2 ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % atLeastLessThan_add_Un
% 5.31/5.65 thf(fact_8800_atLeastLessThanSuc,axiom,
% 5.31/5.65 ! [M2: nat,N: nat] :
% 5.31/5.65 ( ( ( ord_less_eq_nat @ M2 @ N )
% 5.31/5.65 => ( ( set_or4665077453230672383an_nat @ M2 @ ( suc @ N ) )
% 5.31/5.65 = ( insert_nat @ N @ ( set_or4665077453230672383an_nat @ M2 @ N ) ) ) )
% 5.31/5.65 & ( ~ ( ord_less_eq_nat @ M2 @ N )
% 5.31/5.65 => ( ( set_or4665077453230672383an_nat @ M2 @ ( suc @ N ) )
% 5.31/5.65 = bot_bot_set_nat ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % atLeastLessThanSuc
% 5.31/5.65 thf(fact_8801_prod__Suc__Suc__fact,axiom,
% 5.31/5.65 ! [N: nat] :
% 5.31/5.65 ( ( groups708209901874060359at_nat @ suc @ ( set_or4665077453230672383an_nat @ ( suc @ zero_zero_nat ) @ N ) )
% 5.31/5.65 = ( semiri1408675320244567234ct_nat @ N ) ) ).
% 5.31/5.65
% 5.31/5.65 % prod_Suc_Suc_fact
% 5.31/5.65 thf(fact_8802_prod__Suc__fact,axiom,
% 5.31/5.65 ! [N: nat] :
% 5.31/5.65 ( ( groups708209901874060359at_nat @ suc @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) )
% 5.31/5.65 = ( semiri1408675320244567234ct_nat @ N ) ) ).
% 5.31/5.65
% 5.31/5.65 % prod_Suc_fact
% 5.31/5.65 thf(fact_8803_subset__eq__atLeast0__lessThan__card,axiom,
% 5.31/5.65 ! [N6: set_nat,N: nat] :
% 5.31/5.65 ( ( ord_less_eq_set_nat @ N6 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) )
% 5.31/5.65 => ( ord_less_eq_nat @ ( finite_card_nat @ N6 ) @ N ) ) ).
% 5.31/5.65
% 5.31/5.65 % subset_eq_atLeast0_lessThan_card
% 5.31/5.65 thf(fact_8804_card__sum__le__nat__sum,axiom,
% 5.31/5.65 ! [S3: set_nat] :
% 5.31/5.65 ( ord_less_eq_nat
% 5.31/5.65 @ ( groups3542108847815614940at_nat
% 5.31/5.65 @ ^ [X4: nat] : X4
% 5.31/5.65 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( finite_card_nat @ S3 ) ) )
% 5.31/5.65 @ ( groups3542108847815614940at_nat
% 5.31/5.65 @ ^ [X4: nat] : X4
% 5.31/5.65 @ S3 ) ) ).
% 5.31/5.65
% 5.31/5.65 % card_sum_le_nat_sum
% 5.31/5.65 thf(fact_8805_atLeastLessThan__nat__numeral,axiom,
% 5.31/5.65 ! [M2: nat,K2: num] :
% 5.31/5.65 ( ( ( ord_less_eq_nat @ M2 @ ( pred_numeral @ K2 ) )
% 5.31/5.65 => ( ( set_or4665077453230672383an_nat @ M2 @ ( numeral_numeral_nat @ K2 ) )
% 5.31/5.65 = ( insert_nat @ ( pred_numeral @ K2 ) @ ( set_or4665077453230672383an_nat @ M2 @ ( pred_numeral @ K2 ) ) ) ) )
% 5.31/5.65 & ( ~ ( ord_less_eq_nat @ M2 @ ( pred_numeral @ K2 ) )
% 5.31/5.65 => ( ( set_or4665077453230672383an_nat @ M2 @ ( numeral_numeral_nat @ K2 ) )
% 5.31/5.65 = bot_bot_set_nat ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % atLeastLessThan_nat_numeral
% 5.31/5.65 thf(fact_8806_atLeast1__lessThan__eq__remove0,axiom,
% 5.31/5.65 ! [N: nat] :
% 5.31/5.65 ( ( set_or4665077453230672383an_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.31/5.65 = ( minus_minus_set_nat @ ( set_ord_lessThan_nat @ N ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % atLeast1_lessThan_eq_remove0
% 5.31/5.65 thf(fact_8807_xor__int__rec,axiom,
% 5.31/5.65 ( bit_se6526347334894502574or_int
% 5.31/5.65 = ( ^ [K3: int,L2: int] :
% 5.31/5.65 ( plus_plus_int
% 5.31/5.65 @ ( zero_n2684676970156552555ol_int
% 5.31/5.65 @ ( ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K3 ) )
% 5.31/5.65 != ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L2 ) ) ) )
% 5.31/5.65 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se6526347334894502574or_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % xor_int_rec
% 5.31/5.65 thf(fact_8808_sum__power2,axiom,
% 5.31/5.65 ! [K2: nat] :
% 5.31/5.65 ( ( groups3542108847815614940at_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ K2 ) )
% 5.31/5.65 = ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K2 ) @ one_one_nat ) ) ).
% 5.31/5.65
% 5.31/5.65 % sum_power2
% 5.31/5.65 thf(fact_8809_Chebyshev__sum__upper__nat,axiom,
% 5.31/5.65 ! [N: nat,A: nat > nat,B: nat > nat] :
% 5.31/5.65 ( ! [I3: nat,J3: nat] :
% 5.31/5.65 ( ( ord_less_eq_nat @ I3 @ J3 )
% 5.31/5.65 => ( ( ord_less_nat @ J3 @ N )
% 5.31/5.65 => ( ord_less_eq_nat @ ( A @ I3 ) @ ( A @ J3 ) ) ) )
% 5.31/5.65 => ( ! [I3: nat,J3: nat] :
% 5.31/5.65 ( ( ord_less_eq_nat @ I3 @ J3 )
% 5.31/5.65 => ( ( ord_less_nat @ J3 @ N )
% 5.31/5.65 => ( ord_less_eq_nat @ ( B @ J3 ) @ ( B @ I3 ) ) ) )
% 5.31/5.65 => ( ord_less_eq_nat
% 5.31/5.65 @ ( times_times_nat @ N
% 5.31/5.65 @ ( groups3542108847815614940at_nat
% 5.31/5.65 @ ^ [I: nat] : ( times_times_nat @ ( A @ I ) @ ( B @ I ) )
% 5.31/5.65 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) )
% 5.31/5.65 @ ( times_times_nat @ ( groups3542108847815614940at_nat @ A @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) @ ( groups3542108847815614940at_nat @ B @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % Chebyshev_sum_upper_nat
% 5.31/5.65 thf(fact_8810_xor__int__unfold,axiom,
% 5.31/5.65 ( bit_se6526347334894502574or_int
% 5.31/5.65 = ( ^ [K3: int,L2: int] :
% 5.31/5.65 ( if_int
% 5.31/5.65 @ ( K3
% 5.31/5.65 = ( uminus_uminus_int @ one_one_int ) )
% 5.31/5.65 @ ( bit_ri7919022796975470100ot_int @ L2 )
% 5.31/5.65 @ ( if_int
% 5.31/5.65 @ ( L2
% 5.31/5.65 = ( uminus_uminus_int @ one_one_int ) )
% 5.31/5.65 @ ( bit_ri7919022796975470100ot_int @ K3 )
% 5.31/5.65 @ ( if_int @ ( K3 = zero_zero_int ) @ L2 @ ( if_int @ ( L2 = zero_zero_int ) @ K3 @ ( plus_plus_int @ ( abs_abs_int @ ( minus_minus_int @ ( modulo_modulo_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( modulo_modulo_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se6526347334894502574or_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % xor_int_unfold
% 5.31/5.65 thf(fact_8811_exp__two__pi__i_H,axiom,
% 5.31/5.65 ( ( exp_complex @ ( times_times_complex @ imaginary_unit @ ( times_times_complex @ ( real_V4546457046886955230omplex @ pi ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) )
% 5.31/5.65 = one_one_complex ) ).
% 5.31/5.65
% 5.31/5.65 % exp_two_pi_i'
% 5.31/5.65 thf(fact_8812_finite__atLeastLessThan__int,axiom,
% 5.31/5.65 ! [L: int,U: int] : ( finite_finite_int @ ( set_or4662586982721622107an_int @ L @ U ) ) ).
% 5.31/5.65
% 5.31/5.65 % finite_atLeastLessThan_int
% 5.31/5.65 thf(fact_8813_card__atLeastLessThan__int,axiom,
% 5.31/5.65 ! [L: int,U: int] :
% 5.31/5.65 ( ( finite_card_int @ ( set_or4662586982721622107an_int @ L @ U ) )
% 5.31/5.65 = ( nat2 @ ( minus_minus_int @ U @ L ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % card_atLeastLessThan_int
% 5.31/5.65 thf(fact_8814_exp__pi__i_H,axiom,
% 5.31/5.65 ( ( exp_complex @ ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ pi ) ) )
% 5.31/5.65 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.31/5.65
% 5.31/5.65 % exp_pi_i'
% 5.31/5.65 thf(fact_8815_exp__pi__i,axiom,
% 5.31/5.65 ( ( exp_complex @ ( times_times_complex @ ( real_V4546457046886955230omplex @ pi ) @ imaginary_unit ) )
% 5.31/5.65 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.31/5.65
% 5.31/5.65 % exp_pi_i
% 5.31/5.65 thf(fact_8816_exp__two__pi__i,axiom,
% 5.31/5.65 ( ( exp_complex @ ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( real_V4546457046886955230omplex @ pi ) ) @ imaginary_unit ) )
% 5.31/5.65 = one_one_complex ) ).
% 5.31/5.65
% 5.31/5.65 % exp_two_pi_i
% 5.31/5.65 thf(fact_8817_complex__exp__exists,axiom,
% 5.31/5.65 ! [Z3: complex] :
% 5.31/5.65 ? [A3: complex,R4: real] :
% 5.31/5.65 ( Z3
% 5.31/5.65 = ( times_times_complex @ ( real_V4546457046886955230omplex @ R4 ) @ ( exp_complex @ A3 ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % complex_exp_exists
% 5.31/5.65 thf(fact_8818_finite__atLeastZeroLessThan__int,axiom,
% 5.31/5.65 ! [U: int] : ( finite_finite_int @ ( set_or4662586982721622107an_int @ zero_zero_int @ U ) ) ).
% 5.31/5.65
% 5.31/5.65 % finite_atLeastZeroLessThan_int
% 5.31/5.65 thf(fact_8819_atLeastLessThanPlusOne__atLeastAtMost__int,axiom,
% 5.31/5.65 ! [L: int,U: int] :
% 5.31/5.65 ( ( set_or4662586982721622107an_int @ L @ ( plus_plus_int @ U @ one_one_int ) )
% 5.31/5.65 = ( set_or1266510415728281911st_int @ L @ U ) ) ).
% 5.31/5.65
% 5.31/5.65 % atLeastLessThanPlusOne_atLeastAtMost_int
% 5.31/5.65 thf(fact_8820_Complex__mult__complex__of__real,axiom,
% 5.31/5.65 ! [X: real,Y: real,R3: real] :
% 5.31/5.65 ( ( times_times_complex @ ( complex2 @ X @ Y ) @ ( real_V4546457046886955230omplex @ R3 ) )
% 5.31/5.65 = ( complex2 @ ( times_times_real @ X @ R3 ) @ ( times_times_real @ Y @ R3 ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % Complex_mult_complex_of_real
% 5.31/5.65 thf(fact_8821_complex__of__real__mult__Complex,axiom,
% 5.31/5.65 ! [R3: real,X: real,Y: real] :
% 5.31/5.65 ( ( times_times_complex @ ( real_V4546457046886955230omplex @ R3 ) @ ( complex2 @ X @ Y ) )
% 5.31/5.65 = ( complex2 @ ( times_times_real @ R3 @ X ) @ ( times_times_real @ R3 @ Y ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % complex_of_real_mult_Complex
% 5.31/5.65 thf(fact_8822_Complex__eq,axiom,
% 5.31/5.65 ( complex2
% 5.31/5.65 = ( ^ [A5: real,B4: real] : ( plus_plus_complex @ ( real_V4546457046886955230omplex @ A5 ) @ ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ B4 ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % Complex_eq
% 5.31/5.65 thf(fact_8823_cis__conv__exp,axiom,
% 5.31/5.65 ( cis
% 5.31/5.65 = ( ^ [B4: real] : ( exp_complex @ ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ B4 ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % cis_conv_exp
% 5.31/5.65 thf(fact_8824_card__atLeastZeroLessThan__int,axiom,
% 5.31/5.65 ! [U: int] :
% 5.31/5.65 ( ( finite_card_int @ ( set_or4662586982721622107an_int @ zero_zero_int @ U ) )
% 5.31/5.65 = ( nat2 @ U ) ) ).
% 5.31/5.65
% 5.31/5.65 % card_atLeastZeroLessThan_int
% 5.31/5.65 thf(fact_8825_complex__of__real__i,axiom,
% 5.31/5.65 ! [R3: real] :
% 5.31/5.65 ( ( times_times_complex @ ( real_V4546457046886955230omplex @ R3 ) @ imaginary_unit )
% 5.31/5.65 = ( complex2 @ zero_zero_real @ R3 ) ) ).
% 5.31/5.65
% 5.31/5.65 % complex_of_real_i
% 5.31/5.65 thf(fact_8826_i__complex__of__real,axiom,
% 5.31/5.65 ! [R3: real] :
% 5.31/5.65 ( ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ R3 ) )
% 5.31/5.65 = ( complex2 @ zero_zero_real @ R3 ) ) ).
% 5.31/5.65
% 5.31/5.65 % i_complex_of_real
% 5.31/5.65 thf(fact_8827_complex__split__polar,axiom,
% 5.31/5.65 ! [Z3: complex] :
% 5.31/5.65 ? [R4: real,A3: real] :
% 5.31/5.65 ( Z3
% 5.31/5.65 = ( times_times_complex @ ( real_V4546457046886955230omplex @ R4 ) @ ( plus_plus_complex @ ( real_V4546457046886955230omplex @ ( cos_real @ A3 ) ) @ ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ ( sin_real @ A3 ) ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % complex_split_polar
% 5.31/5.65 thf(fact_8828_and__not__numerals_I5_J,axiom,
% 5.31/5.65 ! [M2: num,N: num] :
% 5.31/5.65 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ M2 ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 5.31/5.65 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M2 ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % and_not_numerals(5)
% 5.31/5.65 thf(fact_8829_and__not__numerals_I6_J,axiom,
% 5.31/5.65 ! [M2: num,N: num] :
% 5.31/5.65 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ M2 ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 5.31/5.65 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M2 ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % and_not_numerals(6)
% 5.31/5.65 thf(fact_8830_and__not__numerals_I9_J,axiom,
% 5.31/5.65 ! [M2: num,N: num] :
% 5.31/5.65 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ M2 ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 5.31/5.65 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M2 ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % and_not_numerals(9)
% 5.31/5.65 thf(fact_8831_or__not__numerals_I6_J,axiom,
% 5.31/5.65 ! [M2: num,N: num] :
% 5.31/5.65 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit0 @ M2 ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 5.31/5.65 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M2 ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % or_not_numerals(6)
% 5.31/5.65 thf(fact_8832_cmod__unit__one,axiom,
% 5.31/5.65 ! [A: real] :
% 5.31/5.65 ( ( real_V1022390504157884413omplex @ ( plus_plus_complex @ ( real_V4546457046886955230omplex @ ( cos_real @ A ) ) @ ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ ( sin_real @ A ) ) ) ) )
% 5.31/5.65 = one_one_real ) ).
% 5.31/5.65
% 5.31/5.65 % cmod_unit_one
% 5.31/5.65 thf(fact_8833_cmod__complex__polar,axiom,
% 5.31/5.65 ! [R3: real,A: real] :
% 5.31/5.65 ( ( real_V1022390504157884413omplex @ ( times_times_complex @ ( real_V4546457046886955230omplex @ R3 ) @ ( plus_plus_complex @ ( real_V4546457046886955230omplex @ ( cos_real @ A ) ) @ ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ ( sin_real @ A ) ) ) ) ) )
% 5.31/5.65 = ( abs_abs_real @ R3 ) ) ).
% 5.31/5.65
% 5.31/5.65 % cmod_complex_polar
% 5.31/5.65 thf(fact_8834_or__not__numerals_I5_J,axiom,
% 5.31/5.65 ! [M2: num,N: num] :
% 5.31/5.65 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit0 @ M2 ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 5.31/5.65 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M2 ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % or_not_numerals(5)
% 5.31/5.65 thf(fact_8835_and__not__numerals_I8_J,axiom,
% 5.31/5.65 ! [M2: num,N: num] :
% 5.31/5.65 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ M2 ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 5.31/5.65 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M2 ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % and_not_numerals(8)
% 5.31/5.65 thf(fact_8836_or__not__numerals_I8_J,axiom,
% 5.31/5.65 ! [M2: num,N: num] :
% 5.31/5.65 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit1 @ M2 ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 5.31/5.65 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M2 ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % or_not_numerals(8)
% 5.31/5.65 thf(fact_8837_or__not__numerals_I9_J,axiom,
% 5.31/5.65 ! [M2: num,N: num] :
% 5.31/5.65 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit1 @ M2 ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 5.31/5.65 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M2 ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % or_not_numerals(9)
% 5.31/5.65 thf(fact_8838_not__int__rec,axiom,
% 5.31/5.65 ( bit_ri7919022796975470100ot_int
% 5.31/5.65 = ( ^ [K3: int] : ( plus_plus_int @ ( zero_n2684676970156552555ol_int @ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K3 ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_ri7919022796975470100ot_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % not_int_rec
% 5.31/5.65 thf(fact_8839_Cauchy__iff2,axiom,
% 5.31/5.65 ( topolo4055970368930404560y_real
% 5.31/5.65 = ( ^ [X7: nat > real] :
% 5.31/5.65 ! [J: nat] :
% 5.31/5.65 ? [M9: nat] :
% 5.31/5.65 ! [M6: nat] :
% 5.31/5.65 ( ( ord_less_eq_nat @ M9 @ M6 )
% 5.31/5.65 => ! [N4: nat] :
% 5.31/5.65 ( ( ord_less_eq_nat @ M9 @ N4 )
% 5.31/5.65 => ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ ( X7 @ M6 ) @ ( X7 @ N4 ) ) ) @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ J ) ) ) ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % Cauchy_iff2
% 5.31/5.65 thf(fact_8840_VEBT_Osize__gen_I1_J,axiom,
% 5.31/5.65 ! [X11: option4927543243414619207at_nat,X12: nat,X13: list_VEBT_VEBT,X14: vEBT_VEBT] :
% 5.31/5.65 ( ( vEBT_size_VEBT @ ( vEBT_Node @ X11 @ X12 @ X13 @ X14 ) )
% 5.31/5.65 = ( plus_plus_nat @ ( plus_plus_nat @ ( size_list_VEBT_VEBT @ vEBT_size_VEBT @ X13 ) @ ( vEBT_size_VEBT @ X14 ) ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % VEBT.size_gen(1)
% 5.31/5.65 thf(fact_8841_VEBT_Osize_I3_J,axiom,
% 5.31/5.65 ! [X11: option4927543243414619207at_nat,X12: nat,X13: list_VEBT_VEBT,X14: vEBT_VEBT] :
% 5.31/5.65 ( ( size_size_VEBT_VEBT @ ( vEBT_Node @ X11 @ X12 @ X13 @ X14 ) )
% 5.31/5.65 = ( plus_plus_nat @ ( plus_plus_nat @ ( size_list_VEBT_VEBT @ size_size_VEBT_VEBT @ X13 ) @ ( size_size_VEBT_VEBT @ X14 ) ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % VEBT.size(3)
% 5.31/5.65 thf(fact_8842_divmod__step__integer__def,axiom,
% 5.31/5.65 ( unique4921790084139445826nteger
% 5.31/5.65 = ( ^ [L2: num] :
% 5.31/5.65 ( produc6916734918728496179nteger
% 5.31/5.65 @ ^ [Q5: code_integer,R: code_integer] : ( if_Pro6119634080678213985nteger @ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ L2 ) @ R ) @ ( produc1086072967326762835nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q5 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ R @ ( numera6620942414471956472nteger @ L2 ) ) ) @ ( produc1086072967326762835nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q5 ) @ R ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % divmod_step_integer_def
% 5.31/5.65 thf(fact_8843_complex__div__cnj,axiom,
% 5.31/5.65 ( divide1717551699836669952omplex
% 5.31/5.65 = ( ^ [A5: complex,B4: complex] : ( divide1717551699836669952omplex @ ( times_times_complex @ A5 @ ( cnj @ B4 ) ) @ ( real_V4546457046886955230omplex @ ( power_power_real @ ( real_V1022390504157884413omplex @ B4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % complex_div_cnj
% 5.31/5.65 thf(fact_8844_list__decode_Opsimps_I2_J,axiom,
% 5.31/5.65 ! [N: nat] :
% 5.31/5.65 ( ( accp_nat @ nat_list_decode_rel @ ( suc @ N ) )
% 5.31/5.65 => ( ( nat_list_decode @ ( suc @ N ) )
% 5.31/5.65 = ( produc2761476792215241774st_nat
% 5.31/5.65 @ ^ [X4: nat,Y4: nat] : ( cons_nat @ X4 @ ( nat_list_decode @ Y4 ) )
% 5.31/5.65 @ ( nat_prod_decode @ N ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % list_decode.psimps(2)
% 5.31/5.65 thf(fact_8845_complex__cnj__mult,axiom,
% 5.31/5.65 ! [X: complex,Y: complex] :
% 5.31/5.65 ( ( cnj @ ( times_times_complex @ X @ Y ) )
% 5.31/5.65 = ( times_times_complex @ ( cnj @ X ) @ ( cnj @ Y ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % complex_cnj_mult
% 5.31/5.65 thf(fact_8846_list__decode__eq,axiom,
% 5.31/5.65 ! [X: nat,Y: nat] :
% 5.31/5.65 ( ( ( nat_list_decode @ X )
% 5.31/5.65 = ( nat_list_decode @ Y ) )
% 5.31/5.65 = ( X = Y ) ) ).
% 5.31/5.65
% 5.31/5.65 % list_decode_eq
% 5.31/5.65 thf(fact_8847_times__integer__code_I1_J,axiom,
% 5.31/5.65 ! [K2: code_integer] :
% 5.31/5.65 ( ( times_3573771949741848930nteger @ K2 @ zero_z3403309356797280102nteger )
% 5.31/5.65 = zero_z3403309356797280102nteger ) ).
% 5.31/5.65
% 5.31/5.65 % times_integer_code(1)
% 5.31/5.65 thf(fact_8848_times__integer__code_I2_J,axiom,
% 5.31/5.65 ! [L: code_integer] :
% 5.31/5.65 ( ( times_3573771949741848930nteger @ zero_z3403309356797280102nteger @ L )
% 5.31/5.65 = zero_z3403309356797280102nteger ) ).
% 5.31/5.65
% 5.31/5.65 % times_integer_code(2)
% 5.31/5.65 thf(fact_8849_zero__natural_Orsp,axiom,
% 5.31/5.65 zero_zero_nat = zero_zero_nat ).
% 5.31/5.65
% 5.31/5.65 % zero_natural.rsp
% 5.31/5.65 thf(fact_8850_list__decode_Osimps_I2_J,axiom,
% 5.31/5.65 ! [N: nat] :
% 5.31/5.65 ( ( nat_list_decode @ ( suc @ N ) )
% 5.31/5.65 = ( produc2761476792215241774st_nat
% 5.31/5.65 @ ^ [X4: nat,Y4: nat] : ( cons_nat @ X4 @ ( nat_list_decode @ Y4 ) )
% 5.31/5.65 @ ( nat_prod_decode @ N ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % list_decode.simps(2)
% 5.31/5.65 thf(fact_8851_complex__mod__mult__cnj,axiom,
% 5.31/5.65 ! [Z3: complex] :
% 5.31/5.65 ( ( real_V1022390504157884413omplex @ ( times_times_complex @ Z3 @ ( cnj @ Z3 ) ) )
% 5.31/5.65 = ( power_power_real @ ( real_V1022390504157884413omplex @ Z3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % complex_mod_mult_cnj
% 5.31/5.65 thf(fact_8852_complex__norm__square,axiom,
% 5.31/5.65 ! [Z3: complex] :
% 5.31/5.65 ( ( real_V4546457046886955230omplex @ ( power_power_real @ ( real_V1022390504157884413omplex @ Z3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.31/5.65 = ( times_times_complex @ Z3 @ ( cnj @ Z3 ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % complex_norm_square
% 5.31/5.65 thf(fact_8853_integer__of__int__code,axiom,
% 5.31/5.65 ( code_integer_of_int
% 5.31/5.65 = ( ^ [K3: int] :
% 5.31/5.65 ( if_Code_integer @ ( ord_less_int @ K3 @ zero_zero_int ) @ ( uminus1351360451143612070nteger @ ( code_integer_of_int @ ( uminus_uminus_int @ K3 ) ) )
% 5.31/5.65 @ ( if_Code_integer @ ( K3 = zero_zero_int ) @ zero_z3403309356797280102nteger
% 5.31/5.65 @ ( if_Code_integer
% 5.31/5.65 @ ( ( modulo_modulo_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.31/5.65 = zero_zero_int )
% 5.31/5.65 @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( code_integer_of_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 5.31/5.65 @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( code_integer_of_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ one_one_Code_integer ) ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % integer_of_int_code
% 5.31/5.65 thf(fact_8854_list__decode_Opelims,axiom,
% 5.31/5.65 ! [X: nat,Y: list_nat] :
% 5.31/5.65 ( ( ( nat_list_decode @ X )
% 5.31/5.65 = Y )
% 5.31/5.65 => ( ( accp_nat @ nat_list_decode_rel @ X )
% 5.31/5.65 => ( ( ( X = zero_zero_nat )
% 5.31/5.65 => ( ( Y = nil_nat )
% 5.31/5.65 => ~ ( accp_nat @ nat_list_decode_rel @ zero_zero_nat ) ) )
% 5.31/5.65 => ~ ! [N3: nat] :
% 5.31/5.65 ( ( X
% 5.31/5.65 = ( suc @ N3 ) )
% 5.31/5.65 => ( ( Y
% 5.31/5.65 = ( produc2761476792215241774st_nat
% 5.31/5.65 @ ^ [X4: nat,Y4: nat] : ( cons_nat @ X4 @ ( nat_list_decode @ Y4 ) )
% 5.31/5.65 @ ( nat_prod_decode @ N3 ) ) )
% 5.31/5.65 => ~ ( accp_nat @ nat_list_decode_rel @ ( suc @ N3 ) ) ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % list_decode.pelims
% 5.31/5.65 thf(fact_8855_list__decode_Oelims,axiom,
% 5.31/5.65 ! [X: nat,Y: list_nat] :
% 5.31/5.65 ( ( ( nat_list_decode @ X )
% 5.31/5.65 = Y )
% 5.31/5.65 => ( ( ( X = zero_zero_nat )
% 5.31/5.65 => ( Y != nil_nat ) )
% 5.31/5.65 => ~ ! [N3: nat] :
% 5.31/5.65 ( ( X
% 5.31/5.65 = ( suc @ N3 ) )
% 5.31/5.65 => ( Y
% 5.31/5.65 != ( produc2761476792215241774st_nat
% 5.31/5.65 @ ^ [X4: nat,Y4: nat] : ( cons_nat @ X4 @ ( nat_list_decode @ Y4 ) )
% 5.31/5.65 @ ( nat_prod_decode @ N3 ) ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % list_decode.elims
% 5.31/5.65 thf(fact_8856_cnj__add__mult__eq__Re,axiom,
% 5.31/5.65 ! [Z3: complex,W2: complex] :
% 5.31/5.65 ( ( plus_plus_complex @ ( times_times_complex @ Z3 @ ( cnj @ W2 ) ) @ ( times_times_complex @ ( cnj @ Z3 ) @ W2 ) )
% 5.31/5.65 = ( real_V4546457046886955230omplex @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( re @ ( times_times_complex @ Z3 @ ( cnj @ W2 ) ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % cnj_add_mult_eq_Re
% 5.31/5.65 thf(fact_8857_list__encode_Ocases,axiom,
% 5.31/5.65 ! [X: list_nat] :
% 5.31/5.65 ( ( X != nil_nat )
% 5.31/5.65 => ~ ! [X3: nat,Xs3: list_nat] :
% 5.31/5.65 ( X
% 5.31/5.65 != ( cons_nat @ X3 @ Xs3 ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % list_encode.cases
% 5.31/5.65 thf(fact_8858_times__integer_Oabs__eq,axiom,
% 5.31/5.65 ! [Xa2: int,X: int] :
% 5.31/5.65 ( ( times_3573771949741848930nteger @ ( code_integer_of_int @ Xa2 ) @ ( code_integer_of_int @ X ) )
% 5.31/5.65 = ( code_integer_of_int @ ( times_times_int @ Xa2 @ X ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % times_integer.abs_eq
% 5.31/5.65 thf(fact_8859_scaleR__complex_Osimps_I1_J,axiom,
% 5.31/5.65 ! [R3: real,X: complex] :
% 5.31/5.65 ( ( re @ ( real_V2046097035970521341omplex @ R3 @ X ) )
% 5.31/5.65 = ( times_times_real @ R3 @ ( re @ X ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % scaleR_complex.simps(1)
% 5.31/5.65 thf(fact_8860_list__decode_Osimps_I1_J,axiom,
% 5.31/5.65 ( ( nat_list_decode @ zero_zero_nat )
% 5.31/5.65 = nil_nat ) ).
% 5.31/5.65
% 5.31/5.65 % list_decode.simps(1)
% 5.31/5.65 thf(fact_8861_Re__complex__div__eq__0,axiom,
% 5.31/5.65 ! [A: complex,B: complex] :
% 5.31/5.65 ( ( ( re @ ( divide1717551699836669952omplex @ A @ B ) )
% 5.31/5.65 = zero_zero_real )
% 5.31/5.65 = ( ( re @ ( times_times_complex @ A @ ( cnj @ B ) ) )
% 5.31/5.65 = zero_zero_real ) ) ).
% 5.31/5.65
% 5.31/5.65 % Re_complex_div_eq_0
% 5.31/5.65 thf(fact_8862_complex__mod__sqrt__Re__mult__cnj,axiom,
% 5.31/5.65 ( real_V1022390504157884413omplex
% 5.31/5.65 = ( ^ [Z4: complex] : ( sqrt @ ( re @ ( times_times_complex @ Z4 @ ( cnj @ Z4 ) ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % complex_mod_sqrt_Re_mult_cnj
% 5.31/5.65 thf(fact_8863_Re__complex__div__gt__0,axiom,
% 5.31/5.65 ! [A: complex,B: complex] :
% 5.31/5.65 ( ( ord_less_real @ zero_zero_real @ ( re @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 5.31/5.65 = ( ord_less_real @ zero_zero_real @ ( re @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % Re_complex_div_gt_0
% 5.31/5.65 thf(fact_8864_Re__complex__div__lt__0,axiom,
% 5.31/5.65 ! [A: complex,B: complex] :
% 5.31/5.65 ( ( ord_less_real @ ( re @ ( divide1717551699836669952omplex @ A @ B ) ) @ zero_zero_real )
% 5.31/5.65 = ( ord_less_real @ ( re @ ( times_times_complex @ A @ ( cnj @ B ) ) ) @ zero_zero_real ) ) ).
% 5.31/5.65
% 5.31/5.65 % Re_complex_div_lt_0
% 5.31/5.65 thf(fact_8865_Re__complex__div__le__0,axiom,
% 5.31/5.65 ! [A: complex,B: complex] :
% 5.31/5.65 ( ( ord_less_eq_real @ ( re @ ( divide1717551699836669952omplex @ A @ B ) ) @ zero_zero_real )
% 5.31/5.65 = ( ord_less_eq_real @ ( re @ ( times_times_complex @ A @ ( cnj @ B ) ) ) @ zero_zero_real ) ) ).
% 5.31/5.65
% 5.31/5.65 % Re_complex_div_le_0
% 5.31/5.65 thf(fact_8866_Re__complex__div__ge__0,axiom,
% 5.31/5.65 ! [A: complex,B: complex] :
% 5.31/5.65 ( ( ord_less_eq_real @ zero_zero_real @ ( re @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 5.31/5.65 = ( ord_less_eq_real @ zero_zero_real @ ( re @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % Re_complex_div_ge_0
% 5.31/5.65 thf(fact_8867_list__decode_Opsimps_I1_J,axiom,
% 5.31/5.65 ( ( accp_nat @ nat_list_decode_rel @ zero_zero_nat )
% 5.31/5.65 => ( ( nat_list_decode @ zero_zero_nat )
% 5.31/5.65 = nil_nat ) ) ).
% 5.31/5.65
% 5.31/5.65 % list_decode.psimps(1)
% 5.31/5.65 thf(fact_8868_cos__n__Re__cis__pow__n,axiom,
% 5.31/5.65 ! [N: nat,A: real] :
% 5.31/5.65 ( ( cos_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ A ) )
% 5.31/5.65 = ( re @ ( power_power_complex @ ( cis @ A ) @ N ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % cos_n_Re_cis_pow_n
% 5.31/5.65 thf(fact_8869_complex__add__cnj,axiom,
% 5.31/5.65 ! [Z3: complex] :
% 5.31/5.65 ( ( plus_plus_complex @ Z3 @ ( cnj @ Z3 ) )
% 5.31/5.65 = ( real_V4546457046886955230omplex @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( re @ Z3 ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % complex_add_cnj
% 5.31/5.65 thf(fact_8870_list__encode_Oelims,axiom,
% 5.31/5.65 ! [X: list_nat,Y: nat] :
% 5.31/5.65 ( ( ( nat_list_encode @ X )
% 5.31/5.65 = Y )
% 5.31/5.65 => ( ( ( X = nil_nat )
% 5.31/5.65 => ( Y != zero_zero_nat ) )
% 5.31/5.65 => ~ ! [X3: nat,Xs3: list_nat] :
% 5.31/5.65 ( ( X
% 5.31/5.65 = ( cons_nat @ X3 @ Xs3 ) )
% 5.31/5.65 => ( Y
% 5.31/5.65 != ( suc @ ( nat_prod_encode @ ( product_Pair_nat_nat @ X3 @ ( nat_list_encode @ Xs3 ) ) ) ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % list_encode.elims
% 5.31/5.65 thf(fact_8871_Complex__divide,axiom,
% 5.31/5.65 ( divide1717551699836669952omplex
% 5.31/5.65 = ( ^ [X4: complex,Y4: complex] : ( complex2 @ ( divide_divide_real @ ( plus_plus_real @ ( times_times_real @ ( re @ X4 ) @ ( re @ Y4 ) ) @ ( times_times_real @ ( im @ X4 ) @ ( im @ Y4 ) ) ) @ ( plus_plus_real @ ( power_power_real @ ( re @ Y4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Y4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ ( im @ X4 ) @ ( re @ Y4 ) ) @ ( times_times_real @ ( re @ X4 ) @ ( im @ Y4 ) ) ) @ ( plus_plus_real @ ( power_power_real @ ( re @ Y4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Y4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % Complex_divide
% 5.31/5.65 thf(fact_8872_Re__Reals__divide,axiom,
% 5.31/5.65 ! [R3: complex,Z3: complex] :
% 5.31/5.65 ( ( member_complex @ R3 @ real_V2521375963428798218omplex )
% 5.31/5.65 => ( ( re @ ( divide1717551699836669952omplex @ R3 @ Z3 ) )
% 5.31/5.65 = ( divide_divide_real @ ( times_times_real @ ( re @ R3 ) @ ( re @ Z3 ) ) @ ( power_power_real @ ( real_V1022390504157884413omplex @ Z3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % Re_Reals_divide
% 5.31/5.65 thf(fact_8873_list__encode__inverse,axiom,
% 5.31/5.65 ! [X: list_nat] :
% 5.31/5.65 ( ( nat_list_decode @ ( nat_list_encode @ X ) )
% 5.31/5.65 = X ) ).
% 5.31/5.65
% 5.31/5.65 % list_encode_inverse
% 5.31/5.65 thf(fact_8874_list__decode__inverse,axiom,
% 5.31/5.65 ! [N: nat] :
% 5.31/5.65 ( ( nat_list_encode @ ( nat_list_decode @ N ) )
% 5.31/5.65 = N ) ).
% 5.31/5.65
% 5.31/5.65 % list_decode_inverse
% 5.31/5.65 thf(fact_8875_complex__In__mult__cnj__zero,axiom,
% 5.31/5.65 ! [Z3: complex] :
% 5.31/5.65 ( ( im @ ( times_times_complex @ Z3 @ ( cnj @ Z3 ) ) )
% 5.31/5.65 = zero_zero_real ) ).
% 5.31/5.65
% 5.31/5.65 % complex_In_mult_cnj_zero
% 5.31/5.65 thf(fact_8876_Im__i__times,axiom,
% 5.31/5.65 ! [Z3: complex] :
% 5.31/5.65 ( ( im @ ( times_times_complex @ imaginary_unit @ Z3 ) )
% 5.31/5.65 = ( re @ Z3 ) ) ).
% 5.31/5.65
% 5.31/5.65 % Im_i_times
% 5.31/5.65 thf(fact_8877_real__eq__imaginary__iff,axiom,
% 5.31/5.65 ! [Y: complex,X: complex] :
% 5.31/5.65 ( ( member_complex @ Y @ real_V2521375963428798218omplex )
% 5.31/5.65 => ( ( member_complex @ X @ real_V2521375963428798218omplex )
% 5.31/5.65 => ( ( X
% 5.31/5.65 = ( times_times_complex @ imaginary_unit @ Y ) )
% 5.31/5.65 = ( ( X = zero_zero_complex )
% 5.31/5.65 & ( Y = zero_zero_complex ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % real_eq_imaginary_iff
% 5.31/5.65 thf(fact_8878_imaginary__eq__real__iff,axiom,
% 5.31/5.65 ! [Y: complex,X: complex] :
% 5.31/5.65 ( ( member_complex @ Y @ real_V2521375963428798218omplex )
% 5.31/5.65 => ( ( member_complex @ X @ real_V2521375963428798218omplex )
% 5.31/5.65 => ( ( ( times_times_complex @ imaginary_unit @ Y )
% 5.31/5.65 = X )
% 5.31/5.65 = ( ( X = zero_zero_complex )
% 5.31/5.65 & ( Y = zero_zero_complex ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % imaginary_eq_real_iff
% 5.31/5.65 thf(fact_8879_Re__i__times,axiom,
% 5.31/5.65 ! [Z3: complex] :
% 5.31/5.65 ( ( re @ ( times_times_complex @ imaginary_unit @ Z3 ) )
% 5.31/5.65 = ( uminus_uminus_real @ ( im @ Z3 ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % Re_i_times
% 5.31/5.65 thf(fact_8880_list__encode__eq,axiom,
% 5.31/5.65 ! [X: list_nat,Y: list_nat] :
% 5.31/5.65 ( ( ( nat_list_encode @ X )
% 5.31/5.65 = ( nat_list_encode @ Y ) )
% 5.31/5.65 = ( X = Y ) ) ).
% 5.31/5.65
% 5.31/5.65 % list_encode_eq
% 5.31/5.65 thf(fact_8881_scaleR__complex_Osimps_I2_J,axiom,
% 5.31/5.65 ! [R3: real,X: complex] :
% 5.31/5.65 ( ( im @ ( real_V2046097035970521341omplex @ R3 @ X ) )
% 5.31/5.65 = ( times_times_real @ R3 @ ( im @ X ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % scaleR_complex.simps(2)
% 5.31/5.65 thf(fact_8882_list__encode_Osimps_I1_J,axiom,
% 5.31/5.65 ( ( nat_list_encode @ nil_nat )
% 5.31/5.65 = zero_zero_nat ) ).
% 5.31/5.65
% 5.31/5.65 % list_encode.simps(1)
% 5.31/5.65 thf(fact_8883_times__complex_Osimps_I2_J,axiom,
% 5.31/5.65 ! [X: complex,Y: complex] :
% 5.31/5.65 ( ( im @ ( times_times_complex @ X @ Y ) )
% 5.31/5.65 = ( plus_plus_real @ ( times_times_real @ ( re @ X ) @ ( im @ Y ) ) @ ( times_times_real @ ( im @ X ) @ ( re @ Y ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % times_complex.simps(2)
% 5.31/5.65 thf(fact_8884_times__complex_Osimps_I1_J,axiom,
% 5.31/5.65 ! [X: complex,Y: complex] :
% 5.31/5.65 ( ( re @ ( times_times_complex @ X @ Y ) )
% 5.31/5.65 = ( minus_minus_real @ ( times_times_real @ ( re @ X ) @ ( re @ Y ) ) @ ( times_times_real @ ( im @ X ) @ ( im @ Y ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % times_complex.simps(1)
% 5.31/5.65 thf(fact_8885_Im__complex__div__eq__0,axiom,
% 5.31/5.65 ! [A: complex,B: complex] :
% 5.31/5.65 ( ( ( im @ ( divide1717551699836669952omplex @ A @ B ) )
% 5.31/5.65 = zero_zero_real )
% 5.31/5.65 = ( ( im @ ( times_times_complex @ A @ ( cnj @ B ) ) )
% 5.31/5.65 = zero_zero_real ) ) ).
% 5.31/5.65
% 5.31/5.65 % Im_complex_div_eq_0
% 5.31/5.65 thf(fact_8886_scaleR__complex_Ocode,axiom,
% 5.31/5.65 ( real_V2046097035970521341omplex
% 5.31/5.65 = ( ^ [R: real,X4: complex] : ( complex2 @ ( times_times_real @ R @ ( re @ X4 ) ) @ ( times_times_real @ R @ ( im @ X4 ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % scaleR_complex.code
% 5.31/5.65 thf(fact_8887_Im__Reals__divide,axiom,
% 5.31/5.65 ! [R3: complex,Z3: complex] :
% 5.31/5.65 ( ( member_complex @ R3 @ real_V2521375963428798218omplex )
% 5.31/5.65 => ( ( im @ ( divide1717551699836669952omplex @ R3 @ Z3 ) )
% 5.31/5.65 = ( divide_divide_real @ ( times_times_real @ ( uminus_uminus_real @ ( re @ R3 ) ) @ ( im @ Z3 ) ) @ ( power_power_real @ ( real_V1022390504157884413omplex @ Z3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % Im_Reals_divide
% 5.31/5.65 thf(fact_8888_Im__complex__div__lt__0,axiom,
% 5.31/5.65 ! [A: complex,B: complex] :
% 5.31/5.65 ( ( ord_less_real @ ( im @ ( divide1717551699836669952omplex @ A @ B ) ) @ zero_zero_real )
% 5.31/5.65 = ( ord_less_real @ ( im @ ( times_times_complex @ A @ ( cnj @ B ) ) ) @ zero_zero_real ) ) ).
% 5.31/5.65
% 5.31/5.65 % Im_complex_div_lt_0
% 5.31/5.65 thf(fact_8889_Im__complex__div__gt__0,axiom,
% 5.31/5.65 ! [A: complex,B: complex] :
% 5.31/5.65 ( ( ord_less_real @ zero_zero_real @ ( im @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 5.31/5.65 = ( ord_less_real @ zero_zero_real @ ( im @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % Im_complex_div_gt_0
% 5.31/5.65 thf(fact_8890_Im__complex__div__ge__0,axiom,
% 5.31/5.65 ! [A: complex,B: complex] :
% 5.31/5.65 ( ( ord_less_eq_real @ zero_zero_real @ ( im @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 5.31/5.65 = ( ord_less_eq_real @ zero_zero_real @ ( im @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % Im_complex_div_ge_0
% 5.31/5.65 thf(fact_8891_Im__complex__div__le__0,axiom,
% 5.31/5.65 ! [A: complex,B: complex] :
% 5.31/5.65 ( ( ord_less_eq_real @ ( im @ ( divide1717551699836669952omplex @ A @ B ) ) @ zero_zero_real )
% 5.31/5.65 = ( ord_less_eq_real @ ( im @ ( times_times_complex @ A @ ( cnj @ B ) ) ) @ zero_zero_real ) ) ).
% 5.31/5.65
% 5.31/5.65 % Im_complex_div_le_0
% 5.31/5.65 thf(fact_8892_sin__n__Im__cis__pow__n,axiom,
% 5.31/5.65 ! [N: nat,A: real] :
% 5.31/5.65 ( ( sin_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ A ) )
% 5.31/5.65 = ( im @ ( power_power_complex @ ( cis @ A ) @ N ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % sin_n_Im_cis_pow_n
% 5.31/5.65 thf(fact_8893_Re__exp,axiom,
% 5.31/5.65 ! [Z3: complex] :
% 5.31/5.65 ( ( re @ ( exp_complex @ Z3 ) )
% 5.31/5.65 = ( times_times_real @ ( exp_real @ ( re @ Z3 ) ) @ ( cos_real @ ( im @ Z3 ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % Re_exp
% 5.31/5.65 thf(fact_8894_Im__exp,axiom,
% 5.31/5.65 ! [Z3: complex] :
% 5.31/5.65 ( ( im @ ( exp_complex @ Z3 ) )
% 5.31/5.65 = ( times_times_real @ ( exp_real @ ( re @ Z3 ) ) @ ( sin_real @ ( im @ Z3 ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % Im_exp
% 5.31/5.65 thf(fact_8895_complex__eq,axiom,
% 5.31/5.65 ! [A: complex] :
% 5.31/5.65 ( A
% 5.31/5.65 = ( plus_plus_complex @ ( real_V4546457046886955230omplex @ ( re @ A ) ) @ ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ ( im @ A ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % complex_eq
% 5.31/5.65 thf(fact_8896_times__complex_Ocode,axiom,
% 5.31/5.65 ( times_times_complex
% 5.31/5.65 = ( ^ [X4: complex,Y4: complex] : ( complex2 @ ( minus_minus_real @ ( times_times_real @ ( re @ X4 ) @ ( re @ Y4 ) ) @ ( times_times_real @ ( im @ X4 ) @ ( im @ Y4 ) ) ) @ ( plus_plus_real @ ( times_times_real @ ( re @ X4 ) @ ( im @ Y4 ) ) @ ( times_times_real @ ( im @ X4 ) @ ( re @ Y4 ) ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % times_complex.code
% 5.31/5.65 thf(fact_8897_complex__div__gt__0,axiom,
% 5.31/5.65 ! [A: complex,B: complex] :
% 5.31/5.65 ( ( ( ord_less_real @ zero_zero_real @ ( re @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 5.31/5.65 = ( ord_less_real @ zero_zero_real @ ( re @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) )
% 5.31/5.65 & ( ( ord_less_real @ zero_zero_real @ ( im @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 5.31/5.65 = ( ord_less_real @ zero_zero_real @ ( im @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % complex_div_gt_0
% 5.31/5.65 thf(fact_8898_exp__eq__polar,axiom,
% 5.31/5.65 ( exp_complex
% 5.31/5.65 = ( ^ [Z4: complex] : ( times_times_complex @ ( real_V4546457046886955230omplex @ ( exp_real @ ( re @ Z4 ) ) ) @ ( cis @ ( im @ Z4 ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % exp_eq_polar
% 5.31/5.65 thf(fact_8899_Im__power2,axiom,
% 5.31/5.65 ! [X: complex] :
% 5.31/5.65 ( ( im @ ( power_power_complex @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.31/5.65 = ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( re @ X ) ) @ ( im @ X ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % Im_power2
% 5.31/5.65 thf(fact_8900_list__encode_Osimps_I2_J,axiom,
% 5.31/5.65 ! [X: nat,Xs2: list_nat] :
% 5.31/5.65 ( ( nat_list_encode @ ( cons_nat @ X @ Xs2 ) )
% 5.31/5.65 = ( suc @ ( nat_prod_encode @ ( product_Pair_nat_nat @ X @ ( nat_list_encode @ Xs2 ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % list_encode.simps(2)
% 5.31/5.65 thf(fact_8901_complex__diff__cnj,axiom,
% 5.31/5.65 ! [Z3: complex] :
% 5.31/5.65 ( ( minus_minus_complex @ Z3 @ ( cnj @ Z3 ) )
% 5.31/5.65 = ( times_times_complex @ ( real_V4546457046886955230omplex @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( im @ Z3 ) ) ) @ imaginary_unit ) ) ).
% 5.31/5.65
% 5.31/5.65 % complex_diff_cnj
% 5.31/5.65 thf(fact_8902_Re__divide,axiom,
% 5.31/5.65 ! [X: complex,Y: complex] :
% 5.31/5.65 ( ( re @ ( divide1717551699836669952omplex @ X @ Y ) )
% 5.31/5.65 = ( 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 ) ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % Re_divide
% 5.31/5.65 thf(fact_8903_complex__mult__cnj,axiom,
% 5.31/5.65 ! [Z3: complex] :
% 5.31/5.65 ( ( times_times_complex @ Z3 @ ( cnj @ Z3 ) )
% 5.31/5.65 = ( real_V4546457046886955230omplex @ ( plus_plus_real @ ( power_power_real @ ( re @ Z3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Z3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % complex_mult_cnj
% 5.31/5.65 thf(fact_8904_Im__divide,axiom,
% 5.31/5.65 ! [X: complex,Y: complex] :
% 5.31/5.65 ( ( im @ ( divide1717551699836669952omplex @ X @ Y ) )
% 5.31/5.65 = ( 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 ) ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % Im_divide
% 5.31/5.65 thf(fact_8905_complex__abs__le__norm,axiom,
% 5.31/5.65 ! [Z3: complex] : ( ord_less_eq_real @ ( plus_plus_real @ ( abs_abs_real @ ( re @ Z3 ) ) @ ( abs_abs_real @ ( im @ Z3 ) ) ) @ ( times_times_real @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( real_V1022390504157884413omplex @ Z3 ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % complex_abs_le_norm
% 5.31/5.65 thf(fact_8906_csqrt_Ocode,axiom,
% 5.31/5.65 ( csqrt
% 5.31/5.65 = ( ^ [Z4: complex] :
% 5.31/5.65 ( complex2 @ ( sqrt @ ( divide_divide_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ Z4 ) @ ( re @ Z4 ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.31/5.65 @ ( times_times_real
% 5.31/5.65 @ ( if_real
% 5.31/5.65 @ ( ( im @ Z4 )
% 5.31/5.65 = zero_zero_real )
% 5.31/5.65 @ one_one_real
% 5.31/5.65 @ ( sgn_sgn_real @ ( im @ Z4 ) ) )
% 5.31/5.65 @ ( sqrt @ ( divide_divide_real @ ( minus_minus_real @ ( real_V1022390504157884413omplex @ Z4 ) @ ( re @ Z4 ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % csqrt.code
% 5.31/5.65 thf(fact_8907_csqrt_Osimps_I2_J,axiom,
% 5.31/5.65 ! [Z3: complex] :
% 5.31/5.65 ( ( im @ ( csqrt @ Z3 ) )
% 5.31/5.65 = ( times_times_real
% 5.31/5.65 @ ( if_real
% 5.31/5.65 @ ( ( im @ Z3 )
% 5.31/5.65 = zero_zero_real )
% 5.31/5.65 @ one_one_real
% 5.31/5.65 @ ( sgn_sgn_real @ ( im @ Z3 ) ) )
% 5.31/5.65 @ ( sqrt @ ( divide_divide_real @ ( minus_minus_real @ ( real_V1022390504157884413omplex @ Z3 ) @ ( re @ Z3 ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % csqrt.simps(2)
% 5.31/5.65 thf(fact_8908_csqrt__of__real__nonpos,axiom,
% 5.31/5.65 ! [X: complex] :
% 5.31/5.65 ( ( ( im @ X )
% 5.31/5.65 = zero_zero_real )
% 5.31/5.65 => ( ( ord_less_eq_real @ ( re @ X ) @ zero_zero_real )
% 5.31/5.65 => ( ( csqrt @ X )
% 5.31/5.65 = ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ ( sqrt @ ( abs_abs_real @ ( re @ X ) ) ) ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % csqrt_of_real_nonpos
% 5.31/5.65 thf(fact_8909_csqrt__minus,axiom,
% 5.31/5.65 ! [X: complex] :
% 5.31/5.65 ( ( ( ord_less_real @ ( im @ X ) @ zero_zero_real )
% 5.31/5.65 | ( ( ( im @ X )
% 5.31/5.65 = zero_zero_real )
% 5.31/5.65 & ( ord_less_eq_real @ zero_zero_real @ ( re @ X ) ) ) )
% 5.31/5.65 => ( ( csqrt @ ( uminus1482373934393186551omplex @ X ) )
% 5.31/5.65 = ( times_times_complex @ imaginary_unit @ ( csqrt @ X ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % csqrt_minus
% 5.31/5.65 thf(fact_8910_bezw__0,axiom,
% 5.31/5.65 ! [X: nat] :
% 5.31/5.65 ( ( bezw @ X @ zero_zero_nat )
% 5.31/5.65 = ( product_Pair_int_int @ one_one_int @ zero_zero_int ) ) ).
% 5.31/5.65
% 5.31/5.65 % bezw_0
% 5.31/5.65 thf(fact_8911_push__bit__of__Suc__0,axiom,
% 5.31/5.65 ! [N: nat] :
% 5.31/5.65 ( ( bit_se547839408752420682it_nat @ N @ ( suc @ zero_zero_nat ) )
% 5.31/5.65 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.31/5.65
% 5.31/5.65 % push_bit_of_Suc_0
% 5.31/5.65 thf(fact_8912_nat_Odisc__eq__case_I1_J,axiom,
% 5.31/5.65 ! [Nat: nat] :
% 5.31/5.65 ( ( Nat = zero_zero_nat )
% 5.31/5.65 = ( case_nat_o @ $true
% 5.31/5.65 @ ^ [Uu3: nat] : $false
% 5.31/5.65 @ Nat ) ) ).
% 5.31/5.65
% 5.31/5.65 % nat.disc_eq_case(1)
% 5.31/5.65 thf(fact_8913_nat_Odisc__eq__case_I2_J,axiom,
% 5.31/5.65 ! [Nat: nat] :
% 5.31/5.65 ( ( Nat != zero_zero_nat )
% 5.31/5.65 = ( case_nat_o @ $false
% 5.31/5.65 @ ^ [Uu3: nat] : $true
% 5.31/5.65 @ Nat ) ) ).
% 5.31/5.65
% 5.31/5.65 % nat.disc_eq_case(2)
% 5.31/5.65 thf(fact_8914_bit__push__bit__iff__int,axiom,
% 5.31/5.65 ! [M2: nat,K2: int,N: nat] :
% 5.31/5.65 ( ( bit_se1146084159140164899it_int @ ( bit_se545348938243370406it_int @ M2 @ K2 ) @ N )
% 5.31/5.65 = ( ( ord_less_eq_nat @ M2 @ N )
% 5.31/5.65 & ( bit_se1146084159140164899it_int @ K2 @ ( minus_minus_nat @ N @ M2 ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % bit_push_bit_iff_int
% 5.31/5.65 thf(fact_8915_bit__push__bit__iff__nat,axiom,
% 5.31/5.65 ! [M2: nat,Q2: nat,N: nat] :
% 5.31/5.65 ( ( bit_se1148574629649215175it_nat @ ( bit_se547839408752420682it_nat @ M2 @ Q2 ) @ N )
% 5.31/5.65 = ( ( ord_less_eq_nat @ M2 @ N )
% 5.31/5.65 & ( bit_se1148574629649215175it_nat @ Q2 @ ( minus_minus_nat @ N @ M2 ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % bit_push_bit_iff_nat
% 5.31/5.65 thf(fact_8916_less__eq__nat_Osimps_I2_J,axiom,
% 5.31/5.65 ! [M2: nat,N: nat] :
% 5.31/5.65 ( ( ord_less_eq_nat @ ( suc @ M2 ) @ N )
% 5.31/5.65 = ( case_nat_o @ $false @ ( ord_less_eq_nat @ M2 ) @ N ) ) ).
% 5.31/5.65
% 5.31/5.65 % less_eq_nat.simps(2)
% 5.31/5.65 thf(fact_8917_max__Suc2,axiom,
% 5.31/5.65 ! [M2: nat,N: nat] :
% 5.31/5.65 ( ( ord_max_nat @ M2 @ ( suc @ N ) )
% 5.31/5.65 = ( case_nat_nat @ ( suc @ N )
% 5.31/5.65 @ ^ [M7: nat] : ( suc @ ( ord_max_nat @ M7 @ N ) )
% 5.31/5.65 @ M2 ) ) ).
% 5.31/5.65
% 5.31/5.65 % max_Suc2
% 5.31/5.65 thf(fact_8918_max__Suc1,axiom,
% 5.31/5.65 ! [N: nat,M2: nat] :
% 5.31/5.65 ( ( ord_max_nat @ ( suc @ N ) @ M2 )
% 5.31/5.65 = ( case_nat_nat @ ( suc @ N )
% 5.31/5.65 @ ^ [M7: nat] : ( suc @ ( ord_max_nat @ N @ M7 ) )
% 5.31/5.65 @ M2 ) ) ).
% 5.31/5.65
% 5.31/5.65 % max_Suc1
% 5.31/5.65 thf(fact_8919_diff__Suc,axiom,
% 5.31/5.65 ! [M2: nat,N: nat] :
% 5.31/5.65 ( ( minus_minus_nat @ M2 @ ( suc @ N ) )
% 5.31/5.65 = ( case_nat_nat @ zero_zero_nat
% 5.31/5.65 @ ^ [K3: nat] : K3
% 5.31/5.65 @ ( minus_minus_nat @ M2 @ N ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % diff_Suc
% 5.31/5.65 thf(fact_8920_push__bit__nat__def,axiom,
% 5.31/5.65 ( bit_se547839408752420682it_nat
% 5.31/5.65 = ( ^ [N4: nat,M6: nat] : ( times_times_nat @ M6 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % push_bit_nat_def
% 5.31/5.65 thf(fact_8921_push__bit__int__def,axiom,
% 5.31/5.65 ( bit_se545348938243370406it_int
% 5.31/5.65 = ( ^ [N4: nat,K3: int] : ( times_times_int @ K3 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N4 ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % push_bit_int_def
% 5.31/5.65 thf(fact_8922_pred__def,axiom,
% 5.31/5.65 ( pred
% 5.31/5.65 = ( case_nat_nat @ zero_zero_nat
% 5.31/5.65 @ ^ [X24: nat] : X24 ) ) ).
% 5.31/5.65
% 5.31/5.65 % pred_def
% 5.31/5.65 thf(fact_8923_Suc__0__mod__numeral,axiom,
% 5.31/5.65 ! [K2: num] :
% 5.31/5.65 ( ( modulo_modulo_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ K2 ) )
% 5.31/5.65 = ( product_snd_nat_nat @ ( unique5055182867167087721od_nat @ one @ K2 ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % Suc_0_mod_numeral
% 5.31/5.65 thf(fact_8924_Suc__0__div__numeral,axiom,
% 5.31/5.65 ! [K2: num] :
% 5.31/5.65 ( ( divide_divide_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ K2 ) )
% 5.31/5.65 = ( product_fst_nat_nat @ ( unique5055182867167087721od_nat @ one @ K2 ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % Suc_0_div_numeral
% 5.31/5.65 thf(fact_8925_nat__of__integer__code,axiom,
% 5.31/5.65 ( code_nat_of_integer
% 5.31/5.65 = ( ^ [K3: code_integer] :
% 5.31/5.65 ( if_nat @ ( ord_le3102999989581377725nteger @ K3 @ zero_z3403309356797280102nteger ) @ zero_zero_nat
% 5.31/5.65 @ ( produc1555791787009142072er_nat
% 5.31/5.65 @ ^ [L2: code_integer,J: code_integer] : ( if_nat @ ( J = zero_z3403309356797280102nteger ) @ ( plus_plus_nat @ ( code_nat_of_integer @ L2 ) @ ( code_nat_of_integer @ L2 ) ) @ ( plus_plus_nat @ ( plus_plus_nat @ ( code_nat_of_integer @ L2 ) @ ( code_nat_of_integer @ L2 ) ) @ one_one_nat ) )
% 5.31/5.65 @ ( code_divmod_integer @ K3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % nat_of_integer_code
% 5.31/5.65 thf(fact_8926_drop__bit__of__Suc__0,axiom,
% 5.31/5.65 ! [N: nat] :
% 5.31/5.65 ( ( bit_se8570568707652914677it_nat @ N @ ( suc @ zero_zero_nat ) )
% 5.31/5.65 = ( zero_n2687167440665602831ol_nat @ ( N = zero_zero_nat ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % drop_bit_of_Suc_0
% 5.31/5.65 thf(fact_8927_drop__bit__Suc__minus__bit0,axiom,
% 5.31/5.65 ! [N: nat,K2: num] :
% 5.31/5.65 ( ( bit_se8568078237143864401it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K2 ) ) ) )
% 5.31/5.65 = ( bit_se8568078237143864401it_int @ N @ ( uminus_uminus_int @ ( numeral_numeral_int @ K2 ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % drop_bit_Suc_minus_bit0
% 5.31/5.65 thf(fact_8928_fst__divmod__nat,axiom,
% 5.31/5.65 ! [M2: nat,N: nat] :
% 5.31/5.65 ( ( product_fst_nat_nat @ ( divmod_nat @ M2 @ N ) )
% 5.31/5.65 = ( divide_divide_nat @ M2 @ N ) ) ).
% 5.31/5.65
% 5.31/5.65 % fst_divmod_nat
% 5.31/5.65 thf(fact_8929_nat__of__integer__non__positive,axiom,
% 5.31/5.65 ! [K2: code_integer] :
% 5.31/5.65 ( ( ord_le3102999989581377725nteger @ K2 @ zero_z3403309356797280102nteger )
% 5.31/5.65 => ( ( code_nat_of_integer @ K2 )
% 5.31/5.65 = zero_zero_nat ) ) ).
% 5.31/5.65
% 5.31/5.65 % nat_of_integer_non_positive
% 5.31/5.65 thf(fact_8930_snd__divmod__nat,axiom,
% 5.31/5.65 ! [M2: nat,N: nat] :
% 5.31/5.65 ( ( product_snd_nat_nat @ ( divmod_nat @ M2 @ N ) )
% 5.31/5.65 = ( modulo_modulo_nat @ M2 @ N ) ) ).
% 5.31/5.65
% 5.31/5.65 % snd_divmod_nat
% 5.31/5.65 thf(fact_8931_drop__bit__Suc__minus__bit1,axiom,
% 5.31/5.65 ! [N: nat,K2: num] :
% 5.31/5.65 ( ( bit_se8568078237143864401it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K2 ) ) ) )
% 5.31/5.65 = ( bit_se8568078237143864401it_int @ N @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ K2 ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % drop_bit_Suc_minus_bit1
% 5.31/5.65 thf(fact_8932_nat__of__integer__code__post_I1_J,axiom,
% 5.31/5.65 ( ( code_nat_of_integer @ zero_z3403309356797280102nteger )
% 5.31/5.65 = zero_zero_nat ) ).
% 5.31/5.65
% 5.31/5.65 % nat_of_integer_code_post(1)
% 5.31/5.65 thf(fact_8933_int__of__integer__code,axiom,
% 5.31/5.65 ( code_int_of_integer
% 5.31/5.65 = ( ^ [K3: code_integer] :
% 5.31/5.65 ( if_int @ ( ord_le6747313008572928689nteger @ K3 @ zero_z3403309356797280102nteger ) @ ( uminus_uminus_int @ ( code_int_of_integer @ ( uminus1351360451143612070nteger @ K3 ) ) )
% 5.31/5.65 @ ( if_int @ ( K3 = zero_z3403309356797280102nteger ) @ zero_zero_int
% 5.31/5.65 @ ( produc1553301316500091796er_int
% 5.31/5.65 @ ^ [L2: code_integer,J: code_integer] : ( if_int @ ( J = zero_z3403309356797280102nteger ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( code_int_of_integer @ L2 ) ) @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( code_int_of_integer @ L2 ) ) @ one_one_int ) )
% 5.31/5.65 @ ( code_divmod_integer @ K3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % int_of_integer_code
% 5.31/5.65 thf(fact_8934_times__integer_Orep__eq,axiom,
% 5.31/5.65 ! [X: code_integer,Xa2: code_integer] :
% 5.31/5.65 ( ( code_int_of_integer @ ( times_3573771949741848930nteger @ X @ Xa2 ) )
% 5.31/5.65 = ( times_times_int @ ( code_int_of_integer @ X ) @ ( code_int_of_integer @ Xa2 ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % times_integer.rep_eq
% 5.31/5.65 thf(fact_8935_bezw__non__0,axiom,
% 5.31/5.65 ! [Y: nat,X: nat] :
% 5.31/5.65 ( ( ord_less_nat @ zero_zero_nat @ Y )
% 5.31/5.65 => ( ( bezw @ X @ Y )
% 5.31/5.65 = ( 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 ) ) ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % bezw_non_0
% 5.31/5.65 thf(fact_8936_bezw_Oelims,axiom,
% 5.31/5.65 ! [X: nat,Xa2: nat,Y: product_prod_int_int] :
% 5.31/5.65 ( ( ( bezw @ X @ Xa2 )
% 5.31/5.65 = Y )
% 5.31/5.65 => ( ( ( Xa2 = zero_zero_nat )
% 5.31/5.65 => ( Y
% 5.31/5.65 = ( product_Pair_int_int @ one_one_int @ zero_zero_int ) ) )
% 5.31/5.65 & ( ( Xa2 != zero_zero_nat )
% 5.31/5.65 => ( Y
% 5.31/5.65 = ( 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 ) ) ) ) ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % bezw.elims
% 5.31/5.65 thf(fact_8937_bezw_Osimps,axiom,
% 5.31/5.65 ( bezw
% 5.31/5.65 = ( ^ [X4: nat,Y4: nat] : ( if_Pro3027730157355071871nt_int @ ( Y4 = zero_zero_nat ) @ ( product_Pair_int_int @ one_one_int @ zero_zero_int ) @ ( product_Pair_int_int @ ( product_snd_int_int @ ( bezw @ Y4 @ ( modulo_modulo_nat @ X4 @ Y4 ) ) ) @ ( minus_minus_int @ ( product_fst_int_int @ ( bezw @ Y4 @ ( modulo_modulo_nat @ X4 @ Y4 ) ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ Y4 @ ( modulo_modulo_nat @ X4 @ Y4 ) ) ) @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ X4 @ Y4 ) ) ) ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % bezw.simps
% 5.31/5.65 thf(fact_8938_one__mod__minus__numeral,axiom,
% 5.31/5.65 ! [N: num] :
% 5.31/5.65 ( ( modulo_modulo_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.31/5.65 = ( uminus_uminus_int @ ( adjust_mod @ ( numeral_numeral_int @ N ) @ ( product_snd_int_int @ ( unique5052692396658037445od_int @ one @ N ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % one_mod_minus_numeral
% 5.31/5.65 thf(fact_8939_minus__one__mod__numeral,axiom,
% 5.31/5.65 ! [N: num] :
% 5.31/5.65 ( ( modulo_modulo_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ N ) )
% 5.31/5.65 = ( adjust_mod @ ( numeral_numeral_int @ N ) @ ( product_snd_int_int @ ( unique5052692396658037445od_int @ one @ N ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % minus_one_mod_numeral
% 5.31/5.65 thf(fact_8940_numeral__mod__minus__numeral,axiom,
% 5.31/5.65 ! [M2: num,N: num] :
% 5.31/5.65 ( ( modulo_modulo_int @ ( numeral_numeral_int @ M2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.31/5.65 = ( uminus_uminus_int @ ( adjust_mod @ ( numeral_numeral_int @ N ) @ ( product_snd_int_int @ ( unique5052692396658037445od_int @ M2 @ N ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % numeral_mod_minus_numeral
% 5.31/5.65 thf(fact_8941_minus__numeral__mod__numeral,axiom,
% 5.31/5.65 ! [M2: num,N: num] :
% 5.31/5.65 ( ( modulo_modulo_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ ( numeral_numeral_int @ N ) )
% 5.31/5.65 = ( adjust_mod @ ( numeral_numeral_int @ N ) @ ( product_snd_int_int @ ( unique5052692396658037445od_int @ M2 @ N ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % minus_numeral_mod_numeral
% 5.31/5.65 thf(fact_8942_Divides_Oadjust__mod__def,axiom,
% 5.31/5.65 ( adjust_mod
% 5.31/5.65 = ( ^ [L2: int,R: int] : ( if_int @ ( R = zero_zero_int ) @ zero_zero_int @ ( minus_minus_int @ L2 @ R ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % Divides.adjust_mod_def
% 5.31/5.65 thf(fact_8943_bezw_Opelims,axiom,
% 5.31/5.65 ! [X: nat,Xa2: nat,Y: product_prod_int_int] :
% 5.31/5.65 ( ( ( bezw @ X @ Xa2 )
% 5.31/5.65 = Y )
% 5.31/5.65 => ( ( accp_P4275260045618599050at_nat @ bezw_rel @ ( product_Pair_nat_nat @ X @ Xa2 ) )
% 5.31/5.65 => ~ ( ( ( ( Xa2 = zero_zero_nat )
% 5.31/5.65 => ( Y
% 5.31/5.65 = ( product_Pair_int_int @ one_one_int @ zero_zero_int ) ) )
% 5.31/5.65 & ( ( Xa2 != zero_zero_nat )
% 5.31/5.65 => ( Y
% 5.31/5.65 = ( 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 ) ) ) ) ) ) ) )
% 5.31/5.65 => ~ ( accp_P4275260045618599050at_nat @ bezw_rel @ ( product_Pair_nat_nat @ X @ Xa2 ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % bezw.pelims
% 5.31/5.65 thf(fact_8944_card__greaterThanLessThan__int,axiom,
% 5.31/5.65 ! [L: int,U: int] :
% 5.31/5.65 ( ( finite_card_int @ ( set_or5832277885323065728an_int @ L @ U ) )
% 5.31/5.65 = ( nat2 @ ( minus_minus_int @ U @ ( plus_plus_int @ L @ one_one_int ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % card_greaterThanLessThan_int
% 5.31/5.65 thf(fact_8945_finite__greaterThanLessThan__int,axiom,
% 5.31/5.65 ! [L: int,U: int] : ( finite_finite_int @ ( set_or5832277885323065728an_int @ L @ U ) ) ).
% 5.31/5.65
% 5.31/5.65 % finite_greaterThanLessThan_int
% 5.31/5.65 thf(fact_8946_atLeastPlusOneLessThan__greaterThanLessThan__int,axiom,
% 5.31/5.65 ! [L: int,U: int] :
% 5.31/5.65 ( ( set_or4662586982721622107an_int @ ( plus_plus_int @ L @ one_one_int ) @ U )
% 5.31/5.65 = ( set_or5832277885323065728an_int @ L @ U ) ) ).
% 5.31/5.65
% 5.31/5.65 % atLeastPlusOneLessThan_greaterThanLessThan_int
% 5.31/5.65 thf(fact_8947_prod__decode__aux_Opelims,axiom,
% 5.31/5.65 ! [X: nat,Xa2: nat,Y: product_prod_nat_nat] :
% 5.31/5.65 ( ( ( nat_prod_decode_aux @ X @ Xa2 )
% 5.31/5.65 = Y )
% 5.31/5.65 => ( ( accp_P4275260045618599050at_nat @ nat_pr5047031295181774490ux_rel @ ( product_Pair_nat_nat @ X @ Xa2 ) )
% 5.31/5.65 => ~ ( ( ( ( ord_less_eq_nat @ Xa2 @ X )
% 5.31/5.65 => ( Y
% 5.31/5.65 = ( product_Pair_nat_nat @ Xa2 @ ( minus_minus_nat @ X @ Xa2 ) ) ) )
% 5.31/5.65 & ( ~ ( ord_less_eq_nat @ Xa2 @ X )
% 5.31/5.65 => ( Y
% 5.31/5.65 = ( nat_prod_decode_aux @ ( suc @ X ) @ ( minus_minus_nat @ Xa2 @ ( suc @ X ) ) ) ) ) )
% 5.31/5.65 => ~ ( accp_P4275260045618599050at_nat @ nat_pr5047031295181774490ux_rel @ ( product_Pair_nat_nat @ X @ Xa2 ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % prod_decode_aux.pelims
% 5.31/5.65 thf(fact_8948_finite__greaterThanLessThan,axiom,
% 5.31/5.65 ! [L: nat,U: nat] : ( finite_finite_nat @ ( set_or5834768355832116004an_nat @ L @ U ) ) ).
% 5.31/5.65
% 5.31/5.65 % finite_greaterThanLessThan
% 5.31/5.65 thf(fact_8949_Suc__funpow,axiom,
% 5.31/5.65 ! [N: nat] :
% 5.31/5.65 ( ( compow_nat_nat @ N @ suc )
% 5.31/5.65 = ( plus_plus_nat @ N ) ) ).
% 5.31/5.65
% 5.31/5.65 % Suc_funpow
% 5.31/5.65 thf(fact_8950_card__greaterThanLessThan,axiom,
% 5.31/5.65 ! [L: nat,U: nat] :
% 5.31/5.65 ( ( finite_card_nat @ ( set_or5834768355832116004an_nat @ L @ U ) )
% 5.31/5.65 = ( minus_minus_nat @ U @ ( suc @ L ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % card_greaterThanLessThan
% 5.31/5.65 thf(fact_8951_atLeastSucLessThan__greaterThanLessThan,axiom,
% 5.31/5.65 ! [L: nat,U: nat] :
% 5.31/5.65 ( ( set_or4665077453230672383an_nat @ ( suc @ L ) @ U )
% 5.31/5.65 = ( set_or5834768355832116004an_nat @ L @ U ) ) ).
% 5.31/5.65
% 5.31/5.65 % atLeastSucLessThan_greaterThanLessThan
% 5.31/5.65 thf(fact_8952_sub__BitM__One__eq,axiom,
% 5.31/5.65 ! [N: num] :
% 5.31/5.65 ( ( neg_numeral_sub_int @ ( bitM @ N ) @ one )
% 5.31/5.65 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( neg_numeral_sub_int @ N @ one ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % sub_BitM_One_eq
% 5.31/5.65 thf(fact_8953_bij__betw__nth__root__unity,axiom,
% 5.31/5.65 ! [C2: complex,N: nat] :
% 5.31/5.65 ( ( C2 != zero_zero_complex )
% 5.31/5.65 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.65 => ( bij_be1856998921033663316omplex @ ( times_times_complex @ ( times_times_complex @ ( real_V4546457046886955230omplex @ ( root @ N @ ( real_V1022390504157884413omplex @ C2 ) ) ) @ ( cis @ ( divide_divide_real @ ( arg @ C2 ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) )
% 5.31/5.65 @ ( collect_complex
% 5.31/5.65 @ ^ [Z4: complex] :
% 5.31/5.65 ( ( power_power_complex @ Z4 @ N )
% 5.31/5.65 = one_one_complex ) )
% 5.31/5.65 @ ( collect_complex
% 5.31/5.65 @ ^ [Z4: complex] :
% 5.31/5.65 ( ( power_power_complex @ Z4 @ N )
% 5.31/5.65 = C2 ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % bij_betw_nth_root_unity
% 5.31/5.65 thf(fact_8954_max__nat_Osemilattice__neutr__order__axioms,axiom,
% 5.31/5.65 ( semila1623282765462674594er_nat @ ord_max_nat @ zero_zero_nat
% 5.31/5.65 @ ^ [X4: nat,Y4: nat] : ( ord_less_eq_nat @ Y4 @ X4 )
% 5.31/5.65 @ ^ [X4: nat,Y4: nat] : ( ord_less_nat @ Y4 @ X4 ) ) ).
% 5.31/5.65
% 5.31/5.65 % max_nat.semilattice_neutr_order_axioms
% 5.31/5.65 thf(fact_8955_real__root__Suc__0,axiom,
% 5.31/5.65 ! [X: real] :
% 5.31/5.65 ( ( root @ ( suc @ zero_zero_nat ) @ X )
% 5.31/5.65 = X ) ).
% 5.31/5.65
% 5.31/5.65 % real_root_Suc_0
% 5.31/5.65 thf(fact_8956_real__root__eq__iff,axiom,
% 5.31/5.65 ! [N: nat,X: real,Y: real] :
% 5.31/5.65 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.65 => ( ( ( root @ N @ X )
% 5.31/5.65 = ( root @ N @ Y ) )
% 5.31/5.65 = ( X = Y ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % real_root_eq_iff
% 5.31/5.65 thf(fact_8957_root__0,axiom,
% 5.31/5.65 ! [X: real] :
% 5.31/5.65 ( ( root @ zero_zero_nat @ X )
% 5.31/5.65 = zero_zero_real ) ).
% 5.31/5.65
% 5.31/5.65 % root_0
% 5.31/5.65 thf(fact_8958_real__root__eq__0__iff,axiom,
% 5.31/5.65 ! [N: nat,X: real] :
% 5.31/5.65 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.65 => ( ( ( root @ N @ X )
% 5.31/5.65 = zero_zero_real )
% 5.31/5.65 = ( X = zero_zero_real ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % real_root_eq_0_iff
% 5.31/5.65 thf(fact_8959_real__root__less__iff,axiom,
% 5.31/5.65 ! [N: nat,X: real,Y: real] :
% 5.31/5.65 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.65 => ( ( ord_less_real @ ( root @ N @ X ) @ ( root @ N @ Y ) )
% 5.31/5.65 = ( ord_less_real @ X @ Y ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % real_root_less_iff
% 5.31/5.65 thf(fact_8960_real__root__le__iff,axiom,
% 5.31/5.65 ! [N: nat,X: real,Y: real] :
% 5.31/5.65 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.65 => ( ( ord_less_eq_real @ ( root @ N @ X ) @ ( root @ N @ Y ) )
% 5.31/5.65 = ( ord_less_eq_real @ X @ Y ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % real_root_le_iff
% 5.31/5.65 thf(fact_8961_real__root__one,axiom,
% 5.31/5.65 ! [N: nat] :
% 5.31/5.65 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.65 => ( ( root @ N @ one_one_real )
% 5.31/5.65 = one_one_real ) ) ).
% 5.31/5.65
% 5.31/5.65 % real_root_one
% 5.31/5.65 thf(fact_8962_real__root__eq__1__iff,axiom,
% 5.31/5.65 ! [N: nat,X: real] :
% 5.31/5.65 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.65 => ( ( ( root @ N @ X )
% 5.31/5.65 = one_one_real )
% 5.31/5.65 = ( X = one_one_real ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % real_root_eq_1_iff
% 5.31/5.65 thf(fact_8963_real__root__gt__0__iff,axiom,
% 5.31/5.65 ! [N: nat,Y: real] :
% 5.31/5.65 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.65 => ( ( ord_less_real @ zero_zero_real @ ( root @ N @ Y ) )
% 5.31/5.65 = ( ord_less_real @ zero_zero_real @ Y ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % real_root_gt_0_iff
% 5.31/5.65 thf(fact_8964_real__root__lt__0__iff,axiom,
% 5.31/5.65 ! [N: nat,X: real] :
% 5.31/5.65 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.65 => ( ( ord_less_real @ ( root @ N @ X ) @ zero_zero_real )
% 5.31/5.65 = ( ord_less_real @ X @ zero_zero_real ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % real_root_lt_0_iff
% 5.31/5.65 thf(fact_8965_real__root__ge__0__iff,axiom,
% 5.31/5.65 ! [N: nat,Y: real] :
% 5.31/5.65 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.65 => ( ( ord_less_eq_real @ zero_zero_real @ ( root @ N @ Y ) )
% 5.31/5.65 = ( ord_less_eq_real @ zero_zero_real @ Y ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % real_root_ge_0_iff
% 5.31/5.65 thf(fact_8966_real__root__le__0__iff,axiom,
% 5.31/5.65 ! [N: nat,X: real] :
% 5.31/5.65 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.65 => ( ( ord_less_eq_real @ ( root @ N @ X ) @ zero_zero_real )
% 5.31/5.65 = ( ord_less_eq_real @ X @ zero_zero_real ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % real_root_le_0_iff
% 5.31/5.65 thf(fact_8967_real__root__gt__1__iff,axiom,
% 5.31/5.65 ! [N: nat,Y: real] :
% 5.31/5.65 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.65 => ( ( ord_less_real @ one_one_real @ ( root @ N @ Y ) )
% 5.31/5.65 = ( ord_less_real @ one_one_real @ Y ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % real_root_gt_1_iff
% 5.31/5.65 thf(fact_8968_real__root__lt__1__iff,axiom,
% 5.31/5.65 ! [N: nat,X: real] :
% 5.31/5.65 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.65 => ( ( ord_less_real @ ( root @ N @ X ) @ one_one_real )
% 5.31/5.65 = ( ord_less_real @ X @ one_one_real ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % real_root_lt_1_iff
% 5.31/5.65 thf(fact_8969_real__root__ge__1__iff,axiom,
% 5.31/5.65 ! [N: nat,Y: real] :
% 5.31/5.65 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.65 => ( ( ord_less_eq_real @ one_one_real @ ( root @ N @ Y ) )
% 5.31/5.65 = ( ord_less_eq_real @ one_one_real @ Y ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % real_root_ge_1_iff
% 5.31/5.65 thf(fact_8970_real__root__le__1__iff,axiom,
% 5.31/5.65 ! [N: nat,X: real] :
% 5.31/5.65 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.65 => ( ( ord_less_eq_real @ ( root @ N @ X ) @ one_one_real )
% 5.31/5.65 = ( ord_less_eq_real @ X @ one_one_real ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % real_root_le_1_iff
% 5.31/5.65 thf(fact_8971_real__root__pow__pos2,axiom,
% 5.31/5.65 ! [N: nat,X: real] :
% 5.31/5.65 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.65 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.31/5.65 => ( ( power_power_real @ ( root @ N @ X ) @ N )
% 5.31/5.65 = X ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % real_root_pow_pos2
% 5.31/5.65 thf(fact_8972_real__root__mult__exp,axiom,
% 5.31/5.65 ! [M2: nat,N: nat,X: real] :
% 5.31/5.65 ( ( root @ ( times_times_nat @ M2 @ N ) @ X )
% 5.31/5.65 = ( root @ M2 @ ( root @ N @ X ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % real_root_mult_exp
% 5.31/5.65 thf(fact_8973_real__root__mult,axiom,
% 5.31/5.65 ! [N: nat,X: real,Y: real] :
% 5.31/5.65 ( ( root @ N @ ( times_times_real @ X @ Y ) )
% 5.31/5.65 = ( times_times_real @ ( root @ N @ X ) @ ( root @ N @ Y ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % real_root_mult
% 5.31/5.65 thf(fact_8974_real__root__less__mono,axiom,
% 5.31/5.65 ! [N: nat,X: real,Y: real] :
% 5.31/5.65 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.65 => ( ( ord_less_real @ X @ Y )
% 5.31/5.65 => ( ord_less_real @ ( root @ N @ X ) @ ( root @ N @ Y ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % real_root_less_mono
% 5.31/5.65 thf(fact_8975_real__root__le__mono,axiom,
% 5.31/5.65 ! [N: nat,X: real,Y: real] :
% 5.31/5.65 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.65 => ( ( ord_less_eq_real @ X @ Y )
% 5.31/5.65 => ( ord_less_eq_real @ ( root @ N @ X ) @ ( root @ N @ Y ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % real_root_le_mono
% 5.31/5.65 thf(fact_8976_real__root__power,axiom,
% 5.31/5.65 ! [N: nat,X: real,K2: nat] :
% 5.31/5.65 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.65 => ( ( root @ N @ ( power_power_real @ X @ K2 ) )
% 5.31/5.65 = ( power_power_real @ ( root @ N @ X ) @ K2 ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % real_root_power
% 5.31/5.65 thf(fact_8977_real__root__abs,axiom,
% 5.31/5.65 ! [N: nat,X: real] :
% 5.31/5.65 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.65 => ( ( root @ N @ ( abs_abs_real @ X ) )
% 5.31/5.65 = ( abs_abs_real @ ( root @ N @ X ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % real_root_abs
% 5.31/5.65 thf(fact_8978_sgn__root,axiom,
% 5.31/5.65 ! [N: nat,X: real] :
% 5.31/5.65 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.65 => ( ( sgn_sgn_real @ ( root @ N @ X ) )
% 5.31/5.65 = ( sgn_sgn_real @ X ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % sgn_root
% 5.31/5.65 thf(fact_8979_real__root__gt__zero,axiom,
% 5.31/5.65 ! [N: nat,X: real] :
% 5.31/5.65 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.65 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.31/5.65 => ( ord_less_real @ zero_zero_real @ ( root @ N @ X ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % real_root_gt_zero
% 5.31/5.65 thf(fact_8980_real__root__strict__decreasing,axiom,
% 5.31/5.65 ! [N: nat,N6: nat,X: real] :
% 5.31/5.65 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.65 => ( ( ord_less_nat @ N @ N6 )
% 5.31/5.65 => ( ( ord_less_real @ one_one_real @ X )
% 5.31/5.65 => ( ord_less_real @ ( root @ N6 @ X ) @ ( root @ N @ X ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % real_root_strict_decreasing
% 5.31/5.65 thf(fact_8981_root__abs__power,axiom,
% 5.31/5.65 ! [N: nat,Y: real] :
% 5.31/5.65 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.65 => ( ( abs_abs_real @ ( root @ N @ ( power_power_real @ Y @ N ) ) )
% 5.31/5.65 = ( abs_abs_real @ Y ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % root_abs_power
% 5.31/5.65 thf(fact_8982_real__root__pos__pos,axiom,
% 5.31/5.65 ! [N: nat,X: real] :
% 5.31/5.65 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.65 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.31/5.65 => ( ord_less_eq_real @ zero_zero_real @ ( root @ N @ X ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % real_root_pos_pos
% 5.31/5.65 thf(fact_8983_real__root__strict__increasing,axiom,
% 5.31/5.65 ! [N: nat,N6: nat,X: real] :
% 5.31/5.65 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.65 => ( ( ord_less_nat @ N @ N6 )
% 5.31/5.65 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.31/5.65 => ( ( ord_less_real @ X @ one_one_real )
% 5.31/5.65 => ( ord_less_real @ ( root @ N @ X ) @ ( root @ N6 @ X ) ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % real_root_strict_increasing
% 5.31/5.65 thf(fact_8984_real__root__decreasing,axiom,
% 5.31/5.65 ! [N: nat,N6: nat,X: real] :
% 5.31/5.65 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.65 => ( ( ord_less_eq_nat @ N @ N6 )
% 5.31/5.65 => ( ( ord_less_eq_real @ one_one_real @ X )
% 5.31/5.65 => ( ord_less_eq_real @ ( root @ N6 @ X ) @ ( root @ N @ X ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % real_root_decreasing
% 5.31/5.65 thf(fact_8985_real__root__pow__pos,axiom,
% 5.31/5.65 ! [N: nat,X: real] :
% 5.31/5.65 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.65 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.31/5.65 => ( ( power_power_real @ ( root @ N @ X ) @ N )
% 5.31/5.65 = X ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % real_root_pow_pos
% 5.31/5.65 thf(fact_8986_real__root__pos__unique,axiom,
% 5.31/5.65 ! [N: nat,Y: real,X: real] :
% 5.31/5.65 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.65 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.31/5.65 => ( ( ( power_power_real @ Y @ N )
% 5.31/5.65 = X )
% 5.31/5.65 => ( ( root @ N @ X )
% 5.31/5.65 = Y ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % real_root_pos_unique
% 5.31/5.65 thf(fact_8987_real__root__power__cancel,axiom,
% 5.31/5.65 ! [N: nat,X: real] :
% 5.31/5.65 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.65 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.31/5.65 => ( ( root @ N @ ( power_power_real @ X @ N ) )
% 5.31/5.65 = X ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % real_root_power_cancel
% 5.31/5.65 thf(fact_8988_real__root__increasing,axiom,
% 5.31/5.65 ! [N: nat,N6: nat,X: real] :
% 5.31/5.65 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.65 => ( ( ord_less_eq_nat @ N @ N6 )
% 5.31/5.65 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.31/5.65 => ( ( ord_less_eq_real @ X @ one_one_real )
% 5.31/5.65 => ( ord_less_eq_real @ ( root @ N @ X ) @ ( root @ N6 @ X ) ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % real_root_increasing
% 5.31/5.65 thf(fact_8989_sgn__power__root,axiom,
% 5.31/5.65 ! [N: nat,X: real] :
% 5.31/5.65 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.65 => ( ( times_times_real @ ( sgn_sgn_real @ ( root @ N @ X ) ) @ ( power_power_real @ ( abs_abs_real @ ( root @ N @ X ) ) @ N ) )
% 5.31/5.65 = X ) ) ).
% 5.31/5.65
% 5.31/5.65 % sgn_power_root
% 5.31/5.65 thf(fact_8990_root__sgn__power,axiom,
% 5.31/5.65 ! [N: nat,Y: real] :
% 5.31/5.65 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.65 => ( ( root @ N @ ( times_times_real @ ( sgn_sgn_real @ Y ) @ ( power_power_real @ ( abs_abs_real @ Y ) @ N ) ) )
% 5.31/5.65 = Y ) ) ).
% 5.31/5.65
% 5.31/5.65 % root_sgn_power
% 5.31/5.65 thf(fact_8991_ln__root,axiom,
% 5.31/5.65 ! [N: nat,B: real] :
% 5.31/5.65 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.65 => ( ( ord_less_real @ zero_zero_real @ B )
% 5.31/5.65 => ( ( ln_ln_real @ ( root @ N @ B ) )
% 5.31/5.65 = ( divide_divide_real @ ( ln_ln_real @ B ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % ln_root
% 5.31/5.65 thf(fact_8992_log__root,axiom,
% 5.31/5.65 ! [N: nat,A: real,B: real] :
% 5.31/5.65 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.65 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.31/5.65 => ( ( log2 @ B @ ( root @ N @ A ) )
% 5.31/5.65 = ( divide_divide_real @ ( log2 @ B @ A ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % log_root
% 5.31/5.65 thf(fact_8993_log__base__root,axiom,
% 5.31/5.65 ! [N: nat,B: real,X: real] :
% 5.31/5.65 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.65 => ( ( ord_less_real @ zero_zero_real @ B )
% 5.31/5.65 => ( ( log2 @ ( root @ N @ B ) @ X )
% 5.31/5.65 = ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( log2 @ B @ X ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % log_base_root
% 5.31/5.65 thf(fact_8994_split__root,axiom,
% 5.31/5.65 ! [P2: real > $o,N: nat,X: real] :
% 5.31/5.65 ( ( P2 @ ( root @ N @ X ) )
% 5.31/5.65 = ( ( ( N = zero_zero_nat )
% 5.31/5.65 => ( P2 @ zero_zero_real ) )
% 5.31/5.65 & ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.65 => ! [Y4: real] :
% 5.31/5.65 ( ( ( times_times_real @ ( sgn_sgn_real @ Y4 ) @ ( power_power_real @ ( abs_abs_real @ Y4 ) @ N ) )
% 5.31/5.65 = X )
% 5.31/5.65 => ( P2 @ Y4 ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % split_root
% 5.31/5.65 thf(fact_8995_root__powr__inverse,axiom,
% 5.31/5.65 ! [N: nat,X: real] :
% 5.31/5.65 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.65 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.31/5.65 => ( ( root @ N @ X )
% 5.31/5.65 = ( powr_real @ X @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % root_powr_inverse
% 5.31/5.65 thf(fact_8996_powr__powr,axiom,
% 5.31/5.65 ! [X: real,A: real,B: real] :
% 5.31/5.65 ( ( powr_real @ ( powr_real @ X @ A ) @ B )
% 5.31/5.65 = ( powr_real @ X @ ( times_times_real @ A @ B ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % powr_powr
% 5.31/5.65 thf(fact_8997_powr__mult,axiom,
% 5.31/5.65 ! [X: real,Y: real,A: real] :
% 5.31/5.65 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.31/5.65 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.31/5.65 => ( ( powr_real @ ( times_times_real @ X @ Y ) @ A )
% 5.31/5.65 = ( times_times_real @ ( powr_real @ X @ A ) @ ( powr_real @ Y @ A ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % powr_mult
% 5.31/5.65 thf(fact_8998_divide__powr__uminus,axiom,
% 5.31/5.65 ! [A: real,B: real,C2: real] :
% 5.31/5.65 ( ( divide_divide_real @ A @ ( powr_real @ B @ C2 ) )
% 5.31/5.65 = ( times_times_real @ A @ ( powr_real @ B @ ( uminus_uminus_real @ C2 ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % divide_powr_uminus
% 5.31/5.65 thf(fact_8999_ln__powr,axiom,
% 5.31/5.65 ! [X: real,Y: real] :
% 5.31/5.65 ( ( X != zero_zero_real )
% 5.31/5.65 => ( ( ln_ln_real @ ( powr_real @ X @ Y ) )
% 5.31/5.65 = ( times_times_real @ Y @ ( ln_ln_real @ X ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % ln_powr
% 5.31/5.65 thf(fact_9000_log__powr,axiom,
% 5.31/5.65 ! [X: real,B: real,Y: real] :
% 5.31/5.65 ( ( X != zero_zero_real )
% 5.31/5.65 => ( ( log2 @ B @ ( powr_real @ X @ Y ) )
% 5.31/5.65 = ( times_times_real @ Y @ ( log2 @ B @ X ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % log_powr
% 5.31/5.65 thf(fact_9001_powr__mult__base,axiom,
% 5.31/5.65 ! [X: real,Y: real] :
% 5.31/5.65 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.31/5.65 => ( ( times_times_real @ X @ ( powr_real @ X @ Y ) )
% 5.31/5.65 = ( powr_real @ X @ ( plus_plus_real @ one_one_real @ Y ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % powr_mult_base
% 5.31/5.65 thf(fact_9002_ln__powr__bound2,axiom,
% 5.31/5.65 ! [X: real,A: real] :
% 5.31/5.65 ( ( ord_less_real @ one_one_real @ X )
% 5.31/5.65 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.31/5.65 => ( ord_less_eq_real @ ( powr_real @ ( ln_ln_real @ X ) @ A ) @ ( times_times_real @ ( powr_real @ A @ A ) @ X ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % ln_powr_bound2
% 5.31/5.65 thf(fact_9003_log__add__eq__powr,axiom,
% 5.31/5.65 ! [B: real,X: real,Y: real] :
% 5.31/5.65 ( ( ord_less_real @ zero_zero_real @ B )
% 5.31/5.65 => ( ( B != one_one_real )
% 5.31/5.65 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.31/5.65 => ( ( plus_plus_real @ ( log2 @ B @ X ) @ Y )
% 5.31/5.65 = ( log2 @ B @ ( times_times_real @ X @ ( powr_real @ B @ Y ) ) ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % log_add_eq_powr
% 5.31/5.65 thf(fact_9004_add__log__eq__powr,axiom,
% 5.31/5.65 ! [B: real,X: real,Y: real] :
% 5.31/5.65 ( ( ord_less_real @ zero_zero_real @ B )
% 5.31/5.65 => ( ( B != one_one_real )
% 5.31/5.65 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.31/5.65 => ( ( plus_plus_real @ Y @ ( log2 @ B @ X ) )
% 5.31/5.65 = ( log2 @ B @ ( times_times_real @ ( powr_real @ B @ Y ) @ X ) ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % add_log_eq_powr
% 5.31/5.65 thf(fact_9005_log__minus__eq__powr,axiom,
% 5.31/5.65 ! [B: real,X: real,Y: real] :
% 5.31/5.65 ( ( ord_less_real @ zero_zero_real @ B )
% 5.31/5.65 => ( ( B != one_one_real )
% 5.31/5.65 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.31/5.65 => ( ( minus_minus_real @ ( log2 @ B @ X ) @ Y )
% 5.31/5.65 = ( log2 @ B @ ( times_times_real @ X @ ( powr_real @ B @ ( uminus_uminus_real @ Y ) ) ) ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % log_minus_eq_powr
% 5.31/5.65 thf(fact_9006_times__int_Oabs__eq,axiom,
% 5.31/5.65 ! [Xa2: product_prod_nat_nat,X: product_prod_nat_nat] :
% 5.31/5.65 ( ( times_times_int @ ( abs_Integ @ Xa2 ) @ ( abs_Integ @ X ) )
% 5.31/5.65 = ( abs_Integ
% 5.31/5.65 @ ( produc27273713700761075at_nat
% 5.31/5.65 @ ^ [X4: nat,Y4: nat] :
% 5.31/5.65 ( produc2626176000494625587at_nat
% 5.31/5.65 @ ^ [U2: nat,V3: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ X4 @ U2 ) @ ( times_times_nat @ Y4 @ V3 ) ) @ ( plus_plus_nat @ ( times_times_nat @ X4 @ V3 ) @ ( times_times_nat @ Y4 @ U2 ) ) ) )
% 5.31/5.65 @ Xa2
% 5.31/5.65 @ X ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % times_int.abs_eq
% 5.31/5.65 thf(fact_9007_num__of__nat_Osimps_I2_J,axiom,
% 5.31/5.65 ! [N: nat] :
% 5.31/5.65 ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.65 => ( ( num_of_nat @ ( suc @ N ) )
% 5.31/5.65 = ( inc @ ( num_of_nat @ N ) ) ) )
% 5.31/5.65 & ( ~ ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.65 => ( ( num_of_nat @ ( suc @ N ) )
% 5.31/5.65 = one ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % num_of_nat.simps(2)
% 5.31/5.65 thf(fact_9008_num__of__nat__numeral__eq,axiom,
% 5.31/5.65 ! [Q2: num] :
% 5.31/5.65 ( ( num_of_nat @ ( numeral_numeral_nat @ Q2 ) )
% 5.31/5.65 = Q2 ) ).
% 5.31/5.65
% 5.31/5.65 % num_of_nat_numeral_eq
% 5.31/5.65 thf(fact_9009_eq__Abs__Integ,axiom,
% 5.31/5.65 ! [Z3: int] :
% 5.31/5.65 ~ ! [X3: nat,Y3: nat] :
% 5.31/5.65 ( Z3
% 5.31/5.65 != ( abs_Integ @ ( product_Pair_nat_nat @ X3 @ Y3 ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % eq_Abs_Integ
% 5.31/5.65 thf(fact_9010_num__of__nat_Osimps_I1_J,axiom,
% 5.31/5.65 ( ( num_of_nat @ zero_zero_nat )
% 5.31/5.65 = one ) ).
% 5.31/5.65
% 5.31/5.65 % num_of_nat.simps(1)
% 5.31/5.65 thf(fact_9011_zero__int__def,axiom,
% 5.31/5.65 ( zero_zero_int
% 5.31/5.65 = ( abs_Integ @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % zero_int_def
% 5.31/5.65 thf(fact_9012_int__def,axiom,
% 5.31/5.65 ( semiri1314217659103216013at_int
% 5.31/5.65 = ( ^ [N4: nat] : ( abs_Integ @ ( product_Pair_nat_nat @ N4 @ zero_zero_nat ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % int_def
% 5.31/5.65 thf(fact_9013_numeral__num__of__nat,axiom,
% 5.31/5.65 ! [N: nat] :
% 5.31/5.65 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.65 => ( ( numeral_numeral_nat @ ( num_of_nat @ N ) )
% 5.31/5.65 = N ) ) ).
% 5.31/5.65
% 5.31/5.65 % numeral_num_of_nat
% 5.31/5.65 thf(fact_9014_num__of__nat__One,axiom,
% 5.31/5.65 ! [N: nat] :
% 5.31/5.65 ( ( ord_less_eq_nat @ N @ one_one_nat )
% 5.31/5.65 => ( ( num_of_nat @ N )
% 5.31/5.65 = one ) ) ).
% 5.31/5.65
% 5.31/5.65 % num_of_nat_One
% 5.31/5.65 thf(fact_9015_uminus__int_Oabs__eq,axiom,
% 5.31/5.65 ! [X: product_prod_nat_nat] :
% 5.31/5.65 ( ( uminus_uminus_int @ ( abs_Integ @ X ) )
% 5.31/5.65 = ( abs_Integ
% 5.31/5.65 @ ( produc2626176000494625587at_nat
% 5.31/5.65 @ ^ [X4: nat,Y4: nat] : ( product_Pair_nat_nat @ Y4 @ X4 )
% 5.31/5.65 @ X ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % uminus_int.abs_eq
% 5.31/5.65 thf(fact_9016_one__int__def,axiom,
% 5.31/5.65 ( one_one_int
% 5.31/5.65 = ( abs_Integ @ ( product_Pair_nat_nat @ one_one_nat @ zero_zero_nat ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % one_int_def
% 5.31/5.65 thf(fact_9017_num__of__nat__double,axiom,
% 5.31/5.65 ! [N: nat] :
% 5.31/5.65 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.65 => ( ( num_of_nat @ ( plus_plus_nat @ N @ N ) )
% 5.31/5.65 = ( bit0 @ ( num_of_nat @ N ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % num_of_nat_double
% 5.31/5.65 thf(fact_9018_num__of__nat__plus__distrib,axiom,
% 5.31/5.65 ! [M2: nat,N: nat] :
% 5.31/5.65 ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 5.31/5.65 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.65 => ( ( num_of_nat @ ( plus_plus_nat @ M2 @ N ) )
% 5.31/5.65 = ( plus_plus_num @ ( num_of_nat @ M2 ) @ ( num_of_nat @ N ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % num_of_nat_plus_distrib
% 5.31/5.65 thf(fact_9019_less__eq__int_Oabs__eq,axiom,
% 5.31/5.65 ! [Xa2: product_prod_nat_nat,X: product_prod_nat_nat] :
% 5.31/5.65 ( ( ord_less_eq_int @ ( abs_Integ @ Xa2 ) @ ( abs_Integ @ X ) )
% 5.31/5.65 = ( produc8739625826339149834_nat_o
% 5.31/5.65 @ ^ [X4: nat,Y4: nat] :
% 5.31/5.65 ( produc6081775807080527818_nat_o
% 5.31/5.65 @ ^ [U2: nat,V3: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ X4 @ V3 ) @ ( plus_plus_nat @ U2 @ Y4 ) ) )
% 5.31/5.65 @ Xa2
% 5.31/5.65 @ X ) ) ).
% 5.31/5.65
% 5.31/5.65 % less_eq_int.abs_eq
% 5.31/5.65 thf(fact_9020_plus__int_Oabs__eq,axiom,
% 5.31/5.65 ! [Xa2: product_prod_nat_nat,X: product_prod_nat_nat] :
% 5.31/5.65 ( ( plus_plus_int @ ( abs_Integ @ Xa2 ) @ ( abs_Integ @ X ) )
% 5.31/5.65 = ( abs_Integ
% 5.31/5.65 @ ( produc27273713700761075at_nat
% 5.31/5.65 @ ^ [X4: nat,Y4: nat] :
% 5.31/5.65 ( produc2626176000494625587at_nat
% 5.31/5.65 @ ^ [U2: nat,V3: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X4 @ U2 ) @ ( plus_plus_nat @ Y4 @ V3 ) ) )
% 5.31/5.65 @ Xa2
% 5.31/5.65 @ X ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % plus_int.abs_eq
% 5.31/5.65 thf(fact_9021_minus__int_Oabs__eq,axiom,
% 5.31/5.65 ! [Xa2: product_prod_nat_nat,X: product_prod_nat_nat] :
% 5.31/5.65 ( ( minus_minus_int @ ( abs_Integ @ Xa2 ) @ ( abs_Integ @ X ) )
% 5.31/5.65 = ( abs_Integ
% 5.31/5.65 @ ( produc27273713700761075at_nat
% 5.31/5.65 @ ^ [X4: nat,Y4: nat] :
% 5.31/5.65 ( produc2626176000494625587at_nat
% 5.31/5.65 @ ^ [U2: nat,V3: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X4 @ V3 ) @ ( plus_plus_nat @ Y4 @ U2 ) ) )
% 5.31/5.65 @ Xa2
% 5.31/5.65 @ X ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % minus_int.abs_eq
% 5.31/5.65 thf(fact_9022_sorted__list__of__set__atMost__Suc,axiom,
% 5.31/5.65 ! [K2: nat] :
% 5.31/5.65 ( ( linord2614967742042102400et_nat @ ( set_ord_atMost_nat @ ( suc @ K2 ) ) )
% 5.31/5.65 = ( append_nat @ ( linord2614967742042102400et_nat @ ( set_ord_atMost_nat @ K2 ) ) @ ( cons_nat @ ( suc @ K2 ) @ nil_nat ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % sorted_list_of_set_atMost_Suc
% 5.31/5.65 thf(fact_9023_sorted__list__of__set__lessThan__Suc,axiom,
% 5.31/5.65 ! [K2: nat] :
% 5.31/5.65 ( ( linord2614967742042102400et_nat @ ( set_ord_lessThan_nat @ ( suc @ K2 ) ) )
% 5.31/5.65 = ( append_nat @ ( linord2614967742042102400et_nat @ ( set_ord_lessThan_nat @ K2 ) ) @ ( cons_nat @ K2 @ nil_nat ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % sorted_list_of_set_lessThan_Suc
% 5.31/5.65 thf(fact_9024_sorted__list__of__set__greaterThanLessThan,axiom,
% 5.31/5.65 ! [I2: nat,J2: nat] :
% 5.31/5.65 ( ( ord_less_nat @ ( suc @ I2 ) @ J2 )
% 5.31/5.65 => ( ( linord2614967742042102400et_nat @ ( set_or5834768355832116004an_nat @ I2 @ J2 ) )
% 5.31/5.65 = ( cons_nat @ ( suc @ I2 ) @ ( linord2614967742042102400et_nat @ ( set_or5834768355832116004an_nat @ ( suc @ I2 ) @ J2 ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % sorted_list_of_set_greaterThanLessThan
% 5.31/5.65 thf(fact_9025_nth__sorted__list__of__set__greaterThanLessThan,axiom,
% 5.31/5.65 ! [N: nat,J2: nat,I2: nat] :
% 5.31/5.65 ( ( ord_less_nat @ N @ ( minus_minus_nat @ J2 @ ( suc @ I2 ) ) )
% 5.31/5.65 => ( ( nth_nat @ ( linord2614967742042102400et_nat @ ( set_or5834768355832116004an_nat @ I2 @ J2 ) ) @ N )
% 5.31/5.65 = ( suc @ ( plus_plus_nat @ I2 @ N ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % nth_sorted_list_of_set_greaterThanLessThan
% 5.31/5.65 thf(fact_9026_less__eq__int_Orep__eq,axiom,
% 5.31/5.65 ( ord_less_eq_int
% 5.31/5.65 = ( ^ [X4: int,Xa3: int] :
% 5.31/5.65 ( produc8739625826339149834_nat_o
% 5.31/5.65 @ ^ [Y4: nat,Z4: nat] :
% 5.31/5.65 ( produc6081775807080527818_nat_o
% 5.31/5.65 @ ^ [U2: nat,V3: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ Y4 @ V3 ) @ ( plus_plus_nat @ U2 @ Z4 ) ) )
% 5.31/5.65 @ ( rep_Integ @ X4 )
% 5.31/5.65 @ ( rep_Integ @ Xa3 ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % less_eq_int.rep_eq
% 5.31/5.65 thf(fact_9027_image__minus__const__atLeastLessThan__nat,axiom,
% 5.31/5.65 ! [C2: nat,Y: nat,X: nat] :
% 5.31/5.65 ( ( ( ord_less_nat @ C2 @ Y )
% 5.31/5.65 => ( ( image_nat_nat
% 5.31/5.65 @ ^ [I: nat] : ( minus_minus_nat @ I @ C2 )
% 5.31/5.65 @ ( set_or4665077453230672383an_nat @ X @ Y ) )
% 5.31/5.65 = ( set_or4665077453230672383an_nat @ ( minus_minus_nat @ X @ C2 ) @ ( minus_minus_nat @ Y @ C2 ) ) ) )
% 5.31/5.65 & ( ~ ( ord_less_nat @ C2 @ Y )
% 5.31/5.65 => ( ( ( ord_less_nat @ X @ Y )
% 5.31/5.65 => ( ( image_nat_nat
% 5.31/5.65 @ ^ [I: nat] : ( minus_minus_nat @ I @ C2 )
% 5.31/5.65 @ ( set_or4665077453230672383an_nat @ X @ Y ) )
% 5.31/5.65 = ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) )
% 5.31/5.65 & ( ~ ( ord_less_nat @ X @ Y )
% 5.31/5.65 => ( ( image_nat_nat
% 5.31/5.65 @ ^ [I: nat] : ( minus_minus_nat @ I @ C2 )
% 5.31/5.65 @ ( set_or4665077453230672383an_nat @ X @ Y ) )
% 5.31/5.65 = bot_bot_set_nat ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % image_minus_const_atLeastLessThan_nat
% 5.31/5.65 thf(fact_9028_bij__betw__Suc,axiom,
% 5.31/5.65 ! [M5: set_nat,N6: set_nat] :
% 5.31/5.65 ( ( bij_betw_nat_nat @ suc @ M5 @ N6 )
% 5.31/5.65 = ( ( image_nat_nat @ suc @ M5 )
% 5.31/5.65 = N6 ) ) ).
% 5.31/5.65
% 5.31/5.65 % bij_betw_Suc
% 5.31/5.65 thf(fact_9029_image__Suc__atLeastAtMost,axiom,
% 5.31/5.65 ! [I2: nat,J2: nat] :
% 5.31/5.65 ( ( image_nat_nat @ suc @ ( set_or1269000886237332187st_nat @ I2 @ J2 ) )
% 5.31/5.65 = ( set_or1269000886237332187st_nat @ ( suc @ I2 ) @ ( suc @ J2 ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % image_Suc_atLeastAtMost
% 5.31/5.65 thf(fact_9030_image__Suc__atLeastLessThan,axiom,
% 5.31/5.65 ! [I2: nat,J2: nat] :
% 5.31/5.65 ( ( image_nat_nat @ suc @ ( set_or4665077453230672383an_nat @ I2 @ J2 ) )
% 5.31/5.65 = ( set_or4665077453230672383an_nat @ ( suc @ I2 ) @ ( suc @ J2 ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % image_Suc_atLeastLessThan
% 5.31/5.65 thf(fact_9031_zero__notin__Suc__image,axiom,
% 5.31/5.65 ! [A4: set_nat] :
% 5.31/5.65 ~ ( member_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ A4 ) ) ).
% 5.31/5.65
% 5.31/5.65 % zero_notin_Suc_image
% 5.31/5.65 thf(fact_9032_image__Suc__lessThan,axiom,
% 5.31/5.65 ! [N: nat] :
% 5.31/5.65 ( ( image_nat_nat @ suc @ ( set_ord_lessThan_nat @ N ) )
% 5.31/5.65 = ( set_or1269000886237332187st_nat @ one_one_nat @ N ) ) ).
% 5.31/5.65
% 5.31/5.65 % image_Suc_lessThan
% 5.31/5.65 thf(fact_9033_image__Suc__atMost,axiom,
% 5.31/5.65 ! [N: nat] :
% 5.31/5.65 ( ( image_nat_nat @ suc @ ( set_ord_atMost_nat @ N ) )
% 5.31/5.65 = ( set_or1269000886237332187st_nat @ one_one_nat @ ( suc @ N ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % image_Suc_atMost
% 5.31/5.65 thf(fact_9034_atLeast0__atMost__Suc__eq__insert__0,axiom,
% 5.31/5.65 ! [N: nat] :
% 5.31/5.65 ( ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) )
% 5.31/5.65 = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % atLeast0_atMost_Suc_eq_insert_0
% 5.31/5.65 thf(fact_9035_atLeast0__lessThan__Suc__eq__insert__0,axiom,
% 5.31/5.65 ! [N: nat] :
% 5.31/5.65 ( ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( suc @ N ) )
% 5.31/5.65 = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % atLeast0_lessThan_Suc_eq_insert_0
% 5.31/5.65 thf(fact_9036_lessThan__Suc__eq__insert__0,axiom,
% 5.31/5.65 ! [N: nat] :
% 5.31/5.65 ( ( set_ord_lessThan_nat @ ( suc @ N ) )
% 5.31/5.65 = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % lessThan_Suc_eq_insert_0
% 5.31/5.65 thf(fact_9037_atMost__Suc__eq__insert__0,axiom,
% 5.31/5.65 ! [N: nat] :
% 5.31/5.65 ( ( set_ord_atMost_nat @ ( suc @ N ) )
% 5.31/5.65 = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % atMost_Suc_eq_insert_0
% 5.31/5.65 thf(fact_9038_nth__sorted__list__of__set__greaterThanAtMost,axiom,
% 5.31/5.65 ! [N: nat,J2: nat,I2: nat] :
% 5.31/5.65 ( ( ord_less_nat @ N @ ( minus_minus_nat @ J2 @ I2 ) )
% 5.31/5.65 => ( ( nth_nat @ ( linord2614967742042102400et_nat @ ( set_or6659071591806873216st_nat @ I2 @ J2 ) ) @ N )
% 5.31/5.65 = ( suc @ ( plus_plus_nat @ I2 @ N ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % nth_sorted_list_of_set_greaterThanAtMost
% 5.31/5.65 thf(fact_9039_uminus__int__def,axiom,
% 5.31/5.65 ( uminus_uminus_int
% 5.31/5.65 = ( map_fu3667384564859982768at_int @ rep_Integ @ abs_Integ
% 5.31/5.65 @ ( produc2626176000494625587at_nat
% 5.31/5.65 @ ^ [X4: nat,Y4: nat] : ( product_Pair_nat_nat @ Y4 @ X4 ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % uminus_int_def
% 5.31/5.65 thf(fact_9040_rat__inverse__code,axiom,
% 5.31/5.65 ! [P: rat] :
% 5.31/5.65 ( ( quotient_of @ ( inverse_inverse_rat @ P ) )
% 5.31/5.65 = ( produc4245557441103728435nt_int
% 5.31/5.65 @ ^ [A5: int,B4: int] : ( if_Pro3027730157355071871nt_int @ ( A5 = zero_zero_int ) @ ( product_Pair_int_int @ zero_zero_int @ one_one_int ) @ ( product_Pair_int_int @ ( times_times_int @ ( sgn_sgn_int @ A5 ) @ B4 ) @ ( abs_abs_int @ A5 ) ) )
% 5.31/5.65 @ ( quotient_of @ P ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % rat_inverse_code
% 5.31/5.65 thf(fact_9041_finite__greaterThanAtMost,axiom,
% 5.31/5.65 ! [L: nat,U: nat] : ( finite_finite_nat @ ( set_or6659071591806873216st_nat @ L @ U ) ) ).
% 5.31/5.65
% 5.31/5.65 % finite_greaterThanAtMost
% 5.31/5.65 thf(fact_9042_card__greaterThanAtMost,axiom,
% 5.31/5.65 ! [L: nat,U: nat] :
% 5.31/5.65 ( ( finite_card_nat @ ( set_or6659071591806873216st_nat @ L @ U ) )
% 5.31/5.65 = ( minus_minus_nat @ U @ L ) ) ).
% 5.31/5.65
% 5.31/5.65 % card_greaterThanAtMost
% 5.31/5.65 thf(fact_9043_divide__rat__def,axiom,
% 5.31/5.65 ( divide_divide_rat
% 5.31/5.65 = ( ^ [Q5: rat,R: rat] : ( times_times_rat @ Q5 @ ( inverse_inverse_rat @ R ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % divide_rat_def
% 5.31/5.65 thf(fact_9044_rat__less__eq__code,axiom,
% 5.31/5.65 ( ord_less_eq_rat
% 5.31/5.65 = ( ^ [P5: rat,Q5: rat] :
% 5.31/5.65 ( produc4947309494688390418_int_o
% 5.31/5.65 @ ^ [A5: int,C3: int] :
% 5.31/5.65 ( produc4947309494688390418_int_o
% 5.31/5.65 @ ^ [B4: int,D2: int] : ( ord_less_eq_int @ ( times_times_int @ A5 @ D2 ) @ ( times_times_int @ C3 @ B4 ) )
% 5.31/5.65 @ ( quotient_of @ Q5 ) )
% 5.31/5.65 @ ( quotient_of @ P5 ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % rat_less_eq_code
% 5.31/5.65 thf(fact_9045_rat__less__code,axiom,
% 5.31/5.65 ( ord_less_rat
% 5.31/5.65 = ( ^ [P5: rat,Q5: rat] :
% 5.31/5.65 ( produc4947309494688390418_int_o
% 5.31/5.65 @ ^ [A5: int,C3: int] :
% 5.31/5.65 ( produc4947309494688390418_int_o
% 5.31/5.65 @ ^ [B4: int,D2: int] : ( ord_less_int @ ( times_times_int @ A5 @ D2 ) @ ( times_times_int @ C3 @ B4 ) )
% 5.31/5.65 @ ( quotient_of @ Q5 ) )
% 5.31/5.65 @ ( quotient_of @ P5 ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % rat_less_code
% 5.31/5.65 thf(fact_9046_atLeastSucAtMost__greaterThanAtMost,axiom,
% 5.31/5.65 ! [L: nat,U: nat] :
% 5.31/5.65 ( ( set_or1269000886237332187st_nat @ ( suc @ L ) @ U )
% 5.31/5.65 = ( set_or6659071591806873216st_nat @ L @ U ) ) ).
% 5.31/5.65
% 5.31/5.65 % atLeastSucAtMost_greaterThanAtMost
% 5.31/5.65 thf(fact_9047_image__int__atLeastAtMost,axiom,
% 5.31/5.65 ! [A: nat,B: nat] :
% 5.31/5.65 ( ( image_nat_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 5.31/5.65 = ( set_or1266510415728281911st_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % image_int_atLeastAtMost
% 5.31/5.65 thf(fact_9048_image__int__atLeastLessThan,axiom,
% 5.31/5.65 ! [A: nat,B: nat] :
% 5.31/5.65 ( ( image_nat_int @ semiri1314217659103216013at_int @ ( set_or4665077453230672383an_nat @ A @ B ) )
% 5.31/5.65 = ( set_or4662586982721622107an_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % image_int_atLeastLessThan
% 5.31/5.65 thf(fact_9049_sorted__list__of__set__greaterThanAtMost,axiom,
% 5.31/5.65 ! [I2: nat,J2: nat] :
% 5.31/5.65 ( ( ord_less_eq_nat @ ( suc @ I2 ) @ J2 )
% 5.31/5.65 => ( ( linord2614967742042102400et_nat @ ( set_or6659071591806873216st_nat @ I2 @ J2 ) )
% 5.31/5.65 = ( cons_nat @ ( suc @ I2 ) @ ( linord2614967742042102400et_nat @ ( set_or6659071591806873216st_nat @ ( suc @ I2 ) @ J2 ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % sorted_list_of_set_greaterThanAtMost
% 5.31/5.65 thf(fact_9050_image__add__int__atLeastLessThan,axiom,
% 5.31/5.65 ! [L: int,U: int] :
% 5.31/5.65 ( ( image_int_int
% 5.31/5.65 @ ^ [X4: int] : ( plus_plus_int @ X4 @ L )
% 5.31/5.65 @ ( set_or4662586982721622107an_int @ zero_zero_int @ ( minus_minus_int @ U @ L ) ) )
% 5.31/5.65 = ( set_or4662586982721622107an_int @ L @ U ) ) ).
% 5.31/5.65
% 5.31/5.65 % image_add_int_atLeastLessThan
% 5.31/5.65 thf(fact_9051_image__atLeastZeroLessThan__int,axiom,
% 5.31/5.65 ! [U: int] :
% 5.31/5.65 ( ( ord_less_eq_int @ zero_zero_int @ U )
% 5.31/5.65 => ( ( set_or4662586982721622107an_int @ zero_zero_int @ U )
% 5.31/5.65 = ( image_nat_int @ semiri1314217659103216013at_int @ ( set_ord_lessThan_nat @ ( nat2 @ U ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % image_atLeastZeroLessThan_int
% 5.31/5.65 thf(fact_9052_times__int__def,axiom,
% 5.31/5.65 ( times_times_int
% 5.31/5.65 = ( map_fu4960017516451851995nt_int @ rep_Integ @ ( map_fu3667384564859982768at_int @ rep_Integ @ abs_Integ )
% 5.31/5.65 @ ( produc27273713700761075at_nat
% 5.31/5.65 @ ^ [X4: nat,Y4: nat] :
% 5.31/5.65 ( produc2626176000494625587at_nat
% 5.31/5.65 @ ^ [U2: nat,V3: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ X4 @ U2 ) @ ( times_times_nat @ Y4 @ V3 ) ) @ ( plus_plus_nat @ ( times_times_nat @ X4 @ V3 ) @ ( times_times_nat @ Y4 @ U2 ) ) ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % times_int_def
% 5.31/5.65 thf(fact_9053_minus__int__def,axiom,
% 5.31/5.65 ( minus_minus_int
% 5.31/5.65 = ( map_fu4960017516451851995nt_int @ rep_Integ @ ( map_fu3667384564859982768at_int @ rep_Integ @ abs_Integ )
% 5.31/5.65 @ ( produc27273713700761075at_nat
% 5.31/5.65 @ ^ [X4: nat,Y4: nat] :
% 5.31/5.65 ( produc2626176000494625587at_nat
% 5.31/5.65 @ ^ [U2: nat,V3: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X4 @ V3 ) @ ( plus_plus_nat @ Y4 @ U2 ) ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % minus_int_def
% 5.31/5.65 thf(fact_9054_plus__int__def,axiom,
% 5.31/5.65 ( plus_plus_int
% 5.31/5.65 = ( map_fu4960017516451851995nt_int @ rep_Integ @ ( map_fu3667384564859982768at_int @ rep_Integ @ abs_Integ )
% 5.31/5.65 @ ( produc27273713700761075at_nat
% 5.31/5.65 @ ^ [X4: nat,Y4: nat] :
% 5.31/5.65 ( produc2626176000494625587at_nat
% 5.31/5.65 @ ^ [U2: nat,V3: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X4 @ U2 ) @ ( plus_plus_nat @ Y4 @ V3 ) ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % plus_int_def
% 5.31/5.65 thf(fact_9055_rat__minus__code,axiom,
% 5.31/5.65 ! [P: rat,Q2: rat] :
% 5.31/5.65 ( ( quotient_of @ ( minus_minus_rat @ P @ Q2 ) )
% 5.31/5.65 = ( produc4245557441103728435nt_int
% 5.31/5.65 @ ^ [A5: int,C3: int] :
% 5.31/5.65 ( produc4245557441103728435nt_int
% 5.31/5.65 @ ^ [B4: int,D2: int] : ( normalize @ ( product_Pair_int_int @ ( minus_minus_int @ ( times_times_int @ A5 @ D2 ) @ ( times_times_int @ B4 @ C3 ) ) @ ( times_times_int @ C3 @ D2 ) ) )
% 5.31/5.65 @ ( quotient_of @ Q2 ) )
% 5.31/5.65 @ ( quotient_of @ P ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % rat_minus_code
% 5.31/5.65 thf(fact_9056_finite__greaterThanAtMost__int,axiom,
% 5.31/5.65 ! [L: int,U: int] : ( finite_finite_int @ ( set_or6656581121297822940st_int @ L @ U ) ) ).
% 5.31/5.65
% 5.31/5.65 % finite_greaterThanAtMost_int
% 5.31/5.65 thf(fact_9057_card__greaterThanAtMost__int,axiom,
% 5.31/5.65 ! [L: int,U: int] :
% 5.31/5.65 ( ( finite_card_int @ ( set_or6656581121297822940st_int @ L @ U ) )
% 5.31/5.65 = ( nat2 @ ( minus_minus_int @ U @ L ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % card_greaterThanAtMost_int
% 5.31/5.65 thf(fact_9058_atLeastPlusOneAtMost__greaterThanAtMost__int,axiom,
% 5.31/5.65 ! [L: int,U: int] :
% 5.31/5.65 ( ( set_or1266510415728281911st_int @ ( plus_plus_int @ L @ one_one_int ) @ U )
% 5.31/5.65 = ( set_or6656581121297822940st_int @ L @ U ) ) ).
% 5.31/5.65
% 5.31/5.65 % atLeastPlusOneAtMost_greaterThanAtMost_int
% 5.31/5.65 thf(fact_9059_normalize__crossproduct,axiom,
% 5.31/5.65 ! [Q2: int,S2: int,P: int,R3: int] :
% 5.31/5.65 ( ( Q2 != zero_zero_int )
% 5.31/5.65 => ( ( S2 != zero_zero_int )
% 5.31/5.65 => ( ( ( normalize @ ( product_Pair_int_int @ P @ Q2 ) )
% 5.31/5.65 = ( normalize @ ( product_Pair_int_int @ R3 @ S2 ) ) )
% 5.31/5.65 => ( ( times_times_int @ P @ S2 )
% 5.31/5.65 = ( times_times_int @ R3 @ Q2 ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % normalize_crossproduct
% 5.31/5.65 thf(fact_9060_rat__times__code,axiom,
% 5.31/5.65 ! [P: rat,Q2: rat] :
% 5.31/5.65 ( ( quotient_of @ ( times_times_rat @ P @ Q2 ) )
% 5.31/5.65 = ( produc4245557441103728435nt_int
% 5.31/5.65 @ ^ [A5: int,C3: int] :
% 5.31/5.65 ( produc4245557441103728435nt_int
% 5.31/5.65 @ ^ [B4: int,D2: int] : ( normalize @ ( product_Pair_int_int @ ( times_times_int @ A5 @ B4 ) @ ( times_times_int @ C3 @ D2 ) ) )
% 5.31/5.65 @ ( quotient_of @ Q2 ) )
% 5.31/5.65 @ ( quotient_of @ P ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % rat_times_code
% 5.31/5.65 thf(fact_9061_rat__divide__code,axiom,
% 5.31/5.65 ! [P: rat,Q2: rat] :
% 5.31/5.65 ( ( quotient_of @ ( divide_divide_rat @ P @ Q2 ) )
% 5.31/5.65 = ( produc4245557441103728435nt_int
% 5.31/5.65 @ ^ [A5: int,C3: int] :
% 5.31/5.65 ( produc4245557441103728435nt_int
% 5.31/5.65 @ ^ [B4: int,D2: int] : ( normalize @ ( product_Pair_int_int @ ( times_times_int @ A5 @ D2 ) @ ( times_times_int @ C3 @ B4 ) ) )
% 5.31/5.65 @ ( quotient_of @ Q2 ) )
% 5.31/5.65 @ ( quotient_of @ P ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % rat_divide_code
% 5.31/5.65 thf(fact_9062_rat__plus__code,axiom,
% 5.31/5.65 ! [P: rat,Q2: rat] :
% 5.31/5.65 ( ( quotient_of @ ( plus_plus_rat @ P @ Q2 ) )
% 5.31/5.65 = ( produc4245557441103728435nt_int
% 5.31/5.65 @ ^ [A5: int,C3: int] :
% 5.31/5.65 ( produc4245557441103728435nt_int
% 5.31/5.65 @ ^ [B4: int,D2: int] : ( normalize @ ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ A5 @ D2 ) @ ( times_times_int @ B4 @ C3 ) ) @ ( times_times_int @ C3 @ D2 ) ) )
% 5.31/5.65 @ ( quotient_of @ Q2 ) )
% 5.31/5.65 @ ( quotient_of @ P ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % rat_plus_code
% 5.31/5.65 thf(fact_9063_list__encode_Opelims,axiom,
% 5.31/5.65 ! [X: list_nat,Y: nat] :
% 5.31/5.65 ( ( ( nat_list_encode @ X )
% 5.31/5.65 = Y )
% 5.31/5.65 => ( ( accp_list_nat @ nat_list_encode_rel @ X )
% 5.31/5.65 => ( ( ( X = nil_nat )
% 5.31/5.65 => ( ( Y = zero_zero_nat )
% 5.31/5.65 => ~ ( accp_list_nat @ nat_list_encode_rel @ nil_nat ) ) )
% 5.31/5.65 => ~ ! [X3: nat,Xs3: list_nat] :
% 5.31/5.65 ( ( X
% 5.31/5.65 = ( cons_nat @ X3 @ Xs3 ) )
% 5.31/5.65 => ( ( Y
% 5.31/5.65 = ( suc @ ( nat_prod_encode @ ( product_Pair_nat_nat @ X3 @ ( nat_list_encode @ Xs3 ) ) ) ) )
% 5.31/5.65 => ~ ( accp_list_nat @ nat_list_encode_rel @ ( cons_nat @ X3 @ Xs3 ) ) ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % list_encode.pelims
% 5.31/5.65 thf(fact_9064_upt__rec__numeral,axiom,
% 5.31/5.65 ! [M2: num,N: num] :
% 5.31/5.65 ( ( ( ord_less_nat @ ( numeral_numeral_nat @ M2 ) @ ( numeral_numeral_nat @ N ) )
% 5.31/5.65 => ( ( upt @ ( numeral_numeral_nat @ M2 ) @ ( numeral_numeral_nat @ N ) )
% 5.31/5.65 = ( cons_nat @ ( numeral_numeral_nat @ M2 ) @ ( upt @ ( suc @ ( numeral_numeral_nat @ M2 ) ) @ ( numeral_numeral_nat @ N ) ) ) ) )
% 5.31/5.65 & ( ~ ( ord_less_nat @ ( numeral_numeral_nat @ M2 ) @ ( numeral_numeral_nat @ N ) )
% 5.31/5.65 => ( ( upt @ ( numeral_numeral_nat @ M2 ) @ ( numeral_numeral_nat @ N ) )
% 5.31/5.65 = nil_nat ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % upt_rec_numeral
% 5.31/5.65 thf(fact_9065_tl__upt,axiom,
% 5.31/5.65 ! [M2: nat,N: nat] :
% 5.31/5.65 ( ( tl_nat @ ( upt @ M2 @ N ) )
% 5.31/5.65 = ( upt @ ( suc @ M2 ) @ N ) ) ).
% 5.31/5.65
% 5.31/5.65 % tl_upt
% 5.31/5.65 thf(fact_9066_length__upt,axiom,
% 5.31/5.65 ! [I2: nat,J2: nat] :
% 5.31/5.65 ( ( size_size_list_nat @ ( upt @ I2 @ J2 ) )
% 5.31/5.65 = ( minus_minus_nat @ J2 @ I2 ) ) ).
% 5.31/5.65
% 5.31/5.65 % length_upt
% 5.31/5.65 thf(fact_9067_take__upt,axiom,
% 5.31/5.65 ! [I2: nat,M2: nat,N: nat] :
% 5.31/5.65 ( ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ M2 ) @ N )
% 5.31/5.65 => ( ( take_nat @ M2 @ ( upt @ I2 @ N ) )
% 5.31/5.65 = ( upt @ I2 @ ( plus_plus_nat @ I2 @ M2 ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % take_upt
% 5.31/5.65 thf(fact_9068_upt__conv__Nil,axiom,
% 5.31/5.65 ! [J2: nat,I2: nat] :
% 5.31/5.65 ( ( ord_less_eq_nat @ J2 @ I2 )
% 5.31/5.65 => ( ( upt @ I2 @ J2 )
% 5.31/5.65 = nil_nat ) ) ).
% 5.31/5.65
% 5.31/5.65 % upt_conv_Nil
% 5.31/5.65 thf(fact_9069_upt__eq__Nil__conv,axiom,
% 5.31/5.65 ! [I2: nat,J2: nat] :
% 5.31/5.65 ( ( ( upt @ I2 @ J2 )
% 5.31/5.65 = nil_nat )
% 5.31/5.65 = ( ( J2 = zero_zero_nat )
% 5.31/5.65 | ( ord_less_eq_nat @ J2 @ I2 ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % upt_eq_Nil_conv
% 5.31/5.65 thf(fact_9070_atLeastAtMost__upt,axiom,
% 5.31/5.65 ( set_or1269000886237332187st_nat
% 5.31/5.65 = ( ^ [N4: nat,M6: nat] : ( set_nat2 @ ( upt @ N4 @ ( suc @ M6 ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % atLeastAtMost_upt
% 5.31/5.65 thf(fact_9071_atLeast__upt,axiom,
% 5.31/5.65 ( set_ord_lessThan_nat
% 5.31/5.65 = ( ^ [N4: nat] : ( set_nat2 @ ( upt @ zero_zero_nat @ N4 ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % atLeast_upt
% 5.31/5.65 thf(fact_9072_upt__conv__Cons__Cons,axiom,
% 5.31/5.65 ! [M2: nat,N: nat,Ns: list_nat,Q2: nat] :
% 5.31/5.65 ( ( ( cons_nat @ M2 @ ( cons_nat @ N @ Ns ) )
% 5.31/5.65 = ( upt @ M2 @ Q2 ) )
% 5.31/5.65 = ( ( cons_nat @ N @ Ns )
% 5.31/5.65 = ( upt @ ( suc @ M2 ) @ Q2 ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % upt_conv_Cons_Cons
% 5.31/5.65 thf(fact_9073_upt__0,axiom,
% 5.31/5.65 ! [I2: nat] :
% 5.31/5.65 ( ( upt @ I2 @ zero_zero_nat )
% 5.31/5.65 = nil_nat ) ).
% 5.31/5.65
% 5.31/5.65 % upt_0
% 5.31/5.65 thf(fact_9074_greaterThanAtMost__upt,axiom,
% 5.31/5.65 ( set_or6659071591806873216st_nat
% 5.31/5.65 = ( ^ [N4: nat,M6: nat] : ( set_nat2 @ ( upt @ ( suc @ N4 ) @ ( suc @ M6 ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % greaterThanAtMost_upt
% 5.31/5.65 thf(fact_9075_greaterThanLessThan__upt,axiom,
% 5.31/5.65 ( set_or5834768355832116004an_nat
% 5.31/5.65 = ( ^ [N4: nat,M6: nat] : ( set_nat2 @ ( upt @ ( suc @ N4 ) @ M6 ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % greaterThanLessThan_upt
% 5.31/5.65 thf(fact_9076_atMost__upto,axiom,
% 5.31/5.65 ( set_ord_atMost_nat
% 5.31/5.65 = ( ^ [N4: nat] : ( set_nat2 @ ( upt @ zero_zero_nat @ ( suc @ N4 ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % atMost_upto
% 5.31/5.65 thf(fact_9077_upt__conv__Cons,axiom,
% 5.31/5.65 ! [I2: nat,J2: nat] :
% 5.31/5.65 ( ( ord_less_nat @ I2 @ J2 )
% 5.31/5.65 => ( ( upt @ I2 @ J2 )
% 5.31/5.65 = ( cons_nat @ I2 @ ( upt @ ( suc @ I2 ) @ J2 ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % upt_conv_Cons
% 5.31/5.65 thf(fact_9078_upt__add__eq__append,axiom,
% 5.31/5.65 ! [I2: nat,J2: nat,K2: nat] :
% 5.31/5.65 ( ( ord_less_eq_nat @ I2 @ J2 )
% 5.31/5.65 => ( ( upt @ I2 @ ( plus_plus_nat @ J2 @ K2 ) )
% 5.31/5.65 = ( append_nat @ ( upt @ I2 @ J2 ) @ ( upt @ J2 @ ( plus_plus_nat @ J2 @ K2 ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % upt_add_eq_append
% 5.31/5.65 thf(fact_9079_upt__rec,axiom,
% 5.31/5.65 ( upt
% 5.31/5.65 = ( ^ [I: nat,J: nat] : ( if_list_nat @ ( ord_less_nat @ I @ J ) @ ( cons_nat @ I @ ( upt @ ( suc @ I ) @ J ) ) @ nil_nat ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % upt_rec
% 5.31/5.65 thf(fact_9080_upt__Suc,axiom,
% 5.31/5.65 ! [I2: nat,J2: nat] :
% 5.31/5.65 ( ( ( ord_less_eq_nat @ I2 @ J2 )
% 5.31/5.65 => ( ( upt @ I2 @ ( suc @ J2 ) )
% 5.31/5.65 = ( append_nat @ ( upt @ I2 @ J2 ) @ ( cons_nat @ J2 @ nil_nat ) ) ) )
% 5.31/5.65 & ( ~ ( ord_less_eq_nat @ I2 @ J2 )
% 5.31/5.65 => ( ( upt @ I2 @ ( suc @ J2 ) )
% 5.31/5.65 = nil_nat ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % upt_Suc
% 5.31/5.65 thf(fact_9081_upt__Suc__append,axiom,
% 5.31/5.65 ! [I2: nat,J2: nat] :
% 5.31/5.65 ( ( ord_less_eq_nat @ I2 @ J2 )
% 5.31/5.65 => ( ( upt @ I2 @ ( suc @ J2 ) )
% 5.31/5.65 = ( append_nat @ ( upt @ I2 @ J2 ) @ ( cons_nat @ J2 @ nil_nat ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % upt_Suc_append
% 5.31/5.65 thf(fact_9082_mono__Suc,axiom,
% 5.31/5.65 order_mono_nat_nat @ suc ).
% 5.31/5.65
% 5.31/5.65 % mono_Suc
% 5.31/5.65 thf(fact_9083_mono__times__nat,axiom,
% 5.31/5.65 ! [N: nat] :
% 5.31/5.65 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.65 => ( order_mono_nat_nat @ ( times_times_nat @ N ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % mono_times_nat
% 5.31/5.65 thf(fact_9084_mono__ge2__power__minus__self,axiom,
% 5.31/5.65 ! [K2: nat] :
% 5.31/5.65 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K2 )
% 5.31/5.65 => ( order_mono_nat_nat
% 5.31/5.65 @ ^ [M6: nat] : ( minus_minus_nat @ ( power_power_nat @ K2 @ M6 ) @ M6 ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % mono_ge2_power_minus_self
% 5.31/5.65 thf(fact_9085_sum__list__upt,axiom,
% 5.31/5.65 ! [M2: nat,N: nat] :
% 5.31/5.65 ( ( ord_less_eq_nat @ M2 @ N )
% 5.31/5.65 => ( ( groups4561878855575611511st_nat @ ( upt @ M2 @ N ) )
% 5.31/5.65 = ( groups3542108847815614940at_nat
% 5.31/5.65 @ ^ [X4: nat] : X4
% 5.31/5.65 @ ( set_or4665077453230672383an_nat @ M2 @ N ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % sum_list_upt
% 5.31/5.65 thf(fact_9086_map__Suc__upt,axiom,
% 5.31/5.65 ! [M2: nat,N: nat] :
% 5.31/5.65 ( ( map_nat_nat @ suc @ ( upt @ M2 @ N ) )
% 5.31/5.65 = ( upt @ ( suc @ M2 ) @ ( suc @ N ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % map_Suc_upt
% 5.31/5.65 thf(fact_9087_map__add__upt,axiom,
% 5.31/5.65 ! [N: nat,M2: nat] :
% 5.31/5.65 ( ( map_nat_nat
% 5.31/5.65 @ ^ [I: nat] : ( plus_plus_nat @ I @ N )
% 5.31/5.65 @ ( upt @ zero_zero_nat @ M2 ) )
% 5.31/5.65 = ( upt @ N @ ( plus_plus_nat @ M2 @ N ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % map_add_upt
% 5.31/5.65 thf(fact_9088_map__decr__upt,axiom,
% 5.31/5.65 ! [M2: nat,N: nat] :
% 5.31/5.65 ( ( map_nat_nat
% 5.31/5.65 @ ^ [N4: nat] : ( minus_minus_nat @ N4 @ ( suc @ zero_zero_nat ) )
% 5.31/5.65 @ ( upt @ ( suc @ M2 ) @ ( suc @ N ) ) )
% 5.31/5.65 = ( upt @ M2 @ N ) ) ).
% 5.31/5.65
% 5.31/5.65 % map_decr_upt
% 5.31/5.65 thf(fact_9089_card__length__sum__list__rec,axiom,
% 5.31/5.65 ! [M2: nat,N6: nat] :
% 5.31/5.65 ( ( ord_less_eq_nat @ one_one_nat @ M2 )
% 5.31/5.65 => ( ( finite_card_list_nat
% 5.31/5.65 @ ( collect_list_nat
% 5.31/5.65 @ ^ [L2: list_nat] :
% 5.31/5.65 ( ( ( size_size_list_nat @ L2 )
% 5.31/5.65 = M2 )
% 5.31/5.65 & ( ( groups4561878855575611511st_nat @ L2 )
% 5.31/5.65 = N6 ) ) ) )
% 5.31/5.65 = ( plus_plus_nat
% 5.31/5.65 @ ( finite_card_list_nat
% 5.31/5.65 @ ( collect_list_nat
% 5.31/5.65 @ ^ [L2: list_nat] :
% 5.31/5.65 ( ( ( size_size_list_nat @ L2 )
% 5.31/5.65 = ( minus_minus_nat @ M2 @ one_one_nat ) )
% 5.31/5.65 & ( ( groups4561878855575611511st_nat @ L2 )
% 5.31/5.65 = N6 ) ) ) )
% 5.31/5.65 @ ( finite_card_list_nat
% 5.31/5.65 @ ( collect_list_nat
% 5.31/5.65 @ ^ [L2: list_nat] :
% 5.31/5.65 ( ( ( size_size_list_nat @ L2 )
% 5.31/5.65 = M2 )
% 5.31/5.65 & ( ( plus_plus_nat @ ( groups4561878855575611511st_nat @ L2 ) @ one_one_nat )
% 5.31/5.65 = N6 ) ) ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % card_length_sum_list_rec
% 5.31/5.65 thf(fact_9090_card__length__sum__list,axiom,
% 5.31/5.65 ! [M2: nat,N6: nat] :
% 5.31/5.65 ( ( finite_card_list_nat
% 5.31/5.65 @ ( collect_list_nat
% 5.31/5.65 @ ^ [L2: list_nat] :
% 5.31/5.65 ( ( ( size_size_list_nat @ L2 )
% 5.31/5.65 = M2 )
% 5.31/5.65 & ( ( groups4561878855575611511st_nat @ L2 )
% 5.31/5.65 = N6 ) ) ) )
% 5.31/5.65 = ( binomial @ ( minus_minus_nat @ ( plus_plus_nat @ N6 @ M2 ) @ one_one_nat ) @ N6 ) ) ).
% 5.31/5.65
% 5.31/5.65 % card_length_sum_list
% 5.31/5.65 thf(fact_9091_range__mod,axiom,
% 5.31/5.65 ! [N: nat] :
% 5.31/5.65 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.65 => ( ( image_nat_nat
% 5.31/5.65 @ ^ [M6: nat] : ( modulo_modulo_nat @ M6 @ N )
% 5.31/5.65 @ top_top_set_nat )
% 5.31/5.65 = ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % range_mod
% 5.31/5.65 thf(fact_9092_UNIV__nat__eq,axiom,
% 5.31/5.65 ( top_top_set_nat
% 5.31/5.65 = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ top_top_set_nat ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % UNIV_nat_eq
% 5.31/5.65 thf(fact_9093_range__mult,axiom,
% 5.31/5.65 ! [A: real] :
% 5.31/5.65 ( ( ( A = zero_zero_real )
% 5.31/5.65 => ( ( image_real_real @ ( times_times_real @ A ) @ top_top_set_real )
% 5.31/5.65 = ( insert_real @ zero_zero_real @ bot_bot_set_real ) ) )
% 5.31/5.65 & ( ( A != zero_zero_real )
% 5.31/5.65 => ( ( image_real_real @ ( times_times_real @ A ) @ top_top_set_real )
% 5.31/5.65 = top_top_set_real ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % range_mult
% 5.31/5.65 thf(fact_9094_sorted__upt,axiom,
% 5.31/5.65 ! [M2: nat,N: nat] : ( sorted_wrt_nat @ ord_less_eq_nat @ ( upt @ M2 @ N ) ) ).
% 5.31/5.65
% 5.31/5.65 % sorted_upt
% 5.31/5.65 thf(fact_9095_surj__prod__decode,axiom,
% 5.31/5.65 ( ( image_5846123807819985514at_nat @ nat_prod_decode @ top_top_set_nat )
% 5.31/5.65 = top_to4669805908274784177at_nat ) ).
% 5.31/5.65
% 5.31/5.65 % surj_prod_decode
% 5.31/5.65 thf(fact_9096_bij__prod__decode,axiom,
% 5.31/5.65 bij_be8693218025023041337at_nat @ nat_prod_decode @ top_top_set_nat @ top_to4669805908274784177at_nat ).
% 5.31/5.65
% 5.31/5.65 % bij_prod_decode
% 5.31/5.65 thf(fact_9097_surj__list__decode,axiom,
% 5.31/5.65 ( ( image_nat_list_nat @ nat_list_decode @ top_top_set_nat )
% 5.31/5.65 = top_top_set_list_nat ) ).
% 5.31/5.65
% 5.31/5.65 % surj_list_decode
% 5.31/5.65 thf(fact_9098_bij__list__decode,axiom,
% 5.31/5.65 bij_be6293887246118711976st_nat @ nat_list_decode @ top_top_set_nat @ top_top_set_list_nat ).
% 5.31/5.65
% 5.31/5.65 % bij_list_decode
% 5.31/5.65 thf(fact_9099_surj__list__encode,axiom,
% 5.31/5.65 ( ( image_list_nat_nat @ nat_list_encode @ top_top_set_list_nat )
% 5.31/5.65 = top_top_set_nat ) ).
% 5.31/5.65
% 5.31/5.65 % surj_list_encode
% 5.31/5.65 thf(fact_9100_bij__list__encode,axiom,
% 5.31/5.65 bij_be8532844293280997160at_nat @ nat_list_encode @ top_top_set_list_nat @ top_top_set_nat ).
% 5.31/5.65
% 5.31/5.65 % bij_list_encode
% 5.31/5.65 thf(fact_9101_surj__prod__encode,axiom,
% 5.31/5.65 ( ( image_2486076414777270412at_nat @ nat_prod_encode @ top_to4669805908274784177at_nat )
% 5.31/5.65 = top_top_set_nat ) ).
% 5.31/5.65
% 5.31/5.65 % surj_prod_encode
% 5.31/5.65 thf(fact_9102_bij__prod__encode,axiom,
% 5.31/5.65 bij_be5333170631980326235at_nat @ nat_prod_encode @ top_to4669805908274784177at_nat @ top_top_set_nat ).
% 5.31/5.65
% 5.31/5.65 % bij_prod_encode
% 5.31/5.65 thf(fact_9103_sorted__wrt__less__idx,axiom,
% 5.31/5.65 ! [Ns: list_nat,I2: nat] :
% 5.31/5.65 ( ( sorted_wrt_nat @ ord_less_nat @ Ns )
% 5.31/5.65 => ( ( ord_less_nat @ I2 @ ( size_size_list_nat @ Ns ) )
% 5.31/5.65 => ( ord_less_eq_nat @ I2 @ ( nth_nat @ Ns @ I2 ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % sorted_wrt_less_idx
% 5.31/5.65 thf(fact_9104_root__def,axiom,
% 5.31/5.65 ( root
% 5.31/5.65 = ( ^ [N4: nat,X4: real] :
% 5.31/5.65 ( if_real @ ( N4 = zero_zero_nat ) @ zero_zero_real
% 5.31/5.65 @ ( the_in5290026491893676941l_real @ top_top_set_real
% 5.31/5.65 @ ^ [Y4: real] : ( times_times_real @ ( sgn_sgn_real @ Y4 ) @ ( power_power_real @ ( abs_abs_real @ Y4 ) @ N4 ) )
% 5.31/5.65 @ X4 ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % root_def
% 5.31/5.65 thf(fact_9105_DERIV__even__real__root,axiom,
% 5.31/5.65 ! [N: nat,X: real] :
% 5.31/5.65 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.65 => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.31/5.65 => ( ( ord_less_real @ X @ zero_zero_real )
% 5.31/5.65 => ( 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 ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % DERIV_even_real_root
% 5.31/5.65 thf(fact_9106_DERIV__real__root__generic,axiom,
% 5.31/5.65 ! [N: nat,X: real,D3: real] :
% 5.31/5.65 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.65 => ( ( X != zero_zero_real )
% 5.31/5.65 => ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.31/5.65 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.31/5.65 => ( D3
% 5.31/5.65 = ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( root @ N @ X ) @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) )
% 5.31/5.65 => ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.31/5.65 => ( ( ord_less_real @ X @ zero_zero_real )
% 5.31/5.65 => ( D3
% 5.31/5.65 = ( 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 ) ) ) ) ) ) ) ) )
% 5.31/5.65 => ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.31/5.65 => ( D3
% 5.31/5.65 = ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( root @ N @ X ) @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) ) )
% 5.31/5.65 => ( has_fi5821293074295781190e_real @ ( root @ N ) @ D3 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % DERIV_real_root_generic
% 5.31/5.65 thf(fact_9107_DERIV__arctan__series,axiom,
% 5.31/5.65 ! [X: real] :
% 5.31/5.65 ( ( ord_less_real @ ( abs_abs_real @ X ) @ one_one_real )
% 5.31/5.65 => ( has_fi5821293074295781190e_real
% 5.31/5.65 @ ^ [X9: real] :
% 5.31/5.65 ( suminf_real
% 5.31/5.65 @ ^ [K3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K3 ) @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( times_times_nat @ K3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) @ ( power_power_real @ X9 @ ( plus_plus_nat @ ( times_times_nat @ K3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) )
% 5.31/5.65 @ ( suminf_real
% 5.31/5.65 @ ^ [K3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K3 ) @ ( power_power_real @ X @ ( times_times_nat @ K3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.31/5.65 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % DERIV_arctan_series
% 5.31/5.65 thf(fact_9108_DERIV__fun__pow,axiom,
% 5.31/5.65 ! [G2: real > real,M2: real,X: real,N: nat] :
% 5.31/5.65 ( ( has_fi5821293074295781190e_real @ G2 @ M2 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.31/5.65 => ( has_fi5821293074295781190e_real
% 5.31/5.65 @ ^ [X4: real] : ( power_power_real @ ( G2 @ X4 ) @ N )
% 5.31/5.65 @ ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( G2 @ X ) @ ( minus_minus_nat @ N @ one_one_nat ) ) ) @ M2 )
% 5.31/5.65 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % DERIV_fun_pow
% 5.31/5.65 thf(fact_9109_has__real__derivative__powr,axiom,
% 5.31/5.65 ! [Z3: real,R3: real] :
% 5.31/5.65 ( ( ord_less_real @ zero_zero_real @ Z3 )
% 5.31/5.65 => ( has_fi5821293074295781190e_real
% 5.31/5.65 @ ^ [Z4: real] : ( powr_real @ Z4 @ R3 )
% 5.31/5.65 @ ( times_times_real @ R3 @ ( powr_real @ Z3 @ ( minus_minus_real @ R3 @ one_one_real ) ) )
% 5.31/5.65 @ ( topolo2177554685111907308n_real @ Z3 @ top_top_set_real ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % has_real_derivative_powr
% 5.31/5.65 thf(fact_9110_DERIV__series_H,axiom,
% 5.31/5.65 ! [F2: real > nat > real,F5: real > nat > real,X0: real,A: real,B: real,L5: nat > real] :
% 5.31/5.65 ( ! [N3: nat] :
% 5.31/5.65 ( has_fi5821293074295781190e_real
% 5.31/5.65 @ ^ [X4: real] : ( F2 @ X4 @ N3 )
% 5.31/5.65 @ ( F5 @ X0 @ N3 )
% 5.31/5.65 @ ( topolo2177554685111907308n_real @ X0 @ top_top_set_real ) )
% 5.31/5.65 => ( ! [X3: real] :
% 5.31/5.65 ( ( member_real @ X3 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 5.31/5.65 => ( summable_real @ ( F2 @ X3 ) ) )
% 5.31/5.65 => ( ( member_real @ X0 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 5.31/5.65 => ( ( summable_real @ ( F5 @ X0 ) )
% 5.31/5.65 => ( ( summable_real @ L5 )
% 5.31/5.65 => ( ! [N3: nat,X3: real,Y3: real] :
% 5.31/5.65 ( ( member_real @ X3 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 5.31/5.65 => ( ( member_real @ Y3 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 5.31/5.65 => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( F2 @ X3 @ N3 ) @ ( F2 @ Y3 @ N3 ) ) ) @ ( times_times_real @ ( L5 @ N3 ) @ ( abs_abs_real @ ( minus_minus_real @ X3 @ Y3 ) ) ) ) ) )
% 5.31/5.65 => ( has_fi5821293074295781190e_real
% 5.31/5.65 @ ^ [X4: real] : ( suminf_real @ ( F2 @ X4 ) )
% 5.31/5.65 @ ( suminf_real @ ( F5 @ X0 ) )
% 5.31/5.65 @ ( topolo2177554685111907308n_real @ X0 @ top_top_set_real ) ) ) ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % DERIV_series'
% 5.31/5.65 thf(fact_9111_DERIV__log,axiom,
% 5.31/5.65 ! [X: real,B: real] :
% 5.31/5.65 ( ( ord_less_real @ zero_zero_real @ X )
% 5.31/5.65 => ( has_fi5821293074295781190e_real @ ( log2 @ B ) @ ( divide_divide_real @ one_one_real @ ( times_times_real @ ( ln_ln_real @ B ) @ X ) ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % DERIV_log
% 5.31/5.65 thf(fact_9112_DERIV__fun__powr,axiom,
% 5.31/5.65 ! [G2: real > real,M2: real,X: real,R3: real] :
% 5.31/5.65 ( ( has_fi5821293074295781190e_real @ G2 @ M2 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.31/5.65 => ( ( ord_less_real @ zero_zero_real @ ( G2 @ X ) )
% 5.31/5.65 => ( has_fi5821293074295781190e_real
% 5.31/5.65 @ ^ [X4: real] : ( powr_real @ ( G2 @ X4 ) @ R3 )
% 5.31/5.65 @ ( times_times_real @ ( times_times_real @ R3 @ ( powr_real @ ( G2 @ X ) @ ( minus_minus_real @ R3 @ ( semiri5074537144036343181t_real @ one_one_nat ) ) ) ) @ M2 )
% 5.31/5.65 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % DERIV_fun_powr
% 5.31/5.65 thf(fact_9113_DERIV__powr,axiom,
% 5.31/5.65 ! [G2: real > real,M2: real,X: real,F2: real > real,R3: real] :
% 5.31/5.65 ( ( has_fi5821293074295781190e_real @ G2 @ M2 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.31/5.65 => ( ( ord_less_real @ zero_zero_real @ ( G2 @ X ) )
% 5.31/5.65 => ( ( has_fi5821293074295781190e_real @ F2 @ R3 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.31/5.65 => ( has_fi5821293074295781190e_real
% 5.31/5.65 @ ^ [X4: real] : ( powr_real @ ( G2 @ X4 ) @ ( F2 @ X4 ) )
% 5.31/5.65 @ ( times_times_real @ ( powr_real @ ( G2 @ X ) @ ( F2 @ X ) ) @ ( plus_plus_real @ ( times_times_real @ R3 @ ( ln_ln_real @ ( G2 @ X ) ) ) @ ( divide_divide_real @ ( times_times_real @ M2 @ ( F2 @ X ) ) @ ( G2 @ X ) ) ) )
% 5.31/5.65 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % DERIV_powr
% 5.31/5.65 thf(fact_9114_DERIV__power__series_H,axiom,
% 5.31/5.65 ! [R2: real,F2: nat > real,X0: real] :
% 5.31/5.65 ( ! [X3: real] :
% 5.31/5.65 ( ( member_real @ X3 @ ( set_or1633881224788618240n_real @ ( uminus_uminus_real @ R2 ) @ R2 ) )
% 5.31/5.65 => ( summable_real
% 5.31/5.65 @ ^ [N4: nat] : ( times_times_real @ ( times_times_real @ ( F2 @ N4 ) @ ( semiri5074537144036343181t_real @ ( suc @ N4 ) ) ) @ ( power_power_real @ X3 @ N4 ) ) ) )
% 5.31/5.65 => ( ( member_real @ X0 @ ( set_or1633881224788618240n_real @ ( uminus_uminus_real @ R2 ) @ R2 ) )
% 5.31/5.65 => ( ( ord_less_real @ zero_zero_real @ R2 )
% 5.31/5.65 => ( has_fi5821293074295781190e_real
% 5.31/5.65 @ ^ [X4: real] :
% 5.31/5.65 ( suminf_real
% 5.31/5.65 @ ^ [N4: nat] : ( times_times_real @ ( F2 @ N4 ) @ ( power_power_real @ X4 @ ( suc @ N4 ) ) ) )
% 5.31/5.65 @ ( suminf_real
% 5.31/5.65 @ ^ [N4: nat] : ( times_times_real @ ( times_times_real @ ( F2 @ N4 ) @ ( semiri5074537144036343181t_real @ ( suc @ N4 ) ) ) @ ( power_power_real @ X0 @ N4 ) ) )
% 5.31/5.65 @ ( topolo2177554685111907308n_real @ X0 @ top_top_set_real ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % DERIV_power_series'
% 5.31/5.65 thf(fact_9115_DERIV__real__root,axiom,
% 5.31/5.65 ! [N: nat,X: real] :
% 5.31/5.65 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.65 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.31/5.65 => ( 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 ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % DERIV_real_root
% 5.31/5.65 thf(fact_9116_Maclaurin__all__le,axiom,
% 5.31/5.65 ! [Diff: nat > real > real,F2: real > real,X: real,N: nat] :
% 5.31/5.65 ( ( ( Diff @ zero_zero_nat )
% 5.31/5.65 = F2 )
% 5.31/5.65 => ( ! [M: nat,X3: real] : ( has_fi5821293074295781190e_real @ ( Diff @ M ) @ ( Diff @ ( suc @ M ) @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.31/5.65 => ? [T6: real] :
% 5.31/5.65 ( ( ord_less_eq_real @ ( abs_abs_real @ T6 ) @ ( abs_abs_real @ X ) )
% 5.31/5.65 & ( ( F2 @ X )
% 5.31/5.65 = ( plus_plus_real
% 5.31/5.65 @ ( groups6591440286371151544t_real
% 5.31/5.65 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ X @ M6 ) )
% 5.31/5.65 @ ( set_ord_lessThan_nat @ N ) )
% 5.31/5.65 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T6 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % Maclaurin_all_le
% 5.31/5.65 thf(fact_9117_Maclaurin__all__le__objl,axiom,
% 5.31/5.65 ! [Diff: nat > real > real,F2: real > real,X: real,N: nat] :
% 5.31/5.65 ( ( ( ( Diff @ zero_zero_nat )
% 5.31/5.65 = F2 )
% 5.31/5.65 & ! [M: nat,X3: real] : ( has_fi5821293074295781190e_real @ ( Diff @ M ) @ ( Diff @ ( suc @ M ) @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) )
% 5.31/5.65 => ? [T6: real] :
% 5.31/5.65 ( ( ord_less_eq_real @ ( abs_abs_real @ T6 ) @ ( abs_abs_real @ X ) )
% 5.31/5.65 & ( ( F2 @ X )
% 5.31/5.65 = ( plus_plus_real
% 5.31/5.65 @ ( groups6591440286371151544t_real
% 5.31/5.65 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ X @ M6 ) )
% 5.31/5.65 @ ( set_ord_lessThan_nat @ N ) )
% 5.31/5.65 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T6 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % Maclaurin_all_le_objl
% 5.31/5.65 thf(fact_9118_DERIV__odd__real__root,axiom,
% 5.31/5.65 ! [N: nat,X: real] :
% 5.31/5.65 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.31/5.65 => ( ( X != zero_zero_real )
% 5.31/5.65 => ( 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 ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % DERIV_odd_real_root
% 5.31/5.65 thf(fact_9119_Maclaurin__minus,axiom,
% 5.31/5.65 ! [H: real,N: nat,Diff: nat > real > real,F2: real > real] :
% 5.31/5.65 ( ( ord_less_real @ H @ zero_zero_real )
% 5.31/5.65 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.65 => ( ( ( Diff @ zero_zero_nat )
% 5.31/5.65 = F2 )
% 5.31/5.65 => ( ! [M: nat,T6: real] :
% 5.31/5.65 ( ( ( ord_less_nat @ M @ N )
% 5.31/5.65 & ( ord_less_eq_real @ H @ T6 )
% 5.31/5.65 & ( ord_less_eq_real @ T6 @ zero_zero_real ) )
% 5.31/5.65 => ( has_fi5821293074295781190e_real @ ( Diff @ M ) @ ( Diff @ ( suc @ M ) @ T6 ) @ ( topolo2177554685111907308n_real @ T6 @ top_top_set_real ) ) )
% 5.31/5.65 => ? [T6: real] :
% 5.31/5.65 ( ( ord_less_real @ H @ T6 )
% 5.31/5.65 & ( ord_less_real @ T6 @ zero_zero_real )
% 5.31/5.65 & ( ( F2 @ H )
% 5.31/5.65 = ( plus_plus_real
% 5.31/5.65 @ ( groups6591440286371151544t_real
% 5.31/5.65 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ H @ M6 ) )
% 5.31/5.65 @ ( set_ord_lessThan_nat @ N ) )
% 5.31/5.65 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T6 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ H @ N ) ) ) ) ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % Maclaurin_minus
% 5.31/5.65 thf(fact_9120_Maclaurin2,axiom,
% 5.31/5.65 ! [H: real,Diff: nat > real > real,F2: real > real,N: nat] :
% 5.31/5.65 ( ( ord_less_real @ zero_zero_real @ H )
% 5.31/5.65 => ( ( ( Diff @ zero_zero_nat )
% 5.31/5.65 = F2 )
% 5.31/5.65 => ( ! [M: nat,T6: real] :
% 5.31/5.65 ( ( ( ord_less_nat @ M @ N )
% 5.31/5.65 & ( ord_less_eq_real @ zero_zero_real @ T6 )
% 5.31/5.65 & ( ord_less_eq_real @ T6 @ H ) )
% 5.31/5.65 => ( has_fi5821293074295781190e_real @ ( Diff @ M ) @ ( Diff @ ( suc @ M ) @ T6 ) @ ( topolo2177554685111907308n_real @ T6 @ top_top_set_real ) ) )
% 5.31/5.65 => ? [T6: real] :
% 5.31/5.65 ( ( ord_less_real @ zero_zero_real @ T6 )
% 5.31/5.65 & ( ord_less_eq_real @ T6 @ H )
% 5.31/5.65 & ( ( F2 @ H )
% 5.31/5.65 = ( plus_plus_real
% 5.31/5.65 @ ( groups6591440286371151544t_real
% 5.31/5.65 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ H @ M6 ) )
% 5.31/5.65 @ ( set_ord_lessThan_nat @ N ) )
% 5.31/5.65 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T6 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ H @ N ) ) ) ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % Maclaurin2
% 5.31/5.65 thf(fact_9121_Maclaurin,axiom,
% 5.31/5.65 ! [H: real,N: nat,Diff: nat > real > real,F2: real > real] :
% 5.31/5.65 ( ( ord_less_real @ zero_zero_real @ H )
% 5.31/5.65 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.65 => ( ( ( Diff @ zero_zero_nat )
% 5.31/5.65 = F2 )
% 5.31/5.65 => ( ! [M: nat,T6: real] :
% 5.31/5.65 ( ( ( ord_less_nat @ M @ N )
% 5.31/5.65 & ( ord_less_eq_real @ zero_zero_real @ T6 )
% 5.31/5.65 & ( ord_less_eq_real @ T6 @ H ) )
% 5.31/5.65 => ( has_fi5821293074295781190e_real @ ( Diff @ M ) @ ( Diff @ ( suc @ M ) @ T6 ) @ ( topolo2177554685111907308n_real @ T6 @ top_top_set_real ) ) )
% 5.31/5.65 => ? [T6: real] :
% 5.31/5.65 ( ( ord_less_real @ zero_zero_real @ T6 )
% 5.31/5.65 & ( ord_less_real @ T6 @ H )
% 5.31/5.65 & ( ( F2 @ H )
% 5.31/5.65 = ( plus_plus_real
% 5.31/5.65 @ ( groups6591440286371151544t_real
% 5.31/5.65 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ H @ M6 ) )
% 5.31/5.65 @ ( set_ord_lessThan_nat @ N ) )
% 5.31/5.65 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T6 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ H @ N ) ) ) ) ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % Maclaurin
% 5.31/5.65 thf(fact_9122_Maclaurin__all__lt,axiom,
% 5.31/5.65 ! [Diff: nat > real > real,F2: real > real,N: nat,X: real] :
% 5.31/5.65 ( ( ( Diff @ zero_zero_nat )
% 5.31/5.65 = F2 )
% 5.31/5.65 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.65 => ( ( X != zero_zero_real )
% 5.31/5.65 => ( ! [M: nat,X3: real] : ( has_fi5821293074295781190e_real @ ( Diff @ M ) @ ( Diff @ ( suc @ M ) @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.31/5.65 => ? [T6: real] :
% 5.31/5.65 ( ( ord_less_real @ zero_zero_real @ ( abs_abs_real @ T6 ) )
% 5.31/5.65 & ( ord_less_real @ ( abs_abs_real @ T6 ) @ ( abs_abs_real @ X ) )
% 5.31/5.65 & ( ( F2 @ X )
% 5.31/5.65 = ( plus_plus_real
% 5.31/5.65 @ ( groups6591440286371151544t_real
% 5.31/5.65 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ X @ M6 ) )
% 5.31/5.65 @ ( set_ord_lessThan_nat @ N ) )
% 5.31/5.65 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T6 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % Maclaurin_all_lt
% 5.31/5.65 thf(fact_9123_Maclaurin__bi__le,axiom,
% 5.31/5.65 ! [Diff: nat > real > real,F2: real > real,N: nat,X: real] :
% 5.31/5.65 ( ( ( Diff @ zero_zero_nat )
% 5.31/5.65 = F2 )
% 5.31/5.65 => ( ! [M: nat,T6: real] :
% 5.31/5.65 ( ( ( ord_less_nat @ M @ N )
% 5.31/5.65 & ( ord_less_eq_real @ ( abs_abs_real @ T6 ) @ ( abs_abs_real @ X ) ) )
% 5.31/5.65 => ( has_fi5821293074295781190e_real @ ( Diff @ M ) @ ( Diff @ ( suc @ M ) @ T6 ) @ ( topolo2177554685111907308n_real @ T6 @ top_top_set_real ) ) )
% 5.31/5.65 => ? [T6: real] :
% 5.31/5.65 ( ( ord_less_eq_real @ ( abs_abs_real @ T6 ) @ ( abs_abs_real @ X ) )
% 5.31/5.65 & ( ( F2 @ X )
% 5.31/5.65 = ( plus_plus_real
% 5.31/5.65 @ ( groups6591440286371151544t_real
% 5.31/5.65 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ X @ M6 ) )
% 5.31/5.65 @ ( set_ord_lessThan_nat @ N ) )
% 5.31/5.65 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T6 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % Maclaurin_bi_le
% 5.31/5.65 thf(fact_9124_Taylor__down,axiom,
% 5.31/5.65 ! [N: nat,Diff: nat > real > real,F2: real > real,A: real,B: real,C2: real] :
% 5.31/5.65 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.65 => ( ( ( Diff @ zero_zero_nat )
% 5.31/5.65 = F2 )
% 5.31/5.65 => ( ! [M: nat,T6: real] :
% 5.31/5.65 ( ( ( ord_less_nat @ M @ N )
% 5.31/5.65 & ( ord_less_eq_real @ A @ T6 )
% 5.31/5.65 & ( ord_less_eq_real @ T6 @ B ) )
% 5.31/5.65 => ( has_fi5821293074295781190e_real @ ( Diff @ M ) @ ( Diff @ ( suc @ M ) @ T6 ) @ ( topolo2177554685111907308n_real @ T6 @ top_top_set_real ) ) )
% 5.31/5.65 => ( ( ord_less_real @ A @ C2 )
% 5.31/5.65 => ( ( ord_less_eq_real @ C2 @ B )
% 5.31/5.65 => ? [T6: real] :
% 5.31/5.65 ( ( ord_less_real @ A @ T6 )
% 5.31/5.65 & ( ord_less_real @ T6 @ C2 )
% 5.31/5.65 & ( ( F2 @ A )
% 5.31/5.65 = ( plus_plus_real
% 5.31/5.65 @ ( groups6591440286371151544t_real
% 5.31/5.65 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ C2 ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ ( minus_minus_real @ A @ C2 ) @ M6 ) )
% 5.31/5.65 @ ( set_ord_lessThan_nat @ N ) )
% 5.31/5.65 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T6 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ ( minus_minus_real @ A @ C2 ) @ N ) ) ) ) ) ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % Taylor_down
% 5.31/5.65 thf(fact_9125_Taylor__up,axiom,
% 5.31/5.65 ! [N: nat,Diff: nat > real > real,F2: real > real,A: real,B: real,C2: real] :
% 5.31/5.65 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.65 => ( ( ( Diff @ zero_zero_nat )
% 5.31/5.65 = F2 )
% 5.31/5.65 => ( ! [M: nat,T6: real] :
% 5.31/5.65 ( ( ( ord_less_nat @ M @ N )
% 5.31/5.65 & ( ord_less_eq_real @ A @ T6 )
% 5.31/5.65 & ( ord_less_eq_real @ T6 @ B ) )
% 5.31/5.65 => ( has_fi5821293074295781190e_real @ ( Diff @ M ) @ ( Diff @ ( suc @ M ) @ T6 ) @ ( topolo2177554685111907308n_real @ T6 @ top_top_set_real ) ) )
% 5.31/5.65 => ( ( ord_less_eq_real @ A @ C2 )
% 5.31/5.65 => ( ( ord_less_real @ C2 @ B )
% 5.31/5.65 => ? [T6: real] :
% 5.31/5.65 ( ( ord_less_real @ C2 @ T6 )
% 5.31/5.65 & ( ord_less_real @ T6 @ B )
% 5.31/5.65 & ( ( F2 @ B )
% 5.31/5.65 = ( plus_plus_real
% 5.31/5.65 @ ( groups6591440286371151544t_real
% 5.31/5.65 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ C2 ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ ( minus_minus_real @ B @ C2 ) @ M6 ) )
% 5.31/5.65 @ ( set_ord_lessThan_nat @ N ) )
% 5.31/5.65 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T6 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ ( minus_minus_real @ B @ C2 ) @ N ) ) ) ) ) ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % Taylor_up
% 5.31/5.65 thf(fact_9126_Taylor,axiom,
% 5.31/5.65 ! [N: nat,Diff: nat > real > real,F2: real > real,A: real,B: real,C2: real,X: real] :
% 5.31/5.65 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.65 => ( ( ( Diff @ zero_zero_nat )
% 5.31/5.65 = F2 )
% 5.31/5.65 => ( ! [M: nat,T6: real] :
% 5.31/5.65 ( ( ( ord_less_nat @ M @ N )
% 5.31/5.65 & ( ord_less_eq_real @ A @ T6 )
% 5.31/5.65 & ( ord_less_eq_real @ T6 @ B ) )
% 5.31/5.65 => ( has_fi5821293074295781190e_real @ ( Diff @ M ) @ ( Diff @ ( suc @ M ) @ T6 ) @ ( topolo2177554685111907308n_real @ T6 @ top_top_set_real ) ) )
% 5.31/5.65 => ( ( ord_less_eq_real @ A @ C2 )
% 5.31/5.65 => ( ( ord_less_eq_real @ C2 @ B )
% 5.31/5.65 => ( ( ord_less_eq_real @ A @ X )
% 5.31/5.65 => ( ( ord_less_eq_real @ X @ B )
% 5.31/5.65 => ( ( X != C2 )
% 5.31/5.65 => ? [T6: real] :
% 5.31/5.65 ( ( ( ord_less_real @ X @ C2 )
% 5.31/5.65 => ( ( ord_less_real @ X @ T6 )
% 5.31/5.65 & ( ord_less_real @ T6 @ C2 ) ) )
% 5.31/5.65 & ( ~ ( ord_less_real @ X @ C2 )
% 5.31/5.65 => ( ( ord_less_real @ C2 @ T6 )
% 5.31/5.65 & ( ord_less_real @ T6 @ X ) ) )
% 5.31/5.65 & ( ( F2 @ X )
% 5.31/5.65 = ( plus_plus_real
% 5.31/5.65 @ ( groups6591440286371151544t_real
% 5.31/5.65 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ C2 ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ ( minus_minus_real @ X @ C2 ) @ M6 ) )
% 5.31/5.65 @ ( set_ord_lessThan_nat @ N ) )
% 5.31/5.65 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T6 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ ( minus_minus_real @ X @ C2 ) @ N ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % Taylor
% 5.31/5.65 thf(fact_9127_Maclaurin__lemma2,axiom,
% 5.31/5.65 ! [N: nat,H: real,Diff: nat > real > real,K2: nat,B5: real] :
% 5.31/5.65 ( ! [M: nat,T6: real] :
% 5.31/5.65 ( ( ( ord_less_nat @ M @ N )
% 5.31/5.65 & ( ord_less_eq_real @ zero_zero_real @ T6 )
% 5.31/5.65 & ( ord_less_eq_real @ T6 @ H ) )
% 5.31/5.65 => ( has_fi5821293074295781190e_real @ ( Diff @ M ) @ ( Diff @ ( suc @ M ) @ T6 ) @ ( topolo2177554685111907308n_real @ T6 @ top_top_set_real ) ) )
% 5.31/5.65 => ( ( N
% 5.31/5.65 = ( suc @ K2 ) )
% 5.31/5.65 => ! [M3: nat,T7: real] :
% 5.31/5.65 ( ( ( ord_less_nat @ M3 @ N )
% 5.31/5.65 & ( ord_less_eq_real @ zero_zero_real @ T7 )
% 5.31/5.65 & ( ord_less_eq_real @ T7 @ H ) )
% 5.31/5.65 => ( has_fi5821293074295781190e_real
% 5.31/5.65 @ ^ [U2: real] :
% 5.31/5.65 ( minus_minus_real @ ( Diff @ M3 @ U2 )
% 5.31/5.65 @ ( plus_plus_real
% 5.31/5.65 @ ( groups6591440286371151544t_real
% 5.31/5.65 @ ^ [P5: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ ( plus_plus_nat @ M3 @ P5 ) @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ P5 ) ) @ ( power_power_real @ U2 @ P5 ) )
% 5.31/5.65 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ M3 ) ) )
% 5.31/5.65 @ ( times_times_real @ B5 @ ( divide_divide_real @ ( power_power_real @ U2 @ ( minus_minus_nat @ N @ M3 ) ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N @ M3 ) ) ) ) ) )
% 5.31/5.65 @ ( minus_minus_real @ ( Diff @ ( suc @ M3 ) @ T7 )
% 5.31/5.65 @ ( plus_plus_real
% 5.31/5.65 @ ( groups6591440286371151544t_real
% 5.31/5.65 @ ^ [P5: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ ( plus_plus_nat @ ( suc @ M3 ) @ P5 ) @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ P5 ) ) @ ( power_power_real @ T7 @ P5 ) )
% 5.31/5.65 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ ( suc @ M3 ) ) ) )
% 5.31/5.65 @ ( times_times_real @ B5 @ ( divide_divide_real @ ( power_power_real @ T7 @ ( minus_minus_nat @ N @ ( suc @ M3 ) ) ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N @ ( suc @ M3 ) ) ) ) ) ) )
% 5.31/5.65 @ ( topolo2177554685111907308n_real @ T7 @ top_top_set_real ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % Maclaurin_lemma2
% 5.31/5.65 thf(fact_9128_DERIV__pow,axiom,
% 5.31/5.65 ! [N: nat,X: real,S2: set_real] :
% 5.31/5.65 ( has_fi5821293074295781190e_real
% 5.31/5.65 @ ^ [X4: real] : ( power_power_real @ X4 @ N )
% 5.31/5.65 @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ X @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) )
% 5.31/5.65 @ ( topolo2177554685111907308n_real @ X @ S2 ) ) ).
% 5.31/5.65
% 5.31/5.65 % DERIV_pow
% 5.31/5.65 thf(fact_9129_DERIV__const__ratio__const,axiom,
% 5.31/5.65 ! [A: real,B: real,F2: real > real,K2: real] :
% 5.31/5.65 ( ( A != B )
% 5.31/5.65 => ( ! [X3: real] : ( has_fi5821293074295781190e_real @ F2 @ K2 @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.31/5.65 => ( ( minus_minus_real @ ( F2 @ B ) @ ( F2 @ A ) )
% 5.31/5.65 = ( times_times_real @ ( minus_minus_real @ B @ A ) @ K2 ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % DERIV_const_ratio_const
% 5.31/5.65 thf(fact_9130_MVT2,axiom,
% 5.31/5.65 ! [A: real,B: real,F2: real > real,F5: real > real] :
% 5.31/5.65 ( ( ord_less_real @ A @ B )
% 5.31/5.65 => ( ! [X3: real] :
% 5.31/5.65 ( ( ord_less_eq_real @ A @ X3 )
% 5.31/5.65 => ( ( ord_less_eq_real @ X3 @ B )
% 5.31/5.65 => ( has_fi5821293074295781190e_real @ F2 @ ( F5 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) ) )
% 5.31/5.65 => ? [Z: real] :
% 5.31/5.65 ( ( ord_less_real @ A @ Z )
% 5.31/5.65 & ( ord_less_real @ Z @ B )
% 5.31/5.65 & ( ( minus_minus_real @ ( F2 @ B ) @ ( F2 @ A ) )
% 5.31/5.65 = ( times_times_real @ ( minus_minus_real @ B @ A ) @ ( F5 @ Z ) ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % MVT2
% 5.31/5.65 thf(fact_9131_GMVT_H,axiom,
% 5.31/5.65 ! [A: real,B: real,F2: real > real,G2: real > real,G3: real > real,F5: real > real] :
% 5.31/5.65 ( ( ord_less_real @ A @ B )
% 5.31/5.65 => ( ! [Z: real] :
% 5.31/5.65 ( ( ord_less_eq_real @ A @ Z )
% 5.31/5.65 => ( ( ord_less_eq_real @ Z @ B )
% 5.31/5.65 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ Z @ top_top_set_real ) @ F2 ) ) )
% 5.31/5.65 => ( ! [Z: real] :
% 5.31/5.65 ( ( ord_less_eq_real @ A @ Z )
% 5.31/5.65 => ( ( ord_less_eq_real @ Z @ B )
% 5.31/5.65 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ Z @ top_top_set_real ) @ G2 ) ) )
% 5.31/5.65 => ( ! [Z: real] :
% 5.31/5.65 ( ( ord_less_real @ A @ Z )
% 5.31/5.65 => ( ( ord_less_real @ Z @ B )
% 5.31/5.65 => ( has_fi5821293074295781190e_real @ G2 @ ( G3 @ Z ) @ ( topolo2177554685111907308n_real @ Z @ top_top_set_real ) ) ) )
% 5.31/5.65 => ( ! [Z: real] :
% 5.31/5.65 ( ( ord_less_real @ A @ Z )
% 5.31/5.65 => ( ( ord_less_real @ Z @ B )
% 5.31/5.65 => ( has_fi5821293074295781190e_real @ F2 @ ( F5 @ Z ) @ ( topolo2177554685111907308n_real @ Z @ top_top_set_real ) ) ) )
% 5.31/5.65 => ? [C: real] :
% 5.31/5.65 ( ( ord_less_real @ A @ C )
% 5.31/5.65 & ( ord_less_real @ C @ B )
% 5.31/5.65 & ( ( times_times_real @ ( minus_minus_real @ ( F2 @ B ) @ ( F2 @ A ) ) @ ( G3 @ C ) )
% 5.31/5.65 = ( times_times_real @ ( minus_minus_real @ ( G2 @ B ) @ ( G2 @ A ) ) @ ( F5 @ C ) ) ) ) ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % GMVT'
% 5.31/5.65 thf(fact_9132_summable__Leibniz_I3_J,axiom,
% 5.31/5.65 ! [A: nat > real] :
% 5.31/5.65 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.31/5.65 => ( ( topolo6980174941875973593q_real @ A )
% 5.31/5.65 => ( ( ord_less_real @ ( A @ zero_zero_nat ) @ zero_zero_real )
% 5.31/5.65 => ! [N8: nat] :
% 5.31/5.65 ( member_real
% 5.31/5.65 @ ( suminf_real
% 5.31/5.65 @ ^ [I: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I ) @ ( A @ I ) ) )
% 5.31/5.65 @ ( set_or1222579329274155063t_real
% 5.31/5.65 @ ( groups6591440286371151544t_real
% 5.31/5.65 @ ^ [I: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I ) @ ( A @ I ) )
% 5.31/5.65 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N8 ) @ one_one_nat ) ) )
% 5.31/5.65 @ ( groups6591440286371151544t_real
% 5.31/5.65 @ ^ [I: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I ) @ ( A @ I ) )
% 5.31/5.65 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N8 ) ) ) ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % summable_Leibniz(3)
% 5.31/5.65 thf(fact_9133_summable__Leibniz_I2_J,axiom,
% 5.31/5.65 ! [A: nat > real] :
% 5.31/5.65 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.31/5.65 => ( ( topolo6980174941875973593q_real @ A )
% 5.31/5.65 => ( ( ord_less_real @ zero_zero_real @ ( A @ zero_zero_nat ) )
% 5.31/5.65 => ! [N8: nat] :
% 5.31/5.65 ( member_real
% 5.31/5.65 @ ( suminf_real
% 5.31/5.65 @ ^ [I: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I ) @ ( A @ I ) ) )
% 5.31/5.65 @ ( set_or1222579329274155063t_real
% 5.31/5.65 @ ( groups6591440286371151544t_real
% 5.31/5.65 @ ^ [I: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I ) @ ( A @ I ) )
% 5.31/5.65 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N8 ) ) )
% 5.31/5.65 @ ( groups6591440286371151544t_real
% 5.31/5.65 @ ^ [I: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I ) @ ( A @ I ) )
% 5.31/5.65 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N8 ) @ one_one_nat ) ) ) ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % summable_Leibniz(2)
% 5.31/5.65 thf(fact_9134_summable__Leibniz_H_I4_J,axiom,
% 5.31/5.65 ! [A: nat > real,N: nat] :
% 5.31/5.65 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.31/5.65 => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N3 ) )
% 5.31/5.65 => ( ! [N3: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N3 ) ) @ ( A @ N3 ) )
% 5.31/5.65 => ( ord_less_eq_real
% 5.31/5.65 @ ( suminf_real
% 5.31/5.65 @ ^ [I: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I ) @ ( A @ I ) ) )
% 5.31/5.65 @ ( groups6591440286371151544t_real
% 5.31/5.65 @ ^ [I: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I ) @ ( A @ I ) )
% 5.31/5.65 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % summable_Leibniz'(4)
% 5.31/5.65 thf(fact_9135_mult__nat__left__at__top,axiom,
% 5.31/5.65 ! [C2: nat] :
% 5.31/5.65 ( ( ord_less_nat @ zero_zero_nat @ C2 )
% 5.31/5.65 => ( filterlim_nat_nat @ ( times_times_nat @ C2 ) @ at_top_nat @ at_top_nat ) ) ).
% 5.31/5.65
% 5.31/5.65 % mult_nat_left_at_top
% 5.31/5.65 thf(fact_9136_mult__nat__right__at__top,axiom,
% 5.31/5.65 ! [C2: nat] :
% 5.31/5.65 ( ( ord_less_nat @ zero_zero_nat @ C2 )
% 5.31/5.65 => ( filterlim_nat_nat
% 5.31/5.65 @ ^ [X4: nat] : ( times_times_nat @ X4 @ C2 )
% 5.31/5.65 @ at_top_nat
% 5.31/5.65 @ at_top_nat ) ) ).
% 5.31/5.65
% 5.31/5.65 % mult_nat_right_at_top
% 5.31/5.65 thf(fact_9137_nested__sequence__unique,axiom,
% 5.31/5.65 ! [F2: nat > real,G2: nat > real] :
% 5.31/5.65 ( ! [N3: nat] : ( ord_less_eq_real @ ( F2 @ N3 ) @ ( F2 @ ( suc @ N3 ) ) )
% 5.31/5.65 => ( ! [N3: nat] : ( ord_less_eq_real @ ( G2 @ ( suc @ N3 ) ) @ ( G2 @ N3 ) )
% 5.31/5.65 => ( ! [N3: nat] : ( ord_less_eq_real @ ( F2 @ N3 ) @ ( G2 @ N3 ) )
% 5.31/5.65 => ( ( filterlim_nat_real
% 5.31/5.65 @ ^ [N4: nat] : ( minus_minus_real @ ( F2 @ N4 ) @ ( G2 @ N4 ) )
% 5.31/5.65 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.31/5.65 @ at_top_nat )
% 5.31/5.65 => ? [L4: real] :
% 5.31/5.65 ( ! [N8: nat] : ( ord_less_eq_real @ ( F2 @ N8 ) @ L4 )
% 5.31/5.65 & ( filterlim_nat_real @ F2 @ ( topolo2815343760600316023s_real @ L4 ) @ at_top_nat )
% 5.31/5.65 & ! [N8: nat] : ( ord_less_eq_real @ L4 @ ( G2 @ N8 ) )
% 5.31/5.65 & ( filterlim_nat_real @ G2 @ ( topolo2815343760600316023s_real @ L4 ) @ at_top_nat ) ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % nested_sequence_unique
% 5.31/5.65 thf(fact_9138_LIMSEQ__inverse__zero,axiom,
% 5.31/5.65 ! [X8: nat > real] :
% 5.31/5.65 ( ! [R4: real] :
% 5.31/5.65 ? [N7: nat] :
% 5.31/5.65 ! [N3: nat] :
% 5.31/5.65 ( ( ord_less_eq_nat @ N7 @ N3 )
% 5.31/5.65 => ( ord_less_real @ R4 @ ( X8 @ N3 ) ) )
% 5.31/5.65 => ( filterlim_nat_real
% 5.31/5.65 @ ^ [N4: nat] : ( inverse_inverse_real @ ( X8 @ N4 ) )
% 5.31/5.65 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.31/5.65 @ at_top_nat ) ) ).
% 5.31/5.65
% 5.31/5.65 % LIMSEQ_inverse_zero
% 5.31/5.65 thf(fact_9139_LIMSEQ__inverse__real__of__nat,axiom,
% 5.31/5.65 ( filterlim_nat_real
% 5.31/5.65 @ ^ [N4: nat] : ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N4 ) ) )
% 5.31/5.65 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.31/5.65 @ at_top_nat ) ).
% 5.31/5.65
% 5.31/5.65 % LIMSEQ_inverse_real_of_nat
% 5.31/5.65 thf(fact_9140_LIMSEQ__inverse__real__of__nat__add,axiom,
% 5.31/5.65 ! [R3: real] :
% 5.31/5.65 ( filterlim_nat_real
% 5.31/5.65 @ ^ [N4: nat] : ( plus_plus_real @ R3 @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N4 ) ) ) )
% 5.31/5.65 @ ( topolo2815343760600316023s_real @ R3 )
% 5.31/5.65 @ at_top_nat ) ).
% 5.31/5.65
% 5.31/5.65 % LIMSEQ_inverse_real_of_nat_add
% 5.31/5.65 thf(fact_9141_increasing__LIMSEQ,axiom,
% 5.31/5.65 ! [F2: nat > real,L: real] :
% 5.31/5.65 ( ! [N3: nat] : ( ord_less_eq_real @ ( F2 @ N3 ) @ ( F2 @ ( suc @ N3 ) ) )
% 5.31/5.65 => ( ! [N3: nat] : ( ord_less_eq_real @ ( F2 @ N3 ) @ L )
% 5.31/5.65 => ( ! [E2: real] :
% 5.31/5.65 ( ( ord_less_real @ zero_zero_real @ E2 )
% 5.31/5.65 => ? [N8: nat] : ( ord_less_eq_real @ L @ ( plus_plus_real @ ( F2 @ N8 ) @ E2 ) ) )
% 5.31/5.65 => ( filterlim_nat_real @ F2 @ ( topolo2815343760600316023s_real @ L ) @ at_top_nat ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % increasing_LIMSEQ
% 5.31/5.65 thf(fact_9142_LIMSEQ__inverse__real__of__nat__add__minus,axiom,
% 5.31/5.65 ! [R3: real] :
% 5.31/5.65 ( filterlim_nat_real
% 5.31/5.65 @ ^ [N4: nat] : ( plus_plus_real @ R3 @ ( uminus_uminus_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N4 ) ) ) ) )
% 5.31/5.65 @ ( topolo2815343760600316023s_real @ R3 )
% 5.31/5.65 @ at_top_nat ) ).
% 5.31/5.65
% 5.31/5.65 % LIMSEQ_inverse_real_of_nat_add_minus
% 5.31/5.65 thf(fact_9143_LIMSEQ__inverse__real__of__nat__add__minus__mult,axiom,
% 5.31/5.65 ! [R3: real] :
% 5.31/5.65 ( filterlim_nat_real
% 5.31/5.65 @ ^ [N4: nat] : ( times_times_real @ R3 @ ( plus_plus_real @ one_one_real @ ( uminus_uminus_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N4 ) ) ) ) ) )
% 5.31/5.65 @ ( topolo2815343760600316023s_real @ R3 )
% 5.31/5.65 @ at_top_nat ) ).
% 5.31/5.65
% 5.31/5.65 % LIMSEQ_inverse_real_of_nat_add_minus_mult
% 5.31/5.65 thf(fact_9144_summable__Leibniz_I1_J,axiom,
% 5.31/5.65 ! [A: nat > real] :
% 5.31/5.65 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.31/5.65 => ( ( topolo6980174941875973593q_real @ A )
% 5.31/5.65 => ( summable_real
% 5.31/5.65 @ ^ [N4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N4 ) @ ( A @ N4 ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % summable_Leibniz(1)
% 5.31/5.65 thf(fact_9145_summable,axiom,
% 5.31/5.65 ! [A: nat > real] :
% 5.31/5.65 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.31/5.65 => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N3 ) )
% 5.31/5.65 => ( ! [N3: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N3 ) ) @ ( A @ N3 ) )
% 5.31/5.65 => ( summable_real
% 5.31/5.65 @ ^ [N4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N4 ) @ ( A @ N4 ) ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % summable
% 5.31/5.65 thf(fact_9146_cos__diff__limit__1,axiom,
% 5.31/5.65 ! [Theta: nat > real,Theta2: real] :
% 5.31/5.65 ( ( filterlim_nat_real
% 5.31/5.65 @ ^ [J: nat] : ( cos_real @ ( minus_minus_real @ ( Theta @ J ) @ Theta2 ) )
% 5.31/5.65 @ ( topolo2815343760600316023s_real @ one_one_real )
% 5.31/5.65 @ at_top_nat )
% 5.31/5.65 => ~ ! [K: nat > int] :
% 5.31/5.65 ~ ( filterlim_nat_real
% 5.31/5.65 @ ^ [J: nat] : ( minus_minus_real @ ( Theta @ J ) @ ( times_times_real @ ( ring_1_of_int_real @ ( K @ J ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 5.31/5.65 @ ( topolo2815343760600316023s_real @ Theta2 )
% 5.31/5.65 @ at_top_nat ) ) ).
% 5.31/5.65
% 5.31/5.65 % cos_diff_limit_1
% 5.31/5.65 thf(fact_9147_cos__limit__1,axiom,
% 5.31/5.65 ! [Theta: nat > real] :
% 5.31/5.65 ( ( filterlim_nat_real
% 5.31/5.65 @ ^ [J: nat] : ( cos_real @ ( Theta @ J ) )
% 5.31/5.65 @ ( topolo2815343760600316023s_real @ one_one_real )
% 5.31/5.65 @ at_top_nat )
% 5.31/5.65 => ? [K: nat > int] :
% 5.31/5.65 ( filterlim_nat_real
% 5.31/5.65 @ ^ [J: nat] : ( minus_minus_real @ ( Theta @ J ) @ ( times_times_real @ ( ring_1_of_int_real @ ( K @ J ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 5.31/5.65 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.31/5.65 @ at_top_nat ) ) ).
% 5.31/5.65
% 5.31/5.65 % cos_limit_1
% 5.31/5.65 thf(fact_9148_summable__Leibniz_I4_J,axiom,
% 5.31/5.65 ! [A: nat > real] :
% 5.31/5.65 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.31/5.65 => ( ( topolo6980174941875973593q_real @ A )
% 5.31/5.65 => ( filterlim_nat_real
% 5.31/5.65 @ ^ [N4: nat] :
% 5.31/5.65 ( groups6591440286371151544t_real
% 5.31/5.65 @ ^ [I: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I ) @ ( A @ I ) )
% 5.31/5.65 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) ) )
% 5.31/5.65 @ ( topolo2815343760600316023s_real
% 5.31/5.65 @ ( suminf_real
% 5.31/5.65 @ ^ [I: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I ) @ ( A @ I ) ) ) )
% 5.31/5.65 @ at_top_nat ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % summable_Leibniz(4)
% 5.31/5.65 thf(fact_9149_zeroseq__arctan__series,axiom,
% 5.31/5.65 ! [X: real] :
% 5.31/5.65 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 5.31/5.65 => ( filterlim_nat_real
% 5.31/5.65 @ ^ [N4: nat] : ( times_times_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( times_times_nat @ N4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) @ ( power_power_real @ X @ ( plus_plus_nat @ ( times_times_nat @ N4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) )
% 5.31/5.65 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.31/5.65 @ at_top_nat ) ) ).
% 5.31/5.65
% 5.31/5.65 % zeroseq_arctan_series
% 5.31/5.65 thf(fact_9150_summable__Leibniz_H_I2_J,axiom,
% 5.31/5.65 ! [A: nat > real,N: nat] :
% 5.31/5.65 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.31/5.65 => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N3 ) )
% 5.31/5.65 => ( ! [N3: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N3 ) ) @ ( A @ N3 ) )
% 5.31/5.65 => ( ord_less_eq_real
% 5.31/5.65 @ ( groups6591440286371151544t_real
% 5.31/5.65 @ ^ [I: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I ) @ ( A @ I ) )
% 5.31/5.65 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.31/5.65 @ ( suminf_real
% 5.31/5.65 @ ^ [I: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I ) @ ( A @ I ) ) ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % summable_Leibniz'(2)
% 5.31/5.65 thf(fact_9151_summable__Leibniz_H_I3_J,axiom,
% 5.31/5.65 ! [A: nat > real] :
% 5.31/5.65 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.31/5.65 => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N3 ) )
% 5.31/5.65 => ( ! [N3: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N3 ) ) @ ( A @ N3 ) )
% 5.31/5.65 => ( filterlim_nat_real
% 5.31/5.65 @ ^ [N4: nat] :
% 5.31/5.65 ( groups6591440286371151544t_real
% 5.31/5.65 @ ^ [I: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I ) @ ( A @ I ) )
% 5.31/5.65 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) ) )
% 5.31/5.65 @ ( topolo2815343760600316023s_real
% 5.31/5.65 @ ( suminf_real
% 5.31/5.65 @ ^ [I: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I ) @ ( A @ I ) ) ) )
% 5.31/5.65 @ at_top_nat ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % summable_Leibniz'(3)
% 5.31/5.65 thf(fact_9152_sums__alternating__upper__lower,axiom,
% 5.31/5.65 ! [A: nat > real] :
% 5.31/5.65 ( ! [N3: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N3 ) ) @ ( A @ N3 ) )
% 5.31/5.65 => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N3 ) )
% 5.31/5.65 => ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.31/5.65 => ? [L4: real] :
% 5.31/5.65 ( ! [N8: nat] :
% 5.31/5.65 ( ord_less_eq_real
% 5.31/5.65 @ ( groups6591440286371151544t_real
% 5.31/5.65 @ ^ [I: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I ) @ ( A @ I ) )
% 5.31/5.65 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N8 ) ) )
% 5.31/5.65 @ L4 )
% 5.31/5.65 & ( filterlim_nat_real
% 5.31/5.65 @ ^ [N4: nat] :
% 5.31/5.65 ( groups6591440286371151544t_real
% 5.31/5.65 @ ^ [I: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I ) @ ( A @ I ) )
% 5.31/5.65 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) ) )
% 5.31/5.65 @ ( topolo2815343760600316023s_real @ L4 )
% 5.31/5.65 @ at_top_nat )
% 5.31/5.65 & ! [N8: nat] :
% 5.31/5.65 ( ord_less_eq_real @ L4
% 5.31/5.65 @ ( groups6591440286371151544t_real
% 5.31/5.65 @ ^ [I: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I ) @ ( A @ I ) )
% 5.31/5.65 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N8 ) @ one_one_nat ) ) ) )
% 5.31/5.65 & ( filterlim_nat_real
% 5.31/5.65 @ ^ [N4: nat] :
% 5.31/5.65 ( groups6591440286371151544t_real
% 5.31/5.65 @ ^ [I: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I ) @ ( A @ I ) )
% 5.31/5.65 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) @ one_one_nat ) ) )
% 5.31/5.65 @ ( topolo2815343760600316023s_real @ L4 )
% 5.31/5.65 @ at_top_nat ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % sums_alternating_upper_lower
% 5.31/5.65 thf(fact_9153_summable__Leibniz_I5_J,axiom,
% 5.31/5.65 ! [A: nat > real] :
% 5.31/5.65 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.31/5.65 => ( ( topolo6980174941875973593q_real @ A )
% 5.31/5.65 => ( filterlim_nat_real
% 5.31/5.65 @ ^ [N4: nat] :
% 5.31/5.65 ( groups6591440286371151544t_real
% 5.31/5.65 @ ^ [I: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I ) @ ( A @ I ) )
% 5.31/5.65 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) @ one_one_nat ) ) )
% 5.31/5.65 @ ( topolo2815343760600316023s_real
% 5.31/5.65 @ ( suminf_real
% 5.31/5.65 @ ^ [I: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I ) @ ( A @ I ) ) ) )
% 5.31/5.65 @ at_top_nat ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % summable_Leibniz(5)
% 5.31/5.65 thf(fact_9154_summable__Leibniz_H_I5_J,axiom,
% 5.31/5.65 ! [A: nat > real] :
% 5.31/5.65 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.31/5.65 => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N3 ) )
% 5.31/5.65 => ( ! [N3: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N3 ) ) @ ( A @ N3 ) )
% 5.31/5.65 => ( filterlim_nat_real
% 5.31/5.65 @ ^ [N4: nat] :
% 5.31/5.65 ( groups6591440286371151544t_real
% 5.31/5.65 @ ^ [I: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I ) @ ( A @ I ) )
% 5.31/5.65 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) @ one_one_nat ) ) )
% 5.31/5.65 @ ( topolo2815343760600316023s_real
% 5.31/5.65 @ ( suminf_real
% 5.31/5.65 @ ^ [I: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I ) @ ( A @ I ) ) ) )
% 5.31/5.65 @ at_top_nat ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % summable_Leibniz'(5)
% 5.31/5.65 thf(fact_9155_real__bounded__linear,axiom,
% 5.31/5.65 ( real_V5970128139526366754l_real
% 5.31/5.65 = ( ^ [F4: real > real] :
% 5.31/5.65 ? [C3: real] :
% 5.31/5.65 ( F4
% 5.31/5.65 = ( ^ [X4: real] : ( times_times_real @ X4 @ C3 ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % real_bounded_linear
% 5.31/5.65 thf(fact_9156_filterlim__Suc,axiom,
% 5.31/5.65 filterlim_nat_nat @ suc @ at_top_nat @ at_top_nat ).
% 5.31/5.65
% 5.31/5.65 % filterlim_Suc
% 5.31/5.65 thf(fact_9157_tendsto__exp__limit__at__right,axiom,
% 5.31/5.65 ! [X: real] :
% 5.31/5.65 ( filterlim_real_real
% 5.31/5.65 @ ^ [Y4: real] : ( powr_real @ ( plus_plus_real @ one_one_real @ ( times_times_real @ X @ Y4 ) ) @ ( divide_divide_real @ one_one_real @ Y4 ) )
% 5.31/5.65 @ ( topolo2815343760600316023s_real @ ( exp_real @ X ) )
% 5.31/5.65 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % tendsto_exp_limit_at_right
% 5.31/5.65 thf(fact_9158_GMVT,axiom,
% 5.31/5.65 ! [A: real,B: real,F2: real > real,G2: real > real] :
% 5.31/5.65 ( ( ord_less_real @ A @ B )
% 5.31/5.65 => ( ! [X3: real] :
% 5.31/5.65 ( ( ( ord_less_eq_real @ A @ X3 )
% 5.31/5.65 & ( ord_less_eq_real @ X3 @ B ) )
% 5.31/5.65 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) @ F2 ) )
% 5.31/5.65 => ( ! [X3: real] :
% 5.31/5.65 ( ( ( ord_less_real @ A @ X3 )
% 5.31/5.65 & ( ord_less_real @ X3 @ B ) )
% 5.31/5.65 => ( differ6690327859849518006l_real @ F2 @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) )
% 5.31/5.65 => ( ! [X3: real] :
% 5.31/5.65 ( ( ( ord_less_eq_real @ A @ X3 )
% 5.31/5.65 & ( ord_less_eq_real @ X3 @ B ) )
% 5.31/5.65 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) @ G2 ) )
% 5.31/5.65 => ( ! [X3: real] :
% 5.31/5.65 ( ( ( ord_less_real @ A @ X3 )
% 5.31/5.65 & ( ord_less_real @ X3 @ B ) )
% 5.31/5.65 => ( differ6690327859849518006l_real @ G2 @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) )
% 5.31/5.65 => ? [G_c: real,F_c: real,C: real] :
% 5.31/5.65 ( ( has_fi5821293074295781190e_real @ G2 @ G_c @ ( topolo2177554685111907308n_real @ C @ top_top_set_real ) )
% 5.31/5.65 & ( has_fi5821293074295781190e_real @ F2 @ F_c @ ( topolo2177554685111907308n_real @ C @ top_top_set_real ) )
% 5.31/5.65 & ( ord_less_real @ A @ C )
% 5.31/5.65 & ( ord_less_real @ C @ B )
% 5.31/5.65 & ( ( times_times_real @ ( minus_minus_real @ ( F2 @ B ) @ ( F2 @ A ) ) @ G_c )
% 5.31/5.65 = ( times_times_real @ ( minus_minus_real @ ( G2 @ B ) @ ( G2 @ A ) ) @ F_c ) ) ) ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % GMVT
% 5.31/5.65 thf(fact_9159_eventually__sequentially__Suc,axiom,
% 5.31/5.65 ! [P2: nat > $o] :
% 5.31/5.65 ( ( eventually_nat
% 5.31/5.65 @ ^ [I: nat] : ( P2 @ ( suc @ I ) )
% 5.31/5.65 @ at_top_nat )
% 5.31/5.65 = ( eventually_nat @ P2 @ at_top_nat ) ) ).
% 5.31/5.65
% 5.31/5.65 % eventually_sequentially_Suc
% 5.31/5.65 thf(fact_9160_eventually__sequentially,axiom,
% 5.31/5.65 ! [P2: nat > $o] :
% 5.31/5.65 ( ( eventually_nat @ P2 @ at_top_nat )
% 5.31/5.65 = ( ? [N5: nat] :
% 5.31/5.65 ! [N4: nat] :
% 5.31/5.65 ( ( ord_less_eq_nat @ N5 @ N4 )
% 5.31/5.65 => ( P2 @ N4 ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % eventually_sequentially
% 5.31/5.65 thf(fact_9161_eventually__sequentiallyI,axiom,
% 5.31/5.65 ! [C2: nat,P2: nat > $o] :
% 5.31/5.65 ( ! [X3: nat] :
% 5.31/5.65 ( ( ord_less_eq_nat @ C2 @ X3 )
% 5.31/5.65 => ( P2 @ X3 ) )
% 5.31/5.65 => ( eventually_nat @ P2 @ at_top_nat ) ) ).
% 5.31/5.65
% 5.31/5.65 % eventually_sequentiallyI
% 5.31/5.65 thf(fact_9162_le__sequentially,axiom,
% 5.31/5.65 ! [F3: filter_nat] :
% 5.31/5.65 ( ( ord_le2510731241096832064er_nat @ F3 @ at_top_nat )
% 5.31/5.65 = ( ! [N5: nat] : ( eventually_nat @ ( ord_less_eq_nat @ N5 ) @ F3 ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % le_sequentially
% 5.31/5.65 thf(fact_9163_atLeast__0,axiom,
% 5.31/5.65 ( ( set_ord_atLeast_nat @ zero_zero_nat )
% 5.31/5.65 = top_top_set_nat ) ).
% 5.31/5.65
% 5.31/5.65 % atLeast_0
% 5.31/5.65 thf(fact_9164_atLeast__Suc__greaterThan,axiom,
% 5.31/5.65 ! [K2: nat] :
% 5.31/5.65 ( ( set_ord_atLeast_nat @ ( suc @ K2 ) )
% 5.31/5.65 = ( set_or1210151606488870762an_nat @ K2 ) ) ).
% 5.31/5.65
% 5.31/5.65 % atLeast_Suc_greaterThan
% 5.31/5.65 thf(fact_9165_greaterThan__0,axiom,
% 5.31/5.65 ( ( set_or1210151606488870762an_nat @ zero_zero_nat )
% 5.31/5.65 = ( image_nat_nat @ suc @ top_top_set_nat ) ) ).
% 5.31/5.65
% 5.31/5.65 % greaterThan_0
% 5.31/5.65 thf(fact_9166_greaterThan__Suc,axiom,
% 5.31/5.65 ! [K2: nat] :
% 5.31/5.65 ( ( set_or1210151606488870762an_nat @ ( suc @ K2 ) )
% 5.31/5.65 = ( minus_minus_set_nat @ ( set_or1210151606488870762an_nat @ K2 ) @ ( insert_nat @ ( suc @ K2 ) @ bot_bot_set_nat ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % greaterThan_Suc
% 5.31/5.65 thf(fact_9167_atLeast__Suc,axiom,
% 5.31/5.65 ! [K2: nat] :
% 5.31/5.65 ( ( set_ord_atLeast_nat @ ( suc @ K2 ) )
% 5.31/5.65 = ( minus_minus_set_nat @ ( set_ord_atLeast_nat @ K2 ) @ ( insert_nat @ K2 @ bot_bot_set_nat ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % atLeast_Suc
% 5.31/5.65 thf(fact_9168_filterlim__pow__at__bot__even,axiom,
% 5.31/5.65 ! [N: nat,F2: real > real,F3: filter_real] :
% 5.31/5.65 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.65 => ( ( filterlim_real_real @ F2 @ at_bot_real @ F3 )
% 5.31/5.65 => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.31/5.65 => ( filterlim_real_real
% 5.31/5.65 @ ^ [X4: real] : ( power_power_real @ ( F2 @ X4 ) @ N )
% 5.31/5.65 @ at_top_real
% 5.31/5.65 @ F3 ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % filterlim_pow_at_bot_even
% 5.31/5.65 thf(fact_9169_GreatestI__ex__nat,axiom,
% 5.31/5.65 ! [P2: nat > $o,B: nat] :
% 5.31/5.65 ( ? [X_1: nat] : ( P2 @ X_1 )
% 5.31/5.65 => ( ! [Y3: nat] :
% 5.31/5.65 ( ( P2 @ Y3 )
% 5.31/5.65 => ( ord_less_eq_nat @ Y3 @ B ) )
% 5.31/5.65 => ( P2 @ ( order_Greatest_nat @ P2 ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % GreatestI_ex_nat
% 5.31/5.65 thf(fact_9170_Greatest__le__nat,axiom,
% 5.31/5.65 ! [P2: nat > $o,K2: nat,B: nat] :
% 5.31/5.65 ( ( P2 @ K2 )
% 5.31/5.65 => ( ! [Y3: nat] :
% 5.31/5.65 ( ( P2 @ Y3 )
% 5.31/5.65 => ( ord_less_eq_nat @ Y3 @ B ) )
% 5.31/5.65 => ( ord_less_eq_nat @ K2 @ ( order_Greatest_nat @ P2 ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % Greatest_le_nat
% 5.31/5.65 thf(fact_9171_GreatestI__nat,axiom,
% 5.31/5.65 ! [P2: nat > $o,K2: nat,B: nat] :
% 5.31/5.65 ( ( P2 @ K2 )
% 5.31/5.65 => ( ! [Y3: nat] :
% 5.31/5.65 ( ( P2 @ Y3 )
% 5.31/5.65 => ( ord_less_eq_nat @ Y3 @ B ) )
% 5.31/5.65 => ( P2 @ ( order_Greatest_nat @ P2 ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % GreatestI_nat
% 5.31/5.65 thf(fact_9172_filterlim__pow__at__bot__odd,axiom,
% 5.31/5.65 ! [N: nat,F2: real > real,F3: filter_real] :
% 5.31/5.65 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.65 => ( ( filterlim_real_real @ F2 @ at_bot_real @ F3 )
% 5.31/5.65 => ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.31/5.65 => ( filterlim_real_real
% 5.31/5.65 @ ^ [X4: real] : ( power_power_real @ ( F2 @ X4 ) @ N )
% 5.31/5.65 @ at_bot_real
% 5.31/5.65 @ F3 ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % filterlim_pow_at_bot_odd
% 5.31/5.65 thf(fact_9173_MVT,axiom,
% 5.31/5.65 ! [A: real,B: real,F2: real > real] :
% 5.31/5.65 ( ( ord_less_real @ A @ B )
% 5.31/5.65 => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F2 )
% 5.31/5.65 => ( ! [X3: real] :
% 5.31/5.65 ( ( ord_less_real @ A @ X3 )
% 5.31/5.65 => ( ( ord_less_real @ X3 @ B )
% 5.31/5.65 => ( differ6690327859849518006l_real @ F2 @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) ) )
% 5.31/5.65 => ? [L4: real,Z: real] :
% 5.31/5.65 ( ( ord_less_real @ A @ Z )
% 5.31/5.65 & ( ord_less_real @ Z @ B )
% 5.31/5.65 & ( has_fi5821293074295781190e_real @ F2 @ L4 @ ( topolo2177554685111907308n_real @ Z @ top_top_set_real ) )
% 5.31/5.65 & ( ( minus_minus_real @ ( F2 @ B ) @ ( F2 @ A ) )
% 5.31/5.65 = ( times_times_real @ ( minus_minus_real @ B @ A ) @ L4 ) ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % MVT
% 5.31/5.65 thf(fact_9174_inj__sgn__power,axiom,
% 5.31/5.65 ! [N: nat] :
% 5.31/5.65 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.65 => ( inj_on_real_real
% 5.31/5.65 @ ^ [Y4: real] : ( times_times_real @ ( sgn_sgn_real @ Y4 ) @ ( power_power_real @ ( abs_abs_real @ Y4 ) @ N ) )
% 5.31/5.65 @ top_top_set_real ) ) ).
% 5.31/5.65
% 5.31/5.65 % inj_sgn_power
% 5.31/5.65 thf(fact_9175_UN__lessThan__UNIV,axiom,
% 5.31/5.65 ( ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ set_ord_lessThan_nat @ top_top_set_nat ) )
% 5.31/5.65 = top_top_set_nat ) ).
% 5.31/5.65
% 5.31/5.65 % UN_lessThan_UNIV
% 5.31/5.65 thf(fact_9176_UN__atMost__UNIV,axiom,
% 5.31/5.65 ( ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ set_ord_atMost_nat @ top_top_set_nat ) )
% 5.31/5.65 = top_top_set_nat ) ).
% 5.31/5.65
% 5.31/5.65 % UN_atMost_UNIV
% 5.31/5.65 thf(fact_9177_UN__atLeast__UNIV,axiom,
% 5.31/5.65 ( ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ set_ord_atLeast_nat @ top_top_set_nat ) )
% 5.31/5.65 = top_top_set_nat ) ).
% 5.31/5.65
% 5.31/5.65 % UN_atLeast_UNIV
% 5.31/5.65 thf(fact_9178_Sup__nat__empty,axiom,
% 5.31/5.65 ( ( complete_Sup_Sup_nat @ bot_bot_set_nat )
% 5.31/5.65 = zero_zero_nat ) ).
% 5.31/5.65
% 5.31/5.65 % Sup_nat_empty
% 5.31/5.65 thf(fact_9179_inj__list__encode,axiom,
% 5.31/5.65 ! [A4: set_list_nat] : ( inj_on_list_nat_nat @ nat_list_encode @ A4 ) ).
% 5.31/5.65
% 5.31/5.65 % inj_list_encode
% 5.31/5.65 thf(fact_9180_inj__list__decode,axiom,
% 5.31/5.65 ! [A4: set_nat] : ( inj_on_nat_list_nat @ nat_list_decode @ A4 ) ).
% 5.31/5.65
% 5.31/5.65 % inj_list_decode
% 5.31/5.65 thf(fact_9181_inj__prod__encode,axiom,
% 5.31/5.65 ! [A4: set_Pr1261947904930325089at_nat] : ( inj_on2178005380612969504at_nat @ nat_prod_encode @ A4 ) ).
% 5.31/5.65
% 5.31/5.65 % inj_prod_encode
% 5.31/5.65 thf(fact_9182_inj__Suc,axiom,
% 5.31/5.65 ! [N6: set_nat] : ( inj_on_nat_nat @ suc @ N6 ) ).
% 5.31/5.65
% 5.31/5.65 % inj_Suc
% 5.31/5.65 thf(fact_9183_inj__prod__decode,axiom,
% 5.31/5.65 ! [A4: set_nat] : ( inj_on5538052773655684606at_nat @ nat_prod_decode @ A4 ) ).
% 5.31/5.65
% 5.31/5.65 % inj_prod_decode
% 5.31/5.65 thf(fact_9184_inj__on__diff__nat,axiom,
% 5.31/5.65 ! [N6: set_nat,K2: nat] :
% 5.31/5.65 ( ! [N3: nat] :
% 5.31/5.65 ( ( member_nat @ N3 @ N6 )
% 5.31/5.65 => ( ord_less_eq_nat @ K2 @ N3 ) )
% 5.31/5.65 => ( inj_on_nat_nat
% 5.31/5.65 @ ^ [N4: nat] : ( minus_minus_nat @ N4 @ K2 )
% 5.31/5.65 @ N6 ) ) ).
% 5.31/5.65
% 5.31/5.65 % inj_on_diff_nat
% 5.31/5.65 thf(fact_9185_inj__on__set__encode,axiom,
% 5.31/5.65 inj_on_set_nat_nat @ nat_set_encode @ ( collect_set_nat @ finite_finite_nat ) ).
% 5.31/5.65
% 5.31/5.65 % inj_on_set_encode
% 5.31/5.65 thf(fact_9186_INT__greaterThan__UNIV,axiom,
% 5.31/5.65 ( ( comple7806235888213564991et_nat @ ( image_nat_set_nat @ set_or1210151606488870762an_nat @ top_top_set_nat ) )
% 5.31/5.65 = bot_bot_set_nat ) ).
% 5.31/5.65
% 5.31/5.65 % INT_greaterThan_UNIV
% 5.31/5.65 thf(fact_9187_Gcd__eq__Max,axiom,
% 5.31/5.65 ! [M5: set_nat] :
% 5.31/5.65 ( ( finite_finite_nat @ M5 )
% 5.31/5.65 => ( ( M5 != bot_bot_set_nat )
% 5.31/5.65 => ( ~ ( member_nat @ zero_zero_nat @ M5 )
% 5.31/5.65 => ( ( gcd_Gcd_nat @ M5 )
% 5.31/5.65 = ( lattic8265883725875713057ax_nat
% 5.31/5.65 @ ( comple7806235888213564991et_nat
% 5.31/5.65 @ ( image_nat_set_nat
% 5.31/5.65 @ ^ [M6: nat] :
% 5.31/5.65 ( collect_nat
% 5.31/5.65 @ ^ [D2: nat] : ( dvd_dvd_nat @ D2 @ M6 ) )
% 5.31/5.65 @ M5 ) ) ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % Gcd_eq_Max
% 5.31/5.65 thf(fact_9188_Max__divisors__self__nat,axiom,
% 5.31/5.65 ! [N: nat] :
% 5.31/5.65 ( ( N != zero_zero_nat )
% 5.31/5.65 => ( ( lattic8265883725875713057ax_nat
% 5.31/5.65 @ ( collect_nat
% 5.31/5.65 @ ^ [D2: nat] : ( dvd_dvd_nat @ D2 @ N ) ) )
% 5.31/5.65 = N ) ) ).
% 5.31/5.65
% 5.31/5.65 % Max_divisors_self_nat
% 5.31/5.65 thf(fact_9189_Sup__nat__def,axiom,
% 5.31/5.65 ( complete_Sup_Sup_nat
% 5.31/5.65 = ( ^ [X7: set_nat] : ( if_nat @ ( X7 = bot_bot_set_nat ) @ zero_zero_nat @ ( lattic8265883725875713057ax_nat @ X7 ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % Sup_nat_def
% 5.31/5.65 thf(fact_9190_card__le__Suc__Max,axiom,
% 5.31/5.65 ! [S3: set_nat] :
% 5.31/5.65 ( ( finite_finite_nat @ S3 )
% 5.31/5.65 => ( ord_less_eq_nat @ ( finite_card_nat @ S3 ) @ ( suc @ ( lattic8265883725875713057ax_nat @ S3 ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % card_le_Suc_Max
% 5.31/5.65 thf(fact_9191_divide__nat__def,axiom,
% 5.31/5.65 ( divide_divide_nat
% 5.31/5.65 = ( ^ [M6: nat,N4: nat] :
% 5.31/5.65 ( if_nat @ ( N4 = zero_zero_nat ) @ zero_zero_nat
% 5.31/5.65 @ ( lattic8265883725875713057ax_nat
% 5.31/5.65 @ ( collect_nat
% 5.31/5.65 @ ^ [K3: nat] : ( ord_less_eq_nat @ ( times_times_nat @ K3 @ N4 ) @ M6 ) ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % divide_nat_def
% 5.31/5.65 thf(fact_9192_VEBT__internal_Ovalid_H_Oelims_I1_J,axiom,
% 5.31/5.65 ! [X: vEBT_VEBT,Xa2: nat,Y: $o] :
% 5.31/5.65 ( ( ( vEBT_VEBT_valid @ X @ Xa2 )
% 5.31/5.65 = Y )
% 5.31/5.65 => ( ( ? [Uu2: $o,Uv2: $o] :
% 5.31/5.65 ( X
% 5.31/5.65 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 5.31/5.65 => ( Y
% 5.31/5.65 = ( Xa2 != one_one_nat ) ) )
% 5.31/5.65 => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.31/5.65 ( ( X
% 5.31/5.65 = ( vEBT_Node @ Mima @ Deg2 @ TreeList @ Summary2 ) )
% 5.31/5.65 => ( Y
% 5.31/5.65 = ( ~ ( ( Deg2 = Xa2 )
% 5.31/5.65 & ! [X4: vEBT_VEBT] :
% 5.31/5.65 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.31/5.65 => ( vEBT_VEBT_valid @ X4 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.31/5.65 & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.31/5.65 & ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 5.31/5.65 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.31/5.65 & ( case_o184042715313410164at_nat
% 5.31/5.65 @ ( ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X7 )
% 5.31/5.65 & ! [X4: vEBT_VEBT] :
% 5.31/5.65 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.31/5.65 => ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X7 ) ) )
% 5.31/5.65 @ ( produc6081775807080527818_nat_o
% 5.31/5.65 @ ^ [Mi3: nat,Ma3: nat] :
% 5.31/5.65 ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 5.31/5.65 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.31/5.65 & ! [I: nat] :
% 5.31/5.65 ( ( ord_less_nat @ I @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.31/5.65 => ( ( ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I ) @ X7 ) )
% 5.31/5.65 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I ) ) )
% 5.31/5.65 & ( ( Mi3 = Ma3 )
% 5.31/5.65 => ! [X4: vEBT_VEBT] :
% 5.31/5.65 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.31/5.65 => ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X7 ) ) )
% 5.31/5.65 & ( ( Mi3 != Ma3 )
% 5.31/5.65 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList @ Ma3 )
% 5.31/5.65 & ! [X4: nat] :
% 5.31/5.65 ( ( ord_less_nat @ X4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.31/5.65 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList @ X4 )
% 5.31/5.65 => ( ( ord_less_nat @ Mi3 @ X4 )
% 5.31/5.65 & ( ord_less_eq_nat @ X4 @ Ma3 ) ) ) ) ) ) ) )
% 5.31/5.65 @ Mima ) ) ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % VEBT_internal.valid'.elims(1)
% 5.31/5.65 thf(fact_9193_VEBT__internal_Ovalid_H_Oelims_I2_J,axiom,
% 5.31/5.65 ! [X: vEBT_VEBT,Xa2: nat] :
% 5.31/5.65 ( ( vEBT_VEBT_valid @ X @ Xa2 )
% 5.31/5.65 => ( ( ? [Uu2: $o,Uv2: $o] :
% 5.31/5.65 ( X
% 5.31/5.65 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 5.31/5.65 => ( Xa2 != one_one_nat ) )
% 5.31/5.65 => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.31/5.65 ( ( X
% 5.31/5.65 = ( vEBT_Node @ Mima @ Deg2 @ TreeList @ Summary2 ) )
% 5.31/5.65 => ~ ( ( Deg2 = Xa2 )
% 5.31/5.65 & ! [X5: vEBT_VEBT] :
% 5.31/5.65 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.31/5.65 => ( vEBT_VEBT_valid @ X5 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.31/5.65 & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.31/5.65 & ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 5.31/5.65 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.31/5.65 & ( case_o184042715313410164at_nat
% 5.31/5.65 @ ( ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X7 )
% 5.31/5.65 & ! [X4: vEBT_VEBT] :
% 5.31/5.65 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.31/5.65 => ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X7 ) ) )
% 5.31/5.65 @ ( produc6081775807080527818_nat_o
% 5.31/5.65 @ ^ [Mi3: nat,Ma3: nat] :
% 5.31/5.65 ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 5.31/5.65 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.31/5.65 & ! [I: nat] :
% 5.31/5.65 ( ( ord_less_nat @ I @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.31/5.65 => ( ( ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I ) @ X7 ) )
% 5.31/5.65 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I ) ) )
% 5.31/5.65 & ( ( Mi3 = Ma3 )
% 5.31/5.65 => ! [X4: vEBT_VEBT] :
% 5.31/5.65 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.31/5.65 => ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X7 ) ) )
% 5.31/5.65 & ( ( Mi3 != Ma3 )
% 5.31/5.65 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList @ Ma3 )
% 5.31/5.65 & ! [X4: nat] :
% 5.31/5.65 ( ( ord_less_nat @ X4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.31/5.65 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList @ X4 )
% 5.31/5.65 => ( ( ord_less_nat @ Mi3 @ X4 )
% 5.31/5.65 & ( ord_less_eq_nat @ X4 @ Ma3 ) ) ) ) ) ) ) )
% 5.31/5.65 @ Mima ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % VEBT_internal.valid'.elims(2)
% 5.31/5.65 thf(fact_9194_VEBT__internal_Ovalid_H_Oelims_I3_J,axiom,
% 5.31/5.65 ! [X: vEBT_VEBT,Xa2: nat] :
% 5.31/5.65 ( ~ ( vEBT_VEBT_valid @ X @ Xa2 )
% 5.31/5.65 => ( ( ? [Uu2: $o,Uv2: $o] :
% 5.31/5.65 ( X
% 5.31/5.65 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 5.31/5.65 => ( Xa2 = one_one_nat ) )
% 5.31/5.65 => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.31/5.65 ( ( X
% 5.31/5.65 = ( vEBT_Node @ Mima @ Deg2 @ TreeList @ Summary2 ) )
% 5.31/5.65 => ( ( Deg2 = Xa2 )
% 5.31/5.65 & ! [X3: vEBT_VEBT] :
% 5.31/5.65 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.31/5.65 => ( vEBT_VEBT_valid @ X3 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.31/5.65 & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.31/5.65 & ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 5.31/5.65 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.31/5.65 & ( case_o184042715313410164at_nat
% 5.31/5.65 @ ( ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X7 )
% 5.31/5.65 & ! [X4: vEBT_VEBT] :
% 5.31/5.65 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.31/5.65 => ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X7 ) ) )
% 5.31/5.65 @ ( produc6081775807080527818_nat_o
% 5.31/5.65 @ ^ [Mi3: nat,Ma3: nat] :
% 5.31/5.65 ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 5.31/5.65 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.31/5.65 & ! [I: nat] :
% 5.31/5.65 ( ( ord_less_nat @ I @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.31/5.65 => ( ( ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I ) @ X7 ) )
% 5.31/5.65 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I ) ) )
% 5.31/5.65 & ( ( Mi3 = Ma3 )
% 5.31/5.65 => ! [X4: vEBT_VEBT] :
% 5.31/5.65 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.31/5.65 => ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X7 ) ) )
% 5.31/5.65 & ( ( Mi3 != Ma3 )
% 5.31/5.65 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList @ Ma3 )
% 5.31/5.65 & ! [X4: nat] :
% 5.31/5.65 ( ( ord_less_nat @ X4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.31/5.65 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList @ X4 )
% 5.31/5.65 => ( ( ord_less_nat @ Mi3 @ X4 )
% 5.31/5.65 & ( ord_less_eq_nat @ X4 @ Ma3 ) ) ) ) ) ) ) )
% 5.31/5.65 @ Mima ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % VEBT_internal.valid'.elims(3)
% 5.31/5.65 thf(fact_9195_VEBT__internal_Ovalid_H_Osimps_I2_J,axiom,
% 5.31/5.65 ! [Mima2: option4927543243414619207at_nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,Deg3: nat] :
% 5.31/5.65 ( ( vEBT_VEBT_valid @ ( vEBT_Node @ Mima2 @ Deg @ TreeList2 @ Summary ) @ Deg3 )
% 5.31/5.65 = ( ( Deg = Deg3 )
% 5.31/5.65 & ! [X4: vEBT_VEBT] :
% 5.31/5.65 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.31/5.65 => ( vEBT_VEBT_valid @ X4 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.31/5.65 & ( vEBT_VEBT_valid @ Summary @ ( minus_minus_nat @ Deg @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.31/5.65 & ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 5.31/5.65 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.31/5.65 & ( case_o184042715313410164at_nat
% 5.31/5.65 @ ( ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ Summary @ X7 )
% 5.31/5.65 & ! [X4: vEBT_VEBT] :
% 5.31/5.65 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.31/5.65 => ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X7 ) ) )
% 5.31/5.65 @ ( produc6081775807080527818_nat_o
% 5.31/5.65 @ ^ [Mi3: nat,Ma3: nat] :
% 5.31/5.65 ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 5.31/5.65 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 5.31/5.65 & ! [I: nat] :
% 5.31/5.65 ( ( ord_less_nat @ I @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.31/5.65 => ( ( ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I ) @ X7 ) )
% 5.31/5.65 = ( vEBT_V8194947554948674370ptions @ Summary @ I ) ) )
% 5.31/5.65 & ( ( Mi3 = Ma3 )
% 5.31/5.65 => ! [X4: vEBT_VEBT] :
% 5.31/5.65 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.31/5.65 => ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X7 ) ) )
% 5.31/5.65 & ( ( Mi3 != Ma3 )
% 5.31/5.65 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ Ma3 )
% 5.31/5.65 & ! [X4: nat] :
% 5.31/5.65 ( ( ord_less_nat @ X4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 5.31/5.65 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ X4 )
% 5.31/5.65 => ( ( ord_less_nat @ Mi3 @ X4 )
% 5.31/5.65 & ( ord_less_eq_nat @ X4 @ Ma3 ) ) ) ) ) ) ) )
% 5.31/5.65 @ Mima2 ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % VEBT_internal.valid'.simps(2)
% 5.31/5.65 thf(fact_9196_VEBT__internal_Ovalid_H_Opelims_I3_J,axiom,
% 5.31/5.65 ! [X: vEBT_VEBT,Xa2: nat] :
% 5.31/5.65 ( ~ ( vEBT_VEBT_valid @ X @ Xa2 )
% 5.31/5.65 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 5.31/5.65 => ( ! [Uu2: $o,Uv2: $o] :
% 5.31/5.65 ( ( X
% 5.31/5.65 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 5.31/5.65 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ Xa2 ) )
% 5.31/5.65 => ( Xa2 = one_one_nat ) ) )
% 5.31/5.65 => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.31/5.65 ( ( X
% 5.31/5.65 = ( vEBT_Node @ Mima @ Deg2 @ TreeList @ Summary2 ) )
% 5.31/5.65 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Mima @ Deg2 @ TreeList @ Summary2 ) @ Xa2 ) )
% 5.31/5.65 => ( ( Deg2 = Xa2 )
% 5.31/5.65 & ! [X3: vEBT_VEBT] :
% 5.31/5.65 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.31/5.65 => ( vEBT_VEBT_valid @ X3 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.31/5.65 & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.31/5.65 & ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 5.31/5.65 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.31/5.65 & ( case_o184042715313410164at_nat
% 5.31/5.65 @ ( ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X7 )
% 5.31/5.65 & ! [X4: vEBT_VEBT] :
% 5.31/5.65 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.31/5.65 => ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X7 ) ) )
% 5.31/5.65 @ ( produc6081775807080527818_nat_o
% 5.31/5.65 @ ^ [Mi3: nat,Ma3: nat] :
% 5.31/5.65 ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 5.31/5.65 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.31/5.65 & ! [I: nat] :
% 5.31/5.65 ( ( ord_less_nat @ I @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.31/5.65 => ( ( ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I ) @ X7 ) )
% 5.31/5.65 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I ) ) )
% 5.31/5.65 & ( ( Mi3 = Ma3 )
% 5.31/5.65 => ! [X4: vEBT_VEBT] :
% 5.31/5.65 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.31/5.65 => ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X7 ) ) )
% 5.31/5.65 & ( ( Mi3 != Ma3 )
% 5.31/5.65 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList @ Ma3 )
% 5.31/5.65 & ! [X4: nat] :
% 5.31/5.65 ( ( ord_less_nat @ X4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.31/5.65 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList @ X4 )
% 5.31/5.65 => ( ( ord_less_nat @ Mi3 @ X4 )
% 5.31/5.65 & ( ord_less_eq_nat @ X4 @ Ma3 ) ) ) ) ) ) ) )
% 5.31/5.65 @ Mima ) ) ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % VEBT_internal.valid'.pelims(3)
% 5.31/5.65 thf(fact_9197_VEBT__internal_Ovalid_H_Opelims_I2_J,axiom,
% 5.31/5.65 ! [X: vEBT_VEBT,Xa2: nat] :
% 5.31/5.65 ( ( vEBT_VEBT_valid @ X @ Xa2 )
% 5.31/5.65 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 5.31/5.65 => ( ! [Uu2: $o,Uv2: $o] :
% 5.31/5.65 ( ( X
% 5.31/5.65 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 5.31/5.65 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ Xa2 ) )
% 5.31/5.65 => ( Xa2 != one_one_nat ) ) )
% 5.31/5.65 => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.31/5.65 ( ( X
% 5.31/5.65 = ( vEBT_Node @ Mima @ Deg2 @ TreeList @ Summary2 ) )
% 5.31/5.65 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Mima @ Deg2 @ TreeList @ Summary2 ) @ Xa2 ) )
% 5.31/5.65 => ~ ( ( Deg2 = Xa2 )
% 5.31/5.65 & ! [X5: vEBT_VEBT] :
% 5.31/5.65 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.31/5.65 => ( vEBT_VEBT_valid @ X5 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.31/5.65 & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.31/5.65 & ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 5.31/5.65 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.31/5.65 & ( case_o184042715313410164at_nat
% 5.31/5.65 @ ( ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X7 )
% 5.31/5.65 & ! [X4: vEBT_VEBT] :
% 5.31/5.65 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.31/5.65 => ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X7 ) ) )
% 5.31/5.65 @ ( produc6081775807080527818_nat_o
% 5.31/5.65 @ ^ [Mi3: nat,Ma3: nat] :
% 5.31/5.65 ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 5.31/5.65 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.31/5.65 & ! [I: nat] :
% 5.31/5.65 ( ( ord_less_nat @ I @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.31/5.65 => ( ( ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I ) @ X7 ) )
% 5.31/5.65 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I ) ) )
% 5.31/5.65 & ( ( Mi3 = Ma3 )
% 5.31/5.65 => ! [X4: vEBT_VEBT] :
% 5.31/5.65 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.31/5.65 => ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X7 ) ) )
% 5.31/5.65 & ( ( Mi3 != Ma3 )
% 5.31/5.65 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList @ Ma3 )
% 5.31/5.65 & ! [X4: nat] :
% 5.31/5.65 ( ( ord_less_nat @ X4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.31/5.65 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList @ X4 )
% 5.31/5.65 => ( ( ord_less_nat @ Mi3 @ X4 )
% 5.31/5.65 & ( ord_less_eq_nat @ X4 @ Ma3 ) ) ) ) ) ) ) )
% 5.31/5.65 @ Mima ) ) ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % VEBT_internal.valid'.pelims(2)
% 5.31/5.65 thf(fact_9198_VEBT__internal_Ovalid_H_Opelims_I1_J,axiom,
% 5.31/5.65 ! [X: vEBT_VEBT,Xa2: nat,Y: $o] :
% 5.31/5.65 ( ( ( vEBT_VEBT_valid @ X @ Xa2 )
% 5.31/5.65 = Y )
% 5.31/5.65 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 5.31/5.65 => ( ! [Uu2: $o,Uv2: $o] :
% 5.31/5.65 ( ( X
% 5.31/5.65 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 5.31/5.65 => ( ( Y
% 5.31/5.65 = ( Xa2 = one_one_nat ) )
% 5.31/5.65 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ Xa2 ) ) ) )
% 5.31/5.65 => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.31/5.65 ( ( X
% 5.31/5.65 = ( vEBT_Node @ Mima @ Deg2 @ TreeList @ Summary2 ) )
% 5.31/5.65 => ( ( Y
% 5.31/5.65 = ( ( Deg2 = Xa2 )
% 5.31/5.65 & ! [X4: vEBT_VEBT] :
% 5.31/5.65 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.31/5.65 => ( vEBT_VEBT_valid @ X4 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.31/5.65 & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.31/5.65 & ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 5.31/5.65 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.31/5.65 & ( case_o184042715313410164at_nat
% 5.31/5.65 @ ( ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X7 )
% 5.31/5.65 & ! [X4: vEBT_VEBT] :
% 5.31/5.65 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.31/5.65 => ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X7 ) ) )
% 5.31/5.65 @ ( produc6081775807080527818_nat_o
% 5.31/5.65 @ ^ [Mi3: nat,Ma3: nat] :
% 5.31/5.65 ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 5.31/5.65 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.31/5.65 & ! [I: nat] :
% 5.31/5.65 ( ( ord_less_nat @ I @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.31/5.65 => ( ( ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I ) @ X7 ) )
% 5.31/5.65 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I ) ) )
% 5.31/5.65 & ( ( Mi3 = Ma3 )
% 5.31/5.65 => ! [X4: vEBT_VEBT] :
% 5.31/5.65 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.31/5.65 => ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X7 ) ) )
% 5.31/5.65 & ( ( Mi3 != Ma3 )
% 5.31/5.65 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList @ Ma3 )
% 5.31/5.65 & ! [X4: nat] :
% 5.31/5.65 ( ( ord_less_nat @ X4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.31/5.65 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList @ X4 )
% 5.31/5.65 => ( ( ord_less_nat @ Mi3 @ X4 )
% 5.31/5.65 & ( ord_less_eq_nat @ X4 @ Ma3 ) ) ) ) ) ) ) )
% 5.31/5.65 @ Mima ) ) )
% 5.31/5.65 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Mima @ Deg2 @ TreeList @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % VEBT_internal.valid'.pelims(1)
% 5.31/5.65 thf(fact_9199_min__Suc__Suc,axiom,
% 5.31/5.65 ! [M2: nat,N: nat] :
% 5.31/5.65 ( ( ord_min_nat @ ( suc @ M2 ) @ ( suc @ N ) )
% 5.31/5.65 = ( suc @ ( ord_min_nat @ M2 @ N ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % min_Suc_Suc
% 5.31/5.65 thf(fact_9200_min__0L,axiom,
% 5.31/5.65 ! [N: nat] :
% 5.31/5.65 ( ( ord_min_nat @ zero_zero_nat @ N )
% 5.31/5.65 = zero_zero_nat ) ).
% 5.31/5.65
% 5.31/5.65 % min_0L
% 5.31/5.65 thf(fact_9201_min__0R,axiom,
% 5.31/5.65 ! [N: nat] :
% 5.31/5.65 ( ( ord_min_nat @ N @ zero_zero_nat )
% 5.31/5.65 = zero_zero_nat ) ).
% 5.31/5.65
% 5.31/5.65 % min_0R
% 5.31/5.65 thf(fact_9202_take__bit__num__simps_I1_J,axiom,
% 5.31/5.65 ! [M2: num] :
% 5.31/5.65 ( ( bit_take_bit_num @ zero_zero_nat @ M2 )
% 5.31/5.65 = none_num ) ).
% 5.31/5.65
% 5.31/5.65 % take_bit_num_simps(1)
% 5.31/5.65 thf(fact_9203_take__bit__num__simps_I2_J,axiom,
% 5.31/5.65 ! [N: nat] :
% 5.31/5.65 ( ( bit_take_bit_num @ ( suc @ N ) @ one )
% 5.31/5.65 = ( some_num @ one ) ) ).
% 5.31/5.65
% 5.31/5.65 % take_bit_num_simps(2)
% 5.31/5.65 thf(fact_9204_take__bit__num__simps_I3_J,axiom,
% 5.31/5.65 ! [N: nat,M2: num] :
% 5.31/5.65 ( ( bit_take_bit_num @ ( suc @ N ) @ ( bit0 @ M2 ) )
% 5.31/5.65 = ( case_o6005452278849405969um_num @ none_num
% 5.31/5.65 @ ^ [Q5: num] : ( some_num @ ( bit0 @ Q5 ) )
% 5.31/5.65 @ ( bit_take_bit_num @ N @ M2 ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % take_bit_num_simps(3)
% 5.31/5.65 thf(fact_9205_min__numeral__Suc,axiom,
% 5.31/5.65 ! [K2: num,N: nat] :
% 5.31/5.65 ( ( ord_min_nat @ ( numeral_numeral_nat @ K2 ) @ ( suc @ N ) )
% 5.31/5.65 = ( suc @ ( ord_min_nat @ ( pred_numeral @ K2 ) @ N ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % min_numeral_Suc
% 5.31/5.65 thf(fact_9206_min__Suc__numeral,axiom,
% 5.31/5.65 ! [N: nat,K2: num] :
% 5.31/5.65 ( ( ord_min_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ K2 ) )
% 5.31/5.65 = ( suc @ ( ord_min_nat @ N @ ( pred_numeral @ K2 ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % min_Suc_numeral
% 5.31/5.65 thf(fact_9207_take__bit__num__simps_I4_J,axiom,
% 5.31/5.65 ! [N: nat,M2: num] :
% 5.31/5.65 ( ( bit_take_bit_num @ ( suc @ N ) @ ( bit1 @ M2 ) )
% 5.31/5.65 = ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_take_bit_num @ N @ M2 ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % take_bit_num_simps(4)
% 5.31/5.65 thf(fact_9208_min__diff,axiom,
% 5.31/5.65 ! [M2: nat,I2: nat,N: nat] :
% 5.31/5.65 ( ( ord_min_nat @ ( minus_minus_nat @ M2 @ I2 ) @ ( minus_minus_nat @ N @ I2 ) )
% 5.31/5.65 = ( minus_minus_nat @ ( ord_min_nat @ M2 @ N ) @ I2 ) ) ).
% 5.31/5.65
% 5.31/5.65 % min_diff
% 5.31/5.65 thf(fact_9209_nat__mult__min__left,axiom,
% 5.31/5.65 ! [M2: nat,N: nat,Q2: nat] :
% 5.31/5.65 ( ( times_times_nat @ ( ord_min_nat @ M2 @ N ) @ Q2 )
% 5.31/5.65 = ( ord_min_nat @ ( times_times_nat @ M2 @ Q2 ) @ ( times_times_nat @ N @ Q2 ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % nat_mult_min_left
% 5.31/5.65 thf(fact_9210_nat__mult__min__right,axiom,
% 5.31/5.65 ! [M2: nat,N: nat,Q2: nat] :
% 5.31/5.65 ( ( times_times_nat @ M2 @ ( ord_min_nat @ N @ Q2 ) )
% 5.31/5.65 = ( ord_min_nat @ ( times_times_nat @ M2 @ N ) @ ( times_times_nat @ M2 @ Q2 ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % nat_mult_min_right
% 5.31/5.65 thf(fact_9211_inf__nat__def,axiom,
% 5.31/5.65 inf_inf_nat = ord_min_nat ).
% 5.31/5.65
% 5.31/5.65 % inf_nat_def
% 5.31/5.65 thf(fact_9212_min__Suc1,axiom,
% 5.31/5.65 ! [N: nat,M2: nat] :
% 5.31/5.65 ( ( ord_min_nat @ ( suc @ N ) @ M2 )
% 5.31/5.65 = ( case_nat_nat @ zero_zero_nat
% 5.31/5.65 @ ^ [M7: nat] : ( suc @ ( ord_min_nat @ N @ M7 ) )
% 5.31/5.65 @ M2 ) ) ).
% 5.31/5.65
% 5.31/5.65 % min_Suc1
% 5.31/5.65 thf(fact_9213_min__Suc2,axiom,
% 5.31/5.65 ! [M2: nat,N: nat] :
% 5.31/5.65 ( ( ord_min_nat @ M2 @ ( suc @ N ) )
% 5.31/5.65 = ( case_nat_nat @ zero_zero_nat
% 5.31/5.65 @ ^ [M7: nat] : ( suc @ ( ord_min_nat @ M7 @ N ) )
% 5.31/5.65 @ M2 ) ) ).
% 5.31/5.65
% 5.31/5.65 % min_Suc2
% 5.31/5.65 thf(fact_9214_take__bit__num__def,axiom,
% 5.31/5.65 ( bit_take_bit_num
% 5.31/5.65 = ( ^ [N4: nat,M6: num] :
% 5.31/5.65 ( if_option_num
% 5.31/5.65 @ ( ( bit_se2925701944663578781it_nat @ N4 @ ( numeral_numeral_nat @ M6 ) )
% 5.31/5.65 = zero_zero_nat )
% 5.31/5.65 @ none_num
% 5.31/5.65 @ ( some_num @ ( num_of_nat @ ( bit_se2925701944663578781it_nat @ N4 @ ( numeral_numeral_nat @ M6 ) ) ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % take_bit_num_def
% 5.31/5.65 thf(fact_9215_pred__nat__def,axiom,
% 5.31/5.65 ( pred_nat
% 5.31/5.65 = ( collec3392354462482085612at_nat
% 5.31/5.65 @ ( produc6081775807080527818_nat_o
% 5.31/5.65 @ ^ [M6: nat,N4: nat] :
% 5.31/5.65 ( N4
% 5.31/5.65 = ( suc @ M6 ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % pred_nat_def
% 5.31/5.65 thf(fact_9216_Rats__eq__int__div__nat,axiom,
% 5.31/5.65 ( field_5140801741446780682s_real
% 5.31/5.65 = ( collect_real
% 5.31/5.65 @ ^ [Uu3: real] :
% 5.31/5.65 ? [I: int,N4: nat] :
% 5.31/5.65 ( ( Uu3
% 5.31/5.65 = ( divide_divide_real @ ( ring_1_of_int_real @ I ) @ ( semiri5074537144036343181t_real @ N4 ) ) )
% 5.31/5.65 & ( N4 != zero_zero_nat ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % Rats_eq_int_div_nat
% 5.31/5.65 thf(fact_9217_card_Ocomp__fun__commute__on,axiom,
% 5.31/5.65 ( ( comp_nat_nat_nat @ suc @ suc )
% 5.31/5.65 = ( comp_nat_nat_nat @ suc @ suc ) ) ).
% 5.31/5.65
% 5.31/5.65 % card.comp_fun_commute_on
% 5.31/5.65 thf(fact_9218_divmod__integer__eq__cases,axiom,
% 5.31/5.65 ( code_divmod_integer
% 5.31/5.65 = ( ^ [K3: code_integer,L2: code_integer] :
% 5.31/5.65 ( if_Pro6119634080678213985nteger @ ( K3 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger )
% 5.31/5.65 @ ( if_Pro6119634080678213985nteger @ ( L2 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ K3 )
% 5.31/5.65 @ ( comp_C1593894019821074884nteger @ ( comp_C8797469213163452608nteger @ produc6499014454317279255nteger @ times_3573771949741848930nteger ) @ sgn_sgn_Code_integer @ L2
% 5.31/5.65 @ ( if_Pro6119634080678213985nteger
% 5.31/5.65 @ ( ( sgn_sgn_Code_integer @ K3 )
% 5.31/5.65 = ( sgn_sgn_Code_integer @ L2 ) )
% 5.31/5.65 @ ( code_divmod_abs @ K3 @ L2 )
% 5.31/5.65 @ ( produc6916734918728496179nteger
% 5.31/5.65 @ ^ [R: code_integer,S6: code_integer] : ( if_Pro6119634080678213985nteger @ ( S6 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( uminus1351360451143612070nteger @ R ) @ zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ R ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ ( abs_abs_Code_integer @ L2 ) @ S6 ) ) )
% 5.31/5.65 @ ( code_divmod_abs @ K3 @ L2 ) ) ) ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % divmod_integer_eq_cases
% 5.31/5.65 thf(fact_9219_less__eq,axiom,
% 5.31/5.65 ! [M2: nat,N: nat] :
% 5.31/5.65 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ M2 @ N ) @ ( transi6264000038957366511cl_nat @ pred_nat ) )
% 5.31/5.65 = ( ord_less_nat @ M2 @ N ) ) ).
% 5.31/5.65
% 5.31/5.65 % less_eq
% 5.31/5.65 thf(fact_9220_pred__nat__trancl__eq__le,axiom,
% 5.31/5.65 ! [M2: nat,N: nat] :
% 5.31/5.65 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ M2 @ N ) @ ( transi2905341329935302413cl_nat @ pred_nat ) )
% 5.31/5.65 = ( ord_less_eq_nat @ M2 @ N ) ) ).
% 5.31/5.65
% 5.31/5.65 % pred_nat_trancl_eq_le
% 5.31/5.65 thf(fact_9221_bezw__aux,axiom,
% 5.31/5.65 ! [X: nat,Y: nat] :
% 5.31/5.65 ( ( semiri1314217659103216013at_int @ ( gcd_gcd_nat @ X @ Y ) )
% 5.31/5.65 = ( 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 ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % bezw_aux
% 5.31/5.65 thf(fact_9222_gcd__0__left__nat,axiom,
% 5.31/5.65 ! [X: nat] :
% 5.31/5.65 ( ( gcd_gcd_nat @ zero_zero_nat @ X )
% 5.31/5.65 = X ) ).
% 5.31/5.65
% 5.31/5.65 % gcd_0_left_nat
% 5.31/5.65 thf(fact_9223_gcd__0__nat,axiom,
% 5.31/5.65 ! [X: nat] :
% 5.31/5.65 ( ( gcd_gcd_nat @ X @ zero_zero_nat )
% 5.31/5.65 = X ) ).
% 5.31/5.65
% 5.31/5.65 % gcd_0_nat
% 5.31/5.65 thf(fact_9224_gcd__nat_Oright__neutral,axiom,
% 5.31/5.65 ! [A: nat] :
% 5.31/5.65 ( ( gcd_gcd_nat @ A @ zero_zero_nat )
% 5.31/5.65 = A ) ).
% 5.31/5.65
% 5.31/5.65 % gcd_nat.right_neutral
% 5.31/5.65 thf(fact_9225_gcd__nat_Oneutr__eq__iff,axiom,
% 5.31/5.65 ! [A: nat,B: nat] :
% 5.31/5.65 ( ( zero_zero_nat
% 5.31/5.65 = ( gcd_gcd_nat @ A @ B ) )
% 5.31/5.65 = ( ( A = zero_zero_nat )
% 5.31/5.65 & ( B = zero_zero_nat ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % gcd_nat.neutr_eq_iff
% 5.31/5.65 thf(fact_9226_gcd__nat_Oleft__neutral,axiom,
% 5.31/5.65 ! [A: nat] :
% 5.31/5.65 ( ( gcd_gcd_nat @ zero_zero_nat @ A )
% 5.31/5.65 = A ) ).
% 5.31/5.65
% 5.31/5.65 % gcd_nat.left_neutral
% 5.31/5.65 thf(fact_9227_gcd__nat_Oeq__neutr__iff,axiom,
% 5.31/5.65 ! [A: nat,B: nat] :
% 5.31/5.65 ( ( ( gcd_gcd_nat @ A @ B )
% 5.31/5.65 = zero_zero_nat )
% 5.31/5.65 = ( ( A = zero_zero_nat )
% 5.31/5.65 & ( B = zero_zero_nat ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % gcd_nat.eq_neutr_iff
% 5.31/5.65 thf(fact_9228_gcd__Suc__0,axiom,
% 5.31/5.65 ! [M2: nat] :
% 5.31/5.65 ( ( gcd_gcd_nat @ M2 @ ( suc @ zero_zero_nat ) )
% 5.31/5.65 = ( suc @ zero_zero_nat ) ) ).
% 5.31/5.65
% 5.31/5.65 % gcd_Suc_0
% 5.31/5.65 thf(fact_9229_gcd__pos__nat,axiom,
% 5.31/5.65 ! [M2: nat,N: nat] :
% 5.31/5.65 ( ( ord_less_nat @ zero_zero_nat @ ( gcd_gcd_nat @ M2 @ N ) )
% 5.31/5.65 = ( ( M2 != zero_zero_nat )
% 5.31/5.65 | ( N != zero_zero_nat ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % gcd_pos_nat
% 5.31/5.65 thf(fact_9230_gcd__diff2__nat,axiom,
% 5.31/5.65 ! [M2: nat,N: nat] :
% 5.31/5.65 ( ( ord_less_eq_nat @ M2 @ N )
% 5.31/5.65 => ( ( gcd_gcd_nat @ ( minus_minus_nat @ N @ M2 ) @ N )
% 5.31/5.65 = ( gcd_gcd_nat @ M2 @ N ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % gcd_diff2_nat
% 5.31/5.65 thf(fact_9231_gcd__diff1__nat,axiom,
% 5.31/5.65 ! [N: nat,M2: nat] :
% 5.31/5.65 ( ( ord_less_eq_nat @ N @ M2 )
% 5.31/5.65 => ( ( gcd_gcd_nat @ ( minus_minus_nat @ M2 @ N ) @ N )
% 5.31/5.65 = ( gcd_gcd_nat @ M2 @ N ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % gcd_diff1_nat
% 5.31/5.65 thf(fact_9232_gcd__le1__nat,axiom,
% 5.31/5.65 ! [A: nat,B: nat] :
% 5.31/5.65 ( ( A != zero_zero_nat )
% 5.31/5.65 => ( ord_less_eq_nat @ ( gcd_gcd_nat @ A @ B ) @ A ) ) ).
% 5.31/5.65
% 5.31/5.65 % gcd_le1_nat
% 5.31/5.65 thf(fact_9233_gcd__le2__nat,axiom,
% 5.31/5.65 ! [B: nat,A: nat] :
% 5.31/5.65 ( ( B != zero_zero_nat )
% 5.31/5.65 => ( ord_less_eq_nat @ ( gcd_gcd_nat @ A @ B ) @ B ) ) ).
% 5.31/5.65
% 5.31/5.65 % gcd_le2_nat
% 5.31/5.65 thf(fact_9234_gcd__mult__distrib__nat,axiom,
% 5.31/5.65 ! [K2: nat,M2: nat,N: nat] :
% 5.31/5.65 ( ( times_times_nat @ K2 @ ( gcd_gcd_nat @ M2 @ N ) )
% 5.31/5.65 = ( gcd_gcd_nat @ ( times_times_nat @ K2 @ M2 ) @ ( times_times_nat @ K2 @ N ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % gcd_mult_distrib_nat
% 5.31/5.65 thf(fact_9235_gcd__non__0__nat,axiom,
% 5.31/5.65 ! [Y: nat,X: nat] :
% 5.31/5.65 ( ( Y != zero_zero_nat )
% 5.31/5.65 => ( ( gcd_gcd_nat @ X @ Y )
% 5.31/5.65 = ( gcd_gcd_nat @ Y @ ( modulo_modulo_nat @ X @ Y ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % gcd_non_0_nat
% 5.31/5.65 thf(fact_9236_gcd__nat_Osimps,axiom,
% 5.31/5.65 ( gcd_gcd_nat
% 5.31/5.65 = ( ^ [X4: nat,Y4: nat] : ( if_nat @ ( Y4 = zero_zero_nat ) @ X4 @ ( gcd_gcd_nat @ Y4 @ ( modulo_modulo_nat @ X4 @ Y4 ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % gcd_nat.simps
% 5.31/5.65 thf(fact_9237_gcd__nat_Oelims,axiom,
% 5.31/5.65 ! [X: nat,Xa2: nat,Y: nat] :
% 5.31/5.65 ( ( ( gcd_gcd_nat @ X @ Xa2 )
% 5.31/5.65 = Y )
% 5.31/5.65 => ( ( ( Xa2 = zero_zero_nat )
% 5.31/5.65 => ( Y = X ) )
% 5.31/5.65 & ( ( Xa2 != zero_zero_nat )
% 5.31/5.65 => ( Y
% 5.31/5.65 = ( gcd_gcd_nat @ Xa2 @ ( modulo_modulo_nat @ X @ Xa2 ) ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % gcd_nat.elims
% 5.31/5.65 thf(fact_9238_bezout__nat,axiom,
% 5.31/5.65 ! [A: nat,B: nat] :
% 5.31/5.65 ( ( A != zero_zero_nat )
% 5.31/5.65 => ? [X3: nat,Y3: nat] :
% 5.31/5.65 ( ( times_times_nat @ A @ X3 )
% 5.31/5.65 = ( plus_plus_nat @ ( times_times_nat @ B @ Y3 ) @ ( gcd_gcd_nat @ A @ B ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % bezout_nat
% 5.31/5.65 thf(fact_9239_bezout__gcd__nat_H,axiom,
% 5.31/5.65 ! [B: nat,A: nat] :
% 5.31/5.65 ? [X3: nat,Y3: nat] :
% 5.31/5.65 ( ( ( ord_less_eq_nat @ ( times_times_nat @ B @ Y3 ) @ ( times_times_nat @ A @ X3 ) )
% 5.31/5.65 & ( ( minus_minus_nat @ ( times_times_nat @ A @ X3 ) @ ( times_times_nat @ B @ Y3 ) )
% 5.31/5.65 = ( gcd_gcd_nat @ A @ B ) ) )
% 5.31/5.65 | ( ( ord_less_eq_nat @ ( times_times_nat @ A @ Y3 ) @ ( times_times_nat @ B @ X3 ) )
% 5.31/5.65 & ( ( minus_minus_nat @ ( times_times_nat @ B @ X3 ) @ ( times_times_nat @ A @ Y3 ) )
% 5.31/5.65 = ( gcd_gcd_nat @ A @ B ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % bezout_gcd_nat'
% 5.31/5.65 thf(fact_9240_Field__natLeq__on,axiom,
% 5.31/5.65 ! [N: nat] :
% 5.31/5.65 ( ( field_nat
% 5.31/5.65 @ ( collec3392354462482085612at_nat
% 5.31/5.65 @ ( produc6081775807080527818_nat_o
% 5.31/5.65 @ ^ [X4: nat,Y4: nat] :
% 5.31/5.65 ( ( ord_less_nat @ X4 @ N )
% 5.31/5.65 & ( ord_less_nat @ Y4 @ N )
% 5.31/5.65 & ( ord_less_eq_nat @ X4 @ Y4 ) ) ) ) )
% 5.31/5.65 = ( collect_nat
% 5.31/5.65 @ ^ [X4: nat] : ( ord_less_nat @ X4 @ N ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % Field_natLeq_on
% 5.31/5.65 thf(fact_9241_gcd__nat_Osemilattice__neutr__order__axioms,axiom,
% 5.31/5.65 ( semila1623282765462674594er_nat @ gcd_gcd_nat @ zero_zero_nat @ dvd_dvd_nat
% 5.31/5.65 @ ^ [M6: nat,N4: nat] :
% 5.31/5.65 ( ( dvd_dvd_nat @ M6 @ N4 )
% 5.31/5.65 & ( M6 != N4 ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % gcd_nat.semilattice_neutr_order_axioms
% 5.31/5.65 thf(fact_9242_gcd__is__Max__divisors__nat,axiom,
% 5.31/5.65 ! [N: nat,M2: nat] :
% 5.31/5.65 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.65 => ( ( gcd_gcd_nat @ M2 @ N )
% 5.31/5.65 = ( lattic8265883725875713057ax_nat
% 5.31/5.65 @ ( collect_nat
% 5.31/5.65 @ ^ [D2: nat] :
% 5.31/5.65 ( ( dvd_dvd_nat @ D2 @ M2 )
% 5.31/5.65 & ( dvd_dvd_nat @ D2 @ N ) ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % gcd_is_Max_divisors_nat
% 5.31/5.65 thf(fact_9243_gcd__nat_Opelims,axiom,
% 5.31/5.65 ! [X: nat,Xa2: nat,Y: nat] :
% 5.31/5.65 ( ( ( gcd_gcd_nat @ X @ Xa2 )
% 5.31/5.65 = Y )
% 5.31/5.65 => ( ( accp_P4275260045618599050at_nat @ gcd_nat_rel @ ( product_Pair_nat_nat @ X @ Xa2 ) )
% 5.31/5.65 => ~ ( ( ( ( Xa2 = zero_zero_nat )
% 5.31/5.65 => ( Y = X ) )
% 5.31/5.65 & ( ( Xa2 != zero_zero_nat )
% 5.31/5.65 => ( Y
% 5.31/5.65 = ( gcd_gcd_nat @ Xa2 @ ( modulo_modulo_nat @ X @ Xa2 ) ) ) ) )
% 5.31/5.65 => ~ ( accp_P4275260045618599050at_nat @ gcd_nat_rel @ ( product_Pair_nat_nat @ X @ Xa2 ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % gcd_nat.pelims
% 5.31/5.65 thf(fact_9244_gcd__mult__distrib__int,axiom,
% 5.31/5.65 ! [K2: int,M2: int,N: int] :
% 5.31/5.65 ( ( times_times_int @ ( abs_abs_int @ K2 ) @ ( gcd_gcd_int @ M2 @ N ) )
% 5.31/5.65 = ( gcd_gcd_int @ ( times_times_int @ K2 @ M2 ) @ ( times_times_int @ K2 @ N ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % gcd_mult_distrib_int
% 5.31/5.65 thf(fact_9245_bezout__int,axiom,
% 5.31/5.65 ! [X: int,Y: int] :
% 5.31/5.65 ? [U3: int,V: int] :
% 5.31/5.65 ( ( plus_plus_int @ ( times_times_int @ U3 @ X ) @ ( times_times_int @ V @ Y ) )
% 5.31/5.65 = ( gcd_gcd_int @ X @ Y ) ) ).
% 5.31/5.65
% 5.31/5.65 % bezout_int
% 5.31/5.65 thf(fact_9246_strict__mono__imp__increasing,axiom,
% 5.31/5.65 ! [F2: nat > nat,N: nat] :
% 5.31/5.65 ( ( order_5726023648592871131at_nat @ F2 )
% 5.31/5.65 => ( ord_less_eq_nat @ N @ ( F2 @ N ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % strict_mono_imp_increasing
% 5.31/5.65 thf(fact_9247_DeMoivre2,axiom,
% 5.31/5.65 ! [R3: real,A: real,N: nat] :
% 5.31/5.65 ( ( power_power_complex @ ( rcis @ R3 @ A ) @ N )
% 5.31/5.65 = ( rcis @ ( power_power_real @ R3 @ N ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ A ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % DeMoivre2
% 5.31/5.65 thf(fact_9248_Re__rcis,axiom,
% 5.31/5.65 ! [R3: real,A: real] :
% 5.31/5.65 ( ( re @ ( rcis @ R3 @ A ) )
% 5.31/5.65 = ( times_times_real @ R3 @ ( cos_real @ A ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % Re_rcis
% 5.31/5.65 thf(fact_9249_Im__rcis,axiom,
% 5.31/5.65 ! [R3: real,A: real] :
% 5.31/5.65 ( ( im @ ( rcis @ R3 @ A ) )
% 5.31/5.65 = ( times_times_real @ R3 @ ( sin_real @ A ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % Im_rcis
% 5.31/5.65 thf(fact_9250_rcis__mult,axiom,
% 5.31/5.65 ! [R1: real,A: real,R22: real,B: real] :
% 5.31/5.65 ( ( times_times_complex @ ( rcis @ R1 @ A ) @ ( rcis @ R22 @ B ) )
% 5.31/5.65 = ( rcis @ ( times_times_real @ R1 @ R22 ) @ ( plus_plus_real @ A @ B ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % rcis_mult
% 5.31/5.65 thf(fact_9251_rcis__def,axiom,
% 5.31/5.65 ( rcis
% 5.31/5.65 = ( ^ [R: real,A5: real] : ( times_times_complex @ ( real_V4546457046886955230omplex @ R ) @ ( cis @ A5 ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % rcis_def
% 5.31/5.65 thf(fact_9252_eventually__prod__sequentially,axiom,
% 5.31/5.65 ! [P2: product_prod_nat_nat > $o] :
% 5.31/5.65 ( ( eventu1038000079068216329at_nat @ P2 @ ( prod_filter_nat_nat @ at_top_nat @ at_top_nat ) )
% 5.31/5.65 = ( ? [N5: nat] :
% 5.31/5.65 ! [M6: nat] :
% 5.31/5.65 ( ( ord_less_eq_nat @ N5 @ M6 )
% 5.31/5.65 => ! [N4: nat] :
% 5.31/5.65 ( ( ord_less_eq_nat @ N5 @ N4 )
% 5.31/5.65 => ( P2 @ ( product_Pair_nat_nat @ N4 @ M6 ) ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % eventually_prod_sequentially
% 5.31/5.65 thf(fact_9253_sqr_Osimps_I3_J,axiom,
% 5.31/5.65 ! [N: num] :
% 5.31/5.65 ( ( sqr @ ( bit1 @ N ) )
% 5.31/5.65 = ( bit1 @ ( bit0 @ ( plus_plus_num @ ( sqr @ N ) @ N ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % sqr.simps(3)
% 5.31/5.65 thf(fact_9254_sqr_Osimps_I2_J,axiom,
% 5.31/5.65 ! [N: num] :
% 5.31/5.65 ( ( sqr @ ( bit0 @ N ) )
% 5.31/5.65 = ( bit0 @ ( bit0 @ ( sqr @ N ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % sqr.simps(2)
% 5.31/5.65 thf(fact_9255_sqr_Osimps_I1_J,axiom,
% 5.31/5.65 ( ( sqr @ one )
% 5.31/5.65 = one ) ).
% 5.31/5.65
% 5.31/5.65 % sqr.simps(1)
% 5.31/5.65 thf(fact_9256_sqr__conv__mult,axiom,
% 5.31/5.65 ( sqr
% 5.31/5.65 = ( ^ [X4: num] : ( times_times_num @ X4 @ X4 ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % sqr_conv_mult
% 5.31/5.65 thf(fact_9257_pow_Osimps_I3_J,axiom,
% 5.31/5.65 ! [X: num,Y: num] :
% 5.31/5.65 ( ( pow @ X @ ( bit1 @ Y ) )
% 5.31/5.65 = ( times_times_num @ ( sqr @ ( pow @ X @ Y ) ) @ X ) ) ).
% 5.31/5.65
% 5.31/5.65 % pow.simps(3)
% 5.31/5.65 thf(fact_9258_pow_Osimps_I1_J,axiom,
% 5.31/5.65 ! [X: num] :
% 5.31/5.65 ( ( pow @ X @ one )
% 5.31/5.65 = X ) ).
% 5.31/5.65
% 5.31/5.65 % pow.simps(1)
% 5.31/5.65 thf(fact_9259_pow_Osimps_I2_J,axiom,
% 5.31/5.65 ! [X: num,Y: num] :
% 5.31/5.65 ( ( pow @ X @ ( bit0 @ Y ) )
% 5.31/5.65 = ( sqr @ ( pow @ X @ Y ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % pow.simps(2)
% 5.31/5.65 thf(fact_9260_natLeq__on__wo__rel,axiom,
% 5.31/5.65 ! [N: nat] :
% 5.31/5.65 ( bNF_We3818239936649020644el_nat
% 5.31/5.65 @ ( collec3392354462482085612at_nat
% 5.31/5.65 @ ( produc6081775807080527818_nat_o
% 5.31/5.65 @ ^ [X4: nat,Y4: nat] :
% 5.31/5.65 ( ( ord_less_nat @ X4 @ N )
% 5.31/5.65 & ( ord_less_nat @ Y4 @ N )
% 5.31/5.65 & ( ord_less_eq_nat @ X4 @ Y4 ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % natLeq_on_wo_rel
% 5.31/5.65 thf(fact_9261_pairs__le__eq__Sigma,axiom,
% 5.31/5.65 ! [M2: nat] :
% 5.31/5.65 ( ( collec3392354462482085612at_nat
% 5.31/5.65 @ ( produc6081775807080527818_nat_o
% 5.31/5.65 @ ^ [I: nat,J: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ I @ J ) @ M2 ) ) )
% 5.31/5.65 = ( produc457027306803732586at_nat @ ( set_ord_atMost_nat @ M2 )
% 5.31/5.65 @ ^ [R: nat] : ( set_ord_atMost_nat @ ( minus_minus_nat @ M2 @ R ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % pairs_le_eq_Sigma
% 5.31/5.65 thf(fact_9262_finite__vimage__Suc__iff,axiom,
% 5.31/5.65 ! [F3: set_nat] :
% 5.31/5.65 ( ( finite_finite_nat @ ( vimage_nat_nat @ suc @ F3 ) )
% 5.31/5.65 = ( finite_finite_nat @ F3 ) ) ).
% 5.31/5.65
% 5.31/5.65 % finite_vimage_Suc_iff
% 5.31/5.65 thf(fact_9263_coprime__Suc__0__right,axiom,
% 5.31/5.65 ! [N: nat] : ( algebr934650988132801477me_nat @ N @ ( suc @ zero_zero_nat ) ) ).
% 5.31/5.65
% 5.31/5.65 % coprime_Suc_0_right
% 5.31/5.65 thf(fact_9264_coprime__Suc__0__left,axiom,
% 5.31/5.65 ! [N: nat] : ( algebr934650988132801477me_nat @ ( suc @ zero_zero_nat ) @ N ) ).
% 5.31/5.65
% 5.31/5.65 % coprime_Suc_0_left
% 5.31/5.65 thf(fact_9265_coprime__Suc__left__nat,axiom,
% 5.31/5.65 ! [N: nat] : ( algebr934650988132801477me_nat @ ( suc @ N ) @ N ) ).
% 5.31/5.65
% 5.31/5.65 % coprime_Suc_left_nat
% 5.31/5.65 thf(fact_9266_coprime__Suc__right__nat,axiom,
% 5.31/5.65 ! [N: nat] : ( algebr934650988132801477me_nat @ N @ ( suc @ N ) ) ).
% 5.31/5.65
% 5.31/5.65 % coprime_Suc_right_nat
% 5.31/5.65 thf(fact_9267_coprime__crossproduct__nat,axiom,
% 5.31/5.65 ! [A: nat,D: nat,B: nat,C2: nat] :
% 5.31/5.65 ( ( algebr934650988132801477me_nat @ A @ D )
% 5.31/5.65 => ( ( algebr934650988132801477me_nat @ B @ C2 )
% 5.31/5.65 => ( ( ( times_times_nat @ A @ C2 )
% 5.31/5.65 = ( times_times_nat @ B @ D ) )
% 5.31/5.65 = ( ( A = B )
% 5.31/5.65 & ( C2 = D ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % coprime_crossproduct_nat
% 5.31/5.65 thf(fact_9268_vimage__Suc__insert__Suc,axiom,
% 5.31/5.65 ! [N: nat,A4: set_nat] :
% 5.31/5.65 ( ( vimage_nat_nat @ suc @ ( insert_nat @ ( suc @ N ) @ A4 ) )
% 5.31/5.65 = ( insert_nat @ N @ ( vimage_nat_nat @ suc @ A4 ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % vimage_Suc_insert_Suc
% 5.31/5.65 thf(fact_9269_vimage__Suc__insert__0,axiom,
% 5.31/5.65 ! [A4: set_nat] :
% 5.31/5.65 ( ( vimage_nat_nat @ suc @ ( insert_nat @ zero_zero_nat @ A4 ) )
% 5.31/5.65 = ( vimage_nat_nat @ suc @ A4 ) ) ).
% 5.31/5.65
% 5.31/5.65 % vimage_Suc_insert_0
% 5.31/5.65 thf(fact_9270_coprime__diff__one__left__nat,axiom,
% 5.31/5.65 ! [N: nat] :
% 5.31/5.65 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.65 => ( algebr934650988132801477me_nat @ ( minus_minus_nat @ N @ one_one_nat ) @ N ) ) ).
% 5.31/5.65
% 5.31/5.65 % coprime_diff_one_left_nat
% 5.31/5.65 thf(fact_9271_coprime__diff__one__right__nat,axiom,
% 5.31/5.65 ! [N: nat] :
% 5.31/5.65 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.65 => ( algebr934650988132801477me_nat @ N @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % coprime_diff_one_right_nat
% 5.31/5.65 thf(fact_9272_Rats__abs__nat__div__natE,axiom,
% 5.31/5.65 ! [X: real] :
% 5.31/5.65 ( ( member_real @ X @ field_5140801741446780682s_real )
% 5.31/5.65 => ~ ! [M: nat,N3: nat] :
% 5.31/5.65 ( ( N3 != zero_zero_nat )
% 5.31/5.65 => ( ( ( abs_abs_real @ X )
% 5.31/5.65 = ( divide_divide_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N3 ) ) )
% 5.31/5.65 => ~ ( algebr934650988132801477me_nat @ M @ N3 ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % Rats_abs_nat_div_natE
% 5.31/5.65 thf(fact_9273_set__decode__div__2,axiom,
% 5.31/5.65 ! [X: nat] :
% 5.31/5.65 ( ( nat_set_decode @ ( divide_divide_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.31/5.65 = ( vimage_nat_nat @ suc @ ( nat_set_decode @ X ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % set_decode_div_2
% 5.31/5.65 thf(fact_9274_set__encode__vimage__Suc,axiom,
% 5.31/5.65 ! [A4: set_nat] :
% 5.31/5.65 ( ( nat_set_encode @ ( vimage_nat_nat @ suc @ A4 ) )
% 5.31/5.65 = ( divide_divide_nat @ ( nat_set_encode @ A4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % set_encode_vimage_Suc
% 5.31/5.65 thf(fact_9275_Restr__natLeq,axiom,
% 5.31/5.65 ! [N: nat] :
% 5.31/5.65 ( ( inf_in2572325071724192079at_nat @ bNF_Ca8665028551170535155natLeq
% 5.31/5.65 @ ( produc457027306803732586at_nat
% 5.31/5.65 @ ( collect_nat
% 5.31/5.65 @ ^ [X4: nat] : ( ord_less_nat @ X4 @ N ) )
% 5.31/5.65 @ ^ [Uu3: nat] :
% 5.31/5.65 ( collect_nat
% 5.31/5.65 @ ^ [X4: nat] : ( ord_less_nat @ X4 @ N ) ) ) )
% 5.31/5.65 = ( collec3392354462482085612at_nat
% 5.31/5.65 @ ( produc6081775807080527818_nat_o
% 5.31/5.65 @ ^ [X4: nat,Y4: nat] :
% 5.31/5.65 ( ( ord_less_nat @ X4 @ N )
% 5.31/5.65 & ( ord_less_nat @ Y4 @ N )
% 5.31/5.65 & ( ord_less_eq_nat @ X4 @ Y4 ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % Restr_natLeq
% 5.31/5.65 thf(fact_9276_of__nat__eq__id,axiom,
% 5.31/5.65 semiri1316708129612266289at_nat = id_nat ).
% 5.31/5.65
% 5.31/5.65 % of_nat_eq_id
% 5.31/5.65 thf(fact_9277_coprime__crossproduct__int,axiom,
% 5.31/5.65 ! [A: int,D: int,B: int,C2: int] :
% 5.31/5.65 ( ( algebr932160517623751201me_int @ A @ D )
% 5.31/5.65 => ( ( algebr932160517623751201me_int @ B @ C2 )
% 5.31/5.65 => ( ( ( times_times_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ C2 ) )
% 5.31/5.65 = ( times_times_int @ ( abs_abs_int @ B ) @ ( abs_abs_int @ D ) ) )
% 5.31/5.65 = ( ( ( abs_abs_int @ A )
% 5.31/5.65 = ( abs_abs_int @ B ) )
% 5.31/5.65 & ( ( abs_abs_int @ C2 )
% 5.31/5.65 = ( abs_abs_int @ D ) ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % coprime_crossproduct_int
% 5.31/5.65 thf(fact_9278_natLeq__Linear__order,axiom,
% 5.31/5.65 order_4473980167227706203on_nat @ ( field_nat @ bNF_Ca8665028551170535155natLeq ) @ bNF_Ca8665028551170535155natLeq ).
% 5.31/5.65
% 5.31/5.65 % natLeq_Linear_order
% 5.31/5.65 thf(fact_9279_natLeq__Total,axiom,
% 5.31/5.65 total_on_nat @ ( field_nat @ bNF_Ca8665028551170535155natLeq ) @ bNF_Ca8665028551170535155natLeq ).
% 5.31/5.65
% 5.31/5.65 % natLeq_Total
% 5.31/5.65 thf(fact_9280_natLeq__Refl,axiom,
% 5.31/5.65 refl_on_nat @ ( field_nat @ bNF_Ca8665028551170535155natLeq ) @ bNF_Ca8665028551170535155natLeq ).
% 5.31/5.65
% 5.31/5.65 % natLeq_Refl
% 5.31/5.65 thf(fact_9281_natLeq__natLess__Id,axiom,
% 5.31/5.65 ( bNF_Ca8459412986667044542atLess
% 5.31/5.65 = ( minus_1356011639430497352at_nat @ bNF_Ca8665028551170535155natLeq @ id_nat2 ) ) ).
% 5.31/5.65
% 5.31/5.65 % natLeq_natLess_Id
% 5.31/5.65 thf(fact_9282_Field__natLeq,axiom,
% 5.31/5.65 ( ( field_nat @ bNF_Ca8665028551170535155natLeq )
% 5.31/5.65 = top_top_set_nat ) ).
% 5.31/5.65
% 5.31/5.65 % Field_natLeq
% 5.31/5.65 thf(fact_9283_natLeq__def,axiom,
% 5.31/5.65 ( bNF_Ca8665028551170535155natLeq
% 5.31/5.65 = ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ ord_less_eq_nat ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % natLeq_def
% 5.31/5.65 thf(fact_9284_Restr__natLeq2,axiom,
% 5.31/5.65 ! [N: nat] :
% 5.31/5.65 ( ( inf_in2572325071724192079at_nat @ bNF_Ca8665028551170535155natLeq
% 5.31/5.65 @ ( produc457027306803732586at_nat @ ( order_underS_nat @ bNF_Ca8665028551170535155natLeq @ N )
% 5.31/5.65 @ ^ [Uu3: nat] : ( order_underS_nat @ bNF_Ca8665028551170535155natLeq @ N ) ) )
% 5.31/5.65 = ( collec3392354462482085612at_nat
% 5.31/5.65 @ ( produc6081775807080527818_nat_o
% 5.31/5.65 @ ^ [X4: nat,Y4: nat] :
% 5.31/5.65 ( ( ord_less_nat @ X4 @ N )
% 5.31/5.65 & ( ord_less_nat @ Y4 @ N )
% 5.31/5.65 & ( ord_less_eq_nat @ X4 @ Y4 ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % Restr_natLeq2
% 5.31/5.65 thf(fact_9285_natLeq__underS__less,axiom,
% 5.31/5.65 ! [N: nat] :
% 5.31/5.65 ( ( order_underS_nat @ bNF_Ca8665028551170535155natLeq @ N )
% 5.31/5.65 = ( collect_nat
% 5.31/5.65 @ ^ [X4: nat] : ( ord_less_nat @ X4 @ N ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % natLeq_underS_less
% 5.31/5.65 thf(fact_9286_pair__lessI2,axiom,
% 5.31/5.65 ! [A: nat,B: nat,S2: nat,T: nat] :
% 5.31/5.65 ( ( ord_less_eq_nat @ A @ B )
% 5.31/5.65 => ( ( ord_less_nat @ S2 @ T )
% 5.31/5.65 => ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ ( product_Pair_nat_nat @ A @ S2 ) @ ( product_Pair_nat_nat @ B @ T ) ) @ fun_pair_less ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % pair_lessI2
% 5.31/5.65 thf(fact_9287_pair__less__iff1,axiom,
% 5.31/5.65 ! [X: nat,Y: nat,Z3: nat] :
% 5.31/5.65 ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ ( product_Pair_nat_nat @ X @ Z3 ) ) @ fun_pair_less )
% 5.31/5.65 = ( ord_less_nat @ Y @ Z3 ) ) ).
% 5.31/5.65
% 5.31/5.65 % pair_less_iff1
% 5.31/5.65 thf(fact_9288_pair__lessI1,axiom,
% 5.31/5.65 ! [A: nat,B: nat,S2: nat,T: nat] :
% 5.31/5.65 ( ( ord_less_nat @ A @ B )
% 5.31/5.65 => ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ ( product_Pair_nat_nat @ A @ S2 ) @ ( product_Pair_nat_nat @ B @ T ) ) @ fun_pair_less ) ) ).
% 5.31/5.65
% 5.31/5.65 % pair_lessI1
% 5.31/5.65 thf(fact_9289_pair__leqI2,axiom,
% 5.31/5.65 ! [A: nat,B: nat,S2: nat,T: nat] :
% 5.31/5.65 ( ( ord_less_eq_nat @ A @ B )
% 5.31/5.65 => ( ( ord_less_eq_nat @ S2 @ T )
% 5.31/5.65 => ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ ( product_Pair_nat_nat @ A @ S2 ) @ ( product_Pair_nat_nat @ B @ T ) ) @ fun_pair_leq ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % pair_leqI2
% 5.31/5.65 thf(fact_9290_pair__leqI1,axiom,
% 5.31/5.65 ! [A: nat,B: nat,S2: nat,T: nat] :
% 5.31/5.65 ( ( ord_less_nat @ A @ B )
% 5.31/5.65 => ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ ( product_Pair_nat_nat @ A @ S2 ) @ ( product_Pair_nat_nat @ B @ T ) ) @ fun_pair_leq ) ) ).
% 5.31/5.65
% 5.31/5.65 % pair_leqI1
% 5.31/5.65 thf(fact_9291_length__upto,axiom,
% 5.31/5.65 ! [I2: int,J2: int] :
% 5.31/5.65 ( ( size_size_list_int @ ( upto @ I2 @ J2 ) )
% 5.31/5.65 = ( nat2 @ ( plus_plus_int @ ( minus_minus_int @ J2 @ I2 ) @ one_one_int ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % length_upto
% 5.31/5.65 thf(fact_9292_gcd__nat_Oordering__top__axioms,axiom,
% 5.31/5.65 ( ordering_top_nat @ dvd_dvd_nat
% 5.31/5.65 @ ^ [M6: nat,N4: nat] :
% 5.31/5.65 ( ( dvd_dvd_nat @ M6 @ N4 )
% 5.31/5.65 & ( M6 != N4 ) )
% 5.31/5.65 @ zero_zero_nat ) ).
% 5.31/5.65
% 5.31/5.65 % gcd_nat.ordering_top_axioms
% 5.31/5.65 thf(fact_9293_bot__nat__0_Oordering__top__axioms,axiom,
% 5.31/5.65 ( ordering_top_nat
% 5.31/5.65 @ ^ [X4: nat,Y4: nat] : ( ord_less_eq_nat @ Y4 @ X4 )
% 5.31/5.65 @ ^ [X4: nat,Y4: nat] : ( ord_less_nat @ Y4 @ X4 )
% 5.31/5.65 @ zero_zero_nat ) ).
% 5.31/5.65
% 5.31/5.65 % bot_nat_0.ordering_top_axioms
% 5.31/5.65 thf(fact_9294_ratrel__iff,axiom,
% 5.31/5.65 ( ratrel
% 5.31/5.65 = ( ^ [X4: product_prod_int_int,Y4: product_prod_int_int] :
% 5.31/5.65 ( ( ( product_snd_int_int @ X4 )
% 5.31/5.65 != zero_zero_int )
% 5.31/5.65 & ( ( product_snd_int_int @ Y4 )
% 5.31/5.65 != zero_zero_int )
% 5.31/5.65 & ( ( times_times_int @ ( product_fst_int_int @ X4 ) @ ( product_snd_int_int @ Y4 ) )
% 5.31/5.65 = ( times_times_int @ ( product_fst_int_int @ Y4 ) @ ( product_snd_int_int @ X4 ) ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % ratrel_iff
% 5.31/5.65 thf(fact_9295_ratrel__def,axiom,
% 5.31/5.65 ( ratrel
% 5.31/5.65 = ( ^ [X4: product_prod_int_int,Y4: product_prod_int_int] :
% 5.31/5.65 ( ( ( product_snd_int_int @ X4 )
% 5.31/5.65 != zero_zero_int )
% 5.31/5.65 & ( ( product_snd_int_int @ Y4 )
% 5.31/5.65 != zero_zero_int )
% 5.31/5.65 & ( ( times_times_int @ ( product_fst_int_int @ X4 ) @ ( product_snd_int_int @ Y4 ) )
% 5.31/5.65 = ( times_times_int @ ( product_fst_int_int @ Y4 ) @ ( product_snd_int_int @ X4 ) ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % ratrel_def
% 5.31/5.65 thf(fact_9296_plus__rat_Oabs__eq,axiom,
% 5.31/5.65 ! [Xa2: product_prod_int_int,X: product_prod_int_int] :
% 5.31/5.65 ( ( ratrel @ Xa2 @ Xa2 )
% 5.31/5.65 => ( ( ratrel @ X @ X )
% 5.31/5.65 => ( ( plus_plus_rat @ ( abs_Rat @ Xa2 ) @ ( abs_Rat @ X ) )
% 5.31/5.65 = ( abs_Rat @ ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( product_fst_int_int @ Xa2 ) @ ( product_snd_int_int @ X ) ) @ ( times_times_int @ ( product_fst_int_int @ X ) @ ( product_snd_int_int @ Xa2 ) ) ) @ ( times_times_int @ ( product_snd_int_int @ Xa2 ) @ ( product_snd_int_int @ X ) ) ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % plus_rat.abs_eq
% 5.31/5.65 thf(fact_9297_times__rat_Oabs__eq,axiom,
% 5.31/5.65 ! [Xa2: product_prod_int_int,X: product_prod_int_int] :
% 5.31/5.65 ( ( ratrel @ Xa2 @ Xa2 )
% 5.31/5.65 => ( ( ratrel @ X @ X )
% 5.31/5.65 => ( ( times_times_rat @ ( abs_Rat @ Xa2 ) @ ( abs_Rat @ X ) )
% 5.31/5.65 = ( abs_Rat @ ( product_Pair_int_int @ ( times_times_int @ ( product_fst_int_int @ Xa2 ) @ ( product_fst_int_int @ X ) ) @ ( times_times_int @ ( product_snd_int_int @ Xa2 ) @ ( product_snd_int_int @ X ) ) ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % times_rat.abs_eq
% 5.31/5.65 thf(fact_9298_Rat_Opositive_Oabs__eq,axiom,
% 5.31/5.65 ! [X: product_prod_int_int] :
% 5.31/5.65 ( ( ratrel @ X @ X )
% 5.31/5.65 => ( ( positive @ ( abs_Rat @ X ) )
% 5.31/5.65 = ( ord_less_int @ zero_zero_int @ ( times_times_int @ ( product_fst_int_int @ X ) @ ( product_snd_int_int @ X ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % Rat.positive.abs_eq
% 5.31/5.65 thf(fact_9299_Rat_Opositive__mult,axiom,
% 5.31/5.65 ! [X: rat,Y: rat] :
% 5.31/5.65 ( ( positive @ X )
% 5.31/5.65 => ( ( positive @ Y )
% 5.31/5.65 => ( positive @ ( times_times_rat @ X @ Y ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % Rat.positive_mult
% 5.31/5.65 thf(fact_9300_Rat_Opositive_Orep__eq,axiom,
% 5.31/5.65 ( positive
% 5.31/5.65 = ( ^ [X4: rat] : ( ord_less_int @ zero_zero_int @ ( times_times_int @ ( product_fst_int_int @ ( rep_Rat @ X4 ) ) @ ( product_snd_int_int @ ( rep_Rat @ X4 ) ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % Rat.positive.rep_eq
% 5.31/5.65 thf(fact_9301_Rat_Opositive_Orsp,axiom,
% 5.31/5.65 ( bNF_re8699439704749558557nt_o_o @ ratrel
% 5.31/5.65 @ ^ [Y5: $o,Z2: $o] : ( Y5 = Z2 )
% 5.31/5.65 @ ^ [X4: product_prod_int_int] : ( ord_less_int @ zero_zero_int @ ( times_times_int @ ( product_fst_int_int @ X4 ) @ ( product_snd_int_int @ X4 ) ) )
% 5.31/5.65 @ ^ [X4: product_prod_int_int] : ( ord_less_int @ zero_zero_int @ ( times_times_int @ ( product_fst_int_int @ X4 ) @ ( product_snd_int_int @ X4 ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % Rat.positive.rsp
% 5.31/5.65 thf(fact_9302_Rat_Opositive__def,axiom,
% 5.31/5.65 ( positive
% 5.31/5.65 = ( map_fu898904425404107465nt_o_o @ rep_Rat @ id_o
% 5.31/5.65 @ ^ [X4: product_prod_int_int] : ( ord_less_int @ zero_zero_int @ ( times_times_int @ ( product_fst_int_int @ X4 ) @ ( product_snd_int_int @ X4 ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % Rat.positive_def
% 5.31/5.65 thf(fact_9303_less__eq__natural_Orsp,axiom,
% 5.31/5.65 ( bNF_re578469030762574527_nat_o
% 5.31/5.65 @ ^ [Y5: nat,Z2: nat] : ( Y5 = Z2 )
% 5.31/5.65 @ ( bNF_re4705727531993890431at_o_o
% 5.31/5.65 @ ^ [Y5: nat,Z2: nat] : ( Y5 = Z2 )
% 5.31/5.65 @ ^ [Y5: $o,Z2: $o] : ( Y5 = Z2 ) )
% 5.31/5.65 @ ord_less_eq_nat
% 5.31/5.65 @ ord_less_eq_nat ) ).
% 5.31/5.65
% 5.31/5.65 % less_eq_natural.rsp
% 5.31/5.65 thf(fact_9304_Suc_Orsp,axiom,
% 5.31/5.65 ( bNF_re5653821019739307937at_nat
% 5.31/5.65 @ ^ [Y5: nat,Z2: nat] : ( Y5 = Z2 )
% 5.31/5.65 @ ^ [Y5: nat,Z2: nat] : ( Y5 = Z2 )
% 5.31/5.65 @ suc
% 5.31/5.65 @ suc ) ).
% 5.31/5.65
% 5.31/5.65 % Suc.rsp
% 5.31/5.65 thf(fact_9305_times__integer_Orsp,axiom,
% 5.31/5.65 ( bNF_re711492959462206631nt_int
% 5.31/5.65 @ ^ [Y5: int,Z2: int] : ( Y5 = Z2 )
% 5.31/5.65 @ ( bNF_re4712519889275205905nt_int
% 5.31/5.65 @ ^ [Y5: int,Z2: int] : ( Y5 = Z2 )
% 5.31/5.65 @ ^ [Y5: int,Z2: int] : ( Y5 = Z2 ) )
% 5.31/5.65 @ times_times_int
% 5.31/5.65 @ times_times_int ) ).
% 5.31/5.65
% 5.31/5.65 % times_integer.rsp
% 5.31/5.65 thf(fact_9306_times__natural_Orsp,axiom,
% 5.31/5.65 ( bNF_re1345281282404953727at_nat
% 5.31/5.65 @ ^ [Y5: nat,Z2: nat] : ( Y5 = Z2 )
% 5.31/5.65 @ ( bNF_re5653821019739307937at_nat
% 5.31/5.65 @ ^ [Y5: nat,Z2: nat] : ( Y5 = Z2 )
% 5.31/5.65 @ ^ [Y5: nat,Z2: nat] : ( Y5 = Z2 ) )
% 5.31/5.65 @ times_times_nat
% 5.31/5.65 @ times_times_nat ) ).
% 5.31/5.65
% 5.31/5.65 % times_natural.rsp
% 5.31/5.65 thf(fact_9307_times__rat_Orsp,axiom,
% 5.31/5.65 ( bNF_re5228765855967844073nt_int @ ratrel @ ( bNF_re7145576690424134365nt_int @ ratrel @ ratrel )
% 5.31/5.65 @ ^ [X4: product_prod_int_int,Y4: product_prod_int_int] : ( product_Pair_int_int @ ( times_times_int @ ( product_fst_int_int @ X4 ) @ ( product_fst_int_int @ Y4 ) ) @ ( times_times_int @ ( product_snd_int_int @ X4 ) @ ( product_snd_int_int @ Y4 ) ) )
% 5.31/5.65 @ ^ [X4: product_prod_int_int,Y4: product_prod_int_int] : ( product_Pair_int_int @ ( times_times_int @ ( product_fst_int_int @ X4 ) @ ( product_fst_int_int @ Y4 ) ) @ ( times_times_int @ ( product_snd_int_int @ X4 ) @ ( product_snd_int_int @ Y4 ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % times_rat.rsp
% 5.31/5.65 thf(fact_9308_plus__rat_Orsp,axiom,
% 5.31/5.65 ( bNF_re5228765855967844073nt_int @ ratrel @ ( bNF_re7145576690424134365nt_int @ ratrel @ ratrel )
% 5.31/5.65 @ ^ [X4: product_prod_int_int,Y4: product_prod_int_int] : ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( product_fst_int_int @ X4 ) @ ( product_snd_int_int @ Y4 ) ) @ ( times_times_int @ ( product_fst_int_int @ Y4 ) @ ( product_snd_int_int @ X4 ) ) ) @ ( times_times_int @ ( product_snd_int_int @ X4 ) @ ( product_snd_int_int @ Y4 ) ) )
% 5.31/5.65 @ ^ [X4: product_prod_int_int,Y4: product_prod_int_int] : ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( product_fst_int_int @ X4 ) @ ( product_snd_int_int @ Y4 ) ) @ ( times_times_int @ ( product_fst_int_int @ Y4 ) @ ( product_snd_int_int @ X4 ) ) ) @ ( times_times_int @ ( product_snd_int_int @ X4 ) @ ( product_snd_int_int @ Y4 ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % plus_rat.rsp
% 5.31/5.65 thf(fact_9309_plus__rat_Otransfer,axiom,
% 5.31/5.65 ( bNF_re7627151682743391978at_rat @ pcr_rat @ ( bNF_re8279943556446156061nt_rat @ pcr_rat @ pcr_rat )
% 5.31/5.65 @ ^ [X4: product_prod_int_int,Y4: product_prod_int_int] : ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( product_fst_int_int @ X4 ) @ ( product_snd_int_int @ Y4 ) ) @ ( times_times_int @ ( product_fst_int_int @ Y4 ) @ ( product_snd_int_int @ X4 ) ) ) @ ( times_times_int @ ( product_snd_int_int @ X4 ) @ ( product_snd_int_int @ Y4 ) ) )
% 5.31/5.65 @ plus_plus_rat ) ).
% 5.31/5.65
% 5.31/5.65 % plus_rat.transfer
% 5.31/5.65 thf(fact_9310_Rat_Opositive_Otransfer,axiom,
% 5.31/5.65 ( bNF_re1494630372529172596at_o_o @ pcr_rat
% 5.31/5.65 @ ^ [Y5: $o,Z2: $o] : ( Y5 = Z2 )
% 5.31/5.65 @ ^ [X4: product_prod_int_int] : ( ord_less_int @ zero_zero_int @ ( times_times_int @ ( product_fst_int_int @ X4 ) @ ( product_snd_int_int @ X4 ) ) )
% 5.31/5.65 @ positive ) ).
% 5.31/5.65
% 5.31/5.65 % Rat.positive.transfer
% 5.31/5.65 thf(fact_9311_times__rat_Otransfer,axiom,
% 5.31/5.65 ( bNF_re7627151682743391978at_rat @ pcr_rat @ ( bNF_re8279943556446156061nt_rat @ pcr_rat @ pcr_rat )
% 5.31/5.65 @ ^ [X4: product_prod_int_int,Y4: product_prod_int_int] : ( product_Pair_int_int @ ( times_times_int @ ( product_fst_int_int @ X4 ) @ ( product_fst_int_int @ Y4 ) ) @ ( times_times_int @ ( product_snd_int_int @ X4 ) @ ( product_snd_int_int @ Y4 ) ) )
% 5.31/5.65 @ times_times_rat ) ).
% 5.31/5.65
% 5.31/5.65 % times_rat.transfer
% 5.31/5.65 thf(fact_9312_times__int_Otransfer,axiom,
% 5.31/5.65 ( bNF_re7408651293131936558nt_int @ pcr_int @ ( bNF_re7400052026677387805at_int @ pcr_int @ pcr_int )
% 5.31/5.65 @ ( produc27273713700761075at_nat
% 5.31/5.65 @ ^ [X4: nat,Y4: nat] :
% 5.31/5.65 ( produc2626176000494625587at_nat
% 5.31/5.65 @ ^ [U2: nat,V3: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ X4 @ U2 ) @ ( times_times_nat @ Y4 @ V3 ) ) @ ( plus_plus_nat @ ( times_times_nat @ X4 @ V3 ) @ ( times_times_nat @ Y4 @ U2 ) ) ) ) )
% 5.31/5.65 @ times_times_int ) ).
% 5.31/5.65
% 5.31/5.65 % times_int.transfer
% 5.31/5.65 thf(fact_9313_minus__int_Otransfer,axiom,
% 5.31/5.65 ( bNF_re7408651293131936558nt_int @ pcr_int @ ( bNF_re7400052026677387805at_int @ pcr_int @ pcr_int )
% 5.31/5.65 @ ( produc27273713700761075at_nat
% 5.31/5.65 @ ^ [X4: nat,Y4: nat] :
% 5.31/5.65 ( produc2626176000494625587at_nat
% 5.31/5.65 @ ^ [U2: nat,V3: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X4 @ V3 ) @ ( plus_plus_nat @ Y4 @ U2 ) ) ) )
% 5.31/5.65 @ minus_minus_int ) ).
% 5.31/5.65
% 5.31/5.65 % minus_int.transfer
% 5.31/5.65 thf(fact_9314_zero__int_Otransfer,axiom,
% 5.31/5.65 pcr_int @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) @ zero_zero_int ).
% 5.31/5.65
% 5.31/5.65 % zero_int.transfer
% 5.31/5.65 thf(fact_9315_int__transfer,axiom,
% 5.31/5.65 ( bNF_re6830278522597306478at_int
% 5.31/5.65 @ ^ [Y5: nat,Z2: nat] : ( Y5 = Z2 )
% 5.31/5.65 @ pcr_int
% 5.31/5.65 @ ^ [N4: nat] : ( product_Pair_nat_nat @ N4 @ zero_zero_nat )
% 5.31/5.65 @ semiri1314217659103216013at_int ) ).
% 5.31/5.65
% 5.31/5.65 % int_transfer
% 5.31/5.65 thf(fact_9316_uminus__int_Otransfer,axiom,
% 5.31/5.65 ( bNF_re7400052026677387805at_int @ pcr_int @ pcr_int
% 5.31/5.65 @ ( produc2626176000494625587at_nat
% 5.31/5.65 @ ^ [X4: nat,Y4: nat] : ( product_Pair_nat_nat @ Y4 @ X4 ) )
% 5.31/5.65 @ uminus_uminus_int ) ).
% 5.31/5.65
% 5.31/5.65 % uminus_int.transfer
% 5.31/5.65 thf(fact_9317_one__int_Otransfer,axiom,
% 5.31/5.65 pcr_int @ ( product_Pair_nat_nat @ one_one_nat @ zero_zero_nat ) @ one_one_int ).
% 5.31/5.65
% 5.31/5.65 % one_int.transfer
% 5.31/5.65 thf(fact_9318_less__eq__int_Otransfer,axiom,
% 5.31/5.65 ( bNF_re717283939379294677_int_o @ pcr_int
% 5.31/5.65 @ ( bNF_re6644619430987730960nt_o_o @ pcr_int
% 5.31/5.65 @ ^ [Y5: $o,Z2: $o] : ( Y5 = Z2 ) )
% 5.31/5.65 @ ( produc8739625826339149834_nat_o
% 5.31/5.65 @ ^ [X4: nat,Y4: nat] :
% 5.31/5.65 ( produc6081775807080527818_nat_o
% 5.31/5.65 @ ^ [U2: nat,V3: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ X4 @ V3 ) @ ( plus_plus_nat @ U2 @ Y4 ) ) ) )
% 5.31/5.65 @ ord_less_eq_int ) ).
% 5.31/5.65
% 5.31/5.65 % less_eq_int.transfer
% 5.31/5.65 thf(fact_9319_plus__int_Otransfer,axiom,
% 5.31/5.65 ( bNF_re7408651293131936558nt_int @ pcr_int @ ( bNF_re7400052026677387805at_int @ pcr_int @ pcr_int )
% 5.31/5.65 @ ( produc27273713700761075at_nat
% 5.31/5.65 @ ^ [X4: nat,Y4: nat] :
% 5.31/5.65 ( produc2626176000494625587at_nat
% 5.31/5.65 @ ^ [U2: nat,V3: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X4 @ U2 ) @ ( plus_plus_nat @ Y4 @ V3 ) ) ) )
% 5.31/5.65 @ plus_plus_int ) ).
% 5.31/5.65
% 5.31/5.65 % plus_int.transfer
% 5.31/5.65 thf(fact_9320_times__int_Orsp,axiom,
% 5.31/5.65 ( bNF_re3099431351363272937at_nat @ intrel @ ( bNF_re2241393799969408733at_nat @ intrel @ intrel )
% 5.31/5.65 @ ( produc27273713700761075at_nat
% 5.31/5.65 @ ^ [X4: nat,Y4: nat] :
% 5.31/5.65 ( produc2626176000494625587at_nat
% 5.31/5.65 @ ^ [U2: nat,V3: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ X4 @ U2 ) @ ( times_times_nat @ Y4 @ V3 ) ) @ ( plus_plus_nat @ ( times_times_nat @ X4 @ V3 ) @ ( times_times_nat @ Y4 @ U2 ) ) ) ) )
% 5.31/5.65 @ ( produc27273713700761075at_nat
% 5.31/5.65 @ ^ [X4: nat,Y4: nat] :
% 5.31/5.65 ( produc2626176000494625587at_nat
% 5.31/5.65 @ ^ [U2: nat,V3: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ X4 @ U2 ) @ ( times_times_nat @ Y4 @ V3 ) ) @ ( plus_plus_nat @ ( times_times_nat @ X4 @ V3 ) @ ( times_times_nat @ Y4 @ U2 ) ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % times_int.rsp
% 5.31/5.65 thf(fact_9321_minus__int_Orsp,axiom,
% 5.31/5.65 ( bNF_re3099431351363272937at_nat @ intrel @ ( bNF_re2241393799969408733at_nat @ intrel @ intrel )
% 5.31/5.65 @ ( produc27273713700761075at_nat
% 5.31/5.65 @ ^ [X4: nat,Y4: nat] :
% 5.31/5.65 ( produc2626176000494625587at_nat
% 5.31/5.65 @ ^ [U2: nat,V3: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X4 @ V3 ) @ ( plus_plus_nat @ Y4 @ U2 ) ) ) )
% 5.31/5.65 @ ( produc27273713700761075at_nat
% 5.31/5.65 @ ^ [X4: nat,Y4: nat] :
% 5.31/5.65 ( produc2626176000494625587at_nat
% 5.31/5.65 @ ^ [U2: nat,V3: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X4 @ V3 ) @ ( plus_plus_nat @ Y4 @ U2 ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % minus_int.rsp
% 5.31/5.65 thf(fact_9322_intrel__iff,axiom,
% 5.31/5.65 ! [X: nat,Y: nat,U: nat,V2: nat] :
% 5.31/5.65 ( ( intrel @ ( product_Pair_nat_nat @ X @ Y ) @ ( product_Pair_nat_nat @ U @ V2 ) )
% 5.31/5.65 = ( ( plus_plus_nat @ X @ V2 )
% 5.31/5.65 = ( plus_plus_nat @ U @ Y ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % intrel_iff
% 5.31/5.65 thf(fact_9323_zero__int_Orsp,axiom,
% 5.31/5.65 intrel @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ).
% 5.31/5.65
% 5.31/5.65 % zero_int.rsp
% 5.31/5.65 thf(fact_9324_uminus__int_Orsp,axiom,
% 5.31/5.65 ( bNF_re2241393799969408733at_nat @ intrel @ intrel
% 5.31/5.65 @ ( produc2626176000494625587at_nat
% 5.31/5.65 @ ^ [X4: nat,Y4: nat] : ( product_Pair_nat_nat @ Y4 @ X4 ) )
% 5.31/5.65 @ ( produc2626176000494625587at_nat
% 5.31/5.65 @ ^ [X4: nat,Y4: nat] : ( product_Pair_nat_nat @ Y4 @ X4 ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % uminus_int.rsp
% 5.31/5.65 thf(fact_9325_one__int_Orsp,axiom,
% 5.31/5.65 intrel @ ( product_Pair_nat_nat @ one_one_nat @ zero_zero_nat ) @ ( product_Pair_nat_nat @ one_one_nat @ zero_zero_nat ) ).
% 5.31/5.65
% 5.31/5.65 % one_int.rsp
% 5.31/5.65 thf(fact_9326_less__eq__int_Orsp,axiom,
% 5.31/5.65 ( bNF_re4202695980764964119_nat_o @ intrel
% 5.31/5.65 @ ( bNF_re3666534408544137501at_o_o @ intrel
% 5.31/5.65 @ ^ [Y5: $o,Z2: $o] : ( Y5 = Z2 ) )
% 5.31/5.65 @ ( produc8739625826339149834_nat_o
% 5.31/5.65 @ ^ [X4: nat,Y4: nat] :
% 5.31/5.65 ( produc6081775807080527818_nat_o
% 5.31/5.65 @ ^ [U2: nat,V3: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ X4 @ V3 ) @ ( plus_plus_nat @ U2 @ Y4 ) ) ) )
% 5.31/5.65 @ ( produc8739625826339149834_nat_o
% 5.31/5.65 @ ^ [X4: nat,Y4: nat] :
% 5.31/5.65 ( produc6081775807080527818_nat_o
% 5.31/5.65 @ ^ [U2: nat,V3: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ X4 @ V3 ) @ ( plus_plus_nat @ U2 @ Y4 ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % less_eq_int.rsp
% 5.31/5.65 thf(fact_9327_plus__int_Orsp,axiom,
% 5.31/5.65 ( bNF_re3099431351363272937at_nat @ intrel @ ( bNF_re2241393799969408733at_nat @ intrel @ intrel )
% 5.31/5.65 @ ( produc27273713700761075at_nat
% 5.31/5.65 @ ^ [X4: nat,Y4: nat] :
% 5.31/5.65 ( produc2626176000494625587at_nat
% 5.31/5.65 @ ^ [U2: nat,V3: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X4 @ U2 ) @ ( plus_plus_nat @ Y4 @ V3 ) ) ) )
% 5.31/5.65 @ ( produc27273713700761075at_nat
% 5.31/5.65 @ ^ [X4: nat,Y4: nat] :
% 5.31/5.65 ( produc2626176000494625587at_nat
% 5.31/5.65 @ ^ [U2: nat,V3: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X4 @ U2 ) @ ( plus_plus_nat @ Y4 @ V3 ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % plus_int.rsp
% 5.31/5.65 thf(fact_9328_less__eq__enat__def,axiom,
% 5.31/5.65 ( ord_le2932123472753598470d_enat
% 5.31/5.65 = ( ^ [M6: extended_enat] :
% 5.31/5.65 ( extended_case_enat_o
% 5.31/5.65 @ ^ [N1: nat] :
% 5.31/5.65 ( extended_case_enat_o
% 5.31/5.65 @ ^ [M1: nat] : ( ord_less_eq_nat @ M1 @ N1 )
% 5.31/5.65 @ $false
% 5.31/5.65 @ M6 )
% 5.31/5.65 @ $true ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % less_eq_enat_def
% 5.31/5.65 thf(fact_9329_natLeq__Well__order,axiom,
% 5.31/5.65 order_2888998067076097458on_nat @ ( field_nat @ bNF_Ca8665028551170535155natLeq ) @ bNF_Ca8665028551170535155natLeq ).
% 5.31/5.65
% 5.31/5.65 % natLeq_Well_order
% 5.31/5.65 thf(fact_9330_natLeq__on__well__order__on,axiom,
% 5.31/5.65 ! [N: nat] :
% 5.31/5.65 ( order_2888998067076097458on_nat
% 5.31/5.65 @ ( collect_nat
% 5.31/5.65 @ ^ [X4: nat] : ( ord_less_nat @ X4 @ N ) )
% 5.31/5.65 @ ( collec3392354462482085612at_nat
% 5.31/5.65 @ ( produc6081775807080527818_nat_o
% 5.31/5.65 @ ^ [X4: nat,Y4: nat] :
% 5.31/5.65 ( ( ord_less_nat @ X4 @ N )
% 5.31/5.65 & ( ord_less_nat @ Y4 @ N )
% 5.31/5.65 & ( ord_less_eq_nat @ X4 @ Y4 ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % natLeq_on_well_order_on
% 5.31/5.65 thf(fact_9331_natLeq__on__Well__order,axiom,
% 5.31/5.65 ! [N: nat] :
% 5.31/5.65 ( order_2888998067076097458on_nat
% 5.31/5.65 @ ( field_nat
% 5.31/5.65 @ ( collec3392354462482085612at_nat
% 5.31/5.65 @ ( produc6081775807080527818_nat_o
% 5.31/5.65 @ ^ [X4: nat,Y4: nat] :
% 5.31/5.65 ( ( ord_less_nat @ X4 @ N )
% 5.31/5.65 & ( ord_less_nat @ Y4 @ N )
% 5.31/5.65 & ( ord_less_eq_nat @ X4 @ Y4 ) ) ) ) )
% 5.31/5.65 @ ( collec3392354462482085612at_nat
% 5.31/5.65 @ ( produc6081775807080527818_nat_o
% 5.31/5.65 @ ^ [X4: nat,Y4: nat] :
% 5.31/5.65 ( ( ord_less_nat @ X4 @ N )
% 5.31/5.65 & ( ord_less_nat @ Y4 @ N )
% 5.31/5.65 & ( ord_less_eq_nat @ X4 @ Y4 ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % natLeq_on_Well_order
% 5.31/5.65 thf(fact_9332_inj__on__char__of__nat,axiom,
% 5.31/5.65 inj_on_nat_char @ unique3096191561947761185of_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % inj_on_char_of_nat
% 5.31/5.65 thf(fact_9333_UNIV__char__of__nat,axiom,
% 5.31/5.65 ( top_top_set_char
% 5.31/5.65 = ( image_nat_char @ unique3096191561947761185of_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % UNIV_char_of_nat
% 5.31/5.65 thf(fact_9334_range__nat__of__char,axiom,
% 5.31/5.65 ( ( image_char_nat @ comm_s629917340098488124ar_nat @ top_top_set_char )
% 5.31/5.65 = ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % range_nat_of_char
% 5.31/5.65 thf(fact_9335_plus__rat__def,axiom,
% 5.31/5.65 ( plus_plus_rat
% 5.31/5.65 = ( map_fu4333342158222067775at_rat @ rep_Rat @ ( map_fu5673905371560938248nt_rat @ rep_Rat @ abs_Rat )
% 5.31/5.65 @ ^ [X4: product_prod_int_int,Y4: product_prod_int_int] : ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( product_fst_int_int @ X4 ) @ ( product_snd_int_int @ Y4 ) ) @ ( times_times_int @ ( product_fst_int_int @ Y4 ) @ ( product_snd_int_int @ X4 ) ) ) @ ( times_times_int @ ( product_snd_int_int @ X4 ) @ ( product_snd_int_int @ Y4 ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % plus_rat_def
% 5.31/5.65 thf(fact_9336_diff__rat,axiom,
% 5.31/5.65 ! [B: int,D: int,A: int,C2: int] :
% 5.31/5.65 ( ( B != zero_zero_int )
% 5.31/5.65 => ( ( D != zero_zero_int )
% 5.31/5.65 => ( ( minus_minus_rat @ ( fract @ A @ B ) @ ( fract @ C2 @ D ) )
% 5.31/5.65 = ( fract @ ( minus_minus_int @ ( times_times_int @ A @ D ) @ ( times_times_int @ C2 @ B ) ) @ ( times_times_int @ B @ D ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % diff_rat
% 5.31/5.65 thf(fact_9337_sgn__rat,axiom,
% 5.31/5.65 ! [A: int,B: int] :
% 5.31/5.65 ( ( sgn_sgn_rat @ ( fract @ A @ B ) )
% 5.31/5.65 = ( ring_1_of_int_rat @ ( times_times_int @ ( sgn_sgn_int @ A ) @ ( sgn_sgn_int @ B ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % sgn_rat
% 5.31/5.65 thf(fact_9338_mult__rat,axiom,
% 5.31/5.65 ! [A: int,B: int,C2: int,D: int] :
% 5.31/5.65 ( ( times_times_rat @ ( fract @ A @ B ) @ ( fract @ C2 @ D ) )
% 5.31/5.65 = ( fract @ ( times_times_int @ A @ C2 ) @ ( times_times_int @ B @ D ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % mult_rat
% 5.31/5.65 thf(fact_9339_divide__rat,axiom,
% 5.31/5.65 ! [A: int,B: int,C2: int,D: int] :
% 5.31/5.65 ( ( divide_divide_rat @ ( fract @ A @ B ) @ ( fract @ C2 @ D ) )
% 5.31/5.65 = ( fract @ ( times_times_int @ A @ D ) @ ( times_times_int @ B @ C2 ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % divide_rat
% 5.31/5.65 thf(fact_9340_less__rat,axiom,
% 5.31/5.65 ! [B: int,D: int,A: int,C2: int] :
% 5.31/5.65 ( ( B != zero_zero_int )
% 5.31/5.65 => ( ( D != zero_zero_int )
% 5.31/5.65 => ( ( ord_less_rat @ ( fract @ A @ B ) @ ( fract @ C2 @ D ) )
% 5.31/5.65 = ( ord_less_int @ ( times_times_int @ ( times_times_int @ A @ D ) @ ( times_times_int @ B @ D ) ) @ ( times_times_int @ ( times_times_int @ C2 @ B ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % less_rat
% 5.31/5.65 thf(fact_9341_add__rat,axiom,
% 5.31/5.65 ! [B: int,D: int,A: int,C2: int] :
% 5.31/5.65 ( ( B != zero_zero_int )
% 5.31/5.65 => ( ( D != zero_zero_int )
% 5.31/5.65 => ( ( plus_plus_rat @ ( fract @ A @ B ) @ ( fract @ C2 @ D ) )
% 5.31/5.65 = ( fract @ ( plus_plus_int @ ( times_times_int @ A @ D ) @ ( times_times_int @ C2 @ B ) ) @ ( times_times_int @ B @ D ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % add_rat
% 5.31/5.65 thf(fact_9342_le__rat,axiom,
% 5.31/5.65 ! [B: int,D: int,A: int,C2: int] :
% 5.31/5.65 ( ( B != zero_zero_int )
% 5.31/5.65 => ( ( D != zero_zero_int )
% 5.31/5.65 => ( ( ord_less_eq_rat @ ( fract @ A @ B ) @ ( fract @ C2 @ D ) )
% 5.31/5.65 = ( ord_less_eq_int @ ( times_times_int @ ( times_times_int @ A @ D ) @ ( times_times_int @ B @ D ) ) @ ( times_times_int @ ( times_times_int @ C2 @ B ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % le_rat
% 5.31/5.65 thf(fact_9343_mult__rat__cancel,axiom,
% 5.31/5.65 ! [C2: int,A: int,B: int] :
% 5.31/5.65 ( ( C2 != zero_zero_int )
% 5.31/5.65 => ( ( fract @ ( times_times_int @ C2 @ A ) @ ( times_times_int @ C2 @ B ) )
% 5.31/5.65 = ( fract @ A @ B ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % mult_rat_cancel
% 5.31/5.65 thf(fact_9344_eq__rat_I1_J,axiom,
% 5.31/5.65 ! [B: int,D: int,A: int,C2: int] :
% 5.31/5.65 ( ( B != zero_zero_int )
% 5.31/5.65 => ( ( D != zero_zero_int )
% 5.31/5.65 => ( ( ( fract @ A @ B )
% 5.31/5.65 = ( fract @ C2 @ D ) )
% 5.31/5.65 = ( ( times_times_int @ A @ D )
% 5.31/5.65 = ( times_times_int @ C2 @ B ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % eq_rat(1)
% 5.31/5.65 thf(fact_9345_positive__rat,axiom,
% 5.31/5.65 ! [A: int,B: int] :
% 5.31/5.65 ( ( positive @ ( fract @ A @ B ) )
% 5.31/5.65 = ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % positive_rat
% 5.31/5.65 thf(fact_9346_times__rat__def,axiom,
% 5.31/5.65 ( times_times_rat
% 5.31/5.65 = ( map_fu4333342158222067775at_rat @ rep_Rat @ ( map_fu5673905371560938248nt_rat @ rep_Rat @ abs_Rat )
% 5.31/5.65 @ ^ [X4: product_prod_int_int,Y4: product_prod_int_int] : ( product_Pair_int_int @ ( times_times_int @ ( product_fst_int_int @ X4 ) @ ( product_fst_int_int @ Y4 ) ) @ ( times_times_int @ ( product_snd_int_int @ X4 ) @ ( product_snd_int_int @ Y4 ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % times_rat_def
% 5.31/5.65 thf(fact_9347_integer__of__char__code,axiom,
% 5.31/5.65 ! [B0: $o,B1: $o,B22: $o,B32: $o,B42: $o,B52: $o,B62: $o,B72: $o] :
% 5.31/5.65 ( ( integer_of_char @ ( char2 @ B0 @ B1 @ B22 @ B32 @ B42 @ B52 @ B62 @ B72 ) )
% 5.31/5.65 = ( 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 ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % integer_of_char_code
% 5.31/5.65 thf(fact_9348_char_Osize_I2_J,axiom,
% 5.31/5.65 ! [X1: $o,X2: $o,X33: $o,X42: $o,X52: $o,X62: $o,X72: $o,X82: $o] :
% 5.31/5.65 ( ( size_size_char @ ( char2 @ X1 @ X2 @ X33 @ X42 @ X52 @ X62 @ X72 @ X82 ) )
% 5.31/5.65 = zero_zero_nat ) ).
% 5.31/5.65
% 5.31/5.65 % char.size(2)
% 5.31/5.65 thf(fact_9349_char_Osize__gen,axiom,
% 5.31/5.65 ! [X1: $o,X2: $o,X33: $o,X42: $o,X52: $o,X62: $o,X72: $o,X82: $o] :
% 5.31/5.65 ( ( size_char @ ( char2 @ X1 @ X2 @ X33 @ X42 @ X52 @ X62 @ X72 @ X82 ) )
% 5.31/5.65 = zero_zero_nat ) ).
% 5.31/5.65
% 5.31/5.65 % char.size_gen
% 5.31/5.65 thf(fact_9350_numeral__le__enat__iff,axiom,
% 5.31/5.65 ! [M2: num,N: nat] :
% 5.31/5.65 ( ( ord_le2932123472753598470d_enat @ ( numera1916890842035813515d_enat @ M2 ) @ ( extended_enat2 @ N ) )
% 5.31/5.65 = ( ord_less_eq_nat @ ( numeral_numeral_nat @ M2 ) @ N ) ) ).
% 5.31/5.65
% 5.31/5.65 % numeral_le_enat_iff
% 5.31/5.65 thf(fact_9351_idiff__enat__0__right,axiom,
% 5.31/5.65 ! [N: extended_enat] :
% 5.31/5.65 ( ( minus_3235023915231533773d_enat @ N @ ( extended_enat2 @ zero_zero_nat ) )
% 5.31/5.65 = N ) ).
% 5.31/5.65
% 5.31/5.65 % idiff_enat_0_right
% 5.31/5.65 thf(fact_9352_idiff__enat__0,axiom,
% 5.31/5.65 ! [N: extended_enat] :
% 5.31/5.65 ( ( minus_3235023915231533773d_enat @ ( extended_enat2 @ zero_zero_nat ) @ N )
% 5.31/5.65 = ( extended_enat2 @ zero_zero_nat ) ) ).
% 5.31/5.65
% 5.31/5.65 % idiff_enat_0
% 5.31/5.65 thf(fact_9353_times__enat__simps_I1_J,axiom,
% 5.31/5.65 ! [M2: nat,N: nat] :
% 5.31/5.65 ( ( times_7803423173614009249d_enat @ ( extended_enat2 @ M2 ) @ ( extended_enat2 @ N ) )
% 5.31/5.65 = ( extended_enat2 @ ( times_times_nat @ M2 @ N ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % times_enat_simps(1)
% 5.31/5.65 thf(fact_9354_enat__ord__simps_I1_J,axiom,
% 5.31/5.65 ! [M2: nat,N: nat] :
% 5.31/5.65 ( ( ord_le2932123472753598470d_enat @ ( extended_enat2 @ M2 ) @ ( extended_enat2 @ N ) )
% 5.31/5.65 = ( ord_less_eq_nat @ M2 @ N ) ) ).
% 5.31/5.65
% 5.31/5.65 % enat_ord_simps(1)
% 5.31/5.65 thf(fact_9355_Suc__ile__eq,axiom,
% 5.31/5.65 ! [M2: nat,N: extended_enat] :
% 5.31/5.65 ( ( ord_le2932123472753598470d_enat @ ( extended_enat2 @ ( suc @ M2 ) ) @ N )
% 5.31/5.65 = ( ord_le72135733267957522d_enat @ ( extended_enat2 @ M2 ) @ N ) ) ).
% 5.31/5.65
% 5.31/5.65 % Suc_ile_eq
% 5.31/5.65 thf(fact_9356_enat__0__iff_I2_J,axiom,
% 5.31/5.65 ! [X: nat] :
% 5.31/5.65 ( ( zero_z5237406670263579293d_enat
% 5.31/5.65 = ( extended_enat2 @ X ) )
% 5.31/5.65 = ( X = zero_zero_nat ) ) ).
% 5.31/5.65
% 5.31/5.65 % enat_0_iff(2)
% 5.31/5.65 thf(fact_9357_enat__0__iff_I1_J,axiom,
% 5.31/5.65 ! [X: nat] :
% 5.31/5.65 ( ( ( extended_enat2 @ X )
% 5.31/5.65 = zero_z5237406670263579293d_enat )
% 5.31/5.65 = ( X = zero_zero_nat ) ) ).
% 5.31/5.65
% 5.31/5.65 % enat_0_iff(1)
% 5.31/5.65 thf(fact_9358_zero__enat__def,axiom,
% 5.31/5.65 ( zero_z5237406670263579293d_enat
% 5.31/5.65 = ( extended_enat2 @ zero_zero_nat ) ) ).
% 5.31/5.65
% 5.31/5.65 % zero_enat_def
% 5.31/5.65 thf(fact_9359_iadd__le__enat__iff,axiom,
% 5.31/5.65 ! [X: extended_enat,Y: extended_enat,N: nat] :
% 5.31/5.65 ( ( ord_le2932123472753598470d_enat @ ( plus_p3455044024723400733d_enat @ X @ Y ) @ ( extended_enat2 @ N ) )
% 5.31/5.65 = ( ? [Y8: nat,X9: nat] :
% 5.31/5.65 ( ( X
% 5.31/5.65 = ( extended_enat2 @ X9 ) )
% 5.31/5.65 & ( Y
% 5.31/5.65 = ( extended_enat2 @ Y8 ) )
% 5.31/5.65 & ( ord_less_eq_nat @ ( plus_plus_nat @ X9 @ Y8 ) @ N ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % iadd_le_enat_iff
% 5.31/5.65 thf(fact_9360_elimnum,axiom,
% 5.31/5.65 ! [Info2: option4927543243414619207at_nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat] :
% 5.31/5.65 ( ( vEBT_invar_vebt @ ( vEBT_Node @ Info2 @ Deg @ TreeList2 @ Summary ) @ N )
% 5.31/5.65 => ( ( vEBT_VEBT_elim_dead @ ( vEBT_Node @ Info2 @ Deg @ TreeList2 @ Summary ) @ ( extended_enat2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.31/5.65 = ( vEBT_Node @ Info2 @ Deg @ TreeList2 @ Summary ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % elimnum
% 5.31/5.65 thf(fact_9361_VEBT__internal_Oelim__dead_Osimps_I3_J,axiom,
% 5.31/5.65 ! [Info2: option4927543243414619207at_nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,L: nat] :
% 5.31/5.65 ( ( vEBT_VEBT_elim_dead @ ( vEBT_Node @ Info2 @ Deg @ TreeList2 @ Summary ) @ ( extended_enat2 @ L ) )
% 5.31/5.65 = ( vEBT_Node @ Info2 @ Deg
% 5.31/5.65 @ ( take_VEBT_VEBT @ ( divide_divide_nat @ L @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.31/5.65 @ ( map_VE8901447254227204932T_VEBT
% 5.31/5.65 @ ^ [T2: vEBT_VEBT] : ( vEBT_VEBT_elim_dead @ T2 @ ( extended_enat2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.31/5.65 @ TreeList2 ) )
% 5.31/5.65 @ ( vEBT_VEBT_elim_dead @ Summary @ ( extended_enat2 @ ( divide_divide_nat @ L @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % VEBT_internal.elim_dead.simps(3)
% 5.31/5.65 thf(fact_9362_enat__0__less__mult__iff,axiom,
% 5.31/5.65 ! [M2: extended_enat,N: extended_enat] :
% 5.31/5.65 ( ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ ( times_7803423173614009249d_enat @ M2 @ N ) )
% 5.31/5.65 = ( ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ M2 )
% 5.31/5.65 & ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ N ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % enat_0_less_mult_iff
% 5.31/5.65 thf(fact_9363_imult__is__0,axiom,
% 5.31/5.65 ! [M2: extended_enat,N: extended_enat] :
% 5.31/5.65 ( ( ( times_7803423173614009249d_enat @ M2 @ N )
% 5.31/5.65 = zero_z5237406670263579293d_enat )
% 5.31/5.65 = ( ( M2 = zero_z5237406670263579293d_enat )
% 5.31/5.65 | ( N = zero_z5237406670263579293d_enat ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % imult_is_0
% 5.31/5.65 thf(fact_9364_VEBT__internal_Oelim__dead_Osimps_I1_J,axiom,
% 5.31/5.65 ! [A: $o,B: $o,Uu: extended_enat] :
% 5.31/5.65 ( ( vEBT_VEBT_elim_dead @ ( vEBT_Leaf @ A @ B ) @ Uu )
% 5.31/5.65 = ( vEBT_Leaf @ A @ B ) ) ).
% 5.31/5.65
% 5.31/5.65 % VEBT_internal.elim_dead.simps(1)
% 5.31/5.65 thf(fact_9365_VEBT__internal_Oelim__dead_Oelims,axiom,
% 5.31/5.65 ! [X: vEBT_VEBT,Xa2: extended_enat,Y: vEBT_VEBT] :
% 5.31/5.65 ( ( ( vEBT_VEBT_elim_dead @ X @ Xa2 )
% 5.31/5.65 = Y )
% 5.31/5.65 => ( ! [A3: $o,B3: $o] :
% 5.31/5.65 ( ( X
% 5.31/5.65 = ( vEBT_Leaf @ A3 @ B3 ) )
% 5.31/5.65 => ( Y
% 5.31/5.65 != ( vEBT_Leaf @ A3 @ B3 ) ) )
% 5.31/5.65 => ( ! [Info: option4927543243414619207at_nat,Deg2: nat,TreeList: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.31/5.65 ( ( X
% 5.31/5.65 = ( vEBT_Node @ Info @ Deg2 @ TreeList @ Summary2 ) )
% 5.31/5.65 => ( ( Xa2 = extend5688581933313929465d_enat )
% 5.31/5.65 => ( Y
% 5.31/5.65 != ( vEBT_Node @ Info @ Deg2
% 5.31/5.65 @ ( map_VE8901447254227204932T_VEBT
% 5.31/5.65 @ ^ [T2: vEBT_VEBT] : ( vEBT_VEBT_elim_dead @ T2 @ ( extended_enat2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.31/5.65 @ TreeList )
% 5.31/5.65 @ ( vEBT_VEBT_elim_dead @ Summary2 @ extend5688581933313929465d_enat ) ) ) ) )
% 5.31/5.65 => ~ ! [Info: option4927543243414619207at_nat,Deg2: nat,TreeList: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.31/5.65 ( ( X
% 5.31/5.65 = ( vEBT_Node @ Info @ Deg2 @ TreeList @ Summary2 ) )
% 5.31/5.65 => ! [L4: nat] :
% 5.31/5.65 ( ( Xa2
% 5.31/5.65 = ( extended_enat2 @ L4 ) )
% 5.31/5.65 => ( Y
% 5.31/5.65 != ( vEBT_Node @ Info @ Deg2
% 5.31/5.65 @ ( take_VEBT_VEBT @ ( divide_divide_nat @ L4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.31/5.65 @ ( map_VE8901447254227204932T_VEBT
% 5.31/5.65 @ ^ [T2: vEBT_VEBT] : ( vEBT_VEBT_elim_dead @ T2 @ ( extended_enat2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.31/5.65 @ TreeList ) )
% 5.31/5.65 @ ( vEBT_VEBT_elim_dead @ Summary2 @ ( extended_enat2 @ ( divide_divide_nat @ L4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % VEBT_internal.elim_dead.elims
% 5.31/5.65 thf(fact_9366_VEBT__internal_Oelim__dead_Osimps_I2_J,axiom,
% 5.31/5.65 ! [Info2: option4927543243414619207at_nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.31/5.65 ( ( vEBT_VEBT_elim_dead @ ( vEBT_Node @ Info2 @ Deg @ TreeList2 @ Summary ) @ extend5688581933313929465d_enat )
% 5.31/5.65 = ( vEBT_Node @ Info2 @ Deg
% 5.31/5.65 @ ( map_VE8901447254227204932T_VEBT
% 5.31/5.65 @ ^ [T2: vEBT_VEBT] : ( vEBT_VEBT_elim_dead @ T2 @ ( extended_enat2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.31/5.65 @ TreeList2 )
% 5.31/5.65 @ ( vEBT_VEBT_elim_dead @ Summary @ extend5688581933313929465d_enat ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % VEBT_internal.elim_dead.simps(2)
% 5.31/5.65 thf(fact_9367_elimcomplete,axiom,
% 5.31/5.65 ! [Info2: option4927543243414619207at_nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat] :
% 5.31/5.65 ( ( vEBT_invar_vebt @ ( vEBT_Node @ Info2 @ Deg @ TreeList2 @ Summary ) @ N )
% 5.31/5.65 => ( ( vEBT_VEBT_elim_dead @ ( vEBT_Node @ Info2 @ Deg @ TreeList2 @ Summary ) @ extend5688581933313929465d_enat )
% 5.31/5.65 = ( vEBT_Node @ Info2 @ Deg @ TreeList2 @ Summary ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % elimcomplete
% 5.31/5.65 thf(fact_9368_times__enat__simps_I2_J,axiom,
% 5.31/5.65 ( ( times_7803423173614009249d_enat @ extend5688581933313929465d_enat @ extend5688581933313929465d_enat )
% 5.31/5.65 = extend5688581933313929465d_enat ) ).
% 5.31/5.65
% 5.31/5.65 % times_enat_simps(2)
% 5.31/5.65 thf(fact_9369_times__enat__simps_I3_J,axiom,
% 5.31/5.65 ! [N: nat] :
% 5.31/5.65 ( ( ( N = zero_zero_nat )
% 5.31/5.65 => ( ( times_7803423173614009249d_enat @ extend5688581933313929465d_enat @ ( extended_enat2 @ N ) )
% 5.31/5.65 = zero_z5237406670263579293d_enat ) )
% 5.31/5.65 & ( ( N != zero_zero_nat )
% 5.31/5.65 => ( ( times_7803423173614009249d_enat @ extend5688581933313929465d_enat @ ( extended_enat2 @ N ) )
% 5.31/5.65 = extend5688581933313929465d_enat ) ) ) ).
% 5.31/5.65
% 5.31/5.65 % times_enat_simps(3)
% 5.31/5.65 thf(fact_9370_times__enat__simps_I4_J,axiom,
% 5.31/5.65 ! [M2: nat] :
% 5.31/5.65 ( ( ( M2 = zero_zero_nat )
% 5.31/5.65 => ( ( times_7803423173614009249d_enat @ ( extended_enat2 @ M2 ) @ extend5688581933313929465d_enat )
% 5.31/5.65 = zero_z5237406670263579293d_enat ) )
% 5.31/5.66 & ( ( M2 != zero_zero_nat )
% 5.31/5.66 => ( ( times_7803423173614009249d_enat @ ( extended_enat2 @ M2 ) @ extend5688581933313929465d_enat )
% 5.31/5.66 = extend5688581933313929465d_enat ) ) ) ).
% 5.31/5.66
% 5.31/5.66 % times_enat_simps(4)
% 5.31/5.66 thf(fact_9371_imult__is__infinity,axiom,
% 5.31/5.66 ! [A: extended_enat,B: extended_enat] :
% 5.31/5.66 ( ( ( times_7803423173614009249d_enat @ A @ B )
% 5.31/5.66 = extend5688581933313929465d_enat )
% 5.31/5.66 = ( ( ( A = extend5688581933313929465d_enat )
% 5.31/5.66 & ( B != zero_z5237406670263579293d_enat ) )
% 5.31/5.66 | ( ( B = extend5688581933313929465d_enat )
% 5.31/5.66 & ( A != zero_z5237406670263579293d_enat ) ) ) ) ).
% 5.31/5.66
% 5.31/5.66 % imult_is_infinity
% 5.31/5.66 thf(fact_9372_VEBT__internal_Oelim__dead_Ocases,axiom,
% 5.31/5.66 ! [X: produc7272778201969148633d_enat] :
% 5.31/5.66 ( ! [A3: $o,B3: $o,Uu2: extended_enat] :
% 5.31/5.66 ( X
% 5.31/5.66 != ( produc581526299967858633d_enat @ ( vEBT_Leaf @ A3 @ B3 ) @ Uu2 ) )
% 5.31/5.66 => ( ! [Info: option4927543243414619207at_nat,Deg2: nat,TreeList: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.31/5.66 ( X
% 5.31/5.66 != ( produc581526299967858633d_enat @ ( vEBT_Node @ Info @ Deg2 @ TreeList @ Summary2 ) @ extend5688581933313929465d_enat ) )
% 5.31/5.66 => ~ ! [Info: option4927543243414619207at_nat,Deg2: nat,TreeList: list_VEBT_VEBT,Summary2: vEBT_VEBT,L4: nat] :
% 5.31/5.66 ( X
% 5.31/5.66 != ( produc581526299967858633d_enat @ ( vEBT_Node @ Info @ Deg2 @ TreeList @ Summary2 ) @ ( extended_enat2 @ L4 ) ) ) ) ) ).
% 5.31/5.66
% 5.31/5.66 % VEBT_internal.elim_dead.cases
% 5.31/5.66 thf(fact_9373_imult__infinity,axiom,
% 5.31/5.66 ! [N: extended_enat] :
% 5.31/5.66 ( ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ N )
% 5.31/5.66 => ( ( times_7803423173614009249d_enat @ extend5688581933313929465d_enat @ N )
% 5.31/5.66 = extend5688581933313929465d_enat ) ) ).
% 5.31/5.66
% 5.31/5.66 % imult_infinity
% 5.31/5.66 thf(fact_9374_imult__infinity__right,axiom,
% 5.31/5.66 ! [N: extended_enat] :
% 5.31/5.66 ( ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ N )
% 5.31/5.66 => ( ( times_7803423173614009249d_enat @ N @ extend5688581933313929465d_enat )
% 5.31/5.66 = extend5688581933313929465d_enat ) ) ).
% 5.31/5.66
% 5.31/5.66 % imult_infinity_right
% 5.31/5.66 thf(fact_9375_times__enat__def,axiom,
% 5.31/5.66 ( times_7803423173614009249d_enat
% 5.31/5.66 = ( ^ [M6: extended_enat,N4: extended_enat] :
% 5.31/5.66 ( extend3600170679010898289d_enat
% 5.31/5.66 @ ^ [O: nat] :
% 5.31/5.66 ( extend3600170679010898289d_enat
% 5.31/5.66 @ ^ [P5: nat] : ( extended_enat2 @ ( times_times_nat @ O @ P5 ) )
% 5.31/5.66 @ ( if_Extended_enat @ ( O = zero_zero_nat ) @ zero_z5237406670263579293d_enat @ extend5688581933313929465d_enat )
% 5.31/5.66 @ N4 )
% 5.31/5.66 @ ( if_Extended_enat @ ( N4 = zero_z5237406670263579293d_enat ) @ zero_z5237406670263579293d_enat @ extend5688581933313929465d_enat )
% 5.31/5.66 @ M6 ) ) ) ).
% 5.31/5.66
% 5.31/5.66 % times_enat_def
% 5.31/5.66 thf(fact_9376_VEBT__internal_Oelim__dead_Opelims,axiom,
% 5.31/5.66 ! [X: vEBT_VEBT,Xa2: extended_enat,Y: vEBT_VEBT] :
% 5.31/5.66 ( ( ( vEBT_VEBT_elim_dead @ X @ Xa2 )
% 5.31/5.66 = Y )
% 5.31/5.66 => ( ( accp_P6183159247885693666d_enat @ vEBT_V312737461966249ad_rel @ ( produc581526299967858633d_enat @ X @ Xa2 ) )
% 5.31/5.66 => ( ! [A3: $o,B3: $o] :
% 5.31/5.66 ( ( X
% 5.31/5.66 = ( vEBT_Leaf @ A3 @ B3 ) )
% 5.31/5.66 => ( ( Y
% 5.31/5.66 = ( vEBT_Leaf @ A3 @ B3 ) )
% 5.31/5.66 => ~ ( accp_P6183159247885693666d_enat @ vEBT_V312737461966249ad_rel @ ( produc581526299967858633d_enat @ ( vEBT_Leaf @ A3 @ B3 ) @ Xa2 ) ) ) )
% 5.31/5.66 => ( ! [Info: option4927543243414619207at_nat,Deg2: nat,TreeList: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.31/5.66 ( ( X
% 5.31/5.66 = ( vEBT_Node @ Info @ Deg2 @ TreeList @ Summary2 ) )
% 5.31/5.66 => ( ( Xa2 = extend5688581933313929465d_enat )
% 5.31/5.66 => ( ( Y
% 5.31/5.66 = ( vEBT_Node @ Info @ Deg2
% 5.31/5.66 @ ( map_VE8901447254227204932T_VEBT
% 5.31/5.66 @ ^ [T2: vEBT_VEBT] : ( vEBT_VEBT_elim_dead @ T2 @ ( extended_enat2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.31/5.66 @ TreeList )
% 5.31/5.66 @ ( vEBT_VEBT_elim_dead @ Summary2 @ extend5688581933313929465d_enat ) ) )
% 5.31/5.66 => ~ ( accp_P6183159247885693666d_enat @ vEBT_V312737461966249ad_rel @ ( produc581526299967858633d_enat @ ( vEBT_Node @ Info @ Deg2 @ TreeList @ Summary2 ) @ extend5688581933313929465d_enat ) ) ) ) )
% 5.31/5.66 => ~ ! [Info: option4927543243414619207at_nat,Deg2: nat,TreeList: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.31/5.66 ( ( X
% 5.31/5.66 = ( vEBT_Node @ Info @ Deg2 @ TreeList @ Summary2 ) )
% 5.31/5.66 => ! [L4: nat] :
% 5.31/5.66 ( ( Xa2
% 5.31/5.66 = ( extended_enat2 @ L4 ) )
% 5.31/5.66 => ( ( Y
% 5.31/5.66 = ( vEBT_Node @ Info @ Deg2
% 5.31/5.66 @ ( take_VEBT_VEBT @ ( divide_divide_nat @ L4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.31/5.66 @ ( map_VE8901447254227204932T_VEBT
% 5.31/5.66 @ ^ [T2: vEBT_VEBT] : ( vEBT_VEBT_elim_dead @ T2 @ ( extended_enat2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.31/5.66 @ TreeList ) )
% 5.31/5.66 @ ( vEBT_VEBT_elim_dead @ Summary2 @ ( extended_enat2 @ ( divide_divide_nat @ L4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) )
% 5.31/5.66 => ~ ( accp_P6183159247885693666d_enat @ vEBT_V312737461966249ad_rel @ ( produc581526299967858633d_enat @ ( vEBT_Node @ Info @ Deg2 @ TreeList @ Summary2 ) @ ( extended_enat2 @ L4 ) ) ) ) ) ) ) ) ) ) ).
% 5.31/5.66
% 5.31/5.66 % VEBT_internal.elim_dead.pelims
% 5.31/5.66 thf(fact_9377_eSuc__def,axiom,
% 5.31/5.66 ( extended_eSuc
% 5.31/5.66 = ( extend3600170679010898289d_enat
% 5.31/5.66 @ ^ [N4: nat] : ( extended_enat2 @ ( suc @ N4 ) )
% 5.31/5.66 @ extend5688581933313929465d_enat ) ) ).
% 5.31/5.66
% 5.31/5.66 % eSuc_def
% 5.31/5.66 thf(fact_9378_binomial__def,axiom,
% 5.31/5.66 ( binomial
% 5.31/5.66 = ( ^ [N4: nat,K3: nat] :
% 5.31/5.66 ( finite_card_set_nat
% 5.31/5.66 @ ( collect_set_nat
% 5.31/5.66 @ ^ [K7: set_nat] :
% 5.31/5.66 ( ( member_set_nat @ K7 @ ( pow_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N4 ) ) )
% 5.31/5.66 & ( ( finite_card_nat @ K7 )
% 5.31/5.66 = K3 ) ) ) ) ) ) ).
% 5.31/5.66
% 5.31/5.66 % binomial_def
% 5.31/5.66 thf(fact_9379_enat__eSuc__iff,axiom,
% 5.31/5.66 ! [Y: nat,X: extended_enat] :
% 5.31/5.66 ( ( ( extended_enat2 @ Y )
% 5.31/5.66 = ( extended_eSuc @ X ) )
% 5.31/5.66 = ( ? [N4: nat] :
% 5.31/5.66 ( ( Y
% 5.31/5.66 = ( suc @ N4 ) )
% 5.31/5.66 & ( ( extended_enat2 @ N4 )
% 5.31/5.66 = X ) ) ) ) ).
% 5.31/5.66
% 5.31/5.66 % enat_eSuc_iff
% 5.31/5.66 thf(fact_9380_eSuc__enat__iff,axiom,
% 5.31/5.66 ! [X: extended_enat,Y: nat] :
% 5.31/5.66 ( ( ( extended_eSuc @ X )
% 5.31/5.66 = ( extended_enat2 @ Y ) )
% 5.31/5.66 = ( ? [N4: nat] :
% 5.31/5.66 ( ( Y
% 5.31/5.66 = ( suc @ N4 ) )
% 5.31/5.66 & ( X
% 5.31/5.66 = ( extended_enat2 @ N4 ) ) ) ) ) ).
% 5.31/5.66
% 5.31/5.66 % eSuc_enat_iff
% 5.31/5.66 thf(fact_9381_eSuc__enat,axiom,
% 5.31/5.66 ! [N: nat] :
% 5.31/5.66 ( ( extended_eSuc @ ( extended_enat2 @ N ) )
% 5.31/5.66 = ( extended_enat2 @ ( suc @ N ) ) ) ).
% 5.31/5.66
% 5.31/5.66 % eSuc_enat
% 5.31/5.66 thf(fact_9382_mult__eSuc__right,axiom,
% 5.31/5.66 ! [M2: extended_enat,N: extended_enat] :
% 5.31/5.66 ( ( times_7803423173614009249d_enat @ M2 @ ( extended_eSuc @ N ) )
% 5.31/5.66 = ( plus_p3455044024723400733d_enat @ M2 @ ( times_7803423173614009249d_enat @ M2 @ N ) ) ) ).
% 5.31/5.66
% 5.31/5.66 % mult_eSuc_right
% 5.31/5.66 thf(fact_9383_mult__eSuc,axiom,
% 5.31/5.66 ! [M2: extended_enat,N: extended_enat] :
% 5.31/5.66 ( ( times_7803423173614009249d_enat @ ( extended_eSuc @ M2 ) @ N )
% 5.31/5.66 = ( plus_p3455044024723400733d_enat @ N @ ( times_7803423173614009249d_enat @ M2 @ N ) ) ) ).
% 5.31/5.66
% 5.31/5.66 % mult_eSuc
% 5.31/5.66 thf(fact_9384_less__than__iff,axiom,
% 5.31/5.66 ! [X: nat,Y: nat] :
% 5.31/5.66 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ less_than )
% 5.31/5.66 = ( ord_less_nat @ X @ Y ) ) ).
% 5.31/5.66
% 5.31/5.66 % less_than_iff
% 5.31/5.66 thf(fact_9385_Real_Opositive_Orsp,axiom,
% 5.31/5.66 ( bNF_re728719798268516973at_o_o @ realrel
% 5.31/5.66 @ ^ [Y5: $o,Z2: $o] : ( Y5 = Z2 )
% 5.31/5.66 @ ^ [X7: nat > rat] :
% 5.31/5.66 ? [R: rat] :
% 5.31/5.66 ( ( ord_less_rat @ zero_zero_rat @ R )
% 5.31/5.66 & ? [K3: nat] :
% 5.31/5.66 ! [N4: nat] :
% 5.31/5.66 ( ( ord_less_eq_nat @ K3 @ N4 )
% 5.31/5.66 => ( ord_less_rat @ R @ ( X7 @ N4 ) ) ) )
% 5.31/5.66 @ ^ [X7: nat > rat] :
% 5.31/5.66 ? [R: rat] :
% 5.31/5.66 ( ( ord_less_rat @ zero_zero_rat @ R )
% 5.31/5.66 & ? [K3: nat] :
% 5.31/5.66 ! [N4: nat] :
% 5.31/5.66 ( ( ord_less_eq_nat @ K3 @ N4 )
% 5.31/5.66 => ( ord_less_rat @ R @ ( X7 @ N4 ) ) ) ) ) ).
% 5.31/5.66
% 5.31/5.66 % Real.positive.rsp
% 5.31/5.66 thf(fact_9386_Gcd__nat__set__eq__fold,axiom,
% 5.31/5.66 ! [Xs2: list_nat] :
% 5.31/5.66 ( ( gcd_Gcd_nat @ ( set_nat2 @ Xs2 ) )
% 5.31/5.66 = ( fold_nat_nat @ gcd_gcd_nat @ Xs2 @ zero_zero_nat ) ) ).
% 5.31/5.66
% 5.31/5.66 % Gcd_nat_set_eq_fold
% 5.31/5.66 thf(fact_9387_times__real_Orsp,axiom,
% 5.31/5.66 ( bNF_re1962705104956426057at_rat @ realrel @ ( bNF_re895249473297799549at_rat @ realrel @ realrel )
% 5.31/5.66 @ ^ [X7: nat > rat,Y9: nat > rat,N4: nat] : ( times_times_rat @ ( X7 @ N4 ) @ ( Y9 @ N4 ) )
% 5.31/5.66 @ ^ [X7: nat > rat,Y9: nat > rat,N4: nat] : ( times_times_rat @ ( X7 @ N4 ) @ ( Y9 @ N4 ) ) ) ).
% 5.31/5.66
% 5.31/5.66 % times_real.rsp
% 5.31/5.66 thf(fact_9388_Real_Opositive_Otransfer,axiom,
% 5.31/5.66 ( bNF_re4297313714947099218al_o_o @ pcr_real
% 5.31/5.66 @ ^ [Y5: $o,Z2: $o] : ( Y5 = Z2 )
% 5.31/5.66 @ ^ [X7: nat > rat] :
% 5.31/5.66 ? [R: rat] :
% 5.31/5.66 ( ( ord_less_rat @ zero_zero_rat @ R )
% 5.31/5.66 & ? [K3: nat] :
% 5.31/5.66 ! [N4: nat] :
% 5.31/5.66 ( ( ord_less_eq_nat @ K3 @ N4 )
% 5.31/5.66 => ( ord_less_rat @ R @ ( X7 @ N4 ) ) ) )
% 5.31/5.66 @ positive2 ) ).
% 5.31/5.66
% 5.31/5.66 % Real.positive.transfer
% 5.31/5.66 thf(fact_9389_Real_Opositive__mult,axiom,
% 5.31/5.66 ! [X: real,Y: real] :
% 5.31/5.66 ( ( positive2 @ X )
% 5.31/5.66 => ( ( positive2 @ Y )
% 5.31/5.66 => ( positive2 @ ( times_times_real @ X @ Y ) ) ) ) ).
% 5.31/5.66
% 5.31/5.66 % Real.positive_mult
% 5.31/5.66 thf(fact_9390_times__real_Otransfer,axiom,
% 5.31/5.66 ( bNF_re4695409256820837752l_real @ pcr_real @ ( bNF_re3023117138289059399t_real @ pcr_real @ pcr_real )
% 5.31/5.66 @ ^ [X7: nat > rat,Y9: nat > rat,N4: nat] : ( times_times_rat @ ( X7 @ N4 ) @ ( Y9 @ N4 ) )
% 5.31/5.66 @ times_times_real ) ).
% 5.31/5.66
% 5.31/5.66 % times_real.transfer
% 5.31/5.66 thf(fact_9391_Real_Opositive_Orep__eq,axiom,
% 5.31/5.66 ( positive2
% 5.31/5.66 = ( ^ [X4: real] :
% 5.31/5.66 ? [R: rat] :
% 5.31/5.66 ( ( ord_less_rat @ zero_zero_rat @ R )
% 5.31/5.66 & ? [K3: nat] :
% 5.31/5.66 ! [N4: nat] :
% 5.31/5.66 ( ( ord_less_eq_nat @ K3 @ N4 )
% 5.31/5.66 => ( ord_less_rat @ R @ ( rep_real @ X4 @ N4 ) ) ) ) ) ) ).
% 5.31/5.66
% 5.31/5.66 % Real.positive.rep_eq
% 5.31/5.66 thf(fact_9392_Real_Opositive__def,axiom,
% 5.31/5.66 ( positive2
% 5.31/5.66 = ( map_fu1856342031159181835at_o_o @ rep_real @ id_o
% 5.31/5.66 @ ^ [X7: nat > rat] :
% 5.31/5.66 ? [R: rat] :
% 5.31/5.66 ( ( ord_less_rat @ zero_zero_rat @ R )
% 5.31/5.66 & ? [K3: nat] :
% 5.31/5.66 ! [N4: nat] :
% 5.31/5.66 ( ( ord_less_eq_nat @ K3 @ N4 )
% 5.31/5.66 => ( ord_less_rat @ R @ ( X7 @ N4 ) ) ) ) ) ) ).
% 5.31/5.66
% 5.31/5.66 % Real.positive_def
% 5.31/5.66 thf(fact_9393_Real_Opositive_Oabs__eq,axiom,
% 5.31/5.66 ! [X: nat > rat] :
% 5.31/5.66 ( ( realrel @ X @ X )
% 5.31/5.66 => ( ( positive2 @ ( real2 @ X ) )
% 5.31/5.66 = ( ? [R: rat] :
% 5.31/5.66 ( ( ord_less_rat @ zero_zero_rat @ R )
% 5.31/5.66 & ? [K3: nat] :
% 5.31/5.66 ! [N4: nat] :
% 5.31/5.66 ( ( ord_less_eq_nat @ K3 @ N4 )
% 5.31/5.66 => ( ord_less_rat @ R @ ( X @ N4 ) ) ) ) ) ) ) ).
% 5.31/5.66
% 5.31/5.66 % Real.positive.abs_eq
% 5.31/5.66 thf(fact_9394_times__real_Oabs__eq,axiom,
% 5.31/5.66 ! [Xa2: nat > rat,X: nat > rat] :
% 5.31/5.66 ( ( realrel @ Xa2 @ Xa2 )
% 5.31/5.66 => ( ( realrel @ X @ X )
% 5.31/5.66 => ( ( times_times_real @ ( real2 @ Xa2 ) @ ( real2 @ X ) )
% 5.31/5.66 = ( real2
% 5.31/5.66 @ ^ [N4: nat] : ( times_times_rat @ ( Xa2 @ N4 ) @ ( X @ N4 ) ) ) ) ) ) ).
% 5.31/5.66
% 5.31/5.66 % times_real.abs_eq
% 5.31/5.66 thf(fact_9395_le__Real,axiom,
% 5.31/5.66 ! [X8: nat > rat,Y7: nat > rat] :
% 5.31/5.66 ( ( cauchy @ X8 )
% 5.31/5.66 => ( ( cauchy @ Y7 )
% 5.31/5.66 => ( ( ord_less_eq_real @ ( real2 @ X8 ) @ ( real2 @ Y7 ) )
% 5.31/5.66 = ( ! [R: rat] :
% 5.31/5.66 ( ( ord_less_rat @ zero_zero_rat @ R )
% 5.31/5.66 => ? [K3: nat] :
% 5.31/5.66 ! [N4: nat] :
% 5.31/5.66 ( ( ord_less_eq_nat @ K3 @ N4 )
% 5.31/5.66 => ( ord_less_eq_rat @ ( X8 @ N4 ) @ ( plus_plus_rat @ ( Y7 @ N4 ) @ R ) ) ) ) ) ) ) ) ).
% 5.31/5.66
% 5.31/5.66 % le_Real
% 5.31/5.66 thf(fact_9396_not__positive__Real,axiom,
% 5.31/5.66 ! [X8: nat > rat] :
% 5.31/5.66 ( ( cauchy @ X8 )
% 5.31/5.66 => ( ( ~ ( positive2 @ ( real2 @ X8 ) ) )
% 5.31/5.66 = ( ! [R: rat] :
% 5.31/5.66 ( ( ord_less_rat @ zero_zero_rat @ R )
% 5.31/5.66 => ? [K3: nat] :
% 5.31/5.66 ! [N4: nat] :
% 5.31/5.66 ( ( ord_less_eq_nat @ K3 @ N4 )
% 5.31/5.66 => ( ord_less_eq_rat @ ( X8 @ N4 ) @ R ) ) ) ) ) ) ).
% 5.31/5.66
% 5.31/5.66 % not_positive_Real
% 5.31/5.66 thf(fact_9397_cauchy__mult,axiom,
% 5.31/5.66 ! [X8: nat > rat,Y7: nat > rat] :
% 5.31/5.66 ( ( cauchy @ X8 )
% 5.31/5.66 => ( ( cauchy @ Y7 )
% 5.31/5.66 => ( cauchy
% 5.31/5.66 @ ^ [N4: nat] : ( times_times_rat @ ( X8 @ N4 ) @ ( Y7 @ N4 ) ) ) ) ) ).
% 5.31/5.66
% 5.31/5.66 % cauchy_mult
% 5.31/5.66 thf(fact_9398_mult__Real,axiom,
% 5.31/5.66 ! [X8: nat > rat,Y7: nat > rat] :
% 5.31/5.66 ( ( cauchy @ X8 )
% 5.31/5.66 => ( ( cauchy @ Y7 )
% 5.31/5.66 => ( ( times_times_real @ ( real2 @ X8 ) @ ( real2 @ Y7 ) )
% 5.31/5.66 = ( real2
% 5.31/5.66 @ ^ [N4: nat] : ( times_times_rat @ ( X8 @ N4 ) @ ( Y7 @ N4 ) ) ) ) ) ) ).
% 5.31/5.66
% 5.31/5.66 % mult_Real
% 5.31/5.66 thf(fact_9399_cauchyD,axiom,
% 5.31/5.66 ! [X8: nat > rat,R3: rat] :
% 5.31/5.66 ( ( cauchy @ X8 )
% 5.31/5.66 => ( ( ord_less_rat @ zero_zero_rat @ R3 )
% 5.31/5.66 => ? [K: nat] :
% 5.31/5.66 ! [M3: nat] :
% 5.31/5.66 ( ( ord_less_eq_nat @ K @ M3 )
% 5.31/5.66 => ! [N8: nat] :
% 5.31/5.66 ( ( ord_less_eq_nat @ K @ N8 )
% 5.31/5.66 => ( ord_less_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( X8 @ M3 ) @ ( X8 @ N8 ) ) ) @ R3 ) ) ) ) ) ).
% 5.31/5.66
% 5.31/5.66 % cauchyD
% 5.31/5.66 thf(fact_9400_cauchyI,axiom,
% 5.31/5.66 ! [X8: nat > rat] :
% 5.31/5.66 ( ! [R4: rat] :
% 5.31/5.66 ( ( ord_less_rat @ zero_zero_rat @ R4 )
% 5.31/5.66 => ? [K4: nat] :
% 5.31/5.66 ! [M: nat] :
% 5.31/5.66 ( ( ord_less_eq_nat @ K4 @ M )
% 5.31/5.66 => ! [N3: nat] :
% 5.31/5.66 ( ( ord_less_eq_nat @ K4 @ N3 )
% 5.31/5.66 => ( ord_less_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( X8 @ M ) @ ( X8 @ N3 ) ) ) @ R4 ) ) ) )
% 5.31/5.66 => ( cauchy @ X8 ) ) ).
% 5.31/5.66
% 5.31/5.66 % cauchyI
% 5.31/5.66 thf(fact_9401_cauchy__def,axiom,
% 5.31/5.66 ( cauchy
% 5.31/5.66 = ( ^ [X7: nat > rat] :
% 5.31/5.66 ! [R: rat] :
% 5.31/5.66 ( ( ord_less_rat @ zero_zero_rat @ R )
% 5.31/5.66 => ? [K3: nat] :
% 5.31/5.66 ! [M6: nat] :
% 5.31/5.66 ( ( ord_less_eq_nat @ K3 @ M6 )
% 5.31/5.66 => ! [N4: nat] :
% 5.31/5.66 ( ( ord_less_eq_nat @ K3 @ N4 )
% 5.31/5.66 => ( ord_less_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( X7 @ M6 ) @ ( X7 @ N4 ) ) ) @ R ) ) ) ) ) ) ).
% 5.31/5.66
% 5.31/5.66 % cauchy_def
% 5.31/5.66 thf(fact_9402_positive__Real,axiom,
% 5.31/5.66 ! [X8: nat > rat] :
% 5.31/5.66 ( ( cauchy @ X8 )
% 5.31/5.66 => ( ( positive2 @ ( real2 @ X8 ) )
% 5.31/5.66 = ( ? [R: rat] :
% 5.31/5.66 ( ( ord_less_rat @ zero_zero_rat @ R )
% 5.31/5.66 & ? [K3: nat] :
% 5.31/5.66 ! [N4: nat] :
% 5.31/5.66 ( ( ord_less_eq_nat @ K3 @ N4 )
% 5.31/5.66 => ( ord_less_rat @ R @ ( X8 @ N4 ) ) ) ) ) ) ) ).
% 5.31/5.66
% 5.31/5.66 % positive_Real
% 5.31/5.66 thf(fact_9403_cauchy__not__vanishes__cases,axiom,
% 5.31/5.66 ! [X8: nat > rat] :
% 5.31/5.66 ( ( cauchy @ X8 )
% 5.31/5.66 => ( ~ ( vanishes @ X8 )
% 5.31/5.66 => ? [B3: rat] :
% 5.31/5.66 ( ( ord_less_rat @ zero_zero_rat @ B3 )
% 5.31/5.66 & ? [K: nat] :
% 5.31/5.66 ( ! [N8: nat] :
% 5.31/5.66 ( ( ord_less_eq_nat @ K @ N8 )
% 5.31/5.66 => ( ord_less_rat @ B3 @ ( uminus_uminus_rat @ ( X8 @ N8 ) ) ) )
% 5.31/5.66 | ! [N8: nat] :
% 5.31/5.66 ( ( ord_less_eq_nat @ K @ N8 )
% 5.31/5.66 => ( ord_less_rat @ B3 @ ( X8 @ N8 ) ) ) ) ) ) ) ).
% 5.31/5.66
% 5.31/5.66 % cauchy_not_vanishes_cases
% 5.31/5.66 thf(fact_9404_cauchy__not__vanishes,axiom,
% 5.31/5.66 ! [X8: nat > rat] :
% 5.31/5.66 ( ( cauchy @ X8 )
% 5.31/5.66 => ( ~ ( vanishes @ X8 )
% 5.31/5.66 => ? [B3: rat] :
% 5.31/5.66 ( ( ord_less_rat @ zero_zero_rat @ B3 )
% 5.31/5.66 & ? [K: nat] :
% 5.31/5.66 ! [N8: nat] :
% 5.31/5.66 ( ( ord_less_eq_nat @ K @ N8 )
% 5.31/5.66 => ( ord_less_rat @ B3 @ ( abs_abs_rat @ ( X8 @ N8 ) ) ) ) ) ) ) ).
% 5.31/5.66
% 5.31/5.66 % cauchy_not_vanishes
% 5.31/5.66 thf(fact_9405_vanishesD,axiom,
% 5.31/5.66 ! [X8: nat > rat,R3: rat] :
% 5.31/5.66 ( ( vanishes @ X8 )
% 5.31/5.66 => ( ( ord_less_rat @ zero_zero_rat @ R3 )
% 5.31/5.66 => ? [K: nat] :
% 5.31/5.66 ! [N8: nat] :
% 5.31/5.66 ( ( ord_less_eq_nat @ K @ N8 )
% 5.31/5.66 => ( ord_less_rat @ ( abs_abs_rat @ ( X8 @ N8 ) ) @ R3 ) ) ) ) ).
% 5.31/5.66
% 5.31/5.66 % vanishesD
% 5.31/5.66 thf(fact_9406_vanishesI,axiom,
% 5.31/5.66 ! [X8: nat > rat] :
% 5.31/5.66 ( ! [R4: rat] :
% 5.31/5.66 ( ( ord_less_rat @ zero_zero_rat @ R4 )
% 5.31/5.66 => ? [K4: nat] :
% 5.31/5.66 ! [N3: nat] :
% 5.31/5.66 ( ( ord_less_eq_nat @ K4 @ N3 )
% 5.31/5.66 => ( ord_less_rat @ ( abs_abs_rat @ ( X8 @ N3 ) ) @ R4 ) ) )
% 5.31/5.66 => ( vanishes @ X8 ) ) ).
% 5.31/5.66
% 5.31/5.66 % vanishesI
% 5.31/5.66 thf(fact_9407_vanishes__def,axiom,
% 5.31/5.66 ( vanishes
% 5.31/5.66 = ( ^ [X7: nat > rat] :
% 5.31/5.66 ! [R: rat] :
% 5.31/5.66 ( ( ord_less_rat @ zero_zero_rat @ R )
% 5.31/5.66 => ? [K3: nat] :
% 5.31/5.66 ! [N4: nat] :
% 5.31/5.66 ( ( ord_less_eq_nat @ K3 @ N4 )
% 5.31/5.66 => ( ord_less_rat @ ( abs_abs_rat @ ( X7 @ N4 ) ) @ R ) ) ) ) ) ).
% 5.31/5.66
% 5.31/5.66 % vanishes_def
% 5.31/5.66 thf(fact_9408_vanishes__mult__bounded,axiom,
% 5.31/5.66 ! [X8: nat > rat,Y7: nat > rat] :
% 5.31/5.66 ( ? [A6: rat] :
% 5.31/5.66 ( ( ord_less_rat @ zero_zero_rat @ A6 )
% 5.31/5.66 & ! [N3: nat] : ( ord_less_rat @ ( abs_abs_rat @ ( X8 @ N3 ) ) @ A6 ) )
% 5.31/5.66 => ( ( vanishes @ Y7 )
% 5.31/5.66 => ( vanishes
% 5.31/5.66 @ ^ [N4: nat] : ( times_times_rat @ ( X8 @ N4 ) @ ( Y7 @ N4 ) ) ) ) ) ).
% 5.31/5.66
% 5.31/5.66 % vanishes_mult_bounded
% 5.31/5.66 thf(fact_9409_surj__int__decode,axiom,
% 5.31/5.66 ( ( image_nat_int @ nat_int_decode @ top_top_set_nat )
% 5.31/5.66 = top_top_set_int ) ).
% 5.31/5.66
% 5.31/5.66 % surj_int_decode
% 5.31/5.66 thf(fact_9410_bij__int__decode,axiom,
% 5.31/5.66 bij_betw_nat_int @ nat_int_decode @ top_top_set_nat @ top_top_set_int ).
% 5.31/5.66
% 5.31/5.66 % bij_int_decode
% 5.31/5.66 thf(fact_9411_inj__int__decode,axiom,
% 5.31/5.66 ! [A4: set_nat] : ( inj_on_nat_int @ nat_int_decode @ A4 ) ).
% 5.31/5.66
% 5.31/5.66 % inj_int_decode
% 5.31/5.66 thf(fact_9412_int__decode__eq,axiom,
% 5.31/5.66 ! [X: nat,Y: nat] :
% 5.31/5.66 ( ( ( nat_int_decode @ X )
% 5.31/5.66 = ( nat_int_decode @ Y ) )
% 5.31/5.66 = ( X = Y ) ) ).
% 5.31/5.66
% 5.31/5.66 % int_decode_eq
% 5.31/5.66 thf(fact_9413_nat__to__rat__surj__def,axiom,
% 5.31/5.66 ( nat_to_rat_surj
% 5.31/5.66 = ( ^ [N4: nat] :
% 5.31/5.66 ( produc6207742614233964070at_rat
% 5.31/5.66 @ ^ [A5: nat,B4: nat] : ( fract @ ( nat_int_decode @ A5 ) @ ( nat_int_decode @ B4 ) )
% 5.31/5.66 @ ( nat_prod_decode @ N4 ) ) ) ) ).
% 5.31/5.66
% 5.31/5.66 % nat_to_rat_surj_def
% 5.31/5.66 thf(fact_9414_bij__int__encode,axiom,
% 5.31/5.66 bij_betw_int_nat @ nat_int_encode @ top_top_set_int @ top_top_set_nat ).
% 5.31/5.66
% 5.31/5.66 % bij_int_encode
% 5.31/5.66 thf(fact_9415_int__encode__inverse,axiom,
% 5.31/5.66 ! [X: int] :
% 5.31/5.66 ( ( nat_int_decode @ ( nat_int_encode @ X ) )
% 5.31/5.66 = X ) ).
% 5.31/5.66
% 5.31/5.66 % int_encode_inverse
% 5.31/5.66 thf(fact_9416_int__decode__inverse,axiom,
% 5.31/5.66 ! [N: nat] :
% 5.31/5.66 ( ( nat_int_encode @ ( nat_int_decode @ N ) )
% 5.31/5.66 = N ) ).
% 5.31/5.66
% 5.31/5.66 % int_decode_inverse
% 5.31/5.66 thf(fact_9417_inj__int__encode,axiom,
% 5.31/5.66 ! [A4: set_int] : ( inj_on_int_nat @ nat_int_encode @ A4 ) ).
% 5.31/5.66
% 5.31/5.66 % inj_int_encode
% 5.31/5.66 thf(fact_9418_int__encode__eq,axiom,
% 5.31/5.66 ! [X: int,Y: int] :
% 5.31/5.66 ( ( ( nat_int_encode @ X )
% 5.31/5.66 = ( nat_int_encode @ Y ) )
% 5.31/5.66 = ( X = Y ) ) ).
% 5.31/5.66
% 5.31/5.66 % int_encode_eq
% 5.31/5.66 thf(fact_9419_surj__int__encode,axiom,
% 5.31/5.66 ( ( image_int_nat @ nat_int_encode @ top_top_set_int )
% 5.31/5.66 = top_top_set_nat ) ).
% 5.31/5.66
% 5.31/5.66 % surj_int_encode
% 5.31/5.66 thf(fact_9420_linear__scale__real,axiom,
% 5.31/5.66 ! [F2: real > real,R3: real,B: real] :
% 5.31/5.66 ( ( real_V4572627801940501177l_real @ F2 )
% 5.31/5.66 => ( ( F2 @ ( times_times_real @ R3 @ B ) )
% 5.31/5.66 = ( times_times_real @ R3 @ ( F2 @ B ) ) ) ) ).
% 5.31/5.66
% 5.31/5.66 % linear_scale_real
% 5.31/5.66 thf(fact_9421_real__linearD,axiom,
% 5.31/5.66 ! [F2: real > real] :
% 5.31/5.66 ( ( real_V4572627801940501177l_real @ F2 )
% 5.31/5.66 => ~ ! [C: real] :
% 5.31/5.66 ( F2
% 5.31/5.66 != ( times_times_real @ C ) ) ) ).
% 5.31/5.66
% 5.31/5.66 % real_linearD
% 5.31/5.66 thf(fact_9422_natLeq__Partial__order,axiom,
% 5.31/5.66 order_5251275573222108571on_nat @ ( field_nat @ bNF_Ca8665028551170535155natLeq ) @ bNF_Ca8665028551170535155natLeq ).
% 5.31/5.66
% 5.31/5.66 % natLeq_Partial_order
% 5.31/5.66 thf(fact_9423_natLeq__Preorder,axiom,
% 5.31/5.66 order_4861654808422542329on_nat @ ( field_nat @ bNF_Ca8665028551170535155natLeq ) @ bNF_Ca8665028551170535155natLeq ).
% 5.31/5.66
% 5.31/5.66 % natLeq_Preorder
% 5.31/5.66 thf(fact_9424_less__eq__int__def,axiom,
% 5.31/5.66 ( ord_less_eq_int
% 5.31/5.66 = ( map_fu434086159418415080_int_o @ rep_Integ @ ( map_fu4826362097070443709at_o_o @ rep_Integ @ id_o )
% 5.31/5.66 @ ( produc8739625826339149834_nat_o
% 5.31/5.66 @ ^ [X4: nat,Y4: nat] :
% 5.31/5.66 ( produc6081775807080527818_nat_o
% 5.31/5.66 @ ^ [U2: nat,V3: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ X4 @ V3 ) @ ( plus_plus_nat @ U2 @ Y4 ) ) ) ) ) ) ).
% 5.31/5.66
% 5.31/5.66 % less_eq_int_def
% 5.31/5.66 thf(fact_9425_int__encode__def,axiom,
% 5.31/5.66 ( nat_int_encode
% 5.31/5.66 = ( ^ [I: int] : ( nat_sum_encode @ ( if_Sum_sum_nat_nat @ ( ord_less_eq_int @ zero_zero_int @ I ) @ ( sum_Inl_nat_nat @ ( nat2 @ I ) ) @ ( sum_Inr_nat_nat @ ( nat2 @ ( minus_minus_int @ ( uminus_uminus_int @ I ) @ one_one_int ) ) ) ) ) ) ) ).
% 5.31/5.66
% 5.31/5.66 % int_encode_def
% 5.31/5.66 thf(fact_9426_surj__sum__encode,axiom,
% 5.31/5.66 ( ( image_1320371278474632150at_nat @ nat_sum_encode @ top_to6661820994512907621at_nat )
% 5.31/5.66 = top_top_set_nat ) ).
% 5.31/5.66
% 5.31/5.66 % surj_sum_encode
% 5.31/5.66 thf(fact_9427_inj__sum__encode,axiom,
% 5.31/5.66 ! [A4: set_Sum_sum_nat_nat] : ( inj_on6343450744447823682at_nat @ nat_sum_encode @ A4 ) ).
% 5.31/5.66
% 5.31/5.66 % inj_sum_encode
% 5.31/5.66 thf(fact_9428_sum__encode__eq,axiom,
% 5.31/5.66 ! [X: sum_sum_nat_nat,Y: sum_sum_nat_nat] :
% 5.31/5.66 ( ( ( nat_sum_encode @ X )
% 5.31/5.66 = ( nat_sum_encode @ Y ) )
% 5.31/5.66 = ( X = Y ) ) ).
% 5.31/5.66
% 5.31/5.66 % sum_encode_eq
% 5.31/5.66 thf(fact_9429_bij__sum__encode,axiom,
% 5.31/5.66 bij_be5432664580149595207at_nat @ nat_sum_encode @ top_to6661820994512907621at_nat @ top_top_set_nat ).
% 5.31/5.66
% 5.31/5.66 % bij_sum_encode
% 5.31/5.66 thf(fact_9430_le__sum__encode__Inl,axiom,
% 5.31/5.66 ! [X: nat,Y: nat] :
% 5.31/5.66 ( ( ord_less_eq_nat @ X @ Y )
% 5.31/5.66 => ( ord_less_eq_nat @ X @ ( nat_sum_encode @ ( sum_Inl_nat_nat @ Y ) ) ) ) ).
% 5.31/5.66
% 5.31/5.66 % le_sum_encode_Inl
% 5.31/5.66 thf(fact_9431_le__sum__encode__Inr,axiom,
% 5.31/5.66 ! [X: nat,Y: nat] :
% 5.31/5.66 ( ( ord_less_eq_nat @ X @ Y )
% 5.31/5.66 => ( ord_less_eq_nat @ X @ ( nat_sum_encode @ ( sum_Inr_nat_nat @ Y ) ) ) ) ).
% 5.31/5.66
% 5.31/5.66 % le_sum_encode_Inr
% 5.31/5.66 thf(fact_9432_sum__decode__def,axiom,
% 5.31/5.66 ( nat_sum_decode
% 5.31/5.66 = ( ^ [N4: nat] : ( if_Sum_sum_nat_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) @ ( sum_Inl_nat_nat @ ( divide_divide_nat @ N4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( sum_Inr_nat_nat @ ( divide_divide_nat @ N4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.31/5.66
% 5.31/5.66 % sum_decode_def
% 5.31/5.66 thf(fact_9433_sum__encode__inverse,axiom,
% 5.31/5.66 ! [X: sum_sum_nat_nat] :
% 5.31/5.66 ( ( nat_sum_decode @ ( nat_sum_encode @ X ) )
% 5.31/5.66 = X ) ).
% 5.31/5.66
% 5.31/5.66 % sum_encode_inverse
% 5.31/5.66 thf(fact_9434_sum__decode__inverse,axiom,
% 5.31/5.66 ! [N: nat] :
% 5.31/5.66 ( ( nat_sum_encode @ ( nat_sum_decode @ N ) )
% 5.31/5.66 = N ) ).
% 5.31/5.66
% 5.31/5.66 % sum_decode_inverse
% 5.31/5.66 thf(fact_9435_bij__sum__decode,axiom,
% 5.31/5.66 bij_be4790990086886966983at_nat @ nat_sum_decode @ top_top_set_nat @ top_to6661820994512907621at_nat ).
% 5.31/5.66
% 5.31/5.66 % bij_sum_decode
% 5.31/5.66 thf(fact_9436_sum__decode__eq,axiom,
% 5.31/5.66 ! [X: nat,Y: nat] :
% 5.31/5.66 ( ( ( nat_sum_decode @ X )
% 5.31/5.66 = ( nat_sum_decode @ Y ) )
% 5.31/5.66 = ( X = Y ) ) ).
% 5.31/5.66
% 5.31/5.66 % sum_decode_eq
% 5.31/5.66 thf(fact_9437_inj__sum__decode,axiom,
% 5.31/5.66 ! [A4: set_nat] : ( inj_on5701776251185195458at_nat @ nat_sum_decode @ A4 ) ).
% 5.31/5.66
% 5.31/5.66 % inj_sum_decode
% 5.31/5.66 thf(fact_9438_surj__sum__decode,axiom,
% 5.31/5.66 ( ( image_678696785212003926at_nat @ nat_sum_decode @ top_top_set_nat )
% 5.31/5.66 = top_to6661820994512907621at_nat ) ).
% 5.31/5.66
% 5.31/5.66 % surj_sum_decode
% 5.31/5.66 thf(fact_9439_nth__item_Opinduct,axiom,
% 5.31/5.66 ! [A0: nat,P2: nat > $o] :
% 5.31/5.66 ( ( accp_nat @ nth_item_rel @ A0 )
% 5.31/5.66 => ( ( ( accp_nat @ nth_item_rel @ zero_zero_nat )
% 5.31/5.66 => ( P2 @ zero_zero_nat ) )
% 5.31/5.66 => ( ! [N3: nat] :
% 5.31/5.66 ( ( accp_nat @ nth_item_rel @ ( suc @ N3 ) )
% 5.31/5.66 => ( ! [A6: nat,Aa: nat] :
% 5.31/5.66 ( ( ( nat_sum_decode @ N3 )
% 5.31/5.66 = ( sum_Inl_nat_nat @ A6 ) )
% 5.31/5.66 => ( ( ( nat_sum_decode @ A6 )
% 5.31/5.66 = ( sum_Inl_nat_nat @ Aa ) )
% 5.31/5.66 => ( P2 @ Aa ) ) )
% 5.31/5.66 => ( ! [A6: nat,B6: nat] :
% 5.31/5.66 ( ( ( nat_sum_decode @ N3 )
% 5.31/5.66 = ( sum_Inl_nat_nat @ A6 ) )
% 5.31/5.66 => ( ( ( nat_sum_decode @ A6 )
% 5.31/5.66 = ( sum_Inr_nat_nat @ B6 ) )
% 5.31/5.66 => ( P2 @ B6 ) ) )
% 5.31/5.66 => ( ! [B6: nat,Ba: nat,X5: nat,Y6: nat] :
% 5.31/5.66 ( ( ( nat_sum_decode @ N3 )
% 5.31/5.66 = ( sum_Inr_nat_nat @ B6 ) )
% 5.31/5.66 => ( ( ( nat_sum_decode @ B6 )
% 5.31/5.66 = ( sum_Inr_nat_nat @ Ba ) )
% 5.31/5.66 => ( ( ( product_Pair_nat_nat @ X5 @ Y6 )
% 5.31/5.66 = ( nat_prod_decode @ Ba ) )
% 5.31/5.66 => ( P2 @ X5 ) ) ) )
% 5.31/5.66 => ( ! [B6: nat,Ba: nat,X5: nat,Y6: nat] :
% 5.31/5.66 ( ( ( nat_sum_decode @ N3 )
% 5.31/5.66 = ( sum_Inr_nat_nat @ B6 ) )
% 5.31/5.66 => ( ( ( nat_sum_decode @ B6 )
% 5.31/5.66 = ( sum_Inr_nat_nat @ Ba ) )
% 5.31/5.66 => ( ( ( product_Pair_nat_nat @ X5 @ Y6 )
% 5.31/5.66 = ( nat_prod_decode @ Ba ) )
% 5.31/5.66 => ( P2 @ Y6 ) ) ) )
% 5.31/5.66 => ( P2 @ ( suc @ N3 ) ) ) ) ) ) )
% 5.31/5.66 => ( P2 @ A0 ) ) ) ) ).
% 5.31/5.66
% 5.31/5.66 % nth_item.pinduct
% 5.31/5.66 thf(fact_9440_int__decode__def,axiom,
% 5.31/5.66 ( nat_int_decode
% 5.31/5.66 = ( ^ [N4: nat] :
% 5.31/5.66 ( sum_ca7763040182479039464nt_nat @ semiri1314217659103216013at_int
% 5.31/5.66 @ ^ [B4: nat] : ( minus_minus_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ B4 ) ) @ one_one_int )
% 5.31/5.66 @ ( nat_sum_decode @ N4 ) ) ) ) ).
% 5.31/5.66
% 5.31/5.66 % int_decode_def
% 5.31/5.66 thf(fact_9441_sum__encode__def,axiom,
% 5.31/5.66 ( nat_sum_encode
% 5.31/5.66 = ( sum_ca6763686470577984908at_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.31/5.66 @ ^ [B4: nat] : ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B4 ) ) ) ) ).
% 5.31/5.66
% 5.31/5.66 % sum_encode_def
% 5.31/5.66 thf(fact_9442_enat__def,axiom,
% 5.31/5.66 ( extended_enat2
% 5.31/5.66 = ( ^ [N4: nat] : ( extended_Abs_enat @ ( some_nat @ N4 ) ) ) ) ).
% 5.31/5.66
% 5.31/5.66 % enat_def
% 5.31/5.66 thf(fact_9443_Bseq__monoseq__convergent_H__dec,axiom,
% 5.31/5.66 ! [F2: nat > real,M5: nat] :
% 5.31/5.66 ( ( bfun_nat_real
% 5.31/5.66 @ ^ [N4: nat] : ( F2 @ ( plus_plus_nat @ N4 @ M5 ) )
% 5.31/5.66 @ at_top_nat )
% 5.31/5.66 => ( ! [M: nat,N3: nat] :
% 5.31/5.66 ( ( ord_less_eq_nat @ M5 @ M )
% 5.31/5.66 => ( ( ord_less_eq_nat @ M @ N3 )
% 5.31/5.66 => ( ord_less_eq_real @ ( F2 @ N3 ) @ ( F2 @ M ) ) ) )
% 5.31/5.66 => ( topolo7531315842566124627t_real @ F2 ) ) ) ).
% 5.31/5.66
% 5.31/5.66 % Bseq_monoseq_convergent'_dec
% 5.31/5.66 thf(fact_9444_Bseq__monoseq__convergent_H__inc,axiom,
% 5.31/5.66 ! [F2: nat > real,M5: nat] :
% 5.31/5.66 ( ( bfun_nat_real
% 5.31/5.66 @ ^ [N4: nat] : ( F2 @ ( plus_plus_nat @ N4 @ M5 ) )
% 5.31/5.66 @ at_top_nat )
% 5.31/5.66 => ( ! [M: nat,N3: nat] :
% 5.31/5.66 ( ( ord_less_eq_nat @ M5 @ M )
% 5.31/5.66 => ( ( ord_less_eq_nat @ M @ N3 )
% 5.31/5.66 => ( ord_less_eq_real @ ( F2 @ M ) @ ( F2 @ N3 ) ) ) )
% 5.31/5.66 => ( topolo7531315842566124627t_real @ F2 ) ) ) ).
% 5.31/5.66
% 5.31/5.66 % Bseq_monoseq_convergent'_inc
% 5.31/5.66 thf(fact_9445_Bseq__mono__convergent,axiom,
% 5.31/5.66 ! [X8: nat > real] :
% 5.31/5.66 ( ( bfun_nat_real @ X8 @ at_top_nat )
% 5.31/5.66 => ( ! [M: nat,N3: nat] :
% 5.31/5.66 ( ( ord_less_eq_nat @ M @ N3 )
% 5.31/5.66 => ( ord_less_eq_real @ ( X8 @ M ) @ ( X8 @ N3 ) ) )
% 5.31/5.66 => ( topolo7531315842566124627t_real @ X8 ) ) ) ).
% 5.31/5.66
% 5.31/5.66 % Bseq_mono_convergent
% 5.31/5.66 thf(fact_9446_lcm__altdef__int,axiom,
% 5.31/5.66 ( gcd_lcm_int
% 5.31/5.66 = ( ^ [A5: int,B4: int] : ( divide_divide_int @ ( times_times_int @ ( abs_abs_int @ A5 ) @ ( abs_abs_int @ B4 ) ) @ ( gcd_gcd_int @ A5 @ B4 ) ) ) ) ).
% 5.31/5.66
% 5.31/5.66 % lcm_altdef_int
% 5.31/5.66 thf(fact_9447_prod__gcd__lcm__int,axiom,
% 5.31/5.66 ! [M2: int,N: int] :
% 5.31/5.66 ( ( times_times_int @ ( abs_abs_int @ M2 ) @ ( abs_abs_int @ N ) )
% 5.31/5.66 = ( times_times_int @ ( gcd_gcd_int @ M2 @ N ) @ ( gcd_lcm_int @ M2 @ N ) ) ) ).
% 5.31/5.66
% 5.31/5.66 % prod_gcd_lcm_int
% 5.31/5.66 thf(fact_9448_lcm__0__iff__nat,axiom,
% 5.31/5.66 ! [M2: nat,N: nat] :
% 5.31/5.66 ( ( ( gcd_lcm_nat @ M2 @ N )
% 5.31/5.66 = zero_zero_nat )
% 5.31/5.66 = ( ( M2 = zero_zero_nat )
% 5.31/5.66 | ( N = zero_zero_nat ) ) ) ).
% 5.31/5.66
% 5.31/5.66 % lcm_0_iff_nat
% 5.31/5.66 thf(fact_9449_lcm__1__iff__nat,axiom,
% 5.31/5.66 ! [M2: nat,N: nat] :
% 5.31/5.66 ( ( ( gcd_lcm_nat @ M2 @ N )
% 5.31/5.66 = ( suc @ zero_zero_nat ) )
% 5.31/5.66 = ( ( M2
% 5.31/5.66 = ( suc @ zero_zero_nat ) )
% 5.31/5.66 & ( N
% 5.31/5.66 = ( suc @ zero_zero_nat ) ) ) ) ).
% 5.31/5.66
% 5.31/5.66 % lcm_1_iff_nat
% 5.31/5.66 thf(fact_9450_prod__gcd__lcm__nat,axiom,
% 5.31/5.66 ( times_times_nat
% 5.31/5.66 = ( ^ [M6: nat,N4: nat] : ( times_times_nat @ ( gcd_gcd_nat @ M6 @ N4 ) @ ( gcd_lcm_nat @ M6 @ N4 ) ) ) ) ).
% 5.31/5.66
% 5.31/5.66 % prod_gcd_lcm_nat
% 5.31/5.66 thf(fact_9451_lcm__pos__nat,axiom,
% 5.31/5.66 ! [M2: nat,N: nat] :
% 5.31/5.66 ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 5.31/5.66 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.66 => ( ord_less_nat @ zero_zero_nat @ ( gcd_lcm_nat @ M2 @ N ) ) ) ) ).
% 5.31/5.66
% 5.31/5.66 % lcm_pos_nat
% 5.31/5.66 thf(fact_9452_lcm__code__integer,axiom,
% 5.31/5.66 ( gcd_lcm_Code_integer
% 5.31/5.66 = ( ^ [A5: code_integer,B4: code_integer] : ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ A5 ) @ ( abs_abs_Code_integer @ B4 ) ) @ ( gcd_gcd_Code_integer @ A5 @ B4 ) ) ) ) ).
% 5.31/5.66
% 5.31/5.66 % lcm_code_integer
% 5.31/5.66 thf(fact_9453_lcm__nat__def,axiom,
% 5.31/5.66 ( gcd_lcm_nat
% 5.31/5.66 = ( ^ [X4: nat,Y4: nat] : ( divide_divide_nat @ ( times_times_nat @ X4 @ Y4 ) @ ( gcd_gcd_nat @ X4 @ Y4 ) ) ) ) ).
% 5.31/5.66
% 5.31/5.66 % lcm_nat_def
% 5.31/5.66 thf(fact_9454_Lcm__eq__Max__nat,axiom,
% 5.31/5.66 ! [M5: set_nat] :
% 5.31/5.66 ( ( finite_finite_nat @ M5 )
% 5.31/5.66 => ( ( M5 != bot_bot_set_nat )
% 5.31/5.66 => ( ~ ( member_nat @ zero_zero_nat @ M5 )
% 5.31/5.66 => ( ! [M: nat,N3: nat] :
% 5.31/5.66 ( ( member_nat @ M @ M5 )
% 5.31/5.66 => ( ( member_nat @ N3 @ M5 )
% 5.31/5.66 => ( member_nat @ ( gcd_lcm_nat @ M @ N3 ) @ M5 ) ) )
% 5.31/5.66 => ( ( gcd_Lcm_nat @ M5 )
% 5.31/5.66 = ( lattic8265883725875713057ax_nat @ M5 ) ) ) ) ) ) ).
% 5.31/5.66
% 5.31/5.66 % Lcm_eq_Max_nat
% 5.31/5.66 thf(fact_9455_Lcm__eq__0__I__nat,axiom,
% 5.31/5.66 ! [A4: set_nat] :
% 5.31/5.66 ( ( member_nat @ zero_zero_nat @ A4 )
% 5.31/5.66 => ( ( gcd_Lcm_nat @ A4 )
% 5.31/5.66 = zero_zero_nat ) ) ).
% 5.31/5.66
% 5.31/5.66 % Lcm_eq_0_I_nat
% 5.31/5.66 thf(fact_9456_Lcm__0__iff__nat,axiom,
% 5.31/5.66 ! [A4: set_nat] :
% 5.31/5.66 ( ( finite_finite_nat @ A4 )
% 5.31/5.66 => ( ( ( gcd_Lcm_nat @ A4 )
% 5.31/5.66 = zero_zero_nat )
% 5.31/5.66 = ( member_nat @ zero_zero_nat @ A4 ) ) ) ).
% 5.31/5.66
% 5.31/5.66 % Lcm_0_iff_nat
% 5.31/5.66 thf(fact_9457_Lcm__nat__infinite,axiom,
% 5.31/5.66 ! [M5: set_nat] :
% 5.31/5.66 ( ~ ( finite_finite_nat @ M5 )
% 5.31/5.66 => ( ( gcd_Lcm_nat @ M5 )
% 5.31/5.66 = zero_zero_nat ) ) ).
% 5.31/5.66
% 5.31/5.66 % Lcm_nat_infinite
% 5.31/5.66 thf(fact_9458_Lcm__nat__def,axiom,
% 5.31/5.66 ( gcd_Lcm_nat
% 5.31/5.66 = ( ^ [M9: set_nat] : ( if_nat @ ( finite_finite_nat @ M9 ) @ ( lattic7826324295020591184_F_nat @ gcd_lcm_nat @ one_one_nat @ M9 ) @ zero_zero_nat ) ) ) ).
% 5.31/5.66
% 5.31/5.66 % Lcm_nat_def
% 5.31/5.66 thf(fact_9459_unit__factor__simps_I1_J,axiom,
% 5.31/5.66 ( ( unit_f2748546683901255202or_nat @ zero_zero_nat )
% 5.31/5.66 = zero_zero_nat ) ).
% 5.31/5.66
% 5.31/5.66 % unit_factor_simps(1)
% 5.31/5.66 thf(fact_9460_unit__factor__simps_I2_J,axiom,
% 5.31/5.66 ! [N: nat] :
% 5.31/5.66 ( ( unit_f2748546683901255202or_nat @ ( suc @ N ) )
% 5.31/5.66 = one_one_nat ) ).
% 5.31/5.66
% 5.31/5.66 % unit_factor_simps(2)
% 5.31/5.66 thf(fact_9461_unit__factor__nat__def,axiom,
% 5.31/5.66 ( unit_f2748546683901255202or_nat
% 5.31/5.66 = ( ^ [N4: nat] : ( if_nat @ ( N4 = zero_zero_nat ) @ zero_zero_nat @ one_one_nat ) ) ) ).
% 5.31/5.66
% 5.31/5.66 % unit_factor_nat_def
% 5.31/5.66 thf(fact_9462_times__num__def,axiom,
% 5.31/5.66 ( times_times_num
% 5.31/5.66 = ( ^ [M6: num,N4: num] : ( num_of_nat @ ( times_times_nat @ ( nat_of_num @ M6 ) @ ( nat_of_num @ N4 ) ) ) ) ) ).
% 5.31/5.66
% 5.31/5.66 % times_num_def
% 5.31/5.66 thf(fact_9463_nat__of__num__code_I2_J,axiom,
% 5.31/5.66 ! [N: num] :
% 5.31/5.66 ( ( nat_of_num @ ( bit0 @ N ) )
% 5.31/5.66 = ( plus_plus_nat @ ( nat_of_num @ N ) @ ( nat_of_num @ N ) ) ) ).
% 5.31/5.66
% 5.31/5.66 % nat_of_num_code(2)
% 5.31/5.66 thf(fact_9464_less__eq__num__def,axiom,
% 5.31/5.66 ( ord_less_eq_num
% 5.31/5.66 = ( ^ [M6: num,N4: num] : ( ord_less_eq_nat @ ( nat_of_num @ M6 ) @ ( nat_of_num @ N4 ) ) ) ) ).
% 5.31/5.66
% 5.31/5.66 % less_eq_num_def
% 5.31/5.66 thf(fact_9465_less__num__def,axiom,
% 5.31/5.66 ( ord_less_num
% 5.31/5.66 = ( ^ [M6: num,N4: num] : ( ord_less_nat @ ( nat_of_num @ M6 ) @ ( nat_of_num @ N4 ) ) ) ) ).
% 5.31/5.66
% 5.31/5.66 % less_num_def
% 5.31/5.66 thf(fact_9466_nat__of__num__inc,axiom,
% 5.31/5.66 ! [X: num] :
% 5.31/5.66 ( ( nat_of_num @ ( inc @ X ) )
% 5.31/5.66 = ( suc @ ( nat_of_num @ X ) ) ) ).
% 5.31/5.66
% 5.31/5.66 % nat_of_num_inc
% 5.31/5.66 thf(fact_9467_nat__of__num__mult,axiom,
% 5.31/5.66 ! [X: num,Y: num] :
% 5.31/5.66 ( ( nat_of_num @ ( times_times_num @ X @ Y ) )
% 5.31/5.66 = ( times_times_nat @ ( nat_of_num @ X ) @ ( nat_of_num @ Y ) ) ) ).
% 5.31/5.66
% 5.31/5.66 % nat_of_num_mult
% 5.31/5.66 thf(fact_9468_nat__of__num__numeral,axiom,
% 5.31/5.66 nat_of_num = numeral_numeral_nat ).
% 5.31/5.66
% 5.31/5.66 % nat_of_num_numeral
% 5.31/5.66 thf(fact_9469_num__eq__iff,axiom,
% 5.31/5.66 ( ( ^ [Y5: num,Z2: num] : ( Y5 = Z2 ) )
% 5.31/5.66 = ( ^ [X4: num,Y4: num] :
% 5.31/5.66 ( ( nat_of_num @ X4 )
% 5.31/5.66 = ( nat_of_num @ Y4 ) ) ) ) ).
% 5.31/5.66
% 5.31/5.66 % num_eq_iff
% 5.31/5.66 thf(fact_9470_nat__of__num__inverse,axiom,
% 5.31/5.66 ! [X: num] :
% 5.31/5.66 ( ( num_of_nat @ ( nat_of_num @ X ) )
% 5.31/5.66 = X ) ).
% 5.31/5.66
% 5.31/5.66 % nat_of_num_inverse
% 5.31/5.66 thf(fact_9471_nat__of__num_Osimps_I2_J,axiom,
% 5.31/5.66 ! [X: num] :
% 5.31/5.66 ( ( nat_of_num @ ( bit0 @ X ) )
% 5.31/5.66 = ( plus_plus_nat @ ( nat_of_num @ X ) @ ( nat_of_num @ X ) ) ) ).
% 5.31/5.66
% 5.31/5.66 % nat_of_num.simps(2)
% 5.31/5.66 thf(fact_9472_nat__of__num__pos,axiom,
% 5.31/5.66 ! [X: num] : ( ord_less_nat @ zero_zero_nat @ ( nat_of_num @ X ) ) ).
% 5.31/5.66
% 5.31/5.66 % nat_of_num_pos
% 5.31/5.66 thf(fact_9473_nat__of__num__neq__0,axiom,
% 5.31/5.66 ! [X: num] :
% 5.31/5.66 ( ( nat_of_num @ X )
% 5.31/5.66 != zero_zero_nat ) ).
% 5.31/5.66
% 5.31/5.66 % nat_of_num_neq_0
% 5.31/5.66 thf(fact_9474_nat__of__num__code_I1_J,axiom,
% 5.31/5.66 ( ( nat_of_num @ one )
% 5.31/5.66 = one_one_nat ) ).
% 5.31/5.66
% 5.31/5.66 % nat_of_num_code(1)
% 5.31/5.66 thf(fact_9475_nat__of__num__add,axiom,
% 5.31/5.66 ! [X: num,Y: num] :
% 5.31/5.66 ( ( nat_of_num @ ( plus_plus_num @ X @ Y ) )
% 5.31/5.66 = ( plus_plus_nat @ ( nat_of_num @ X ) @ ( nat_of_num @ Y ) ) ) ).
% 5.31/5.66
% 5.31/5.66 % nat_of_num_add
% 5.31/5.66 thf(fact_9476_nat__of__num__sqr,axiom,
% 5.31/5.66 ! [X: num] :
% 5.31/5.66 ( ( nat_of_num @ ( sqr @ X ) )
% 5.31/5.66 = ( times_times_nat @ ( nat_of_num @ X ) @ ( nat_of_num @ X ) ) ) ).
% 5.31/5.66
% 5.31/5.66 % nat_of_num_sqr
% 5.31/5.66 thf(fact_9477_nat__of__num_Osimps_I1_J,axiom,
% 5.31/5.66 ( ( nat_of_num @ one )
% 5.31/5.66 = ( suc @ zero_zero_nat ) ) ).
% 5.31/5.66
% 5.31/5.66 % nat_of_num.simps(1)
% 5.31/5.66 thf(fact_9478_nat__of__num_Osimps_I3_J,axiom,
% 5.31/5.66 ! [X: num] :
% 5.31/5.66 ( ( nat_of_num @ ( bit1 @ X ) )
% 5.31/5.66 = ( suc @ ( plus_plus_nat @ ( nat_of_num @ X ) @ ( nat_of_num @ X ) ) ) ) ).
% 5.31/5.66
% 5.31/5.66 % nat_of_num.simps(3)
% 5.31/5.66 thf(fact_9479_num__of__nat__inverse,axiom,
% 5.31/5.66 ! [N: nat] :
% 5.31/5.66 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.31/5.66 => ( ( nat_of_num @ ( num_of_nat @ N ) )
% 5.31/5.66 = N ) ) ).
% 5.31/5.66
% 5.31/5.66 % num_of_nat_inverse
% 5.31/5.66 thf(fact_9480_nat__of__num__code_I3_J,axiom,
% 5.31/5.66 ! [N: num] :
% 5.31/5.66 ( ( nat_of_num @ ( bit1 @ N ) )
% 5.31/5.66 = ( suc @ ( plus_plus_nat @ ( nat_of_num @ N ) @ ( nat_of_num @ N ) ) ) ) ).
% 5.31/5.66
% 5.31/5.66 % nat_of_num_code(3)
% 5.31/5.66 thf(fact_9481_plus__num__def,axiom,
% 5.31/5.66 ( plus_plus_num
% 5.31/5.66 = ( ^ [M6: num,N4: num] : ( num_of_nat @ ( plus_plus_nat @ ( nat_of_num @ M6 ) @ ( nat_of_num @ N4 ) ) ) ) ) ).
% 5.31/5.66
% 5.31/5.66 % plus_num_def
% 5.31/5.66 thf(fact_9482_natLeq__trans,axiom,
% 5.31/5.66 trans_nat @ bNF_Ca8665028551170535155natLeq ).
% 5.31/5.66
% 5.31/5.66 % natLeq_trans
% 5.31/5.66 thf(fact_9483_natLeq__antisym,axiom,
% 5.31/5.66 antisym_nat @ bNF_Ca8665028551170535155natLeq ).
% 5.31/5.66
% 5.31/5.66 % natLeq_antisym
% 5.31/5.66 thf(fact_9484_VEBT__internal_Olesseq_Oelims_I3_J,axiom,
% 5.31/5.66 ! [X: option_nat,Xa2: option_nat] :
% 5.31/5.66 ( ~ ( vEBT_VEBT_lesseq @ X @ Xa2 )
% 5.31/5.66 => ~ ( vEBT_V2881884560877996034ft_nat @ ord_less_eq_nat @ X @ Xa2 ) ) ).
% 5.31/5.66
% 5.31/5.66 % VEBT_internal.lesseq.elims(3)
% 5.31/5.66 thf(fact_9485_VEBT__internal_Olesseq_Oelims_I2_J,axiom,
% 5.31/5.66 ! [X: option_nat,Xa2: option_nat] :
% 5.31/5.66 ( ( vEBT_VEBT_lesseq @ X @ Xa2 )
% 5.31/5.66 => ( vEBT_V2881884560877996034ft_nat @ ord_less_eq_nat @ X @ Xa2 ) ) ).
% 5.31/5.66
% 5.31/5.66 % VEBT_internal.lesseq.elims(2)
% 5.31/5.66 thf(fact_9486_VEBT__internal_Olesseq_Oelims_I1_J,axiom,
% 5.31/5.66 ! [X: option_nat,Xa2: option_nat,Y: $o] :
% 5.31/5.66 ( ( ( vEBT_VEBT_lesseq @ X @ Xa2 )
% 5.31/5.66 = Y )
% 5.31/5.66 => ( Y
% 5.31/5.66 = ( vEBT_V2881884560877996034ft_nat @ ord_less_eq_nat @ X @ Xa2 ) ) ) ).
% 5.31/5.66
% 5.31/5.66 % VEBT_internal.lesseq.elims(1)
% 5.31/5.66 thf(fact_9487_VEBT__internal_Olesseq_Osimps,axiom,
% 5.31/5.66 ( vEBT_VEBT_lesseq
% 5.31/5.66 = ( vEBT_V2881884560877996034ft_nat @ ord_less_eq_nat ) ) ).
% 5.31/5.66
% 5.31/5.66 % VEBT_internal.lesseq.simps
% 5.31/5.66 thf(fact_9488_integer__of__nat__0,axiom,
% 5.31/5.66 ( ( code_integer_of_nat @ zero_zero_nat )
% 5.31/5.66 = zero_z3403309356797280102nteger ) ).
% 5.31/5.66
% 5.31/5.66 % integer_of_nat_0
% 5.31/5.66 thf(fact_9489_natural__decr,axiom,
% 5.31/5.66 ! [N: code_natural] :
% 5.31/5.66 ( ( N != zero_z2226904508553997617atural )
% 5.31/5.66 => ( ord_less_nat @ ( minus_minus_nat @ ( code_nat_of_natural @ N ) @ ( suc @ zero_zero_nat ) ) @ ( code_nat_of_natural @ N ) ) ) ).
% 5.31/5.66
% 5.31/5.66 % natural_decr
% 5.31/5.66 thf(fact_9490_times__natural_Orep__eq,axiom,
% 5.31/5.66 ! [X: code_natural,Xa2: code_natural] :
% 5.31/5.66 ( ( code_nat_of_natural @ ( times_2397367101498566445atural @ X @ Xa2 ) )
% 5.31/5.66 = ( times_times_nat @ ( code_nat_of_natural @ X ) @ ( code_nat_of_natural @ Xa2 ) ) ) ).
% 5.31/5.66
% 5.31/5.66 % times_natural.rep_eq
% 5.31/5.66 thf(fact_9491_zero__natural_Orep__eq,axiom,
% 5.31/5.66 ( ( code_nat_of_natural @ zero_z2226904508553997617atural )
% 5.31/5.66 = zero_zero_nat ) ).
% 5.31/5.66
% 5.31/5.66 % zero_natural.rep_eq
% 5.31/5.66 thf(fact_9492_less__eq__natural_Orep__eq,axiom,
% 5.31/5.66 ( ord_le1926595141338095240atural
% 5.31/5.66 = ( ^ [X4: code_natural,Xa3: code_natural] : ( ord_less_eq_nat @ ( code_nat_of_natural @ X4 ) @ ( code_nat_of_natural @ Xa3 ) ) ) ) ).
% 5.31/5.66
% 5.31/5.66 % less_eq_natural.rep_eq
% 5.31/5.66 thf(fact_9493_next_Osimps,axiom,
% 5.31/5.66 ! [V2: code_natural,W2: code_natural] :
% 5.31/5.66 ( ( next @ ( produc3574140220909816553atural @ V2 @ W2 ) )
% 5.31/5.66 = ( produc6639722614265839536atural @ ( plus_p4538020629002901425atural @ ( minus_shift @ ( numera5444537566228673987atural @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( minus_shift @ ( numera5444537566228673987atural @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( times_2397367101498566445atural @ ( modulo8411746178871703098atural @ V2 @ ( numera5444537566228673987atural @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( numera5444537566228673987atural @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( times_2397367101498566445atural @ ( divide5121882707175180666atural @ V2 @ ( numera5444537566228673987atural @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( numera5444537566228673987atural @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( plus_p4538020629002901425atural @ ( minus_shift @ ( numera5444537566228673987atural @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( times_2397367101498566445atural @ ( modulo8411746178871703098atural @ W2 @ ( numera5444537566228673987atural @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( numera5444537566228673987atural @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( times_2397367101498566445atural @ ( divide5121882707175180666atural @ W2 @ ( numera5444537566228673987atural @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( numera5444537566228673987atural @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ one_one_Code_natural ) ) @ one_one_Code_natural ) @ ( produc3574140220909816553atural @ ( minus_shift @ ( numera5444537566228673987atural @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( times_2397367101498566445atural @ ( modulo8411746178871703098atural @ V2 @ ( numera5444537566228673987atural @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( numera5444537566228673987atural @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( times_2397367101498566445atural @ ( divide5121882707175180666atural @ V2 @ ( numera5444537566228673987atural @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( numera5444537566228673987atural @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( minus_shift @ ( numera5444537566228673987atural @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( times_2397367101498566445atural @ ( modulo8411746178871703098atural @ W2 @ ( numera5444537566228673987atural @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( numera5444537566228673987atural @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( times_2397367101498566445atural @ ( divide5121882707175180666atural @ W2 @ ( numera5444537566228673987atural @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( numera5444537566228673987atural @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.31/5.66
% 5.31/5.66 % next.simps
% 5.31/5.66 thf(fact_9494_Random_Orange__def,axiom,
% 5.31/5.66 ( range
% 5.31/5.66 = ( ^ [K3: code_natural] :
% 5.31/5.66 ( produc5538323210962509403atural
% 5.31/5.66 @ ( iterat8892046348760725948atural @ ( log @ ( numera5444537566228673987atural @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ K3 )
% 5.31/5.66 @ ^ [L2: code_natural] :
% 5.31/5.66 ( produc5538323210962509403atural @ next
% 5.31/5.66 @ ^ [V3: code_natural] : ( produc6639722614265839536atural @ ( plus_p4538020629002901425atural @ V3 @ ( times_2397367101498566445atural @ L2 @ ( numera5444537566228673987atural @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
% 5.31/5.66 @ one_one_Code_natural )
% 5.31/5.66 @ ^ [V3: code_natural] : ( produc6639722614265839536atural @ ( modulo8411746178871703098atural @ V3 @ K3 ) ) ) ) ) ).
% 5.31/5.66
% 5.31/5.66 % Random.range_def
% 5.31/5.66 thf(fact_9495_Suc_Orep__eq,axiom,
% 5.31/5.66 ! [X: code_natural] :
% 5.31/5.66 ( ( code_nat_of_natural @ ( code_Suc @ X ) )
% 5.31/5.66 = ( suc @ ( code_nat_of_natural @ X ) ) ) ).
% 5.31/5.66
% 5.31/5.66 % Suc.rep_eq
% 5.31/5.66 thf(fact_9496_Suc_Oabs__eq,axiom,
% 5.31/5.66 ! [X: nat] :
% 5.31/5.66 ( ( code_Suc @ ( code_natural_of_nat @ X ) )
% 5.31/5.66 = ( code_natural_of_nat @ ( suc @ X ) ) ) ).
% 5.31/5.66
% 5.31/5.66 % Suc.abs_eq
% 5.31/5.66 thf(fact_9497_less__eq__natural_Oabs__eq,axiom,
% 5.31/5.66 ! [Xa2: nat,X: nat] :
% 5.31/5.66 ( ( ord_le1926595141338095240atural @ ( code_natural_of_nat @ Xa2 ) @ ( code_natural_of_nat @ X ) )
% 5.31/5.66 = ( ord_less_eq_nat @ Xa2 @ X ) ) ).
% 5.31/5.66
% 5.31/5.66 % less_eq_natural.abs_eq
% 5.31/5.66 thf(fact_9498_times__natural_Oabs__eq,axiom,
% 5.31/5.66 ! [Xa2: nat,X: nat] :
% 5.31/5.66 ( ( times_2397367101498566445atural @ ( code_natural_of_nat @ Xa2 ) @ ( code_natural_of_nat @ X ) )
% 5.31/5.66 = ( code_natural_of_nat @ ( times_times_nat @ Xa2 @ X ) ) ) ).
% 5.31/5.66
% 5.31/5.66 % times_natural.abs_eq
% 5.31/5.66 thf(fact_9499_less__nat__rel,axiom,
% 5.31/5.66 ( ord_less_nat
% 5.31/5.66 = ( transi2163837189807498211lp_nat
% 5.31/5.66 @ ^ [M6: nat,N4: nat] :
% 5.31/5.66 ( N4
% 5.31/5.66 = ( suc @ M6 ) ) ) ) ).
% 5.31/5.66
% 5.31/5.66 % less_nat_rel
% 5.31/5.66 thf(fact_9500_zero__natural__def,axiom,
% 5.31/5.66 ( zero_z2226904508553997617atural
% 5.31/5.66 = ( code_natural_of_nat @ zero_zero_nat ) ) ).
% 5.31/5.66
% 5.31/5.66 % zero_natural_def
% 5.31/5.66 thf(fact_9501_Code__Numeral_OSuc__def,axiom,
% 5.31/5.66 ( code_Suc
% 5.31/5.66 = ( map_fu1239815594074539274atural @ code_nat_of_natural @ code_natural_of_nat @ suc ) ) ).
% 5.31/5.66
% 5.31/5.66 % Code_Numeral.Suc_def
% 5.31/5.66 thf(fact_9502_times__natural__def,axiom,
% 5.31/5.66 ( times_2397367101498566445atural
% 5.31/5.66 = ( map_fu6549440983881763648atural @ code_nat_of_natural @ ( map_fu1239815594074539274atural @ code_nat_of_natural @ code_natural_of_nat ) @ times_times_nat ) ) ).
% 5.31/5.66
% 5.31/5.66 % times_natural_def
% 5.31/5.66 thf(fact_9503_typerep_Osize__neq,axiom,
% 5.31/5.66 ! [X: typerep] :
% 5.31/5.66 ( ( size_size_typerep @ X )
% 5.31/5.66 != zero_zero_nat ) ).
% 5.31/5.66
% 5.31/5.66 % typerep.size_neq
% 5.31/5.66 thf(fact_9504_typerep_Osize_I2_J,axiom,
% 5.31/5.66 ! [X1: literal,X2: list_typerep] :
% 5.31/5.66 ( ( size_size_typerep @ ( typerep2 @ X1 @ X2 ) )
% 5.31/5.66 = ( plus_plus_nat @ ( size_list_typerep @ size_size_typerep @ X2 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.31/5.66
% 5.31/5.66 % typerep.size(2)
% 5.31/5.66 thf(fact_9505_typerep_Osize__gen,axiom,
% 5.31/5.66 ! [X1: literal,X2: list_typerep] :
% 5.31/5.66 ( ( size_typerep @ ( typerep2 @ X1 @ X2 ) )
% 5.31/5.66 = ( plus_plus_nat @ ( size_list_typerep @ size_typerep @ X2 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.31/5.66
% 5.31/5.66 % typerep.size_gen
% 5.31/5.66 thf(fact_9506_max__nat_Osemilattice__neutr__axioms,axiom,
% 5.31/5.66 semila9081495762789891438tr_nat @ ord_max_nat @ zero_zero_nat ).
% 5.31/5.66
% 5.31/5.66 % max_nat.semilattice_neutr_axioms
% 5.31/5.66 thf(fact_9507_gcd__nat_Osemilattice__neutr__axioms,axiom,
% 5.31/5.66 semila9081495762789891438tr_nat @ gcd_gcd_nat @ zero_zero_nat ).
% 5.31/5.66
% 5.31/5.66 % gcd_nat.semilattice_neutr_axioms
% 5.31/5.66 thf(fact_9508_real__times__code,axiom,
% 5.31/5.66 ! [X: rat,Y: rat] :
% 5.31/5.66 ( ( times_times_real @ ( ratreal @ X ) @ ( ratreal @ Y ) )
% 5.31/5.66 = ( ratreal @ ( times_times_rat @ X @ Y ) ) ) ).
% 5.31/5.66
% 5.31/5.66 % real_times_code
% 5.31/5.66 thf(fact_9509_max__nat_Omonoid__axioms,axiom,
% 5.31/5.66 monoid_nat @ ord_max_nat @ zero_zero_nat ).
% 5.31/5.66
% 5.31/5.66 % max_nat.monoid_axioms
% 5.31/5.66 thf(fact_9510_gcd__nat_Omonoid__axioms,axiom,
% 5.31/5.66 monoid_nat @ gcd_gcd_nat @ zero_zero_nat ).
% 5.31/5.66
% 5.31/5.66 % gcd_nat.monoid_axioms
% 5.31/5.66 thf(fact_9511_natLeq__Card__order,axiom,
% 5.31/5.66 bNF_Ca1281551314933786834on_nat @ ( field_nat @ bNF_Ca8665028551170535155natLeq ) @ bNF_Ca8665028551170535155natLeq ).
% 5.31/5.66
% 5.31/5.66 % natLeq_Card_order
% 5.31/5.66 thf(fact_9512_card__of__nat,axiom,
% 5.31/5.66 member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ ( bNF_Ca3793111618940312692of_nat @ top_top_set_nat ) @ bNF_Ca8665028551170535155natLeq ) @ bNF_We5258908940166488438at_nat ).
% 5.31/5.66
% 5.31/5.66 % card_of_nat
% 5.31/5.66 thf(fact_9513_card__of__Field__natLeq,axiom,
% 5.31/5.66 member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ ( bNF_Ca3793111618940312692of_nat @ ( field_nat @ bNF_Ca8665028551170535155natLeq ) ) @ bNF_Ca8665028551170535155natLeq ) @ bNF_We5258908940166488438at_nat ).
% 5.31/5.66
% 5.31/5.66 % card_of_Field_natLeq
% 5.31/5.66
% 5.31/5.66 % Helper facts (35)
% 5.31/5.66 thf(help_If_2_1_If_001t__Int__Oint_T,axiom,
% 5.31/5.66 ! [X: int,Y: int] :
% 5.31/5.66 ( ( if_int @ $false @ X @ Y )
% 5.31/5.66 = Y ) ).
% 5.31/5.66
% 5.31/5.66 thf(help_If_1_1_If_001t__Int__Oint_T,axiom,
% 5.31/5.66 ! [X: int,Y: int] :
% 5.31/5.66 ( ( if_int @ $true @ X @ Y )
% 5.31/5.66 = X ) ).
% 5.31/5.66
% 5.31/5.66 thf(help_If_2_1_If_001t__Nat__Onat_T,axiom,
% 5.31/5.66 ! [X: nat,Y: nat] :
% 5.31/5.66 ( ( if_nat @ $false @ X @ Y )
% 5.31/5.66 = Y ) ).
% 5.31/5.66
% 5.31/5.66 thf(help_If_1_1_If_001t__Nat__Onat_T,axiom,
% 5.31/5.66 ! [X: nat,Y: nat] :
% 5.31/5.66 ( ( if_nat @ $true @ X @ Y )
% 5.31/5.66 = X ) ).
% 5.31/5.66
% 5.31/5.66 thf(help_If_2_1_If_001t__Num__Onum_T,axiom,
% 5.31/5.66 ! [X: num,Y: num] :
% 5.31/5.66 ( ( if_num @ $false @ X @ Y )
% 5.31/5.66 = Y ) ).
% 5.31/5.66
% 5.31/5.66 thf(help_If_1_1_If_001t__Num__Onum_T,axiom,
% 5.31/5.66 ! [X: num,Y: num] :
% 5.31/5.66 ( ( if_num @ $true @ X @ Y )
% 5.31/5.66 = X ) ).
% 5.31/5.66
% 5.31/5.66 thf(help_If_2_1_If_001t__Rat__Orat_T,axiom,
% 5.31/5.66 ! [X: rat,Y: rat] :
% 5.31/5.66 ( ( if_rat @ $false @ X @ Y )
% 5.31/5.66 = Y ) ).
% 5.31/5.66
% 5.31/5.66 thf(help_If_1_1_If_001t__Rat__Orat_T,axiom,
% 5.31/5.66 ! [X: rat,Y: rat] :
% 5.31/5.66 ( ( if_rat @ $true @ X @ Y )
% 5.31/5.66 = X ) ).
% 5.31/5.66
% 5.31/5.66 thf(help_If_2_1_If_001t__Real__Oreal_T,axiom,
% 5.31/5.66 ! [X: real,Y: real] :
% 5.31/5.66 ( ( if_real @ $false @ X @ Y )
% 5.31/5.66 = Y ) ).
% 5.31/5.66
% 5.31/5.66 thf(help_If_1_1_If_001t__Real__Oreal_T,axiom,
% 5.31/5.66 ! [X: real,Y: real] :
% 5.31/5.66 ( ( if_real @ $true @ X @ Y )
% 5.31/5.66 = X ) ).
% 5.31/5.66
% 5.31/5.66 thf(help_If_2_1_If_001t__Complex__Ocomplex_T,axiom,
% 5.31/5.66 ! [X: complex,Y: complex] :
% 5.31/5.66 ( ( if_complex @ $false @ X @ Y )
% 5.31/5.66 = Y ) ).
% 5.31/5.66
% 5.31/5.66 thf(help_If_1_1_If_001t__Complex__Ocomplex_T,axiom,
% 5.31/5.66 ! [X: complex,Y: complex] :
% 5.31/5.66 ( ( if_complex @ $true @ X @ Y )
% 5.31/5.66 = X ) ).
% 5.31/5.66
% 5.31/5.66 thf(help_If_2_1_If_001t__Extended____Nat__Oenat_T,axiom,
% 5.31/5.66 ! [X: extended_enat,Y: extended_enat] :
% 5.31/5.66 ( ( if_Extended_enat @ $false @ X @ Y )
% 5.31/5.66 = Y ) ).
% 5.31/5.66
% 5.31/5.66 thf(help_If_1_1_If_001t__Extended____Nat__Oenat_T,axiom,
% 5.31/5.66 ! [X: extended_enat,Y: extended_enat] :
% 5.31/5.66 ( ( if_Extended_enat @ $true @ X @ Y )
% 5.31/5.66 = X ) ).
% 5.31/5.66
% 5.31/5.66 thf(help_If_2_1_If_001t__Code____Numeral__Ointeger_T,axiom,
% 5.31/5.66 ! [X: code_integer,Y: code_integer] :
% 5.31/5.66 ( ( if_Code_integer @ $false @ X @ Y )
% 5.31/5.66 = Y ) ).
% 5.31/5.66
% 5.31/5.66 thf(help_If_1_1_If_001t__Code____Numeral__Ointeger_T,axiom,
% 5.31/5.66 ! [X: code_integer,Y: code_integer] :
% 5.31/5.66 ( ( if_Code_integer @ $true @ X @ Y )
% 5.31/5.66 = X ) ).
% 5.31/5.66
% 5.31/5.66 thf(help_If_2_1_If_001t__Set__Oset_It__Nat__Onat_J_T,axiom,
% 5.31/5.66 ! [X: set_nat,Y: set_nat] :
% 5.31/5.66 ( ( if_set_nat @ $false @ X @ Y )
% 5.31/5.66 = Y ) ).
% 5.31/5.66
% 5.31/5.66 thf(help_If_1_1_If_001t__Set__Oset_It__Nat__Onat_J_T,axiom,
% 5.31/5.66 ! [X: set_nat,Y: set_nat] :
% 5.31/5.66 ( ( if_set_nat @ $true @ X @ Y )
% 5.31/5.66 = X ) ).
% 5.31/5.66
% 5.31/5.66 thf(help_If_2_1_If_001t__VEBT____Definitions__OVEBT_T,axiom,
% 5.31/5.66 ! [X: vEBT_VEBT,Y: vEBT_VEBT] :
% 5.31/5.66 ( ( if_VEBT_VEBT @ $false @ X @ Y )
% 5.31/5.66 = Y ) ).
% 5.31/5.66
% 5.31/5.66 thf(help_If_1_1_If_001t__VEBT____Definitions__OVEBT_T,axiom,
% 5.31/5.66 ! [X: vEBT_VEBT,Y: vEBT_VEBT] :
% 5.31/5.66 ( ( if_VEBT_VEBT @ $true @ X @ Y )
% 5.31/5.66 = X ) ).
% 5.31/5.66
% 5.31/5.66 thf(help_If_2_1_If_001t__List__Olist_It__Nat__Onat_J_T,axiom,
% 5.31/5.66 ! [X: list_nat,Y: list_nat] :
% 5.31/5.66 ( ( if_list_nat @ $false @ X @ Y )
% 5.31/5.66 = Y ) ).
% 5.31/5.66
% 5.31/5.66 thf(help_If_1_1_If_001t__List__Olist_It__Nat__Onat_J_T,axiom,
% 5.31/5.66 ! [X: list_nat,Y: list_nat] :
% 5.31/5.66 ( ( if_list_nat @ $true @ X @ Y )
% 5.31/5.66 = X ) ).
% 5.31/5.66
% 5.31/5.66 thf(help_If_2_1_If_001t__Option__Ooption_It__Nat__Onat_J_T,axiom,
% 5.31/5.66 ! [X: option_nat,Y: option_nat] :
% 5.31/5.66 ( ( if_option_nat @ $false @ X @ Y )
% 5.31/5.66 = Y ) ).
% 5.31/5.66
% 5.31/5.66 thf(help_If_1_1_If_001t__Option__Ooption_It__Nat__Onat_J_T,axiom,
% 5.31/5.66 ! [X: option_nat,Y: option_nat] :
% 5.31/5.66 ( ( if_option_nat @ $true @ X @ Y )
% 5.31/5.66 = X ) ).
% 5.31/5.66
% 5.31/5.66 thf(help_If_2_1_If_001t__Option__Ooption_It__Num__Onum_J_T,axiom,
% 5.31/5.66 ! [X: option_num,Y: option_num] :
% 5.31/5.66 ( ( if_option_num @ $false @ X @ Y )
% 5.31/5.66 = Y ) ).
% 5.31/5.66
% 5.31/5.66 thf(help_If_1_1_If_001t__Option__Ooption_It__Num__Onum_J_T,axiom,
% 5.31/5.66 ! [X: option_num,Y: option_num] :
% 5.31/5.66 ( ( if_option_num @ $true @ X @ Y )
% 5.31/5.66 = X ) ).
% 5.31/5.66
% 5.31/5.66 thf(help_If_2_1_If_001t__Sum____Type__Osum_It__Nat__Onat_Mt__Nat__Onat_J_T,axiom,
% 5.31/5.66 ! [X: sum_sum_nat_nat,Y: sum_sum_nat_nat] :
% 5.31/5.66 ( ( if_Sum_sum_nat_nat @ $false @ X @ Y )
% 5.31/5.66 = Y ) ).
% 5.31/5.66
% 5.31/5.66 thf(help_If_1_1_If_001t__Sum____Type__Osum_It__Nat__Onat_Mt__Nat__Onat_J_T,axiom,
% 5.31/5.66 ! [X: sum_sum_nat_nat,Y: sum_sum_nat_nat] :
% 5.31/5.66 ( ( if_Sum_sum_nat_nat @ $true @ X @ Y )
% 5.31/5.66 = X ) ).
% 5.31/5.66
% 5.31/5.66 thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_T,axiom,
% 5.31/5.66 ! [X: product_prod_int_int,Y: product_prod_int_int] :
% 5.31/5.66 ( ( if_Pro3027730157355071871nt_int @ $false @ X @ Y )
% 5.31/5.66 = Y ) ).
% 5.31/5.66
% 5.31/5.66 thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_T,axiom,
% 5.31/5.66 ! [X: product_prod_int_int,Y: product_prod_int_int] :
% 5.31/5.66 ( ( if_Pro3027730157355071871nt_int @ $true @ X @ Y )
% 5.31/5.66 = X ) ).
% 5.31/5.66
% 5.31/5.66 thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_T,axiom,
% 6.73/7.03 ! [X: product_prod_nat_nat,Y: product_prod_nat_nat] :
% 6.73/7.03 ( ( if_Pro6206227464963214023at_nat @ $false @ X @ Y )
% 6.73/7.03 = Y ) ).
% 6.73/7.03
% 6.73/7.03 thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_T,axiom,
% 6.73/7.03 ! [X: product_prod_nat_nat,Y: product_prod_nat_nat] :
% 6.73/7.03 ( ( if_Pro6206227464963214023at_nat @ $true @ X @ Y )
% 6.73/7.03 = X ) ).
% 6.73/7.03
% 6.73/7.03 thf(help_If_3_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_T,axiom,
% 6.73/7.03 ! [P2: $o] :
% 6.73/7.03 ( ( P2 = $true )
% 6.73/7.03 | ( P2 = $false ) ) ).
% 6.73/7.03
% 6.73/7.03 thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_T,axiom,
% 6.73/7.03 ! [X: produc8923325533196201883nteger,Y: produc8923325533196201883nteger] :
% 6.73/7.03 ( ( if_Pro6119634080678213985nteger @ $false @ X @ Y )
% 6.73/7.03 = Y ) ).
% 6.73/7.03
% 6.73/7.03 thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_T,axiom,
% 6.73/7.03 ! [X: produc8923325533196201883nteger,Y: produc8923325533196201883nteger] :
% 6.73/7.03 ( ( if_Pro6119634080678213985nteger @ $true @ X @ Y )
% 6.73/7.03 = X ) ).
% 6.73/7.03
% 6.73/7.03 % Conjectures (1)
% 6.73/7.03 thf(conj_0,conjecture,
% 6.73/7.03 ( info
% 6.73/7.03 = ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) ) ).
% 6.73/7.03
% 6.73/7.03 %------------------------------------------------------------------------------
% 6.73/7.03 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.o9zfIIUxlf/cvc5---1.0.5_3022.p...
% 6.73/7.03 (declare-sort $$unsorted 0)
% 6.73/7.03 (declare-sort tptp.produc5542196010084753463at_nat 0)
% 6.73/7.03 (declare-sort tptp.produc5491161045314408544at_nat 0)
% 6.73/7.03 (declare-sort tptp.set_Pr4333006031979791559at_nat 0)
% 6.73/7.03 (declare-sort tptp.produc424102278133772007at_nat 0)
% 6.73/7.03 (declare-sort tptp.set_Pr1542805901266377927at_nat 0)
% 6.73/7.03 (declare-sort tptp.list_P5464809261938338413at_nat 0)
% 6.73/7.03 (declare-sort tptp.set_Pr4329608150637261639at_nat 0)
% 6.73/7.03 (declare-sort tptp.produc1193250871479095198on_num 0)
% 6.73/7.03 (declare-sort tptp.produc8306885398267862888on_nat 0)
% 6.73/7.03 (declare-sort tptp.produc6121120109295599847at_nat 0)
% 6.73/7.03 (declare-sort tptp.produc4471711990508489141at_nat 0)
% 6.73/7.03 (declare-sort tptp.produc6392793444374437607at_nat 0)
% 6.73/7.03 (declare-sort tptp.produc7036089656553540234on_num 0)
% 6.73/7.03 (declare-sort tptp.produc2233624965454879586on_nat 0)
% 6.73/7.03 (declare-sort tptp.produc3843707927480180839at_nat 0)
% 6.73/7.03 (declare-sort tptp.list_P8469869581646625389at_nat 0)
% 6.73/7.03 (declare-sort tptp.set_Pr8693737435421807431at_nat 0)
% 6.73/7.03 (declare-sort tptp.produc5835291356934675326atural 0)
% 6.73/7.03 (declare-sort tptp.set_Pr1916528119006554503T_VEBT 0)
% 6.73/7.03 (declare-sort tptp.produc859450856879609959at_nat 0)
% 6.73/7.03 (declare-sort tptp.set_Pr7565137564259432987nteger 0)
% 6.73/7.03 (declare-sort tptp.produc9211091688327510695T_VEBT 0)
% 6.73/7.03 (declare-sort tptp.set_Pr8894456036836396799st_nat 0)
% 6.73/7.03 (declare-sort tptp.set_Pr4080907618048478043st_int 0)
% 6.73/7.03 (declare-sort tptp.set_Pr1262583345697558789T_VEBT 0)
% 6.73/7.03 (declare-sort tptp.produc862207588354017979nteger 0)
% 6.73/7.03 (declare-sort tptp.set_Pr7508168486584781291list_o 0)
% 6.73/7.03 (declare-sort tptp.set_Pr5170412164475753123T_VEBT 0)
% 6.73/7.03 (declare-sort tptp.list_s9130966667114977576at_nat 0)
% 6.73/7.03 (declare-sort tptp.produc1097915047028332489st_nat 0)
% 6.73/7.03 (declare-sort tptp.produc7831203938951381541st_int 0)
% 6.73/7.03 (declare-sort tptp.produc872621073311890639T_VEBT 0)
% 6.73/7.03 (declare-sort tptp.set_Pr3451248702717554689st_nat 0)
% 6.73/7.03 (declare-sort tptp.set_Pr765067013931698361st_int 0)
% 6.73/7.03 (declare-sort tptp.list_P7413028617227757229T_VEBT 0)
% 6.73/7.03 (declare-sort tptp.set_Pr6192946355708809607T_VEBT 0)
% 6.73/7.03 (declare-sort tptp.list_P6254988961118846195et_nat 0)
% 6.73/7.03 (declare-sort tptp.list_P5578671422887162913nteger 0)
% 6.73/7.03 (declare-sort tptp.set_Pr5488025237498180813et_nat 0)
% 6.73/7.03 (declare-sort tptp.set_Pr4811707699266497531nteger 0)
% 6.73/7.03 (declare-sort tptp.produc3447558737645232053on_num 0)
% 6.73/7.03 (declare-sort tptp.produc4953844613479565601on_nat 0)
% 6.73/7.03 (declare-sort tptp.produc3962069817607390347list_o 0)
% 6.73/7.03 (declare-sort tptp.produc1922972420619397443T_VEBT 0)
% 6.73/7.03 (declare-sort tptp.set_Pr1150278048023938153list_o 0)
% 6.73/7.03 (declare-sort tptp.set_Pr591367044826345187st_nat 0)
% 6.73/7.03 (declare-sort tptp.set_Pr5001190662893202239st_int 0)
% 6.73/7.03 (declare-sort tptp.produc7248412053542808358at_nat 0)
% 6.73/7.03 (declare-sort tptp.list_P4108580160459392801omplex 0)
% 6.73/7.03 (declare-sort tptp.list_P7977503562704621835T_VEBT 0)
% 6.73/7.03 (declare-sort tptp.set_Pr216944050393469383omplex 0)
% 6.73/7.03 (declare-sort tptp.set_Pr4085867452638698417T_VEBT 0)
% 6.73/7.03 (declare-sort tptp.list_P9162950289778280392at_nat 0)
% 6.73/7.03 (declare-sort tptp.list_P2623026923184700063T_real 0)
% 6.73/7.03 (declare-sort tptp.list_P877281246627933069T_VEBT 0)
% 6.73/7.03 (declare-sort tptp.produc1828647624359046049st_nat 0)
% 6.73/7.03 (declare-sort tptp.produc1186641810826059865st_int 0)
% 6.73/7.03 (declare-sort tptp.set_Pr7765410600122031685T_real 0)
% 6.73/7.03 (declare-sort tptp.set_Pr6019664923565264691T_VEBT 0)
% 6.73/7.03 (declare-sort tptp.list_P7037539587688870467BT_nat 0)
% 6.73/7.03 (declare-sort tptp.list_P4547456442757143711BT_int 0)
% 6.73/7.03 (declare-sort tptp.list_P5647936690300460905T_VEBT 0)
% 6.73/7.03 (declare-sort tptp.set_Pr6227168374412355847list_o 0)
% 6.73/7.03 (declare-sort tptp.produc8243902056947475879T_VEBT 0)
% 6.73/7.03 (declare-sort tptp.list_s1210847774152347623at_nat 0)
% 6.73/7.03 (declare-sort tptp.list_P7664491975274850627omplex 0)
% 6.73/7.03 (declare-sort tptp.set_Pr7556676689462069481BT_nat 0)
% 6.73/7.03 (declare-sort tptp.set_Pr5066593544530342725BT_int 0)
% 6.73/7.03 (declare-sort tptp.set_Pr6167073792073659919T_VEBT 0)
% 6.73/7.03 (declare-sort tptp.set_se7855581050983116737at_nat 0)
% 6.73/7.03 (declare-sort tptp.set_Pr5085853215250843933omplex 0)
% 6.73/7.03 (declare-sort tptp.produc7819656566062154093et_nat 0)
% 6.73/7.03 (declare-sort tptp.produc7822875418678951345atural 0)
% 6.73/7.03 (declare-sort tptp.produc8923325533196201883nteger 0)
% 6.73/7.03 (declare-sort tptp.produc7272778201969148633d_enat 0)
% 6.73/7.03 (declare-sort tptp.list_P3881527313128557121omplex 0)
% 6.73/7.03 (declare-sort tptp.list_P7647014805210017729x_real 0)
% 6.73/7.03 (declare-sort tptp.produc149729814636038835list_o 0)
% 6.73/7.03 (declare-sort tptp.produc4203922736317485613st_nat 0)
% 6.73/7.03 (declare-sort tptp.produc1713839591385758857st_int 0)
% 6.73/7.03 (declare-sort tptp.set_Pr6591433984475009307omplex 0)
% 6.73/7.03 (declare-sort tptp.set_Pr1133549439701694107x_real 0)
% 6.73/7.03 (declare-sort tptp.list_P3126845725202233233VEBT_o 0)
% 6.73/7.03 (declare-sort tptp.list_P1797514011394873281omplex 0)
% 6.73/7.03 (declare-sort tptp.list_P4696196834278971493ex_nat 0)
% 6.73/7.03 (declare-sort tptp.list_P2206113689347244737ex_int 0)
% 6.73/7.03 (declare-sort tptp.list_P7495141550334521929T_VEBT 0)
% 6.73/7.03 (declare-sort tptp.produc8380087813684007313omplex 0)
% 6.73/7.03 (declare-sort tptp.produc7151440242714718331T_VEBT 0)
% 6.73/7.03 (declare-sort tptp.set_Pr3175402225741728619VEBT_o 0)
% 6.73/7.03 (declare-sort tptp.set_Pr1846070511934368667omplex 0)
% 6.73/7.03 (declare-sort tptp.set_Pr4744753334818466879ex_nat 0)
% 6.73/7.03 (declare-sort tptp.set_Pr2254670189886740123ex_int 0)
% 6.73/7.03 (declare-sort tptp.set_Pr7543698050874017315T_VEBT 0)
% 6.73/7.03 (declare-sort tptp.option4927543243414619207at_nat 0)
% 6.73/7.03 (declare-sort tptp.list_P8689742595348180415l_real 0)
% 6.73/7.03 (declare-sort tptp.filter1242075044329608583at_nat 0)
% 6.73/7.03 (declare-sort tptp.set_Pr6218003697084177305l_real 0)
% 6.73/7.03 (declare-sort tptp.list_P6834414599653733731al_nat 0)
% 6.73/7.03 (declare-sort tptp.list_P4344331454722006975al_int 0)
% 6.73/7.03 (declare-sort tptp.list_P6863124054624500543t_real 0)
% 6.73/7.03 (declare-sort tptp.produc5170161368751668367T_real 0)
% 6.73/7.03 (declare-sort tptp.produc3757001726724277373T_VEBT 0)
% 6.73/7.03 (declare-sort tptp.set_Pr3510011417693777981al_nat 0)
% 6.73/7.03 (declare-sort tptp.set_Pr1019928272762051225al_int 0)
% 6.73/7.03 (declare-sort tptp.set_Pr3538720872664544793t_real 0)
% 6.73/7.03 (declare-sort tptp.produc7102631898165422375list_o 0)
% 6.73/7.03 (declare-sort tptp.list_P6011104703257516679at_nat 0)
% 6.73/7.03 (declare-sort tptp.list_P3521021558325789923at_int 0)
% 6.73/7.03 (declare-sort tptp.list_P5707943133018811711nt_int 0)
% 6.73/7.03 (declare-sort tptp.produc9072475918466114483BT_nat 0)
% 6.73/7.03 (declare-sort tptp.produc4894624898956917775BT_int 0)
% 6.73/7.03 (declare-sort tptp.produc8025551001238799321T_VEBT 0)
% 6.73/7.03 (declare-sort tptp.list_P7942624414058669295plex_o 0)
% 6.73/7.03 (declare-sort tptp.list_P3924974545808530565omplex 0)
% 6.73/7.03 (declare-sort tptp.set_Pr1261947904930325089at_nat 0)
% 6.73/7.03 (declare-sort tptp.set_Pr958786334691620121nt_int 0)
% 6.73/7.03 (declare-sort tptp.produc4411394909380815293omplex 0)
% 6.73/7.03 (declare-sort tptp.set_Pr216032351708956309plex_o 0)
% 6.73/7.03 (declare-sort tptp.set_Pr5421754520313593387omplex 0)
% 6.73/7.03 (declare-sort tptp.list_C4705013386053401436er_nat 0)
% 6.73/7.03 (declare-sort tptp.set_Sum_sum_nat_nat 0)
% 6.73/7.03 (declare-sort tptp.list_P3595434254542482545real_o 0)
% 6.73/7.03 (declare-sort tptp.list_P5232166724548748803o_real 0)
% 6.73/7.03 (declare-sort tptp.produc6979889472282505531omplex 0)
% 6.73/7.03 (declare-sort tptp.produc8892588492097263291x_real 0)
% 6.73/7.03 (declare-sort tptp.list_list_VEBT_VEBT 0)
% 6.73/7.03 (declare-sort tptp.set_Pr4936984352647145239real_o 0)
% 6.73/7.03 (declare-sort tptp.set_Pr6573716822653411497o_real 0)
% 6.73/7.03 (declare-sort tptp.set_list_list_nat 0)
% 6.73/7.03 (declare-sort tptp.list_P7333126701944960589_nat_o 0)
% 6.73/7.03 (declare-sort tptp.list_P6285523579766656935_o_nat 0)
% 6.73/7.03 (declare-sort tptp.list_P3795440434834930179_o_int 0)
% 6.73/7.03 (declare-sort tptp.set_list_VEBT_VEBT 0)
% 6.73/7.03 (declare-sort tptp.produc334124729049499915VEBT_o 0)
% 6.73/7.03 (declare-sort tptp.produc5838698208256999739omplex 0)
% 6.73/7.03 (declare-sort tptp.produc1799700322190218207ex_nat 0)
% 6.73/7.03 (declare-sort tptp.produc6845221339535797307ex_int 0)
% 6.73/7.03 (declare-sort tptp.produc2504756804600209347T_VEBT 0)
% 6.73/7.03 (declare-sort tptp.set_Pr3149072824959771635_nat_o 0)
% 6.73/7.03 (declare-sort tptp.set_Pr2101469702781467981_o_nat 0)
% 6.73/7.03 (declare-sort tptp.set_Pr8834758594704517033_o_int 0)
% 6.73/7.03 (declare-sort tptp.set_list_set_nat 0)
% 6.73/7.03 (declare-sort tptp.produc2422161461964618553l_real 0)
% 6.73/7.03 (declare-sort tptp.produc3741383161447143261al_nat 0)
% 6.73/7.03 (declare-sort tptp.produc8786904178792722361al_int 0)
% 6.73/7.03 (declare-sort tptp.produc679980390762269497t_real 0)
% 6.73/7.03 (declare-sort tptp.product_prod_nat_nat 0)
% 6.73/7.03 (declare-sort tptp.product_prod_nat_int 0)
% 6.73/7.03 (declare-sort tptp.product_prod_int_int 0)
% 6.73/7.03 (declare-sort tptp.list_P4002435161011370285od_o_o 0)
% 6.73/7.03 (declare-sort tptp.set_list_complex 0)
% 6.73/7.03 (declare-sort tptp.produc6088675342482847199plex_o 0)
% 6.73/7.03 (declare-sort tptp.produc648051720047351925omplex 0)
% 6.73/7.03 (declare-sort tptp.set_Product_prod_o_o 0)
% 6.73/7.03 (declare-sort tptp.list_nat_nat 0)
% 6.73/7.03 (declare-sort tptp.list_int_nat 0)
% 6.73/7.03 (declare-sort tptp.option_VEBT_VEBT 0)
% 6.73/7.03 (declare-sort tptp.sum_sum_nat_nat 0)
% 6.73/7.03 (declare-sort tptp.product_prod_real_o 0)
% 6.73/7.03 (declare-sort tptp.product_prod_o_real 0)
% 6.73/7.03 (declare-sort tptp.list_list_nat 0)
% 6.73/7.03 (declare-sort tptp.list_list_int 0)
% 6.73/7.03 (declare-sort tptp.list_VEBT_VEBT 0)
% 6.73/7.03 (declare-sort tptp.set_list_nat 0)
% 6.73/7.03 (declare-sort tptp.set_list_int 0)
% 6.73/7.03 (declare-sort tptp.product_prod_nat_o 0)
% 6.73/7.03 (declare-sort tptp.product_prod_o_nat 0)
% 6.73/7.03 (declare-sort tptp.product_prod_o_int 0)
% 6.73/7.03 (declare-sort tptp.list_set_nat 0)
% 6.73/7.03 (declare-sort tptp.list_Code_integer 0)
% 6.73/7.03 (declare-sort tptp.set_VEBT_VEBT 0)
% 6.73/7.03 (declare-sort tptp.set_set_nat 0)
% 6.73/7.03 (declare-sort tptp.set_Code_integer 0)
% 6.73/7.03 (declare-sort tptp.list_list_o 0)
% 6.73/7.03 (declare-sort tptp.list_typerep 0)
% 6.73/7.03 (declare-sort tptp.list_complex 0)
% 6.73/7.03 (declare-sort tptp.set_list_o 0)
% 6.73/7.03 (declare-sort tptp.product_prod_o_o 0)
% 6.73/7.03 (declare-sort tptp.set_complex 0)
% 6.73/7.03 (declare-sort tptp.filter_real 0)
% 6.73/7.03 (declare-sort tptp.option_num 0)
% 6.73/7.03 (declare-sort tptp.option_nat 0)
% 6.73/7.03 (declare-sort tptp.option_int 0)
% 6.73/7.03 (declare-sort tptp.filter_nat 0)
% 6.73/7.03 (declare-sort tptp.set_char 0)
% 6.73/7.03 (declare-sort tptp.list_real 0)
% 6.73/7.03 (declare-sort tptp.set_real 0)
% 6.73/7.03 (declare-sort tptp.list_num 0)
% 6.73/7.03 (declare-sort tptp.list_nat 0)
% 6.73/7.03 (declare-sort tptp.list_int 0)
% 6.73/7.03 (declare-sort tptp.vEBT_VEBT 0)
% 6.73/7.03 (declare-sort tptp.set_rat 0)
% 6.73/7.03 (declare-sort tptp.set_num 0)
% 6.73/7.03 (declare-sort tptp.set_nat 0)
% 6.73/7.03 (declare-sort tptp.set_int 0)
% 6.73/7.03 (declare-sort tptp.code_natural 0)
% 6.73/7.03 (declare-sort tptp.code_integer 0)
% 6.73/7.03 (declare-sort tptp.option_o 0)
% 6.73/7.03 (declare-sort tptp.extended_enat 0)
% 6.73/7.03 (declare-sort tptp.list_o 0)
% 6.73/7.03 (declare-sort tptp.typerep 0)
% 6.73/7.03 (declare-sort tptp.complex 0)
% 6.73/7.03 (declare-sort tptp.literal 0)
% 6.73/7.03 (declare-sort tptp.set_o 0)
% 6.73/7.03 (declare-sort tptp.char 0)
% 6.73/7.03 (declare-sort tptp.real 0)
% 6.73/7.03 (declare-sort tptp.rat 0)
% 6.73/7.03 (declare-sort tptp.num 0)
% 6.73/7.03 (declare-sort tptp.nat 0)
% 6.73/7.03 (declare-sort tptp.int 0)
% 6.73/7.03 (declare-fun tptp.archim7802044766580827645g_real (tptp.real) tptp.int)
% 6.73/7.03 (declare-fun tptp.archim6058952711729229775r_real (tptp.real) tptp.int)
% 6.73/7.03 (declare-fun tptp.bNF_Ca3793111618940312692of_nat (tptp.set_nat) tptp.set_Pr1261947904930325089at_nat)
% 6.73/7.03 (declare-fun tptp.bNF_Ca1281551314933786834on_nat (tptp.set_nat tptp.set_Pr1261947904930325089at_nat) Bool)
% 6.73/7.03 (declare-fun tptp.bNF_Ca8665028551170535155natLeq () tptp.set_Pr1261947904930325089at_nat)
% 6.73/7.03 (declare-fun tptp.bNF_Ca8459412986667044542atLess () tptp.set_Pr1261947904930325089at_nat)
% 6.73/7.03 (declare-fun tptp.bNF_Ca8987285221972644271er_int (tptp.set_Pr4811707699266497531nteger (-> tptp.code_integer tptp.int)) Bool)
% 6.73/7.03 (declare-fun tptp.bNF_Ca8989775692481694547er_nat (tptp.set_Pr4811707699266497531nteger (-> tptp.code_integer tptp.nat)) Bool)
% 6.73/7.03 (declare-fun tptp.bNF_Ca5547107478637473181er_num (tptp.set_Pr4811707699266497531nteger (-> tptp.code_integer tptp.num)) Bool)
% 6.73/7.03 (declare-fun tptp.bNF_Ca8354645632395198811er_rat (tptp.set_Pr4811707699266497531nteger (-> tptp.code_integer tptp.rat)) Bool)
% 6.73/7.03 (declare-fun tptp.bNF_Ca1968104039914474786nt_nat (tptp.set_Pr958786334691620121nt_int (-> tptp.int tptp.nat)) Bool)
% 6.73/7.03 (declare-fun tptp.bNF_Ca7748807862925029228nt_num (tptp.set_Pr958786334691620121nt_int (-> tptp.int tptp.num)) Bool)
% 6.73/7.03 (declare-fun tptp.bNF_Ca1332973979827979050nt_rat (tptp.set_Pr958786334691620121nt_int (-> tptp.int tptp.rat)) Bool)
% 6.73/7.03 (declare-fun tptp.bNF_Ca968750328013420230at_nat (tptp.set_Pr1261947904930325089at_nat (-> tptp.nat tptp.nat)) Bool)
% 6.73/7.03 (declare-fun tptp.bNF_Ca6749454151023974672at_num (tptp.set_Pr1261947904930325089at_nat (-> tptp.nat tptp.num)) Bool)
% 6.73/7.03 (declare-fun tptp.bNF_Ca333620267926924494at_rat (tptp.set_Pr1261947904930325089at_nat (-> tptp.nat tptp.rat)) Bool)
% 6.73/7.03 (declare-fun tptp.bNF_re1962705104956426057at_rat ((-> (-> tptp.nat tptp.rat) (-> tptp.nat tptp.rat) Bool) (-> (-> (-> tptp.nat tptp.rat) tptp.nat tptp.rat) (-> (-> tptp.nat tptp.rat) tptp.nat tptp.rat) Bool) (-> (-> tptp.nat tptp.rat) (-> tptp.nat tptp.rat) tptp.nat tptp.rat) (-> (-> tptp.nat tptp.rat) (-> tptp.nat tptp.rat) tptp.nat tptp.rat)) Bool)
% 6.73/7.03 (declare-fun tptp.bNF_re895249473297799549at_rat ((-> (-> tptp.nat tptp.rat) (-> tptp.nat tptp.rat) Bool) (-> (-> tptp.nat tptp.rat) (-> tptp.nat tptp.rat) Bool) (-> (-> tptp.nat tptp.rat) tptp.nat tptp.rat) (-> (-> tptp.nat tptp.rat) tptp.nat tptp.rat)) Bool)
% 6.73/7.03 (declare-fun tptp.bNF_re728719798268516973at_o_o ((-> (-> tptp.nat tptp.rat) (-> tptp.nat tptp.rat) Bool) (-> Bool Bool Bool) (-> (-> tptp.nat tptp.rat) Bool) (-> (-> tptp.nat tptp.rat) Bool)) Bool)
% 6.73/7.03 (declare-fun tptp.bNF_re4695409256820837752l_real ((-> (-> tptp.nat tptp.rat) tptp.real Bool) (-> (-> (-> tptp.nat tptp.rat) tptp.nat tptp.rat) (-> tptp.real tptp.real) Bool) (-> (-> tptp.nat tptp.rat) (-> tptp.nat tptp.rat) tptp.nat tptp.rat) (-> tptp.real tptp.real tptp.real)) Bool)
% 6.73/7.03 (declare-fun tptp.bNF_re3023117138289059399t_real ((-> (-> tptp.nat tptp.rat) tptp.real Bool) (-> (-> tptp.nat tptp.rat) tptp.real Bool) (-> (-> tptp.nat tptp.rat) tptp.nat tptp.rat) (-> tptp.real tptp.real)) Bool)
% 6.73/7.03 (declare-fun tptp.bNF_re4297313714947099218al_o_o ((-> (-> tptp.nat tptp.rat) tptp.real Bool) (-> Bool Bool Bool) (-> (-> tptp.nat tptp.rat) Bool) (-> tptp.real Bool)) Bool)
% 6.73/7.03 (declare-fun tptp.bNF_re711492959462206631nt_int ((-> tptp.int tptp.int Bool) (-> (-> tptp.int tptp.int) (-> tptp.int tptp.int) Bool) (-> tptp.int tptp.int tptp.int) (-> tptp.int tptp.int tptp.int)) Bool)
% 6.73/7.03 (declare-fun tptp.bNF_re4712519889275205905nt_int ((-> tptp.int tptp.int Bool) (-> tptp.int tptp.int Bool) (-> tptp.int tptp.int) (-> tptp.int tptp.int)) Bool)
% 6.73/7.03 (declare-fun tptp.bNF_re578469030762574527_nat_o ((-> tptp.nat tptp.nat Bool) (-> (-> tptp.nat Bool) (-> tptp.nat Bool) Bool) (-> tptp.nat tptp.nat Bool) (-> tptp.nat tptp.nat Bool)) Bool)
% 6.73/7.03 (declare-fun tptp.bNF_re1345281282404953727at_nat ((-> tptp.nat tptp.nat Bool) (-> (-> tptp.nat tptp.nat) (-> tptp.nat tptp.nat) Bool) (-> tptp.nat tptp.nat tptp.nat) (-> tptp.nat tptp.nat tptp.nat)) Bool)
% 6.73/7.03 (declare-fun tptp.bNF_re4705727531993890431at_o_o ((-> tptp.nat tptp.nat Bool) (-> Bool Bool Bool) (-> tptp.nat Bool) (-> tptp.nat Bool)) Bool)
% 6.73/7.03 (declare-fun tptp.bNF_re5653821019739307937at_nat ((-> tptp.nat tptp.nat Bool) (-> tptp.nat tptp.nat Bool) (-> tptp.nat tptp.nat) (-> tptp.nat tptp.nat)) Bool)
% 6.73/7.03 (declare-fun tptp.bNF_re6830278522597306478at_int ((-> tptp.nat tptp.nat Bool) (-> tptp.product_prod_nat_nat tptp.int Bool) (-> tptp.nat tptp.product_prod_nat_nat) (-> tptp.nat tptp.int)) Bool)
% 6.73/7.03 (declare-fun tptp.bNF_re5228765855967844073nt_int ((-> tptp.product_prod_int_int tptp.product_prod_int_int Bool) (-> (-> tptp.product_prod_int_int tptp.product_prod_int_int) (-> tptp.product_prod_int_int tptp.product_prod_int_int) Bool) (-> tptp.product_prod_int_int tptp.product_prod_int_int tptp.product_prod_int_int) (-> tptp.product_prod_int_int tptp.product_prod_int_int tptp.product_prod_int_int)) Bool)
% 6.73/7.03 (declare-fun tptp.bNF_re8699439704749558557nt_o_o ((-> tptp.product_prod_int_int tptp.product_prod_int_int Bool) (-> Bool Bool Bool) (-> tptp.product_prod_int_int Bool) (-> tptp.product_prod_int_int Bool)) Bool)
% 6.73/7.03 (declare-fun tptp.bNF_re7145576690424134365nt_int ((-> tptp.product_prod_int_int tptp.product_prod_int_int Bool) (-> tptp.product_prod_int_int tptp.product_prod_int_int Bool) (-> tptp.product_prod_int_int tptp.product_prod_int_int) (-> tptp.product_prod_int_int tptp.product_prod_int_int)) Bool)
% 6.73/7.03 (declare-fun tptp.bNF_re7627151682743391978at_rat ((-> tptp.product_prod_int_int tptp.rat Bool) (-> (-> tptp.product_prod_int_int tptp.product_prod_int_int) (-> tptp.rat tptp.rat) Bool) (-> tptp.product_prod_int_int tptp.product_prod_int_int tptp.product_prod_int_int) (-> tptp.rat tptp.rat tptp.rat)) Bool)
% 6.73/7.03 (declare-fun tptp.bNF_re1494630372529172596at_o_o ((-> tptp.product_prod_int_int tptp.rat Bool) (-> Bool Bool Bool) (-> tptp.product_prod_int_int Bool) (-> tptp.rat Bool)) Bool)
% 6.73/7.03 (declare-fun tptp.bNF_re8279943556446156061nt_rat ((-> tptp.product_prod_int_int tptp.rat Bool) (-> tptp.product_prod_int_int tptp.rat Bool) (-> tptp.product_prod_int_int tptp.product_prod_int_int) (-> tptp.rat tptp.rat)) Bool)
% 6.73/7.03 (declare-fun tptp.bNF_re717283939379294677_int_o ((-> tptp.product_prod_nat_nat tptp.int Bool) (-> (-> tptp.product_prod_nat_nat Bool) (-> tptp.int Bool) Bool) (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool) (-> tptp.int tptp.int Bool)) Bool)
% 6.73/7.03 (declare-fun tptp.bNF_re7408651293131936558nt_int ((-> tptp.product_prod_nat_nat tptp.int Bool) (-> (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat) (-> tptp.int tptp.int) Bool) (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat) (-> tptp.int tptp.int tptp.int)) Bool)
% 6.73/7.03 (declare-fun tptp.bNF_re6644619430987730960nt_o_o ((-> tptp.product_prod_nat_nat tptp.int Bool) (-> Bool Bool Bool) (-> tptp.product_prod_nat_nat Bool) (-> tptp.int Bool)) Bool)
% 6.73/7.03 (declare-fun tptp.bNF_re7400052026677387805at_int ((-> tptp.product_prod_nat_nat tptp.int Bool) (-> tptp.product_prod_nat_nat tptp.int Bool) (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat) (-> tptp.int tptp.int)) Bool)
% 6.73/7.03 (declare-fun tptp.bNF_re4202695980764964119_nat_o ((-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool) (-> (-> tptp.product_prod_nat_nat Bool) (-> tptp.product_prod_nat_nat Bool) Bool) (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool) (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)) Bool)
% 6.73/7.03 (declare-fun tptp.bNF_re3099431351363272937at_nat ((-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool) (-> (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat) (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat) Bool) (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat) (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)) Bool)
% 6.73/7.03 (declare-fun tptp.bNF_re3666534408544137501at_o_o ((-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool) (-> Bool Bool Bool) (-> tptp.product_prod_nat_nat Bool) (-> tptp.product_prod_nat_nat Bool)) Bool)
% 6.73/7.03 (declare-fun tptp.bNF_re2241393799969408733at_nat ((-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool) (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool) (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat) (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat)) Bool)
% 6.73/7.03 (declare-fun tptp.bNF_We5258908940166488438at_nat () tptp.set_Pr4329608150637261639at_nat)
% 6.73/7.03 (declare-fun tptp.bNF_We3818239936649020644el_nat (tptp.set_Pr1261947904930325089at_nat) Bool)
% 6.73/7.03 (declare-fun tptp.binomial (tptp.nat tptp.nat) tptp.nat)
% 6.73/7.03 (declare-fun tptp.gbinom8545251970709558553nteger (tptp.code_integer tptp.nat) tptp.code_integer)
% 6.73/7.03 (declare-fun tptp.gbinomial_complex (tptp.complex tptp.nat) tptp.complex)
% 6.73/7.03 (declare-fun tptp.gbinomial_int (tptp.int tptp.nat) tptp.int)
% 6.73/7.03 (declare-fun tptp.gbinomial_nat (tptp.nat tptp.nat) tptp.nat)
% 6.73/7.03 (declare-fun tptp.gbinomial_rat (tptp.rat tptp.nat) tptp.rat)
% 6.73/7.03 (declare-fun tptp.gbinomial_real (tptp.real tptp.nat) tptp.real)
% 6.73/7.03 (declare-fun tptp.bit_and_int_rel (tptp.product_prod_int_int tptp.product_prod_int_int) Bool)
% 6.73/7.03 (declare-fun tptp.bit_concat_bit (tptp.nat tptp.int tptp.int) tptp.int)
% 6.73/7.03 (declare-fun tptp.bit_ri7919022796975470100ot_int (tptp.int) tptp.int)
% 6.73/7.03 (declare-fun tptp.bit_ri6519982836138164636nteger (tptp.nat tptp.code_integer) tptp.code_integer)
% 6.73/7.03 (declare-fun tptp.bit_ri631733984087533419it_int (tptp.nat tptp.int) tptp.int)
% 6.73/7.03 (declare-fun tptp.bit_se3949692690581998587nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 6.73/7.03 (declare-fun tptp.bit_se725231765392027082nd_int (tptp.int tptp.int) tptp.int)
% 6.73/7.03 (declare-fun tptp.bit_se727722235901077358nd_nat (tptp.nat tptp.nat) tptp.nat)
% 6.73/7.03 (declare-fun tptp.bit_se8568078237143864401it_int (tptp.nat tptp.int) tptp.int)
% 6.73/7.03 (declare-fun tptp.bit_se8570568707652914677it_nat (tptp.nat tptp.nat) tptp.nat)
% 6.73/7.03 (declare-fun tptp.bit_se1345352211410354436nteger (tptp.nat tptp.code_integer) tptp.code_integer)
% 6.73/7.03 (declare-fun tptp.bit_se168947363167071951atural (tptp.nat tptp.code_natural) tptp.code_natural)
% 6.73/7.03 (declare-fun tptp.bit_se2159334234014336723it_int (tptp.nat tptp.int) tptp.int)
% 6.73/7.03 (declare-fun tptp.bit_se2161824704523386999it_nat (tptp.nat tptp.nat) tptp.nat)
% 6.73/7.03 (declare-fun tptp.bit_se2002935070580805687sk_nat (tptp.nat) tptp.nat)
% 6.73/7.03 (declare-fun tptp.bit_se1409905431419307370or_int (tptp.int tptp.int) tptp.int)
% 6.73/7.03 (declare-fun tptp.bit_se1412395901928357646or_nat (tptp.nat tptp.nat) tptp.nat)
% 6.73/7.03 (declare-fun tptp.bit_se545348938243370406it_int (tptp.nat tptp.int) tptp.int)
% 6.73/7.03 (declare-fun tptp.bit_se547839408752420682it_nat (tptp.nat tptp.nat) tptp.nat)
% 6.73/7.03 (declare-fun tptp.bit_se2793503036327961859nteger (tptp.nat tptp.code_integer) tptp.code_integer)
% 6.73/7.03 (declare-fun tptp.bit_se1617098188084679374atural (tptp.nat tptp.code_natural) tptp.code_natural)
% 6.73/7.03 (declare-fun tptp.bit_se7879613467334960850it_int (tptp.nat tptp.int) tptp.int)
% 6.73/7.03 (declare-fun tptp.bit_se7882103937844011126it_nat (tptp.nat tptp.nat) tptp.nat)
% 6.73/7.03 (declare-fun tptp.bit_se2923211474154528505it_int (tptp.nat tptp.int) tptp.int)
% 6.73/7.03 (declare-fun tptp.bit_se2925701944663578781it_nat (tptp.nat tptp.nat) tptp.nat)
% 6.73/7.03 (declare-fun tptp.bit_se7083795435491715335atural (tptp.nat tptp.code_natural) tptp.code_natural)
% 6.73/7.03 (declare-fun tptp.bit_se4203085406695923979it_int (tptp.nat tptp.int) tptp.int)
% 6.73/7.03 (declare-fun tptp.bit_se4205575877204974255it_nat (tptp.nat tptp.nat) tptp.nat)
% 6.73/7.03 (declare-fun tptp.bit_se6526347334894502574or_int (tptp.int tptp.int) tptp.int)
% 6.73/7.03 (declare-fun tptp.bit_se6528837805403552850or_nat (tptp.nat tptp.nat) tptp.nat)
% 6.73/7.03 (declare-fun tptp.bit_se1146084159140164899it_int (tptp.int tptp.nat) Bool)
% 6.73/7.03 (declare-fun tptp.bit_se1148574629649215175it_nat (tptp.nat tptp.nat) Bool)
% 6.73/7.03 (declare-fun tptp.bit_take_bit_num (tptp.nat tptp.num) tptp.option_num)
% 6.73/7.03 (declare-fun tptp.code_Suc (tptp.code_natural) tptp.code_natural)
% 6.73/7.03 (declare-fun tptp.code_divmod_abs (tptp.code_integer tptp.code_integer) tptp.produc8923325533196201883nteger)
% 6.73/7.03 (declare-fun tptp.code_divmod_integer (tptp.code_integer tptp.code_integer) tptp.produc8923325533196201883nteger)
% 6.73/7.03 (declare-fun tptp.code_int_of_integer (tptp.code_integer) tptp.int)
% 6.73/7.03 (declare-fun tptp.code_integer_of_int (tptp.int) tptp.code_integer)
% 6.73/7.03 (declare-fun tptp.code_integer_of_nat (tptp.nat) tptp.code_integer)
% 6.73/7.03 (declare-fun tptp.code_nat_of_integer (tptp.code_integer) tptp.nat)
% 6.73/7.03 (declare-fun tptp.code_nat_of_natural (tptp.code_natural) tptp.nat)
% 6.73/7.03 (declare-fun tptp.code_natural_of_nat (tptp.nat) tptp.code_natural)
% 6.73/7.03 (declare-fun tptp.comple7806235888213564991et_nat (tptp.set_set_nat) tptp.set_nat)
% 6.73/7.03 (declare-fun tptp.complete_Sup_Sup_nat (tptp.set_nat) tptp.nat)
% 6.73/7.03 (declare-fun tptp.comple7399068483239264473et_nat (tptp.set_set_nat) tptp.set_nat)
% 6.73/7.03 (declare-fun tptp.arg (tptp.complex) tptp.real)
% 6.73/7.03 (declare-fun tptp.cis (tptp.real) tptp.complex)
% 6.73/7.03 (declare-fun tptp.cnj (tptp.complex) tptp.complex)
% 6.73/7.03 (declare-fun tptp.complex2 (tptp.real tptp.real) tptp.complex)
% 6.73/7.03 (declare-fun tptp.im (tptp.complex) tptp.real)
% 6.73/7.03 (declare-fun tptp.re (tptp.complex) tptp.real)
% 6.73/7.03 (declare-fun tptp.csqrt (tptp.complex) tptp.complex)
% 6.73/7.03 (declare-fun tptp.imaginary_unit () tptp.complex)
% 6.73/7.03 (declare-fun tptp.rcis (tptp.real tptp.real) tptp.complex)
% 6.73/7.03 (declare-fun tptp.nat_to_rat_surj (tptp.nat) tptp.rat)
% 6.73/7.03 (declare-fun tptp.nth_item_rel (tptp.nat tptp.nat) Bool)
% 6.73/7.03 (declare-fun tptp.differ6690327859849518006l_real ((-> tptp.real tptp.real) tptp.filter_real) Bool)
% 6.73/7.03 (declare-fun tptp.has_fi5821293074295781190e_real ((-> tptp.real tptp.real) tptp.real tptp.filter_real) Bool)
% 6.73/7.03 (declare-fun tptp.adjust_div (tptp.product_prod_int_int) tptp.int)
% 6.73/7.03 (declare-fun tptp.adjust_mod (tptp.int tptp.int) tptp.int)
% 6.73/7.03 (declare-fun tptp.divmod_nat (tptp.nat tptp.nat) tptp.product_prod_nat_nat)
% 6.73/7.03 (declare-fun tptp.eucl_rel_int (tptp.int tptp.int tptp.product_prod_int_int) Bool)
% 6.73/7.03 (declare-fun tptp.unique5706413561485394159nteger (tptp.produc8923325533196201883nteger) Bool)
% 6.73/7.03 (declare-fun tptp.unique6319869463603278526ux_int (tptp.product_prod_int_int) Bool)
% 6.73/7.03 (declare-fun tptp.unique6322359934112328802ux_nat (tptp.product_prod_nat_nat) Bool)
% 6.73/7.03 (declare-fun tptp.unique3479559517661332726nteger (tptp.num tptp.num) tptp.produc8923325533196201883nteger)
% 6.73/7.03 (declare-fun tptp.unique5052692396658037445od_int (tptp.num tptp.num) tptp.product_prod_int_int)
% 6.73/7.03 (declare-fun tptp.unique5055182867167087721od_nat (tptp.num tptp.num) tptp.product_prod_nat_nat)
% 6.73/7.03 (declare-fun tptp.unique4921790084139445826nteger (tptp.num tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger)
% 6.73/7.03 (declare-fun tptp.unique5024387138958732305ep_int (tptp.num tptp.product_prod_int_int) tptp.product_prod_int_int)
% 6.73/7.03 (declare-fun tptp.unique5026877609467782581ep_nat (tptp.num tptp.product_prod_nat_nat) tptp.product_prod_nat_nat)
% 6.73/7.03 (declare-fun tptp.extended_eSuc (tptp.extended_enat) tptp.extended_enat)
% 6.73/7.03 (declare-fun tptp.extended_enat2 (tptp.nat) tptp.extended_enat)
% 6.73/7.03 (declare-fun tptp.extended_Abs_enat (tptp.option_nat) tptp.extended_enat)
% 6.73/7.03 (declare-fun tptp.extended_case_enat_o ((-> tptp.nat Bool) Bool tptp.extended_enat) Bool)
% 6.73/7.03 (declare-fun tptp.extend3600170679010898289d_enat ((-> tptp.nat tptp.extended_enat) tptp.extended_enat tptp.extended_enat) tptp.extended_enat)
% 6.73/7.03 (declare-fun tptp.extend5688581933313929465d_enat () tptp.extended_enat)
% 6.73/7.03 (declare-fun tptp.comm_s8582702949713902594nteger (tptp.code_integer tptp.nat) tptp.code_integer)
% 6.73/7.03 (declare-fun tptp.comm_s2602460028002588243omplex (tptp.complex tptp.nat) tptp.complex)
% 6.73/7.03 (declare-fun tptp.comm_s4660882817536571857er_int (tptp.int tptp.nat) tptp.int)
% 6.73/7.03 (declare-fun tptp.comm_s4663373288045622133er_nat (tptp.nat tptp.nat) tptp.nat)
% 6.73/7.03 (declare-fun tptp.comm_s4028243227959126397er_rat (tptp.rat tptp.nat) tptp.rat)
% 6.73/7.03 (declare-fun tptp.comm_s7457072308508201937r_real (tptp.real tptp.nat) tptp.real)
% 6.73/7.03 (declare-fun tptp.semiri3624122377584611663nteger (tptp.nat) tptp.code_integer)
% 6.73/7.03 (declare-fun tptp.semiri2447717529341329178atural (tptp.nat) tptp.code_natural)
% 6.73/7.03 (declare-fun tptp.semiri5044797733671781792omplex (tptp.nat) tptp.complex)
% 6.73/7.03 (declare-fun tptp.semiri4449623510593786356d_enat (tptp.nat) tptp.extended_enat)
% 6.73/7.03 (declare-fun tptp.semiri1406184849735516958ct_int (tptp.nat) tptp.int)
% 6.73/7.03 (declare-fun tptp.semiri1408675320244567234ct_nat (tptp.nat) tptp.nat)
% 6.73/7.03 (declare-fun tptp.semiri773545260158071498ct_rat (tptp.nat) tptp.rat)
% 6.73/7.03 (declare-fun tptp.semiri2265585572941072030t_real (tptp.nat) tptp.real)
% 6.73/7.03 (declare-fun tptp.invers8013647133539491842omplex (tptp.complex) tptp.complex)
% 6.73/7.03 (declare-fun tptp.inverse_inverse_rat (tptp.rat) tptp.rat)
% 6.73/7.03 (declare-fun tptp.inverse_inverse_real (tptp.real) tptp.real)
% 6.73/7.03 (declare-fun tptp.at_bot_real () tptp.filter_real)
% 6.73/7.03 (declare-fun tptp.at_top_nat () tptp.filter_nat)
% 6.73/7.03 (declare-fun tptp.at_top_real () tptp.filter_real)
% 6.73/7.03 (declare-fun tptp.eventually_nat ((-> tptp.nat Bool) tptp.filter_nat) Bool)
% 6.73/7.03 (declare-fun tptp.eventu1038000079068216329at_nat ((-> tptp.product_prod_nat_nat Bool) tptp.filter1242075044329608583at_nat) Bool)
% 6.73/7.03 (declare-fun tptp.filterlim_nat_nat ((-> tptp.nat tptp.nat) tptp.filter_nat tptp.filter_nat) Bool)
% 6.73/7.03 (declare-fun tptp.filterlim_nat_real ((-> tptp.nat tptp.real) tptp.filter_real tptp.filter_nat) Bool)
% 6.73/7.03 (declare-fun tptp.filterlim_real_real ((-> tptp.real tptp.real) tptp.filter_real tptp.filter_real) Bool)
% 6.73/7.03 (declare-fun tptp.prod_filter_nat_nat (tptp.filter_nat tptp.filter_nat) tptp.filter1242075044329608583at_nat)
% 6.73/7.03 (declare-fun tptp.finite_card_o (tptp.set_o) tptp.nat)
% 6.73/7.03 (declare-fun tptp.finite_card_complex (tptp.set_complex) tptp.nat)
% 6.73/7.03 (declare-fun tptp.finite_card_int (tptp.set_int) tptp.nat)
% 6.73/7.03 (declare-fun tptp.finite_card_list_o (tptp.set_list_o) tptp.nat)
% 6.73/7.03 (declare-fun tptp.finite5120063068150530198omplex (tptp.set_list_complex) tptp.nat)
% 6.73/7.03 (declare-fun tptp.finite_card_list_int (tptp.set_list_int) tptp.nat)
% 6.73/7.03 (declare-fun tptp.finite7325466520557071688st_nat (tptp.set_list_list_nat) tptp.nat)
% 6.73/7.03 (declare-fun tptp.finite_card_list_nat (tptp.set_list_nat) tptp.nat)
% 6.73/7.03 (declare-fun tptp.finite5631907774883551598et_nat (tptp.set_list_set_nat) tptp.nat)
% 6.73/7.03 (declare-fun tptp.finite5915292604075114978T_VEBT (tptp.set_list_VEBT_VEBT) tptp.nat)
% 6.73/7.03 (declare-fun tptp.finite_card_nat (tptp.set_nat) tptp.nat)
% 6.73/7.03 (declare-fun tptp.finite711546835091564841at_nat (tptp.set_Pr1261947904930325089at_nat) tptp.nat)
% 6.73/7.03 (declare-fun tptp.finite_card_real (tptp.set_real) tptp.nat)
% 6.73/7.03 (declare-fun tptp.finite_card_set_nat (tptp.set_set_nat) tptp.nat)
% 6.73/7.03 (declare-fun tptp.finite7802652506058667612T_VEBT (tptp.set_VEBT_VEBT) tptp.nat)
% 6.73/7.03 (declare-fun tptp.finite_finite_o (tptp.set_o) Bool)
% 6.73/7.03 (declare-fun tptp.finite3207457112153483333omplex (tptp.set_complex) Bool)
% 6.73/7.03 (declare-fun tptp.finite_finite_int (tptp.set_int) Bool)
% 6.73/7.03 (declare-fun tptp.finite_finite_list_o (tptp.set_list_o) Bool)
% 6.73/7.03 (declare-fun tptp.finite8712137658972009173omplex (tptp.set_list_complex) Bool)
% 6.73/7.03 (declare-fun tptp.finite3922522038869484883st_int (tptp.set_list_int) Bool)
% 6.73/7.03 (declare-fun tptp.finite8100373058378681591st_nat (tptp.set_list_nat) Bool)
% 6.73/7.03 (declare-fun tptp.finite3004134309566078307T_VEBT (tptp.set_list_VEBT_VEBT) Bool)
% 6.73/7.03 (declare-fun tptp.finite_finite_nat (tptp.set_nat) Bool)
% 6.73/7.03 (declare-fun tptp.finite_finite_num (tptp.set_num) Bool)
% 6.73/7.03 (declare-fun tptp.finite6177210948735845034at_nat (tptp.set_Pr1261947904930325089at_nat) Bool)
% 6.73/7.03 (declare-fun tptp.finite_finite_rat (tptp.set_rat) Bool)
% 6.73/7.03 (declare-fun tptp.finite_finite_real (tptp.set_real) Bool)
% 6.73/7.03 (declare-fun tptp.finite1152437895449049373et_nat (tptp.set_set_nat) Bool)
% 6.73/7.03 (declare-fun tptp.finite5795047828879050333T_VEBT (tptp.set_VEBT_VEBT) Bool)
% 6.73/7.03 (declare-fun tptp.bij_be1856998921033663316omplex ((-> tptp.complex tptp.complex) tptp.set_complex tptp.set_complex) Bool)
% 6.73/7.03 (declare-fun tptp.bij_betw_int_nat ((-> tptp.int tptp.nat) tptp.set_int tptp.set_nat) Bool)
% 6.73/7.03 (declare-fun tptp.bij_be8532844293280997160at_nat ((-> tptp.list_nat tptp.nat) tptp.set_list_nat tptp.set_nat) Bool)
% 6.73/7.03 (declare-fun tptp.bij_betw_nat_complex ((-> tptp.nat tptp.complex) tptp.set_nat tptp.set_complex) Bool)
% 6.73/7.03 (declare-fun tptp.bij_betw_nat_int ((-> tptp.nat tptp.int) tptp.set_nat tptp.set_int) Bool)
% 6.73/7.03 (declare-fun tptp.bij_be6293887246118711976st_nat ((-> tptp.nat tptp.list_nat) tptp.set_nat tptp.set_list_nat) Bool)
% 6.73/7.03 (declare-fun tptp.bij_betw_nat_nat ((-> tptp.nat tptp.nat) tptp.set_nat tptp.set_nat) Bool)
% 6.73/7.03 (declare-fun tptp.bij_be8693218025023041337at_nat ((-> tptp.nat tptp.product_prod_nat_nat) tptp.set_nat tptp.set_Pr1261947904930325089at_nat) Bool)
% 6.73/7.03 (declare-fun tptp.bij_be4790990086886966983at_nat ((-> tptp.nat tptp.sum_sum_nat_nat) tptp.set_nat tptp.set_Sum_sum_nat_nat) Bool)
% 6.73/7.03 (declare-fun tptp.bij_be5333170631980326235at_nat ((-> tptp.product_prod_nat_nat tptp.nat) tptp.set_Pr1261947904930325089at_nat tptp.set_nat) Bool)
% 6.73/7.03 (declare-fun tptp.bij_be5432664580149595207at_nat ((-> tptp.sum_sum_nat_nat tptp.nat) tptp.set_Sum_sum_nat_nat tptp.set_nat) Bool)
% 6.73/7.03 (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)
% 6.73/7.03 (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)
% 6.73/7.03 (declare-fun tptp.comp_nat_nat_nat ((-> tptp.nat tptp.nat) (-> tptp.nat tptp.nat) tptp.nat) tptp.nat)
% 6.73/7.03 (declare-fun tptp.id_o (Bool) Bool)
% 6.73/7.03 (declare-fun tptp.id_nat (tptp.nat) tptp.nat)
% 6.73/7.03 (declare-fun tptp.inj_on_int_nat ((-> tptp.int tptp.nat) tptp.set_int) Bool)
% 6.73/7.03 (declare-fun tptp.inj_on_list_nat_nat ((-> tptp.list_nat tptp.nat) tptp.set_list_nat) Bool)
% 6.73/7.03 (declare-fun tptp.inj_on_nat_int ((-> tptp.nat tptp.int) tptp.set_nat) Bool)
% 6.73/7.03 (declare-fun tptp.inj_on_nat_list_nat ((-> tptp.nat tptp.list_nat) tptp.set_nat) Bool)
% 6.73/7.03 (declare-fun tptp.inj_on_nat_nat ((-> tptp.nat tptp.nat) tptp.set_nat) Bool)
% 6.73/7.03 (declare-fun tptp.inj_on5538052773655684606at_nat ((-> tptp.nat tptp.product_prod_nat_nat) tptp.set_nat) Bool)
% 6.73/7.03 (declare-fun tptp.inj_on_nat_char ((-> tptp.nat tptp.char) tptp.set_nat) Bool)
% 6.73/7.03 (declare-fun tptp.inj_on5701776251185195458at_nat ((-> tptp.nat tptp.sum_sum_nat_nat) tptp.set_nat) Bool)
% 6.73/7.03 (declare-fun tptp.inj_on2178005380612969504at_nat ((-> tptp.product_prod_nat_nat tptp.nat) tptp.set_Pr1261947904930325089at_nat) Bool)
% 6.73/7.03 (declare-fun tptp.inj_on_real_real ((-> tptp.real tptp.real) tptp.set_real) Bool)
% 6.73/7.03 (declare-fun tptp.inj_on_set_nat_nat ((-> tptp.set_nat tptp.nat) tptp.set_set_nat) Bool)
% 6.73/7.03 (declare-fun tptp.inj_on6343450744447823682at_nat ((-> tptp.sum_sum_nat_nat tptp.nat) tptp.set_Sum_sum_nat_nat) Bool)
% 6.73/7.03 (declare-fun tptp.map_fu6549440983881763648atural ((-> tptp.code_natural tptp.nat) (-> (-> tptp.nat tptp.nat) tptp.code_natural tptp.code_natural) (-> tptp.nat tptp.nat tptp.nat) tptp.code_natural tptp.code_natural) tptp.code_natural)
% 6.73/7.03 (declare-fun tptp.map_fu1239815594074539274atural ((-> tptp.code_natural tptp.nat) (-> tptp.nat tptp.code_natural) (-> tptp.nat tptp.nat) tptp.code_natural) tptp.code_natural)
% 6.73/7.03 (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)
% 6.73/7.03 (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)
% 6.73/7.03 (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)
% 6.73/7.03 (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)
% 6.73/7.03 (declare-fun tptp.map_fu4333342158222067775at_rat ((-> tptp.rat tptp.product_prod_int_int) (-> (-> tptp.product_prod_int_int tptp.product_prod_int_int) tptp.rat tptp.rat) (-> tptp.product_prod_int_int tptp.product_prod_int_int tptp.product_prod_int_int) tptp.rat tptp.rat) tptp.rat)
% 6.73/7.03 (declare-fun tptp.map_fu898904425404107465nt_o_o ((-> tptp.rat tptp.product_prod_int_int) (-> Bool Bool) (-> tptp.product_prod_int_int Bool) tptp.rat) Bool)
% 6.73/7.03 (declare-fun tptp.map_fu5673905371560938248nt_rat ((-> tptp.rat tptp.product_prod_int_int) (-> tptp.product_prod_int_int tptp.rat) (-> tptp.product_prod_int_int tptp.product_prod_int_int) tptp.rat) tptp.rat)
% 6.73/7.03 (declare-fun tptp.map_fu1856342031159181835at_o_o ((-> tptp.real tptp.nat tptp.rat) (-> Bool Bool) (-> (-> tptp.nat tptp.rat) Bool) tptp.real) Bool)
% 6.73/7.03 (declare-fun tptp.the_in5290026491893676941l_real (tptp.set_real (-> tptp.real tptp.real) tptp.real) tptp.real)
% 6.73/7.03 (declare-fun tptp.fun_pair_leq () tptp.set_Pr8693737435421807431at_nat)
% 6.73/7.03 (declare-fun tptp.fun_pair_less () tptp.set_Pr8693737435421807431at_nat)
% 6.73/7.03 (declare-fun tptp.gcd_Gcd_int (tptp.set_int) tptp.int)
% 6.73/7.03 (declare-fun tptp.gcd_Gcd_nat (tptp.set_nat) tptp.nat)
% 6.73/7.03 (declare-fun tptp.gcd_Lcm_nat (tptp.set_nat) tptp.nat)
% 6.73/7.03 (declare-fun tptp.bezw (tptp.nat tptp.nat) tptp.product_prod_int_int)
% 6.73/7.03 (declare-fun tptp.bezw_rel (tptp.product_prod_nat_nat tptp.product_prod_nat_nat) Bool)
% 6.73/7.03 (declare-fun tptp.gcd_gcd_Code_integer (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 6.73/7.03 (declare-fun tptp.gcd_gcd_int (tptp.int tptp.int) tptp.int)
% 6.73/7.03 (declare-fun tptp.gcd_gcd_nat (tptp.nat tptp.nat) tptp.nat)
% 6.73/7.03 (declare-fun tptp.gcd_lcm_Code_integer (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 6.73/7.03 (declare-fun tptp.gcd_lcm_int (tptp.int tptp.int) tptp.int)
% 6.73/7.03 (declare-fun tptp.gcd_lcm_nat (tptp.nat tptp.nat) tptp.nat)
% 6.73/7.03 (declare-fun tptp.gcd_nat_rel (tptp.product_prod_nat_nat tptp.product_prod_nat_nat) Bool)
% 6.73/7.03 (declare-fun tptp.semiri4256215615220890538in_int (tptp.set_int) tptp.int)
% 6.73/7.03 (declare-fun tptp.semiri4258706085729940814in_nat (tptp.set_nat) tptp.nat)
% 6.73/7.03 (declare-fun tptp.abs_abs_Code_integer (tptp.code_integer) tptp.code_integer)
% 6.73/7.03 (declare-fun tptp.abs_abs_complex (tptp.complex) tptp.complex)
% 6.73/7.03 (declare-fun tptp.abs_abs_int (tptp.int) tptp.int)
% 6.73/7.03 (declare-fun tptp.abs_abs_rat (tptp.rat) tptp.rat)
% 6.73/7.03 (declare-fun tptp.abs_abs_real (tptp.real) tptp.real)
% 6.73/7.03 (declare-fun tptp.minus_8373710615458151222nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 6.73/7.03 (declare-fun tptp.minus_7197305767214868737atural (tptp.code_natural tptp.code_natural) tptp.code_natural)
% 6.73/7.03 (declare-fun tptp.minus_minus_complex (tptp.complex tptp.complex) tptp.complex)
% 6.73/7.03 (declare-fun tptp.minus_3235023915231533773d_enat (tptp.extended_enat tptp.extended_enat) tptp.extended_enat)
% 6.73/7.03 (declare-fun tptp.minus_minus_int (tptp.int tptp.int) tptp.int)
% 6.73/7.03 (declare-fun tptp.minus_minus_nat (tptp.nat tptp.nat) tptp.nat)
% 6.73/7.03 (declare-fun tptp.minus_minus_rat (tptp.rat tptp.rat) tptp.rat)
% 6.73/7.03 (declare-fun tptp.minus_minus_real (tptp.real tptp.real) tptp.real)
% 6.73/7.03 (declare-fun tptp.minus_minus_set_o (tptp.set_o tptp.set_o) tptp.set_o)
% 6.73/7.03 (declare-fun tptp.minus_811609699411566653omplex (tptp.set_complex tptp.set_complex) tptp.set_complex)
% 6.73/7.03 (declare-fun tptp.minus_minus_set_int (tptp.set_int tptp.set_int) tptp.set_int)
% 6.73/7.03 (declare-fun tptp.minus_7954133019191499631st_nat (tptp.set_list_nat tptp.set_list_nat) tptp.set_list_nat)
% 6.73/7.03 (declare-fun tptp.minus_minus_set_nat (tptp.set_nat tptp.set_nat) tptp.set_nat)
% 6.73/7.03 (declare-fun tptp.minus_1356011639430497352at_nat (tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat) tptp.set_Pr1261947904930325089at_nat)
% 6.73/7.03 (declare-fun tptp.minus_minus_set_real (tptp.set_real tptp.set_real) tptp.set_real)
% 6.73/7.03 (declare-fun tptp.minus_2163939370556025621et_nat (tptp.set_set_nat tptp.set_set_nat) tptp.set_set_nat)
% 6.73/7.03 (declare-fun tptp.minus_5127226145743854075T_VEBT (tptp.set_VEBT_VEBT tptp.set_VEBT_VEBT) tptp.set_VEBT_VEBT)
% 6.73/7.03 (declare-fun tptp.monoid_nat ((-> tptp.nat tptp.nat tptp.nat) tptp.nat) Bool)
% 6.73/7.03 (declare-fun tptp.one_one_Code_integer () tptp.code_integer)
% 6.73/7.03 (declare-fun tptp.one_one_Code_natural () tptp.code_natural)
% 6.73/7.03 (declare-fun tptp.one_one_complex () tptp.complex)
% 6.73/7.03 (declare-fun tptp.one_on7984719198319812577d_enat () tptp.extended_enat)
% 6.73/7.03 (declare-fun tptp.one_one_int () tptp.int)
% 6.73/7.03 (declare-fun tptp.one_one_nat () tptp.nat)
% 6.73/7.03 (declare-fun tptp.one_one_rat () tptp.rat)
% 6.73/7.03 (declare-fun tptp.one_one_real () tptp.real)
% 6.73/7.03 (declare-fun tptp.plus_p5714425477246183910nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 6.73/7.03 (declare-fun tptp.plus_p4538020629002901425atural (tptp.code_natural tptp.code_natural) tptp.code_natural)
% 6.73/7.03 (declare-fun tptp.plus_plus_complex (tptp.complex tptp.complex) tptp.complex)
% 6.73/7.03 (declare-fun tptp.plus_p3455044024723400733d_enat (tptp.extended_enat tptp.extended_enat) tptp.extended_enat)
% 6.73/7.03 (declare-fun tptp.plus_plus_int (tptp.int tptp.int) tptp.int)
% 6.73/7.03 (declare-fun tptp.plus_plus_nat (tptp.nat tptp.nat) tptp.nat)
% 6.73/7.03 (declare-fun tptp.plus_plus_num (tptp.num tptp.num) tptp.num)
% 6.73/7.03 (declare-fun tptp.plus_plus_rat (tptp.rat tptp.rat) tptp.rat)
% 6.73/7.03 (declare-fun tptp.plus_plus_real (tptp.real tptp.real) tptp.real)
% 6.73/7.03 (declare-fun tptp.sgn_sgn_Code_integer (tptp.code_integer) tptp.code_integer)
% 6.73/7.03 (declare-fun tptp.sgn_sgn_int (tptp.int) tptp.int)
% 6.73/7.03 (declare-fun tptp.sgn_sgn_rat (tptp.rat) tptp.rat)
% 6.73/7.03 (declare-fun tptp.sgn_sgn_real (tptp.real) tptp.real)
% 6.73/7.03 (declare-fun tptp.times_3573771949741848930nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 6.73/7.03 (declare-fun tptp.times_2397367101498566445atural (tptp.code_natural tptp.code_natural) tptp.code_natural)
% 6.73/7.03 (declare-fun tptp.times_times_complex (tptp.complex tptp.complex) tptp.complex)
% 6.73/7.03 (declare-fun tptp.times_7803423173614009249d_enat (tptp.extended_enat tptp.extended_enat) tptp.extended_enat)
% 6.73/7.03 (declare-fun tptp.times_times_int (tptp.int tptp.int) tptp.int)
% 6.73/7.03 (declare-fun tptp.times_times_nat (tptp.nat tptp.nat) tptp.nat)
% 6.73/7.03 (declare-fun tptp.times_times_num (tptp.num tptp.num) tptp.num)
% 6.73/7.03 (declare-fun tptp.times_times_rat (tptp.rat tptp.rat) tptp.rat)
% 6.73/7.03 (declare-fun tptp.times_times_real (tptp.real tptp.real) tptp.real)
% 6.73/7.03 (declare-fun tptp.uminus1351360451143612070nteger (tptp.code_integer) tptp.code_integer)
% 6.73/7.03 (declare-fun tptp.uminus1482373934393186551omplex (tptp.complex) tptp.complex)
% 6.73/7.03 (declare-fun tptp.uminus_uminus_int (tptp.int) tptp.int)
% 6.73/7.03 (declare-fun tptp.uminus_uminus_rat (tptp.rat) tptp.rat)
% 6.73/7.03 (declare-fun tptp.uminus_uminus_real (tptp.real) tptp.real)
% 6.73/7.03 (declare-fun tptp.uminus8566677241136511917omplex (tptp.set_complex) tptp.set_complex)
% 6.73/7.03 (declare-fun tptp.uminus1532241313380277803et_int (tptp.set_int) tptp.set_int)
% 6.73/7.03 (declare-fun tptp.uminus5710092332889474511et_nat (tptp.set_nat) tptp.set_nat)
% 6.73/7.03 (declare-fun tptp.uminus6524753893492686040at_nat (tptp.set_Pr1261947904930325089at_nat) tptp.set_Pr1261947904930325089at_nat)
% 6.73/7.03 (declare-fun tptp.uminus612125837232591019t_real (tptp.set_real) tptp.set_real)
% 6.73/7.03 (declare-fun tptp.zero_z3403309356797280102nteger () tptp.code_integer)
% 6.73/7.03 (declare-fun tptp.zero_z2226904508553997617atural () tptp.code_natural)
% 6.73/7.03 (declare-fun tptp.zero_zero_complex () tptp.complex)
% 6.73/7.03 (declare-fun tptp.zero_z5237406670263579293d_enat () tptp.extended_enat)
% 6.73/7.03 (declare-fun tptp.zero_zero_int () tptp.int)
% 6.73/7.03 (declare-fun tptp.zero_zero_nat () tptp.nat)
% 6.73/7.03 (declare-fun tptp.zero_zero_rat () tptp.rat)
% 6.73/7.03 (declare-fun tptp.zero_zero_real () tptp.real)
% 6.73/7.03 (declare-fun tptp.groups8507830703676809646_o_nat ((-> Bool tptp.nat) tptp.set_o) tptp.nat)
% 6.73/7.03 (declare-fun tptp.groups6621422865394947399nteger ((-> tptp.complex tptp.code_integer) tptp.set_complex) tptp.code_integer)
% 6.73/7.03 (declare-fun tptp.groups7754918857620584856omplex ((-> tptp.complex tptp.complex) tptp.set_complex) tptp.complex)
% 6.73/7.03 (declare-fun tptp.groups5690904116761175830ex_int ((-> tptp.complex tptp.int) tptp.set_complex) tptp.int)
% 6.73/7.03 (declare-fun tptp.groups5693394587270226106ex_nat ((-> tptp.complex tptp.nat) tptp.set_complex) tptp.nat)
% 6.73/7.03 (declare-fun tptp.groups5058264527183730370ex_rat ((-> tptp.complex tptp.rat) tptp.set_complex) tptp.rat)
% 6.73/7.03 (declare-fun tptp.groups5808333547571424918x_real ((-> tptp.complex tptp.real) tptp.set_complex) tptp.real)
% 6.73/7.03 (declare-fun tptp.groups7873554091576472773nteger ((-> tptp.int tptp.code_integer) tptp.set_int) tptp.code_integer)
% 6.73/7.03 (declare-fun tptp.groups3049146728041665814omplex ((-> tptp.int tptp.complex) tptp.set_int) tptp.complex)
% 6.73/7.03 (declare-fun tptp.groups4538972089207619220nt_int ((-> tptp.int tptp.int) tptp.set_int) tptp.int)
% 6.73/7.03 (declare-fun tptp.groups4541462559716669496nt_nat ((-> tptp.int tptp.nat) tptp.set_int) tptp.nat)
% 6.73/7.03 (declare-fun tptp.groups3906332499630173760nt_rat ((-> tptp.int tptp.rat) tptp.set_int) tptp.rat)
% 6.73/7.03 (declare-fun tptp.groups8778361861064173332t_real ((-> tptp.int tptp.real) tptp.set_int) tptp.real)
% 6.73/7.03 (declare-fun tptp.groups6529277132148336714omplex ((-> tptp.list_nat tptp.complex) tptp.set_list_nat) tptp.complex)
% 6.73/7.03 (declare-fun tptp.groups4396056296759096172at_nat ((-> tptp.list_nat tptp.nat) tptp.set_list_nat) tptp.nat)
% 6.73/7.03 (declare-fun tptp.groups8399112307953289288t_real ((-> tptp.list_nat tptp.real) tptp.set_list_nat) tptp.real)
% 6.73/7.03 (declare-fun tptp.groups7501900531339628137nteger ((-> tptp.nat tptp.code_integer) tptp.set_nat) tptp.code_integer)
% 6.73/7.03 (declare-fun tptp.groups2073611262835488442omplex ((-> tptp.nat tptp.complex) tptp.set_nat) tptp.complex)
% 6.73/7.03 (declare-fun tptp.groups7108830773950497114d_enat ((-> tptp.nat tptp.extended_enat) tptp.set_nat) tptp.extended_enat)
% 6.73/7.03 (declare-fun tptp.groups3539618377306564664at_int ((-> tptp.nat tptp.int) tptp.set_nat) tptp.int)
% 6.73/7.03 (declare-fun tptp.groups3542108847815614940at_nat ((-> tptp.nat tptp.nat) tptp.set_nat) tptp.nat)
% 6.73/7.03 (declare-fun tptp.groups2906978787729119204at_rat ((-> tptp.nat tptp.rat) tptp.set_nat) tptp.rat)
% 6.73/7.03 (declare-fun tptp.groups6591440286371151544t_real ((-> tptp.nat tptp.real) tptp.set_nat) tptp.real)
% 6.73/7.03 (declare-fun tptp.groups7713935264441627589nteger ((-> tptp.real tptp.code_integer) tptp.set_real) tptp.code_integer)
% 6.73/7.03 (declare-fun tptp.groups5754745047067104278omplex ((-> tptp.real tptp.complex) tptp.set_real) tptp.complex)
% 6.73/7.03 (declare-fun tptp.groups1932886352136224148al_int ((-> tptp.real tptp.int) tptp.set_real) tptp.int)
% 6.73/7.03 (declare-fun tptp.groups1935376822645274424al_nat ((-> tptp.real tptp.nat) tptp.set_real) tptp.nat)
% 6.73/7.03 (declare-fun tptp.groups1300246762558778688al_rat ((-> tptp.real tptp.rat) tptp.set_real) tptp.rat)
% 6.73/7.03 (declare-fun tptp.groups8097168146408367636l_real ((-> tptp.real tptp.real) tptp.set_real) tptp.real)
% 6.73/7.03 (declare-fun tptp.groups8255218700646806128omplex ((-> tptp.set_nat tptp.complex) tptp.set_set_nat) tptp.complex)
% 6.73/7.03 (declare-fun tptp.groups8294997508430121362at_nat ((-> tptp.set_nat tptp.nat) tptp.set_set_nat) tptp.nat)
% 6.73/7.03 (declare-fun tptp.groups5107569545109728110t_real ((-> tptp.set_nat tptp.real) tptp.set_set_nat) tptp.real)
% 6.73/7.03 (declare-fun tptp.groups771621172384141258BT_nat ((-> tptp.vEBT_VEBT tptp.nat) tptp.set_VEBT_VEBT) tptp.nat)
% 6.73/7.03 (declare-fun tptp.groups8682486955453173170nteger ((-> tptp.complex tptp.code_integer) tptp.set_complex) tptp.code_integer)
% 6.73/7.03 (declare-fun tptp.groups3708469109370488835omplex ((-> tptp.complex tptp.complex) tptp.set_complex) tptp.complex)
% 6.73/7.03 (declare-fun tptp.groups858564598930262913ex_int ((-> tptp.complex tptp.int) tptp.set_complex) tptp.int)
% 6.73/7.03 (declare-fun tptp.groups861055069439313189ex_nat ((-> tptp.complex tptp.nat) tptp.set_complex) tptp.nat)
% 6.73/7.03 (declare-fun tptp.groups225925009352817453ex_rat ((-> tptp.complex tptp.rat) tptp.set_complex) tptp.rat)
% 6.73/7.03 (declare-fun tptp.groups766887009212190081x_real ((-> tptp.complex tptp.real) tptp.set_complex) tptp.real)
% 6.73/7.03 (declare-fun tptp.groups3827104343326376752nteger ((-> tptp.int tptp.code_integer) tptp.set_int) tptp.code_integer)
% 6.73/7.03 (declare-fun tptp.groups7440179247065528705omplex ((-> tptp.int tptp.complex) tptp.set_int) tptp.complex)
% 6.73/7.03 (declare-fun tptp.groups1705073143266064639nt_int ((-> tptp.int tptp.int) tptp.set_int) tptp.int)
% 6.73/7.03 (declare-fun tptp.groups1707563613775114915nt_nat ((-> tptp.int tptp.nat) tptp.set_int) tptp.nat)
% 6.73/7.03 (declare-fun tptp.groups1072433553688619179nt_rat ((-> tptp.int tptp.rat) tptp.set_int) tptp.rat)
% 6.73/7.03 (declare-fun tptp.groups2316167850115554303t_real ((-> tptp.int tptp.real) tptp.set_int) tptp.real)
% 6.73/7.03 (declare-fun tptp.groups3455450783089532116nteger ((-> tptp.nat tptp.code_integer) tptp.set_nat) tptp.code_integer)
% 6.73/7.03 (declare-fun tptp.groups6464643781859351333omplex ((-> tptp.nat tptp.complex) tptp.set_nat) tptp.complex)
% 6.73/7.03 (declare-fun tptp.groups705719431365010083at_int ((-> tptp.nat tptp.int) tptp.set_nat) tptp.int)
% 6.73/7.03 (declare-fun tptp.groups708209901874060359at_nat ((-> tptp.nat tptp.nat) tptp.set_nat) tptp.nat)
% 6.73/7.03 (declare-fun tptp.groups73079841787564623at_rat ((-> tptp.nat tptp.rat) tptp.set_nat) tptp.rat)
% 6.73/7.03 (declare-fun tptp.groups129246275422532515t_real ((-> tptp.nat tptp.real) tptp.set_nat) tptp.real)
% 6.73/7.03 (declare-fun tptp.groups8110221916422527690omplex ((-> tptp.product_prod_nat_nat tptp.complex) tptp.set_Pr1261947904930325089at_nat) tptp.complex)
% 6.73/7.03 (declare-fun tptp.groups6225526099057966256nteger ((-> tptp.real tptp.code_integer) tptp.set_real) tptp.code_integer)
% 6.73/7.03 (declare-fun tptp.groups713298508707869441omplex ((-> tptp.real tptp.complex) tptp.set_real) tptp.complex)
% 6.73/7.03 (declare-fun tptp.groups4694064378042380927al_int ((-> tptp.real tptp.int) tptp.set_real) tptp.int)
% 6.73/7.03 (declare-fun tptp.groups4696554848551431203al_nat ((-> tptp.real tptp.nat) tptp.set_real) tptp.nat)
% 6.73/7.03 (declare-fun tptp.groups4061424788464935467al_rat ((-> tptp.real tptp.rat) tptp.set_real) tptp.rat)
% 6.73/7.03 (declare-fun tptp.groups1681761925125756287l_real ((-> tptp.real tptp.real) tptp.set_real) tptp.real)
% 6.73/7.03 (declare-fun tptp.groups9116527308978886569_o_int ((-> Bool tptp.int) tptp.int tptp.list_o) tptp.int)
% 6.73/7.03 (declare-fun tptp.groups4561878855575611511st_nat (tptp.list_nat) tptp.nat)
% 6.73/7.03 (declare-fun tptp.the_real ((-> tptp.real Bool)) tptp.real)
% 6.73/7.03 (declare-fun tptp.if_Code_integer (Bool tptp.code_integer tptp.code_integer) tptp.code_integer)
% 6.73/7.03 (declare-fun tptp.if_complex (Bool tptp.complex tptp.complex) tptp.complex)
% 6.73/7.03 (declare-fun tptp.if_Extended_enat (Bool tptp.extended_enat tptp.extended_enat) tptp.extended_enat)
% 6.73/7.03 (declare-fun tptp.if_int (Bool tptp.int tptp.int) tptp.int)
% 6.73/7.03 (declare-fun tptp.if_list_nat (Bool tptp.list_nat tptp.list_nat) tptp.list_nat)
% 6.73/7.03 (declare-fun tptp.if_nat (Bool tptp.nat tptp.nat) tptp.nat)
% 6.73/7.03 (declare-fun tptp.if_num (Bool tptp.num tptp.num) tptp.num)
% 6.73/7.03 (declare-fun tptp.if_option_nat (Bool tptp.option_nat tptp.option_nat) tptp.option_nat)
% 6.73/7.03 (declare-fun tptp.if_option_num (Bool tptp.option_num tptp.option_num) tptp.option_num)
% 6.73/7.03 (declare-fun tptp.if_Pro6119634080678213985nteger (Bool tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger)
% 6.73/7.03 (declare-fun tptp.if_Pro3027730157355071871nt_int (Bool tptp.product_prod_int_int tptp.product_prod_int_int) tptp.product_prod_int_int)
% 6.73/7.03 (declare-fun tptp.if_Pro6206227464963214023at_nat (Bool tptp.product_prod_nat_nat tptp.product_prod_nat_nat) tptp.product_prod_nat_nat)
% 6.73/7.03 (declare-fun tptp.if_rat (Bool tptp.rat tptp.rat) tptp.rat)
% 6.73/7.03 (declare-fun tptp.if_real (Bool tptp.real tptp.real) tptp.real)
% 6.73/7.03 (declare-fun tptp.if_set_nat (Bool tptp.set_nat tptp.set_nat) tptp.set_nat)
% 6.73/7.03 (declare-fun tptp.if_Sum_sum_nat_nat (Bool tptp.sum_sum_nat_nat tptp.sum_sum_nat_nat) tptp.sum_sum_nat_nat)
% 6.73/7.03 (declare-fun tptp.if_VEBT_VEBT (Bool tptp.vEBT_VEBT tptp.vEBT_VEBT) tptp.vEBT_VEBT)
% 6.73/7.03 (declare-fun tptp.infini8530281810654367211te_nat (tptp.set_nat tptp.nat) tptp.nat)
% 6.73/7.03 (declare-fun tptp.abs_Integ (tptp.product_prod_nat_nat) tptp.int)
% 6.73/7.03 (declare-fun tptp.rep_Integ (tptp.int) tptp.product_prod_nat_nat)
% 6.73/7.03 (declare-fun tptp.intrel (tptp.product_prod_nat_nat tptp.product_prod_nat_nat) Bool)
% 6.73/7.03 (declare-fun tptp.nat2 (tptp.int) tptp.nat)
% 6.73/7.03 (declare-fun tptp.pcr_int (tptp.product_prod_nat_nat tptp.int) Bool)
% 6.73/7.03 (declare-fun tptp.ring_1_Ints_real () tptp.set_real)
% 6.73/7.03 (declare-fun tptp.ring_1_of_int_rat (tptp.int) tptp.rat)
% 6.73/7.03 (declare-fun tptp.ring_1_of_int_real (tptp.int) tptp.real)
% 6.73/7.03 (declare-fun tptp.inf_inf_int (tptp.int tptp.int) tptp.int)
% 6.73/7.03 (declare-fun tptp.inf_inf_nat (tptp.nat tptp.nat) tptp.nat)
% 6.73/7.03 (declare-fun tptp.inf_inf_rat (tptp.rat tptp.rat) tptp.rat)
% 6.73/7.03 (declare-fun tptp.inf_inf_set_complex (tptp.set_complex tptp.set_complex) tptp.set_complex)
% 6.73/7.03 (declare-fun tptp.inf_inf_set_int (tptp.set_int tptp.set_int) tptp.set_int)
% 6.73/7.03 (declare-fun tptp.inf_inf_set_nat (tptp.set_nat tptp.set_nat) tptp.set_nat)
% 6.73/7.03 (declare-fun tptp.inf_inf_set_num (tptp.set_num tptp.set_num) tptp.set_num)
% 6.73/7.03 (declare-fun tptp.inf_in2572325071724192079at_nat (tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat) tptp.set_Pr1261947904930325089at_nat)
% 6.73/7.03 (declare-fun tptp.inf_inf_set_rat (tptp.set_rat tptp.set_rat) tptp.set_rat)
% 6.73/7.03 (declare-fun tptp.inf_inf_set_real (tptp.set_real tptp.set_real) tptp.set_real)
% 6.73/7.03 (declare-fun tptp.semila9081495762789891438tr_nat ((-> tptp.nat tptp.nat tptp.nat) tptp.nat) Bool)
% 6.73/7.03 (declare-fun tptp.semila1623282765462674594er_nat ((-> tptp.nat tptp.nat tptp.nat) tptp.nat (-> tptp.nat tptp.nat Bool) (-> tptp.nat tptp.nat Bool)) Bool)
% 6.73/7.03 (declare-fun tptp.sup_sup_int (tptp.int tptp.int) tptp.int)
% 6.73/7.03 (declare-fun tptp.sup_sup_nat (tptp.nat tptp.nat) tptp.nat)
% 6.73/7.03 (declare-fun tptp.sup_sup_rat (tptp.rat tptp.rat) tptp.rat)
% 6.73/7.03 (declare-fun tptp.sup_sup_set_complex (tptp.set_complex tptp.set_complex) tptp.set_complex)
% 6.73/7.03 (declare-fun tptp.sup_sup_set_int (tptp.set_int tptp.set_int) tptp.set_int)
% 6.73/7.03 (declare-fun tptp.sup_sup_set_list_nat (tptp.set_list_nat tptp.set_list_nat) tptp.set_list_nat)
% 6.73/7.03 (declare-fun tptp.sup_sup_set_nat (tptp.set_nat tptp.set_nat) tptp.set_nat)
% 6.73/7.03 (declare-fun tptp.sup_sup_set_num (tptp.set_num tptp.set_num) tptp.set_num)
% 6.73/7.03 (declare-fun tptp.sup_su6327502436637775413at_nat (tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat) tptp.set_Pr1261947904930325089at_nat)
% 6.73/7.03 (declare-fun tptp.sup_sup_set_rat (tptp.set_rat tptp.set_rat) tptp.set_rat)
% 6.73/7.03 (declare-fun tptp.sup_sup_set_real (tptp.set_real tptp.set_real) tptp.set_real)
% 6.73/7.03 (declare-fun tptp.sup_sup_set_set_nat (tptp.set_set_nat tptp.set_set_nat) tptp.set_set_nat)
% 6.73/7.03 (declare-fun tptp.lattic8265883725875713057ax_nat (tptp.set_nat) tptp.nat)
% 6.73/7.03 (declare-fun tptp.lattic5364784637807008409ex_nat ((-> tptp.complex tptp.nat) tptp.set_complex) tptp.complex)
% 6.73/7.03 (declare-fun tptp.lattic1922116423962787043ex_num ((-> tptp.complex tptp.num) tptp.set_complex) tptp.complex)
% 6.73/7.03 (declare-fun tptp.lattic4729654577720512673ex_rat ((-> tptp.complex tptp.rat) tptp.set_complex) tptp.complex)
% 6.73/7.03 (declare-fun tptp.lattic5003618458639192673nt_num ((-> tptp.int tptp.num) tptp.set_int) tptp.int)
% 6.73/7.03 (declare-fun tptp.lattic7811156612396918303nt_rat ((-> tptp.int tptp.rat) tptp.set_int) tptp.int)
% 6.73/7.03 (declare-fun tptp.lattic7446932960582359483at_nat ((-> tptp.nat tptp.nat) tptp.set_nat) tptp.nat)
% 6.73/7.03 (declare-fun tptp.lattic4004264746738138117at_num ((-> tptp.nat tptp.num) tptp.set_nat) tptp.nat)
% 6.73/7.03 (declare-fun tptp.lattic6811802900495863747at_rat ((-> tptp.nat tptp.rat) tptp.set_nat) tptp.nat)
% 6.73/7.03 (declare-fun tptp.lattic1613168225601753569al_num ((-> tptp.real tptp.num) tptp.set_real) tptp.real)
% 6.73/7.03 (declare-fun tptp.lattic4420706379359479199al_rat ((-> tptp.real tptp.rat) tptp.set_real) tptp.real)
% 6.73/7.03 (declare-fun tptp.lattic7826324295020591184_F_nat ((-> tptp.nat tptp.nat tptp.nat) tptp.nat tptp.set_nat) tptp.nat)
% 6.73/7.03 (declare-fun tptp.bfun_nat_real ((-> tptp.nat tptp.real) tptp.filter_nat) Bool)
% 6.73/7.03 (declare-fun tptp.append_nat (tptp.list_nat tptp.list_nat) tptp.list_nat)
% 6.73/7.03 (declare-fun tptp.concat_o (tptp.list_list_o) tptp.list_o)
% 6.73/7.03 (declare-fun tptp.concat_int (tptp.list_list_int) tptp.list_int)
% 6.73/7.03 (declare-fun tptp.concat_nat (tptp.list_list_nat) tptp.list_nat)
% 6.73/7.03 (declare-fun tptp.concat_VEBT_VEBT (tptp.list_list_VEBT_VEBT) tptp.list_VEBT_VEBT)
% 6.73/7.03 (declare-fun tptp.count_list_o (tptp.list_o Bool) tptp.nat)
% 6.73/7.03 (declare-fun tptp.count_list_complex (tptp.list_complex tptp.complex) tptp.nat)
% 6.73/7.03 (declare-fun tptp.count_list_int (tptp.list_int tptp.int) tptp.nat)
% 6.73/7.03 (declare-fun tptp.count_list_nat (tptp.list_nat tptp.nat) tptp.nat)
% 6.73/7.03 (declare-fun tptp.count_list_real (tptp.list_real tptp.real) tptp.nat)
% 6.73/7.03 (declare-fun tptp.count_list_set_nat (tptp.list_set_nat tptp.set_nat) tptp.nat)
% 6.73/7.03 (declare-fun tptp.count_list_VEBT_VEBT (tptp.list_VEBT_VEBT tptp.vEBT_VEBT) tptp.nat)
% 6.73/7.03 (declare-fun tptp.distinct_o (tptp.list_o) Bool)
% 6.73/7.03 (declare-fun tptp.distinct_complex (tptp.list_complex) Bool)
% 6.73/7.03 (declare-fun tptp.distinct_int (tptp.list_int) Bool)
% 6.73/7.03 (declare-fun tptp.distinct_list_nat (tptp.list_list_nat) Bool)
% 6.73/7.03 (declare-fun tptp.distinct_nat (tptp.list_nat) Bool)
% 6.73/7.03 (declare-fun tptp.distin6923225563576452346at_nat (tptp.list_P6011104703257516679at_nat) Bool)
% 6.73/7.03 (declare-fun tptp.distinct_real (tptp.list_real) Bool)
% 6.73/7.03 (declare-fun tptp.distinct_set_nat (tptp.list_set_nat) Bool)
% 6.73/7.03 (declare-fun tptp.distinct_VEBT_VEBT (tptp.list_VEBT_VEBT) Bool)
% 6.73/7.03 (declare-fun tptp.enumerate_o (tptp.nat tptp.list_o) tptp.list_P7333126701944960589_nat_o)
% 6.73/7.03 (declare-fun tptp.enumerate_int (tptp.nat tptp.list_int) tptp.list_P3521021558325789923at_int)
% 6.73/7.03 (declare-fun tptp.enumerate_nat (tptp.nat tptp.list_nat) tptp.list_P6011104703257516679at_nat)
% 6.73/7.03 (declare-fun tptp.enumerate_VEBT_VEBT (tptp.nat tptp.list_VEBT_VEBT) tptp.list_P5647936690300460905T_VEBT)
% 6.73/7.03 (declare-fun tptp.find_o ((-> Bool Bool) tptp.list_o) tptp.option_o)
% 6.73/7.03 (declare-fun tptp.find_int ((-> tptp.int Bool) tptp.list_int) tptp.option_int)
% 6.73/7.03 (declare-fun tptp.find_nat ((-> tptp.nat Bool) tptp.list_nat) tptp.option_nat)
% 6.73/7.03 (declare-fun tptp.find_num ((-> tptp.num Bool) tptp.list_num) tptp.option_num)
% 6.73/7.03 (declare-fun tptp.find_P8199882355184865565at_nat ((-> tptp.product_prod_nat_nat Bool) tptp.list_P6011104703257516679at_nat) tptp.option4927543243414619207at_nat)
% 6.73/7.03 (declare-fun tptp.find_VEBT_VEBT ((-> tptp.vEBT_VEBT Bool) tptp.list_VEBT_VEBT) tptp.option_VEBT_VEBT)
% 6.73/7.03 (declare-fun tptp.fold_nat_nat ((-> tptp.nat tptp.nat tptp.nat) tptp.list_nat tptp.nat) tptp.nat)
% 6.73/7.03 (declare-fun tptp.lenlex_o (tptp.set_Product_prod_o_o) tptp.set_Pr6227168374412355847list_o)
% 6.73/7.03 (declare-fun tptp.lenlex_Code_integer (tptp.set_Pr4811707699266497531nteger) tptp.set_Pr7565137564259432987nteger)
% 6.73/7.03 (declare-fun tptp.lenlex_int (tptp.set_Pr958786334691620121nt_int) tptp.set_Pr765067013931698361st_int)
% 6.73/7.03 (declare-fun tptp.lenlex_nat (tptp.set_Pr1261947904930325089at_nat) tptp.set_Pr3451248702717554689st_nat)
% 6.73/7.03 (declare-fun tptp.lenlex325483962726685836at_nat (tptp.set_Pr8693737435421807431at_nat) tptp.set_Pr1542805901266377927at_nat)
% 6.73/7.03 (declare-fun tptp.lenlex1357538814655152620at_nat (tptp.set_Pr4329608150637261639at_nat) tptp.set_Pr4333006031979791559at_nat)
% 6.73/7.03 (declare-fun tptp.lenlex_VEBT_VEBT (tptp.set_Pr6192946355708809607T_VEBT) tptp.set_Pr1916528119006554503T_VEBT)
% 6.73/7.03 (declare-fun tptp.lex_o (tptp.set_Product_prod_o_o) tptp.set_Pr6227168374412355847list_o)
% 6.73/7.03 (declare-fun tptp.lex_Code_integer (tptp.set_Pr4811707699266497531nteger) tptp.set_Pr7565137564259432987nteger)
% 6.73/7.03 (declare-fun tptp.lex_int (tptp.set_Pr958786334691620121nt_int) tptp.set_Pr765067013931698361st_int)
% 6.73/7.03 (declare-fun tptp.lex_nat (tptp.set_Pr1261947904930325089at_nat) tptp.set_Pr3451248702717554689st_nat)
% 6.73/7.03 (declare-fun tptp.lex_Pr8571645452597969515at_nat (tptp.set_Pr8693737435421807431at_nat) tptp.set_Pr1542805901266377927at_nat)
% 6.73/7.03 (declare-fun tptp.lex_se2245640040323279819at_nat (tptp.set_Pr4329608150637261639at_nat) tptp.set_Pr4333006031979791559at_nat)
% 6.73/7.03 (declare-fun tptp.lex_VEBT_VEBT (tptp.set_Pr6192946355708809607T_VEBT) tptp.set_Pr1916528119006554503T_VEBT)
% 6.73/7.03 (declare-fun tptp.linord2614967742042102400et_nat (tptp.set_nat) tptp.list_nat)
% 6.73/7.03 (declare-fun tptp.cons_C1897838848541180310er_nat ((-> tptp.code_integer tptp.nat) tptp.list_C4705013386053401436er_nat) tptp.list_C4705013386053401436er_nat)
% 6.73/7.03 (declare-fun tptp.cons_int_nat ((-> tptp.int tptp.nat) tptp.list_int_nat) tptp.list_int_nat)
% 6.73/7.03 (declare-fun tptp.cons_nat_nat ((-> tptp.nat tptp.nat) tptp.list_nat_nat) tptp.list_nat_nat)
% 6.73/7.03 (declare-fun tptp.cons_P4861729644591583992at_nat ((-> tptp.product_prod_nat_nat tptp.nat) tptp.list_P9162950289778280392at_nat) tptp.list_P9162950289778280392at_nat)
% 6.73/7.03 (declare-fun tptp.cons_s2538900923071588440at_nat ((-> tptp.set_Pr1261947904930325089at_nat tptp.nat) tptp.list_s9130966667114977576at_nat) tptp.list_s9130966667114977576at_nat)
% 6.73/7.03 (declare-fun tptp.cons_o (Bool tptp.list_o) tptp.list_o)
% 6.73/7.03 (declare-fun tptp.cons_Code_integer (tptp.code_integer tptp.list_Code_integer) tptp.list_Code_integer)
% 6.73/7.03 (declare-fun tptp.cons_complex (tptp.complex tptp.list_complex) tptp.list_complex)
% 6.73/7.03 (declare-fun tptp.cons_int (tptp.int tptp.list_int) tptp.list_int)
% 6.73/7.03 (declare-fun tptp.cons_nat (tptp.nat tptp.list_nat) tptp.list_nat)
% 6.73/7.03 (declare-fun tptp.cons_num (tptp.num tptp.list_num) tptp.list_num)
% 6.73/7.03 (declare-fun tptp.cons_P9044669534377732177nteger (tptp.produc8923325533196201883nteger tptp.list_P5578671422887162913nteger) tptp.list_P5578671422887162913nteger)
% 6.73/7.03 (declare-fun tptp.cons_P3334398858971670639nt_int (tptp.product_prod_int_int tptp.list_P5707943133018811711nt_int) tptp.list_P5707943133018811711nt_int)
% 6.73/7.03 (declare-fun tptp.cons_P6512896166579812791at_nat (tptp.product_prod_nat_nat tptp.list_P6011104703257516679at_nat) tptp.list_P6011104703257516679at_nat)
% 6.73/7.03 (declare-fun tptp.cons_P8732206157123786781at_nat (tptp.produc859450856879609959at_nat tptp.list_P8469869581646625389at_nat) tptp.list_P8469869581646625389at_nat)
% 6.73/7.03 (declare-fun tptp.cons_P3940603068885512221at_nat (tptp.produc3843707927480180839at_nat tptp.list_P5464809261938338413at_nat) tptp.list_P5464809261938338413at_nat)
% 6.73/7.03 (declare-fun tptp.cons_real (tptp.real tptp.list_real) tptp.list_real)
% 6.73/7.03 (declare-fun tptp.cons_set_nat (tptp.set_nat tptp.list_set_nat) tptp.list_set_nat)
% 6.73/7.03 (declare-fun tptp.cons_s6881495754146722583at_nat (tptp.set_Pr1261947904930325089at_nat tptp.list_s1210847774152347623at_nat) tptp.list_s1210847774152347623at_nat)
% 6.73/7.03 (declare-fun tptp.cons_VEBT_VEBT (tptp.vEBT_VEBT tptp.list_VEBT_VEBT) tptp.list_VEBT_VEBT)
% 6.73/7.03 (declare-fun tptp.nil_nat () tptp.list_nat)
% 6.73/7.03 (declare-fun tptp.map_nat_nat ((-> tptp.nat tptp.nat) tptp.list_nat) tptp.list_nat)
% 6.73/7.03 (declare-fun tptp.map_VE8901447254227204932T_VEBT ((-> tptp.vEBT_VEBT tptp.vEBT_VEBT) tptp.list_VEBT_VEBT) tptp.list_VEBT_VEBT)
% 6.73/7.03 (declare-fun tptp.set_o2 (tptp.list_o) tptp.set_o)
% 6.73/7.03 (declare-fun tptp.set_Code_integer2 (tptp.list_Code_integer) tptp.set_Code_integer)
% 6.73/7.03 (declare-fun tptp.set_complex2 (tptp.list_complex) tptp.set_complex)
% 6.73/7.03 (declare-fun tptp.set_int2 (tptp.list_int) tptp.set_int)
% 6.73/7.03 (declare-fun tptp.set_list_o2 (tptp.list_list_o) tptp.set_list_o)
% 6.73/7.03 (declare-fun tptp.set_list_int2 (tptp.list_list_int) tptp.set_list_int)
% 6.73/7.03 (declare-fun tptp.set_list_nat2 (tptp.list_list_nat) tptp.set_list_nat)
% 6.73/7.03 (declare-fun tptp.set_list_VEBT_VEBT2 (tptp.list_list_VEBT_VEBT) tptp.set_list_VEBT_VEBT)
% 6.73/7.03 (declare-fun tptp.set_nat2 (tptp.list_nat) tptp.set_nat)
% 6.73/7.03 (declare-fun tptp.set_Pr1389080609085208608omplex (tptp.list_P3924974545808530565omplex) tptp.set_Pr5421754520313593387omplex)
% 6.73/7.03 (declare-fun tptp.set_Pr2600826154070092190o_real (tptp.list_P5232166724548748803o_real) tptp.set_Pr6573716822653411497o_real)
% 6.73/7.03 (declare-fun tptp.set_Pr655345902815428824T_VEBT (tptp.list_P7495141550334521929T_VEBT) tptp.set_Pr7543698050874017315T_VEBT)
% 6.73/7.03 (declare-fun tptp.set_Pr920681315882439344nteger (tptp.list_P5578671422887162913nteger) tptp.set_Pr4811707699266497531nteger)
% 6.73/7.03 (declare-fun tptp.set_Pr6829704231520703882plex_o (tptp.list_P7942624414058669295plex_o) tptp.set_Pr216032351708956309plex_o)
% 6.73/7.03 (declare-fun tptp.set_Pr8199049879907524818omplex (tptp.list_P7664491975274850627omplex) tptp.set_Pr5085853215250843933omplex)
% 6.73/7.03 (declare-fun tptp.set_Pr4995810437751016784ex_int (tptp.list_P2206113689347244737ex_int) tptp.set_Pr2254670189886740123ex_int)
% 6.73/7.03 (declare-fun tptp.set_Pr9173661457260213492ex_nat (tptp.list_P4696196834278971493ex_nat) tptp.set_Pr4744753334818466879ex_nat)
% 6.73/7.03 (declare-fun tptp.set_Pr1225976482156248400x_real (tptp.list_P7647014805210017729x_real) tptp.set_Pr1133549439701694107x_real)
% 6.73/7.03 (declare-fun tptp.set_Pr5158653123227461798T_VEBT (tptp.list_P7977503562704621835T_VEBT) tptp.set_Pr4085867452638698417T_VEBT)
% 6.73/7.03 (declare-fun tptp.set_Pr3989287306472219216omplex (tptp.list_P1797514011394873281omplex) tptp.set_Pr1846070511934368667omplex)
% 6.73/7.03 (declare-fun tptp.set_Pr2470121279949933262nt_int (tptp.list_P5707943133018811711nt_int) tptp.set_Pr958786334691620121nt_int)
% 6.73/7.03 (declare-fun tptp.set_Pr112895574167722958t_real (tptp.list_P6863124054624500543t_real) tptp.set_Pr3538720872664544793t_real)
% 6.73/7.03 (declare-fun tptp.set_Pr5648618587558075414at_nat (tptp.list_P6011104703257516679at_nat) tptp.set_Pr1261947904930325089at_nat)
% 6.73/7.03 (declare-fun tptp.set_Pr5518436109238095868at_nat (tptp.list_P8469869581646625389at_nat) tptp.set_Pr8693737435421807431at_nat)
% 6.73/7.03 (declare-fun tptp.set_Pr5196769464307566348real_o (tptp.list_P3595434254542482545real_o) tptp.set_Pr4936984352647145239real_o)
% 6.73/7.03 (declare-fun tptp.set_Pr8536649499196266448omplex (tptp.list_P3881527313128557121omplex) tptp.set_Pr6591433984475009307omplex)
% 6.73/7.03 (declare-fun tptp.set_Pr8219819362198175822al_int (tptp.list_P4344331454722006975al_int) tptp.set_Pr1019928272762051225al_int)
% 6.73/7.03 (declare-fun tptp.set_Pr3174298344852596722al_nat (tptp.list_P6834414599653733731al_nat) tptp.set_Pr3510011417693777981al_nat)
% 6.73/7.03 (declare-fun tptp.set_Pr5999470521830281550l_real (tptp.list_P8689742595348180415l_real) tptp.set_Pr6218003697084177305l_real)
% 6.73/7.03 (declare-fun tptp.set_Pr8897343066327330088T_VEBT (tptp.list_P877281246627933069T_VEBT) tptp.set_Pr6019664923565264691T_VEBT)
% 6.73/7.03 (declare-fun tptp.set_Pr9040384385603167362et_nat (tptp.list_P6254988961118846195et_nat) tptp.set_Pr5488025237498180813et_nat)
% 6.73/7.03 (declare-fun tptp.set_Pr3765526544606949372at_nat (tptp.list_P5464809261938338413at_nat) tptp.set_Pr4329608150637261639at_nat)
% 6.73/7.03 (declare-fun tptp.set_Pr7708085864119495200VEBT_o (tptp.list_P3126845725202233233VEBT_o) tptp.set_Pr3175402225741728619VEBT_o)
% 6.73/7.03 (declare-fun tptp.set_Pr6387300694196750780omplex (tptp.list_P4108580160459392801omplex) tptp.set_Pr216944050393469383omplex)
% 6.73/7.03 (declare-fun tptp.set_Pr2853735649769556538BT_int (tptp.list_P4547456442757143711BT_int) tptp.set_Pr5066593544530342725BT_int)
% 6.73/7.03 (declare-fun tptp.set_Pr7031586669278753246BT_nat (tptp.list_P7037539587688870467BT_nat) tptp.set_Pr7556676689462069481BT_nat)
% 6.73/7.03 (declare-fun tptp.set_Pr1087130671499945274T_real (tptp.list_P2623026923184700063T_real) tptp.set_Pr7765410600122031685T_real)
% 6.73/7.03 (declare-fun tptp.set_Pr9182192707038809660T_VEBT (tptp.list_P7413028617227757229T_VEBT) tptp.set_Pr6192946355708809607T_VEBT)
% 6.73/7.03 (declare-fun tptp.set_real2 (tptp.list_real) tptp.set_real)
% 6.73/7.03 (declare-fun tptp.set_set_nat2 (tptp.list_set_nat) tptp.set_set_nat)
% 6.73/7.03 (declare-fun tptp.set_se5049602875457034614at_nat (tptp.list_s1210847774152347623at_nat) tptp.set_se7855581050983116737at_nat)
% 6.73/7.03 (declare-fun tptp.set_VEBT_VEBT2 (tptp.list_VEBT_VEBT) tptp.set_VEBT_VEBT)
% 6.73/7.03 (declare-fun tptp.size_list_typerep ((-> tptp.typerep tptp.nat) tptp.list_typerep) tptp.nat)
% 6.73/7.03 (declare-fun tptp.size_list_VEBT_VEBT ((-> tptp.vEBT_VEBT tptp.nat) tptp.list_VEBT_VEBT) tptp.nat)
% 6.73/7.03 (declare-fun tptp.tl_nat (tptp.list_nat) tptp.list_nat)
% 6.73/7.03 (declare-fun tptp.list_update_o (tptp.list_o tptp.nat Bool) tptp.list_o)
% 6.73/7.03 (declare-fun tptp.list_u5447711078246177391nteger (tptp.list_Code_integer tptp.nat tptp.code_integer) tptp.list_Code_integer)
% 6.73/7.03 (declare-fun tptp.list_update_complex (tptp.list_complex tptp.nat tptp.complex) tptp.list_complex)
% 6.73/7.03 (declare-fun tptp.list_update_int (tptp.list_int tptp.nat tptp.int) tptp.list_int)
% 6.73/7.03 (declare-fun tptp.list_update_nat (tptp.list_nat tptp.nat tptp.nat) tptp.list_nat)
% 6.73/7.03 (declare-fun tptp.list_u2254550707601501961nteger (tptp.list_P5578671422887162913nteger tptp.nat tptp.produc8923325533196201883nteger) tptp.list_P5578671422887162913nteger)
% 6.73/7.03 (declare-fun tptp.list_u3002344382305578791nt_int (tptp.list_P5707943133018811711nt_int tptp.nat tptp.product_prod_int_int) tptp.list_P5707943133018811711nt_int)
% 6.73/7.03 (declare-fun tptp.list_u6180841689913720943at_nat (tptp.list_P6011104703257516679at_nat tptp.nat tptp.product_prod_nat_nat) tptp.list_P6011104703257516679at_nat)
% 6.73/7.03 (declare-fun tptp.list_u5003261594476800725at_nat (tptp.list_P8469869581646625389at_nat tptp.nat tptp.produc859450856879609959at_nat) tptp.list_P8469869581646625389at_nat)
% 6.73/7.03 (declare-fun tptp.list_u4696772448584712917at_nat (tptp.list_P5464809261938338413at_nat tptp.nat tptp.produc3843707927480180839at_nat) tptp.list_P5464809261938338413at_nat)
% 6.73/7.03 (declare-fun tptp.list_u6961636818849549845T_VEBT (tptp.list_P7413028617227757229T_VEBT tptp.nat tptp.produc8243902056947475879T_VEBT) tptp.list_P7413028617227757229T_VEBT)
% 6.73/7.03 (declare-fun tptp.list_update_real (tptp.list_real tptp.nat tptp.real) tptp.list_real)
% 6.73/7.03 (declare-fun tptp.list_update_set_nat (tptp.list_set_nat tptp.nat tptp.set_nat) tptp.list_set_nat)
% 6.73/7.03 (declare-fun tptp.list_u8444657558853818831at_nat (tptp.list_s1210847774152347623at_nat tptp.nat tptp.set_Pr1261947904930325089at_nat) tptp.list_s1210847774152347623at_nat)
% 6.73/7.03 (declare-fun tptp.list_u1324408373059187874T_VEBT (tptp.list_VEBT_VEBT tptp.nat tptp.vEBT_VEBT) tptp.list_VEBT_VEBT)
% 6.73/7.03 (declare-fun tptp.listrel_o_o (tptp.set_Product_prod_o_o) tptp.set_Pr6227168374412355847list_o)
% 6.73/7.03 (declare-fun tptp.listrel_o_int (tptp.set_Pr8834758594704517033_o_int) tptp.set_Pr5001190662893202239st_int)
% 6.73/7.03 (declare-fun tptp.listrel_o_nat (tptp.set_Pr2101469702781467981_o_nat) tptp.set_Pr591367044826345187st_nat)
% 6.73/7.03 (declare-fun tptp.listrel_o_VEBT_VEBT (tptp.set_Pr7543698050874017315T_VEBT) tptp.set_Pr5170412164475753123T_VEBT)
% 6.73/7.03 (declare-fun tptp.listre5734910445319291053nteger (tptp.set_Pr4811707699266497531nteger) tptp.set_Pr7565137564259432987nteger)
% 6.73/7.03 (declare-fun tptp.listrel_int_int (tptp.set_Pr958786334691620121nt_int) tptp.set_Pr765067013931698361st_int)
% 6.73/7.03 (declare-fun tptp.listrel_nat_o (tptp.set_Pr3149072824959771635_nat_o) tptp.set_Pr1150278048023938153list_o)
% 6.73/7.03 (declare-fun tptp.listrel_nat_nat (tptp.set_Pr1261947904930325089at_nat) tptp.set_Pr3451248702717554689st_nat)
% 6.73/7.03 (declare-fun tptp.listre5761932458788874033T_VEBT (tptp.set_Pr6167073792073659919T_VEBT) tptp.set_Pr1262583345697558789T_VEBT)
% 6.73/7.03 (declare-fun tptp.listre818007680106770737at_nat (tptp.set_Pr8693737435421807431at_nat) tptp.set_Pr1542805901266377927at_nat)
% 6.73/7.03 (declare-fun tptp.listre2047417242196832561at_nat (tptp.set_Pr4329608150637261639at_nat) tptp.set_Pr4333006031979791559at_nat)
% 6.73/7.03 (declare-fun tptp.listrel_VEBT_VEBT_o (tptp.set_Pr3175402225741728619VEBT_o) tptp.set_Pr7508168486584781291list_o)
% 6.73/7.03 (declare-fun tptp.listre5898179758603845167BT_int (tptp.set_Pr5066593544530342725BT_int) tptp.set_Pr4080907618048478043st_int)
% 6.73/7.03 (declare-fun tptp.listre5900670229112895443BT_nat (tptp.set_Pr7556676689462069481BT_nat) tptp.set_Pr8894456036836396799st_nat)
% 6.73/7.03 (declare-fun tptp.listre1230615542750757617T_VEBT (tptp.set_Pr6192946355708809607T_VEBT) tptp.set_Pr1916528119006554503T_VEBT)
% 6.73/7.03 (declare-fun tptp.measur8870801148506250077nteger (tptp.list_C4705013386053401436er_nat) tptp.set_Pr4811707699266497531nteger)
% 6.73/7.03 (declare-fun tptp.measures_int (tptp.list_int_nat) tptp.set_Pr958786334691620121nt_int)
% 6.73/7.03 (declare-fun tptp.measures_nat (tptp.list_nat_nat) tptp.set_Pr1261947904930325089at_nat)
% 6.73/7.03 (declare-fun tptp.measur2679027848233739777at_nat (tptp.list_P9162950289778280392at_nat) tptp.set_Pr8693737435421807431at_nat)
% 6.73/7.03 (declare-fun tptp.measur2694323259624372065at_nat (tptp.list_s9130966667114977576at_nat) tptp.set_Pr4329608150637261639at_nat)
% 6.73/7.03 (declare-fun tptp.nth_o (tptp.list_o tptp.nat) Bool)
% 6.73/7.03 (declare-fun tptp.nth_Code_integer (tptp.list_Code_integer tptp.nat) tptp.code_integer)
% 6.73/7.03 (declare-fun tptp.nth_complex (tptp.list_complex tptp.nat) tptp.complex)
% 6.73/7.03 (declare-fun tptp.nth_int (tptp.list_int tptp.nat) tptp.int)
% 6.73/7.03 (declare-fun tptp.nth_nat (tptp.list_nat tptp.nat) tptp.nat)
% 6.73/7.03 (declare-fun tptp.nth_num (tptp.list_num tptp.nat) tptp.num)
% 6.73/7.03 (declare-fun tptp.nth_Product_prod_o_o (tptp.list_P4002435161011370285od_o_o tptp.nat) tptp.product_prod_o_o)
% 6.73/7.03 (declare-fun tptp.nth_Pr1649062631805364268_o_int (tptp.list_P3795440434834930179_o_int tptp.nat) tptp.product_prod_o_int)
% 6.73/7.03 (declare-fun tptp.nth_Pr5826913651314560976_o_nat (tptp.list_P6285523579766656935_o_nat tptp.nat) tptp.product_prod_o_nat)
% 6.73/7.03 (declare-fun tptp.nth_Pr6777367263587873994T_VEBT (tptp.list_P7495141550334521929T_VEBT tptp.nat) tptp.produc2504756804600209347T_VEBT)
% 6.73/7.03 (declare-fun tptp.nth_Pr2304437835452373666nteger (tptp.list_P5578671422887162913nteger tptp.nat) tptp.produc8923325533196201883nteger)
% 6.73/7.03 (declare-fun tptp.nth_Pr112076138515278198_nat_o (tptp.list_P7333126701944960589_nat_o tptp.nat) tptp.product_prod_nat_o)
% 6.73/7.03 (declare-fun tptp.nth_Pr3440142176431000676at_int (tptp.list_P3521021558325789923at_int tptp.nat) tptp.product_prod_nat_int)
% 6.73/7.03 (declare-fun tptp.nth_Pr7617993195940197384at_nat (tptp.list_P6011104703257516679at_nat tptp.nat) tptp.product_prod_nat_nat)
% 6.73/7.03 (declare-fun tptp.nth_Pr744662078594809490T_VEBT (tptp.list_P5647936690300460905T_VEBT tptp.nat) tptp.produc8025551001238799321T_VEBT)
% 6.73/7.03 (declare-fun tptp.nth_Pr4606735188037164562VEBT_o (tptp.list_P3126845725202233233VEBT_o tptp.nat) tptp.produc334124729049499915VEBT_o)
% 6.73/7.03 (declare-fun tptp.nth_Pr6837108013167703752BT_int (tptp.list_P4547456442757143711BT_int tptp.nat) tptp.produc4894624898956917775BT_int)
% 6.73/7.03 (declare-fun tptp.nth_Pr1791586995822124652BT_nat (tptp.list_P7037539587688870467BT_nat tptp.nat) tptp.produc9072475918466114483BT_nat)
% 6.73/7.03 (declare-fun tptp.nth_Pr4953567300277697838T_VEBT (tptp.list_P7413028617227757229T_VEBT tptp.nat) tptp.produc8243902056947475879T_VEBT)
% 6.73/7.03 (declare-fun tptp.nth_real (tptp.list_real tptp.nat) tptp.real)
% 6.73/7.03 (declare-fun tptp.nth_set_nat (tptp.list_set_nat tptp.nat) tptp.set_nat)
% 6.73/7.03 (declare-fun tptp.nth_VEBT_VEBT (tptp.list_VEBT_VEBT tptp.nat) tptp.vEBT_VEBT)
% 6.73/7.03 (declare-fun tptp.product_o_o (tptp.list_o tptp.list_o) tptp.list_P4002435161011370285od_o_o)
% 6.73/7.03 (declare-fun tptp.product_o_int (tptp.list_o tptp.list_int) tptp.list_P3795440434834930179_o_int)
% 6.73/7.03 (declare-fun tptp.product_o_nat (tptp.list_o tptp.list_nat) tptp.list_P6285523579766656935_o_nat)
% 6.73/7.03 (declare-fun tptp.product_o_VEBT_VEBT (tptp.list_o tptp.list_VEBT_VEBT) tptp.list_P7495141550334521929T_VEBT)
% 6.73/7.03 (declare-fun tptp.produc8792966785426426881nteger (tptp.list_Code_integer tptp.list_Code_integer) tptp.list_P5578671422887162913nteger)
% 6.73/7.03 (declare-fun tptp.product_nat_o (tptp.list_nat tptp.list_o) tptp.list_P7333126701944960589_nat_o)
% 6.73/7.03 (declare-fun tptp.produc7156399406898700509T_VEBT (tptp.list_nat tptp.list_VEBT_VEBT) tptp.list_P5647936690300460905T_VEBT)
% 6.73/7.03 (declare-fun tptp.product_VEBT_VEBT_o (tptp.list_VEBT_VEBT tptp.list_o) tptp.list_P3126845725202233233VEBT_o)
% 6.73/7.03 (declare-fun tptp.produc7292646706713671643BT_int (tptp.list_VEBT_VEBT tptp.list_int) tptp.list_P4547456442757143711BT_int)
% 6.73/7.03 (declare-fun tptp.produc7295137177222721919BT_nat (tptp.list_VEBT_VEBT tptp.list_nat) tptp.list_P7037539587688870467BT_nat)
% 6.73/7.03 (declare-fun tptp.produc4743750530478302277T_VEBT (tptp.list_VEBT_VEBT tptp.list_VEBT_VEBT) tptp.list_P7413028617227757229T_VEBT)
% 6.73/7.03 (declare-fun tptp.product_lists_o (tptp.list_list_o) tptp.list_list_o)
% 6.73/7.03 (declare-fun tptp.product_lists_int (tptp.list_list_int) tptp.list_list_int)
% 6.73/7.03 (declare-fun tptp.product_lists_nat (tptp.list_list_nat) tptp.list_list_nat)
% 6.73/7.03 (declare-fun tptp.produc3021084454716106787T_VEBT (tptp.list_list_VEBT_VEBT) tptp.list_list_VEBT_VEBT)
% 6.73/7.03 (declare-fun tptp.replicate_o (tptp.nat Bool) tptp.list_o)
% 6.73/7.03 (declare-fun tptp.replicate_complex (tptp.nat tptp.complex) tptp.list_complex)
% 6.73/7.03 (declare-fun tptp.replicate_int (tptp.nat tptp.int) tptp.list_int)
% 6.73/7.03 (declare-fun tptp.replicate_nat (tptp.nat tptp.nat) tptp.list_nat)
% 6.73/7.03 (declare-fun tptp.replicate_real (tptp.nat tptp.real) tptp.list_real)
% 6.73/7.03 (declare-fun tptp.replicate_set_nat (tptp.nat tptp.set_nat) tptp.list_set_nat)
% 6.73/7.03 (declare-fun tptp.replicate_VEBT_VEBT (tptp.nat tptp.vEBT_VEBT) tptp.list_VEBT_VEBT)
% 6.73/7.03 (declare-fun tptp.rotate1_o (tptp.list_o) tptp.list_o)
% 6.73/7.03 (declare-fun tptp.rotate1_int (tptp.list_int) tptp.list_int)
% 6.73/7.03 (declare-fun tptp.rotate1_nat (tptp.list_nat) tptp.list_nat)
% 6.73/7.03 (declare-fun tptp.rotate1_VEBT_VEBT (tptp.list_VEBT_VEBT) tptp.list_VEBT_VEBT)
% 6.73/7.03 (declare-fun tptp.sorted_wrt_nat ((-> tptp.nat tptp.nat Bool) tptp.list_nat) Bool)
% 6.73/7.03 (declare-fun tptp.take_nat (tptp.nat tptp.list_nat) tptp.list_nat)
% 6.73/7.03 (declare-fun tptp.take_VEBT_VEBT (tptp.nat tptp.list_VEBT_VEBT) tptp.list_VEBT_VEBT)
% 6.73/7.03 (declare-fun tptp.upt (tptp.nat tptp.nat) tptp.list_nat)
% 6.73/7.03 (declare-fun tptp.upto (tptp.int tptp.int) tptp.list_int)
% 6.73/7.03 (declare-fun tptp.zip_o_o (tptp.list_o tptp.list_o) tptp.list_P4002435161011370285od_o_o)
% 6.73/7.03 (declare-fun tptp.zip_o_complex (tptp.list_o tptp.list_complex) tptp.list_P3924974545808530565omplex)
% 6.73/7.03 (declare-fun tptp.zip_o_int (tptp.list_o tptp.list_int) tptp.list_P3795440434834930179_o_int)
% 6.73/7.03 (declare-fun tptp.zip_o_nat (tptp.list_o tptp.list_nat) tptp.list_P6285523579766656935_o_nat)
% 6.73/7.03 (declare-fun tptp.zip_o_real (tptp.list_o tptp.list_real) tptp.list_P5232166724548748803o_real)
% 6.73/7.03 (declare-fun tptp.zip_o_VEBT_VEBT (tptp.list_o tptp.list_VEBT_VEBT) tptp.list_P7495141550334521929T_VEBT)
% 6.73/7.03 (declare-fun tptp.zip_Co3543743374963494515nteger (tptp.list_Code_integer tptp.list_Code_integer) tptp.list_P5578671422887162913nteger)
% 6.73/7.03 (declare-fun tptp.zip_complex_o (tptp.list_complex tptp.list_o) tptp.list_P7942624414058669295plex_o)
% 6.73/7.03 (declare-fun tptp.zip_complex_complex (tptp.list_complex tptp.list_complex) tptp.list_P7664491975274850627omplex)
% 6.73/7.03 (declare-fun tptp.zip_complex_int (tptp.list_complex tptp.list_int) tptp.list_P2206113689347244737ex_int)
% 6.73/7.03 (declare-fun tptp.zip_complex_nat (tptp.list_complex tptp.list_nat) tptp.list_P4696196834278971493ex_nat)
% 6.73/7.03 (declare-fun tptp.zip_complex_real (tptp.list_complex tptp.list_real) tptp.list_P7647014805210017729x_real)
% 6.73/7.03 (declare-fun tptp.zip_co9157518722488180109T_VEBT (tptp.list_complex tptp.list_VEBT_VEBT) tptp.list_P7977503562704621835T_VEBT)
% 6.73/7.03 (declare-fun tptp.zip_int_complex (tptp.list_int tptp.list_complex) tptp.list_P1797514011394873281omplex)
% 6.73/7.03 (declare-fun tptp.zip_int_int (tptp.list_int tptp.list_int) tptp.list_P5707943133018811711nt_int)
% 6.73/7.03 (declare-fun tptp.zip_int_real (tptp.list_int tptp.list_real) tptp.list_P6863124054624500543t_real)
% 6.73/7.03 (declare-fun tptp.zip_nat_nat (tptp.list_nat tptp.list_nat) tptp.list_P6011104703257516679at_nat)
% 6.73/7.03 (declare-fun tptp.zip_nat_VEBT_VEBT (tptp.list_nat tptp.list_VEBT_VEBT) tptp.list_P5647936690300460905T_VEBT)
% 6.73/7.03 (declare-fun tptp.zip_Pr4664179122662387191at_nat (tptp.list_P6011104703257516679at_nat tptp.list_P6011104703257516679at_nat) tptp.list_P8469869581646625389at_nat)
% 6.73/7.03 (declare-fun tptp.zip_real_o (tptp.list_real tptp.list_o) tptp.list_P3595434254542482545real_o)
% 6.73/7.03 (declare-fun tptp.zip_real_complex (tptp.list_real tptp.list_complex) tptp.list_P3881527313128557121omplex)
% 6.73/7.03 (declare-fun tptp.zip_real_int (tptp.list_real tptp.list_int) tptp.list_P4344331454722006975al_int)
% 6.73/7.03 (declare-fun tptp.zip_real_nat (tptp.list_real tptp.list_nat) tptp.list_P6834414599653733731al_nat)
% 6.73/7.03 (declare-fun tptp.zip_real_real (tptp.list_real tptp.list_real) tptp.list_P8689742595348180415l_real)
% 6.73/7.03 (declare-fun tptp.zip_real_VEBT_VEBT (tptp.list_real tptp.list_VEBT_VEBT) tptp.list_P877281246627933069T_VEBT)
% 6.73/7.03 (declare-fun tptp.zip_set_nat_set_nat (tptp.list_set_nat tptp.list_set_nat) tptp.list_P6254988961118846195et_nat)
% 6.73/7.03 (declare-fun tptp.zip_se5600341670672612855at_nat (tptp.list_s1210847774152347623at_nat tptp.list_s1210847774152347623at_nat) tptp.list_P5464809261938338413at_nat)
% 6.73/7.03 (declare-fun tptp.zip_VEBT_VEBT_o (tptp.list_VEBT_VEBT tptp.list_o) tptp.list_P3126845725202233233VEBT_o)
% 6.73/7.03 (declare-fun tptp.zip_VE2794733401258833515omplex (tptp.list_VEBT_VEBT tptp.list_complex) tptp.list_P4108580160459392801omplex)
% 6.73/7.03 (declare-fun tptp.zip_VEBT_VEBT_int (tptp.list_VEBT_VEBT tptp.list_int) tptp.list_P4547456442757143711BT_int)
% 6.73/7.03 (declare-fun tptp.zip_VEBT_VEBT_nat (tptp.list_VEBT_VEBT tptp.list_nat) tptp.list_P7037539587688870467BT_nat)
% 6.73/7.03 (declare-fun tptp.zip_VEBT_VEBT_real (tptp.list_VEBT_VEBT tptp.list_real) tptp.list_P2623026923184700063T_real)
% 6.73/7.03 (declare-fun tptp.zip_VE537291747668921783T_VEBT (tptp.list_VEBT_VEBT tptp.list_VEBT_VEBT) tptp.list_P7413028617227757229T_VEBT)
% 6.73/7.03 (declare-fun tptp.suc (tptp.nat) tptp.nat)
% 6.73/7.03 (declare-fun tptp.compow_nat_nat (tptp.nat (-> tptp.nat tptp.nat) tptp.nat) tptp.nat)
% 6.73/7.03 (declare-fun tptp.case_nat_o (Bool (-> tptp.nat Bool) tptp.nat) Bool)
% 6.73/7.03 (declare-fun tptp.case_nat_nat (tptp.nat (-> tptp.nat tptp.nat) tptp.nat) tptp.nat)
% 6.73/7.03 (declare-fun tptp.pred (tptp.nat) tptp.nat)
% 6.73/7.03 (declare-fun tptp.semiri4939895301339042750nteger (tptp.nat) tptp.code_integer)
% 6.73/7.03 (declare-fun tptp.semiri3763490453095760265atural (tptp.nat) tptp.code_natural)
% 6.73/7.03 (declare-fun tptp.semiri8010041392384452111omplex (tptp.nat) tptp.complex)
% 6.73/7.03 (declare-fun tptp.semiri4216267220026989637d_enat (tptp.nat) tptp.extended_enat)
% 6.73/7.03 (declare-fun tptp.semiri1314217659103216013at_int (tptp.nat) tptp.int)
% 6.73/7.03 (declare-fun tptp.semiri1316708129612266289at_nat (tptp.nat) tptp.nat)
% 6.73/7.03 (declare-fun tptp.semiri681578069525770553at_rat (tptp.nat) tptp.rat)
% 6.73/7.03 (declare-fun tptp.semiri5074537144036343181t_real (tptp.nat) tptp.real)
% 6.73/7.03 (declare-fun tptp.semiri4055485073559036834nteger ((-> tptp.code_integer tptp.code_integer) tptp.nat tptp.code_integer) tptp.code_integer)
% 6.73/7.03 (declare-fun tptp.semiri2816024913162550771omplex ((-> tptp.complex tptp.complex) tptp.nat tptp.complex) tptp.complex)
% 6.73/7.03 (declare-fun tptp.semiri8420488043553186161ux_int ((-> tptp.int tptp.int) tptp.nat tptp.int) tptp.int)
% 6.73/7.03 (declare-fun tptp.semiri8422978514062236437ux_nat ((-> tptp.nat tptp.nat) tptp.nat tptp.nat) tptp.nat)
% 6.73/7.03 (declare-fun tptp.semiri7787848453975740701ux_rat ((-> tptp.rat tptp.rat) tptp.nat tptp.rat) tptp.rat)
% 6.73/7.03 (declare-fun tptp.semiri7260567687927622513x_real ((-> tptp.real tptp.real) tptp.nat tptp.real) tptp.real)
% 6.73/7.03 (declare-fun tptp.size_size_list_o (tptp.list_o) tptp.nat)
% 6.73/7.03 (declare-fun tptp.size_s3445333598471063425nteger (tptp.list_Code_integer) tptp.nat)
% 6.73/7.03 (declare-fun tptp.size_s3451745648224563538omplex (tptp.list_complex) tptp.nat)
% 6.73/7.03 (declare-fun tptp.size_size_list_int (tptp.list_int) tptp.nat)
% 6.73/7.03 (declare-fun tptp.size_s2710708370519433104list_o (tptp.list_list_o) tptp.nat)
% 6.73/7.03 (declare-fun tptp.size_s533118279054570080st_int (tptp.list_list_int) tptp.nat)
% 6.73/7.03 (declare-fun tptp.size_s3023201423986296836st_nat (tptp.list_list_nat) tptp.nat)
% 6.73/7.03 (declare-fun tptp.size_s8217280938318005548T_VEBT (tptp.list_list_VEBT_VEBT) tptp.nat)
% 6.73/7.03 (declare-fun tptp.size_size_list_nat (tptp.list_nat) tptp.nat)
% 6.73/7.03 (declare-fun tptp.size_size_list_num (tptp.list_num) tptp.nat)
% 6.73/7.03 (declare-fun tptp.size_s1515746228057227161od_o_o (tptp.list_P4002435161011370285od_o_o) tptp.nat)
% 6.73/7.03 (declare-fun tptp.size_s2953683556165314199_o_int (tptp.list_P3795440434834930179_o_int) tptp.nat)
% 6.73/7.03 (declare-fun tptp.size_s5443766701097040955_o_nat (tptp.list_P6285523579766656935_o_nat) tptp.nat)
% 6.73/7.03 (declare-fun tptp.size_s4313452262239582901T_VEBT (tptp.list_P7495141550334521929T_VEBT) tptp.nat)
% 6.73/7.03 (declare-fun tptp.size_s6491369823275344609_nat_o (tptp.list_P7333126701944960589_nat_o) tptp.nat)
% 6.73/7.03 (declare-fun tptp.size_s2970893825323803983at_int (tptp.list_P3521021558325789923at_int) tptp.nat)
% 6.73/7.03 (declare-fun tptp.size_s5460976970255530739at_nat (tptp.list_P6011104703257516679at_nat) tptp.nat)
% 6.73/7.03 (declare-fun tptp.size_s4762443039079500285T_VEBT (tptp.list_P5647936690300460905T_VEBT) tptp.nat)
% 6.73/7.03 (declare-fun tptp.size_s9168528473962070013VEBT_o (tptp.list_P3126845725202233233VEBT_o) tptp.nat)
% 6.73/7.03 (declare-fun tptp.size_s3661962791536183091BT_int (tptp.list_P4547456442757143711BT_int) tptp.nat)
% 6.73/7.03 (declare-fun tptp.size_s6152045936467909847BT_nat (tptp.list_P7037539587688870467BT_nat) tptp.nat)
% 6.73/7.03 (declare-fun tptp.size_s7466405169056248089T_VEBT (tptp.list_P7413028617227757229T_VEBT) tptp.nat)
% 6.73/7.03 (declare-fun tptp.size_size_list_real (tptp.list_real) tptp.nat)
% 6.73/7.03 (declare-fun tptp.size_s3254054031482475050et_nat (tptp.list_set_nat) tptp.nat)
% 6.73/7.03 (declare-fun tptp.size_s8736152011456118867at_nat (tptp.list_s1210847774152347623at_nat) tptp.nat)
% 6.73/7.03 (declare-fun tptp.size_s6755466524823107622T_VEBT (tptp.list_VEBT_VEBT) tptp.nat)
% 6.73/7.03 (declare-fun tptp.size_size_num (tptp.num) tptp.nat)
% 6.73/7.03 (declare-fun tptp.size_size_option_nat (tptp.option_nat) tptp.nat)
% 6.73/7.03 (declare-fun tptp.size_size_option_num (tptp.option_num) tptp.nat)
% 6.73/7.03 (declare-fun tptp.size_s170228958280169651at_nat (tptp.option4927543243414619207at_nat) tptp.nat)
% 6.73/7.03 (declare-fun tptp.size_size_char (tptp.char) tptp.nat)
% 6.73/7.03 (declare-fun tptp.size_size_typerep (tptp.typerep) tptp.nat)
% 6.73/7.03 (declare-fun tptp.size_size_VEBT_VEBT (tptp.vEBT_VEBT) tptp.nat)
% 6.73/7.03 (declare-fun tptp.nat_int_decode (tptp.nat) tptp.int)
% 6.73/7.03 (declare-fun tptp.nat_int_encode (tptp.int) tptp.nat)
% 6.73/7.03 (declare-fun tptp.nat_list_decode (tptp.nat) tptp.list_nat)
% 6.73/7.03 (declare-fun tptp.nat_list_decode_rel (tptp.nat tptp.nat) Bool)
% 6.73/7.03 (declare-fun tptp.nat_list_encode (tptp.list_nat) tptp.nat)
% 6.73/7.03 (declare-fun tptp.nat_list_encode_rel (tptp.list_nat tptp.list_nat) Bool)
% 6.73/7.03 (declare-fun tptp.nat_prod_decode (tptp.nat) tptp.product_prod_nat_nat)
% 6.73/7.03 (declare-fun tptp.nat_prod_decode_aux (tptp.nat tptp.nat) tptp.product_prod_nat_nat)
% 6.73/7.03 (declare-fun tptp.nat_pr5047031295181774490ux_rel (tptp.product_prod_nat_nat tptp.product_prod_nat_nat) Bool)
% 6.73/7.03 (declare-fun tptp.nat_prod_encode (tptp.product_prod_nat_nat) tptp.nat)
% 6.73/7.03 (declare-fun tptp.nat_set_decode (tptp.nat) tptp.set_nat)
% 6.73/7.03 (declare-fun tptp.nat_set_encode (tptp.set_nat) tptp.nat)
% 6.73/7.03 (declare-fun tptp.nat_sum_decode (tptp.nat) tptp.sum_sum_nat_nat)
% 6.73/7.03 (declare-fun tptp.nat_sum_encode (tptp.sum_sum_nat_nat) tptp.nat)
% 6.73/7.03 (declare-fun tptp.nat_triangle (tptp.nat) tptp.nat)
% 6.73/7.03 (declare-fun tptp.root (tptp.nat tptp.real) tptp.real)
% 6.73/7.03 (declare-fun tptp.sqrt (tptp.real) tptp.real)
% 6.73/7.03 (declare-fun tptp.bitM (tptp.num) tptp.num)
% 6.73/7.03 (declare-fun tptp.inc (tptp.num) tptp.num)
% 6.73/7.03 (declare-fun tptp.nat_of_num (tptp.num) tptp.nat)
% 6.73/7.03 (declare-fun tptp.neg_nu8804712462038260780nteger (tptp.code_integer) tptp.code_integer)
% 6.73/7.03 (declare-fun tptp.neg_nu7009210354673126013omplex (tptp.complex) tptp.complex)
% 6.73/7.03 (declare-fun tptp.neg_numeral_dbl_int (tptp.int) tptp.int)
% 6.73/7.03 (declare-fun tptp.neg_numeral_dbl_rat (tptp.rat) tptp.rat)
% 6.73/7.03 (declare-fun tptp.neg_numeral_dbl_real (tptp.real) tptp.real)
% 6.73/7.03 (declare-fun tptp.neg_nu7757733837767384882nteger (tptp.code_integer) tptp.code_integer)
% 6.73/7.03 (declare-fun tptp.neg_nu6511756317524482435omplex (tptp.complex) tptp.complex)
% 6.73/7.03 (declare-fun tptp.neg_nu3811975205180677377ec_int (tptp.int) tptp.int)
% 6.73/7.03 (declare-fun tptp.neg_nu3179335615603231917ec_rat (tptp.rat) tptp.rat)
% 6.73/7.03 (declare-fun tptp.neg_nu6075765906172075777c_real (tptp.real) tptp.real)
% 6.73/7.03 (declare-fun tptp.neg_nu5831290666863070958nteger (tptp.code_integer) tptp.code_integer)
% 6.73/7.03 (declare-fun tptp.neg_nu8557863876264182079omplex (tptp.complex) tptp.complex)
% 6.73/7.03 (declare-fun tptp.neg_nu5851722552734809277nc_int (tptp.int) tptp.int)
% 6.73/7.03 (declare-fun tptp.neg_nu5219082963157363817nc_rat (tptp.rat) tptp.rat)
% 6.73/7.03 (declare-fun tptp.neg_nu8295874005876285629c_real (tptp.real) tptp.real)
% 6.73/7.03 (declare-fun tptp.neg_numeral_sub_int (tptp.num tptp.num) tptp.int)
% 6.73/7.03 (declare-fun tptp.bit0 (tptp.num) tptp.num)
% 6.73/7.03 (declare-fun tptp.bit1 (tptp.num) tptp.num)
% 6.73/7.03 (declare-fun tptp.one () tptp.num)
% 6.73/7.03 (declare-fun tptp.size_num (tptp.num) tptp.nat)
% 6.73/7.03 (declare-fun tptp.num_of_nat (tptp.nat) tptp.num)
% 6.73/7.03 (declare-fun tptp.numera6620942414471956472nteger (tptp.num) tptp.code_integer)
% 6.73/7.03 (declare-fun tptp.numera5444537566228673987atural (tptp.num) tptp.code_natural)
% 6.73/7.03 (declare-fun tptp.numera6690914467698888265omplex (tptp.num) tptp.complex)
% 6.73/7.03 (declare-fun tptp.numera1916890842035813515d_enat (tptp.num) tptp.extended_enat)
% 6.73/7.03 (declare-fun tptp.numeral_numeral_int (tptp.num) tptp.int)
% 6.73/7.03 (declare-fun tptp.numeral_numeral_nat (tptp.num) tptp.nat)
% 6.73/7.03 (declare-fun tptp.numeral_numeral_rat (tptp.num) tptp.rat)
% 6.73/7.03 (declare-fun tptp.numeral_numeral_real (tptp.num) tptp.real)
% 6.73/7.03 (declare-fun tptp.pow (tptp.num tptp.num) tptp.num)
% 6.73/7.03 (declare-fun tptp.pred_numeral (tptp.num) tptp.nat)
% 6.73/7.03 (declare-fun tptp.sqr (tptp.num) tptp.num)
% 6.73/7.03 (declare-fun tptp.none_nat () tptp.option_nat)
% 6.73/7.03 (declare-fun tptp.none_num () tptp.option_num)
% 6.73/7.03 (declare-fun tptp.none_P5556105721700978146at_nat () tptp.option4927543243414619207at_nat)
% 6.73/7.03 (declare-fun tptp.some_o (Bool) tptp.option_o)
% 6.73/7.03 (declare-fun tptp.some_int (tptp.int) tptp.option_int)
% 6.73/7.03 (declare-fun tptp.some_nat (tptp.nat) tptp.option_nat)
% 6.73/7.03 (declare-fun tptp.some_num (tptp.num) tptp.option_num)
% 6.73/7.03 (declare-fun tptp.some_P7363390416028606310at_nat (tptp.product_prod_nat_nat) tptp.option4927543243414619207at_nat)
% 6.73/7.03 (declare-fun tptp.some_VEBT_VEBT (tptp.vEBT_VEBT) tptp.option_VEBT_VEBT)
% 6.73/7.03 (declare-fun tptp.case_o184042715313410164at_nat (Bool (-> tptp.product_prod_nat_nat Bool) tptp.option4927543243414619207at_nat) Bool)
% 6.73/7.03 (declare-fun tptp.case_option_num_num (tptp.num (-> tptp.num tptp.num) tptp.option_num) tptp.num)
% 6.73/7.03 (declare-fun tptp.case_o6005452278849405969um_num (tptp.option_num (-> tptp.num tptp.option_num) tptp.option_num) tptp.option_num)
% 6.73/7.03 (declare-fun tptp.size_option_nat ((-> tptp.nat tptp.nat) tptp.option_nat) tptp.nat)
% 6.73/7.03 (declare-fun tptp.size_option_num ((-> tptp.num tptp.nat) tptp.option_num) tptp.nat)
% 6.73/7.03 (declare-fun tptp.size_o8335143837870341156at_nat ((-> tptp.product_prod_nat_nat tptp.nat) tptp.option4927543243414619207at_nat) tptp.nat)
% 6.73/7.03 (declare-fun tptp.the_nat (tptp.option_nat) tptp.nat)
% 6.73/7.03 (declare-fun tptp.the_num (tptp.option_num) tptp.num)
% 6.73/7.03 (declare-fun tptp.the_Pr8591224930841456533at_nat (tptp.option4927543243414619207at_nat) tptp.product_prod_nat_nat)
% 6.73/7.03 (declare-fun tptp.order_4473980167227706203on_nat (tptp.set_nat tptp.set_Pr1261947904930325089at_nat) Bool)
% 6.73/7.03 (declare-fun tptp.order_5251275573222108571on_nat (tptp.set_nat tptp.set_Pr1261947904930325089at_nat) Bool)
% 6.73/7.03 (declare-fun tptp.order_4861654808422542329on_nat (tptp.set_nat tptp.set_Pr1261947904930325089at_nat) Bool)
% 6.73/7.03 (declare-fun tptp.order_underS_nat (tptp.set_Pr1261947904930325089at_nat tptp.nat) tptp.set_nat)
% 6.73/7.03 (declare-fun tptp.order_2888998067076097458on_nat (tptp.set_nat tptp.set_Pr1261947904930325089at_nat) Bool)
% 6.73/7.03 (declare-fun tptp.bot_bot_nat () tptp.nat)
% 6.73/7.03 (declare-fun tptp.bot_bot_set_o () tptp.set_o)
% 6.73/7.03 (declare-fun tptp.bot_bot_set_complex () tptp.set_complex)
% 6.73/7.03 (declare-fun tptp.bot_bot_set_int () tptp.set_int)
% 6.73/7.03 (declare-fun tptp.bot_bot_set_list_nat () tptp.set_list_nat)
% 6.73/7.03 (declare-fun tptp.bot_bot_set_nat () tptp.set_nat)
% 6.73/7.03 (declare-fun tptp.bot_bot_set_num () tptp.set_num)
% 6.73/7.03 (declare-fun tptp.bot_bo2099793752762293965at_nat () tptp.set_Pr1261947904930325089at_nat)
% 6.73/7.03 (declare-fun tptp.bot_bot_set_rat () tptp.set_rat)
% 6.73/7.03 (declare-fun tptp.bot_bot_set_real () tptp.set_real)
% 6.73/7.03 (declare-fun tptp.bot_bot_set_set_nat () tptp.set_set_nat)
% 6.73/7.03 (declare-fun tptp.bot_bo8194388402131092736T_VEBT () tptp.set_VEBT_VEBT)
% 6.73/7.03 (declare-fun tptp.ord_Least_nat ((-> tptp.nat Bool)) tptp.nat)
% 6.73/7.03 (declare-fun tptp.ord_le6747313008572928689nteger (tptp.code_integer tptp.code_integer) Bool)
% 6.73/7.03 (declare-fun tptp.ord_le72135733267957522d_enat (tptp.extended_enat tptp.extended_enat) Bool)
% 6.73/7.03 (declare-fun tptp.ord_less_int (tptp.int tptp.int) Bool)
% 6.73/7.03 (declare-fun tptp.ord_less_nat (tptp.nat tptp.nat) Bool)
% 6.73/7.03 (declare-fun tptp.ord_less_num (tptp.num tptp.num) Bool)
% 6.73/7.03 (declare-fun tptp.ord_less_rat (tptp.rat tptp.rat) Bool)
% 6.73/7.03 (declare-fun tptp.ord_less_real (tptp.real tptp.real) Bool)
% 6.73/7.03 (declare-fun tptp.ord_less_set_complex (tptp.set_complex tptp.set_complex) Bool)
% 6.73/7.03 (declare-fun tptp.ord_less_set_int (tptp.set_int tptp.set_int) Bool)
% 6.73/7.03 (declare-fun tptp.ord_less_set_nat (tptp.set_nat tptp.set_nat) Bool)
% 6.73/7.03 (declare-fun tptp.ord_less_set_num (tptp.set_num tptp.set_num) Bool)
% 6.73/7.03 (declare-fun tptp.ord_less_set_rat (tptp.set_rat tptp.set_rat) Bool)
% 6.73/7.03 (declare-fun tptp.ord_less_set_real (tptp.set_real tptp.set_real) Bool)
% 6.73/7.03 (declare-fun tptp.ord_less_set_set_nat (tptp.set_set_nat tptp.set_set_nat) Bool)
% 6.73/7.03 (declare-fun tptp.ord_le3102999989581377725nteger (tptp.code_integer tptp.code_integer) Bool)
% 6.73/7.03 (declare-fun tptp.ord_le1926595141338095240atural (tptp.code_natural tptp.code_natural) Bool)
% 6.73/7.03 (declare-fun tptp.ord_le2932123472753598470d_enat (tptp.extended_enat tptp.extended_enat) Bool)
% 6.73/7.03 (declare-fun tptp.ord_le2510731241096832064er_nat (tptp.filter_nat tptp.filter_nat) Bool)
% 6.73/7.03 (declare-fun tptp.ord_less_eq_int (tptp.int tptp.int) Bool)
% 6.73/7.03 (declare-fun tptp.ord_less_eq_nat (tptp.nat tptp.nat) Bool)
% 6.73/7.03 (declare-fun tptp.ord_less_eq_num (tptp.num tptp.num) Bool)
% 6.73/7.03 (declare-fun tptp.ord_less_eq_rat (tptp.rat tptp.rat) Bool)
% 6.73/7.03 (declare-fun tptp.ord_less_eq_real (tptp.real tptp.real) Bool)
% 6.73/7.03 (declare-fun tptp.ord_less_eq_set_o (tptp.set_o tptp.set_o) Bool)
% 6.73/7.03 (declare-fun tptp.ord_le211207098394363844omplex (tptp.set_complex tptp.set_complex) Bool)
% 6.73/7.03 (declare-fun tptp.ord_less_eq_set_int (tptp.set_int tptp.set_int) Bool)
% 6.73/7.03 (declare-fun tptp.ord_le6045566169113846134st_nat (tptp.set_list_nat tptp.set_list_nat) Bool)
% 6.73/7.03 (declare-fun tptp.ord_less_eq_set_nat (tptp.set_nat tptp.set_nat) Bool)
% 6.73/7.03 (declare-fun tptp.ord_less_eq_set_num (tptp.set_num tptp.set_num) Bool)
% 6.73/7.03 (declare-fun tptp.ord_le3146513528884898305at_nat (tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat) Bool)
% 6.73/7.03 (declare-fun tptp.ord_less_eq_set_rat (tptp.set_rat tptp.set_rat) Bool)
% 6.73/7.03 (declare-fun tptp.ord_less_eq_set_real (tptp.set_real tptp.set_real) Bool)
% 6.73/7.03 (declare-fun tptp.ord_le6893508408891458716et_nat (tptp.set_set_nat tptp.set_set_nat) Bool)
% 6.73/7.03 (declare-fun tptp.ord_le4337996190870823476T_VEBT (tptp.set_VEBT_VEBT tptp.set_VEBT_VEBT) Bool)
% 6.73/7.03 (declare-fun tptp.ord_max_Code_integer (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 6.73/7.03 (declare-fun tptp.ord_ma741700101516333627d_enat (tptp.extended_enat tptp.extended_enat) tptp.extended_enat)
% 6.73/7.03 (declare-fun tptp.ord_max_int (tptp.int tptp.int) tptp.int)
% 6.73/7.03 (declare-fun tptp.ord_max_nat (tptp.nat tptp.nat) tptp.nat)
% 6.73/7.03 (declare-fun tptp.ord_max_num (tptp.num tptp.num) tptp.num)
% 6.73/7.03 (declare-fun tptp.ord_max_rat (tptp.rat tptp.rat) tptp.rat)
% 6.73/7.03 (declare-fun tptp.ord_max_real (tptp.real tptp.real) tptp.real)
% 6.73/7.03 (declare-fun tptp.ord_max_set_int (tptp.set_int tptp.set_int) tptp.set_int)
% 6.73/7.03 (declare-fun tptp.ord_max_set_nat (tptp.set_nat tptp.set_nat) tptp.set_nat)
% 6.73/7.03 (declare-fun tptp.ord_max_set_real (tptp.set_real tptp.set_real) tptp.set_real)
% 6.73/7.03 (declare-fun tptp.ord_min_nat (tptp.nat tptp.nat) tptp.nat)
% 6.73/7.03 (declare-fun tptp.order_Greatest_nat ((-> tptp.nat Bool)) tptp.nat)
% 6.73/7.03 (declare-fun tptp.order_mono_nat_nat ((-> tptp.nat tptp.nat)) Bool)
% 6.73/7.03 (declare-fun tptp.order_5726023648592871131at_nat ((-> tptp.nat tptp.nat)) Bool)
% 6.73/7.03 (declare-fun tptp.ordering_top_nat ((-> tptp.nat tptp.nat Bool) (-> tptp.nat tptp.nat Bool) tptp.nat) Bool)
% 6.73/7.03 (declare-fun tptp.top_top_set_int () tptp.set_int)
% 6.73/7.03 (declare-fun tptp.top_top_set_list_nat () tptp.set_list_nat)
% 6.73/7.03 (declare-fun tptp.top_top_set_nat () tptp.set_nat)
% 6.73/7.03 (declare-fun tptp.top_to4669805908274784177at_nat () tptp.set_Pr1261947904930325089at_nat)
% 6.73/7.03 (declare-fun tptp.top_top_set_real () tptp.set_real)
% 6.73/7.03 (declare-fun tptp.top_top_set_char () tptp.set_char)
% 6.73/7.03 (declare-fun tptp.top_to6661820994512907621at_nat () tptp.set_Sum_sum_nat_nat)
% 6.73/7.03 (declare-fun tptp.power_8256067586552552935nteger (tptp.code_integer tptp.nat) tptp.code_integer)
% 6.73/7.03 (declare-fun tptp.power_7079662738309270450atural (tptp.code_natural tptp.nat) tptp.code_natural)
% 6.73/7.03 (declare-fun tptp.power_power_complex (tptp.complex tptp.nat) tptp.complex)
% 6.73/7.03 (declare-fun tptp.power_8040749407984259932d_enat (tptp.extended_enat tptp.nat) tptp.extended_enat)
% 6.73/7.03 (declare-fun tptp.power_power_int (tptp.int tptp.nat) tptp.int)
% 6.73/7.03 (declare-fun tptp.power_power_nat (tptp.nat tptp.nat) tptp.nat)
% 6.73/7.03 (declare-fun tptp.power_power_rat (tptp.rat tptp.nat) tptp.rat)
% 6.73/7.03 (declare-fun tptp.power_power_real (tptp.real tptp.nat) tptp.real)
% 6.73/7.03 (declare-fun tptp.produc4035269172776083154on_nat ((-> tptp.nat tptp.nat Bool) tptp.produc4953844613479565601on_nat) tptp.produc2233624965454879586on_nat)
% 6.73/7.03 (declare-fun tptp.produc3209952032786966637at_nat ((-> tptp.nat tptp.nat tptp.nat) tptp.produc7248412053542808358at_nat) tptp.produc4471711990508489141at_nat)
% 6.73/7.03 (declare-fun tptp.produc8929957630744042906on_nat ((-> tptp.nat tptp.nat tptp.nat) tptp.produc4953844613479565601on_nat) tptp.produc8306885398267862888on_nat)
% 6.73/7.03 (declare-fun tptp.produc3576312749637752826on_num ((-> tptp.num tptp.num Bool) tptp.produc3447558737645232053on_num) tptp.produc7036089656553540234on_num)
% 6.73/7.03 (declare-fun tptp.produc5778274026573060048on_num ((-> tptp.num tptp.num tptp.num) tptp.produc3447558737645232053on_num) tptp.produc1193250871479095198on_num)
% 6.73/7.03 (declare-fun tptp.produc3994169339658061776at_nat ((-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool) tptp.produc6121120109295599847at_nat) tptp.produc5491161045314408544at_nat)
% 6.73/7.03 (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)
% 6.73/7.03 (declare-fun tptp.product_Pair_o_o (Bool Bool) tptp.product_prod_o_o)
% 6.73/7.03 (declare-fun tptp.produc414345526774272751omplex (Bool tptp.complex) tptp.produc648051720047351925omplex)
% 6.73/7.03 (declare-fun tptp.product_Pair_o_int (Bool tptp.int) tptp.product_prod_o_int)
% 6.73/7.03 (declare-fun tptp.product_Pair_o_nat (Bool tptp.nat) tptp.product_prod_o_nat)
% 6.73/7.03 (declare-fun tptp.product_Pair_o_real (Bool tptp.real) tptp.product_prod_o_real)
% 6.73/7.03 (declare-fun tptp.produc2982872950893828659T_VEBT (Bool tptp.vEBT_VEBT) tptp.produc2504756804600209347T_VEBT)
% 6.73/7.03 (declare-fun tptp.produc1086072967326762835nteger (tptp.code_integer tptp.code_integer) tptp.produc8923325533196201883nteger)
% 6.73/7.03 (declare-fun tptp.produc3574140220909816553atural (tptp.code_natural tptp.code_natural) tptp.produc7822875418678951345atural)
% 6.73/7.03 (declare-fun tptp.produc6639722614265839536atural (tptp.code_natural tptp.produc7822875418678951345atural) tptp.produc5835291356934675326atural)
% 6.73/7.03 (declare-fun tptp.produc2908979694703026321plex_o (tptp.complex Bool) tptp.produc6088675342482847199plex_o)
% 6.73/7.03 (declare-fun tptp.produc101793102246108661omplex (tptp.complex tptp.complex) tptp.produc4411394909380815293omplex)
% 6.73/7.03 (declare-fun tptp.produc1367138851071493491ex_int (tptp.complex tptp.int) tptp.produc6845221339535797307ex_int)
% 6.73/7.03 (declare-fun tptp.produc1369629321580543767ex_nat (tptp.complex tptp.nat) tptp.produc1799700322190218207ex_nat)
% 6.73/7.03 (declare-fun tptp.produc1746590499379883635x_real (tptp.complex tptp.real) tptp.produc8892588492097263291x_real)
% 6.73/7.03 (declare-fun tptp.produc2757191886755552429T_VEBT (tptp.complex tptp.vEBT_VEBT) tptp.produc7151440242714718331T_VEBT)
% 6.73/7.03 (declare-fun tptp.produc7948753499206759283omplex (tptp.int tptp.complex) tptp.produc5838698208256999739omplex)
% 6.73/7.03 (declare-fun tptp.product_Pair_int_int (tptp.int tptp.int) tptp.product_prod_int_int)
% 6.73/7.03 (declare-fun tptp.produc801115645435158769t_real (tptp.int tptp.real) tptp.produc679980390762269497t_real)
% 6.73/7.03 (declare-fun tptp.produc8435520187683070743list_o (tptp.list_o tptp.list_o) tptp.produc7102631898165422375list_o)
% 6.73/7.03 (declare-fun tptp.produc2951025481305455875st_int (tptp.list_o tptp.list_int) tptp.produc1713839591385758857st_int)
% 6.73/7.03 (declare-fun tptp.produc7128876500814652583st_nat (tptp.list_o tptp.list_nat) tptp.produc4203922736317485613st_nat)
% 6.73/7.03 (declare-fun tptp.produc6043759678074843571T_VEBT (tptp.list_o tptp.list_VEBT_VEBT) tptp.produc1922972420619397443T_VEBT)
% 6.73/7.03 (declare-fun tptp.produc750622340256944499nteger (tptp.list_Code_integer tptp.list_Code_integer) tptp.produc862207588354017979nteger)
% 6.73/7.03 (declare-fun tptp.produc364263696895485585st_int (tptp.list_int tptp.list_int) tptp.produc1186641810826059865st_int)
% 6.73/7.03 (declare-fun tptp.produc699922362453767013list_o (tptp.list_nat tptp.list_o) tptp.produc149729814636038835list_o)
% 6.73/7.03 (declare-fun tptp.produc2694037385005941721st_nat (tptp.list_nat tptp.list_nat) tptp.produc1828647624359046049st_nat)
% 6.73/7.03 (declare-fun tptp.produc8335345208264861441T_VEBT (tptp.list_nat tptp.list_VEBT_VEBT) tptp.produc872621073311890639T_VEBT)
% 6.73/7.03 (declare-fun tptp.produc5943733680697469783at_nat (tptp.list_P6011104703257516679at_nat tptp.list_P6011104703257516679at_nat) tptp.produc6392793444374437607at_nat)
% 6.73/7.03 (declare-fun tptp.produc7536900900485677911at_nat (tptp.list_s1210847774152347623at_nat tptp.list_s1210847774152347623at_nat) tptp.produc424102278133772007at_nat)
% 6.73/7.03 (declare-fun tptp.produc2717590391345394939list_o (tptp.list_VEBT_VEBT tptp.list_o) tptp.produc3962069817607390347list_o)
% 6.73/7.03 (declare-fun tptp.produc1392282695434103839st_int (tptp.list_VEBT_VEBT tptp.list_int) tptp.produc7831203938951381541st_int)
% 6.73/7.03 (declare-fun tptp.produc5570133714943300547st_nat (tptp.list_VEBT_VEBT tptp.list_nat) tptp.produc1097915047028332489st_nat)
% 6.73/7.03 (declare-fun tptp.produc3897820843166775703T_VEBT (tptp.list_VEBT_VEBT tptp.list_VEBT_VEBT) tptp.produc9211091688327510695T_VEBT)
% 6.73/7.03 (declare-fun tptp.product_Pair_nat_o (tptp.nat Bool) tptp.product_prod_nat_o)
% 6.73/7.03 (declare-fun tptp.product_Pair_nat_int (tptp.nat tptp.int) tptp.product_prod_nat_int)
% 6.73/7.03 (declare-fun tptp.product_Pair_nat_nat (tptp.nat tptp.nat) tptp.product_prod_nat_nat)
% 6.73/7.03 (declare-fun tptp.produc487386426758144856at_nat (tptp.nat tptp.product_prod_nat_nat) tptp.produc7248412053542808358at_nat)
% 6.73/7.03 (declare-fun tptp.produc599794634098209291T_VEBT (tptp.nat tptp.vEBT_VEBT) tptp.produc8025551001238799321T_VEBT)
% 6.73/7.03 (declare-fun tptp.produc5098337634421038937on_nat (tptp.option_nat tptp.option_nat) tptp.produc4953844613479565601on_nat)
% 6.73/7.03 (declare-fun tptp.produc8585076106096196333on_num (tptp.option_num tptp.option_num) tptp.produc3447558737645232053on_num)
% 6.73/7.03 (declare-fun tptp.produc488173922507101015at_nat (tptp.option4927543243414619207at_nat tptp.option4927543243414619207at_nat) tptp.produc6121120109295599847at_nat)
% 6.73/7.03 (declare-fun tptp.produc6161850002892822231at_nat (tptp.product_prod_nat_nat tptp.product_prod_nat_nat) tptp.produc859450856879609959at_nat)
% 6.73/7.03 (declare-fun tptp.product_Pair_real_o (tptp.real Bool) tptp.product_prod_real_o)
% 6.73/7.03 (declare-fun tptp.produc1693001998875562995omplex (tptp.real tptp.complex) tptp.produc6979889472282505531omplex)
% 6.73/7.03 (declare-fun tptp.produc3179012173361985393al_int (tptp.real tptp.int) tptp.produc8786904178792722361al_int)
% 6.73/7.03 (declare-fun tptp.produc3181502643871035669al_nat (tptp.real tptp.nat) tptp.produc3741383161447143261al_nat)
% 6.73/7.03 (declare-fun tptp.produc4511245868158468465l_real (tptp.real tptp.real) tptp.produc2422161461964618553l_real)
% 6.73/7.03 (declare-fun tptp.produc6931449550656315951T_VEBT (tptp.real tptp.vEBT_VEBT) tptp.produc3757001726724277373T_VEBT)
% 6.73/7.03 (declare-fun tptp.produc4532415448927165861et_nat (tptp.set_nat tptp.set_nat) tptp.produc7819656566062154093et_nat)
% 6.73/7.03 (declare-fun tptp.produc2922128104949294807at_nat (tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat) tptp.produc3843707927480180839at_nat)
% 6.73/7.03 (declare-fun tptp.produc8721562602347293563VEBT_o (tptp.vEBT_VEBT Bool) tptp.produc334124729049499915VEBT_o)
% 6.73/7.03 (declare-fun tptp.produc5617778602380981643omplex (tptp.vEBT_VEBT tptp.complex) tptp.produc8380087813684007313omplex)
% 6.73/7.03 (declare-fun tptp.produc581526299967858633d_enat (tptp.vEBT_VEBT tptp.extended_enat) tptp.produc7272778201969148633d_enat)
% 6.73/7.03 (declare-fun tptp.produc736041933913180425BT_int (tptp.vEBT_VEBT tptp.int) tptp.produc4894624898956917775BT_int)
% 6.73/7.03 (declare-fun tptp.produc738532404422230701BT_nat (tptp.vEBT_VEBT tptp.nat) tptp.produc9072475918466114483BT_nat)
% 6.73/7.03 (declare-fun tptp.produc8117437818029410057T_real (tptp.vEBT_VEBT tptp.real) tptp.produc5170161368751668367T_real)
% 6.73/7.03 (declare-fun tptp.produc537772716801021591T_VEBT (tptp.vEBT_VEBT tptp.vEBT_VEBT) tptp.produc8243902056947475879T_VEBT)
% 6.73/7.03 (declare-fun tptp.produc457027306803732586at_nat (tptp.set_nat (-> tptp.nat tptp.set_nat)) tptp.set_Pr1261947904930325089at_nat)
% 6.73/7.03 (declare-fun tptp.produc6499014454317279255nteger ((-> tptp.code_integer tptp.code_integer) tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger)
% 6.73/7.03 (declare-fun tptp.produc1553301316500091796er_int ((-> tptp.code_integer tptp.code_integer tptp.int) tptp.produc8923325533196201883nteger) tptp.int)
% 6.73/7.03 (declare-fun tptp.produc1555791787009142072er_nat ((-> tptp.code_integer tptp.code_integer tptp.nat) tptp.produc8923325533196201883nteger) tptp.nat)
% 6.73/7.03 (declare-fun tptp.produc6916734918728496179nteger ((-> tptp.code_integer tptp.code_integer tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger)
% 6.73/7.03 (declare-fun tptp.produc4947309494688390418_int_o ((-> tptp.int tptp.int Bool) tptp.product_prod_int_int) Bool)
% 6.73/7.03 (declare-fun tptp.produc8211389475949308722nt_int ((-> tptp.int tptp.int tptp.int) tptp.product_prod_int_int) tptp.int)
% 6.73/7.03 (declare-fun tptp.produc4245557441103728435nt_int ((-> tptp.int tptp.int tptp.product_prod_int_int) tptp.product_prod_int_int) tptp.product_prod_int_int)
% 6.73/7.03 (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)
% 6.73/7.03 (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)
% 6.73/7.03 (declare-fun tptp.produc6081775807080527818_nat_o ((-> tptp.nat tptp.nat Bool) tptp.product_prod_nat_nat) Bool)
% 6.73/7.03 (declare-fun tptp.produc2761476792215241774st_nat ((-> tptp.nat tptp.nat tptp.list_nat) tptp.product_prod_nat_nat) tptp.list_nat)
% 6.73/7.03 (declare-fun tptp.produc6842872674320459806at_nat ((-> tptp.nat tptp.nat tptp.nat) tptp.product_prod_nat_nat) tptp.nat)
% 6.73/7.03 (declare-fun tptp.produc2626176000494625587at_nat ((-> tptp.nat tptp.nat tptp.product_prod_nat_nat) tptp.product_prod_nat_nat) tptp.product_prod_nat_nat)
% 6.73/7.03 (declare-fun tptp.produc6207742614233964070at_rat ((-> tptp.nat tptp.nat tptp.rat) tptp.product_prod_nat_nat) tptp.rat)
% 6.73/7.03 (declare-fun tptp.product_fst_int_int (tptp.product_prod_int_int) tptp.int)
% 6.73/7.03 (declare-fun tptp.product_fst_nat_nat (tptp.product_prod_nat_nat) tptp.nat)
% 6.73/7.03 (declare-fun tptp.product_snd_int_int (tptp.product_prod_int_int) tptp.int)
% 6.73/7.03 (declare-fun tptp.product_snd_nat_nat (tptp.product_prod_nat_nat) tptp.nat)
% 6.73/7.03 (declare-fun tptp.produc5538323210962509403atural ((-> tptp.produc7822875418678951345atural tptp.produc5835291356934675326atural) (-> tptp.code_natural tptp.produc7822875418678951345atural tptp.produc5835291356934675326atural) tptp.produc7822875418678951345atural) tptp.produc5835291356934675326atural)
% 6.73/7.03 (declare-fun tptp.iterat8892046348760725948atural (tptp.code_natural (-> tptp.code_natural tptp.produc7822875418678951345atural tptp.produc5835291356934675326atural) tptp.code_natural tptp.produc7822875418678951345atural) tptp.produc5835291356934675326atural)
% 6.73/7.03 (declare-fun tptp.log (tptp.code_natural tptp.code_natural) tptp.code_natural)
% 6.73/7.03 (declare-fun tptp.minus_shift (tptp.code_natural tptp.code_natural tptp.code_natural) tptp.code_natural)
% 6.73/7.03 (declare-fun tptp.next (tptp.produc7822875418678951345atural) tptp.produc5835291356934675326atural)
% 6.73/7.03 (declare-fun tptp.range (tptp.code_natural tptp.produc7822875418678951345atural) tptp.produc5835291356934675326atural)
% 6.73/7.03 (declare-fun tptp.abs_Rat (tptp.product_prod_int_int) tptp.rat)
% 6.73/7.03 (declare-fun tptp.fract (tptp.int tptp.int) tptp.rat)
% 6.73/7.03 (declare-fun tptp.rep_Rat (tptp.rat) tptp.product_prod_int_int)
% 6.73/7.03 (declare-fun tptp.field_5140801741446780682s_real () tptp.set_real)
% 6.73/7.03 (declare-fun tptp.normalize (tptp.product_prod_int_int) tptp.product_prod_int_int)
% 6.73/7.03 (declare-fun tptp.pcr_rat (tptp.product_prod_int_int tptp.rat) Bool)
% 6.73/7.03 (declare-fun tptp.positive (tptp.rat) Bool)
% 6.73/7.03 (declare-fun tptp.quotient_of (tptp.rat) tptp.product_prod_int_int)
% 6.73/7.03 (declare-fun tptp.ratrel (tptp.product_prod_int_int tptp.product_prod_int_int) Bool)
% 6.73/7.03 (declare-fun tptp.ratreal (tptp.rat) tptp.real)
% 6.73/7.03 (declare-fun tptp.real2 ((-> tptp.nat tptp.rat)) tptp.real)
% 6.73/7.03 (declare-fun tptp.cauchy ((-> tptp.nat tptp.rat)) Bool)
% 6.73/7.03 (declare-fun tptp.pcr_real ((-> tptp.nat tptp.rat) tptp.real) Bool)
% 6.73/7.03 (declare-fun tptp.positive2 (tptp.real) Bool)
% 6.73/7.03 (declare-fun tptp.realrel ((-> tptp.nat tptp.rat) (-> tptp.nat tptp.rat)) Bool)
% 6.73/7.03 (declare-fun tptp.rep_real (tptp.real tptp.nat) tptp.rat)
% 6.73/7.03 (declare-fun tptp.vanishes ((-> tptp.nat tptp.rat)) Bool)
% 6.73/7.03 (declare-fun tptp.real_V2521375963428798218omplex () tptp.set_complex)
% 6.73/7.03 (declare-fun tptp.real_V5970128139526366754l_real ((-> tptp.real tptp.real)) Bool)
% 6.73/7.03 (declare-fun tptp.real_V4572627801940501177l_real ((-> tptp.real tptp.real)) Bool)
% 6.73/7.03 (declare-fun tptp.real_V1022390504157884413omplex (tptp.complex) tptp.real)
% 6.73/7.03 (declare-fun tptp.real_V7735802525324610683m_real (tptp.real) tptp.real)
% 6.73/7.03 (declare-fun tptp.real_V4546457046886955230omplex (tptp.real) tptp.complex)
% 6.73/7.03 (declare-fun tptp.real_V2046097035970521341omplex (tptp.real tptp.complex) tptp.complex)
% 6.73/7.03 (declare-fun tptp.real_V1485227260804924795R_real (tptp.real tptp.real) tptp.real)
% 6.73/7.03 (declare-fun tptp.field_nat (tptp.set_Pr1261947904930325089at_nat) tptp.set_nat)
% 6.73/7.03 (declare-fun tptp.id_nat2 () tptp.set_Pr1261947904930325089at_nat)
% 6.73/7.03 (declare-fun tptp.antisym_nat (tptp.set_Pr1261947904930325089at_nat) Bool)
% 6.73/7.03 (declare-fun tptp.refl_on_nat (tptp.set_nat tptp.set_Pr1261947904930325089at_nat) Bool)
% 6.73/7.03 (declare-fun tptp.total_on_nat (tptp.set_nat tptp.set_Pr1261947904930325089at_nat) Bool)
% 6.73/7.03 (declare-fun tptp.trans_nat (tptp.set_Pr1261947904930325089at_nat) Bool)
% 6.73/7.03 (declare-fun tptp.algebr932160517623751201me_int (tptp.int tptp.int) Bool)
% 6.73/7.03 (declare-fun tptp.algebr934650988132801477me_nat (tptp.nat tptp.nat) Bool)
% 6.73/7.03 (declare-fun tptp.divide6298287555418463151nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 6.73/7.03 (declare-fun tptp.divide5121882707175180666atural (tptp.code_natural tptp.code_natural) tptp.code_natural)
% 6.73/7.03 (declare-fun tptp.divide1717551699836669952omplex (tptp.complex tptp.complex) tptp.complex)
% 6.73/7.03 (declare-fun tptp.divide_divide_int (tptp.int tptp.int) tptp.int)
% 6.73/7.03 (declare-fun tptp.divide_divide_nat (tptp.nat tptp.nat) tptp.nat)
% 6.73/7.03 (declare-fun tptp.divide_divide_rat (tptp.rat tptp.rat) tptp.rat)
% 6.73/7.03 (declare-fun tptp.divide_divide_real (tptp.real tptp.real) tptp.real)
% 6.73/7.03 (declare-fun tptp.dvd_dvd_Code_integer (tptp.code_integer tptp.code_integer) Bool)
% 6.73/7.03 (declare-fun tptp.dvd_dvd_Code_natural (tptp.code_natural tptp.code_natural) Bool)
% 6.73/7.03 (declare-fun tptp.dvd_dvd_complex (tptp.complex tptp.complex) Bool)
% 6.73/7.03 (declare-fun tptp.dvd_dvd_int (tptp.int tptp.int) Bool)
% 6.73/7.03 (declare-fun tptp.dvd_dvd_nat (tptp.nat tptp.nat) Bool)
% 6.73/7.03 (declare-fun tptp.dvd_dvd_rat (tptp.rat tptp.rat) Bool)
% 6.73/7.03 (declare-fun tptp.dvd_dvd_real (tptp.real tptp.real) Bool)
% 6.73/7.03 (declare-fun tptp.modulo364778990260209775nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 6.73/7.03 (declare-fun tptp.modulo8411746178871703098atural (tptp.code_natural tptp.code_natural) tptp.code_natural)
% 6.73/7.03 (declare-fun tptp.modulo_modulo_int (tptp.int tptp.int) tptp.int)
% 6.73/7.03 (declare-fun tptp.modulo_modulo_nat (tptp.nat tptp.nat) tptp.nat)
% 6.73/7.03 (declare-fun tptp.unit_f2748546683901255202or_nat (tptp.nat) tptp.nat)
% 6.73/7.03 (declare-fun tptp.zero_n356916108424825756nteger (Bool) tptp.code_integer)
% 6.73/7.03 (declare-fun tptp.zero_n8403883297036319079atural (Bool) tptp.code_natural)
% 6.73/7.03 (declare-fun tptp.zero_n1201886186963655149omplex (Bool) tptp.complex)
% 6.73/7.03 (declare-fun tptp.zero_n2684676970156552555ol_int (Bool) tptp.int)
% 6.73/7.03 (declare-fun tptp.zero_n2687167440665602831ol_nat (Bool) tptp.nat)
% 6.73/7.03 (declare-fun tptp.zero_n2052037380579107095ol_rat (Bool) tptp.rat)
% 6.73/7.03 (declare-fun tptp.zero_n3304061248610475627l_real (Bool) tptp.real)
% 6.73/7.03 (declare-fun tptp.suminf_real ((-> tptp.nat tptp.real)) tptp.real)
% 6.73/7.03 (declare-fun tptp.summable_real ((-> tptp.nat tptp.real)) Bool)
% 6.73/7.03 (declare-fun tptp.sums_complex ((-> tptp.nat tptp.complex) tptp.complex) Bool)
% 6.73/7.03 (declare-fun tptp.sums_int ((-> tptp.nat tptp.int) tptp.int) Bool)
% 6.73/7.03 (declare-fun tptp.sums_nat ((-> tptp.nat tptp.nat) tptp.nat) Bool)
% 6.73/7.03 (declare-fun tptp.sums_real ((-> tptp.nat tptp.real) tptp.real) Bool)
% 6.73/7.03 (declare-fun tptp.collect_complex ((-> tptp.complex Bool)) tptp.set_complex)
% 6.73/7.03 (declare-fun tptp.collect_int ((-> tptp.int Bool)) tptp.set_int)
% 6.73/7.03 (declare-fun tptp.collect_list_o ((-> tptp.list_o Bool)) tptp.set_list_o)
% 6.73/7.03 (declare-fun tptp.collect_list_complex ((-> tptp.list_complex Bool)) tptp.set_list_complex)
% 6.73/7.03 (declare-fun tptp.collect_list_int ((-> tptp.list_int Bool)) tptp.set_list_int)
% 6.73/7.03 (declare-fun tptp.collec5989764272469232197st_nat ((-> tptp.list_list_nat Bool)) tptp.set_list_list_nat)
% 6.73/7.03 (declare-fun tptp.collect_list_nat ((-> tptp.list_nat Bool)) tptp.set_list_nat)
% 6.73/7.03 (declare-fun tptp.collect_list_set_nat ((-> tptp.list_set_nat Bool)) tptp.set_list_set_nat)
% 6.73/7.03 (declare-fun tptp.collec5608196760682091941T_VEBT ((-> tptp.list_VEBT_VEBT Bool)) tptp.set_list_VEBT_VEBT)
% 6.73/7.03 (declare-fun tptp.collect_nat ((-> tptp.nat Bool)) tptp.set_nat)
% 6.73/7.03 (declare-fun tptp.collect_num ((-> tptp.num Bool)) tptp.set_num)
% 6.73/7.03 (declare-fun tptp.collec3392354462482085612at_nat ((-> tptp.product_prod_nat_nat Bool)) tptp.set_Pr1261947904930325089at_nat)
% 6.73/7.03 (declare-fun tptp.collect_rat ((-> tptp.rat Bool)) tptp.set_rat)
% 6.73/7.03 (declare-fun tptp.collect_real ((-> tptp.real Bool)) tptp.set_real)
% 6.73/7.03 (declare-fun tptp.collect_set_nat ((-> tptp.set_nat Bool)) tptp.set_set_nat)
% 6.73/7.03 (declare-fun tptp.pow_nat (tptp.set_nat) tptp.set_set_nat)
% 6.73/7.03 (declare-fun tptp.image_int_int ((-> tptp.int tptp.int) tptp.set_int) tptp.set_int)
% 6.73/7.03 (declare-fun tptp.image_int_nat ((-> tptp.int tptp.nat) tptp.set_int) tptp.set_nat)
% 6.73/7.03 (declare-fun tptp.image_list_nat_nat ((-> tptp.list_nat tptp.nat) tptp.set_list_nat) tptp.set_nat)
% 6.73/7.03 (declare-fun tptp.image_nat_int ((-> tptp.nat tptp.int) tptp.set_nat) tptp.set_int)
% 6.73/7.03 (declare-fun tptp.image_nat_list_nat ((-> tptp.nat tptp.list_nat) tptp.set_nat) tptp.set_list_nat)
% 6.73/7.03 (declare-fun tptp.image_nat_nat ((-> tptp.nat tptp.nat) tptp.set_nat) tptp.set_nat)
% 6.73/7.03 (declare-fun tptp.image_5846123807819985514at_nat ((-> tptp.nat tptp.product_prod_nat_nat) tptp.set_nat) tptp.set_Pr1261947904930325089at_nat)
% 6.73/7.03 (declare-fun tptp.image_nat_set_nat ((-> tptp.nat tptp.set_nat) tptp.set_nat) tptp.set_set_nat)
% 6.73/7.03 (declare-fun tptp.image_nat_char ((-> tptp.nat tptp.char) tptp.set_nat) tptp.set_char)
% 6.73/7.03 (declare-fun tptp.image_678696785212003926at_nat ((-> tptp.nat tptp.sum_sum_nat_nat) tptp.set_nat) tptp.set_Sum_sum_nat_nat)
% 6.73/7.03 (declare-fun tptp.image_2486076414777270412at_nat ((-> tptp.product_prod_nat_nat tptp.nat) tptp.set_Pr1261947904930325089at_nat) tptp.set_nat)
% 6.73/7.03 (declare-fun tptp.image_real_real ((-> tptp.real tptp.real) tptp.set_real) tptp.set_real)
% 6.73/7.03 (declare-fun tptp.image_char_nat ((-> tptp.char tptp.nat) tptp.set_char) tptp.set_nat)
% 6.73/7.03 (declare-fun tptp.image_1320371278474632150at_nat ((-> tptp.sum_sum_nat_nat tptp.nat) tptp.set_Sum_sum_nat_nat) tptp.set_nat)
% 6.73/7.03 (declare-fun tptp.insert_o (Bool tptp.set_o) tptp.set_o)
% 6.73/7.03 (declare-fun tptp.insert_complex (tptp.complex tptp.set_complex) tptp.set_complex)
% 6.73/7.03 (declare-fun tptp.insert_int (tptp.int tptp.set_int) tptp.set_int)
% 6.73/7.03 (declare-fun tptp.insert_list_nat (tptp.list_nat tptp.set_list_nat) tptp.set_list_nat)
% 6.73/7.03 (declare-fun tptp.insert_nat (tptp.nat tptp.set_nat) tptp.set_nat)
% 6.73/7.03 (declare-fun tptp.insert_num (tptp.num tptp.set_num) tptp.set_num)
% 6.73/7.03 (declare-fun tptp.insert8211810215607154385at_nat (tptp.product_prod_nat_nat tptp.set_Pr1261947904930325089at_nat) tptp.set_Pr1261947904930325089at_nat)
% 6.73/7.03 (declare-fun tptp.insert_rat (tptp.rat tptp.set_rat) tptp.set_rat)
% 6.73/7.03 (declare-fun tptp.insert_real (tptp.real tptp.set_real) tptp.set_real)
% 6.73/7.03 (declare-fun tptp.insert_set_nat (tptp.set_nat tptp.set_set_nat) tptp.set_set_nat)
% 6.73/7.03 (declare-fun tptp.insert_VEBT_VEBT (tptp.vEBT_VEBT tptp.set_VEBT_VEBT) tptp.set_VEBT_VEBT)
% 6.73/7.03 (declare-fun tptp.vimage_nat_nat ((-> tptp.nat tptp.nat) tptp.set_nat) tptp.set_nat)
% 6.73/7.03 (declare-fun tptp.set_fo1084959871951514735nteger ((-> tptp.nat tptp.code_integer tptp.code_integer) tptp.nat tptp.nat tptp.code_integer) tptp.code_integer)
% 6.73/7.03 (declare-fun tptp.set_fo1517530859248394432omplex ((-> tptp.nat tptp.complex tptp.complex) tptp.nat tptp.nat tptp.complex) tptp.complex)
% 6.73/7.03 (declare-fun tptp.set_fo2581907887559384638at_int ((-> tptp.nat tptp.int tptp.int) tptp.nat tptp.nat tptp.int) tptp.int)
% 6.73/7.03 (declare-fun tptp.set_fo2584398358068434914at_nat ((-> tptp.nat tptp.nat tptp.nat) tptp.nat tptp.nat tptp.nat) tptp.nat)
% 6.73/7.03 (declare-fun tptp.set_fo1949268297981939178at_rat ((-> tptp.nat tptp.rat tptp.rat) tptp.nat tptp.nat tptp.rat) tptp.rat)
% 6.73/7.03 (declare-fun tptp.set_fo3111899725591712190t_real ((-> tptp.nat tptp.real tptp.real) tptp.nat tptp.nat tptp.real) tptp.real)
% 6.73/7.03 (declare-fun tptp.set_or1266510415728281911st_int (tptp.int tptp.int) tptp.set_int)
% 6.73/7.03 (declare-fun tptp.set_or1269000886237332187st_nat (tptp.nat tptp.nat) tptp.set_nat)
% 6.73/7.03 (declare-fun tptp.set_or7049704709247886629st_num (tptp.num tptp.num) tptp.set_num)
% 6.73/7.03 (declare-fun tptp.set_or633870826150836451st_rat (tptp.rat tptp.rat) tptp.set_rat)
% 6.73/7.03 (declare-fun tptp.set_or1222579329274155063t_real (tptp.real tptp.real) tptp.set_real)
% 6.73/7.03 (declare-fun tptp.set_or4548717258645045905et_nat (tptp.set_nat tptp.set_nat) tptp.set_set_nat)
% 6.73/7.03 (declare-fun tptp.set_or4662586982721622107an_int (tptp.int tptp.int) tptp.set_int)
% 6.73/7.03 (declare-fun tptp.set_or4665077453230672383an_nat (tptp.nat tptp.nat) tptp.set_nat)
% 6.73/7.03 (declare-fun tptp.set_ord_atLeast_nat (tptp.nat) tptp.set_nat)
% 6.73/7.03 (declare-fun tptp.set_ord_atMost_int (tptp.int) tptp.set_int)
% 6.73/7.03 (declare-fun tptp.set_ord_atMost_nat (tptp.nat) tptp.set_nat)
% 6.73/7.03 (declare-fun tptp.set_ord_atMost_num (tptp.num) tptp.set_num)
% 6.73/7.03 (declare-fun tptp.set_ord_atMost_rat (tptp.rat) tptp.set_rat)
% 6.73/7.03 (declare-fun tptp.set_ord_atMost_real (tptp.real) tptp.set_real)
% 6.73/7.03 (declare-fun tptp.set_or4236626031148496127et_nat (tptp.set_nat) tptp.set_set_nat)
% 6.73/7.03 (declare-fun tptp.set_or6656581121297822940st_int (tptp.int tptp.int) tptp.set_int)
% 6.73/7.03 (declare-fun tptp.set_or6659071591806873216st_nat (tptp.nat tptp.nat) tptp.set_nat)
% 6.73/7.03 (declare-fun tptp.set_or5832277885323065728an_int (tptp.int tptp.int) tptp.set_int)
% 6.73/7.03 (declare-fun tptp.set_or5834768355832116004an_nat (tptp.nat tptp.nat) tptp.set_nat)
% 6.73/7.03 (declare-fun tptp.set_or1633881224788618240n_real (tptp.real tptp.real) tptp.set_real)
% 6.73/7.03 (declare-fun tptp.set_or1210151606488870762an_nat (tptp.nat) tptp.set_nat)
% 6.73/7.03 (declare-fun tptp.set_or5849166863359141190n_real (tptp.real) tptp.set_real)
% 6.73/7.03 (declare-fun tptp.set_ord_lessThan_int (tptp.int) tptp.set_int)
% 6.73/7.03 (declare-fun tptp.set_ord_lessThan_nat (tptp.nat) tptp.set_nat)
% 6.73/7.03 (declare-fun tptp.set_ord_lessThan_num (tptp.num) tptp.set_num)
% 6.73/7.03 (declare-fun tptp.set_ord_lessThan_rat (tptp.rat) tptp.set_rat)
% 6.73/7.03 (declare-fun tptp.set_or5984915006950818249n_real (tptp.real) tptp.set_real)
% 6.73/7.03 (declare-fun tptp.set_or890127255671739683et_nat (tptp.set_nat) tptp.set_set_nat)
% 6.73/7.03 (declare-fun tptp.char2 (Bool Bool Bool Bool Bool Bool Bool Bool) tptp.char)
% 6.73/7.03 (declare-fun tptp.size_char (tptp.char) tptp.nat)
% 6.73/7.03 (declare-fun tptp.comm_s629917340098488124ar_nat (tptp.char) tptp.nat)
% 6.73/7.03 (declare-fun tptp.integer_of_char (tptp.char) tptp.code_integer)
% 6.73/7.03 (declare-fun tptp.unique3096191561947761185of_nat (tptp.nat) tptp.char)
% 6.73/7.03 (declare-fun tptp.sum_Inl_nat_nat (tptp.nat) tptp.sum_sum_nat_nat)
% 6.73/7.03 (declare-fun tptp.sum_Inr_nat_nat (tptp.nat) tptp.sum_sum_nat_nat)
% 6.73/7.03 (declare-fun tptp.sum_ca7763040182479039464nt_nat ((-> tptp.nat tptp.int) (-> tptp.nat tptp.int) tptp.sum_sum_nat_nat) tptp.int)
% 6.73/7.03 (declare-fun tptp.sum_ca6763686470577984908at_nat ((-> tptp.nat tptp.nat) (-> tptp.nat tptp.nat) tptp.sum_sum_nat_nat) tptp.nat)
% 6.73/7.03 (declare-fun tptp.topolo4422821103128117721l_real (tptp.filter_real (-> tptp.real tptp.real)) Bool)
% 6.73/7.03 (declare-fun tptp.topolo5044208981011980120l_real (tptp.set_real (-> tptp.real tptp.real)) Bool)
% 6.73/7.03 (declare-fun tptp.topolo6980174941875973593q_real ((-> tptp.nat tptp.real)) Bool)
% 6.73/7.03 (declare-fun tptp.topolo2177554685111907308n_real (tptp.real tptp.set_real) tptp.filter_real)
% 6.73/7.03 (declare-fun tptp.topolo7531315842566124627t_real ((-> tptp.nat tptp.real)) Bool)
% 6.73/7.03 (declare-fun tptp.topolo2815343760600316023s_real (tptp.real) tptp.filter_real)
% 6.73/7.03 (declare-fun tptp.topolo4055970368930404560y_real ((-> tptp.nat tptp.real)) Bool)
% 6.73/7.03 (declare-fun tptp.arccos (tptp.real) tptp.real)
% 6.73/7.03 (declare-fun tptp.arcosh_real (tptp.real) tptp.real)
% 6.73/7.03 (declare-fun tptp.arctan (tptp.real) tptp.real)
% 6.73/7.03 (declare-fun tptp.arsinh_real (tptp.real) tptp.real)
% 6.73/7.03 (declare-fun tptp.artanh_real (tptp.real) tptp.real)
% 6.73/7.03 (declare-fun tptp.cos_complex (tptp.complex) tptp.complex)
% 6.73/7.03 (declare-fun tptp.cos_real (tptp.real) tptp.real)
% 6.73/7.03 (declare-fun tptp.cos_coeff (tptp.nat) tptp.real)
% 6.73/7.03 (declare-fun tptp.cot_real (tptp.real) tptp.real)
% 6.73/7.03 (declare-fun tptp.exp_complex (tptp.complex) tptp.complex)
% 6.73/7.03 (declare-fun tptp.exp_real (tptp.real) tptp.real)
% 6.73/7.03 (declare-fun tptp.ln_ln_real (tptp.real) tptp.real)
% 6.73/7.03 (declare-fun tptp.log2 (tptp.real tptp.real) tptp.real)
% 6.73/7.03 (declare-fun tptp.pi () tptp.real)
% 6.73/7.03 (declare-fun tptp.powr_real (tptp.real tptp.real) tptp.real)
% 6.73/7.03 (declare-fun tptp.sin_complex (tptp.complex) tptp.complex)
% 6.73/7.03 (declare-fun tptp.sin_real (tptp.real) tptp.real)
% 6.73/7.03 (declare-fun tptp.sin_coeff (tptp.nat) tptp.real)
% 6.73/7.03 (declare-fun tptp.tan_real (tptp.real) tptp.real)
% 6.73/7.03 (declare-fun tptp.tanh_real (tptp.real) tptp.real)
% 6.73/7.03 (declare-fun tptp.transi2905341329935302413cl_nat (tptp.set_Pr1261947904930325089at_nat) tptp.set_Pr1261947904930325089at_nat)
% 6.73/7.03 (declare-fun tptp.transi6264000038957366511cl_nat (tptp.set_Pr1261947904930325089at_nat) tptp.set_Pr1261947904930325089at_nat)
% 6.73/7.03 (declare-fun tptp.transi2163837189807498211lp_nat ((-> tptp.nat tptp.nat Bool) tptp.nat tptp.nat) Bool)
% 6.73/7.03 (declare-fun tptp.typerep2 (tptp.literal tptp.list_typerep) tptp.typerep)
% 6.73/7.03 (declare-fun tptp.size_typerep (tptp.typerep) tptp.nat)
% 6.73/7.03 (declare-fun tptp.vEBT_Leaf (Bool Bool) tptp.vEBT_VEBT)
% 6.73/7.03 (declare-fun tptp.vEBT_Node (tptp.option4927543243414619207at_nat tptp.nat tptp.list_VEBT_VEBT tptp.vEBT_VEBT) tptp.vEBT_VEBT)
% 6.73/7.03 (declare-fun tptp.vEBT_size_VEBT (tptp.vEBT_VEBT) tptp.nat)
% 6.73/7.03 (declare-fun tptp.vEBT_V8194947554948674370ptions (tptp.vEBT_VEBT tptp.nat) Bool)
% 6.73/7.03 (declare-fun tptp.vEBT_VEBT_elim_dead (tptp.vEBT_VEBT tptp.extended_enat) tptp.vEBT_VEBT)
% 6.73/7.03 (declare-fun tptp.vEBT_V312737461966249ad_rel (tptp.produc7272778201969148633d_enat tptp.produc7272778201969148633d_enat) Bool)
% 6.73/7.03 (declare-fun tptp.vEBT_VEBT_high (tptp.nat tptp.nat) tptp.nat)
% 6.73/7.03 (declare-fun tptp.vEBT_V5917875025757280293ildren (tptp.nat tptp.list_VEBT_VEBT tptp.nat) Bool)
% 6.73/7.03 (declare-fun tptp.vEBT_VEBT_low (tptp.nat tptp.nat) tptp.nat)
% 6.73/7.03 (declare-fun tptp.vEBT_VEBT_membermima (tptp.vEBT_VEBT tptp.nat) Bool)
% 6.73/7.03 (declare-fun tptp.vEBT_V4351362008482014158ma_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 6.73/7.03 (declare-fun tptp.vEBT_V5719532721284313246member (tptp.vEBT_VEBT tptp.nat) Bool)
% 6.73/7.03 (declare-fun tptp.vEBT_V5765760719290551771er_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 6.73/7.03 (declare-fun tptp.vEBT_VEBT_valid (tptp.vEBT_VEBT tptp.nat) Bool)
% 6.73/7.03 (declare-fun tptp.vEBT_VEBT_valid_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 6.73/7.03 (declare-fun tptp.vEBT_invar_vebt (tptp.vEBT_VEBT tptp.nat) Bool)
% 6.73/7.03 (declare-fun tptp.vEBT_set_vebt (tptp.vEBT_VEBT) tptp.set_nat)
% 6.73/7.03 (declare-fun tptp.vEBT_vebt_buildup (tptp.nat) tptp.vEBT_VEBT)
% 6.73/7.03 (declare-fun tptp.vEBT_v4011308405150292612up_rel (tptp.nat tptp.nat) Bool)
% 6.73/7.03 (declare-fun tptp.vEBT_vebt_delete (tptp.vEBT_VEBT tptp.nat) tptp.vEBT_VEBT)
% 6.73/7.03 (declare-fun tptp.vEBT_vebt_delete_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 6.73/7.03 (declare-fun tptp.vEBT_VEBT_insert (tptp.vEBT_VEBT tptp.nat) tptp.vEBT_VEBT)
% 6.73/7.03 (declare-fun tptp.vEBT_VEBT_insert_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 6.73/7.03 (declare-fun tptp.vEBT_vebt_insert (tptp.vEBT_VEBT tptp.nat) tptp.vEBT_VEBT)
% 6.73/7.03 (declare-fun tptp.vEBT_vebt_insert_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 6.73/7.03 (declare-fun tptp.vEBT_VEBT_bit_concat (tptp.nat tptp.nat tptp.nat) tptp.nat)
% 6.73/7.03 (declare-fun tptp.vEBT_VEBT_minNull (tptp.vEBT_VEBT) Bool)
% 6.73/7.03 (declare-fun tptp.vEBT_V6963167321098673237ll_rel (tptp.vEBT_VEBT tptp.vEBT_VEBT) Bool)
% 6.73/7.03 (declare-fun tptp.vEBT_VEBT_set_vebt (tptp.vEBT_VEBT) tptp.set_nat)
% 6.73/7.03 (declare-fun tptp.vEBT_vebt_member (tptp.vEBT_VEBT tptp.nat) Bool)
% 6.73/7.03 (declare-fun tptp.vEBT_vebt_member_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 6.73/7.03 (declare-fun tptp.vEBT_VEBT_add (tptp.option_nat tptp.option_nat) tptp.option_nat)
% 6.73/7.03 (declare-fun tptp.vEBT_VEBT_greater (tptp.option_nat tptp.option_nat) Bool)
% 6.73/7.03 (declare-fun tptp.vEBT_VEBT_less (tptp.option_nat tptp.option_nat) Bool)
% 6.73/7.03 (declare-fun tptp.vEBT_VEBT_lesseq (tptp.option_nat tptp.option_nat) Bool)
% 6.73/7.03 (declare-fun tptp.vEBT_VEBT_max_in_set (tptp.set_nat tptp.nat) Bool)
% 6.73/7.03 (declare-fun tptp.vEBT_VEBT_min_in_set (tptp.set_nat tptp.nat) Bool)
% 6.73/7.03 (declare-fun tptp.vEBT_VEBT_mul (tptp.option_nat tptp.option_nat) tptp.option_nat)
% 6.73/7.03 (declare-fun tptp.vEBT_V2881884560877996034ft_nat ((-> tptp.nat tptp.nat Bool) tptp.option_nat tptp.option_nat) Bool)
% 6.73/7.03 (declare-fun tptp.vEBT_V4262088993061758097ft_nat ((-> tptp.nat tptp.nat tptp.nat) tptp.option_nat tptp.option_nat) tptp.option_nat)
% 6.73/7.03 (declare-fun tptp.vEBT_V819420779217536731ft_num ((-> tptp.num tptp.num tptp.num) tptp.option_num tptp.option_num) tptp.option_num)
% 6.73/7.03 (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)
% 6.73/7.03 (declare-fun tptp.vEBT_VEBT_power (tptp.option_nat tptp.option_nat) tptp.option_nat)
% 6.73/7.03 (declare-fun tptp.vEBT_vebt_maxt (tptp.vEBT_VEBT) tptp.option_nat)
% 6.73/7.03 (declare-fun tptp.vEBT_vebt_maxt_rel (tptp.vEBT_VEBT tptp.vEBT_VEBT) Bool)
% 6.73/7.03 (declare-fun tptp.vEBT_vebt_mint (tptp.vEBT_VEBT) tptp.option_nat)
% 6.73/7.03 (declare-fun tptp.vEBT_vebt_mint_rel (tptp.vEBT_VEBT tptp.vEBT_VEBT) Bool)
% 6.73/7.03 (declare-fun tptp.vEBT_is_pred_in_set (tptp.set_nat tptp.nat tptp.nat) Bool)
% 6.73/7.03 (declare-fun tptp.vEBT_vebt_pred (tptp.vEBT_VEBT tptp.nat) tptp.option_nat)
% 6.73/7.03 (declare-fun tptp.vEBT_vebt_pred_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 6.73/7.03 (declare-fun tptp.vEBT_is_succ_in_set (tptp.set_nat tptp.nat tptp.nat) Bool)
% 6.73/7.03 (declare-fun tptp.vEBT_vebt_succ (tptp.vEBT_VEBT tptp.nat) tptp.option_nat)
% 6.73/7.03 (declare-fun tptp.vEBT_vebt_succ_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 6.73/7.03 (declare-fun tptp.accp_list_nat ((-> tptp.list_nat tptp.list_nat Bool) tptp.list_nat) Bool)
% 6.73/7.03 (declare-fun tptp.accp_nat ((-> tptp.nat tptp.nat Bool) tptp.nat) Bool)
% 6.73/7.03 (declare-fun tptp.accp_P1096762738010456898nt_int ((-> tptp.product_prod_int_int tptp.product_prod_int_int Bool) tptp.product_prod_int_int) Bool)
% 6.73/7.03 (declare-fun tptp.accp_P4275260045618599050at_nat ((-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool) tptp.product_prod_nat_nat) Bool)
% 6.73/7.03 (declare-fun tptp.accp_P6183159247885693666d_enat ((-> tptp.produc7272778201969148633d_enat tptp.produc7272778201969148633d_enat Bool) tptp.produc7272778201969148633d_enat) Bool)
% 6.73/7.03 (declare-fun tptp.accp_P2887432264394892906BT_nat ((-> tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat Bool) tptp.produc9072475918466114483BT_nat) Bool)
% 6.73/7.03 (declare-fun tptp.accp_VEBT_VEBT ((-> tptp.vEBT_VEBT tptp.vEBT_VEBT Bool) tptp.vEBT_VEBT) Bool)
% 6.73/7.03 (declare-fun tptp.less_than () tptp.set_Pr1261947904930325089at_nat)
% 6.73/7.03 (declare-fun tptp.pred_nat () tptp.set_Pr1261947904930325089at_nat)
% 6.73/7.03 (declare-fun tptp.member_o (Bool tptp.set_o) Bool)
% 6.73/7.03 (declare-fun tptp.member_Code_integer (tptp.code_integer tptp.set_Code_integer) Bool)
% 6.73/7.03 (declare-fun tptp.member_complex (tptp.complex tptp.set_complex) Bool)
% 6.73/7.03 (declare-fun tptp.member_int (tptp.int tptp.set_int) Bool)
% 6.73/7.03 (declare-fun tptp.member_list_o (tptp.list_o tptp.set_list_o) Bool)
% 6.73/7.03 (declare-fun tptp.member_list_int (tptp.list_int tptp.set_list_int) Bool)
% 6.73/7.03 (declare-fun tptp.member_list_nat (tptp.list_nat tptp.set_list_nat) Bool)
% 6.73/7.03 (declare-fun tptp.member2936631157270082147T_VEBT (tptp.list_VEBT_VEBT tptp.set_list_VEBT_VEBT) Bool)
% 6.73/7.03 (declare-fun tptp.member_nat (tptp.nat tptp.set_nat) Bool)
% 6.73/7.03 (declare-fun tptp.member_num (tptp.num tptp.set_num) Bool)
% 6.73/7.03 (declare-fun tptp.member7466972457876170832od_o_o (tptp.product_prod_o_o tptp.set_Product_prod_o_o) Bool)
% 6.73/7.03 (declare-fun tptp.member1046615901120239500omplex (tptp.produc648051720047351925omplex tptp.set_Pr5421754520313593387omplex) Bool)
% 6.73/7.03 (declare-fun tptp.member7847949116333733898_o_int (tptp.product_prod_o_int tptp.set_Pr8834758594704517033_o_int) Bool)
% 6.73/7.03 (declare-fun tptp.member2802428098988154798_o_nat (tptp.product_prod_o_nat tptp.set_Pr2101469702781467981_o_nat) Bool)
% 6.73/7.03 (declare-fun tptp.member7400031367953476362o_real (tptp.product_prod_o_real tptp.set_Pr6573716822653411497o_real) Bool)
% 6.73/7.03 (declare-fun tptp.member5477980866518848620T_VEBT (tptp.produc2504756804600209347T_VEBT tptp.set_Pr7543698050874017315T_VEBT) Bool)
% 6.73/7.03 (declare-fun tptp.member157494554546826820nteger (tptp.produc8923325533196201883nteger tptp.set_Pr4811707699266497531nteger) Bool)
% 6.73/7.03 (declare-fun tptp.member6487239523555734774plex_o (tptp.produc6088675342482847199plex_o tptp.set_Pr216032351708956309plex_o) Bool)
% 6.73/7.03 (declare-fun tptp.member5793383173714906214omplex (tptp.produc4411394909380815293omplex tptp.set_Pr5085853215250843933omplex) Bool)
% 6.73/7.03 (declare-fun tptp.member595073364599660772ex_int (tptp.produc6845221339535797307ex_int tptp.set_Pr2254670189886740123ex_int) Bool)
% 6.73/7.03 (declare-fun tptp.member4772924384108857480ex_nat (tptp.produc1799700322190218207ex_nat tptp.set_Pr4744753334818466879ex_nat) Bool)
% 6.73/7.03 (declare-fun tptp.member47443559803733732x_real (tptp.produc8892588492097263291x_real tptp.set_Pr1133549439701694107x_real) Bool)
% 6.73/7.03 (declare-fun tptp.member1978952105866562066T_VEBT (tptp.produc7151440242714718331T_VEBT tptp.set_Pr4085867452638698417T_VEBT) Bool)
% 6.73/7.03 (declare-fun tptp.member8811922270175639012omplex (tptp.produc5838698208256999739omplex tptp.set_Pr1846070511934368667omplex) Bool)
% 6.73/7.03 (declare-fun tptp.member5262025264175285858nt_int (tptp.product_prod_int_int tptp.set_Pr958786334691620121nt_int) Bool)
% 6.73/7.03 (declare-fun tptp.member2744130022092475746t_real (tptp.produc679980390762269497t_real tptp.set_Pr3538720872664544793t_real) Bool)
% 6.73/7.03 (declare-fun tptp.member4159035015898711888list_o (tptp.produc7102631898165422375list_o tptp.set_Pr6227168374412355847list_o) Bool)
% 6.73/7.03 (declare-fun tptp.member8253032945758599840st_int (tptp.produc1713839591385758857st_int tptp.set_Pr5001190662893202239st_int) Bool)
% 6.73/7.03 (declare-fun tptp.member1519744053835550788st_nat (tptp.produc4203922736317485613st_nat tptp.set_Pr591367044826345187st_nat) Bool)
% 6.73/7.03 (declare-fun tptp.member1087064965665443052T_VEBT (tptp.produc1922972420619397443T_VEBT tptp.set_Pr5170412164475753123T_VEBT) Bool)
% 6.73/7.03 (declare-fun tptp.member749217712838834276nteger (tptp.produc862207588354017979nteger tptp.set_Pr7565137564259432987nteger) Bool)
% 6.73/7.03 (declare-fun tptp.member6698963635872716290st_int (tptp.produc1186641810826059865st_int tptp.set_Pr765067013931698361st_int) Bool)
% 6.73/7.03 (declare-fun tptp.member6688923169008879818list_o (tptp.produc149729814636038835list_o tptp.set_Pr1150278048023938153list_o) Bool)
% 6.73/7.03 (declare-fun tptp.member7340969449405702474st_nat (tptp.produc1828647624359046049st_nat tptp.set_Pr3451248702717554689st_nat) Bool)
% 6.73/7.03 (declare-fun tptp.member5968030670617646438T_VEBT (tptp.produc872621073311890639T_VEBT tptp.set_Pr1262583345697558789T_VEBT) Bool)
% 6.73/7.03 (declare-fun tptp.member6693912407220327184at_nat (tptp.produc6392793444374437607at_nat tptp.set_Pr1542805901266377927at_nat) Bool)
% 6.73/7.03 (declare-fun tptp.member4080735728053443344at_nat (tptp.produc424102278133772007at_nat tptp.set_Pr4333006031979791559at_nat) Bool)
% 6.73/7.03 (declare-fun tptp.member3126162362653435956list_o (tptp.produc3962069817607390347list_o tptp.set_Pr7508168486584781291list_o) Bool)
% 6.73/7.03 (declare-fun tptp.member3703241499402361532st_int (tptp.produc7831203938951381541st_int tptp.set_Pr4080907618048478043st_int) Bool)
% 6.73/7.03 (declare-fun tptp.member6193324644334088288st_nat (tptp.produc1097915047028332489st_nat tptp.set_Pr8894456036836396799st_nat) Bool)
% 6.73/7.03 (declare-fun tptp.member4439316823752958928T_VEBT (tptp.produc9211091688327510695T_VEBT tptp.set_Pr1916528119006554503T_VEBT) Bool)
% 6.73/7.03 (declare-fun tptp.member8440522571783428010at_nat (tptp.product_prod_nat_nat tptp.set_Pr1261947904930325089at_nat) Bool)
% 6.73/7.03 (declare-fun tptp.member8549952807677709168T_VEBT (tptp.produc8025551001238799321T_VEBT tptp.set_Pr6167073792073659919T_VEBT) Bool)
% 6.73/7.03 (declare-fun tptp.member8206827879206165904at_nat (tptp.produc859450856879609959at_nat tptp.set_Pr8693737435421807431at_nat) Bool)
% 6.73/7.03 (declare-fun tptp.member772602641336174712real_o (tptp.product_prod_real_o tptp.set_Pr4936984352647145239real_o) Bool)
% 6.73/7.03 (declare-fun tptp.member7358116576843751780omplex (tptp.produc6979889472282505531omplex tptp.set_Pr6591433984475009307omplex) Bool)
% 6.73/7.03 (declare-fun tptp.member1627681773268152802al_int (tptp.produc8786904178792722361al_int tptp.set_Pr1019928272762051225al_int) Bool)
% 6.73/7.03 (declare-fun tptp.member5805532792777349510al_nat (tptp.produc3741383161447143261al_nat tptp.set_Pr3510011417693777981al_nat) Bool)
% 6.73/7.03 (declare-fun tptp.member7849222048561428706l_real (tptp.produc2422161461964618553l_real tptp.set_Pr6218003697084177305l_real) Bool)
% 6.73/7.03 (declare-fun tptp.member7262085504369356948T_VEBT (tptp.produc3757001726724277373T_VEBT tptp.set_Pr6019664923565264691T_VEBT) Bool)
% 6.73/7.03 (declare-fun tptp.member8277197624267554838et_nat (tptp.produc7819656566062154093et_nat tptp.set_Pr5488025237498180813et_nat) Bool)
% 6.73/7.03 (declare-fun tptp.member8757157785044589968at_nat (tptp.produc3843707927480180839at_nat tptp.set_Pr4329608150637261639at_nat) Bool)
% 6.73/7.03 (declare-fun tptp.member3307348790968139188VEBT_o (tptp.produc334124729049499915VEBT_o tptp.set_Pr3175402225741728619VEBT_o) Bool)
% 6.73/7.03 (declare-fun tptp.member3207599676835851048omplex (tptp.produc8380087813684007313omplex tptp.set_Pr216944050393469383omplex) Bool)
% 6.73/7.03 (declare-fun tptp.member5419026705395827622BT_int (tptp.produc4894624898956917775BT_int tptp.set_Pr5066593544530342725BT_int) Bool)
% 6.73/7.03 (declare-fun tptp.member373505688050248522BT_nat (tptp.produc9072475918466114483BT_nat tptp.set_Pr7556676689462069481BT_nat) Bool)
% 6.73/7.03 (declare-fun tptp.member8675245146396747942T_real (tptp.produc5170161368751668367T_real tptp.set_Pr7765410600122031685T_real) Bool)
% 6.73/7.03 (declare-fun tptp.member568628332442017744T_VEBT (tptp.produc8243902056947475879T_VEBT tptp.set_Pr6192946355708809607T_VEBT) Bool)
% 6.73/7.03 (declare-fun tptp.member_rat (tptp.rat tptp.set_rat) Bool)
% 6.73/7.03 (declare-fun tptp.member_real (tptp.real tptp.set_real) Bool)
% 6.73/7.03 (declare-fun tptp.member_set_nat (tptp.set_nat tptp.set_set_nat) Bool)
% 6.73/7.03 (declare-fun tptp.member2643936169264416010at_nat (tptp.set_Pr1261947904930325089at_nat tptp.set_se7855581050983116737at_nat) Bool)
% 6.73/7.03 (declare-fun tptp.member_VEBT_VEBT (tptp.vEBT_VEBT tptp.set_VEBT_VEBT) Bool)
% 6.73/7.03 (declare-fun tptp.a () Bool)
% 6.73/7.03 (declare-fun tptp.b () Bool)
% 6.73/7.03 (declare-fun tptp.deg () tptp.nat)
% 6.73/7.03 (declare-fun tptp.info () tptp.option4927543243414619207at_nat)
% 6.73/7.03 (declare-fun tptp.m () tptp.nat)
% 6.73/7.03 (declare-fun tptp.ma () tptp.nat)
% 6.73/7.03 (declare-fun tptp.mi () tptp.nat)
% 6.73/7.03 (declare-fun tptp.na () tptp.nat)
% 6.73/7.03 (declare-fun tptp.sa () tptp.vEBT_VEBT)
% 6.73/7.03 (declare-fun tptp.summary () tptp.vEBT_VEBT)
% 6.73/7.03 (declare-fun tptp.summary2 () tptp.vEBT_VEBT)
% 6.73/7.03 (declare-fun tptp.treeList () tptp.list_VEBT_VEBT)
% 6.73/7.03 (declare-fun tptp.treeList2 () tptp.list_VEBT_VEBT)
% 6.73/7.03 (assert (@ (@ tptp.ord_less_eq_nat tptp.mi) tptp.ma))
% 6.73/7.03 (assert (forall ((X2 tptp.product_prod_nat_nat) (Y2 tptp.product_prod_nat_nat)) (= (= (@ tptp.some_P7363390416028606310at_nat X2) (@ tptp.some_P7363390416028606310at_nat Y2)) (= X2 Y2))))
% 6.73/7.03 (assert (forall ((X2 tptp.nat) (Y2 tptp.nat)) (= (= (@ tptp.some_nat X2) (@ tptp.some_nat Y2)) (= X2 Y2))))
% 6.73/7.03 (assert (forall ((X2 tptp.num) (Y2 tptp.num)) (= (= (@ tptp.some_num X2) (@ tptp.some_num Y2)) (= X2 Y2))))
% 6.73/7.03 (assert (forall ((X1 tptp.code_integer) (X2 tptp.code_integer) (Y1 tptp.code_integer) (Y2 tptp.code_integer)) (= (= (@ (@ tptp.produc1086072967326762835nteger X1) X2) (@ (@ tptp.produc1086072967326762835nteger Y1) Y2)) (and (= X1 Y1) (= X2 Y2)))))
% 6.73/7.03 (assert (forall ((X1 tptp.product_prod_nat_nat) (X2 tptp.product_prod_nat_nat) (Y1 tptp.product_prod_nat_nat) (Y2 tptp.product_prod_nat_nat)) (= (= (@ (@ tptp.produc6161850002892822231at_nat X1) X2) (@ (@ tptp.produc6161850002892822231at_nat Y1) Y2)) (and (= X1 Y1) (= X2 Y2)))))
% 6.73/7.03 (assert (forall ((X1 tptp.set_Pr1261947904930325089at_nat) (X2 tptp.set_Pr1261947904930325089at_nat) (Y1 tptp.set_Pr1261947904930325089at_nat) (Y2 tptp.set_Pr1261947904930325089at_nat)) (= (= (@ (@ tptp.produc2922128104949294807at_nat X1) X2) (@ (@ tptp.produc2922128104949294807at_nat Y1) Y2)) (and (= X1 Y1) (= X2 Y2)))))
% 6.73/7.03 (assert (forall ((X1 tptp.nat) (X2 tptp.nat) (Y1 tptp.nat) (Y2 tptp.nat)) (= (= (@ (@ tptp.product_Pair_nat_nat X1) X2) (@ (@ tptp.product_Pair_nat_nat Y1) Y2)) (and (= X1 Y1) (= X2 Y2)))))
% 6.73/7.03 (assert (forall ((X1 tptp.int) (X2 tptp.int) (Y1 tptp.int) (Y2 tptp.int)) (= (= (@ (@ tptp.product_Pair_int_int X1) X2) (@ (@ tptp.product_Pair_int_int Y1) Y2)) (and (= X1 Y1) (= X2 Y2)))))
% 6.73/7.03 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (A2 tptp.code_integer) (B2 tptp.code_integer)) (= (= (@ (@ tptp.produc1086072967326762835nteger A) B) (@ (@ tptp.produc1086072967326762835nteger A2) B2)) (and (= A A2) (= B B2)))))
% 6.73/7.03 (assert (forall ((A tptp.product_prod_nat_nat) (B tptp.product_prod_nat_nat) (A2 tptp.product_prod_nat_nat) (B2 tptp.product_prod_nat_nat)) (= (= (@ (@ tptp.produc6161850002892822231at_nat A) B) (@ (@ tptp.produc6161850002892822231at_nat A2) B2)) (and (= A A2) (= B B2)))))
% 6.73/7.03 (assert (forall ((A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat) (A2 tptp.set_Pr1261947904930325089at_nat) (B2 tptp.set_Pr1261947904930325089at_nat)) (= (= (@ (@ tptp.produc2922128104949294807at_nat A) B) (@ (@ tptp.produc2922128104949294807at_nat A2) B2)) (and (= A A2) (= B B2)))))
% 6.73/7.03 (assert (forall ((A tptp.nat) (B tptp.nat) (A2 tptp.nat) (B2 tptp.nat)) (= (= (@ (@ tptp.product_Pair_nat_nat A) B) (@ (@ tptp.product_Pair_nat_nat A2) B2)) (and (= A A2) (= B B2)))))
% 6.73/7.03 (assert (forall ((A tptp.int) (B tptp.int) (A2 tptp.int) (B2 tptp.int)) (= (= (@ (@ tptp.product_Pair_int_int A) B) (@ (@ tptp.product_Pair_int_int A2) B2)) (and (= A A2) (= B B2)))))
% 6.73/7.03 (assert (forall ((X tptp.product_prod_nat_nat)) (not (forall ((K tptp.nat) (M tptp.nat)) (not (= X (@ (@ tptp.product_Pair_nat_nat K) M)))))))
% 6.73/7.03 (assert (forall ((Y tptp.produc8923325533196201883nteger)) (not (forall ((A3 tptp.code_integer) (B3 tptp.code_integer)) (not (= Y (@ (@ tptp.produc1086072967326762835nteger A3) B3)))))))
% 6.73/7.03 (assert (forall ((Y tptp.produc859450856879609959at_nat)) (not (forall ((A3 tptp.product_prod_nat_nat) (B3 tptp.product_prod_nat_nat)) (not (= Y (@ (@ tptp.produc6161850002892822231at_nat A3) B3)))))))
% 6.73/7.03 (assert (forall ((Y tptp.produc3843707927480180839at_nat)) (not (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (not (= Y (@ (@ tptp.produc2922128104949294807at_nat A3) B3)))))))
% 6.73/7.03 (assert (forall ((Y tptp.product_prod_nat_nat)) (not (forall ((A3 tptp.nat) (B3 tptp.nat)) (not (= Y (@ (@ tptp.product_Pair_nat_nat A3) B3)))))))
% 6.73/7.03 (assert (forall ((Y tptp.product_prod_int_int)) (not (forall ((A3 tptp.int) (B3 tptp.int)) (not (= Y (@ (@ tptp.product_Pair_int_int A3) B3)))))))
% 6.73/7.03 (assert (forall ((P tptp.produc8923325533196201883nteger)) (exists ((X3 tptp.code_integer) (Y3 tptp.code_integer)) (= P (@ (@ tptp.produc1086072967326762835nteger X3) Y3)))))
% 6.73/7.03 (assert (forall ((P tptp.produc859450856879609959at_nat)) (exists ((X3 tptp.product_prod_nat_nat) (Y3 tptp.product_prod_nat_nat)) (= P (@ (@ tptp.produc6161850002892822231at_nat X3) Y3)))))
% 6.73/7.03 (assert (forall ((P tptp.produc3843707927480180839at_nat)) (exists ((X3 tptp.set_Pr1261947904930325089at_nat) (Y3 tptp.set_Pr1261947904930325089at_nat)) (= P (@ (@ tptp.produc2922128104949294807at_nat X3) Y3)))))
% 6.73/7.03 (assert (forall ((P tptp.product_prod_nat_nat)) (exists ((X3 tptp.nat) (Y3 tptp.nat)) (= P (@ (@ tptp.product_Pair_nat_nat X3) Y3)))))
% 6.73/7.03 (assert (forall ((P tptp.product_prod_int_int)) (exists ((X3 tptp.int) (Y3 tptp.int)) (= P (@ (@ tptp.product_Pair_int_int X3) Y3)))))
% 6.73/7.03 (assert (forall ((P2 (-> tptp.produc8923325533196201883nteger Bool)) (P tptp.produc8923325533196201883nteger)) (=> (forall ((A3 tptp.code_integer) (B3 tptp.code_integer)) (@ P2 (@ (@ tptp.produc1086072967326762835nteger A3) B3))) (@ P2 P))))
% 6.73/7.03 (assert (forall ((P2 (-> tptp.produc859450856879609959at_nat Bool)) (P tptp.produc859450856879609959at_nat)) (=> (forall ((A3 tptp.product_prod_nat_nat) (B3 tptp.product_prod_nat_nat)) (@ P2 (@ (@ tptp.produc6161850002892822231at_nat A3) B3))) (@ P2 P))))
% 6.73/7.03 (assert (forall ((P2 (-> tptp.produc3843707927480180839at_nat Bool)) (P tptp.produc3843707927480180839at_nat)) (=> (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (@ P2 (@ (@ tptp.produc2922128104949294807at_nat A3) B3))) (@ P2 P))))
% 6.73/7.03 (assert (forall ((P2 (-> tptp.product_prod_nat_nat Bool)) (P tptp.product_prod_nat_nat)) (=> (forall ((A3 tptp.nat) (B3 tptp.nat)) (@ P2 (@ (@ tptp.product_Pair_nat_nat A3) B3))) (@ P2 P))))
% 6.73/7.03 (assert (forall ((P2 (-> tptp.product_prod_int_int Bool)) (P tptp.product_prod_int_int)) (=> (forall ((A3 tptp.int) (B3 tptp.int)) (@ P2 (@ (@ tptp.product_Pair_int_int A3) B3))) (@ P2 P))))
% 6.73/7.03 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (A2 tptp.code_integer) (B2 tptp.code_integer)) (=> (= (@ (@ tptp.produc1086072967326762835nteger A) B) (@ (@ tptp.produc1086072967326762835nteger A2) B2)) (not (=> (= A A2) (not (= B B2)))))))
% 6.73/7.03 (assert (forall ((A tptp.product_prod_nat_nat) (B tptp.product_prod_nat_nat) (A2 tptp.product_prod_nat_nat) (B2 tptp.product_prod_nat_nat)) (=> (= (@ (@ tptp.produc6161850002892822231at_nat A) B) (@ (@ tptp.produc6161850002892822231at_nat A2) B2)) (not (=> (= A A2) (not (= B B2)))))))
% 6.73/7.03 (assert (forall ((A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat) (A2 tptp.set_Pr1261947904930325089at_nat) (B2 tptp.set_Pr1261947904930325089at_nat)) (=> (= (@ (@ tptp.produc2922128104949294807at_nat A) B) (@ (@ tptp.produc2922128104949294807at_nat A2) B2)) (not (=> (= A A2) (not (= B B2)))))))
% 6.73/7.03 (assert (forall ((A tptp.nat) (B tptp.nat) (A2 tptp.nat) (B2 tptp.nat)) (=> (= (@ (@ tptp.product_Pair_nat_nat A) B) (@ (@ tptp.product_Pair_nat_nat A2) B2)) (not (=> (= A A2) (not (= B B2)))))))
% 6.73/7.03 (assert (forall ((A tptp.int) (B tptp.int) (A2 tptp.int) (B2 tptp.int)) (=> (= (@ (@ tptp.product_Pair_int_int A) B) (@ (@ tptp.product_Pair_int_int A2) B2)) (not (=> (= A A2) (not (= B B2)))))))
% 6.73/7.03 (assert (forall ((Y tptp.produc859450856879609959at_nat)) (not (forall ((A3 tptp.product_prod_nat_nat) (B3 tptp.nat) (C tptp.nat)) (not (= Y (@ (@ tptp.produc6161850002892822231at_nat A3) (@ (@ tptp.product_Pair_nat_nat B3) C))))))))
% 6.73/7.03 (assert (= tptp.vEBT_VEBT_max_in_set (lambda ((Xs tptp.set_nat) (X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) Xs) (forall ((Y4 tptp.nat)) (=> (@ (@ tptp.member_nat Y4) Xs) (@ (@ tptp.ord_less_eq_nat Y4) X4)))))))
% 6.73/7.03 (assert (= tptp.vEBT_VEBT_min_in_set (lambda ((Xs tptp.set_nat) (X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) Xs) (forall ((Y4 tptp.nat)) (=> (@ (@ tptp.member_nat Y4) Xs) (@ (@ tptp.ord_less_eq_nat X4) Y4)))))))
% 6.73/7.03 (assert (= tptp.ord_less_eq_nat (lambda ((X4 tptp.nat) (Y4 tptp.nat)) (@ (@ tptp.vEBT_VEBT_lesseq (@ tptp.some_nat X4)) (@ tptp.some_nat Y4)))))
% 6.73/7.03 (assert (forall ((P2 (-> tptp.produc859450856879609959at_nat Bool)) (X tptp.produc859450856879609959at_nat)) (=> (forall ((A3 tptp.product_prod_nat_nat) (B3 tptp.nat) (C tptp.nat)) (@ P2 (@ (@ tptp.produc6161850002892822231at_nat A3) (@ (@ tptp.product_Pair_nat_nat B3) C)))) (@ P2 X))))
% 6.73/7.03 (assert (forall ((X tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat X) X)))
% 6.73/7.03 (assert (forall ((X tptp.rat)) (@ (@ tptp.ord_less_eq_rat X) X)))
% 6.73/7.03 (assert (forall ((X tptp.num)) (@ (@ tptp.ord_less_eq_num X) X)))
% 6.73/7.03 (assert (forall ((X tptp.nat)) (@ (@ tptp.ord_less_eq_nat X) X)))
% 6.73/7.03 (assert (forall ((X tptp.int)) (@ (@ tptp.ord_less_eq_int X) X)))
% 6.73/7.03 (assert (forall ((A tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat A) A)))
% 6.73/7.03 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_eq_rat A) A)))
% 6.73/7.03 (assert (forall ((A tptp.num)) (@ (@ tptp.ord_less_eq_num A) A)))
% 6.73/7.03 (assert (forall ((A tptp.nat)) (@ (@ tptp.ord_less_eq_nat A) A)))
% 6.73/7.03 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int A) A)))
% 6.73/7.03 (assert (= tptp.bNF_Ca8354645632395198811er_rat (lambda ((R tptp.set_Pr4811707699266497531nteger) (As (-> tptp.code_integer tptp.rat))) (forall ((I tptp.code_integer) (J tptp.code_integer)) (=> (@ (@ tptp.member157494554546826820nteger (@ (@ tptp.produc1086072967326762835nteger I) J)) R) (@ (@ tptp.ord_less_eq_rat (@ As I)) (@ As J)))))))
% 6.73/7.03 (assert (= tptp.bNF_Ca333620267926924494at_rat (lambda ((R tptp.set_Pr1261947904930325089at_nat) (As (-> tptp.nat tptp.rat))) (forall ((I tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat I) J)) R) (@ (@ tptp.ord_less_eq_rat (@ As I)) (@ As J)))))))
% 6.73/7.03 (assert (= tptp.bNF_Ca1332973979827979050nt_rat (lambda ((R tptp.set_Pr958786334691620121nt_int) (As (-> tptp.int tptp.rat))) (forall ((I tptp.int) (J tptp.int)) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int I) J)) R) (@ (@ tptp.ord_less_eq_rat (@ As I)) (@ As J)))))))
% 6.73/7.03 (assert (= tptp.bNF_Ca5547107478637473181er_num (lambda ((R tptp.set_Pr4811707699266497531nteger) (As (-> tptp.code_integer tptp.num))) (forall ((I tptp.code_integer) (J tptp.code_integer)) (=> (@ (@ tptp.member157494554546826820nteger (@ (@ tptp.produc1086072967326762835nteger I) J)) R) (@ (@ tptp.ord_less_eq_num (@ As I)) (@ As J)))))))
% 6.73/7.03 (assert (= tptp.bNF_Ca6749454151023974672at_num (lambda ((R tptp.set_Pr1261947904930325089at_nat) (As (-> tptp.nat tptp.num))) (forall ((I tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat I) J)) R) (@ (@ tptp.ord_less_eq_num (@ As I)) (@ As J)))))))
% 6.73/7.03 (assert (= tptp.bNF_Ca7748807862925029228nt_num (lambda ((R tptp.set_Pr958786334691620121nt_int) (As (-> tptp.int tptp.num))) (forall ((I tptp.int) (J tptp.int)) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int I) J)) R) (@ (@ tptp.ord_less_eq_num (@ As I)) (@ As J)))))))
% 6.73/7.03 (assert (= tptp.bNF_Ca8989775692481694547er_nat (lambda ((R tptp.set_Pr4811707699266497531nteger) (As (-> tptp.code_integer tptp.nat))) (forall ((I tptp.code_integer) (J tptp.code_integer)) (=> (@ (@ tptp.member157494554546826820nteger (@ (@ tptp.produc1086072967326762835nteger I) J)) R) (@ (@ tptp.ord_less_eq_nat (@ As I)) (@ As J)))))))
% 6.73/7.03 (assert (= tptp.bNF_Ca968750328013420230at_nat (lambda ((R tptp.set_Pr1261947904930325089at_nat) (As (-> tptp.nat tptp.nat))) (forall ((I tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat I) J)) R) (@ (@ tptp.ord_less_eq_nat (@ As I)) (@ As J)))))))
% 6.73/7.03 (assert (= tptp.bNF_Ca1968104039914474786nt_nat (lambda ((R tptp.set_Pr958786334691620121nt_int) (As (-> tptp.int tptp.nat))) (forall ((I tptp.int) (J tptp.int)) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int I) J)) R) (@ (@ tptp.ord_less_eq_nat (@ As I)) (@ As J)))))))
% 6.73/7.03 (assert (= tptp.bNF_Ca8987285221972644271er_int (lambda ((R tptp.set_Pr4811707699266497531nteger) (As (-> tptp.code_integer tptp.int))) (forall ((I tptp.code_integer) (J tptp.code_integer)) (=> (@ (@ tptp.member157494554546826820nteger (@ (@ tptp.produc1086072967326762835nteger I) J)) R) (@ (@ tptp.ord_less_eq_int (@ As I)) (@ As J)))))))
% 6.73/7.03 (assert (forall ((X tptp.produc4471711990508489141at_nat)) (not (forall ((F (-> tptp.nat tptp.nat tptp.nat)) (A3 tptp.nat) (B3 tptp.nat) (Acc tptp.nat)) (not (= X (@ (@ tptp.produc3209952032786966637at_nat F) (@ (@ tptp.produc487386426758144856at_nat A3) (@ (@ tptp.product_Pair_nat_nat B3) Acc)))))))))
% 6.73/7.03 (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)))))
% 6.73/7.03 (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)))))
% 6.73/7.03 (assert (forall ((F2 (-> tptp.nat tptp.set_nat)) (N tptp.nat) (N2 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_set_nat (@ F2 N3)) (@ F2 (@ tptp.suc N3)))) (=> (@ (@ tptp.ord_less_eq_nat N) N2) (@ (@ tptp.ord_less_eq_set_nat (@ F2 N)) (@ F2 N2))))))
% 6.73/7.03 (assert (forall ((F2 (-> tptp.nat tptp.rat)) (N tptp.nat) (N2 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_rat (@ F2 N3)) (@ F2 (@ tptp.suc N3)))) (=> (@ (@ tptp.ord_less_eq_nat N) N2) (@ (@ tptp.ord_less_eq_rat (@ F2 N)) (@ F2 N2))))))
% 6.73/7.03 (assert (forall ((F2 (-> tptp.nat tptp.num)) (N tptp.nat) (N2 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_num (@ F2 N3)) (@ F2 (@ tptp.suc N3)))) (=> (@ (@ tptp.ord_less_eq_nat N) N2) (@ (@ tptp.ord_less_eq_num (@ F2 N)) (@ F2 N2))))))
% 6.73/7.03 (assert (forall ((F2 (-> tptp.nat tptp.nat)) (N tptp.nat) (N2 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ F2 N3)) (@ F2 (@ tptp.suc N3)))) (=> (@ (@ tptp.ord_less_eq_nat N) N2) (@ (@ tptp.ord_less_eq_nat (@ F2 N)) (@ F2 N2))))))
% 6.73/7.03 (assert (forall ((F2 (-> tptp.nat tptp.int)) (N tptp.nat) (N2 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ F2 N3)) (@ F2 (@ tptp.suc N3)))) (=> (@ (@ tptp.ord_less_eq_nat N) N2) (@ (@ tptp.ord_less_eq_int (@ F2 N)) (@ F2 N2))))))
% 6.73/7.03 (assert (forall ((F2 (-> tptp.nat tptp.set_nat)) (N tptp.nat) (N2 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_set_nat (@ F2 (@ tptp.suc N3))) (@ F2 N3))) (=> (@ (@ tptp.ord_less_eq_nat N) N2) (@ (@ tptp.ord_less_eq_set_nat (@ F2 N2)) (@ F2 N))))))
% 6.73/7.03 (assert (forall ((F2 (-> tptp.nat tptp.rat)) (N tptp.nat) (N2 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_rat (@ F2 (@ tptp.suc N3))) (@ F2 N3))) (=> (@ (@ tptp.ord_less_eq_nat N) N2) (@ (@ tptp.ord_less_eq_rat (@ F2 N2)) (@ F2 N))))))
% 6.73/7.03 (assert (forall ((F2 (-> tptp.nat tptp.num)) (N tptp.nat) (N2 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_num (@ F2 (@ tptp.suc N3))) (@ F2 N3))) (=> (@ (@ tptp.ord_less_eq_nat N) N2) (@ (@ tptp.ord_less_eq_num (@ F2 N2)) (@ F2 N))))))
% 6.73/7.03 (assert (forall ((F2 (-> tptp.nat tptp.nat)) (N tptp.nat) (N2 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ F2 (@ tptp.suc N3))) (@ F2 N3))) (=> (@ (@ tptp.ord_less_eq_nat N) N2) (@ (@ tptp.ord_less_eq_nat (@ F2 N2)) (@ F2 N))))))
% 6.73/7.03 (assert (forall ((F2 (-> tptp.nat tptp.int)) (N tptp.nat) (N2 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ F2 (@ tptp.suc N3))) (@ F2 N3))) (=> (@ (@ tptp.ord_less_eq_nat N) N2) (@ (@ tptp.ord_less_eq_int (@ F2 N2)) (@ F2 N))))))
% 6.73/7.03 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat N) N)))
% 6.73/7.03 (assert (forall ((I2 tptp.nat) (J2 tptp.nat) (K2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat I2))) (=> (@ _let_1 J2) (=> (@ (@ tptp.ord_less_eq_nat J2) K2) (@ _let_1 K2))))))
% 6.73/7.03 (assert (= tptp.deg (@ tptp.suc tptp.zero_zero_nat)))
% 6.73/7.03 (assert (forall ((Nat tptp.nat) (Nat2 tptp.nat)) (= (= (@ tptp.suc Nat) (@ tptp.suc Nat2)) (= Nat Nat2))))
% 6.73/7.03 (assert (forall ((X2 tptp.nat) (Y2 tptp.nat)) (= (= (@ tptp.suc X2) (@ tptp.suc Y2)) (= X2 Y2))))
% 6.73/7.03 (assert (forall ((X tptp.product_prod_nat_nat) (Y tptp.product_prod_nat_nat)) (= (= (@ tptp.nat_prod_encode X) (@ tptp.nat_prod_encode Y)) (= X Y))))
% 6.73/7.03 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) (@ tptp.suc M2)) (@ (@ tptp.ord_less_eq_nat N) M2))))
% 6.73/7.03 (assert (forall ((N tptp.nat)) (not (= N (@ tptp.suc N)))))
% 6.73/7.03 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (= (@ tptp.suc X) (@ tptp.suc Y)) (= X Y))))
% 6.73/7.03 (assert (forall ((M2 tptp.nat) (N tptp.nat) (R2 (-> tptp.nat tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (=> (forall ((X3 tptp.nat)) (@ (@ R2 X3) X3)) (=> (forall ((X3 tptp.nat) (Y3 tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ R2 X3))) (=> (@ _let_1 Y3) (=> (@ (@ R2 Y3) Z) (@ _let_1 Z))))) (=> (forall ((N3 tptp.nat)) (@ (@ R2 N3) (@ tptp.suc N3))) (@ (@ R2 M2) N)))))))
% 6.73/7.03 (assert (forall ((M2 tptp.nat) (N tptp.nat) (P2 (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (=> (@ P2 M2) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N3) (=> (@ P2 N3) (@ P2 (@ tptp.suc N3))))) (@ P2 N))))))
% 6.73/7.03 (assert (forall ((A tptp.int) (P2 (-> tptp.int Bool))) (= (@ (@ tptp.member_int A) (@ tptp.collect_int P2)) (@ P2 A))))
% 6.73/7.03 (assert (forall ((A tptp.complex) (P2 (-> tptp.complex Bool))) (= (@ (@ tptp.member_complex A) (@ tptp.collect_complex P2)) (@ P2 A))))
% 6.73/7.03 (assert (forall ((A tptp.real) (P2 (-> tptp.real Bool))) (= (@ (@ tptp.member_real A) (@ tptp.collect_real P2)) (@ P2 A))))
% 6.73/7.03 (assert (forall ((A tptp.list_nat) (P2 (-> tptp.list_nat Bool))) (= (@ (@ tptp.member_list_nat A) (@ tptp.collect_list_nat P2)) (@ P2 A))))
% 6.73/7.03 (assert (forall ((A tptp.set_nat) (P2 (-> tptp.set_nat Bool))) (= (@ (@ tptp.member_set_nat A) (@ tptp.collect_set_nat P2)) (@ P2 A))))
% 6.73/7.03 (assert (forall ((A tptp.nat) (P2 (-> tptp.nat Bool))) (= (@ (@ tptp.member_nat A) (@ tptp.collect_nat P2)) (@ P2 A))))
% 6.73/7.03 (assert (forall ((A4 tptp.set_int)) (= (@ tptp.collect_int (lambda ((X4 tptp.int)) (@ (@ tptp.member_int X4) A4))) A4)))
% 6.73/7.03 (assert (forall ((A4 tptp.set_complex)) (= (@ tptp.collect_complex (lambda ((X4 tptp.complex)) (@ (@ tptp.member_complex X4) A4))) A4)))
% 6.73/7.03 (assert (forall ((A4 tptp.set_real)) (= (@ tptp.collect_real (lambda ((X4 tptp.real)) (@ (@ tptp.member_real X4) A4))) A4)))
% 6.73/7.03 (assert (forall ((A4 tptp.set_list_nat)) (= (@ tptp.collect_list_nat (lambda ((X4 tptp.list_nat)) (@ (@ tptp.member_list_nat X4) A4))) A4)))
% 6.73/7.03 (assert (forall ((A4 tptp.set_set_nat)) (= (@ tptp.collect_set_nat (lambda ((X4 tptp.set_nat)) (@ (@ tptp.member_set_nat X4) A4))) A4)))
% 6.73/7.03 (assert (forall ((A4 tptp.set_nat)) (= (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (@ (@ tptp.member_nat X4) A4))) A4)))
% 6.73/7.03 (assert (forall ((P2 (-> tptp.complex Bool)) (Q (-> tptp.complex Bool))) (=> (forall ((X3 tptp.complex)) (= (@ P2 X3) (@ Q X3))) (= (@ tptp.collect_complex P2) (@ tptp.collect_complex Q)))))
% 6.73/7.03 (assert (forall ((P2 (-> tptp.real Bool)) (Q (-> tptp.real Bool))) (=> (forall ((X3 tptp.real)) (= (@ P2 X3) (@ Q X3))) (= (@ tptp.collect_real P2) (@ tptp.collect_real Q)))))
% 6.73/7.03 (assert (forall ((P2 (-> tptp.list_nat Bool)) (Q (-> tptp.list_nat Bool))) (=> (forall ((X3 tptp.list_nat)) (= (@ P2 X3) (@ Q X3))) (= (@ tptp.collect_list_nat P2) (@ tptp.collect_list_nat Q)))))
% 6.73/7.03 (assert (forall ((P2 (-> tptp.set_nat Bool)) (Q (-> tptp.set_nat Bool))) (=> (forall ((X3 tptp.set_nat)) (= (@ P2 X3) (@ Q X3))) (= (@ tptp.collect_set_nat P2) (@ tptp.collect_set_nat Q)))))
% 6.73/7.03 (assert (forall ((P2 (-> tptp.nat Bool)) (Q (-> tptp.nat Bool))) (=> (forall ((X3 tptp.nat)) (= (@ P2 X3) (@ Q X3))) (= (@ tptp.collect_nat P2) (@ tptp.collect_nat Q)))))
% 6.73/7.03 (assert (forall ((P2 (-> tptp.nat Bool)) (N tptp.nat)) (=> (forall ((N3 tptp.nat)) (=> (forall ((M3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M3)) N3) (@ P2 M3))) (@ P2 N3))) (@ P2 N))))
% 6.73/7.03 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (not (@ (@ tptp.ord_less_eq_nat M2) N)) (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) M2))))
% 6.73/7.03 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) N))))
% 6.73/7.03 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.ord_less_eq_nat M2))) (= (@ _let_2 _let_1) (or (@ _let_2 N) (= M2 _let_1)))))))
% 6.73/7.03 (assert (forall ((N tptp.nat) (M4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) M4) (exists ((M tptp.nat)) (= M4 (@ tptp.suc M))))))
% 6.73/7.03 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat M2))) (=> (@ _let_1 N) (@ _let_1 (@ tptp.suc N))))))
% 6.73/7.03 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.ord_less_eq_nat M2))) (=> (@ _let_2 _let_1) (=> (not (@ _let_2 N)) (= M2 _let_1)))))))
% 6.73/7.03 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M2)) N) (@ (@ tptp.ord_less_eq_nat M2) N))))
% 6.73/7.03 (assert (forall ((Y tptp.set_nat) (X tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat Y) X) (= (@ (@ tptp.ord_less_eq_set_nat X) Y) (= X Y)))))
% 6.73/7.03 (assert (forall ((Y tptp.rat) (X tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat Y) X) (= (@ (@ tptp.ord_less_eq_rat X) Y) (= X Y)))))
% 6.73/7.03 (assert (forall ((Y tptp.num) (X tptp.num)) (=> (@ (@ tptp.ord_less_eq_num Y) X) (= (@ (@ tptp.ord_less_eq_num X) Y) (= X Y)))))
% 6.73/7.03 (assert (forall ((Y tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Y) X) (= (@ (@ tptp.ord_less_eq_nat X) Y) (= X Y)))))
% 6.73/7.03 (assert (forall ((Y tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Y) X) (= (@ (@ tptp.ord_less_eq_int X) Y) (= X Y)))))
% 6.73/7.03 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (not (@ (@ tptp.ord_less_eq_rat X) Y)) (@ (@ tptp.ord_less_eq_rat Y) X))))
% 6.73/7.03 (assert (forall ((X tptp.num) (Y tptp.num)) (=> (not (@ (@ tptp.ord_less_eq_num X) Y)) (@ (@ tptp.ord_less_eq_num Y) X))))
% 6.73/7.03 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (not (@ (@ tptp.ord_less_eq_nat X) Y)) (@ (@ tptp.ord_less_eq_nat Y) X))))
% 6.73/7.03 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (not (@ (@ tptp.ord_less_eq_int X) Y)) (@ (@ tptp.ord_less_eq_int Y) X))))
% 6.73/7.03 (assert (forall ((A tptp.rat) (B tptp.rat) (F2 (-> tptp.rat tptp.rat)) (C2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (= (@ F2 B) C2) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y3) (@ (@ tptp.ord_less_eq_rat (@ F2 X3)) (@ F2 Y3)))) (@ (@ tptp.ord_less_eq_rat (@ F2 A)) C2))))))
% 6.73/7.03 (assert (forall ((A tptp.rat) (B tptp.rat) (F2 (-> tptp.rat tptp.num)) (C2 tptp.num)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (= (@ F2 B) C2) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y3) (@ (@ tptp.ord_less_eq_num (@ F2 X3)) (@ F2 Y3)))) (@ (@ tptp.ord_less_eq_num (@ F2 A)) C2))))))
% 6.73/7.03 (assert (forall ((A tptp.rat) (B tptp.rat) (F2 (-> tptp.rat tptp.nat)) (C2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (= (@ F2 B) C2) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y3) (@ (@ tptp.ord_less_eq_nat (@ F2 X3)) (@ F2 Y3)))) (@ (@ tptp.ord_less_eq_nat (@ F2 A)) C2))))))
% 6.73/7.03 (assert (forall ((A tptp.rat) (B tptp.rat) (F2 (-> tptp.rat tptp.int)) (C2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (= (@ F2 B) C2) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y3) (@ (@ tptp.ord_less_eq_int (@ F2 X3)) (@ F2 Y3)))) (@ (@ tptp.ord_less_eq_int (@ F2 A)) C2))))))
% 6.73/7.03 (assert (forall ((A tptp.num) (B tptp.num) (F2 (-> tptp.num tptp.rat)) (C2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (= (@ F2 B) C2) (=> (forall ((X3 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y3) (@ (@ tptp.ord_less_eq_rat (@ F2 X3)) (@ F2 Y3)))) (@ (@ tptp.ord_less_eq_rat (@ F2 A)) C2))))))
% 6.73/7.03 (assert (forall ((A tptp.num) (B tptp.num) (F2 (-> tptp.num tptp.num)) (C2 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (= (@ F2 B) C2) (=> (forall ((X3 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y3) (@ (@ tptp.ord_less_eq_num (@ F2 X3)) (@ F2 Y3)))) (@ (@ tptp.ord_less_eq_num (@ F2 A)) C2))))))
% 6.73/7.03 (assert (forall ((A tptp.num) (B tptp.num) (F2 (-> tptp.num tptp.nat)) (C2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (= (@ F2 B) C2) (=> (forall ((X3 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y3) (@ (@ tptp.ord_less_eq_nat (@ F2 X3)) (@ F2 Y3)))) (@ (@ tptp.ord_less_eq_nat (@ F2 A)) C2))))))
% 6.73/7.03 (assert (forall ((A tptp.num) (B tptp.num) (F2 (-> tptp.num tptp.int)) (C2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (= (@ F2 B) C2) (=> (forall ((X3 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y3) (@ (@ tptp.ord_less_eq_int (@ F2 X3)) (@ F2 Y3)))) (@ (@ tptp.ord_less_eq_int (@ F2 A)) C2))))))
% 6.73/7.03 (assert (forall ((A tptp.nat) (B tptp.nat) (F2 (-> tptp.nat tptp.rat)) (C2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (= (@ F2 B) C2) (=> (forall ((X3 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) Y3) (@ (@ tptp.ord_less_eq_rat (@ F2 X3)) (@ F2 Y3)))) (@ (@ tptp.ord_less_eq_rat (@ F2 A)) C2))))))
% 6.73/7.03 (assert (forall ((A tptp.nat) (B tptp.nat) (F2 (-> tptp.nat tptp.num)) (C2 tptp.num)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (= (@ F2 B) C2) (=> (forall ((X3 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) Y3) (@ (@ tptp.ord_less_eq_num (@ F2 X3)) (@ F2 Y3)))) (@ (@ tptp.ord_less_eq_num (@ F2 A)) C2))))))
% 6.73/7.03 (assert (forall ((A tptp.rat) (F2 (-> tptp.rat tptp.rat)) (B tptp.rat) (C2 tptp.rat)) (=> (= A (@ F2 B)) (=> (@ (@ tptp.ord_less_eq_rat B) C2) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y3) (@ (@ tptp.ord_less_eq_rat (@ F2 X3)) (@ F2 Y3)))) (@ (@ tptp.ord_less_eq_rat A) (@ F2 C2)))))))
% 6.73/7.03 (assert (forall ((A tptp.num) (F2 (-> tptp.rat tptp.num)) (B tptp.rat) (C2 tptp.rat)) (=> (= A (@ F2 B)) (=> (@ (@ tptp.ord_less_eq_rat B) C2) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y3) (@ (@ tptp.ord_less_eq_num (@ F2 X3)) (@ F2 Y3)))) (@ (@ tptp.ord_less_eq_num A) (@ F2 C2)))))))
% 6.73/7.03 (assert (forall ((A tptp.nat) (F2 (-> tptp.rat tptp.nat)) (B tptp.rat) (C2 tptp.rat)) (=> (= A (@ F2 B)) (=> (@ (@ tptp.ord_less_eq_rat B) C2) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y3) (@ (@ tptp.ord_less_eq_nat (@ F2 X3)) (@ F2 Y3)))) (@ (@ tptp.ord_less_eq_nat A) (@ F2 C2)))))))
% 6.73/7.03 (assert (forall ((A tptp.int) (F2 (-> tptp.rat tptp.int)) (B tptp.rat) (C2 tptp.rat)) (=> (= A (@ F2 B)) (=> (@ (@ tptp.ord_less_eq_rat B) C2) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y3) (@ (@ tptp.ord_less_eq_int (@ F2 X3)) (@ F2 Y3)))) (@ (@ tptp.ord_less_eq_int A) (@ F2 C2)))))))
% 6.73/7.03 (assert (forall ((A tptp.rat) (F2 (-> tptp.num tptp.rat)) (B tptp.num) (C2 tptp.num)) (=> (= A (@ F2 B)) (=> (@ (@ tptp.ord_less_eq_num B) C2) (=> (forall ((X3 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y3) (@ (@ tptp.ord_less_eq_rat (@ F2 X3)) (@ F2 Y3)))) (@ (@ tptp.ord_less_eq_rat A) (@ F2 C2)))))))
% 6.73/7.03 (assert (forall ((A tptp.num) (F2 (-> tptp.num tptp.num)) (B tptp.num) (C2 tptp.num)) (=> (= A (@ F2 B)) (=> (@ (@ tptp.ord_less_eq_num B) C2) (=> (forall ((X3 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y3) (@ (@ tptp.ord_less_eq_num (@ F2 X3)) (@ F2 Y3)))) (@ (@ tptp.ord_less_eq_num A) (@ F2 C2)))))))
% 6.73/7.03 (assert (forall ((A tptp.nat) (F2 (-> tptp.num tptp.nat)) (B tptp.num) (C2 tptp.num)) (=> (= A (@ F2 B)) (=> (@ (@ tptp.ord_less_eq_num B) C2) (=> (forall ((X3 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y3) (@ (@ tptp.ord_less_eq_nat (@ F2 X3)) (@ F2 Y3)))) (@ (@ tptp.ord_less_eq_nat A) (@ F2 C2)))))))
% 6.73/7.03 (assert (forall ((A tptp.int) (F2 (-> tptp.num tptp.int)) (B tptp.num) (C2 tptp.num)) (=> (= A (@ F2 B)) (=> (@ (@ tptp.ord_less_eq_num B) C2) (=> (forall ((X3 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y3) (@ (@ tptp.ord_less_eq_int (@ F2 X3)) (@ F2 Y3)))) (@ (@ tptp.ord_less_eq_int A) (@ F2 C2)))))))
% 6.73/7.03 (assert (forall ((A tptp.rat) (F2 (-> tptp.nat tptp.rat)) (B tptp.nat) (C2 tptp.nat)) (=> (= A (@ F2 B)) (=> (@ (@ tptp.ord_less_eq_nat B) C2) (=> (forall ((X3 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) Y3) (@ (@ tptp.ord_less_eq_rat (@ F2 X3)) (@ F2 Y3)))) (@ (@ tptp.ord_less_eq_rat A) (@ F2 C2)))))))
% 6.73/7.03 (assert (forall ((A tptp.num) (F2 (-> tptp.nat tptp.num)) (B tptp.nat) (C2 tptp.nat)) (=> (= A (@ F2 B)) (=> (@ (@ tptp.ord_less_eq_nat B) C2) (=> (forall ((X3 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) Y3) (@ (@ tptp.ord_less_eq_num (@ F2 X3)) (@ F2 Y3)))) (@ (@ tptp.ord_less_eq_num A) (@ F2 C2)))))))
% 6.73/7.03 (assert (forall ((X tptp.rat) (Y tptp.rat)) (or (@ (@ tptp.ord_less_eq_rat X) Y) (@ (@ tptp.ord_less_eq_rat Y) X))))
% 6.73/7.03 (assert (forall ((X tptp.num) (Y tptp.num)) (or (@ (@ tptp.ord_less_eq_num X) Y) (@ (@ tptp.ord_less_eq_num Y) X))))
% 6.73/7.03 (assert (forall ((X tptp.nat) (Y tptp.nat)) (or (@ (@ tptp.ord_less_eq_nat X) Y) (@ (@ tptp.ord_less_eq_nat Y) X))))
% 6.73/7.03 (assert (forall ((X tptp.int) (Y tptp.int)) (or (@ (@ tptp.ord_less_eq_int X) Y) (@ (@ tptp.ord_less_eq_int Y) X))))
% 6.73/7.03 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat)) (=> (= X Y) (@ (@ tptp.ord_less_eq_set_nat X) Y))))
% 6.73/7.03 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (= X Y) (@ (@ tptp.ord_less_eq_rat X) Y))))
% 6.73/7.03 (assert (forall ((X tptp.num) (Y tptp.num)) (=> (= X Y) (@ (@ tptp.ord_less_eq_num X) Y))))
% 6.73/7.03 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (= X Y) (@ (@ tptp.ord_less_eq_nat X) Y))))
% 6.73/7.03 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (= X Y) (@ (@ tptp.ord_less_eq_int X) Y))))
% 6.73/7.03 (assert (forall ((A tptp.rat) (B tptp.rat) (F2 (-> tptp.rat tptp.rat)) (C2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat (@ F2 B)) C2) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y3) (@ (@ tptp.ord_less_eq_rat (@ F2 X3)) (@ F2 Y3)))) (@ (@ tptp.ord_less_eq_rat (@ F2 A)) C2))))))
% 6.73/7.03 (assert (forall ((A tptp.rat) (B tptp.rat) (F2 (-> tptp.rat tptp.num)) (C2 tptp.num)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_num (@ F2 B)) C2) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y3) (@ (@ tptp.ord_less_eq_num (@ F2 X3)) (@ F2 Y3)))) (@ (@ tptp.ord_less_eq_num (@ F2 A)) C2))))))
% 6.73/7.03 (assert (forall ((A tptp.rat) (B tptp.rat) (F2 (-> tptp.rat tptp.nat)) (C2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_nat (@ F2 B)) C2) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y3) (@ (@ tptp.ord_less_eq_nat (@ F2 X3)) (@ F2 Y3)))) (@ (@ tptp.ord_less_eq_nat (@ F2 A)) C2))))))
% 6.73/7.03 (assert (forall ((A tptp.rat) (B tptp.rat) (F2 (-> tptp.rat tptp.int)) (C2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_int (@ F2 B)) C2) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y3) (@ (@ tptp.ord_less_eq_int (@ F2 X3)) (@ F2 Y3)))) (@ (@ tptp.ord_less_eq_int (@ F2 A)) C2))))))
% 6.73/7.03 (assert (forall ((A tptp.num) (B tptp.num) (F2 (-> tptp.num tptp.rat)) (C2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (@ (@ tptp.ord_less_eq_rat (@ F2 B)) C2) (=> (forall ((X3 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y3) (@ (@ tptp.ord_less_eq_rat (@ F2 X3)) (@ F2 Y3)))) (@ (@ tptp.ord_less_eq_rat (@ F2 A)) C2))))))
% 6.73/7.03 (assert (forall ((A tptp.num) (B tptp.num) (F2 (-> tptp.num tptp.num)) (C2 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (@ (@ tptp.ord_less_eq_num (@ F2 B)) C2) (=> (forall ((X3 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y3) (@ (@ tptp.ord_less_eq_num (@ F2 X3)) (@ F2 Y3)))) (@ (@ tptp.ord_less_eq_num (@ F2 A)) C2))))))
% 6.73/7.03 (assert (forall ((A tptp.num) (B tptp.num) (F2 (-> tptp.num tptp.nat)) (C2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (@ (@ tptp.ord_less_eq_nat (@ F2 B)) C2) (=> (forall ((X3 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y3) (@ (@ tptp.ord_less_eq_nat (@ F2 X3)) (@ F2 Y3)))) (@ (@ tptp.ord_less_eq_nat (@ F2 A)) C2))))))
% 6.73/7.03 (assert (forall ((A tptp.num) (B tptp.num) (F2 (-> tptp.num tptp.int)) (C2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (@ (@ tptp.ord_less_eq_int (@ F2 B)) C2) (=> (forall ((X3 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y3) (@ (@ tptp.ord_less_eq_int (@ F2 X3)) (@ F2 Y3)))) (@ (@ tptp.ord_less_eq_int (@ F2 A)) C2))))))
% 6.73/7.03 (assert (forall ((A tptp.nat) (B tptp.nat) (F2 (-> tptp.nat tptp.rat)) (C2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_rat (@ F2 B)) C2) (=> (forall ((X3 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) Y3) (@ (@ tptp.ord_less_eq_rat (@ F2 X3)) (@ F2 Y3)))) (@ (@ tptp.ord_less_eq_rat (@ F2 A)) C2))))))
% 6.73/7.03 (assert (forall ((A tptp.nat) (B tptp.nat) (F2 (-> tptp.nat tptp.num)) (C2 tptp.num)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_num (@ F2 B)) C2) (=> (forall ((X3 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) Y3) (@ (@ tptp.ord_less_eq_num (@ F2 X3)) (@ F2 Y3)))) (@ (@ tptp.ord_less_eq_num (@ F2 A)) C2))))))
% 6.73/7.03 (assert (forall ((A tptp.rat) (F2 (-> tptp.rat tptp.rat)) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat A))) (=> (@ _let_1 (@ F2 B)) (=> (@ (@ tptp.ord_less_eq_rat B) C2) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y3) (@ (@ tptp.ord_less_eq_rat (@ F2 X3)) (@ F2 Y3)))) (@ _let_1 (@ F2 C2))))))))
% 6.73/7.03 (assert (forall ((A tptp.rat) (F2 (-> tptp.num tptp.rat)) (B tptp.num) (C2 tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_rat A))) (=> (@ _let_1 (@ F2 B)) (=> (@ (@ tptp.ord_less_eq_num B) C2) (=> (forall ((X3 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y3) (@ (@ tptp.ord_less_eq_rat (@ F2 X3)) (@ F2 Y3)))) (@ _let_1 (@ F2 C2))))))))
% 6.73/7.03 (assert (forall ((A tptp.rat) (F2 (-> tptp.nat tptp.rat)) (B tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_rat A))) (=> (@ _let_1 (@ F2 B)) (=> (@ (@ tptp.ord_less_eq_nat B) C2) (=> (forall ((X3 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) Y3) (@ (@ tptp.ord_less_eq_rat (@ F2 X3)) (@ F2 Y3)))) (@ _let_1 (@ F2 C2))))))))
% 6.73/7.03 (assert (forall ((A tptp.rat) (F2 (-> tptp.int tptp.rat)) (B tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_rat A))) (=> (@ _let_1 (@ F2 B)) (=> (@ (@ tptp.ord_less_eq_int B) C2) (=> (forall ((X3 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X3) Y3) (@ (@ tptp.ord_less_eq_rat (@ F2 X3)) (@ F2 Y3)))) (@ _let_1 (@ F2 C2))))))))
% 6.73/7.03 (assert (forall ((A tptp.num) (F2 (-> tptp.rat tptp.num)) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_num A))) (=> (@ _let_1 (@ F2 B)) (=> (@ (@ tptp.ord_less_eq_rat B) C2) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y3) (@ (@ tptp.ord_less_eq_num (@ F2 X3)) (@ F2 Y3)))) (@ _let_1 (@ F2 C2))))))))
% 6.73/7.03 (assert (forall ((A tptp.num) (F2 (-> tptp.num tptp.num)) (B tptp.num) (C2 tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_num A))) (=> (@ _let_1 (@ F2 B)) (=> (@ (@ tptp.ord_less_eq_num B) C2) (=> (forall ((X3 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y3) (@ (@ tptp.ord_less_eq_num (@ F2 X3)) (@ F2 Y3)))) (@ _let_1 (@ F2 C2))))))))
% 6.73/7.03 (assert (forall ((A tptp.num) (F2 (-> tptp.nat tptp.num)) (B tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_num A))) (=> (@ _let_1 (@ F2 B)) (=> (@ (@ tptp.ord_less_eq_nat B) C2) (=> (forall ((X3 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) Y3) (@ (@ tptp.ord_less_eq_num (@ F2 X3)) (@ F2 Y3)))) (@ _let_1 (@ F2 C2))))))))
% 6.73/7.03 (assert (forall ((A tptp.num) (F2 (-> tptp.int tptp.num)) (B tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_num A))) (=> (@ _let_1 (@ F2 B)) (=> (@ (@ tptp.ord_less_eq_int B) C2) (=> (forall ((X3 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X3) Y3) (@ (@ tptp.ord_less_eq_num (@ F2 X3)) (@ F2 Y3)))) (@ _let_1 (@ F2 C2))))))))
% 6.73/7.03 (assert (forall ((A tptp.nat) (F2 (-> tptp.rat tptp.nat)) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_nat A))) (=> (@ _let_1 (@ F2 B)) (=> (@ (@ tptp.ord_less_eq_rat B) C2) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y3) (@ (@ tptp.ord_less_eq_nat (@ F2 X3)) (@ F2 Y3)))) (@ _let_1 (@ F2 C2))))))))
% 6.73/7.03 (assert (forall ((A tptp.nat) (F2 (-> tptp.num tptp.nat)) (B tptp.num) (C2 tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_nat A))) (=> (@ _let_1 (@ F2 B)) (=> (@ (@ tptp.ord_less_eq_num B) C2) (=> (forall ((X3 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y3) (@ (@ tptp.ord_less_eq_nat (@ F2 X3)) (@ F2 Y3)))) (@ _let_1 (@ F2 C2))))))))
% 6.73/7.03 (assert (= (lambda ((Y5 tptp.set_nat) (Z2 tptp.set_nat)) (= Y5 Z2)) (lambda ((A5 tptp.set_nat) (B4 tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat A5) B4) (@ (@ tptp.ord_less_eq_set_nat B4) A5)))))
% 6.73/7.03 (assert (= (lambda ((Y5 tptp.rat) (Z2 tptp.rat)) (= Y5 Z2)) (lambda ((A5 tptp.rat) (B4 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat A5) B4) (@ (@ tptp.ord_less_eq_rat B4) A5)))))
% 6.73/7.03 (assert (= (lambda ((Y5 tptp.num) (Z2 tptp.num)) (= Y5 Z2)) (lambda ((A5 tptp.num) (B4 tptp.num)) (and (@ (@ tptp.ord_less_eq_num A5) B4) (@ (@ tptp.ord_less_eq_num B4) A5)))))
% 6.73/7.04 (assert (= (lambda ((Y5 tptp.nat) (Z2 tptp.nat)) (= Y5 Z2)) (lambda ((A5 tptp.nat) (B4 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat A5) B4) (@ (@ tptp.ord_less_eq_nat B4) A5)))))
% 6.73/7.04 (assert (= (lambda ((Y5 tptp.int) (Z2 tptp.int)) (= Y5 Z2)) (lambda ((A5 tptp.int) (B4 tptp.int)) (and (@ (@ tptp.ord_less_eq_int A5) B4) (@ (@ tptp.ord_less_eq_int B4) A5)))))
% 6.73/7.04 (assert (forall ((A tptp.set_nat) (B tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A) B) (=> (@ (@ tptp.ord_less_eq_set_nat B) A) (= A B)))))
% 6.73/7.04 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat B) A) (= A B)))))
% 6.73/7.04 (assert (forall ((A tptp.num) (B tptp.num)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (@ (@ tptp.ord_less_eq_num B) A) (= A B)))))
% 6.73/7.04 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat B) A) (= A B)))))
% 6.73/7.04 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_eq_int B) A) (= A B)))))
% 6.73/7.04 (assert (forall ((B tptp.set_nat) (A tptp.set_nat) (C2 tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat C2))) (=> (@ (@ tptp.ord_less_eq_set_nat B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 6.73/7.04 (assert (forall ((B tptp.rat) (A tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat C2))) (=> (@ (@ tptp.ord_less_eq_rat B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 6.73/7.04 (assert (forall ((B tptp.num) (A tptp.num) (C2 tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_num C2))) (=> (@ (@ tptp.ord_less_eq_num B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 6.73/7.04 (assert (forall ((B tptp.nat) (A tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat C2))) (=> (@ (@ tptp.ord_less_eq_nat B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 6.73/7.04 (assert (forall ((B tptp.int) (A tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int C2))) (=> (@ (@ tptp.ord_less_eq_int B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 6.73/7.04 (assert (forall ((B tptp.set_nat) (A tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat B) A) (=> (@ (@ tptp.ord_less_eq_set_nat A) B) (= A B)))))
% 6.73/7.04 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat B) A) (=> (@ (@ tptp.ord_less_eq_rat A) B) (= A B)))))
% 6.73/7.04 (assert (forall ((B tptp.num) (A tptp.num)) (=> (@ (@ tptp.ord_less_eq_num B) A) (=> (@ (@ tptp.ord_less_eq_num A) B) (= A B)))))
% 6.73/7.04 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B) A) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= A B)))))
% 6.73/7.04 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B) A) (=> (@ (@ tptp.ord_less_eq_int A) B) (= A B)))))
% 6.73/7.04 (assert (= (lambda ((Y5 tptp.set_nat) (Z2 tptp.set_nat)) (= Y5 Z2)) (lambda ((A5 tptp.set_nat) (B4 tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat B4) A5) (@ (@ tptp.ord_less_eq_set_nat A5) B4)))))
% 6.73/7.04 (assert (= (lambda ((Y5 tptp.rat) (Z2 tptp.rat)) (= Y5 Z2)) (lambda ((A5 tptp.rat) (B4 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat B4) A5) (@ (@ tptp.ord_less_eq_rat A5) B4)))))
% 6.73/7.04 (assert (= (lambda ((Y5 tptp.num) (Z2 tptp.num)) (= Y5 Z2)) (lambda ((A5 tptp.num) (B4 tptp.num)) (and (@ (@ tptp.ord_less_eq_num B4) A5) (@ (@ tptp.ord_less_eq_num A5) B4)))))
% 6.73/7.04 (assert (= (lambda ((Y5 tptp.nat) (Z2 tptp.nat)) (= Y5 Z2)) (lambda ((A5 tptp.nat) (B4 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat B4) A5) (@ (@ tptp.ord_less_eq_nat A5) B4)))))
% 6.73/7.04 (assert (= (lambda ((Y5 tptp.int) (Z2 tptp.int)) (= Y5 Z2)) (lambda ((A5 tptp.int) (B4 tptp.int)) (and (@ (@ tptp.ord_less_eq_int B4) A5) (@ (@ tptp.ord_less_eq_int A5) B4)))))
% 6.73/7.04 (assert (forall ((P2 (-> tptp.rat tptp.rat Bool)) (A tptp.rat) (B tptp.rat)) (=> (forall ((A3 tptp.rat) (B3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A3) B3) (@ (@ P2 A3) B3))) (=> (forall ((A3 tptp.rat) (B3 tptp.rat)) (=> (@ (@ P2 B3) A3) (@ (@ P2 A3) B3))) (@ (@ P2 A) B)))))
% 6.73/7.04 (assert (forall ((P2 (-> tptp.num tptp.num Bool)) (A tptp.num) (B tptp.num)) (=> (forall ((A3 tptp.num) (B3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num A3) B3) (@ (@ P2 A3) B3))) (=> (forall ((A3 tptp.num) (B3 tptp.num)) (=> (@ (@ P2 B3) A3) (@ (@ P2 A3) B3))) (@ (@ P2 A) B)))))
% 6.73/7.04 (assert (forall ((P2 (-> tptp.nat tptp.nat Bool)) (A tptp.nat) (B tptp.nat)) (=> (forall ((A3 tptp.nat) (B3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A3) B3) (@ (@ P2 A3) B3))) (=> (forall ((A3 tptp.nat) (B3 tptp.nat)) (=> (@ (@ P2 B3) A3) (@ (@ P2 A3) B3))) (@ (@ P2 A) B)))))
% 6.73/7.04 (assert (forall ((P2 (-> tptp.int tptp.int Bool)) (A tptp.int) (B tptp.int)) (=> (forall ((A3 tptp.int) (B3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A3) B3) (@ (@ P2 A3) B3))) (=> (forall ((A3 tptp.int) (B3 tptp.int)) (=> (@ (@ P2 B3) A3) (@ (@ P2 A3) B3))) (@ (@ P2 A) B)))))
% 6.73/7.04 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat) (Z3 tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_set_nat Y) Z3) (@ _let_1 Z3))))))
% 6.73/7.04 (assert (forall ((X tptp.rat) (Y tptp.rat) (Z3 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_rat Y) Z3) (@ _let_1 Z3))))))
% 6.73/7.04 (assert (forall ((X tptp.num) (Y tptp.num) (Z3 tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_num X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_num Y) Z3) (@ _let_1 Z3))))))
% 6.73/7.04 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z3 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_nat Y) Z3) (@ _let_1 Z3))))))
% 6.73/7.04 (assert (forall ((X tptp.int) (Y tptp.int) (Z3 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_int Y) Z3) (@ _let_1 Z3))))))
% 6.73/7.04 (assert (forall ((A tptp.set_nat) (B tptp.set_nat) (C2 tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_set_nat B) C2) (@ _let_1 C2))))))
% 6.73/7.04 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_rat B) C2) (@ _let_1 C2))))))
% 6.73/7.04 (assert (forall ((A tptp.num) (B tptp.num) (C2 tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_num A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_num B) C2) (@ _let_1 C2))))))
% 6.73/7.04 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_nat B) C2) (@ _let_1 C2))))))
% 6.73/7.04 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_int B) C2) (@ _let_1 C2))))))
% 6.73/7.04 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat X) Y) (=> (@ (@ tptp.ord_less_eq_set_nat Y) X) (= X Y)))))
% 6.73/7.04 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X) Y) (=> (@ (@ tptp.ord_less_eq_rat Y) X) (= X Y)))))
% 6.73/7.04 (assert (forall ((X tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X) Y) (=> (@ (@ tptp.ord_less_eq_num Y) X) (= X Y)))))
% 6.73/7.04 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X) Y) (=> (@ (@ tptp.ord_less_eq_nat Y) X) (= X Y)))))
% 6.73/7.04 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X) Y) (=> (@ (@ tptp.ord_less_eq_int Y) X) (= X Y)))))
% 6.73/7.04 (assert (forall ((A tptp.set_nat) (B tptp.set_nat) (C2 tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat A))) (=> (@ _let_1 B) (=> (= B C2) (@ _let_1 C2))))))
% 6.73/7.04 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat A))) (=> (@ _let_1 B) (=> (= B C2) (@ _let_1 C2))))))
% 6.73/7.04 (assert (forall ((A tptp.num) (B tptp.num) (C2 tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_num A))) (=> (@ _let_1 B) (=> (= B C2) (@ _let_1 C2))))))
% 6.73/7.04 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat A))) (=> (@ _let_1 B) (=> (= B C2) (@ _let_1 C2))))))
% 6.73/7.04 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int A))) (=> (@ _let_1 B) (=> (= B C2) (@ _let_1 C2))))))
% 6.73/7.04 (assert (forall ((A tptp.set_nat) (B tptp.set_nat) (C2 tptp.set_nat)) (=> (= A B) (=> (@ (@ tptp.ord_less_eq_set_nat B) C2) (@ (@ tptp.ord_less_eq_set_nat A) C2)))))
% 6.73/7.04 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (=> (= A B) (=> (@ (@ tptp.ord_less_eq_rat B) C2) (@ (@ tptp.ord_less_eq_rat A) C2)))))
% 6.73/7.04 (assert (forall ((A tptp.num) (B tptp.num) (C2 tptp.num)) (=> (= A B) (=> (@ (@ tptp.ord_less_eq_num B) C2) (@ (@ tptp.ord_less_eq_num A) C2)))))
% 6.73/7.04 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (=> (= A B) (=> (@ (@ tptp.ord_less_eq_nat B) C2) (@ (@ tptp.ord_less_eq_nat A) C2)))))
% 6.73/7.04 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (=> (= A B) (=> (@ (@ tptp.ord_less_eq_int B) C2) (@ (@ tptp.ord_less_eq_int A) C2)))))
% 6.73/7.04 (assert (= (lambda ((Y5 tptp.set_nat) (Z2 tptp.set_nat)) (= Y5 Z2)) (lambda ((X4 tptp.set_nat) (Y4 tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat X4) Y4) (@ (@ tptp.ord_less_eq_set_nat Y4) X4)))))
% 6.73/7.04 (assert (= (lambda ((Y5 tptp.rat) (Z2 tptp.rat)) (= Y5 Z2)) (lambda ((X4 tptp.rat) (Y4 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat X4) Y4) (@ (@ tptp.ord_less_eq_rat Y4) X4)))))
% 6.73/7.04 (assert (= (lambda ((Y5 tptp.num) (Z2 tptp.num)) (= Y5 Z2)) (lambda ((X4 tptp.num) (Y4 tptp.num)) (and (@ (@ tptp.ord_less_eq_num X4) Y4) (@ (@ tptp.ord_less_eq_num Y4) X4)))))
% 6.73/7.04 (assert (= (lambda ((Y5 tptp.nat) (Z2 tptp.nat)) (= Y5 Z2)) (lambda ((X4 tptp.nat) (Y4 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat X4) Y4) (@ (@ tptp.ord_less_eq_nat Y4) X4)))))
% 6.73/7.04 (assert (= (lambda ((Y5 tptp.int) (Z2 tptp.int)) (= Y5 Z2)) (lambda ((X4 tptp.int) (Y4 tptp.int)) (and (@ (@ tptp.ord_less_eq_int X4) Y4) (@ (@ tptp.ord_less_eq_int Y4) X4)))))
% 6.73/7.04 (assert (forall ((X tptp.rat) (Y tptp.rat) (Z3 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 Z3))) (let ((_let_4 (@ _let_3 X))) (let ((_let_5 (@ tptp.ord_less_eq_rat Y))) (let ((_let_6 (@ _let_5 Z3))) (let ((_let_7 (@ _let_5 X))) (let ((_let_8 (@ _let_3 Y))) (let ((_let_9 (@ _let_1 Z3))) (=> (=> _let_2 (not _let_6)) (=> (=> _let_7 (not _let_9)) (=> (=> _let_9 (not _let_8)) (=> (=> _let_8 (not _let_7)) (=> (=> _let_6 (not _let_4)) (not (=> _let_4 (not _let_2)))))))))))))))))))
% 6.73/7.04 (assert (forall ((X tptp.num) (Y tptp.num) (Z3 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 Z3))) (let ((_let_4 (@ _let_3 X))) (let ((_let_5 (@ tptp.ord_less_eq_num Y))) (let ((_let_6 (@ _let_5 Z3))) (let ((_let_7 (@ _let_5 X))) (let ((_let_8 (@ _let_3 Y))) (let ((_let_9 (@ _let_1 Z3))) (=> (=> _let_2 (not _let_6)) (=> (=> _let_7 (not _let_9)) (=> (=> _let_9 (not _let_8)) (=> (=> _let_8 (not _let_7)) (=> (=> _let_6 (not _let_4)) (not (=> _let_4 (not _let_2)))))))))))))))))))
% 6.73/7.04 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z3 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat X))) (let ((_let_2 (@ _let_1 Y))) (let ((_let_3 (@ tptp.ord_less_eq_nat Z3))) (let ((_let_4 (@ _let_3 X))) (let ((_let_5 (@ tptp.ord_less_eq_nat Y))) (let ((_let_6 (@ _let_5 Z3))) (let ((_let_7 (@ _let_5 X))) (let ((_let_8 (@ _let_3 Y))) (let ((_let_9 (@ _let_1 Z3))) (=> (=> _let_2 (not _let_6)) (=> (=> _let_7 (not _let_9)) (=> (=> _let_9 (not _let_8)) (=> (=> _let_8 (not _let_7)) (=> (=> _let_6 (not _let_4)) (not (=> _let_4 (not _let_2)))))))))))))))))))
% 6.73/7.04 (assert (forall ((X tptp.int) (Y tptp.int) (Z3 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int X))) (let ((_let_2 (@ _let_1 Y))) (let ((_let_3 (@ tptp.ord_less_eq_int Z3))) (let ((_let_4 (@ _let_3 X))) (let ((_let_5 (@ tptp.ord_less_eq_int Y))) (let ((_let_6 (@ _let_5 Z3))) (let ((_let_7 (@ _let_5 X))) (let ((_let_8 (@ _let_3 Y))) (let ((_let_9 (@ _let_1 Z3))) (=> (=> _let_2 (not _let_6)) (=> (=> _let_7 (not _let_9)) (=> (=> _let_9 (not _let_8)) (=> (=> _let_8 (not _let_7)) (=> (=> _let_6 (not _let_4)) (not (=> _let_4 (not _let_2)))))))))))))))))))
% 6.73/7.04 (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))))))
% 6.73/7.04 (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))))))
% 6.73/7.04 (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))))))
% 6.73/7.04 (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))))))
% 6.73/7.04 (assert (forall ((P2 (-> tptp.nat Bool)) (X tptp.nat) (M5 tptp.nat)) (=> (@ P2 X) (=> (forall ((X3 tptp.nat)) (=> (@ P2 X3) (@ (@ tptp.ord_less_eq_nat X3) M5))) (not (forall ((M tptp.nat)) (=> (@ P2 M) (not (forall ((X5 tptp.nat)) (=> (@ P2 X5) (@ (@ tptp.ord_less_eq_nat X5) M)))))))))))
% 6.73/7.04 (assert (forall ((P2 (-> tptp.nat Bool)) (K2 tptp.nat) (B tptp.nat)) (=> (@ P2 K2) (=> (forall ((Y3 tptp.nat)) (=> (@ P2 Y3) (@ (@ tptp.ord_less_eq_nat Y3) B))) (exists ((X3 tptp.nat)) (and (@ P2 X3) (forall ((Y6 tptp.nat)) (=> (@ P2 Y6) (@ (@ tptp.ord_less_eq_nat Y6) X3)))))))))
% 6.73/7.04 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (or (@ (@ tptp.ord_less_eq_nat M2) N) (@ (@ tptp.ord_less_eq_nat N) M2))))
% 6.73/7.04 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (=> (@ (@ tptp.ord_less_eq_nat N) M2) (= M2 N)))))
% 6.73/7.04 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (= M2 N) (@ (@ tptp.ord_less_eq_nat M2) N))))
% 6.73/7.04 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) N)))
% 6.73/7.04 (assert (forall ((A tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A)))
% 6.73/7.04 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat N) tptp.zero_zero_nat) (= N tptp.zero_zero_nat))))
% 6.73/7.04 (assert (forall ((A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.zero_zero_nat) (= A tptp.zero_zero_nat))))
% 6.73/7.04 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat A) tptp.zero_zero_nat) (= A tptp.zero_zero_nat))))
% 6.73/7.04 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) N)))
% 6.73/7.04 (assert (forall ((N tptp.nat)) (=> (not (= N tptp.zero_zero_nat)) (exists ((M tptp.nat)) (= N (@ tptp.suc M))))))
% 6.73/7.04 (assert (forall ((M2 tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc M2)))))
% 6.73/7.04 (assert (forall ((M2 tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc M2)))))
% 6.73/7.04 (assert (forall ((M2 tptp.nat)) (not (= (@ tptp.suc M2) tptp.zero_zero_nat))))
% 6.73/7.04 (assert (forall ((P2 (-> tptp.nat Bool)) (K2 tptp.nat)) (=> (@ P2 K2) (=> (forall ((N3 tptp.nat)) (=> (@ P2 (@ tptp.suc N3)) (@ P2 N3))) (@ P2 tptp.zero_zero_nat)))))
% 6.73/7.04 (assert (forall ((P2 (-> tptp.nat tptp.nat Bool)) (M2 tptp.nat) (N tptp.nat)) (=> (forall ((X3 tptp.nat)) (@ (@ P2 X3) tptp.zero_zero_nat)) (=> (forall ((Y3 tptp.nat)) (@ (@ P2 tptp.zero_zero_nat) (@ tptp.suc Y3))) (=> (forall ((X3 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ P2 X3) Y3) (@ (@ P2 (@ tptp.suc X3)) (@ tptp.suc Y3)))) (@ (@ P2 M2) N))))))
% 6.73/7.04 (assert (forall ((X tptp.nat)) (=> (not (= X tptp.zero_zero_nat)) (not (forall ((N3 tptp.nat)) (not (= X (@ tptp.suc N3))))))))
% 6.73/7.04 (assert (forall ((X2 tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc X2)))))
% 6.73/7.04 (assert (forall ((Nat2 tptp.nat)) (not (= (@ tptp.suc Nat2) tptp.zero_zero_nat))))
% 6.73/7.04 (assert (forall ((Nat2 tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc Nat2)))))
% 6.73/7.04 (assert (forall ((Nat tptp.nat) (X2 tptp.nat)) (=> (= Nat (@ tptp.suc X2)) (not (= Nat tptp.zero_zero_nat)))))
% 6.73/7.04 (assert (forall ((Y tptp.nat)) (=> (not (= Y tptp.zero_zero_nat)) (not (forall ((Nat3 tptp.nat)) (not (= Y (@ tptp.suc Nat3))))))))
% 6.73/7.04 (assert (forall ((P2 (-> tptp.nat Bool)) (N tptp.nat)) (=> (@ P2 tptp.zero_zero_nat) (=> (forall ((N3 tptp.nat)) (=> (@ P2 N3) (@ P2 (@ tptp.suc N3)))) (@ P2 N)))))
% 6.73/7.04 (assert (@ (@ tptp.vEBT_invar_vebt tptp.sa) tptp.deg))
% 6.73/7.04 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat N) tptp.zero_zero_nat) (= N tptp.zero_zero_nat))))
% 6.73/7.04 (assert (forall ((X2 tptp.product_prod_nat_nat)) (= (@ tptp.size_s170228958280169651at_nat (@ tptp.some_P7363390416028606310at_nat X2)) (@ tptp.suc tptp.zero_zero_nat))))
% 6.73/7.04 (assert (forall ((X2 tptp.nat)) (= (@ tptp.size_size_option_nat (@ tptp.some_nat X2)) (@ tptp.suc tptp.zero_zero_nat))))
% 6.73/7.04 (assert (forall ((X2 tptp.num)) (= (@ tptp.size_size_option_num (@ tptp.some_num X2)) (@ tptp.suc tptp.zero_zero_nat))))
% 6.73/7.04 (assert (forall ((X tptp.nat)) (=> (not (= X tptp.zero_zero_nat)) (=> (not (= X (@ tptp.suc tptp.zero_zero_nat))) (not (forall ((Va tptp.nat)) (not (= X (@ tptp.suc (@ tptp.suc Va))))))))))
% 6.73/7.04 (assert (forall ((P2 (-> tptp.nat Bool))) (=> (not (@ P2 tptp.zero_zero_nat)) (=> (exists ((X_1 tptp.nat)) (@ P2 X_1)) (exists ((N3 tptp.nat)) (and (not (@ P2 N3)) (@ P2 (@ tptp.suc N3))))))))
% 6.73/7.04 (assert (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) tptp.zero_zero_real))
% 6.73/7.04 (assert (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) tptp.zero_zero_rat))
% 6.73/7.04 (assert (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) tptp.zero_zero_nat))
% 6.73/7.04 (assert (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) tptp.zero_zero_int))
% 6.73/7.04 (assert (forall ((X tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) X)))
% 6.73/7.04 (assert (forall ((Q2 tptp.code_integer) (R3 tptp.code_integer)) (= (@ tptp.unique5706413561485394159nteger (@ (@ tptp.produc1086072967326762835nteger Q2) R3)) (= R3 tptp.zero_z3403309356797280102nteger))))
% 6.73/7.04 (assert (forall ((Q2 tptp.nat) (R3 tptp.nat)) (= (@ tptp.unique6322359934112328802ux_nat (@ (@ tptp.product_Pair_nat_nat Q2) R3)) (= R3 tptp.zero_zero_nat))))
% 6.73/7.04 (assert (forall ((Q2 tptp.int) (R3 tptp.int)) (= (@ tptp.unique6319869463603278526ux_int (@ (@ tptp.product_Pair_int_int Q2) R3)) (= R3 tptp.zero_zero_int))))
% 6.73/7.04 (assert (forall ((M2 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 M2) N)) (and (@ _let_1 M2) (@ _let_1 N))))))
% 6.73/7.04 (assert (= tptp.sa (@ (@ tptp.vEBT_Leaf tptp.a) tptp.b)))
% 6.73/7.04 (assert (forall ((T tptp.vEBT_VEBT)) (not (@ (@ tptp.vEBT_invar_vebt T) tptp.zero_zero_nat))))
% 6.73/7.04 (assert (forall ((T tptp.vEBT_VEBT)) (not (@ (@ tptp.vEBT_invar_vebt T) tptp.zero_zero_nat))))
% 6.73/7.04 (assert (forall ((A Bool) (B Bool)) (not (@ (@ tptp.vEBT_invar_vebt (@ (@ tptp.vEBT_Leaf A) B)) tptp.zero_zero_nat))))
% 6.73/7.04 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (= (@ tptp.nat_prod_decode X) (@ tptp.nat_prod_decode Y)) (= X Y))))
% 6.73/7.04 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (@ (@ tptp.vEBT_invar_vebt (@ (@ tptp.vEBT_VEBT_insert T) X)) N))))
% 6.73/7.04 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (= (@ (@ tptp.times_times_nat M2) N) tptp.zero_zero_nat) (or (= M2 tptp.zero_zero_nat) (= N tptp.zero_zero_nat)))))
% 6.73/7.04 (assert (forall ((M2 tptp.nat)) (= (@ (@ tptp.times_times_nat M2) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 6.73/7.04 (assert (forall ((K2 tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K2))) (= (= (@ _let_1 M2) (@ _let_1 N)) (or (= M2 N) (= K2 tptp.zero_zero_nat))))))
% 6.73/7.04 (assert (forall ((M2 tptp.nat) (K2 tptp.nat) (N tptp.nat)) (= (= (@ (@ tptp.times_times_nat M2) K2) (@ (@ tptp.times_times_nat N) K2)) (or (= M2 N) (= K2 tptp.zero_zero_nat)))))
% 6.73/7.04 (assert (forall ((N tptp.nat)) (= (@ tptp.nat_prod_encode (@ tptp.nat_prod_decode N)) N)))
% 6.73/7.04 (assert (forall ((X tptp.product_prod_nat_nat)) (= (@ tptp.nat_prod_decode (@ tptp.nat_prod_encode X)) X)))
% 6.73/7.04 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (= _let_1 (@ (@ tptp.times_times_nat M2) N)) (and (= M2 _let_1) (= N _let_1))))))
% 6.73/7.04 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (= (@ (@ tptp.times_times_nat M2) N) _let_1) (and (= M2 _let_1) (= N _let_1))))))
% 6.73/7.04 (assert (forall ((B tptp.real) (A tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.times_times_real B))) (let ((_let_2 (@ tptp.times_times_real A))) (= (@ _let_1 (@ _let_2 C2)) (@ _let_2 (@ _let_1 C2)))))))
% 6.73/7.04 (assert (forall ((B tptp.rat) (A tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat B))) (let ((_let_2 (@ tptp.times_times_rat A))) (= (@ _let_1 (@ _let_2 C2)) (@ _let_2 (@ _let_1 C2)))))))
% 6.73/7.04 (assert (forall ((B tptp.nat) (A tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat B))) (let ((_let_2 (@ tptp.times_times_nat A))) (= (@ _let_1 (@ _let_2 C2)) (@ _let_2 (@ _let_1 C2)))))))
% 6.73/7.04 (assert (forall ((B tptp.int) (A tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int B))) (let ((_let_2 (@ tptp.times_times_int A))) (= (@ _let_1 (@ _let_2 C2)) (@ _let_2 (@ _let_1 C2)))))))
% 6.73/7.04 (assert (= tptp.times_times_real (lambda ((A5 tptp.real) (B4 tptp.real)) (@ (@ tptp.times_times_real B4) A5))))
% 6.73/7.04 (assert (= tptp.times_times_rat (lambda ((A5 tptp.rat) (B4 tptp.rat)) (@ (@ tptp.times_times_rat B4) A5))))
% 6.73/7.04 (assert (= tptp.times_times_nat (lambda ((A5 tptp.nat) (B4 tptp.nat)) (@ (@ tptp.times_times_nat B4) A5))))
% 6.73/7.04 (assert (= tptp.times_times_int (lambda ((A5 tptp.int) (B4 tptp.int)) (@ (@ tptp.times_times_int B4) A5))))
% 6.73/7.04 (assert (forall ((A tptp.real) (B tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.times_times_real A))) (= (@ (@ tptp.times_times_real (@ _let_1 B)) C2) (@ _let_1 (@ (@ tptp.times_times_real B) C2))))))
% 6.73/7.04 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat A))) (= (@ (@ tptp.times_times_rat (@ _let_1 B)) C2) (@ _let_1 (@ (@ tptp.times_times_rat B) C2))))))
% 6.73/7.04 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (= (@ (@ tptp.times_times_nat (@ _let_1 B)) C2) (@ _let_1 (@ (@ tptp.times_times_nat B) C2))))))
% 6.73/7.04 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (= (@ (@ tptp.times_times_int (@ _let_1 B)) C2) (@ _let_1 (@ (@ tptp.times_times_int B) C2))))))
% 6.73/7.04 (assert (forall ((A tptp.real) (B tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.times_times_real A))) (= (@ (@ tptp.times_times_real (@ _let_1 B)) C2) (@ _let_1 (@ (@ tptp.times_times_real B) C2))))))
% 6.73/7.04 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat A))) (= (@ (@ tptp.times_times_rat (@ _let_1 B)) C2) (@ _let_1 (@ (@ tptp.times_times_rat B) C2))))))
% 6.73/7.04 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (= (@ (@ tptp.times_times_nat (@ _let_1 B)) C2) (@ _let_1 (@ (@ tptp.times_times_nat B) C2))))))
% 6.73/7.04 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (= (@ (@ tptp.times_times_int (@ _let_1 B)) C2) (@ _let_1 (@ (@ tptp.times_times_int B) C2))))))
% 6.73/7.04 (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)))))
% 6.73/7.04 (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)))))
% 6.73/7.04 (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)))))
% 6.73/7.04 (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)))))
% 6.73/7.04 (assert (forall ((X tptp.num) (Y tptp.num)) (=> (not (= (@ tptp.size_size_num X) (@ tptp.size_size_num Y))) (not (= X Y)))))
% 6.73/7.04 (assert (forall ((K2 tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.suc K2)))) (= (= (@ _let_1 M2) (@ _let_1 N)) (= M2 N)))))
% 6.73/7.04 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.zero_zero_nat) N) tptp.zero_zero_nat)))
% 6.73/7.04 (assert (forall ((I2 tptp.nat) (J2 tptp.nat) (K2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K2))) (=> (@ (@ tptp.ord_less_eq_nat I2) J2) (@ (@ tptp.ord_less_eq_nat (@ _let_1 I2)) (@ _let_1 J2))))))
% 6.73/7.04 (assert (forall ((I2 tptp.nat) (J2 tptp.nat) (K2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat I2) K2)) (@ (@ tptp.times_times_nat J2) K2)))))
% 6.73/7.04 (assert (forall ((I2 tptp.nat) (J2 tptp.nat) (K2 tptp.nat) (L tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J2) (=> (@ (@ tptp.ord_less_eq_nat K2) L) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat I2) K2)) (@ (@ tptp.times_times_nat J2) L))))))
% 6.73/7.04 (assert (forall ((M2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat M2) (@ (@ tptp.times_times_nat M2) M2))))
% 6.73/7.04 (assert (forall ((M2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat M2))) (@ (@ tptp.ord_less_eq_nat M2) (@ _let_1 (@ _let_1 M2))))))
% 6.73/7.04 (assert (forall ((K2 tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.suc K2)))) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 M2)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat M2) N)))))
% 6.73/7.04 (assert (forall ((X tptp.complex)) (= (= tptp.zero_zero_complex X) (= X tptp.zero_zero_complex))))
% 6.73/7.04 (assert (forall ((X tptp.real)) (= (= tptp.zero_zero_real X) (= X tptp.zero_zero_real))))
% 6.73/7.04 (assert (forall ((X tptp.rat)) (= (= tptp.zero_zero_rat X) (= X tptp.zero_zero_rat))))
% 6.73/7.04 (assert (forall ((X tptp.nat)) (= (= tptp.zero_zero_nat X) (= X tptp.zero_zero_nat))))
% 6.73/7.04 (assert (forall ((X tptp.int)) (= (= tptp.zero_zero_int X) (= X tptp.zero_zero_int))))
% 6.73/7.04 (assert (forall ((A tptp.complex) (C2 tptp.complex) (B tptp.complex)) (= (= (@ (@ tptp.times_times_complex A) C2) (@ (@ tptp.times_times_complex B) C2)) (or (= C2 tptp.zero_zero_complex) (= A B)))))
% 6.73/7.04 (assert (forall ((A tptp.real) (C2 tptp.real) (B tptp.real)) (= (= (@ (@ tptp.times_times_real A) C2) (@ (@ tptp.times_times_real B) C2)) (or (= C2 tptp.zero_zero_real) (= A B)))))
% 6.73/7.04 (assert (forall ((A tptp.rat) (C2 tptp.rat) (B tptp.rat)) (= (= (@ (@ tptp.times_times_rat A) C2) (@ (@ tptp.times_times_rat B) C2)) (or (= C2 tptp.zero_zero_rat) (= A B)))))
% 6.73/7.04 (assert (forall ((A tptp.nat) (C2 tptp.nat) (B tptp.nat)) (= (= (@ (@ tptp.times_times_nat A) C2) (@ (@ tptp.times_times_nat B) C2)) (or (= C2 tptp.zero_zero_nat) (= A B)))))
% 6.73/7.04 (assert (forall ((A tptp.int) (C2 tptp.int) (B tptp.int)) (= (= (@ (@ tptp.times_times_int A) C2) (@ (@ tptp.times_times_int B) C2)) (or (= C2 tptp.zero_zero_int) (= A B)))))
% 6.73/7.04 (assert (forall ((C2 tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex C2))) (= (= (@ _let_1 A) (@ _let_1 B)) (or (= C2 tptp.zero_zero_complex) (= A B))))))
% 6.73/7.04 (assert (forall ((C2 tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real C2))) (= (= (@ _let_1 A) (@ _let_1 B)) (or (= C2 tptp.zero_zero_real) (= A B))))))
% 6.73/7.04 (assert (forall ((C2 tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C2))) (= (= (@ _let_1 A) (@ _let_1 B)) (or (= C2 tptp.zero_zero_rat) (= A B))))))
% 6.73/7.04 (assert (forall ((C2 tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C2))) (= (= (@ _let_1 A) (@ _let_1 B)) (or (= C2 tptp.zero_zero_nat) (= A B))))))
% 6.73/7.04 (assert (forall ((C2 tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C2))) (= (= (@ _let_1 A) (@ _let_1 B)) (or (= C2 tptp.zero_zero_int) (= A B))))))
% 6.73/7.04 (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)))))
% 6.73/7.04 (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)))))
% 6.73/7.04 (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)))))
% 6.73/7.04 (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)))))
% 6.73/7.04 (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)))))
% 6.73/7.04 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex A) tptp.zero_zero_complex) tptp.zero_zero_complex)))
% 6.73/7.04 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real A) tptp.zero_zero_real) tptp.zero_zero_real)))
% 6.73/7.04 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat A) tptp.zero_zero_rat) tptp.zero_zero_rat)))
% 6.73/7.04 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat A) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 6.73/7.04 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int A) tptp.zero_zero_int) tptp.zero_zero_int)))
% 6.73/7.04 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex tptp.zero_zero_complex) A) tptp.zero_zero_complex)))
% 6.73/7.04 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real tptp.zero_zero_real) A) tptp.zero_zero_real)))
% 6.73/7.04 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat tptp.zero_zero_rat) A) tptp.zero_zero_rat)))
% 6.73/7.04 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)))
% 6.73/7.04 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int tptp.zero_zero_int) A) tptp.zero_zero_int)))
% 6.73/7.04 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z3 tptp.nat)) (= (= (@ (@ tptp.times_times_nat X) Y) Z3) (= (@ (@ tptp.vEBT_VEBT_mul (@ tptp.some_nat X)) (@ tptp.some_nat Y)) (@ tptp.some_nat Z3)))))
% 6.73/7.04 (assert (forall ((A Bool) (B Bool)) (@ (@ tptp.vEBT_invar_vebt (@ (@ tptp.vEBT_Leaf A) B)) (@ tptp.suc tptp.zero_zero_nat))))
% 6.73/7.04 (assert (forall ((A tptp.real) (B tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.times_times_real C2))) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C2) (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B)))))))
% 6.73/7.04 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C2))) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C2) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B)))))))
% 6.73/7.04 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C2))) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C2) (@ (@ tptp.ord_less_eq_nat (@ _let_1 A)) (@ _let_1 B)))))))
% 6.73/7.04 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int C2))) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C2) (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B)))))))
% 6.73/7.04 (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)))))))
% 6.73/7.04 (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)))))))
% 6.73/7.04 (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)))))))
% 6.73/7.04 (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)))))
% 6.73/7.04 (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)))))
% 6.73/7.04 (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)))))
% 6.73/7.04 (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)))))
% 6.73/7.04 (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)))))
% 6.73/7.04 (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)))))
% 6.73/7.04 (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)))))
% 6.73/7.04 (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)))))
% 6.73/7.04 (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)))))
% 6.73/7.04 (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)))))
% 6.73/7.04 (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)))))
% 6.73/7.04 (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)))))
% 6.73/7.04 (assert (forall ((X21 Bool) (X22 Bool) (Y21 Bool) (Y22 Bool)) (= (= (@ (@ tptp.vEBT_Leaf X21) X22) (@ (@ tptp.vEBT_Leaf Y21) Y22)) (and (= X21 Y21) (= X22 Y22)))))
% 6.73/7.04 (assert (= tptp.vEBT_VEBT_mul (@ tptp.vEBT_V4262088993061758097ft_nat tptp.times_times_nat)))
% 6.73/7.04 (assert (forall ((X21 Bool) (X22 Bool)) (= (@ tptp.size_size_VEBT_VEBT (@ (@ tptp.vEBT_Leaf X21) X22)) tptp.zero_zero_nat)))
% 6.73/7.04 (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))))))
% 6.73/7.04 (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))))))
% 6.73/7.04 (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))))))
% 6.73/7.04 (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))))))
% 6.73/7.04 (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))))))
% 6.73/7.04 (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)))))
% 6.73/7.04 (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)))))
% 6.73/7.04 (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)))))
% 6.73/7.04 (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)))))
% 6.73/7.04 (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)))))
% 6.73/7.04 (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))))))
% 6.73/7.04 (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))))))
% 6.73/7.04 (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))))))
% 6.73/7.04 (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))))))
% 6.73/7.04 (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))))))
% 6.73/7.04 (assert (forall ((C2 tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex C2))) (=> (not (= C2 tptp.zero_zero_complex)) (= (= (@ _let_1 A) (@ _let_1 B)) (= A B))))))
% 6.73/7.04 (assert (forall ((C2 tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real C2))) (=> (not (= C2 tptp.zero_zero_real)) (= (= (@ _let_1 A) (@ _let_1 B)) (= A B))))))
% 6.73/7.04 (assert (forall ((C2 tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C2))) (=> (not (= C2 tptp.zero_zero_rat)) (= (= (@ _let_1 A) (@ _let_1 B)) (= A B))))))
% 6.73/7.04 (assert (forall ((C2 tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C2))) (=> (not (= C2 tptp.zero_zero_nat)) (= (= (@ _let_1 A) (@ _let_1 B)) (= A B))))))
% 6.73/7.04 (assert (forall ((C2 tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C2))) (=> (not (= C2 tptp.zero_zero_int)) (= (= (@ _let_1 A) (@ _let_1 B)) (= A B))))))
% 6.73/7.04 (assert (forall ((C2 tptp.complex) (A tptp.complex) (B tptp.complex)) (=> (not (= C2 tptp.zero_zero_complex)) (= (= (@ (@ tptp.times_times_complex A) C2) (@ (@ tptp.times_times_complex B) C2)) (= A B)))))
% 6.73/7.04 (assert (forall ((C2 tptp.real) (A tptp.real) (B tptp.real)) (=> (not (= C2 tptp.zero_zero_real)) (= (= (@ (@ tptp.times_times_real A) C2) (@ (@ tptp.times_times_real B) C2)) (= A B)))))
% 6.73/7.04 (assert (forall ((C2 tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (not (= C2 tptp.zero_zero_rat)) (= (= (@ (@ tptp.times_times_rat A) C2) (@ (@ tptp.times_times_rat B) C2)) (= A B)))))
% 6.73/7.04 (assert (forall ((C2 tptp.nat) (A tptp.nat) (B tptp.nat)) (=> (not (= C2 tptp.zero_zero_nat)) (= (= (@ (@ tptp.times_times_nat A) C2) (@ (@ tptp.times_times_nat B) C2)) (= A B)))))
% 6.73/7.04 (assert (forall ((C2 tptp.int) (A tptp.int) (B tptp.int)) (=> (not (= C2 tptp.zero_zero_int)) (= (= (@ (@ tptp.times_times_int A) C2) (@ (@ tptp.times_times_int B) C2)) (= A B)))))
% 6.73/7.04 (assert (forall ((A tptp.real) (B tptp.real) (C2 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 C2) D) (=> (@ _let_1 B) (=> (@ _let_1 C2) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) C2)) (@ (@ tptp.times_times_real B) D)))))))))
% 6.73/7.04 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 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 C2) D) (=> (@ _let_1 B) (=> (@ _let_1 C2) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C2)) (@ (@ tptp.times_times_rat B) D)))))))))
% 6.73/7.04 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 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 C2) D) (=> (@ _let_1 B) (=> (@ _let_1 C2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A) C2)) (@ (@ tptp.times_times_nat B) D)))))))))
% 6.73/7.04 (assert (forall ((A tptp.int) (B tptp.int) (C2 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 C2) D) (=> (@ _let_1 B) (=> (@ _let_1 C2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) C2)) (@ (@ tptp.times_times_int B) D)))))))))
% 6.73/7.04 (assert (forall ((A tptp.real) (B tptp.real) (C2 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 C2) D) (=> (@ _let_1 A) (=> (@ _let_1 C2) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) C2)) (@ (@ tptp.times_times_real B) D)))))))))
% 6.73/7.04 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 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 C2) D) (=> (@ _let_1 A) (=> (@ _let_1 C2) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C2)) (@ (@ tptp.times_times_rat B) D)))))))))
% 6.73/7.04 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 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 C2) D) (=> (@ _let_1 A) (=> (@ _let_1 C2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A) C2)) (@ (@ tptp.times_times_nat B) D)))))))))
% 6.73/7.04 (assert (forall ((A tptp.int) (B tptp.int) (C2 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 C2) D) (=> (@ _let_1 A) (=> (@ _let_1 C2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) C2)) (@ (@ tptp.times_times_int B) D)))))))))
% 6.73/7.04 (assert (forall ((A tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.times_times_real A) A))))
% 6.73/7.04 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.times_times_rat A) A))))
% 6.73/7.04 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.times_times_int A) A))))
% 6.73/7.04 (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))))))
% 6.73/7.04 (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))))))
% 6.73/7.04 (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))))))
% 6.73/7.04 (assert (forall ((B tptp.real) (A tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.times_times_real C2))) (=> (@ (@ tptp.ord_less_eq_real B) A) (=> (@ (@ tptp.ord_less_eq_real C2) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B)))))))
% 6.73/7.04 (assert (forall ((B tptp.rat) (A tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C2))) (=> (@ (@ tptp.ord_less_eq_rat B) A) (=> (@ (@ tptp.ord_less_eq_rat C2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B)))))))
% 6.73/7.04 (assert (forall ((B tptp.int) (A tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int C2))) (=> (@ (@ tptp.ord_less_eq_int B) A) (=> (@ (@ tptp.ord_less_eq_int C2) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B)))))))
% 6.73/7.04 (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))))))
% 6.73/7.04 (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))))))
% 6.73/7.04 (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))))))
% 6.73/7.04 (assert (forall ((A tptp.real) (B tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.times_times_real C2))) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C2) (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B)))))))
% 6.73/7.04 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C2))) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C2) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B)))))))
% 6.73/7.04 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C2))) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C2) (@ (@ tptp.ord_less_eq_nat (@ _let_1 A)) (@ _let_1 B)))))))
% 6.73/7.04 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int C2))) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C2) (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B)))))))
% 6.73/7.04 (assert (forall ((B tptp.real) (A tptp.real) (C2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real B) A) (=> (@ (@ tptp.ord_less_eq_real C2) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) C2)) (@ (@ tptp.times_times_real B) C2))))))
% 6.73/7.04 (assert (forall ((B tptp.rat) (A tptp.rat) (C2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat B) A) (=> (@ (@ tptp.ord_less_eq_rat C2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C2)) (@ (@ tptp.times_times_rat B) C2))))))
% 6.73/7.04 (assert (forall ((B tptp.int) (A tptp.int) (C2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B) A) (=> (@ (@ tptp.ord_less_eq_int C2) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) C2)) (@ (@ tptp.times_times_int B) C2))))))
% 6.73/7.04 (assert (forall ((A tptp.real) (B tptp.real) (C2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C2) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) C2)) (@ (@ tptp.times_times_real B) C2))))))
% 6.73/7.04 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C2) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C2)) (@ (@ tptp.times_times_rat B) C2))))))
% 6.73/7.04 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A) C2)) (@ (@ tptp.times_times_nat B) C2))))))
% 6.73/7.04 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) C2)) (@ (@ tptp.times_times_int B) C2))))))
% 6.73/7.04 (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)))))))
% 6.73/7.04 (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)))))))
% 6.73/7.04 (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)))))))
% 6.73/7.04 (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)))))
% 6.73/7.04 (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)))))
% 6.73/7.04 (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)))))
% 6.73/7.04 (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)))))
% 6.73/7.04 (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)))))))
% 6.73/7.04 (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)))))))
% 6.73/7.04 (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)))))))
% 6.73/7.04 (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)))))))
% 6.73/7.04 (assert (= tptp.vEBT_VEBT_valid tptp.vEBT_invar_vebt))
% 6.73/7.04 (assert (forall ((T tptp.vEBT_VEBT) (D tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) D) (@ (@ tptp.vEBT_VEBT_valid T) D))))
% 6.73/7.04 (assert (forall ((T tptp.vEBT_VEBT) (D tptp.nat)) (=> (@ (@ tptp.vEBT_VEBT_valid T) D) (@ (@ tptp.vEBT_invar_vebt T) D))))
% 6.73/7.04 (assert (forall ((T tptp.vEBT_VEBT)) (= (@ (@ tptp.vEBT_invar_vebt T) tptp.one_one_nat) (exists ((A5 Bool) (B4 Bool)) (= T (@ (@ tptp.vEBT_Leaf A5) B4))))))
% 6.73/7.04 (assert (forall ((T tptp.vEBT_VEBT)) (=> (@ (@ tptp.vEBT_invar_vebt T) tptp.one_one_nat) (exists ((A3 Bool) (B3 Bool)) (= T (@ (@ tptp.vEBT_Leaf A3) B3))))))
% 6.73/7.04 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (= N tptp.one_one_nat) (exists ((A3 Bool) (B3 Bool)) (= T (@ (@ tptp.vEBT_Leaf A3) B3)))))))
% 6.73/7.04 (assert (forall ((K2 tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K2))) (= (= (@ _let_1 M2) (@ _let_1 N)) (or (= K2 tptp.zero_zero_nat) (= M2 N))))))
% 6.73/7.04 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))
% 6.73/7.04 (assert (forall ((X21 Bool) (X22 Bool)) (= (@ tptp.vEBT_size_VEBT (@ (@ tptp.vEBT_Leaf X21) X22)) tptp.zero_zero_nat)))
% 6.73/7.04 (assert (forall ((Tree tptp.vEBT_VEBT) (N tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt Tree) (@ tptp.suc (@ tptp.suc N))) (exists ((Info tptp.option4927543243414619207at_nat) (TreeList tptp.list_VEBT_VEBT) (S tptp.vEBT_VEBT)) (= Tree (@ (@ (@ (@ tptp.vEBT_Node Info) (@ tptp.suc (@ tptp.suc N))) TreeList) S))))))
% 6.73/7.04 (assert (= (@ tptp.vEBT_VEBT_set_vebt (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat tptp.mi) tptp.ma))) tptp.deg) tptp.treeList2) tptp.summary2)) (@ tptp.vEBT_VEBT_set_vebt tptp.sa)))
% 6.73/7.04 (assert (forall ((Info2 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 Info2) Deg) TreeList2) Summary)) N) (= Deg N))))
% 6.73/7.04 (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)))))
% 6.73/7.04 (assert (forall ((N tptp.nat)) (= (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)) (= N tptp.zero_zero_nat))))
% 6.73/7.04 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger tptp.one_one_Code_integer) A) A)))
% 6.73/7.04 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex tptp.one_one_complex) A) A)))
% 6.73/7.04 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real tptp.one_one_real) A) A)))
% 6.73/7.04 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat tptp.one_one_rat) A) A)))
% 6.73/7.04 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.one_one_nat) A) A)))
% 6.73/7.04 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int tptp.one_one_int) A) A)))
% 6.73/7.04 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger A) tptp.one_one_Code_integer) A)))
% 6.73/7.04 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex A) tptp.one_one_complex) A)))
% 6.73/7.04 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real A) tptp.one_one_real) A)))
% 6.73/7.04 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat A) tptp.one_one_rat) A)))
% 6.73/7.04 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat A) tptp.one_one_nat) A)))
% 6.73/7.04 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int A) tptp.one_one_int) A)))
% 6.73/7.04 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.suc M2)) (@ tptp.suc N)) (@ (@ tptp.ord_less_nat M2) N))))
% 6.73/7.04 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) N) (@ (@ tptp.ord_less_nat (@ tptp.suc M2)) (@ tptp.suc N)))))
% 6.73/7.04 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_nat N) (@ tptp.suc N))))
% 6.73/7.04 (assert (forall ((A tptp.nat)) (= (not (= A tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A))))
% 6.73/7.04 (assert (forall ((N tptp.nat)) (= (not (= N tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))
% 6.73/7.04 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) tptp.zero_zero_nat))))
% 6.73/7.04 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (= tptp.one_one_nat (@ (@ tptp.times_times_nat M2) N)) (and (= M2 tptp.one_one_nat) (= N tptp.one_one_nat)))))
% 6.73/7.04 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (= (@ (@ tptp.times_times_nat M2) N) tptp.one_one_nat) (and (= M2 tptp.one_one_nat) (= N tptp.one_one_nat)))))
% 6.73/7.04 (assert (@ (@ tptp.vEBT_invar_vebt tptp.summary2) tptp.m))
% 6.73/7.04 (assert (forall ((C2 tptp.code_integer) (B tptp.code_integer)) (= (= C2 (@ (@ tptp.times_3573771949741848930nteger C2) B)) (or (= C2 tptp.zero_z3403309356797280102nteger) (= B tptp.one_one_Code_integer)))))
% 6.73/7.04 (assert (forall ((C2 tptp.complex) (B tptp.complex)) (= (= C2 (@ (@ tptp.times_times_complex C2) B)) (or (= C2 tptp.zero_zero_complex) (= B tptp.one_one_complex)))))
% 6.73/7.04 (assert (forall ((C2 tptp.real) (B tptp.real)) (= (= C2 (@ (@ tptp.times_times_real C2) B)) (or (= C2 tptp.zero_zero_real) (= B tptp.one_one_real)))))
% 6.73/7.04 (assert (forall ((C2 tptp.rat) (B tptp.rat)) (= (= C2 (@ (@ tptp.times_times_rat C2) B)) (or (= C2 tptp.zero_zero_rat) (= B tptp.one_one_rat)))))
% 6.73/7.04 (assert (forall ((C2 tptp.int) (B tptp.int)) (= (= C2 (@ (@ tptp.times_times_int C2) B)) (or (= C2 tptp.zero_zero_int) (= B tptp.one_one_int)))))
% 6.73/7.04 (assert (forall ((C2 tptp.code_integer) (A tptp.code_integer)) (= (= (@ (@ tptp.times_3573771949741848930nteger C2) A) C2) (or (= C2 tptp.zero_z3403309356797280102nteger) (= A tptp.one_one_Code_integer)))))
% 6.73/7.04 (assert (forall ((C2 tptp.complex) (A tptp.complex)) (= (= (@ (@ tptp.times_times_complex C2) A) C2) (or (= C2 tptp.zero_zero_complex) (= A tptp.one_one_complex)))))
% 6.73/7.04 (assert (forall ((C2 tptp.real) (A tptp.real)) (= (= (@ (@ tptp.times_times_real C2) A) C2) (or (= C2 tptp.zero_zero_real) (= A tptp.one_one_real)))))
% 6.73/7.04 (assert (forall ((C2 tptp.rat) (A tptp.rat)) (= (= (@ (@ tptp.times_times_rat C2) A) C2) (or (= C2 tptp.zero_zero_rat) (= A tptp.one_one_rat)))))
% 6.73/7.04 (assert (forall ((C2 tptp.int) (A tptp.int)) (= (= (@ (@ tptp.times_times_int C2) A) C2) (or (= C2 tptp.zero_zero_int) (= A tptp.one_one_int)))))
% 6.73/7.04 (assert (forall ((C2 tptp.code_integer) (B tptp.code_integer)) (= (= C2 (@ (@ tptp.times_3573771949741848930nteger B) C2)) (or (= C2 tptp.zero_z3403309356797280102nteger) (= B tptp.one_one_Code_integer)))))
% 6.73/7.04 (assert (forall ((C2 tptp.complex) (B tptp.complex)) (= (= C2 (@ (@ tptp.times_times_complex B) C2)) (or (= C2 tptp.zero_zero_complex) (= B tptp.one_one_complex)))))
% 6.73/7.04 (assert (forall ((C2 tptp.real) (B tptp.real)) (= (= C2 (@ (@ tptp.times_times_real B) C2)) (or (= C2 tptp.zero_zero_real) (= B tptp.one_one_real)))))
% 6.73/7.04 (assert (forall ((C2 tptp.rat) (B tptp.rat)) (= (= C2 (@ (@ tptp.times_times_rat B) C2)) (or (= C2 tptp.zero_zero_rat) (= B tptp.one_one_rat)))))
% 6.73/7.04 (assert (forall ((C2 tptp.int) (B tptp.int)) (= (= C2 (@ (@ tptp.times_times_int B) C2)) (or (= C2 tptp.zero_zero_int) (= B tptp.one_one_int)))))
% 6.73/7.04 (assert (forall ((A tptp.code_integer) (C2 tptp.code_integer)) (= (= (@ (@ tptp.times_3573771949741848930nteger A) C2) C2) (or (= C2 tptp.zero_z3403309356797280102nteger) (= A tptp.one_one_Code_integer)))))
% 6.73/7.04 (assert (forall ((A tptp.complex) (C2 tptp.complex)) (= (= (@ (@ tptp.times_times_complex A) C2) C2) (or (= C2 tptp.zero_zero_complex) (= A tptp.one_one_complex)))))
% 6.73/7.04 (assert (forall ((A tptp.real) (C2 tptp.real)) (= (= (@ (@ tptp.times_times_real A) C2) C2) (or (= C2 tptp.zero_zero_real) (= A tptp.one_one_real)))))
% 6.73/7.04 (assert (forall ((A tptp.rat) (C2 tptp.rat)) (= (= (@ (@ tptp.times_times_rat A) C2) C2) (or (= C2 tptp.zero_zero_rat) (= A tptp.one_one_rat)))))
% 6.73/7.04 (assert (forall ((A tptp.int) (C2 tptp.int)) (= (= (@ (@ tptp.times_times_int A) C2) C2) (or (= C2 tptp.zero_zero_int) (= A tptp.one_one_int)))))
% 6.73/7.04 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.suc N))))
% 6.73/7.04 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_nat N) (@ tptp.suc tptp.zero_zero_nat)) (= N tptp.zero_zero_nat))))
% 6.73/7.04 (assert (forall ((K2 tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K2))) (= (@ (@ tptp.ord_less_nat (@ _let_1 M2)) (@ _let_1 N)) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K2) (@ (@ tptp.ord_less_nat M2) N))))))
% 6.73/7.04 (assert (forall ((M2 tptp.nat) (K2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat M2) K2)) (@ (@ tptp.times_times_nat N) K2)) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K2) (@ (@ tptp.ord_less_nat M2) N)))))
% 6.73/7.04 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ (@ tptp.times_times_nat M2) N)) (and (@ _let_1 M2) (@ _let_1 N))))))
% 6.73/7.04 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_nat N) tptp.one_one_nat) (= N tptp.zero_zero_nat))))
% 6.73/7.04 (assert (forall ((K2 tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K2))) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 M2)) (@ _let_1 N)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K2) (@ (@ tptp.ord_less_eq_nat M2) N))))))
% 6.73/7.04 (assert (forall ((M2 tptp.nat) (K2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat M2) K2)) (@ (@ tptp.times_times_nat N) K2)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K2) (@ (@ tptp.ord_less_eq_nat M2) N)))))
% 6.73/7.04 (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)))))
% 6.73/7.04 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (not (= X Y)) (=> (not (@ (@ tptp.ord_less_real X) Y)) (@ (@ tptp.ord_less_real Y) X)))))
% 6.73/7.04 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (not (= X Y)) (=> (not (@ (@ tptp.ord_less_rat X) Y)) (@ (@ tptp.ord_less_rat Y) X)))))
% 6.73/7.04 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (not (= X Y)) (=> (not (@ (@ tptp.ord_less_int X) Y)) (@ (@ tptp.ord_less_int Y) X)))))
% 6.73/7.04 (assert (forall ((X tptp.real)) (exists ((Y3 tptp.real)) (@ (@ tptp.ord_less_real Y3) X))))
% 6.73/7.04 (assert (forall ((X tptp.rat)) (exists ((Y3 tptp.rat)) (@ (@ tptp.ord_less_rat Y3) X))))
% 6.73/7.04 (assert (forall ((X tptp.int)) (exists ((Y3 tptp.int)) (@ (@ tptp.ord_less_int Y3) X))))
% 6.73/7.04 (assert (forall ((X tptp.real)) (exists ((X_12 tptp.real)) (@ (@ tptp.ord_less_real X) X_12))))
% 6.73/7.04 (assert (forall ((X tptp.rat)) (exists ((X_12 tptp.rat)) (@ (@ tptp.ord_less_rat X) X_12))))
% 6.73/7.04 (assert (forall ((X tptp.nat)) (exists ((X_12 tptp.nat)) (@ (@ tptp.ord_less_nat X) X_12))))
% 6.73/7.04 (assert (forall ((X tptp.int)) (exists ((X_12 tptp.int)) (@ (@ tptp.ord_less_int X) X_12))))
% 6.73/7.04 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X) Y) (exists ((Z tptp.real)) (and (@ (@ tptp.ord_less_real X) Z) (@ (@ tptp.ord_less_real Z) Y))))))
% 6.73/7.04 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat X) Y) (exists ((Z tptp.rat)) (and (@ (@ tptp.ord_less_rat X) Z) (@ (@ tptp.ord_less_rat Z) Y))))))
% 6.73/7.04 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X) Y) (not (= X Y)))))
% 6.73/7.04 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat X) Y) (not (= X Y)))))
% 6.73/7.04 (assert (forall ((X tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_num X) Y) (not (= X Y)))))
% 6.73/7.04 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Y) (not (= X Y)))))
% 6.73/7.04 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int X) Y) (not (= X Y)))))
% 6.73/7.04 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (not (@ (@ tptp.ord_less_real B) A)))))
% 6.73/7.04 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (not (@ (@ tptp.ord_less_rat B) A)))))
% 6.73/7.04 (assert (forall ((A tptp.num) (B tptp.num)) (=> (@ (@ tptp.ord_less_num A) B) (not (@ (@ tptp.ord_less_num B) A)))))
% 6.73/7.04 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (not (@ (@ tptp.ord_less_nat B) A)))))
% 6.73/7.04 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (not (@ (@ tptp.ord_less_int B) A)))))
% 6.73/7.04 (assert (forall ((A tptp.real) (B tptp.real) (C2 tptp.real)) (=> (= A B) (=> (@ (@ tptp.ord_less_real B) C2) (@ (@ tptp.ord_less_real A) C2)))))
% 6.73/7.04 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (=> (= A B) (=> (@ (@ tptp.ord_less_rat B) C2) (@ (@ tptp.ord_less_rat A) C2)))))
% 6.73/7.04 (assert (forall ((A tptp.num) (B tptp.num) (C2 tptp.num)) (=> (= A B) (=> (@ (@ tptp.ord_less_num B) C2) (@ (@ tptp.ord_less_num A) C2)))))
% 6.73/7.04 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (=> (= A B) (=> (@ (@ tptp.ord_less_nat B) C2) (@ (@ tptp.ord_less_nat A) C2)))))
% 6.73/7.04 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (=> (= A B) (=> (@ (@ tptp.ord_less_int B) C2) (@ (@ tptp.ord_less_int A) C2)))))
% 6.73/7.04 (assert (forall ((A tptp.real) (B tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real A))) (=> (@ _let_1 B) (=> (= B C2) (@ _let_1 C2))))))
% 6.73/7.04 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A))) (=> (@ _let_1 B) (=> (= B C2) (@ _let_1 C2))))))
% 6.73/7.04 (assert (forall ((A tptp.num) (B tptp.num) (C2 tptp.num)) (let ((_let_1 (@ tptp.ord_less_num A))) (=> (@ _let_1 B) (=> (= B C2) (@ _let_1 C2))))))
% 6.73/7.04 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat A))) (=> (@ _let_1 B) (=> (= B C2) (@ _let_1 C2))))))
% 6.73/7.04 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int A))) (=> (@ _let_1 B) (=> (= B C2) (@ _let_1 C2))))))
% 6.73/7.04 (assert (forall ((P2 (-> tptp.nat Bool)) (A tptp.nat)) (=> (forall ((X3 tptp.nat)) (=> (forall ((Y6 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Y6) X3) (@ P2 Y6))) (@ P2 X3))) (@ P2 A))))
% 6.73/7.04 (assert (forall ((Y tptp.real) (X tptp.real)) (=> (not (@ (@ tptp.ord_less_real Y) X)) (= (not (@ (@ tptp.ord_less_real X) Y)) (= X Y)))))
% 6.73/7.04 (assert (forall ((Y tptp.rat) (X tptp.rat)) (=> (not (@ (@ tptp.ord_less_rat Y) X)) (= (not (@ (@ tptp.ord_less_rat X) Y)) (= X Y)))))
% 6.73/7.04 (assert (forall ((Y tptp.num) (X tptp.num)) (=> (not (@ (@ tptp.ord_less_num Y) X)) (= (not (@ (@ tptp.ord_less_num X) Y)) (= X Y)))))
% 6.73/7.04 (assert (forall ((Y tptp.nat) (X tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat Y) X)) (= (not (@ (@ tptp.ord_less_nat X) Y)) (= X Y)))))
% 6.73/7.04 (assert (forall ((Y tptp.int) (X tptp.int)) (=> (not (@ (@ tptp.ord_less_int Y) X)) (= (not (@ (@ tptp.ord_less_int X) Y)) (= X Y)))))
% 6.73/7.04 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (not (@ (@ tptp.ord_less_real X) Y)) (=> (not (= X Y)) (@ (@ tptp.ord_less_real Y) X)))))
% 6.73/7.04 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (not (@ (@ tptp.ord_less_rat X) Y)) (=> (not (= X Y)) (@ (@ tptp.ord_less_rat Y) X)))))
% 6.73/7.04 (assert (forall ((X tptp.num) (Y tptp.num)) (=> (not (@ (@ tptp.ord_less_num X) Y)) (=> (not (= X Y)) (@ (@ tptp.ord_less_num Y) X)))))
% 6.73/7.04 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat X) Y)) (=> (not (= X Y)) (@ (@ tptp.ord_less_nat Y) X)))))
% 6.73/7.04 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (not (@ (@ tptp.ord_less_int X) Y)) (=> (not (= X Y)) (@ (@ tptp.ord_less_int Y) X)))))
% 6.73/7.04 (assert (forall ((B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real B) A) (not (@ (@ tptp.ord_less_real A) B)))))
% 6.73/7.04 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat B) A) (not (@ (@ tptp.ord_less_rat A) B)))))
% 6.73/7.04 (assert (forall ((B tptp.num) (A tptp.num)) (=> (@ (@ tptp.ord_less_num B) A) (not (@ (@ tptp.ord_less_num A) B)))))
% 6.73/7.04 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat B) A) (not (@ (@ tptp.ord_less_nat A) B)))))
% 6.73/7.04 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int B) A) (not (@ (@ tptp.ord_less_int A) B)))))
% 6.73/7.04 (assert (forall ((A tptp.real)) (not (@ (@ tptp.ord_less_real A) A))))
% 6.73/7.04 (assert (forall ((A tptp.rat)) (not (@ (@ tptp.ord_less_rat A) A))))
% 6.73/7.04 (assert (forall ((A tptp.num)) (not (@ (@ tptp.ord_less_num A) A))))
% 6.73/7.04 (assert (forall ((A tptp.nat)) (not (@ (@ tptp.ord_less_nat A) A))))
% 6.73/7.04 (assert (forall ((A tptp.int)) (not (@ (@ tptp.ord_less_int A) A))))
% 6.73/7.04 (assert (= (lambda ((P3 (-> tptp.nat Bool))) (exists ((X6 tptp.nat)) (@ P3 X6))) (lambda ((P4 (-> tptp.nat Bool))) (exists ((N4 tptp.nat)) (and (@ P4 N4) (forall ((M6 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M6) N4) (not (@ P4 M6)))))))))
% 6.73/7.04 (assert (forall ((P2 (-> tptp.real tptp.real Bool)) (A tptp.real) (B tptp.real)) (=> (forall ((A3 tptp.real) (B3 tptp.real)) (=> (@ (@ tptp.ord_less_real A3) B3) (@ (@ P2 A3) B3))) (=> (forall ((A3 tptp.real)) (@ (@ P2 A3) A3)) (=> (forall ((A3 tptp.real) (B3 tptp.real)) (=> (@ (@ P2 B3) A3) (@ (@ P2 A3) B3))) (@ (@ P2 A) B))))))
% 6.73/7.04 (assert (forall ((P2 (-> tptp.rat tptp.rat Bool)) (A tptp.rat) (B tptp.rat)) (=> (forall ((A3 tptp.rat) (B3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat A3) B3) (@ (@ P2 A3) B3))) (=> (forall ((A3 tptp.rat)) (@ (@ P2 A3) A3)) (=> (forall ((A3 tptp.rat) (B3 tptp.rat)) (=> (@ (@ P2 B3) A3) (@ (@ P2 A3) B3))) (@ (@ P2 A) B))))))
% 6.73/7.04 (assert (forall ((P2 (-> tptp.num tptp.num Bool)) (A tptp.num) (B tptp.num)) (=> (forall ((A3 tptp.num) (B3 tptp.num)) (=> (@ (@ tptp.ord_less_num A3) B3) (@ (@ P2 A3) B3))) (=> (forall ((A3 tptp.num)) (@ (@ P2 A3) A3)) (=> (forall ((A3 tptp.num) (B3 tptp.num)) (=> (@ (@ P2 B3) A3) (@ (@ P2 A3) B3))) (@ (@ P2 A) B))))))
% 6.73/7.04 (assert (forall ((P2 (-> tptp.nat tptp.nat Bool)) (A tptp.nat) (B tptp.nat)) (=> (forall ((A3 tptp.nat) (B3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A3) B3) (@ (@ P2 A3) B3))) (=> (forall ((A3 tptp.nat)) (@ (@ P2 A3) A3)) (=> (forall ((A3 tptp.nat) (B3 tptp.nat)) (=> (@ (@ P2 B3) A3) (@ (@ P2 A3) B3))) (@ (@ P2 A) B))))))
% 6.73/7.04 (assert (forall ((P2 (-> tptp.int tptp.int Bool)) (A tptp.int) (B tptp.int)) (=> (forall ((A3 tptp.int) (B3 tptp.int)) (=> (@ (@ tptp.ord_less_int A3) B3) (@ (@ P2 A3) B3))) (=> (forall ((A3 tptp.int)) (@ (@ P2 A3) A3)) (=> (forall ((A3 tptp.int) (B3 tptp.int)) (=> (@ (@ P2 B3) A3) (@ (@ P2 A3) B3))) (@ (@ P2 A) B))))))
% 6.73/7.04 (assert (forall ((A tptp.real) (B tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_real B) C2) (@ _let_1 C2))))))
% 6.73/7.04 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_rat B) C2) (@ _let_1 C2))))))
% 6.73/7.04 (assert (forall ((A tptp.num) (B tptp.num) (C2 tptp.num)) (let ((_let_1 (@ tptp.ord_less_num A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_num B) C2) (@ _let_1 C2))))))
% 6.73/7.04 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_nat B) C2) (@ _let_1 C2))))))
% 6.73/7.04 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_int B) C2) (@ _let_1 C2))))))
% 6.73/7.04 (assert (forall ((X tptp.real) (Y tptp.real)) (= (not (@ (@ tptp.ord_less_real X) Y)) (or (@ (@ tptp.ord_less_real Y) X) (= X Y)))))
% 6.73/7.04 (assert (forall ((X tptp.rat) (Y tptp.rat)) (= (not (@ (@ tptp.ord_less_rat X) Y)) (or (@ (@ tptp.ord_less_rat Y) X) (= X Y)))))
% 6.73/7.04 (assert (forall ((X tptp.num) (Y tptp.num)) (= (not (@ (@ tptp.ord_less_num X) Y)) (or (@ (@ tptp.ord_less_num Y) X) (= X Y)))))
% 6.73/7.04 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (not (@ (@ tptp.ord_less_nat X) Y)) (or (@ (@ tptp.ord_less_nat Y) X) (= X Y)))))
% 6.73/7.04 (assert (forall ((X tptp.int) (Y tptp.int)) (= (not (@ (@ tptp.ord_less_int X) Y)) (or (@ (@ tptp.ord_less_int Y) X) (= X Y)))))
% 6.73/7.04 (assert (forall ((B tptp.real) (A tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real C2))) (=> (@ (@ tptp.ord_less_real B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 6.73/7.04 (assert (forall ((B tptp.rat) (A tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat C2))) (=> (@ (@ tptp.ord_less_rat B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 6.73/7.04 (assert (forall ((B tptp.num) (A tptp.num) (C2 tptp.num)) (let ((_let_1 (@ tptp.ord_less_num C2))) (=> (@ (@ tptp.ord_less_num B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 6.73/7.04 (assert (forall ((B tptp.nat) (A tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat C2))) (=> (@ (@ tptp.ord_less_nat B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 6.73/7.04 (assert (forall ((B tptp.int) (A tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int C2))) (=> (@ (@ tptp.ord_less_int B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 6.73/7.04 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (not (= A B)))))
% 6.73/7.04 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (not (= A B)))))
% 6.73/7.04 (assert (forall ((A tptp.num) (B tptp.num)) (=> (@ (@ tptp.ord_less_num A) B) (not (= A B)))))
% 6.73/7.04 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (not (= A B)))))
% 6.73/7.04 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (not (= A B)))))
% 6.73/7.04 (assert (forall ((B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real B) A) (not (= A B)))))
% 6.73/7.04 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat B) A) (not (= A B)))))
% 6.73/7.04 (assert (forall ((B tptp.num) (A tptp.num)) (=> (@ (@ tptp.ord_less_num B) A) (not (= A B)))))
% 6.73/7.04 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat B) A) (not (= A B)))))
% 6.73/7.04 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int B) A) (not (= A B)))))
% 6.73/7.04 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (not (= M2 N)) (or (@ (@ tptp.ord_less_nat M2) N) (@ (@ tptp.ord_less_nat N) M2)))))
% 6.73/7.04 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) N))))
% 6.73/7.04 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) M2) (not (= M2 N)))))
% 6.73/7.04 (assert (forall ((S2 tptp.nat) (T tptp.nat)) (=> (@ (@ tptp.ord_less_nat S2) T) (not (= S2 T)))))
% 6.73/7.04 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) N))))
% 6.73/7.04 (assert (forall ((P2 (-> tptp.nat Bool)) (N tptp.nat)) (=> (forall ((N3 tptp.nat)) (=> (forall ((M3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M3) N3) (@ P2 M3))) (@ P2 N3))) (@ P2 N))))
% 6.73/7.04 (assert (forall ((P2 (-> tptp.nat Bool)) (N tptp.nat)) (=> (forall ((N3 tptp.nat)) (=> (not (@ P2 N3)) (exists ((M3 tptp.nat)) (and (@ (@ tptp.ord_less_nat M3) N3) (not (@ P2 M3)))))) (@ P2 N))))
% 6.73/7.04 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (not (= X Y)) (=> (not (@ (@ tptp.ord_less_nat X) Y)) (@ (@ tptp.ord_less_nat Y) X)))))
% 6.73/7.04 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (not (= X Y)) (=> (not (@ (@ tptp.ord_less_real X) Y)) (@ (@ tptp.ord_less_real Y) X)))))
% 6.73/7.04 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (not (= X Y)) (=> (not (@ (@ tptp.ord_less_rat X) Y)) (@ (@ tptp.ord_less_rat Y) X)))))
% 6.73/7.04 (assert (forall ((X tptp.num) (Y tptp.num)) (=> (not (= X Y)) (=> (not (@ (@ tptp.ord_less_num X) Y)) (@ (@ tptp.ord_less_num Y) X)))))
% 6.73/7.04 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (not (= X Y)) (=> (not (@ (@ tptp.ord_less_nat X) Y)) (@ (@ tptp.ord_less_nat Y) X)))))
% 6.73/7.04 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (not (= X Y)) (=> (not (@ (@ tptp.ord_less_int X) Y)) (@ (@ tptp.ord_less_int Y) X)))))
% 6.73/7.04 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X) Y) (not (@ (@ tptp.ord_less_real Y) X)))))
% 6.73/7.04 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat X) Y) (not (@ (@ tptp.ord_less_rat Y) X)))))
% 6.73/7.04 (assert (forall ((X tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_num X) Y) (not (@ (@ tptp.ord_less_num Y) X)))))
% 6.73/7.04 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Y) (not (@ (@ tptp.ord_less_nat Y) X)))))
% 6.73/7.04 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int X) Y) (not (@ (@ tptp.ord_less_int Y) X)))))
% 6.73/7.04 (assert (forall ((X tptp.real) (Y tptp.real)) (= (not (= X Y)) (or (@ (@ tptp.ord_less_real X) Y) (@ (@ tptp.ord_less_real Y) X)))))
% 6.73/7.04 (assert (forall ((X tptp.rat) (Y tptp.rat)) (= (not (= X Y)) (or (@ (@ tptp.ord_less_rat X) Y) (@ (@ tptp.ord_less_rat Y) X)))))
% 6.73/7.04 (assert (forall ((X tptp.num) (Y tptp.num)) (= (not (= X Y)) (or (@ (@ tptp.ord_less_num X) Y) (@ (@ tptp.ord_less_num Y) X)))))
% 6.73/7.04 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (not (= X Y)) (or (@ (@ tptp.ord_less_nat X) Y) (@ (@ tptp.ord_less_nat Y) X)))))
% 6.73/7.04 (assert (forall ((X tptp.int) (Y tptp.int)) (= (not (= X Y)) (or (@ (@ tptp.ord_less_int X) Y) (@ (@ tptp.ord_less_int Y) X)))))
% 6.73/7.04 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (not (@ (@ tptp.ord_less_real B) A)))))
% 6.73/7.04 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (not (@ (@ tptp.ord_less_rat B) A)))))
% 6.73/7.04 (assert (forall ((A tptp.num) (B tptp.num)) (=> (@ (@ tptp.ord_less_num A) B) (not (@ (@ tptp.ord_less_num B) A)))))
% 6.73/7.04 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (not (@ (@ tptp.ord_less_nat B) A)))))
% 6.73/7.04 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (not (@ (@ tptp.ord_less_int B) A)))))
% 6.73/7.04 (assert (forall ((X tptp.real) (Y tptp.real) (Z3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_real Y) Z3) (@ _let_1 Z3))))))
% 6.73/7.04 (assert (forall ((X tptp.rat) (Y tptp.rat) (Z3 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_rat Y) Z3) (@ _let_1 Z3))))))
% 6.73/7.04 (assert (forall ((X tptp.num) (Y tptp.num) (Z3 tptp.num)) (let ((_let_1 (@ tptp.ord_less_num X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_num Y) Z3) (@ _let_1 Z3))))))
% 6.73/7.04 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z3 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_nat Y) Z3) (@ _let_1 Z3))))))
% 6.73/7.04 (assert (forall ((X tptp.int) (Y tptp.int) (Z3 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_int Y) Z3) (@ _let_1 Z3))))))
% 6.73/7.04 (assert (forall ((A tptp.real) (F2 (-> tptp.real tptp.real)) (B tptp.real) (C2 tptp.real)) (=> (= A (@ F2 B)) (=> (@ (@ tptp.ord_less_real B) C2) (=> (forall ((X3 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Y3) (@ (@ tptp.ord_less_real (@ F2 X3)) (@ F2 Y3)))) (@ (@ tptp.ord_less_real A) (@ F2 C2)))))))
% 6.73/7.04 (assert (forall ((A tptp.rat) (F2 (-> tptp.real tptp.rat)) (B tptp.real) (C2 tptp.real)) (=> (= A (@ F2 B)) (=> (@ (@ tptp.ord_less_real B) C2) (=> (forall ((X3 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Y3) (@ (@ tptp.ord_less_rat (@ F2 X3)) (@ F2 Y3)))) (@ (@ tptp.ord_less_rat A) (@ F2 C2)))))))
% 6.73/7.04 (assert (forall ((A tptp.num) (F2 (-> tptp.real tptp.num)) (B tptp.real) (C2 tptp.real)) (=> (= A (@ F2 B)) (=> (@ (@ tptp.ord_less_real B) C2) (=> (forall ((X3 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Y3) (@ (@ tptp.ord_less_num (@ F2 X3)) (@ F2 Y3)))) (@ (@ tptp.ord_less_num A) (@ F2 C2)))))))
% 6.73/7.04 (assert (forall ((A tptp.nat) (F2 (-> tptp.real tptp.nat)) (B tptp.real) (C2 tptp.real)) (=> (= A (@ F2 B)) (=> (@ (@ tptp.ord_less_real B) C2) (=> (forall ((X3 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Y3) (@ (@ tptp.ord_less_nat (@ F2 X3)) (@ F2 Y3)))) (@ (@ tptp.ord_less_nat A) (@ F2 C2)))))))
% 6.73/7.04 (assert (forall ((A tptp.int) (F2 (-> tptp.real tptp.int)) (B tptp.real) (C2 tptp.real)) (=> (= A (@ F2 B)) (=> (@ (@ tptp.ord_less_real B) C2) (=> (forall ((X3 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Y3) (@ (@ tptp.ord_less_int (@ F2 X3)) (@ F2 Y3)))) (@ (@ tptp.ord_less_int A) (@ F2 C2)))))))
% 6.73/7.04 (assert (forall ((A tptp.real) (F2 (-> tptp.rat tptp.real)) (B tptp.rat) (C2 tptp.rat)) (=> (= A (@ F2 B)) (=> (@ (@ tptp.ord_less_rat B) C2) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y3) (@ (@ tptp.ord_less_real (@ F2 X3)) (@ F2 Y3)))) (@ (@ tptp.ord_less_real A) (@ F2 C2)))))))
% 6.73/7.04 (assert (forall ((A tptp.rat) (F2 (-> tptp.rat tptp.rat)) (B tptp.rat) (C2 tptp.rat)) (=> (= A (@ F2 B)) (=> (@ (@ tptp.ord_less_rat B) C2) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y3) (@ (@ tptp.ord_less_rat (@ F2 X3)) (@ F2 Y3)))) (@ (@ tptp.ord_less_rat A) (@ F2 C2)))))))
% 6.73/7.04 (assert (forall ((A tptp.num) (F2 (-> tptp.rat tptp.num)) (B tptp.rat) (C2 tptp.rat)) (=> (= A (@ F2 B)) (=> (@ (@ tptp.ord_less_rat B) C2) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y3) (@ (@ tptp.ord_less_num (@ F2 X3)) (@ F2 Y3)))) (@ (@ tptp.ord_less_num A) (@ F2 C2)))))))
% 6.73/7.04 (assert (forall ((A tptp.nat) (F2 (-> tptp.rat tptp.nat)) (B tptp.rat) (C2 tptp.rat)) (=> (= A (@ F2 B)) (=> (@ (@ tptp.ord_less_rat B) C2) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y3) (@ (@ tptp.ord_less_nat (@ F2 X3)) (@ F2 Y3)))) (@ (@ tptp.ord_less_nat A) (@ F2 C2)))))))
% 6.73/7.04 (assert (forall ((A tptp.int) (F2 (-> tptp.rat tptp.int)) (B tptp.rat) (C2 tptp.rat)) (=> (= A (@ F2 B)) (=> (@ (@ tptp.ord_less_rat B) C2) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y3) (@ (@ tptp.ord_less_int (@ F2 X3)) (@ F2 Y3)))) (@ (@ tptp.ord_less_int A) (@ F2 C2)))))))
% 6.73/7.04 (assert (forall ((A tptp.real) (B tptp.real) (F2 (-> tptp.real tptp.real)) (C2 tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (=> (= (@ F2 B) C2) (=> (forall ((X3 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Y3) (@ (@ tptp.ord_less_real (@ F2 X3)) (@ F2 Y3)))) (@ (@ tptp.ord_less_real (@ F2 A)) C2))))))
% 6.73/7.04 (assert (forall ((A tptp.real) (B tptp.real) (F2 (-> tptp.real tptp.rat)) (C2 tptp.rat)) (=> (@ (@ tptp.ord_less_real A) B) (=> (= (@ F2 B) C2) (=> (forall ((X3 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Y3) (@ (@ tptp.ord_less_rat (@ F2 X3)) (@ F2 Y3)))) (@ (@ tptp.ord_less_rat (@ F2 A)) C2))))))
% 6.73/7.04 (assert (forall ((A tptp.real) (B tptp.real) (F2 (-> tptp.real tptp.num)) (C2 tptp.num)) (=> (@ (@ tptp.ord_less_real A) B) (=> (= (@ F2 B) C2) (=> (forall ((X3 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Y3) (@ (@ tptp.ord_less_num (@ F2 X3)) (@ F2 Y3)))) (@ (@ tptp.ord_less_num (@ F2 A)) C2))))))
% 6.73/7.04 (assert (forall ((A tptp.real) (B tptp.real) (F2 (-> tptp.real tptp.nat)) (C2 tptp.nat)) (=> (@ (@ tptp.ord_less_real A) B) (=> (= (@ F2 B) C2) (=> (forall ((X3 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Y3) (@ (@ tptp.ord_less_nat (@ F2 X3)) (@ F2 Y3)))) (@ (@ tptp.ord_less_nat (@ F2 A)) C2))))))
% 6.73/7.04 (assert (forall ((A tptp.real) (B tptp.real) (F2 (-> tptp.real tptp.int)) (C2 tptp.int)) (=> (@ (@ tptp.ord_less_real A) B) (=> (= (@ F2 B) C2) (=> (forall ((X3 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Y3) (@ (@ tptp.ord_less_int (@ F2 X3)) (@ F2 Y3)))) (@ (@ tptp.ord_less_int (@ F2 A)) C2))))))
% 6.73/7.04 (assert (forall ((A tptp.rat) (B tptp.rat) (F2 (-> tptp.rat tptp.real)) (C2 tptp.real)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (= (@ F2 B) C2) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y3) (@ (@ tptp.ord_less_real (@ F2 X3)) (@ F2 Y3)))) (@ (@ tptp.ord_less_real (@ F2 A)) C2))))))
% 6.73/7.04 (assert (forall ((A tptp.rat) (B tptp.rat) (F2 (-> tptp.rat tptp.rat)) (C2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (= (@ F2 B) C2) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y3) (@ (@ tptp.ord_less_rat (@ F2 X3)) (@ F2 Y3)))) (@ (@ tptp.ord_less_rat (@ F2 A)) C2))))))
% 6.73/7.04 (assert (forall ((A tptp.rat) (B tptp.rat) (F2 (-> tptp.rat tptp.num)) (C2 tptp.num)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (= (@ F2 B) C2) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y3) (@ (@ tptp.ord_less_num (@ F2 X3)) (@ F2 Y3)))) (@ (@ tptp.ord_less_num (@ F2 A)) C2))))))
% 6.73/7.04 (assert (forall ((A tptp.rat) (B tptp.rat) (F2 (-> tptp.rat tptp.nat)) (C2 tptp.nat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (= (@ F2 B) C2) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y3) (@ (@ tptp.ord_less_nat (@ F2 X3)) (@ F2 Y3)))) (@ (@ tptp.ord_less_nat (@ F2 A)) C2))))))
% 6.73/7.04 (assert (forall ((A tptp.rat) (B tptp.rat) (F2 (-> tptp.rat tptp.int)) (C2 tptp.int)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (= (@ F2 B) C2) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y3) (@ (@ tptp.ord_less_int (@ F2 X3)) (@ F2 Y3)))) (@ (@ tptp.ord_less_int (@ F2 A)) C2))))))
% 6.73/7.04 (assert (forall ((X tptp.real)) (not (@ (@ tptp.ord_less_real X) X))))
% 6.73/7.04 (assert (forall ((X tptp.rat)) (not (@ (@ tptp.ord_less_rat X) X))))
% 6.73/7.04 (assert (forall ((X tptp.num)) (not (@ (@ tptp.ord_less_num X) X))))
% 6.73/7.04 (assert (forall ((X tptp.nat)) (not (@ (@ tptp.ord_less_nat X) X))))
% 6.73/7.04 (assert (forall ((X tptp.int)) (not (@ (@ tptp.ord_less_int X) X))))
% 6.73/7.04 (assert (forall ((A tptp.real) (F2 (-> tptp.real tptp.real)) (B tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real A))) (=> (@ _let_1 (@ F2 B)) (=> (@ (@ tptp.ord_less_real B) C2) (=> (forall ((X3 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Y3) (@ (@ tptp.ord_less_real (@ F2 X3)) (@ F2 Y3)))) (@ _let_1 (@ F2 C2))))))))
% 6.73/7.04 (assert (forall ((A tptp.real) (F2 (-> tptp.rat tptp.real)) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_real A))) (=> (@ _let_1 (@ F2 B)) (=> (@ (@ tptp.ord_less_rat B) C2) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y3) (@ (@ tptp.ord_less_real (@ F2 X3)) (@ F2 Y3)))) (@ _let_1 (@ F2 C2))))))))
% 6.73/7.04 (assert (forall ((A tptp.real) (F2 (-> tptp.num tptp.real)) (B tptp.num) (C2 tptp.num)) (let ((_let_1 (@ tptp.ord_less_real A))) (=> (@ _let_1 (@ F2 B)) (=> (@ (@ tptp.ord_less_num B) C2) (=> (forall ((X3 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_num X3) Y3) (@ (@ tptp.ord_less_real (@ F2 X3)) (@ F2 Y3)))) (@ _let_1 (@ F2 C2))))))))
% 6.73/7.04 (assert (forall ((A tptp.real) (F2 (-> tptp.nat tptp.real)) (B tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_real A))) (=> (@ _let_1 (@ F2 B)) (=> (@ (@ tptp.ord_less_nat B) C2) (=> (forall ((X3 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Y3) (@ (@ tptp.ord_less_real (@ F2 X3)) (@ F2 Y3)))) (@ _let_1 (@ F2 C2))))))))
% 6.73/7.04 (assert (forall ((A tptp.real) (F2 (-> tptp.int tptp.real)) (B tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_real A))) (=> (@ _let_1 (@ F2 B)) (=> (@ (@ tptp.ord_less_int B) C2) (=> (forall ((X3 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Y3) (@ (@ tptp.ord_less_real (@ F2 X3)) (@ F2 Y3)))) (@ _let_1 (@ F2 C2))))))))
% 6.73/7.04 (assert (forall ((A tptp.rat) (F2 (-> tptp.real tptp.rat)) (B tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_rat A))) (=> (@ _let_1 (@ F2 B)) (=> (@ (@ tptp.ord_less_real B) C2) (=> (forall ((X3 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Y3) (@ (@ tptp.ord_less_rat (@ F2 X3)) (@ F2 Y3)))) (@ _let_1 (@ F2 C2))))))))
% 6.73/7.04 (assert (forall ((A tptp.rat) (F2 (-> tptp.rat tptp.rat)) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A))) (=> (@ _let_1 (@ F2 B)) (=> (@ (@ tptp.ord_less_rat B) C2) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y3) (@ (@ tptp.ord_less_rat (@ F2 X3)) (@ F2 Y3)))) (@ _let_1 (@ F2 C2))))))))
% 6.73/7.04 (assert (forall ((A tptp.rat) (F2 (-> tptp.num tptp.rat)) (B tptp.num) (C2 tptp.num)) (let ((_let_1 (@ tptp.ord_less_rat A))) (=> (@ _let_1 (@ F2 B)) (=> (@ (@ tptp.ord_less_num B) C2) (=> (forall ((X3 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_num X3) Y3) (@ (@ tptp.ord_less_rat (@ F2 X3)) (@ F2 Y3)))) (@ _let_1 (@ F2 C2))))))))
% 6.73/7.04 (assert (forall ((A tptp.rat) (F2 (-> tptp.nat tptp.rat)) (B tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_rat A))) (=> (@ _let_1 (@ F2 B)) (=> (@ (@ tptp.ord_less_nat B) C2) (=> (forall ((X3 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Y3) (@ (@ tptp.ord_less_rat (@ F2 X3)) (@ F2 Y3)))) (@ _let_1 (@ F2 C2))))))))
% 6.73/7.04 (assert (forall ((A tptp.rat) (F2 (-> tptp.int tptp.rat)) (B tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_rat A))) (=> (@ _let_1 (@ F2 B)) (=> (@ (@ tptp.ord_less_int B) C2) (=> (forall ((X3 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Y3) (@ (@ tptp.ord_less_rat (@ F2 X3)) (@ F2 Y3)))) (@ _let_1 (@ F2 C2))))))))
% 6.73/7.04 (assert (forall ((A tptp.real) (B tptp.real) (F2 (-> tptp.real tptp.real)) (C2 tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_real (@ F2 B)) C2) (=> (forall ((X3 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Y3) (@ (@ tptp.ord_less_real (@ F2 X3)) (@ F2 Y3)))) (@ (@ tptp.ord_less_real (@ F2 A)) C2))))))
% 6.73/7.04 (assert (forall ((A tptp.real) (B tptp.real) (F2 (-> tptp.real tptp.rat)) (C2 tptp.rat)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_rat (@ F2 B)) C2) (=> (forall ((X3 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Y3) (@ (@ tptp.ord_less_rat (@ F2 X3)) (@ F2 Y3)))) (@ (@ tptp.ord_less_rat (@ F2 A)) C2))))))
% 6.73/7.04 (assert (forall ((A tptp.real) (B tptp.real) (F2 (-> tptp.real tptp.num)) (C2 tptp.num)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_num (@ F2 B)) C2) (=> (forall ((X3 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Y3) (@ (@ tptp.ord_less_num (@ F2 X3)) (@ F2 Y3)))) (@ (@ tptp.ord_less_num (@ F2 A)) C2))))))
% 6.73/7.04 (assert (forall ((A tptp.real) (B tptp.real) (F2 (-> tptp.real tptp.nat)) (C2 tptp.nat)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_nat (@ F2 B)) C2) (=> (forall ((X3 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Y3) (@ (@ tptp.ord_less_nat (@ F2 X3)) (@ F2 Y3)))) (@ (@ tptp.ord_less_nat (@ F2 A)) C2))))))
% 6.73/7.04 (assert (forall ((A tptp.real) (B tptp.real) (F2 (-> tptp.real tptp.int)) (C2 tptp.int)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_int (@ F2 B)) C2) (=> (forall ((X3 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Y3) (@ (@ tptp.ord_less_int (@ F2 X3)) (@ F2 Y3)))) (@ (@ tptp.ord_less_int (@ F2 A)) C2))))))
% 6.73/7.04 (assert (forall ((A tptp.rat) (B tptp.rat) (F2 (-> tptp.rat tptp.real)) (C2 tptp.real)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_real (@ F2 B)) C2) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y3) (@ (@ tptp.ord_less_real (@ F2 X3)) (@ F2 Y3)))) (@ (@ tptp.ord_less_real (@ F2 A)) C2))))))
% 6.73/7.04 (assert (forall ((A tptp.rat) (B tptp.rat) (F2 (-> tptp.rat tptp.rat)) (C2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_rat (@ F2 B)) C2) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y3) (@ (@ tptp.ord_less_rat (@ F2 X3)) (@ F2 Y3)))) (@ (@ tptp.ord_less_rat (@ F2 A)) C2))))))
% 6.73/7.04 (assert (forall ((A tptp.rat) (B tptp.rat) (F2 (-> tptp.rat tptp.num)) (C2 tptp.num)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_num (@ F2 B)) C2) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y3) (@ (@ tptp.ord_less_num (@ F2 X3)) (@ F2 Y3)))) (@ (@ tptp.ord_less_num (@ F2 A)) C2))))))
% 6.73/7.04 (assert (forall ((A tptp.rat) (B tptp.rat) (F2 (-> tptp.rat tptp.nat)) (C2 tptp.nat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_nat (@ F2 B)) C2) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y3) (@ (@ tptp.ord_less_nat (@ F2 X3)) (@ F2 Y3)))) (@ (@ tptp.ord_less_nat (@ F2 A)) C2))))))
% 6.73/7.04 (assert (forall ((A tptp.rat) (B tptp.rat) (F2 (-> tptp.rat tptp.int)) (C2 tptp.int)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_int (@ F2 B)) C2) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y3) (@ (@ tptp.ord_less_int (@ F2 X3)) (@ F2 Y3)))) (@ (@ tptp.ord_less_int (@ F2 A)) C2))))))
% 6.73/7.04 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X) Y) (not (@ (@ tptp.ord_less_real Y) X)))))
% 6.73/7.04 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat X) Y) (not (@ (@ tptp.ord_less_rat Y) X)))))
% 6.73/7.04 (assert (forall ((X tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_num X) Y) (not (@ (@ tptp.ord_less_num Y) X)))))
% 6.73/7.04 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Y) (not (@ (@ tptp.ord_less_nat Y) X)))))
% 6.73/7.04 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int X) Y) (not (@ (@ tptp.ord_less_int Y) X)))))
% 6.73/7.04 (assert (forall ((X tptp.real) (Y tptp.real) (P2 Bool)) (=> (@ (@ tptp.ord_less_real X) Y) (=> (@ (@ tptp.ord_less_real Y) X) P2))))
% 6.73/7.04 (assert (forall ((X tptp.rat) (Y tptp.rat) (P2 Bool)) (=> (@ (@ tptp.ord_less_rat X) Y) (=> (@ (@ tptp.ord_less_rat Y) X) P2))))
% 6.73/7.04 (assert (forall ((X tptp.num) (Y tptp.num) (P2 Bool)) (=> (@ (@ tptp.ord_less_num X) Y) (=> (@ (@ tptp.ord_less_num Y) X) P2))))
% 6.73/7.04 (assert (forall ((X tptp.nat) (Y tptp.nat) (P2 Bool)) (=> (@ (@ tptp.ord_less_nat X) Y) (=> (@ (@ tptp.ord_less_nat Y) X) P2))))
% 6.73/7.04 (assert (forall ((X tptp.int) (Y tptp.int) (P2 Bool)) (=> (@ (@ tptp.ord_less_int X) Y) (=> (@ (@ tptp.ord_less_int Y) X) P2))))
% 6.73/7.04 (assert (forall ((X tptp.real) (Y tptp.real)) (or (@ (@ tptp.ord_less_real X) Y) (= X Y) (@ (@ tptp.ord_less_real Y) X))))
% 6.73/7.04 (assert (forall ((X tptp.rat) (Y tptp.rat)) (or (@ (@ tptp.ord_less_rat X) Y) (= X Y) (@ (@ tptp.ord_less_rat Y) X))))
% 6.73/7.04 (assert (forall ((X tptp.num) (Y tptp.num)) (or (@ (@ tptp.ord_less_num X) Y) (= X Y) (@ (@ tptp.ord_less_num Y) X))))
% 6.73/7.04 (assert (forall ((X tptp.nat) (Y tptp.nat)) (or (@ (@ tptp.ord_less_nat X) Y) (= X Y) (@ (@ tptp.ord_less_nat Y) X))))
% 6.73/7.04 (assert (forall ((X tptp.int) (Y tptp.int)) (or (@ (@ tptp.ord_less_int X) Y) (= X Y) (@ (@ tptp.ord_less_int Y) X))))
% 6.73/7.04 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X) Y) (not (= X Y)))))
% 6.73/7.04 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat X) Y) (not (= X Y)))))
% 6.73/7.04 (assert (forall ((X tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_num X) Y) (not (= X Y)))))
% 6.73/7.04 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Y) (not (= X Y)))))
% 6.73/7.04 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int X) Y) (not (= X Y)))))
% 6.73/7.04 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X) Y) (not (= Y X)))))
% 6.73/7.04 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat X) Y) (not (= Y X)))))
% 6.73/7.04 (assert (forall ((X tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_num X) Y) (not (= Y X)))))
% 6.73/7.04 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Y) (not (= Y X)))))
% 6.73/7.04 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int X) Y) (not (= Y X)))))
% 6.73/7.04 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X) Y) (not (@ (@ tptp.ord_less_real Y) X)))))
% 6.73/7.04 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat X) Y) (not (@ (@ tptp.ord_less_rat Y) X)))))
% 6.73/7.04 (assert (forall ((X tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_num X) Y) (not (@ (@ tptp.ord_less_num Y) X)))))
% 6.73/7.04 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Y) (not (@ (@ tptp.ord_less_nat Y) X)))))
% 6.73/7.04 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int X) Y) (not (@ (@ tptp.ord_less_int Y) X)))))
% 6.73/7.04 (assert (not (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) tptp.one_one_Code_integer)))
% 6.73/7.04 (assert (not (@ (@ tptp.ord_less_real tptp.one_one_real) tptp.one_one_real)))
% 6.73/7.04 (assert (not (@ (@ tptp.ord_less_rat tptp.one_one_rat) tptp.one_one_rat)))
% 6.73/7.04 (assert (not (@ (@ tptp.ord_less_nat tptp.one_one_nat) tptp.one_one_nat)))
% 6.73/7.04 (assert (not (@ (@ tptp.ord_less_int tptp.one_one_int) tptp.one_one_int)))
% 6.73/7.04 (assert (forall ((X tptp.code_integer)) (= (= tptp.one_one_Code_integer X) (= X tptp.one_one_Code_integer))))
% 6.73/7.04 (assert (forall ((X tptp.complex)) (= (= tptp.one_one_complex X) (= X tptp.one_one_complex))))
% 6.73/7.04 (assert (forall ((X tptp.real)) (= (= tptp.one_one_real X) (= X tptp.one_one_real))))
% 6.73/7.04 (assert (forall ((X tptp.nat)) (= (= tptp.one_one_nat X) (= X tptp.one_one_nat))))
% 6.73/7.04 (assert (forall ((X tptp.int)) (= (= tptp.one_one_int X) (= X tptp.one_one_int))))
% 6.73/7.04 (assert (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) tptp.one_one_Code_integer))
% 6.73/7.04 (assert (@ (@ tptp.ord_less_real tptp.zero_zero_real) tptp.one_one_real))
% 6.73/7.04 (assert (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) tptp.one_one_rat))
% 6.73/7.04 (assert (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) tptp.one_one_nat))
% 6.73/7.04 (assert (@ (@ tptp.ord_less_int tptp.zero_zero_int) tptp.one_one_int))
% 6.73/7.04 (assert (not (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) tptp.zero_z3403309356797280102nteger)))
% 6.73/7.04 (assert (not (@ (@ tptp.ord_less_real tptp.one_one_real) tptp.zero_zero_real)))
% 6.73/7.04 (assert (not (@ (@ tptp.ord_less_rat tptp.one_one_rat) tptp.zero_zero_rat)))
% 6.73/7.04 (assert (not (@ (@ tptp.ord_less_nat tptp.one_one_nat) tptp.zero_zero_nat)))
% 6.73/7.04 (assert (not (@ (@ tptp.ord_less_int tptp.one_one_int) tptp.zero_zero_int)))
% 6.73/7.04 (assert (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) tptp.one_one_Code_integer))
% 6.73/7.04 (assert (@ (@ tptp.ord_less_real tptp.zero_zero_real) tptp.one_one_real))
% 6.73/7.04 (assert (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) tptp.one_one_rat))
% 6.73/7.04 (assert (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) tptp.one_one_nat))
% 6.73/7.04 (assert (@ (@ tptp.ord_less_int tptp.zero_zero_int) tptp.one_one_int))
% 6.73/7.04 (assert (forall ((F2 (-> tptp.nat tptp.real)) (N tptp.nat) (M2 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_real (@ F2 N3)) (@ F2 (@ tptp.suc N3)))) (= (@ (@ tptp.ord_less_real (@ F2 N)) (@ F2 M2)) (@ (@ tptp.ord_less_nat N) M2)))))
% 6.73/7.04 (assert (forall ((F2 (-> tptp.nat tptp.rat)) (N tptp.nat) (M2 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_rat (@ F2 N3)) (@ F2 (@ tptp.suc N3)))) (= (@ (@ tptp.ord_less_rat (@ F2 N)) (@ F2 M2)) (@ (@ tptp.ord_less_nat N) M2)))))
% 6.73/7.04 (assert (forall ((F2 (-> tptp.nat tptp.num)) (N tptp.nat) (M2 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_num (@ F2 N3)) (@ F2 (@ tptp.suc N3)))) (= (@ (@ tptp.ord_less_num (@ F2 N)) (@ F2 M2)) (@ (@ tptp.ord_less_nat N) M2)))))
% 6.73/7.04 (assert (forall ((F2 (-> tptp.nat tptp.nat)) (N tptp.nat) (M2 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_nat (@ F2 N3)) (@ F2 (@ tptp.suc N3)))) (= (@ (@ tptp.ord_less_nat (@ F2 N)) (@ F2 M2)) (@ (@ tptp.ord_less_nat N) M2)))))
% 6.73/7.04 (assert (forall ((F2 (-> tptp.nat tptp.int)) (N tptp.nat) (M2 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_int (@ F2 N3)) (@ F2 (@ tptp.suc N3)))) (= (@ (@ tptp.ord_less_int (@ F2 N)) (@ F2 M2)) (@ (@ tptp.ord_less_nat N) M2)))))
% 6.73/7.04 (assert (forall ((F2 (-> tptp.nat tptp.real)) (N tptp.nat) (N2 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_real (@ F2 N3)) (@ F2 (@ tptp.suc N3)))) (=> (@ (@ tptp.ord_less_nat N) N2) (@ (@ tptp.ord_less_real (@ F2 N)) (@ F2 N2))))))
% 6.73/7.04 (assert (forall ((F2 (-> tptp.nat tptp.rat)) (N tptp.nat) (N2 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_rat (@ F2 N3)) (@ F2 (@ tptp.suc N3)))) (=> (@ (@ tptp.ord_less_nat N) N2) (@ (@ tptp.ord_less_rat (@ F2 N)) (@ F2 N2))))))
% 6.73/7.04 (assert (forall ((F2 (-> tptp.nat tptp.num)) (N tptp.nat) (N2 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_num (@ F2 N3)) (@ F2 (@ tptp.suc N3)))) (=> (@ (@ tptp.ord_less_nat N) N2) (@ (@ tptp.ord_less_num (@ F2 N)) (@ F2 N2))))))
% 6.73/7.04 (assert (forall ((F2 (-> tptp.nat tptp.nat)) (N tptp.nat) (N2 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_nat (@ F2 N3)) (@ F2 (@ tptp.suc N3)))) (=> (@ (@ tptp.ord_less_nat N) N2) (@ (@ tptp.ord_less_nat (@ F2 N)) (@ F2 N2))))))
% 6.73/7.04 (assert (forall ((F2 (-> tptp.nat tptp.int)) (N tptp.nat) (N2 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_int (@ F2 N3)) (@ F2 (@ tptp.suc N3)))) (=> (@ (@ tptp.ord_less_nat N) N2) (@ (@ tptp.ord_less_int (@ F2 N)) (@ F2 N2))))))
% 6.73/7.04 (assert (forall ((M2 tptp.code_integer) (N tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer))) (=> (@ _let_1 M2) (=> (@ _let_1 N) (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger M2) N)))))))
% 6.73/7.04 (assert (forall ((M2 tptp.real) (N tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ _let_1 M2) (=> (@ _let_1 N) (@ _let_1 (@ (@ tptp.times_times_real M2) N)))))))
% 6.73/7.04 (assert (forall ((M2 tptp.rat) (N tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.one_one_rat))) (=> (@ _let_1 M2) (=> (@ _let_1 N) (@ _let_1 (@ (@ tptp.times_times_rat M2) N)))))))
% 6.73/7.04 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.one_one_nat))) (=> (@ _let_1 M2) (=> (@ _let_1 N) (@ _let_1 (@ (@ tptp.times_times_nat M2) N)))))))
% 6.73/7.04 (assert (forall ((M2 tptp.int) (N tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.one_one_int))) (=> (@ _let_1 M2) (=> (@ _let_1 N) (@ _let_1 (@ (@ tptp.times_times_int M2) N)))))))
% 6.73/7.04 (assert (forall ((Uu Bool) (Uv Bool) (D tptp.nat)) (= (@ (@ tptp.vEBT_VEBT_valid (@ (@ tptp.vEBT_Leaf Uu) Uv)) D) (= D tptp.one_one_nat))))
% 6.73/7.04 (assert (forall ((N tptp.nat) (P2 (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ P2 tptp.one_one_nat) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N3) (=> (@ P2 N3) (@ P2 (@ tptp.suc N3))))) (@ P2 N))))))
% 6.73/7.04 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) Y) (or (@ (@ tptp.ord_less_real X) Y) (= X Y)))))
% 6.73/7.04 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat X) Y) (or (@ (@ tptp.ord_less_set_nat X) Y) (= X Y)))))
% 6.73/7.04 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X) Y) (or (@ (@ tptp.ord_less_rat X) Y) (= X Y)))))
% 6.73/7.04 (assert (forall ((X tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X) Y) (or (@ (@ tptp.ord_less_num X) Y) (= X Y)))))
% 6.73/7.04 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X) Y) (or (@ (@ tptp.ord_less_nat X) Y) (= X Y)))))
% 6.73/7.04 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X) Y) (or (@ (@ tptp.ord_less_int X) Y) (= X Y)))))
% 6.73/7.04 (assert (forall ((X tptp.real) (Y tptp.real)) (or (@ (@ tptp.ord_less_eq_real X) Y) (@ (@ tptp.ord_less_real Y) X))))
% 6.73/7.04 (assert (forall ((X tptp.rat) (Y tptp.rat)) (or (@ (@ tptp.ord_less_eq_rat X) Y) (@ (@ tptp.ord_less_rat Y) X))))
% 6.73/7.04 (assert (forall ((X tptp.num) (Y tptp.num)) (or (@ (@ tptp.ord_less_eq_num X) Y) (@ (@ tptp.ord_less_num Y) X))))
% 6.73/7.04 (assert (forall ((X tptp.nat) (Y tptp.nat)) (or (@ (@ tptp.ord_less_eq_nat X) Y) (@ (@ tptp.ord_less_nat Y) X))))
% 6.73/7.04 (assert (forall ((X tptp.int) (Y tptp.int)) (or (@ (@ tptp.ord_less_eq_int X) Y) (@ (@ tptp.ord_less_int Y) X))))
% 6.73/7.04 (assert (forall ((A tptp.real) (B tptp.real) (F2 (-> tptp.real tptp.real)) (C2 tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_eq_real (@ F2 B)) C2) (=> (forall ((X3 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Y3) (@ (@ tptp.ord_less_real (@ F2 X3)) (@ F2 Y3)))) (@ (@ tptp.ord_less_real (@ F2 A)) C2))))))
% 6.73/7.04 (assert (forall ((A tptp.rat) (B tptp.rat) (F2 (-> tptp.rat tptp.real)) (C2 tptp.real)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_eq_real (@ F2 B)) C2) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y3) (@ (@ tptp.ord_less_real (@ F2 X3)) (@ F2 Y3)))) (@ (@ tptp.ord_less_real (@ F2 A)) C2))))))
% 6.73/7.04 (assert (forall ((A tptp.num) (B tptp.num) (F2 (-> tptp.num tptp.real)) (C2 tptp.real)) (=> (@ (@ tptp.ord_less_num A) B) (=> (@ (@ tptp.ord_less_eq_real (@ F2 B)) C2) (=> (forall ((X3 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_num X3) Y3) (@ (@ tptp.ord_less_real (@ F2 X3)) (@ F2 Y3)))) (@ (@ tptp.ord_less_real (@ F2 A)) C2))))))
% 6.73/7.04 (assert (forall ((A tptp.nat) (B tptp.nat) (F2 (-> tptp.nat tptp.real)) (C2 tptp.real)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_eq_real (@ F2 B)) C2) (=> (forall ((X3 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Y3) (@ (@ tptp.ord_less_real (@ F2 X3)) (@ F2 Y3)))) (@ (@ tptp.ord_less_real (@ F2 A)) C2))))))
% 6.73/7.04 (assert (forall ((A tptp.int) (B tptp.int) (F2 (-> tptp.int tptp.real)) (C2 tptp.real)) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_eq_real (@ F2 B)) C2) (=> (forall ((X3 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Y3) (@ (@ tptp.ord_less_real (@ F2 X3)) (@ F2 Y3)))) (@ (@ tptp.ord_less_real (@ F2 A)) C2))))))
% 6.73/7.04 (assert (forall ((A tptp.real) (B tptp.real) (F2 (-> tptp.real tptp.rat)) (C2 tptp.rat)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_eq_rat (@ F2 B)) C2) (=> (forall ((X3 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Y3) (@ (@ tptp.ord_less_rat (@ F2 X3)) (@ F2 Y3)))) (@ (@ tptp.ord_less_rat (@ F2 A)) C2))))))
% 6.73/7.04 (assert (forall ((A tptp.rat) (B tptp.rat) (F2 (-> tptp.rat tptp.rat)) (C2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat (@ F2 B)) C2) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y3) (@ (@ tptp.ord_less_rat (@ F2 X3)) (@ F2 Y3)))) (@ (@ tptp.ord_less_rat (@ F2 A)) C2))))))
% 6.73/7.04 (assert (forall ((A tptp.num) (B tptp.num) (F2 (-> tptp.num tptp.rat)) (C2 tptp.rat)) (=> (@ (@ tptp.ord_less_num A) B) (=> (@ (@ tptp.ord_less_eq_rat (@ F2 B)) C2) (=> (forall ((X3 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_num X3) Y3) (@ (@ tptp.ord_less_rat (@ F2 X3)) (@ F2 Y3)))) (@ (@ tptp.ord_less_rat (@ F2 A)) C2))))))
% 6.73/7.04 (assert (forall ((A tptp.nat) (B tptp.nat) (F2 (-> tptp.nat tptp.rat)) (C2 tptp.rat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_eq_rat (@ F2 B)) C2) (=> (forall ((X3 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Y3) (@ (@ tptp.ord_less_rat (@ F2 X3)) (@ F2 Y3)))) (@ (@ tptp.ord_less_rat (@ F2 A)) C2))))))
% 6.73/7.04 (assert (forall ((A tptp.int) (B tptp.int) (F2 (-> tptp.int tptp.rat)) (C2 tptp.rat)) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_eq_rat (@ F2 B)) C2) (=> (forall ((X3 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Y3) (@ (@ tptp.ord_less_rat (@ F2 X3)) (@ F2 Y3)))) (@ (@ tptp.ord_less_rat (@ F2 A)) C2))))))
% 6.73/7.04 (assert (forall ((A tptp.real) (F2 (-> tptp.rat tptp.real)) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_real A))) (=> (@ _let_1 (@ F2 B)) (=> (@ (@ tptp.ord_less_eq_rat B) C2) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y3) (@ (@ tptp.ord_less_eq_real (@ F2 X3)) (@ F2 Y3)))) (@ _let_1 (@ F2 C2))))))))
% 6.73/7.04 (assert (forall ((A tptp.rat) (F2 (-> tptp.rat tptp.rat)) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A))) (=> (@ _let_1 (@ F2 B)) (=> (@ (@ tptp.ord_less_eq_rat B) C2) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y3) (@ (@ tptp.ord_less_eq_rat (@ F2 X3)) (@ F2 Y3)))) (@ _let_1 (@ F2 C2))))))))
% 6.73/7.04 (assert (forall ((A tptp.num) (F2 (-> tptp.rat tptp.num)) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_num A))) (=> (@ _let_1 (@ F2 B)) (=> (@ (@ tptp.ord_less_eq_rat B) C2) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y3) (@ (@ tptp.ord_less_eq_num (@ F2 X3)) (@ F2 Y3)))) (@ _let_1 (@ F2 C2))))))))
% 6.73/7.04 (assert (forall ((A tptp.nat) (F2 (-> tptp.rat tptp.nat)) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_nat A))) (=> (@ _let_1 (@ F2 B)) (=> (@ (@ tptp.ord_less_eq_rat B) C2) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y3) (@ (@ tptp.ord_less_eq_nat (@ F2 X3)) (@ F2 Y3)))) (@ _let_1 (@ F2 C2))))))))
% 6.73/7.04 (assert (forall ((A tptp.int) (F2 (-> tptp.rat tptp.int)) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_int A))) (=> (@ _let_1 (@ F2 B)) (=> (@ (@ tptp.ord_less_eq_rat B) C2) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y3) (@ (@ tptp.ord_less_eq_int (@ F2 X3)) (@ F2 Y3)))) (@ _let_1 (@ F2 C2))))))))
% 6.73/7.04 (assert (forall ((A tptp.real) (F2 (-> tptp.num tptp.real)) (B tptp.num) (C2 tptp.num)) (let ((_let_1 (@ tptp.ord_less_real A))) (=> (@ _let_1 (@ F2 B)) (=> (@ (@ tptp.ord_less_eq_num B) C2) (=> (forall ((X3 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y3) (@ (@ tptp.ord_less_eq_real (@ F2 X3)) (@ F2 Y3)))) (@ _let_1 (@ F2 C2))))))))
% 6.73/7.04 (assert (forall ((A tptp.rat) (F2 (-> tptp.num tptp.rat)) (B tptp.num) (C2 tptp.num)) (let ((_let_1 (@ tptp.ord_less_rat A))) (=> (@ _let_1 (@ F2 B)) (=> (@ (@ tptp.ord_less_eq_num B) C2) (=> (forall ((X3 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y3) (@ (@ tptp.ord_less_eq_rat (@ F2 X3)) (@ F2 Y3)))) (@ _let_1 (@ F2 C2))))))))
% 6.73/7.04 (assert (forall ((A tptp.num) (F2 (-> tptp.num tptp.num)) (B tptp.num) (C2 tptp.num)) (let ((_let_1 (@ tptp.ord_less_num A))) (=> (@ _let_1 (@ F2 B)) (=> (@ (@ tptp.ord_less_eq_num B) C2) (=> (forall ((X3 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y3) (@ (@ tptp.ord_less_eq_num (@ F2 X3)) (@ F2 Y3)))) (@ _let_1 (@ F2 C2))))))))
% 6.73/7.04 (assert (forall ((A tptp.nat) (F2 (-> tptp.num tptp.nat)) (B tptp.num) (C2 tptp.num)) (let ((_let_1 (@ tptp.ord_less_nat A))) (=> (@ _let_1 (@ F2 B)) (=> (@ (@ tptp.ord_less_eq_num B) C2) (=> (forall ((X3 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y3) (@ (@ tptp.ord_less_eq_nat (@ F2 X3)) (@ F2 Y3)))) (@ _let_1 (@ F2 C2))))))))
% 6.73/7.04 (assert (forall ((A tptp.int) (F2 (-> tptp.num tptp.int)) (B tptp.num) (C2 tptp.num)) (let ((_let_1 (@ tptp.ord_less_int A))) (=> (@ _let_1 (@ F2 B)) (=> (@ (@ tptp.ord_less_eq_num B) C2) (=> (forall ((X3 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y3) (@ (@ tptp.ord_less_eq_int (@ F2 X3)) (@ F2 Y3)))) (@ _let_1 (@ F2 C2))))))))
% 6.73/7.04 (assert (forall ((A tptp.rat) (B tptp.rat) (F2 (-> tptp.rat tptp.real)) (C2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_real (@ F2 B)) C2) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y3) (@ (@ tptp.ord_less_eq_real (@ F2 X3)) (@ F2 Y3)))) (@ (@ tptp.ord_less_real (@ F2 A)) C2))))))
% 6.73/7.04 (assert (forall ((A tptp.rat) (B tptp.rat) (F2 (-> tptp.rat tptp.rat)) (C2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_rat (@ F2 B)) C2) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y3) (@ (@ tptp.ord_less_eq_rat (@ F2 X3)) (@ F2 Y3)))) (@ (@ tptp.ord_less_rat (@ F2 A)) C2))))))
% 6.73/7.04 (assert (forall ((A tptp.rat) (B tptp.rat) (F2 (-> tptp.rat tptp.num)) (C2 tptp.num)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_num (@ F2 B)) C2) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y3) (@ (@ tptp.ord_less_eq_num (@ F2 X3)) (@ F2 Y3)))) (@ (@ tptp.ord_less_num (@ F2 A)) C2))))))
% 6.73/7.04 (assert (forall ((A tptp.rat) (B tptp.rat) (F2 (-> tptp.rat tptp.nat)) (C2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_nat (@ F2 B)) C2) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y3) (@ (@ tptp.ord_less_eq_nat (@ F2 X3)) (@ F2 Y3)))) (@ (@ tptp.ord_less_nat (@ F2 A)) C2))))))
% 6.73/7.04 (assert (forall ((A tptp.rat) (B tptp.rat) (F2 (-> tptp.rat tptp.int)) (C2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_int (@ F2 B)) C2) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y3) (@ (@ tptp.ord_less_eq_int (@ F2 X3)) (@ F2 Y3)))) (@ (@ tptp.ord_less_int (@ F2 A)) C2))))))
% 6.73/7.04 (assert (forall ((A tptp.num) (B tptp.num) (F2 (-> tptp.num tptp.real)) (C2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (@ (@ tptp.ord_less_real (@ F2 B)) C2) (=> (forall ((X3 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y3) (@ (@ tptp.ord_less_eq_real (@ F2 X3)) (@ F2 Y3)))) (@ (@ tptp.ord_less_real (@ F2 A)) C2))))))
% 6.73/7.04 (assert (forall ((A tptp.num) (B tptp.num) (F2 (-> tptp.num tptp.rat)) (C2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (@ (@ tptp.ord_less_rat (@ F2 B)) C2) (=> (forall ((X3 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y3) (@ (@ tptp.ord_less_eq_rat (@ F2 X3)) (@ F2 Y3)))) (@ (@ tptp.ord_less_rat (@ F2 A)) C2))))))
% 6.73/7.04 (assert (forall ((A tptp.num) (B tptp.num) (F2 (-> tptp.num tptp.num)) (C2 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (@ (@ tptp.ord_less_num (@ F2 B)) C2) (=> (forall ((X3 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y3) (@ (@ tptp.ord_less_eq_num (@ F2 X3)) (@ F2 Y3)))) (@ (@ tptp.ord_less_num (@ F2 A)) C2))))))
% 6.73/7.04 (assert (forall ((A tptp.num) (B tptp.num) (F2 (-> tptp.num tptp.nat)) (C2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (@ (@ tptp.ord_less_nat (@ F2 B)) C2) (=> (forall ((X3 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y3) (@ (@ tptp.ord_less_eq_nat (@ F2 X3)) (@ F2 Y3)))) (@ (@ tptp.ord_less_nat (@ F2 A)) C2))))))
% 6.73/7.04 (assert (forall ((A tptp.num) (B tptp.num) (F2 (-> tptp.num tptp.int)) (C2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (@ (@ tptp.ord_less_int (@ F2 B)) C2) (=> (forall ((X3 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y3) (@ (@ tptp.ord_less_eq_int (@ F2 X3)) (@ F2 Y3)))) (@ (@ tptp.ord_less_int (@ F2 A)) C2))))))
% 6.73/7.04 (assert (forall ((A tptp.real) (F2 (-> tptp.real tptp.real)) (B tptp.real) (C2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) (@ F2 B)) (=> (@ (@ tptp.ord_less_real B) C2) (=> (forall ((X3 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Y3) (@ (@ tptp.ord_less_real (@ F2 X3)) (@ F2 Y3)))) (@ (@ tptp.ord_less_real A) (@ F2 C2)))))))
% 6.73/7.04 (assert (forall ((A tptp.real) (F2 (-> tptp.rat tptp.real)) (B tptp.rat) (C2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_real A) (@ F2 B)) (=> (@ (@ tptp.ord_less_rat B) C2) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y3) (@ (@ tptp.ord_less_real (@ F2 X3)) (@ F2 Y3)))) (@ (@ tptp.ord_less_real A) (@ F2 C2)))))))
% 6.73/7.04 (assert (forall ((A tptp.real) (F2 (-> tptp.num tptp.real)) (B tptp.num) (C2 tptp.num)) (=> (@ (@ tptp.ord_less_eq_real A) (@ F2 B)) (=> (@ (@ tptp.ord_less_num B) C2) (=> (forall ((X3 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_num X3) Y3) (@ (@ tptp.ord_less_real (@ F2 X3)) (@ F2 Y3)))) (@ (@ tptp.ord_less_real A) (@ F2 C2)))))))
% 6.73/7.04 (assert (forall ((A tptp.real) (F2 (-> tptp.nat tptp.real)) (B tptp.nat) (C2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_real A) (@ F2 B)) (=> (@ (@ tptp.ord_less_nat B) C2) (=> (forall ((X3 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Y3) (@ (@ tptp.ord_less_real (@ F2 X3)) (@ F2 Y3)))) (@ (@ tptp.ord_less_real A) (@ F2 C2)))))))
% 6.73/7.04 (assert (forall ((A tptp.real) (F2 (-> tptp.int tptp.real)) (B tptp.int) (C2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_real A) (@ F2 B)) (=> (@ (@ tptp.ord_less_int B) C2) (=> (forall ((X3 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Y3) (@ (@ tptp.ord_less_real (@ F2 X3)) (@ F2 Y3)))) (@ (@ tptp.ord_less_real A) (@ F2 C2)))))))
% 6.73/7.04 (assert (forall ((A tptp.rat) (F2 (-> tptp.real tptp.rat)) (B tptp.real) (C2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_rat A) (@ F2 B)) (=> (@ (@ tptp.ord_less_real B) C2) (=> (forall ((X3 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Y3) (@ (@ tptp.ord_less_rat (@ F2 X3)) (@ F2 Y3)))) (@ (@ tptp.ord_less_rat A) (@ F2 C2)))))))
% 6.73/7.04 (assert (forall ((A tptp.rat) (F2 (-> tptp.rat tptp.rat)) (B tptp.rat) (C2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) (@ F2 B)) (=> (@ (@ tptp.ord_less_rat B) C2) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y3) (@ (@ tptp.ord_less_rat (@ F2 X3)) (@ F2 Y3)))) (@ (@ tptp.ord_less_rat A) (@ F2 C2)))))))
% 6.73/7.04 (assert (forall ((A tptp.rat) (F2 (-> tptp.num tptp.rat)) (B tptp.num) (C2 tptp.num)) (=> (@ (@ tptp.ord_less_eq_rat A) (@ F2 B)) (=> (@ (@ tptp.ord_less_num B) C2) (=> (forall ((X3 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_num X3) Y3) (@ (@ tptp.ord_less_rat (@ F2 X3)) (@ F2 Y3)))) (@ (@ tptp.ord_less_rat A) (@ F2 C2)))))))
% 6.73/7.04 (assert (forall ((A tptp.rat) (F2 (-> tptp.nat tptp.rat)) (B tptp.nat) (C2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_rat A) (@ F2 B)) (=> (@ (@ tptp.ord_less_nat B) C2) (=> (forall ((X3 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Y3) (@ (@ tptp.ord_less_rat (@ F2 X3)) (@ F2 Y3)))) (@ (@ tptp.ord_less_rat A) (@ F2 C2)))))))
% 6.73/7.04 (assert (forall ((A tptp.rat) (F2 (-> tptp.int tptp.rat)) (B tptp.int) (C2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_rat A) (@ F2 B)) (=> (@ (@ tptp.ord_less_int B) C2) (=> (forall ((X3 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Y3) (@ (@ tptp.ord_less_rat (@ F2 X3)) (@ F2 Y3)))) (@ (@ tptp.ord_less_rat A) (@ F2 C2)))))))
% 6.73/7.04 (assert (forall ((X tptp.real) (Y tptp.real) (Z3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_real Y) Z3) (@ _let_1 Z3))))))
% 6.73/7.04 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat) (Z3 tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_set_nat X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_set_nat Y) Z3) (@ _let_1 Z3))))))
% 6.73/7.04 (assert (forall ((X tptp.rat) (Y tptp.rat) (Z3 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_rat Y) Z3) (@ _let_1 Z3))))))
% 6.73/7.04 (assert (forall ((X tptp.num) (Y tptp.num) (Z3 tptp.num)) (let ((_let_1 (@ tptp.ord_less_num X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_num Y) Z3) (@ _let_1 Z3))))))
% 6.73/7.04 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z3 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_nat Y) Z3) (@ _let_1 Z3))))))
% 6.73/7.04 (assert (forall ((X tptp.int) (Y tptp.int) (Z3 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_int Y) Z3) (@ _let_1 Z3))))))
% 6.73/7.04 (assert (forall ((X tptp.real) (Y tptp.real) (Z3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) Y) (=> (@ (@ tptp.ord_less_real Y) Z3) (@ (@ tptp.ord_less_real X) Z3)))))
% 6.73/7.04 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat) (Z3 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat X) Y) (=> (@ (@ tptp.ord_less_set_nat Y) Z3) (@ (@ tptp.ord_less_set_nat X) Z3)))))
% 6.73/7.04 (assert (forall ((X tptp.rat) (Y tptp.rat) (Z3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X) Y) (=> (@ (@ tptp.ord_less_rat Y) Z3) (@ (@ tptp.ord_less_rat X) Z3)))))
% 6.73/7.04 (assert (forall ((X tptp.num) (Y tptp.num) (Z3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X) Y) (=> (@ (@ tptp.ord_less_num Y) Z3) (@ (@ tptp.ord_less_num X) Z3)))))
% 6.73/7.04 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X) Y) (=> (@ (@ tptp.ord_less_nat Y) Z3) (@ (@ tptp.ord_less_nat X) Z3)))))
% 6.73/7.04 (assert (forall ((X tptp.int) (Y tptp.int) (Z3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X) Y) (=> (@ (@ tptp.ord_less_int Y) Z3) (@ (@ tptp.ord_less_int X) Z3)))))
% 6.73/7.04 (assert (forall ((A tptp.real) (B tptp.real)) (=> (not (= A B)) (=> (@ (@ tptp.ord_less_eq_real A) B) (@ (@ tptp.ord_less_real A) B)))))
% 6.73/7.04 (assert (forall ((A tptp.set_nat) (B tptp.set_nat)) (=> (not (= A B)) (=> (@ (@ tptp.ord_less_eq_set_nat A) B) (@ (@ tptp.ord_less_set_nat A) B)))))
% 6.73/7.04 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (not (= A B)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (@ (@ tptp.ord_less_rat A) B)))))
% 6.73/7.04 (assert (forall ((A tptp.num) (B tptp.num)) (=> (not (= A B)) (=> (@ (@ tptp.ord_less_eq_num A) B) (@ (@ tptp.ord_less_num A) B)))))
% 6.73/7.04 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (not (= A B)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (@ (@ tptp.ord_less_nat A) B)))))
% 6.73/7.04 (assert (forall ((A tptp.int) (B tptp.int)) (=> (not (= A B)) (=> (@ (@ tptp.ord_less_eq_int A) B) (@ (@ tptp.ord_less_int A) B)))))
% 6.73/7.04 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (not (= A B)) (@ (@ tptp.ord_less_real A) B)))))
% 6.73/7.04 (assert (forall ((A tptp.set_nat) (B tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A) B) (=> (not (= A B)) (@ (@ tptp.ord_less_set_nat A) B)))))
% 6.73/7.04 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (not (= A B)) (@ (@ tptp.ord_less_rat A) B)))))
% 6.73/7.04 (assert (forall ((A tptp.num) (B tptp.num)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (not (= A B)) (@ (@ tptp.ord_less_num A) B)))))
% 6.73/7.04 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (not (= A B)) (@ (@ tptp.ord_less_nat A) B)))))
% 6.73/7.04 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (not (= A B)) (@ (@ tptp.ord_less_int A) B)))))
% 6.73/7.04 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X) Y) (@ (@ tptp.ord_less_eq_real X) Y))))
% 6.73/7.04 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat X) Y) (@ (@ tptp.ord_less_eq_set_nat X) Y))))
% 6.73/7.04 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat X) Y) (@ (@ tptp.ord_less_eq_rat X) Y))))
% 6.73/7.04 (assert (forall ((X tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_num X) Y) (@ (@ tptp.ord_less_eq_num X) Y))))
% 6.73/7.04 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Y) (@ (@ tptp.ord_less_eq_nat X) Y))))
% 6.73/7.04 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int X) Y) (@ (@ tptp.ord_less_eq_int X) Y))))
% 6.73/7.04 (assert (forall ((X tptp.real) (Y tptp.real)) (= (not (@ (@ tptp.ord_less_real X) Y)) (@ (@ tptp.ord_less_eq_real Y) X))))
% 6.73/7.04 (assert (forall ((X tptp.rat) (Y tptp.rat)) (= (not (@ (@ tptp.ord_less_rat X) Y)) (@ (@ tptp.ord_less_eq_rat Y) X))))
% 6.73/7.04 (assert (forall ((X tptp.num) (Y tptp.num)) (= (not (@ (@ tptp.ord_less_num X) Y)) (@ (@ tptp.ord_less_eq_num Y) X))))
% 6.73/7.04 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (not (@ (@ tptp.ord_less_nat X) Y)) (@ (@ tptp.ord_less_eq_nat Y) X))))
% 6.73/7.04 (assert (forall ((X tptp.int) (Y tptp.int)) (= (not (@ (@ tptp.ord_less_int X) Y)) (@ (@ tptp.ord_less_eq_int Y) X))))
% 6.73/7.04 (assert (forall ((X tptp.real) (Y tptp.real)) (= (not (@ (@ tptp.ord_less_eq_real X) Y)) (@ (@ tptp.ord_less_real Y) X))))
% 6.73/7.04 (assert (forall ((X tptp.rat) (Y tptp.rat)) (= (not (@ (@ tptp.ord_less_eq_rat X) Y)) (@ (@ tptp.ord_less_rat Y) X))))
% 6.73/7.04 (assert (forall ((X tptp.num) (Y tptp.num)) (= (not (@ (@ tptp.ord_less_eq_num X) Y)) (@ (@ tptp.ord_less_num Y) X))))
% 6.73/7.04 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (not (@ (@ tptp.ord_less_eq_nat X) Y)) (@ (@ tptp.ord_less_nat Y) X))))
% 6.73/7.04 (assert (forall ((X tptp.int) (Y tptp.int)) (= (not (@ (@ tptp.ord_less_eq_int X) Y)) (@ (@ tptp.ord_less_int Y) X))))
% 6.73/7.04 (assert (= tptp.ord_less_real (lambda ((X4 tptp.real) (Y4 tptp.real)) (and (@ (@ tptp.ord_less_eq_real X4) Y4) (not (= X4 Y4))))))
% 6.73/7.04 (assert (= tptp.ord_less_set_nat (lambda ((X4 tptp.set_nat) (Y4 tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat X4) Y4) (not (= X4 Y4))))))
% 6.73/7.04 (assert (= tptp.ord_less_rat (lambda ((X4 tptp.rat) (Y4 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat X4) Y4) (not (= X4 Y4))))))
% 6.73/7.04 (assert (= tptp.ord_less_num (lambda ((X4 tptp.num) (Y4 tptp.num)) (and (@ (@ tptp.ord_less_eq_num X4) Y4) (not (= X4 Y4))))))
% 6.73/7.04 (assert (= tptp.ord_less_nat (lambda ((X4 tptp.nat) (Y4 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat X4) Y4) (not (= X4 Y4))))))
% 6.73/7.04 (assert (= tptp.ord_less_int (lambda ((X4 tptp.int) (Y4 tptp.int)) (and (@ (@ tptp.ord_less_eq_int X4) Y4) (not (= X4 Y4))))))
% 6.73/7.04 (assert (= tptp.ord_less_eq_real (lambda ((X4 tptp.real) (Y4 tptp.real)) (or (@ (@ tptp.ord_less_real X4) Y4) (= X4 Y4)))))
% 6.73/7.04 (assert (= tptp.ord_less_eq_set_nat (lambda ((X4 tptp.set_nat) (Y4 tptp.set_nat)) (or (@ (@ tptp.ord_less_set_nat X4) Y4) (= X4 Y4)))))
% 6.73/7.04 (assert (= tptp.ord_less_eq_rat (lambda ((X4 tptp.rat) (Y4 tptp.rat)) (or (@ (@ tptp.ord_less_rat X4) Y4) (= X4 Y4)))))
% 6.73/7.04 (assert (= tptp.ord_less_eq_num (lambda ((X4 tptp.num) (Y4 tptp.num)) (or (@ (@ tptp.ord_less_num X4) Y4) (= X4 Y4)))))
% 6.73/7.04 (assert (= tptp.ord_less_eq_nat (lambda ((X4 tptp.nat) (Y4 tptp.nat)) (or (@ (@ tptp.ord_less_nat X4) Y4) (= X4 Y4)))))
% 6.73/7.04 (assert (= tptp.ord_less_eq_int (lambda ((X4 tptp.int) (Y4 tptp.int)) (or (@ (@ tptp.ord_less_int X4) Y4) (= X4 Y4)))))
% 6.73/7.04 (assert (forall ((B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real B) A) (@ (@ tptp.ord_less_eq_real B) A))))
% 6.73/7.04 (assert (forall ((B tptp.set_nat) (A tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat B) A) (@ (@ tptp.ord_less_eq_set_nat B) A))))
% 6.73/7.04 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat B) A) (@ (@ tptp.ord_less_eq_rat B) A))))
% 6.73/7.04 (assert (forall ((B tptp.num) (A tptp.num)) (=> (@ (@ tptp.ord_less_num B) A) (@ (@ tptp.ord_less_eq_num B) A))))
% 6.73/7.04 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat B) A) (@ (@ tptp.ord_less_eq_nat B) A))))
% 6.73/7.04 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int B) A) (@ (@ tptp.ord_less_eq_int B) A))))
% 6.73/7.04 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (@ (@ tptp.ord_less_eq_real A) B))))
% 6.73/7.04 (assert (forall ((A tptp.set_nat) (B tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat A) B) (@ (@ tptp.ord_less_eq_set_nat A) B))))
% 6.73/7.04 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (@ (@ tptp.ord_less_eq_rat A) B))))
% 6.73/7.04 (assert (forall ((A tptp.num) (B tptp.num)) (=> (@ (@ tptp.ord_less_num A) B) (@ (@ tptp.ord_less_eq_num A) B))))
% 6.73/7.04 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (@ (@ tptp.ord_less_eq_nat A) B))))
% 6.73/7.04 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (@ (@ tptp.ord_less_eq_int A) B))))
% 6.73/7.04 (assert (= tptp.ord_less_real (lambda ((B4 tptp.real) (A5 tptp.real)) (and (@ (@ tptp.ord_less_eq_real B4) A5) (not (@ (@ tptp.ord_less_eq_real A5) B4))))))
% 6.73/7.04 (assert (= tptp.ord_less_set_nat (lambda ((B4 tptp.set_nat) (A5 tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat B4) A5) (not (@ (@ tptp.ord_less_eq_set_nat A5) B4))))))
% 6.73/7.04 (assert (= tptp.ord_less_rat (lambda ((B4 tptp.rat) (A5 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat B4) A5) (not (@ (@ tptp.ord_less_eq_rat A5) B4))))))
% 6.73/7.04 (assert (= tptp.ord_less_num (lambda ((B4 tptp.num) (A5 tptp.num)) (and (@ (@ tptp.ord_less_eq_num B4) A5) (not (@ (@ tptp.ord_less_eq_num A5) B4))))))
% 6.73/7.04 (assert (= tptp.ord_less_nat (lambda ((B4 tptp.nat) (A5 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat B4) A5) (not (@ (@ tptp.ord_less_eq_nat A5) B4))))))
% 6.73/7.04 (assert (= tptp.ord_less_int (lambda ((B4 tptp.int) (A5 tptp.int)) (and (@ (@ tptp.ord_less_eq_int B4) A5) (not (@ (@ tptp.ord_less_eq_int A5) B4))))))
% 6.73/7.04 (assert (forall ((B tptp.real) (A tptp.real) (C2 tptp.real)) (=> (@ (@ tptp.ord_less_real B) A) (=> (@ (@ tptp.ord_less_eq_real C2) B) (@ (@ tptp.ord_less_real C2) A)))))
% 6.73/7.04 (assert (forall ((B tptp.set_nat) (A tptp.set_nat) (C2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat B) A) (=> (@ (@ tptp.ord_less_eq_set_nat C2) B) (@ (@ tptp.ord_less_set_nat C2) A)))))
% 6.73/7.04 (assert (forall ((B tptp.rat) (A tptp.rat) (C2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat B) A) (=> (@ (@ tptp.ord_less_eq_rat C2) B) (@ (@ tptp.ord_less_rat C2) A)))))
% 6.73/7.04 (assert (forall ((B tptp.num) (A tptp.num) (C2 tptp.num)) (=> (@ (@ tptp.ord_less_num B) A) (=> (@ (@ tptp.ord_less_eq_num C2) B) (@ (@ tptp.ord_less_num C2) A)))))
% 6.73/7.04 (assert (forall ((B tptp.nat) (A tptp.nat) (C2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat B) A) (=> (@ (@ tptp.ord_less_eq_nat C2) B) (@ (@ tptp.ord_less_nat C2) A)))))
% 6.73/7.04 (assert (forall ((B tptp.int) (A tptp.int) (C2 tptp.int)) (=> (@ (@ tptp.ord_less_int B) A) (=> (@ (@ tptp.ord_less_eq_int C2) B) (@ (@ tptp.ord_less_int C2) A)))))
% 6.73/7.04 (assert (forall ((B tptp.real) (A tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real C2))) (=> (@ (@ tptp.ord_less_eq_real B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 6.73/7.04 (assert (forall ((B tptp.set_nat) (A tptp.set_nat) (C2 tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_set_nat C2))) (=> (@ (@ tptp.ord_less_eq_set_nat B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 6.73/7.04 (assert (forall ((B tptp.rat) (A tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat C2))) (=> (@ (@ tptp.ord_less_eq_rat B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 6.73/7.04 (assert (forall ((B tptp.num) (A tptp.num) (C2 tptp.num)) (let ((_let_1 (@ tptp.ord_less_num C2))) (=> (@ (@ tptp.ord_less_eq_num B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 6.73/7.04 (assert (forall ((B tptp.nat) (A tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat C2))) (=> (@ (@ tptp.ord_less_eq_nat B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 6.73/7.04 (assert (forall ((B tptp.int) (A tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int C2))) (=> (@ (@ tptp.ord_less_eq_int B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 6.73/7.04 (assert (= tptp.ord_less_real (lambda ((B4 tptp.real) (A5 tptp.real)) (and (@ (@ tptp.ord_less_eq_real B4) A5) (not (= A5 B4))))))
% 6.73/7.04 (assert (= tptp.ord_less_set_nat (lambda ((B4 tptp.set_nat) (A5 tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat B4) A5) (not (= A5 B4))))))
% 6.73/7.04 (assert (= tptp.ord_less_rat (lambda ((B4 tptp.rat) (A5 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat B4) A5) (not (= A5 B4))))))
% 6.73/7.04 (assert (= tptp.ord_less_num (lambda ((B4 tptp.num) (A5 tptp.num)) (and (@ (@ tptp.ord_less_eq_num B4) A5) (not (= A5 B4))))))
% 6.73/7.04 (assert (= tptp.ord_less_nat (lambda ((B4 tptp.nat) (A5 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat B4) A5) (not (= A5 B4))))))
% 6.73/7.04 (assert (= tptp.ord_less_int (lambda ((B4 tptp.int) (A5 tptp.int)) (and (@ (@ tptp.ord_less_eq_int B4) A5) (not (= A5 B4))))))
% 6.73/7.04 (assert (= tptp.ord_less_eq_real (lambda ((B4 tptp.real) (A5 tptp.real)) (or (@ (@ tptp.ord_less_real B4) A5) (= A5 B4)))))
% 6.73/7.04 (assert (= tptp.ord_less_eq_set_nat (lambda ((B4 tptp.set_nat) (A5 tptp.set_nat)) (or (@ (@ tptp.ord_less_set_nat B4) A5) (= A5 B4)))))
% 6.73/7.04 (assert (= tptp.ord_less_eq_rat (lambda ((B4 tptp.rat) (A5 tptp.rat)) (or (@ (@ tptp.ord_less_rat B4) A5) (= A5 B4)))))
% 6.73/7.04 (assert (= tptp.ord_less_eq_num (lambda ((B4 tptp.num) (A5 tptp.num)) (or (@ (@ tptp.ord_less_num B4) A5) (= A5 B4)))))
% 6.73/7.04 (assert (= tptp.ord_less_eq_nat (lambda ((B4 tptp.nat) (A5 tptp.nat)) (or (@ (@ tptp.ord_less_nat B4) A5) (= A5 B4)))))
% 6.73/7.04 (assert (= tptp.ord_less_eq_int (lambda ((B4 tptp.int) (A5 tptp.int)) (or (@ (@ tptp.ord_less_int B4) A5) (= A5 B4)))))
% 6.73/7.04 (assert (forall ((X tptp.real) (Y tptp.real) (Z3 tptp.real)) (=> (@ (@ tptp.ord_less_real X) Y) (=> (forall ((W tptp.real)) (=> (@ (@ tptp.ord_less_real X) W) (=> (@ (@ tptp.ord_less_real W) Y) (@ (@ tptp.ord_less_eq_real W) Z3)))) (@ (@ tptp.ord_less_eq_real Y) Z3)))))
% 6.73/7.04 (assert (forall ((X tptp.rat) (Y tptp.rat) (Z3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X) Y) (=> (forall ((W tptp.rat)) (=> (@ (@ tptp.ord_less_rat X) W) (=> (@ (@ tptp.ord_less_rat W) Y) (@ (@ tptp.ord_less_eq_rat W) Z3)))) (@ (@ tptp.ord_less_eq_rat Y) Z3)))))
% 6.73/7.04 (assert (forall ((Z3 tptp.real) (X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real Z3) X) (=> (forall ((W tptp.real)) (=> (@ (@ tptp.ord_less_real Z3) W) (=> (@ (@ tptp.ord_less_real W) X) (@ (@ tptp.ord_less_eq_real Y) W)))) (@ (@ tptp.ord_less_eq_real Y) Z3)))))
% 6.73/7.04 (assert (forall ((Z3 tptp.rat) (X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z3) X) (=> (forall ((W tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z3) W) (=> (@ (@ tptp.ord_less_rat W) X) (@ (@ tptp.ord_less_eq_rat Y) W)))) (@ (@ tptp.ord_less_eq_rat Y) Z3)))))
% 6.73/7.04 (assert (= tptp.ord_less_real (lambda ((A5 tptp.real) (B4 tptp.real)) (and (@ (@ tptp.ord_less_eq_real A5) B4) (not (@ (@ tptp.ord_less_eq_real B4) A5))))))
% 6.73/7.04 (assert (= tptp.ord_less_set_nat (lambda ((A5 tptp.set_nat) (B4 tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat A5) B4) (not (@ (@ tptp.ord_less_eq_set_nat B4) A5))))))
% 6.73/7.04 (assert (= tptp.ord_less_rat (lambda ((A5 tptp.rat) (B4 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat A5) B4) (not (@ (@ tptp.ord_less_eq_rat B4) A5))))))
% 6.73/7.04 (assert (= tptp.ord_less_num (lambda ((A5 tptp.num) (B4 tptp.num)) (and (@ (@ tptp.ord_less_eq_num A5) B4) (not (@ (@ tptp.ord_less_eq_num B4) A5))))))
% 6.73/7.04 (assert (= tptp.ord_less_nat (lambda ((A5 tptp.nat) (B4 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat A5) B4) (not (@ (@ tptp.ord_less_eq_nat B4) A5))))))
% 6.73/7.04 (assert (= tptp.ord_less_int (lambda ((A5 tptp.int) (B4 tptp.int)) (and (@ (@ tptp.ord_less_eq_int A5) B4) (not (@ (@ tptp.ord_less_eq_int B4) A5))))))
% 6.73/7.04 (assert (forall ((A tptp.real) (B tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_real B) C2) (@ _let_1 C2))))))
% 6.73/7.04 (assert (forall ((A tptp.set_nat) (B tptp.set_nat) (C2 tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_set_nat A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_set_nat B) C2) (@ _let_1 C2))))))
% 6.73/7.04 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_rat B) C2) (@ _let_1 C2))))))
% 6.73/7.04 (assert (forall ((A tptp.num) (B tptp.num) (C2 tptp.num)) (let ((_let_1 (@ tptp.ord_less_num A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_num B) C2) (@ _let_1 C2))))))
% 6.73/7.04 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_nat B) C2) (@ _let_1 C2))))))
% 6.73/7.04 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_int B) C2) (@ _let_1 C2))))))
% 6.73/7.04 (assert (forall ((A tptp.real) (B tptp.real) (C2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_real B) C2) (@ (@ tptp.ord_less_real A) C2)))))
% 6.73/7.04 (assert (forall ((A tptp.set_nat) (B tptp.set_nat) (C2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A) B) (=> (@ (@ tptp.ord_less_set_nat B) C2) (@ (@ tptp.ord_less_set_nat A) C2)))))
% 6.73/7.04 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_rat B) C2) (@ (@ tptp.ord_less_rat A) C2)))))
% 6.73/7.04 (assert (forall ((A tptp.num) (B tptp.num) (C2 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (@ (@ tptp.ord_less_num B) C2) (@ (@ tptp.ord_less_num A) C2)))))
% 6.73/7.04 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_nat B) C2) (@ (@ tptp.ord_less_nat A) C2)))))
% 6.73/7.04 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_int B) C2) (@ (@ tptp.ord_less_int A) C2)))))
% 6.73/7.04 (assert (= tptp.ord_less_real (lambda ((A5 tptp.real) (B4 tptp.real)) (and (@ (@ tptp.ord_less_eq_real A5) B4) (not (= A5 B4))))))
% 6.73/7.04 (assert (= tptp.ord_less_set_nat (lambda ((A5 tptp.set_nat) (B4 tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat A5) B4) (not (= A5 B4))))))
% 6.73/7.04 (assert (= tptp.ord_less_rat (lambda ((A5 tptp.rat) (B4 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat A5) B4) (not (= A5 B4))))))
% 6.73/7.04 (assert (= tptp.ord_less_num (lambda ((A5 tptp.num) (B4 tptp.num)) (and (@ (@ tptp.ord_less_eq_num A5) B4) (not (= A5 B4))))))
% 6.73/7.04 (assert (= tptp.ord_less_nat (lambda ((A5 tptp.nat) (B4 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat A5) B4) (not (= A5 B4))))))
% 6.73/7.04 (assert (= tptp.ord_less_int (lambda ((A5 tptp.int) (B4 tptp.int)) (and (@ (@ tptp.ord_less_eq_int A5) B4) (not (= A5 B4))))))
% 6.73/7.04 (assert (= tptp.ord_less_eq_real (lambda ((A5 tptp.real) (B4 tptp.real)) (or (@ (@ tptp.ord_less_real A5) B4) (= A5 B4)))))
% 6.73/7.04 (assert (= tptp.ord_less_eq_set_nat (lambda ((A5 tptp.set_nat) (B4 tptp.set_nat)) (or (@ (@ tptp.ord_less_set_nat A5) B4) (= A5 B4)))))
% 6.73/7.04 (assert (= tptp.ord_less_eq_rat (lambda ((A5 tptp.rat) (B4 tptp.rat)) (or (@ (@ tptp.ord_less_rat A5) B4) (= A5 B4)))))
% 6.73/7.04 (assert (= tptp.ord_less_eq_num (lambda ((A5 tptp.num) (B4 tptp.num)) (or (@ (@ tptp.ord_less_num A5) B4) (= A5 B4)))))
% 6.73/7.04 (assert (= tptp.ord_less_eq_nat (lambda ((A5 tptp.nat) (B4 tptp.nat)) (or (@ (@ tptp.ord_less_nat A5) B4) (= A5 B4)))))
% 6.73/7.04 (assert (= tptp.ord_less_eq_int (lambda ((A5 tptp.int) (B4 tptp.int)) (or (@ (@ tptp.ord_less_int A5) B4) (= A5 B4)))))
% 6.73/7.04 (assert (forall ((Y tptp.real) (X tptp.real)) (=> (not (@ (@ tptp.ord_less_eq_real Y) X)) (@ (@ tptp.ord_less_real X) Y))))
% 6.73/7.04 (assert (forall ((Y tptp.rat) (X tptp.rat)) (=> (not (@ (@ tptp.ord_less_eq_rat Y) X)) (@ (@ tptp.ord_less_rat X) Y))))
% 6.73/7.04 (assert (forall ((Y tptp.num) (X tptp.num)) (=> (not (@ (@ tptp.ord_less_eq_num Y) X)) (@ (@ tptp.ord_less_num X) Y))))
% 6.73/7.04 (assert (forall ((Y tptp.nat) (X tptp.nat)) (=> (not (@ (@ tptp.ord_less_eq_nat Y) X)) (@ (@ tptp.ord_less_nat X) Y))))
% 6.73/7.04 (assert (forall ((Y tptp.int) (X tptp.int)) (=> (not (@ (@ tptp.ord_less_eq_int Y) X)) (@ (@ tptp.ord_less_int X) Y))))
% 6.73/7.04 (assert (= tptp.ord_less_real (lambda ((X4 tptp.real) (Y4 tptp.real)) (and (@ (@ tptp.ord_less_eq_real X4) Y4) (not (@ (@ tptp.ord_less_eq_real Y4) X4))))))
% 6.73/7.04 (assert (= tptp.ord_less_set_nat (lambda ((X4 tptp.set_nat) (Y4 tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat X4) Y4) (not (@ (@ tptp.ord_less_eq_set_nat Y4) X4))))))
% 6.73/7.04 (assert (= tptp.ord_less_rat (lambda ((X4 tptp.rat) (Y4 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat X4) Y4) (not (@ (@ tptp.ord_less_eq_rat Y4) X4))))))
% 6.73/7.04 (assert (= tptp.ord_less_num (lambda ((X4 tptp.num) (Y4 tptp.num)) (and (@ (@ tptp.ord_less_eq_num X4) Y4) (not (@ (@ tptp.ord_less_eq_num Y4) X4))))))
% 6.73/7.04 (assert (= tptp.ord_less_nat (lambda ((X4 tptp.nat) (Y4 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat X4) Y4) (not (@ (@ tptp.ord_less_eq_nat Y4) X4))))))
% 6.73/7.04 (assert (= tptp.ord_less_int (lambda ((X4 tptp.int) (Y4 tptp.int)) (and (@ (@ tptp.ord_less_eq_int X4) Y4) (not (@ (@ tptp.ord_less_eq_int Y4) X4))))))
% 6.73/7.04 (assert (forall ((Y tptp.real) (Z3 tptp.real)) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Y) (@ (@ tptp.ord_less_eq_real X3) Z3))) (@ (@ tptp.ord_less_eq_real Y) Z3))))
% 6.73/7.04 (assert (forall ((Y tptp.rat) (Z3 tptp.rat)) (=> (forall ((X3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y) (@ (@ tptp.ord_less_eq_rat X3) Z3))) (@ (@ tptp.ord_less_eq_rat Y) Z3))))
% 6.73/7.04 (assert (forall ((Z3 tptp.real) (Y tptp.real)) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real Z3) X3) (@ (@ tptp.ord_less_eq_real Y) X3))) (@ (@ tptp.ord_less_eq_real Y) Z3))))
% 6.73/7.04 (assert (forall ((Z3 tptp.rat) (Y tptp.rat)) (=> (forall ((X3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z3) X3) (@ (@ tptp.ord_less_eq_rat Y) X3))) (@ (@ tptp.ord_less_eq_rat Y) Z3))))
% 6.73/7.04 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) Y) (= (not (@ (@ tptp.ord_less_real X) Y)) (= X Y)))))
% 6.73/7.04 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat X) Y) (= (not (@ (@ tptp.ord_less_set_nat X) Y)) (= X Y)))))
% 6.73/7.04 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X) Y) (= (not (@ (@ tptp.ord_less_rat X) Y)) (= X Y)))))
% 6.73/7.04 (assert (forall ((X tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X) Y) (= (not (@ (@ tptp.ord_less_num X) Y)) (= X Y)))))
% 6.73/7.04 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X) Y) (= (not (@ (@ tptp.ord_less_nat X) Y)) (= X Y)))))
% 6.73/7.04 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X) Y) (= (not (@ (@ tptp.ord_less_int X) Y)) (= X Y)))))
% 6.73/7.04 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (not (@ (@ tptp.ord_less_real X) Y)) (= (@ (@ tptp.ord_less_eq_real X) Y) (= X Y)))))
% 6.73/7.04 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat)) (=> (not (@ (@ tptp.ord_less_set_nat X) Y)) (= (@ (@ tptp.ord_less_eq_set_nat X) Y) (= X Y)))))
% 6.73/7.04 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (not (@ (@ tptp.ord_less_rat X) Y)) (= (@ (@ tptp.ord_less_eq_rat X) Y) (= X Y)))))
% 6.73/7.04 (assert (forall ((X tptp.num) (Y tptp.num)) (=> (not (@ (@ tptp.ord_less_num X) Y)) (= (@ (@ tptp.ord_less_eq_num X) Y) (= X Y)))))
% 6.73/7.04 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat X) Y)) (= (@ (@ tptp.ord_less_eq_nat X) Y) (= X Y)))))
% 6.73/7.04 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (not (@ (@ tptp.ord_less_int X) Y)) (= (@ (@ tptp.ord_less_eq_int X) Y) (= X Y)))))
% 6.73/7.04 (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)))))
% 6.73/7.04 (assert (forall ((A tptp.set_nat) (B tptp.set_nat)) (= (not (@ (@ tptp.ord_less_set_nat A) B)) (or (not (@ (@ tptp.ord_less_eq_set_nat A) B)) (= A B)))))
% 6.73/7.04 (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)))))
% 6.73/7.04 (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)))))
% 6.73/7.04 (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)))))
% 6.73/7.04 (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)))))
% 6.73/7.04 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (not (@ (@ tptp.ord_less_real X) Y)) (@ (@ tptp.ord_less_eq_real Y) X))))
% 6.73/7.04 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (not (@ (@ tptp.ord_less_rat X) Y)) (@ (@ tptp.ord_less_eq_rat Y) X))))
% 6.73/7.04 (assert (forall ((X tptp.num) (Y tptp.num)) (=> (not (@ (@ tptp.ord_less_num X) Y)) (@ (@ tptp.ord_less_eq_num Y) X))))
% 6.73/7.04 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat X) Y)) (@ (@ tptp.ord_less_eq_nat Y) X))))
% 6.73/7.04 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (not (@ (@ tptp.ord_less_int X) Y)) (@ (@ tptp.ord_less_eq_int Y) X))))
% 6.73/7.04 (assert (forall ((Y tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real Y) X) (not (@ (@ tptp.ord_less_real X) Y)))))
% 6.73/7.04 (assert (forall ((Y tptp.set_nat) (X tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat Y) X) (not (@ (@ tptp.ord_less_set_nat X) Y)))))
% 6.73/7.04 (assert (forall ((Y tptp.rat) (X tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat Y) X) (not (@ (@ tptp.ord_less_rat X) Y)))))
% 6.73/7.04 (assert (forall ((Y tptp.num) (X tptp.num)) (=> (@ (@ tptp.ord_less_eq_num Y) X) (not (@ (@ tptp.ord_less_num X) Y)))))
% 6.73/7.04 (assert (forall ((Y tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Y) X) (not (@ (@ tptp.ord_less_nat X) Y)))))
% 6.73/7.04 (assert (forall ((Y tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Y) X) (not (@ (@ tptp.ord_less_int X) Y)))))
% 6.73/7.04 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (not (= N tptp.zero_zero_nat)))))
% 6.73/7.04 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) N) (not (= N tptp.zero_zero_nat)))))
% 6.73/7.04 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) tptp.zero_zero_nat))))
% 6.73/7.04 (assert (forall ((N tptp.nat)) (=> (not (= N tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))
% 6.73/7.04 (assert (not (@ (@ tptp.ord_less_real tptp.zero_zero_real) tptp.zero_zero_real)))
% 6.73/7.04 (assert (not (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) tptp.zero_zero_rat)))
% 6.73/7.04 (assert (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 6.73/7.04 (assert (not (@ (@ tptp.ord_less_int tptp.zero_zero_int) tptp.zero_zero_int)))
% 6.73/7.04 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat N))) (=> (not (@ _let_1 M2)) (= (@ _let_1 (@ tptp.suc M2)) (= N M2))))))
% 6.73/7.04 (assert (forall ((I2 tptp.nat) (J2 tptp.nat) (P2 (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_nat I2) J2) (=> (forall ((I3 tptp.nat)) (=> (= J2 (@ tptp.suc I3)) (@ P2 I3))) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) J2) (=> (@ P2 (@ tptp.suc I3)) (@ P2 I3)))) (@ P2 I2))))))
% 6.73/7.04 (assert (forall ((I2 tptp.nat) (J2 tptp.nat) (P2 (-> tptp.nat tptp.nat Bool))) (=> (@ (@ tptp.ord_less_nat I2) J2) (=> (forall ((I3 tptp.nat)) (@ (@ P2 I3) (@ tptp.suc I3))) (=> (forall ((I3 tptp.nat) (J3 tptp.nat) (K tptp.nat)) (let ((_let_1 (@ P2 I3))) (=> (@ (@ tptp.ord_less_nat I3) J3) (=> (@ (@ tptp.ord_less_nat J3) K) (=> (@ _let_1 J3) (=> (@ (@ P2 J3) K) (@ _let_1 K))))))) (@ (@ P2 I2) J2))))))
% 6.73/7.04 (assert (forall ((I2 tptp.nat) (J2 tptp.nat) (K2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) J2) (=> (@ (@ tptp.ord_less_nat J2) K2) (@ (@ tptp.ord_less_nat (@ tptp.suc I2)) K2)))))
% 6.73/7.04 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc M2)) (@ tptp.suc N)) (@ (@ tptp.ord_less_nat M2) N))))
% 6.73/7.04 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat N))) (=> (not (@ _let_1 M2)) (=> (@ _let_1 (@ tptp.suc M2)) (= M2 N))))))
% 6.73/7.04 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.suc N)) M2) (exists ((M7 tptp.nat)) (and (= M2 (@ tptp.suc M7)) (@ (@ tptp.ord_less_nat N) M7))))))
% 6.73/7.04 (assert (forall ((N tptp.nat) (P2 (-> tptp.nat Bool))) (= (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.suc N)) (@ P2 I))) (and (@ P2 N) (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) N) (@ P2 I)))))))
% 6.73/7.04 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (not (@ (@ tptp.ord_less_nat M2) N)) (@ (@ tptp.ord_less_nat N) (@ tptp.suc M2)))))
% 6.73/7.04 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat M2))) (= (@ _let_1 (@ tptp.suc N)) (or (@ _let_1 N) (= M2 N))))))
% 6.73/7.04 (assert (forall ((N tptp.nat) (P2 (-> tptp.nat Bool))) (= (exists ((I tptp.nat)) (and (@ (@ tptp.ord_less_nat I) (@ tptp.suc N)) (@ P2 I))) (or (@ P2 N) (exists ((I tptp.nat)) (and (@ (@ tptp.ord_less_nat I) N) (@ P2 I)))))))
% 6.73/7.04 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat M2))) (=> (@ _let_1 N) (@ _let_1 (@ tptp.suc N))))))
% 6.73/7.04 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat M2))) (=> (@ _let_1 (@ tptp.suc N)) (=> (not (@ _let_1 N)) (= M2 N))))))
% 6.73/7.04 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc M2))) (=> (@ (@ tptp.ord_less_nat M2) N) (=> (not (= _let_1 N)) (@ (@ tptp.ord_less_nat _let_1) N))))))
% 6.73/7.04 (assert (forall ((I2 tptp.nat) (K2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc I2)) K2) (not (forall ((J3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) J3) (not (= K2 (@ tptp.suc J3)))))))))
% 6.73/7.04 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc M2)) N) (@ (@ tptp.ord_less_nat M2) N))))
% 6.73/7.04 (assert (forall ((I2 tptp.nat) (K2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) K2) (=> (not (= K2 (@ tptp.suc I2))) (not (forall ((J3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) J3) (not (= K2 (@ tptp.suc J3))))))))))
% 6.73/7.04 (assert (forall ((X11 tptp.option4927543243414619207at_nat) (X12 tptp.nat) (X13 tptp.list_VEBT_VEBT) (X14 tptp.vEBT_VEBT) (X21 Bool) (X22 Bool)) (not (= (@ (@ (@ (@ tptp.vEBT_Node X11) X12) X13) X14) (@ (@ tptp.vEBT_Leaf X21) X22)))))
% 6.73/7.04 (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) (X222 Bool)) (not (= Y (@ (@ tptp.vEBT_Leaf X212) X222))))))))
% 6.73/7.04 (assert (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) tptp.one_one_Code_integer))
% 6.73/7.04 (assert (@ (@ tptp.ord_less_eq_real tptp.one_one_real) tptp.one_one_real))
% 6.73/7.04 (assert (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) tptp.one_one_rat))
% 6.73/7.04 (assert (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) tptp.one_one_nat))
% 6.73/7.04 (assert (@ (@ tptp.ord_less_eq_int tptp.one_one_int) tptp.one_one_int))
% 6.73/7.04 (assert (not (= tptp.zero_z3403309356797280102nteger tptp.one_one_Code_integer)))
% 6.73/7.04 (assert (not (= tptp.zero_zero_complex tptp.one_one_complex)))
% 6.73/7.04 (assert (not (= tptp.zero_zero_real tptp.one_one_real)))
% 6.73/7.04 (assert (not (= tptp.zero_zero_rat tptp.one_one_rat)))
% 6.73/7.04 (assert (not (= tptp.zero_zero_nat tptp.one_one_nat)))
% 6.73/7.04 (assert (not (= tptp.zero_zero_int tptp.one_one_int)))
% 6.73/7.04 (assert (forall ((A tptp.nat)) (not (@ (@ tptp.ord_less_nat A) tptp.zero_zero_nat))))
% 6.73/7.04 (assert (forall ((N tptp.nat)) (=> (not (= N tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))
% 6.73/7.04 (assert (forall ((N tptp.nat)) (= (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)) (= N tptp.zero_zero_nat))))
% 6.73/7.04 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) tptp.zero_zero_nat))))
% 6.73/7.04 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) tptp.zero_zero_nat))))
% 6.73/7.04 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) N) (not (= N tptp.zero_zero_nat)))))
% 6.73/7.04 (assert (forall ((P2 (-> tptp.nat Bool)) (N tptp.nat)) (=> (@ P2 tptp.zero_zero_nat) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N3) (=> (not (@ P2 N3)) (exists ((M3 tptp.nat)) (and (@ (@ tptp.ord_less_nat M3) N3) (not (@ P2 M3))))))) (@ P2 N)))))
% 6.73/7.04 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger A) tptp.one_one_Code_integer) A)))
% 6.73/7.04 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex A) tptp.one_one_complex) A)))
% 6.73/7.04 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real A) tptp.one_one_real) A)))
% 6.73/7.04 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat A) tptp.one_one_rat) A)))
% 6.73/7.04 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat A) tptp.one_one_nat) A)))
% 6.73/7.04 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int A) tptp.one_one_int) A)))
% 6.73/7.04 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger tptp.one_one_Code_integer) A) A)))
% 6.73/7.04 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex tptp.one_one_complex) A) A)))
% 6.73/7.04 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real tptp.one_one_real) A) A)))
% 6.73/7.04 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat tptp.one_one_rat) A) A)))
% 6.73/7.04 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.one_one_nat) A) A)))
% 6.73/7.04 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int tptp.one_one_int) A) A)))
% 6.73/7.04 (assert (forall ((F2 (-> tptp.nat tptp.nat)) (I2 tptp.nat) (J2 tptp.nat)) (=> (forall ((I3 tptp.nat) (J3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) J3) (@ (@ tptp.ord_less_nat (@ F2 I3)) (@ F2 J3)))) (=> (@ (@ tptp.ord_less_eq_nat I2) J2) (@ (@ tptp.ord_less_eq_nat (@ F2 I2)) (@ F2 J2))))))
% 6.73/7.04 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (=> (not (= M2 N)) (@ (@ tptp.ord_less_nat M2) N)))))
% 6.73/7.04 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (or (@ (@ tptp.ord_less_nat M2) N) (= M2 N)) (@ (@ tptp.ord_less_eq_nat M2) N))))
% 6.73/7.04 (assert (= tptp.ord_less_eq_nat (lambda ((M6 tptp.nat) (N4 tptp.nat)) (or (@ (@ tptp.ord_less_nat M6) N4) (= M6 N4)))))
% 6.73/7.04 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) N) (@ (@ tptp.ord_less_eq_nat M2) N))))
% 6.73/7.04 (assert (= tptp.ord_less_nat (lambda ((M6 tptp.nat) (N4 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat M6) N4) (not (= M6 N4))))))
% 6.73/7.04 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.one_one_nat) N) N)))
% 6.73/7.04 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.times_times_nat N) tptp.one_one_nat) N)))
% 6.73/7.04 (assert (forall ((K2 tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K2) (= (= (@ _let_1 M2) (@ _let_1 N)) (= M2 N))))))
% 6.73/7.04 (assert (forall ((K2 tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K2) (= (@ (@ tptp.ord_less_nat (@ _let_1 M2)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat M2) N))))))
% 6.73/7.04 (assert (forall ((A tptp.code_integer) (C2 tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.times_3573771949741848930nteger A) C2)) C2) (and (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) C2) (@ (@ tptp.ord_le6747313008572928689nteger A) tptp.one_one_Code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger C2) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) A))))))
% 6.73/7.04 (assert (forall ((A tptp.real) (C2 tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C2)) C2) (and (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C2) (@ (@ tptp.ord_less_real A) tptp.one_one_real)) (=> (@ (@ tptp.ord_less_eq_real C2) tptp.zero_zero_real) (@ (@ tptp.ord_less_real tptp.one_one_real) A))))))
% 6.73/7.04 (assert (forall ((A tptp.rat) (C2 tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C2)) C2) (and (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C2) (@ (@ tptp.ord_less_rat A) tptp.one_one_rat)) (=> (@ (@ tptp.ord_less_eq_rat C2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat tptp.one_one_rat) A))))))
% 6.73/7.04 (assert (forall ((A tptp.int) (C2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) C2)) C2) (and (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C2) (@ (@ tptp.ord_less_int A) tptp.one_one_int)) (=> (@ (@ tptp.ord_less_eq_int C2) tptp.zero_zero_int) (@ (@ tptp.ord_less_int tptp.one_one_int) A))))))
% 6.73/7.04 (assert (forall ((C2 tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger C2) (@ (@ tptp.times_3573771949741848930nteger B) C2)) (and (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) C2) (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) B)) (=> (@ (@ tptp.ord_le3102999989581377725nteger C2) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger B) tptp.one_one_Code_integer))))))
% 6.73/7.04 (assert (forall ((C2 tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_real C2) (@ (@ tptp.times_times_real B) C2)) (and (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C2) (@ (@ tptp.ord_less_real tptp.one_one_real) B)) (=> (@ (@ tptp.ord_less_eq_real C2) tptp.zero_zero_real) (@ (@ tptp.ord_less_real B) tptp.one_one_real))))))
% 6.73/7.04 (assert (forall ((C2 tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat C2) (@ (@ tptp.times_times_rat B) C2)) (and (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C2) (@ (@ tptp.ord_less_rat tptp.one_one_rat) B)) (=> (@ (@ tptp.ord_less_eq_rat C2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B) tptp.one_one_rat))))))
% 6.73/7.04 (assert (forall ((C2 tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_int C2) (@ (@ tptp.times_times_int B) C2)) (and (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C2) (@ (@ tptp.ord_less_int tptp.one_one_int) B)) (=> (@ (@ tptp.ord_less_eq_int C2) tptp.zero_zero_int) (@ (@ tptp.ord_less_int B) tptp.one_one_int))))))
% 6.73/7.04 (assert (forall ((C2 tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.times_3573771949741848930nteger C2) A)) C2) (and (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) C2) (@ (@ tptp.ord_le6747313008572928689nteger A) tptp.one_one_Code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger C2) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) A))))))
% 6.73/7.04 (assert (forall ((C2 tptp.real) (A tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real C2) A)) C2) (and (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C2) (@ (@ tptp.ord_less_real A) tptp.one_one_real)) (=> (@ (@ tptp.ord_less_eq_real C2) tptp.zero_zero_real) (@ (@ tptp.ord_less_real tptp.one_one_real) A))))))
% 6.73/7.04 (assert (forall ((C2 tptp.rat) (A tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat C2) A)) C2) (and (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C2) (@ (@ tptp.ord_less_rat A) tptp.one_one_rat)) (=> (@ (@ tptp.ord_less_eq_rat C2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat tptp.one_one_rat) A))))))
% 6.73/7.04 (assert (forall ((C2 tptp.int) (A tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int C2) A)) C2) (and (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C2) (@ (@ tptp.ord_less_int A) tptp.one_one_int)) (=> (@ (@ tptp.ord_less_eq_int C2) tptp.zero_zero_int) (@ (@ tptp.ord_less_int tptp.one_one_int) A))))))
% 6.73/7.04 (assert (forall ((C2 tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger C2) (@ (@ tptp.times_3573771949741848930nteger C2) B)) (and (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) C2) (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) B)) (=> (@ (@ tptp.ord_le3102999989581377725nteger C2) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger B) tptp.one_one_Code_integer))))))
% 6.73/7.04 (assert (forall ((C2 tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_real C2) (@ (@ tptp.times_times_real C2) B)) (and (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C2) (@ (@ tptp.ord_less_real tptp.one_one_real) B)) (=> (@ (@ tptp.ord_less_eq_real C2) tptp.zero_zero_real) (@ (@ tptp.ord_less_real B) tptp.one_one_real))))))
% 6.73/7.04 (assert (forall ((C2 tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat C2) (@ (@ tptp.times_times_rat C2) B)) (and (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C2) (@ (@ tptp.ord_less_rat tptp.one_one_rat) B)) (=> (@ (@ tptp.ord_less_eq_rat C2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B) tptp.one_one_rat))))))
% 6.73/7.04 (assert (forall ((C2 tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_int C2) (@ (@ tptp.times_times_int C2) B)) (and (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C2) (@ (@ tptp.ord_less_int tptp.one_one_int) B)) (=> (@ (@ tptp.ord_less_eq_int C2) tptp.zero_zero_int) (@ (@ tptp.ord_less_int B) tptp.one_one_int))))))
% 6.73/7.04 (assert (forall ((A tptp.code_integer) (C2 tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.times_3573771949741848930nteger A) C2)) C2) (and (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) C2) (@ (@ tptp.ord_le3102999989581377725nteger A) tptp.one_one_Code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger C2) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) A))))))
% 6.73/7.04 (assert (forall ((A tptp.real) (C2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) C2)) C2) (and (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C2) (@ (@ tptp.ord_less_eq_real A) tptp.one_one_real)) (=> (@ (@ tptp.ord_less_real C2) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) A))))))
% 6.73/7.04 (assert (forall ((A tptp.rat) (C2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C2)) C2) (and (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C2) (@ (@ tptp.ord_less_eq_rat A) tptp.one_one_rat)) (=> (@ (@ tptp.ord_less_rat C2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) A))))))
% 6.73/7.04 (assert (forall ((A tptp.int) (C2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) C2)) C2) (and (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C2) (@ (@ tptp.ord_less_eq_int A) tptp.one_one_int)) (=> (@ (@ tptp.ord_less_int C2) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) A))))))
% 6.73/7.04 (assert (forall ((C2 tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger C2) (@ (@ tptp.times_3573771949741848930nteger B) C2)) (and (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) C2) (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) B)) (=> (@ (@ tptp.ord_le6747313008572928689nteger C2) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le3102999989581377725nteger B) tptp.one_one_Code_integer))))))
% 6.73/7.04 (assert (forall ((C2 tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_eq_real C2) (@ (@ tptp.times_times_real B) C2)) (and (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C2) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) B)) (=> (@ (@ tptp.ord_less_real C2) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real B) tptp.one_one_real))))))
% 6.73/7.04 (assert (forall ((C2 tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat C2) (@ (@ tptp.times_times_rat B) C2)) (and (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C2) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) B)) (=> (@ (@ tptp.ord_less_rat C2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat B) tptp.one_one_rat))))))
% 6.73/7.04 (assert (forall ((C2 tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_int C2) (@ (@ tptp.times_times_int B) C2)) (and (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C2) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) B)) (=> (@ (@ tptp.ord_less_int C2) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int B) tptp.one_one_int))))))
% 6.73/7.04 (assert (forall ((C2 tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.times_3573771949741848930nteger C2) A)) C2) (and (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) C2) (@ (@ tptp.ord_le3102999989581377725nteger A) tptp.one_one_Code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger C2) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) A))))))
% 6.73/7.04 (assert (forall ((C2 tptp.real) (A tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real C2) A)) C2) (and (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C2) (@ (@ tptp.ord_less_eq_real A) tptp.one_one_real)) (=> (@ (@ tptp.ord_less_real C2) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) A))))))
% 6.73/7.04 (assert (forall ((C2 tptp.rat) (A tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat C2) A)) C2) (and (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C2) (@ (@ tptp.ord_less_eq_rat A) tptp.one_one_rat)) (=> (@ (@ tptp.ord_less_rat C2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) A))))))
% 6.73/7.04 (assert (forall ((C2 tptp.int) (A tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int C2) A)) C2) (and (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C2) (@ (@ tptp.ord_less_eq_int A) tptp.one_one_int)) (=> (@ (@ tptp.ord_less_int C2) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) A))))))
% 6.73/7.04 (assert (forall ((C2 tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger C2) (@ (@ tptp.times_3573771949741848930nteger C2) B)) (and (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) C2) (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) B)) (=> (@ (@ tptp.ord_le6747313008572928689nteger C2) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le3102999989581377725nteger B) tptp.one_one_Code_integer))))))
% 6.73/7.04 (assert (forall ((C2 tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_eq_real C2) (@ (@ tptp.times_times_real C2) B)) (and (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C2) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) B)) (=> (@ (@ tptp.ord_less_real C2) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real B) tptp.one_one_real))))))
% 6.73/7.04 (assert (forall ((C2 tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat C2) (@ (@ tptp.times_times_rat C2) B)) (and (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C2) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) B)) (=> (@ (@ tptp.ord_less_rat C2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat B) tptp.one_one_rat))))))
% 6.73/7.04 (assert (forall ((C2 tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_int C2) (@ (@ tptp.times_times_int C2) B)) (and (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C2) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) B)) (=> (@ (@ tptp.ord_less_int C2) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int B) tptp.one_one_int))))))
% 6.73/7.04 (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))))))
% 6.73/7.04 (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))))))
% 6.73/7.04 (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))))))
% 6.73/7.04 (assert (forall ((A tptp.real)) (not (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) A)) tptp.zero_zero_real))))
% 6.73/7.04 (assert (forall ((A tptp.rat)) (not (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) A)) tptp.zero_zero_rat))))
% 6.73/7.04 (assert (forall ((A tptp.int)) (not (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) A)) tptp.zero_zero_int))))
% 6.73/7.04 (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)))))))
% 6.73/7.04 (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)))))))
% 6.73/7.04 (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)))))))
% 6.73/7.04 (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)))))
% 6.73/7.04 (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)))))
% 6.73/7.04 (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)))))
% 6.73/7.04 (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)))))
% 6.73/7.04 (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)))))
% 6.73/7.04 (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)))))
% 6.73/7.04 (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)))))
% 6.73/7.04 (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)))))
% 6.73/7.04 (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)))))))
% 6.73/7.04 (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)))))))
% 6.73/7.04 (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)))))))
% 6.73/7.04 (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)))))))
% 6.73/7.04 (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)))))
% 6.73/7.04 (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)))))
% 6.73/7.04 (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)))))
% 6.73/7.04 (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)))))
% 6.73/7.04 (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)))))))
% 6.73/7.04 (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)))))))
% 6.73/7.04 (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)))))))
% 6.73/7.04 (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))))))
% 6.73/7.04 (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))))))
% 6.73/7.04 (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))))))
% 6.73/7.04 (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))))))
% 6.73/7.04 (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))))))
% 6.73/7.04 (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))))))
% 6.73/7.04 (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))))))
% 6.73/7.04 (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))))))
% 6.73/7.04 (assert (forall ((C2 tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real C2))) (=> (@ (@ tptp.ord_less_real C2) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_real B) A))))))
% 6.73/7.04 (assert (forall ((C2 tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C2))) (=> (@ (@ tptp.ord_less_rat C2) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_rat B) A))))))
% 6.73/7.04 (assert (forall ((C2 tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C2))) (=> (@ (@ tptp.ord_less_int C2) tptp.zero_zero_int) (= (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_int B) A))))))
% 6.73/7.04 (assert (forall ((C2 tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real C2))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C2) (= (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_real A) B))))))
% 6.73/7.04 (assert (forall ((C2 tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C2))) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C2) (= (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_rat A) B))))))
% 6.73/7.04 (assert (forall ((C2 tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C2))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C2) (= (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_int A) B))))))
% 6.73/7.04 (assert (forall ((B tptp.real) (A tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.times_times_real C2))) (=> (@ (@ tptp.ord_less_real B) A) (=> (@ (@ tptp.ord_less_real C2) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B)))))))
% 6.73/7.04 (assert (forall ((B tptp.rat) (A tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C2))) (=> (@ (@ tptp.ord_less_rat B) A) (=> (@ (@ tptp.ord_less_rat C2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B)))))))
% 6.73/7.04 (assert (forall ((B tptp.int) (A tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int C2))) (=> (@ (@ tptp.ord_less_int B) A) (=> (@ (@ tptp.ord_less_int C2) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B)))))))
% 6.73/7.04 (assert (forall ((A tptp.real) (B tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.times_times_real C2))) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C2) (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B)))))))
% 6.73/7.04 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C2))) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C2) (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B)))))))
% 6.73/7.04 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C2))) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C2) (@ (@ tptp.ord_less_nat (@ _let_1 A)) (@ _let_1 B)))))))
% 6.73/7.04 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int C2))) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C2) (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B)))))))
% 6.73/7.04 (assert (forall ((C2 tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real C2))) (= (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B)) (or (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) C2) (@ (@ tptp.ord_less_real A) B)) (and (@ (@ tptp.ord_less_real C2) tptp.zero_zero_real) (@ (@ tptp.ord_less_real B) A)))))))
% 6.73/7.04 (assert (forall ((C2 tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C2))) (= (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B)) (or (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C2) (@ (@ tptp.ord_less_rat A) B)) (and (@ (@ tptp.ord_less_rat C2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B) A)))))))
% 6.73/7.04 (assert (forall ((C2 tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C2))) (= (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B)) (or (and (@ (@ tptp.ord_less_int tptp.zero_zero_int) C2) (@ (@ tptp.ord_less_int A) B)) (and (@ (@ tptp.ord_less_int C2) tptp.zero_zero_int) (@ (@ tptp.ord_less_int B) A)))))))
% 6.73/7.04 (assert (forall ((B tptp.real) (A tptp.real) (C2 tptp.real)) (=> (@ (@ tptp.ord_less_real B) A) (=> (@ (@ tptp.ord_less_real C2) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C2)) (@ (@ tptp.times_times_real B) C2))))))
% 6.73/7.04 (assert (forall ((B tptp.rat) (A tptp.rat) (C2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat B) A) (=> (@ (@ tptp.ord_less_rat C2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C2)) (@ (@ tptp.times_times_rat B) C2))))))
% 6.73/7.04 (assert (forall ((B tptp.int) (A tptp.int) (C2 tptp.int)) (=> (@ (@ tptp.ord_less_int B) A) (=> (@ (@ tptp.ord_less_int C2) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) C2)) (@ (@ tptp.times_times_int B) C2))))))
% 6.73/7.04 (assert (forall ((A tptp.real) (B tptp.real) (C2 tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C2) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C2)) (@ (@ tptp.times_times_real B) C2))))))
% 6.73/7.04 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C2) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C2)) (@ (@ tptp.times_times_rat B) C2))))))
% 6.73/7.04 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C2) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A) C2)) (@ (@ tptp.times_times_nat B) C2))))))
% 6.73/7.04 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C2) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) C2)) (@ (@ tptp.times_times_int B) C2))))))
% 6.73/7.04 (assert (forall ((A tptp.real) (C2 tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C2)) (@ (@ tptp.times_times_real B) C2)) (or (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) C2) (@ (@ tptp.ord_less_real A) B)) (and (@ (@ tptp.ord_less_real C2) tptp.zero_zero_real) (@ (@ tptp.ord_less_real B) A))))))
% 6.73/7.04 (assert (forall ((A tptp.rat) (C2 tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C2)) (@ (@ tptp.times_times_rat B) C2)) (or (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C2) (@ (@ tptp.ord_less_rat A) B)) (and (@ (@ tptp.ord_less_rat C2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B) A))))))
% 6.73/7.04 (assert (forall ((A tptp.int) (C2 tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) C2)) (@ (@ tptp.times_times_int B) C2)) (or (and (@ (@ tptp.ord_less_int tptp.zero_zero_int) C2) (@ (@ tptp.ord_less_int A) B)) (and (@ (@ tptp.ord_less_int C2) tptp.zero_zero_int) (@ (@ tptp.ord_less_int B) A))))))
% 6.73/7.04 (assert (forall ((A tptp.real) (B tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.times_times_real C2))) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C2) (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B)))))))
% 6.73/7.04 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C2))) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C2) (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B)))))))
% 6.73/7.04 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C2))) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C2) (@ (@ tptp.ord_less_nat (@ _let_1 A)) (@ _let_1 B)))))))
% 6.73/7.04 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int C2))) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C2) (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B)))))))
% 6.73/7.04 (assert (not (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) tptp.zero_z3403309356797280102nteger)))
% 6.73/7.04 (assert (not (@ (@ tptp.ord_less_eq_real tptp.one_one_real) tptp.zero_zero_real)))
% 6.73/7.04 (assert (not (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) tptp.zero_zero_rat)))
% 6.73/7.04 (assert (not (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) tptp.zero_zero_nat)))
% 6.73/7.04 (assert (not (@ (@ tptp.ord_less_eq_int tptp.one_one_int) tptp.zero_zero_int)))
% 6.73/7.04 (assert (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) tptp.one_one_Code_integer))
% 6.73/7.04 (assert (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) tptp.one_one_real))
% 6.73/7.04 (assert (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) tptp.one_one_rat))
% 6.73/7.04 (assert (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) tptp.one_one_nat))
% 6.73/7.04 (assert (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) tptp.one_one_int))
% 6.73/7.04 (assert (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) tptp.one_one_Code_integer))
% 6.73/7.04 (assert (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) tptp.one_one_real))
% 6.73/7.04 (assert (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) tptp.one_one_rat))
% 6.73/7.04 (assert (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) tptp.one_one_nat))
% 6.73/7.04 (assert (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) tptp.one_one_int))
% 6.73/7.04 (assert (forall ((K2 tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K2) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 M2)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat M2) N))))))
% 6.73/7.04 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat M2) (@ tptp.suc N)) (or (= M2 tptp.zero_zero_nat) (exists ((J tptp.nat)) (and (= M2 (@ tptp.suc J)) (@ (@ tptp.ord_less_nat J) N)))))))
% 6.73/7.04 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (exists ((M tptp.nat)) (= N (@ tptp.suc M))))))
% 6.73/7.04 (assert (forall ((N tptp.nat) (P2 (-> tptp.nat Bool))) (= (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.suc N)) (@ P2 I))) (and (@ P2 tptp.zero_zero_nat) (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) N) (@ P2 (@ tptp.suc I))))))))
% 6.73/7.04 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (exists ((M6 tptp.nat)) (= N (@ tptp.suc M6))))))
% 6.73/7.04 (assert (forall ((N tptp.nat) (P2 (-> tptp.nat Bool))) (= (exists ((I tptp.nat)) (and (@ (@ tptp.ord_less_nat I) (@ tptp.suc N)) (@ P2 I))) (or (@ P2 tptp.zero_zero_nat) (exists ((I tptp.nat)) (and (@ (@ tptp.ord_less_nat I) N) (@ P2 (@ tptp.suc I))))))))
% 6.73/7.04 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (@ (@ tptp.ord_less_nat M2) (@ tptp.suc N)))))
% 6.73/7.04 (assert (= tptp.ord_less_nat (lambda ((N4 tptp.nat) (__flatten_var_0 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N4)) __flatten_var_0))))
% 6.73/7.04 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat M2) (@ tptp.suc N)) (@ (@ tptp.ord_less_eq_nat M2) N))))
% 6.73/7.04 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ (@ tptp.ord_less_nat N) (@ tptp.suc M2)) (= N M2)))))
% 6.73/7.04 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M2)) N) (@ (@ tptp.ord_less_nat M2) N))))
% 6.73/7.04 (assert (forall ((I2 tptp.nat) (J2 tptp.nat) (P2 (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat I2) J2) (=> (@ P2 J2) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) N3) (=> (@ (@ tptp.ord_less_nat N3) J2) (=> (@ P2 (@ tptp.suc N3)) (@ P2 N3))))) (@ P2 I2))))))
% 6.73/7.04 (assert (forall ((I2 tptp.nat) (J2 tptp.nat) (P2 (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat I2) J2) (=> (@ P2 I2) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) N3) (=> (@ (@ tptp.ord_less_nat N3) J2) (=> (@ P2 N3) (@ P2 (@ tptp.suc N3)))))) (@ P2 J2))))))
% 6.73/7.04 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M2)) N) (@ (@ tptp.ord_less_nat M2) N))))
% 6.73/7.04 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) N) (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M2)) N))))
% 6.73/7.04 (assert (forall ((P2 (-> tptp.nat Bool)) (N tptp.nat)) (=> (@ P2 N) (=> (not (@ P2 tptp.zero_zero_nat)) (exists ((K tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat K) N) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) K) (not (@ P2 I4)))) (@ P2 K)))))))
% 6.73/7.04 (assert (forall ((K2 tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.suc K2)))) (= (@ (@ tptp.ord_less_nat (@ _let_1 M2)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat M2) N)))))
% 6.73/7.04 (assert (forall ((I2 tptp.nat) (J2 tptp.nat) (K2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) J2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K2) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat I2) K2)) (@ (@ tptp.times_times_nat J2) K2))))))
% 6.73/7.04 (assert (forall ((I2 tptp.nat) (J2 tptp.nat) (K2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K2))) (=> (@ (@ tptp.ord_less_nat I2) J2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K2) (@ (@ tptp.ord_less_nat (@ _let_1 I2)) (@ _let_1 J2)))))))
% 6.73/7.04 (assert (= tptp.one_one_nat (@ tptp.suc tptp.zero_zero_nat)))
% 6.73/7.04 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (= M2 (@ (@ tptp.times_times_nat M2) N)) (or (= N tptp.one_one_nat) (= M2 tptp.zero_zero_nat)))))
% 6.73/7.04 (assert (forall ((A tptp.real) (B tptp.real) (C2 tptp.real) (D tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_eq_real C2) D) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C2) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C2)) (@ (@ tptp.times_times_real B) D))))))))
% 6.73/7.04 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat) (D tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat C2) D) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C2) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C2)) (@ (@ tptp.times_times_rat B) D))))))))
% 6.73/7.04 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat) (D tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat C2) D) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C2) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A) C2)) (@ (@ tptp.times_times_nat B) D))))))))
% 6.73/7.04 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int) (D tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_eq_int C2) D) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C2) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) C2)) (@ (@ tptp.times_times_int B) D))))))))
% 6.73/7.04 (assert (forall ((A tptp.real) (B tptp.real) (C2 tptp.real) (D tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_real C2) D) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C2) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C2)) (@ (@ tptp.times_times_real B) D))))))))
% 6.73/7.04 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat) (D tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_rat C2) D) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C2) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C2)) (@ (@ tptp.times_times_rat B) D))))))))
% 6.73/7.04 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat) (D tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_nat C2) D) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C2) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A) C2)) (@ (@ tptp.times_times_nat B) D))))))))
% 6.73/7.04 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int) (D tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_int C2) D) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C2) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) C2)) (@ (@ tptp.times_times_int B) D))))))))
% 6.73/7.04 (assert (forall ((A tptp.real) (C2 tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) C2)) (@ (@ tptp.times_times_real B) C2)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C2) (@ (@ tptp.ord_less_eq_real A) B)))))
% 6.73/7.04 (assert (forall ((A tptp.rat) (C2 tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C2)) (@ (@ tptp.times_times_rat B) C2)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C2) (@ (@ tptp.ord_less_eq_rat A) B)))))
% 6.73/7.04 (assert (forall ((A tptp.nat) (C2 tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A) C2)) (@ (@ tptp.times_times_nat B) C2)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C2) (@ (@ tptp.ord_less_eq_nat A) B)))))
% 6.73/7.04 (assert (forall ((A tptp.int) (C2 tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) C2)) (@ (@ tptp.times_times_int B) C2)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C2) (@ (@ tptp.ord_less_eq_int A) B)))))
% 6.73/7.04 (assert (forall ((C2 tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real C2))) (=> (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C2) (@ (@ tptp.ord_less_eq_real A) B))))))
% 6.73/7.04 (assert (forall ((C2 tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C2))) (=> (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C2) (@ (@ tptp.ord_less_eq_rat A) B))))))
% 6.73/7.04 (assert (forall ((C2 tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C2))) (=> (@ (@ tptp.ord_less_eq_nat (@ _let_1 A)) (@ _let_1 B)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C2) (@ (@ tptp.ord_less_eq_nat A) B))))))
% 6.73/7.04 (assert (forall ((C2 tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C2))) (=> (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C2) (@ (@ tptp.ord_less_eq_int A) B))))))
% 6.73/7.04 (assert (forall ((C2 tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real C2))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C2) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_real A) B))))))
% 6.73/7.04 (assert (forall ((C2 tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C2))) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C2) (= (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_rat A) B))))))
% 6.73/7.04 (assert (forall ((C2 tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C2))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C2) (= (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_int A) B))))))
% 6.73/7.04 (assert (forall ((C2 tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real C2))) (=> (@ (@ tptp.ord_less_real C2) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_real B) A))))))
% 6.73/7.04 (assert (forall ((C2 tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C2))) (=> (@ (@ tptp.ord_less_rat C2) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_rat B) A))))))
% 6.73/7.04 (assert (forall ((C2 tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C2))) (=> (@ (@ tptp.ord_less_int C2) tptp.zero_zero_int) (= (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_int B) A))))))
% 6.73/7.04 (assert (forall ((A tptp.real) (C2 tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C2)) (@ (@ tptp.times_times_real B) C2)) (and (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C2) (@ (@ tptp.ord_less_real A) B)) (=> (@ (@ tptp.ord_less_eq_real C2) tptp.zero_zero_real) (@ (@ tptp.ord_less_real B) A))))))
% 6.73/7.04 (assert (forall ((A tptp.rat) (C2 tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C2)) (@ (@ tptp.times_times_rat B) C2)) (and (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C2) (@ (@ tptp.ord_less_rat A) B)) (=> (@ (@ tptp.ord_less_eq_rat C2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B) A))))))
% 6.73/7.04 (assert (forall ((A tptp.int) (C2 tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) C2)) (@ (@ tptp.times_times_int B) C2)) (and (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C2) (@ (@ tptp.ord_less_int A) B)) (=> (@ (@ tptp.ord_less_eq_int C2) tptp.zero_zero_int) (@ (@ tptp.ord_less_int B) A))))))
% 6.73/7.04 (assert (forall ((A tptp.real) (B tptp.real) (C2 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 C2) D) (=> (@ _let_1 A) (=> (@ _let_1 C2) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C2)) (@ (@ tptp.times_times_real B) D)))))))))
% 6.73/7.04 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 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 C2) D) (=> (@ _let_1 A) (=> (@ _let_1 C2) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C2)) (@ (@ tptp.times_times_rat B) D)))))))))
% 6.73/7.04 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 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 C2) D) (=> (@ _let_1 A) (=> (@ _let_1 C2) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A) C2)) (@ (@ tptp.times_times_nat B) D)))))))))
% 6.73/7.04 (assert (forall ((A tptp.int) (B tptp.int) (C2 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 C2) D) (=> (@ _let_1 A) (=> (@ _let_1 C2) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) C2)) (@ (@ tptp.times_times_int B) D)))))))))
% 6.73/7.04 (assert (forall ((A tptp.real) (C2 tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C2)) (@ (@ tptp.times_times_real B) C2)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C2) (@ (@ tptp.ord_less_real A) B)))))
% 6.73/7.04 (assert (forall ((A tptp.rat) (C2 tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C2)) (@ (@ tptp.times_times_rat B) C2)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C2) (@ (@ tptp.ord_less_rat A) B)))))
% 6.73/7.04 (assert (forall ((A tptp.nat) (C2 tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A) C2)) (@ (@ tptp.times_times_nat B) C2)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C2) (@ (@ tptp.ord_less_nat A) B)))))
% 6.73/7.04 (assert (forall ((A tptp.int) (C2 tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) C2)) (@ (@ tptp.times_times_int B) C2)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C2) (@ (@ tptp.ord_less_int A) B)))))
% 6.73/7.04 (assert (forall ((C2 tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real C2))) (= (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B)) (and (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C2) (@ (@ tptp.ord_less_real A) B)) (=> (@ (@ tptp.ord_less_eq_real C2) tptp.zero_zero_real) (@ (@ tptp.ord_less_real B) A)))))))
% 6.73/7.04 (assert (forall ((C2 tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C2))) (= (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B)) (and (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C2) (@ (@ tptp.ord_less_rat A) B)) (=> (@ (@ tptp.ord_less_eq_rat C2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B) A)))))))
% 6.73/7.04 (assert (forall ((C2 tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C2))) (= (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B)) (and (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C2) (@ (@ tptp.ord_less_int A) B)) (=> (@ (@ tptp.ord_less_eq_int C2) tptp.zero_zero_int) (@ (@ tptp.ord_less_int B) A)))))))
% 6.73/7.04 (assert (forall ((A tptp.real) (B tptp.real) (C2 tptp.real) (D tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_real C2) D) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) B) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C2) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C2)) (@ (@ tptp.times_times_real B) D))))))))
% 6.73/7.04 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat) (D tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_rat C2) D) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) B) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C2) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C2)) (@ (@ tptp.times_times_rat B) D))))))))
% 6.73/7.04 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat) (D tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_nat C2) D) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C2) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A) C2)) (@ (@ tptp.times_times_nat B) D))))))))
% 6.73/7.04 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int) (D tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_int C2) D) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C2) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) C2)) (@ (@ tptp.times_times_int B) D))))))))
% 6.73/7.04 (assert (forall ((C2 tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real C2))) (=> (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C2) (@ (@ tptp.ord_less_real A) B))))))
% 6.73/7.04 (assert (forall ((C2 tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C2))) (=> (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C2) (@ (@ tptp.ord_less_rat A) B))))))
% 6.73/7.04 (assert (forall ((C2 tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C2))) (=> (@ (@ tptp.ord_less_nat (@ _let_1 A)) (@ _let_1 B)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C2) (@ (@ tptp.ord_less_nat A) B))))))
% 6.73/7.04 (assert (forall ((C2 tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C2))) (=> (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C2) (@ (@ tptp.ord_less_int A) B))))))
% 6.73/7.04 (assert (forall ((A tptp.real) (C2 tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) C2)) (@ (@ tptp.times_times_real B) C2)) (and (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C2) (@ (@ tptp.ord_less_eq_real A) B)) (=> (@ (@ tptp.ord_less_real C2) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real B) A))))))
% 6.73/7.04 (assert (forall ((A tptp.rat) (C2 tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C2)) (@ (@ tptp.times_times_rat B) C2)) (and (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C2) (@ (@ tptp.ord_less_eq_rat A) B)) (=> (@ (@ tptp.ord_less_rat C2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat B) A))))))
% 6.73/7.04 (assert (forall ((A tptp.int) (C2 tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) C2)) (@ (@ tptp.times_times_int B) C2)) (and (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C2) (@ (@ tptp.ord_less_eq_int A) B)) (=> (@ (@ tptp.ord_less_int C2) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int B) A))))))
% 6.73/7.04 (assert (forall ((C2 tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real C2))) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B)) (and (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C2) (@ (@ tptp.ord_less_eq_real A) B)) (=> (@ (@ tptp.ord_less_real C2) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real B) A)))))))
% 6.73/7.04 (assert (forall ((C2 tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C2))) (= (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B)) (and (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C2) (@ (@ tptp.ord_less_eq_rat A) B)) (=> (@ (@ tptp.ord_less_rat C2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat B) A)))))))
% 6.73/7.04 (assert (forall ((C2 tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C2))) (= (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B)) (and (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C2) (@ (@ tptp.ord_less_eq_int A) B)) (=> (@ (@ tptp.ord_less_int C2) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int B) A)))))))
% 6.73/7.04 (assert (forall ((X tptp.produc9072475918466114483BT_nat)) (=> (forall ((A3 Bool) (B3 Bool) (X3 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf A3) B3)) X3)))) (=> (forall ((Uu2 tptp.option4927543243414619207at_nat) (Uv2 tptp.list_VEBT_VEBT) (Uw tptp.vEBT_VEBT) (Ux tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node Uu2) tptp.zero_zero_nat) Uv2) Uw)) Ux)))) (not (forall ((Uy tptp.option4927543243414619207at_nat) (V tptp.nat) (TreeList tptp.list_VEBT_VEBT) (S tptp.vEBT_VEBT) (X3 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node Uy) (@ tptp.suc V)) TreeList) S)) X3)))))))))
% 6.73/7.04 (assert (forall ((C2 tptp.code_integer) (A tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger C2) tptp.one_one_Code_integer) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.times_3573771949741848930nteger A) C2)) A)))))
% 6.73/7.04 (assert (forall ((C2 tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_eq_real C2) tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) C2)) A)))))
% 6.73/7.04 (assert (forall ((C2 tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat C2) tptp.one_one_rat) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C2)) A)))))
% 6.73/7.04 (assert (forall ((C2 tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat C2) tptp.one_one_nat) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A) C2)) A)))))
% 6.73/7.04 (assert (forall ((C2 tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int C2) tptp.one_one_int) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) C2)) A)))))
% 6.73/7.04 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger A) tptp.one_one_Code_integer) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) B) (=> (@ (@ tptp.ord_le3102999989581377725nteger B) tptp.one_one_Code_integer) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.times_3573771949741848930nteger A) B)) tptp.one_one_Code_integer))))))
% 6.73/7.04 (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))))))
% 6.73/7.04 (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))))))
% 6.73/7.04 (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))))))
% 6.73/7.04 (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))))))
% 6.73/7.04 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_le3102999989581377725nteger Y) tptp.one_one_Code_integer) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.times_3573771949741848930nteger X) Y)) X)))))))
% 6.73/7.04 (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)))))))
% 6.73/7.04 (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)))))))
% 6.73/7.04 (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)))))))
% 6.73/7.04 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_le3102999989581377725nteger Y) tptp.one_one_Code_integer) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.times_3573771949741848930nteger Y) X)) X)))))))
% 6.73/7.04 (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)))))))
% 6.73/7.04 (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)))))))
% 6.73/7.04 (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)))))))
% 6.73/7.04 (assert (forall ((P2 (-> tptp.nat Bool)) (N tptp.nat)) (=> (@ P2 N) (=> (not (@ P2 tptp.zero_zero_nat)) (exists ((K tptp.nat)) (and (@ (@ tptp.ord_less_nat K) N) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I4) K) (not (@ P2 I4)))) (@ P2 (@ tptp.suc K))))))))
% 6.73/7.04 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)) M2) (@ (@ tptp.ord_less_nat N) (@ (@ tptp.times_times_nat N) M2))))))
% 6.73/7.04 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)) M2) (@ (@ tptp.ord_less_nat N) (@ (@ tptp.times_times_nat M2) N))))))
% 6.73/7.04 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)))) (=> (@ _let_1 N) (=> (@ _let_1 M2) (@ _let_1 (@ (@ tptp.times_times_nat M2) N)))))))
% 6.73/7.04 (assert (= tptp.ord_less_nat (lambda ((Y4 tptp.nat) (X4 tptp.nat)) (@ (@ tptp.vEBT_VEBT_greater (@ tptp.some_nat X4)) (@ tptp.some_nat Y4)))))
% 6.73/7.04 (assert (= tptp.ord_less_nat (lambda ((X4 tptp.nat) (Y4 tptp.nat)) (@ (@ tptp.vEBT_VEBT_less (@ tptp.some_nat X4)) (@ tptp.some_nat Y4)))))
% 6.73/7.04 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.vEBT_invar_vebt (@ tptp.vEBT_vebt_buildup N)) N))))
% 6.73/7.04 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (forall ((Z tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Z) (=> (@ (@ tptp.ord_less_real Z) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real Z) X)) Y)))) (@ (@ tptp.ord_less_eq_real X) Y))))
% 6.73/7.04 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (forall ((Z tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Z) (=> (@ (@ tptp.ord_less_rat Z) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat Z) X)) Y)))) (@ (@ tptp.ord_less_eq_rat X) Y))))
% 6.73/7.04 (assert (forall ((S2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.vEBT_invar_vebt S2) tptp.m) (=> (= (@ tptp.vEBT_VEBT_set_vebt tptp.summary2) (@ tptp.vEBT_VEBT_set_vebt S2)) (= S2 tptp.summary2)))))
% 6.73/7.04 (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)))))
% 6.73/7.04 (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))))))
% 6.73/7.04 (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)))))
% 6.73/7.04 (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))))))
% 6.73/7.04 (assert (forall ((Z3 tptp.real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.times_times_real Z3))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Z3) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_real X) Y))))))
% 6.73/7.04 (assert (forall ((Z3 tptp.rat) (X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat Z3))) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Z3) (= (@ (@ tptp.ord_less_eq_rat (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_rat X) Y))))))
% 6.73/7.04 (assert (forall ((Z3 tptp.int) (X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.times_times_int Z3))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z3) (= (@ (@ tptp.ord_less_eq_int (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_int X) Y))))))
% 6.73/7.04 (assert (forall ((Z3 tptp.real) (X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Z3) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real X) Z3)) (@ (@ tptp.times_times_real Y) Z3)) (@ (@ tptp.ord_less_eq_real X) Y)))))
% 6.73/7.04 (assert (forall ((Z3 tptp.rat) (X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Z3) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat X) Z3)) (@ (@ tptp.times_times_rat Y) Z3)) (@ (@ tptp.ord_less_eq_rat X) Y)))))
% 6.73/7.04 (assert (forall ((Z3 tptp.int) (X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z3) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int X) Z3)) (@ (@ tptp.times_times_int Y) Z3)) (@ (@ tptp.ord_less_eq_int X) Y)))))
% 6.73/7.04 (assert (forall ((T tptp.vEBT_VEBT) (H tptp.nat) (K2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.vEBT_invar_vebt T) H) (=> (@ (@ tptp.vEBT_invar_vebt K2) H) (=> (= (@ tptp.vEBT_VEBT_set_vebt T) (@ tptp.vEBT_VEBT_set_vebt K2)) (= (@ tptp.vEBT_vebt_mint T) (@ tptp.vEBT_vebt_mint K2)))))))
% 6.73/7.04 (assert (forall ((T tptp.vEBT_VEBT) (H tptp.nat) (K2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.vEBT_invar_vebt T) H) (=> (@ (@ tptp.vEBT_invar_vebt K2) H) (=> (= (@ tptp.vEBT_VEBT_set_vebt T) (@ tptp.vEBT_VEBT_set_vebt K2)) (= (@ tptp.vEBT_vebt_maxt T) (@ tptp.vEBT_vebt_maxt K2)))))))
% 6.73/7.04 (assert (= tptp.m tptp.na))
% 6.73/7.04 (assert (= (@ tptp.vEBT_vebt_buildup tptp.zero_zero_nat) (@ (@ tptp.vEBT_Leaf false) false)))
% 6.73/7.04 (assert (= (@ tptp.vEBT_vebt_buildup (@ tptp.suc tptp.zero_zero_nat)) (@ (@ tptp.vEBT_Leaf false) false)))
% 6.73/7.04 (assert (forall ((Z3 tptp.real) (X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Z3) (= (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real X) Z3)) (@ (@ tptp.times_times_real Y) Z3)) (@ (@ tptp.ord_less_real X) Y)))))
% 6.73/7.04 (assert (forall ((Z3 tptp.rat) (X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Z3) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat X) Z3)) (@ (@ tptp.times_times_rat Y) Z3)) (@ (@ tptp.ord_less_rat X) Y)))))
% 6.73/7.04 (assert (forall ((Z3 tptp.int) (X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z3) (= (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int X) Z3)) (@ (@ tptp.times_times_int Y) Z3)) (@ (@ tptp.ord_less_int X) Y)))))
% 6.73/7.04 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Ux2 tptp.nat) (Uy2 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))) Ux2) Uy2) Uz)) (@ tptp.some_nat Ma))))
% 6.73/7.04 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Ux2 tptp.nat) (Uy2 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))) Ux2) Uy2) Uz)) (@ tptp.some_nat Mi))))
% 6.73/7.04 (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))))))
% 6.73/7.04 (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))))))
% 6.73/7.04 (assert (forall ((N tptp.nat) (X tptp.nat)) (not (@ (@ tptp.vEBT_V5719532721284313246member (@ tptp.vEBT_vebt_buildup N)) X))))
% 6.73/7.04 (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)))))
% 6.73/7.04 (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)))))
% 6.73/7.04 (assert (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.insert_nat tptp.mi) (@ (@ tptp.insert_nat tptp.ma) tptp.bot_bot_set_nat))) (@ tptp.vEBT_VEBT_set_vebt (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat tptp.mi) tptp.ma))) tptp.deg) tptp.treeList2) tptp.summary2))))
% 6.73/7.04 (assert (forall ((X tptp.produc9072475918466114483BT_nat)) (=> (forall ((A3 Bool) (B3 Bool) (X3 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf A3) B3)) X3)))) (not (forall ((Info tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT) (X3 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node Info) Deg2) TreeList) Summary2)) X3))))))))
% 6.73/7.04 (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))))))
% 6.73/7.04 (assert (forall ((F2 (-> 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 F2) (@ tptp.some_P7363390416028606310at_nat A)) (@ tptp.some_P7363390416028606310at_nat B)) (@ tptp.some_P7363390416028606310at_nat (@ (@ F2 A) B)))))
% 6.73/7.04 (assert (forall ((F2 (-> tptp.num tptp.num tptp.num)) (A tptp.num) (B tptp.num)) (= (@ (@ (@ tptp.vEBT_V819420779217536731ft_num F2) (@ tptp.some_num A)) (@ tptp.some_num B)) (@ tptp.some_num (@ (@ F2 A) B)))))
% 6.73/7.04 (assert (forall ((F2 (-> tptp.nat tptp.nat tptp.nat)) (A tptp.nat) (B tptp.nat)) (= (@ (@ (@ tptp.vEBT_V4262088993061758097ft_nat F2) (@ tptp.some_nat A)) (@ tptp.some_nat B)) (@ tptp.some_nat (@ (@ F2 A) B)))))
% 6.73/7.04 (assert (forall ((N tptp.nat)) (= (@ tptp.vEBT_VEBT_set_vebt (@ tptp.vEBT_vebt_buildup N)) tptp.bot_bot_set_nat)))
% 6.73/7.04 (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 ((Z4 tptp.nat)) (=> (and (@ (@ tptp.vEBT_vebt_member T) Z4) (@ (@ tptp.ord_less_nat Z4) X)) (@ (@ tptp.ord_less_eq_nat Z4) Y)))))))
% 6.73/7.04 (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 ((Z4 tptp.nat)) (=> (and (@ (@ tptp.vEBT_vebt_member T) Z4) (@ (@ tptp.ord_less_nat X) Z4)) (@ (@ tptp.ord_less_eq_nat Y) Z4)))))))
% 6.73/7.04 (assert (= tptp.deg (@ (@ tptp.plus_plus_nat tptp.na) tptp.m)))
% 6.73/7.04 (assert (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 tptp.treeList2)) (and (@ (@ tptp.vEBT_invar_vebt X5) tptp.na) (forall ((Xa tptp.vEBT_VEBT)) (=> (@ (@ tptp.vEBT_invar_vebt Xa) tptp.na) (=> (= (@ tptp.vEBT_VEBT_set_vebt X5) (@ tptp.vEBT_VEBT_set_vebt Xa)) (= Xa X5))))))))
% 6.73/7.04 (assert (forall ((A tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A) tptp.bot_bot_set_int) (= A tptp.bot_bot_set_int))))
% 6.73/7.04 (assert (forall ((A tptp.set_real)) (=> (@ (@ tptp.ord_less_eq_set_real A) tptp.bot_bot_set_real) (= A tptp.bot_bot_set_real))))
% 6.73/7.04 (assert (forall ((A tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A) tptp.bot_bot_set_nat) (= A tptp.bot_bot_set_nat))))
% 6.73/7.04 (assert (forall ((A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.bot_bot_nat) (= A tptp.bot_bot_nat))))
% 6.73/7.04 (assert (forall ((A tptp.set_int)) (= (@ (@ tptp.ord_less_eq_set_int A) tptp.bot_bot_set_int) (= A tptp.bot_bot_set_int))))
% 6.73/7.04 (assert (forall ((A tptp.set_real)) (= (@ (@ tptp.ord_less_eq_set_real A) tptp.bot_bot_set_real) (= A tptp.bot_bot_set_real))))
% 6.73/7.04 (assert (forall ((A tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat A) tptp.bot_bot_set_nat) (= A tptp.bot_bot_set_nat))))
% 6.73/7.04 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat A) tptp.bot_bot_nat) (= A tptp.bot_bot_nat))))
% 6.73/7.04 (assert (forall ((A tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int tptp.bot_bot_set_int) A)))
% 6.73/7.04 (assert (forall ((A tptp.set_real)) (@ (@ tptp.ord_less_eq_set_real tptp.bot_bot_set_real) A)))
% 6.73/7.04 (assert (forall ((A tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat tptp.bot_bot_set_nat) A)))
% 6.73/7.04 (assert (forall ((A tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.bot_bot_nat) A)))
% 6.73/7.04 (assert (forall ((A tptp.set_nat)) (not (@ (@ tptp.ord_less_set_nat A) tptp.bot_bot_set_nat))))
% 6.73/7.04 (assert (forall ((A tptp.set_int)) (not (@ (@ tptp.ord_less_set_int A) tptp.bot_bot_set_int))))
% 6.73/7.04 (assert (forall ((A tptp.set_real)) (not (@ (@ tptp.ord_less_set_real A) tptp.bot_bot_set_real))))
% 6.73/7.04 (assert (forall ((A tptp.nat)) (not (@ (@ tptp.ord_less_nat A) tptp.bot_bot_nat))))
% 6.73/7.04 (assert (forall ((A tptp.set_nat)) (= (not (= A tptp.bot_bot_set_nat)) (@ (@ tptp.ord_less_set_nat tptp.bot_bot_set_nat) A))))
% 6.73/7.04 (assert (forall ((A tptp.set_int)) (= (not (= A tptp.bot_bot_set_int)) (@ (@ tptp.ord_less_set_int tptp.bot_bot_set_int) A))))
% 6.73/7.04 (assert (forall ((A tptp.set_real)) (= (not (= A tptp.bot_bot_set_real)) (@ (@ tptp.ord_less_set_real tptp.bot_bot_set_real) A))))
% 6.73/7.04 (assert (forall ((A tptp.nat)) (= (not (= A tptp.bot_bot_nat)) (@ (@ tptp.ord_less_nat tptp.bot_bot_nat) A))))
% 6.73/7.04 (assert (forall ((Uu tptp.option4927543243414619207at_nat) (Uv tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT) (Ux2 tptp.nat)) (not (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ (@ (@ tptp.vEBT_Node Uu) tptp.zero_zero_nat) Uv) Uw2)) Ux2))))
% 6.73/7.04 (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))))))))
% 6.73/7.04 (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))))))
% 6.73/7.04 (assert (forall ((V2 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 V2)) (@ tptp.suc tptp.zero_zero_nat)) Vb) Vc)) X))))
% 6.73/7.04 (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))))))))
% 6.73/7.04 (assert (forall ((V2 tptp.product_prod_nat_nat) (Uy2 tptp.list_VEBT_VEBT) (Uz tptp.vEBT_VEBT) (X tptp.nat)) (not (@ (@ tptp.vEBT_vebt_member (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Uy2) Uz)) X))))
% 6.73/7.04 (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)))))
% 6.73/7.04 (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)))))
% 6.73/7.04 (assert (forall ((N tptp.nat) (X tptp.nat)) (not (@ (@ tptp.vEBT_VEBT_membermima (@ tptp.vEBT_vebt_buildup N)) X))))
% 6.73/7.04 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (= (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.vEBT_vebt_delete T) X)) Y) (and (not (= X Y)) (@ (@ tptp.vEBT_vebt_member T) Y))))))
% 6.73/7.04 (assert (forall ((X tptp.produc9072475918466114483BT_nat)) (=> (forall ((Uu2 Bool) (Uv2 Bool) (Uw tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf Uu2) Uv2)) Uw)))) (=> (forall ((Ux tptp.list_VEBT_VEBT) (Uy tptp.vEBT_VEBT) (Uz2 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) tptp.zero_zero_nat) Ux) Uy)) Uz2)))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va2 tptp.list_VEBT_VEBT) (Vb2 tptp.vEBT_VEBT) (X3 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) Va2) Vb2)) X3)))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (V tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT) (X3 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc V)) TreeList) Vc2)) X3)))) (not (forall ((V tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Vd tptp.vEBT_VEBT) (X3 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) (@ tptp.suc V)) TreeList) Vd)) X3)))))))))))
% 6.73/7.04 (assert (=> (= tptp.mi tptp.ma) (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 tptp.treeList2)) (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X5) X_1)))))))
% 6.73/7.04 (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)))))))))
% 6.73/7.04 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (@ (@ tptp.vEBT_invar_vebt (@ (@ tptp.vEBT_vebt_delete T) X)) N))))
% 6.73/7.04 (assert (forall ((T tptp.vEBT_VEBT) (X tptp.nat)) (=> (= (@ tptp.vEBT_vebt_maxt T) (@ tptp.some_nat X)) (@ (@ tptp.vEBT_V8194947554948674370ptions T) X))))
% 6.73/7.04 (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))))))
% 6.73/7.04 (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)))))
% 6.73/7.04 (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)))))
% 6.73/7.04 (assert (= tptp.vEBT_V8194947554948674370ptions (lambda ((T2 tptp.vEBT_VEBT) (X4 tptp.nat)) (or (@ (@ tptp.vEBT_V5719532721284313246member T2) X4) (@ (@ tptp.vEBT_VEBT_membermima T2) X4)))))
% 6.73/7.04 (assert (forall ((B tptp.real) (A tptp.real) (C2 tptp.real)) (= (= (@ (@ tptp.plus_plus_real B) A) (@ (@ tptp.plus_plus_real C2) A)) (= B C2))))
% 6.73/7.04 (assert (forall ((B tptp.rat) (A tptp.rat) (C2 tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat B) A) (@ (@ tptp.plus_plus_rat C2) A)) (= B C2))))
% 6.73/7.04 (assert (forall ((B tptp.nat) (A tptp.nat) (C2 tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat B) A) (@ (@ tptp.plus_plus_nat C2) A)) (= B C2))))
% 6.73/7.04 (assert (forall ((B tptp.int) (A tptp.int) (C2 tptp.int)) (= (= (@ (@ tptp.plus_plus_int B) A) (@ (@ tptp.plus_plus_int C2) A)) (= B C2))))
% 6.73/7.04 (assert (forall ((A tptp.real) (B tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A))) (= (= (@ _let_1 B) (@ _let_1 C2)) (= B C2)))))
% 6.73/7.04 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat A))) (= (= (@ _let_1 B) (@ _let_1 C2)) (= B C2)))))
% 6.73/7.04 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A))) (= (= (@ _let_1 B) (@ _let_1 C2)) (= B C2)))))
% 6.73/7.04 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A))) (= (= (@ _let_1 B) (@ _let_1 C2)) (= B C2)))))
% 6.73/7.04 (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 ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X5) X_1))))) (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary) X_1))))))))
% 6.73/7.04 (assert (forall ((C2 tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real C2))) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_real A) B)))))
% 6.73/7.04 (assert (forall ((C2 tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat C2))) (= (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_rat A) B)))))
% 6.73/7.04 (assert (forall ((C2 tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C2))) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_nat A) B)))))
% 6.73/7.04 (assert (forall ((C2 tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C2))) (= (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_int A) B)))))
% 6.73/7.04 (assert (forall ((A tptp.real) (C2 tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A) C2)) (@ (@ tptp.plus_plus_real B) C2)) (@ (@ tptp.ord_less_eq_real A) B))))
% 6.73/7.04 (assert (forall ((A tptp.rat) (C2 tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A) C2)) (@ (@ tptp.plus_plus_rat B) C2)) (@ (@ tptp.ord_less_eq_rat A) B))))
% 6.73/7.04 (assert (forall ((A tptp.nat) (C2 tptp.nat) (B tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A) C2)) (@ (@ tptp.plus_plus_nat B) C2)) (@ (@ tptp.ord_less_eq_nat A) B))))
% 6.73/7.04 (assert (forall ((A tptp.int) (C2 tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A) C2)) (@ (@ tptp.plus_plus_int B) C2)) (@ (@ tptp.ord_less_eq_int A) B))))
% 6.73/7.04 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex A) tptp.zero_zero_complex) A)))
% 6.73/7.04 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real A) tptp.zero_zero_real) A)))
% 6.73/7.04 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat A) tptp.zero_zero_rat) A)))
% 6.73/7.04 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.plus_plus_nat A) tptp.zero_zero_nat) A)))
% 6.73/7.04 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int A) tptp.zero_zero_int) A)))
% 6.73/7.04 (assert (forall ((A tptp.real)) (= (= tptp.zero_zero_real (@ (@ tptp.plus_plus_real A) A)) (= A tptp.zero_zero_real))))
% 6.73/7.04 (assert (forall ((A tptp.rat)) (= (= tptp.zero_zero_rat (@ (@ tptp.plus_plus_rat A) A)) (= A tptp.zero_zero_rat))))
% 6.73/7.04 (assert (forall ((A tptp.int)) (= (= tptp.zero_zero_int (@ (@ tptp.plus_plus_int A) A)) (= A tptp.zero_zero_int))))
% 6.73/7.04 (assert (forall ((B tptp.complex) (A tptp.complex)) (= (= (@ (@ tptp.plus_plus_complex B) A) A) (= B tptp.zero_zero_complex))))
% 6.73/7.04 (assert (forall ((B tptp.real) (A tptp.real)) (= (= (@ (@ tptp.plus_plus_real B) A) A) (= B tptp.zero_zero_real))))
% 6.73/7.04 (assert (forall ((B tptp.rat) (A tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat B) A) A) (= B tptp.zero_zero_rat))))
% 6.73/7.04 (assert (forall ((B tptp.nat) (A tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat B) A) A) (= B tptp.zero_zero_nat))))
% 6.73/7.04 (assert (forall ((B tptp.int) (A tptp.int)) (= (= (@ (@ tptp.plus_plus_int B) A) A) (= B tptp.zero_zero_int))))
% 6.73/7.04 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= (@ (@ tptp.plus_plus_complex A) B) A) (= B tptp.zero_zero_complex))))
% 6.73/7.04 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ (@ tptp.plus_plus_real A) B) A) (= B tptp.zero_zero_real))))
% 6.73/7.04 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat A) B) A) (= B tptp.zero_zero_rat))))
% 6.73/7.04 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat A) B) A) (= B tptp.zero_zero_nat))))
% 6.73/7.04 (assert (forall ((A tptp.int) (B tptp.int)) (= (= (@ (@ tptp.plus_plus_int A) B) A) (= B tptp.zero_zero_int))))
% 6.73/7.04 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= A (@ (@ tptp.plus_plus_complex B) A)) (= B tptp.zero_zero_complex))))
% 6.73/7.04 (assert (forall ((A tptp.real) (B tptp.real)) (= (= A (@ (@ tptp.plus_plus_real B) A)) (= B tptp.zero_zero_real))))
% 6.73/7.04 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= A (@ (@ tptp.plus_plus_rat B) A)) (= B tptp.zero_zero_rat))))
% 6.73/7.04 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (= A (@ (@ tptp.plus_plus_nat B) A)) (= B tptp.zero_zero_nat))))
% 6.73/7.04 (assert (forall ((A tptp.int) (B tptp.int)) (= (= A (@ (@ tptp.plus_plus_int B) A)) (= B tptp.zero_zero_int))))
% 6.73/7.04 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= A (@ (@ tptp.plus_plus_complex A) B)) (= B tptp.zero_zero_complex))))
% 6.73/7.04 (assert (forall ((A tptp.real) (B tptp.real)) (= (= A (@ (@ tptp.plus_plus_real A) B)) (= B tptp.zero_zero_real))))
% 6.73/7.04 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= A (@ (@ tptp.plus_plus_rat A) B)) (= B tptp.zero_zero_rat))))
% 6.73/7.04 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (= A (@ (@ tptp.plus_plus_nat A) B)) (= B tptp.zero_zero_nat))))
% 6.73/7.04 (assert (forall ((A tptp.int) (B tptp.int)) (= (= A (@ (@ tptp.plus_plus_int A) B)) (= B tptp.zero_zero_int))))
% 6.73/7.04 (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)))))
% 6.73/7.04 (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)))))
% 6.73/7.04 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex tptp.zero_zero_complex) A) A)))
% 6.73/7.04 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real tptp.zero_zero_real) A) A)))
% 6.73/7.04 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat tptp.zero_zero_rat) A) A)))
% 6.73/7.04 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.plus_plus_nat tptp.zero_zero_nat) A) A)))
% 6.73/7.04 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int tptp.zero_zero_int) A) A)))
% 6.73/7.04 (assert (forall ((A tptp.real) (C2 tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) C2)) (@ (@ tptp.plus_plus_real B) C2)) (@ (@ tptp.ord_less_real A) B))))
% 6.73/7.04 (assert (forall ((A tptp.rat) (C2 tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) C2)) (@ (@ tptp.plus_plus_rat B) C2)) (@ (@ tptp.ord_less_rat A) B))))
% 6.73/7.04 (assert (forall ((A tptp.nat) (C2 tptp.nat) (B tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) C2)) (@ (@ tptp.plus_plus_nat B) C2)) (@ (@ tptp.ord_less_nat A) B))))
% 6.73/7.04 (assert (forall ((A tptp.int) (C2 tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) C2)) (@ (@ tptp.plus_plus_int B) C2)) (@ (@ tptp.ord_less_int A) B))))
% 6.73/7.04 (assert (forall ((C2 tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real C2))) (= (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_real A) B)))))
% 6.73/7.04 (assert (forall ((C2 tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat C2))) (= (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_rat A) B)))))
% 6.73/7.04 (assert (forall ((C2 tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C2))) (= (@ (@ tptp.ord_less_nat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_nat A) B)))))
% 6.73/7.04 (assert (forall ((C2 tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C2))) (= (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_int A) B)))))
% 6.73/7.04 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat M2))) (= (@ _let_1 (@ tptp.suc N)) (@ tptp.suc (@ _let_1 N))))))
% 6.73/7.04 (assert (forall ((M2 tptp.nat)) (= (@ (@ tptp.plus_plus_nat M2) tptp.zero_zero_nat) M2)))
% 6.73/7.04 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat M2) N) tptp.zero_zero_nat) (and (= M2 tptp.zero_zero_nat) (= N tptp.zero_zero_nat)))))
% 6.73/7.04 (assert (forall ((K2 tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K2))) (= (@ (@ tptp.ord_less_nat (@ _let_1 M2)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat M2) N)))))
% 6.73/7.04 (assert (forall ((K2 tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K2))) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 M2)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat M2) N)))))
% 6.73/7.04 (assert (forall ((X tptp.option4927543243414619207at_nat)) (= (forall ((Y4 tptp.product_prod_nat_nat)) (not (= X (@ tptp.some_P7363390416028606310at_nat Y4)))) (= X tptp.none_P5556105721700978146at_nat))))
% 6.73/7.04 (assert (forall ((X tptp.option_nat)) (= (forall ((Y4 tptp.nat)) (not (= X (@ tptp.some_nat Y4)))) (= X tptp.none_nat))))
% 6.73/7.04 (assert (forall ((X tptp.option_num)) (= (forall ((Y4 tptp.num)) (not (= X (@ tptp.some_num Y4)))) (= X tptp.none_num))))
% 6.73/7.04 (assert (forall ((X tptp.option4927543243414619207at_nat)) (= (not (= X tptp.none_P5556105721700978146at_nat)) (exists ((Y4 tptp.product_prod_nat_nat)) (= X (@ tptp.some_P7363390416028606310at_nat Y4))))))
% 6.73/7.04 (assert (forall ((X tptp.option_nat)) (= (not (= X tptp.none_nat)) (exists ((Y4 tptp.nat)) (= X (@ tptp.some_nat Y4))))))
% 6.73/7.04 (assert (forall ((X tptp.option_num)) (= (not (= X tptp.none_num)) (exists ((Y4 tptp.num)) (= X (@ tptp.some_num Y4))))))
% 6.73/7.04 (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))))
% 6.73/7.04 (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))))
% 6.73/7.04 (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))))
% 6.73/7.04 (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))))
% 6.73/7.04 (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))))
% 6.73/7.04 (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))))
% 6.73/7.04 (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))))
% 6.73/7.04 (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))))
% 6.73/7.04 (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))))
% 6.73/7.04 (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))))
% 6.73/7.04 (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))))
% 6.73/7.04 (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))))
% 6.73/7.04 (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))))
% 6.73/7.04 (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))))
% 6.73/7.04 (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))))
% 6.73/7.04 (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))))
% 6.73/7.04 (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))))
% 6.73/7.04 (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))))
% 6.73/7.04 (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))))
% 6.73/7.04 (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)))))
% 6.73/7.04 (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)))))
% 6.73/7.04 (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)))))
% 6.73/7.04 (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)))))
% 6.73/7.04 (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)))))
% 6.73/7.04 (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)))))
% 6.73/7.04 (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))))
% 6.73/7.04 (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))))
% 6.73/7.04 (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))))
% 6.73/7.04 (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))))
% 6.73/7.04 (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))))
% 6.73/7.04 (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))))
% 6.73/7.04 (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))))
% 6.73/7.04 (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))))
% 6.73/7.04 (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))))
% 6.73/7.04 (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))))
% 6.73/7.04 (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))))
% 6.73/7.04 (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))))
% 6.73/7.04 (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))))
% 6.73/7.04 (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))))
% 6.73/7.04 (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))))
% 6.73/7.04 (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))))
% 6.73/7.04 (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))))
% 6.73/7.04 (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))))
% 6.73/7.04 (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))))
% 6.73/7.04 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M2) N)) (or (@ _let_1 M2) (@ _let_1 N))))))
% 6.73/7.04 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat M2))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.plus_plus_nat M2) (@ _let_1 N))))))
% 6.73/7.04 (assert (forall ((B tptp.real) (A tptp.real) (C2 tptp.real)) (=> (= (@ (@ tptp.plus_plus_real B) A) (@ (@ tptp.plus_plus_real C2) A)) (= B C2))))
% 6.73/7.04 (assert (forall ((B tptp.rat) (A tptp.rat) (C2 tptp.rat)) (=> (= (@ (@ tptp.plus_plus_rat B) A) (@ (@ tptp.plus_plus_rat C2) A)) (= B C2))))
% 6.73/7.04 (assert (forall ((B tptp.nat) (A tptp.nat) (C2 tptp.nat)) (=> (= (@ (@ tptp.plus_plus_nat B) A) (@ (@ tptp.plus_plus_nat C2) A)) (= B C2))))
% 6.73/7.04 (assert (forall ((B tptp.int) (A tptp.int) (C2 tptp.int)) (=> (= (@ (@ tptp.plus_plus_int B) A) (@ (@ tptp.plus_plus_int C2) A)) (= B C2))))
% 6.73/7.04 (assert (forall ((A tptp.real) (B tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A))) (=> (= (@ _let_1 B) (@ _let_1 C2)) (= B C2)))))
% 6.73/7.04 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat A))) (=> (= (@ _let_1 B) (@ _let_1 C2)) (= B C2)))))
% 6.73/7.04 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A))) (=> (= (@ _let_1 B) (@ _let_1 C2)) (= B C2)))))
% 6.73/7.04 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A))) (=> (= (@ _let_1 B) (@ _let_1 C2)) (= B C2)))))
% 6.73/7.04 (assert (forall ((B tptp.real) (A tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real B))) (let ((_let_2 (@ tptp.plus_plus_real A))) (= (@ _let_1 (@ _let_2 C2)) (@ _let_2 (@ _let_1 C2)))))))
% 6.73/7.04 (assert (forall ((B tptp.rat) (A tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat B))) (let ((_let_2 (@ tptp.plus_plus_rat A))) (= (@ _let_1 (@ _let_2 C2)) (@ _let_2 (@ _let_1 C2)))))))
% 6.73/7.04 (assert (forall ((B tptp.nat) (A tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat B))) (let ((_let_2 (@ tptp.plus_plus_nat A))) (= (@ _let_1 (@ _let_2 C2)) (@ _let_2 (@ _let_1 C2)))))))
% 6.73/7.04 (assert (forall ((B tptp.int) (A tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int B))) (let ((_let_2 (@ tptp.plus_plus_int A))) (= (@ _let_1 (@ _let_2 C2)) (@ _let_2 (@ _let_1 C2)))))))
% 6.73/7.04 (assert (= tptp.plus_plus_real (lambda ((A5 tptp.real) (B4 tptp.real)) (@ (@ tptp.plus_plus_real B4) A5))))
% 6.73/7.04 (assert (= tptp.plus_plus_rat (lambda ((A5 tptp.rat) (B4 tptp.rat)) (@ (@ tptp.plus_plus_rat B4) A5))))
% 6.73/7.04 (assert (= tptp.plus_plus_nat (lambda ((A5 tptp.nat) (B4 tptp.nat)) (@ (@ tptp.plus_plus_nat B4) A5))))
% 6.73/7.04 (assert (= tptp.plus_plus_int (lambda ((A5 tptp.int) (B4 tptp.int)) (@ (@ tptp.plus_plus_int B4) A5))))
% 6.73/7.04 (assert (forall ((B tptp.real) (A tptp.real) (C2 tptp.real)) (= (= (@ (@ tptp.plus_plus_real B) A) (@ (@ tptp.plus_plus_real C2) A)) (= B C2))))
% 6.73/7.04 (assert (forall ((B tptp.rat) (A tptp.rat) (C2 tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat B) A) (@ (@ tptp.plus_plus_rat C2) A)) (= B C2))))
% 6.73/7.04 (assert (forall ((B tptp.int) (A tptp.int) (C2 tptp.int)) (= (= (@ (@ tptp.plus_plus_int B) A) (@ (@ tptp.plus_plus_int C2) A)) (= B C2))))
% 6.73/7.04 (assert (forall ((A tptp.real) (B tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A))) (= (= (@ _let_1 B) (@ _let_1 C2)) (= B C2)))))
% 6.73/7.04 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat A))) (= (= (@ _let_1 B) (@ _let_1 C2)) (= B C2)))))
% 6.73/7.04 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A))) (= (= (@ _let_1 B) (@ _let_1 C2)) (= B C2)))))
% 6.73/7.04 (assert (forall ((A tptp.real) (B tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A))) (= (@ (@ tptp.plus_plus_real (@ _let_1 B)) C2) (@ _let_1 (@ (@ tptp.plus_plus_real B) C2))))))
% 6.73/7.04 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat A))) (= (@ (@ tptp.plus_plus_rat (@ _let_1 B)) C2) (@ _let_1 (@ (@ tptp.plus_plus_rat B) C2))))))
% 6.73/7.04 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A))) (= (@ (@ tptp.plus_plus_nat (@ _let_1 B)) C2) (@ _let_1 (@ (@ tptp.plus_plus_nat B) C2))))))
% 6.73/7.04 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A))) (= (@ (@ tptp.plus_plus_int (@ _let_1 B)) C2) (@ _let_1 (@ (@ tptp.plus_plus_int B) C2))))))
% 6.73/7.04 (assert (forall ((B5 tptp.real) (K2 tptp.real) (B tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A))) (let ((_let_2 (@ tptp.plus_plus_real K2))) (=> (= B5 (@ _let_2 B)) (= (@ _let_1 B5) (@ _let_2 (@ _let_1 B))))))))
% 6.73/7.04 (assert (forall ((B5 tptp.rat) (K2 tptp.rat) (B tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat A))) (let ((_let_2 (@ tptp.plus_plus_rat K2))) (=> (= B5 (@ _let_2 B)) (= (@ _let_1 B5) (@ _let_2 (@ _let_1 B))))))))
% 6.73/7.04 (assert (forall ((B5 tptp.nat) (K2 tptp.nat) (B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A))) (let ((_let_2 (@ tptp.plus_plus_nat K2))) (=> (= B5 (@ _let_2 B)) (= (@ _let_1 B5) (@ _let_2 (@ _let_1 B))))))))
% 6.73/7.04 (assert (forall ((B5 tptp.int) (K2 tptp.int) (B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A))) (let ((_let_2 (@ tptp.plus_plus_int K2))) (=> (= B5 (@ _let_2 B)) (= (@ _let_1 B5) (@ _let_2 (@ _let_1 B))))))))
% 6.73/7.04 (assert (forall ((A4 tptp.real) (K2 tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real K2))) (=> (= A4 (@ _let_1 A)) (= (@ (@ tptp.plus_plus_real A4) B) (@ _let_1 (@ (@ tptp.plus_plus_real A) B)))))))
% 6.73/7.04 (assert (forall ((A4 tptp.rat) (K2 tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat K2))) (=> (= A4 (@ _let_1 A)) (= (@ (@ tptp.plus_plus_rat A4) B) (@ _let_1 (@ (@ tptp.plus_plus_rat A) B)))))))
% 6.73/7.04 (assert (forall ((A4 tptp.nat) (K2 tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K2))) (=> (= A4 (@ _let_1 A)) (= (@ (@ tptp.plus_plus_nat A4) B) (@ _let_1 (@ (@ tptp.plus_plus_nat A) B)))))))
% 6.73/7.04 (assert (forall ((A4 tptp.int) (K2 tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int K2))) (=> (= A4 (@ _let_1 A)) (= (@ (@ tptp.plus_plus_int A4) B) (@ _let_1 (@ (@ tptp.plus_plus_int A) B)))))))
% 6.73/7.04 (assert (forall ((I2 tptp.real) (J2 tptp.real) (K2 tptp.real) (L tptp.real)) (=> (and (= I2 J2) (= K2 L)) (= (@ (@ tptp.plus_plus_real I2) K2) (@ (@ tptp.plus_plus_real J2) L)))))
% 6.73/7.04 (assert (forall ((I2 tptp.rat) (J2 tptp.rat) (K2 tptp.rat) (L tptp.rat)) (=> (and (= I2 J2) (= K2 L)) (= (@ (@ tptp.plus_plus_rat I2) K2) (@ (@ tptp.plus_plus_rat J2) L)))))
% 6.73/7.04 (assert (forall ((I2 tptp.nat) (J2 tptp.nat) (K2 tptp.nat) (L tptp.nat)) (=> (and (= I2 J2) (= K2 L)) (= (@ (@ tptp.plus_plus_nat I2) K2) (@ (@ tptp.plus_plus_nat J2) L)))))
% 6.73/7.04 (assert (forall ((I2 tptp.int) (J2 tptp.int) (K2 tptp.int) (L tptp.int)) (=> (and (= I2 J2) (= K2 L)) (= (@ (@ tptp.plus_plus_int I2) K2) (@ (@ tptp.plus_plus_int J2) L)))))
% 6.73/7.04 (assert (forall ((A tptp.real) (B tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A))) (= (@ (@ tptp.plus_plus_real (@ _let_1 B)) C2) (@ _let_1 (@ (@ tptp.plus_plus_real B) C2))))))
% 6.73/7.04 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat A))) (= (@ (@ tptp.plus_plus_rat (@ _let_1 B)) C2) (@ _let_1 (@ (@ tptp.plus_plus_rat B) C2))))))
% 6.73/7.04 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A))) (= (@ (@ tptp.plus_plus_int (@ _let_1 B)) C2) (@ _let_1 (@ (@ tptp.plus_plus_int B) C2))))))
% 6.73/7.04 (assert (forall ((A tptp.real) (B tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A))) (= (@ (@ tptp.plus_plus_real (@ _let_1 B)) C2) (@ _let_1 (@ (@ tptp.plus_plus_real B) C2))))))
% 6.73/7.04 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat A))) (= (@ (@ tptp.plus_plus_rat (@ _let_1 B)) C2) (@ _let_1 (@ (@ tptp.plus_plus_rat B) C2))))))
% 6.73/7.04 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A))) (= (@ (@ tptp.plus_plus_nat (@ _let_1 B)) C2) (@ _let_1 (@ (@ tptp.plus_plus_nat B) C2))))))
% 6.73/7.04 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A))) (= (@ (@ tptp.plus_plus_int (@ _let_1 B)) C2) (@ _let_1 (@ (@ tptp.plus_plus_int B) C2))))))
% 6.73/7.04 (assert (= tptp.bot_bot_nat tptp.zero_zero_nat))
% 6.73/7.04 (assert (forall ((Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT) (Uz tptp.nat)) (not (@ (@ tptp.vEBT_VEBT_membermima (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) tptp.zero_zero_nat) Ux2) Uy2)) Uz))))
% 6.73/7.04 (assert (forall ((I2 tptp.real) (J2 tptp.real) (K2 tptp.real) (L tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real I2) J2) (= K2 L)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real I2) K2)) (@ (@ tptp.plus_plus_real J2) L)))))
% 6.73/7.04 (assert (forall ((I2 tptp.rat) (J2 tptp.rat) (K2 tptp.rat) (L tptp.rat)) (=> (and (@ (@ tptp.ord_less_eq_rat I2) J2) (= K2 L)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat I2) K2)) (@ (@ tptp.plus_plus_rat J2) L)))))
% 6.73/7.04 (assert (forall ((I2 tptp.nat) (J2 tptp.nat) (K2 tptp.nat) (L tptp.nat)) (=> (and (@ (@ tptp.ord_less_eq_nat I2) J2) (= K2 L)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I2) K2)) (@ (@ tptp.plus_plus_nat J2) L)))))
% 6.73/7.04 (assert (forall ((I2 tptp.int) (J2 tptp.int) (K2 tptp.int) (L tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int I2) J2) (= K2 L)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int I2) K2)) (@ (@ tptp.plus_plus_int J2) L)))))
% 6.73/7.04 (assert (forall ((I2 tptp.real) (J2 tptp.real) (K2 tptp.real) (L tptp.real)) (=> (and (= I2 J2) (@ (@ tptp.ord_less_eq_real K2) L)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real I2) K2)) (@ (@ tptp.plus_plus_real J2) L)))))
% 6.73/7.04 (assert (forall ((I2 tptp.rat) (J2 tptp.rat) (K2 tptp.rat) (L tptp.rat)) (=> (and (= I2 J2) (@ (@ tptp.ord_less_eq_rat K2) L)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat I2) K2)) (@ (@ tptp.plus_plus_rat J2) L)))))
% 6.73/7.04 (assert (forall ((I2 tptp.nat) (J2 tptp.nat) (K2 tptp.nat) (L tptp.nat)) (=> (and (= I2 J2) (@ (@ tptp.ord_less_eq_nat K2) L)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I2) K2)) (@ (@ tptp.plus_plus_nat J2) L)))))
% 6.73/7.04 (assert (forall ((I2 tptp.int) (J2 tptp.int) (K2 tptp.int) (L tptp.int)) (=> (and (= I2 J2) (@ (@ tptp.ord_less_eq_int K2) L)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int I2) K2)) (@ (@ tptp.plus_plus_int J2) L)))))
% 6.73/7.04 (assert (forall ((I2 tptp.real) (J2 tptp.real) (K2 tptp.real) (L tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real I2) J2) (@ (@ tptp.ord_less_eq_real K2) L)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real I2) K2)) (@ (@ tptp.plus_plus_real J2) L)))))
% 6.73/7.04 (assert (forall ((I2 tptp.rat) (J2 tptp.rat) (K2 tptp.rat) (L tptp.rat)) (=> (and (@ (@ tptp.ord_less_eq_rat I2) J2) (@ (@ tptp.ord_less_eq_rat K2) L)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat I2) K2)) (@ (@ tptp.plus_plus_rat J2) L)))))
% 6.73/7.04 (assert (forall ((I2 tptp.nat) (J2 tptp.nat) (K2 tptp.nat) (L tptp.nat)) (=> (and (@ (@ tptp.ord_less_eq_nat I2) J2) (@ (@ tptp.ord_less_eq_nat K2) L)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I2) K2)) (@ (@ tptp.plus_plus_nat J2) L)))))
% 6.73/7.04 (assert (forall ((I2 tptp.int) (J2 tptp.int) (K2 tptp.int) (L tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int I2) J2) (@ (@ tptp.ord_less_eq_int K2) L)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int I2) K2)) (@ (@ tptp.plus_plus_int J2) L)))))
% 6.73/7.04 (assert (forall ((A tptp.real) (B tptp.real) (C2 tptp.real) (D tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real C2) D) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A) C2)) (@ (@ tptp.plus_plus_real B) D))))))
% 6.73/7.04 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat) (D tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat C2) D) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A) C2)) (@ (@ tptp.plus_plus_rat B) D))))))
% 6.73/7.04 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat) (D tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat C2) D) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A) C2)) (@ (@ tptp.plus_plus_nat B) D))))))
% 6.73/7.04 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int) (D tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_eq_int C2) D) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A) C2)) (@ (@ tptp.plus_plus_int B) D))))))
% 6.73/7.04 (assert (forall ((A tptp.real) (B tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real C2))) (=> (@ (@ tptp.ord_less_eq_real A) B) (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B))))))
% 6.73/7.04 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat C2))) (=> (@ (@ tptp.ord_less_eq_rat A) B) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B))))))
% 6.73/7.04 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C2))) (=> (@ (@ tptp.ord_less_eq_nat A) B) (@ (@ tptp.ord_less_eq_nat (@ _let_1 A)) (@ _let_1 B))))))
% 6.73/7.04 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C2))) (=> (@ (@ tptp.ord_less_eq_int A) B) (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B))))))
% 6.73/7.04 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (not (forall ((C tptp.nat)) (not (= B (@ (@ tptp.plus_plus_nat A) C))))))))
% 6.73/7.04 (assert (forall ((A tptp.real) (B tptp.real) (C2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A) C2)) (@ (@ tptp.plus_plus_real B) C2)))))
% 6.73/7.04 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A) C2)) (@ (@ tptp.plus_plus_rat B) C2)))))
% 6.73/7.04 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A) C2)) (@ (@ tptp.plus_plus_nat B) C2)))))
% 6.73/7.04 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A) C2)) (@ (@ tptp.plus_plus_int B) C2)))))
% 6.73/7.04 (assert (= tptp.ord_less_eq_nat (lambda ((A5 tptp.nat) (B4 tptp.nat)) (exists ((C3 tptp.nat)) (= B4 (@ (@ tptp.plus_plus_nat A5) C3))))))
% 6.73/7.04 (assert (forall ((C2 tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real C2))) (=> (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_real A) B)))))
% 6.73/7.04 (assert (forall ((C2 tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat C2))) (=> (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_rat A) B)))))
% 6.73/7.04 (assert (forall ((C2 tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C2))) (=> (@ (@ tptp.ord_less_eq_nat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_nat A) B)))))
% 6.73/7.04 (assert (forall ((C2 tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C2))) (=> (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_int A) B)))))
% 6.73/7.04 (assert (forall ((A tptp.real) (C2 tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A) C2)) (@ (@ tptp.plus_plus_real B) C2)) (@ (@ tptp.ord_less_eq_real A) B))))
% 6.73/7.04 (assert (forall ((A tptp.rat) (C2 tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A) C2)) (@ (@ tptp.plus_plus_rat B) C2)) (@ (@ tptp.ord_less_eq_rat A) B))))
% 6.73/7.04 (assert (forall ((A tptp.nat) (C2 tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A) C2)) (@ (@ tptp.plus_plus_nat B) C2)) (@ (@ tptp.ord_less_eq_nat A) B))))
% 6.73/7.04 (assert (forall ((A tptp.int) (C2 tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A) C2)) (@ (@ tptp.plus_plus_int B) C2)) (@ (@ tptp.ord_less_eq_int A) B))))
% 6.73/7.04 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex tptp.zero_zero_complex) A) A)))
% 6.73/7.04 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real tptp.zero_zero_real) A) A)))
% 6.73/7.04 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat tptp.zero_zero_rat) A) A)))
% 6.73/7.04 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.plus_plus_nat tptp.zero_zero_nat) A) A)))
% 6.73/7.04 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int tptp.zero_zero_int) A) A)))
% 6.73/7.04 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex A) tptp.zero_zero_complex) A)))
% 6.73/7.04 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real A) tptp.zero_zero_real) A)))
% 6.73/7.04 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat A) tptp.zero_zero_rat) A)))
% 6.73/7.04 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.plus_plus_nat A) tptp.zero_zero_nat) A)))
% 6.73/7.04 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int A) tptp.zero_zero_int) A)))
% 6.73/7.04 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex tptp.zero_zero_complex) A) A)))
% 6.73/7.04 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real tptp.zero_zero_real) A) A)))
% 6.73/7.04 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat tptp.zero_zero_rat) A) A)))
% 6.73/7.04 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int tptp.zero_zero_int) A) A)))
% 6.73/7.04 (assert (forall ((A tptp.real) (C2 tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) C2)) (@ (@ tptp.plus_plus_real B) C2)) (@ (@ tptp.ord_less_real A) B))))
% 6.73/7.04 (assert (forall ((A tptp.rat) (C2 tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) C2)) (@ (@ tptp.plus_plus_rat B) C2)) (@ (@ tptp.ord_less_rat A) B))))
% 6.73/7.04 (assert (forall ((A tptp.nat) (C2 tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) C2)) (@ (@ tptp.plus_plus_nat B) C2)) (@ (@ tptp.ord_less_nat A) B))))
% 6.73/7.04 (assert (forall ((A tptp.int) (C2 tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) C2)) (@ (@ tptp.plus_plus_int B) C2)) (@ (@ tptp.ord_less_int A) B))))
% 6.73/7.04 (assert (forall ((C2 tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real C2))) (=> (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_real A) B)))))
% 6.73/7.04 (assert (forall ((C2 tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat C2))) (=> (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_rat A) B)))))
% 6.73/7.04 (assert (forall ((C2 tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C2))) (=> (@ (@ tptp.ord_less_nat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_nat A) B)))))
% 6.73/7.04 (assert (forall ((C2 tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C2))) (=> (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_int A) B)))))
% 6.73/7.04 (assert (forall ((A tptp.real) (B tptp.real) (C2 tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) C2)) (@ (@ tptp.plus_plus_real B) C2)))))
% 6.73/7.04 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) C2)) (@ (@ tptp.plus_plus_rat B) C2)))))
% 6.73/7.04 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) C2)) (@ (@ tptp.plus_plus_nat B) C2)))))
% 6.73/7.04 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) C2)) (@ (@ tptp.plus_plus_int B) C2)))))
% 6.73/7.04 (assert (forall ((A tptp.real) (B tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real C2))) (=> (@ (@ tptp.ord_less_real A) B) (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B))))))
% 6.73/7.04 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat C2))) (=> (@ (@ tptp.ord_less_rat A) B) (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B))))))
% 6.73/7.04 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C2))) (=> (@ (@ tptp.ord_less_nat A) B) (@ (@ tptp.ord_less_nat (@ _let_1 A)) (@ _let_1 B))))))
% 6.73/7.04 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C2))) (=> (@ (@ tptp.ord_less_int A) B) (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B))))))
% 6.73/7.04 (assert (forall ((A tptp.real) (B tptp.real) (C2 tptp.real) (D tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_real C2) D) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) C2)) (@ (@ tptp.plus_plus_real B) D))))))
% 6.73/7.04 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat) (D tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_rat C2) D) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) C2)) (@ (@ tptp.plus_plus_rat B) D))))))
% 6.73/7.04 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat) (D tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_nat C2) D) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) C2)) (@ (@ tptp.plus_plus_nat B) D))))))
% 6.73/7.04 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int) (D tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_int C2) D) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) C2)) (@ (@ tptp.plus_plus_int B) D))))))
% 6.73/7.04 (assert (forall ((I2 tptp.real) (J2 tptp.real) (K2 tptp.real) (L tptp.real)) (=> (and (@ (@ tptp.ord_less_real I2) J2) (= K2 L)) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real I2) K2)) (@ (@ tptp.plus_plus_real J2) L)))))
% 6.73/7.04 (assert (forall ((I2 tptp.rat) (J2 tptp.rat) (K2 tptp.rat) (L tptp.rat)) (=> (and (@ (@ tptp.ord_less_rat I2) J2) (= K2 L)) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat I2) K2)) (@ (@ tptp.plus_plus_rat J2) L)))))
% 6.73/7.04 (assert (forall ((I2 tptp.nat) (J2 tptp.nat) (K2 tptp.nat) (L tptp.nat)) (=> (and (@ (@ tptp.ord_less_nat I2) J2) (= K2 L)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I2) K2)) (@ (@ tptp.plus_plus_nat J2) L)))))
% 6.73/7.04 (assert (forall ((I2 tptp.int) (J2 tptp.int) (K2 tptp.int) (L tptp.int)) (=> (and (@ (@ tptp.ord_less_int I2) J2) (= K2 L)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int I2) K2)) (@ (@ tptp.plus_plus_int J2) L)))))
% 6.73/7.04 (assert (forall ((I2 tptp.real) (J2 tptp.real) (K2 tptp.real) (L tptp.real)) (=> (and (= I2 J2) (@ (@ tptp.ord_less_real K2) L)) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real I2) K2)) (@ (@ tptp.plus_plus_real J2) L)))))
% 6.73/7.04 (assert (forall ((I2 tptp.rat) (J2 tptp.rat) (K2 tptp.rat) (L tptp.rat)) (=> (and (= I2 J2) (@ (@ tptp.ord_less_rat K2) L)) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat I2) K2)) (@ (@ tptp.plus_plus_rat J2) L)))))
% 6.73/7.04 (assert (forall ((I2 tptp.nat) (J2 tptp.nat) (K2 tptp.nat) (L tptp.nat)) (=> (and (= I2 J2) (@ (@ tptp.ord_less_nat K2) L)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I2) K2)) (@ (@ tptp.plus_plus_nat J2) L)))))
% 6.73/7.04 (assert (forall ((I2 tptp.int) (J2 tptp.int) (K2 tptp.int) (L tptp.int)) (=> (and (= I2 J2) (@ (@ tptp.ord_less_int K2) L)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int I2) K2)) (@ (@ tptp.plus_plus_int J2) L)))))
% 6.73/7.04 (assert (forall ((I2 tptp.real) (J2 tptp.real) (K2 tptp.real) (L tptp.real)) (=> (and (@ (@ tptp.ord_less_real I2) J2) (@ (@ tptp.ord_less_real K2) L)) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real I2) K2)) (@ (@ tptp.plus_plus_real J2) L)))))
% 6.73/7.04 (assert (forall ((I2 tptp.rat) (J2 tptp.rat) (K2 tptp.rat) (L tptp.rat)) (=> (and (@ (@ tptp.ord_less_rat I2) J2) (@ (@ tptp.ord_less_rat K2) L)) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat I2) K2)) (@ (@ tptp.plus_plus_rat J2) L)))))
% 6.73/7.04 (assert (forall ((I2 tptp.nat) (J2 tptp.nat) (K2 tptp.nat) (L tptp.nat)) (=> (and (@ (@ tptp.ord_less_nat I2) J2) (@ (@ tptp.ord_less_nat K2) L)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I2) K2)) (@ (@ tptp.plus_plus_nat J2) L)))))
% 6.73/7.04 (assert (forall ((I2 tptp.int) (J2 tptp.int) (K2 tptp.int) (L tptp.int)) (=> (and (@ (@ tptp.ord_less_int I2) J2) (@ (@ tptp.ord_less_int K2) L)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int I2) K2)) (@ (@ tptp.plus_plus_int J2) L)))))
% 6.73/7.04 (assert (forall ((A tptp.real) (B tptp.real) (C2 tptp.real)) (= (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real A) B)) C2) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) C2)) (@ (@ tptp.times_times_real B) C2)))))
% 6.73/7.04 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (= (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat A) B)) C2) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) C2)) (@ (@ tptp.times_times_rat B) C2)))))
% 6.73/7.04 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int A) B)) C2) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) C2)) (@ (@ tptp.times_times_int B) C2)))))
% 6.73/7.04 (assert (forall ((A tptp.real) (B tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.times_times_real A))) (= (@ _let_1 (@ (@ tptp.plus_plus_real B) C2)) (@ (@ tptp.plus_plus_real (@ _let_1 B)) (@ _let_1 C2))))))
% 6.73/7.04 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat B) C2)) (@ (@ tptp.plus_plus_rat (@ _let_1 B)) (@ _let_1 C2))))))
% 6.73/7.04 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (= (@ _let_1 (@ (@ tptp.plus_plus_int B) C2)) (@ (@ tptp.plus_plus_int (@ _let_1 B)) (@ _let_1 C2))))))
% 6.73/7.04 (assert (forall ((A tptp.real) (B tptp.real) (C2 tptp.real)) (= (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real A) B)) C2) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) C2)) (@ (@ tptp.times_times_real B) C2)))))
% 6.73/7.04 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (= (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat A) B)) C2) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) C2)) (@ (@ tptp.times_times_rat B) C2)))))
% 6.73/7.04 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat A) B)) C2) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat A) C2)) (@ (@ tptp.times_times_nat B) C2)))))
% 6.73/7.04 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int A) B)) C2) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) C2)) (@ (@ tptp.times_times_int B) C2)))))
% 6.73/7.04 (assert (forall ((A tptp.real) (B tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.times_times_real A))) (= (@ _let_1 (@ (@ tptp.plus_plus_real B) C2)) (@ (@ tptp.plus_plus_real (@ _let_1 B)) (@ _let_1 C2))))))
% 6.73/7.04 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat B) C2)) (@ (@ tptp.plus_plus_rat (@ _let_1 B)) (@ _let_1 C2))))))
% 6.73/7.04 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat B) C2)) (@ (@ tptp.plus_plus_nat (@ _let_1 B)) (@ _let_1 C2))))))
% 6.73/7.04 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (= (@ _let_1 (@ (@ tptp.plus_plus_int B) C2)) (@ (@ tptp.plus_plus_int (@ _let_1 B)) (@ _let_1 C2))))))
% 6.73/7.04 (assert (forall ((A tptp.real) (B tptp.real) (C2 tptp.real)) (= (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real A) B)) C2) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) C2)) (@ (@ tptp.times_times_real B) C2)))))
% 6.73/7.04 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (= (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat A) B)) C2) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) C2)) (@ (@ tptp.times_times_rat B) C2)))))
% 6.73/7.04 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat A) B)) C2) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat A) C2)) (@ (@ tptp.times_times_nat B) C2)))))
% 6.73/7.04 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int A) B)) C2) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) C2)) (@ (@ tptp.times_times_int B) C2)))))
% 6.73/7.04 (assert (forall ((A tptp.real) (E tptp.real) (B tptp.real) (C2 tptp.real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) E)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real B) E)) C2)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real A) B)) E)) C2))))
% 6.73/7.04 (assert (forall ((A tptp.rat) (E tptp.rat) (B tptp.rat) (C2 tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) E)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B) E)) C2)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat A) B)) E)) C2))))
% 6.73/7.04 (assert (forall ((A tptp.nat) (E tptp.nat) (B tptp.nat) (C2 tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat A) E)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat B) E)) C2)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat A) B)) E)) C2))))
% 6.73/7.04 (assert (forall ((A tptp.int) (E tptp.int) (B tptp.int) (C2 tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) E)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) E)) C2)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int A) B)) E)) C2))))
% 6.73/7.04 (assert (forall ((X tptp.option4927543243414619207at_nat) (P2 (-> tptp.option4927543243414619207at_nat tptp.option4927543243414619207at_nat Bool)) (Y tptp.option4927543243414619207at_nat)) (let ((_let_1 (@ (@ P2 X) Y))) (=> (=> (= X tptp.none_P5556105721700978146at_nat) _let_1) (=> (=> (= Y tptp.none_P5556105721700978146at_nat) _let_1) (=> (forall ((A3 tptp.product_prod_nat_nat) (B3 tptp.product_prod_nat_nat)) (=> (= X (@ tptp.some_P7363390416028606310at_nat A3)) (=> (= Y (@ tptp.some_P7363390416028606310at_nat B3)) (@ (@ P2 X) Y)))) _let_1))))))
% 6.73/7.04 (assert (forall ((X tptp.option4927543243414619207at_nat) (P2 (-> tptp.option4927543243414619207at_nat tptp.option_nat Bool)) (Y tptp.option_nat)) (let ((_let_1 (@ (@ P2 X) Y))) (=> (=> (= X tptp.none_P5556105721700978146at_nat) _let_1) (=> (=> (= Y tptp.none_nat) _let_1) (=> (forall ((A3 tptp.product_prod_nat_nat) (B3 tptp.nat)) (=> (= X (@ tptp.some_P7363390416028606310at_nat A3)) (=> (= Y (@ tptp.some_nat B3)) (@ (@ P2 X) Y)))) _let_1))))))
% 6.73/7.04 (assert (forall ((X tptp.option4927543243414619207at_nat) (P2 (-> tptp.option4927543243414619207at_nat tptp.option_num Bool)) (Y tptp.option_num)) (let ((_let_1 (@ (@ P2 X) Y))) (=> (=> (= X tptp.none_P5556105721700978146at_nat) _let_1) (=> (=> (= Y tptp.none_num) _let_1) (=> (forall ((A3 tptp.product_prod_nat_nat) (B3 tptp.num)) (=> (= X (@ tptp.some_P7363390416028606310at_nat A3)) (=> (= Y (@ tptp.some_num B3)) (@ (@ P2 X) Y)))) _let_1))))))
% 6.73/7.04 (assert (forall ((X tptp.option_nat) (P2 (-> tptp.option_nat tptp.option4927543243414619207at_nat Bool)) (Y tptp.option4927543243414619207at_nat)) (let ((_let_1 (@ (@ P2 X) Y))) (=> (=> (= X tptp.none_nat) _let_1) (=> (=> (= Y tptp.none_P5556105721700978146at_nat) _let_1) (=> (forall ((A3 tptp.nat) (B3 tptp.product_prod_nat_nat)) (=> (= X (@ tptp.some_nat A3)) (=> (= Y (@ tptp.some_P7363390416028606310at_nat B3)) (@ (@ P2 X) Y)))) _let_1))))))
% 6.73/7.04 (assert (forall ((X tptp.option_nat) (P2 (-> tptp.option_nat tptp.option_nat Bool)) (Y tptp.option_nat)) (let ((_let_1 (@ (@ P2 X) Y))) (=> (=> (= X tptp.none_nat) _let_1) (=> (=> (= Y tptp.none_nat) _let_1) (=> (forall ((A3 tptp.nat) (B3 tptp.nat)) (=> (= X (@ tptp.some_nat A3)) (=> (= Y (@ tptp.some_nat B3)) (@ (@ P2 X) Y)))) _let_1))))))
% 6.73/7.04 (assert (forall ((X tptp.option_nat) (P2 (-> tptp.option_nat tptp.option_num Bool)) (Y tptp.option_num)) (let ((_let_1 (@ (@ P2 X) Y))) (=> (=> (= X tptp.none_nat) _let_1) (=> (=> (= Y tptp.none_num) _let_1) (=> (forall ((A3 tptp.nat) (B3 tptp.num)) (=> (= X (@ tptp.some_nat A3)) (=> (= Y (@ tptp.some_num B3)) (@ (@ P2 X) Y)))) _let_1))))))
% 6.73/7.04 (assert (forall ((X tptp.option_num) (P2 (-> tptp.option_num tptp.option4927543243414619207at_nat Bool)) (Y tptp.option4927543243414619207at_nat)) (let ((_let_1 (@ (@ P2 X) Y))) (=> (=> (= X tptp.none_num) _let_1) (=> (=> (= Y tptp.none_P5556105721700978146at_nat) _let_1) (=> (forall ((A3 tptp.num) (B3 tptp.product_prod_nat_nat)) (=> (= X (@ tptp.some_num A3)) (=> (= Y (@ tptp.some_P7363390416028606310at_nat B3)) (@ (@ P2 X) Y)))) _let_1))))))
% 6.73/7.04 (assert (forall ((X tptp.option_num) (P2 (-> tptp.option_num tptp.option_nat Bool)) (Y tptp.option_nat)) (let ((_let_1 (@ (@ P2 X) Y))) (=> (=> (= X tptp.none_num) _let_1) (=> (=> (= Y tptp.none_nat) _let_1) (=> (forall ((A3 tptp.num) (B3 tptp.nat)) (=> (= X (@ tptp.some_num A3)) (=> (= Y (@ tptp.some_nat B3)) (@ (@ P2 X) Y)))) _let_1))))))
% 6.73/7.04 (assert (forall ((X tptp.option_num) (P2 (-> tptp.option_num tptp.option_num Bool)) (Y tptp.option_num)) (let ((_let_1 (@ (@ P2 X) Y))) (=> (=> (= X tptp.none_num) _let_1) (=> (=> (= Y tptp.none_num) _let_1) (=> (forall ((A3 tptp.num) (B3 tptp.num)) (=> (= X (@ tptp.some_num A3)) (=> (= Y (@ tptp.some_num B3)) (@ (@ P2 X) Y)))) _let_1))))))
% 6.73/7.04 (assert (= (lambda ((P3 (-> tptp.option4927543243414619207at_nat Bool))) (forall ((X6 tptp.option4927543243414619207at_nat)) (@ P3 X6))) (lambda ((P4 (-> tptp.option4927543243414619207at_nat Bool))) (and (@ P4 tptp.none_P5556105721700978146at_nat) (forall ((X4 tptp.product_prod_nat_nat)) (@ P4 (@ tptp.some_P7363390416028606310at_nat X4)))))))
% 6.73/7.04 (assert (= (lambda ((P3 (-> tptp.option_nat Bool))) (forall ((X6 tptp.option_nat)) (@ P3 X6))) (lambda ((P4 (-> tptp.option_nat Bool))) (and (@ P4 tptp.none_nat) (forall ((X4 tptp.nat)) (@ P4 (@ tptp.some_nat X4)))))))
% 6.73/7.04 (assert (= (lambda ((P3 (-> tptp.option_num Bool))) (forall ((X6 tptp.option_num)) (@ P3 X6))) (lambda ((P4 (-> tptp.option_num Bool))) (and (@ P4 tptp.none_num) (forall ((X4 tptp.num)) (@ P4 (@ tptp.some_num X4)))))))
% 6.73/7.04 (assert (= (lambda ((P3 (-> tptp.option4927543243414619207at_nat Bool))) (exists ((X6 tptp.option4927543243414619207at_nat)) (@ P3 X6))) (lambda ((P4 (-> tptp.option4927543243414619207at_nat Bool))) (or (@ P4 tptp.none_P5556105721700978146at_nat) (exists ((X4 tptp.product_prod_nat_nat)) (@ P4 (@ tptp.some_P7363390416028606310at_nat X4)))))))
% 6.73/7.04 (assert (= (lambda ((P3 (-> tptp.option_nat Bool))) (exists ((X6 tptp.option_nat)) (@ P3 X6))) (lambda ((P4 (-> tptp.option_nat Bool))) (or (@ P4 tptp.none_nat) (exists ((X4 tptp.nat)) (@ P4 (@ tptp.some_nat X4)))))))
% 6.73/7.04 (assert (= (lambda ((P3 (-> tptp.option_num Bool))) (exists ((X6 tptp.option_num)) (@ P3 X6))) (lambda ((P4 (-> tptp.option_num Bool))) (or (@ P4 tptp.none_num) (exists ((X4 tptp.num)) (@ P4 (@ tptp.some_num X4)))))))
% 6.73/7.04 (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))))))))
% 6.73/7.04 (assert (forall ((Y tptp.option_nat)) (=> (not (= Y tptp.none_nat)) (not (forall ((X23 tptp.nat)) (not (= Y (@ tptp.some_nat X23))))))))
% 6.73/7.04 (assert (forall ((Y tptp.option_num)) (=> (not (= Y tptp.none_num)) (not (forall ((X23 tptp.num)) (not (= Y (@ tptp.some_num X23))))))))
% 6.73/7.04 (assert (forall ((Option tptp.option4927543243414619207at_nat) (X2 tptp.product_prod_nat_nat)) (=> (= Option (@ tptp.some_P7363390416028606310at_nat X2)) (not (= Option tptp.none_P5556105721700978146at_nat)))))
% 6.73/7.04 (assert (forall ((Option tptp.option_nat) (X2 tptp.nat)) (=> (= Option (@ tptp.some_nat X2)) (not (= Option tptp.none_nat)))))
% 6.73/7.04 (assert (forall ((Option tptp.option_num) (X2 tptp.num)) (=> (= Option (@ tptp.some_num X2)) (not (= Option tptp.none_num)))))
% 6.73/7.04 (assert (forall ((X2 tptp.product_prod_nat_nat)) (not (= tptp.none_P5556105721700978146at_nat (@ tptp.some_P7363390416028606310at_nat X2)))))
% 6.73/7.04 (assert (forall ((X2 tptp.nat)) (not (= tptp.none_nat (@ tptp.some_nat X2)))))
% 6.73/7.04 (assert (forall ((X2 tptp.num)) (not (= tptp.none_num (@ tptp.some_num X2)))))
% 6.73/7.04 (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 ((Uw (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)) (V tptp.product_prod_nat_nat)) (not (= X (@ (@ tptp.produc2899441246263362727at_nat Uw) (@ (@ tptp.produc488173922507101015at_nat (@ tptp.some_P7363390416028606310at_nat V)) tptp.none_P5556105721700978146at_nat))))) (not (forall ((F (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)) (A3 tptp.product_prod_nat_nat) (B3 tptp.product_prod_nat_nat)) (not (= X (@ (@ tptp.produc2899441246263362727at_nat F) (@ (@ tptp.produc488173922507101015at_nat (@ tptp.some_P7363390416028606310at_nat A3)) (@ tptp.some_P7363390416028606310at_nat B3)))))))))))
% 6.73/7.04 (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 ((Uw (-> tptp.nat tptp.nat tptp.nat)) (V tptp.nat)) (not (= X (@ (@ tptp.produc8929957630744042906on_nat Uw) (@ (@ tptp.produc5098337634421038937on_nat (@ tptp.some_nat V)) tptp.none_nat))))) (not (forall ((F (-> tptp.nat tptp.nat tptp.nat)) (A3 tptp.nat) (B3 tptp.nat)) (not (= X (@ (@ tptp.produc8929957630744042906on_nat F) (@ (@ tptp.produc5098337634421038937on_nat (@ tptp.some_nat A3)) (@ tptp.some_nat B3)))))))))))
% 6.73/7.04 (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 ((Uw (-> tptp.num tptp.num tptp.num)) (V tptp.num)) (not (= X (@ (@ tptp.produc5778274026573060048on_num Uw) (@ (@ tptp.produc8585076106096196333on_num (@ tptp.some_num V)) tptp.none_num))))) (not (forall ((F (-> tptp.num tptp.num tptp.num)) (A3 tptp.num) (B3 tptp.num)) (not (= X (@ (@ tptp.produc5778274026573060048on_num F) (@ (@ tptp.produc8585076106096196333on_num (@ tptp.some_num A3)) (@ tptp.some_num B3)))))))))))
% 6.73/7.04 (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 ((Uw (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)) (V tptp.product_prod_nat_nat)) (not (= X (@ (@ tptp.produc3994169339658061776at_nat Uw) (@ (@ tptp.produc488173922507101015at_nat (@ tptp.some_P7363390416028606310at_nat V)) tptp.none_P5556105721700978146at_nat))))) (not (forall ((F (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)) (X3 tptp.product_prod_nat_nat) (Y3 tptp.product_prod_nat_nat)) (not (= X (@ (@ tptp.produc3994169339658061776at_nat F) (@ (@ tptp.produc488173922507101015at_nat (@ tptp.some_P7363390416028606310at_nat X3)) (@ tptp.some_P7363390416028606310at_nat Y3)))))))))))
% 6.73/7.04 (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 ((Uw (-> tptp.nat tptp.nat Bool)) (V tptp.nat)) (not (= X (@ (@ tptp.produc4035269172776083154on_nat Uw) (@ (@ tptp.produc5098337634421038937on_nat (@ tptp.some_nat V)) tptp.none_nat))))) (not (forall ((F (-> tptp.nat tptp.nat Bool)) (X3 tptp.nat) (Y3 tptp.nat)) (not (= X (@ (@ tptp.produc4035269172776083154on_nat F) (@ (@ tptp.produc5098337634421038937on_nat (@ tptp.some_nat X3)) (@ tptp.some_nat Y3)))))))))))
% 6.73/7.04 (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 ((Uw (-> tptp.num tptp.num Bool)) (V tptp.num)) (not (= X (@ (@ tptp.produc3576312749637752826on_num Uw) (@ (@ tptp.produc8585076106096196333on_num (@ tptp.some_num V)) tptp.none_num))))) (not (forall ((F (-> tptp.num tptp.num Bool)) (X3 tptp.num) (Y3 tptp.num)) (not (= X (@ (@ tptp.produc3576312749637752826on_num F) (@ (@ tptp.produc8585076106096196333on_num (@ tptp.some_num X3)) (@ tptp.some_num Y3)))))))))))
% 6.73/7.04 (assert (forall ((A4 tptp.nat) (K2 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K2))) (=> (= A4 (@ _let_1 A)) (= (@ tptp.suc A4) (@ _let_1 (@ tptp.suc A)))))))
% 6.73/7.04 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ tptp.suc M2)) N) (@ tptp.suc (@ (@ tptp.plus_plus_nat M2) N)))))
% 6.73/7.04 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ tptp.suc M2)) N) (@ (@ tptp.plus_plus_nat M2) (@ tptp.suc N)))))
% 6.73/7.04 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (= (@ (@ tptp.plus_plus_nat M2) N) M2) (= N tptp.zero_zero_nat))))
% 6.73/7.04 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.plus_plus_nat tptp.zero_zero_nat) N) N)))
% 6.73/7.04 (assert (forall ((K2 tptp.nat) (L tptp.nat) (M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat K2) L) (=> (= (@ (@ tptp.plus_plus_nat M2) L) (@ (@ tptp.plus_plus_nat K2) N)) (@ (@ tptp.ord_less_nat M2) N)))))
% 6.73/7.04 (assert (forall ((I2 tptp.nat) (J2 tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat I2))) (=> (@ _let_1 J2) (@ _let_1 (@ (@ tptp.plus_plus_nat M2) J2))))))
% 6.73/7.04 (assert (forall ((I2 tptp.nat) (J2 tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat I2))) (=> (@ _let_1 J2) (@ _let_1 (@ (@ tptp.plus_plus_nat J2) M2))))))
% 6.73/7.04 (assert (forall ((I2 tptp.nat) (J2 tptp.nat) (K2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) J2) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I2) K2)) (@ (@ tptp.plus_plus_nat J2) K2)))))
% 6.73/7.04 (assert (forall ((J2 tptp.nat) (I2 tptp.nat)) (not (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat J2) I2)) I2))))
% 6.73/7.04 (assert (forall ((I2 tptp.nat) (J2 tptp.nat)) (not (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I2) J2)) I2))))
% 6.73/7.04 (assert (forall ((I2 tptp.nat) (J2 tptp.nat) (K2 tptp.nat) (L tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) J2) (=> (@ (@ tptp.ord_less_nat K2) L) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I2) K2)) (@ (@ tptp.plus_plus_nat J2) L))))))
% 6.73/7.04 (assert (forall ((I2 tptp.nat) (J2 tptp.nat) (K2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I2) J2)) K2) (@ (@ tptp.ord_less_nat I2) K2))))
% 6.73/7.04 (assert (forall ((M2 tptp.nat) (K2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat M2) K2)) N) (not (=> (@ (@ tptp.ord_less_eq_nat M2) N) (not (@ (@ tptp.ord_less_eq_nat K2) N)))))))
% 6.73/7.04 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat N) (@ (@ tptp.plus_plus_nat N) M2))))
% 6.73/7.04 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat N) (@ (@ tptp.plus_plus_nat M2) N))))
% 6.73/7.04 (assert (forall ((M2 tptp.nat) (K2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat M2) K2)) N) (@ (@ tptp.ord_less_eq_nat M2) N))))
% 6.73/7.04 (assert (forall ((M2 tptp.nat) (K2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat M2) K2)) N) (@ (@ tptp.ord_less_eq_nat K2) N))))
% 6.73/7.04 (assert (forall ((K2 tptp.nat) (L tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K2) L) (exists ((N3 tptp.nat)) (= L (@ (@ tptp.plus_plus_nat K2) N3))))))
% 6.73/7.04 (assert (forall ((I2 tptp.nat) (J2 tptp.nat) (K2 tptp.nat) (L tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J2) (=> (@ (@ tptp.ord_less_eq_nat K2) L) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I2) K2)) (@ (@ tptp.plus_plus_nat J2) L))))))
% 6.73/7.04 (assert (forall ((I2 tptp.nat) (J2 tptp.nat) (K2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I2) K2)) (@ (@ tptp.plus_plus_nat J2) K2)))))
% 6.73/7.04 (assert (forall ((I2 tptp.nat) (J2 tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat I2))) (=> (@ _let_1 J2) (@ _let_1 (@ (@ tptp.plus_plus_nat J2) M2))))))
% 6.73/7.04 (assert (forall ((I2 tptp.nat) (J2 tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat I2))) (=> (@ _let_1 J2) (@ _let_1 (@ (@ tptp.plus_plus_nat M2) J2))))))
% 6.73/7.04 (assert (= tptp.ord_less_eq_nat (lambda ((M6 tptp.nat) (N4 tptp.nat)) (exists ((K3 tptp.nat)) (= N4 (@ (@ tptp.plus_plus_nat M6) K3))))))
% 6.73/7.04 (assert (forall ((K2 tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K2))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M2) N)) (@ (@ tptp.plus_plus_nat (@ _let_1 M2)) (@ _let_1 N))))))
% 6.73/7.04 (assert (forall ((M2 tptp.nat) (N tptp.nat) (K2 tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat M2) N)) K2) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat M2) K2)) (@ (@ tptp.times_times_nat N) K2)))))
% 6.73/7.04 (assert (forall ((I2 tptp.nat) (U tptp.nat) (J2 tptp.nat) (K2 tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I2) U)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J2) U)) K2)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat I2) J2)) U)) K2))))
% 6.73/7.04 (assert (forall ((Uu Bool) (Uv Bool) (Uw2 tptp.nat)) (not (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.vEBT_Leaf Uu) Uv)) Uw2))))
% 6.73/7.04 (assert (forall ((A tptp.real) (C2 tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real C2) B) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A) C2)) B)))))
% 6.73/7.04 (assert (forall ((A tptp.rat) (C2 tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_rat C2) B) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A) C2)) B)))))
% 6.73/7.04 (assert (forall ((A tptp.nat) (C2 tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_eq_nat C2) B) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A) C2)) B)))))
% 6.73/7.04 (assert (forall ((A tptp.int) (C2 tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_eq_int C2) B) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A) C2)) B)))))
% 6.73/7.04 (assert (forall ((A tptp.real) (B tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real B))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ _let_1 C2) (@ _let_1 (@ (@ tptp.plus_plus_real A) C2)))))))
% 6.73/7.04 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat B))) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ _let_1 C2) (@ _let_1 (@ (@ tptp.plus_plus_rat A) C2)))))))
% 6.73/7.04 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat B))) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ _let_1 C2) (@ _let_1 (@ (@ tptp.plus_plus_nat A) C2)))))))
% 6.73/7.04 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int B))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ _let_1 C2) (@ _let_1 (@ (@ tptp.plus_plus_int A) C2)))))))
% 6.73/7.04 (assert (forall ((C2 tptp.real) (A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real C2) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real A) B) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A) C2)) B)))))
% 6.73/7.04 (assert (forall ((C2 tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat C2) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_rat A) B) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A) C2)) B)))))
% 6.73/7.04 (assert (forall ((C2 tptp.nat) (A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat C2) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_eq_nat A) B) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A) C2)) B)))))
% 6.73/7.04 (assert (forall ((C2 tptp.int) (A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int C2) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_eq_int A) B) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A) C2)) B)))))
% 6.73/7.04 (assert (forall ((C2 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) C2) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.plus_plus_real A) C2)))))))
% 6.73/7.04 (assert (forall ((C2 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) C2) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.plus_plus_rat A) C2)))))))
% 6.73/7.04 (assert (forall ((C2 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) C2) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.plus_plus_nat A) C2)))))))
% 6.73/7.04 (assert (forall ((C2 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) C2) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.plus_plus_int A) C2)))))))
% 6.73/7.04 (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)))))))
% 6.73/7.04 (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)))))))
% 6.73/7.04 (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)))))))
% 6.73/7.04 (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)))))))
% 6.73/7.04 (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)))))
% 6.73/7.04 (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)))))
% 6.73/7.04 (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)))))
% 6.73/7.04 (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)))))
% 6.73/7.04 (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))))))))
% 6.73/7.04 (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))))))))
% 6.73/7.04 (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))))))))
% 6.73/7.04 (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))))))))
% 6.73/7.04 (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)))))))
% 6.73/7.04 (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)))))))
% 6.73/7.04 (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)))))))
% 6.73/7.04 (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)))))))
% 6.73/7.04 (assert (forall ((A tptp.real) (B tptp.real) (C2 tptp.real) (D tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_eq_real C2) D) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) C2)) (@ (@ tptp.plus_plus_real B) D))))))
% 6.73/7.04 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat) (D tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat C2) D) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) C2)) (@ (@ tptp.plus_plus_rat B) D))))))
% 6.73/7.04 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat) (D tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat C2) D) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) C2)) (@ (@ tptp.plus_plus_nat B) D))))))
% 6.73/7.04 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int) (D tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_eq_int C2) D) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) C2)) (@ (@ tptp.plus_plus_int B) D))))))
% 6.73/7.04 (assert (forall ((A tptp.real) (B tptp.real) (C2 tptp.real) (D tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_real C2) D) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) C2)) (@ (@ tptp.plus_plus_real B) D))))))
% 6.73/7.04 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat) (D tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_rat C2) D) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) C2)) (@ (@ tptp.plus_plus_rat B) D))))))
% 6.73/7.04 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat) (D tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_nat C2) D) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) C2)) (@ (@ tptp.plus_plus_nat B) D))))))
% 6.73/7.04 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int) (D tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_int C2) D) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) C2)) (@ (@ tptp.plus_plus_int B) D))))))
% 6.73/7.04 (assert (forall ((I2 tptp.real) (J2 tptp.real) (K2 tptp.real) (L tptp.real)) (=> (and (@ (@ tptp.ord_less_real I2) J2) (@ (@ tptp.ord_less_eq_real K2) L)) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real I2) K2)) (@ (@ tptp.plus_plus_real J2) L)))))
% 6.73/7.04 (assert (forall ((I2 tptp.rat) (J2 tptp.rat) (K2 tptp.rat) (L tptp.rat)) (=> (and (@ (@ tptp.ord_less_rat I2) J2) (@ (@ tptp.ord_less_eq_rat K2) L)) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat I2) K2)) (@ (@ tptp.plus_plus_rat J2) L)))))
% 6.73/7.04 (assert (forall ((I2 tptp.nat) (J2 tptp.nat) (K2 tptp.nat) (L tptp.nat)) (=> (and (@ (@ tptp.ord_less_nat I2) J2) (@ (@ tptp.ord_less_eq_nat K2) L)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I2) K2)) (@ (@ tptp.plus_plus_nat J2) L)))))
% 6.73/7.04 (assert (forall ((I2 tptp.int) (J2 tptp.int) (K2 tptp.int) (L tptp.int)) (=> (and (@ (@ tptp.ord_less_int I2) J2) (@ (@ tptp.ord_less_eq_int K2) L)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int I2) K2)) (@ (@ tptp.plus_plus_int J2) L)))))
% 6.73/7.04 (assert (forall ((I2 tptp.real) (J2 tptp.real) (K2 tptp.real) (L tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real I2) J2) (@ (@ tptp.ord_less_real K2) L)) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real I2) K2)) (@ (@ tptp.plus_plus_real J2) L)))))
% 6.73/7.04 (assert (forall ((I2 tptp.rat) (J2 tptp.rat) (K2 tptp.rat) (L tptp.rat)) (=> (and (@ (@ tptp.ord_less_eq_rat I2) J2) (@ (@ tptp.ord_less_rat K2) L)) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat I2) K2)) (@ (@ tptp.plus_plus_rat J2) L)))))
% 6.73/7.04 (assert (forall ((I2 tptp.nat) (J2 tptp.nat) (K2 tptp.nat) (L tptp.nat)) (=> (and (@ (@ tptp.ord_less_eq_nat I2) J2) (@ (@ tptp.ord_less_nat K2) L)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I2) K2)) (@ (@ tptp.plus_plus_nat J2) L)))))
% 6.73/7.04 (assert (forall ((I2 tptp.int) (J2 tptp.int) (K2 tptp.int) (L tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int I2) J2) (@ (@ tptp.ord_less_int K2) L)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int I2) K2)) (@ (@ tptp.plus_plus_int J2) L)))))
% 6.73/7.04 (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)))))
% 6.73/7.04 (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)))))
% 6.73/7.04 (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)))))
% 6.73/7.04 (assert (forall ((A tptp.real) (B tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real B))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (@ _let_1 C2) (@ _let_1 (@ (@ tptp.plus_plus_real A) C2)))))))
% 6.73/7.04 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat B))) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (=> (@ _let_1 C2) (@ _let_1 (@ (@ tptp.plus_plus_rat A) C2)))))))
% 6.73/7.04 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat B))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A) (=> (@ _let_1 C2) (@ _let_1 (@ (@ tptp.plus_plus_nat A) C2)))))))
% 6.73/7.04 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int B))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (=> (@ _let_1 C2) (@ _let_1 (@ (@ tptp.plus_plus_int A) C2)))))))
% 6.73/7.04 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (not (forall ((C tptp.nat)) (=> (= B (@ (@ tptp.plus_plus_nat A) C)) (= C tptp.zero_zero_nat)))))))
% 6.73/7.04 (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)))))))
% 6.73/7.04 (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)))))))
% 6.73/7.04 (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)))))))
% 6.73/7.04 (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)))))))
% 6.73/7.04 (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)))))
% 6.73/7.04 (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)))))
% 6.73/7.04 (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)))))
% 6.73/7.04 (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)))))
% 6.73/7.04 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A) B) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.plus_p5714425477246183910nteger A) tptp.one_one_Code_integer)) (@ (@ tptp.plus_p5714425477246183910nteger B) tptp.one_one_Code_integer)))))
% 6.73/7.04 (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)))))
% 6.73/7.04 (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)))))
% 6.73/7.04 (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)))))
% 6.73/7.04 (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)))))
% 6.73/7.04 (assert (forall ((A tptp.code_integer)) (@ (@ tptp.ord_le6747313008572928689nteger A) (@ (@ tptp.plus_p5714425477246183910nteger A) tptp.one_one_Code_integer))))
% 6.73/7.04 (assert (forall ((A tptp.real)) (@ (@ tptp.ord_less_real A) (@ (@ tptp.plus_plus_real A) tptp.one_one_real))))
% 6.73/7.04 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_rat A) (@ (@ tptp.plus_plus_rat A) tptp.one_one_rat))))
% 6.73/7.04 (assert (forall ((A tptp.nat)) (@ (@ tptp.ord_less_nat A) (@ (@ tptp.plus_plus_nat A) tptp.one_one_nat))))
% 6.73/7.04 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_int A) (@ (@ tptp.plus_plus_int A) tptp.one_one_int))))
% 6.73/7.04 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (= (@ (@ tptp.plus_plus_nat M2) N) _let_1) (or (and (= M2 _let_1) (= N tptp.zero_zero_nat)) (and (= M2 tptp.zero_zero_nat) (= N _let_1)))))))
% 6.73/7.04 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (= _let_1 (@ (@ tptp.plus_plus_nat M2) N)) (or (and (= M2 _let_1) (= N tptp.zero_zero_nat)) (and (= M2 tptp.zero_zero_nat) (= N _let_1)))))))
% 6.73/7.04 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) N) (not (forall ((Q3 tptp.nat)) (not (= N (@ tptp.suc (@ (@ tptp.plus_plus_nat M2) Q3)))))))))
% 6.73/7.04 (assert (forall ((I2 tptp.nat) (M2 tptp.nat)) (@ (@ tptp.ord_less_nat I2) (@ tptp.suc (@ (@ tptp.plus_plus_nat I2) M2)))))
% 6.73/7.04 (assert (forall ((I2 tptp.nat) (M2 tptp.nat)) (@ (@ tptp.ord_less_nat I2) (@ tptp.suc (@ (@ tptp.plus_plus_nat M2) I2)))))
% 6.73/7.04 (assert (= tptp.ord_less_nat (lambda ((M6 tptp.nat) (N4 tptp.nat)) (exists ((K3 tptp.nat)) (= N4 (@ tptp.suc (@ (@ tptp.plus_plus_nat M6) K3)))))))
% 6.73/7.04 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) N) (exists ((K tptp.nat)) (= N (@ tptp.suc (@ (@ tptp.plus_plus_nat M2) K)))))))
% 6.73/7.04 (assert (forall ((I2 tptp.nat) (J2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) J2) (exists ((K tptp.nat)) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (@ (@ tptp.plus_plus_nat I2) K) J2))))))
% 6.73/7.04 (assert (forall ((F2 (-> tptp.nat tptp.nat)) (M2 tptp.nat) (K2 tptp.nat)) (=> (forall ((M tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N3) (@ (@ tptp.ord_less_nat (@ F2 M)) (@ F2 N3)))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ F2 M2)) K2)) (@ F2 (@ (@ tptp.plus_plus_nat M2) K2))))))
% 6.73/7.04 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.times_times_nat (@ tptp.suc M2)) N) (@ (@ tptp.plus_plus_nat N) (@ (@ tptp.times_times_nat M2) N)))))
% 6.73/7.04 (assert (= tptp.suc (lambda ((N4 tptp.nat)) (@ (@ tptp.plus_plus_nat N4) tptp.one_one_nat))))
% 6.73/7.04 (assert (= (@ tptp.plus_plus_nat tptp.one_one_nat) tptp.suc))
% 6.73/7.04 (assert (= tptp.suc (@ tptp.plus_plus_nat tptp.one_one_nat)))
% 6.73/7.04 (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 ((Uw tptp.nat) (Ux tptp.list_VEBT_VEBT) (Uy tptp.vEBT_VEBT)) (not (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uw) Ux) Uy)))) (not (forall ((Uz2 tptp.product_prod_nat_nat) (Va2 tptp.nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (not (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat Uz2)) Va2) Vb2) Vc2)))))))))))
% 6.73/7.04 (assert (forall ((Uw2 (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)) (V2 tptp.product_prod_nat_nat)) (= (@ (@ (@ tptp.vEBT_V1502963449132264192at_nat Uw2) (@ tptp.some_P7363390416028606310at_nat V2)) tptp.none_P5556105721700978146at_nat) tptp.none_P5556105721700978146at_nat)))
% 6.73/7.04 (assert (forall ((Uw2 (-> tptp.num tptp.num tptp.num)) (V2 tptp.num)) (= (@ (@ (@ tptp.vEBT_V819420779217536731ft_num Uw2) (@ tptp.some_num V2)) tptp.none_num) tptp.none_num)))
% 6.73/7.04 (assert (forall ((Uw2 (-> tptp.nat tptp.nat tptp.nat)) (V2 tptp.nat)) (= (@ (@ (@ tptp.vEBT_V4262088993061758097ft_nat Uw2) (@ tptp.some_nat V2)) tptp.none_nat) tptp.none_nat)))
% 6.73/7.04 (assert (forall ((X (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)) (Xa2 tptp.option4927543243414619207at_nat) (Xb tptp.option4927543243414619207at_nat) (Y tptp.option4927543243414619207at_nat)) (let ((_let_1 (not (= Y tptp.none_P5556105721700978146at_nat)))) (=> (= (@ (@ (@ tptp.vEBT_V1502963449132264192at_nat X) Xa2) Xb) Y) (=> (=> (= Xa2 tptp.none_P5556105721700978146at_nat) _let_1) (=> (=> (exists ((V tptp.product_prod_nat_nat)) (= Xa2 (@ tptp.some_P7363390416028606310at_nat V))) (=> (= Xb tptp.none_P5556105721700978146at_nat) _let_1)) (not (forall ((A3 tptp.product_prod_nat_nat)) (=> (= Xa2 (@ tptp.some_P7363390416028606310at_nat A3)) (forall ((B3 tptp.product_prod_nat_nat)) (=> (= Xb (@ tptp.some_P7363390416028606310at_nat B3)) (not (= Y (@ tptp.some_P7363390416028606310at_nat (@ (@ X A3) B3)))))))))))))))
% 6.73/7.04 (assert (forall ((X (-> tptp.num tptp.num tptp.num)) (Xa2 tptp.option_num) (Xb tptp.option_num) (Y tptp.option_num)) (let ((_let_1 (not (= Y tptp.none_num)))) (=> (= (@ (@ (@ tptp.vEBT_V819420779217536731ft_num X) Xa2) Xb) Y) (=> (=> (= Xa2 tptp.none_num) _let_1) (=> (=> (exists ((V tptp.num)) (= Xa2 (@ tptp.some_num V))) (=> (= Xb tptp.none_num) _let_1)) (not (forall ((A3 tptp.num)) (=> (= Xa2 (@ tptp.some_num A3)) (forall ((B3 tptp.num)) (=> (= Xb (@ tptp.some_num B3)) (not (= Y (@ tptp.some_num (@ (@ X A3) B3)))))))))))))))
% 6.73/7.04 (assert (forall ((X (-> tptp.nat tptp.nat tptp.nat)) (Xa2 tptp.option_nat) (Xb tptp.option_nat) (Y tptp.option_nat)) (let ((_let_1 (not (= Y tptp.none_nat)))) (=> (= (@ (@ (@ tptp.vEBT_V4262088993061758097ft_nat X) Xa2) Xb) Y) (=> (=> (= Xa2 tptp.none_nat) _let_1) (=> (=> (exists ((V tptp.nat)) (= Xa2 (@ tptp.some_nat V))) (=> (= Xb tptp.none_nat) _let_1)) (not (forall ((A3 tptp.nat)) (=> (= Xa2 (@ tptp.some_nat A3)) (forall ((B3 tptp.nat)) (=> (= Xb (@ tptp.some_nat B3)) (not (= Y (@ tptp.some_nat (@ (@ X A3) B3)))))))))))))))
% 6.73/7.04 (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))))
% 6.73/7.04 (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))))
% 6.73/7.04 (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)))))
% 6.73/7.04 (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)))))
% 6.73/7.04 (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)))))
% 6.73/7.04 (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)))))
% 6.73/7.04 (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)))))))
% 6.73/7.04 (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)))))))
% 6.73/7.04 (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)))))))
% 6.73/7.04 (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)))))))
% 6.73/7.04 (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)))))
% 6.73/7.04 (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)))))
% 6.73/7.04 (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)))))
% 6.73/7.04 (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)))))
% 6.73/7.04 (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)))))))
% 6.73/7.04 (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)))))))
% 6.73/7.04 (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)))))))
% 6.73/7.04 (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)))))))
% 6.73/7.04 (assert (forall ((A tptp.real) (B tptp.real) (C2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_eq_real B) C2) (@ (@ tptp.ord_less_real B) (@ (@ tptp.plus_plus_real A) C2))))))
% 6.73/7.04 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_eq_rat B) C2) (@ (@ tptp.ord_less_rat B) (@ (@ tptp.plus_plus_rat A) C2))))))
% 6.73/7.04 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_eq_nat B) C2) (@ (@ tptp.ord_less_nat B) (@ (@ tptp.plus_plus_nat A) C2))))))
% 6.73/7.04 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_eq_int B) C2) (@ (@ tptp.ord_less_int B) (@ (@ tptp.plus_plus_int A) C2))))))
% 6.73/7.04 (assert (forall ((A tptp.real) (B tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real B))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ _let_1 C2) (@ _let_1 (@ (@ tptp.plus_plus_real A) C2)))))))
% 6.73/7.04 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat B))) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ _let_1 C2) (@ _let_1 (@ (@ tptp.plus_plus_rat A) C2)))))))
% 6.73/7.04 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat B))) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ _let_1 C2) (@ _let_1 (@ (@ tptp.plus_plus_nat A) C2)))))))
% 6.73/7.04 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int B))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ _let_1 C2) (@ _let_1 (@ (@ tptp.plus_plus_int A) C2)))))))
% 6.73/7.04 (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)))))
% 6.73/7.04 (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)))))
% 6.73/7.04 (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)))))
% 6.73/7.04 (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))))
% 6.73/7.04 (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))))
% 6.73/7.04 (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))))
% 6.73/7.04 (assert (= tptp.ord_le6747313008572928689nteger (lambda ((A5 tptp.code_integer) (__flatten_var_0 tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.plus_p5714425477246183910nteger A5) tptp.one_one_Code_integer)) __flatten_var_0))))
% 6.73/7.04 (assert (= tptp.ord_less_nat (lambda ((A5 tptp.nat) (__flatten_var_0 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A5) tptp.one_one_nat)) __flatten_var_0))))
% 6.73/7.04 (assert (= tptp.ord_less_int (lambda ((A5 tptp.int) (__flatten_var_0 tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A5) tptp.one_one_int)) __flatten_var_0))))
% 6.73/7.04 (assert (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ (@ tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer) tptp.one_one_Code_integer)))
% 6.73/7.04 (assert (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real tptp.one_one_real) tptp.one_one_real)))
% 6.73/7.04 (assert (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.plus_plus_rat tptp.one_one_rat) tptp.one_one_rat)))
% 6.73/7.04 (assert (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) tptp.one_one_nat)))
% 6.73/7.04 (assert (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int tptp.one_one_int) tptp.one_one_int)))
% 6.73/7.04 (assert (= (@ tptp.size_size_option_nat tptp.none_nat) (@ tptp.suc tptp.zero_zero_nat)))
% 6.73/7.04 (assert (= (@ tptp.size_s170228958280169651at_nat tptp.none_P5556105721700978146at_nat) (@ tptp.suc tptp.zero_zero_nat)))
% 6.73/7.04 (assert (= (@ tptp.size_size_option_num tptp.none_num) (@ tptp.suc tptp.zero_zero_nat)))
% 6.73/7.04 (assert (forall ((X tptp.code_integer) (A tptp.code_integer) (Y tptp.code_integer) (U tptp.code_integer) (V2 tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (=> (@ (@ tptp.ord_le3102999989581377725nteger X) A) (=> (@ (@ tptp.ord_le3102999989581377725nteger Y) A) (=> (@ _let_1 U) (=> (@ _let_1 V2) (=> (= (@ (@ tptp.plus_p5714425477246183910nteger U) V2) tptp.one_one_Code_integer) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger U) X)) (@ (@ tptp.times_3573771949741848930nteger V2) Y))) A)))))))))
% 6.73/7.04 (assert (forall ((X tptp.real) (A tptp.real) (Y tptp.real) (U tptp.real) (V2 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 V2) (=> (= (@ (@ tptp.plus_plus_real U) V2) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real U) X)) (@ (@ tptp.times_times_real V2) Y))) A)))))))))
% 6.73/7.04 (assert (forall ((X tptp.rat) (A tptp.rat) (Y tptp.rat) (U tptp.rat) (V2 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 V2) (=> (= (@ (@ tptp.plus_plus_rat U) V2) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat U) X)) (@ (@ tptp.times_times_rat V2) Y))) A)))))))))
% 6.73/7.04 (assert (forall ((X tptp.int) (A tptp.int) (Y tptp.int) (U tptp.int) (V2 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 V2) (=> (= (@ (@ tptp.plus_plus_int U) V2) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int U) X)) (@ (@ tptp.times_times_int V2) Y))) A)))))))))
% 6.73/7.04 (assert (forall ((X tptp.vEBT_VEBT) (Y tptp.option_nat)) (=> (= (@ tptp.vEBT_vebt_mint X) Y) (=> (forall ((A3 Bool) (B3 Bool)) (=> (= X (@ (@ tptp.vEBT_Leaf A3) B3)) (not (and (=> A3 (= Y (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A3) (and (=> B3 (= Y (@ tptp.some_nat tptp.one_one_nat))) (=> (not B3) (= Y tptp.none_nat)))))))) (=> (=> (exists ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw))) (not (= Y tptp.none_nat))) (not (forall ((Mi2 tptp.nat)) (=> (exists ((Ma2 tptp.nat) (Ux tptp.nat) (Uy tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) Ux) Uy) Uz2))) (not (= Y (@ tptp.some_nat Mi2)))))))))))
% 6.73/7.04 (assert (forall ((X tptp.vEBT_VEBT) (Y tptp.option_nat)) (=> (= (@ tptp.vEBT_vebt_maxt X) Y) (=> (forall ((A3 Bool) (B3 Bool)) (=> (= X (@ (@ tptp.vEBT_Leaf A3) B3)) (not (and (=> B3 (= Y (@ tptp.some_nat tptp.one_one_nat))) (=> (not B3) (and (=> A3 (= Y (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A3) (= Y tptp.none_nat)))))))) (=> (=> (exists ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw))) (not (= Y tptp.none_nat))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat)) (=> (exists ((Ux tptp.nat) (Uy tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) Ux) Uy) Uz2))) (not (= Y (@ tptp.some_nat Ma2)))))))))))
% 6.73/7.04 (assert (forall ((X tptp.vEBT_VEBT)) (=> (forall ((A3 Bool) (B3 Bool)) (not (= X (@ (@ tptp.vEBT_Leaf A3) B3)))) (=> (forall ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw tptp.vEBT_VEBT)) (not (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw)))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Ux tptp.nat) (Uy tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (not (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) Ux) Uy) Uz2)))))))))
% 6.73/7.04 (assert (forall ((X tptp.code_integer) (A tptp.code_integer) (Y tptp.code_integer) (U tptp.code_integer) (V2 tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (=> (@ (@ tptp.ord_le6747313008572928689nteger X) A) (=> (@ (@ tptp.ord_le6747313008572928689nteger Y) A) (=> (@ _let_1 U) (=> (@ _let_1 V2) (=> (= (@ (@ tptp.plus_p5714425477246183910nteger U) V2) tptp.one_one_Code_integer) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger U) X)) (@ (@ tptp.times_3573771949741848930nteger V2) Y))) A)))))))))
% 6.73/7.04 (assert (forall ((X tptp.real) (A tptp.real) (Y tptp.real) (U tptp.real) (V2 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 V2) (=> (= (@ (@ tptp.plus_plus_real U) V2) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real U) X)) (@ (@ tptp.times_times_real V2) Y))) A)))))))))
% 6.73/7.04 (assert (forall ((X tptp.rat) (A tptp.rat) (Y tptp.rat) (U tptp.rat) (V2 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 V2) (=> (= (@ (@ tptp.plus_plus_rat U) V2) tptp.one_one_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat U) X)) (@ (@ tptp.times_times_rat V2) Y))) A)))))))))
% 6.73/7.04 (assert (forall ((X tptp.int) (A tptp.int) (Y tptp.int) (U tptp.int) (V2 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 V2) (=> (= (@ (@ tptp.plus_plus_int U) V2) tptp.one_one_int) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int U) X)) (@ (@ tptp.times_times_int V2) Y))) A)))))))))
% 6.73/7.04 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Va3 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) Va3) Vb)) X) (or (= X Mi) (= X Ma)))))
% 6.73/7.04 (assert (forall ((X tptp.produc9072475918466114483BT_nat)) (=> (forall ((A3 Bool) (B3 Bool) (X3 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf A3) B3)) X3)))) (=> (forall ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw tptp.vEBT_VEBT) (X3 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw)) X3)))) (=> (forall ((V tptp.product_prod_nat_nat) (Uy tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT) (X3 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V)) tptp.zero_zero_nat) Uy) Uz2)) X3)))) (=> (forall ((V tptp.product_prod_nat_nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT) (X3 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V)) (@ tptp.suc tptp.zero_zero_nat)) Vb2) Vc2)) X3)))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT) (X3 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc (@ tptp.suc Va))) TreeList) Summary2)) X3)))))))))))
% 6.73/7.04 (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))))))))
% 6.73/7.04 (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))))))))
% 6.73/7.04 (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))))))
% 6.73/7.04 (assert (forall ((X tptp.produc9072475918466114483BT_nat)) (=> (forall ((Uu2 Bool) (Uv2 Bool)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf Uu2) Uv2)) tptp.zero_zero_nat)))) (=> (forall ((A3 Bool) (Uw Bool)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf A3) Uw)) (@ tptp.suc tptp.zero_zero_nat))))) (=> (forall ((A3 Bool) (B3 Bool) (Va tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf A3) B3)) (@ tptp.suc (@ tptp.suc Va)))))) (=> (forall ((Uy tptp.nat) (Uz2 tptp.list_VEBT_VEBT) (Va2 tptp.vEBT_VEBT) (Vb2 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uy) Uz2) Va2)) Vb2)))) (=> (forall ((V tptp.product_prod_nat_nat) (Vd tptp.list_VEBT_VEBT) (Ve tptp.vEBT_VEBT) (Vf tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V)) tptp.zero_zero_nat) Vd) Ve)) Vf)))) (=> (forall ((V tptp.product_prod_nat_nat) (Vh tptp.list_VEBT_VEBT) (Vi tptp.vEBT_VEBT) (Vj tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V)) (@ tptp.suc tptp.zero_zero_nat)) Vh) Vi)) Vj)))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT) (X3 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc (@ tptp.suc Va))) TreeList) Summary2)) X3)))))))))))))
% 6.73/7.04 (assert (forall ((X tptp.produc9072475918466114483BT_nat)) (=> (forall ((Uu2 Bool) (B3 Bool)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf Uu2) B3)) tptp.zero_zero_nat)))) (=> (forall ((Uv2 Bool) (Uw Bool) (N3 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf Uv2) Uw)) (@ tptp.suc N3))))) (=> (forall ((Ux tptp.nat) (Uy tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT) (Va2 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Ux) Uy) Uz2)) Va2)))) (=> (forall ((V tptp.product_prod_nat_nat) (Vc2 tptp.list_VEBT_VEBT) (Vd tptp.vEBT_VEBT) (Ve tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V)) tptp.zero_zero_nat) Vc2) Vd)) Ve)))) (=> (forall ((V tptp.product_prod_nat_nat) (Vg tptp.list_VEBT_VEBT) (Vh tptp.vEBT_VEBT) (Vi tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V)) (@ tptp.suc tptp.zero_zero_nat)) Vg) Vh)) Vi)))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT) (X3 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc (@ tptp.suc Va))) TreeList) Summary2)) X3))))))))))))
% 6.73/7.04 (assert (forall ((X tptp.produc9072475918466114483BT_nat)) (=> (forall ((A3 Bool) (B3 Bool)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf A3) B3)) tptp.zero_zero_nat)))) (=> (forall ((A3 Bool) (B3 Bool)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf A3) B3)) (@ tptp.suc tptp.zero_zero_nat))))) (=> (forall ((A3 Bool) (B3 Bool) (N3 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf A3) B3)) (@ tptp.suc (@ tptp.suc N3)))))) (=> (forall ((Deg2 tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT) (Uu2 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Deg2) TreeList) Summary2)) Uu2)))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (TrLst tptp.list_VEBT_VEBT) (Smry tptp.vEBT_VEBT) (X3 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) tptp.zero_zero_nat) TrLst) Smry)) X3)))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Tr tptp.list_VEBT_VEBT) (Sm tptp.vEBT_VEBT) (X3 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc tptp.zero_zero_nat)) Tr) Sm)) X3)))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT) (X3 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc (@ tptp.suc Va))) TreeList) Summary2)) X3)))))))))))))
% 6.73/7.04 (assert (forall ((X tptp.produc9072475918466114483BT_nat)) (=> (forall ((A3 Bool) (B3 Bool) (X3 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf A3) B3)) X3)))) (=> (forall ((Info tptp.option4927543243414619207at_nat) (Ts tptp.list_VEBT_VEBT) (S tptp.vEBT_VEBT) (X3 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node Info) tptp.zero_zero_nat) Ts) S)) X3)))) (=> (forall ((Info tptp.option4927543243414619207at_nat) (Ts tptp.list_VEBT_VEBT) (S tptp.vEBT_VEBT) (X3 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node Info) (@ tptp.suc tptp.zero_zero_nat)) Ts) S)) X3)))) (=> (forall ((V tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT) (X3 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) (@ tptp.suc (@ tptp.suc V))) TreeList) Summary2)) X3)))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT) (X3 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc (@ tptp.suc Va))) TreeList) Summary2)) X3)))))))))))
% 6.73/7.04 (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)))))
% 6.73/7.04 (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)))))
% 6.73/7.04 (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)))))
% 6.73/7.04 (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)))))
% 6.73/7.04 (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)))))
% 6.73/7.04 (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)))))
% 6.73/7.04 (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)))))
% 6.73/7.04 (assert (forall ((Uv Bool) (Uw2 Bool) (N tptp.nat)) (= (@ (@ tptp.vEBT_vebt_succ (@ (@ tptp.vEBT_Leaf Uv) Uw2)) (@ tptp.suc N)) tptp.none_nat)))
% 6.73/7.04 (assert (forall ((Uu Bool) (Uv Bool)) (= (@ (@ tptp.vEBT_vebt_pred (@ (@ tptp.vEBT_Leaf Uu) Uv)) tptp.zero_zero_nat) tptp.none_nat)))
% 6.73/7.04 (assert (forall ((V2 tptp.product_prod_nat_nat) (Vc tptp.list_VEBT_VEBT) (Vd2 tptp.vEBT_VEBT) (Ve2 tptp.nat)) (= (@ (@ tptp.vEBT_vebt_succ (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Vc) Vd2)) Ve2) tptp.none_nat)))
% 6.73/7.04 (assert (forall ((V2 tptp.product_prod_nat_nat) (Vd2 tptp.list_VEBT_VEBT) (Ve2 tptp.vEBT_VEBT) (Vf2 tptp.nat)) (= (@ (@ tptp.vEBT_vebt_pred (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Vd2) Ve2)) Vf2) tptp.none_nat)))
% 6.73/7.04 (assert (forall ((V2 tptp.product_prod_nat_nat) (Vh2 tptp.list_VEBT_VEBT) (Vi2 tptp.vEBT_VEBT) (Vj2 tptp.nat)) (= (@ (@ tptp.vEBT_vebt_pred (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vh2) Vi2)) Vj2) tptp.none_nat)))
% 6.73/7.04 (assert (forall ((V2 tptp.product_prod_nat_nat) (Vg2 tptp.list_VEBT_VEBT) (Vh2 tptp.vEBT_VEBT) (Vi2 tptp.nat)) (= (@ (@ tptp.vEBT_vebt_succ (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vg2) Vh2)) Vi2) tptp.none_nat)))
% 6.73/7.04 (assert (forall ((A Bool) (Uw2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_vebt_pred (@ (@ tptp.vEBT_Leaf A) Uw2)) (@ tptp.suc tptp.zero_zero_nat)))) (and (=> A (= _let_1 (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A) (= _let_1 tptp.none_nat))))))
% 6.73/7.04 (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))))))
% 6.73/7.04 (assert (forall ((B Bool) (A Bool) (Va3 tptp.nat)) (let ((_let_1 (@ (@ tptp.vEBT_vebt_pred (@ (@ tptp.vEBT_Leaf A) B)) (@ tptp.suc (@ tptp.suc Va3))))) (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))))))))
% 6.73/7.04 (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))))
% 6.73/7.04 (assert (forall ((A Bool) (B Bool)) (= (@ (@ tptp.vEBT_vebt_delete (@ (@ tptp.vEBT_Leaf A) B)) tptp.zero_zero_nat) (@ (@ tptp.vEBT_Leaf false) B))))
% 6.73/7.04 (assert (= tptp.vEBT_is_pred_in_set (lambda ((Xs tptp.set_nat) (X4 tptp.nat) (Y4 tptp.nat)) (and (@ (@ tptp.member_nat Y4) Xs) (@ (@ tptp.ord_less_nat Y4) X4) (forall ((Z4 tptp.nat)) (=> (@ (@ tptp.member_nat Z4) Xs) (=> (@ (@ tptp.ord_less_nat Z4) X4) (@ (@ tptp.ord_less_eq_nat Z4) Y4))))))))
% 6.73/7.04 (assert (= tptp.vEBT_is_succ_in_set (lambda ((Xs tptp.set_nat) (X4 tptp.nat) (Y4 tptp.nat)) (and (@ (@ tptp.member_nat Y4) Xs) (@ (@ tptp.ord_less_nat X4) Y4) (forall ((Z4 tptp.nat)) (=> (@ (@ tptp.member_nat Z4) Xs) (=> (@ (@ tptp.ord_less_nat X4) Z4) (@ (@ tptp.ord_less_eq_nat Y4) Z4))))))))
% 6.73/7.04 (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)))))
% 6.73/7.04 (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)))))
% 6.73/7.04 (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)))))
% 6.73/7.04 (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))))))
% 6.73/7.04 (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))))))
% 6.73/7.04 (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))))))
% 6.73/7.04 (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)))))
% 6.73/7.04 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (TrLst2 tptp.list_VEBT_VEBT) (Smry2 tptp.vEBT_VEBT) (X tptp.nat)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) tptp.zero_zero_nat) TrLst2) Smry2))) (= (@ (@ tptp.vEBT_vebt_delete _let_1) X) _let_1))))
% 6.73/7.04 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Tr2 tptp.list_VEBT_VEBT) (Sm2 tptp.vEBT_VEBT) (X tptp.nat)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) (@ tptp.suc tptp.zero_zero_nat)) Tr2) Sm2))) (= (@ (@ tptp.vEBT_vebt_delete _let_1) X) _let_1))))
% 6.73/7.04 (assert (= tptp.vEBT_VEBT_add (@ tptp.vEBT_V4262088993061758097ft_nat tptp.plus_plus_nat)))
% 6.73/7.04 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (= (@ tptp.vEBT_VEBT_set_vebt (@ (@ tptp.vEBT_vebt_delete T) X)) (@ (@ tptp.minus_minus_set_nat (@ tptp.vEBT_set_vebt T)) (@ (@ tptp.insert_nat X) tptp.bot_bot_set_nat))))))
% 6.73/7.04 (assert (forall ((A tptp.real)) (= (= (@ (@ tptp.plus_plus_real A) A) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 6.73/7.04 (assert (forall ((A tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat A) A) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))))
% 6.73/7.04 (assert (forall ((A tptp.int)) (= (= (@ (@ tptp.plus_plus_int A) A) tptp.zero_zero_int) (= A tptp.zero_zero_int))))
% 6.73/7.04 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z3 tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat X) Y) Z3) (= (@ (@ tptp.vEBT_VEBT_add (@ tptp.some_nat X)) (@ tptp.some_nat Y)) (@ tptp.some_nat Z3)))))
% 6.73/7.04 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (= (@ tptp.vEBT_VEBT_set_vebt (@ (@ tptp.vEBT_vebt_delete T) X)) (@ (@ tptp.minus_minus_set_nat (@ tptp.vEBT_VEBT_set_vebt T)) (@ (@ tptp.insert_nat X) tptp.bot_bot_set_nat))))))
% 6.73/7.04 (assert (forall ((X tptp.nat) (Z3 tptp.nat) (A4 tptp.set_nat) (B5 tptp.set_nat)) (=> (@ (@ tptp.ord_less_nat X) Z3) (=> (@ (@ tptp.vEBT_VEBT_max_in_set A4) Z3) (=> (@ tptp.finite_finite_nat B5) (=> (= A4 B5) (exists ((X_12 tptp.nat)) (@ (@ (@ tptp.vEBT_is_succ_in_set A4) X) X_12))))))))
% 6.73/7.04 (assert (forall ((Z3 tptp.nat) (X tptp.nat) (A4 tptp.set_nat)) (=> (@ (@ tptp.ord_less_nat Z3) X) (=> (@ (@ tptp.vEBT_VEBT_min_in_set A4) Z3) (=> (@ tptp.finite_finite_nat A4) (exists ((X_12 tptp.nat)) (@ (@ (@ tptp.vEBT_is_pred_in_set A4) X) X_12)))))))
% 6.73/7.04 (assert (forall ((X tptp.complex) (Xs2 tptp.list_complex)) (=> (@ (@ tptp.member_complex X) (@ tptp.set_complex2 Xs2)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_s3451745648224563538omplex Xs2)))))
% 6.73/7.04 (assert (forall ((X tptp.real) (Xs2 tptp.list_real)) (=> (@ (@ tptp.member_real X) (@ tptp.set_real2 Xs2)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_size_list_real Xs2)))))
% 6.73/7.04 (assert (forall ((X tptp.set_nat) (Xs2 tptp.list_set_nat)) (=> (@ (@ tptp.member_set_nat X) (@ tptp.set_set_nat2 Xs2)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_s3254054031482475050et_nat Xs2)))))
% 6.73/7.04 (assert (forall ((X tptp.vEBT_VEBT) (Xs2 tptp.list_VEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 Xs2)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_s6755466524823107622T_VEBT Xs2)))))
% 6.73/7.04 (assert (forall ((X Bool) (Xs2 tptp.list_o)) (=> (@ (@ tptp.member_o X) (@ tptp.set_o2 Xs2)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_size_list_o Xs2)))))
% 6.73/7.04 (assert (forall ((X tptp.nat) (Xs2 tptp.list_nat)) (=> (@ (@ tptp.member_nat X) (@ tptp.set_nat2 Xs2)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_size_list_nat Xs2)))))
% 6.73/7.04 (assert (forall ((X tptp.int) (Xs2 tptp.list_int)) (=> (@ (@ tptp.member_int X) (@ tptp.set_int2 Xs2)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_size_list_int Xs2)))))
% 6.73/7.04 (assert (forall ((X (-> tptp.product_prod_nat_nat tptp.nat)) (X2 tptp.product_prod_nat_nat)) (= (@ (@ tptp.size_o8335143837870341156at_nat X) (@ tptp.some_P7363390416028606310at_nat X2)) (@ (@ tptp.plus_plus_nat (@ X X2)) (@ tptp.suc tptp.zero_zero_nat)))))
% 6.73/7.04 (assert (forall ((X (-> tptp.nat tptp.nat)) (X2 tptp.nat)) (= (@ (@ tptp.size_option_nat X) (@ tptp.some_nat X2)) (@ (@ tptp.plus_plus_nat (@ X X2)) (@ tptp.suc tptp.zero_zero_nat)))))
% 6.73/7.04 (assert (forall ((X (-> tptp.num tptp.nat)) (X2 tptp.num)) (= (@ (@ tptp.size_option_num X) (@ tptp.some_num X2)) (@ (@ tptp.plus_plus_nat (@ X X2)) (@ tptp.suc tptp.zero_zero_nat)))))
% 6.73/7.04 (assert (forall ((R3 tptp.complex) (A tptp.complex) (B tptp.complex) (C2 tptp.complex) (D tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex R3))) (=> (not (= R3 tptp.zero_zero_complex)) (=> (and (= A B) (not (= C2 D))) (not (= (@ (@ tptp.plus_plus_complex A) (@ _let_1 C2)) (@ (@ tptp.plus_plus_complex B) (@ _let_1 D)))))))))
% 6.73/7.04 (assert (forall ((R3 tptp.real) (A tptp.real) (B tptp.real) (C2 tptp.real) (D tptp.real)) (let ((_let_1 (@ tptp.times_times_real R3))) (=> (not (= R3 tptp.zero_zero_real)) (=> (and (= A B) (not (= C2 D))) (not (= (@ (@ tptp.plus_plus_real A) (@ _let_1 C2)) (@ (@ tptp.plus_plus_real B) (@ _let_1 D)))))))))
% 6.73/7.04 (assert (forall ((R3 tptp.rat) (A tptp.rat) (B tptp.rat) (C2 tptp.rat) (D tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat R3))) (=> (not (= R3 tptp.zero_zero_rat)) (=> (and (= A B) (not (= C2 D))) (not (= (@ (@ tptp.plus_plus_rat A) (@ _let_1 C2)) (@ (@ tptp.plus_plus_rat B) (@ _let_1 D)))))))))
% 6.73/7.04 (assert (forall ((R3 tptp.nat) (A tptp.nat) (B tptp.nat) (C2 tptp.nat) (D tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat R3))) (=> (not (= R3 tptp.zero_zero_nat)) (=> (and (= A B) (not (= C2 D))) (not (= (@ (@ tptp.plus_plus_nat A) (@ _let_1 C2)) (@ (@ tptp.plus_plus_nat B) (@ _let_1 D)))))))))
% 6.73/7.04 (assert (forall ((R3 tptp.int) (A tptp.int) (B tptp.int) (C2 tptp.int) (D tptp.int)) (let ((_let_1 (@ tptp.times_times_int R3))) (=> (not (= R3 tptp.zero_zero_int)) (=> (and (= A B) (not (= C2 D))) (not (= (@ (@ tptp.plus_plus_int A) (@ _let_1 C2)) (@ (@ tptp.plus_plus_int B) (@ _let_1 D)))))))))
% 6.73/7.04 (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)))))
% 6.73/7.04 (assert (forall ((Xs2 tptp.set_nat) (A tptp.nat)) (=> (not (exists ((X_12 tptp.nat)) (@ (@ (@ tptp.vEBT_is_pred_in_set Xs2) A) X_12))) (=> (@ tptp.finite_finite_nat Xs2) (not (exists ((X5 tptp.nat)) (and (@ (@ tptp.member_nat X5) Xs2) (@ (@ tptp.ord_less_nat X5) A))))))))
% 6.73/7.04 (assert (forall ((Xs2 tptp.set_nat) (A tptp.nat)) (=> (not (exists ((X_12 tptp.nat)) (@ (@ (@ tptp.vEBT_is_succ_in_set Xs2) A) X_12))) (=> (@ tptp.finite_finite_nat Xs2) (not (exists ((X5 tptp.nat)) (and (@ (@ tptp.member_nat X5) Xs2) (@ (@ tptp.ord_less_nat A) X5))))))))
% 6.73/7.04 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.minus_minus_complex A) A) tptp.zero_zero_complex)))
% 6.73/7.04 (assert (forall ((A tptp.real)) (= (@ (@ tptp.minus_minus_real A) A) tptp.zero_zero_real)))
% 6.73/7.04 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.minus_minus_rat A) A) tptp.zero_zero_rat)))
% 6.73/7.04 (assert (forall ((A tptp.int)) (= (@ (@ tptp.minus_minus_int A) A) tptp.zero_zero_int)))
% 6.73/7.04 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.minus_minus_complex A) tptp.zero_zero_complex) A)))
% 6.73/7.04 (assert (forall ((A tptp.real)) (= (@ (@ tptp.minus_minus_real A) tptp.zero_zero_real) A)))
% 6.73/7.04 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.minus_minus_rat A) tptp.zero_zero_rat) A)))
% 6.73/7.04 (assert (forall ((A tptp.int)) (= (@ (@ tptp.minus_minus_int A) tptp.zero_zero_int) A)))
% 6.73/7.04 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.minus_minus_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)))
% 6.73/7.04 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.minus_minus_complex A) tptp.zero_zero_complex) A)))
% 6.73/7.04 (assert (forall ((A tptp.real)) (= (@ (@ tptp.minus_minus_real A) tptp.zero_zero_real) A)))
% 6.73/7.04 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.minus_minus_rat A) tptp.zero_zero_rat) A)))
% 6.73/7.04 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.minus_minus_nat A) tptp.zero_zero_nat) A)))
% 6.73/7.04 (assert (forall ((A tptp.int)) (= (@ (@ tptp.minus_minus_int A) tptp.zero_zero_int) A)))
% 6.73/7.04 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.minus_minus_complex A) A) tptp.zero_zero_complex)))
% 6.73/7.04 (assert (forall ((A tptp.real)) (= (@ (@ tptp.minus_minus_real A) A) tptp.zero_zero_real)))
% 6.73/7.04 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.minus_minus_rat A) A) tptp.zero_zero_rat)))
% 6.73/7.04 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.minus_minus_nat A) A) tptp.zero_zero_nat)))
% 6.73/7.04 (assert (forall ((A tptp.int)) (= (@ (@ tptp.minus_minus_int A) A) tptp.zero_zero_int)))
% 6.73/7.04 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A) B)) B) A)))
% 6.73/7.04 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A) B)) B) A)))
% 6.73/7.04 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat A) B)) B) A)))
% 6.73/7.04 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A) B)) B) A)))
% 6.73/7.04 (assert (forall ((A tptp.real) (C2 tptp.real) (B tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A) C2)) (@ (@ tptp.plus_plus_real B) C2)) (@ (@ tptp.minus_minus_real A) B))))
% 6.73/7.04 (assert (forall ((A tptp.rat) (C2 tptp.rat) (B tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A) C2)) (@ (@ tptp.plus_plus_rat B) C2)) (@ (@ tptp.minus_minus_rat A) B))))
% 6.73/7.04 (assert (forall ((A tptp.nat) (C2 tptp.nat) (B tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat A) C2)) (@ (@ tptp.plus_plus_nat B) C2)) (@ (@ tptp.minus_minus_nat A) B))))
% 6.73/7.04 (assert (forall ((A tptp.int) (C2 tptp.int) (B tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A) C2)) (@ (@ tptp.plus_plus_int B) C2)) (@ (@ tptp.minus_minus_int A) B))))
% 6.73/7.04 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A) B)) A) B)))
% 6.73/7.04 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A) B)) A) B)))
% 6.73/7.04 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat A) B)) A) B)))
% 6.73/7.04 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A) B)) A) B)))
% 6.73/7.04 (assert (forall ((C2 tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real C2))) (= (@ (@ tptp.minus_minus_real (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.minus_minus_real A) B)))))
% 6.73/7.04 (assert (forall ((C2 tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat C2))) (= (@ (@ tptp.minus_minus_rat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.minus_minus_rat A) B)))))
% 6.73/7.04 (assert (forall ((C2 tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C2))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.minus_minus_nat A) B)))))
% 6.73/7.04 (assert (forall ((C2 tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C2))) (= (@ (@ tptp.minus_minus_int (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.minus_minus_int A) B)))))
% 6.73/7.04 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.minus_minus_real A) B)) B) A)))
% 6.73/7.04 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.minus_minus_rat A) B)) B) A)))
% 6.73/7.04 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int A) B)) B) A)))
% 6.73/7.04 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A) B)) B) A)))
% 6.73/7.04 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A) B)) B) A)))
% 6.73/7.04 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A) B)) B) A)))
% 6.73/7.04 (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))))
% 6.73/7.04 (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))))
% 6.73/7.04 (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))))
% 6.73/7.04 (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))))
% 6.73/7.04 (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))))
% 6.73/7.04 (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))))
% 6.73/7.04 (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))))
% 6.73/7.04 (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))))
% 6.73/7.04 (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))))
% 6.73/7.04 (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))))
% 6.73/7.04 (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))))
% 6.73/7.04 (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))))
% 6.73/7.04 (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))))
% 6.73/7.04 (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))))
% 6.73/7.04 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.minus_minus_nat A) (@ (@ tptp.plus_plus_nat A) B)) tptp.zero_zero_nat)))
% 6.73/7.04 (assert (= (@ (@ tptp.minus_8373710615458151222nteger tptp.one_one_Code_integer) tptp.one_one_Code_integer) tptp.zero_z3403309356797280102nteger))
% 6.73/7.04 (assert (= (@ (@ tptp.minus_minus_complex tptp.one_one_complex) tptp.one_one_complex) tptp.zero_zero_complex))
% 6.73/7.04 (assert (= (@ (@ tptp.minus_minus_real tptp.one_one_real) tptp.one_one_real) tptp.zero_zero_real))
% 6.73/7.04 (assert (= (@ (@ tptp.minus_minus_rat tptp.one_one_rat) tptp.one_one_rat) tptp.zero_zero_rat))
% 6.73/7.04 (assert (= (@ (@ tptp.minus_minus_int tptp.one_one_int) tptp.one_one_int) tptp.zero_zero_int))
% 6.73/7.04 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (Ys tptp.list_VEBT_VEBT)) (=> (not (= (@ tptp.size_s6755466524823107622T_VEBT Xs2) (@ tptp.size_s6755466524823107622T_VEBT Ys))) (not (= Xs2 Ys)))))
% 6.73/7.04 (assert (forall ((Xs2 tptp.list_o) (Ys tptp.list_o)) (=> (not (= (@ tptp.size_size_list_o Xs2) (@ tptp.size_size_list_o Ys))) (not (= Xs2 Ys)))))
% 6.73/7.04 (assert (forall ((Xs2 tptp.list_nat) (Ys tptp.list_nat)) (=> (not (= (@ tptp.size_size_list_nat Xs2) (@ tptp.size_size_list_nat Ys))) (not (= Xs2 Ys)))))
% 6.73/7.04 (assert (forall ((Xs2 tptp.list_int) (Ys tptp.list_int)) (=> (not (= (@ tptp.size_size_list_int Xs2) (@ tptp.size_size_list_int Ys))) (not (= Xs2 Ys)))))
% 6.73/7.04 (assert (forall ((N tptp.nat)) (exists ((Xs3 tptp.list_VEBT_VEBT)) (= (@ tptp.size_s6755466524823107622T_VEBT Xs3) N))))
% 6.73/7.04 (assert (forall ((N tptp.nat)) (exists ((Xs3 tptp.list_o)) (= (@ tptp.size_size_list_o Xs3) N))))
% 6.73/7.04 (assert (forall ((N tptp.nat)) (exists ((Xs3 tptp.list_nat)) (= (@ tptp.size_size_list_nat Xs3) N))))
% 6.73/7.04 (assert (forall ((N tptp.nat)) (exists ((Xs3 tptp.list_int)) (= (@ tptp.size_size_list_int Xs3) N))))
% 6.73/7.04 (assert (forall ((A tptp.rat) (C2 tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.minus_minus_rat A))) (= (@ (@ tptp.minus_minus_rat (@ _let_1 C2)) B) (@ (@ tptp.minus_minus_rat (@ _let_1 B)) C2)))))
% 6.73/7.04 (assert (forall ((A tptp.nat) (C2 tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat A))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 C2)) B) (@ (@ tptp.minus_minus_nat (@ _let_1 B)) C2)))))
% 6.73/7.04 (assert (forall ((A tptp.int) (C2 tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int A))) (= (@ (@ tptp.minus_minus_int (@ _let_1 C2)) B) (@ (@ tptp.minus_minus_int (@ _let_1 B)) C2)))))
% 6.73/7.04 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat) (D tptp.rat)) (=> (= (@ (@ tptp.minus_minus_rat A) B) (@ (@ tptp.minus_minus_rat C2) D)) (= (= A B) (= C2 D)))))
% 6.73/7.04 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int) (D tptp.int)) (=> (= (@ (@ tptp.minus_minus_int A) B) (@ (@ tptp.minus_minus_int C2) D)) (= (= A B) (= C2 D)))))
% 6.73/7.04 (assert (forall ((A tptp.rat) (B tptp.rat) (D tptp.rat) (C2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat D) C2) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat A) C2)) (@ (@ tptp.minus_minus_rat B) D))))))
% 6.73/7.04 (assert (forall ((A tptp.int) (B tptp.int) (D tptp.int) (C2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_eq_int D) C2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int A) C2)) (@ (@ tptp.minus_minus_int B) D))))))
% 6.73/7.04 (assert (forall ((B tptp.rat) (A tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.minus_minus_rat C2))) (=> (@ (@ tptp.ord_less_eq_rat B) A) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B))))))
% 6.73/7.04 (assert (forall ((B tptp.int) (A tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int C2))) (=> (@ (@ tptp.ord_less_eq_int B) A) (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B))))))
% 6.73/7.04 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat A) C2)) (@ (@ tptp.minus_minus_rat B) C2)))))
% 6.73/7.04 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int A) C2)) (@ (@ tptp.minus_minus_int B) C2)))))
% 6.73/7.04 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat) (D tptp.rat)) (=> (= (@ (@ tptp.minus_minus_rat A) B) (@ (@ tptp.minus_minus_rat C2) D)) (= (@ (@ tptp.ord_less_eq_rat A) B) (@ (@ tptp.ord_less_eq_rat C2) D)))))
% 6.73/7.04 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int) (D tptp.int)) (=> (= (@ (@ tptp.minus_minus_int A) B) (@ (@ tptp.minus_minus_int C2) D)) (= (@ (@ tptp.ord_less_eq_int A) B) (@ (@ tptp.ord_less_eq_int C2) D)))))
% 6.73/7.04 (assert (= (lambda ((Y5 tptp.complex) (Z2 tptp.complex)) (= Y5 Z2)) (lambda ((A5 tptp.complex) (B4 tptp.complex)) (= (@ (@ tptp.minus_minus_complex A5) B4) tptp.zero_zero_complex))))
% 6.73/7.04 (assert (= (lambda ((Y5 tptp.real) (Z2 tptp.real)) (= Y5 Z2)) (lambda ((A5 tptp.real) (B4 tptp.real)) (= (@ (@ tptp.minus_minus_real A5) B4) tptp.zero_zero_real))))
% 6.73/7.04 (assert (= (lambda ((Y5 tptp.rat) (Z2 tptp.rat)) (= Y5 Z2)) (lambda ((A5 tptp.rat) (B4 tptp.rat)) (= (@ (@ tptp.minus_minus_rat A5) B4) tptp.zero_zero_rat))))
% 6.73/7.04 (assert (= (lambda ((Y5 tptp.int) (Z2 tptp.int)) (= Y5 Z2)) (lambda ((A5 tptp.int) (B4 tptp.int)) (= (@ (@ tptp.minus_minus_int A5) B4) tptp.zero_zero_int))))
% 6.73/7.04 (assert (forall ((A tptp.real) (B tptp.real) (C2 tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real A) C2)) (@ (@ tptp.minus_minus_real B) C2)))))
% 6.73/7.04 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat A) C2)) (@ (@ tptp.minus_minus_rat B) C2)))))
% 6.73/7.04 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (@ (@ tptp.ord_less_int (@ (@ tptp.minus_minus_int A) C2)) (@ (@ tptp.minus_minus_int B) C2)))))
% 6.73/7.04 (assert (forall ((B tptp.real) (A tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.minus_minus_real C2))) (=> (@ (@ tptp.ord_less_real B) A) (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B))))))
% 6.73/7.04 (assert (forall ((B tptp.rat) (A tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.minus_minus_rat C2))) (=> (@ (@ tptp.ord_less_rat B) A) (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B))))))
% 6.73/7.04 (assert (forall ((B tptp.int) (A tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int C2))) (=> (@ (@ tptp.ord_less_int B) A) (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B))))))
% 6.73/7.04 (assert (forall ((A tptp.real) (B tptp.real) (C2 tptp.real) (D tptp.real)) (=> (= (@ (@ tptp.minus_minus_real A) B) (@ (@ tptp.minus_minus_real C2) D)) (= (@ (@ tptp.ord_less_real A) B) (@ (@ tptp.ord_less_real C2) D)))))
% 6.73/7.04 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat) (D tptp.rat)) (=> (= (@ (@ tptp.minus_minus_rat A) B) (@ (@ tptp.minus_minus_rat C2) D)) (= (@ (@ tptp.ord_less_rat A) B) (@ (@ tptp.ord_less_rat C2) D)))))
% 6.73/7.04 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int) (D tptp.int)) (=> (= (@ (@ tptp.minus_minus_int A) B) (@ (@ tptp.minus_minus_int C2) D)) (= (@ (@ tptp.ord_less_int A) B) (@ (@ tptp.ord_less_int C2) D)))))
% 6.73/7.04 (assert (forall ((A tptp.real) (B tptp.real) (D tptp.real) (C2 tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_real D) C2) (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real A) C2)) (@ (@ tptp.minus_minus_real B) D))))))
% 6.73/7.04 (assert (forall ((A tptp.rat) (B tptp.rat) (D tptp.rat) (C2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_rat D) C2) (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat A) C2)) (@ (@ tptp.minus_minus_rat B) D))))))
% 6.73/7.04 (assert (forall ((A tptp.int) (B tptp.int) (D tptp.int) (C2 tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_int D) C2) (@ (@ tptp.ord_less_int (@ (@ tptp.minus_minus_int A) C2)) (@ (@ tptp.minus_minus_int B) D))))))
% 6.73/7.04 (assert (forall ((A tptp.real) (B tptp.real) (C2 tptp.real)) (= (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real A) B)) C2) (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real A) C2)) (@ (@ tptp.times_times_real B) C2)))))
% 6.73/7.04 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (= (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat A) B)) C2) (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat A) C2)) (@ (@ tptp.times_times_rat B) C2)))))
% 6.73/7.04 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int A) B)) C2) (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int A) C2)) (@ (@ tptp.times_times_int B) C2)))))
% 6.73/7.04 (assert (forall ((A tptp.real) (B tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.times_times_real A))) (= (@ _let_1 (@ (@ tptp.minus_minus_real B) C2)) (@ (@ tptp.minus_minus_real (@ _let_1 B)) (@ _let_1 C2))))))
% 6.73/7.04 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat A))) (= (@ _let_1 (@ (@ tptp.minus_minus_rat B) C2)) (@ (@ tptp.minus_minus_rat (@ _let_1 B)) (@ _let_1 C2))))))
% 6.73/7.04 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (= (@ _let_1 (@ (@ tptp.minus_minus_int B) C2)) (@ (@ tptp.minus_minus_int (@ _let_1 B)) (@ _let_1 C2))))))
% 6.73/7.04 (assert (forall ((B tptp.real) (C2 tptp.real) (A tptp.real)) (= (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real B) C2)) A) (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real B) A)) (@ (@ tptp.times_times_real C2) A)))))
% 6.73/7.04 (assert (forall ((B tptp.rat) (C2 tptp.rat) (A tptp.rat)) (= (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat B) C2)) A) (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat B) A)) (@ (@ tptp.times_times_rat C2) A)))))
% 6.73/7.04 (assert (forall ((B tptp.nat) (C2 tptp.nat) (A tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat B) C2)) A) (@ (@ tptp.minus_minus_nat (@ (@ tptp.times_times_nat B) A)) (@ (@ tptp.times_times_nat C2) A)))))
% 6.73/7.04 (assert (forall ((B tptp.int) (C2 tptp.int) (A tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int B) C2)) A) (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int B) A)) (@ (@ tptp.times_times_int C2) A)))))
% 6.73/7.04 (assert (forall ((A tptp.real) (B tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.times_times_real A))) (= (@ _let_1 (@ (@ tptp.minus_minus_real B) C2)) (@ (@ tptp.minus_minus_real (@ _let_1 B)) (@ _let_1 C2))))))
% 6.73/7.04 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat A))) (= (@ _let_1 (@ (@ tptp.minus_minus_rat B) C2)) (@ (@ tptp.minus_minus_rat (@ _let_1 B)) (@ _let_1 C2))))))
% 6.73/7.04 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (= (@ _let_1 (@ (@ tptp.minus_minus_nat B) C2)) (@ (@ tptp.minus_minus_nat (@ _let_1 B)) (@ _let_1 C2))))))
% 6.73/7.04 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (= (@ _let_1 (@ (@ tptp.minus_minus_int B) C2)) (@ (@ tptp.minus_minus_int (@ _let_1 B)) (@ _let_1 C2))))))
% 6.73/7.04 (assert (forall ((A tptp.real) (B tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.minus_minus_real A))) (= (@ (@ tptp.minus_minus_real (@ _let_1 B)) C2) (@ _let_1 (@ (@ tptp.plus_plus_real B) C2))))))
% 6.73/7.04 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.minus_minus_rat A))) (= (@ (@ tptp.minus_minus_rat (@ _let_1 B)) C2) (@ _let_1 (@ (@ tptp.plus_plus_rat B) C2))))))
% 6.73/7.04 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat A))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 B)) C2) (@ _let_1 (@ (@ tptp.plus_plus_nat B) C2))))))
% 6.73/7.04 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int A))) (= (@ (@ tptp.minus_minus_int (@ _let_1 B)) C2) (@ _let_1 (@ (@ tptp.plus_plus_int B) C2))))))
% 6.73/7.04 (assert (forall ((C2 tptp.real) (B tptp.real) (A tptp.real)) (=> (= (@ (@ tptp.plus_plus_real C2) B) A) (= C2 (@ (@ tptp.minus_minus_real A) B)))))
% 6.73/7.04 (assert (forall ((C2 tptp.rat) (B tptp.rat) (A tptp.rat)) (=> (= (@ (@ tptp.plus_plus_rat C2) B) A) (= C2 (@ (@ tptp.minus_minus_rat A) B)))))
% 6.73/7.04 (assert (forall ((C2 tptp.nat) (B tptp.nat) (A tptp.nat)) (=> (= (@ (@ tptp.plus_plus_nat C2) B) A) (= C2 (@ (@ tptp.minus_minus_nat A) B)))))
% 6.73/7.04 (assert (forall ((C2 tptp.int) (B tptp.int) (A tptp.int)) (=> (= (@ (@ tptp.plus_plus_int C2) B) A) (= C2 (@ (@ tptp.minus_minus_int A) B)))))
% 6.73/7.04 (assert (forall ((A tptp.real) (B tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.minus_minus_real A))) (= (@ _let_1 (@ (@ tptp.plus_plus_real B) C2)) (@ (@ tptp.minus_minus_real (@ _let_1 C2)) B)))))
% 6.73/7.04 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.minus_minus_rat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat B) C2)) (@ (@ tptp.minus_minus_rat (@ _let_1 C2)) B)))))
% 6.73/7.04 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int A))) (= (@ _let_1 (@ (@ tptp.plus_plus_int B) C2)) (@ (@ tptp.minus_minus_int (@ _let_1 C2)) B)))))
% 6.73/7.04 (assert (forall ((A tptp.real) (B tptp.real) (C2 tptp.real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.minus_minus_real A) B)) C2) (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A) C2)) B))))
% 6.73/7.04 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.minus_minus_rat A) B)) C2) (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A) C2)) B))))
% 6.73/7.04 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int A) B)) C2) (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A) C2)) B))))
% 6.73/7.04 (assert (forall ((A tptp.real) (B tptp.real) (C2 tptp.real)) (= (@ (@ tptp.minus_minus_real A) (@ (@ tptp.minus_minus_real B) C2)) (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A) C2)) B))))
% 6.73/7.04 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (= (@ (@ tptp.minus_minus_rat A) (@ (@ tptp.minus_minus_rat B) C2)) (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A) C2)) B))))
% 6.73/7.04 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (= (@ (@ tptp.minus_minus_int A) (@ (@ tptp.minus_minus_int B) C2)) (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A) C2)) B))))
% 6.73/7.04 (assert (forall ((A tptp.real) (B tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A))) (= (@ _let_1 (@ (@ tptp.minus_minus_real B) C2)) (@ (@ tptp.minus_minus_real (@ _let_1 B)) C2)))))
% 6.73/7.04 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat A))) (= (@ _let_1 (@ (@ tptp.minus_minus_rat B) C2)) (@ (@ tptp.minus_minus_rat (@ _let_1 B)) C2)))))
% 6.73/7.04 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A))) (= (@ _let_1 (@ (@ tptp.minus_minus_int B) C2)) (@ (@ tptp.minus_minus_int (@ _let_1 B)) C2)))))
% 6.73/7.04 (assert (forall ((A tptp.real) (C2 tptp.real) (B tptp.real)) (= (= A (@ (@ tptp.minus_minus_real C2) B)) (= (@ (@ tptp.plus_plus_real A) B) C2))))
% 6.73/7.04 (assert (forall ((A tptp.rat) (C2 tptp.rat) (B tptp.rat)) (= (= A (@ (@ tptp.minus_minus_rat C2) B)) (= (@ (@ tptp.plus_plus_rat A) B) C2))))
% 6.73/7.04 (assert (forall ((A tptp.int) (C2 tptp.int) (B tptp.int)) (= (= A (@ (@ tptp.minus_minus_int C2) B)) (= (@ (@ tptp.plus_plus_int A) B) C2))))
% 6.73/7.04 (assert (forall ((A tptp.real) (B tptp.real) (C2 tptp.real)) (= (= (@ (@ tptp.minus_minus_real A) B) C2) (= A (@ (@ tptp.plus_plus_real C2) B)))))
% 6.73/7.04 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (= (= (@ (@ tptp.minus_minus_rat A) B) C2) (= A (@ (@ tptp.plus_plus_rat C2) B)))))
% 6.73/7.04 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (= (= (@ (@ tptp.minus_minus_int A) B) C2) (= A (@ (@ tptp.plus_plus_int C2) B)))))
% 6.73/7.04 (assert (forall ((A4 tptp.real) (K2 tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real K2))) (=> (= A4 (@ _let_1 A)) (= (@ (@ tptp.minus_minus_real A4) B) (@ _let_1 (@ (@ tptp.minus_minus_real A) B)))))))
% 6.73/7.04 (assert (forall ((A4 tptp.rat) (K2 tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat K2))) (=> (= A4 (@ _let_1 A)) (= (@ (@ tptp.minus_minus_rat A4) B) (@ _let_1 (@ (@ tptp.minus_minus_rat A) B)))))))
% 6.73/7.04 (assert (forall ((A4 tptp.int) (K2 tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int K2))) (=> (= A4 (@ _let_1 A)) (= (@ (@ tptp.minus_minus_int A4) B) (@ _let_1 (@ (@ tptp.minus_minus_int A) B)))))))
% 6.73/7.04 (assert (= tptp.finite_finite_nat (lambda ((N5 tptp.set_nat)) (exists ((M6 tptp.nat)) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) N5) (@ (@ tptp.ord_less_nat X4) M6)))))))
% 6.73/7.04 (assert (forall ((N6 tptp.set_nat) (N tptp.nat)) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) N6) (@ (@ tptp.ord_less_nat X3) N))) (@ tptp.finite_finite_nat N6))))
% 6.73/7.04 (assert (= tptp.finite_finite_nat (lambda ((N5 tptp.set_nat)) (exists ((M6 tptp.nat)) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) N5) (@ (@ tptp.ord_less_eq_nat X4) M6)))))))
% 6.73/7.04 (assert (= tptp.ord_less_eq_real (lambda ((A5 tptp.real) (B4 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real A5) B4)) tptp.zero_zero_real))))
% 6.73/7.04 (assert (= tptp.ord_less_eq_rat (lambda ((A5 tptp.rat) (B4 tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat A5) B4)) tptp.zero_zero_rat))))
% 6.73/7.04 (assert (= tptp.ord_less_eq_int (lambda ((A5 tptp.int) (B4 tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int A5) B4)) tptp.zero_zero_int))))
% 6.73/7.04 (assert (= tptp.ord_less_real (lambda ((A5 tptp.real) (B4 tptp.real)) (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real A5) B4)) tptp.zero_zero_real))))
% 6.73/7.04 (assert (= tptp.ord_less_rat (lambda ((A5 tptp.rat) (B4 tptp.rat)) (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat A5) B4)) tptp.zero_zero_rat))))
% 6.73/7.04 (assert (= tptp.ord_less_int (lambda ((A5 tptp.int) (B4 tptp.int)) (@ (@ tptp.ord_less_int (@ (@ tptp.minus_minus_int A5) B4)) tptp.zero_zero_int))))
% 6.73/7.04 (assert (forall ((I2 tptp.real) (K2 tptp.real) (N tptp.real) (J2 tptp.real)) (let ((_let_1 (@ (@ tptp.ord_less_eq_real N) (@ (@ tptp.plus_plus_real J2) K2)))) (let ((_let_2 (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real I2) K2)) N))) (=> _let_2 (=> _let_1 (=> _let_2 (=> _let_1 (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real N) K2)) J2)))))))))
% 6.73/7.04 (assert (forall ((I2 tptp.rat) (K2 tptp.rat) (N tptp.rat) (J2 tptp.rat)) (let ((_let_1 (@ (@ tptp.ord_less_eq_rat N) (@ (@ tptp.plus_plus_rat J2) K2)))) (let ((_let_2 (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat I2) K2)) N))) (=> _let_2 (=> _let_1 (=> _let_2 (=> _let_1 (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat N) K2)) J2)))))))))
% 6.73/7.04 (assert (forall ((I2 tptp.nat) (K2 tptp.nat) (N tptp.nat) (J2 tptp.nat)) (let ((_let_1 (@ (@ tptp.ord_less_eq_nat N) (@ (@ tptp.plus_plus_nat J2) K2)))) (let ((_let_2 (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I2) K2)) N))) (=> _let_2 (=> _let_1 (=> _let_2 (=> _let_1 (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat N) K2)) J2)))))))))
% 6.73/7.04 (assert (forall ((I2 tptp.int) (K2 tptp.int) (N tptp.int) (J2 tptp.int)) (let ((_let_1 (@ (@ tptp.ord_less_eq_int N) (@ (@ tptp.plus_plus_int J2) K2)))) (let ((_let_2 (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int I2) K2)) N))) (=> _let_2 (=> _let_1 (=> _let_2 (=> _let_1 (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int N) K2)) J2)))))))))
% 6.73/7.04 (assert (forall ((I2 tptp.real) (K2 tptp.real) (N tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real I2) K2)) N) (@ (@ tptp.ord_less_eq_real I2) (@ (@ tptp.minus_minus_real N) K2)))))
% 6.73/7.04 (assert (forall ((I2 tptp.rat) (K2 tptp.rat) (N tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat I2) K2)) N) (@ (@ tptp.ord_less_eq_rat I2) (@ (@ tptp.minus_minus_rat N) K2)))))
% 6.73/7.04 (assert (forall ((I2 tptp.nat) (K2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I2) K2)) N) (@ (@ tptp.ord_less_eq_nat I2) (@ (@ tptp.minus_minus_nat N) K2)))))
% 6.73/7.04 (assert (forall ((I2 tptp.int) (K2 tptp.int) (N tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int I2) K2)) N) (@ (@ tptp.ord_less_eq_int I2) (@ (@ tptp.minus_minus_int N) K2)))))
% 6.73/7.04 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ (@ tptp.ord_less_eq_nat A) B))) (=> _let_1 (=> _let_1 (= (= (@ (@ tptp.minus_minus_nat B) A) C2) (= B (@ (@ tptp.plus_plus_nat C2) A))))))))
% 6.73/7.04 (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))))
% 6.73/7.04 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= (@ (@ tptp.minus_minus_nat C2) (@ (@ tptp.minus_minus_nat B) A)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat C2) A)) B)))))
% 6.73/7.04 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat B) C2)) A) (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat B) A)) C2)))))
% 6.73/7.04 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat B) A)) C2) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat B) C2)) A)))))
% 6.73/7.04 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C2))) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= (@ (@ tptp.minus_minus_nat (@ _let_1 B)) A) (@ _let_1 (@ (@ tptp.minus_minus_nat B) A)))))))
% 6.73/7.04 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C2))) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= (@ _let_1 (@ (@ tptp.minus_minus_nat B) A)) (@ (@ tptp.minus_minus_nat (@ _let_1 B)) A))))))
% 6.73/7.04 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= (@ (@ tptp.ord_less_eq_nat C2) (@ (@ tptp.minus_minus_nat B) A)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat C2) A)) B)))))
% 6.73/7.04 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (@ (@ tptp.ord_less_eq_nat C2) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat B) C2)) A)))))
% 6.73/7.04 (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))))
% 6.73/7.04 (assert (forall ((A tptp.real) (C2 tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_eq_real A) (@ (@ tptp.minus_minus_real C2) B)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A) B)) C2))))
% 6.73/7.04 (assert (forall ((A tptp.rat) (C2 tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat A) (@ (@ tptp.minus_minus_rat C2) B)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A) B)) C2))))
% 6.73/7.04 (assert (forall ((A tptp.int) (C2 tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.minus_minus_int C2) B)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A) B)) C2))))
% 6.73/7.04 (assert (forall ((A tptp.real) (B tptp.real) (C2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real A) B)) C2) (@ (@ tptp.ord_less_eq_real A) (@ (@ tptp.plus_plus_real C2) B)))))
% 6.73/7.04 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat A) B)) C2) (@ (@ tptp.ord_less_eq_rat A) (@ (@ tptp.plus_plus_rat C2) B)))))
% 6.73/7.04 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int A) B)) C2) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.plus_plus_int C2) B)))))
% 6.73/7.04 (assert (forall ((A tptp.real) (C2 tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_real A) (@ (@ tptp.minus_minus_real C2) B)) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) B)) C2))))
% 6.73/7.04 (assert (forall ((A tptp.rat) (C2 tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat A) (@ (@ tptp.minus_minus_rat C2) B)) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) B)) C2))))
% 6.73/7.04 (assert (forall ((A tptp.int) (C2 tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_int A) (@ (@ tptp.minus_minus_int C2) B)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) B)) C2))))
% 6.73/7.04 (assert (forall ((A tptp.real) (B tptp.real) (C2 tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real A) B)) C2) (@ (@ tptp.ord_less_real A) (@ (@ tptp.plus_plus_real C2) B)))))
% 6.73/7.04 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat A) B)) C2) (@ (@ tptp.ord_less_rat A) (@ (@ tptp.plus_plus_rat C2) B)))))
% 6.73/7.04 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.minus_minus_int A) B)) C2) (@ (@ tptp.ord_less_int A) (@ (@ tptp.plus_plus_int C2) B)))))
% 6.73/7.04 (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))))
% 6.73/7.04 (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))))
% 6.73/7.04 (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))))
% 6.73/7.04 (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))))
% 6.73/7.04 (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)))))
% 6.73/7.04 (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)))))
% 6.73/7.04 (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)))))
% 6.73/7.04 (assert (forall ((A tptp.real) (E tptp.real) (C2 tptp.real) (B tptp.real) (D tptp.real)) (= (= (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) E)) C2) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real B) E)) D)) (= C2 (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real B) A)) E)) D)))))
% 6.73/7.04 (assert (forall ((A tptp.rat) (E tptp.rat) (C2 tptp.rat) (B tptp.rat) (D tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) E)) C2) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B) E)) D)) (= C2 (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat B) A)) E)) D)))))
% 6.73/7.04 (assert (forall ((A tptp.int) (E tptp.int) (C2 tptp.int) (B tptp.int) (D tptp.int)) (= (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) E)) C2) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) E)) D)) (= C2 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int B) A)) E)) D)))))
% 6.73/7.04 (assert (forall ((A tptp.real) (E tptp.real) (C2 tptp.real) (B tptp.real) (D tptp.real)) (= (= (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) E)) C2) (@ (@ 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)) C2) D))))
% 6.73/7.04 (assert (forall ((A tptp.rat) (E tptp.rat) (C2 tptp.rat) (B tptp.rat) (D tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) E)) C2) (@ (@ 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)) C2) D))))
% 6.73/7.04 (assert (forall ((A tptp.int) (E tptp.int) (C2 tptp.int) (B tptp.int) (D tptp.int)) (= (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) E)) C2) (@ (@ 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)) C2) D))))
% 6.73/7.04 (assert (forall ((A tptp.real) (E tptp.real) (C2 tptp.real) (B tptp.real) (D tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) E)) C2)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real B) E)) D)) (@ (@ tptp.ord_less_eq_real C2) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real B) A)) E)) D)))))
% 6.73/7.04 (assert (forall ((A tptp.rat) (E tptp.rat) (C2 tptp.rat) (B tptp.rat) (D tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) E)) C2)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B) E)) D)) (@ (@ tptp.ord_less_eq_rat C2) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat B) A)) E)) D)))))
% 6.73/7.04 (assert (forall ((A tptp.int) (E tptp.int) (C2 tptp.int) (B tptp.int) (D tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) E)) C2)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) E)) D)) (@ (@ tptp.ord_less_eq_int C2) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int B) A)) E)) D)))))
% 6.73/7.04 (assert (forall ((A tptp.real) (E tptp.real) (C2 tptp.real) (B tptp.real) (D tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) E)) C2)) (@ (@ 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)) C2)) D))))
% 6.73/7.04 (assert (forall ((A tptp.rat) (E tptp.rat) (C2 tptp.rat) (B tptp.rat) (D tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) E)) C2)) (@ (@ 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)) C2)) D))))
% 6.73/7.04 (assert (forall ((A tptp.int) (E tptp.int) (C2 tptp.int) (B tptp.int) (D tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) E)) C2)) (@ (@ 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)) C2)) D))))
% 6.73/7.04 (assert (forall ((A tptp.real) (E tptp.real) (C2 tptp.real) (B tptp.real) (D tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) E)) C2)) (@ (@ 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)) C2)) D))))
% 6.73/7.04 (assert (forall ((A tptp.rat) (E tptp.rat) (C2 tptp.rat) (B tptp.rat) (D tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) E)) C2)) (@ (@ 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)) C2)) D))))
% 6.73/7.04 (assert (forall ((A tptp.int) (E tptp.int) (C2 tptp.int) (B tptp.int) (D tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) E)) C2)) (@ (@ 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)) C2)) D))))
% 6.73/7.04 (assert (forall ((A tptp.real) (E tptp.real) (C2 tptp.real) (B tptp.real) (D tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) E)) C2)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real B) E)) D)) (@ (@ tptp.ord_less_real C2) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real B) A)) E)) D)))))
% 6.73/7.04 (assert (forall ((A tptp.rat) (E tptp.rat) (C2 tptp.rat) (B tptp.rat) (D tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) E)) C2)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B) E)) D)) (@ (@ tptp.ord_less_rat C2) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat B) A)) E)) D)))))
% 6.73/7.04 (assert (forall ((A tptp.int) (E tptp.int) (C2 tptp.int) (B tptp.int) (D tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) E)) C2)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) E)) D)) (@ (@ tptp.ord_less_int C2) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int B) A)) E)) D)))))
% 6.73/7.04 (assert (forall ((X tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.times_3573771949741848930nteger X) X)) tptp.one_one_Code_integer) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.plus_p5714425477246183910nteger X) tptp.one_one_Code_integer)) (@ (@ tptp.minus_8373710615458151222nteger X) tptp.one_one_Code_integer)))))
% 6.73/7.04 (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)))))
% 6.73/7.04 (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)))))
% 6.73/7.04 (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)))))
% 6.73/7.04 (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)))))
% 6.73/7.04 (assert (forall ((S3 tptp.set_complex) (P2 (-> tptp.set_complex Bool)) (F2 (-> tptp.complex tptp.rat))) (=> (@ tptp.finite3207457112153483333omplex S3) (=> (@ P2 tptp.bot_bot_set_complex) (=> (forall ((X3 tptp.complex) (S4 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex S4) (=> (forall ((Y6 tptp.complex)) (=> (@ (@ tptp.member_complex Y6) S4) (@ (@ tptp.ord_less_eq_rat (@ F2 Y6)) (@ F2 X3)))) (=> (@ P2 S4) (@ P2 (@ (@ tptp.insert_complex X3) S4)))))) (@ P2 S3))))))
% 6.73/7.04 (assert (forall ((S3 tptp.set_nat) (P2 (-> tptp.set_nat Bool)) (F2 (-> tptp.nat tptp.rat))) (=> (@ tptp.finite_finite_nat S3) (=> (@ P2 tptp.bot_bot_set_nat) (=> (forall ((X3 tptp.nat) (S4 tptp.set_nat)) (=> (@ tptp.finite_finite_nat S4) (=> (forall ((Y6 tptp.nat)) (=> (@ (@ tptp.member_nat Y6) S4) (@ (@ tptp.ord_less_eq_rat (@ F2 Y6)) (@ F2 X3)))) (=> (@ P2 S4) (@ P2 (@ (@ tptp.insert_nat X3) S4)))))) (@ P2 S3))))))
% 6.73/7.04 (assert (forall ((S3 tptp.set_int) (P2 (-> tptp.set_int Bool)) (F2 (-> tptp.int tptp.rat))) (=> (@ tptp.finite_finite_int S3) (=> (@ P2 tptp.bot_bot_set_int) (=> (forall ((X3 tptp.int) (S4 tptp.set_int)) (=> (@ tptp.finite_finite_int S4) (=> (forall ((Y6 tptp.int)) (=> (@ (@ tptp.member_int Y6) S4) (@ (@ tptp.ord_less_eq_rat (@ F2 Y6)) (@ F2 X3)))) (=> (@ P2 S4) (@ P2 (@ (@ tptp.insert_int X3) S4)))))) (@ P2 S3))))))
% 6.73/7.04 (assert (forall ((S3 tptp.set_real) (P2 (-> tptp.set_real Bool)) (F2 (-> tptp.real tptp.rat))) (=> (@ tptp.finite_finite_real S3) (=> (@ P2 tptp.bot_bot_set_real) (=> (forall ((X3 tptp.real) (S4 tptp.set_real)) (=> (@ tptp.finite_finite_real S4) (=> (forall ((Y6 tptp.real)) (=> (@ (@ tptp.member_real Y6) S4) (@ (@ tptp.ord_less_eq_rat (@ F2 Y6)) (@ F2 X3)))) (=> (@ P2 S4) (@ P2 (@ (@ tptp.insert_real X3) S4)))))) (@ P2 S3))))))
% 6.73/7.04 (assert (forall ((S3 tptp.set_complex) (P2 (-> tptp.set_complex Bool)) (F2 (-> tptp.complex tptp.num))) (=> (@ tptp.finite3207457112153483333omplex S3) (=> (@ P2 tptp.bot_bot_set_complex) (=> (forall ((X3 tptp.complex) (S4 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex S4) (=> (forall ((Y6 tptp.complex)) (=> (@ (@ tptp.member_complex Y6) S4) (@ (@ tptp.ord_less_eq_num (@ F2 Y6)) (@ F2 X3)))) (=> (@ P2 S4) (@ P2 (@ (@ tptp.insert_complex X3) S4)))))) (@ P2 S3))))))
% 6.73/7.04 (assert (forall ((S3 tptp.set_nat) (P2 (-> tptp.set_nat Bool)) (F2 (-> tptp.nat tptp.num))) (=> (@ tptp.finite_finite_nat S3) (=> (@ P2 tptp.bot_bot_set_nat) (=> (forall ((X3 tptp.nat) (S4 tptp.set_nat)) (=> (@ tptp.finite_finite_nat S4) (=> (forall ((Y6 tptp.nat)) (=> (@ (@ tptp.member_nat Y6) S4) (@ (@ tptp.ord_less_eq_num (@ F2 Y6)) (@ F2 X3)))) (=> (@ P2 S4) (@ P2 (@ (@ tptp.insert_nat X3) S4)))))) (@ P2 S3))))))
% 6.73/7.04 (assert (forall ((S3 tptp.set_int) (P2 (-> tptp.set_int Bool)) (F2 (-> tptp.int tptp.num))) (=> (@ tptp.finite_finite_int S3) (=> (@ P2 tptp.bot_bot_set_int) (=> (forall ((X3 tptp.int) (S4 tptp.set_int)) (=> (@ tptp.finite_finite_int S4) (=> (forall ((Y6 tptp.int)) (=> (@ (@ tptp.member_int Y6) S4) (@ (@ tptp.ord_less_eq_num (@ F2 Y6)) (@ F2 X3)))) (=> (@ P2 S4) (@ P2 (@ (@ tptp.insert_int X3) S4)))))) (@ P2 S3))))))
% 6.73/7.04 (assert (forall ((S3 tptp.set_real) (P2 (-> tptp.set_real Bool)) (F2 (-> tptp.real tptp.num))) (=> (@ tptp.finite_finite_real S3) (=> (@ P2 tptp.bot_bot_set_real) (=> (forall ((X3 tptp.real) (S4 tptp.set_real)) (=> (@ tptp.finite_finite_real S4) (=> (forall ((Y6 tptp.real)) (=> (@ (@ tptp.member_real Y6) S4) (@ (@ tptp.ord_less_eq_num (@ F2 Y6)) (@ F2 X3)))) (=> (@ P2 S4) (@ P2 (@ (@ tptp.insert_real X3) S4)))))) (@ P2 S3))))))
% 6.73/7.04 (assert (forall ((S3 tptp.set_complex) (P2 (-> tptp.set_complex Bool)) (F2 (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex S3) (=> (@ P2 tptp.bot_bot_set_complex) (=> (forall ((X3 tptp.complex) (S4 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex S4) (=> (forall ((Y6 tptp.complex)) (=> (@ (@ tptp.member_complex Y6) S4) (@ (@ tptp.ord_less_eq_nat (@ F2 Y6)) (@ F2 X3)))) (=> (@ P2 S4) (@ P2 (@ (@ tptp.insert_complex X3) S4)))))) (@ P2 S3))))))
% 6.73/7.04 (assert (forall ((S3 tptp.set_nat) (P2 (-> tptp.set_nat Bool)) (F2 (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_nat S3) (=> (@ P2 tptp.bot_bot_set_nat) (=> (forall ((X3 tptp.nat) (S4 tptp.set_nat)) (=> (@ tptp.finite_finite_nat S4) (=> (forall ((Y6 tptp.nat)) (=> (@ (@ tptp.member_nat Y6) S4) (@ (@ tptp.ord_less_eq_nat (@ F2 Y6)) (@ F2 X3)))) (=> (@ P2 S4) (@ P2 (@ (@ tptp.insert_nat X3) S4)))))) (@ P2 S3))))))
% 6.73/7.04 (assert (forall ((P2 (-> tptp.list_VEBT_VEBT Bool)) (Xs2 tptp.list_VEBT_VEBT)) (=> (forall ((Xs3 tptp.list_VEBT_VEBT)) (=> (forall ((Ys2 tptp.list_VEBT_VEBT)) (=> (@ (@ tptp.ord_less_nat (@ tptp.size_s6755466524823107622T_VEBT Ys2)) (@ tptp.size_s6755466524823107622T_VEBT Xs3)) (@ P2 Ys2))) (@ P2 Xs3))) (@ P2 Xs2))))
% 6.73/7.04 (assert (forall ((P2 (-> tptp.list_o Bool)) (Xs2 tptp.list_o)) (=> (forall ((Xs3 tptp.list_o)) (=> (forall ((Ys2 tptp.list_o)) (=> (@ (@ tptp.ord_less_nat (@ tptp.size_size_list_o Ys2)) (@ tptp.size_size_list_o Xs3)) (@ P2 Ys2))) (@ P2 Xs3))) (@ P2 Xs2))))
% 6.73/7.04 (assert (forall ((P2 (-> tptp.list_nat Bool)) (Xs2 tptp.list_nat)) (=> (forall ((Xs3 tptp.list_nat)) (=> (forall ((Ys2 tptp.list_nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.size_size_list_nat Ys2)) (@ tptp.size_size_list_nat Xs3)) (@ P2 Ys2))) (@ P2 Xs3))) (@ P2 Xs2))))
% 6.73/7.04 (assert (forall ((P2 (-> tptp.list_int Bool)) (Xs2 tptp.list_int)) (=> (forall ((Xs3 tptp.list_int)) (=> (forall ((Ys2 tptp.list_int)) (=> (@ (@ tptp.ord_less_nat (@ tptp.size_size_list_int Ys2)) (@ tptp.size_size_list_int Xs3)) (@ P2 Ys2))) (@ P2 Xs3))) (@ P2 Xs2))))
% 6.73/7.04 (assert (forall ((B tptp.complex) (A tptp.complex)) (= (= B (@ (@ tptp.plus_plus_complex B) A)) (= A tptp.zero_zero_complex))))
% 6.73/7.04 (assert (forall ((B tptp.real) (A tptp.real)) (= (= B (@ (@ tptp.plus_plus_real B) A)) (= A tptp.zero_zero_real))))
% 6.73/7.04 (assert (forall ((B tptp.rat) (A tptp.rat)) (= (= B (@ (@ tptp.plus_plus_rat B) A)) (= A tptp.zero_zero_rat))))
% 6.73/7.04 (assert (forall ((B tptp.nat) (A tptp.nat)) (= (= B (@ (@ tptp.plus_plus_nat B) A)) (= A tptp.zero_zero_nat))))
% 6.73/7.04 (assert (forall ((B tptp.int) (A tptp.int)) (= (= B (@ (@ tptp.plus_plus_int B) A)) (= A tptp.zero_zero_int))))
% 6.73/7.04 (assert (forall ((W2 tptp.real) (Y tptp.real) (X tptp.real) (Z3 tptp.real)) (let ((_let_1 (@ tptp.times_times_real X))) (let ((_let_2 (@ tptp.times_times_real W2))) (= (= (@ (@ tptp.plus_plus_real (@ _let_2 Y)) (@ _let_1 Z3)) (@ (@ tptp.plus_plus_real (@ _let_2 Z3)) (@ _let_1 Y))) (or (= W2 X) (= Y Z3)))))))
% 6.73/7.04 (assert (forall ((W2 tptp.rat) (Y tptp.rat) (X tptp.rat) (Z3 tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat X))) (let ((_let_2 (@ tptp.times_times_rat W2))) (= (= (@ (@ tptp.plus_plus_rat (@ _let_2 Y)) (@ _let_1 Z3)) (@ (@ tptp.plus_plus_rat (@ _let_2 Z3)) (@ _let_1 Y))) (or (= W2 X) (= Y Z3)))))))
% 6.73/7.04 (assert (forall ((W2 tptp.nat) (Y tptp.nat) (X tptp.nat) (Z3 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat X))) (let ((_let_2 (@ tptp.times_times_nat W2))) (= (= (@ (@ tptp.plus_plus_nat (@ _let_2 Y)) (@ _let_1 Z3)) (@ (@ tptp.plus_plus_nat (@ _let_2 Z3)) (@ _let_1 Y))) (or (= W2 X) (= Y Z3)))))))
% 6.73/7.04 (assert (forall ((W2 tptp.int) (Y tptp.int) (X tptp.int) (Z3 tptp.int)) (let ((_let_1 (@ tptp.times_times_int X))) (let ((_let_2 (@ tptp.times_times_int W2))) (= (= (@ (@ tptp.plus_plus_int (@ _let_2 Y)) (@ _let_1 Z3)) (@ (@ tptp.plus_plus_int (@ _let_2 Z3)) (@ _let_1 Y))) (or (= W2 X) (= Y Z3)))))))
% 6.73/7.04 (assert (forall ((A tptp.real) (B tptp.real) (C2 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 (= C2 D))) (not (= (@ (@ tptp.plus_plus_real (@ _let_2 C2)) (@ _let_1 D)) (@ (@ tptp.plus_plus_real (@ _let_2 D)) (@ _let_1 C2)))))))))
% 6.73/7.04 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 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 (= C2 D))) (not (= (@ (@ tptp.plus_plus_rat (@ _let_2 C2)) (@ _let_1 D)) (@ (@ tptp.plus_plus_rat (@ _let_2 D)) (@ _let_1 C2)))))))))
% 6.73/7.04 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 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 (= C2 D))) (not (= (@ (@ tptp.plus_plus_nat (@ _let_2 C2)) (@ _let_1 D)) (@ (@ tptp.plus_plus_nat (@ _let_2 D)) (@ _let_1 C2)))))))))
% 6.73/7.04 (assert (forall ((A tptp.int) (B tptp.int) (C2 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 (= C2 D))) (not (= (@ (@ tptp.plus_plus_int (@ _let_2 C2)) (@ _let_1 D)) (@ (@ tptp.plus_plus_int (@ _let_2 D)) (@ _let_1 C2)))))))))
% 6.73/7.04 (assert (forall ((X (-> tptp.nat tptp.nat))) (= (@ (@ tptp.size_option_nat X) tptp.none_nat) (@ tptp.suc tptp.zero_zero_nat))))
% 6.73/7.04 (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))))
% 6.73/7.04 (assert (forall ((X (-> tptp.num tptp.nat))) (= (@ (@ tptp.size_option_num X) tptp.none_num) (@ tptp.suc tptp.zero_zero_nat))))
% 6.73/7.04 (assert (forall ((A4 tptp.set_real)) (=> (@ tptp.finite_finite_real A4) (=> (not (= A4 tptp.bot_bot_set_real)) (exists ((X3 tptp.real)) (and (@ (@ tptp.member_real X3) A4) (forall ((Xa tptp.real)) (=> (@ (@ tptp.member_real Xa) A4) (=> (@ (@ tptp.ord_less_eq_real Xa) X3) (= X3 Xa))))))))))
% 6.73/7.04 (assert (forall ((A4 tptp.set_set_nat)) (=> (@ tptp.finite1152437895449049373et_nat A4) (=> (not (= A4 tptp.bot_bot_set_set_nat)) (exists ((X3 tptp.set_nat)) (and (@ (@ tptp.member_set_nat X3) A4) (forall ((Xa tptp.set_nat)) (=> (@ (@ tptp.member_set_nat Xa) A4) (=> (@ (@ tptp.ord_less_eq_set_nat Xa) X3) (= X3 Xa))))))))))
% 6.73/7.04 (assert (forall ((A4 tptp.set_rat)) (=> (@ tptp.finite_finite_rat A4) (=> (not (= A4 tptp.bot_bot_set_rat)) (exists ((X3 tptp.rat)) (and (@ (@ tptp.member_rat X3) A4) (forall ((Xa tptp.rat)) (=> (@ (@ tptp.member_rat Xa) A4) (=> (@ (@ tptp.ord_less_eq_rat Xa) X3) (= X3 Xa))))))))))
% 6.73/7.04 (assert (forall ((A4 tptp.set_num)) (=> (@ tptp.finite_finite_num A4) (=> (not (= A4 tptp.bot_bot_set_num)) (exists ((X3 tptp.num)) (and (@ (@ tptp.member_num X3) A4) (forall ((Xa tptp.num)) (=> (@ (@ tptp.member_num Xa) A4) (=> (@ (@ tptp.ord_less_eq_num Xa) X3) (= X3 Xa))))))))))
% 6.73/7.04 (assert (forall ((A4 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A4) (=> (not (= A4 tptp.bot_bot_set_nat)) (exists ((X3 tptp.nat)) (and (@ (@ tptp.member_nat X3) A4) (forall ((Xa tptp.nat)) (=> (@ (@ tptp.member_nat Xa) A4) (=> (@ (@ tptp.ord_less_eq_nat Xa) X3) (= X3 Xa))))))))))
% 6.73/7.04 (assert (forall ((A4 tptp.set_int)) (=> (@ tptp.finite_finite_int A4) (=> (not (= A4 tptp.bot_bot_set_int)) (exists ((X3 tptp.int)) (and (@ (@ tptp.member_int X3) A4) (forall ((Xa tptp.int)) (=> (@ (@ tptp.member_int Xa) A4) (=> (@ (@ tptp.ord_less_eq_int Xa) X3) (= X3 Xa))))))))))
% 6.73/7.04 (assert (forall ((A4 tptp.set_real)) (=> (@ tptp.finite_finite_real A4) (=> (not (= A4 tptp.bot_bot_set_real)) (exists ((X3 tptp.real)) (and (@ (@ tptp.member_real X3) A4) (forall ((Xa tptp.real)) (=> (@ (@ tptp.member_real Xa) A4) (=> (@ (@ tptp.ord_less_eq_real X3) Xa) (= X3 Xa))))))))))
% 6.73/7.04 (assert (forall ((A4 tptp.set_set_nat)) (=> (@ tptp.finite1152437895449049373et_nat A4) (=> (not (= A4 tptp.bot_bot_set_set_nat)) (exists ((X3 tptp.set_nat)) (and (@ (@ tptp.member_set_nat X3) A4) (forall ((Xa tptp.set_nat)) (=> (@ (@ tptp.member_set_nat Xa) A4) (=> (@ (@ tptp.ord_less_eq_set_nat X3) Xa) (= X3 Xa))))))))))
% 6.73/7.04 (assert (forall ((A4 tptp.set_rat)) (=> (@ tptp.finite_finite_rat A4) (=> (not (= A4 tptp.bot_bot_set_rat)) (exists ((X3 tptp.rat)) (and (@ (@ tptp.member_rat X3) A4) (forall ((Xa tptp.rat)) (=> (@ (@ tptp.member_rat Xa) A4) (=> (@ (@ tptp.ord_less_eq_rat X3) Xa) (= X3 Xa))))))))))
% 6.73/7.04 (assert (forall ((A4 tptp.set_num)) (=> (@ tptp.finite_finite_num A4) (=> (not (= A4 tptp.bot_bot_set_num)) (exists ((X3 tptp.num)) (and (@ (@ tptp.member_num X3) A4) (forall ((Xa tptp.num)) (=> (@ (@ tptp.member_num Xa) A4) (=> (@ (@ tptp.ord_less_eq_num X3) Xa) (= X3 Xa))))))))))
% 6.73/7.04 (assert (forall ((A4 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A4) (=> (not (= A4 tptp.bot_bot_set_nat)) (exists ((X3 tptp.nat)) (and (@ (@ tptp.member_nat X3) A4) (forall ((Xa tptp.nat)) (=> (@ (@ tptp.member_nat Xa) A4) (=> (@ (@ tptp.ord_less_eq_nat X3) Xa) (= X3 Xa))))))))))
% 6.73/7.04 (assert (forall ((A4 tptp.set_int)) (=> (@ tptp.finite_finite_int A4) (=> (not (= A4 tptp.bot_bot_set_int)) (exists ((X3 tptp.int)) (and (@ (@ tptp.member_int X3) A4) (forall ((Xa tptp.int)) (=> (@ (@ tptp.member_int Xa) A4) (=> (@ (@ tptp.ord_less_eq_int X3) Xa) (= X3 Xa))))))))))
% 6.73/7.04 (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))))))
% 6.73/7.04 (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))))))
% 6.73/7.04 (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))))))
% 6.73/7.04 (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))))
% 6.73/7.04 (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))))
% 6.73/7.04 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat)) (= (= (@ (@ tptp.minus_1356011639430497352at_nat X) Y) tptp.bot_bo2099793752762293965at_nat) (@ (@ tptp.ord_le3146513528884898305at_nat X) Y))))
% 6.73/7.04 (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))))
% 6.73/7.04 (assert (forall ((T tptp.vEBT_VEBT)) (=> (@ tptp.vEBT_VEBT_minNull T) (= (@ tptp.vEBT_vebt_mint T) tptp.none_nat))))
% 6.73/7.04 (assert (forall ((T tptp.vEBT_VEBT)) (=> (= (@ tptp.vEBT_vebt_mint T) tptp.none_nat) (@ tptp.vEBT_VEBT_minNull T))))
% 6.73/7.04 (assert (forall ((X tptp.vEBT_VEBT) (Y tptp.option_nat)) (=> (= (@ tptp.vEBT_vebt_maxt X) Y) (=> (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_vebt_maxt_rel) X) (=> (forall ((A3 Bool) (B3 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A3) B3))) (=> (= X _let_1) (=> (and (=> B3 (= Y (@ tptp.some_nat tptp.one_one_nat))) (=> (not B3) (and (=> A3 (= Y (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A3) (= Y tptp.none_nat))))) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_vebt_maxt_rel) _let_1)))))) (=> (forall ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw))) (=> (= 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) (Ux tptp.nat) (Uy 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))) Ux) Uy) Uz2))) (=> (= X _let_1) (=> (= Y (@ tptp.some_nat Ma2)) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_vebt_maxt_rel) _let_1)))))))))))))
% 6.73/7.04 (assert (forall ((X tptp.vEBT_VEBT) (Y tptp.option_nat)) (=> (= (@ tptp.vEBT_vebt_mint X) Y) (=> (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_vebt_mint_rel) X) (=> (forall ((A3 Bool) (B3 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A3) B3))) (=> (= X _let_1) (=> (and (=> A3 (= Y (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A3) (and (=> B3 (= Y (@ tptp.some_nat tptp.one_one_nat))) (=> (not B3) (= Y tptp.none_nat))))) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_vebt_mint_rel) _let_1)))))) (=> (forall ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw))) (=> (= 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) (Ux tptp.nat) (Uy 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))) Ux) Uy) Uz2))) (=> (= X _let_1) (=> (= Y (@ tptp.some_nat Mi2)) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_vebt_mint_rel) _let_1)))))))))))))
% 6.73/7.04 (assert (forall ((S3 tptp.set_nat)) (= (not (@ tptp.finite_finite_nat S3)) (forall ((M6 tptp.nat)) (exists ((N4 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat M6) N4) (@ (@ tptp.member_nat N4) S3)))))))
% 6.73/7.04 (assert (forall ((Xs2 tptp.list_complex) (P2 (-> tptp.complex Bool)) (N tptp.nat)) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ tptp.set_complex2 Xs2)) (@ P2 X3))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s3451745648224563538omplex Xs2)) (@ P2 (@ (@ tptp.nth_complex Xs2) N))))))
% 6.73/7.04 (assert (forall ((Xs2 tptp.list_real) (P2 (-> tptp.real Bool)) (N tptp.nat)) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) (@ tptp.set_real2 Xs2)) (@ P2 X3))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_real Xs2)) (@ P2 (@ (@ tptp.nth_real Xs2) N))))))
% 6.73/7.04 (assert (forall ((Xs2 tptp.list_set_nat) (P2 (-> tptp.set_nat Bool)) (N tptp.nat)) (=> (forall ((X3 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat X3) (@ tptp.set_set_nat2 Xs2)) (@ P2 X3))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s3254054031482475050et_nat Xs2)) (@ P2 (@ (@ tptp.nth_set_nat Xs2) N))))))
% 6.73/7.04 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (P2 (-> tptp.vEBT_VEBT Bool)) (N tptp.nat)) (=> (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 Xs2)) (@ P2 X3))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (@ P2 (@ (@ tptp.nth_VEBT_VEBT Xs2) N))))))
% 6.73/7.04 (assert (forall ((Xs2 tptp.list_o) (P2 (-> Bool Bool)) (N tptp.nat)) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) (@ tptp.set_o2 Xs2)) (@ P2 X3))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_o Xs2)) (@ P2 (@ (@ tptp.nth_o Xs2) N))))))
% 6.73/7.04 (assert (forall ((Xs2 tptp.list_nat) (P2 (-> tptp.nat Bool)) (N tptp.nat)) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ tptp.set_nat2 Xs2)) (@ P2 X3))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_nat Xs2)) (@ P2 (@ (@ tptp.nth_nat Xs2) N))))))
% 6.73/7.04 (assert (forall ((Xs2 tptp.list_int) (P2 (-> tptp.int Bool)) (N tptp.nat)) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ tptp.set_int2 Xs2)) (@ P2 X3))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_int Xs2)) (@ P2 (@ (@ tptp.nth_int Xs2) N))))))
% 6.73/7.04 (assert (forall ((T tptp.vEBT_VEBT)) (=> (not (@ tptp.vEBT_VEBT_minNull T)) (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions T) X_12)))))
% 6.73/7.04 (assert (forall ((T tptp.vEBT_VEBT) (X tptp.nat)) (=> (@ tptp.vEBT_VEBT_minNull T) (not (@ (@ tptp.vEBT_vebt_member T) X)))))
% 6.73/7.04 (assert (forall ((M2 tptp.nat) (N tptp.nat) (K2 tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat (@ tptp.suc M2)) N)) (@ tptp.suc K2)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat M2) N)) K2))))
% 6.73/7.04 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc M2)) (@ tptp.suc N)) (@ (@ tptp.minus_minus_nat M2) N))))
% 6.73/7.04 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.minus_minus_nat tptp.zero_zero_nat) N) tptp.zero_zero_nat)))
% 6.73/7.04 (assert (forall ((M2 tptp.nat)) (= (@ (@ tptp.minus_minus_nat M2) M2) tptp.zero_zero_nat)))
% 6.73/7.04 (assert (forall ((I2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat N))) (=> (@ (@ tptp.ord_less_eq_nat I2) N) (= (@ _let_1 (@ _let_1 I2)) I2)))))
% 6.73/7.04 (assert (forall ((I2 tptp.nat) (J2 tptp.nat) (K2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat I2))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 J2)) K2) (@ _let_1 (@ (@ tptp.plus_plus_nat J2) K2))))))
% 6.73/7.04 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat N) M2)) (@ (@ tptp.ord_less_nat M2) N))))
% 6.73/7.04 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ (@ tptp.minus_minus_nat M2) N) tptp.zero_zero_nat))))
% 6.73/7.04 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (= (@ (@ tptp.minus_minus_nat M2) N) tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_nat M2) N))))
% 6.73/7.04 (assert (forall ((K2 tptp.nat) (J2 tptp.nat) (I2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat I2))) (=> (@ (@ tptp.ord_less_eq_nat K2) J2) (= (@ _let_1 (@ (@ tptp.minus_minus_nat J2) K2)) (@ (@ tptp.minus_minus_nat (@ _let_1 J2)) K2))))))
% 6.73/7.04 (assert (forall ((K2 tptp.nat) (J2 tptp.nat) (I2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K2) J2) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat J2) K2)) I2) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat J2) I2)) K2)))))
% 6.73/7.04 (assert (forall ((K2 tptp.nat) (J2 tptp.nat) (I2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K2) J2) (= (@ (@ tptp.minus_minus_nat I2) (@ (@ tptp.minus_minus_nat J2) K2)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat I2) K2)) J2)))))
% 6.73/7.04 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc N)) tptp.one_one_nat) N)))
% 6.73/7.04 (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))))
% 6.73/7.04 (assert (forall ((K2 tptp.nat) (J2 tptp.nat) (I2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K2) J2) (= (@ (@ tptp.minus_minus_nat I2) (@ tptp.suc (@ (@ tptp.minus_minus_nat J2) K2))) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat I2) K2)) (@ tptp.suc J2))))))
% 6.73/7.04 (assert (forall ((K2 tptp.nat) (J2 tptp.nat) (I2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K2) J2) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc (@ (@ tptp.minus_minus_nat J2) K2))) I2) (@ (@ tptp.minus_minus_nat (@ tptp.suc J2)) (@ (@ tptp.plus_plus_nat K2) I2))))))
% 6.73/7.04 (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))))
% 6.73/7.04 (assert (forall ((P2 (-> tptp.nat Bool)) (K2 tptp.nat) (I2 tptp.nat)) (=> (@ P2 K2) (=> (forall ((N3 tptp.nat)) (=> (@ P2 (@ tptp.suc N3)) (@ P2 N3))) (@ P2 (@ (@ tptp.minus_minus_nat K2) I2))))))
% 6.73/7.04 (assert (forall ((M2 tptp.nat)) (= (@ (@ tptp.minus_minus_nat M2) tptp.zero_zero_nat) M2)))
% 6.73/7.04 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (= (@ (@ tptp.minus_minus_nat M2) N) tptp.zero_zero_nat) (=> (= (@ (@ tptp.minus_minus_nat N) M2) tptp.zero_zero_nat) (= M2 N)))))
% 6.73/7.04 (assert (forall ((M2 tptp.nat) (N tptp.nat) (L tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat L))) (let ((_let_2 (@ tptp.ord_less_nat M2))) (=> (@ _let_2 N) (=> (@ _let_2 L) (@ (@ tptp.ord_less_nat (@ _let_1 N)) (@ _let_1 M2))))))))
% 6.73/7.04 (assert (forall ((J2 tptp.nat) (K2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat J2) K2) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat J2) N)) K2))))
% 6.73/7.04 (assert (forall ((M2 tptp.nat) (N tptp.nat) (L tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat L))) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (@ (@ tptp.ord_less_eq_nat (@ _let_1 N)) (@ _let_1 M2))))))
% 6.73/7.04 (assert (forall ((A tptp.nat) (C2 tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat B))) (let ((_let_2 (@ tptp.minus_minus_nat C2))) (=> (@ (@ tptp.ord_less_eq_nat A) C2) (=> (@ _let_1 C2) (= (@ (@ tptp.ord_less_eq_nat (@ _let_2 A)) (@ _let_2 B)) (@ _let_1 A))))))))
% 6.73/7.04 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat M2) N)) M2)))
% 6.73/7.04 (assert (forall ((M2 tptp.nat) (N tptp.nat) (L tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat M2) L)) (@ (@ tptp.minus_minus_nat N) L)))))
% 6.73/7.04 (assert (forall ((K2 tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat M2))) (let ((_let_2 (@ tptp.ord_less_eq_nat K2))) (=> (@ _let_2 M2) (=> (@ _let_2 N) (= (@ (@ tptp.minus_minus_nat (@ _let_1 K2)) (@ (@ tptp.minus_minus_nat N) K2)) (@ _let_1 N))))))))
% 6.73/7.04 (assert (forall ((K2 tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat K2))) (=> (@ _let_1 M2) (=> (@ _let_1 N) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat M2) K2)) (@ (@ tptp.minus_minus_nat N) K2)) (@ (@ tptp.ord_less_eq_nat M2) N)))))))
% 6.73/7.04 (assert (forall ((K2 tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat K2))) (=> (@ _let_1 M2) (=> (@ _let_1 N) (= (= (@ (@ tptp.minus_minus_nat M2) K2) (@ (@ tptp.minus_minus_nat N) K2)) (= M2 N)))))))
% 6.73/7.04 (assert (forall ((K2 tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K2))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 M2)) (@ _let_1 N)) (@ (@ tptp.minus_minus_nat M2) N)))))
% 6.73/7.04 (assert (forall ((M2 tptp.nat) (K2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M2) K2)) (@ (@ tptp.plus_plus_nat N) K2)) (@ (@ tptp.minus_minus_nat M2) N))))
% 6.73/7.04 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat N) M2)) N) M2)))
% 6.73/7.04 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M2) N)) N) M2)))
% 6.73/7.04 (assert (forall ((M2 tptp.nat) (N tptp.nat) (K2 tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat M2) N)) K2) (@ (@ tptp.minus_minus_nat (@ (@ tptp.times_times_nat M2) K2)) (@ (@ tptp.times_times_nat N) K2)))))
% 6.73/7.04 (assert (forall ((K2 tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K2))) (= (@ _let_1 (@ (@ tptp.minus_minus_nat M2) N)) (@ (@ tptp.minus_minus_nat (@ _let_1 M2)) (@ _let_1 N))))))
% 6.73/7.04 (assert (@ tptp.vEBT_VEBT_minNull (@ (@ tptp.vEBT_Leaf false) false)))
% 6.73/7.04 (assert (forall ((Uv Bool)) (not (@ tptp.vEBT_VEBT_minNull (@ (@ tptp.vEBT_Leaf true) Uv)))))
% 6.73/7.04 (assert (forall ((Uu Bool)) (not (@ tptp.vEBT_VEBT_minNull (@ (@ tptp.vEBT_Leaf Uu) true)))))
% 6.73/7.04 (assert (= (lambda ((Y5 tptp.list_VEBT_VEBT) (Z2 tptp.list_VEBT_VEBT)) (= Y5 Z2)) (lambda ((Xs tptp.list_VEBT_VEBT) (Ys3 tptp.list_VEBT_VEBT)) (and (= (@ tptp.size_s6755466524823107622T_VEBT Xs) (@ tptp.size_s6755466524823107622T_VEBT Ys3)) (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (= (@ (@ tptp.nth_VEBT_VEBT Xs) I) (@ (@ tptp.nth_VEBT_VEBT Ys3) I))))))))
% 6.73/7.04 (assert (= (lambda ((Y5 tptp.list_o) (Z2 tptp.list_o)) (= Y5 Z2)) (lambda ((Xs tptp.list_o) (Ys3 tptp.list_o)) (and (= (@ tptp.size_size_list_o Xs) (@ tptp.size_size_list_o Ys3)) (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_o Xs)) (= (@ (@ tptp.nth_o Xs) I) (@ (@ tptp.nth_o Ys3) I))))))))
% 6.73/7.04 (assert (= (lambda ((Y5 tptp.list_nat) (Z2 tptp.list_nat)) (= Y5 Z2)) (lambda ((Xs tptp.list_nat) (Ys3 tptp.list_nat)) (and (= (@ tptp.size_size_list_nat Xs) (@ tptp.size_size_list_nat Ys3)) (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_nat Xs)) (= (@ (@ tptp.nth_nat Xs) I) (@ (@ tptp.nth_nat Ys3) I))))))))
% 6.73/7.04 (assert (= (lambda ((Y5 tptp.list_int) (Z2 tptp.list_int)) (= Y5 Z2)) (lambda ((Xs tptp.list_int) (Ys3 tptp.list_int)) (and (= (@ tptp.size_size_list_int Xs) (@ tptp.size_size_list_int Ys3)) (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_int Xs)) (= (@ (@ tptp.nth_int Xs) I) (@ (@ tptp.nth_int Ys3) I))))))))
% 6.73/7.04 (assert (forall ((K2 tptp.nat) (P2 (-> tptp.nat tptp.vEBT_VEBT Bool))) (= (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) K2) (exists ((X7 tptp.vEBT_VEBT)) (@ (@ P2 I) X7)))) (exists ((Xs tptp.list_VEBT_VEBT)) (and (= (@ tptp.size_s6755466524823107622T_VEBT Xs) K2) (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) K2) (@ (@ P2 I) (@ (@ tptp.nth_VEBT_VEBT Xs) I)))))))))
% 6.73/7.04 (assert (forall ((K2 tptp.nat) (P2 (-> tptp.nat Bool Bool))) (= (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) K2) (exists ((X7 Bool)) (@ (@ P2 I) X7)))) (exists ((Xs tptp.list_o)) (and (= (@ tptp.size_size_list_o Xs) K2) (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) K2) (@ (@ P2 I) (@ (@ tptp.nth_o Xs) I)))))))))
% 6.73/7.04 (assert (forall ((K2 tptp.nat) (P2 (-> tptp.nat tptp.nat Bool))) (= (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) K2) (exists ((X7 tptp.nat)) (@ (@ P2 I) X7)))) (exists ((Xs tptp.list_nat)) (and (= (@ tptp.size_size_list_nat Xs) K2) (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) K2) (@ (@ P2 I) (@ (@ tptp.nth_nat Xs) I)))))))))
% 6.73/7.04 (assert (forall ((K2 tptp.nat) (P2 (-> tptp.nat tptp.int Bool))) (= (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) K2) (exists ((X7 tptp.int)) (@ (@ P2 I) X7)))) (exists ((Xs tptp.list_int)) (and (= (@ tptp.size_size_list_int Xs) K2) (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) K2) (@ (@ P2 I) (@ (@ tptp.nth_int Xs) I)))))))))
% 6.73/7.04 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (Ys tptp.list_VEBT_VEBT)) (=> (= (@ tptp.size_s6755466524823107622T_VEBT Xs2) (@ tptp.size_s6755466524823107622T_VEBT Ys)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (= (@ (@ tptp.nth_VEBT_VEBT Xs2) I3) (@ (@ tptp.nth_VEBT_VEBT Ys) I3)))) (= Xs2 Ys)))))
% 6.73/7.04 (assert (forall ((Xs2 tptp.list_o) (Ys tptp.list_o)) (=> (= (@ tptp.size_size_list_o Xs2) (@ tptp.size_size_list_o Ys)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_o Xs2)) (= (@ (@ tptp.nth_o Xs2) I3) (@ (@ tptp.nth_o Ys) I3)))) (= Xs2 Ys)))))
% 6.73/7.04 (assert (forall ((Xs2 tptp.list_nat) (Ys tptp.list_nat)) (=> (= (@ tptp.size_size_list_nat Xs2) (@ tptp.size_size_list_nat Ys)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_nat Xs2)) (= (@ (@ tptp.nth_nat Xs2) I3) (@ (@ tptp.nth_nat Ys) I3)))) (= Xs2 Ys)))))
% 6.73/7.04 (assert (forall ((Xs2 tptp.list_int) (Ys tptp.list_int)) (=> (= (@ tptp.size_size_list_int Xs2) (@ tptp.size_size_list_int Ys)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_int Xs2)) (= (@ (@ tptp.nth_int Xs2) I3) (@ (@ tptp.nth_int Ys) I3)))) (= Xs2 Ys)))))
% 6.73/7.04 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat M2) N)) (@ tptp.suc M2))))
% 6.73/7.04 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat M2))) (=> (@ (@ tptp.ord_less_nat N) M2) (= (@ tptp.suc (@ _let_1 (@ tptp.suc N))) (@ _let_1 N))))))
% 6.73/7.04 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 N) (=> (@ _let_1 M2) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat M2) N)) M2))))))
% 6.73/7.04 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M2) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc M2)) N) (@ tptp.suc (@ (@ tptp.minus_minus_nat M2) N))))))
% 6.73/7.04 (assert (forall ((K2 tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat K2))) (=> (@ _let_1 M2) (=> (@ _let_1 N) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat M2) K2)) (@ (@ tptp.minus_minus_nat N) K2)) (@ (@ tptp.ord_less_nat M2) N)))))))
% 6.73/7.04 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat C2) A) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat A) C2)) (@ (@ tptp.minus_minus_nat B) C2))))))
% 6.73/7.04 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (= (@ (@ tptp.minus_minus_nat N) (@ (@ tptp.plus_plus_nat N) M2)) tptp.zero_zero_nat)))
% 6.73/7.04 (assert (forall ((M5 tptp.set_list_VEBT_VEBT)) (=> (@ tptp.finite3004134309566078307T_VEBT M5) (exists ((N3 tptp.nat)) (forall ((X5 tptp.list_VEBT_VEBT)) (=> (@ (@ tptp.member2936631157270082147T_VEBT X5) M5) (@ (@ tptp.ord_less_nat (@ tptp.size_s6755466524823107622T_VEBT X5)) N3)))))))
% 6.73/7.04 (assert (forall ((M5 tptp.set_list_o)) (=> (@ tptp.finite_finite_list_o M5) (exists ((N3 tptp.nat)) (forall ((X5 tptp.list_o)) (=> (@ (@ tptp.member_list_o X5) M5) (@ (@ tptp.ord_less_nat (@ tptp.size_size_list_o X5)) N3)))))))
% 6.73/7.04 (assert (forall ((M5 tptp.set_list_nat)) (=> (@ tptp.finite8100373058378681591st_nat M5) (exists ((N3 tptp.nat)) (forall ((X5 tptp.list_nat)) (=> (@ (@ tptp.member_list_nat X5) M5) (@ (@ tptp.ord_less_nat (@ tptp.size_size_list_nat X5)) N3)))))))
% 6.73/7.04 (assert (forall ((M5 tptp.set_list_int)) (=> (@ tptp.finite3922522038869484883st_int M5) (exists ((N3 tptp.nat)) (forall ((X5 tptp.list_int)) (=> (@ (@ tptp.member_list_int X5) M5) (@ (@ tptp.ord_less_nat (@ tptp.size_size_list_int X5)) N3)))))))
% 6.73/7.04 (assert (forall ((I2 tptp.nat) (J2 tptp.nat) (K2 tptp.nat)) (= (@ (@ tptp.ord_less_nat I2) (@ (@ tptp.minus_minus_nat J2) K2)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I2) K2)) J2))))
% 6.73/7.04 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat M2) N)) (= (@ (@ tptp.plus_plus_nat N) (@ (@ tptp.minus_minus_nat M2) N)) M2))))
% 6.73/7.04 (assert (forall ((J2 tptp.nat) (K2 tptp.nat) (I2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat J2) K2)) I2) (@ (@ tptp.ord_less_eq_nat J2) (@ (@ tptp.plus_plus_nat I2) K2)))))
% 6.73/7.04 (assert (forall ((K2 tptp.nat) (J2 tptp.nat) (I2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K2) J2) (= (@ (@ tptp.ord_less_eq_nat I2) (@ (@ tptp.minus_minus_nat J2) K2)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I2) K2)) J2)))))
% 6.73/7.04 (assert (forall ((K2 tptp.nat) (J2 tptp.nat) (I2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat I2))) (=> (@ (@ tptp.ord_less_eq_nat K2) J2) (= (@ (@ tptp.minus_minus_nat (@ _let_1 J2)) K2) (@ _let_1 (@ (@ tptp.minus_minus_nat J2) K2)))))))
% 6.73/7.04 (assert (forall ((K2 tptp.nat) (J2 tptp.nat) (I2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K2) J2) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat J2) I2)) K2) (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat J2) K2)) I2)))))
% 6.73/7.04 (assert (forall ((I2 tptp.nat) (J2 tptp.nat) (K2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J2) (= (= (@ (@ tptp.minus_minus_nat J2) I2) K2) (= J2 (@ (@ tptp.plus_plus_nat K2) I2))))))
% 6.73/7.04 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat M2))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.minus_minus_nat (@ _let_1 tptp.one_one_nat)) N)))))
% 6.73/7.04 (assert (forall ((Uz tptp.product_prod_nat_nat) (Va3 tptp.nat) (Vb tptp.list_VEBT_VEBT) (Vc tptp.vEBT_VEBT)) (not (@ tptp.vEBT_VEBT_minNull (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat Uz)) Va3) Vb) Vc)))))
% 6.73/7.04 (assert (forall ((N tptp.nat) (Xs2 tptp.list_complex)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s3451745648224563538omplex Xs2)) (@ (@ tptp.member_complex (@ (@ tptp.nth_complex Xs2) N)) (@ tptp.set_complex2 Xs2)))))
% 6.73/7.04 (assert (forall ((N tptp.nat) (Xs2 tptp.list_real)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_real Xs2)) (@ (@ tptp.member_real (@ (@ tptp.nth_real Xs2) N)) (@ tptp.set_real2 Xs2)))))
% 6.73/7.04 (assert (forall ((N tptp.nat) (Xs2 tptp.list_set_nat)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s3254054031482475050et_nat Xs2)) (@ (@ tptp.member_set_nat (@ (@ tptp.nth_set_nat Xs2) N)) (@ tptp.set_set_nat2 Xs2)))))
% 6.73/7.04 (assert (forall ((N tptp.nat) (Xs2 tptp.list_VEBT_VEBT)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (@ (@ tptp.member_VEBT_VEBT (@ (@ tptp.nth_VEBT_VEBT Xs2) N)) (@ tptp.set_VEBT_VEBT2 Xs2)))))
% 6.73/7.04 (assert (forall ((N tptp.nat) (Xs2 tptp.list_o)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_o Xs2)) (@ (@ tptp.member_o (@ (@ tptp.nth_o Xs2) N)) (@ tptp.set_o2 Xs2)))))
% 6.73/7.04 (assert (forall ((N tptp.nat) (Xs2 tptp.list_nat)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_nat Xs2)) (@ (@ tptp.member_nat (@ (@ tptp.nth_nat Xs2) N)) (@ tptp.set_nat2 Xs2)))))
% 6.73/7.04 (assert (forall ((N tptp.nat) (Xs2 tptp.list_int)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_int Xs2)) (@ (@ tptp.member_int (@ (@ tptp.nth_int Xs2) N)) (@ tptp.set_int2 Xs2)))))
% 6.73/7.04 (assert (forall ((N tptp.nat) (Xs2 tptp.list_VEBT_VEBT) (P2 (-> tptp.vEBT_VEBT Bool))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (=> (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 Xs2)) (@ P2 X3))) (@ P2 (@ (@ tptp.nth_VEBT_VEBT Xs2) N))))))
% 6.73/7.04 (assert (forall ((N tptp.nat) (Xs2 tptp.list_o) (P2 (-> Bool Bool))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_o Xs2)) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) (@ tptp.set_o2 Xs2)) (@ P2 X3))) (@ P2 (@ (@ tptp.nth_o Xs2) N))))))
% 6.73/7.04 (assert (forall ((N tptp.nat) (Xs2 tptp.list_nat) (P2 (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_nat Xs2)) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ tptp.set_nat2 Xs2)) (@ P2 X3))) (@ P2 (@ (@ tptp.nth_nat Xs2) N))))))
% 6.73/7.04 (assert (forall ((N tptp.nat) (Xs2 tptp.list_int) (P2 (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_int Xs2)) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ tptp.set_int2 Xs2)) (@ P2 X3))) (@ P2 (@ (@ tptp.nth_int Xs2) N))))))
% 6.73/7.04 (assert (forall ((X tptp.complex) (Xs2 tptp.list_complex)) (= (@ (@ tptp.member_complex X) (@ tptp.set_complex2 Xs2)) (exists ((I tptp.nat)) (and (@ (@ tptp.ord_less_nat I) (@ tptp.size_s3451745648224563538omplex Xs2)) (= (@ (@ tptp.nth_complex Xs2) I) X))))))
% 6.73/7.04 (assert (forall ((X tptp.real) (Xs2 tptp.list_real)) (= (@ (@ tptp.member_real X) (@ tptp.set_real2 Xs2)) (exists ((I tptp.nat)) (and (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_real Xs2)) (= (@ (@ tptp.nth_real Xs2) I) X))))))
% 6.73/7.04 (assert (forall ((X tptp.set_nat) (Xs2 tptp.list_set_nat)) (= (@ (@ tptp.member_set_nat X) (@ tptp.set_set_nat2 Xs2)) (exists ((I tptp.nat)) (and (@ (@ tptp.ord_less_nat I) (@ tptp.size_s3254054031482475050et_nat Xs2)) (= (@ (@ tptp.nth_set_nat Xs2) I) X))))))
% 6.73/7.04 (assert (forall ((X tptp.vEBT_VEBT) (Xs2 tptp.list_VEBT_VEBT)) (= (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 Xs2)) (exists ((I tptp.nat)) (and (@ (@ tptp.ord_less_nat I) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (= (@ (@ tptp.nth_VEBT_VEBT Xs2) I) X))))))
% 6.73/7.04 (assert (forall ((X Bool) (Xs2 tptp.list_o)) (= (@ (@ tptp.member_o X) (@ tptp.set_o2 Xs2)) (exists ((I tptp.nat)) (and (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_o Xs2)) (= (@ (@ tptp.nth_o Xs2) I) X))))))
% 6.73/7.04 (assert (forall ((X tptp.nat) (Xs2 tptp.list_nat)) (= (@ (@ tptp.member_nat X) (@ tptp.set_nat2 Xs2)) (exists ((I tptp.nat)) (and (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_nat Xs2)) (= (@ (@ tptp.nth_nat Xs2) I) X))))))
% 6.73/7.04 (assert (forall ((X tptp.int) (Xs2 tptp.list_int)) (= (@ (@ tptp.member_int X) (@ tptp.set_int2 Xs2)) (exists ((I tptp.nat)) (and (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_int Xs2)) (= (@ (@ tptp.nth_int Xs2) I) X))))))
% 6.73/7.04 (assert (forall ((Xs2 tptp.list_complex) (P2 (-> tptp.complex Bool)) (X tptp.complex)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_s3451745648224563538omplex Xs2)) (@ P2 (@ (@ tptp.nth_complex Xs2) I3)))) (=> (@ (@ tptp.member_complex X) (@ tptp.set_complex2 Xs2)) (@ P2 X)))))
% 6.73/7.04 (assert (forall ((Xs2 tptp.list_real) (P2 (-> tptp.real Bool)) (X tptp.real)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_real Xs2)) (@ P2 (@ (@ tptp.nth_real Xs2) I3)))) (=> (@ (@ tptp.member_real X) (@ tptp.set_real2 Xs2)) (@ P2 X)))))
% 6.73/7.04 (assert (forall ((Xs2 tptp.list_set_nat) (P2 (-> tptp.set_nat Bool)) (X tptp.set_nat)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_s3254054031482475050et_nat Xs2)) (@ P2 (@ (@ tptp.nth_set_nat Xs2) I3)))) (=> (@ (@ tptp.member_set_nat X) (@ tptp.set_set_nat2 Xs2)) (@ P2 X)))))
% 6.73/7.04 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (P2 (-> tptp.vEBT_VEBT Bool)) (X tptp.vEBT_VEBT)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (@ P2 (@ (@ tptp.nth_VEBT_VEBT Xs2) I3)))) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 Xs2)) (@ P2 X)))))
% 6.73/7.04 (assert (forall ((Xs2 tptp.list_o) (P2 (-> Bool Bool)) (X Bool)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_o Xs2)) (@ P2 (@ (@ tptp.nth_o Xs2) I3)))) (=> (@ (@ tptp.member_o X) (@ tptp.set_o2 Xs2)) (@ P2 X)))))
% 6.73/7.04 (assert (forall ((Xs2 tptp.list_nat) (P2 (-> tptp.nat Bool)) (X tptp.nat)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_nat Xs2)) (@ P2 (@ (@ tptp.nth_nat Xs2) I3)))) (=> (@ (@ tptp.member_nat X) (@ tptp.set_nat2 Xs2)) (@ P2 X)))))
% 6.73/7.04 (assert (forall ((Xs2 tptp.list_int) (P2 (-> tptp.int Bool)) (X tptp.int)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_int Xs2)) (@ P2 (@ (@ tptp.nth_int Xs2) I3)))) (=> (@ (@ tptp.member_int X) (@ tptp.set_int2 Xs2)) (@ P2 X)))))
% 6.73/7.04 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (P2 (-> tptp.vEBT_VEBT Bool))) (= (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 Xs2)) (@ P2 X4))) (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (@ P2 (@ (@ tptp.nth_VEBT_VEBT Xs2) I)))))))
% 6.73/7.04 (assert (forall ((Xs2 tptp.list_o) (P2 (-> Bool Bool))) (= (forall ((X4 Bool)) (=> (@ (@ tptp.member_o X4) (@ tptp.set_o2 Xs2)) (@ P2 X4))) (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_o Xs2)) (@ P2 (@ (@ tptp.nth_o Xs2) I)))))))
% 6.73/7.04 (assert (forall ((Xs2 tptp.list_nat) (P2 (-> tptp.nat Bool))) (= (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) (@ tptp.set_nat2 Xs2)) (@ P2 X4))) (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_nat Xs2)) (@ P2 (@ (@ tptp.nth_nat Xs2) I)))))))
% 6.73/7.04 (assert (forall ((Xs2 tptp.list_int) (P2 (-> tptp.int Bool))) (= (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) (@ tptp.set_int2 Xs2)) (@ P2 X4))) (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_int Xs2)) (@ P2 (@ (@ tptp.nth_int Xs2) I)))))))
% 6.73/7.04 (assert (forall ((N tptp.nat) (I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat N) (@ tptp.suc I2))) N))))
% 6.73/7.04 (assert (forall ((P2 (-> tptp.nat Bool)) (A tptp.nat) (B tptp.nat)) (= (@ P2 (@ (@ tptp.minus_minus_nat A) B)) (and (=> (@ (@ tptp.ord_less_nat A) B) (@ P2 tptp.zero_zero_nat)) (forall ((D2 tptp.nat)) (=> (= A (@ (@ tptp.plus_plus_nat B) D2)) (@ P2 D2)))))))
% 6.73/7.04 (assert (forall ((P2 (-> tptp.nat Bool)) (A tptp.nat) (B tptp.nat)) (= (@ P2 (@ (@ tptp.minus_minus_nat A) B)) (not (or (and (@ (@ tptp.ord_less_nat A) B) (not (@ P2 tptp.zero_zero_nat))) (exists ((D2 tptp.nat)) (and (= A (@ (@ tptp.plus_plus_nat B) D2)) (not (@ P2 D2)))))))))
% 6.73/7.04 (assert (forall ((K2 tptp.nat) (J2 tptp.nat) (I2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K2) J2) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat J2) K2)) I2) (@ (@ tptp.ord_less_nat J2) (@ (@ tptp.plus_plus_nat I2) K2))))))
% 6.73/7.04 (assert (forall ((J2 tptp.nat) (I2 tptp.nat) (U tptp.nat) (M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat J2) I2) (= (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I2) U)) M2) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J2) U)) N)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat I2) J2)) U)) M2) N)))))
% 6.73/7.04 (assert (forall ((I2 tptp.nat) (J2 tptp.nat) (U tptp.nat) (M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J2) (= (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I2) U)) M2) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J2) U)) N)) (= M2 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat J2) I2)) U)) N))))))
% 6.73/7.04 (assert (forall ((J2 tptp.nat) (I2 tptp.nat) (U tptp.nat) (M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat J2) I2) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I2) U)) M2)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J2) U)) N)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat I2) J2)) U)) M2)) N)))))
% 6.73/7.04 (assert (forall ((I2 tptp.nat) (J2 tptp.nat) (U tptp.nat) (M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J2) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I2) U)) M2)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J2) U)) N)) (@ (@ tptp.ord_less_eq_nat M2) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat J2) I2)) U)) N))))))
% 6.73/7.04 (assert (forall ((J2 tptp.nat) (I2 tptp.nat) (U tptp.nat) (M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat J2) I2) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I2) U)) M2)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J2) U)) N)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat I2) J2)) U)) M2)) N)))))
% 6.73/7.04 (assert (forall ((I2 tptp.nat) (J2 tptp.nat) (U tptp.nat) (M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J2) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I2) U)) M2)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J2) U)) N)) (@ (@ tptp.minus_minus_nat M2) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat J2) I2)) U)) N))))))
% 6.73/7.04 (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) (Va2 tptp.nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (not (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat Uz2)) Va2) Vb2) Vc2))))))))))
% 6.73/7.04 (assert (forall ((X tptp.vEBT_VEBT)) (=> (@ tptp.vEBT_VEBT_minNull X) (=> (not (= X (@ (@ tptp.vEBT_Leaf false) false))) (not (forall ((Uw tptp.nat) (Ux tptp.list_VEBT_VEBT) (Uy tptp.vEBT_VEBT)) (not (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uw) Ux) Uy)))))))))
% 6.73/7.04 (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))))))
% 6.73/7.04 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc M2)) N) (@ (@ tptp.minus_minus_nat M2) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat))))))
% 6.73/7.04 (assert (= tptp.plus_plus_nat (lambda ((M6 tptp.nat) (N4 tptp.nat)) (@ (@ (@ tptp.if_nat (= M6 tptp.zero_zero_nat)) N4) (@ tptp.suc (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat M6) tptp.one_one_nat)) N4))))))
% 6.73/7.04 (assert (forall ((J2 tptp.nat) (I2 tptp.nat) (U tptp.nat) (M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat J2) I2) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I2) U)) M2)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J2) U)) N)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat I2) J2)) U)) M2)) N)))))
% 6.73/7.04 (assert (forall ((I2 tptp.nat) (J2 tptp.nat) (U tptp.nat) (M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J2) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I2) U)) M2)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J2) U)) N)) (@ (@ tptp.ord_less_nat M2) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat J2) I2)) U)) N))))))
% 6.73/7.04 (assert (= tptp.times_times_nat (lambda ((M6 tptp.nat) (N4 tptp.nat)) (@ (@ (@ tptp.if_nat (= M6 tptp.zero_zero_nat)) tptp.zero_zero_nat) (@ (@ tptp.plus_plus_nat N4) (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat M6) tptp.one_one_nat)) N4))))))
% 6.73/7.04 (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 ((Uw tptp.nat) (Ux tptp.list_VEBT_VEBT) (Uy tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uw) Ux) Uy))) _let_1) (not (=> (exists ((Uz2 tptp.product_prod_nat_nat) (Va2 tptp.nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat Uz2)) Va2) Vb2) Vc2))) Y))))))))))
% 6.73/7.04 (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)))))))))
% 6.73/7.04 (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)))))))))
% 6.73/7.04 (assert (forall ((A4 tptp.set_real) (A tptp.real)) (=> (@ tptp.finite_finite_real A4) (=> (@ (@ tptp.member_real A) A4) (exists ((X3 tptp.real)) (and (@ (@ tptp.member_real X3) A4) (@ (@ tptp.ord_less_eq_real X3) A) (forall ((Xa tptp.real)) (=> (@ (@ tptp.member_real Xa) A4) (=> (@ (@ tptp.ord_less_eq_real Xa) X3) (= X3 Xa))))))))))
% 6.73/7.04 (assert (forall ((A4 tptp.set_set_nat) (A tptp.set_nat)) (=> (@ tptp.finite1152437895449049373et_nat A4) (=> (@ (@ tptp.member_set_nat A) A4) (exists ((X3 tptp.set_nat)) (and (@ (@ tptp.member_set_nat X3) A4) (@ (@ tptp.ord_less_eq_set_nat X3) A) (forall ((Xa tptp.set_nat)) (=> (@ (@ tptp.member_set_nat Xa) A4) (=> (@ (@ tptp.ord_less_eq_set_nat Xa) X3) (= X3 Xa))))))))))
% 6.73/7.04 (assert (forall ((A4 tptp.set_rat) (A tptp.rat)) (=> (@ tptp.finite_finite_rat A4) (=> (@ (@ tptp.member_rat A) A4) (exists ((X3 tptp.rat)) (and (@ (@ tptp.member_rat X3) A4) (@ (@ tptp.ord_less_eq_rat X3) A) (forall ((Xa tptp.rat)) (=> (@ (@ tptp.member_rat Xa) A4) (=> (@ (@ tptp.ord_less_eq_rat Xa) X3) (= X3 Xa))))))))))
% 6.73/7.04 (assert (forall ((A4 tptp.set_num) (A tptp.num)) (=> (@ tptp.finite_finite_num A4) (=> (@ (@ tptp.member_num A) A4) (exists ((X3 tptp.num)) (and (@ (@ tptp.member_num X3) A4) (@ (@ tptp.ord_less_eq_num X3) A) (forall ((Xa tptp.num)) (=> (@ (@ tptp.member_num Xa) A4) (=> (@ (@ tptp.ord_less_eq_num Xa) X3) (= X3 Xa))))))))))
% 6.73/7.04 (assert (forall ((A4 tptp.set_nat) (A tptp.nat)) (=> (@ tptp.finite_finite_nat A4) (=> (@ (@ tptp.member_nat A) A4) (exists ((X3 tptp.nat)) (and (@ (@ tptp.member_nat X3) A4) (@ (@ tptp.ord_less_eq_nat X3) A) (forall ((Xa tptp.nat)) (=> (@ (@ tptp.member_nat Xa) A4) (=> (@ (@ tptp.ord_less_eq_nat Xa) X3) (= X3 Xa))))))))))
% 6.73/7.04 (assert (forall ((A4 tptp.set_int) (A tptp.int)) (=> (@ tptp.finite_finite_int A4) (=> (@ (@ tptp.member_int A) A4) (exists ((X3 tptp.int)) (and (@ (@ tptp.member_int X3) A4) (@ (@ tptp.ord_less_eq_int X3) A) (forall ((Xa tptp.int)) (=> (@ (@ tptp.member_int Xa) A4) (=> (@ (@ tptp.ord_less_eq_int Xa) X3) (= X3 Xa))))))))))
% 6.73/7.04 (assert (forall ((A4 tptp.set_real) (A tptp.real)) (=> (@ tptp.finite_finite_real A4) (=> (@ (@ tptp.member_real A) A4) (exists ((X3 tptp.real)) (and (@ (@ tptp.member_real X3) A4) (@ (@ tptp.ord_less_eq_real A) X3) (forall ((Xa tptp.real)) (=> (@ (@ tptp.member_real Xa) A4) (=> (@ (@ tptp.ord_less_eq_real X3) Xa) (= X3 Xa))))))))))
% 6.73/7.04 (assert (forall ((A4 tptp.set_set_nat) (A tptp.set_nat)) (=> (@ tptp.finite1152437895449049373et_nat A4) (=> (@ (@ tptp.member_set_nat A) A4) (exists ((X3 tptp.set_nat)) (and (@ (@ tptp.member_set_nat X3) A4) (@ (@ tptp.ord_less_eq_set_nat A) X3) (forall ((Xa tptp.set_nat)) (=> (@ (@ tptp.member_set_nat Xa) A4) (=> (@ (@ tptp.ord_less_eq_set_nat X3) Xa) (= X3 Xa))))))))))
% 6.73/7.04 (assert (forall ((A4 tptp.set_rat) (A tptp.rat)) (=> (@ tptp.finite_finite_rat A4) (=> (@ (@ tptp.member_rat A) A4) (exists ((X3 tptp.rat)) (and (@ (@ tptp.member_rat X3) A4) (@ (@ tptp.ord_less_eq_rat A) X3) (forall ((Xa tptp.rat)) (=> (@ (@ tptp.member_rat Xa) A4) (=> (@ (@ tptp.ord_less_eq_rat X3) Xa) (= X3 Xa))))))))))
% 6.73/7.04 (assert (forall ((A4 tptp.set_num) (A tptp.num)) (=> (@ tptp.finite_finite_num A4) (=> (@ (@ tptp.member_num A) A4) (exists ((X3 tptp.num)) (and (@ (@ tptp.member_num X3) A4) (@ (@ tptp.ord_less_eq_num A) X3) (forall ((Xa tptp.num)) (=> (@ (@ tptp.member_num Xa) A4) (=> (@ (@ tptp.ord_less_eq_num X3) Xa) (= X3 Xa))))))))))
% 6.73/7.04 (assert (forall ((A4 tptp.set_nat) (A tptp.nat)) (=> (@ tptp.finite_finite_nat A4) (=> (@ (@ tptp.member_nat A) A4) (exists ((X3 tptp.nat)) (and (@ (@ tptp.member_nat X3) A4) (@ (@ tptp.ord_less_eq_nat A) X3) (forall ((Xa tptp.nat)) (=> (@ (@ tptp.member_nat Xa) A4) (=> (@ (@ tptp.ord_less_eq_nat X3) Xa) (= X3 Xa))))))))))
% 6.73/7.04 (assert (forall ((A4 tptp.set_int) (A tptp.int)) (=> (@ tptp.finite_finite_int A4) (=> (@ (@ tptp.member_int A) A4) (exists ((X3 tptp.int)) (and (@ (@ tptp.member_int X3) A4) (@ (@ tptp.ord_less_eq_int A) X3) (forall ((Xa tptp.int)) (=> (@ (@ tptp.member_int Xa) A4) (=> (@ (@ tptp.ord_less_eq_int X3) Xa) (= X3 Xa))))))))))
% 6.73/7.04 (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 ((Uw tptp.nat) (Ux tptp.list_VEBT_VEBT) (Uy tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uw) Ux) Uy))) (=> (= X _let_1) (=> Y (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel) _let_1)))))) (not (forall ((Uz2 tptp.product_prod_nat_nat) (Va2 tptp.nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat Uz2)) Va2) Vb2) Vc2))) (=> (= X _let_1) (=> (not Y) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel) _let_1)))))))))))))))))
% 6.73/7.04 (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 ((Uw tptp.nat) (Ux tptp.list_VEBT_VEBT) (Uy tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uw) Ux) Uy))) (=> (= X _let_1) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel) _let_1)))))))))))))
% 6.73/7.04 (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) (Va2 tptp.nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat Uz2)) Va2) Vb2) Vc2))) (=> (= X _let_1) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel) _let_1))))))))))))
% 6.73/7.04 (assert (forall ((M2 tptp.nat) (Xs2 tptp.list_VEBT_VEBT) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (= (@ (@ tptp.nth_Pr744662078594809490T_VEBT (@ (@ tptp.enumerate_VEBT_VEBT N) Xs2)) M2) (@ (@ tptp.produc599794634098209291T_VEBT (@ (@ tptp.plus_plus_nat N) M2)) (@ (@ tptp.nth_VEBT_VEBT Xs2) M2))))))
% 6.73/7.04 (assert (forall ((M2 tptp.nat) (Xs2 tptp.list_o) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) (@ tptp.size_size_list_o Xs2)) (= (@ (@ tptp.nth_Pr112076138515278198_nat_o (@ (@ tptp.enumerate_o N) Xs2)) M2) (@ (@ tptp.product_Pair_nat_o (@ (@ tptp.plus_plus_nat N) M2)) (@ (@ tptp.nth_o Xs2) M2))))))
% 6.73/7.04 (assert (forall ((M2 tptp.nat) (Xs2 tptp.list_nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) (@ tptp.size_size_list_nat Xs2)) (= (@ (@ tptp.nth_Pr7617993195940197384at_nat (@ (@ tptp.enumerate_nat N) Xs2)) M2) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat N) M2)) (@ (@ tptp.nth_nat Xs2) M2))))))
% 6.73/7.04 (assert (forall ((M2 tptp.nat) (Xs2 tptp.list_int) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) (@ tptp.size_size_list_int Xs2)) (= (@ (@ tptp.nth_Pr3440142176431000676at_int (@ (@ tptp.enumerate_int N) Xs2)) M2) (@ (@ tptp.product_Pair_nat_int (@ (@ tptp.plus_plus_nat N) M2)) (@ (@ tptp.nth_int Xs2) M2))))))
% 6.73/7.04 (assert (forall ((S3 tptp.set_complex) (Y tptp.complex) (F2 (-> tptp.complex tptp.rat))) (=> (@ tptp.finite3207457112153483333omplex S3) (=> (not (= S3 tptp.bot_bot_set_complex)) (=> (@ (@ tptp.member_complex Y) S3) (@ (@ tptp.ord_less_eq_rat (@ F2 (@ (@ tptp.lattic4729654577720512673ex_rat F2) S3))) (@ F2 Y)))))))
% 6.73/7.04 (assert (forall ((S3 tptp.set_nat) (Y tptp.nat) (F2 (-> tptp.nat tptp.rat))) (=> (@ tptp.finite_finite_nat S3) (=> (not (= S3 tptp.bot_bot_set_nat)) (=> (@ (@ tptp.member_nat Y) S3) (@ (@ tptp.ord_less_eq_rat (@ F2 (@ (@ tptp.lattic6811802900495863747at_rat F2) S3))) (@ F2 Y)))))))
% 6.73/7.04 (assert (forall ((S3 tptp.set_int) (Y tptp.int) (F2 (-> tptp.int tptp.rat))) (=> (@ tptp.finite_finite_int S3) (=> (not (= S3 tptp.bot_bot_set_int)) (=> (@ (@ tptp.member_int Y) S3) (@ (@ tptp.ord_less_eq_rat (@ F2 (@ (@ tptp.lattic7811156612396918303nt_rat F2) S3))) (@ F2 Y)))))))
% 6.73/7.04 (assert (forall ((S3 tptp.set_real) (Y tptp.real) (F2 (-> tptp.real tptp.rat))) (=> (@ tptp.finite_finite_real S3) (=> (not (= S3 tptp.bot_bot_set_real)) (=> (@ (@ tptp.member_real Y) S3) (@ (@ tptp.ord_less_eq_rat (@ F2 (@ (@ tptp.lattic4420706379359479199al_rat F2) S3))) (@ F2 Y)))))))
% 6.73/7.04 (assert (forall ((S3 tptp.set_complex) (Y tptp.complex) (F2 (-> tptp.complex tptp.num))) (=> (@ tptp.finite3207457112153483333omplex S3) (=> (not (= S3 tptp.bot_bot_set_complex)) (=> (@ (@ tptp.member_complex Y) S3) (@ (@ tptp.ord_less_eq_num (@ F2 (@ (@ tptp.lattic1922116423962787043ex_num F2) S3))) (@ F2 Y)))))))
% 6.73/7.04 (assert (forall ((S3 tptp.set_nat) (Y tptp.nat) (F2 (-> tptp.nat tptp.num))) (=> (@ tptp.finite_finite_nat S3) (=> (not (= S3 tptp.bot_bot_set_nat)) (=> (@ (@ tptp.member_nat Y) S3) (@ (@ tptp.ord_less_eq_num (@ F2 (@ (@ tptp.lattic4004264746738138117at_num F2) S3))) (@ F2 Y)))))))
% 6.73/7.04 (assert (forall ((S3 tptp.set_int) (Y tptp.int) (F2 (-> tptp.int tptp.num))) (=> (@ tptp.finite_finite_int S3) (=> (not (= S3 tptp.bot_bot_set_int)) (=> (@ (@ tptp.member_int Y) S3) (@ (@ tptp.ord_less_eq_num (@ F2 (@ (@ tptp.lattic5003618458639192673nt_num F2) S3))) (@ F2 Y)))))))
% 6.73/7.04 (assert (forall ((S3 tptp.set_real) (Y tptp.real) (F2 (-> tptp.real tptp.num))) (=> (@ tptp.finite_finite_real S3) (=> (not (= S3 tptp.bot_bot_set_real)) (=> (@ (@ tptp.member_real Y) S3) (@ (@ tptp.ord_less_eq_num (@ F2 (@ (@ tptp.lattic1613168225601753569al_num F2) S3))) (@ F2 Y)))))))
% 6.73/7.04 (assert (forall ((S3 tptp.set_complex) (Y tptp.complex) (F2 (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex S3) (=> (not (= S3 tptp.bot_bot_set_complex)) (=> (@ (@ tptp.member_complex Y) S3) (@ (@ tptp.ord_less_eq_nat (@ F2 (@ (@ tptp.lattic5364784637807008409ex_nat F2) S3))) (@ F2 Y)))))))
% 6.73/7.04 (assert (forall ((S3 tptp.set_nat) (Y tptp.nat) (F2 (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_nat S3) (=> (not (= S3 tptp.bot_bot_set_nat)) (=> (@ (@ tptp.member_nat Y) S3) (@ (@ tptp.ord_less_eq_nat (@ F2 (@ (@ tptp.lattic7446932960582359483at_nat F2) S3))) (@ F2 Y)))))))
% 6.73/7.04 (assert (forall ((P2 (-> tptp.nat tptp.nat Bool)) (A tptp.nat) (B tptp.nat)) (=> (forall ((A3 tptp.nat) (B3 tptp.nat)) (= (@ (@ P2 A3) B3) (@ (@ P2 B3) A3))) (=> (forall ((A3 tptp.nat)) (@ (@ P2 A3) tptp.zero_zero_nat)) (=> (forall ((A3 tptp.nat) (B3 tptp.nat)) (let ((_let_1 (@ P2 A3))) (=> (@ _let_1 B3) (@ _let_1 (@ (@ tptp.plus_plus_nat A3) B3))))) (@ (@ P2 A) B))))))
% 6.73/7.04 (assert (forall ((N tptp.nat) (P2 (-> tptp.nat Bool)) (M2 tptp.nat)) (=> (forall ((K tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) K) (@ P2 K))) (=> (forall ((K tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat K) I4) (@ P2 I4))) (@ P2 K)))) (@ P2 M2)))))
% 6.73/7.04 (assert (forall ((Xs2 tptp.list_list_VEBT_VEBT) (N tptp.nat)) (=> (forall ((X3 tptp.list_VEBT_VEBT)) (=> (@ (@ tptp.member2936631157270082147T_VEBT X3) (@ tptp.set_list_VEBT_VEBT2 Xs2)) (= (@ tptp.size_s6755466524823107622T_VEBT X3) N))) (= (@ tptp.size_s6755466524823107622T_VEBT (@ tptp.concat_VEBT_VEBT Xs2)) (@ (@ tptp.times_times_nat (@ tptp.size_s8217280938318005548T_VEBT Xs2)) N)))))
% 6.73/7.04 (assert (forall ((Xs2 tptp.list_list_o) (N tptp.nat)) (=> (forall ((X3 tptp.list_o)) (=> (@ (@ tptp.member_list_o X3) (@ tptp.set_list_o2 Xs2)) (= (@ tptp.size_size_list_o X3) N))) (= (@ tptp.size_size_list_o (@ tptp.concat_o Xs2)) (@ (@ tptp.times_times_nat (@ tptp.size_s2710708370519433104list_o Xs2)) N)))))
% 6.73/7.04 (assert (forall ((Xs2 tptp.list_list_nat) (N tptp.nat)) (=> (forall ((X3 tptp.list_nat)) (=> (@ (@ tptp.member_list_nat X3) (@ tptp.set_list_nat2 Xs2)) (= (@ tptp.size_size_list_nat X3) N))) (= (@ tptp.size_size_list_nat (@ tptp.concat_nat Xs2)) (@ (@ tptp.times_times_nat (@ tptp.size_s3023201423986296836st_nat Xs2)) N)))))
% 6.73/7.04 (assert (forall ((Xs2 tptp.list_list_int) (N tptp.nat)) (=> (forall ((X3 tptp.list_int)) (=> (@ (@ tptp.member_list_int X3) (@ tptp.set_list_int2 Xs2)) (= (@ tptp.size_size_list_int X3) N))) (= (@ tptp.size_size_list_int (@ tptp.concat_int Xs2)) (@ (@ tptp.times_times_nat (@ tptp.size_s533118279054570080st_int Xs2)) N)))))
% 6.73/7.04 (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)))))
% 6.73/7.04 (assert (forall ((N tptp.nat) (Xs2 tptp.list_VEBT_VEBT)) (= (@ tptp.size_s4762443039079500285T_VEBT (@ (@ tptp.enumerate_VEBT_VEBT N) Xs2)) (@ tptp.size_s6755466524823107622T_VEBT Xs2))))
% 6.73/7.04 (assert (forall ((N tptp.nat) (Xs2 tptp.list_o)) (= (@ tptp.size_s6491369823275344609_nat_o (@ (@ tptp.enumerate_o N) Xs2)) (@ tptp.size_size_list_o Xs2))))
% 6.73/7.04 (assert (forall ((N tptp.nat) (Xs2 tptp.list_nat)) (= (@ tptp.size_s5460976970255530739at_nat (@ (@ tptp.enumerate_nat N) Xs2)) (@ tptp.size_size_list_nat Xs2))))
% 6.73/7.04 (assert (forall ((N tptp.nat) (Xs2 tptp.list_int)) (= (@ tptp.size_s2970893825323803983at_int (@ (@ tptp.enumerate_int N) Xs2)) (@ tptp.size_size_list_int Xs2))))
% 6.73/7.04 (assert (= (@ tptp.nat_triangle tptp.zero_zero_nat) tptp.zero_zero_nat))
% 6.73/7.04 (assert (forall ((I2 tptp.nat) (J2 tptp.nat) (K2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat I2))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 J2)) K2) (@ (@ tptp.minus_minus_nat (@ _let_1 K2)) J2)))))
% 6.73/7.04 (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))))))))))
% 6.73/7.04 (assert (= tptp.nat_prod_decode_aux (lambda ((K3 tptp.nat) (M6 tptp.nat)) (let ((_let_1 (@ tptp.suc K3))) (@ (@ (@ tptp.if_Pro6206227464963214023at_nat (@ (@ tptp.ord_less_eq_nat M6) K3)) (@ (@ tptp.product_Pair_nat_nat M6) (@ (@ tptp.minus_minus_nat K3) M6))) (@ (@ tptp.nat_prod_decode_aux _let_1) (@ (@ tptp.minus_minus_nat M6) _let_1)))))))
% 6.73/7.04 (assert (forall ((K2 tptp.nat) (M2 tptp.nat)) (= (@ tptp.nat_prod_encode (@ (@ tptp.nat_prod_decode_aux K2) M2)) (@ (@ tptp.plus_plus_nat (@ tptp.nat_triangle K2)) M2))))
% 6.73/7.04 (assert (forall ((K2 tptp.nat) (M2 tptp.nat)) (= (@ tptp.nat_prod_decode (@ (@ tptp.plus_plus_nat (@ tptp.nat_triangle K2)) M2)) (@ (@ tptp.nat_prod_decode_aux K2) M2))))
% 6.73/7.04 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (Xss tptp.list_list_VEBT_VEBT)) (=> (@ (@ tptp.member2936631157270082147T_VEBT Xs2) (@ tptp.set_list_VEBT_VEBT2 (@ tptp.produc3021084454716106787T_VEBT Xss))) (= (@ tptp.size_s6755466524823107622T_VEBT Xs2) (@ tptp.size_s8217280938318005548T_VEBT Xss)))))
% 6.73/7.04 (assert (forall ((Xs2 tptp.list_o) (Xss tptp.list_list_o)) (=> (@ (@ tptp.member_list_o Xs2) (@ tptp.set_list_o2 (@ tptp.product_lists_o Xss))) (= (@ tptp.size_size_list_o Xs2) (@ tptp.size_s2710708370519433104list_o Xss)))))
% 6.73/7.04 (assert (forall ((Xs2 tptp.list_nat) (Xss tptp.list_list_nat)) (=> (@ (@ tptp.member_list_nat Xs2) (@ tptp.set_list_nat2 (@ tptp.product_lists_nat Xss))) (= (@ tptp.size_size_list_nat Xs2) (@ tptp.size_s3023201423986296836st_nat Xss)))))
% 6.73/7.04 (assert (forall ((Xs2 tptp.list_int) (Xss tptp.list_list_int)) (=> (@ (@ tptp.member_list_int Xs2) (@ tptp.set_list_int2 (@ tptp.product_lists_int Xss))) (= (@ tptp.size_size_list_int Xs2) (@ tptp.size_s533118279054570080st_int Xss)))))
% 6.73/7.04 (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)))))))
% 6.73/7.04 (assert (forall ((P2 (-> tptp.real Bool)) (D3 tptp.real) (Q (-> tptp.real Bool))) (=> (forall ((X3 tptp.real) (K tptp.real)) (= (@ P2 X3) (@ P2 (@ (@ tptp.minus_minus_real X3) (@ (@ tptp.times_times_real K) D3))))) (=> (forall ((X3 tptp.real) (K tptp.real)) (= (@ Q X3) (@ Q (@ (@ tptp.minus_minus_real X3) (@ (@ tptp.times_times_real K) D3))))) (forall ((X5 tptp.real) (K4 tptp.real)) (let ((_let_1 (@ (@ tptp.minus_minus_real X5) (@ (@ tptp.times_times_real K4) D3)))) (= (or (@ P2 X5) (@ Q X5)) (or (@ P2 _let_1) (@ Q _let_1)))))))))
% 6.73/7.04 (assert (forall ((P2 (-> tptp.rat Bool)) (D3 tptp.rat) (Q (-> tptp.rat Bool))) (=> (forall ((X3 tptp.rat) (K tptp.rat)) (= (@ P2 X3) (@ P2 (@ (@ tptp.minus_minus_rat X3) (@ (@ tptp.times_times_rat K) D3))))) (=> (forall ((X3 tptp.rat) (K tptp.rat)) (= (@ Q X3) (@ Q (@ (@ tptp.minus_minus_rat X3) (@ (@ tptp.times_times_rat K) D3))))) (forall ((X5 tptp.rat) (K4 tptp.rat)) (let ((_let_1 (@ (@ tptp.minus_minus_rat X5) (@ (@ tptp.times_times_rat K4) D3)))) (= (or (@ P2 X5) (@ Q X5)) (or (@ P2 _let_1) (@ Q _let_1)))))))))
% 6.73/7.04 (assert (forall ((P2 (-> tptp.int Bool)) (D3 tptp.int) (Q (-> tptp.int Bool))) (=> (forall ((X3 tptp.int) (K tptp.int)) (= (@ P2 X3) (@ P2 (@ (@ tptp.minus_minus_int X3) (@ (@ tptp.times_times_int K) D3))))) (=> (forall ((X3 tptp.int) (K tptp.int)) (= (@ Q X3) (@ Q (@ (@ tptp.minus_minus_int X3) (@ (@ tptp.times_times_int K) D3))))) (forall ((X5 tptp.int) (K4 tptp.int)) (let ((_let_1 (@ (@ tptp.minus_minus_int X5) (@ (@ tptp.times_times_int K4) D3)))) (= (or (@ P2 X5) (@ Q X5)) (or (@ P2 _let_1) (@ Q _let_1)))))))))
% 6.73/7.04 (assert (forall ((P2 (-> tptp.real Bool)) (D3 tptp.real) (Q (-> tptp.real Bool))) (=> (forall ((X3 tptp.real) (K tptp.real)) (= (@ P2 X3) (@ P2 (@ (@ tptp.minus_minus_real X3) (@ (@ tptp.times_times_real K) D3))))) (=> (forall ((X3 tptp.real) (K tptp.real)) (= (@ Q X3) (@ Q (@ (@ tptp.minus_minus_real X3) (@ (@ tptp.times_times_real K) D3))))) (forall ((X5 tptp.real) (K4 tptp.real)) (let ((_let_1 (@ (@ tptp.minus_minus_real X5) (@ (@ tptp.times_times_real K4) D3)))) (= (and (@ P2 X5) (@ Q X5)) (and (@ P2 _let_1) (@ Q _let_1)))))))))
% 6.73/7.04 (assert (forall ((P2 (-> tptp.rat Bool)) (D3 tptp.rat) (Q (-> tptp.rat Bool))) (=> (forall ((X3 tptp.rat) (K tptp.rat)) (= (@ P2 X3) (@ P2 (@ (@ tptp.minus_minus_rat X3) (@ (@ tptp.times_times_rat K) D3))))) (=> (forall ((X3 tptp.rat) (K tptp.rat)) (= (@ Q X3) (@ Q (@ (@ tptp.minus_minus_rat X3) (@ (@ tptp.times_times_rat K) D3))))) (forall ((X5 tptp.rat) (K4 tptp.rat)) (let ((_let_1 (@ (@ tptp.minus_minus_rat X5) (@ (@ tptp.times_times_rat K4) D3)))) (= (and (@ P2 X5) (@ Q X5)) (and (@ P2 _let_1) (@ Q _let_1)))))))))
% 6.73/7.04 (assert (forall ((P2 (-> tptp.int Bool)) (D3 tptp.int) (Q (-> tptp.int Bool))) (=> (forall ((X3 tptp.int) (K tptp.int)) (= (@ P2 X3) (@ P2 (@ (@ tptp.minus_minus_int X3) (@ (@ tptp.times_times_int K) D3))))) (=> (forall ((X3 tptp.int) (K tptp.int)) (= (@ Q X3) (@ Q (@ (@ tptp.minus_minus_int X3) (@ (@ tptp.times_times_int K) D3))))) (forall ((X5 tptp.int) (K4 tptp.int)) (let ((_let_1 (@ (@ tptp.minus_minus_int X5) (@ (@ tptp.times_times_int K4) D3)))) (= (and (@ P2 X5) (@ Q X5)) (and (@ P2 _let_1) (@ Q _let_1)))))))))
% 6.73/7.04 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex A) tptp.zero_zero_complex) A)))
% 6.73/7.04 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real A) tptp.zero_zero_real) A)))
% 6.73/7.04 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat A) tptp.zero_zero_rat) A)))
% 6.73/7.04 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.plus_plus_nat A) tptp.zero_zero_nat) A)))
% 6.73/7.04 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int A) tptp.zero_zero_int) A)))
% 6.73/7.04 (assert (= (@ tptp.gcd_Gcd_nat tptp.bot_bot_set_nat) tptp.zero_zero_nat))
% 6.73/7.04 (assert (= (@ tptp.gcd_Gcd_int tptp.bot_bot_set_int) tptp.zero_zero_int))
% 6.73/7.04 (assert (forall ((A4 tptp.set_int)) (= (= (@ tptp.gcd_Gcd_int A4) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_set_int A4) (@ (@ tptp.insert_int tptp.zero_zero_int) tptp.bot_bot_set_int)))))
% 6.73/7.04 (assert (forall ((A4 tptp.set_nat)) (= (= (@ tptp.gcd_Gcd_nat A4) tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_set_nat A4) (@ (@ tptp.insert_nat tptp.zero_zero_nat) tptp.bot_bot_set_nat)))))
% 6.73/7.04 (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)))))
% 6.73/7.04 (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)))))
% 6.73/7.04 (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)))))
% 6.73/7.04 (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)))))
% 6.73/7.04 (assert (forall ((A tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat A) A)))
% 6.73/7.04 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_eq_rat A) A)))
% 6.73/7.04 (assert (forall ((A tptp.num)) (@ (@ tptp.ord_less_eq_num A) A)))
% 6.73/7.04 (assert (forall ((A tptp.nat)) (@ (@ tptp.ord_less_eq_nat A) A)))
% 6.73/7.04 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int A) A)))
% 6.73/7.04 (assert (= tptp.nat_prod_decode (@ tptp.nat_prod_decode_aux tptp.zero_zero_nat)))
% 6.73/7.04 (assert (forall ((B2 tptp.real) (A2 tptp.real)) (= (not (@ (@ tptp.ord_less_eq_real B2) A2)) (@ (@ tptp.ord_less_real A2) B2))))
% 6.73/7.04 (assert (forall ((B2 tptp.rat) (A2 tptp.rat)) (= (not (@ (@ tptp.ord_less_eq_rat B2) A2)) (@ (@ tptp.ord_less_rat A2) B2))))
% 6.73/7.04 (assert (forall ((B2 tptp.num) (A2 tptp.num)) (= (not (@ (@ tptp.ord_less_eq_num B2) A2)) (@ (@ tptp.ord_less_num A2) B2))))
% 6.73/7.04 (assert (forall ((B2 tptp.nat) (A2 tptp.nat)) (= (not (@ (@ tptp.ord_less_eq_nat B2) A2)) (@ (@ tptp.ord_less_nat A2) B2))))
% 6.73/7.04 (assert (forall ((B2 tptp.int) (A2 tptp.int)) (= (not (@ (@ tptp.ord_less_eq_int B2) A2)) (@ (@ tptp.ord_less_int A2) B2))))
% 6.73/7.04 (assert (forall ((T tptp.real)) (exists ((Z tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real Z) X5) (not (@ (@ tptp.ord_less_eq_real X5) T)))))))
% 6.73/7.04 (assert (forall ((T tptp.rat)) (exists ((Z tptp.rat)) (forall ((X5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z) X5) (not (@ (@ tptp.ord_less_eq_rat X5) T)))))))
% 6.73/7.04 (assert (forall ((T tptp.num)) (exists ((Z tptp.num)) (forall ((X5 tptp.num)) (=> (@ (@ tptp.ord_less_num Z) X5) (not (@ (@ tptp.ord_less_eq_num X5) T)))))))
% 6.73/7.04 (assert (forall ((T tptp.nat)) (exists ((Z tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z) X5) (not (@ (@ tptp.ord_less_eq_nat X5) T)))))))
% 6.73/7.04 (assert (forall ((T tptp.int)) (exists ((Z tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int Z) X5) (not (@ (@ tptp.ord_less_eq_int X5) T)))))))
% 6.73/7.04 (assert (forall ((T tptp.real)) (exists ((Z tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real Z) X5) (@ (@ tptp.ord_less_eq_real T) X5))))))
% 6.73/7.04 (assert (forall ((T tptp.rat)) (exists ((Z tptp.rat)) (forall ((X5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z) X5) (@ (@ tptp.ord_less_eq_rat T) X5))))))
% 6.73/7.04 (assert (forall ((T tptp.num)) (exists ((Z tptp.num)) (forall ((X5 tptp.num)) (=> (@ (@ tptp.ord_less_num Z) X5) (@ (@ tptp.ord_less_eq_num T) X5))))))
% 6.73/7.04 (assert (forall ((T tptp.nat)) (exists ((Z tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z) X5) (@ (@ tptp.ord_less_eq_nat T) X5))))))
% 6.73/7.04 (assert (forall ((T tptp.int)) (exists ((Z tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int Z) X5) (@ (@ tptp.ord_less_eq_int T) X5))))))
% 6.73/7.04 (assert (forall ((T tptp.real)) (exists ((Z tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Z) (@ (@ tptp.ord_less_eq_real X5) T))))))
% 6.73/7.04 (assert (forall ((T tptp.rat)) (exists ((Z tptp.rat)) (forall ((X5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X5) Z) (@ (@ tptp.ord_less_eq_rat X5) T))))))
% 6.73/7.04 (assert (forall ((T tptp.num)) (exists ((Z tptp.num)) (forall ((X5 tptp.num)) (=> (@ (@ tptp.ord_less_num X5) Z) (@ (@ tptp.ord_less_eq_num X5) T))))))
% 6.73/7.04 (assert (forall ((T tptp.nat)) (exists ((Z tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Z) (@ (@ tptp.ord_less_eq_nat X5) T))))))
% 6.73/7.04 (assert (forall ((T tptp.int)) (exists ((Z tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int X5) Z) (@ (@ tptp.ord_less_eq_int X5) T))))))
% 6.73/7.04 (assert (forall ((T tptp.real)) (exists ((Z tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Z) (not (@ (@ tptp.ord_less_eq_real T) X5)))))))
% 6.73/7.04 (assert (forall ((T tptp.rat)) (exists ((Z tptp.rat)) (forall ((X5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X5) Z) (not (@ (@ tptp.ord_less_eq_rat T) X5)))))))
% 6.73/7.04 (assert (forall ((T tptp.num)) (exists ((Z tptp.num)) (forall ((X5 tptp.num)) (=> (@ (@ tptp.ord_less_num X5) Z) (not (@ (@ tptp.ord_less_eq_num T) X5)))))))
% 6.73/7.04 (assert (forall ((T tptp.nat)) (exists ((Z tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Z) (not (@ (@ tptp.ord_less_eq_nat T) X5)))))))
% 6.73/7.04 (assert (forall ((T tptp.int)) (exists ((Z tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int X5) Z) (not (@ (@ tptp.ord_less_eq_int T) X5)))))))
% 6.73/7.04 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (Ys tptp.list_VEBT_VEBT)) (= (@ tptp.size_s7466405169056248089T_VEBT (@ (@ tptp.produc4743750530478302277T_VEBT Xs2) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (@ tptp.size_s6755466524823107622T_VEBT Ys)))))
% 6.73/7.04 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (Ys tptp.list_o)) (= (@ tptp.size_s9168528473962070013VEBT_o (@ (@ tptp.product_VEBT_VEBT_o Xs2) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (@ tptp.size_size_list_o Ys)))))
% 6.73/7.04 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (Ys tptp.list_nat)) (= (@ tptp.size_s6152045936467909847BT_nat (@ (@ tptp.produc7295137177222721919BT_nat Xs2) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (@ tptp.size_size_list_nat Ys)))))
% 6.73/7.04 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (Ys tptp.list_int)) (= (@ tptp.size_s3661962791536183091BT_int (@ (@ tptp.produc7292646706713671643BT_int Xs2) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (@ tptp.size_size_list_int Ys)))))
% 6.73/7.04 (assert (forall ((Xs2 tptp.list_o) (Ys tptp.list_VEBT_VEBT)) (= (@ tptp.size_s4313452262239582901T_VEBT (@ (@ tptp.product_o_VEBT_VEBT Xs2) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_o Xs2)) (@ tptp.size_s6755466524823107622T_VEBT Ys)))))
% 6.73/7.04 (assert (forall ((Xs2 tptp.list_o) (Ys tptp.list_o)) (= (@ tptp.size_s1515746228057227161od_o_o (@ (@ tptp.product_o_o Xs2) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_o Xs2)) (@ tptp.size_size_list_o Ys)))))
% 6.73/7.04 (assert (forall ((Xs2 tptp.list_o) (Ys tptp.list_nat)) (= (@ tptp.size_s5443766701097040955_o_nat (@ (@ tptp.product_o_nat Xs2) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_o Xs2)) (@ tptp.size_size_list_nat Ys)))))
% 6.73/7.04 (assert (forall ((Xs2 tptp.list_o) (Ys tptp.list_int)) (= (@ tptp.size_s2953683556165314199_o_int (@ (@ tptp.product_o_int Xs2) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_o Xs2)) (@ tptp.size_size_list_int Ys)))))
% 6.73/7.04 (assert (forall ((Xs2 tptp.list_nat) (Ys tptp.list_VEBT_VEBT)) (= (@ tptp.size_s4762443039079500285T_VEBT (@ (@ tptp.produc7156399406898700509T_VEBT Xs2) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_nat Xs2)) (@ tptp.size_s6755466524823107622T_VEBT Ys)))))
% 6.73/7.04 (assert (forall ((Xs2 tptp.list_nat) (Ys tptp.list_o)) (= (@ tptp.size_s6491369823275344609_nat_o (@ (@ tptp.product_nat_o Xs2) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_nat Xs2)) (@ tptp.size_size_list_o Ys)))))
% 6.73/7.04 (assert (forall ((A tptp.real) (B tptp.real) (P2 (-> tptp.real Bool))) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ P2 A) (=> (not (@ P2 B)) (exists ((C tptp.real)) (and (@ (@ tptp.ord_less_eq_real A) C) (@ (@ tptp.ord_less_eq_real C) B) (forall ((X5 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real A) X5) (@ (@ tptp.ord_less_real X5) C)) (@ P2 X5))) (forall ((D4 tptp.real)) (=> (forall ((X3 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real A) X3) (@ (@ tptp.ord_less_real X3) D4)) (@ P2 X3))) (@ (@ tptp.ord_less_eq_real D4) C))))))))))
% 6.73/7.04 (assert (forall ((A tptp.nat) (B tptp.nat) (P2 (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ P2 A) (=> (not (@ P2 B)) (exists ((C tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat A) C) (@ (@ tptp.ord_less_eq_nat C) B) (forall ((X5 tptp.nat)) (=> (and (@ (@ tptp.ord_less_eq_nat A) X5) (@ (@ tptp.ord_less_nat X5) C)) (@ P2 X5))) (forall ((D4 tptp.nat)) (=> (forall ((X3 tptp.nat)) (=> (and (@ (@ tptp.ord_less_eq_nat A) X3) (@ (@ tptp.ord_less_nat X3) D4)) (@ P2 X3))) (@ (@ tptp.ord_less_eq_nat D4) C))))))))))
% 6.73/7.04 (assert (forall ((A tptp.int) (B tptp.int) (P2 (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ P2 A) (=> (not (@ P2 B)) (exists ((C tptp.int)) (and (@ (@ tptp.ord_less_eq_int A) C) (@ (@ tptp.ord_less_eq_int C) B) (forall ((X5 tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int A) X5) (@ (@ tptp.ord_less_int X5) C)) (@ P2 X5))) (forall ((D4 tptp.int)) (=> (forall ((X3 tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int A) X3) (@ (@ tptp.ord_less_int X3) D4)) (@ P2 X3))) (@ (@ tptp.ord_less_eq_int D4) C))))))))))
% 6.73/7.04 (assert (forall ((V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (X tptp.nat)) (let ((_let_1 (@ tptp.suc (@ tptp.suc V2)))) (= (@ (@ 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)))))
% 6.73/7.04 (assert (forall ((I2 tptp.nat) (Xs2 tptp.list_Code_integer) (Ys tptp.list_Code_integer)) (let ((_let_1 (@ tptp.ord_less_nat I2))) (=> (@ _let_1 (@ tptp.size_s3445333598471063425nteger Xs2)) (=> (@ _let_1 (@ tptp.size_s3445333598471063425nteger Ys)) (= (@ (@ tptp.nth_Pr2304437835452373666nteger (@ (@ tptp.zip_Co3543743374963494515nteger Xs2) Ys)) I2) (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.nth_Code_integer Xs2) I2)) (@ (@ tptp.nth_Code_integer Ys) I2))))))))
% 6.73/7.04 (assert (forall ((I2 tptp.nat) (Xs2 tptp.list_VEBT_VEBT) (Ys tptp.list_VEBT_VEBT)) (let ((_let_1 (@ tptp.ord_less_nat I2))) (=> (@ _let_1 (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (=> (@ _let_1 (@ tptp.size_s6755466524823107622T_VEBT Ys)) (= (@ (@ tptp.nth_Pr4953567300277697838T_VEBT (@ (@ tptp.zip_VE537291747668921783T_VEBT Xs2) Ys)) I2) (@ (@ tptp.produc537772716801021591T_VEBT (@ (@ tptp.nth_VEBT_VEBT Xs2) I2)) (@ (@ tptp.nth_VEBT_VEBT Ys) I2))))))))
% 6.73/7.04 (assert (forall ((I2 tptp.nat) (Xs2 tptp.list_VEBT_VEBT) (Ys tptp.list_o)) (let ((_let_1 (@ tptp.ord_less_nat I2))) (=> (@ _let_1 (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (=> (@ _let_1 (@ tptp.size_size_list_o Ys)) (= (@ (@ tptp.nth_Pr4606735188037164562VEBT_o (@ (@ tptp.zip_VEBT_VEBT_o Xs2) Ys)) I2) (@ (@ tptp.produc8721562602347293563VEBT_o (@ (@ tptp.nth_VEBT_VEBT Xs2) I2)) (@ (@ tptp.nth_o Ys) I2))))))))
% 6.73/7.04 (assert (forall ((I2 tptp.nat) (Xs2 tptp.list_VEBT_VEBT) (Ys tptp.list_nat)) (let ((_let_1 (@ tptp.ord_less_nat I2))) (=> (@ _let_1 (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (=> (@ _let_1 (@ tptp.size_size_list_nat Ys)) (= (@ (@ tptp.nth_Pr1791586995822124652BT_nat (@ (@ tptp.zip_VEBT_VEBT_nat Xs2) Ys)) I2) (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.nth_VEBT_VEBT Xs2) I2)) (@ (@ tptp.nth_nat Ys) I2))))))))
% 6.73/7.04 (assert (forall ((I2 tptp.nat) (Xs2 tptp.list_VEBT_VEBT) (Ys tptp.list_int)) (let ((_let_1 (@ tptp.ord_less_nat I2))) (=> (@ _let_1 (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (=> (@ _let_1 (@ tptp.size_size_list_int Ys)) (= (@ (@ tptp.nth_Pr6837108013167703752BT_int (@ (@ tptp.zip_VEBT_VEBT_int Xs2) Ys)) I2) (@ (@ tptp.produc736041933913180425BT_int (@ (@ tptp.nth_VEBT_VEBT Xs2) I2)) (@ (@ tptp.nth_int Ys) I2))))))))
% 6.73/7.04 (assert (forall ((I2 tptp.nat) (Xs2 tptp.list_o) (Ys tptp.list_VEBT_VEBT)) (let ((_let_1 (@ tptp.ord_less_nat I2))) (=> (@ _let_1 (@ tptp.size_size_list_o Xs2)) (=> (@ _let_1 (@ tptp.size_s6755466524823107622T_VEBT Ys)) (= (@ (@ tptp.nth_Pr6777367263587873994T_VEBT (@ (@ tptp.zip_o_VEBT_VEBT Xs2) Ys)) I2) (@ (@ tptp.produc2982872950893828659T_VEBT (@ (@ tptp.nth_o Xs2) I2)) (@ (@ tptp.nth_VEBT_VEBT Ys) I2))))))))
% 6.73/7.04 (assert (forall ((I2 tptp.nat) (Xs2 tptp.list_o) (Ys tptp.list_o)) (let ((_let_1 (@ tptp.ord_less_nat I2))) (=> (@ _let_1 (@ tptp.size_size_list_o Xs2)) (=> (@ _let_1 (@ tptp.size_size_list_o Ys)) (= (@ (@ tptp.nth_Product_prod_o_o (@ (@ tptp.zip_o_o Xs2) Ys)) I2) (@ (@ tptp.product_Pair_o_o (@ (@ tptp.nth_o Xs2) I2)) (@ (@ tptp.nth_o Ys) I2))))))))
% 6.73/7.04 (assert (forall ((I2 tptp.nat) (Xs2 tptp.list_o) (Ys tptp.list_nat)) (let ((_let_1 (@ tptp.ord_less_nat I2))) (=> (@ _let_1 (@ tptp.size_size_list_o Xs2)) (=> (@ _let_1 (@ tptp.size_size_list_nat Ys)) (= (@ (@ tptp.nth_Pr5826913651314560976_o_nat (@ (@ tptp.zip_o_nat Xs2) Ys)) I2) (@ (@ tptp.product_Pair_o_nat (@ (@ tptp.nth_o Xs2) I2)) (@ (@ tptp.nth_nat Ys) I2))))))))
% 6.73/7.04 (assert (forall ((I2 tptp.nat) (Xs2 tptp.list_o) (Ys tptp.list_int)) (let ((_let_1 (@ tptp.ord_less_nat I2))) (=> (@ _let_1 (@ tptp.size_size_list_o Xs2)) (=> (@ _let_1 (@ tptp.size_size_list_int Ys)) (= (@ (@ tptp.nth_Pr1649062631805364268_o_int (@ (@ tptp.zip_o_int Xs2) Ys)) I2) (@ (@ tptp.product_Pair_o_int (@ (@ tptp.nth_o Xs2) I2)) (@ (@ tptp.nth_int Ys) I2))))))))
% 6.73/7.04 (assert (forall ((I2 tptp.nat) (Xs2 tptp.list_nat) (Ys tptp.list_VEBT_VEBT)) (let ((_let_1 (@ tptp.ord_less_nat I2))) (=> (@ _let_1 (@ tptp.size_size_list_nat Xs2)) (=> (@ _let_1 (@ tptp.size_s6755466524823107622T_VEBT Ys)) (= (@ (@ tptp.nth_Pr744662078594809490T_VEBT (@ (@ tptp.zip_nat_VEBT_VEBT Xs2) Ys)) I2) (@ (@ tptp.produc599794634098209291T_VEBT (@ (@ tptp.nth_nat Xs2) I2)) (@ (@ tptp.nth_VEBT_VEBT Ys) I2))))))))
% 6.73/7.04 (assert (forall ((X tptp.product_prod_nat_nat) (P2 (-> tptp.product_prod_nat_nat Bool)) (Xs2 tptp.list_P6011104703257516679at_nat)) (= (= (@ tptp.some_P7363390416028606310at_nat X) (@ (@ tptp.find_P8199882355184865565at_nat P2) Xs2)) (exists ((I tptp.nat)) (let ((_let_1 (@ (@ tptp.nth_Pr7617993195940197384at_nat Xs2) I))) (and (@ (@ tptp.ord_less_nat I) (@ tptp.size_s5460976970255530739at_nat Xs2)) (@ P2 _let_1) (= X _let_1) (forall ((J tptp.nat)) (=> (@ (@ tptp.ord_less_nat J) I) (not (@ P2 (@ (@ tptp.nth_Pr7617993195940197384at_nat Xs2) J)))))))))))
% 6.73/7.04 (assert (forall ((X tptp.num) (P2 (-> tptp.num Bool)) (Xs2 tptp.list_num)) (= (= (@ tptp.some_num X) (@ (@ tptp.find_num P2) Xs2)) (exists ((I tptp.nat)) (let ((_let_1 (@ (@ tptp.nth_num Xs2) I))) (and (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_num Xs2)) (@ P2 _let_1) (= X _let_1) (forall ((J tptp.nat)) (=> (@ (@ tptp.ord_less_nat J) I) (not (@ P2 (@ (@ tptp.nth_num Xs2) J)))))))))))
% 6.73/7.04 (assert (forall ((X tptp.vEBT_VEBT) (P2 (-> tptp.vEBT_VEBT Bool)) (Xs2 tptp.list_VEBT_VEBT)) (= (= (@ tptp.some_VEBT_VEBT X) (@ (@ tptp.find_VEBT_VEBT P2) Xs2)) (exists ((I tptp.nat)) (let ((_let_1 (@ (@ tptp.nth_VEBT_VEBT Xs2) I))) (and (@ (@ tptp.ord_less_nat I) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (@ P2 _let_1) (= X _let_1) (forall ((J tptp.nat)) (=> (@ (@ tptp.ord_less_nat J) I) (not (@ P2 (@ (@ tptp.nth_VEBT_VEBT Xs2) J)))))))))))
% 6.73/7.04 (assert (forall ((X Bool) (P2 (-> Bool Bool)) (Xs2 tptp.list_o)) (= (= (@ tptp.some_o X) (@ (@ tptp.find_o P2) Xs2)) (exists ((I tptp.nat)) (let ((_let_1 (@ (@ tptp.nth_o Xs2) I))) (and (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_o Xs2)) (@ P2 _let_1) (= X _let_1) (forall ((J tptp.nat)) (=> (@ (@ tptp.ord_less_nat J) I) (not (@ P2 (@ (@ tptp.nth_o Xs2) J)))))))))))
% 6.73/7.04 (assert (forall ((X tptp.nat) (P2 (-> tptp.nat Bool)) (Xs2 tptp.list_nat)) (= (= (@ tptp.some_nat X) (@ (@ tptp.find_nat P2) Xs2)) (exists ((I tptp.nat)) (let ((_let_1 (@ (@ tptp.nth_nat Xs2) I))) (and (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_nat Xs2)) (@ P2 _let_1) (= X _let_1) (forall ((J tptp.nat)) (=> (@ (@ tptp.ord_less_nat J) I) (not (@ P2 (@ (@ tptp.nth_nat Xs2) J)))))))))))
% 6.73/7.04 (assert (forall ((X tptp.int) (P2 (-> tptp.int Bool)) (Xs2 tptp.list_int)) (= (= (@ tptp.some_int X) (@ (@ tptp.find_int P2) Xs2)) (exists ((I tptp.nat)) (let ((_let_1 (@ (@ tptp.nth_int Xs2) I))) (and (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_int Xs2)) (@ P2 _let_1) (= X _let_1) (forall ((J tptp.nat)) (=> (@ (@ tptp.ord_less_nat J) I) (not (@ P2 (@ (@ tptp.nth_int Xs2) J)))))))))))
% 6.73/7.04 (assert (forall ((P2 (-> tptp.product_prod_nat_nat Bool)) (Xs2 tptp.list_P6011104703257516679at_nat) (X tptp.product_prod_nat_nat)) (= (= (@ (@ tptp.find_P8199882355184865565at_nat P2) Xs2) (@ tptp.some_P7363390416028606310at_nat X)) (exists ((I tptp.nat)) (let ((_let_1 (@ (@ tptp.nth_Pr7617993195940197384at_nat Xs2) I))) (and (@ (@ tptp.ord_less_nat I) (@ tptp.size_s5460976970255530739at_nat Xs2)) (@ P2 _let_1) (= X _let_1) (forall ((J tptp.nat)) (=> (@ (@ tptp.ord_less_nat J) I) (not (@ P2 (@ (@ tptp.nth_Pr7617993195940197384at_nat Xs2) J)))))))))))
% 6.73/7.04 (assert (forall ((P2 (-> tptp.num Bool)) (Xs2 tptp.list_num) (X tptp.num)) (= (= (@ (@ tptp.find_num P2) Xs2) (@ tptp.some_num X)) (exists ((I tptp.nat)) (let ((_let_1 (@ (@ tptp.nth_num Xs2) I))) (and (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_num Xs2)) (@ P2 _let_1) (= X _let_1) (forall ((J tptp.nat)) (=> (@ (@ tptp.ord_less_nat J) I) (not (@ P2 (@ (@ tptp.nth_num Xs2) J)))))))))))
% 6.73/7.04 (assert (forall ((P2 (-> tptp.vEBT_VEBT Bool)) (Xs2 tptp.list_VEBT_VEBT) (X tptp.vEBT_VEBT)) (= (= (@ (@ tptp.find_VEBT_VEBT P2) Xs2) (@ tptp.some_VEBT_VEBT X)) (exists ((I tptp.nat)) (let ((_let_1 (@ (@ tptp.nth_VEBT_VEBT Xs2) I))) (and (@ (@ tptp.ord_less_nat I) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (@ P2 _let_1) (= X _let_1) (forall ((J tptp.nat)) (=> (@ (@ tptp.ord_less_nat J) I) (not (@ P2 (@ (@ tptp.nth_VEBT_VEBT Xs2) J)))))))))))
% 6.73/7.04 (assert (forall ((P2 (-> Bool Bool)) (Xs2 tptp.list_o) (X Bool)) (= (= (@ (@ tptp.find_o P2) Xs2) (@ tptp.some_o X)) (exists ((I tptp.nat)) (let ((_let_1 (@ (@ tptp.nth_o Xs2) I))) (and (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_o Xs2)) (@ P2 _let_1) (= X _let_1) (forall ((J tptp.nat)) (=> (@ (@ tptp.ord_less_nat J) I) (not (@ P2 (@ (@ tptp.nth_o Xs2) J)))))))))))
% 6.73/7.04 (assert (forall ((P2 (-> tptp.nat Bool)) (Xs2 tptp.list_nat) (X tptp.nat)) (= (= (@ (@ tptp.find_nat P2) Xs2) (@ tptp.some_nat X)) (exists ((I tptp.nat)) (let ((_let_1 (@ (@ tptp.nth_nat Xs2) I))) (and (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_nat Xs2)) (@ P2 _let_1) (= X _let_1) (forall ((J tptp.nat)) (=> (@ (@ tptp.ord_less_nat J) I) (not (@ P2 (@ (@ tptp.nth_nat Xs2) J)))))))))))
% 6.73/7.04 (assert (forall ((P2 (-> tptp.int Bool)) (Xs2 tptp.list_int) (X tptp.int)) (= (= (@ (@ tptp.find_int P2) Xs2) (@ tptp.some_int X)) (exists ((I tptp.nat)) (let ((_let_1 (@ (@ tptp.nth_int Xs2) I))) (and (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_int Xs2)) (@ P2 _let_1) (= X _let_1) (forall ((J tptp.nat)) (=> (@ (@ tptp.ord_less_nat J) I) (not (@ P2 (@ (@ tptp.nth_int Xs2) J)))))))))))
% 6.73/7.04 (assert (forall ((N tptp.nat) (X tptp.vEBT_VEBT) (Xs2 tptp.list_VEBT_VEBT)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.nth_VEBT_VEBT (@ (@ tptp.cons_VEBT_VEBT X) Xs2)) N) (@ (@ tptp.nth_VEBT_VEBT Xs2) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat))))))
% 6.73/7.04 (assert (forall ((N tptp.nat) (X tptp.nat) (Xs2 tptp.list_nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.nth_nat (@ (@ tptp.cons_nat X) Xs2)) N) (@ (@ tptp.nth_nat Xs2) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat))))))
% 6.73/7.04 (assert (forall ((Xs2 tptp.list_VEBT_VEBT)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_s6755466524823107622T_VEBT Xs2)) tptp.one_one_nat) (= (@ tptp.rotate1_VEBT_VEBT Xs2) Xs2))))
% 6.73/7.04 (assert (forall ((Xs2 tptp.list_o)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_o Xs2)) tptp.one_one_nat) (= (@ tptp.rotate1_o Xs2) Xs2))))
% 6.73/7.04 (assert (forall ((Xs2 tptp.list_nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_nat Xs2)) tptp.one_one_nat) (= (@ tptp.rotate1_nat Xs2) Xs2))))
% 6.73/7.04 (assert (forall ((Xs2 tptp.list_int)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_int Xs2)) tptp.one_one_nat) (= (@ tptp.rotate1_int Xs2) Xs2))))
% 6.73/7.04 (assert (forall ((Xs2 tptp.list_VEBT_VEBT)) (= (@ tptp.size_s6755466524823107622T_VEBT (@ tptp.rotate1_VEBT_VEBT Xs2)) (@ tptp.size_s6755466524823107622T_VEBT Xs2))))
% 6.73/7.04 (assert (forall ((Xs2 tptp.list_o)) (= (@ tptp.size_size_list_o (@ tptp.rotate1_o Xs2)) (@ tptp.size_size_list_o Xs2))))
% 6.73/7.04 (assert (forall ((Xs2 tptp.list_nat)) (= (@ tptp.size_size_list_nat (@ tptp.rotate1_nat Xs2)) (@ tptp.size_size_list_nat Xs2))))
% 6.73/7.04 (assert (forall ((Xs2 tptp.list_int)) (= (@ tptp.size_size_list_int (@ tptp.rotate1_int Xs2)) (@ tptp.size_size_list_int Xs2))))
% 6.73/7.04 (assert (forall ((X tptp.vEBT_VEBT) (Xs2 tptp.list_VEBT_VEBT) (N tptp.nat)) (= (@ (@ tptp.nth_VEBT_VEBT (@ (@ tptp.cons_VEBT_VEBT X) Xs2)) (@ tptp.suc N)) (@ (@ tptp.nth_VEBT_VEBT Xs2) N))))
% 6.73/7.04 (assert (forall ((X tptp.nat) (Xs2 tptp.list_nat) (N tptp.nat)) (= (@ (@ tptp.nth_nat (@ (@ tptp.cons_nat X) Xs2)) (@ tptp.suc N)) (@ (@ tptp.nth_nat Xs2) N))))
% 6.73/7.04 (assert (forall ((X tptp.vEBT_VEBT) (Xs2 tptp.list_VEBT_VEBT)) (= (@ (@ tptp.nth_VEBT_VEBT (@ (@ tptp.cons_VEBT_VEBT X) Xs2)) tptp.zero_zero_nat) X)))
% 6.73/7.04 (assert (forall ((X tptp.nat) (Xs2 tptp.list_nat)) (= (@ (@ tptp.nth_nat (@ (@ tptp.cons_nat X) Xs2)) tptp.zero_zero_nat) X)))
% 6.73/7.04 (assert (forall ((X tptp.code_integer) (Xs2 tptp.list_Code_integer) (Y tptp.code_integer) (Ys tptp.list_Code_integer)) (= (@ (@ tptp.zip_Co3543743374963494515nteger (@ (@ tptp.cons_Code_integer X) Xs2)) (@ (@ tptp.cons_Code_integer Y) Ys)) (@ (@ tptp.cons_P9044669534377732177nteger (@ (@ tptp.produc1086072967326762835nteger X) Y)) (@ (@ tptp.zip_Co3543743374963494515nteger Xs2) Ys)))))
% 6.73/7.04 (assert (forall ((X tptp.product_prod_nat_nat) (Xs2 tptp.list_P6011104703257516679at_nat) (Y tptp.product_prod_nat_nat) (Ys tptp.list_P6011104703257516679at_nat)) (= (@ (@ tptp.zip_Pr4664179122662387191at_nat (@ (@ tptp.cons_P6512896166579812791at_nat X) Xs2)) (@ (@ tptp.cons_P6512896166579812791at_nat Y) Ys)) (@ (@ tptp.cons_P8732206157123786781at_nat (@ (@ tptp.produc6161850002892822231at_nat X) Y)) (@ (@ tptp.zip_Pr4664179122662387191at_nat Xs2) Ys)))))
% 6.73/7.04 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat) (Xs2 tptp.list_s1210847774152347623at_nat) (Y tptp.set_Pr1261947904930325089at_nat) (Ys tptp.list_s1210847774152347623at_nat)) (= (@ (@ tptp.zip_se5600341670672612855at_nat (@ (@ tptp.cons_s6881495754146722583at_nat X) Xs2)) (@ (@ tptp.cons_s6881495754146722583at_nat Y) Ys)) (@ (@ tptp.cons_P3940603068885512221at_nat (@ (@ tptp.produc2922128104949294807at_nat X) Y)) (@ (@ tptp.zip_se5600341670672612855at_nat Xs2) Ys)))))
% 6.73/7.04 (assert (forall ((X tptp.nat) (Xs2 tptp.list_nat) (Y tptp.nat) (Ys tptp.list_nat)) (= (@ (@ tptp.zip_nat_nat (@ (@ tptp.cons_nat X) Xs2)) (@ (@ tptp.cons_nat Y) Ys)) (@ (@ tptp.cons_P6512896166579812791at_nat (@ (@ tptp.product_Pair_nat_nat X) Y)) (@ (@ tptp.zip_nat_nat Xs2) Ys)))))
% 6.73/7.04 (assert (forall ((X tptp.int) (Xs2 tptp.list_int) (Y tptp.int) (Ys tptp.list_int)) (= (@ (@ tptp.zip_int_int (@ (@ tptp.cons_int X) Xs2)) (@ (@ tptp.cons_int Y) Ys)) (@ (@ tptp.cons_P3334398858971670639nt_int (@ (@ tptp.product_Pair_int_int X) Y)) (@ (@ tptp.zip_int_int Xs2) Ys)))))
% 6.73/7.04 (assert (forall ((N tptp.nat) (X tptp.nat) (Xs2 tptp.list_nat)) (= (@ (@ tptp.enumerate_nat N) (@ (@ tptp.cons_nat X) Xs2)) (@ (@ tptp.cons_P6512896166579812791at_nat (@ (@ tptp.product_Pair_nat_nat N) X)) (@ (@ tptp.enumerate_nat (@ tptp.suc N)) Xs2)))))
% 6.73/7.04 (assert (forall ((Xs2 tptp.list_Code_integer) (Ys tptp.list_Code_integer) (Xy tptp.produc8923325533196201883nteger) (Xys tptp.list_P5578671422887162913nteger)) (=> (= (@ (@ tptp.zip_Co3543743374963494515nteger Xs2) Ys) (@ (@ tptp.cons_P9044669534377732177nteger Xy) Xys)) (not (forall ((X3 tptp.code_integer) (Xs4 tptp.list_Code_integer)) (=> (= Xs2 (@ (@ tptp.cons_Code_integer X3) Xs4)) (forall ((Y3 tptp.code_integer) (Ys4 tptp.list_Code_integer)) (=> (= Ys (@ (@ tptp.cons_Code_integer Y3) Ys4)) (=> (= Xy (@ (@ tptp.produc1086072967326762835nteger X3) Y3)) (not (= Xys (@ (@ tptp.zip_Co3543743374963494515nteger Xs4) Ys4))))))))))))
% 6.73/7.04 (assert (forall ((Xs2 tptp.list_P6011104703257516679at_nat) (Ys tptp.list_P6011104703257516679at_nat) (Xy tptp.produc859450856879609959at_nat) (Xys tptp.list_P8469869581646625389at_nat)) (=> (= (@ (@ tptp.zip_Pr4664179122662387191at_nat Xs2) Ys) (@ (@ tptp.cons_P8732206157123786781at_nat Xy) Xys)) (not (forall ((X3 tptp.product_prod_nat_nat) (Xs4 tptp.list_P6011104703257516679at_nat)) (=> (= Xs2 (@ (@ tptp.cons_P6512896166579812791at_nat X3) Xs4)) (forall ((Y3 tptp.product_prod_nat_nat) (Ys4 tptp.list_P6011104703257516679at_nat)) (=> (= Ys (@ (@ tptp.cons_P6512896166579812791at_nat Y3) Ys4)) (=> (= Xy (@ (@ tptp.produc6161850002892822231at_nat X3) Y3)) (not (= Xys (@ (@ tptp.zip_Pr4664179122662387191at_nat Xs4) Ys4))))))))))))
% 6.73/7.04 (assert (forall ((Xs2 tptp.list_s1210847774152347623at_nat) (Ys tptp.list_s1210847774152347623at_nat) (Xy tptp.produc3843707927480180839at_nat) (Xys tptp.list_P5464809261938338413at_nat)) (=> (= (@ (@ tptp.zip_se5600341670672612855at_nat Xs2) Ys) (@ (@ tptp.cons_P3940603068885512221at_nat Xy) Xys)) (not (forall ((X3 tptp.set_Pr1261947904930325089at_nat) (Xs4 tptp.list_s1210847774152347623at_nat)) (=> (= Xs2 (@ (@ tptp.cons_s6881495754146722583at_nat X3) Xs4)) (forall ((Y3 tptp.set_Pr1261947904930325089at_nat) (Ys4 tptp.list_s1210847774152347623at_nat)) (=> (= Ys (@ (@ tptp.cons_s6881495754146722583at_nat Y3) Ys4)) (=> (= Xy (@ (@ tptp.produc2922128104949294807at_nat X3) Y3)) (not (= Xys (@ (@ tptp.zip_se5600341670672612855at_nat Xs4) Ys4))))))))))))
% 6.73/7.04 (assert (forall ((Xs2 tptp.list_nat) (Ys tptp.list_nat) (Xy tptp.product_prod_nat_nat) (Xys tptp.list_P6011104703257516679at_nat)) (=> (= (@ (@ tptp.zip_nat_nat Xs2) Ys) (@ (@ tptp.cons_P6512896166579812791at_nat Xy) Xys)) (not (forall ((X3 tptp.nat) (Xs4 tptp.list_nat)) (=> (= Xs2 (@ (@ tptp.cons_nat X3) Xs4)) (forall ((Y3 tptp.nat) (Ys4 tptp.list_nat)) (=> (= Ys (@ (@ tptp.cons_nat Y3) Ys4)) (=> (= Xy (@ (@ tptp.product_Pair_nat_nat X3) Y3)) (not (= Xys (@ (@ tptp.zip_nat_nat Xs4) Ys4))))))))))))
% 6.73/7.04 (assert (forall ((Xs2 tptp.list_int) (Ys tptp.list_int) (Xy tptp.product_prod_int_int) (Xys tptp.list_P5707943133018811711nt_int)) (=> (= (@ (@ tptp.zip_int_int Xs2) Ys) (@ (@ tptp.cons_P3334398858971670639nt_int Xy) Xys)) (not (forall ((X3 tptp.int) (Xs4 tptp.list_int)) (=> (= Xs2 (@ (@ tptp.cons_int X3) Xs4)) (forall ((Y3 tptp.int) (Ys4 tptp.list_int)) (=> (= Ys (@ (@ tptp.cons_int Y3) Ys4)) (=> (= Xy (@ (@ tptp.product_Pair_int_int X3) Y3)) (not (= Xys (@ (@ tptp.zip_int_int Xs4) Ys4))))))))))))
% 6.73/7.04 (assert (forall ((P2 (-> tptp.product_prod_nat_nat Bool)) (X tptp.product_prod_nat_nat) (Xs2 tptp.list_P6011104703257516679at_nat)) (let ((_let_1 (@ tptp.find_P8199882355184865565at_nat P2))) (let ((_let_2 (@ _let_1 (@ (@ tptp.cons_P6512896166579812791at_nat X) Xs2)))) (let ((_let_3 (@ P2 X))) (and (=> _let_3 (= _let_2 (@ tptp.some_P7363390416028606310at_nat X))) (=> (not _let_3) (= _let_2 (@ _let_1 Xs2)))))))))
% 6.73/7.04 (assert (forall ((P2 (-> tptp.nat Bool)) (X tptp.nat) (Xs2 tptp.list_nat)) (let ((_let_1 (@ tptp.find_nat P2))) (let ((_let_2 (@ _let_1 (@ (@ tptp.cons_nat X) Xs2)))) (let ((_let_3 (@ P2 X))) (and (=> _let_3 (= _let_2 (@ tptp.some_nat X))) (=> (not _let_3) (= _let_2 (@ _let_1 Xs2)))))))))
% 6.73/7.04 (assert (forall ((P2 (-> tptp.num Bool)) (X tptp.num) (Xs2 tptp.list_num)) (let ((_let_1 (@ tptp.find_num P2))) (let ((_let_2 (@ _let_1 (@ (@ tptp.cons_num X) Xs2)))) (let ((_let_3 (@ P2 X))) (and (=> _let_3 (= _let_2 (@ tptp.some_num X))) (=> (not _let_3) (= _let_2 (@ _let_1 Xs2)))))))))
% 6.73/7.04 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer) (Xs2 tptp.list_Code_integer) (Ys tptp.list_Code_integer)) (=> (@ (@ tptp.member157494554546826820nteger (@ (@ tptp.produc1086072967326762835nteger X) Y)) (@ tptp.set_Pr920681315882439344nteger (@ (@ tptp.zip_Co3543743374963494515nteger Xs2) Ys))) (@ (@ tptp.member_Code_integer Y) (@ tptp.set_Code_integer2 Ys)))))
% 6.73/7.04 (assert (forall ((X tptp.product_prod_nat_nat) (Y tptp.product_prod_nat_nat) (Xs2 tptp.list_P6011104703257516679at_nat) (Ys tptp.list_P6011104703257516679at_nat)) (=> (@ (@ tptp.member8206827879206165904at_nat (@ (@ tptp.produc6161850002892822231at_nat X) Y)) (@ tptp.set_Pr5518436109238095868at_nat (@ (@ tptp.zip_Pr4664179122662387191at_nat Xs2) Ys))) (@ (@ tptp.member8440522571783428010at_nat Y) (@ tptp.set_Pr5648618587558075414at_nat Ys)))))
% 6.73/7.04 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat) (Xs2 tptp.list_s1210847774152347623at_nat) (Ys tptp.list_s1210847774152347623at_nat)) (=> (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat X) Y)) (@ tptp.set_Pr3765526544606949372at_nat (@ (@ tptp.zip_se5600341670672612855at_nat Xs2) Ys))) (@ (@ tptp.member2643936169264416010at_nat Y) (@ tptp.set_se5049602875457034614at_nat Ys)))))
% 6.73/7.04 (assert (forall ((X tptp.nat) (Y tptp.nat) (Xs2 tptp.list_nat) (Ys tptp.list_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X) Y)) (@ tptp.set_Pr5648618587558075414at_nat (@ (@ tptp.zip_nat_nat Xs2) Ys))) (@ (@ tptp.member_nat Y) (@ tptp.set_nat2 Ys)))))
% 6.73/7.04 (assert (forall ((X tptp.int) (Y tptp.int) (Xs2 tptp.list_int) (Ys tptp.list_int)) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X) Y)) (@ tptp.set_Pr2470121279949933262nt_int (@ (@ tptp.zip_int_int Xs2) Ys))) (@ (@ tptp.member_int Y) (@ tptp.set_int2 Ys)))))
% 6.73/7.04 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer) (Xs2 tptp.list_Code_integer) (Ys tptp.list_Code_integer)) (=> (@ (@ tptp.member157494554546826820nteger (@ (@ tptp.produc1086072967326762835nteger X) Y)) (@ tptp.set_Pr920681315882439344nteger (@ (@ tptp.zip_Co3543743374963494515nteger Xs2) Ys))) (@ (@ tptp.member_Code_integer X) (@ tptp.set_Code_integer2 Xs2)))))
% 6.73/7.04 (assert (forall ((X tptp.product_prod_nat_nat) (Y tptp.product_prod_nat_nat) (Xs2 tptp.list_P6011104703257516679at_nat) (Ys tptp.list_P6011104703257516679at_nat)) (=> (@ (@ tptp.member8206827879206165904at_nat (@ (@ tptp.produc6161850002892822231at_nat X) Y)) (@ tptp.set_Pr5518436109238095868at_nat (@ (@ tptp.zip_Pr4664179122662387191at_nat Xs2) Ys))) (@ (@ tptp.member8440522571783428010at_nat X) (@ tptp.set_Pr5648618587558075414at_nat Xs2)))))
% 6.73/7.04 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat) (Xs2 tptp.list_s1210847774152347623at_nat) (Ys tptp.list_s1210847774152347623at_nat)) (=> (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat X) Y)) (@ tptp.set_Pr3765526544606949372at_nat (@ (@ tptp.zip_se5600341670672612855at_nat Xs2) Ys))) (@ (@ tptp.member2643936169264416010at_nat X) (@ tptp.set_se5049602875457034614at_nat Xs2)))))
% 6.73/7.04 (assert (forall ((X tptp.nat) (Y tptp.nat) (Xs2 tptp.list_nat) (Ys tptp.list_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X) Y)) (@ tptp.set_Pr5648618587558075414at_nat (@ (@ tptp.zip_nat_nat Xs2) Ys))) (@ (@ tptp.member_nat X) (@ tptp.set_nat2 Xs2)))))
% 6.73/7.04 (assert (forall ((X tptp.int) (Y tptp.int) (Xs2 tptp.list_int) (Ys tptp.list_int)) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X) Y)) (@ tptp.set_Pr2470121279949933262nt_int (@ (@ tptp.zip_int_int Xs2) Ys))) (@ (@ tptp.member_int X) (@ tptp.set_int2 Xs2)))))
% 6.73/7.04 (assert (forall ((X tptp.complex) (Y tptp.complex) (Xs2 tptp.list_complex) (Ys tptp.list_complex)) (=> (@ (@ tptp.member5793383173714906214omplex (@ (@ tptp.produc101793102246108661omplex X) Y)) (@ tptp.set_Pr8199049879907524818omplex (@ (@ tptp.zip_complex_complex Xs2) Ys))) (not (=> (@ (@ tptp.member_complex X) (@ tptp.set_complex2 Xs2)) (not (@ (@ tptp.member_complex Y) (@ tptp.set_complex2 Ys))))))))
% 6.73/7.04 (assert (forall ((X tptp.complex) (Y tptp.real) (Xs2 tptp.list_complex) (Ys tptp.list_real)) (=> (@ (@ tptp.member47443559803733732x_real (@ (@ tptp.produc1746590499379883635x_real X) Y)) (@ tptp.set_Pr1225976482156248400x_real (@ (@ tptp.zip_complex_real Xs2) Ys))) (not (=> (@ (@ tptp.member_complex X) (@ tptp.set_complex2 Xs2)) (not (@ (@ tptp.member_real Y) (@ tptp.set_real2 Ys))))))))
% 6.73/7.04 (assert (forall ((X tptp.complex) (Y tptp.int) (Xs2 tptp.list_complex) (Ys tptp.list_int)) (=> (@ (@ tptp.member595073364599660772ex_int (@ (@ tptp.produc1367138851071493491ex_int X) Y)) (@ tptp.set_Pr4995810437751016784ex_int (@ (@ tptp.zip_complex_int Xs2) Ys))) (not (=> (@ (@ tptp.member_complex X) (@ tptp.set_complex2 Xs2)) (not (@ (@ tptp.member_int Y) (@ tptp.set_int2 Ys))))))))
% 6.73/7.04 (assert (forall ((X tptp.real) (Y tptp.complex) (Xs2 tptp.list_real) (Ys tptp.list_complex)) (=> (@ (@ tptp.member7358116576843751780omplex (@ (@ tptp.produc1693001998875562995omplex X) Y)) (@ tptp.set_Pr8536649499196266448omplex (@ (@ tptp.zip_real_complex Xs2) Ys))) (not (=> (@ (@ tptp.member_real X) (@ tptp.set_real2 Xs2)) (not (@ (@ tptp.member_complex Y) (@ tptp.set_complex2 Ys))))))))
% 6.73/7.04 (assert (forall ((X tptp.real) (Y tptp.real) (Xs2 tptp.list_real) (Ys tptp.list_real)) (=> (@ (@ tptp.member7849222048561428706l_real (@ (@ tptp.produc4511245868158468465l_real X) Y)) (@ tptp.set_Pr5999470521830281550l_real (@ (@ tptp.zip_real_real Xs2) Ys))) (not (=> (@ (@ tptp.member_real X) (@ tptp.set_real2 Xs2)) (not (@ (@ tptp.member_real Y) (@ tptp.set_real2 Ys))))))))
% 6.73/7.04 (assert (forall ((X tptp.real) (Y tptp.int) (Xs2 tptp.list_real) (Ys tptp.list_int)) (=> (@ (@ tptp.member1627681773268152802al_int (@ (@ tptp.produc3179012173361985393al_int X) Y)) (@ tptp.set_Pr8219819362198175822al_int (@ (@ tptp.zip_real_int Xs2) Ys))) (not (=> (@ (@ tptp.member_real X) (@ tptp.set_real2 Xs2)) (not (@ (@ tptp.member_int Y) (@ tptp.set_int2 Ys))))))))
% 6.73/7.04 (assert (forall ((X tptp.int) (Y tptp.complex) (Xs2 tptp.list_int) (Ys tptp.list_complex)) (=> (@ (@ tptp.member8811922270175639012omplex (@ (@ tptp.produc7948753499206759283omplex X) Y)) (@ tptp.set_Pr3989287306472219216omplex (@ (@ tptp.zip_int_complex Xs2) Ys))) (not (=> (@ (@ tptp.member_int X) (@ tptp.set_int2 Xs2)) (not (@ (@ tptp.member_complex Y) (@ tptp.set_complex2 Ys))))))))
% 6.73/7.04 (assert (forall ((X tptp.int) (Y tptp.real) (Xs2 tptp.list_int) (Ys tptp.list_real)) (=> (@ (@ tptp.member2744130022092475746t_real (@ (@ tptp.produc801115645435158769t_real X) Y)) (@ tptp.set_Pr112895574167722958t_real (@ (@ tptp.zip_int_real Xs2) Ys))) (not (=> (@ (@ tptp.member_int X) (@ tptp.set_int2 Xs2)) (not (@ (@ tptp.member_real Y) (@ tptp.set_real2 Ys))))))))
% 6.73/7.04 (assert (forall ((X tptp.complex) (Y tptp.vEBT_VEBT) (Xs2 tptp.list_complex) (Ys tptp.list_VEBT_VEBT)) (=> (@ (@ tptp.member1978952105866562066T_VEBT (@ (@ tptp.produc2757191886755552429T_VEBT X) Y)) (@ tptp.set_Pr5158653123227461798T_VEBT (@ (@ tptp.zip_co9157518722488180109T_VEBT Xs2) Ys))) (not (=> (@ (@ tptp.member_complex X) (@ tptp.set_complex2 Xs2)) (not (@ (@ tptp.member_VEBT_VEBT Y) (@ tptp.set_VEBT_VEBT2 Ys))))))))
% 6.73/7.04 (assert (forall ((X tptp.real) (Y tptp.vEBT_VEBT) (Xs2 tptp.list_real) (Ys tptp.list_VEBT_VEBT)) (=> (@ (@ tptp.member7262085504369356948T_VEBT (@ (@ tptp.produc6931449550656315951T_VEBT X) Y)) (@ tptp.set_Pr8897343066327330088T_VEBT (@ (@ tptp.zip_real_VEBT_VEBT Xs2) Ys))) (not (=> (@ (@ tptp.member_real X) (@ tptp.set_real2 Xs2)) (not (@ (@ tptp.member_VEBT_VEBT Y) (@ tptp.set_VEBT_VEBT2 Ys))))))))
% 6.73/7.04 (assert (forall ((A tptp.complex) (B tptp.complex) (Xs2 tptp.list_complex)) (= (@ (@ tptp.member5793383173714906214omplex (@ (@ tptp.produc101793102246108661omplex A) B)) (@ tptp.set_Pr8199049879907524818omplex (@ (@ tptp.zip_complex_complex Xs2) Xs2))) (and (@ (@ tptp.member_complex A) (@ tptp.set_complex2 Xs2)) (= A B)))))
% 6.73/7.04 (assert (forall ((A tptp.real) (B tptp.real) (Xs2 tptp.list_real)) (= (@ (@ tptp.member7849222048561428706l_real (@ (@ tptp.produc4511245868158468465l_real A) B)) (@ tptp.set_Pr5999470521830281550l_real (@ (@ tptp.zip_real_real Xs2) Xs2))) (and (@ (@ tptp.member_real A) (@ tptp.set_real2 Xs2)) (= A B)))))
% 6.73/7.04 (assert (forall ((A tptp.set_nat) (B tptp.set_nat) (Xs2 tptp.list_set_nat)) (= (@ (@ tptp.member8277197624267554838et_nat (@ (@ tptp.produc4532415448927165861et_nat A) B)) (@ tptp.set_Pr9040384385603167362et_nat (@ (@ tptp.zip_set_nat_set_nat Xs2) Xs2))) (and (@ (@ tptp.member_set_nat A) (@ tptp.set_set_nat2 Xs2)) (= A B)))))
% 6.73/7.04 (assert (forall ((A tptp.vEBT_VEBT) (B tptp.vEBT_VEBT) (Xs2 tptp.list_VEBT_VEBT)) (= (@ (@ tptp.member568628332442017744T_VEBT (@ (@ tptp.produc537772716801021591T_VEBT A) B)) (@ tptp.set_Pr9182192707038809660T_VEBT (@ (@ tptp.zip_VE537291747668921783T_VEBT Xs2) Xs2))) (and (@ (@ tptp.member_VEBT_VEBT A) (@ tptp.set_VEBT_VEBT2 Xs2)) (= A B)))))
% 6.73/7.04 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (Xs2 tptp.list_Code_integer)) (= (@ (@ tptp.member157494554546826820nteger (@ (@ tptp.produc1086072967326762835nteger A) B)) (@ tptp.set_Pr920681315882439344nteger (@ (@ tptp.zip_Co3543743374963494515nteger Xs2) Xs2))) (and (@ (@ tptp.member_Code_integer A) (@ tptp.set_Code_integer2 Xs2)) (= A B)))))
% 6.73/7.04 (assert (forall ((A tptp.product_prod_nat_nat) (B tptp.product_prod_nat_nat) (Xs2 tptp.list_P6011104703257516679at_nat)) (= (@ (@ tptp.member8206827879206165904at_nat (@ (@ tptp.produc6161850002892822231at_nat A) B)) (@ tptp.set_Pr5518436109238095868at_nat (@ (@ tptp.zip_Pr4664179122662387191at_nat Xs2) Xs2))) (and (@ (@ tptp.member8440522571783428010at_nat A) (@ tptp.set_Pr5648618587558075414at_nat Xs2)) (= A B)))))
% 6.73/7.04 (assert (forall ((A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat) (Xs2 tptp.list_s1210847774152347623at_nat)) (= (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat A) B)) (@ tptp.set_Pr3765526544606949372at_nat (@ (@ tptp.zip_se5600341670672612855at_nat Xs2) Xs2))) (and (@ (@ tptp.member2643936169264416010at_nat A) (@ tptp.set_se5049602875457034614at_nat Xs2)) (= A B)))))
% 6.73/7.04 (assert (forall ((A tptp.nat) (B tptp.nat) (Xs2 tptp.list_nat)) (= (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat A) B)) (@ tptp.set_Pr5648618587558075414at_nat (@ (@ tptp.zip_nat_nat Xs2) Xs2))) (and (@ (@ tptp.member_nat A) (@ tptp.set_nat2 Xs2)) (= A B)))))
% 6.73/7.04 (assert (forall ((A tptp.int) (B tptp.int) (Xs2 tptp.list_int)) (= (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int A) B)) (@ tptp.set_Pr2470121279949933262nt_int (@ (@ tptp.zip_int_int Xs2) Xs2))) (and (@ (@ tptp.member_int A) (@ tptp.set_int2 Xs2)) (= A B)))))
% 6.73/7.04 (assert (forall ((N tptp.nat) (Xs2 tptp.list_VEBT_VEBT)) (= (= (@ tptp.suc N) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (exists ((Y4 tptp.vEBT_VEBT) (Ys3 tptp.list_VEBT_VEBT)) (and (= Xs2 (@ (@ tptp.cons_VEBT_VEBT Y4) Ys3)) (= (@ tptp.size_s6755466524823107622T_VEBT Ys3) N))))))
% 6.73/7.04 (assert (forall ((N tptp.nat) (Xs2 tptp.list_o)) (= (= (@ tptp.suc N) (@ tptp.size_size_list_o Xs2)) (exists ((Y4 Bool) (Ys3 tptp.list_o)) (and (= Xs2 (@ (@ tptp.cons_o Y4) Ys3)) (= (@ tptp.size_size_list_o Ys3) N))))))
% 6.73/7.04 (assert (forall ((N tptp.nat) (Xs2 tptp.list_nat)) (= (= (@ tptp.suc N) (@ tptp.size_size_list_nat Xs2)) (exists ((Y4 tptp.nat) (Ys3 tptp.list_nat)) (and (= Xs2 (@ (@ tptp.cons_nat Y4) Ys3)) (= (@ tptp.size_size_list_nat Ys3) N))))))
% 6.73/7.04 (assert (forall ((N tptp.nat) (Xs2 tptp.list_int)) (= (= (@ tptp.suc N) (@ tptp.size_size_list_int Xs2)) (exists ((Y4 tptp.int) (Ys3 tptp.list_int)) (and (= Xs2 (@ (@ tptp.cons_int Y4) Ys3)) (= (@ tptp.size_size_list_int Ys3) N))))))
% 6.73/7.04 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (N tptp.nat)) (= (= (@ tptp.size_s6755466524823107622T_VEBT Xs2) (@ tptp.suc N)) (exists ((Y4 tptp.vEBT_VEBT) (Ys3 tptp.list_VEBT_VEBT)) (and (= Xs2 (@ (@ tptp.cons_VEBT_VEBT Y4) Ys3)) (= (@ tptp.size_s6755466524823107622T_VEBT Ys3) N))))))
% 6.73/7.04 (assert (forall ((Xs2 tptp.list_o) (N tptp.nat)) (= (= (@ tptp.size_size_list_o Xs2) (@ tptp.suc N)) (exists ((Y4 Bool) (Ys3 tptp.list_o)) (and (= Xs2 (@ (@ tptp.cons_o Y4) Ys3)) (= (@ tptp.size_size_list_o Ys3) N))))))
% 6.73/7.04 (assert (forall ((Xs2 tptp.list_nat) (N tptp.nat)) (= (= (@ tptp.size_size_list_nat Xs2) (@ tptp.suc N)) (exists ((Y4 tptp.nat) (Ys3 tptp.list_nat)) (and (= Xs2 (@ (@ tptp.cons_nat Y4) Ys3)) (= (@ tptp.size_size_list_nat Ys3) N))))))
% 6.73/7.04 (assert (forall ((Xs2 tptp.list_int) (N tptp.nat)) (= (= (@ tptp.size_size_list_int Xs2) (@ tptp.suc N)) (exists ((Y4 tptp.int) (Ys3 tptp.list_int)) (and (= Xs2 (@ (@ tptp.cons_int Y4) Ys3)) (= (@ tptp.size_size_list_int Ys3) N))))))
% 6.73/7.04 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (Ys tptp.list_VEBT_VEBT) (X tptp.vEBT_VEBT)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (@ tptp.size_s6755466524823107622T_VEBT Ys)) (not (= Xs2 (@ (@ tptp.cons_VEBT_VEBT X) Ys))))))
% 6.73/7.04 (assert (forall ((Xs2 tptp.list_o) (Ys tptp.list_o) (X Bool)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_o Xs2)) (@ tptp.size_size_list_o Ys)) (not (= Xs2 (@ (@ tptp.cons_o X) Ys))))))
% 6.73/7.04 (assert (forall ((Xs2 tptp.list_nat) (Ys tptp.list_nat) (X tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_nat Xs2)) (@ tptp.size_size_list_nat Ys)) (not (= Xs2 (@ (@ tptp.cons_nat X) Ys))))))
% 6.73/7.04 (assert (forall ((Xs2 tptp.list_int) (Ys tptp.list_int) (X tptp.int)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_int Xs2)) (@ tptp.size_size_list_int Ys)) (not (= Xs2 (@ (@ tptp.cons_int X) Ys))))))
% 6.73/7.04 (assert (forall ((Info2 tptp.option4927543243414619207at_nat) (Ts2 tptp.list_VEBT_VEBT) (S2 tptp.vEBT_VEBT) (X tptp.nat)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info2) tptp.zero_zero_nat) Ts2) S2))) (= (@ (@ tptp.vEBT_vebt_insert _let_1) X) _let_1))))
% 6.73/7.04 (assert (forall ((Xs2 tptp.list_Code_integer) (Ys tptp.list_Code_integer) (X tptp.code_integer)) (=> (= (@ tptp.size_s3445333598471063425nteger Xs2) (@ tptp.size_s3445333598471063425nteger Ys)) (=> (@ (@ tptp.member_Code_integer X) (@ tptp.set_Code_integer2 Xs2)) (not (forall ((Y3 tptp.code_integer)) (not (@ (@ tptp.member157494554546826820nteger (@ (@ tptp.produc1086072967326762835nteger X) Y3)) (@ tptp.set_Pr920681315882439344nteger (@ (@ tptp.zip_Co3543743374963494515nteger Xs2) Ys))))))))))
% 6.73/7.04 (assert (forall ((Xs2 tptp.list_complex) (Ys tptp.list_VEBT_VEBT) (X tptp.complex)) (=> (= (@ tptp.size_s3451745648224563538omplex Xs2) (@ tptp.size_s6755466524823107622T_VEBT Ys)) (=> (@ (@ tptp.member_complex X) (@ tptp.set_complex2 Xs2)) (not (forall ((Y3 tptp.vEBT_VEBT)) (not (@ (@ tptp.member1978952105866562066T_VEBT (@ (@ tptp.produc2757191886755552429T_VEBT X) Y3)) (@ tptp.set_Pr5158653123227461798T_VEBT (@ (@ tptp.zip_co9157518722488180109T_VEBT Xs2) Ys))))))))))
% 6.73/7.04 (assert (forall ((Xs2 tptp.list_real) (Ys tptp.list_VEBT_VEBT) (X tptp.real)) (=> (= (@ tptp.size_size_list_real Xs2) (@ tptp.size_s6755466524823107622T_VEBT Ys)) (=> (@ (@ tptp.member_real X) (@ tptp.set_real2 Xs2)) (not (forall ((Y3 tptp.vEBT_VEBT)) (not (@ (@ tptp.member7262085504369356948T_VEBT (@ (@ tptp.produc6931449550656315951T_VEBT X) Y3)) (@ tptp.set_Pr8897343066327330088T_VEBT (@ (@ tptp.zip_real_VEBT_VEBT Xs2) Ys))))))))))
% 6.73/7.04 (assert (forall ((Xs2 tptp.list_complex) (Ys tptp.list_o) (X tptp.complex)) (=> (= (@ tptp.size_s3451745648224563538omplex Xs2) (@ tptp.size_size_list_o Ys)) (=> (@ (@ tptp.member_complex X) (@ tptp.set_complex2 Xs2)) (not (forall ((Y3 Bool)) (not (@ (@ tptp.member6487239523555734774plex_o (@ (@ tptp.produc2908979694703026321plex_o X) Y3)) (@ tptp.set_Pr6829704231520703882plex_o (@ (@ tptp.zip_complex_o Xs2) Ys))))))))))
% 6.73/7.04 (assert (forall ((Xs2 tptp.list_real) (Ys tptp.list_o) (X tptp.real)) (=> (= (@ tptp.size_size_list_real Xs2) (@ tptp.size_size_list_o Ys)) (=> (@ (@ tptp.member_real X) (@ tptp.set_real2 Xs2)) (not (forall ((Y3 Bool)) (not (@ (@ tptp.member772602641336174712real_o (@ (@ tptp.product_Pair_real_o X) Y3)) (@ tptp.set_Pr5196769464307566348real_o (@ (@ tptp.zip_real_o Xs2) Ys))))))))))
% 6.73/7.04 (assert (forall ((Xs2 tptp.list_complex) (Ys tptp.list_nat) (X tptp.complex)) (=> (= (@ tptp.size_s3451745648224563538omplex Xs2) (@ tptp.size_size_list_nat Ys)) (=> (@ (@ tptp.member_complex X) (@ tptp.set_complex2 Xs2)) (not (forall ((Y3 tptp.nat)) (not (@ (@ tptp.member4772924384108857480ex_nat (@ (@ tptp.produc1369629321580543767ex_nat X) Y3)) (@ tptp.set_Pr9173661457260213492ex_nat (@ (@ tptp.zip_complex_nat Xs2) Ys))))))))))
% 6.73/7.04 (assert (forall ((Xs2 tptp.list_real) (Ys tptp.list_nat) (X tptp.real)) (=> (= (@ tptp.size_size_list_real Xs2) (@ tptp.size_size_list_nat Ys)) (=> (@ (@ tptp.member_real X) (@ tptp.set_real2 Xs2)) (not (forall ((Y3 tptp.nat)) (not (@ (@ tptp.member5805532792777349510al_nat (@ (@ tptp.produc3181502643871035669al_nat X) Y3)) (@ tptp.set_Pr3174298344852596722al_nat (@ (@ tptp.zip_real_nat Xs2) Ys))))))))))
% 6.73/7.04 (assert (forall ((Xs2 tptp.list_complex) (Ys tptp.list_int) (X tptp.complex)) (=> (= (@ tptp.size_s3451745648224563538omplex Xs2) (@ tptp.size_size_list_int Ys)) (=> (@ (@ tptp.member_complex X) (@ tptp.set_complex2 Xs2)) (not (forall ((Y3 tptp.int)) (not (@ (@ tptp.member595073364599660772ex_int (@ (@ tptp.produc1367138851071493491ex_int X) Y3)) (@ tptp.set_Pr4995810437751016784ex_int (@ (@ tptp.zip_complex_int Xs2) Ys))))))))))
% 6.73/7.04 (assert (forall ((Xs2 tptp.list_real) (Ys tptp.list_int) (X tptp.real)) (=> (= (@ tptp.size_size_list_real Xs2) (@ tptp.size_size_list_int Ys)) (=> (@ (@ tptp.member_real X) (@ tptp.set_real2 Xs2)) (not (forall ((Y3 tptp.int)) (not (@ (@ tptp.member1627681773268152802al_int (@ (@ tptp.produc3179012173361985393al_int X) Y3)) (@ tptp.set_Pr8219819362198175822al_int (@ (@ tptp.zip_real_int Xs2) Ys))))))))))
% 6.73/7.04 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (Ys tptp.list_VEBT_VEBT) (X tptp.vEBT_VEBT)) (=> (= (@ tptp.size_s6755466524823107622T_VEBT Xs2) (@ tptp.size_s6755466524823107622T_VEBT Ys)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 Xs2)) (not (forall ((Y3 tptp.vEBT_VEBT)) (not (@ (@ tptp.member568628332442017744T_VEBT (@ (@ tptp.produc537772716801021591T_VEBT X) Y3)) (@ tptp.set_Pr9182192707038809660T_VEBT (@ (@ tptp.zip_VE537291747668921783T_VEBT Xs2) Ys))))))))))
% 6.73/7.04 (assert (forall ((Xs2 tptp.list_Code_integer) (Ys tptp.list_Code_integer) (Y tptp.code_integer)) (=> (= (@ tptp.size_s3445333598471063425nteger Xs2) (@ tptp.size_s3445333598471063425nteger Ys)) (=> (@ (@ tptp.member_Code_integer Y) (@ tptp.set_Code_integer2 Ys)) (not (forall ((X3 tptp.code_integer)) (not (@ (@ tptp.member157494554546826820nteger (@ (@ tptp.produc1086072967326762835nteger X3) Y)) (@ tptp.set_Pr920681315882439344nteger (@ (@ tptp.zip_Co3543743374963494515nteger Xs2) Ys))))))))))
% 6.73/7.04 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (Ys tptp.list_complex) (Y tptp.complex)) (=> (= (@ tptp.size_s6755466524823107622T_VEBT Xs2) (@ tptp.size_s3451745648224563538omplex Ys)) (=> (@ (@ tptp.member_complex Y) (@ tptp.set_complex2 Ys)) (not (forall ((X3 tptp.vEBT_VEBT)) (not (@ (@ tptp.member3207599676835851048omplex (@ (@ tptp.produc5617778602380981643omplex X3) Y)) (@ tptp.set_Pr6387300694196750780omplex (@ (@ tptp.zip_VE2794733401258833515omplex Xs2) Ys))))))))))
% 6.73/7.04 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (Ys tptp.list_real) (Y tptp.real)) (=> (= (@ tptp.size_s6755466524823107622T_VEBT Xs2) (@ tptp.size_size_list_real Ys)) (=> (@ (@ tptp.member_real Y) (@ tptp.set_real2 Ys)) (not (forall ((X3 tptp.vEBT_VEBT)) (not (@ (@ tptp.member8675245146396747942T_real (@ (@ tptp.produc8117437818029410057T_real X3) Y)) (@ tptp.set_Pr1087130671499945274T_real (@ (@ tptp.zip_VEBT_VEBT_real Xs2) Ys))))))))))
% 6.73/7.04 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (Ys tptp.list_VEBT_VEBT) (Y tptp.vEBT_VEBT)) (=> (= (@ tptp.size_s6755466524823107622T_VEBT Xs2) (@ tptp.size_s6755466524823107622T_VEBT Ys)) (=> (@ (@ tptp.member_VEBT_VEBT Y) (@ tptp.set_VEBT_VEBT2 Ys)) (not (forall ((X3 tptp.vEBT_VEBT)) (not (@ (@ tptp.member568628332442017744T_VEBT (@ (@ tptp.produc537772716801021591T_VEBT X3) Y)) (@ tptp.set_Pr9182192707038809660T_VEBT (@ (@ tptp.zip_VE537291747668921783T_VEBT Xs2) Ys))))))))))
% 6.73/7.04 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (Ys tptp.list_o) (Y Bool)) (=> (= (@ tptp.size_s6755466524823107622T_VEBT Xs2) (@ tptp.size_size_list_o Ys)) (=> (@ (@ tptp.member_o Y) (@ tptp.set_o2 Ys)) (not (forall ((X3 tptp.vEBT_VEBT)) (not (@ (@ tptp.member3307348790968139188VEBT_o (@ (@ tptp.produc8721562602347293563VEBT_o X3) Y)) (@ tptp.set_Pr7708085864119495200VEBT_o (@ (@ tptp.zip_VEBT_VEBT_o Xs2) Ys))))))))))
% 6.73/7.04 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (Ys tptp.list_nat) (Y tptp.nat)) (=> (= (@ tptp.size_s6755466524823107622T_VEBT Xs2) (@ tptp.size_size_list_nat Ys)) (=> (@ (@ tptp.member_nat Y) (@ tptp.set_nat2 Ys)) (not (forall ((X3 tptp.vEBT_VEBT)) (not (@ (@ tptp.member373505688050248522BT_nat (@ (@ tptp.produc738532404422230701BT_nat X3) Y)) (@ tptp.set_Pr7031586669278753246BT_nat (@ (@ tptp.zip_VEBT_VEBT_nat Xs2) Ys))))))))))
% 6.73/7.04 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (Ys tptp.list_int) (Y tptp.int)) (=> (= (@ tptp.size_s6755466524823107622T_VEBT Xs2) (@ tptp.size_size_list_int Ys)) (=> (@ (@ tptp.member_int Y) (@ tptp.set_int2 Ys)) (not (forall ((X3 tptp.vEBT_VEBT)) (not (@ (@ tptp.member5419026705395827622BT_int (@ (@ tptp.produc736041933913180425BT_int X3) Y)) (@ tptp.set_Pr2853735649769556538BT_int (@ (@ tptp.zip_VEBT_VEBT_int Xs2) Ys))))))))))
% 6.73/7.04 (assert (forall ((Xs2 tptp.list_o) (Ys tptp.list_complex) (Y tptp.complex)) (=> (= (@ tptp.size_size_list_o Xs2) (@ tptp.size_s3451745648224563538omplex Ys)) (=> (@ (@ tptp.member_complex Y) (@ tptp.set_complex2 Ys)) (not (forall ((X3 Bool)) (not (@ (@ tptp.member1046615901120239500omplex (@ (@ tptp.produc414345526774272751omplex X3) Y)) (@ tptp.set_Pr1389080609085208608omplex (@ (@ tptp.zip_o_complex Xs2) Ys))))))))))
% 6.73/7.04 (assert (forall ((Xs2 tptp.list_o) (Ys tptp.list_real) (Y tptp.real)) (=> (= (@ tptp.size_size_list_o Xs2) (@ tptp.size_size_list_real Ys)) (=> (@ (@ tptp.member_real Y) (@ tptp.set_real2 Ys)) (not (forall ((X3 Bool)) (not (@ (@ tptp.member7400031367953476362o_real (@ (@ tptp.product_Pair_o_real X3) Y)) (@ tptp.set_Pr2600826154070092190o_real (@ (@ tptp.zip_o_real Xs2) Ys))))))))))
% 6.73/7.04 (assert (forall ((Xs2 tptp.list_o) (Ys tptp.list_VEBT_VEBT) (Y tptp.vEBT_VEBT)) (=> (= (@ tptp.size_size_list_o Xs2) (@ tptp.size_s6755466524823107622T_VEBT Ys)) (=> (@ (@ tptp.member_VEBT_VEBT Y) (@ tptp.set_VEBT_VEBT2 Ys)) (not (forall ((X3 Bool)) (not (@ (@ tptp.member5477980866518848620T_VEBT (@ (@ tptp.produc2982872950893828659T_VEBT X3) Y)) (@ tptp.set_Pr655345902815428824T_VEBT (@ (@ tptp.zip_o_VEBT_VEBT Xs2) Ys))))))))))
% 6.73/7.04 (assert (forall ((N tptp.nat) (Xs2 tptp.list_VEBT_VEBT)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (exists ((X4 tptp.vEBT_VEBT) (Ys3 tptp.list_VEBT_VEBT)) (and (= Xs2 (@ (@ tptp.cons_VEBT_VEBT X4) Ys3)) (@ (@ tptp.ord_less_eq_nat N) (@ tptp.size_s6755466524823107622T_VEBT Ys3)))))))
% 6.73/7.04 (assert (forall ((N tptp.nat) (Xs2 tptp.list_o)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) (@ tptp.size_size_list_o Xs2)) (exists ((X4 Bool) (Ys3 tptp.list_o)) (and (= Xs2 (@ (@ tptp.cons_o X4) Ys3)) (@ (@ tptp.ord_less_eq_nat N) (@ tptp.size_size_list_o Ys3)))))))
% 6.73/7.04 (assert (forall ((N tptp.nat) (Xs2 tptp.list_nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) (@ tptp.size_size_list_nat Xs2)) (exists ((X4 tptp.nat) (Ys3 tptp.list_nat)) (and (= Xs2 (@ (@ tptp.cons_nat X4) Ys3)) (@ (@ tptp.ord_less_eq_nat N) (@ tptp.size_size_list_nat Ys3)))))))
% 6.73/7.04 (assert (forall ((N tptp.nat) (Xs2 tptp.list_int)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) (@ tptp.size_size_list_int Xs2)) (exists ((X4 tptp.int) (Ys3 tptp.list_int)) (and (= Xs2 (@ (@ tptp.cons_int X4) Ys3)) (@ (@ tptp.ord_less_eq_nat N) (@ tptp.size_size_list_int Ys3)))))))
% 6.73/7.04 (assert (forall ((A Bool) (B Bool) (X tptp.nat)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A) B))) (= (@ (@ tptp.vEBT_VEBT_insert _let_1) X) (@ (@ tptp.vEBT_vebt_insert _let_1) X)))))
% 6.73/7.04 (assert (forall ((Info2 tptp.option4927543243414619207at_nat) (Ts2 tptp.list_VEBT_VEBT) (S2 tptp.vEBT_VEBT) (X tptp.nat)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info2) (@ tptp.suc tptp.zero_zero_nat)) Ts2) S2))) (= (@ (@ tptp.vEBT_vebt_insert _let_1) X) _let_1))))
% 6.73/7.04 (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))))))))))))
% 6.73/7.04 (assert (forall ((X21 tptp.vEBT_VEBT) (X22 tptp.list_VEBT_VEBT)) (= (@ tptp.size_s6755466524823107622T_VEBT (@ (@ tptp.cons_VEBT_VEBT X21) X22)) (@ (@ tptp.plus_plus_nat (@ tptp.size_s6755466524823107622T_VEBT X22)) (@ tptp.suc tptp.zero_zero_nat)))))
% 6.73/7.04 (assert (forall ((X21 Bool) (X22 tptp.list_o)) (= (@ tptp.size_size_list_o (@ (@ tptp.cons_o X21) X22)) (@ (@ tptp.plus_plus_nat (@ tptp.size_size_list_o X22)) (@ tptp.suc tptp.zero_zero_nat)))))
% 6.73/7.04 (assert (forall ((X21 tptp.nat) (X22 tptp.list_nat)) (= (@ tptp.size_size_list_nat (@ (@ tptp.cons_nat X21) X22)) (@ (@ tptp.plus_plus_nat (@ tptp.size_size_list_nat X22)) (@ tptp.suc tptp.zero_zero_nat)))))
% 6.73/7.04 (assert (forall ((X21 tptp.int) (X22 tptp.list_int)) (= (@ tptp.size_size_list_int (@ (@ tptp.cons_int X21) X22)) (@ (@ tptp.plus_plus_nat (@ tptp.size_size_list_int X22)) (@ tptp.suc tptp.zero_zero_nat)))))
% 6.73/7.04 (assert (forall ((N tptp.nat) (X tptp.vEBT_VEBT) (Xs2 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.nth_VEBT_VEBT (@ (@ tptp.cons_VEBT_VEBT X) Xs2)) N))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 X)) (=> (not _let_2) (= _let_1 (@ (@ tptp.nth_VEBT_VEBT Xs2) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)))))))))
% 6.73/7.04 (assert (forall ((N tptp.nat) (X tptp.nat) (Xs2 tptp.list_nat)) (let ((_let_1 (@ (@ tptp.nth_nat (@ (@ tptp.cons_nat X) Xs2)) N))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 X)) (=> (not _let_2) (= _let_1 (@ (@ tptp.nth_nat Xs2) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)))))))))
% 6.73/7.05 (assert (forall ((X tptp.complex) (Xs2 tptp.list_complex) (N tptp.nat)) (=> (not (@ (@ tptp.member_complex X) (@ tptp.set_complex2 Xs2))) (=> (@ (@ tptp.ord_less_eq_nat N) (@ tptp.size_s3451745648224563538omplex Xs2)) (= (= (@ (@ tptp.nth_complex (@ (@ tptp.cons_complex X) Xs2)) N) X) (= N tptp.zero_zero_nat))))))
% 6.73/7.05 (assert (forall ((X tptp.real) (Xs2 tptp.list_real) (N tptp.nat)) (=> (not (@ (@ tptp.member_real X) (@ tptp.set_real2 Xs2))) (=> (@ (@ tptp.ord_less_eq_nat N) (@ tptp.size_size_list_real Xs2)) (= (= (@ (@ tptp.nth_real (@ (@ tptp.cons_real X) Xs2)) N) X) (= N tptp.zero_zero_nat))))))
% 6.73/7.05 (assert (forall ((X tptp.set_nat) (Xs2 tptp.list_set_nat) (N tptp.nat)) (=> (not (@ (@ tptp.member_set_nat X) (@ tptp.set_set_nat2 Xs2))) (=> (@ (@ tptp.ord_less_eq_nat N) (@ tptp.size_s3254054031482475050et_nat Xs2)) (= (= (@ (@ tptp.nth_set_nat (@ (@ tptp.cons_set_nat X) Xs2)) N) X) (= N tptp.zero_zero_nat))))))
% 6.73/7.05 (assert (forall ((X tptp.vEBT_VEBT) (Xs2 tptp.list_VEBT_VEBT) (N tptp.nat)) (=> (not (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 Xs2))) (=> (@ (@ tptp.ord_less_eq_nat N) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (= (= (@ (@ tptp.nth_VEBT_VEBT (@ (@ tptp.cons_VEBT_VEBT X) Xs2)) N) X) (= N tptp.zero_zero_nat))))))
% 6.73/7.05 (assert (forall ((X Bool) (Xs2 tptp.list_o) (N tptp.nat)) (=> (not (@ (@ tptp.member_o X) (@ tptp.set_o2 Xs2))) (=> (@ (@ tptp.ord_less_eq_nat N) (@ tptp.size_size_list_o Xs2)) (= (= (@ (@ tptp.nth_o (@ (@ tptp.cons_o X) Xs2)) N) X) (= N tptp.zero_zero_nat))))))
% 6.73/7.05 (assert (forall ((X tptp.nat) (Xs2 tptp.list_nat) (N tptp.nat)) (=> (not (@ (@ tptp.member_nat X) (@ tptp.set_nat2 Xs2))) (=> (@ (@ tptp.ord_less_eq_nat N) (@ tptp.size_size_list_nat Xs2)) (= (= (@ (@ tptp.nth_nat (@ (@ tptp.cons_nat X) Xs2)) N) X) (= N tptp.zero_zero_nat))))))
% 6.73/7.05 (assert (forall ((X tptp.int) (Xs2 tptp.list_int) (N tptp.nat)) (=> (not (@ (@ tptp.member_int X) (@ tptp.set_int2 Xs2))) (=> (@ (@ tptp.ord_less_eq_nat N) (@ tptp.size_size_list_int Xs2)) (= (= (@ (@ tptp.nth_int (@ (@ tptp.cons_int X) Xs2)) N) X) (= N tptp.zero_zero_nat))))))
% 6.73/7.05 (assert (forall ((X tptp.vEBT_VEBT) (Y tptp.vEBT_VEBT) (Xs2 tptp.list_VEBT_VEBT) (N tptp.nat)) (=> (not (= X Y)) (= (= (@ (@ tptp.nth_VEBT_VEBT (@ (@ tptp.cons_VEBT_VEBT X) Xs2)) N) Y) (and (= (@ (@ tptp.nth_VEBT_VEBT Xs2) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) Y) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))))
% 6.73/7.05 (assert (forall ((X tptp.nat) (Y tptp.nat) (Xs2 tptp.list_nat) (N tptp.nat)) (=> (not (= X Y)) (= (= (@ (@ tptp.nth_nat (@ (@ tptp.cons_nat X) Xs2)) N) Y) (and (= (@ (@ tptp.nth_nat Xs2) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) Y) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))))
% 6.73/7.05 (assert (forall ((X tptp.vEBT_VEBT) (Xs2 tptp.list_VEBT_VEBT)) (= (@ tptp.size_s6755466524823107622T_VEBT (@ (@ tptp.cons_VEBT_VEBT X) Xs2)) (@ tptp.suc (@ tptp.size_s6755466524823107622T_VEBT Xs2)))))
% 6.73/7.05 (assert (forall ((X Bool) (Xs2 tptp.list_o)) (= (@ tptp.size_size_list_o (@ (@ tptp.cons_o X) Xs2)) (@ tptp.suc (@ tptp.size_size_list_o Xs2)))))
% 6.73/7.05 (assert (forall ((X tptp.nat) (Xs2 tptp.list_nat)) (= (@ tptp.size_size_list_nat (@ (@ tptp.cons_nat X) Xs2)) (@ tptp.suc (@ tptp.size_size_list_nat Xs2)))))
% 6.73/7.05 (assert (forall ((X tptp.int) (Xs2 tptp.list_int)) (= (@ tptp.size_size_list_int (@ (@ tptp.cons_int X) Xs2)) (@ tptp.suc (@ tptp.size_size_list_int Xs2)))))
% 6.73/7.05 (assert (= (@ tptp.neg_nu5831290666863070958nteger tptp.zero_z3403309356797280102nteger) tptp.one_one_Code_integer))
% 6.73/7.05 (assert (= (@ tptp.neg_nu8557863876264182079omplex tptp.zero_zero_complex) tptp.one_one_complex))
% 6.73/7.05 (assert (= (@ tptp.neg_nu8295874005876285629c_real tptp.zero_zero_real) tptp.one_one_real))
% 6.73/7.05 (assert (= (@ tptp.neg_nu5219082963157363817nc_rat tptp.zero_zero_rat) tptp.one_one_rat))
% 6.73/7.05 (assert (= (@ tptp.neg_nu5851722552734809277nc_int tptp.zero_zero_int) tptp.one_one_int))
% 6.73/7.05 (assert (forall ((S3 tptp.set_nat) (N tptp.nat)) (let ((_let_1 (@ tptp.infini8530281810654367211te_nat S3))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.infini8530281810654367211te_nat (@ (@ tptp.minus_minus_set_nat S3) (@ (@ tptp.insert_nat (@ _let_1 tptp.zero_zero_nat)) tptp.bot_bot_set_nat))) N)))))
% 6.73/7.05 (assert (= tptp.neg_nu7757733837767384882nteger (lambda ((X4 tptp.code_integer)) (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.plus_p5714425477246183910nteger X4) X4)) tptp.one_one_Code_integer))))
% 6.73/7.05 (assert (= tptp.neg_nu6511756317524482435omplex (lambda ((X4 tptp.complex)) (@ (@ tptp.minus_minus_complex (@ (@ tptp.plus_plus_complex X4) X4)) tptp.one_one_complex))))
% 6.73/7.05 (assert (= tptp.neg_nu6075765906172075777c_real (lambda ((X4 tptp.real)) (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real X4) X4)) tptp.one_one_real))))
% 6.73/7.05 (assert (= tptp.neg_nu3179335615603231917ec_rat (lambda ((X4 tptp.rat)) (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat X4) X4)) tptp.one_one_rat))))
% 6.73/7.05 (assert (= tptp.neg_nu3811975205180677377ec_int (lambda ((X4 tptp.int)) (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int X4) X4)) tptp.one_one_int))))
% 6.73/7.05 (assert (forall ((A4 tptp.set_int)) (= (= (@ tptp.semiri4256215615220890538in_int A4) tptp.zero_zero_int) (and (@ (@ tptp.ord_less_eq_set_int A4) (@ (@ tptp.insert_int tptp.zero_zero_int) tptp.bot_bot_set_int)) (@ tptp.finite_finite_int A4)))))
% 6.73/7.05 (assert (forall ((A4 tptp.set_nat)) (= (= (@ tptp.semiri4258706085729940814in_nat A4) tptp.zero_zero_nat) (and (@ (@ tptp.ord_less_eq_set_nat A4) (@ (@ tptp.insert_nat tptp.zero_zero_nat) tptp.bot_bot_set_nat)) (@ tptp.finite_finite_nat A4)))))
% 6.73/7.05 (assert (forall ((B tptp.code_integer) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger B))) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) B) (=> (@ (@ tptp.ord_le6747313008572928689nteger B) tptp.one_one_Code_integer) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ _let_1 M2)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat N) M2)))))))
% 6.73/7.05 (assert (forall ((B tptp.real) (M2 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 M2)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat N) M2)))))))
% 6.73/7.05 (assert (forall ((B tptp.rat) (M2 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 M2)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat N) M2)))))))
% 6.73/7.05 (assert (forall ((B tptp.nat) (M2 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 M2)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat N) M2)))))))
% 6.73/7.05 (assert (forall ((B tptp.int) (M2 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 M2)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat N) M2)))))))
% 6.73/7.05 (assert (forall ((N tptp.nat) (Y tptp.set_real) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_real Y)) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_real (@ (@ tptp.insert_real X) Y))) N)))))
% 6.73/7.05 (assert (forall ((N tptp.nat) (Y tptp.set_nat) (X tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat Y)) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat (@ (@ tptp.insert_nat X) Y))) N)))))
% 6.73/7.05 (assert (forall ((N tptp.nat) (Y tptp.set_complex) (X tptp.complex)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_complex Y)) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_complex (@ (@ tptp.insert_complex X) Y))) N)))))
% 6.73/7.05 (assert (forall ((N tptp.nat) (Y tptp.set_int) (X tptp.int)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_int Y)) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_int (@ (@ tptp.insert_int X) Y))) N)))))
% 6.73/7.05 (assert (forall ((N tptp.nat) (Y tptp.set_list_nat) (X tptp.list_nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_list_nat Y)) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_list_nat (@ (@ tptp.insert_list_nat X) Y))) N)))))
% 6.73/7.05 (assert (forall ((N tptp.nat) (Y tptp.set_set_nat) (X tptp.set_nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_set_nat Y)) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_set_nat (@ (@ tptp.insert_set_nat X) Y))) N)))))
% 6.73/7.05 (assert (forall ((X tptp.complex) (Xs2 tptp.list_complex)) (=> (not (@ (@ tptp.member_complex X) (@ tptp.set_complex2 Xs2))) (= (@ (@ tptp.count_list_complex Xs2) X) tptp.zero_zero_nat))))
% 6.73/7.05 (assert (forall ((X tptp.real) (Xs2 tptp.list_real)) (=> (not (@ (@ tptp.member_real X) (@ tptp.set_real2 Xs2))) (= (@ (@ tptp.count_list_real Xs2) X) tptp.zero_zero_nat))))
% 6.73/7.05 (assert (forall ((X tptp.set_nat) (Xs2 tptp.list_set_nat)) (=> (not (@ (@ tptp.member_set_nat X) (@ tptp.set_set_nat2 Xs2))) (= (@ (@ tptp.count_list_set_nat Xs2) X) tptp.zero_zero_nat))))
% 6.73/7.05 (assert (forall ((X tptp.int) (Xs2 tptp.list_int)) (=> (not (@ (@ tptp.member_int X) (@ tptp.set_int2 Xs2))) (= (@ (@ tptp.count_list_int Xs2) X) tptp.zero_zero_nat))))
% 6.73/7.05 (assert (forall ((X tptp.vEBT_VEBT) (Xs2 tptp.list_VEBT_VEBT)) (=> (not (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 Xs2))) (= (@ (@ tptp.count_list_VEBT_VEBT Xs2) X) tptp.zero_zero_nat))))
% 6.73/7.05 (assert (forall ((X tptp.nat) (Xs2 tptp.list_nat)) (=> (not (@ (@ tptp.member_nat X) (@ tptp.set_nat2 Xs2))) (= (@ (@ tptp.count_list_nat Xs2) X) tptp.zero_zero_nat))))
% 6.73/7.05 (assert (forall ((M2 tptp.code_integer) (Ms tptp.list_Code_integer) (N tptp.code_integer) (Ns tptp.list_Code_integer) (R3 tptp.set_Pr4811707699266497531nteger)) (let ((_let_1 (@ tptp.lenlex_Code_integer R3))) (let ((_let_2 (@ tptp.size_s3445333598471063425nteger Ns))) (let ((_let_3 (@ tptp.size_s3445333598471063425nteger Ms))) (= (@ (@ tptp.member749217712838834276nteger (@ (@ tptp.produc750622340256944499nteger (@ (@ tptp.cons_Code_integer M2) Ms)) (@ (@ tptp.cons_Code_integer N) Ns))) _let_1) (or (@ (@ tptp.ord_less_nat _let_3) _let_2) (and (= _let_3 _let_2) (@ (@ tptp.member157494554546826820nteger (@ (@ tptp.produc1086072967326762835nteger M2) N)) R3)) (and (= M2 N) (@ (@ tptp.member749217712838834276nteger (@ (@ tptp.produc750622340256944499nteger Ms) Ns)) _let_1)))))))))
% 6.73/7.05 (assert (forall ((M2 tptp.product_prod_nat_nat) (Ms tptp.list_P6011104703257516679at_nat) (N tptp.product_prod_nat_nat) (Ns tptp.list_P6011104703257516679at_nat) (R3 tptp.set_Pr8693737435421807431at_nat)) (let ((_let_1 (@ tptp.lenlex325483962726685836at_nat R3))) (let ((_let_2 (@ tptp.size_s5460976970255530739at_nat Ns))) (let ((_let_3 (@ tptp.size_s5460976970255530739at_nat Ms))) (= (@ (@ tptp.member6693912407220327184at_nat (@ (@ tptp.produc5943733680697469783at_nat (@ (@ tptp.cons_P6512896166579812791at_nat M2) Ms)) (@ (@ tptp.cons_P6512896166579812791at_nat N) Ns))) _let_1) (or (@ (@ tptp.ord_less_nat _let_3) _let_2) (and (= _let_3 _let_2) (@ (@ tptp.member8206827879206165904at_nat (@ (@ tptp.produc6161850002892822231at_nat M2) N)) R3)) (and (= M2 N) (@ (@ tptp.member6693912407220327184at_nat (@ (@ tptp.produc5943733680697469783at_nat Ms) Ns)) _let_1)))))))))
% 6.73/7.05 (assert (forall ((M2 tptp.set_Pr1261947904930325089at_nat) (Ms tptp.list_s1210847774152347623at_nat) (N tptp.set_Pr1261947904930325089at_nat) (Ns tptp.list_s1210847774152347623at_nat) (R3 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.lenlex1357538814655152620at_nat R3))) (let ((_let_2 (@ tptp.size_s8736152011456118867at_nat Ns))) (let ((_let_3 (@ tptp.size_s8736152011456118867at_nat Ms))) (= (@ (@ tptp.member4080735728053443344at_nat (@ (@ tptp.produc7536900900485677911at_nat (@ (@ tptp.cons_s6881495754146722583at_nat M2) Ms)) (@ (@ tptp.cons_s6881495754146722583at_nat N) Ns))) _let_1) (or (@ (@ tptp.ord_less_nat _let_3) _let_2) (and (= _let_3 _let_2) (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat M2) N)) R3)) (and (= M2 N) (@ (@ tptp.member4080735728053443344at_nat (@ (@ tptp.produc7536900900485677911at_nat Ms) Ns)) _let_1)))))))))
% 6.73/7.05 (assert (forall ((M2 tptp.vEBT_VEBT) (Ms tptp.list_VEBT_VEBT) (N tptp.vEBT_VEBT) (Ns tptp.list_VEBT_VEBT) (R3 tptp.set_Pr6192946355708809607T_VEBT)) (let ((_let_1 (@ tptp.lenlex_VEBT_VEBT R3))) (let ((_let_2 (@ tptp.size_s6755466524823107622T_VEBT Ns))) (let ((_let_3 (@ tptp.size_s6755466524823107622T_VEBT Ms))) (= (@ (@ tptp.member4439316823752958928T_VEBT (@ (@ tptp.produc3897820843166775703T_VEBT (@ (@ tptp.cons_VEBT_VEBT M2) Ms)) (@ (@ tptp.cons_VEBT_VEBT N) Ns))) _let_1) (or (@ (@ tptp.ord_less_nat _let_3) _let_2) (and (= _let_3 _let_2) (@ (@ tptp.member568628332442017744T_VEBT (@ (@ tptp.produc537772716801021591T_VEBT M2) N)) R3)) (and (= M2 N) (@ (@ tptp.member4439316823752958928T_VEBT (@ (@ tptp.produc3897820843166775703T_VEBT Ms) Ns)) _let_1)))))))))
% 6.73/7.05 (assert (forall ((M2 Bool) (Ms tptp.list_o) (N Bool) (Ns tptp.list_o) (R3 tptp.set_Product_prod_o_o)) (let ((_let_1 (@ tptp.lenlex_o R3))) (let ((_let_2 (@ tptp.size_size_list_o Ns))) (let ((_let_3 (@ tptp.size_size_list_o Ms))) (= (@ (@ tptp.member4159035015898711888list_o (@ (@ tptp.produc8435520187683070743list_o (@ (@ tptp.cons_o M2) Ms)) (@ (@ tptp.cons_o N) Ns))) _let_1) (or (@ (@ tptp.ord_less_nat _let_3) _let_2) (and (= _let_3 _let_2) (@ (@ tptp.member7466972457876170832od_o_o (@ (@ tptp.product_Pair_o_o M2) N)) R3)) (and (= M2 N) (@ (@ tptp.member4159035015898711888list_o (@ (@ tptp.produc8435520187683070743list_o Ms) Ns)) _let_1)))))))))
% 6.73/7.05 (assert (forall ((M2 tptp.nat) (Ms tptp.list_nat) (N tptp.nat) (Ns tptp.list_nat) (R3 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.lenlex_nat R3))) (let ((_let_2 (@ tptp.size_size_list_nat Ns))) (let ((_let_3 (@ tptp.size_size_list_nat Ms))) (= (@ (@ tptp.member7340969449405702474st_nat (@ (@ tptp.produc2694037385005941721st_nat (@ (@ tptp.cons_nat M2) Ms)) (@ (@ tptp.cons_nat N) Ns))) _let_1) (or (@ (@ tptp.ord_less_nat _let_3) _let_2) (and (= _let_3 _let_2) (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat M2) N)) R3)) (and (= M2 N) (@ (@ tptp.member7340969449405702474st_nat (@ (@ tptp.produc2694037385005941721st_nat Ms) Ns)) _let_1)))))))))
% 6.73/7.05 (assert (forall ((M2 tptp.int) (Ms tptp.list_int) (N tptp.int) (Ns tptp.list_int) (R3 tptp.set_Pr958786334691620121nt_int)) (let ((_let_1 (@ tptp.lenlex_int R3))) (let ((_let_2 (@ tptp.size_size_list_int Ns))) (let ((_let_3 (@ tptp.size_size_list_int Ms))) (= (@ (@ tptp.member6698963635872716290st_int (@ (@ tptp.produc364263696895485585st_int (@ (@ tptp.cons_int M2) Ms)) (@ (@ tptp.cons_int N) Ns))) _let_1) (or (@ (@ tptp.ord_less_nat _let_3) _let_2) (and (= _let_3 _let_2) (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int M2) N)) R3)) (and (= M2 N) (@ (@ tptp.member6698963635872716290st_int (@ (@ tptp.produc364263696895485585st_int Ms) Ns)) _let_1)))))))))
% 6.73/7.05 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z3 tptp.nat)) (= (= (@ (@ tptp.power_power_nat X) Y) Z3) (= (@ (@ tptp.vEBT_VEBT_power (@ tptp.some_nat X)) (@ tptp.some_nat Y)) (@ tptp.some_nat Z3)))))
% 6.73/7.05 (assert (= tptp.vEBT_VEBT_power (@ tptp.vEBT_V4262088993061758097ft_nat tptp.power_power_nat)))
% 6.73/7.05 (assert (forall ((X tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (= (@ (@ tptp.power_power_nat X) M2) _let_1) (or (= M2 tptp.zero_zero_nat) (= X _let_1))))))
% 6.73/7.05 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (@ (@ tptp.power_power_nat _let_1) N) _let_1))))
% 6.73/7.05 (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))))))
% 6.73/7.05 (assert (= (@ tptp.neg_nu7757733837767384882nteger tptp.one_one_Code_integer) tptp.one_one_Code_integer))
% 6.73/7.05 (assert (= (@ tptp.neg_nu6511756317524482435omplex tptp.one_one_complex) tptp.one_one_complex))
% 6.73/7.05 (assert (= (@ tptp.neg_nu6075765906172075777c_real tptp.one_one_real) tptp.one_one_real))
% 6.73/7.05 (assert (= (@ tptp.neg_nu3811975205180677377ec_int tptp.one_one_int) tptp.one_one_int))
% 6.73/7.05 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_rat tptp.zero_zero_rat) (@ tptp.suc N)) tptp.zero_zero_rat)))
% 6.73/7.05 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_nat tptp.zero_zero_nat) (@ tptp.suc N)) tptp.zero_zero_nat)))
% 6.73/7.05 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_real tptp.zero_zero_real) (@ tptp.suc N)) tptp.zero_zero_real)))
% 6.73/7.05 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_int tptp.zero_zero_int) (@ tptp.suc N)) tptp.zero_zero_int)))
% 6.73/7.05 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_complex tptp.zero_zero_complex) (@ tptp.suc N)) tptp.zero_zero_complex)))
% 6.73/7.05 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.power_power_nat A) (@ tptp.suc tptp.zero_zero_nat)) A)))
% 6.73/7.05 (assert (forall ((A tptp.real)) (= (@ (@ tptp.power_power_real A) (@ tptp.suc tptp.zero_zero_nat)) A)))
% 6.73/7.05 (assert (forall ((A tptp.int)) (= (@ (@ tptp.power_power_int A) (@ tptp.suc tptp.zero_zero_nat)) A)))
% 6.73/7.05 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.power_power_complex A) (@ tptp.suc tptp.zero_zero_nat)) A)))
% 6.73/7.05 (assert (= (@ tptp.finite_card_complex tptp.bot_bot_set_complex) tptp.zero_zero_nat))
% 6.73/7.05 (assert (= (@ tptp.finite_card_list_nat tptp.bot_bot_set_list_nat) tptp.zero_zero_nat))
% 6.73/7.05 (assert (= (@ tptp.finite_card_set_nat tptp.bot_bot_set_set_nat) tptp.zero_zero_nat))
% 6.73/7.05 (assert (= (@ tptp.finite_card_nat tptp.bot_bot_set_nat) tptp.zero_zero_nat))
% 6.73/7.05 (assert (= (@ tptp.finite_card_int tptp.bot_bot_set_int) tptp.zero_zero_nat))
% 6.73/7.05 (assert (= (@ tptp.finite_card_real tptp.bot_bot_set_real) tptp.zero_zero_nat))
% 6.73/7.05 (assert (forall ((A4 tptp.set_list_nat)) (=> (not (@ tptp.finite8100373058378681591st_nat A4)) (= (@ tptp.finite_card_list_nat A4) tptp.zero_zero_nat))))
% 6.73/7.05 (assert (forall ((A4 tptp.set_set_nat)) (=> (not (@ tptp.finite1152437895449049373et_nat A4)) (= (@ tptp.finite_card_set_nat A4) tptp.zero_zero_nat))))
% 6.73/7.05 (assert (forall ((A4 tptp.set_nat)) (=> (not (@ tptp.finite_finite_nat A4)) (= (@ tptp.finite_card_nat A4) tptp.zero_zero_nat))))
% 6.73/7.05 (assert (forall ((A4 tptp.set_int)) (=> (not (@ tptp.finite_finite_int A4)) (= (@ tptp.finite_card_int A4) tptp.zero_zero_nat))))
% 6.73/7.05 (assert (forall ((A4 tptp.set_complex)) (=> (not (@ tptp.finite3207457112153483333omplex A4)) (= (@ tptp.finite_card_complex A4) tptp.zero_zero_nat))))
% 6.73/7.05 (assert (= (@ tptp.semiri4258706085729940814in_nat tptp.bot_bot_set_nat) tptp.zero_zero_nat))
% 6.73/7.05 (assert (= (@ tptp.semiri4256215615220890538in_int tptp.bot_bot_set_int) tptp.zero_zero_int))
% 6.73/7.05 (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)))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (assert (forall ((A4 tptp.set_list_nat)) (=> (@ tptp.finite8100373058378681591st_nat A4) (= (= (@ tptp.finite_card_list_nat A4) tptp.zero_zero_nat) (= A4 tptp.bot_bot_set_list_nat)))))
% 6.73/7.05 (assert (forall ((A4 tptp.set_set_nat)) (=> (@ tptp.finite1152437895449049373et_nat A4) (= (= (@ tptp.finite_card_set_nat A4) tptp.zero_zero_nat) (= A4 tptp.bot_bot_set_set_nat)))))
% 6.73/7.05 (assert (forall ((A4 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex A4) (= (= (@ tptp.finite_card_complex A4) tptp.zero_zero_nat) (= A4 tptp.bot_bot_set_complex)))))
% 6.73/7.05 (assert (forall ((A4 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A4) (= (= (@ tptp.finite_card_nat A4) tptp.zero_zero_nat) (= A4 tptp.bot_bot_set_nat)))))
% 6.73/7.05 (assert (forall ((A4 tptp.set_int)) (=> (@ tptp.finite_finite_int A4) (= (= (@ tptp.finite_card_int A4) tptp.zero_zero_nat) (= A4 tptp.bot_bot_set_int)))))
% 6.73/7.05 (assert (forall ((A4 tptp.set_real)) (=> (@ tptp.finite_finite_real A4) (= (= (@ tptp.finite_card_real A4) tptp.zero_zero_nat) (= A4 tptp.bot_bot_set_real)))))
% 6.73/7.05 (assert (forall ((A4 tptp.set_real) (X tptp.real)) (=> (@ tptp.finite_finite_real A4) (=> (not (@ (@ tptp.member_real X) A4)) (= (@ tptp.finite_card_real (@ (@ tptp.insert_real X) A4)) (@ tptp.suc (@ tptp.finite_card_real A4)))))))
% 6.73/7.05 (assert (forall ((A4 tptp.set_list_nat) (X tptp.list_nat)) (=> (@ tptp.finite8100373058378681591st_nat A4) (=> (not (@ (@ tptp.member_list_nat X) A4)) (= (@ tptp.finite_card_list_nat (@ (@ tptp.insert_list_nat X) A4)) (@ tptp.suc (@ tptp.finite_card_list_nat A4)))))))
% 6.73/7.05 (assert (forall ((A4 tptp.set_set_nat) (X tptp.set_nat)) (=> (@ tptp.finite1152437895449049373et_nat A4) (=> (not (@ (@ tptp.member_set_nat X) A4)) (= (@ tptp.finite_card_set_nat (@ (@ tptp.insert_set_nat X) A4)) (@ tptp.suc (@ tptp.finite_card_set_nat A4)))))))
% 6.73/7.05 (assert (forall ((A4 tptp.set_nat) (X tptp.nat)) (=> (@ tptp.finite_finite_nat A4) (=> (not (@ (@ tptp.member_nat X) A4)) (= (@ tptp.finite_card_nat (@ (@ tptp.insert_nat X) A4)) (@ tptp.suc (@ tptp.finite_card_nat A4)))))))
% 6.73/7.05 (assert (forall ((A4 tptp.set_int) (X tptp.int)) (=> (@ tptp.finite_finite_int A4) (=> (not (@ (@ tptp.member_int X) A4)) (= (@ tptp.finite_card_int (@ (@ tptp.insert_int X) A4)) (@ tptp.suc (@ tptp.finite_card_int A4)))))))
% 6.73/7.05 (assert (forall ((A4 tptp.set_complex) (X tptp.complex)) (=> (@ tptp.finite3207457112153483333omplex A4) (=> (not (@ (@ tptp.member_complex X) A4)) (= (@ tptp.finite_card_complex (@ (@ tptp.insert_complex X) A4)) (@ tptp.suc (@ tptp.finite_card_complex A4)))))))
% 6.73/7.05 (assert (forall ((B tptp.code_integer) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger B))) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) B) (=> (@ (@ tptp.ord_le6747313008572928689nteger B) tptp.one_one_Code_integer) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ _let_1 M2)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat N) M2)))))))
% 6.73/7.05 (assert (forall ((B tptp.real) (M2 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 M2)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat N) M2)))))))
% 6.73/7.05 (assert (forall ((B tptp.rat) (M2 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 M2)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat N) M2)))))))
% 6.73/7.05 (assert (forall ((B tptp.nat) (M2 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 M2)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat N) M2)))))))
% 6.73/7.05 (assert (forall ((B tptp.int) (M2 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 M2)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat N) M2)))))))
% 6.73/7.05 (assert (forall ((B tptp.code_integer) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger B))) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) B) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_nat X) Y))))))
% 6.73/7.05 (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))))))
% 6.73/7.05 (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))))))
% 6.73/7.05 (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))))))
% 6.73/7.05 (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))))))
% 6.73/7.05 (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))))))))
% 6.73/7.05 (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))))))))
% 6.73/7.05 (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))))))))
% 6.73/7.05 (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))))))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (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)))))))
% 6.73/7.05 (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)))))))
% 6.73/7.05 (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)))))))
% 6.73/7.05 (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)))))))
% 6.73/7.05 (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)))))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (assert (forall ((A tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (= (@ _let_1 (@ (@ tptp.times_times_nat M2) N)) (@ (@ tptp.power_power_nat (@ _let_1 M2)) N)))))
% 6.73/7.05 (assert (forall ((A tptp.real) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A))) (= (@ _let_1 (@ (@ tptp.times_times_nat M2) N)) (@ (@ tptp.power_power_real (@ _let_1 M2)) N)))))
% 6.73/7.05 (assert (forall ((A tptp.int) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (= (@ _let_1 (@ (@ tptp.times_times_nat M2) N)) (@ (@ tptp.power_power_int (@ _let_1 M2)) N)))))
% 6.73/7.05 (assert (forall ((A tptp.complex) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex A))) (= (@ _let_1 (@ (@ tptp.times_times_nat M2) N)) (@ (@ tptp.power_power_complex (@ _let_1 M2)) N)))))
% 6.73/7.05 (assert (forall ((S3 tptp.set_nat) (N tptp.nat)) (=> (@ tptp.finite_finite_nat S3) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.finite_card_nat S3)) (@ (@ tptp.ord_less_eq_nat N) (@ (@ tptp.infini8530281810654367211te_nat S3) N))))))
% 6.73/7.05 (assert (forall ((R3 tptp.set_Pr4811707699266497531nteger) (Xs2 tptp.list_Code_integer)) (=> (forall ((X3 tptp.code_integer)) (not (@ (@ tptp.member157494554546826820nteger (@ (@ tptp.produc1086072967326762835nteger X3) X3)) R3))) (not (@ (@ tptp.member749217712838834276nteger (@ (@ tptp.produc750622340256944499nteger Xs2) Xs2)) (@ tptp.lenlex_Code_integer R3))))))
% 6.73/7.05 (assert (forall ((R3 tptp.set_Pr8693737435421807431at_nat) (Xs2 tptp.list_P6011104703257516679at_nat)) (=> (forall ((X3 tptp.product_prod_nat_nat)) (not (@ (@ tptp.member8206827879206165904at_nat (@ (@ tptp.produc6161850002892822231at_nat X3) X3)) R3))) (not (@ (@ tptp.member6693912407220327184at_nat (@ (@ tptp.produc5943733680697469783at_nat Xs2) Xs2)) (@ tptp.lenlex325483962726685836at_nat R3))))))
% 6.73/7.05 (assert (forall ((R3 tptp.set_Pr4329608150637261639at_nat) (Xs2 tptp.list_s1210847774152347623at_nat)) (=> (forall ((X3 tptp.set_Pr1261947904930325089at_nat)) (not (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat X3) X3)) R3))) (not (@ (@ tptp.member4080735728053443344at_nat (@ (@ tptp.produc7536900900485677911at_nat Xs2) Xs2)) (@ tptp.lenlex1357538814655152620at_nat R3))))))
% 6.73/7.05 (assert (forall ((R3 tptp.set_Pr1261947904930325089at_nat) (Xs2 tptp.list_nat)) (=> (forall ((X3 tptp.nat)) (not (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X3) X3)) R3))) (not (@ (@ tptp.member7340969449405702474st_nat (@ (@ tptp.produc2694037385005941721st_nat Xs2) Xs2)) (@ tptp.lenlex_nat R3))))))
% 6.73/7.05 (assert (forall ((R3 tptp.set_Pr958786334691620121nt_int) (Xs2 tptp.list_int)) (=> (forall ((X3 tptp.int)) (not (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X3) X3)) R3))) (not (@ (@ tptp.member6698963635872716290st_int (@ (@ tptp.produc364263696895485585st_int Xs2) Xs2)) (@ tptp.lenlex_int R3))))))
% 6.73/7.05 (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))))))
% 6.73/7.05 (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))))))
% 6.73/7.05 (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))))))
% 6.73/7.05 (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))))))
% 6.73/7.05 (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))))))
% 6.73/7.05 (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))))))
% 6.73/7.05 (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))))))
% 6.73/7.05 (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))))))
% 6.73/7.05 (assert (forall ((S3 tptp.set_nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.infini8530281810654367211te_nat S3))) (=> (@ tptp.finite_finite_nat S3) (=> (@ (@ tptp.ord_less_nat _let_1) (@ tptp.finite_card_nat S3)) (@ (@ tptp.ord_less_nat (@ _let_2 N)) (@ _let_2 _let_1))))))))
% 6.73/7.05 (assert (forall ((B5 tptp.set_real) (A4 tptp.set_real) (R3 (-> tptp.real tptp.real Bool))) (=> (@ tptp.finite_finite_real B5) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) A4) (exists ((B6 tptp.real)) (and (@ (@ tptp.member_real B6) B5) (@ (@ R3 A3) B6))))) (=> (forall ((A1 tptp.real) (A22 tptp.real) (B3 tptp.real)) (=> (@ (@ tptp.member_real A1) A4) (=> (@ (@ tptp.member_real A22) A4) (=> (@ (@ tptp.member_real B3) B5) (=> (@ (@ R3 A1) B3) (=> (@ (@ R3 A22) B3) (= A1 A22))))))) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_real A4)) (@ tptp.finite_card_real B5)))))))
% 6.73/7.05 (assert (forall ((B5 tptp.set_real) (A4 tptp.set_nat) (R3 (-> tptp.nat tptp.real Bool))) (=> (@ tptp.finite_finite_real B5) (=> (forall ((A3 tptp.nat)) (=> (@ (@ tptp.member_nat A3) A4) (exists ((B6 tptp.real)) (and (@ (@ tptp.member_real B6) B5) (@ (@ R3 A3) B6))))) (=> (forall ((A1 tptp.nat) (A22 tptp.nat) (B3 tptp.real)) (=> (@ (@ tptp.member_nat A1) A4) (=> (@ (@ tptp.member_nat A22) A4) (=> (@ (@ tptp.member_real B3) B5) (=> (@ (@ R3 A1) B3) (=> (@ (@ R3 A22) B3) (= A1 A22))))))) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat A4)) (@ tptp.finite_card_real B5)))))))
% 6.73/7.05 (assert (forall ((B5 tptp.set_real) (A4 tptp.set_complex) (R3 (-> tptp.complex tptp.real Bool))) (=> (@ tptp.finite_finite_real B5) (=> (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) A4) (exists ((B6 tptp.real)) (and (@ (@ tptp.member_real B6) B5) (@ (@ R3 A3) B6))))) (=> (forall ((A1 tptp.complex) (A22 tptp.complex) (B3 tptp.real)) (=> (@ (@ tptp.member_complex A1) A4) (=> (@ (@ tptp.member_complex A22) A4) (=> (@ (@ tptp.member_real B3) B5) (=> (@ (@ R3 A1) B3) (=> (@ (@ R3 A22) B3) (= A1 A22))))))) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_complex A4)) (@ tptp.finite_card_real B5)))))))
% 6.73/7.05 (assert (forall ((B5 tptp.set_real) (A4 tptp.set_int) (R3 (-> tptp.int tptp.real Bool))) (=> (@ tptp.finite_finite_real B5) (=> (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) A4) (exists ((B6 tptp.real)) (and (@ (@ tptp.member_real B6) B5) (@ (@ R3 A3) B6))))) (=> (forall ((A1 tptp.int) (A22 tptp.int) (B3 tptp.real)) (=> (@ (@ tptp.member_int A1) A4) (=> (@ (@ tptp.member_int A22) A4) (=> (@ (@ tptp.member_real B3) B5) (=> (@ (@ R3 A1) B3) (=> (@ (@ R3 A22) B3) (= A1 A22))))))) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_int A4)) (@ tptp.finite_card_real B5)))))))
% 6.73/7.05 (assert (forall ((B5 tptp.set_nat) (A4 tptp.set_real) (R3 (-> tptp.real tptp.nat Bool))) (=> (@ tptp.finite_finite_nat B5) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) A4) (exists ((B6 tptp.nat)) (and (@ (@ tptp.member_nat B6) B5) (@ (@ R3 A3) B6))))) (=> (forall ((A1 tptp.real) (A22 tptp.real) (B3 tptp.nat)) (=> (@ (@ tptp.member_real A1) A4) (=> (@ (@ tptp.member_real A22) A4) (=> (@ (@ tptp.member_nat B3) B5) (=> (@ (@ R3 A1) B3) (=> (@ (@ R3 A22) B3) (= A1 A22))))))) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_real A4)) (@ tptp.finite_card_nat B5)))))))
% 6.73/7.05 (assert (forall ((B5 tptp.set_nat) (A4 tptp.set_nat) (R3 (-> tptp.nat tptp.nat Bool))) (=> (@ tptp.finite_finite_nat B5) (=> (forall ((A3 tptp.nat)) (=> (@ (@ tptp.member_nat A3) A4) (exists ((B6 tptp.nat)) (and (@ (@ tptp.member_nat B6) B5) (@ (@ R3 A3) B6))))) (=> (forall ((A1 tptp.nat) (A22 tptp.nat) (B3 tptp.nat)) (=> (@ (@ tptp.member_nat A1) A4) (=> (@ (@ tptp.member_nat A22) A4) (=> (@ (@ tptp.member_nat B3) B5) (=> (@ (@ R3 A1) B3) (=> (@ (@ R3 A22) B3) (= A1 A22))))))) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat A4)) (@ tptp.finite_card_nat B5)))))))
% 6.73/7.05 (assert (forall ((B5 tptp.set_nat) (A4 tptp.set_complex) (R3 (-> tptp.complex tptp.nat Bool))) (=> (@ tptp.finite_finite_nat B5) (=> (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) A4) (exists ((B6 tptp.nat)) (and (@ (@ tptp.member_nat B6) B5) (@ (@ R3 A3) B6))))) (=> (forall ((A1 tptp.complex) (A22 tptp.complex) (B3 tptp.nat)) (=> (@ (@ tptp.member_complex A1) A4) (=> (@ (@ tptp.member_complex A22) A4) (=> (@ (@ tptp.member_nat B3) B5) (=> (@ (@ R3 A1) B3) (=> (@ (@ R3 A22) B3) (= A1 A22))))))) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_complex A4)) (@ tptp.finite_card_nat B5)))))))
% 6.73/7.05 (assert (forall ((B5 tptp.set_nat) (A4 tptp.set_int) (R3 (-> tptp.int tptp.nat Bool))) (=> (@ tptp.finite_finite_nat B5) (=> (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) A4) (exists ((B6 tptp.nat)) (and (@ (@ tptp.member_nat B6) B5) (@ (@ R3 A3) B6))))) (=> (forall ((A1 tptp.int) (A22 tptp.int) (B3 tptp.nat)) (=> (@ (@ tptp.member_int A1) A4) (=> (@ (@ tptp.member_int A22) A4) (=> (@ (@ tptp.member_nat B3) B5) (=> (@ (@ R3 A1) B3) (=> (@ (@ R3 A22) B3) (= A1 A22))))))) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_int A4)) (@ tptp.finite_card_nat B5)))))))
% 6.73/7.05 (assert (forall ((B5 tptp.set_int) (A4 tptp.set_real) (R3 (-> tptp.real tptp.int Bool))) (=> (@ tptp.finite_finite_int B5) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) A4) (exists ((B6 tptp.int)) (and (@ (@ tptp.member_int B6) B5) (@ (@ R3 A3) B6))))) (=> (forall ((A1 tptp.real) (A22 tptp.real) (B3 tptp.int)) (=> (@ (@ tptp.member_real A1) A4) (=> (@ (@ tptp.member_real A22) A4) (=> (@ (@ tptp.member_int B3) B5) (=> (@ (@ R3 A1) B3) (=> (@ (@ R3 A22) B3) (= A1 A22))))))) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_real A4)) (@ tptp.finite_card_int B5)))))))
% 6.73/7.05 (assert (forall ((B5 tptp.set_int) (A4 tptp.set_nat) (R3 (-> tptp.nat tptp.int Bool))) (=> (@ tptp.finite_finite_int B5) (=> (forall ((A3 tptp.nat)) (=> (@ (@ tptp.member_nat A3) A4) (exists ((B6 tptp.int)) (and (@ (@ tptp.member_int B6) B5) (@ (@ R3 A3) B6))))) (=> (forall ((A1 tptp.nat) (A22 tptp.nat) (B3 tptp.int)) (=> (@ (@ tptp.member_nat A1) A4) (=> (@ (@ tptp.member_nat A22) A4) (=> (@ (@ tptp.member_int B3) B5) (=> (@ (@ R3 A1) B3) (=> (@ (@ R3 A22) B3) (= A1 A22))))))) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat A4)) (@ tptp.finite_card_int B5)))))))
% 6.73/7.05 (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))))))
% 6.73/7.05 (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))))))
% 6.73/7.05 (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))))))
% 6.73/7.05 (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))))))
% 6.73/7.05 (assert (forall ((A4 tptp.set_real) (X tptp.real)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_real A4)) (@ tptp.finite_card_real (@ (@ tptp.insert_real X) A4)))))
% 6.73/7.05 (assert (forall ((A4 tptp.set_nat) (X tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat A4)) (@ tptp.finite_card_nat (@ (@ tptp.insert_nat X) A4)))))
% 6.73/7.05 (assert (forall ((A4 tptp.set_complex) (X tptp.complex)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_complex A4)) (@ tptp.finite_card_complex (@ (@ tptp.insert_complex X) A4)))))
% 6.73/7.05 (assert (forall ((A4 tptp.set_int) (X tptp.int)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_int A4)) (@ tptp.finite_card_int (@ (@ tptp.insert_int X) A4)))))
% 6.73/7.05 (assert (forall ((A4 tptp.set_list_nat) (X tptp.list_nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_list_nat A4)) (@ tptp.finite_card_list_nat (@ (@ tptp.insert_list_nat X) A4)))))
% 6.73/7.05 (assert (forall ((A4 tptp.set_set_nat) (X tptp.set_nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_set_nat A4)) (@ tptp.finite_card_set_nat (@ (@ tptp.insert_set_nat X) A4)))))
% 6.73/7.05 (assert (forall ((A tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_8256067586552552935nteger A) N))))))
% 6.73/7.05 (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))))))
% 6.73/7.05 (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))))))
% 6.73/7.05 (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))))))
% 6.73/7.05 (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))))))
% 6.73/7.05 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer) (N tptp.nat)) (=> (= (@ (@ tptp.times_3573771949741848930nteger X) Y) tptp.one_one_Code_integer) (= (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.power_8256067586552552935nteger X) N)) (@ (@ tptp.power_8256067586552552935nteger Y) N)) tptp.one_one_Code_integer))))
% 6.73/7.05 (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))))
% 6.73/7.05 (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))))
% 6.73/7.05 (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))))
% 6.73/7.05 (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))))
% 6.73/7.05 (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))))
% 6.73/7.05 (assert (forall ((X8 tptp.set_nat) (Y7 tptp.set_nat)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.finite_card_nat X8)) (= (@ (@ tptp.infini8530281810654367211te_nat X8) I3) (@ (@ tptp.infini8530281810654367211te_nat Y7) I3)))) (=> (@ tptp.finite_finite_nat X8) (=> (@ tptp.finite_finite_nat Y7) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat X8)) (@ tptp.finite_card_nat Y7)) (@ (@ tptp.ord_less_eq_set_nat X8) Y7)))))))
% 6.73/7.05 (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))))))
% 6.73/7.05 (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))))))
% 6.73/7.05 (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))))))
% 6.73/7.05 (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))))))
% 6.73/7.05 (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))))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.power_8256067586552552935nteger A) tptp.zero_zero_nat) tptp.one_one_Code_integer)))
% 6.73/7.05 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.power_power_nat A) tptp.zero_zero_nat) tptp.one_one_nat)))
% 6.73/7.05 (assert (forall ((A tptp.real)) (= (@ (@ tptp.power_power_real A) tptp.zero_zero_nat) tptp.one_one_real)))
% 6.73/7.05 (assert (forall ((A tptp.int)) (= (@ (@ tptp.power_power_int A) tptp.zero_zero_nat) tptp.one_one_int)))
% 6.73/7.05 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.power_power_complex A) tptp.zero_zero_nat) tptp.one_one_complex)))
% 6.73/7.05 (assert (forall ((A tptp.complex) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M2) N)) (@ (@ tptp.times_times_complex (@ _let_1 M2)) (@ _let_1 N))))))
% 6.73/7.05 (assert (forall ((A tptp.real) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M2) N)) (@ (@ tptp.times_times_real (@ _let_1 M2)) (@ _let_1 N))))))
% 6.73/7.05 (assert (forall ((A tptp.rat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M2) N)) (@ (@ tptp.times_times_rat (@ _let_1 M2)) (@ _let_1 N))))))
% 6.73/7.05 (assert (forall ((A tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M2) N)) (@ (@ tptp.times_times_nat (@ _let_1 M2)) (@ _let_1 N))))))
% 6.73/7.05 (assert (forall ((A tptp.int) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M2) N)) (@ (@ tptp.times_times_int (@ _let_1 M2)) (@ _let_1 N))))))
% 6.73/7.05 (assert (forall ((I2 tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat I2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) I2) (=> (@ (@ tptp.ord_less_nat (@ _let_1 M2)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat M2) N))))))
% 6.73/7.05 (assert (forall ((S3 tptp.set_nat) (N tptp.nat)) (=> (not (@ tptp.finite_finite_nat S3)) (@ (@ tptp.ord_less_eq_nat N) (@ (@ tptp.infini8530281810654367211te_nat S3) N)))))
% 6.73/7.05 (assert (forall ((A4 tptp.set_list_nat)) (= (= (@ tptp.finite_card_list_nat A4) tptp.zero_zero_nat) (or (= A4 tptp.bot_bot_set_list_nat) (not (@ tptp.finite8100373058378681591st_nat A4))))))
% 6.73/7.05 (assert (forall ((A4 tptp.set_set_nat)) (= (= (@ tptp.finite_card_set_nat A4) tptp.zero_zero_nat) (or (= A4 tptp.bot_bot_set_set_nat) (not (@ tptp.finite1152437895449049373et_nat A4))))))
% 6.73/7.05 (assert (forall ((A4 tptp.set_complex)) (= (= (@ tptp.finite_card_complex A4) tptp.zero_zero_nat) (or (= A4 tptp.bot_bot_set_complex) (not (@ tptp.finite3207457112153483333omplex A4))))))
% 6.73/7.05 (assert (forall ((A4 tptp.set_nat)) (= (= (@ tptp.finite_card_nat A4) tptp.zero_zero_nat) (or (= A4 tptp.bot_bot_set_nat) (not (@ tptp.finite_finite_nat A4))))))
% 6.73/7.05 (assert (forall ((A4 tptp.set_int)) (= (= (@ tptp.finite_card_int A4) tptp.zero_zero_nat) (or (= A4 tptp.bot_bot_set_int) (not (@ tptp.finite_finite_int A4))))))
% 6.73/7.05 (assert (forall ((A4 tptp.set_real)) (= (= (@ tptp.finite_card_real A4) tptp.zero_zero_nat) (or (= A4 tptp.bot_bot_set_real) (not (@ tptp.finite_finite_real A4))))))
% 6.73/7.05 (assert (forall ((A4 tptp.set_list_nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.finite_card_list_nat A4)) (@ tptp.finite8100373058378681591st_nat A4))))
% 6.73/7.05 (assert (forall ((A4 tptp.set_set_nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.finite_card_set_nat A4)) (@ tptp.finite1152437895449049373et_nat A4))))
% 6.73/7.05 (assert (forall ((A4 tptp.set_nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.finite_card_nat A4)) (@ tptp.finite_finite_nat A4))))
% 6.73/7.05 (assert (forall ((A4 tptp.set_int)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.finite_card_int A4)) (@ tptp.finite_finite_int A4))))
% 6.73/7.05 (assert (forall ((A4 tptp.set_complex)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.finite_card_complex A4)) (@ tptp.finite3207457112153483333omplex A4))))
% 6.73/7.05 (assert (forall ((A4 tptp.set_real) (X tptp.real)) (let ((_let_1 (@ tptp.finite_card_real A4))) (let ((_let_2 (@ tptp.finite_card_real (@ (@ tptp.insert_real X) A4)))) (let ((_let_3 (@ (@ tptp.member_real X) A4))) (=> (@ tptp.finite_finite_real A4) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ tptp.suc _let_1))))))))))
% 6.73/7.05 (assert (forall ((A4 tptp.set_list_nat) (X tptp.list_nat)) (let ((_let_1 (@ tptp.finite_card_list_nat A4))) (let ((_let_2 (@ tptp.finite_card_list_nat (@ (@ tptp.insert_list_nat X) A4)))) (let ((_let_3 (@ (@ tptp.member_list_nat X) A4))) (=> (@ tptp.finite8100373058378681591st_nat A4) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ tptp.suc _let_1))))))))))
% 6.73/7.05 (assert (forall ((A4 tptp.set_set_nat) (X tptp.set_nat)) (let ((_let_1 (@ tptp.finite_card_set_nat A4))) (let ((_let_2 (@ tptp.finite_card_set_nat (@ (@ tptp.insert_set_nat X) A4)))) (let ((_let_3 (@ (@ tptp.member_set_nat X) A4))) (=> (@ tptp.finite1152437895449049373et_nat A4) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ tptp.suc _let_1))))))))))
% 6.73/7.05 (assert (forall ((A4 tptp.set_nat) (X tptp.nat)) (let ((_let_1 (@ tptp.finite_card_nat A4))) (let ((_let_2 (@ tptp.finite_card_nat (@ (@ tptp.insert_nat X) A4)))) (let ((_let_3 (@ (@ tptp.member_nat X) A4))) (=> (@ tptp.finite_finite_nat A4) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ tptp.suc _let_1))))))))))
% 6.73/7.05 (assert (forall ((A4 tptp.set_int) (X tptp.int)) (let ((_let_1 (@ tptp.finite_card_int A4))) (let ((_let_2 (@ tptp.finite_card_int (@ (@ tptp.insert_int X) A4)))) (let ((_let_3 (@ (@ tptp.member_int X) A4))) (=> (@ tptp.finite_finite_int A4) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ tptp.suc _let_1))))))))))
% 6.73/7.05 (assert (forall ((A4 tptp.set_complex) (X tptp.complex)) (let ((_let_1 (@ tptp.finite_card_complex A4))) (let ((_let_2 (@ tptp.finite_card_complex (@ (@ tptp.insert_complex X) A4)))) (let ((_let_3 (@ (@ tptp.member_complex X) A4))) (=> (@ tptp.finite3207457112153483333omplex A4) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ tptp.suc _let_1))))))))))
% 6.73/7.05 (assert (forall ((A4 tptp.set_real) (K2 tptp.nat)) (= (= (@ tptp.finite_card_real A4) (@ tptp.suc K2)) (exists ((B4 tptp.real) (B7 tptp.set_real)) (and (= A4 (@ (@ tptp.insert_real B4) B7)) (not (@ (@ tptp.member_real B4) B7)) (= (@ tptp.finite_card_real B7) K2) (@ tptp.finite_finite_real B7))))))
% 6.73/7.05 (assert (forall ((A4 tptp.set_list_nat) (K2 tptp.nat)) (= (= (@ tptp.finite_card_list_nat A4) (@ tptp.suc K2)) (exists ((B4 tptp.list_nat) (B7 tptp.set_list_nat)) (and (= A4 (@ (@ tptp.insert_list_nat B4) B7)) (not (@ (@ tptp.member_list_nat B4) B7)) (= (@ tptp.finite_card_list_nat B7) K2) (@ tptp.finite8100373058378681591st_nat B7))))))
% 6.73/7.05 (assert (forall ((A4 tptp.set_set_nat) (K2 tptp.nat)) (= (= (@ tptp.finite_card_set_nat A4) (@ tptp.suc K2)) (exists ((B4 tptp.set_nat) (B7 tptp.set_set_nat)) (and (= A4 (@ (@ tptp.insert_set_nat B4) B7)) (not (@ (@ tptp.member_set_nat B4) B7)) (= (@ tptp.finite_card_set_nat B7) K2) (@ tptp.finite1152437895449049373et_nat B7))))))
% 6.73/7.05 (assert (forall ((A4 tptp.set_nat) (K2 tptp.nat)) (= (= (@ tptp.finite_card_nat A4) (@ tptp.suc K2)) (exists ((B4 tptp.nat) (B7 tptp.set_nat)) (and (= A4 (@ (@ tptp.insert_nat B4) B7)) (not (@ (@ tptp.member_nat B4) B7)) (= (@ tptp.finite_card_nat B7) K2) (@ tptp.finite_finite_nat B7))))))
% 6.73/7.05 (assert (forall ((A4 tptp.set_int) (K2 tptp.nat)) (= (= (@ tptp.finite_card_int A4) (@ tptp.suc K2)) (exists ((B4 tptp.int) (B7 tptp.set_int)) (and (= A4 (@ (@ tptp.insert_int B4) B7)) (not (@ (@ tptp.member_int B4) B7)) (= (@ tptp.finite_card_int B7) K2) (@ tptp.finite_finite_int B7))))))
% 6.73/7.05 (assert (forall ((A4 tptp.set_complex) (K2 tptp.nat)) (= (= (@ tptp.finite_card_complex A4) (@ tptp.suc K2)) (exists ((B4 tptp.complex) (B7 tptp.set_complex)) (and (= A4 (@ (@ tptp.insert_complex B4) B7)) (not (@ (@ tptp.member_complex B4) B7)) (= (@ tptp.finite_card_complex B7) K2) (@ tptp.finite3207457112153483333omplex B7))))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (assert (forall ((B5 tptp.set_list_nat) (A4 tptp.set_list_nat)) (=> (@ tptp.finite8100373058378681591st_nat B5) (=> (@ (@ tptp.ord_le6045566169113846134st_nat A4) B5) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_list_nat A4)) (@ tptp.finite_card_list_nat B5))))))
% 6.73/7.05 (assert (forall ((B5 tptp.set_set_nat) (A4 tptp.set_set_nat)) (=> (@ tptp.finite1152437895449049373et_nat B5) (=> (@ (@ tptp.ord_le6893508408891458716et_nat A4) B5) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_set_nat A4)) (@ tptp.finite_card_set_nat B5))))))
% 6.73/7.05 (assert (forall ((B5 tptp.set_int) (A4 tptp.set_int)) (=> (@ tptp.finite_finite_int B5) (=> (@ (@ tptp.ord_less_eq_set_int A4) B5) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_int A4)) (@ tptp.finite_card_int B5))))))
% 6.73/7.05 (assert (forall ((B5 tptp.set_complex) (A4 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex B5) (=> (@ (@ tptp.ord_le211207098394363844omplex A4) B5) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_complex A4)) (@ tptp.finite_card_complex B5))))))
% 6.73/7.05 (assert (forall ((B5 tptp.set_nat) (A4 tptp.set_nat)) (=> (@ tptp.finite_finite_nat B5) (=> (@ (@ tptp.ord_less_eq_set_nat A4) B5) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat A4)) (@ tptp.finite_card_nat B5))))))
% 6.73/7.05 (assert (forall ((B5 tptp.set_list_nat) (A4 tptp.set_list_nat)) (=> (@ tptp.finite8100373058378681591st_nat B5) (=> (@ (@ tptp.ord_le6045566169113846134st_nat A4) B5) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_list_nat B5)) (@ tptp.finite_card_list_nat A4)) (= A4 B5))))))
% 6.73/7.05 (assert (forall ((B5 tptp.set_set_nat) (A4 tptp.set_set_nat)) (=> (@ tptp.finite1152437895449049373et_nat B5) (=> (@ (@ tptp.ord_le6893508408891458716et_nat A4) B5) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_set_nat B5)) (@ tptp.finite_card_set_nat A4)) (= A4 B5))))))
% 6.73/7.05 (assert (forall ((B5 tptp.set_int) (A4 tptp.set_int)) (=> (@ tptp.finite_finite_int B5) (=> (@ (@ tptp.ord_less_eq_set_int A4) B5) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_int B5)) (@ tptp.finite_card_int A4)) (= A4 B5))))))
% 6.73/7.05 (assert (forall ((B5 tptp.set_complex) (A4 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex B5) (=> (@ (@ tptp.ord_le211207098394363844omplex A4) B5) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_complex B5)) (@ tptp.finite_card_complex A4)) (= A4 B5))))))
% 6.73/7.05 (assert (forall ((B5 tptp.set_nat) (A4 tptp.set_nat)) (=> (@ tptp.finite_finite_nat B5) (=> (@ (@ tptp.ord_less_eq_set_nat A4) B5) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat B5)) (@ tptp.finite_card_nat A4)) (= A4 B5))))))
% 6.73/7.05 (assert (forall ((F3 tptp.set_list_nat) (C4 tptp.nat)) (=> (forall ((G tptp.set_list_nat)) (=> (@ (@ tptp.ord_le6045566169113846134st_nat G) F3) (=> (@ tptp.finite8100373058378681591st_nat G) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_list_nat G)) C4)))) (and (@ tptp.finite8100373058378681591st_nat F3) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_list_nat F3)) C4)))))
% 6.73/7.05 (assert (forall ((F3 tptp.set_set_nat) (C4 tptp.nat)) (=> (forall ((G tptp.set_set_nat)) (=> (@ (@ tptp.ord_le6893508408891458716et_nat G) F3) (=> (@ tptp.finite1152437895449049373et_nat G) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_set_nat G)) C4)))) (and (@ tptp.finite1152437895449049373et_nat F3) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_set_nat F3)) C4)))))
% 6.73/7.05 (assert (forall ((F3 tptp.set_int) (C4 tptp.nat)) (=> (forall ((G tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int G) F3) (=> (@ tptp.finite_finite_int G) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_int G)) C4)))) (and (@ tptp.finite_finite_int F3) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_int F3)) C4)))))
% 6.73/7.05 (assert (forall ((F3 tptp.set_complex) (C4 tptp.nat)) (=> (forall ((G tptp.set_complex)) (=> (@ (@ tptp.ord_le211207098394363844omplex G) F3) (=> (@ tptp.finite3207457112153483333omplex G) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_complex G)) C4)))) (and (@ tptp.finite3207457112153483333omplex F3) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_complex F3)) C4)))))
% 6.73/7.05 (assert (forall ((F3 tptp.set_nat) (C4 tptp.nat)) (=> (forall ((G tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat G) F3) (=> (@ tptp.finite_finite_nat G) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat G)) C4)))) (and (@ tptp.finite_finite_nat F3) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat F3)) C4)))))
% 6.73/7.05 (assert (forall ((N tptp.nat) (S3 tptp.set_list_nat)) (=> (@ (@ tptp.ord_less_eq_nat N) (@ tptp.finite_card_list_nat S3)) (not (forall ((T3 tptp.set_list_nat)) (=> (@ (@ tptp.ord_le6045566169113846134st_nat T3) S3) (=> (= (@ tptp.finite_card_list_nat T3) N) (not (@ tptp.finite8100373058378681591st_nat T3)))))))))
% 6.73/7.05 (assert (forall ((N tptp.nat) (S3 tptp.set_set_nat)) (=> (@ (@ tptp.ord_less_eq_nat N) (@ tptp.finite_card_set_nat S3)) (not (forall ((T3 tptp.set_set_nat)) (=> (@ (@ tptp.ord_le6893508408891458716et_nat T3) S3) (=> (= (@ tptp.finite_card_set_nat T3) N) (not (@ tptp.finite1152437895449049373et_nat T3)))))))))
% 6.73/7.05 (assert (forall ((N tptp.nat) (S3 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_nat N) (@ tptp.finite_card_int S3)) (not (forall ((T3 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int T3) S3) (=> (= (@ tptp.finite_card_int T3) N) (not (@ tptp.finite_finite_int T3)))))))))
% 6.73/7.05 (assert (forall ((N tptp.nat) (S3 tptp.set_complex)) (=> (@ (@ tptp.ord_less_eq_nat N) (@ tptp.finite_card_complex S3)) (not (forall ((T3 tptp.set_complex)) (=> (@ (@ tptp.ord_le211207098394363844omplex T3) S3) (=> (= (@ tptp.finite_card_complex T3) N) (not (@ tptp.finite3207457112153483333omplex T3)))))))))
% 6.73/7.05 (assert (forall ((N tptp.nat) (S3 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_nat N) (@ tptp.finite_card_nat S3)) (not (forall ((T3 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat T3) S3) (=> (= (@ tptp.finite_card_nat T3) N) (not (@ tptp.finite_finite_nat T3)))))))))
% 6.73/7.05 (assert (forall ((A tptp.code_integer) (N tptp.nat)) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A) (=> (@ (@ tptp.ord_le3102999989581377725nteger A) tptp.one_one_Code_integer) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.power_8256067586552552935nteger A) N)) tptp.one_one_Code_integer)))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (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))))))))
% 6.73/7.05 (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))))))))
% 6.73/7.05 (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))))))))
% 6.73/7.05 (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))))))))
% 6.73/7.05 (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))))))
% 6.73/7.05 (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))))))
% 6.73/7.05 (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))))))
% 6.73/7.05 (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))))))
% 6.73/7.05 (assert (forall ((A tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_8256067586552552935nteger A) N))) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) A) (@ (@ tptp.ord_le6747313008572928689nteger _let_1) (@ (@ tptp.times_3573771949741848930nteger A) _let_1))))))
% 6.73/7.05 (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))))))
% 6.73/7.05 (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))))))
% 6.73/7.05 (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))))))
% 6.73/7.05 (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))))))
% 6.73/7.05 (assert (forall ((A tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger A) (@ (@ tptp.power_8256067586552552935nteger A) N)))))))
% 6.73/7.05 (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)))))))
% 6.73/7.05 (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)))))))
% 6.73/7.05 (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)))))))
% 6.73/7.05 (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)))))))
% 6.73/7.05 (assert (forall ((A4 tptp.set_list_nat) (B5 tptp.set_list_nat)) (=> (@ tptp.finite8100373058378681591st_nat A4) (=> (@ tptp.finite8100373058378681591st_nat B5) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_list_nat A4)) (@ tptp.finite_card_list_nat B5)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_list_nat (@ (@ tptp.minus_7954133019191499631st_nat A4) B5))) (@ tptp.finite_card_list_nat (@ (@ tptp.minus_7954133019191499631st_nat B5) A4))))))))
% 6.73/7.05 (assert (forall ((A4 tptp.set_set_nat) (B5 tptp.set_set_nat)) (=> (@ tptp.finite1152437895449049373et_nat A4) (=> (@ tptp.finite1152437895449049373et_nat B5) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_set_nat A4)) (@ tptp.finite_card_set_nat B5)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_set_nat (@ (@ tptp.minus_2163939370556025621et_nat A4) B5))) (@ tptp.finite_card_set_nat (@ (@ tptp.minus_2163939370556025621et_nat B5) A4))))))))
% 6.73/7.05 (assert (forall ((A4 tptp.set_int) (B5 tptp.set_int)) (=> (@ tptp.finite_finite_int A4) (=> (@ tptp.finite_finite_int B5) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_int A4)) (@ tptp.finite_card_int B5)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_int (@ (@ tptp.minus_minus_set_int A4) B5))) (@ tptp.finite_card_int (@ (@ tptp.minus_minus_set_int B5) A4))))))))
% 6.73/7.05 (assert (forall ((A4 tptp.set_complex) (B5 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex A4) (=> (@ tptp.finite3207457112153483333omplex B5) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_complex A4)) (@ tptp.finite_card_complex B5)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_complex (@ (@ tptp.minus_811609699411566653omplex A4) B5))) (@ tptp.finite_card_complex (@ (@ tptp.minus_811609699411566653omplex B5) A4))))))))
% 6.73/7.05 (assert (forall ((A4 tptp.set_Pr1261947904930325089at_nat) (B5 tptp.set_Pr1261947904930325089at_nat)) (=> (@ tptp.finite6177210948735845034at_nat A4) (=> (@ tptp.finite6177210948735845034at_nat B5) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite711546835091564841at_nat A4)) (@ tptp.finite711546835091564841at_nat B5)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite711546835091564841at_nat (@ (@ tptp.minus_1356011639430497352at_nat A4) B5))) (@ tptp.finite711546835091564841at_nat (@ (@ tptp.minus_1356011639430497352at_nat B5) A4))))))))
% 6.73/7.05 (assert (forall ((A4 tptp.set_nat) (B5 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A4) (=> (@ tptp.finite_finite_nat B5) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat A4)) (@ tptp.finite_card_nat B5)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat (@ (@ tptp.minus_minus_set_nat A4) B5))) (@ tptp.finite_card_nat (@ (@ tptp.minus_minus_set_nat B5) A4))))))))
% 6.73/7.05 (assert (forall ((Xs2 tptp.list_complex)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_complex (@ tptp.set_complex2 Xs2))) (@ tptp.size_s3451745648224563538omplex Xs2))))
% 6.73/7.05 (assert (forall ((Xs2 tptp.list_list_nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_list_nat (@ tptp.set_list_nat2 Xs2))) (@ tptp.size_s3023201423986296836st_nat Xs2))))
% 6.73/7.05 (assert (forall ((Xs2 tptp.list_set_nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_set_nat (@ tptp.set_set_nat2 Xs2))) (@ tptp.size_s3254054031482475050et_nat Xs2))))
% 6.73/7.05 (assert (forall ((Xs2 tptp.list_VEBT_VEBT)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite7802652506058667612T_VEBT (@ tptp.set_VEBT_VEBT2 Xs2))) (@ tptp.size_s6755466524823107622T_VEBT Xs2))))
% 6.73/7.05 (assert (forall ((Xs2 tptp.list_o)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_o (@ tptp.set_o2 Xs2))) (@ tptp.size_size_list_o Xs2))))
% 6.73/7.05 (assert (forall ((Xs2 tptp.list_nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat (@ tptp.set_nat2 Xs2))) (@ tptp.size_size_list_nat Xs2))))
% 6.73/7.05 (assert (forall ((Xs2 tptp.list_int)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_int (@ tptp.set_int2 Xs2))) (@ tptp.size_size_list_int Xs2))))
% 6.73/7.05 (assert (forall ((A tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_8256067586552552935nteger A) (@ tptp.suc N)))))))
% 6.73/7.05 (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)))))))
% 6.73/7.05 (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)))))))
% 6.73/7.05 (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)))))))
% 6.73/7.05 (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)))))))
% 6.73/7.05 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_8256067586552552935nteger tptp.zero_z3403309356797280102nteger) N))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_Code_integer)) (=> (not _let_2) (= _let_1 tptp.zero_z3403309356797280102nteger)))))))
% 6.73/7.05 (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)))))))
% 6.73/7.05 (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)))))))
% 6.73/7.05 (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)))))))
% 6.73/7.05 (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)))))))
% 6.73/7.05 (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)))))))
% 6.73/7.05 (assert (forall ((N tptp.nat) (N6 tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger A))) (=> (@ (@ tptp.ord_less_eq_nat N) N6) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) A) (@ (@ tptp.ord_le3102999989581377725nteger (@ _let_1 N)) (@ _let_1 N6)))))))
% 6.73/7.05 (assert (forall ((N tptp.nat) (N6 tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_eq_nat N) N6) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) A) (@ (@ tptp.ord_less_eq_real (@ _let_1 N)) (@ _let_1 N6)))))))
% 6.73/7.05 (assert (forall ((N tptp.nat) (N6 tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat A))) (=> (@ (@ tptp.ord_less_eq_nat N) N6) (=> (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) A) (@ (@ tptp.ord_less_eq_rat (@ _let_1 N)) (@ _let_1 N6)))))))
% 6.73/7.05 (assert (forall ((N tptp.nat) (N6 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_eq_nat N) N6) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) A) (@ (@ tptp.ord_less_eq_nat (@ _let_1 N)) (@ _let_1 N6)))))))
% 6.73/7.05 (assert (forall ((N tptp.nat) (N6 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_eq_nat N) N6) (=> (@ (@ tptp.ord_less_eq_int tptp.one_one_int) A) (@ (@ tptp.ord_less_eq_int (@ _let_1 N)) (@ _let_1 N6)))))))
% 6.73/7.05 (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))))
% 6.73/7.05 (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))))
% 6.73/7.05 (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))))
% 6.73/7.05 (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))))
% 6.73/7.05 (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))))
% 6.73/7.05 (assert (forall ((Ms tptp.list_VEBT_VEBT) (Ns tptp.list_VEBT_VEBT) (R3 tptp.set_Pr6192946355708809607T_VEBT)) (=> (@ (@ tptp.member4439316823752958928T_VEBT (@ (@ tptp.produc3897820843166775703T_VEBT Ms) Ns)) (@ tptp.lenlex_VEBT_VEBT R3)) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_s6755466524823107622T_VEBT Ms)) (@ tptp.size_s6755466524823107622T_VEBT Ns)))))
% 6.73/7.05 (assert (forall ((Ms tptp.list_o) (Ns tptp.list_o) (R3 tptp.set_Product_prod_o_o)) (=> (@ (@ tptp.member4159035015898711888list_o (@ (@ tptp.produc8435520187683070743list_o Ms) Ns)) (@ tptp.lenlex_o R3)) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_o Ms)) (@ tptp.size_size_list_o Ns)))))
% 6.73/7.05 (assert (forall ((Ms tptp.list_nat) (Ns tptp.list_nat) (R3 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.member7340969449405702474st_nat (@ (@ tptp.produc2694037385005941721st_nat Ms) Ns)) (@ tptp.lenlex_nat R3)) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_nat Ms)) (@ tptp.size_size_list_nat Ns)))))
% 6.73/7.05 (assert (forall ((Ms tptp.list_int) (Ns tptp.list_int) (R3 tptp.set_Pr958786334691620121nt_int)) (=> (@ (@ tptp.member6698963635872716290st_int (@ (@ tptp.produc364263696895485585st_int Ms) Ns)) (@ tptp.lenlex_int R3)) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_int Ms)) (@ tptp.size_size_list_int Ns)))))
% 6.73/7.05 (assert (forall ((N tptp.nat) (K2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)) N) (@ (@ tptp.ord_less_nat K2) (@ (@ tptp.power_power_nat N) K2)))))
% 6.73/7.05 (assert (forall ((I2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat (@ tptp.suc tptp.zero_zero_nat)))) (=> (@ _let_1 I2) (@ _let_1 (@ (@ tptp.power_power_nat I2) N))))))
% 6.73/7.05 (assert (forall ((S3 tptp.set_nat) (N tptp.nat)) (let ((_let_1 (@ tptp.infini8530281810654367211te_nat S3))) (=> (not (@ tptp.finite_finite_nat S3)) (@ (@ tptp.ord_less_nat (@ _let_1 N)) (@ _let_1 (@ tptp.suc N)))))))
% 6.73/7.05 (assert (forall ((A4 tptp.set_list_nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.finite_card_list_nat A4)) (and (not (= A4 tptp.bot_bot_set_list_nat)) (@ tptp.finite8100373058378681591st_nat A4)))))
% 6.73/7.05 (assert (forall ((A4 tptp.set_set_nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.finite_card_set_nat A4)) (and (not (= A4 tptp.bot_bot_set_set_nat)) (@ tptp.finite1152437895449049373et_nat A4)))))
% 6.73/7.05 (assert (forall ((A4 tptp.set_complex)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.finite_card_complex A4)) (and (not (= A4 tptp.bot_bot_set_complex)) (@ tptp.finite3207457112153483333omplex A4)))))
% 6.73/7.05 (assert (forall ((A4 tptp.set_nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.finite_card_nat A4)) (and (not (= A4 tptp.bot_bot_set_nat)) (@ tptp.finite_finite_nat A4)))))
% 6.73/7.05 (assert (forall ((A4 tptp.set_int)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.finite_card_int A4)) (and (not (= A4 tptp.bot_bot_set_int)) (@ tptp.finite_finite_int A4)))))
% 6.73/7.05 (assert (forall ((A4 tptp.set_real)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.finite_card_real A4)) (and (not (= A4 tptp.bot_bot_set_real)) (@ tptp.finite_finite_real A4)))))
% 6.73/7.05 (assert (forall ((A4 tptp.set_complex)) (= (= (@ tptp.finite_card_complex A4) (@ tptp.suc tptp.zero_zero_nat)) (exists ((X4 tptp.complex)) (= A4 (@ (@ tptp.insert_complex X4) tptp.bot_bot_set_complex))))))
% 6.73/7.05 (assert (forall ((A4 tptp.set_list_nat)) (= (= (@ tptp.finite_card_list_nat A4) (@ tptp.suc tptp.zero_zero_nat)) (exists ((X4 tptp.list_nat)) (= A4 (@ (@ tptp.insert_list_nat X4) tptp.bot_bot_set_list_nat))))))
% 6.73/7.05 (assert (forall ((A4 tptp.set_set_nat)) (= (= (@ tptp.finite_card_set_nat A4) (@ tptp.suc tptp.zero_zero_nat)) (exists ((X4 tptp.set_nat)) (= A4 (@ (@ tptp.insert_set_nat X4) tptp.bot_bot_set_set_nat))))))
% 6.73/7.05 (assert (forall ((A4 tptp.set_nat)) (= (= (@ tptp.finite_card_nat A4) (@ tptp.suc tptp.zero_zero_nat)) (exists ((X4 tptp.nat)) (= A4 (@ (@ tptp.insert_nat X4) tptp.bot_bot_set_nat))))))
% 6.73/7.05 (assert (forall ((A4 tptp.set_int)) (= (= (@ tptp.finite_card_int A4) (@ tptp.suc tptp.zero_zero_nat)) (exists ((X4 tptp.int)) (= A4 (@ (@ tptp.insert_int X4) tptp.bot_bot_set_int))))))
% 6.73/7.05 (assert (forall ((A4 tptp.set_real)) (= (= (@ tptp.finite_card_real A4) (@ tptp.suc tptp.zero_zero_nat)) (exists ((X4 tptp.real)) (= A4 (@ (@ tptp.insert_real X4) tptp.bot_bot_set_real))))))
% 6.73/7.05 (assert (forall ((A4 tptp.set_complex) (K2 tptp.nat)) (=> (= (@ tptp.finite_card_complex A4) (@ tptp.suc K2)) (exists ((B3 tptp.complex) (B8 tptp.set_complex)) (and (= A4 (@ (@ tptp.insert_complex B3) B8)) (not (@ (@ tptp.member_complex B3) B8)) (= (@ tptp.finite_card_complex B8) K2) (=> (= K2 tptp.zero_zero_nat) (= B8 tptp.bot_bot_set_complex)))))))
% 6.73/7.05 (assert (forall ((A4 tptp.set_list_nat) (K2 tptp.nat)) (=> (= (@ tptp.finite_card_list_nat A4) (@ tptp.suc K2)) (exists ((B3 tptp.list_nat) (B8 tptp.set_list_nat)) (and (= A4 (@ (@ tptp.insert_list_nat B3) B8)) (not (@ (@ tptp.member_list_nat B3) B8)) (= (@ tptp.finite_card_list_nat B8) K2) (=> (= K2 tptp.zero_zero_nat) (= B8 tptp.bot_bot_set_list_nat)))))))
% 6.73/7.05 (assert (forall ((A4 tptp.set_set_nat) (K2 tptp.nat)) (=> (= (@ tptp.finite_card_set_nat A4) (@ tptp.suc K2)) (exists ((B3 tptp.set_nat) (B8 tptp.set_set_nat)) (and (= A4 (@ (@ tptp.insert_set_nat B3) B8)) (not (@ (@ tptp.member_set_nat B3) B8)) (= (@ tptp.finite_card_set_nat B8) K2) (=> (= K2 tptp.zero_zero_nat) (= B8 tptp.bot_bot_set_set_nat)))))))
% 6.73/7.05 (assert (forall ((A4 tptp.set_nat) (K2 tptp.nat)) (=> (= (@ tptp.finite_card_nat A4) (@ tptp.suc K2)) (exists ((B3 tptp.nat) (B8 tptp.set_nat)) (and (= A4 (@ (@ tptp.insert_nat B3) B8)) (not (@ (@ tptp.member_nat B3) B8)) (= (@ tptp.finite_card_nat B8) K2) (=> (= K2 tptp.zero_zero_nat) (= B8 tptp.bot_bot_set_nat)))))))
% 6.73/7.05 (assert (forall ((A4 tptp.set_int) (K2 tptp.nat)) (=> (= (@ tptp.finite_card_int A4) (@ tptp.suc K2)) (exists ((B3 tptp.int) (B8 tptp.set_int)) (and (= A4 (@ (@ tptp.insert_int B3) B8)) (not (@ (@ tptp.member_int B3) B8)) (= (@ tptp.finite_card_int B8) K2) (=> (= K2 tptp.zero_zero_nat) (= B8 tptp.bot_bot_set_int)))))))
% 6.73/7.05 (assert (forall ((A4 tptp.set_real) (K2 tptp.nat)) (=> (= (@ tptp.finite_card_real A4) (@ tptp.suc K2)) (exists ((B3 tptp.real) (B8 tptp.set_real)) (and (= A4 (@ (@ tptp.insert_real B3) B8)) (not (@ (@ tptp.member_real B3) B8)) (= (@ tptp.finite_card_real B8) K2) (=> (= K2 tptp.zero_zero_nat) (= B8 tptp.bot_bot_set_real)))))))
% 6.73/7.05 (assert (forall ((A4 tptp.set_complex) (K2 tptp.nat)) (= (= (@ tptp.finite_card_complex A4) (@ tptp.suc K2)) (exists ((B4 tptp.complex) (B7 tptp.set_complex)) (and (= A4 (@ (@ tptp.insert_complex B4) B7)) (not (@ (@ tptp.member_complex B4) B7)) (= (@ tptp.finite_card_complex B7) K2) (=> (= K2 tptp.zero_zero_nat) (= B7 tptp.bot_bot_set_complex)))))))
% 6.73/7.05 (assert (forall ((A4 tptp.set_list_nat) (K2 tptp.nat)) (= (= (@ tptp.finite_card_list_nat A4) (@ tptp.suc K2)) (exists ((B4 tptp.list_nat) (B7 tptp.set_list_nat)) (and (= A4 (@ (@ tptp.insert_list_nat B4) B7)) (not (@ (@ tptp.member_list_nat B4) B7)) (= (@ tptp.finite_card_list_nat B7) K2) (=> (= K2 tptp.zero_zero_nat) (= B7 tptp.bot_bot_set_list_nat)))))))
% 6.73/7.05 (assert (forall ((A4 tptp.set_set_nat) (K2 tptp.nat)) (= (= (@ tptp.finite_card_set_nat A4) (@ tptp.suc K2)) (exists ((B4 tptp.set_nat) (B7 tptp.set_set_nat)) (and (= A4 (@ (@ tptp.insert_set_nat B4) B7)) (not (@ (@ tptp.member_set_nat B4) B7)) (= (@ tptp.finite_card_set_nat B7) K2) (=> (= K2 tptp.zero_zero_nat) (= B7 tptp.bot_bot_set_set_nat)))))))
% 6.73/7.05 (assert (forall ((A4 tptp.set_nat) (K2 tptp.nat)) (= (= (@ tptp.finite_card_nat A4) (@ tptp.suc K2)) (exists ((B4 tptp.nat) (B7 tptp.set_nat)) (and (= A4 (@ (@ tptp.insert_nat B4) B7)) (not (@ (@ tptp.member_nat B4) B7)) (= (@ tptp.finite_card_nat B7) K2) (=> (= K2 tptp.zero_zero_nat) (= B7 tptp.bot_bot_set_nat)))))))
% 6.73/7.05 (assert (forall ((A4 tptp.set_int) (K2 tptp.nat)) (= (= (@ tptp.finite_card_int A4) (@ tptp.suc K2)) (exists ((B4 tptp.int) (B7 tptp.set_int)) (and (= A4 (@ (@ tptp.insert_int B4) B7)) (not (@ (@ tptp.member_int B4) B7)) (= (@ tptp.finite_card_int B7) K2) (=> (= K2 tptp.zero_zero_nat) (= B7 tptp.bot_bot_set_int)))))))
% 6.73/7.05 (assert (forall ((A4 tptp.set_real) (K2 tptp.nat)) (= (= (@ tptp.finite_card_real A4) (@ tptp.suc K2)) (exists ((B4 tptp.real) (B7 tptp.set_real)) (and (= A4 (@ (@ tptp.insert_real B4) B7)) (not (@ (@ tptp.member_real B4) B7)) (= (@ tptp.finite_card_real B7) K2) (=> (= K2 tptp.zero_zero_nat) (= B7 tptp.bot_bot_set_real)))))))
% 6.73/7.05 (assert (forall ((A4 tptp.set_list_nat)) (=> (@ tptp.finite8100373058378681591st_nat A4) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_list_nat A4)) (@ tptp.suc tptp.zero_zero_nat)) (forall ((X4 tptp.list_nat)) (=> (@ (@ tptp.member_list_nat X4) A4) (forall ((Y4 tptp.list_nat)) (=> (@ (@ tptp.member_list_nat Y4) A4) (= X4 Y4)))))))))
% 6.73/7.05 (assert (forall ((A4 tptp.set_set_nat)) (=> (@ tptp.finite1152437895449049373et_nat A4) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_set_nat A4)) (@ tptp.suc tptp.zero_zero_nat)) (forall ((X4 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat X4) A4) (forall ((Y4 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat Y4) A4) (= X4 Y4)))))))))
% 6.73/7.05 (assert (forall ((A4 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A4) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat A4)) (@ tptp.suc tptp.zero_zero_nat)) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) A4) (forall ((Y4 tptp.nat)) (=> (@ (@ tptp.member_nat Y4) A4) (= X4 Y4)))))))))
% 6.73/7.05 (assert (forall ((A4 tptp.set_int)) (=> (@ tptp.finite_finite_int A4) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_int A4)) (@ tptp.suc tptp.zero_zero_nat)) (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) A4) (forall ((Y4 tptp.int)) (=> (@ (@ tptp.member_int Y4) A4) (= X4 Y4)))))))))
% 6.73/7.05 (assert (forall ((A4 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex A4) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_complex A4)) (@ tptp.suc tptp.zero_zero_nat)) (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) A4) (forall ((Y4 tptp.complex)) (=> (@ (@ tptp.member_complex Y4) A4) (= X4 Y4)))))))))
% 6.73/7.05 (assert (forall ((N tptp.nat) (A4 tptp.set_real)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) (@ tptp.finite_card_real A4)) (exists ((A5 tptp.real) (B7 tptp.set_real)) (and (= A4 (@ (@ tptp.insert_real A5) B7)) (not (@ (@ tptp.member_real A5) B7)) (@ (@ tptp.ord_less_eq_nat N) (@ tptp.finite_card_real B7)) (@ tptp.finite_finite_real B7))))))
% 6.73/7.05 (assert (forall ((N tptp.nat) (A4 tptp.set_list_nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) (@ tptp.finite_card_list_nat A4)) (exists ((A5 tptp.list_nat) (B7 tptp.set_list_nat)) (and (= A4 (@ (@ tptp.insert_list_nat A5) B7)) (not (@ (@ tptp.member_list_nat A5) B7)) (@ (@ tptp.ord_less_eq_nat N) (@ tptp.finite_card_list_nat B7)) (@ tptp.finite8100373058378681591st_nat B7))))))
% 6.73/7.05 (assert (forall ((N tptp.nat) (A4 tptp.set_set_nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) (@ tptp.finite_card_set_nat A4)) (exists ((A5 tptp.set_nat) (B7 tptp.set_set_nat)) (and (= A4 (@ (@ tptp.insert_set_nat A5) B7)) (not (@ (@ tptp.member_set_nat A5) B7)) (@ (@ tptp.ord_less_eq_nat N) (@ tptp.finite_card_set_nat B7)) (@ tptp.finite1152437895449049373et_nat B7))))))
% 6.73/7.05 (assert (forall ((N tptp.nat) (A4 tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) (@ tptp.finite_card_nat A4)) (exists ((A5 tptp.nat) (B7 tptp.set_nat)) (and (= A4 (@ (@ tptp.insert_nat A5) B7)) (not (@ (@ tptp.member_nat A5) B7)) (@ (@ tptp.ord_less_eq_nat N) (@ tptp.finite_card_nat B7)) (@ tptp.finite_finite_nat B7))))))
% 6.73/7.05 (assert (forall ((N tptp.nat) (A4 tptp.set_int)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) (@ tptp.finite_card_int A4)) (exists ((A5 tptp.int) (B7 tptp.set_int)) (and (= A4 (@ (@ tptp.insert_int A5) B7)) (not (@ (@ tptp.member_int A5) B7)) (@ (@ tptp.ord_less_eq_nat N) (@ tptp.finite_card_int B7)) (@ tptp.finite_finite_int B7))))))
% 6.73/7.05 (assert (forall ((N tptp.nat) (A4 tptp.set_complex)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) (@ tptp.finite_card_complex A4)) (exists ((A5 tptp.complex) (B7 tptp.set_complex)) (and (= A4 (@ (@ tptp.insert_complex A5) B7)) (not (@ (@ tptp.member_complex A5) B7)) (@ (@ tptp.ord_less_eq_nat N) (@ tptp.finite_card_complex B7)) (@ tptp.finite3207457112153483333omplex B7))))))
% 6.73/7.05 (assert (forall ((A tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_8256067586552552935nteger A) N))) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A) (=> (@ (@ tptp.ord_le6747313008572928689nteger A) tptp.one_one_Code_integer) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.times_3573771949741848930nteger A) _let_1)) _let_1))))))
% 6.73/7.05 (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))))))
% 6.73/7.05 (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))))))
% 6.73/7.05 (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))))))
% 6.73/7.05 (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))))))
% 6.73/7.05 (assert (forall ((A tptp.code_integer) (N tptp.nat)) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A) (=> (@ (@ tptp.ord_le3102999989581377725nteger A) tptp.one_one_Code_integer) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.power_8256067586552552935nteger A) (@ tptp.suc N))) A)))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (assert (forall ((A tptp.code_integer) (N tptp.nat)) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A) (=> (@ (@ tptp.ord_le6747313008572928689nteger A) tptp.one_one_Code_integer) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.power_8256067586552552935nteger A) (@ tptp.suc N))) tptp.one_one_Code_integer)))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (assert (forall ((A4 tptp.set_complex) (X tptp.complex)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_complex (@ (@ tptp.minus_811609699411566653omplex A4) (@ (@ tptp.insert_complex X) tptp.bot_bot_set_complex)))) (@ tptp.finite_card_complex A4))))
% 6.73/7.05 (assert (forall ((A4 tptp.set_list_nat) (X tptp.list_nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_list_nat (@ (@ tptp.minus_7954133019191499631st_nat A4) (@ (@ tptp.insert_list_nat X) tptp.bot_bot_set_list_nat)))) (@ tptp.finite_card_list_nat A4))))
% 6.73/7.05 (assert (forall ((A4 tptp.set_set_nat) (X tptp.set_nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_set_nat (@ (@ tptp.minus_2163939370556025621et_nat A4) (@ (@ tptp.insert_set_nat X) tptp.bot_bot_set_set_nat)))) (@ tptp.finite_card_set_nat A4))))
% 6.73/7.05 (assert (forall ((A4 tptp.set_int) (X tptp.int)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_int (@ (@ tptp.minus_minus_set_int A4) (@ (@ tptp.insert_int X) tptp.bot_bot_set_int)))) (@ tptp.finite_card_int A4))))
% 6.73/7.05 (assert (forall ((A4 tptp.set_real) (X tptp.real)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_real (@ (@ tptp.minus_minus_set_real A4) (@ (@ tptp.insert_real X) tptp.bot_bot_set_real)))) (@ tptp.finite_card_real A4))))
% 6.73/7.05 (assert (forall ((A4 tptp.set_Pr1261947904930325089at_nat) (X tptp.product_prod_nat_nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite711546835091564841at_nat (@ (@ tptp.minus_1356011639430497352at_nat A4) (@ (@ tptp.insert8211810215607154385at_nat X) tptp.bot_bo2099793752762293965at_nat)))) (@ tptp.finite711546835091564841at_nat A4))))
% 6.73/7.05 (assert (forall ((A4 tptp.set_nat) (X tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat (@ (@ tptp.minus_minus_set_nat A4) (@ (@ tptp.insert_nat X) tptp.bot_bot_set_nat)))) (@ tptp.finite_card_nat A4))))
% 6.73/7.05 (assert (forall ((N tptp.nat) (N6 tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger A))) (=> (@ (@ tptp.ord_less_nat N) N6) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A) (=> (@ (@ tptp.ord_le6747313008572928689nteger A) tptp.one_one_Code_integer) (@ (@ tptp.ord_le6747313008572928689nteger (@ _let_1 N6)) (@ _let_1 N))))))))
% 6.73/7.05 (assert (forall ((N tptp.nat) (N6 tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_nat N) N6) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_real A) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ _let_1 N6)) (@ _let_1 N))))))))
% 6.73/7.05 (assert (forall ((N tptp.nat) (N6 tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat A))) (=> (@ (@ tptp.ord_less_nat N) N6) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_rat A) tptp.one_one_rat) (@ (@ tptp.ord_less_rat (@ _let_1 N6)) (@ _let_1 N))))))))
% 6.73/7.05 (assert (forall ((N tptp.nat) (N6 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_nat N) N6) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat A) tptp.one_one_nat) (@ (@ tptp.ord_less_nat (@ _let_1 N6)) (@ _let_1 N))))))))
% 6.73/7.05 (assert (forall ((N tptp.nat) (N6 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_nat N) N6) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int A) tptp.one_one_int) (@ (@ tptp.ord_less_int (@ _let_1 N6)) (@ _let_1 N))))))))
% 6.73/7.05 (assert (forall ((N tptp.nat) (N6 tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger A))) (=> (@ (@ tptp.ord_less_eq_nat N) N6) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A) (=> (@ (@ tptp.ord_le3102999989581377725nteger A) tptp.one_one_Code_integer) (@ (@ tptp.ord_le3102999989581377725nteger (@ _let_1 N6)) (@ _let_1 N))))))))
% 6.73/7.05 (assert (forall ((N tptp.nat) (N6 tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_eq_nat N) N6) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_eq_real A) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ _let_1 N6)) (@ _let_1 N))))))))
% 6.73/7.05 (assert (forall ((N tptp.nat) (N6 tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat A))) (=> (@ (@ tptp.ord_less_eq_nat N) N6) (=> (@ (@ 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 N6)) (@ _let_1 N))))))))
% 6.73/7.05 (assert (forall ((N tptp.nat) (N6 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_eq_nat N) N6) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.one_one_nat) (@ (@ tptp.ord_less_eq_nat (@ _let_1 N6)) (@ _let_1 N))))))))
% 6.73/7.05 (assert (forall ((N tptp.nat) (N6 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_eq_nat N) N6) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_eq_int A) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ _let_1 N6)) (@ _let_1 N))))))))
% 6.73/7.05 (assert (forall ((A tptp.code_integer) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger A))) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) A) (=> (@ (@ tptp.ord_le3102999989581377725nteger (@ _let_1 M2)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat M2) N))))))
% 6.73/7.05 (assert (forall ((A tptp.real) (M2 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 M2)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat M2) N))))))
% 6.73/7.05 (assert (forall ((A tptp.rat) (M2 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 M2)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat M2) N))))))
% 6.73/7.05 (assert (forall ((A tptp.nat) (M2 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 M2)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat M2) N))))))
% 6.73/7.05 (assert (forall ((A tptp.int) (M2 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 M2)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat M2) N))))))
% 6.73/7.05 (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))))))))
% 6.73/7.05 (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))))))))
% 6.73/7.05 (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))))))))
% 6.73/7.05 (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))))))))
% 6.73/7.05 (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))))))))
% 6.73/7.05 (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))))))))
% 6.73/7.05 (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))))))))
% 6.73/7.05 (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))))))))
% 6.73/7.05 (assert (forall ((B5 tptp.set_list_nat) (A4 tptp.set_list_nat)) (=> (@ tptp.finite8100373058378681591st_nat B5) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat (@ tptp.finite_card_list_nat A4)) (@ tptp.finite_card_list_nat B5))) (@ tptp.finite_card_list_nat (@ (@ tptp.minus_7954133019191499631st_nat A4) B5))))))
% 6.73/7.05 (assert (forall ((B5 tptp.set_set_nat) (A4 tptp.set_set_nat)) (=> (@ tptp.finite1152437895449049373et_nat B5) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat (@ tptp.finite_card_set_nat A4)) (@ tptp.finite_card_set_nat B5))) (@ tptp.finite_card_set_nat (@ (@ tptp.minus_2163939370556025621et_nat A4) B5))))))
% 6.73/7.05 (assert (forall ((B5 tptp.set_int) (A4 tptp.set_int)) (=> (@ tptp.finite_finite_int B5) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat (@ tptp.finite_card_int A4)) (@ tptp.finite_card_int B5))) (@ tptp.finite_card_int (@ (@ tptp.minus_minus_set_int A4) B5))))))
% 6.73/7.05 (assert (forall ((B5 tptp.set_complex) (A4 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex B5) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat (@ tptp.finite_card_complex A4)) (@ tptp.finite_card_complex B5))) (@ tptp.finite_card_complex (@ (@ tptp.minus_811609699411566653omplex A4) B5))))))
% 6.73/7.05 (assert (forall ((B5 tptp.set_Pr1261947904930325089at_nat) (A4 tptp.set_Pr1261947904930325089at_nat)) (=> (@ tptp.finite6177210948735845034at_nat B5) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat (@ tptp.finite711546835091564841at_nat A4)) (@ tptp.finite711546835091564841at_nat B5))) (@ tptp.finite711546835091564841at_nat (@ (@ tptp.minus_1356011639430497352at_nat A4) B5))))))
% 6.73/7.05 (assert (forall ((B5 tptp.set_nat) (A4 tptp.set_nat)) (=> (@ tptp.finite_finite_nat B5) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat (@ tptp.finite_card_nat A4)) (@ tptp.finite_card_nat B5))) (@ tptp.finite_card_nat (@ (@ tptp.minus_minus_set_nat A4) B5))))))
% 6.73/7.05 (assert (forall ((A tptp.code_integer) (N tptp.nat)) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_le3102999989581377725nteger A) (@ (@ tptp.power_8256067586552552935nteger A) N))))))
% 6.73/7.05 (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))))))
% 6.73/7.05 (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))))))
% 6.73/7.05 (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))))))
% 6.73/7.05 (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))))))
% 6.73/7.05 (assert (forall ((A tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer))) (=> (@ _let_1 A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ _let_1 (@ (@ tptp.power_8256067586552552935nteger A) N)))))))
% 6.73/7.05 (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)))))))
% 6.73/7.05 (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)))))))
% 6.73/7.05 (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)))))))
% 6.73/7.05 (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)))))))
% 6.73/7.05 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (X tptp.vEBT_VEBT)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.count_list_VEBT_VEBT Xs2) X)) (@ tptp.size_s6755466524823107622T_VEBT Xs2))))
% 6.73/7.05 (assert (forall ((Xs2 tptp.list_o) (X Bool)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.count_list_o Xs2) X)) (@ tptp.size_size_list_o Xs2))))
% 6.73/7.05 (assert (forall ((Xs2 tptp.list_nat) (X tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.count_list_nat Xs2) X)) (@ tptp.size_size_list_nat Xs2))))
% 6.73/7.05 (assert (forall ((Xs2 tptp.list_int) (X tptp.int)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.count_list_int Xs2) X)) (@ tptp.size_size_list_int Xs2))))
% 6.73/7.05 (assert (= tptp.neg_nu5831290666863070958nteger (lambda ((X4 tptp.code_integer)) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.plus_p5714425477246183910nteger X4) X4)) tptp.one_one_Code_integer))))
% 6.73/7.05 (assert (= tptp.neg_nu8557863876264182079omplex (lambda ((X4 tptp.complex)) (@ (@ tptp.plus_plus_complex (@ (@ tptp.plus_plus_complex X4) X4)) tptp.one_one_complex))))
% 6.73/7.05 (assert (= tptp.neg_nu8295874005876285629c_real (lambda ((X4 tptp.real)) (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real X4) X4)) tptp.one_one_real))))
% 6.73/7.05 (assert (= tptp.neg_nu5219082963157363817nc_rat (lambda ((X4 tptp.rat)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.plus_plus_rat X4) X4)) tptp.one_one_rat))))
% 6.73/7.05 (assert (= tptp.neg_nu5851722552734809277nc_int (lambda ((X4 tptp.int)) (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int X4) X4)) tptp.one_one_int))))
% 6.73/7.05 (assert (forall ((A4 tptp.set_list_nat) (X tptp.list_nat)) (=> (@ tptp.finite8100373058378681591st_nat A4) (=> (@ (@ tptp.member_list_nat X) A4) (= (@ tptp.finite_card_list_nat A4) (@ tptp.suc (@ tptp.finite_card_list_nat (@ (@ tptp.minus_7954133019191499631st_nat A4) (@ (@ tptp.insert_list_nat X) tptp.bot_bot_set_list_nat)))))))))
% 6.73/7.05 (assert (forall ((A4 tptp.set_set_nat) (X tptp.set_nat)) (=> (@ tptp.finite1152437895449049373et_nat A4) (=> (@ (@ tptp.member_set_nat X) A4) (= (@ tptp.finite_card_set_nat A4) (@ tptp.suc (@ tptp.finite_card_set_nat (@ (@ tptp.minus_2163939370556025621et_nat A4) (@ (@ tptp.insert_set_nat X) tptp.bot_bot_set_set_nat)))))))))
% 6.73/7.05 (assert (forall ((A4 tptp.set_complex) (X tptp.complex)) (=> (@ tptp.finite3207457112153483333omplex A4) (=> (@ (@ tptp.member_complex X) A4) (= (@ tptp.finite_card_complex A4) (@ tptp.suc (@ tptp.finite_card_complex (@ (@ tptp.minus_811609699411566653omplex A4) (@ (@ tptp.insert_complex X) tptp.bot_bot_set_complex)))))))))
% 6.73/7.05 (assert (forall ((A4 tptp.set_int) (X tptp.int)) (=> (@ tptp.finite_finite_int A4) (=> (@ (@ tptp.member_int X) A4) (= (@ tptp.finite_card_int A4) (@ tptp.suc (@ tptp.finite_card_int (@ (@ tptp.minus_minus_set_int A4) (@ (@ tptp.insert_int X) tptp.bot_bot_set_int)))))))))
% 6.73/7.05 (assert (forall ((A4 tptp.set_real) (X tptp.real)) (=> (@ tptp.finite_finite_real A4) (=> (@ (@ tptp.member_real X) A4) (= (@ tptp.finite_card_real A4) (@ tptp.suc (@ tptp.finite_card_real (@ (@ tptp.minus_minus_set_real A4) (@ (@ tptp.insert_real X) tptp.bot_bot_set_real)))))))))
% 6.73/7.05 (assert (forall ((A4 tptp.set_Pr1261947904930325089at_nat) (X tptp.product_prod_nat_nat)) (=> (@ tptp.finite6177210948735845034at_nat A4) (=> (@ (@ tptp.member8440522571783428010at_nat X) A4) (= (@ tptp.finite711546835091564841at_nat A4) (@ tptp.suc (@ tptp.finite711546835091564841at_nat (@ (@ tptp.minus_1356011639430497352at_nat A4) (@ (@ tptp.insert8211810215607154385at_nat X) tptp.bot_bo2099793752762293965at_nat)))))))))
% 6.73/7.05 (assert (forall ((A4 tptp.set_nat) (X tptp.nat)) (=> (@ tptp.finite_finite_nat A4) (=> (@ (@ tptp.member_nat X) A4) (= (@ tptp.finite_card_nat A4) (@ tptp.suc (@ tptp.finite_card_nat (@ (@ tptp.minus_minus_set_nat A4) (@ (@ tptp.insert_nat X) tptp.bot_bot_set_nat)))))))))
% 6.73/7.05 (assert (forall ((A4 tptp.set_list_nat) (X tptp.list_nat)) (let ((_let_1 (@ tptp.insert_list_nat X))) (=> (@ tptp.finite8100373058378681591st_nat A4) (= (@ tptp.finite_card_list_nat (@ _let_1 A4)) (@ tptp.suc (@ tptp.finite_card_list_nat (@ (@ tptp.minus_7954133019191499631st_nat A4) (@ _let_1 tptp.bot_bot_set_list_nat)))))))))
% 6.73/7.05 (assert (forall ((A4 tptp.set_set_nat) (X tptp.set_nat)) (let ((_let_1 (@ tptp.insert_set_nat X))) (=> (@ tptp.finite1152437895449049373et_nat A4) (= (@ tptp.finite_card_set_nat (@ _let_1 A4)) (@ tptp.suc (@ tptp.finite_card_set_nat (@ (@ tptp.minus_2163939370556025621et_nat A4) (@ _let_1 tptp.bot_bot_set_set_nat)))))))))
% 6.73/7.05 (assert (forall ((A4 tptp.set_complex) (X tptp.complex)) (let ((_let_1 (@ tptp.insert_complex X))) (=> (@ tptp.finite3207457112153483333omplex A4) (= (@ tptp.finite_card_complex (@ _let_1 A4)) (@ tptp.suc (@ tptp.finite_card_complex (@ (@ tptp.minus_811609699411566653omplex A4) (@ _let_1 tptp.bot_bot_set_complex)))))))))
% 6.73/7.05 (assert (forall ((A4 tptp.set_int) (X tptp.int)) (let ((_let_1 (@ tptp.insert_int X))) (=> (@ tptp.finite_finite_int A4) (= (@ tptp.finite_card_int (@ _let_1 A4)) (@ tptp.suc (@ tptp.finite_card_int (@ (@ tptp.minus_minus_set_int A4) (@ _let_1 tptp.bot_bot_set_int)))))))))
% 6.73/7.05 (assert (forall ((A4 tptp.set_real) (X tptp.real)) (let ((_let_1 (@ tptp.insert_real X))) (=> (@ tptp.finite_finite_real A4) (= (@ tptp.finite_card_real (@ _let_1 A4)) (@ tptp.suc (@ tptp.finite_card_real (@ (@ tptp.minus_minus_set_real A4) (@ _let_1 tptp.bot_bot_set_real)))))))))
% 6.73/7.05 (assert (forall ((A4 tptp.set_Pr1261947904930325089at_nat) (X tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.insert8211810215607154385at_nat X))) (=> (@ tptp.finite6177210948735845034at_nat A4) (= (@ tptp.finite711546835091564841at_nat (@ _let_1 A4)) (@ tptp.suc (@ tptp.finite711546835091564841at_nat (@ (@ tptp.minus_1356011639430497352at_nat A4) (@ _let_1 tptp.bot_bo2099793752762293965at_nat)))))))))
% 6.73/7.05 (assert (forall ((A4 tptp.set_nat) (X tptp.nat)) (let ((_let_1 (@ tptp.insert_nat X))) (=> (@ tptp.finite_finite_nat A4) (= (@ tptp.finite_card_nat (@ _let_1 A4)) (@ tptp.suc (@ tptp.finite_card_nat (@ (@ tptp.minus_minus_set_nat A4) (@ _let_1 tptp.bot_bot_set_nat)))))))))
% 6.73/7.05 (assert (forall ((A4 tptp.set_list_nat) (X tptp.list_nat)) (=> (@ tptp.finite8100373058378681591st_nat A4) (=> (@ (@ tptp.member_list_nat X) A4) (= (@ tptp.suc (@ tptp.finite_card_list_nat (@ (@ tptp.minus_7954133019191499631st_nat A4) (@ (@ tptp.insert_list_nat X) tptp.bot_bot_set_list_nat)))) (@ tptp.finite_card_list_nat A4))))))
% 6.73/7.05 (assert (forall ((A4 tptp.set_set_nat) (X tptp.set_nat)) (=> (@ tptp.finite1152437895449049373et_nat A4) (=> (@ (@ tptp.member_set_nat X) A4) (= (@ tptp.suc (@ tptp.finite_card_set_nat (@ (@ tptp.minus_2163939370556025621et_nat A4) (@ (@ tptp.insert_set_nat X) tptp.bot_bot_set_set_nat)))) (@ tptp.finite_card_set_nat A4))))))
% 6.73/7.05 (assert (forall ((A4 tptp.set_complex) (X tptp.complex)) (=> (@ tptp.finite3207457112153483333omplex A4) (=> (@ (@ tptp.member_complex X) A4) (= (@ tptp.suc (@ tptp.finite_card_complex (@ (@ tptp.minus_811609699411566653omplex A4) (@ (@ tptp.insert_complex X) tptp.bot_bot_set_complex)))) (@ tptp.finite_card_complex A4))))))
% 6.73/7.05 (assert (forall ((A4 tptp.set_int) (X tptp.int)) (=> (@ tptp.finite_finite_int A4) (=> (@ (@ tptp.member_int X) A4) (= (@ tptp.suc (@ tptp.finite_card_int (@ (@ tptp.minus_minus_set_int A4) (@ (@ tptp.insert_int X) tptp.bot_bot_set_int)))) (@ tptp.finite_card_int A4))))))
% 6.73/7.05 (assert (forall ((A4 tptp.set_real) (X tptp.real)) (=> (@ tptp.finite_finite_real A4) (=> (@ (@ tptp.member_real X) A4) (= (@ tptp.suc (@ tptp.finite_card_real (@ (@ tptp.minus_minus_set_real A4) (@ (@ tptp.insert_real X) tptp.bot_bot_set_real)))) (@ tptp.finite_card_real A4))))))
% 6.73/7.05 (assert (forall ((A4 tptp.set_Pr1261947904930325089at_nat) (X tptp.product_prod_nat_nat)) (=> (@ tptp.finite6177210948735845034at_nat A4) (=> (@ (@ tptp.member8440522571783428010at_nat X) A4) (= (@ tptp.suc (@ tptp.finite711546835091564841at_nat (@ (@ tptp.minus_1356011639430497352at_nat A4) (@ (@ tptp.insert8211810215607154385at_nat X) tptp.bot_bo2099793752762293965at_nat)))) (@ tptp.finite711546835091564841at_nat A4))))))
% 6.73/7.05 (assert (forall ((A4 tptp.set_nat) (X tptp.nat)) (=> (@ tptp.finite_finite_nat A4) (=> (@ (@ tptp.member_nat X) A4) (= (@ tptp.suc (@ tptp.finite_card_nat (@ (@ tptp.minus_minus_set_nat A4) (@ (@ tptp.insert_nat X) tptp.bot_bot_set_nat)))) (@ tptp.finite_card_nat A4))))))
% 6.73/7.05 (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)))))))
% 6.73/7.05 (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)))))))
% 6.73/7.05 (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)))))))
% 6.73/7.05 (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)))))))
% 6.73/7.05 (assert (= tptp.power_8256067586552552935nteger (lambda ((P5 tptp.code_integer) (M6 tptp.nat)) (@ (@ (@ tptp.if_Code_integer (= M6 tptp.zero_zero_nat)) tptp.one_one_Code_integer) (@ (@ tptp.times_3573771949741848930nteger P5) (@ (@ tptp.power_8256067586552552935nteger P5) (@ (@ tptp.minus_minus_nat M6) tptp.one_one_nat)))))))
% 6.73/7.05 (assert (= tptp.power_power_complex (lambda ((P5 tptp.complex) (M6 tptp.nat)) (@ (@ (@ tptp.if_complex (= M6 tptp.zero_zero_nat)) tptp.one_one_complex) (@ (@ tptp.times_times_complex P5) (@ (@ tptp.power_power_complex P5) (@ (@ tptp.minus_minus_nat M6) tptp.one_one_nat)))))))
% 6.73/7.05 (assert (= tptp.power_power_real (lambda ((P5 tptp.real) (M6 tptp.nat)) (@ (@ (@ tptp.if_real (= M6 tptp.zero_zero_nat)) tptp.one_one_real) (@ (@ tptp.times_times_real P5) (@ (@ tptp.power_power_real P5) (@ (@ tptp.minus_minus_nat M6) tptp.one_one_nat)))))))
% 6.73/7.05 (assert (= tptp.power_power_rat (lambda ((P5 tptp.rat) (M6 tptp.nat)) (@ (@ (@ tptp.if_rat (= M6 tptp.zero_zero_nat)) tptp.one_one_rat) (@ (@ tptp.times_times_rat P5) (@ (@ tptp.power_power_rat P5) (@ (@ tptp.minus_minus_nat M6) tptp.one_one_nat)))))))
% 6.73/7.05 (assert (= tptp.power_power_nat (lambda ((P5 tptp.nat) (M6 tptp.nat)) (@ (@ (@ tptp.if_nat (= M6 tptp.zero_zero_nat)) tptp.one_one_nat) (@ (@ tptp.times_times_nat P5) (@ (@ tptp.power_power_nat P5) (@ (@ tptp.minus_minus_nat M6) tptp.one_one_nat)))))))
% 6.73/7.05 (assert (= tptp.power_power_int (lambda ((P5 tptp.int) (M6 tptp.nat)) (@ (@ (@ tptp.if_int (= M6 tptp.zero_zero_nat)) tptp.one_one_int) (@ (@ tptp.times_times_int P5) (@ (@ tptp.power_power_int P5) (@ (@ tptp.minus_minus_nat M6) tptp.one_one_nat)))))))
% 6.73/7.05 (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))))))
% 6.73/7.05 (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))))))
% 6.73/7.05 (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))))))
% 6.73/7.05 (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))))))
% 6.73/7.05 (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))))))
% 6.73/7.05 (assert (forall ((X tptp.code_integer) (Xs2 tptp.list_Code_integer) (Y tptp.code_integer) (Ys tptp.list_Code_integer) (R3 tptp.set_Pr4811707699266497531nteger)) (let ((_let_1 (@ tptp.lex_Code_integer R3))) (= (@ (@ tptp.member749217712838834276nteger (@ (@ tptp.produc750622340256944499nteger (@ (@ tptp.cons_Code_integer X) Xs2)) (@ (@ tptp.cons_Code_integer Y) Ys))) _let_1) (or (and (@ (@ tptp.member157494554546826820nteger (@ (@ tptp.produc1086072967326762835nteger X) Y)) R3) (= (@ tptp.size_s3445333598471063425nteger Xs2) (@ tptp.size_s3445333598471063425nteger Ys))) (and (= X Y) (@ (@ tptp.member749217712838834276nteger (@ (@ tptp.produc750622340256944499nteger Xs2) Ys)) _let_1)))))))
% 6.73/7.05 (assert (forall ((X tptp.product_prod_nat_nat) (Xs2 tptp.list_P6011104703257516679at_nat) (Y tptp.product_prod_nat_nat) (Ys tptp.list_P6011104703257516679at_nat) (R3 tptp.set_Pr8693737435421807431at_nat)) (let ((_let_1 (@ tptp.lex_Pr8571645452597969515at_nat R3))) (= (@ (@ tptp.member6693912407220327184at_nat (@ (@ tptp.produc5943733680697469783at_nat (@ (@ tptp.cons_P6512896166579812791at_nat X) Xs2)) (@ (@ tptp.cons_P6512896166579812791at_nat Y) Ys))) _let_1) (or (and (@ (@ tptp.member8206827879206165904at_nat (@ (@ tptp.produc6161850002892822231at_nat X) Y)) R3) (= (@ tptp.size_s5460976970255530739at_nat Xs2) (@ tptp.size_s5460976970255530739at_nat Ys))) (and (= X Y) (@ (@ tptp.member6693912407220327184at_nat (@ (@ tptp.produc5943733680697469783at_nat Xs2) Ys)) _let_1)))))))
% 6.73/7.05 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat) (Xs2 tptp.list_s1210847774152347623at_nat) (Y tptp.set_Pr1261947904930325089at_nat) (Ys tptp.list_s1210847774152347623at_nat) (R3 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.lex_se2245640040323279819at_nat R3))) (= (@ (@ tptp.member4080735728053443344at_nat (@ (@ tptp.produc7536900900485677911at_nat (@ (@ tptp.cons_s6881495754146722583at_nat X) Xs2)) (@ (@ tptp.cons_s6881495754146722583at_nat Y) Ys))) _let_1) (or (and (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat X) Y)) R3) (= (@ tptp.size_s8736152011456118867at_nat Xs2) (@ tptp.size_s8736152011456118867at_nat Ys))) (and (= X Y) (@ (@ tptp.member4080735728053443344at_nat (@ (@ tptp.produc7536900900485677911at_nat Xs2) Ys)) _let_1)))))))
% 6.73/7.05 (assert (forall ((X tptp.vEBT_VEBT) (Xs2 tptp.list_VEBT_VEBT) (Y tptp.vEBT_VEBT) (Ys tptp.list_VEBT_VEBT) (R3 tptp.set_Pr6192946355708809607T_VEBT)) (let ((_let_1 (@ tptp.lex_VEBT_VEBT R3))) (= (@ (@ tptp.member4439316823752958928T_VEBT (@ (@ tptp.produc3897820843166775703T_VEBT (@ (@ tptp.cons_VEBT_VEBT X) Xs2)) (@ (@ tptp.cons_VEBT_VEBT Y) Ys))) _let_1) (or (and (@ (@ tptp.member568628332442017744T_VEBT (@ (@ tptp.produc537772716801021591T_VEBT X) Y)) R3) (= (@ tptp.size_s6755466524823107622T_VEBT Xs2) (@ tptp.size_s6755466524823107622T_VEBT Ys))) (and (= X Y) (@ (@ tptp.member4439316823752958928T_VEBT (@ (@ tptp.produc3897820843166775703T_VEBT Xs2) Ys)) _let_1)))))))
% 6.73/7.05 (assert (forall ((X Bool) (Xs2 tptp.list_o) (Y Bool) (Ys tptp.list_o) (R3 tptp.set_Product_prod_o_o)) (let ((_let_1 (@ tptp.lex_o R3))) (= (@ (@ tptp.member4159035015898711888list_o (@ (@ tptp.produc8435520187683070743list_o (@ (@ tptp.cons_o X) Xs2)) (@ (@ tptp.cons_o Y) Ys))) _let_1) (or (and (@ (@ tptp.member7466972457876170832od_o_o (@ (@ tptp.product_Pair_o_o X) Y)) R3) (= (@ tptp.size_size_list_o Xs2) (@ tptp.size_size_list_o Ys))) (and (= X Y) (@ (@ tptp.member4159035015898711888list_o (@ (@ tptp.produc8435520187683070743list_o Xs2) Ys)) _let_1)))))))
% 6.73/7.05 (assert (forall ((X tptp.nat) (Xs2 tptp.list_nat) (Y tptp.nat) (Ys tptp.list_nat) (R3 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.lex_nat R3))) (= (@ (@ tptp.member7340969449405702474st_nat (@ (@ tptp.produc2694037385005941721st_nat (@ (@ tptp.cons_nat X) Xs2)) (@ (@ tptp.cons_nat Y) Ys))) _let_1) (or (and (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X) Y)) R3) (= (@ tptp.size_size_list_nat Xs2) (@ tptp.size_size_list_nat Ys))) (and (= X Y) (@ (@ tptp.member7340969449405702474st_nat (@ (@ tptp.produc2694037385005941721st_nat Xs2) Ys)) _let_1)))))))
% 6.73/7.05 (assert (forall ((X tptp.int) (Xs2 tptp.list_int) (Y tptp.int) (Ys tptp.list_int) (R3 tptp.set_Pr958786334691620121nt_int)) (let ((_let_1 (@ tptp.lex_int R3))) (= (@ (@ tptp.member6698963635872716290st_int (@ (@ tptp.produc364263696895485585st_int (@ (@ tptp.cons_int X) Xs2)) (@ (@ tptp.cons_int Y) Ys))) _let_1) (or (and (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X) Y)) R3) (= (@ tptp.size_size_list_int Xs2) (@ tptp.size_size_list_int Ys))) (and (= X Y) (@ (@ tptp.member6698963635872716290st_int (@ (@ tptp.produc364263696895485585st_int Xs2) Ys)) _let_1)))))))
% 6.73/7.05 (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 ((X3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) X3) (= (@ (@ tptp.power_power_real X3) N) A) (forall ((Y6 tptp.real)) (=> (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y6) (= (@ (@ tptp.power_power_real Y6) N) A)) (= Y6 X3)))))))))
% 6.73/7.05 (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 ((R4 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) R4) (= (@ (@ tptp.power_power_real R4) N) A)))))))
% 6.73/7.05 (assert (and (= tptp.sa (@ (@ (@ (@ tptp.vEBT_Node tptp.info) tptp.deg) tptp.treeList) tptp.summary)) (= tptp.deg (@ (@ tptp.plus_plus_nat tptp.na) tptp.m)) (= (@ tptp.size_s6755466524823107622T_VEBT tptp.treeList) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.m)) (@ (@ tptp.vEBT_invar_vebt tptp.summary) tptp.m) (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 tptp.treeList)) (@ (@ tptp.vEBT_invar_vebt X5) tptp.na)))))
% 6.73/7.05 (assert (forall ((Xs2 tptp.list_Code_integer) (Ys tptp.list_Code_integer) (R3 tptp.set_Pr4811707699266497531nteger)) (= (@ (@ tptp.member749217712838834276nteger (@ (@ tptp.produc750622340256944499nteger Xs2) Ys)) (@ tptp.listre5734910445319291053nteger R3)) (and (= (@ tptp.size_s3445333598471063425nteger Xs2) (@ tptp.size_s3445333598471063425nteger Ys)) (forall ((N4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N4) (@ tptp.size_s3445333598471063425nteger Xs2)) (@ (@ tptp.member157494554546826820nteger (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.nth_Code_integer Xs2) N4)) (@ (@ tptp.nth_Code_integer Ys) N4))) R3)))))))
% 6.73/7.05 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (Ys tptp.list_VEBT_VEBT) (R3 tptp.set_Pr6192946355708809607T_VEBT)) (= (@ (@ tptp.member4439316823752958928T_VEBT (@ (@ tptp.produc3897820843166775703T_VEBT Xs2) Ys)) (@ tptp.listre1230615542750757617T_VEBT R3)) (and (= (@ tptp.size_s6755466524823107622T_VEBT Xs2) (@ tptp.size_s6755466524823107622T_VEBT Ys)) (forall ((N4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N4) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (@ (@ tptp.member568628332442017744T_VEBT (@ (@ tptp.produc537772716801021591T_VEBT (@ (@ tptp.nth_VEBT_VEBT Xs2) N4)) (@ (@ tptp.nth_VEBT_VEBT Ys) N4))) R3)))))))
% 6.73/7.05 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (Ys tptp.list_o) (R3 tptp.set_Pr3175402225741728619VEBT_o)) (= (@ (@ tptp.member3126162362653435956list_o (@ (@ tptp.produc2717590391345394939list_o Xs2) Ys)) (@ tptp.listrel_VEBT_VEBT_o R3)) (and (= (@ tptp.size_s6755466524823107622T_VEBT Xs2) (@ tptp.size_size_list_o Ys)) (forall ((N4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N4) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (@ (@ tptp.member3307348790968139188VEBT_o (@ (@ tptp.produc8721562602347293563VEBT_o (@ (@ tptp.nth_VEBT_VEBT Xs2) N4)) (@ (@ tptp.nth_o Ys) N4))) R3)))))))
% 6.73/7.05 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (Ys tptp.list_nat) (R3 tptp.set_Pr7556676689462069481BT_nat)) (= (@ (@ tptp.member6193324644334088288st_nat (@ (@ tptp.produc5570133714943300547st_nat Xs2) Ys)) (@ tptp.listre5900670229112895443BT_nat R3)) (and (= (@ tptp.size_s6755466524823107622T_VEBT Xs2) (@ tptp.size_size_list_nat Ys)) (forall ((N4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N4) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (@ (@ tptp.member373505688050248522BT_nat (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.nth_VEBT_VEBT Xs2) N4)) (@ (@ tptp.nth_nat Ys) N4))) R3)))))))
% 6.73/7.05 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (Ys tptp.list_int) (R3 tptp.set_Pr5066593544530342725BT_int)) (= (@ (@ tptp.member3703241499402361532st_int (@ (@ tptp.produc1392282695434103839st_int Xs2) Ys)) (@ tptp.listre5898179758603845167BT_int R3)) (and (= (@ tptp.size_s6755466524823107622T_VEBT Xs2) (@ tptp.size_size_list_int Ys)) (forall ((N4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N4) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (@ (@ tptp.member5419026705395827622BT_int (@ (@ tptp.produc736041933913180425BT_int (@ (@ tptp.nth_VEBT_VEBT Xs2) N4)) (@ (@ tptp.nth_int Ys) N4))) R3)))))))
% 6.73/7.05 (assert (forall ((Xs2 tptp.list_o) (Ys tptp.list_VEBT_VEBT) (R3 tptp.set_Pr7543698050874017315T_VEBT)) (= (@ (@ tptp.member1087064965665443052T_VEBT (@ (@ tptp.produc6043759678074843571T_VEBT Xs2) Ys)) (@ tptp.listrel_o_VEBT_VEBT R3)) (and (= (@ tptp.size_size_list_o Xs2) (@ tptp.size_s6755466524823107622T_VEBT Ys)) (forall ((N4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N4) (@ tptp.size_size_list_o Xs2)) (@ (@ tptp.member5477980866518848620T_VEBT (@ (@ tptp.produc2982872950893828659T_VEBT (@ (@ tptp.nth_o Xs2) N4)) (@ (@ tptp.nth_VEBT_VEBT Ys) N4))) R3)))))))
% 6.73/7.05 (assert (forall ((Xs2 tptp.list_o) (Ys tptp.list_o) (R3 tptp.set_Product_prod_o_o)) (= (@ (@ tptp.member4159035015898711888list_o (@ (@ tptp.produc8435520187683070743list_o Xs2) Ys)) (@ tptp.listrel_o_o R3)) (and (= (@ tptp.size_size_list_o Xs2) (@ tptp.size_size_list_o Ys)) (forall ((N4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N4) (@ tptp.size_size_list_o Xs2)) (@ (@ tptp.member7466972457876170832od_o_o (@ (@ tptp.product_Pair_o_o (@ (@ tptp.nth_o Xs2) N4)) (@ (@ tptp.nth_o Ys) N4))) R3)))))))
% 6.73/7.05 (assert (forall ((Xs2 tptp.list_o) (Ys tptp.list_nat) (R3 tptp.set_Pr2101469702781467981_o_nat)) (= (@ (@ tptp.member1519744053835550788st_nat (@ (@ tptp.produc7128876500814652583st_nat Xs2) Ys)) (@ tptp.listrel_o_nat R3)) (and (= (@ tptp.size_size_list_o Xs2) (@ tptp.size_size_list_nat Ys)) (forall ((N4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N4) (@ tptp.size_size_list_o Xs2)) (@ (@ tptp.member2802428098988154798_o_nat (@ (@ tptp.product_Pair_o_nat (@ (@ tptp.nth_o Xs2) N4)) (@ (@ tptp.nth_nat Ys) N4))) R3)))))))
% 6.73/7.05 (assert (forall ((Xs2 tptp.list_o) (Ys tptp.list_int) (R3 tptp.set_Pr8834758594704517033_o_int)) (= (@ (@ tptp.member8253032945758599840st_int (@ (@ tptp.produc2951025481305455875st_int Xs2) Ys)) (@ tptp.listrel_o_int R3)) (and (= (@ tptp.size_size_list_o Xs2) (@ tptp.size_size_list_int Ys)) (forall ((N4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N4) (@ tptp.size_size_list_o Xs2)) (@ (@ tptp.member7847949116333733898_o_int (@ (@ tptp.product_Pair_o_int (@ (@ tptp.nth_o Xs2) N4)) (@ (@ tptp.nth_int Ys) N4))) R3)))))))
% 6.73/7.05 (assert (forall ((Xs2 tptp.list_nat) (Ys tptp.list_VEBT_VEBT) (R3 tptp.set_Pr6167073792073659919T_VEBT)) (= (@ (@ tptp.member5968030670617646438T_VEBT (@ (@ tptp.produc8335345208264861441T_VEBT Xs2) Ys)) (@ tptp.listre5761932458788874033T_VEBT R3)) (and (= (@ tptp.size_size_list_nat Xs2) (@ tptp.size_s6755466524823107622T_VEBT Ys)) (forall ((N4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N4) (@ tptp.size_size_list_nat Xs2)) (@ (@ tptp.member8549952807677709168T_VEBT (@ (@ tptp.produc599794634098209291T_VEBT (@ (@ tptp.nth_nat Xs2) N4)) (@ (@ tptp.nth_VEBT_VEBT Ys) N4))) R3)))))))
% 6.73/7.05 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer) (F2 (-> tptp.code_integer tptp.nat)) (Fs tptp.list_C4705013386053401436er_nat)) (let ((_let_1 (@ tptp.member157494554546826820nteger (@ (@ tptp.produc1086072967326762835nteger X) Y)))) (let ((_let_2 (@ F2 Y))) (let ((_let_3 (@ F2 X))) (= (@ _let_1 (@ tptp.measur8870801148506250077nteger (@ (@ tptp.cons_C1897838848541180310er_nat F2) Fs))) (or (@ (@ tptp.ord_less_nat _let_3) _let_2) (and (= _let_3 _let_2) (@ _let_1 (@ tptp.measur8870801148506250077nteger Fs))))))))))
% 6.73/7.05 (assert (forall ((X tptp.product_prod_nat_nat) (Y tptp.product_prod_nat_nat) (F2 (-> tptp.product_prod_nat_nat tptp.nat)) (Fs tptp.list_P9162950289778280392at_nat)) (let ((_let_1 (@ tptp.member8206827879206165904at_nat (@ (@ tptp.produc6161850002892822231at_nat X) Y)))) (let ((_let_2 (@ F2 Y))) (let ((_let_3 (@ F2 X))) (= (@ _let_1 (@ tptp.measur2679027848233739777at_nat (@ (@ tptp.cons_P4861729644591583992at_nat F2) Fs))) (or (@ (@ tptp.ord_less_nat _let_3) _let_2) (and (= _let_3 _let_2) (@ _let_1 (@ tptp.measur2679027848233739777at_nat Fs))))))))))
% 6.73/7.05 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat) (F2 (-> tptp.set_Pr1261947904930325089at_nat tptp.nat)) (Fs tptp.list_s9130966667114977576at_nat)) (let ((_let_1 (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat X) Y)))) (let ((_let_2 (@ F2 Y))) (let ((_let_3 (@ F2 X))) (= (@ _let_1 (@ tptp.measur2694323259624372065at_nat (@ (@ tptp.cons_s2538900923071588440at_nat F2) Fs))) (or (@ (@ tptp.ord_less_nat _let_3) _let_2) (and (= _let_3 _let_2) (@ _let_1 (@ tptp.measur2694323259624372065at_nat Fs))))))))))
% 6.73/7.05 (assert (forall ((X tptp.nat) (Y tptp.nat) (F2 (-> tptp.nat tptp.nat)) (Fs tptp.list_nat_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X) Y)))) (let ((_let_2 (@ F2 Y))) (let ((_let_3 (@ F2 X))) (= (@ _let_1 (@ tptp.measures_nat (@ (@ tptp.cons_nat_nat F2) Fs))) (or (@ (@ tptp.ord_less_nat _let_3) _let_2) (and (= _let_3 _let_2) (@ _let_1 (@ tptp.measures_nat Fs))))))))))
% 6.73/7.05 (assert (forall ((X tptp.int) (Y tptp.int) (F2 (-> tptp.int tptp.nat)) (Fs tptp.list_int_nat)) (let ((_let_1 (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X) Y)))) (let ((_let_2 (@ F2 Y))) (let ((_let_3 (@ F2 X))) (= (@ _let_1 (@ tptp.measures_int (@ (@ tptp.cons_int_nat F2) Fs))) (or (@ (@ tptp.ord_less_nat _let_3) _let_2) (and (= _let_3 _let_2) (@ _let_1 (@ tptp.measures_int Fs))))))))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (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))))))
% 6.73/7.05 (assert (not (forall ((TreeList3 tptp.list_VEBT_VEBT) (Summary3 tptp.vEBT_VEBT) (Info tptp.option4927543243414619207at_nat)) (not (and (= tptp.sa (@ (@ (@ (@ tptp.vEBT_Node Info) tptp.deg) TreeList3) Summary3)) (= tptp.deg (@ (@ tptp.plus_plus_nat tptp.na) tptp.m)) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.m)) (@ (@ tptp.vEBT_invar_vebt Summary3) tptp.m) (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 TreeList3)) (@ (@ tptp.vEBT_invar_vebt X5) tptp.na))))))))
% 6.73/7.05 (assert (forall ((I2 tptp.nat) (N tptp.nat) (P2 (-> tptp.nat Bool)) (X tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) N) (=> (@ P2 X) (@ P2 (@ (@ tptp.nth_nat (@ (@ tptp.replicate_nat N) X)) I2))))))
% 6.73/7.05 (assert (forall ((I2 tptp.nat) (N tptp.nat) (P2 (-> tptp.vEBT_VEBT Bool)) (X tptp.vEBT_VEBT)) (=> (@ (@ tptp.ord_less_nat I2) N) (=> (@ P2 X) (@ P2 (@ (@ tptp.nth_VEBT_VEBT (@ (@ tptp.replicate_VEBT_VEBT N) X)) I2))))))
% 6.73/7.05 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (= (@ tptp.numera1916890842035813515d_enat M2) (@ tptp.numera1916890842035813515d_enat N)) (= M2 N))))
% 6.73/7.05 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (= (@ tptp.numera6690914467698888265omplex M2) (@ tptp.numera6690914467698888265omplex N)) (= M2 N))))
% 6.73/7.05 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (= (@ tptp.numeral_numeral_real M2) (@ tptp.numeral_numeral_real N)) (= M2 N))))
% 6.73/7.05 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (= (@ tptp.numeral_numeral_nat M2) (@ tptp.numeral_numeral_nat N)) (= M2 N))))
% 6.73/7.05 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (= (@ tptp.numeral_numeral_int M2) (@ tptp.numeral_numeral_int N)) (= M2 N))))
% 6.73/7.05 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_num (@ tptp.bit0 M2)) (@ tptp.bit0 N)) (@ tptp.bit0 (@ tptp.bit0 (@ (@ tptp.times_times_num M2) N))))))
% 6.73/7.05 (assert (forall ((M2 tptp.num)) (= (@ (@ tptp.times_times_num M2) tptp.one) M2)))
% 6.73/7.05 (assert (forall ((N tptp.num)) (= (@ (@ tptp.times_times_num tptp.one) N) N)))
% 6.73/7.05 (assert (@ (@ tptp.ord_less_nat tptp.ma) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.deg)))
% 6.73/7.05 (assert (= (@ tptp.size_s6755466524823107622T_VEBT tptp.treeList2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.m)))
% 6.73/7.05 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (= (@ tptp.semiri5074537144036343181t_real M2) (@ tptp.semiri5074537144036343181t_real N)) (= M2 N))))
% 6.73/7.05 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (= (@ tptp.semiri1314217659103216013at_int M2) (@ tptp.semiri1314217659103216013at_int N)) (= M2 N))))
% 6.73/7.05 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (= (@ tptp.semiri1316708129612266289at_nat M2) (@ tptp.semiri1316708129612266289at_nat N)) (= M2 N))))
% 6.73/7.05 (assert (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.deg))
% 6.73/7.05 (assert (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.m)) (= (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT tptp.treeList2) I4)) X7)) (@ (@ tptp.vEBT_V8194947554948674370ptions tptp.summary2) I4)))))
% 6.73/7.05 (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))))))
% 6.73/7.05 (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_invar_vebt (@ (@ tptp.vEBT_vebt_insert T) X)) N)))))
% 6.73/7.05 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_le2932123472753598470d_enat (@ tptp.numera1916890842035813515d_enat M2)) (@ tptp.numera1916890842035813515d_enat N)) (@ (@ tptp.ord_less_eq_num M2) N))))
% 6.73/7.05 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real M2)) (@ tptp.numeral_numeral_real N)) (@ (@ tptp.ord_less_eq_num M2) N))))
% 6.73/7.05 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.numeral_numeral_rat M2)) (@ tptp.numeral_numeral_rat N)) (@ (@ tptp.ord_less_eq_num M2) N))))
% 6.73/7.05 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat M2)) (@ tptp.numeral_numeral_nat N)) (@ (@ tptp.ord_less_eq_num M2) N))))
% 6.73/7.05 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int M2)) (@ tptp.numeral_numeral_int N)) (@ (@ tptp.ord_less_eq_num M2) N))))
% 6.73/7.05 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_rat (@ tptp.numeral_numeral_rat M2)) (@ tptp.numeral_numeral_rat N)) (@ (@ tptp.ord_less_num M2) N))))
% 6.73/7.05 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_le72135733267957522d_enat (@ tptp.numera1916890842035813515d_enat M2)) (@ tptp.numera1916890842035813515d_enat N)) (@ (@ tptp.ord_less_num M2) N))))
% 6.73/7.05 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real M2)) (@ tptp.numeral_numeral_real N)) (@ (@ tptp.ord_less_num M2) N))))
% 6.73/7.05 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_nat (@ tptp.numeral_numeral_nat M2)) (@ tptp.numeral_numeral_nat N)) (@ (@ tptp.ord_less_num M2) N))))
% 6.73/7.05 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int M2)) (@ tptp.numeral_numeral_int N)) (@ (@ tptp.ord_less_num M2) N))))
% 6.73/7.05 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat M2)) (@ tptp.numeral_numeral_rat N)) (@ tptp.numeral_numeral_rat (@ (@ tptp.times_times_num M2) N)))))
% 6.73/7.05 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.times_7803423173614009249d_enat (@ tptp.numera1916890842035813515d_enat M2)) (@ tptp.numera1916890842035813515d_enat N)) (@ tptp.numera1916890842035813515d_enat (@ (@ tptp.times_times_num M2) N)))))
% 6.73/7.05 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex M2)) (@ tptp.numera6690914467698888265omplex N)) (@ tptp.numera6690914467698888265omplex (@ (@ tptp.times_times_num M2) N)))))
% 6.73/7.05 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real M2)) (@ tptp.numeral_numeral_real N)) (@ tptp.numeral_numeral_real (@ (@ tptp.times_times_num M2) N)))))
% 6.73/7.05 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat M2)) (@ tptp.numeral_numeral_nat N)) (@ tptp.numeral_numeral_nat (@ (@ tptp.times_times_num M2) N)))))
% 6.73/7.05 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int M2)) (@ tptp.numeral_numeral_int N)) (@ tptp.numeral_numeral_int (@ (@ tptp.times_times_num M2) N)))))
% 6.73/7.05 (assert (forall ((V2 tptp.num) (W2 tptp.num) (Z3 tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat V2)) (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat W2)) Z3)) (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat (@ (@ tptp.times_times_num V2) W2))) Z3))))
% 6.73/7.05 (assert (forall ((V2 tptp.num) (W2 tptp.num) (Z3 tptp.extended_enat)) (= (@ (@ tptp.times_7803423173614009249d_enat (@ tptp.numera1916890842035813515d_enat V2)) (@ (@ tptp.times_7803423173614009249d_enat (@ tptp.numera1916890842035813515d_enat W2)) Z3)) (@ (@ tptp.times_7803423173614009249d_enat (@ tptp.numera1916890842035813515d_enat (@ (@ tptp.times_times_num V2) W2))) Z3))))
% 6.73/7.05 (assert (forall ((V2 tptp.num) (W2 tptp.num) (Z3 tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex V2)) (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex W2)) Z3)) (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ (@ tptp.times_times_num V2) W2))) Z3))))
% 6.73/7.05 (assert (forall ((V2 tptp.num) (W2 tptp.num) (Z3 tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real V2)) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real W2)) Z3)) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ (@ tptp.times_times_num V2) W2))) Z3))))
% 6.73/7.05 (assert (forall ((V2 tptp.num) (W2 tptp.num) (Z3 tptp.nat)) (= (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat V2)) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat W2)) Z3)) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ (@ tptp.times_times_num V2) W2))) Z3))))
% 6.73/7.05 (assert (forall ((V2 tptp.num) (W2 tptp.num) (Z3 tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int V2)) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int W2)) Z3)) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ (@ tptp.times_times_num V2) W2))) Z3))))
% 6.73/7.05 (assert (forall ((V2 tptp.num) (W2 tptp.num) (Z3 tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ tptp.numeral_numeral_rat V2)) (@ (@ tptp.plus_plus_rat (@ tptp.numeral_numeral_rat W2)) Z3)) (@ (@ tptp.plus_plus_rat (@ tptp.numeral_numeral_rat (@ (@ tptp.plus_plus_num V2) W2))) Z3))))
% 6.73/7.05 (assert (forall ((V2 tptp.num) (W2 tptp.num) (Z3 tptp.extended_enat)) (= (@ (@ tptp.plus_p3455044024723400733d_enat (@ tptp.numera1916890842035813515d_enat V2)) (@ (@ tptp.plus_p3455044024723400733d_enat (@ tptp.numera1916890842035813515d_enat W2)) Z3)) (@ (@ tptp.plus_p3455044024723400733d_enat (@ tptp.numera1916890842035813515d_enat (@ (@ tptp.plus_plus_num V2) W2))) Z3))))
% 6.73/7.05 (assert (forall ((V2 tptp.num) (W2 tptp.num) (Z3 tptp.complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.numera6690914467698888265omplex V2)) (@ (@ tptp.plus_plus_complex (@ tptp.numera6690914467698888265omplex W2)) Z3)) (@ (@ tptp.plus_plus_complex (@ tptp.numera6690914467698888265omplex (@ (@ tptp.plus_plus_num V2) W2))) Z3))))
% 6.73/7.05 (assert (forall ((V2 tptp.num) (W2 tptp.num) (Z3 tptp.real)) (= (@ (@ tptp.plus_plus_real (@ tptp.numeral_numeral_real V2)) (@ (@ tptp.plus_plus_real (@ tptp.numeral_numeral_real W2)) Z3)) (@ (@ tptp.plus_plus_real (@ tptp.numeral_numeral_real (@ (@ tptp.plus_plus_num V2) W2))) Z3))))
% 6.73/7.05 (assert (forall ((V2 tptp.num) (W2 tptp.num) (Z3 tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat V2)) (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat W2)) Z3)) (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num V2) W2))) Z3))))
% 6.73/7.05 (assert (forall ((V2 tptp.num) (W2 tptp.num) (Z3 tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.numeral_numeral_int V2)) (@ (@ tptp.plus_plus_int (@ tptp.numeral_numeral_int W2)) Z3)) (@ (@ tptp.plus_plus_int (@ tptp.numeral_numeral_int (@ (@ tptp.plus_plus_num V2) W2))) Z3))))
% 6.73/7.05 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.plus_plus_rat (@ tptp.numeral_numeral_rat M2)) (@ tptp.numeral_numeral_rat N)) (@ tptp.numeral_numeral_rat (@ (@ tptp.plus_plus_num M2) N)))))
% 6.73/7.05 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.plus_p3455044024723400733d_enat (@ tptp.numera1916890842035813515d_enat M2)) (@ tptp.numera1916890842035813515d_enat N)) (@ tptp.numera1916890842035813515d_enat (@ (@ tptp.plus_plus_num M2) N)))))
% 6.73/7.05 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.plus_plus_complex (@ tptp.numera6690914467698888265omplex M2)) (@ tptp.numera6690914467698888265omplex N)) (@ tptp.numera6690914467698888265omplex (@ (@ tptp.plus_plus_num M2) N)))))
% 6.73/7.05 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.plus_plus_real (@ tptp.numeral_numeral_real M2)) (@ tptp.numeral_numeral_real N)) (@ tptp.numeral_numeral_real (@ (@ tptp.plus_plus_num M2) N)))))
% 6.73/7.05 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat M2)) (@ tptp.numeral_numeral_nat N)) (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M2) N)))))
% 6.73/7.05 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.plus_plus_int (@ tptp.numeral_numeral_int M2)) (@ tptp.numeral_numeral_int N)) (@ tptp.numeral_numeral_int (@ (@ tptp.plus_plus_num M2) N)))))
% 6.73/7.05 (assert (forall ((N tptp.num)) (= (@ (@ tptp.times_times_num (@ tptp.bit0 tptp.one)) N) (@ tptp.bit0 N))))
% 6.73/7.05 (assert (forall ((A tptp.nat) (M2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.power_power_nat A))) (= (@ (@ tptp.power_power_nat (@ _let_1 (@ tptp.numeral_numeral_nat M2))) (@ tptp.numeral_numeral_nat N)) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.times_times_num M2) N)))))))
% 6.73/7.05 (assert (forall ((A tptp.real) (M2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.power_power_real A))) (= (@ (@ tptp.power_power_real (@ _let_1 (@ tptp.numeral_numeral_nat M2))) (@ tptp.numeral_numeral_nat N)) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.times_times_num M2) N)))))))
% 6.73/7.05 (assert (forall ((A tptp.int) (M2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.power_power_int A))) (= (@ (@ tptp.power_power_int (@ _let_1 (@ tptp.numeral_numeral_nat M2))) (@ tptp.numeral_numeral_nat N)) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.times_times_num M2) N)))))))
% 6.73/7.05 (assert (forall ((A tptp.complex) (M2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.power_power_complex A))) (= (@ (@ tptp.power_power_complex (@ _let_1 (@ tptp.numeral_numeral_nat M2))) (@ tptp.numeral_numeral_nat N)) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.times_times_num M2) N)))))))
% 6.73/7.05 (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))))))
% 6.73/7.05 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (= (@ tptp.some_nat M2) (@ tptp.vEBT_vebt_mint T)) (@ (@ tptp.ord_less_nat M2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))))
% 6.73/7.05 (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))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (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))))))))
% 6.73/7.05 (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))))))
% 6.73/7.05 (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))))))
% 6.73/7.05 (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)))))))))
% 6.73/7.05 (assert (forall ((M2 tptp.nat) (X tptp.vEBT_VEBT) (N tptp.nat) (Y tptp.vEBT_VEBT)) (= (= (@ (@ tptp.replicate_VEBT_VEBT M2) X) (@ (@ tptp.replicate_VEBT_VEBT N) Y)) (and (= M2 N) (=> (not (= M2 tptp.zero_zero_nat)) (= X Y))))))
% 6.73/7.05 (assert (forall ((N tptp.nat) (X tptp.vEBT_VEBT)) (= (@ tptp.size_s6755466524823107622T_VEBT (@ (@ tptp.replicate_VEBT_VEBT N) X)) N)))
% 6.73/7.05 (assert (forall ((N tptp.nat) (X Bool)) (= (@ tptp.size_size_list_o (@ (@ tptp.replicate_o N) X)) N)))
% 6.73/7.05 (assert (forall ((N tptp.nat) (X tptp.nat)) (= (@ tptp.size_size_list_nat (@ (@ tptp.replicate_nat N) X)) N)))
% 6.73/7.05 (assert (forall ((N tptp.nat) (X tptp.int)) (= (@ tptp.size_size_list_int (@ (@ tptp.replicate_int N) X)) N)))
% 6.73/7.05 (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))))))
% 6.73/7.05 (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))))))
% 6.73/7.05 (assert (forall ((TreeList2 tptp.list_VEBT_VEBT) (N tptp.nat) (M2 tptp.nat)) (=> (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList2)) (@ (@ tptp.vEBT_invar_vebt X3) N))) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M2)) (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N)))))
% 6.73/7.05 (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))))))
% 6.73/7.05 (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))))))
% 6.73/7.05 (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))))))
% 6.73/7.05 (assert (= tptp.vEBT_VEBT_bit_concat (lambda ((H2 tptp.nat) (L2 tptp.nat) (D2 tptp.nat)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat H2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) D2))) L2))))
% 6.73/7.05 (assert (forall ((V2 tptp.num) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat V2)))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat B) C2)) (@ (@ tptp.plus_plus_rat (@ _let_1 B)) (@ _let_1 C2))))))
% 6.73/7.05 (assert (forall ((V2 tptp.num) (B tptp.extended_enat) (C2 tptp.extended_enat)) (let ((_let_1 (@ tptp.times_7803423173614009249d_enat (@ tptp.numera1916890842035813515d_enat V2)))) (= (@ _let_1 (@ (@ tptp.plus_p3455044024723400733d_enat B) C2)) (@ (@ tptp.plus_p3455044024723400733d_enat (@ _let_1 B)) (@ _let_1 C2))))))
% 6.73/7.05 (assert (forall ((V2 tptp.num) (B tptp.complex) (C2 tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex V2)))) (= (@ _let_1 (@ (@ tptp.plus_plus_complex B) C2)) (@ (@ tptp.plus_plus_complex (@ _let_1 B)) (@ _let_1 C2))))))
% 6.73/7.05 (assert (forall ((V2 tptp.num) (B tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.times_times_real (@ tptp.numeral_numeral_real V2)))) (= (@ _let_1 (@ (@ tptp.plus_plus_real B) C2)) (@ (@ tptp.plus_plus_real (@ _let_1 B)) (@ _let_1 C2))))))
% 6.73/7.05 (assert (forall ((V2 tptp.num) (B tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat V2)))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat B) C2)) (@ (@ tptp.plus_plus_nat (@ _let_1 B)) (@ _let_1 C2))))))
% 6.73/7.05 (assert (forall ((V2 tptp.num) (B tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int (@ tptp.numeral_numeral_int V2)))) (= (@ _let_1 (@ (@ tptp.plus_plus_int B) C2)) (@ (@ tptp.plus_plus_int (@ _let_1 B)) (@ _let_1 C2))))))
% 6.73/7.05 (assert (forall ((A tptp.rat) (B tptp.rat) (V2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat V2))) (= (@ (@ 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))))))
% 6.73/7.05 (assert (forall ((A tptp.extended_enat) (B tptp.extended_enat) (V2 tptp.num)) (let ((_let_1 (@ tptp.numera1916890842035813515d_enat V2))) (= (@ (@ tptp.times_7803423173614009249d_enat (@ (@ tptp.plus_p3455044024723400733d_enat A) B)) _let_1) (@ (@ tptp.plus_p3455044024723400733d_enat (@ (@ tptp.times_7803423173614009249d_enat A) _let_1)) (@ (@ tptp.times_7803423173614009249d_enat B) _let_1))))))
% 6.73/7.05 (assert (forall ((A tptp.complex) (B tptp.complex) (V2 tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex V2))) (= (@ (@ 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))))))
% 6.73/7.05 (assert (forall ((A tptp.real) (B tptp.real) (V2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real V2))) (= (@ (@ 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))))))
% 6.73/7.05 (assert (forall ((A tptp.nat) (B tptp.nat) (V2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat V2))) (= (@ (@ 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))))))
% 6.73/7.05 (assert (forall ((A tptp.int) (B tptp.int) (V2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int V2))) (= (@ (@ 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))))))
% 6.73/7.05 (assert (forall ((N tptp.num)) (= (= (@ tptp.numera6620942414471956472nteger N) tptp.one_one_Code_integer) (= N tptp.one))))
% 6.73/7.05 (assert (forall ((N tptp.num)) (= (= (@ tptp.numera1916890842035813515d_enat N) tptp.one_on7984719198319812577d_enat) (= N tptp.one))))
% 6.73/7.05 (assert (forall ((N tptp.num)) (= (= (@ tptp.numera6690914467698888265omplex N) tptp.one_one_complex) (= N tptp.one))))
% 6.73/7.05 (assert (forall ((N tptp.num)) (= (= (@ tptp.numeral_numeral_real N) tptp.one_one_real) (= N tptp.one))))
% 6.73/7.05 (assert (forall ((N tptp.num)) (= (= (@ tptp.numeral_numeral_nat N) tptp.one_one_nat) (= N tptp.one))))
% 6.73/7.05 (assert (forall ((N tptp.num)) (= (= (@ tptp.numeral_numeral_int N) tptp.one_one_int) (= N tptp.one))))
% 6.73/7.05 (assert (forall ((N tptp.num)) (= (= tptp.one_one_Code_integer (@ tptp.numera6620942414471956472nteger N)) (= tptp.one N))))
% 6.73/7.05 (assert (forall ((N tptp.num)) (= (= tptp.one_on7984719198319812577d_enat (@ tptp.numera1916890842035813515d_enat N)) (= tptp.one N))))
% 6.73/7.05 (assert (forall ((N tptp.num)) (= (= tptp.one_one_complex (@ tptp.numera6690914467698888265omplex N)) (= tptp.one N))))
% 6.73/7.05 (assert (forall ((N tptp.num)) (= (= tptp.one_one_real (@ tptp.numeral_numeral_real N)) (= tptp.one N))))
% 6.73/7.05 (assert (forall ((N tptp.num)) (= (= tptp.one_one_nat (@ tptp.numeral_numeral_nat N)) (= tptp.one N))))
% 6.73/7.05 (assert (forall ((N tptp.num)) (= (= tptp.one_one_int (@ tptp.numeral_numeral_int N)) (= tptp.one N))))
% 6.73/7.05 (assert (forall ((A tptp.rat) (B tptp.rat) (V2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat V2))) (= (@ (@ 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))))))
% 6.73/7.05 (assert (forall ((A tptp.complex) (B tptp.complex) (V2 tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex V2))) (= (@ (@ 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))))))
% 6.73/7.05 (assert (forall ((A tptp.real) (B tptp.real) (V2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real V2))) (= (@ (@ 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))))))
% 6.73/7.05 (assert (forall ((A tptp.int) (B tptp.int) (V2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int V2))) (= (@ (@ 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))))))
% 6.73/7.05 (assert (forall ((V2 tptp.num) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat V2)))) (= (@ _let_1 (@ (@ tptp.minus_minus_rat B) C2)) (@ (@ tptp.minus_minus_rat (@ _let_1 B)) (@ _let_1 C2))))))
% 6.73/7.05 (assert (forall ((V2 tptp.num) (B tptp.complex) (C2 tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex V2)))) (= (@ _let_1 (@ (@ tptp.minus_minus_complex B) C2)) (@ (@ tptp.minus_minus_complex (@ _let_1 B)) (@ _let_1 C2))))))
% 6.73/7.05 (assert (forall ((V2 tptp.num) (B tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.times_times_real (@ tptp.numeral_numeral_real V2)))) (= (@ _let_1 (@ (@ tptp.minus_minus_real B) C2)) (@ (@ tptp.minus_minus_real (@ _let_1 B)) (@ _let_1 C2))))))
% 6.73/7.05 (assert (forall ((V2 tptp.num) (B tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int (@ tptp.numeral_numeral_int V2)))) (= (@ _let_1 (@ (@ tptp.minus_minus_int B) C2)) (@ (@ tptp.minus_minus_int (@ _let_1 B)) (@ _let_1 C2))))))
% 6.73/7.05 (assert (forall ((K2 tptp.num)) (= (@ (@ tptp.power_power_rat tptp.zero_zero_rat) (@ tptp.numeral_numeral_nat K2)) tptp.zero_zero_rat)))
% 6.73/7.05 (assert (forall ((K2 tptp.num)) (= (@ (@ tptp.power_power_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat K2)) tptp.zero_zero_nat)))
% 6.73/7.05 (assert (forall ((K2 tptp.num)) (= (@ (@ tptp.power_power_real tptp.zero_zero_real) (@ tptp.numeral_numeral_nat K2)) tptp.zero_zero_real)))
% 6.73/7.05 (assert (forall ((K2 tptp.num)) (= (@ (@ tptp.power_power_int tptp.zero_zero_int) (@ tptp.numeral_numeral_nat K2)) tptp.zero_zero_int)))
% 6.73/7.05 (assert (forall ((K2 tptp.num)) (= (@ (@ tptp.power_power_complex tptp.zero_zero_complex) (@ tptp.numeral_numeral_nat K2)) tptp.zero_zero_complex)))
% 6.73/7.05 (assert (forall ((N tptp.num)) (= (@ tptp.suc (@ tptp.numeral_numeral_nat N)) (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num N) tptp.one)))))
% 6.73/7.05 (assert (forall ((A tptp.complex) (M2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.power_power_complex A))) (= (@ (@ tptp.times_times_complex (@ _let_1 (@ tptp.numeral_numeral_nat M2))) (@ _let_1 (@ tptp.numeral_numeral_nat N))) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M2) N)))))))
% 6.73/7.05 (assert (forall ((A tptp.real) (M2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.power_power_real A))) (= (@ (@ tptp.times_times_real (@ _let_1 (@ tptp.numeral_numeral_nat M2))) (@ _let_1 (@ tptp.numeral_numeral_nat N))) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M2) N)))))))
% 6.73/7.05 (assert (forall ((A tptp.rat) (M2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.power_power_rat A))) (= (@ (@ tptp.times_times_rat (@ _let_1 (@ tptp.numeral_numeral_nat M2))) (@ _let_1 (@ tptp.numeral_numeral_nat N))) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M2) N)))))))
% 6.73/7.05 (assert (forall ((A tptp.nat) (M2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.power_power_nat A))) (= (@ (@ tptp.times_times_nat (@ _let_1 (@ tptp.numeral_numeral_nat M2))) (@ _let_1 (@ tptp.numeral_numeral_nat N))) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M2) N)))))))
% 6.73/7.05 (assert (forall ((A tptp.int) (M2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.power_power_int A))) (= (@ (@ tptp.times_times_int (@ _let_1 (@ tptp.numeral_numeral_nat M2))) (@ _let_1 (@ tptp.numeral_numeral_nat N))) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M2) N)))))))
% 6.73/7.05 (assert (forall ((A tptp.complex) (M2 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 M2))) (@ (@ 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 M2) N)))) B)))))
% 6.73/7.05 (assert (forall ((A tptp.real) (M2 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 M2))) (@ (@ 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 M2) N)))) B)))))
% 6.73/7.05 (assert (forall ((A tptp.rat) (M2 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 M2))) (@ (@ 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 M2) N)))) B)))))
% 6.73/7.05 (assert (forall ((A tptp.nat) (M2 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 M2))) (@ (@ 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 M2) N)))) B)))))
% 6.73/7.05 (assert (forall ((A tptp.int) (M2 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 M2))) (@ (@ 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 M2) N)))) B)))))
% 6.73/7.05 (assert (forall ((M2 tptp.nat)) (= (= (@ tptp.semiri8010041392384452111omplex M2) tptp.zero_zero_complex) (= M2 tptp.zero_zero_nat))))
% 6.73/7.05 (assert (forall ((M2 tptp.nat)) (= (= (@ tptp.semiri681578069525770553at_rat M2) tptp.zero_zero_rat) (= M2 tptp.zero_zero_nat))))
% 6.73/7.05 (assert (forall ((M2 tptp.nat)) (= (= (@ tptp.semiri5074537144036343181t_real M2) tptp.zero_zero_real) (= M2 tptp.zero_zero_nat))))
% 6.73/7.05 (assert (forall ((M2 tptp.nat)) (= (= (@ tptp.semiri1314217659103216013at_int M2) tptp.zero_zero_int) (= M2 tptp.zero_zero_nat))))
% 6.73/7.05 (assert (forall ((M2 tptp.nat)) (= (= (@ tptp.semiri1316708129612266289at_nat M2) tptp.zero_zero_nat) (= M2 tptp.zero_zero_nat))))
% 6.73/7.05 (assert (forall ((N tptp.nat)) (= (= tptp.zero_zero_complex (@ tptp.semiri8010041392384452111omplex N)) (= tptp.zero_zero_nat N))))
% 6.73/7.05 (assert (forall ((N tptp.nat)) (= (= tptp.zero_zero_rat (@ tptp.semiri681578069525770553at_rat N)) (= tptp.zero_zero_nat N))))
% 6.73/7.05 (assert (forall ((N tptp.nat)) (= (= tptp.zero_zero_real (@ tptp.semiri5074537144036343181t_real N)) (= tptp.zero_zero_nat N))))
% 6.73/7.05 (assert (forall ((N tptp.nat)) (= (= tptp.zero_zero_int (@ tptp.semiri1314217659103216013at_int N)) (= tptp.zero_zero_nat N))))
% 6.73/7.05 (assert (forall ((N tptp.nat)) (= (= tptp.zero_zero_nat (@ tptp.semiri1316708129612266289at_nat N)) (= tptp.zero_zero_nat N))))
% 6.73/7.05 (assert (= (@ tptp.semiri8010041392384452111omplex tptp.zero_zero_nat) tptp.zero_zero_complex))
% 6.73/7.05 (assert (= (@ tptp.semiri681578069525770553at_rat tptp.zero_zero_nat) tptp.zero_zero_rat))
% 6.73/7.05 (assert (= (@ tptp.semiri5074537144036343181t_real tptp.zero_zero_nat) tptp.zero_zero_real))
% 6.73/7.05 (assert (= (@ tptp.semiri1314217659103216013at_int tptp.zero_zero_nat) tptp.zero_zero_int))
% 6.73/7.05 (assert (= (@ tptp.semiri1316708129612266289at_nat tptp.zero_zero_nat) tptp.zero_zero_nat))
% 6.73/7.05 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_rat (@ tptp.semiri681578069525770553at_rat M2)) (@ tptp.semiri681578069525770553at_rat N)) (@ (@ tptp.ord_less_nat M2) N))))
% 6.73/7.05 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real M2)) (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.ord_less_nat M2) N))))
% 6.73/7.05 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int M2)) (@ tptp.semiri1314217659103216013at_int N)) (@ (@ tptp.ord_less_nat M2) N))))
% 6.73/7.05 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.semiri1316708129612266289at_nat M2)) (@ tptp.semiri1316708129612266289at_nat N)) (@ (@ tptp.ord_less_nat M2) N))))
% 6.73/7.05 (assert (forall ((N tptp.num)) (= (@ tptp.semiri4216267220026989637d_enat (@ tptp.numeral_numeral_nat N)) (@ tptp.numera1916890842035813515d_enat N))))
% 6.73/7.05 (assert (forall ((N tptp.num)) (= (@ tptp.semiri8010041392384452111omplex (@ tptp.numeral_numeral_nat N)) (@ tptp.numera6690914467698888265omplex N))))
% 6.73/7.05 (assert (forall ((N tptp.num)) (= (@ tptp.semiri5074537144036343181t_real (@ tptp.numeral_numeral_nat N)) (@ tptp.numeral_numeral_real N))))
% 6.73/7.05 (assert (forall ((N tptp.num)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.numeral_numeral_nat N)) (@ tptp.numeral_numeral_int N))))
% 6.73/7.05 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N))) (= (@ tptp.semiri1316708129612266289at_nat _let_1) _let_1))))
% 6.73/7.05 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real M2)) (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.ord_less_eq_nat M2) N))))
% 6.73/7.05 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.semiri681578069525770553at_rat M2)) (@ tptp.semiri681578069525770553at_rat N)) (@ (@ tptp.ord_less_eq_nat M2) N))))
% 6.73/7.05 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1316708129612266289at_nat M2)) (@ tptp.semiri1316708129612266289at_nat N)) (@ (@ tptp.ord_less_eq_nat M2) N))))
% 6.73/7.05 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int M2)) (@ tptp.semiri1314217659103216013at_int N)) (@ (@ tptp.ord_less_eq_nat M2) N))))
% 6.73/7.05 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.plus_plus_nat M2) N)) (@ (@ tptp.plus_plus_rat (@ tptp.semiri681578069525770553at_rat M2)) (@ tptp.semiri681578069525770553at_rat N)))))
% 6.73/7.05 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.plus_plus_nat M2) N)) (@ (@ tptp.plus_plus_real (@ tptp.semiri5074537144036343181t_real M2)) (@ tptp.semiri5074537144036343181t_real N)))))
% 6.73/7.05 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.plus_plus_nat M2) N)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int M2)) (@ tptp.semiri1314217659103216013at_int N)))))
% 6.73/7.05 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.plus_plus_nat M2) N)) (@ (@ tptp.plus_plus_nat (@ tptp.semiri1316708129612266289at_nat M2)) (@ tptp.semiri1316708129612266289at_nat N)))))
% 6.73/7.05 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.times_times_nat M2) N)) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat M2)) (@ tptp.semiri681578069525770553at_rat N)))))
% 6.73/7.05 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.times_times_nat M2) N)) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real M2)) (@ tptp.semiri5074537144036343181t_real N)))))
% 6.73/7.05 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.times_times_nat M2) N)) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int M2)) (@ tptp.semiri1314217659103216013at_int N)))))
% 6.73/7.05 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.times_times_nat M2) N)) (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat M2)) (@ tptp.semiri1316708129612266289at_nat N)))))
% 6.73/7.05 (assert (forall ((N tptp.nat)) (= (= (@ tptp.semiri4939895301339042750nteger N) tptp.one_one_Code_integer) (= N tptp.one_one_nat))))
% 6.73/7.05 (assert (forall ((N tptp.nat)) (= (= (@ tptp.semiri8010041392384452111omplex N) tptp.one_one_complex) (= N tptp.one_one_nat))))
% 6.73/7.05 (assert (forall ((N tptp.nat)) (= (= (@ tptp.semiri5074537144036343181t_real N) tptp.one_one_real) (= N tptp.one_one_nat))))
% 6.73/7.05 (assert (forall ((N tptp.nat)) (= (= (@ tptp.semiri1314217659103216013at_int N) tptp.one_one_int) (= N tptp.one_one_nat))))
% 6.73/7.05 (assert (forall ((N tptp.nat)) (= (= (@ tptp.semiri1316708129612266289at_nat N) tptp.one_one_nat) (= N tptp.one_one_nat))))
% 6.73/7.05 (assert (forall ((N tptp.nat)) (= (= tptp.one_one_Code_integer (@ tptp.semiri4939895301339042750nteger N)) (= N tptp.one_one_nat))))
% 6.73/7.05 (assert (forall ((N tptp.nat)) (= (= tptp.one_one_complex (@ tptp.semiri8010041392384452111omplex N)) (= N tptp.one_one_nat))))
% 6.73/7.05 (assert (forall ((N tptp.nat)) (= (= tptp.one_one_real (@ tptp.semiri5074537144036343181t_real N)) (= N tptp.one_one_nat))))
% 6.73/7.05 (assert (forall ((N tptp.nat)) (= (= tptp.one_one_int (@ tptp.semiri1314217659103216013at_int N)) (= N tptp.one_one_nat))))
% 6.73/7.05 (assert (forall ((N tptp.nat)) (= (= tptp.one_one_nat (@ tptp.semiri1316708129612266289at_nat N)) (= N tptp.one_one_nat))))
% 6.73/7.05 (assert (= (@ tptp.semiri4939895301339042750nteger tptp.one_one_nat) tptp.one_one_Code_integer))
% 6.73/7.05 (assert (= (@ tptp.semiri8010041392384452111omplex tptp.one_one_nat) tptp.one_one_complex))
% 6.73/7.05 (assert (= (@ tptp.semiri5074537144036343181t_real tptp.one_one_nat) tptp.one_one_real))
% 6.73/7.05 (assert (= (@ tptp.semiri1314217659103216013at_int tptp.one_one_nat) tptp.one_one_int))
% 6.73/7.05 (assert (= (@ tptp.semiri1316708129612266289at_nat tptp.one_one_nat) tptp.one_one_nat))
% 6.73/7.05 (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))))))
% 6.73/7.05 (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))))))
% 6.73/7.05 (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))))))
% 6.73/7.05 (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))))))
% 6.73/7.05 (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))))))
% 6.73/7.05 (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))))))
% 6.73/7.05 (assert (forall ((N tptp.nat) (A tptp.nat) (P2 (-> tptp.nat Bool))) (= (exists ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) (@ tptp.set_nat2 (@ (@ tptp.replicate_nat N) A))) (@ P2 X4))) (and (@ P2 A) (not (= N tptp.zero_zero_nat))))))
% 6.73/7.05 (assert (forall ((N tptp.nat) (A tptp.vEBT_VEBT) (P2 (-> tptp.vEBT_VEBT Bool))) (= (exists ((X4 tptp.vEBT_VEBT)) (and (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 (@ (@ tptp.replicate_VEBT_VEBT N) A))) (@ P2 X4))) (and (@ P2 A) (not (= N tptp.zero_zero_nat))))))
% 6.73/7.05 (assert (forall ((N tptp.nat) (A tptp.nat) (P2 (-> tptp.nat Bool))) (= (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) (@ tptp.set_nat2 (@ (@ tptp.replicate_nat N) A))) (@ P2 X4))) (or (@ P2 A) (= N tptp.zero_zero_nat)))))
% 6.73/7.05 (assert (forall ((N tptp.nat) (A tptp.vEBT_VEBT) (P2 (-> tptp.vEBT_VEBT Bool))) (= (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 (@ (@ tptp.replicate_VEBT_VEBT N) A))) (@ P2 X4))) (or (@ P2 A) (= N tptp.zero_zero_nat)))))
% 6.73/7.05 (assert (forall ((N tptp.num)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.numera6620942414471956472nteger N)) tptp.one_one_Code_integer) (@ (@ tptp.ord_less_eq_num N) tptp.one))))
% 6.73/7.05 (assert (forall ((N tptp.num)) (= (@ (@ tptp.ord_le2932123472753598470d_enat (@ tptp.numera1916890842035813515d_enat N)) tptp.one_on7984719198319812577d_enat) (@ (@ tptp.ord_less_eq_num N) tptp.one))))
% 6.73/7.05 (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))))
% 6.73/7.05 (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))))
% 6.73/7.05 (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))))
% 6.73/7.05 (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))))
% 6.73/7.05 (assert (forall ((N tptp.num)) (= (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) (@ tptp.numera6620942414471956472nteger N)) (@ (@ tptp.ord_less_num tptp.one) N))))
% 6.73/7.05 (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))))
% 6.73/7.05 (assert (forall ((N tptp.num)) (= (@ (@ tptp.ord_le72135733267957522d_enat tptp.one_on7984719198319812577d_enat) (@ tptp.numera1916890842035813515d_enat N)) (@ (@ tptp.ord_less_num tptp.one) N))))
% 6.73/7.05 (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))))
% 6.73/7.05 (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))))
% 6.73/7.05 (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))))
% 6.73/7.05 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer) (@ tptp.numera6620942414471956472nteger N)) (@ tptp.numera6620942414471956472nteger (@ (@ tptp.plus_plus_num tptp.one) N)))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_p3455044024723400733d_enat tptp.one_on7984719198319812577d_enat) (@ tptp.numera1916890842035813515d_enat N)) (@ tptp.numera1916890842035813515d_enat (@ (@ tptp.plus_plus_num tptp.one) N)))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.numera6620942414471956472nteger N)) tptp.one_one_Code_integer) (@ tptp.numera6620942414471956472nteger (@ (@ tptp.plus_plus_num N) tptp.one)))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_p3455044024723400733d_enat (@ tptp.numera1916890842035813515d_enat N)) tptp.one_on7984719198319812577d_enat) (@ tptp.numera1916890842035813515d_enat (@ (@ tptp.plus_plus_num N) tptp.one)))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (assert (forall ((M2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real M2)) tptp.zero_zero_real) (= M2 tptp.zero_zero_nat))))
% 6.73/7.05 (assert (forall ((M2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.semiri681578069525770553at_rat M2)) tptp.zero_zero_rat) (= M2 tptp.zero_zero_nat))))
% 6.73/7.05 (assert (forall ((M2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1316708129612266289at_nat M2)) tptp.zero_zero_nat) (= M2 tptp.zero_zero_nat))))
% 6.73/7.05 (assert (forall ((M2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int M2)) tptp.zero_zero_int) (= M2 tptp.zero_zero_nat))))
% 6.73/7.05 (assert (forall ((M2 tptp.nat)) (= (@ tptp.semiri4939895301339042750nteger (@ tptp.suc M2)) (@ (@ tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer) (@ tptp.semiri4939895301339042750nteger M2)))))
% 6.73/7.05 (assert (forall ((M2 tptp.nat)) (= (@ tptp.semiri8010041392384452111omplex (@ tptp.suc M2)) (@ (@ tptp.plus_plus_complex tptp.one_one_complex) (@ tptp.semiri8010041392384452111omplex M2)))))
% 6.73/7.05 (assert (forall ((M2 tptp.nat)) (= (@ tptp.semiri681578069525770553at_rat (@ tptp.suc M2)) (@ (@ tptp.plus_plus_rat tptp.one_one_rat) (@ tptp.semiri681578069525770553at_rat M2)))))
% 6.73/7.05 (assert (forall ((M2 tptp.nat)) (= (@ tptp.semiri5074537144036343181t_real (@ tptp.suc M2)) (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real M2)))))
% 6.73/7.05 (assert (forall ((M2 tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.suc M2)) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ tptp.semiri1314217659103216013at_int M2)))))
% 6.73/7.05 (assert (forall ((M2 tptp.nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ tptp.suc M2)) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ tptp.semiri1316708129612266289at_nat M2)))))
% 6.73/7.05 (assert (= (@ (@ tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer) tptp.one_one_Code_integer) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))
% 6.73/7.05 (assert (= (@ (@ tptp.plus_plus_rat tptp.one_one_rat) tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))
% 6.73/7.05 (assert (= (@ (@ tptp.plus_p3455044024723400733d_enat tptp.one_on7984719198319812577d_enat) tptp.one_on7984719198319812577d_enat) (@ tptp.numera1916890842035813515d_enat (@ tptp.bit0 tptp.one))))
% 6.73/7.05 (assert (= (@ (@ tptp.plus_plus_complex tptp.one_one_complex) tptp.one_one_complex) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))
% 6.73/7.05 (assert (= (@ (@ tptp.plus_plus_real tptp.one_one_real) tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))
% 6.73/7.05 (assert (= (@ (@ tptp.plus_plus_nat tptp.one_one_nat) tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))
% 6.73/7.05 (assert (= (@ (@ tptp.plus_plus_int tptp.one_one_int) tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))
% 6.73/7.05 (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))))
% 6.73/7.05 (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))))
% 6.73/7.05 (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))))
% 6.73/7.05 (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))))
% 6.73/7.05 (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))))
% 6.73/7.05 (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))))
% 6.73/7.05 (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))))
% 6.73/7.05 (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))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (@ tptp.suc (@ tptp.suc N)))))
% 6.73/7.05 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.plus_plus_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.suc (@ tptp.suc N)))))
% 6.73/7.05 (assert (= (@ tptp.suc tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))
% 6.73/7.05 (assert (forall ((B tptp.nat) (W2 tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real B)) W2)) (@ tptp.semiri5074537144036343181t_real X)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat B) W2)) X))))
% 6.73/7.05 (assert (forall ((B tptp.nat) (W2 tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat (@ tptp.semiri681578069525770553at_rat B)) W2)) (@ tptp.semiri681578069525770553at_rat X)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat B) W2)) X))))
% 6.73/7.05 (assert (forall ((B tptp.nat) (W2 tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat B)) W2)) (@ tptp.semiri1316708129612266289at_nat X)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat B) W2)) X))))
% 6.73/7.05 (assert (forall ((B tptp.nat) (W2 tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int B)) W2)) (@ tptp.semiri1314217659103216013at_int X)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat B) W2)) X))))
% 6.73/7.05 (assert (forall ((X tptp.nat) (B tptp.nat) (W2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real X)) (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real B)) W2)) (@ (@ tptp.ord_less_eq_nat X) (@ (@ tptp.power_power_nat B) W2)))))
% 6.73/7.05 (assert (forall ((X tptp.nat) (B tptp.nat) (W2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.semiri681578069525770553at_rat X)) (@ (@ tptp.power_power_rat (@ tptp.semiri681578069525770553at_rat B)) W2)) (@ (@ tptp.ord_less_eq_nat X) (@ (@ tptp.power_power_nat B) W2)))))
% 6.73/7.05 (assert (forall ((X tptp.nat) (B tptp.nat) (W2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1316708129612266289at_nat X)) (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat B)) W2)) (@ (@ tptp.ord_less_eq_nat X) (@ (@ tptp.power_power_nat B) W2)))))
% 6.73/7.05 (assert (forall ((X tptp.nat) (B tptp.nat) (W2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int X)) (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int B)) W2)) (@ (@ tptp.ord_less_eq_nat X) (@ (@ tptp.power_power_nat B) W2)))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (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))))))))
% 6.73/7.05 (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))))))))
% 6.73/7.05 (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))))))))
% 6.73/7.05 (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))))))))
% 6.73/7.05 (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))))
% 6.73/7.05 (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))))
% 6.73/7.05 (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))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (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))))))
% 6.73/7.05 (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))))))
% 6.73/7.05 (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))))))
% 6.73/7.05 (assert (forall ((I2 tptp.num) (N tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real I2)) N)) (@ tptp.semiri5074537144036343181t_real X)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N)) X))))
% 6.73/7.05 (assert (forall ((I2 tptp.num) (N tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat I2)) N)) (@ tptp.semiri681578069525770553at_rat X)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N)) X))))
% 6.73/7.05 (assert (forall ((I2 tptp.num) (N tptp.nat) (X tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N)))) (= (@ _let_1 (@ tptp.semiri1316708129612266289at_nat X)) (@ _let_1 X)))))
% 6.73/7.05 (assert (forall ((I2 tptp.num) (N tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int I2)) N)) (@ tptp.semiri1314217659103216013at_int X)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N)) X))))
% 6.73/7.05 (assert (forall ((X tptp.nat) (I2 tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real X)) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real I2)) N)) (@ (@ tptp.ord_less_eq_nat X) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N)))))
% 6.73/7.05 (assert (forall ((X tptp.nat) (I2 tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.semiri681578069525770553at_rat X)) (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat I2)) N)) (@ (@ tptp.ord_less_eq_nat X) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N)))))
% 6.73/7.05 (assert (forall ((X tptp.nat) (I2 tptp.num) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N))) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1316708129612266289at_nat X)) _let_1) (@ (@ tptp.ord_less_eq_nat X) _let_1)))))
% 6.73/7.05 (assert (forall ((X tptp.nat) (I2 tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int X)) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int I2)) N)) (@ (@ tptp.ord_less_eq_nat X) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N)))))
% 6.73/7.05 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat M2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) N) (@ (@ tptp.ord_less_eq_nat M2) N))))
% 6.73/7.05 (assert (forall ((M2 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 M2) _let_1)) (@ (@ tptp.power_power_nat N) _let_1)) (@ (@ tptp.ord_less_eq_nat M2) N)))))
% 6.73/7.05 (assert (forall ((K2 tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) K2) (@ (@ tptp.ord_less_eq_nat M2) (@ (@ tptp.power_power_nat K2) M2)))))
% 6.73/7.05 (assert (forall ((S3 tptp.set_nat)) (= (= (@ tptp.finite_card_nat S3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (exists ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) S3) (exists ((Y4 tptp.nat)) (and (@ (@ tptp.member_nat Y4) S3) (not (= X4 Y4)) (forall ((Z4 tptp.nat)) (=> (@ (@ tptp.member_nat Z4) S3) (or (= Z4 X4) (= Z4 Y4)))))))))))
% 6.73/7.05 (assert (forall ((S3 tptp.set_complex)) (= (= (@ tptp.finite_card_complex S3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (exists ((X4 tptp.complex)) (and (@ (@ tptp.member_complex X4) S3) (exists ((Y4 tptp.complex)) (and (@ (@ tptp.member_complex Y4) S3) (not (= X4 Y4)) (forall ((Z4 tptp.complex)) (=> (@ (@ tptp.member_complex Z4) S3) (or (= Z4 X4) (= Z4 Y4)))))))))))
% 6.73/7.05 (assert (forall ((S3 tptp.set_int)) (= (= (@ tptp.finite_card_int S3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (exists ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) S3) (exists ((Y4 tptp.int)) (and (@ (@ tptp.member_int Y4) S3) (not (= X4 Y4)) (forall ((Z4 tptp.int)) (=> (@ (@ tptp.member_int Z4) S3) (or (= Z4 X4) (= Z4 Y4)))))))))))
% 6.73/7.05 (assert (forall ((S3 tptp.set_list_nat)) (= (= (@ tptp.finite_card_list_nat S3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (exists ((X4 tptp.list_nat)) (and (@ (@ tptp.member_list_nat X4) S3) (exists ((Y4 tptp.list_nat)) (and (@ (@ tptp.member_list_nat Y4) S3) (not (= X4 Y4)) (forall ((Z4 tptp.list_nat)) (=> (@ (@ tptp.member_list_nat Z4) S3) (or (= Z4 X4) (= Z4 Y4)))))))))))
% 6.73/7.05 (assert (forall ((S3 tptp.set_set_nat)) (= (= (@ tptp.finite_card_set_nat S3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (exists ((X4 tptp.set_nat)) (and (@ (@ tptp.member_set_nat X4) S3) (exists ((Y4 tptp.set_nat)) (and (@ (@ tptp.member_set_nat Y4) S3) (not (= X4 Y4)) (forall ((Z4 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat Z4) S3) (or (= Z4 X4) (= Z4 Y4)))))))))))
% 6.73/7.05 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (forall ((Y6 tptp.real)) (exists ((N3 tptp.nat)) (@ (@ tptp.ord_less_real Y6) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N3)) X)))))))
% 6.73/7.05 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_num tptp.one) N) (@ (@ tptp.plus_plus_num N) tptp.one))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numera1916890842035813515d_enat N))) (= (@ tptp.numera1916890842035813515d_enat (@ tptp.bit0 N)) (@ (@ tptp.plus_p3455044024723400733d_enat _let_1) _let_1)))))
% 6.73/7.05 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex N))) (= (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 N)) (@ (@ tptp.plus_plus_complex _let_1) _let_1)))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat A) (@ tptp.numeral_numeral_rat tptp.one)) A)))
% 6.73/7.05 (assert (forall ((A tptp.extended_enat)) (= (@ (@ tptp.times_7803423173614009249d_enat A) (@ tptp.numera1916890842035813515d_enat tptp.one)) A)))
% 6.73/7.05 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex A) (@ tptp.numera6690914467698888265omplex tptp.one)) A)))
% 6.73/7.05 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real A) (@ tptp.numeral_numeral_real tptp.one)) A)))
% 6.73/7.05 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat A) (@ tptp.numeral_numeral_nat tptp.one)) A)))
% 6.73/7.05 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int A) (@ tptp.numeral_numeral_int tptp.one)) A)))
% 6.73/7.05 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat tptp.one)) A) A)))
% 6.73/7.05 (assert (forall ((A tptp.extended_enat)) (= (@ (@ tptp.times_7803423173614009249d_enat (@ tptp.numera1916890842035813515d_enat tptp.one)) A) A)))
% 6.73/7.05 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex tptp.one)) A) A)))
% 6.73/7.05 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real tptp.one)) A) A)))
% 6.73/7.05 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat tptp.one)) A) A)))
% 6.73/7.05 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int tptp.one)) A) A)))
% 6.73/7.05 (assert (= (@ tptp.numera6620942414471956472nteger tptp.one) tptp.one_one_Code_integer))
% 6.73/7.05 (assert (= (@ tptp.numera1916890842035813515d_enat tptp.one) tptp.one_on7984719198319812577d_enat))
% 6.73/7.05 (assert (= (@ tptp.numera6690914467698888265omplex tptp.one) tptp.one_one_complex))
% 6.73/7.05 (assert (= (@ tptp.numeral_numeral_real tptp.one) tptp.one_one_real))
% 6.73/7.05 (assert (= (@ tptp.numeral_numeral_nat tptp.one) tptp.one_one_nat))
% 6.73/7.05 (assert (= (@ tptp.numeral_numeral_int tptp.one) tptp.one_one_int))
% 6.73/7.05 (assert (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))
% 6.73/7.05 (assert (= (@ tptp.numeral_numeral_nat tptp.one) tptp.one_one_nat))
% 6.73/7.05 (assert (forall ((X tptp.num)) (= (@ (@ tptp.ord_less_eq_num X) tptp.one) (= X tptp.one))))
% 6.73/7.05 (assert (forall ((Z3 tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))) Z3) (@ (@ tptp.plus_plus_rat Z3) Z3))))
% 6.73/7.05 (assert (forall ((Z3 tptp.extended_enat)) (= (@ (@ tptp.times_7803423173614009249d_enat (@ tptp.numera1916890842035813515d_enat (@ tptp.bit0 tptp.one))) Z3) (@ (@ tptp.plus_p3455044024723400733d_enat Z3) Z3))))
% 6.73/7.05 (assert (forall ((Z3 tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))) Z3) (@ (@ tptp.plus_plus_complex Z3) Z3))))
% 6.73/7.05 (assert (forall ((Z3 tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) Z3) (@ (@ tptp.plus_plus_real Z3) Z3))))
% 6.73/7.05 (assert (forall ((Z3 tptp.nat)) (= (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Z3) (@ (@ tptp.plus_plus_nat Z3) Z3))))
% 6.73/7.05 (assert (forall ((Z3 tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) Z3) (@ (@ tptp.plus_plus_int Z3) Z3))))
% 6.73/7.05 (assert (forall ((Z3 tptp.rat)) (= (@ (@ tptp.times_times_rat Z3) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_plus_rat Z3) Z3))))
% 6.73/7.05 (assert (forall ((Z3 tptp.extended_enat)) (= (@ (@ tptp.times_7803423173614009249d_enat Z3) (@ tptp.numera1916890842035813515d_enat (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_p3455044024723400733d_enat Z3) Z3))))
% 6.73/7.05 (assert (forall ((Z3 tptp.complex)) (= (@ (@ tptp.times_times_complex Z3) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_plus_complex Z3) Z3))))
% 6.73/7.05 (assert (forall ((Z3 tptp.real)) (= (@ (@ tptp.times_times_real Z3) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_plus_real Z3) Z3))))
% 6.73/7.05 (assert (forall ((Z3 tptp.nat)) (= (@ (@ tptp.times_times_nat Z3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_plus_nat Z3) Z3))))
% 6.73/7.05 (assert (forall ((Z3 tptp.int)) (= (@ (@ tptp.times_times_int Z3) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_plus_int Z3) Z3))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (assert (forall ((A tptp.extended_enat) (B tptp.extended_enat)) (let ((_let_1 (@ tptp.plus_p3455044024723400733d_enat A))) (= (@ _let_1 (@ _let_1 B)) (@ (@ tptp.plus_p3455044024723400733d_enat (@ (@ tptp.times_7803423173614009249d_enat (@ tptp.numera1916890842035813515d_enat (@ tptp.bit0 tptp.one))) A)) B)))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (assert (= (@ (@ tptp.power_power_rat tptp.zero_zero_rat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_rat))
% 6.73/7.05 (assert (= (@ (@ tptp.power_power_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_nat))
% 6.73/7.05 (assert (= (@ (@ tptp.power_power_real tptp.zero_zero_real) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_real))
% 6.73/7.05 (assert (= (@ (@ tptp.power_power_int tptp.zero_zero_int) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_int))
% 6.73/7.05 (assert (= (@ (@ tptp.power_power_complex tptp.zero_zero_complex) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_complex))
% 6.73/7.05 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.power_power_complex A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.times_times_complex A) A))))
% 6.73/7.05 (assert (forall ((A tptp.real)) (= (@ (@ tptp.power_power_real A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.times_times_real A) A))))
% 6.73/7.05 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.power_power_rat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.times_times_rat A) A))))
% 6.73/7.05 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.power_power_nat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.times_times_nat A) A))))
% 6.73/7.05 (assert (forall ((A tptp.int)) (= (@ (@ tptp.power_power_int A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.times_times_int A) A))))
% 6.73/7.05 (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))))
% 6.73/7.05 (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))))
% 6.73/7.05 (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))))
% 6.73/7.05 (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))))
% 6.73/7.05 (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))))
% 6.73/7.05 (assert (= (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)) (@ tptp.suc (@ tptp.suc tptp.zero_zero_nat))))
% 6.73/7.05 (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))))))
% 6.73/7.05 (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))))))
% 6.73/7.05 (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))))))
% 6.73/7.05 (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))))))
% 6.73/7.05 (assert (forall ((K2 tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat K2))) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) K2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat M2) N)) (@ (@ tptp.minus_minus_nat (@ _let_1 M2)) (@ _let_1 N)))))))
% 6.73/7.05 (assert (= (@ (@ tptp.plus_plus_nat tptp.one_one_nat) tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))
% 6.73/7.05 (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)))))))
% 6.73/7.05 (assert (forall ((X tptp.extended_enat) (Y tptp.extended_enat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ (@ tptp.power_8040749407984259932d_enat (@ (@ tptp.plus_p3455044024723400733d_enat X) Y)) _let_2) (@ (@ tptp.plus_p3455044024723400733d_enat (@ (@ tptp.plus_p3455044024723400733d_enat (@ (@ tptp.power_8040749407984259932d_enat X) _let_2)) (@ (@ tptp.power_8040749407984259932d_enat Y) _let_2))) (@ (@ tptp.times_7803423173614009249d_enat (@ (@ tptp.times_7803423173614009249d_enat (@ tptp.numera1916890842035813515d_enat _let_1)) X)) Y)))))))
% 6.73/7.05 (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)))))))
% 6.73/7.05 (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)))))))
% 6.73/7.05 (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))))))
% 6.73/7.05 (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)))))))
% 6.73/7.05 (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)))))))
% 6.73/7.05 (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)))))))
% 6.73/7.05 (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)))))))
% 6.73/7.05 (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)))))))
% 6.73/7.05 (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)))))))
% 6.73/7.05 (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)))))))
% 6.73/7.05 (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))))))
% 6.73/7.05 (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))))))
% 6.73/7.05 (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))))))
% 6.73/7.05 (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))))))
% 6.73/7.05 (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))))))))
% 6.73/7.05 (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))))))))
% 6.73/7.05 (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))))))))
% 6.73/7.05 (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))))))))
% 6.73/7.05 (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))))))
% 6.73/7.05 (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))))))
% 6.73/7.05 (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))))))
% 6.73/7.05 (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))))
% 6.73/7.05 (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))))
% 6.73/7.05 (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))))
% 6.73/7.05 (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))))))
% 6.73/7.05 (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))))))
% 6.73/7.05 (assert (forall ((S3 tptp.set_complex)) (= (= (@ tptp.finite_card_complex S3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (exists ((X4 tptp.complex) (Y4 tptp.complex)) (and (= S3 (@ (@ tptp.insert_complex X4) (@ (@ tptp.insert_complex Y4) tptp.bot_bot_set_complex))) (not (= X4 Y4)))))))
% 6.73/7.05 (assert (forall ((S3 tptp.set_list_nat)) (= (= (@ tptp.finite_card_list_nat S3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (exists ((X4 tptp.list_nat) (Y4 tptp.list_nat)) (and (= S3 (@ (@ tptp.insert_list_nat X4) (@ (@ tptp.insert_list_nat Y4) tptp.bot_bot_set_list_nat))) (not (= X4 Y4)))))))
% 6.73/7.05 (assert (forall ((S3 tptp.set_set_nat)) (= (= (@ tptp.finite_card_set_nat S3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (exists ((X4 tptp.set_nat) (Y4 tptp.set_nat)) (and (= S3 (@ (@ tptp.insert_set_nat X4) (@ (@ tptp.insert_set_nat Y4) tptp.bot_bot_set_set_nat))) (not (= X4 Y4)))))))
% 6.73/7.05 (assert (forall ((S3 tptp.set_nat)) (= (= (@ tptp.finite_card_nat S3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (exists ((X4 tptp.nat) (Y4 tptp.nat)) (and (= S3 (@ (@ tptp.insert_nat X4) (@ (@ tptp.insert_nat Y4) tptp.bot_bot_set_nat))) (not (= X4 Y4)))))))
% 6.73/7.05 (assert (forall ((S3 tptp.set_int)) (= (= (@ tptp.finite_card_int S3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (exists ((X4 tptp.int) (Y4 tptp.int)) (and (= S3 (@ (@ tptp.insert_int X4) (@ (@ tptp.insert_int Y4) tptp.bot_bot_set_int))) (not (= X4 Y4)))))))
% 6.73/7.05 (assert (forall ((S3 tptp.set_real)) (= (= (@ tptp.finite_card_real S3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (exists ((X4 tptp.real) (Y4 tptp.real)) (and (= S3 (@ (@ tptp.insert_real X4) (@ (@ tptp.insert_real Y4) tptp.bot_bot_set_real))) (not (= X4 Y4)))))))
% 6.73/7.05 (assert (= (@ tptp.numeral_numeral_nat tptp.one) (@ tptp.suc tptp.zero_zero_nat)))
% 6.73/7.05 (assert (forall ((V2 tptp.num) (N tptp.nat)) (= (@ tptp.suc (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat V2)) N)) (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num V2) tptp.one))) N))))
% 6.73/7.05 (assert (forall ((X tptp.real)) (exists ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real X) (@ tptp.semiri5074537144036343181t_real N3)))))
% 6.73/7.05 (assert (forall ((X tptp.rat)) (exists ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_rat X) (@ tptp.semiri681578069525770553at_rat N3)))))
% 6.73/7.05 (assert (forall ((X tptp.rat)) (exists ((N3 tptp.nat)) (@ (@ tptp.ord_less_rat X) (@ tptp.semiri681578069525770553at_rat N3)))))
% 6.73/7.05 (assert (forall ((X tptp.real)) (exists ((N3 tptp.nat)) (@ (@ tptp.ord_less_real X) (@ tptp.semiri5074537144036343181t_real N3)))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (assert (= tptp.ord_less_int (lambda ((W3 tptp.int) (Z4 tptp.int)) (exists ((N4 tptp.nat)) (= Z4 (@ (@ tptp.plus_plus_int W3) (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N4))))))))
% 6.73/7.05 (assert (forall ((N tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int N)) tptp.one_one_int))))
% 6.73/7.05 (assert (forall ((A tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.suc A)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int A)) tptp.one_one_int))))
% 6.73/7.05 (assert (forall ((N tptp.num)) (not (= tptp.zero_zero_rat (@ tptp.numeral_numeral_rat N)))))
% 6.73/7.05 (assert (forall ((N tptp.num)) (not (= tptp.zero_z5237406670263579293d_enat (@ tptp.numera1916890842035813515d_enat N)))))
% 6.73/7.05 (assert (forall ((N tptp.num)) (not (= tptp.zero_zero_complex (@ tptp.numera6690914467698888265omplex N)))))
% 6.73/7.05 (assert (forall ((N tptp.num)) (not (= tptp.zero_zero_real (@ tptp.numeral_numeral_real N)))))
% 6.73/7.05 (assert (forall ((N tptp.num)) (not (= tptp.zero_zero_nat (@ tptp.numeral_numeral_nat N)))))
% 6.73/7.05 (assert (forall ((N tptp.num)) (not (= tptp.zero_zero_int (@ tptp.numeral_numeral_int N)))))
% 6.73/7.05 (assert (= (@ tptp.semiri1314217659103216013at_int tptp.zero_zero_nat) tptp.zero_zero_int))
% 6.73/7.05 (assert (= tptp.ord_less_eq_nat (lambda ((N4 tptp.nat) (M6 tptp.nat)) (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real N4)) (@ (@ tptp.plus_plus_real (@ tptp.semiri5074537144036343181t_real M6)) tptp.one_one_real)))))
% 6.73/7.05 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int M2)) (@ tptp.semiri1314217659103216013at_int N)) (@ (@ tptp.ord_less_eq_nat M2) N))))
% 6.73/7.05 (assert (= tptp.ord_less_eq_nat (lambda ((A5 tptp.nat) (B4 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int A5)) (@ tptp.semiri1314217659103216013at_int B4)))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (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))))))
% 6.73/7.05 (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))))))
% 6.73/7.05 (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))))))
% 6.73/7.05 (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))))))
% 6.73/7.05 (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))))))
% 6.73/7.05 (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))))))
% 6.73/7.05 (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))))))
% 6.73/7.05 (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))))))
% 6.73/7.05 (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))))))
% 6.73/7.05 (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))))))
% 6.73/7.05 (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)))))))
% 6.73/7.05 (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)))))))
% 6.73/7.05 (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)))))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (assert (= (@ tptp.size_size_num tptp.one) tptp.zero_zero_nat))
% 6.73/7.05 (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)))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (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)))))))
% 6.73/7.05 (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)))))))
% 6.73/7.05 (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)))))))
% 6.73/7.05 (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)))))))
% 6.73/7.05 (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)))))))
% 6.73/7.05 (assert (forall ((B tptp.nat) (K2 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) K2) (exists ((N3 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (and (@ (@ tptp.ord_less_eq_nat (@ _let_1 N3)) K2) (@ (@ tptp.ord_less_nat K2) (@ _let_1 (@ (@ tptp.plus_plus_nat N3) tptp.one_one_nat))))))))))
% 6.73/7.05 (assert (forall ((B tptp.nat) (K2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (@ _let_1 B) (=> (@ _let_1 K2) (exists ((N3 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (and (@ (@ tptp.ord_less_nat (@ _let_1 N3)) K2) (@ (@ tptp.ord_less_eq_nat K2) (@ _let_1 (@ (@ tptp.plus_plus_nat N3) tptp.one_one_nat)))))))))))
% 6.73/7.05 (assert (forall ((Deg tptp.nat) (X tptp.nat) (Info2 tptp.option4927543243414619207at_nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info2) Deg) TreeList2) Summary))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_insert _let_1) X))) (let ((_let_3 (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Deg)) X))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ (@ tptp.vEBT_vebt_insert _let_1) X)))))))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (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))))
% 6.73/7.05 (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))))
% 6.73/7.05 (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))))
% 6.73/7.05 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y tptp.vEBT_VEBT)) (=> (= (@ (@ tptp.vEBT_VEBT_insert X) Xa2) Y) (=> (forall ((A3 Bool) (B3 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A3) B3))) (=> (= X _let_1) (not (= Y (@ (@ tptp.vEBT_vebt_insert _let_1) Xa2)))))) (not (forall ((Info tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info) Deg2) TreeList) Summary2))) (let ((_let_2 (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Deg2)) Xa2))) (=> (= X _let_1) (not (and (=> _let_2 (= Y _let_1)) (=> (not _let_2) (= Y (@ (@ tptp.vEBT_vebt_insert _let_1) Xa2))))))))))))))
% 6.73/7.05 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.semiri5074537144036343181t_real N))))
% 6.73/7.05 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.semiri681578069525770553at_rat N))))
% 6.73/7.05 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ tptp.semiri1316708129612266289at_nat N))))
% 6.73/7.05 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.semiri1314217659103216013at_int N))))
% 6.73/7.05 (assert (forall ((M2 tptp.nat)) (not (@ (@ tptp.ord_less_rat (@ tptp.semiri681578069525770553at_rat M2)) tptp.zero_zero_rat))))
% 6.73/7.05 (assert (forall ((M2 tptp.nat)) (not (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real M2)) tptp.zero_zero_real))))
% 6.73/7.05 (assert (forall ((M2 tptp.nat)) (not (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int M2)) tptp.zero_zero_int))))
% 6.73/7.05 (assert (forall ((M2 tptp.nat)) (not (@ (@ tptp.ord_less_nat (@ tptp.semiri1316708129612266289at_nat M2)) tptp.zero_zero_nat))))
% 6.73/7.05 (assert (forall ((N tptp.nat)) (not (= (@ tptp.semiri8010041392384452111omplex (@ tptp.suc N)) tptp.zero_zero_complex))))
% 6.73/7.05 (assert (forall ((N tptp.nat)) (not (= (@ tptp.semiri681578069525770553at_rat (@ tptp.suc N)) tptp.zero_zero_rat))))
% 6.73/7.05 (assert (forall ((N tptp.nat)) (not (= (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N)) tptp.zero_zero_real))))
% 6.73/7.05 (assert (forall ((N tptp.nat)) (not (= (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N)) tptp.zero_zero_int))))
% 6.73/7.05 (assert (forall ((N tptp.nat)) (not (= (@ tptp.semiri1316708129612266289at_nat (@ tptp.suc N)) tptp.zero_zero_nat))))
% 6.73/7.05 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_rat (@ tptp.semiri681578069525770553at_rat M2)) (@ tptp.semiri681578069525770553at_rat N)) (@ (@ tptp.ord_less_nat M2) N))))
% 6.73/7.05 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real M2)) (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.ord_less_nat M2) N))))
% 6.73/7.05 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int M2)) (@ tptp.semiri1314217659103216013at_int N)) (@ (@ tptp.ord_less_nat M2) N))))
% 6.73/7.05 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.semiri1316708129612266289at_nat M2)) (@ tptp.semiri1316708129612266289at_nat N)) (@ (@ tptp.ord_less_nat M2) N))))
% 6.73/7.05 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) N) (@ (@ tptp.ord_less_rat (@ tptp.semiri681578069525770553at_rat M2)) (@ tptp.semiri681578069525770553at_rat N)))))
% 6.73/7.05 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) N) (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real M2)) (@ tptp.semiri5074537144036343181t_real N)))))
% 6.73/7.05 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) N) (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int M2)) (@ tptp.semiri1314217659103216013at_int N)))))
% 6.73/7.05 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) N) (@ (@ tptp.ord_less_nat (@ tptp.semiri1316708129612266289at_nat M2)) (@ tptp.semiri1316708129612266289at_nat N)))))
% 6.73/7.05 (assert (forall ((I2 tptp.nat) (J2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J2) (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real I2)) (@ tptp.semiri5074537144036343181t_real J2)))))
% 6.73/7.05 (assert (forall ((I2 tptp.nat) (J2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J2) (@ (@ tptp.ord_less_eq_rat (@ tptp.semiri681578069525770553at_rat I2)) (@ tptp.semiri681578069525770553at_rat J2)))))
% 6.73/7.05 (assert (forall ((I2 tptp.nat) (J2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J2) (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1316708129612266289at_nat I2)) (@ tptp.semiri1316708129612266289at_nat J2)))))
% 6.73/7.05 (assert (forall ((I2 tptp.nat) (J2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J2) (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int I2)) (@ tptp.semiri1314217659103216013at_int J2)))))
% 6.73/7.05 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ tptp.numera1916890842035813515d_enat N))))
% 6.73/7.05 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.numeral_numeral_real N))))
% 6.73/7.05 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.numeral_numeral_rat N))))
% 6.73/7.05 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat N))))
% 6.73/7.05 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.numeral_numeral_int N))))
% 6.73/7.05 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_le2932123472753598470d_enat (@ tptp.numera1916890842035813515d_enat N)) tptp.zero_z5237406670263579293d_enat))))
% 6.73/7.05 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real N)) tptp.zero_zero_real))))
% 6.73/7.05 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_eq_rat (@ tptp.numeral_numeral_rat N)) tptp.zero_zero_rat))))
% 6.73/7.05 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat N)) tptp.zero_zero_nat))))
% 6.73/7.05 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int N)) tptp.zero_zero_int))))
% 6.73/7.05 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_rat (@ tptp.numeral_numeral_rat N)) tptp.zero_zero_rat))))
% 6.73/7.05 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_le72135733267957522d_enat (@ tptp.numera1916890842035813515d_enat N)) tptp.zero_z5237406670263579293d_enat))))
% 6.73/7.05 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real N)) tptp.zero_zero_real))))
% 6.73/7.05 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_nat (@ tptp.numeral_numeral_nat N)) tptp.zero_zero_nat))))
% 6.73/7.05 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int N)) tptp.zero_zero_int))))
% 6.73/7.05 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.numeral_numeral_rat N))))
% 6.73/7.05 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat) (@ tptp.numera1916890842035813515d_enat N))))
% 6.73/7.05 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.numeral_numeral_real N))))
% 6.73/7.05 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat N))))
% 6.73/7.05 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.numeral_numeral_int N))))
% 6.73/7.05 (assert (forall ((N tptp.nat) (X tptp.nat)) (= (@ (@ tptp.replicate_nat (@ tptp.suc N)) X) (@ (@ tptp.cons_nat X) (@ (@ tptp.replicate_nat N) X)))))
% 6.73/7.05 (assert (forall ((N tptp.nat) (X tptp.vEBT_VEBT)) (= (@ (@ tptp.replicate_VEBT_VEBT (@ tptp.suc N)) X) (@ (@ tptp.cons_VEBT_VEBT X) (@ (@ tptp.replicate_VEBT_VEBT N) X)))))
% 6.73/7.05 (assert (forall ((X tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 C2) (=> (forall ((M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real M)) X)) C2))) (= X tptp.zero_zero_real)))))))
% 6.73/7.05 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (@ tptp.numera6620942414471956472nteger N))))
% 6.73/7.05 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.one_on7984719198319812577d_enat) (@ tptp.numera1916890842035813515d_enat N))))
% 6.73/7.05 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.numeral_numeral_real N))))
% 6.73/7.05 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat N))))
% 6.73/7.05 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat N))))
% 6.73/7.05 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.numeral_numeral_int N))))
% 6.73/7.05 (assert (forall ((K2 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K2) (not (forall ((N3 tptp.nat)) (=> (= K2 (@ tptp.semiri1314217659103216013at_int N3)) (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N3))))))))
% 6.73/7.05 (assert (forall ((K2 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K2) (exists ((N3 tptp.nat)) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N3) (= K2 (@ tptp.semiri1314217659103216013at_int N3)))))))
% 6.73/7.05 (assert (forall ((I2 tptp.int) (J2 tptp.int) (K2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int K2)))) (=> (@ (@ tptp.ord_less_int I2) J2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K2) (@ (@ tptp.ord_less_int (@ _let_1 I2)) (@ _let_1 J2)))))))
% 6.73/7.05 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.numera6620942414471956472nteger N)) tptp.one_one_Code_integer))))
% 6.73/7.05 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_rat (@ tptp.numeral_numeral_rat N)) tptp.one_one_rat))))
% 6.73/7.05 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_le72135733267957522d_enat (@ tptp.numera1916890842035813515d_enat N)) tptp.one_on7984719198319812577d_enat))))
% 6.73/7.05 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real N)) tptp.one_one_real))))
% 6.73/7.05 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_nat (@ tptp.numeral_numeral_nat N)) tptp.one_one_nat))))
% 6.73/7.05 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int N)) tptp.one_one_int))))
% 6.73/7.05 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger X))) (= (@ (@ tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer) _let_1) (@ (@ tptp.plus_p5714425477246183910nteger _let_1) tptp.one_one_Code_integer)))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numera1916890842035813515d_enat X))) (= (@ (@ tptp.plus_p3455044024723400733d_enat tptp.one_on7984719198319812577d_enat) _let_1) (@ (@ tptp.plus_p3455044024723400733d_enat _let_1) tptp.one_on7984719198319812577d_enat)))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (X tptp.vEBT_VEBT)) (=> (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 Xs2)) (= X3 X))) (= (@ (@ tptp.replicate_VEBT_VEBT (@ tptp.size_s6755466524823107622T_VEBT Xs2)) X) Xs2))))
% 6.73/7.05 (assert (forall ((Xs2 tptp.list_o) (X Bool)) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) (@ tptp.set_o2 Xs2)) (= X3 X))) (= (@ (@ tptp.replicate_o (@ tptp.size_size_list_o Xs2)) X) Xs2))))
% 6.73/7.05 (assert (forall ((Xs2 tptp.list_nat) (X tptp.nat)) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ tptp.set_nat2 Xs2)) (= X3 X))) (= (@ (@ tptp.replicate_nat (@ tptp.size_size_list_nat Xs2)) X) Xs2))))
% 6.73/7.05 (assert (forall ((Xs2 tptp.list_int) (X tptp.int)) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ tptp.set_int2 Xs2)) (= X3 X))) (= (@ (@ tptp.replicate_int (@ tptp.size_size_list_int Xs2)) X) Xs2))))
% 6.73/7.05 (assert (forall ((Xs2 tptp.list_complex) (N tptp.nat) (X tptp.complex)) (=> (= (@ tptp.size_s3451745648224563538omplex Xs2) N) (=> (forall ((Y3 tptp.complex)) (=> (@ (@ tptp.member_complex Y3) (@ tptp.set_complex2 Xs2)) (= Y3 X))) (= Xs2 (@ (@ tptp.replicate_complex N) X))))))
% 6.73/7.05 (assert (forall ((Xs2 tptp.list_real) (N tptp.nat) (X tptp.real)) (=> (= (@ tptp.size_size_list_real Xs2) N) (=> (forall ((Y3 tptp.real)) (=> (@ (@ tptp.member_real Y3) (@ tptp.set_real2 Xs2)) (= Y3 X))) (= Xs2 (@ (@ tptp.replicate_real N) X))))))
% 6.73/7.05 (assert (forall ((Xs2 tptp.list_set_nat) (N tptp.nat) (X tptp.set_nat)) (=> (= (@ tptp.size_s3254054031482475050et_nat Xs2) N) (=> (forall ((Y3 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat Y3) (@ tptp.set_set_nat2 Xs2)) (= Y3 X))) (= Xs2 (@ (@ tptp.replicate_set_nat N) X))))))
% 6.73/7.05 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (N tptp.nat) (X tptp.vEBT_VEBT)) (=> (= (@ tptp.size_s6755466524823107622T_VEBT Xs2) N) (=> (forall ((Y3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT Y3) (@ tptp.set_VEBT_VEBT2 Xs2)) (= Y3 X))) (= Xs2 (@ (@ tptp.replicate_VEBT_VEBT N) X))))))
% 6.73/7.05 (assert (forall ((Xs2 tptp.list_o) (N tptp.nat) (X Bool)) (=> (= (@ tptp.size_size_list_o Xs2) N) (=> (forall ((Y3 Bool)) (=> (@ (@ tptp.member_o Y3) (@ tptp.set_o2 Xs2)) (= Y3 X))) (= Xs2 (@ (@ tptp.replicate_o N) X))))))
% 6.73/7.05 (assert (forall ((Xs2 tptp.list_nat) (N tptp.nat) (X tptp.nat)) (=> (= (@ tptp.size_size_list_nat Xs2) N) (=> (forall ((Y3 tptp.nat)) (=> (@ (@ tptp.member_nat Y3) (@ tptp.set_nat2 Xs2)) (= Y3 X))) (= Xs2 (@ (@ tptp.replicate_nat N) X))))))
% 6.73/7.05 (assert (forall ((Xs2 tptp.list_int) (N tptp.nat) (X tptp.int)) (=> (= (@ tptp.size_size_list_int Xs2) N) (=> (forall ((Y3 tptp.int)) (=> (@ (@ tptp.member_int Y3) (@ tptp.set_int2 Xs2)) (= Y3 X))) (= Xs2 (@ (@ tptp.replicate_int N) X))))))
% 6.73/7.05 (assert (forall ((TreeList2 tptp.list_VEBT_VEBT) (N tptp.nat) (Summary tptp.vEBT_VEBT) (M2 tptp.nat) (Deg tptp.nat)) (=> (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList2)) (@ (@ tptp.vEBT_invar_vebt X3) N))) (=> (@ (@ tptp.vEBT_invar_vebt Summary) M2) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M2)) (=> (= M2 N) (=> (= Deg (@ (@ tptp.plus_plus_nat N) M2)) (=> (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary) X_12))) (=> (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X3) X_12))))) (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Deg) TreeList2) Summary)) Deg))))))))))
% 6.73/7.05 (assert (forall ((TreeList2 tptp.list_VEBT_VEBT) (N tptp.nat) (Summary tptp.vEBT_VEBT) (M2 tptp.nat) (Deg tptp.nat)) (=> (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList2)) (@ (@ tptp.vEBT_invar_vebt X3) N))) (=> (@ (@ tptp.vEBT_invar_vebt Summary) M2) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M2)) (=> (= M2 (@ tptp.suc N)) (=> (= Deg (@ (@ tptp.plus_plus_nat N) M2)) (=> (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary) X_12))) (=> (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X3) X_12))))) (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Deg) TreeList2) Summary)) Deg))))))))))
% 6.73/7.05 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (Ys tptp.list_VEBT_VEBT) (R3 tptp.set_Pr6192946355708809607T_VEBT)) (=> (@ (@ tptp.member4439316823752958928T_VEBT (@ (@ tptp.produc3897820843166775703T_VEBT Xs2) Ys)) (@ tptp.listre1230615542750757617T_VEBT R3)) (= (@ tptp.size_s6755466524823107622T_VEBT Xs2) (@ tptp.size_s6755466524823107622T_VEBT Ys)))))
% 6.73/7.05 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (Ys tptp.list_o) (R3 tptp.set_Pr3175402225741728619VEBT_o)) (=> (@ (@ tptp.member3126162362653435956list_o (@ (@ tptp.produc2717590391345394939list_o Xs2) Ys)) (@ tptp.listrel_VEBT_VEBT_o R3)) (= (@ tptp.size_s6755466524823107622T_VEBT Xs2) (@ tptp.size_size_list_o Ys)))))
% 6.73/7.05 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (Ys tptp.list_nat) (R3 tptp.set_Pr7556676689462069481BT_nat)) (=> (@ (@ tptp.member6193324644334088288st_nat (@ (@ tptp.produc5570133714943300547st_nat Xs2) Ys)) (@ tptp.listre5900670229112895443BT_nat R3)) (= (@ tptp.size_s6755466524823107622T_VEBT Xs2) (@ tptp.size_size_list_nat Ys)))))
% 6.73/7.05 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (Ys tptp.list_int) (R3 tptp.set_Pr5066593544530342725BT_int)) (=> (@ (@ tptp.member3703241499402361532st_int (@ (@ tptp.produc1392282695434103839st_int Xs2) Ys)) (@ tptp.listre5898179758603845167BT_int R3)) (= (@ tptp.size_s6755466524823107622T_VEBT Xs2) (@ tptp.size_size_list_int Ys)))))
% 6.73/7.05 (assert (forall ((Xs2 tptp.list_o) (Ys tptp.list_VEBT_VEBT) (R3 tptp.set_Pr7543698050874017315T_VEBT)) (=> (@ (@ tptp.member1087064965665443052T_VEBT (@ (@ tptp.produc6043759678074843571T_VEBT Xs2) Ys)) (@ tptp.listrel_o_VEBT_VEBT R3)) (= (@ tptp.size_size_list_o Xs2) (@ tptp.size_s6755466524823107622T_VEBT Ys)))))
% 6.73/7.05 (assert (forall ((Xs2 tptp.list_o) (Ys tptp.list_o) (R3 tptp.set_Product_prod_o_o)) (=> (@ (@ tptp.member4159035015898711888list_o (@ (@ tptp.produc8435520187683070743list_o Xs2) Ys)) (@ tptp.listrel_o_o R3)) (= (@ tptp.size_size_list_o Xs2) (@ tptp.size_size_list_o Ys)))))
% 6.73/7.05 (assert (forall ((Xs2 tptp.list_o) (Ys tptp.list_nat) (R3 tptp.set_Pr2101469702781467981_o_nat)) (=> (@ (@ tptp.member1519744053835550788st_nat (@ (@ tptp.produc7128876500814652583st_nat Xs2) Ys)) (@ tptp.listrel_o_nat R3)) (= (@ tptp.size_size_list_o Xs2) (@ tptp.size_size_list_nat Ys)))))
% 6.73/7.05 (assert (forall ((Xs2 tptp.list_o) (Ys tptp.list_int) (R3 tptp.set_Pr8834758594704517033_o_int)) (=> (@ (@ tptp.member8253032945758599840st_int (@ (@ tptp.produc2951025481305455875st_int Xs2) Ys)) (@ tptp.listrel_o_int R3)) (= (@ tptp.size_size_list_o Xs2) (@ tptp.size_size_list_int Ys)))))
% 6.73/7.05 (assert (forall ((Xs2 tptp.list_nat) (Ys tptp.list_VEBT_VEBT) (R3 tptp.set_Pr6167073792073659919T_VEBT)) (=> (@ (@ tptp.member5968030670617646438T_VEBT (@ (@ tptp.produc8335345208264861441T_VEBT Xs2) Ys)) (@ tptp.listre5761932458788874033T_VEBT R3)) (= (@ tptp.size_size_list_nat Xs2) (@ tptp.size_s6755466524823107622T_VEBT Ys)))))
% 6.73/7.05 (assert (forall ((Xs2 tptp.list_nat) (Ys tptp.list_o) (R3 tptp.set_Pr3149072824959771635_nat_o)) (=> (@ (@ tptp.member6688923169008879818list_o (@ (@ tptp.produc699922362453767013list_o Xs2) Ys)) (@ tptp.listrel_nat_o R3)) (= (@ tptp.size_size_list_nat Xs2) (@ tptp.size_size_list_o Ys)))))
% 6.73/7.05 (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))))))
% 6.73/7.05 (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))))))
% 6.73/7.05 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M2) (= (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.minus_minus_nat M2) N)) (@ (@ tptp.minus_minus_rat (@ tptp.semiri681578069525770553at_rat M2)) (@ tptp.semiri681578069525770553at_rat N))))))
% 6.73/7.05 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M2) (= (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.minus_minus_nat M2) N)) (@ (@ tptp.minus_minus_real (@ tptp.semiri5074537144036343181t_real M2)) (@ tptp.semiri5074537144036343181t_real N))))))
% 6.73/7.05 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M2) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.minus_minus_nat M2) N)) (@ (@ tptp.minus_minus_int (@ tptp.semiri1314217659103216013at_int M2)) (@ tptp.semiri1314217659103216013at_int N))))))
% 6.73/7.05 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M2) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.minus_minus_nat M2) N)) (@ (@ tptp.minus_minus_nat (@ tptp.semiri1316708129612266289at_nat M2)) (@ tptp.semiri1316708129612266289at_nat N))))))
% 6.73/7.05 (assert (forall ((P2 (-> tptp.int Bool)) (X tptp.nat) (Y tptp.nat)) (= (@ P2 (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.minus_minus_nat X) Y))) (and (=> (@ (@ tptp.ord_less_eq_nat Y) X) (@ P2 (@ (@ tptp.minus_minus_int (@ tptp.semiri1314217659103216013at_int X)) (@ tptp.semiri1314217659103216013at_int Y)))) (=> (@ (@ tptp.ord_less_nat X) Y) (@ P2 tptp.zero_zero_int))))))
% 6.73/7.05 (assert (forall ((X2 tptp.num)) (= (@ tptp.size_size_num (@ tptp.bit0 X2)) (@ (@ tptp.plus_plus_nat (@ tptp.size_size_num X2)) (@ tptp.suc tptp.zero_zero_nat)))))
% 6.73/7.05 (assert (forall ((A tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (exists ((R4 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) R4) (= (@ (@ tptp.power_power_real R4) (@ tptp.suc N)) A))))))
% 6.73/7.05 (assert (forall ((Xs2 tptp.list_Code_integer) (Y tptp.code_integer) (Ys tptp.list_Code_integer) (R3 tptp.set_Pr4811707699266497531nteger)) (=> (@ (@ tptp.member749217712838834276nteger (@ (@ tptp.produc750622340256944499nteger Xs2) (@ (@ tptp.cons_Code_integer Y) Ys))) (@ tptp.listre5734910445319291053nteger R3)) (not (forall ((X3 tptp.code_integer) (Xs3 tptp.list_Code_integer)) (=> (= Xs2 (@ (@ tptp.cons_Code_integer X3) Xs3)) (=> (@ (@ tptp.member157494554546826820nteger (@ (@ tptp.produc1086072967326762835nteger X3) Y)) R3) (not (@ (@ tptp.member749217712838834276nteger (@ (@ tptp.produc750622340256944499nteger Xs3) Ys)) (@ tptp.listre5734910445319291053nteger R3))))))))))
% 6.73/7.05 (assert (forall ((Xs2 tptp.list_P6011104703257516679at_nat) (Y tptp.product_prod_nat_nat) (Ys tptp.list_P6011104703257516679at_nat) (R3 tptp.set_Pr8693737435421807431at_nat)) (=> (@ (@ tptp.member6693912407220327184at_nat (@ (@ tptp.produc5943733680697469783at_nat Xs2) (@ (@ tptp.cons_P6512896166579812791at_nat Y) Ys))) (@ tptp.listre818007680106770737at_nat R3)) (not (forall ((X3 tptp.product_prod_nat_nat) (Xs3 tptp.list_P6011104703257516679at_nat)) (=> (= Xs2 (@ (@ tptp.cons_P6512896166579812791at_nat X3) Xs3)) (=> (@ (@ tptp.member8206827879206165904at_nat (@ (@ tptp.produc6161850002892822231at_nat X3) Y)) R3) (not (@ (@ tptp.member6693912407220327184at_nat (@ (@ tptp.produc5943733680697469783at_nat Xs3) Ys)) (@ tptp.listre818007680106770737at_nat R3))))))))))
% 6.73/7.05 (assert (forall ((Xs2 tptp.list_s1210847774152347623at_nat) (Y tptp.set_Pr1261947904930325089at_nat) (Ys tptp.list_s1210847774152347623at_nat) (R3 tptp.set_Pr4329608150637261639at_nat)) (=> (@ (@ tptp.member4080735728053443344at_nat (@ (@ tptp.produc7536900900485677911at_nat Xs2) (@ (@ tptp.cons_s6881495754146722583at_nat Y) Ys))) (@ tptp.listre2047417242196832561at_nat R3)) (not (forall ((X3 tptp.set_Pr1261947904930325089at_nat) (Xs3 tptp.list_s1210847774152347623at_nat)) (=> (= Xs2 (@ (@ tptp.cons_s6881495754146722583at_nat X3) Xs3)) (=> (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat X3) Y)) R3) (not (@ (@ tptp.member4080735728053443344at_nat (@ (@ tptp.produc7536900900485677911at_nat Xs3) Ys)) (@ tptp.listre2047417242196832561at_nat R3))))))))))
% 6.73/7.05 (assert (forall ((Xs2 tptp.list_nat) (Y tptp.nat) (Ys tptp.list_nat) (R3 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.member7340969449405702474st_nat (@ (@ tptp.produc2694037385005941721st_nat Xs2) (@ (@ tptp.cons_nat Y) Ys))) (@ tptp.listrel_nat_nat R3)) (not (forall ((X3 tptp.nat) (Xs3 tptp.list_nat)) (=> (= Xs2 (@ (@ tptp.cons_nat X3) Xs3)) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X3) Y)) R3) (not (@ (@ tptp.member7340969449405702474st_nat (@ (@ tptp.produc2694037385005941721st_nat Xs3) Ys)) (@ tptp.listrel_nat_nat R3))))))))))
% 6.73/7.05 (assert (forall ((Xs2 tptp.list_int) (Y tptp.int) (Ys tptp.list_int) (R3 tptp.set_Pr958786334691620121nt_int)) (=> (@ (@ tptp.member6698963635872716290st_int (@ (@ tptp.produc364263696895485585st_int Xs2) (@ (@ tptp.cons_int Y) Ys))) (@ tptp.listrel_int_int R3)) (not (forall ((X3 tptp.int) (Xs3 tptp.list_int)) (=> (= Xs2 (@ (@ tptp.cons_int X3) Xs3)) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X3) Y)) R3) (not (@ (@ tptp.member6698963635872716290st_int (@ (@ tptp.produc364263696895485585st_int Xs3) Ys)) (@ tptp.listrel_int_int R3))))))))))
% 6.73/7.05 (assert (forall ((Y tptp.code_integer) (Ys tptp.list_Code_integer) (Xs2 tptp.list_Code_integer) (R3 tptp.set_Pr4811707699266497531nteger)) (=> (@ (@ tptp.member749217712838834276nteger (@ (@ tptp.produc750622340256944499nteger (@ (@ tptp.cons_Code_integer Y) Ys)) Xs2)) (@ tptp.listre5734910445319291053nteger R3)) (not (forall ((Y3 tptp.code_integer) (Ys5 tptp.list_Code_integer)) (=> (= Xs2 (@ (@ tptp.cons_Code_integer Y3) Ys5)) (=> (@ (@ tptp.member157494554546826820nteger (@ (@ tptp.produc1086072967326762835nteger Y) Y3)) R3) (not (@ (@ tptp.member749217712838834276nteger (@ (@ tptp.produc750622340256944499nteger Ys) Ys5)) (@ tptp.listre5734910445319291053nteger R3))))))))))
% 6.73/7.05 (assert (forall ((Y tptp.product_prod_nat_nat) (Ys tptp.list_P6011104703257516679at_nat) (Xs2 tptp.list_P6011104703257516679at_nat) (R3 tptp.set_Pr8693737435421807431at_nat)) (=> (@ (@ tptp.member6693912407220327184at_nat (@ (@ tptp.produc5943733680697469783at_nat (@ (@ tptp.cons_P6512896166579812791at_nat Y) Ys)) Xs2)) (@ tptp.listre818007680106770737at_nat R3)) (not (forall ((Y3 tptp.product_prod_nat_nat) (Ys5 tptp.list_P6011104703257516679at_nat)) (=> (= Xs2 (@ (@ tptp.cons_P6512896166579812791at_nat Y3) Ys5)) (=> (@ (@ tptp.member8206827879206165904at_nat (@ (@ tptp.produc6161850002892822231at_nat Y) Y3)) R3) (not (@ (@ tptp.member6693912407220327184at_nat (@ (@ tptp.produc5943733680697469783at_nat Ys) Ys5)) (@ tptp.listre818007680106770737at_nat R3))))))))))
% 6.73/7.05 (assert (forall ((Y tptp.set_Pr1261947904930325089at_nat) (Ys tptp.list_s1210847774152347623at_nat) (Xs2 tptp.list_s1210847774152347623at_nat) (R3 tptp.set_Pr4329608150637261639at_nat)) (=> (@ (@ tptp.member4080735728053443344at_nat (@ (@ tptp.produc7536900900485677911at_nat (@ (@ tptp.cons_s6881495754146722583at_nat Y) Ys)) Xs2)) (@ tptp.listre2047417242196832561at_nat R3)) (not (forall ((Y3 tptp.set_Pr1261947904930325089at_nat) (Ys5 tptp.list_s1210847774152347623at_nat)) (=> (= Xs2 (@ (@ tptp.cons_s6881495754146722583at_nat Y3) Ys5)) (=> (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat Y) Y3)) R3) (not (@ (@ tptp.member4080735728053443344at_nat (@ (@ tptp.produc7536900900485677911at_nat Ys) Ys5)) (@ tptp.listre2047417242196832561at_nat R3))))))))))
% 6.73/7.05 (assert (forall ((Y tptp.nat) (Ys tptp.list_nat) (Xs2 tptp.list_nat) (R3 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.member7340969449405702474st_nat (@ (@ tptp.produc2694037385005941721st_nat (@ (@ tptp.cons_nat Y) Ys)) Xs2)) (@ tptp.listrel_nat_nat R3)) (not (forall ((Y3 tptp.nat) (Ys5 tptp.list_nat)) (=> (= Xs2 (@ (@ tptp.cons_nat Y3) Ys5)) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat Y) Y3)) R3) (not (@ (@ tptp.member7340969449405702474st_nat (@ (@ tptp.produc2694037385005941721st_nat Ys) Ys5)) (@ tptp.listrel_nat_nat R3))))))))))
% 6.73/7.05 (assert (forall ((Y tptp.int) (Ys tptp.list_int) (Xs2 tptp.list_int) (R3 tptp.set_Pr958786334691620121nt_int)) (=> (@ (@ tptp.member6698963635872716290st_int (@ (@ tptp.produc364263696895485585st_int (@ (@ tptp.cons_int Y) Ys)) Xs2)) (@ tptp.listrel_int_int R3)) (not (forall ((Y3 tptp.int) (Ys5 tptp.list_int)) (=> (= Xs2 (@ (@ tptp.cons_int Y3) Ys5)) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int Y) Y3)) R3) (not (@ (@ tptp.member6698963635872716290st_int (@ (@ tptp.produc364263696895485585st_int Ys) Ys5)) (@ tptp.listrel_int_int R3))))))))))
% 6.73/7.05 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer) (R3 tptp.set_Pr4811707699266497531nteger) (Xs2 tptp.list_Code_integer) (Ys tptp.list_Code_integer)) (let ((_let_1 (@ tptp.listre5734910445319291053nteger R3))) (=> (@ (@ tptp.member157494554546826820nteger (@ (@ tptp.produc1086072967326762835nteger X) Y)) R3) (=> (@ (@ tptp.member749217712838834276nteger (@ (@ tptp.produc750622340256944499nteger Xs2) Ys)) _let_1) (@ (@ tptp.member749217712838834276nteger (@ (@ tptp.produc750622340256944499nteger (@ (@ tptp.cons_Code_integer X) Xs2)) (@ (@ tptp.cons_Code_integer Y) Ys))) _let_1))))))
% 6.73/7.05 (assert (forall ((X tptp.product_prod_nat_nat) (Y tptp.product_prod_nat_nat) (R3 tptp.set_Pr8693737435421807431at_nat) (Xs2 tptp.list_P6011104703257516679at_nat) (Ys tptp.list_P6011104703257516679at_nat)) (let ((_let_1 (@ tptp.listre818007680106770737at_nat R3))) (=> (@ (@ tptp.member8206827879206165904at_nat (@ (@ tptp.produc6161850002892822231at_nat X) Y)) R3) (=> (@ (@ tptp.member6693912407220327184at_nat (@ (@ tptp.produc5943733680697469783at_nat Xs2) Ys)) _let_1) (@ (@ tptp.member6693912407220327184at_nat (@ (@ tptp.produc5943733680697469783at_nat (@ (@ tptp.cons_P6512896166579812791at_nat X) Xs2)) (@ (@ tptp.cons_P6512896166579812791at_nat Y) Ys))) _let_1))))))
% 6.73/7.05 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat) (R3 tptp.set_Pr4329608150637261639at_nat) (Xs2 tptp.list_s1210847774152347623at_nat) (Ys tptp.list_s1210847774152347623at_nat)) (let ((_let_1 (@ tptp.listre2047417242196832561at_nat R3))) (=> (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat X) Y)) R3) (=> (@ (@ tptp.member4080735728053443344at_nat (@ (@ tptp.produc7536900900485677911at_nat Xs2) Ys)) _let_1) (@ (@ tptp.member4080735728053443344at_nat (@ (@ tptp.produc7536900900485677911at_nat (@ (@ tptp.cons_s6881495754146722583at_nat X) Xs2)) (@ (@ tptp.cons_s6881495754146722583at_nat Y) Ys))) _let_1))))))
% 6.73/7.05 (assert (forall ((X tptp.nat) (Y tptp.nat) (R3 tptp.set_Pr1261947904930325089at_nat) (Xs2 tptp.list_nat) (Ys tptp.list_nat)) (let ((_let_1 (@ tptp.listrel_nat_nat R3))) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X) Y)) R3) (=> (@ (@ tptp.member7340969449405702474st_nat (@ (@ tptp.produc2694037385005941721st_nat Xs2) Ys)) _let_1) (@ (@ tptp.member7340969449405702474st_nat (@ (@ tptp.produc2694037385005941721st_nat (@ (@ tptp.cons_nat X) Xs2)) (@ (@ tptp.cons_nat Y) Ys))) _let_1))))))
% 6.73/7.05 (assert (forall ((X tptp.int) (Y tptp.int) (R3 tptp.set_Pr958786334691620121nt_int) (Xs2 tptp.list_int) (Ys tptp.list_int)) (let ((_let_1 (@ tptp.listrel_int_int R3))) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X) Y)) R3) (=> (@ (@ tptp.member6698963635872716290st_int (@ (@ tptp.produc364263696895485585st_int Xs2) Ys)) _let_1) (@ (@ tptp.member6698963635872716290st_int (@ (@ tptp.produc364263696895485585st_int (@ (@ tptp.cons_int X) Xs2)) (@ (@ tptp.cons_int Y) Ys))) _let_1))))))
% 6.73/7.05 (assert (forall ((F2 (-> tptp.code_integer tptp.nat)) (X tptp.code_integer) (Y tptp.code_integer) (Fs tptp.list_C4705013386053401436er_nat)) (=> (@ (@ tptp.ord_less_nat (@ F2 X)) (@ F2 Y)) (@ (@ tptp.member157494554546826820nteger (@ (@ tptp.produc1086072967326762835nteger X) Y)) (@ tptp.measur8870801148506250077nteger (@ (@ tptp.cons_C1897838848541180310er_nat F2) Fs))))))
% 6.73/7.05 (assert (forall ((F2 (-> tptp.product_prod_nat_nat tptp.nat)) (X tptp.product_prod_nat_nat) (Y tptp.product_prod_nat_nat) (Fs tptp.list_P9162950289778280392at_nat)) (=> (@ (@ tptp.ord_less_nat (@ F2 X)) (@ F2 Y)) (@ (@ tptp.member8206827879206165904at_nat (@ (@ tptp.produc6161850002892822231at_nat X) Y)) (@ tptp.measur2679027848233739777at_nat (@ (@ tptp.cons_P4861729644591583992at_nat F2) Fs))))))
% 6.73/7.05 (assert (forall ((F2 (-> tptp.set_Pr1261947904930325089at_nat tptp.nat)) (X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat) (Fs tptp.list_s9130966667114977576at_nat)) (=> (@ (@ tptp.ord_less_nat (@ F2 X)) (@ F2 Y)) (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat X) Y)) (@ tptp.measur2694323259624372065at_nat (@ (@ tptp.cons_s2538900923071588440at_nat F2) Fs))))))
% 6.73/7.05 (assert (forall ((F2 (-> tptp.nat tptp.nat)) (X tptp.nat) (Y tptp.nat) (Fs tptp.list_nat_nat)) (=> (@ (@ tptp.ord_less_nat (@ F2 X)) (@ F2 Y)) (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X) Y)) (@ tptp.measures_nat (@ (@ tptp.cons_nat_nat F2) Fs))))))
% 6.73/7.05 (assert (forall ((F2 (-> tptp.int tptp.nat)) (X tptp.int) (Y tptp.int) (Fs tptp.list_int_nat)) (=> (@ (@ tptp.ord_less_nat (@ F2 X)) (@ F2 Y)) (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X) Y)) (@ tptp.measures_int (@ (@ tptp.cons_int_nat F2) Fs))))))
% 6.73/7.05 (assert (forall ((F2 (-> tptp.code_integer tptp.nat)) (X tptp.code_integer) (Y tptp.code_integer) (Fs tptp.list_C4705013386053401436er_nat)) (let ((_let_1 (@ tptp.member157494554546826820nteger (@ (@ tptp.produc1086072967326762835nteger X) Y)))) (=> (@ (@ tptp.ord_less_eq_nat (@ F2 X)) (@ F2 Y)) (=> (@ _let_1 (@ tptp.measur8870801148506250077nteger Fs)) (@ _let_1 (@ tptp.measur8870801148506250077nteger (@ (@ tptp.cons_C1897838848541180310er_nat F2) Fs))))))))
% 6.73/7.05 (assert (forall ((F2 (-> tptp.product_prod_nat_nat tptp.nat)) (X tptp.product_prod_nat_nat) (Y tptp.product_prod_nat_nat) (Fs tptp.list_P9162950289778280392at_nat)) (let ((_let_1 (@ tptp.member8206827879206165904at_nat (@ (@ tptp.produc6161850002892822231at_nat X) Y)))) (=> (@ (@ tptp.ord_less_eq_nat (@ F2 X)) (@ F2 Y)) (=> (@ _let_1 (@ tptp.measur2679027848233739777at_nat Fs)) (@ _let_1 (@ tptp.measur2679027848233739777at_nat (@ (@ tptp.cons_P4861729644591583992at_nat F2) Fs))))))))
% 6.73/7.05 (assert (forall ((F2 (-> tptp.set_Pr1261947904930325089at_nat tptp.nat)) (X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat) (Fs tptp.list_s9130966667114977576at_nat)) (let ((_let_1 (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat X) Y)))) (=> (@ (@ tptp.ord_less_eq_nat (@ F2 X)) (@ F2 Y)) (=> (@ _let_1 (@ tptp.measur2694323259624372065at_nat Fs)) (@ _let_1 (@ tptp.measur2694323259624372065at_nat (@ (@ tptp.cons_s2538900923071588440at_nat F2) Fs))))))))
% 6.73/7.05 (assert (forall ((F2 (-> tptp.nat tptp.nat)) (X tptp.nat) (Y tptp.nat) (Fs tptp.list_nat_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X) Y)))) (=> (@ (@ tptp.ord_less_eq_nat (@ F2 X)) (@ F2 Y)) (=> (@ _let_1 (@ tptp.measures_nat Fs)) (@ _let_1 (@ tptp.measures_nat (@ (@ tptp.cons_nat_nat F2) Fs))))))))
% 6.73/7.05 (assert (forall ((F2 (-> tptp.int tptp.nat)) (X tptp.int) (Y tptp.int) (Fs tptp.list_int_nat)) (let ((_let_1 (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X) Y)))) (=> (@ (@ tptp.ord_less_eq_nat (@ F2 X)) (@ F2 Y)) (=> (@ _let_1 (@ tptp.measures_int Fs)) (@ _let_1 (@ tptp.measures_int (@ (@ tptp.cons_int_nat F2) Fs))))))))
% 6.73/7.05 (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))))
% 6.73/7.05 (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))))
% 6.73/7.05 (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))))
% 6.73/7.05 (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))))
% 6.73/7.05 (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))))))))
% 6.73/7.05 (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))))))))
% 6.73/7.05 (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))))))))
% 6.73/7.05 (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))))))))
% 6.73/7.05 (assert (forall ((X tptp.nat) (Xs2 tptp.list_nat) (N tptp.nat) (Y tptp.nat)) (= (= (@ (@ tptp.cons_nat X) Xs2) (@ (@ tptp.replicate_nat N) Y)) (and (= X Y) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= Xs2 (@ (@ tptp.replicate_nat (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) X))))))
% 6.73/7.05 (assert (forall ((X tptp.vEBT_VEBT) (Xs2 tptp.list_VEBT_VEBT) (N tptp.nat) (Y tptp.vEBT_VEBT)) (= (= (@ (@ tptp.cons_VEBT_VEBT X) Xs2) (@ (@ tptp.replicate_VEBT_VEBT N) Y)) (and (= X Y) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= Xs2 (@ (@ tptp.replicate_VEBT_VEBT (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) X))))))
% 6.73/7.05 (assert (forall ((L tptp.num) (R3 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 L) (@ (@ tptp.product_Pair_nat_nat Q2) R3)))) (let ((_let_3 (@ tptp.numeral_numeral_nat L))) (let ((_let_4 (@ (@ tptp.ord_less_eq_nat _let_3) R3))) (and (=> _let_4 (= _let_2 (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat)) (@ (@ tptp.minus_minus_nat R3) _let_3)))) (=> (not _let_4) (= _let_2 (@ (@ tptp.product_Pair_nat_nat _let_1) R3))))))))))
% 6.73/7.05 (assert (forall ((L tptp.num) (R3 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 L) (@ (@ tptp.product_Pair_int_int Q2) R3)))) (let ((_let_3 (@ tptp.numeral_numeral_int L))) (let ((_let_4 (@ (@ tptp.ord_less_eq_int _let_3) R3))) (and (=> _let_4 (= _let_2 (@ (@ tptp.product_Pair_int_int (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int)) (@ (@ tptp.minus_minus_int R3) _let_3)))) (=> (not _let_4) (= _let_2 (@ (@ tptp.product_Pair_int_int _let_1) R3))))))))))
% 6.73/7.05 (assert (forall ((L tptp.num) (R3 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 L) (@ (@ tptp.produc1086072967326762835nteger Q2) R3)))) (let ((_let_3 (@ tptp.numera6620942414471956472nteger L))) (let ((_let_4 (@ (@ tptp.ord_le3102999989581377725nteger _let_3) R3))) (and (=> _let_4 (= _let_2 (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.plus_p5714425477246183910nteger _let_1) tptp.one_one_Code_integer)) (@ (@ tptp.minus_8373710615458151222nteger R3) _let_3)))) (=> (not _let_4) (= _let_2 (@ (@ tptp.produc1086072967326762835nteger _let_1) R3))))))))))
% 6.73/7.05 (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 ((M tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (and (= (@ tptp.some_nat M) (@ tptp.vEBT_vebt_mint Summary)) (@ (@ tptp.ord_less_nat M) (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.minus_minus_nat N) (@ (@ tptp.divide_divide_nat N) _let_1))))))))))))
% 6.73/7.05 (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.sup_sup_set_nat (@ tptp.vEBT_set_vebt T)) (@ (@ tptp.insert_nat X) tptp.bot_bot_set_nat)) (@ tptp.vEBT_set_vebt (@ (@ tptp.vEBT_vebt_insert T) X)))))))
% 6.73/7.05 (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.sup_sup_set_nat (@ tptp.vEBT_VEBT_set_vebt T)) (@ (@ tptp.insert_nat X) tptp.bot_bot_set_nat)) (@ tptp.vEBT_VEBT_set_vebt (@ (@ tptp.vEBT_vebt_insert T) X)))))))
% 6.73/7.05 (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))))))
% 6.73/7.05 (assert (forall ((P2 (-> tptp.nat Bool)) (N tptp.nat)) (=> (@ P2 tptp.zero_zero_nat) (=> (forall ((N3 tptp.nat)) (=> (@ P2 N3) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N3) (@ P2 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N3))))) (=> (forall ((N3 tptp.nat)) (=> (@ P2 N3) (@ P2 (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N3))))) (@ P2 N))))))
% 6.73/7.05 (assert (forall ((P2 (-> tptp.nat Bool)) (N tptp.nat)) (=> (@ P2 tptp.zero_zero_nat) (=> (@ P2 tptp.one_one_nat) (=> (forall ((N3 tptp.nat)) (=> (@ P2 N3) (@ P2 (@ (@ tptp.plus_plus_nat N3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ P2 N))))))
% 6.73/7.05 (assert (forall ((N tptp.nat) (M2 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) M2)) tptp.zero_zero_nat))))))
% 6.73/7.05 (assert (forall ((N tptp.nat) (M2 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) M2)) tptp.zero_zero_int))))))
% 6.73/7.05 (assert (forall ((M2 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 M2) N)) tptp.zero_zero_nat)) (not (= (@ _let_1 M2) tptp.zero_zero_nat))))))
% 6.73/7.05 (assert (forall ((M2 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 M2) N)) tptp.zero_zero_int)) (not (= (@ _let_1 M2) tptp.zero_zero_int))))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (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)))))))
% 6.73/7.05 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.divide_divide_nat A) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 6.73/7.05 (assert (forall ((A tptp.int)) (= (@ (@ tptp.divide_divide_int A) tptp.zero_zero_int) tptp.zero_zero_int)))
% 6.73/7.05 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.divide_divide_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)))
% 6.73/7.05 (assert (forall ((A tptp.int)) (= (@ (@ tptp.divide_divide_int tptp.zero_zero_int) A) tptp.zero_zero_int)))
% 6.73/7.05 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) tptp.zero_zero_complex) tptp.zero_zero_complex)))
% 6.73/7.05 (assert (forall ((A tptp.real)) (= (@ (@ tptp.divide_divide_real A) tptp.zero_zero_real) tptp.zero_zero_real)))
% 6.73/7.05 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.divide_divide_rat A) tptp.zero_zero_rat) tptp.zero_zero_rat)))
% 6.73/7.05 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.divide_divide_nat A) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 6.73/7.05 (assert (forall ((A tptp.int)) (= (@ (@ tptp.divide_divide_int A) tptp.zero_zero_int) tptp.zero_zero_int)))
% 6.73/7.05 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex tptp.zero_zero_complex) A) tptp.zero_zero_complex)))
% 6.73/7.05 (assert (forall ((A tptp.real)) (= (@ (@ tptp.divide_divide_real tptp.zero_zero_real) A) tptp.zero_zero_real)))
% 6.73/7.05 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.divide_divide_rat tptp.zero_zero_rat) A) tptp.zero_zero_rat)))
% 6.73/7.05 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.divide_divide_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)))
% 6.73/7.05 (assert (forall ((A tptp.int)) (= (@ (@ tptp.divide_divide_int tptp.zero_zero_int) A) tptp.zero_zero_int)))
% 6.73/7.05 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) tptp.zero_zero_complex) tptp.zero_zero_complex)))
% 6.73/7.05 (assert (forall ((A tptp.real)) (= (@ (@ tptp.divide_divide_real A) tptp.zero_zero_real) tptp.zero_zero_real)))
% 6.73/7.05 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.divide_divide_rat A) tptp.zero_zero_rat) tptp.zero_zero_rat)))
% 6.73/7.05 (assert (forall ((A tptp.complex) (C2 tptp.complex) (B tptp.complex)) (= (= (@ (@ tptp.divide1717551699836669952omplex A) C2) (@ (@ tptp.divide1717551699836669952omplex B) C2)) (or (= C2 tptp.zero_zero_complex) (= A B)))))
% 6.73/7.05 (assert (forall ((A tptp.real) (C2 tptp.real) (B tptp.real)) (= (= (@ (@ tptp.divide_divide_real A) C2) (@ (@ tptp.divide_divide_real B) C2)) (or (= C2 tptp.zero_zero_real) (= A B)))))
% 6.73/7.05 (assert (forall ((A tptp.rat) (C2 tptp.rat) (B tptp.rat)) (= (= (@ (@ tptp.divide_divide_rat A) C2) (@ (@ tptp.divide_divide_rat B) C2)) (or (= C2 tptp.zero_zero_rat) (= A B)))))
% 6.73/7.05 (assert (forall ((C2 tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.divide1717551699836669952omplex C2))) (= (= (@ _let_1 A) (@ _let_1 B)) (or (= C2 tptp.zero_zero_complex) (= A B))))))
% 6.73/7.05 (assert (forall ((C2 tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.divide_divide_real C2))) (= (= (@ _let_1 A) (@ _let_1 B)) (or (= C2 tptp.zero_zero_real) (= A B))))))
% 6.73/7.05 (assert (forall ((C2 tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.divide_divide_rat C2))) (= (= (@ _let_1 A) (@ _let_1 B)) (or (= C2 tptp.zero_zero_rat) (= A B))))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (assert (forall ((A tptp.complex) (B tptp.complex) (C2 tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex A))) (= (@ _let_1 (@ (@ tptp.divide1717551699836669952omplex B) C2)) (@ (@ tptp.divide1717551699836669952omplex (@ _let_1 B)) C2)))))
% 6.73/7.05 (assert (forall ((A tptp.real) (B tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.times_times_real A))) (= (@ _let_1 (@ (@ tptp.divide_divide_real B) C2)) (@ (@ tptp.divide_divide_real (@ _let_1 B)) C2)))))
% 6.73/7.05 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat A))) (= (@ _let_1 (@ (@ tptp.divide_divide_rat B) C2)) (@ (@ tptp.divide_divide_rat (@ _let_1 B)) C2)))))
% 6.73/7.05 (assert (forall ((A tptp.complex) (B tptp.complex) (C2 tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) (@ (@ tptp.divide1717551699836669952omplex B) C2)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex A) C2)) B))))
% 6.73/7.05 (assert (forall ((A tptp.real) (B tptp.real) (C2 tptp.real)) (= (@ (@ tptp.divide_divide_real A) (@ (@ tptp.divide_divide_real B) C2)) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real A) C2)) B))))
% 6.73/7.05 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (= (@ (@ tptp.divide_divide_rat A) (@ (@ tptp.divide_divide_rat B) C2)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat A) C2)) B))))
% 6.73/7.05 (assert (forall ((A tptp.complex) (B tptp.complex) (C2 tptp.complex)) (let ((_let_1 (@ tptp.divide1717551699836669952omplex A))) (= (@ (@ tptp.divide1717551699836669952omplex (@ _let_1 B)) C2) (@ _let_1 (@ (@ tptp.times_times_complex B) C2))))))
% 6.73/7.05 (assert (forall ((A tptp.real) (B tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.divide_divide_real A))) (= (@ (@ tptp.divide_divide_real (@ _let_1 B)) C2) (@ _let_1 (@ (@ tptp.times_times_real B) C2))))))
% 6.73/7.05 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.divide_divide_rat A))) (= (@ (@ tptp.divide_divide_rat (@ _let_1 B)) C2) (@ _let_1 (@ (@ tptp.times_times_rat B) C2))))))
% 6.73/7.05 (assert (forall ((B tptp.complex) (C2 tptp.complex) (A tptp.complex)) (= (@ (@ tptp.times_times_complex (@ (@ tptp.divide1717551699836669952omplex B) C2)) A) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex B) A)) C2))))
% 6.73/7.05 (assert (forall ((B tptp.real) (C2 tptp.real) (A tptp.real)) (= (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real B) C2)) A) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real B) A)) C2))))
% 6.73/7.05 (assert (forall ((B tptp.rat) (C2 tptp.rat) (A tptp.rat)) (= (@ (@ tptp.times_times_rat (@ (@ tptp.divide_divide_rat B) C2)) A) (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat B) A)) C2))))
% 6.73/7.05 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.divide6298287555418463151nteger A) tptp.one_one_Code_integer) A)))
% 6.73/7.05 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) tptp.one_one_complex) A)))
% 6.73/7.05 (assert (forall ((A tptp.real)) (= (@ (@ tptp.divide_divide_real A) tptp.one_one_real) A)))
% 6.73/7.05 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.divide_divide_rat A) tptp.one_one_rat) A)))
% 6.73/7.05 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.divide_divide_nat A) tptp.one_one_nat) A)))
% 6.73/7.05 (assert (forall ((A tptp.int)) (= (@ (@ tptp.divide_divide_int A) tptp.one_one_int) A)))
% 6.73/7.05 (assert (forall ((I2 tptp.set_nat) (L tptp.set_nat) (U tptp.set_nat)) (= (@ (@ tptp.member_set_nat I2) (@ (@ tptp.set_or4548717258645045905et_nat L) U)) (and (@ (@ tptp.ord_less_eq_set_nat L) I2) (@ (@ tptp.ord_less_eq_set_nat I2) U)))))
% 6.73/7.05 (assert (forall ((I2 tptp.rat) (L tptp.rat) (U tptp.rat)) (= (@ (@ tptp.member_rat I2) (@ (@ tptp.set_or633870826150836451st_rat L) U)) (and (@ (@ tptp.ord_less_eq_rat L) I2) (@ (@ tptp.ord_less_eq_rat I2) U)))))
% 6.73/7.05 (assert (forall ((I2 tptp.num) (L tptp.num) (U tptp.num)) (= (@ (@ tptp.member_num I2) (@ (@ tptp.set_or7049704709247886629st_num L) U)) (and (@ (@ tptp.ord_less_eq_num L) I2) (@ (@ tptp.ord_less_eq_num I2) U)))))
% 6.73/7.05 (assert (forall ((I2 tptp.nat) (L tptp.nat) (U tptp.nat)) (= (@ (@ tptp.member_nat I2) (@ (@ tptp.set_or1269000886237332187st_nat L) U)) (and (@ (@ tptp.ord_less_eq_nat L) I2) (@ (@ tptp.ord_less_eq_nat I2) U)))))
% 6.73/7.05 (assert (forall ((I2 tptp.int) (L tptp.int) (U tptp.int)) (= (@ (@ tptp.member_int I2) (@ (@ tptp.set_or1266510415728281911st_int L) U)) (and (@ (@ tptp.ord_less_eq_int L) I2) (@ (@ tptp.ord_less_eq_int I2) U)))))
% 6.73/7.05 (assert (forall ((I2 tptp.real) (L tptp.real) (U tptp.real)) (= (@ (@ tptp.member_real I2) (@ (@ tptp.set_or1222579329274155063t_real L) U)) (and (@ (@ tptp.ord_less_eq_real L) I2) (@ (@ tptp.ord_less_eq_real I2) U)))))
% 6.73/7.05 (assert (forall ((L tptp.set_nat) (H tptp.set_nat) (L3 tptp.set_nat) (H3 tptp.set_nat)) (= (= (@ (@ tptp.set_or4548717258645045905et_nat L) H) (@ (@ tptp.set_or4548717258645045905et_nat L3) H3)) (or (and (= L L3) (= H H3)) (and (not (@ (@ tptp.ord_less_eq_set_nat L) H)) (not (@ (@ tptp.ord_less_eq_set_nat L3) H3)))))))
% 6.73/7.05 (assert (forall ((L tptp.rat) (H tptp.rat) (L3 tptp.rat) (H3 tptp.rat)) (= (= (@ (@ tptp.set_or633870826150836451st_rat L) H) (@ (@ tptp.set_or633870826150836451st_rat L3) H3)) (or (and (= L L3) (= H H3)) (and (not (@ (@ tptp.ord_less_eq_rat L) H)) (not (@ (@ tptp.ord_less_eq_rat L3) H3)))))))
% 6.73/7.05 (assert (forall ((L tptp.num) (H tptp.num) (L3 tptp.num) (H3 tptp.num)) (= (= (@ (@ tptp.set_or7049704709247886629st_num L) H) (@ (@ tptp.set_or7049704709247886629st_num L3) H3)) (or (and (= L L3) (= H H3)) (and (not (@ (@ tptp.ord_less_eq_num L) H)) (not (@ (@ tptp.ord_less_eq_num L3) H3)))))))
% 6.73/7.05 (assert (forall ((L tptp.nat) (H tptp.nat) (L3 tptp.nat) (H3 tptp.nat)) (= (= (@ (@ tptp.set_or1269000886237332187st_nat L) H) (@ (@ tptp.set_or1269000886237332187st_nat L3) H3)) (or (and (= L L3) (= H H3)) (and (not (@ (@ tptp.ord_less_eq_nat L) H)) (not (@ (@ tptp.ord_less_eq_nat L3) H3)))))))
% 6.73/7.05 (assert (forall ((L tptp.int) (H tptp.int) (L3 tptp.int) (H3 tptp.int)) (= (= (@ (@ tptp.set_or1266510415728281911st_int L) H) (@ (@ tptp.set_or1266510415728281911st_int L3) H3)) (or (and (= L L3) (= H H3)) (and (not (@ (@ tptp.ord_less_eq_int L) H)) (not (@ (@ tptp.ord_less_eq_int L3) H3)))))))
% 6.73/7.05 (assert (forall ((L tptp.real) (H tptp.real) (L3 tptp.real) (H3 tptp.real)) (= (= (@ (@ tptp.set_or1222579329274155063t_real L) H) (@ (@ tptp.set_or1222579329274155063t_real L3) H3)) (or (and (= L L3) (= H H3)) (and (not (@ (@ tptp.ord_less_eq_real L) H)) (not (@ (@ tptp.ord_less_eq_real L3) H3)))))))
% 6.73/7.05 (assert (forall ((L tptp.nat) (U tptp.nat)) (@ tptp.finite_finite_nat (@ (@ tptp.set_or1269000886237332187st_nat L) U))))
% 6.73/7.05 (assert (forall ((A tptp.complex) (B tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex A) B)) A) B))))
% 6.73/7.05 (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))))
% 6.73/7.05 (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))))
% 6.73/7.05 (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))))
% 6.73/7.05 (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))))
% 6.73/7.05 (assert (forall ((B tptp.complex) (A tptp.complex)) (=> (not (= B tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex A) B)) B) A))))
% 6.73/7.05 (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))))
% 6.73/7.05 (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))))
% 6.73/7.05 (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))))
% 6.73/7.05 (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))))
% 6.73/7.05 (assert (forall ((C2 tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex C2))) (let ((_let_2 (@ (@ tptp.divide1717551699836669952omplex (@ _let_1 A)) (@ _let_1 B)))) (let ((_let_3 (= C2 tptp.zero_zero_complex))) (and (=> _let_3 (= _let_2 tptp.zero_zero_complex)) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide1717551699836669952omplex A) B)))))))))
% 6.73/7.05 (assert (forall ((C2 tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real C2))) (let ((_let_2 (@ (@ tptp.divide_divide_real (@ _let_1 A)) (@ _let_1 B)))) (let ((_let_3 (= C2 tptp.zero_zero_real))) (and (=> _let_3 (= _let_2 tptp.zero_zero_real)) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_real A) B)))))))))
% 6.73/7.05 (assert (forall ((C2 tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C2))) (let ((_let_2 (@ (@ tptp.divide_divide_rat (@ _let_1 A)) (@ _let_1 B)))) (let ((_let_3 (= C2 tptp.zero_zero_rat))) (and (=> _let_3 (= _let_2 tptp.zero_zero_rat)) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_rat A) B)))))))))
% 6.73/7.05 (assert (forall ((C2 tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex C2))) (=> (not (= C2 tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.divide1717551699836669952omplex A) B))))))
% 6.73/7.05 (assert (forall ((C2 tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real C2))) (=> (not (= C2 tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.divide_divide_real A) B))))))
% 6.73/7.05 (assert (forall ((C2 tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C2))) (=> (not (= C2 tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.divide_divide_rat A) B))))))
% 6.73/7.05 (assert (forall ((C2 tptp.complex) (A tptp.complex) (B tptp.complex)) (=> (not (= C2 tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex C2) A)) (@ (@ tptp.times_times_complex B) C2)) (@ (@ tptp.divide1717551699836669952omplex A) B)))))
% 6.73/7.05 (assert (forall ((C2 tptp.real) (A tptp.real) (B tptp.real)) (=> (not (= C2 tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real C2) A)) (@ (@ tptp.times_times_real B) C2)) (@ (@ tptp.divide_divide_real A) B)))))
% 6.73/7.05 (assert (forall ((C2 tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (not (= C2 tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat C2) A)) (@ (@ tptp.times_times_rat B) C2)) (@ (@ tptp.divide_divide_rat A) B)))))
% 6.73/7.05 (assert (forall ((C2 tptp.complex) (A tptp.complex) (B tptp.complex)) (=> (not (= C2 tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex A) C2)) (@ (@ tptp.times_times_complex B) C2)) (@ (@ tptp.divide1717551699836669952omplex A) B)))))
% 6.73/7.05 (assert (forall ((C2 tptp.real) (A tptp.real) (B tptp.real)) (=> (not (= C2 tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real A) C2)) (@ (@ tptp.times_times_real B) C2)) (@ (@ tptp.divide_divide_real A) B)))))
% 6.73/7.05 (assert (forall ((C2 tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (not (= C2 tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat A) C2)) (@ (@ tptp.times_times_rat B) C2)) (@ (@ tptp.divide_divide_rat A) B)))))
% 6.73/7.05 (assert (forall ((C2 tptp.complex) (A tptp.complex) (B tptp.complex)) (=> (not (= C2 tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex A) C2)) (@ (@ tptp.times_times_complex C2) B)) (@ (@ tptp.divide1717551699836669952omplex A) B)))))
% 6.73/7.05 (assert (forall ((C2 tptp.real) (A tptp.real) (B tptp.real)) (=> (not (= C2 tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real A) C2)) (@ (@ tptp.times_times_real C2) B)) (@ (@ tptp.divide_divide_real A) B)))))
% 6.73/7.05 (assert (forall ((C2 tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (not (= C2 tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat A) C2)) (@ (@ tptp.times_times_rat C2) B)) (@ (@ tptp.divide_divide_rat A) B)))))
% 6.73/7.05 (assert (forall ((A tptp.code_integer)) (=> (not (= A tptp.zero_z3403309356797280102nteger)) (= (@ (@ tptp.divide6298287555418463151nteger A) A) tptp.one_one_Code_integer))))
% 6.73/7.05 (assert (forall ((A tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) A) tptp.one_one_complex))))
% 6.73/7.05 (assert (forall ((A tptp.real)) (=> (not (= A tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real A) A) tptp.one_one_real))))
% 6.73/7.05 (assert (forall ((A tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat A) A) tptp.one_one_rat))))
% 6.73/7.05 (assert (forall ((A tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat A) A) tptp.one_one_nat))))
% 6.73/7.05 (assert (forall ((A tptp.int)) (=> (not (= A tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int A) A) tptp.one_one_int))))
% 6.73/7.05 (assert (forall ((A tptp.real)) (= (= tptp.zero_zero_real (@ (@ tptp.divide_divide_real tptp.one_one_real) A)) (= A tptp.zero_zero_real))))
% 6.73/7.05 (assert (forall ((A tptp.rat)) (= (= tptp.zero_zero_rat (@ (@ tptp.divide_divide_rat tptp.one_one_rat) A)) (= A tptp.zero_zero_rat))))
% 6.73/7.05 (assert (forall ((A tptp.real)) (= (= (@ (@ tptp.divide_divide_real tptp.one_one_real) A) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 6.73/7.05 (assert (forall ((A tptp.rat)) (= (= (@ (@ tptp.divide_divide_rat tptp.one_one_rat) A) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (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)))))))
% 6.73/7.05 (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)))))))
% 6.73/7.05 (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)))))))
% 6.73/7.05 (assert (forall ((A tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) A) tptp.one_one_complex))))
% 6.73/7.05 (assert (forall ((A tptp.real)) (=> (not (= A tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real A) A) tptp.one_one_real))))
% 6.73/7.05 (assert (forall ((A tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat A) A) tptp.one_one_rat))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (assert (forall ((A tptp.set_nat) (B tptp.set_nat)) (= (= (@ (@ tptp.set_or4548717258645045905et_nat A) B) tptp.bot_bot_set_set_nat) (not (@ (@ tptp.ord_less_eq_set_nat A) B)))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (assert (forall ((A tptp.set_nat) (B tptp.set_nat)) (= (= tptp.bot_bot_set_set_nat (@ (@ tptp.set_or4548717258645045905et_nat A) B)) (not (@ (@ tptp.ord_less_eq_set_nat A) B)))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (assert (forall ((A tptp.set_nat) (B tptp.set_nat) (C2 tptp.set_nat) (D tptp.set_nat)) (= (@ (@ tptp.ord_le6893508408891458716et_nat (@ (@ tptp.set_or4548717258645045905et_nat A) B)) (@ (@ tptp.set_or4548717258645045905et_nat C2) D)) (or (not (@ (@ tptp.ord_less_eq_set_nat A) B)) (and (@ (@ tptp.ord_less_eq_set_nat C2) A) (@ (@ tptp.ord_less_eq_set_nat B) D))))))
% 6.73/7.05 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat) (D tptp.rat)) (= (@ (@ tptp.ord_less_eq_set_rat (@ (@ tptp.set_or633870826150836451st_rat A) B)) (@ (@ tptp.set_or633870826150836451st_rat C2) D)) (or (not (@ (@ tptp.ord_less_eq_rat A) B)) (and (@ (@ tptp.ord_less_eq_rat C2) A) (@ (@ tptp.ord_less_eq_rat B) D))))))
% 6.73/7.05 (assert (forall ((A tptp.num) (B tptp.num) (C2 tptp.num) (D tptp.num)) (= (@ (@ tptp.ord_less_eq_set_num (@ (@ tptp.set_or7049704709247886629st_num A) B)) (@ (@ tptp.set_or7049704709247886629st_num C2) D)) (or (not (@ (@ tptp.ord_less_eq_num A) B)) (and (@ (@ tptp.ord_less_eq_num C2) A) (@ (@ tptp.ord_less_eq_num B) D))))))
% 6.73/7.05 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat) (D tptp.nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.set_or1269000886237332187st_nat A) B)) (@ (@ tptp.set_or1269000886237332187st_nat C2) D)) (or (not (@ (@ tptp.ord_less_eq_nat A) B)) (and (@ (@ tptp.ord_less_eq_nat C2) A) (@ (@ tptp.ord_less_eq_nat B) D))))))
% 6.73/7.05 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int) (D tptp.int)) (= (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.set_or1266510415728281911st_int A) B)) (@ (@ tptp.set_or1266510415728281911st_int C2) D)) (or (not (@ (@ tptp.ord_less_eq_int A) B)) (and (@ (@ tptp.ord_less_eq_int C2) A) (@ (@ tptp.ord_less_eq_int B) D))))))
% 6.73/7.05 (assert (forall ((A tptp.real) (B tptp.real) (C2 tptp.real) (D tptp.real)) (= (@ (@ tptp.ord_less_eq_set_real (@ (@ tptp.set_or1222579329274155063t_real A) B)) (@ (@ tptp.set_or1222579329274155063t_real C2) D)) (or (not (@ (@ tptp.ord_less_eq_real A) B)) (and (@ (@ tptp.ord_less_eq_real C2) A) (@ (@ tptp.ord_less_eq_real B) D))))))
% 6.73/7.05 (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))))
% 6.73/7.05 (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))))
% 6.73/7.05 (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))))
% 6.73/7.05 (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))))
% 6.73/7.05 (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))))
% 6.73/7.05 (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))))
% 6.73/7.05 (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))))
% 6.73/7.05 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.set_or1269000886237332187st_nat A) A) (@ (@ tptp.insert_nat A) tptp.bot_bot_set_nat))))
% 6.73/7.05 (assert (forall ((A tptp.int)) (= (@ (@ tptp.set_or1266510415728281911st_int A) A) (@ (@ tptp.insert_int A) tptp.bot_bot_set_int))))
% 6.73/7.05 (assert (forall ((A tptp.real)) (= (@ (@ tptp.set_or1222579329274155063t_real A) A) (@ (@ tptp.insert_real A) tptp.bot_bot_set_real))))
% 6.73/7.05 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (= (= (@ (@ tptp.set_or1269000886237332187st_nat A) B) (@ (@ tptp.insert_nat C2) tptp.bot_bot_set_nat)) (and (= A B) (= B C2)))))
% 6.73/7.05 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (= (= (@ (@ tptp.set_or1266510415728281911st_int A) B) (@ (@ tptp.insert_int C2) tptp.bot_bot_set_int)) (and (= A B) (= B C2)))))
% 6.73/7.05 (assert (forall ((A tptp.real) (B tptp.real) (C2 tptp.real)) (= (= (@ (@ tptp.set_or1222579329274155063t_real A) B) (@ (@ tptp.insert_real C2) tptp.bot_bot_set_real)) (and (= A B) (= B C2)))))
% 6.73/7.05 (assert (forall ((K2 tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K2))) (let ((_let_2 (@ (@ tptp.divide_divide_nat (@ _let_1 M2)) (@ _let_1 N)))) (let ((_let_3 (= K2 tptp.zero_zero_nat))) (and (=> _let_3 (= _let_2 tptp.zero_zero_nat)) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_nat M2) N)))))))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (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))))
% 6.73/7.05 (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))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (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))))))
% 6.73/7.05 (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))))))
% 6.73/7.05 (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))))
% 6.73/7.05 (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))))
% 6.73/7.05 (assert (forall ((B tptp.real) (W2 tptp.num) (A tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real W2))) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real B) _let_1)) A) (@ (@ tptp.ord_less_eq_real B) (@ (@ tptp.times_times_real A) _let_1))))))
% 6.73/7.05 (assert (forall ((B tptp.rat) (W2 tptp.num) (A tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_rat W2))) (= (@ (@ 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))))))
% 6.73/7.05 (assert (forall ((A tptp.real) (B tptp.real) (W2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real W2))) (= (@ (@ 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)))))
% 6.73/7.05 (assert (forall ((A tptp.rat) (B tptp.rat) (W2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat W2))) (= (@ (@ 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)))))
% 6.73/7.05 (assert (forall ((B tptp.complex) (W2 tptp.num) (A tptp.complex)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex W2))) (let ((_let_2 (= _let_1 tptp.zero_zero_complex))) (= (= (@ (@ tptp.divide1717551699836669952omplex B) _let_1) A) (and (=> (not _let_2) (= B (@ (@ tptp.times_times_complex A) _let_1))) (=> _let_2 (= A tptp.zero_zero_complex))))))))
% 6.73/7.05 (assert (forall ((B tptp.real) (W2 tptp.num) (A tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real W2))) (let ((_let_2 (= _let_1 tptp.zero_zero_real))) (= (= (@ (@ tptp.divide_divide_real B) _let_1) A) (and (=> (not _let_2) (= B (@ (@ tptp.times_times_real A) _let_1))) (=> _let_2 (= A tptp.zero_zero_real))))))))
% 6.73/7.05 (assert (forall ((B tptp.rat) (W2 tptp.num) (A tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_rat W2))) (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))))))))
% 6.73/7.05 (assert (forall ((A tptp.complex) (B tptp.complex) (W2 tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex W2))) (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))))))))
% 6.73/7.05 (assert (forall ((A tptp.real) (B tptp.real) (W2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real W2))) (let ((_let_2 (= _let_1 tptp.zero_zero_real))) (= (= A (@ (@ tptp.divide_divide_real B) _let_1)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_real A) _let_1) B)) (=> _let_2 (= A tptp.zero_zero_real))))))))
% 6.73/7.05 (assert (forall ((A tptp.rat) (B tptp.rat) (W2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat W2))) (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))))))))
% 6.73/7.05 (assert (forall ((A tptp.real) (B tptp.real) (W2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real W2))) (= (@ (@ tptp.ord_less_real A) (@ (@ tptp.divide_divide_real B) _let_1)) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) _let_1)) B)))))
% 6.73/7.05 (assert (forall ((A tptp.rat) (B tptp.rat) (W2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat W2))) (= (@ (@ tptp.ord_less_rat A) (@ (@ tptp.divide_divide_rat B) _let_1)) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) _let_1)) B)))))
% 6.73/7.05 (assert (forall ((B tptp.real) (W2 tptp.num) (A tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real W2))) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real B) _let_1)) A) (@ (@ tptp.ord_less_real B) (@ (@ tptp.times_times_real A) _let_1))))))
% 6.73/7.05 (assert (forall ((B tptp.rat) (W2 tptp.num) (A tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_rat W2))) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat B) _let_1)) A) (@ (@ tptp.ord_less_rat B) (@ (@ tptp.times_times_rat A) _let_1))))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (assert (forall ((N tptp.num) (M2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real N)) (@ tptp.semiri5074537144036343181t_real M2)) (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat N)) M2))))
% 6.73/7.05 (assert (forall ((L tptp.nat) (U tptp.nat)) (= (@ tptp.finite_card_nat (@ (@ tptp.set_or1269000886237332187st_nat L) U)) (@ (@ tptp.minus_minus_nat (@ tptp.suc U)) L))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (assert (= (@ (@ tptp.divide6298287555418463151nteger tptp.one_one_Code_integer) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) tptp.zero_z3403309356797280102nteger))
% 6.73/7.05 (assert (= (@ (@ tptp.divide_divide_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_nat))
% 6.73/7.05 (assert (= (@ (@ tptp.divide_divide_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) tptp.zero_zero_int))
% 6.73/7.05 (assert (forall ((D tptp.int) (P2 (-> tptp.int Bool)) (K2 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (=> (forall ((X3 tptp.int)) (=> (@ P2 X3) (@ P2 (@ (@ tptp.minus_minus_int X3) D)))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K2) (forall ((X5 tptp.int)) (=> (@ P2 X5) (@ P2 (@ (@ tptp.minus_minus_int X5) (@ (@ tptp.times_times_int K2) D))))))))))
% 6.73/7.05 (assert (forall ((D tptp.int) (P1 (-> tptp.int Bool)) (P2 (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (=> (forall ((X3 tptp.int) (K tptp.int)) (= (@ P1 X3) (@ P1 (@ (@ tptp.minus_minus_int X3) (@ (@ tptp.times_times_int K) D))))) (=> (exists ((Z5 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Z5) (= (@ P2 X3) (@ P1 X3))))) (=> (exists ((X_1 tptp.int)) (@ P1 X_1)) (exists ((X_12 tptp.int)) (@ P2 X_12))))))))
% 6.73/7.05 (assert (forall ((D tptp.int) (P6 (-> tptp.int Bool)) (P2 (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (=> (forall ((X3 tptp.int) (K tptp.int)) (= (@ P6 X3) (@ P6 (@ (@ tptp.minus_minus_int X3) (@ (@ tptp.times_times_int K) D))))) (=> (exists ((Z5 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int Z5) X3) (= (@ P2 X3) (@ P6 X3))))) (=> (exists ((X_1 tptp.int)) (@ P6 X_1)) (exists ((X_12 tptp.int)) (@ P2 X_12))))))))
% 6.73/7.05 (assert (forall ((L tptp.int)) (= (@ (@ tptp.times_times_int tptp.zero_zero_int) L) tptp.zero_zero_int)))
% 6.73/7.05 (assert (forall ((K2 tptp.int)) (= (@ (@ tptp.times_times_int K2) tptp.zero_zero_int) tptp.zero_zero_int)))
% 6.73/7.05 (assert (forall ((M2 tptp.int) (N tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) M2) (= (= (@ (@ tptp.times_times_int M2) N) tptp.one_one_int) (and (= M2 tptp.one_one_int) (= N tptp.one_one_int))))))
% 6.73/7.05 (assert (forall ((I2 tptp.int) (J2 tptp.int) (K2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int K2))) (=> (@ (@ tptp.ord_less_int I2) J2) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K2) (@ (@ tptp.ord_less_int (@ _let_1 I2)) (@ _let_1 J2)))))))
% 6.73/7.05 (assert (forall ((B tptp.int) (Q4 tptp.int) (R5 tptp.int) (Q2 tptp.int) (R3 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int B))) (let ((_let_2 (@ tptp.times_times_int B))) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ _let_2 Q4)) R5)) (@ (@ tptp.plus_plus_int (@ _let_2 Q2)) R3)) (=> (@ (@ tptp.ord_less_eq_int R3) tptp.zero_zero_int) (=> (@ _let_1 R3) (=> (@ _let_1 R5) (@ (@ tptp.ord_less_eq_int Q2) Q4)))))))))
% 6.73/7.05 (assert (forall ((B tptp.int) (Q4 tptp.int) (R5 tptp.int) (Q2 tptp.int) (R3 tptp.int)) (let ((_let_1 (@ tptp.times_times_int B))) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ _let_1 Q4)) R5)) (@ (@ tptp.plus_plus_int (@ _let_1 Q2)) R3)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) R5) (=> (@ (@ tptp.ord_less_int R5) B) (=> (@ (@ tptp.ord_less_int R3) B) (@ (@ tptp.ord_less_eq_int Q4) Q2))))))))
% 6.73/7.05 (assert (forall ((B tptp.int) (Q2 tptp.int) (R3 tptp.int) (B2 tptp.int) (Q4 tptp.int) (R5 tptp.int)) (let ((_let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B2) Q4)) R5))) (=> (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) Q2)) R3) _let_1) (=> (@ (@ tptp.ord_less_int _let_1) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int R3) B) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) R5) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B2) (=> (@ (@ tptp.ord_less_eq_int B2) B) (@ (@ tptp.ord_less_eq_int Q4) Q2))))))))))
% 6.73/7.05 (assert (forall ((B tptp.int) (Q2 tptp.int) (R3 tptp.int) (B2 tptp.int) (Q4 tptp.int) (R5 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 B2) Q4)) R5))) (=> (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) Q2)) R3) _let_2) (=> (@ _let_1 _let_2) (=> (@ (@ tptp.ord_less_int R5) B2) (=> (@ _let_1 R3) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B2) (=> (@ (@ tptp.ord_less_eq_int B2) B) (@ (@ tptp.ord_less_eq_int Q2) Q4)))))))))))
% 6.73/7.05 (assert (forall ((B2 tptp.int) (Q4 tptp.int) (R5 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B2) Q4)) R5)) (=> (@ (@ tptp.ord_less_int R5) B2) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B2) (@ _let_1 Q4)))))))
% 6.73/7.05 (assert (forall ((D tptp.int) (P2 (-> tptp.int Bool)) (K2 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (=> (forall ((X3 tptp.int)) (=> (@ P2 X3) (@ P2 (@ (@ tptp.plus_plus_int X3) D)))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K2) (forall ((X5 tptp.int)) (=> (@ P2 X5) (@ P2 (@ (@ tptp.plus_plus_int X5) (@ (@ tptp.times_times_int K2) D))))))))))
% 6.73/7.05 (assert (forall ((L tptp.rat) (M2 tptp.rat) (U tptp.rat)) (let ((_let_1 (@ tptp.set_or633870826150836451st_rat L))) (=> (@ (@ tptp.ord_less_eq_rat L) M2) (=> (@ (@ tptp.ord_less_eq_rat M2) U) (= (@ (@ tptp.sup_sup_set_rat (@ _let_1 M2)) (@ (@ tptp.set_or633870826150836451st_rat M2) U)) (@ _let_1 U)))))))
% 6.73/7.05 (assert (forall ((L tptp.num) (M2 tptp.num) (U tptp.num)) (let ((_let_1 (@ tptp.set_or7049704709247886629st_num L))) (=> (@ (@ tptp.ord_less_eq_num L) M2) (=> (@ (@ tptp.ord_less_eq_num M2) U) (= (@ (@ tptp.sup_sup_set_num (@ _let_1 M2)) (@ (@ tptp.set_or7049704709247886629st_num M2) U)) (@ _let_1 U)))))))
% 6.73/7.05 (assert (forall ((L tptp.nat) (M2 tptp.nat) (U tptp.nat)) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat L))) (=> (@ (@ tptp.ord_less_eq_nat L) M2) (=> (@ (@ tptp.ord_less_eq_nat M2) U) (= (@ (@ tptp.sup_sup_set_nat (@ _let_1 M2)) (@ (@ tptp.set_or1269000886237332187st_nat M2) U)) (@ _let_1 U)))))))
% 6.73/7.05 (assert (forall ((L tptp.int) (M2 tptp.int) (U tptp.int)) (let ((_let_1 (@ tptp.set_or1266510415728281911st_int L))) (=> (@ (@ tptp.ord_less_eq_int L) M2) (=> (@ (@ tptp.ord_less_eq_int M2) U) (= (@ (@ tptp.sup_sup_set_int (@ _let_1 M2)) (@ (@ tptp.set_or1266510415728281911st_int M2) U)) (@ _let_1 U)))))))
% 6.73/7.05 (assert (forall ((L tptp.real) (M2 tptp.real) (U tptp.real)) (let ((_let_1 (@ tptp.set_or1222579329274155063t_real L))) (=> (@ (@ tptp.ord_less_eq_real L) M2) (=> (@ (@ tptp.ord_less_eq_real M2) U) (= (@ (@ tptp.sup_sup_set_real (@ _let_1 M2)) (@ (@ tptp.set_or1222579329274155063t_real M2) U)) (@ _let_1 U)))))))
% 6.73/7.05 (assert (forall ((W2 tptp.int) (Z1 tptp.int) (Z22 tptp.int)) (let ((_let_1 (@ tptp.times_times_int W2))) (= (@ _let_1 (@ (@ tptp.plus_plus_int Z1) Z22)) (@ (@ tptp.plus_plus_int (@ _let_1 Z1)) (@ _let_1 Z22))))))
% 6.73/7.05 (assert (forall ((Z1 tptp.int) (Z22 tptp.int) (W2 tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int Z1) Z22)) W2) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int Z1) W2)) (@ (@ tptp.times_times_int Z22) W2)))))
% 6.73/7.05 (assert (forall ((Z1 tptp.int) (Z22 tptp.int) (W2 tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int Z1) Z22)) W2) (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int Z1) W2)) (@ (@ tptp.times_times_int Z22) W2)))))
% 6.73/7.05 (assert (forall ((W2 tptp.int) (Z1 tptp.int) (Z22 tptp.int)) (let ((_let_1 (@ tptp.times_times_int W2))) (= (@ _let_1 (@ (@ tptp.minus_minus_int Z1) Z22)) (@ (@ tptp.minus_minus_int (@ _let_1 Z1)) (@ _let_1 Z22))))))
% 6.73/7.05 (assert (forall ((A tptp.complex) (B tptp.complex) (C2 tptp.complex)) (let ((_let_1 (@ tptp.divide1717551699836669952omplex A))) (= (@ (@ tptp.divide1717551699836669952omplex (@ _let_1 B)) C2) (@ _let_1 (@ (@ tptp.times_times_complex C2) B))))))
% 6.73/7.05 (assert (forall ((A tptp.real) (B tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.divide_divide_real A))) (= (@ (@ tptp.divide_divide_real (@ _let_1 B)) C2) (@ _let_1 (@ (@ tptp.times_times_real C2) B))))))
% 6.73/7.05 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.divide_divide_rat A))) (= (@ (@ tptp.divide_divide_rat (@ _let_1 B)) C2) (@ _let_1 (@ (@ tptp.times_times_rat C2) B))))))
% 6.73/7.05 (assert (forall ((X tptp.complex) (Y tptp.complex) (Z3 tptp.complex) (W2 tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.divide1717551699836669952omplex X) Y)) (@ (@ tptp.divide1717551699836669952omplex Z3) W2)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex X) W2)) (@ (@ tptp.times_times_complex Y) Z3)))))
% 6.73/7.05 (assert (forall ((X tptp.real) (Y tptp.real) (Z3 tptp.real) (W2 tptp.real)) (= (@ (@ tptp.divide_divide_real (@ (@ tptp.divide_divide_real X) Y)) (@ (@ tptp.divide_divide_real Z3) W2)) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real X) W2)) (@ (@ tptp.times_times_real Y) Z3)))))
% 6.73/7.05 (assert (forall ((X tptp.rat) (Y tptp.rat) (Z3 tptp.rat) (W2 tptp.rat)) (= (@ (@ tptp.divide_divide_rat (@ (@ tptp.divide_divide_rat X) Y)) (@ (@ tptp.divide_divide_rat Z3) W2)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat X) W2)) (@ (@ tptp.times_times_rat Y) Z3)))))
% 6.73/7.05 (assert (forall ((X tptp.complex) (Y tptp.complex) (Z3 tptp.complex) (W2 tptp.complex)) (= (@ (@ tptp.times_times_complex (@ (@ tptp.divide1717551699836669952omplex X) Y)) (@ (@ tptp.divide1717551699836669952omplex Z3) W2)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex X) Z3)) (@ (@ tptp.times_times_complex Y) W2)))))
% 6.73/7.05 (assert (forall ((X tptp.real) (Y tptp.real) (Z3 tptp.real) (W2 tptp.real)) (= (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real X) Y)) (@ (@ tptp.divide_divide_real Z3) W2)) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real X) Z3)) (@ (@ tptp.times_times_real Y) W2)))))
% 6.73/7.05 (assert (forall ((X tptp.rat) (Y tptp.rat) (Z3 tptp.rat) (W2 tptp.rat)) (= (@ (@ tptp.times_times_rat (@ (@ tptp.divide_divide_rat X) Y)) (@ (@ tptp.divide_divide_rat Z3) W2)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat X) Z3)) (@ (@ tptp.times_times_rat Y) W2)))))
% 6.73/7.05 (assert (forall ((A tptp.set_nat) (B tptp.set_nat) (C2 tptp.set_nat) (D tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat C2))) (= (@ (@ tptp.ord_less_set_set_nat (@ (@ tptp.set_or4548717258645045905et_nat A) B)) (@ (@ tptp.set_or4548717258645045905et_nat C2) D)) (and (or (not (@ (@ tptp.ord_less_eq_set_nat A) B)) (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_set_nat B) D) (or (@ (@ tptp.ord_less_set_nat C2) A) (@ (@ tptp.ord_less_set_nat B) D)))) (@ _let_1 D))))))
% 6.73/7.05 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat) (D tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat C2))) (= (@ (@ tptp.ord_less_set_rat (@ (@ tptp.set_or633870826150836451st_rat A) B)) (@ (@ tptp.set_or633870826150836451st_rat C2) 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 C2) A) (@ (@ tptp.ord_less_rat B) D)))) (@ _let_1 D))))))
% 6.73/7.05 (assert (forall ((A tptp.num) (B tptp.num) (C2 tptp.num) (D tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_num C2))) (= (@ (@ tptp.ord_less_set_num (@ (@ tptp.set_or7049704709247886629st_num A) B)) (@ (@ tptp.set_or7049704709247886629st_num C2) 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 C2) A) (@ (@ tptp.ord_less_num B) D)))) (@ _let_1 D))))))
% 6.73/7.05 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat) (D tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat C2))) (= (@ (@ tptp.ord_less_set_nat (@ (@ tptp.set_or1269000886237332187st_nat A) B)) (@ (@ tptp.set_or1269000886237332187st_nat C2) 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 C2) A) (@ (@ tptp.ord_less_nat B) D)))) (@ _let_1 D))))))
% 6.73/7.05 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int) (D tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int C2))) (= (@ (@ tptp.ord_less_set_int (@ (@ tptp.set_or1266510415728281911st_int A) B)) (@ (@ tptp.set_or1266510415728281911st_int C2) 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 C2) A) (@ (@ tptp.ord_less_int B) D)))) (@ _let_1 D))))))
% 6.73/7.05 (assert (forall ((A tptp.real) (B tptp.real) (C2 tptp.real) (D tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real C2))) (= (@ (@ tptp.ord_less_set_real (@ (@ tptp.set_or1222579329274155063t_real A) B)) (@ (@ tptp.set_or1222579329274155063t_real C2) 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 C2) A) (@ (@ tptp.ord_less_real B) D)))) (@ _let_1 D))))))
% 6.73/7.05 (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))))))
% 6.73/7.05 (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))))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (assert (forall ((A tptp.real) (B tptp.real) (C2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real C2) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real B) C2)) (@ (@ tptp.divide_divide_real A) C2))))))
% 6.73/7.05 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat C2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat B) C2)) (@ (@ tptp.divide_divide_rat A) C2))))))
% 6.73/7.05 (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))))))
% 6.73/7.05 (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))))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (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)))))))
% 6.73/7.05 (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)))))))
% 6.73/7.05 (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)))))))
% 6.73/7.05 (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)))))))
% 6.73/7.05 (assert (forall ((A tptp.real) (B tptp.real) (C2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C2) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real A) C2)) (@ (@ tptp.divide_divide_real B) C2))))))
% 6.73/7.05 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C2) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat A) C2)) (@ (@ tptp.divide_divide_rat B) C2))))))
% 6.73/7.05 (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)))))))
% 6.73/7.05 (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)))))))
% 6.73/7.05 (assert (forall ((B tptp.real) (A tptp.real) (C2 tptp.real)) (=> (@ (@ tptp.ord_less_real B) A) (=> (@ (@ tptp.ord_less_real C2) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real A) C2)) (@ (@ tptp.divide_divide_real B) C2))))))
% 6.73/7.05 (assert (forall ((B tptp.rat) (A tptp.rat) (C2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat B) A) (=> (@ (@ tptp.ord_less_rat C2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat A) C2)) (@ (@ tptp.divide_divide_rat B) C2))))))
% 6.73/7.05 (assert (forall ((A tptp.real) (B tptp.real) (C2 tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C2) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real A) C2)) (@ (@ tptp.divide_divide_real B) C2))))))
% 6.73/7.05 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C2) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat A) C2)) (@ (@ tptp.divide_divide_rat B) C2))))))
% 6.73/7.05 (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)))))))
% 6.73/7.05 (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)))))))
% 6.73/7.05 (assert (forall ((A tptp.real) (C2 tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real A) C2)) (@ (@ tptp.divide_divide_real B) C2)) (and (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C2) (@ (@ tptp.ord_less_real A) B)) (=> (@ (@ tptp.ord_less_real C2) tptp.zero_zero_real) (@ (@ tptp.ord_less_real B) A)) (not (= C2 tptp.zero_zero_real))))))
% 6.73/7.05 (assert (forall ((A tptp.rat) (C2 tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat A) C2)) (@ (@ tptp.divide_divide_rat B) C2)) (and (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C2) (@ (@ tptp.ord_less_rat A) B)) (=> (@ (@ tptp.ord_less_rat C2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B) A)) (not (= C2 tptp.zero_zero_rat))))))
% 6.73/7.05 (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)))))))
% 6.73/7.05 (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)))))))
% 6.73/7.05 (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)))))))
% 6.73/7.05 (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)))))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (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))))))
% 6.73/7.05 (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))))))
% 6.73/7.05 (assert (forall ((N tptp.nat) (P2 (-> tptp.nat Bool))) (= (forall ((M6 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M6) N) (@ P2 M6))) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)) (@ P2 X4))))))
% 6.73/7.05 (assert (forall ((N tptp.nat) (P2 (-> tptp.nat Bool))) (= (exists ((M6 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat M6) N) (@ P2 M6))) (exists ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)) (@ P2 X4))))))
% 6.73/7.05 (assert (forall ((Y tptp.complex) (Z3 tptp.complex) (X tptp.complex) (W2 tptp.complex)) (=> (not (= Y tptp.zero_zero_complex)) (=> (not (= Z3 tptp.zero_zero_complex)) (= (= (@ (@ tptp.divide1717551699836669952omplex X) Y) (@ (@ tptp.divide1717551699836669952omplex W2) Z3)) (= (@ (@ tptp.times_times_complex X) Z3) (@ (@ tptp.times_times_complex W2) Y)))))))
% 6.73/7.05 (assert (forall ((Y tptp.real) (Z3 tptp.real) (X tptp.real) (W2 tptp.real)) (=> (not (= Y tptp.zero_zero_real)) (=> (not (= Z3 tptp.zero_zero_real)) (= (= (@ (@ tptp.divide_divide_real X) Y) (@ (@ tptp.divide_divide_real W2) Z3)) (= (@ (@ tptp.times_times_real X) Z3) (@ (@ tptp.times_times_real W2) Y)))))))
% 6.73/7.05 (assert (forall ((Y tptp.rat) (Z3 tptp.rat) (X tptp.rat) (W2 tptp.rat)) (=> (not (= Y tptp.zero_zero_rat)) (=> (not (= Z3 tptp.zero_zero_rat)) (= (= (@ (@ tptp.divide_divide_rat X) Y) (@ (@ tptp.divide_divide_rat W2) Z3)) (= (@ (@ tptp.times_times_rat X) Z3) (@ (@ tptp.times_times_rat W2) Y)))))))
% 6.73/7.05 (assert (forall ((B tptp.complex) (C2 tptp.complex) (A tptp.complex)) (let ((_let_1 (= C2 tptp.zero_zero_complex))) (= (= (@ (@ tptp.divide1717551699836669952omplex B) C2) A) (and (=> (not _let_1) (= B (@ (@ tptp.times_times_complex A) C2))) (=> _let_1 (= A tptp.zero_zero_complex)))))))
% 6.73/7.05 (assert (forall ((B tptp.real) (C2 tptp.real) (A tptp.real)) (let ((_let_1 (= C2 tptp.zero_zero_real))) (= (= (@ (@ tptp.divide_divide_real B) C2) A) (and (=> (not _let_1) (= B (@ (@ tptp.times_times_real A) C2))) (=> _let_1 (= A tptp.zero_zero_real)))))))
% 6.73/7.05 (assert (forall ((B tptp.rat) (C2 tptp.rat) (A tptp.rat)) (let ((_let_1 (= C2 tptp.zero_zero_rat))) (= (= (@ (@ tptp.divide_divide_rat B) C2) A) (and (=> (not _let_1) (= B (@ (@ tptp.times_times_rat A) C2))) (=> _let_1 (= A tptp.zero_zero_rat)))))))
% 6.73/7.05 (assert (forall ((A tptp.complex) (B tptp.complex) (C2 tptp.complex)) (let ((_let_1 (= C2 tptp.zero_zero_complex))) (= (= A (@ (@ tptp.divide1717551699836669952omplex B) C2)) (and (=> (not _let_1) (= (@ (@ tptp.times_times_complex A) C2) B)) (=> _let_1 (= A tptp.zero_zero_complex)))))))
% 6.73/7.05 (assert (forall ((A tptp.real) (B tptp.real) (C2 tptp.real)) (let ((_let_1 (= C2 tptp.zero_zero_real))) (= (= A (@ (@ tptp.divide_divide_real B) C2)) (and (=> (not _let_1) (= (@ (@ tptp.times_times_real A) C2) B)) (=> _let_1 (= A tptp.zero_zero_real)))))))
% 6.73/7.05 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (= C2 tptp.zero_zero_rat))) (= (= A (@ (@ tptp.divide_divide_rat B) C2)) (and (=> (not _let_1) (= (@ (@ tptp.times_times_rat A) C2) B)) (=> _let_1 (= A tptp.zero_zero_rat)))))))
% 6.73/7.05 (assert (forall ((C2 tptp.complex) (B tptp.complex) (A tptp.complex)) (=> (not (= C2 tptp.zero_zero_complex)) (=> (= B (@ (@ tptp.times_times_complex A) C2)) (= (@ (@ tptp.divide1717551699836669952omplex B) C2) A)))))
% 6.73/7.05 (assert (forall ((C2 tptp.real) (B tptp.real) (A tptp.real)) (=> (not (= C2 tptp.zero_zero_real)) (=> (= B (@ (@ tptp.times_times_real A) C2)) (= (@ (@ tptp.divide_divide_real B) C2) A)))))
% 6.73/7.05 (assert (forall ((C2 tptp.rat) (B tptp.rat) (A tptp.rat)) (=> (not (= C2 tptp.zero_zero_rat)) (=> (= B (@ (@ tptp.times_times_rat A) C2)) (= (@ (@ tptp.divide_divide_rat B) C2) A)))))
% 6.73/7.05 (assert (forall ((C2 tptp.complex) (A tptp.complex) (B tptp.complex)) (=> (not (= C2 tptp.zero_zero_complex)) (=> (= (@ (@ tptp.times_times_complex A) C2) B) (= A (@ (@ tptp.divide1717551699836669952omplex B) C2))))))
% 6.73/7.05 (assert (forall ((C2 tptp.real) (A tptp.real) (B tptp.real)) (=> (not (= C2 tptp.zero_zero_real)) (=> (= (@ (@ tptp.times_times_real A) C2) B) (= A (@ (@ tptp.divide_divide_real B) C2))))))
% 6.73/7.05 (assert (forall ((C2 tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (not (= C2 tptp.zero_zero_rat)) (=> (= (@ (@ tptp.times_times_rat A) C2) B) (= A (@ (@ tptp.divide_divide_rat B) C2))))))
% 6.73/7.05 (assert (forall ((C2 tptp.complex) (B tptp.complex) (A tptp.complex)) (=> (not (= C2 tptp.zero_zero_complex)) (= (= (@ (@ tptp.divide1717551699836669952omplex B) C2) A) (= B (@ (@ tptp.times_times_complex A) C2))))))
% 6.73/7.05 (assert (forall ((C2 tptp.real) (B tptp.real) (A tptp.real)) (=> (not (= C2 tptp.zero_zero_real)) (= (= (@ (@ tptp.divide_divide_real B) C2) A) (= B (@ (@ tptp.times_times_real A) C2))))))
% 6.73/7.05 (assert (forall ((C2 tptp.rat) (B tptp.rat) (A tptp.rat)) (=> (not (= C2 tptp.zero_zero_rat)) (= (= (@ (@ tptp.divide_divide_rat B) C2) A) (= B (@ (@ tptp.times_times_rat A) C2))))))
% 6.73/7.05 (assert (forall ((C2 tptp.complex) (A tptp.complex) (B tptp.complex)) (=> (not (= C2 tptp.zero_zero_complex)) (= (= A (@ (@ tptp.divide1717551699836669952omplex B) C2)) (= (@ (@ tptp.times_times_complex A) C2) B)))))
% 6.73/7.05 (assert (forall ((C2 tptp.real) (A tptp.real) (B tptp.real)) (=> (not (= C2 tptp.zero_zero_real)) (= (= A (@ (@ tptp.divide_divide_real B) C2)) (= (@ (@ tptp.times_times_real A) C2) B)))))
% 6.73/7.05 (assert (forall ((C2 tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (not (= C2 tptp.zero_zero_rat)) (= (= A (@ (@ tptp.divide_divide_rat B) C2)) (= (@ (@ tptp.times_times_rat A) C2) B)))))
% 6.73/7.05 (assert (forall ((B tptp.complex) (A tptp.complex)) (=> (not (= B tptp.zero_zero_complex)) (= (= (@ (@ tptp.divide1717551699836669952omplex A) B) tptp.one_one_complex) (= A B)))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) (@ tptp.numera6690914467698888265omplex tptp.one)) A)))
% 6.73/7.05 (assert (forall ((A tptp.real)) (= (@ (@ tptp.divide_divide_real A) (@ tptp.numeral_numeral_real tptp.one)) A)))
% 6.73/7.05 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.divide_divide_rat A) (@ tptp.numeral_numeral_rat tptp.one)) A)))
% 6.73/7.05 (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)))))))
% 6.73/7.05 (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)))))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (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))))))
% 6.73/7.05 (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))))))
% 6.73/7.05 (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)))))))
% 6.73/7.05 (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)))))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (assert (forall ((A tptp.real) (C2 tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real A) C2)) (@ (@ tptp.divide_divide_real B) C2)) (and (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C2) (@ (@ tptp.ord_less_eq_real A) B)) (=> (@ (@ tptp.ord_less_real C2) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real B) A))))))
% 6.73/7.05 (assert (forall ((A tptp.rat) (C2 tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat A) C2)) (@ (@ tptp.divide_divide_rat B) C2)) (and (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C2) (@ (@ tptp.ord_less_eq_rat A) B)) (=> (@ (@ tptp.ord_less_rat C2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat B) A))))))
% 6.73/7.05 (assert (forall ((X tptp.real) (Y tptp.real) (W2 tptp.real) (Z3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ (@ tptp.ord_less_eq_real X) Y) (=> (@ _let_1 W2) (=> (@ (@ tptp.ord_less_real W2) Z3) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real X) Z3)) (@ (@ tptp.divide_divide_real Y) W2)))))))))
% 6.73/7.05 (assert (forall ((X tptp.rat) (Y tptp.rat) (W2 tptp.rat) (Z3 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 W2) (=> (@ (@ tptp.ord_less_rat W2) Z3) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat X) Z3)) (@ (@ tptp.divide_divide_rat Y) W2)))))))))
% 6.73/7.05 (assert (forall ((X tptp.real) (Y tptp.real) (W2 tptp.real) (Z3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_real X) Y) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) W2) (=> (@ (@ tptp.ord_less_eq_real W2) Z3) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real X) Z3)) (@ (@ tptp.divide_divide_real Y) W2))))))))
% 6.73/7.05 (assert (forall ((X tptp.rat) (Y tptp.rat) (W2 tptp.rat) (Z3 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) W2) (=> (@ (@ tptp.ord_less_eq_rat W2) Z3) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat X) Z3)) (@ (@ tptp.divide_divide_rat Y) W2))))))))
% 6.73/7.05 (assert (forall ((Y tptp.real) (X tptp.real) (W2 tptp.real) (Z3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (=> (@ (@ tptp.ord_less_eq_real X) Y) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) W2) (=> (@ (@ tptp.ord_less_eq_real W2) Z3) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real X) Z3)) (@ (@ tptp.divide_divide_real Y) W2))))))))
% 6.73/7.05 (assert (forall ((Y tptp.rat) (X tptp.rat) (W2 tptp.rat) (Z3 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) W2) (=> (@ (@ tptp.ord_less_eq_rat W2) Z3) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat X) Z3)) (@ (@ tptp.divide_divide_rat Y) W2))))))))
% 6.73/7.05 (assert (forall ((C2 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) C2) (= (@ _let_1 (@ (@ tptp.times_times_nat B) C2)) (@ (@ tptp.divide_divide_nat (@ _let_1 B)) C2))))))
% 6.73/7.05 (assert (forall ((C2 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) C2) (= (@ _let_1 (@ (@ tptp.times_times_int B) C2)) (@ (@ tptp.divide_divide_int (@ _let_1 B)) C2))))))
% 6.73/7.05 (assert (forall ((B tptp.real) (C2 tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (let ((_let_2 (@ (@ tptp.ord_less_real C2) tptp.zero_zero_real))) (let ((_let_3 (@ (@ tptp.times_times_real A) C2))) (let ((_let_4 (@ _let_1 C2))) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real B) C2)) 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))))))))))))
% 6.73/7.05 (assert (forall ((B tptp.rat) (C2 tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (let ((_let_2 (@ (@ tptp.ord_less_rat C2) tptp.zero_zero_rat))) (let ((_let_3 (@ (@ tptp.times_times_rat A) C2))) (let ((_let_4 (@ _let_1 C2))) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat B) C2)) 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))))))))))))
% 6.73/7.05 (assert (forall ((A tptp.real) (B tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real A))) (let ((_let_2 (@ (@ tptp.ord_less_real C2) tptp.zero_zero_real))) (let ((_let_3 (@ (@ tptp.times_times_real A) C2))) (let ((_let_4 (@ (@ tptp.ord_less_real tptp.zero_zero_real) C2))) (= (@ _let_1 (@ (@ tptp.divide_divide_real B) C2)) (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))))))))))))
% 6.73/7.05 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A))) (let ((_let_2 (@ (@ tptp.ord_less_rat C2) tptp.zero_zero_rat))) (let ((_let_3 (@ (@ tptp.times_times_rat A) C2))) (let ((_let_4 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C2))) (= (@ _let_1 (@ (@ tptp.divide_divide_rat B) C2)) (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))))))))))))
% 6.73/7.05 (assert (forall ((C2 tptp.real) (B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real C2) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real B) C2)) A) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C2)) B)))))
% 6.73/7.05 (assert (forall ((C2 tptp.rat) (B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat C2) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat B) C2)) A) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C2)) B)))))
% 6.73/7.05 (assert (forall ((C2 tptp.real) (A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real C2) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_real A) (@ (@ tptp.divide_divide_real B) C2)) (@ (@ tptp.ord_less_real B) (@ (@ tptp.times_times_real A) C2))))))
% 6.73/7.05 (assert (forall ((C2 tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat C2) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_rat A) (@ (@ tptp.divide_divide_rat B) C2)) (@ (@ tptp.ord_less_rat B) (@ (@ tptp.times_times_rat A) C2))))))
% 6.73/7.05 (assert (forall ((C2 tptp.real) (B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C2) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real B) C2)) A) (@ (@ tptp.ord_less_real B) (@ (@ tptp.times_times_real A) C2))))))
% 6.73/7.05 (assert (forall ((C2 tptp.rat) (B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C2) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat B) C2)) A) (@ (@ tptp.ord_less_rat B) (@ (@ tptp.times_times_rat A) C2))))))
% 6.73/7.05 (assert (forall ((C2 tptp.real) (A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C2) (= (@ (@ tptp.ord_less_real A) (@ (@ tptp.divide_divide_real B) C2)) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C2)) B)))))
% 6.73/7.05 (assert (forall ((C2 tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C2) (= (@ (@ tptp.ord_less_rat A) (@ (@ tptp.divide_divide_rat B) C2)) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C2)) B)))))
% 6.73/7.05 (assert (forall ((Y tptp.real) (X tptp.real) (Z3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (=> (@ (@ tptp.ord_less_real X) (@ (@ tptp.times_times_real Z3) Y)) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real X) Y)) Z3)))))
% 6.73/7.05 (assert (forall ((Y tptp.rat) (X tptp.rat) (Z3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y) (=> (@ (@ tptp.ord_less_rat X) (@ (@ tptp.times_times_rat Z3) Y)) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat X) Y)) Z3)))))
% 6.73/7.05 (assert (forall ((Y tptp.real) (Z3 tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real Z3) Y)) X) (@ (@ tptp.ord_less_real Z3) (@ (@ tptp.divide_divide_real X) Y))))))
% 6.73/7.05 (assert (forall ((Y tptp.rat) (Z3 tptp.rat) (X tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat Z3) Y)) X) (@ (@ tptp.ord_less_rat Z3) (@ (@ tptp.divide_divide_rat X) Y))))))
% 6.73/7.05 (assert (forall ((B tptp.real) (A tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.divide_divide_real C2))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_real B) A) (=> (@ _let_2 C2) (=> (@ _let_2 (@ (@ tptp.times_times_real A) B)) (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B)))))))))
% 6.73/7.05 (assert (forall ((B tptp.rat) (A tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.divide_divide_rat C2))) (let ((_let_2 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ (@ tptp.ord_less_rat B) A) (=> (@ _let_2 C2) (=> (@ _let_2 (@ (@ tptp.times_times_rat A) B)) (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B)))))))))
% 6.73/7.05 (assert (forall ((A tptp.real) (B tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.divide_divide_real C2))) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_real C2) 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))))))))
% 6.73/7.05 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.divide_divide_rat C2))) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_rat C2) 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))))))))
% 6.73/7.05 (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)))))))
% 6.73/7.05 (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)))))))
% 6.73/7.05 (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))))))
% 6.73/7.05 (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))))))
% 6.73/7.05 (assert (forall ((B tptp.complex) (C2 tptp.complex) (W2 tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex W2))) (let ((_let_2 (= C2 tptp.zero_zero_complex))) (= (= (@ (@ tptp.divide1717551699836669952omplex B) C2) _let_1) (and (=> (not _let_2) (= B (@ (@ tptp.times_times_complex _let_1) C2))) (=> _let_2 (= _let_1 tptp.zero_zero_complex))))))))
% 6.73/7.05 (assert (forall ((B tptp.real) (C2 tptp.real) (W2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real W2))) (let ((_let_2 (= C2 tptp.zero_zero_real))) (= (= (@ (@ tptp.divide_divide_real B) C2) _let_1) (and (=> (not _let_2) (= B (@ (@ tptp.times_times_real _let_1) C2))) (=> _let_2 (= _let_1 tptp.zero_zero_real))))))))
% 6.73/7.05 (assert (forall ((B tptp.rat) (C2 tptp.rat) (W2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat W2))) (let ((_let_2 (= C2 tptp.zero_zero_rat))) (= (= (@ (@ tptp.divide_divide_rat B) C2) _let_1) (and (=> (not _let_2) (= B (@ (@ tptp.times_times_rat _let_1) C2))) (=> _let_2 (= _let_1 tptp.zero_zero_rat))))))))
% 6.73/7.05 (assert (forall ((W2 tptp.num) (B tptp.complex) (C2 tptp.complex)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex W2))) (let ((_let_2 (= C2 tptp.zero_zero_complex))) (= (= _let_1 (@ (@ tptp.divide1717551699836669952omplex B) C2)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_complex _let_1) C2) B)) (=> _let_2 (= _let_1 tptp.zero_zero_complex))))))))
% 6.73/7.05 (assert (forall ((W2 tptp.num) (B tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real W2))) (let ((_let_2 (= C2 tptp.zero_zero_real))) (= (= _let_1 (@ (@ tptp.divide_divide_real B) C2)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_real _let_1) C2) B)) (=> _let_2 (= _let_1 tptp.zero_zero_real))))))))
% 6.73/7.05 (assert (forall ((W2 tptp.num) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_rat W2))) (let ((_let_2 (= C2 tptp.zero_zero_rat))) (= (= _let_1 (@ (@ tptp.divide_divide_rat B) C2)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_rat _let_1) C2) B)) (=> _let_2 (= _let_1 tptp.zero_zero_rat))))))))
% 6.73/7.05 (assert (forall ((Z3 tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ (@ tptp.plus_plus_complex (@ (@ tptp.divide1717551699836669952omplex A) Z3)) B))) (let ((_let_2 (= Z3 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) Z3))) Z3))))))))
% 6.73/7.05 (assert (forall ((Z3 tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ (@ tptp.plus_plus_real (@ (@ tptp.divide_divide_real A) Z3)) B))) (let ((_let_2 (= Z3 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) Z3))) Z3))))))))
% 6.73/7.05 (assert (forall ((Z3 tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ (@ tptp.plus_plus_rat (@ (@ tptp.divide_divide_rat A) Z3)) B))) (let ((_let_2 (= Z3 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) Z3))) Z3))))))))
% 6.73/7.05 (assert (forall ((Z3 tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ (@ tptp.plus_plus_complex A) (@ (@ tptp.divide1717551699836669952omplex B) Z3)))) (let ((_let_2 (= Z3 tptp.zero_zero_complex))) (and (=> _let_2 (= _let_1 A)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex A) Z3)) B)) Z3))))))))
% 6.73/7.05 (assert (forall ((Z3 tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ (@ tptp.plus_plus_real A) (@ (@ tptp.divide_divide_real B) Z3)))) (let ((_let_2 (= Z3 tptp.zero_zero_real))) (and (=> _let_2 (= _let_1 A)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) Z3)) B)) Z3))))))))
% 6.73/7.05 (assert (forall ((Z3 tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ (@ tptp.plus_plus_rat A) (@ (@ tptp.divide_divide_rat B) Z3)))) (let ((_let_2 (= Z3 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) Z3)) B)) Z3))))))))
% 6.73/7.05 (assert (forall ((Y tptp.complex) (Z3 tptp.complex) (X tptp.complex) (W2 tptp.complex)) (=> (not (= Y tptp.zero_zero_complex)) (=> (not (= Z3 tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.divide1717551699836669952omplex X) Y)) (@ (@ tptp.divide1717551699836669952omplex W2) Z3)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex X) Z3)) (@ (@ tptp.times_times_complex W2) Y))) (@ (@ tptp.times_times_complex Y) Z3)))))))
% 6.73/7.05 (assert (forall ((Y tptp.real) (Z3 tptp.real) (X tptp.real) (W2 tptp.real)) (=> (not (= Y tptp.zero_zero_real)) (=> (not (= Z3 tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.divide_divide_real X) Y)) (@ (@ tptp.divide_divide_real W2) Z3)) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X) Z3)) (@ (@ tptp.times_times_real W2) Y))) (@ (@ tptp.times_times_real Y) Z3)))))))
% 6.73/7.05 (assert (forall ((Y tptp.rat) (Z3 tptp.rat) (X tptp.rat) (W2 tptp.rat)) (=> (not (= Y tptp.zero_zero_rat)) (=> (not (= Z3 tptp.zero_zero_rat)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.divide_divide_rat X) Y)) (@ (@ tptp.divide_divide_rat W2) Z3)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X) Z3)) (@ (@ tptp.times_times_rat W2) Y))) (@ (@ tptp.times_times_rat Y) Z3)))))))
% 6.73/7.05 (assert (forall ((Y tptp.complex) (X tptp.complex) (Z3 tptp.complex)) (=> (not (= Y tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.divide1717551699836669952omplex X) Y)) Z3) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex X) (@ (@ tptp.times_times_complex Z3) Y))) Y)))))
% 6.73/7.05 (assert (forall ((Y tptp.real) (X tptp.real) (Z3 tptp.real)) (=> (not (= Y tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.divide_divide_real X) Y)) Z3) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X) (@ (@ tptp.times_times_real Z3) Y))) Y)))))
% 6.73/7.05 (assert (forall ((Y tptp.rat) (X tptp.rat) (Z3 tptp.rat)) (=> (not (= Y tptp.zero_zero_rat)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.divide_divide_rat X) Y)) Z3) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat X) (@ (@ tptp.times_times_rat Z3) Y))) Y)))))
% 6.73/7.05 (assert (forall ((Y tptp.complex) (Z3 tptp.complex) (X tptp.complex)) (=> (not (= Y tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex Z3) (@ (@ tptp.divide1717551699836669952omplex X) Y)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex X) (@ (@ tptp.times_times_complex Z3) Y))) Y)))))
% 6.73/7.05 (assert (forall ((Y tptp.real) (Z3 tptp.real) (X tptp.real)) (=> (not (= Y tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real Z3) (@ (@ tptp.divide_divide_real X) Y)) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X) (@ (@ tptp.times_times_real Z3) Y))) Y)))))
% 6.73/7.05 (assert (forall ((Y tptp.rat) (Z3 tptp.rat) (X tptp.rat)) (=> (not (= Y tptp.zero_zero_rat)) (= (@ (@ tptp.plus_plus_rat Z3) (@ (@ tptp.divide_divide_rat X) Y)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat X) (@ (@ tptp.times_times_rat Z3) Y))) Y)))))
% 6.73/7.05 (assert (forall ((Z3 tptp.complex) (X tptp.complex) (Y tptp.complex)) (=> (not (= Z3 tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex X) (@ (@ tptp.divide1717551699836669952omplex Y) Z3)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex X) Z3)) Y)) Z3)))))
% 6.73/7.05 (assert (forall ((Z3 tptp.real) (X tptp.real) (Y tptp.real)) (=> (not (= Z3 tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real X) (@ (@ tptp.divide_divide_real Y) Z3)) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X) Z3)) Y)) Z3)))))
% 6.73/7.05 (assert (forall ((Z3 tptp.rat) (X tptp.rat) (Y tptp.rat)) (=> (not (= Z3 tptp.zero_zero_rat)) (= (@ (@ tptp.plus_plus_rat X) (@ (@ tptp.divide_divide_rat Y) Z3)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X) Z3)) Y)) Z3)))))
% 6.73/7.05 (assert (forall ((Z3 tptp.complex) (X tptp.complex) (Y tptp.complex)) (=> (not (= Z3 tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.divide1717551699836669952omplex X) Z3)) Y) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex X) (@ (@ tptp.times_times_complex Y) Z3))) Z3)))))
% 6.73/7.05 (assert (forall ((Z3 tptp.real) (X tptp.real) (Y tptp.real)) (=> (not (= Z3 tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.divide_divide_real X) Z3)) Y) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X) (@ (@ tptp.times_times_real Y) Z3))) Z3)))))
% 6.73/7.05 (assert (forall ((Z3 tptp.rat) (X tptp.rat) (Y tptp.rat)) (=> (not (= Z3 tptp.zero_zero_rat)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.divide_divide_rat X) Z3)) Y) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat X) (@ (@ tptp.times_times_rat Y) Z3))) Z3)))))
% 6.73/7.05 (assert (forall ((Z3 tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ (@ tptp.minus_minus_complex A) (@ (@ tptp.divide1717551699836669952omplex B) Z3)))) (let ((_let_2 (= Z3 tptp.zero_zero_complex))) (and (=> _let_2 (= _let_1 A)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex A) Z3)) B)) Z3))))))))
% 6.73/7.05 (assert (forall ((Z3 tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ (@ tptp.minus_minus_real A) (@ (@ tptp.divide_divide_real B) Z3)))) (let ((_let_2 (= Z3 tptp.zero_zero_real))) (and (=> _let_2 (= _let_1 A)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real A) Z3)) B)) Z3))))))))
% 6.73/7.05 (assert (forall ((Z3 tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ (@ tptp.minus_minus_rat A) (@ (@ tptp.divide_divide_rat B) Z3)))) (let ((_let_2 (= Z3 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) Z3)) B)) Z3))))))))
% 6.73/7.05 (assert (forall ((Y tptp.complex) (Z3 tptp.complex) (X tptp.complex) (W2 tptp.complex)) (=> (not (= Y tptp.zero_zero_complex)) (=> (not (= Z3 tptp.zero_zero_complex)) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.divide1717551699836669952omplex X) Y)) (@ (@ tptp.divide1717551699836669952omplex W2) Z3)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex X) Z3)) (@ (@ tptp.times_times_complex W2) Y))) (@ (@ tptp.times_times_complex Y) Z3)))))))
% 6.73/7.05 (assert (forall ((Y tptp.real) (Z3 tptp.real) (X tptp.real) (W2 tptp.real)) (=> (not (= Y tptp.zero_zero_real)) (=> (not (= Z3 tptp.zero_zero_real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real X) Y)) (@ (@ tptp.divide_divide_real W2) Z3)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real X) Z3)) (@ (@ tptp.times_times_real W2) Y))) (@ (@ tptp.times_times_real Y) Z3)))))))
% 6.73/7.05 (assert (forall ((Y tptp.rat) (Z3 tptp.rat) (X tptp.rat) (W2 tptp.rat)) (=> (not (= Y tptp.zero_zero_rat)) (=> (not (= Z3 tptp.zero_zero_rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.divide_divide_rat X) Y)) (@ (@ tptp.divide_divide_rat W2) Z3)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat X) Z3)) (@ (@ tptp.times_times_rat W2) Y))) (@ (@ tptp.times_times_rat Y) Z3)))))))
% 6.73/7.05 (assert (forall ((Z3 tptp.complex) (X tptp.complex) (Y tptp.complex)) (=> (not (= Z3 tptp.zero_zero_complex)) (= (@ (@ tptp.minus_minus_complex X) (@ (@ tptp.divide1717551699836669952omplex Y) Z3)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex X) Z3)) Y)) Z3)))))
% 6.73/7.05 (assert (forall ((Z3 tptp.real) (X tptp.real) (Y tptp.real)) (=> (not (= Z3 tptp.zero_zero_real)) (= (@ (@ tptp.minus_minus_real X) (@ (@ tptp.divide_divide_real Y) Z3)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real X) Z3)) Y)) Z3)))))
% 6.73/7.05 (assert (forall ((Z3 tptp.rat) (X tptp.rat) (Y tptp.rat)) (=> (not (= Z3 tptp.zero_zero_rat)) (= (@ (@ tptp.minus_minus_rat X) (@ (@ tptp.divide_divide_rat Y) Z3)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat X) Z3)) Y)) Z3)))))
% 6.73/7.05 (assert (forall ((Z3 tptp.complex) (X tptp.complex) (Y tptp.complex)) (=> (not (= Z3 tptp.zero_zero_complex)) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.divide1717551699836669952omplex X) Z3)) Y) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex X) (@ (@ tptp.times_times_complex Y) Z3))) Z3)))))
% 6.73/7.05 (assert (forall ((Z3 tptp.real) (X tptp.real) (Y tptp.real)) (=> (not (= Z3 tptp.zero_zero_real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real X) Z3)) Y) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real X) (@ (@ tptp.times_times_real Y) Z3))) Z3)))))
% 6.73/7.05 (assert (forall ((Z3 tptp.rat) (X tptp.rat) (Y tptp.rat)) (=> (not (= Z3 tptp.zero_zero_rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.divide_divide_rat X) Z3)) Y) (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat X) (@ (@ tptp.times_times_rat Y) Z3))) Z3)))))
% 6.73/7.05 (assert (forall ((A4 tptp.set_complex) (B5 tptp.set_complex)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_complex (@ (@ tptp.sup_sup_set_complex A4) B5))) (@ (@ tptp.plus_plus_nat (@ tptp.finite_card_complex A4)) (@ tptp.finite_card_complex B5)))))
% 6.73/7.05 (assert (forall ((A4 tptp.set_int) (B5 tptp.set_int)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_int (@ (@ tptp.sup_sup_set_int A4) B5))) (@ (@ tptp.plus_plus_nat (@ tptp.finite_card_int A4)) (@ tptp.finite_card_int B5)))))
% 6.73/7.05 (assert (forall ((A4 tptp.set_list_nat) (B5 tptp.set_list_nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_list_nat (@ (@ tptp.sup_sup_set_list_nat A4) B5))) (@ (@ tptp.plus_plus_nat (@ tptp.finite_card_list_nat A4)) (@ tptp.finite_card_list_nat B5)))))
% 6.73/7.05 (assert (forall ((A4 tptp.set_set_nat) (B5 tptp.set_set_nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_set_nat (@ (@ tptp.sup_sup_set_set_nat A4) B5))) (@ (@ tptp.plus_plus_nat (@ tptp.finite_card_set_nat A4)) (@ tptp.finite_card_set_nat B5)))))
% 6.73/7.05 (assert (forall ((A4 tptp.set_nat) (B5 tptp.set_nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat (@ (@ tptp.sup_sup_set_nat A4) B5))) (@ (@ tptp.plus_plus_nat (@ tptp.finite_card_nat A4)) (@ tptp.finite_card_nat B5)))))
% 6.73/7.05 (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)))))))
% 6.73/7.05 (assert (forall ((K2 tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K2) (= (@ (@ tptp.divide_divide_nat (@ _let_1 M2)) (@ _let_1 N)) (@ (@ tptp.divide_divide_nat M2) N))))))
% 6.73/7.05 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ (@ tptp.set_or1269000886237332187st_nat M2) N) (@ (@ tptp.insert_nat M2) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M2)) N))))))
% 6.73/7.05 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat M2))) (let ((_let_2 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_nat M2) _let_2) (= (@ _let_1 _let_2) (@ (@ tptp.insert_nat _let_2) (@ _let_1 N))))))))
% 6.73/7.05 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ (@ tptp.insert_nat M2) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M2)) N)) (@ (@ tptp.set_or1269000886237332187st_nat M2) N)))))
% 6.73/7.05 (assert (forall ((N6 tptp.set_nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_set_nat N6) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)) (@ tptp.finite_finite_nat N6))))
% 6.73/7.05 (assert (forall ((B tptp.real) (C2 tptp.real) (A tptp.real)) (let ((_let_1 (@ (@ tptp.ord_less_real C2) tptp.zero_zero_real))) (let ((_let_2 (@ (@ tptp.times_times_real A) C2))) (let ((_let_3 (@ (@ tptp.ord_less_real tptp.zero_zero_real) C2))) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real B) C2)) 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)))))))))))
% 6.73/7.05 (assert (forall ((B tptp.rat) (C2 tptp.rat) (A tptp.rat)) (let ((_let_1 (@ (@ tptp.ord_less_rat C2) tptp.zero_zero_rat))) (let ((_let_2 (@ (@ tptp.times_times_rat A) C2))) (let ((_let_3 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C2))) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat B) C2)) 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)))))))))))
% 6.73/7.05 (assert (forall ((A tptp.real) (B tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real A))) (let ((_let_2 (@ (@ tptp.ord_less_real C2) tptp.zero_zero_real))) (let ((_let_3 (@ (@ tptp.times_times_real A) C2))) (let ((_let_4 (@ (@ tptp.ord_less_real tptp.zero_zero_real) C2))) (= (@ _let_1 (@ (@ tptp.divide_divide_real B) C2)) (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))))))))))))
% 6.73/7.05 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat A))) (let ((_let_2 (@ (@ tptp.ord_less_rat C2) tptp.zero_zero_rat))) (let ((_let_3 (@ (@ tptp.times_times_rat A) C2))) (let ((_let_4 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C2))) (= (@ _let_1 (@ (@ tptp.divide_divide_rat B) C2)) (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))))))))))))
% 6.73/7.05 (assert (forall ((B tptp.real) (A tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.divide_divide_real C2))) (=> (@ (@ tptp.ord_less_eq_real B) A) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C2) (=> (@ (@ 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))))))))
% 6.73/7.05 (assert (forall ((B tptp.rat) (A tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.divide_divide_rat C2))) (=> (@ (@ tptp.ord_less_eq_rat B) A) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C2) (=> (@ (@ 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))))))))
% 6.73/7.05 (assert (forall ((C2 tptp.real) (B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real C2) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real B) C2)) A) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) C2)) B)))))
% 6.73/7.05 (assert (forall ((C2 tptp.rat) (B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat C2) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat B) C2)) A) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C2)) B)))))
% 6.73/7.05 (assert (forall ((C2 tptp.real) (A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real C2) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_eq_real A) (@ (@ tptp.divide_divide_real B) C2)) (@ (@ tptp.ord_less_eq_real B) (@ (@ tptp.times_times_real A) C2))))))
% 6.73/7.05 (assert (forall ((C2 tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat C2) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_eq_rat A) (@ (@ tptp.divide_divide_rat B) C2)) (@ (@ tptp.ord_less_eq_rat B) (@ (@ tptp.times_times_rat A) C2))))))
% 6.73/7.05 (assert (forall ((C2 tptp.real) (B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C2) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real B) C2)) A) (@ (@ tptp.ord_less_eq_real B) (@ (@ tptp.times_times_real A) C2))))))
% 6.73/7.05 (assert (forall ((C2 tptp.rat) (B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C2) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat B) C2)) A) (@ (@ tptp.ord_less_eq_rat B) (@ (@ tptp.times_times_rat A) C2))))))
% 6.73/7.05 (assert (forall ((C2 tptp.real) (A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C2) (= (@ (@ tptp.ord_less_eq_real A) (@ (@ tptp.divide_divide_real B) C2)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) C2)) B)))))
% 6.73/7.05 (assert (forall ((C2 tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C2) (= (@ (@ tptp.ord_less_eq_rat A) (@ (@ tptp.divide_divide_rat B) C2)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C2)) B)))))
% 6.73/7.05 (assert (forall ((Y tptp.real) (X tptp.real) (Z3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (=> (@ (@ tptp.ord_less_eq_real X) (@ (@ tptp.times_times_real Z3) Y)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real X) Y)) Z3)))))
% 6.73/7.05 (assert (forall ((Y tptp.rat) (X tptp.rat) (Z3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y) (=> (@ (@ tptp.ord_less_eq_rat X) (@ (@ tptp.times_times_rat Z3) Y)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat X) Y)) Z3)))))
% 6.73/7.05 (assert (forall ((Y tptp.real) (Z3 tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real Z3) Y)) X) (@ (@ tptp.ord_less_eq_real Z3) (@ (@ tptp.divide_divide_real X) Y))))))
% 6.73/7.05 (assert (forall ((Y tptp.rat) (Z3 tptp.rat) (X tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y) (=> (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat Z3) Y)) X) (@ (@ tptp.ord_less_eq_rat Z3) (@ (@ tptp.divide_divide_rat X) Y))))))
% 6.73/7.05 (assert (forall ((A tptp.real) (B tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.divide_divide_real C2))) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real C2) 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))))))))
% 6.73/7.05 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.divide_divide_rat C2))) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat C2) 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))))))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (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))))))
% 6.73/7.05 (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))))))
% 6.73/7.05 (assert (forall ((B tptp.real) (C2 tptp.real) (W2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real W2))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (let ((_let_3 (@ (@ tptp.ord_less_real C2) tptp.zero_zero_real))) (let ((_let_4 (@ (@ tptp.times_times_real _let_1) C2))) (let ((_let_5 (@ _let_2 C2))) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real B) C2)) _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)))))))))))))
% 6.73/7.05 (assert (forall ((B tptp.rat) (C2 tptp.rat) (W2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat W2))) (let ((_let_2 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (let ((_let_3 (@ (@ tptp.ord_less_rat C2) tptp.zero_zero_rat))) (let ((_let_4 (@ (@ tptp.times_times_rat _let_1) C2))) (let ((_let_5 (@ _let_2 C2))) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat B) C2)) _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)))))))))))))
% 6.73/7.05 (assert (forall ((W2 tptp.num) (B tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real W2))) (let ((_let_2 (@ tptp.ord_less_real _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_real C2) tptp.zero_zero_real))) (let ((_let_4 (@ (@ tptp.times_times_real _let_1) C2))) (let ((_let_5 (@ (@ tptp.ord_less_real tptp.zero_zero_real) C2))) (= (@ _let_2 (@ (@ tptp.divide_divide_real B) C2)) (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)))))))))))))
% 6.73/7.05 (assert (forall ((W2 tptp.num) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_rat W2))) (let ((_let_2 (@ tptp.ord_less_rat _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_rat C2) tptp.zero_zero_rat))) (let ((_let_4 (@ (@ tptp.times_times_rat _let_1) C2))) (let ((_let_5 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C2))) (= (@ _let_2 (@ (@ tptp.divide_divide_rat B) C2)) (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)))))))))))))
% 6.73/7.05 (assert (forall ((Y tptp.real) (Z3 tptp.real) (X tptp.real) (W2 tptp.real)) (=> (not (= Y tptp.zero_zero_real)) (=> (not (= Z3 tptp.zero_zero_real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real X) Y)) (@ (@ tptp.divide_divide_real W2) Z3)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real X) Z3)) (@ (@ tptp.times_times_real W2) Y))) (@ (@ tptp.times_times_real Y) Z3))) tptp.zero_zero_real))))))
% 6.73/7.05 (assert (forall ((Y tptp.rat) (Z3 tptp.rat) (X tptp.rat) (W2 tptp.rat)) (=> (not (= Y tptp.zero_zero_rat)) (=> (not (= Z3 tptp.zero_zero_rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat X) Y)) (@ (@ tptp.divide_divide_rat W2) Z3)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat X) Z3)) (@ (@ tptp.times_times_rat W2) Y))) (@ (@ tptp.times_times_rat Y) Z3))) tptp.zero_zero_rat))))))
% 6.73/7.05 (assert (forall ((Y tptp.real) (Z3 tptp.real) (X tptp.real) (W2 tptp.real)) (=> (not (= Y tptp.zero_zero_real)) (=> (not (= Z3 tptp.zero_zero_real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real X) Y)) (@ (@ tptp.divide_divide_real W2) Z3)) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real X) Z3)) (@ (@ tptp.times_times_real W2) Y))) (@ (@ tptp.times_times_real Y) Z3))) tptp.zero_zero_real))))))
% 6.73/7.05 (assert (forall ((Y tptp.rat) (Z3 tptp.rat) (X tptp.rat) (W2 tptp.rat)) (=> (not (= Y tptp.zero_zero_rat)) (=> (not (= Z3 tptp.zero_zero_rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat X) Y)) (@ (@ tptp.divide_divide_rat W2) Z3)) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat X) Z3)) (@ (@ tptp.times_times_rat W2) Y))) (@ (@ tptp.times_times_rat Y) Z3))) tptp.zero_zero_rat))))))
% 6.73/7.05 (assert (forall ((A tptp.complex) (N tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex A))) (=> (not (= A tptp.zero_zero_complex)) (=> (@ (@ tptp.ord_less_eq_nat N) M2) (= (@ _let_1 (@ (@ tptp.minus_minus_nat M2) N)) (@ (@ tptp.divide1717551699836669952omplex (@ _let_1 M2)) (@ _let_1 N))))))))
% 6.73/7.05 (assert (forall ((A tptp.real) (N tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (not (= A tptp.zero_zero_real)) (=> (@ (@ tptp.ord_less_eq_nat N) M2) (= (@ _let_1 (@ (@ tptp.minus_minus_nat M2) N)) (@ (@ tptp.divide_divide_real (@ _let_1 M2)) (@ _let_1 N))))))))
% 6.73/7.05 (assert (forall ((A tptp.rat) (N tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat A))) (=> (not (= A tptp.zero_zero_rat)) (=> (@ (@ tptp.ord_less_eq_nat N) M2) (= (@ _let_1 (@ (@ tptp.minus_minus_nat M2) N)) (@ (@ tptp.divide_divide_rat (@ _let_1 M2)) (@ _let_1 N))))))))
% 6.73/7.05 (assert (forall ((A tptp.nat) (N tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (not (= A tptp.zero_zero_nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M2) (= (@ _let_1 (@ (@ tptp.minus_minus_nat M2) N)) (@ (@ tptp.divide_divide_nat (@ _let_1 M2)) (@ _let_1 N))))))))
% 6.73/7.05 (assert (forall ((A tptp.int) (N tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (not (= A tptp.zero_zero_int)) (=> (@ (@ tptp.ord_less_eq_nat N) M2) (= (@ _let_1 (@ (@ tptp.minus_minus_nat M2) N)) (@ (@ tptp.divide_divide_int (@ _let_1 M2)) (@ _let_1 N))))))))
% 6.73/7.05 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (not (@ (@ tptp.ord_less_nat M2) N)) (= (@ (@ tptp.divide_divide_nat M2) N) (@ tptp.suc (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat M2) N)) N)))))))
% 6.73/7.05 (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))))))
% 6.73/7.05 (assert (forall ((A tptp.real) (C2 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) C2))) (@ (@ 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 C2) _let_2))))))))
% 6.73/7.05 (assert (forall ((B tptp.real) (C2 tptp.real) (W2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real W2))) (let ((_let_2 (@ (@ tptp.ord_less_real C2) tptp.zero_zero_real))) (let ((_let_3 (@ (@ tptp.times_times_real _let_1) C2))) (let ((_let_4 (@ (@ tptp.ord_less_real tptp.zero_zero_real) C2))) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real B) C2)) _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))))))))))))
% 6.73/7.05 (assert (forall ((B tptp.rat) (C2 tptp.rat) (W2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat W2))) (let ((_let_2 (@ (@ tptp.ord_less_rat C2) tptp.zero_zero_rat))) (let ((_let_3 (@ (@ tptp.times_times_rat _let_1) C2))) (let ((_let_4 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C2))) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat B) C2)) _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))))))))))))
% 6.73/7.05 (assert (forall ((W2 tptp.num) (B tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real W2))) (let ((_let_2 (@ tptp.ord_less_eq_real _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_real C2) tptp.zero_zero_real))) (let ((_let_4 (@ (@ tptp.times_times_real _let_1) C2))) (let ((_let_5 (@ (@ tptp.ord_less_real tptp.zero_zero_real) C2))) (= (@ _let_2 (@ (@ tptp.divide_divide_real B) C2)) (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)))))))))))))
% 6.73/7.05 (assert (forall ((W2 tptp.num) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_rat W2))) (let ((_let_2 (@ tptp.ord_less_eq_rat _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_rat C2) tptp.zero_zero_rat))) (let ((_let_4 (@ (@ tptp.times_times_rat _let_1) C2))) (let ((_let_5 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C2))) (= (@ _let_2 (@ (@ tptp.divide_divide_rat B) C2)) (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)))))))))))))
% 6.73/7.05 (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))))))))
% 6.73/7.05 (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))))))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (assert (forall ((U tptp.real) (V2 tptp.real) (R3 tptp.real) (S2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real U) V2) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) R3) (=> (@ (@ tptp.ord_less_eq_real R3) S2) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real U) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real R3) (@ (@ tptp.minus_minus_real V2) U))) S2))) V2))))))
% 6.73/7.05 (assert (forall ((U tptp.rat) (V2 tptp.rat) (R3 tptp.rat) (S2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat U) V2) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) R3) (=> (@ (@ tptp.ord_less_eq_rat R3) S2) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat U) (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat R3) (@ (@ tptp.minus_minus_rat V2) U))) S2))) V2))))))
% 6.73/7.05 (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)))))))
% 6.73/7.05 (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)))))))
% 6.73/7.05 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_real tptp.one_one_real))) (=> (@ (@ tptp.ord_less_eq_nat N) M2) (=> (not (= N tptp.zero_zero_nat)) (@ (@ tptp.ord_less_eq_real (@ _let_1 (@ tptp.semiri5074537144036343181t_real M2))) (@ _let_1 (@ tptp.semiri5074537144036343181t_real N))))))))
% 6.73/7.05 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_rat tptp.one_one_rat))) (=> (@ (@ tptp.ord_less_eq_nat N) M2) (=> (not (= N tptp.zero_zero_nat)) (@ (@ tptp.ord_less_eq_rat (@ _let_1 (@ tptp.semiri681578069525770553at_rat M2))) (@ _let_1 (@ tptp.semiri681578069525770553at_rat N))))))))
% 6.73/7.05 (assert (= tptp.nat_triangle (lambda ((N4 tptp.nat)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat N4) (@ tptp.suc N4))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 6.73/7.05 (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))))))))))
% 6.73/7.05 (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))))))))))
% 6.73/7.05 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (not (= (@ _let_1 M2) (@ tptp.suc (@ _let_1 N)))))))
% 6.73/7.05 (assert (forall ((M2 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 M2)) (@ _let_1 N))))))
% 6.73/7.05 (assert (forall ((M2 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 M2) N)) tptp.zero_zero_nat)) (not (= (@ _let_1 N) tptp.zero_zero_nat))))))
% 6.73/7.05 (assert (forall ((M2 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 M2) N)) tptp.zero_zero_int)) (not (= (@ _let_1 N) tptp.zero_zero_int))))))
% 6.73/7.05 (assert (= (@ (@ tptp.divide6298287555418463151nteger tptp.one_one_Code_integer) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) tptp.zero_z3403309356797280102nteger))
% 6.73/7.05 (assert (= (@ (@ tptp.divide_divide_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_nat))
% 6.73/7.05 (assert (= (@ (@ tptp.divide_divide_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) tptp.zero_zero_int))
% 6.73/7.05 (assert (forall ((M2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.divide_divide_nat (@ tptp.suc (@ tptp.suc M2))) _let_1) (@ tptp.suc (@ (@ tptp.divide_divide_nat M2) _let_1))))))
% 6.73/7.05 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (= (@ tptp.vEBT_set_vebt (@ (@ tptp.vEBT_VEBT_insert T) X)) (@ (@ tptp.inf_inf_set_nat (@ (@ tptp.sup_sup_set_nat (@ tptp.vEBT_set_vebt T)) (@ (@ tptp.insert_nat X) tptp.bot_bot_set_nat))) (@ (@ 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)))))))
% 6.73/7.05 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat M2) N)) N) M2))))
% 6.73/7.05 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat N) M2)) N) M2))))
% 6.73/7.05 (assert (forall ((B tptp.nat) (A tptp.nat) (C2 tptp.nat)) (=> (not (= B tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat A) (@ (@ tptp.times_times_nat C2) B))) B) (@ (@ tptp.plus_plus_nat C2) (@ (@ tptp.divide_divide_nat A) B))))))
% 6.73/7.05 (assert (forall ((B tptp.int) (A tptp.int) (C2 tptp.int)) (=> (not (= B tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int A) (@ (@ tptp.times_times_int C2) B))) B) (@ (@ tptp.plus_plus_int C2) (@ (@ tptp.divide_divide_int A) B))))))
% 6.73/7.05 (assert (forall ((B tptp.nat) (A tptp.nat) (C2 tptp.nat)) (=> (not (= B tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat A) (@ (@ tptp.times_times_nat B) C2))) B) (@ (@ tptp.plus_plus_nat C2) (@ (@ tptp.divide_divide_nat A) B))))))
% 6.73/7.05 (assert (forall ((B tptp.int) (A tptp.int) (C2 tptp.int)) (=> (not (= B tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int A) (@ (@ tptp.times_times_int B) C2))) B) (@ (@ tptp.plus_plus_int C2) (@ (@ tptp.divide_divide_int A) B))))))
% 6.73/7.05 (assert (forall ((B tptp.nat) (C2 tptp.nat) (A tptp.nat)) (=> (not (= B tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat C2) B)) A)) B) (@ (@ tptp.plus_plus_nat C2) (@ (@ tptp.divide_divide_nat A) B))))))
% 6.73/7.05 (assert (forall ((B tptp.int) (C2 tptp.int) (A tptp.int)) (=> (not (= B tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int C2) B)) A)) B) (@ (@ tptp.plus_plus_int C2) (@ (@ tptp.divide_divide_int A) B))))))
% 6.73/7.05 (assert (forall ((V2 tptp.num) (W2 tptp.num)) (= (@ (@ tptp.divide_divide_int (@ tptp.numeral_numeral_int (@ tptp.bit0 V2))) (@ tptp.numeral_numeral_int (@ tptp.bit0 W2))) (@ (@ tptp.divide_divide_int (@ tptp.numeral_numeral_int V2)) (@ tptp.numeral_numeral_int W2)))))
% 6.73/7.05 (assert (forall ((R3 tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.times_times_real R3))) (= (@ (@ tptp.divide_divide_real (@ _let_1 A)) (@ _let_1 R3)) (@ (@ tptp.divide_divide_real A) R3)))))
% 6.73/7.05 (assert (forall ((C2 tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C2))) (let ((_let_2 (@ (@ tptp.divide_divide_nat (@ _let_1 A)) (@ _let_1 B)))) (let ((_let_3 (= C2 tptp.zero_zero_nat))) (and (=> _let_3 (= _let_2 tptp.zero_zero_nat)) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_nat A) B)))))))))
% 6.73/7.05 (assert (forall ((C2 tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C2))) (let ((_let_2 (@ (@ tptp.divide_divide_int (@ _let_1 A)) (@ _let_1 B)))) (let ((_let_3 (= C2 tptp.zero_zero_int))) (and (=> _let_3 (= _let_2 tptp.zero_zero_int)) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_int A) B)))))))))
% 6.73/7.05 (assert (forall ((C2 tptp.nat) (A tptp.nat) (B tptp.nat)) (=> (not (= C2 tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat A) C2)) (@ (@ tptp.times_times_nat B) C2)) (@ (@ tptp.divide_divide_nat A) B)))))
% 6.73/7.05 (assert (forall ((C2 tptp.int) (A tptp.int) (B tptp.int)) (=> (not (= C2 tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int A) C2)) (@ (@ tptp.times_times_int B) C2)) (@ (@ tptp.divide_divide_int A) B)))))
% 6.73/7.05 (assert (forall ((C2 tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C2))) (=> (not (= C2 tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.divide_divide_nat A) B))))))
% 6.73/7.05 (assert (forall ((C2 tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C2))) (=> (not (= C2 tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.divide_divide_int A) B))))))
% 6.73/7.05 (assert (forall ((M2 tptp.nat)) (= (@ (@ tptp.divide_divide_nat M2) (@ tptp.suc tptp.zero_zero_nat)) M2)))
% 6.73/7.05 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) N) (= (@ (@ tptp.divide_divide_nat M2) N) tptp.zero_zero_nat))))
% 6.73/7.05 (assert (forall ((B tptp.nat) (C2 tptp.nat) (A tptp.nat)) (=> (not (= B tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat B) C2)) A)) B) (@ (@ tptp.plus_plus_nat C2) (@ (@ tptp.divide_divide_nat A) B))))))
% 6.73/7.05 (assert (forall ((B tptp.int) (C2 tptp.int) (A tptp.int)) (=> (not (= B tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) C2)) A)) B) (@ (@ tptp.plus_plus_int C2) (@ (@ tptp.divide_divide_int A) B))))))
% 6.73/7.05 (assert (forall ((C2 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) C2) (= (@ _let_1 (@ (@ tptp.times_times_int B) C2)) (@ (@ tptp.divide_divide_int (@ _let_1 B)) C2))))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (assert (forall ((M2 tptp.int) (N tptp.int)) (let ((_let_1 (@ tptp.set_or1266510415728281911st_int M2))) (let ((_let_2 (@ (@ tptp.plus_plus_int tptp.one_one_int) N))) (=> (@ (@ tptp.ord_less_eq_int M2) _let_2) (= (@ _let_1 _let_2) (@ (@ tptp.insert_int _let_2) (@ _let_1 N))))))))
% 6.73/7.05 (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)))))))
% 6.73/7.05 (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))))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (assert (forall ((K2 tptp.int) (I2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 K2) (= (@ _let_1 (@ (@ tptp.divide_divide_int I2) K2)) (@ (@ tptp.ord_less_eq_int K2) I2))))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (assert (forall ((L tptp.int) (K2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_eq_int L) K2) (=> (@ _let_1 L) (@ _let_1 (@ (@ tptp.divide_divide_int K2) L)))))))
% 6.73/7.05 (assert (forall ((K2 tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.divide_divide_int K2) L)) (or (= K2 tptp.zero_zero_int) (= L tptp.zero_zero_int) (and (@ _let_1 K2) (@ _let_1 L)) (and (@ (@ tptp.ord_less_int K2) tptp.zero_zero_int) (@ (@ tptp.ord_less_int L) tptp.zero_zero_int)))))))
% 6.73/7.05 (assert (forall ((A tptp.int) (B2 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) B2) (=> (@ (@ tptp.ord_less_eq_int B2) B) (@ (@ tptp.ord_less_eq_int (@ _let_1 B2)) (@ _let_1 B))))))))
% 6.73/7.05 (assert (forall ((A tptp.int) (A2 tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) A2) (=> (@ (@ tptp.ord_less_int B) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.divide_divide_int A2) B)) (@ (@ tptp.divide_divide_int A) B))))))
% 6.73/7.05 (assert (forall ((I2 tptp.int) (K2 tptp.int)) (= (= (@ (@ tptp.divide_divide_int I2) K2) tptp.zero_zero_int) (or (= K2 tptp.zero_zero_int) (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) I2) (@ (@ tptp.ord_less_int I2) K2)) (and (@ (@ tptp.ord_less_eq_int I2) tptp.zero_zero_int) (@ (@ tptp.ord_less_int K2) I2))))))
% 6.73/7.05 (assert (forall ((A tptp.int) (B2 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) B2) (=> (@ (@ tptp.ord_less_eq_int B2) B) (@ (@ tptp.ord_less_eq_int (@ _let_1 B)) (@ _let_1 B2))))))))
% 6.73/7.05 (assert (forall ((A tptp.int) (A2 tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) A2) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.divide_divide_int A) B)) (@ (@ tptp.divide_divide_int A2) B))))))
% 6.73/7.05 (assert (forall ((X tptp.int) (K2 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) X) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) K2) (@ (@ tptp.ord_less_int (@ (@ tptp.divide_divide_int X) K2)) X)))))
% 6.73/7.05 (assert (forall ((D tptp.int) (P2 (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (=> (forall ((X3 tptp.int) (K tptp.int)) (= (@ P2 X3) (@ P2 (@ (@ tptp.minus_minus_int X3) (@ (@ tptp.times_times_int K) D))))) (= (exists ((X7 tptp.int)) (@ P2 X7)) (exists ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D)) (@ P2 X4))))))))
% 6.73/7.05 (assert (forall ((P2 (-> tptp.int Bool)) (N tptp.int) (K2 tptp.int)) (= (@ P2 (@ (@ tptp.divide_divide_int N) K2)) (and (=> (= K2 tptp.zero_zero_int) (@ P2 tptp.zero_zero_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K2) (forall ((I tptp.int) (J tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) J) (@ (@ tptp.ord_less_int J) K2) (= N (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int K2) I)) J))) (@ P2 I)))) (=> (@ (@ tptp.ord_less_int K2) tptp.zero_zero_int) (forall ((I tptp.int) (J tptp.int)) (=> (and (@ (@ tptp.ord_less_int K2) J) (@ (@ tptp.ord_less_eq_int J) tptp.zero_zero_int) (= N (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int K2) I)) J))) (@ P2 I))))))))
% 6.73/7.05 (assert (forall ((A tptp.int) (B tptp.int) (Q2 tptp.int) (R3 tptp.int)) (=> (= A (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) Q2)) R3)) (=> (@ (@ tptp.ord_less_eq_int R3) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int B) R3) (= (@ (@ tptp.divide_divide_int A) B) Q2))))))
% 6.73/7.05 (assert (forall ((A tptp.int) (B tptp.int) (Q2 tptp.int) (R3 tptp.int)) (=> (= A (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) Q2)) R3)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) R3) (=> (@ (@ tptp.ord_less_int R3) B) (= (@ (@ tptp.divide_divide_int A) B) Q2))))))
% 6.73/7.05 (assert (forall ((D3 tptp.int) (P2 (-> tptp.int Bool)) (P6 (-> tptp.int Bool)) (B5 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D3) (=> (exists ((Z5 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Z5) (= (@ P2 X3) (@ P6 X3))))) (=> (forall ((X3 tptp.int)) (=> (forall ((Xa tptp.int)) (=> (@ (@ tptp.member_int Xa) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D3)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) B5) (not (= X3 (@ (@ tptp.plus_plus_int Xb2) Xa))))))) (=> (@ P2 X3) (@ P2 (@ (@ tptp.minus_minus_int X3) D3))))) (=> (forall ((X3 tptp.int) (K tptp.int)) (= (@ P6 X3) (@ P6 (@ (@ tptp.minus_minus_int X3) (@ (@ tptp.times_times_int K) D3))))) (= (exists ((X7 tptp.int)) (@ P2 X7)) (or (exists ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D3)) (@ P6 X4))) (exists ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D3)) (exists ((Y4 tptp.int)) (and (@ (@ tptp.member_int Y4) B5) (@ P2 (@ (@ tptp.plus_plus_int Y4) X4))))))))))))))
% 6.73/7.05 (assert (forall ((D3 tptp.int) (P2 (-> tptp.int Bool)) (P6 (-> tptp.int Bool)) (A4 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D3) (=> (exists ((Z5 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int Z5) X3) (= (@ P2 X3) (@ P6 X3))))) (=> (forall ((X3 tptp.int)) (=> (forall ((Xa tptp.int)) (=> (@ (@ tptp.member_int Xa) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D3)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) A4) (not (= X3 (@ (@ tptp.minus_minus_int Xb2) Xa))))))) (=> (@ P2 X3) (@ P2 (@ (@ tptp.plus_plus_int X3) D3))))) (=> (forall ((X3 tptp.int) (K tptp.int)) (= (@ P6 X3) (@ P6 (@ (@ tptp.minus_minus_int X3) (@ (@ tptp.times_times_int K) D3))))) (= (exists ((X7 tptp.int)) (@ P2 X7)) (or (exists ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D3)) (@ P6 X4))) (exists ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D3)) (exists ((Y4 tptp.int)) (and (@ (@ tptp.member_int Y4) A4) (@ P2 (@ (@ tptp.minus_minus_int Y4) X4))))))))))))))
% 6.73/7.05 (assert (forall ((M2 tptp.nat) (K2 tptp.int)) (let ((_let_1 (@ tptp.power_power_int K2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M2) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K2) (= (@ (@ tptp.divide_divide_int (@ _let_1 M2)) K2) (@ _let_1 (@ (@ tptp.minus_minus_nat M2) (@ tptp.suc tptp.zero_zero_nat)))))))))
% 6.73/7.05 (assert (forall ((L tptp.int) (K2 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) L) (=> (@ (@ tptp.ord_less_eq_int L) K2) (= (@ (@ tptp.divide_divide_int K2) L) (@ (@ tptp.plus_plus_int (@ (@ tptp.divide_divide_int (@ (@ tptp.minus_minus_int K2) L)) L)) tptp.one_one_int))))))
% 6.73/7.05 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.divide_divide_nat M2) N)) M2)))
% 6.73/7.05 (assert (forall ((M2 tptp.nat) (N tptp.nat) (K2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.divide_divide_nat M2) K2)) (@ (@ tptp.divide_divide_nat N) K2)))))
% 6.73/7.05 (assert (forall ((M2 tptp.nat) (N tptp.nat) (Q2 tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat M2))) (= (@ _let_1 (@ (@ tptp.times_times_nat N) Q2)) (@ (@ tptp.divide_divide_nat (@ _let_1 N)) Q2)))))
% 6.73/7.05 (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))))))
% 6.73/7.05 (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))))))
% 6.73/7.05 (assert (forall ((A tptp.int) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int N))) (let ((_let_2 (@ tptp.semiri1314217659103216013at_int M2))) (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)))))))
% 6.73/7.05 (assert (forall ((A tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri1316708129612266289at_nat N))) (let ((_let_2 (@ tptp.semiri1316708129612266289at_nat M2))) (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)))))))
% 6.73/7.05 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (= (@ (@ tptp.divide_divide_nat M2) N) tptp.zero_zero_nat) (or (@ (@ tptp.ord_less_nat M2) N) (= N tptp.zero_zero_nat)))))
% 6.73/7.05 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.divide_divide_nat M2) N)) (@ (@ tptp.divide_divide_nat (@ tptp.suc M2)) N))))
% 6.73/7.05 (assert (forall ((M2 tptp.nat) (I2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) (@ (@ tptp.times_times_nat I2) N)) (@ (@ tptp.ord_less_nat (@ (@ tptp.divide_divide_nat M2) N)) I2))))
% 6.73/7.05 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat N) (@ (@ tptp.divide_divide_nat M2) N))) M2)))
% 6.73/7.05 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat M2) N)) N)) M2)))
% 6.73/7.05 (assert (forall ((A tptp.nat) (K2 tptp.num) (L tptp.num)) (let ((_let_1 (@ tptp.divide_divide_nat A))) (= (@ (@ tptp.divide_divide_nat (@ _let_1 (@ tptp.numeral_numeral_nat K2))) (@ tptp.numeral_numeral_nat L)) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.times_times_num K2) L)))))))
% 6.73/7.05 (assert (forall ((A tptp.int) (K2 tptp.num) (L tptp.num)) (let ((_let_1 (@ tptp.divide_divide_int A))) (= (@ (@ tptp.divide_divide_int (@ _let_1 (@ tptp.numeral_numeral_int K2))) (@ tptp.numeral_numeral_int L)) (@ _let_1 (@ tptp.numeral_numeral_int (@ (@ tptp.times_times_num K2) L)))))))
% 6.73/7.05 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (=> (not (= B tptp.zero_z3403309356797280102nteger)) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.plus_p5714425477246183910nteger B) A)) B) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.divide6298287555418463151nteger A) B)) tptp.one_one_Code_integer)))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (=> (not (= B tptp.zero_z3403309356797280102nteger)) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B)) B) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.divide6298287555418463151nteger A) B)) tptp.one_one_Code_integer)))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (assert (forall ((M2 tptp.nat) (N tptp.nat) (K2 tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat K2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M2) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (@ (@ tptp.ord_less_eq_nat (@ _let_1 N)) (@ _let_1 M2)))))))
% 6.73/7.05 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ (@ tptp.divide_divide_nat M2) N)) (and (@ (@ tptp.ord_less_eq_nat N) M2) (@ _let_1 N))))))
% 6.73/7.05 (assert (forall ((Q2 tptp.nat) (M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) Q2) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.divide_divide_nat M2) Q2)) N) (@ (@ tptp.ord_less_nat M2) (@ (@ tptp.times_times_nat N) Q2))))))
% 6.73/7.05 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) N) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M2) (@ (@ tptp.ord_less_nat (@ (@ tptp.divide_divide_nat M2) N)) M2)))))
% 6.73/7.05 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M2) (= (= (@ (@ tptp.divide_divide_nat M2) N) M2) (= N tptp.one_one_nat)))))
% 6.73/7.05 (assert (= tptp.divide_divide_nat (lambda ((M6 tptp.nat) (N4 tptp.nat)) (@ (@ (@ tptp.if_nat (or (@ (@ tptp.ord_less_nat M6) N4) (= N4 tptp.zero_zero_nat))) tptp.zero_zero_nat) (@ tptp.suc (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat M6) N4)) N4))))))
% 6.73/7.05 (assert (forall ((N tptp.nat) (Q2 tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat N))) (=> (@ (@ tptp.ord_less_eq_nat (@ _let_1 Q2)) M2) (=> (@ (@ tptp.ord_less_nat M2) (@ _let_1 (@ tptp.suc Q2))) (= (@ (@ tptp.divide_divide_nat M2) N) Q2))))))
% 6.73/7.05 (assert (forall ((Q2 tptp.nat) (M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) Q2) (= (@ (@ tptp.ord_less_eq_nat M2) (@ (@ tptp.divide_divide_nat N) Q2)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat M2) Q2)) N)))))
% 6.73/7.05 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_nat M2) (@ (@ tptp.plus_plus_nat N) (@ (@ tptp.times_times_nat N) (@ (@ tptp.divide_divide_nat M2) N)))))))
% 6.73/7.05 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_nat M2) (@ (@ tptp.plus_plus_nat N) (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat M2) N)) N))))))
% 6.73/7.05 (assert (forall ((P2 (-> tptp.nat Bool)) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (= N tptp.zero_zero_nat))) (= (@ P2 (@ (@ tptp.divide_divide_nat M2) N)) (and (=> _let_1 (@ P2 tptp.zero_zero_nat)) (=> (not _let_1) (forall ((I tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_nat J) N) (=> (= M2 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat N) I)) J)) (@ P2 I))))))))))
% 6.73/7.05 (assert (forall ((A tptp.code_integer) (N tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger A))) (let ((_let_2 (@ (@ tptp.divide6298287555418463151nteger (@ _let_1 M2)) (@ _let_1 N)))) (let ((_let_3 (@ (@ tptp.ord_less_eq_nat N) M2))) (=> (not (= A tptp.zero_z3403309356797280102nteger)) (and (=> _let_3 (= _let_2 (@ _let_1 (@ (@ tptp.minus_minus_nat M2) N)))) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide6298287555418463151nteger tptp.one_one_Code_integer) (@ _let_1 (@ (@ tptp.minus_minus_nat N) M2))))))))))))
% 6.73/7.05 (assert (forall ((A tptp.nat) (N tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (let ((_let_2 (@ (@ tptp.divide_divide_nat (@ _let_1 M2)) (@ _let_1 N)))) (let ((_let_3 (@ (@ tptp.ord_less_eq_nat N) M2))) (=> (not (= A tptp.zero_zero_nat)) (and (=> _let_3 (= _let_2 (@ _let_1 (@ (@ tptp.minus_minus_nat M2) N)))) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_nat tptp.one_one_nat) (@ _let_1 (@ (@ tptp.minus_minus_nat N) M2))))))))))))
% 6.73/7.05 (assert (forall ((A tptp.int) (N tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (let ((_let_2 (@ (@ tptp.divide_divide_int (@ _let_1 M2)) (@ _let_1 N)))) (let ((_let_3 (@ (@ tptp.ord_less_eq_nat N) M2))) (=> (not (= A tptp.zero_zero_int)) (and (=> _let_3 (= _let_2 (@ _let_1 (@ (@ tptp.minus_minus_nat M2) N)))) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_int tptp.one_one_int) (@ _let_1 (@ (@ tptp.minus_minus_nat N) M2))))))))))))
% 6.73/7.05 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_eq_nat N) M2) (= (@ (@ tptp.divide_divide_nat M2) N) (@ tptp.suc (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat M2) N)) N)))))))
% 6.73/7.05 (assert (forall ((P2 (-> tptp.nat Bool)) (M2 tptp.nat) (N tptp.nat)) (= (@ P2 (@ (@ tptp.divide_divide_nat M2) N)) (or (and (= N tptp.zero_zero_nat) (@ P2 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)) M2) (@ (@ tptp.ord_less_nat M2) (@ _let_1 (@ tptp.suc Q5))) (@ P2 Q5))))))))
% 6.73/7.05 (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)))))))
% 6.73/7.05 (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))))))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (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)))))))
% 6.73/7.05 (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)))))))
% 6.73/7.05 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se2793503036327961859nteger tptp.zero_zero_nat) A) (@ (@ tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer) (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.divide6298287555418463151nteger A) _let_1)))))))
% 6.73/7.05 (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)))))))
% 6.73/7.05 (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)))))))
% 6.73/7.05 (assert (=> (not (= tptp.mi tptp.ma)) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.m)) (and (=> (= (@ (@ tptp.vEBT_VEBT_high tptp.ma) tptp.na) I4) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT tptp.treeList2) I4)) (@ (@ tptp.vEBT_VEBT_low tptp.ma) tptp.na))) (forall ((X5 tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X5) tptp.na) I4) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT tptp.treeList2) I4)) (@ (@ tptp.vEBT_VEBT_low X5) tptp.na))) (and (@ (@ tptp.ord_less_nat tptp.mi) X5) (@ (@ tptp.ord_less_eq_nat X5) tptp.ma)))))))))
% 6.73/7.05 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_le2932123472753598470d_enat (@ tptp.numera1916890842035813515d_enat M2)) (@ tptp.numera1916890842035813515d_enat N)) (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat M2)) (@ tptp.numeral_numeral_nat N)))))
% 6.73/7.05 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat) (Z3 tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.sup_sup_set_nat X) Y)) Z3) (and (@ (@ tptp.ord_less_eq_set_nat X) Z3) (@ (@ tptp.ord_less_eq_set_nat Y) Z3)))))
% 6.73/7.05 (assert (forall ((X tptp.rat) (Y tptp.rat) (Z3 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.sup_sup_rat X) Y)) Z3) (and (@ (@ tptp.ord_less_eq_rat X) Z3) (@ (@ tptp.ord_less_eq_rat Y) Z3)))))
% 6.73/7.05 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z3 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.sup_sup_nat X) Y)) Z3) (and (@ (@ tptp.ord_less_eq_nat X) Z3) (@ (@ tptp.ord_less_eq_nat Y) Z3)))))
% 6.73/7.05 (assert (forall ((X tptp.int) (Y tptp.int) (Z3 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.sup_sup_int X) Y)) Z3) (and (@ (@ tptp.ord_less_eq_int X) Z3) (@ (@ tptp.ord_less_eq_int Y) Z3)))))
% 6.73/7.05 (assert (forall ((B tptp.set_nat) (C2 tptp.set_nat) (A tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.sup_sup_set_nat B) C2)) A) (and (@ (@ tptp.ord_less_eq_set_nat B) A) (@ (@ tptp.ord_less_eq_set_nat C2) A)))))
% 6.73/7.05 (assert (forall ((B tptp.rat) (C2 tptp.rat) (A tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.sup_sup_rat B) C2)) A) (and (@ (@ tptp.ord_less_eq_rat B) A) (@ (@ tptp.ord_less_eq_rat C2) A)))))
% 6.73/7.05 (assert (forall ((B tptp.nat) (C2 tptp.nat) (A tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.sup_sup_nat B) C2)) A) (and (@ (@ tptp.ord_less_eq_nat B) A) (@ (@ tptp.ord_less_eq_nat C2) A)))))
% 6.73/7.05 (assert (forall ((B tptp.int) (C2 tptp.int) (A tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.sup_sup_int B) C2)) A) (and (@ (@ tptp.ord_less_eq_int B) A) (@ (@ tptp.ord_less_eq_int C2) A)))))
% 6.73/7.05 (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)))
% 6.73/7.05 (assert (forall ((L tptp.int) (U tptp.int)) (@ tptp.finite_finite_int (@ (@ tptp.set_or1266510415728281911st_int L) U))))
% 6.73/7.05 (assert (= tptp.vEBT_VEBT_high (lambda ((X4 tptp.nat) (N4 tptp.nat)) (@ (@ tptp.divide_divide_nat X4) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N4)))))
% 6.73/7.05 (assert (forall ((Ma tptp.nat) (N tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_nat Ma) (@ _let_1 (@ (@ tptp.plus_plus_nat N) M2))) (@ (@ tptp.ord_less_nat (@ (@ tptp.vEBT_VEBT_high Ma) N)) (@ _let_1 M2))))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat) (Z3 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.ord_le3146513528884898305at_nat X))) (= (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat Y) Z3)) (and (@ _let_1 Y) (@ _let_1 Z3))))))
% 6.73/7.05 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat) (Z3 tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat X))) (= (@ _let_1 (@ (@ tptp.inf_inf_set_nat Y) Z3)) (and (@ _let_1 Y) (@ _let_1 Z3))))))
% 6.73/7.05 (assert (forall ((X tptp.rat) (Y tptp.rat) (Z3 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat X))) (= (@ _let_1 (@ (@ tptp.inf_inf_rat Y) Z3)) (and (@ _let_1 Y) (@ _let_1 Z3))))))
% 6.73/7.05 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z3 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat X))) (= (@ _let_1 (@ (@ tptp.inf_inf_nat Y) Z3)) (and (@ _let_1 Y) (@ _let_1 Z3))))))
% 6.73/7.05 (assert (forall ((X tptp.int) (Y tptp.int) (Z3 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int X))) (= (@ _let_1 (@ (@ tptp.inf_inf_int Y) Z3)) (and (@ _let_1 Y) (@ _let_1 Z3))))))
% 6.73/7.05 (assert (forall ((A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat) (C2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.ord_le3146513528884898305at_nat A))) (= (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat B) C2)) (and (@ _let_1 B) (@ _let_1 C2))))))
% 6.73/7.05 (assert (forall ((A tptp.set_nat) (B tptp.set_nat) (C2 tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat A))) (= (@ _let_1 (@ (@ tptp.inf_inf_set_nat B) C2)) (and (@ _let_1 B) (@ _let_1 C2))))))
% 6.73/7.05 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat A))) (= (@ _let_1 (@ (@ tptp.inf_inf_rat B) C2)) (and (@ _let_1 B) (@ _let_1 C2))))))
% 6.73/7.05 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat A))) (= (@ _let_1 (@ (@ tptp.inf_inf_nat B) C2)) (and (@ _let_1 B) (@ _let_1 C2))))))
% 6.73/7.05 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int A))) (= (@ _let_1 (@ (@ tptp.inf_inf_int B) C2)) (and (@ _let_1 B) (@ _let_1 C2))))))
% 6.73/7.05 (assert (forall ((Info2 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 Info2) 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)))))))))
% 6.73/7.05 (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)))))))
% 6.73/7.05 (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)))))))))))
% 6.73/7.05 (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))))))))
% 6.73/7.05 (assert (forall ((X tptp.nat) (N tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ (@ tptp.ord_less_nat X) (@ _let_1 (@ (@ tptp.plus_plus_nat N) M2))) (=> (@ _let_2 N) (=> (@ _let_2 M2) (@ (@ tptp.ord_less_nat (@ (@ tptp.vEBT_VEBT_low X) N)) (@ _let_1 N)))))))))
% 6.73/7.05 (assert (forall ((X tptp.nat) (N tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ (@ tptp.ord_less_nat X) (@ _let_1 (@ (@ tptp.plus_plus_nat N) M2))) (=> (@ _let_2 N) (=> (@ _let_2 M2) (@ (@ tptp.ord_less_nat (@ (@ tptp.vEBT_VEBT_high X) N)) (@ _let_1 M2)))))))))
% 6.73/7.05 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.inf_in2572325071724192079at_nat X) Y)) Y)))
% 6.73/7.05 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.inf_inf_set_nat X) Y)) Y)))
% 6.73/7.05 (assert (forall ((X tptp.rat) (Y tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.inf_inf_rat X) Y)) Y)))
% 6.73/7.05 (assert (forall ((X tptp.nat) (Y tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.inf_inf_nat X) Y)) Y)))
% 6.73/7.05 (assert (forall ((X tptp.int) (Y tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.inf_inf_int X) Y)) Y)))
% 6.73/7.05 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.inf_in2572325071724192079at_nat X) Y)) X)))
% 6.73/7.05 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.inf_inf_set_nat X) Y)) X)))
% 6.73/7.05 (assert (forall ((X tptp.rat) (Y tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.inf_inf_rat X) Y)) X)))
% 6.73/7.05 (assert (forall ((X tptp.nat) (Y tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.inf_inf_nat X) Y)) X)))
% 6.73/7.05 (assert (forall ((X tptp.int) (Y tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.inf_inf_int X) Y)) X)))
% 6.73/7.05 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.inf_in2572325071724192079at_nat X) Y)) X)))
% 6.73/7.05 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.inf_inf_set_nat X) Y)) X)))
% 6.73/7.05 (assert (forall ((X tptp.rat) (Y tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.inf_inf_rat X) Y)) X)))
% 6.73/7.05 (assert (forall ((X tptp.nat) (Y tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.inf_inf_nat X) Y)) X)))
% 6.73/7.05 (assert (forall ((X tptp.int) (Y tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.inf_inf_int X) Y)) X)))
% 6.73/7.05 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.inf_in2572325071724192079at_nat X) Y)) Y)))
% 6.73/7.05 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.inf_inf_set_nat X) Y)) Y)))
% 6.73/7.05 (assert (forall ((X tptp.rat) (Y tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.inf_inf_rat X) Y)) Y)))
% 6.73/7.05 (assert (forall ((X tptp.nat) (Y tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.inf_inf_nat X) Y)) Y)))
% 6.73/7.05 (assert (forall ((X tptp.int) (Y tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.inf_inf_int X) Y)) Y)))
% 6.73/7.05 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat) (A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.ord_le3146513528884898305at_nat X))) (=> (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat A) B)) (not (=> (@ _let_1 A) (not (@ _let_1 B))))))))
% 6.73/7.05 (assert (forall ((X tptp.set_nat) (A tptp.set_nat) (B tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat X))) (=> (@ _let_1 (@ (@ tptp.inf_inf_set_nat A) B)) (not (=> (@ _let_1 A) (not (@ _let_1 B))))))))
% 6.73/7.05 (assert (forall ((X tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat X))) (=> (@ _let_1 (@ (@ tptp.inf_inf_rat A) B)) (not (=> (@ _let_1 A) (not (@ _let_1 B))))))))
% 6.73/7.05 (assert (forall ((X tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat X))) (=> (@ _let_1 (@ (@ tptp.inf_inf_nat A) B)) (not (=> (@ _let_1 A) (not (@ _let_1 B))))))))
% 6.73/7.05 (assert (forall ((X tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int X))) (=> (@ _let_1 (@ (@ tptp.inf_inf_int A) B)) (not (=> (@ _let_1 A) (not (@ _let_1 B))))))))
% 6.73/7.05 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat) (A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.ord_le3146513528884898305at_nat X))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat A) B)))))))
% 6.73/7.05 (assert (forall ((X tptp.set_nat) (A tptp.set_nat) (B tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat X))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.inf_inf_set_nat A) B)))))))
% 6.73/7.05 (assert (forall ((X tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat X))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.inf_inf_rat A) B)))))))
% 6.73/7.05 (assert (forall ((X tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat X))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.inf_inf_nat A) B)))))))
% 6.73/7.05 (assert (forall ((X tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int X))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.inf_inf_int A) B)))))))
% 6.73/7.05 (assert (forall ((A tptp.set_Pr1261947904930325089at_nat) (C2 tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat) (D tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_le3146513528884898305at_nat A) C2) (=> (@ (@ tptp.ord_le3146513528884898305at_nat B) D) (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.inf_in2572325071724192079at_nat A) B)) (@ (@ tptp.inf_in2572325071724192079at_nat C2) D))))))
% 6.73/7.05 (assert (forall ((A tptp.set_nat) (C2 tptp.set_nat) (B tptp.set_nat) (D tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A) C2) (=> (@ (@ tptp.ord_less_eq_set_nat B) D) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.inf_inf_set_nat A) B)) (@ (@ tptp.inf_inf_set_nat C2) D))))))
% 6.73/7.05 (assert (forall ((A tptp.rat) (C2 tptp.rat) (B tptp.rat) (D tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) C2) (=> (@ (@ tptp.ord_less_eq_rat B) D) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.inf_inf_rat A) B)) (@ (@ tptp.inf_inf_rat C2) D))))))
% 6.73/7.05 (assert (forall ((A tptp.nat) (C2 tptp.nat) (B tptp.nat) (D tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) C2) (=> (@ (@ tptp.ord_less_eq_nat B) D) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.inf_inf_nat A) B)) (@ (@ tptp.inf_inf_nat C2) D))))))
% 6.73/7.05 (assert (forall ((A tptp.int) (C2 tptp.int) (B tptp.int) (D tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) C2) (=> (@ (@ tptp.ord_less_eq_int B) D) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.inf_inf_int A) B)) (@ (@ tptp.inf_inf_int C2) D))))))
% 6.73/7.05 (assert (forall ((A tptp.set_Pr1261947904930325089at_nat) (X tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_le3146513528884898305at_nat A) X) (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.inf_in2572325071724192079at_nat A) B)) X))))
% 6.73/7.05 (assert (forall ((A tptp.set_nat) (X tptp.set_nat) (B tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A) X) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.inf_inf_set_nat A) B)) X))))
% 6.73/7.05 (assert (forall ((A tptp.rat) (X tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) X) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.inf_inf_rat A) B)) X))))
% 6.73/7.05 (assert (forall ((A tptp.nat) (X tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) X) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.inf_inf_nat A) B)) X))))
% 6.73/7.05 (assert (forall ((A tptp.int) (X tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) X) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.inf_inf_int A) B)) X))))
% 6.73/7.05 (assert (forall ((B tptp.set_Pr1261947904930325089at_nat) (X tptp.set_Pr1261947904930325089at_nat) (A tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_le3146513528884898305at_nat B) X) (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.inf_in2572325071724192079at_nat A) B)) X))))
% 6.73/7.05 (assert (forall ((B tptp.set_nat) (X tptp.set_nat) (A tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat B) X) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.inf_inf_set_nat A) B)) X))))
% 6.73/7.05 (assert (forall ((B tptp.rat) (X tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat B) X) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.inf_inf_rat A) B)) X))))
% 6.73/7.05 (assert (forall ((B tptp.nat) (X tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B) X) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.inf_inf_nat A) B)) X))))
% 6.73/7.05 (assert (forall ((B tptp.int) (X tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B) X) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.inf_inf_int A) B)) X))))
% 6.73/7.05 (assert (forall ((A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_le3146513528884898305at_nat A) B) (= A (@ (@ tptp.inf_in2572325071724192079at_nat A) B)))))
% 6.73/7.05 (assert (forall ((A tptp.set_nat) (B tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A) B) (= A (@ (@ tptp.inf_inf_set_nat A) B)))))
% 6.73/7.05 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (= A (@ (@ tptp.inf_inf_rat A) B)))))
% 6.73/7.05 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= A (@ (@ tptp.inf_inf_nat A) B)))))
% 6.73/7.05 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (= A (@ (@ tptp.inf_inf_int A) B)))))
% 6.73/7.05 (assert (forall ((A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (=> (= A (@ (@ tptp.inf_in2572325071724192079at_nat A) B)) (@ (@ tptp.ord_le3146513528884898305at_nat A) B))))
% 6.73/7.05 (assert (forall ((A tptp.set_nat) (B tptp.set_nat)) (=> (= A (@ (@ tptp.inf_inf_set_nat A) B)) (@ (@ tptp.ord_less_eq_set_nat A) B))))
% 6.73/7.05 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (= A (@ (@ tptp.inf_inf_rat A) B)) (@ (@ tptp.ord_less_eq_rat A) B))))
% 6.73/7.05 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (= A (@ (@ tptp.inf_inf_nat A) B)) (@ (@ tptp.ord_less_eq_nat A) B))))
% 6.73/7.05 (assert (forall ((A tptp.int) (B tptp.int)) (=> (= A (@ (@ tptp.inf_inf_int A) B)) (@ (@ tptp.ord_less_eq_int A) B))))
% 6.73/7.05 (assert (forall ((F2 (-> tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat)) (X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat)) (=> (forall ((X3 tptp.set_Pr1261947904930325089at_nat) (Y3 tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ F2 X3) Y3)) X3)) (=> (forall ((X3 tptp.set_Pr1261947904930325089at_nat) (Y3 tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ F2 X3) Y3)) Y3)) (=> (forall ((X3 tptp.set_Pr1261947904930325089at_nat) (Y3 tptp.set_Pr1261947904930325089at_nat) (Z tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.ord_le3146513528884898305at_nat X3))) (=> (@ _let_1 Y3) (=> (@ _let_1 Z) (@ _let_1 (@ (@ F2 Y3) Z)))))) (= (@ (@ tptp.inf_in2572325071724192079at_nat X) Y) (@ (@ F2 X) Y)))))))
% 6.73/7.05 (assert (forall ((F2 (-> tptp.set_nat tptp.set_nat tptp.set_nat)) (X tptp.set_nat) (Y tptp.set_nat)) (=> (forall ((X3 tptp.set_nat) (Y3 tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat (@ (@ F2 X3) Y3)) X3)) (=> (forall ((X3 tptp.set_nat) (Y3 tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat (@ (@ F2 X3) Y3)) Y3)) (=> (forall ((X3 tptp.set_nat) (Y3 tptp.set_nat) (Z tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat X3))) (=> (@ _let_1 Y3) (=> (@ _let_1 Z) (@ _let_1 (@ (@ F2 Y3) Z)))))) (= (@ (@ tptp.inf_inf_set_nat X) Y) (@ (@ F2 X) Y)))))))
% 6.73/7.05 (assert (forall ((F2 (-> tptp.rat tptp.rat tptp.rat)) (X tptp.rat) (Y tptp.rat)) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ (@ F2 X3) Y3)) X3)) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ (@ F2 X3) Y3)) Y3)) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat) (Z tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat X3))) (=> (@ _let_1 Y3) (=> (@ _let_1 Z) (@ _let_1 (@ (@ F2 Y3) Z)))))) (= (@ (@ tptp.inf_inf_rat X) Y) (@ (@ F2 X) Y)))))))
% 6.73/7.05 (assert (forall ((F2 (-> tptp.nat tptp.nat tptp.nat)) (X tptp.nat) (Y tptp.nat)) (=> (forall ((X3 tptp.nat) (Y3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ F2 X3) Y3)) X3)) (=> (forall ((X3 tptp.nat) (Y3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ F2 X3) Y3)) Y3)) (=> (forall ((X3 tptp.nat) (Y3 tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat X3))) (=> (@ _let_1 Y3) (=> (@ _let_1 Z) (@ _let_1 (@ (@ F2 Y3) Z)))))) (= (@ (@ tptp.inf_inf_nat X) Y) (@ (@ F2 X) Y)))))))
% 6.73/7.05 (assert (forall ((F2 (-> tptp.int tptp.int tptp.int)) (X tptp.int) (Y tptp.int)) (=> (forall ((X3 tptp.int) (Y3 tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ F2 X3) Y3)) X3)) (=> (forall ((X3 tptp.int) (Y3 tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ F2 X3) Y3)) Y3)) (=> (forall ((X3 tptp.int) (Y3 tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int X3))) (=> (@ _let_1 Y3) (=> (@ _let_1 Z) (@ _let_1 (@ (@ F2 Y3) Z)))))) (= (@ (@ tptp.inf_inf_int X) Y) (@ (@ F2 X) Y)))))))
% 6.73/7.05 (assert (= tptp.ord_le3146513528884898305at_nat (lambda ((X4 tptp.set_Pr1261947904930325089at_nat) (Y4 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat X4) Y4) X4))))
% 6.73/7.05 (assert (= tptp.ord_less_eq_set_nat (lambda ((X4 tptp.set_nat) (Y4 tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat X4) Y4) X4))))
% 6.73/7.05 (assert (= tptp.ord_less_eq_rat (lambda ((X4 tptp.rat) (Y4 tptp.rat)) (= (@ (@ tptp.inf_inf_rat X4) Y4) X4))))
% 6.73/7.05 (assert (= tptp.ord_less_eq_nat (lambda ((X4 tptp.nat) (Y4 tptp.nat)) (= (@ (@ tptp.inf_inf_nat X4) Y4) X4))))
% 6.73/7.05 (assert (= tptp.ord_less_eq_int (lambda ((X4 tptp.int) (Y4 tptp.int)) (= (@ (@ tptp.inf_inf_int X4) Y4) X4))))
% 6.73/7.05 (assert (forall ((A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_le3146513528884898305at_nat A) B) (= (@ (@ tptp.inf_in2572325071724192079at_nat A) B) A))))
% 6.73/7.05 (assert (forall ((A tptp.set_nat) (B tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A) B) (= (@ (@ tptp.inf_inf_set_nat A) B) A))))
% 6.73/7.05 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (= (@ (@ tptp.inf_inf_rat A) B) A))))
% 6.73/7.05 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= (@ (@ tptp.inf_inf_nat A) B) A))))
% 6.73/7.05 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (= (@ (@ tptp.inf_inf_int A) B) A))))
% 6.73/7.05 (assert (forall ((B tptp.set_Pr1261947904930325089at_nat) (A tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_le3146513528884898305at_nat B) A) (= (@ (@ tptp.inf_in2572325071724192079at_nat A) B) B))))
% 6.73/7.05 (assert (forall ((B tptp.set_nat) (A tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat B) A) (= (@ (@ tptp.inf_inf_set_nat A) B) B))))
% 6.73/7.05 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat B) A) (= (@ (@ tptp.inf_inf_rat A) B) B))))
% 6.73/7.05 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B) A) (= (@ (@ tptp.inf_inf_nat A) B) B))))
% 6.73/7.05 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B) A) (= (@ (@ tptp.inf_inf_int A) B) B))))
% 6.73/7.05 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_le3146513528884898305at_nat X) Y) (= (@ (@ tptp.inf_in2572325071724192079at_nat X) Y) X))))
% 6.73/7.05 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat X) Y) (= (@ (@ tptp.inf_inf_set_nat X) Y) X))))
% 6.73/7.05 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X) Y) (= (@ (@ tptp.inf_inf_rat X) Y) X))))
% 6.73/7.05 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X) Y) (= (@ (@ tptp.inf_inf_nat X) Y) X))))
% 6.73/7.05 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X) Y) (= (@ (@ tptp.inf_inf_int X) Y) X))))
% 6.73/7.05 (assert (forall ((Y tptp.set_Pr1261947904930325089at_nat) (X tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_le3146513528884898305at_nat Y) X) (= (@ (@ tptp.inf_in2572325071724192079at_nat X) Y) Y))))
% 6.73/7.05 (assert (forall ((Y tptp.set_nat) (X tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat Y) X) (= (@ (@ tptp.inf_inf_set_nat X) Y) Y))))
% 6.73/7.05 (assert (forall ((Y tptp.rat) (X tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat Y) X) (= (@ (@ tptp.inf_inf_rat X) Y) Y))))
% 6.73/7.05 (assert (forall ((Y tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Y) X) (= (@ (@ tptp.inf_inf_nat X) Y) Y))))
% 6.73/7.05 (assert (forall ((Y tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Y) X) (= (@ (@ tptp.inf_inf_int X) Y) Y))))
% 6.73/7.05 (assert (forall ((A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat) (C2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.ord_le3146513528884898305at_nat A))) (=> (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat B) C2)) (not (=> (@ _let_1 B) (not (@ _let_1 C2))))))))
% 6.73/7.05 (assert (forall ((A tptp.set_nat) (B tptp.set_nat) (C2 tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat A))) (=> (@ _let_1 (@ (@ tptp.inf_inf_set_nat B) C2)) (not (=> (@ _let_1 B) (not (@ _let_1 C2))))))))
% 6.73/7.05 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat A))) (=> (@ _let_1 (@ (@ tptp.inf_inf_rat B) C2)) (not (=> (@ _let_1 B) (not (@ _let_1 C2))))))))
% 6.73/7.05 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat A))) (=> (@ _let_1 (@ (@ tptp.inf_inf_nat B) C2)) (not (=> (@ _let_1 B) (not (@ _let_1 C2))))))))
% 6.73/7.05 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int A))) (=> (@ _let_1 (@ (@ tptp.inf_inf_int B) C2)) (not (=> (@ _let_1 B) (not (@ _let_1 C2))))))))
% 6.73/7.05 (assert (forall ((A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat) (C2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.ord_le3146513528884898305at_nat A))) (=> (@ _let_1 B) (=> (@ _let_1 C2) (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat B) C2)))))))
% 6.73/7.05 (assert (forall ((A tptp.set_nat) (B tptp.set_nat) (C2 tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat A))) (=> (@ _let_1 B) (=> (@ _let_1 C2) (@ _let_1 (@ (@ tptp.inf_inf_set_nat B) C2)))))))
% 6.73/7.05 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat A))) (=> (@ _let_1 B) (=> (@ _let_1 C2) (@ _let_1 (@ (@ tptp.inf_inf_rat B) C2)))))))
% 6.73/7.05 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat A))) (=> (@ _let_1 B) (=> (@ _let_1 C2) (@ _let_1 (@ (@ tptp.inf_inf_nat B) C2)))))))
% 6.73/7.05 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int A))) (=> (@ _let_1 B) (=> (@ _let_1 C2) (@ _let_1 (@ (@ tptp.inf_inf_int B) C2)))))))
% 6.73/7.05 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat) (Z3 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.ord_le3146513528884898305at_nat X))) (=> (@ _let_1 Y) (=> (@ _let_1 Z3) (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat Y) Z3)))))))
% 6.73/7.05 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat) (Z3 tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat X))) (=> (@ _let_1 Y) (=> (@ _let_1 Z3) (@ _let_1 (@ (@ tptp.inf_inf_set_nat Y) Z3)))))))
% 6.73/7.05 (assert (forall ((X tptp.rat) (Y tptp.rat) (Z3 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat X))) (=> (@ _let_1 Y) (=> (@ _let_1 Z3) (@ _let_1 (@ (@ tptp.inf_inf_rat Y) Z3)))))))
% 6.73/7.05 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z3 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat X))) (=> (@ _let_1 Y) (=> (@ _let_1 Z3) (@ _let_1 (@ (@ tptp.inf_inf_nat Y) Z3)))))))
% 6.73/7.05 (assert (forall ((X tptp.int) (Y tptp.int) (Z3 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int X))) (=> (@ _let_1 Y) (=> (@ _let_1 Z3) (@ _let_1 (@ (@ tptp.inf_inf_int Y) Z3)))))))
% 6.73/7.05 (assert (= tptp.ord_le3146513528884898305at_nat (lambda ((A5 tptp.set_Pr1261947904930325089at_nat) (B4 tptp.set_Pr1261947904930325089at_nat)) (= A5 (@ (@ tptp.inf_in2572325071724192079at_nat A5) B4)))))
% 6.73/7.05 (assert (= tptp.ord_less_eq_set_nat (lambda ((A5 tptp.set_nat) (B4 tptp.set_nat)) (= A5 (@ (@ tptp.inf_inf_set_nat A5) B4)))))
% 6.73/7.05 (assert (= tptp.ord_less_eq_rat (lambda ((A5 tptp.rat) (B4 tptp.rat)) (= A5 (@ (@ tptp.inf_inf_rat A5) B4)))))
% 6.73/7.05 (assert (= tptp.ord_less_eq_nat (lambda ((A5 tptp.nat) (B4 tptp.nat)) (= A5 (@ (@ tptp.inf_inf_nat A5) B4)))))
% 6.73/7.05 (assert (= tptp.ord_less_eq_int (lambda ((A5 tptp.int) (B4 tptp.int)) (= A5 (@ (@ tptp.inf_inf_int A5) B4)))))
% 6.73/7.05 (assert (forall ((A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.inf_in2572325071724192079at_nat A) B)) A)))
% 6.73/7.05 (assert (forall ((A tptp.set_nat) (B tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.inf_inf_set_nat A) B)) A)))
% 6.73/7.05 (assert (forall ((A tptp.rat) (B tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.inf_inf_rat A) B)) A)))
% 6.73/7.05 (assert (forall ((A tptp.nat) (B tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.inf_inf_nat A) B)) A)))
% 6.73/7.05 (assert (forall ((A tptp.int) (B tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.inf_inf_int A) B)) A)))
% 6.73/7.05 (assert (forall ((A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.inf_in2572325071724192079at_nat A) B)) B)))
% 6.73/7.05 (assert (forall ((A tptp.set_nat) (B tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.inf_inf_set_nat A) B)) B)))
% 6.73/7.05 (assert (forall ((A tptp.rat) (B tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.inf_inf_rat A) B)) B)))
% 6.73/7.05 (assert (forall ((A tptp.nat) (B tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.inf_inf_nat A) B)) B)))
% 6.73/7.05 (assert (forall ((A tptp.int) (B tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.inf_inf_int A) B)) B)))
% 6.73/7.05 (assert (= tptp.ord_le3146513528884898305at_nat (lambda ((A5 tptp.set_Pr1261947904930325089at_nat) (B4 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat A5) B4) A5))))
% 6.73/7.05 (assert (= tptp.ord_less_eq_set_nat (lambda ((A5 tptp.set_nat) (B4 tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat A5) B4) A5))))
% 6.73/7.05 (assert (= tptp.ord_less_eq_rat (lambda ((A5 tptp.rat) (B4 tptp.rat)) (= (@ (@ tptp.inf_inf_rat A5) B4) A5))))
% 6.73/7.05 (assert (= tptp.ord_less_eq_nat (lambda ((A5 tptp.nat) (B4 tptp.nat)) (= (@ (@ tptp.inf_inf_nat A5) B4) A5))))
% 6.73/7.05 (assert (= tptp.ord_less_eq_int (lambda ((A5 tptp.int) (B4 tptp.int)) (= (@ (@ tptp.inf_inf_int A5) B4) A5))))
% 6.73/7.05 (assert (= tptp.ord_le3146513528884898305at_nat (lambda ((B4 tptp.set_Pr1261947904930325089at_nat) (A5 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat A5) B4) B4))))
% 6.73/7.05 (assert (= tptp.ord_less_eq_set_nat (lambda ((B4 tptp.set_nat) (A5 tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat A5) B4) B4))))
% 6.73/7.05 (assert (= tptp.ord_less_eq_rat (lambda ((B4 tptp.rat) (A5 tptp.rat)) (= (@ (@ tptp.inf_inf_rat A5) B4) B4))))
% 6.73/7.05 (assert (= tptp.ord_less_eq_nat (lambda ((B4 tptp.nat) (A5 tptp.nat)) (= (@ (@ tptp.inf_inf_nat A5) B4) B4))))
% 6.73/7.05 (assert (= tptp.ord_less_eq_int (lambda ((B4 tptp.int) (A5 tptp.int)) (= (@ (@ tptp.inf_inf_int A5) B4) B4))))
% 6.73/7.05 (assert (forall ((A tptp.set_Pr1261947904930325089at_nat) (C2 tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_le3146513528884898305at_nat A) C2) (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.inf_in2572325071724192079at_nat A) B)) C2))))
% 6.73/7.05 (assert (forall ((A tptp.set_nat) (C2 tptp.set_nat) (B tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A) C2) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.inf_inf_set_nat A) B)) C2))))
% 6.73/7.05 (assert (forall ((A tptp.rat) (C2 tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) C2) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.inf_inf_rat A) B)) C2))))
% 6.73/7.05 (assert (forall ((A tptp.nat) (C2 tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) C2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.inf_inf_nat A) B)) C2))))
% 6.73/7.05 (assert (forall ((A tptp.int) (C2 tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) C2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.inf_inf_int A) B)) C2))))
% 6.73/7.05 (assert (forall ((B tptp.set_Pr1261947904930325089at_nat) (C2 tptp.set_Pr1261947904930325089at_nat) (A tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_le3146513528884898305at_nat B) C2) (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.inf_in2572325071724192079at_nat A) B)) C2))))
% 6.73/7.05 (assert (forall ((B tptp.set_nat) (C2 tptp.set_nat) (A tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat B) C2) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.inf_inf_set_nat A) B)) C2))))
% 6.73/7.05 (assert (forall ((B tptp.rat) (C2 tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat B) C2) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.inf_inf_rat A) B)) C2))))
% 6.73/7.05 (assert (forall ((B tptp.nat) (C2 tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B) C2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.inf_inf_nat A) B)) C2))))
% 6.73/7.05 (assert (forall ((B tptp.int) (C2 tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B) C2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.inf_inf_int A) B)) C2))))
% 6.73/7.05 (assert (forall ((C2 tptp.set_nat) (B tptp.set_nat) (A tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat C2))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.sup_sup_set_nat A) B))))))
% 6.73/7.05 (assert (forall ((C2 tptp.rat) (B tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat C2))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.sup_sup_rat A) B))))))
% 6.73/7.05 (assert (forall ((C2 tptp.nat) (B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat C2))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.sup_sup_nat A) B))))))
% 6.73/7.05 (assert (forall ((C2 tptp.int) (B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int C2))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.sup_sup_int A) B))))))
% 6.73/7.05 (assert (forall ((C2 tptp.set_nat) (A tptp.set_nat) (B tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat C2))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.sup_sup_set_nat A) B))))))
% 6.73/7.05 (assert (forall ((C2 tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat C2))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.sup_sup_rat A) B))))))
% 6.73/7.05 (assert (forall ((C2 tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat C2))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.sup_sup_nat A) B))))))
% 6.73/7.05 (assert (forall ((C2 tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int C2))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.sup_sup_int A) B))))))
% 6.73/7.05 (assert (= tptp.ord_less_eq_set_nat (lambda ((A5 tptp.set_nat) (B4 tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat A5) B4) B4))))
% 6.73/7.05 (assert (= tptp.ord_less_eq_rat (lambda ((A5 tptp.rat) (B4 tptp.rat)) (= (@ (@ tptp.sup_sup_rat A5) B4) B4))))
% 6.73/7.05 (assert (= tptp.ord_less_eq_nat (lambda ((A5 tptp.nat) (B4 tptp.nat)) (= (@ (@ tptp.sup_sup_nat A5) B4) B4))))
% 6.73/7.05 (assert (= tptp.ord_less_eq_int (lambda ((A5 tptp.int) (B4 tptp.int)) (= (@ (@ tptp.sup_sup_int A5) B4) B4))))
% 6.73/7.05 (assert (= tptp.ord_less_eq_set_nat (lambda ((B4 tptp.set_nat) (A5 tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat A5) B4) A5))))
% 6.73/7.05 (assert (= tptp.ord_less_eq_rat (lambda ((B4 tptp.rat) (A5 tptp.rat)) (= (@ (@ tptp.sup_sup_rat A5) B4) A5))))
% 6.73/7.05 (assert (= tptp.ord_less_eq_nat (lambda ((B4 tptp.nat) (A5 tptp.nat)) (= (@ (@ tptp.sup_sup_nat A5) B4) A5))))
% 6.73/7.05 (assert (= tptp.ord_less_eq_int (lambda ((B4 tptp.int) (A5 tptp.int)) (= (@ (@ tptp.sup_sup_int A5) B4) A5))))
% 6.73/7.05 (assert (forall ((B tptp.set_nat) (A tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat B) (@ (@ tptp.sup_sup_set_nat A) B))))
% 6.73/7.05 (assert (forall ((B tptp.rat) (A tptp.rat)) (@ (@ tptp.ord_less_eq_rat B) (@ (@ tptp.sup_sup_rat A) B))))
% 6.73/7.05 (assert (forall ((B tptp.nat) (A tptp.nat)) (@ (@ tptp.ord_less_eq_nat B) (@ (@ tptp.sup_sup_nat A) B))))
% 6.73/7.05 (assert (forall ((B tptp.int) (A tptp.int)) (@ (@ tptp.ord_less_eq_int B) (@ (@ tptp.sup_sup_int A) B))))
% 6.73/7.05 (assert (forall ((A tptp.set_nat) (B tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat A) (@ (@ tptp.sup_sup_set_nat A) B))))
% 6.73/7.05 (assert (forall ((A tptp.rat) (B tptp.rat)) (@ (@ tptp.ord_less_eq_rat A) (@ (@ tptp.sup_sup_rat A) B))))
% 6.73/7.05 (assert (forall ((A tptp.nat) (B tptp.nat)) (@ (@ tptp.ord_less_eq_nat A) (@ (@ tptp.sup_sup_nat A) B))))
% 6.73/7.05 (assert (forall ((A tptp.int) (B tptp.int)) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.sup_sup_int A) B))))
% 6.73/7.05 (assert (= tptp.ord_less_eq_set_nat (lambda ((B4 tptp.set_nat) (A5 tptp.set_nat)) (= A5 (@ (@ tptp.sup_sup_set_nat A5) B4)))))
% 6.73/7.05 (assert (= tptp.ord_less_eq_rat (lambda ((B4 tptp.rat) (A5 tptp.rat)) (= A5 (@ (@ tptp.sup_sup_rat A5) B4)))))
% 6.73/7.05 (assert (= tptp.ord_less_eq_nat (lambda ((B4 tptp.nat) (A5 tptp.nat)) (= A5 (@ (@ tptp.sup_sup_nat A5) B4)))))
% 6.73/7.05 (assert (= tptp.ord_less_eq_int (lambda ((B4 tptp.int) (A5 tptp.int)) (= A5 (@ (@ tptp.sup_sup_int A5) B4)))))
% 6.73/7.05 (assert (forall ((B tptp.set_nat) (A tptp.set_nat) (C2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat B) A) (=> (@ (@ tptp.ord_less_eq_set_nat C2) A) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.sup_sup_set_nat B) C2)) A)))))
% 6.73/7.05 (assert (forall ((B tptp.rat) (A tptp.rat) (C2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat B) A) (=> (@ (@ tptp.ord_less_eq_rat C2) A) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.sup_sup_rat B) C2)) A)))))
% 6.73/7.05 (assert (forall ((B tptp.nat) (A tptp.nat) (C2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B) A) (=> (@ (@ tptp.ord_less_eq_nat C2) A) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.sup_sup_nat B) C2)) A)))))
% 6.73/7.05 (assert (forall ((B tptp.int) (A tptp.int) (C2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B) A) (=> (@ (@ tptp.ord_less_eq_int C2) A) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.sup_sup_int B) C2)) A)))))
% 6.73/7.05 (assert (forall ((B tptp.set_nat) (C2 tptp.set_nat) (A tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.sup_sup_set_nat B) C2)) A) (not (=> (@ (@ tptp.ord_less_eq_set_nat B) A) (not (@ (@ tptp.ord_less_eq_set_nat C2) A)))))))
% 6.73/7.05 (assert (forall ((B tptp.rat) (C2 tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.sup_sup_rat B) C2)) A) (not (=> (@ (@ tptp.ord_less_eq_rat B) A) (not (@ (@ tptp.ord_less_eq_rat C2) A)))))))
% 6.73/7.05 (assert (forall ((B tptp.nat) (C2 tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.sup_sup_nat B) C2)) A) (not (=> (@ (@ tptp.ord_less_eq_nat B) A) (not (@ (@ tptp.ord_less_eq_nat C2) A)))))))
% 6.73/7.05 (assert (forall ((B tptp.int) (C2 tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.sup_sup_int B) C2)) A) (not (=> (@ (@ tptp.ord_less_eq_int B) A) (not (@ (@ tptp.ord_less_eq_int C2) A)))))))
% 6.73/7.05 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat X) Y) (= (@ (@ tptp.sup_sup_set_nat X) Y) Y))))
% 6.73/7.05 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X) Y) (= (@ (@ tptp.sup_sup_rat X) Y) Y))))
% 6.73/7.05 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X) Y) (= (@ (@ tptp.sup_sup_nat X) Y) Y))))
% 6.73/7.05 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X) Y) (= (@ (@ tptp.sup_sup_int X) Y) Y))))
% 6.73/7.05 (assert (forall ((Y tptp.set_nat) (X tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat Y) X) (= (@ (@ tptp.sup_sup_set_nat X) Y) X))))
% 6.73/7.05 (assert (forall ((Y tptp.rat) (X tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat Y) X) (= (@ (@ tptp.sup_sup_rat X) Y) X))))
% 6.73/7.05 (assert (forall ((Y tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Y) X) (= (@ (@ tptp.sup_sup_nat X) Y) X))))
% 6.73/7.05 (assert (forall ((Y tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Y) X) (= (@ (@ tptp.sup_sup_int X) Y) X))))
% 6.73/7.05 (assert (forall ((A tptp.set_nat) (B tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A) B) (= (@ (@ tptp.sup_sup_set_nat A) B) B))))
% 6.73/7.05 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (= (@ (@ tptp.sup_sup_rat A) B) B))))
% 6.73/7.05 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= (@ (@ tptp.sup_sup_nat A) B) B))))
% 6.73/7.05 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (= (@ (@ tptp.sup_sup_int A) B) B))))
% 6.73/7.05 (assert (forall ((B tptp.set_nat) (A tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat B) A) (= (@ (@ tptp.sup_sup_set_nat A) B) A))))
% 6.73/7.05 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat B) A) (= (@ (@ tptp.sup_sup_rat A) B) A))))
% 6.73/7.05 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B) A) (= (@ (@ tptp.sup_sup_nat A) B) A))))
% 6.73/7.05 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B) A) (= (@ (@ tptp.sup_sup_int A) B) A))))
% 6.73/7.05 (assert (forall ((F2 (-> tptp.set_nat tptp.set_nat tptp.set_nat)) (X tptp.set_nat) (Y tptp.set_nat)) (=> (forall ((X3 tptp.set_nat) (Y3 tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat X3) (@ (@ F2 X3) Y3))) (=> (forall ((X3 tptp.set_nat) (Y3 tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat Y3) (@ (@ F2 X3) Y3))) (=> (forall ((X3 tptp.set_nat) (Y3 tptp.set_nat) (Z tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat Y3) X3) (=> (@ (@ tptp.ord_less_eq_set_nat Z) X3) (@ (@ tptp.ord_less_eq_set_nat (@ (@ F2 Y3) Z)) X3)))) (= (@ (@ tptp.sup_sup_set_nat X) Y) (@ (@ F2 X) Y)))))))
% 6.73/7.05 (assert (forall ((F2 (-> tptp.rat tptp.rat tptp.rat)) (X tptp.rat) (Y tptp.rat)) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (@ (@ tptp.ord_less_eq_rat X3) (@ (@ F2 X3) Y3))) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (@ (@ tptp.ord_less_eq_rat Y3) (@ (@ F2 X3) Y3))) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat) (Z tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat Y3) X3) (=> (@ (@ tptp.ord_less_eq_rat Z) X3) (@ (@ tptp.ord_less_eq_rat (@ (@ F2 Y3) Z)) X3)))) (= (@ (@ tptp.sup_sup_rat X) Y) (@ (@ F2 X) Y)))))))
% 6.73/7.05 (assert (forall ((F2 (-> tptp.nat tptp.nat tptp.nat)) (X tptp.nat) (Y tptp.nat)) (=> (forall ((X3 tptp.nat) (Y3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat X3) (@ (@ F2 X3) Y3))) (=> (forall ((X3 tptp.nat) (Y3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat Y3) (@ (@ F2 X3) Y3))) (=> (forall ((X3 tptp.nat) (Y3 tptp.nat) (Z tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Y3) X3) (=> (@ (@ tptp.ord_less_eq_nat Z) X3) (@ (@ tptp.ord_less_eq_nat (@ (@ F2 Y3) Z)) X3)))) (= (@ (@ tptp.sup_sup_nat X) Y) (@ (@ F2 X) Y)))))))
% 6.73/7.05 (assert (forall ((F2 (-> tptp.int tptp.int tptp.int)) (X tptp.int) (Y tptp.int)) (=> (forall ((X3 tptp.int) (Y3 tptp.int)) (@ (@ tptp.ord_less_eq_int X3) (@ (@ F2 X3) Y3))) (=> (forall ((X3 tptp.int) (Y3 tptp.int)) (@ (@ tptp.ord_less_eq_int Y3) (@ (@ F2 X3) Y3))) (=> (forall ((X3 tptp.int) (Y3 tptp.int) (Z tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Y3) X3) (=> (@ (@ tptp.ord_less_eq_int Z) X3) (@ (@ tptp.ord_less_eq_int (@ (@ F2 Y3) Z)) X3)))) (= (@ (@ tptp.sup_sup_int X) Y) (@ (@ F2 X) Y)))))))
% 6.73/7.05 (assert (forall ((A tptp.set_nat) (B tptp.set_nat)) (=> (= A (@ (@ tptp.sup_sup_set_nat A) B)) (@ (@ tptp.ord_less_eq_set_nat B) A))))
% 6.73/7.05 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (= A (@ (@ tptp.sup_sup_rat A) B)) (@ (@ tptp.ord_less_eq_rat B) A))))
% 6.73/7.05 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (= A (@ (@ tptp.sup_sup_nat A) B)) (@ (@ tptp.ord_less_eq_nat B) A))))
% 6.73/7.05 (assert (forall ((A tptp.int) (B tptp.int)) (=> (= A (@ (@ tptp.sup_sup_int A) B)) (@ (@ tptp.ord_less_eq_int B) A))))
% 6.73/7.05 (assert (forall ((B tptp.set_nat) (A tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat B) A) (= A (@ (@ tptp.sup_sup_set_nat A) B)))))
% 6.73/7.05 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat B) A) (= A (@ (@ tptp.sup_sup_rat A) B)))))
% 6.73/7.05 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B) A) (= A (@ (@ tptp.sup_sup_nat A) B)))))
% 6.73/7.05 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B) A) (= A (@ (@ tptp.sup_sup_int A) B)))))
% 6.73/7.05 (assert (= tptp.ord_less_eq_set_nat (lambda ((X4 tptp.set_nat) (Y4 tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat X4) Y4) Y4))))
% 6.73/7.05 (assert (= tptp.ord_less_eq_rat (lambda ((X4 tptp.rat) (Y4 tptp.rat)) (= (@ (@ tptp.sup_sup_rat X4) Y4) Y4))))
% 6.73/7.05 (assert (= tptp.ord_less_eq_nat (lambda ((X4 tptp.nat) (Y4 tptp.nat)) (= (@ (@ tptp.sup_sup_nat X4) Y4) Y4))))
% 6.73/7.05 (assert (= tptp.ord_less_eq_int (lambda ((X4 tptp.int) (Y4 tptp.int)) (= (@ (@ tptp.sup_sup_int X4) Y4) Y4))))
% 6.73/7.05 (assert (forall ((Y tptp.set_nat) (X tptp.set_nat) (Z3 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat Y) X) (=> (@ (@ tptp.ord_less_eq_set_nat Z3) X) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.sup_sup_set_nat Y) Z3)) X)))))
% 6.73/7.05 (assert (forall ((Y tptp.rat) (X tptp.rat) (Z3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat Y) X) (=> (@ (@ tptp.ord_less_eq_rat Z3) X) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.sup_sup_rat Y) Z3)) X)))))
% 6.73/7.05 (assert (forall ((Y tptp.nat) (X tptp.nat) (Z3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Y) X) (=> (@ (@ tptp.ord_less_eq_nat Z3) X) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.sup_sup_nat Y) Z3)) X)))))
% 6.73/7.05 (assert (forall ((Y tptp.int) (X tptp.int) (Z3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Y) X) (=> (@ (@ tptp.ord_less_eq_int Z3) X) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.sup_sup_int Y) Z3)) X)))))
% 6.73/7.05 (assert (forall ((A tptp.set_nat) (C2 tptp.set_nat) (B tptp.set_nat) (D tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A) C2) (=> (@ (@ tptp.ord_less_eq_set_nat B) D) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.sup_sup_set_nat A) B)) (@ (@ tptp.sup_sup_set_nat C2) D))))))
% 6.73/7.05 (assert (forall ((A tptp.rat) (C2 tptp.rat) (B tptp.rat) (D tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) C2) (=> (@ (@ tptp.ord_less_eq_rat B) D) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.sup_sup_rat A) B)) (@ (@ tptp.sup_sup_rat C2) D))))))
% 6.73/7.05 (assert (forall ((A tptp.nat) (C2 tptp.nat) (B tptp.nat) (D tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) C2) (=> (@ (@ tptp.ord_less_eq_nat B) D) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.sup_sup_nat A) B)) (@ (@ tptp.sup_sup_nat C2) D))))))
% 6.73/7.05 (assert (forall ((A tptp.int) (C2 tptp.int) (B tptp.int) (D tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) C2) (=> (@ (@ tptp.ord_less_eq_int B) D) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.sup_sup_int A) B)) (@ (@ tptp.sup_sup_int C2) D))))))
% 6.73/7.05 (assert (forall ((C2 tptp.set_nat) (A tptp.set_nat) (D tptp.set_nat) (B tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat C2) A) (=> (@ (@ tptp.ord_less_eq_set_nat D) B) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.sup_sup_set_nat C2) D)) (@ (@ tptp.sup_sup_set_nat A) B))))))
% 6.73/7.05 (assert (forall ((C2 tptp.rat) (A tptp.rat) (D tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat C2) A) (=> (@ (@ tptp.ord_less_eq_rat D) B) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.sup_sup_rat C2) D)) (@ (@ tptp.sup_sup_rat A) B))))))
% 6.73/7.05 (assert (forall ((C2 tptp.nat) (A tptp.nat) (D tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat C2) A) (=> (@ (@ tptp.ord_less_eq_nat D) B) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.sup_sup_nat C2) D)) (@ (@ tptp.sup_sup_nat A) B))))))
% 6.73/7.05 (assert (forall ((C2 tptp.int) (A tptp.int) (D tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int C2) A) (=> (@ (@ tptp.ord_less_eq_int D) B) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.sup_sup_int C2) D)) (@ (@ tptp.sup_sup_int A) B))))))
% 6.73/7.05 (assert (forall ((X tptp.set_nat) (B tptp.set_nat) (A tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat X))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.sup_sup_set_nat A) B))))))
% 6.73/7.05 (assert (forall ((X tptp.rat) (B tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat X))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.sup_sup_rat A) B))))))
% 6.73/7.05 (assert (forall ((X tptp.nat) (B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat X))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.sup_sup_nat A) B))))))
% 6.73/7.05 (assert (forall ((X tptp.int) (B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int X))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.sup_sup_int A) B))))))
% 6.73/7.05 (assert (forall ((X tptp.set_nat) (A tptp.set_nat) (B tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat X))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.sup_sup_set_nat A) B))))))
% 6.73/7.05 (assert (forall ((X tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat X))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.sup_sup_rat A) B))))))
% 6.73/7.05 (assert (forall ((X tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat X))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.sup_sup_nat A) B))))))
% 6.73/7.05 (assert (forall ((X tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int X))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.sup_sup_int A) B))))))
% 6.73/7.05 (assert (forall ((Y tptp.set_nat) (X tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat Y) (@ (@ tptp.sup_sup_set_nat X) Y))))
% 6.73/7.05 (assert (forall ((Y tptp.rat) (X tptp.rat)) (@ (@ tptp.ord_less_eq_rat Y) (@ (@ tptp.sup_sup_rat X) Y))))
% 6.73/7.05 (assert (forall ((Y tptp.nat) (X tptp.nat)) (@ (@ tptp.ord_less_eq_nat Y) (@ (@ tptp.sup_sup_nat X) Y))))
% 6.73/7.05 (assert (forall ((Y tptp.int) (X tptp.int)) (@ (@ tptp.ord_less_eq_int Y) (@ (@ tptp.sup_sup_int X) Y))))
% 6.73/7.05 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat X) (@ (@ tptp.sup_sup_set_nat X) Y))))
% 6.73/7.05 (assert (forall ((X tptp.rat) (Y tptp.rat)) (@ (@ tptp.ord_less_eq_rat X) (@ (@ tptp.sup_sup_rat X) Y))))
% 6.73/7.05 (assert (forall ((X tptp.nat) (Y tptp.nat)) (@ (@ tptp.ord_less_eq_nat X) (@ (@ tptp.sup_sup_nat X) Y))))
% 6.73/7.05 (assert (forall ((X tptp.int) (Y tptp.int)) (@ (@ tptp.ord_less_eq_int X) (@ (@ tptp.sup_sup_int X) Y))))
% 6.73/7.05 (assert (forall ((A tptp.set_nat) (X tptp.set_nat) (B tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A) X) (=> (@ (@ tptp.ord_less_eq_set_nat B) X) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.sup_sup_set_nat A) B)) X)))))
% 6.73/7.05 (assert (forall ((A tptp.rat) (X tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) X) (=> (@ (@ tptp.ord_less_eq_rat B) X) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.sup_sup_rat A) B)) X)))))
% 6.73/7.05 (assert (forall ((A tptp.nat) (X tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) X) (=> (@ (@ tptp.ord_less_eq_nat B) X) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.sup_sup_nat A) B)) X)))))
% 6.73/7.05 (assert (forall ((A tptp.int) (X tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) X) (=> (@ (@ tptp.ord_less_eq_int B) X) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.sup_sup_int A) B)) X)))))
% 6.73/7.05 (assert (forall ((A tptp.set_nat) (B tptp.set_nat) (X tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.sup_sup_set_nat A) B)) X) (not (=> (@ (@ tptp.ord_less_eq_set_nat A) X) (not (@ (@ tptp.ord_less_eq_set_nat B) X)))))))
% 6.73/7.05 (assert (forall ((A tptp.rat) (B tptp.rat) (X tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.sup_sup_rat A) B)) X) (not (=> (@ (@ tptp.ord_less_eq_rat A) X) (not (@ (@ tptp.ord_less_eq_rat B) X)))))))
% 6.73/7.05 (assert (forall ((A tptp.nat) (B tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.sup_sup_nat A) B)) X) (not (=> (@ (@ tptp.ord_less_eq_nat A) X) (not (@ (@ tptp.ord_less_eq_nat B) X)))))))
% 6.73/7.05 (assert (forall ((A tptp.int) (B tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.sup_sup_int A) B)) X) (not (=> (@ (@ tptp.ord_less_eq_int A) X) (not (@ (@ tptp.ord_less_eq_int B) X)))))))
% 6.73/7.05 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat X) (@ (@ tptp.sup_sup_set_nat X) Y))))
% 6.73/7.05 (assert (forall ((X tptp.rat) (Y tptp.rat)) (@ (@ tptp.ord_less_eq_rat X) (@ (@ tptp.sup_sup_rat X) Y))))
% 6.73/7.05 (assert (forall ((X tptp.nat) (Y tptp.nat)) (@ (@ tptp.ord_less_eq_nat X) (@ (@ tptp.sup_sup_nat X) Y))))
% 6.73/7.05 (assert (forall ((X tptp.int) (Y tptp.int)) (@ (@ tptp.ord_less_eq_int X) (@ (@ tptp.sup_sup_int X) Y))))
% 6.73/7.05 (assert (forall ((Y tptp.set_nat) (X tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat Y) (@ (@ tptp.sup_sup_set_nat X) Y))))
% 6.73/7.05 (assert (forall ((Y tptp.rat) (X tptp.rat)) (@ (@ tptp.ord_less_eq_rat Y) (@ (@ tptp.sup_sup_rat X) Y))))
% 6.73/7.05 (assert (forall ((Y tptp.nat) (X tptp.nat)) (@ (@ tptp.ord_less_eq_nat Y) (@ (@ tptp.sup_sup_nat X) Y))))
% 6.73/7.05 (assert (forall ((Y tptp.int) (X tptp.int)) (@ (@ tptp.ord_less_eq_int Y) (@ (@ tptp.sup_sup_int X) Y))))
% 6.73/7.05 (assert (forall ((TreeList2 tptp.list_VEBT_VEBT) (N tptp.nat) (Summary tptp.vEBT_VEBT) (M2 tptp.nat) (Deg tptp.nat) (Mi tptp.nat) (Ma tptp.nat)) (let ((_let_1 (= Mi Ma))) (let ((_let_2 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList2)) (@ (@ tptp.vEBT_invar_vebt X3) N))) (=> (@ (@ tptp.vEBT_invar_vebt Summary) M2) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList2) (@ _let_2 M2)) (=> (= M2 N) (=> (= Deg (@ (@ tptp.plus_plus_nat N) M2)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M2)) (= (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I3)) X7)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary) I3)))) (=> (=> _let_1 (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X3) X_12)))))) (=> (@ (@ tptp.ord_less_eq_nat Mi) Ma) (=> (@ (@ tptp.ord_less_nat Ma) (@ _let_2 Deg)) (=> (=> (not _let_1) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M2)) (and (=> (= (@ (@ tptp.vEBT_VEBT_high Ma) N) I3) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I3)) (@ (@ tptp.vEBT_VEBT_low Ma) N))) (forall ((X3 tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X3) N) I3) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I3)) (@ (@ tptp.vEBT_VEBT_low X3) N))) (and (@ (@ tptp.ord_less_nat Mi) X3) (@ (@ tptp.ord_less_eq_nat X3) Ma)))))))) (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList2) Summary)) Deg)))))))))))))))
% 6.73/7.05 (assert (forall ((TreeList2 tptp.list_VEBT_VEBT) (N tptp.nat) (Summary tptp.vEBT_VEBT) (M2 tptp.nat) (Deg tptp.nat) (Mi tptp.nat) (Ma tptp.nat)) (let ((_let_1 (= Mi Ma))) (let ((_let_2 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList2)) (@ (@ tptp.vEBT_invar_vebt X3) N))) (=> (@ (@ tptp.vEBT_invar_vebt Summary) M2) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList2) (@ _let_2 M2)) (=> (= M2 (@ tptp.suc N)) (=> (= Deg (@ (@ tptp.plus_plus_nat N) M2)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M2)) (= (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I3)) X7)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary) I3)))) (=> (=> _let_1 (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X3) X_12)))))) (=> (@ (@ tptp.ord_less_eq_nat Mi) Ma) (=> (@ (@ tptp.ord_less_nat Ma) (@ _let_2 Deg)) (=> (=> (not _let_1) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M2)) (and (=> (= (@ (@ tptp.vEBT_VEBT_high Ma) N) I3) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I3)) (@ (@ tptp.vEBT_VEBT_low Ma) N))) (forall ((X3 tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X3) N) I3) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I3)) (@ (@ tptp.vEBT_VEBT_low X3) N))) (and (@ (@ tptp.ord_less_nat Mi) X3) (@ (@ tptp.ord_less_eq_nat X3) Ma)))))))) (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList2) Summary)) Deg)))))))))))))))
% 6.73/7.05 (assert (forall ((A12 tptp.vEBT_VEBT) (A23 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt A12) A23) (=> (=> (exists ((A3 Bool) (B3 Bool)) (= A12 (@ (@ tptp.vEBT_Leaf A3) B3))) (not (= A23 (@ tptp.suc tptp.zero_zero_nat)))) (=> (forall ((TreeList tptp.list_VEBT_VEBT) (N3 tptp.nat) (Summary2 tptp.vEBT_VEBT) (M tptp.nat) (Deg2 tptp.nat)) (=> (= A12 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Deg2) TreeList) Summary2)) (=> (= A23 Deg2) (=> (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 TreeList)) (@ (@ tptp.vEBT_invar_vebt X5) N3))) (=> (@ (@ tptp.vEBT_invar_vebt Summary2) M) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M)) (=> (= M N3) (=> (= Deg2 (@ (@ tptp.plus_plus_nat N3) M)) (=> (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) X_1))) (not (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 TreeList)) (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X5) X_1))))))))))))))) (=> (forall ((TreeList tptp.list_VEBT_VEBT) (N3 tptp.nat) (Summary2 tptp.vEBT_VEBT) (M tptp.nat) (Deg2 tptp.nat)) (=> (= A12 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Deg2) TreeList) Summary2)) (=> (= A23 Deg2) (=> (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 TreeList)) (@ (@ tptp.vEBT_invar_vebt X5) N3))) (=> (@ (@ tptp.vEBT_invar_vebt Summary2) M) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M)) (=> (= M (@ tptp.suc N3)) (=> (= Deg2 (@ (@ tptp.plus_plus_nat N3) M)) (=> (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) X_1))) (not (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 TreeList)) (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X5) X_1))))))))))))))) (=> (forall ((TreeList tptp.list_VEBT_VEBT) (N3 tptp.nat) (Summary2 tptp.vEBT_VEBT) (M 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) TreeList) Summary2)) (=> (= A23 Deg2) (=> (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 TreeList)) (@ (@ tptp.vEBT_invar_vebt X5) N3))) (=> (@ (@ tptp.vEBT_invar_vebt Summary2) M) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList) (@ _let_2 M)) (=> (= M N3) (=> (= Deg2 (@ (@ tptp.plus_plus_nat N3) M)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M)) (= (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I4)) X7)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I4)))) (=> (=> _let_1 (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 TreeList)) (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X5) X_1)))))) (=> (@ (@ tptp.ord_less_eq_nat Mi2) Ma2) (=> (@ (@ tptp.ord_less_nat Ma2) (@ _let_2 Deg2)) (not (=> (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 Ma2) N3) I4) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I4)) (@ (@ tptp.vEBT_VEBT_low Ma2) N3))) (forall ((X5 tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X5) N3) I4) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I4)) (@ (@ tptp.vEBT_VEBT_low X5) N3))) (and (@ (@ tptp.ord_less_nat Mi2) X5) (@ (@ tptp.ord_less_eq_nat X5) Ma2))))))))))))))))))))))) (not (forall ((TreeList tptp.list_VEBT_VEBT) (N3 tptp.nat) (Summary2 tptp.vEBT_VEBT) (M 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) TreeList) Summary2)) (=> (= A23 Deg2) (=> (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 TreeList)) (@ (@ tptp.vEBT_invar_vebt X5) N3))) (=> (@ (@ tptp.vEBT_invar_vebt Summary2) M) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList) (@ _let_2 M)) (=> (= M (@ tptp.suc N3)) (=> (= Deg2 (@ (@ tptp.plus_plus_nat N3) M)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M)) (= (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I4)) X7)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I4)))) (=> (=> _let_1 (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 TreeList)) (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X5) X_1)))))) (=> (@ (@ tptp.ord_less_eq_nat Mi2) Ma2) (=> (@ (@ tptp.ord_less_nat Ma2) (@ _let_2 Deg2)) (not (=> (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 Ma2) N3) I4) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I4)) (@ (@ tptp.vEBT_VEBT_low Ma2) N3))) (forall ((X5 tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X5) N3) I4) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I4)) (@ (@ tptp.vEBT_VEBT_low X5) N3))) (and (@ (@ tptp.ord_less_nat Mi2) X5) (@ (@ tptp.ord_less_eq_nat X5) Ma2)))))))))))))))))))))))))))))))
% 6.73/7.05 (assert (= tptp.vEBT_invar_vebt (lambda ((A13 tptp.vEBT_VEBT) (A24 tptp.nat)) (or (and (exists ((A5 Bool) (B4 Bool)) (= A13 (@ (@ tptp.vEBT_Leaf A5) B4))) (= A24 (@ tptp.suc tptp.zero_zero_nat))) (exists ((TreeList4 tptp.list_VEBT_VEBT) (N4 tptp.nat) (Summary4 tptp.vEBT_VEBT)) (and (= A13 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) A24) TreeList4) Summary4)) (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList4)) (@ (@ tptp.vEBT_invar_vebt X4) N4))) (@ (@ tptp.vEBT_invar_vebt Summary4) N4) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList4) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N4)) (= A24 (@ (@ tptp.plus_plus_nat N4) N4)) (not (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary4) X7))) (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList4)) (not (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X4) X7))))))) (exists ((TreeList4 tptp.list_VEBT_VEBT) (N4 tptp.nat) (Summary4 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc N4))) (and (= A13 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) A24) TreeList4) Summary4)) (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList4)) (@ (@ tptp.vEBT_invar_vebt X4) N4))) (@ (@ tptp.vEBT_invar_vebt Summary4) _let_1) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList4) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_1)) (= A24 (@ (@ tptp.plus_plus_nat N4) _let_1)) (not (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary4) X7))) (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList4)) (not (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X4) X7)))))))) (exists ((TreeList4 tptp.list_VEBT_VEBT) (N4 tptp.nat) (Summary4 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 (= A13 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi3) Ma3))) A24) TreeList4) Summary4)) (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList4)) (@ (@ tptp.vEBT_invar_vebt X4) N4))) (@ (@ tptp.vEBT_invar_vebt Summary4) N4) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList4) (@ _let_2 N4)) (= A24 (@ (@ tptp.plus_plus_nat N4) N4)) (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N4)) (= (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList4) I)) X7)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary4) I)))) (=> _let_1 (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList4)) (not (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X4) X7)))))) (@ (@ tptp.ord_less_eq_nat Mi3) Ma3) (@ (@ tptp.ord_less_nat Ma3) (@ _let_2 A24)) (=> (not _let_1) (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N4)) (and (=> (= (@ (@ tptp.vEBT_VEBT_high Ma3) N4) I) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList4) I)) (@ (@ tptp.vEBT_VEBT_low Ma3) N4))) (forall ((X4 tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X4) N4) I) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList4) I)) (@ (@ tptp.vEBT_VEBT_low X4) N4))) (and (@ (@ tptp.ord_less_nat Mi3) X4) (@ (@ tptp.ord_less_eq_nat X4) Ma3)))))))))))) (exists ((TreeList4 tptp.list_VEBT_VEBT) (N4 tptp.nat) (Summary4 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 N4))) (and (= A13 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi3) Ma3))) A24) TreeList4) Summary4)) (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList4)) (@ (@ tptp.vEBT_invar_vebt X4) N4))) (@ (@ tptp.vEBT_invar_vebt Summary4) _let_3) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList4) (@ _let_2 _let_3)) (= A24 (@ (@ tptp.plus_plus_nat N4) _let_3)) (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.suc N4))) (= (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList4) I)) X7)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary4) I)))) (=> _let_1 (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList4)) (not (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X4) X7)))))) (@ (@ tptp.ord_less_eq_nat Mi3) Ma3) (@ (@ tptp.ord_less_nat Ma3) (@ _let_2 A24)) (=> (not _let_1) (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.suc N4))) (and (=> (= (@ (@ tptp.vEBT_VEBT_high Ma3) N4) I) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList4) I)) (@ (@ tptp.vEBT_VEBT_low Ma3) N4))) (forall ((X4 tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X4) N4) I) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList4) I)) (@ (@ tptp.vEBT_VEBT_low X4) N4))) (and (@ (@ tptp.ord_less_nat Mi3) X4) (@ (@ tptp.ord_less_eq_nat X4) Ma3)))))))))))))))))
% 6.73/7.05 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat) (Z3 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.inf_in2572325071724192079at_nat X))) (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.sup_su6327502436637775413at_nat (@ _let_1 Y)) (@ _let_1 Z3))) (@ _let_1 (@ (@ tptp.sup_su6327502436637775413at_nat Y) Z3))))))
% 6.73/7.05 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat) (Z3 tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat X))) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.sup_sup_set_nat (@ _let_1 Y)) (@ _let_1 Z3))) (@ _let_1 (@ (@ tptp.sup_sup_set_nat Y) Z3))))))
% 6.73/7.05 (assert (forall ((X tptp.rat) (Y tptp.rat) (Z3 tptp.rat)) (let ((_let_1 (@ tptp.inf_inf_rat X))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.sup_sup_rat (@ _let_1 Y)) (@ _let_1 Z3))) (@ _let_1 (@ (@ tptp.sup_sup_rat Y) Z3))))))
% 6.73/7.05 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z3 tptp.nat)) (let ((_let_1 (@ tptp.inf_inf_nat X))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.sup_sup_nat (@ _let_1 Y)) (@ _let_1 Z3))) (@ _let_1 (@ (@ tptp.sup_sup_nat Y) Z3))))))
% 6.73/7.05 (assert (forall ((X tptp.int) (Y tptp.int) (Z3 tptp.int)) (let ((_let_1 (@ tptp.inf_inf_int X))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.sup_sup_int (@ _let_1 Y)) (@ _let_1 Z3))) (@ _let_1 (@ (@ tptp.sup_sup_int Y) Z3))))))
% 6.73/7.05 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat) (Z3 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.sup_su6327502436637775413at_nat X))) (@ (@ tptp.ord_le3146513528884898305at_nat (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat Y) Z3))) (@ (@ tptp.inf_in2572325071724192079at_nat (@ _let_1 Y)) (@ _let_1 Z3))))))
% 6.73/7.05 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat) (Z3 tptp.set_nat)) (let ((_let_1 (@ tptp.sup_sup_set_nat X))) (@ (@ tptp.ord_less_eq_set_nat (@ _let_1 (@ (@ tptp.inf_inf_set_nat Y) Z3))) (@ (@ tptp.inf_inf_set_nat (@ _let_1 Y)) (@ _let_1 Z3))))))
% 6.73/7.05 (assert (forall ((X tptp.rat) (Y tptp.rat) (Z3 tptp.rat)) (let ((_let_1 (@ tptp.sup_sup_rat X))) (@ (@ tptp.ord_less_eq_rat (@ _let_1 (@ (@ tptp.inf_inf_rat Y) Z3))) (@ (@ tptp.inf_inf_rat (@ _let_1 Y)) (@ _let_1 Z3))))))
% 6.73/7.05 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z3 tptp.nat)) (let ((_let_1 (@ tptp.sup_sup_nat X))) (@ (@ tptp.ord_less_eq_nat (@ _let_1 (@ (@ tptp.inf_inf_nat Y) Z3))) (@ (@ tptp.inf_inf_nat (@ _let_1 Y)) (@ _let_1 Z3))))))
% 6.73/7.05 (assert (forall ((X tptp.int) (Y tptp.int) (Z3 tptp.int)) (let ((_let_1 (@ tptp.sup_sup_int X))) (@ (@ tptp.ord_less_eq_int (@ _let_1 (@ (@ tptp.inf_inf_int Y) Z3))) (@ (@ tptp.inf_inf_int (@ _let_1 Y)) (@ _let_1 Z3))))))
% 6.73/7.05 (assert (= tptp.vEBT_V5917875025757280293ildren (lambda ((N4 tptp.nat) (TreeList4 tptp.list_VEBT_VEBT) (X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList4) (@ (@ tptp.vEBT_VEBT_high X4) N4))) (@ (@ tptp.vEBT_VEBT_low X4) N4)))))
% 6.73/7.05 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (N tptp.nat) (Va3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat Va3) _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 Va3))) (=> (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)))))))))))
% 6.73/7.05 (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)))))))))
% 6.73/7.05 (assert (forall ((A4 tptp.set_nat) (N tptp.nat)) (=> (@ tptp.finite_finite_nat A4) (=> (not (@ (@ tptp.member_nat N) A4)) (= (@ tptp.nat_set_encode (@ (@ tptp.insert_nat N) A4)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (@ tptp.nat_set_encode A4)))))))
% 6.73/7.05 (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))))))
% 6.73/7.05 (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))))))
% 6.73/7.05 (assert (forall ((X tptp.nat) (Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (Xn tptp.nat) (H tptp.nat) (Summary tptp.vEBT_VEBT) (TreeList2 tptp.list_VEBT_VEBT) (L 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 H) (=> (= 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) L) (=> (@ (@ tptp.ord_less_nat _let_5) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)) (=> (= Newnode (@ (@ tptp.vEBT_vebt_delete (@ _let_4 H)) L)) (=> (= Newlist (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList2) H) 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 H) _let_3)) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ (@ tptp.nth_VEBT_VEBT Newlist) H))))) Ma)))) Deg) Newlist) Summary))))))))))))))))))))
% 6.73/7.05 (assert (forall ((Mi tptp.nat) (X tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (H tptp.nat) (L 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 H) (=> (= (@ (@ tptp.vEBT_VEBT_low X) _let_2) L) (=> (= Newnode (@ (@ tptp.vEBT_vebt_delete (@ (@ tptp.nth_VEBT_VEBT TreeList2) H)) L)) (=> (not (@ tptp.vEBT_VEBT_minNull Newnode)) (=> (= Newlist (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList2) H) 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 H) (@ (@ tptp.power_power_nat _let_1) _let_2))) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ (@ tptp.nth_VEBT_VEBT Newlist) H))))) Ma)))) Deg) Newlist) Summary)))))))))))))))))
% 6.73/7.05 (assert (forall ((B tptp.int) (A tptp.int) (Q2 tptp.int) (R3 tptp.int)) (let ((_let_1 (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.product_Pair_int_int 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 R3)) (@ (@ (@ tptp.eucl_rel_int (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ _let_1 A))) (@ _let_1 B)) (@ _let_2 (@ (@ tptp.minus_minus_int (@ _let_1 R3)) tptp.one_one_int)))))))))
% 6.73/7.05 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (I2 tptp.nat) (X tptp.vEBT_VEBT)) (= (@ tptp.size_s6755466524823107622T_VEBT (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs2) I2) X)) (@ tptp.size_s6755466524823107622T_VEBT Xs2))))
% 6.73/7.05 (assert (forall ((Xs2 tptp.list_o) (I2 tptp.nat) (X Bool)) (= (@ tptp.size_size_list_o (@ (@ (@ tptp.list_update_o Xs2) I2) X)) (@ tptp.size_size_list_o Xs2))))
% 6.73/7.05 (assert (forall ((Xs2 tptp.list_nat) (I2 tptp.nat) (X tptp.nat)) (= (@ tptp.size_size_list_nat (@ (@ (@ tptp.list_update_nat Xs2) I2) X)) (@ tptp.size_size_list_nat Xs2))))
% 6.73/7.05 (assert (forall ((Xs2 tptp.list_int) (I2 tptp.nat) (X tptp.int)) (= (@ tptp.size_size_list_int (@ (@ (@ tptp.list_update_int Xs2) I2) X)) (@ tptp.size_size_list_int Xs2))))
% 6.73/7.05 (assert (forall ((Option tptp.option4927543243414619207at_nat)) (=> (not (= Option tptp.none_P5556105721700978146at_nat)) (= (@ tptp.some_P7363390416028606310at_nat (@ tptp.the_Pr8591224930841456533at_nat Option)) Option))))
% 6.73/7.05 (assert (forall ((Option tptp.option_nat)) (=> (not (= Option tptp.none_nat)) (= (@ tptp.some_nat (@ tptp.the_nat Option)) Option))))
% 6.73/7.05 (assert (forall ((Option tptp.option_num)) (=> (not (= Option tptp.none_num)) (= (@ tptp.some_num (@ tptp.the_num Option)) Option))))
% 6.73/7.05 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (I2 tptp.nat) (X tptp.vEBT_VEBT)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_s6755466524823107622T_VEBT Xs2)) I2) (= (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs2) I2) X) Xs2))))
% 6.73/7.05 (assert (forall ((Xs2 tptp.list_o) (I2 tptp.nat) (X Bool)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_o Xs2)) I2) (= (@ (@ (@ tptp.list_update_o Xs2) I2) X) Xs2))))
% 6.73/7.05 (assert (forall ((Xs2 tptp.list_nat) (I2 tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_nat Xs2)) I2) (= (@ (@ (@ tptp.list_update_nat Xs2) I2) X) Xs2))))
% 6.73/7.05 (assert (forall ((Xs2 tptp.list_int) (I2 tptp.nat) (X tptp.int)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_int Xs2)) I2) (= (@ (@ (@ tptp.list_update_int Xs2) I2) X) Xs2))))
% 6.73/7.05 (assert (= (@ tptp.nat_set_encode tptp.bot_bot_set_nat) tptp.zero_zero_nat))
% 6.73/7.05 (assert (forall ((I2 tptp.nat) (Xs2 tptp.list_VEBT_VEBT) (X tptp.vEBT_VEBT)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (= (@ (@ tptp.nth_VEBT_VEBT (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs2) I2) X)) I2) X))))
% 6.73/7.05 (assert (forall ((I2 tptp.nat) (Xs2 tptp.list_o) (X Bool)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_o Xs2)) (= (@ (@ tptp.nth_o (@ (@ (@ tptp.list_update_o Xs2) I2) X)) I2) X))))
% 6.73/7.05 (assert (forall ((I2 tptp.nat) (Xs2 tptp.list_nat) (X tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_nat Xs2)) (= (@ (@ tptp.nth_nat (@ (@ (@ tptp.list_update_nat Xs2) I2) X)) I2) X))))
% 6.73/7.05 (assert (forall ((I2 tptp.nat) (Xs2 tptp.list_int) (X tptp.int)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_int Xs2)) (= (@ (@ tptp.nth_int (@ (@ (@ tptp.list_update_int Xs2) I2) X)) I2) X))))
% 6.73/7.05 (assert (forall ((I2 tptp.nat) (Xs2 tptp.list_VEBT_VEBT) (J2 tptp.nat)) (let ((_let_1 (@ tptp.nth_VEBT_VEBT Xs2))) (let ((_let_2 (@ tptp.size_s6755466524823107622T_VEBT Xs2))) (=> (@ (@ tptp.ord_less_nat I2) _let_2) (=> (@ (@ tptp.ord_less_nat J2) _let_2) (= (@ tptp.set_VEBT_VEBT2 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs2) I2) (@ _let_1 J2))) J2) (@ _let_1 I2))) (@ tptp.set_VEBT_VEBT2 Xs2))))))))
% 6.73/7.05 (assert (forall ((I2 tptp.nat) (Xs2 tptp.list_o) (J2 tptp.nat)) (let ((_let_1 (@ tptp.nth_o Xs2))) (let ((_let_2 (@ tptp.size_size_list_o Xs2))) (=> (@ (@ tptp.ord_less_nat I2) _let_2) (=> (@ (@ tptp.ord_less_nat J2) _let_2) (= (@ tptp.set_o2 (@ (@ (@ tptp.list_update_o (@ (@ (@ tptp.list_update_o Xs2) I2) (@ _let_1 J2))) J2) (@ _let_1 I2))) (@ tptp.set_o2 Xs2))))))))
% 6.73/7.05 (assert (forall ((I2 tptp.nat) (Xs2 tptp.list_nat) (J2 tptp.nat)) (let ((_let_1 (@ tptp.nth_nat Xs2))) (let ((_let_2 (@ tptp.size_size_list_nat Xs2))) (=> (@ (@ tptp.ord_less_nat I2) _let_2) (=> (@ (@ tptp.ord_less_nat J2) _let_2) (= (@ tptp.set_nat2 (@ (@ (@ tptp.list_update_nat (@ (@ (@ tptp.list_update_nat Xs2) I2) (@ _let_1 J2))) J2) (@ _let_1 I2))) (@ tptp.set_nat2 Xs2))))))))
% 6.73/7.05 (assert (forall ((I2 tptp.nat) (Xs2 tptp.list_int) (J2 tptp.nat)) (let ((_let_1 (@ tptp.nth_int Xs2))) (let ((_let_2 (@ tptp.size_size_list_int Xs2))) (=> (@ (@ tptp.ord_less_nat I2) _let_2) (=> (@ (@ tptp.ord_less_nat J2) _let_2) (= (@ tptp.set_int2 (@ (@ (@ tptp.list_update_int (@ (@ (@ tptp.list_update_int Xs2) I2) (@ _let_1 J2))) J2) (@ _let_1 I2))) (@ tptp.set_int2 Xs2))))))))
% 6.73/7.05 (assert (forall ((A tptp.int) (B tptp.int) (Q2 tptp.int) (R3 tptp.int) (Q4 tptp.int) (R5 tptp.int)) (let ((_let_1 (@ (@ tptp.eucl_rel_int A) B))) (=> (@ _let_1 (@ (@ tptp.product_Pair_int_int Q2) R3)) (=> (@ _let_1 (@ (@ tptp.product_Pair_int_int Q4) R5)) (= Q2 Q4))))))
% 6.73/7.05 (assert (forall ((A tptp.int) (B tptp.int) (Q2 tptp.int) (R3 tptp.int) (Q4 tptp.int) (R5 tptp.int)) (let ((_let_1 (@ (@ tptp.eucl_rel_int A) B))) (=> (@ _let_1 (@ (@ tptp.product_Pair_int_int Q2) R3)) (=> (@ _let_1 (@ (@ tptp.product_Pair_int_int Q4) R5)) (= R3 R5))))))
% 6.73/7.05 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (I2 tptp.nat) (X tptp.vEBT_VEBT) (Ys tptp.list_VEBT_VEBT) (Y tptp.vEBT_VEBT)) (= (@ (@ tptp.zip_VE537291747668921783T_VEBT (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs2) I2) X)) (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Ys) I2) Y)) (@ (@ (@ tptp.list_u6961636818849549845T_VEBT (@ (@ tptp.zip_VE537291747668921783T_VEBT Xs2) Ys)) I2) (@ (@ tptp.produc537772716801021591T_VEBT X) Y)))))
% 6.73/7.05 (assert (forall ((Xs2 tptp.list_Code_integer) (I2 tptp.nat) (X tptp.code_integer) (Ys tptp.list_Code_integer) (Y tptp.code_integer)) (= (@ (@ tptp.zip_Co3543743374963494515nteger (@ (@ (@ tptp.list_u5447711078246177391nteger Xs2) I2) X)) (@ (@ (@ tptp.list_u5447711078246177391nteger Ys) I2) Y)) (@ (@ (@ tptp.list_u2254550707601501961nteger (@ (@ tptp.zip_Co3543743374963494515nteger Xs2) Ys)) I2) (@ (@ tptp.produc1086072967326762835nteger X) Y)))))
% 6.73/7.05 (assert (forall ((Xs2 tptp.list_P6011104703257516679at_nat) (I2 tptp.nat) (X tptp.product_prod_nat_nat) (Ys tptp.list_P6011104703257516679at_nat) (Y tptp.product_prod_nat_nat)) (= (@ (@ tptp.zip_Pr4664179122662387191at_nat (@ (@ (@ tptp.list_u6180841689913720943at_nat Xs2) I2) X)) (@ (@ (@ tptp.list_u6180841689913720943at_nat Ys) I2) Y)) (@ (@ (@ tptp.list_u5003261594476800725at_nat (@ (@ tptp.zip_Pr4664179122662387191at_nat Xs2) Ys)) I2) (@ (@ tptp.produc6161850002892822231at_nat X) Y)))))
% 6.73/7.05 (assert (forall ((Xs2 tptp.list_s1210847774152347623at_nat) (I2 tptp.nat) (X tptp.set_Pr1261947904930325089at_nat) (Ys tptp.list_s1210847774152347623at_nat) (Y tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.zip_se5600341670672612855at_nat (@ (@ (@ tptp.list_u8444657558853818831at_nat Xs2) I2) X)) (@ (@ (@ tptp.list_u8444657558853818831at_nat Ys) I2) Y)) (@ (@ (@ tptp.list_u4696772448584712917at_nat (@ (@ tptp.zip_se5600341670672612855at_nat Xs2) Ys)) I2) (@ (@ tptp.produc2922128104949294807at_nat X) Y)))))
% 6.73/7.05 (assert (forall ((Xs2 tptp.list_nat) (I2 tptp.nat) (X tptp.nat) (Ys tptp.list_nat) (Y tptp.nat)) (= (@ (@ tptp.zip_nat_nat (@ (@ (@ tptp.list_update_nat Xs2) I2) X)) (@ (@ (@ tptp.list_update_nat Ys) I2) Y)) (@ (@ (@ tptp.list_u6180841689913720943at_nat (@ (@ tptp.zip_nat_nat Xs2) Ys)) I2) (@ (@ tptp.product_Pair_nat_nat X) Y)))))
% 6.73/7.05 (assert (forall ((Xs2 tptp.list_int) (I2 tptp.nat) (X tptp.int) (Ys tptp.list_int) (Y tptp.int)) (= (@ (@ tptp.zip_int_int (@ (@ (@ tptp.list_update_int Xs2) I2) X)) (@ (@ (@ tptp.list_update_int Ys) I2) Y)) (@ (@ (@ tptp.list_u3002344382305578791nt_int (@ (@ tptp.zip_int_int Xs2) Ys)) I2) (@ (@ tptp.product_Pair_int_int X) Y)))))
% 6.73/7.05 (assert (forall ((X2 tptp.product_prod_nat_nat)) (= (@ tptp.the_Pr8591224930841456533at_nat (@ tptp.some_P7363390416028606310at_nat X2)) X2)))
% 6.73/7.05 (assert (forall ((X2 tptp.nat)) (= (@ tptp.the_nat (@ tptp.some_nat X2)) X2)))
% 6.73/7.05 (assert (forall ((X2 tptp.num)) (= (@ tptp.the_num (@ tptp.some_num X2)) X2)))
% 6.73/7.05 (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)))))))
% 6.73/7.05 (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)))))))
% 6.73/7.05 (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)))))))
% 6.73/7.05 (assert (forall ((K2 tptp.int)) (@ (@ (@ tptp.eucl_rel_int K2) tptp.zero_zero_int) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) K2))))
% 6.73/7.05 (assert (forall ((K2 tptp.int) (L tptp.int) (Q2 tptp.int) (R3 tptp.int)) (=> (@ (@ (@ tptp.eucl_rel_int K2) L) (@ (@ tptp.product_Pair_int_int Q2) R3)) (= (@ (@ tptp.divide_divide_int K2) L) Q2))))
% 6.73/7.05 (assert (forall ((X tptp.nat) (Xs2 tptp.list_nat) (I2 tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.cons_nat X))) (= (@ (@ (@ tptp.list_update_nat (@ _let_1 Xs2)) (@ tptp.suc I2)) Y) (@ _let_1 (@ (@ (@ tptp.list_update_nat Xs2) I2) Y))))))
% 6.73/7.05 (assert (forall ((X tptp.vEBT_VEBT) (Xs2 tptp.list_VEBT_VEBT) (I2 tptp.nat) (Y tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.cons_VEBT_VEBT X))) (= (@ (@ (@ tptp.list_u1324408373059187874T_VEBT (@ _let_1 Xs2)) (@ tptp.suc I2)) Y) (@ _let_1 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs2) I2) Y))))))
% 6.73/7.05 (assert (forall ((X tptp.nat) (Xs2 tptp.list_nat) (Y tptp.nat)) (= (@ (@ (@ tptp.list_update_nat (@ (@ tptp.cons_nat X) Xs2)) tptp.zero_zero_nat) Y) (@ (@ tptp.cons_nat Y) Xs2))))
% 6.73/7.05 (assert (forall ((X tptp.vEBT_VEBT) (Xs2 tptp.list_VEBT_VEBT) (Y tptp.vEBT_VEBT)) (= (@ (@ (@ tptp.list_u1324408373059187874T_VEBT (@ (@ tptp.cons_VEBT_VEBT X) Xs2)) tptp.zero_zero_nat) Y) (@ (@ tptp.cons_VEBT_VEBT Y) Xs2))))
% 6.73/7.05 (assert (forall ((A4 tptp.set_nat) (B5 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A4) (=> (@ tptp.finite_finite_nat B5) (= (= (@ tptp.nat_set_encode A4) (@ tptp.nat_set_encode B5)) (= A4 B5))))))
% 6.73/7.05 (assert (forall ((Option tptp.option4927543243414619207at_nat)) (=> (not (= Option tptp.none_P5556105721700978146at_nat)) (= Option (@ tptp.some_P7363390416028606310at_nat (@ tptp.the_Pr8591224930841456533at_nat Option))))))
% 6.73/7.05 (assert (forall ((Option tptp.option_nat)) (=> (not (= Option tptp.none_nat)) (= Option (@ tptp.some_nat (@ tptp.the_nat Option))))))
% 6.73/7.05 (assert (forall ((Option tptp.option_num)) (=> (not (= Option tptp.none_num)) (= Option (@ tptp.some_num (@ tptp.the_num Option))))))
% 6.73/7.05 (assert (forall ((L tptp.int) (K2 tptp.int) (Q2 tptp.int)) (=> (not (= L tptp.zero_zero_int)) (=> (= K2 (@ (@ tptp.times_times_int Q2) L)) (@ (@ (@ tptp.eucl_rel_int K2) L) (@ (@ tptp.product_Pair_int_int Q2) tptp.zero_zero_int))))))
% 6.73/7.05 (assert (forall ((N tptp.nat) (Xs2 tptp.list_complex) (X tptp.complex)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s3451745648224563538omplex Xs2)) (@ (@ tptp.member_complex X) (@ tptp.set_complex2 (@ (@ (@ tptp.list_update_complex Xs2) N) X))))))
% 6.73/7.05 (assert (forall ((N tptp.nat) (Xs2 tptp.list_real) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_real Xs2)) (@ (@ tptp.member_real X) (@ tptp.set_real2 (@ (@ (@ tptp.list_update_real Xs2) N) X))))))
% 6.73/7.05 (assert (forall ((N tptp.nat) (Xs2 tptp.list_set_nat) (X tptp.set_nat)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s3254054031482475050et_nat Xs2)) (@ (@ tptp.member_set_nat X) (@ tptp.set_set_nat2 (@ (@ (@ tptp.list_update_set_nat Xs2) N) X))))))
% 6.73/7.05 (assert (forall ((N tptp.nat) (Xs2 tptp.list_VEBT_VEBT) (X tptp.vEBT_VEBT)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs2) N) X))))))
% 6.73/7.05 (assert (forall ((N tptp.nat) (Xs2 tptp.list_o) (X Bool)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_o Xs2)) (@ (@ tptp.member_o X) (@ tptp.set_o2 (@ (@ (@ tptp.list_update_o Xs2) N) X))))))
% 6.73/7.05 (assert (forall ((N tptp.nat) (Xs2 tptp.list_nat) (X tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_nat Xs2)) (@ (@ tptp.member_nat X) (@ tptp.set_nat2 (@ (@ (@ tptp.list_update_nat Xs2) N) X))))))
% 6.73/7.05 (assert (forall ((N tptp.nat) (Xs2 tptp.list_int) (X tptp.int)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_int Xs2)) (@ (@ tptp.member_int X) (@ tptp.set_int2 (@ (@ (@ tptp.list_update_int Xs2) N) X))))))
% 6.73/7.05 (assert (forall ((I2 tptp.nat) (Xs2 tptp.list_VEBT_VEBT) (X tptp.vEBT_VEBT)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (= (= (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs2) I2) X) Xs2) (= (@ (@ tptp.nth_VEBT_VEBT Xs2) I2) X)))))
% 6.73/7.05 (assert (forall ((I2 tptp.nat) (Xs2 tptp.list_o) (X Bool)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_o Xs2)) (= (= (@ (@ (@ tptp.list_update_o Xs2) I2) X) Xs2) (= (@ (@ tptp.nth_o Xs2) I2) X)))))
% 6.73/7.05 (assert (forall ((I2 tptp.nat) (Xs2 tptp.list_nat) (X tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_nat Xs2)) (= (= (@ (@ (@ tptp.list_update_nat Xs2) I2) X) Xs2) (= (@ (@ tptp.nth_nat Xs2) I2) X)))))
% 6.73/7.05 (assert (forall ((I2 tptp.nat) (Xs2 tptp.list_int) (X tptp.int)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_int Xs2)) (= (= (@ (@ (@ tptp.list_update_int Xs2) I2) X) Xs2) (= (@ (@ tptp.nth_int Xs2) I2) X)))))
% 6.73/7.05 (assert (forall ((I2 tptp.nat) (Xs2 tptp.list_VEBT_VEBT) (J2 tptp.nat) (X tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ tptp.nth_VEBT_VEBT (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs2) I2) X)) J2))) (let ((_let_2 (= I2 J2))) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (and (=> _let_2 (= _let_1 X)) (=> (not _let_2) (= _let_1 (@ (@ tptp.nth_VEBT_VEBT Xs2) J2)))))))))
% 6.73/7.05 (assert (forall ((I2 tptp.nat) (Xs2 tptp.list_o) (X Bool) (J2 tptp.nat)) (let ((_let_1 (= I2 J2))) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_o Xs2)) (= (@ (@ tptp.nth_o (@ (@ (@ tptp.list_update_o Xs2) I2) X)) J2) (and (=> _let_1 X) (=> (not _let_1) (@ (@ tptp.nth_o Xs2) J2))))))))
% 6.73/7.05 (assert (forall ((I2 tptp.nat) (Xs2 tptp.list_nat) (J2 tptp.nat) (X tptp.nat)) (let ((_let_1 (@ (@ tptp.nth_nat (@ (@ (@ tptp.list_update_nat Xs2) I2) X)) J2))) (let ((_let_2 (= I2 J2))) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_nat Xs2)) (and (=> _let_2 (= _let_1 X)) (=> (not _let_2) (= _let_1 (@ (@ tptp.nth_nat Xs2) J2)))))))))
% 6.73/7.05 (assert (forall ((I2 tptp.nat) (Xs2 tptp.list_int) (J2 tptp.nat) (X tptp.int)) (let ((_let_1 (@ (@ tptp.nth_int (@ (@ (@ tptp.list_update_int Xs2) I2) X)) J2))) (let ((_let_2 (= I2 J2))) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_int Xs2)) (and (=> _let_2 (= _let_1 X)) (=> (not _let_2) (= _let_1 (@ (@ tptp.nth_int Xs2) J2)))))))))
% 6.73/7.05 (assert (forall ((A4 tptp.set_nat)) (=> (not (@ tptp.finite_finite_nat A4)) (= (@ tptp.nat_set_encode A4) tptp.zero_zero_nat))))
% 6.73/7.05 (assert (forall ((K2 tptp.int) (L tptp.int) (Q2 tptp.int) (R3 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int L))) (let ((_let_2 (@ _let_1 tptp.zero_zero_int))) (let ((_let_3 (@ (@ tptp.ord_less_int tptp.zero_zero_int) L))) (= (@ (@ (@ tptp.eucl_rel_int K2) L) (@ (@ tptp.product_Pair_int_int Q2) R3)) (and (= K2 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int L) Q2)) R3)) (=> _let_3 (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) R3) (@ (@ tptp.ord_less_int R3) L))) (=> (not _let_3) (and (=> _let_2 (and (@ _let_1 R3) (@ (@ tptp.ord_less_eq_int R3) tptp.zero_zero_int))) (=> (not _let_2) (= Q2 tptp.zero_zero_int)))))))))))
% 6.73/7.05 (assert (forall ((B tptp.int) (A tptp.int) (Q2 tptp.int) (R3 tptp.int)) (let ((_let_1 (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.plus_plus_int tptp.one_one_int))) (let ((_let_3 (@ tptp.product_Pair_int_int Q2))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B) (=> (@ (@ (@ tptp.eucl_rel_int A) B) (@ _let_3 R3)) (@ (@ (@ tptp.eucl_rel_int (@ _let_2 (@ _let_1 A))) (@ _let_1 B)) (@ _let_3 (@ _let_2 (@ _let_1 R3)))))))))))
% 6.73/7.05 (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)))))))))))))
% 6.73/7.05 (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))))))))))))))
% 6.73/7.05 (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)))))))))))))))))))))
% 6.73/7.05 (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)))))))))))))))
% 6.73/7.05 (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)))))))))))))))
% 6.73/7.05 (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)))))))))))))))))))))
% 6.73/7.05 (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)))))))))))))))))))))))))))
% 6.73/7.05 (assert (forall ((X tptp.nat) (Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (Xn tptp.nat) (H tptp.nat) (Summary tptp.vEBT_VEBT) (TreeList2 tptp.list_VEBT_VEBT) (L tptp.nat)) (let ((_let_1 (@ tptp.nth_VEBT_VEBT TreeList2))) (let ((_let_2 (@ (@ tptp.vEBT_vebt_delete (@ _let_1 H)) L))) (let ((_let_3 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList2) H) _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) H))) (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 H) (=> (= 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) L) (=> (@ (@ 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 H) _let_7)) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ _let_4 H))))) Ma)))) Deg) _let_3) Summary))))))))))))))))))))))))))
% 6.73/7.05 (assert (= tptp.vEBT_VEBT_set_vebt (lambda ((T2 tptp.vEBT_VEBT)) (@ tptp.collect_nat (@ tptp.vEBT_vebt_member T2)))))
% 6.73/7.05 (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 ((Y4 tptp.nat)) (and (@ (@ tptp.vEBT_vebt_member T) Y4) (@ (@ tptp.ord_less_nat Y4) X)))) tptp.bot_bot_set_nat)))))
% 6.73/7.05 (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 ((Y4 tptp.nat)) (and (@ (@ tptp.vEBT_vebt_member T) Y4) (@ (@ tptp.ord_less_nat X) Y4)))) tptp.bot_bot_set_nat)))))
% 6.73/7.05 (assert (forall ((B tptp.rat) (C2 tptp.rat) (A tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.ord_max_rat B) C2)) A) (and (@ (@ tptp.ord_less_eq_rat B) A) (@ (@ tptp.ord_less_eq_rat C2) A)))))
% 6.73/7.05 (assert (forall ((B tptp.num) (C2 tptp.num) (A tptp.num)) (= (@ (@ tptp.ord_less_eq_num (@ (@ tptp.ord_max_num B) C2)) A) (and (@ (@ tptp.ord_less_eq_num B) A) (@ (@ tptp.ord_less_eq_num C2) A)))))
% 6.73/7.05 (assert (forall ((B tptp.nat) (C2 tptp.nat) (A tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.ord_max_nat B) C2)) A) (and (@ (@ tptp.ord_less_eq_nat B) A) (@ (@ tptp.ord_less_eq_nat C2) A)))))
% 6.73/7.05 (assert (forall ((B tptp.int) (C2 tptp.int) (A tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.ord_max_int B) C2)) A) (and (@ (@ tptp.ord_less_eq_int B) A) (@ (@ tptp.ord_less_eq_int C2) A)))))
% 6.73/7.05 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (= (@ (@ tptp.ord_max_rat A) B) B))))
% 6.73/7.05 (assert (forall ((A tptp.num) (B tptp.num)) (=> (@ (@ tptp.ord_less_eq_num A) B) (= (@ (@ tptp.ord_max_num A) B) B))))
% 6.73/7.05 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= (@ (@ tptp.ord_max_nat A) B) B))))
% 6.73/7.05 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (= (@ (@ tptp.ord_max_int A) B) B))))
% 6.73/7.05 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat B) A) (= (@ (@ tptp.ord_max_rat A) B) A))))
% 6.73/7.05 (assert (forall ((B tptp.num) (A tptp.num)) (=> (@ (@ tptp.ord_less_eq_num B) A) (= (@ (@ tptp.ord_max_num A) B) A))))
% 6.73/7.05 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B) A) (= (@ (@ tptp.ord_max_nat A) B) A))))
% 6.73/7.05 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B) A) (= (@ (@ tptp.ord_max_int A) B) A))))
% 6.73/7.05 (assert (forall ((X tptp.set_nat)) (= (@ (@ tptp.ord_max_set_nat tptp.bot_bot_set_nat) X) X)))
% 6.73/7.05 (assert (forall ((X tptp.set_int)) (= (@ (@ tptp.ord_max_set_int tptp.bot_bot_set_int) X) X)))
% 6.73/7.05 (assert (forall ((X tptp.set_real)) (= (@ (@ tptp.ord_max_set_real tptp.bot_bot_set_real) X) X)))
% 6.73/7.05 (assert (forall ((X tptp.nat)) (= (@ (@ tptp.ord_max_nat tptp.bot_bot_nat) X) X)))
% 6.73/7.05 (assert (forall ((X tptp.set_nat)) (= (@ (@ tptp.ord_max_set_nat X) tptp.bot_bot_set_nat) X)))
% 6.73/7.05 (assert (forall ((X tptp.set_int)) (= (@ (@ tptp.ord_max_set_int X) tptp.bot_bot_set_int) X)))
% 6.73/7.05 (assert (forall ((X tptp.set_real)) (= (@ (@ tptp.ord_max_set_real X) tptp.bot_bot_set_real) X)))
% 6.73/7.05 (assert (forall ((X tptp.nat)) (= (@ (@ tptp.ord_max_nat X) tptp.bot_bot_nat) X)))
% 6.73/7.05 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_max_nat (@ tptp.suc M2)) (@ tptp.suc N)) (@ tptp.suc (@ (@ tptp.ord_max_nat M2) N)))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.ord_max_nat tptp.zero_zero_nat) A) A)))
% 6.73/7.05 (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)))))
% 6.73/7.05 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.ord_max_nat A) tptp.zero_zero_nat) A)))
% 6.73/7.05 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_max_nat tptp.zero_zero_nat) N) N)))
% 6.73/7.05 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_max_nat N) tptp.zero_zero_nat) N)))
% 6.73/7.05 (assert (forall ((K2 tptp.nat)) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_nat N4) K2))))))
% 6.73/7.05 (assert (forall ((U tptp.num) (V2 tptp.num)) (let ((_let_1 (@ tptp.numera1916890842035813515d_enat U))) (let ((_let_2 (@ tptp.numera1916890842035813515d_enat V2))) (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)))))))))
% 6.73/7.05 (assert (forall ((U tptp.num) (V2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real U))) (let ((_let_2 (@ tptp.numeral_numeral_real V2))) (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)))))))))
% 6.73/7.05 (assert (forall ((U tptp.num) (V2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat U))) (let ((_let_2 (@ tptp.numeral_numeral_rat V2))) (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)))))))))
% 6.73/7.05 (assert (forall ((U tptp.num) (V2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat U))) (let ((_let_2 (@ tptp.numeral_numeral_nat V2))) (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)))))))))
% 6.73/7.05 (assert (forall ((U tptp.num) (V2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int U))) (let ((_let_2 (@ tptp.numeral_numeral_int V2))) (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)))))))))
% 6.73/7.05 (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))))
% 6.73/7.05 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numera1916890842035813515d_enat X))) (= (@ (@ tptp.ord_ma741700101516333627d_enat tptp.zero_z5237406670263579293d_enat) _let_1) _let_1))))
% 6.73/7.05 (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))))
% 6.73/7.05 (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))))
% 6.73/7.05 (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))))
% 6.73/7.05 (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))))
% 6.73/7.05 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numera1916890842035813515d_enat X))) (= (@ (@ tptp.ord_ma741700101516333627d_enat _let_1) tptp.zero_z5237406670263579293d_enat) _let_1))))
% 6.73/7.05 (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))))
% 6.73/7.05 (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))))
% 6.73/7.05 (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))))
% 6.73/7.05 (assert (= (@ (@ tptp.ord_max_Code_integer tptp.one_one_Code_integer) tptp.zero_z3403309356797280102nteger) tptp.one_one_Code_integer))
% 6.73/7.05 (assert (= (@ (@ tptp.ord_max_real tptp.one_one_real) tptp.zero_zero_real) tptp.one_one_real))
% 6.73/7.05 (assert (= (@ (@ tptp.ord_max_rat tptp.one_one_rat) tptp.zero_zero_rat) tptp.one_one_rat))
% 6.73/7.05 (assert (= (@ (@ tptp.ord_max_nat tptp.one_one_nat) tptp.zero_zero_nat) tptp.one_one_nat))
% 6.73/7.05 (assert (= (@ (@ tptp.ord_max_int tptp.one_one_int) tptp.zero_zero_int) tptp.one_one_int))
% 6.73/7.05 (assert (= (@ (@ tptp.ord_max_Code_integer tptp.zero_z3403309356797280102nteger) tptp.one_one_Code_integer) tptp.one_one_Code_integer))
% 6.73/7.05 (assert (= (@ (@ tptp.ord_max_real tptp.zero_zero_real) tptp.one_one_real) tptp.one_one_real))
% 6.73/7.05 (assert (= (@ (@ tptp.ord_max_rat tptp.zero_zero_rat) tptp.one_one_rat) tptp.one_one_rat))
% 6.73/7.05 (assert (= (@ (@ tptp.ord_max_nat tptp.zero_zero_nat) tptp.one_one_nat) tptp.one_one_nat))
% 6.73/7.05 (assert (= (@ (@ tptp.ord_max_int tptp.zero_zero_int) tptp.one_one_int) tptp.one_one_int))
% 6.73/7.05 (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))))
% 6.73/7.05 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numera1916890842035813515d_enat X))) (= (@ (@ tptp.ord_ma741700101516333627d_enat tptp.one_on7984719198319812577d_enat) _let_1) _let_1))))
% 6.73/7.05 (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))))
% 6.73/7.05 (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))))
% 6.73/7.05 (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))))
% 6.73/7.05 (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))))
% 6.73/7.05 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numera1916890842035813515d_enat X))) (= (@ (@ tptp.ord_ma741700101516333627d_enat _let_1) tptp.one_on7984719198319812577d_enat) _let_1))))
% 6.73/7.05 (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))))
% 6.73/7.05 (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))))
% 6.73/7.05 (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))))
% 6.73/7.05 (assert (forall ((N tptp.nat)) (= (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((I tptp.nat)) (@ (@ tptp.ord_less_eq_nat I) N)))) (@ tptp.suc N))))
% 6.73/7.05 (assert (forall ((Mi tptp.nat) (X tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (H tptp.nat) (L tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ tptp.vEBT_vebt_delete (@ (@ tptp.nth_VEBT_VEBT TreeList2) H)) L))) (let ((_let_2 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList2) H) _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) H))) (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 H) (=> (= (@ (@ tptp.vEBT_VEBT_low X) _let_5) L) (=> (@ (@ 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 H) _let_6)) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ _let_3 H))))) Ma)))) Deg) _let_2) Summary)))))))))))))))))))))))
% 6.73/7.05 (assert (forall ((Mi tptp.nat) (X tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (H tptp.nat) (L 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 H) (=> (= (@ (@ tptp.vEBT_VEBT_low X) _let_4) L) (=> (= Newnode (@ (@ tptp.vEBT_vebt_delete (@ (@ tptp.nth_VEBT_VEBT TreeList2) H)) L)) (=> (@ tptp.vEBT_VEBT_minNull Newnode) (=> (= Sn (@ (@ tptp.vEBT_vebt_delete Summary) H)) (=> (= Newlist (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList2) H) 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))))))))))))))))))))
% 6.73/7.05 (assert (forall ((Mi tptp.nat) (X tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (H tptp.nat) (L 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) H))) (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 H) (=> (= (@ (@ tptp.vEBT_VEBT_low X) _let_3) L) (=> (= Newnode (@ (@ tptp.vEBT_vebt_delete (@ (@ tptp.nth_VEBT_VEBT TreeList2) H)) L)) (=> (= Newlist (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList2) H) 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 H) _let_4)) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ _let_1 H))))) Ma)))) Deg) Newlist) Summary))))))))))))))))))))))))))
% 6.73/7.05 (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)))))))))))))))))))))))
% 6.73/7.05 (assert (forall ((X tptp.nat) (Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (Xn tptp.nat) (H tptp.nat) (Summary tptp.vEBT_VEBT) (TreeList2 tptp.list_VEBT_VEBT) (L 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 H) (=> (= 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) L) (=> (@ (@ tptp.ord_less_nat _let_7) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)) (=> (= Newnode (@ (@ tptp.vEBT_vebt_delete (@ _let_6 H)) L)) (=> (= Newlist (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList2) H) Newnode)) (=> (@ tptp.vEBT_VEBT_minNull Newnode) (=> (= Sn (@ (@ tptp.vEBT_vebt_delete Summary) H)) (= (@ (@ 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)))))))))))))))))))))))
% 6.73/7.05 (assert (forall ((X tptp.nat) (Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (Xn tptp.nat) (H tptp.nat) (Summary tptp.vEBT_VEBT) (TreeList2 tptp.list_VEBT_VEBT) (L 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) H))) (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 H) (=> (= 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) L) (=> (@ (@ tptp.ord_less_nat _let_13) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)) (=> (= Newnode (@ (@ tptp.vEBT_vebt_delete (@ _let_12 H)) L)) (=> (= Newlist (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList2) H) 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 H) _let_4)) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ _let_1 H))))) Ma)))) Deg) Newlist) Summary)))))))))))))))))))))))))))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (assert (= tptp.ord_max_set_nat (lambda ((A5 tptp.set_nat) (B4 tptp.set_nat)) (@ (@ (@ tptp.if_set_nat (@ (@ tptp.ord_less_eq_set_nat A5) B4)) B4) A5))))
% 6.73/7.05 (assert (= tptp.ord_max_rat (lambda ((A5 tptp.rat) (B4 tptp.rat)) (@ (@ (@ tptp.if_rat (@ (@ tptp.ord_less_eq_rat A5) B4)) B4) A5))))
% 6.73/7.05 (assert (= tptp.ord_max_num (lambda ((A5 tptp.num) (B4 tptp.num)) (@ (@ (@ tptp.if_num (@ (@ tptp.ord_less_eq_num A5) B4)) B4) A5))))
% 6.73/7.05 (assert (= tptp.ord_max_nat (lambda ((A5 tptp.nat) (B4 tptp.nat)) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_eq_nat A5) B4)) B4) A5))))
% 6.73/7.05 (assert (= tptp.ord_max_int (lambda ((A5 tptp.int) (B4 tptp.int)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_eq_int A5) B4)) B4) A5))))
% 6.73/7.05 (assert (= tptp.sup_sup_nat tptp.ord_max_nat))
% 6.73/7.05 (assert (= (lambda ((H2 tptp.complex)) tptp.zero_zero_complex) (@ tptp.times_times_complex tptp.zero_zero_complex)))
% 6.73/7.05 (assert (= (lambda ((H2 tptp.real)) tptp.zero_zero_real) (@ tptp.times_times_real tptp.zero_zero_real)))
% 6.73/7.05 (assert (= (lambda ((H2 tptp.rat)) tptp.zero_zero_rat) (@ tptp.times_times_rat tptp.zero_zero_rat)))
% 6.73/7.05 (assert (= (lambda ((H2 tptp.nat)) tptp.zero_zero_nat) (@ tptp.times_times_nat tptp.zero_zero_nat)))
% 6.73/7.05 (assert (= (lambda ((H2 tptp.int)) tptp.zero_zero_int) (@ tptp.times_times_int tptp.zero_zero_int)))
% 6.73/7.05 (assert (= (lambda ((X4 tptp.code_integer)) X4) (@ tptp.times_3573771949741848930nteger tptp.one_one_Code_integer)))
% 6.73/7.05 (assert (= (lambda ((X4 tptp.complex)) X4) (@ tptp.times_times_complex tptp.one_one_complex)))
% 6.73/7.05 (assert (= (lambda ((X4 tptp.real)) X4) (@ tptp.times_times_real tptp.one_one_real)))
% 6.73/7.05 (assert (= (lambda ((X4 tptp.rat)) X4) (@ tptp.times_times_rat tptp.one_one_rat)))
% 6.73/7.05 (assert (= (lambda ((X4 tptp.nat)) X4) (@ tptp.times_times_nat tptp.one_one_nat)))
% 6.73/7.05 (assert (= (lambda ((X4 tptp.int)) X4) (@ tptp.times_times_int tptp.one_one_int)))
% 6.73/7.05 (assert (forall ((P2 (-> tptp.nat Bool)) (I2 tptp.nat)) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((K3 tptp.nat)) (and (@ P2 K3) (@ (@ tptp.ord_less_nat K3) I2)))))))
% 6.73/7.05 (assert (forall ((F2 (-> tptp.nat tptp.nat)) (U tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat N3) (@ F2 N3))) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ F2 N4)) U)))))))
% 6.73/7.05 (assert (forall ((C2 tptp.rat) (A tptp.rat) (D tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat C2) A) (=> (@ (@ tptp.ord_less_eq_rat D) B) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.ord_max_rat C2) D)) (@ (@ tptp.ord_max_rat A) B))))))
% 6.73/7.05 (assert (forall ((C2 tptp.num) (A tptp.num) (D tptp.num) (B tptp.num)) (=> (@ (@ tptp.ord_less_eq_num C2) A) (=> (@ (@ tptp.ord_less_eq_num D) B) (@ (@ tptp.ord_less_eq_num (@ (@ tptp.ord_max_num C2) D)) (@ (@ tptp.ord_max_num A) B))))))
% 6.73/7.05 (assert (forall ((C2 tptp.nat) (A tptp.nat) (D tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat C2) A) (=> (@ (@ tptp.ord_less_eq_nat D) B) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.ord_max_nat C2) D)) (@ (@ tptp.ord_max_nat A) B))))))
% 6.73/7.05 (assert (forall ((C2 tptp.int) (A tptp.int) (D tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int C2) A) (=> (@ (@ tptp.ord_less_eq_int D) B) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.ord_max_int C2) D)) (@ (@ tptp.ord_max_int A) B))))))
% 6.73/7.05 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat B) A) (= A (@ (@ tptp.ord_max_rat A) B)))))
% 6.73/7.05 (assert (forall ((B tptp.num) (A tptp.num)) (=> (@ (@ tptp.ord_less_eq_num B) A) (= A (@ (@ tptp.ord_max_num A) B)))))
% 6.73/7.05 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B) A) (= A (@ (@ tptp.ord_max_nat A) B)))))
% 6.73/7.05 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B) A) (= A (@ (@ tptp.ord_max_int A) B)))))
% 6.73/7.05 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (= A (@ (@ tptp.ord_max_rat A) B)) (@ (@ tptp.ord_less_eq_rat B) A))))
% 6.73/7.05 (assert (forall ((A tptp.num) (B tptp.num)) (=> (= A (@ (@ tptp.ord_max_num A) B)) (@ (@ tptp.ord_less_eq_num B) A))))
% 6.73/7.05 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (= A (@ (@ tptp.ord_max_nat A) B)) (@ (@ tptp.ord_less_eq_nat B) A))))
% 6.73/7.05 (assert (forall ((A tptp.int) (B tptp.int)) (=> (= A (@ (@ tptp.ord_max_int A) B)) (@ (@ tptp.ord_less_eq_int B) A))))
% 6.73/7.05 (assert (forall ((B tptp.rat) (C2 tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.ord_max_rat B) C2)) A) (not (=> (@ (@ tptp.ord_less_eq_rat B) A) (not (@ (@ tptp.ord_less_eq_rat C2) A)))))))
% 6.73/7.05 (assert (forall ((B tptp.num) (C2 tptp.num) (A tptp.num)) (=> (@ (@ tptp.ord_less_eq_num (@ (@ tptp.ord_max_num B) C2)) A) (not (=> (@ (@ tptp.ord_less_eq_num B) A) (not (@ (@ tptp.ord_less_eq_num C2) A)))))))
% 6.73/7.05 (assert (forall ((B tptp.nat) (C2 tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.ord_max_nat B) C2)) A) (not (=> (@ (@ tptp.ord_less_eq_nat B) A) (not (@ (@ tptp.ord_less_eq_nat C2) A)))))))
% 6.73/7.05 (assert (forall ((B tptp.int) (C2 tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.ord_max_int B) C2)) A) (not (=> (@ (@ tptp.ord_less_eq_int B) A) (not (@ (@ tptp.ord_less_eq_int C2) A)))))))
% 6.73/7.05 (assert (forall ((B tptp.rat) (A tptp.rat) (C2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat B) A) (=> (@ (@ tptp.ord_less_eq_rat C2) A) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.ord_max_rat B) C2)) A)))))
% 6.73/7.05 (assert (forall ((B tptp.num) (A tptp.num) (C2 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num B) A) (=> (@ (@ tptp.ord_less_eq_num C2) A) (@ (@ tptp.ord_less_eq_num (@ (@ tptp.ord_max_num B) C2)) A)))))
% 6.73/7.05 (assert (forall ((B tptp.nat) (A tptp.nat) (C2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B) A) (=> (@ (@ tptp.ord_less_eq_nat C2) A) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.ord_max_nat B) C2)) A)))))
% 6.73/7.05 (assert (forall ((B tptp.int) (A tptp.int) (C2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B) A) (=> (@ (@ tptp.ord_less_eq_int C2) A) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.ord_max_int B) C2)) A)))))
% 6.73/7.05 (assert (= tptp.ord_less_eq_rat (lambda ((B4 tptp.rat) (A5 tptp.rat)) (= A5 (@ (@ tptp.ord_max_rat A5) B4)))))
% 6.73/7.05 (assert (= tptp.ord_less_eq_num (lambda ((B4 tptp.num) (A5 tptp.num)) (= A5 (@ (@ tptp.ord_max_num A5) B4)))))
% 6.73/7.05 (assert (= tptp.ord_less_eq_nat (lambda ((B4 tptp.nat) (A5 tptp.nat)) (= A5 (@ (@ tptp.ord_max_nat A5) B4)))))
% 6.73/7.05 (assert (= tptp.ord_less_eq_int (lambda ((B4 tptp.int) (A5 tptp.int)) (= A5 (@ (@ tptp.ord_max_int A5) B4)))))
% 6.73/7.05 (assert (forall ((A tptp.rat) (B tptp.rat)) (@ (@ tptp.ord_less_eq_rat A) (@ (@ tptp.ord_max_rat A) B))))
% 6.73/7.05 (assert (forall ((A tptp.num) (B tptp.num)) (@ (@ tptp.ord_less_eq_num A) (@ (@ tptp.ord_max_num A) B))))
% 6.73/7.05 (assert (forall ((A tptp.nat) (B tptp.nat)) (@ (@ tptp.ord_less_eq_nat A) (@ (@ tptp.ord_max_nat A) B))))
% 6.73/7.05 (assert (forall ((A tptp.int) (B tptp.int)) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.ord_max_int A) B))))
% 6.73/7.05 (assert (forall ((B tptp.rat) (A tptp.rat)) (@ (@ tptp.ord_less_eq_rat B) (@ (@ tptp.ord_max_rat A) B))))
% 6.73/7.05 (assert (forall ((B tptp.num) (A tptp.num)) (@ (@ tptp.ord_less_eq_num B) (@ (@ tptp.ord_max_num A) B))))
% 6.73/7.05 (assert (forall ((B tptp.nat) (A tptp.nat)) (@ (@ tptp.ord_less_eq_nat B) (@ (@ tptp.ord_max_nat A) B))))
% 6.73/7.05 (assert (forall ((B tptp.int) (A tptp.int)) (@ (@ tptp.ord_less_eq_int B) (@ (@ tptp.ord_max_int A) B))))
% 6.73/7.05 (assert (forall ((Z3 tptp.rat) (X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat Z3))) (= (@ _let_1 (@ (@ tptp.ord_max_rat X) Y)) (or (@ _let_1 X) (@ _let_1 Y))))))
% 6.73/7.05 (assert (forall ((Z3 tptp.num) (X tptp.num) (Y tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_num Z3))) (= (@ _let_1 (@ (@ tptp.ord_max_num X) Y)) (or (@ _let_1 X) (@ _let_1 Y))))))
% 6.73/7.05 (assert (forall ((Z3 tptp.nat) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat Z3))) (= (@ _let_1 (@ (@ tptp.ord_max_nat X) Y)) (or (@ _let_1 X) (@ _let_1 Y))))))
% 6.73/7.05 (assert (forall ((Z3 tptp.int) (X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int Z3))) (= (@ _let_1 (@ (@ tptp.ord_max_int X) Y)) (or (@ _let_1 X) (@ _let_1 Y))))))
% 6.73/7.05 (assert (= tptp.ord_less_eq_rat (lambda ((B4 tptp.rat) (A5 tptp.rat)) (= (@ (@ tptp.ord_max_rat A5) B4) A5))))
% 6.73/7.05 (assert (= tptp.ord_less_eq_num (lambda ((B4 tptp.num) (A5 tptp.num)) (= (@ (@ tptp.ord_max_num A5) B4) A5))))
% 6.73/7.05 (assert (= tptp.ord_less_eq_nat (lambda ((B4 tptp.nat) (A5 tptp.nat)) (= (@ (@ tptp.ord_max_nat A5) B4) A5))))
% 6.73/7.05 (assert (= tptp.ord_less_eq_int (lambda ((B4 tptp.int) (A5 tptp.int)) (= (@ (@ tptp.ord_max_int A5) B4) A5))))
% 6.73/7.05 (assert (= tptp.ord_less_eq_rat (lambda ((A5 tptp.rat) (B4 tptp.rat)) (= (@ (@ tptp.ord_max_rat A5) B4) B4))))
% 6.73/7.05 (assert (= tptp.ord_less_eq_num (lambda ((A5 tptp.num) (B4 tptp.num)) (= (@ (@ tptp.ord_max_num A5) B4) B4))))
% 6.73/7.05 (assert (= tptp.ord_less_eq_nat (lambda ((A5 tptp.nat) (B4 tptp.nat)) (= (@ (@ tptp.ord_max_nat A5) B4) B4))))
% 6.73/7.05 (assert (= tptp.ord_less_eq_int (lambda ((A5 tptp.int) (B4 tptp.int)) (= (@ (@ tptp.ord_max_int A5) B4) B4))))
% 6.73/7.05 (assert (forall ((C2 tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat C2))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.ord_max_rat A) B))))))
% 6.73/7.05 (assert (forall ((C2 tptp.num) (A tptp.num) (B tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_num C2))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.ord_max_num A) B))))))
% 6.73/7.05 (assert (forall ((C2 tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat C2))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.ord_max_nat A) B))))))
% 6.73/7.05 (assert (forall ((C2 tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int C2))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.ord_max_int A) B))))))
% 6.73/7.05 (assert (forall ((C2 tptp.rat) (B tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat C2))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.ord_max_rat A) B))))))
% 6.73/7.05 (assert (forall ((C2 tptp.num) (B tptp.num) (A tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_num C2))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.ord_max_num A) B))))))
% 6.73/7.05 (assert (forall ((C2 tptp.nat) (B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat C2))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.ord_max_nat A) B))))))
% 6.73/7.05 (assert (forall ((C2 tptp.int) (B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int C2))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.ord_max_int A) B))))))
% 6.73/7.05 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat X) Y) (= (@ (@ tptp.ord_max_set_nat X) Y) Y))))
% 6.73/7.05 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X) Y) (= (@ (@ tptp.ord_max_rat X) Y) Y))))
% 6.73/7.05 (assert (forall ((X tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X) Y) (= (@ (@ tptp.ord_max_num X) Y) Y))))
% 6.73/7.05 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X) Y) (= (@ (@ tptp.ord_max_nat X) Y) Y))))
% 6.73/7.05 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X) Y) (= (@ (@ tptp.ord_max_int X) Y) Y))))
% 6.73/7.05 (assert (forall ((Y tptp.set_nat) (X tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat Y) X) (= (@ (@ tptp.ord_max_set_nat X) Y) X))))
% 6.73/7.05 (assert (forall ((Y tptp.rat) (X tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat Y) X) (= (@ (@ tptp.ord_max_rat X) Y) X))))
% 6.73/7.05 (assert (forall ((Y tptp.num) (X tptp.num)) (=> (@ (@ tptp.ord_less_eq_num Y) X) (= (@ (@ tptp.ord_max_num X) Y) X))))
% 6.73/7.05 (assert (forall ((Y tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Y) X) (= (@ (@ tptp.ord_max_nat X) Y) X))))
% 6.73/7.05 (assert (forall ((Y tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Y) X) (= (@ (@ tptp.ord_max_int X) Y) X))))
% 6.73/7.05 (assert (= tptp.ord_max_set_nat (lambda ((A5 tptp.set_nat) (B4 tptp.set_nat)) (@ (@ (@ tptp.if_set_nat (@ (@ tptp.ord_less_eq_set_nat A5) B4)) B4) A5))))
% 6.73/7.05 (assert (= tptp.ord_max_rat (lambda ((A5 tptp.rat) (B4 tptp.rat)) (@ (@ (@ tptp.if_rat (@ (@ tptp.ord_less_eq_rat A5) B4)) B4) A5))))
% 6.73/7.05 (assert (= tptp.ord_max_num (lambda ((A5 tptp.num) (B4 tptp.num)) (@ (@ (@ tptp.if_num (@ (@ tptp.ord_less_eq_num A5) B4)) B4) A5))))
% 6.73/7.05 (assert (= tptp.ord_max_nat (lambda ((A5 tptp.nat) (B4 tptp.nat)) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_eq_nat A5) B4)) B4) A5))))
% 6.73/7.05 (assert (= tptp.ord_max_int (lambda ((A5 tptp.int) (B4 tptp.int)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_eq_int A5) B4)) B4) A5))))
% 6.73/7.05 (assert (forall ((X tptp.real) (Y tptp.real) (Z3 tptp.real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.ord_max_real X) Y)) Z3) (@ (@ tptp.ord_max_real (@ (@ tptp.plus_plus_real X) Z3)) (@ (@ tptp.plus_plus_real Y) Z3)))))
% 6.73/7.05 (assert (forall ((X tptp.rat) (Y tptp.rat) (Z3 tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.ord_max_rat X) Y)) Z3) (@ (@ tptp.ord_max_rat (@ (@ tptp.plus_plus_rat X) Z3)) (@ (@ tptp.plus_plus_rat Y) Z3)))))
% 6.73/7.05 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z3 tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.ord_max_nat X) Y)) Z3) (@ (@ tptp.ord_max_nat (@ (@ tptp.plus_plus_nat X) Z3)) (@ (@ tptp.plus_plus_nat Y) Z3)))))
% 6.73/7.05 (assert (forall ((X tptp.int) (Y tptp.int) (Z3 tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.ord_max_int X) Y)) Z3) (@ (@ tptp.ord_max_int (@ (@ tptp.plus_plus_int X) Z3)) (@ (@ tptp.plus_plus_int Y) Z3)))))
% 6.73/7.05 (assert (forall ((X tptp.real) (Y tptp.real) (Z3 tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real X))) (= (@ _let_1 (@ (@ tptp.ord_max_real Y) Z3)) (@ (@ tptp.ord_max_real (@ _let_1 Y)) (@ _let_1 Z3))))))
% 6.73/7.05 (assert (forall ((X tptp.rat) (Y tptp.rat) (Z3 tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat X))) (= (@ _let_1 (@ (@ tptp.ord_max_rat Y) Z3)) (@ (@ tptp.ord_max_rat (@ _let_1 Y)) (@ _let_1 Z3))))))
% 6.73/7.05 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z3 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat X))) (= (@ _let_1 (@ (@ tptp.ord_max_nat Y) Z3)) (@ (@ tptp.ord_max_nat (@ _let_1 Y)) (@ _let_1 Z3))))))
% 6.73/7.05 (assert (forall ((X tptp.int) (Y tptp.int) (Z3 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int X))) (= (@ _let_1 (@ (@ tptp.ord_max_int Y) Z3)) (@ (@ tptp.ord_max_int (@ _let_1 Y)) (@ _let_1 Z3))))))
% 6.73/7.05 (assert (forall ((X tptp.rat) (Y tptp.rat) (Z3 tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.ord_max_rat X) Y)) Z3) (@ (@ tptp.ord_max_rat (@ (@ tptp.minus_minus_rat X) Z3)) (@ (@ tptp.minus_minus_rat Y) Z3)))))
% 6.73/7.05 (assert (forall ((X tptp.int) (Y tptp.int) (Z3 tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.ord_max_int X) Y)) Z3) (@ (@ tptp.ord_max_int (@ (@ tptp.minus_minus_int X) Z3)) (@ (@ tptp.minus_minus_int Y) Z3)))))
% 6.73/7.05 (assert (forall ((M2 tptp.nat) (N tptp.nat) (Q2 tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.ord_max_nat M2) N)) Q2) (@ (@ tptp.ord_max_nat (@ (@ tptp.plus_plus_nat M2) Q2)) (@ (@ tptp.plus_plus_nat N) Q2)))))
% 6.73/7.05 (assert (forall ((M2 tptp.nat) (N tptp.nat) (Q2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat M2))) (= (@ _let_1 (@ (@ tptp.ord_max_nat N) Q2)) (@ (@ tptp.ord_max_nat (@ _let_1 N)) (@ _let_1 Q2))))))
% 6.73/7.05 (assert (= tptp.vEBT_set_vebt (lambda ((T2 tptp.vEBT_VEBT)) (@ tptp.collect_nat (@ tptp.vEBT_V8194947554948674370ptions T2)))))
% 6.73/7.05 (assert (forall ((M2 tptp.nat) (N tptp.nat) (Q2 tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.ord_max_nat M2) N)) Q2) (@ (@ tptp.ord_max_nat (@ (@ tptp.times_times_nat M2) Q2)) (@ (@ tptp.times_times_nat N) Q2)))))
% 6.73/7.05 (assert (forall ((M2 tptp.nat) (N tptp.nat) (Q2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat M2))) (= (@ _let_1 (@ (@ tptp.ord_max_nat N) Q2)) (@ (@ tptp.ord_max_nat (@ _let_1 N)) (@ _let_1 Q2))))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numera1916890842035813515d_enat N))) (= (@ tptp.numera1916890842035813515d_enat (@ tptp.bit0 N)) (@ (@ tptp.plus_p3455044024723400733d_enat _let_1) _let_1)))))
% 6.73/7.05 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex N))) (= (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 N)) (@ (@ tptp.plus_plus_complex _let_1) _let_1)))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (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)))))
% 6.73/7.05 (assert (= tptp.ord_less_eq_nat (lambda ((A5 tptp.nat) (B4 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int A5)) (@ tptp.semiri1314217659103216013at_int B4)))))
% 6.73/7.05 (assert (forall ((Z3 tptp.complex) (W2 tptp.num)) (let ((_let_1 (@ tptp.power_power_complex Z3))) (let ((_let_2 (@ _let_1 (@ tptp.numeral_numeral_nat W2)))) (= (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 W2))) (@ (@ tptp.times_times_complex _let_2) _let_2))))))
% 6.73/7.05 (assert (forall ((Z3 tptp.real) (W2 tptp.num)) (let ((_let_1 (@ tptp.power_power_real Z3))) (let ((_let_2 (@ _let_1 (@ tptp.numeral_numeral_nat W2)))) (= (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 W2))) (@ (@ tptp.times_times_real _let_2) _let_2))))))
% 6.73/7.06 (assert (forall ((Z3 tptp.rat) (W2 tptp.num)) (let ((_let_1 (@ tptp.power_power_rat Z3))) (let ((_let_2 (@ _let_1 (@ tptp.numeral_numeral_nat W2)))) (= (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 W2))) (@ (@ tptp.times_times_rat _let_2) _let_2))))))
% 6.73/7.06 (assert (forall ((Z3 tptp.nat) (W2 tptp.num)) (let ((_let_1 (@ tptp.power_power_nat Z3))) (let ((_let_2 (@ _let_1 (@ tptp.numeral_numeral_nat W2)))) (= (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 W2))) (@ (@ tptp.times_times_nat _let_2) _let_2))))))
% 6.73/7.06 (assert (forall ((Z3 tptp.int) (W2 tptp.num)) (let ((_let_1 (@ tptp.power_power_int Z3))) (let ((_let_2 (@ _let_1 (@ tptp.numeral_numeral_nat W2)))) (= (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 W2))) (@ (@ tptp.times_times_int _let_2) _let_2))))))
% 6.73/7.06 (assert (forall ((M5 tptp.set_nat) (I2 tptp.nat)) (=> (@ (@ tptp.member_nat tptp.zero_zero_nat) M5) (not (= (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((K3 tptp.nat)) (and (@ (@ tptp.member_nat K3) M5) (@ (@ tptp.ord_less_nat K3) (@ tptp.suc I2)))))) tptp.zero_zero_nat)))))
% 6.73/7.06 (assert (forall ((M5 tptp.set_nat) (I2 tptp.nat)) (=> (@ (@ tptp.member_nat tptp.zero_zero_nat) M5) (= (@ tptp.suc (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((K3 tptp.nat)) (and (@ (@ tptp.member_nat (@ tptp.suc K3)) M5) (@ (@ tptp.ord_less_nat K3) I2)))))) (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((K3 tptp.nat)) (and (@ (@ tptp.member_nat K3) M5) (@ (@ tptp.ord_less_nat K3) (@ tptp.suc I2))))))))))
% 6.73/7.06 (assert (forall ((M5 tptp.set_nat) (I2 tptp.nat)) (=> (not (@ (@ tptp.member_nat tptp.zero_zero_nat) M5)) (= (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((K3 tptp.nat)) (and (@ (@ tptp.member_nat (@ tptp.suc K3)) M5) (@ (@ tptp.ord_less_nat K3) I2))))) (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((K3 tptp.nat)) (and (@ (@ tptp.member_nat K3) M5) (@ (@ tptp.ord_less_nat K3) (@ tptp.suc I2))))))))))
% 6.73/7.06 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat N) M2)) M2) (@ (@ tptp.ord_max_nat N) M2))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_complex) (N tptp.nat)) (=> (@ tptp.finite3207457112153483333omplex A4) (@ tptp.finite8712137658972009173omplex (@ tptp.collect_list_complex (lambda ((Xs tptp.list_complex)) (and (@ (@ tptp.ord_le211207098394363844omplex (@ tptp.set_complex2 Xs)) A4) (= (@ tptp.size_s3451745648224563538omplex Xs) N))))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_VEBT_VEBT) (N tptp.nat)) (=> (@ tptp.finite5795047828879050333T_VEBT A4) (@ tptp.finite3004134309566078307T_VEBT (@ tptp.collec5608196760682091941T_VEBT (lambda ((Xs tptp.list_VEBT_VEBT)) (and (@ (@ tptp.ord_le4337996190870823476T_VEBT (@ tptp.set_VEBT_VEBT2 Xs)) A4) (= (@ tptp.size_s6755466524823107622T_VEBT Xs) N))))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_o) (N tptp.nat)) (=> (@ tptp.finite_finite_o A4) (@ tptp.finite_finite_list_o (@ tptp.collect_list_o (lambda ((Xs tptp.list_o)) (and (@ (@ tptp.ord_less_eq_set_o (@ tptp.set_o2 Xs)) A4) (= (@ tptp.size_size_list_o Xs) N))))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_int) (N tptp.nat)) (=> (@ tptp.finite_finite_int A4) (@ tptp.finite3922522038869484883st_int (@ tptp.collect_list_int (lambda ((Xs tptp.list_int)) (and (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_int2 Xs)) A4) (= (@ tptp.size_size_list_int Xs) N))))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_nat) (N tptp.nat)) (=> (@ tptp.finite_finite_nat A4) (@ tptp.finite8100373058378681591st_nat (@ tptp.collect_list_nat (lambda ((Xs tptp.list_nat)) (and (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_nat2 Xs)) A4) (= (@ tptp.size_size_list_nat Xs) N))))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_list_nat) (N tptp.nat)) (=> (@ tptp.finite8100373058378681591st_nat A4) (= (@ tptp.finite7325466520557071688st_nat (@ tptp.collec5989764272469232197st_nat (lambda ((Xs tptp.list_list_nat)) (and (@ (@ tptp.ord_le6045566169113846134st_nat (@ tptp.set_list_nat2 Xs)) A4) (= (@ tptp.size_s3023201423986296836st_nat Xs) N))))) (@ (@ tptp.power_power_nat (@ tptp.finite_card_list_nat A4)) N)))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_set_nat) (N tptp.nat)) (=> (@ tptp.finite1152437895449049373et_nat A4) (= (@ tptp.finite5631907774883551598et_nat (@ tptp.collect_list_set_nat (lambda ((Xs tptp.list_set_nat)) (and (@ (@ tptp.ord_le6893508408891458716et_nat (@ tptp.set_set_nat2 Xs)) A4) (= (@ tptp.size_s3254054031482475050et_nat Xs) N))))) (@ (@ tptp.power_power_nat (@ tptp.finite_card_set_nat A4)) N)))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_complex) (N tptp.nat)) (=> (@ tptp.finite3207457112153483333omplex A4) (= (@ tptp.finite5120063068150530198omplex (@ tptp.collect_list_complex (lambda ((Xs tptp.list_complex)) (and (@ (@ tptp.ord_le211207098394363844omplex (@ tptp.set_complex2 Xs)) A4) (= (@ tptp.size_s3451745648224563538omplex Xs) N))))) (@ (@ tptp.power_power_nat (@ tptp.finite_card_complex A4)) N)))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_VEBT_VEBT) (N tptp.nat)) (=> (@ tptp.finite5795047828879050333T_VEBT A4) (= (@ tptp.finite5915292604075114978T_VEBT (@ tptp.collec5608196760682091941T_VEBT (lambda ((Xs tptp.list_VEBT_VEBT)) (and (@ (@ tptp.ord_le4337996190870823476T_VEBT (@ tptp.set_VEBT_VEBT2 Xs)) A4) (= (@ tptp.size_s6755466524823107622T_VEBT Xs) N))))) (@ (@ tptp.power_power_nat (@ tptp.finite7802652506058667612T_VEBT A4)) N)))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_o) (N tptp.nat)) (=> (@ tptp.finite_finite_o A4) (= (@ tptp.finite_card_list_o (@ tptp.collect_list_o (lambda ((Xs tptp.list_o)) (and (@ (@ tptp.ord_less_eq_set_o (@ tptp.set_o2 Xs)) A4) (= (@ tptp.size_size_list_o Xs) N))))) (@ (@ tptp.power_power_nat (@ tptp.finite_card_o A4)) N)))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_int) (N tptp.nat)) (=> (@ tptp.finite_finite_int A4) (= (@ tptp.finite_card_list_int (@ tptp.collect_list_int (lambda ((Xs tptp.list_int)) (and (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_int2 Xs)) A4) (= (@ tptp.size_size_list_int Xs) N))))) (@ (@ tptp.power_power_nat (@ tptp.finite_card_int A4)) N)))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_nat) (N tptp.nat)) (=> (@ tptp.finite_finite_nat A4) (= (@ tptp.finite_card_list_nat (@ tptp.collect_list_nat (lambda ((Xs tptp.list_nat)) (and (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_nat2 Xs)) A4) (= (@ tptp.size_size_list_nat Xs) N))))) (@ (@ tptp.power_power_nat (@ tptp.finite_card_nat A4)) N)))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_complex) (N tptp.nat)) (=> (@ tptp.finite3207457112153483333omplex A4) (@ tptp.finite8712137658972009173omplex (@ tptp.collect_list_complex (lambda ((Xs tptp.list_complex)) (and (@ (@ tptp.ord_le211207098394363844omplex (@ tptp.set_complex2 Xs)) A4) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_s3451745648224563538omplex Xs)) N))))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_VEBT_VEBT) (N tptp.nat)) (=> (@ tptp.finite5795047828879050333T_VEBT A4) (@ tptp.finite3004134309566078307T_VEBT (@ tptp.collec5608196760682091941T_VEBT (lambda ((Xs tptp.list_VEBT_VEBT)) (and (@ (@ tptp.ord_le4337996190870823476T_VEBT (@ tptp.set_VEBT_VEBT2 Xs)) A4) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_s6755466524823107622T_VEBT Xs)) N))))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_o) (N tptp.nat)) (=> (@ tptp.finite_finite_o A4) (@ tptp.finite_finite_list_o (@ tptp.collect_list_o (lambda ((Xs tptp.list_o)) (and (@ (@ tptp.ord_less_eq_set_o (@ tptp.set_o2 Xs)) A4) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_o Xs)) N))))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_int) (N tptp.nat)) (=> (@ tptp.finite_finite_int A4) (@ tptp.finite3922522038869484883st_int (@ tptp.collect_list_int (lambda ((Xs tptp.list_int)) (and (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_int2 Xs)) A4) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_int Xs)) N))))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_nat) (N tptp.nat)) (=> (@ tptp.finite_finite_nat A4) (@ tptp.finite8100373058378681591st_nat (@ tptp.collect_list_nat (lambda ((Xs tptp.list_nat)) (and (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_nat2 Xs)) A4) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_nat Xs)) N))))))))
% 6.73/7.06 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Va3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (X tptp.nat)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va3)))) (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)))))))))))
% 6.73/7.06 (assert (forall ((Uy2 tptp.option4927543243414619207at_nat) (V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (S2 tptp.vEBT_VEBT) (X tptp.nat)) (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 X) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (= (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ (@ (@ tptp.vEBT_Node Uy2) _let_1) TreeList2) S2)) X) (and (=> _let_4 (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_3)) (@ (@ tptp.vEBT_VEBT_low X) _let_2))) _let_4))))))))
% 6.73/7.06 (assert (forall ((V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Vd2 tptp.vEBT_VEBT) (X tptp.nat)) (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 X) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (= (@ (@ tptp.vEBT_VEBT_membermima (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1) TreeList2) Vd2)) X) (and (=> _let_4 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_3)) (@ (@ tptp.vEBT_VEBT_low X) _let_2))) _let_4))))))))
% 6.73/7.06 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y tptp.vEBT_VEBT)) (=> (= (@ (@ tptp.vEBT_vebt_insert X) Xa2) Y) (=> (forall ((A3 Bool) (B3 Bool)) (let ((_let_1 (@ tptp.vEBT_Leaf A3))) (let ((_let_2 (@ _let_1 B3))) (let ((_let_3 (= Xa2 tptp.one_one_nat))) (let ((_let_4 (= Xa2 tptp.zero_zero_nat))) (=> (= X _let_2) (not (and (=> _let_4 (= Y (@ (@ tptp.vEBT_Leaf true) B3))) (=> (not _let_4) (and (=> _let_3 (= Y (@ _let_1 true))) (=> (not _let_3) (= Y _let_2)))))))))))) (=> (forall ((Info tptp.option4927543243414619207at_nat) (Ts tptp.list_VEBT_VEBT) (S tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info) tptp.zero_zero_nat) Ts) S))) (=> (= X _let_1) (not (= Y _let_1))))) (=> (forall ((Info tptp.option4927543243414619207at_nat) (Ts tptp.list_VEBT_VEBT) (S tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info) (@ tptp.suc tptp.zero_zero_nat)) Ts) S))) (=> (= X _let_1) (not (= Y _let_1))))) (=> (forall ((V tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc V)))) (=> (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1) TreeList) Summary2)) (not (= Y (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Xa2) Xa2))) _let_1) TreeList) Summary2)))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList) 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 TreeList) _let_6))) (=> (= X _let_2) (not (= Y (@ (@ (@ tptp.if_VEBT_VEBT (and (@ (@ tptp.ord_less_nat _let_6) (@ tptp.size_s6755466524823107622T_VEBT TreeList)) (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 TreeList) _let_6) (@ (@ tptp.vEBT_vebt_insert _let_7) (@ (@ tptp.vEBT_VEBT_low _let_5) _let_3)))) (@ (@ (@ tptp.if_VEBT_VEBT (@ tptp.vEBT_VEBT_minNull _let_7)) (@ (@ tptp.vEBT_vebt_insert Summary2) _let_6)) Summary2))) _let_2))))))))))))))))))))
% 6.73/7.06 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Va3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (X tptp.nat)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va3)))) (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))))))))))))))))
% 6.73/7.06 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Vc tptp.vEBT_VEBT) (X tptp.nat)) (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 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)))))))))
% 6.73/7.06 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (not (@ (@ tptp.vEBT_V5719532721284313246member X) Xa2)) (=> (forall ((A3 Bool) (B3 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (=> (= X (@ (@ tptp.vEBT_Leaf A3) B3)) (and (=> _let_2 A3) (=> (not _let_2) (and (=> _let_1 B3) _let_1))))))) (=> (forall ((Uu2 tptp.option4927543243414619207at_nat) (Uv2 tptp.list_VEBT_VEBT) (Uw tptp.vEBT_VEBT)) (not (= X (@ (@ (@ (@ tptp.vEBT_Node Uu2) tptp.zero_zero_nat) Uv2) Uw)))) (not (forall ((Uy tptp.option4927543243414619207at_nat) (V tptp.nat) (TreeList tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V)) (@ 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 TreeList)))) (=> (exists ((S tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node Uy) (@ tptp.suc V)) TreeList) S))) (and (=> _let_3 (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3))))))))))))
% 6.73/7.06 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (@ (@ tptp.vEBT_V5719532721284313246member X) Xa2) (=> (forall ((A3 Bool) (B3 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (=> (= X (@ (@ tptp.vEBT_Leaf A3) B3)) (not (and (=> _let_2 A3) (=> (not _let_2) (and (=> _let_1 B3) _let_1)))))))) (not (forall ((Uy tptp.option4927543243414619207at_nat) (V tptp.nat) (TreeList tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V)) (@ 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 TreeList)))) (=> (exists ((S tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node Uy) (@ tptp.suc V)) TreeList) S))) (not (and (=> _let_3 (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3))))))))))))
% 6.73/7.06 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y Bool)) (=> (= (@ (@ tptp.vEBT_V5719532721284313246member X) Xa2) Y) (=> (forall ((A3 Bool) (B3 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (=> (= X (@ (@ tptp.vEBT_Leaf A3) B3)) (= Y (not (and (=> _let_2 A3) (=> (not _let_2) (and (=> _let_1 B3) _let_1))))))))) (=> (=> (exists ((Uu2 tptp.option4927543243414619207at_nat) (Uv2 tptp.list_VEBT_VEBT) (Uw tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node Uu2) tptp.zero_zero_nat) Uv2) Uw))) Y) (not (forall ((Uy tptp.option4927543243414619207at_nat) (V tptp.nat) (TreeList tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V)) (@ 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 TreeList)))) (=> (exists ((S tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node Uy) (@ tptp.suc V)) TreeList) S))) (= Y (not (and (=> _let_3 (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3))))))))))))))
% 6.73/7.06 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (@ (@ tptp.vEBT_VEBT_membermima X) Xa2) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat)) (=> (exists ((Va2 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) Va2) Vb2))) (not (or (= Xa2 Mi2) (= Xa2 Ma2))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (V tptp.nat) (TreeList tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V)) (@ 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 TreeList)))) (=> (exists ((Vc2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc V)) TreeList) Vc2))) (not (or (= Xa2 Mi2) (= Xa2 Ma2) (and (=> _let_3 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3)))))))) (not (forall ((V tptp.nat) (TreeList tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V)) (@ 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 TreeList)))) (=> (exists ((Vd tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) (@ tptp.suc V)) TreeList) Vd))) (not (and (=> _let_3 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3)))))))))))))
% 6.73/7.06 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (@ (@ tptp.vEBT_vebt_member X) Xa2) (=> (forall ((A3 Bool) (B3 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (=> (= X (@ (@ tptp.vEBT_Leaf A3) B3)) (not (and (=> _let_2 A3) (=> (not _let_2) (and (=> _let_1 B3) _let_1)))))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va tptp.nat) (TreeList tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc (@ tptp.suc Va))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList)))) (let ((_let_4 (not (@ (@ tptp.ord_less_nat Ma2) Xa2)))) (let ((_let_5 (not (@ (@ tptp.ord_less_nat Xa2) Mi2)))) (=> (exists ((Summary2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc (@ tptp.suc Va))) TreeList) 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 TreeList) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3))))))))))))))))))))
% 6.73/7.06 (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 ((Ux tptp.list_VEBT_VEBT) (Uy tptp.vEBT_VEBT)) (not (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) tptp.zero_zero_nat) Ux) Uy)))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat)) (=> (exists ((Va2 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) Va2) Vb2))) (or (= Xa2 Mi2) (= Xa2 Ma2)))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (V tptp.nat) (TreeList tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V)) (@ 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 TreeList)))) (=> (exists ((Vc2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc V)) TreeList) Vc2))) (or (= Xa2 Mi2) (= Xa2 Ma2) (and (=> _let_3 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3))))))) (not (forall ((V tptp.nat) (TreeList tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V)) (@ 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 TreeList)))) (=> (exists ((Vd tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) (@ tptp.suc V)) TreeList) Vd))) (and (=> _let_3 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3))))))))))))))
% 6.73/7.06 (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 ((Ux tptp.list_VEBT_VEBT) (Uy tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) tptp.zero_zero_nat) Ux) Uy))) Y) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat)) (=> (exists ((Va2 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) Va2) Vb2))) (= Y (not (or (= Xa2 Mi2) (= Xa2 Ma2)))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (V tptp.nat) (TreeList tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V)) (@ 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 TreeList)))) (=> (exists ((Vc2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc V)) TreeList) Vc2))) (= Y (not (or (= Xa2 Mi2) (= Xa2 Ma2) (and (=> _let_3 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3))))))))) (not (forall ((V tptp.nat) (TreeList tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V)) (@ 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 TreeList)))) (=> (exists ((Vd tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) (@ tptp.suc V)) TreeList) Vd))) (= Y (not (and (=> _let_3 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3))))))))))))))))
% 6.73/7.06 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (not (@ (@ tptp.vEBT_vebt_member X) Xa2)) (=> (forall ((A3 Bool) (B3 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (=> (= X (@ (@ tptp.vEBT_Leaf A3) B3)) (and (=> _let_2 A3) (=> (not _let_2) (and (=> _let_1 B3) _let_1))))))) (=> (forall ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw tptp.vEBT_VEBT)) (not (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw)))) (=> (forall ((V tptp.product_prod_nat_nat) (Uy tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (not (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V)) tptp.zero_zero_nat) Uy) Uz2)))) (=> (forall ((V tptp.product_prod_nat_nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (not (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V)) (@ tptp.suc tptp.zero_zero_nat)) Vb2) Vc2)))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va tptp.nat) (TreeList tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc (@ tptp.suc Va))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList)))) (let ((_let_4 (not (@ (@ tptp.ord_less_nat Ma2) Xa2)))) (let ((_let_5 (not (@ (@ tptp.ord_less_nat Xa2) Mi2)))) (=> (exists ((Summary2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc (@ tptp.suc Va))) TreeList) 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 TreeList) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3))))))))))))))))))))))
% 6.73/7.06 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y Bool)) (=> (= (@ (@ tptp.vEBT_vebt_member X) Xa2) Y) (=> (forall ((A3 Bool) (B3 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (=> (= X (@ (@ tptp.vEBT_Leaf A3) B3)) (= Y (not (and (=> _let_2 A3) (=> (not _let_2) (and (=> _let_1 B3) _let_1))))))))) (=> (=> (exists ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw))) Y) (=> (=> (exists ((V tptp.product_prod_nat_nat) (Uy tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V)) tptp.zero_zero_nat) Uy) Uz2))) Y) (=> (=> (exists ((V tptp.product_prod_nat_nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V)) (@ tptp.suc tptp.zero_zero_nat)) Vb2) Vc2))) Y) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va tptp.nat) (TreeList tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc (@ tptp.suc Va))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList)))) (let ((_let_4 (not (@ (@ tptp.ord_less_nat Ma2) Xa2)))) (let ((_let_5 (not (@ (@ tptp.ord_less_nat Xa2) Mi2)))) (=> (exists ((Summary2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc (@ tptp.suc Va))) TreeList) 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 TreeList) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3))))))))))))))))))))))))
% 6.73/7.06 (assert (forall ((Ma tptp.nat) (X tptp.nat) (Mi tptp.nat) (Va3 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 Va3)))) (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))))))))))))))))))
% 6.73/7.06 (assert (forall ((X tptp.nat) (Mi tptp.nat) (Ma tptp.nat) (Va3 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 Va3)))) (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))))))))))))))))))
% 6.73/7.06 (assert (forall ((X tptp.nat) (Mi tptp.nat) (Ma tptp.nat) (Va3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va3)))) (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)))))))))))))))))))))))))))))))))
% 6.73/7.06 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y tptp.vEBT_VEBT)) (=> (= (@ (@ tptp.vEBT_vebt_delete X) Xa2) Y) (=> (forall ((A3 Bool) (B3 Bool)) (=> (= X (@ (@ tptp.vEBT_Leaf A3) B3)) (=> (= Xa2 tptp.zero_zero_nat) (not (= Y (@ (@ tptp.vEBT_Leaf false) B3)))))) (=> (forall ((A3 Bool)) (=> (exists ((B3 Bool)) (= X (@ (@ tptp.vEBT_Leaf A3) B3))) (=> (= Xa2 (@ tptp.suc tptp.zero_zero_nat)) (not (= Y (@ (@ tptp.vEBT_Leaf A3) false)))))) (=> (forall ((A3 Bool) (B3 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A3) B3))) (=> (= X _let_1) (=> (exists ((N3 tptp.nat)) (= Xa2 (@ tptp.suc (@ tptp.suc N3)))) (not (= Y _let_1)))))) (=> (forall ((Deg2 tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Deg2) TreeList) Summary2))) (=> (= X _let_1) (not (= Y _let_1))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (TrLst tptp.list_VEBT_VEBT) (Smry tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) tptp.zero_zero_nat) TrLst) Smry))) (=> (= X _let_1) (not (= Y _let_1))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Tr tptp.list_VEBT_VEBT) (Sm tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc tptp.zero_zero_nat)) Tr) Sm))) (=> (= X _let_1) (not (= Y _let_1))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList) 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 TreeList))) (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 TreeList) _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) TreeList) Summary2))) (=> (not _let_23) (= Y (@ (@ (@ tptp.if_VEBT_VEBT (@ (@ tptp.ord_less_nat _let_12) (@ tptp.size_s6755466524823107622T_VEBT TreeList))) (@ (@ (@ 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)))))))))))))))))))))))))))))))))))))))))))
% 6.73/7.06 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y tptp.option_nat)) (let ((_let_1 (not (= Y tptp.none_nat)))) (=> (= (@ (@ tptp.vEBT_vebt_succ X) Xa2) Y) (=> (forall ((Uu2 Bool) (B3 Bool)) (=> (= X (@ (@ tptp.vEBT_Leaf Uu2) B3)) (=> (= Xa2 tptp.zero_zero_nat) (not (and (=> B3 (= Y (@ tptp.some_nat tptp.one_one_nat))) (=> (not B3) (= Y tptp.none_nat))))))) (=> (=> (exists ((Uv2 Bool) (Uw Bool)) (= X (@ (@ tptp.vEBT_Leaf Uv2) Uw))) (=> (exists ((N3 tptp.nat)) (= Xa2 (@ tptp.suc N3))) _let_1)) (=> (=> (exists ((Ux tptp.nat) (Uy tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Ux) Uy) Uz2))) _let_1) (=> (=> (exists ((V tptp.product_prod_nat_nat) (Vc2 tptp.list_VEBT_VEBT) (Vd tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V)) tptp.zero_zero_nat) Vc2) Vd))) _let_1) (=> (=> (exists ((V tptp.product_prod_nat_nat) (Vg tptp.list_VEBT_VEBT) (Vh tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V)) (@ tptp.suc tptp.zero_zero_nat)) Vg) Vh))) _let_1) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va tptp.nat) (TreeList 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 Va)))) (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 TreeList))) (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) TreeList) 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 TreeList))) (@ (@ (@ 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))))))))))))))))))))))))))))
% 6.73/7.06 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y tptp.option_nat)) (let ((_let_1 (not (= Y tptp.none_nat)))) (=> (= (@ (@ tptp.vEBT_vebt_pred X) Xa2) Y) (=> (=> (exists ((Uu2 Bool) (Uv2 Bool)) (= X (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) (=> (= Xa2 tptp.zero_zero_nat) _let_1)) (=> (forall ((A3 Bool)) (=> (exists ((Uw Bool)) (= X (@ (@ tptp.vEBT_Leaf A3) Uw))) (=> (= Xa2 (@ tptp.suc tptp.zero_zero_nat)) (not (and (=> A3 (= Y (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A3) (= Y tptp.none_nat))))))) (=> (forall ((A3 Bool) (B3 Bool)) (=> (= X (@ (@ tptp.vEBT_Leaf A3) B3)) (=> (exists ((Va tptp.nat)) (= Xa2 (@ tptp.suc (@ tptp.suc Va)))) (not (and (=> B3 (= Y (@ tptp.some_nat tptp.one_one_nat))) (=> (not B3) (and (=> A3 (= Y (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A3) (= Y tptp.none_nat))))))))) (=> (=> (exists ((Uy tptp.nat) (Uz2 tptp.list_VEBT_VEBT) (Va2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uy) Uz2) Va2))) _let_1) (=> (=> (exists ((V tptp.product_prod_nat_nat) (Vd tptp.list_VEBT_VEBT) (Ve tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V)) tptp.zero_zero_nat) Vd) Ve))) _let_1) (=> (=> (exists ((V tptp.product_prod_nat_nat) (Vh tptp.list_VEBT_VEBT) (Vi tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V)) (@ tptp.suc tptp.zero_zero_nat)) Vh) Vi))) _let_1) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va tptp.nat) (TreeList 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 Va)))) (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 TreeList))) (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) TreeList) 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 TreeList))) (@ (@ (@ 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)))))))))))))))))))))))))))))
% 6.73/7.06 (assert (forall ((N tptp.nat) (C2 tptp.complex)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((Z4 tptp.complex)) (= (@ (@ tptp.power_power_complex Z4) N) C2)))))))
% 6.73/7.06 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_real (@ tptp.collect_real (lambda ((Z4 tptp.real)) (= (@ (@ tptp.power_power_real Z4) N) tptp.one_one_real))))) N))))
% 6.73/7.06 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_complex (@ tptp.collect_complex (lambda ((Z4 tptp.complex)) (= (@ (@ tptp.power_power_complex Z4) N) tptp.one_one_complex))))) N))))
% 6.73/7.06 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N) (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((Z4 tptp.real)) (= (@ (@ tptp.power_power_real Z4) N) tptp.one_one_real)))))))
% 6.73/7.06 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N) (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((Z4 tptp.complex)) (= (@ (@ tptp.power_power_complex Z4) N) tptp.one_one_complex)))))))
% 6.73/7.06 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y tptp.option_nat)) (=> (= (@ (@ tptp.vEBT_vebt_succ X) Xa2) Y) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_succ_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa2)) (=> (forall ((Uu2 Bool) (B3 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu2) B3))) (=> (= X _let_1) (=> (= Xa2 tptp.zero_zero_nat) (=> (and (=> B3 (= Y (@ tptp.some_nat tptp.one_one_nat))) (=> (not B3) (= Y tptp.none_nat))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_succ_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) tptp.zero_zero_nat)))))))) (=> (forall ((Uv2 Bool) (Uw Bool)) (=> (= X (@ (@ tptp.vEBT_Leaf Uv2) Uw)) (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) Uw)) _let_1))))))))) (=> (forall ((Ux tptp.nat) (Uy tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Ux) Uy) 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 ((V tptp.product_prod_nat_nat) (Vc2 tptp.list_VEBT_VEBT) (Vd tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V)) tptp.zero_zero_nat) Vc2) Vd))) (=> (= X _let_1) (=> (= Y tptp.none_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_succ_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((V tptp.product_prod_nat_nat) (Vg tptp.list_VEBT_VEBT) (Vh tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V)) (@ tptp.suc tptp.zero_zero_nat)) Vg) Vh))) (=> (= X _let_1) (=> (= Y tptp.none_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_succ_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList) 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 TreeList))) (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 TreeList))) (@ (@ (@ 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))))))))))))))))))))))))))))
% 6.73/7.06 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y tptp.option_nat)) (=> (= (@ (@ tptp.vEBT_vebt_pred X) Xa2) Y) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_pred_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa2)) (=> (forall ((Uu2 Bool) (Uv2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) (=> (= X _let_1) (=> (= Xa2 tptp.zero_zero_nat) (=> (= Y tptp.none_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_pred_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) tptp.zero_zero_nat)))))))) (=> (forall ((A3 Bool) (Uw Bool)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (let ((_let_2 (@ (@ tptp.vEBT_Leaf A3) Uw))) (=> (= X _let_2) (=> (= Xa2 _let_1) (=> (and (=> A3 (= Y (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A3) (= Y tptp.none_nat))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_pred_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) _let_1))))))))) (=> (forall ((A3 Bool) (B3 Bool)) (=> (= X (@ (@ tptp.vEBT_Leaf A3) B3)) (forall ((Va tptp.nat)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va)))) (=> (= Xa2 _let_1) (=> (and (=> B3 (= Y (@ tptp.some_nat tptp.one_one_nat))) (=> (not B3) (and (=> A3 (= Y (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A3) (= Y tptp.none_nat))))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_pred_rel) (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf A3) B3)) _let_1))))))))) (=> (forall ((Uy tptp.nat) (Uz2 tptp.list_VEBT_VEBT) (Va2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uy) Uz2) Va2))) (=> (= X _let_1) (=> (= Y tptp.none_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_pred_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((V tptp.product_prod_nat_nat) (Vd tptp.list_VEBT_VEBT) (Ve tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V)) tptp.zero_zero_nat) Vd) Ve))) (=> (= X _let_1) (=> (= Y tptp.none_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_pred_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((V tptp.product_prod_nat_nat) (Vh tptp.list_VEBT_VEBT) (Vi tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V)) (@ tptp.suc tptp.zero_zero_nat)) Vh) Vi))) (=> (= X _let_1) (=> (= Y tptp.none_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_pred_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList) 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 TreeList))) (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 TreeList))) (@ (@ (@ 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)))))))))))))))))))))))))))))
% 6.73/7.06 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y tptp.vEBT_VEBT)) (=> (= (@ (@ tptp.vEBT_vebt_delete X) Xa2) Y) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_delete_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa2)) (=> (forall ((A3 Bool) (B3 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A3) B3))) (=> (= X _let_1) (=> (= Xa2 tptp.zero_zero_nat) (=> (= Y (@ (@ tptp.vEBT_Leaf false) B3)) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_delete_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) tptp.zero_zero_nat)))))))) (=> (forall ((A3 Bool) (B3 Bool)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (let ((_let_2 (@ tptp.vEBT_Leaf A3))) (let ((_let_3 (@ _let_2 B3))) (=> (= X _let_3) (=> (= Xa2 _let_1) (=> (= Y (@ _let_2 false)) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_delete_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_3) _let_1)))))))))) (=> (forall ((A3 Bool) (B3 Bool)) (=> (= X (@ (@ tptp.vEBT_Leaf A3) B3)) (forall ((N3 tptp.nat)) (let ((_let_1 (@ tptp.suc (@ tptp.suc N3)))) (let ((_let_2 (@ (@ tptp.vEBT_Leaf A3) B3))) (=> (= Xa2 _let_1) (=> (= Y _let_2) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_delete_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) _let_1)))))))))) (=> (forall ((Deg2 tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Deg2) TreeList) Summary2))) (=> (= X _let_1) (=> (= Y _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_delete_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (TrLst tptp.list_VEBT_VEBT) (Smry tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) tptp.zero_zero_nat) TrLst) Smry))) (=> (= X _let_1) (=> (= Y _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_delete_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Tr tptp.list_VEBT_VEBT) (Sm tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc tptp.zero_zero_nat)) Tr) Sm))) (=> (= X _let_1) (=> (= Y _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_delete_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList) 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 TreeList))) (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 TreeList) _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) TreeList) Summary2))) (=> (not _let_23) (= Y (@ (@ (@ tptp.if_VEBT_VEBT (@ (@ tptp.ord_less_nat _let_12) (@ tptp.size_s6755466524823107622T_VEBT TreeList))) (@ (@ (@ 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)))))))))))))))))))))))))))))))))))))))))
% 6.73/7.06 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y tptp.vEBT_VEBT)) (=> (= (@ (@ tptp.vEBT_vebt_insert X) Xa2) Y) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_insert_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa2)) (=> (forall ((A3 Bool) (B3 Bool)) (let ((_let_1 (@ tptp.vEBT_Leaf A3))) (let ((_let_2 (@ _let_1 B3))) (let ((_let_3 (= Xa2 tptp.one_one_nat))) (let ((_let_4 (= Xa2 tptp.zero_zero_nat))) (=> (= X _let_2) (=> (and (=> _let_4 (= Y (@ (@ tptp.vEBT_Leaf true) B3))) (=> (not _let_4) (and (=> _let_3 (= Y (@ _let_1 true))) (=> (not _let_3) (= Y _let_2))))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_insert_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa2)))))))))) (=> (forall ((Info tptp.option4927543243414619207at_nat) (Ts tptp.list_VEBT_VEBT) (S tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info) tptp.zero_zero_nat) Ts) S))) (=> (= X _let_1) (=> (= Y _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_insert_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((Info tptp.option4927543243414619207at_nat) (Ts tptp.list_VEBT_VEBT) (S tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info) (@ tptp.suc tptp.zero_zero_nat)) Ts) S))) (=> (= X _let_1) (=> (= Y _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_insert_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((V tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc V)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1) TreeList) Summary2))) (=> (= X _let_2) (=> (= Y (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Xa2) Xa2))) _let_1) TreeList) Summary2)) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_insert_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa2)))))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList) 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 TreeList) _let_6))) (=> (= X _let_2) (=> (= Y (@ (@ (@ tptp.if_VEBT_VEBT (and (@ (@ tptp.ord_less_nat _let_6) (@ tptp.size_s6755466524823107622T_VEBT TreeList)) (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 TreeList) _let_6) (@ (@ tptp.vEBT_vebt_insert _let_7) (@ (@ tptp.vEBT_VEBT_low _let_5) _let_3)))) (@ (@ (@ tptp.if_VEBT_VEBT (@ tptp.vEBT_VEBT_minNull _let_7)) (@ (@ tptp.vEBT_vebt_insert Summary2) _let_6)) Summary2))) _let_2)) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_insert_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa2))))))))))))))))))))))
% 6.73/7.06 (assert (= tptp.vEBT_VEBT_low (lambda ((X4 tptp.nat) (N4 tptp.nat)) (@ (@ tptp.modulo_modulo_nat X4) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N4)))))
% 6.73/7.06 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)))
% 6.73/7.06 (assert (forall ((A tptp.int)) (= (@ (@ tptp.modulo_modulo_int tptp.zero_zero_int) A) tptp.zero_zero_int)))
% 6.73/7.06 (assert (forall ((A tptp.code_natural)) (= (@ (@ tptp.modulo8411746178871703098atural tptp.zero_z2226904508553997617atural) A) tptp.zero_z2226904508553997617atural)))
% 6.73/7.06 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat A) tptp.zero_zero_nat) A)))
% 6.73/7.06 (assert (forall ((A tptp.int)) (= (@ (@ tptp.modulo_modulo_int A) tptp.zero_zero_int) A)))
% 6.73/7.06 (assert (forall ((A tptp.code_natural)) (= (@ (@ tptp.modulo8411746178871703098atural A) tptp.zero_z2226904508553997617atural) A)))
% 6.73/7.06 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat A) A) tptp.zero_zero_nat)))
% 6.73/7.06 (assert (forall ((A tptp.int)) (= (@ (@ tptp.modulo_modulo_int A) A) tptp.zero_zero_int)))
% 6.73/7.06 (assert (forall ((A tptp.code_natural)) (= (@ (@ tptp.modulo8411746178871703098atural A) A) tptp.zero_z2226904508553997617atural)))
% 6.73/7.06 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)))
% 6.73/7.06 (assert (forall ((A tptp.int)) (= (@ (@ tptp.modulo_modulo_int tptp.zero_zero_int) A) tptp.zero_zero_int)))
% 6.73/7.06 (assert (forall ((A tptp.code_natural)) (= (@ (@ tptp.modulo8411746178871703098atural tptp.zero_z2226904508553997617atural) A) tptp.zero_z2226904508553997617atural)))
% 6.73/7.06 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat A) B)) B) tptp.zero_zero_nat)))
% 6.73/7.06 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int A) B)) B) tptp.zero_zero_int)))
% 6.73/7.06 (assert (forall ((A tptp.code_natural) (B tptp.code_natural)) (= (@ (@ tptp.modulo8411746178871703098atural (@ (@ tptp.times_2397367101498566445atural A) B)) B) tptp.zero_z2226904508553997617atural)))
% 6.73/7.06 (assert (forall ((B tptp.nat) (A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat B) A)) B) tptp.zero_zero_nat)))
% 6.73/7.06 (assert (forall ((B tptp.int) (A tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int B) A)) B) tptp.zero_zero_int)))
% 6.73/7.06 (assert (forall ((B tptp.code_natural) (A tptp.code_natural)) (= (@ (@ tptp.modulo8411746178871703098atural (@ (@ tptp.times_2397367101498566445atural B) A)) B) tptp.zero_z2226904508553997617atural)))
% 6.73/7.06 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger A) tptp.one_one_Code_integer) tptp.zero_z3403309356797280102nteger)))
% 6.73/7.06 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat A) tptp.one_one_nat) tptp.zero_zero_nat)))
% 6.73/7.06 (assert (forall ((A tptp.int)) (= (@ (@ tptp.modulo_modulo_int A) tptp.one_one_int) tptp.zero_zero_int)))
% 6.73/7.06 (assert (forall ((A tptp.code_natural)) (= (@ (@ tptp.modulo8411746178871703098atural A) tptp.one_one_Code_natural) tptp.zero_z2226904508553997617atural)))
% 6.73/7.06 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger A) tptp.one_one_Code_integer) tptp.zero_z3403309356797280102nteger)))
% 6.73/7.06 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat A) tptp.one_one_nat) tptp.zero_zero_nat)))
% 6.73/7.06 (assert (forall ((A tptp.int)) (= (@ (@ tptp.modulo_modulo_int A) tptp.one_one_int) tptp.zero_zero_int)))
% 6.73/7.06 (assert (forall ((A tptp.code_natural)) (= (@ (@ tptp.modulo8411746178871703098atural A) tptp.one_one_Code_natural) tptp.zero_z2226904508553997617atural)))
% 6.73/7.06 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.modulo_modulo_nat A) B)) B) tptp.zero_zero_nat)))
% 6.73/7.06 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.modulo_modulo_int A) B)) B) tptp.zero_zero_int)))
% 6.73/7.06 (assert (forall ((A tptp.code_natural) (B tptp.code_natural)) (= (@ (@ tptp.divide5121882707175180666atural (@ (@ tptp.modulo8411746178871703098atural A) B)) B) tptp.zero_z2226904508553997617atural)))
% 6.73/7.06 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.modulo_modulo_nat A) B)) B) tptp.zero_zero_nat)))
% 6.73/7.06 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.modulo_modulo_int A) B)) B) tptp.zero_zero_int)))
% 6.73/7.06 (assert (forall ((A tptp.code_natural) (B tptp.code_natural)) (= (@ (@ tptp.divide5121882707175180666atural (@ (@ tptp.modulo8411746178871703098atural A) B)) B) tptp.zero_z2226904508553997617atural)))
% 6.73/7.06 (assert (forall ((A tptp.nat) (C2 tptp.nat) (B tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat A) (@ (@ tptp.times_times_nat C2) B))) B) (@ (@ tptp.modulo_modulo_nat A) B))))
% 6.73/7.06 (assert (forall ((A tptp.int) (C2 tptp.int) (B tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int A) (@ (@ tptp.times_times_int C2) B))) B) (@ (@ tptp.modulo_modulo_int A) B))))
% 6.73/7.06 (assert (forall ((A tptp.code_natural) (C2 tptp.code_natural) (B tptp.code_natural)) (= (@ (@ tptp.modulo8411746178871703098atural (@ (@ tptp.plus_p4538020629002901425atural A) (@ (@ tptp.times_2397367101498566445atural C2) B))) B) (@ (@ tptp.modulo8411746178871703098atural A) B))))
% 6.73/7.06 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat A) (@ (@ tptp.times_times_nat B) C2))) B) (@ (@ tptp.modulo_modulo_nat A) B))))
% 6.73/7.06 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int A) (@ (@ tptp.times_times_int B) C2))) B) (@ (@ tptp.modulo_modulo_int A) B))))
% 6.73/7.06 (assert (forall ((A tptp.code_natural) (B tptp.code_natural) (C2 tptp.code_natural)) (= (@ (@ tptp.modulo8411746178871703098atural (@ (@ tptp.plus_p4538020629002901425atural A) (@ (@ tptp.times_2397367101498566445atural B) C2))) B) (@ (@ tptp.modulo8411746178871703098atural A) B))))
% 6.73/7.06 (assert (forall ((C2 tptp.nat) (B tptp.nat) (A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat C2) B)) A)) B) (@ (@ tptp.modulo_modulo_nat A) B))))
% 6.73/7.06 (assert (forall ((C2 tptp.int) (B tptp.int) (A tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int C2) B)) A)) B) (@ (@ tptp.modulo_modulo_int A) B))))
% 6.73/7.06 (assert (forall ((C2 tptp.code_natural) (B tptp.code_natural) (A tptp.code_natural)) (= (@ (@ tptp.modulo8411746178871703098atural (@ (@ tptp.plus_p4538020629002901425atural (@ (@ tptp.times_2397367101498566445atural C2) B)) A)) B) (@ (@ tptp.modulo8411746178871703098atural A) B))))
% 6.73/7.06 (assert (forall ((B tptp.nat) (C2 tptp.nat) (A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat B) C2)) A)) B) (@ (@ tptp.modulo_modulo_nat A) B))))
% 6.73/7.06 (assert (forall ((B tptp.int) (C2 tptp.int) (A tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) C2)) A)) B) (@ (@ tptp.modulo_modulo_int A) B))))
% 6.73/7.06 (assert (forall ((B tptp.code_natural) (C2 tptp.code_natural) (A tptp.code_natural)) (= (@ (@ tptp.modulo8411746178871703098atural (@ (@ tptp.plus_p4538020629002901425atural (@ (@ tptp.times_2397367101498566445atural B) C2)) A)) B) (@ (@ tptp.modulo8411746178871703098atural A) B))))
% 6.73/7.06 (assert (forall ((M2 tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat M2) (@ tptp.suc tptp.zero_zero_nat)) tptp.zero_zero_nat)))
% 6.73/7.06 (assert (forall ((N tptp.nat) (K2 tptp.nat) (M2 tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat N) K2)) M2))) N) (@ (@ tptp.modulo_modulo_nat (@ tptp.suc M2)) N))))
% 6.73/7.06 (assert (forall ((K2 tptp.nat) (N tptp.nat) (M2 tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat K2) N)) M2))) N) (@ (@ tptp.modulo_modulo_nat (@ tptp.suc M2)) N))))
% 6.73/7.06 (assert (forall ((M2 tptp.nat) (N tptp.nat) (K2 tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ (@ tptp.plus_plus_nat M2) (@ (@ tptp.times_times_nat N) K2)))) N) (@ (@ tptp.modulo_modulo_nat (@ tptp.suc M2)) N))))
% 6.73/7.06 (assert (forall ((M2 tptp.nat) (K2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ (@ tptp.plus_plus_nat M2) (@ (@ tptp.times_times_nat K2) N)))) N) (@ (@ tptp.modulo_modulo_nat (@ tptp.suc M2)) N))))
% 6.73/7.06 (assert (forall ((M2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ tptp.suc M2))) _let_1) (@ (@ tptp.modulo_modulo_nat M2) _let_1)))))
% 6.73/7.06 (assert (forall ((K2 tptp.num) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat K2))) (=> (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)))))
% 6.73/7.06 (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)))))
% 6.73/7.06 (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)))))
% 6.73/7.06 (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)))))
% 6.73/7.06 (assert (forall ((A tptp.code_natural)) (let ((_let_1 (@ (@ tptp.modulo8411746178871703098atural A) (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one))))) (= (not (= _let_1 tptp.zero_z2226904508553997617atural)) (= _let_1 tptp.one_one_Code_natural)))))
% 6.73/7.06 (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)))))
% 6.73/7.06 (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)))))
% 6.73/7.06 (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)))))
% 6.73/7.06 (assert (forall ((A tptp.code_natural)) (let ((_let_1 (@ (@ tptp.modulo8411746178871703098atural A) (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one))))) (= (not (= _let_1 tptp.one_one_Code_natural)) (= _let_1 tptp.zero_z2226904508553997617atural)))))
% 6.73/7.06 (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)))))
% 6.73/7.06 (assert (forall ((M2 tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat M2) M2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_nat)))
% 6.73/7.06 (assert (forall ((M2 tptp.nat)) (let ((_let_1 (@ (@ tptp.modulo_modulo_nat M2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) _let_1) (= _let_1 tptp.one_one_nat)))))
% 6.73/7.06 (assert (forall ((A tptp.nat) (C2 tptp.nat) (B tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat (@ (@ tptp.modulo_modulo_nat A) C2)) (@ (@ tptp.modulo_modulo_nat B) C2))) C2) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat A) B)) C2))))
% 6.73/7.06 (assert (forall ((A tptp.int) (C2 tptp.int) (B tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int (@ (@ tptp.modulo_modulo_int A) C2)) (@ (@ tptp.modulo_modulo_int B) C2))) C2) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int A) B)) C2))))
% 6.73/7.06 (assert (forall ((A tptp.code_natural) (C2 tptp.code_natural) (B tptp.code_natural)) (= (@ (@ tptp.modulo8411746178871703098atural (@ (@ tptp.times_2397367101498566445atural (@ (@ tptp.modulo8411746178871703098atural A) C2)) (@ (@ tptp.modulo8411746178871703098atural B) C2))) C2) (@ (@ tptp.modulo8411746178871703098atural (@ (@ tptp.times_2397367101498566445atural A) B)) C2))))
% 6.73/7.06 (assert (forall ((A tptp.nat) (C2 tptp.nat) (A2 tptp.nat) (B tptp.nat) (B2 tptp.nat)) (=> (= (@ (@ tptp.modulo_modulo_nat A) C2) (@ (@ tptp.modulo_modulo_nat A2) C2)) (=> (= (@ (@ tptp.modulo_modulo_nat B) C2) (@ (@ tptp.modulo_modulo_nat B2) C2)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat A) B)) C2) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat A2) B2)) C2))))))
% 6.73/7.06 (assert (forall ((A tptp.int) (C2 tptp.int) (A2 tptp.int) (B tptp.int) (B2 tptp.int)) (=> (= (@ (@ tptp.modulo_modulo_int A) C2) (@ (@ tptp.modulo_modulo_int A2) C2)) (=> (= (@ (@ tptp.modulo_modulo_int B) C2) (@ (@ tptp.modulo_modulo_int B2) C2)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int A) B)) C2) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int A2) B2)) C2))))))
% 6.73/7.06 (assert (forall ((A tptp.code_natural) (C2 tptp.code_natural) (A2 tptp.code_natural) (B tptp.code_natural) (B2 tptp.code_natural)) (=> (= (@ (@ tptp.modulo8411746178871703098atural A) C2) (@ (@ tptp.modulo8411746178871703098atural A2) C2)) (=> (= (@ (@ tptp.modulo8411746178871703098atural B) C2) (@ (@ tptp.modulo8411746178871703098atural B2) C2)) (= (@ (@ tptp.modulo8411746178871703098atural (@ (@ tptp.times_2397367101498566445atural A) B)) C2) (@ (@ tptp.modulo8411746178871703098atural (@ (@ tptp.times_2397367101498566445atural A2) B2)) C2))))))
% 6.73/7.06 (assert (forall ((A tptp.nat) (C2 tptp.nat) (B tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat A) C2)) (@ (@ tptp.times_times_nat B) C2)) (@ (@ tptp.times_times_nat (@ (@ tptp.modulo_modulo_nat A) B)) C2))))
% 6.73/7.06 (assert (forall ((A tptp.int) (C2 tptp.int) (B tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int A) C2)) (@ (@ tptp.times_times_int B) C2)) (@ (@ tptp.times_times_int (@ (@ tptp.modulo_modulo_int A) B)) C2))))
% 6.73/7.06 (assert (forall ((A tptp.code_natural) (C2 tptp.code_natural) (B tptp.code_natural)) (= (@ (@ tptp.modulo8411746178871703098atural (@ (@ tptp.times_2397367101498566445atural A) C2)) (@ (@ tptp.times_2397367101498566445atural B) C2)) (@ (@ tptp.times_2397367101498566445atural (@ (@ tptp.modulo8411746178871703098atural A) B)) C2))))
% 6.73/7.06 (assert (forall ((C2 tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C2))) (= (@ _let_1 (@ (@ tptp.modulo_modulo_nat A) B)) (@ (@ tptp.modulo_modulo_nat (@ _let_1 A)) (@ _let_1 B))))))
% 6.73/7.06 (assert (forall ((C2 tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C2))) (= (@ _let_1 (@ (@ tptp.modulo_modulo_int A) B)) (@ (@ tptp.modulo_modulo_int (@ _let_1 A)) (@ _let_1 B))))))
% 6.73/7.06 (assert (forall ((C2 tptp.code_natural) (A tptp.code_natural) (B tptp.code_natural)) (let ((_let_1 (@ tptp.times_2397367101498566445atural C2))) (= (@ _let_1 (@ (@ tptp.modulo8411746178871703098atural A) B)) (@ (@ tptp.modulo8411746178871703098atural (@ _let_1 A)) (@ _let_1 B))))))
% 6.73/7.06 (assert (forall ((A tptp.nat) (C2 tptp.nat) (B tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat (@ (@ tptp.modulo_modulo_nat A) C2)) B)) C2) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat A) B)) C2))))
% 6.73/7.06 (assert (forall ((A tptp.int) (C2 tptp.int) (B tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int (@ (@ tptp.modulo_modulo_int A) C2)) B)) C2) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int A) B)) C2))))
% 6.73/7.06 (assert (forall ((A tptp.code_natural) (C2 tptp.code_natural) (B tptp.code_natural)) (= (@ (@ tptp.modulo8411746178871703098atural (@ (@ tptp.times_2397367101498566445atural (@ (@ tptp.modulo8411746178871703098atural A) C2)) B)) C2) (@ (@ tptp.modulo8411746178871703098atural (@ (@ tptp.times_2397367101498566445atural A) B)) C2))))
% 6.73/7.06 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (= (@ (@ tptp.modulo_modulo_nat (@ _let_1 (@ (@ tptp.modulo_modulo_nat B) C2))) C2) (@ (@ tptp.modulo_modulo_nat (@ _let_1 B)) C2)))))
% 6.73/7.06 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (= (@ (@ tptp.modulo_modulo_int (@ _let_1 (@ (@ tptp.modulo_modulo_int B) C2))) C2) (@ (@ tptp.modulo_modulo_int (@ _let_1 B)) C2)))))
% 6.73/7.06 (assert (forall ((A tptp.code_natural) (B tptp.code_natural) (C2 tptp.code_natural)) (let ((_let_1 (@ tptp.times_2397367101498566445atural A))) (= (@ (@ tptp.modulo8411746178871703098atural (@ _let_1 (@ (@ tptp.modulo8411746178871703098atural B) C2))) C2) (@ (@ tptp.modulo8411746178871703098atural (@ _let_1 B)) C2)))))
% 6.73/7.06 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ tptp.suc (@ (@ tptp.modulo_modulo_nat M2) N)))) N) (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ tptp.suc M2))) N))))
% 6.73/7.06 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ (@ tptp.modulo_modulo_nat M2) N))) N) (@ (@ tptp.modulo_modulo_nat (@ tptp.suc M2)) N))))
% 6.73/7.06 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.modulo_modulo_nat M2) N)) M2)))
% 6.73/7.06 (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))))
% 6.73/7.06 (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))))
% 6.73/7.06 (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))))
% 6.73/7.06 (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))))
% 6.73/7.06 (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))))
% 6.73/7.06 (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))))
% 6.73/7.06 (assert (forall ((A tptp.code_natural) (B tptp.code_natural)) (= (= (@ (@ tptp.modulo8411746178871703098atural A) B) A) (= (@ (@ tptp.divide5121882707175180666atural A) B) tptp.zero_z2226904508553997617atural))))
% 6.73/7.06 (assert (forall ((M2 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 M2))) _let_2) (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 N))) _let_2)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat M2)) _let_1) (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat N)) _let_1)))))))
% 6.73/7.06 (assert (forall ((M2 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 M2))) _let_2) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N))) _let_2)) (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int M2)) _let_1) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int N)) _let_1)))))))
% 6.73/7.06 (assert (forall ((M2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat tptp.one))) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat M2)) _let_1) (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat N)) _let_1)))))
% 6.73/7.06 (assert (forall ((M2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int tptp.one))) (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int M2)) _let_1) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int N)) _let_1)))))
% 6.73/7.06 (assert (forall ((A tptp.int) (C2 tptp.int) (B tptp.int)) (=> (= (@ (@ tptp.modulo_modulo_int A) C2) (@ (@ tptp.modulo_modulo_int B) C2)) (not (forall ((D5 tptp.int)) (not (= B (@ (@ tptp.plus_plus_int A) (@ (@ tptp.times_times_int C2) D5)))))))))
% 6.73/7.06 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc (@ (@ tptp.modulo_modulo_nat M2) N)))) (let ((_let_2 (@ (@ tptp.modulo_modulo_nat (@ tptp.suc M2)) N))) (let ((_let_3 (= _let_1 N))) (and (=> _let_3 (= _let_2 tptp.zero_zero_nat)) (=> (not _let_3) (= _let_2 _let_1))))))))
% 6.73/7.06 (assert (forall ((P2 (-> tptp.nat Bool)) (N tptp.nat) (P tptp.nat) (M2 tptp.nat)) (=> (@ P2 N) (=> (@ (@ tptp.ord_less_nat N) P) (=> (@ (@ tptp.ord_less_nat M2) P) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N3) P) (=> (@ P2 N3) (@ P2 (@ (@ tptp.modulo_modulo_nat (@ tptp.suc N3)) P))))) (@ P2 M2)))))))
% 6.73/7.06 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_nat (@ (@ tptp.modulo_modulo_nat M2) N)) N))))
% 6.73/7.06 (assert (forall ((P2 (-> tptp.nat tptp.nat Bool)) (M2 tptp.nat) (N tptp.nat)) (=> (forall ((M tptp.nat)) (@ (@ P2 M) tptp.zero_zero_nat)) (=> (forall ((M tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N3) (=> (@ (@ P2 N3) (@ (@ tptp.modulo_modulo_nat M) N3)) (@ (@ P2 M) N3)))) (@ (@ P2 M2) N)))))
% 6.73/7.06 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.modulo_modulo_nat M2) (@ tptp.suc N))) N)))
% 6.73/7.06 (assert (forall ((M2 tptp.nat) (D tptp.nat)) (=> (= (@ (@ tptp.modulo_modulo_nat M2) D) tptp.zero_zero_nat) (exists ((Q3 tptp.nat)) (= M2 (@ (@ tptp.times_times_nat D) Q3))))))
% 6.73/7.06 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat M2) N)) (= (@ (@ tptp.modulo_modulo_nat M2) N) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.minus_minus_nat M2) N)) N)))))
% 6.73/7.06 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M2) (= (@ (@ tptp.modulo_modulo_nat M2) N) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.minus_minus_nat M2) N)) N)))))
% 6.73/7.06 (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))))))))
% 6.73/7.06 (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)))))
% 6.73/7.06 (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)))))
% 6.73/7.06 (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)))))
% 6.73/7.06 (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)))))
% 6.73/7.06 (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))))
% 6.73/7.06 (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))))
% 6.73/7.06 (assert (forall ((N tptp.num)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat N)) (@ tptp.numeral_numeral_nat tptp.one)) tptp.zero_zero_nat)))
% 6.73/7.06 (assert (forall ((N tptp.num)) (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int N)) (@ tptp.numeral_numeral_int tptp.one)) tptp.zero_zero_int)))
% 6.73/7.06 (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))))))
% 6.73/7.06 (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))))))
% 6.73/7.06 (assert (forall ((M2 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 M2))) _let_1) (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat tptp.one)) _let_1))))))
% 6.73/7.06 (assert (forall ((M2 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 M2))) _let_1) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int tptp.one)) _let_1))))))
% 6.73/7.06 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (= (@ (@ tptp.divide_divide_nat (@ _let_1 B)) C2) (@ (@ tptp.plus_plus_nat (@ _let_1 (@ (@ tptp.divide_divide_nat B) C2))) (@ (@ tptp.divide_divide_nat (@ _let_1 (@ (@ tptp.modulo_modulo_nat B) C2))) C2))))))
% 6.73/7.06 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (= (@ (@ tptp.divide_divide_int (@ _let_1 B)) C2) (@ (@ tptp.plus_plus_int (@ _let_1 (@ (@ tptp.divide_divide_int B) C2))) (@ (@ tptp.divide_divide_int (@ _let_1 (@ (@ tptp.modulo_modulo_int B) C2))) C2))))))
% 6.73/7.06 (assert (forall ((A tptp.code_natural) (B tptp.code_natural) (C2 tptp.code_natural)) (let ((_let_1 (@ tptp.times_2397367101498566445atural A))) (= (@ (@ tptp.divide5121882707175180666atural (@ _let_1 B)) C2) (@ (@ tptp.plus_p4538020629002901425atural (@ _let_1 (@ (@ tptp.divide5121882707175180666atural B) C2))) (@ (@ tptp.divide5121882707175180666atural (@ _let_1 (@ (@ tptp.modulo8411746178871703098atural B) C2))) C2))))))
% 6.73/7.06 (assert (forall ((B tptp.nat) (A tptp.nat) (C2 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))) C2) (@ (@ tptp.plus_plus_nat A) C2))))
% 6.73/7.06 (assert (forall ((B tptp.int) (A tptp.int) (C2 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))) C2) (@ (@ tptp.plus_plus_int A) C2))))
% 6.73/7.06 (assert (forall ((B tptp.code_natural) (A tptp.code_natural) (C2 tptp.code_natural)) (= (@ (@ tptp.plus_p4538020629002901425atural (@ (@ tptp.plus_p4538020629002901425atural (@ (@ tptp.times_2397367101498566445atural B) (@ (@ tptp.divide5121882707175180666atural A) B))) (@ (@ tptp.modulo8411746178871703098atural A) B))) C2) (@ (@ tptp.plus_p4538020629002901425atural A) C2))))
% 6.73/7.06 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 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))) C2) (@ (@ tptp.plus_plus_nat A) C2))))
% 6.73/7.06 (assert (forall ((A tptp.int) (B tptp.int) (C2 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))) C2) (@ (@ tptp.plus_plus_int A) C2))))
% 6.73/7.06 (assert (forall ((A tptp.code_natural) (B tptp.code_natural) (C2 tptp.code_natural)) (= (@ (@ tptp.plus_p4538020629002901425atural (@ (@ tptp.plus_p4538020629002901425atural (@ (@ tptp.times_2397367101498566445atural (@ (@ tptp.divide5121882707175180666atural A) B)) B)) (@ (@ tptp.modulo8411746178871703098atural A) B))) C2) (@ (@ tptp.plus_p4538020629002901425atural A) C2))))
% 6.73/7.06 (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)))))
% 6.73/7.06 (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)))))
% 6.73/7.06 (assert (forall ((A tptp.code_natural) (B tptp.code_natural)) (= A (@ (@ tptp.plus_p4538020629002901425atural (@ (@ tptp.times_2397367101498566445atural (@ (@ tptp.divide5121882707175180666atural A) B)) B)) (@ (@ tptp.modulo8411746178871703098atural A) B)))))
% 6.73/7.06 (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)))
% 6.73/7.06 (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)))
% 6.73/7.06 (assert (forall ((A tptp.code_natural) (B tptp.code_natural)) (= (@ (@ tptp.plus_p4538020629002901425atural (@ (@ tptp.times_2397367101498566445atural (@ (@ tptp.divide5121882707175180666atural A) B)) B)) (@ (@ tptp.modulo8411746178871703098atural A) B)) A)))
% 6.73/7.06 (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)))
% 6.73/7.06 (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)))
% 6.73/7.06 (assert (forall ((A tptp.code_natural) (B tptp.code_natural)) (= (@ (@ tptp.plus_p4538020629002901425atural (@ (@ tptp.modulo8411746178871703098atural A) B)) (@ (@ tptp.times_2397367101498566445atural (@ (@ tptp.divide5121882707175180666atural A) B)) B)) A)))
% 6.73/7.06 (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)))
% 6.73/7.06 (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)))
% 6.73/7.06 (assert (forall ((A tptp.code_natural) (B tptp.code_natural)) (= (@ (@ tptp.plus_p4538020629002901425atural (@ (@ tptp.modulo8411746178871703098atural A) B)) (@ (@ tptp.times_2397367101498566445atural B) (@ (@ tptp.divide5121882707175180666atural A) B))) A)))
% 6.73/7.06 (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)))
% 6.73/7.06 (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)))
% 6.73/7.06 (assert (forall ((B tptp.code_natural) (A tptp.code_natural)) (= (@ (@ tptp.plus_p4538020629002901425atural (@ (@ tptp.times_2397367101498566445atural B) (@ (@ tptp.divide5121882707175180666atural A) B))) (@ (@ tptp.modulo8411746178871703098atural A) B)) A)))
% 6.73/7.06 (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))))
% 6.73/7.06 (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))))
% 6.73/7.06 (assert (forall ((A tptp.code_natural) (B tptp.code_natural)) (= (@ (@ tptp.minus_7197305767214868737atural A) (@ (@ tptp.times_2397367101498566445atural (@ (@ tptp.divide5121882707175180666atural A) B)) B)) (@ (@ tptp.modulo8411746178871703098atural A) B))))
% 6.73/7.06 (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))))
% 6.73/7.06 (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))))
% 6.73/7.06 (assert (forall ((A tptp.code_natural) (B tptp.code_natural)) (= (@ (@ tptp.minus_7197305767214868737atural A) (@ (@ tptp.modulo8411746178871703098atural A) B)) (@ (@ tptp.times_2397367101498566445atural (@ (@ tptp.divide5121882707175180666atural A) B)) B))))
% 6.73/7.06 (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)))))
% 6.73/7.06 (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)))))
% 6.73/7.06 (assert (forall ((A tptp.code_natural) (B tptp.code_natural)) (= (@ (@ tptp.minus_7197305767214868737atural A) (@ (@ tptp.modulo8411746178871703098atural A) B)) (@ (@ tptp.times_2397367101498566445atural B) (@ (@ tptp.divide5121882707175180666atural A) B)))))
% 6.73/7.06 (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))))
% 6.73/7.06 (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))))
% 6.73/7.06 (assert (forall ((A tptp.code_natural) (B tptp.code_natural)) (= (@ (@ tptp.minus_7197305767214868737atural A) (@ (@ tptp.times_2397367101498566445atural B) (@ (@ tptp.divide5121882707175180666atural A) B))) (@ (@ tptp.modulo8411746178871703098atural A) B))))
% 6.73/7.06 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.modulo_modulo_nat M2) N)) N))))
% 6.73/7.06 (assert (forall ((A4 tptp.nat) (B5 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat A4) B5) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (= (@ (@ tptp.modulo_modulo_nat A4) N) tptp.zero_zero_nat) (=> (= (@ (@ tptp.modulo_modulo_nat B5) N) tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.divide_divide_nat A4) N)) (@ (@ tptp.divide_divide_nat B5) N))))))))
% 6.73/7.06 (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))))))))
% 6.73/7.06 (assert (forall ((M2 tptp.nat) (Q2 tptp.nat) (N tptp.nat)) (=> (= (@ (@ tptp.modulo_modulo_nat M2) Q2) (@ (@ tptp.modulo_modulo_nat N) Q2)) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (not (forall ((S tptp.nat)) (not (= N (@ (@ tptp.plus_plus_nat M2) (@ (@ tptp.times_times_nat Q2) S))))))))))
% 6.73/7.06 (assert (forall ((M2 tptp.nat) (Q2 tptp.nat) (N tptp.nat)) (=> (= (@ (@ tptp.modulo_modulo_nat M2) Q2) (@ (@ tptp.modulo_modulo_nat N) Q2)) (=> (@ (@ tptp.ord_less_eq_nat N) M2) (not (forall ((S tptp.nat)) (not (= M2 (@ (@ tptp.plus_plus_nat N) (@ (@ tptp.times_times_nat Q2) S))))))))))
% 6.73/7.06 (assert (forall ((M2 tptp.nat) (N tptp.nat) (Q2 tptp.nat)) (let ((_let_1 (@ tptp.modulo_modulo_nat M2))) (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 M2) N)) Q2))) (@ _let_1 N)))))))
% 6.73/7.06 (assert (forall ((A4 tptp.nat) (N tptp.nat)) (= A4 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat A4) N)) N)) (@ (@ tptp.modulo_modulo_nat A4) N)))))
% 6.73/7.06 (assert (= tptp.modulo_modulo_nat (lambda ((M6 tptp.nat) (N4 tptp.nat)) (@ (@ tptp.minus_minus_nat M6) (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat M6) N4)) N4)))))
% 6.73/7.06 (assert (forall ((A tptp.code_natural) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri3763490453095760265atural M2))) (let ((_let_2 (@ tptp.modulo8411746178871703098atural A))) (let ((_let_3 (@ tptp.semiri3763490453095760265atural N))) (let ((_let_4 (@ tptp.times_2397367101498566445atural _let_1))) (= (@ _let_2 (@ _let_4 _let_3)) (@ (@ tptp.plus_p4538020629002901425atural (@ _let_4 (@ (@ tptp.modulo8411746178871703098atural (@ (@ tptp.divide5121882707175180666atural A) _let_1)) _let_3))) (@ _let_2 _let_1)))))))))
% 6.73/7.06 (assert (forall ((A tptp.int) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int M2))) (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)))))))))
% 6.73/7.06 (assert (forall ((A tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri1316708129612266289at_nat M2))) (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)))))))))
% 6.73/7.06 (assert (forall ((P2 (-> tptp.nat Bool)) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (= N tptp.zero_zero_nat))) (= (@ P2 (@ (@ tptp.modulo_modulo_nat M2) N)) (and (=> _let_1 (@ P2 M2)) (=> (not _let_1) (forall ((I tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_nat J) N) (=> (= M2 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat N) I)) J)) (@ P2 J))))))))))
% 6.73/7.06 (assert (forall ((C2 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) C2) (= (@ _let_1 (@ _let_2 C2)) (@ (@ tptp.plus_plus_nat (@ _let_2 (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.divide_divide_nat A) B)) C2))) (@ _let_1 B))))))))
% 6.73/7.06 (assert (forall ((C2 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) C2) (= (@ _let_1 (@ _let_2 C2)) (@ (@ tptp.plus_plus_int (@ _let_2 (@ (@ tptp.modulo_modulo_int (@ (@ tptp.divide_divide_int A) B)) C2))) (@ _let_1 B))))))))
% 6.73/7.06 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)) M2) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ (@ tptp.times_times_nat M2) N))) M2) tptp.one_one_nat))))
% 6.73/7.06 (assert (forall ((N tptp.nat) (Xs2 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ tptp.size_s6755466524823107622T_VEBT Xs2))) (=> (@ (@ tptp.ord_less_nat N) _let_1) (= (@ (@ tptp.nth_VEBT_VEBT (@ tptp.rotate1_VEBT_VEBT Xs2)) N) (@ (@ tptp.nth_VEBT_VEBT Xs2) (@ (@ tptp.modulo_modulo_nat (@ tptp.suc N)) _let_1)))))))
% 6.73/7.06 (assert (forall ((N tptp.nat) (Xs2 tptp.list_o)) (let ((_let_1 (@ tptp.size_size_list_o Xs2))) (=> (@ (@ tptp.ord_less_nat N) _let_1) (= (@ (@ tptp.nth_o (@ tptp.rotate1_o Xs2)) N) (@ (@ tptp.nth_o Xs2) (@ (@ tptp.modulo_modulo_nat (@ tptp.suc N)) _let_1)))))))
% 6.73/7.06 (assert (forall ((N tptp.nat) (Xs2 tptp.list_nat)) (let ((_let_1 (@ tptp.size_size_list_nat Xs2))) (=> (@ (@ tptp.ord_less_nat N) _let_1) (= (@ (@ tptp.nth_nat (@ tptp.rotate1_nat Xs2)) N) (@ (@ tptp.nth_nat Xs2) (@ (@ tptp.modulo_modulo_nat (@ tptp.suc N)) _let_1)))))))
% 6.73/7.06 (assert (forall ((N tptp.nat) (Xs2 tptp.list_int)) (let ((_let_1 (@ tptp.size_size_list_int Xs2))) (=> (@ (@ tptp.ord_less_nat N) _let_1) (= (@ (@ tptp.nth_int (@ tptp.rotate1_int Xs2)) N) (@ (@ tptp.nth_int Xs2) (@ (@ tptp.modulo_modulo_nat (@ tptp.suc N)) _let_1)))))))
% 6.73/7.06 (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))))))))
% 6.73/7.06 (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))))))))
% 6.73/7.06 (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)))))
% 6.73/7.06 (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)))))
% 6.73/7.06 (assert (forall ((A tptp.code_natural)) (let ((_let_1 (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one)))) (=> (= (@ (@ tptp.divide5121882707175180666atural A) _let_1) A) (= (@ (@ tptp.plus_p4538020629002901425atural A) (@ (@ tptp.modulo8411746178871703098atural A) _let_1)) tptp.zero_z2226904508553997617atural)))))
% 6.73/7.06 (assert (forall ((A4 tptp.nat) (B5 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat A4) B5) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.divide_divide_nat A4) N)) (@ (@ (@ tptp.if_nat (= (@ (@ tptp.modulo_modulo_nat B5) N) tptp.zero_zero_nat)) tptp.one_one_nat) tptp.zero_zero_nat))) (@ (@ tptp.divide_divide_nat B5) N))))))
% 6.73/7.06 (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)))))))))
% 6.73/7.06 (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)))))))))
% 6.73/7.06 (assert (forall ((M2 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 M2))) (=> (@ (@ tptp.ord_less_eq_nat M2) 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) M2)))) _let_2)))))))
% 6.73/7.06 (assert (forall ((M2 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 M2))) (=> (@ (@ tptp.ord_less_eq_nat M2) 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) M2)))) _let_2)))))))
% 6.73/7.06 (assert (forall ((M2 tptp.nat) (N tptp.nat) (A tptp.code_natural)) (let ((_let_1 (@ tptp.power_7079662738309270450atural (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 M2))) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ (@ tptp.modulo8411746178871703098atural (@ (@ tptp.times_2397367101498566445atural A) _let_2)) (@ _let_1 N)) (@ (@ tptp.times_2397367101498566445atural (@ (@ tptp.modulo8411746178871703098atural A) (@ _let_1 (@ (@ tptp.minus_minus_nat N) M2)))) _let_2)))))))
% 6.73/7.06 (assert (forall ((M2 tptp.nat) (X tptp.nat)) (let ((_let_1 (@ tptp.modulo_modulo_nat X))) (let ((_let_2 (@ _let_1 M2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M2)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M2) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) X) (or (= _let_3 _let_2) (= _let_3 (@ (@ tptp.plus_plus_nat _let_2) M2))))))))))
% 6.73/7.06 (assert (forall ((M2 tptp.int) (X tptp.int)) (let ((_let_1 (@ tptp.modulo_modulo_int X))) (let ((_let_2 (@ _let_1 M2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) M2)))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) M2) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X) (or (= _let_3 _let_2) (= _let_3 (@ (@ tptp.plus_plus_int _let_2) M2))))))))))
% 6.73/7.06 (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)))))))))
% 6.73/7.06 (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)))))))))
% 6.73/7.06 (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))))))))
% 6.73/7.06 (assert (forall ((N tptp.nat) (A tptp.code_natural)) (let ((_let_1 (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se7083795435491715335atural (@ tptp.suc N)) A) (@ (@ tptp.plus_p4538020629002901425atural (@ (@ tptp.modulo8411746178871703098atural A) _let_1)) (@ (@ tptp.times_2397367101498566445atural _let_1) (@ (@ tptp.bit_se7083795435491715335atural N) (@ (@ tptp.divide5121882707175180666atural A) _let_1))))))))
% 6.73/7.06 (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))))))))
% 6.73/7.06 (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))))))))
% 6.73/7.06 (assert (forall ((N tptp.nat) (A tptp.code_natural)) (let ((_let_1 (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se1617098188084679374atural (@ tptp.suc N)) A) (@ (@ tptp.plus_p4538020629002901425atural (@ (@ tptp.modulo8411746178871703098atural A) _let_1)) (@ (@ tptp.times_2397367101498566445atural _let_1) (@ (@ tptp.bit_se1617098188084679374atural N) (@ (@ tptp.divide5121882707175180666atural A) _let_1))))))))
% 6.73/7.06 (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))))))))
% 6.73/7.06 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.finite_card_complex (@ tptp.collect_complex (lambda ((Z4 tptp.complex)) (= (@ (@ tptp.power_power_complex Z4) N) tptp.one_one_complex)))) N))))
% 6.73/7.06 (assert (forall ((C2 tptp.complex) (N tptp.nat)) (=> (not (= C2 tptp.zero_zero_complex)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.finite_card_complex (@ tptp.collect_complex (lambda ((Z4 tptp.complex)) (= (@ (@ tptp.power_power_complex Z4) N) C2)))) N)))))
% 6.73/7.06 (assert (forall ((N tptp.nat) (Xs2 tptp.list_Code_integer) (Ys tptp.list_Code_integer)) (let ((_let_1 (@ tptp.size_s3445333598471063425nteger Ys))) (=> (@ (@ tptp.ord_less_nat N) (@ (@ tptp.times_times_nat (@ tptp.size_s3445333598471063425nteger Xs2)) _let_1)) (= (@ (@ tptp.nth_Pr2304437835452373666nteger (@ (@ tptp.produc8792966785426426881nteger Xs2) Ys)) N) (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.nth_Code_integer Xs2) (@ (@ tptp.divide_divide_nat N) _let_1))) (@ (@ tptp.nth_Code_integer Ys) (@ (@ tptp.modulo_modulo_nat N) _let_1))))))))
% 6.73/7.06 (assert (forall ((N tptp.nat) (Xs2 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 Xs2)) _let_1)) (= (@ (@ tptp.nth_Pr4953567300277697838T_VEBT (@ (@ tptp.produc4743750530478302277T_VEBT Xs2) Ys)) N) (@ (@ tptp.produc537772716801021591T_VEBT (@ (@ tptp.nth_VEBT_VEBT Xs2) (@ (@ tptp.divide_divide_nat N) _let_1))) (@ (@ tptp.nth_VEBT_VEBT Ys) (@ (@ tptp.modulo_modulo_nat N) _let_1))))))))
% 6.73/7.06 (assert (forall ((N tptp.nat) (Xs2 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 Xs2)) _let_1)) (= (@ (@ tptp.nth_Pr4606735188037164562VEBT_o (@ (@ tptp.product_VEBT_VEBT_o Xs2) Ys)) N) (@ (@ tptp.produc8721562602347293563VEBT_o (@ (@ tptp.nth_VEBT_VEBT Xs2) (@ (@ tptp.divide_divide_nat N) _let_1))) (@ (@ tptp.nth_o Ys) (@ (@ tptp.modulo_modulo_nat N) _let_1))))))))
% 6.73/7.06 (assert (forall ((N tptp.nat) (Xs2 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 Xs2)) _let_1)) (= (@ (@ tptp.nth_Pr1791586995822124652BT_nat (@ (@ tptp.produc7295137177222721919BT_nat Xs2) Ys)) N) (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.nth_VEBT_VEBT Xs2) (@ (@ tptp.divide_divide_nat N) _let_1))) (@ (@ tptp.nth_nat Ys) (@ (@ tptp.modulo_modulo_nat N) _let_1))))))))
% 6.73/7.06 (assert (forall ((N tptp.nat) (Xs2 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 Xs2)) _let_1)) (= (@ (@ tptp.nth_Pr6837108013167703752BT_int (@ (@ tptp.produc7292646706713671643BT_int Xs2) Ys)) N) (@ (@ tptp.produc736041933913180425BT_int (@ (@ tptp.nth_VEBT_VEBT Xs2) (@ (@ tptp.divide_divide_nat N) _let_1))) (@ (@ tptp.nth_int Ys) (@ (@ tptp.modulo_modulo_nat N) _let_1))))))))
% 6.73/7.06 (assert (forall ((N tptp.nat) (Xs2 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 Xs2)) _let_1)) (= (@ (@ tptp.nth_Pr6777367263587873994T_VEBT (@ (@ tptp.product_o_VEBT_VEBT Xs2) Ys)) N) (@ (@ tptp.produc2982872950893828659T_VEBT (@ (@ tptp.nth_o Xs2) (@ (@ tptp.divide_divide_nat N) _let_1))) (@ (@ tptp.nth_VEBT_VEBT Ys) (@ (@ tptp.modulo_modulo_nat N) _let_1))))))))
% 6.73/7.06 (assert (forall ((N tptp.nat) (Xs2 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 Xs2)) _let_1)) (= (@ (@ tptp.nth_Product_prod_o_o (@ (@ tptp.product_o_o Xs2) Ys)) N) (@ (@ tptp.product_Pair_o_o (@ (@ tptp.nth_o Xs2) (@ (@ tptp.divide_divide_nat N) _let_1))) (@ (@ tptp.nth_o Ys) (@ (@ tptp.modulo_modulo_nat N) _let_1))))))))
% 6.73/7.06 (assert (forall ((N tptp.nat) (Xs2 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 Xs2)) _let_1)) (= (@ (@ tptp.nth_Pr5826913651314560976_o_nat (@ (@ tptp.product_o_nat Xs2) Ys)) N) (@ (@ tptp.product_Pair_o_nat (@ (@ tptp.nth_o Xs2) (@ (@ tptp.divide_divide_nat N) _let_1))) (@ (@ tptp.nth_nat Ys) (@ (@ tptp.modulo_modulo_nat N) _let_1))))))))
% 6.73/7.06 (assert (forall ((N tptp.nat) (Xs2 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 Xs2)) _let_1)) (= (@ (@ tptp.nth_Pr1649062631805364268_o_int (@ (@ tptp.product_o_int Xs2) Ys)) N) (@ (@ tptp.product_Pair_o_int (@ (@ tptp.nth_o Xs2) (@ (@ tptp.divide_divide_nat N) _let_1))) (@ (@ tptp.nth_int Ys) (@ (@ tptp.modulo_modulo_nat N) _let_1))))))))
% 6.73/7.06 (assert (forall ((N tptp.nat) (Xs2 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 Xs2)) _let_1)) (= (@ (@ tptp.nth_Pr744662078594809490T_VEBT (@ (@ tptp.produc7156399406898700509T_VEBT Xs2) Ys)) N) (@ (@ tptp.produc599794634098209291T_VEBT (@ (@ tptp.nth_nat Xs2) (@ (@ tptp.divide_divide_nat N) _let_1))) (@ (@ tptp.nth_VEBT_VEBT Ys) (@ (@ tptp.modulo_modulo_nat N) _let_1))))))))
% 6.73/7.06 (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))))))))))
% 6.73/7.06 (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))))))))))
% 6.73/7.06 (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))))))))))
% 6.73/7.06 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y tptp.vEBT_VEBT)) (=> (= (@ (@ tptp.vEBT_VEBT_insert X) Xa2) Y) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_insert_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa2)) (=> (forall ((A3 Bool) (B3 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A3) B3))) (=> (= X _let_1) (=> (= Y (@ (@ tptp.vEBT_vebt_insert _let_1) Xa2)) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_insert_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (not (forall ((Info tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info) Deg2) TreeList) Summary2))) (let ((_let_2 (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Deg2)) Xa2))) (=> (= X _let_1) (=> (and (=> _let_2 (= Y _let_1)) (=> (not _let_2) (= Y (@ (@ tptp.vEBT_vebt_insert _let_1) Xa2)))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_insert_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))))))))))
% 6.73/7.06 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y Bool)) (=> (= (@ (@ tptp.vEBT_vebt_member X) Xa2) Y) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa2)) (=> (forall ((A3 Bool) (B3 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A3) B3))) (let ((_let_2 (= Xa2 tptp.one_one_nat))) (let ((_let_3 (= Xa2 tptp.zero_zero_nat))) (=> (= X _let_1) (=> (= Y (and (=> _let_3 A3) (=> (not _let_3) (and (=> _let_2 B3) _let_2)))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))))) (=> (forall ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw))) (=> (= X _let_1) (=> (not Y) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((V tptp.product_prod_nat_nat) (Uy tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V)) tptp.zero_zero_nat) Uy) Uz2))) (=> (= X _let_1) (=> (not Y) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((V tptp.product_prod_nat_nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V)) (@ tptp.suc tptp.zero_zero_nat)) Vb2) Vc2))) (=> (= X _let_1) (=> (not Y) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList) 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 TreeList)))) (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 TreeList) _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))))))))))))))))))))))
% 6.73/7.06 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (not (@ (@ tptp.vEBT_vebt_member X) Xa2)) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa2)) (=> (forall ((A3 Bool) (B3 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (let ((_let_3 (@ (@ tptp.vEBT_Leaf A3) B3))) (=> (= X _let_3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_3) Xa2)) (and (=> _let_2 A3) (=> (not _let_2) (and (=> _let_1 B3) _let_1))))))))) (=> (forall ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw))) (=> (= X _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2)))))) (=> (forall ((V tptp.product_prod_nat_nat) (Uy tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V)) tptp.zero_zero_nat) Uy) Uz2))) (=> (= X _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2)))))) (=> (forall ((V tptp.product_prod_nat_nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V)) (@ tptp.suc tptp.zero_zero_nat)) Vb2) Vc2))) (=> (= X _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2)))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList)))) (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) TreeList) 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 TreeList) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_2))) _let_4))))))))))))))))))))))))))
% 6.73/7.06 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y Bool)) (=> (= (@ (@ tptp.vEBT_V5719532721284313246member X) Xa2) Y) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa2)) (=> (forall ((A3 Bool) (B3 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A3) B3))) (let ((_let_2 (= Xa2 tptp.one_one_nat))) (let ((_let_3 (= Xa2 tptp.zero_zero_nat))) (=> (= X _let_1) (=> (= Y (and (=> _let_3 A3) (=> (not _let_3) (and (=> _let_2 B3) _let_2)))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))))) (=> (forall ((Uu2 tptp.option4927543243414619207at_nat) (Uv2 tptp.list_VEBT_VEBT) (Uw tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Uu2) tptp.zero_zero_nat) Uv2) Uw))) (=> (= X _let_1) (=> (not Y) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (not (forall ((Uy tptp.option4927543243414619207at_nat) (V tptp.nat) (TreeList tptp.list_VEBT_VEBT) (S tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node Uy) _let_1) TreeList) S))) (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 TreeList)))) (=> (= X _let_2) (=> (= Y (and (=> _let_5 (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.nth_VEBT_VEBT TreeList) _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))))))))))))))))))
% 6.73/7.06 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (@ (@ tptp.vEBT_V5719532721284313246member X) Xa2) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa2)) (=> (forall ((A3 Bool) (B3 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (let ((_let_3 (@ (@ tptp.vEBT_Leaf A3) B3))) (=> (= X _let_3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_3) Xa2)) (not (and (=> _let_2 A3) (=> (not _let_2) (and (=> _let_1 B3) _let_1)))))))))) (not (forall ((Uy tptp.option4927543243414619207at_nat) (V tptp.nat) (TreeList tptp.list_VEBT_VEBT) (S tptp.vEBT_VEBT)) (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 Xa2) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList)))) (let ((_let_5 (@ (@ (@ (@ tptp.vEBT_Node Uy) _let_1) TreeList) S))) (=> (= 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 TreeList) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_2))) _let_4))))))))))))))))
% 6.73/7.06 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (not (@ (@ tptp.vEBT_V5719532721284313246member X) Xa2)) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa2)) (=> (forall ((A3 Bool) (B3 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (let ((_let_3 (@ (@ tptp.vEBT_Leaf A3) B3))) (=> (= X _let_3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_3) Xa2)) (and (=> _let_2 A3) (=> (not _let_2) (and (=> _let_1 B3) _let_1))))))))) (=> (forall ((Uu2 tptp.option4927543243414619207at_nat) (Uv2 tptp.list_VEBT_VEBT) (Uw tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Uu2) tptp.zero_zero_nat) Uv2) Uw))) (=> (= X _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2)))))) (not (forall ((Uy tptp.option4927543243414619207at_nat) (V tptp.nat) (TreeList tptp.list_VEBT_VEBT) (S tptp.vEBT_VEBT)) (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 Xa2) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList)))) (let ((_let_5 (@ (@ (@ (@ tptp.vEBT_Node Uy) _let_1) TreeList) S))) (=> (= 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 TreeList) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_2))) _let_4))))))))))))))))
% 6.73/7.06 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (@ (@ tptp.vEBT_vebt_member X) Xa2) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa2)) (=> (forall ((A3 Bool) (B3 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (let ((_let_3 (@ (@ tptp.vEBT_Leaf A3) B3))) (=> (= X _let_3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_3) Xa2)) (not (and (=> _let_2 A3) (=> (not _let_2) (and (=> _let_1 B3) _let_1)))))))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList)))) (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) TreeList) 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 TreeList) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_2))) _let_4))))))))))))))))))))))))
% 6.73/7.06 (assert (forall ((V2 tptp.num) (W2 tptp.num)) (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit0 V2))) (@ tptp.numeral_numeral_int (@ tptp.bit0 W2))) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int V2)) (@ tptp.numeral_numeral_int W2))))))
% 6.73/7.06 (assert (forall ((M2 tptp.int) (K2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) M2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.modulo_modulo_int M2) K2)) M2))))
% 6.73/7.06 (assert (forall ((M2 tptp.int) (D tptp.int)) (= (= (@ (@ tptp.modulo_modulo_int M2) D) tptp.zero_zero_int) (exists ((Q5 tptp.int)) (= M2 (@ (@ tptp.times_times_int D) Q5))))))
% 6.73/7.06 (assert (forall ((M2 tptp.int) (D tptp.int)) (=> (= (@ (@ tptp.modulo_modulo_int M2) D) tptp.zero_zero_int) (exists ((Q3 tptp.int)) (= M2 (@ (@ tptp.times_times_int D) Q3))))))
% 6.73/7.06 (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)))))
% 6.73/7.06 (assert (forall ((K2 tptp.int) (L tptp.int) (Q2 tptp.int) (R3 tptp.int)) (=> (@ (@ (@ tptp.eucl_rel_int K2) L) (@ (@ tptp.product_Pair_int_int Q2) R3)) (= (@ (@ tptp.modulo_modulo_int K2) L) R3))))
% 6.73/7.06 (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)))))))
% 6.73/7.06 (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))))))
% 6.73/7.06 (assert (forall ((I2 tptp.int) (K2 tptp.int)) (= (= (@ (@ tptp.modulo_modulo_int I2) K2) I2) (or (= K2 tptp.zero_zero_int) (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) I2) (@ (@ tptp.ord_less_int I2) K2)) (and (@ (@ tptp.ord_less_eq_int I2) tptp.zero_zero_int) (@ (@ tptp.ord_less_int K2) I2))))))
% 6.73/7.06 (assert (forall ((A4 tptp.int) (N tptp.int)) (= A4 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int A4) N)) N)) (@ (@ tptp.modulo_modulo_int A4) N)))))
% 6.73/7.06 (assert (forall ((K2 tptp.int) (L tptp.int)) (@ (@ (@ tptp.eucl_rel_int K2) L) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.divide_divide_int K2) L)) (@ (@ tptp.modulo_modulo_int K2) L)))))
% 6.73/7.06 (assert (forall ((L tptp.int) (K2 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) L) (=> (@ (@ tptp.ord_less_eq_int L) K2) (= (@ (@ tptp.modulo_modulo_int K2) L) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.minus_minus_int K2) L)) L))))))
% 6.73/7.06 (assert (forall ((A tptp.int) (B tptp.int) (Q2 tptp.int) (R3 tptp.int)) (=> (= A (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) Q2)) R3)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) R3) (=> (@ (@ tptp.ord_less_int R3) B) (= (@ (@ tptp.modulo_modulo_int A) B) R3))))))
% 6.73/7.06 (assert (forall ((A tptp.int) (B tptp.int) (Q2 tptp.int) (R3 tptp.int)) (=> (= A (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) Q2)) R3)) (=> (@ (@ tptp.ord_less_eq_int R3) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int B) R3) (= (@ (@ tptp.modulo_modulo_int A) B) R3))))))
% 6.73/7.06 (assert (forall ((P2 (-> tptp.int Bool)) (N tptp.int) (K2 tptp.int)) (= (@ P2 (@ (@ tptp.modulo_modulo_int N) K2)) (and (=> (= K2 tptp.zero_zero_int) (@ P2 N)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K2) (forall ((I tptp.int) (J tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) J) (@ (@ tptp.ord_less_int J) K2) (= N (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int K2) I)) J))) (@ P2 J)))) (=> (@ (@ tptp.ord_less_int K2) tptp.zero_zero_int) (forall ((I tptp.int) (J tptp.int)) (=> (and (@ (@ tptp.ord_less_int K2) J) (@ (@ tptp.ord_less_eq_int J) tptp.zero_zero_int) (= N (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int K2) I)) J))) (@ P2 J))))))))
% 6.73/7.06 (assert (forall ((C2 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) C2) (= (@ _let_1 (@ _let_2 C2)) (@ (@ tptp.plus_plus_int (@ _let_2 (@ (@ tptp.modulo_modulo_int (@ (@ tptp.divide_divide_int A) B)) C2))) (@ _let_1 B))))))))
% 6.73/7.06 (assert (forall ((K2 tptp.int) (P2 (-> tptp.int tptp.int Bool)) (N tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K2) (= (@ (@ P2 (@ (@ tptp.divide_divide_int N) K2)) (@ (@ tptp.modulo_modulo_int N) K2)) (forall ((I tptp.int) (J tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) J) (@ (@ tptp.ord_less_int J) K2) (= N (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int K2) I)) J))) (@ (@ P2 I) J)))))))
% 6.73/7.06 (assert (forall ((K2 tptp.int) (P2 (-> tptp.int tptp.int Bool)) (N tptp.int)) (=> (@ (@ tptp.ord_less_int K2) tptp.zero_zero_int) (= (@ (@ P2 (@ (@ tptp.divide_divide_int N) K2)) (@ (@ tptp.modulo_modulo_int N) K2)) (forall ((I tptp.int) (J tptp.int)) (=> (and (@ (@ tptp.ord_less_int K2) J) (@ (@ tptp.ord_less_eq_int J) tptp.zero_zero_int) (= N (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int K2) I)) J))) (@ (@ P2 I) J)))))))
% 6.73/7.06 (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)))))))))
% 6.73/7.06 (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))))))
% 6.73/7.06 (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 ((Ux tptp.list_VEBT_VEBT) (Uy tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) tptp.zero_zero_nat) Ux) Uy))) (=> (= 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) (Va2 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) Va2) 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) (V tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList) 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 TreeList)))) (=> (= X _let_2) (=> (= Y (or (= Xa2 Mi2) (= Xa2 Ma2) (and (=> _let_5 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList) _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 ((V tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Vd tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1) TreeList) Vd))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_3))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_4) (@ tptp.size_s6755466524823107622T_VEBT TreeList)))) (=> (= X _let_2) (=> (= Y (and (=> _let_5 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList) _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))))))))))))))))))))
% 6.73/7.06 (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 ((Ux tptp.list_VEBT_VEBT) (Uy tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) tptp.zero_zero_nat) Ux) Uy))) (=> (= 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) (Va2 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) Va2) 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) (V tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (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 Xa2) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList)))) (let ((_let_5 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList) 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 TreeList) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_2))) _let_4)))))))))) (not (forall ((V tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Vd tptp.vEBT_VEBT)) (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 Xa2) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList)))) (let ((_let_5 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1) TreeList) Vd))) (=> (= X _let_5) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_5) Xa2)) (and (=> _let_4 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_2))) _let_4))))))))))))))))))
% 6.73/7.06 (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) (Va2 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) Va2) 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) (V tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (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 Xa2) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList)))) (let ((_let_5 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList) 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 TreeList) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_2))) _let_4))))))))))) (not (forall ((V tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Vd tptp.vEBT_VEBT)) (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 Xa2) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList)))) (let ((_let_5 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1) TreeList) Vd))) (=> (= X _let_5) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_5) Xa2)) (not (and (=> _let_4 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_2))) _let_4)))))))))))))))))
% 6.73/7.06 (assert (= (@ tptp.arcosh_real tptp.one_one_real) tptp.zero_zero_real))
% 6.73/7.06 (assert (forall ((H tptp.real) (Z3 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 Z3))) (let ((_let_5 (@ (@ tptp.plus_plus_real Z3) H))) (=> (not (= H tptp.zero_zero_real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real Z3)) K5) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real _let_5)) K5) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real _let_5) N)) (@ _let_4 N))) H)) (@ _let_3 (@ _let_4 _let_2))))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ _let_3 (@ tptp.semiri5074537144036343181t_real _let_2))) (@ (@ tptp.power_power_real K5) (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ tptp.real_V7735802525324610683m_real H)))))))))))))
% 6.73/7.06 (assert (forall ((H tptp.complex) (Z3 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 Z3))) (let ((_let_4 (@ (@ tptp.plus_plus_complex Z3) H))) (=> (not (= H tptp.zero_zero_complex)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex Z3)) K5) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex _let_4)) K5) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ (@ tptp.power_power_complex _let_4) N)) (@ _let_3 N))) H)) (@ (@ 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 H))))))))))))
% 6.73/7.06 (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))))))))
% 6.73/7.06 (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))))))))
% 6.73/7.06 (assert (forall ((N tptp.nat) (A tptp.code_natural)) (let ((_let_1 (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se168947363167071951atural (@ tptp.suc N)) A) (@ (@ tptp.plus_p4538020629002901425atural (@ (@ tptp.modulo8411746178871703098atural A) _let_1)) (@ (@ tptp.times_2397367101498566445atural _let_1) (@ (@ tptp.bit_se168947363167071951atural N) (@ (@ tptp.divide5121882707175180666atural A) _let_1))))))))
% 6.73/7.06 (assert (= (@ tptp.artanh_real tptp.zero_zero_real) tptp.zero_zero_real))
% 6.73/7.06 (assert (forall ((W2 tptp.num) (A tptp.real)) (let ((_let_1 (@ tptp.times_times_real (@ tptp.numeral_numeral_real W2)))) (= (@ tptp.real_V7735802525324610683m_real (@ _let_1 A)) (@ _let_1 (@ tptp.real_V7735802525324610683m_real A))))))
% 6.73/7.06 (assert (forall ((W2 tptp.num) (A tptp.complex)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex W2)) A)) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real W2)) (@ tptp.real_V1022390504157884413omplex A)))))
% 6.73/7.06 (assert (forall ((A tptp.real) (W2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real W2))) (= (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.times_times_real A) _let_1)) (@ (@ tptp.times_times_real (@ tptp.real_V7735802525324610683m_real A)) _let_1)))))
% 6.73/7.06 (assert (forall ((A tptp.complex) (W2 tptp.num)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.times_times_complex A) (@ tptp.numera6690914467698888265omplex W2))) (@ (@ tptp.times_times_real (@ tptp.real_V1022390504157884413omplex A)) (@ tptp.numeral_numeral_real W2)))))
% 6.73/7.06 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real X)) tptp.zero_zero_real) (= X tptp.zero_zero_real))))
% 6.73/7.06 (assert (forall ((X tptp.complex)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex X)) tptp.zero_zero_real) (= X tptp.zero_zero_complex))))
% 6.73/7.06 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.real_V7735802525324610683m_real X)) (not (= X tptp.zero_zero_real)))))
% 6.73/7.06 (assert (forall ((X tptp.complex)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.real_V1022390504157884413omplex X)) (not (= X tptp.zero_zero_complex)))))
% 6.73/7.06 (assert (= (@ tptp.real_V7735802525324610683m_real tptp.zero_zero_real) tptp.zero_zero_real))
% 6.73/7.06 (assert (= (@ tptp.real_V1022390504157884413omplex tptp.zero_zero_complex) tptp.zero_zero_real))
% 6.73/7.06 (assert (forall ((X tptp.real)) (= (= (@ tptp.real_V7735802525324610683m_real X) tptp.zero_zero_real) (= X tptp.zero_zero_real))))
% 6.73/7.06 (assert (forall ((X tptp.complex)) (= (= (@ tptp.real_V1022390504157884413omplex X) tptp.zero_zero_real) (= X tptp.zero_zero_complex))))
% 6.73/7.06 (assert (forall ((Z3 tptp.real) (W2 tptp.real) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real Z3)) tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real W2)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real Z3) M2)) (@ (@ tptp.power_power_real W2) M2)))) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real M2)) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real Z3) W2))))))))
% 6.73/7.06 (assert (forall ((Z3 tptp.complex) (W2 tptp.complex) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex Z3)) tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex W2)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex (@ (@ tptp.power_power_complex Z3) M2)) (@ (@ tptp.power_power_complex W2) M2)))) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real M2)) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex Z3) W2))))))))
% 6.73/7.06 (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)))))
% 6.73/7.06 (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)))))
% 6.73/7.06 (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))))))
% 6.73/7.06 (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))))))
% 6.73/7.06 (assert (forall ((W2 tptp.real) (N tptp.nat) (Z3 tptp.real)) (=> (= (@ (@ tptp.power_power_real W2) N) (@ (@ tptp.power_power_real Z3) N)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.real_V7735802525324610683m_real W2) (@ tptp.real_V7735802525324610683m_real Z3))))))
% 6.73/7.06 (assert (forall ((W2 tptp.complex) (N tptp.nat) (Z3 tptp.complex)) (=> (= (@ (@ tptp.power_power_complex W2) N) (@ (@ tptp.power_power_complex Z3) N)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.real_V1022390504157884413omplex W2) (@ tptp.real_V1022390504157884413omplex Z3))))))
% 6.73/7.06 (assert (forall ((X tptp.real) (R3 tptp.real) (Y tptp.real) (S2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real X)) R3) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real Y)) S2) (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.times_times_real X) Y))) (@ (@ tptp.times_times_real R3) S2))))))
% 6.73/7.06 (assert (forall ((X tptp.complex) (R3 tptp.real) (Y tptp.complex) (S2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex X)) R3) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex Y)) S2) (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.times_times_complex X) Y))) (@ (@ tptp.times_times_real R3) S2))))))
% 6.73/7.06 (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)))))
% 6.73/7.06 (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)))))
% 6.73/7.06 (assert (forall ((W2 tptp.real) (N tptp.nat)) (=> (= (@ (@ tptp.power_power_real W2) N) tptp.one_one_real) (or (= (@ tptp.real_V7735802525324610683m_real W2) tptp.one_one_real) (= N tptp.zero_zero_nat)))))
% 6.73/7.06 (assert (forall ((W2 tptp.complex) (N tptp.nat)) (=> (= (@ (@ tptp.power_power_complex W2) N) tptp.one_one_complex) (or (= (@ tptp.real_V1022390504157884413omplex W2) tptp.one_one_real) (= N tptp.zero_zero_nat)))))
% 6.73/7.06 (assert (= (@ tptp.arsinh_real tptp.zero_zero_real) tptp.zero_zero_real))
% 6.73/7.06 (assert (forall ((X tptp.nat) (Y tptp.vEBT_VEBT)) (let ((_let_1 (not (= Y (@ (@ tptp.vEBT_Leaf false) false))))) (=> (= (@ tptp.vEBT_vebt_buildup X) Y) (=> (=> (= X tptp.zero_zero_nat) _let_1) (=> (=> (= X (@ tptp.suc tptp.zero_zero_nat)) _let_1) (not (forall ((Va tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_2) _let_1))) (let ((_let_4 (@ tptp.suc _let_3))) (let ((_let_5 (@ tptp.vEBT_vebt_buildup _let_3))) (let ((_let_6 (@ tptp.power_power_nat _let_1))) (let ((_let_7 (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_2))) (let ((_let_8 (@ (@ tptp.dvd_dvd_nat _let_1) _let_2))) (=> (= X _let_2) (not (and (=> _let_8 (= Y (@ (@ _let_7 (@ (@ tptp.replicate_VEBT_VEBT (@ _let_6 _let_3)) _let_5)) _let_5))) (=> (not _let_8) (= Y (@ (@ _let_7 (@ (@ tptp.replicate_VEBT_VEBT (@ _let_6 _let_4)) _let_5)) (@ tptp.vEBT_vebt_buildup _let_4)))))))))))))))))))))))
% 6.73/7.06 (assert (forall ((I5 tptp.set_real) (X (-> tptp.real tptp.code_integer)) (Y (-> tptp.real tptp.code_integer))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I tptp.real)) (and (@ (@ tptp.member_real I) I5) (not (= (@ X I) tptp.one_one_Code_integer)))))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I tptp.real)) (and (@ (@ tptp.member_real I) I5) (not (= (@ Y I) tptp.one_one_Code_integer)))))) (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I tptp.real)) (and (@ (@ tptp.member_real I) I5) (not (= (@ (@ tptp.times_3573771949741848930nteger (@ X I)) (@ Y I)) tptp.one_one_Code_integer))))))))))
% 6.73/7.06 (assert (forall ((I5 tptp.set_nat) (X (-> tptp.nat tptp.code_integer)) (Y (-> tptp.nat tptp.code_integer))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I tptp.nat)) (and (@ (@ tptp.member_nat I) I5) (not (= (@ X I) tptp.one_one_Code_integer)))))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I tptp.nat)) (and (@ (@ tptp.member_nat I) I5) (not (= (@ Y I) tptp.one_one_Code_integer)))))) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I tptp.nat)) (and (@ (@ tptp.member_nat I) I5) (not (= (@ (@ tptp.times_3573771949741848930nteger (@ X I)) (@ Y I)) tptp.one_one_Code_integer))))))))))
% 6.73/7.06 (assert (forall ((I5 tptp.set_int) (X (-> tptp.int tptp.code_integer)) (Y (-> tptp.int tptp.code_integer))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I tptp.int)) (and (@ (@ tptp.member_int I) I5) (not (= (@ X I) tptp.one_one_Code_integer)))))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I tptp.int)) (and (@ (@ tptp.member_int I) I5) (not (= (@ Y I) tptp.one_one_Code_integer)))))) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I tptp.int)) (and (@ (@ tptp.member_int I) I5) (not (= (@ (@ tptp.times_3573771949741848930nteger (@ X I)) (@ Y I)) tptp.one_one_Code_integer))))))))))
% 6.73/7.06 (assert (forall ((I5 tptp.set_complex) (X (-> tptp.complex tptp.code_integer)) (Y (-> tptp.complex tptp.code_integer))) (=> (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I tptp.complex)) (and (@ (@ tptp.member_complex I) I5) (not (= (@ X I) tptp.one_one_Code_integer)))))) (=> (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I tptp.complex)) (and (@ (@ tptp.member_complex I) I5) (not (= (@ Y I) tptp.one_one_Code_integer)))))) (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I tptp.complex)) (and (@ (@ tptp.member_complex I) I5) (not (= (@ (@ tptp.times_3573771949741848930nteger (@ X I)) (@ Y I)) tptp.one_one_Code_integer))))))))))
% 6.73/7.06 (assert (forall ((I5 tptp.set_real) (X (-> tptp.real tptp.complex)) (Y (-> tptp.real tptp.complex))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I tptp.real)) (and (@ (@ tptp.member_real I) I5) (not (= (@ X I) tptp.one_one_complex)))))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I tptp.real)) (and (@ (@ tptp.member_real I) I5) (not (= (@ Y I) tptp.one_one_complex)))))) (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I tptp.real)) (and (@ (@ tptp.member_real I) I5) (not (= (@ (@ tptp.times_times_complex (@ X I)) (@ Y I)) tptp.one_one_complex))))))))))
% 6.73/7.06 (assert (forall ((I5 tptp.set_nat) (X (-> tptp.nat tptp.complex)) (Y (-> tptp.nat tptp.complex))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I tptp.nat)) (and (@ (@ tptp.member_nat I) I5) (not (= (@ X I) tptp.one_one_complex)))))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I tptp.nat)) (and (@ (@ tptp.member_nat I) I5) (not (= (@ Y I) tptp.one_one_complex)))))) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I tptp.nat)) (and (@ (@ tptp.member_nat I) I5) (not (= (@ (@ tptp.times_times_complex (@ X I)) (@ Y I)) tptp.one_one_complex))))))))))
% 6.73/7.06 (assert (forall ((I5 tptp.set_int) (X (-> tptp.int tptp.complex)) (Y (-> tptp.int tptp.complex))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I tptp.int)) (and (@ (@ tptp.member_int I) I5) (not (= (@ X I) tptp.one_one_complex)))))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I tptp.int)) (and (@ (@ tptp.member_int I) I5) (not (= (@ Y I) tptp.one_one_complex)))))) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I tptp.int)) (and (@ (@ tptp.member_int I) I5) (not (= (@ (@ tptp.times_times_complex (@ X I)) (@ Y I)) tptp.one_one_complex))))))))))
% 6.73/7.06 (assert (forall ((I5 tptp.set_complex) (X (-> tptp.complex tptp.complex)) (Y (-> tptp.complex tptp.complex))) (=> (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I tptp.complex)) (and (@ (@ tptp.member_complex I) I5) (not (= (@ X I) tptp.one_one_complex)))))) (=> (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I tptp.complex)) (and (@ (@ tptp.member_complex I) I5) (not (= (@ Y I) tptp.one_one_complex)))))) (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I tptp.complex)) (and (@ (@ tptp.member_complex I) I5) (not (= (@ (@ tptp.times_times_complex (@ X I)) (@ Y I)) tptp.one_one_complex))))))))))
% 6.73/7.06 (assert (forall ((I5 tptp.set_real) (X (-> tptp.real tptp.real)) (Y (-> tptp.real tptp.real))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I tptp.real)) (and (@ (@ tptp.member_real I) I5) (not (= (@ X I) tptp.one_one_real)))))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I tptp.real)) (and (@ (@ tptp.member_real I) I5) (not (= (@ Y I) tptp.one_one_real)))))) (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I tptp.real)) (and (@ (@ tptp.member_real I) I5) (not (= (@ (@ tptp.times_times_real (@ X I)) (@ Y I)) tptp.one_one_real))))))))))
% 6.73/7.06 (assert (forall ((I5 tptp.set_nat) (X (-> tptp.nat tptp.real)) (Y (-> tptp.nat tptp.real))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I tptp.nat)) (and (@ (@ tptp.member_nat I) I5) (not (= (@ X I) tptp.one_one_real)))))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I tptp.nat)) (and (@ (@ tptp.member_nat I) I5) (not (= (@ Y I) tptp.one_one_real)))))) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I tptp.nat)) (and (@ (@ tptp.member_nat I) I5) (not (= (@ (@ tptp.times_times_real (@ X I)) (@ Y I)) tptp.one_one_real))))))))))
% 6.73/7.06 (assert (forall ((N tptp.nat) (M2 tptp.nat) (X tptp.complex)) (let ((_let_1 (@ tptp.power_power_complex X))) (let ((_let_2 (@ (@ tptp.groups2073611262835488442omplex _let_1) (@ (@ tptp.set_or1269000886237332187st_nat M2) N)))) (let ((_let_3 (= X tptp.one_one_complex))) (let ((_let_4 (@ (@ tptp.ord_less_nat N) M2))) (and (=> _let_4 (= _let_2 tptp.zero_zero_complex)) (=> (not _let_4) (and (=> _let_3 (= _let_2 (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat)) M2)))) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ _let_1 M2)) (@ _let_1 (@ tptp.suc N)))) (@ (@ tptp.minus_minus_complex tptp.one_one_complex) X)))))))))))))
% 6.73/7.06 (assert (forall ((N tptp.nat) (M2 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 M2) N)))) (let ((_let_3 (= X tptp.one_one_rat))) (let ((_let_4 (@ (@ tptp.ord_less_nat N) M2))) (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)) M2)))) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ _let_1 M2)) (@ _let_1 (@ tptp.suc N)))) (@ (@ tptp.minus_minus_rat tptp.one_one_rat) X)))))))))))))
% 6.73/7.06 (assert (forall ((N tptp.nat) (M2 tptp.nat) (X tptp.real)) (let ((_let_1 (@ tptp.power_power_real X))) (let ((_let_2 (@ (@ tptp.groups6591440286371151544t_real _let_1) (@ (@ tptp.set_or1269000886237332187st_nat M2) N)))) (let ((_let_3 (= X tptp.one_one_real))) (let ((_let_4 (@ (@ tptp.ord_less_nat N) M2))) (and (=> _let_4 (= _let_2 tptp.zero_zero_real)) (=> (not _let_4) (and (=> _let_3 (= _let_2 (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat)) M2)))) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ _let_1 M2)) (@ _let_1 (@ tptp.suc N)))) (@ (@ tptp.minus_minus_real tptp.one_one_real) X)))))))))))))
% 6.73/7.06 (assert (forall ((I5 tptp.set_real) (X (-> tptp.real tptp.complex)) (Y (-> tptp.real tptp.complex))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I tptp.real)) (and (@ (@ tptp.member_real I) I5) (not (= (@ X I) tptp.zero_zero_complex)))))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I tptp.real)) (and (@ (@ tptp.member_real I) I5) (not (= (@ Y I) tptp.zero_zero_complex)))))) (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I tptp.real)) (and (@ (@ tptp.member_real I) I5) (not (= (@ (@ tptp.plus_plus_complex (@ X I)) (@ Y I)) tptp.zero_zero_complex))))))))))
% 6.73/7.06 (assert (forall ((I5 tptp.set_nat) (X (-> tptp.nat tptp.complex)) (Y (-> tptp.nat tptp.complex))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I tptp.nat)) (and (@ (@ tptp.member_nat I) I5) (not (= (@ X I) tptp.zero_zero_complex)))))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I tptp.nat)) (and (@ (@ tptp.member_nat I) I5) (not (= (@ Y I) tptp.zero_zero_complex)))))) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I tptp.nat)) (and (@ (@ tptp.member_nat I) I5) (not (= (@ (@ tptp.plus_plus_complex (@ X I)) (@ Y I)) tptp.zero_zero_complex))))))))))
% 6.73/7.06 (assert (forall ((I5 tptp.set_int) (X (-> tptp.int tptp.complex)) (Y (-> tptp.int tptp.complex))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I tptp.int)) (and (@ (@ tptp.member_int I) I5) (not (= (@ X I) tptp.zero_zero_complex)))))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I tptp.int)) (and (@ (@ tptp.member_int I) I5) (not (= (@ Y I) tptp.zero_zero_complex)))))) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I tptp.int)) (and (@ (@ tptp.member_int I) I5) (not (= (@ (@ tptp.plus_plus_complex (@ X I)) (@ Y I)) tptp.zero_zero_complex))))))))))
% 6.73/7.06 (assert (forall ((I5 tptp.set_complex) (X (-> tptp.complex tptp.complex)) (Y (-> tptp.complex tptp.complex))) (=> (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I tptp.complex)) (and (@ (@ tptp.member_complex I) I5) (not (= (@ X I) tptp.zero_zero_complex)))))) (=> (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I tptp.complex)) (and (@ (@ tptp.member_complex I) I5) (not (= (@ Y I) tptp.zero_zero_complex)))))) (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I tptp.complex)) (and (@ (@ tptp.member_complex I) I5) (not (= (@ (@ tptp.plus_plus_complex (@ X I)) (@ Y I)) tptp.zero_zero_complex))))))))))
% 6.73/7.06 (assert (forall ((I5 tptp.set_real) (X (-> tptp.real tptp.real)) (Y (-> tptp.real tptp.real))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I tptp.real)) (and (@ (@ tptp.member_real I) I5) (not (= (@ X I) tptp.zero_zero_real)))))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I tptp.real)) (and (@ (@ tptp.member_real I) I5) (not (= (@ Y I) tptp.zero_zero_real)))))) (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I tptp.real)) (and (@ (@ tptp.member_real I) I5) (not (= (@ (@ tptp.plus_plus_real (@ X I)) (@ Y I)) tptp.zero_zero_real))))))))))
% 6.73/7.06 (assert (forall ((I5 tptp.set_nat) (X (-> tptp.nat tptp.real)) (Y (-> tptp.nat tptp.real))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I tptp.nat)) (and (@ (@ tptp.member_nat I) I5) (not (= (@ X I) tptp.zero_zero_real)))))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I tptp.nat)) (and (@ (@ tptp.member_nat I) I5) (not (= (@ Y I) tptp.zero_zero_real)))))) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I tptp.nat)) (and (@ (@ tptp.member_nat I) I5) (not (= (@ (@ tptp.plus_plus_real (@ X I)) (@ Y I)) tptp.zero_zero_real))))))))))
% 6.73/7.06 (assert (forall ((I5 tptp.set_int) (X (-> tptp.int tptp.real)) (Y (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I tptp.int)) (and (@ (@ tptp.member_int I) I5) (not (= (@ X I) tptp.zero_zero_real)))))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I tptp.int)) (and (@ (@ tptp.member_int I) I5) (not (= (@ Y I) tptp.zero_zero_real)))))) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I tptp.int)) (and (@ (@ tptp.member_int I) I5) (not (= (@ (@ tptp.plus_plus_real (@ X I)) (@ Y I)) tptp.zero_zero_real))))))))))
% 6.73/7.06 (assert (forall ((I5 tptp.set_complex) (X (-> tptp.complex tptp.real)) (Y (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I tptp.complex)) (and (@ (@ tptp.member_complex I) I5) (not (= (@ X I) tptp.zero_zero_real)))))) (=> (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I tptp.complex)) (and (@ (@ tptp.member_complex I) I5) (not (= (@ Y I) tptp.zero_zero_real)))))) (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I tptp.complex)) (and (@ (@ tptp.member_complex I) I5) (not (= (@ (@ tptp.plus_plus_real (@ X I)) (@ Y I)) tptp.zero_zero_real))))))))))
% 6.73/7.06 (assert (forall ((I5 tptp.set_real) (X (-> tptp.real tptp.rat)) (Y (-> tptp.real tptp.rat))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I tptp.real)) (and (@ (@ tptp.member_real I) I5) (not (= (@ X I) tptp.zero_zero_rat)))))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I tptp.real)) (and (@ (@ tptp.member_real I) I5) (not (= (@ Y I) tptp.zero_zero_rat)))))) (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I tptp.real)) (and (@ (@ tptp.member_real I) I5) (not (= (@ (@ tptp.plus_plus_rat (@ X I)) (@ Y I)) tptp.zero_zero_rat))))))))))
% 6.73/7.06 (assert (forall ((I5 tptp.set_nat) (X (-> tptp.nat tptp.rat)) (Y (-> tptp.nat tptp.rat))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I tptp.nat)) (and (@ (@ tptp.member_nat I) I5) (not (= (@ X I) tptp.zero_zero_rat)))))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I tptp.nat)) (and (@ (@ tptp.member_nat I) I5) (not (= (@ Y I) tptp.zero_zero_rat)))))) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I tptp.nat)) (and (@ (@ tptp.member_nat I) I5) (not (= (@ (@ tptp.plus_plus_rat (@ X I)) (@ Y I)) tptp.zero_zero_rat))))))))))
% 6.73/7.06 (assert (forall ((Z3 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real Z3)) tptp.one_one_real) (@ (@ tptp.sums_real (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N4))) (@ (@ tptp.power_power_real Z3) N4)))) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real tptp.one_one_real) Z3)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 6.73/7.06 (assert (forall ((Z3 tptp.complex)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex Z3)) tptp.one_one_real) (@ (@ tptp.sums_complex (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex (@ tptp.suc N4))) (@ (@ tptp.power_power_complex Z3) N4)))) (@ (@ tptp.divide1717551699836669952omplex tptp.one_one_complex) (@ (@ tptp.power_power_complex (@ (@ tptp.minus_minus_complex tptp.one_one_complex) Z3)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 6.73/7.06 (assert (forall ((Z3 tptp.complex) (N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numera6690914467698888265omplex _let_1))) (let ((_let_3 (@ tptp.numeral_numeral_nat _let_1))) (let ((_let_4 (@ (@ tptp.times_times_nat _let_3) N))) (= (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.times_times_complex _let_2) Z3)) _let_4) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.power_power_nat _let_3) _let_4))) (@ (@ tptp.comm_s2602460028002588243omplex Z3) N))) (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.plus_plus_complex Z3) (@ (@ tptp.divide1717551699836669952omplex tptp.one_one_complex) _let_2))) N)))))))))
% 6.73/7.06 (assert (forall ((Z3 tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_rat _let_1))) (let ((_let_3 (@ tptp.numeral_numeral_nat _let_1))) (let ((_let_4 (@ (@ tptp.times_times_nat _let_3) N))) (= (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.times_times_rat _let_2) Z3)) _let_4) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.power_power_nat _let_3) _let_4))) (@ (@ tptp.comm_s4028243227959126397er_rat Z3) N))) (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.plus_plus_rat Z3) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) _let_2))) N)))))))))
% 6.73/7.06 (assert (forall ((Z3 tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_real _let_1))) (let ((_let_3 (@ tptp.numeral_numeral_nat _let_1))) (let ((_let_4 (@ (@ tptp.times_times_nat _let_3) N))) (= (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.times_times_real _let_2) Z3)) _let_4) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.power_power_nat _let_3) _let_4))) (@ (@ tptp.comm_s7457072308508201937r_real Z3) N))) (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.plus_plus_real Z3) (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_2))) N)))))))))
% 6.73/7.06 (assert (forall ((A tptp.complex)) (@ (@ tptp.dvd_dvd_complex A) tptp.zero_zero_complex)))
% 6.73/7.06 (assert (forall ((A tptp.real)) (@ (@ tptp.dvd_dvd_real A) tptp.zero_zero_real)))
% 6.73/7.06 (assert (forall ((A tptp.rat)) (@ (@ tptp.dvd_dvd_rat A) tptp.zero_zero_rat)))
% 6.73/7.06 (assert (forall ((A tptp.nat)) (@ (@ tptp.dvd_dvd_nat A) tptp.zero_zero_nat)))
% 6.73/7.06 (assert (forall ((A tptp.int)) (@ (@ tptp.dvd_dvd_int A) tptp.zero_zero_int)))
% 6.73/7.06 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.dvd_dvd_complex tptp.zero_zero_complex) A) (= A tptp.zero_zero_complex))))
% 6.73/7.06 (assert (forall ((A tptp.real)) (= (@ (@ tptp.dvd_dvd_real tptp.zero_zero_real) A) (= A tptp.zero_zero_real))))
% 6.73/7.06 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.dvd_dvd_rat tptp.zero_zero_rat) A) (= A tptp.zero_zero_rat))))
% 6.73/7.06 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.dvd_dvd_nat tptp.zero_zero_nat) A) (= A tptp.zero_zero_nat))))
% 6.73/7.06 (assert (forall ((A tptp.int)) (= (@ (@ tptp.dvd_dvd_int tptp.zero_zero_int) A) (= A tptp.zero_zero_int))))
% 6.73/7.06 (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)))))
% 6.73/7.06 (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)))))
% 6.73/7.06 (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)))))
% 6.73/7.06 (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)))))
% 6.73/7.06 (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)))))
% 6.73/7.06 (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)))))
% 6.73/7.06 (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)))))
% 6.73/7.06 (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)))))
% 6.73/7.06 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (=> (@ _let_1 B) (=> (@ _let_1 C2) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.divide_divide_nat B) A)) (@ (@ tptp.divide_divide_nat C2) A)) (@ (@ tptp.dvd_dvd_nat B) C2)))))))
% 6.73/7.06 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (=> (@ _let_1 B) (=> (@ _let_1 C2) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.divide_divide_int B) A)) (@ (@ tptp.divide_divide_int C2) A)) (@ (@ tptp.dvd_dvd_int B) C2)))))))
% 6.73/7.06 (assert (forall ((M2 tptp.nat)) (= (@ (@ tptp.dvd_dvd_nat M2) tptp.one_one_nat) (= M2 tptp.one_one_nat))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((Uu3 tptp.nat)) tptp.zero_zero_nat)) A4) tptp.zero_zero_nat)))
% 6.73/7.06 (assert (forall ((A4 tptp.set_int)) (= (@ (@ tptp.groups4538972089207619220nt_int (lambda ((Uu3 tptp.int)) tptp.zero_zero_int)) A4) tptp.zero_zero_int)))
% 6.73/7.06 (assert (forall ((A4 tptp.set_nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((Uu3 tptp.nat)) tptp.zero_zero_real)) A4) tptp.zero_zero_real)))
% 6.73/7.06 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat B) A)) (@ (@ tptp.times_times_nat C2) A)) (@ (@ tptp.dvd_dvd_nat B) C2)))))
% 6.73/7.06 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (=> (not (= A tptp.zero_zero_int)) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int B) A)) (@ (@ tptp.times_times_int C2) A)) (@ (@ tptp.dvd_dvd_int B) C2)))))
% 6.73/7.06 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 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 C2)) (@ (@ tptp.dvd_dvd_nat B) C2))))))
% 6.73/7.06 (assert (forall ((A tptp.int) (B tptp.int) (C2 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 C2)) (@ (@ tptp.dvd_dvd_int B) C2))))))
% 6.73/7.06 (assert (forall ((A tptp.complex) (C2 tptp.complex) (B tptp.complex)) (= (@ (@ tptp.dvd_dvd_complex (@ (@ tptp.times_times_complex A) C2)) (@ (@ tptp.times_times_complex B) C2)) (or (= C2 tptp.zero_zero_complex) (@ (@ tptp.dvd_dvd_complex A) B)))))
% 6.73/7.06 (assert (forall ((A tptp.real) (C2 tptp.real) (B tptp.real)) (= (@ (@ tptp.dvd_dvd_real (@ (@ tptp.times_times_real A) C2)) (@ (@ tptp.times_times_real B) C2)) (or (= C2 tptp.zero_zero_real) (@ (@ tptp.dvd_dvd_real A) B)))))
% 6.73/7.06 (assert (forall ((A tptp.rat) (C2 tptp.rat) (B tptp.rat)) (= (@ (@ tptp.dvd_dvd_rat (@ (@ tptp.times_times_rat A) C2)) (@ (@ tptp.times_times_rat B) C2)) (or (= C2 tptp.zero_zero_rat) (@ (@ tptp.dvd_dvd_rat A) B)))))
% 6.73/7.06 (assert (forall ((A tptp.int) (C2 tptp.int) (B tptp.int)) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A) C2)) (@ (@ tptp.times_times_int B) C2)) (or (= C2 tptp.zero_zero_int) (@ (@ tptp.dvd_dvd_int A) B)))))
% 6.73/7.06 (assert (forall ((C2 tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex C2))) (= (@ (@ tptp.dvd_dvd_complex (@ _let_1 A)) (@ _let_1 B)) (or (= C2 tptp.zero_zero_complex) (@ (@ tptp.dvd_dvd_complex A) B))))))
% 6.73/7.06 (assert (forall ((C2 tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real C2))) (= (@ (@ tptp.dvd_dvd_real (@ _let_1 A)) (@ _let_1 B)) (or (= C2 tptp.zero_zero_real) (@ (@ tptp.dvd_dvd_real A) B))))))
% 6.73/7.06 (assert (forall ((C2 tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C2))) (= (@ (@ tptp.dvd_dvd_rat (@ _let_1 A)) (@ _let_1 B)) (or (= C2 tptp.zero_zero_rat) (@ (@ tptp.dvd_dvd_rat A) B))))))
% 6.73/7.06 (assert (forall ((C2 tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C2))) (= (@ (@ tptp.dvd_dvd_int (@ _let_1 A)) (@ _let_1 B)) (or (= C2 tptp.zero_zero_int) (@ (@ tptp.dvd_dvd_int A) B))))))
% 6.73/7.06 (assert (forall ((A tptp.real) (B tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real A))) (= (@ _let_1 (@ (@ tptp.plus_plus_real B) (@ (@ tptp.times_times_real C2) A))) (@ _let_1 B)))))
% 6.73/7.06 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat B) (@ (@ tptp.times_times_rat C2) A))) (@ _let_1 B)))))
% 6.73/7.06 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat B) (@ (@ tptp.times_times_nat C2) A))) (@ _let_1 B)))))
% 6.73/7.06 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (= (@ _let_1 (@ (@ tptp.plus_plus_int B) (@ (@ tptp.times_times_int C2) A))) (@ _let_1 B)))))
% 6.73/7.06 (assert (forall ((A tptp.real) (C2 tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real A))) (= (@ _let_1 (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real C2) A)) B)) (@ _let_1 B)))))
% 6.73/7.06 (assert (forall ((A tptp.rat) (C2 tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat C2) A)) B)) (@ _let_1 B)))))
% 6.73/7.06 (assert (forall ((A tptp.nat) (C2 tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat C2) A)) B)) (@ _let_1 B)))))
% 6.73/7.06 (assert (forall ((A tptp.int) (C2 tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (= (@ _let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int C2) A)) B)) (@ _let_1 B)))))
% 6.73/7.06 (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)))))
% 6.73/7.06 (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)))))
% 6.73/7.06 (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)))))
% 6.73/7.06 (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))))
% 6.73/7.06 (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))))
% 6.73/7.06 (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))))
% 6.73/7.06 (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))))
% 6.73/7.06 (assert (forall ((C2 tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat C2))) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat A) B)) C2) (@ (@ tptp.plus_plus_nat (@ (@ tptp.divide_divide_nat A) C2)) (@ (@ tptp.divide_divide_nat B) C2))))))))
% 6.73/7.06 (assert (forall ((C2 tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int C2))) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int A) B)) C2) (@ (@ tptp.plus_plus_int (@ (@ tptp.divide_divide_int A) C2)) (@ (@ tptp.divide_divide_int B) C2))))))))
% 6.73/7.06 (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)))))
% 6.73/7.06 (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)))))
% 6.73/7.06 (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)))))
% 6.73/7.06 (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))))
% 6.73/7.06 (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))))
% 6.73/7.06 (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))))
% 6.73/7.06 (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)))))
% 6.73/7.06 (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)))))
% 6.73/7.06 (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)))))
% 6.73/7.06 (assert (forall ((G2 (-> tptp.nat tptp.complex))) (= (@ (@ tptp.groups2073611262835488442omplex G2) tptp.bot_bot_set_nat) tptp.zero_zero_complex)))
% 6.73/7.06 (assert (forall ((G2 (-> tptp.nat tptp.rat))) (= (@ (@ tptp.groups2906978787729119204at_rat G2) tptp.bot_bot_set_nat) tptp.zero_zero_rat)))
% 6.73/7.06 (assert (forall ((G2 (-> tptp.nat tptp.int))) (= (@ (@ tptp.groups3539618377306564664at_int G2) tptp.bot_bot_set_nat) tptp.zero_zero_int)))
% 6.73/7.06 (assert (forall ((G2 (-> tptp.int tptp.complex))) (= (@ (@ tptp.groups3049146728041665814omplex G2) tptp.bot_bot_set_int) tptp.zero_zero_complex)))
% 6.73/7.06 (assert (forall ((G2 (-> tptp.int tptp.real))) (= (@ (@ tptp.groups8778361861064173332t_real G2) tptp.bot_bot_set_int) tptp.zero_zero_real)))
% 6.73/7.06 (assert (forall ((G2 (-> tptp.int tptp.rat))) (= (@ (@ tptp.groups3906332499630173760nt_rat G2) tptp.bot_bot_set_int) tptp.zero_zero_rat)))
% 6.73/7.06 (assert (forall ((G2 (-> tptp.int tptp.nat))) (= (@ (@ tptp.groups4541462559716669496nt_nat G2) tptp.bot_bot_set_int) tptp.zero_zero_nat)))
% 6.73/7.06 (assert (forall ((G2 (-> tptp.real tptp.complex))) (= (@ (@ tptp.groups5754745047067104278omplex G2) tptp.bot_bot_set_real) tptp.zero_zero_complex)))
% 6.73/7.06 (assert (forall ((G2 (-> tptp.real tptp.real))) (= (@ (@ tptp.groups8097168146408367636l_real G2) tptp.bot_bot_set_real) tptp.zero_zero_real)))
% 6.73/7.06 (assert (forall ((G2 (-> tptp.real tptp.rat))) (= (@ (@ tptp.groups1300246762558778688al_rat G2) tptp.bot_bot_set_real) tptp.zero_zero_rat)))
% 6.73/7.06 (assert (forall ((A4 tptp.set_nat) (G2 (-> tptp.nat tptp.complex))) (=> (not (@ tptp.finite_finite_nat A4)) (= (@ (@ tptp.groups2073611262835488442omplex G2) A4) tptp.zero_zero_complex))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_int) (G2 (-> tptp.int tptp.complex))) (=> (not (@ tptp.finite_finite_int A4)) (= (@ (@ tptp.groups3049146728041665814omplex G2) A4) tptp.zero_zero_complex))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_complex) (G2 (-> tptp.complex tptp.complex))) (=> (not (@ tptp.finite3207457112153483333omplex A4)) (= (@ (@ tptp.groups7754918857620584856omplex G2) A4) tptp.zero_zero_complex))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_int) (G2 (-> tptp.int tptp.real))) (=> (not (@ tptp.finite_finite_int A4)) (= (@ (@ tptp.groups8778361861064173332t_real G2) A4) tptp.zero_zero_real))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_complex) (G2 (-> tptp.complex tptp.real))) (=> (not (@ tptp.finite3207457112153483333omplex A4)) (= (@ (@ tptp.groups5808333547571424918x_real G2) A4) tptp.zero_zero_real))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_nat) (G2 (-> tptp.nat tptp.rat))) (=> (not (@ tptp.finite_finite_nat A4)) (= (@ (@ tptp.groups2906978787729119204at_rat G2) A4) tptp.zero_zero_rat))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_int) (G2 (-> tptp.int tptp.rat))) (=> (not (@ tptp.finite_finite_int A4)) (= (@ (@ tptp.groups3906332499630173760nt_rat G2) A4) tptp.zero_zero_rat))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_complex) (G2 (-> tptp.complex tptp.rat))) (=> (not (@ tptp.finite3207457112153483333omplex A4)) (= (@ (@ tptp.groups5058264527183730370ex_rat G2) A4) tptp.zero_zero_rat))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_int) (G2 (-> tptp.int tptp.nat))) (=> (not (@ tptp.finite_finite_int A4)) (= (@ (@ tptp.groups4541462559716669496nt_nat G2) A4) tptp.zero_zero_nat))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_complex) (G2 (-> tptp.complex tptp.nat))) (=> (not (@ tptp.finite3207457112153483333omplex A4)) (= (@ (@ tptp.groups5693394587270226106ex_nat G2) A4) tptp.zero_zero_nat))))
% 6.73/7.06 (assert (forall ((F3 tptp.set_int) (F2 (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int F3) (= (= (@ (@ tptp.groups4541462559716669496nt_nat F2) F3) tptp.zero_zero_nat) (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) F3) (= (@ F2 X4) tptp.zero_zero_nat)))))))
% 6.73/7.06 (assert (forall ((F3 tptp.set_complex) (F2 (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex F3) (= (= (@ (@ tptp.groups5693394587270226106ex_nat F2) F3) tptp.zero_zero_nat) (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) F3) (= (@ F2 X4) tptp.zero_zero_nat)))))))
% 6.73/7.06 (assert (forall ((F3 tptp.set_nat) (F2 (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_nat F3) (= (= (@ (@ tptp.groups3542108847815614940at_nat F2) F3) tptp.zero_zero_nat) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) F3) (= (@ F2 X4) tptp.zero_zero_nat)))))))
% 6.73/7.06 (assert (forall ((C2 tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int C2))) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.minus_minus_int A) B)) C2) (@ (@ tptp.minus_minus_int (@ (@ tptp.divide_divide_int A) C2)) (@ (@ tptp.divide_divide_int B) C2))))))))
% 6.73/7.06 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) B) (= (@ (@ tptp.modulo_modulo_nat B) A) tptp.zero_zero_nat))))
% 6.73/7.06 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) B) (= (@ (@ tptp.modulo_modulo_int B) A) tptp.zero_zero_int))))
% 6.73/7.06 (assert (forall ((A tptp.code_natural) (B tptp.code_natural)) (=> (@ (@ tptp.dvd_dvd_Code_natural A) B) (= (@ (@ tptp.modulo8411746178871703098atural B) A) tptp.zero_z2226904508553997617atural))))
% 6.73/7.06 (assert (forall ((K2 tptp.nat)) (@ (@ tptp.dvd_dvd_nat (@ tptp.suc tptp.zero_zero_nat)) K2)))
% 6.73/7.06 (assert (forall ((M2 tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (@ (@ tptp.dvd_dvd_nat M2) _let_1) (= M2 _let_1)))))
% 6.73/7.06 (assert (forall ((K2 tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K2))) (= (@ (@ tptp.dvd_dvd_nat (@ _let_1 M2)) (@ _let_1 N)) (or (= K2 tptp.zero_zero_nat) (@ (@ tptp.dvd_dvd_nat M2) N))))))
% 6.73/7.06 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.comm_s8582702949713902594nteger A) tptp.zero_zero_nat) tptp.one_one_Code_integer)))
% 6.73/7.06 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.comm_s2602460028002588243omplex A) tptp.zero_zero_nat) tptp.one_one_complex)))
% 6.73/7.06 (assert (forall ((A tptp.real)) (= (@ (@ tptp.comm_s7457072308508201937r_real A) tptp.zero_zero_nat) tptp.one_one_real)))
% 6.73/7.06 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.comm_s4663373288045622133er_nat A) tptp.zero_zero_nat) tptp.one_one_nat)))
% 6.73/7.06 (assert (forall ((A tptp.int)) (= (@ (@ tptp.comm_s4660882817536571857er_int A) tptp.zero_zero_nat) tptp.one_one_int)))
% 6.73/7.06 (assert (forall ((S3 tptp.set_real) (A tptp.real) (B (-> tptp.real tptp.complex))) (let ((_let_1 (@ (@ tptp.member_real A) S3))) (=> (@ tptp.finite_finite_real S3) (and (=> _let_1 (= (@ (@ tptp.groups5754745047067104278omplex (lambda ((K3 tptp.real)) (@ (@ (@ tptp.if_complex (= K3 A)) (@ B K3)) tptp.zero_zero_complex))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups5754745047067104278omplex (lambda ((K3 tptp.real)) (@ (@ (@ tptp.if_complex (= K3 A)) (@ B K3)) tptp.zero_zero_complex))) S3) tptp.zero_zero_complex)))))))
% 6.73/7.06 (assert (forall ((S3 tptp.set_nat) (A tptp.nat) (B (-> tptp.nat tptp.complex))) (let ((_let_1 (@ (@ tptp.member_nat A) S3))) (=> (@ tptp.finite_finite_nat S3) (and (=> _let_1 (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((K3 tptp.nat)) (@ (@ (@ tptp.if_complex (= K3 A)) (@ B K3)) tptp.zero_zero_complex))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((K3 tptp.nat)) (@ (@ (@ tptp.if_complex (= K3 A)) (@ B K3)) tptp.zero_zero_complex))) S3) tptp.zero_zero_complex)))))))
% 6.73/7.06 (assert (forall ((S3 tptp.set_int) (A tptp.int) (B (-> tptp.int tptp.complex))) (let ((_let_1 (@ (@ tptp.member_int A) S3))) (=> (@ tptp.finite_finite_int S3) (and (=> _let_1 (= (@ (@ tptp.groups3049146728041665814omplex (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_complex (= K3 A)) (@ B K3)) tptp.zero_zero_complex))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups3049146728041665814omplex (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_complex (= K3 A)) (@ B K3)) tptp.zero_zero_complex))) S3) tptp.zero_zero_complex)))))))
% 6.73/7.06 (assert (forall ((S3 tptp.set_complex) (A tptp.complex) (B (-> tptp.complex tptp.complex))) (let ((_let_1 (@ (@ tptp.member_complex A) S3))) (=> (@ tptp.finite3207457112153483333omplex S3) (and (=> _let_1 (= (@ (@ tptp.groups7754918857620584856omplex (lambda ((K3 tptp.complex)) (@ (@ (@ tptp.if_complex (= K3 A)) (@ B K3)) tptp.zero_zero_complex))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups7754918857620584856omplex (lambda ((K3 tptp.complex)) (@ (@ (@ tptp.if_complex (= K3 A)) (@ B K3)) tptp.zero_zero_complex))) S3) tptp.zero_zero_complex)))))))
% 6.73/7.06 (assert (forall ((S3 tptp.set_real) (A tptp.real) (B (-> tptp.real tptp.real))) (let ((_let_1 (@ (@ tptp.member_real A) S3))) (=> (@ tptp.finite_finite_real S3) (and (=> _let_1 (= (@ (@ tptp.groups8097168146408367636l_real (lambda ((K3 tptp.real)) (@ (@ (@ tptp.if_real (= K3 A)) (@ B K3)) tptp.zero_zero_real))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups8097168146408367636l_real (lambda ((K3 tptp.real)) (@ (@ (@ tptp.if_real (= K3 A)) (@ B K3)) tptp.zero_zero_real))) S3) tptp.zero_zero_real)))))))
% 6.73/7.06 (assert (forall ((S3 tptp.set_int) (A tptp.int) (B (-> tptp.int tptp.real))) (let ((_let_1 (@ (@ tptp.member_int A) S3))) (=> (@ tptp.finite_finite_int S3) (and (=> _let_1 (= (@ (@ tptp.groups8778361861064173332t_real (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_real (= K3 A)) (@ B K3)) tptp.zero_zero_real))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups8778361861064173332t_real (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_real (= K3 A)) (@ B K3)) tptp.zero_zero_real))) S3) tptp.zero_zero_real)))))))
% 6.73/7.06 (assert (forall ((S3 tptp.set_complex) (A tptp.complex) (B (-> tptp.complex tptp.real))) (let ((_let_1 (@ (@ tptp.member_complex A) S3))) (=> (@ tptp.finite3207457112153483333omplex S3) (and (=> _let_1 (= (@ (@ tptp.groups5808333547571424918x_real (lambda ((K3 tptp.complex)) (@ (@ (@ tptp.if_real (= K3 A)) (@ B K3)) tptp.zero_zero_real))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups5808333547571424918x_real (lambda ((K3 tptp.complex)) (@ (@ (@ tptp.if_real (= K3 A)) (@ B K3)) tptp.zero_zero_real))) S3) tptp.zero_zero_real)))))))
% 6.73/7.06 (assert (forall ((S3 tptp.set_real) (A tptp.real) (B (-> tptp.real tptp.rat))) (let ((_let_1 (@ (@ tptp.member_real A) S3))) (=> (@ tptp.finite_finite_real S3) (and (=> _let_1 (= (@ (@ tptp.groups1300246762558778688al_rat (lambda ((K3 tptp.real)) (@ (@ (@ tptp.if_rat (= K3 A)) (@ B K3)) tptp.zero_zero_rat))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups1300246762558778688al_rat (lambda ((K3 tptp.real)) (@ (@ (@ tptp.if_rat (= K3 A)) (@ B K3)) tptp.zero_zero_rat))) S3) tptp.zero_zero_rat)))))))
% 6.73/7.06 (assert (forall ((S3 tptp.set_nat) (A tptp.nat) (B (-> tptp.nat tptp.rat))) (let ((_let_1 (@ (@ tptp.member_nat A) S3))) (=> (@ tptp.finite_finite_nat S3) (and (=> _let_1 (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ (@ tptp.if_rat (= K3 A)) (@ B K3)) tptp.zero_zero_rat))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ (@ tptp.if_rat (= K3 A)) (@ B K3)) tptp.zero_zero_rat))) S3) tptp.zero_zero_rat)))))))
% 6.73/7.06 (assert (forall ((S3 tptp.set_int) (A tptp.int) (B (-> tptp.int tptp.rat))) (let ((_let_1 (@ (@ tptp.member_int A) S3))) (=> (@ tptp.finite_finite_int S3) (and (=> _let_1 (= (@ (@ tptp.groups3906332499630173760nt_rat (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_rat (= K3 A)) (@ B K3)) tptp.zero_zero_rat))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups3906332499630173760nt_rat (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_rat (= K3 A)) (@ B K3)) tptp.zero_zero_rat))) S3) tptp.zero_zero_rat)))))))
% 6.73/7.06 (assert (forall ((S3 tptp.set_real) (A tptp.real) (B (-> tptp.real tptp.complex))) (let ((_let_1 (@ (@ tptp.member_real A) S3))) (=> (@ tptp.finite_finite_real S3) (and (=> _let_1 (= (@ (@ tptp.groups5754745047067104278omplex (lambda ((K3 tptp.real)) (@ (@ (@ tptp.if_complex (= A K3)) (@ B K3)) tptp.zero_zero_complex))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups5754745047067104278omplex (lambda ((K3 tptp.real)) (@ (@ (@ tptp.if_complex (= A K3)) (@ B K3)) tptp.zero_zero_complex))) S3) tptp.zero_zero_complex)))))))
% 6.73/7.06 (assert (forall ((S3 tptp.set_nat) (A tptp.nat) (B (-> tptp.nat tptp.complex))) (let ((_let_1 (@ (@ tptp.member_nat A) S3))) (=> (@ tptp.finite_finite_nat S3) (and (=> _let_1 (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((K3 tptp.nat)) (@ (@ (@ tptp.if_complex (= A K3)) (@ B K3)) tptp.zero_zero_complex))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((K3 tptp.nat)) (@ (@ (@ tptp.if_complex (= A K3)) (@ B K3)) tptp.zero_zero_complex))) S3) tptp.zero_zero_complex)))))))
% 6.73/7.06 (assert (forall ((S3 tptp.set_int) (A tptp.int) (B (-> tptp.int tptp.complex))) (let ((_let_1 (@ (@ tptp.member_int A) S3))) (=> (@ tptp.finite_finite_int S3) (and (=> _let_1 (= (@ (@ tptp.groups3049146728041665814omplex (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_complex (= A K3)) (@ B K3)) tptp.zero_zero_complex))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups3049146728041665814omplex (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_complex (= A K3)) (@ B K3)) tptp.zero_zero_complex))) S3) tptp.zero_zero_complex)))))))
% 6.73/7.06 (assert (forall ((S3 tptp.set_complex) (A tptp.complex) (B (-> tptp.complex tptp.complex))) (let ((_let_1 (@ (@ tptp.member_complex A) S3))) (=> (@ tptp.finite3207457112153483333omplex S3) (and (=> _let_1 (= (@ (@ tptp.groups7754918857620584856omplex (lambda ((K3 tptp.complex)) (@ (@ (@ tptp.if_complex (= A K3)) (@ B K3)) tptp.zero_zero_complex))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups7754918857620584856omplex (lambda ((K3 tptp.complex)) (@ (@ (@ tptp.if_complex (= A K3)) (@ B K3)) tptp.zero_zero_complex))) S3) tptp.zero_zero_complex)))))))
% 6.73/7.06 (assert (forall ((S3 tptp.set_real) (A tptp.real) (B (-> tptp.real tptp.real))) (let ((_let_1 (@ (@ tptp.member_real A) S3))) (=> (@ tptp.finite_finite_real S3) (and (=> _let_1 (= (@ (@ tptp.groups8097168146408367636l_real (lambda ((K3 tptp.real)) (@ (@ (@ tptp.if_real (= A K3)) (@ B K3)) tptp.zero_zero_real))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups8097168146408367636l_real (lambda ((K3 tptp.real)) (@ (@ (@ tptp.if_real (= A K3)) (@ B K3)) tptp.zero_zero_real))) S3) tptp.zero_zero_real)))))))
% 6.73/7.06 (assert (forall ((S3 tptp.set_int) (A tptp.int) (B (-> tptp.int tptp.real))) (let ((_let_1 (@ (@ tptp.member_int A) S3))) (=> (@ tptp.finite_finite_int S3) (and (=> _let_1 (= (@ (@ tptp.groups8778361861064173332t_real (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_real (= A K3)) (@ B K3)) tptp.zero_zero_real))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups8778361861064173332t_real (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_real (= A K3)) (@ B K3)) tptp.zero_zero_real))) S3) tptp.zero_zero_real)))))))
% 6.73/7.06 (assert (forall ((S3 tptp.set_complex) (A tptp.complex) (B (-> tptp.complex tptp.real))) (let ((_let_1 (@ (@ tptp.member_complex A) S3))) (=> (@ tptp.finite3207457112153483333omplex S3) (and (=> _let_1 (= (@ (@ tptp.groups5808333547571424918x_real (lambda ((K3 tptp.complex)) (@ (@ (@ tptp.if_real (= A K3)) (@ B K3)) tptp.zero_zero_real))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups5808333547571424918x_real (lambda ((K3 tptp.complex)) (@ (@ (@ tptp.if_real (= A K3)) (@ B K3)) tptp.zero_zero_real))) S3) tptp.zero_zero_real)))))))
% 6.73/7.06 (assert (forall ((S3 tptp.set_real) (A tptp.real) (B (-> tptp.real tptp.rat))) (let ((_let_1 (@ (@ tptp.member_real A) S3))) (=> (@ tptp.finite_finite_real S3) (and (=> _let_1 (= (@ (@ tptp.groups1300246762558778688al_rat (lambda ((K3 tptp.real)) (@ (@ (@ tptp.if_rat (= A K3)) (@ B K3)) tptp.zero_zero_rat))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups1300246762558778688al_rat (lambda ((K3 tptp.real)) (@ (@ (@ tptp.if_rat (= A K3)) (@ B K3)) tptp.zero_zero_rat))) S3) tptp.zero_zero_rat)))))))
% 6.73/7.06 (assert (forall ((S3 tptp.set_nat) (A tptp.nat) (B (-> tptp.nat tptp.rat))) (let ((_let_1 (@ (@ tptp.member_nat A) S3))) (=> (@ tptp.finite_finite_nat S3) (and (=> _let_1 (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ (@ tptp.if_rat (= A K3)) (@ B K3)) tptp.zero_zero_rat))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ (@ tptp.if_rat (= A K3)) (@ B K3)) tptp.zero_zero_rat))) S3) tptp.zero_zero_rat)))))))
% 6.73/7.06 (assert (forall ((S3 tptp.set_int) (A tptp.int) (B (-> tptp.int tptp.rat))) (let ((_let_1 (@ (@ tptp.member_int A) S3))) (=> (@ tptp.finite_finite_int S3) (and (=> _let_1 (= (@ (@ tptp.groups3906332499630173760nt_rat (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_rat (= A K3)) (@ B K3)) tptp.zero_zero_rat))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups3906332499630173760nt_rat (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_rat (= A K3)) (@ B K3)) tptp.zero_zero_rat))) S3) tptp.zero_zero_rat)))))))
% 6.73/7.06 (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)))))
% 6.73/7.06 (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)))))
% 6.73/7.06 (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)))))
% 6.73/7.06 (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))))
% 6.73/7.06 (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))))
% 6.73/7.06 (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))))
% 6.73/7.06 (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)))))
% 6.73/7.06 (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)))))
% 6.73/7.06 (assert (forall ((Y tptp.rat) (A4 tptp.set_nat)) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((X4 tptp.nat)) Y)) A4) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat (@ tptp.finite_card_nat A4))) Y))))
% 6.73/7.06 (assert (forall ((Y tptp.rat) (A4 tptp.set_complex)) (= (@ (@ tptp.groups5058264527183730370ex_rat (lambda ((X4 tptp.complex)) Y)) A4) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat (@ tptp.finite_card_complex A4))) Y))))
% 6.73/7.06 (assert (forall ((Y tptp.rat) (A4 tptp.set_int)) (= (@ (@ tptp.groups3906332499630173760nt_rat (lambda ((X4 tptp.int)) Y)) A4) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat (@ tptp.finite_card_int A4))) Y))))
% 6.73/7.06 (assert (forall ((Y tptp.real) (A4 tptp.set_complex)) (= (@ (@ tptp.groups5808333547571424918x_real (lambda ((X4 tptp.complex)) Y)) A4) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ tptp.finite_card_complex A4))) Y))))
% 6.73/7.06 (assert (forall ((Y tptp.real) (A4 tptp.set_int)) (= (@ (@ tptp.groups8778361861064173332t_real (lambda ((X4 tptp.int)) Y)) A4) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ tptp.finite_card_int A4))) Y))))
% 6.73/7.06 (assert (forall ((Y tptp.int) (A4 tptp.set_nat)) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((X4 tptp.nat)) Y)) A4) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int (@ tptp.finite_card_nat A4))) Y))))
% 6.73/7.06 (assert (forall ((Y tptp.int) (A4 tptp.set_complex)) (= (@ (@ tptp.groups5690904116761175830ex_int (lambda ((X4 tptp.complex)) Y)) A4) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int (@ tptp.finite_card_complex A4))) Y))))
% 6.73/7.06 (assert (forall ((Y tptp.nat) (A4 tptp.set_complex)) (= (@ (@ tptp.groups5693394587270226106ex_nat (lambda ((X4 tptp.complex)) Y)) A4) (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat (@ tptp.finite_card_complex A4))) Y))))
% 6.73/7.06 (assert (forall ((Y tptp.nat) (A4 tptp.set_int)) (= (@ (@ tptp.groups4541462559716669496nt_nat (lambda ((X4 tptp.int)) Y)) A4) (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat (@ tptp.finite_card_int A4))) Y))))
% 6.73/7.06 (assert (forall ((Y tptp.nat) (A4 tptp.set_nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X4 tptp.nat)) Y)) A4) (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat (@ tptp.finite_card_nat A4))) Y))))
% 6.73/7.06 (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))))))
% 6.73/7.06 (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))))))
% 6.73/7.06 (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)))))
% 6.73/7.06 (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))))))
% 6.73/7.06 (assert (forall ((A (-> tptp.nat tptp.complex)) (X tptp.complex)) (= (@ (@ tptp.sums_complex (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_complex (@ A N4)) (@ (@ tptp.power_power_complex tptp.zero_zero_complex) N4)))) X) (= (@ A tptp.zero_zero_nat) X))))
% 6.73/7.06 (assert (forall ((A (-> tptp.nat tptp.real)) (X tptp.real)) (= (@ (@ tptp.sums_real (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_real (@ A N4)) (@ (@ tptp.power_power_real tptp.zero_zero_real) N4)))) X) (= (@ A tptp.zero_zero_nat) X))))
% 6.73/7.06 (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))))))
% 6.73/7.06 (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)))))))
% 6.73/7.06 (assert (forall ((N tptp.nat) (M2 tptp.nat) (G2 (-> tptp.nat tptp.complex))) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M2))) (let ((_let_3 (@ tptp.groups2073611262835488442omplex G2))) (let ((_let_4 (@ _let_3 (@ _let_2 _let_1)))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_1) M2))) (and (=> _let_5 (= _let_4 tptp.zero_zero_complex)) (=> (not _let_5) (= _let_4 (@ (@ tptp.plus_plus_complex (@ _let_3 (@ _let_2 N))) (@ G2 _let_1))))))))))))
% 6.73/7.06 (assert (forall ((N tptp.nat) (M2 tptp.nat) (G2 (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M2))) (let ((_let_3 (@ tptp.groups2906978787729119204at_rat G2))) (let ((_let_4 (@ _let_3 (@ _let_2 _let_1)))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_1) M2))) (and (=> _let_5 (= _let_4 tptp.zero_zero_rat)) (=> (not _let_5) (= _let_4 (@ (@ tptp.plus_plus_rat (@ _let_3 (@ _let_2 N))) (@ G2 _let_1))))))))))))
% 6.73/7.06 (assert (forall ((N tptp.nat) (M2 tptp.nat) (G2 (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M2))) (let ((_let_3 (@ tptp.groups3539618377306564664at_int G2))) (let ((_let_4 (@ _let_3 (@ _let_2 _let_1)))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_1) M2))) (and (=> _let_5 (= _let_4 tptp.zero_zero_int)) (=> (not _let_5) (= _let_4 (@ (@ tptp.plus_plus_int (@ _let_3 (@ _let_2 N))) (@ G2 _let_1))))))))))))
% 6.73/7.06 (assert (forall ((N tptp.nat) (M2 tptp.nat) (G2 (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M2))) (let ((_let_3 (@ tptp.groups3542108847815614940at_nat G2))) (let ((_let_4 (@ _let_3 (@ _let_2 _let_1)))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_1) M2))) (and (=> _let_5 (= _let_4 tptp.zero_zero_nat)) (=> (not _let_5) (= _let_4 (@ (@ tptp.plus_plus_nat (@ _let_3 (@ _let_2 N))) (@ G2 _let_1))))))))))))
% 6.73/7.06 (assert (forall ((N tptp.nat) (M2 tptp.nat) (G2 (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M2))) (let ((_let_3 (@ tptp.groups6591440286371151544t_real G2))) (let ((_let_4 (@ _let_3 (@ _let_2 _let_1)))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_1) M2))) (and (=> _let_5 (= _let_4 tptp.zero_zero_real)) (=> (not _let_5) (= _let_4 (@ (@ tptp.plus_plus_real (@ _let_3 (@ _let_2 N))) (@ G2 _let_1))))))))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_nat) (C2 (-> tptp.nat tptp.complex))) (let ((_let_1 (and (@ tptp.finite_finite_nat A4) (@ (@ tptp.member_nat tptp.zero_zero_nat) A4)))) (and (=> _let_1 (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I tptp.nat)) (@ (@ tptp.times_times_complex (@ C2 I)) (@ (@ tptp.power_power_complex tptp.zero_zero_complex) I)))) A4) (@ C2 tptp.zero_zero_nat))) (=> (not _let_1) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I tptp.nat)) (@ (@ tptp.times_times_complex (@ C2 I)) (@ (@ tptp.power_power_complex tptp.zero_zero_complex) I)))) A4) tptp.zero_zero_complex))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_nat) (C2 (-> tptp.nat tptp.rat))) (let ((_let_1 (and (@ tptp.finite_finite_nat A4) (@ (@ tptp.member_nat tptp.zero_zero_nat) A4)))) (and (=> _let_1 (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I tptp.nat)) (@ (@ tptp.times_times_rat (@ C2 I)) (@ (@ tptp.power_power_rat tptp.zero_zero_rat) I)))) A4) (@ C2 tptp.zero_zero_nat))) (=> (not _let_1) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I tptp.nat)) (@ (@ tptp.times_times_rat (@ C2 I)) (@ (@ tptp.power_power_rat tptp.zero_zero_rat) I)))) A4) tptp.zero_zero_rat))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_nat) (C2 (-> tptp.nat tptp.real))) (let ((_let_1 (and (@ tptp.finite_finite_nat A4) (@ (@ tptp.member_nat tptp.zero_zero_nat) A4)))) (and (=> _let_1 (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I tptp.nat)) (@ (@ tptp.times_times_real (@ C2 I)) (@ (@ tptp.power_power_real tptp.zero_zero_real) I)))) A4) (@ C2 tptp.zero_zero_nat))) (=> (not _let_1) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I tptp.nat)) (@ (@ tptp.times_times_real (@ C2 I)) (@ (@ tptp.power_power_real tptp.zero_zero_real) I)))) A4) tptp.zero_zero_real))))))
% 6.73/7.06 (assert (forall ((A tptp.real) (W2 tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (let ((_let_2 (@ tptp.numeral_numeral_nat W2))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_2))) (= (@ _let_1 (@ (@ tptp.power_power_real A) _let_2)) (or _let_3 (and (not _let_3) (@ _let_1 A)))))))))
% 6.73/7.06 (assert (forall ((A tptp.rat) (W2 tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (let ((_let_2 (@ tptp.numeral_numeral_nat W2))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_2))) (= (@ _let_1 (@ (@ tptp.power_power_rat A) _let_2)) (or _let_3 (and (not _let_3) (@ _let_1 A)))))))))
% 6.73/7.06 (assert (forall ((A tptp.int) (W2 tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_2 (@ tptp.numeral_numeral_nat W2))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_2))) (= (@ _let_1 (@ (@ tptp.power_power_int A) _let_2)) (or _let_3 (and (not _let_3) (@ _let_1 A)))))))))
% 6.73/7.06 (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))))))
% 6.73/7.06 (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))))))
% 6.73/7.06 (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)))))
% 6.73/7.06 (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)))))
% 6.73/7.06 (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)))))
% 6.73/7.06 (assert (forall ((A tptp.real) (W2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat W2))) (= (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real A) _let_1)) tptp.zero_zero_real) (and (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_1)) (@ (@ tptp.ord_less_real A) tptp.zero_zero_real))))))
% 6.73/7.06 (assert (forall ((A tptp.rat) (W2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat W2))) (= (@ (@ 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))))))
% 6.73/7.06 (assert (forall ((A tptp.int) (W2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat W2))) (= (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int A) _let_1)) tptp.zero_zero_int) (and (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_1)) (@ (@ tptp.ord_less_int A) tptp.zero_zero_int))))))
% 6.73/7.06 (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))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_nat) (C2 (-> tptp.nat tptp.complex)) (D (-> tptp.nat tptp.complex))) (let ((_let_1 (and (@ tptp.finite_finite_nat A4) (@ (@ tptp.member_nat tptp.zero_zero_nat) A4)))) (and (=> _let_1 (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I tptp.nat)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex (@ C2 I)) (@ (@ tptp.power_power_complex tptp.zero_zero_complex) I))) (@ D I)))) A4) (@ (@ tptp.divide1717551699836669952omplex (@ C2 tptp.zero_zero_nat)) (@ D tptp.zero_zero_nat)))) (=> (not _let_1) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I tptp.nat)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex (@ C2 I)) (@ (@ tptp.power_power_complex tptp.zero_zero_complex) I))) (@ D I)))) A4) tptp.zero_zero_complex))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_nat) (C2 (-> tptp.nat tptp.rat)) (D (-> tptp.nat tptp.rat))) (let ((_let_1 (and (@ tptp.finite_finite_nat A4) (@ (@ tptp.member_nat tptp.zero_zero_nat) A4)))) (and (=> _let_1 (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I tptp.nat)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat (@ C2 I)) (@ (@ tptp.power_power_rat tptp.zero_zero_rat) I))) (@ D I)))) A4) (@ (@ tptp.divide_divide_rat (@ C2 tptp.zero_zero_nat)) (@ D tptp.zero_zero_nat)))) (=> (not _let_1) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I tptp.nat)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat (@ C2 I)) (@ (@ tptp.power_power_rat tptp.zero_zero_rat) I))) (@ D I)))) A4) tptp.zero_zero_rat))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_nat) (C2 (-> tptp.nat tptp.real)) (D (-> tptp.nat tptp.real))) (let ((_let_1 (and (@ tptp.finite_finite_nat A4) (@ (@ tptp.member_nat tptp.zero_zero_nat) A4)))) (and (=> _let_1 (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I tptp.nat)) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ C2 I)) (@ (@ tptp.power_power_real tptp.zero_zero_real) I))) (@ D I)))) A4) (@ (@ tptp.divide_divide_real (@ C2 tptp.zero_zero_nat)) (@ D tptp.zero_zero_nat)))) (=> (not _let_1) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I tptp.nat)) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ C2 I)) (@ (@ tptp.power_power_real tptp.zero_zero_real) I))) (@ D I)))) A4) tptp.zero_zero_real))))))
% 6.73/7.06 (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)))))
% 6.73/7.06 (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)))))
% 6.73/7.06 (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)))))
% 6.73/7.06 (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)))))
% 6.73/7.06 (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)))))
% 6.73/7.06 (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)))))
% 6.73/7.06 (assert (forall ((A tptp.real) (W2 tptp.num)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (let ((_let_2 (@ tptp.numeral_numeral_nat W2))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_2))) (= (@ _let_1 (@ (@ tptp.power_power_real A) _let_2)) (or (= _let_2 tptp.zero_zero_nat) (and _let_3 (not (= A tptp.zero_zero_real))) (and (not _let_3) (@ _let_1 A)))))))))
% 6.73/7.06 (assert (forall ((A tptp.rat) (W2 tptp.num)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (let ((_let_2 (@ tptp.numeral_numeral_nat W2))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_2))) (= (@ _let_1 (@ (@ tptp.power_power_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)))))))))
% 6.73/7.06 (assert (forall ((A tptp.int) (W2 tptp.num)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (let ((_let_2 (@ tptp.numeral_numeral_nat W2))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_2))) (= (@ _let_1 (@ (@ tptp.power_power_int A) _let_2)) (or (= _let_2 tptp.zero_zero_nat) (and _let_3 (not (= A tptp.zero_zero_int))) (and (not _let_3) (@ _let_1 A)))))))))
% 6.73/7.06 (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))))))
% 6.73/7.06 (assert (forall ((A tptp.real) (W2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat W2))) (let ((_let_2 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_1))) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real A) _let_1)) tptp.zero_zero_real) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) _let_1) (or (and (not _let_2) (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real)) (and _let_2 (= A tptp.zero_zero_real)))))))))
% 6.73/7.06 (assert (forall ((A tptp.rat) (W2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat W2))) (let ((_let_2 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_1))) (= (@ (@ tptp.ord_less_eq_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)))))))))
% 6.73/7.06 (assert (forall ((A tptp.int) (W2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat W2))) (let ((_let_2 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_1))) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A) _let_1)) tptp.zero_zero_int) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) _let_1) (or (and (not _let_2) (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int)) (and _let_2 (= A tptp.zero_zero_int)))))))))
% 6.73/7.06 (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))))))))
% 6.73/7.06 (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))))))))
% 6.73/7.06 (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))))))))
% 6.73/7.06 (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))))))))))
% 6.73/7.06 (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))))))))))
% 6.73/7.06 (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))))))))))
% 6.73/7.06 (assert (forall ((A tptp.code_natural) (N tptp.nat)) (let ((_let_1 (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.power_7079662738309270450atural _let_1) N))) (let ((_let_3 (@ tptp.plus_p4538020629002901425atural tptp.one_one_Code_natural))) (=> (@ (@ tptp.dvd_dvd_Code_natural _let_1) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.modulo8411746178871703098atural (@ _let_3 A)) _let_2) (@ _let_3 (@ (@ tptp.modulo8411746178871703098atural A) _let_2))))))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_nat) (G2 (-> tptp.nat tptp.nat))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A4) (= (@ G2 X3) tptp.zero_zero_nat))) (= (@ (@ tptp.groups3542108847815614940at_nat G2) A4) tptp.zero_zero_nat))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_int) (G2 (-> tptp.int tptp.int))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A4) (= (@ G2 X3) tptp.zero_zero_int))) (= (@ (@ tptp.groups4538972089207619220nt_int G2) A4) tptp.zero_zero_int))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_nat) (G2 (-> tptp.nat tptp.real))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A4) (= (@ G2 X3) tptp.zero_zero_real))) (= (@ (@ tptp.groups6591440286371151544t_real G2) A4) tptp.zero_zero_real))))
% 6.73/7.06 (assert (forall ((G2 (-> tptp.complex tptp.complex)) (A4 tptp.set_complex)) (=> (not (= (@ (@ tptp.groups7754918857620584856omplex G2) A4) tptp.zero_zero_complex)) (not (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) A4) (= (@ G2 A3) tptp.zero_zero_complex)))))))
% 6.73/7.06 (assert (forall ((G2 (-> tptp.real tptp.complex)) (A4 tptp.set_real)) (=> (not (= (@ (@ tptp.groups5754745047067104278omplex G2) A4) tptp.zero_zero_complex)) (not (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) A4) (= (@ G2 A3) tptp.zero_zero_complex)))))))
% 6.73/7.06 (assert (forall ((G2 (-> tptp.nat tptp.complex)) (A4 tptp.set_nat)) (=> (not (= (@ (@ tptp.groups2073611262835488442omplex G2) A4) tptp.zero_zero_complex)) (not (forall ((A3 tptp.nat)) (=> (@ (@ tptp.member_nat A3) A4) (= (@ G2 A3) tptp.zero_zero_complex)))))))
% 6.73/7.06 (assert (forall ((G2 (-> tptp.int tptp.complex)) (A4 tptp.set_int)) (=> (not (= (@ (@ tptp.groups3049146728041665814omplex G2) A4) tptp.zero_zero_complex)) (not (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) A4) (= (@ G2 A3) tptp.zero_zero_complex)))))))
% 6.73/7.06 (assert (forall ((G2 (-> tptp.complex tptp.real)) (A4 tptp.set_complex)) (=> (not (= (@ (@ tptp.groups5808333547571424918x_real G2) A4) tptp.zero_zero_real)) (not (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) A4) (= (@ G2 A3) tptp.zero_zero_real)))))))
% 6.73/7.06 (assert (forall ((G2 (-> tptp.real tptp.real)) (A4 tptp.set_real)) (=> (not (= (@ (@ tptp.groups8097168146408367636l_real G2) A4) tptp.zero_zero_real)) (not (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) A4) (= (@ G2 A3) tptp.zero_zero_real)))))))
% 6.73/7.06 (assert (forall ((G2 (-> tptp.int tptp.real)) (A4 tptp.set_int)) (=> (not (= (@ (@ tptp.groups8778361861064173332t_real G2) A4) tptp.zero_zero_real)) (not (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) A4) (= (@ G2 A3) tptp.zero_zero_real)))))))
% 6.73/7.06 (assert (forall ((G2 (-> tptp.complex tptp.rat)) (A4 tptp.set_complex)) (=> (not (= (@ (@ tptp.groups5058264527183730370ex_rat G2) A4) tptp.zero_zero_rat)) (not (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) A4) (= (@ G2 A3) tptp.zero_zero_rat)))))))
% 6.73/7.06 (assert (forall ((G2 (-> tptp.real tptp.rat)) (A4 tptp.set_real)) (=> (not (= (@ (@ tptp.groups1300246762558778688al_rat G2) A4) tptp.zero_zero_rat)) (not (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) A4) (= (@ G2 A3) tptp.zero_zero_rat)))))))
% 6.73/7.06 (assert (forall ((G2 (-> tptp.nat tptp.rat)) (A4 tptp.set_nat)) (=> (not (= (@ (@ tptp.groups2906978787729119204at_rat G2) A4) tptp.zero_zero_rat)) (not (forall ((A3 tptp.nat)) (=> (@ (@ tptp.member_nat A3) A4) (= (@ G2 A3) tptp.zero_zero_rat)))))))
% 6.73/7.06 (assert (forall ((K5 tptp.set_complex) (F2 (-> tptp.complex tptp.rat)) (G2 (-> tptp.complex tptp.rat))) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) K5) (@ (@ tptp.ord_less_eq_rat (@ F2 I3)) (@ G2 I3)))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups5058264527183730370ex_rat F2) K5)) (@ (@ tptp.groups5058264527183730370ex_rat G2) K5)))))
% 6.73/7.06 (assert (forall ((K5 tptp.set_real) (F2 (-> tptp.real tptp.rat)) (G2 (-> tptp.real tptp.rat))) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) K5) (@ (@ tptp.ord_less_eq_rat (@ F2 I3)) (@ G2 I3)))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups1300246762558778688al_rat F2) K5)) (@ (@ tptp.groups1300246762558778688al_rat G2) K5)))))
% 6.73/7.06 (assert (forall ((K5 tptp.set_nat) (F2 (-> tptp.nat tptp.rat)) (G2 (-> tptp.nat tptp.rat))) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.member_nat I3) K5) (@ (@ tptp.ord_less_eq_rat (@ F2 I3)) (@ G2 I3)))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups2906978787729119204at_rat F2) K5)) (@ (@ tptp.groups2906978787729119204at_rat G2) K5)))))
% 6.73/7.06 (assert (forall ((K5 tptp.set_int) (F2 (-> tptp.int tptp.rat)) (G2 (-> tptp.int tptp.rat))) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) K5) (@ (@ tptp.ord_less_eq_rat (@ F2 I3)) (@ G2 I3)))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups3906332499630173760nt_rat F2) K5)) (@ (@ tptp.groups3906332499630173760nt_rat G2) K5)))))
% 6.73/7.06 (assert (forall ((K5 tptp.set_complex) (F2 (-> tptp.complex tptp.nat)) (G2 (-> tptp.complex tptp.nat))) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) K5) (@ (@ tptp.ord_less_eq_nat (@ F2 I3)) (@ G2 I3)))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups5693394587270226106ex_nat F2) K5)) (@ (@ tptp.groups5693394587270226106ex_nat G2) K5)))))
% 6.73/7.06 (assert (forall ((K5 tptp.set_real) (F2 (-> tptp.real tptp.nat)) (G2 (-> tptp.real tptp.nat))) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) K5) (@ (@ tptp.ord_less_eq_nat (@ F2 I3)) (@ G2 I3)))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups1935376822645274424al_nat F2) K5)) (@ (@ tptp.groups1935376822645274424al_nat G2) K5)))))
% 6.73/7.06 (assert (forall ((K5 tptp.set_int) (F2 (-> tptp.int tptp.nat)) (G2 (-> tptp.int tptp.nat))) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) K5) (@ (@ tptp.ord_less_eq_nat (@ F2 I3)) (@ G2 I3)))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups4541462559716669496nt_nat F2) K5)) (@ (@ tptp.groups4541462559716669496nt_nat G2) K5)))))
% 6.73/7.06 (assert (forall ((K5 tptp.set_complex) (F2 (-> tptp.complex tptp.int)) (G2 (-> tptp.complex tptp.int))) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) K5) (@ (@ tptp.ord_less_eq_int (@ F2 I3)) (@ G2 I3)))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.groups5690904116761175830ex_int F2) K5)) (@ (@ tptp.groups5690904116761175830ex_int G2) K5)))))
% 6.73/7.06 (assert (forall ((K5 tptp.set_real) (F2 (-> tptp.real tptp.int)) (G2 (-> tptp.real tptp.int))) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) K5) (@ (@ tptp.ord_less_eq_int (@ F2 I3)) (@ G2 I3)))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.groups1932886352136224148al_int F2) K5)) (@ (@ tptp.groups1932886352136224148al_int G2) K5)))))
% 6.73/7.06 (assert (forall ((K5 tptp.set_nat) (F2 (-> tptp.nat tptp.int)) (G2 (-> tptp.nat tptp.int))) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.member_nat I3) K5) (@ (@ tptp.ord_less_eq_int (@ F2 I3)) (@ G2 I3)))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.groups3539618377306564664at_int F2) K5)) (@ (@ tptp.groups3539618377306564664at_int G2) K5)))))
% 6.73/7.06 (assert (forall ((R3 tptp.nat) (F2 (-> tptp.nat tptp.nat)) (A4 tptp.set_nat)) (= (@ (@ tptp.times_times_nat R3) (@ (@ tptp.groups3542108847815614940at_nat F2) A4)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_nat R3) (@ F2 N4)))) A4))))
% 6.73/7.06 (assert (forall ((R3 tptp.int) (F2 (-> tptp.int tptp.int)) (A4 tptp.set_int)) (= (@ (@ tptp.times_times_int R3) (@ (@ tptp.groups4538972089207619220nt_int F2) A4)) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((N4 tptp.int)) (@ (@ tptp.times_times_int R3) (@ F2 N4)))) A4))))
% 6.73/7.06 (assert (forall ((R3 tptp.real) (F2 (-> tptp.nat tptp.real)) (A4 tptp.set_nat)) (= (@ (@ tptp.times_times_real R3) (@ (@ tptp.groups6591440286371151544t_real F2) A4)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_real R3) (@ F2 N4)))) A4))))
% 6.73/7.06 (assert (forall ((F2 (-> tptp.nat tptp.nat)) (A4 tptp.set_nat) (R3 tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.groups3542108847815614940at_nat F2) A4)) R3) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_nat (@ F2 N4)) R3))) A4))))
% 6.73/7.06 (assert (forall ((F2 (-> tptp.int tptp.int)) (A4 tptp.set_int) (R3 tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.groups4538972089207619220nt_int F2) A4)) R3) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((N4 tptp.int)) (@ (@ tptp.times_times_int (@ F2 N4)) R3))) A4))))
% 6.73/7.06 (assert (forall ((F2 (-> tptp.nat tptp.real)) (A4 tptp.set_nat) (R3 tptp.real)) (= (@ (@ tptp.times_times_real (@ (@ tptp.groups6591440286371151544t_real F2) A4)) R3) (@ (@ tptp.groups6591440286371151544t_real (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_real (@ F2 N4)) R3))) A4))))
% 6.73/7.06 (assert (forall ((F2 (-> tptp.nat tptp.nat)) (A4 tptp.set_nat) (G2 (-> tptp.nat tptp.nat)) (B5 tptp.set_nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.groups3542108847815614940at_nat F2) A4)) (@ (@ tptp.groups3542108847815614940at_nat G2) B5)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I tptp.nat)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((J tptp.nat)) (@ (@ tptp.times_times_nat (@ F2 I)) (@ G2 J)))) B5))) A4))))
% 6.73/7.06 (assert (forall ((F2 (-> tptp.int tptp.int)) (A4 tptp.set_int) (G2 (-> tptp.int tptp.int)) (B5 tptp.set_int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.groups4538972089207619220nt_int F2) A4)) (@ (@ tptp.groups4538972089207619220nt_int G2) B5)) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((I tptp.int)) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((J tptp.int)) (@ (@ tptp.times_times_int (@ F2 I)) (@ G2 J)))) B5))) A4))))
% 6.73/7.06 (assert (forall ((F2 (-> tptp.nat tptp.real)) (A4 tptp.set_nat) (G2 (-> tptp.nat tptp.real)) (B5 tptp.set_nat)) (= (@ (@ tptp.times_times_real (@ (@ tptp.groups6591440286371151544t_real F2) A4)) (@ (@ tptp.groups6591440286371151544t_real G2) B5)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((J tptp.nat)) (@ (@ tptp.times_times_real (@ F2 I)) (@ G2 J)))) B5))) A4))))
% 6.73/7.06 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat M2) N) (=> (@ (@ tptp.dvd_dvd_nat N) M2) (= M2 N)))))
% 6.73/7.06 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (=> (@ _let_1 B) (=> (@ (@ tptp.dvd_dvd_nat B) C2) (@ _let_1 C2))))))
% 6.73/7.06 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (=> (@ _let_1 B) (=> (@ (@ tptp.dvd_dvd_int B) C2) (@ _let_1 C2))))))
% 6.73/7.06 (assert (forall ((A tptp.nat)) (@ (@ tptp.dvd_dvd_nat A) A)))
% 6.73/7.06 (assert (forall ((A tptp.int)) (@ (@ tptp.dvd_dvd_int A) A)))
% 6.73/7.06 (assert (= tptp.dvd_dvd_complex (lambda ((A5 tptp.complex) (B4 tptp.complex)) (=> (= A5 tptp.zero_zero_complex) (= B4 tptp.zero_zero_complex)))))
% 6.73/7.06 (assert (= tptp.dvd_dvd_real (lambda ((A5 tptp.real) (B4 tptp.real)) (=> (= A5 tptp.zero_zero_real) (= B4 tptp.zero_zero_real)))))
% 6.73/7.06 (assert (= tptp.dvd_dvd_rat (lambda ((A5 tptp.rat) (B4 tptp.rat)) (=> (= A5 tptp.zero_zero_rat) (= B4 tptp.zero_zero_rat)))))
% 6.73/7.06 (assert (forall ((A tptp.complex)) (=> (@ (@ tptp.dvd_dvd_complex tptp.zero_zero_complex) A) (= A tptp.zero_zero_complex))))
% 6.73/7.06 (assert (forall ((A tptp.real)) (=> (@ (@ tptp.dvd_dvd_real tptp.zero_zero_real) A) (= A tptp.zero_zero_real))))
% 6.73/7.06 (assert (forall ((A tptp.rat)) (=> (@ (@ tptp.dvd_dvd_rat tptp.zero_zero_rat) A) (= A tptp.zero_zero_rat))))
% 6.73/7.06 (assert (forall ((A tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat tptp.zero_zero_nat) A) (= A tptp.zero_zero_nat))))
% 6.73/7.06 (assert (forall ((A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int tptp.zero_zero_int) A) (= A tptp.zero_zero_int))))
% 6.73/7.06 (assert (forall ((P tptp.nat) (A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat P) (@ (@ tptp.times_times_nat A) B)) (not (forall ((X3 tptp.nat) (Y3 tptp.nat)) (=> (= P (@ (@ tptp.times_times_nat X3) Y3)) (=> (@ (@ tptp.dvd_dvd_nat X3) A) (not (@ (@ tptp.dvd_dvd_nat Y3) B)))))))))
% 6.73/7.06 (assert (forall ((P tptp.int) (A tptp.int) (B tptp.int)) (=> (@ (@ tptp.dvd_dvd_int P) (@ (@ tptp.times_times_int A) B)) (not (forall ((X3 tptp.int) (Y3 tptp.int)) (=> (= P (@ (@ tptp.times_times_int X3) Y3)) (=> (@ (@ tptp.dvd_dvd_int X3) A) (not (@ (@ tptp.dvd_dvd_int Y3) B)))))))))
% 6.73/7.06 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) (@ (@ tptp.times_times_nat B) C2)) (exists ((B9 tptp.nat) (C5 tptp.nat)) (and (= A (@ (@ tptp.times_times_nat B9) C5)) (@ (@ tptp.dvd_dvd_nat B9) B) (@ (@ tptp.dvd_dvd_nat C5) C2))))))
% 6.73/7.06 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) (@ (@ tptp.times_times_int B) C2)) (exists ((B9 tptp.int) (C5 tptp.int)) (and (= A (@ (@ tptp.times_times_int B9) C5)) (@ (@ tptp.dvd_dvd_int B9) B) (@ (@ tptp.dvd_dvd_int C5) C2))))))
% 6.73/7.06 (assert (forall ((B tptp.real) (A tptp.real)) (=> (@ (@ tptp.dvd_dvd_real B) A) (not (forall ((K tptp.real)) (not (= A (@ (@ tptp.times_times_real B) K))))))))
% 6.73/7.06 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.dvd_dvd_rat B) A) (not (forall ((K tptp.rat)) (not (= A (@ (@ tptp.times_times_rat B) K))))))))
% 6.73/7.06 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B) A) (not (forall ((K tptp.nat)) (not (= A (@ (@ tptp.times_times_nat B) K))))))))
% 6.73/7.06 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B) A) (not (forall ((K tptp.int)) (not (= A (@ (@ tptp.times_times_int B) K))))))))
% 6.73/7.06 (assert (forall ((A tptp.real) (B tptp.real) (K2 tptp.real)) (=> (= A (@ (@ tptp.times_times_real B) K2)) (@ (@ tptp.dvd_dvd_real B) A))))
% 6.73/7.06 (assert (forall ((A tptp.rat) (B tptp.rat) (K2 tptp.rat)) (=> (= A (@ (@ tptp.times_times_rat B) K2)) (@ (@ tptp.dvd_dvd_rat B) A))))
% 6.73/7.06 (assert (forall ((A tptp.nat) (B tptp.nat) (K2 tptp.nat)) (=> (= A (@ (@ tptp.times_times_nat B) K2)) (@ (@ tptp.dvd_dvd_nat B) A))))
% 6.73/7.06 (assert (forall ((A tptp.int) (B tptp.int) (K2 tptp.int)) (=> (= A (@ (@ tptp.times_times_int B) K2)) (@ (@ tptp.dvd_dvd_int B) A))))
% 6.73/7.06 (assert (= tptp.dvd_dvd_real (lambda ((B4 tptp.real) (A5 tptp.real)) (exists ((K3 tptp.real)) (= A5 (@ (@ tptp.times_times_real B4) K3))))))
% 6.73/7.06 (assert (= tptp.dvd_dvd_rat (lambda ((B4 tptp.rat) (A5 tptp.rat)) (exists ((K3 tptp.rat)) (= A5 (@ (@ tptp.times_times_rat B4) K3))))))
% 6.73/7.06 (assert (= tptp.dvd_dvd_nat (lambda ((B4 tptp.nat) (A5 tptp.nat)) (exists ((K3 tptp.nat)) (= A5 (@ (@ tptp.times_times_nat B4) K3))))))
% 6.73/7.06 (assert (= tptp.dvd_dvd_int (lambda ((B4 tptp.int) (A5 tptp.int)) (exists ((K3 tptp.int)) (= A5 (@ (@ tptp.times_times_int B4) K3))))))
% 6.73/7.06 (assert (forall ((A tptp.real) (C2 tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real A))) (=> (@ _let_1 C2) (@ _let_1 (@ (@ tptp.times_times_real B) C2))))))
% 6.73/7.06 (assert (forall ((A tptp.rat) (C2 tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat A))) (=> (@ _let_1 C2) (@ _let_1 (@ (@ tptp.times_times_rat B) C2))))))
% 6.73/7.06 (assert (forall ((A tptp.nat) (C2 tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (=> (@ _let_1 C2) (@ _let_1 (@ (@ tptp.times_times_nat B) C2))))))
% 6.73/7.06 (assert (forall ((A tptp.int) (C2 tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (=> (@ _let_1 C2) (@ _let_1 (@ (@ tptp.times_times_int B) C2))))))
% 6.73/7.06 (assert (forall ((A tptp.real) (B tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real A))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_times_real B) C2))))))
% 6.73/7.06 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat A))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_times_rat B) C2))))))
% 6.73/7.06 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_times_nat B) C2))))))
% 6.73/7.06 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_times_int B) C2))))))
% 6.73/7.06 (assert (forall ((A tptp.real) (B tptp.real) (C2 tptp.real)) (=> (@ (@ tptp.dvd_dvd_real (@ (@ tptp.times_times_real A) B)) C2) (@ (@ tptp.dvd_dvd_real A) C2))))
% 6.73/7.06 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (=> (@ (@ tptp.dvd_dvd_rat (@ (@ tptp.times_times_rat A) B)) C2) (@ (@ tptp.dvd_dvd_rat A) C2))))
% 6.73/7.06 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat A) B)) C2) (@ (@ tptp.dvd_dvd_nat A) C2))))
% 6.73/7.06 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A) B)) C2) (@ (@ tptp.dvd_dvd_int A) C2))))
% 6.73/7.06 (assert (forall ((A tptp.real) (B tptp.real)) (@ (@ tptp.dvd_dvd_real A) (@ (@ tptp.times_times_real A) B))))
% 6.73/7.06 (assert (forall ((A tptp.rat) (B tptp.rat)) (@ (@ tptp.dvd_dvd_rat A) (@ (@ tptp.times_times_rat A) B))))
% 6.73/7.06 (assert (forall ((A tptp.nat) (B tptp.nat)) (@ (@ tptp.dvd_dvd_nat A) (@ (@ tptp.times_times_nat A) B))))
% 6.73/7.06 (assert (forall ((A tptp.int) (B tptp.int)) (@ (@ tptp.dvd_dvd_int A) (@ (@ tptp.times_times_int A) B))))
% 6.73/7.06 (assert (forall ((A tptp.real) (B tptp.real) (C2 tptp.real) (D tptp.real)) (=> (@ (@ tptp.dvd_dvd_real A) B) (=> (@ (@ tptp.dvd_dvd_real C2) D) (@ (@ tptp.dvd_dvd_real (@ (@ tptp.times_times_real A) C2)) (@ (@ tptp.times_times_real B) D))))))
% 6.73/7.06 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat) (D tptp.rat)) (=> (@ (@ tptp.dvd_dvd_rat A) B) (=> (@ (@ tptp.dvd_dvd_rat C2) D) (@ (@ tptp.dvd_dvd_rat (@ (@ tptp.times_times_rat A) C2)) (@ (@ tptp.times_times_rat B) D))))))
% 6.73/7.06 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat) (D tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) B) (=> (@ (@ tptp.dvd_dvd_nat C2) D) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat A) C2)) (@ (@ tptp.times_times_nat B) D))))))
% 6.73/7.06 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int) (D tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) B) (=> (@ (@ tptp.dvd_dvd_int C2) D) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A) C2)) (@ (@ tptp.times_times_int B) D))))))
% 6.73/7.06 (assert (forall ((A tptp.real) (B tptp.real) (C2 tptp.real)) (=> (@ (@ tptp.dvd_dvd_real (@ (@ tptp.times_times_real A) B)) C2) (@ (@ tptp.dvd_dvd_real B) C2))))
% 6.73/7.06 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (=> (@ (@ tptp.dvd_dvd_rat (@ (@ tptp.times_times_rat A) B)) C2) (@ (@ tptp.dvd_dvd_rat B) C2))))
% 6.73/7.06 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat A) B)) C2) (@ (@ tptp.dvd_dvd_nat B) C2))))
% 6.73/7.06 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A) B)) C2) (@ (@ tptp.dvd_dvd_int B) C2))))
% 6.73/7.06 (assert (forall ((A tptp.real) (B tptp.real)) (@ (@ tptp.dvd_dvd_real A) (@ (@ tptp.times_times_real B) A))))
% 6.73/7.06 (assert (forall ((A tptp.rat) (B tptp.rat)) (@ (@ tptp.dvd_dvd_rat A) (@ (@ tptp.times_times_rat B) A))))
% 6.73/7.06 (assert (forall ((A tptp.nat) (B tptp.nat)) (@ (@ tptp.dvd_dvd_nat A) (@ (@ tptp.times_times_nat B) A))))
% 6.73/7.06 (assert (forall ((A tptp.int) (B tptp.int)) (@ (@ tptp.dvd_dvd_int A) (@ (@ tptp.times_times_int B) A))))
% 6.73/7.06 (assert (forall ((A tptp.real) (B tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real A))) (=> (@ _let_1 B) (= (@ _let_1 (@ (@ tptp.plus_plus_real B) C2)) (@ _let_1 C2))))))
% 6.73/7.06 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat A))) (=> (@ _let_1 B) (= (@ _let_1 (@ (@ tptp.plus_plus_rat B) C2)) (@ _let_1 C2))))))
% 6.73/7.06 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (=> (@ _let_1 B) (= (@ _let_1 (@ (@ tptp.plus_plus_nat B) C2)) (@ _let_1 C2))))))
% 6.73/7.06 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (=> (@ _let_1 B) (= (@ _let_1 (@ (@ tptp.plus_plus_int B) C2)) (@ _let_1 C2))))))
% 6.73/7.06 (assert (forall ((A tptp.real) (C2 tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real A))) (=> (@ _let_1 C2) (= (@ _let_1 (@ (@ tptp.plus_plus_real B) C2)) (@ _let_1 B))))))
% 6.73/7.06 (assert (forall ((A tptp.rat) (C2 tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat A))) (=> (@ _let_1 C2) (= (@ _let_1 (@ (@ tptp.plus_plus_rat B) C2)) (@ _let_1 B))))))
% 6.73/7.06 (assert (forall ((A tptp.nat) (C2 tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (=> (@ _let_1 C2) (= (@ _let_1 (@ (@ tptp.plus_plus_nat B) C2)) (@ _let_1 B))))))
% 6.73/7.06 (assert (forall ((A tptp.int) (C2 tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (=> (@ _let_1 C2) (= (@ _let_1 (@ (@ tptp.plus_plus_int B) C2)) (@ _let_1 B))))))
% 6.73/7.06 (assert (forall ((A tptp.real) (B tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real A))) (=> (@ _let_1 B) (=> (@ _let_1 C2) (@ _let_1 (@ (@ tptp.plus_plus_real B) C2)))))))
% 6.73/7.06 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat A))) (=> (@ _let_1 B) (=> (@ _let_1 C2) (@ _let_1 (@ (@ tptp.plus_plus_rat B) C2)))))))
% 6.73/7.06 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (=> (@ _let_1 B) (=> (@ _let_1 C2) (@ _let_1 (@ (@ tptp.plus_plus_nat B) C2)))))))
% 6.73/7.06 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (=> (@ _let_1 B) (=> (@ _let_1 C2) (@ _let_1 (@ (@ tptp.plus_plus_int B) C2)))))))
% 6.73/7.06 (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))))))
% 6.73/7.06 (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))))))
% 6.73/7.06 (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))))))
% 6.73/7.06 (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)))))
% 6.73/7.06 (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)))))
% 6.73/7.06 (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)))))
% 6.73/7.06 (assert (forall ((A tptp.code_integer)) (@ (@ tptp.dvd_dvd_Code_integer tptp.one_one_Code_integer) A)))
% 6.73/7.06 (assert (forall ((A tptp.complex)) (@ (@ tptp.dvd_dvd_complex tptp.one_one_complex) A)))
% 6.73/7.06 (assert (forall ((A tptp.real)) (@ (@ tptp.dvd_dvd_real tptp.one_one_real) A)))
% 6.73/7.06 (assert (forall ((A tptp.nat)) (@ (@ tptp.dvd_dvd_nat tptp.one_one_nat) A)))
% 6.73/7.06 (assert (forall ((A tptp.int)) (@ (@ tptp.dvd_dvd_int tptp.one_one_int) A)))
% 6.73/7.06 (assert (forall ((X tptp.rat) (Y tptp.rat) (Z3 tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat X))) (=> (@ _let_1 Y) (=> (@ _let_1 Z3) (@ _let_1 (@ (@ tptp.minus_minus_rat Y) Z3)))))))
% 6.73/7.06 (assert (forall ((X tptp.int) (Y tptp.int) (Z3 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int X))) (=> (@ _let_1 Y) (=> (@ _let_1 Z3) (@ _let_1 (@ (@ tptp.minus_minus_int Y) Z3)))))))
% 6.73/7.06 (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)))))))
% 6.73/7.06 (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)))))))
% 6.73/7.06 (assert (forall ((A tptp.complex) (C2 tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.dvd_dvd_complex C2))) (=> (= (@ (@ tptp.divide1717551699836669952omplex A) C2) (@ (@ tptp.divide1717551699836669952omplex B) C2)) (=> (@ _let_1 A) (=> (@ _let_1 B) (= A B)))))))
% 6.73/7.06 (assert (forall ((A tptp.real) (C2 tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real C2))) (=> (= (@ (@ tptp.divide_divide_real A) C2) (@ (@ tptp.divide_divide_real B) C2)) (=> (@ _let_1 A) (=> (@ _let_1 B) (= A B)))))))
% 6.73/7.06 (assert (forall ((A tptp.rat) (C2 tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat C2))) (=> (= (@ (@ tptp.divide_divide_rat A) C2) (@ (@ tptp.divide_divide_rat B) C2)) (=> (@ _let_1 A) (=> (@ _let_1 B) (= A B)))))))
% 6.73/7.06 (assert (forall ((A tptp.nat) (C2 tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat C2))) (=> (= (@ (@ tptp.divide_divide_nat A) C2) (@ (@ tptp.divide_divide_nat B) C2)) (=> (@ _let_1 A) (=> (@ _let_1 B) (= A B)))))))
% 6.73/7.06 (assert (forall ((A tptp.int) (C2 tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int C2))) (=> (= (@ (@ tptp.divide_divide_int A) C2) (@ (@ tptp.divide_divide_int B) C2)) (=> (@ _let_1 A) (=> (@ _let_1 B) (= A B)))))))
% 6.73/7.06 (assert (forall ((C2 tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.dvd_dvd_complex C2))) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (= (@ (@ tptp.divide1717551699836669952omplex A) C2) (@ (@ tptp.divide1717551699836669952omplex B) C2)) (= A B)))))))
% 6.73/7.06 (assert (forall ((C2 tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real C2))) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (= (@ (@ tptp.divide_divide_real A) C2) (@ (@ tptp.divide_divide_real B) C2)) (= A B)))))))
% 6.73/7.06 (assert (forall ((C2 tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat C2))) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (= (@ (@ tptp.divide_divide_rat A) C2) (@ (@ tptp.divide_divide_rat B) C2)) (= A B)))))))
% 6.73/7.06 (assert (forall ((C2 tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat C2))) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (= (@ (@ tptp.divide_divide_nat A) C2) (@ (@ tptp.divide_divide_nat B) C2)) (= A B)))))))
% 6.73/7.06 (assert (forall ((C2 tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int C2))) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (= (@ (@ tptp.divide_divide_int A) C2) (@ (@ tptp.divide_divide_int B) C2)) (= A B)))))))
% 6.73/7.06 (assert (forall ((A tptp.nat)) (@ (@ tptp.dvd_dvd_nat A) tptp.zero_zero_nat)))
% 6.73/7.06 (assert (forall ((A tptp.nat)) (not (and (@ (@ tptp.dvd_dvd_nat tptp.zero_zero_nat) A) (not (= tptp.zero_zero_nat A))))))
% 6.73/7.06 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.dvd_dvd_nat tptp.zero_zero_nat) A) (= A tptp.zero_zero_nat))))
% 6.73/7.06 (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)))))
% 6.73/7.06 (assert (forall ((A tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat tptp.zero_zero_nat) A) (= A tptp.zero_zero_nat))))
% 6.73/7.06 (assert (forall ((C2 tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat C2))) (=> (@ _let_1 (@ (@ tptp.modulo_modulo_nat A) B)) (=> (@ _let_1 B) (@ _let_1 A))))))
% 6.73/7.06 (assert (forall ((C2 tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int C2))) (=> (@ _let_1 (@ (@ tptp.modulo_modulo_int A) B)) (=> (@ _let_1 B) (@ _let_1 A))))))
% 6.73/7.06 (assert (forall ((C2 tptp.code_natural) (A tptp.code_natural) (B tptp.code_natural)) (let ((_let_1 (@ tptp.dvd_dvd_Code_natural C2))) (=> (@ _let_1 (@ (@ tptp.modulo8411746178871703098atural A) B)) (=> (@ _let_1 B) (@ _let_1 A))))))
% 6.73/7.06 (assert (forall ((C2 tptp.nat) (B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat C2))) (=> (@ _let_1 B) (= (@ _let_1 (@ (@ tptp.modulo_modulo_nat A) B)) (@ _let_1 A))))))
% 6.73/7.06 (assert (forall ((C2 tptp.int) (B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int C2))) (=> (@ _let_1 B) (= (@ _let_1 (@ (@ tptp.modulo_modulo_int A) B)) (@ _let_1 A))))))
% 6.73/7.06 (assert (forall ((C2 tptp.code_natural) (B tptp.code_natural) (A tptp.code_natural)) (let ((_let_1 (@ tptp.dvd_dvd_Code_natural C2))) (=> (@ _let_1 B) (= (@ _let_1 (@ (@ tptp.modulo8411746178871703098atural A) B)) (@ _let_1 A))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_complex) (F2 (-> tptp.complex tptp.real))) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) A4) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F2 X3)))) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.groups5808333547571424918x_real F2) A4)))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_real) (F2 (-> tptp.real tptp.real))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) A4) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F2 X3)))) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.groups8097168146408367636l_real F2) A4)))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_int) (F2 (-> tptp.int tptp.real))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A4) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F2 X3)))) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.groups8778361861064173332t_real F2) A4)))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_complex) (F2 (-> tptp.complex tptp.rat))) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) A4) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F2 X3)))) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.groups5058264527183730370ex_rat F2) A4)))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_real) (F2 (-> tptp.real tptp.rat))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) A4) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F2 X3)))) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.groups1300246762558778688al_rat F2) A4)))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_nat) (F2 (-> tptp.nat tptp.rat))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A4) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F2 X3)))) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.groups2906978787729119204at_rat F2) A4)))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_int) (F2 (-> tptp.int tptp.rat))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A4) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F2 X3)))) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.groups3906332499630173760nt_rat F2) A4)))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_complex) (F2 (-> tptp.complex tptp.nat))) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) A4) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F2 X3)))) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ (@ tptp.groups5693394587270226106ex_nat F2) A4)))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_real) (F2 (-> tptp.real tptp.nat))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) A4) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F2 X3)))) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ (@ tptp.groups1935376822645274424al_nat F2) A4)))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_int) (F2 (-> tptp.int tptp.nat))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A4) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F2 X3)))) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ (@ tptp.groups4541462559716669496nt_nat F2) A4)))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_complex) (F2 (-> tptp.complex tptp.real))) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) A4) (@ (@ tptp.ord_less_eq_real (@ F2 X3)) tptp.zero_zero_real))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups5808333547571424918x_real F2) A4)) tptp.zero_zero_real))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_real) (F2 (-> tptp.real tptp.real))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) A4) (@ (@ tptp.ord_less_eq_real (@ F2 X3)) tptp.zero_zero_real))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups8097168146408367636l_real F2) A4)) tptp.zero_zero_real))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_int) (F2 (-> tptp.int tptp.real))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A4) (@ (@ tptp.ord_less_eq_real (@ F2 X3)) tptp.zero_zero_real))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups8778361861064173332t_real F2) A4)) tptp.zero_zero_real))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_complex) (F2 (-> tptp.complex tptp.rat))) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) A4) (@ (@ tptp.ord_less_eq_rat (@ F2 X3)) tptp.zero_zero_rat))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups5058264527183730370ex_rat F2) A4)) tptp.zero_zero_rat))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_real) (F2 (-> tptp.real tptp.rat))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) A4) (@ (@ tptp.ord_less_eq_rat (@ F2 X3)) tptp.zero_zero_rat))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups1300246762558778688al_rat F2) A4)) tptp.zero_zero_rat))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_nat) (F2 (-> tptp.nat tptp.rat))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A4) (@ (@ tptp.ord_less_eq_rat (@ F2 X3)) tptp.zero_zero_rat))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups2906978787729119204at_rat F2) A4)) tptp.zero_zero_rat))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_int) (F2 (-> tptp.int tptp.rat))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A4) (@ (@ tptp.ord_less_eq_rat (@ F2 X3)) tptp.zero_zero_rat))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups3906332499630173760nt_rat F2) A4)) tptp.zero_zero_rat))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_complex) (F2 (-> tptp.complex tptp.nat))) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) A4) (@ (@ tptp.ord_less_eq_nat (@ F2 X3)) tptp.zero_zero_nat))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups5693394587270226106ex_nat F2) A4)) tptp.zero_zero_nat))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_real) (F2 (-> tptp.real tptp.nat))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) A4) (@ (@ tptp.ord_less_eq_nat (@ F2 X3)) tptp.zero_zero_nat))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups1935376822645274424al_nat F2) A4)) tptp.zero_zero_nat))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_int) (F2 (-> tptp.int tptp.nat))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A4) (@ (@ tptp.ord_less_eq_nat (@ F2 X3)) tptp.zero_zero_nat))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups4541462559716669496nt_nat F2) A4)) tptp.zero_zero_nat))))
% 6.73/7.06 (assert (forall ((K2 tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat K2))) (=> (@ _let_1 M2) (=> (@ _let_1 N) (@ _let_1 (@ (@ tptp.minus_minus_nat M2) N)))))))
% 6.73/7.06 (assert (forall ((F2 (-> tptp.real tptp.rat)) (I5 tptp.set_real) (G2 (-> tptp.real tptp.rat)) (I2 tptp.real)) (=> (= (@ (@ tptp.groups1300246762558778688al_rat F2) I5) (@ (@ tptp.groups1300246762558778688al_rat G2) I5)) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) I5) (@ (@ tptp.ord_less_eq_rat (@ F2 I3)) (@ G2 I3)))) (=> (@ (@ tptp.member_real I2) I5) (=> (@ tptp.finite_finite_real I5) (= (@ F2 I2) (@ G2 I2))))))))
% 6.73/7.06 (assert (forall ((F2 (-> tptp.nat tptp.rat)) (I5 tptp.set_nat) (G2 (-> tptp.nat tptp.rat)) (I2 tptp.nat)) (=> (= (@ (@ tptp.groups2906978787729119204at_rat F2) I5) (@ (@ tptp.groups2906978787729119204at_rat G2) I5)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.member_nat I3) I5) (@ (@ tptp.ord_less_eq_rat (@ F2 I3)) (@ G2 I3)))) (=> (@ (@ tptp.member_nat I2) I5) (=> (@ tptp.finite_finite_nat I5) (= (@ F2 I2) (@ G2 I2))))))))
% 6.73/7.06 (assert (forall ((F2 (-> tptp.int tptp.rat)) (I5 tptp.set_int) (G2 (-> tptp.int tptp.rat)) (I2 tptp.int)) (=> (= (@ (@ tptp.groups3906332499630173760nt_rat F2) I5) (@ (@ tptp.groups3906332499630173760nt_rat G2) I5)) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) I5) (@ (@ tptp.ord_less_eq_rat (@ F2 I3)) (@ G2 I3)))) (=> (@ (@ tptp.member_int I2) I5) (=> (@ tptp.finite_finite_int I5) (= (@ F2 I2) (@ G2 I2))))))))
% 6.73/7.06 (assert (forall ((F2 (-> tptp.complex tptp.rat)) (I5 tptp.set_complex) (G2 (-> tptp.complex tptp.rat)) (I2 tptp.complex)) (=> (= (@ (@ tptp.groups5058264527183730370ex_rat F2) I5) (@ (@ tptp.groups5058264527183730370ex_rat G2) I5)) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) I5) (@ (@ tptp.ord_less_eq_rat (@ F2 I3)) (@ G2 I3)))) (=> (@ (@ tptp.member_complex I2) I5) (=> (@ tptp.finite3207457112153483333omplex I5) (= (@ F2 I2) (@ G2 I2))))))))
% 6.73/7.06 (assert (forall ((F2 (-> tptp.real tptp.nat)) (I5 tptp.set_real) (G2 (-> tptp.real tptp.nat)) (I2 tptp.real)) (=> (= (@ (@ tptp.groups1935376822645274424al_nat F2) I5) (@ (@ tptp.groups1935376822645274424al_nat G2) I5)) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) I5) (@ (@ tptp.ord_less_eq_nat (@ F2 I3)) (@ G2 I3)))) (=> (@ (@ tptp.member_real I2) I5) (=> (@ tptp.finite_finite_real I5) (= (@ F2 I2) (@ G2 I2))))))))
% 6.73/7.06 (assert (forall ((F2 (-> tptp.int tptp.nat)) (I5 tptp.set_int) (G2 (-> tptp.int tptp.nat)) (I2 tptp.int)) (=> (= (@ (@ tptp.groups4541462559716669496nt_nat F2) I5) (@ (@ tptp.groups4541462559716669496nt_nat G2) I5)) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) I5) (@ (@ tptp.ord_less_eq_nat (@ F2 I3)) (@ G2 I3)))) (=> (@ (@ tptp.member_int I2) I5) (=> (@ tptp.finite_finite_int I5) (= (@ F2 I2) (@ G2 I2))))))))
% 6.73/7.06 (assert (forall ((F2 (-> tptp.complex tptp.nat)) (I5 tptp.set_complex) (G2 (-> tptp.complex tptp.nat)) (I2 tptp.complex)) (=> (= (@ (@ tptp.groups5693394587270226106ex_nat F2) I5) (@ (@ tptp.groups5693394587270226106ex_nat G2) I5)) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) I5) (@ (@ tptp.ord_less_eq_nat (@ F2 I3)) (@ G2 I3)))) (=> (@ (@ tptp.member_complex I2) I5) (=> (@ tptp.finite3207457112153483333omplex I5) (= (@ F2 I2) (@ G2 I2))))))))
% 6.73/7.06 (assert (forall ((F2 (-> tptp.real tptp.int)) (I5 tptp.set_real) (G2 (-> tptp.real tptp.int)) (I2 tptp.real)) (=> (= (@ (@ tptp.groups1932886352136224148al_int F2) I5) (@ (@ tptp.groups1932886352136224148al_int G2) I5)) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) I5) (@ (@ tptp.ord_less_eq_int (@ F2 I3)) (@ G2 I3)))) (=> (@ (@ tptp.member_real I2) I5) (=> (@ tptp.finite_finite_real I5) (= (@ F2 I2) (@ G2 I2))))))))
% 6.73/7.06 (assert (forall ((F2 (-> tptp.nat tptp.int)) (I5 tptp.set_nat) (G2 (-> tptp.nat tptp.int)) (I2 tptp.nat)) (=> (= (@ (@ tptp.groups3539618377306564664at_int F2) I5) (@ (@ tptp.groups3539618377306564664at_int G2) I5)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.member_nat I3) I5) (@ (@ tptp.ord_less_eq_int (@ F2 I3)) (@ G2 I3)))) (=> (@ (@ tptp.member_nat I2) I5) (=> (@ tptp.finite_finite_nat I5) (= (@ F2 I2) (@ G2 I2))))))))
% 6.73/7.06 (assert (forall ((F2 (-> tptp.complex tptp.int)) (I5 tptp.set_complex) (G2 (-> tptp.complex tptp.int)) (I2 tptp.complex)) (=> (= (@ (@ tptp.groups5690904116761175830ex_int F2) I5) (@ (@ tptp.groups5690904116761175830ex_int G2) I5)) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) I5) (@ (@ tptp.ord_less_eq_int (@ F2 I3)) (@ G2 I3)))) (=> (@ (@ tptp.member_complex I2) I5) (=> (@ tptp.finite3207457112153483333omplex I5) (= (@ F2 I2) (@ G2 I2))))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_nat) (F2 (-> tptp.nat tptp.nat)) (G2 (-> tptp.nat tptp.nat))) (=> (not (@ (@ tptp.member_nat tptp.zero_zero_nat) A4)) (=> (forall ((X3 tptp.nat)) (let ((_let_1 (@ tptp.suc X3))) (=> (@ (@ tptp.member_nat _let_1) A4) (= (@ F2 _let_1) (@ G2 _let_1))))) (= (@ (@ tptp.groups3542108847815614940at_nat F2) A4) (@ (@ tptp.groups3542108847815614940at_nat G2) A4))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_nat) (F2 (-> tptp.nat tptp.real)) (G2 (-> tptp.nat tptp.real))) (=> (not (@ (@ tptp.member_nat tptp.zero_zero_nat) A4)) (=> (forall ((X3 tptp.nat)) (let ((_let_1 (@ tptp.suc X3))) (=> (@ (@ tptp.member_nat _let_1) A4) (= (@ F2 _let_1) (@ G2 _let_1))))) (= (@ (@ tptp.groups6591440286371151544t_real F2) A4) (@ (@ tptp.groups6591440286371151544t_real G2) A4))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_real) (G2 (-> tptp.real tptp.complex)) (P2 (-> tptp.real Bool))) (=> (@ tptp.finite_finite_real A4) (= (@ (@ tptp.groups5754745047067104278omplex G2) (@ tptp.collect_real (lambda ((X4 tptp.real)) (and (@ (@ tptp.member_real X4) A4) (@ P2 X4))))) (@ (@ tptp.groups5754745047067104278omplex (lambda ((X4 tptp.real)) (@ (@ (@ tptp.if_complex (@ P2 X4)) (@ G2 X4)) tptp.zero_zero_complex))) A4)))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_nat) (G2 (-> tptp.nat tptp.complex)) (P2 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat A4) (= (@ (@ tptp.groups2073611262835488442omplex G2) (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) A4) (@ P2 X4))))) (@ (@ tptp.groups2073611262835488442omplex (lambda ((X4 tptp.nat)) (@ (@ (@ tptp.if_complex (@ P2 X4)) (@ G2 X4)) tptp.zero_zero_complex))) A4)))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_int) (G2 (-> tptp.int tptp.complex)) (P2 (-> tptp.int Bool))) (=> (@ tptp.finite_finite_int A4) (= (@ (@ tptp.groups3049146728041665814omplex G2) (@ tptp.collect_int (lambda ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) A4) (@ P2 X4))))) (@ (@ tptp.groups3049146728041665814omplex (lambda ((X4 tptp.int)) (@ (@ (@ tptp.if_complex (@ P2 X4)) (@ G2 X4)) tptp.zero_zero_complex))) A4)))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_complex) (G2 (-> tptp.complex tptp.complex)) (P2 (-> tptp.complex Bool))) (=> (@ tptp.finite3207457112153483333omplex A4) (= (@ (@ tptp.groups7754918857620584856omplex G2) (@ tptp.collect_complex (lambda ((X4 tptp.complex)) (and (@ (@ tptp.member_complex X4) A4) (@ P2 X4))))) (@ (@ tptp.groups7754918857620584856omplex (lambda ((X4 tptp.complex)) (@ (@ (@ tptp.if_complex (@ P2 X4)) (@ G2 X4)) tptp.zero_zero_complex))) A4)))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_real) (G2 (-> tptp.real tptp.real)) (P2 (-> tptp.real Bool))) (=> (@ tptp.finite_finite_real A4) (= (@ (@ tptp.groups8097168146408367636l_real G2) (@ tptp.collect_real (lambda ((X4 tptp.real)) (and (@ (@ tptp.member_real X4) A4) (@ P2 X4))))) (@ (@ tptp.groups8097168146408367636l_real (lambda ((X4 tptp.real)) (@ (@ (@ tptp.if_real (@ P2 X4)) (@ G2 X4)) tptp.zero_zero_real))) A4)))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_int) (G2 (-> tptp.int tptp.real)) (P2 (-> tptp.int Bool))) (=> (@ tptp.finite_finite_int A4) (= (@ (@ tptp.groups8778361861064173332t_real G2) (@ tptp.collect_int (lambda ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) A4) (@ P2 X4))))) (@ (@ tptp.groups8778361861064173332t_real (lambda ((X4 tptp.int)) (@ (@ (@ tptp.if_real (@ P2 X4)) (@ G2 X4)) tptp.zero_zero_real))) A4)))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_complex) (G2 (-> tptp.complex tptp.real)) (P2 (-> tptp.complex Bool))) (=> (@ tptp.finite3207457112153483333omplex A4) (= (@ (@ tptp.groups5808333547571424918x_real G2) (@ tptp.collect_complex (lambda ((X4 tptp.complex)) (and (@ (@ tptp.member_complex X4) A4) (@ P2 X4))))) (@ (@ tptp.groups5808333547571424918x_real (lambda ((X4 tptp.complex)) (@ (@ (@ tptp.if_real (@ P2 X4)) (@ G2 X4)) tptp.zero_zero_real))) A4)))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_real) (G2 (-> tptp.real tptp.rat)) (P2 (-> tptp.real Bool))) (=> (@ tptp.finite_finite_real A4) (= (@ (@ tptp.groups1300246762558778688al_rat G2) (@ tptp.collect_real (lambda ((X4 tptp.real)) (and (@ (@ tptp.member_real X4) A4) (@ P2 X4))))) (@ (@ tptp.groups1300246762558778688al_rat (lambda ((X4 tptp.real)) (@ (@ (@ tptp.if_rat (@ P2 X4)) (@ G2 X4)) tptp.zero_zero_rat))) A4)))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_nat) (G2 (-> tptp.nat tptp.rat)) (P2 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat A4) (= (@ (@ tptp.groups2906978787729119204at_rat G2) (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) A4) (@ P2 X4))))) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((X4 tptp.nat)) (@ (@ (@ tptp.if_rat (@ P2 X4)) (@ G2 X4)) tptp.zero_zero_rat))) A4)))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_int) (G2 (-> tptp.int tptp.rat)) (P2 (-> tptp.int Bool))) (=> (@ tptp.finite_finite_int A4) (= (@ (@ tptp.groups3906332499630173760nt_rat G2) (@ tptp.collect_int (lambda ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) A4) (@ P2 X4))))) (@ (@ tptp.groups3906332499630173760nt_rat (lambda ((X4 tptp.int)) (@ (@ (@ tptp.if_rat (@ P2 X4)) (@ G2 X4)) tptp.zero_zero_rat))) A4)))))
% 6.73/7.06 (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))))
% 6.73/7.06 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_eq_set_real (@ tptp.collect_real (lambda ((C3 tptp.real)) (@ (@ tptp.dvd_dvd_real C3) A)))) (@ tptp.collect_real (lambda ((C3 tptp.real)) (@ (@ tptp.dvd_dvd_real C3) B)))) (@ (@ tptp.dvd_dvd_real A) B))))
% 6.73/7.06 (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))))
% 6.73/7.06 (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))))
% 6.73/7.06 (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))))))
% 6.73/7.06 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_set_real (@ tptp.collect_real (lambda ((C3 tptp.real)) (@ (@ tptp.dvd_dvd_real C3) A)))) (@ tptp.collect_real (lambda ((C3 tptp.real)) (@ (@ tptp.dvd_dvd_real C3) B)))) (and (@ (@ tptp.dvd_dvd_real A) B) (not (@ (@ tptp.dvd_dvd_real B) A))))))
% 6.73/7.06 (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))))))
% 6.73/7.06 (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))))))
% 6.73/7.06 (assert (forall ((S2 tptp.set_int) (T tptp.set_int) (G2 (-> tptp.int tptp.real)) (I2 (-> tptp.int tptp.int)) (F2 (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int S2) (=> (@ tptp.finite_finite_int T) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) T) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ G2 X3)))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) S2) (exists ((Xa tptp.int)) (and (@ (@ tptp.member_int Xa) T) (= (@ I2 Xa) X3) (@ (@ tptp.ord_less_eq_real (@ F2 X3)) (@ G2 Xa)))))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups8778361861064173332t_real F2) S2)) (@ (@ tptp.groups8778361861064173332t_real G2) T))))))))
% 6.73/7.06 (assert (forall ((S2 tptp.set_int) (T tptp.set_complex) (G2 (-> tptp.complex tptp.real)) (I2 (-> tptp.complex tptp.int)) (F2 (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int S2) (=> (@ tptp.finite3207457112153483333omplex T) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) T) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ G2 X3)))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) S2) (exists ((Xa tptp.complex)) (and (@ (@ tptp.member_complex Xa) T) (= (@ I2 Xa) X3) (@ (@ tptp.ord_less_eq_real (@ F2 X3)) (@ G2 Xa)))))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups8778361861064173332t_real F2) S2)) (@ (@ tptp.groups5808333547571424918x_real G2) T))))))))
% 6.73/7.06 (assert (forall ((S2 tptp.set_complex) (T tptp.set_int) (G2 (-> tptp.int tptp.real)) (I2 (-> tptp.int tptp.complex)) (F2 (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex S2) (=> (@ tptp.finite_finite_int T) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) T) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ G2 X3)))) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) S2) (exists ((Xa tptp.int)) (and (@ (@ tptp.member_int Xa) T) (= (@ I2 Xa) X3) (@ (@ tptp.ord_less_eq_real (@ F2 X3)) (@ G2 Xa)))))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups5808333547571424918x_real F2) S2)) (@ (@ tptp.groups8778361861064173332t_real G2) T))))))))
% 6.73/7.06 (assert (forall ((S2 tptp.set_complex) (T tptp.set_complex) (G2 (-> tptp.complex tptp.real)) (I2 (-> tptp.complex tptp.complex)) (F2 (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex S2) (=> (@ tptp.finite3207457112153483333omplex T) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) T) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ G2 X3)))) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) S2) (exists ((Xa tptp.complex)) (and (@ (@ tptp.member_complex Xa) T) (= (@ I2 Xa) X3) (@ (@ tptp.ord_less_eq_real (@ F2 X3)) (@ G2 Xa)))))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups5808333547571424918x_real F2) S2)) (@ (@ tptp.groups5808333547571424918x_real G2) T))))))))
% 6.73/7.06 (assert (forall ((S2 tptp.set_nat) (T tptp.set_nat) (G2 (-> tptp.nat tptp.rat)) (I2 (-> tptp.nat tptp.nat)) (F2 (-> tptp.nat tptp.rat))) (=> (@ tptp.finite_finite_nat S2) (=> (@ tptp.finite_finite_nat T) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) T) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ G2 X3)))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) S2) (exists ((Xa tptp.nat)) (and (@ (@ tptp.member_nat Xa) T) (= (@ I2 Xa) X3) (@ (@ tptp.ord_less_eq_rat (@ F2 X3)) (@ G2 Xa)))))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups2906978787729119204at_rat F2) S2)) (@ (@ tptp.groups2906978787729119204at_rat G2) T))))))))
% 6.73/7.06 (assert (forall ((S2 tptp.set_nat) (T tptp.set_int) (G2 (-> tptp.int tptp.rat)) (I2 (-> tptp.int tptp.nat)) (F2 (-> tptp.nat tptp.rat))) (=> (@ tptp.finite_finite_nat S2) (=> (@ tptp.finite_finite_int T) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) T) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ G2 X3)))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) S2) (exists ((Xa tptp.int)) (and (@ (@ tptp.member_int Xa) T) (= (@ I2 Xa) X3) (@ (@ tptp.ord_less_eq_rat (@ F2 X3)) (@ G2 Xa)))))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups2906978787729119204at_rat F2) S2)) (@ (@ tptp.groups3906332499630173760nt_rat G2) T))))))))
% 6.73/7.06 (assert (forall ((S2 tptp.set_nat) (T tptp.set_complex) (G2 (-> tptp.complex tptp.rat)) (I2 (-> tptp.complex tptp.nat)) (F2 (-> tptp.nat tptp.rat))) (=> (@ tptp.finite_finite_nat S2) (=> (@ tptp.finite3207457112153483333omplex T) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) T) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ G2 X3)))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) S2) (exists ((Xa tptp.complex)) (and (@ (@ tptp.member_complex Xa) T) (= (@ I2 Xa) X3) (@ (@ tptp.ord_less_eq_rat (@ F2 X3)) (@ G2 Xa)))))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups2906978787729119204at_rat F2) S2)) (@ (@ tptp.groups5058264527183730370ex_rat G2) T))))))))
% 6.73/7.06 (assert (forall ((S2 tptp.set_int) (T tptp.set_nat) (G2 (-> tptp.nat tptp.rat)) (I2 (-> tptp.nat tptp.int)) (F2 (-> tptp.int tptp.rat))) (=> (@ tptp.finite_finite_int S2) (=> (@ tptp.finite_finite_nat T) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) T) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ G2 X3)))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) S2) (exists ((Xa tptp.nat)) (and (@ (@ tptp.member_nat Xa) T) (= (@ I2 Xa) X3) (@ (@ tptp.ord_less_eq_rat (@ F2 X3)) (@ G2 Xa)))))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups3906332499630173760nt_rat F2) S2)) (@ (@ tptp.groups2906978787729119204at_rat G2) T))))))))
% 6.73/7.06 (assert (forall ((S2 tptp.set_int) (T tptp.set_int) (G2 (-> tptp.int tptp.rat)) (I2 (-> tptp.int tptp.int)) (F2 (-> tptp.int tptp.rat))) (=> (@ tptp.finite_finite_int S2) (=> (@ tptp.finite_finite_int T) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) T) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ G2 X3)))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) S2) (exists ((Xa tptp.int)) (and (@ (@ tptp.member_int Xa) T) (= (@ I2 Xa) X3) (@ (@ tptp.ord_less_eq_rat (@ F2 X3)) (@ G2 Xa)))))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups3906332499630173760nt_rat F2) S2)) (@ (@ tptp.groups3906332499630173760nt_rat G2) T))))))))
% 6.73/7.06 (assert (forall ((S2 tptp.set_int) (T tptp.set_complex) (G2 (-> tptp.complex tptp.rat)) (I2 (-> tptp.complex tptp.int)) (F2 (-> tptp.int tptp.rat))) (=> (@ tptp.finite_finite_int S2) (=> (@ tptp.finite3207457112153483333omplex T) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) T) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ G2 X3)))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) S2) (exists ((Xa tptp.complex)) (and (@ (@ tptp.member_complex Xa) T) (= (@ I2 Xa) X3) (@ (@ tptp.ord_less_eq_rat (@ F2 X3)) (@ G2 Xa)))))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups3906332499630173760nt_rat F2) S2)) (@ (@ tptp.groups5058264527183730370ex_rat G2) T))))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_real) (F2 (-> tptp.real tptp.real))) (=> (@ tptp.finite_finite_real A4) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) A4) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F2 X3)))) (= (= (@ (@ tptp.groups8097168146408367636l_real F2) A4) tptp.zero_zero_real) (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) A4) (= (@ F2 X4) tptp.zero_zero_real))))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_int) (F2 (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int A4) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A4) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F2 X3)))) (= (= (@ (@ tptp.groups8778361861064173332t_real F2) A4) tptp.zero_zero_real) (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) A4) (= (@ F2 X4) tptp.zero_zero_real))))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_complex) (F2 (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex A4) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) A4) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F2 X3)))) (= (= (@ (@ tptp.groups5808333547571424918x_real F2) A4) tptp.zero_zero_real) (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) A4) (= (@ F2 X4) tptp.zero_zero_real))))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_real) (F2 (-> tptp.real tptp.rat))) (=> (@ tptp.finite_finite_real A4) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) A4) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F2 X3)))) (= (= (@ (@ tptp.groups1300246762558778688al_rat F2) A4) tptp.zero_zero_rat) (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) A4) (= (@ F2 X4) tptp.zero_zero_rat))))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_nat) (F2 (-> tptp.nat tptp.rat))) (=> (@ tptp.finite_finite_nat A4) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A4) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F2 X3)))) (= (= (@ (@ tptp.groups2906978787729119204at_rat F2) A4) tptp.zero_zero_rat) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) A4) (= (@ F2 X4) tptp.zero_zero_rat))))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_int) (F2 (-> tptp.int tptp.rat))) (=> (@ tptp.finite_finite_int A4) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A4) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F2 X3)))) (= (= (@ (@ tptp.groups3906332499630173760nt_rat F2) A4) tptp.zero_zero_rat) (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) A4) (= (@ F2 X4) tptp.zero_zero_rat))))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_complex) (F2 (-> tptp.complex tptp.rat))) (=> (@ tptp.finite3207457112153483333omplex A4) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) A4) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F2 X3)))) (= (= (@ (@ tptp.groups5058264527183730370ex_rat F2) A4) tptp.zero_zero_rat) (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) A4) (= (@ F2 X4) tptp.zero_zero_rat))))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_real) (F2 (-> tptp.real tptp.nat))) (=> (@ tptp.finite_finite_real A4) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) A4) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F2 X3)))) (= (= (@ (@ tptp.groups1935376822645274424al_nat F2) A4) tptp.zero_zero_nat) (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) A4) (= (@ F2 X4) tptp.zero_zero_nat))))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_int) (F2 (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int A4) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A4) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F2 X3)))) (= (= (@ (@ tptp.groups4541462559716669496nt_nat F2) A4) tptp.zero_zero_nat) (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) A4) (= (@ F2 X4) tptp.zero_zero_nat))))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_complex) (F2 (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex A4) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) A4) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F2 X3)))) (= (= (@ (@ tptp.groups5693394587270226106ex_nat F2) A4) tptp.zero_zero_nat) (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) A4) (= (@ F2 X4) tptp.zero_zero_nat))))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_int) (F2 (-> tptp.int tptp.real)) (G2 (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int A4) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A4) (@ (@ tptp.ord_less_eq_real (@ F2 X3)) (@ G2 X3)))) (=> (exists ((X5 tptp.int)) (and (@ (@ tptp.member_int X5) A4) (@ (@ tptp.ord_less_real (@ F2 X5)) (@ G2 X5)))) (@ (@ tptp.ord_less_real (@ (@ tptp.groups8778361861064173332t_real F2) A4)) (@ (@ tptp.groups8778361861064173332t_real G2) A4)))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_complex) (F2 (-> tptp.complex tptp.real)) (G2 (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex A4) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) A4) (@ (@ tptp.ord_less_eq_real (@ F2 X3)) (@ G2 X3)))) (=> (exists ((X5 tptp.complex)) (and (@ (@ tptp.member_complex X5) A4) (@ (@ tptp.ord_less_real (@ F2 X5)) (@ G2 X5)))) (@ (@ tptp.ord_less_real (@ (@ tptp.groups5808333547571424918x_real F2) A4)) (@ (@ tptp.groups5808333547571424918x_real G2) A4)))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_nat) (F2 (-> tptp.nat tptp.rat)) (G2 (-> tptp.nat tptp.rat))) (=> (@ tptp.finite_finite_nat A4) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A4) (@ (@ tptp.ord_less_eq_rat (@ F2 X3)) (@ G2 X3)))) (=> (exists ((X5 tptp.nat)) (and (@ (@ tptp.member_nat X5) A4) (@ (@ tptp.ord_less_rat (@ F2 X5)) (@ G2 X5)))) (@ (@ tptp.ord_less_rat (@ (@ tptp.groups2906978787729119204at_rat F2) A4)) (@ (@ tptp.groups2906978787729119204at_rat G2) A4)))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_int) (F2 (-> tptp.int tptp.rat)) (G2 (-> tptp.int tptp.rat))) (=> (@ tptp.finite_finite_int A4) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A4) (@ (@ tptp.ord_less_eq_rat (@ F2 X3)) (@ G2 X3)))) (=> (exists ((X5 tptp.int)) (and (@ (@ tptp.member_int X5) A4) (@ (@ tptp.ord_less_rat (@ F2 X5)) (@ G2 X5)))) (@ (@ tptp.ord_less_rat (@ (@ tptp.groups3906332499630173760nt_rat F2) A4)) (@ (@ tptp.groups3906332499630173760nt_rat G2) A4)))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_complex) (F2 (-> tptp.complex tptp.rat)) (G2 (-> tptp.complex tptp.rat))) (=> (@ tptp.finite3207457112153483333omplex A4) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) A4) (@ (@ tptp.ord_less_eq_rat (@ F2 X3)) (@ G2 X3)))) (=> (exists ((X5 tptp.complex)) (and (@ (@ tptp.member_complex X5) A4) (@ (@ tptp.ord_less_rat (@ F2 X5)) (@ G2 X5)))) (@ (@ tptp.ord_less_rat (@ (@ tptp.groups5058264527183730370ex_rat F2) A4)) (@ (@ tptp.groups5058264527183730370ex_rat G2) A4)))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_int) (F2 (-> tptp.int tptp.nat)) (G2 (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int A4) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A4) (@ (@ tptp.ord_less_eq_nat (@ F2 X3)) (@ G2 X3)))) (=> (exists ((X5 tptp.int)) (and (@ (@ tptp.member_int X5) A4) (@ (@ tptp.ord_less_nat (@ F2 X5)) (@ G2 X5)))) (@ (@ tptp.ord_less_nat (@ (@ tptp.groups4541462559716669496nt_nat F2) A4)) (@ (@ tptp.groups4541462559716669496nt_nat G2) A4)))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_complex) (F2 (-> tptp.complex tptp.nat)) (G2 (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex A4) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) A4) (@ (@ tptp.ord_less_eq_nat (@ F2 X3)) (@ G2 X3)))) (=> (exists ((X5 tptp.complex)) (and (@ (@ tptp.member_complex X5) A4) (@ (@ tptp.ord_less_nat (@ F2 X5)) (@ G2 X5)))) (@ (@ tptp.ord_less_nat (@ (@ tptp.groups5693394587270226106ex_nat F2) A4)) (@ (@ tptp.groups5693394587270226106ex_nat G2) A4)))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_nat) (F2 (-> tptp.nat tptp.int)) (G2 (-> tptp.nat tptp.int))) (=> (@ tptp.finite_finite_nat A4) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A4) (@ (@ tptp.ord_less_eq_int (@ F2 X3)) (@ G2 X3)))) (=> (exists ((X5 tptp.nat)) (and (@ (@ tptp.member_nat X5) A4) (@ (@ tptp.ord_less_int (@ F2 X5)) (@ G2 X5)))) (@ (@ tptp.ord_less_int (@ (@ tptp.groups3539618377306564664at_int F2) A4)) (@ (@ tptp.groups3539618377306564664at_int G2) A4)))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_complex) (F2 (-> tptp.complex tptp.int)) (G2 (-> tptp.complex tptp.int))) (=> (@ tptp.finite3207457112153483333omplex A4) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) A4) (@ (@ tptp.ord_less_eq_int (@ F2 X3)) (@ G2 X3)))) (=> (exists ((X5 tptp.complex)) (and (@ (@ tptp.member_complex X5) A4) (@ (@ tptp.ord_less_int (@ F2 X5)) (@ G2 X5)))) (@ (@ tptp.ord_less_int (@ (@ tptp.groups5690904116761175830ex_int F2) A4)) (@ (@ tptp.groups5690904116761175830ex_int G2) A4)))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_nat) (F2 (-> tptp.nat tptp.nat)) (G2 (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_nat A4) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A4) (@ (@ tptp.ord_less_eq_nat (@ F2 X3)) (@ G2 X3)))) (=> (exists ((X5 tptp.nat)) (and (@ (@ tptp.member_nat X5) A4) (@ (@ tptp.ord_less_nat (@ F2 X5)) (@ G2 X5)))) (@ (@ tptp.ord_less_nat (@ (@ tptp.groups3542108847815614940at_nat F2) A4)) (@ (@ tptp.groups3542108847815614940at_nat G2) A4)))))))
% 6.73/7.06 (assert (forall ((R2 (-> tptp.complex tptp.complex Bool)) (S3 tptp.set_nat) (H (-> tptp.nat tptp.complex)) (G2 (-> tptp.nat tptp.complex))) (=> (@ (@ R2 tptp.zero_zero_complex) tptp.zero_zero_complex) (=> (forall ((X15 tptp.complex) (Y15 tptp.complex) (X23 tptp.complex) (Y23 tptp.complex)) (=> (and (@ (@ R2 X15) X23) (@ (@ R2 Y15) Y23)) (@ (@ R2 (@ (@ tptp.plus_plus_complex X15) Y15)) (@ (@ tptp.plus_plus_complex X23) Y23)))) (=> (@ tptp.finite_finite_nat S3) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) S3) (@ (@ R2 (@ H X3)) (@ G2 X3)))) (@ (@ R2 (@ (@ tptp.groups2073611262835488442omplex H) S3)) (@ (@ tptp.groups2073611262835488442omplex G2) S3))))))))
% 6.73/7.06 (assert (forall ((R2 (-> tptp.complex tptp.complex Bool)) (S3 tptp.set_int) (H (-> tptp.int tptp.complex)) (G2 (-> tptp.int tptp.complex))) (=> (@ (@ R2 tptp.zero_zero_complex) tptp.zero_zero_complex) (=> (forall ((X15 tptp.complex) (Y15 tptp.complex) (X23 tptp.complex) (Y23 tptp.complex)) (=> (and (@ (@ R2 X15) X23) (@ (@ R2 Y15) Y23)) (@ (@ R2 (@ (@ tptp.plus_plus_complex X15) Y15)) (@ (@ tptp.plus_plus_complex X23) Y23)))) (=> (@ tptp.finite_finite_int S3) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) S3) (@ (@ R2 (@ H X3)) (@ G2 X3)))) (@ (@ R2 (@ (@ tptp.groups3049146728041665814omplex H) S3)) (@ (@ tptp.groups3049146728041665814omplex G2) S3))))))))
% 6.73/7.06 (assert (forall ((R2 (-> tptp.complex tptp.complex Bool)) (S3 tptp.set_complex) (H (-> tptp.complex tptp.complex)) (G2 (-> tptp.complex tptp.complex))) (=> (@ (@ R2 tptp.zero_zero_complex) tptp.zero_zero_complex) (=> (forall ((X15 tptp.complex) (Y15 tptp.complex) (X23 tptp.complex) (Y23 tptp.complex)) (=> (and (@ (@ R2 X15) X23) (@ (@ R2 Y15) Y23)) (@ (@ R2 (@ (@ tptp.plus_plus_complex X15) Y15)) (@ (@ tptp.plus_plus_complex X23) Y23)))) (=> (@ tptp.finite3207457112153483333omplex S3) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) S3) (@ (@ R2 (@ H X3)) (@ G2 X3)))) (@ (@ R2 (@ (@ tptp.groups7754918857620584856omplex H) S3)) (@ (@ tptp.groups7754918857620584856omplex G2) S3))))))))
% 6.73/7.06 (assert (forall ((R2 (-> tptp.real tptp.real Bool)) (S3 tptp.set_int) (H (-> tptp.int tptp.real)) (G2 (-> tptp.int tptp.real))) (=> (@ (@ R2 tptp.zero_zero_real) tptp.zero_zero_real) (=> (forall ((X15 tptp.real) (Y15 tptp.real) (X23 tptp.real) (Y23 tptp.real)) (=> (and (@ (@ R2 X15) X23) (@ (@ R2 Y15) Y23)) (@ (@ R2 (@ (@ tptp.plus_plus_real X15) Y15)) (@ (@ tptp.plus_plus_real X23) Y23)))) (=> (@ tptp.finite_finite_int S3) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) S3) (@ (@ R2 (@ H X3)) (@ G2 X3)))) (@ (@ R2 (@ (@ tptp.groups8778361861064173332t_real H) S3)) (@ (@ tptp.groups8778361861064173332t_real G2) S3))))))))
% 6.73/7.06 (assert (forall ((R2 (-> tptp.real tptp.real Bool)) (S3 tptp.set_complex) (H (-> tptp.complex tptp.real)) (G2 (-> tptp.complex tptp.real))) (=> (@ (@ R2 tptp.zero_zero_real) tptp.zero_zero_real) (=> (forall ((X15 tptp.real) (Y15 tptp.real) (X23 tptp.real) (Y23 tptp.real)) (=> (and (@ (@ R2 X15) X23) (@ (@ R2 Y15) Y23)) (@ (@ R2 (@ (@ tptp.plus_plus_real X15) Y15)) (@ (@ tptp.plus_plus_real X23) Y23)))) (=> (@ tptp.finite3207457112153483333omplex S3) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) S3) (@ (@ R2 (@ H X3)) (@ G2 X3)))) (@ (@ R2 (@ (@ tptp.groups5808333547571424918x_real H) S3)) (@ (@ tptp.groups5808333547571424918x_real G2) S3))))))))
% 6.73/7.06 (assert (forall ((R2 (-> tptp.rat tptp.rat Bool)) (S3 tptp.set_nat) (H (-> tptp.nat tptp.rat)) (G2 (-> tptp.nat tptp.rat))) (=> (@ (@ R2 tptp.zero_zero_rat) tptp.zero_zero_rat) (=> (forall ((X15 tptp.rat) (Y15 tptp.rat) (X23 tptp.rat) (Y23 tptp.rat)) (=> (and (@ (@ R2 X15) X23) (@ (@ R2 Y15) Y23)) (@ (@ R2 (@ (@ tptp.plus_plus_rat X15) Y15)) (@ (@ tptp.plus_plus_rat X23) Y23)))) (=> (@ tptp.finite_finite_nat S3) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) S3) (@ (@ R2 (@ H X3)) (@ G2 X3)))) (@ (@ R2 (@ (@ tptp.groups2906978787729119204at_rat H) S3)) (@ (@ tptp.groups2906978787729119204at_rat G2) S3))))))))
% 6.73/7.06 (assert (forall ((R2 (-> tptp.rat tptp.rat Bool)) (S3 tptp.set_int) (H (-> tptp.int tptp.rat)) (G2 (-> tptp.int tptp.rat))) (=> (@ (@ R2 tptp.zero_zero_rat) tptp.zero_zero_rat) (=> (forall ((X15 tptp.rat) (Y15 tptp.rat) (X23 tptp.rat) (Y23 tptp.rat)) (=> (and (@ (@ R2 X15) X23) (@ (@ R2 Y15) Y23)) (@ (@ R2 (@ (@ tptp.plus_plus_rat X15) Y15)) (@ (@ tptp.plus_plus_rat X23) Y23)))) (=> (@ tptp.finite_finite_int S3) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) S3) (@ (@ R2 (@ H X3)) (@ G2 X3)))) (@ (@ R2 (@ (@ tptp.groups3906332499630173760nt_rat H) S3)) (@ (@ tptp.groups3906332499630173760nt_rat G2) S3))))))))
% 6.73/7.06 (assert (forall ((R2 (-> tptp.rat tptp.rat Bool)) (S3 tptp.set_complex) (H (-> tptp.complex tptp.rat)) (G2 (-> tptp.complex tptp.rat))) (=> (@ (@ R2 tptp.zero_zero_rat) tptp.zero_zero_rat) (=> (forall ((X15 tptp.rat) (Y15 tptp.rat) (X23 tptp.rat) (Y23 tptp.rat)) (=> (and (@ (@ R2 X15) X23) (@ (@ R2 Y15) Y23)) (@ (@ R2 (@ (@ tptp.plus_plus_rat X15) Y15)) (@ (@ tptp.plus_plus_rat X23) Y23)))) (=> (@ tptp.finite3207457112153483333omplex S3) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) S3) (@ (@ R2 (@ H X3)) (@ G2 X3)))) (@ (@ R2 (@ (@ tptp.groups5058264527183730370ex_rat H) S3)) (@ (@ tptp.groups5058264527183730370ex_rat G2) S3))))))))
% 6.73/7.06 (assert (forall ((R2 (-> tptp.nat tptp.nat Bool)) (S3 tptp.set_int) (H (-> tptp.int tptp.nat)) (G2 (-> tptp.int tptp.nat))) (=> (@ (@ R2 tptp.zero_zero_nat) tptp.zero_zero_nat) (=> (forall ((X15 tptp.nat) (Y15 tptp.nat) (X23 tptp.nat) (Y23 tptp.nat)) (=> (and (@ (@ R2 X15) X23) (@ (@ R2 Y15) Y23)) (@ (@ R2 (@ (@ tptp.plus_plus_nat X15) Y15)) (@ (@ tptp.plus_plus_nat X23) Y23)))) (=> (@ tptp.finite_finite_int S3) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) S3) (@ (@ R2 (@ H X3)) (@ G2 X3)))) (@ (@ R2 (@ (@ tptp.groups4541462559716669496nt_nat H) S3)) (@ (@ tptp.groups4541462559716669496nt_nat G2) S3))))))))
% 6.73/7.06 (assert (forall ((R2 (-> tptp.nat tptp.nat Bool)) (S3 tptp.set_complex) (H (-> tptp.complex tptp.nat)) (G2 (-> tptp.complex tptp.nat))) (=> (@ (@ R2 tptp.zero_zero_nat) tptp.zero_zero_nat) (=> (forall ((X15 tptp.nat) (Y15 tptp.nat) (X23 tptp.nat) (Y23 tptp.nat)) (=> (and (@ (@ R2 X15) X23) (@ (@ R2 Y15) Y23)) (@ (@ R2 (@ (@ tptp.plus_plus_nat X15) Y15)) (@ (@ tptp.plus_plus_nat X23) Y23)))) (=> (@ tptp.finite3207457112153483333omplex S3) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) S3) (@ (@ R2 (@ H X3)) (@ G2 X3)))) (@ (@ R2 (@ (@ tptp.groups5693394587270226106ex_nat H) S3)) (@ (@ tptp.groups5693394587270226106ex_nat G2) S3))))))))
% 6.73/7.06 (assert (forall ((S5 tptp.set_real) (T4 tptp.set_real) (S3 tptp.set_real) (I2 (-> tptp.real tptp.real)) (J2 (-> tptp.real tptp.real)) (T5 tptp.set_real) (G2 (-> tptp.real tptp.complex)) (H (-> tptp.real tptp.complex))) (=> (@ tptp.finite_finite_real S5) (=> (@ tptp.finite_finite_real T4) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) (@ (@ tptp.minus_minus_set_real S3) S5)) (= (@ I2 (@ J2 A3)) A3))) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) (@ (@ tptp.minus_minus_set_real S3) S5)) (@ (@ tptp.member_real (@ J2 A3)) (@ (@ tptp.minus_minus_set_real T5) T4)))) (=> (forall ((B3 tptp.real)) (=> (@ (@ tptp.member_real B3) (@ (@ tptp.minus_minus_set_real T5) T4)) (= (@ J2 (@ I2 B3)) B3))) (=> (forall ((B3 tptp.real)) (=> (@ (@ tptp.member_real B3) (@ (@ tptp.minus_minus_set_real T5) T4)) (@ (@ tptp.member_real (@ I2 B3)) (@ (@ tptp.minus_minus_set_real S3) S5)))) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) S5) (= (@ G2 A3) tptp.zero_zero_complex))) (=> (forall ((B3 tptp.real)) (=> (@ (@ tptp.member_real B3) T4) (= (@ H B3) tptp.zero_zero_complex))) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) S3) (= (@ H (@ J2 A3)) (@ G2 A3)))) (= (@ (@ tptp.groups5754745047067104278omplex G2) S3) (@ (@ tptp.groups5754745047067104278omplex H) T5)))))))))))))
% 6.73/7.06 (assert (forall ((S5 tptp.set_real) (T4 tptp.set_int) (S3 tptp.set_real) (I2 (-> tptp.int tptp.real)) (J2 (-> tptp.real tptp.int)) (T5 tptp.set_int) (G2 (-> tptp.real tptp.complex)) (H (-> tptp.int tptp.complex))) (=> (@ tptp.finite_finite_real S5) (=> (@ tptp.finite_finite_int T4) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) (@ (@ tptp.minus_minus_set_real S3) S5)) (= (@ I2 (@ J2 A3)) A3))) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) (@ (@ tptp.minus_minus_set_real S3) S5)) (@ (@ tptp.member_int (@ J2 A3)) (@ (@ tptp.minus_minus_set_int T5) T4)))) (=> (forall ((B3 tptp.int)) (=> (@ (@ tptp.member_int B3) (@ (@ tptp.minus_minus_set_int T5) T4)) (= (@ J2 (@ I2 B3)) B3))) (=> (forall ((B3 tptp.int)) (=> (@ (@ tptp.member_int B3) (@ (@ tptp.minus_minus_set_int T5) T4)) (@ (@ tptp.member_real (@ I2 B3)) (@ (@ tptp.minus_minus_set_real S3) S5)))) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) S5) (= (@ G2 A3) tptp.zero_zero_complex))) (=> (forall ((B3 tptp.int)) (=> (@ (@ tptp.member_int B3) T4) (= (@ H B3) tptp.zero_zero_complex))) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) S3) (= (@ H (@ J2 A3)) (@ G2 A3)))) (= (@ (@ tptp.groups5754745047067104278omplex G2) S3) (@ (@ tptp.groups3049146728041665814omplex H) T5)))))))))))))
% 6.73/7.06 (assert (forall ((S5 tptp.set_real) (T4 tptp.set_complex) (S3 tptp.set_real) (I2 (-> tptp.complex tptp.real)) (J2 (-> tptp.real tptp.complex)) (T5 tptp.set_complex) (G2 (-> tptp.real tptp.complex)) (H (-> tptp.complex tptp.complex))) (=> (@ tptp.finite_finite_real S5) (=> (@ tptp.finite3207457112153483333omplex T4) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) (@ (@ tptp.minus_minus_set_real S3) S5)) (= (@ I2 (@ J2 A3)) A3))) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) (@ (@ tptp.minus_minus_set_real S3) S5)) (@ (@ tptp.member_complex (@ J2 A3)) (@ (@ tptp.minus_811609699411566653omplex T5) T4)))) (=> (forall ((B3 tptp.complex)) (=> (@ (@ tptp.member_complex B3) (@ (@ tptp.minus_811609699411566653omplex T5) T4)) (= (@ J2 (@ I2 B3)) B3))) (=> (forall ((B3 tptp.complex)) (=> (@ (@ tptp.member_complex B3) (@ (@ tptp.minus_811609699411566653omplex T5) T4)) (@ (@ tptp.member_real (@ I2 B3)) (@ (@ tptp.minus_minus_set_real S3) S5)))) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) S5) (= (@ G2 A3) tptp.zero_zero_complex))) (=> (forall ((B3 tptp.complex)) (=> (@ (@ tptp.member_complex B3) T4) (= (@ H B3) tptp.zero_zero_complex))) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) S3) (= (@ H (@ J2 A3)) (@ G2 A3)))) (= (@ (@ tptp.groups5754745047067104278omplex G2) S3) (@ (@ tptp.groups7754918857620584856omplex H) T5)))))))))))))
% 6.73/7.06 (assert (forall ((S5 tptp.set_int) (T4 tptp.set_real) (S3 tptp.set_int) (I2 (-> tptp.real tptp.int)) (J2 (-> tptp.int tptp.real)) (T5 tptp.set_real) (G2 (-> tptp.int tptp.complex)) (H (-> tptp.real tptp.complex))) (=> (@ tptp.finite_finite_int S5) (=> (@ tptp.finite_finite_real T4) (=> (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) (@ (@ tptp.minus_minus_set_int S3) S5)) (= (@ I2 (@ J2 A3)) A3))) (=> (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) (@ (@ tptp.minus_minus_set_int S3) S5)) (@ (@ tptp.member_real (@ J2 A3)) (@ (@ tptp.minus_minus_set_real T5) T4)))) (=> (forall ((B3 tptp.real)) (=> (@ (@ tptp.member_real B3) (@ (@ tptp.minus_minus_set_real T5) T4)) (= (@ J2 (@ I2 B3)) B3))) (=> (forall ((B3 tptp.real)) (=> (@ (@ tptp.member_real B3) (@ (@ tptp.minus_minus_set_real T5) T4)) (@ (@ tptp.member_int (@ I2 B3)) (@ (@ tptp.minus_minus_set_int S3) S5)))) (=> (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) S5) (= (@ G2 A3) tptp.zero_zero_complex))) (=> (forall ((B3 tptp.real)) (=> (@ (@ tptp.member_real B3) T4) (= (@ H B3) tptp.zero_zero_complex))) (=> (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) S3) (= (@ H (@ J2 A3)) (@ G2 A3)))) (= (@ (@ tptp.groups3049146728041665814omplex G2) S3) (@ (@ tptp.groups5754745047067104278omplex H) T5)))))))))))))
% 6.73/7.06 (assert (forall ((S5 tptp.set_int) (T4 tptp.set_int) (S3 tptp.set_int) (I2 (-> tptp.int tptp.int)) (J2 (-> tptp.int tptp.int)) (T5 tptp.set_int) (G2 (-> tptp.int tptp.complex)) (H (-> tptp.int tptp.complex))) (=> (@ tptp.finite_finite_int S5) (=> (@ tptp.finite_finite_int T4) (=> (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) (@ (@ tptp.minus_minus_set_int S3) S5)) (= (@ I2 (@ J2 A3)) A3))) (=> (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) (@ (@ tptp.minus_minus_set_int S3) S5)) (@ (@ tptp.member_int (@ J2 A3)) (@ (@ tptp.minus_minus_set_int T5) T4)))) (=> (forall ((B3 tptp.int)) (=> (@ (@ tptp.member_int B3) (@ (@ tptp.minus_minus_set_int T5) T4)) (= (@ J2 (@ I2 B3)) B3))) (=> (forall ((B3 tptp.int)) (=> (@ (@ tptp.member_int B3) (@ (@ tptp.minus_minus_set_int T5) T4)) (@ (@ tptp.member_int (@ I2 B3)) (@ (@ tptp.minus_minus_set_int S3) S5)))) (=> (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) S5) (= (@ G2 A3) tptp.zero_zero_complex))) (=> (forall ((B3 tptp.int)) (=> (@ (@ tptp.member_int B3) T4) (= (@ H B3) tptp.zero_zero_complex))) (=> (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) S3) (= (@ H (@ J2 A3)) (@ G2 A3)))) (= (@ (@ tptp.groups3049146728041665814omplex G2) S3) (@ (@ tptp.groups3049146728041665814omplex H) T5)))))))))))))
% 6.73/7.06 (assert (forall ((S5 tptp.set_int) (T4 tptp.set_complex) (S3 tptp.set_int) (I2 (-> tptp.complex tptp.int)) (J2 (-> tptp.int tptp.complex)) (T5 tptp.set_complex) (G2 (-> tptp.int tptp.complex)) (H (-> tptp.complex tptp.complex))) (=> (@ tptp.finite_finite_int S5) (=> (@ tptp.finite3207457112153483333omplex T4) (=> (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) (@ (@ tptp.minus_minus_set_int S3) S5)) (= (@ I2 (@ J2 A3)) A3))) (=> (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) (@ (@ tptp.minus_minus_set_int S3) S5)) (@ (@ tptp.member_complex (@ J2 A3)) (@ (@ tptp.minus_811609699411566653omplex T5) T4)))) (=> (forall ((B3 tptp.complex)) (=> (@ (@ tptp.member_complex B3) (@ (@ tptp.minus_811609699411566653omplex T5) T4)) (= (@ J2 (@ I2 B3)) B3))) (=> (forall ((B3 tptp.complex)) (=> (@ (@ tptp.member_complex B3) (@ (@ tptp.minus_811609699411566653omplex T5) T4)) (@ (@ tptp.member_int (@ I2 B3)) (@ (@ tptp.minus_minus_set_int S3) S5)))) (=> (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) S5) (= (@ G2 A3) tptp.zero_zero_complex))) (=> (forall ((B3 tptp.complex)) (=> (@ (@ tptp.member_complex B3) T4) (= (@ H B3) tptp.zero_zero_complex))) (=> (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) S3) (= (@ H (@ J2 A3)) (@ G2 A3)))) (= (@ (@ tptp.groups3049146728041665814omplex G2) S3) (@ (@ tptp.groups7754918857620584856omplex H) T5)))))))))))))
% 6.73/7.06 (assert (forall ((S5 tptp.set_complex) (T4 tptp.set_real) (S3 tptp.set_complex) (I2 (-> tptp.real tptp.complex)) (J2 (-> tptp.complex tptp.real)) (T5 tptp.set_real) (G2 (-> tptp.complex tptp.complex)) (H (-> tptp.real tptp.complex))) (=> (@ tptp.finite3207457112153483333omplex S5) (=> (@ tptp.finite_finite_real T4) (=> (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) (@ (@ tptp.minus_811609699411566653omplex S3) S5)) (= (@ I2 (@ J2 A3)) A3))) (=> (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) (@ (@ tptp.minus_811609699411566653omplex S3) S5)) (@ (@ tptp.member_real (@ J2 A3)) (@ (@ tptp.minus_minus_set_real T5) T4)))) (=> (forall ((B3 tptp.real)) (=> (@ (@ tptp.member_real B3) (@ (@ tptp.minus_minus_set_real T5) T4)) (= (@ J2 (@ I2 B3)) B3))) (=> (forall ((B3 tptp.real)) (=> (@ (@ tptp.member_real B3) (@ (@ tptp.minus_minus_set_real T5) T4)) (@ (@ tptp.member_complex (@ I2 B3)) (@ (@ tptp.minus_811609699411566653omplex S3) S5)))) (=> (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) S5) (= (@ G2 A3) tptp.zero_zero_complex))) (=> (forall ((B3 tptp.real)) (=> (@ (@ tptp.member_real B3) T4) (= (@ H B3) tptp.zero_zero_complex))) (=> (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) S3) (= (@ H (@ J2 A3)) (@ G2 A3)))) (= (@ (@ tptp.groups7754918857620584856omplex G2) S3) (@ (@ tptp.groups5754745047067104278omplex H) T5)))))))))))))
% 6.73/7.06 (assert (forall ((S5 tptp.set_complex) (T4 tptp.set_int) (S3 tptp.set_complex) (I2 (-> tptp.int tptp.complex)) (J2 (-> tptp.complex tptp.int)) (T5 tptp.set_int) (G2 (-> tptp.complex tptp.complex)) (H (-> tptp.int tptp.complex))) (=> (@ tptp.finite3207457112153483333omplex S5) (=> (@ tptp.finite_finite_int T4) (=> (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) (@ (@ tptp.minus_811609699411566653omplex S3) S5)) (= (@ I2 (@ J2 A3)) A3))) (=> (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) (@ (@ tptp.minus_811609699411566653omplex S3) S5)) (@ (@ tptp.member_int (@ J2 A3)) (@ (@ tptp.minus_minus_set_int T5) T4)))) (=> (forall ((B3 tptp.int)) (=> (@ (@ tptp.member_int B3) (@ (@ tptp.minus_minus_set_int T5) T4)) (= (@ J2 (@ I2 B3)) B3))) (=> (forall ((B3 tptp.int)) (=> (@ (@ tptp.member_int B3) (@ (@ tptp.minus_minus_set_int T5) T4)) (@ (@ tptp.member_complex (@ I2 B3)) (@ (@ tptp.minus_811609699411566653omplex S3) S5)))) (=> (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) S5) (= (@ G2 A3) tptp.zero_zero_complex))) (=> (forall ((B3 tptp.int)) (=> (@ (@ tptp.member_int B3) T4) (= (@ H B3) tptp.zero_zero_complex))) (=> (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) S3) (= (@ H (@ J2 A3)) (@ G2 A3)))) (= (@ (@ tptp.groups7754918857620584856omplex G2) S3) (@ (@ tptp.groups3049146728041665814omplex H) T5)))))))))))))
% 6.73/7.06 (assert (forall ((S5 tptp.set_complex) (T4 tptp.set_complex) (S3 tptp.set_complex) (I2 (-> tptp.complex tptp.complex)) (J2 (-> tptp.complex tptp.complex)) (T5 tptp.set_complex) (G2 (-> tptp.complex tptp.complex)) (H (-> tptp.complex tptp.complex))) (=> (@ tptp.finite3207457112153483333omplex S5) (=> (@ tptp.finite3207457112153483333omplex T4) (=> (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) (@ (@ tptp.minus_811609699411566653omplex S3) S5)) (= (@ I2 (@ J2 A3)) A3))) (=> (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) (@ (@ tptp.minus_811609699411566653omplex S3) S5)) (@ (@ tptp.member_complex (@ J2 A3)) (@ (@ tptp.minus_811609699411566653omplex T5) T4)))) (=> (forall ((B3 tptp.complex)) (=> (@ (@ tptp.member_complex B3) (@ (@ tptp.minus_811609699411566653omplex T5) T4)) (= (@ J2 (@ I2 B3)) B3))) (=> (forall ((B3 tptp.complex)) (=> (@ (@ tptp.member_complex B3) (@ (@ tptp.minus_811609699411566653omplex T5) T4)) (@ (@ tptp.member_complex (@ I2 B3)) (@ (@ tptp.minus_811609699411566653omplex S3) S5)))) (=> (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) S5) (= (@ G2 A3) tptp.zero_zero_complex))) (=> (forall ((B3 tptp.complex)) (=> (@ (@ tptp.member_complex B3) T4) (= (@ H B3) tptp.zero_zero_complex))) (=> (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) S3) (= (@ H (@ J2 A3)) (@ G2 A3)))) (= (@ (@ tptp.groups7754918857620584856omplex G2) S3) (@ (@ tptp.groups7754918857620584856omplex H) T5)))))))))))))
% 6.73/7.06 (assert (forall ((S5 tptp.set_real) (T4 tptp.set_real) (S3 tptp.set_real) (I2 (-> tptp.real tptp.real)) (J2 (-> tptp.real tptp.real)) (T5 tptp.set_real) (G2 (-> tptp.real tptp.real)) (H (-> tptp.real tptp.real))) (=> (@ tptp.finite_finite_real S5) (=> (@ tptp.finite_finite_real T4) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) (@ (@ tptp.minus_minus_set_real S3) S5)) (= (@ I2 (@ J2 A3)) A3))) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) (@ (@ tptp.minus_minus_set_real S3) S5)) (@ (@ tptp.member_real (@ J2 A3)) (@ (@ tptp.minus_minus_set_real T5) T4)))) (=> (forall ((B3 tptp.real)) (=> (@ (@ tptp.member_real B3) (@ (@ tptp.minus_minus_set_real T5) T4)) (= (@ J2 (@ I2 B3)) B3))) (=> (forall ((B3 tptp.real)) (=> (@ (@ tptp.member_real B3) (@ (@ tptp.minus_minus_set_real T5) T4)) (@ (@ tptp.member_real (@ I2 B3)) (@ (@ tptp.minus_minus_set_real S3) S5)))) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) S5) (= (@ G2 A3) tptp.zero_zero_real))) (=> (forall ((B3 tptp.real)) (=> (@ (@ tptp.member_real B3) T4) (= (@ H B3) tptp.zero_zero_real))) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) S3) (= (@ H (@ J2 A3)) (@ G2 A3)))) (= (@ (@ tptp.groups8097168146408367636l_real G2) S3) (@ (@ tptp.groups8097168146408367636l_real H) T5)))))))))))))
% 6.73/7.06 (assert (not (@ (@ tptp.dvd_dvd_Code_integer tptp.zero_z3403309356797280102nteger) tptp.one_one_Code_integer)))
% 6.73/7.06 (assert (not (@ (@ tptp.dvd_dvd_nat tptp.zero_zero_nat) tptp.one_one_nat)))
% 6.73/7.06 (assert (not (@ (@ tptp.dvd_dvd_int tptp.zero_zero_int) tptp.one_one_int)))
% 6.73/7.06 (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)))))
% 6.73/7.06 (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)))))
% 6.73/7.06 (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)))))
% 6.73/7.06 (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)))))
% 6.73/7.06 (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)))))
% 6.73/7.06 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C2 tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer) (= (= (@ (@ tptp.times_3573771949741848930nteger B) A) (@ (@ tptp.times_3573771949741848930nteger C2) A)) (= B C2)))))
% 6.73/7.06 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (= (= (@ (@ tptp.times_times_nat B) A) (@ (@ tptp.times_times_nat C2) A)) (= B C2)))))
% 6.73/7.06 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (= (= (@ (@ tptp.times_times_int B) A) (@ (@ tptp.times_times_int C2) A)) (= B C2)))))
% 6.73/7.06 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C2 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 C2)) (= B C2))))))
% 6.73/7.06 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (=> (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (= (= (@ _let_1 B) (@ _let_1 C2)) (= B C2))))))
% 6.73/7.06 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (=> (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (= (= (@ _let_1 B) (@ _let_1 C2)) (= B C2))))))
% 6.73/7.06 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C2 tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer) (= (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.times_3573771949741848930nteger A) B)) C2) (@ (@ tptp.dvd_dvd_Code_integer B) C2)))))
% 6.73/7.06 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat A) B)) C2) (@ (@ tptp.dvd_dvd_nat B) C2)))))
% 6.73/7.06 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A) B)) C2) (@ (@ tptp.dvd_dvd_int B) C2)))))
% 6.73/7.06 (assert (forall ((B tptp.code_integer) (A tptp.code_integer) (C2 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) C2)) (@ _let_1 C2))))))
% 6.73/7.06 (assert (forall ((B tptp.nat) (A tptp.nat) (C2 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) C2)) (@ _let_1 C2))))))
% 6.73/7.06 (assert (forall ((B tptp.int) (A tptp.int) (C2 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) C2)) (@ _let_1 C2))))))
% 6.73/7.06 (assert (forall ((B tptp.code_integer) (A tptp.code_integer) (C2 tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer) (= (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.times_3573771949741848930nteger A) B)) C2) (@ (@ tptp.dvd_dvd_Code_integer A) C2)))))
% 6.73/7.06 (assert (forall ((B tptp.nat) (A tptp.nat) (C2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat A) B)) C2) (@ (@ tptp.dvd_dvd_nat A) C2)))))
% 6.73/7.06 (assert (forall ((B tptp.int) (A tptp.int) (C2 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A) B)) C2) (@ (@ tptp.dvd_dvd_int A) C2)))))
% 6.73/7.06 (assert (forall ((B tptp.code_integer) (A tptp.code_integer) (C2 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 C2) B)) (@ _let_1 C2))))))
% 6.73/7.06 (assert (forall ((B tptp.nat) (A tptp.nat) (C2 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 C2) B)) (@ _let_1 C2))))))
% 6.73/7.06 (assert (forall ((B tptp.int) (A tptp.int) (C2 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 C2) B)) (@ _let_1 C2))))))
% 6.73/7.06 (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)))))
% 6.73/7.06 (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)))))
% 6.73/7.06 (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)))))
% 6.73/7.06 (assert (forall ((C2 tptp.nat) (B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat C2) B) (= (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat B) C2)) A) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat B) A)) C2)))))
% 6.73/7.06 (assert (forall ((C2 tptp.int) (B tptp.int) (A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int C2) B) (= (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int B) C2)) A) (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int B) A)) C2)))))
% 6.73/7.06 (assert (forall ((C2 tptp.nat) (B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (=> (@ (@ tptp.dvd_dvd_nat C2) B) (= (@ _let_1 (@ (@ tptp.divide_divide_nat B) C2)) (@ (@ tptp.divide_divide_nat (@ _let_1 B)) C2))))))
% 6.73/7.06 (assert (forall ((C2 tptp.int) (B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (=> (@ (@ tptp.dvd_dvd_int C2) B) (= (@ _let_1 (@ (@ tptp.divide_divide_int B) C2)) (@ (@ tptp.divide_divide_int (@ _let_1 B)) C2))))))
% 6.73/7.06 (assert (forall ((C2 tptp.nat) (B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat A))) (=> (@ (@ tptp.dvd_dvd_nat C2) B) (=> (@ (@ tptp.dvd_dvd_nat B) A) (= (@ _let_1 (@ (@ tptp.divide_divide_nat B) C2)) (@ (@ tptp.times_times_nat (@ _let_1 B)) C2)))))))
% 6.73/7.06 (assert (forall ((C2 tptp.int) (B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A))) (=> (@ (@ tptp.dvd_dvd_int C2) B) (=> (@ (@ tptp.dvd_dvd_int B) A) (= (@ _let_1 (@ (@ tptp.divide_divide_int B) C2)) (@ (@ tptp.times_times_int (@ _let_1 B)) C2)))))))
% 6.73/7.06 (assert (forall ((B tptp.nat) (C2 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat A))) (let ((_let_2 (@ (@ tptp.times_times_nat B) C2))) (=> (@ (@ tptp.dvd_dvd_nat _let_2) A) (= (@ _let_1 _let_2) (@ (@ tptp.divide_divide_nat (@ _let_1 B)) C2)))))))
% 6.73/7.06 (assert (forall ((B tptp.int) (C2 tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A))) (let ((_let_2 (@ (@ tptp.times_times_int B) C2))) (=> (@ (@ tptp.dvd_dvd_int _let_2) A) (= (@ _let_1 _let_2) (@ (@ tptp.divide_divide_int (@ _let_1 B)) C2)))))))
% 6.73/7.06 (assert (forall ((A tptp.nat) (C2 tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat A) C2)) B) (@ (@ tptp.dvd_dvd_nat A) (@ (@ tptp.divide_divide_nat B) C2)))))
% 6.73/7.06 (assert (forall ((A tptp.int) (C2 tptp.int) (B tptp.int)) (=> (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A) C2)) B) (@ (@ tptp.dvd_dvd_int A) (@ (@ tptp.divide_divide_int B) C2)))))
% 6.73/7.06 (assert (forall ((B tptp.nat) (A tptp.nat) (D tptp.nat) (C2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B) A) (=> (@ (@ tptp.dvd_dvd_nat D) C2) (= (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat A) B)) (@ (@ tptp.divide_divide_nat C2) D)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat A) C2)) (@ (@ tptp.times_times_nat B) D)))))))
% 6.73/7.06 (assert (forall ((B tptp.int) (A tptp.int) (D tptp.int) (C2 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B) A) (=> (@ (@ tptp.dvd_dvd_int D) C2) (= (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int A) B)) (@ (@ tptp.divide_divide_int C2) D)) (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int A) C2)) (@ (@ tptp.times_times_int B) D)))))))
% 6.73/7.06 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C2 tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer) (= (= (@ (@ tptp.divide6298287555418463151nteger B) A) (@ (@ tptp.divide6298287555418463151nteger C2) A)) (= B C2)))))
% 6.73/7.06 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (= (= (@ (@ tptp.divide_divide_nat B) A) (@ (@ tptp.divide_divide_nat C2) A)) (= B C2)))))
% 6.73/7.06 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (= (= (@ (@ tptp.divide_divide_int B) A) (@ (@ tptp.divide_divide_int C2) A)) (= B C2)))))
% 6.73/7.06 (assert (forall ((B tptp.code_integer) (A tptp.code_integer) (C2 tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer) (= (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.divide6298287555418463151nteger A) B)) C2) (@ (@ tptp.dvd_dvd_Code_integer A) C2)))))
% 6.73/7.06 (assert (forall ((B tptp.nat) (A tptp.nat) (C2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.divide_divide_nat A) B)) C2) (@ (@ tptp.dvd_dvd_nat A) C2)))))
% 6.73/7.06 (assert (forall ((B tptp.int) (A tptp.int) (C2 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.divide_divide_int A) B)) C2) (@ (@ tptp.dvd_dvd_int A) C2)))))
% 6.73/7.06 (assert (forall ((B tptp.code_integer) (A tptp.code_integer) (C2 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 C2) B)) (@ _let_1 C2))))))
% 6.73/7.06 (assert (forall ((B tptp.nat) (A tptp.nat) (C2 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 C2) B)) (@ _let_1 C2))))))
% 6.73/7.06 (assert (forall ((B tptp.int) (A tptp.int) (C2 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 C2) B)) (@ _let_1 C2))))))
% 6.73/7.06 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (= (@ (@ tptp.modulo_modulo_nat A) B) tptp.zero_zero_nat) (@ (@ tptp.dvd_dvd_nat B) A))))
% 6.73/7.06 (assert (forall ((A tptp.int) (B tptp.int)) (= (= (@ (@ tptp.modulo_modulo_int A) B) tptp.zero_zero_int) (@ (@ tptp.dvd_dvd_int B) A))))
% 6.73/7.06 (assert (forall ((A tptp.code_natural) (B tptp.code_natural)) (= (= (@ (@ tptp.modulo8411746178871703098atural A) B) tptp.zero_z2226904508553997617atural) (@ (@ tptp.dvd_dvd_Code_natural B) A))))
% 6.73/7.06 (assert (= tptp.dvd_dvd_nat (lambda ((A5 tptp.nat) (B4 tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat B4) A5) tptp.zero_zero_nat))))
% 6.73/7.06 (assert (= tptp.dvd_dvd_int (lambda ((A5 tptp.int) (B4 tptp.int)) (= (@ (@ tptp.modulo_modulo_int B4) A5) tptp.zero_zero_int))))
% 6.73/7.06 (assert (= tptp.dvd_dvd_Code_natural (lambda ((A5 tptp.code_natural) (B4 tptp.code_natural)) (= (@ (@ tptp.modulo8411746178871703098atural B4) A5) tptp.zero_z2226904508553997617atural))))
% 6.73/7.06 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (= (@ (@ tptp.modulo_modulo_nat A) B) tptp.zero_zero_nat) (@ (@ tptp.dvd_dvd_nat B) A))))
% 6.73/7.06 (assert (forall ((A tptp.int) (B tptp.int)) (=> (= (@ (@ tptp.modulo_modulo_int A) B) tptp.zero_zero_int) (@ (@ tptp.dvd_dvd_int B) A))))
% 6.73/7.06 (assert (forall ((A tptp.code_natural) (B tptp.code_natural)) (=> (= (@ (@ tptp.modulo8411746178871703098atural A) B) tptp.zero_z2226904508553997617atural) (@ (@ tptp.dvd_dvd_Code_natural B) A))))
% 6.73/7.06 (assert (forall ((X tptp.nat) (Y tptp.nat) (N tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat X) Y) (=> (@ (@ tptp.ord_less_eq_nat N) M2) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.power_power_nat X) N)) (@ (@ tptp.power_power_nat Y) M2))))))
% 6.73/7.06 (assert (forall ((X tptp.real) (Y tptp.real) (N tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_real X) Y) (=> (@ (@ tptp.ord_less_eq_nat N) M2) (@ (@ tptp.dvd_dvd_real (@ (@ tptp.power_power_real X) N)) (@ (@ tptp.power_power_real Y) M2))))))
% 6.73/7.06 (assert (forall ((X tptp.int) (Y tptp.int) (N tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_int X) Y) (=> (@ (@ tptp.ord_less_eq_nat N) M2) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.power_power_int X) N)) (@ (@ tptp.power_power_int Y) M2))))))
% 6.73/7.06 (assert (forall ((X tptp.complex) (Y tptp.complex) (N tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_complex X) Y) (=> (@ (@ tptp.ord_less_eq_nat N) M2) (@ (@ tptp.dvd_dvd_complex (@ (@ tptp.power_power_complex X) N)) (@ (@ tptp.power_power_complex Y) M2))))))
% 6.73/7.06 (assert (forall ((A tptp.nat) (N tptp.nat) (B tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.dvd_dvd_nat (@ _let_1 N)) B) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (@ (@ tptp.dvd_dvd_nat (@ _let_1 M2)) B))))))
% 6.73/7.06 (assert (forall ((A tptp.real) (N tptp.nat) (B tptp.real) (M2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.dvd_dvd_real (@ _let_1 N)) B) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (@ (@ tptp.dvd_dvd_real (@ _let_1 M2)) B))))))
% 6.73/7.06 (assert (forall ((A tptp.int) (N tptp.nat) (B tptp.int) (M2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.dvd_dvd_int (@ _let_1 N)) B) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (@ (@ tptp.dvd_dvd_int (@ _let_1 M2)) B))))))
% 6.73/7.06 (assert (forall ((A tptp.complex) (N tptp.nat) (B tptp.complex) (M2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex A))) (=> (@ (@ tptp.dvd_dvd_complex (@ _let_1 N)) B) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (@ (@ tptp.dvd_dvd_complex (@ _let_1 M2)) B))))))
% 6.73/7.06 (assert (forall ((M2 tptp.nat) (N tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (@ (@ tptp.dvd_dvd_nat (@ _let_1 M2)) (@ _let_1 N))))))
% 6.73/7.06 (assert (forall ((M2 tptp.nat) (N tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (@ (@ tptp.dvd_dvd_real (@ _let_1 M2)) (@ _let_1 N))))))
% 6.73/7.06 (assert (forall ((M2 tptp.nat) (N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (@ (@ tptp.dvd_dvd_int (@ _let_1 M2)) (@ _let_1 N))))))
% 6.73/7.06 (assert (forall ((M2 tptp.nat) (N tptp.nat) (A tptp.complex)) (let ((_let_1 (@ tptp.power_power_complex A))) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (@ (@ tptp.dvd_dvd_complex (@ _let_1 M2)) (@ _let_1 N))))))
% 6.73/7.06 (assert (forall ((B tptp.nat) (A tptp.nat)) (@ (@ tptp.dvd_dvd_nat B) (@ (@ tptp.minus_minus_nat A) (@ (@ tptp.modulo_modulo_nat A) B)))))
% 6.73/7.06 (assert (forall ((B tptp.int) (A tptp.int)) (@ (@ tptp.dvd_dvd_int B) (@ (@ tptp.minus_minus_int A) (@ (@ tptp.modulo_modulo_int A) B)))))
% 6.73/7.06 (assert (forall ((B tptp.code_natural) (A tptp.code_natural)) (@ (@ tptp.dvd_dvd_Code_natural B) (@ (@ tptp.minus_7197305767214868737atural A) (@ (@ tptp.modulo8411746178871703098atural A) B)))))
% 6.73/7.06 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 N) (=> (@ (@ tptp.dvd_dvd_nat M2) N) (@ _let_1 M2))))))
% 6.73/7.06 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M2) (=> (@ (@ tptp.ord_less_nat M2) N) (not (@ (@ tptp.dvd_dvd_nat N) M2))))))
% 6.73/7.06 (assert (forall ((X tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X) (@ _let_1 (@ (@ tptp.comm_s7457072308508201937r_real X) N))))))
% 6.73/7.06 (assert (forall ((X tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 X) (@ _let_1 (@ (@ tptp.comm_s4028243227959126397er_rat X) N))))))
% 6.73/7.06 (assert (forall ((X tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 X) (@ _let_1 (@ (@ tptp.comm_s4663373288045622133er_nat X) N))))))
% 6.73/7.06 (assert (forall ((X tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 X) (@ _let_1 (@ (@ tptp.comm_s4660882817536571857er_int X) N))))))
% 6.73/7.06 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat M2))) (= (@ _let_1 (@ (@ tptp.minus_minus_nat N) M2)) (or (@ (@ tptp.ord_less_nat N) M2) (@ _let_1 N))))))
% 6.73/7.06 (assert (forall ((S2 tptp.set_real) (F2 (-> tptp.real tptp.real)) (I2 tptp.real)) (=> (@ tptp.finite_finite_real S2) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) S2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F2 I3)))) (=> (= (@ (@ tptp.groups8097168146408367636l_real F2) S2) tptp.zero_zero_real) (=> (@ (@ tptp.member_real I2) S2) (= (@ F2 I2) tptp.zero_zero_real)))))))
% 6.73/7.06 (assert (forall ((S2 tptp.set_int) (F2 (-> tptp.int tptp.real)) (I2 tptp.int)) (=> (@ tptp.finite_finite_int S2) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) S2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F2 I3)))) (=> (= (@ (@ tptp.groups8778361861064173332t_real F2) S2) tptp.zero_zero_real) (=> (@ (@ tptp.member_int I2) S2) (= (@ F2 I2) tptp.zero_zero_real)))))))
% 6.73/7.06 (assert (forall ((S2 tptp.set_complex) (F2 (-> tptp.complex tptp.real)) (I2 tptp.complex)) (=> (@ tptp.finite3207457112153483333omplex S2) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) S2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F2 I3)))) (=> (= (@ (@ tptp.groups5808333547571424918x_real F2) S2) tptp.zero_zero_real) (=> (@ (@ tptp.member_complex I2) S2) (= (@ F2 I2) tptp.zero_zero_real)))))))
% 6.73/7.06 (assert (forall ((S2 tptp.set_real) (F2 (-> tptp.real tptp.rat)) (I2 tptp.real)) (=> (@ tptp.finite_finite_real S2) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) S2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F2 I3)))) (=> (= (@ (@ tptp.groups1300246762558778688al_rat F2) S2) tptp.zero_zero_rat) (=> (@ (@ tptp.member_real I2) S2) (= (@ F2 I2) tptp.zero_zero_rat)))))))
% 6.73/7.06 (assert (forall ((S2 tptp.set_nat) (F2 (-> tptp.nat tptp.rat)) (I2 tptp.nat)) (=> (@ tptp.finite_finite_nat S2) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.member_nat I3) S2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F2 I3)))) (=> (= (@ (@ tptp.groups2906978787729119204at_rat F2) S2) tptp.zero_zero_rat) (=> (@ (@ tptp.member_nat I2) S2) (= (@ F2 I2) tptp.zero_zero_rat)))))))
% 6.73/7.06 (assert (forall ((S2 tptp.set_int) (F2 (-> tptp.int tptp.rat)) (I2 tptp.int)) (=> (@ tptp.finite_finite_int S2) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) S2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F2 I3)))) (=> (= (@ (@ tptp.groups3906332499630173760nt_rat F2) S2) tptp.zero_zero_rat) (=> (@ (@ tptp.member_int I2) S2) (= (@ F2 I2) tptp.zero_zero_rat)))))))
% 6.73/7.06 (assert (forall ((S2 tptp.set_complex) (F2 (-> tptp.complex tptp.rat)) (I2 tptp.complex)) (=> (@ tptp.finite3207457112153483333omplex S2) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) S2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F2 I3)))) (=> (= (@ (@ tptp.groups5058264527183730370ex_rat F2) S2) tptp.zero_zero_rat) (=> (@ (@ tptp.member_complex I2) S2) (= (@ F2 I2) tptp.zero_zero_rat)))))))
% 6.73/7.06 (assert (forall ((S2 tptp.set_real) (F2 (-> tptp.real tptp.nat)) (I2 tptp.real)) (=> (@ tptp.finite_finite_real S2) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) S2) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F2 I3)))) (=> (= (@ (@ tptp.groups1935376822645274424al_nat F2) S2) tptp.zero_zero_nat) (=> (@ (@ tptp.member_real I2) S2) (= (@ F2 I2) tptp.zero_zero_nat)))))))
% 6.73/7.06 (assert (forall ((S2 tptp.set_int) (F2 (-> tptp.int tptp.nat)) (I2 tptp.int)) (=> (@ tptp.finite_finite_int S2) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) S2) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F2 I3)))) (=> (= (@ (@ tptp.groups4541462559716669496nt_nat F2) S2) tptp.zero_zero_nat) (=> (@ (@ tptp.member_int I2) S2) (= (@ F2 I2) tptp.zero_zero_nat)))))))
% 6.73/7.06 (assert (forall ((S2 tptp.set_complex) (F2 (-> tptp.complex tptp.nat)) (I2 tptp.complex)) (=> (@ tptp.finite3207457112153483333omplex S2) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) S2) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F2 I3)))) (=> (= (@ (@ tptp.groups5693394587270226106ex_nat F2) S2) tptp.zero_zero_nat) (=> (@ (@ tptp.member_complex I2) S2) (= (@ F2 I2) tptp.zero_zero_nat)))))))
% 6.73/7.06 (assert (forall ((S2 tptp.set_real) (F2 (-> tptp.real tptp.real)) (B5 tptp.real) (I2 tptp.real)) (=> (@ tptp.finite_finite_real S2) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) S2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F2 I3)))) (=> (= (@ (@ tptp.groups8097168146408367636l_real F2) S2) B5) (=> (@ (@ tptp.member_real I2) S2) (@ (@ tptp.ord_less_eq_real (@ F2 I2)) B5)))))))
% 6.73/7.06 (assert (forall ((S2 tptp.set_int) (F2 (-> tptp.int tptp.real)) (B5 tptp.real) (I2 tptp.int)) (=> (@ tptp.finite_finite_int S2) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) S2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F2 I3)))) (=> (= (@ (@ tptp.groups8778361861064173332t_real F2) S2) B5) (=> (@ (@ tptp.member_int I2) S2) (@ (@ tptp.ord_less_eq_real (@ F2 I2)) B5)))))))
% 6.73/7.06 (assert (forall ((S2 tptp.set_complex) (F2 (-> tptp.complex tptp.real)) (B5 tptp.real) (I2 tptp.complex)) (=> (@ tptp.finite3207457112153483333omplex S2) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) S2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F2 I3)))) (=> (= (@ (@ tptp.groups5808333547571424918x_real F2) S2) B5) (=> (@ (@ tptp.member_complex I2) S2) (@ (@ tptp.ord_less_eq_real (@ F2 I2)) B5)))))))
% 6.73/7.06 (assert (forall ((S2 tptp.set_real) (F2 (-> tptp.real tptp.rat)) (B5 tptp.rat) (I2 tptp.real)) (=> (@ tptp.finite_finite_real S2) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) S2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F2 I3)))) (=> (= (@ (@ tptp.groups1300246762558778688al_rat F2) S2) B5) (=> (@ (@ tptp.member_real I2) S2) (@ (@ tptp.ord_less_eq_rat (@ F2 I2)) B5)))))))
% 6.73/7.06 (assert (forall ((S2 tptp.set_nat) (F2 (-> tptp.nat tptp.rat)) (B5 tptp.rat) (I2 tptp.nat)) (=> (@ tptp.finite_finite_nat S2) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.member_nat I3) S2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F2 I3)))) (=> (= (@ (@ tptp.groups2906978787729119204at_rat F2) S2) B5) (=> (@ (@ tptp.member_nat I2) S2) (@ (@ tptp.ord_less_eq_rat (@ F2 I2)) B5)))))))
% 6.73/7.06 (assert (forall ((S2 tptp.set_int) (F2 (-> tptp.int tptp.rat)) (B5 tptp.rat) (I2 tptp.int)) (=> (@ tptp.finite_finite_int S2) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) S2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F2 I3)))) (=> (= (@ (@ tptp.groups3906332499630173760nt_rat F2) S2) B5) (=> (@ (@ tptp.member_int I2) S2) (@ (@ tptp.ord_less_eq_rat (@ F2 I2)) B5)))))))
% 6.73/7.06 (assert (forall ((S2 tptp.set_complex) (F2 (-> tptp.complex tptp.rat)) (B5 tptp.rat) (I2 tptp.complex)) (=> (@ tptp.finite3207457112153483333omplex S2) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) S2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F2 I3)))) (=> (= (@ (@ tptp.groups5058264527183730370ex_rat F2) S2) B5) (=> (@ (@ tptp.member_complex I2) S2) (@ (@ tptp.ord_less_eq_rat (@ F2 I2)) B5)))))))
% 6.73/7.06 (assert (forall ((S2 tptp.set_real) (F2 (-> tptp.real tptp.nat)) (B5 tptp.nat) (I2 tptp.real)) (=> (@ tptp.finite_finite_real S2) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) S2) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F2 I3)))) (=> (= (@ (@ tptp.groups1935376822645274424al_nat F2) S2) B5) (=> (@ (@ tptp.member_real I2) S2) (@ (@ tptp.ord_less_eq_nat (@ F2 I2)) B5)))))))
% 6.73/7.06 (assert (forall ((S2 tptp.set_int) (F2 (-> tptp.int tptp.nat)) (B5 tptp.nat) (I2 tptp.int)) (=> (@ tptp.finite_finite_int S2) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) S2) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F2 I3)))) (=> (= (@ (@ tptp.groups4541462559716669496nt_nat F2) S2) B5) (=> (@ (@ tptp.member_int I2) S2) (@ (@ tptp.ord_less_eq_nat (@ F2 I2)) B5)))))))
% 6.73/7.06 (assert (forall ((S2 tptp.set_complex) (F2 (-> tptp.complex tptp.nat)) (B5 tptp.nat) (I2 tptp.complex)) (=> (@ tptp.finite3207457112153483333omplex S2) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) S2) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F2 I3)))) (=> (= (@ (@ tptp.groups5693394587270226106ex_nat F2) S2) B5) (=> (@ (@ tptp.member_complex I2) S2) (@ (@ tptp.ord_less_eq_nat (@ F2 I2)) B5)))))))
% 6.73/7.06 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat M2))) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ _let_1 N) (@ _let_1 (@ (@ tptp.minus_minus_nat N) M2)))))))
% 6.73/7.06 (assert (forall ((K2 tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat K2))) (=> (@ _let_1 (@ (@ tptp.minus_minus_nat M2) N)) (=> (@ _let_1 M2) (=> (@ (@ tptp.ord_less_eq_nat N) M2) (@ _let_1 N)))))))
% 6.73/7.06 (assert (forall ((K2 tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat K2))) (=> (@ _let_1 (@ (@ tptp.minus_minus_nat M2) N)) (=> (@ _let_1 N) (=> (@ (@ tptp.ord_less_eq_nat N) M2) (@ _let_1 M2)))))))
% 6.73/7.06 (assert (forall ((A tptp.complex) (N tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.comm_s2602460028002588243omplex A))) (=> (= (@ _let_1 N) tptp.zero_zero_complex) (=> (@ (@ tptp.ord_less_eq_nat N) M2) (= (@ _let_1 M2) tptp.zero_zero_complex))))))
% 6.73/7.06 (assert (forall ((A tptp.real) (N tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.comm_s7457072308508201937r_real A))) (=> (= (@ _let_1 N) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_nat N) M2) (= (@ _let_1 M2) tptp.zero_zero_real))))))
% 6.73/7.06 (assert (forall ((A tptp.rat) (N tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.comm_s4028243227959126397er_rat A))) (=> (= (@ _let_1 N) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_nat N) M2) (= (@ _let_1 M2) tptp.zero_zero_rat))))))
% 6.73/7.06 (assert (forall ((A tptp.complex) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.comm_s2602460028002588243omplex A))) (=> (not (= (@ _let_1 M2) tptp.zero_zero_complex)) (=> (@ (@ tptp.ord_less_eq_nat N) M2) (not (= (@ _let_1 N) tptp.zero_zero_complex)))))))
% 6.73/7.06 (assert (forall ((A tptp.real) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.comm_s7457072308508201937r_real A))) (=> (not (= (@ _let_1 M2) tptp.zero_zero_real)) (=> (@ (@ tptp.ord_less_eq_nat N) M2) (not (= (@ _let_1 N) tptp.zero_zero_real)))))))
% 6.73/7.06 (assert (forall ((A tptp.rat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.comm_s4028243227959126397er_rat A))) (=> (not (= (@ _let_1 M2) tptp.zero_zero_rat)) (=> (@ (@ tptp.ord_less_eq_nat N) M2) (not (= (@ _let_1 N) tptp.zero_zero_rat)))))))
% 6.73/7.06 (assert (forall ((A tptp.nat) (B tptp.nat)) (exists ((D5 tptp.nat) (X3 tptp.nat) (Y3 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (let ((_let_2 (@ tptp.times_times_nat B))) (let ((_let_3 (@ tptp.dvd_dvd_nat D5))) (and (@ _let_3 A) (@ _let_3 B) (or (= (@ _let_1 X3) (@ (@ tptp.plus_plus_nat (@ _let_2 Y3)) D5)) (= (@ _let_2 X3) (@ (@ tptp.plus_plus_nat (@ _let_1 Y3)) D5))))))))))
% 6.73/7.06 (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 ((X3 tptp.nat) (Y3 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (let ((_let_2 (@ (@ tptp.plus_plus_nat A) B))) (let ((_let_3 (@ tptp.times_times_nat _let_2))) (let ((_let_4 (@ tptp.dvd_dvd_nat D))) (and (@ _let_4 A) (@ _let_4 _let_2) (or (= (@ _let_1 X3) (@ (@ tptp.plus_plus_nat (@ _let_3 Y3)) D)) (= (@ _let_3 X3) (@ (@ tptp.plus_plus_nat (@ _let_1 Y3)) D)))))))))))))))))
% 6.73/7.06 (assert (forall ((A tptp.nat) (B tptp.nat)) (exists ((D5 tptp.nat) (X3 tptp.nat) (Y3 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (let ((_let_2 (@ tptp.times_times_nat B))) (let ((_let_3 (@ tptp.dvd_dvd_nat D5))) (and (@ _let_3 A) (@ _let_3 B) (or (= (@ (@ tptp.minus_minus_nat (@ _let_1 X3)) (@ _let_2 Y3)) D5) (= (@ (@ tptp.minus_minus_nat (@ _let_2 X3)) (@ _let_1 Y3)) D5)))))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_real) (G2 (-> tptp.real tptp.complex)) (B5 tptp.set_real)) (=> (@ tptp.finite_finite_real A4) (= (@ (@ tptp.groups5754745047067104278omplex G2) (@ (@ tptp.inf_inf_set_real A4) B5)) (@ (@ tptp.groups5754745047067104278omplex (lambda ((X4 tptp.real)) (@ (@ (@ tptp.if_complex (@ (@ tptp.member_real X4) B5)) (@ G2 X4)) tptp.zero_zero_complex))) A4)))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_int) (G2 (-> tptp.int tptp.complex)) (B5 tptp.set_int)) (=> (@ tptp.finite_finite_int A4) (= (@ (@ tptp.groups3049146728041665814omplex G2) (@ (@ tptp.inf_inf_set_int A4) B5)) (@ (@ tptp.groups3049146728041665814omplex (lambda ((X4 tptp.int)) (@ (@ (@ tptp.if_complex (@ (@ tptp.member_int X4) B5)) (@ G2 X4)) tptp.zero_zero_complex))) A4)))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_complex) (G2 (-> tptp.complex tptp.complex)) (B5 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex A4) (= (@ (@ tptp.groups7754918857620584856omplex G2) (@ (@ tptp.inf_inf_set_complex A4) B5)) (@ (@ tptp.groups7754918857620584856omplex (lambda ((X4 tptp.complex)) (@ (@ (@ tptp.if_complex (@ (@ tptp.member_complex X4) B5)) (@ G2 X4)) tptp.zero_zero_complex))) A4)))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_real) (G2 (-> tptp.real tptp.real)) (B5 tptp.set_real)) (=> (@ tptp.finite_finite_real A4) (= (@ (@ tptp.groups8097168146408367636l_real G2) (@ (@ tptp.inf_inf_set_real A4) B5)) (@ (@ tptp.groups8097168146408367636l_real (lambda ((X4 tptp.real)) (@ (@ (@ tptp.if_real (@ (@ tptp.member_real X4) B5)) (@ G2 X4)) tptp.zero_zero_real))) A4)))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_int) (G2 (-> tptp.int tptp.real)) (B5 tptp.set_int)) (=> (@ tptp.finite_finite_int A4) (= (@ (@ tptp.groups8778361861064173332t_real G2) (@ (@ tptp.inf_inf_set_int A4) B5)) (@ (@ tptp.groups8778361861064173332t_real (lambda ((X4 tptp.int)) (@ (@ (@ tptp.if_real (@ (@ tptp.member_int X4) B5)) (@ G2 X4)) tptp.zero_zero_real))) A4)))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_complex) (G2 (-> tptp.complex tptp.real)) (B5 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex A4) (= (@ (@ tptp.groups5808333547571424918x_real G2) (@ (@ tptp.inf_inf_set_complex A4) B5)) (@ (@ tptp.groups5808333547571424918x_real (lambda ((X4 tptp.complex)) (@ (@ (@ tptp.if_real (@ (@ tptp.member_complex X4) B5)) (@ G2 X4)) tptp.zero_zero_real))) A4)))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_real) (G2 (-> tptp.real tptp.rat)) (B5 tptp.set_real)) (=> (@ tptp.finite_finite_real A4) (= (@ (@ tptp.groups1300246762558778688al_rat G2) (@ (@ tptp.inf_inf_set_real A4) B5)) (@ (@ tptp.groups1300246762558778688al_rat (lambda ((X4 tptp.real)) (@ (@ (@ tptp.if_rat (@ (@ tptp.member_real X4) B5)) (@ G2 X4)) tptp.zero_zero_rat))) A4)))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_int) (G2 (-> tptp.int tptp.rat)) (B5 tptp.set_int)) (=> (@ tptp.finite_finite_int A4) (= (@ (@ tptp.groups3906332499630173760nt_rat G2) (@ (@ tptp.inf_inf_set_int A4) B5)) (@ (@ tptp.groups3906332499630173760nt_rat (lambda ((X4 tptp.int)) (@ (@ (@ tptp.if_rat (@ (@ tptp.member_int X4) B5)) (@ G2 X4)) tptp.zero_zero_rat))) A4)))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_complex) (G2 (-> tptp.complex tptp.rat)) (B5 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex A4) (= (@ (@ tptp.groups5058264527183730370ex_rat G2) (@ (@ tptp.inf_inf_set_complex A4) B5)) (@ (@ tptp.groups5058264527183730370ex_rat (lambda ((X4 tptp.complex)) (@ (@ (@ tptp.if_rat (@ (@ tptp.member_complex X4) B5)) (@ G2 X4)) tptp.zero_zero_rat))) A4)))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_real) (G2 (-> tptp.real tptp.nat)) (B5 tptp.set_real)) (=> (@ tptp.finite_finite_real A4) (= (@ (@ tptp.groups1935376822645274424al_nat G2) (@ (@ tptp.inf_inf_set_real A4) B5)) (@ (@ tptp.groups1935376822645274424al_nat (lambda ((X4 tptp.real)) (@ (@ (@ tptp.if_nat (@ (@ tptp.member_real X4) B5)) (@ G2 X4)) tptp.zero_zero_nat))) A4)))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_real) (G2 (-> tptp.real tptp.complex))) (let ((_let_1 (@ tptp.groups5754745047067104278omplex G2))) (=> (@ tptp.finite_finite_real A4) (= (@ _let_1 (@ (@ tptp.minus_minus_set_real A4) (@ tptp.collect_real (lambda ((X4 tptp.real)) (= (@ G2 X4) tptp.zero_zero_complex))))) (@ _let_1 A4))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_int) (G2 (-> tptp.int tptp.complex))) (let ((_let_1 (@ tptp.groups3049146728041665814omplex G2))) (=> (@ tptp.finite_finite_int A4) (= (@ _let_1 (@ (@ tptp.minus_minus_set_int A4) (@ tptp.collect_int (lambda ((X4 tptp.int)) (= (@ G2 X4) tptp.zero_zero_complex))))) (@ _let_1 A4))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_complex) (G2 (-> tptp.complex tptp.complex))) (let ((_let_1 (@ tptp.groups7754918857620584856omplex G2))) (=> (@ tptp.finite3207457112153483333omplex A4) (= (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A4) (@ tptp.collect_complex (lambda ((X4 tptp.complex)) (= (@ G2 X4) tptp.zero_zero_complex))))) (@ _let_1 A4))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_real) (G2 (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.groups8097168146408367636l_real G2))) (=> (@ tptp.finite_finite_real A4) (= (@ _let_1 (@ (@ tptp.minus_minus_set_real A4) (@ tptp.collect_real (lambda ((X4 tptp.real)) (= (@ G2 X4) tptp.zero_zero_real))))) (@ _let_1 A4))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_int) (G2 (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups8778361861064173332t_real G2))) (=> (@ tptp.finite_finite_int A4) (= (@ _let_1 (@ (@ tptp.minus_minus_set_int A4) (@ tptp.collect_int (lambda ((X4 tptp.int)) (= (@ G2 X4) tptp.zero_zero_real))))) (@ _let_1 A4))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_complex) (G2 (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups5808333547571424918x_real G2))) (=> (@ tptp.finite3207457112153483333omplex A4) (= (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A4) (@ tptp.collect_complex (lambda ((X4 tptp.complex)) (= (@ G2 X4) tptp.zero_zero_real))))) (@ _let_1 A4))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_real) (G2 (-> tptp.real tptp.rat))) (let ((_let_1 (@ tptp.groups1300246762558778688al_rat G2))) (=> (@ tptp.finite_finite_real A4) (= (@ _let_1 (@ (@ tptp.minus_minus_set_real A4) (@ tptp.collect_real (lambda ((X4 tptp.real)) (= (@ G2 X4) tptp.zero_zero_rat))))) (@ _let_1 A4))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_int) (G2 (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups3906332499630173760nt_rat G2))) (=> (@ tptp.finite_finite_int A4) (= (@ _let_1 (@ (@ tptp.minus_minus_set_int A4) (@ tptp.collect_int (lambda ((X4 tptp.int)) (= (@ G2 X4) tptp.zero_zero_rat))))) (@ _let_1 A4))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_complex) (G2 (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups5058264527183730370ex_rat G2))) (=> (@ tptp.finite3207457112153483333omplex A4) (= (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A4) (@ tptp.collect_complex (lambda ((X4 tptp.complex)) (= (@ G2 X4) tptp.zero_zero_rat))))) (@ _let_1 A4))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_real) (G2 (-> tptp.real tptp.nat))) (let ((_let_1 (@ tptp.groups1935376822645274424al_nat G2))) (=> (@ tptp.finite_finite_real A4) (= (@ _let_1 (@ (@ tptp.minus_minus_set_real A4) (@ tptp.collect_real (lambda ((X4 tptp.real)) (= (@ G2 X4) tptp.zero_zero_nat))))) (@ _let_1 A4))))))
% 6.73/7.06 (assert (forall ((G2 (-> tptp.nat tptp.nat)) (M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat G2) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M2)) (@ tptp.suc N))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I tptp.nat)) (@ G2 (@ tptp.suc I)))) (@ (@ tptp.set_or1269000886237332187st_nat M2) N)))))
% 6.73/7.06 (assert (forall ((G2 (-> tptp.nat tptp.real)) (M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real G2) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M2)) (@ tptp.suc N))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I tptp.nat)) (@ G2 (@ tptp.suc I)))) (@ (@ tptp.set_or1269000886237332187st_nat M2) N)))))
% 6.73/7.06 (assert (forall ((G2 (-> tptp.nat tptp.nat)) (M2 tptp.nat) (K2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat G2) (@ (@ tptp.set_or1269000886237332187st_nat (@ (@ tptp.plus_plus_nat M2) K2)) (@ (@ tptp.plus_plus_nat N) K2))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I tptp.nat)) (@ G2 (@ (@ tptp.plus_plus_nat I) K2)))) (@ (@ tptp.set_or1269000886237332187st_nat M2) N)))))
% 6.73/7.06 (assert (forall ((G2 (-> tptp.nat tptp.real)) (M2 tptp.nat) (K2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real G2) (@ (@ tptp.set_or1269000886237332187st_nat (@ (@ tptp.plus_plus_nat M2) K2)) (@ (@ tptp.plus_plus_nat N) K2))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I tptp.nat)) (@ G2 (@ (@ tptp.plus_plus_nat I) K2)))) (@ (@ tptp.set_or1269000886237332187st_nat M2) N)))))
% 6.73/7.06 (assert (forall ((I5 tptp.set_real) (I2 tptp.real) (F2 (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ tptp.finite_finite_real I5) (=> (@ (@ tptp.member_real I2) I5) (=> (@ _let_1 (@ F2 I2)) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) I5) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F2 I3)))) (@ _let_1 (@ (@ tptp.groups8097168146408367636l_real F2) I5)))))))))
% 6.73/7.06 (assert (forall ((I5 tptp.set_int) (I2 tptp.int) (F2 (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ tptp.finite_finite_int I5) (=> (@ (@ tptp.member_int I2) I5) (=> (@ _let_1 (@ F2 I2)) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) I5) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F2 I3)))) (@ _let_1 (@ (@ tptp.groups8778361861064173332t_real F2) I5)))))))))
% 6.73/7.06 (assert (forall ((I5 tptp.set_complex) (I2 tptp.complex) (F2 (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ tptp.finite3207457112153483333omplex I5) (=> (@ (@ tptp.member_complex I2) I5) (=> (@ _let_1 (@ F2 I2)) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) I5) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F2 I3)))) (@ _let_1 (@ (@ tptp.groups5808333547571424918x_real F2) I5)))))))))
% 6.73/7.06 (assert (forall ((I5 tptp.set_real) (I2 tptp.real) (F2 (-> tptp.real tptp.rat))) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ tptp.finite_finite_real I5) (=> (@ (@ tptp.member_real I2) I5) (=> (@ _let_1 (@ F2 I2)) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) I5) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F2 I3)))) (@ _let_1 (@ (@ tptp.groups1300246762558778688al_rat F2) I5)))))))))
% 6.73/7.06 (assert (forall ((I5 tptp.set_nat) (I2 tptp.nat) (F2 (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ tptp.finite_finite_nat I5) (=> (@ (@ tptp.member_nat I2) I5) (=> (@ _let_1 (@ F2 I2)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.member_nat I3) I5) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F2 I3)))) (@ _let_1 (@ (@ tptp.groups2906978787729119204at_rat F2) I5)))))))))
% 6.73/7.06 (assert (forall ((I5 tptp.set_int) (I2 tptp.int) (F2 (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ tptp.finite_finite_int I5) (=> (@ (@ tptp.member_int I2) I5) (=> (@ _let_1 (@ F2 I2)) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) I5) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F2 I3)))) (@ _let_1 (@ (@ tptp.groups3906332499630173760nt_rat F2) I5)))))))))
% 6.73/7.06 (assert (forall ((I5 tptp.set_complex) (I2 tptp.complex) (F2 (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ tptp.finite3207457112153483333omplex I5) (=> (@ (@ tptp.member_complex I2) I5) (=> (@ _let_1 (@ F2 I2)) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) I5) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F2 I3)))) (@ _let_1 (@ (@ tptp.groups5058264527183730370ex_rat F2) I5)))))))))
% 6.73/7.06 (assert (forall ((I5 tptp.set_real) (I2 tptp.real) (F2 (-> tptp.real tptp.nat))) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ tptp.finite_finite_real I5) (=> (@ (@ tptp.member_real I2) I5) (=> (@ _let_1 (@ F2 I2)) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) I5) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F2 I3)))) (@ _let_1 (@ (@ tptp.groups1935376822645274424al_nat F2) I5)))))))))
% 6.73/7.06 (assert (forall ((I5 tptp.set_int) (I2 tptp.int) (F2 (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ tptp.finite_finite_int I5) (=> (@ (@ tptp.member_int I2) I5) (=> (@ _let_1 (@ F2 I2)) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) I5) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F2 I3)))) (@ _let_1 (@ (@ tptp.groups4541462559716669496nt_nat F2) I5)))))))))
% 6.73/7.06 (assert (forall ((I5 tptp.set_complex) (I2 tptp.complex) (F2 (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ tptp.finite3207457112153483333omplex I5) (=> (@ (@ tptp.member_complex I2) I5) (=> (@ _let_1 (@ F2 I2)) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) I5) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F2 I3)))) (@ _let_1 (@ (@ tptp.groups5693394587270226106ex_nat F2) I5)))))))))
% 6.73/7.06 (assert (forall ((I5 tptp.set_complex) (F2 (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex I5) (=> (not (= I5 tptp.bot_bot_set_complex)) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) I5) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F2 I3)))) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.groups5808333547571424918x_real F2) I5)))))))
% 6.73/7.06 (assert (forall ((I5 tptp.set_int) (F2 (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int I5) (=> (not (= I5 tptp.bot_bot_set_int)) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) I5) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F2 I3)))) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.groups8778361861064173332t_real F2) I5)))))))
% 6.73/7.06 (assert (forall ((I5 tptp.set_real) (F2 (-> tptp.real tptp.real))) (=> (@ tptp.finite_finite_real I5) (=> (not (= I5 tptp.bot_bot_set_real)) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) I5) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F2 I3)))) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.groups8097168146408367636l_real F2) I5)))))))
% 6.73/7.06 (assert (forall ((I5 tptp.set_complex) (F2 (-> tptp.complex tptp.rat))) (=> (@ tptp.finite3207457112153483333omplex I5) (=> (not (= I5 tptp.bot_bot_set_complex)) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) I5) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ F2 I3)))) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.groups5058264527183730370ex_rat F2) I5)))))))
% 6.73/7.06 (assert (forall ((I5 tptp.set_nat) (F2 (-> tptp.nat tptp.rat))) (=> (@ tptp.finite_finite_nat I5) (=> (not (= I5 tptp.bot_bot_set_nat)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.member_nat I3) I5) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ F2 I3)))) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.groups2906978787729119204at_rat F2) I5)))))))
% 6.73/7.06 (assert (forall ((I5 tptp.set_int) (F2 (-> tptp.int tptp.rat))) (=> (@ tptp.finite_finite_int I5) (=> (not (= I5 tptp.bot_bot_set_int)) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) I5) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ F2 I3)))) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.groups3906332499630173760nt_rat F2) I5)))))))
% 6.73/7.06 (assert (forall ((I5 tptp.set_real) (F2 (-> tptp.real tptp.rat))) (=> (@ tptp.finite_finite_real I5) (=> (not (= I5 tptp.bot_bot_set_real)) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) I5) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ F2 I3)))) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.groups1300246762558778688al_rat F2) I5)))))))
% 6.73/7.06 (assert (forall ((I5 tptp.set_complex) (F2 (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex I5) (=> (not (= I5 tptp.bot_bot_set_complex)) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) I5) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F2 I3)))) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.groups5693394587270226106ex_nat F2) I5)))))))
% 6.73/7.06 (assert (forall ((I5 tptp.set_int) (F2 (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int I5) (=> (not (= I5 tptp.bot_bot_set_int)) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) I5) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F2 I3)))) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.groups4541462559716669496nt_nat F2) I5)))))))
% 6.73/7.06 (assert (forall ((I5 tptp.set_real) (F2 (-> tptp.real tptp.nat))) (=> (@ tptp.finite_finite_real I5) (=> (not (= I5 tptp.bot_bot_set_real)) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) I5) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F2 I3)))) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.groups1935376822645274424al_nat F2) I5)))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_real) (K5 tptp.real) (F2 (-> tptp.real tptp.real))) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) A4) (@ (@ tptp.ord_less_eq_real K5) (@ F2 I3)))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ tptp.finite_card_real A4))) K5)) (@ (@ tptp.groups8097168146408367636l_real F2) A4)))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_complex) (K5 tptp.real) (F2 (-> tptp.complex tptp.real))) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) A4) (@ (@ tptp.ord_less_eq_real K5) (@ F2 I3)))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ tptp.finite_card_complex A4))) K5)) (@ (@ tptp.groups5808333547571424918x_real F2) A4)))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_int) (K5 tptp.real) (F2 (-> tptp.int tptp.real))) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) A4) (@ (@ tptp.ord_less_eq_real K5) (@ F2 I3)))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ tptp.finite_card_int A4))) K5)) (@ (@ tptp.groups8778361861064173332t_real F2) A4)))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_real) (K5 tptp.rat) (F2 (-> tptp.real tptp.rat))) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) A4) (@ (@ tptp.ord_less_eq_rat K5) (@ F2 I3)))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat (@ tptp.finite_card_real A4))) K5)) (@ (@ tptp.groups1300246762558778688al_rat F2) A4)))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_nat) (K5 tptp.rat) (F2 (-> tptp.nat tptp.rat))) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.member_nat I3) A4) (@ (@ tptp.ord_less_eq_rat K5) (@ F2 I3)))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat (@ tptp.finite_card_nat A4))) K5)) (@ (@ tptp.groups2906978787729119204at_rat F2) A4)))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_complex) (K5 tptp.rat) (F2 (-> tptp.complex tptp.rat))) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) A4) (@ (@ tptp.ord_less_eq_rat K5) (@ F2 I3)))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat (@ tptp.finite_card_complex A4))) K5)) (@ (@ tptp.groups5058264527183730370ex_rat F2) A4)))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_int) (K5 tptp.rat) (F2 (-> tptp.int tptp.rat))) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) A4) (@ (@ tptp.ord_less_eq_rat K5) (@ F2 I3)))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat (@ tptp.finite_card_int A4))) K5)) (@ (@ tptp.groups3906332499630173760nt_rat F2) A4)))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_real) (K5 tptp.nat) (F2 (-> tptp.real tptp.nat))) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) A4) (@ (@ tptp.ord_less_eq_nat K5) (@ F2 I3)))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat (@ tptp.finite_card_real A4))) K5)) (@ (@ tptp.groups1935376822645274424al_nat F2) A4)))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_complex) (K5 tptp.nat) (F2 (-> tptp.complex tptp.nat))) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) A4) (@ (@ tptp.ord_less_eq_nat K5) (@ F2 I3)))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat (@ tptp.finite_card_complex A4))) K5)) (@ (@ tptp.groups5693394587270226106ex_nat F2) A4)))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_int) (K5 tptp.nat) (F2 (-> tptp.int tptp.nat))) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) A4) (@ (@ tptp.ord_less_eq_nat K5) (@ F2 I3)))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat (@ tptp.finite_card_int A4))) K5)) (@ (@ tptp.groups4541462559716669496nt_nat F2) A4)))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_real) (F2 (-> tptp.real tptp.real)) (K5 tptp.real)) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) A4) (@ (@ tptp.ord_less_eq_real (@ F2 I3)) K5))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups8097168146408367636l_real F2) A4)) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ tptp.finite_card_real A4))) K5)))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_complex) (F2 (-> tptp.complex tptp.real)) (K5 tptp.real)) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) A4) (@ (@ tptp.ord_less_eq_real (@ F2 I3)) K5))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups5808333547571424918x_real F2) A4)) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ tptp.finite_card_complex A4))) K5)))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_int) (F2 (-> tptp.int tptp.real)) (K5 tptp.real)) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) A4) (@ (@ tptp.ord_less_eq_real (@ F2 I3)) K5))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups8778361861064173332t_real F2) A4)) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ tptp.finite_card_int A4))) K5)))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_real) (F2 (-> tptp.real tptp.rat)) (K5 tptp.rat)) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) A4) (@ (@ tptp.ord_less_eq_rat (@ F2 I3)) K5))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups1300246762558778688al_rat F2) A4)) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat (@ tptp.finite_card_real A4))) K5)))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_nat) (F2 (-> tptp.nat tptp.rat)) (K5 tptp.rat)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.member_nat I3) A4) (@ (@ tptp.ord_less_eq_rat (@ F2 I3)) K5))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups2906978787729119204at_rat F2) A4)) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat (@ tptp.finite_card_nat A4))) K5)))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_complex) (F2 (-> tptp.complex tptp.rat)) (K5 tptp.rat)) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) A4) (@ (@ tptp.ord_less_eq_rat (@ F2 I3)) K5))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups5058264527183730370ex_rat F2) A4)) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat (@ tptp.finite_card_complex A4))) K5)))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_int) (F2 (-> tptp.int tptp.rat)) (K5 tptp.rat)) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) A4) (@ (@ tptp.ord_less_eq_rat (@ F2 I3)) K5))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups3906332499630173760nt_rat F2) A4)) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat (@ tptp.finite_card_int A4))) K5)))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_real) (F2 (-> tptp.real tptp.nat)) (K5 tptp.nat)) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) A4) (@ (@ tptp.ord_less_eq_nat (@ F2 I3)) K5))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups1935376822645274424al_nat F2) A4)) (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat (@ tptp.finite_card_real A4))) K5)))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_complex) (F2 (-> tptp.complex tptp.nat)) (K5 tptp.nat)) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) A4) (@ (@ tptp.ord_less_eq_nat (@ F2 I3)) K5))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups5693394587270226106ex_nat F2) A4)) (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat (@ tptp.finite_card_complex A4))) K5)))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_int) (F2 (-> tptp.int tptp.nat)) (K5 tptp.nat)) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) A4) (@ (@ tptp.ord_less_eq_nat (@ F2 I3)) K5))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups4541462559716669496nt_nat F2) A4)) (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat (@ tptp.finite_card_int A4))) K5)))))
% 6.73/7.06 (assert (forall ((T5 tptp.set_real) (S3 tptp.set_real) (G2 (-> tptp.real tptp.complex)) (H (-> tptp.real tptp.complex))) (=> (@ tptp.finite_finite_real T5) (=> (@ (@ tptp.ord_less_eq_set_real S3) T5) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) (@ (@ tptp.minus_minus_set_real T5) S3)) (= (@ G2 X3) tptp.zero_zero_complex))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) S3) (= (@ G2 X3) (@ H X3)))) (= (@ (@ tptp.groups5754745047067104278omplex G2) T5) (@ (@ tptp.groups5754745047067104278omplex H) S3))))))))
% 6.73/7.06 (assert (forall ((T5 tptp.set_int) (S3 tptp.set_int) (G2 (-> tptp.int tptp.complex)) (H (-> tptp.int tptp.complex))) (=> (@ tptp.finite_finite_int T5) (=> (@ (@ tptp.ord_less_eq_set_int S3) T5) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.minus_minus_set_int T5) S3)) (= (@ G2 X3) tptp.zero_zero_complex))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) S3) (= (@ G2 X3) (@ H X3)))) (= (@ (@ tptp.groups3049146728041665814omplex G2) T5) (@ (@ tptp.groups3049146728041665814omplex H) S3))))))))
% 6.73/7.06 (assert (forall ((T5 tptp.set_complex) (S3 tptp.set_complex) (G2 (-> tptp.complex tptp.complex)) (H (-> tptp.complex tptp.complex))) (=> (@ tptp.finite3207457112153483333omplex T5) (=> (@ (@ tptp.ord_le211207098394363844omplex S3) T5) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ (@ tptp.minus_811609699411566653omplex T5) S3)) (= (@ G2 X3) tptp.zero_zero_complex))) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) S3) (= (@ G2 X3) (@ H X3)))) (= (@ (@ tptp.groups7754918857620584856omplex G2) T5) (@ (@ tptp.groups7754918857620584856omplex H) S3))))))))
% 6.73/7.06 (assert (forall ((T5 tptp.set_real) (S3 tptp.set_real) (G2 (-> tptp.real tptp.real)) (H (-> tptp.real tptp.real))) (=> (@ tptp.finite_finite_real T5) (=> (@ (@ tptp.ord_less_eq_set_real S3) T5) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) (@ (@ tptp.minus_minus_set_real T5) S3)) (= (@ G2 X3) tptp.zero_zero_real))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) S3) (= (@ G2 X3) (@ H X3)))) (= (@ (@ tptp.groups8097168146408367636l_real G2) T5) (@ (@ tptp.groups8097168146408367636l_real H) S3))))))))
% 6.73/7.06 (assert (forall ((T5 tptp.set_int) (S3 tptp.set_int) (G2 (-> tptp.int tptp.real)) (H (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int T5) (=> (@ (@ tptp.ord_less_eq_set_int S3) T5) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.minus_minus_set_int T5) S3)) (= (@ G2 X3) tptp.zero_zero_real))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) S3) (= (@ G2 X3) (@ H X3)))) (= (@ (@ tptp.groups8778361861064173332t_real G2) T5) (@ (@ tptp.groups8778361861064173332t_real H) S3))))))))
% 6.73/7.06 (assert (forall ((T5 tptp.set_complex) (S3 tptp.set_complex) (G2 (-> tptp.complex tptp.real)) (H (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex T5) (=> (@ (@ tptp.ord_le211207098394363844omplex S3) T5) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ (@ tptp.minus_811609699411566653omplex T5) S3)) (= (@ G2 X3) tptp.zero_zero_real))) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) S3) (= (@ G2 X3) (@ H X3)))) (= (@ (@ tptp.groups5808333547571424918x_real G2) T5) (@ (@ tptp.groups5808333547571424918x_real H) S3))))))))
% 6.73/7.06 (assert (forall ((T5 tptp.set_real) (S3 tptp.set_real) (G2 (-> tptp.real tptp.rat)) (H (-> tptp.real tptp.rat))) (=> (@ tptp.finite_finite_real T5) (=> (@ (@ tptp.ord_less_eq_set_real S3) T5) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) (@ (@ tptp.minus_minus_set_real T5) S3)) (= (@ G2 X3) tptp.zero_zero_rat))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) S3) (= (@ G2 X3) (@ H X3)))) (= (@ (@ tptp.groups1300246762558778688al_rat G2) T5) (@ (@ tptp.groups1300246762558778688al_rat H) S3))))))))
% 6.73/7.06 (assert (forall ((T5 tptp.set_int) (S3 tptp.set_int) (G2 (-> tptp.int tptp.rat)) (H (-> tptp.int tptp.rat))) (=> (@ tptp.finite_finite_int T5) (=> (@ (@ tptp.ord_less_eq_set_int S3) T5) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.minus_minus_set_int T5) S3)) (= (@ G2 X3) tptp.zero_zero_rat))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) S3) (= (@ G2 X3) (@ H X3)))) (= (@ (@ tptp.groups3906332499630173760nt_rat G2) T5) (@ (@ tptp.groups3906332499630173760nt_rat H) S3))))))))
% 6.73/7.06 (assert (forall ((T5 tptp.set_complex) (S3 tptp.set_complex) (G2 (-> tptp.complex tptp.rat)) (H (-> tptp.complex tptp.rat))) (=> (@ tptp.finite3207457112153483333omplex T5) (=> (@ (@ tptp.ord_le211207098394363844omplex S3) T5) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ (@ tptp.minus_811609699411566653omplex T5) S3)) (= (@ G2 X3) tptp.zero_zero_rat))) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) S3) (= (@ G2 X3) (@ H X3)))) (= (@ (@ tptp.groups5058264527183730370ex_rat G2) T5) (@ (@ tptp.groups5058264527183730370ex_rat H) S3))))))))
% 6.73/7.06 (assert (forall ((T5 tptp.set_real) (S3 tptp.set_real) (G2 (-> tptp.real tptp.nat)) (H (-> tptp.real tptp.nat))) (=> (@ tptp.finite_finite_real T5) (=> (@ (@ tptp.ord_less_eq_set_real S3) T5) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) (@ (@ tptp.minus_minus_set_real T5) S3)) (= (@ G2 X3) tptp.zero_zero_nat))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) S3) (= (@ G2 X3) (@ H X3)))) (= (@ (@ tptp.groups1935376822645274424al_nat G2) T5) (@ (@ tptp.groups1935376822645274424al_nat H) S3))))))))
% 6.73/7.06 (assert (forall ((T5 tptp.set_real) (S3 tptp.set_real) (H (-> tptp.real tptp.complex)) (G2 (-> tptp.real tptp.complex))) (=> (@ tptp.finite_finite_real T5) (=> (@ (@ tptp.ord_less_eq_set_real S3) T5) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) (@ (@ tptp.minus_minus_set_real T5) S3)) (= (@ H X3) tptp.zero_zero_complex))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) S3) (= (@ G2 X3) (@ H X3)))) (= (@ (@ tptp.groups5754745047067104278omplex G2) S3) (@ (@ tptp.groups5754745047067104278omplex H) T5))))))))
% 6.73/7.06 (assert (forall ((T5 tptp.set_int) (S3 tptp.set_int) (H (-> tptp.int tptp.complex)) (G2 (-> tptp.int tptp.complex))) (=> (@ tptp.finite_finite_int T5) (=> (@ (@ tptp.ord_less_eq_set_int S3) T5) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.minus_minus_set_int T5) S3)) (= (@ H X3) tptp.zero_zero_complex))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) S3) (= (@ G2 X3) (@ H X3)))) (= (@ (@ tptp.groups3049146728041665814omplex G2) S3) (@ (@ tptp.groups3049146728041665814omplex H) T5))))))))
% 6.73/7.06 (assert (forall ((T5 tptp.set_complex) (S3 tptp.set_complex) (H (-> tptp.complex tptp.complex)) (G2 (-> tptp.complex tptp.complex))) (=> (@ tptp.finite3207457112153483333omplex T5) (=> (@ (@ tptp.ord_le211207098394363844omplex S3) T5) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ (@ tptp.minus_811609699411566653omplex T5) S3)) (= (@ H X3) tptp.zero_zero_complex))) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) S3) (= (@ G2 X3) (@ H X3)))) (= (@ (@ tptp.groups7754918857620584856omplex G2) S3) (@ (@ tptp.groups7754918857620584856omplex H) T5))))))))
% 6.73/7.06 (assert (forall ((T5 tptp.set_real) (S3 tptp.set_real) (H (-> tptp.real tptp.real)) (G2 (-> tptp.real tptp.real))) (=> (@ tptp.finite_finite_real T5) (=> (@ (@ tptp.ord_less_eq_set_real S3) T5) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) (@ (@ tptp.minus_minus_set_real T5) S3)) (= (@ H X3) tptp.zero_zero_real))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) S3) (= (@ G2 X3) (@ H X3)))) (= (@ (@ tptp.groups8097168146408367636l_real G2) S3) (@ (@ tptp.groups8097168146408367636l_real H) T5))))))))
% 6.73/7.06 (assert (forall ((T5 tptp.set_int) (S3 tptp.set_int) (H (-> tptp.int tptp.real)) (G2 (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int T5) (=> (@ (@ tptp.ord_less_eq_set_int S3) T5) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.minus_minus_set_int T5) S3)) (= (@ H X3) tptp.zero_zero_real))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) S3) (= (@ G2 X3) (@ H X3)))) (= (@ (@ tptp.groups8778361861064173332t_real G2) S3) (@ (@ tptp.groups8778361861064173332t_real H) T5))))))))
% 6.73/7.06 (assert (forall ((T5 tptp.set_complex) (S3 tptp.set_complex) (H (-> tptp.complex tptp.real)) (G2 (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex T5) (=> (@ (@ tptp.ord_le211207098394363844omplex S3) T5) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ (@ tptp.minus_811609699411566653omplex T5) S3)) (= (@ H X3) tptp.zero_zero_real))) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) S3) (= (@ G2 X3) (@ H X3)))) (= (@ (@ tptp.groups5808333547571424918x_real G2) S3) (@ (@ tptp.groups5808333547571424918x_real H) T5))))))))
% 6.73/7.06 (assert (forall ((T5 tptp.set_real) (S3 tptp.set_real) (H (-> tptp.real tptp.rat)) (G2 (-> tptp.real tptp.rat))) (=> (@ tptp.finite_finite_real T5) (=> (@ (@ tptp.ord_less_eq_set_real S3) T5) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) (@ (@ tptp.minus_minus_set_real T5) S3)) (= (@ H X3) tptp.zero_zero_rat))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) S3) (= (@ G2 X3) (@ H X3)))) (= (@ (@ tptp.groups1300246762558778688al_rat G2) S3) (@ (@ tptp.groups1300246762558778688al_rat H) T5))))))))
% 6.73/7.06 (assert (forall ((T5 tptp.set_int) (S3 tptp.set_int) (H (-> tptp.int tptp.rat)) (G2 (-> tptp.int tptp.rat))) (=> (@ tptp.finite_finite_int T5) (=> (@ (@ tptp.ord_less_eq_set_int S3) T5) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.minus_minus_set_int T5) S3)) (= (@ H X3) tptp.zero_zero_rat))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) S3) (= (@ G2 X3) (@ H X3)))) (= (@ (@ tptp.groups3906332499630173760nt_rat G2) S3) (@ (@ tptp.groups3906332499630173760nt_rat H) T5))))))))
% 6.73/7.06 (assert (forall ((T5 tptp.set_complex) (S3 tptp.set_complex) (H (-> tptp.complex tptp.rat)) (G2 (-> tptp.complex tptp.rat))) (=> (@ tptp.finite3207457112153483333omplex T5) (=> (@ (@ tptp.ord_le211207098394363844omplex S3) T5) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ (@ tptp.minus_811609699411566653omplex T5) S3)) (= (@ H X3) tptp.zero_zero_rat))) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) S3) (= (@ G2 X3) (@ H X3)))) (= (@ (@ tptp.groups5058264527183730370ex_rat G2) S3) (@ (@ tptp.groups5058264527183730370ex_rat H) T5))))))))
% 6.73/7.06 (assert (forall ((T5 tptp.set_real) (S3 tptp.set_real) (H (-> tptp.real tptp.nat)) (G2 (-> tptp.real tptp.nat))) (=> (@ tptp.finite_finite_real T5) (=> (@ (@ tptp.ord_less_eq_set_real S3) T5) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) (@ (@ tptp.minus_minus_set_real T5) S3)) (= (@ H X3) tptp.zero_zero_nat))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) S3) (= (@ G2 X3) (@ H X3)))) (= (@ (@ tptp.groups1935376822645274424al_nat G2) S3) (@ (@ tptp.groups1935376822645274424al_nat H) T5))))))))
% 6.73/7.06 (assert (forall ((T5 tptp.set_int) (S3 tptp.set_int) (G2 (-> tptp.int tptp.complex))) (let ((_let_1 (@ tptp.groups3049146728041665814omplex G2))) (=> (@ tptp.finite_finite_int T5) (=> (@ (@ tptp.ord_less_eq_set_int S3) T5) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.minus_minus_set_int T5) S3)) (= (@ G2 X3) tptp.zero_zero_complex))) (= (@ _let_1 T5) (@ _let_1 S3))))))))
% 6.73/7.06 (assert (forall ((T5 tptp.set_complex) (S3 tptp.set_complex) (G2 (-> tptp.complex tptp.complex))) (let ((_let_1 (@ tptp.groups7754918857620584856omplex G2))) (=> (@ tptp.finite3207457112153483333omplex T5) (=> (@ (@ tptp.ord_le211207098394363844omplex S3) T5) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ (@ tptp.minus_811609699411566653omplex T5) S3)) (= (@ G2 X3) tptp.zero_zero_complex))) (= (@ _let_1 T5) (@ _let_1 S3))))))))
% 6.73/7.06 (assert (forall ((T5 tptp.set_int) (S3 tptp.set_int) (G2 (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups8778361861064173332t_real G2))) (=> (@ tptp.finite_finite_int T5) (=> (@ (@ tptp.ord_less_eq_set_int S3) T5) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.minus_minus_set_int T5) S3)) (= (@ G2 X3) tptp.zero_zero_real))) (= (@ _let_1 T5) (@ _let_1 S3))))))))
% 6.73/7.06 (assert (forall ((T5 tptp.set_complex) (S3 tptp.set_complex) (G2 (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups5808333547571424918x_real G2))) (=> (@ tptp.finite3207457112153483333omplex T5) (=> (@ (@ tptp.ord_le211207098394363844omplex S3) T5) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ (@ tptp.minus_811609699411566653omplex T5) S3)) (= (@ G2 X3) tptp.zero_zero_real))) (= (@ _let_1 T5) (@ _let_1 S3))))))))
% 6.73/7.06 (assert (forall ((T5 tptp.set_int) (S3 tptp.set_int) (G2 (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups3906332499630173760nt_rat G2))) (=> (@ tptp.finite_finite_int T5) (=> (@ (@ tptp.ord_less_eq_set_int S3) T5) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.minus_minus_set_int T5) S3)) (= (@ G2 X3) tptp.zero_zero_rat))) (= (@ _let_1 T5) (@ _let_1 S3))))))))
% 6.73/7.06 (assert (forall ((T5 tptp.set_complex) (S3 tptp.set_complex) (G2 (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups5058264527183730370ex_rat G2))) (=> (@ tptp.finite3207457112153483333omplex T5) (=> (@ (@ tptp.ord_le211207098394363844omplex S3) T5) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ (@ tptp.minus_811609699411566653omplex T5) S3)) (= (@ G2 X3) tptp.zero_zero_rat))) (= (@ _let_1 T5) (@ _let_1 S3))))))))
% 6.73/7.06 (assert (forall ((T5 tptp.set_int) (S3 tptp.set_int) (G2 (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups4541462559716669496nt_nat G2))) (=> (@ tptp.finite_finite_int T5) (=> (@ (@ tptp.ord_less_eq_set_int S3) T5) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.minus_minus_set_int T5) S3)) (= (@ G2 X3) tptp.zero_zero_nat))) (= (@ _let_1 T5) (@ _let_1 S3))))))))
% 6.73/7.06 (assert (forall ((T5 tptp.set_complex) (S3 tptp.set_complex) (G2 (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups5693394587270226106ex_nat G2))) (=> (@ tptp.finite3207457112153483333omplex T5) (=> (@ (@ tptp.ord_le211207098394363844omplex S3) T5) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ (@ tptp.minus_811609699411566653omplex T5) S3)) (= (@ G2 X3) tptp.zero_zero_nat))) (= (@ _let_1 T5) (@ _let_1 S3))))))))
% 6.73/7.06 (assert (forall ((T5 tptp.set_complex) (S3 tptp.set_complex) (G2 (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.groups5690904116761175830ex_int G2))) (=> (@ tptp.finite3207457112153483333omplex T5) (=> (@ (@ tptp.ord_le211207098394363844omplex S3) T5) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ (@ tptp.minus_811609699411566653omplex T5) S3)) (= (@ G2 X3) tptp.zero_zero_int))) (= (@ _let_1 T5) (@ _let_1 S3))))))))
% 6.73/7.06 (assert (forall ((T5 tptp.set_nat) (S3 tptp.set_nat) (G2 (-> tptp.nat tptp.complex))) (let ((_let_1 (@ tptp.groups2073611262835488442omplex G2))) (=> (@ tptp.finite_finite_nat T5) (=> (@ (@ tptp.ord_less_eq_set_nat S3) T5) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ (@ tptp.minus_minus_set_nat T5) S3)) (= (@ G2 X3) tptp.zero_zero_complex))) (= (@ _let_1 T5) (@ _let_1 S3))))))))
% 6.73/7.06 (assert (forall ((T5 tptp.set_int) (S3 tptp.set_int) (G2 (-> tptp.int tptp.complex))) (let ((_let_1 (@ tptp.groups3049146728041665814omplex G2))) (=> (@ tptp.finite_finite_int T5) (=> (@ (@ tptp.ord_less_eq_set_int S3) T5) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.minus_minus_set_int T5) S3)) (= (@ G2 X3) tptp.zero_zero_complex))) (= (@ _let_1 S3) (@ _let_1 T5))))))))
% 6.73/7.06 (assert (forall ((T5 tptp.set_complex) (S3 tptp.set_complex) (G2 (-> tptp.complex tptp.complex))) (let ((_let_1 (@ tptp.groups7754918857620584856omplex G2))) (=> (@ tptp.finite3207457112153483333omplex T5) (=> (@ (@ tptp.ord_le211207098394363844omplex S3) T5) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ (@ tptp.minus_811609699411566653omplex T5) S3)) (= (@ G2 X3) tptp.zero_zero_complex))) (= (@ _let_1 S3) (@ _let_1 T5))))))))
% 6.73/7.06 (assert (forall ((T5 tptp.set_int) (S3 tptp.set_int) (G2 (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups8778361861064173332t_real G2))) (=> (@ tptp.finite_finite_int T5) (=> (@ (@ tptp.ord_less_eq_set_int S3) T5) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.minus_minus_set_int T5) S3)) (= (@ G2 X3) tptp.zero_zero_real))) (= (@ _let_1 S3) (@ _let_1 T5))))))))
% 6.73/7.06 (assert (forall ((T5 tptp.set_complex) (S3 tptp.set_complex) (G2 (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups5808333547571424918x_real G2))) (=> (@ tptp.finite3207457112153483333omplex T5) (=> (@ (@ tptp.ord_le211207098394363844omplex S3) T5) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ (@ tptp.minus_811609699411566653omplex T5) S3)) (= (@ G2 X3) tptp.zero_zero_real))) (= (@ _let_1 S3) (@ _let_1 T5))))))))
% 6.73/7.06 (assert (forall ((T5 tptp.set_int) (S3 tptp.set_int) (G2 (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups3906332499630173760nt_rat G2))) (=> (@ tptp.finite_finite_int T5) (=> (@ (@ tptp.ord_less_eq_set_int S3) T5) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.minus_minus_set_int T5) S3)) (= (@ G2 X3) tptp.zero_zero_rat))) (= (@ _let_1 S3) (@ _let_1 T5))))))))
% 6.73/7.06 (assert (forall ((T5 tptp.set_complex) (S3 tptp.set_complex) (G2 (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups5058264527183730370ex_rat G2))) (=> (@ tptp.finite3207457112153483333omplex T5) (=> (@ (@ tptp.ord_le211207098394363844omplex S3) T5) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ (@ tptp.minus_811609699411566653omplex T5) S3)) (= (@ G2 X3) tptp.zero_zero_rat))) (= (@ _let_1 S3) (@ _let_1 T5))))))))
% 6.73/7.06 (assert (forall ((T5 tptp.set_int) (S3 tptp.set_int) (G2 (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups4541462559716669496nt_nat G2))) (=> (@ tptp.finite_finite_int T5) (=> (@ (@ tptp.ord_less_eq_set_int S3) T5) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.minus_minus_set_int T5) S3)) (= (@ G2 X3) tptp.zero_zero_nat))) (= (@ _let_1 S3) (@ _let_1 T5))))))))
% 6.73/7.06 (assert (forall ((T5 tptp.set_complex) (S3 tptp.set_complex) (G2 (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups5693394587270226106ex_nat G2))) (=> (@ tptp.finite3207457112153483333omplex T5) (=> (@ (@ tptp.ord_le211207098394363844omplex S3) T5) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ (@ tptp.minus_811609699411566653omplex T5) S3)) (= (@ G2 X3) tptp.zero_zero_nat))) (= (@ _let_1 S3) (@ _let_1 T5))))))))
% 6.73/7.06 (assert (forall ((T5 tptp.set_complex) (S3 tptp.set_complex) (G2 (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.groups5690904116761175830ex_int G2))) (=> (@ tptp.finite3207457112153483333omplex T5) (=> (@ (@ tptp.ord_le211207098394363844omplex S3) T5) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ (@ tptp.minus_811609699411566653omplex T5) S3)) (= (@ G2 X3) tptp.zero_zero_int))) (= (@ _let_1 S3) (@ _let_1 T5))))))))
% 6.73/7.06 (assert (forall ((T5 tptp.set_nat) (S3 tptp.set_nat) (G2 (-> tptp.nat tptp.complex))) (let ((_let_1 (@ tptp.groups2073611262835488442omplex G2))) (=> (@ tptp.finite_finite_nat T5) (=> (@ (@ tptp.ord_less_eq_set_nat S3) T5) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ (@ tptp.minus_minus_set_nat T5) S3)) (= (@ G2 X3) tptp.zero_zero_complex))) (= (@ _let_1 S3) (@ _let_1 T5))))))))
% 6.73/7.06 (assert (forall ((C4 tptp.set_real) (A4 tptp.set_real) (B5 tptp.set_real) (G2 (-> tptp.real tptp.complex)) (H (-> tptp.real tptp.complex))) (let ((_let_1 (@ tptp.groups5754745047067104278omplex H))) (let ((_let_2 (@ tptp.groups5754745047067104278omplex G2))) (=> (@ tptp.finite_finite_real C4) (=> (@ (@ tptp.ord_less_eq_set_real A4) C4) (=> (@ (@ tptp.ord_less_eq_set_real B5) C4) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) (@ (@ tptp.minus_minus_set_real C4) A4)) (= (@ G2 A3) tptp.zero_zero_complex))) (=> (forall ((B3 tptp.real)) (=> (@ (@ tptp.member_real B3) (@ (@ tptp.minus_minus_set_real C4) B5)) (= (@ H B3) tptp.zero_zero_complex))) (=> (= (@ _let_2 C4) (@ _let_1 C4)) (= (@ _let_2 A4) (@ _let_1 B5))))))))))))
% 6.73/7.06 (assert (forall ((C4 tptp.set_int) (A4 tptp.set_int) (B5 tptp.set_int) (G2 (-> tptp.int tptp.complex)) (H (-> tptp.int tptp.complex))) (let ((_let_1 (@ tptp.groups3049146728041665814omplex H))) (let ((_let_2 (@ tptp.groups3049146728041665814omplex G2))) (=> (@ tptp.finite_finite_int C4) (=> (@ (@ tptp.ord_less_eq_set_int A4) C4) (=> (@ (@ tptp.ord_less_eq_set_int B5) C4) (=> (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) (@ (@ tptp.minus_minus_set_int C4) A4)) (= (@ G2 A3) tptp.zero_zero_complex))) (=> (forall ((B3 tptp.int)) (=> (@ (@ tptp.member_int B3) (@ (@ tptp.minus_minus_set_int C4) B5)) (= (@ H B3) tptp.zero_zero_complex))) (=> (= (@ _let_2 C4) (@ _let_1 C4)) (= (@ _let_2 A4) (@ _let_1 B5))))))))))))
% 6.73/7.06 (assert (forall ((C4 tptp.set_complex) (A4 tptp.set_complex) (B5 tptp.set_complex) (G2 (-> tptp.complex tptp.complex)) (H (-> tptp.complex tptp.complex))) (let ((_let_1 (@ tptp.groups7754918857620584856omplex H))) (let ((_let_2 (@ tptp.groups7754918857620584856omplex G2))) (=> (@ tptp.finite3207457112153483333omplex C4) (=> (@ (@ tptp.ord_le211207098394363844omplex A4) C4) (=> (@ (@ tptp.ord_le211207098394363844omplex B5) C4) (=> (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) (@ (@ tptp.minus_811609699411566653omplex C4) A4)) (= (@ G2 A3) tptp.zero_zero_complex))) (=> (forall ((B3 tptp.complex)) (=> (@ (@ tptp.member_complex B3) (@ (@ tptp.minus_811609699411566653omplex C4) B5)) (= (@ H B3) tptp.zero_zero_complex))) (=> (= (@ _let_2 C4) (@ _let_1 C4)) (= (@ _let_2 A4) (@ _let_1 B5))))))))))))
% 6.73/7.06 (assert (forall ((C4 tptp.set_real) (A4 tptp.set_real) (B5 tptp.set_real) (G2 (-> tptp.real tptp.real)) (H (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.groups8097168146408367636l_real H))) (let ((_let_2 (@ tptp.groups8097168146408367636l_real G2))) (=> (@ tptp.finite_finite_real C4) (=> (@ (@ tptp.ord_less_eq_set_real A4) C4) (=> (@ (@ tptp.ord_less_eq_set_real B5) C4) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) (@ (@ tptp.minus_minus_set_real C4) A4)) (= (@ G2 A3) tptp.zero_zero_real))) (=> (forall ((B3 tptp.real)) (=> (@ (@ tptp.member_real B3) (@ (@ tptp.minus_minus_set_real C4) B5)) (= (@ H B3) tptp.zero_zero_real))) (=> (= (@ _let_2 C4) (@ _let_1 C4)) (= (@ _let_2 A4) (@ _let_1 B5))))))))))))
% 6.73/7.06 (assert (forall ((C4 tptp.set_int) (A4 tptp.set_int) (B5 tptp.set_int) (G2 (-> tptp.int tptp.real)) (H (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups8778361861064173332t_real H))) (let ((_let_2 (@ tptp.groups8778361861064173332t_real G2))) (=> (@ tptp.finite_finite_int C4) (=> (@ (@ tptp.ord_less_eq_set_int A4) C4) (=> (@ (@ tptp.ord_less_eq_set_int B5) C4) (=> (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) (@ (@ tptp.minus_minus_set_int C4) A4)) (= (@ G2 A3) tptp.zero_zero_real))) (=> (forall ((B3 tptp.int)) (=> (@ (@ tptp.member_int B3) (@ (@ tptp.minus_minus_set_int C4) B5)) (= (@ H B3) tptp.zero_zero_real))) (=> (= (@ _let_2 C4) (@ _let_1 C4)) (= (@ _let_2 A4) (@ _let_1 B5))))))))))))
% 6.73/7.06 (assert (forall ((C4 tptp.set_complex) (A4 tptp.set_complex) (B5 tptp.set_complex) (G2 (-> tptp.complex tptp.real)) (H (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups5808333547571424918x_real H))) (let ((_let_2 (@ tptp.groups5808333547571424918x_real G2))) (=> (@ tptp.finite3207457112153483333omplex C4) (=> (@ (@ tptp.ord_le211207098394363844omplex A4) C4) (=> (@ (@ tptp.ord_le211207098394363844omplex B5) C4) (=> (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) (@ (@ tptp.minus_811609699411566653omplex C4) A4)) (= (@ G2 A3) tptp.zero_zero_real))) (=> (forall ((B3 tptp.complex)) (=> (@ (@ tptp.member_complex B3) (@ (@ tptp.minus_811609699411566653omplex C4) B5)) (= (@ H B3) tptp.zero_zero_real))) (=> (= (@ _let_2 C4) (@ _let_1 C4)) (= (@ _let_2 A4) (@ _let_1 B5))))))))))))
% 6.73/7.06 (assert (forall ((C4 tptp.set_real) (A4 tptp.set_real) (B5 tptp.set_real) (G2 (-> tptp.real tptp.rat)) (H (-> tptp.real tptp.rat))) (let ((_let_1 (@ tptp.groups1300246762558778688al_rat H))) (let ((_let_2 (@ tptp.groups1300246762558778688al_rat G2))) (=> (@ tptp.finite_finite_real C4) (=> (@ (@ tptp.ord_less_eq_set_real A4) C4) (=> (@ (@ tptp.ord_less_eq_set_real B5) C4) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) (@ (@ tptp.minus_minus_set_real C4) A4)) (= (@ G2 A3) tptp.zero_zero_rat))) (=> (forall ((B3 tptp.real)) (=> (@ (@ tptp.member_real B3) (@ (@ tptp.minus_minus_set_real C4) B5)) (= (@ H B3) tptp.zero_zero_rat))) (=> (= (@ _let_2 C4) (@ _let_1 C4)) (= (@ _let_2 A4) (@ _let_1 B5))))))))))))
% 6.73/7.06 (assert (forall ((C4 tptp.set_int) (A4 tptp.set_int) (B5 tptp.set_int) (G2 (-> tptp.int tptp.rat)) (H (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups3906332499630173760nt_rat H))) (let ((_let_2 (@ tptp.groups3906332499630173760nt_rat G2))) (=> (@ tptp.finite_finite_int C4) (=> (@ (@ tptp.ord_less_eq_set_int A4) C4) (=> (@ (@ tptp.ord_less_eq_set_int B5) C4) (=> (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) (@ (@ tptp.minus_minus_set_int C4) A4)) (= (@ G2 A3) tptp.zero_zero_rat))) (=> (forall ((B3 tptp.int)) (=> (@ (@ tptp.member_int B3) (@ (@ tptp.minus_minus_set_int C4) B5)) (= (@ H B3) tptp.zero_zero_rat))) (=> (= (@ _let_2 C4) (@ _let_1 C4)) (= (@ _let_2 A4) (@ _let_1 B5))))))))))))
% 6.73/7.06 (assert (forall ((C4 tptp.set_complex) (A4 tptp.set_complex) (B5 tptp.set_complex) (G2 (-> tptp.complex tptp.rat)) (H (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups5058264527183730370ex_rat H))) (let ((_let_2 (@ tptp.groups5058264527183730370ex_rat G2))) (=> (@ tptp.finite3207457112153483333omplex C4) (=> (@ (@ tptp.ord_le211207098394363844omplex A4) C4) (=> (@ (@ tptp.ord_le211207098394363844omplex B5) C4) (=> (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) (@ (@ tptp.minus_811609699411566653omplex C4) A4)) (= (@ G2 A3) tptp.zero_zero_rat))) (=> (forall ((B3 tptp.complex)) (=> (@ (@ tptp.member_complex B3) (@ (@ tptp.minus_811609699411566653omplex C4) B5)) (= (@ H B3) tptp.zero_zero_rat))) (=> (= (@ _let_2 C4) (@ _let_1 C4)) (= (@ _let_2 A4) (@ _let_1 B5))))))))))))
% 6.73/7.06 (assert (forall ((C4 tptp.set_real) (A4 tptp.set_real) (B5 tptp.set_real) (G2 (-> tptp.real tptp.nat)) (H (-> tptp.real tptp.nat))) (let ((_let_1 (@ tptp.groups1935376822645274424al_nat H))) (let ((_let_2 (@ tptp.groups1935376822645274424al_nat G2))) (=> (@ tptp.finite_finite_real C4) (=> (@ (@ tptp.ord_less_eq_set_real A4) C4) (=> (@ (@ tptp.ord_less_eq_set_real B5) C4) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) (@ (@ tptp.minus_minus_set_real C4) A4)) (= (@ G2 A3) tptp.zero_zero_nat))) (=> (forall ((B3 tptp.real)) (=> (@ (@ tptp.member_real B3) (@ (@ tptp.minus_minus_set_real C4) B5)) (= (@ H B3) tptp.zero_zero_nat))) (=> (= (@ _let_2 C4) (@ _let_1 C4)) (= (@ _let_2 A4) (@ _let_1 B5))))))))))))
% 6.73/7.06 (assert (forall ((C4 tptp.set_real) (A4 tptp.set_real) (B5 tptp.set_real) (G2 (-> tptp.real tptp.complex)) (H (-> tptp.real tptp.complex))) (let ((_let_1 (@ tptp.groups5754745047067104278omplex H))) (let ((_let_2 (@ tptp.groups5754745047067104278omplex G2))) (=> (@ tptp.finite_finite_real C4) (=> (@ (@ tptp.ord_less_eq_set_real A4) C4) (=> (@ (@ tptp.ord_less_eq_set_real B5) C4) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) (@ (@ tptp.minus_minus_set_real C4) A4)) (= (@ G2 A3) tptp.zero_zero_complex))) (=> (forall ((B3 tptp.real)) (=> (@ (@ tptp.member_real B3) (@ (@ tptp.minus_minus_set_real C4) B5)) (= (@ H B3) tptp.zero_zero_complex))) (= (= (@ _let_2 A4) (@ _let_1 B5)) (= (@ _let_2 C4) (@ _let_1 C4))))))))))))
% 6.73/7.06 (assert (forall ((C4 tptp.set_int) (A4 tptp.set_int) (B5 tptp.set_int) (G2 (-> tptp.int tptp.complex)) (H (-> tptp.int tptp.complex))) (let ((_let_1 (@ tptp.groups3049146728041665814omplex H))) (let ((_let_2 (@ tptp.groups3049146728041665814omplex G2))) (=> (@ tptp.finite_finite_int C4) (=> (@ (@ tptp.ord_less_eq_set_int A4) C4) (=> (@ (@ tptp.ord_less_eq_set_int B5) C4) (=> (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) (@ (@ tptp.minus_minus_set_int C4) A4)) (= (@ G2 A3) tptp.zero_zero_complex))) (=> (forall ((B3 tptp.int)) (=> (@ (@ tptp.member_int B3) (@ (@ tptp.minus_minus_set_int C4) B5)) (= (@ H B3) tptp.zero_zero_complex))) (= (= (@ _let_2 A4) (@ _let_1 B5)) (= (@ _let_2 C4) (@ _let_1 C4))))))))))))
% 6.73/7.06 (assert (forall ((C4 tptp.set_complex) (A4 tptp.set_complex) (B5 tptp.set_complex) (G2 (-> tptp.complex tptp.complex)) (H (-> tptp.complex tptp.complex))) (let ((_let_1 (@ tptp.groups7754918857620584856omplex H))) (let ((_let_2 (@ tptp.groups7754918857620584856omplex G2))) (=> (@ tptp.finite3207457112153483333omplex C4) (=> (@ (@ tptp.ord_le211207098394363844omplex A4) C4) (=> (@ (@ tptp.ord_le211207098394363844omplex B5) C4) (=> (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) (@ (@ tptp.minus_811609699411566653omplex C4) A4)) (= (@ G2 A3) tptp.zero_zero_complex))) (=> (forall ((B3 tptp.complex)) (=> (@ (@ tptp.member_complex B3) (@ (@ tptp.minus_811609699411566653omplex C4) B5)) (= (@ H B3) tptp.zero_zero_complex))) (= (= (@ _let_2 A4) (@ _let_1 B5)) (= (@ _let_2 C4) (@ _let_1 C4))))))))))))
% 6.73/7.06 (assert (forall ((C4 tptp.set_real) (A4 tptp.set_real) (B5 tptp.set_real) (G2 (-> tptp.real tptp.real)) (H (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.groups8097168146408367636l_real H))) (let ((_let_2 (@ tptp.groups8097168146408367636l_real G2))) (=> (@ tptp.finite_finite_real C4) (=> (@ (@ tptp.ord_less_eq_set_real A4) C4) (=> (@ (@ tptp.ord_less_eq_set_real B5) C4) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) (@ (@ tptp.minus_minus_set_real C4) A4)) (= (@ G2 A3) tptp.zero_zero_real))) (=> (forall ((B3 tptp.real)) (=> (@ (@ tptp.member_real B3) (@ (@ tptp.minus_minus_set_real C4) B5)) (= (@ H B3) tptp.zero_zero_real))) (= (= (@ _let_2 A4) (@ _let_1 B5)) (= (@ _let_2 C4) (@ _let_1 C4))))))))))))
% 6.73/7.06 (assert (forall ((C4 tptp.set_int) (A4 tptp.set_int) (B5 tptp.set_int) (G2 (-> tptp.int tptp.real)) (H (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups8778361861064173332t_real H))) (let ((_let_2 (@ tptp.groups8778361861064173332t_real G2))) (=> (@ tptp.finite_finite_int C4) (=> (@ (@ tptp.ord_less_eq_set_int A4) C4) (=> (@ (@ tptp.ord_less_eq_set_int B5) C4) (=> (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) (@ (@ tptp.minus_minus_set_int C4) A4)) (= (@ G2 A3) tptp.zero_zero_real))) (=> (forall ((B3 tptp.int)) (=> (@ (@ tptp.member_int B3) (@ (@ tptp.minus_minus_set_int C4) B5)) (= (@ H B3) tptp.zero_zero_real))) (= (= (@ _let_2 A4) (@ _let_1 B5)) (= (@ _let_2 C4) (@ _let_1 C4))))))))))))
% 6.73/7.06 (assert (forall ((C4 tptp.set_complex) (A4 tptp.set_complex) (B5 tptp.set_complex) (G2 (-> tptp.complex tptp.real)) (H (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups5808333547571424918x_real H))) (let ((_let_2 (@ tptp.groups5808333547571424918x_real G2))) (=> (@ tptp.finite3207457112153483333omplex C4) (=> (@ (@ tptp.ord_le211207098394363844omplex A4) C4) (=> (@ (@ tptp.ord_le211207098394363844omplex B5) C4) (=> (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) (@ (@ tptp.minus_811609699411566653omplex C4) A4)) (= (@ G2 A3) tptp.zero_zero_real))) (=> (forall ((B3 tptp.complex)) (=> (@ (@ tptp.member_complex B3) (@ (@ tptp.minus_811609699411566653omplex C4) B5)) (= (@ H B3) tptp.zero_zero_real))) (= (= (@ _let_2 A4) (@ _let_1 B5)) (= (@ _let_2 C4) (@ _let_1 C4))))))))))))
% 6.73/7.06 (assert (forall ((C4 tptp.set_real) (A4 tptp.set_real) (B5 tptp.set_real) (G2 (-> tptp.real tptp.rat)) (H (-> tptp.real tptp.rat))) (let ((_let_1 (@ tptp.groups1300246762558778688al_rat H))) (let ((_let_2 (@ tptp.groups1300246762558778688al_rat G2))) (=> (@ tptp.finite_finite_real C4) (=> (@ (@ tptp.ord_less_eq_set_real A4) C4) (=> (@ (@ tptp.ord_less_eq_set_real B5) C4) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) (@ (@ tptp.minus_minus_set_real C4) A4)) (= (@ G2 A3) tptp.zero_zero_rat))) (=> (forall ((B3 tptp.real)) (=> (@ (@ tptp.member_real B3) (@ (@ tptp.minus_minus_set_real C4) B5)) (= (@ H B3) tptp.zero_zero_rat))) (= (= (@ _let_2 A4) (@ _let_1 B5)) (= (@ _let_2 C4) (@ _let_1 C4))))))))))))
% 6.73/7.06 (assert (forall ((C4 tptp.set_int) (A4 tptp.set_int) (B5 tptp.set_int) (G2 (-> tptp.int tptp.rat)) (H (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups3906332499630173760nt_rat H))) (let ((_let_2 (@ tptp.groups3906332499630173760nt_rat G2))) (=> (@ tptp.finite_finite_int C4) (=> (@ (@ tptp.ord_less_eq_set_int A4) C4) (=> (@ (@ tptp.ord_less_eq_set_int B5) C4) (=> (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) (@ (@ tptp.minus_minus_set_int C4) A4)) (= (@ G2 A3) tptp.zero_zero_rat))) (=> (forall ((B3 tptp.int)) (=> (@ (@ tptp.member_int B3) (@ (@ tptp.minus_minus_set_int C4) B5)) (= (@ H B3) tptp.zero_zero_rat))) (= (= (@ _let_2 A4) (@ _let_1 B5)) (= (@ _let_2 C4) (@ _let_1 C4))))))))))))
% 6.73/7.06 (assert (forall ((C4 tptp.set_complex) (A4 tptp.set_complex) (B5 tptp.set_complex) (G2 (-> tptp.complex tptp.rat)) (H (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups5058264527183730370ex_rat H))) (let ((_let_2 (@ tptp.groups5058264527183730370ex_rat G2))) (=> (@ tptp.finite3207457112153483333omplex C4) (=> (@ (@ tptp.ord_le211207098394363844omplex A4) C4) (=> (@ (@ tptp.ord_le211207098394363844omplex B5) C4) (=> (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) (@ (@ tptp.minus_811609699411566653omplex C4) A4)) (= (@ G2 A3) tptp.zero_zero_rat))) (=> (forall ((B3 tptp.complex)) (=> (@ (@ tptp.member_complex B3) (@ (@ tptp.minus_811609699411566653omplex C4) B5)) (= (@ H B3) tptp.zero_zero_rat))) (= (= (@ _let_2 A4) (@ _let_1 B5)) (= (@ _let_2 C4) (@ _let_1 C4))))))))))))
% 6.73/7.06 (assert (forall ((C4 tptp.set_real) (A4 tptp.set_real) (B5 tptp.set_real) (G2 (-> tptp.real tptp.nat)) (H (-> tptp.real tptp.nat))) (let ((_let_1 (@ tptp.groups1935376822645274424al_nat H))) (let ((_let_2 (@ tptp.groups1935376822645274424al_nat G2))) (=> (@ tptp.finite_finite_real C4) (=> (@ (@ tptp.ord_less_eq_set_real A4) C4) (=> (@ (@ tptp.ord_less_eq_set_real B5) C4) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) (@ (@ tptp.minus_minus_set_real C4) A4)) (= (@ G2 A3) tptp.zero_zero_nat))) (=> (forall ((B3 tptp.real)) (=> (@ (@ tptp.member_real B3) (@ (@ tptp.minus_minus_set_real C4) B5)) (= (@ H B3) tptp.zero_zero_nat))) (= (= (@ _let_2 A4) (@ _let_1 B5)) (= (@ _let_2 C4) (@ _let_1 C4))))))))))))
% 6.73/7.06 (assert (forall ((T5 tptp.set_real) (S3 tptp.set_real) (H (-> tptp.real tptp.complex)) (G2 (-> tptp.real tptp.complex))) (=> (@ tptp.finite_finite_real T5) (=> (@ tptp.finite_finite_real S3) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) (@ (@ tptp.minus_minus_set_real T5) S3)) (= (@ H I3) tptp.zero_zero_complex))) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) (@ (@ tptp.minus_minus_set_real S3) T5)) (= (@ G2 I3) tptp.zero_zero_complex))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) (@ (@ tptp.inf_inf_set_real S3) T5)) (= (@ G2 X3) (@ H X3)))) (= (@ (@ tptp.groups5754745047067104278omplex G2) S3) (@ (@ tptp.groups5754745047067104278omplex H) T5)))))))))
% 6.73/7.06 (assert (forall ((T5 tptp.set_int) (S3 tptp.set_int) (H (-> tptp.int tptp.complex)) (G2 (-> tptp.int tptp.complex))) (=> (@ tptp.finite_finite_int T5) (=> (@ tptp.finite_finite_int S3) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) (@ (@ tptp.minus_minus_set_int T5) S3)) (= (@ H I3) tptp.zero_zero_complex))) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) (@ (@ tptp.minus_minus_set_int S3) T5)) (= (@ G2 I3) tptp.zero_zero_complex))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.inf_inf_set_int S3) T5)) (= (@ G2 X3) (@ H X3)))) (= (@ (@ tptp.groups3049146728041665814omplex G2) S3) (@ (@ tptp.groups3049146728041665814omplex H) T5)))))))))
% 6.73/7.06 (assert (forall ((T5 tptp.set_complex) (S3 tptp.set_complex) (H (-> tptp.complex tptp.complex)) (G2 (-> tptp.complex tptp.complex))) (=> (@ tptp.finite3207457112153483333omplex T5) (=> (@ tptp.finite3207457112153483333omplex S3) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) (@ (@ tptp.minus_811609699411566653omplex T5) S3)) (= (@ H I3) tptp.zero_zero_complex))) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) (@ (@ tptp.minus_811609699411566653omplex S3) T5)) (= (@ G2 I3) tptp.zero_zero_complex))) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ (@ tptp.inf_inf_set_complex S3) T5)) (= (@ G2 X3) (@ H X3)))) (= (@ (@ tptp.groups7754918857620584856omplex G2) S3) (@ (@ tptp.groups7754918857620584856omplex H) T5)))))))))
% 6.73/7.06 (assert (forall ((T5 tptp.set_real) (S3 tptp.set_real) (H (-> tptp.real tptp.real)) (G2 (-> tptp.real tptp.real))) (=> (@ tptp.finite_finite_real T5) (=> (@ tptp.finite_finite_real S3) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) (@ (@ tptp.minus_minus_set_real T5) S3)) (= (@ H I3) tptp.zero_zero_real))) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) (@ (@ tptp.minus_minus_set_real S3) T5)) (= (@ G2 I3) tptp.zero_zero_real))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) (@ (@ tptp.inf_inf_set_real S3) T5)) (= (@ G2 X3) (@ H X3)))) (= (@ (@ tptp.groups8097168146408367636l_real G2) S3) (@ (@ tptp.groups8097168146408367636l_real H) T5)))))))))
% 6.73/7.06 (assert (forall ((T5 tptp.set_int) (S3 tptp.set_int) (H (-> tptp.int tptp.real)) (G2 (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int T5) (=> (@ tptp.finite_finite_int S3) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) (@ (@ tptp.minus_minus_set_int T5) S3)) (= (@ H I3) tptp.zero_zero_real))) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) (@ (@ tptp.minus_minus_set_int S3) T5)) (= (@ G2 I3) tptp.zero_zero_real))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.inf_inf_set_int S3) T5)) (= (@ G2 X3) (@ H X3)))) (= (@ (@ tptp.groups8778361861064173332t_real G2) S3) (@ (@ tptp.groups8778361861064173332t_real H) T5)))))))))
% 6.73/7.06 (assert (forall ((T5 tptp.set_complex) (S3 tptp.set_complex) (H (-> tptp.complex tptp.real)) (G2 (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex T5) (=> (@ tptp.finite3207457112153483333omplex S3) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) (@ (@ tptp.minus_811609699411566653omplex T5) S3)) (= (@ H I3) tptp.zero_zero_real))) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) (@ (@ tptp.minus_811609699411566653omplex S3) T5)) (= (@ G2 I3) tptp.zero_zero_real))) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ (@ tptp.inf_inf_set_complex S3) T5)) (= (@ G2 X3) (@ H X3)))) (= (@ (@ tptp.groups5808333547571424918x_real G2) S3) (@ (@ tptp.groups5808333547571424918x_real H) T5)))))))))
% 6.73/7.06 (assert (forall ((T5 tptp.set_real) (S3 tptp.set_real) (H (-> tptp.real tptp.rat)) (G2 (-> tptp.real tptp.rat))) (=> (@ tptp.finite_finite_real T5) (=> (@ tptp.finite_finite_real S3) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) (@ (@ tptp.minus_minus_set_real T5) S3)) (= (@ H I3) tptp.zero_zero_rat))) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) (@ (@ tptp.minus_minus_set_real S3) T5)) (= (@ G2 I3) tptp.zero_zero_rat))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) (@ (@ tptp.inf_inf_set_real S3) T5)) (= (@ G2 X3) (@ H X3)))) (= (@ (@ tptp.groups1300246762558778688al_rat G2) S3) (@ (@ tptp.groups1300246762558778688al_rat H) T5)))))))))
% 6.73/7.06 (assert (forall ((T5 tptp.set_int) (S3 tptp.set_int) (H (-> tptp.int tptp.rat)) (G2 (-> tptp.int tptp.rat))) (=> (@ tptp.finite_finite_int T5) (=> (@ tptp.finite_finite_int S3) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) (@ (@ tptp.minus_minus_set_int T5) S3)) (= (@ H I3) tptp.zero_zero_rat))) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) (@ (@ tptp.minus_minus_set_int S3) T5)) (= (@ G2 I3) tptp.zero_zero_rat))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.inf_inf_set_int S3) T5)) (= (@ G2 X3) (@ H X3)))) (= (@ (@ tptp.groups3906332499630173760nt_rat G2) S3) (@ (@ tptp.groups3906332499630173760nt_rat H) T5)))))))))
% 6.73/7.06 (assert (forall ((T5 tptp.set_complex) (S3 tptp.set_complex) (H (-> tptp.complex tptp.rat)) (G2 (-> tptp.complex tptp.rat))) (=> (@ tptp.finite3207457112153483333omplex T5) (=> (@ tptp.finite3207457112153483333omplex S3) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) (@ (@ tptp.minus_811609699411566653omplex T5) S3)) (= (@ H I3) tptp.zero_zero_rat))) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) (@ (@ tptp.minus_811609699411566653omplex S3) T5)) (= (@ G2 I3) tptp.zero_zero_rat))) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ (@ tptp.inf_inf_set_complex S3) T5)) (= (@ G2 X3) (@ H X3)))) (= (@ (@ tptp.groups5058264527183730370ex_rat G2) S3) (@ (@ tptp.groups5058264527183730370ex_rat H) T5)))))))))
% 6.73/7.06 (assert (forall ((T5 tptp.set_real) (S3 tptp.set_real) (H (-> tptp.real tptp.nat)) (G2 (-> tptp.real tptp.nat))) (=> (@ tptp.finite_finite_real T5) (=> (@ tptp.finite_finite_real S3) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) (@ (@ tptp.minus_minus_set_real T5) S3)) (= (@ H I3) tptp.zero_zero_nat))) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) (@ (@ tptp.minus_minus_set_real S3) T5)) (= (@ G2 I3) tptp.zero_zero_nat))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) (@ (@ tptp.inf_inf_set_real S3) T5)) (= (@ G2 X3) (@ H X3)))) (= (@ (@ tptp.groups1935376822645274424al_nat G2) S3) (@ (@ tptp.groups1935376822645274424al_nat H) T5)))))))))
% 6.73/7.06 (assert (forall ((P2 (-> tptp.complex Bool)) (L tptp.complex)) (= (exists ((X4 tptp.complex)) (@ P2 (@ (@ tptp.times_times_complex L) X4))) (exists ((X4 tptp.complex)) (and (@ (@ tptp.dvd_dvd_complex L) (@ (@ tptp.plus_plus_complex X4) tptp.zero_zero_complex)) (@ P2 X4))))))
% 6.73/7.06 (assert (forall ((P2 (-> tptp.real Bool)) (L tptp.real)) (= (exists ((X4 tptp.real)) (@ P2 (@ (@ tptp.times_times_real L) X4))) (exists ((X4 tptp.real)) (and (@ (@ tptp.dvd_dvd_real L) (@ (@ tptp.plus_plus_real X4) tptp.zero_zero_real)) (@ P2 X4))))))
% 6.73/7.06 (assert (forall ((P2 (-> tptp.rat Bool)) (L tptp.rat)) (= (exists ((X4 tptp.rat)) (@ P2 (@ (@ tptp.times_times_rat L) X4))) (exists ((X4 tptp.rat)) (and (@ (@ tptp.dvd_dvd_rat L) (@ (@ tptp.plus_plus_rat X4) tptp.zero_zero_rat)) (@ P2 X4))))))
% 6.73/7.06 (assert (forall ((P2 (-> tptp.nat Bool)) (L tptp.nat)) (= (exists ((X4 tptp.nat)) (@ P2 (@ (@ tptp.times_times_nat L) X4))) (exists ((X4 tptp.nat)) (and (@ (@ tptp.dvd_dvd_nat L) (@ (@ tptp.plus_plus_nat X4) tptp.zero_zero_nat)) (@ P2 X4))))))
% 6.73/7.06 (assert (forall ((P2 (-> tptp.int Bool)) (L tptp.int)) (= (exists ((X4 tptp.int)) (@ P2 (@ (@ tptp.times_times_int L) X4))) (exists ((X4 tptp.int)) (and (@ (@ tptp.dvd_dvd_int L) (@ (@ tptp.plus_plus_int X4) tptp.zero_zero_int)) (@ P2 X4))))))
% 6.73/7.06 (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 ((C tptp.code_integer)) (not (= B (@ (@ tptp.times_3573771949741848930nteger A) C)))))))))
% 6.73/7.06 (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 ((C tptp.nat)) (not (= B (@ (@ tptp.times_times_nat A) C)))))))))
% 6.73/7.06 (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 ((C tptp.int)) (not (= B (@ (@ tptp.times_times_int A) C)))))))))
% 6.73/7.06 (assert (forall ((A tptp.nat) (C2 tptp.nat) (B tptp.nat) (D tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (=> (not (= C2 tptp.zero_zero_nat)) (=> (@ (@ tptp.dvd_dvd_nat A) B) (=> (@ (@ tptp.dvd_dvd_nat C2) D) (= (= (@ (@ tptp.divide_divide_nat B) A) (@ (@ tptp.divide_divide_nat D) C2)) (= (@ (@ tptp.times_times_nat B) C2) (@ (@ tptp.times_times_nat A) D)))))))))
% 6.73/7.06 (assert (forall ((A tptp.int) (C2 tptp.int) (B tptp.int) (D tptp.int)) (=> (not (= A tptp.zero_zero_int)) (=> (not (= C2 tptp.zero_zero_int)) (=> (@ (@ tptp.dvd_dvd_int A) B) (=> (@ (@ tptp.dvd_dvd_int C2) D) (= (= (@ (@ tptp.divide_divide_int B) A) (@ (@ tptp.divide_divide_int D) C2)) (= (@ (@ tptp.times_times_int B) C2) (@ (@ tptp.times_times_int A) D)))))))))
% 6.73/7.06 (assert (forall ((C2 tptp.nat) (B tptp.nat) (A tptp.nat)) (=> (not (= C2 tptp.zero_zero_nat)) (=> (@ (@ tptp.dvd_dvd_nat C2) B) (= (@ (@ tptp.dvd_dvd_nat A) (@ (@ tptp.divide_divide_nat B) C2)) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat A) C2)) B))))))
% 6.73/7.06 (assert (forall ((C2 tptp.int) (B tptp.int) (A tptp.int)) (=> (not (= C2 tptp.zero_zero_int)) (=> (@ (@ tptp.dvd_dvd_int C2) B) (= (@ (@ tptp.dvd_dvd_int A) (@ (@ tptp.divide_divide_int B) C2)) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A) C2)) B))))))
% 6.73/7.06 (assert (forall ((B tptp.nat) (A tptp.nat) (C2 tptp.nat)) (=> (not (= B tptp.zero_zero_nat)) (=> (@ (@ tptp.dvd_dvd_nat B) A) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.divide_divide_nat A) B)) C2) (@ (@ tptp.dvd_dvd_nat A) (@ (@ tptp.times_times_nat C2) B)))))))
% 6.73/7.06 (assert (forall ((B tptp.int) (A tptp.int) (C2 tptp.int)) (=> (not (= B tptp.zero_zero_int)) (=> (@ (@ tptp.dvd_dvd_int B) A) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.divide_divide_int A) B)) C2) (@ (@ tptp.dvd_dvd_int A) (@ (@ tptp.times_times_int C2) B)))))))
% 6.73/7.06 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (=> (@ (@ tptp.dvd_dvd_nat A) B) (= (= (@ (@ tptp.divide_divide_nat B) A) C2) (= B (@ (@ tptp.times_times_nat C2) A)))))))
% 6.73/7.06 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (=> (not (= A tptp.zero_zero_int)) (=> (@ (@ tptp.dvd_dvd_int A) B) (= (= (@ (@ tptp.divide_divide_int B) A) C2) (= B (@ (@ tptp.times_times_int C2) A)))))))
% 6.73/7.06 (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)))))
% 6.73/7.06 (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)))))
% 6.73/7.06 (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)))))
% 6.73/7.06 (assert (forall ((D tptp.real) (D3 tptp.real) (T tptp.real)) (=> (@ (@ tptp.dvd_dvd_real D) D3) (forall ((X5 tptp.real) (K4 tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real D))) (= (not (@ _let_1 (@ (@ tptp.plus_plus_real X5) T))) (not (@ _let_1 (@ (@ tptp.plus_plus_real (@ (@ tptp.minus_minus_real X5) (@ (@ tptp.times_times_real K4) D3))) T)))))))))
% 6.73/7.06 (assert (forall ((D tptp.rat) (D3 tptp.rat) (T tptp.rat)) (=> (@ (@ tptp.dvd_dvd_rat D) D3) (forall ((X5 tptp.rat) (K4 tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat D))) (= (not (@ _let_1 (@ (@ tptp.plus_plus_rat X5) T))) (not (@ _let_1 (@ (@ tptp.plus_plus_rat (@ (@ tptp.minus_minus_rat X5) (@ (@ tptp.times_times_rat K4) D3))) T)))))))))
% 6.73/7.06 (assert (forall ((D tptp.int) (D3 tptp.int) (T tptp.int)) (=> (@ (@ tptp.dvd_dvd_int D) D3) (forall ((X5 tptp.int) (K4 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int D))) (= (not (@ _let_1 (@ (@ tptp.plus_plus_int X5) T))) (not (@ _let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int X5) (@ (@ tptp.times_times_int K4) D3))) T)))))))))
% 6.73/7.06 (assert (forall ((D tptp.real) (D3 tptp.real) (T tptp.real)) (=> (@ (@ tptp.dvd_dvd_real D) D3) (forall ((X5 tptp.real) (K4 tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real D))) (= (@ _let_1 (@ (@ tptp.plus_plus_real X5) T)) (@ _let_1 (@ (@ tptp.plus_plus_real (@ (@ tptp.minus_minus_real X5) (@ (@ tptp.times_times_real K4) D3))) T))))))))
% 6.73/7.06 (assert (forall ((D tptp.rat) (D3 tptp.rat) (T tptp.rat)) (=> (@ (@ tptp.dvd_dvd_rat D) D3) (forall ((X5 tptp.rat) (K4 tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat D))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat X5) T)) (@ _let_1 (@ (@ tptp.plus_plus_rat (@ (@ tptp.minus_minus_rat X5) (@ (@ tptp.times_times_rat K4) D3))) T))))))))
% 6.73/7.06 (assert (forall ((D tptp.int) (D3 tptp.int) (T tptp.int)) (=> (@ (@ tptp.dvd_dvd_int D) D3) (forall ((X5 tptp.int) (K4 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int D))) (= (@ _let_1 (@ (@ tptp.plus_plus_int X5) T)) (@ _let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int X5) (@ (@ tptp.times_times_int K4) D3))) T))))))))
% 6.73/7.06 (assert (forall ((B tptp.code_integer) (A tptp.code_integer) (C2 tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer) (= (= (@ (@ tptp.divide6298287555418463151nteger A) B) C2) (= A (@ (@ tptp.times_3573771949741848930nteger C2) B))))))
% 6.73/7.06 (assert (forall ((B tptp.nat) (A tptp.nat) (C2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat) (= (= (@ (@ tptp.divide_divide_nat A) B) C2) (= A (@ (@ tptp.times_times_nat C2) B))))))
% 6.73/7.06 (assert (forall ((B tptp.int) (A tptp.int) (C2 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int) (= (= (@ (@ tptp.divide_divide_int A) B) C2) (= A (@ (@ tptp.times_times_int C2) B))))))
% 6.73/7.06 (assert (forall ((B tptp.code_integer) (A tptp.code_integer) (C2 tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer) (= (= A (@ (@ tptp.divide6298287555418463151nteger C2) B)) (= (@ (@ tptp.times_3573771949741848930nteger A) B) C2)))))
% 6.73/7.06 (assert (forall ((B tptp.nat) (A tptp.nat) (C2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat) (= (= A (@ (@ tptp.divide_divide_nat C2) B)) (= (@ (@ tptp.times_times_nat A) B) C2)))))
% 6.73/7.06 (assert (forall ((B tptp.int) (A tptp.int) (C2 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int) (= (= A (@ (@ tptp.divide_divide_int C2) B)) (= (@ (@ tptp.times_times_int A) B) C2)))))
% 6.73/7.06 (assert (forall ((C2 tptp.code_integer) (B tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.divide6298287555418463151nteger A))) (=> (@ (@ tptp.dvd_dvd_Code_integer C2) tptp.one_one_Code_integer) (=> (@ (@ tptp.dvd_dvd_Code_integer B) A) (= (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger B) C2)) (@ (@ tptp.divide6298287555418463151nteger (@ _let_1 B)) C2)))))))
% 6.73/7.06 (assert (forall ((C2 tptp.nat) (B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat A))) (=> (@ (@ tptp.dvd_dvd_nat C2) tptp.one_one_nat) (=> (@ (@ tptp.dvd_dvd_nat B) A) (= (@ _let_1 (@ (@ tptp.times_times_nat B) C2)) (@ (@ tptp.divide_divide_nat (@ _let_1 B)) C2)))))))
% 6.73/7.06 (assert (forall ((C2 tptp.int) (B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A))) (=> (@ (@ tptp.dvd_dvd_int C2) tptp.one_one_int) (=> (@ (@ tptp.dvd_dvd_int B) A) (= (@ _let_1 (@ (@ tptp.times_times_int B) C2)) (@ (@ tptp.divide_divide_int (@ _let_1 B)) C2)))))))
% 6.73/7.06 (assert (forall ((B tptp.code_integer) (A tptp.code_integer) (C2 tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer) (= (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.divide6298287555418463151nteger A) B)) C2) (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.times_3573771949741848930nteger A) C2)) B)))))
% 6.73/7.06 (assert (forall ((B tptp.nat) (A tptp.nat) (C2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat) (= (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat A) B)) C2) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat A) C2)) B)))))
% 6.73/7.06 (assert (forall ((B tptp.int) (A tptp.int) (C2 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int) (= (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int A) B)) C2) (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int A) C2)) B)))))
% 6.73/7.06 (assert (forall ((C2 tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger A))) (=> (@ (@ tptp.dvd_dvd_Code_integer C2) tptp.one_one_Code_integer) (= (@ _let_1 (@ (@ tptp.divide6298287555418463151nteger B) C2)) (@ (@ tptp.divide6298287555418463151nteger (@ _let_1 B)) C2))))))
% 6.73/7.06 (assert (forall ((C2 tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (=> (@ (@ tptp.dvd_dvd_nat C2) tptp.one_one_nat) (= (@ _let_1 (@ (@ tptp.divide_divide_nat B) C2)) (@ (@ tptp.divide_divide_nat (@ _let_1 B)) C2))))))
% 6.73/7.06 (assert (forall ((C2 tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (=> (@ (@ tptp.dvd_dvd_int C2) tptp.one_one_int) (= (@ _let_1 (@ (@ tptp.divide_divide_int B) C2)) (@ (@ tptp.divide_divide_int (@ _let_1 B)) C2))))))
% 6.73/7.06 (assert (forall ((B tptp.code_integer) (C2 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 C2) tptp.one_one_Code_integer) (= (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger B) C2)) (@ (@ tptp.divide6298287555418463151nteger (@ _let_1 B)) C2)))))))
% 6.73/7.06 (assert (forall ((B tptp.nat) (C2 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 C2) tptp.one_one_nat) (= (@ _let_1 (@ (@ tptp.times_times_nat B) C2)) (@ (@ tptp.divide_divide_nat (@ _let_1 B)) C2)))))))
% 6.73/7.06 (assert (forall ((B tptp.int) (C2 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 C2) tptp.one_one_int) (= (@ _let_1 (@ (@ tptp.times_times_int B) C2)) (@ (@ tptp.divide_divide_int (@ _let_1 B)) C2)))))))
% 6.73/7.06 (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)))))
% 6.73/7.06 (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)))))
% 6.73/7.06 (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)))))
% 6.73/7.06 (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))))
% 6.73/7.06 (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))))
% 6.73/7.06 (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))))
% 6.73/7.06 (assert (forall ((B tptp.code_natural) (A tptp.code_natural)) (=> (@ (@ tptp.dvd_dvd_Code_natural B) tptp.one_one_Code_natural) (= (@ (@ tptp.modulo8411746178871703098atural A) B) tptp.zero_z2226904508553997617atural))))
% 6.73/7.06 (assert (forall ((X tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.comm_s7457072308508201937r_real X) N)))))
% 6.73/7.06 (assert (forall ((X tptp.rat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) X) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.comm_s4028243227959126397er_rat X) N)))))
% 6.73/7.06 (assert (forall ((X tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) X) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ (@ tptp.comm_s4663373288045622133er_nat X) N)))))
% 6.73/7.06 (assert (forall ((X tptp.int) (N tptp.nat)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) X) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.comm_s4660882817536571857er_int X) N)))))
% 6.73/7.06 (assert (forall ((K2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat K2) N) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_eq_nat K2) N)))))
% 6.73/7.06 (assert (forall ((K2 tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K2))) (=> (@ (@ tptp.dvd_dvd_nat (@ _let_1 M2)) (@ _let_1 N)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K2) (@ (@ tptp.dvd_dvd_nat M2) N))))))
% 6.73/7.06 (assert (forall ((K2 tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K2) (= (@ (@ tptp.dvd_dvd_nat (@ _let_1 M2)) (@ _let_1 N)) (@ (@ tptp.dvd_dvd_nat M2) N))))))
% 6.73/7.06 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.comm_s8582702949713902594nteger tptp.zero_z3403309356797280102nteger) N))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_Code_integer)) (=> (not _let_2) (= _let_1 tptp.zero_z3403309356797280102nteger)))))))
% 6.73/7.06 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.comm_s2602460028002588243omplex tptp.zero_zero_complex) N))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_complex)) (=> (not _let_2) (= _let_1 tptp.zero_zero_complex)))))))
% 6.73/7.06 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.comm_s7457072308508201937r_real tptp.zero_zero_real) N))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_real)) (=> (not _let_2) (= _let_1 tptp.zero_zero_real)))))))
% 6.73/7.06 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.comm_s4028243227959126397er_rat tptp.zero_zero_rat) N))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_rat)) (=> (not _let_2) (= _let_1 tptp.zero_zero_rat)))))))
% 6.73/7.06 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.comm_s4663373288045622133er_nat tptp.zero_zero_nat) N))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_nat)) (=> (not _let_2) (= _let_1 tptp.zero_zero_nat)))))))
% 6.73/7.06 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.comm_s4660882817536571857er_int tptp.zero_zero_int) N))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_int)) (=> (not _let_2) (= _let_1 tptp.zero_zero_int)))))))
% 6.73/7.06 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (exists ((D5 tptp.nat) (X3 tptp.nat) (Y3 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat D5))) (and (@ _let_1 A) (@ _let_1 B) (= (@ (@ tptp.times_times_nat A) X3) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat B) Y3)) D5))))))))
% 6.73/7.06 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.modulo_modulo_nat M2) N)) (not (@ (@ tptp.dvd_dvd_nat N) M2)))))
% 6.73/7.06 (assert (forall ((N tptp.nat) (M2 tptp.nat) (Q2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M2) (= (= (@ (@ tptp.modulo_modulo_nat M2) Q2) (@ (@ tptp.modulo_modulo_nat N) Q2)) (@ (@ tptp.dvd_dvd_nat Q2) (@ (@ tptp.minus_minus_nat M2) N))))))
% 6.73/7.06 (assert (forall ((X tptp.complex) (M2 tptp.nat) (I5 tptp.set_nat)) (let ((_let_1 (@ tptp.power_power_complex X))) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I tptp.nat)) (@ (@ tptp.power_power_complex X) (@ (@ tptp.plus_plus_nat M2) I)))) I5) (@ (@ tptp.times_times_complex (@ _let_1 M2)) (@ (@ tptp.groups2073611262835488442omplex _let_1) I5))))))
% 6.73/7.06 (assert (forall ((X tptp.rat) (M2 tptp.nat) (I5 tptp.set_nat)) (let ((_let_1 (@ tptp.power_power_rat X))) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I tptp.nat)) (@ (@ tptp.power_power_rat X) (@ (@ tptp.plus_plus_nat M2) I)))) I5) (@ (@ tptp.times_times_rat (@ _let_1 M2)) (@ (@ tptp.groups2906978787729119204at_rat _let_1) I5))))))
% 6.73/7.06 (assert (forall ((X tptp.int) (M2 tptp.nat) (I5 tptp.set_nat)) (let ((_let_1 (@ tptp.power_power_int X))) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((I tptp.nat)) (@ (@ tptp.power_power_int X) (@ (@ tptp.plus_plus_nat M2) I)))) I5) (@ (@ tptp.times_times_int (@ _let_1 M2)) (@ (@ tptp.groups3539618377306564664at_int _let_1) I5))))))
% 6.73/7.06 (assert (forall ((X tptp.real) (M2 tptp.nat) (I5 tptp.set_nat)) (let ((_let_1 (@ tptp.power_power_real X))) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I tptp.nat)) (@ (@ tptp.power_power_real X) (@ (@ tptp.plus_plus_nat M2) I)))) I5) (@ (@ tptp.times_times_real (@ _let_1 M2)) (@ (@ tptp.groups6591440286371151544t_real _let_1) I5))))))
% 6.73/7.06 (assert (forall ((B5 tptp.set_real) (A4 tptp.set_real) (F2 (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.groups8097168146408367636l_real F2))) (=> (@ tptp.finite_finite_real B5) (=> (@ (@ tptp.ord_less_eq_set_real A4) B5) (=> (forall ((B3 tptp.real)) (=> (@ (@ tptp.member_real B3) (@ (@ tptp.minus_minus_set_real B5) A4)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F2 B3)))) (@ (@ tptp.ord_less_eq_real (@ _let_1 A4)) (@ _let_1 B5))))))))
% 6.73/7.06 (assert (forall ((B5 tptp.set_int) (A4 tptp.set_int) (F2 (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups8778361861064173332t_real F2))) (=> (@ tptp.finite_finite_int B5) (=> (@ (@ tptp.ord_less_eq_set_int A4) B5) (=> (forall ((B3 tptp.int)) (=> (@ (@ tptp.member_int B3) (@ (@ tptp.minus_minus_set_int B5) A4)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F2 B3)))) (@ (@ tptp.ord_less_eq_real (@ _let_1 A4)) (@ _let_1 B5))))))))
% 6.73/7.06 (assert (forall ((B5 tptp.set_complex) (A4 tptp.set_complex) (F2 (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups5808333547571424918x_real F2))) (=> (@ tptp.finite3207457112153483333omplex B5) (=> (@ (@ tptp.ord_le211207098394363844omplex A4) B5) (=> (forall ((B3 tptp.complex)) (=> (@ (@ tptp.member_complex B3) (@ (@ tptp.minus_811609699411566653omplex B5) A4)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F2 B3)))) (@ (@ tptp.ord_less_eq_real (@ _let_1 A4)) (@ _let_1 B5))))))))
% 6.73/7.06 (assert (forall ((B5 tptp.set_real) (A4 tptp.set_real) (F2 (-> tptp.real tptp.rat))) (let ((_let_1 (@ tptp.groups1300246762558778688al_rat F2))) (=> (@ tptp.finite_finite_real B5) (=> (@ (@ tptp.ord_less_eq_set_real A4) B5) (=> (forall ((B3 tptp.real)) (=> (@ (@ tptp.member_real B3) (@ (@ tptp.minus_minus_set_real B5) A4)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F2 B3)))) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A4)) (@ _let_1 B5))))))))
% 6.73/7.06 (assert (forall ((B5 tptp.set_int) (A4 tptp.set_int) (F2 (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups3906332499630173760nt_rat F2))) (=> (@ tptp.finite_finite_int B5) (=> (@ (@ tptp.ord_less_eq_set_int A4) B5) (=> (forall ((B3 tptp.int)) (=> (@ (@ tptp.member_int B3) (@ (@ tptp.minus_minus_set_int B5) A4)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F2 B3)))) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A4)) (@ _let_1 B5))))))))
% 6.73/7.06 (assert (forall ((B5 tptp.set_complex) (A4 tptp.set_complex) (F2 (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups5058264527183730370ex_rat F2))) (=> (@ tptp.finite3207457112153483333omplex B5) (=> (@ (@ tptp.ord_le211207098394363844omplex A4) B5) (=> (forall ((B3 tptp.complex)) (=> (@ (@ tptp.member_complex B3) (@ (@ tptp.minus_811609699411566653omplex B5) A4)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F2 B3)))) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A4)) (@ _let_1 B5))))))))
% 6.73/7.06 (assert (forall ((B5 tptp.set_real) (A4 tptp.set_real) (F2 (-> tptp.real tptp.nat))) (let ((_let_1 (@ tptp.groups1935376822645274424al_nat F2))) (=> (@ tptp.finite_finite_real B5) (=> (@ (@ tptp.ord_less_eq_set_real A4) B5) (=> (forall ((B3 tptp.real)) (=> (@ (@ tptp.member_real B3) (@ (@ tptp.minus_minus_set_real B5) A4)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F2 B3)))) (@ (@ tptp.ord_less_eq_nat (@ _let_1 A4)) (@ _let_1 B5))))))))
% 6.73/7.06 (assert (forall ((B5 tptp.set_int) (A4 tptp.set_int) (F2 (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups4541462559716669496nt_nat F2))) (=> (@ tptp.finite_finite_int B5) (=> (@ (@ tptp.ord_less_eq_set_int A4) B5) (=> (forall ((B3 tptp.int)) (=> (@ (@ tptp.member_int B3) (@ (@ tptp.minus_minus_set_int B5) A4)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F2 B3)))) (@ (@ tptp.ord_less_eq_nat (@ _let_1 A4)) (@ _let_1 B5))))))))
% 6.73/7.06 (assert (forall ((B5 tptp.set_complex) (A4 tptp.set_complex) (F2 (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups5693394587270226106ex_nat F2))) (=> (@ tptp.finite3207457112153483333omplex B5) (=> (@ (@ tptp.ord_le211207098394363844omplex A4) B5) (=> (forall ((B3 tptp.complex)) (=> (@ (@ tptp.member_complex B3) (@ (@ tptp.minus_811609699411566653omplex B5) A4)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F2 B3)))) (@ (@ tptp.ord_less_eq_nat (@ _let_1 A4)) (@ _let_1 B5))))))))
% 6.73/7.06 (assert (forall ((B5 tptp.set_real) (A4 tptp.set_real) (F2 (-> tptp.real tptp.int))) (let ((_let_1 (@ tptp.groups1932886352136224148al_int F2))) (=> (@ tptp.finite_finite_real B5) (=> (@ (@ tptp.ord_less_eq_set_real A4) B5) (=> (forall ((B3 tptp.real)) (=> (@ (@ tptp.member_real B3) (@ (@ tptp.minus_minus_set_real B5) A4)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F2 B3)))) (@ (@ tptp.ord_less_eq_int (@ _let_1 A4)) (@ _let_1 B5))))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_int) (B5 tptp.set_int) (G2 (-> tptp.int tptp.complex))) (let ((_let_1 (@ tptp.groups3049146728041665814omplex G2))) (=> (@ tptp.finite_finite_int A4) (=> (@ tptp.finite_finite_int B5) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.inf_inf_set_int A4) B5)) (= (@ G2 X3) tptp.zero_zero_complex))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_int A4) B5)) (@ (@ tptp.plus_plus_complex (@ _let_1 A4)) (@ _let_1 B5)))))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_complex) (B5 tptp.set_complex) (G2 (-> tptp.complex tptp.complex))) (let ((_let_1 (@ tptp.groups7754918857620584856omplex G2))) (=> (@ tptp.finite3207457112153483333omplex A4) (=> (@ tptp.finite3207457112153483333omplex B5) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ (@ tptp.inf_inf_set_complex A4) B5)) (= (@ G2 X3) tptp.zero_zero_complex))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_complex A4) B5)) (@ (@ tptp.plus_plus_complex (@ _let_1 A4)) (@ _let_1 B5)))))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_int) (B5 tptp.set_int) (G2 (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups8778361861064173332t_real G2))) (=> (@ tptp.finite_finite_int A4) (=> (@ tptp.finite_finite_int B5) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.inf_inf_set_int A4) B5)) (= (@ G2 X3) tptp.zero_zero_real))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_int A4) B5)) (@ (@ tptp.plus_plus_real (@ _let_1 A4)) (@ _let_1 B5)))))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_complex) (B5 tptp.set_complex) (G2 (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups5808333547571424918x_real G2))) (=> (@ tptp.finite3207457112153483333omplex A4) (=> (@ tptp.finite3207457112153483333omplex B5) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ (@ tptp.inf_inf_set_complex A4) B5)) (= (@ G2 X3) tptp.zero_zero_real))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_complex A4) B5)) (@ (@ tptp.plus_plus_real (@ _let_1 A4)) (@ _let_1 B5)))))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_int) (B5 tptp.set_int) (G2 (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups3906332499630173760nt_rat G2))) (=> (@ tptp.finite_finite_int A4) (=> (@ tptp.finite_finite_int B5) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.inf_inf_set_int A4) B5)) (= (@ G2 X3) tptp.zero_zero_rat))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_int A4) B5)) (@ (@ tptp.plus_plus_rat (@ _let_1 A4)) (@ _let_1 B5)))))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_complex) (B5 tptp.set_complex) (G2 (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups5058264527183730370ex_rat G2))) (=> (@ tptp.finite3207457112153483333omplex A4) (=> (@ tptp.finite3207457112153483333omplex B5) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ (@ tptp.inf_inf_set_complex A4) B5)) (= (@ G2 X3) tptp.zero_zero_rat))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_complex A4) B5)) (@ (@ tptp.plus_plus_rat (@ _let_1 A4)) (@ _let_1 B5)))))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_int) (B5 tptp.set_int) (G2 (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups4541462559716669496nt_nat G2))) (=> (@ tptp.finite_finite_int A4) (=> (@ tptp.finite_finite_int B5) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.inf_inf_set_int A4) B5)) (= (@ G2 X3) tptp.zero_zero_nat))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_int A4) B5)) (@ (@ tptp.plus_plus_nat (@ _let_1 A4)) (@ _let_1 B5)))))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_complex) (B5 tptp.set_complex) (G2 (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups5693394587270226106ex_nat G2))) (=> (@ tptp.finite3207457112153483333omplex A4) (=> (@ tptp.finite3207457112153483333omplex B5) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ (@ tptp.inf_inf_set_complex A4) B5)) (= (@ G2 X3) tptp.zero_zero_nat))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_complex A4) B5)) (@ (@ tptp.plus_plus_nat (@ _let_1 A4)) (@ _let_1 B5)))))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_complex) (B5 tptp.set_complex) (G2 (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.groups5690904116761175830ex_int G2))) (=> (@ tptp.finite3207457112153483333omplex A4) (=> (@ tptp.finite3207457112153483333omplex B5) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ (@ tptp.inf_inf_set_complex A4) B5)) (= (@ G2 X3) tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_complex A4) B5)) (@ (@ tptp.plus_plus_int (@ _let_1 A4)) (@ _let_1 B5)))))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_nat) (B5 tptp.set_nat) (G2 (-> tptp.nat tptp.complex))) (let ((_let_1 (@ tptp.groups2073611262835488442omplex G2))) (=> (@ tptp.finite_finite_nat A4) (=> (@ tptp.finite_finite_nat B5) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ (@ tptp.inf_inf_set_nat A4) B5)) (= (@ G2 X3) tptp.zero_zero_complex))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_nat A4) B5)) (@ (@ tptp.plus_plus_complex (@ _let_1 A4)) (@ _let_1 B5)))))))))
% 6.73/7.06 (assert (forall ((G2 (-> tptp.nat tptp.nat)) (N tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat N) M2))) (= (@ (@ tptp.groups3542108847815614940at_nat G2) _let_1) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I tptp.nat)) (@ G2 (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M2) N)) I)))) _let_1)))))
% 6.73/7.06 (assert (forall ((G2 (-> tptp.nat tptp.real)) (N tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat N) M2))) (= (@ (@ tptp.groups6591440286371151544t_real G2) _let_1) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I tptp.nat)) (@ G2 (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M2) N)) I)))) _let_1)))))
% 6.73/7.06 (assert (forall ((M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M2) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((D2 tptp.nat)) (@ (@ tptp.dvd_dvd_nat D2) M2)))))))
% 6.73/7.06 (assert (forall ((A (-> tptp.nat tptp.complex))) (@ (@ tptp.sums_complex (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_complex (@ A N4)) (@ (@ tptp.power_power_complex tptp.zero_zero_complex) N4)))) (@ A tptp.zero_zero_nat))))
% 6.73/7.06 (assert (forall ((A (-> tptp.nat tptp.real))) (@ (@ tptp.sums_real (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_real (@ A N4)) (@ (@ tptp.power_power_real tptp.zero_zero_real) N4)))) (@ A tptp.zero_zero_nat))))
% 6.73/7.06 (assert (forall ((F2 (-> tptp.nat tptp.complex)) (K2 tptp.nat)) (let ((_let_1 (@ tptp.groups2073611262835488442omplex F2))) (=> (= (@ F2 tptp.zero_zero_nat) tptp.zero_zero_complex) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) K2)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) K2)))))))
% 6.73/7.06 (assert (forall ((F2 (-> tptp.nat tptp.rat)) (K2 tptp.nat)) (let ((_let_1 (@ tptp.groups2906978787729119204at_rat F2))) (=> (= (@ F2 tptp.zero_zero_nat) tptp.zero_zero_rat) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) K2)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) K2)))))))
% 6.73/7.06 (assert (forall ((F2 (-> tptp.nat tptp.int)) (K2 tptp.nat)) (let ((_let_1 (@ tptp.groups3539618377306564664at_int F2))) (=> (= (@ F2 tptp.zero_zero_nat) tptp.zero_zero_int) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) K2)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) K2)))))))
% 6.73/7.06 (assert (forall ((F2 (-> tptp.nat tptp.nat)) (K2 tptp.nat)) (let ((_let_1 (@ tptp.groups3542108847815614940at_nat F2))) (=> (= (@ F2 tptp.zero_zero_nat) tptp.zero_zero_nat) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) K2)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) K2)))))))
% 6.73/7.06 (assert (forall ((F2 (-> tptp.nat tptp.real)) (K2 tptp.nat)) (let ((_let_1 (@ tptp.groups6591440286371151544t_real F2))) (=> (= (@ F2 tptp.zero_zero_nat) tptp.zero_zero_real) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) K2)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) K2)))))))
% 6.73/7.06 (assert (forall ((G2 (-> 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 G2))) (= (@ _let_3 (@ _let_2 _let_1)) (@ (@ tptp.plus_plus_rat (@ _let_3 (@ _let_2 N))) (@ G2 _let_1))))))))
% 6.73/7.06 (assert (forall ((G2 (-> 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 G2))) (= (@ _let_3 (@ _let_2 _let_1)) (@ (@ tptp.plus_plus_int (@ _let_3 (@ _let_2 N))) (@ G2 _let_1))))))))
% 6.73/7.06 (assert (forall ((G2 (-> 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 G2))) (= (@ _let_3 (@ _let_2 _let_1)) (@ (@ tptp.plus_plus_nat (@ _let_3 (@ _let_2 N))) (@ G2 _let_1))))))))
% 6.73/7.06 (assert (forall ((G2 (-> 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 G2))) (= (@ _let_3 (@ _let_2 _let_1)) (@ (@ tptp.plus_plus_real (@ _let_3 (@ _let_2 N))) (@ G2 _let_1))))))))
% 6.73/7.06 (assert (forall ((M2 tptp.nat) (N tptp.nat) (G2 (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups2906978787729119204at_rat G2))) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M2) N)) (@ (@ tptp.plus_plus_rat (@ G2 M2)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M2)) N))))))))
% 6.73/7.06 (assert (forall ((M2 tptp.nat) (N tptp.nat) (G2 (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.groups3539618377306564664at_int G2))) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M2) N)) (@ (@ tptp.plus_plus_int (@ G2 M2)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M2)) N))))))))
% 6.73/7.06 (assert (forall ((M2 tptp.nat) (N tptp.nat) (G2 (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.groups3542108847815614940at_nat G2))) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M2) N)) (@ (@ tptp.plus_plus_nat (@ G2 M2)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M2)) N))))))))
% 6.73/7.06 (assert (forall ((M2 tptp.nat) (N tptp.nat) (G2 (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.groups6591440286371151544t_real G2))) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M2) N)) (@ (@ tptp.plus_plus_real (@ G2 M2)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M2)) N))))))))
% 6.73/7.06 (assert (forall ((M2 tptp.nat) (N tptp.nat) (G2 (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat M2))) (let ((_let_2 (@ tptp.groups2906978787729119204at_rat G2))) (let ((_let_3 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_nat M2) _let_3) (= (@ _let_2 (@ _let_1 _let_3)) (@ (@ tptp.plus_plus_rat (@ G2 _let_3)) (@ _let_2 (@ _let_1 N))))))))))
% 6.73/7.06 (assert (forall ((M2 tptp.nat) (N tptp.nat) (G2 (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat M2))) (let ((_let_2 (@ tptp.groups3539618377306564664at_int G2))) (let ((_let_3 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_nat M2) _let_3) (= (@ _let_2 (@ _let_1 _let_3)) (@ (@ tptp.plus_plus_int (@ G2 _let_3)) (@ _let_2 (@ _let_1 N))))))))))
% 6.73/7.06 (assert (forall ((M2 tptp.nat) (N tptp.nat) (G2 (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat M2))) (let ((_let_2 (@ tptp.groups3542108847815614940at_nat G2))) (let ((_let_3 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_nat M2) _let_3) (= (@ _let_2 (@ _let_1 _let_3)) (@ (@ tptp.plus_plus_nat (@ G2 _let_3)) (@ _let_2 (@ _let_1 N))))))))))
% 6.73/7.06 (assert (forall ((M2 tptp.nat) (N tptp.nat) (G2 (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat M2))) (let ((_let_2 (@ tptp.groups6591440286371151544t_real G2))) (let ((_let_3 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_nat M2) _let_3) (= (@ _let_2 (@ _let_1 _let_3)) (@ (@ tptp.plus_plus_real (@ G2 _let_3)) (@ _let_2 (@ _let_1 N))))))))))
% 6.73/7.06 (assert (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_nat))
% 6.73/7.06 (assert (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) tptp.zero_zero_int))
% 6.73/7.06 (assert (forall ((A tptp.code_integer) (C2 tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer) (not (=> (not (= A tptp.zero_z3403309356797280102nteger)) (forall ((B3 tptp.code_integer)) (let ((_let_1 (@ tptp.divide6298287555418463151nteger tptp.one_one_Code_integer))) (=> (not (= B3 tptp.zero_z3403309356797280102nteger)) (=> (@ (@ tptp.dvd_dvd_Code_integer B3) tptp.one_one_Code_integer) (=> (= (@ _let_1 A) B3) (=> (= (@ _let_1 B3) A) (=> (= (@ (@ tptp.times_3573771949741848930nteger A) B3) tptp.one_one_Code_integer) (not (= (@ (@ tptp.divide6298287555418463151nteger C2) A) (@ (@ tptp.times_3573771949741848930nteger C2) B3)))))))))))))))
% 6.73/7.06 (assert (forall ((A tptp.nat) (C2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (not (=> (not (= A tptp.zero_zero_nat)) (forall ((B3 tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat tptp.one_one_nat))) (=> (not (= B3 tptp.zero_zero_nat)) (=> (@ (@ tptp.dvd_dvd_nat B3) tptp.one_one_nat) (=> (= (@ _let_1 A) B3) (=> (= (@ _let_1 B3) A) (=> (= (@ (@ tptp.times_times_nat A) B3) tptp.one_one_nat) (not (= (@ (@ tptp.divide_divide_nat C2) A) (@ (@ tptp.times_times_nat C2) B3)))))))))))))))
% 6.73/7.06 (assert (forall ((A tptp.int) (C2 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (not (=> (not (= A tptp.zero_zero_int)) (forall ((B3 tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int tptp.one_one_int))) (=> (not (= B3 tptp.zero_zero_int)) (=> (@ (@ tptp.dvd_dvd_int B3) tptp.one_one_int) (=> (= (@ _let_1 A) B3) (=> (= (@ _let_1 B3) A) (=> (= (@ (@ tptp.times_times_int A) B3) tptp.one_one_int) (not (= (@ (@ tptp.divide_divide_int C2) A) (@ (@ tptp.times_times_int C2) B3)))))))))))))))
% 6.73/7.06 (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))))))
% 6.73/7.06 (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))))))
% 6.73/7.06 (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))))))
% 6.73/7.06 (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))))))
% 6.73/7.06 (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))))))
% 6.73/7.06 (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))))))
% 6.73/7.06 (assert (forall ((A tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) A) (not (forall ((B3 tptp.nat)) (not (= A (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) B3))))))))
% 6.73/7.06 (assert (forall ((A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) A) (not (forall ((B3 tptp.int)) (not (= A (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) B3))))))))
% 6.73/7.06 (assert (forall ((X tptp.code_integer) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger X))) (=> (not (= X tptp.zero_z3403309356797280102nteger)) (= (@ (@ tptp.dvd_dvd_Code_integer (@ _let_1 M2)) (@ _let_1 N)) (or (@ (@ tptp.dvd_dvd_Code_integer X) tptp.one_one_Code_integer) (@ (@ tptp.ord_less_eq_nat M2) N)))))))
% 6.73/7.06 (assert (forall ((X tptp.nat) (M2 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 M2)) (@ _let_1 N)) (or (@ (@ tptp.dvd_dvd_nat X) tptp.one_one_nat) (@ (@ tptp.ord_less_eq_nat M2) N)))))))
% 6.73/7.06 (assert (forall ((X tptp.int) (M2 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 M2)) (@ _let_1 N)) (or (@ (@ tptp.dvd_dvd_int X) tptp.one_one_int) (@ (@ tptp.ord_less_eq_nat M2) N)))))))
% 6.73/7.06 (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)))))
% 6.73/7.06 (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)))))
% 6.73/7.06 (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)))))
% 6.73/7.06 (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)))))
% 6.73/7.06 (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)))))
% 6.73/7.06 (assert (forall ((B5 tptp.set_real) (A4 tptp.set_real) (B tptp.real) (F2 (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.groups8097168146408367636l_real F2))) (=> (@ tptp.finite_finite_real B5) (=> (@ (@ tptp.ord_less_eq_set_real A4) B5) (=> (@ (@ tptp.member_real B) (@ (@ tptp.minus_minus_set_real B5) A4)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F2 B)) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) B5) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F2 X3)))) (@ (@ tptp.ord_less_real (@ _let_1 A4)) (@ _let_1 B5))))))))))
% 6.73/7.06 (assert (forall ((B5 tptp.set_int) (A4 tptp.set_int) (B tptp.int) (F2 (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups8778361861064173332t_real F2))) (=> (@ tptp.finite_finite_int B5) (=> (@ (@ tptp.ord_less_eq_set_int A4) B5) (=> (@ (@ tptp.member_int B) (@ (@ tptp.minus_minus_set_int B5) A4)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F2 B)) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) B5) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F2 X3)))) (@ (@ tptp.ord_less_real (@ _let_1 A4)) (@ _let_1 B5))))))))))
% 6.73/7.06 (assert (forall ((B5 tptp.set_complex) (A4 tptp.set_complex) (B tptp.complex) (F2 (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups5808333547571424918x_real F2))) (=> (@ tptp.finite3207457112153483333omplex B5) (=> (@ (@ tptp.ord_le211207098394363844omplex A4) B5) (=> (@ (@ tptp.member_complex B) (@ (@ tptp.minus_811609699411566653omplex B5) A4)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F2 B)) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) B5) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F2 X3)))) (@ (@ tptp.ord_less_real (@ _let_1 A4)) (@ _let_1 B5))))))))))
% 6.73/7.06 (assert (forall ((B5 tptp.set_real) (A4 tptp.set_real) (B tptp.real) (F2 (-> tptp.real tptp.rat))) (let ((_let_1 (@ tptp.groups1300246762558778688al_rat F2))) (=> (@ tptp.finite_finite_real B5) (=> (@ (@ tptp.ord_less_eq_set_real A4) B5) (=> (@ (@ tptp.member_real B) (@ (@ tptp.minus_minus_set_real B5) A4)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ F2 B)) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) B5) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F2 X3)))) (@ (@ tptp.ord_less_rat (@ _let_1 A4)) (@ _let_1 B5))))))))))
% 6.73/7.06 (assert (forall ((B5 tptp.set_int) (A4 tptp.set_int) (B tptp.int) (F2 (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups3906332499630173760nt_rat F2))) (=> (@ tptp.finite_finite_int B5) (=> (@ (@ tptp.ord_less_eq_set_int A4) B5) (=> (@ (@ tptp.member_int B) (@ (@ tptp.minus_minus_set_int B5) A4)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ F2 B)) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) B5) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F2 X3)))) (@ (@ tptp.ord_less_rat (@ _let_1 A4)) (@ _let_1 B5))))))))))
% 6.73/7.06 (assert (forall ((B5 tptp.set_complex) (A4 tptp.set_complex) (B tptp.complex) (F2 (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups5058264527183730370ex_rat F2))) (=> (@ tptp.finite3207457112153483333omplex B5) (=> (@ (@ tptp.ord_le211207098394363844omplex A4) B5) (=> (@ (@ tptp.member_complex B) (@ (@ tptp.minus_811609699411566653omplex B5) A4)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ F2 B)) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) B5) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F2 X3)))) (@ (@ tptp.ord_less_rat (@ _let_1 A4)) (@ _let_1 B5))))))))))
% 6.73/7.06 (assert (forall ((B5 tptp.set_real) (A4 tptp.set_real) (B tptp.real) (F2 (-> tptp.real tptp.nat))) (let ((_let_1 (@ tptp.groups1935376822645274424al_nat F2))) (=> (@ tptp.finite_finite_real B5) (=> (@ (@ tptp.ord_less_eq_set_real A4) B5) (=> (@ (@ tptp.member_real B) (@ (@ tptp.minus_minus_set_real B5) A4)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F2 B)) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) B5) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F2 X3)))) (@ (@ tptp.ord_less_nat (@ _let_1 A4)) (@ _let_1 B5))))))))))
% 6.73/7.06 (assert (forall ((B5 tptp.set_int) (A4 tptp.set_int) (B tptp.int) (F2 (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups4541462559716669496nt_nat F2))) (=> (@ tptp.finite_finite_int B5) (=> (@ (@ tptp.ord_less_eq_set_int A4) B5) (=> (@ (@ tptp.member_int B) (@ (@ tptp.minus_minus_set_int B5) A4)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F2 B)) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) B5) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F2 X3)))) (@ (@ tptp.ord_less_nat (@ _let_1 A4)) (@ _let_1 B5))))))))))
% 6.73/7.06 (assert (forall ((B5 tptp.set_complex) (A4 tptp.set_complex) (B tptp.complex) (F2 (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups5693394587270226106ex_nat F2))) (=> (@ tptp.finite3207457112153483333omplex B5) (=> (@ (@ tptp.ord_le211207098394363844omplex A4) B5) (=> (@ (@ tptp.member_complex B) (@ (@ tptp.minus_811609699411566653omplex B5) A4)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F2 B)) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) B5) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F2 X3)))) (@ (@ tptp.ord_less_nat (@ _let_1 A4)) (@ _let_1 B5))))))))))
% 6.73/7.06 (assert (forall ((B5 tptp.set_real) (A4 tptp.set_real) (B tptp.real) (F2 (-> tptp.real tptp.int))) (let ((_let_1 (@ tptp.groups1932886352136224148al_int F2))) (=> (@ tptp.finite_finite_real B5) (=> (@ (@ tptp.ord_less_eq_set_real A4) B5) (=> (@ (@ tptp.member_real B) (@ (@ tptp.minus_minus_set_real B5) A4)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ F2 B)) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) B5) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F2 X3)))) (@ (@ tptp.ord_less_int (@ _let_1 A4)) (@ _let_1 B5))))))))))
% 6.73/7.06 (assert (forall ((I2 tptp.complex) (A4 tptp.set_complex) (F2 (-> tptp.complex tptp.real))) (=> (@ (@ tptp.member_complex I2) A4) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ (@ tptp.minus_811609699411566653omplex A4) (@ (@ tptp.insert_complex I2) tptp.bot_bot_set_complex))) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F2 X3)))) (=> (@ tptp.finite3207457112153483333omplex A4) (@ (@ tptp.ord_less_eq_real (@ F2 I2)) (@ (@ tptp.groups5808333547571424918x_real F2) A4)))))))
% 6.73/7.06 (assert (forall ((I2 tptp.int) (A4 tptp.set_int) (F2 (-> tptp.int tptp.real))) (=> (@ (@ tptp.member_int I2) A4) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.minus_minus_set_int A4) (@ (@ tptp.insert_int I2) tptp.bot_bot_set_int))) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F2 X3)))) (=> (@ tptp.finite_finite_int A4) (@ (@ tptp.ord_less_eq_real (@ F2 I2)) (@ (@ tptp.groups8778361861064173332t_real F2) A4)))))))
% 6.73/7.06 (assert (forall ((I2 tptp.real) (A4 tptp.set_real) (F2 (-> tptp.real tptp.real))) (=> (@ (@ tptp.member_real I2) A4) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) (@ (@ tptp.minus_minus_set_real A4) (@ (@ tptp.insert_real I2) tptp.bot_bot_set_real))) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F2 X3)))) (=> (@ tptp.finite_finite_real A4) (@ (@ tptp.ord_less_eq_real (@ F2 I2)) (@ (@ tptp.groups8097168146408367636l_real F2) A4)))))))
% 6.73/7.06 (assert (forall ((I2 tptp.complex) (A4 tptp.set_complex) (F2 (-> tptp.complex tptp.rat))) (=> (@ (@ tptp.member_complex I2) A4) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ (@ tptp.minus_811609699411566653omplex A4) (@ (@ tptp.insert_complex I2) tptp.bot_bot_set_complex))) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F2 X3)))) (=> (@ tptp.finite3207457112153483333omplex A4) (@ (@ tptp.ord_less_eq_rat (@ F2 I2)) (@ (@ tptp.groups5058264527183730370ex_rat F2) A4)))))))
% 6.73/7.06 (assert (forall ((I2 tptp.int) (A4 tptp.set_int) (F2 (-> tptp.int tptp.rat))) (=> (@ (@ tptp.member_int I2) A4) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.minus_minus_set_int A4) (@ (@ tptp.insert_int I2) tptp.bot_bot_set_int))) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F2 X3)))) (=> (@ tptp.finite_finite_int A4) (@ (@ tptp.ord_less_eq_rat (@ F2 I2)) (@ (@ tptp.groups3906332499630173760nt_rat F2) A4)))))))
% 6.73/7.06 (assert (forall ((I2 tptp.real) (A4 tptp.set_real) (F2 (-> tptp.real tptp.rat))) (=> (@ (@ tptp.member_real I2) A4) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) (@ (@ tptp.minus_minus_set_real A4) (@ (@ tptp.insert_real I2) tptp.bot_bot_set_real))) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F2 X3)))) (=> (@ tptp.finite_finite_real A4) (@ (@ tptp.ord_less_eq_rat (@ F2 I2)) (@ (@ tptp.groups1300246762558778688al_rat F2) A4)))))))
% 6.73/7.06 (assert (forall ((I2 tptp.nat) (A4 tptp.set_nat) (F2 (-> tptp.nat tptp.rat))) (=> (@ (@ tptp.member_nat I2) A4) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ (@ tptp.minus_minus_set_nat A4) (@ (@ tptp.insert_nat I2) tptp.bot_bot_set_nat))) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F2 X3)))) (=> (@ tptp.finite_finite_nat A4) (@ (@ tptp.ord_less_eq_rat (@ F2 I2)) (@ (@ tptp.groups2906978787729119204at_rat F2) A4)))))))
% 6.73/7.06 (assert (forall ((I2 tptp.complex) (A4 tptp.set_complex) (F2 (-> tptp.complex tptp.nat))) (=> (@ (@ tptp.member_complex I2) A4) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ (@ tptp.minus_811609699411566653omplex A4) (@ (@ tptp.insert_complex I2) tptp.bot_bot_set_complex))) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F2 X3)))) (=> (@ tptp.finite3207457112153483333omplex A4) (@ (@ tptp.ord_less_eq_nat (@ F2 I2)) (@ (@ tptp.groups5693394587270226106ex_nat F2) A4)))))))
% 6.73/7.06 (assert (forall ((I2 tptp.int) (A4 tptp.set_int) (F2 (-> tptp.int tptp.nat))) (=> (@ (@ tptp.member_int I2) A4) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.minus_minus_set_int A4) (@ (@ tptp.insert_int I2) tptp.bot_bot_set_int))) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F2 X3)))) (=> (@ tptp.finite_finite_int A4) (@ (@ tptp.ord_less_eq_nat (@ F2 I2)) (@ (@ tptp.groups4541462559716669496nt_nat F2) A4)))))))
% 6.73/7.06 (assert (forall ((I2 tptp.real) (A4 tptp.set_real) (F2 (-> tptp.real tptp.nat))) (=> (@ (@ tptp.member_real I2) A4) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) (@ (@ tptp.minus_minus_set_real A4) (@ (@ tptp.insert_real I2) tptp.bot_bot_set_real))) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F2 X3)))) (=> (@ tptp.finite_finite_real A4) (@ (@ tptp.ord_less_eq_nat (@ F2 I2)) (@ (@ tptp.groups1935376822645274424al_nat F2) A4)))))))
% 6.73/7.06 (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)))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_real) (F2 (-> tptp.real tptp.rat)) (K5 tptp.rat)) (let ((_let_1 (@ tptp.finite_card_real A4))) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) A4) (@ (@ tptp.ord_less_rat (@ F2 I3)) K5))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) _let_1) (@ (@ tptp.ord_less_rat (@ (@ tptp.groups1300246762558778688al_rat F2) A4)) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat _let_1)) K5)))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_nat) (F2 (-> tptp.nat tptp.rat)) (K5 tptp.rat)) (let ((_let_1 (@ tptp.finite_card_nat A4))) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.member_nat I3) A4) (@ (@ tptp.ord_less_rat (@ F2 I3)) K5))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) _let_1) (@ (@ tptp.ord_less_rat (@ (@ tptp.groups2906978787729119204at_rat F2) A4)) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat _let_1)) K5)))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_complex) (F2 (-> tptp.complex tptp.rat)) (K5 tptp.rat)) (let ((_let_1 (@ tptp.finite_card_complex A4))) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) A4) (@ (@ tptp.ord_less_rat (@ F2 I3)) K5))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) _let_1) (@ (@ tptp.ord_less_rat (@ (@ tptp.groups5058264527183730370ex_rat F2) A4)) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat _let_1)) K5)))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_int) (F2 (-> tptp.int tptp.rat)) (K5 tptp.rat)) (let ((_let_1 (@ tptp.finite_card_int A4))) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) A4) (@ (@ tptp.ord_less_rat (@ F2 I3)) K5))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) _let_1) (@ (@ tptp.ord_less_rat (@ (@ tptp.groups3906332499630173760nt_rat F2) A4)) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat _let_1)) K5)))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_real) (F2 (-> tptp.real tptp.real)) (K5 tptp.real)) (let ((_let_1 (@ tptp.finite_card_real A4))) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) A4) (@ (@ tptp.ord_less_real (@ F2 I3)) K5))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) _let_1) (@ (@ tptp.ord_less_real (@ (@ tptp.groups8097168146408367636l_real F2) A4)) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real _let_1)) K5)))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_complex) (F2 (-> tptp.complex tptp.real)) (K5 tptp.real)) (let ((_let_1 (@ tptp.finite_card_complex A4))) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) A4) (@ (@ tptp.ord_less_real (@ F2 I3)) K5))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) _let_1) (@ (@ tptp.ord_less_real (@ (@ tptp.groups5808333547571424918x_real F2) A4)) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real _let_1)) K5)))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_int) (F2 (-> tptp.int tptp.real)) (K5 tptp.real)) (let ((_let_1 (@ tptp.finite_card_int A4))) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) A4) (@ (@ tptp.ord_less_real (@ F2 I3)) K5))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) _let_1) (@ (@ tptp.ord_less_real (@ (@ tptp.groups8778361861064173332t_real F2) A4)) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real _let_1)) K5)))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_real) (F2 (-> tptp.real tptp.int)) (K5 tptp.int)) (let ((_let_1 (@ tptp.finite_card_real A4))) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) A4) (@ (@ tptp.ord_less_int (@ F2 I3)) K5))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) _let_1) (@ (@ tptp.ord_less_int (@ (@ tptp.groups1932886352136224148al_int F2) A4)) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int _let_1)) K5)))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_nat) (F2 (-> tptp.nat tptp.int)) (K5 tptp.int)) (let ((_let_1 (@ tptp.finite_card_nat A4))) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.member_nat I3) A4) (@ (@ tptp.ord_less_int (@ F2 I3)) K5))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) _let_1) (@ (@ tptp.ord_less_int (@ (@ tptp.groups3539618377306564664at_int F2) A4)) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int _let_1)) K5)))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_complex) (F2 (-> tptp.complex tptp.int)) (K5 tptp.int)) (let ((_let_1 (@ tptp.finite_card_complex A4))) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) A4) (@ (@ tptp.ord_less_int (@ F2 I3)) K5))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) _let_1) (@ (@ tptp.ord_less_int (@ (@ tptp.groups5690904116761175830ex_int F2) A4)) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int _let_1)) K5)))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_complex) (F2 (-> tptp.complex tptp.real)) (K5 tptp.real)) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) A4) (@ (@ tptp.ord_less_eq_real (@ F2 I3)) (@ (@ tptp.divide_divide_real K5) (@ tptp.semiri5074537144036343181t_real (@ tptp.finite_card_complex A4)))))) (=> (@ tptp.finite3207457112153483333omplex A4) (=> (not (= A4 tptp.bot_bot_set_complex)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups5808333547571424918x_real F2) A4)) K5))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_int) (F2 (-> tptp.int tptp.real)) (K5 tptp.real)) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) A4) (@ (@ tptp.ord_less_eq_real (@ F2 I3)) (@ (@ tptp.divide_divide_real K5) (@ tptp.semiri5074537144036343181t_real (@ tptp.finite_card_int A4)))))) (=> (@ tptp.finite_finite_int A4) (=> (not (= A4 tptp.bot_bot_set_int)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups8778361861064173332t_real F2) A4)) K5))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_real) (F2 (-> tptp.real tptp.real)) (K5 tptp.real)) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) A4) (@ (@ tptp.ord_less_eq_real (@ F2 I3)) (@ (@ tptp.divide_divide_real K5) (@ tptp.semiri5074537144036343181t_real (@ tptp.finite_card_real A4)))))) (=> (@ tptp.finite_finite_real A4) (=> (not (= A4 tptp.bot_bot_set_real)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups8097168146408367636l_real F2) A4)) K5))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_complex) (F2 (-> tptp.complex tptp.rat)) (K5 tptp.rat)) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) A4) (@ (@ tptp.ord_less_eq_rat (@ F2 I3)) (@ (@ tptp.divide_divide_rat K5) (@ tptp.semiri681578069525770553at_rat (@ tptp.finite_card_complex A4)))))) (=> (@ tptp.finite3207457112153483333omplex A4) (=> (not (= A4 tptp.bot_bot_set_complex)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups5058264527183730370ex_rat F2) A4)) K5))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_nat) (F2 (-> tptp.nat tptp.rat)) (K5 tptp.rat)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.member_nat I3) A4) (@ (@ tptp.ord_less_eq_rat (@ F2 I3)) (@ (@ tptp.divide_divide_rat K5) (@ tptp.semiri681578069525770553at_rat (@ tptp.finite_card_nat A4)))))) (=> (@ tptp.finite_finite_nat A4) (=> (not (= A4 tptp.bot_bot_set_nat)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups2906978787729119204at_rat F2) A4)) K5))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_int) (F2 (-> tptp.int tptp.rat)) (K5 tptp.rat)) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) A4) (@ (@ tptp.ord_less_eq_rat (@ F2 I3)) (@ (@ tptp.divide_divide_rat K5) (@ tptp.semiri681578069525770553at_rat (@ tptp.finite_card_int A4)))))) (=> (@ tptp.finite_finite_int A4) (=> (not (= A4 tptp.bot_bot_set_int)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups3906332499630173760nt_rat F2) A4)) K5))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_real) (F2 (-> tptp.real tptp.rat)) (K5 tptp.rat)) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) A4) (@ (@ tptp.ord_less_eq_rat (@ F2 I3)) (@ (@ tptp.divide_divide_rat K5) (@ tptp.semiri681578069525770553at_rat (@ tptp.finite_card_real A4)))))) (=> (@ tptp.finite_finite_real A4) (=> (not (= A4 tptp.bot_bot_set_real)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups1300246762558778688al_rat F2) A4)) K5))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_nat) (F2 (-> tptp.nat tptp.real)) (K5 tptp.real)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.member_nat I3) A4) (@ (@ tptp.ord_less_eq_real (@ F2 I3)) (@ (@ tptp.divide_divide_real K5) (@ tptp.semiri5074537144036343181t_real (@ tptp.finite_card_nat A4)))))) (=> (@ tptp.finite_finite_nat A4) (=> (not (= A4 tptp.bot_bot_set_nat)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups6591440286371151544t_real F2) A4)) K5))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_list_nat) (F2 (-> tptp.list_nat tptp.real)) (K5 tptp.real)) (=> (forall ((I3 tptp.list_nat)) (=> (@ (@ tptp.member_list_nat I3) A4) (@ (@ tptp.ord_less_eq_real (@ F2 I3)) (@ (@ tptp.divide_divide_real K5) (@ tptp.semiri5074537144036343181t_real (@ tptp.finite_card_list_nat A4)))))) (=> (@ tptp.finite8100373058378681591st_nat A4) (=> (not (= A4 tptp.bot_bot_set_list_nat)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups8399112307953289288t_real F2) A4)) K5))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_set_nat) (F2 (-> tptp.set_nat tptp.real)) (K5 tptp.real)) (=> (forall ((I3 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat I3) A4) (@ (@ tptp.ord_less_eq_real (@ F2 I3)) (@ (@ tptp.divide_divide_real K5) (@ tptp.semiri5074537144036343181t_real (@ tptp.finite_card_set_nat A4)))))) (=> (@ tptp.finite1152437895449049373et_nat A4) (=> (not (= A4 tptp.bot_bot_set_set_nat)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups5107569545109728110t_real F2) A4)) K5))))))
% 6.73/7.06 (assert (forall ((A tptp.code_integer) (N tptp.nat)) (= (@ (@ tptp.comm_s8582702949713902594nteger A) (@ tptp.suc N)) (@ (@ tptp.times_3573771949741848930nteger A) (@ (@ tptp.comm_s8582702949713902594nteger (@ (@ tptp.plus_p5714425477246183910nteger A) tptp.one_one_Code_integer)) N)))))
% 6.73/7.06 (assert (forall ((A tptp.complex) (N tptp.nat)) (= (@ (@ tptp.comm_s2602460028002588243omplex A) (@ tptp.suc N)) (@ (@ tptp.times_times_complex A) (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.plus_plus_complex A) tptp.one_one_complex)) N)))))
% 6.73/7.06 (assert (forall ((A tptp.real) (N tptp.nat)) (= (@ (@ tptp.comm_s7457072308508201937r_real A) (@ tptp.suc N)) (@ (@ tptp.times_times_real A) (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.plus_plus_real A) tptp.one_one_real)) N)))))
% 6.73/7.06 (assert (forall ((A tptp.rat) (N tptp.nat)) (= (@ (@ tptp.comm_s4028243227959126397er_rat A) (@ tptp.suc N)) (@ (@ tptp.times_times_rat A) (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.plus_plus_rat A) tptp.one_one_rat)) N)))))
% 6.73/7.06 (assert (forall ((A tptp.nat) (N tptp.nat)) (= (@ (@ tptp.comm_s4663373288045622133er_nat A) (@ tptp.suc N)) (@ (@ tptp.times_times_nat A) (@ (@ tptp.comm_s4663373288045622133er_nat (@ (@ tptp.plus_plus_nat A) tptp.one_one_nat)) N)))))
% 6.73/7.06 (assert (forall ((A tptp.int) (N tptp.nat)) (= (@ (@ tptp.comm_s4660882817536571857er_int A) (@ tptp.suc N)) (@ (@ tptp.times_times_int A) (@ (@ tptp.comm_s4660882817536571857er_int (@ (@ tptp.plus_plus_int A) tptp.one_one_int)) N)))))
% 6.73/7.06 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M2) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat M2) N)) M2) (= N tptp.one_one_nat)))))
% 6.73/7.06 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M2) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat N) M2)) M2) (= N tptp.one_one_nat)))))
% 6.73/7.06 (assert (forall ((Z3 tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.comm_s4028243227959126397er_rat Z3))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat Z3) (@ tptp.semiri681578069525770553at_rat N))) (@ _let_1 N))))))
% 6.73/7.06 (assert (forall ((Z3 tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.comm_s7457072308508201937r_real Z3))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real Z3) (@ tptp.semiri5074537144036343181t_real N))) (@ _let_1 N))))))
% 6.73/7.06 (assert (forall ((Z3 tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.comm_s4660882817536571857er_int Z3))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int Z3) (@ tptp.semiri1314217659103216013at_int N))) (@ _let_1 N))))))
% 6.73/7.06 (assert (forall ((Z3 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.comm_s4663373288045622133er_nat Z3))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat Z3) (@ tptp.semiri1316708129612266289at_nat N))) (@ _let_1 N))))))
% 6.73/7.06 (assert (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.comm_s4028243227959126397er_rat A))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_rat (@ _let_1 N)) (@ (@ tptp.plus_plus_rat A) (@ tptp.semiri681578069525770553at_rat N)))))))
% 6.73/7.06 (assert (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.comm_s7457072308508201937r_real A))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_real (@ _let_1 N)) (@ (@ tptp.plus_plus_real A) (@ tptp.semiri5074537144036343181t_real N)))))))
% 6.73/7.06 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.comm_s4660882817536571857er_int A))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_int (@ _let_1 N)) (@ (@ tptp.plus_plus_int A) (@ tptp.semiri1314217659103216013at_int N)))))))
% 6.73/7.06 (assert (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.comm_s4663373288045622133er_nat A))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_nat (@ _let_1 N)) (@ (@ tptp.plus_plus_nat A) (@ tptp.semiri1316708129612266289at_nat N)))))))
% 6.73/7.06 (assert (forall ((Q2 tptp.nat) (N tptp.nat) (R3 tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat R3) M2))) (let ((_let_2 (@ tptp.dvd_dvd_nat M2))) (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)))))))))))
% 6.73/7.06 (assert (forall ((I2 tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat I2))) (=> (@ (@ tptp.dvd_dvd_nat (@ _let_1 M2)) (@ _let_1 N)) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) I2) (@ (@ tptp.ord_less_eq_nat M2) N))))))
% 6.73/7.06 (assert (forall ((Z3 tptp.rat) (N tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.comm_s4028243227959126397er_rat Z3))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N) M2)) (@ (@ tptp.times_times_rat (@ _let_1 N)) (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.plus_plus_rat Z3) (@ tptp.semiri681578069525770553at_rat N))) M2))))))
% 6.73/7.06 (assert (forall ((Z3 tptp.real) (N tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.comm_s7457072308508201937r_real Z3))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N) M2)) (@ (@ tptp.times_times_real (@ _let_1 N)) (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.plus_plus_real Z3) (@ tptp.semiri5074537144036343181t_real N))) M2))))))
% 6.73/7.06 (assert (forall ((Z3 tptp.int) (N tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.comm_s4660882817536571857er_int Z3))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N) M2)) (@ (@ tptp.times_times_int (@ _let_1 N)) (@ (@ tptp.comm_s4660882817536571857er_int (@ (@ tptp.plus_plus_int Z3) (@ tptp.semiri1314217659103216013at_int N))) M2))))))
% 6.73/7.06 (assert (forall ((Z3 tptp.nat) (N tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.comm_s4663373288045622133er_nat Z3))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N) M2)) (@ (@ tptp.times_times_nat (@ _let_1 N)) (@ (@ tptp.comm_s4663373288045622133er_nat (@ (@ tptp.plus_plus_nat Z3) (@ tptp.semiri1316708129612266289at_nat N))) M2))))))
% 6.73/7.06 (assert (forall ((R3 tptp.nat) (N tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat R3) N) (=> (@ (@ tptp.ord_less_eq_nat R3) M2) (=> (@ (@ tptp.dvd_dvd_nat N) (@ (@ tptp.minus_minus_nat M2) R3)) (= (@ (@ tptp.modulo_modulo_nat M2) N) R3))))))
% 6.73/7.06 (assert (forall ((M2 tptp.nat) (N tptp.nat) (G2 (-> tptp.nat tptp.rat))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M2) N))) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.groups2906978787729119204at_rat G2) _let_1)) (@ G2 (@ tptp.suc N))) (@ (@ tptp.plus_plus_rat (@ G2 M2)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I tptp.nat)) (@ G2 (@ tptp.suc I)))) _let_1)))))))
% 6.73/7.06 (assert (forall ((M2 tptp.nat) (N tptp.nat) (G2 (-> tptp.nat tptp.int))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M2) N))) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.groups3539618377306564664at_int G2) _let_1)) (@ G2 (@ tptp.suc N))) (@ (@ tptp.plus_plus_int (@ G2 M2)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I tptp.nat)) (@ G2 (@ tptp.suc I)))) _let_1)))))))
% 6.73/7.06 (assert (forall ((M2 tptp.nat) (N tptp.nat) (G2 (-> tptp.nat tptp.nat))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M2) N))) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.groups3542108847815614940at_nat G2) _let_1)) (@ G2 (@ tptp.suc N))) (@ (@ tptp.plus_plus_nat (@ G2 M2)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I tptp.nat)) (@ G2 (@ tptp.suc I)))) _let_1)))))))
% 6.73/7.06 (assert (forall ((M2 tptp.nat) (N tptp.nat) (G2 (-> tptp.nat tptp.real))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M2) N))) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real G2) _let_1)) (@ G2 (@ tptp.suc N))) (@ (@ tptp.plus_plus_real (@ G2 M2)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I tptp.nat)) (@ G2 (@ tptp.suc I)))) _let_1)))))))
% 6.73/7.06 (assert (forall ((M2 tptp.nat) (N tptp.nat) (F2 (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_nat M2) _let_1) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I tptp.nat)) (@ (@ tptp.minus_minus_rat (@ F2 (@ tptp.suc I))) (@ F2 I)))) (@ (@ tptp.set_or1269000886237332187st_nat M2) N)) (@ (@ tptp.minus_minus_rat (@ F2 _let_1)) (@ F2 M2)))))))
% 6.73/7.06 (assert (forall ((M2 tptp.nat) (N tptp.nat) (F2 (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_nat M2) _let_1) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((I tptp.nat)) (@ (@ tptp.minus_minus_int (@ F2 (@ tptp.suc I))) (@ F2 I)))) (@ (@ tptp.set_or1269000886237332187st_nat M2) N)) (@ (@ tptp.minus_minus_int (@ F2 _let_1)) (@ F2 M2)))))))
% 6.73/7.06 (assert (forall ((M2 tptp.nat) (N tptp.nat) (F2 (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_nat M2) _let_1) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I tptp.nat)) (@ (@ tptp.minus_minus_real (@ F2 (@ tptp.suc I))) (@ F2 I)))) (@ (@ tptp.set_or1269000886237332187st_nat M2) N)) (@ (@ tptp.minus_minus_real (@ F2 _let_1)) (@ F2 M2)))))))
% 6.73/7.06 (assert (forall ((S3 tptp.set_real) (F2 (-> tptp.real tptp.complex)) (K5 tptp.real)) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) S3) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ F2 X3))) K5))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.groups5754745047067104278omplex F2) S3))) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ tptp.finite_card_real S3))) K5)))))
% 6.73/7.06 (assert (forall ((S3 tptp.set_nat) (F2 (-> tptp.nat tptp.complex)) (K5 tptp.real)) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) S3) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ F2 X3))) K5))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.groups2073611262835488442omplex F2) S3))) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ tptp.finite_card_nat S3))) K5)))))
% 6.73/7.06 (assert (forall ((S3 tptp.set_complex) (F2 (-> tptp.complex tptp.complex)) (K5 tptp.real)) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) S3) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ F2 X3))) K5))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.groups7754918857620584856omplex F2) S3))) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ tptp.finite_card_complex S3))) K5)))))
% 6.73/7.06 (assert (forall ((S3 tptp.set_int) (F2 (-> tptp.int tptp.complex)) (K5 tptp.real)) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) S3) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ F2 X3))) K5))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.groups3049146728041665814omplex F2) S3))) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ tptp.finite_card_int S3))) K5)))))
% 6.73/7.06 (assert (forall ((S3 tptp.set_list_nat) (F2 (-> tptp.list_nat tptp.complex)) (K5 tptp.real)) (=> (forall ((X3 tptp.list_nat)) (=> (@ (@ tptp.member_list_nat X3) S3) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ F2 X3))) K5))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.groups6529277132148336714omplex F2) S3))) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ tptp.finite_card_list_nat S3))) K5)))))
% 6.73/7.06 (assert (forall ((S3 tptp.set_set_nat) (F2 (-> tptp.set_nat tptp.complex)) (K5 tptp.real)) (=> (forall ((X3 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat X3) S3) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ F2 X3))) K5))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.groups8255218700646806128omplex F2) S3))) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ tptp.finite_card_set_nat S3))) K5)))))
% 6.73/7.06 (assert (forall ((S3 tptp.set_nat) (F2 (-> tptp.nat tptp.real)) (K5 tptp.real)) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) S3) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ F2 X3))) K5))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.groups6591440286371151544t_real F2) S3))) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ tptp.finite_card_nat S3))) K5)))))
% 6.73/7.06 (assert (forall ((M2 tptp.nat) (N tptp.nat) (G2 (-> tptp.nat tptp.rat)) (P tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N))) (let ((_let_2 (@ _let_1 P))) (let ((_let_3 (@ _let_1 tptp.one_one_nat))) (let ((_let_4 (@ tptp.groups2906978787729119204at_rat G2))) (let ((_let_5 (@ tptp.set_or1269000886237332187st_nat M2))) (=> (@ (@ tptp.ord_less_eq_nat M2) _let_3) (= (@ _let_4 (@ _let_5 _let_2)) (@ (@ tptp.plus_plus_rat (@ _let_4 (@ _let_5 N))) (@ _let_4 (@ (@ tptp.set_or1269000886237332187st_nat _let_3) _let_2))))))))))))
% 6.73/7.06 (assert (forall ((M2 tptp.nat) (N tptp.nat) (G2 (-> tptp.nat tptp.int)) (P tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N))) (let ((_let_2 (@ _let_1 P))) (let ((_let_3 (@ _let_1 tptp.one_one_nat))) (let ((_let_4 (@ tptp.groups3539618377306564664at_int G2))) (let ((_let_5 (@ tptp.set_or1269000886237332187st_nat M2))) (=> (@ (@ tptp.ord_less_eq_nat M2) _let_3) (= (@ _let_4 (@ _let_5 _let_2)) (@ (@ tptp.plus_plus_int (@ _let_4 (@ _let_5 N))) (@ _let_4 (@ (@ tptp.set_or1269000886237332187st_nat _let_3) _let_2))))))))))))
% 6.73/7.06 (assert (forall ((M2 tptp.nat) (N tptp.nat) (G2 (-> tptp.nat tptp.nat)) (P tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N))) (let ((_let_2 (@ _let_1 P))) (let ((_let_3 (@ _let_1 tptp.one_one_nat))) (let ((_let_4 (@ tptp.groups3542108847815614940at_nat G2))) (let ((_let_5 (@ tptp.set_or1269000886237332187st_nat M2))) (=> (@ (@ tptp.ord_less_eq_nat M2) _let_3) (= (@ _let_4 (@ _let_5 _let_2)) (@ (@ tptp.plus_plus_nat (@ _let_4 (@ _let_5 N))) (@ _let_4 (@ (@ tptp.set_or1269000886237332187st_nat _let_3) _let_2))))))))))))
% 6.73/7.06 (assert (forall ((M2 tptp.nat) (N tptp.nat) (G2 (-> tptp.nat tptp.real)) (P tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N))) (let ((_let_2 (@ _let_1 P))) (let ((_let_3 (@ _let_1 tptp.one_one_nat))) (let ((_let_4 (@ tptp.groups6591440286371151544t_real G2))) (let ((_let_5 (@ tptp.set_or1269000886237332187st_nat M2))) (=> (@ (@ tptp.ord_less_eq_nat M2) _let_3) (= (@ _let_4 (@ _let_5 _let_2)) (@ (@ tptp.plus_plus_real (@ _let_4 (@ _let_5 N))) (@ _let_4 (@ (@ tptp.set_or1269000886237332187st_nat _let_3) _let_2))))))))))))
% 6.73/7.06 (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)))))
% 6.73/7.06 (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)))))
% 6.73/7.06 (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)))))
% 6.73/7.06 (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)))))
% 6.73/7.06 (assert (forall ((A tptp.code_natural)) (let ((_let_1 (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.dvd_dvd_Code_natural _let_1) A) (= (@ (@ tptp.modulo8411746178871703098atural A) _let_1) tptp.zero_z2226904508553997617atural)))))
% 6.73/7.06 (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))))))
% 6.73/7.06 (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))))))
% 6.73/7.06 (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))))))
% 6.73/7.06 (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))))
% 6.73/7.06 (assert (forall ((K2 tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat K2))) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) K2) (= (@ (@ tptp.dvd_dvd_nat (@ _let_1 M2)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat M2) N))))))
% 6.73/7.06 (assert (forall ((M2 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se4205575877204974255it_nat M2) A)) (or (@ _let_1 A) (= M2 tptp.zero_zero_nat))))))
% 6.73/7.06 (assert (forall ((M2 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se4203085406695923979it_int M2) A)) (or (@ _let_1 A) (= M2 tptp.zero_zero_nat))))))
% 6.73/7.06 (assert (= tptp.nat_set_encode (@ tptp.groups3542108847815614940at_nat (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 6.73/7.06 (assert (forall ((M2 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se7882103937844011126it_nat M2) A)) (and (@ _let_1 A) (not (= M2 tptp.zero_zero_nat)))))))
% 6.73/7.06 (assert (forall ((M2 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se7879613467334960850it_int M2) A)) (and (@ _let_1 A) (not (= M2 tptp.zero_zero_nat)))))))
% 6.73/7.06 (assert (forall ((M2 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se2161824704523386999it_nat M2) A)) (not (= (@ _let_1 A) (= M2 tptp.zero_zero_nat)))))))
% 6.73/7.06 (assert (forall ((M2 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se2159334234014336723it_int M2) A)) (not (= (@ _let_1 A) (= M2 tptp.zero_zero_nat)))))))
% 6.73/7.06 (assert (forall ((M2 tptp.nat) (N tptp.nat) (Z3 tptp.rat)) (let ((_let_1 (@ tptp.comm_s4028243227959126397er_rat Z3))) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ _let_1 N) (@ (@ tptp.times_times_rat (@ _let_1 M2)) (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.plus_plus_rat Z3) (@ tptp.semiri681578069525770553at_rat M2))) (@ (@ tptp.minus_minus_nat N) M2))))))))
% 6.73/7.06 (assert (forall ((M2 tptp.nat) (N tptp.nat) (Z3 tptp.real)) (let ((_let_1 (@ tptp.comm_s7457072308508201937r_real Z3))) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ _let_1 N) (@ (@ tptp.times_times_real (@ _let_1 M2)) (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.plus_plus_real Z3) (@ tptp.semiri5074537144036343181t_real M2))) (@ (@ tptp.minus_minus_nat N) M2))))))))
% 6.73/7.06 (assert (forall ((M2 tptp.nat) (N tptp.nat) (Z3 tptp.int)) (let ((_let_1 (@ tptp.comm_s4660882817536571857er_int Z3))) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ _let_1 N) (@ (@ tptp.times_times_int (@ _let_1 M2)) (@ (@ tptp.comm_s4660882817536571857er_int (@ (@ tptp.plus_plus_int Z3) (@ tptp.semiri1314217659103216013at_int M2))) (@ (@ tptp.minus_minus_nat N) M2))))))))
% 6.73/7.06 (assert (forall ((M2 tptp.nat) (N tptp.nat) (Z3 tptp.nat)) (let ((_let_1 (@ tptp.comm_s4663373288045622133er_nat Z3))) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ _let_1 N) (@ (@ tptp.times_times_nat (@ _let_1 M2)) (@ (@ tptp.comm_s4663373288045622133er_nat (@ (@ tptp.plus_plus_nat Z3) (@ tptp.semiri1316708129612266289at_nat M2))) (@ (@ tptp.minus_minus_nat N) M2))))))))
% 6.73/7.06 (assert (forall ((A tptp.code_integer)) (=> (not (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) A)) (not (forall ((B3 tptp.code_integer)) (not (= A (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) B3)) tptp.one_one_Code_integer))))))))
% 6.73/7.06 (assert (forall ((A tptp.nat)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) A)) (not (forall ((B3 tptp.nat)) (not (= A (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) B3)) tptp.one_one_nat))))))))
% 6.73/7.06 (assert (forall ((A tptp.int)) (=> (not (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) A)) (not (forall ((B3 tptp.int)) (not (= A (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) B3)) tptp.one_one_int))))))))
% 6.73/7.06 (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))))))))
% 6.73/7.06 (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))))))))
% 6.73/7.06 (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))))))))
% 6.73/7.06 (assert (forall ((A tptp.code_natural)) (let ((_let_1 (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.modulo8411746178871703098atural A) _let_1))) (let ((_let_3 (@ (@ tptp.dvd_dvd_Code_natural _let_1) A))) (and (=> _let_3 (= _let_2 tptp.zero_z2226904508553997617atural)) (=> (not _let_3) (= _let_2 tptp.one_one_Code_natural))))))))
% 6.73/7.06 (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))))))))))
% 6.73/7.06 (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))))))))))
% 6.73/7.06 (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))))))))))
% 6.73/7.06 (assert (forall ((A tptp.code_natural)) (let ((_let_1 (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.modulo8411746178871703098atural A) _let_1))) (let ((_let_3 (@ (@ tptp.dvd_dvd_Code_natural _let_1) A))) (=> (=> _let_3 (not (= _let_2 tptp.zero_z2226904508553997617atural))) (not (=> (not _let_3) (not (= _let_2 tptp.one_one_Code_natural))))))))))
% 6.73/7.06 (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)))))
% 6.73/7.06 (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)))))
% 6.73/7.06 (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)))))
% 6.73/7.06 (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))))))
% 6.73/7.06 (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))))))
% 6.73/7.06 (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))))))
% 6.73/7.06 (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))))))))
% 6.73/7.06 (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))))))))
% 6.73/7.06 (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))))))))
% 6.73/7.06 (assert (forall ((M2 tptp.nat) (N tptp.nat) (F2 (-> tptp.nat tptp.complex))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M2) N))) (let ((_let_2 (@ (@ tptp.ord_less_eq_nat M2) N))) (and (=> _let_2 (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((K3 tptp.nat)) (@ (@ tptp.minus_minus_complex (@ F2 K3)) (@ F2 (@ (@ tptp.plus_plus_nat K3) tptp.one_one_nat))))) _let_1) (@ (@ tptp.minus_minus_complex (@ F2 M2)) (@ F2 (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat))))) (=> (not _let_2) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((K3 tptp.nat)) (@ (@ tptp.minus_minus_complex (@ F2 K3)) (@ F2 (@ (@ tptp.plus_plus_nat K3) tptp.one_one_nat))))) _let_1) tptp.zero_zero_complex)))))))
% 6.73/7.06 (assert (forall ((M2 tptp.nat) (N tptp.nat) (F2 (-> tptp.nat tptp.rat))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M2) N))) (let ((_let_2 (@ (@ tptp.ord_less_eq_nat M2) N))) (and (=> _let_2 (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ tptp.minus_minus_rat (@ F2 K3)) (@ F2 (@ (@ tptp.plus_plus_nat K3) tptp.one_one_nat))))) _let_1) (@ (@ tptp.minus_minus_rat (@ F2 M2)) (@ F2 (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat))))) (=> (not _let_2) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ tptp.minus_minus_rat (@ F2 K3)) (@ F2 (@ (@ tptp.plus_plus_nat K3) tptp.one_one_nat))))) _let_1) tptp.zero_zero_rat)))))))
% 6.73/7.06 (assert (forall ((M2 tptp.nat) (N tptp.nat) (F2 (-> tptp.nat tptp.int))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M2) N))) (let ((_let_2 (@ (@ tptp.ord_less_eq_nat M2) N))) (and (=> _let_2 (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((K3 tptp.nat)) (@ (@ tptp.minus_minus_int (@ F2 K3)) (@ F2 (@ (@ tptp.plus_plus_nat K3) tptp.one_one_nat))))) _let_1) (@ (@ tptp.minus_minus_int (@ F2 M2)) (@ F2 (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat))))) (=> (not _let_2) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((K3 tptp.nat)) (@ (@ tptp.minus_minus_int (@ F2 K3)) (@ F2 (@ (@ tptp.plus_plus_nat K3) tptp.one_one_nat))))) _let_1) tptp.zero_zero_int)))))))
% 6.73/7.06 (assert (forall ((M2 tptp.nat) (N tptp.nat) (F2 (-> tptp.nat tptp.real))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M2) N))) (let ((_let_2 (@ (@ tptp.ord_less_eq_nat M2) N))) (and (=> _let_2 (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.minus_minus_real (@ F2 K3)) (@ F2 (@ (@ tptp.plus_plus_nat K3) tptp.one_one_nat))))) _let_1) (@ (@ tptp.minus_minus_real (@ F2 M2)) (@ F2 (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat))))) (=> (not _let_2) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.minus_minus_real (@ F2 K3)) (@ F2 (@ (@ tptp.plus_plus_nat K3) tptp.one_one_nat))))) _let_1) tptp.zero_zero_real)))))))
% 6.73/7.06 (assert (forall ((M2 tptp.nat) (N tptp.nat) (F2 (-> tptp.nat tptp.rat))) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ tptp.minus_minus_rat (@ F2 K3)) (@ F2 (@ (@ tptp.minus_minus_nat K3) tptp.one_one_nat))))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M2)) N)) (@ (@ tptp.minus_minus_rat (@ F2 N)) (@ F2 M2))))))
% 6.73/7.06 (assert (forall ((M2 tptp.nat) (N tptp.nat) (F2 (-> tptp.nat tptp.int))) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((K3 tptp.nat)) (@ (@ tptp.minus_minus_int (@ F2 K3)) (@ F2 (@ (@ tptp.minus_minus_nat K3) tptp.one_one_nat))))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M2)) N)) (@ (@ tptp.minus_minus_int (@ F2 N)) (@ F2 M2))))))
% 6.73/7.06 (assert (forall ((M2 tptp.nat) (N tptp.nat) (F2 (-> tptp.nat tptp.real))) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.minus_minus_real (@ F2 K3)) (@ F2 (@ (@ tptp.minus_minus_nat K3) tptp.one_one_nat))))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M2)) N)) (@ (@ tptp.minus_minus_real (@ F2 N)) (@ F2 M2))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A4) (= (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.nat_set_encode A4)) (not (@ (@ tptp.member_nat tptp.zero_zero_nat) A4))))))
% 6.73/7.06 (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))))))))
% 6.73/7.06 (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))))))))
% 6.73/7.06 (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))))))))
% 6.73/7.06 (assert (forall ((M2 tptp.nat) (N tptp.nat) (X tptp.code_integer)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger X))) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.minus_8373710615458151222nteger tptp.one_one_Code_integer) X)) (@ (@ tptp.groups7501900531339628137nteger _let_1) (@ (@ tptp.set_or1269000886237332187st_nat M2) N))) (@ (@ tptp.minus_8373710615458151222nteger (@ _let_1 M2)) (@ _let_1 (@ tptp.suc N))))))))
% 6.73/7.06 (assert (forall ((M2 tptp.nat) (N tptp.nat) (X tptp.complex)) (let ((_let_1 (@ tptp.power_power_complex X))) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex tptp.one_one_complex) X)) (@ (@ tptp.groups2073611262835488442omplex _let_1) (@ (@ tptp.set_or1269000886237332187st_nat M2) N))) (@ (@ tptp.minus_minus_complex (@ _let_1 M2)) (@ _let_1 (@ tptp.suc N))))))))
% 6.73/7.06 (assert (forall ((M2 tptp.nat) (N tptp.nat) (X tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat X))) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat tptp.one_one_rat) X)) (@ (@ tptp.groups2906978787729119204at_rat _let_1) (@ (@ tptp.set_or1269000886237332187st_nat M2) N))) (@ (@ tptp.minus_minus_rat (@ _let_1 M2)) (@ _let_1 (@ tptp.suc N))))))))
% 6.73/7.06 (assert (forall ((M2 tptp.nat) (N tptp.nat) (X tptp.int)) (let ((_let_1 (@ tptp.power_power_int X))) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int tptp.one_one_int) X)) (@ (@ tptp.groups3539618377306564664at_int _let_1) (@ (@ tptp.set_or1269000886237332187st_nat M2) N))) (@ (@ tptp.minus_minus_int (@ _let_1 M2)) (@ _let_1 (@ tptp.suc N))))))))
% 6.73/7.06 (assert (forall ((M2 tptp.nat) (N tptp.nat) (X tptp.real)) (let ((_let_1 (@ tptp.power_power_real X))) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real tptp.one_one_real) X)) (@ (@ tptp.groups6591440286371151544t_real _let_1) (@ (@ tptp.set_or1269000886237332187st_nat M2) N))) (@ (@ tptp.minus_minus_real (@ _let_1 M2)) (@ _let_1 (@ tptp.suc N))))))))
% 6.73/7.06 (assert (forall ((G2 (-> tptp.nat tptp.rat)) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.groups2906978787729119204at_rat G2) (@ (@ tptp.set_or1269000886237332187st_nat (@ _let_1 M2)) (@ tptp.suc (@ _let_1 N)))) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I))) (@ (@ tptp.plus_plus_rat (@ G2 _let_1)) (@ G2 (@ tptp.suc _let_1)))))) (@ (@ tptp.set_or1269000886237332187st_nat M2) N))))))
% 6.73/7.06 (assert (forall ((G2 (-> tptp.nat tptp.int)) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.groups3539618377306564664at_int G2) (@ (@ tptp.set_or1269000886237332187st_nat (@ _let_1 M2)) (@ tptp.suc (@ _let_1 N)))) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I))) (@ (@ tptp.plus_plus_int (@ G2 _let_1)) (@ G2 (@ tptp.suc _let_1)))))) (@ (@ tptp.set_or1269000886237332187st_nat M2) N))))))
% 6.73/7.06 (assert (forall ((G2 (-> tptp.nat tptp.nat)) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.groups3542108847815614940at_nat G2) (@ (@ tptp.set_or1269000886237332187st_nat (@ _let_1 M2)) (@ tptp.suc (@ _let_1 N)))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I))) (@ (@ tptp.plus_plus_nat (@ G2 _let_1)) (@ G2 (@ tptp.suc _let_1)))))) (@ (@ tptp.set_or1269000886237332187st_nat M2) N))))))
% 6.73/7.06 (assert (forall ((G2 (-> tptp.nat tptp.real)) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.groups6591440286371151544t_real G2) (@ (@ tptp.set_or1269000886237332187st_nat (@ _let_1 M2)) (@ tptp.suc (@ _let_1 N)))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I))) (@ (@ tptp.plus_plus_real (@ G2 _let_1)) (@ G2 (@ tptp.suc _let_1)))))) (@ (@ tptp.set_or1269000886237332187st_nat M2) N))))))
% 6.73/7.06 (assert (forall ((M2 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 M2)) tptp.one_one_Code_integer)) (@ _let_2 N))) (@ (@ tptp.ord_less_eq_nat M2) N))))))
% 6.73/7.06 (assert (forall ((M2 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 M2)) tptp.one_one_nat)) (@ _let_2 N))) (@ (@ tptp.ord_less_eq_nat M2) N))))))
% 6.73/7.06 (assert (forall ((M2 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 M2)) tptp.one_one_int)) (@ _let_2 N))) (@ (@ tptp.ord_less_eq_nat M2) N))))))
% 6.73/7.06 (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))))))))
% 6.73/7.06 (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))))))))
% 6.73/7.06 (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))))))))
% 6.73/7.06 (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))))))))
% 6.73/7.06 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X4 tptp.nat)) X4)) (@ (@ 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))))))
% 6.73/7.06 (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))))))))
% 6.73/7.06 (assert (forall ((M2 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 M2)) tptp.one_one_Code_integer)) _let_3)) (or (= _let_3 tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_less_eq_nat M2) N))))))))
% 6.73/7.06 (assert (forall ((M2 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 M2)) tptp.one_one_nat)) _let_3)) (or (= _let_3 tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_nat M2) N))))))))
% 6.73/7.06 (assert (forall ((M2 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 M2)) tptp.one_one_int)) _let_3)) (or (= _let_3 tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_nat M2) N))))))))
% 6.73/7.06 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri4939895301339042750nteger N))) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups7501900531339628137nteger tptp.semiri4939895301339042750nteger) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N))) (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.plus_p5714425477246183910nteger _let_1) tptp.one_one_Code_integer))))))
% 6.73/7.06 (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))))))
% 6.73/7.06 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri4216267220026989637d_enat N))) (= (@ (@ tptp.times_7803423173614009249d_enat (@ tptp.numera1916890842035813515d_enat (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups7108830773950497114d_enat tptp.semiri4216267220026989637d_enat) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N))) (@ (@ tptp.times_7803423173614009249d_enat _let_1) (@ (@ tptp.plus_p3455044024723400733d_enat _let_1) tptp.one_on7984719198319812577d_enat))))))
% 6.73/7.06 (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))))))
% 6.73/7.06 (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))))))
% 6.73/7.06 (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))))))
% 6.73/7.06 (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))))))
% 6.73/7.06 (assert (forall ((A tptp.code_integer) (D tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri4939895301339042750nteger N))) (let ((_let_2 (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (= (@ _let_2 (@ (@ tptp.groups7501900531339628137nteger (lambda ((I tptp.nat)) (@ (@ tptp.plus_p5714425477246183910nteger A) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.semiri4939895301339042750nteger I)) D)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N))) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.plus_p5714425477246183910nteger _let_1) tptp.one_one_Code_integer)) (@ (@ tptp.plus_p5714425477246183910nteger (@ _let_2 A)) (@ (@ tptp.times_3573771949741848930nteger _let_1) D))))))))
% 6.73/7.06 (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 ((I tptp.nat)) (@ (@ tptp.plus_plus_rat A) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat I)) 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))))))))
% 6.73/7.06 (assert (forall ((A tptp.extended_enat) (D tptp.extended_enat) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri4216267220026989637d_enat N))) (let ((_let_2 (@ tptp.times_7803423173614009249d_enat (@ tptp.numera1916890842035813515d_enat (@ tptp.bit0 tptp.one))))) (= (@ _let_2 (@ (@ tptp.groups7108830773950497114d_enat (lambda ((I tptp.nat)) (@ (@ tptp.plus_p3455044024723400733d_enat A) (@ (@ tptp.times_7803423173614009249d_enat (@ tptp.semiri4216267220026989637d_enat I)) D)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N))) (@ (@ tptp.times_7803423173614009249d_enat (@ (@ tptp.plus_p3455044024723400733d_enat _let_1) tptp.one_on7984719198319812577d_enat)) (@ (@ tptp.plus_p3455044024723400733d_enat (@ _let_2 A)) (@ (@ tptp.times_7803423173614009249d_enat _let_1) D))))))))
% 6.73/7.06 (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 ((I tptp.nat)) (@ (@ tptp.plus_plus_complex A) (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex I)) 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))))))))
% 6.73/7.06 (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 ((I tptp.nat)) (@ (@ tptp.plus_plus_int A) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int I)) 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))))))))
% 6.73/7.06 (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 ((I tptp.nat)) (@ (@ tptp.plus_plus_nat A) (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat I)) 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))))))))
% 6.73/7.06 (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 ((I tptp.nat)) (@ (@ tptp.plus_plus_real A) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real I)) 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))))))))
% 6.73/7.06 (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 ((I tptp.nat)) (@ (@ tptp.plus_plus_nat A) (@ (@ tptp.times_times_nat I) 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)))))
% 6.73/7.06 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X4 tptp.nat)) X4)) (@ (@ tptp.set_or1269000886237332187st_nat M2) 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 M2) (@ (@ tptp.minus_minus_nat M2) tptp.one_one_nat)))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 6.73/7.06 (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))))))
% 6.73/7.06 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri4939895301339042750nteger N))) (= (@ (@ tptp.groups7501900531339628137nteger tptp.semiri4939895301339042750nteger) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)) (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.plus_p5714425477246183910nteger _let_1) tptp.one_one_Code_integer))) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))))))
% 6.73/7.06 (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)))))))
% 6.73/7.06 (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)))))))
% 6.73/7.06 (assert (forall ((A tptp.code_integer) (D tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.semiri4939895301339042750nteger N))) (= (@ (@ tptp.groups7501900531339628137nteger (lambda ((I tptp.nat)) (@ (@ tptp.plus_p5714425477246183910nteger A) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.semiri4939895301339042750nteger I)) D)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)) (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.plus_p5714425477246183910nteger _let_2) tptp.one_one_Code_integer)) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger _let_1) A)) (@ (@ tptp.times_3573771949741848930nteger _let_2) D)))) _let_1))))))
% 6.73/7.06 (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 ((I tptp.nat)) (@ (@ tptp.plus_plus_int A) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int I)) 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))))))
% 6.73/7.06 (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 ((I tptp.nat)) (@ (@ tptp.plus_plus_nat A) (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat I)) 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))))))
% 6.73/7.06 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri4939895301339042750nteger N))) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups7501900531339628137nteger tptp.semiri4939895301339042750nteger) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N))) (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.plus_p5714425477246183910nteger _let_1) tptp.one_one_Code_integer))))))
% 6.73/7.06 (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))))))
% 6.73/7.06 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri4216267220026989637d_enat N))) (= (@ (@ tptp.times_7803423173614009249d_enat (@ tptp.numera1916890842035813515d_enat (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups7108830773950497114d_enat tptp.semiri4216267220026989637d_enat) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N))) (@ (@ tptp.times_7803423173614009249d_enat _let_1) (@ (@ tptp.plus_p3455044024723400733d_enat _let_1) tptp.one_on7984719198319812577d_enat))))))
% 6.73/7.06 (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))))))
% 6.73/7.06 (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))))))
% 6.73/7.06 (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))))))
% 6.73/7.06 (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))))))
% 6.73/7.06 (assert (forall ((A tptp.nat) (M2 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 M2))) _let_4)) (or (@ (@ tptp.ord_less_nat N) M2) (= _let_4 tptp.zero_zero_nat) (and (@ (@ tptp.ord_less_eq_nat M2) N) (@ _let_3 (@ (@ tptp.divide_divide_nat A) (@ _let_2 (@ (@ tptp.minus_minus_nat N) M2)))))))))))))
% 6.73/7.06 (assert (forall ((A tptp.int) (M2 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 M2))) _let_4)) (or (@ (@ tptp.ord_less_nat N) M2) (= _let_4 tptp.zero_zero_int) (and (@ (@ tptp.ord_less_eq_nat M2) N) (@ _let_3 (@ (@ tptp.divide_divide_int A) (@ _let_2 (@ (@ tptp.minus_minus_nat N) M2)))))))))))))
% 6.73/7.06 (assert (forall ((X tptp.complex) (M2 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 M2) (@ (@ tptp.plus_plus_nat M2) 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 M2)) (@ _let_1 (@ _let_2 (@ tptp.suc N))))) (@ _let_1 X)))))))))))
% 6.73/7.06 (assert (forall ((X tptp.rat) (M2 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 M2) (@ (@ tptp.plus_plus_nat M2) 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 M2)) (@ _let_1 (@ _let_2 (@ tptp.suc N))))) (@ _let_1 X)))))))))))
% 6.73/7.06 (assert (forall ((X tptp.real) (M2 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 M2) (@ (@ tptp.plus_plus_nat M2) 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 M2)) (@ _let_1 (@ _let_2 (@ tptp.suc N))))) (@ _let_1 X)))))))))))
% 6.73/7.06 (assert (forall ((Va3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.suc (@ tptp.suc Va3)))) (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))))))))))))))))
% 6.73/7.06 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri4939895301339042750nteger N))) (= (@ (@ tptp.groups7501900531339628137nteger tptp.semiri4939895301339042750nteger) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N)) (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.plus_p5714425477246183910nteger _let_1) tptp.one_one_Code_integer))) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))))))
% 6.73/7.06 (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)))))))
% 6.73/7.06 (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)))))))
% 6.73/7.06 (assert (@ (@ tptp.sums_real (lambda ((N4 tptp.nat)) (@ (@ tptp.power_power_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.suc N4)))) tptp.one_one_real))
% 6.73/7.06 (assert (@ (@ tptp.sums_complex (lambda ((N4 tptp.nat)) tptp.zero_zero_complex)) tptp.zero_zero_complex))
% 6.73/7.06 (assert (@ (@ tptp.sums_real (lambda ((N4 tptp.nat)) tptp.zero_zero_real)) tptp.zero_zero_real))
% 6.73/7.06 (assert (@ (@ tptp.sums_nat (lambda ((N4 tptp.nat)) tptp.zero_zero_nat)) tptp.zero_zero_nat))
% 6.73/7.06 (assert (@ (@ tptp.sums_int (lambda ((N4 tptp.nat)) tptp.zero_zero_int)) tptp.zero_zero_int))
% 6.73/7.06 (assert (forall ((M2 tptp.nat) (Z3 tptp.complex)) (@ (@ tptp.sums_complex (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ (@ tptp.if_complex (= N4 M2)) tptp.one_one_complex) tptp.zero_zero_complex)) (@ (@ tptp.power_power_complex Z3) N4)))) (@ (@ tptp.power_power_complex Z3) M2))))
% 6.73/7.06 (assert (forall ((M2 tptp.nat) (Z3 tptp.real)) (@ (@ tptp.sums_real (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ (@ tptp.if_real (= N4 M2)) tptp.one_one_real) tptp.zero_zero_real)) (@ (@ tptp.power_power_real Z3) N4)))) (@ (@ tptp.power_power_real Z3) M2))))
% 6.73/7.06 (assert (forall ((M2 tptp.nat) (Z3 tptp.int)) (@ (@ tptp.sums_int (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_int (@ (@ (@ tptp.if_int (= N4 M2)) tptp.one_one_int) tptp.zero_zero_int)) (@ (@ tptp.power_power_int Z3) N4)))) (@ (@ tptp.power_power_int Z3) M2))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_nat) (F2 (-> tptp.nat tptp.complex))) (=> (@ tptp.finite_finite_nat A4) (@ (@ tptp.sums_complex (lambda ((R tptp.nat)) (@ (@ (@ tptp.if_complex (@ (@ tptp.member_nat R) A4)) (@ F2 R)) tptp.zero_zero_complex))) (@ (@ tptp.groups2073611262835488442omplex F2) A4)))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_nat) (F2 (-> tptp.nat tptp.int))) (=> (@ tptp.finite_finite_nat A4) (@ (@ tptp.sums_int (lambda ((R tptp.nat)) (@ (@ (@ tptp.if_int (@ (@ tptp.member_nat R) A4)) (@ F2 R)) tptp.zero_zero_int))) (@ (@ tptp.groups3539618377306564664at_int F2) A4)))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_nat) (F2 (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_nat A4) (@ (@ tptp.sums_nat (lambda ((R tptp.nat)) (@ (@ (@ tptp.if_nat (@ (@ tptp.member_nat R) A4)) (@ F2 R)) tptp.zero_zero_nat))) (@ (@ tptp.groups3542108847815614940at_nat F2) A4)))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_nat) (F2 (-> tptp.nat tptp.real))) (=> (@ tptp.finite_finite_nat A4) (@ (@ tptp.sums_real (lambda ((R tptp.nat)) (@ (@ (@ tptp.if_real (@ (@ tptp.member_nat R) A4)) (@ F2 R)) tptp.zero_zero_real))) (@ (@ tptp.groups6591440286371151544t_real F2) A4)))))
% 6.73/7.06 (assert (forall ((P2 (-> tptp.nat Bool)) (F2 (-> tptp.nat tptp.complex))) (let ((_let_1 (@ tptp.collect_nat P2))) (=> (@ tptp.finite_finite_nat _let_1) (@ (@ tptp.sums_complex (lambda ((R tptp.nat)) (@ (@ (@ tptp.if_complex (@ P2 R)) (@ F2 R)) tptp.zero_zero_complex))) (@ (@ tptp.groups2073611262835488442omplex F2) _let_1))))))
% 6.73/7.06 (assert (forall ((P2 (-> tptp.nat Bool)) (F2 (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.collect_nat P2))) (=> (@ tptp.finite_finite_nat _let_1) (@ (@ tptp.sums_int (lambda ((R tptp.nat)) (@ (@ (@ tptp.if_int (@ P2 R)) (@ F2 R)) tptp.zero_zero_int))) (@ (@ tptp.groups3539618377306564664at_int F2) _let_1))))))
% 6.73/7.06 (assert (forall ((P2 (-> tptp.nat Bool)) (F2 (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.collect_nat P2))) (=> (@ tptp.finite_finite_nat _let_1) (@ (@ tptp.sums_nat (lambda ((R tptp.nat)) (@ (@ (@ tptp.if_nat (@ P2 R)) (@ F2 R)) tptp.zero_zero_nat))) (@ (@ tptp.groups3542108847815614940at_nat F2) _let_1))))))
% 6.73/7.06 (assert (forall ((P2 (-> tptp.nat Bool)) (F2 (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.collect_nat P2))) (=> (@ tptp.finite_finite_nat _let_1) (@ (@ tptp.sums_real (lambda ((R tptp.nat)) (@ (@ (@ tptp.if_real (@ P2 R)) (@ F2 R)) tptp.zero_zero_real))) (@ (@ tptp.groups6591440286371151544t_real F2) _let_1))))))
% 6.73/7.06 (assert (forall ((N6 tptp.set_nat) (F2 (-> tptp.nat tptp.complex))) (=> (@ tptp.finite_finite_nat N6) (=> (forall ((N3 tptp.nat)) (=> (not (@ (@ tptp.member_nat N3) N6)) (= (@ F2 N3) tptp.zero_zero_complex))) (@ (@ tptp.sums_complex F2) (@ (@ tptp.groups2073611262835488442omplex F2) N6))))))
% 6.73/7.06 (assert (forall ((N6 tptp.set_nat) (F2 (-> tptp.nat tptp.int))) (=> (@ tptp.finite_finite_nat N6) (=> (forall ((N3 tptp.nat)) (=> (not (@ (@ tptp.member_nat N3) N6)) (= (@ F2 N3) tptp.zero_zero_int))) (@ (@ tptp.sums_int F2) (@ (@ tptp.groups3539618377306564664at_int F2) N6))))))
% 6.73/7.06 (assert (forall ((N6 tptp.set_nat) (F2 (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_nat N6) (=> (forall ((N3 tptp.nat)) (=> (not (@ (@ tptp.member_nat N3) N6)) (= (@ F2 N3) tptp.zero_zero_nat))) (@ (@ tptp.sums_nat F2) (@ (@ tptp.groups3542108847815614940at_nat F2) N6))))))
% 6.73/7.06 (assert (forall ((N6 tptp.set_nat) (F2 (-> tptp.nat tptp.real))) (=> (@ tptp.finite_finite_nat N6) (=> (forall ((N3 tptp.nat)) (=> (not (@ (@ tptp.member_nat N3) N6)) (= (@ F2 N3) tptp.zero_zero_real))) (@ (@ tptp.sums_real F2) (@ (@ tptp.groups6591440286371151544t_real F2) N6))))))
% 6.73/7.06 (assert (forall ((N tptp.nat) (F2 (-> tptp.nat tptp.complex)) (S2 tptp.complex)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) N) (= (@ F2 I3) tptp.zero_zero_complex))) (= (@ (@ tptp.sums_complex (lambda ((I tptp.nat)) (@ F2 (@ (@ tptp.plus_plus_nat I) N)))) S2) (@ (@ tptp.sums_complex F2) S2)))))
% 6.73/7.06 (assert (forall ((N tptp.nat) (F2 (-> tptp.nat tptp.real)) (S2 tptp.real)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) N) (= (@ F2 I3) tptp.zero_zero_real))) (= (@ (@ tptp.sums_real (lambda ((I tptp.nat)) (@ F2 (@ (@ tptp.plus_plus_nat I) N)))) S2) (@ (@ tptp.sums_real F2) S2)))))
% 6.73/7.06 (assert (forall ((K2 tptp.int) (M2 tptp.int) (T tptp.int)) (let ((_let_1 (@ tptp.times_times_int K2))) (=> (not (= K2 tptp.zero_zero_int)) (= (@ (@ tptp.dvd_dvd_int M2) T) (@ (@ tptp.dvd_dvd_int (@ _let_1 M2)) (@ _let_1 T)))))))
% 6.73/7.06 (assert (forall ((K2 tptp.int) (M2 tptp.int) (N tptp.int)) (let ((_let_1 (@ tptp.times_times_int K2))) (=> (@ (@ tptp.dvd_dvd_int (@ _let_1 M2)) (@ _let_1 N)) (=> (not (= K2 tptp.zero_zero_int)) (@ (@ tptp.dvd_dvd_int M2) N))))))
% 6.73/7.06 (assert (forall ((A tptp.int) (D tptp.int) (X tptp.int) (T tptp.int) (C2 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 C2) D))) T))))))))
% 6.73/7.06 (assert (forall ((K2 tptp.int) (N tptp.int) (M2 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int K2))) (= (@ _let_1 (@ (@ tptp.plus_plus_int N) (@ (@ tptp.times_times_int K2) M2))) (@ _let_1 N)))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_complex) (G2 (-> tptp.complex tptp.nat)) (F2 (-> tptp.complex tptp.nat))) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) A4) (@ (@ tptp.ord_less_eq_nat (@ G2 X3)) (@ F2 X3)))) (= (@ (@ tptp.groups5693394587270226106ex_nat (lambda ((X4 tptp.complex)) (@ (@ tptp.minus_minus_nat (@ F2 X4)) (@ G2 X4)))) A4) (@ (@ tptp.minus_minus_nat (@ (@ tptp.groups5693394587270226106ex_nat F2) A4)) (@ (@ tptp.groups5693394587270226106ex_nat G2) A4))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_real) (G2 (-> tptp.real tptp.nat)) (F2 (-> tptp.real tptp.nat))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) A4) (@ (@ tptp.ord_less_eq_nat (@ G2 X3)) (@ F2 X3)))) (= (@ (@ tptp.groups1935376822645274424al_nat (lambda ((X4 tptp.real)) (@ (@ tptp.minus_minus_nat (@ F2 X4)) (@ G2 X4)))) A4) (@ (@ tptp.minus_minus_nat (@ (@ tptp.groups1935376822645274424al_nat F2) A4)) (@ (@ tptp.groups1935376822645274424al_nat G2) A4))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_set_nat) (G2 (-> tptp.set_nat tptp.nat)) (F2 (-> tptp.set_nat tptp.nat))) (=> (forall ((X3 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat X3) A4) (@ (@ tptp.ord_less_eq_nat (@ G2 X3)) (@ F2 X3)))) (= (@ (@ tptp.groups8294997508430121362at_nat (lambda ((X4 tptp.set_nat)) (@ (@ tptp.minus_minus_nat (@ F2 X4)) (@ G2 X4)))) A4) (@ (@ tptp.minus_minus_nat (@ (@ tptp.groups8294997508430121362at_nat F2) A4)) (@ (@ tptp.groups8294997508430121362at_nat G2) A4))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_int) (G2 (-> tptp.int tptp.nat)) (F2 (-> tptp.int tptp.nat))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A4) (@ (@ tptp.ord_less_eq_nat (@ G2 X3)) (@ F2 X3)))) (= (@ (@ tptp.groups4541462559716669496nt_nat (lambda ((X4 tptp.int)) (@ (@ tptp.minus_minus_nat (@ F2 X4)) (@ G2 X4)))) A4) (@ (@ tptp.minus_minus_nat (@ (@ tptp.groups4541462559716669496nt_nat F2) A4)) (@ (@ tptp.groups4541462559716669496nt_nat G2) A4))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_nat) (G2 (-> tptp.nat tptp.nat)) (F2 (-> tptp.nat tptp.nat))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A4) (@ (@ tptp.ord_less_eq_nat (@ G2 X3)) (@ F2 X3)))) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X4 tptp.nat)) (@ (@ tptp.minus_minus_nat (@ F2 X4)) (@ G2 X4)))) A4) (@ (@ tptp.minus_minus_nat (@ (@ tptp.groups3542108847815614940at_nat F2) A4)) (@ (@ tptp.groups3542108847815614940at_nat G2) A4))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_int) (F2 (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int A4) (= (= (@ (@ tptp.groups4541462559716669496nt_nat F2) A4) (@ tptp.suc tptp.zero_zero_nat)) (exists ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) A4) (= (@ F2 X4) (@ tptp.suc tptp.zero_zero_nat)) (forall ((Y4 tptp.int)) (=> (@ (@ tptp.member_int Y4) A4) (=> (not (= X4 Y4)) (= (@ F2 Y4) tptp.zero_zero_nat))))))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_complex) (F2 (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex A4) (= (= (@ (@ tptp.groups5693394587270226106ex_nat F2) A4) (@ tptp.suc tptp.zero_zero_nat)) (exists ((X4 tptp.complex)) (and (@ (@ tptp.member_complex X4) A4) (= (@ F2 X4) (@ tptp.suc tptp.zero_zero_nat)) (forall ((Y4 tptp.complex)) (=> (@ (@ tptp.member_complex Y4) A4) (=> (not (= X4 Y4)) (= (@ F2 Y4) tptp.zero_zero_nat))))))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_nat) (F2 (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_nat A4) (= (= (@ (@ tptp.groups3542108847815614940at_nat F2) A4) (@ tptp.suc tptp.zero_zero_nat)) (exists ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) A4) (= (@ F2 X4) (@ tptp.suc tptp.zero_zero_nat)) (forall ((Y4 tptp.nat)) (=> (@ (@ tptp.member_nat Y4) A4) (=> (not (= X4 Y4)) (= (@ F2 Y4) tptp.zero_zero_nat))))))))))
% 6.73/7.06 (assert (forall ((F2 (-> tptp.nat tptp.nat)) (A4 tptp.set_nat) (N tptp.nat)) (=> (= (@ (@ tptp.groups3542108847815614940at_nat F2) A4) (@ tptp.suc N)) (exists ((X3 tptp.nat)) (and (@ (@ tptp.member_nat X3) A4) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F2 X3)))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_int) (F2 (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int A4) (= (= (@ (@ tptp.groups4541462559716669496nt_nat F2) A4) tptp.one_one_nat) (exists ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) A4) (= (@ F2 X4) tptp.one_one_nat) (forall ((Y4 tptp.int)) (=> (@ (@ tptp.member_int Y4) A4) (=> (not (= X4 Y4)) (= (@ F2 Y4) tptp.zero_zero_nat))))))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_complex) (F2 (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex A4) (= (= (@ (@ tptp.groups5693394587270226106ex_nat F2) A4) tptp.one_one_nat) (exists ((X4 tptp.complex)) (and (@ (@ tptp.member_complex X4) A4) (= (@ F2 X4) tptp.one_one_nat) (forall ((Y4 tptp.complex)) (=> (@ (@ tptp.member_complex Y4) A4) (=> (not (= X4 Y4)) (= (@ F2 Y4) tptp.zero_zero_nat))))))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_nat) (F2 (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_nat A4) (= (= (@ (@ tptp.groups3542108847815614940at_nat F2) A4) tptp.one_one_nat) (exists ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) A4) (= (@ F2 X4) tptp.one_one_nat) (forall ((Y4 tptp.nat)) (=> (@ (@ tptp.member_nat Y4) A4) (=> (not (= X4 Y4)) (= (@ F2 Y4) tptp.zero_zero_nat))))))))))
% 6.73/7.06 (assert (forall ((F2 (-> tptp.complex tptp.nat)) (A4 tptp.set_complex)) (= (@ (@ tptp.groups5693394587270226106ex_nat (lambda ((X4 tptp.complex)) (@ tptp.suc (@ F2 X4)))) A4) (@ (@ tptp.plus_plus_nat (@ (@ tptp.groups5693394587270226106ex_nat F2) A4)) (@ tptp.finite_card_complex A4)))))
% 6.73/7.06 (assert (forall ((F2 (-> tptp.int tptp.nat)) (A4 tptp.set_int)) (= (@ (@ tptp.groups4541462559716669496nt_nat (lambda ((X4 tptp.int)) (@ tptp.suc (@ F2 X4)))) A4) (@ (@ tptp.plus_plus_nat (@ (@ tptp.groups4541462559716669496nt_nat F2) A4)) (@ tptp.finite_card_int A4)))))
% 6.73/7.06 (assert (forall ((F2 (-> tptp.list_nat tptp.nat)) (A4 tptp.set_list_nat)) (= (@ (@ tptp.groups4396056296759096172at_nat (lambda ((X4 tptp.list_nat)) (@ tptp.suc (@ F2 X4)))) A4) (@ (@ tptp.plus_plus_nat (@ (@ tptp.groups4396056296759096172at_nat F2) A4)) (@ tptp.finite_card_list_nat A4)))))
% 6.73/7.06 (assert (forall ((F2 (-> tptp.set_nat tptp.nat)) (A4 tptp.set_set_nat)) (= (@ (@ tptp.groups8294997508430121362at_nat (lambda ((X4 tptp.set_nat)) (@ tptp.suc (@ F2 X4)))) A4) (@ (@ tptp.plus_plus_nat (@ (@ tptp.groups8294997508430121362at_nat F2) A4)) (@ tptp.finite_card_set_nat A4)))))
% 6.73/7.06 (assert (forall ((F2 (-> tptp.nat tptp.nat)) (A4 tptp.set_nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X4 tptp.nat)) (@ tptp.suc (@ F2 X4)))) A4) (@ (@ tptp.plus_plus_nat (@ (@ tptp.groups3542108847815614940at_nat F2) A4)) (@ tptp.finite_card_nat A4)))))
% 6.73/7.06 (assert (forall ((S3 tptp.set_real) (T5 tptp.set_real) (R2 (-> tptp.real tptp.real Bool)) (K2 tptp.nat)) (=> (@ tptp.finite_finite_real S3) (=> (@ tptp.finite_finite_real T5) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) T5) (= (@ tptp.finite_card_real (@ tptp.collect_real (lambda ((I tptp.real)) (and (@ (@ tptp.member_real I) S3) (@ (@ R2 I) X3))))) K2))) (= (@ (@ tptp.groups1935376822645274424al_nat (lambda ((I tptp.real)) (@ tptp.finite_card_real (@ tptp.collect_real (lambda ((J tptp.real)) (and (@ (@ tptp.member_real J) T5) (@ (@ R2 I) J))))))) S3) (@ (@ tptp.times_times_nat K2) (@ tptp.finite_card_real T5))))))))
% 6.73/7.06 (assert (forall ((S3 tptp.set_real) (T5 tptp.set_nat) (R2 (-> tptp.real tptp.nat Bool)) (K2 tptp.nat)) (=> (@ tptp.finite_finite_real S3) (=> (@ tptp.finite_finite_nat T5) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) T5) (= (@ tptp.finite_card_real (@ tptp.collect_real (lambda ((I tptp.real)) (and (@ (@ tptp.member_real I) S3) (@ (@ R2 I) X3))))) K2))) (= (@ (@ tptp.groups1935376822645274424al_nat (lambda ((I tptp.real)) (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((J tptp.nat)) (and (@ (@ tptp.member_nat J) T5) (@ (@ R2 I) J))))))) S3) (@ (@ tptp.times_times_nat K2) (@ tptp.finite_card_nat T5))))))))
% 6.73/7.06 (assert (forall ((S3 tptp.set_real) (T5 tptp.set_int) (R2 (-> tptp.real tptp.int Bool)) (K2 tptp.nat)) (=> (@ tptp.finite_finite_real S3) (=> (@ tptp.finite_finite_int T5) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) T5) (= (@ tptp.finite_card_real (@ tptp.collect_real (lambda ((I tptp.real)) (and (@ (@ tptp.member_real I) S3) (@ (@ R2 I) X3))))) K2))) (= (@ (@ tptp.groups1935376822645274424al_nat (lambda ((I tptp.real)) (@ tptp.finite_card_int (@ tptp.collect_int (lambda ((J tptp.int)) (and (@ (@ tptp.member_int J) T5) (@ (@ R2 I) J))))))) S3) (@ (@ tptp.times_times_nat K2) (@ tptp.finite_card_int T5))))))))
% 6.73/7.06 (assert (forall ((S3 tptp.set_real) (T5 tptp.set_complex) (R2 (-> tptp.real tptp.complex Bool)) (K2 tptp.nat)) (=> (@ tptp.finite_finite_real S3) (=> (@ tptp.finite3207457112153483333omplex T5) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) T5) (= (@ tptp.finite_card_real (@ tptp.collect_real (lambda ((I tptp.real)) (and (@ (@ tptp.member_real I) S3) (@ (@ R2 I) X3))))) K2))) (= (@ (@ tptp.groups1935376822645274424al_nat (lambda ((I tptp.real)) (@ tptp.finite_card_complex (@ tptp.collect_complex (lambda ((J tptp.complex)) (and (@ (@ tptp.member_complex J) T5) (@ (@ R2 I) J))))))) S3) (@ (@ tptp.times_times_nat K2) (@ tptp.finite_card_complex T5))))))))
% 6.73/7.06 (assert (forall ((S3 tptp.set_int) (T5 tptp.set_real) (R2 (-> tptp.int tptp.real Bool)) (K2 tptp.nat)) (=> (@ tptp.finite_finite_int S3) (=> (@ tptp.finite_finite_real T5) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) T5) (= (@ tptp.finite_card_int (@ tptp.collect_int (lambda ((I tptp.int)) (and (@ (@ tptp.member_int I) S3) (@ (@ R2 I) X3))))) K2))) (= (@ (@ tptp.groups4541462559716669496nt_nat (lambda ((I tptp.int)) (@ tptp.finite_card_real (@ tptp.collect_real (lambda ((J tptp.real)) (and (@ (@ tptp.member_real J) T5) (@ (@ R2 I) J))))))) S3) (@ (@ tptp.times_times_nat K2) (@ tptp.finite_card_real T5))))))))
% 6.73/7.06 (assert (forall ((S3 tptp.set_int) (T5 tptp.set_nat) (R2 (-> tptp.int tptp.nat Bool)) (K2 tptp.nat)) (=> (@ tptp.finite_finite_int S3) (=> (@ tptp.finite_finite_nat T5) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) T5) (= (@ tptp.finite_card_int (@ tptp.collect_int (lambda ((I tptp.int)) (and (@ (@ tptp.member_int I) S3) (@ (@ R2 I) X3))))) K2))) (= (@ (@ tptp.groups4541462559716669496nt_nat (lambda ((I tptp.int)) (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((J tptp.nat)) (and (@ (@ tptp.member_nat J) T5) (@ (@ R2 I) J))))))) S3) (@ (@ tptp.times_times_nat K2) (@ tptp.finite_card_nat T5))))))))
% 6.73/7.06 (assert (forall ((S3 tptp.set_int) (T5 tptp.set_int) (R2 (-> tptp.int tptp.int Bool)) (K2 tptp.nat)) (=> (@ tptp.finite_finite_int S3) (=> (@ tptp.finite_finite_int T5) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) T5) (= (@ tptp.finite_card_int (@ tptp.collect_int (lambda ((I tptp.int)) (and (@ (@ tptp.member_int I) S3) (@ (@ R2 I) X3))))) K2))) (= (@ (@ tptp.groups4541462559716669496nt_nat (lambda ((I tptp.int)) (@ tptp.finite_card_int (@ tptp.collect_int (lambda ((J tptp.int)) (and (@ (@ tptp.member_int J) T5) (@ (@ R2 I) J))))))) S3) (@ (@ tptp.times_times_nat K2) (@ tptp.finite_card_int T5))))))))
% 6.73/7.06 (assert (forall ((S3 tptp.set_int) (T5 tptp.set_complex) (R2 (-> tptp.int tptp.complex Bool)) (K2 tptp.nat)) (=> (@ tptp.finite_finite_int S3) (=> (@ tptp.finite3207457112153483333omplex T5) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) T5) (= (@ tptp.finite_card_int (@ tptp.collect_int (lambda ((I tptp.int)) (and (@ (@ tptp.member_int I) S3) (@ (@ R2 I) X3))))) K2))) (= (@ (@ tptp.groups4541462559716669496nt_nat (lambda ((I tptp.int)) (@ tptp.finite_card_complex (@ tptp.collect_complex (lambda ((J tptp.complex)) (and (@ (@ tptp.member_complex J) T5) (@ (@ R2 I) J))))))) S3) (@ (@ tptp.times_times_nat K2) (@ tptp.finite_card_complex T5))))))))
% 6.73/7.06 (assert (forall ((S3 tptp.set_complex) (T5 tptp.set_real) (R2 (-> tptp.complex tptp.real Bool)) (K2 tptp.nat)) (=> (@ tptp.finite3207457112153483333omplex S3) (=> (@ tptp.finite_finite_real T5) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) T5) (= (@ tptp.finite_card_complex (@ tptp.collect_complex (lambda ((I tptp.complex)) (and (@ (@ tptp.member_complex I) S3) (@ (@ R2 I) X3))))) K2))) (= (@ (@ tptp.groups5693394587270226106ex_nat (lambda ((I tptp.complex)) (@ tptp.finite_card_real (@ tptp.collect_real (lambda ((J tptp.real)) (and (@ (@ tptp.member_real J) T5) (@ (@ R2 I) J))))))) S3) (@ (@ tptp.times_times_nat K2) (@ tptp.finite_card_real T5))))))))
% 6.73/7.06 (assert (forall ((S3 tptp.set_complex) (T5 tptp.set_nat) (R2 (-> tptp.complex tptp.nat Bool)) (K2 tptp.nat)) (=> (@ tptp.finite3207457112153483333omplex S3) (=> (@ tptp.finite_finite_nat T5) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) T5) (= (@ tptp.finite_card_complex (@ tptp.collect_complex (lambda ((I tptp.complex)) (and (@ (@ tptp.member_complex I) S3) (@ (@ R2 I) X3))))) K2))) (= (@ (@ tptp.groups5693394587270226106ex_nat (lambda ((I tptp.complex)) (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((J tptp.nat)) (and (@ (@ tptp.member_nat J) T5) (@ (@ R2 I) J))))))) S3) (@ (@ tptp.times_times_nat K2) (@ tptp.finite_card_nat T5))))))))
% 6.73/7.06 (assert (forall ((K2 tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.modulo_modulo_int K2) L)) (or (@ (@ tptp.dvd_dvd_int L) K2) (and (= L tptp.zero_zero_int) (@ _let_1 K2)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) L))))))
% 6.73/7.06 (assert (forall ((Xs2 tptp.list_complex) (X8 tptp.set_complex)) (=> (@ (@ tptp.ord_le211207098394363844omplex (@ tptp.set_complex2 Xs2)) X8) (=> (@ tptp.finite3207457112153483333omplex X8) (= (@ (@ tptp.groups5693394587270226106ex_nat (@ tptp.count_list_complex Xs2)) X8) (@ tptp.size_s3451745648224563538omplex Xs2))))))
% 6.73/7.06 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (X8 tptp.set_VEBT_VEBT)) (=> (@ (@ tptp.ord_le4337996190870823476T_VEBT (@ tptp.set_VEBT_VEBT2 Xs2)) X8) (=> (@ tptp.finite5795047828879050333T_VEBT X8) (= (@ (@ tptp.groups771621172384141258BT_nat (@ tptp.count_list_VEBT_VEBT Xs2)) X8) (@ tptp.size_s6755466524823107622T_VEBT Xs2))))))
% 6.73/7.06 (assert (forall ((Xs2 tptp.list_o) (X8 tptp.set_o)) (=> (@ (@ tptp.ord_less_eq_set_o (@ tptp.set_o2 Xs2)) X8) (=> (@ tptp.finite_finite_o X8) (= (@ (@ tptp.groups8507830703676809646_o_nat (@ tptp.count_list_o Xs2)) X8) (@ tptp.size_size_list_o Xs2))))))
% 6.73/7.06 (assert (forall ((Xs2 tptp.list_int) (X8 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_int2 Xs2)) X8) (=> (@ tptp.finite_finite_int X8) (= (@ (@ tptp.groups4541462559716669496nt_nat (@ tptp.count_list_int Xs2)) X8) (@ tptp.size_size_list_int Xs2))))))
% 6.73/7.06 (assert (forall ((Xs2 tptp.list_nat) (X8 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_nat2 Xs2)) X8) (=> (@ tptp.finite_finite_nat X8) (= (@ (@ tptp.groups3542108847815614940at_nat (@ tptp.count_list_nat Xs2)) X8) (@ tptp.size_size_list_nat Xs2))))))
% 6.73/7.06 (assert (forall ((F2 (-> tptp.nat tptp.real)) (G2 (-> tptp.nat tptp.real)) (S2 tptp.real) (T tptp.real)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ F2 N3)) (@ G2 N3))) (=> (@ (@ tptp.sums_real F2) S2) (=> (@ (@ tptp.sums_real G2) T) (@ (@ tptp.ord_less_eq_real S2) T))))))
% 6.73/7.06 (assert (forall ((F2 (-> tptp.nat tptp.nat)) (G2 (-> tptp.nat tptp.nat)) (S2 tptp.nat) (T tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ F2 N3)) (@ G2 N3))) (=> (@ (@ tptp.sums_nat F2) S2) (=> (@ (@ tptp.sums_nat G2) T) (@ (@ tptp.ord_less_eq_nat S2) T))))))
% 6.73/7.06 (assert (forall ((F2 (-> tptp.nat tptp.int)) (G2 (-> tptp.nat tptp.int)) (S2 tptp.int) (T tptp.int)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ F2 N3)) (@ G2 N3))) (=> (@ (@ tptp.sums_int F2) S2) (=> (@ (@ tptp.sums_int G2) T) (@ (@ tptp.ord_less_eq_int S2) T))))))
% 6.73/7.06 (assert (forall ((F2 (-> tptp.nat tptp.complex))) (=> (forall ((N3 tptp.nat)) (= (@ F2 N3) tptp.zero_zero_complex)) (@ (@ tptp.sums_complex F2) tptp.zero_zero_complex))))
% 6.73/7.06 (assert (forall ((F2 (-> tptp.nat tptp.real))) (=> (forall ((N3 tptp.nat)) (= (@ F2 N3) tptp.zero_zero_real)) (@ (@ tptp.sums_real F2) tptp.zero_zero_real))))
% 6.73/7.06 (assert (forall ((F2 (-> tptp.nat tptp.nat))) (=> (forall ((N3 tptp.nat)) (= (@ F2 N3) tptp.zero_zero_nat)) (@ (@ tptp.sums_nat F2) tptp.zero_zero_nat))))
% 6.73/7.06 (assert (forall ((F2 (-> tptp.nat tptp.int))) (=> (forall ((N3 tptp.nat)) (= (@ F2 N3) tptp.zero_zero_int)) (@ (@ tptp.sums_int F2) tptp.zero_zero_int))))
% 6.73/7.06 (assert (forall ((I2 tptp.nat) (F2 (-> tptp.nat tptp.complex))) (@ (@ tptp.sums_complex (lambda ((R tptp.nat)) (@ (@ (@ tptp.if_complex (= R I2)) (@ F2 R)) tptp.zero_zero_complex))) (@ F2 I2))))
% 6.73/7.06 (assert (forall ((I2 tptp.nat) (F2 (-> tptp.nat tptp.real))) (@ (@ tptp.sums_real (lambda ((R tptp.nat)) (@ (@ (@ tptp.if_real (= R I2)) (@ F2 R)) tptp.zero_zero_real))) (@ F2 I2))))
% 6.73/7.06 (assert (forall ((I2 tptp.nat) (F2 (-> tptp.nat tptp.nat))) (@ (@ tptp.sums_nat (lambda ((R tptp.nat)) (@ (@ (@ tptp.if_nat (= R I2)) (@ F2 R)) tptp.zero_zero_nat))) (@ F2 I2))))
% 6.73/7.06 (assert (forall ((I2 tptp.nat) (F2 (-> tptp.nat tptp.int))) (@ (@ tptp.sums_int (lambda ((R tptp.nat)) (@ (@ (@ tptp.if_int (= R I2)) (@ F2 R)) tptp.zero_zero_int))) (@ F2 I2))))
% 6.73/7.06 (assert (forall ((F2 (-> tptp.nat tptp.real)) (A tptp.real) (C2 tptp.real)) (=> (@ (@ tptp.sums_real F2) A) (@ (@ tptp.sums_real (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_real (@ F2 N4)) C2))) (@ (@ tptp.times_times_real A) C2)))))
% 6.73/7.06 (assert (forall ((F2 (-> tptp.nat tptp.real)) (A tptp.real) (C2 tptp.real)) (=> (@ (@ tptp.sums_real F2) A) (@ (@ tptp.sums_real (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_real C2) (@ F2 N4)))) (@ (@ tptp.times_times_real C2) A)))))
% 6.73/7.06 (assert (forall ((M2 tptp.int) (N tptp.int)) (=> (@ (@ tptp.ord_less_eq_int M2) N) (= (@ (@ tptp.groups4538972089207619220nt_int (lambda ((X4 tptp.int)) X4)) (@ (@ tptp.set_or1266510415728281911st_int M2) 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 M2) (@ (@ tptp.minus_minus_int M2) tptp.one_one_int)))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))))))
% 6.73/7.06 (assert (forall ((C2 tptp.complex) (F2 (-> tptp.nat tptp.complex)) (D tptp.complex)) (=> (not (= C2 tptp.zero_zero_complex)) (= (@ (@ tptp.sums_complex (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_complex C2) (@ F2 N4)))) (@ (@ tptp.times_times_complex C2) D)) (@ (@ tptp.sums_complex F2) D)))))
% 6.73/7.06 (assert (forall ((C2 tptp.real) (F2 (-> tptp.nat tptp.real)) (D tptp.real)) (=> (not (= C2 tptp.zero_zero_real)) (= (@ (@ tptp.sums_real (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_real C2) (@ F2 N4)))) (@ (@ tptp.times_times_real C2) D)) (@ (@ tptp.sums_real F2) D)))))
% 6.73/7.06 (assert (forall ((C2 tptp.complex) (F2 (-> tptp.nat tptp.complex)) (D tptp.complex)) (=> (not (= C2 tptp.zero_zero_complex)) (= (@ (@ tptp.sums_complex (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_complex (@ F2 N4)) C2))) (@ (@ tptp.times_times_complex D) C2)) (@ (@ tptp.sums_complex F2) D)))))
% 6.73/7.06 (assert (forall ((C2 tptp.real) (F2 (-> tptp.nat tptp.real)) (D tptp.real)) (=> (not (= C2 tptp.zero_zero_real)) (= (@ (@ tptp.sums_real (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_real (@ F2 N4)) C2))) (@ (@ tptp.times_times_real D) C2)) (@ (@ tptp.sums_real F2) D)))))
% 6.73/7.06 (assert (forall ((C2 tptp.complex) (F2 (-> tptp.nat tptp.complex)) (A tptp.complex)) (=> (@ (@ tptp.sums_complex (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_complex C2) (@ F2 N4)))) A) (=> (not (= C2 tptp.zero_zero_complex)) (@ (@ tptp.sums_complex F2) (@ (@ tptp.divide1717551699836669952omplex A) C2))))))
% 6.73/7.06 (assert (forall ((C2 tptp.real) (F2 (-> tptp.nat tptp.real)) (A tptp.real)) (=> (@ (@ tptp.sums_real (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_real C2) (@ F2 N4)))) A) (=> (not (= C2 tptp.zero_zero_real)) (@ (@ tptp.sums_real F2) (@ (@ tptp.divide_divide_real A) C2))))))
% 6.73/7.06 (assert (forall ((F2 (-> tptp.nat tptp.complex)) (S2 tptp.complex)) (=> (= (@ F2 tptp.zero_zero_nat) tptp.zero_zero_complex) (=> (@ (@ tptp.sums_complex (lambda ((N4 tptp.nat)) (@ F2 (@ tptp.suc N4)))) S2) (@ (@ tptp.sums_complex F2) S2)))))
% 6.73/7.06 (assert (forall ((F2 (-> tptp.nat tptp.real)) (S2 tptp.real)) (=> (= (@ F2 tptp.zero_zero_nat) tptp.zero_zero_real) (=> (@ (@ tptp.sums_real (lambda ((N4 tptp.nat)) (@ F2 (@ tptp.suc N4)))) S2) (@ (@ tptp.sums_real F2) S2)))))
% 6.73/7.06 (assert (forall ((F2 (-> tptp.nat tptp.real)) (S2 tptp.real)) (= (@ (@ tptp.sums_real (lambda ((N4 tptp.nat)) (@ F2 (@ tptp.suc N4)))) S2) (@ (@ tptp.sums_real F2) (@ (@ tptp.plus_plus_real S2) (@ F2 tptp.zero_zero_nat))))))
% 6.73/7.06 (assert (forall ((F2 (-> tptp.nat tptp.real)) (L tptp.real)) (=> (@ (@ tptp.sums_real (lambda ((N4 tptp.nat)) (@ F2 (@ tptp.suc N4)))) L) (@ (@ tptp.sums_real F2) (@ (@ tptp.plus_plus_real L) (@ F2 tptp.zero_zero_nat))))))
% 6.73/7.06 (assert (forall ((F2 (-> tptp.nat tptp.nat)) (L tptp.nat)) (=> (@ (@ tptp.sums_nat (lambda ((N4 tptp.nat)) (@ F2 (@ tptp.suc N4)))) L) (@ (@ tptp.sums_nat F2) (@ (@ tptp.plus_plus_nat L) (@ F2 tptp.zero_zero_nat))))))
% 6.73/7.06 (assert (forall ((F2 (-> tptp.nat tptp.int)) (L tptp.int)) (=> (@ (@ tptp.sums_int (lambda ((N4 tptp.nat)) (@ F2 (@ tptp.suc N4)))) L) (@ (@ tptp.sums_int F2) (@ (@ tptp.plus_plus_int L) (@ F2 tptp.zero_zero_nat))))))
% 6.73/7.06 (assert (forall ((Z3 tptp.complex) (N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.suc N))) (= (@ (@ tptp.times_times_complex (@ (@ tptp.comm_s2602460028002588243omplex Z3) _let_2)) (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.plus_plus_complex Z3) (@ (@ tptp.divide1717551699836669952omplex tptp.one_one_complex) (@ tptp.numera6690914467698888265omplex _let_1)))) _let_2)) (@ (@ tptp.groups6464643781859351333omplex (lambda ((K3 tptp.nat)) (@ (@ tptp.plus_plus_complex Z3) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.semiri8010041392384452111omplex K3)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat _let_1)) N)) tptp.one_one_nat))))))))
% 6.73/7.06 (assert (forall ((Z3 tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.suc N))) (= (@ (@ tptp.times_times_rat (@ (@ tptp.comm_s4028243227959126397er_rat Z3) _let_2)) (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.plus_plus_rat Z3) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat _let_1)))) _let_2)) (@ (@ tptp.groups73079841787564623at_rat (lambda ((K3 tptp.nat)) (@ (@ tptp.plus_plus_rat Z3) (@ (@ tptp.divide_divide_rat (@ tptp.semiri681578069525770553at_rat K3)) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat _let_1)) N)) tptp.one_one_nat))))))))
% 6.73/7.06 (assert (forall ((Z3 tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.suc N))) (= (@ (@ tptp.times_times_real (@ (@ tptp.comm_s7457072308508201937r_real Z3) _let_2)) (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.plus_plus_real Z3) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real _let_1)))) _let_2)) (@ (@ tptp.groups129246275422532515t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.plus_plus_real Z3) (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real K3)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat _let_1)) N)) tptp.one_one_nat))))))))
% 6.73/7.06 (assert (forall ((H tptp.complex) (Z3 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 Z3))) (=> (not (= H tptp.zero_zero_complex)) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ (@ tptp.power_power_complex (@ (@ tptp.plus_plus_complex Z3) H)) N)) (@ _let_2 N))) H)) (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex N)) (@ _let_2 _let_1))) (@ (@ tptp.times_times_complex H) (@ (@ tptp.groups2073611262835488442omplex (lambda ((P5 tptp.nat)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((Q5 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex (@ (@ tptp.plus_plus_complex Z3) H)) Q5)) (@ (@ tptp.power_power_complex Z3) (@ (@ 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))) P5))))) (@ tptp.set_ord_lessThan_nat _let_1)))))))))
% 6.73/7.06 (assert (forall ((H tptp.rat) (Z3 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 Z3))) (=> (not (= H tptp.zero_zero_rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.power_power_rat (@ (@ tptp.plus_plus_rat Z3) H)) N)) (@ _let_2 N))) H)) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat N)) (@ _let_2 _let_1))) (@ (@ tptp.times_times_rat H) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((P5 tptp.nat)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((Q5 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ (@ tptp.plus_plus_rat Z3) H)) Q5)) (@ (@ tptp.power_power_rat Z3) (@ (@ 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))) P5))))) (@ tptp.set_ord_lessThan_nat _let_1)))))))))
% 6.73/7.06 (assert (forall ((H tptp.real) (Z3 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 Z3))) (=> (not (= H tptp.zero_zero_real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real Z3) H)) N)) (@ _let_2 N))) H)) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ _let_2 _let_1))) (@ (@ tptp.times_times_real H) (@ (@ tptp.groups6591440286371151544t_real (lambda ((P5 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((Q5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real Z3) H)) Q5)) (@ (@ tptp.power_power_real Z3) (@ (@ 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))) P5))))) (@ tptp.set_ord_lessThan_nat _let_1)))))))))
% 6.73/7.06 (assert (= tptp.comm_s8582702949713902594nteger (lambda ((A5 tptp.code_integer) (N4 tptp.nat)) (@ (@ (@ tptp.if_Code_integer (= N4 tptp.zero_zero_nat)) tptp.one_one_Code_integer) (@ (@ (@ (@ tptp.set_fo1084959871951514735nteger (lambda ((O tptp.nat) (__flatten_var_0 tptp.code_integer)) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.plus_p5714425477246183910nteger A5) (@ tptp.semiri4939895301339042750nteger O))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat N4) tptp.one_one_nat)) tptp.one_one_Code_integer)))))
% 6.73/7.06 (assert (= tptp.comm_s2602460028002588243omplex (lambda ((A5 tptp.complex) (N4 tptp.nat)) (@ (@ (@ tptp.if_complex (= N4 tptp.zero_zero_nat)) tptp.one_one_complex) (@ (@ (@ (@ tptp.set_fo1517530859248394432omplex (lambda ((O tptp.nat) (__flatten_var_0 tptp.complex)) (@ (@ tptp.times_times_complex (@ (@ tptp.plus_plus_complex A5) (@ tptp.semiri8010041392384452111omplex O))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat N4) tptp.one_one_nat)) tptp.one_one_complex)))))
% 6.73/7.06 (assert (= tptp.comm_s4028243227959126397er_rat (lambda ((A5 tptp.rat) (N4 tptp.nat)) (@ (@ (@ tptp.if_rat (= N4 tptp.zero_zero_nat)) tptp.one_one_rat) (@ (@ (@ (@ tptp.set_fo1949268297981939178at_rat (lambda ((O tptp.nat) (__flatten_var_0 tptp.rat)) (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat A5) (@ tptp.semiri681578069525770553at_rat O))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat N4) tptp.one_one_nat)) tptp.one_one_rat)))))
% 6.73/7.06 (assert (= tptp.comm_s7457072308508201937r_real (lambda ((A5 tptp.real) (N4 tptp.nat)) (@ (@ (@ tptp.if_real (= N4 tptp.zero_zero_nat)) tptp.one_one_real) (@ (@ (@ (@ tptp.set_fo3111899725591712190t_real (lambda ((O tptp.nat) (__flatten_var_0 tptp.real)) (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real A5) (@ tptp.semiri5074537144036343181t_real O))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat N4) tptp.one_one_nat)) tptp.one_one_real)))))
% 6.73/7.06 (assert (= tptp.comm_s4660882817536571857er_int (lambda ((A5 tptp.int) (N4 tptp.nat)) (@ (@ (@ tptp.if_int (= N4 tptp.zero_zero_nat)) tptp.one_one_int) (@ (@ (@ (@ tptp.set_fo2581907887559384638at_int (lambda ((O tptp.nat) (__flatten_var_0 tptp.int)) (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int A5) (@ tptp.semiri1314217659103216013at_int O))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat N4) tptp.one_one_nat)) tptp.one_one_int)))))
% 6.73/7.06 (assert (= tptp.comm_s4663373288045622133er_nat (lambda ((A5 tptp.nat) (N4 tptp.nat)) (@ (@ (@ tptp.if_nat (= N4 tptp.zero_zero_nat)) tptp.one_one_nat) (@ (@ (@ (@ tptp.set_fo2584398358068434914at_nat (lambda ((O tptp.nat) (__flatten_var_0 tptp.nat)) (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat A5) (@ tptp.semiri1316708129612266289at_nat O))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat N4) tptp.one_one_nat)) tptp.one_one_nat)))))
% 6.73/7.06 (assert (= tptp.semiri4939895301339042750nteger (lambda ((N4 tptp.nat)) (@ (@ (@ tptp.semiri4055485073559036834nteger (lambda ((I tptp.code_integer)) (@ (@ tptp.plus_p5714425477246183910nteger I) tptp.one_one_Code_integer))) N4) tptp.zero_z3403309356797280102nteger))))
% 6.73/7.06 (assert (= tptp.semiri8010041392384452111omplex (lambda ((N4 tptp.nat)) (@ (@ (@ tptp.semiri2816024913162550771omplex (lambda ((I tptp.complex)) (@ (@ tptp.plus_plus_complex I) tptp.one_one_complex))) N4) tptp.zero_zero_complex))))
% 6.73/7.06 (assert (= tptp.semiri681578069525770553at_rat (lambda ((N4 tptp.nat)) (@ (@ (@ tptp.semiri7787848453975740701ux_rat (lambda ((I tptp.rat)) (@ (@ tptp.plus_plus_rat I) tptp.one_one_rat))) N4) tptp.zero_zero_rat))))
% 6.73/7.06 (assert (= tptp.semiri5074537144036343181t_real (lambda ((N4 tptp.nat)) (@ (@ (@ tptp.semiri7260567687927622513x_real (lambda ((I tptp.real)) (@ (@ tptp.plus_plus_real I) tptp.one_one_real))) N4) tptp.zero_zero_real))))
% 6.73/7.06 (assert (= tptp.semiri1314217659103216013at_int (lambda ((N4 tptp.nat)) (@ (@ (@ tptp.semiri8420488043553186161ux_int (lambda ((I tptp.int)) (@ (@ tptp.plus_plus_int I) tptp.one_one_int))) N4) tptp.zero_zero_int))))
% 6.73/7.06 (assert (= tptp.semiri1316708129612266289at_nat (lambda ((N4 tptp.nat)) (@ (@ (@ tptp.semiri8422978514062236437ux_nat (lambda ((I tptp.nat)) (@ (@ tptp.plus_plus_nat I) tptp.one_one_nat))) N4) tptp.zero_zero_nat))))
% 6.73/7.06 (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)))))))
% 6.73/7.06 (assert (forall ((N tptp.nat) (K2 tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ (@ tptp.bit_concat_bit (@ tptp.suc N)) K2) L) (@ (@ tptp.plus_plus_int (@ (@ tptp.modulo_modulo_int K2) _let_1)) (@ (@ tptp.times_times_int _let_1) (@ (@ (@ tptp.bit_concat_bit N) (@ (@ tptp.divide_divide_int K2) _let_1)) L)))))))
% 6.73/7.06 (assert (= (@ tptp.neg_nu8804712462038260780nteger tptp.one_one_Code_integer) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))
% 6.73/7.06 (assert (= (@ tptp.neg_nu7009210354673126013omplex tptp.one_one_complex) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))
% 6.73/7.06 (assert (= (@ tptp.neg_numeral_dbl_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))
% 6.73/7.06 (assert (= (@ tptp.neg_numeral_dbl_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))
% 6.73/7.06 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (= (@ tptp.set_ord_lessThan_nat X) (@ tptp.set_ord_lessThan_nat Y)) (= X Y))))
% 6.73/7.06 (assert (forall ((I2 tptp.set_nat) (K2 tptp.set_nat)) (= (@ (@ tptp.member_set_nat I2) (@ tptp.set_or890127255671739683et_nat K2)) (@ (@ tptp.ord_less_set_nat I2) K2))))
% 6.73/7.06 (assert (forall ((I2 tptp.real) (K2 tptp.real)) (= (@ (@ tptp.member_real I2) (@ tptp.set_or5984915006950818249n_real K2)) (@ (@ tptp.ord_less_real I2) K2))))
% 6.73/7.06 (assert (forall ((I2 tptp.rat) (K2 tptp.rat)) (= (@ (@ tptp.member_rat I2) (@ tptp.set_ord_lessThan_rat K2)) (@ (@ tptp.ord_less_rat I2) K2))))
% 6.73/7.06 (assert (forall ((I2 tptp.num) (K2 tptp.num)) (= (@ (@ tptp.member_num I2) (@ tptp.set_ord_lessThan_num K2)) (@ (@ tptp.ord_less_num I2) K2))))
% 6.73/7.06 (assert (forall ((I2 tptp.int) (K2 tptp.int)) (= (@ (@ tptp.member_int I2) (@ tptp.set_ord_lessThan_int K2)) (@ (@ tptp.ord_less_int I2) K2))))
% 6.73/7.06 (assert (forall ((I2 tptp.nat) (K2 tptp.nat)) (= (@ (@ tptp.member_nat I2) (@ tptp.set_ord_lessThan_nat K2)) (@ (@ tptp.ord_less_nat I2) K2))))
% 6.73/7.06 (assert (forall ((K2 tptp.nat)) (@ tptp.finite_finite_nat (@ tptp.set_ord_lessThan_nat K2))))
% 6.73/7.06 (assert (forall ((K2 tptp.int) (L tptp.int)) (= (@ (@ (@ tptp.bit_concat_bit tptp.zero_zero_nat) K2) L) L)))
% 6.73/7.06 (assert (forall ((U tptp.nat)) (= (@ tptp.finite_card_nat (@ tptp.set_ord_lessThan_nat U)) U)))
% 6.73/7.06 (assert (= (@ tptp.neg_nu7009210354673126013omplex tptp.zero_zero_complex) tptp.zero_zero_complex))
% 6.73/7.06 (assert (= (@ tptp.neg_numeral_dbl_real tptp.zero_zero_real) tptp.zero_zero_real))
% 6.73/7.06 (assert (= (@ tptp.neg_numeral_dbl_rat tptp.zero_zero_rat) tptp.zero_zero_rat))
% 6.73/7.06 (assert (= (@ tptp.neg_numeral_dbl_int tptp.zero_zero_int) tptp.zero_zero_int))
% 6.73/7.06 (assert (forall ((A4 tptp.set_nat) (F2 (-> tptp.nat tptp.complex))) (=> (@ tptp.finite_finite_nat A4) (= (= (@ (@ tptp.groups6464643781859351333omplex F2) A4) tptp.zero_zero_complex) (exists ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) A4) (= (@ F2 X4) tptp.zero_zero_complex)))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_int) (F2 (-> tptp.int tptp.complex))) (=> (@ tptp.finite_finite_int A4) (= (= (@ (@ tptp.groups7440179247065528705omplex F2) A4) tptp.zero_zero_complex) (exists ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) A4) (= (@ F2 X4) tptp.zero_zero_complex)))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_complex) (F2 (-> tptp.complex tptp.complex))) (=> (@ tptp.finite3207457112153483333omplex A4) (= (= (@ (@ tptp.groups3708469109370488835omplex F2) A4) tptp.zero_zero_complex) (exists ((X4 tptp.complex)) (and (@ (@ tptp.member_complex X4) A4) (= (@ F2 X4) tptp.zero_zero_complex)))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_nat) (F2 (-> tptp.nat tptp.real))) (=> (@ tptp.finite_finite_nat A4) (= (= (@ (@ tptp.groups129246275422532515t_real F2) A4) tptp.zero_zero_real) (exists ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) A4) (= (@ F2 X4) tptp.zero_zero_real)))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_int) (F2 (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int A4) (= (= (@ (@ tptp.groups2316167850115554303t_real F2) A4) tptp.zero_zero_real) (exists ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) A4) (= (@ F2 X4) tptp.zero_zero_real)))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_complex) (F2 (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex A4) (= (= (@ (@ tptp.groups766887009212190081x_real F2) A4) tptp.zero_zero_real) (exists ((X4 tptp.complex)) (and (@ (@ tptp.member_complex X4) A4) (= (@ F2 X4) tptp.zero_zero_real)))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_nat) (F2 (-> tptp.nat tptp.rat))) (=> (@ tptp.finite_finite_nat A4) (= (= (@ (@ tptp.groups73079841787564623at_rat F2) A4) tptp.zero_zero_rat) (exists ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) A4) (= (@ F2 X4) tptp.zero_zero_rat)))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_int) (F2 (-> tptp.int tptp.rat))) (=> (@ tptp.finite_finite_int A4) (= (= (@ (@ tptp.groups1072433553688619179nt_rat F2) A4) tptp.zero_zero_rat) (exists ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) A4) (= (@ F2 X4) tptp.zero_zero_rat)))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_complex) (F2 (-> tptp.complex tptp.rat))) (=> (@ tptp.finite3207457112153483333omplex A4) (= (= (@ (@ tptp.groups225925009352817453ex_rat F2) A4) tptp.zero_zero_rat) (exists ((X4 tptp.complex)) (and (@ (@ tptp.member_complex X4) A4) (= (@ F2 X4) tptp.zero_zero_rat)))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_int) (F2 (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int A4) (= (= (@ (@ tptp.groups1707563613775114915nt_nat F2) A4) tptp.zero_zero_nat) (exists ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) A4) (= (@ F2 X4) tptp.zero_zero_nat)))))))
% 6.73/7.06 (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))))
% 6.73/7.06 (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))))
% 6.73/7.06 (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))))
% 6.73/7.06 (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))))
% 6.73/7.06 (assert (= (@ tptp.set_ord_lessThan_nat tptp.zero_zero_nat) tptp.bot_bot_set_nat))
% 6.73/7.06 (assert (forall ((K2 tptp.num)) (= (@ tptp.neg_nu7009210354673126013omplex (@ tptp.numera6690914467698888265omplex K2)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 K2)))))
% 6.73/7.06 (assert (forall ((K2 tptp.num)) (= (@ tptp.neg_numeral_dbl_real (@ tptp.numeral_numeral_real K2)) (@ tptp.numeral_numeral_real (@ tptp.bit0 K2)))))
% 6.73/7.06 (assert (forall ((K2 tptp.num)) (= (@ tptp.neg_numeral_dbl_int (@ tptp.numeral_numeral_int K2)) (@ tptp.numeral_numeral_int (@ tptp.bit0 K2)))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_real) (X tptp.real) (G2 (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.groups1681761925125756287l_real G2))) (=> (@ tptp.finite_finite_real A4) (=> (not (@ (@ tptp.member_real X) A4)) (= (@ _let_1 (@ (@ tptp.insert_real X) A4)) (@ (@ tptp.times_times_real (@ G2 X)) (@ _let_1 A4))))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_nat) (X tptp.nat) (G2 (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.groups129246275422532515t_real G2))) (=> (@ tptp.finite_finite_nat A4) (=> (not (@ (@ tptp.member_nat X) A4)) (= (@ _let_1 (@ (@ tptp.insert_nat X) A4)) (@ (@ tptp.times_times_real (@ G2 X)) (@ _let_1 A4))))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_int) (X tptp.int) (G2 (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups2316167850115554303t_real G2))) (=> (@ tptp.finite_finite_int A4) (=> (not (@ (@ tptp.member_int X) A4)) (= (@ _let_1 (@ (@ tptp.insert_int X) A4)) (@ (@ tptp.times_times_real (@ G2 X)) (@ _let_1 A4))))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_complex) (X tptp.complex) (G2 (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups766887009212190081x_real G2))) (=> (@ tptp.finite3207457112153483333omplex A4) (=> (not (@ (@ tptp.member_complex X) A4)) (= (@ _let_1 (@ (@ tptp.insert_complex X) A4)) (@ (@ tptp.times_times_real (@ G2 X)) (@ _let_1 A4))))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_real) (X tptp.real) (G2 (-> tptp.real tptp.rat))) (let ((_let_1 (@ tptp.groups4061424788464935467al_rat G2))) (=> (@ tptp.finite_finite_real A4) (=> (not (@ (@ tptp.member_real X) A4)) (= (@ _let_1 (@ (@ tptp.insert_real X) A4)) (@ (@ tptp.times_times_rat (@ G2 X)) (@ _let_1 A4))))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_nat) (X tptp.nat) (G2 (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups73079841787564623at_rat G2))) (=> (@ tptp.finite_finite_nat A4) (=> (not (@ (@ tptp.member_nat X) A4)) (= (@ _let_1 (@ (@ tptp.insert_nat X) A4)) (@ (@ tptp.times_times_rat (@ G2 X)) (@ _let_1 A4))))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_int) (X tptp.int) (G2 (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups1072433553688619179nt_rat G2))) (=> (@ tptp.finite_finite_int A4) (=> (not (@ (@ tptp.member_int X) A4)) (= (@ _let_1 (@ (@ tptp.insert_int X) A4)) (@ (@ tptp.times_times_rat (@ G2 X)) (@ _let_1 A4))))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_complex) (X tptp.complex) (G2 (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups225925009352817453ex_rat G2))) (=> (@ tptp.finite3207457112153483333omplex A4) (=> (not (@ (@ tptp.member_complex X) A4)) (= (@ _let_1 (@ (@ tptp.insert_complex X) A4)) (@ (@ tptp.times_times_rat (@ G2 X)) (@ _let_1 A4))))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_real) (X tptp.real) (G2 (-> tptp.real tptp.nat))) (let ((_let_1 (@ tptp.groups4696554848551431203al_nat G2))) (=> (@ tptp.finite_finite_real A4) (=> (not (@ (@ tptp.member_real X) A4)) (= (@ _let_1 (@ (@ tptp.insert_real X) A4)) (@ (@ tptp.times_times_nat (@ G2 X)) (@ _let_1 A4))))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_int) (X tptp.int) (G2 (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups1707563613775114915nt_nat G2))) (=> (@ tptp.finite_finite_int A4) (=> (not (@ (@ tptp.member_int X) A4)) (= (@ _let_1 (@ (@ tptp.insert_int X) A4)) (@ (@ tptp.times_times_nat (@ G2 X)) (@ _let_1 A4))))))))
% 6.73/7.06 (assert (forall ((G2 (-> tptp.nat tptp.rat)) (N tptp.nat)) (let ((_let_1 (@ tptp.groups2906978787729119204at_rat G2))) (= (@ _let_1 (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) (@ (@ tptp.plus_plus_rat (@ _let_1 (@ tptp.set_ord_lessThan_nat N))) (@ G2 N))))))
% 6.73/7.06 (assert (forall ((G2 (-> tptp.nat tptp.int)) (N tptp.nat)) (let ((_let_1 (@ tptp.groups3539618377306564664at_int G2))) (= (@ _let_1 (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) (@ (@ tptp.plus_plus_int (@ _let_1 (@ tptp.set_ord_lessThan_nat N))) (@ G2 N))))))
% 6.73/7.06 (assert (forall ((G2 (-> tptp.nat tptp.nat)) (N tptp.nat)) (let ((_let_1 (@ tptp.groups3542108847815614940at_nat G2))) (= (@ _let_1 (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) (@ (@ tptp.plus_plus_nat (@ _let_1 (@ tptp.set_ord_lessThan_nat N))) (@ G2 N))))))
% 6.73/7.06 (assert (forall ((G2 (-> tptp.nat tptp.real)) (N tptp.nat)) (let ((_let_1 (@ tptp.groups6591440286371151544t_real G2))) (= (@ _let_1 (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) (@ (@ tptp.plus_plus_real (@ _let_1 (@ tptp.set_ord_lessThan_nat N))) (@ G2 N))))))
% 6.73/7.06 (assert (forall ((K2 tptp.int)) (let ((_let_1 (@ (@ tptp.insert_int K2) tptp.bot_bot_set_int))) (= (@ (@ tptp.minus_minus_set_int _let_1) (@ tptp.set_ord_lessThan_int K2)) _let_1))))
% 6.73/7.06 (assert (forall ((K2 tptp.real)) (let ((_let_1 (@ (@ tptp.insert_real K2) tptp.bot_bot_set_real))) (= (@ (@ tptp.minus_minus_set_real _let_1) (@ tptp.set_or5984915006950818249n_real K2)) _let_1))))
% 6.73/7.06 (assert (forall ((K2 tptp.nat)) (let ((_let_1 (@ (@ tptp.insert_nat K2) tptp.bot_bot_set_nat))) (= (@ (@ tptp.minus_minus_set_nat _let_1) (@ tptp.set_ord_lessThan_nat K2)) _let_1))))
% 6.73/7.06 (assert (forall ((G2 (-> tptp.nat tptp.real)) (N tptp.nat)) (let ((_let_1 (@ tptp.groups129246275422532515t_real G2))) (= (@ _let_1 (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) (@ (@ tptp.times_times_real (@ _let_1 (@ tptp.set_ord_lessThan_nat N))) (@ G2 N))))))
% 6.73/7.06 (assert (forall ((G2 (-> tptp.nat tptp.rat)) (N tptp.nat)) (let ((_let_1 (@ tptp.groups73079841787564623at_rat G2))) (= (@ _let_1 (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) (@ (@ tptp.times_times_rat (@ _let_1 (@ tptp.set_ord_lessThan_nat N))) (@ G2 N))))))
% 6.73/7.06 (assert (forall ((G2 (-> tptp.nat tptp.int)) (N tptp.nat)) (let ((_let_1 (@ tptp.groups705719431365010083at_int G2))) (= (@ _let_1 (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) (@ (@ tptp.times_times_int (@ _let_1 (@ tptp.set_ord_lessThan_nat N))) (@ G2 N))))))
% 6.73/7.06 (assert (forall ((G2 (-> tptp.nat tptp.nat)) (N tptp.nat)) (let ((_let_1 (@ tptp.groups708209901874060359at_nat G2))) (= (@ _let_1 (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) (@ (@ tptp.times_times_nat (@ _let_1 (@ tptp.set_ord_lessThan_nat N))) (@ G2 N))))))
% 6.73/7.06 (assert (forall ((N tptp.nat) (M2 tptp.nat) (G2 (-> tptp.nat tptp.code_integer))) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M2))) (let ((_let_3 (@ tptp.groups3455450783089532116nteger G2))) (let ((_let_4 (@ _let_3 (@ _let_2 _let_1)))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_1) M2))) (and (=> _let_5 (= _let_4 tptp.one_one_Code_integer)) (=> (not _let_5) (= _let_4 (@ (@ tptp.times_3573771949741848930nteger (@ _let_3 (@ _let_2 N))) (@ G2 _let_1))))))))))))
% 6.73/7.06 (assert (forall ((N tptp.nat) (M2 tptp.nat) (G2 (-> tptp.nat tptp.complex))) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M2))) (let ((_let_3 (@ tptp.groups6464643781859351333omplex G2))) (let ((_let_4 (@ _let_3 (@ _let_2 _let_1)))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_1) M2))) (and (=> _let_5 (= _let_4 tptp.one_one_complex)) (=> (not _let_5) (= _let_4 (@ (@ tptp.times_times_complex (@ _let_3 (@ _let_2 N))) (@ G2 _let_1))))))))))))
% 6.73/7.06 (assert (forall ((N tptp.nat) (M2 tptp.nat) (G2 (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M2))) (let ((_let_3 (@ tptp.groups129246275422532515t_real G2))) (let ((_let_4 (@ _let_3 (@ _let_2 _let_1)))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_1) M2))) (and (=> _let_5 (= _let_4 tptp.one_one_real)) (=> (not _let_5) (= _let_4 (@ (@ tptp.times_times_real (@ _let_3 (@ _let_2 N))) (@ G2 _let_1))))))))))))
% 6.73/7.06 (assert (forall ((N tptp.nat) (M2 tptp.nat) (G2 (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M2))) (let ((_let_3 (@ tptp.groups73079841787564623at_rat G2))) (let ((_let_4 (@ _let_3 (@ _let_2 _let_1)))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_1) M2))) (and (=> _let_5 (= _let_4 tptp.one_one_rat)) (=> (not _let_5) (= _let_4 (@ (@ tptp.times_times_rat (@ _let_3 (@ _let_2 N))) (@ G2 _let_1))))))))))))
% 6.73/7.06 (assert (forall ((N tptp.nat) (M2 tptp.nat) (G2 (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M2))) (let ((_let_3 (@ tptp.groups705719431365010083at_int G2))) (let ((_let_4 (@ _let_3 (@ _let_2 _let_1)))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_1) M2))) (and (=> _let_5 (= _let_4 tptp.one_one_int)) (=> (not _let_5) (= _let_4 (@ (@ tptp.times_times_int (@ _let_3 (@ _let_2 N))) (@ G2 _let_1))))))))))))
% 6.73/7.06 (assert (forall ((N tptp.nat) (M2 tptp.nat) (G2 (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M2))) (let ((_let_3 (@ tptp.groups708209901874060359at_nat G2))) (let ((_let_4 (@ _let_3 (@ _let_2 _let_1)))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_1) M2))) (and (=> _let_5 (= _let_4 tptp.one_one_nat)) (=> (not _let_5) (= _let_4 (@ (@ tptp.times_times_nat (@ _let_3 (@ _let_2 N))) (@ G2 _let_1))))))))))))
% 6.73/7.06 (assert (forall ((G2 (-> tptp.nat tptp.int)) (N tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat N))) (= (@ (@ tptp.groups705719431365010083at_int (lambda ((I tptp.nat)) (@ G2 (@ (@ tptp.minus_minus_nat N) (@ tptp.suc I))))) _let_1) (@ (@ tptp.groups705719431365010083at_int G2) _let_1)))))
% 6.73/7.06 (assert (forall ((G2 (-> tptp.nat tptp.nat)) (N tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat N))) (= (@ (@ tptp.groups708209901874060359at_nat (lambda ((I tptp.nat)) (@ G2 (@ (@ tptp.minus_minus_nat N) (@ tptp.suc I))))) _let_1) (@ (@ tptp.groups708209901874060359at_nat G2) _let_1)))))
% 6.73/7.06 (assert (forall ((X tptp.int)) (not (= (@ tptp.set_ord_lessThan_int X) tptp.bot_bot_set_int))))
% 6.73/7.06 (assert (forall ((X tptp.real)) (not (= (@ tptp.set_or5984915006950818249n_real X) tptp.bot_bot_set_real))))
% 6.73/7.06 (assert (forall ((A tptp.int)) (not (@ tptp.finite_finite_int (@ tptp.set_ord_lessThan_int A)))))
% 6.73/7.06 (assert (forall ((G2 (-> tptp.nat tptp.int)) (H (-> tptp.nat tptp.int)) (A4 tptp.set_nat)) (= (@ (@ tptp.groups705719431365010083at_int (lambda ((X4 tptp.nat)) (@ (@ tptp.times_times_int (@ G2 X4)) (@ H X4)))) A4) (@ (@ tptp.times_times_int (@ (@ tptp.groups705719431365010083at_int G2) A4)) (@ (@ tptp.groups705719431365010083at_int H) A4)))))
% 6.73/7.06 (assert (forall ((G2 (-> tptp.int tptp.int)) (H (-> tptp.int tptp.int)) (A4 tptp.set_int)) (= (@ (@ tptp.groups1705073143266064639nt_int (lambda ((X4 tptp.int)) (@ (@ tptp.times_times_int (@ G2 X4)) (@ H X4)))) A4) (@ (@ tptp.times_times_int (@ (@ tptp.groups1705073143266064639nt_int G2) A4)) (@ (@ tptp.groups1705073143266064639nt_int H) A4)))))
% 6.73/7.06 (assert (forall ((G2 (-> tptp.nat tptp.nat)) (H (-> tptp.nat tptp.nat)) (A4 tptp.set_nat)) (= (@ (@ tptp.groups708209901874060359at_nat (lambda ((X4 tptp.nat)) (@ (@ tptp.times_times_nat (@ G2 X4)) (@ H X4)))) A4) (@ (@ tptp.times_times_nat (@ (@ tptp.groups708209901874060359at_nat G2) A4)) (@ (@ tptp.groups708209901874060359at_nat H) A4)))))
% 6.73/7.06 (assert (= tptp.set_or890127255671739683et_nat (lambda ((U2 tptp.set_nat)) (@ tptp.collect_set_nat (lambda ((X4 tptp.set_nat)) (@ (@ tptp.ord_less_set_nat X4) U2))))))
% 6.73/7.06 (assert (= tptp.set_or5984915006950818249n_real (lambda ((U2 tptp.real)) (@ tptp.collect_real (lambda ((X4 tptp.real)) (@ (@ tptp.ord_less_real X4) U2))))))
% 6.73/7.06 (assert (= tptp.set_ord_lessThan_rat (lambda ((U2 tptp.rat)) (@ tptp.collect_rat (lambda ((X4 tptp.rat)) (@ (@ tptp.ord_less_rat X4) U2))))))
% 6.73/7.06 (assert (= tptp.set_ord_lessThan_num (lambda ((U2 tptp.num)) (@ tptp.collect_num (lambda ((X4 tptp.num)) (@ (@ tptp.ord_less_num X4) U2))))))
% 6.73/7.06 (assert (= tptp.set_ord_lessThan_int (lambda ((U2 tptp.int)) (@ tptp.collect_int (lambda ((X4 tptp.int)) (@ (@ tptp.ord_less_int X4) U2))))))
% 6.73/7.06 (assert (= tptp.set_ord_lessThan_nat (lambda ((U2 tptp.nat)) (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (@ (@ tptp.ord_less_nat X4) U2))))))
% 6.73/7.06 (assert (forall ((G2 (-> tptp.nat tptp.real)) (N tptp.nat)) (= (@ (@ tptp.groups129246275422532515t_real G2) (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) (@ (@ tptp.times_times_real (@ G2 tptp.zero_zero_nat)) (@ (@ tptp.groups129246275422532515t_real (lambda ((I tptp.nat)) (@ G2 (@ tptp.suc I)))) (@ tptp.set_ord_lessThan_nat N))))))
% 6.73/7.06 (assert (forall ((G2 (-> tptp.nat tptp.rat)) (N tptp.nat)) (= (@ (@ tptp.groups73079841787564623at_rat G2) (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) (@ (@ tptp.times_times_rat (@ G2 tptp.zero_zero_nat)) (@ (@ tptp.groups73079841787564623at_rat (lambda ((I tptp.nat)) (@ G2 (@ tptp.suc I)))) (@ tptp.set_ord_lessThan_nat N))))))
% 6.73/7.06 (assert (forall ((G2 (-> tptp.nat tptp.int)) (N tptp.nat)) (= (@ (@ tptp.groups705719431365010083at_int G2) (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) (@ (@ tptp.times_times_int (@ G2 tptp.zero_zero_nat)) (@ (@ tptp.groups705719431365010083at_int (lambda ((I tptp.nat)) (@ G2 (@ tptp.suc I)))) (@ tptp.set_ord_lessThan_nat N))))))
% 6.73/7.06 (assert (forall ((G2 (-> tptp.nat tptp.nat)) (N tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat G2) (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) (@ (@ tptp.times_times_nat (@ G2 tptp.zero_zero_nat)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I tptp.nat)) (@ G2 (@ tptp.suc I)))) (@ tptp.set_ord_lessThan_nat N))))))
% 6.73/7.06 (assert (forall ((G2 (-> tptp.nat tptp.int)) (N tptp.nat)) (= (@ (@ tptp.groups705719431365010083at_int G2) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N)) (@ (@ tptp.groups705719431365010083at_int (lambda ((K3 tptp.nat)) (@ G2 (@ tptp.suc K3)))) (@ tptp.set_ord_lessThan_nat N)))))
% 6.73/7.06 (assert (forall ((G2 (-> tptp.nat tptp.nat)) (N tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat G2) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((K3 tptp.nat)) (@ G2 (@ tptp.suc K3)))) (@ tptp.set_ord_lessThan_nat N)))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_complex) (F2 (-> tptp.complex tptp.real)) (G2 (-> tptp.complex tptp.real))) (=> (forall ((I3 tptp.complex)) (let ((_let_1 (@ F2 I3))) (=> (@ (@ tptp.member_complex I3) A4) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) (@ G2 I3)))))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups766887009212190081x_real F2) A4)) (@ (@ tptp.groups766887009212190081x_real G2) A4)))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_real) (F2 (-> tptp.real tptp.real)) (G2 (-> tptp.real tptp.real))) (=> (forall ((I3 tptp.real)) (let ((_let_1 (@ F2 I3))) (=> (@ (@ tptp.member_real I3) A4) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) (@ G2 I3)))))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups1681761925125756287l_real F2) A4)) (@ (@ tptp.groups1681761925125756287l_real G2) A4)))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_nat) (F2 (-> tptp.nat tptp.real)) (G2 (-> tptp.nat tptp.real))) (=> (forall ((I3 tptp.nat)) (let ((_let_1 (@ F2 I3))) (=> (@ (@ tptp.member_nat I3) A4) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) (@ G2 I3)))))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups129246275422532515t_real F2) A4)) (@ (@ tptp.groups129246275422532515t_real G2) A4)))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_int) (F2 (-> tptp.int tptp.real)) (G2 (-> tptp.int tptp.real))) (=> (forall ((I3 tptp.int)) (let ((_let_1 (@ F2 I3))) (=> (@ (@ tptp.member_int I3) A4) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) (@ G2 I3)))))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups2316167850115554303t_real F2) A4)) (@ (@ tptp.groups2316167850115554303t_real G2) A4)))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_complex) (F2 (-> tptp.complex tptp.rat)) (G2 (-> tptp.complex tptp.rat))) (=> (forall ((I3 tptp.complex)) (let ((_let_1 (@ F2 I3))) (=> (@ (@ tptp.member_complex I3) A4) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1) (@ (@ tptp.ord_less_eq_rat _let_1) (@ G2 I3)))))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups225925009352817453ex_rat F2) A4)) (@ (@ tptp.groups225925009352817453ex_rat G2) A4)))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_real) (F2 (-> tptp.real tptp.rat)) (G2 (-> tptp.real tptp.rat))) (=> (forall ((I3 tptp.real)) (let ((_let_1 (@ F2 I3))) (=> (@ (@ tptp.member_real I3) A4) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1) (@ (@ tptp.ord_less_eq_rat _let_1) (@ G2 I3)))))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups4061424788464935467al_rat F2) A4)) (@ (@ tptp.groups4061424788464935467al_rat G2) A4)))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_nat) (F2 (-> tptp.nat tptp.rat)) (G2 (-> tptp.nat tptp.rat))) (=> (forall ((I3 tptp.nat)) (let ((_let_1 (@ F2 I3))) (=> (@ (@ tptp.member_nat I3) A4) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1) (@ (@ tptp.ord_less_eq_rat _let_1) (@ G2 I3)))))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups73079841787564623at_rat F2) A4)) (@ (@ tptp.groups73079841787564623at_rat G2) A4)))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_int) (F2 (-> tptp.int tptp.rat)) (G2 (-> tptp.int tptp.rat))) (=> (forall ((I3 tptp.int)) (let ((_let_1 (@ F2 I3))) (=> (@ (@ tptp.member_int I3) A4) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1) (@ (@ tptp.ord_less_eq_rat _let_1) (@ G2 I3)))))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups1072433553688619179nt_rat F2) A4)) (@ (@ tptp.groups1072433553688619179nt_rat G2) A4)))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_complex) (F2 (-> tptp.complex tptp.nat)) (G2 (-> tptp.complex tptp.nat))) (=> (forall ((I3 tptp.complex)) (let ((_let_1 (@ F2 I3))) (=> (@ (@ tptp.member_complex I3) A4) (and (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) _let_1) (@ (@ tptp.ord_less_eq_nat _let_1) (@ G2 I3)))))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups861055069439313189ex_nat F2) A4)) (@ (@ tptp.groups861055069439313189ex_nat G2) A4)))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_real) (F2 (-> tptp.real tptp.nat)) (G2 (-> tptp.real tptp.nat))) (=> (forall ((I3 tptp.real)) (let ((_let_1 (@ F2 I3))) (=> (@ (@ tptp.member_real I3) A4) (and (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) _let_1) (@ (@ tptp.ord_less_eq_nat _let_1) (@ G2 I3)))))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups4696554848551431203al_nat F2) A4)) (@ (@ tptp.groups4696554848551431203al_nat G2) A4)))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_nat) (F2 (-> tptp.nat tptp.int))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A4) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F2 X3)))) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.groups705719431365010083at_int F2) A4)))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_int) (F2 (-> tptp.int tptp.int))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A4) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F2 X3)))) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.groups1705073143266064639nt_int F2) A4)))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_nat) (F2 (-> tptp.nat tptp.nat))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A4) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F2 X3)))) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ (@ tptp.groups708209901874060359at_nat F2) A4)))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_nat) (F2 (-> tptp.nat tptp.int))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A4) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ F2 X3)))) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.groups705719431365010083at_int F2) A4)))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_int) (F2 (-> tptp.int tptp.int))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A4) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ F2 X3)))) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.groups1705073143266064639nt_int F2) A4)))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_nat) (F2 (-> tptp.nat tptp.nat))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A4) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F2 X3)))) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.groups708209901874060359at_nat F2) A4)))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_complex) (F2 (-> tptp.complex tptp.code_integer))) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) A4) (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (@ F2 X3)))) (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (@ (@ tptp.groups8682486955453173170nteger F2) A4)))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_real) (F2 (-> tptp.real tptp.code_integer))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) A4) (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (@ F2 X3)))) (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (@ (@ tptp.groups6225526099057966256nteger F2) A4)))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_nat) (F2 (-> tptp.nat tptp.code_integer))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A4) (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (@ F2 X3)))) (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (@ (@ tptp.groups3455450783089532116nteger F2) A4)))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_int) (F2 (-> tptp.int tptp.code_integer))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A4) (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (@ F2 X3)))) (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (@ (@ tptp.groups3827104343326376752nteger F2) A4)))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_complex) (F2 (-> tptp.complex tptp.real))) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) A4) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F2 X3)))) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ (@ tptp.groups766887009212190081x_real F2) A4)))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_real) (F2 (-> tptp.real tptp.real))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) A4) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F2 X3)))) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ (@ tptp.groups1681761925125756287l_real F2) A4)))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_nat) (F2 (-> tptp.nat tptp.real))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A4) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F2 X3)))) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ (@ tptp.groups129246275422532515t_real F2) A4)))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_int) (F2 (-> tptp.int tptp.real))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A4) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F2 X3)))) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ (@ tptp.groups2316167850115554303t_real F2) A4)))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_complex) (F2 (-> tptp.complex tptp.rat))) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) A4) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ F2 X3)))) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ (@ tptp.groups225925009352817453ex_rat F2) A4)))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_real) (F2 (-> tptp.real tptp.rat))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) A4) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ F2 X3)))) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ (@ tptp.groups4061424788464935467al_rat F2) A4)))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_nat) (F2 (-> tptp.nat tptp.complex))) (=> (@ tptp.finite_finite_nat A4) (=> (exists ((X5 tptp.nat)) (and (@ (@ tptp.member_nat X5) A4) (= (@ F2 X5) tptp.zero_zero_complex))) (= (@ (@ tptp.groups6464643781859351333omplex F2) A4) tptp.zero_zero_complex)))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_int) (F2 (-> tptp.int tptp.complex))) (=> (@ tptp.finite_finite_int A4) (=> (exists ((X5 tptp.int)) (and (@ (@ tptp.member_int X5) A4) (= (@ F2 X5) tptp.zero_zero_complex))) (= (@ (@ tptp.groups7440179247065528705omplex F2) A4) tptp.zero_zero_complex)))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_complex) (F2 (-> tptp.complex tptp.complex))) (=> (@ tptp.finite3207457112153483333omplex A4) (=> (exists ((X5 tptp.complex)) (and (@ (@ tptp.member_complex X5) A4) (= (@ F2 X5) tptp.zero_zero_complex))) (= (@ (@ tptp.groups3708469109370488835omplex F2) A4) tptp.zero_zero_complex)))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_nat) (F2 (-> tptp.nat tptp.real))) (=> (@ tptp.finite_finite_nat A4) (=> (exists ((X5 tptp.nat)) (and (@ (@ tptp.member_nat X5) A4) (= (@ F2 X5) tptp.zero_zero_real))) (= (@ (@ tptp.groups129246275422532515t_real F2) A4) tptp.zero_zero_real)))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_int) (F2 (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int A4) (=> (exists ((X5 tptp.int)) (and (@ (@ tptp.member_int X5) A4) (= (@ F2 X5) tptp.zero_zero_real))) (= (@ (@ tptp.groups2316167850115554303t_real F2) A4) tptp.zero_zero_real)))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_complex) (F2 (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex A4) (=> (exists ((X5 tptp.complex)) (and (@ (@ tptp.member_complex X5) A4) (= (@ F2 X5) tptp.zero_zero_real))) (= (@ (@ tptp.groups766887009212190081x_real F2) A4) tptp.zero_zero_real)))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_nat) (F2 (-> tptp.nat tptp.rat))) (=> (@ tptp.finite_finite_nat A4) (=> (exists ((X5 tptp.nat)) (and (@ (@ tptp.member_nat X5) A4) (= (@ F2 X5) tptp.zero_zero_rat))) (= (@ (@ tptp.groups73079841787564623at_rat F2) A4) tptp.zero_zero_rat)))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_int) (F2 (-> tptp.int tptp.rat))) (=> (@ tptp.finite_finite_int A4) (=> (exists ((X5 tptp.int)) (and (@ (@ tptp.member_int X5) A4) (= (@ F2 X5) tptp.zero_zero_rat))) (= (@ (@ tptp.groups1072433553688619179nt_rat F2) A4) tptp.zero_zero_rat)))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_complex) (F2 (-> tptp.complex tptp.rat))) (=> (@ tptp.finite3207457112153483333omplex A4) (=> (exists ((X5 tptp.complex)) (and (@ (@ tptp.member_complex X5) A4) (= (@ F2 X5) tptp.zero_zero_rat))) (= (@ (@ tptp.groups225925009352817453ex_rat F2) A4) tptp.zero_zero_rat)))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_int) (F2 (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int A4) (=> (exists ((X5 tptp.int)) (and (@ (@ tptp.member_int X5) A4) (= (@ F2 X5) tptp.zero_zero_nat))) (= (@ (@ tptp.groups1707563613775114915nt_nat F2) A4) tptp.zero_zero_nat)))))
% 6.73/7.06 (assert (forall ((F2 (-> tptp.nat tptp.code_integer)) (A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.groups3455450783089532116nteger F2) (@ (@ tptp.set_or1269000886237332187st_nat A) B)) (@ (@ (@ (@ tptp.set_fo1084959871951514735nteger (lambda ((A5 tptp.nat) (__flatten_var_0 tptp.code_integer)) (@ (@ tptp.times_3573771949741848930nteger (@ F2 A5)) __flatten_var_0))) A) B) tptp.one_one_Code_integer))))
% 6.73/7.06 (assert (forall ((F2 (-> tptp.nat tptp.complex)) (A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.groups6464643781859351333omplex F2) (@ (@ tptp.set_or1269000886237332187st_nat A) B)) (@ (@ (@ (@ tptp.set_fo1517530859248394432omplex (lambda ((A5 tptp.nat) (__flatten_var_0 tptp.complex)) (@ (@ tptp.times_times_complex (@ F2 A5)) __flatten_var_0))) A) B) tptp.one_one_complex))))
% 6.73/7.06 (assert (forall ((F2 (-> tptp.nat tptp.real)) (A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.groups129246275422532515t_real F2) (@ (@ tptp.set_or1269000886237332187st_nat A) B)) (@ (@ (@ (@ tptp.set_fo3111899725591712190t_real (lambda ((A5 tptp.nat) (__flatten_var_0 tptp.real)) (@ (@ tptp.times_times_real (@ F2 A5)) __flatten_var_0))) A) B) tptp.one_one_real))))
% 6.73/7.06 (assert (forall ((F2 (-> tptp.nat tptp.rat)) (A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.groups73079841787564623at_rat F2) (@ (@ tptp.set_or1269000886237332187st_nat A) B)) (@ (@ (@ (@ tptp.set_fo1949268297981939178at_rat (lambda ((A5 tptp.nat) (__flatten_var_0 tptp.rat)) (@ (@ tptp.times_times_rat (@ F2 A5)) __flatten_var_0))) A) B) tptp.one_one_rat))))
% 6.73/7.06 (assert (forall ((F2 (-> tptp.nat tptp.int)) (A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.groups705719431365010083at_int F2) (@ (@ tptp.set_or1269000886237332187st_nat A) B)) (@ (@ (@ (@ tptp.set_fo2581907887559384638at_int (lambda ((A5 tptp.nat) (__flatten_var_0 tptp.int)) (@ (@ tptp.times_times_int (@ F2 A5)) __flatten_var_0))) A) B) tptp.one_one_int))))
% 6.73/7.06 (assert (forall ((F2 (-> tptp.nat tptp.nat)) (A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat F2) (@ (@ tptp.set_or1269000886237332187st_nat A) B)) (@ (@ (@ (@ tptp.set_fo2584398358068434914at_nat (lambda ((A5 tptp.nat) (__flatten_var_0 tptp.nat)) (@ (@ tptp.times_times_nat (@ F2 A5)) __flatten_var_0))) A) B) tptp.one_one_nat))))
% 6.73/7.06 (assert (forall ((N tptp.nat)) (= (= (@ tptp.set_ord_lessThan_nat N) tptp.bot_bot_set_nat) (= N tptp.bot_bot_nat))))
% 6.73/7.06 (assert (forall ((M2 tptp.real) (N tptp.real)) (= (@ (@ tptp.ord_less_set_real (@ tptp.set_or5984915006950818249n_real M2)) (@ tptp.set_or5984915006950818249n_real N)) (@ (@ tptp.ord_less_real M2) N))))
% 6.73/7.06 (assert (forall ((M2 tptp.rat) (N tptp.rat)) (= (@ (@ tptp.ord_less_set_rat (@ tptp.set_ord_lessThan_rat M2)) (@ tptp.set_ord_lessThan_rat N)) (@ (@ tptp.ord_less_rat M2) N))))
% 6.73/7.06 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_set_num (@ tptp.set_ord_lessThan_num M2)) (@ tptp.set_ord_lessThan_num N)) (@ (@ tptp.ord_less_num M2) N))))
% 6.73/7.06 (assert (forall ((M2 tptp.int) (N tptp.int)) (= (@ (@ tptp.ord_less_set_int (@ tptp.set_ord_lessThan_int M2)) (@ tptp.set_ord_lessThan_int N)) (@ (@ tptp.ord_less_int M2) N))))
% 6.73/7.06 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_set_nat (@ tptp.set_ord_lessThan_nat M2)) (@ tptp.set_ord_lessThan_nat N)) (@ (@ tptp.ord_less_nat M2) N))))
% 6.73/7.06 (assert (forall ((K2 tptp.nat)) (= (@ tptp.set_ord_lessThan_nat (@ tptp.suc K2)) (@ (@ tptp.insert_nat K2) (@ tptp.set_ord_lessThan_nat K2)))))
% 6.73/7.06 (assert (forall ((N tptp.nat)) (= (= (@ tptp.set_ord_lessThan_nat N) tptp.bot_bot_set_nat) (= N tptp.zero_zero_nat))))
% 6.73/7.06 (assert (= tptp.neg_numeral_dbl_real (lambda ((X4 tptp.real)) (@ (@ tptp.plus_plus_real X4) X4))))
% 6.73/7.06 (assert (= tptp.neg_numeral_dbl_rat (lambda ((X4 tptp.rat)) (@ (@ tptp.plus_plus_rat X4) X4))))
% 6.73/7.06 (assert (= tptp.neg_numeral_dbl_int (lambda ((X4 tptp.int)) (@ (@ tptp.plus_plus_int X4) X4))))
% 6.73/7.06 (assert (forall ((G2 (-> tptp.nat tptp.int)) (M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups705719431365010083at_int G2) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M2)) (@ tptp.suc N))) (@ (@ tptp.groups705719431365010083at_int (lambda ((I tptp.nat)) (@ G2 (@ tptp.suc I)))) (@ (@ tptp.set_or1269000886237332187st_nat M2) N)))))
% 6.73/7.06 (assert (forall ((G2 (-> tptp.nat tptp.nat)) (M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat G2) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M2)) (@ tptp.suc N))) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I tptp.nat)) (@ G2 (@ tptp.suc I)))) (@ (@ tptp.set_or1269000886237332187st_nat M2) N)))))
% 6.73/7.06 (assert (forall ((G2 (-> tptp.nat tptp.int)) (M2 tptp.nat) (K2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups705719431365010083at_int G2) (@ (@ tptp.set_or1269000886237332187st_nat (@ (@ tptp.plus_plus_nat M2) K2)) (@ (@ tptp.plus_plus_nat N) K2))) (@ (@ tptp.groups705719431365010083at_int (lambda ((I tptp.nat)) (@ G2 (@ (@ tptp.plus_plus_nat I) K2)))) (@ (@ tptp.set_or1269000886237332187st_nat M2) N)))))
% 6.73/7.06 (assert (forall ((G2 (-> tptp.nat tptp.nat)) (M2 tptp.nat) (K2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat G2) (@ (@ tptp.set_or1269000886237332187st_nat (@ (@ tptp.plus_plus_nat M2) K2)) (@ (@ tptp.plus_plus_nat N) K2))) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I tptp.nat)) (@ G2 (@ (@ tptp.plus_plus_nat I) K2)))) (@ (@ tptp.set_or1269000886237332187st_nat M2) N)))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_complex) (F2 (-> tptp.complex tptp.code_integer))) (=> (forall ((X3 tptp.complex)) (let ((_let_1 (@ F2 X3))) (=> (@ (@ tptp.member_complex X3) A4) (and (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) _let_1) (@ (@ tptp.ord_le3102999989581377725nteger _let_1) tptp.one_one_Code_integer))))) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.groups8682486955453173170nteger F2) A4)) tptp.one_one_Code_integer))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_real) (F2 (-> tptp.real tptp.code_integer))) (=> (forall ((X3 tptp.real)) (let ((_let_1 (@ F2 X3))) (=> (@ (@ tptp.member_real X3) A4) (and (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) _let_1) (@ (@ tptp.ord_le3102999989581377725nteger _let_1) tptp.one_one_Code_integer))))) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.groups6225526099057966256nteger F2) A4)) tptp.one_one_Code_integer))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_nat) (F2 (-> tptp.nat tptp.code_integer))) (=> (forall ((X3 tptp.nat)) (let ((_let_1 (@ F2 X3))) (=> (@ (@ tptp.member_nat X3) A4) (and (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) _let_1) (@ (@ tptp.ord_le3102999989581377725nteger _let_1) tptp.one_one_Code_integer))))) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.groups3455450783089532116nteger F2) A4)) tptp.one_one_Code_integer))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_int) (F2 (-> tptp.int tptp.code_integer))) (=> (forall ((X3 tptp.int)) (let ((_let_1 (@ F2 X3))) (=> (@ (@ tptp.member_int X3) A4) (and (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) _let_1) (@ (@ tptp.ord_le3102999989581377725nteger _let_1) tptp.one_one_Code_integer))))) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.groups3827104343326376752nteger F2) A4)) tptp.one_one_Code_integer))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_complex) (F2 (-> tptp.complex tptp.real))) (=> (forall ((X3 tptp.complex)) (let ((_let_1 (@ F2 X3))) (=> (@ (@ tptp.member_complex X3) A4) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) tptp.one_one_real))))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups766887009212190081x_real F2) A4)) tptp.one_one_real))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_real) (F2 (-> tptp.real tptp.real))) (=> (forall ((X3 tptp.real)) (let ((_let_1 (@ F2 X3))) (=> (@ (@ tptp.member_real X3) A4) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) tptp.one_one_real))))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups1681761925125756287l_real F2) A4)) tptp.one_one_real))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_nat) (F2 (-> tptp.nat tptp.real))) (=> (forall ((X3 tptp.nat)) (let ((_let_1 (@ F2 X3))) (=> (@ (@ tptp.member_nat X3) A4) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) tptp.one_one_real))))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups129246275422532515t_real F2) A4)) tptp.one_one_real))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_int) (F2 (-> tptp.int tptp.real))) (=> (forall ((X3 tptp.int)) (let ((_let_1 (@ F2 X3))) (=> (@ (@ tptp.member_int X3) A4) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) tptp.one_one_real))))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups2316167850115554303t_real F2) A4)) tptp.one_one_real))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_complex) (F2 (-> tptp.complex tptp.rat))) (=> (forall ((X3 tptp.complex)) (let ((_let_1 (@ F2 X3))) (=> (@ (@ tptp.member_complex X3) A4) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1) (@ (@ tptp.ord_less_eq_rat _let_1) tptp.one_one_rat))))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups225925009352817453ex_rat F2) A4)) tptp.one_one_rat))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_real) (F2 (-> tptp.real tptp.rat))) (=> (forall ((X3 tptp.real)) (let ((_let_1 (@ F2 X3))) (=> (@ (@ tptp.member_real X3) A4) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1) (@ (@ tptp.ord_less_eq_rat _let_1) tptp.one_one_rat))))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups4061424788464935467al_rat F2) A4)) tptp.one_one_rat))))
% 6.73/7.06 (assert (forall ((R2 (-> tptp.code_integer tptp.code_integer Bool)) (S3 tptp.set_nat) (H (-> tptp.nat tptp.code_integer)) (G2 (-> tptp.nat tptp.code_integer))) (=> (@ (@ R2 tptp.one_one_Code_integer) tptp.one_one_Code_integer) (=> (forall ((X15 tptp.code_integer) (Y15 tptp.code_integer) (X23 tptp.code_integer) (Y23 tptp.code_integer)) (=> (and (@ (@ R2 X15) X23) (@ (@ R2 Y15) Y23)) (@ (@ R2 (@ (@ tptp.times_3573771949741848930nteger X15) Y15)) (@ (@ tptp.times_3573771949741848930nteger X23) Y23)))) (=> (@ tptp.finite_finite_nat S3) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) S3) (@ (@ R2 (@ H X3)) (@ G2 X3)))) (@ (@ R2 (@ (@ tptp.groups3455450783089532116nteger H) S3)) (@ (@ tptp.groups3455450783089532116nteger G2) S3))))))))
% 6.73/7.06 (assert (forall ((R2 (-> tptp.code_integer tptp.code_integer Bool)) (S3 tptp.set_int) (H (-> tptp.int tptp.code_integer)) (G2 (-> tptp.int tptp.code_integer))) (=> (@ (@ R2 tptp.one_one_Code_integer) tptp.one_one_Code_integer) (=> (forall ((X15 tptp.code_integer) (Y15 tptp.code_integer) (X23 tptp.code_integer) (Y23 tptp.code_integer)) (=> (and (@ (@ R2 X15) X23) (@ (@ R2 Y15) Y23)) (@ (@ R2 (@ (@ tptp.times_3573771949741848930nteger X15) Y15)) (@ (@ tptp.times_3573771949741848930nteger X23) Y23)))) (=> (@ tptp.finite_finite_int S3) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) S3) (@ (@ R2 (@ H X3)) (@ G2 X3)))) (@ (@ R2 (@ (@ tptp.groups3827104343326376752nteger H) S3)) (@ (@ tptp.groups3827104343326376752nteger G2) S3))))))))
% 6.73/7.06 (assert (forall ((R2 (-> tptp.code_integer tptp.code_integer Bool)) (S3 tptp.set_complex) (H (-> tptp.complex tptp.code_integer)) (G2 (-> tptp.complex tptp.code_integer))) (=> (@ (@ R2 tptp.one_one_Code_integer) tptp.one_one_Code_integer) (=> (forall ((X15 tptp.code_integer) (Y15 tptp.code_integer) (X23 tptp.code_integer) (Y23 tptp.code_integer)) (=> (and (@ (@ R2 X15) X23) (@ (@ R2 Y15) Y23)) (@ (@ R2 (@ (@ tptp.times_3573771949741848930nteger X15) Y15)) (@ (@ tptp.times_3573771949741848930nteger X23) Y23)))) (=> (@ tptp.finite3207457112153483333omplex S3) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) S3) (@ (@ R2 (@ H X3)) (@ G2 X3)))) (@ (@ R2 (@ (@ tptp.groups8682486955453173170nteger H) S3)) (@ (@ tptp.groups8682486955453173170nteger G2) S3))))))))
% 6.73/7.06 (assert (forall ((R2 (-> tptp.complex tptp.complex Bool)) (S3 tptp.set_nat) (H (-> tptp.nat tptp.complex)) (G2 (-> tptp.nat tptp.complex))) (=> (@ (@ R2 tptp.one_one_complex) tptp.one_one_complex) (=> (forall ((X15 tptp.complex) (Y15 tptp.complex) (X23 tptp.complex) (Y23 tptp.complex)) (=> (and (@ (@ R2 X15) X23) (@ (@ R2 Y15) Y23)) (@ (@ R2 (@ (@ tptp.times_times_complex X15) Y15)) (@ (@ tptp.times_times_complex X23) Y23)))) (=> (@ tptp.finite_finite_nat S3) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) S3) (@ (@ R2 (@ H X3)) (@ G2 X3)))) (@ (@ R2 (@ (@ tptp.groups6464643781859351333omplex H) S3)) (@ (@ tptp.groups6464643781859351333omplex G2) S3))))))))
% 6.73/7.06 (assert (forall ((R2 (-> tptp.complex tptp.complex Bool)) (S3 tptp.set_int) (H (-> tptp.int tptp.complex)) (G2 (-> tptp.int tptp.complex))) (=> (@ (@ R2 tptp.one_one_complex) tptp.one_one_complex) (=> (forall ((X15 tptp.complex) (Y15 tptp.complex) (X23 tptp.complex) (Y23 tptp.complex)) (=> (and (@ (@ R2 X15) X23) (@ (@ R2 Y15) Y23)) (@ (@ R2 (@ (@ tptp.times_times_complex X15) Y15)) (@ (@ tptp.times_times_complex X23) Y23)))) (=> (@ tptp.finite_finite_int S3) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) S3) (@ (@ R2 (@ H X3)) (@ G2 X3)))) (@ (@ R2 (@ (@ tptp.groups7440179247065528705omplex H) S3)) (@ (@ tptp.groups7440179247065528705omplex G2) S3))))))))
% 6.73/7.06 (assert (forall ((R2 (-> tptp.complex tptp.complex Bool)) (S3 tptp.set_complex) (H (-> tptp.complex tptp.complex)) (G2 (-> tptp.complex tptp.complex))) (=> (@ (@ R2 tptp.one_one_complex) tptp.one_one_complex) (=> (forall ((X15 tptp.complex) (Y15 tptp.complex) (X23 tptp.complex) (Y23 tptp.complex)) (=> (and (@ (@ R2 X15) X23) (@ (@ R2 Y15) Y23)) (@ (@ R2 (@ (@ tptp.times_times_complex X15) Y15)) (@ (@ tptp.times_times_complex X23) Y23)))) (=> (@ tptp.finite3207457112153483333omplex S3) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) S3) (@ (@ R2 (@ H X3)) (@ G2 X3)))) (@ (@ R2 (@ (@ tptp.groups3708469109370488835omplex H) S3)) (@ (@ tptp.groups3708469109370488835omplex G2) S3))))))))
% 6.73/7.06 (assert (forall ((R2 (-> tptp.real tptp.real Bool)) (S3 tptp.set_nat) (H (-> tptp.nat tptp.real)) (G2 (-> tptp.nat tptp.real))) (=> (@ (@ R2 tptp.one_one_real) tptp.one_one_real) (=> (forall ((X15 tptp.real) (Y15 tptp.real) (X23 tptp.real) (Y23 tptp.real)) (=> (and (@ (@ R2 X15) X23) (@ (@ R2 Y15) Y23)) (@ (@ R2 (@ (@ tptp.times_times_real X15) Y15)) (@ (@ tptp.times_times_real X23) Y23)))) (=> (@ tptp.finite_finite_nat S3) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) S3) (@ (@ R2 (@ H X3)) (@ G2 X3)))) (@ (@ R2 (@ (@ tptp.groups129246275422532515t_real H) S3)) (@ (@ tptp.groups129246275422532515t_real G2) S3))))))))
% 6.73/7.06 (assert (forall ((R2 (-> tptp.real tptp.real Bool)) (S3 tptp.set_int) (H (-> tptp.int tptp.real)) (G2 (-> tptp.int tptp.real))) (=> (@ (@ R2 tptp.one_one_real) tptp.one_one_real) (=> (forall ((X15 tptp.real) (Y15 tptp.real) (X23 tptp.real) (Y23 tptp.real)) (=> (and (@ (@ R2 X15) X23) (@ (@ R2 Y15) Y23)) (@ (@ R2 (@ (@ tptp.times_times_real X15) Y15)) (@ (@ tptp.times_times_real X23) Y23)))) (=> (@ tptp.finite_finite_int S3) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) S3) (@ (@ R2 (@ H X3)) (@ G2 X3)))) (@ (@ R2 (@ (@ tptp.groups2316167850115554303t_real H) S3)) (@ (@ tptp.groups2316167850115554303t_real G2) S3))))))))
% 6.73/7.06 (assert (forall ((R2 (-> tptp.real tptp.real Bool)) (S3 tptp.set_complex) (H (-> tptp.complex tptp.real)) (G2 (-> tptp.complex tptp.real))) (=> (@ (@ R2 tptp.one_one_real) tptp.one_one_real) (=> (forall ((X15 tptp.real) (Y15 tptp.real) (X23 tptp.real) (Y23 tptp.real)) (=> (and (@ (@ R2 X15) X23) (@ (@ R2 Y15) Y23)) (@ (@ R2 (@ (@ tptp.times_times_real X15) Y15)) (@ (@ tptp.times_times_real X23) Y23)))) (=> (@ tptp.finite3207457112153483333omplex S3) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) S3) (@ (@ R2 (@ H X3)) (@ G2 X3)))) (@ (@ R2 (@ (@ tptp.groups766887009212190081x_real H) S3)) (@ (@ tptp.groups766887009212190081x_real G2) S3))))))))
% 6.73/7.06 (assert (forall ((R2 (-> tptp.rat tptp.rat Bool)) (S3 tptp.set_nat) (H (-> tptp.nat tptp.rat)) (G2 (-> tptp.nat tptp.rat))) (=> (@ (@ R2 tptp.one_one_rat) tptp.one_one_rat) (=> (forall ((X15 tptp.rat) (Y15 tptp.rat) (X23 tptp.rat) (Y23 tptp.rat)) (=> (and (@ (@ R2 X15) X23) (@ (@ R2 Y15) Y23)) (@ (@ R2 (@ (@ tptp.times_times_rat X15) Y15)) (@ (@ tptp.times_times_rat X23) Y23)))) (=> (@ tptp.finite_finite_nat S3) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) S3) (@ (@ R2 (@ H X3)) (@ G2 X3)))) (@ (@ R2 (@ (@ tptp.groups73079841787564623at_rat H) S3)) (@ (@ tptp.groups73079841787564623at_rat G2) S3))))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_real) (X tptp.real) (G2 (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.groups1681761925125756287l_real G2))) (let ((_let_2 (@ _let_1 A4))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_real X) A4)))) (let ((_let_4 (@ (@ tptp.member_real X) A4))) (=> (@ tptp.finite_finite_real A4) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.times_times_real (@ G2 X)) _let_2)))))))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_nat) (X tptp.nat) (G2 (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.groups129246275422532515t_real G2))) (let ((_let_2 (@ _let_1 A4))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_nat X) A4)))) (let ((_let_4 (@ (@ tptp.member_nat X) A4))) (=> (@ tptp.finite_finite_nat A4) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.times_times_real (@ G2 X)) _let_2)))))))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_int) (X tptp.int) (G2 (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups2316167850115554303t_real G2))) (let ((_let_2 (@ _let_1 A4))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_int X) A4)))) (let ((_let_4 (@ (@ tptp.member_int X) A4))) (=> (@ tptp.finite_finite_int A4) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.times_times_real (@ G2 X)) _let_2)))))))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_complex) (X tptp.complex) (G2 (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups766887009212190081x_real G2))) (let ((_let_2 (@ _let_1 A4))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_complex X) A4)))) (let ((_let_4 (@ (@ tptp.member_complex X) A4))) (=> (@ tptp.finite3207457112153483333omplex A4) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.times_times_real (@ G2 X)) _let_2)))))))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_real) (X tptp.real) (G2 (-> tptp.real tptp.rat))) (let ((_let_1 (@ tptp.groups4061424788464935467al_rat G2))) (let ((_let_2 (@ _let_1 A4))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_real X) A4)))) (let ((_let_4 (@ (@ tptp.member_real X) A4))) (=> (@ tptp.finite_finite_real A4) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.times_times_rat (@ G2 X)) _let_2)))))))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_nat) (X tptp.nat) (G2 (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups73079841787564623at_rat G2))) (let ((_let_2 (@ _let_1 A4))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_nat X) A4)))) (let ((_let_4 (@ (@ tptp.member_nat X) A4))) (=> (@ tptp.finite_finite_nat A4) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.times_times_rat (@ G2 X)) _let_2)))))))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_int) (X tptp.int) (G2 (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups1072433553688619179nt_rat G2))) (let ((_let_2 (@ _let_1 A4))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_int X) A4)))) (let ((_let_4 (@ (@ tptp.member_int X) A4))) (=> (@ tptp.finite_finite_int A4) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.times_times_rat (@ G2 X)) _let_2)))))))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_complex) (X tptp.complex) (G2 (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups225925009352817453ex_rat G2))) (let ((_let_2 (@ _let_1 A4))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_complex X) A4)))) (let ((_let_4 (@ (@ tptp.member_complex X) A4))) (=> (@ tptp.finite3207457112153483333omplex A4) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.times_times_rat (@ G2 X)) _let_2)))))))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_real) (X tptp.real) (G2 (-> tptp.real tptp.nat))) (let ((_let_1 (@ tptp.groups4696554848551431203al_nat G2))) (let ((_let_2 (@ _let_1 A4))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_real X) A4)))) (let ((_let_4 (@ (@ tptp.member_real X) A4))) (=> (@ tptp.finite_finite_real A4) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.times_times_nat (@ G2 X)) _let_2)))))))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_int) (X tptp.int) (G2 (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups1707563613775114915nt_nat G2))) (let ((_let_2 (@ _let_1 A4))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_int X) A4)))) (let ((_let_4 (@ (@ tptp.member_int X) A4))) (=> (@ tptp.finite_finite_int A4) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.times_times_nat (@ G2 X)) _let_2)))))))))))
% 6.73/7.06 (assert (forall ((L tptp.nat) (U tptp.nat)) (= (@ (@ tptp.inf_inf_set_nat (@ tptp.set_ord_lessThan_nat L)) (@ (@ tptp.set_or1269000886237332187st_nat L) U)) tptp.bot_bot_set_nat)))
% 6.73/7.06 (assert (forall ((L tptp.int) (U tptp.int)) (= (@ (@ tptp.inf_inf_set_int (@ tptp.set_ord_lessThan_int L)) (@ (@ tptp.set_or1266510415728281911st_int L) U)) tptp.bot_bot_set_int)))
% 6.73/7.06 (assert (forall ((L tptp.real) (U tptp.real)) (= (@ (@ tptp.inf_inf_set_real (@ tptp.set_or5984915006950818249n_real L)) (@ (@ tptp.set_or1222579329274155063t_real L) U)) tptp.bot_bot_set_real)))
% 6.73/7.06 (assert (forall ((G2 (-> tptp.nat tptp.int)) (N tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat N) M2))) (= (@ (@ tptp.groups705719431365010083at_int G2) _let_1) (@ (@ tptp.groups705719431365010083at_int (lambda ((I tptp.nat)) (@ G2 (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M2) N)) I)))) _let_1)))))
% 6.73/7.06 (assert (forall ((G2 (-> tptp.nat tptp.nat)) (N tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat N) M2))) (= (@ (@ tptp.groups708209901874060359at_nat G2) _let_1) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I tptp.nat)) (@ G2 (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M2) N)) I)))) _let_1)))))
% 6.73/7.06 (assert (forall ((G2 (-> tptp.nat tptp.nat)) (N tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat N))) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I tptp.nat)) (@ G2 (@ (@ tptp.minus_minus_nat N) (@ tptp.suc I))))) _let_1) (@ (@ tptp.groups3542108847815614940at_nat G2) _let_1)))))
% 6.73/7.06 (assert (forall ((G2 (-> tptp.nat tptp.real)) (N tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat N))) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I tptp.nat)) (@ G2 (@ (@ tptp.minus_minus_nat N) (@ tptp.suc I))))) _let_1) (@ (@ tptp.groups6591440286371151544t_real G2) _let_1)))))
% 6.73/7.06 (assert (forall ((Q (-> tptp.nat tptp.nat)) (P2 (-> tptp.nat tptp.nat)) (N tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat N))) (=> (forall ((X3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ Q X3)) (@ P2 X3))) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.groups3542108847815614940at_nat P2) _let_1)) (@ (@ tptp.groups3542108847815614940at_nat Q) _let_1)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X4 tptp.nat)) (@ (@ tptp.minus_minus_nat (@ P2 X4)) (@ Q X4)))) _let_1))))))
% 6.73/7.06 (assert (forall ((I5 tptp.set_real) (I2 tptp.real) (F2 (-> tptp.real tptp.code_integer))) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer))) (=> (@ tptp.finite_finite_real I5) (=> (@ (@ tptp.member_real I2) I5) (=> (@ _let_1 (@ F2 I2)) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) I5) (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (@ F2 I3)))) (@ _let_1 (@ (@ tptp.groups6225526099057966256nteger F2) I5)))))))))
% 6.73/7.06 (assert (forall ((I5 tptp.set_nat) (I2 tptp.nat) (F2 (-> tptp.nat tptp.code_integer))) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer))) (=> (@ tptp.finite_finite_nat I5) (=> (@ (@ tptp.member_nat I2) I5) (=> (@ _let_1 (@ F2 I2)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.member_nat I3) I5) (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (@ F2 I3)))) (@ _let_1 (@ (@ tptp.groups3455450783089532116nteger F2) I5)))))))))
% 6.73/7.06 (assert (forall ((I5 tptp.set_int) (I2 tptp.int) (F2 (-> tptp.int tptp.code_integer))) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer))) (=> (@ tptp.finite_finite_int I5) (=> (@ (@ tptp.member_int I2) I5) (=> (@ _let_1 (@ F2 I2)) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) I5) (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (@ F2 I3)))) (@ _let_1 (@ (@ tptp.groups3827104343326376752nteger F2) I5)))))))))
% 6.73/7.06 (assert (forall ((I5 tptp.set_complex) (I2 tptp.complex) (F2 (-> tptp.complex tptp.code_integer))) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer))) (=> (@ tptp.finite3207457112153483333omplex I5) (=> (@ (@ tptp.member_complex I2) I5) (=> (@ _let_1 (@ F2 I2)) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) I5) (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (@ F2 I3)))) (@ _let_1 (@ (@ tptp.groups8682486955453173170nteger F2) I5)))))))))
% 6.73/7.06 (assert (forall ((I5 tptp.set_real) (I2 tptp.real) (F2 (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ tptp.finite_finite_real I5) (=> (@ (@ tptp.member_real I2) I5) (=> (@ _let_1 (@ F2 I2)) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) I5) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F2 I3)))) (@ _let_1 (@ (@ tptp.groups1681761925125756287l_real F2) I5)))))))))
% 6.73/7.06 (assert (forall ((I5 tptp.set_nat) (I2 tptp.nat) (F2 (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ tptp.finite_finite_nat I5) (=> (@ (@ tptp.member_nat I2) I5) (=> (@ _let_1 (@ F2 I2)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.member_nat I3) I5) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F2 I3)))) (@ _let_1 (@ (@ tptp.groups129246275422532515t_real F2) I5)))))))))
% 6.73/7.06 (assert (forall ((I5 tptp.set_int) (I2 tptp.int) (F2 (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ tptp.finite_finite_int I5) (=> (@ (@ tptp.member_int I2) I5) (=> (@ _let_1 (@ F2 I2)) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) I5) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F2 I3)))) (@ _let_1 (@ (@ tptp.groups2316167850115554303t_real F2) I5)))))))))
% 6.73/7.06 (assert (forall ((I5 tptp.set_complex) (I2 tptp.complex) (F2 (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ tptp.finite3207457112153483333omplex I5) (=> (@ (@ tptp.member_complex I2) I5) (=> (@ _let_1 (@ F2 I2)) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) I5) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F2 I3)))) (@ _let_1 (@ (@ tptp.groups766887009212190081x_real F2) I5)))))))))
% 6.73/7.06 (assert (forall ((I5 tptp.set_real) (I2 tptp.real) (F2 (-> tptp.real tptp.rat))) (let ((_let_1 (@ tptp.ord_less_rat tptp.one_one_rat))) (=> (@ tptp.finite_finite_real I5) (=> (@ (@ tptp.member_real I2) I5) (=> (@ _let_1 (@ F2 I2)) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) I5) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ F2 I3)))) (@ _let_1 (@ (@ tptp.groups4061424788464935467al_rat F2) I5)))))))))
% 6.73/7.06 (assert (forall ((I5 tptp.set_nat) (I2 tptp.nat) (F2 (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.ord_less_rat tptp.one_one_rat))) (=> (@ tptp.finite_finite_nat I5) (=> (@ (@ tptp.member_nat I2) I5) (=> (@ _let_1 (@ F2 I2)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.member_nat I3) I5) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ F2 I3)))) (@ _let_1 (@ (@ tptp.groups73079841787564623at_rat F2) I5)))))))))
% 6.73/7.06 (assert (forall ((B5 tptp.set_int) (A4 tptp.set_int) (G2 (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups2316167850115554303t_real G2))) (=> (@ (@ tptp.ord_less_eq_set_int B5) A4) (=> (@ tptp.finite_finite_int A4) (= (@ _let_1 A4) (@ (@ tptp.times_times_real (@ _let_1 (@ (@ tptp.minus_minus_set_int A4) B5))) (@ _let_1 B5))))))))
% 6.73/7.06 (assert (forall ((B5 tptp.set_complex) (A4 tptp.set_complex) (G2 (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups766887009212190081x_real G2))) (=> (@ (@ tptp.ord_le211207098394363844omplex B5) A4) (=> (@ tptp.finite3207457112153483333omplex A4) (= (@ _let_1 A4) (@ (@ tptp.times_times_real (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A4) B5))) (@ _let_1 B5))))))))
% 6.73/7.06 (assert (forall ((B5 tptp.set_int) (A4 tptp.set_int) (G2 (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups1072433553688619179nt_rat G2))) (=> (@ (@ tptp.ord_less_eq_set_int B5) A4) (=> (@ tptp.finite_finite_int A4) (= (@ _let_1 A4) (@ (@ tptp.times_times_rat (@ _let_1 (@ (@ tptp.minus_minus_set_int A4) B5))) (@ _let_1 B5))))))))
% 6.73/7.06 (assert (forall ((B5 tptp.set_complex) (A4 tptp.set_complex) (G2 (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups225925009352817453ex_rat G2))) (=> (@ (@ tptp.ord_le211207098394363844omplex B5) A4) (=> (@ tptp.finite3207457112153483333omplex A4) (= (@ _let_1 A4) (@ (@ tptp.times_times_rat (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A4) B5))) (@ _let_1 B5))))))))
% 6.73/7.06 (assert (forall ((B5 tptp.set_int) (A4 tptp.set_int) (G2 (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups1707563613775114915nt_nat G2))) (=> (@ (@ tptp.ord_less_eq_set_int B5) A4) (=> (@ tptp.finite_finite_int A4) (= (@ _let_1 A4) (@ (@ tptp.times_times_nat (@ _let_1 (@ (@ tptp.minus_minus_set_int A4) B5))) (@ _let_1 B5))))))))
% 6.73/7.06 (assert (forall ((B5 tptp.set_complex) (A4 tptp.set_complex) (G2 (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups861055069439313189ex_nat G2))) (=> (@ (@ tptp.ord_le211207098394363844omplex B5) A4) (=> (@ tptp.finite3207457112153483333omplex A4) (= (@ _let_1 A4) (@ (@ tptp.times_times_nat (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A4) B5))) (@ _let_1 B5))))))))
% 6.73/7.06 (assert (forall ((B5 tptp.set_complex) (A4 tptp.set_complex) (G2 (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.groups858564598930262913ex_int G2))) (=> (@ (@ tptp.ord_le211207098394363844omplex B5) A4) (=> (@ tptp.finite3207457112153483333omplex A4) (= (@ _let_1 A4) (@ (@ tptp.times_times_int (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A4) B5))) (@ _let_1 B5))))))))
% 6.73/7.06 (assert (forall ((B5 tptp.set_nat) (A4 tptp.set_nat) (G2 (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.groups129246275422532515t_real G2))) (=> (@ (@ tptp.ord_less_eq_set_nat B5) A4) (=> (@ tptp.finite_finite_nat A4) (= (@ _let_1 A4) (@ (@ tptp.times_times_real (@ _let_1 (@ (@ tptp.minus_minus_set_nat A4) B5))) (@ _let_1 B5))))))))
% 6.73/7.06 (assert (forall ((B5 tptp.set_nat) (A4 tptp.set_nat) (G2 (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups73079841787564623at_rat G2))) (=> (@ (@ tptp.ord_less_eq_set_nat B5) A4) (=> (@ tptp.finite_finite_nat A4) (= (@ _let_1 A4) (@ (@ tptp.times_times_rat (@ _let_1 (@ (@ tptp.minus_minus_set_nat A4) B5))) (@ _let_1 B5))))))))
% 6.73/7.06 (assert (forall ((B5 tptp.set_nat) (A4 tptp.set_nat) (G2 (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.groups705719431365010083at_int G2))) (=> (@ (@ tptp.ord_less_eq_set_nat B5) A4) (=> (@ tptp.finite_finite_nat A4) (= (@ _let_1 A4) (@ (@ tptp.times_times_int (@ _let_1 (@ (@ tptp.minus_minus_set_nat A4) B5))) (@ _let_1 B5))))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_int) (B5 tptp.set_int) (G2 (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups2316167850115554303t_real G2))) (=> (@ tptp.finite_finite_int A4) (=> (@ tptp.finite_finite_int B5) (= (@ (@ tptp.times_times_real (@ _let_1 (@ (@ tptp.sup_sup_set_int A4) B5))) (@ _let_1 (@ (@ tptp.inf_inf_set_int A4) B5))) (@ (@ tptp.times_times_real (@ _let_1 A4)) (@ _let_1 B5))))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_complex) (B5 tptp.set_complex) (G2 (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups766887009212190081x_real G2))) (=> (@ tptp.finite3207457112153483333omplex A4) (=> (@ tptp.finite3207457112153483333omplex B5) (= (@ (@ tptp.times_times_real (@ _let_1 (@ (@ tptp.sup_sup_set_complex A4) B5))) (@ _let_1 (@ (@ tptp.inf_inf_set_complex A4) B5))) (@ (@ tptp.times_times_real (@ _let_1 A4)) (@ _let_1 B5))))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_nat) (B5 tptp.set_nat) (G2 (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.groups129246275422532515t_real G2))) (=> (@ tptp.finite_finite_nat A4) (=> (@ tptp.finite_finite_nat B5) (= (@ (@ tptp.times_times_real (@ _let_1 (@ (@ tptp.sup_sup_set_nat A4) B5))) (@ _let_1 (@ (@ tptp.inf_inf_set_nat A4) B5))) (@ (@ tptp.times_times_real (@ _let_1 A4)) (@ _let_1 B5))))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_int) (B5 tptp.set_int) (G2 (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups1072433553688619179nt_rat G2))) (=> (@ tptp.finite_finite_int A4) (=> (@ tptp.finite_finite_int B5) (= (@ (@ tptp.times_times_rat (@ _let_1 (@ (@ tptp.sup_sup_set_int A4) B5))) (@ _let_1 (@ (@ tptp.inf_inf_set_int A4) B5))) (@ (@ tptp.times_times_rat (@ _let_1 A4)) (@ _let_1 B5))))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_complex) (B5 tptp.set_complex) (G2 (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups225925009352817453ex_rat G2))) (=> (@ tptp.finite3207457112153483333omplex A4) (=> (@ tptp.finite3207457112153483333omplex B5) (= (@ (@ tptp.times_times_rat (@ _let_1 (@ (@ tptp.sup_sup_set_complex A4) B5))) (@ _let_1 (@ (@ tptp.inf_inf_set_complex A4) B5))) (@ (@ tptp.times_times_rat (@ _let_1 A4)) (@ _let_1 B5))))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_nat) (B5 tptp.set_nat) (G2 (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups73079841787564623at_rat G2))) (=> (@ tptp.finite_finite_nat A4) (=> (@ tptp.finite_finite_nat B5) (= (@ (@ tptp.times_times_rat (@ _let_1 (@ (@ tptp.sup_sup_set_nat A4) B5))) (@ _let_1 (@ (@ tptp.inf_inf_set_nat A4) B5))) (@ (@ tptp.times_times_rat (@ _let_1 A4)) (@ _let_1 B5))))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_int) (B5 tptp.set_int) (G2 (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups1707563613775114915nt_nat G2))) (=> (@ tptp.finite_finite_int A4) (=> (@ tptp.finite_finite_int B5) (= (@ (@ tptp.times_times_nat (@ _let_1 (@ (@ tptp.sup_sup_set_int A4) B5))) (@ _let_1 (@ (@ tptp.inf_inf_set_int A4) B5))) (@ (@ tptp.times_times_nat (@ _let_1 A4)) (@ _let_1 B5))))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_complex) (B5 tptp.set_complex) (G2 (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups861055069439313189ex_nat G2))) (=> (@ tptp.finite3207457112153483333omplex A4) (=> (@ tptp.finite3207457112153483333omplex B5) (= (@ (@ tptp.times_times_nat (@ _let_1 (@ (@ tptp.sup_sup_set_complex A4) B5))) (@ _let_1 (@ (@ tptp.inf_inf_set_complex A4) B5))) (@ (@ tptp.times_times_nat (@ _let_1 A4)) (@ _let_1 B5))))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_complex) (B5 tptp.set_complex) (G2 (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.groups858564598930262913ex_int G2))) (=> (@ tptp.finite3207457112153483333omplex A4) (=> (@ tptp.finite3207457112153483333omplex B5) (= (@ (@ tptp.times_times_int (@ _let_1 (@ (@ tptp.sup_sup_set_complex A4) B5))) (@ _let_1 (@ (@ tptp.inf_inf_set_complex A4) B5))) (@ (@ tptp.times_times_int (@ _let_1 A4)) (@ _let_1 B5))))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_nat) (B5 tptp.set_nat) (G2 (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.groups705719431365010083at_int G2))) (=> (@ tptp.finite_finite_nat A4) (=> (@ tptp.finite_finite_nat B5) (= (@ (@ tptp.times_times_int (@ _let_1 (@ (@ tptp.sup_sup_set_nat A4) B5))) (@ _let_1 (@ (@ tptp.inf_inf_set_nat A4) B5))) (@ (@ tptp.times_times_int (@ _let_1 A4)) (@ _let_1 B5))))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_int) (G2 (-> tptp.int tptp.real)) (B5 tptp.set_int)) (let ((_let_1 (@ tptp.groups2316167850115554303t_real G2))) (=> (@ tptp.finite_finite_int A4) (= (@ _let_1 A4) (@ (@ tptp.times_times_real (@ _let_1 (@ (@ tptp.inf_inf_set_int A4) B5))) (@ _let_1 (@ (@ tptp.minus_minus_set_int A4) B5))))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_complex) (G2 (-> tptp.complex tptp.real)) (B5 tptp.set_complex)) (let ((_let_1 (@ tptp.groups766887009212190081x_real G2))) (=> (@ tptp.finite3207457112153483333omplex A4) (= (@ _let_1 A4) (@ (@ tptp.times_times_real (@ _let_1 (@ (@ tptp.inf_inf_set_complex A4) B5))) (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A4) B5))))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_nat) (G2 (-> tptp.nat tptp.real)) (B5 tptp.set_nat)) (let ((_let_1 (@ tptp.groups129246275422532515t_real G2))) (=> (@ tptp.finite_finite_nat A4) (= (@ _let_1 A4) (@ (@ tptp.times_times_real (@ _let_1 (@ (@ tptp.inf_inf_set_nat A4) B5))) (@ _let_1 (@ (@ tptp.minus_minus_set_nat A4) B5))))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_int) (G2 (-> tptp.int tptp.rat)) (B5 tptp.set_int)) (let ((_let_1 (@ tptp.groups1072433553688619179nt_rat G2))) (=> (@ tptp.finite_finite_int A4) (= (@ _let_1 A4) (@ (@ tptp.times_times_rat (@ _let_1 (@ (@ tptp.inf_inf_set_int A4) B5))) (@ _let_1 (@ (@ tptp.minus_minus_set_int A4) B5))))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_complex) (G2 (-> tptp.complex tptp.rat)) (B5 tptp.set_complex)) (let ((_let_1 (@ tptp.groups225925009352817453ex_rat G2))) (=> (@ tptp.finite3207457112153483333omplex A4) (= (@ _let_1 A4) (@ (@ tptp.times_times_rat (@ _let_1 (@ (@ tptp.inf_inf_set_complex A4) B5))) (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A4) B5))))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_nat) (G2 (-> tptp.nat tptp.rat)) (B5 tptp.set_nat)) (let ((_let_1 (@ tptp.groups73079841787564623at_rat G2))) (=> (@ tptp.finite_finite_nat A4) (= (@ _let_1 A4) (@ (@ tptp.times_times_rat (@ _let_1 (@ (@ tptp.inf_inf_set_nat A4) B5))) (@ _let_1 (@ (@ tptp.minus_minus_set_nat A4) B5))))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_int) (G2 (-> tptp.int tptp.nat)) (B5 tptp.set_int)) (let ((_let_1 (@ tptp.groups1707563613775114915nt_nat G2))) (=> (@ tptp.finite_finite_int A4) (= (@ _let_1 A4) (@ (@ tptp.times_times_nat (@ _let_1 (@ (@ tptp.inf_inf_set_int A4) B5))) (@ _let_1 (@ (@ tptp.minus_minus_set_int A4) B5))))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_complex) (G2 (-> tptp.complex tptp.nat)) (B5 tptp.set_complex)) (let ((_let_1 (@ tptp.groups861055069439313189ex_nat G2))) (=> (@ tptp.finite3207457112153483333omplex A4) (= (@ _let_1 A4) (@ (@ tptp.times_times_nat (@ _let_1 (@ (@ tptp.inf_inf_set_complex A4) B5))) (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A4) B5))))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_complex) (G2 (-> tptp.complex tptp.int)) (B5 tptp.set_complex)) (let ((_let_1 (@ tptp.groups858564598930262913ex_int G2))) (=> (@ tptp.finite3207457112153483333omplex A4) (= (@ _let_1 A4) (@ (@ tptp.times_times_int (@ _let_1 (@ (@ tptp.inf_inf_set_complex A4) B5))) (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A4) B5))))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_nat) (G2 (-> tptp.nat tptp.int)) (B5 tptp.set_nat)) (let ((_let_1 (@ tptp.groups705719431365010083at_int G2))) (=> (@ tptp.finite_finite_nat A4) (= (@ _let_1 A4) (@ (@ tptp.times_times_int (@ _let_1 (@ (@ tptp.inf_inf_set_nat A4) B5))) (@ _let_1 (@ (@ tptp.minus_minus_set_nat A4) B5))))))))
% 6.73/7.06 (assert (forall ((G2 (-> tptp.nat tptp.real)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat))) (let ((_let_3 (@ tptp.groups129246275422532515t_real G2))) (= (@ _let_3 (@ _let_2 _let_1)) (@ (@ tptp.times_times_real (@ _let_3 (@ _let_2 N))) (@ G2 _let_1))))))))
% 6.73/7.06 (assert (forall ((G2 (-> tptp.nat tptp.rat)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat))) (let ((_let_3 (@ tptp.groups73079841787564623at_rat G2))) (= (@ _let_3 (@ _let_2 _let_1)) (@ (@ tptp.times_times_rat (@ _let_3 (@ _let_2 N))) (@ G2 _let_1))))))))
% 6.73/7.06 (assert (forall ((G2 (-> tptp.nat tptp.int)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat))) (let ((_let_3 (@ tptp.groups705719431365010083at_int G2))) (= (@ _let_3 (@ _let_2 _let_1)) (@ (@ tptp.times_times_int (@ _let_3 (@ _let_2 N))) (@ G2 _let_1))))))))
% 6.73/7.06 (assert (forall ((G2 (-> tptp.nat tptp.nat)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat))) (let ((_let_3 (@ tptp.groups708209901874060359at_nat G2))) (= (@ _let_3 (@ _let_2 _let_1)) (@ (@ tptp.times_times_nat (@ _let_3 (@ _let_2 N))) (@ G2 _let_1))))))))
% 6.73/7.06 (assert (forall ((M2 tptp.nat) (N tptp.nat) (G2 (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.groups129246275422532515t_real G2))) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M2) N)) (@ (@ tptp.times_times_real (@ G2 M2)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M2)) N))))))))
% 6.73/7.06 (assert (forall ((M2 tptp.nat) (N tptp.nat) (G2 (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups73079841787564623at_rat G2))) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M2) N)) (@ (@ tptp.times_times_rat (@ G2 M2)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M2)) N))))))))
% 6.73/7.06 (assert (forall ((M2 tptp.nat) (N tptp.nat) (G2 (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.groups705719431365010083at_int G2))) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M2) N)) (@ (@ tptp.times_times_int (@ G2 M2)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M2)) N))))))))
% 6.73/7.06 (assert (forall ((M2 tptp.nat) (N tptp.nat) (G2 (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.groups708209901874060359at_nat G2))) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M2) N)) (@ (@ tptp.times_times_nat (@ G2 M2)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M2)) N))))))))
% 6.73/7.06 (assert (forall ((M2 tptp.nat) (N tptp.nat) (G2 (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat M2))) (let ((_let_2 (@ tptp.groups129246275422532515t_real G2))) (let ((_let_3 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_nat M2) _let_3) (= (@ _let_2 (@ _let_1 _let_3)) (@ (@ tptp.times_times_real (@ G2 _let_3)) (@ _let_2 (@ _let_1 N))))))))))
% 6.73/7.06 (assert (forall ((M2 tptp.nat) (N tptp.nat) (G2 (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat M2))) (let ((_let_2 (@ tptp.groups73079841787564623at_rat G2))) (let ((_let_3 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_nat M2) _let_3) (= (@ _let_2 (@ _let_1 _let_3)) (@ (@ tptp.times_times_rat (@ G2 _let_3)) (@ _let_2 (@ _let_1 N))))))))))
% 6.73/7.06 (assert (forall ((M2 tptp.nat) (N tptp.nat) (G2 (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat M2))) (let ((_let_2 (@ tptp.groups705719431365010083at_int G2))) (let ((_let_3 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_nat M2) _let_3) (= (@ _let_2 (@ _let_1 _let_3)) (@ (@ tptp.times_times_int (@ G2 _let_3)) (@ _let_2 (@ _let_1 N))))))))))
% 6.73/7.06 (assert (forall ((M2 tptp.nat) (N tptp.nat) (G2 (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat M2))) (let ((_let_2 (@ tptp.groups708209901874060359at_nat G2))) (let ((_let_3 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_nat M2) _let_3) (= (@ _let_2 (@ _let_1 _let_3)) (@ (@ tptp.times_times_nat (@ G2 _let_3)) (@ _let_2 (@ _let_1 N))))))))))
% 6.73/7.06 (assert (forall ((X tptp.real) (K2 tptp.real)) (let ((_let_1 (@ (@ tptp.insert_real X) tptp.bot_bot_set_real))) (let ((_let_2 (@ (@ tptp.inf_inf_set_real (@ tptp.set_or5984915006950818249n_real K2)) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_real X) K2))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 tptp.bot_bot_set_real))))))))
% 6.73/7.06 (assert (forall ((X tptp.rat) (K2 tptp.rat)) (let ((_let_1 (@ (@ tptp.insert_rat X) tptp.bot_bot_set_rat))) (let ((_let_2 (@ (@ tptp.inf_inf_set_rat (@ tptp.set_ord_lessThan_rat K2)) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_rat X) K2))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 tptp.bot_bot_set_rat))))))))
% 6.73/7.06 (assert (forall ((X tptp.num) (K2 tptp.num)) (let ((_let_1 (@ (@ tptp.insert_num X) tptp.bot_bot_set_num))) (let ((_let_2 (@ (@ tptp.inf_inf_set_num (@ tptp.set_ord_lessThan_num K2)) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_num X) K2))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 tptp.bot_bot_set_num))))))))
% 6.73/7.06 (assert (forall ((X tptp.int) (K2 tptp.int)) (let ((_let_1 (@ (@ tptp.insert_int X) tptp.bot_bot_set_int))) (let ((_let_2 (@ (@ tptp.inf_inf_set_int (@ tptp.set_ord_lessThan_int K2)) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_int X) K2))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 tptp.bot_bot_set_int))))))))
% 6.73/7.06 (assert (forall ((X tptp.nat) (K2 tptp.nat)) (let ((_let_1 (@ (@ tptp.insert_nat X) tptp.bot_bot_set_nat))) (let ((_let_2 (@ (@ tptp.inf_inf_set_nat (@ tptp.set_ord_lessThan_nat K2)) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat X) K2))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 tptp.bot_bot_set_nat))))))))
% 6.73/7.06 (assert (forall ((M2 tptp.nat) (N tptp.nat) (G2 (-> tptp.nat tptp.real))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M2) N))) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ (@ tptp.times_times_real (@ (@ tptp.groups129246275422532515t_real G2) _let_1)) (@ G2 (@ tptp.suc N))) (@ (@ tptp.times_times_real (@ G2 M2)) (@ (@ tptp.groups129246275422532515t_real (lambda ((I tptp.nat)) (@ G2 (@ tptp.suc I)))) _let_1)))))))
% 6.73/7.06 (assert (forall ((M2 tptp.nat) (N tptp.nat) (G2 (-> tptp.nat tptp.rat))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M2) N))) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ (@ tptp.times_times_rat (@ (@ tptp.groups73079841787564623at_rat G2) _let_1)) (@ G2 (@ tptp.suc N))) (@ (@ tptp.times_times_rat (@ G2 M2)) (@ (@ tptp.groups73079841787564623at_rat (lambda ((I tptp.nat)) (@ G2 (@ tptp.suc I)))) _let_1)))))))
% 6.73/7.06 (assert (forall ((M2 tptp.nat) (N tptp.nat) (G2 (-> tptp.nat tptp.int))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M2) N))) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ (@ tptp.times_times_int (@ (@ tptp.groups705719431365010083at_int G2) _let_1)) (@ G2 (@ tptp.suc N))) (@ (@ tptp.times_times_int (@ G2 M2)) (@ (@ tptp.groups705719431365010083at_int (lambda ((I tptp.nat)) (@ G2 (@ tptp.suc I)))) _let_1)))))))
% 6.73/7.06 (assert (forall ((M2 tptp.nat) (N tptp.nat) (G2 (-> tptp.nat tptp.nat))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M2) N))) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ (@ tptp.times_times_nat (@ (@ tptp.groups708209901874060359at_nat G2) _let_1)) (@ G2 (@ tptp.suc N))) (@ (@ tptp.times_times_nat (@ G2 M2)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I tptp.nat)) (@ G2 (@ tptp.suc I)))) _let_1)))))))
% 6.73/7.06 (assert (forall ((G2 (-> tptp.nat tptp.rat)) (N tptp.nat)) (= (@ (@ tptp.groups2906978787729119204at_rat G2) (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) (@ (@ tptp.plus_plus_rat (@ G2 tptp.zero_zero_nat)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I tptp.nat)) (@ G2 (@ tptp.suc I)))) (@ tptp.set_ord_lessThan_nat N))))))
% 6.73/7.06 (assert (forall ((G2 (-> tptp.nat tptp.int)) (N tptp.nat)) (= (@ (@ tptp.groups3539618377306564664at_int G2) (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) (@ (@ tptp.plus_plus_int (@ G2 tptp.zero_zero_nat)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I tptp.nat)) (@ G2 (@ tptp.suc I)))) (@ tptp.set_ord_lessThan_nat N))))))
% 6.73/7.06 (assert (forall ((G2 (-> tptp.nat tptp.nat)) (N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat G2) (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) (@ (@ tptp.plus_plus_nat (@ G2 tptp.zero_zero_nat)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I tptp.nat)) (@ G2 (@ tptp.suc I)))) (@ tptp.set_ord_lessThan_nat N))))))
% 6.73/7.06 (assert (forall ((G2 (-> tptp.nat tptp.real)) (N tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real G2) (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) (@ (@ tptp.plus_plus_real (@ G2 tptp.zero_zero_nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I tptp.nat)) (@ G2 (@ tptp.suc I)))) (@ tptp.set_ord_lessThan_nat N))))))
% 6.73/7.06 (assert (forall ((F2 (-> tptp.nat tptp.rat)) (M2 tptp.nat)) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((N4 tptp.nat)) (@ (@ tptp.minus_minus_rat (@ F2 N4)) (@ F2 (@ tptp.suc N4))))) (@ tptp.set_ord_lessThan_nat M2)) (@ (@ tptp.minus_minus_rat (@ F2 tptp.zero_zero_nat)) (@ F2 M2)))))
% 6.73/7.06 (assert (forall ((F2 (-> tptp.nat tptp.int)) (M2 tptp.nat)) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((N4 tptp.nat)) (@ (@ tptp.minus_minus_int (@ F2 N4)) (@ F2 (@ tptp.suc N4))))) (@ tptp.set_ord_lessThan_nat M2)) (@ (@ tptp.minus_minus_int (@ F2 tptp.zero_zero_nat)) (@ F2 M2)))))
% 6.73/7.06 (assert (forall ((F2 (-> tptp.nat tptp.real)) (M2 tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((N4 tptp.nat)) (@ (@ tptp.minus_minus_real (@ F2 N4)) (@ F2 (@ tptp.suc N4))))) (@ tptp.set_ord_lessThan_nat M2)) (@ (@ tptp.minus_minus_real (@ F2 tptp.zero_zero_nat)) (@ F2 M2)))))
% 6.73/7.06 (assert (forall ((F2 (-> tptp.nat tptp.rat)) (M2 tptp.nat)) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((N4 tptp.nat)) (@ (@ tptp.minus_minus_rat (@ F2 (@ tptp.suc N4))) (@ F2 N4)))) (@ tptp.set_ord_lessThan_nat M2)) (@ (@ tptp.minus_minus_rat (@ F2 M2)) (@ F2 tptp.zero_zero_nat)))))
% 6.73/7.06 (assert (forall ((F2 (-> tptp.nat tptp.int)) (M2 tptp.nat)) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((N4 tptp.nat)) (@ (@ tptp.minus_minus_int (@ F2 (@ tptp.suc N4))) (@ F2 N4)))) (@ tptp.set_ord_lessThan_nat M2)) (@ (@ tptp.minus_minus_int (@ F2 M2)) (@ F2 tptp.zero_zero_nat)))))
% 6.73/7.06 (assert (forall ((F2 (-> tptp.nat tptp.real)) (M2 tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((N4 tptp.nat)) (@ (@ tptp.minus_minus_real (@ F2 (@ tptp.suc N4))) (@ F2 N4)))) (@ tptp.set_ord_lessThan_nat M2)) (@ (@ tptp.minus_minus_real (@ F2 M2)) (@ F2 tptp.zero_zero_nat)))))
% 6.73/7.06 (assert (forall ((F2 (-> tptp.nat tptp.rat)) (N tptp.nat) (R3 tptp.rat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat N))) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.groups2906978787729119204at_rat F2) _let_1)) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat N)) R3)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I tptp.nat)) (@ (@ tptp.minus_minus_rat (@ F2 I)) R3))) _let_1)))))
% 6.73/7.06 (assert (forall ((F2 (-> tptp.nat tptp.int)) (N tptp.nat) (R3 tptp.int)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat N))) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.groups3539618377306564664at_int F2) _let_1)) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int N)) R3)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I tptp.nat)) (@ (@ tptp.minus_minus_int (@ F2 I)) R3))) _let_1)))))
% 6.73/7.06 (assert (forall ((F2 (-> tptp.nat tptp.real)) (N tptp.nat) (R3 tptp.real)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat N))) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.groups6591440286371151544t_real F2) _let_1)) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) R3)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I tptp.nat)) (@ (@ tptp.minus_minus_real (@ F2 I)) R3))) _let_1)))))
% 6.73/7.06 (assert (forall ((G2 (-> tptp.nat tptp.nat)) (N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat G2) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K3 tptp.nat)) (@ G2 (@ tptp.suc K3)))) (@ tptp.set_ord_lessThan_nat N)))))
% 6.73/7.06 (assert (forall ((G2 (-> tptp.nat tptp.real)) (N tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real G2) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ G2 (@ tptp.suc K3)))) (@ tptp.set_ord_lessThan_nat N)))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_complex) (F2 (-> tptp.complex tptp.real)) (G2 (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex A4) (=> (forall ((I3 tptp.complex)) (let ((_let_1 (@ F2 I3))) (=> (@ (@ tptp.member_complex I3) A4) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_real _let_1) (@ G2 I3)))))) (=> (not (= A4 tptp.bot_bot_set_complex)) (@ (@ tptp.ord_less_real (@ (@ tptp.groups766887009212190081x_real F2) A4)) (@ (@ tptp.groups766887009212190081x_real G2) A4)))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_nat) (F2 (-> tptp.nat tptp.real)) (G2 (-> tptp.nat tptp.real))) (=> (@ tptp.finite_finite_nat A4) (=> (forall ((I3 tptp.nat)) (let ((_let_1 (@ F2 I3))) (=> (@ (@ tptp.member_nat I3) A4) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_real _let_1) (@ G2 I3)))))) (=> (not (= A4 tptp.bot_bot_set_nat)) (@ (@ tptp.ord_less_real (@ (@ tptp.groups129246275422532515t_real F2) A4)) (@ (@ tptp.groups129246275422532515t_real G2) A4)))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_int) (F2 (-> tptp.int tptp.real)) (G2 (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int A4) (=> (forall ((I3 tptp.int)) (let ((_let_1 (@ F2 I3))) (=> (@ (@ tptp.member_int I3) A4) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_real _let_1) (@ G2 I3)))))) (=> (not (= A4 tptp.bot_bot_set_int)) (@ (@ tptp.ord_less_real (@ (@ tptp.groups2316167850115554303t_real F2) A4)) (@ (@ tptp.groups2316167850115554303t_real G2) A4)))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_real) (F2 (-> tptp.real tptp.real)) (G2 (-> tptp.real tptp.real))) (=> (@ tptp.finite_finite_real A4) (=> (forall ((I3 tptp.real)) (let ((_let_1 (@ F2 I3))) (=> (@ (@ tptp.member_real I3) A4) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_real _let_1) (@ G2 I3)))))) (=> (not (= A4 tptp.bot_bot_set_real)) (@ (@ tptp.ord_less_real (@ (@ tptp.groups1681761925125756287l_real F2) A4)) (@ (@ tptp.groups1681761925125756287l_real G2) A4)))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_complex) (F2 (-> tptp.complex tptp.rat)) (G2 (-> tptp.complex tptp.rat))) (=> (@ tptp.finite3207457112153483333omplex A4) (=> (forall ((I3 tptp.complex)) (let ((_let_1 (@ F2 I3))) (=> (@ (@ tptp.member_complex I3) A4) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1) (@ (@ tptp.ord_less_rat _let_1) (@ G2 I3)))))) (=> (not (= A4 tptp.bot_bot_set_complex)) (@ (@ tptp.ord_less_rat (@ (@ tptp.groups225925009352817453ex_rat F2) A4)) (@ (@ tptp.groups225925009352817453ex_rat G2) A4)))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_nat) (F2 (-> tptp.nat tptp.rat)) (G2 (-> tptp.nat tptp.rat))) (=> (@ tptp.finite_finite_nat A4) (=> (forall ((I3 tptp.nat)) (let ((_let_1 (@ F2 I3))) (=> (@ (@ tptp.member_nat I3) A4) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1) (@ (@ tptp.ord_less_rat _let_1) (@ G2 I3)))))) (=> (not (= A4 tptp.bot_bot_set_nat)) (@ (@ tptp.ord_less_rat (@ (@ tptp.groups73079841787564623at_rat F2) A4)) (@ (@ tptp.groups73079841787564623at_rat G2) A4)))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_int) (F2 (-> tptp.int tptp.rat)) (G2 (-> tptp.int tptp.rat))) (=> (@ tptp.finite_finite_int A4) (=> (forall ((I3 tptp.int)) (let ((_let_1 (@ F2 I3))) (=> (@ (@ tptp.member_int I3) A4) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1) (@ (@ tptp.ord_less_rat _let_1) (@ G2 I3)))))) (=> (not (= A4 tptp.bot_bot_set_int)) (@ (@ tptp.ord_less_rat (@ (@ tptp.groups1072433553688619179nt_rat F2) A4)) (@ (@ tptp.groups1072433553688619179nt_rat G2) A4)))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_real) (F2 (-> tptp.real tptp.rat)) (G2 (-> tptp.real tptp.rat))) (=> (@ tptp.finite_finite_real A4) (=> (forall ((I3 tptp.real)) (let ((_let_1 (@ F2 I3))) (=> (@ (@ tptp.member_real I3) A4) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1) (@ (@ tptp.ord_less_rat _let_1) (@ G2 I3)))))) (=> (not (= A4 tptp.bot_bot_set_real)) (@ (@ tptp.ord_less_rat (@ (@ tptp.groups4061424788464935467al_rat F2) A4)) (@ (@ tptp.groups4061424788464935467al_rat G2) A4)))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_complex) (F2 (-> tptp.complex tptp.nat)) (G2 (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex A4) (=> (forall ((I3 tptp.complex)) (let ((_let_1 (@ F2 I3))) (=> (@ (@ tptp.member_complex I3) A4) (and (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) _let_1) (@ (@ tptp.ord_less_nat _let_1) (@ G2 I3)))))) (=> (not (= A4 tptp.bot_bot_set_complex)) (@ (@ tptp.ord_less_nat (@ (@ tptp.groups861055069439313189ex_nat F2) A4)) (@ (@ tptp.groups861055069439313189ex_nat G2) A4)))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_int) (F2 (-> tptp.int tptp.nat)) (G2 (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int A4) (=> (forall ((I3 tptp.int)) (let ((_let_1 (@ F2 I3))) (=> (@ (@ tptp.member_int I3) A4) (and (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) _let_1) (@ (@ tptp.ord_less_nat _let_1) (@ G2 I3)))))) (=> (not (= A4 tptp.bot_bot_set_int)) (@ (@ tptp.ord_less_nat (@ (@ tptp.groups1707563613775114915nt_nat F2) A4)) (@ (@ tptp.groups1707563613775114915nt_nat G2) A4)))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_complex) (X tptp.complex) (G2 (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups766887009212190081x_real G2))) (=> (@ tptp.finite3207457112153483333omplex A4) (=> (@ (@ tptp.member_complex X) A4) (= (@ _let_1 A4) (@ (@ tptp.times_times_real (@ G2 X)) (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A4) (@ (@ tptp.insert_complex X) tptp.bot_bot_set_complex))))))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_int) (X tptp.int) (G2 (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups2316167850115554303t_real G2))) (=> (@ tptp.finite_finite_int A4) (=> (@ (@ tptp.member_int X) A4) (= (@ _let_1 A4) (@ (@ tptp.times_times_real (@ G2 X)) (@ _let_1 (@ (@ tptp.minus_minus_set_int A4) (@ (@ tptp.insert_int X) tptp.bot_bot_set_int))))))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_real) (X tptp.real) (G2 (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.groups1681761925125756287l_real G2))) (=> (@ tptp.finite_finite_real A4) (=> (@ (@ tptp.member_real X) A4) (= (@ _let_1 A4) (@ (@ tptp.times_times_real (@ G2 X)) (@ _let_1 (@ (@ tptp.minus_minus_set_real A4) (@ (@ tptp.insert_real X) tptp.bot_bot_set_real))))))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_nat) (X tptp.nat) (G2 (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.groups129246275422532515t_real G2))) (=> (@ tptp.finite_finite_nat A4) (=> (@ (@ tptp.member_nat X) A4) (= (@ _let_1 A4) (@ (@ tptp.times_times_real (@ G2 X)) (@ _let_1 (@ (@ tptp.minus_minus_set_nat A4) (@ (@ tptp.insert_nat X) tptp.bot_bot_set_nat))))))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_complex) (X tptp.complex) (G2 (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups225925009352817453ex_rat G2))) (=> (@ tptp.finite3207457112153483333omplex A4) (=> (@ (@ tptp.member_complex X) A4) (= (@ _let_1 A4) (@ (@ tptp.times_times_rat (@ G2 X)) (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A4) (@ (@ tptp.insert_complex X) tptp.bot_bot_set_complex))))))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_int) (X tptp.int) (G2 (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups1072433553688619179nt_rat G2))) (=> (@ tptp.finite_finite_int A4) (=> (@ (@ tptp.member_int X) A4) (= (@ _let_1 A4) (@ (@ tptp.times_times_rat (@ G2 X)) (@ _let_1 (@ (@ tptp.minus_minus_set_int A4) (@ (@ tptp.insert_int X) tptp.bot_bot_set_int))))))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_real) (X tptp.real) (G2 (-> tptp.real tptp.rat))) (let ((_let_1 (@ tptp.groups4061424788464935467al_rat G2))) (=> (@ tptp.finite_finite_real A4) (=> (@ (@ tptp.member_real X) A4) (= (@ _let_1 A4) (@ (@ tptp.times_times_rat (@ G2 X)) (@ _let_1 (@ (@ tptp.minus_minus_set_real A4) (@ (@ tptp.insert_real X) tptp.bot_bot_set_real))))))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_nat) (X tptp.nat) (G2 (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups73079841787564623at_rat G2))) (=> (@ tptp.finite_finite_nat A4) (=> (@ (@ tptp.member_nat X) A4) (= (@ _let_1 A4) (@ (@ tptp.times_times_rat (@ G2 X)) (@ _let_1 (@ (@ tptp.minus_minus_set_nat A4) (@ (@ tptp.insert_nat X) tptp.bot_bot_set_nat))))))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_complex) (X tptp.complex) (G2 (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups861055069439313189ex_nat G2))) (=> (@ tptp.finite3207457112153483333omplex A4) (=> (@ (@ tptp.member_complex X) A4) (= (@ _let_1 A4) (@ (@ tptp.times_times_nat (@ G2 X)) (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A4) (@ (@ tptp.insert_complex X) tptp.bot_bot_set_complex))))))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_int) (X tptp.int) (G2 (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups1707563613775114915nt_nat G2))) (=> (@ tptp.finite_finite_int A4) (=> (@ (@ tptp.member_int X) A4) (= (@ _let_1 A4) (@ (@ tptp.times_times_nat (@ G2 X)) (@ _let_1 (@ (@ tptp.minus_minus_set_int A4) (@ (@ tptp.insert_int X) tptp.bot_bot_set_int))))))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_complex) (G2 (-> tptp.complex tptp.real)) (X tptp.complex)) (let ((_let_1 (@ tptp.insert_complex X))) (let ((_let_2 (@ tptp.groups766887009212190081x_real G2))) (=> (@ tptp.finite3207457112153483333omplex A4) (= (@ _let_2 (@ _let_1 A4)) (@ (@ tptp.times_times_real (@ G2 X)) (@ _let_2 (@ (@ tptp.minus_811609699411566653omplex A4) (@ _let_1 tptp.bot_bot_set_complex))))))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_int) (G2 (-> tptp.int tptp.real)) (X tptp.int)) (let ((_let_1 (@ tptp.insert_int X))) (let ((_let_2 (@ tptp.groups2316167850115554303t_real G2))) (=> (@ tptp.finite_finite_int A4) (= (@ _let_2 (@ _let_1 A4)) (@ (@ tptp.times_times_real (@ G2 X)) (@ _let_2 (@ (@ tptp.minus_minus_set_int A4) (@ _let_1 tptp.bot_bot_set_int))))))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_real) (G2 (-> tptp.real tptp.real)) (X tptp.real)) (let ((_let_1 (@ tptp.insert_real X))) (let ((_let_2 (@ tptp.groups1681761925125756287l_real G2))) (=> (@ tptp.finite_finite_real A4) (= (@ _let_2 (@ _let_1 A4)) (@ (@ tptp.times_times_real (@ G2 X)) (@ _let_2 (@ (@ tptp.minus_minus_set_real A4) (@ _let_1 tptp.bot_bot_set_real))))))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_nat) (G2 (-> tptp.nat tptp.real)) (X tptp.nat)) (let ((_let_1 (@ tptp.insert_nat X))) (let ((_let_2 (@ tptp.groups129246275422532515t_real G2))) (=> (@ tptp.finite_finite_nat A4) (= (@ _let_2 (@ _let_1 A4)) (@ (@ tptp.times_times_real (@ G2 X)) (@ _let_2 (@ (@ tptp.minus_minus_set_nat A4) (@ _let_1 tptp.bot_bot_set_nat))))))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_complex) (G2 (-> tptp.complex tptp.rat)) (X tptp.complex)) (let ((_let_1 (@ tptp.insert_complex X))) (let ((_let_2 (@ tptp.groups225925009352817453ex_rat G2))) (=> (@ tptp.finite3207457112153483333omplex A4) (= (@ _let_2 (@ _let_1 A4)) (@ (@ tptp.times_times_rat (@ G2 X)) (@ _let_2 (@ (@ tptp.minus_811609699411566653omplex A4) (@ _let_1 tptp.bot_bot_set_complex))))))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_int) (G2 (-> tptp.int tptp.rat)) (X tptp.int)) (let ((_let_1 (@ tptp.insert_int X))) (let ((_let_2 (@ tptp.groups1072433553688619179nt_rat G2))) (=> (@ tptp.finite_finite_int A4) (= (@ _let_2 (@ _let_1 A4)) (@ (@ tptp.times_times_rat (@ G2 X)) (@ _let_2 (@ (@ tptp.minus_minus_set_int A4) (@ _let_1 tptp.bot_bot_set_int))))))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_real) (G2 (-> tptp.real tptp.rat)) (X tptp.real)) (let ((_let_1 (@ tptp.insert_real X))) (let ((_let_2 (@ tptp.groups4061424788464935467al_rat G2))) (=> (@ tptp.finite_finite_real A4) (= (@ _let_2 (@ _let_1 A4)) (@ (@ tptp.times_times_rat (@ G2 X)) (@ _let_2 (@ (@ tptp.minus_minus_set_real A4) (@ _let_1 tptp.bot_bot_set_real))))))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_nat) (G2 (-> tptp.nat tptp.rat)) (X tptp.nat)) (let ((_let_1 (@ tptp.insert_nat X))) (let ((_let_2 (@ tptp.groups73079841787564623at_rat G2))) (=> (@ tptp.finite_finite_nat A4) (= (@ _let_2 (@ _let_1 A4)) (@ (@ tptp.times_times_rat (@ G2 X)) (@ _let_2 (@ (@ tptp.minus_minus_set_nat A4) (@ _let_1 tptp.bot_bot_set_nat))))))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_complex) (G2 (-> tptp.complex tptp.nat)) (X tptp.complex)) (let ((_let_1 (@ tptp.insert_complex X))) (let ((_let_2 (@ tptp.groups861055069439313189ex_nat G2))) (=> (@ tptp.finite3207457112153483333omplex A4) (= (@ _let_2 (@ _let_1 A4)) (@ (@ tptp.times_times_nat (@ G2 X)) (@ _let_2 (@ (@ tptp.minus_811609699411566653omplex A4) (@ _let_1 tptp.bot_bot_set_complex))))))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_int) (G2 (-> tptp.int tptp.nat)) (X tptp.int)) (let ((_let_1 (@ tptp.insert_int X))) (let ((_let_2 (@ tptp.groups1707563613775114915nt_nat G2))) (=> (@ tptp.finite_finite_int A4) (= (@ _let_2 (@ _let_1 A4)) (@ (@ tptp.times_times_nat (@ G2 X)) (@ _let_2 (@ (@ tptp.minus_minus_set_int A4) (@ _let_1 tptp.bot_bot_set_int))))))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_int) (B5 tptp.set_int) (G2 (-> tptp.int tptp.code_integer))) (let ((_let_1 (@ tptp.groups3827104343326376752nteger G2))) (=> (@ tptp.finite_finite_int A4) (=> (@ tptp.finite_finite_int B5) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.inf_inf_set_int A4) B5)) (= (@ G2 X3) tptp.one_one_Code_integer))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_int A4) B5)) (@ (@ tptp.times_3573771949741848930nteger (@ _let_1 A4)) (@ _let_1 B5)))))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_complex) (B5 tptp.set_complex) (G2 (-> tptp.complex tptp.code_integer))) (let ((_let_1 (@ tptp.groups8682486955453173170nteger G2))) (=> (@ tptp.finite3207457112153483333omplex A4) (=> (@ tptp.finite3207457112153483333omplex B5) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ (@ tptp.inf_inf_set_complex A4) B5)) (= (@ G2 X3) tptp.one_one_Code_integer))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_complex A4) B5)) (@ (@ tptp.times_3573771949741848930nteger (@ _let_1 A4)) (@ _let_1 B5)))))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_int) (B5 tptp.set_int) (G2 (-> tptp.int tptp.complex))) (let ((_let_1 (@ tptp.groups7440179247065528705omplex G2))) (=> (@ tptp.finite_finite_int A4) (=> (@ tptp.finite_finite_int B5) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.inf_inf_set_int A4) B5)) (= (@ G2 X3) tptp.one_one_complex))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_int A4) B5)) (@ (@ tptp.times_times_complex (@ _let_1 A4)) (@ _let_1 B5)))))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_complex) (B5 tptp.set_complex) (G2 (-> tptp.complex tptp.complex))) (let ((_let_1 (@ tptp.groups3708469109370488835omplex G2))) (=> (@ tptp.finite3207457112153483333omplex A4) (=> (@ tptp.finite3207457112153483333omplex B5) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ (@ tptp.inf_inf_set_complex A4) B5)) (= (@ G2 X3) tptp.one_one_complex))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_complex A4) B5)) (@ (@ tptp.times_times_complex (@ _let_1 A4)) (@ _let_1 B5)))))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_nat) (B5 tptp.set_nat) (G2 (-> tptp.nat tptp.code_integer))) (let ((_let_1 (@ tptp.groups3455450783089532116nteger G2))) (=> (@ tptp.finite_finite_nat A4) (=> (@ tptp.finite_finite_nat B5) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ (@ tptp.inf_inf_set_nat A4) B5)) (= (@ G2 X3) tptp.one_one_Code_integer))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_nat A4) B5)) (@ (@ tptp.times_3573771949741848930nteger (@ _let_1 A4)) (@ _let_1 B5)))))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_nat) (B5 tptp.set_nat) (G2 (-> tptp.nat tptp.complex))) (let ((_let_1 (@ tptp.groups6464643781859351333omplex G2))) (=> (@ tptp.finite_finite_nat A4) (=> (@ tptp.finite_finite_nat B5) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ (@ tptp.inf_inf_set_nat A4) B5)) (= (@ G2 X3) tptp.one_one_complex))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_nat A4) B5)) (@ (@ tptp.times_times_complex (@ _let_1 A4)) (@ _let_1 B5)))))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_int) (B5 tptp.set_int) (G2 (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups2316167850115554303t_real G2))) (=> (@ tptp.finite_finite_int A4) (=> (@ tptp.finite_finite_int B5) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.inf_inf_set_int A4) B5)) (= (@ G2 X3) tptp.one_one_real))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_int A4) B5)) (@ (@ tptp.times_times_real (@ _let_1 A4)) (@ _let_1 B5)))))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_complex) (B5 tptp.set_complex) (G2 (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups766887009212190081x_real G2))) (=> (@ tptp.finite3207457112153483333omplex A4) (=> (@ tptp.finite3207457112153483333omplex B5) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ (@ tptp.inf_inf_set_complex A4) B5)) (= (@ G2 X3) tptp.one_one_real))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_complex A4) B5)) (@ (@ tptp.times_times_real (@ _let_1 A4)) (@ _let_1 B5)))))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_nat) (B5 tptp.set_nat) (G2 (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.groups129246275422532515t_real G2))) (=> (@ tptp.finite_finite_nat A4) (=> (@ tptp.finite_finite_nat B5) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ (@ tptp.inf_inf_set_nat A4) B5)) (= (@ G2 X3) tptp.one_one_real))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_nat A4) B5)) (@ (@ tptp.times_times_real (@ _let_1 A4)) (@ _let_1 B5)))))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_int) (B5 tptp.set_int) (G2 (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups1072433553688619179nt_rat G2))) (=> (@ tptp.finite_finite_int A4) (=> (@ tptp.finite_finite_int B5) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.inf_inf_set_int A4) B5)) (= (@ G2 X3) tptp.one_one_rat))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_int A4) B5)) (@ (@ tptp.times_times_rat (@ _let_1 A4)) (@ _let_1 B5)))))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_complex) (B5 tptp.set_complex) (G2 (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups766887009212190081x_real G2))) (=> (@ tptp.finite3207457112153483333omplex A4) (=> (@ tptp.finite3207457112153483333omplex B5) (=> (= (@ (@ tptp.inf_inf_set_complex A4) B5) tptp.bot_bot_set_complex) (= (@ _let_1 (@ (@ tptp.sup_sup_set_complex A4) B5)) (@ (@ tptp.times_times_real (@ _let_1 A4)) (@ _let_1 B5)))))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_nat) (B5 tptp.set_nat) (G2 (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.groups129246275422532515t_real G2))) (=> (@ tptp.finite_finite_nat A4) (=> (@ tptp.finite_finite_nat B5) (=> (= (@ (@ tptp.inf_inf_set_nat A4) B5) tptp.bot_bot_set_nat) (= (@ _let_1 (@ (@ tptp.sup_sup_set_nat A4) B5)) (@ (@ tptp.times_times_real (@ _let_1 A4)) (@ _let_1 B5)))))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_int) (B5 tptp.set_int) (G2 (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups2316167850115554303t_real G2))) (=> (@ tptp.finite_finite_int A4) (=> (@ tptp.finite_finite_int B5) (=> (= (@ (@ tptp.inf_inf_set_int A4) B5) tptp.bot_bot_set_int) (= (@ _let_1 (@ (@ tptp.sup_sup_set_int A4) B5)) (@ (@ tptp.times_times_real (@ _let_1 A4)) (@ _let_1 B5)))))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_real) (B5 tptp.set_real) (G2 (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.groups1681761925125756287l_real G2))) (=> (@ tptp.finite_finite_real A4) (=> (@ tptp.finite_finite_real B5) (=> (= (@ (@ tptp.inf_inf_set_real A4) B5) tptp.bot_bot_set_real) (= (@ _let_1 (@ (@ tptp.sup_sup_set_real A4) B5)) (@ (@ tptp.times_times_real (@ _let_1 A4)) (@ _let_1 B5)))))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_complex) (B5 tptp.set_complex) (G2 (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups225925009352817453ex_rat G2))) (=> (@ tptp.finite3207457112153483333omplex A4) (=> (@ tptp.finite3207457112153483333omplex B5) (=> (= (@ (@ tptp.inf_inf_set_complex A4) B5) tptp.bot_bot_set_complex) (= (@ _let_1 (@ (@ tptp.sup_sup_set_complex A4) B5)) (@ (@ tptp.times_times_rat (@ _let_1 A4)) (@ _let_1 B5)))))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_nat) (B5 tptp.set_nat) (G2 (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups73079841787564623at_rat G2))) (=> (@ tptp.finite_finite_nat A4) (=> (@ tptp.finite_finite_nat B5) (=> (= (@ (@ tptp.inf_inf_set_nat A4) B5) tptp.bot_bot_set_nat) (= (@ _let_1 (@ (@ tptp.sup_sup_set_nat A4) B5)) (@ (@ tptp.times_times_rat (@ _let_1 A4)) (@ _let_1 B5)))))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_int) (B5 tptp.set_int) (G2 (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups1072433553688619179nt_rat G2))) (=> (@ tptp.finite_finite_int A4) (=> (@ tptp.finite_finite_int B5) (=> (= (@ (@ tptp.inf_inf_set_int A4) B5) tptp.bot_bot_set_int) (= (@ _let_1 (@ (@ tptp.sup_sup_set_int A4) B5)) (@ (@ tptp.times_times_rat (@ _let_1 A4)) (@ _let_1 B5)))))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_real) (B5 tptp.set_real) (G2 (-> tptp.real tptp.rat))) (let ((_let_1 (@ tptp.groups4061424788464935467al_rat G2))) (=> (@ tptp.finite_finite_real A4) (=> (@ tptp.finite_finite_real B5) (=> (= (@ (@ tptp.inf_inf_set_real A4) B5) tptp.bot_bot_set_real) (= (@ _let_1 (@ (@ tptp.sup_sup_set_real A4) B5)) (@ (@ tptp.times_times_rat (@ _let_1 A4)) (@ _let_1 B5)))))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_complex) (B5 tptp.set_complex) (G2 (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups861055069439313189ex_nat G2))) (=> (@ tptp.finite3207457112153483333omplex A4) (=> (@ tptp.finite3207457112153483333omplex B5) (=> (= (@ (@ tptp.inf_inf_set_complex A4) B5) tptp.bot_bot_set_complex) (= (@ _let_1 (@ (@ tptp.sup_sup_set_complex A4) B5)) (@ (@ tptp.times_times_nat (@ _let_1 A4)) (@ _let_1 B5)))))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_int) (B5 tptp.set_int) (G2 (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups1707563613775114915nt_nat G2))) (=> (@ tptp.finite_finite_int A4) (=> (@ tptp.finite_finite_int B5) (=> (= (@ (@ tptp.inf_inf_set_int A4) B5) tptp.bot_bot_set_int) (= (@ _let_1 (@ (@ tptp.sup_sup_set_int A4) B5)) (@ (@ tptp.times_times_nat (@ _let_1 A4)) (@ _let_1 B5)))))))))
% 6.73/7.06 (assert (forall ((N tptp.nat) (K2 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 K2)) (@ _let_1 N)))))
% 6.73/7.06 (assert (forall ((K2 tptp.nat) (K6 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.binomial N))) (=> (@ (@ tptp.ord_less_eq_nat K2) 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 K2)) (@ _let_1 K6)))))))
% 6.73/7.06 (assert (forall ((K2 tptp.nat) (K6 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.binomial N))) (=> (@ (@ tptp.ord_less_eq_nat K2) K6) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.divide_divide_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) K2) (=> (@ (@ tptp.ord_less_eq_nat K6) N) (@ (@ tptp.ord_less_eq_nat (@ _let_1 K6)) (@ _let_1 K2))))))))
% 6.73/7.06 (assert (forall ((N tptp.nat) (K2 tptp.nat)) (let ((_let_1 (@ tptp.binomial N))) (@ (@ tptp.ord_less_eq_nat (@ _let_1 K2)) (@ _let_1 (@ (@ tptp.divide_divide_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_int) (B5 tptp.set_int) (G2 (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups2316167850115554303t_real G2))) (=> (@ tptp.finite_finite_int A4) (=> (@ tptp.finite_finite_int B5) (= (@ _let_1 (@ (@ tptp.sup_sup_set_int A4) B5)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ _let_1 (@ (@ tptp.minus_minus_set_int A4) B5))) (@ _let_1 (@ (@ tptp.minus_minus_set_int B5) A4)))) (@ _let_1 (@ (@ tptp.inf_inf_set_int A4) B5)))))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_complex) (B5 tptp.set_complex) (G2 (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups766887009212190081x_real G2))) (=> (@ tptp.finite3207457112153483333omplex A4) (=> (@ tptp.finite3207457112153483333omplex B5) (= (@ _let_1 (@ (@ tptp.sup_sup_set_complex A4) B5)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A4) B5))) (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex B5) A4)))) (@ _let_1 (@ (@ tptp.inf_inf_set_complex A4) B5)))))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_nat) (B5 tptp.set_nat) (G2 (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.groups129246275422532515t_real G2))) (=> (@ tptp.finite_finite_nat A4) (=> (@ tptp.finite_finite_nat B5) (= (@ _let_1 (@ (@ tptp.sup_sup_set_nat A4) B5)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ _let_1 (@ (@ tptp.minus_minus_set_nat A4) B5))) (@ _let_1 (@ (@ tptp.minus_minus_set_nat B5) A4)))) (@ _let_1 (@ (@ tptp.inf_inf_set_nat A4) B5)))))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_int) (B5 tptp.set_int) (G2 (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups1072433553688619179nt_rat G2))) (=> (@ tptp.finite_finite_int A4) (=> (@ tptp.finite_finite_int B5) (= (@ _let_1 (@ (@ tptp.sup_sup_set_int A4) B5)) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ _let_1 (@ (@ tptp.minus_minus_set_int A4) B5))) (@ _let_1 (@ (@ tptp.minus_minus_set_int B5) A4)))) (@ _let_1 (@ (@ tptp.inf_inf_set_int A4) B5)))))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_complex) (B5 tptp.set_complex) (G2 (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups225925009352817453ex_rat G2))) (=> (@ tptp.finite3207457112153483333omplex A4) (=> (@ tptp.finite3207457112153483333omplex B5) (= (@ _let_1 (@ (@ tptp.sup_sup_set_complex A4) B5)) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A4) B5))) (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex B5) A4)))) (@ _let_1 (@ (@ tptp.inf_inf_set_complex A4) B5)))))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_nat) (B5 tptp.set_nat) (G2 (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups73079841787564623at_rat G2))) (=> (@ tptp.finite_finite_nat A4) (=> (@ tptp.finite_finite_nat B5) (= (@ _let_1 (@ (@ tptp.sup_sup_set_nat A4) B5)) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ _let_1 (@ (@ tptp.minus_minus_set_nat A4) B5))) (@ _let_1 (@ (@ tptp.minus_minus_set_nat B5) A4)))) (@ _let_1 (@ (@ tptp.inf_inf_set_nat A4) B5)))))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_int) (B5 tptp.set_int) (G2 (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups1707563613775114915nt_nat G2))) (=> (@ tptp.finite_finite_int A4) (=> (@ tptp.finite_finite_int B5) (= (@ _let_1 (@ (@ tptp.sup_sup_set_int A4) B5)) (@ (@ tptp.times_times_nat (@ (@ tptp.times_times_nat (@ _let_1 (@ (@ tptp.minus_minus_set_int A4) B5))) (@ _let_1 (@ (@ tptp.minus_minus_set_int B5) A4)))) (@ _let_1 (@ (@ tptp.inf_inf_set_int A4) B5)))))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_complex) (B5 tptp.set_complex) (G2 (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups861055069439313189ex_nat G2))) (=> (@ tptp.finite3207457112153483333omplex A4) (=> (@ tptp.finite3207457112153483333omplex B5) (= (@ _let_1 (@ (@ tptp.sup_sup_set_complex A4) B5)) (@ (@ tptp.times_times_nat (@ (@ tptp.times_times_nat (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A4) B5))) (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex B5) A4)))) (@ _let_1 (@ (@ tptp.inf_inf_set_complex A4) B5)))))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_complex) (B5 tptp.set_complex) (G2 (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.groups858564598930262913ex_int G2))) (=> (@ tptp.finite3207457112153483333omplex A4) (=> (@ tptp.finite3207457112153483333omplex B5) (= (@ _let_1 (@ (@ tptp.sup_sup_set_complex A4) B5)) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A4) B5))) (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex B5) A4)))) (@ _let_1 (@ (@ tptp.inf_inf_set_complex A4) B5)))))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_nat) (B5 tptp.set_nat) (G2 (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.groups705719431365010083at_int G2))) (=> (@ tptp.finite_finite_nat A4) (=> (@ tptp.finite_finite_nat B5) (= (@ _let_1 (@ (@ tptp.sup_sup_set_nat A4) B5)) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int (@ _let_1 (@ (@ tptp.minus_minus_set_nat A4) B5))) (@ _let_1 (@ (@ tptp.minus_minus_set_nat B5) A4)))) (@ _let_1 (@ (@ tptp.inf_inf_set_nat A4) B5)))))))))
% 6.73/7.06 (assert (forall ((M2 tptp.nat) (N tptp.nat) (G2 (-> tptp.nat tptp.real)) (P tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N))) (let ((_let_2 (@ _let_1 P))) (let ((_let_3 (@ _let_1 tptp.one_one_nat))) (let ((_let_4 (@ tptp.groups129246275422532515t_real G2))) (let ((_let_5 (@ tptp.set_or1269000886237332187st_nat M2))) (=> (@ (@ tptp.ord_less_eq_nat M2) _let_3) (= (@ _let_4 (@ _let_5 _let_2)) (@ (@ tptp.times_times_real (@ _let_4 (@ _let_5 N))) (@ _let_4 (@ (@ tptp.set_or1269000886237332187st_nat _let_3) _let_2))))))))))))
% 6.73/7.06 (assert (forall ((M2 tptp.nat) (N tptp.nat) (G2 (-> tptp.nat tptp.rat)) (P tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N))) (let ((_let_2 (@ _let_1 P))) (let ((_let_3 (@ _let_1 tptp.one_one_nat))) (let ((_let_4 (@ tptp.groups73079841787564623at_rat G2))) (let ((_let_5 (@ tptp.set_or1269000886237332187st_nat M2))) (=> (@ (@ tptp.ord_less_eq_nat M2) _let_3) (= (@ _let_4 (@ _let_5 _let_2)) (@ (@ tptp.times_times_rat (@ _let_4 (@ _let_5 N))) (@ _let_4 (@ (@ tptp.set_or1269000886237332187st_nat _let_3) _let_2))))))))))))
% 6.73/7.06 (assert (forall ((M2 tptp.nat) (N tptp.nat) (G2 (-> tptp.nat tptp.int)) (P tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N))) (let ((_let_2 (@ _let_1 P))) (let ((_let_3 (@ _let_1 tptp.one_one_nat))) (let ((_let_4 (@ tptp.groups705719431365010083at_int G2))) (let ((_let_5 (@ tptp.set_or1269000886237332187st_nat M2))) (=> (@ (@ tptp.ord_less_eq_nat M2) _let_3) (= (@ _let_4 (@ _let_5 _let_2)) (@ (@ tptp.times_times_int (@ _let_4 (@ _let_5 N))) (@ _let_4 (@ (@ tptp.set_or1269000886237332187st_nat _let_3) _let_2))))))))))))
% 6.73/7.06 (assert (forall ((M2 tptp.nat) (N tptp.nat) (G2 (-> tptp.nat tptp.nat)) (P tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N))) (let ((_let_2 (@ _let_1 P))) (let ((_let_3 (@ _let_1 tptp.one_one_nat))) (let ((_let_4 (@ tptp.groups708209901874060359at_nat G2))) (let ((_let_5 (@ tptp.set_or1269000886237332187st_nat M2))) (=> (@ (@ tptp.ord_less_eq_nat M2) _let_3) (= (@ _let_4 (@ _let_5 _let_2)) (@ (@ tptp.times_times_nat (@ _let_4 (@ _let_5 N))) (@ _let_4 (@ (@ tptp.set_or1269000886237332187st_nat _let_3) _let_2))))))))))))
% 6.73/7.06 (assert (= tptp.set_fo2584398358068434914at_nat (lambda ((F4 (-> tptp.nat tptp.nat tptp.nat)) (A5 tptp.nat) (B4 tptp.nat) (Acc2 tptp.nat)) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat B4) A5)) Acc2) (@ (@ (@ (@ tptp.set_fo2584398358068434914at_nat F4) (@ (@ tptp.plus_plus_nat A5) tptp.one_one_nat)) B4) (@ (@ F4 A5) Acc2))))))
% 6.73/7.06 (assert (forall ((X (-> tptp.nat tptp.nat tptp.nat)) (Xa2 tptp.nat) (Xb tptp.nat) (Xc tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.set_fo2584398358068434914at_nat X))) (let ((_let_2 (@ (@ tptp.ord_less_nat Xb) Xa2))) (=> (= (@ (@ (@ _let_1 Xa2) Xb) Xc) Y) (and (=> _let_2 (= Y Xc)) (=> (not _let_2) (= Y (@ (@ (@ _let_1 (@ (@ tptp.plus_plus_nat Xa2) tptp.one_one_nat)) Xb) (@ (@ X Xa2) Xc))))))))))
% 6.73/7.06 (assert (forall ((S3 tptp.set_complex) (A tptp.complex) (B (-> tptp.complex tptp.real)) (C2 (-> tptp.complex tptp.real))) (let ((_let_1 (@ (@ tptp.groups766887009212190081x_real C2) (@ (@ tptp.minus_811609699411566653omplex S3) (@ (@ tptp.insert_complex A) tptp.bot_bot_set_complex))))) (let ((_let_2 (@ (@ tptp.member_complex A) S3))) (=> (@ tptp.finite3207457112153483333omplex S3) (and (=> _let_2 (= (@ (@ tptp.groups766887009212190081x_real (lambda ((K3 tptp.complex)) (@ (@ (@ tptp.if_real (= K3 A)) (@ B K3)) (@ C2 K3)))) S3) (@ (@ tptp.times_times_real (@ B A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups766887009212190081x_real (lambda ((K3 tptp.complex)) (@ (@ (@ tptp.if_real (= K3 A)) (@ B K3)) (@ C2 K3)))) S3) _let_1))))))))
% 6.73/7.06 (assert (forall ((S3 tptp.set_int) (A tptp.int) (B (-> tptp.int tptp.real)) (C2 (-> tptp.int tptp.real))) (let ((_let_1 (@ (@ tptp.groups2316167850115554303t_real C2) (@ (@ tptp.minus_minus_set_int S3) (@ (@ tptp.insert_int A) tptp.bot_bot_set_int))))) (let ((_let_2 (@ (@ tptp.member_int A) S3))) (=> (@ tptp.finite_finite_int S3) (and (=> _let_2 (= (@ (@ tptp.groups2316167850115554303t_real (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_real (= K3 A)) (@ B K3)) (@ C2 K3)))) S3) (@ (@ tptp.times_times_real (@ B A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups2316167850115554303t_real (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_real (= K3 A)) (@ B K3)) (@ C2 K3)))) S3) _let_1))))))))
% 6.73/7.06 (assert (forall ((S3 tptp.set_real) (A tptp.real) (B (-> tptp.real tptp.real)) (C2 (-> tptp.real tptp.real))) (let ((_let_1 (@ (@ tptp.groups1681761925125756287l_real C2) (@ (@ tptp.minus_minus_set_real S3) (@ (@ tptp.insert_real A) tptp.bot_bot_set_real))))) (let ((_let_2 (@ (@ tptp.member_real A) S3))) (=> (@ tptp.finite_finite_real S3) (and (=> _let_2 (= (@ (@ tptp.groups1681761925125756287l_real (lambda ((K3 tptp.real)) (@ (@ (@ tptp.if_real (= K3 A)) (@ B K3)) (@ C2 K3)))) S3) (@ (@ tptp.times_times_real (@ B A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups1681761925125756287l_real (lambda ((K3 tptp.real)) (@ (@ (@ tptp.if_real (= K3 A)) (@ B K3)) (@ C2 K3)))) S3) _let_1))))))))
% 6.73/7.06 (assert (forall ((S3 tptp.set_nat) (A tptp.nat) (B (-> tptp.nat tptp.real)) (C2 (-> tptp.nat tptp.real))) (let ((_let_1 (@ (@ tptp.groups129246275422532515t_real C2) (@ (@ tptp.minus_minus_set_nat S3) (@ (@ tptp.insert_nat A) tptp.bot_bot_set_nat))))) (let ((_let_2 (@ (@ tptp.member_nat A) S3))) (=> (@ tptp.finite_finite_nat S3) (and (=> _let_2 (= (@ (@ tptp.groups129246275422532515t_real (lambda ((K3 tptp.nat)) (@ (@ (@ tptp.if_real (= K3 A)) (@ B K3)) (@ C2 K3)))) S3) (@ (@ tptp.times_times_real (@ B A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups129246275422532515t_real (lambda ((K3 tptp.nat)) (@ (@ (@ tptp.if_real (= K3 A)) (@ B K3)) (@ C2 K3)))) S3) _let_1))))))))
% 6.73/7.06 (assert (forall ((S3 tptp.set_complex) (A tptp.complex) (B (-> tptp.complex tptp.rat)) (C2 (-> tptp.complex tptp.rat))) (let ((_let_1 (@ (@ tptp.groups225925009352817453ex_rat C2) (@ (@ tptp.minus_811609699411566653omplex S3) (@ (@ tptp.insert_complex A) tptp.bot_bot_set_complex))))) (let ((_let_2 (@ (@ tptp.member_complex A) S3))) (=> (@ tptp.finite3207457112153483333omplex S3) (and (=> _let_2 (= (@ (@ tptp.groups225925009352817453ex_rat (lambda ((K3 tptp.complex)) (@ (@ (@ tptp.if_rat (= K3 A)) (@ B K3)) (@ C2 K3)))) S3) (@ (@ tptp.times_times_rat (@ B A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups225925009352817453ex_rat (lambda ((K3 tptp.complex)) (@ (@ (@ tptp.if_rat (= K3 A)) (@ B K3)) (@ C2 K3)))) S3) _let_1))))))))
% 6.73/7.06 (assert (forall ((S3 tptp.set_int) (A tptp.int) (B (-> tptp.int tptp.rat)) (C2 (-> tptp.int tptp.rat))) (let ((_let_1 (@ (@ tptp.groups1072433553688619179nt_rat C2) (@ (@ tptp.minus_minus_set_int S3) (@ (@ tptp.insert_int A) tptp.bot_bot_set_int))))) (let ((_let_2 (@ (@ tptp.member_int A) S3))) (=> (@ tptp.finite_finite_int S3) (and (=> _let_2 (= (@ (@ tptp.groups1072433553688619179nt_rat (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_rat (= K3 A)) (@ B K3)) (@ C2 K3)))) S3) (@ (@ tptp.times_times_rat (@ B A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups1072433553688619179nt_rat (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_rat (= K3 A)) (@ B K3)) (@ C2 K3)))) S3) _let_1))))))))
% 6.73/7.06 (assert (forall ((S3 tptp.set_real) (A tptp.real) (B (-> tptp.real tptp.rat)) (C2 (-> tptp.real tptp.rat))) (let ((_let_1 (@ (@ tptp.groups4061424788464935467al_rat C2) (@ (@ tptp.minus_minus_set_real S3) (@ (@ tptp.insert_real A) tptp.bot_bot_set_real))))) (let ((_let_2 (@ (@ tptp.member_real A) S3))) (=> (@ tptp.finite_finite_real S3) (and (=> _let_2 (= (@ (@ tptp.groups4061424788464935467al_rat (lambda ((K3 tptp.real)) (@ (@ (@ tptp.if_rat (= K3 A)) (@ B K3)) (@ C2 K3)))) S3) (@ (@ tptp.times_times_rat (@ B A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups4061424788464935467al_rat (lambda ((K3 tptp.real)) (@ (@ (@ tptp.if_rat (= K3 A)) (@ B K3)) (@ C2 K3)))) S3) _let_1))))))))
% 6.73/7.06 (assert (forall ((S3 tptp.set_nat) (A tptp.nat) (B (-> tptp.nat tptp.rat)) (C2 (-> tptp.nat tptp.rat))) (let ((_let_1 (@ (@ tptp.groups73079841787564623at_rat C2) (@ (@ tptp.minus_minus_set_nat S3) (@ (@ tptp.insert_nat A) tptp.bot_bot_set_nat))))) (let ((_let_2 (@ (@ tptp.member_nat A) S3))) (=> (@ tptp.finite_finite_nat S3) (and (=> _let_2 (= (@ (@ tptp.groups73079841787564623at_rat (lambda ((K3 tptp.nat)) (@ (@ (@ tptp.if_rat (= K3 A)) (@ B K3)) (@ C2 K3)))) S3) (@ (@ tptp.times_times_rat (@ B A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups73079841787564623at_rat (lambda ((K3 tptp.nat)) (@ (@ (@ tptp.if_rat (= K3 A)) (@ B K3)) (@ C2 K3)))) S3) _let_1))))))))
% 6.73/7.06 (assert (forall ((S3 tptp.set_complex) (A tptp.complex) (B (-> tptp.complex tptp.nat)) (C2 (-> tptp.complex tptp.nat))) (let ((_let_1 (@ (@ tptp.groups861055069439313189ex_nat C2) (@ (@ tptp.minus_811609699411566653omplex S3) (@ (@ tptp.insert_complex A) tptp.bot_bot_set_complex))))) (let ((_let_2 (@ (@ tptp.member_complex A) S3))) (=> (@ tptp.finite3207457112153483333omplex S3) (and (=> _let_2 (= (@ (@ tptp.groups861055069439313189ex_nat (lambda ((K3 tptp.complex)) (@ (@ (@ tptp.if_nat (= K3 A)) (@ B K3)) (@ C2 K3)))) S3) (@ (@ tptp.times_times_nat (@ B A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups861055069439313189ex_nat (lambda ((K3 tptp.complex)) (@ (@ (@ tptp.if_nat (= K3 A)) (@ B K3)) (@ C2 K3)))) S3) _let_1))))))))
% 6.73/7.06 (assert (forall ((S3 tptp.set_int) (A tptp.int) (B (-> tptp.int tptp.nat)) (C2 (-> tptp.int tptp.nat))) (let ((_let_1 (@ (@ tptp.groups1707563613775114915nt_nat C2) (@ (@ tptp.minus_minus_set_int S3) (@ (@ tptp.insert_int A) tptp.bot_bot_set_int))))) (let ((_let_2 (@ (@ tptp.member_int A) S3))) (=> (@ tptp.finite_finite_int S3) (and (=> _let_2 (= (@ (@ tptp.groups1707563613775114915nt_nat (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_nat (= K3 A)) (@ B K3)) (@ C2 K3)))) S3) (@ (@ tptp.times_times_nat (@ B A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups1707563613775114915nt_nat (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_nat (= K3 A)) (@ B K3)) (@ C2 K3)))) S3) _let_1))))))))
% 6.73/7.06 (assert (forall ((X tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger X))) (= (@ (@ tptp.minus_8373710615458151222nteger (@ _let_1 N)) tptp.one_one_Code_integer) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.minus_8373710615458151222nteger X) tptp.one_one_Code_integer)) (@ (@ tptp.groups7501900531339628137nteger _let_1) (@ tptp.set_ord_lessThan_nat N)))))))
% 6.73/7.06 (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)))))))
% 6.73/7.06 (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)))))))
% 6.73/7.06 (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)))))))
% 6.73/7.06 (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)))))))
% 6.73/7.06 (assert (forall ((X tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger X))) (let ((_let_2 (@ tptp.minus_8373710615458151222nteger tptp.one_one_Code_integer))) (= (@ _let_2 (@ _let_1 N)) (@ (@ tptp.times_3573771949741848930nteger (@ _let_2 X)) (@ (@ tptp.groups7501900531339628137nteger _let_1) (@ tptp.set_ord_lessThan_nat N))))))))
% 6.73/7.06 (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))))))))
% 6.73/7.06 (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))))))))
% 6.73/7.06 (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))))))))
% 6.73/7.06 (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))))))))
% 6.73/7.06 (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)))))))
% 6.73/7.06 (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)))))))
% 6.73/7.06 (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)))))))
% 6.73/7.06 (assert (forall ((B5 tptp.set_real) (A4 tptp.set_real) (F2 (-> tptp.real tptp.code_integer))) (let ((_let_1 (@ tptp.groups6225526099057966256nteger F2))) (=> (@ tptp.finite_finite_real B5) (=> (@ (@ tptp.ord_less_eq_set_real A4) B5) (=> (forall ((B3 tptp.real)) (=> (@ (@ tptp.member_real B3) (@ (@ tptp.minus_minus_set_real B5) A4)) (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (@ F2 B3)))) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) A4) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ F2 A3)))) (@ (@ tptp.ord_le3102999989581377725nteger (@ _let_1 A4)) (@ _let_1 B5)))))))))
% 6.73/7.06 (assert (forall ((B5 tptp.set_int) (A4 tptp.set_int) (F2 (-> tptp.int tptp.code_integer))) (let ((_let_1 (@ tptp.groups3827104343326376752nteger F2))) (=> (@ tptp.finite_finite_int B5) (=> (@ (@ tptp.ord_less_eq_set_int A4) B5) (=> (forall ((B3 tptp.int)) (=> (@ (@ tptp.member_int B3) (@ (@ tptp.minus_minus_set_int B5) A4)) (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (@ F2 B3)))) (=> (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) A4) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ F2 A3)))) (@ (@ tptp.ord_le3102999989581377725nteger (@ _let_1 A4)) (@ _let_1 B5)))))))))
% 6.73/7.06 (assert (forall ((B5 tptp.set_complex) (A4 tptp.set_complex) (F2 (-> tptp.complex tptp.code_integer))) (let ((_let_1 (@ tptp.groups8682486955453173170nteger F2))) (=> (@ tptp.finite3207457112153483333omplex B5) (=> (@ (@ tptp.ord_le211207098394363844omplex A4) B5) (=> (forall ((B3 tptp.complex)) (=> (@ (@ tptp.member_complex B3) (@ (@ tptp.minus_811609699411566653omplex B5) A4)) (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (@ F2 B3)))) (=> (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) A4) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ F2 A3)))) (@ (@ tptp.ord_le3102999989581377725nteger (@ _let_1 A4)) (@ _let_1 B5)))))))))
% 6.73/7.06 (assert (forall ((B5 tptp.set_real) (A4 tptp.set_real) (F2 (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.groups1681761925125756287l_real F2))) (=> (@ tptp.finite_finite_real B5) (=> (@ (@ tptp.ord_less_eq_set_real A4) B5) (=> (forall ((B3 tptp.real)) (=> (@ (@ tptp.member_real B3) (@ (@ tptp.minus_minus_set_real B5) A4)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F2 B3)))) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) A4) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F2 A3)))) (@ (@ tptp.ord_less_eq_real (@ _let_1 A4)) (@ _let_1 B5)))))))))
% 6.73/7.06 (assert (forall ((B5 tptp.set_int) (A4 tptp.set_int) (F2 (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups2316167850115554303t_real F2))) (=> (@ tptp.finite_finite_int B5) (=> (@ (@ tptp.ord_less_eq_set_int A4) B5) (=> (forall ((B3 tptp.int)) (=> (@ (@ tptp.member_int B3) (@ (@ tptp.minus_minus_set_int B5) A4)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F2 B3)))) (=> (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) A4) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F2 A3)))) (@ (@ tptp.ord_less_eq_real (@ _let_1 A4)) (@ _let_1 B5)))))))))
% 6.73/7.06 (assert (forall ((B5 tptp.set_complex) (A4 tptp.set_complex) (F2 (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups766887009212190081x_real F2))) (=> (@ tptp.finite3207457112153483333omplex B5) (=> (@ (@ tptp.ord_le211207098394363844omplex A4) B5) (=> (forall ((B3 tptp.complex)) (=> (@ (@ tptp.member_complex B3) (@ (@ tptp.minus_811609699411566653omplex B5) A4)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F2 B3)))) (=> (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) A4) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F2 A3)))) (@ (@ tptp.ord_less_eq_real (@ _let_1 A4)) (@ _let_1 B5)))))))))
% 6.73/7.06 (assert (forall ((B5 tptp.set_real) (A4 tptp.set_real) (F2 (-> tptp.real tptp.rat))) (let ((_let_1 (@ tptp.groups4061424788464935467al_rat F2))) (=> (@ tptp.finite_finite_real B5) (=> (@ (@ tptp.ord_less_eq_set_real A4) B5) (=> (forall ((B3 tptp.real)) (=> (@ (@ tptp.member_real B3) (@ (@ tptp.minus_minus_set_real B5) A4)) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ F2 B3)))) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) A4) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F2 A3)))) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A4)) (@ _let_1 B5)))))))))
% 6.73/7.06 (assert (forall ((B5 tptp.set_int) (A4 tptp.set_int) (F2 (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups1072433553688619179nt_rat F2))) (=> (@ tptp.finite_finite_int B5) (=> (@ (@ tptp.ord_less_eq_set_int A4) B5) (=> (forall ((B3 tptp.int)) (=> (@ (@ tptp.member_int B3) (@ (@ tptp.minus_minus_set_int B5) A4)) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ F2 B3)))) (=> (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) A4) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F2 A3)))) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A4)) (@ _let_1 B5)))))))))
% 6.73/7.06 (assert (forall ((B5 tptp.set_complex) (A4 tptp.set_complex) (F2 (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups225925009352817453ex_rat F2))) (=> (@ tptp.finite3207457112153483333omplex B5) (=> (@ (@ tptp.ord_le211207098394363844omplex A4) B5) (=> (forall ((B3 tptp.complex)) (=> (@ (@ tptp.member_complex B3) (@ (@ tptp.minus_811609699411566653omplex B5) A4)) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ F2 B3)))) (=> (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) A4) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F2 A3)))) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A4)) (@ _let_1 B5)))))))))
% 6.73/7.06 (assert (forall ((B5 tptp.set_real) (A4 tptp.set_real) (F2 (-> tptp.real tptp.int))) (let ((_let_1 (@ tptp.groups4694064378042380927al_int F2))) (=> (@ tptp.finite_finite_real B5) (=> (@ (@ tptp.ord_less_eq_set_real A4) B5) (=> (forall ((B3 tptp.real)) (=> (@ (@ tptp.member_real B3) (@ (@ tptp.minus_minus_set_real B5) A4)) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ F2 B3)))) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) A4) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F2 A3)))) (@ (@ tptp.ord_less_eq_int (@ _let_1 A4)) (@ _let_1 B5)))))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_real) (F2 (-> tptp.real tptp.code_integer)) (N tptp.code_integer) (K2 tptp.nat)) (=> (forall ((I3 tptp.real)) (let ((_let_1 (@ F2 I3))) (=> (@ (@ tptp.member_real I3) A4) (and (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) _let_1) (@ (@ tptp.ord_le3102999989581377725nteger _let_1) N))))) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_real A4)) K2) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) N) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.groups6225526099057966256nteger F2) A4)) (@ (@ tptp.power_8256067586552552935nteger N) K2)))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_nat) (F2 (-> tptp.nat tptp.code_integer)) (N tptp.code_integer) (K2 tptp.nat)) (=> (forall ((I3 tptp.nat)) (let ((_let_1 (@ F2 I3))) (=> (@ (@ tptp.member_nat I3) A4) (and (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) _let_1) (@ (@ tptp.ord_le3102999989581377725nteger _let_1) N))))) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat A4)) K2) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) N) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.groups3455450783089532116nteger F2) A4)) (@ (@ tptp.power_8256067586552552935nteger N) K2)))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_complex) (F2 (-> tptp.complex tptp.code_integer)) (N tptp.code_integer) (K2 tptp.nat)) (=> (forall ((I3 tptp.complex)) (let ((_let_1 (@ F2 I3))) (=> (@ (@ tptp.member_complex I3) A4) (and (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) _let_1) (@ (@ tptp.ord_le3102999989581377725nteger _let_1) N))))) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_complex A4)) K2) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) N) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.groups8682486955453173170nteger F2) A4)) (@ (@ tptp.power_8256067586552552935nteger N) K2)))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_int) (F2 (-> tptp.int tptp.code_integer)) (N tptp.code_integer) (K2 tptp.nat)) (=> (forall ((I3 tptp.int)) (let ((_let_1 (@ F2 I3))) (=> (@ (@ tptp.member_int I3) A4) (and (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) _let_1) (@ (@ tptp.ord_le3102999989581377725nteger _let_1) N))))) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_int A4)) K2) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) N) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.groups3827104343326376752nteger F2) A4)) (@ (@ tptp.power_8256067586552552935nteger N) K2)))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_real) (F2 (-> tptp.real tptp.real)) (N tptp.real) (K2 tptp.nat)) (=> (forall ((I3 tptp.real)) (let ((_let_1 (@ F2 I3))) (=> (@ (@ tptp.member_real I3) A4) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) N))))) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_real A4)) K2) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) N) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups1681761925125756287l_real F2) A4)) (@ (@ tptp.power_power_real N) K2)))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_nat) (F2 (-> tptp.nat tptp.real)) (N tptp.real) (K2 tptp.nat)) (=> (forall ((I3 tptp.nat)) (let ((_let_1 (@ F2 I3))) (=> (@ (@ tptp.member_nat I3) A4) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) N))))) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat A4)) K2) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) N) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups129246275422532515t_real F2) A4)) (@ (@ tptp.power_power_real N) K2)))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_complex) (F2 (-> tptp.complex tptp.real)) (N tptp.real) (K2 tptp.nat)) (=> (forall ((I3 tptp.complex)) (let ((_let_1 (@ F2 I3))) (=> (@ (@ tptp.member_complex I3) A4) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) N))))) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_complex A4)) K2) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) N) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups766887009212190081x_real F2) A4)) (@ (@ tptp.power_power_real N) K2)))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_int) (F2 (-> tptp.int tptp.real)) (N tptp.real) (K2 tptp.nat)) (=> (forall ((I3 tptp.int)) (let ((_let_1 (@ F2 I3))) (=> (@ (@ tptp.member_int I3) A4) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) N))))) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_int A4)) K2) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) N) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups2316167850115554303t_real F2) A4)) (@ (@ tptp.power_power_real N) K2)))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_real) (F2 (-> tptp.real tptp.rat)) (N tptp.rat) (K2 tptp.nat)) (=> (forall ((I3 tptp.real)) (let ((_let_1 (@ F2 I3))) (=> (@ (@ tptp.member_real I3) A4) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1) (@ (@ tptp.ord_less_eq_rat _let_1) N))))) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_real A4)) K2) (=> (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) N) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups4061424788464935467al_rat F2) A4)) (@ (@ tptp.power_power_rat N) K2)))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_nat) (F2 (-> tptp.nat tptp.rat)) (N tptp.rat) (K2 tptp.nat)) (=> (forall ((I3 tptp.nat)) (let ((_let_1 (@ F2 I3))) (=> (@ (@ tptp.member_nat I3) A4) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1) (@ (@ tptp.ord_less_eq_rat _let_1) N))))) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat A4)) K2) (=> (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) N) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups73079841787564623at_rat F2) A4)) (@ (@ tptp.power_power_rat N) K2)))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_int) (B5 tptp.set_int) (F2 (-> tptp.int tptp.complex))) (let ((_let_1 (@ tptp.groups7440179247065528705omplex F2))) (=> (@ tptp.finite_finite_int A4) (=> (@ tptp.finite_finite_int B5) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.inf_inf_set_int A4) B5)) (not (= (@ F2 X3) tptp.zero_zero_complex)))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_int A4) B5)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex (@ _let_1 A4)) (@ _let_1 B5))) (@ _let_1 (@ (@ tptp.inf_inf_set_int A4) B5))))))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_complex) (B5 tptp.set_complex) (F2 (-> tptp.complex tptp.complex))) (let ((_let_1 (@ tptp.groups3708469109370488835omplex F2))) (=> (@ tptp.finite3207457112153483333omplex A4) (=> (@ tptp.finite3207457112153483333omplex B5) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ (@ tptp.inf_inf_set_complex A4) B5)) (not (= (@ F2 X3) tptp.zero_zero_complex)))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_complex A4) B5)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex (@ _let_1 A4)) (@ _let_1 B5))) (@ _let_1 (@ (@ tptp.inf_inf_set_complex A4) B5))))))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_nat) (B5 tptp.set_nat) (F2 (-> tptp.nat tptp.complex))) (let ((_let_1 (@ tptp.groups6464643781859351333omplex F2))) (=> (@ tptp.finite_finite_nat A4) (=> (@ tptp.finite_finite_nat B5) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ (@ tptp.inf_inf_set_nat A4) B5)) (not (= (@ F2 X3) tptp.zero_zero_complex)))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_nat A4) B5)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex (@ _let_1 A4)) (@ _let_1 B5))) (@ _let_1 (@ (@ tptp.inf_inf_set_nat A4) B5))))))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_int) (B5 tptp.set_int) (F2 (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups2316167850115554303t_real F2))) (=> (@ tptp.finite_finite_int A4) (=> (@ tptp.finite_finite_int B5) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.inf_inf_set_int A4) B5)) (not (= (@ F2 X3) tptp.zero_zero_real)))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_int A4) B5)) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ _let_1 A4)) (@ _let_1 B5))) (@ _let_1 (@ (@ tptp.inf_inf_set_int A4) B5))))))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_complex) (B5 tptp.set_complex) (F2 (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups766887009212190081x_real F2))) (=> (@ tptp.finite3207457112153483333omplex A4) (=> (@ tptp.finite3207457112153483333omplex B5) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ (@ tptp.inf_inf_set_complex A4) B5)) (not (= (@ F2 X3) tptp.zero_zero_real)))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_complex A4) B5)) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ _let_1 A4)) (@ _let_1 B5))) (@ _let_1 (@ (@ tptp.inf_inf_set_complex A4) B5))))))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_nat) (B5 tptp.set_nat) (F2 (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.groups129246275422532515t_real F2))) (=> (@ tptp.finite_finite_nat A4) (=> (@ tptp.finite_finite_nat B5) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ (@ tptp.inf_inf_set_nat A4) B5)) (not (= (@ F2 X3) tptp.zero_zero_real)))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_nat A4) B5)) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ _let_1 A4)) (@ _let_1 B5))) (@ _let_1 (@ (@ tptp.inf_inf_set_nat A4) B5))))))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_int) (B5 tptp.set_int) (F2 (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups1072433553688619179nt_rat F2))) (=> (@ tptp.finite_finite_int A4) (=> (@ tptp.finite_finite_int B5) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.inf_inf_set_int A4) B5)) (not (= (@ F2 X3) tptp.zero_zero_rat)))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_int A4) B5)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat (@ _let_1 A4)) (@ _let_1 B5))) (@ _let_1 (@ (@ tptp.inf_inf_set_int A4) B5))))))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_complex) (B5 tptp.set_complex) (F2 (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups225925009352817453ex_rat F2))) (=> (@ tptp.finite3207457112153483333omplex A4) (=> (@ tptp.finite3207457112153483333omplex B5) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ (@ tptp.inf_inf_set_complex A4) B5)) (not (= (@ F2 X3) tptp.zero_zero_rat)))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_complex A4) B5)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat (@ _let_1 A4)) (@ _let_1 B5))) (@ _let_1 (@ (@ tptp.inf_inf_set_complex A4) B5))))))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_nat) (B5 tptp.set_nat) (F2 (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups73079841787564623at_rat F2))) (=> (@ tptp.finite_finite_nat A4) (=> (@ tptp.finite_finite_nat B5) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ (@ tptp.inf_inf_set_nat A4) B5)) (not (= (@ F2 X3) tptp.zero_zero_rat)))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_nat A4) B5)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat (@ _let_1 A4)) (@ _let_1 B5))) (@ _let_1 (@ (@ tptp.inf_inf_set_nat A4) B5))))))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_Pr1261947904930325089at_nat) (B5 tptp.set_Pr1261947904930325089at_nat) (F2 (-> tptp.product_prod_nat_nat tptp.complex))) (let ((_let_1 (@ tptp.groups8110221916422527690omplex F2))) (=> (@ tptp.finite6177210948735845034at_nat A4) (=> (@ tptp.finite6177210948735845034at_nat B5) (=> (forall ((X3 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat X3) (@ (@ tptp.inf_in2572325071724192079at_nat A4) B5)) (not (= (@ F2 X3) tptp.zero_zero_complex)))) (= (@ _let_1 (@ (@ tptp.sup_su6327502436637775413at_nat A4) B5)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex (@ _let_1 A4)) (@ _let_1 B5))) (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat A4) B5))))))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_complex) (F2 (-> tptp.complex tptp.complex)) (A tptp.complex)) (let ((_let_1 (@ tptp.groups3708469109370488835omplex F2))) (let ((_let_2 (@ _let_1 A4))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A4) (@ (@ tptp.insert_complex A) tptp.bot_bot_set_complex))))) (let ((_let_4 (@ (@ tptp.member_complex A) A4))) (let ((_let_5 (@ F2 A))) (=> (@ tptp.finite3207457112153483333omplex A4) (=> (not (= _let_5 tptp.zero_zero_complex)) (and (=> _let_4 (= _let_3 (@ (@ tptp.divide1717551699836669952omplex _let_2) _let_5))) (=> (not _let_4) (= _let_3 _let_2))))))))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_int) (F2 (-> tptp.int tptp.complex)) (A tptp.int)) (let ((_let_1 (@ tptp.groups7440179247065528705omplex F2))) (let ((_let_2 (@ _let_1 A4))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_minus_set_int A4) (@ (@ tptp.insert_int A) tptp.bot_bot_set_int))))) (let ((_let_4 (@ (@ tptp.member_int A) A4))) (let ((_let_5 (@ F2 A))) (=> (@ tptp.finite_finite_int A4) (=> (not (= _let_5 tptp.zero_zero_complex)) (and (=> _let_4 (= _let_3 (@ (@ tptp.divide1717551699836669952omplex _let_2) _let_5))) (=> (not _let_4) (= _let_3 _let_2))))))))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_real) (F2 (-> tptp.real tptp.complex)) (A tptp.real)) (let ((_let_1 (@ tptp.groups713298508707869441omplex F2))) (let ((_let_2 (@ _let_1 A4))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_minus_set_real A4) (@ (@ tptp.insert_real A) tptp.bot_bot_set_real))))) (let ((_let_4 (@ (@ tptp.member_real A) A4))) (let ((_let_5 (@ F2 A))) (=> (@ tptp.finite_finite_real A4) (=> (not (= _let_5 tptp.zero_zero_complex)) (and (=> _let_4 (= _let_3 (@ (@ tptp.divide1717551699836669952omplex _let_2) _let_5))) (=> (not _let_4) (= _let_3 _let_2))))))))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_nat) (F2 (-> tptp.nat tptp.complex)) (A tptp.nat)) (let ((_let_1 (@ tptp.groups6464643781859351333omplex F2))) (let ((_let_2 (@ _let_1 A4))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_minus_set_nat A4) (@ (@ tptp.insert_nat A) tptp.bot_bot_set_nat))))) (let ((_let_4 (@ (@ tptp.member_nat A) A4))) (let ((_let_5 (@ F2 A))) (=> (@ tptp.finite_finite_nat A4) (=> (not (= _let_5 tptp.zero_zero_complex)) (and (=> _let_4 (= _let_3 (@ (@ tptp.divide1717551699836669952omplex _let_2) _let_5))) (=> (not _let_4) (= _let_3 _let_2))))))))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_complex) (F2 (-> tptp.complex tptp.real)) (A tptp.complex)) (let ((_let_1 (@ tptp.groups766887009212190081x_real F2))) (let ((_let_2 (@ _let_1 A4))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A4) (@ (@ tptp.insert_complex A) tptp.bot_bot_set_complex))))) (let ((_let_4 (@ (@ tptp.member_complex A) A4))) (let ((_let_5 (@ F2 A))) (=> (@ tptp.finite3207457112153483333omplex A4) (=> (not (= _let_5 tptp.zero_zero_real)) (and (=> _let_4 (= _let_3 (@ (@ tptp.divide_divide_real _let_2) _let_5))) (=> (not _let_4) (= _let_3 _let_2))))))))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_int) (F2 (-> tptp.int tptp.real)) (A tptp.int)) (let ((_let_1 (@ tptp.groups2316167850115554303t_real F2))) (let ((_let_2 (@ _let_1 A4))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_minus_set_int A4) (@ (@ tptp.insert_int A) tptp.bot_bot_set_int))))) (let ((_let_4 (@ (@ tptp.member_int A) A4))) (let ((_let_5 (@ F2 A))) (=> (@ tptp.finite_finite_int A4) (=> (not (= _let_5 tptp.zero_zero_real)) (and (=> _let_4 (= _let_3 (@ (@ tptp.divide_divide_real _let_2) _let_5))) (=> (not _let_4) (= _let_3 _let_2))))))))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_real) (F2 (-> tptp.real tptp.real)) (A tptp.real)) (let ((_let_1 (@ tptp.groups1681761925125756287l_real F2))) (let ((_let_2 (@ _let_1 A4))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_minus_set_real A4) (@ (@ tptp.insert_real A) tptp.bot_bot_set_real))))) (let ((_let_4 (@ (@ tptp.member_real A) A4))) (let ((_let_5 (@ F2 A))) (=> (@ tptp.finite_finite_real A4) (=> (not (= _let_5 tptp.zero_zero_real)) (and (=> _let_4 (= _let_3 (@ (@ tptp.divide_divide_real _let_2) _let_5))) (=> (not _let_4) (= _let_3 _let_2))))))))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_nat) (F2 (-> tptp.nat tptp.real)) (A tptp.nat)) (let ((_let_1 (@ tptp.groups129246275422532515t_real F2))) (let ((_let_2 (@ _let_1 A4))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_minus_set_nat A4) (@ (@ tptp.insert_nat A) tptp.bot_bot_set_nat))))) (let ((_let_4 (@ (@ tptp.member_nat A) A4))) (let ((_let_5 (@ F2 A))) (=> (@ tptp.finite_finite_nat A4) (=> (not (= _let_5 tptp.zero_zero_real)) (and (=> _let_4 (= _let_3 (@ (@ tptp.divide_divide_real _let_2) _let_5))) (=> (not _let_4) (= _let_3 _let_2))))))))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_complex) (F2 (-> tptp.complex tptp.rat)) (A tptp.complex)) (let ((_let_1 (@ tptp.groups225925009352817453ex_rat F2))) (let ((_let_2 (@ _let_1 A4))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A4) (@ (@ tptp.insert_complex A) tptp.bot_bot_set_complex))))) (let ((_let_4 (@ (@ tptp.member_complex A) A4))) (let ((_let_5 (@ F2 A))) (=> (@ tptp.finite3207457112153483333omplex A4) (=> (not (= _let_5 tptp.zero_zero_rat)) (and (=> _let_4 (= _let_3 (@ (@ tptp.divide_divide_rat _let_2) _let_5))) (=> (not _let_4) (= _let_3 _let_2))))))))))))
% 6.73/7.06 (assert (forall ((A4 tptp.set_int) (F2 (-> tptp.int tptp.rat)) (A tptp.int)) (let ((_let_1 (@ tptp.groups1072433553688619179nt_rat F2))) (let ((_let_2 (@ _let_1 A4))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_minus_set_int A4) (@ (@ tptp.insert_int A) tptp.bot_bot_set_int))))) (let ((_let_4 (@ (@ tptp.member_int A) A4))) (let ((_let_5 (@ F2 A))) (=> (@ tptp.finite_finite_int A4) (=> (not (= _let_5 tptp.zero_zero_rat)) (and (=> _let_4 (= _let_3 (@ (@ tptp.divide_divide_rat _let_2) _let_5))) (=> (not _let_4) (= _let_3 _let_2))))))))))))
% 6.73/7.06 (assert (forall ((K2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.binomial N))) (=> (@ (@ tptp.ord_less_nat K2) (@ (@ tptp.divide_divide_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_nat (@ _let_1 K2)) (@ _let_1 (@ tptp.suc K2)))))))
% 6.73/7.06 (assert (forall ((K2 tptp.nat) (K6 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.binomial N))) (=> (@ (@ tptp.ord_less_nat K2) K6) (=> (@ (@ tptp.ord_less_eq_nat N) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) K2)) (=> (@ (@ tptp.ord_less_eq_nat K6) N) (@ (@ tptp.ord_less_nat (@ _let_1 K6)) (@ _let_1 K2))))))))
% 6.73/7.06 (assert (forall ((K2 tptp.nat) (K6 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.binomial N))) (=> (@ (@ tptp.ord_less_nat K2) 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 K2)) (@ _let_1 K6)))))))
% 6.73/7.06 (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))))))))
% 6.73/7.06 (assert (forall ((S3 tptp.set_real) (A tptp.real) (B (-> tptp.real tptp.complex)) (C2 tptp.complex)) (let ((_let_1 (@ tptp.finite_card_real S3))) (let ((_let_2 (@ tptp.power_power_complex C2))) (let ((_let_3 (@ (@ tptp.member_real A) S3))) (=> (@ tptp.finite_finite_real S3) (and (=> _let_3 (= (@ (@ tptp.groups713298508707869441omplex (lambda ((K3 tptp.real)) (@ (@ (@ tptp.if_complex (= K3 A)) (@ B K3)) C2))) S3) (@ (@ tptp.times_times_complex (@ B A)) (@ _let_2 (@ (@ tptp.minus_minus_nat _let_1) tptp.one_one_nat))))) (=> (not _let_3) (= (@ (@ tptp.groups713298508707869441omplex (lambda ((K3 tptp.real)) (@ (@ (@ tptp.if_complex (= K3 A)) (@ B K3)) C2))) S3) (@ _let_2 _let_1))))))))))
% 6.73/7.06 (assert (forall ((S3 tptp.set_nat) (A tptp.nat) (B (-> tptp.nat tptp.complex)) (C2 tptp.complex)) (let ((_let_1 (@ tptp.finite_card_nat S3))) (let ((_let_2 (@ tptp.power_power_complex C2))) (let ((_let_3 (@ (@ tptp.member_nat A) S3))) (=> (@ tptp.finite_finite_nat S3) (and (=> _let_3 (= (@ (@ tptp.groups6464643781859351333omplex (lambda ((K3 tptp.nat)) (@ (@ (@ tptp.if_complex (= K3 A)) (@ B K3)) C2))) S3) (@ (@ tptp.times_times_complex (@ B A)) (@ _let_2 (@ (@ tptp.minus_minus_nat _let_1) tptp.one_one_nat))))) (=> (not _let_3) (= (@ (@ tptp.groups6464643781859351333omplex (lambda ((K3 tptp.nat)) (@ (@ (@ tptp.if_complex (= K3 A)) (@ B K3)) C2))) S3) (@ _let_2 _let_1))))))))))
% 6.73/7.06 (assert (forall ((S3 tptp.set_int) (A tptp.int) (B (-> tptp.int tptp.complex)) (C2 tptp.complex)) (let ((_let_1 (@ tptp.finite_card_int S3))) (let ((_let_2 (@ tptp.power_power_complex C2))) (let ((_let_3 (@ (@ tptp.member_int A) S3))) (=> (@ tptp.finite_finite_int S3) (and (=> _let_3 (= (@ (@ tptp.groups7440179247065528705omplex (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_complex (= K3 A)) (@ B K3)) C2))) S3) (@ (@ tptp.times_times_complex (@ B A)) (@ _let_2 (@ (@ tptp.minus_minus_nat _let_1) tptp.one_one_nat))))) (=> (not _let_3) (= (@ (@ tptp.groups7440179247065528705omplex (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_complex (= K3 A)) (@ B K3)) C2))) S3) (@ _let_2 _let_1))))))))))
% 6.73/7.06 (assert (forall ((S3 tptp.set_complex) (A tptp.complex) (B (-> tptp.complex tptp.complex)) (C2 tptp.complex)) (let ((_let_1 (@ tptp.finite_card_complex S3))) (let ((_let_2 (@ tptp.power_power_complex C2))) (let ((_let_3 (@ (@ tptp.member_complex A) S3))) (=> (@ tptp.finite3207457112153483333omplex S3) (and (=> _let_3 (= (@ (@ tptp.groups3708469109370488835omplex (lambda ((K3 tptp.complex)) (@ (@ (@ tptp.if_complex (= K3 A)) (@ B K3)) C2))) S3) (@ (@ tptp.times_times_complex (@ B A)) (@ _let_2 (@ (@ tptp.minus_minus_nat _let_1) tptp.one_one_nat))))) (=> (not _let_3) (= (@ (@ tptp.groups3708469109370488835omplex (lambda ((K3 tptp.complex)) (@ (@ (@ tptp.if_complex (= K3 A)) (@ B K3)) C2))) S3) (@ _let_2 _let_1))))))))))
% 6.73/7.06 (assert (forall ((S3 tptp.set_real) (A tptp.real) (B (-> tptp.real tptp.real)) (C2 tptp.real)) (let ((_let_1 (@ tptp.finite_card_real S3))) (let ((_let_2 (@ tptp.power_power_real C2))) (let ((_let_3 (@ (@ tptp.member_real A) S3))) (=> (@ tptp.finite_finite_real S3) (and (=> _let_3 (= (@ (@ tptp.groups1681761925125756287l_real (lambda ((K3 tptp.real)) (@ (@ (@ tptp.if_real (= K3 A)) (@ B K3)) C2))) S3) (@ (@ tptp.times_times_real (@ B A)) (@ _let_2 (@ (@ tptp.minus_minus_nat _let_1) tptp.one_one_nat))))) (=> (not _let_3) (= (@ (@ tptp.groups1681761925125756287l_real (lambda ((K3 tptp.real)) (@ (@ (@ tptp.if_real (= K3 A)) (@ B K3)) C2))) S3) (@ _let_2 _let_1))))))))))
% 6.73/7.06 (assert (forall ((S3 tptp.set_nat) (A tptp.nat) (B (-> tptp.nat tptp.real)) (C2 tptp.real)) (let ((_let_1 (@ tptp.finite_card_nat S3))) (let ((_let_2 (@ tptp.power_power_real C2))) (let ((_let_3 (@ (@ tptp.member_nat A) S3))) (=> (@ tptp.finite_finite_nat S3) (and (=> _let_3 (= (@ (@ tptp.groups129246275422532515t_real (lambda ((K3 tptp.nat)) (@ (@ (@ tptp.if_real (= K3 A)) (@ B K3)) C2))) S3) (@ (@ tptp.times_times_real (@ B A)) (@ _let_2 (@ (@ tptp.minus_minus_nat _let_1) tptp.one_one_nat))))) (=> (not _let_3) (= (@ (@ tptp.groups129246275422532515t_real (lambda ((K3 tptp.nat)) (@ (@ (@ tptp.if_real (= K3 A)) (@ B K3)) C2))) S3) (@ _let_2 _let_1))))))))))
% 6.73/7.06 (assert (forall ((S3 tptp.set_int) (A tptp.int) (B (-> tptp.int tptp.real)) (C2 tptp.real)) (let ((_let_1 (@ tptp.finite_card_int S3))) (let ((_let_2 (@ tptp.power_power_real C2))) (let ((_let_3 (@ (@ tptp.member_int A) S3))) (=> (@ tptp.finite_finite_int S3) (and (=> _let_3 (= (@ (@ tptp.groups2316167850115554303t_real (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_real (= K3 A)) (@ B K3)) C2))) S3) (@ (@ tptp.times_times_real (@ B A)) (@ _let_2 (@ (@ tptp.minus_minus_nat _let_1) tptp.one_one_nat))))) (=> (not _let_3) (= (@ (@ tptp.groups2316167850115554303t_real (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_real (= K3 A)) (@ B K3)) C2))) S3) (@ _let_2 _let_1))))))))))
% 6.73/7.06 (assert (forall ((S3 tptp.set_complex) (A tptp.complex) (B (-> tptp.complex tptp.real)) (C2 tptp.real)) (let ((_let_1 (@ tptp.finite_card_complex S3))) (let ((_let_2 (@ tptp.power_power_real C2))) (let ((_let_3 (@ (@ tptp.member_complex A) S3))) (=> (@ tptp.finite3207457112153483333omplex S3) (and (=> _let_3 (= (@ (@ tptp.groups766887009212190081x_real (lambda ((K3 tptp.complex)) (@ (@ (@ tptp.if_real (= K3 A)) (@ B K3)) C2))) S3) (@ (@ tptp.times_times_real (@ B A)) (@ _let_2 (@ (@ tptp.minus_minus_nat _let_1) tptp.one_one_nat))))) (=> (not _let_3) (= (@ (@ tptp.groups766887009212190081x_real (lambda ((K3 tptp.complex)) (@ (@ (@ tptp.if_real (= K3 A)) (@ B K3)) C2))) S3) (@ _let_2 _let_1))))))))))
% 6.73/7.06 (assert (forall ((S3 tptp.set_real) (A tptp.real) (B (-> tptp.real tptp.rat)) (C2 tptp.rat)) (let ((_let_1 (@ tptp.finite_card_real S3))) (let ((_let_2 (@ tptp.power_power_rat C2))) (let ((_let_3 (@ (@ tptp.member_real A) S3))) (=> (@ tptp.finite_finite_real S3) (and (=> _let_3 (= (@ (@ tptp.groups4061424788464935467al_rat (lambda ((K3 tptp.real)) (@ (@ (@ tptp.if_rat (= K3 A)) (@ B K3)) C2))) S3) (@ (@ tptp.times_times_rat (@ B A)) (@ _let_2 (@ (@ tptp.minus_minus_nat _let_1) tptp.one_one_nat))))) (=> (not _let_3) (= (@ (@ tptp.groups4061424788464935467al_rat (lambda ((K3 tptp.real)) (@ (@ (@ tptp.if_rat (= K3 A)) (@ B K3)) C2))) S3) (@ _let_2 _let_1))))))))))
% 6.73/7.06 (assert (forall ((S3 tptp.set_nat) (A tptp.nat) (B (-> tptp.nat tptp.rat)) (C2 tptp.rat)) (let ((_let_1 (@ tptp.finite_card_nat S3))) (let ((_let_2 (@ tptp.power_power_rat C2))) (let ((_let_3 (@ (@ tptp.member_nat A) S3))) (=> (@ tptp.finite_finite_nat S3) (and (=> _let_3 (= (@ (@ tptp.groups73079841787564623at_rat (lambda ((K3 tptp.nat)) (@ (@ (@ tptp.if_rat (= K3 A)) (@ B K3)) C2))) S3) (@ (@ tptp.times_times_rat (@ B A)) (@ _let_2 (@ (@ tptp.minus_minus_nat _let_1) tptp.one_one_nat))))) (=> (not _let_3) (= (@ (@ tptp.groups73079841787564623at_rat (lambda ((K3 tptp.nat)) (@ (@ (@ tptp.if_rat (= K3 A)) (@ B K3)) C2))) S3) (@ _let_2 _let_1))))))))))
% 6.73/7.06 (assert (forall ((A tptp.rat) (N tptp.nat)) (= (@ (@ tptp.comm_s4028243227959126397er_rat A) (@ tptp.suc N)) (@ (@ tptp.groups73079841787564623at_rat (lambda ((I tptp.nat)) (@ (@ tptp.plus_plus_rat A) (@ tptp.semiri681578069525770553at_rat I)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)))))
% 6.73/7.06 (assert (forall ((A tptp.real) (N tptp.nat)) (= (@ (@ tptp.comm_s7457072308508201937r_real A) (@ tptp.suc N)) (@ (@ tptp.groups129246275422532515t_real (lambda ((I tptp.nat)) (@ (@ tptp.plus_plus_real A) (@ tptp.semiri5074537144036343181t_real I)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)))))
% 6.73/7.06 (assert (forall ((A tptp.int) (N tptp.nat)) (= (@ (@ tptp.comm_s4660882817536571857er_int A) (@ tptp.suc N)) (@ (@ tptp.groups705719431365010083at_int (lambda ((I tptp.nat)) (@ (@ tptp.plus_plus_int A) (@ tptp.semiri1314217659103216013at_int I)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)))))
% 6.73/7.06 (assert (forall ((A tptp.nat) (N tptp.nat)) (= (@ (@ tptp.comm_s4663373288045622133er_nat A) (@ tptp.suc N)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I tptp.nat)) (@ (@ tptp.plus_plus_nat A) (@ tptp.semiri1316708129612266289at_nat I)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)))))
% 6.73/7.06 (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)))))))))))
% 6.73/7.06 (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)))))))))))
% 6.73/7.06 (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)))))))))))
% 6.73/7.06 (assert (forall ((Z3 tptp.complex) (H tptp.complex) (M2 tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat M2))) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((P5 tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex Z3))) (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex (@ (@ tptp.plus_plus_complex Z3) H)) (@ (@ tptp.minus_minus_nat M2) P5))) (@ _let_1 P5))) (@ _let_1 M2))))) _let_1) (@ (@ tptp.groups2073611262835488442omplex (lambda ((P5 tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat M2) P5))) (let ((_let_2 (@ tptp.power_power_complex Z3))) (@ (@ tptp.times_times_complex (@ _let_2 P5)) (@ (@ tptp.minus_minus_complex (@ (@ tptp.power_power_complex (@ (@ tptp.plus_plus_complex Z3) H)) _let_1)) (@ _let_2 _let_1))))))) _let_1)))))
% 6.73/7.06 (assert (forall ((Z3 tptp.rat) (H tptp.rat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat M2))) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((P5 tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat Z3))) (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ (@ tptp.plus_plus_rat Z3) H)) (@ (@ tptp.minus_minus_nat M2) P5))) (@ _let_1 P5))) (@ _let_1 M2))))) _let_1) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((P5 tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat M2) P5))) (let ((_let_2 (@ tptp.power_power_rat Z3))) (@ (@ tptp.times_times_rat (@ _let_2 P5)) (@ (@ tptp.minus_minus_rat (@ (@ tptp.power_power_rat (@ (@ tptp.plus_plus_rat Z3) H)) _let_1)) (@ _let_2 _let_1))))))) _let_1)))))
% 6.73/7.06 (assert (forall ((Z3 tptp.int) (H tptp.int) (M2 tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat M2))) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((P5 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int Z3))) (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ (@ tptp.plus_plus_int Z3) H)) (@ (@ tptp.minus_minus_nat M2) P5))) (@ _let_1 P5))) (@ _let_1 M2))))) _let_1) (@ (@ tptp.groups3539618377306564664at_int (lambda ((P5 tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat M2) P5))) (let ((_let_2 (@ tptp.power_power_int Z3))) (@ (@ tptp.times_times_int (@ _let_2 P5)) (@ (@ tptp.minus_minus_int (@ (@ tptp.power_power_int (@ (@ tptp.plus_plus_int Z3) H)) _let_1)) (@ _let_2 _let_1))))))) _let_1)))))
% 6.73/7.06 (assert (forall ((Z3 tptp.real) (H tptp.real) (M2 tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat M2))) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((P5 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real Z3))) (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real Z3) H)) (@ (@ tptp.minus_minus_nat M2) P5))) (@ _let_1 P5))) (@ _let_1 M2))))) _let_1) (@ (@ tptp.groups6591440286371151544t_real (lambda ((P5 tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat M2) P5))) (let ((_let_2 (@ tptp.power_power_real Z3))) (@ (@ tptp.times_times_real (@ _let_2 P5)) (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real Z3) H)) _let_1)) (@ _let_2 _let_1))))))) _let_1)))))
% 6.73/7.06 (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 ((P5 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex X) P5)) (@ (@ tptp.power_power_complex Y) (@ (@ tptp.minus_minus_nat N) P5))))) (@ tptp.set_ord_lessThan_nat _let_1)))))))
% 6.73/7.06 (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 ((P5 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat X) P5)) (@ (@ tptp.power_power_rat Y) (@ (@ tptp.minus_minus_nat N) P5))))) (@ tptp.set_ord_lessThan_nat _let_1)))))))
% 6.73/7.06 (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 ((P5 tptp.nat)) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int X) P5)) (@ (@ tptp.power_power_int Y) (@ (@ tptp.minus_minus_nat N) P5))))) (@ tptp.set_ord_lessThan_nat _let_1)))))))
% 6.73/7.06 (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 ((P5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real X) P5)) (@ (@ tptp.power_power_real Y) (@ (@ tptp.minus_minus_nat N) P5))))) (@ tptp.set_ord_lessThan_nat _let_1)))))))
% 6.73/7.06 (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 ((I tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex Y) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc I)))) (@ (@ tptp.power_power_complex X) I)))) (@ tptp.set_ord_lessThan_nat N))))))
% 6.73/7.06 (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 ((I tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat Y) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc I)))) (@ (@ tptp.power_power_rat X) I)))) (@ tptp.set_ord_lessThan_nat N))))))
% 6.73/7.06 (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 ((I tptp.nat)) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int Y) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc I)))) (@ (@ tptp.power_power_int X) I)))) (@ tptp.set_ord_lessThan_nat N))))))
% 6.73/7.07 (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 ((I tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real Y) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc I)))) (@ (@ tptp.power_power_real X) I)))) (@ tptp.set_ord_lessThan_nat N))))))
% 6.73/7.07 (assert (forall ((N tptp.nat) (F2 (-> tptp.nat tptp.rat)) (K5 tptp.rat) (K2 tptp.nat)) (=> (forall ((P7 tptp.nat)) (=> (@ (@ tptp.ord_less_nat P7) N) (@ (@ tptp.ord_less_eq_rat (@ F2 P7)) K5))) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) K5) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups2906978787729119204at_rat F2) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.minus_minus_nat N) K2)))) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat N)) K5))))))
% 6.73/7.07 (assert (forall ((N tptp.nat) (F2 (-> tptp.nat tptp.int)) (K5 tptp.int) (K2 tptp.nat)) (=> (forall ((P7 tptp.nat)) (=> (@ (@ tptp.ord_less_nat P7) N) (@ (@ tptp.ord_less_eq_int (@ F2 P7)) K5))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K5) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.groups3539618377306564664at_int F2) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.minus_minus_nat N) K2)))) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int N)) K5))))))
% 6.73/7.07 (assert (forall ((N tptp.nat) (F2 (-> tptp.nat tptp.nat)) (K5 tptp.nat) (K2 tptp.nat)) (=> (forall ((P7 tptp.nat)) (=> (@ (@ tptp.ord_less_nat P7) N) (@ (@ tptp.ord_less_eq_nat (@ F2 P7)) K5))) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) K5) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups3542108847815614940at_nat F2) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.minus_minus_nat N) K2)))) (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat N)) K5))))))
% 6.73/7.07 (assert (forall ((N tptp.nat) (F2 (-> tptp.nat tptp.real)) (K5 tptp.real) (K2 tptp.nat)) (=> (forall ((P7 tptp.nat)) (=> (@ (@ tptp.ord_less_nat P7) N) (@ (@ tptp.ord_less_eq_real (@ F2 P7)) K5))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) K5) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups6591440286371151544t_real F2) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.minus_minus_nat N) K2)))) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) K5))))))
% 6.73/7.07 (assert (forall ((G2 (-> tptp.nat tptp.real)) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.groups129246275422532515t_real G2) (@ (@ tptp.set_or1269000886237332187st_nat (@ _let_1 M2)) (@ tptp.suc (@ _let_1 N)))) (@ (@ tptp.groups129246275422532515t_real (lambda ((I tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I))) (@ (@ tptp.times_times_real (@ G2 _let_1)) (@ G2 (@ tptp.suc _let_1)))))) (@ (@ tptp.set_or1269000886237332187st_nat M2) N))))))
% 6.73/7.07 (assert (forall ((G2 (-> tptp.nat tptp.rat)) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.groups73079841787564623at_rat G2) (@ (@ tptp.set_or1269000886237332187st_nat (@ _let_1 M2)) (@ tptp.suc (@ _let_1 N)))) (@ (@ tptp.groups73079841787564623at_rat (lambda ((I tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I))) (@ (@ tptp.times_times_rat (@ G2 _let_1)) (@ G2 (@ tptp.suc _let_1)))))) (@ (@ tptp.set_or1269000886237332187st_nat M2) N))))))
% 6.73/7.07 (assert (forall ((G2 (-> tptp.nat tptp.int)) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.groups705719431365010083at_int G2) (@ (@ tptp.set_or1269000886237332187st_nat (@ _let_1 M2)) (@ tptp.suc (@ _let_1 N)))) (@ (@ tptp.groups705719431365010083at_int (lambda ((I tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I))) (@ (@ tptp.times_times_int (@ G2 _let_1)) (@ G2 (@ tptp.suc _let_1)))))) (@ (@ tptp.set_or1269000886237332187st_nat M2) N))))))
% 6.73/7.07 (assert (forall ((G2 (-> tptp.nat tptp.nat)) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.groups708209901874060359at_nat G2) (@ (@ tptp.set_or1269000886237332187st_nat (@ _let_1 M2)) (@ tptp.suc (@ _let_1 N)))) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I))) (@ (@ tptp.times_times_nat (@ G2 _let_1)) (@ G2 (@ tptp.suc _let_1)))))) (@ (@ tptp.set_or1269000886237332187st_nat M2) N))))))
% 6.73/7.07 (assert (forall ((F2 (-> tptp.nat tptp.complex)) (A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.groups2073611262835488442omplex F2) (@ (@ tptp.set_or1269000886237332187st_nat A) B)) (@ (@ (@ (@ tptp.set_fo1517530859248394432omplex (lambda ((A5 tptp.nat) (__flatten_var_0 tptp.complex)) (@ (@ tptp.plus_plus_complex (@ F2 A5)) __flatten_var_0))) A) B) tptp.zero_zero_complex))))
% 6.73/7.07 (assert (forall ((F2 (-> tptp.nat tptp.rat)) (A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.groups2906978787729119204at_rat F2) (@ (@ tptp.set_or1269000886237332187st_nat A) B)) (@ (@ (@ (@ tptp.set_fo1949268297981939178at_rat (lambda ((A5 tptp.nat) (__flatten_var_0 tptp.rat)) (@ (@ tptp.plus_plus_rat (@ F2 A5)) __flatten_var_0))) A) B) tptp.zero_zero_rat))))
% 6.73/7.07 (assert (forall ((F2 (-> tptp.nat tptp.int)) (A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.groups3539618377306564664at_int F2) (@ (@ tptp.set_or1269000886237332187st_nat A) B)) (@ (@ (@ (@ tptp.set_fo2581907887559384638at_int (lambda ((A5 tptp.nat) (__flatten_var_0 tptp.int)) (@ (@ tptp.plus_plus_int (@ F2 A5)) __flatten_var_0))) A) B) tptp.zero_zero_int))))
% 6.73/7.07 (assert (forall ((F2 (-> tptp.nat tptp.nat)) (A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat F2) (@ (@ tptp.set_or1269000886237332187st_nat A) B)) (@ (@ (@ (@ tptp.set_fo2584398358068434914at_nat (lambda ((A5 tptp.nat) (__flatten_var_0 tptp.nat)) (@ (@ tptp.plus_plus_nat (@ F2 A5)) __flatten_var_0))) A) B) tptp.zero_zero_nat))))
% 6.73/7.07 (assert (forall ((F2 (-> tptp.nat tptp.real)) (A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real F2) (@ (@ tptp.set_or1269000886237332187st_nat A) B)) (@ (@ (@ (@ tptp.set_fo3111899725591712190t_real (lambda ((A5 tptp.nat) (__flatten_var_0 tptp.real)) (@ (@ tptp.plus_plus_real (@ F2 A5)) __flatten_var_0))) A) B) tptp.zero_zero_real))))
% 6.73/7.07 (assert (forall ((A tptp.rat) (N tptp.nat)) (= (@ (@ tptp.comm_s4028243227959126397er_rat A) (@ tptp.suc N)) (@ (@ tptp.groups73079841787564623at_rat (lambda ((I tptp.nat)) (@ (@ tptp.plus_plus_rat A) (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.minus_minus_nat N) I))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)))))
% 6.73/7.07 (assert (forall ((A tptp.real) (N tptp.nat)) (= (@ (@ tptp.comm_s7457072308508201937r_real A) (@ tptp.suc N)) (@ (@ tptp.groups129246275422532515t_real (lambda ((I tptp.nat)) (@ (@ tptp.plus_plus_real A) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.minus_minus_nat N) I))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)))))
% 6.73/7.07 (assert (forall ((A tptp.int) (N tptp.nat)) (= (@ (@ tptp.comm_s4660882817536571857er_int A) (@ tptp.suc N)) (@ (@ tptp.groups705719431365010083at_int (lambda ((I tptp.nat)) (@ (@ tptp.plus_plus_int A) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.minus_minus_nat N) I))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)))))
% 6.73/7.07 (assert (forall ((A tptp.nat) (N tptp.nat)) (= (@ (@ tptp.comm_s4663373288045622133er_nat A) (@ tptp.suc N)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I tptp.nat)) (@ (@ tptp.plus_plus_nat A) (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.minus_minus_nat N) I))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)))))
% 6.73/7.07 (assert (forall ((X tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_8373710615458151222nteger tptp.one_one_Code_integer))) (= (@ _let_1 (@ (@ tptp.power_8256067586552552935nteger X) N)) (@ (@ tptp.times_3573771949741848930nteger (@ _let_1 X)) (@ (@ tptp.groups7501900531339628137nteger (lambda ((I tptp.nat)) (@ (@ tptp.power_8256067586552552935nteger X) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc I))))) (@ tptp.set_ord_lessThan_nat N)))))))
% 6.73/7.07 (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 ((I tptp.nat)) (@ (@ tptp.power_power_complex X) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc I))))) (@ tptp.set_ord_lessThan_nat N)))))))
% 6.73/7.07 (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 ((I tptp.nat)) (@ (@ tptp.power_power_rat X) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc I))))) (@ tptp.set_ord_lessThan_nat N)))))))
% 6.73/7.07 (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 ((I tptp.nat)) (@ (@ tptp.power_power_int X) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc I))))) (@ tptp.set_ord_lessThan_nat N)))))))
% 6.73/7.07 (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 ((I tptp.nat)) (@ (@ tptp.power_power_real X) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc I))))) (@ tptp.set_ord_lessThan_nat N)))))))
% 6.73/7.07 (assert (forall ((F2 (-> tptp.nat tptp.real)) (G2 (-> tptp.nat tptp.real)) (N tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat N))) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I tptp.nat)) (@ (@ (@ tptp.if_real (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I)) (@ F2 I)) (@ G2 I)))) (@ 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 ((I tptp.nat)) (@ F2 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I)))) _let_1)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I tptp.nat)) (@ G2 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I)) tptp.one_one_nat)))) _let_1))))))
% 6.73/7.07 (assert (forall ((N tptp.nat) (K2 tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.binomial N) K2)) (@ (@ tptp.ord_less_eq_nat K2) N))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.binomial N) tptp.zero_zero_nat) tptp.one_one_nat)))
% 6.73/7.07 (assert (forall ((N tptp.nat) (K2 tptp.nat)) (let ((_let_1 (@ tptp.suc K2))) (let ((_let_2 (@ tptp.binomial N))) (= (@ (@ tptp.binomial (@ tptp.suc N)) _let_1) (@ (@ tptp.plus_plus_nat (@ _let_2 K2)) (@ _let_2 _let_1)))))))
% 6.73/7.07 (assert (forall ((N tptp.nat) (K2 tptp.nat)) (= (= (@ (@ tptp.binomial N) K2) tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat N) K2))))
% 6.73/7.07 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.binomial N) (@ tptp.suc tptp.zero_zero_nat)) N)))
% 6.73/7.07 (assert (forall ((K2 tptp.nat)) (= (@ (@ tptp.binomial tptp.zero_zero_nat) (@ tptp.suc K2)) tptp.zero_zero_nat)))
% 6.73/7.07 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (= (@ (@ tptp.binomial _let_1) N) _let_1))))
% 6.73/7.07 (assert (forall ((A4 tptp.set_int) (F2 (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int A4) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.groups1707563613775114915nt_nat F2) A4)) (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) A4) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F2 X4))))))))
% 6.73/7.07 (assert (forall ((A4 tptp.set_complex) (F2 (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex A4) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.groups861055069439313189ex_nat F2) A4)) (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) A4) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F2 X4))))))))
% 6.73/7.07 (assert (forall ((A4 tptp.set_nat) (F2 (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_nat A4) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.groups708209901874060359at_nat F2) A4)) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) A4) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F2 X4))))))))
% 6.73/7.07 (assert (forall ((I2 tptp.nat) (J2 tptp.nat)) (= (@ (@ tptp.groups705719431365010083at_int tptp.semiri1314217659103216013at_int) (@ (@ tptp.set_or1269000886237332187st_nat I2) J2)) (@ (@ tptp.groups1705073143266064639nt_int (lambda ((X4 tptp.int)) X4)) (@ (@ tptp.set_or1266510415728281911st_int (@ tptp.semiri1314217659103216013at_int I2)) (@ tptp.semiri1314217659103216013at_int J2))))))
% 6.73/7.07 (assert (forall ((I2 tptp.nat) (J2 tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat I2) J2))) (= (@ (@ tptp.groups705719431365010083at_int tptp.semiri1314217659103216013at_int) (@ (@ tptp.set_or1269000886237332187st_nat I2) _let_1)) (@ (@ tptp.groups1705073143266064639nt_int (lambda ((X4 tptp.int)) X4)) (@ (@ tptp.set_or1266510415728281911st_int (@ tptp.semiri1314217659103216013at_int I2)) (@ tptp.semiri1314217659103216013at_int _let_1)))))))
% 6.73/7.07 (assert (forall ((N tptp.nat) (K2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) K2) (= (@ (@ tptp.binomial N) K2) tptp.zero_zero_nat))))
% 6.73/7.07 (assert (forall ((K2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.suc K2))) (= (@ (@ tptp.times_times_nat _let_2) (@ (@ tptp.binomial _let_1) _let_2)) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.binomial N) K2)))))))
% 6.73/7.07 (assert (forall ((N tptp.nat) (K2 tptp.nat)) (let ((_let_1 (@ tptp.suc K2))) (let ((_let_2 (@ tptp.suc N))) (= (@ (@ tptp.times_times_nat _let_2) (@ (@ tptp.binomial N) K2)) (@ (@ tptp.times_times_nat (@ (@ tptp.binomial _let_2) _let_1)) _let_1))))))
% 6.73/7.07 (assert (forall ((K2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.binomial N))) (=> (@ (@ tptp.ord_less_eq_nat K2) N) (= (@ _let_1 K2) (@ _let_1 (@ (@ tptp.minus_minus_nat N) K2)))))))
% 6.73/7.07 (assert (forall ((M2 tptp.nat) (R3 tptp.nat) (K2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat M2))) (let ((_let_2 (@ _let_1 R3))) (let ((_let_3 (@ tptp.binomial (@ (@ tptp.plus_plus_nat _let_2) K2)))) (let ((_let_4 (@ _let_1 K2))) (= (@ (@ tptp.times_times_nat (@ _let_3 _let_4)) (@ (@ tptp.binomial _let_4) K2)) (@ (@ tptp.times_times_nat (@ _let_3 K2)) (@ (@ tptp.binomial _let_2) M2)))))))))
% 6.73/7.07 (assert (forall ((R3 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat R3) N) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.binomial N) R3)) (@ (@ tptp.power_power_nat N) R3)))))
% 6.73/7.07 (assert (forall ((K2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K2) N) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.binomial N) K2)))))
% 6.73/7.07 (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)))))))
% 6.73/7.07 (assert (forall ((N tptp.nat) (K2 tptp.nat)) (let ((_let_1 (@ tptp.suc K2))) (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) K2))) _let_1))))))
% 6.73/7.07 (assert (forall ((K2 tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.binomial N))) (=> (@ (@ tptp.ord_less_eq_nat K2) M2) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ (@ tptp.times_times_nat (@ _let_1 M2)) (@ (@ tptp.binomial M2) K2)) (@ (@ tptp.times_times_nat (@ _let_1 K2)) (@ (@ tptp.binomial (@ (@ tptp.minus_minus_nat N) K2)) (@ (@ tptp.minus_minus_nat M2) K2)))))))))
% 6.73/7.07 (assert (forall ((N tptp.nat) (K2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat N))) (= (@ (@ tptp.times_times_nat (@ _let_1 K2)) (@ (@ tptp.binomial N) K2)) (@ (@ tptp.times_times_nat N) (@ (@ tptp.binomial (@ _let_1 tptp.one_one_nat)) K2))))))
% 6.73/7.07 (assert (forall ((K2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc K2))) (= (@ (@ 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)) K2))))))
% 6.73/7.07 (assert (forall ((F2 (-> tptp.nat tptp.nat)) (Mm tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K3 tptp.nat)) (@ F2 (@ tptp.suc K3)))) (@ tptp.set_ord_lessThan_nat Mm)) (@ (@ tptp.groups3542108847815614940at_nat F2) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) Mm)))))
% 6.73/7.07 (assert (forall ((F2 (-> tptp.nat tptp.real)) (Mm tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ F2 (@ tptp.suc K3)))) (@ tptp.set_ord_lessThan_nat Mm)) (@ (@ tptp.groups6591440286371151544t_real F2) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) Mm)))))
% 6.73/7.07 (assert (forall ((K2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K2) N) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real N)) (@ tptp.semiri5074537144036343181t_real K2))) K2)) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.binomial N) K2))))))
% 6.73/7.07 (assert (forall ((K2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K2) N) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat (@ (@ tptp.divide_divide_rat (@ tptp.semiri681578069525770553at_rat N)) (@ tptp.semiri681578069525770553at_rat K2))) K2)) (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.binomial N) K2))))))
% 6.73/7.07 (assert (forall ((N tptp.nat) (K2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.binomial N) K2)) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))
% 6.73/7.07 (assert (forall ((N tptp.nat) (K2 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 K2) (= (@ (@ tptp.binomial N) K2) (@ (@ tptp.plus_plus_nat (@ _let_1 (@ (@ tptp.minus_minus_nat K2) tptp.one_one_nat))) (@ _let_1 K2)))))))))
% 6.73/7.07 (assert (forall ((K2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K2) (= (@ (@ tptp.times_times_nat K2) (@ (@ tptp.binomial N) K2)) (@ (@ tptp.times_times_nat N) (@ (@ tptp.binomial (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) (@ (@ tptp.minus_minus_nat K2) tptp.one_one_nat)))))))
% 6.73/7.07 (assert (forall ((N tptp.nat) (K2 tptp.nat)) (let ((_let_1 (@ tptp.binomial (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)))) (let ((_let_2 (@ tptp.suc K2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.binomial N) _let_2) (@ (@ tptp.plus_plus_nat (@ _let_1 _let_2)) (@ _let_1 K2))))))))
% 6.73/7.07 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.times_times_rat _let_1) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I tptp.nat)) (@ (@ (@ tptp.if_rat (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I))) (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.binomial N) I))) tptp.zero_zero_rat))) (@ tptp.set_ord_atMost_nat N))) (@ (@ tptp.power_power_rat _let_1) N))))))
% 6.73/7.07 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.times_times_complex _let_1) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I tptp.nat)) (@ (@ (@ tptp.if_complex (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I))) (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.binomial N) I))) tptp.zero_zero_complex))) (@ tptp.set_ord_atMost_nat N))) (@ (@ tptp.power_power_complex _let_1) N))))))
% 6.73/7.07 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I tptp.nat)) (@ (@ (@ tptp.if_int (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I))) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.binomial N) I))) tptp.zero_zero_int))) (@ tptp.set_ord_atMost_nat N))) (@ (@ tptp.power_power_int _let_1) N))))))
% 6.73/7.07 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.times_times_real _let_1) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I tptp.nat)) (@ (@ (@ tptp.if_real (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I))) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.binomial N) I))) tptp.zero_zero_real))) (@ tptp.set_ord_atMost_nat N))) (@ (@ tptp.power_power_real _let_1) N))))))
% 6.73/7.07 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.times_times_rat _let_1) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I tptp.nat)) (@ (@ (@ tptp.if_rat (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I)) (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.binomial N) I))) tptp.zero_zero_rat))) (@ tptp.set_ord_atMost_nat N))) (@ (@ tptp.power_power_rat _let_1) N))))))
% 6.73/7.07 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.times_times_complex _let_1) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I tptp.nat)) (@ (@ (@ tptp.if_complex (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I)) (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.binomial N) I))) tptp.zero_zero_complex))) (@ tptp.set_ord_atMost_nat N))) (@ (@ tptp.power_power_complex _let_1) N))))))
% 6.73/7.07 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I tptp.nat)) (@ (@ (@ tptp.if_int (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I)) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.binomial N) I))) tptp.zero_zero_int))) (@ tptp.set_ord_atMost_nat N))) (@ (@ tptp.power_power_int _let_1) N))))))
% 6.73/7.07 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.times_times_real _let_1) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I tptp.nat)) (@ (@ (@ tptp.if_real (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I)) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.binomial N) I))) tptp.zero_zero_real))) (@ tptp.set_ord_atMost_nat N))) (@ (@ tptp.power_power_real _let_1) N))))))
% 6.73/7.07 (assert (forall ((A4 tptp.set_list_nat) (K2 tptp.nat)) (let ((_let_1 (@ tptp.finite_card_list_nat A4))) (=> (@ tptp.finite8100373058378681591st_nat A4) (=> (@ (@ tptp.ord_less_eq_nat K2) _let_1) (= (@ tptp.finite7325466520557071688st_nat (@ tptp.collec5989764272469232197st_nat (lambda ((Xs tptp.list_list_nat)) (and (= (@ tptp.size_s3023201423986296836st_nat Xs) K2) (@ tptp.distinct_list_nat Xs) (@ (@ tptp.ord_le6045566169113846134st_nat (@ tptp.set_list_nat2 Xs)) A4))))) (@ (@ tptp.groups708209901874060359at_nat (lambda ((X4 tptp.nat)) X4)) (@ (@ tptp.set_or1269000886237332187st_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat _let_1) K2)) tptp.one_one_nat)) _let_1))))))))
% 6.73/7.07 (assert (forall ((A4 tptp.set_set_nat) (K2 tptp.nat)) (let ((_let_1 (@ tptp.finite_card_set_nat A4))) (=> (@ tptp.finite1152437895449049373et_nat A4) (=> (@ (@ tptp.ord_less_eq_nat K2) _let_1) (= (@ tptp.finite5631907774883551598et_nat (@ tptp.collect_list_set_nat (lambda ((Xs tptp.list_set_nat)) (and (= (@ tptp.size_s3254054031482475050et_nat Xs) K2) (@ tptp.distinct_set_nat Xs) (@ (@ tptp.ord_le6893508408891458716et_nat (@ tptp.set_set_nat2 Xs)) A4))))) (@ (@ tptp.groups708209901874060359at_nat (lambda ((X4 tptp.nat)) X4)) (@ (@ tptp.set_or1269000886237332187st_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat _let_1) K2)) tptp.one_one_nat)) _let_1))))))))
% 6.73/7.07 (assert (forall ((A4 tptp.set_complex) (K2 tptp.nat)) (let ((_let_1 (@ tptp.finite_card_complex A4))) (=> (@ tptp.finite3207457112153483333omplex A4) (=> (@ (@ tptp.ord_less_eq_nat K2) _let_1) (= (@ tptp.finite5120063068150530198omplex (@ tptp.collect_list_complex (lambda ((Xs tptp.list_complex)) (and (= (@ tptp.size_s3451745648224563538omplex Xs) K2) (@ tptp.distinct_complex Xs) (@ (@ tptp.ord_le211207098394363844omplex (@ tptp.set_complex2 Xs)) A4))))) (@ (@ tptp.groups708209901874060359at_nat (lambda ((X4 tptp.nat)) X4)) (@ (@ tptp.set_or1269000886237332187st_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat _let_1) K2)) tptp.one_one_nat)) _let_1))))))))
% 6.73/7.07 (assert (forall ((A4 tptp.set_VEBT_VEBT) (K2 tptp.nat)) (let ((_let_1 (@ tptp.finite7802652506058667612T_VEBT A4))) (=> (@ tptp.finite5795047828879050333T_VEBT A4) (=> (@ (@ tptp.ord_less_eq_nat K2) _let_1) (= (@ tptp.finite5915292604075114978T_VEBT (@ tptp.collec5608196760682091941T_VEBT (lambda ((Xs tptp.list_VEBT_VEBT)) (and (= (@ tptp.size_s6755466524823107622T_VEBT Xs) K2) (@ tptp.distinct_VEBT_VEBT Xs) (@ (@ tptp.ord_le4337996190870823476T_VEBT (@ tptp.set_VEBT_VEBT2 Xs)) A4))))) (@ (@ tptp.groups708209901874060359at_nat (lambda ((X4 tptp.nat)) X4)) (@ (@ tptp.set_or1269000886237332187st_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat _let_1) K2)) tptp.one_one_nat)) _let_1))))))))
% 6.73/7.07 (assert (forall ((A4 tptp.set_o) (K2 tptp.nat)) (let ((_let_1 (@ tptp.finite_card_o A4))) (=> (@ tptp.finite_finite_o A4) (=> (@ (@ tptp.ord_less_eq_nat K2) _let_1) (= (@ tptp.finite_card_list_o (@ tptp.collect_list_o (lambda ((Xs tptp.list_o)) (and (= (@ tptp.size_size_list_o Xs) K2) (@ tptp.distinct_o Xs) (@ (@ tptp.ord_less_eq_set_o (@ tptp.set_o2 Xs)) A4))))) (@ (@ tptp.groups708209901874060359at_nat (lambda ((X4 tptp.nat)) X4)) (@ (@ tptp.set_or1269000886237332187st_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat _let_1) K2)) tptp.one_one_nat)) _let_1))))))))
% 6.73/7.07 (assert (forall ((A4 tptp.set_int) (K2 tptp.nat)) (let ((_let_1 (@ tptp.finite_card_int A4))) (=> (@ tptp.finite_finite_int A4) (=> (@ (@ tptp.ord_less_eq_nat K2) _let_1) (= (@ tptp.finite_card_list_int (@ tptp.collect_list_int (lambda ((Xs tptp.list_int)) (and (= (@ tptp.size_size_list_int Xs) K2) (@ tptp.distinct_int Xs) (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_int2 Xs)) A4))))) (@ (@ tptp.groups708209901874060359at_nat (lambda ((X4 tptp.nat)) X4)) (@ (@ tptp.set_or1269000886237332187st_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat _let_1) K2)) tptp.one_one_nat)) _let_1))))))))
% 6.73/7.07 (assert (forall ((A4 tptp.set_nat) (K2 tptp.nat)) (let ((_let_1 (@ tptp.finite_card_nat A4))) (=> (@ tptp.finite_finite_nat A4) (=> (@ (@ tptp.ord_less_eq_nat K2) _let_1) (= (@ tptp.finite_card_list_nat (@ tptp.collect_list_nat (lambda ((Xs tptp.list_nat)) (and (= (@ tptp.size_size_list_nat Xs) K2) (@ tptp.distinct_nat Xs) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_nat2 Xs)) A4))))) (@ (@ tptp.groups708209901874060359at_nat (lambda ((X4 tptp.nat)) X4)) (@ (@ tptp.set_or1269000886237332187st_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat _let_1) K2)) tptp.one_one_nat)) _let_1))))))))
% 6.73/7.07 (assert (forall ((R3 tptp.complex) (M2 tptp.nat)) (let ((_let_1 (@ tptp.suc M2))) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.gbinomial_complex R3) K3)) (@ (@ tptp.minus_minus_complex (@ (@ tptp.divide1717551699836669952omplex R3) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) (@ tptp.semiri8010041392384452111omplex K3))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) M2)) (@ (@ tptp.times_times_complex (@ (@ tptp.divide1717551699836669952omplex (@ tptp.semiri8010041392384452111omplex _let_1)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) (@ (@ tptp.gbinomial_complex R3) _let_1))))))
% 6.73/7.07 (assert (forall ((R3 tptp.rat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.suc M2))) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.gbinomial_rat R3) K3)) (@ (@ tptp.minus_minus_rat (@ (@ tptp.divide_divide_rat R3) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one)))) (@ tptp.semiri681578069525770553at_rat K3))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) M2)) (@ (@ tptp.times_times_rat (@ (@ tptp.divide_divide_rat (@ tptp.semiri681578069525770553at_rat _let_1)) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.gbinomial_rat R3) _let_1))))))
% 6.73/7.07 (assert (forall ((R3 tptp.real) (M2 tptp.nat)) (let ((_let_1 (@ tptp.suc M2))) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.gbinomial_real R3) K3)) (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real R3) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.semiri5074537144036343181t_real K3))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) M2)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real _let_1)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ (@ tptp.gbinomial_real R3) _let_1))))))
% 6.73/7.07 (assert (forall ((X tptp.nat) (Y tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (let ((_let_2 (@ tptp.accp_nat tptp.vEBT_v4011308405150292612up_rel))) (let ((_let_3 (= Y (@ (@ tptp.vEBT_Leaf false) false)))) (=> (= (@ tptp.vEBT_vebt_buildup X) Y) (=> (@ _let_2 X) (=> (=> (= X tptp.zero_zero_nat) (=> _let_3 (not (@ _let_2 tptp.zero_zero_nat)))) (=> (=> (= X _let_1) (=> _let_3 (not (@ _let_2 _let_1)))) (not (forall ((Va tptp.nat)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_1) _let_2))) (let ((_let_4 (@ tptp.suc _let_3))) (let ((_let_5 (@ tptp.vEBT_vebt_buildup _let_3))) (let ((_let_6 (@ tptp.power_power_nat _let_2))) (let ((_let_7 (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1))) (let ((_let_8 (@ (@ tptp.dvd_dvd_nat _let_2) _let_1))) (=> (= X _let_1) (=> (and (=> _let_8 (= Y (@ (@ _let_7 (@ (@ tptp.replicate_VEBT_VEBT (@ _let_6 _let_3)) _let_5)) _let_5))) (=> (not _let_8) (= Y (@ (@ _let_7 (@ (@ tptp.replicate_VEBT_VEBT (@ _let_6 _let_4)) _let_5)) (@ tptp.vEBT_vebt_buildup _let_4))))) (not (@ (@ tptp.accp_nat tptp.vEBT_v4011308405150292612up_rel) _let_1)))))))))))))))))))))))
% 6.73/7.07 (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)))))))
% 6.73/7.07 (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)))))))
% 6.73/7.07 (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)))))))
% 6.73/7.07 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (= (@ tptp.set_ord_atMost_nat X) (@ tptp.set_ord_atMost_nat Y)) (= X Y))))
% 6.73/7.07 (assert (forall ((I2 tptp.real) (K2 tptp.real)) (= (@ (@ tptp.member_real I2) (@ tptp.set_ord_atMost_real K2)) (@ (@ tptp.ord_less_eq_real I2) K2))))
% 6.73/7.07 (assert (forall ((I2 tptp.set_nat) (K2 tptp.set_nat)) (= (@ (@ tptp.member_set_nat I2) (@ tptp.set_or4236626031148496127et_nat K2)) (@ (@ tptp.ord_less_eq_set_nat I2) K2))))
% 6.73/7.07 (assert (forall ((I2 tptp.rat) (K2 tptp.rat)) (= (@ (@ tptp.member_rat I2) (@ tptp.set_ord_atMost_rat K2)) (@ (@ tptp.ord_less_eq_rat I2) K2))))
% 6.73/7.07 (assert (forall ((I2 tptp.num) (K2 tptp.num)) (= (@ (@ tptp.member_num I2) (@ tptp.set_ord_atMost_num K2)) (@ (@ tptp.ord_less_eq_num I2) K2))))
% 6.73/7.07 (assert (forall ((I2 tptp.int) (K2 tptp.int)) (= (@ (@ tptp.member_int I2) (@ tptp.set_ord_atMost_int K2)) (@ (@ tptp.ord_less_eq_int I2) K2))))
% 6.73/7.07 (assert (forall ((I2 tptp.nat) (K2 tptp.nat)) (= (@ (@ tptp.member_nat I2) (@ tptp.set_ord_atMost_nat K2)) (@ (@ tptp.ord_less_eq_nat I2) K2))))
% 6.73/7.07 (assert (forall ((P2 Bool) (Q Bool)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.zero_n2052037380579107095ol_rat P2)) (@ tptp.zero_n2052037380579107095ol_rat Q)) (=> P2 Q))))
% 6.73/7.07 (assert (forall ((P2 Bool) (Q Bool)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.zero_n2687167440665602831ol_nat P2)) (@ tptp.zero_n2687167440665602831ol_nat Q)) (=> P2 Q))))
% 6.73/7.07 (assert (forall ((P2 Bool) (Q Bool)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.zero_n2684676970156552555ol_int P2)) (@ tptp.zero_n2684676970156552555ol_int Q)) (=> P2 Q))))
% 6.73/7.07 (assert (forall ((P2 Bool) (Q Bool)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.zero_n356916108424825756nteger P2)) (@ tptp.zero_n356916108424825756nteger Q)) (=> P2 Q))))
% 6.73/7.07 (assert (= (@ tptp.zero_n1201886186963655149omplex false) tptp.zero_zero_complex))
% 6.73/7.07 (assert (= (@ tptp.zero_n3304061248610475627l_real false) tptp.zero_zero_real))
% 6.73/7.07 (assert (= (@ tptp.zero_n2052037380579107095ol_rat false) tptp.zero_zero_rat))
% 6.73/7.07 (assert (= (@ tptp.zero_n2687167440665602831ol_nat false) tptp.zero_zero_nat))
% 6.73/7.07 (assert (= (@ tptp.zero_n2684676970156552555ol_int false) tptp.zero_zero_int))
% 6.73/7.07 (assert (= (@ tptp.zero_n356916108424825756nteger false) tptp.zero_z3403309356797280102nteger))
% 6.73/7.07 (assert (forall ((P2 Bool)) (= (= (@ tptp.zero_n1201886186963655149omplex P2) tptp.zero_zero_complex) (not P2))))
% 6.73/7.07 (assert (forall ((P2 Bool)) (= (= (@ tptp.zero_n3304061248610475627l_real P2) tptp.zero_zero_real) (not P2))))
% 6.73/7.07 (assert (forall ((P2 Bool)) (= (= (@ tptp.zero_n2052037380579107095ol_rat P2) tptp.zero_zero_rat) (not P2))))
% 6.73/7.07 (assert (forall ((P2 Bool)) (= (= (@ tptp.zero_n2687167440665602831ol_nat P2) tptp.zero_zero_nat) (not P2))))
% 6.73/7.07 (assert (forall ((P2 Bool)) (= (= (@ tptp.zero_n2684676970156552555ol_int P2) tptp.zero_zero_int) (not P2))))
% 6.73/7.07 (assert (forall ((P2 Bool)) (= (= (@ tptp.zero_n356916108424825756nteger P2) tptp.zero_z3403309356797280102nteger) (not P2))))
% 6.73/7.07 (assert (forall ((P2 Bool) (Q Bool)) (= (@ (@ tptp.ord_less_real (@ tptp.zero_n3304061248610475627l_real P2)) (@ tptp.zero_n3304061248610475627l_real Q)) (and (not P2) Q))))
% 6.73/7.07 (assert (forall ((P2 Bool) (Q Bool)) (= (@ (@ tptp.ord_less_rat (@ tptp.zero_n2052037380579107095ol_rat P2)) (@ tptp.zero_n2052037380579107095ol_rat Q)) (and (not P2) Q))))
% 6.73/7.07 (assert (forall ((P2 Bool) (Q Bool)) (= (@ (@ tptp.ord_less_nat (@ tptp.zero_n2687167440665602831ol_nat P2)) (@ tptp.zero_n2687167440665602831ol_nat Q)) (and (not P2) Q))))
% 6.73/7.07 (assert (forall ((P2 Bool) (Q Bool)) (= (@ (@ tptp.ord_less_int (@ tptp.zero_n2684676970156552555ol_int P2)) (@ tptp.zero_n2684676970156552555ol_int Q)) (and (not P2) Q))))
% 6.73/7.07 (assert (forall ((P2 Bool) (Q Bool)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.zero_n356916108424825756nteger P2)) (@ tptp.zero_n356916108424825756nteger Q)) (and (not P2) Q))))
% 6.73/7.07 (assert (forall ((P2 Bool)) (= (= (@ tptp.zero_n1201886186963655149omplex P2) tptp.one_one_complex) P2)))
% 6.73/7.07 (assert (forall ((P2 Bool)) (= (= (@ tptp.zero_n3304061248610475627l_real P2) tptp.one_one_real) P2)))
% 6.73/7.07 (assert (forall ((P2 Bool)) (= (= (@ tptp.zero_n2687167440665602831ol_nat P2) tptp.one_one_nat) P2)))
% 6.73/7.07 (assert (forall ((P2 Bool)) (= (= (@ tptp.zero_n2684676970156552555ol_int P2) tptp.one_one_int) P2)))
% 6.73/7.07 (assert (forall ((P2 Bool)) (= (= (@ tptp.zero_n356916108424825756nteger P2) tptp.one_one_Code_integer) P2)))
% 6.73/7.07 (assert (= (@ tptp.zero_n1201886186963655149omplex true) tptp.one_one_complex))
% 6.73/7.07 (assert (= (@ tptp.zero_n3304061248610475627l_real true) tptp.one_one_real))
% 6.73/7.07 (assert (= (@ tptp.zero_n2687167440665602831ol_nat true) tptp.one_one_nat))
% 6.73/7.07 (assert (= (@ tptp.zero_n2684676970156552555ol_int true) tptp.one_one_int))
% 6.73/7.07 (assert (= (@ tptp.zero_n356916108424825756nteger true) tptp.one_one_Code_integer))
% 6.73/7.07 (assert (forall ((P2 Bool)) (= (@ tptp.semiri5074537144036343181t_real (@ tptp.zero_n2687167440665602831ol_nat P2)) (@ tptp.zero_n3304061248610475627l_real P2))))
% 6.73/7.07 (assert (forall ((P2 Bool)) (let ((_let_1 (@ tptp.zero_n2687167440665602831ol_nat P2))) (= (@ tptp.semiri1316708129612266289at_nat _let_1) _let_1))))
% 6.73/7.07 (assert (forall ((P2 Bool)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.zero_n2687167440665602831ol_nat P2)) (@ tptp.zero_n2684676970156552555ol_int P2))))
% 6.73/7.07 (assert (forall ((P2 Bool)) (= (@ tptp.semiri4939895301339042750nteger (@ tptp.zero_n2687167440665602831ol_nat P2)) (@ tptp.zero_n356916108424825756nteger P2))))
% 6.73/7.07 (assert (forall ((P2 Bool) (Q Bool)) (= (@ tptp.zero_n2687167440665602831ol_nat (or P2 Q)) (@ (@ tptp.ord_max_nat (@ tptp.zero_n2687167440665602831ol_nat P2)) (@ tptp.zero_n2687167440665602831ol_nat Q)))))
% 6.73/7.07 (assert (forall ((P2 Bool) (Q Bool)) (= (@ tptp.zero_n2684676970156552555ol_int (or P2 Q)) (@ (@ tptp.ord_max_int (@ tptp.zero_n2684676970156552555ol_int P2)) (@ tptp.zero_n2684676970156552555ol_int Q)))))
% 6.73/7.07 (assert (forall ((P2 Bool) (Q Bool)) (= (@ tptp.zero_n356916108424825756nteger (or P2 Q)) (@ (@ tptp.ord_max_Code_integer (@ tptp.zero_n356916108424825756nteger P2)) (@ tptp.zero_n356916108424825756nteger Q)))))
% 6.73/7.07 (assert (forall ((K2 tptp.nat)) (@ tptp.finite_finite_nat (@ tptp.set_ord_atMost_nat K2))))
% 6.73/7.07 (assert (forall ((P2 Bool)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.zero_n3304061248610475627l_real P2)) P2)))
% 6.73/7.07 (assert (forall ((P2 Bool)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.zero_n2052037380579107095ol_rat P2)) P2)))
% 6.73/7.07 (assert (forall ((P2 Bool)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.zero_n2687167440665602831ol_nat P2)) P2)))
% 6.73/7.07 (assert (forall ((P2 Bool)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.zero_n2684676970156552555ol_int P2)) P2)))
% 6.73/7.07 (assert (forall ((P2 Bool)) (= (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ tptp.zero_n356916108424825756nteger P2)) P2)))
% 6.73/7.07 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat)) (= (@ (@ tptp.ord_le6893508408891458716et_nat (@ tptp.set_or4236626031148496127et_nat X)) (@ tptp.set_or4236626031148496127et_nat Y)) (@ (@ tptp.ord_less_eq_set_nat X) Y))))
% 6.73/7.07 (assert (forall ((X tptp.rat) (Y tptp.rat)) (= (@ (@ tptp.ord_less_eq_set_rat (@ tptp.set_ord_atMost_rat X)) (@ tptp.set_ord_atMost_rat Y)) (@ (@ tptp.ord_less_eq_rat X) Y))))
% 6.73/7.07 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.ord_less_eq_set_num (@ tptp.set_ord_atMost_num X)) (@ tptp.set_ord_atMost_num Y)) (@ (@ tptp.ord_less_eq_num X) Y))))
% 6.73/7.07 (assert (forall ((X tptp.int) (Y tptp.int)) (= (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_ord_atMost_int X)) (@ tptp.set_ord_atMost_int Y)) (@ (@ tptp.ord_less_eq_int X) Y))))
% 6.73/7.07 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_ord_atMost_nat X)) (@ tptp.set_ord_atMost_nat Y)) (@ (@ tptp.ord_less_eq_nat X) Y))))
% 6.73/7.07 (assert (forall ((P2 Bool)) (= (@ (@ tptp.ord_less_real (@ tptp.zero_n3304061248610475627l_real P2)) tptp.one_one_real) (not P2))))
% 6.73/7.07 (assert (forall ((P2 Bool)) (= (@ (@ tptp.ord_less_rat (@ tptp.zero_n2052037380579107095ol_rat P2)) tptp.one_one_rat) (not P2))))
% 6.73/7.07 (assert (forall ((P2 Bool)) (= (@ (@ tptp.ord_less_nat (@ tptp.zero_n2687167440665602831ol_nat P2)) tptp.one_one_nat) (not P2))))
% 6.73/7.07 (assert (forall ((P2 Bool)) (= (@ (@ tptp.ord_less_int (@ tptp.zero_n2684676970156552555ol_int P2)) tptp.one_one_int) (not P2))))
% 6.73/7.07 (assert (forall ((P2 Bool)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.zero_n356916108424825756nteger P2)) tptp.one_one_Code_integer) (not P2))))
% 6.73/7.07 (assert (forall ((P2 Bool)) (= (@ tptp.zero_n1201886186963655149omplex (not P2)) (@ (@ tptp.minus_minus_complex tptp.one_one_complex) (@ tptp.zero_n1201886186963655149omplex P2)))))
% 6.73/7.07 (assert (forall ((P2 Bool)) (= (@ tptp.zero_n3304061248610475627l_real (not P2)) (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ tptp.zero_n3304061248610475627l_real P2)))))
% 6.73/7.07 (assert (forall ((P2 Bool)) (= (@ tptp.zero_n2052037380579107095ol_rat (not P2)) (@ (@ tptp.minus_minus_rat tptp.one_one_rat) (@ tptp.zero_n2052037380579107095ol_rat P2)))))
% 6.73/7.07 (assert (forall ((P2 Bool)) (= (@ tptp.zero_n2684676970156552555ol_int (not P2)) (@ (@ tptp.minus_minus_int tptp.one_one_int) (@ tptp.zero_n2684676970156552555ol_int P2)))))
% 6.73/7.07 (assert (forall ((P2 Bool)) (= (@ tptp.zero_n356916108424825756nteger (not P2)) (@ (@ tptp.minus_8373710615458151222nteger tptp.one_one_Code_integer) (@ tptp.zero_n356916108424825756nteger P2)))))
% 6.73/7.07 (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)))))))
% 6.73/7.07 (assert (forall ((K2 tptp.nat)) (= (@ (@ tptp.gbinomial_complex tptp.zero_zero_complex) (@ tptp.suc K2)) tptp.zero_zero_complex)))
% 6.73/7.07 (assert (forall ((K2 tptp.nat)) (= (@ (@ tptp.gbinomial_real tptp.zero_zero_real) (@ tptp.suc K2)) tptp.zero_zero_real)))
% 6.73/7.07 (assert (forall ((K2 tptp.nat)) (= (@ (@ tptp.gbinomial_rat tptp.zero_zero_rat) (@ tptp.suc K2)) tptp.zero_zero_rat)))
% 6.73/7.07 (assert (forall ((K2 tptp.nat)) (= (@ (@ tptp.gbinomial_nat tptp.zero_zero_nat) (@ tptp.suc K2)) tptp.zero_zero_nat)))
% 6.73/7.07 (assert (forall ((K2 tptp.nat)) (= (@ (@ tptp.gbinomial_int tptp.zero_zero_int) (@ tptp.suc K2)) tptp.zero_zero_int)))
% 6.73/7.07 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.gbinom8545251970709558553nteger A) tptp.zero_zero_nat) tptp.one_one_Code_integer)))
% 6.73/7.07 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.gbinomial_complex A) tptp.zero_zero_nat) tptp.one_one_complex)))
% 6.73/7.07 (assert (forall ((A tptp.real)) (= (@ (@ tptp.gbinomial_real A) tptp.zero_zero_nat) tptp.one_one_real)))
% 6.73/7.07 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.gbinomial_nat A) tptp.zero_zero_nat) tptp.one_one_nat)))
% 6.73/7.07 (assert (forall ((A tptp.int)) (= (@ (@ tptp.gbinomial_int A) tptp.zero_zero_nat) tptp.one_one_int)))
% 6.73/7.07 (assert (forall ((U tptp.nat)) (= (@ tptp.finite_card_nat (@ tptp.set_ord_atMost_nat U)) (@ tptp.suc U))))
% 6.73/7.07 (assert (forall ((L tptp.set_nat) (H tptp.set_nat) (H3 tptp.set_nat)) (= (@ (@ tptp.ord_le6893508408891458716et_nat (@ (@ tptp.set_or4548717258645045905et_nat L) H)) (@ tptp.set_or4236626031148496127et_nat H3)) (or (not (@ (@ tptp.ord_less_eq_set_nat L) H)) (@ (@ tptp.ord_less_eq_set_nat H) H3)))))
% 6.73/7.07 (assert (forall ((L tptp.rat) (H tptp.rat) (H3 tptp.rat)) (= (@ (@ tptp.ord_less_eq_set_rat (@ (@ tptp.set_or633870826150836451st_rat L) H)) (@ tptp.set_ord_atMost_rat H3)) (or (not (@ (@ tptp.ord_less_eq_rat L) H)) (@ (@ tptp.ord_less_eq_rat H) H3)))))
% 6.73/7.07 (assert (forall ((L tptp.num) (H tptp.num) (H3 tptp.num)) (= (@ (@ tptp.ord_less_eq_set_num (@ (@ tptp.set_or7049704709247886629st_num L) H)) (@ tptp.set_ord_atMost_num H3)) (or (not (@ (@ tptp.ord_less_eq_num L) H)) (@ (@ tptp.ord_less_eq_num H) H3)))))
% 6.73/7.07 (assert (forall ((L tptp.nat) (H tptp.nat) (H3 tptp.nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.set_or1269000886237332187st_nat L) H)) (@ tptp.set_ord_atMost_nat H3)) (or (not (@ (@ tptp.ord_less_eq_nat L) H)) (@ (@ tptp.ord_less_eq_nat H) H3)))))
% 6.73/7.07 (assert (forall ((L tptp.int) (H tptp.int) (H3 tptp.int)) (= (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.set_or1266510415728281911st_int L) H)) (@ tptp.set_ord_atMost_int H3)) (or (not (@ (@ tptp.ord_less_eq_int L) H)) (@ (@ tptp.ord_less_eq_int H) H3)))))
% 6.73/7.07 (assert (forall ((L tptp.real) (H tptp.real) (H3 tptp.real)) (= (@ (@ tptp.ord_less_eq_set_real (@ (@ tptp.set_or1222579329274155063t_real L) H)) (@ tptp.set_ord_atMost_real H3)) (or (not (@ (@ tptp.ord_less_eq_real L) H)) (@ (@ tptp.ord_less_eq_real H) H3)))))
% 6.73/7.07 (assert (forall ((G2 (-> tptp.nat tptp.rat)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.groups2906978787729119204at_rat G2))) (= (@ _let_2 (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.plus_plus_rat (@ _let_2 (@ tptp.set_ord_atMost_nat N))) (@ G2 _let_1)))))))
% 6.73/7.07 (assert (forall ((G2 (-> tptp.nat tptp.int)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.groups3539618377306564664at_int G2))) (= (@ _let_2 (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.plus_plus_int (@ _let_2 (@ tptp.set_ord_atMost_nat N))) (@ G2 _let_1)))))))
% 6.73/7.07 (assert (forall ((G2 (-> tptp.nat tptp.nat)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.groups3542108847815614940at_nat G2))) (= (@ _let_2 (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.plus_plus_nat (@ _let_2 (@ tptp.set_ord_atMost_nat N))) (@ G2 _let_1)))))))
% 6.73/7.07 (assert (forall ((G2 (-> tptp.nat tptp.real)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.groups6591440286371151544t_real G2))) (= (@ _let_2 (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.plus_plus_real (@ _let_2 (@ tptp.set_ord_atMost_nat N))) (@ G2 _let_1)))))))
% 6.73/7.07 (assert (forall ((G2 (-> tptp.nat tptp.real)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.groups129246275422532515t_real G2))) (= (@ _let_2 (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.times_times_real (@ _let_2 (@ tptp.set_ord_atMost_nat N))) (@ G2 _let_1)))))))
% 6.73/7.07 (assert (forall ((G2 (-> tptp.nat tptp.rat)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.groups73079841787564623at_rat G2))) (= (@ _let_2 (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.times_times_rat (@ _let_2 (@ tptp.set_ord_atMost_nat N))) (@ G2 _let_1)))))))
% 6.73/7.07 (assert (forall ((G2 (-> tptp.nat tptp.int)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.groups705719431365010083at_int G2))) (= (@ _let_2 (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.times_times_int (@ _let_2 (@ tptp.set_ord_atMost_nat N))) (@ G2 _let_1)))))))
% 6.73/7.07 (assert (forall ((G2 (-> tptp.nat tptp.nat)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.groups708209901874060359at_nat G2))) (= (@ _let_2 (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.times_times_nat (@ _let_2 (@ tptp.set_ord_atMost_nat N))) (@ G2 _let_1)))))))
% 6.73/7.07 (assert (= (@ tptp.set_ord_atMost_nat tptp.zero_zero_nat) (@ (@ tptp.insert_nat tptp.zero_zero_nat) tptp.bot_bot_set_nat)))
% 6.73/7.07 (assert (forall ((I2 tptp.nat) (Xs2 tptp.list_VEBT_VEBT) (J2 tptp.nat)) (let ((_let_1 (@ tptp.nth_VEBT_VEBT Xs2))) (let ((_let_2 (@ tptp.size_s6755466524823107622T_VEBT Xs2))) (=> (@ (@ tptp.ord_less_nat I2) _let_2) (=> (@ (@ tptp.ord_less_nat J2) _let_2) (= (@ tptp.distinct_VEBT_VEBT (@ (@ (@ tptp.list_u1324408373059187874T_VEBT (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs2) I2) (@ _let_1 J2))) J2) (@ _let_1 I2))) (@ tptp.distinct_VEBT_VEBT Xs2))))))))
% 6.73/7.07 (assert (forall ((I2 tptp.nat) (Xs2 tptp.list_o) (J2 tptp.nat)) (let ((_let_1 (@ tptp.nth_o Xs2))) (let ((_let_2 (@ tptp.size_size_list_o Xs2))) (=> (@ (@ tptp.ord_less_nat I2) _let_2) (=> (@ (@ tptp.ord_less_nat J2) _let_2) (= (@ tptp.distinct_o (@ (@ (@ tptp.list_update_o (@ (@ (@ tptp.list_update_o Xs2) I2) (@ _let_1 J2))) J2) (@ _let_1 I2))) (@ tptp.distinct_o Xs2))))))))
% 6.73/7.07 (assert (forall ((I2 tptp.nat) (Xs2 tptp.list_nat) (J2 tptp.nat)) (let ((_let_1 (@ tptp.nth_nat Xs2))) (let ((_let_2 (@ tptp.size_size_list_nat Xs2))) (=> (@ (@ tptp.ord_less_nat I2) _let_2) (=> (@ (@ tptp.ord_less_nat J2) _let_2) (= (@ tptp.distinct_nat (@ (@ (@ tptp.list_update_nat (@ (@ (@ tptp.list_update_nat Xs2) I2) (@ _let_1 J2))) J2) (@ _let_1 I2))) (@ tptp.distinct_nat Xs2))))))))
% 6.73/7.07 (assert (forall ((I2 tptp.nat) (Xs2 tptp.list_int) (J2 tptp.nat)) (let ((_let_1 (@ tptp.nth_int Xs2))) (let ((_let_2 (@ tptp.size_size_list_int Xs2))) (=> (@ (@ tptp.ord_less_nat I2) _let_2) (=> (@ (@ tptp.ord_less_nat J2) _let_2) (= (@ tptp.distinct_int (@ (@ (@ tptp.list_update_int (@ (@ (@ tptp.list_update_int Xs2) I2) (@ _let_1 J2))) J2) (@ _let_1 I2))) (@ tptp.distinct_int Xs2))))))))
% 6.73/7.07 (assert (forall ((A4 tptp.set_real) (F2 (-> tptp.real tptp.real)) (P2 (-> tptp.real Bool))) (=> (@ tptp.finite_finite_real A4) (= (@ (@ tptp.groups8097168146408367636l_real (lambda ((X4 tptp.real)) (@ (@ tptp.times_times_real (@ F2 X4)) (@ tptp.zero_n3304061248610475627l_real (@ P2 X4))))) A4) (@ (@ tptp.groups8097168146408367636l_real F2) (@ (@ tptp.inf_inf_set_real A4) (@ tptp.collect_real P2)))))))
% 6.73/7.07 (assert (forall ((A4 tptp.set_int) (F2 (-> tptp.int tptp.real)) (P2 (-> tptp.int Bool))) (=> (@ tptp.finite_finite_int A4) (= (@ (@ tptp.groups8778361861064173332t_real (lambda ((X4 tptp.int)) (@ (@ tptp.times_times_real (@ F2 X4)) (@ tptp.zero_n3304061248610475627l_real (@ P2 X4))))) A4) (@ (@ tptp.groups8778361861064173332t_real F2) (@ (@ tptp.inf_inf_set_int A4) (@ tptp.collect_int P2)))))))
% 6.73/7.07 (assert (forall ((A4 tptp.set_complex) (F2 (-> tptp.complex tptp.real)) (P2 (-> tptp.complex Bool))) (=> (@ tptp.finite3207457112153483333omplex A4) (= (@ (@ tptp.groups5808333547571424918x_real (lambda ((X4 tptp.complex)) (@ (@ tptp.times_times_real (@ F2 X4)) (@ tptp.zero_n3304061248610475627l_real (@ P2 X4))))) A4) (@ (@ tptp.groups5808333547571424918x_real F2) (@ (@ tptp.inf_inf_set_complex A4) (@ tptp.collect_complex P2)))))))
% 6.73/7.07 (assert (forall ((A4 tptp.set_real) (F2 (-> tptp.real tptp.rat)) (P2 (-> tptp.real Bool))) (=> (@ tptp.finite_finite_real A4) (= (@ (@ tptp.groups1300246762558778688al_rat (lambda ((X4 tptp.real)) (@ (@ tptp.times_times_rat (@ F2 X4)) (@ tptp.zero_n2052037380579107095ol_rat (@ P2 X4))))) A4) (@ (@ tptp.groups1300246762558778688al_rat F2) (@ (@ tptp.inf_inf_set_real A4) (@ tptp.collect_real P2)))))))
% 6.73/7.07 (assert (forall ((A4 tptp.set_int) (F2 (-> tptp.int tptp.rat)) (P2 (-> tptp.int Bool))) (=> (@ tptp.finite_finite_int A4) (= (@ (@ tptp.groups3906332499630173760nt_rat (lambda ((X4 tptp.int)) (@ (@ tptp.times_times_rat (@ F2 X4)) (@ tptp.zero_n2052037380579107095ol_rat (@ P2 X4))))) A4) (@ (@ tptp.groups3906332499630173760nt_rat F2) (@ (@ tptp.inf_inf_set_int A4) (@ tptp.collect_int P2)))))))
% 6.73/7.07 (assert (forall ((A4 tptp.set_complex) (F2 (-> tptp.complex tptp.rat)) (P2 (-> tptp.complex Bool))) (=> (@ tptp.finite3207457112153483333omplex A4) (= (@ (@ tptp.groups5058264527183730370ex_rat (lambda ((X4 tptp.complex)) (@ (@ tptp.times_times_rat (@ F2 X4)) (@ tptp.zero_n2052037380579107095ol_rat (@ P2 X4))))) A4) (@ (@ tptp.groups5058264527183730370ex_rat F2) (@ (@ tptp.inf_inf_set_complex A4) (@ tptp.collect_complex P2)))))))
% 6.73/7.07 (assert (forall ((A4 tptp.set_nat) (F2 (-> tptp.nat tptp.rat)) (P2 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat A4) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((X4 tptp.nat)) (@ (@ tptp.times_times_rat (@ F2 X4)) (@ tptp.zero_n2052037380579107095ol_rat (@ P2 X4))))) A4) (@ (@ tptp.groups2906978787729119204at_rat F2) (@ (@ tptp.inf_inf_set_nat A4) (@ tptp.collect_nat P2)))))))
% 6.73/7.07 (assert (forall ((A4 tptp.set_real) (F2 (-> tptp.real tptp.nat)) (P2 (-> tptp.real Bool))) (=> (@ tptp.finite_finite_real A4) (= (@ (@ tptp.groups1935376822645274424al_nat (lambda ((X4 tptp.real)) (@ (@ tptp.times_times_nat (@ F2 X4)) (@ tptp.zero_n2687167440665602831ol_nat (@ P2 X4))))) A4) (@ (@ tptp.groups1935376822645274424al_nat F2) (@ (@ tptp.inf_inf_set_real A4) (@ tptp.collect_real P2)))))))
% 6.73/7.07 (assert (forall ((A4 tptp.set_int) (F2 (-> tptp.int tptp.nat)) (P2 (-> tptp.int Bool))) (=> (@ tptp.finite_finite_int A4) (= (@ (@ tptp.groups4541462559716669496nt_nat (lambda ((X4 tptp.int)) (@ (@ tptp.times_times_nat (@ F2 X4)) (@ tptp.zero_n2687167440665602831ol_nat (@ P2 X4))))) A4) (@ (@ tptp.groups4541462559716669496nt_nat F2) (@ (@ tptp.inf_inf_set_int A4) (@ tptp.collect_int P2)))))))
% 6.73/7.07 (assert (forall ((A4 tptp.set_complex) (F2 (-> tptp.complex tptp.nat)) (P2 (-> tptp.complex Bool))) (=> (@ tptp.finite3207457112153483333omplex A4) (= (@ (@ tptp.groups5693394587270226106ex_nat (lambda ((X4 tptp.complex)) (@ (@ tptp.times_times_nat (@ F2 X4)) (@ tptp.zero_n2687167440665602831ol_nat (@ P2 X4))))) A4) (@ (@ tptp.groups5693394587270226106ex_nat F2) (@ (@ tptp.inf_inf_set_complex A4) (@ tptp.collect_complex P2)))))))
% 6.73/7.07 (assert (forall ((A4 tptp.set_real) (P2 (-> tptp.real Bool)) (F2 (-> tptp.real tptp.real))) (=> (@ tptp.finite_finite_real A4) (= (@ (@ tptp.groups8097168146408367636l_real (lambda ((X4 tptp.real)) (@ (@ tptp.times_times_real (@ tptp.zero_n3304061248610475627l_real (@ P2 X4))) (@ F2 X4)))) A4) (@ (@ tptp.groups8097168146408367636l_real F2) (@ (@ tptp.inf_inf_set_real A4) (@ tptp.collect_real P2)))))))
% 6.73/7.07 (assert (forall ((A4 tptp.set_int) (P2 (-> tptp.int Bool)) (F2 (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int A4) (= (@ (@ tptp.groups8778361861064173332t_real (lambda ((X4 tptp.int)) (@ (@ tptp.times_times_real (@ tptp.zero_n3304061248610475627l_real (@ P2 X4))) (@ F2 X4)))) A4) (@ (@ tptp.groups8778361861064173332t_real F2) (@ (@ tptp.inf_inf_set_int A4) (@ tptp.collect_int P2)))))))
% 6.73/7.07 (assert (forall ((A4 tptp.set_complex) (P2 (-> tptp.complex Bool)) (F2 (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex A4) (= (@ (@ tptp.groups5808333547571424918x_real (lambda ((X4 tptp.complex)) (@ (@ tptp.times_times_real (@ tptp.zero_n3304061248610475627l_real (@ P2 X4))) (@ F2 X4)))) A4) (@ (@ tptp.groups5808333547571424918x_real F2) (@ (@ tptp.inf_inf_set_complex A4) (@ tptp.collect_complex P2)))))))
% 6.73/7.07 (assert (forall ((A4 tptp.set_real) (P2 (-> tptp.real Bool)) (F2 (-> tptp.real tptp.rat))) (=> (@ tptp.finite_finite_real A4) (= (@ (@ tptp.groups1300246762558778688al_rat (lambda ((X4 tptp.real)) (@ (@ tptp.times_times_rat (@ tptp.zero_n2052037380579107095ol_rat (@ P2 X4))) (@ F2 X4)))) A4) (@ (@ tptp.groups1300246762558778688al_rat F2) (@ (@ tptp.inf_inf_set_real A4) (@ tptp.collect_real P2)))))))
% 6.73/7.07 (assert (forall ((A4 tptp.set_int) (P2 (-> tptp.int Bool)) (F2 (-> tptp.int tptp.rat))) (=> (@ tptp.finite_finite_int A4) (= (@ (@ tptp.groups3906332499630173760nt_rat (lambda ((X4 tptp.int)) (@ (@ tptp.times_times_rat (@ tptp.zero_n2052037380579107095ol_rat (@ P2 X4))) (@ F2 X4)))) A4) (@ (@ tptp.groups3906332499630173760nt_rat F2) (@ (@ tptp.inf_inf_set_int A4) (@ tptp.collect_int P2)))))))
% 6.73/7.07 (assert (forall ((A4 tptp.set_complex) (P2 (-> tptp.complex Bool)) (F2 (-> tptp.complex tptp.rat))) (=> (@ tptp.finite3207457112153483333omplex A4) (= (@ (@ tptp.groups5058264527183730370ex_rat (lambda ((X4 tptp.complex)) (@ (@ tptp.times_times_rat (@ tptp.zero_n2052037380579107095ol_rat (@ P2 X4))) (@ F2 X4)))) A4) (@ (@ tptp.groups5058264527183730370ex_rat F2) (@ (@ tptp.inf_inf_set_complex A4) (@ tptp.collect_complex P2)))))))
% 6.73/7.07 (assert (forall ((A4 tptp.set_nat) (P2 (-> tptp.nat Bool)) (F2 (-> tptp.nat tptp.rat))) (=> (@ tptp.finite_finite_nat A4) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((X4 tptp.nat)) (@ (@ tptp.times_times_rat (@ tptp.zero_n2052037380579107095ol_rat (@ P2 X4))) (@ F2 X4)))) A4) (@ (@ tptp.groups2906978787729119204at_rat F2) (@ (@ tptp.inf_inf_set_nat A4) (@ tptp.collect_nat P2)))))))
% 6.73/7.07 (assert (forall ((A4 tptp.set_real) (P2 (-> tptp.real Bool)) (F2 (-> tptp.real tptp.nat))) (=> (@ tptp.finite_finite_real A4) (= (@ (@ tptp.groups1935376822645274424al_nat (lambda ((X4 tptp.real)) (@ (@ tptp.times_times_nat (@ tptp.zero_n2687167440665602831ol_nat (@ P2 X4))) (@ F2 X4)))) A4) (@ (@ tptp.groups1935376822645274424al_nat F2) (@ (@ tptp.inf_inf_set_real A4) (@ tptp.collect_real P2)))))))
% 6.73/7.07 (assert (forall ((A4 tptp.set_int) (P2 (-> tptp.int Bool)) (F2 (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int A4) (= (@ (@ tptp.groups4541462559716669496nt_nat (lambda ((X4 tptp.int)) (@ (@ tptp.times_times_nat (@ tptp.zero_n2687167440665602831ol_nat (@ P2 X4))) (@ F2 X4)))) A4) (@ (@ tptp.groups4541462559716669496nt_nat F2) (@ (@ tptp.inf_inf_set_int A4) (@ tptp.collect_int P2)))))))
% 6.73/7.07 (assert (forall ((A4 tptp.set_complex) (P2 (-> tptp.complex Bool)) (F2 (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex A4) (= (@ (@ tptp.groups5693394587270226106ex_nat (lambda ((X4 tptp.complex)) (@ (@ tptp.times_times_nat (@ tptp.zero_n2687167440665602831ol_nat (@ P2 X4))) (@ F2 X4)))) A4) (@ (@ tptp.groups5693394587270226106ex_nat F2) (@ (@ tptp.inf_inf_set_complex A4) (@ tptp.collect_complex P2)))))))
% 6.73/7.07 (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)))
% 6.73/7.07 (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)))
% 6.73/7.07 (assert (forall ((B Bool)) (= (@ (@ tptp.divide6298287555418463151nteger (@ tptp.zero_n356916108424825756nteger B)) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) tptp.zero_z3403309356797280102nteger)))
% 6.73/7.07 (assert (forall ((A4 tptp.set_complex) (N tptp.nat)) (=> (@ tptp.finite3207457112153483333omplex A4) (@ tptp.finite8712137658972009173omplex (@ tptp.collect_list_complex (lambda ((Xs tptp.list_complex)) (and (= (@ tptp.size_s3451745648224563538omplex Xs) N) (@ tptp.distinct_complex Xs) (@ (@ tptp.ord_le211207098394363844omplex (@ tptp.set_complex2 Xs)) A4))))))))
% 6.73/7.07 (assert (forall ((A4 tptp.set_VEBT_VEBT) (N tptp.nat)) (=> (@ tptp.finite5795047828879050333T_VEBT A4) (@ tptp.finite3004134309566078307T_VEBT (@ tptp.collec5608196760682091941T_VEBT (lambda ((Xs tptp.list_VEBT_VEBT)) (and (= (@ tptp.size_s6755466524823107622T_VEBT Xs) N) (@ tptp.distinct_VEBT_VEBT Xs) (@ (@ tptp.ord_le4337996190870823476T_VEBT (@ tptp.set_VEBT_VEBT2 Xs)) A4))))))))
% 6.73/7.07 (assert (forall ((A4 tptp.set_o) (N tptp.nat)) (=> (@ tptp.finite_finite_o A4) (@ tptp.finite_finite_list_o (@ tptp.collect_list_o (lambda ((Xs tptp.list_o)) (and (= (@ tptp.size_size_list_o Xs) N) (@ tptp.distinct_o Xs) (@ (@ tptp.ord_less_eq_set_o (@ tptp.set_o2 Xs)) A4))))))))
% 6.73/7.07 (assert (forall ((A4 tptp.set_int) (N tptp.nat)) (=> (@ tptp.finite_finite_int A4) (@ tptp.finite3922522038869484883st_int (@ tptp.collect_list_int (lambda ((Xs tptp.list_int)) (and (= (@ tptp.size_size_list_int Xs) N) (@ tptp.distinct_int Xs) (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_int2 Xs)) A4))))))))
% 6.73/7.07 (assert (forall ((A4 tptp.set_nat) (N tptp.nat)) (=> (@ tptp.finite_finite_nat A4) (@ tptp.finite8100373058378681591st_nat (@ tptp.collect_list_nat (lambda ((Xs tptp.list_nat)) (and (= (@ tptp.size_size_list_nat Xs) N) (@ tptp.distinct_nat Xs) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_nat2 Xs)) A4))))))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.modulo8411746178871703098atural tptp.one_one_Code_natural) (@ (@ tptp.power_7079662738309270450atural (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one))) N)) (@ tptp.zero_n8403883297036319079atural (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (assert (forall ((P Bool) (Q2 Bool)) (= (= (@ tptp.zero_n2687167440665602831ol_nat P) (@ tptp.zero_n2687167440665602831ol_nat Q2)) (= P Q2))))
% 6.73/7.07 (assert (forall ((P Bool) (Q2 Bool)) (= (= (@ tptp.zero_n2684676970156552555ol_int P) (@ tptp.zero_n2684676970156552555ol_int Q2)) (= P Q2))))
% 6.73/7.07 (assert (forall ((P Bool) (Q2 Bool)) (= (= (@ tptp.zero_n356916108424825756nteger P) (@ tptp.zero_n356916108424825756nteger Q2)) (= P Q2))))
% 6.73/7.07 (assert (forall ((P2 Bool) (Q Bool)) (= (@ tptp.zero_n3304061248610475627l_real (and P2 Q)) (@ (@ tptp.times_times_real (@ tptp.zero_n3304061248610475627l_real P2)) (@ tptp.zero_n3304061248610475627l_real Q)))))
% 6.73/7.07 (assert (forall ((P2 Bool) (Q Bool)) (= (@ tptp.zero_n2052037380579107095ol_rat (and P2 Q)) (@ (@ tptp.times_times_rat (@ tptp.zero_n2052037380579107095ol_rat P2)) (@ tptp.zero_n2052037380579107095ol_rat Q)))))
% 6.73/7.07 (assert (forall ((P2 Bool) (Q Bool)) (= (@ tptp.zero_n2687167440665602831ol_nat (and P2 Q)) (@ (@ tptp.times_times_nat (@ tptp.zero_n2687167440665602831ol_nat P2)) (@ tptp.zero_n2687167440665602831ol_nat Q)))))
% 6.73/7.07 (assert (forall ((P2 Bool) (Q Bool)) (= (@ tptp.zero_n2684676970156552555ol_int (and P2 Q)) (@ (@ tptp.times_times_int (@ tptp.zero_n2684676970156552555ol_int P2)) (@ tptp.zero_n2684676970156552555ol_int Q)))))
% 6.73/7.07 (assert (forall ((P2 Bool) (Q Bool)) (= (@ tptp.zero_n356916108424825756nteger (and P2 Q)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.zero_n356916108424825756nteger P2)) (@ tptp.zero_n356916108424825756nteger Q)))))
% 6.73/7.07 (assert (forall ((H tptp.int)) (not (= tptp.bot_bot_set_int (@ tptp.set_ord_atMost_int H)))))
% 6.73/7.07 (assert (forall ((H tptp.real)) (not (= tptp.bot_bot_set_real (@ tptp.set_ord_atMost_real H)))))
% 6.73/7.07 (assert (forall ((H tptp.nat)) (not (= tptp.bot_bot_set_nat (@ tptp.set_ord_atMost_nat H)))))
% 6.73/7.07 (assert (forall ((A tptp.int)) (not (@ tptp.finite_finite_int (@ tptp.set_ord_atMost_int A)))))
% 6.73/7.07 (assert (forall ((H3 tptp.int) (L tptp.int) (H tptp.int)) (not (= (@ tptp.set_ord_atMost_int H3) (@ (@ tptp.set_or1266510415728281911st_int L) H)))))
% 6.73/7.07 (assert (forall ((H3 tptp.real) (L tptp.real) (H tptp.real)) (not (= (@ tptp.set_ord_atMost_real H3) (@ (@ tptp.set_or1222579329274155063t_real L) H)))))
% 6.73/7.07 (assert (= tptp.set_ord_atMost_real (lambda ((U2 tptp.real)) (@ tptp.collect_real (lambda ((X4 tptp.real)) (@ (@ tptp.ord_less_eq_real X4) U2))))))
% 6.73/7.07 (assert (= tptp.set_or4236626031148496127et_nat (lambda ((U2 tptp.set_nat)) (@ tptp.collect_set_nat (lambda ((X4 tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat X4) U2))))))
% 6.73/7.07 (assert (= tptp.set_ord_atMost_rat (lambda ((U2 tptp.rat)) (@ tptp.collect_rat (lambda ((X4 tptp.rat)) (@ (@ tptp.ord_less_eq_rat X4) U2))))))
% 6.73/7.07 (assert (= tptp.set_ord_atMost_num (lambda ((U2 tptp.num)) (@ tptp.collect_num (lambda ((X4 tptp.num)) (@ (@ tptp.ord_less_eq_num X4) U2))))))
% 6.73/7.07 (assert (= tptp.set_ord_atMost_int (lambda ((U2 tptp.int)) (@ tptp.collect_int (lambda ((X4 tptp.int)) (@ (@ tptp.ord_less_eq_int X4) U2))))))
% 6.73/7.07 (assert (= tptp.set_ord_atMost_nat (lambda ((U2 tptp.nat)) (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (@ (@ tptp.ord_less_eq_nat X4) U2))))))
% 6.73/7.07 (assert (forall ((P2 Bool)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.zero_n3304061248610475627l_real P2))))
% 6.73/7.07 (assert (forall ((P2 Bool)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.zero_n2052037380579107095ol_rat P2))))
% 6.73/7.07 (assert (forall ((P2 Bool)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ tptp.zero_n2687167440665602831ol_nat P2))))
% 6.73/7.07 (assert (forall ((P2 Bool)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.zero_n2684676970156552555ol_int P2))))
% 6.73/7.07 (assert (forall ((P2 Bool)) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ tptp.zero_n356916108424825756nteger P2))))
% 6.73/7.07 (assert (forall ((P2 Bool)) (@ (@ tptp.ord_less_eq_real (@ tptp.zero_n3304061248610475627l_real P2)) tptp.one_one_real)))
% 6.73/7.07 (assert (forall ((P2 Bool)) (@ (@ tptp.ord_less_eq_rat (@ tptp.zero_n2052037380579107095ol_rat P2)) tptp.one_one_rat)))
% 6.73/7.07 (assert (forall ((P2 Bool)) (@ (@ tptp.ord_less_eq_nat (@ tptp.zero_n2687167440665602831ol_nat P2)) tptp.one_one_nat)))
% 6.73/7.07 (assert (forall ((P2 Bool)) (@ (@ tptp.ord_less_eq_int (@ tptp.zero_n2684676970156552555ol_int P2)) tptp.one_one_int)))
% 6.73/7.07 (assert (forall ((P2 Bool)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.zero_n356916108424825756nteger P2)) tptp.one_one_Code_integer)))
% 6.73/7.07 (assert (= tptp.zero_n1201886186963655149omplex (lambda ((P5 Bool)) (@ (@ (@ tptp.if_complex P5) tptp.one_one_complex) tptp.zero_zero_complex))))
% 6.73/7.07 (assert (= tptp.zero_n3304061248610475627l_real (lambda ((P5 Bool)) (@ (@ (@ tptp.if_real P5) tptp.one_one_real) tptp.zero_zero_real))))
% 6.73/7.07 (assert (= tptp.zero_n2052037380579107095ol_rat (lambda ((P5 Bool)) (@ (@ (@ tptp.if_rat P5) tptp.one_one_rat) tptp.zero_zero_rat))))
% 6.73/7.07 (assert (= tptp.zero_n2687167440665602831ol_nat (lambda ((P5 Bool)) (@ (@ (@ tptp.if_nat P5) tptp.one_one_nat) tptp.zero_zero_nat))))
% 6.73/7.07 (assert (= tptp.zero_n2684676970156552555ol_int (lambda ((P5 Bool)) (@ (@ (@ tptp.if_int P5) tptp.one_one_int) tptp.zero_zero_int))))
% 6.73/7.07 (assert (= tptp.zero_n356916108424825756nteger (lambda ((P5 Bool)) (@ (@ (@ tptp.if_Code_integer P5) tptp.one_one_Code_integer) tptp.zero_z3403309356797280102nteger))))
% 6.73/7.07 (assert (forall ((P2 (-> tptp.complex Bool)) (P Bool)) (= (@ P2 (@ tptp.zero_n1201886186963655149omplex P)) (and (=> P (@ P2 tptp.one_one_complex)) (=> (not P) (@ P2 tptp.zero_zero_complex))))))
% 6.73/7.07 (assert (forall ((P2 (-> tptp.real Bool)) (P Bool)) (= (@ P2 (@ tptp.zero_n3304061248610475627l_real P)) (and (=> P (@ P2 tptp.one_one_real)) (=> (not P) (@ P2 tptp.zero_zero_real))))))
% 6.73/7.07 (assert (forall ((P2 (-> tptp.rat Bool)) (P Bool)) (= (@ P2 (@ tptp.zero_n2052037380579107095ol_rat P)) (and (=> P (@ P2 tptp.one_one_rat)) (=> (not P) (@ P2 tptp.zero_zero_rat))))))
% 6.73/7.07 (assert (forall ((P2 (-> tptp.nat Bool)) (P Bool)) (= (@ P2 (@ tptp.zero_n2687167440665602831ol_nat P)) (and (=> P (@ P2 tptp.one_one_nat)) (=> (not P) (@ P2 tptp.zero_zero_nat))))))
% 6.73/7.07 (assert (forall ((P2 (-> tptp.int Bool)) (P Bool)) (= (@ P2 (@ tptp.zero_n2684676970156552555ol_int P)) (and (=> P (@ P2 tptp.one_one_int)) (=> (not P) (@ P2 tptp.zero_zero_int))))))
% 6.73/7.07 (assert (forall ((P2 (-> tptp.code_integer Bool)) (P Bool)) (= (@ P2 (@ tptp.zero_n356916108424825756nteger P)) (and (=> P (@ P2 tptp.one_one_Code_integer)) (=> (not P) (@ P2 tptp.zero_z3403309356797280102nteger))))))
% 6.73/7.07 (assert (forall ((P2 (-> tptp.complex Bool)) (P Bool)) (= (@ P2 (@ tptp.zero_n1201886186963655149omplex P)) (not (or (and P (not (@ P2 tptp.one_one_complex))) (and (not P) (not (@ P2 tptp.zero_zero_complex))))))))
% 6.73/7.07 (assert (forall ((P2 (-> tptp.real Bool)) (P Bool)) (= (@ P2 (@ tptp.zero_n3304061248610475627l_real P)) (not (or (and P (not (@ P2 tptp.one_one_real))) (and (not P) (not (@ P2 tptp.zero_zero_real))))))))
% 6.73/7.07 (assert (forall ((P2 (-> tptp.rat Bool)) (P Bool)) (= (@ P2 (@ tptp.zero_n2052037380579107095ol_rat P)) (not (or (and P (not (@ P2 tptp.one_one_rat))) (and (not P) (not (@ P2 tptp.zero_zero_rat))))))))
% 6.73/7.07 (assert (forall ((P2 (-> tptp.nat Bool)) (P Bool)) (= (@ P2 (@ tptp.zero_n2687167440665602831ol_nat P)) (not (or (and P (not (@ P2 tptp.one_one_nat))) (and (not P) (not (@ P2 tptp.zero_zero_nat))))))))
% 6.73/7.07 (assert (forall ((P2 (-> tptp.int Bool)) (P Bool)) (= (@ P2 (@ tptp.zero_n2684676970156552555ol_int P)) (not (or (and P (not (@ P2 tptp.one_one_int))) (and (not P) (not (@ P2 tptp.zero_zero_int))))))))
% 6.73/7.07 (assert (forall ((P2 (-> tptp.code_integer Bool)) (P Bool)) (= (@ P2 (@ tptp.zero_n356916108424825756nteger P)) (not (or (and P (not (@ P2 tptp.one_one_Code_integer))) (and (not P) (not (@ P2 tptp.zero_z3403309356797280102nteger))))))))
% 6.73/7.07 (assert (= tptp.set_ord_atMost_nat (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat)))
% 6.73/7.07 (assert (forall ((K2 tptp.nat)) (= (@ tptp.set_ord_lessThan_nat (@ tptp.suc K2)) (@ tptp.set_ord_atMost_nat K2))))
% 6.73/7.07 (assert (forall ((K2 tptp.nat)) (let ((_let_1 (@ tptp.suc K2))) (= (@ tptp.set_ord_atMost_nat _let_1) (@ (@ tptp.insert_nat _let_1) (@ tptp.set_ord_atMost_nat K2))))))
% 6.73/7.07 (assert (forall ((H tptp.int) (L3 tptp.int) (H3 tptp.int)) (not (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_ord_atMost_int H)) (@ (@ tptp.set_or1266510415728281911st_int L3) H3)))))
% 6.73/7.07 (assert (forall ((H tptp.real) (L3 tptp.real) (H3 tptp.real)) (not (@ (@ tptp.ord_less_eq_set_real (@ tptp.set_ord_atMost_real H)) (@ (@ tptp.set_or1222579329274155063t_real L3) H3)))))
% 6.73/7.07 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (I2 tptp.nat) (J2 tptp.nat)) (let ((_let_1 (@ tptp.nth_VEBT_VEBT Xs2))) (let ((_let_2 (@ tptp.size_s6755466524823107622T_VEBT Xs2))) (=> (@ tptp.distinct_VEBT_VEBT Xs2) (=> (@ (@ tptp.ord_less_nat I2) _let_2) (=> (@ (@ tptp.ord_less_nat J2) _let_2) (= (= (@ _let_1 I2) (@ _let_1 J2)) (= I2 J2)))))))))
% 6.73/7.07 (assert (forall ((Xs2 tptp.list_o) (I2 tptp.nat) (J2 tptp.nat)) (let ((_let_1 (@ tptp.nth_o Xs2))) (let ((_let_2 (@ tptp.size_size_list_o Xs2))) (=> (@ tptp.distinct_o Xs2) (=> (@ (@ tptp.ord_less_nat I2) _let_2) (=> (@ (@ tptp.ord_less_nat J2) _let_2) (= (= (@ _let_1 I2) (@ _let_1 J2)) (= I2 J2)))))))))
% 6.73/7.07 (assert (forall ((Xs2 tptp.list_nat) (I2 tptp.nat) (J2 tptp.nat)) (let ((_let_1 (@ tptp.nth_nat Xs2))) (let ((_let_2 (@ tptp.size_size_list_nat Xs2))) (=> (@ tptp.distinct_nat Xs2) (=> (@ (@ tptp.ord_less_nat I2) _let_2) (=> (@ (@ tptp.ord_less_nat J2) _let_2) (= (= (@ _let_1 I2) (@ _let_1 J2)) (= I2 J2)))))))))
% 6.73/7.07 (assert (forall ((Xs2 tptp.list_int) (I2 tptp.nat) (J2 tptp.nat)) (let ((_let_1 (@ tptp.nth_int Xs2))) (let ((_let_2 (@ tptp.size_size_list_int Xs2))) (=> (@ tptp.distinct_int Xs2) (=> (@ (@ tptp.ord_less_nat I2) _let_2) (=> (@ (@ tptp.ord_less_nat J2) _let_2) (= (= (@ _let_1 I2) (@ _let_1 J2)) (= I2 J2)))))))))
% 6.73/7.07 (assert (= tptp.distinct_VEBT_VEBT (lambda ((Xs tptp.list_VEBT_VEBT)) (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (forall ((J tptp.nat)) (let ((_let_1 (@ tptp.nth_VEBT_VEBT Xs))) (=> (@ (@ tptp.ord_less_nat J) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (=> (not (= I J)) (not (= (@ _let_1 I) (@ _let_1 J))))))))))))
% 6.73/7.07 (assert (= tptp.distinct_o (lambda ((Xs tptp.list_o)) (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_o Xs)) (forall ((J tptp.nat)) (let ((_let_1 (@ tptp.nth_o Xs))) (=> (@ (@ tptp.ord_less_nat J) (@ tptp.size_size_list_o Xs)) (=> (not (= I J)) (not (= (@ _let_1 I) (@ _let_1 J))))))))))))
% 6.73/7.07 (assert (= tptp.distinct_nat (lambda ((Xs tptp.list_nat)) (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_nat Xs)) (forall ((J tptp.nat)) (let ((_let_1 (@ tptp.nth_nat Xs))) (=> (@ (@ tptp.ord_less_nat J) (@ tptp.size_size_list_nat Xs)) (=> (not (= I J)) (not (= (@ _let_1 I) (@ _let_1 J))))))))))))
% 6.73/7.07 (assert (= tptp.distinct_int (lambda ((Xs tptp.list_int)) (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_int Xs)) (forall ((J tptp.nat)) (let ((_let_1 (@ tptp.nth_int Xs))) (=> (@ (@ tptp.ord_less_nat J) (@ tptp.size_size_list_int Xs)) (=> (not (= I J)) (not (= (@ _let_1 I) (@ _let_1 J))))))))))))
% 6.73/7.07 (assert (forall ((Xs2 tptp.list_complex)) (=> (= (@ tptp.finite_card_complex (@ tptp.set_complex2 Xs2)) (@ tptp.size_s3451745648224563538omplex Xs2)) (@ tptp.distinct_complex Xs2))))
% 6.73/7.07 (assert (forall ((Xs2 tptp.list_list_nat)) (=> (= (@ tptp.finite_card_list_nat (@ tptp.set_list_nat2 Xs2)) (@ tptp.size_s3023201423986296836st_nat Xs2)) (@ tptp.distinct_list_nat Xs2))))
% 6.73/7.07 (assert (forall ((Xs2 tptp.list_set_nat)) (=> (= (@ tptp.finite_card_set_nat (@ tptp.set_set_nat2 Xs2)) (@ tptp.size_s3254054031482475050et_nat Xs2)) (@ tptp.distinct_set_nat Xs2))))
% 6.73/7.07 (assert (forall ((Xs2 tptp.list_VEBT_VEBT)) (=> (= (@ tptp.finite7802652506058667612T_VEBT (@ tptp.set_VEBT_VEBT2 Xs2)) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (@ tptp.distinct_VEBT_VEBT Xs2))))
% 6.73/7.07 (assert (forall ((Xs2 tptp.list_o)) (=> (= (@ tptp.finite_card_o (@ tptp.set_o2 Xs2)) (@ tptp.size_size_list_o Xs2)) (@ tptp.distinct_o Xs2))))
% 6.73/7.07 (assert (forall ((Xs2 tptp.list_nat)) (=> (= (@ tptp.finite_card_nat (@ tptp.set_nat2 Xs2)) (@ tptp.size_size_list_nat Xs2)) (@ tptp.distinct_nat Xs2))))
% 6.73/7.07 (assert (forall ((Xs2 tptp.list_int)) (=> (= (@ tptp.finite_card_int (@ tptp.set_int2 Xs2)) (@ tptp.size_size_list_int Xs2)) (@ tptp.distinct_int Xs2))))
% 6.73/7.07 (assert (forall ((Xs2 tptp.list_complex)) (=> (@ tptp.distinct_complex Xs2) (= (@ tptp.finite_card_complex (@ tptp.set_complex2 Xs2)) (@ tptp.size_s3451745648224563538omplex Xs2)))))
% 6.73/7.07 (assert (forall ((Xs2 tptp.list_list_nat)) (=> (@ tptp.distinct_list_nat Xs2) (= (@ tptp.finite_card_list_nat (@ tptp.set_list_nat2 Xs2)) (@ tptp.size_s3023201423986296836st_nat Xs2)))))
% 6.73/7.07 (assert (forall ((Xs2 tptp.list_set_nat)) (=> (@ tptp.distinct_set_nat Xs2) (= (@ tptp.finite_card_set_nat (@ tptp.set_set_nat2 Xs2)) (@ tptp.size_s3254054031482475050et_nat Xs2)))))
% 6.73/7.07 (assert (forall ((Xs2 tptp.list_VEBT_VEBT)) (=> (@ tptp.distinct_VEBT_VEBT Xs2) (= (@ tptp.finite7802652506058667612T_VEBT (@ tptp.set_VEBT_VEBT2 Xs2)) (@ tptp.size_s6755466524823107622T_VEBT Xs2)))))
% 6.73/7.07 (assert (forall ((Xs2 tptp.list_o)) (=> (@ tptp.distinct_o Xs2) (= (@ tptp.finite_card_o (@ tptp.set_o2 Xs2)) (@ tptp.size_size_list_o Xs2)))))
% 6.73/7.07 (assert (forall ((Xs2 tptp.list_nat)) (=> (@ tptp.distinct_nat Xs2) (= (@ tptp.finite_card_nat (@ tptp.set_nat2 Xs2)) (@ tptp.size_size_list_nat Xs2)))))
% 6.73/7.07 (assert (forall ((Xs2 tptp.list_int)) (=> (@ tptp.distinct_int Xs2) (= (@ tptp.finite_card_int (@ tptp.set_int2 Xs2)) (@ tptp.size_size_list_int Xs2)))))
% 6.73/7.07 (assert (forall ((A tptp.complex) (K2 tptp.nat)) (let ((_let_1 (@ tptp.suc K2))) (let ((_let_2 (@ tptp.gbinomial_complex A))) (= (@ (@ tptp.gbinomial_complex (@ (@ tptp.plus_plus_complex A) tptp.one_one_complex)) _let_1) (@ (@ tptp.plus_plus_complex (@ _let_2 K2)) (@ _let_2 _let_1)))))))
% 6.73/7.07 (assert (forall ((A tptp.real) (K2 tptp.nat)) (let ((_let_1 (@ tptp.suc K2))) (let ((_let_2 (@ tptp.gbinomial_real A))) (= (@ (@ tptp.gbinomial_real (@ (@ tptp.plus_plus_real A) tptp.one_one_real)) _let_1) (@ (@ tptp.plus_plus_real (@ _let_2 K2)) (@ _let_2 _let_1)))))))
% 6.73/7.07 (assert (forall ((A tptp.rat) (K2 tptp.nat)) (let ((_let_1 (@ tptp.suc K2))) (let ((_let_2 (@ tptp.gbinomial_rat A))) (= (@ (@ tptp.gbinomial_rat (@ (@ tptp.plus_plus_rat A) tptp.one_one_rat)) _let_1) (@ (@ tptp.plus_plus_rat (@ _let_2 K2)) (@ _let_2 _let_1)))))))
% 6.73/7.07 (assert (forall ((K2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.gbinomial_real (@ tptp.semiri5074537144036343181t_real N)))) (=> (@ (@ tptp.ord_less_eq_nat K2) N) (= (@ _let_1 K2) (@ _let_1 (@ (@ tptp.minus_minus_nat N) K2)))))))
% 6.73/7.07 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_eq_set_real (@ tptp.set_ord_atMost_real A)) (@ tptp.set_or5984915006950818249n_real B)) (@ (@ tptp.ord_less_real A) B))))
% 6.73/7.07 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_set_rat (@ tptp.set_ord_atMost_rat A)) (@ tptp.set_ord_lessThan_rat B)) (@ (@ tptp.ord_less_rat A) B))))
% 6.73/7.07 (assert (forall ((A tptp.num) (B tptp.num)) (= (@ (@ tptp.ord_less_eq_set_num (@ tptp.set_ord_atMost_num A)) (@ tptp.set_ord_lessThan_num B)) (@ (@ tptp.ord_less_num A) B))))
% 6.73/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_ord_atMost_int A)) (@ tptp.set_ord_lessThan_int B)) (@ (@ tptp.ord_less_int A) B))))
% 6.73/7.07 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_ord_atMost_nat A)) (@ tptp.set_ord_lessThan_nat B)) (@ (@ tptp.ord_less_nat A) B))))
% 6.73/7.07 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K3 tptp.nat)) (@ (@ tptp.binomial K3) M2))) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.binomial (@ tptp.suc N)) (@ tptp.suc M2)))))
% 6.73/7.07 (assert (forall ((Xs2 tptp.list_complex) (X tptp.complex)) (=> (@ tptp.distinct_complex Xs2) (=> (@ (@ tptp.member_complex X) (@ tptp.set_complex2 Xs2)) (exists ((X3 tptp.nat)) (and (@ (@ tptp.ord_less_nat X3) (@ tptp.size_s3451745648224563538omplex Xs2)) (= (@ (@ tptp.nth_complex Xs2) X3) X) (forall ((Y6 tptp.nat)) (=> (and (@ (@ tptp.ord_less_nat Y6) (@ tptp.size_s3451745648224563538omplex Xs2)) (= (@ (@ tptp.nth_complex Xs2) Y6) X)) (= Y6 X3)))))))))
% 6.73/7.07 (assert (forall ((Xs2 tptp.list_real) (X tptp.real)) (=> (@ tptp.distinct_real Xs2) (=> (@ (@ tptp.member_real X) (@ tptp.set_real2 Xs2)) (exists ((X3 tptp.nat)) (and (@ (@ tptp.ord_less_nat X3) (@ tptp.size_size_list_real Xs2)) (= (@ (@ tptp.nth_real Xs2) X3) X) (forall ((Y6 tptp.nat)) (=> (and (@ (@ tptp.ord_less_nat Y6) (@ tptp.size_size_list_real Xs2)) (= (@ (@ tptp.nth_real Xs2) Y6) X)) (= Y6 X3)))))))))
% 6.73/7.07 (assert (forall ((Xs2 tptp.list_set_nat) (X tptp.set_nat)) (=> (@ tptp.distinct_set_nat Xs2) (=> (@ (@ tptp.member_set_nat X) (@ tptp.set_set_nat2 Xs2)) (exists ((X3 tptp.nat)) (and (@ (@ tptp.ord_less_nat X3) (@ tptp.size_s3254054031482475050et_nat Xs2)) (= (@ (@ tptp.nth_set_nat Xs2) X3) X) (forall ((Y6 tptp.nat)) (=> (and (@ (@ tptp.ord_less_nat Y6) (@ tptp.size_s3254054031482475050et_nat Xs2)) (= (@ (@ tptp.nth_set_nat Xs2) Y6) X)) (= Y6 X3)))))))))
% 6.73/7.07 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (X tptp.vEBT_VEBT)) (=> (@ tptp.distinct_VEBT_VEBT Xs2) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 Xs2)) (exists ((X3 tptp.nat)) (and (@ (@ tptp.ord_less_nat X3) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (= (@ (@ tptp.nth_VEBT_VEBT Xs2) X3) X) (forall ((Y6 tptp.nat)) (=> (and (@ (@ tptp.ord_less_nat Y6) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (= (@ (@ tptp.nth_VEBT_VEBT Xs2) Y6) X)) (= Y6 X3)))))))))
% 6.73/7.07 (assert (forall ((Xs2 tptp.list_o) (X Bool)) (=> (@ tptp.distinct_o Xs2) (=> (@ (@ tptp.member_o X) (@ tptp.set_o2 Xs2)) (exists ((X3 tptp.nat)) (and (@ (@ tptp.ord_less_nat X3) (@ tptp.size_size_list_o Xs2)) (= (@ (@ tptp.nth_o Xs2) X3) X) (forall ((Y6 tptp.nat)) (=> (and (@ (@ tptp.ord_less_nat Y6) (@ tptp.size_size_list_o Xs2)) (= (@ (@ tptp.nth_o Xs2) Y6) X)) (= Y6 X3)))))))))
% 6.73/7.07 (assert (forall ((Xs2 tptp.list_nat) (X tptp.nat)) (=> (@ tptp.distinct_nat Xs2) (=> (@ (@ tptp.member_nat X) (@ tptp.set_nat2 Xs2)) (exists ((X3 tptp.nat)) (and (@ (@ tptp.ord_less_nat X3) (@ tptp.size_size_list_nat Xs2)) (= (@ (@ tptp.nth_nat Xs2) X3) X) (forall ((Y6 tptp.nat)) (=> (and (@ (@ tptp.ord_less_nat Y6) (@ tptp.size_size_list_nat Xs2)) (= (@ (@ tptp.nth_nat Xs2) Y6) X)) (= Y6 X3)))))))))
% 6.73/7.07 (assert (forall ((Xs2 tptp.list_int) (X tptp.int)) (=> (@ tptp.distinct_int Xs2) (=> (@ (@ tptp.member_int X) (@ tptp.set_int2 Xs2)) (exists ((X3 tptp.nat)) (and (@ (@ tptp.ord_less_nat X3) (@ tptp.size_size_list_int Xs2)) (= (@ (@ tptp.nth_int Xs2) X3) X) (forall ((Y6 tptp.nat)) (=> (and (@ (@ tptp.ord_less_nat Y6) (@ tptp.size_size_list_int Xs2)) (= (@ (@ tptp.nth_int Xs2) Y6) X)) (= Y6 X3)))))))))
% 6.73/7.07 (assert (forall ((M2 tptp.nat) (A tptp.complex) (X tptp.complex) (Y tptp.complex)) (let ((_let_1 (@ tptp.set_ord_atMost_nat M2))) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ (@ tptp.gbinomial_complex (@ (@ tptp.plus_plus_complex (@ tptp.semiri8010041392384452111omplex M2)) A)) K3)) (@ (@ tptp.power_power_complex X) K3))) (@ (@ tptp.power_power_complex Y) (@ (@ tptp.minus_minus_nat M2) K3))))) _let_1) (@ (@ tptp.groups2073611262835488442omplex (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ (@ tptp.gbinomial_complex (@ (@ tptp.minus_minus_complex (@ (@ tptp.plus_plus_complex (@ tptp.semiri8010041392384452111omplex K3)) A)) tptp.one_one_complex)) K3)) (@ (@ tptp.power_power_complex X) K3))) (@ (@ tptp.power_power_complex (@ (@ tptp.plus_plus_complex X) Y)) (@ (@ tptp.minus_minus_nat M2) K3))))) _let_1)))))
% 6.73/7.07 (assert (forall ((M2 tptp.nat) (A tptp.rat) (X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.set_ord_atMost_nat M2))) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ (@ tptp.gbinomial_rat (@ (@ tptp.plus_plus_rat (@ tptp.semiri681578069525770553at_rat M2)) A)) K3)) (@ (@ tptp.power_power_rat X) K3))) (@ (@ tptp.power_power_rat Y) (@ (@ tptp.minus_minus_nat M2) K3))))) _let_1) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ (@ tptp.gbinomial_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat (@ tptp.semiri681578069525770553at_rat K3)) A)) tptp.one_one_rat)) K3)) (@ (@ tptp.power_power_rat X) K3))) (@ (@ tptp.power_power_rat (@ (@ tptp.plus_plus_rat X) Y)) (@ (@ tptp.minus_minus_nat M2) K3))))) _let_1)))))
% 6.73/7.07 (assert (forall ((M2 tptp.nat) (A tptp.real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.set_ord_atMost_nat M2))) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.gbinomial_real (@ (@ tptp.plus_plus_real (@ tptp.semiri5074537144036343181t_real M2)) A)) K3)) (@ (@ tptp.power_power_real X) K3))) (@ (@ tptp.power_power_real Y) (@ (@ tptp.minus_minus_nat M2) K3))))) _let_1) (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.gbinomial_real (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real (@ tptp.semiri5074537144036343181t_real K3)) A)) tptp.one_one_real)) K3)) (@ (@ tptp.power_power_real X) K3))) (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real X) Y)) (@ (@ tptp.minus_minus_nat M2) K3))))) _let_1)))))
% 6.73/7.07 (assert (forall ((A tptp.complex) (K2 tptp.nat)) (let ((_let_1 (@ tptp.gbinomial_complex (@ (@ tptp.minus_minus_complex A) tptp.one_one_complex)))) (let ((_let_2 (@ tptp.suc K2))) (= (@ (@ tptp.gbinomial_complex A) _let_2) (@ (@ tptp.plus_plus_complex (@ _let_1 _let_2)) (@ _let_1 K2)))))))
% 6.73/7.07 (assert (forall ((A tptp.real) (K2 tptp.nat)) (let ((_let_1 (@ tptp.gbinomial_real (@ (@ tptp.minus_minus_real A) tptp.one_one_real)))) (let ((_let_2 (@ tptp.suc K2))) (= (@ (@ tptp.gbinomial_real A) _let_2) (@ (@ tptp.plus_plus_real (@ _let_1 _let_2)) (@ _let_1 K2)))))))
% 6.73/7.07 (assert (forall ((A tptp.rat) (K2 tptp.nat)) (let ((_let_1 (@ tptp.gbinomial_rat (@ (@ tptp.minus_minus_rat A) tptp.one_one_rat)))) (let ((_let_2 (@ tptp.suc K2))) (= (@ (@ tptp.gbinomial_rat A) _let_2) (@ (@ tptp.plus_plus_rat (@ _let_1 _let_2)) (@ _let_1 K2)))))))
% 6.73/7.07 (assert (forall ((A tptp.complex) (K2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_complex A))) (= (@ (@ tptp.times_times_complex (@ _let_1 (@ tptp.semiri8010041392384452111omplex K2))) (@ (@ tptp.gbinomial_complex A) K2)) (@ (@ tptp.times_times_complex A) (@ (@ tptp.gbinomial_complex (@ _let_1 tptp.one_one_complex)) K2))))))
% 6.73/7.07 (assert (forall ((A tptp.rat) (K2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_rat A))) (= (@ (@ tptp.times_times_rat (@ _let_1 (@ tptp.semiri681578069525770553at_rat K2))) (@ (@ tptp.gbinomial_rat A) K2)) (@ (@ tptp.times_times_rat A) (@ (@ tptp.gbinomial_rat (@ _let_1 tptp.one_one_rat)) K2))))))
% 6.73/7.07 (assert (forall ((A tptp.real) (K2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_real A))) (= (@ (@ tptp.times_times_real (@ _let_1 (@ tptp.semiri5074537144036343181t_real K2))) (@ (@ tptp.gbinomial_real A) K2)) (@ (@ tptp.times_times_real A) (@ (@ tptp.gbinomial_real (@ _let_1 tptp.one_one_real)) K2))))))
% 6.73/7.07 (assert (forall ((K2 tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real K2))) (=> (@ (@ tptp.ord_less_eq_real _let_1) A) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ (@ tptp.divide_divide_real A) _let_1)) K2)) (@ (@ tptp.gbinomial_real A) K2))))))
% 6.73/7.07 (assert (forall ((K2 tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.semiri681578069525770553at_rat K2))) (=> (@ (@ tptp.ord_less_eq_rat _let_1) A) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat (@ (@ tptp.divide_divide_rat A) _let_1)) K2)) (@ (@ tptp.gbinomial_rat A) K2))))))
% 6.73/7.07 (assert (forall ((A tptp.rat) (K2 tptp.nat)) (let ((_let_1 (@ tptp.suc K2))) (let ((_let_2 (@ tptp.gbinomial_rat A))) (let ((_let_3 (@ _let_2 K2))) (= (@ (@ tptp.times_times_rat _let_3) A) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat K2)) _let_3)) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat _let_1)) (@ _let_2 _let_1)))))))))
% 6.73/7.07 (assert (forall ((A tptp.real) (K2 tptp.nat)) (let ((_let_1 (@ tptp.suc K2))) (let ((_let_2 (@ tptp.gbinomial_real A))) (let ((_let_3 (@ _let_2 K2))) (= (@ (@ tptp.times_times_real _let_3) A) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real K2)) _let_3)) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real _let_1)) (@ _let_2 _let_1)))))))))
% 6.73/7.07 (assert (forall ((A tptp.rat) (K2 tptp.nat)) (let ((_let_1 (@ tptp.suc K2))) (let ((_let_2 (@ tptp.gbinomial_rat A))) (let ((_let_3 (@ _let_2 K2))) (= (@ (@ tptp.times_times_rat A) _let_3) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat K2)) _let_3)) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat _let_1)) (@ _let_2 _let_1)))))))))
% 6.73/7.07 (assert (forall ((A tptp.real) (K2 tptp.nat)) (let ((_let_1 (@ tptp.suc K2))) (let ((_let_2 (@ tptp.gbinomial_real A))) (let ((_let_3 (@ _let_2 K2))) (= (@ (@ tptp.times_times_real A) _let_3) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real K2)) _let_3)) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real _let_1)) (@ _let_2 _let_1)))))))))
% 6.73/7.07 (assert (forall ((G2 (-> tptp.nat tptp.rat)) (N tptp.nat)) (= (@ (@ tptp.groups2906978787729119204at_rat G2) (@ tptp.set_ord_atMost_nat (@ tptp.suc N))) (@ (@ tptp.plus_plus_rat (@ G2 tptp.zero_zero_nat)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I tptp.nat)) (@ G2 (@ tptp.suc I)))) (@ tptp.set_ord_atMost_nat N))))))
% 6.73/7.07 (assert (forall ((G2 (-> tptp.nat tptp.int)) (N tptp.nat)) (= (@ (@ tptp.groups3539618377306564664at_int G2) (@ tptp.set_ord_atMost_nat (@ tptp.suc N))) (@ (@ tptp.plus_plus_int (@ G2 tptp.zero_zero_nat)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I tptp.nat)) (@ G2 (@ tptp.suc I)))) (@ tptp.set_ord_atMost_nat N))))))
% 6.73/7.07 (assert (forall ((G2 (-> tptp.nat tptp.nat)) (N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat G2) (@ tptp.set_ord_atMost_nat (@ tptp.suc N))) (@ (@ tptp.plus_plus_nat (@ G2 tptp.zero_zero_nat)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I tptp.nat)) (@ G2 (@ tptp.suc I)))) (@ tptp.set_ord_atMost_nat N))))))
% 6.73/7.07 (assert (forall ((G2 (-> tptp.nat tptp.real)) (N tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real G2) (@ tptp.set_ord_atMost_nat (@ tptp.suc N))) (@ (@ tptp.plus_plus_real (@ G2 tptp.zero_zero_nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I tptp.nat)) (@ G2 (@ tptp.suc I)))) (@ tptp.set_ord_atMost_nat N))))))
% 6.73/7.07 (assert (forall ((F2 (-> tptp.nat tptp.rat)) (I2 tptp.nat)) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I tptp.nat)) (@ (@ tptp.minus_minus_rat (@ F2 I)) (@ F2 (@ tptp.suc I))))) (@ tptp.set_ord_atMost_nat I2)) (@ (@ tptp.minus_minus_rat (@ F2 tptp.zero_zero_nat)) (@ F2 (@ tptp.suc I2))))))
% 6.73/7.07 (assert (forall ((F2 (-> tptp.nat tptp.int)) (I2 tptp.nat)) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((I tptp.nat)) (@ (@ tptp.minus_minus_int (@ F2 I)) (@ F2 (@ tptp.suc I))))) (@ tptp.set_ord_atMost_nat I2)) (@ (@ tptp.minus_minus_int (@ F2 tptp.zero_zero_nat)) (@ F2 (@ tptp.suc I2))))))
% 6.73/7.07 (assert (forall ((F2 (-> tptp.nat tptp.real)) (I2 tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I tptp.nat)) (@ (@ tptp.minus_minus_real (@ F2 I)) (@ F2 (@ tptp.suc I))))) (@ tptp.set_ord_atMost_nat I2)) (@ (@ tptp.minus_minus_real (@ F2 tptp.zero_zero_nat)) (@ F2 (@ tptp.suc I2))))))
% 6.73/7.07 (assert (forall ((C2 (-> tptp.nat tptp.complex)) (N tptp.nat) (D (-> tptp.nat tptp.complex))) (= (forall ((X4 tptp.complex)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N))) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I tptp.nat)) (@ (@ tptp.times_times_complex (@ C2 I)) (@ (@ tptp.power_power_complex X4) I)))) _let_1) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I tptp.nat)) (@ (@ tptp.times_times_complex (@ D I)) (@ (@ tptp.power_power_complex X4) I)))) _let_1)))) (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) N) (= (@ C2 I) (@ D I)))))))
% 6.73/7.07 (assert (forall ((C2 (-> tptp.nat tptp.real)) (N tptp.nat) (D (-> tptp.nat tptp.real))) (= (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N))) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I tptp.nat)) (@ (@ tptp.times_times_real (@ C2 I)) (@ (@ tptp.power_power_real X4) I)))) _let_1) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I tptp.nat)) (@ (@ tptp.times_times_real (@ D I)) (@ (@ tptp.power_power_real X4) I)))) _let_1)))) (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) N) (= (@ C2 I) (@ D I)))))))
% 6.73/7.07 (assert (forall ((G2 (-> tptp.nat tptp.real)) (N tptp.nat)) (= (@ (@ tptp.groups129246275422532515t_real G2) (@ tptp.set_ord_atMost_nat (@ tptp.suc N))) (@ (@ tptp.times_times_real (@ G2 tptp.zero_zero_nat)) (@ (@ tptp.groups129246275422532515t_real (lambda ((I tptp.nat)) (@ G2 (@ tptp.suc I)))) (@ tptp.set_ord_atMost_nat N))))))
% 6.73/7.07 (assert (forall ((G2 (-> tptp.nat tptp.rat)) (N tptp.nat)) (= (@ (@ tptp.groups73079841787564623at_rat G2) (@ tptp.set_ord_atMost_nat (@ tptp.suc N))) (@ (@ tptp.times_times_rat (@ G2 tptp.zero_zero_nat)) (@ (@ tptp.groups73079841787564623at_rat (lambda ((I tptp.nat)) (@ G2 (@ tptp.suc I)))) (@ tptp.set_ord_atMost_nat N))))))
% 6.73/7.07 (assert (forall ((G2 (-> tptp.nat tptp.int)) (N tptp.nat)) (= (@ (@ tptp.groups705719431365010083at_int G2) (@ tptp.set_ord_atMost_nat (@ tptp.suc N))) (@ (@ tptp.times_times_int (@ G2 tptp.zero_zero_nat)) (@ (@ tptp.groups705719431365010083at_int (lambda ((I tptp.nat)) (@ G2 (@ tptp.suc I)))) (@ tptp.set_ord_atMost_nat N))))))
% 6.73/7.07 (assert (forall ((G2 (-> tptp.nat tptp.nat)) (N tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat G2) (@ tptp.set_ord_atMost_nat (@ tptp.suc N))) (@ (@ tptp.times_times_nat (@ G2 tptp.zero_zero_nat)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I tptp.nat)) (@ G2 (@ tptp.suc I)))) (@ tptp.set_ord_atMost_nat N))))))
% 6.73/7.07 (assert (forall ((A (-> tptp.nat tptp.nat tptp.nat)) (N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I tptp.nat)) (@ (@ tptp.groups3542108847815614940at_nat (@ A I)) (@ tptp.set_ord_lessThan_nat I)))) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((J tptp.nat)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I tptp.nat)) (@ (@ A I) J))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc J)) N)))) (@ tptp.set_ord_lessThan_nat N)))))
% 6.73/7.07 (assert (forall ((A (-> tptp.nat tptp.nat tptp.real)) (N tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (@ A I)) (@ tptp.set_ord_lessThan_nat I)))) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((J tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I tptp.nat)) (@ (@ A I) J))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc J)) N)))) (@ tptp.set_ord_lessThan_nat N)))))
% 6.73/7.07 (assert (forall ((L tptp.rat) (U tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat L) U) (= (@ (@ tptp.sup_sup_set_rat (@ tptp.set_ord_lessThan_rat L)) (@ (@ tptp.set_or633870826150836451st_rat L) U)) (@ tptp.set_ord_atMost_rat U)))))
% 6.73/7.07 (assert (forall ((L tptp.num) (U tptp.num)) (=> (@ (@ tptp.ord_less_eq_num L) U) (= (@ (@ tptp.sup_sup_set_num (@ tptp.set_ord_lessThan_num L)) (@ (@ tptp.set_or7049704709247886629st_num L) U)) (@ tptp.set_ord_atMost_num U)))))
% 6.73/7.07 (assert (forall ((L tptp.nat) (U tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat L) U) (= (@ (@ tptp.sup_sup_set_nat (@ tptp.set_ord_lessThan_nat L)) (@ (@ tptp.set_or1269000886237332187st_nat L) U)) (@ tptp.set_ord_atMost_nat U)))))
% 6.73/7.07 (assert (forall ((L tptp.int) (U tptp.int)) (=> (@ (@ tptp.ord_less_eq_int L) U) (= (@ (@ tptp.sup_sup_set_int (@ tptp.set_ord_lessThan_int L)) (@ (@ tptp.set_or1266510415728281911st_int L) U)) (@ tptp.set_ord_atMost_int U)))))
% 6.73/7.07 (assert (forall ((L tptp.real) (U tptp.real)) (=> (@ (@ tptp.ord_less_eq_real L) U) (= (@ (@ tptp.sup_sup_set_real (@ tptp.set_or5984915006950818249n_real L)) (@ (@ tptp.set_or1222579329274155063t_real L) U)) (@ tptp.set_ord_atMost_real U)))))
% 6.73/7.07 (assert (forall ((U tptp.int)) (= (@ (@ tptp.sup_sup_set_int (@ tptp.set_ord_lessThan_int U)) (@ (@ tptp.insert_int U) tptp.bot_bot_set_int)) (@ tptp.set_ord_atMost_int U))))
% 6.73/7.07 (assert (forall ((U tptp.real)) (= (@ (@ tptp.sup_sup_set_real (@ tptp.set_or5984915006950818249n_real U)) (@ (@ tptp.insert_real U) tptp.bot_bot_set_real)) (@ tptp.set_ord_atMost_real U))))
% 6.73/7.07 (assert (forall ((U tptp.nat)) (= (@ (@ tptp.sup_sup_set_nat (@ tptp.set_ord_lessThan_nat U)) (@ (@ tptp.insert_nat U) tptp.bot_bot_set_nat)) (@ tptp.set_ord_atMost_nat U))))
% 6.73/7.07 (assert (forall ((A (-> tptp.nat tptp.nat tptp.int)) (N tptp.nat)) (= (@ (@ tptp.groups705719431365010083at_int (lambda ((I tptp.nat)) (@ (@ tptp.groups705719431365010083at_int (@ A I)) (@ tptp.set_ord_lessThan_nat I)))) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.groups705719431365010083at_int (lambda ((J tptp.nat)) (@ (@ tptp.groups705719431365010083at_int (lambda ((I tptp.nat)) (@ (@ A I) J))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc J)) N)))) (@ tptp.set_ord_lessThan_nat N)))))
% 6.73/7.07 (assert (forall ((A (-> tptp.nat tptp.nat tptp.nat)) (N tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat (lambda ((I tptp.nat)) (@ (@ tptp.groups708209901874060359at_nat (@ A I)) (@ tptp.set_ord_lessThan_nat I)))) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((J tptp.nat)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I tptp.nat)) (@ (@ A I) J))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc J)) N)))) (@ tptp.set_ord_lessThan_nat N)))))
% 6.73/7.07 (assert (forall ((R3 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K3 tptp.nat)) (@ (@ tptp.binomial (@ (@ tptp.plus_plus_nat R3) K3)) K3))) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.binomial (@ tptp.suc (@ (@ tptp.plus_plus_nat R3) N))) N))))
% 6.73/7.07 (assert (forall ((K2 tptp.nat) (A tptp.complex)) (let ((_let_1 (@ (@ tptp.plus_plus_complex A) tptp.one_one_complex))) (let ((_let_2 (@ tptp.suc K2))) (= (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex _let_2)) (@ (@ tptp.gbinomial_complex _let_1) _let_2)) (@ (@ tptp.times_times_complex _let_1) (@ (@ tptp.gbinomial_complex A) K2)))))))
% 6.73/7.07 (assert (forall ((K2 tptp.nat) (A tptp.rat)) (let ((_let_1 (@ (@ tptp.plus_plus_rat A) tptp.one_one_rat))) (let ((_let_2 (@ tptp.suc K2))) (= (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat _let_2)) (@ (@ tptp.gbinomial_rat _let_1) _let_2)) (@ (@ tptp.times_times_rat _let_1) (@ (@ tptp.gbinomial_rat A) K2)))))))
% 6.73/7.07 (assert (forall ((K2 tptp.nat) (A tptp.real)) (let ((_let_1 (@ (@ tptp.plus_plus_real A) tptp.one_one_real))) (let ((_let_2 (@ tptp.suc K2))) (= (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real _let_2)) (@ (@ tptp.gbinomial_real _let_1) _let_2)) (@ (@ tptp.times_times_real _let_1) (@ (@ tptp.gbinomial_real A) K2)))))))
% 6.73/7.07 (assert (forall ((K2 tptp.nat) (A tptp.complex)) (let ((_let_1 (@ tptp.suc K2))) (= (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex _let_1)) (@ (@ tptp.gbinomial_complex A) _let_1)) (@ (@ tptp.times_times_complex A) (@ (@ tptp.gbinomial_complex (@ (@ tptp.minus_minus_complex A) tptp.one_one_complex)) K2))))))
% 6.73/7.07 (assert (forall ((K2 tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.suc K2))) (= (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat _let_1)) (@ (@ tptp.gbinomial_rat A) _let_1)) (@ (@ tptp.times_times_rat A) (@ (@ tptp.gbinomial_rat (@ (@ tptp.minus_minus_rat A) tptp.one_one_rat)) K2))))))
% 6.73/7.07 (assert (forall ((K2 tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.suc K2))) (= (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real _let_1)) (@ (@ tptp.gbinomial_real A) _let_1)) (@ (@ tptp.times_times_real A) (@ (@ tptp.gbinomial_real (@ (@ tptp.minus_minus_real A) tptp.one_one_real)) K2))))))
% 6.73/7.07 (assert (forall ((K2 tptp.nat) (M2 tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.gbinomial_rat A))) (=> (@ (@ tptp.ord_less_eq_nat K2) M2) (= (@ (@ tptp.times_times_rat (@ _let_1 M2)) (@ (@ tptp.gbinomial_rat (@ tptp.semiri681578069525770553at_rat M2)) K2)) (@ (@ tptp.times_times_rat (@ _let_1 K2)) (@ (@ tptp.gbinomial_rat (@ (@ tptp.minus_minus_rat A) (@ tptp.semiri681578069525770553at_rat K2))) (@ (@ tptp.minus_minus_nat M2) K2))))))))
% 6.73/7.07 (assert (forall ((K2 tptp.nat) (M2 tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.gbinomial_real A))) (=> (@ (@ tptp.ord_less_eq_nat K2) M2) (= (@ (@ tptp.times_times_real (@ _let_1 M2)) (@ (@ tptp.gbinomial_real (@ tptp.semiri5074537144036343181t_real M2)) K2)) (@ (@ tptp.times_times_real (@ _let_1 K2)) (@ (@ tptp.gbinomial_real (@ (@ tptp.minus_minus_real A) (@ tptp.semiri5074537144036343181t_real K2))) (@ (@ tptp.minus_minus_nat M2) K2))))))))
% 6.73/7.07 (assert (forall ((C2 (-> tptp.nat tptp.complex)) (N tptp.nat) (K2 tptp.nat)) (=> (forall ((W tptp.complex)) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I tptp.nat)) (@ (@ tptp.times_times_complex (@ C2 I)) (@ (@ tptp.power_power_complex W) I)))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_complex)) (=> (@ (@ tptp.ord_less_eq_nat K2) N) (= (@ C2 K2) tptp.zero_zero_complex)))))
% 6.73/7.07 (assert (forall ((C2 (-> tptp.nat tptp.real)) (N tptp.nat) (K2 tptp.nat)) (=> (forall ((W tptp.real)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I tptp.nat)) (@ (@ tptp.times_times_real (@ C2 I)) (@ (@ tptp.power_power_real W) I)))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_real)) (=> (@ (@ tptp.ord_less_eq_nat K2) N) (= (@ C2 K2) tptp.zero_zero_real)))))
% 6.73/7.07 (assert (forall ((C2 (-> tptp.nat tptp.complex)) (N tptp.nat)) (= (forall ((X4 tptp.complex)) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I tptp.nat)) (@ (@ tptp.times_times_complex (@ C2 I)) (@ (@ tptp.power_power_complex X4) I)))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_complex)) (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) N) (= (@ C2 I) tptp.zero_zero_complex))))))
% 6.73/7.07 (assert (forall ((C2 (-> tptp.nat tptp.real)) (N tptp.nat)) (= (forall ((X4 tptp.real)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I tptp.nat)) (@ (@ tptp.times_times_real (@ C2 I)) (@ (@ tptp.power_power_real X4) I)))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_real)) (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) N) (= (@ C2 I) tptp.zero_zero_real))))))
% 6.73/7.07 (assert (forall ((G2 (-> tptp.nat tptp.rat)) (N tptp.nat)) (= (@ (@ tptp.groups2906978787729119204at_rat G2) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.plus_plus_rat (@ G2 tptp.zero_zero_nat)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I tptp.nat)) (@ G2 (@ tptp.suc I)))) (@ tptp.set_ord_lessThan_nat N))))))
% 6.73/7.07 (assert (forall ((G2 (-> tptp.nat tptp.int)) (N tptp.nat)) (= (@ (@ tptp.groups3539618377306564664at_int G2) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.plus_plus_int (@ G2 tptp.zero_zero_nat)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I tptp.nat)) (@ G2 (@ tptp.suc I)))) (@ tptp.set_ord_lessThan_nat N))))))
% 6.73/7.07 (assert (forall ((G2 (-> tptp.nat tptp.nat)) (N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat G2) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.plus_plus_nat (@ G2 tptp.zero_zero_nat)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I tptp.nat)) (@ G2 (@ tptp.suc I)))) (@ tptp.set_ord_lessThan_nat N))))))
% 6.73/7.07 (assert (forall ((G2 (-> tptp.nat tptp.real)) (N tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real G2) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.plus_plus_real (@ G2 tptp.zero_zero_nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I tptp.nat)) (@ G2 (@ tptp.suc I)))) (@ tptp.set_ord_lessThan_nat N))))))
% 6.73/7.07 (assert (forall ((F2 (-> tptp.nat tptp.rat)) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat M2) N))) (let ((_let_2 (@ tptp.groups2906978787729119204at_rat F2))) (= (@ _let_2 (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.plus_plus_rat (@ _let_2 (@ tptp.set_ord_atMost_nat M2))) (@ _let_2 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M2)) _let_1))))))))
% 6.73/7.07 (assert (forall ((F2 (-> tptp.nat tptp.int)) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat M2) N))) (let ((_let_2 (@ tptp.groups3539618377306564664at_int F2))) (= (@ _let_2 (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.plus_plus_int (@ _let_2 (@ tptp.set_ord_atMost_nat M2))) (@ _let_2 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M2)) _let_1))))))))
% 6.73/7.07 (assert (forall ((F2 (-> tptp.nat tptp.nat)) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat M2) N))) (let ((_let_2 (@ tptp.groups3542108847815614940at_nat F2))) (= (@ _let_2 (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.plus_plus_nat (@ _let_2 (@ tptp.set_ord_atMost_nat M2))) (@ _let_2 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M2)) _let_1))))))))
% 6.73/7.07 (assert (forall ((F2 (-> tptp.nat tptp.real)) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat M2) N))) (let ((_let_2 (@ tptp.groups6591440286371151544t_real F2))) (= (@ _let_2 (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.plus_plus_real (@ _let_2 (@ tptp.set_ord_atMost_nat M2))) (@ _let_2 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M2)) _let_1))))))))
% 6.73/7.07 (assert (forall ((G2 (-> tptp.nat tptp.real)) (N tptp.nat)) (= (@ (@ tptp.groups129246275422532515t_real G2) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.times_times_real (@ G2 tptp.zero_zero_nat)) (@ (@ tptp.groups129246275422532515t_real (lambda ((I tptp.nat)) (@ G2 (@ tptp.suc I)))) (@ tptp.set_ord_lessThan_nat N))))))
% 6.73/7.07 (assert (forall ((G2 (-> tptp.nat tptp.rat)) (N tptp.nat)) (= (@ (@ tptp.groups73079841787564623at_rat G2) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.times_times_rat (@ G2 tptp.zero_zero_nat)) (@ (@ tptp.groups73079841787564623at_rat (lambda ((I tptp.nat)) (@ G2 (@ tptp.suc I)))) (@ tptp.set_ord_lessThan_nat N))))))
% 6.73/7.07 (assert (forall ((G2 (-> tptp.nat tptp.int)) (N tptp.nat)) (= (@ (@ tptp.groups705719431365010083at_int G2) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.times_times_int (@ G2 tptp.zero_zero_nat)) (@ (@ tptp.groups705719431365010083at_int (lambda ((I tptp.nat)) (@ G2 (@ tptp.suc I)))) (@ tptp.set_ord_lessThan_nat N))))))
% 6.73/7.07 (assert (forall ((G2 (-> tptp.nat tptp.nat)) (N tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat G2) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.times_times_nat (@ G2 tptp.zero_zero_nat)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I tptp.nat)) (@ G2 (@ tptp.suc I)))) (@ tptp.set_ord_lessThan_nat N))))))
% 6.73/7.07 (assert (forall ((M2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_rat _let_1))) (= (@ (@ tptp.groups2906978787729119204at_rat (@ tptp.gbinomial_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat _let_2) (@ tptp.semiri681578069525770553at_rat M2))) tptp.one_one_rat))) (@ tptp.set_ord_atMost_nat M2)) (@ (@ tptp.power_power_rat _let_2) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat _let_1)) M2)))))))
% 6.73/7.07 (assert (forall ((M2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numera6690914467698888265omplex _let_1))) (= (@ (@ tptp.groups2073611262835488442omplex (@ tptp.gbinomial_complex (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex _let_2) (@ tptp.semiri8010041392384452111omplex M2))) tptp.one_one_complex))) (@ tptp.set_ord_atMost_nat M2)) (@ (@ tptp.power_power_complex _let_2) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat _let_1)) M2)))))))
% 6.73/7.07 (assert (forall ((M2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_real _let_1))) (= (@ (@ tptp.groups6591440286371151544t_real (@ tptp.gbinomial_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real _let_2) (@ tptp.semiri5074537144036343181t_real M2))) tptp.one_one_real))) (@ tptp.set_ord_atMost_nat M2)) (@ (@ tptp.power_power_real _let_2) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat _let_1)) M2)))))))
% 6.73/7.07 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K3 tptp.nat)) (@ (@ tptp.binomial (@ (@ tptp.minus_minus_nat N) K3)) (@ (@ tptp.minus_minus_nat M2) K3)))) (@ tptp.set_ord_atMost_nat M2)) (@ (@ tptp.binomial (@ tptp.suc N)) M2)))))
% 6.73/7.07 (assert (forall ((M2 tptp.nat) (N tptp.nat) (R3 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_nat (@ (@ tptp.binomial M2) K3)) (@ (@ tptp.binomial N) (@ (@ tptp.minus_minus_nat R3) K3))))) (@ tptp.set_ord_atMost_nat R3)) (@ (@ tptp.binomial (@ (@ tptp.plus_plus_nat M2) N)) R3))))
% 6.73/7.07 (assert (forall ((P2 (-> tptp.nat Bool)) (A tptp.nat)) (=> (forall ((A3 tptp.nat)) (=> (= (@ (@ tptp.divide_divide_nat A3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) A3) (@ P2 A3))) (=> (forall ((A3 tptp.nat) (B3 Bool)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.plus_plus_nat (@ tptp.zero_n2687167440665602831ol_nat B3)) (@ (@ tptp.times_times_nat _let_1) A3)))) (=> (@ P2 A3) (=> (= (@ (@ tptp.divide_divide_nat _let_2) _let_1) A3) (@ P2 _let_2)))))) (@ P2 A)))))
% 6.73/7.07 (assert (forall ((P2 (-> tptp.int Bool)) (A tptp.int)) (=> (forall ((A3 tptp.int)) (=> (= (@ (@ tptp.divide_divide_int A3) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) A3) (@ P2 A3))) (=> (forall ((A3 tptp.int) (B3 Bool)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.plus_plus_int (@ tptp.zero_n2684676970156552555ol_int B3)) (@ (@ tptp.times_times_int _let_1) A3)))) (=> (@ P2 A3) (=> (= (@ (@ tptp.divide_divide_int _let_2) _let_1) A3) (@ P2 _let_2)))))) (@ P2 A)))))
% 6.73/7.07 (assert (forall ((P2 (-> tptp.code_integer Bool)) (A tptp.code_integer)) (=> (forall ((A3 tptp.code_integer)) (=> (= (@ (@ tptp.divide6298287555418463151nteger A3) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) A3) (@ P2 A3))) (=> (forall ((A3 tptp.code_integer) (B3 Bool)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.zero_n356916108424825756nteger B3)) (@ (@ tptp.times_3573771949741848930nteger _let_1) A3)))) (=> (@ P2 A3) (=> (= (@ (@ tptp.divide6298287555418463151nteger _let_2) _let_1) A3) (@ P2 _let_2)))))) (@ P2 A)))))
% 6.73/7.07 (assert (forall ((A tptp.complex) (M2 tptp.nat)) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.gbinomial_complex A) K3)) (@ (@ tptp.minus_minus_complex (@ (@ tptp.divide1717551699836669952omplex A) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) (@ tptp.semiri8010041392384452111omplex K3))))) (@ tptp.set_ord_atMost_nat M2)) (@ (@ tptp.times_times_complex (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex (@ tptp.semiri8010041392384452111omplex M2)) tptp.one_one_complex)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) (@ (@ tptp.gbinomial_complex A) (@ (@ tptp.plus_plus_nat M2) tptp.one_one_nat))))))
% 6.73/7.07 (assert (forall ((A tptp.rat) (M2 tptp.nat)) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.gbinomial_rat A) K3)) (@ (@ tptp.minus_minus_rat (@ (@ tptp.divide_divide_rat A) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one)))) (@ tptp.semiri681578069525770553at_rat K3))))) (@ tptp.set_ord_atMost_nat M2)) (@ (@ tptp.times_times_rat (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat (@ tptp.semiri681578069525770553at_rat M2)) tptp.one_one_rat)) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.gbinomial_rat A) (@ (@ tptp.plus_plus_nat M2) tptp.one_one_nat))))))
% 6.73/7.07 (assert (forall ((A tptp.real) (M2 tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.gbinomial_real A) K3)) (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real A) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.semiri5074537144036343181t_real K3))))) (@ tptp.set_ord_atMost_nat M2)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ tptp.semiri5074537144036343181t_real M2)) tptp.one_one_real)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ (@ tptp.gbinomial_real A) (@ (@ tptp.plus_plus_nat M2) tptp.one_one_nat))))))
% 6.73/7.07 (assert (forall ((A tptp.complex) (K2 tptp.nat)) (let ((_let_1 (@ tptp.suc K2))) (let ((_let_2 (@ (@ tptp.plus_plus_complex A) tptp.one_one_complex))) (= (@ (@ tptp.gbinomial_complex _let_2) _let_1) (@ (@ tptp.times_times_complex (@ (@ tptp.divide1717551699836669952omplex _let_2) (@ tptp.semiri8010041392384452111omplex _let_1))) (@ (@ tptp.gbinomial_complex A) K2)))))))
% 6.73/7.07 (assert (forall ((A tptp.rat) (K2 tptp.nat)) (let ((_let_1 (@ tptp.suc K2))) (let ((_let_2 (@ (@ tptp.plus_plus_rat A) tptp.one_one_rat))) (= (@ (@ tptp.gbinomial_rat _let_2) _let_1) (@ (@ tptp.times_times_rat (@ (@ tptp.divide_divide_rat _let_2) (@ tptp.semiri681578069525770553at_rat _let_1))) (@ (@ tptp.gbinomial_rat A) K2)))))))
% 6.73/7.07 (assert (forall ((A tptp.real) (K2 tptp.nat)) (let ((_let_1 (@ tptp.suc K2))) (let ((_let_2 (@ (@ tptp.plus_plus_real A) tptp.one_one_real))) (= (@ (@ tptp.gbinomial_real _let_2) _let_1) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real _let_2) (@ tptp.semiri5074537144036343181t_real _let_1))) (@ (@ tptp.gbinomial_real A) K2)))))))
% 6.73/7.07 (assert (forall ((A tptp.complex) (K2 tptp.nat)) (let ((_let_1 (@ tptp.suc K2))) (let ((_let_2 (@ (@ tptp.plus_plus_complex A) tptp.one_one_complex))) (= (@ (@ tptp.gbinomial_complex _let_2) _let_1) (@ (@ tptp.times_times_complex (@ (@ tptp.gbinomial_complex A) K2)) (@ (@ tptp.divide1717551699836669952omplex _let_2) (@ tptp.semiri8010041392384452111omplex _let_1))))))))
% 6.73/7.07 (assert (forall ((A tptp.rat) (K2 tptp.nat)) (let ((_let_1 (@ tptp.suc K2))) (let ((_let_2 (@ (@ tptp.plus_plus_rat A) tptp.one_one_rat))) (= (@ (@ tptp.gbinomial_rat _let_2) _let_1) (@ (@ tptp.times_times_rat (@ (@ tptp.gbinomial_rat A) K2)) (@ (@ tptp.divide_divide_rat _let_2) (@ tptp.semiri681578069525770553at_rat _let_1))))))))
% 6.73/7.07 (assert (forall ((A tptp.real) (K2 tptp.nat)) (let ((_let_1 (@ tptp.suc K2))) (let ((_let_2 (@ (@ tptp.plus_plus_real A) tptp.one_one_real))) (= (@ (@ tptp.gbinomial_real _let_2) _let_1) (@ (@ tptp.times_times_real (@ (@ tptp.gbinomial_real A) K2)) (@ (@ tptp.divide_divide_real _let_2) (@ tptp.semiri5074537144036343181t_real _let_1))))))))
% 6.73/7.07 (assert (forall ((X tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger X))) (let ((_let_2 (@ tptp.minus_8373710615458151222nteger tptp.one_one_Code_integer))) (= (@ (@ tptp.times_3573771949741848930nteger (@ _let_2 X)) (@ (@ tptp.groups7501900531339628137nteger _let_1) (@ tptp.set_ord_atMost_nat N))) (@ _let_2 (@ _let_1 (@ tptp.suc N))))))))
% 6.73/7.07 (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))) (= (@ (@ tptp.times_times_complex (@ _let_2 X)) (@ (@ tptp.groups2073611262835488442omplex _let_1) (@ tptp.set_ord_atMost_nat N))) (@ _let_2 (@ _let_1 (@ tptp.suc N))))))))
% 6.73/7.07 (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))) (= (@ (@ tptp.times_times_rat (@ _let_2 X)) (@ (@ tptp.groups2906978787729119204at_rat _let_1) (@ tptp.set_ord_atMost_nat N))) (@ _let_2 (@ _let_1 (@ tptp.suc N))))))))
% 6.73/7.07 (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))) (= (@ (@ tptp.times_times_int (@ _let_2 X)) (@ (@ tptp.groups3539618377306564664at_int _let_1) (@ tptp.set_ord_atMost_nat N))) (@ _let_2 (@ _let_1 (@ tptp.suc N))))))))
% 6.73/7.07 (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))) (= (@ (@ tptp.times_times_real (@ _let_2 X)) (@ (@ tptp.groups6591440286371151544t_real _let_1) (@ tptp.set_ord_atMost_nat N))) (@ _let_2 (@ _let_1 (@ tptp.suc N))))))))
% 6.73/7.07 (assert (forall ((C2 (-> tptp.nat tptp.complex)) (N tptp.nat)) (= (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((X4 tptp.complex)) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I tptp.nat)) (@ (@ tptp.times_times_complex (@ C2 I)) (@ (@ tptp.power_power_complex X4) I)))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_complex)))) (exists ((I tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat I) N) (not (= (@ C2 I) tptp.zero_zero_complex)))))))
% 6.73/7.07 (assert (forall ((C2 (-> tptp.nat tptp.real)) (N tptp.nat)) (= (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((X4 tptp.real)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I tptp.nat)) (@ (@ tptp.times_times_real (@ C2 I)) (@ (@ tptp.power_power_real X4) I)))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_real)))) (exists ((I tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat I) N) (not (= (@ C2 I) tptp.zero_zero_real)))))))
% 6.73/7.07 (assert (forall ((C2 (-> tptp.nat tptp.complex)) (K2 tptp.nat) (N tptp.nat)) (=> (not (= (@ C2 K2) tptp.zero_zero_complex)) (=> (@ (@ tptp.ord_less_eq_nat K2) N) (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((Z4 tptp.complex)) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I tptp.nat)) (@ (@ tptp.times_times_complex (@ C2 I)) (@ (@ tptp.power_power_complex Z4) I)))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_complex))))))))
% 6.73/7.07 (assert (forall ((C2 (-> tptp.nat tptp.real)) (K2 tptp.nat) (N tptp.nat)) (=> (not (= (@ C2 K2) tptp.zero_zero_real)) (=> (@ (@ tptp.ord_less_eq_nat K2) N) (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((Z4 tptp.real)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I tptp.nat)) (@ (@ tptp.times_times_real (@ C2 I)) (@ (@ tptp.power_power_real Z4) I)))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_real))))))))
% 6.73/7.07 (assert (forall ((C2 (-> tptp.nat tptp.complex)) (K2 tptp.nat) (N tptp.nat)) (=> (not (= (@ C2 K2) tptp.zero_zero_complex)) (=> (@ (@ tptp.ord_less_eq_nat K2) N) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_complex (@ tptp.collect_complex (lambda ((Z4 tptp.complex)) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I tptp.nat)) (@ (@ tptp.times_times_complex (@ C2 I)) (@ (@ tptp.power_power_complex Z4) I)))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_complex))))) N)))))
% 6.73/7.07 (assert (forall ((C2 (-> tptp.nat tptp.real)) (K2 tptp.nat) (N tptp.nat)) (=> (not (= (@ C2 K2) tptp.zero_zero_real)) (=> (@ (@ tptp.ord_less_eq_nat K2) N) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_real (@ tptp.collect_real (lambda ((Z4 tptp.real)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I tptp.nat)) (@ (@ tptp.times_times_real (@ C2 I)) (@ (@ tptp.power_power_real Z4) I)))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_real))))) N)))))
% 6.73/7.07 (assert (forall ((C2 (-> tptp.nat tptp.complex)) (A tptp.complex) (N tptp.nat)) (=> (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I tptp.nat)) (@ (@ tptp.times_times_complex (@ C2 I)) (@ (@ tptp.power_power_complex A) I)))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_complex) (not (forall ((B3 (-> tptp.nat tptp.complex))) (not (forall ((Z5 tptp.complex)) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I tptp.nat)) (@ (@ tptp.times_times_complex (@ C2 I)) (@ (@ tptp.power_power_complex Z5) I)))) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex Z5) A)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I tptp.nat)) (@ (@ tptp.times_times_complex (@ B3 I)) (@ (@ tptp.power_power_complex Z5) I)))) (@ tptp.set_ord_lessThan_nat N)))))))))))
% 6.73/7.07 (assert (forall ((C2 (-> tptp.nat tptp.rat)) (A tptp.rat) (N tptp.nat)) (=> (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I tptp.nat)) (@ (@ tptp.times_times_rat (@ C2 I)) (@ (@ tptp.power_power_rat A) I)))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_rat) (not (forall ((B3 (-> tptp.nat tptp.rat))) (not (forall ((Z5 tptp.rat)) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I tptp.nat)) (@ (@ tptp.times_times_rat (@ C2 I)) (@ (@ tptp.power_power_rat Z5) I)))) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat Z5) A)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I tptp.nat)) (@ (@ tptp.times_times_rat (@ B3 I)) (@ (@ tptp.power_power_rat Z5) I)))) (@ tptp.set_ord_lessThan_nat N)))))))))))
% 6.73/7.07 (assert (forall ((C2 (-> tptp.nat tptp.int)) (A tptp.int) (N tptp.nat)) (=> (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((I tptp.nat)) (@ (@ tptp.times_times_int (@ C2 I)) (@ (@ tptp.power_power_int A) I)))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_int) (not (forall ((B3 (-> tptp.nat tptp.int))) (not (forall ((Z5 tptp.int)) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((I tptp.nat)) (@ (@ tptp.times_times_int (@ C2 I)) (@ (@ tptp.power_power_int Z5) I)))) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int Z5) A)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I tptp.nat)) (@ (@ tptp.times_times_int (@ B3 I)) (@ (@ tptp.power_power_int Z5) I)))) (@ tptp.set_ord_lessThan_nat N)))))))))))
% 6.73/7.07 (assert (forall ((C2 (-> tptp.nat tptp.real)) (A tptp.real) (N tptp.nat)) (=> (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I tptp.nat)) (@ (@ tptp.times_times_real (@ C2 I)) (@ (@ tptp.power_power_real A) I)))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_real) (not (forall ((B3 (-> tptp.nat tptp.real))) (not (forall ((Z5 tptp.real)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I tptp.nat)) (@ (@ tptp.times_times_real (@ C2 I)) (@ (@ tptp.power_power_real Z5) I)))) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real Z5) A)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I tptp.nat)) (@ (@ tptp.times_times_real (@ B3 I)) (@ (@ tptp.power_power_real Z5) I)))) (@ tptp.set_ord_lessThan_nat N)))))))))))
% 6.73/7.07 (assert (forall ((C2 (-> tptp.nat tptp.complex)) (N tptp.nat) (A tptp.complex)) (exists ((B3 (-> tptp.nat tptp.complex))) (forall ((Z5 tptp.complex)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N))) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I tptp.nat)) (@ (@ tptp.times_times_complex (@ C2 I)) (@ (@ tptp.power_power_complex Z5) I)))) _let_1) (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex Z5) A)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I tptp.nat)) (@ (@ tptp.times_times_complex (@ B3 I)) (@ (@ tptp.power_power_complex Z5) I)))) (@ tptp.set_ord_lessThan_nat N)))) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I tptp.nat)) (@ (@ tptp.times_times_complex (@ C2 I)) (@ (@ tptp.power_power_complex A) I)))) _let_1))))))))
% 6.73/7.07 (assert (forall ((C2 (-> tptp.nat tptp.rat)) (N tptp.nat) (A tptp.rat)) (exists ((B3 (-> tptp.nat tptp.rat))) (forall ((Z5 tptp.rat)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N))) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I tptp.nat)) (@ (@ tptp.times_times_rat (@ C2 I)) (@ (@ tptp.power_power_rat Z5) I)))) _let_1) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat Z5) A)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I tptp.nat)) (@ (@ tptp.times_times_rat (@ B3 I)) (@ (@ tptp.power_power_rat Z5) I)))) (@ tptp.set_ord_lessThan_nat N)))) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I tptp.nat)) (@ (@ tptp.times_times_rat (@ C2 I)) (@ (@ tptp.power_power_rat A) I)))) _let_1))))))))
% 6.73/7.07 (assert (forall ((C2 (-> tptp.nat tptp.int)) (N tptp.nat) (A tptp.int)) (exists ((B3 (-> tptp.nat tptp.int))) (forall ((Z5 tptp.int)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N))) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((I tptp.nat)) (@ (@ tptp.times_times_int (@ C2 I)) (@ (@ tptp.power_power_int Z5) I)))) _let_1) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int Z5) A)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I tptp.nat)) (@ (@ tptp.times_times_int (@ B3 I)) (@ (@ tptp.power_power_int Z5) I)))) (@ tptp.set_ord_lessThan_nat N)))) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I tptp.nat)) (@ (@ tptp.times_times_int (@ C2 I)) (@ (@ tptp.power_power_int A) I)))) _let_1))))))))
% 6.73/7.07 (assert (forall ((C2 (-> tptp.nat tptp.real)) (N tptp.nat) (A tptp.real)) (exists ((B3 (-> tptp.nat tptp.real))) (forall ((Z5 tptp.real)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N))) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I tptp.nat)) (@ (@ tptp.times_times_real (@ C2 I)) (@ (@ tptp.power_power_real Z5) I)))) _let_1) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real Z5) A)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I tptp.nat)) (@ (@ tptp.times_times_real (@ B3 I)) (@ (@ tptp.power_power_real Z5) I)))) (@ tptp.set_ord_lessThan_nat N)))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I tptp.nat)) (@ (@ tptp.times_times_real (@ C2 I)) (@ (@ tptp.power_power_real A) I)))) _let_1))))))))
% 6.73/7.07 (assert (forall ((M2 tptp.nat) (N tptp.nat) (X tptp.complex)) (let ((_let_1 (@ tptp.power_power_complex X))) (let ((_let_2 (@ tptp.groups2073611262835488442omplex _let_1))) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ _let_2 (@ (@ tptp.set_or1269000886237332187st_nat M2) N)) (@ (@ tptp.times_times_complex (@ _let_1 M2)) (@ _let_2 (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat N) M2))))))))))
% 6.73/7.07 (assert (forall ((M2 tptp.nat) (N tptp.nat) (X tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat X))) (let ((_let_2 (@ tptp.groups2906978787729119204at_rat _let_1))) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ _let_2 (@ (@ tptp.set_or1269000886237332187st_nat M2) N)) (@ (@ tptp.times_times_rat (@ _let_1 M2)) (@ _let_2 (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat N) M2))))))))))
% 6.73/7.07 (assert (forall ((M2 tptp.nat) (N tptp.nat) (X tptp.int)) (let ((_let_1 (@ tptp.power_power_int X))) (let ((_let_2 (@ tptp.groups3539618377306564664at_int _let_1))) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ _let_2 (@ (@ tptp.set_or1269000886237332187st_nat M2) N)) (@ (@ tptp.times_times_int (@ _let_1 M2)) (@ _let_2 (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat N) M2))))))))))
% 6.73/7.07 (assert (forall ((M2 tptp.nat) (N tptp.nat) (X tptp.real)) (let ((_let_1 (@ tptp.power_power_real X))) (let ((_let_2 (@ tptp.groups6591440286371151544t_real _let_1))) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ _let_2 (@ (@ tptp.set_or1269000886237332187st_nat M2) N)) (@ (@ tptp.times_times_real (@ _let_1 M2)) (@ _let_2 (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat N) M2))))))))))
% 6.73/7.07 (assert (forall ((A tptp.nat) (B tptp.nat) (N tptp.nat)) (= (@ (@ tptp.power_power_nat (@ (@ tptp.plus_plus_nat A) B)) N) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_nat (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.binomial N) K3))) (@ (@ tptp.power_power_nat A) K3))) (@ (@ tptp.power_power_nat B) (@ (@ tptp.minus_minus_nat N) K3))))) (@ tptp.set_ord_atMost_nat N)))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_7079662738309270450atural (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 M2))) (= (@ (@ tptp.modulo8411746178871703098atural _let_2) (@ _let_1 N)) (@ (@ tptp.times_2397367101498566445atural (@ tptp.zero_n8403883297036319079atural (@ (@ tptp.ord_less_nat M2) N))) _let_2))))))
% 6.73/7.07 (assert (forall ((M2 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 M2))) (= (@ (@ tptp.modulo_modulo_nat _let_2) (@ _let_1 N)) (@ (@ tptp.times_times_nat (@ tptp.zero_n2687167440665602831ol_nat (@ (@ tptp.ord_less_nat M2) N))) _let_2))))))
% 6.73/7.07 (assert (forall ((M2 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 M2))) (= (@ (@ tptp.modulo_modulo_int _let_2) (@ _let_1 N)) (@ (@ tptp.times_times_int (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.ord_less_nat M2) N))) _let_2))))))
% 6.73/7.07 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 M2))) (= (@ (@ tptp.modulo364778990260209775nteger _let_2) (@ _let_1 N)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.zero_n356916108424825756nteger (@ (@ tptp.ord_less_nat M2) N))) _let_2))))))
% 6.73/7.07 (assert (forall ((K2 tptp.nat) (A tptp.complex)) (let ((_let_1 (@ tptp.gbinomial_complex (@ (@ tptp.minus_minus_complex A) tptp.one_one_complex)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K2) (= (@ (@ tptp.gbinomial_complex A) K2) (@ (@ tptp.plus_plus_complex (@ _let_1 (@ (@ tptp.minus_minus_nat K2) tptp.one_one_nat))) (@ _let_1 K2)))))))
% 6.73/7.07 (assert (forall ((K2 tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.gbinomial_real (@ (@ tptp.minus_minus_real A) tptp.one_one_real)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K2) (= (@ (@ tptp.gbinomial_real A) K2) (@ (@ tptp.plus_plus_real (@ _let_1 (@ (@ tptp.minus_minus_nat K2) tptp.one_one_nat))) (@ _let_1 K2)))))))
% 6.73/7.07 (assert (forall ((K2 tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.gbinomial_rat (@ (@ tptp.minus_minus_rat A) tptp.one_one_rat)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K2) (= (@ (@ tptp.gbinomial_rat A) K2) (@ (@ tptp.plus_plus_rat (@ _let_1 (@ (@ tptp.minus_minus_nat K2) tptp.one_one_nat))) (@ _let_1 K2)))))))
% 6.73/7.07 (assert (forall ((G2 (-> tptp.nat tptp.rat)) (N tptp.nat)) (= (@ (@ tptp.groups2906978787729119204at_rat G2) (@ tptp.set_ord_atMost_nat (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I))) (@ (@ tptp.plus_plus_rat (@ G2 _let_1)) (@ G2 (@ tptp.suc _let_1)))))) (@ tptp.set_ord_atMost_nat N)))))
% 6.73/7.07 (assert (forall ((G2 (-> tptp.nat tptp.int)) (N tptp.nat)) (= (@ (@ tptp.groups3539618377306564664at_int G2) (@ tptp.set_ord_atMost_nat (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I))) (@ (@ tptp.plus_plus_int (@ G2 _let_1)) (@ G2 (@ tptp.suc _let_1)))))) (@ tptp.set_ord_atMost_nat N)))))
% 6.73/7.07 (assert (forall ((G2 (-> tptp.nat tptp.nat)) (N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat G2) (@ tptp.set_ord_atMost_nat (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I))) (@ (@ tptp.plus_plus_nat (@ G2 _let_1)) (@ G2 (@ tptp.suc _let_1)))))) (@ tptp.set_ord_atMost_nat N)))))
% 6.73/7.07 (assert (forall ((G2 (-> tptp.nat tptp.real)) (N tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real G2) (@ tptp.set_ord_atMost_nat (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I))) (@ (@ tptp.plus_plus_real (@ G2 _let_1)) (@ G2 (@ tptp.suc _let_1)))))) (@ tptp.set_ord_atMost_nat N)))))
% 6.73/7.07 (assert (forall ((C2 (-> tptp.nat tptp.complex)) (K2 tptp.nat) (N tptp.nat)) (=> (not (= (@ C2 K2) tptp.zero_zero_complex)) (=> (@ (@ tptp.ord_less_eq_nat K2) N) (and (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((Z4 tptp.complex)) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I tptp.nat)) (@ (@ tptp.times_times_complex (@ C2 I)) (@ (@ tptp.power_power_complex Z4) I)))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_complex)))) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_complex (@ tptp.collect_complex (lambda ((Z4 tptp.complex)) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I tptp.nat)) (@ (@ tptp.times_times_complex (@ C2 I)) (@ (@ tptp.power_power_complex Z4) I)))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_complex))))) N))))))
% 6.73/7.07 (assert (forall ((C2 (-> tptp.nat tptp.real)) (K2 tptp.nat) (N tptp.nat)) (=> (not (= (@ C2 K2) tptp.zero_zero_real)) (=> (@ (@ tptp.ord_less_eq_nat K2) N) (and (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((Z4 tptp.real)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I tptp.nat)) (@ (@ tptp.times_times_real (@ C2 I)) (@ (@ tptp.power_power_real Z4) I)))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_real)))) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_real (@ tptp.collect_real (lambda ((Z4 tptp.real)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I tptp.nat)) (@ (@ tptp.times_times_real (@ C2 I)) (@ (@ tptp.power_power_real Z4) I)))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_real))))) N))))))
% 6.73/7.07 (assert (forall ((M2 tptp.nat) (A (-> tptp.nat tptp.complex)) (N tptp.nat) (B (-> tptp.nat tptp.complex)) (X tptp.complex)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) I3) (= (@ A I3) tptp.zero_zero_complex))) (=> (forall ((J3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) J3) (= (@ B J3) tptp.zero_zero_complex))) (= (@ (@ tptp.times_times_complex (@ (@ tptp.groups2073611262835488442omplex (lambda ((I tptp.nat)) (@ (@ tptp.times_times_complex (@ A I)) (@ (@ tptp.power_power_complex X) I)))) (@ tptp.set_ord_atMost_nat M2))) (@ (@ tptp.groups2073611262835488442omplex (lambda ((J tptp.nat)) (@ (@ tptp.times_times_complex (@ B J)) (@ (@ tptp.power_power_complex X) J)))) (@ tptp.set_ord_atMost_nat N))) (@ (@ tptp.groups2073611262835488442omplex (lambda ((R tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.groups2073611262835488442omplex (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_complex (@ A K3)) (@ B (@ (@ tptp.minus_minus_nat R) K3))))) (@ tptp.set_ord_atMost_nat R))) (@ (@ tptp.power_power_complex X) R)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.plus_plus_nat M2) N))))))))
% 6.73/7.07 (assert (forall ((M2 tptp.nat) (A (-> tptp.nat tptp.rat)) (N tptp.nat) (B (-> tptp.nat tptp.rat)) (X tptp.rat)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) I3) (= (@ A I3) tptp.zero_zero_rat))) (=> (forall ((J3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) J3) (= (@ B J3) tptp.zero_zero_rat))) (= (@ (@ tptp.times_times_rat (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I tptp.nat)) (@ (@ tptp.times_times_rat (@ A I)) (@ (@ tptp.power_power_rat X) I)))) (@ tptp.set_ord_atMost_nat M2))) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((J tptp.nat)) (@ (@ tptp.times_times_rat (@ B J)) (@ (@ tptp.power_power_rat X) J)))) (@ tptp.set_ord_atMost_nat N))) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((R tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_rat (@ A K3)) (@ B (@ (@ tptp.minus_minus_nat R) K3))))) (@ tptp.set_ord_atMost_nat R))) (@ (@ tptp.power_power_rat X) R)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.plus_plus_nat M2) N))))))))
% 6.73/7.07 (assert (forall ((M2 tptp.nat) (A (-> tptp.nat tptp.int)) (N tptp.nat) (B (-> tptp.nat tptp.int)) (X tptp.int)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) I3) (= (@ A I3) tptp.zero_zero_int))) (=> (forall ((J3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) J3) (= (@ B J3) tptp.zero_zero_int))) (= (@ (@ tptp.times_times_int (@ (@ tptp.groups3539618377306564664at_int (lambda ((I tptp.nat)) (@ (@ tptp.times_times_int (@ A I)) (@ (@ tptp.power_power_int X) I)))) (@ tptp.set_ord_atMost_nat M2))) (@ (@ tptp.groups3539618377306564664at_int (lambda ((J tptp.nat)) (@ (@ tptp.times_times_int (@ B J)) (@ (@ tptp.power_power_int X) J)))) (@ tptp.set_ord_atMost_nat N))) (@ (@ tptp.groups3539618377306564664at_int (lambda ((R tptp.nat)) (@ (@ tptp.times_times_int (@ (@ tptp.groups3539618377306564664at_int (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_int (@ A K3)) (@ B (@ (@ tptp.minus_minus_nat R) K3))))) (@ tptp.set_ord_atMost_nat R))) (@ (@ tptp.power_power_int X) R)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.plus_plus_nat M2) N))))))))
% 6.73/7.07 (assert (forall ((M2 tptp.nat) (A (-> tptp.nat tptp.real)) (N tptp.nat) (B (-> tptp.nat tptp.real)) (X tptp.real)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) I3) (= (@ A I3) tptp.zero_zero_real))) (=> (forall ((J3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) J3) (= (@ B J3) tptp.zero_zero_real))) (= (@ (@ tptp.times_times_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((I tptp.nat)) (@ (@ tptp.times_times_real (@ A I)) (@ (@ tptp.power_power_real X) I)))) (@ tptp.set_ord_atMost_nat M2))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((J tptp.nat)) (@ (@ tptp.times_times_real (@ B J)) (@ (@ tptp.power_power_real X) J)))) (@ tptp.set_ord_atMost_nat N))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((R tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_real (@ A K3)) (@ B (@ (@ tptp.minus_minus_nat R) K3))))) (@ tptp.set_ord_atMost_nat R))) (@ (@ tptp.power_power_real X) R)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.plus_plus_nat M2) N))))))))
% 6.73/7.07 (assert (forall ((G2 (-> tptp.nat tptp.real)) (N tptp.nat)) (= (@ (@ tptp.groups129246275422532515t_real G2) (@ tptp.set_ord_atMost_nat (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))) (@ (@ tptp.groups129246275422532515t_real (lambda ((I tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I))) (@ (@ tptp.times_times_real (@ G2 _let_1)) (@ G2 (@ tptp.suc _let_1)))))) (@ tptp.set_ord_atMost_nat N)))))
% 6.73/7.07 (assert (forall ((G2 (-> tptp.nat tptp.rat)) (N tptp.nat)) (= (@ (@ tptp.groups73079841787564623at_rat G2) (@ tptp.set_ord_atMost_nat (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))) (@ (@ tptp.groups73079841787564623at_rat (lambda ((I tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I))) (@ (@ tptp.times_times_rat (@ G2 _let_1)) (@ G2 (@ tptp.suc _let_1)))))) (@ tptp.set_ord_atMost_nat N)))))
% 6.73/7.07 (assert (forall ((G2 (-> tptp.nat tptp.int)) (N tptp.nat)) (= (@ (@ tptp.groups705719431365010083at_int G2) (@ tptp.set_ord_atMost_nat (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))) (@ (@ tptp.groups705719431365010083at_int (lambda ((I tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I))) (@ (@ tptp.times_times_int (@ G2 _let_1)) (@ G2 (@ tptp.suc _let_1)))))) (@ tptp.set_ord_atMost_nat N)))))
% 6.73/7.07 (assert (forall ((G2 (-> tptp.nat tptp.nat)) (N tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat G2) (@ tptp.set_ord_atMost_nat (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I))) (@ (@ tptp.times_times_nat (@ G2 _let_1)) (@ G2 (@ tptp.suc _let_1)))))) (@ tptp.set_ord_atMost_nat N)))))
% 6.73/7.07 (assert (forall ((C2 (-> tptp.nat tptp.complex)) (N tptp.nat) (K2 tptp.complex)) (= (forall ((X4 tptp.complex)) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I tptp.nat)) (@ (@ tptp.times_times_complex (@ C2 I)) (@ (@ tptp.power_power_complex X4) I)))) (@ tptp.set_ord_atMost_nat N)) K2)) (and (= (@ C2 tptp.zero_zero_nat) K2) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N)) (= (@ C2 X4) tptp.zero_zero_complex)))))))
% 6.73/7.07 (assert (forall ((C2 (-> tptp.nat tptp.real)) (N tptp.nat) (K2 tptp.real)) (= (forall ((X4 tptp.real)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I tptp.nat)) (@ (@ tptp.times_times_real (@ C2 I)) (@ (@ tptp.power_power_real X4) I)))) (@ tptp.set_ord_atMost_nat N)) K2)) (and (= (@ C2 tptp.zero_zero_nat) K2) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N)) (= (@ C2 X4) tptp.zero_zero_real)))))))
% 6.73/7.07 (assert (forall ((A tptp.complex) (B tptp.complex) (N tptp.nat)) (= (@ (@ tptp.power_power_complex (@ (@ tptp.plus_plus_complex A) B)) N) (@ (@ tptp.groups2073611262835488442omplex (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.binomial N) K3))) (@ (@ tptp.power_power_complex A) K3))) (@ (@ tptp.power_power_complex B) (@ (@ tptp.minus_minus_nat N) K3))))) (@ tptp.set_ord_atMost_nat N)))))
% 6.73/7.07 (assert (forall ((A tptp.rat) (B tptp.rat) (N tptp.nat)) (= (@ (@ tptp.power_power_rat (@ (@ tptp.plus_plus_rat A) B)) N) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.binomial N) K3))) (@ (@ tptp.power_power_rat A) K3))) (@ (@ tptp.power_power_rat B) (@ (@ tptp.minus_minus_nat N) K3))))) (@ tptp.set_ord_atMost_nat N)))))
% 6.73/7.07 (assert (forall ((A tptp.int) (B tptp.int) (N tptp.nat)) (= (@ (@ tptp.power_power_int (@ (@ tptp.plus_plus_int A) B)) N) (@ (@ tptp.groups3539618377306564664at_int (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.binomial N) K3))) (@ (@ tptp.power_power_int A) K3))) (@ (@ tptp.power_power_int B) (@ (@ tptp.minus_minus_nat N) K3))))) (@ tptp.set_ord_atMost_nat N)))))
% 6.73/7.07 (assert (forall ((A tptp.nat) (B tptp.nat) (N tptp.nat)) (= (@ (@ tptp.power_power_nat (@ (@ tptp.plus_plus_nat A) B)) N) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_nat (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.binomial N) K3))) (@ (@ tptp.power_power_nat A) K3))) (@ (@ tptp.power_power_nat B) (@ (@ tptp.minus_minus_nat N) K3))))) (@ tptp.set_ord_atMost_nat N)))))
% 6.73/7.07 (assert (forall ((A tptp.real) (B tptp.real) (N tptp.nat)) (= (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real A) B)) N) (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.binomial N) K3))) (@ (@ tptp.power_power_real A) K3))) (@ (@ tptp.power_power_real B) (@ (@ tptp.minus_minus_nat N) K3))))) (@ tptp.set_ord_atMost_nat N)))))
% 6.73/7.07 (assert (forall ((A tptp.rat) (B tptp.rat) (N tptp.nat)) (= (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.plus_plus_rat A) B)) N) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.binomial N) K3))) (@ (@ tptp.comm_s4028243227959126397er_rat A) K3))) (@ (@ tptp.comm_s4028243227959126397er_rat B) (@ (@ tptp.minus_minus_nat N) K3))))) (@ tptp.set_ord_atMost_nat N)))))
% 6.73/7.07 (assert (forall ((A tptp.int) (B tptp.int) (N tptp.nat)) (= (@ (@ tptp.comm_s4660882817536571857er_int (@ (@ tptp.plus_plus_int A) B)) N) (@ (@ tptp.groups3539618377306564664at_int (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.binomial N) K3))) (@ (@ tptp.comm_s4660882817536571857er_int A) K3))) (@ (@ tptp.comm_s4660882817536571857er_int B) (@ (@ tptp.minus_minus_nat N) K3))))) (@ tptp.set_ord_atMost_nat N)))))
% 6.73/7.07 (assert (forall ((A tptp.real) (B tptp.real) (N tptp.nat)) (= (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.plus_plus_real A) B)) N) (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.binomial N) K3))) (@ (@ tptp.comm_s7457072308508201937r_real A) K3))) (@ (@ tptp.comm_s7457072308508201937r_real B) (@ (@ tptp.minus_minus_nat N) K3))))) (@ tptp.set_ord_atMost_nat N)))))
% 6.73/7.07 (assert (forall ((M2 tptp.nat) (A (-> tptp.nat tptp.nat)) (N tptp.nat) (B (-> tptp.nat tptp.nat)) (X tptp.nat)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) I3) (= (@ A I3) tptp.zero_zero_nat))) (=> (forall ((J3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) J3) (= (@ B J3) tptp.zero_zero_nat))) (= (@ (@ tptp.times_times_nat (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I tptp.nat)) (@ (@ tptp.times_times_nat (@ A I)) (@ (@ tptp.power_power_nat X) I)))) (@ tptp.set_ord_atMost_nat M2))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((J tptp.nat)) (@ (@ tptp.times_times_nat (@ B J)) (@ (@ tptp.power_power_nat X) J)))) (@ tptp.set_ord_atMost_nat N))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((R tptp.nat)) (@ (@ tptp.times_times_nat (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_nat (@ A K3)) (@ B (@ (@ tptp.minus_minus_nat R) K3))))) (@ tptp.set_ord_atMost_nat R))) (@ (@ tptp.power_power_nat X) R)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.plus_plus_nat M2) N))))))))
% 6.73/7.07 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K3 tptp.nat)) (@ (@ tptp.power_power_nat (@ (@ tptp.binomial N) K3)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.binomial (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) N))))
% 6.73/7.07 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (N tptp.nat) (X tptp.vEBT_VEBT)) (=> (@ tptp.distinct_VEBT_VEBT Xs2) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (= (@ tptp.set_VEBT_VEBT2 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs2) N) X)) (@ (@ tptp.insert_VEBT_VEBT X) (@ (@ tptp.minus_5127226145743854075T_VEBT (@ tptp.set_VEBT_VEBT2 Xs2)) (@ (@ tptp.insert_VEBT_VEBT (@ (@ tptp.nth_VEBT_VEBT Xs2) N)) tptp.bot_bo8194388402131092736T_VEBT))))))))
% 6.73/7.07 (assert (forall ((Xs2 tptp.list_o) (N tptp.nat) (X Bool)) (=> (@ tptp.distinct_o Xs2) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_o Xs2)) (= (@ tptp.set_o2 (@ (@ (@ tptp.list_update_o Xs2) N) X)) (@ (@ tptp.insert_o X) (@ (@ tptp.minus_minus_set_o (@ tptp.set_o2 Xs2)) (@ (@ tptp.insert_o (@ (@ tptp.nth_o Xs2) N)) tptp.bot_bot_set_o))))))))
% 6.73/7.07 (assert (forall ((Xs2 tptp.list_int) (N tptp.nat) (X tptp.int)) (=> (@ tptp.distinct_int Xs2) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_int Xs2)) (= (@ tptp.set_int2 (@ (@ (@ tptp.list_update_int Xs2) N) X)) (@ (@ tptp.insert_int X) (@ (@ tptp.minus_minus_set_int (@ tptp.set_int2 Xs2)) (@ (@ tptp.insert_int (@ (@ tptp.nth_int Xs2) N)) tptp.bot_bot_set_int))))))))
% 6.73/7.07 (assert (forall ((Xs2 tptp.list_real) (N tptp.nat) (X tptp.real)) (=> (@ tptp.distinct_real Xs2) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_real Xs2)) (= (@ tptp.set_real2 (@ (@ (@ tptp.list_update_real Xs2) N) X)) (@ (@ tptp.insert_real X) (@ (@ tptp.minus_minus_set_real (@ tptp.set_real2 Xs2)) (@ (@ tptp.insert_real (@ (@ tptp.nth_real Xs2) N)) tptp.bot_bot_set_real))))))))
% 6.73/7.07 (assert (forall ((Xs2 tptp.list_P6011104703257516679at_nat) (N tptp.nat) (X tptp.product_prod_nat_nat)) (=> (@ tptp.distin6923225563576452346at_nat Xs2) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s5460976970255530739at_nat Xs2)) (= (@ tptp.set_Pr5648618587558075414at_nat (@ (@ (@ tptp.list_u6180841689913720943at_nat Xs2) N) X)) (@ (@ tptp.insert8211810215607154385at_nat X) (@ (@ tptp.minus_1356011639430497352at_nat (@ tptp.set_Pr5648618587558075414at_nat Xs2)) (@ (@ tptp.insert8211810215607154385at_nat (@ (@ tptp.nth_Pr7617993195940197384at_nat Xs2) N)) tptp.bot_bo2099793752762293965at_nat))))))))
% 6.73/7.07 (assert (forall ((Xs2 tptp.list_nat) (N tptp.nat) (X tptp.nat)) (=> (@ tptp.distinct_nat Xs2) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_nat Xs2)) (= (@ tptp.set_nat2 (@ (@ (@ tptp.list_update_nat Xs2) N) X)) (@ (@ tptp.insert_nat X) (@ (@ tptp.minus_minus_set_nat (@ tptp.set_nat2 Xs2)) (@ (@ tptp.insert_nat (@ (@ tptp.nth_nat Xs2) N)) tptp.bot_bot_set_nat))))))))
% 6.73/7.07 (assert (forall ((P tptp.nat) (K2 tptp.nat) (G2 (-> tptp.nat tptp.complex)) (H (-> tptp.nat tptp.complex))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) P) (=> (@ (@ tptp.ord_less_eq_nat K2) P) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((J tptp.nat)) (@ (@ (@ tptp.if_complex (@ (@ tptp.ord_less_nat J) K2)) (@ G2 J)) (@ (@ (@ tptp.if_complex (= J K2)) tptp.zero_zero_complex) (@ H (@ (@ tptp.minus_minus_nat J) (@ tptp.suc tptp.zero_zero_nat))))))) (@ tptp.set_ord_atMost_nat P)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((J tptp.nat)) (@ (@ (@ tptp.if_complex (@ (@ tptp.ord_less_nat J) K2)) (@ G2 J)) (@ H J)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat P) (@ tptp.suc tptp.zero_zero_nat)))))))))
% 6.73/7.07 (assert (forall ((P tptp.nat) (K2 tptp.nat) (G2 (-> tptp.nat tptp.rat)) (H (-> tptp.nat tptp.rat))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) P) (=> (@ (@ tptp.ord_less_eq_nat K2) P) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((J tptp.nat)) (@ (@ (@ tptp.if_rat (@ (@ tptp.ord_less_nat J) K2)) (@ G2 J)) (@ (@ (@ tptp.if_rat (= J K2)) tptp.zero_zero_rat) (@ H (@ (@ tptp.minus_minus_nat J) (@ tptp.suc tptp.zero_zero_nat))))))) (@ tptp.set_ord_atMost_nat P)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((J tptp.nat)) (@ (@ (@ tptp.if_rat (@ (@ tptp.ord_less_nat J) K2)) (@ G2 J)) (@ H J)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat P) (@ tptp.suc tptp.zero_zero_nat)))))))))
% 6.73/7.07 (assert (forall ((P tptp.nat) (K2 tptp.nat) (G2 (-> tptp.nat tptp.int)) (H (-> tptp.nat tptp.int))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) P) (=> (@ (@ tptp.ord_less_eq_nat K2) P) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((J tptp.nat)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_nat J) K2)) (@ G2 J)) (@ (@ (@ tptp.if_int (= J K2)) tptp.zero_zero_int) (@ H (@ (@ tptp.minus_minus_nat J) (@ tptp.suc tptp.zero_zero_nat))))))) (@ tptp.set_ord_atMost_nat P)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((J tptp.nat)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_nat J) K2)) (@ G2 J)) (@ H J)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat P) (@ tptp.suc tptp.zero_zero_nat)))))))))
% 6.73/7.07 (assert (forall ((P tptp.nat) (K2 tptp.nat) (G2 (-> tptp.nat tptp.nat)) (H (-> tptp.nat tptp.nat))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) P) (=> (@ (@ tptp.ord_less_eq_nat K2) P) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((J tptp.nat)) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat J) K2)) (@ G2 J)) (@ (@ (@ tptp.if_nat (= J K2)) tptp.zero_zero_nat) (@ H (@ (@ tptp.minus_minus_nat J) (@ tptp.suc tptp.zero_zero_nat))))))) (@ tptp.set_ord_atMost_nat P)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((J tptp.nat)) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat J) K2)) (@ G2 J)) (@ H J)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat P) (@ tptp.suc tptp.zero_zero_nat)))))))))
% 6.73/7.07 (assert (forall ((P tptp.nat) (K2 tptp.nat) (G2 (-> tptp.nat tptp.real)) (H (-> tptp.nat tptp.real))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) P) (=> (@ (@ tptp.ord_less_eq_nat K2) P) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((J tptp.nat)) (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_nat J) K2)) (@ G2 J)) (@ (@ (@ tptp.if_real (= J K2)) tptp.zero_zero_real) (@ H (@ (@ tptp.minus_minus_nat J) (@ tptp.suc tptp.zero_zero_nat))))))) (@ tptp.set_ord_atMost_nat P)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((J tptp.nat)) (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_nat J) K2)) (@ G2 J)) (@ H J)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat P) (@ tptp.suc tptp.zero_zero_nat)))))))))
% 6.73/7.07 (assert (forall ((P tptp.nat) (K2 tptp.nat) (G2 (-> tptp.nat tptp.code_integer)) (H (-> tptp.nat tptp.code_integer))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) P) (=> (@ (@ tptp.ord_less_eq_nat K2) P) (= (@ (@ tptp.groups3455450783089532116nteger (lambda ((J tptp.nat)) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.ord_less_nat J) K2)) (@ G2 J)) (@ (@ (@ tptp.if_Code_integer (= J K2)) tptp.one_one_Code_integer) (@ H (@ (@ tptp.minus_minus_nat J) (@ tptp.suc tptp.zero_zero_nat))))))) (@ tptp.set_ord_atMost_nat P)) (@ (@ tptp.groups3455450783089532116nteger (lambda ((J tptp.nat)) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.ord_less_nat J) K2)) (@ G2 J)) (@ H J)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat P) (@ tptp.suc tptp.zero_zero_nat)))))))))
% 6.73/7.07 (assert (forall ((P tptp.nat) (K2 tptp.nat) (G2 (-> tptp.nat tptp.complex)) (H (-> tptp.nat tptp.complex))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) P) (=> (@ (@ tptp.ord_less_eq_nat K2) P) (= (@ (@ tptp.groups6464643781859351333omplex (lambda ((J tptp.nat)) (@ (@ (@ tptp.if_complex (@ (@ tptp.ord_less_nat J) K2)) (@ G2 J)) (@ (@ (@ tptp.if_complex (= J K2)) tptp.one_one_complex) (@ H (@ (@ tptp.minus_minus_nat J) (@ tptp.suc tptp.zero_zero_nat))))))) (@ tptp.set_ord_atMost_nat P)) (@ (@ tptp.groups6464643781859351333omplex (lambda ((J tptp.nat)) (@ (@ (@ tptp.if_complex (@ (@ tptp.ord_less_nat J) K2)) (@ G2 J)) (@ H J)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat P) (@ tptp.suc tptp.zero_zero_nat)))))))))
% 6.73/7.07 (assert (forall ((P tptp.nat) (K2 tptp.nat) (G2 (-> tptp.nat tptp.real)) (H (-> tptp.nat tptp.real))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) P) (=> (@ (@ tptp.ord_less_eq_nat K2) P) (= (@ (@ tptp.groups129246275422532515t_real (lambda ((J tptp.nat)) (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_nat J) K2)) (@ G2 J)) (@ (@ (@ tptp.if_real (= J K2)) tptp.one_one_real) (@ H (@ (@ tptp.minus_minus_nat J) (@ tptp.suc tptp.zero_zero_nat))))))) (@ tptp.set_ord_atMost_nat P)) (@ (@ tptp.groups129246275422532515t_real (lambda ((J tptp.nat)) (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_nat J) K2)) (@ G2 J)) (@ H J)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat P) (@ tptp.suc tptp.zero_zero_nat)))))))))
% 6.73/7.07 (assert (forall ((P tptp.nat) (K2 tptp.nat) (G2 (-> tptp.nat tptp.int)) (H (-> tptp.nat tptp.int))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) P) (=> (@ (@ tptp.ord_less_eq_nat K2) P) (= (@ (@ tptp.groups705719431365010083at_int (lambda ((J tptp.nat)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_nat J) K2)) (@ G2 J)) (@ (@ (@ tptp.if_int (= J K2)) tptp.one_one_int) (@ H (@ (@ tptp.minus_minus_nat J) (@ tptp.suc tptp.zero_zero_nat))))))) (@ tptp.set_ord_atMost_nat P)) (@ (@ tptp.groups705719431365010083at_int (lambda ((J tptp.nat)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_nat J) K2)) (@ G2 J)) (@ H J)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat P) (@ tptp.suc tptp.zero_zero_nat)))))))))
% 6.73/7.07 (assert (forall ((P tptp.nat) (K2 tptp.nat) (G2 (-> tptp.nat tptp.nat)) (H (-> tptp.nat tptp.nat))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) P) (=> (@ (@ tptp.ord_less_eq_nat K2) P) (= (@ (@ tptp.groups708209901874060359at_nat (lambda ((J tptp.nat)) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat J) K2)) (@ G2 J)) (@ (@ (@ tptp.if_nat (= J K2)) tptp.one_one_nat) (@ H (@ (@ tptp.minus_minus_nat J) (@ tptp.suc tptp.zero_zero_nat))))))) (@ tptp.set_ord_atMost_nat P)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((J tptp.nat)) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat J) K2)) (@ G2 J)) (@ H J)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat P) (@ tptp.suc tptp.zero_zero_nat)))))))))
% 6.73/7.07 (assert (forall ((K2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((J tptp.nat)) (@ (@ tptp.gbinomial_complex (@ tptp.semiri8010041392384452111omplex J)) K2))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)) (@ (@ tptp.gbinomial_complex (@ (@ tptp.plus_plus_complex (@ tptp.semiri8010041392384452111omplex N)) tptp.one_one_complex)) (@ (@ tptp.plus_plus_nat K2) tptp.one_one_nat)))))
% 6.73/7.07 (assert (forall ((K2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((J tptp.nat)) (@ (@ tptp.gbinomial_rat (@ tptp.semiri681578069525770553at_rat J)) K2))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)) (@ (@ tptp.gbinomial_rat (@ (@ tptp.plus_plus_rat (@ tptp.semiri681578069525770553at_rat N)) tptp.one_one_rat)) (@ (@ tptp.plus_plus_nat K2) tptp.one_one_nat)))))
% 6.73/7.07 (assert (forall ((K2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((J tptp.nat)) (@ (@ tptp.gbinomial_real (@ tptp.semiri5074537144036343181t_real J)) K2))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)) (@ (@ tptp.gbinomial_real (@ (@ tptp.plus_plus_real (@ tptp.semiri5074537144036343181t_real N)) tptp.one_one_real)) (@ (@ tptp.plus_plus_nat K2) tptp.one_one_nat)))))
% 6.73/7.07 (assert (forall ((M2 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 M2))) (= (@ (@ 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) M2)))) (@ _let_1 (@ (@ tptp.minus_minus_nat M2) N))))))))
% 6.73/7.07 (assert (forall ((M2 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 M2))) (= (@ (@ 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) M2)))) (@ _let_1 (@ (@ tptp.minus_minus_nat M2) N))))))))
% 6.73/7.07 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 M2))) (= (@ (@ 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) M2)))) (@ _let_1 (@ (@ tptp.minus_minus_nat M2) N))))))))
% 6.73/7.07 (assert (forall ((K2 tptp.nat) (A tptp.complex)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K2) (= (@ (@ tptp.gbinomial_complex A) K2) (@ (@ tptp.times_times_complex (@ (@ tptp.divide1717551699836669952omplex A) (@ tptp.semiri8010041392384452111omplex K2))) (@ (@ tptp.gbinomial_complex (@ (@ tptp.minus_minus_complex A) tptp.one_one_complex)) (@ (@ tptp.minus_minus_nat K2) tptp.one_one_nat)))))))
% 6.73/7.07 (assert (forall ((K2 tptp.nat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K2) (= (@ (@ tptp.gbinomial_rat A) K2) (@ (@ tptp.times_times_rat (@ (@ tptp.divide_divide_rat A) (@ tptp.semiri681578069525770553at_rat K2))) (@ (@ tptp.gbinomial_rat (@ (@ tptp.minus_minus_rat A) tptp.one_one_rat)) (@ (@ tptp.minus_minus_nat K2) tptp.one_one_nat)))))))
% 6.73/7.07 (assert (forall ((K2 tptp.nat) (A tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K2) (= (@ (@ tptp.gbinomial_real A) K2) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real A) (@ tptp.semiri5074537144036343181t_real K2))) (@ (@ tptp.gbinomial_real (@ (@ tptp.minus_minus_real A) tptp.one_one_real)) (@ (@ tptp.minus_minus_nat K2) tptp.one_one_nat)))))))
% 6.73/7.07 (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_atMost_nat N)))) (let ((_let_4 (= X tptp.one_one_complex))) (and (=> _let_4 (= _let_3 (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat)))) (=> (not _let_4) (= _let_3 (@ (@ tptp.divide1717551699836669952omplex (@ _let_1 (@ _let_2 (@ tptp.suc N)))) (@ _let_1 X)))))))))))
% 6.73/7.07 (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_atMost_nat N)))) (let ((_let_4 (= X tptp.one_one_rat))) (and (=> _let_4 (= _let_3 (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat)))) (=> (not _let_4) (= _let_3 (@ (@ tptp.divide_divide_rat (@ _let_1 (@ _let_2 (@ tptp.suc N)))) (@ _let_1 X)))))))))))
% 6.73/7.07 (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_atMost_nat N)))) (let ((_let_4 (= X tptp.one_one_real))) (and (=> _let_4 (= _let_3 (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat)))) (=> (not _let_4) (= _let_3 (@ (@ tptp.divide_divide_real (@ _let_1 (@ _let_2 (@ tptp.suc N)))) (@ _let_1 X)))))))))))
% 6.73/7.07 (assert (forall ((N tptp.nat) (A (-> tptp.nat tptp.complex)) (X tptp.complex) (Y tptp.complex)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.groups2073611262835488442omplex (lambda ((I tptp.nat)) (@ (@ tptp.times_times_complex (@ A I)) (@ (@ tptp.power_power_complex X) I)))) _let_1)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I tptp.nat)) (@ (@ tptp.times_times_complex (@ A I)) (@ (@ tptp.power_power_complex Y) I)))) _let_1)) (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex X) Y)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((J tptp.nat)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ A (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat J) K3)) tptp.one_one_nat))) (@ (@ tptp.power_power_complex Y) K3))) (@ (@ tptp.power_power_complex X) J)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.minus_minus_nat N) J))))) (@ tptp.set_ord_lessThan_nat N))))))))
% 6.73/7.07 (assert (forall ((N tptp.nat) (A (-> tptp.nat tptp.rat)) (X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I tptp.nat)) (@ (@ tptp.times_times_rat (@ A I)) (@ (@ tptp.power_power_rat X) I)))) _let_1)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I tptp.nat)) (@ (@ tptp.times_times_rat (@ A I)) (@ (@ tptp.power_power_rat Y) I)))) _let_1)) (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat X) Y)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((J tptp.nat)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ A (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat J) K3)) tptp.one_one_nat))) (@ (@ tptp.power_power_rat Y) K3))) (@ (@ tptp.power_power_rat X) J)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.minus_minus_nat N) J))))) (@ tptp.set_ord_lessThan_nat N))))))))
% 6.73/7.07 (assert (forall ((N tptp.nat) (A (-> tptp.nat tptp.int)) (X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.groups3539618377306564664at_int (lambda ((I tptp.nat)) (@ (@ tptp.times_times_int (@ A I)) (@ (@ tptp.power_power_int X) I)))) _let_1)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I tptp.nat)) (@ (@ tptp.times_times_int (@ A I)) (@ (@ tptp.power_power_int Y) I)))) _let_1)) (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int X) Y)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((J tptp.nat)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int (@ A (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat J) K3)) tptp.one_one_nat))) (@ (@ tptp.power_power_int Y) K3))) (@ (@ tptp.power_power_int X) J)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.minus_minus_nat N) J))))) (@ tptp.set_ord_lessThan_nat N))))))))
% 6.73/7.07 (assert (forall ((N tptp.nat) (A (-> tptp.nat tptp.real)) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((I tptp.nat)) (@ (@ tptp.times_times_real (@ A I)) (@ (@ tptp.power_power_real X) I)))) _let_1)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I tptp.nat)) (@ (@ tptp.times_times_real (@ A I)) (@ (@ tptp.power_power_real Y) I)))) _let_1)) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real X) Y)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((J tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ A (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat J) K3)) tptp.one_one_nat))) (@ (@ tptp.power_power_real Y) K3))) (@ (@ tptp.power_power_real X) J)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.minus_minus_nat N) J))))) (@ tptp.set_ord_lessThan_nat N))))))))
% 6.73/7.07 (assert (forall ((M2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.times_times_nat _let_1) M2))) (= (@ (@ tptp.groups3542108847815614940at_nat (@ tptp.binomial (@ (@ tptp.plus_plus_nat _let_2) tptp.one_one_nat))) (@ tptp.set_ord_atMost_nat M2)) (@ (@ tptp.power_power_nat _let_1) _let_2))))))
% 6.73/7.07 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I tptp.nat)) (@ (@ tptp.times_times_nat I) (@ (@ tptp.binomial N) I)))) (@ 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))))))
% 6.73/7.07 (assert (forall ((A4 tptp.set_list_nat) (N tptp.nat)) (=> (@ tptp.finite8100373058378681591st_nat A4) (= (@ tptp.finite7325466520557071688st_nat (@ tptp.collec5989764272469232197st_nat (lambda ((Xs tptp.list_list_nat)) (and (@ (@ tptp.ord_le6045566169113846134st_nat (@ tptp.set_list_nat2 Xs)) A4) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_s3023201423986296836st_nat Xs)) N))))) (@ (@ tptp.groups3542108847815614940at_nat (@ tptp.power_power_nat (@ tptp.finite_card_list_nat A4))) (@ tptp.set_ord_atMost_nat N))))))
% 6.73/7.07 (assert (forall ((A4 tptp.set_set_nat) (N tptp.nat)) (=> (@ tptp.finite1152437895449049373et_nat A4) (= (@ tptp.finite5631907774883551598et_nat (@ tptp.collect_list_set_nat (lambda ((Xs tptp.list_set_nat)) (and (@ (@ tptp.ord_le6893508408891458716et_nat (@ tptp.set_set_nat2 Xs)) A4) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_s3254054031482475050et_nat Xs)) N))))) (@ (@ tptp.groups3542108847815614940at_nat (@ tptp.power_power_nat (@ tptp.finite_card_set_nat A4))) (@ tptp.set_ord_atMost_nat N))))))
% 6.73/7.07 (assert (forall ((A4 tptp.set_complex) (N tptp.nat)) (=> (@ tptp.finite3207457112153483333omplex A4) (= (@ tptp.finite5120063068150530198omplex (@ tptp.collect_list_complex (lambda ((Xs tptp.list_complex)) (and (@ (@ tptp.ord_le211207098394363844omplex (@ tptp.set_complex2 Xs)) A4) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_s3451745648224563538omplex Xs)) N))))) (@ (@ tptp.groups3542108847815614940at_nat (@ tptp.power_power_nat (@ tptp.finite_card_complex A4))) (@ tptp.set_ord_atMost_nat N))))))
% 6.73/7.07 (assert (forall ((A4 tptp.set_VEBT_VEBT) (N tptp.nat)) (=> (@ tptp.finite5795047828879050333T_VEBT A4) (= (@ tptp.finite5915292604075114978T_VEBT (@ tptp.collec5608196760682091941T_VEBT (lambda ((Xs tptp.list_VEBT_VEBT)) (and (@ (@ tptp.ord_le4337996190870823476T_VEBT (@ tptp.set_VEBT_VEBT2 Xs)) A4) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_s6755466524823107622T_VEBT Xs)) N))))) (@ (@ tptp.groups3542108847815614940at_nat (@ tptp.power_power_nat (@ tptp.finite7802652506058667612T_VEBT A4))) (@ tptp.set_ord_atMost_nat N))))))
% 6.73/7.07 (assert (forall ((A4 tptp.set_o) (N tptp.nat)) (=> (@ tptp.finite_finite_o A4) (= (@ tptp.finite_card_list_o (@ tptp.collect_list_o (lambda ((Xs tptp.list_o)) (and (@ (@ tptp.ord_less_eq_set_o (@ tptp.set_o2 Xs)) A4) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_o Xs)) N))))) (@ (@ tptp.groups3542108847815614940at_nat (@ tptp.power_power_nat (@ tptp.finite_card_o A4))) (@ tptp.set_ord_atMost_nat N))))))
% 6.73/7.07 (assert (forall ((A4 tptp.set_int) (N tptp.nat)) (=> (@ tptp.finite_finite_int A4) (= (@ tptp.finite_card_list_int (@ tptp.collect_list_int (lambda ((Xs tptp.list_int)) (and (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_int2 Xs)) A4) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_int Xs)) N))))) (@ (@ tptp.groups3542108847815614940at_nat (@ tptp.power_power_nat (@ tptp.finite_card_int A4))) (@ tptp.set_ord_atMost_nat N))))))
% 6.73/7.07 (assert (forall ((A4 tptp.set_nat) (N tptp.nat)) (=> (@ tptp.finite_finite_nat A4) (= (@ tptp.finite_card_list_nat (@ tptp.collect_list_nat (lambda ((Xs tptp.list_nat)) (and (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_nat2 Xs)) A4) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_nat Xs)) N))))) (@ (@ tptp.groups3542108847815614940at_nat (@ tptp.power_power_nat (@ tptp.finite_card_nat A4))) (@ tptp.set_ord_atMost_nat N))))))
% 6.73/7.07 (assert (forall ((E tptp.real) (C2 (-> tptp.nat tptp.complex)) (N tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E) (exists ((M8 tptp.real)) (forall ((Z5 tptp.complex)) (let ((_let_1 (@ tptp.real_V1022390504157884413omplex Z5))) (=> (@ (@ tptp.ord_less_eq_real M8) _let_1) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.groups2073611262835488442omplex (lambda ((I tptp.nat)) (@ (@ tptp.times_times_complex (@ C2 I)) (@ (@ tptp.power_power_complex Z5) I)))) (@ tptp.set_ord_atMost_nat N)))) (@ (@ tptp.times_times_real E) (@ (@ tptp.power_power_real _let_1) (@ tptp.suc N)))))))))))
% 6.73/7.07 (assert (forall ((E tptp.real) (C2 (-> tptp.nat tptp.real)) (N tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E) (exists ((M8 tptp.real)) (forall ((Z5 tptp.real)) (let ((_let_1 (@ tptp.real_V7735802525324610683m_real Z5))) (=> (@ (@ tptp.ord_less_eq_real M8) _let_1) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((I tptp.nat)) (@ (@ tptp.times_times_real (@ C2 I)) (@ (@ tptp.power_power_real Z5) I)))) (@ tptp.set_ord_atMost_nat N)))) (@ (@ tptp.times_times_real E) (@ (@ tptp.power_power_real _let_1) (@ tptp.suc N)))))))))))
% 6.73/7.07 (assert (forall ((N tptp.nat) (A (-> tptp.nat tptp.complex)) (X tptp.complex) (Y tptp.complex)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.groups2073611262835488442omplex (lambda ((I tptp.nat)) (@ (@ tptp.times_times_complex (@ A I)) (@ (@ tptp.power_power_complex X) I)))) _let_1)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I tptp.nat)) (@ (@ tptp.times_times_complex (@ A I)) (@ (@ tptp.power_power_complex Y) I)))) _let_1)) (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex X) Y)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((J tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.groups2073611262835488442omplex (lambda ((I tptp.nat)) (@ (@ tptp.times_times_complex (@ A I)) (@ (@ tptp.power_power_complex Y) (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat I) J)) tptp.one_one_nat))))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc J)) N))) (@ (@ tptp.power_power_complex X) J)))) (@ tptp.set_ord_lessThan_nat N))))))))
% 6.73/7.07 (assert (forall ((N tptp.nat) (A (-> tptp.nat tptp.rat)) (X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I tptp.nat)) (@ (@ tptp.times_times_rat (@ A I)) (@ (@ tptp.power_power_rat X) I)))) _let_1)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I tptp.nat)) (@ (@ tptp.times_times_rat (@ A I)) (@ (@ tptp.power_power_rat Y) I)))) _let_1)) (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat X) Y)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((J tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I tptp.nat)) (@ (@ tptp.times_times_rat (@ A I)) (@ (@ tptp.power_power_rat Y) (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat I) J)) tptp.one_one_nat))))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc J)) N))) (@ (@ tptp.power_power_rat X) J)))) (@ tptp.set_ord_lessThan_nat N))))))))
% 6.73/7.07 (assert (forall ((N tptp.nat) (A (-> tptp.nat tptp.int)) (X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.groups3539618377306564664at_int (lambda ((I tptp.nat)) (@ (@ tptp.times_times_int (@ A I)) (@ (@ tptp.power_power_int X) I)))) _let_1)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I tptp.nat)) (@ (@ tptp.times_times_int (@ A I)) (@ (@ tptp.power_power_int Y) I)))) _let_1)) (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int X) Y)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((J tptp.nat)) (@ (@ tptp.times_times_int (@ (@ tptp.groups3539618377306564664at_int (lambda ((I tptp.nat)) (@ (@ tptp.times_times_int (@ A I)) (@ (@ tptp.power_power_int Y) (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat I) J)) tptp.one_one_nat))))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc J)) N))) (@ (@ tptp.power_power_int X) J)))) (@ tptp.set_ord_lessThan_nat N))))))))
% 6.73/7.07 (assert (forall ((N tptp.nat) (A (-> tptp.nat tptp.real)) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((I tptp.nat)) (@ (@ tptp.times_times_real (@ A I)) (@ (@ tptp.power_power_real X) I)))) _let_1)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I tptp.nat)) (@ (@ tptp.times_times_real (@ A I)) (@ (@ tptp.power_power_real Y) I)))) _let_1)) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real X) Y)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((J tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((I tptp.nat)) (@ (@ tptp.times_times_real (@ A I)) (@ (@ tptp.power_power_real Y) (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat I) J)) tptp.one_one_nat))))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc J)) N))) (@ (@ tptp.power_power_real X) J)))) (@ tptp.set_ord_lessThan_nat N))))))))
% 6.73/7.07 (assert (forall ((K2 tptp.nat) (A4 tptp.set_complex)) (let ((_let_1 (@ tptp.finite_card_complex A4))) (=> (@ (@ tptp.ord_less_nat K2) _let_1) (= (@ tptp.finite5120063068150530198omplex (@ tptp.collect_list_complex (lambda ((Xs tptp.list_complex)) (and (= (@ tptp.size_s3451745648224563538omplex Xs) K2) (@ tptp.distinct_complex Xs) (@ (@ tptp.ord_le211207098394363844omplex (@ tptp.set_complex2 Xs)) A4))))) (@ (@ tptp.groups708209901874060359at_nat (lambda ((X4 tptp.nat)) X4)) (@ (@ tptp.set_or1269000886237332187st_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat _let_1) K2)) tptp.one_one_nat)) _let_1)))))))
% 6.73/7.07 (assert (forall ((K2 tptp.nat) (A4 tptp.set_list_nat)) (let ((_let_1 (@ tptp.finite_card_list_nat A4))) (=> (@ (@ tptp.ord_less_nat K2) _let_1) (= (@ tptp.finite7325466520557071688st_nat (@ tptp.collec5989764272469232197st_nat (lambda ((Xs tptp.list_list_nat)) (and (= (@ tptp.size_s3023201423986296836st_nat Xs) K2) (@ tptp.distinct_list_nat Xs) (@ (@ tptp.ord_le6045566169113846134st_nat (@ tptp.set_list_nat2 Xs)) A4))))) (@ (@ tptp.groups708209901874060359at_nat (lambda ((X4 tptp.nat)) X4)) (@ (@ tptp.set_or1269000886237332187st_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat _let_1) K2)) tptp.one_one_nat)) _let_1)))))))
% 6.73/7.07 (assert (forall ((K2 tptp.nat) (A4 tptp.set_set_nat)) (let ((_let_1 (@ tptp.finite_card_set_nat A4))) (=> (@ (@ tptp.ord_less_nat K2) _let_1) (= (@ tptp.finite5631907774883551598et_nat (@ tptp.collect_list_set_nat (lambda ((Xs tptp.list_set_nat)) (and (= (@ tptp.size_s3254054031482475050et_nat Xs) K2) (@ tptp.distinct_set_nat Xs) (@ (@ tptp.ord_le6893508408891458716et_nat (@ tptp.set_set_nat2 Xs)) A4))))) (@ (@ tptp.groups708209901874060359at_nat (lambda ((X4 tptp.nat)) X4)) (@ (@ tptp.set_or1269000886237332187st_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat _let_1) K2)) tptp.one_one_nat)) _let_1)))))))
% 6.73/7.07 (assert (forall ((K2 tptp.nat) (A4 tptp.set_VEBT_VEBT)) (let ((_let_1 (@ tptp.finite7802652506058667612T_VEBT A4))) (=> (@ (@ tptp.ord_less_nat K2) _let_1) (= (@ tptp.finite5915292604075114978T_VEBT (@ tptp.collec5608196760682091941T_VEBT (lambda ((Xs tptp.list_VEBT_VEBT)) (and (= (@ tptp.size_s6755466524823107622T_VEBT Xs) K2) (@ tptp.distinct_VEBT_VEBT Xs) (@ (@ tptp.ord_le4337996190870823476T_VEBT (@ tptp.set_VEBT_VEBT2 Xs)) A4))))) (@ (@ tptp.groups708209901874060359at_nat (lambda ((X4 tptp.nat)) X4)) (@ (@ tptp.set_or1269000886237332187st_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat _let_1) K2)) tptp.one_one_nat)) _let_1)))))))
% 6.73/7.07 (assert (forall ((K2 tptp.nat) (A4 tptp.set_o)) (let ((_let_1 (@ tptp.finite_card_o A4))) (=> (@ (@ tptp.ord_less_nat K2) _let_1) (= (@ tptp.finite_card_list_o (@ tptp.collect_list_o (lambda ((Xs tptp.list_o)) (and (= (@ tptp.size_size_list_o Xs) K2) (@ tptp.distinct_o Xs) (@ (@ tptp.ord_less_eq_set_o (@ tptp.set_o2 Xs)) A4))))) (@ (@ tptp.groups708209901874060359at_nat (lambda ((X4 tptp.nat)) X4)) (@ (@ tptp.set_or1269000886237332187st_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat _let_1) K2)) tptp.one_one_nat)) _let_1)))))))
% 6.73/7.07 (assert (forall ((K2 tptp.nat) (A4 tptp.set_int)) (let ((_let_1 (@ tptp.finite_card_int A4))) (=> (@ (@ tptp.ord_less_nat K2) _let_1) (= (@ tptp.finite_card_list_int (@ tptp.collect_list_int (lambda ((Xs tptp.list_int)) (and (= (@ tptp.size_size_list_int Xs) K2) (@ tptp.distinct_int Xs) (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_int2 Xs)) A4))))) (@ (@ tptp.groups708209901874060359at_nat (lambda ((X4 tptp.nat)) X4)) (@ (@ tptp.set_or1269000886237332187st_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat _let_1) K2)) tptp.one_one_nat)) _let_1)))))))
% 6.73/7.07 (assert (forall ((K2 tptp.nat) (A4 tptp.set_nat)) (let ((_let_1 (@ tptp.finite_card_nat A4))) (=> (@ (@ tptp.ord_less_nat K2) _let_1) (= (@ tptp.finite_card_list_nat (@ tptp.collect_list_nat (lambda ((Xs tptp.list_nat)) (and (= (@ tptp.size_size_list_nat Xs) K2) (@ tptp.distinct_nat Xs) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_nat2 Xs)) A4))))) (@ (@ tptp.groups708209901874060359at_nat (lambda ((X4 tptp.nat)) X4)) (@ (@ tptp.set_or1269000886237332187st_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat _let_1) K2)) tptp.one_one_nat)) _let_1)))))))
% 6.73/7.07 (assert (forall ((Q2 tptp.int) (R3 tptp.int)) (= (@ tptp.adjust_div (@ (@ tptp.product_Pair_int_int Q2) R3)) (@ (@ tptp.plus_plus_int Q2) (@ tptp.zero_n2684676970156552555ol_int (not (= R3 tptp.zero_zero_int)))))))
% 6.73/7.07 (assert (forall ((A0 tptp.nat) (P2 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.accp_nat tptp.nat_list_decode_rel))) (=> (@ _let_1 A0) (=> (=> (@ _let_1 tptp.zero_zero_nat) (@ P2 tptp.zero_zero_nat)) (=> (forall ((N3 tptp.nat)) (let ((_let_1 (@ tptp.suc N3))) (=> (@ (@ tptp.accp_nat tptp.nat_list_decode_rel) _let_1) (=> (forall ((X5 tptp.nat) (Y6 tptp.nat)) (=> (= (@ (@ tptp.product_Pair_nat_nat X5) Y6) (@ tptp.nat_prod_decode N3)) (@ P2 Y6))) (@ P2 _let_1))))) (@ P2 A0)))))))
% 6.73/7.07 (assert (= tptp.gbinomial_complex (lambda ((A5 tptp.complex) (K3 tptp.nat)) (@ (@ (@ tptp.if_complex (= K3 tptp.zero_zero_nat)) tptp.one_one_complex) (@ (@ tptp.divide1717551699836669952omplex (@ (@ (@ (@ tptp.set_fo1517530859248394432omplex (lambda ((L2 tptp.nat) (__flatten_var_0 tptp.complex)) (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex A5) (@ tptp.semiri8010041392384452111omplex L2))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat K3) tptp.one_one_nat)) tptp.one_one_complex)) (@ tptp.semiri5044797733671781792omplex K3))))))
% 6.73/7.07 (assert (= tptp.gbinomial_rat (lambda ((A5 tptp.rat) (K3 tptp.nat)) (@ (@ (@ tptp.if_rat (= K3 tptp.zero_zero_nat)) tptp.one_one_rat) (@ (@ tptp.divide_divide_rat (@ (@ (@ (@ tptp.set_fo1949268297981939178at_rat (lambda ((L2 tptp.nat) (__flatten_var_0 tptp.rat)) (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat A5) (@ tptp.semiri681578069525770553at_rat L2))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat K3) tptp.one_one_nat)) tptp.one_one_rat)) (@ tptp.semiri773545260158071498ct_rat K3))))))
% 6.73/7.07 (assert (= tptp.gbinomial_real (lambda ((A5 tptp.real) (K3 tptp.nat)) (@ (@ (@ tptp.if_real (= K3 tptp.zero_zero_nat)) tptp.one_one_real) (@ (@ tptp.divide_divide_real (@ (@ (@ (@ tptp.set_fo3111899725591712190t_real (lambda ((L2 tptp.nat) (__flatten_var_0 tptp.real)) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real A5) (@ tptp.semiri5074537144036343181t_real L2))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat K3) tptp.one_one_nat)) tptp.one_one_real)) (@ tptp.semiri2265585572941072030t_real K3))))))
% 6.73/7.07 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) I)) (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.binomial N) I))))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_complex))))
% 6.73/7.07 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.groups7501900531339628137nteger (lambda ((I tptp.nat)) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) I)) (@ tptp.semiri4939895301339042750nteger (@ (@ tptp.binomial N) I))))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_z3403309356797280102nteger))))
% 6.73/7.07 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) I)) (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.binomial N) I))))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_rat))))
% 6.73/7.07 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((I tptp.nat)) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) I)) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.binomial N) I))))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_int))))
% 6.73/7.07 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I)) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.binomial N) I))))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_real))))
% 6.73/7.07 (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))))))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (assert (forall ((A tptp.int)) (= (@ tptp.uminus_uminus_int (@ tptp.uminus_uminus_int A)) A)))
% 6.73/7.07 (assert (forall ((A tptp.real)) (= (@ tptp.uminus_uminus_real (@ tptp.uminus_uminus_real A)) A)))
% 6.73/7.07 (assert (forall ((A tptp.complex)) (= (@ tptp.uminus1482373934393186551omplex (@ tptp.uminus1482373934393186551omplex A)) A)))
% 6.73/7.07 (assert (forall ((A tptp.code_integer)) (= (@ tptp.uminus1351360451143612070nteger (@ tptp.uminus1351360451143612070nteger A)) A)))
% 6.73/7.07 (assert (forall ((A tptp.rat)) (= (@ tptp.uminus_uminus_rat (@ tptp.uminus_uminus_rat A)) A)))
% 6.73/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (= (= (@ tptp.uminus_uminus_int A) (@ tptp.uminus_uminus_int B)) (= A B))))
% 6.73/7.07 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ tptp.uminus_uminus_real A) (@ tptp.uminus_uminus_real B)) (= A B))))
% 6.73/7.07 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= (@ tptp.uminus1482373934393186551omplex A) (@ tptp.uminus1482373934393186551omplex B)) (= A B))))
% 6.73/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= (@ tptp.uminus1351360451143612070nteger A) (@ tptp.uminus1351360451143612070nteger B)) (= A B))))
% 6.73/7.07 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ tptp.uminus_uminus_rat A) (@ tptp.uminus_uminus_rat B)) (= A B))))
% 6.73/7.07 (assert (= tptp.semiri1316708129612266289at_nat (lambda ((N4 tptp.nat)) N4)))
% 6.73/7.07 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ tptp.uminus5710092332889474511et_nat X)) (@ tptp.uminus5710092332889474511et_nat Y)) (@ (@ tptp.ord_less_eq_set_nat Y) X))))
% 6.73/7.07 (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))))
% 6.73/7.07 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger A)) (@ (@ tptp.ord_le3102999989581377725nteger A) B))))
% 6.73/7.07 (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))))
% 6.73/7.07 (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))))
% 6.73/7.07 (assert (forall ((A tptp.int)) (= (= (@ tptp.uminus_uminus_int A) A) (= A tptp.zero_zero_int))))
% 6.73/7.07 (assert (forall ((A tptp.real)) (= (= (@ tptp.uminus_uminus_real A) A) (= A tptp.zero_zero_real))))
% 6.73/7.07 (assert (forall ((A tptp.code_integer)) (= (= (@ tptp.uminus1351360451143612070nteger A) A) (= A tptp.zero_z3403309356797280102nteger))))
% 6.73/7.07 (assert (forall ((A tptp.rat)) (= (= (@ tptp.uminus_uminus_rat A) A) (= A tptp.zero_zero_rat))))
% 6.73/7.07 (assert (forall ((A tptp.int)) (= (= A (@ tptp.uminus_uminus_int A)) (= A tptp.zero_zero_int))))
% 6.73/7.07 (assert (forall ((A tptp.real)) (= (= A (@ tptp.uminus_uminus_real A)) (= A tptp.zero_zero_real))))
% 6.73/7.07 (assert (forall ((A tptp.code_integer)) (= (= A (@ tptp.uminus1351360451143612070nteger A)) (= A tptp.zero_z3403309356797280102nteger))))
% 6.73/7.07 (assert (forall ((A tptp.rat)) (= (= A (@ tptp.uminus_uminus_rat A)) (= A tptp.zero_zero_rat))))
% 6.73/7.07 (assert (forall ((A tptp.int)) (= (= (@ tptp.uminus_uminus_int A) tptp.zero_zero_int) (= A tptp.zero_zero_int))))
% 6.73/7.07 (assert (forall ((A tptp.real)) (= (= (@ tptp.uminus_uminus_real A) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 6.73/7.07 (assert (forall ((A tptp.complex)) (= (= (@ tptp.uminus1482373934393186551omplex A) tptp.zero_zero_complex) (= A tptp.zero_zero_complex))))
% 6.73/7.07 (assert (forall ((A tptp.code_integer)) (= (= (@ tptp.uminus1351360451143612070nteger A) tptp.zero_z3403309356797280102nteger) (= A tptp.zero_z3403309356797280102nteger))))
% 6.73/7.07 (assert (forall ((A tptp.rat)) (= (= (@ tptp.uminus_uminus_rat A) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))))
% 6.73/7.07 (assert (forall ((A tptp.int)) (= (= tptp.zero_zero_int (@ tptp.uminus_uminus_int A)) (= tptp.zero_zero_int A))))
% 6.73/7.07 (assert (forall ((A tptp.real)) (= (= tptp.zero_zero_real (@ tptp.uminus_uminus_real A)) (= tptp.zero_zero_real A))))
% 6.73/7.07 (assert (forall ((A tptp.complex)) (= (= tptp.zero_zero_complex (@ tptp.uminus1482373934393186551omplex A)) (= tptp.zero_zero_complex A))))
% 6.73/7.07 (assert (forall ((A tptp.code_integer)) (= (= tptp.zero_z3403309356797280102nteger (@ tptp.uminus1351360451143612070nteger A)) (= tptp.zero_z3403309356797280102nteger A))))
% 6.73/7.07 (assert (forall ((A tptp.rat)) (= (= tptp.zero_zero_rat (@ tptp.uminus_uminus_rat A)) (= tptp.zero_zero_rat A))))
% 6.73/7.07 (assert (= (@ tptp.uminus_uminus_int tptp.zero_zero_int) tptp.zero_zero_int))
% 6.73/7.07 (assert (= (@ tptp.uminus_uminus_real tptp.zero_zero_real) tptp.zero_zero_real))
% 6.73/7.07 (assert (= (@ tptp.uminus1482373934393186551omplex tptp.zero_zero_complex) tptp.zero_zero_complex))
% 6.73/7.07 (assert (= (@ tptp.uminus1351360451143612070nteger tptp.zero_z3403309356797280102nteger) tptp.zero_z3403309356797280102nteger))
% 6.73/7.07 (assert (= (@ tptp.uminus_uminus_rat tptp.zero_zero_rat) tptp.zero_zero_rat))
% 6.73/7.07 (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))))
% 6.73/7.07 (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))))
% 6.73/7.07 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger A)) (@ (@ tptp.ord_le6747313008572928689nteger A) B))))
% 6.73/7.07 (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))))
% 6.73/7.07 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (= (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) (= M2 N))))
% 6.73/7.07 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (= (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M2)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))) (= M2 N))))
% 6.73/7.07 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (= (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex M2)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N))) (= M2 N))))
% 6.73/7.07 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (= (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M2)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))) (= M2 N))))
% 6.73/7.07 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (= (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M2)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))) (= M2 N))))
% 6.73/7.07 (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))))))
% 6.73/7.07 (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))))))
% 6.73/7.07 (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))))))
% 6.73/7.07 (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))))))
% 6.73/7.07 (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))))))
% 6.73/7.07 (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))))
% 6.73/7.07 (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))))
% 6.73/7.07 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex A)) (@ tptp.uminus1482373934393186551omplex B)) (@ (@ tptp.times_times_complex A) B))))
% 6.73/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger A)) (@ tptp.uminus1351360451143612070nteger B)) (@ (@ tptp.times_3573771949741848930nteger A) B))))
% 6.73/7.07 (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))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex A)) B) (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.times_times_complex A) B)))))
% 6.73/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger A)) B) (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.times_3573771949741848930nteger A) B)))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.plus_plus_int A) (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int A)) B)) B)))
% 6.73/7.07 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.plus_plus_real A) (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A)) B)) B)))
% 6.73/7.07 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.plus_plus_complex A) (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex A)) B)) B)))
% 6.73/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger A) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger A)) B)) B)))
% 6.73/7.07 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.plus_plus_rat A) (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat A)) B)) B)))
% 6.73/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int A)) (@ (@ tptp.plus_plus_int A) B)) B)))
% 6.73/7.07 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A)) (@ (@ tptp.plus_plus_real A) B)) B)))
% 6.73/7.07 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex A)) (@ (@ tptp.plus_plus_complex A) B)) B)))
% 6.73/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger A)) (@ (@ tptp.plus_p5714425477246183910nteger A) B)) B)))
% 6.73/7.07 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat A)) (@ (@ tptp.plus_plus_rat A) B)) B)))
% 6.73/7.07 (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)))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ tptp.uminus_uminus_int (@ (@ tptp.minus_minus_int A) B)) (@ (@ tptp.minus_minus_int B) A))))
% 6.73/7.07 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ tptp.uminus_uminus_real (@ (@ tptp.minus_minus_real A) B)) (@ (@ tptp.minus_minus_real B) A))))
% 6.73/7.07 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.minus_minus_complex A) B)) (@ (@ tptp.minus_minus_complex B) A))))
% 6.73/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.minus_8373710615458151222nteger A) B)) (@ (@ tptp.minus_8373710615458151222nteger B) A))))
% 6.73/7.07 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ tptp.uminus_uminus_rat (@ (@ tptp.minus_minus_rat A) B)) (@ (@ tptp.minus_minus_rat B) A))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (assert (forall ((X tptp.complex) (Y tptp.complex)) (let ((_let_1 (@ tptp.dvd_dvd_complex X))) (= (@ _let_1 (@ tptp.uminus1482373934393186551omplex Y)) (@ _let_1 Y)))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (assert (forall ((X tptp.int) (Y tptp.int)) (= (@ (@ tptp.dvd_dvd_int (@ tptp.uminus_uminus_int X)) Y) (@ (@ tptp.dvd_dvd_int X) Y))))
% 6.73/7.07 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ tptp.dvd_dvd_real (@ tptp.uminus_uminus_real X)) Y) (@ (@ tptp.dvd_dvd_real X) Y))))
% 6.73/7.07 (assert (forall ((X tptp.complex) (Y tptp.complex)) (= (@ (@ tptp.dvd_dvd_complex (@ tptp.uminus1482373934393186551omplex X)) Y) (@ (@ tptp.dvd_dvd_complex X) Y))))
% 6.73/7.07 (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))))
% 6.73/7.07 (assert (forall ((X tptp.rat) (Y tptp.rat)) (= (@ (@ tptp.dvd_dvd_rat (@ tptp.uminus_uminus_rat X)) Y) (@ (@ tptp.dvd_dvd_rat X) Y))))
% 6.73/7.07 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (= (= (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N)) (@ tptp.semiri1314217659103216013at_int M2)) (and (= N tptp.zero_zero_nat) (= M2 tptp.zero_zero_nat)))))
% 6.73/7.07 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_ri631733984087533419it_int N) tptp.zero_zero_int) tptp.zero_zero_int)))
% 6.73/7.07 (assert (forall ((N tptp.nat)) (= (@ tptp.nat_set_encode (@ tptp.nat_set_decode N)) N)))
% 6.73/7.07 (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))))
% 6.73/7.07 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger A)) A) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A))))
% 6.73/7.07 (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))))
% 6.73/7.07 (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))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger A))) (= (@ _let_1 (@ tptp.uminus1351360451143612070nteger A)) (@ _let_1 tptp.zero_z3403309356797280102nteger)))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (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))))
% 6.73/7.07 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger A)) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A))))
% 6.73/7.07 (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))))
% 6.73/7.07 (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))))
% 6.73/7.07 (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))))
% 6.73/7.07 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger A)) (@ (@ tptp.ord_le3102999989581377725nteger A) tptp.zero_z3403309356797280102nteger))))
% 6.73/7.07 (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))))
% 6.73/7.07 (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))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger A))) (= (@ _let_1 (@ tptp.uminus1351360451143612070nteger A)) (@ _let_1 tptp.zero_z3403309356797280102nteger)))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (assert (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int A)) A) (@ (@ tptp.ord_less_int tptp.zero_zero_int) A))))
% 6.73/7.07 (assert (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real A)) A) (@ (@ tptp.ord_less_real tptp.zero_zero_real) A))))
% 6.73/7.07 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger A)) A) (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A))))
% 6.73/7.07 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat A)) A) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A))))
% 6.73/7.07 (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))))
% 6.73/7.07 (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))))
% 6.73/7.07 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger A)) (@ (@ tptp.ord_le6747313008572928689nteger A) tptp.zero_z3403309356797280102nteger))))
% 6.73/7.07 (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))))
% 6.73/7.07 (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))))
% 6.73/7.07 (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))))
% 6.73/7.07 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger A)) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A))))
% 6.73/7.07 (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))))
% 6.73/7.07 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int A) (@ tptp.uminus_uminus_int A)) tptp.zero_zero_int)))
% 6.73/7.07 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real A) (@ tptp.uminus_uminus_real A)) tptp.zero_zero_real)))
% 6.73/7.07 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex A) (@ tptp.uminus1482373934393186551omplex A)) tptp.zero_zero_complex)))
% 6.73/7.07 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger A) (@ tptp.uminus1351360451143612070nteger A)) tptp.zero_z3403309356797280102nteger)))
% 6.73/7.07 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat A) (@ tptp.uminus_uminus_rat A)) tptp.zero_zero_rat)))
% 6.73/7.07 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int A)) A) tptp.zero_zero_int)))
% 6.73/7.07 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A)) A) tptp.zero_zero_real)))
% 6.73/7.07 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex A)) A) tptp.zero_zero_complex)))
% 6.73/7.07 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger A)) A) tptp.zero_z3403309356797280102nteger)))
% 6.73/7.07 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat A)) A) tptp.zero_zero_rat)))
% 6.73/7.07 (assert (forall ((B tptp.int)) (= (@ (@ tptp.minus_minus_int tptp.zero_zero_int) B) (@ tptp.uminus_uminus_int B))))
% 6.73/7.07 (assert (forall ((B tptp.real)) (= (@ (@ tptp.minus_minus_real tptp.zero_zero_real) B) (@ tptp.uminus_uminus_real B))))
% 6.73/7.07 (assert (forall ((B tptp.complex)) (= (@ (@ tptp.minus_minus_complex tptp.zero_zero_complex) B) (@ tptp.uminus1482373934393186551omplex B))))
% 6.73/7.07 (assert (forall ((B tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger tptp.zero_z3403309356797280102nteger) B) (@ tptp.uminus1351360451143612070nteger B))))
% 6.73/7.07 (assert (forall ((B tptp.rat)) (= (@ (@ tptp.minus_minus_rat tptp.zero_zero_rat) B) (@ tptp.uminus_uminus_rat B))))
% 6.73/7.07 (assert (forall ((A tptp.int)) (= (@ (@ tptp.minus_minus_int tptp.zero_zero_int) A) (@ tptp.uminus_uminus_int A))))
% 6.73/7.07 (assert (forall ((A tptp.real)) (= (@ (@ tptp.minus_minus_real tptp.zero_zero_real) A) (@ tptp.uminus_uminus_real A))))
% 6.73/7.07 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.minus_minus_complex tptp.zero_zero_complex) A) (@ tptp.uminus1482373934393186551omplex A))))
% 6.73/7.07 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger tptp.zero_z3403309356797280102nteger) A) (@ tptp.uminus1351360451143612070nteger A))))
% 6.73/7.07 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.minus_minus_rat tptp.zero_zero_rat) A) (@ tptp.uminus_uminus_rat A))))
% 6.73/7.07 (assert (forall ((M2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (let ((_let_2 (@ tptp.numeral_numeral_int M2))) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int _let_2)) (@ tptp.uminus_uminus_int _let_1)) (@ tptp.uminus_uminus_int (@ (@ tptp.plus_plus_int _let_2) _let_1)))))))
% 6.73/7.07 (assert (forall ((M2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real N))) (let ((_let_2 (@ tptp.numeral_numeral_real M2))) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real _let_2)) (@ tptp.uminus_uminus_real _let_1)) (@ tptp.uminus_uminus_real (@ (@ tptp.plus_plus_real _let_2) _let_1)))))))
% 6.73/7.07 (assert (forall ((M2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex N))) (let ((_let_2 (@ tptp.numera6690914467698888265omplex M2))) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex _let_2)) (@ tptp.uminus1482373934393186551omplex _let_1)) (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.plus_plus_complex _let_2) _let_1)))))))
% 6.73/7.07 (assert (forall ((M2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger N))) (let ((_let_2 (@ tptp.numera6620942414471956472nteger M2))) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger _let_2)) (@ tptp.uminus1351360451143612070nteger _let_1)) (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.plus_p5714425477246183910nteger _let_2) _let_1)))))))
% 6.73/7.07 (assert (forall ((M2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat N))) (let ((_let_2 (@ tptp.numeral_numeral_rat M2))) (= (@ (@ 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)))))))
% 6.73/7.07 (assert (forall ((Z3 tptp.int)) (= (@ (@ tptp.times_times_int Z3) (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.uminus_uminus_int Z3))))
% 6.73/7.07 (assert (forall ((Z3 tptp.real)) (= (@ (@ tptp.times_times_real Z3) (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.uminus_uminus_real Z3))))
% 6.73/7.07 (assert (forall ((Z3 tptp.complex)) (= (@ (@ tptp.times_times_complex Z3) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ tptp.uminus1482373934393186551omplex Z3))))
% 6.73/7.07 (assert (forall ((Z3 tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger Z3) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.uminus1351360451143612070nteger Z3))))
% 6.73/7.07 (assert (forall ((Z3 tptp.rat)) (= (@ (@ tptp.times_times_rat Z3) (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.uminus_uminus_rat Z3))))
% 6.73/7.07 (assert (forall ((Z3 tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int tptp.one_one_int)) Z3) (@ tptp.uminus_uminus_int Z3))))
% 6.73/7.07 (assert (forall ((Z3 tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Z3) (@ tptp.uminus_uminus_real Z3))))
% 6.73/7.07 (assert (forall ((Z3 tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) Z3) (@ tptp.uminus1482373934393186551omplex Z3))))
% 6.73/7.07 (assert (forall ((Z3 tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) Z3) (@ tptp.uminus1351360451143612070nteger Z3))))
% 6.73/7.07 (assert (forall ((Z3 tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) Z3) (@ tptp.uminus_uminus_rat Z3))))
% 6.73/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.minus_minus_int A) (@ tptp.uminus_uminus_int B)) (@ (@ tptp.plus_plus_int A) B))))
% 6.73/7.07 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.minus_minus_real A) (@ tptp.uminus_uminus_real B)) (@ (@ tptp.plus_plus_real A) B))))
% 6.73/7.07 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.minus_minus_complex A) (@ tptp.uminus1482373934393186551omplex B)) (@ (@ tptp.plus_plus_complex A) B))))
% 6.73/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger A) (@ tptp.uminus1351360451143612070nteger B)) (@ (@ tptp.plus_p5714425477246183910nteger A) B))))
% 6.73/7.07 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.minus_minus_rat A) (@ tptp.uminus_uminus_rat B)) (@ (@ tptp.plus_plus_rat A) B))))
% 6.73/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int A)) B) (@ (@ tptp.minus_minus_int B) A))))
% 6.73/7.07 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A)) B) (@ (@ tptp.minus_minus_real B) A))))
% 6.73/7.07 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex A)) B) (@ (@ tptp.minus_minus_complex B) A))))
% 6.73/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger A)) B) (@ (@ tptp.minus_8373710615458151222nteger B) A))))
% 6.73/7.07 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat A)) B) (@ (@ tptp.minus_minus_rat B) A))))
% 6.73/7.07 (assert (= (@ tptp.semiri3624122377584611663nteger tptp.zero_zero_nat) tptp.one_one_Code_integer))
% 6.73/7.07 (assert (= (@ tptp.semiri5044797733671781792omplex tptp.zero_zero_nat) tptp.one_one_complex))
% 6.73/7.07 (assert (= (@ tptp.semiri1406184849735516958ct_int tptp.zero_zero_nat) tptp.one_one_int))
% 6.73/7.07 (assert (= (@ tptp.semiri1408675320244567234ct_nat tptp.zero_zero_nat) tptp.one_one_nat))
% 6.73/7.07 (assert (= (@ tptp.semiri2265585572941072030t_real tptp.zero_zero_nat) tptp.one_one_real))
% 6.73/7.07 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N)))) (@ tptp.semiri1314217659103216013at_int M2))))
% 6.73/7.07 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_ri6519982836138164636nteger (@ tptp.suc N)) tptp.one_one_Code_integer) tptp.one_one_Code_integer)))
% 6.73/7.07 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.suc N)) tptp.one_one_int) tptp.one_one_int)))
% 6.73/7.07 (assert (forall ((K2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int K2))) (= (@ tptp.neg_numeral_dbl_int (@ tptp.uminus_uminus_int _let_1)) (@ tptp.uminus_uminus_int (@ tptp.neg_numeral_dbl_int _let_1))))))
% 6.73/7.07 (assert (forall ((K2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real K2))) (= (@ tptp.neg_numeral_dbl_real (@ tptp.uminus_uminus_real _let_1)) (@ tptp.uminus_uminus_real (@ tptp.neg_numeral_dbl_real _let_1))))))
% 6.73/7.07 (assert (forall ((K2 tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex K2))) (= (@ tptp.neg_nu7009210354673126013omplex (@ tptp.uminus1482373934393186551omplex _let_1)) (@ tptp.uminus1482373934393186551omplex (@ tptp.neg_nu7009210354673126013omplex _let_1))))))
% 6.73/7.07 (assert (forall ((K2 tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger K2))) (= (@ tptp.neg_nu8804712462038260780nteger (@ tptp.uminus1351360451143612070nteger _let_1)) (@ tptp.uminus1351360451143612070nteger (@ tptp.neg_nu8804712462038260780nteger _let_1))))))
% 6.73/7.07 (assert (forall ((K2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat K2))) (= (@ tptp.neg_numeral_dbl_rat (@ tptp.uminus_uminus_rat _let_1)) (@ tptp.uminus_uminus_rat (@ tptp.neg_numeral_dbl_rat _let_1))))))
% 6.73/7.07 (assert (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (@ tptp.neg_nu5851722552734809277nc_int _let_1) _let_1)))
% 6.73/7.07 (assert (let ((_let_1 (@ tptp.uminus_uminus_real tptp.one_one_real))) (= (@ tptp.neg_nu8295874005876285629c_real _let_1) _let_1)))
% 6.73/7.07 (assert (let ((_let_1 (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))) (= (@ tptp.neg_nu8557863876264182079omplex _let_1) _let_1)))
% 6.73/7.07 (assert (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (= (@ tptp.neg_nu5831290666863070958nteger _let_1) _let_1)))
% 6.73/7.07 (assert (let ((_let_1 (@ tptp.uminus_uminus_rat tptp.one_one_rat))) (= (@ tptp.neg_nu5219082963157363817nc_rat _let_1) _let_1)))
% 6.73/7.07 (assert (= (@ tptp.nat_set_decode tptp.zero_zero_nat) tptp.bot_bot_set_nat))
% 6.73/7.07 (assert (forall ((A4 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A4) (= (@ tptp.nat_set_decode (@ tptp.nat_set_encode A4)) A4))))
% 6.73/7.07 (assert (= (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.zero_zero_int))
% 6.73/7.07 (assert (= (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.zero_zero_real))
% 6.73/7.07 (assert (= (@ (@ tptp.plus_plus_complex tptp.one_one_complex) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) tptp.zero_zero_complex))
% 6.73/7.07 (assert (= (@ (@ tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.zero_z3403309356797280102nteger))
% 6.73/7.07 (assert (= (@ (@ tptp.plus_plus_rat tptp.one_one_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.zero_zero_rat))
% 6.73/7.07 (assert (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.one_one_int) tptp.zero_zero_int))
% 6.73/7.07 (assert (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.one_one_real) tptp.zero_zero_real))
% 6.73/7.07 (assert (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) tptp.one_one_complex) tptp.zero_zero_complex))
% 6.73/7.07 (assert (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.one_one_Code_integer) tptp.zero_z3403309356797280102nteger))
% 6.73/7.07 (assert (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.one_one_rat) tptp.zero_zero_rat))
% 6.73/7.07 (assert (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (@ (@ tptp.minus_minus_int _let_1) _let_1) tptp.zero_zero_int)))
% 6.73/7.07 (assert (let ((_let_1 (@ tptp.uminus_uminus_real tptp.one_one_real))) (= (@ (@ tptp.minus_minus_real _let_1) _let_1) tptp.zero_zero_real)))
% 6.73/7.07 (assert (let ((_let_1 (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))) (= (@ (@ tptp.minus_minus_complex _let_1) _let_1) tptp.zero_zero_complex)))
% 6.73/7.07 (assert (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (= (@ (@ tptp.minus_8373710615458151222nteger _let_1) _let_1) tptp.zero_z3403309356797280102nteger)))
% 6.73/7.07 (assert (let ((_let_1 (@ tptp.uminus_uminus_rat tptp.one_one_rat))) (= (@ (@ tptp.minus_minus_rat _let_1) _let_1) tptp.zero_zero_rat)))
% 6.73/7.07 (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))))
% 6.73/7.07 (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))))
% 6.73/7.07 (assert (forall ((N tptp.num)) (= (= (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N))) (= N tptp.one))))
% 6.73/7.07 (assert (forall ((N tptp.num)) (= (= (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))) (= N tptp.one))))
% 6.73/7.07 (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))))
% 6.73/7.07 (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))))
% 6.73/7.07 (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))))
% 6.73/7.07 (assert (forall ((N tptp.num)) (= (= (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N)) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (= N tptp.one))))
% 6.73/7.07 (assert (forall ((N tptp.num)) (= (= (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N)) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (= N tptp.one))))
% 6.73/7.07 (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))))
% 6.73/7.07 (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))))
% 6.73/7.07 (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))))
% 6.73/7.07 (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))))
% 6.73/7.07 (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))))
% 6.73/7.07 (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))))
% 6.73/7.07 (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))))
% 6.73/7.07 (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))))
% 6.73/7.07 (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))))
% 6.73/7.07 (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))))
% 6.73/7.07 (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))))
% 6.73/7.07 (assert (forall ((A tptp.int)) (= (@ (@ tptp.modulo_modulo_int A) (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.zero_zero_int)))
% 6.73/7.07 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger A) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.zero_z3403309356797280102nteger)))
% 6.73/7.07 (assert (forall ((U tptp.num) (V2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real U))) (let ((_let_2 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V2)))) (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)))))))))
% 6.73/7.07 (assert (forall ((U tptp.num) (V2 tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger U))) (let ((_let_2 (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger V2)))) (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)))))))))
% 6.73/7.07 (assert (forall ((U tptp.num) (V2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat U))) (let ((_let_2 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V2)))) (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)))))))))
% 6.73/7.07 (assert (forall ((U tptp.num) (V2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int U))) (let ((_let_2 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V2)))) (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)))))))))
% 6.73/7.07 (assert (forall ((U tptp.num) (V2 tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real U)))) (let ((_let_2 (@ tptp.numeral_numeral_real V2))) (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)))))))))
% 6.73/7.07 (assert (forall ((U tptp.num) (V2 tptp.num)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger U)))) (let ((_let_2 (@ tptp.numera6620942414471956472nteger V2))) (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)))))))))
% 6.73/7.07 (assert (forall ((U tptp.num) (V2 tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat U)))) (let ((_let_2 (@ tptp.numeral_numeral_rat V2))) (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)))))))))
% 6.73/7.07 (assert (forall ((U tptp.num) (V2 tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int U)))) (let ((_let_2 (@ tptp.numeral_numeral_int V2))) (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)))))))))
% 6.73/7.07 (assert (forall ((U tptp.num) (V2 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 V2)))) (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)))))))))
% 6.73/7.07 (assert (forall ((U tptp.num) (V2 tptp.num)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger U)))) (let ((_let_2 (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger V2)))) (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)))))))))
% 6.73/7.07 (assert (forall ((U tptp.num) (V2 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 V2)))) (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)))))))))
% 6.73/7.07 (assert (forall ((U tptp.num) (V2 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 V2)))) (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)))))))))
% 6.73/7.07 (assert (= (@ tptp.semiri3624122377584611663nteger (@ tptp.suc tptp.zero_zero_nat)) tptp.one_one_Code_integer))
% 6.73/7.07 (assert (= (@ tptp.semiri5044797733671781792omplex (@ tptp.suc tptp.zero_zero_nat)) tptp.one_one_complex))
% 6.73/7.07 (assert (= (@ tptp.semiri1406184849735516958ct_int (@ tptp.suc tptp.zero_zero_nat)) tptp.one_one_int))
% 6.73/7.07 (assert (= (@ tptp.semiri1408675320244567234ct_nat (@ tptp.suc tptp.zero_zero_nat)) tptp.one_one_nat))
% 6.73/7.07 (assert (= (@ tptp.semiri2265585572941072030t_real (@ tptp.suc tptp.zero_zero_nat)) tptp.one_one_real))
% 6.73/7.07 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (= (@ tptp.semiri773545260158071498ct_rat _let_1) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat _let_1)) (@ tptp.semiri773545260158071498ct_rat N))))))
% 6.73/7.07 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (= (@ tptp.semiri1406184849735516958ct_int _let_1) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int _let_1)) (@ tptp.semiri1406184849735516958ct_int N))))))
% 6.73/7.07 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (= (@ tptp.semiri1408675320244567234ct_nat _let_1) (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat _let_1)) (@ tptp.semiri1408675320244567234ct_nat N))))))
% 6.73/7.07 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (= (@ tptp.semiri2265585572941072030t_real _let_1) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real _let_1)) (@ tptp.semiri2265585572941072030t_real N))))))
% 6.73/7.07 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M2))) (@ tptp.numeral_numeral_int N)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.plus_plus_num M2) N))))))
% 6.73/7.07 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M2))) (@ tptp.numeral_numeral_real N)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ (@ tptp.plus_plus_num M2) N))))))
% 6.73/7.07 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex M2))) (@ tptp.numera6690914467698888265omplex N)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ (@ tptp.plus_plus_num M2) N))))))
% 6.73/7.07 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M2))) (@ tptp.numera6620942414471956472nteger N)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ (@ tptp.plus_plus_num M2) N))))))
% 6.73/7.07 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M2))) (@ tptp.numeral_numeral_rat N)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ (@ tptp.plus_plus_num M2) N))))))
% 6.73/7.07 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.minus_minus_int (@ tptp.numeral_numeral_int M2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) (@ tptp.numeral_numeral_int (@ (@ tptp.plus_plus_num M2) N)))))
% 6.73/7.07 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.minus_minus_real (@ tptp.numeral_numeral_real M2)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))) (@ tptp.numeral_numeral_real (@ (@ tptp.plus_plus_num M2) N)))))
% 6.73/7.07 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.minus_minus_complex (@ tptp.numera6690914467698888265omplex M2)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N))) (@ tptp.numera6690914467698888265omplex (@ (@ tptp.plus_plus_num M2) N)))))
% 6.73/7.07 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.numera6620942414471956472nteger M2)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))) (@ tptp.numera6620942414471956472nteger (@ (@ tptp.plus_plus_num M2) N)))))
% 6.73/7.07 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.minus_minus_rat (@ tptp.numeral_numeral_rat M2)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))) (@ tptp.numeral_numeral_rat (@ (@ tptp.plus_plus_num M2) N)))))
% 6.73/7.07 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int M2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.times_times_num M2) N))))))
% 6.73/7.07 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real M2)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ (@ tptp.times_times_num M2) N))))))
% 6.73/7.07 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex M2)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N))) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ (@ tptp.times_times_num M2) N))))))
% 6.73/7.07 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger M2)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ (@ tptp.times_times_num M2) N))))))
% 6.73/7.07 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat M2)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ (@ tptp.times_times_num M2) N))))))
% 6.73/7.07 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M2))) (@ tptp.numeral_numeral_int N)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.times_times_num M2) N))))))
% 6.73/7.07 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M2))) (@ tptp.numeral_numeral_real N)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ (@ tptp.times_times_num M2) N))))))
% 6.73/7.07 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex M2))) (@ tptp.numera6690914467698888265omplex N)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ (@ tptp.times_times_num M2) N))))))
% 6.73/7.07 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M2))) (@ tptp.numera6620942414471956472nteger N)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ (@ tptp.times_times_num M2) N))))))
% 6.73/7.07 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M2))) (@ tptp.numeral_numeral_rat N)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ (@ tptp.times_times_num M2) N))))))
% 6.73/7.07 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M2))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) (@ tptp.numeral_numeral_int (@ (@ tptp.times_times_num M2) N)))))
% 6.73/7.07 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M2))) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))) (@ tptp.numeral_numeral_real (@ (@ tptp.times_times_num M2) N)))))
% 6.73/7.07 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex M2))) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N))) (@ tptp.numera6690914467698888265omplex (@ (@ tptp.times_times_num M2) N)))))
% 6.73/7.07 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M2))) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))) (@ tptp.numera6620942414471956472nteger (@ (@ tptp.times_times_num M2) N)))))
% 6.73/7.07 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M2))) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))) (@ tptp.numeral_numeral_rat (@ (@ tptp.times_times_num M2) N)))))
% 6.73/7.07 (assert (forall ((V2 tptp.num) (W2 tptp.num) (Y tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V2))) (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int W2))) Y)) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ (@ tptp.times_times_num V2) W2))) Y))))
% 6.73/7.07 (assert (forall ((V2 tptp.num) (W2 tptp.num) (Y tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V2))) (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W2))) Y)) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ (@ tptp.times_times_num V2) W2))) Y))))
% 6.73/7.07 (assert (forall ((V2 tptp.num) (W2 tptp.num) (Y tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex V2))) (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W2))) Y)) (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ (@ tptp.times_times_num V2) W2))) Y))))
% 6.73/7.07 (assert (forall ((V2 tptp.num) (W2 tptp.num) (Y tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger V2))) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger W2))) Y)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ (@ tptp.times_times_num V2) W2))) Y))))
% 6.73/7.07 (assert (forall ((V2 tptp.num) (W2 tptp.num) (Y tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V2))) (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W2))) Y)) (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat (@ (@ tptp.times_times_num V2) W2))) Y))))
% 6.73/7.07 (assert (forall ((V2 tptp.num) (W2 tptp.num) (Y tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int V2)) (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int W2))) Y)) (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.times_times_num V2) W2)))) Y))))
% 6.73/7.07 (assert (forall ((V2 tptp.num) (W2 tptp.num) (Y tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real V2)) (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W2))) Y)) (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ (@ tptp.times_times_num V2) W2)))) Y))))
% 6.73/7.07 (assert (forall ((V2 tptp.num) (W2 tptp.num) (Y tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex V2)) (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W2))) Y)) (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ (@ tptp.times_times_num V2) W2)))) Y))))
% 6.73/7.07 (assert (forall ((V2 tptp.num) (W2 tptp.num) (Y tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger V2)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger W2))) Y)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ (@ tptp.times_times_num V2) W2)))) Y))))
% 6.73/7.07 (assert (forall ((V2 tptp.num) (W2 tptp.num) (Y tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat V2)) (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W2))) Y)) (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ (@ tptp.times_times_num V2) W2)))) Y))))
% 6.73/7.07 (assert (forall ((V2 tptp.num) (W2 tptp.num) (Y tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V2))) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int W2)) Y)) (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.times_times_num V2) W2)))) Y))))
% 6.73/7.07 (assert (forall ((V2 tptp.num) (W2 tptp.num) (Y tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V2))) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real W2)) Y)) (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ (@ tptp.times_times_num V2) W2)))) Y))))
% 6.73/7.07 (assert (forall ((V2 tptp.num) (W2 tptp.num) (Y tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex V2))) (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex W2)) Y)) (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ (@ tptp.times_times_num V2) W2)))) Y))))
% 6.73/7.07 (assert (forall ((V2 tptp.num) (W2 tptp.num) (Y tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger V2))) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger W2)) Y)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ (@ tptp.times_times_num V2) W2)))) Y))))
% 6.73/7.07 (assert (forall ((V2 tptp.num) (W2 tptp.num) (Y tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V2))) (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat W2)) Y)) (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ (@ tptp.times_times_num V2) W2)))) Y))))
% 6.73/7.07 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M2))) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))) (@ (@ tptp.ord_less_eq_num N) M2))))
% 6.73/7.07 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M2))) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))) (@ (@ tptp.ord_less_eq_num N) M2))))
% 6.73/7.07 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M2))) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))) (@ (@ tptp.ord_less_eq_num N) M2))))
% 6.73/7.07 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M2))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) (@ (@ tptp.ord_less_eq_num N) M2))))
% 6.73/7.07 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M2))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) (@ (@ tptp.ord_less_num N) M2))))
% 6.73/7.07 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M2))) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))) (@ (@ tptp.ord_less_num N) M2))))
% 6.73/7.07 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M2))) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))) (@ (@ tptp.ord_less_num N) M2))))
% 6.73/7.07 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M2))) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))) (@ (@ tptp.ord_less_num N) M2))))
% 6.73/7.07 (assert (= (@ tptp.neg_nu3811975205180677377ec_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int tptp.one_one_int)))
% 6.73/7.07 (assert (= (@ tptp.neg_nu6075765906172075777c_real tptp.zero_zero_real) (@ tptp.uminus_uminus_real tptp.one_one_real)))
% 6.73/7.07 (assert (= (@ tptp.neg_nu6511756317524482435omplex tptp.zero_zero_complex) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))
% 6.73/7.07 (assert (= (@ tptp.neg_nu7757733837767384882nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))
% 6.73/7.07 (assert (= (@ tptp.neg_nu3179335615603231917ec_rat tptp.zero_zero_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat)))
% 6.73/7.07 (assert (forall ((M2 tptp.num)) (= (not (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M2)))) (not (= M2 tptp.one)))))
% 6.73/7.07 (assert (forall ((M2 tptp.num)) (= (not (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M2)))) (not (= M2 tptp.one)))))
% 6.73/7.07 (assert (forall ((M2 tptp.num)) (= (not (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M2)))) (not (= M2 tptp.one)))))
% 6.73/7.07 (assert (forall ((M2 tptp.num)) (= (not (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M2)))) (not (= M2 tptp.one)))))
% 6.73/7.07 (assert (forall ((B tptp.real) (W2 tptp.num) (A tptp.real)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W2)))) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real B) _let_1)) A) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) _let_1)) B)))))
% 6.73/7.07 (assert (forall ((B tptp.rat) (W2 tptp.num) (A tptp.rat)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W2)))) (= (@ (@ 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)))))
% 6.73/7.07 (assert (forall ((A tptp.real) (B tptp.real) (W2 tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W2)))) (= (@ (@ tptp.ord_less_eq_real A) (@ (@ tptp.divide_divide_real B) _let_1)) (@ (@ tptp.ord_less_eq_real B) (@ (@ tptp.times_times_real A) _let_1))))))
% 6.73/7.07 (assert (forall ((A tptp.rat) (B tptp.rat) (W2 tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W2)))) (= (@ (@ 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))))))
% 6.73/7.07 (assert (forall ((B tptp.real) (W2 tptp.num) (A tptp.real)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W2)))) (let ((_let_2 (= _let_1 tptp.zero_zero_real))) (= (= (@ (@ tptp.divide_divide_real B) _let_1) A) (and (=> (not _let_2) (= B (@ (@ tptp.times_times_real A) _let_1))) (=> _let_2 (= A tptp.zero_zero_real))))))))
% 6.73/7.07 (assert (forall ((B tptp.complex) (W2 tptp.num) (A tptp.complex)) (let ((_let_1 (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W2)))) (let ((_let_2 (= _let_1 tptp.zero_zero_complex))) (= (= (@ (@ tptp.divide1717551699836669952omplex B) _let_1) A) (and (=> (not _let_2) (= B (@ (@ tptp.times_times_complex A) _let_1))) (=> _let_2 (= A tptp.zero_zero_complex))))))))
% 6.73/7.07 (assert (forall ((B tptp.rat) (W2 tptp.num) (A tptp.rat)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W2)))) (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))))))))
% 6.73/7.07 (assert (forall ((A tptp.real) (B tptp.real) (W2 tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W2)))) (let ((_let_2 (= _let_1 tptp.zero_zero_real))) (= (= A (@ (@ tptp.divide_divide_real B) _let_1)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_real A) _let_1) B)) (=> _let_2 (= A tptp.zero_zero_real))))))))
% 6.73/7.07 (assert (forall ((A tptp.complex) (B tptp.complex) (W2 tptp.num)) (let ((_let_1 (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W2)))) (let ((_let_2 (= _let_1 tptp.zero_zero_complex))) (= (= A (@ (@ tptp.divide1717551699836669952omplex B) _let_1)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_complex A) _let_1) B)) (=> _let_2 (= A tptp.zero_zero_complex))))))))
% 6.73/7.07 (assert (forall ((A tptp.rat) (B tptp.rat) (W2 tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W2)))) (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))))))))
% 6.73/7.07 (assert (forall ((M2 tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M2))) (@ tptp.uminus_uminus_int tptp.one_one_int)) (not (= M2 tptp.one)))))
% 6.73/7.07 (assert (forall ((M2 tptp.num)) (= (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M2))) (@ tptp.uminus_uminus_real tptp.one_one_real)) (not (= M2 tptp.one)))))
% 6.73/7.07 (assert (forall ((M2 tptp.num)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M2))) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (not (= M2 tptp.one)))))
% 6.73/7.07 (assert (forall ((M2 tptp.num)) (= (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M2))) (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (not (= M2 tptp.one)))))
% 6.73/7.07 (assert (forall ((A tptp.real) (B tptp.real) (W2 tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W2)))) (= (@ (@ tptp.ord_less_real A) (@ (@ tptp.divide_divide_real B) _let_1)) (@ (@ tptp.ord_less_real B) (@ (@ tptp.times_times_real A) _let_1))))))
% 6.73/7.07 (assert (forall ((A tptp.rat) (B tptp.rat) (W2 tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W2)))) (= (@ (@ tptp.ord_less_rat A) (@ (@ tptp.divide_divide_rat B) _let_1)) (@ (@ tptp.ord_less_rat B) (@ (@ tptp.times_times_rat A) _let_1))))))
% 6.73/7.07 (assert (forall ((B tptp.real) (W2 tptp.num) (A tptp.real)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W2)))) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real B) _let_1)) A) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) _let_1)) B)))))
% 6.73/7.07 (assert (forall ((B tptp.rat) (W2 tptp.num) (A tptp.rat)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W2)))) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat B) _let_1)) A) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) _let_1)) B)))))
% 6.73/7.07 (assert (forall ((K2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int K2))) (= (@ tptp.neg_nu3811975205180677377ec_int (@ tptp.uminus_uminus_int _let_1)) (@ tptp.uminus_uminus_int (@ tptp.neg_nu5851722552734809277nc_int _let_1))))))
% 6.73/7.07 (assert (forall ((K2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real K2))) (= (@ tptp.neg_nu6075765906172075777c_real (@ tptp.uminus_uminus_real _let_1)) (@ tptp.uminus_uminus_real (@ tptp.neg_nu8295874005876285629c_real _let_1))))))
% 6.73/7.07 (assert (forall ((K2 tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex K2))) (= (@ tptp.neg_nu6511756317524482435omplex (@ tptp.uminus1482373934393186551omplex _let_1)) (@ tptp.uminus1482373934393186551omplex (@ tptp.neg_nu8557863876264182079omplex _let_1))))))
% 6.73/7.07 (assert (forall ((K2 tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger K2))) (= (@ tptp.neg_nu7757733837767384882nteger (@ tptp.uminus1351360451143612070nteger _let_1)) (@ tptp.uminus1351360451143612070nteger (@ tptp.neg_nu5831290666863070958nteger _let_1))))))
% 6.73/7.07 (assert (forall ((K2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat K2))) (= (@ tptp.neg_nu3179335615603231917ec_rat (@ tptp.uminus_uminus_rat _let_1)) (@ tptp.uminus_uminus_rat (@ tptp.neg_nu5219082963157363817nc_rat _let_1))))))
% 6.73/7.07 (assert (forall ((K2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int K2))) (= (@ tptp.neg_nu5851722552734809277nc_int (@ tptp.uminus_uminus_int _let_1)) (@ tptp.uminus_uminus_int (@ tptp.neg_nu3811975205180677377ec_int _let_1))))))
% 6.73/7.07 (assert (forall ((K2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real K2))) (= (@ tptp.neg_nu8295874005876285629c_real (@ tptp.uminus_uminus_real _let_1)) (@ tptp.uminus_uminus_real (@ tptp.neg_nu6075765906172075777c_real _let_1))))))
% 6.73/7.07 (assert (forall ((K2 tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex K2))) (= (@ tptp.neg_nu8557863876264182079omplex (@ tptp.uminus1482373934393186551omplex _let_1)) (@ tptp.uminus1482373934393186551omplex (@ tptp.neg_nu6511756317524482435omplex _let_1))))))
% 6.73/7.07 (assert (forall ((K2 tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger K2))) (= (@ tptp.neg_nu5831290666863070958nteger (@ tptp.uminus1351360451143612070nteger _let_1)) (@ tptp.uminus1351360451143612070nteger (@ tptp.neg_nu7757733837767384882nteger _let_1))))))
% 6.73/7.07 (assert (forall ((K2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat K2))) (= (@ tptp.neg_nu5219082963157363817nc_rat (@ tptp.uminus_uminus_rat _let_1)) (@ tptp.uminus_uminus_rat (@ tptp.neg_nu3179335615603231917ec_rat _let_1))))))
% 6.73/7.07 (assert (forall ((N tptp.nat) (K2 tptp.num)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.suc N)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 K2)))) (@ (@ tptp.times_times_int (@ (@ tptp.bit_ri631733984087533419it_int N) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K2)))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))))
% 6.73/7.07 (assert (forall ((N tptp.nat) (K2 tptp.num)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.suc N)) (@ tptp.numeral_numeral_int (@ tptp.bit0 K2))) (@ (@ tptp.times_times_int (@ (@ tptp.bit_ri631733984087533419it_int N) (@ tptp.numeral_numeral_int K2))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))))
% 6.73/7.07 (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))))))
% 6.73/7.07 (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))))))
% 6.73/7.07 (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))))))
% 6.73/7.07 (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))))))
% 6.73/7.07 (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))))))
% 6.73/7.07 (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))))
% 6.73/7.07 (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))))
% 6.73/7.07 (assert (= (@ (@ tptp.minus_minus_complex tptp.one_one_complex) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))
% 6.73/7.07 (assert (= (@ (@ tptp.minus_8373710615458151222nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))
% 6.73/7.07 (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))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (assert (= (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) tptp.one_one_complex) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))))
% 6.73/7.07 (assert (= (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (assert (forall ((M2 tptp.num)) (= (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M2))) tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.plus_plus_num M2) tptp.one))))))
% 6.73/7.07 (assert (forall ((M2 tptp.num)) (= (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M2))) tptp.one_one_real) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ (@ tptp.plus_plus_num M2) tptp.one))))))
% 6.73/7.07 (assert (forall ((M2 tptp.num)) (= (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex M2))) tptp.one_one_complex) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ (@ tptp.plus_plus_num M2) tptp.one))))))
% 6.73/7.07 (assert (forall ((M2 tptp.num)) (= (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M2))) tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ (@ tptp.plus_plus_num M2) tptp.one))))))
% 6.73/7.07 (assert (forall ((M2 tptp.num)) (= (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M2))) tptp.one_one_rat) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ (@ tptp.plus_plus_num M2) tptp.one))))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (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))))))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (assert (= (@ tptp.neg_nu7009210354673126013omplex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))))
% 6.73/7.07 (assert (= (@ tptp.neg_nu8804712462038260780nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (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)))
% 6.73/7.07 (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)))
% 6.73/7.07 (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)))
% 6.73/7.07 (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)))
% 6.73/7.07 (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)))
% 6.73/7.07 (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)))))))
% 6.73/7.07 (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)))))))
% 6.73/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (= (= A (@ tptp.uminus_uminus_int B)) (= B (@ tptp.uminus_uminus_int A)))))
% 6.73/7.07 (assert (forall ((A tptp.real) (B tptp.real)) (= (= A (@ tptp.uminus_uminus_real B)) (= B (@ tptp.uminus_uminus_real A)))))
% 6.73/7.07 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= A (@ tptp.uminus1482373934393186551omplex B)) (= B (@ tptp.uminus1482373934393186551omplex A)))))
% 6.73/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= A (@ tptp.uminus1351360451143612070nteger B)) (= B (@ tptp.uminus1351360451143612070nteger A)))))
% 6.73/7.07 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= A (@ tptp.uminus_uminus_rat B)) (= B (@ tptp.uminus_uminus_rat A)))))
% 6.73/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (= (= (@ tptp.uminus_uminus_int A) B) (= (@ tptp.uminus_uminus_int B) A))))
% 6.73/7.07 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ tptp.uminus_uminus_real A) B) (= (@ tptp.uminus_uminus_real B) A))))
% 6.73/7.07 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= (@ tptp.uminus1482373934393186551omplex A) B) (= (@ tptp.uminus1482373934393186551omplex B) A))))
% 6.73/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= (@ tptp.uminus1351360451143612070nteger A) B) (= (@ tptp.uminus1351360451143612070nteger B) A))))
% 6.73/7.07 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ tptp.uminus_uminus_rat A) B) (= (@ tptp.uminus_uminus_rat B) A))))
% 6.73/7.07 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1408675320244567234ct_nat M2)) (@ tptp.semiri1408675320244567234ct_nat N)))))
% 6.73/7.07 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat N) (@ tptp.semiri1408675320244567234ct_nat N))))
% 6.73/7.07 (assert (forall ((N tptp.nat)) (not (= (@ tptp.semiri5044797733671781792omplex N) tptp.zero_zero_complex))))
% 6.73/7.07 (assert (forall ((N tptp.nat)) (not (= (@ tptp.semiri773545260158071498ct_rat N) tptp.zero_zero_rat))))
% 6.73/7.07 (assert (forall ((N tptp.nat)) (not (= (@ tptp.semiri1406184849735516958ct_int N) tptp.zero_zero_int))))
% 6.73/7.07 (assert (forall ((N tptp.nat)) (not (= (@ tptp.semiri1408675320244567234ct_nat N) tptp.zero_zero_nat))))
% 6.73/7.07 (assert (forall ((N tptp.nat)) (not (= (@ tptp.semiri2265585572941072030t_real N) tptp.zero_zero_real))))
% 6.73/7.07 (assert (forall ((Y tptp.set_nat) (X tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat (@ tptp.uminus5710092332889474511et_nat Y)) X) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.uminus5710092332889474511et_nat X)) Y))))
% 6.73/7.07 (assert (forall ((Y tptp.set_nat) (X tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat Y) (@ tptp.uminus5710092332889474511et_nat X)) (@ (@ tptp.ord_less_eq_set_nat X) (@ tptp.uminus5710092332889474511et_nat Y)))))
% 6.73/7.07 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat X) Y) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.uminus5710092332889474511et_nat Y)) (@ tptp.uminus5710092332889474511et_nat X)))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger A) B) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger A)))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (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))))
% 6.73/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger A)) B) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger B)) A))))
% 6.73/7.07 (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))))
% 6.73/7.07 (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))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger A) (@ tptp.uminus1351360451143612070nteger B)) (@ (@ tptp.ord_le3102999989581377725nteger B) (@ tptp.uminus1351360451143612070nteger A)))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger A) (@ tptp.uminus1351360451143612070nteger B)) (@ (@ tptp.ord_le6747313008572928689nteger B) (@ tptp.uminus1351360451143612070nteger A)))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (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))))
% 6.73/7.07 (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))))
% 6.73/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger A)) B) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger B)) A))))
% 6.73/7.07 (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))))
% 6.73/7.07 (assert (forall ((M2 tptp.num) (N tptp.num)) (not (= (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M2)) (@ tptp.numeral_numeral_int N)))))
% 6.73/7.07 (assert (forall ((M2 tptp.num) (N tptp.num)) (not (= (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M2)) (@ tptp.numeral_numeral_real N)))))
% 6.73/7.07 (assert (forall ((M2 tptp.num) (N tptp.num)) (not (= (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex M2)) (@ tptp.numera6690914467698888265omplex N)))))
% 6.73/7.07 (assert (forall ((M2 tptp.num) (N tptp.num)) (not (= (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M2)) (@ tptp.numera6620942414471956472nteger N)))))
% 6.73/7.07 (assert (forall ((M2 tptp.num) (N tptp.num)) (not (= (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M2)) (@ tptp.numeral_numeral_rat N)))))
% 6.73/7.07 (assert (forall ((M2 tptp.num) (N tptp.num)) (not (= (@ tptp.numeral_numeral_int M2) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))))))
% 6.73/7.07 (assert (forall ((M2 tptp.num) (N tptp.num)) (not (= (@ tptp.numeral_numeral_real M2) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))))))
% 6.73/7.07 (assert (forall ((M2 tptp.num) (N tptp.num)) (not (= (@ tptp.numera6690914467698888265omplex M2) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N))))))
% 6.73/7.07 (assert (forall ((M2 tptp.num) (N tptp.num)) (not (= (@ tptp.numera6620942414471956472nteger M2) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))))))
% 6.73/7.07 (assert (forall ((M2 tptp.num) (N tptp.num)) (not (= (@ tptp.numeral_numeral_rat M2) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex A)) B) (@ (@ tptp.times_times_complex A) (@ tptp.uminus1482373934393186551omplex B)))))
% 6.73/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger A)) B) (@ (@ tptp.times_3573771949741848930nteger A) (@ tptp.uminus1351360451143612070nteger B)))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (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))))))
% 6.73/7.07 (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))))))
% 6.73/7.07 (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))))))
% 6.73/7.07 (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))))))
% 6.73/7.07 (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))))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (assert (forall ((A4 tptp.int) (K2 tptp.int) (A tptp.int)) (=> (= A4 (@ (@ tptp.plus_plus_int K2) A)) (= (@ tptp.uminus_uminus_int A4) (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int K2)) (@ tptp.uminus_uminus_int A))))))
% 6.73/7.07 (assert (forall ((A4 tptp.real) (K2 tptp.real) (A tptp.real)) (=> (= A4 (@ (@ tptp.plus_plus_real K2) A)) (= (@ tptp.uminus_uminus_real A4) (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real K2)) (@ tptp.uminus_uminus_real A))))))
% 6.73/7.07 (assert (forall ((A4 tptp.complex) (K2 tptp.complex) (A tptp.complex)) (=> (= A4 (@ (@ tptp.plus_plus_complex K2) A)) (= (@ tptp.uminus1482373934393186551omplex A4) (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex K2)) (@ tptp.uminus1482373934393186551omplex A))))))
% 6.73/7.07 (assert (forall ((A4 tptp.code_integer) (K2 tptp.code_integer) (A tptp.code_integer)) (=> (= A4 (@ (@ tptp.plus_p5714425477246183910nteger K2) A)) (= (@ tptp.uminus1351360451143612070nteger A4) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger K2)) (@ tptp.uminus1351360451143612070nteger A))))))
% 6.73/7.07 (assert (forall ((A4 tptp.rat) (K2 tptp.rat) (A tptp.rat)) (=> (= A4 (@ (@ tptp.plus_plus_rat K2) A)) (= (@ tptp.uminus_uminus_rat A4) (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat K2)) (@ tptp.uminus_uminus_rat A))))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (assert (not (= tptp.one_one_int (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 6.73/7.07 (assert (not (= tptp.one_one_real (@ tptp.uminus_uminus_real tptp.one_one_real))))
% 6.73/7.07 (assert (not (= tptp.one_one_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))))
% 6.73/7.07 (assert (not (= tptp.one_one_Code_integer (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 6.73/7.07 (assert (not (= tptp.one_one_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat))))
% 6.73/7.07 (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))))
% 6.73/7.07 (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))))
% 6.73/7.07 (assert (forall ((B tptp.complex) (A tptp.complex)) (= (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex B)) A) (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex A)) B))))
% 6.73/7.07 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger B)) A) (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger A)) B))))
% 6.73/7.07 (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))))
% 6.73/7.07 (assert (forall ((N tptp.nat) (K2 tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.bit_ri631733984087533419it_int N))) (= (@ _let_1 (@ (@ tptp.times_times_int (@ _let_1 K2)) (@ _let_1 L))) (@ _let_1 (@ (@ tptp.times_times_int K2) L))))))
% 6.73/7.07 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M2) (=> (@ (@ tptp.ord_less_nat M2) N) (@ (@ tptp.ord_less_nat (@ tptp.semiri1408675320244567234ct_nat M2)) (@ tptp.semiri1408675320244567234ct_nat N))))))
% 6.73/7.07 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.semiri773545260158071498ct_rat N))))
% 6.73/7.07 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.semiri1406184849735516958ct_int N))))
% 6.73/7.07 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ tptp.semiri1408675320244567234ct_nat N))))
% 6.73/7.07 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.semiri2265585572941072030t_real N))))
% 6.73/7.07 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_rat (@ tptp.semiri773545260158071498ct_rat N)) tptp.zero_zero_rat))))
% 6.73/7.07 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_int (@ tptp.semiri1406184849735516958ct_int N)) tptp.zero_zero_int))))
% 6.73/7.07 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat (@ tptp.semiri1408675320244567234ct_nat N)) tptp.zero_zero_nat))))
% 6.73/7.07 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_real (@ tptp.semiri2265585572941072030t_real N)) tptp.zero_zero_real))))
% 6.73/7.07 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.semiri773545260158071498ct_rat N))))
% 6.73/7.07 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.semiri1406184849735516958ct_int N))))
% 6.73/7.07 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.semiri1408675320244567234ct_nat N))))
% 6.73/7.07 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.semiri2265585572941072030t_real N))))
% 6.73/7.07 (assert (forall ((N tptp.nat)) (@ tptp.finite_finite_nat (@ tptp.nat_set_decode N))))
% 6.73/7.07 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (@ tptp.semiri3624122377584611663nteger N))))
% 6.73/7.07 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ tptp.semiri773545260158071498ct_rat N))))
% 6.73/7.07 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.semiri1406184849735516958ct_int N))))
% 6.73/7.07 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) (@ tptp.semiri1408675320244567234ct_nat N))))
% 6.73/7.07 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.semiri2265585572941072030t_real N))))
% 6.73/7.07 (assert (forall ((M2 tptp.num) (N tptp.num)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M2))) (@ tptp.numeral_numeral_real N))))
% 6.73/7.07 (assert (forall ((M2 tptp.num) (N tptp.num)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M2))) (@ tptp.numera6620942414471956472nteger N))))
% 6.73/7.07 (assert (forall ((M2 tptp.num) (N tptp.num)) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M2))) (@ tptp.numeral_numeral_rat N))))
% 6.73/7.07 (assert (forall ((M2 tptp.num) (N tptp.num)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M2))) (@ tptp.numeral_numeral_int N))))
% 6.73/7.07 (assert (forall ((M2 tptp.num) (N tptp.num)) (not (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real M2)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))))))
% 6.73/7.07 (assert (forall ((M2 tptp.num) (N tptp.num)) (not (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.numera6620942414471956472nteger M2)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))))))
% 6.73/7.07 (assert (forall ((M2 tptp.num) (N tptp.num)) (not (@ (@ tptp.ord_less_eq_rat (@ tptp.numeral_numeral_rat M2)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))))))
% 6.73/7.07 (assert (forall ((M2 tptp.num) (N tptp.num)) (not (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int M2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))))))
% 6.73/7.07 (assert (forall ((N tptp.num)) (not (= tptp.zero_zero_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))))))
% 6.73/7.07 (assert (forall ((N tptp.num)) (not (= tptp.zero_zero_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))))))
% 6.73/7.07 (assert (forall ((N tptp.num)) (not (= tptp.zero_zero_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N))))))
% 6.73/7.07 (assert (forall ((N tptp.num)) (not (= tptp.zero_z3403309356797280102nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))))))
% 6.73/7.07 (assert (forall ((N tptp.num)) (not (= tptp.zero_zero_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))))))
% 6.73/7.07 (assert (forall ((M2 tptp.num) (N tptp.num)) (not (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int M2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))))))
% 6.73/7.07 (assert (forall ((M2 tptp.num) (N tptp.num)) (not (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real M2)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))))))
% 6.73/7.07 (assert (forall ((M2 tptp.num) (N tptp.num)) (not (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.numera6620942414471956472nteger M2)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))))))
% 6.73/7.07 (assert (forall ((M2 tptp.num) (N tptp.num)) (not (@ (@ tptp.ord_less_rat (@ tptp.numeral_numeral_rat M2)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))))))
% 6.73/7.07 (assert (forall ((M2 tptp.num) (N tptp.num)) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M2))) (@ tptp.numeral_numeral_int N))))
% 6.73/7.07 (assert (forall ((M2 tptp.num) (N tptp.num)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M2))) (@ tptp.numeral_numeral_real N))))
% 6.73/7.07 (assert (forall ((M2 tptp.num) (N tptp.num)) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M2))) (@ tptp.numera6620942414471956472nteger N))))
% 6.73/7.07 (assert (forall ((M2 tptp.num) (N tptp.num)) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M2))) (@ tptp.numeral_numeral_rat N))))
% 6.73/7.07 (assert (not (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.uminus_uminus_real tptp.one_one_real))))
% 6.73/7.07 (assert (not (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 6.73/7.07 (assert (not (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat))))
% 6.73/7.07 (assert (not (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 6.73/7.07 (assert (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.one_one_real))
% 6.73/7.07 (assert (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.one_one_Code_integer))
% 6.73/7.07 (assert (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.one_one_rat))
% 6.73/7.07 (assert (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.one_one_int))
% 6.73/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (= (= (@ (@ tptp.plus_plus_int A) B) tptp.zero_zero_int) (= B (@ tptp.uminus_uminus_int A)))))
% 6.73/7.07 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ (@ tptp.plus_plus_real A) B) tptp.zero_zero_real) (= B (@ tptp.uminus_uminus_real A)))))
% 6.73/7.07 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= (@ (@ tptp.plus_plus_complex A) B) tptp.zero_zero_complex) (= B (@ tptp.uminus1482373934393186551omplex A)))))
% 6.73/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= (@ (@ tptp.plus_p5714425477246183910nteger A) B) tptp.zero_z3403309356797280102nteger) (= B (@ tptp.uminus1351360451143612070nteger A)))))
% 6.73/7.07 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat A) B) tptp.zero_zero_rat) (= B (@ tptp.uminus_uminus_rat A)))))
% 6.73/7.07 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int A)) A) tptp.zero_zero_int)))
% 6.73/7.07 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A)) A) tptp.zero_zero_real)))
% 6.73/7.07 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex A)) A) tptp.zero_zero_complex)))
% 6.73/7.07 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger A)) A) tptp.zero_z3403309356797280102nteger)))
% 6.73/7.07 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat A)) A) tptp.zero_zero_rat)))
% 6.73/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (=> (= (@ (@ tptp.plus_plus_int A) B) tptp.zero_zero_int) (= (@ tptp.uminus_uminus_int A) B))))
% 6.73/7.07 (assert (forall ((A tptp.real) (B tptp.real)) (=> (= (@ (@ tptp.plus_plus_real A) B) tptp.zero_zero_real) (= (@ tptp.uminus_uminus_real A) B))))
% 6.73/7.07 (assert (forall ((A tptp.complex) (B tptp.complex)) (=> (= (@ (@ tptp.plus_plus_complex A) B) tptp.zero_zero_complex) (= (@ tptp.uminus1482373934393186551omplex A) B))))
% 6.73/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (= (@ (@ tptp.plus_p5714425477246183910nteger A) B) tptp.zero_z3403309356797280102nteger) (= (@ tptp.uminus1351360451143612070nteger A) B))))
% 6.73/7.07 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (= (@ (@ tptp.plus_plus_rat A) B) tptp.zero_zero_rat) (= (@ tptp.uminus_uminus_rat A) B))))
% 6.73/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (= (= A (@ tptp.uminus_uminus_int B)) (= (@ (@ tptp.plus_plus_int A) B) tptp.zero_zero_int))))
% 6.73/7.07 (assert (forall ((A tptp.real) (B tptp.real)) (= (= A (@ tptp.uminus_uminus_real B)) (= (@ (@ tptp.plus_plus_real A) B) tptp.zero_zero_real))))
% 6.73/7.07 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= A (@ tptp.uminus1482373934393186551omplex B)) (= (@ (@ tptp.plus_plus_complex A) B) tptp.zero_zero_complex))))
% 6.73/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= A (@ tptp.uminus1351360451143612070nteger B)) (= (@ (@ tptp.plus_p5714425477246183910nteger A) B) tptp.zero_z3403309356797280102nteger))))
% 6.73/7.07 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= A (@ tptp.uminus_uminus_rat B)) (= (@ (@ tptp.plus_plus_rat A) B) tptp.zero_zero_rat))))
% 6.73/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (= (= (@ tptp.uminus_uminus_int A) B) (= (@ (@ tptp.plus_plus_int A) B) tptp.zero_zero_int))))
% 6.73/7.07 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ tptp.uminus_uminus_real A) B) (= (@ (@ tptp.plus_plus_real A) B) tptp.zero_zero_real))))
% 6.73/7.07 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= (@ tptp.uminus1482373934393186551omplex A) B) (= (@ (@ tptp.plus_plus_complex A) B) tptp.zero_zero_complex))))
% 6.73/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= (@ tptp.uminus1351360451143612070nteger A) B) (= (@ (@ tptp.plus_p5714425477246183910nteger A) B) tptp.zero_z3403309356797280102nteger))))
% 6.73/7.07 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ tptp.uminus_uminus_rat A) B) (= (@ (@ tptp.plus_plus_rat A) B) tptp.zero_zero_rat))))
% 6.73/7.07 (assert (not (= tptp.zero_zero_int (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 6.73/7.07 (assert (not (= tptp.zero_zero_real (@ tptp.uminus_uminus_real tptp.one_one_real))))
% 6.73/7.07 (assert (not (= tptp.zero_zero_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))))
% 6.73/7.07 (assert (not (= tptp.zero_z3403309356797280102nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 6.73/7.07 (assert (not (= tptp.zero_zero_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat))))
% 6.73/7.07 (assert (not (@ (@ tptp.ord_less_int tptp.one_one_int) (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 6.73/7.07 (assert (not (@ (@ tptp.ord_less_real tptp.one_one_real) (@ tptp.uminus_uminus_real tptp.one_one_real))))
% 6.73/7.07 (assert (not (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 6.73/7.07 (assert (not (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat))))
% 6.73/7.07 (assert (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.one_one_int))
% 6.73/7.07 (assert (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.one_one_real))
% 6.73/7.07 (assert (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.one_one_Code_integer))
% 6.73/7.07 (assert (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.one_one_rat))
% 6.73/7.07 (assert (forall ((W2 tptp.num) (X tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int W2))) (= (@ (@ tptp.times_times_int _let_1) (@ tptp.uminus_uminus_int X)) (@ (@ tptp.times_times_int X) (@ tptp.uminus_uminus_int _let_1))))))
% 6.73/7.07 (assert (forall ((W2 tptp.num) (X tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real W2))) (= (@ (@ tptp.times_times_real _let_1) (@ tptp.uminus_uminus_real X)) (@ (@ tptp.times_times_real X) (@ tptp.uminus_uminus_real _let_1))))))
% 6.73/7.07 (assert (forall ((W2 tptp.num) (X tptp.complex)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex W2))) (= (@ (@ tptp.times_times_complex _let_1) (@ tptp.uminus1482373934393186551omplex X)) (@ (@ tptp.times_times_complex X) (@ tptp.uminus1482373934393186551omplex _let_1))))))
% 6.73/7.07 (assert (forall ((W2 tptp.num) (X tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger W2))) (= (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ tptp.uminus1351360451143612070nteger X)) (@ (@ tptp.times_3573771949741848930nteger X) (@ tptp.uminus1351360451143612070nteger _let_1))))))
% 6.73/7.07 (assert (forall ((W2 tptp.num) (X tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_rat W2))) (= (@ (@ tptp.times_times_rat _let_1) (@ tptp.uminus_uminus_rat X)) (@ (@ tptp.times_times_rat X) (@ tptp.uminus_uminus_rat _let_1))))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (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)))))))
% 6.73/7.07 (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)))))))
% 6.73/7.07 (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)))))))
% 6.73/7.07 (assert (forall ((N tptp.num)) (not (= tptp.one_one_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))))))
% 6.73/7.07 (assert (forall ((N tptp.num)) (not (= tptp.one_one_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))))))
% 6.73/7.07 (assert (forall ((N tptp.num)) (not (= tptp.one_one_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N))))))
% 6.73/7.07 (assert (forall ((N tptp.num)) (not (= tptp.one_one_Code_integer (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))))))
% 6.73/7.07 (assert (forall ((N tptp.num)) (not (= tptp.one_one_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))))))
% 6.73/7.07 (assert (forall ((N tptp.num)) (not (= (@ tptp.numeral_numeral_int N) (@ tptp.uminus_uminus_int tptp.one_one_int)))))
% 6.73/7.07 (assert (forall ((N tptp.num)) (not (= (@ tptp.numeral_numeral_real N) (@ tptp.uminus_uminus_real tptp.one_one_real)))))
% 6.73/7.07 (assert (forall ((N tptp.num)) (not (= (@ tptp.numera6690914467698888265omplex N) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))))
% 6.73/7.07 (assert (forall ((N tptp.num)) (not (= (@ tptp.numera6620942414471956472nteger N) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))))
% 6.73/7.07 (assert (forall ((N tptp.num)) (not (= (@ tptp.numeral_numeral_rat N) (@ tptp.uminus_uminus_rat tptp.one_one_rat)))))
% 6.73/7.07 (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))))))
% 6.73/7.07 (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))))))
% 6.73/7.07 (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))))))
% 6.73/7.07 (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))))))
% 6.73/7.07 (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))))))
% 6.73/7.07 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (@ (@ tptp.ord_less_eq_rat (@ tptp.semiri773545260158071498ct_rat M2)) (@ tptp.semiri773545260158071498ct_rat N)))))
% 6.73/7.07 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1406184849735516958ct_int M2)) (@ tptp.semiri1406184849735516958ct_int N)))))
% 6.73/7.07 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1408675320244567234ct_nat M2)) (@ tptp.semiri1408675320244567234ct_nat N)))))
% 6.73/7.07 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (@ (@ tptp.ord_less_eq_real (@ tptp.semiri2265585572941072030t_real M2)) (@ tptp.semiri2265585572941072030t_real N)))))
% 6.73/7.07 (assert (= tptp.minus_minus_int (lambda ((A5 tptp.int) (B4 tptp.int)) (@ (@ tptp.plus_plus_int A5) (@ tptp.uminus_uminus_int B4)))))
% 6.73/7.07 (assert (= tptp.minus_minus_real (lambda ((A5 tptp.real) (B4 tptp.real)) (@ (@ tptp.plus_plus_real A5) (@ tptp.uminus_uminus_real B4)))))
% 6.73/7.07 (assert (= tptp.minus_minus_complex (lambda ((A5 tptp.complex) (B4 tptp.complex)) (@ (@ tptp.plus_plus_complex A5) (@ tptp.uminus1482373934393186551omplex B4)))))
% 6.73/7.07 (assert (= tptp.minus_8373710615458151222nteger (lambda ((A5 tptp.code_integer) (B4 tptp.code_integer)) (@ (@ tptp.plus_p5714425477246183910nteger A5) (@ tptp.uminus1351360451143612070nteger B4)))))
% 6.73/7.07 (assert (= tptp.minus_minus_rat (lambda ((A5 tptp.rat) (B4 tptp.rat)) (@ (@ tptp.plus_plus_rat A5) (@ tptp.uminus_uminus_rat B4)))))
% 6.73/7.07 (assert (= tptp.minus_minus_int (lambda ((A5 tptp.int) (B4 tptp.int)) (@ (@ tptp.plus_plus_int A5) (@ tptp.uminus_uminus_int B4)))))
% 6.73/7.07 (assert (= tptp.minus_minus_real (lambda ((A5 tptp.real) (B4 tptp.real)) (@ (@ tptp.plus_plus_real A5) (@ tptp.uminus_uminus_real B4)))))
% 6.73/7.07 (assert (= tptp.minus_minus_complex (lambda ((A5 tptp.complex) (B4 tptp.complex)) (@ (@ tptp.plus_plus_complex A5) (@ tptp.uminus1482373934393186551omplex B4)))))
% 6.73/7.07 (assert (= tptp.minus_8373710615458151222nteger (lambda ((A5 tptp.code_integer) (B4 tptp.code_integer)) (@ (@ tptp.plus_p5714425477246183910nteger A5) (@ tptp.uminus1351360451143612070nteger B4)))))
% 6.73/7.07 (assert (= tptp.minus_minus_rat (lambda ((A5 tptp.rat) (B4 tptp.rat)) (@ (@ tptp.plus_plus_rat A5) (@ tptp.uminus_uminus_rat B4)))))
% 6.73/7.07 (assert (forall ((B5 tptp.int) (K2 tptp.int) (B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int A))) (=> (= B5 (@ (@ tptp.plus_plus_int K2) B)) (= (@ _let_1 B5) (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int K2)) (@ _let_1 B)))))))
% 6.73/7.07 (assert (forall ((B5 tptp.real) (K2 tptp.real) (B tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.minus_minus_real A))) (=> (= B5 (@ (@ tptp.plus_plus_real K2) B)) (= (@ _let_1 B5) (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real K2)) (@ _let_1 B)))))))
% 6.73/7.07 (assert (forall ((B5 tptp.complex) (K2 tptp.complex) (B tptp.complex) (A tptp.complex)) (let ((_let_1 (@ tptp.minus_minus_complex A))) (=> (= B5 (@ (@ tptp.plus_plus_complex K2) B)) (= (@ _let_1 B5) (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex K2)) (@ _let_1 B)))))))
% 6.73/7.07 (assert (forall ((B5 tptp.code_integer) (K2 tptp.code_integer) (B tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.minus_8373710615458151222nteger A))) (=> (= B5 (@ (@ tptp.plus_p5714425477246183910nteger K2) B)) (= (@ _let_1 B5) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger K2)) (@ _let_1 B)))))))
% 6.73/7.07 (assert (forall ((B5 tptp.rat) (K2 tptp.rat) (B tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.minus_minus_rat A))) (=> (= B5 (@ (@ tptp.plus_plus_rat K2) B)) (= (@ _let_1 B5) (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat K2)) (@ _let_1 B)))))))
% 6.73/7.07 (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))))))
% 6.73/7.07 (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))))))
% 6.73/7.07 (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))))))
% 6.73/7.07 (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))))))
% 6.73/7.07 (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))))))
% 6.73/7.07 (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)))))))
% 6.73/7.07 (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)))))))
% 6.73/7.07 (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)))))))
% 6.73/7.07 (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)))))))
% 6.73/7.07 (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)))))))
% 6.73/7.07 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M2) (@ (@ tptp.dvd_dvd_int (@ tptp.semiri1406184849735516958ct_int N)) (@ tptp.semiri1406184849735516958ct_int M2)))))
% 6.73/7.07 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M2) (@ (@ tptp.dvd_dvd_nat (@ tptp.semiri1408675320244567234ct_nat N)) (@ tptp.semiri1408675320244567234ct_nat M2)))))
% 6.73/7.07 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M2) (@ (@ tptp.dvd_dvd_real (@ tptp.semiri2265585572941072030t_real N)) (@ tptp.semiri2265585572941072030t_real M2)))))
% 6.73/7.07 (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))))
% 6.73/7.07 (assert (forall ((P2 (-> tptp.int Bool)) (Z3 tptp.int)) (=> (forall ((N3 tptp.nat)) (@ P2 (@ tptp.semiri1314217659103216013at_int N3))) (=> (forall ((N3 tptp.nat)) (@ P2 (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N3))))) (@ P2 Z3)))))
% 6.73/7.07 (assert (forall ((Z3 tptp.int)) (=> (forall ((N3 tptp.nat)) (not (= Z3 (@ tptp.semiri1314217659103216013at_int N3)))) (not (forall ((N3 tptp.nat)) (not (= Z3 (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N3))))))))))
% 6.73/7.07 (assert (forall ((M2 tptp.int) (N tptp.int)) (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (= (@ (@ tptp.times_times_int M2) N) tptp.one_one_int) (or (and (= M2 tptp.one_one_int) (= N tptp.one_one_int)) (and (= M2 _let_1) (= N _let_1)))))))
% 6.73/7.07 (assert (forall ((M2 tptp.int) (N tptp.int)) (=> (= (@ (@ tptp.times_times_int M2) N) tptp.one_one_int) (or (= M2 tptp.one_one_int) (= M2 (@ tptp.uminus_uminus_int tptp.one_one_int))))))
% 6.73/7.07 (assert (forall ((K2 tptp.int) (L tptp.int)) (=> (not (= (@ (@ tptp.modulo_modulo_int (@ tptp.uminus_uminus_int K2)) L) tptp.zero_zero_int)) (not (= (@ (@ tptp.modulo_modulo_int K2) L) tptp.zero_zero_int)))))
% 6.73/7.07 (assert (forall ((K2 tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.modulo_modulo_int K2))) (=> (not (= (@ _let_1 (@ tptp.uminus_uminus_int L)) tptp.zero_zero_int)) (not (= (@ _let_1 L) tptp.zero_zero_int))))))
% 6.73/7.07 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.comm_s2602460028002588243omplex (@ tptp.uminus1482373934393186551omplex (@ tptp.semiri8010041392384452111omplex N))) N) (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) N)) (@ tptp.semiri5044797733671781792omplex N)))))
% 6.73/7.07 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.comm_s8582702949713902594nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.semiri4939895301339042750nteger N))) N) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) N)) (@ tptp.semiri3624122377584611663nteger N)))))
% 6.73/7.07 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.comm_s4028243227959126397er_rat (@ tptp.uminus_uminus_rat (@ tptp.semiri681578069525770553at_rat N))) N) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) N)) (@ tptp.semiri773545260158071498ct_rat N)))))
% 6.73/7.07 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.comm_s4660882817536571857er_int (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N))) N) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) N)) (@ tptp.semiri1406184849735516958ct_int N)))))
% 6.73/7.07 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.comm_s7457072308508201937r_real (@ tptp.uminus_uminus_real (@ tptp.semiri5074537144036343181t_real N))) N) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N)) (@ tptp.semiri2265585572941072030t_real N)))))
% 6.73/7.07 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.semiri1408675320244567234ct_nat N))))
% 6.73/7.07 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) M2) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (@ (@ tptp.dvd_dvd_nat M2) (@ tptp.semiri1408675320244567234ct_nat N))))))
% 6.73/7.07 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))))))
% 6.73/7.07 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))))))
% 6.73/7.07 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))))))
% 6.73/7.07 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))))))
% 6.73/7.07 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))) tptp.zero_zero_real)))
% 6.73/7.07 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))) tptp.zero_z3403309356797280102nteger)))
% 6.73/7.07 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))) tptp.zero_zero_rat)))
% 6.73/7.07 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) tptp.zero_zero_int)))
% 6.73/7.07 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))))))
% 6.73/7.07 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))))))
% 6.73/7.07 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))))))
% 6.73/7.07 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))))))
% 6.73/7.07 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) tptp.zero_zero_int)))
% 6.73/7.07 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))) tptp.zero_zero_real)))
% 6.73/7.07 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))) tptp.zero_z3403309356797280102nteger)))
% 6.73/7.07 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))) tptp.zero_zero_rat)))
% 6.73/7.07 (assert (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.zero_zero_real))
% 6.73/7.07 (assert (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.zero_z3403309356797280102nteger))
% 6.73/7.07 (assert (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.zero_zero_rat))
% 6.73/7.07 (assert (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.zero_zero_int))
% 6.73/7.07 (assert (not (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.uminus_uminus_real tptp.one_one_real))))
% 6.73/7.07 (assert (not (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 6.73/7.07 (assert (not (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat))))
% 6.73/7.07 (assert (not (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 6.73/7.07 (assert (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.zero_zero_int))
% 6.73/7.07 (assert (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.zero_zero_real))
% 6.73/7.07 (assert (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.zero_z3403309356797280102nteger))
% 6.73/7.07 (assert (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.zero_zero_rat))
% 6.73/7.07 (assert (not (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 6.73/7.07 (assert (not (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.uminus_uminus_real tptp.one_one_real))))
% 6.73/7.07 (assert (not (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 6.73/7.07 (assert (not (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat))))
% 6.73/7.07 (assert (forall ((M2 tptp.num)) (not (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M2))))))
% 6.73/7.07 (assert (forall ((M2 tptp.num)) (not (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M2))))))
% 6.73/7.07 (assert (forall ((M2 tptp.num)) (not (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M2))))))
% 6.73/7.07 (assert (forall ((M2 tptp.num)) (not (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M2))))))
% 6.73/7.07 (assert (forall ((M2 tptp.num)) (not (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real M2)) (@ tptp.uminus_uminus_real tptp.one_one_real)))))
% 6.73/7.07 (assert (forall ((M2 tptp.num)) (not (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.numera6620942414471956472nteger M2)) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))))
% 6.73/7.07 (assert (forall ((M2 tptp.num)) (not (@ (@ tptp.ord_less_eq_rat (@ tptp.numeral_numeral_rat M2)) (@ tptp.uminus_uminus_rat tptp.one_one_rat)))))
% 6.73/7.07 (assert (forall ((M2 tptp.num)) (not (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int M2)) (@ tptp.uminus_uminus_int tptp.one_one_int)))))
% 6.73/7.07 (assert (forall ((M2 tptp.num)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M2))) (@ tptp.uminus_uminus_real tptp.one_one_real))))
% 6.73/7.07 (assert (forall ((M2 tptp.num)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M2))) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 6.73/7.07 (assert (forall ((M2 tptp.num)) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M2))) (@ tptp.uminus_uminus_rat tptp.one_one_rat))))
% 6.73/7.07 (assert (forall ((M2 tptp.num)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M2))) (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 6.73/7.07 (assert (forall ((M2 tptp.num)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.numeral_numeral_real M2))))
% 6.73/7.07 (assert (forall ((M2 tptp.num)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.numera6620942414471956472nteger M2))))
% 6.73/7.07 (assert (forall ((M2 tptp.num)) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.numeral_numeral_rat M2))))
% 6.73/7.07 (assert (forall ((M2 tptp.num)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.numeral_numeral_int M2))))
% 6.73/7.07 (assert (forall ((M2 tptp.num)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M2))) tptp.one_one_real)))
% 6.73/7.07 (assert (forall ((M2 tptp.num)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M2))) tptp.one_one_Code_integer)))
% 6.73/7.07 (assert (forall ((M2 tptp.num)) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M2))) tptp.one_one_rat)))
% 6.73/7.07 (assert (forall ((M2 tptp.num)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M2))) tptp.one_one_int)))
% 6.73/7.07 (assert (= tptp.gbinomial_complex (lambda ((A5 tptp.complex) (K3 tptp.nat)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) K3)) (@ (@ tptp.comm_s2602460028002588243omplex (@ tptp.uminus1482373934393186551omplex A5)) K3))) (@ tptp.semiri5044797733671781792omplex K3)))))
% 6.73/7.07 (assert (= tptp.gbinomial_rat (lambda ((A5 tptp.rat) (K3 tptp.nat)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) K3)) (@ (@ tptp.comm_s4028243227959126397er_rat (@ tptp.uminus_uminus_rat A5)) K3))) (@ tptp.semiri773545260158071498ct_rat K3)))))
% 6.73/7.07 (assert (= tptp.gbinomial_real (lambda ((A5 tptp.real) (K3 tptp.nat)) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) K3)) (@ (@ tptp.comm_s7457072308508201937r_real (@ tptp.uminus_uminus_real A5)) K3))) (@ tptp.semiri2265585572941072030t_real K3)))))
% 6.73/7.07 (assert (forall ((M2 tptp.num)) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M2))) tptp.one_one_int)))
% 6.73/7.07 (assert (forall ((M2 tptp.num)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M2))) tptp.one_one_real)))
% 6.73/7.07 (assert (forall ((M2 tptp.num)) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M2))) tptp.one_one_Code_integer)))
% 6.73/7.07 (assert (forall ((M2 tptp.num)) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M2))) tptp.one_one_rat)))
% 6.73/7.07 (assert (forall ((M2 tptp.num)) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.numeral_numeral_int M2))))
% 6.73/7.07 (assert (forall ((M2 tptp.num)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.numeral_numeral_real M2))))
% 6.73/7.07 (assert (forall ((M2 tptp.num)) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.numera6620942414471956472nteger M2))))
% 6.73/7.07 (assert (forall ((M2 tptp.num)) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.numeral_numeral_rat M2))))
% 6.73/7.07 (assert (forall ((M2 tptp.num)) (not (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int M2)) (@ tptp.uminus_uminus_int tptp.one_one_int)))))
% 6.73/7.07 (assert (forall ((M2 tptp.num)) (not (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real M2)) (@ tptp.uminus_uminus_real tptp.one_one_real)))))
% 6.73/7.07 (assert (forall ((M2 tptp.num)) (not (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.numera6620942414471956472nteger M2)) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))))
% 6.73/7.07 (assert (forall ((M2 tptp.num)) (not (@ (@ tptp.ord_less_rat (@ tptp.numeral_numeral_rat M2)) (@ tptp.uminus_uminus_rat tptp.one_one_rat)))))
% 6.73/7.07 (assert (forall ((M2 tptp.num)) (not (@ (@ tptp.ord_less_int tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M2))))))
% 6.73/7.07 (assert (forall ((M2 tptp.num)) (not (@ (@ tptp.ord_less_real tptp.one_one_real) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M2))))))
% 6.73/7.07 (assert (forall ((M2 tptp.num)) (not (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M2))))))
% 6.73/7.07 (assert (forall ((M2 tptp.num)) (not (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M2))))))
% 6.73/7.07 (assert (forall ((M2 tptp.num)) (not (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M2))))))
% 6.73/7.07 (assert (forall ((M2 tptp.num)) (not (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M2))))))
% 6.73/7.07 (assert (forall ((M2 tptp.num)) (not (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M2))))))
% 6.73/7.07 (assert (forall ((M2 tptp.num)) (not (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M2))))))
% 6.73/7.07 (assert (forall ((A tptp.real) (B tptp.real) (C2 tptp.real)) (let ((_let_1 (= C2 tptp.zero_zero_real))) (= (= A (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B) C2))) (and (=> (not _let_1) (= (@ (@ tptp.times_times_real A) C2) (@ tptp.uminus_uminus_real B))) (=> _let_1 (= A tptp.zero_zero_real)))))))
% 6.73/7.07 (assert (forall ((A tptp.complex) (B tptp.complex) (C2 tptp.complex)) (let ((_let_1 (= C2 tptp.zero_zero_complex))) (= (= A (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex B) C2))) (and (=> (not _let_1) (= (@ (@ tptp.times_times_complex A) C2) (@ tptp.uminus1482373934393186551omplex B))) (=> _let_1 (= A tptp.zero_zero_complex)))))))
% 6.73/7.07 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (= C2 tptp.zero_zero_rat))) (= (= A (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C2))) (and (=> (not _let_1) (= (@ (@ tptp.times_times_rat A) C2) (@ tptp.uminus_uminus_rat B))) (=> _let_1 (= A tptp.zero_zero_rat)))))))
% 6.73/7.07 (assert (forall ((B tptp.real) (C2 tptp.real) (A tptp.real)) (let ((_let_1 (= C2 tptp.zero_zero_real))) (= (= (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B) C2)) A) (and (=> (not _let_1) (= (@ tptp.uminus_uminus_real B) (@ (@ tptp.times_times_real A) C2))) (=> _let_1 (= A tptp.zero_zero_real)))))))
% 6.73/7.07 (assert (forall ((B tptp.complex) (C2 tptp.complex) (A tptp.complex)) (let ((_let_1 (= C2 tptp.zero_zero_complex))) (= (= (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex B) C2)) A) (and (=> (not _let_1) (= (@ tptp.uminus1482373934393186551omplex B) (@ (@ tptp.times_times_complex A) C2))) (=> _let_1 (= A tptp.zero_zero_complex)))))))
% 6.73/7.07 (assert (forall ((B tptp.rat) (C2 tptp.rat) (A tptp.rat)) (let ((_let_1 (= C2 tptp.zero_zero_rat))) (= (= (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C2)) A) (and (=> (not _let_1) (= (@ tptp.uminus_uminus_rat B) (@ (@ tptp.times_times_rat A) C2))) (=> _let_1 (= A tptp.zero_zero_rat)))))))
% 6.73/7.07 (assert (forall ((B tptp.real) (A tptp.real) (C2 tptp.real)) (=> (not (= B tptp.zero_zero_real)) (= (= (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real A) B)) C2) (= (@ tptp.uminus_uminus_real A) (@ (@ tptp.times_times_real C2) B))))))
% 6.73/7.07 (assert (forall ((B tptp.complex) (A tptp.complex) (C2 tptp.complex)) (=> (not (= B tptp.zero_zero_complex)) (= (= (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex A) B)) C2) (= (@ tptp.uminus1482373934393186551omplex A) (@ (@ tptp.times_times_complex C2) B))))))
% 6.73/7.07 (assert (forall ((B tptp.rat) (A tptp.rat) (C2 tptp.rat)) (=> (not (= B tptp.zero_zero_rat)) (= (= (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat A) B)) C2) (= (@ tptp.uminus_uminus_rat A) (@ (@ tptp.times_times_rat C2) B))))))
% 6.73/7.07 (assert (forall ((B tptp.real) (C2 tptp.real) (A tptp.real)) (=> (not (= B tptp.zero_zero_real)) (= (= C2 (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real A) B))) (= (@ (@ tptp.times_times_real C2) B) (@ tptp.uminus_uminus_real A))))))
% 6.73/7.07 (assert (forall ((B tptp.complex) (C2 tptp.complex) (A tptp.complex)) (=> (not (= B tptp.zero_zero_complex)) (= (= C2 (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex A) B))) (= (@ (@ tptp.times_times_complex C2) B) (@ tptp.uminus1482373934393186551omplex A))))))
% 6.73/7.07 (assert (forall ((B tptp.rat) (C2 tptp.rat) (A tptp.rat)) (=> (not (= B tptp.zero_zero_rat)) (= (= C2 (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat A) B))) (= (@ (@ tptp.times_times_rat C2) B) (@ tptp.uminus_uminus_rat A))))))
% 6.73/7.07 (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))))
% 6.73/7.07 (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))))
% 6.73/7.07 (assert (forall ((B tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex tptp.one))) B) (@ tptp.uminus1482373934393186551omplex B))))
% 6.73/7.07 (assert (forall ((B tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger tptp.one))) B) (@ tptp.uminus1351360451143612070nteger B))))
% 6.73/7.07 (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))))
% 6.73/7.07 (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))))
% 6.73/7.07 (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))))
% 6.73/7.07 (assert (forall ((B tptp.complex)) (= (@ (@ tptp.times_times_complex B) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex tptp.one))) (@ tptp.uminus1482373934393186551omplex B))))
% 6.73/7.07 (assert (forall ((B tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger B) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger tptp.one))) (@ tptp.uminus1351360451143612070nteger B))))
% 6.73/7.07 (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))))
% 6.73/7.07 (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))))))
% 6.73/7.07 (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))))))
% 6.73/7.07 (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))))))
% 6.73/7.07 (assert (= (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int tptp.one)) (@ tptp.uminus_uminus_int tptp.one_one_int)))
% 6.73/7.07 (assert (= (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real tptp.one)) (@ tptp.uminus_uminus_real tptp.one_one_real)))
% 6.73/7.07 (assert (= (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex tptp.one)) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))
% 6.73/7.07 (assert (= (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger tptp.one)) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))
% 6.73/7.07 (assert (= (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat tptp.one)) (@ tptp.uminus_uminus_rat tptp.one_one_rat)))
% 6.73/7.07 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M2) (=> (@ (@ tptp.ord_less_nat M2) N) (@ (@ tptp.ord_less_rat (@ tptp.semiri773545260158071498ct_rat M2)) (@ tptp.semiri773545260158071498ct_rat N))))))
% 6.73/7.07 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M2) (=> (@ (@ tptp.ord_less_nat M2) N) (@ (@ tptp.ord_less_int (@ tptp.semiri1406184849735516958ct_int M2)) (@ tptp.semiri1406184849735516958ct_int N))))))
% 6.73/7.07 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M2) (=> (@ (@ tptp.ord_less_nat M2) N) (@ (@ tptp.ord_less_nat (@ tptp.semiri1408675320244567234ct_nat M2)) (@ tptp.semiri1408675320244567234ct_nat N))))))
% 6.73/7.07 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M2) (=> (@ (@ tptp.ord_less_nat M2) N) (@ (@ tptp.ord_less_real (@ tptp.semiri2265585572941072030t_real M2)) (@ tptp.semiri2265585572941072030t_real N))))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat)) (= (= (@ (@ tptp.inf_in2572325071724192079at_nat X) Y) tptp.bot_bo2099793752762293965at_nat) (@ (@ tptp.ord_le3146513528884898305at_nat X) (@ tptp.uminus6524753893492686040at_nat Y)))))
% 6.73/7.07 (assert (forall ((X tptp.set_int) (Y tptp.set_int)) (= (= (@ (@ tptp.inf_inf_set_int X) Y) tptp.bot_bot_set_int) (@ (@ tptp.ord_less_eq_set_int X) (@ tptp.uminus1532241313380277803et_int Y)))))
% 6.73/7.07 (assert (forall ((X tptp.set_real) (Y tptp.set_real)) (= (= (@ (@ tptp.inf_inf_set_real X) Y) tptp.bot_bot_set_real) (@ (@ tptp.ord_less_eq_set_real X) (@ tptp.uminus612125837232591019t_real Y)))))
% 6.73/7.07 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat)) (= (= (@ (@ tptp.inf_inf_set_nat X) Y) tptp.bot_bot_set_nat) (@ (@ tptp.ord_less_eq_set_nat X) (@ tptp.uminus5710092332889474511et_nat Y)))))
% 6.73/7.07 (assert (forall ((K2 tptp.nat) (N tptp.nat)) (@ (@ tptp.dvd_dvd_rat (@ (@ tptp.times_times_rat (@ tptp.semiri773545260158071498ct_rat K2)) (@ tptp.semiri773545260158071498ct_rat N))) (@ tptp.semiri773545260158071498ct_rat (@ (@ tptp.plus_plus_nat K2) N)))))
% 6.73/7.07 (assert (forall ((K2 tptp.nat) (N tptp.nat)) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int (@ tptp.semiri1406184849735516958ct_int K2)) (@ tptp.semiri1406184849735516958ct_int N))) (@ tptp.semiri1406184849735516958ct_int (@ (@ tptp.plus_plus_nat K2) N)))))
% 6.73/7.07 (assert (forall ((K2 tptp.nat) (N tptp.nat)) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat (@ tptp.semiri1408675320244567234ct_nat K2)) (@ tptp.semiri1408675320244567234ct_nat N))) (@ tptp.semiri1408675320244567234ct_nat (@ (@ tptp.plus_plus_nat K2) N)))))
% 6.73/7.07 (assert (forall ((K2 tptp.nat) (N tptp.nat)) (@ (@ tptp.dvd_dvd_real (@ (@ tptp.times_times_real (@ tptp.semiri2265585572941072030t_real K2)) (@ tptp.semiri2265585572941072030t_real N))) (@ tptp.semiri2265585572941072030t_real (@ (@ tptp.plus_plus_nat K2) N)))))
% 6.73/7.07 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ (@ tptp.modulo_modulo_int (@ tptp.semiri1406184849735516958ct_int N)) (@ tptp.semiri1406184849735516958ct_int M2)) tptp.zero_zero_int))))
% 6.73/7.07 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ (@ tptp.modulo8411746178871703098atural (@ tptp.semiri2447717529341329178atural N)) (@ tptp.semiri2447717529341329178atural M2)) tptp.zero_z2226904508553997617atural))))
% 6.73/7.07 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.semiri1408675320244567234ct_nat N)) (@ tptp.semiri1408675320244567234ct_nat M2)) tptp.zero_zero_nat))))
% 6.73/7.07 (assert (forall ((P tptp.set_Pr1261947904930325089at_nat) (Q2 tptp.set_Pr1261947904930325089at_nat) (R3 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.ord_le3146513528884898305at_nat P) (@ (@ tptp.sup_su6327502436637775413at_nat Q2) R3)) (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.inf_in2572325071724192079at_nat P) (@ tptp.uminus6524753893492686040at_nat Q2))) R3))))
% 6.73/7.07 (assert (forall ((P tptp.set_nat) (Q2 tptp.set_nat) (R3 tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat P) (@ (@ tptp.sup_sup_set_nat Q2) R3)) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.inf_inf_set_nat P) (@ tptp.uminus5710092332889474511et_nat Q2))) R3))))
% 6.73/7.07 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat) (Z3 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.inf_in2572325071724192079at_nat X) (@ tptp.uminus6524753893492686040at_nat Y))) Z3) (@ (@ tptp.ord_le3146513528884898305at_nat X) (@ (@ tptp.sup_su6327502436637775413at_nat Y) Z3)))))
% 6.73/7.07 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat) (Z3 tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.inf_inf_set_nat X) (@ tptp.uminus5710092332889474511et_nat Y))) Z3) (@ (@ tptp.ord_less_eq_set_nat X) (@ (@ tptp.sup_sup_set_nat Y) Z3)))))
% 6.73/7.07 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat) (Z3 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.inf_in2572325071724192079at_nat X) Y)) Z3) (@ (@ tptp.ord_le3146513528884898305at_nat X) (@ (@ tptp.sup_su6327502436637775413at_nat (@ tptp.uminus6524753893492686040at_nat Y)) Z3)))))
% 6.73/7.07 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat) (Z3 tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.inf_inf_set_nat X) Y)) Z3) (@ (@ tptp.ord_less_eq_set_nat X) (@ (@ tptp.sup_sup_set_nat (@ tptp.uminus5710092332889474511et_nat Y)) Z3)))))
% 6.73/7.07 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.semiri773545260158071498ct_rat N)) (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.power_power_nat N) N)))))
% 6.73/7.07 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1406184849735516958ct_int N)) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.power_power_nat N) N)))))
% 6.73/7.07 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1408675320244567234ct_nat N)) (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.power_power_nat N) N)))))
% 6.73/7.07 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.semiri2265585572941072030t_real N)) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.power_power_nat N) N)))))
% 6.73/7.07 (assert (forall ((M2 tptp.int)) (=> (forall ((N3 tptp.nat)) (not (= M2 (@ tptp.semiri1314217659103216013at_int N3)))) (not (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N3) (not (= M2 (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N3))))))))))
% 6.73/7.07 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int N)) (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int M2))) (and (= N tptp.zero_zero_nat) (= M2 tptp.zero_zero_nat)))))
% 6.73/7.07 (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)))))))))
% 6.73/7.07 (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))))))))))
% 6.73/7.07 (assert (forall ((R3 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat R3) N) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.divide_divide_nat (@ tptp.semiri1408675320244567234ct_nat N)) (@ tptp.semiri1408675320244567234ct_nat (@ (@ tptp.minus_minus_nat N) R3)))) (@ (@ tptp.power_power_nat N) R3)))))
% 6.73/7.07 (assert (forall ((K2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K2) N) (= (@ (@ tptp.times_times_nat (@ (@ tptp.times_times_nat (@ tptp.semiri1408675320244567234ct_nat K2)) (@ tptp.semiri1408675320244567234ct_nat (@ (@ tptp.minus_minus_nat N) K2)))) (@ (@ tptp.binomial N) K2)) (@ tptp.semiri1408675320244567234ct_nat N)))))
% 6.73/7.07 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_set_nat (@ tptp.nat_set_decode M2)) (@ tptp.nat_set_decode N)) (@ (@ tptp.ord_less_eq_nat M2) N))))
% 6.73/7.07 (assert (forall ((A tptp.real) (B tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real A))) (let ((_let_2 (@ (@ tptp.ord_less_real C2) tptp.zero_zero_real))) (let ((_let_3 (@ (@ tptp.times_times_real A) C2))) (let ((_let_4 (@ tptp.uminus_uminus_real B))) (let ((_let_5 (@ (@ tptp.ord_less_real tptp.zero_zero_real) C2))) (= (@ _let_1 (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B) C2))) (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)))))))))))))
% 6.73/7.07 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A))) (let ((_let_2 (@ (@ tptp.ord_less_rat C2) tptp.zero_zero_rat))) (let ((_let_3 (@ (@ tptp.times_times_rat A) C2))) (let ((_let_4 (@ tptp.uminus_uminus_rat B))) (let ((_let_5 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C2))) (= (@ _let_1 (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C2))) (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)))))))))))))
% 6.73/7.07 (assert (forall ((B tptp.real) (C2 tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (let ((_let_2 (@ (@ tptp.ord_less_real C2) tptp.zero_zero_real))) (let ((_let_3 (@ tptp.uminus_uminus_real B))) (let ((_let_4 (@ (@ tptp.times_times_real A) C2))) (let ((_let_5 (@ _let_1 C2))) (= (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B) C2))) 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)))))))))))))
% 6.73/7.07 (assert (forall ((B tptp.rat) (C2 tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (let ((_let_2 (@ (@ tptp.ord_less_rat C2) tptp.zero_zero_rat))) (let ((_let_3 (@ tptp.uminus_uminus_rat B))) (let ((_let_4 (@ (@ tptp.times_times_rat A) C2))) (let ((_let_5 (@ _let_1 C2))) (= (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C2))) 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)))))))))))))
% 6.73/7.07 (assert (forall ((C2 tptp.real) (A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real C2) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_real A) (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B) C2))) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real B)) (@ (@ tptp.times_times_real A) C2))))))
% 6.73/7.07 (assert (forall ((C2 tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat C2) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_rat A) (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C2))) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat B)) (@ (@ tptp.times_times_rat A) C2))))))
% 6.73/7.07 (assert (forall ((C2 tptp.real) (B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real C2) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B) C2))) A) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C2)) (@ tptp.uminus_uminus_real B))))))
% 6.73/7.07 (assert (forall ((C2 tptp.rat) (B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat C2) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C2))) A) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C2)) (@ tptp.uminus_uminus_rat B))))))
% 6.73/7.07 (assert (forall ((C2 tptp.real) (A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C2) (= (@ (@ tptp.ord_less_real A) (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B) C2))) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C2)) (@ tptp.uminus_uminus_real B))))))
% 6.73/7.07 (assert (forall ((C2 tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C2) (= (@ (@ tptp.ord_less_rat A) (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C2))) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C2)) (@ tptp.uminus_uminus_rat B))))))
% 6.73/7.07 (assert (forall ((C2 tptp.real) (B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C2) (= (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B) C2))) A) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real B)) (@ (@ tptp.times_times_real A) C2))))))
% 6.73/7.07 (assert (forall ((C2 tptp.rat) (B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C2) (= (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C2))) A) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat B)) (@ (@ tptp.times_times_rat A) C2))))))
% 6.73/7.07 (assert (forall ((W2 tptp.num) (B tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W2)))) (let ((_let_2 (= C2 tptp.zero_zero_real))) (= (= _let_1 (@ (@ tptp.divide_divide_real B) C2)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_real _let_1) C2) B)) (=> _let_2 (= _let_1 tptp.zero_zero_real))))))))
% 6.73/7.07 (assert (forall ((W2 tptp.num) (B tptp.complex) (C2 tptp.complex)) (let ((_let_1 (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W2)))) (let ((_let_2 (= C2 tptp.zero_zero_complex))) (= (= _let_1 (@ (@ tptp.divide1717551699836669952omplex B) C2)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_complex _let_1) C2) B)) (=> _let_2 (= _let_1 tptp.zero_zero_complex))))))))
% 6.73/7.07 (assert (forall ((W2 tptp.num) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W2)))) (let ((_let_2 (= C2 tptp.zero_zero_rat))) (= (= _let_1 (@ (@ tptp.divide_divide_rat B) C2)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_rat _let_1) C2) B)) (=> _let_2 (= _let_1 tptp.zero_zero_rat))))))))
% 6.73/7.07 (assert (forall ((B tptp.real) (C2 tptp.real) (W2 tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W2)))) (let ((_let_2 (= C2 tptp.zero_zero_real))) (= (= (@ (@ tptp.divide_divide_real B) C2) _let_1) (and (=> (not _let_2) (= B (@ (@ tptp.times_times_real _let_1) C2))) (=> _let_2 (= _let_1 tptp.zero_zero_real))))))))
% 6.73/7.07 (assert (forall ((B tptp.complex) (C2 tptp.complex) (W2 tptp.num)) (let ((_let_1 (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W2)))) (let ((_let_2 (= C2 tptp.zero_zero_complex))) (= (= (@ (@ tptp.divide1717551699836669952omplex B) C2) _let_1) (and (=> (not _let_2) (= B (@ (@ tptp.times_times_complex _let_1) C2))) (=> _let_2 (= _let_1 tptp.zero_zero_complex))))))))
% 6.73/7.07 (assert (forall ((B tptp.rat) (C2 tptp.rat) (W2 tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W2)))) (let ((_let_2 (= C2 tptp.zero_zero_rat))) (= (= (@ (@ tptp.divide_divide_rat B) C2) _let_1) (and (=> (not _let_2) (= B (@ (@ tptp.times_times_rat _let_1) C2))) (=> _let_2 (= _let_1 tptp.zero_zero_rat))))))))
% 6.73/7.07 (assert (forall ((Z3 tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real A) Z3))) B))) (let ((_let_2 (= Z3 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) Z3))) Z3))))))))
% 6.73/7.07 (assert (forall ((Z3 tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex A) Z3))) B))) (let ((_let_2 (= Z3 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) Z3))) Z3))))))))
% 6.73/7.07 (assert (forall ((Z3 tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat A) Z3))) B))) (let ((_let_2 (= Z3 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) Z3))) Z3))))))))
% 6.73/7.07 (assert (forall ((Z3 tptp.real) (X tptp.real) (Y tptp.real)) (=> (not (= Z3 tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real X) Z3))) Y) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real X)) (@ (@ tptp.times_times_real Y) Z3))) Z3)))))
% 6.73/7.07 (assert (forall ((Z3 tptp.complex) (X tptp.complex) (Y tptp.complex)) (=> (not (= Z3 tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex X) Z3))) Y) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex X)) (@ (@ tptp.times_times_complex Y) Z3))) Z3)))))
% 6.73/7.07 (assert (forall ((Z3 tptp.rat) (X tptp.rat) (Y tptp.rat)) (=> (not (= Z3 tptp.zero_zero_rat)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat X) Z3))) Y) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat X)) (@ (@ tptp.times_times_rat Y) Z3))) Z3)))))
% 6.73/7.07 (assert (forall ((K2 tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_int K2) (@ tptp.uminus_uminus_int (@ _let_1 N))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int K2) (@ _let_1 (@ tptp.suc N)))) (@ (@ tptp.bit_ri631733984087533419it_int N) K2))))))
% 6.73/7.07 (assert (forall ((Z3 tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real A) Z3))) B))) (let ((_let_2 (= Z3 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) Z3))) Z3))))))))
% 6.73/7.07 (assert (forall ((Z3 tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex A) Z3))) B))) (let ((_let_2 (= Z3 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) Z3))) Z3))))))))
% 6.73/7.07 (assert (forall ((Z3 tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat A) Z3))) B))) (let ((_let_2 (= Z3 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) Z3))) Z3))))))))
% 6.73/7.07 (assert (forall ((Z3 tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real A) Z3)) B))) (let ((_let_2 (= Z3 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) Z3))) Z3))))))))
% 6.73/7.07 (assert (forall ((Z3 tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ (@ tptp.minus_minus_complex (@ (@ tptp.divide1717551699836669952omplex A) Z3)) B))) (let ((_let_2 (= Z3 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) Z3))) Z3))))))))
% 6.73/7.07 (assert (forall ((Z3 tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ (@ tptp.minus_minus_rat (@ (@ tptp.divide_divide_rat A) Z3)) B))) (let ((_let_2 (= Z3 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) Z3))) Z3))))))))
% 6.73/7.07 (assert (forall ((Z3 tptp.real) (X tptp.real) (Y tptp.real)) (=> (not (= Z3 tptp.zero_zero_real)) (= (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real X) Z3))) Y) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real X)) (@ (@ tptp.times_times_real Y) Z3))) Z3)))))
% 6.73/7.07 (assert (forall ((Z3 tptp.complex) (X tptp.complex) (Y tptp.complex)) (=> (not (= Z3 tptp.zero_zero_complex)) (= (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex X) Z3))) Y) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex X)) (@ (@ tptp.times_times_complex Y) Z3))) Z3)))))
% 6.73/7.07 (assert (forall ((Z3 tptp.rat) (X tptp.rat) (Y tptp.rat)) (=> (not (= Z3 tptp.zero_zero_rat)) (= (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat X) Z3))) Y) (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat X)) (@ (@ tptp.times_times_rat Y) Z3))) Z3)))))
% 6.73/7.07 (assert (forall ((K2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K2) N) (@ (@ tptp.dvd_dvd_rat (@ (@ tptp.times_times_rat (@ tptp.semiri773545260158071498ct_rat K2)) (@ tptp.semiri773545260158071498ct_rat (@ (@ tptp.minus_minus_nat N) K2)))) (@ tptp.semiri773545260158071498ct_rat N)))))
% 6.73/7.07 (assert (forall ((K2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K2) N) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int (@ tptp.semiri1406184849735516958ct_int K2)) (@ tptp.semiri1406184849735516958ct_int (@ (@ tptp.minus_minus_nat N) K2)))) (@ tptp.semiri1406184849735516958ct_int N)))))
% 6.73/7.07 (assert (forall ((K2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K2) N) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat (@ tptp.semiri1408675320244567234ct_nat K2)) (@ tptp.semiri1408675320244567234ct_nat (@ (@ tptp.minus_minus_nat N) K2)))) (@ tptp.semiri1408675320244567234ct_nat N)))))
% 6.73/7.07 (assert (forall ((K2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K2) N) (@ (@ tptp.dvd_dvd_real (@ (@ tptp.times_times_real (@ tptp.semiri2265585572941072030t_real K2)) (@ tptp.semiri2265585572941072030t_real (@ (@ tptp.minus_minus_nat N) K2)))) (@ tptp.semiri2265585572941072030t_real N)))))
% 6.73/7.07 (assert (forall ((K2 tptp.int)) (=> (not (= K2 tptp.zero_zero_int)) (=> (forall ((N3 tptp.nat)) (=> (= K2 (@ tptp.semiri1314217659103216013at_int N3)) (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N3)))) (not (forall ((N3 tptp.nat)) (=> (= K2 (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N3))) (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N3)))))))))
% 6.73/7.07 (assert (forall ((N tptp.nat) (K2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) K2) (= (@ (@ tptp.comm_s2602460028002588243omplex (@ tptp.uminus1482373934393186551omplex (@ tptp.semiri8010041392384452111omplex N))) K2) tptp.zero_zero_complex))))
% 6.73/7.07 (assert (forall ((N tptp.nat) (K2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) K2) (= (@ (@ tptp.comm_s8582702949713902594nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.semiri4939895301339042750nteger N))) K2) tptp.zero_z3403309356797280102nteger))))
% 6.73/7.07 (assert (forall ((N tptp.nat) (K2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) K2) (= (@ (@ tptp.comm_s4028243227959126397er_rat (@ tptp.uminus_uminus_rat (@ tptp.semiri681578069525770553at_rat N))) K2) tptp.zero_zero_rat))))
% 6.73/7.07 (assert (forall ((N tptp.nat) (K2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) K2) (= (@ (@ tptp.comm_s7457072308508201937r_real (@ tptp.uminus_uminus_real (@ tptp.semiri5074537144036343181t_real N))) K2) tptp.zero_zero_real))))
% 6.73/7.07 (assert (forall ((N tptp.nat) (K2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) K2) (= (@ (@ tptp.comm_s4660882817536571857er_int (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N))) K2) tptp.zero_zero_int))))
% 6.73/7.07 (assert (forall ((N tptp.nat) (K2 tptp.nat)) (= (= (@ (@ tptp.comm_s2602460028002588243omplex (@ tptp.uminus1482373934393186551omplex (@ tptp.semiri8010041392384452111omplex N))) K2) tptp.zero_zero_complex) (@ (@ tptp.ord_less_nat N) K2))))
% 6.73/7.07 (assert (forall ((N tptp.nat) (K2 tptp.nat)) (= (= (@ (@ tptp.comm_s8582702949713902594nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.semiri4939895301339042750nteger N))) K2) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_less_nat N) K2))))
% 6.73/7.07 (assert (forall ((N tptp.nat) (K2 tptp.nat)) (= (= (@ (@ tptp.comm_s4028243227959126397er_rat (@ tptp.uminus_uminus_rat (@ tptp.semiri681578069525770553at_rat N))) K2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_nat N) K2))))
% 6.73/7.07 (assert (forall ((N tptp.nat) (K2 tptp.nat)) (= (= (@ (@ tptp.comm_s7457072308508201937r_real (@ tptp.uminus_uminus_real (@ tptp.semiri5074537144036343181t_real N))) K2) tptp.zero_zero_real) (@ (@ tptp.ord_less_nat N) K2))))
% 6.73/7.07 (assert (forall ((N tptp.nat) (K2 tptp.nat)) (= (= (@ (@ tptp.comm_s4660882817536571857er_int (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N))) K2) tptp.zero_zero_int) (@ (@ tptp.ord_less_nat N) K2))))
% 6.73/7.07 (assert (forall ((A tptp.complex) (N tptp.nat)) (= (= (@ (@ tptp.comm_s2602460028002588243omplex A) N) tptp.zero_zero_complex) (exists ((K3 tptp.nat)) (and (@ (@ tptp.ord_less_nat K3) N) (= A (@ tptp.uminus1482373934393186551omplex (@ tptp.semiri8010041392384452111omplex K3))))))))
% 6.73/7.07 (assert (forall ((A tptp.rat) (N tptp.nat)) (= (= (@ (@ tptp.comm_s4028243227959126397er_rat A) N) tptp.zero_zero_rat) (exists ((K3 tptp.nat)) (and (@ (@ tptp.ord_less_nat K3) N) (= A (@ tptp.uminus_uminus_rat (@ tptp.semiri681578069525770553at_rat K3))))))))
% 6.73/7.07 (assert (forall ((A tptp.real) (N tptp.nat)) (= (= (@ (@ tptp.comm_s7457072308508201937r_real A) N) tptp.zero_zero_real) (exists ((K3 tptp.nat)) (and (@ (@ tptp.ord_less_nat K3) N) (= A (@ tptp.uminus_uminus_real (@ tptp.semiri5074537144036343181t_real K3))))))))
% 6.73/7.07 (assert (forall ((K2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K2) N) (not (= (@ (@ tptp.comm_s2602460028002588243omplex (@ tptp.uminus1482373934393186551omplex (@ tptp.semiri8010041392384452111omplex N))) K2) tptp.zero_zero_complex)))))
% 6.73/7.07 (assert (forall ((K2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K2) N) (not (= (@ (@ tptp.comm_s8582702949713902594nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.semiri4939895301339042750nteger N))) K2) tptp.zero_z3403309356797280102nteger)))))
% 6.73/7.07 (assert (forall ((K2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K2) N) (not (= (@ (@ tptp.comm_s4028243227959126397er_rat (@ tptp.uminus_uminus_rat (@ tptp.semiri681578069525770553at_rat N))) K2) tptp.zero_zero_rat)))))
% 6.73/7.07 (assert (forall ((K2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K2) N) (not (= (@ (@ tptp.comm_s7457072308508201937r_real (@ tptp.uminus_uminus_real (@ tptp.semiri5074537144036343181t_real N))) K2) tptp.zero_zero_real)))))
% 6.73/7.07 (assert (forall ((K2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K2) N) (not (= (@ (@ tptp.comm_s4660882817536571857er_int (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N))) K2) tptp.zero_zero_int)))))
% 6.73/7.07 (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)))))))
% 6.73/7.07 (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))))))))
% 6.73/7.07 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N)))) tptp.zero_zero_int)))
% 6.73/7.07 (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)))))
% 6.73/7.07 (assert (forall ((A4 tptp.set_real) (P2 (-> tptp.real Bool)) (H (-> tptp.real tptp.real)) (G2 (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.collect_real P2))) (let ((_let_2 (@ tptp.inf_inf_set_real A4))) (=> (@ tptp.finite_finite_real A4) (= (@ (@ tptp.groups1681761925125756287l_real (lambda ((X4 tptp.real)) (@ (@ (@ tptp.if_real (@ P2 X4)) (@ H X4)) (@ G2 X4)))) A4) (@ (@ tptp.times_times_real (@ (@ tptp.groups1681761925125756287l_real H) (@ _let_2 _let_1))) (@ (@ tptp.groups1681761925125756287l_real G2) (@ _let_2 (@ tptp.uminus612125837232591019t_real _let_1))))))))))
% 6.73/7.07 (assert (forall ((A4 tptp.set_int) (P2 (-> tptp.int Bool)) (H (-> tptp.int tptp.real)) (G2 (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.collect_int P2))) (let ((_let_2 (@ tptp.inf_inf_set_int A4))) (=> (@ tptp.finite_finite_int A4) (= (@ (@ tptp.groups2316167850115554303t_real (lambda ((X4 tptp.int)) (@ (@ (@ tptp.if_real (@ P2 X4)) (@ H X4)) (@ G2 X4)))) A4) (@ (@ tptp.times_times_real (@ (@ tptp.groups2316167850115554303t_real H) (@ _let_2 _let_1))) (@ (@ tptp.groups2316167850115554303t_real G2) (@ _let_2 (@ tptp.uminus1532241313380277803et_int _let_1))))))))))
% 6.73/7.07 (assert (forall ((A4 tptp.set_complex) (P2 (-> tptp.complex Bool)) (H (-> tptp.complex tptp.real)) (G2 (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.collect_complex P2))) (let ((_let_2 (@ tptp.inf_inf_set_complex A4))) (=> (@ tptp.finite3207457112153483333omplex A4) (= (@ (@ tptp.groups766887009212190081x_real (lambda ((X4 tptp.complex)) (@ (@ (@ tptp.if_real (@ P2 X4)) (@ H X4)) (@ G2 X4)))) A4) (@ (@ tptp.times_times_real (@ (@ tptp.groups766887009212190081x_real H) (@ _let_2 _let_1))) (@ (@ tptp.groups766887009212190081x_real G2) (@ _let_2 (@ tptp.uminus8566677241136511917omplex _let_1))))))))))
% 6.73/7.07 (assert (forall ((A4 tptp.set_nat) (P2 (-> tptp.nat Bool)) (H (-> tptp.nat tptp.real)) (G2 (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.collect_nat P2))) (let ((_let_2 (@ tptp.inf_inf_set_nat A4))) (=> (@ tptp.finite_finite_nat A4) (= (@ (@ tptp.groups129246275422532515t_real (lambda ((X4 tptp.nat)) (@ (@ (@ tptp.if_real (@ P2 X4)) (@ H X4)) (@ G2 X4)))) A4) (@ (@ tptp.times_times_real (@ (@ tptp.groups129246275422532515t_real H) (@ _let_2 _let_1))) (@ (@ tptp.groups129246275422532515t_real G2) (@ _let_2 (@ tptp.uminus5710092332889474511et_nat _let_1))))))))))
% 6.73/7.07 (assert (forall ((A4 tptp.set_real) (P2 (-> tptp.real Bool)) (H (-> tptp.real tptp.rat)) (G2 (-> tptp.real tptp.rat))) (let ((_let_1 (@ tptp.collect_real P2))) (let ((_let_2 (@ tptp.inf_inf_set_real A4))) (=> (@ tptp.finite_finite_real A4) (= (@ (@ tptp.groups4061424788464935467al_rat (lambda ((X4 tptp.real)) (@ (@ (@ tptp.if_rat (@ P2 X4)) (@ H X4)) (@ G2 X4)))) A4) (@ (@ tptp.times_times_rat (@ (@ tptp.groups4061424788464935467al_rat H) (@ _let_2 _let_1))) (@ (@ tptp.groups4061424788464935467al_rat G2) (@ _let_2 (@ tptp.uminus612125837232591019t_real _let_1))))))))))
% 6.73/7.07 (assert (forall ((A4 tptp.set_int) (P2 (-> tptp.int Bool)) (H (-> tptp.int tptp.rat)) (G2 (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.collect_int P2))) (let ((_let_2 (@ tptp.inf_inf_set_int A4))) (=> (@ tptp.finite_finite_int A4) (= (@ (@ tptp.groups1072433553688619179nt_rat (lambda ((X4 tptp.int)) (@ (@ (@ tptp.if_rat (@ P2 X4)) (@ H X4)) (@ G2 X4)))) A4) (@ (@ tptp.times_times_rat (@ (@ tptp.groups1072433553688619179nt_rat H) (@ _let_2 _let_1))) (@ (@ tptp.groups1072433553688619179nt_rat G2) (@ _let_2 (@ tptp.uminus1532241313380277803et_int _let_1))))))))))
% 6.73/7.07 (assert (forall ((A4 tptp.set_complex) (P2 (-> tptp.complex Bool)) (H (-> tptp.complex tptp.rat)) (G2 (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.collect_complex P2))) (let ((_let_2 (@ tptp.inf_inf_set_complex A4))) (=> (@ tptp.finite3207457112153483333omplex A4) (= (@ (@ tptp.groups225925009352817453ex_rat (lambda ((X4 tptp.complex)) (@ (@ (@ tptp.if_rat (@ P2 X4)) (@ H X4)) (@ G2 X4)))) A4) (@ (@ tptp.times_times_rat (@ (@ tptp.groups225925009352817453ex_rat H) (@ _let_2 _let_1))) (@ (@ tptp.groups225925009352817453ex_rat G2) (@ _let_2 (@ tptp.uminus8566677241136511917omplex _let_1))))))))))
% 6.73/7.07 (assert (forall ((A4 tptp.set_nat) (P2 (-> tptp.nat Bool)) (H (-> tptp.nat tptp.rat)) (G2 (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.collect_nat P2))) (let ((_let_2 (@ tptp.inf_inf_set_nat A4))) (=> (@ tptp.finite_finite_nat A4) (= (@ (@ tptp.groups73079841787564623at_rat (lambda ((X4 tptp.nat)) (@ (@ (@ tptp.if_rat (@ P2 X4)) (@ H X4)) (@ G2 X4)))) A4) (@ (@ tptp.times_times_rat (@ (@ tptp.groups73079841787564623at_rat H) (@ _let_2 _let_1))) (@ (@ tptp.groups73079841787564623at_rat G2) (@ _let_2 (@ tptp.uminus5710092332889474511et_nat _let_1))))))))))
% 6.73/7.07 (assert (forall ((A4 tptp.set_real) (P2 (-> tptp.real Bool)) (H (-> tptp.real tptp.nat)) (G2 (-> tptp.real tptp.nat))) (let ((_let_1 (@ tptp.collect_real P2))) (let ((_let_2 (@ tptp.inf_inf_set_real A4))) (=> (@ tptp.finite_finite_real A4) (= (@ (@ tptp.groups4696554848551431203al_nat (lambda ((X4 tptp.real)) (@ (@ (@ tptp.if_nat (@ P2 X4)) (@ H X4)) (@ G2 X4)))) A4) (@ (@ tptp.times_times_nat (@ (@ tptp.groups4696554848551431203al_nat H) (@ _let_2 _let_1))) (@ (@ tptp.groups4696554848551431203al_nat G2) (@ _let_2 (@ tptp.uminus612125837232591019t_real _let_1))))))))))
% 6.73/7.07 (assert (forall ((A4 tptp.set_int) (P2 (-> tptp.int Bool)) (H (-> tptp.int tptp.nat)) (G2 (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.collect_int P2))) (let ((_let_2 (@ tptp.inf_inf_set_int A4))) (=> (@ tptp.finite_finite_int A4) (= (@ (@ tptp.groups1707563613775114915nt_nat (lambda ((X4 tptp.int)) (@ (@ (@ tptp.if_nat (@ P2 X4)) (@ H X4)) (@ G2 X4)))) A4) (@ (@ tptp.times_times_nat (@ (@ tptp.groups1707563613775114915nt_nat H) (@ _let_2 _let_1))) (@ (@ tptp.groups1707563613775114915nt_nat G2) (@ _let_2 (@ tptp.uminus1532241313380277803et_int _let_1))))))))))
% 6.73/7.07 (assert (forall ((K2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K2) N) (= (@ (@ tptp.binomial N) K2) (@ (@ tptp.divide_divide_nat (@ tptp.semiri1408675320244567234ct_nat N)) (@ (@ tptp.times_times_nat (@ tptp.semiri1408675320244567234ct_nat K2)) (@ tptp.semiri1408675320244567234ct_nat (@ (@ tptp.minus_minus_nat N) K2))))))))
% 6.73/7.07 (assert (forall ((A tptp.real) (B tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real A))) (let ((_let_2 (@ (@ tptp.ord_less_real C2) tptp.zero_zero_real))) (let ((_let_3 (@ (@ tptp.times_times_real A) C2))) (let ((_let_4 (@ tptp.uminus_uminus_real B))) (let ((_let_5 (@ (@ tptp.ord_less_real tptp.zero_zero_real) C2))) (= (@ _let_1 (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B) C2))) (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)))))))))))))
% 6.73/7.07 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat A))) (let ((_let_2 (@ (@ tptp.ord_less_rat C2) tptp.zero_zero_rat))) (let ((_let_3 (@ (@ tptp.times_times_rat A) C2))) (let ((_let_4 (@ tptp.uminus_uminus_rat B))) (let ((_let_5 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C2))) (= (@ _let_1 (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C2))) (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)))))))))))))
% 6.73/7.07 (assert (forall ((B tptp.real) (C2 tptp.real) (A tptp.real)) (let ((_let_1 (@ (@ tptp.ord_less_real C2) tptp.zero_zero_real))) (let ((_let_2 (@ tptp.uminus_uminus_real B))) (let ((_let_3 (@ (@ tptp.times_times_real A) C2))) (let ((_let_4 (@ (@ tptp.ord_less_real tptp.zero_zero_real) C2))) (= (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B) C2))) 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))))))))))))
% 6.73/7.07 (assert (forall ((B tptp.rat) (C2 tptp.rat) (A tptp.rat)) (let ((_let_1 (@ (@ tptp.ord_less_rat C2) tptp.zero_zero_rat))) (let ((_let_2 (@ tptp.uminus_uminus_rat B))) (let ((_let_3 (@ (@ tptp.times_times_rat A) C2))) (let ((_let_4 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C2))) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C2))) 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))))))))))))
% 6.73/7.07 (assert (forall ((C2 tptp.real) (A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real C2) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_eq_real A) (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B) C2))) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real B)) (@ (@ tptp.times_times_real A) C2))))))
% 6.73/7.07 (assert (forall ((C2 tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat C2) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_eq_rat A) (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C2))) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat B)) (@ (@ tptp.times_times_rat A) C2))))))
% 6.73/7.07 (assert (forall ((C2 tptp.real) (B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real C2) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B) C2))) A) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) C2)) (@ tptp.uminus_uminus_real B))))))
% 6.73/7.07 (assert (forall ((C2 tptp.rat) (B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat C2) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C2))) A) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C2)) (@ tptp.uminus_uminus_rat B))))))
% 6.73/7.07 (assert (forall ((C2 tptp.real) (A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C2) (= (@ (@ tptp.ord_less_eq_real A) (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B) C2))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) C2)) (@ tptp.uminus_uminus_real B))))))
% 6.73/7.07 (assert (forall ((C2 tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C2) (= (@ (@ tptp.ord_less_eq_rat A) (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C2))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C2)) (@ tptp.uminus_uminus_rat B))))))
% 6.73/7.07 (assert (forall ((C2 tptp.real) (B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C2) (= (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B) C2))) A) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real B)) (@ (@ tptp.times_times_real A) C2))))))
% 6.73/7.07 (assert (forall ((C2 tptp.rat) (B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C2) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C2))) A) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat B)) (@ (@ tptp.times_times_rat A) C2))))))
% 6.73/7.07 (assert (forall ((B tptp.real) (C2 tptp.real) (W2 tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W2)))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (let ((_let_3 (@ (@ tptp.ord_less_real C2) tptp.zero_zero_real))) (let ((_let_4 (@ (@ tptp.times_times_real _let_1) C2))) (let ((_let_5 (@ _let_2 C2))) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real B) C2)) _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)))))))))))))
% 6.73/7.07 (assert (forall ((B tptp.rat) (C2 tptp.rat) (W2 tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W2)))) (let ((_let_2 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (let ((_let_3 (@ (@ tptp.ord_less_rat C2) tptp.zero_zero_rat))) (let ((_let_4 (@ (@ tptp.times_times_rat _let_1) C2))) (let ((_let_5 (@ _let_2 C2))) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat B) C2)) _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)))))))))))))
% 6.73/7.07 (assert (forall ((W2 tptp.num) (B tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W2)))) (let ((_let_2 (@ tptp.ord_less_real _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_real C2) tptp.zero_zero_real))) (let ((_let_4 (@ (@ tptp.times_times_real _let_1) C2))) (let ((_let_5 (@ (@ tptp.ord_less_real tptp.zero_zero_real) C2))) (= (@ _let_2 (@ (@ tptp.divide_divide_real B) C2)) (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)))))))))))))
% 6.73/7.07 (assert (forall ((W2 tptp.num) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W2)))) (let ((_let_2 (@ tptp.ord_less_rat _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_rat C2) tptp.zero_zero_rat))) (let ((_let_4 (@ (@ tptp.times_times_rat _let_1) C2))) (let ((_let_5 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C2))) (= (@ _let_2 (@ (@ tptp.divide_divide_rat B) C2)) (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)))))))))))))
% 6.73/7.07 (assert (forall ((K2 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 K2) N) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N) K2)) (@ _let_1 (@ (@ tptp.minus_minus_nat N) K2)))))))
% 6.73/7.07 (assert (forall ((K2 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 K2) N) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N) K2)) (@ _let_1 (@ (@ tptp.minus_minus_nat N) K2)))))))
% 6.73/7.07 (assert (forall ((K2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))) (=> (@ (@ tptp.ord_less_eq_nat K2) N) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N) K2)) (@ _let_1 (@ (@ tptp.minus_minus_nat N) K2)))))))
% 6.73/7.07 (assert (forall ((K2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))) (=> (@ (@ tptp.ord_less_eq_nat K2) N) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N) K2)) (@ _let_1 (@ (@ tptp.minus_minus_nat N) K2)))))))
% 6.73/7.07 (assert (forall ((K2 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 K2) N) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N) K2)) (@ _let_1 (@ (@ tptp.minus_minus_nat N) K2)))))))
% 6.73/7.07 (assert (forall ((K2 tptp.int)) (=> (@ (@ tptp.ord_less_int K2) tptp.zero_zero_int) (not (forall ((N3 tptp.nat)) (=> (= K2 (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N3))) (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N3))))))))
% 6.73/7.07 (assert (forall ((L tptp.int) (K2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) L) (= (@ (@ tptp.modulo_modulo_int (@ tptp.uminus_uminus_int K2)) L) (@ (@ tptp.minus_minus_int (@ (@ tptp.minus_minus_int L) tptp.one_one_int)) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.minus_minus_int K2) tptp.one_one_int)) L))))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (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))))))))))
% 6.73/7.07 (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)))))))))))
% 6.73/7.07 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M2) (= (@ tptp.semiri1408675320244567234ct_nat M2) (@ (@ tptp.times_times_nat (@ tptp.semiri1408675320244567234ct_nat N)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((X4 tptp.nat)) X4)) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc N)) M2)))))))
% 6.73/7.07 (assert (= tptp.bit_ri6519982836138164636nteger (lambda ((N4 tptp.nat) (A5 tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.modulo364778990260209775nteger A5) _let_1))) (@ (@ (@ tptp.if_Code_integer (= N4 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 N4) tptp.one_one_nat)) (@ (@ tptp.divide6298287555418463151nteger A5) _let_1))))))))))
% 6.73/7.07 (assert (= tptp.bit_ri631733984087533419it_int (lambda ((N4 tptp.nat) (A5 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.modulo_modulo_int A5) _let_1))) (@ (@ (@ tptp.if_int (= N4 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 N4) tptp.one_one_nat)) (@ (@ tptp.divide_divide_int A5) _let_1))))))))))
% 6.73/7.07 (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))))))
% 6.73/7.07 (assert (forall ((A tptp.int) (B tptp.int) (Q2 tptp.int) (R3 tptp.int)) (let ((_let_1 (@ tptp.if_int (= R3 tptp.zero_zero_int)))) (let ((_let_2 (@ tptp.uminus_uminus_int Q2))) (=> (@ (@ (@ tptp.eucl_rel_int A) B) (@ (@ tptp.product_Pair_int_int Q2) R3)) (=> (not (= B tptp.zero_zero_int)) (@ (@ (@ tptp.eucl_rel_int (@ tptp.uminus_uminus_int A)) B) (@ (@ tptp.product_Pair_int_int (@ (@ _let_1 _let_2) (@ (@ tptp.minus_minus_int _let_2) tptp.one_one_int))) (@ (@ _let_1 tptp.zero_zero_int) (@ (@ tptp.minus_minus_int B) R3))))))))))
% 6.73/7.07 (assert (forall ((B tptp.real) (C2 tptp.real) (W2 tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W2)))) (let ((_let_2 (@ (@ tptp.ord_less_real C2) tptp.zero_zero_real))) (let ((_let_3 (@ (@ tptp.times_times_real _let_1) C2))) (let ((_let_4 (@ (@ tptp.ord_less_real tptp.zero_zero_real) C2))) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real B) C2)) _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))))))))))))
% 6.73/7.07 (assert (forall ((B tptp.rat) (C2 tptp.rat) (W2 tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W2)))) (let ((_let_2 (@ (@ tptp.ord_less_rat C2) tptp.zero_zero_rat))) (let ((_let_3 (@ (@ tptp.times_times_rat _let_1) C2))) (let ((_let_4 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C2))) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat B) C2)) _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))))))))))))
% 6.73/7.07 (assert (forall ((W2 tptp.num) (B tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W2)))) (let ((_let_2 (@ tptp.ord_less_eq_real _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_real C2) tptp.zero_zero_real))) (let ((_let_4 (@ (@ tptp.times_times_real _let_1) C2))) (let ((_let_5 (@ (@ tptp.ord_less_real tptp.zero_zero_real) C2))) (= (@ _let_2 (@ (@ tptp.divide_divide_real B) C2)) (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)))))))))))))
% 6.73/7.07 (assert (forall ((W2 tptp.num) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W2)))) (let ((_let_2 (@ tptp.ord_less_eq_rat _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_rat C2) tptp.zero_zero_rat))) (let ((_let_4 (@ (@ tptp.times_times_rat _let_1) C2))) (let ((_let_5 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C2))) (= (@ _let_2 (@ (@ tptp.divide_divide_rat B) C2)) (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)))))))))))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (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))))))
% 6.73/7.07 (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))))))
% 6.73/7.07 (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))))))
% 6.73/7.07 (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))))))
% 6.73/7.07 (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))))))
% 6.73/7.07 (assert (= tptp.semiri3624122377584611663nteger (lambda ((M6 tptp.nat)) (@ (@ (@ tptp.if_Code_integer (= M6 tptp.zero_zero_nat)) tptp.one_one_Code_integer) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.semiri4939895301339042750nteger M6)) (@ tptp.semiri3624122377584611663nteger (@ (@ tptp.minus_minus_nat M6) tptp.one_one_nat)))))))
% 6.73/7.07 (assert (= tptp.semiri5044797733671781792omplex (lambda ((M6 tptp.nat)) (@ (@ (@ tptp.if_complex (= M6 tptp.zero_zero_nat)) tptp.one_one_complex) (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex M6)) (@ tptp.semiri5044797733671781792omplex (@ (@ tptp.minus_minus_nat M6) tptp.one_one_nat)))))))
% 6.73/7.07 (assert (= tptp.semiri773545260158071498ct_rat (lambda ((M6 tptp.nat)) (@ (@ (@ tptp.if_rat (= M6 tptp.zero_zero_nat)) tptp.one_one_rat) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat M6)) (@ tptp.semiri773545260158071498ct_rat (@ (@ tptp.minus_minus_nat M6) tptp.one_one_nat)))))))
% 6.73/7.07 (assert (= tptp.semiri1406184849735516958ct_int (lambda ((M6 tptp.nat)) (@ (@ (@ tptp.if_int (= M6 tptp.zero_zero_nat)) tptp.one_one_int) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int M6)) (@ tptp.semiri1406184849735516958ct_int (@ (@ tptp.minus_minus_nat M6) tptp.one_one_nat)))))))
% 6.73/7.07 (assert (= tptp.semiri1408675320244567234ct_nat (lambda ((M6 tptp.nat)) (@ (@ (@ tptp.if_nat (= M6 tptp.zero_zero_nat)) tptp.one_one_nat) (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat M6)) (@ tptp.semiri1408675320244567234ct_nat (@ (@ tptp.minus_minus_nat M6) tptp.one_one_nat)))))))
% 6.73/7.07 (assert (= tptp.semiri2265585572941072030t_real (lambda ((M6 tptp.nat)) (@ (@ (@ tptp.if_real (= M6 tptp.zero_zero_nat)) tptp.one_one_real) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real M6)) (@ tptp.semiri2265585572941072030t_real (@ (@ tptp.minus_minus_nat M6) tptp.one_one_nat)))))))
% 6.73/7.07 (assert (= tptp.semiri1406184849735516958ct_int (lambda ((N4 tptp.nat)) (@ tptp.semiri1314217659103216013at_int (@ (@ (@ (@ tptp.set_fo2584398358068434914at_nat tptp.times_times_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N4) tptp.one_one_nat)))))
% 6.73/7.07 (assert (= tptp.semiri1408675320244567234ct_nat (lambda ((N4 tptp.nat)) (@ tptp.semiri1316708129612266289at_nat (@ (@ (@ (@ tptp.set_fo2584398358068434914at_nat tptp.times_times_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N4) tptp.one_one_nat)))))
% 6.73/7.07 (assert (= tptp.semiri2265585572941072030t_real (lambda ((N4 tptp.nat)) (@ tptp.semiri5074537144036343181t_real (@ (@ (@ (@ tptp.set_fo2584398358068434914at_nat tptp.times_times_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N4) tptp.one_one_nat)))))
% 6.73/7.07 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.semiri773545260158071498ct_rat N) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat N)) (@ tptp.semiri773545260158071498ct_rat (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)))))))
% 6.73/7.07 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.semiri1406184849735516958ct_int N) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int N)) (@ tptp.semiri1406184849735516958ct_int (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)))))))
% 6.73/7.07 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.semiri1408675320244567234ct_nat N) (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat N)) (@ tptp.semiri1408675320244567234ct_nat (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)))))))
% 6.73/7.07 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.semiri2265585572941072030t_real N) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ tptp.semiri2265585572941072030t_real (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)))))))
% 6.73/7.07 (assert (forall ((R3 tptp.complex) (K2 tptp.nat)) (let ((_let_1 (@ tptp.uminus1482373934393186551omplex R3))) (= (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex R3) (@ tptp.semiri8010041392384452111omplex K2))) (@ (@ tptp.comm_s2602460028002588243omplex _let_1) K2)) (@ (@ tptp.times_times_complex R3) (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.plus_plus_complex _let_1) tptp.one_one_complex)) K2))))))
% 6.73/7.07 (assert (forall ((R3 tptp.code_integer) (K2 tptp.nat)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger R3))) (= (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.minus_8373710615458151222nteger R3) (@ tptp.semiri4939895301339042750nteger K2))) (@ (@ tptp.comm_s8582702949713902594nteger _let_1) K2)) (@ (@ tptp.times_3573771949741848930nteger R3) (@ (@ tptp.comm_s8582702949713902594nteger (@ (@ tptp.plus_p5714425477246183910nteger _let_1) tptp.one_one_Code_integer)) K2))))))
% 6.73/7.07 (assert (forall ((R3 tptp.rat) (K2 tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_rat R3))) (= (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat R3) (@ tptp.semiri681578069525770553at_rat K2))) (@ (@ tptp.comm_s4028243227959126397er_rat _let_1) K2)) (@ (@ tptp.times_times_rat R3) (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.plus_plus_rat _let_1) tptp.one_one_rat)) K2))))))
% 6.73/7.07 (assert (forall ((R3 tptp.real) (K2 tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_real R3))) (= (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real R3) (@ tptp.semiri5074537144036343181t_real K2))) (@ (@ tptp.comm_s7457072308508201937r_real _let_1) K2)) (@ (@ tptp.times_times_real R3) (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real)) K2))))))
% 6.73/7.07 (assert (forall ((R3 tptp.int) (K2 tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_int R3))) (= (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int R3) (@ tptp.semiri1314217659103216013at_int K2))) (@ (@ tptp.comm_s4660882817536571857er_int _let_1) K2)) (@ (@ tptp.times_times_int R3) (@ (@ tptp.comm_s4660882817536571857er_int (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int)) K2))))))
% 6.73/7.07 (assert (forall ((K2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))) (= (@ (@ tptp.times_times_complex (@ _let_1 K2)) (@ (@ tptp.gbinomial_complex (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.semiri8010041392384452111omplex N))) tptp.one_one_complex)) K2)) (@ (@ tptp.times_times_complex (@ _let_1 N)) (@ (@ tptp.gbinomial_complex (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.semiri8010041392384452111omplex K2))) tptp.one_one_complex)) N))))))
% 6.73/7.07 (assert (forall ((K2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)))) (= (@ (@ tptp.times_times_rat (@ _let_1 K2)) (@ (@ tptp.gbinomial_rat (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat (@ tptp.semiri681578069525770553at_rat N))) tptp.one_one_rat)) K2)) (@ (@ tptp.times_times_rat (@ _let_1 N)) (@ (@ tptp.gbinomial_rat (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat (@ tptp.semiri681578069525770553at_rat K2))) tptp.one_one_rat)) N))))))
% 6.73/7.07 (assert (forall ((K2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)))) (= (@ (@ tptp.times_times_real (@ _let_1 K2)) (@ (@ tptp.gbinomial_real (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real (@ tptp.semiri5074537144036343181t_real N))) tptp.one_one_real)) K2)) (@ (@ tptp.times_times_real (@ _let_1 N)) (@ (@ tptp.gbinomial_real (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real (@ tptp.semiri5074537144036343181t_real K2))) tptp.one_one_real)) N))))))
% 6.73/7.07 (assert (= tptp.gbinomial_complex (lambda ((A5 tptp.complex) (K3 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) K3)) (@ (@ tptp.gbinomial_complex (@ (@ tptp.minus_minus_complex (@ (@ tptp.minus_minus_complex (@ tptp.semiri8010041392384452111omplex K3)) A5)) tptp.one_one_complex)) K3)))))
% 6.73/7.07 (assert (= tptp.gbinomial_rat (lambda ((A5 tptp.rat) (K3 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) K3)) (@ (@ tptp.gbinomial_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.minus_minus_rat (@ tptp.semiri681578069525770553at_rat K3)) A5)) tptp.one_one_rat)) K3)))))
% 6.73/7.07 (assert (= tptp.gbinomial_real (lambda ((A5 tptp.real) (K3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) K3)) (@ (@ tptp.gbinomial_real (@ (@ tptp.minus_minus_real (@ (@ tptp.minus_minus_real (@ tptp.semiri5074537144036343181t_real K3)) A5)) tptp.one_one_real)) K3)))))
% 6.73/7.07 (assert (forall ((K2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K2) N) (= (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.binomial N) K2)) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.semiri5044797733671781792omplex N)) (@ (@ tptp.times_times_complex (@ tptp.semiri5044797733671781792omplex K2)) (@ tptp.semiri5044797733671781792omplex (@ (@ tptp.minus_minus_nat N) K2))))))))
% 6.73/7.07 (assert (forall ((K2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K2) N) (= (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.binomial N) K2)) (@ (@ tptp.divide_divide_rat (@ tptp.semiri773545260158071498ct_rat N)) (@ (@ tptp.times_times_rat (@ tptp.semiri773545260158071498ct_rat K2)) (@ tptp.semiri773545260158071498ct_rat (@ (@ tptp.minus_minus_nat N) K2))))))))
% 6.73/7.07 (assert (forall ((K2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K2) N) (= (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.binomial N) K2)) (@ (@ tptp.divide_divide_real (@ tptp.semiri2265585572941072030t_real N)) (@ (@ tptp.times_times_real (@ tptp.semiri2265585572941072030t_real K2)) (@ tptp.semiri2265585572941072030t_real (@ (@ tptp.minus_minus_nat N) K2))))))))
% 6.73/7.07 (assert (forall ((K2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K2) N) (= (@ (@ tptp.times_times_complex (@ tptp.semiri5044797733671781792omplex K2)) (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.binomial N) K2))) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.semiri5044797733671781792omplex N)) (@ tptp.semiri5044797733671781792omplex (@ (@ tptp.minus_minus_nat N) K2)))))))
% 6.73/7.07 (assert (forall ((K2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K2) N) (= (@ (@ tptp.times_times_rat (@ tptp.semiri773545260158071498ct_rat K2)) (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.binomial N) K2))) (@ (@ tptp.divide_divide_rat (@ tptp.semiri773545260158071498ct_rat N)) (@ tptp.semiri773545260158071498ct_rat (@ (@ tptp.minus_minus_nat N) K2)))))))
% 6.73/7.07 (assert (forall ((K2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K2) N) (= (@ (@ tptp.times_times_real (@ tptp.semiri2265585572941072030t_real K2)) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.binomial N) K2))) (@ (@ tptp.divide_divide_real (@ tptp.semiri2265585572941072030t_real N)) (@ tptp.semiri2265585572941072030t_real (@ (@ tptp.minus_minus_nat N) K2)))))))
% 6.73/7.07 (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))))))
% 6.73/7.07 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M2) (= (@ (@ tptp.divide_divide_nat (@ tptp.semiri1408675320244567234ct_nat M2)) (@ tptp.semiri1408675320244567234ct_nat N)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((X4 tptp.nat)) X4)) (@ (@ tptp.set_or1269000886237332187st_nat (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat)) M2))))))
% 6.73/7.07 (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))))
% 6.73/7.07 (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))))
% 6.73/7.07 (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))))
% 6.73/7.07 (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))))
% 6.73/7.07 (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))))
% 6.73/7.07 (assert (forall ((A tptp.complex) (K2 tptp.nat)) (= (@ (@ tptp.gbinomial_complex (@ tptp.uminus1482373934393186551omplex A)) K2) (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) K2)) (@ (@ tptp.gbinomial_complex (@ (@ tptp.minus_minus_complex (@ (@ tptp.plus_plus_complex A) (@ tptp.semiri8010041392384452111omplex K2))) tptp.one_one_complex)) K2)))))
% 6.73/7.07 (assert (forall ((A tptp.rat) (K2 tptp.nat)) (= (@ (@ tptp.gbinomial_rat (@ tptp.uminus_uminus_rat A)) K2) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) K2)) (@ (@ tptp.gbinomial_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A) (@ tptp.semiri681578069525770553at_rat K2))) tptp.one_one_rat)) K2)))))
% 6.73/7.07 (assert (forall ((A tptp.real) (K2 tptp.nat)) (= (@ (@ tptp.gbinomial_real (@ tptp.uminus_uminus_real A)) K2) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) K2)) (@ (@ tptp.gbinomial_real (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A) (@ tptp.semiri5074537144036343181t_real K2))) tptp.one_one_real)) K2)))))
% 6.73/7.07 (assert (forall ((N tptp.nat) (K2 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)) K2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_ri631733984087533419it_int N) K2)) (@ (@ tptp.minus_minus_int K2) (@ _let_1 (@ tptp.suc N))))))))
% 6.73/7.07 (assert (forall ((B tptp.complex) (K2 tptp.nat)) (= (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.plus_plus_complex (@ (@ tptp.minus_minus_complex B) (@ tptp.semiri8010041392384452111omplex K2))) tptp.one_one_complex)) K2) (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) K2)) (@ (@ tptp.comm_s2602460028002588243omplex (@ tptp.uminus1482373934393186551omplex B)) K2)))))
% 6.73/7.07 (assert (forall ((B tptp.code_integer) (K2 tptp.nat)) (= (@ (@ tptp.comm_s8582702949713902594nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.minus_8373710615458151222nteger B) (@ tptp.semiri4939895301339042750nteger K2))) tptp.one_one_Code_integer)) K2) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) K2)) (@ (@ tptp.comm_s8582702949713902594nteger (@ tptp.uminus1351360451143612070nteger B)) K2)))))
% 6.73/7.07 (assert (forall ((B tptp.rat) (K2 tptp.nat)) (= (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.minus_minus_rat B) (@ tptp.semiri681578069525770553at_rat K2))) tptp.one_one_rat)) K2) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) K2)) (@ (@ tptp.comm_s4028243227959126397er_rat (@ tptp.uminus_uminus_rat B)) K2)))))
% 6.73/7.07 (assert (forall ((B tptp.real) (K2 tptp.nat)) (= (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.plus_plus_real (@ (@ tptp.minus_minus_real B) (@ tptp.semiri5074537144036343181t_real K2))) tptp.one_one_real)) K2) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) K2)) (@ (@ tptp.comm_s7457072308508201937r_real (@ tptp.uminus_uminus_real B)) K2)))))
% 6.73/7.07 (assert (forall ((B tptp.int) (K2 tptp.nat)) (= (@ (@ tptp.comm_s4660882817536571857er_int (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int B) (@ tptp.semiri1314217659103216013at_int K2))) tptp.one_one_int)) K2) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) K2)) (@ (@ tptp.comm_s4660882817536571857er_int (@ tptp.uminus_uminus_int B)) K2)))))
% 6.73/7.07 (assert (forall ((B tptp.complex) (K2 tptp.nat)) (= (@ (@ tptp.comm_s2602460028002588243omplex (@ tptp.uminus1482373934393186551omplex B)) K2) (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) K2)) (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.plus_plus_complex (@ (@ tptp.minus_minus_complex B) (@ tptp.semiri8010041392384452111omplex K2))) tptp.one_one_complex)) K2)))))
% 6.73/7.07 (assert (forall ((B tptp.code_integer) (K2 tptp.nat)) (= (@ (@ tptp.comm_s8582702949713902594nteger (@ tptp.uminus1351360451143612070nteger B)) K2) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) K2)) (@ (@ tptp.comm_s8582702949713902594nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.minus_8373710615458151222nteger B) (@ tptp.semiri4939895301339042750nteger K2))) tptp.one_one_Code_integer)) K2)))))
% 6.73/7.07 (assert (forall ((B tptp.rat) (K2 tptp.nat)) (= (@ (@ tptp.comm_s4028243227959126397er_rat (@ tptp.uminus_uminus_rat B)) K2) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) K2)) (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.minus_minus_rat B) (@ tptp.semiri681578069525770553at_rat K2))) tptp.one_one_rat)) K2)))))
% 6.73/7.07 (assert (forall ((B tptp.real) (K2 tptp.nat)) (= (@ (@ tptp.comm_s7457072308508201937r_real (@ tptp.uminus_uminus_real B)) K2) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) K2)) (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.plus_plus_real (@ (@ tptp.minus_minus_real B) (@ tptp.semiri5074537144036343181t_real K2))) tptp.one_one_real)) K2)))))
% 6.73/7.07 (assert (forall ((B tptp.int) (K2 tptp.nat)) (= (@ (@ tptp.comm_s4660882817536571857er_int (@ tptp.uminus_uminus_int B)) K2) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) K2)) (@ (@ tptp.comm_s4660882817536571857er_int (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int B) (@ tptp.semiri1314217659103216013at_int K2))) tptp.one_one_int)) K2)))))
% 6.73/7.07 (assert (forall ((P2 (-> tptp.int Bool)) (K2 tptp.int)) (=> (@ P2 tptp.zero_zero_int) (=> (@ P2 (@ tptp.uminus_uminus_int tptp.one_one_int)) (=> (forall ((K tptp.int)) (=> (@ P2 K) (=> (not (= K tptp.zero_zero_int)) (@ P2 (@ (@ tptp.times_times_int K) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))))) (=> (forall ((K tptp.int)) (=> (@ P2 K) (=> (not (= K (@ tptp.uminus_uminus_int tptp.one_one_int))) (@ P2 (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ (@ tptp.times_times_int K) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))))))) (@ P2 K2)))))))
% 6.73/7.07 (assert (forall ((A tptp.complex) (M2 tptp.nat)) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.gbinomial_complex A) K3)) (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) K3)))) (@ tptp.set_ord_atMost_nat M2)) (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) M2)) (@ (@ tptp.gbinomial_complex (@ (@ tptp.minus_minus_complex A) tptp.one_one_complex)) M2)))))
% 6.73/7.07 (assert (forall ((A tptp.rat) (M2 tptp.nat)) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.gbinomial_rat A) K3)) (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) K3)))) (@ tptp.set_ord_atMost_nat M2)) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) M2)) (@ (@ tptp.gbinomial_rat (@ (@ tptp.minus_minus_rat A) tptp.one_one_rat)) M2)))))
% 6.73/7.07 (assert (forall ((A tptp.real) (M2 tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.gbinomial_real A) K3)) (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) K3)))) (@ tptp.set_ord_atMost_nat M2)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) M2)) (@ (@ tptp.gbinomial_real (@ (@ tptp.minus_minus_real A) tptp.one_one_real)) M2)))))
% 6.73/7.07 (assert (forall ((A tptp.complex) (K2 tptp.nat)) (let ((_let_1 (@ tptp.suc K2))) (= (@ (@ tptp.gbinomial_complex A) _let_1) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.groups6464643781859351333omplex (lambda ((I tptp.nat)) (@ (@ tptp.minus_minus_complex A) (@ tptp.semiri8010041392384452111omplex I)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) K2))) (@ tptp.semiri5044797733671781792omplex _let_1))))))
% 6.73/7.07 (assert (forall ((A tptp.rat) (K2 tptp.nat)) (let ((_let_1 (@ tptp.suc K2))) (= (@ (@ tptp.gbinomial_rat A) _let_1) (@ (@ tptp.divide_divide_rat (@ (@ tptp.groups73079841787564623at_rat (lambda ((I tptp.nat)) (@ (@ tptp.minus_minus_rat A) (@ tptp.semiri681578069525770553at_rat I)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) K2))) (@ tptp.semiri773545260158071498ct_rat _let_1))))))
% 6.73/7.07 (assert (forall ((A tptp.real) (K2 tptp.nat)) (let ((_let_1 (@ tptp.suc K2))) (= (@ (@ tptp.gbinomial_real A) _let_1) (@ (@ tptp.divide_divide_real (@ (@ tptp.groups129246275422532515t_real (lambda ((I tptp.nat)) (@ (@ tptp.minus_minus_real A) (@ tptp.semiri5074537144036343181t_real I)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) K2))) (@ tptp.semiri2265585572941072030t_real _let_1))))))
% 6.73/7.07 (assert (forall ((A tptp.int) (K2 tptp.nat)) (let ((_let_1 (@ tptp.suc K2))) (= (@ (@ tptp.gbinomial_int A) _let_1) (@ (@ tptp.divide_divide_int (@ (@ tptp.groups705719431365010083at_int (lambda ((I tptp.nat)) (@ (@ tptp.minus_minus_int A) (@ tptp.semiri1314217659103216013at_int I)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) K2))) (@ tptp.semiri1406184849735516958ct_int _let_1))))))
% 6.73/7.07 (assert (forall ((A tptp.nat) (K2 tptp.nat)) (let ((_let_1 (@ tptp.suc K2))) (= (@ (@ tptp.gbinomial_nat A) _let_1) (@ (@ tptp.divide_divide_nat (@ (@ tptp.groups708209901874060359at_nat (lambda ((I tptp.nat)) (@ (@ tptp.minus_minus_nat A) (@ tptp.semiri1316708129612266289at_nat I)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) K2))) (@ tptp.semiri1408675320244567234ct_nat _let_1))))))
% 6.73/7.07 (assert (forall ((M2 tptp.nat) (A tptp.complex) (X tptp.complex) (Y tptp.complex)) (let ((_let_1 (@ tptp.set_ord_atMost_nat M2))) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ (@ tptp.gbinomial_complex (@ (@ tptp.plus_plus_complex (@ tptp.semiri8010041392384452111omplex M2)) A)) K3)) (@ (@ tptp.power_power_complex X) K3))) (@ (@ tptp.power_power_complex Y) (@ (@ tptp.minus_minus_nat M2) K3))))) _let_1) (@ (@ tptp.groups2073611262835488442omplex (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ (@ tptp.gbinomial_complex (@ tptp.uminus1482373934393186551omplex A)) K3)) (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex X)) K3))) (@ (@ tptp.power_power_complex (@ (@ tptp.plus_plus_complex X) Y)) (@ (@ tptp.minus_minus_nat M2) K3))))) _let_1)))))
% 6.73/7.07 (assert (forall ((M2 tptp.nat) (A tptp.rat) (X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.set_ord_atMost_nat M2))) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ (@ tptp.gbinomial_rat (@ (@ tptp.plus_plus_rat (@ tptp.semiri681578069525770553at_rat M2)) A)) K3)) (@ (@ tptp.power_power_rat X) K3))) (@ (@ tptp.power_power_rat Y) (@ (@ tptp.minus_minus_nat M2) K3))))) _let_1) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ (@ tptp.gbinomial_rat (@ tptp.uminus_uminus_rat A)) K3)) (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat X)) K3))) (@ (@ tptp.power_power_rat (@ (@ tptp.plus_plus_rat X) Y)) (@ (@ tptp.minus_minus_nat M2) K3))))) _let_1)))))
% 6.73/7.07 (assert (forall ((M2 tptp.nat) (A tptp.real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.set_ord_atMost_nat M2))) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.gbinomial_real (@ (@ tptp.plus_plus_real (@ tptp.semiri5074537144036343181t_real M2)) A)) K3)) (@ (@ tptp.power_power_real X) K3))) (@ (@ tptp.power_power_real Y) (@ (@ tptp.minus_minus_nat M2) K3))))) _let_1) (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.gbinomial_real (@ tptp.uminus_uminus_real A)) K3)) (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real X)) K3))) (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real X) Y)) (@ (@ tptp.minus_minus_nat M2) K3))))) _let_1)))))
% 6.73/7.07 (assert (forall ((N tptp.nat) (Z3 tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N) (= (= (@ (@ tptp.power_power_int Z3) N) A) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((I tptp.nat)) (@ (@ tptp.times_times_int (@ (@ (@ tptp.if_int (= I tptp.zero_zero_nat)) (@ tptp.uminus_uminus_int A)) (@ (@ (@ tptp.if_int (= I N)) tptp.one_one_int) tptp.zero_zero_int))) (@ (@ tptp.power_power_int Z3) I)))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_int)))))
% 6.73/7.07 (assert (forall ((N tptp.nat) (Z3 tptp.complex) (A tptp.complex)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N) (= (= (@ (@ tptp.power_power_complex Z3) N) A) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ (@ tptp.if_complex (= I tptp.zero_zero_nat)) (@ tptp.uminus1482373934393186551omplex A)) (@ (@ (@ tptp.if_complex (= I N)) tptp.one_one_complex) tptp.zero_zero_complex))) (@ (@ tptp.power_power_complex Z3) I)))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_complex)))))
% 6.73/7.07 (assert (forall ((N tptp.nat) (Z3 tptp.code_integer) (A tptp.code_integer)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N) (= (= (@ (@ tptp.power_8256067586552552935nteger Z3) N) A) (= (@ (@ tptp.groups7501900531339628137nteger (lambda ((I tptp.nat)) (@ (@ tptp.times_3573771949741848930nteger (@ (@ (@ tptp.if_Code_integer (= I tptp.zero_zero_nat)) (@ tptp.uminus1351360451143612070nteger A)) (@ (@ (@ tptp.if_Code_integer (= I N)) tptp.one_one_Code_integer) tptp.zero_z3403309356797280102nteger))) (@ (@ tptp.power_8256067586552552935nteger Z3) I)))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_z3403309356797280102nteger)))))
% 6.73/7.07 (assert (forall ((N tptp.nat) (Z3 tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N) (= (= (@ (@ tptp.power_power_rat Z3) N) A) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ (@ tptp.if_rat (= I tptp.zero_zero_nat)) (@ tptp.uminus_uminus_rat A)) (@ (@ (@ tptp.if_rat (= I N)) tptp.one_one_rat) tptp.zero_zero_rat))) (@ (@ tptp.power_power_rat Z3) I)))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_rat)))))
% 6.73/7.07 (assert (forall ((N tptp.nat) (Z3 tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N) (= (= (@ (@ tptp.power_power_real Z3) N) A) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I tptp.nat)) (@ (@ tptp.times_times_real (@ (@ (@ tptp.if_real (= I tptp.zero_zero_nat)) (@ tptp.uminus_uminus_real A)) (@ (@ (@ tptp.if_real (= I N)) tptp.one_one_real) tptp.zero_zero_real))) (@ (@ tptp.power_power_real Z3) I)))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_real)))))
% 6.73/7.07 (assert (forall ((N tptp.nat) (Z3 tptp.nat)) (let ((_let_1 (@ tptp.nat_set_decode Z3))) (=> (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)) Z3)) (@ (@ tptp.insert_nat N) _let_1))))))
% 6.73/7.07 (assert (forall ((N tptp.nat)) (=> (not (= N tptp.one_one_nat)) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) I)) (@ tptp.semiri8010041392384452111omplex I))) (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.binomial N) I))))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_complex))))
% 6.73/7.07 (assert (forall ((N tptp.nat)) (=> (not (= N tptp.one_one_nat)) (= (@ (@ tptp.groups7501900531339628137nteger (lambda ((I tptp.nat)) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) I)) (@ tptp.semiri4939895301339042750nteger I))) (@ tptp.semiri4939895301339042750nteger (@ (@ tptp.binomial N) I))))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_z3403309356797280102nteger))))
% 6.73/7.07 (assert (forall ((N tptp.nat)) (=> (not (= N tptp.one_one_nat)) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) I)) (@ tptp.semiri681578069525770553at_rat I))) (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.binomial N) I))))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_rat))))
% 6.73/7.07 (assert (forall ((N tptp.nat)) (=> (not (= N tptp.one_one_nat)) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((I tptp.nat)) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) I)) (@ tptp.semiri1314217659103216013at_int I))) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.binomial N) I))))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_int))))
% 6.73/7.07 (assert (forall ((N tptp.nat)) (=> (not (= N tptp.one_one_nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I)) (@ tptp.semiri5074537144036343181t_real I))) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.binomial N) I))))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_real))))
% 6.73/7.07 (assert (= tptp.nat_set_decode (lambda ((X4 tptp.nat)) (@ tptp.collect_nat (lambda ((N4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (not (@ (@ tptp.dvd_dvd_nat _let_1) (@ (@ tptp.divide_divide_nat X4) (@ (@ tptp.power_power_nat _let_1) N4))))))))))
% 6.73/7.07 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numera6690914467698888265omplex _let_1))) (let ((_let_3 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat _let_1)) N))) (= (@ tptp.semiri5044797733671781792omplex _let_3) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex _let_2) _let_3)) (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.divide1717551699836669952omplex tptp.one_one_complex) _let_2)) N))) (@ tptp.semiri5044797733671781792omplex N))))))))
% 6.73/7.07 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_rat _let_1))) (let ((_let_3 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat _let_1)) N))) (= (@ tptp.semiri773545260158071498ct_rat _let_3) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat _let_2) _let_3)) (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.divide_divide_rat tptp.one_one_rat) _let_2)) N))) (@ tptp.semiri773545260158071498ct_rat N))))))))
% 6.73/7.07 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_real _let_1))) (let ((_let_3 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat _let_1)) N))) (= (@ tptp.semiri2265585572941072030t_real _let_3) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real _let_2) _let_3)) (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_2)) N))) (@ tptp.semiri2265585572941072030t_real N))))))))
% 6.73/7.07 (assert (= tptp.binomial (lambda ((N4 tptp.nat) (K3 tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat N4) K3))) (let ((_let_2 (@ tptp.ord_less_nat N4))) (@ (@ (@ tptp.if_nat (@ _let_2 K3)) tptp.zero_zero_nat) (@ (@ (@ tptp.if_nat (@ _let_2 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) K3))) (@ (@ tptp.binomial N4) _let_1)) (@ (@ tptp.divide_divide_nat (@ (@ (@ (@ tptp.set_fo2584398358068434914at_nat tptp.times_times_nat) (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat)) N4) tptp.one_one_nat)) (@ tptp.semiri1408675320244567234ct_nat K3)))))))))
% 6.73/7.07 (assert (forall ((H tptp.real) (F2 (-> tptp.real tptp.real)) (J2 (-> tptp.nat tptp.real)) (N tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H) (exists ((B8 tptp.real)) (= (@ F2 H) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ J2 M6)) (@ tptp.semiri2265585572941072030t_real M6))) (@ (@ tptp.power_power_real H) M6)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real B8) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real H) N)) (@ tptp.semiri2265585572941072030t_real N)))))))))
% 6.73/7.07 (assert (forall ((X tptp.real) (N tptp.nat) (Diff (-> tptp.nat tptp.complex tptp.real))) (=> (= X tptp.zero_zero_real) (=> (not (= N tptp.zero_zero_nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M6) tptp.zero_zero_complex)) (@ tptp.semiri2265585572941072030t_real M6))) (@ (@ tptp.power_power_real X) M6)))) (@ tptp.set_ord_lessThan_nat N)) (@ (@ Diff tptp.zero_zero_nat) tptp.zero_zero_complex))))))
% 6.73/7.07 (assert (forall ((X tptp.real) (N tptp.nat) (Diff (-> tptp.nat tptp.real tptp.real))) (=> (= X tptp.zero_zero_real) (=> (not (= N tptp.zero_zero_nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M6) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M6))) (@ (@ tptp.power_power_real X) M6)))) (@ tptp.set_ord_lessThan_nat N)) (@ (@ Diff tptp.zero_zero_nat) tptp.zero_zero_real))))))
% 6.73/7.07 (assert (forall ((X tptp.real) (N tptp.nat) (Diff (-> tptp.nat tptp.rat tptp.real))) (=> (= X tptp.zero_zero_real) (=> (not (= N tptp.zero_zero_nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M6) tptp.zero_zero_rat)) (@ tptp.semiri2265585572941072030t_real M6))) (@ (@ tptp.power_power_real X) M6)))) (@ tptp.set_ord_lessThan_nat N)) (@ (@ Diff tptp.zero_zero_nat) tptp.zero_zero_rat))))))
% 6.73/7.07 (assert (forall ((X tptp.real) (N tptp.nat) (Diff (-> tptp.nat tptp.nat tptp.real))) (=> (= X tptp.zero_zero_real) (=> (not (= N tptp.zero_zero_nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M6) tptp.zero_zero_nat)) (@ tptp.semiri2265585572941072030t_real M6))) (@ (@ tptp.power_power_real X) M6)))) (@ tptp.set_ord_lessThan_nat N)) (@ (@ Diff tptp.zero_zero_nat) tptp.zero_zero_nat))))))
% 6.73/7.07 (assert (forall ((X tptp.real) (N tptp.nat) (Diff (-> tptp.nat tptp.int tptp.real))) (=> (= X tptp.zero_zero_real) (=> (not (= N tptp.zero_zero_nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M6) tptp.zero_zero_int)) (@ tptp.semiri2265585572941072030t_real M6))) (@ (@ tptp.power_power_real X) M6)))) (@ tptp.set_ord_lessThan_nat N)) (@ (@ Diff tptp.zero_zero_nat) tptp.zero_zero_int))))))
% 6.73/7.07 (assert (= tptp.sin_coeff (lambda ((N4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_real (@ (@ tptp.dvd_dvd_nat _let_1) N4)) 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 N4) (@ tptp.suc tptp.zero_zero_nat))) _let_1))) (@ tptp.semiri2265585572941072030t_real N4)))))))
% 6.73/7.07 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.suc M2))) (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 M2) N)))))))))
% 6.73/7.07 (assert (forall ((X tptp.real)) (@ (@ tptp.sums_real (lambda ((N4 tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N4)) tptp.one_one_nat))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N4)) (@ tptp.semiri2265585572941072030t_real _let_1))) (@ (@ tptp.power_power_real X) _let_1))))) (@ tptp.sin_real X))))
% 6.73/7.07 (assert (= tptp.bit_se725231765392027082nd_int (lambda ((K3 tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_int _let_1))) (let ((_let_3 (@ tptp.zero_n2684676970156552555ol_int (and (not (@ _let_2 K3)) (not (@ _let_2 L2)))))) (let ((_let_4 (@ (@ tptp.insert_int tptp.zero_zero_int) (@ (@ tptp.insert_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.bot_bot_set_int)))) (@ (@ (@ tptp.if_int (and (@ (@ tptp.member_int K3) _let_4) (@ (@ tptp.member_int L2) _let_4))) (@ tptp.uminus_uminus_int _let_3)) (@ (@ tptp.plus_plus_int _let_3) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se725231765392027082nd_int (@ (@ tptp.divide_divide_int K3) _let_1)) (@ (@ tptp.divide_divide_int L2) _let_1))))))))))))
% 6.73/7.07 (assert (= (@ tptp.sin_complex tptp.zero_zero_complex) tptp.zero_zero_complex))
% 6.73/7.07 (assert (= (@ tptp.sin_real tptp.zero_zero_real) tptp.zero_zero_real))
% 6.73/7.07 (assert (forall ((X tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int X) tptp.zero_zero_int) tptp.zero_zero_int)))
% 6.73/7.07 (assert (forall ((X tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.zero_zero_int) X) tptp.zero_zero_int)))
% 6.73/7.07 (assert (forall ((A tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.zero_zero_int) A) tptp.zero_zero_int)))
% 6.73/7.07 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.bit_se727722235901077358nd_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)))
% 6.73/7.07 (assert (forall ((A tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int A) tptp.zero_zero_int) tptp.zero_zero_int)))
% 6.73/7.07 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.bit_se727722235901077358nd_nat A) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 6.73/7.07 (assert (= (@ tptp.sin_coeff tptp.zero_zero_nat) tptp.zero_zero_real))
% 6.73/7.07 (assert (forall ((X tptp.num)) (= (@ (@ tptp.bit_se3949692690581998587nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 X))) tptp.one_one_Code_integer) tptp.zero_z3403309356797280102nteger)))
% 6.73/7.07 (assert (forall ((X tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 X))) tptp.one_one_int) tptp.zero_zero_int)))
% 6.73/7.07 (assert (forall ((X tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 X))) tptp.one_one_nat) tptp.zero_zero_nat)))
% 6.73/7.07 (assert (forall ((Y tptp.num)) (= (@ (@ tptp.bit_se3949692690581998587nteger tptp.one_one_Code_integer) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 Y))) tptp.zero_z3403309356797280102nteger)))
% 6.73/7.07 (assert (forall ((Y tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 Y))) tptp.zero_zero_int)))
% 6.73/7.07 (assert (forall ((Y tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Y))) tptp.zero_zero_nat)))
% 6.73/7.07 (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))))))
% 6.73/7.07 (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))))))
% 6.73/7.07 (assert (= tptp.bit_se725231765392027082nd_int (lambda ((K3 tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_int _let_1))) (@ (@ tptp.plus_plus_int (@ tptp.zero_n2684676970156552555ol_int (and (not (@ _let_2 K3)) (not (@ _let_2 L2))))) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se725231765392027082nd_int (@ (@ tptp.divide_divide_int K3) _let_1)) (@ (@ tptp.divide_divide_int L2) _let_1)))))))))
% 6.73/7.07 (assert (= tptp.bit_se725231765392027082nd_int (lambda ((K3 tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.uminus_uminus_int tptp.one_one_int))) (@ (@ (@ tptp.if_int (or (= K3 tptp.zero_zero_int) (= L2 tptp.zero_zero_int))) tptp.zero_zero_int) (@ (@ (@ tptp.if_int (= K3 _let_2)) L2) (@ (@ (@ tptp.if_int (= L2 _let_2)) K3) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.modulo_modulo_int K3) _let_1)) (@ (@ tptp.modulo_modulo_int L2) _let_1))) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se725231765392027082nd_int (@ (@ tptp.divide_divide_int K3) _let_1)) (@ (@ tptp.divide_divide_int L2) _let_1))))))))))))
% 6.73/7.07 (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)))))))))))))))
% 6.73/7.07 (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 ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.sin_coeff M6)) (@ (@ tptp.power_power_real X) M6)))) (@ 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))))))))))
% 6.73/7.07 (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 ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.sin_coeff M6)) (@ (@ tptp.power_power_real X) M6)))) (@ 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)))))))))
% 6.73/7.07 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.cos_coeff M6)) (@ (@ tptp.power_power_real tptp.zero_zero_real) M6)))) (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) tptp.one_one_real)))
% 6.73/7.07 (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)))))
% 6.73/7.07 (assert (forall ((X tptp.real) (N tptp.nat)) (exists ((T6 tptp.real)) (= (@ tptp.sin_real X) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.sin_coeff M6)) (@ (@ tptp.power_power_real X) M6)))) (@ tptp.set_ord_lessThan_nat 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)))))))
% 6.73/7.07 (assert (forall ((N tptp.nat) (K2 tptp.num)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.suc N)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 K2)))) (@ (@ 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 K2))) tptp.one_one_int))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) tptp.one_one_int))))
% 6.73/7.07 (assert (forall ((M2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.times_times_num (@ tptp.bit1 M2)))) (= (@ _let_1 (@ tptp.bit0 N)) (@ tptp.bit0 (@ _let_1 N))))))
% 6.73/7.07 (assert (forall ((M2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.bit1 N))) (= (@ (@ tptp.times_times_num (@ tptp.bit0 M2)) _let_1) (@ tptp.bit0 (@ (@ tptp.times_times_num M2) _let_1))))))
% 6.73/7.07 (assert (= (@ tptp.cos_coeff tptp.zero_zero_nat) tptp.one_one_real))
% 6.73/7.07 (assert (forall ((K2 tptp.num)) (= (@ tptp.neg_nu8557863876264182079omplex (@ tptp.numera6690914467698888265omplex K2)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit1 K2)))))
% 6.73/7.07 (assert (forall ((K2 tptp.num)) (= (@ tptp.neg_nu8295874005876285629c_real (@ tptp.numeral_numeral_real K2)) (@ tptp.numeral_numeral_real (@ tptp.bit1 K2)))))
% 6.73/7.07 (assert (forall ((K2 tptp.num)) (= (@ tptp.neg_nu5851722552734809277nc_int (@ tptp.numeral_numeral_int K2)) (@ tptp.numeral_numeral_int (@ tptp.bit1 K2)))))
% 6.73/7.07 (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)))
% 6.73/7.07 (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)))
% 6.73/7.07 (assert (forall ((V2 tptp.num) (W2 tptp.num)) (= (@ (@ tptp.divide_divide_int (@ tptp.numeral_numeral_int (@ tptp.bit1 V2))) (@ tptp.numeral_numeral_int (@ tptp.bit0 W2))) (@ (@ tptp.divide_divide_int (@ tptp.numeral_numeral_int V2)) (@ tptp.numeral_numeral_int W2)))))
% 6.73/7.07 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_num (@ tptp.bit1 M2)) (@ tptp.bit1 N)) (@ tptp.bit1 (@ (@ tptp.plus_plus_num (@ (@ tptp.plus_plus_num M2) N)) (@ tptp.bit0 (@ (@ tptp.times_times_num M2) N)))))))
% 6.73/7.07 (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)))
% 6.73/7.07 (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)))
% 6.73/7.07 (assert (forall ((N tptp.nat)) (= (@ tptp.sin_real (@ (@ tptp.times_times_real tptp.pi) (@ tptp.semiri5074537144036343181t_real N))) tptp.zero_zero_real)))
% 6.73/7.07 (assert (forall ((N tptp.nat)) (= (@ tptp.sin_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) tptp.pi)) tptp.zero_zero_real)))
% 6.73/7.07 (assert (= (@ tptp.neg_nu5831290666863070958nteger tptp.one_one_Code_integer) (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 tptp.one))))
% 6.73/7.07 (assert (= (@ tptp.neg_nu8557863876264182079omplex tptp.one_one_complex) (@ tptp.numera6690914467698888265omplex (@ tptp.bit1 tptp.one))))
% 6.73/7.07 (assert (= (@ tptp.neg_nu8295874005876285629c_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit1 tptp.one))))
% 6.73/7.07 (assert (= (@ tptp.neg_nu5851722552734809277nc_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit1 tptp.one))))
% 6.73/7.07 (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))))))
% 6.73/7.07 (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))))))
% 6.73/7.07 (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))))))
% 6.73/7.07 (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))))))
% 6.73/7.07 (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))))))
% 6.73/7.07 (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))))))
% 6.73/7.07 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat M2))) (= (@ _let_1 (@ tptp.suc (@ tptp.suc (@ tptp.suc N)))) (@ _let_1 (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) N))))))
% 6.73/7.07 (assert (forall ((M2 tptp.nat) (V2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat V2))) (= (@ (@ tptp.divide_divide_nat (@ tptp.suc (@ tptp.suc (@ tptp.suc M2)))) _let_1) (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) M2)) _let_1)))))
% 6.73/7.07 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.modulo_modulo_nat M2))) (= (@ _let_1 (@ tptp.suc (@ tptp.suc (@ tptp.suc N)))) (@ _let_1 (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) N))))))
% 6.73/7.07 (assert (forall ((M2 tptp.nat) (V2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat V2))) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ tptp.suc (@ tptp.suc M2)))) _let_1) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) M2)) _let_1)))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (assert (= (@ tptp.neg_nu6511756317524482435omplex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ tptp.bit1 tptp.one)))))
% 6.73/7.07 (assert (= (@ tptp.neg_nu7757733837767384882nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 tptp.one)))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (assert (= (@ tptp.sin_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) tptp.zero_zero_real))
% 6.73/7.07 (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)))))
% 6.73/7.07 (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))))
% 6.73/7.07 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se3949692690581998587nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 X))) (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 Y))) (@ (@ tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se3949692690581998587nteger (@ tptp.numera6620942414471956472nteger X)) (@ tptp.numera6620942414471956472nteger Y)))))))
% 6.73/7.07 (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)))))))
% 6.73/7.07 (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)))))))
% 6.73/7.07 (assert (forall ((V2 tptp.num) (W2 tptp.num)) (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit1 V2))) (@ tptp.numeral_numeral_int (@ tptp.bit0 W2))) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int V2)) (@ tptp.numeral_numeral_int W2)))) tptp.one_one_int))))
% 6.73/7.07 (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)))
% 6.73/7.07 (assert (forall ((N tptp.nat) (K2 tptp.num)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.suc N)) (@ tptp.numeral_numeral_int (@ tptp.bit1 K2))) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.bit_ri631733984087533419it_int N) (@ tptp.numeral_numeral_int K2))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) tptp.one_one_int))))
% 6.73/7.07 (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)))
% 6.73/7.07 (assert (forall ((Y tptp.num)) (=> (not (= Y tptp.one)) (=> (forall ((X23 tptp.num)) (not (= Y (@ tptp.bit0 X23)))) (not (forall ((X32 tptp.num)) (not (= Y (@ tptp.bit1 X32)))))))))
% 6.73/7.07 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger N))) (= (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 N)) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.plus_p5714425477246183910nteger _let_1) _let_1)) tptp.one_one_Code_integer)))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numera1916890842035813515d_enat N))) (= (@ tptp.numera1916890842035813515d_enat (@ tptp.bit1 N)) (@ (@ tptp.plus_p3455044024723400733d_enat (@ (@ tptp.plus_p3455044024723400733d_enat _let_1) _let_1)) tptp.one_on7984719198319812577d_enat)))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (assert (forall ((N tptp.num)) (= (@ tptp.numeral_numeral_nat (@ tptp.bit1 N)) (@ tptp.suc (@ tptp.numeral_numeral_nat (@ tptp.bit0 N))))))
% 6.73/7.07 (assert (forall ((M2 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 M2))) _let_2) (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 N))) _let_2)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat M2)) _let_1) (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat N)) _let_1)))))))
% 6.73/7.07 (assert (forall ((M2 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 M2))) _let_2) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N))) _let_2)) (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int M2)) _let_1) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int N)) _let_1)))))))
% 6.73/7.07 (assert (forall ((M2 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 M2))) _let_1) (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 N))) _let_1))))))
% 6.73/7.07 (assert (forall ((M2 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 M2))) _let_1) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N))) _let_1))))))
% 6.73/7.07 (assert (forall ((M2 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 M2))) _let_1) (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 N))) _let_1))))))
% 6.73/7.07 (assert (forall ((M2 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 M2))) _let_1) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N))) _let_1))))))
% 6.73/7.07 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger N))) (= (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 N)) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.plus_p5714425477246183910nteger _let_1) _let_1)) tptp.one_one_Code_integer)))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numera1916890842035813515d_enat N))) (= (@ tptp.numera1916890842035813515d_enat (@ tptp.bit1 N)) (@ (@ tptp.plus_p3455044024723400733d_enat (@ (@ tptp.plus_p3455044024723400733d_enat _let_1) _let_1)) tptp.one_on7984719198319812577d_enat)))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (assert (forall ((Z3 tptp.complex) (W2 tptp.num)) (let ((_let_1 (@ tptp.power_power_complex Z3))) (let ((_let_2 (@ _let_1 (@ tptp.numeral_numeral_nat W2)))) (= (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 W2))) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex Z3) _let_2)) _let_2))))))
% 6.73/7.07 (assert (forall ((Z3 tptp.real) (W2 tptp.num)) (let ((_let_1 (@ tptp.power_power_real Z3))) (let ((_let_2 (@ _let_1 (@ tptp.numeral_numeral_nat W2)))) (= (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 W2))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real Z3) _let_2)) _let_2))))))
% 6.73/7.07 (assert (forall ((Z3 tptp.rat) (W2 tptp.num)) (let ((_let_1 (@ tptp.power_power_rat Z3))) (let ((_let_2 (@ _let_1 (@ tptp.numeral_numeral_nat W2)))) (= (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 W2))) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat Z3) _let_2)) _let_2))))))
% 6.73/7.07 (assert (forall ((Z3 tptp.nat) (W2 tptp.num)) (let ((_let_1 (@ tptp.power_power_nat Z3))) (let ((_let_2 (@ _let_1 (@ tptp.numeral_numeral_nat W2)))) (= (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 W2))) (@ (@ tptp.times_times_nat (@ (@ tptp.times_times_nat Z3) _let_2)) _let_2))))))
% 6.73/7.07 (assert (forall ((Z3 tptp.int) (W2 tptp.num)) (let ((_let_1 (@ tptp.power_power_int Z3))) (let ((_let_2 (@ _let_1 (@ tptp.numeral_numeral_nat W2)))) (= (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 W2))) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int Z3) _let_2)) _let_2))))))
% 6.73/7.07 (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))))
% 6.73/7.07 (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))))
% 6.73/7.07 (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))))
% 6.73/7.07 (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))))
% 6.73/7.07 (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))))
% 6.73/7.07 (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))))
% 6.73/7.07 (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))))
% 6.73/7.07 (assert (= (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one)) (@ tptp.suc (@ tptp.suc (@ tptp.suc tptp.zero_zero_nat)))))
% 6.73/7.07 (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))))
% 6.73/7.07 (assert (forall ((X33 tptp.num)) (= (@ tptp.size_size_num (@ tptp.bit1 X33)) (@ (@ tptp.plus_plus_nat (@ tptp.size_size_num X33)) (@ tptp.suc tptp.zero_zero_nat)))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (assert (forall ((M2 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 M2))) _let_1) (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat tptp.one)) _let_1)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat M2)) (@ tptp.numeral_numeral_nat Q2)) tptp.zero_zero_nat)))))
% 6.73/7.07 (assert (forall ((M2 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 M2))) _let_1) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int tptp.one)) _let_1)) (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int M2)) (@ tptp.numeral_numeral_int Q2)) tptp.zero_zero_int)))))
% 6.73/7.07 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.divide_divide_nat (@ tptp.suc (@ tptp.suc (@ tptp.suc M2)))) N) (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) M2)) N))))
% 6.73/7.07 (assert (forall ((S3 tptp.set_complex)) (= (= (@ tptp.finite_card_complex S3) (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) (exists ((X4 tptp.complex) (Y4 tptp.complex) (Z4 tptp.complex)) (and (= S3 (@ (@ tptp.insert_complex X4) (@ (@ tptp.insert_complex Y4) (@ (@ tptp.insert_complex Z4) tptp.bot_bot_set_complex)))) (not (= X4 Y4)) (not (= Y4 Z4)) (not (= X4 Z4)))))))
% 6.73/7.07 (assert (forall ((S3 tptp.set_list_nat)) (= (= (@ tptp.finite_card_list_nat S3) (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) (exists ((X4 tptp.list_nat) (Y4 tptp.list_nat) (Z4 tptp.list_nat)) (and (= S3 (@ (@ tptp.insert_list_nat X4) (@ (@ tptp.insert_list_nat Y4) (@ (@ tptp.insert_list_nat Z4) tptp.bot_bot_set_list_nat)))) (not (= X4 Y4)) (not (= Y4 Z4)) (not (= X4 Z4)))))))
% 6.73/7.07 (assert (forall ((S3 tptp.set_set_nat)) (= (= (@ tptp.finite_card_set_nat S3) (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) (exists ((X4 tptp.set_nat) (Y4 tptp.set_nat) (Z4 tptp.set_nat)) (and (= S3 (@ (@ tptp.insert_set_nat X4) (@ (@ tptp.insert_set_nat Y4) (@ (@ tptp.insert_set_nat Z4) tptp.bot_bot_set_set_nat)))) (not (= X4 Y4)) (not (= Y4 Z4)) (not (= X4 Z4)))))))
% 6.73/7.07 (assert (forall ((S3 tptp.set_nat)) (= (= (@ tptp.finite_card_nat S3) (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) (exists ((X4 tptp.nat) (Y4 tptp.nat) (Z4 tptp.nat)) (and (= S3 (@ (@ tptp.insert_nat X4) (@ (@ tptp.insert_nat Y4) (@ (@ tptp.insert_nat Z4) tptp.bot_bot_set_nat)))) (not (= X4 Y4)) (not (= Y4 Z4)) (not (= X4 Z4)))))))
% 6.73/7.07 (assert (forall ((S3 tptp.set_int)) (= (= (@ tptp.finite_card_int S3) (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) (exists ((X4 tptp.int) (Y4 tptp.int) (Z4 tptp.int)) (and (= S3 (@ (@ tptp.insert_int X4) (@ (@ tptp.insert_int Y4) (@ (@ tptp.insert_int Z4) tptp.bot_bot_set_int)))) (not (= X4 Y4)) (not (= Y4 Z4)) (not (= X4 Z4)))))))
% 6.73/7.07 (assert (forall ((S3 tptp.set_real)) (= (= (@ tptp.finite_card_real S3) (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) (exists ((X4 tptp.real) (Y4 tptp.real) (Z4 tptp.real)) (and (= S3 (@ (@ tptp.insert_real X4) (@ (@ tptp.insert_real Y4) (@ (@ tptp.insert_real Z4) tptp.bot_bot_set_real)))) (not (= X4 Y4)) (not (= Y4 Z4)) (not (= X4 Z4)))))))
% 6.73/7.07 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ tptp.suc (@ tptp.suc M2)))) N) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) M2)) N))))
% 6.73/7.07 (assert (forall ((M2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ (@ tptp.modulo_modulo_nat M2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 _let_1))))) (or (= _let_2 tptp.zero_zero_nat) (= _let_2 tptp.one_one_nat) (= _let_2 (@ tptp.numeral_numeral_nat _let_1)) (= _let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))))))))
% 6.73/7.07 (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))
% 6.73/7.07 (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)))))))
% 6.73/7.07 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (= (@ tptp.sin_coeff _let_1) (@ (@ tptp.divide_divide_real (@ tptp.cos_coeff N)) (@ tptp.semiri5074537144036343181t_real _let_1))))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (assert (= tptp.bit_se727722235901077358nd_nat (lambda ((M6 tptp.nat) (N4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_nat (or (= M6 tptp.zero_zero_nat) (= N4 tptp.zero_zero_nat))) tptp.zero_zero_nat) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.modulo_modulo_nat M6) _let_1)) (@ (@ tptp.modulo_modulo_nat N4) _let_1))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se727722235901077358nd_nat (@ (@ tptp.divide_divide_nat M6) _let_1)) (@ (@ tptp.divide_divide_nat N4) _let_1)))))))))
% 6.73/7.07 (assert (= tptp.bit_se727722235901077358nd_nat (lambda ((M6 tptp.nat) (N4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_nat _let_1))) (@ (@ tptp.plus_plus_nat (@ tptp.zero_n2687167440665602831ol_nat (and (not (@ _let_2 M6)) (not (@ _let_2 N4))))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se727722235901077358nd_nat (@ (@ tptp.divide_divide_nat M6) _let_1)) (@ (@ tptp.divide_divide_nat N4) _let_1)))))))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (= (@ tptp.cos_coeff _let_1) (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real (@ tptp.sin_coeff N))) (@ tptp.semiri5074537144036343181t_real _let_1))))))
% 6.73/7.07 (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))))))))
% 6.73/7.07 (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)))))))
% 6.73/7.07 (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)))))))))))
% 6.73/7.07 (assert (forall ((X tptp.real)) (= (= (@ tptp.sin_real X) tptp.zero_zero_real) (or (exists ((N4 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (and (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat _let_1)) N4) (= X (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N4)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1))))))) (exists ((N4 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (and (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat _let_1)) N4) (= X (@ tptp.uminus_uminus_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N4)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1))))))))))))
% 6.73/7.07 (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 ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.cos_coeff M6)) (@ (@ tptp.power_power_real X) M6)))) (@ 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))))))))))
% 6.73/7.07 (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 ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.cos_coeff M6)) (@ (@ tptp.power_power_real X) M6)))) (@ 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))))))))))
% 6.73/7.07 (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 ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.sin_coeff M6)) (@ (@ tptp.power_power_real X) M6)))) (@ 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))))))))
% 6.73/7.07 (assert (forall ((L tptp.num) (K2 tptp.num)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.numeral_numeral_nat L)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 K2)))) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.pred_numeral L)) (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K2))) tptp.one_one_int))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) tptp.one_one_int))))
% 6.73/7.07 (assert (forall ((M2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.bit1 N))) (let ((_let_2 (@ tptp.bit1 M2))) (let ((_let_3 (@ tptp.unique5055182867167087721od_nat _let_2))) (let ((_let_4 (@ _let_3 _let_1))) (let ((_let_5 (@ (@ tptp.ord_less_num M2) 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)))))))))))))
% 6.73/7.07 (assert (forall ((M2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.bit1 N))) (let ((_let_2 (@ tptp.bit1 M2))) (let ((_let_3 (@ tptp.unique5052692396658037445od_int _let_2))) (let ((_let_4 (@ _let_3 _let_1))) (let ((_let_5 (@ (@ tptp.ord_less_num M2) 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)))))))))))))
% 6.73/7.07 (assert (forall ((M2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.bit1 N))) (let ((_let_2 (@ tptp.bit1 M2))) (let ((_let_3 (@ tptp.unique3479559517661332726nteger _let_2))) (let ((_let_4 (@ _let_3 _let_1))) (let ((_let_5 (@ (@ tptp.ord_less_num M2) 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)))))))))))))
% 6.73/7.07 (assert (forall ((M2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.bit1 N))) (let ((_let_2 (@ tptp.bit0 M2))) (let ((_let_3 (@ tptp.unique5055182867167087721od_nat _let_2))) (let ((_let_4 (@ _let_3 _let_1))) (let ((_let_5 (@ (@ tptp.ord_less_eq_num M2) 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)))))))))))))
% 6.73/7.07 (assert (forall ((M2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.bit1 N))) (let ((_let_2 (@ tptp.bit0 M2))) (let ((_let_3 (@ tptp.unique5052692396658037445od_int _let_2))) (let ((_let_4 (@ _let_3 _let_1))) (let ((_let_5 (@ (@ tptp.ord_less_eq_num M2) 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)))))))))))))
% 6.73/7.07 (assert (forall ((M2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.bit1 N))) (let ((_let_2 (@ tptp.bit0 M2))) (let ((_let_3 (@ tptp.unique3479559517661332726nteger _let_2))) (let ((_let_4 (@ _let_3 _let_1))) (let ((_let_5 (@ (@ tptp.ord_less_eq_num M2) 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)))))))))))))
% 6.73/7.07 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.abs_abs_real A))) (= (@ tptp.abs_abs_real _let_1) _let_1))))
% 6.73/7.07 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.abs_abs_int A))) (= (@ tptp.abs_abs_int _let_1) _let_1))))
% 6.73/7.07 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.abs_abs_Code_integer A))) (= (@ tptp.abs_abs_Code_integer _let_1) _let_1))))
% 6.73/7.07 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.abs_abs_rat A))) (= (@ tptp.abs_abs_rat _let_1) _let_1))))
% 6.73/7.07 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.abs_abs_real A))) (= (@ tptp.abs_abs_real _let_1) _let_1))))
% 6.73/7.07 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.abs_abs_int A))) (= (@ tptp.abs_abs_int _let_1) _let_1))))
% 6.73/7.07 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.abs_abs_Code_integer A))) (= (@ tptp.abs_abs_Code_integer _let_1) _let_1))))
% 6.73/7.07 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.abs_abs_rat A))) (= (@ tptp.abs_abs_rat _let_1) _let_1))))
% 6.73/7.07 (assert (= (@ tptp.abs_abs_Code_integer tptp.zero_z3403309356797280102nteger) tptp.zero_z3403309356797280102nteger))
% 6.73/7.07 (assert (= (@ tptp.abs_abs_complex tptp.zero_zero_complex) tptp.zero_zero_complex))
% 6.73/7.07 (assert (= (@ tptp.abs_abs_real tptp.zero_zero_real) tptp.zero_zero_real))
% 6.73/7.07 (assert (= (@ tptp.abs_abs_rat tptp.zero_zero_rat) tptp.zero_zero_rat))
% 6.73/7.07 (assert (= (@ tptp.abs_abs_int tptp.zero_zero_int) tptp.zero_zero_int))
% 6.73/7.07 (assert (forall ((A tptp.code_integer)) (= (= tptp.zero_z3403309356797280102nteger (@ tptp.abs_abs_Code_integer A)) (= A tptp.zero_z3403309356797280102nteger))))
% 6.73/7.07 (assert (forall ((A tptp.real)) (= (= tptp.zero_zero_real (@ tptp.abs_abs_real A)) (= A tptp.zero_zero_real))))
% 6.73/7.07 (assert (forall ((A tptp.rat)) (= (= tptp.zero_zero_rat (@ tptp.abs_abs_rat A)) (= A tptp.zero_zero_rat))))
% 6.73/7.07 (assert (forall ((A tptp.int)) (= (= tptp.zero_zero_int (@ tptp.abs_abs_int A)) (= A tptp.zero_zero_int))))
% 6.73/7.07 (assert (forall ((A tptp.code_integer)) (= (= (@ tptp.abs_abs_Code_integer A) tptp.zero_z3403309356797280102nteger) (= A tptp.zero_z3403309356797280102nteger))))
% 6.73/7.07 (assert (forall ((A tptp.real)) (= (= (@ tptp.abs_abs_real A) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 6.73/7.07 (assert (forall ((A tptp.rat)) (= (= (@ tptp.abs_abs_rat A) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))))
% 6.73/7.07 (assert (forall ((A tptp.int)) (= (= (@ tptp.abs_abs_int A) tptp.zero_zero_int) (= A tptp.zero_zero_int))))
% 6.73/7.07 (assert (= (@ tptp.abs_abs_Code_integer tptp.zero_z3403309356797280102nteger) tptp.zero_z3403309356797280102nteger))
% 6.73/7.07 (assert (= (@ tptp.abs_abs_real tptp.zero_zero_real) tptp.zero_zero_real))
% 6.73/7.07 (assert (= (@ tptp.abs_abs_rat tptp.zero_zero_rat) tptp.zero_zero_rat))
% 6.73/7.07 (assert (= (@ tptp.abs_abs_int tptp.zero_zero_int) tptp.zero_zero_int))
% 6.73/7.07 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger N))) (= (@ tptp.abs_abs_Code_integer _let_1) _let_1))))
% 6.73/7.07 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat N))) (= (@ tptp.abs_abs_rat _let_1) _let_1))))
% 6.73/7.07 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real N))) (= (@ tptp.abs_abs_real _let_1) _let_1))))
% 6.73/7.07 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (= (@ tptp.abs_abs_int _let_1) _let_1))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (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))))
% 6.73/7.07 (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))))
% 6.73/7.07 (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))))
% 6.73/7.07 (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))))
% 6.73/7.07 (assert (= (@ tptp.abs_abs_rat tptp.one_one_rat) tptp.one_one_rat))
% 6.73/7.07 (assert (= (@ tptp.abs_abs_Code_integer tptp.one_one_Code_integer) tptp.one_one_Code_integer))
% 6.73/7.07 (assert (= (@ tptp.abs_abs_complex tptp.one_one_complex) tptp.one_one_complex))
% 6.73/7.07 (assert (= (@ tptp.abs_abs_real tptp.one_one_real) tptp.one_one_real))
% 6.73/7.07 (assert (= (@ tptp.abs_abs_int tptp.one_one_int) tptp.one_one_int))
% 6.73/7.07 (assert (forall ((A tptp.int)) (= (@ tptp.abs_abs_int (@ tptp.uminus_uminus_int A)) (@ tptp.abs_abs_int A))))
% 6.73/7.07 (assert (forall ((A tptp.real)) (= (@ tptp.abs_abs_real (@ tptp.uminus_uminus_real A)) (@ tptp.abs_abs_real A))))
% 6.73/7.07 (assert (forall ((A tptp.code_integer)) (= (@ tptp.abs_abs_Code_integer (@ tptp.uminus1351360451143612070nteger A)) (@ tptp.abs_abs_Code_integer A))))
% 6.73/7.07 (assert (forall ((A tptp.rat)) (= (@ tptp.abs_abs_rat (@ tptp.uminus_uminus_rat A)) (@ tptp.abs_abs_rat A))))
% 6.73/7.07 (assert (forall ((A tptp.int)) (= (@ tptp.abs_abs_int (@ tptp.uminus_uminus_int A)) (@ tptp.abs_abs_int A))))
% 6.73/7.07 (assert (forall ((A tptp.real)) (= (@ tptp.abs_abs_real (@ tptp.uminus_uminus_real A)) (@ tptp.abs_abs_real A))))
% 6.73/7.07 (assert (forall ((A tptp.complex)) (= (@ tptp.abs_abs_complex (@ tptp.uminus1482373934393186551omplex A)) (@ tptp.abs_abs_complex A))))
% 6.73/7.07 (assert (forall ((A tptp.code_integer)) (= (@ tptp.abs_abs_Code_integer (@ tptp.uminus1351360451143612070nteger A)) (@ tptp.abs_abs_Code_integer A))))
% 6.73/7.07 (assert (forall ((A tptp.rat)) (= (@ tptp.abs_abs_rat (@ tptp.uminus_uminus_rat A)) (@ tptp.abs_abs_rat A))))
% 6.73/7.07 (assert (forall ((M2 tptp.real) (K2 tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real M2))) (= (@ _let_1 (@ tptp.abs_abs_real K2)) (@ _let_1 K2)))))
% 6.73/7.07 (assert (forall ((M2 tptp.int) (K2 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int M2))) (= (@ _let_1 (@ tptp.abs_abs_int K2)) (@ _let_1 K2)))))
% 6.73/7.07 (assert (forall ((M2 tptp.code_integer) (K2 tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer M2))) (= (@ _let_1 (@ tptp.abs_abs_Code_integer K2)) (@ _let_1 K2)))))
% 6.73/7.07 (assert (forall ((M2 tptp.rat) (K2 tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat M2))) (= (@ _let_1 (@ tptp.abs_abs_rat K2)) (@ _let_1 K2)))))
% 6.73/7.07 (assert (forall ((M2 tptp.real) (K2 tptp.real)) (= (@ (@ tptp.dvd_dvd_real (@ tptp.abs_abs_real M2)) K2) (@ (@ tptp.dvd_dvd_real M2) K2))))
% 6.73/7.07 (assert (forall ((M2 tptp.int) (K2 tptp.int)) (= (@ (@ tptp.dvd_dvd_int (@ tptp.abs_abs_int M2)) K2) (@ (@ tptp.dvd_dvd_int M2) K2))))
% 6.73/7.07 (assert (forall ((M2 tptp.code_integer) (K2 tptp.code_integer)) (= (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.abs_abs_Code_integer M2)) K2) (@ (@ tptp.dvd_dvd_Code_integer M2) K2))))
% 6.73/7.07 (assert (forall ((M2 tptp.rat) (K2 tptp.rat)) (= (@ (@ tptp.dvd_dvd_rat (@ tptp.abs_abs_rat M2)) K2) (@ (@ tptp.dvd_dvd_rat M2) K2))))
% 6.73/7.07 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri4939895301339042750nteger N))) (= (@ tptp.abs_abs_Code_integer _let_1) _let_1))))
% 6.73/7.07 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri681578069525770553at_rat N))) (= (@ tptp.abs_abs_rat _let_1) _let_1))))
% 6.73/7.07 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real N))) (= (@ tptp.abs_abs_real _let_1) _let_1))))
% 6.73/7.07 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int N))) (= (@ tptp.abs_abs_int _let_1) _let_1))))
% 6.73/7.07 (assert (forall ((P2 Bool)) (let ((_let_1 (@ tptp.zero_n3304061248610475627l_real P2))) (= (@ tptp.abs_abs_real _let_1) _let_1))))
% 6.73/7.07 (assert (forall ((P2 Bool)) (let ((_let_1 (@ tptp.zero_n2052037380579107095ol_rat P2))) (= (@ tptp.abs_abs_rat _let_1) _let_1))))
% 6.73/7.07 (assert (forall ((P2 Bool)) (let ((_let_1 (@ tptp.zero_n2684676970156552555ol_int P2))) (= (@ tptp.abs_abs_int _let_1) _let_1))))
% 6.73/7.07 (assert (forall ((P2 Bool)) (let ((_let_1 (@ tptp.zero_n356916108424825756nteger P2))) (= (@ tptp.abs_abs_Code_integer _let_1) _let_1))))
% 6.73/7.07 (assert (forall ((A tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A) (= (@ tptp.abs_abs_Code_integer A) A))))
% 6.73/7.07 (assert (forall ((A tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (= (@ tptp.abs_abs_real A) A))))
% 6.73/7.07 (assert (forall ((A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (= (@ tptp.abs_abs_rat A) A))))
% 6.73/7.07 (assert (forall ((A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (= (@ tptp.abs_abs_int A) A))))
% 6.73/7.07 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer A)) A) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A))))
% 6.73/7.07 (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))))
% 6.73/7.07 (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))))
% 6.73/7.07 (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))))
% 6.73/7.07 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer A)) tptp.zero_z3403309356797280102nteger) (= A tptp.zero_z3403309356797280102nteger))))
% 6.73/7.07 (assert (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real A)) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 6.73/7.07 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat A)) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))))
% 6.73/7.07 (assert (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int A)) tptp.zero_zero_int) (= A tptp.zero_zero_int))))
% 6.73/7.07 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ tptp.abs_abs_Code_integer A)) (not (= A tptp.zero_z3403309356797280102nteger)))))
% 6.73/7.07 (assert (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.abs_abs_real A)) (not (= A tptp.zero_zero_real)))))
% 6.73/7.07 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.abs_abs_rat A)) (not (= A tptp.zero_zero_rat)))))
% 6.73/7.07 (assert (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.abs_abs_int A)) (not (= A tptp.zero_zero_int)))))
% 6.73/7.07 (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))))
% 6.73/7.07 (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))))
% 6.73/7.07 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger N))) (= (@ tptp.abs_abs_Code_integer (@ tptp.uminus1351360451143612070nteger _let_1)) _let_1))))
% 6.73/7.07 (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))))
% 6.73/7.07 (assert (= (@ tptp.abs_abs_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.one_one_int))
% 6.73/7.07 (assert (= (@ tptp.abs_abs_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.one_one_real))
% 6.73/7.07 (assert (= (@ tptp.abs_abs_Code_integer (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.one_one_Code_integer))
% 6.73/7.07 (assert (= (@ tptp.abs_abs_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.one_one_rat))
% 6.73/7.07 (assert (= (@ tptp.cos_complex tptp.zero_zero_complex) tptp.one_one_complex))
% 6.73/7.07 (assert (= (@ tptp.cos_real tptp.zero_zero_real) tptp.one_one_real))
% 6.73/7.07 (assert (= (@ tptp.pred_numeral tptp.one) tptp.zero_zero_nat))
% 6.73/7.07 (assert (forall ((K2 tptp.num) (N tptp.nat)) (= (= (@ tptp.numeral_numeral_nat K2) (@ tptp.suc N)) (= (@ tptp.pred_numeral K2) N))))
% 6.73/7.07 (assert (forall ((N tptp.nat) (K2 tptp.num)) (= (= (@ tptp.suc N) (@ tptp.numeral_numeral_nat K2)) (= N (@ tptp.pred_numeral K2)))))
% 6.73/7.07 (assert (forall ((F2 (-> tptp.int tptp.int)) (A4 tptp.set_int)) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.groups4538972089207619220nt_int F2) A4))) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((I tptp.int)) (@ tptp.abs_abs_int (@ F2 I)))) A4))))
% 6.73/7.07 (assert (forall ((F2 (-> tptp.nat tptp.real)) (A4 tptp.set_nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.groups6591440286371151544t_real F2) A4))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I tptp.nat)) (@ tptp.abs_abs_real (@ F2 I)))) A4))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ (@ tptp.divide_divide_real A) (@ tptp.abs_abs_real B))) (or (@ _let_1 A) (= B tptp.zero_zero_real))))))
% 6.73/7.07 (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))))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (assert (forall ((A tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger A) tptp.zero_z3403309356797280102nteger) (= (@ tptp.abs_abs_Code_integer A) (@ tptp.uminus1351360451143612070nteger A)))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (assert (forall ((N tptp.nat) (K2 tptp.num)) (= (@ (@ tptp.ord_less_nat (@ tptp.suc N)) (@ tptp.numeral_numeral_nat K2)) (@ (@ tptp.ord_less_nat N) (@ tptp.pred_numeral K2)))))
% 6.73/7.07 (assert (forall ((K2 tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.numeral_numeral_nat K2)) (@ tptp.suc N)) (@ (@ tptp.ord_less_nat (@ tptp.pred_numeral K2)) N))))
% 6.73/7.07 (assert (forall ((K2 tptp.num)) (= (@ tptp.pred_numeral (@ tptp.bit1 K2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 K2)))))
% 6.73/7.07 (assert (forall ((K2 tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat K2)) (@ tptp.suc N)) (@ (@ tptp.ord_less_eq_nat (@ tptp.pred_numeral K2)) N))))
% 6.73/7.07 (assert (forall ((N tptp.nat) (K2 tptp.num)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) (@ tptp.numeral_numeral_nat K2)) (@ (@ tptp.ord_less_eq_nat N) (@ tptp.pred_numeral K2)))))
% 6.73/7.07 (assert (forall ((K2 tptp.num) (N tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ tptp.numeral_numeral_nat K2)) (@ tptp.suc N)) (@ (@ tptp.minus_minus_nat (@ tptp.pred_numeral K2)) N))))
% 6.73/7.07 (assert (forall ((N tptp.nat) (K2 tptp.num)) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc N)) (@ tptp.numeral_numeral_nat K2)) (@ (@ tptp.minus_minus_nat N) (@ tptp.pred_numeral K2)))))
% 6.73/7.07 (assert (forall ((N tptp.nat) (K2 tptp.num)) (= (@ (@ tptp.ord_max_nat (@ tptp.suc N)) (@ tptp.numeral_numeral_nat K2)) (@ tptp.suc (@ (@ tptp.ord_max_nat N) (@ tptp.pred_numeral K2))))))
% 6.73/7.07 (assert (forall ((K2 tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_max_nat (@ tptp.numeral_numeral_nat K2)) (@ tptp.suc N)) (@ tptp.suc (@ (@ tptp.ord_max_nat (@ tptp.pred_numeral K2)) N)))))
% 6.73/7.07 (assert (forall ((F2 (-> tptp.int tptp.int)) (A4 tptp.set_int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((I tptp.int)) (@ tptp.abs_abs_int (@ F2 I)))) A4))))
% 6.73/7.07 (assert (forall ((F2 (-> tptp.nat tptp.real)) (A4 tptp.set_nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I tptp.nat)) (@ tptp.abs_abs_real (@ F2 I)))) A4))))
% 6.73/7.07 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.divide_divide_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M2))) (@ tptp.numeral_numeral_int N)) (@ tptp.uminus_uminus_int (@ tptp.adjust_div (@ (@ tptp.unique5052692396658037445od_int M2) N))))))
% 6.73/7.07 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.divide_divide_int (@ tptp.numeral_numeral_int M2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) (@ tptp.uminus_uminus_int (@ tptp.adjust_div (@ (@ tptp.unique5052692396658037445od_int M2) N))))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (assert (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.sin_complex X))) (let ((_let_2 (@ tptp.cos_complex X))) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex _let_2) _let_2)) (@ (@ tptp.times_times_complex _let_1) _let_1)) tptp.one_one_complex)))))
% 6.73/7.07 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.sin_real X))) (let ((_let_2 (@ tptp.cos_real X))) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real _let_2) _let_2)) (@ (@ tptp.times_times_real _let_1) _let_1)) tptp.one_one_real)))))
% 6.73/7.07 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int M2)) (@ tptp.numeral_numeral_int N)) (@ tptp.unique6319869463603278526ux_int (@ (@ tptp.unique5052692396658037445od_int N) M2)))))
% 6.73/7.07 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat M2)) (@ tptp.numeral_numeral_nat N)) (@ tptp.unique6322359934112328802ux_nat (@ (@ tptp.unique5055182867167087721od_nat N) M2)))))
% 6.73/7.07 (assert (forall ((M2 tptp.num)) (= (@ (@ tptp.unique3479559517661332726nteger M2) tptp.one) (@ (@ tptp.produc1086072967326762835nteger (@ tptp.numera6620942414471956472nteger M2)) tptp.zero_z3403309356797280102nteger))))
% 6.73/7.07 (assert (forall ((M2 tptp.num)) (= (@ (@ tptp.unique5052692396658037445od_int M2) tptp.one) (@ (@ tptp.product_Pair_int_int (@ tptp.numeral_numeral_int M2)) tptp.zero_zero_int))))
% 6.73/7.07 (assert (forall ((M2 tptp.num)) (= (@ (@ tptp.unique5055182867167087721od_nat M2) tptp.one) (@ (@ tptp.product_Pair_nat_nat (@ tptp.numeral_numeral_nat M2)) tptp.zero_zero_nat))))
% 6.73/7.07 (assert (forall ((N tptp.num)) (= (@ (@ tptp.unique3479559517661332726nteger tptp.one) (@ tptp.bit0 N)) (@ (@ tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger) (@ tptp.numera6620942414471956472nteger tptp.one)))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (assert (forall ((N tptp.num)) (= (@ (@ tptp.unique3479559517661332726nteger tptp.one) (@ tptp.bit1 N)) (@ (@ tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger) (@ tptp.numera6620942414471956472nteger tptp.one)))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (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))))))
% 6.73/7.07 (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))))))
% 6.73/7.07 (assert (= (@ tptp.cos_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) tptp.one_one_real))
% 6.73/7.07 (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))))
% 6.73/7.07 (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))))
% 6.73/7.07 (assert (forall ((L tptp.num) (K2 tptp.num)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.numeral_numeral_nat L)) (@ tptp.numeral_numeral_int (@ tptp.bit0 K2))) (@ (@ tptp.times_times_int (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.pred_numeral L)) (@ tptp.numeral_numeral_int K2))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))))
% 6.73/7.07 (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))))
% 6.73/7.07 (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))))
% 6.73/7.07 (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)))
% 6.73/7.07 (assert (forall ((L tptp.num) (K2 tptp.num)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.numeral_numeral_nat L)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 K2)))) (@ (@ tptp.times_times_int (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.pred_numeral L)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K2)))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))))
% 6.73/7.07 (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))
% 6.73/7.07 (assert (forall ((L tptp.num) (K2 tptp.num)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.numeral_numeral_nat L)) (@ tptp.numeral_numeral_int (@ tptp.bit1 K2))) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.pred_numeral L)) (@ tptp.numeral_numeral_int K2))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) tptp.one_one_int))))
% 6.73/7.07 (assert (forall ((M2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ tptp.cos_real (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real tptp.pi) (@ tptp.semiri5074537144036343181t_real (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat _let_1)) M2))))) (@ tptp.numeral_numeral_real _let_1))) tptp.zero_zero_real))))
% 6.73/7.07 (assert (forall ((A tptp.real)) (@ (@ tptp.ord_less_eq_real A) (@ tptp.abs_abs_real A))))
% 6.73/7.07 (assert (forall ((A tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger A) (@ tptp.abs_abs_Code_integer A))))
% 6.73/7.07 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_eq_rat A) (@ tptp.abs_abs_rat A))))
% 6.73/7.07 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int A) (@ tptp.abs_abs_int A))))
% 6.73/7.07 (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))))
% 6.73/7.07 (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))))
% 6.73/7.07 (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))))
% 6.73/7.07 (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))))
% 6.73/7.07 (assert (forall ((A tptp.code_integer)) (= (= (@ tptp.abs_abs_Code_integer A) tptp.zero_z3403309356797280102nteger) (= A tptp.zero_z3403309356797280102nteger))))
% 6.73/7.07 (assert (forall ((A tptp.complex)) (= (= (@ tptp.abs_abs_complex A) tptp.zero_zero_complex) (= A tptp.zero_zero_complex))))
% 6.73/7.07 (assert (forall ((A tptp.real)) (= (= (@ tptp.abs_abs_real A) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 6.73/7.07 (assert (forall ((A tptp.rat)) (= (= (@ tptp.abs_abs_rat A) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))))
% 6.73/7.07 (assert (forall ((A tptp.int)) (= (= (@ tptp.abs_abs_int A) tptp.zero_zero_int) (= A tptp.zero_zero_int))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (assert (= (@ tptp.abs_abs_rat tptp.one_one_rat) tptp.one_one_rat))
% 6.73/7.07 (assert (= (@ tptp.abs_abs_Code_integer tptp.one_one_Code_integer) tptp.one_one_Code_integer))
% 6.73/7.07 (assert (= (@ tptp.abs_abs_real tptp.one_one_real) tptp.one_one_real))
% 6.73/7.07 (assert (= (@ tptp.abs_abs_int tptp.one_one_int) tptp.one_one_int))
% 6.73/7.07 (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)))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (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))))))
% 6.73/7.07 (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))))))
% 6.73/7.07 (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))))))
% 6.73/7.07 (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))))))
% 6.73/7.07 (assert (forall ((L tptp.real) (K2 tptp.real)) (=> (= (@ tptp.abs_abs_real L) (@ tptp.abs_abs_real K2)) (@ (@ tptp.dvd_dvd_real L) K2))))
% 6.73/7.07 (assert (forall ((L tptp.int) (K2 tptp.int)) (=> (= (@ tptp.abs_abs_int L) (@ tptp.abs_abs_int K2)) (@ (@ tptp.dvd_dvd_int L) K2))))
% 6.73/7.07 (assert (forall ((L tptp.code_integer) (K2 tptp.code_integer)) (=> (= (@ tptp.abs_abs_Code_integer L) (@ tptp.abs_abs_Code_integer K2)) (@ (@ tptp.dvd_dvd_Code_integer L) K2))))
% 6.73/7.07 (assert (forall ((L tptp.rat) (K2 tptp.rat)) (=> (= (@ tptp.abs_abs_rat L) (@ tptp.abs_abs_rat K2)) (@ (@ tptp.dvd_dvd_rat L) K2))))
% 6.73/7.07 (assert (forall ((A tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ tptp.abs_abs_Code_integer A))))
% 6.73/7.07 (assert (forall ((A tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.abs_abs_real A))))
% 6.73/7.07 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.abs_abs_rat A))))
% 6.73/7.07 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.abs_abs_int A))))
% 6.73/7.07 (assert (forall ((A tptp.code_integer)) (not (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.abs_abs_Code_integer A)) tptp.zero_z3403309356797280102nteger))))
% 6.73/7.07 (assert (forall ((A tptp.real)) (not (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real A)) tptp.zero_zero_real))))
% 6.73/7.07 (assert (forall ((A tptp.rat)) (not (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat A)) tptp.zero_zero_rat))))
% 6.73/7.07 (assert (forall ((A tptp.int)) (not (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int A)) tptp.zero_zero_int))))
% 6.73/7.07 (assert (forall ((A tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A) (= (@ tptp.abs_abs_Code_integer A) A))))
% 6.73/7.07 (assert (forall ((A tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (= (@ tptp.abs_abs_real A) A))))
% 6.73/7.07 (assert (forall ((A tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (= (@ tptp.abs_abs_rat A) A))))
% 6.73/7.07 (assert (forall ((A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (= (@ tptp.abs_abs_int A) A))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (assert (forall ((A tptp.code_integer) (C2 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) C2) (=> (@ (@ tptp.ord_le6747313008572928689nteger _let_1) D) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.times_3573771949741848930nteger _let_2) _let_1)) (@ (@ tptp.times_3573771949741848930nteger C2) D))))))))
% 6.73/7.07 (assert (forall ((A tptp.real) (C2 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) C2) (=> (@ (@ tptp.ord_less_real _let_1) D) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real _let_2) _let_1)) (@ (@ tptp.times_times_real C2) D))))))))
% 6.73/7.07 (assert (forall ((A tptp.rat) (C2 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) C2) (=> (@ (@ tptp.ord_less_rat _let_1) D) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat _let_2) _let_1)) (@ (@ tptp.times_times_rat C2) D))))))))
% 6.73/7.07 (assert (forall ((A tptp.int) (C2 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) C2) (=> (@ (@ tptp.ord_less_int _let_1) D) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int _let_2) _let_1)) (@ (@ tptp.times_times_int C2) D))))))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (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))))))
% 6.73/7.07 (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))))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (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))))
% 6.73/7.07 (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))))
% 6.73/7.07 (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))))
% 6.73/7.07 (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))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (assert (forall ((A tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real A)) (@ tptp.abs_abs_real A))))
% 6.73/7.07 (assert (forall ((A tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger A)) (@ tptp.abs_abs_Code_integer A))))
% 6.73/7.07 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat A)) (@ tptp.abs_abs_rat A))))
% 6.73/7.07 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int A)) (@ tptp.abs_abs_int A))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (assert (forall ((X tptp.real) (Y tptp.real)) (exists ((R4 tptp.real) (A3 tptp.real)) (let ((_let_1 (@ tptp.times_times_real R4))) (and (= X (@ _let_1 (@ tptp.cos_real A3))) (= Y (@ _let_1 (@ tptp.sin_real A3))))))))
% 6.73/7.07 (assert (= tptp.numeral_numeral_nat (lambda ((K3 tptp.num)) (@ tptp.suc (@ tptp.pred_numeral K3)))))
% 6.73/7.07 (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)))
% 6.73/7.07 (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))))
% 6.73/7.07 (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))))
% 6.73/7.07 (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))))))
% 6.73/7.07 (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))))))
% 6.73/7.07 (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))))))
% 6.73/7.07 (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))))))
% 6.73/7.07 (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)))))))
% 6.73/7.07 (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)))))))
% 6.73/7.07 (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)))))))
% 6.73/7.07 (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)))))))
% 6.73/7.07 (assert (forall ((X tptp.complex)) (=> (= (@ tptp.cos_complex X) tptp.one_one_complex) (= (@ tptp.sin_complex X) tptp.zero_zero_complex))))
% 6.73/7.07 (assert (forall ((X tptp.real)) (=> (= (@ tptp.cos_real X) tptp.one_one_real) (= (@ tptp.sin_real X) tptp.zero_zero_real))))
% 6.73/7.07 (assert (forall ((A tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ tptp.abs_abs_real A))) tptp.zero_zero_real)))
% 6.73/7.07 (assert (forall ((A tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.abs_abs_Code_integer A))) tptp.zero_z3403309356797280102nteger)))
% 6.73/7.07 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ tptp.abs_abs_rat A))) tptp.zero_zero_rat)))
% 6.73/7.07 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.abs_abs_int A))) tptp.zero_zero_int)))
% 6.73/7.07 (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)))))))
% 6.73/7.07 (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)))))))
% 6.73/7.07 (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)))))))
% 6.73/7.07 (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)))))))
% 6.73/7.07 (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)))))))
% 6.73/7.07 (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)))))))
% 6.73/7.07 (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)))))))
% 6.73/7.07 (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)))))))
% 6.73/7.07 (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))))))
% 6.73/7.07 (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))))))
% 6.73/7.07 (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))))
% 6.73/7.07 (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))))
% 6.73/7.07 (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))))
% 6.73/7.07 (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))))
% 6.73/7.07 (assert (= tptp.abs_abs_int (lambda ((A5 tptp.int)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_int A5) tptp.zero_zero_int)) (@ tptp.uminus_uminus_int A5)) A5))))
% 6.73/7.07 (assert (= tptp.abs_abs_real (lambda ((A5 tptp.real)) (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_real A5) tptp.zero_zero_real)) (@ tptp.uminus_uminus_real A5)) A5))))
% 6.73/7.07 (assert (= tptp.abs_abs_Code_integer (lambda ((A5 tptp.code_integer)) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.ord_le6747313008572928689nteger A5) tptp.zero_z3403309356797280102nteger)) (@ tptp.uminus1351360451143612070nteger A5)) A5))))
% 6.73/7.07 (assert (= tptp.abs_abs_rat (lambda ((A5 tptp.rat)) (@ (@ (@ tptp.if_rat (@ (@ tptp.ord_less_rat A5) tptp.zero_zero_rat)) (@ tptp.uminus_uminus_rat A5)) A5))))
% 6.73/7.07 (assert (= tptp.abs_abs_int (lambda ((A5 tptp.int)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_int A5) tptp.zero_zero_int)) (@ tptp.uminus_uminus_int A5)) A5))))
% 6.73/7.07 (assert (= tptp.abs_abs_real (lambda ((A5 tptp.real)) (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_real A5) tptp.zero_zero_real)) (@ tptp.uminus_uminus_real A5)) A5))))
% 6.73/7.07 (assert (= tptp.abs_abs_Code_integer (lambda ((A5 tptp.code_integer)) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.ord_le6747313008572928689nteger A5) tptp.zero_z3403309356797280102nteger)) (@ tptp.uminus1351360451143612070nteger A5)) A5))))
% 6.73/7.07 (assert (= tptp.abs_abs_rat (lambda ((A5 tptp.rat)) (@ (@ (@ tptp.if_rat (@ (@ tptp.ord_less_rat A5) tptp.zero_zero_rat)) (@ tptp.uminus_uminus_rat A5)) A5))))
% 6.73/7.07 (assert (forall ((A tptp.int)) (=> (@ (@ tptp.ord_less_int A) tptp.zero_zero_int) (= (@ tptp.abs_abs_int A) (@ tptp.uminus_uminus_int A)))))
% 6.73/7.07 (assert (forall ((A tptp.real)) (=> (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (= (@ tptp.abs_abs_real A) (@ tptp.uminus_uminus_real A)))))
% 6.73/7.07 (assert (forall ((A tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A) tptp.zero_z3403309356797280102nteger) (= (@ tptp.abs_abs_Code_integer A) (@ tptp.uminus1351360451143612070nteger A)))))
% 6.73/7.07 (assert (forall ((A tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (= (@ tptp.abs_abs_rat A) (@ tptp.uminus_uminus_rat A)))))
% 6.73/7.07 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ tptp.sin_real (@ (@ tptp.plus_plus_real X) Y)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.sin_real X)) (@ tptp.cos_real Y))) (@ (@ tptp.times_times_real (@ tptp.cos_real X)) (@ tptp.sin_real Y))))))
% 6.73/7.07 (assert (forall ((X tptp.code_integer) (A tptp.code_integer) (R3 tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger X) A))) R3) (and (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.minus_8373710615458151222nteger A) R3)) X) (@ (@ tptp.ord_le3102999989581377725nteger X) (@ (@ tptp.plus_p5714425477246183910nteger A) R3))))))
% 6.73/7.07 (assert (forall ((X tptp.real) (A tptp.real) (R3 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X) A))) R3) (and (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real A) R3)) X) (@ (@ tptp.ord_less_eq_real X) (@ (@ tptp.plus_plus_real A) R3))))))
% 6.73/7.07 (assert (forall ((X tptp.rat) (A tptp.rat) (R3 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat X) A))) R3) (and (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat A) R3)) X) (@ (@ tptp.ord_less_eq_rat X) (@ (@ tptp.plus_plus_rat A) R3))))))
% 6.73/7.07 (assert (forall ((X tptp.int) (A tptp.int) (R3 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int X) A))) R3) (and (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int A) R3)) X) (@ (@ tptp.ord_less_eq_int X) (@ (@ tptp.plus_plus_int A) R3))))))
% 6.73/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C2 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 C2) D)))) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger A) C2))) (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger B) D))))))
% 6.73/7.07 (assert (forall ((A tptp.real) (B tptp.real) (C2 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 C2) D)))) (@ (@ tptp.plus_plus_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real A) C2))) (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real B) D))))))
% 6.73/7.07 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 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 C2) D)))) (@ (@ tptp.plus_plus_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat A) C2))) (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat B) D))))))
% 6.73/7.07 (assert (forall ((A tptp.int) (B tptp.int) (C2 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 C2) D)))) (@ (@ tptp.plus_plus_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int A) C2))) (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int B) D))))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ tptp.sin_real (@ (@ tptp.minus_minus_real X) Y)) (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real (@ tptp.sin_real X)) (@ tptp.cos_real Y))) (@ (@ tptp.times_times_real (@ tptp.cos_real X)) (@ tptp.sin_real Y))))))
% 6.73/7.07 (assert (forall ((X tptp.code_integer) (A tptp.code_integer) (R3 tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger X) A))) R3) (and (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.minus_8373710615458151222nteger A) R3)) X) (@ (@ tptp.ord_le6747313008572928689nteger X) (@ (@ tptp.plus_p5714425477246183910nteger A) R3))))))
% 6.73/7.07 (assert (forall ((X tptp.real) (A tptp.real) (R3 tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X) A))) R3) (and (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real A) R3)) X) (@ (@ tptp.ord_less_real X) (@ (@ tptp.plus_plus_real A) R3))))))
% 6.73/7.07 (assert (forall ((X tptp.rat) (A tptp.rat) (R3 tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat X) A))) R3) (and (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat A) R3)) X) (@ (@ tptp.ord_less_rat X) (@ (@ tptp.plus_plus_rat A) R3))))))
% 6.73/7.07 (assert (forall ((X tptp.int) (A tptp.int) (R3 tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int X) A))) R3) (and (@ (@ tptp.ord_less_int (@ (@ tptp.minus_minus_int A) R3)) X) (@ (@ tptp.ord_less_int X) (@ (@ tptp.plus_plus_int A) R3))))))
% 6.73/7.07 (assert (= tptp.pred_numeral (lambda ((K3 tptp.num)) (@ (@ tptp.minus_minus_nat (@ tptp.numeral_numeral_nat K3)) tptp.one_one_nat))))
% 6.73/7.07 (assert (forall ((K2 tptp.num)) (let ((_let_1 (@ tptp.pred_numeral K2))) (= (@ tptp.set_ord_lessThan_nat (@ tptp.numeral_numeral_nat K2)) (@ (@ tptp.insert_nat _let_1) (@ tptp.set_ord_lessThan_nat _let_1))))))
% 6.73/7.07 (assert (forall ((K2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat K2))) (= (@ tptp.set_ord_atMost_nat _let_1) (@ (@ tptp.insert_nat _let_1) (@ tptp.set_ord_atMost_nat (@ tptp.pred_numeral K2)))))))
% 6.73/7.07 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ tptp.cos_real (@ (@ tptp.plus_plus_real X) Y)) (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real (@ tptp.cos_real X)) (@ tptp.cos_real Y))) (@ (@ tptp.times_times_real (@ tptp.sin_real X)) (@ tptp.sin_real Y))))))
% 6.73/7.07 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ tptp.cos_real (@ (@ tptp.minus_minus_real X) Y)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.cos_real X)) (@ tptp.cos_real Y))) (@ (@ tptp.times_times_real (@ tptp.sin_real X)) (@ tptp.sin_real Y))))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (assert (forall ((X tptp.real)) (=> (= (@ tptp.sin_real X) tptp.zero_zero_real) (= (@ tptp.real_V7735802525324610683m_real (@ tptp.cos_real X)) tptp.one_one_real))))
% 6.73/7.07 (assert (forall ((X tptp.complex)) (=> (= (@ tptp.sin_complex X) tptp.zero_zero_complex) (= (@ tptp.real_V1022390504157884413omplex (@ tptp.cos_complex X)) tptp.one_one_real))))
% 6.73/7.07 (assert (forall ((K2 tptp.num)) (= (@ tptp.semiri773545260158071498ct_rat (@ tptp.numeral_numeral_nat K2)) (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat K2)) (@ tptp.semiri773545260158071498ct_rat (@ tptp.pred_numeral K2))))))
% 6.73/7.07 (assert (forall ((K2 tptp.num)) (= (@ tptp.semiri4449623510593786356d_enat (@ tptp.numeral_numeral_nat K2)) (@ (@ tptp.times_7803423173614009249d_enat (@ tptp.numera1916890842035813515d_enat K2)) (@ tptp.semiri4449623510593786356d_enat (@ tptp.pred_numeral K2))))))
% 6.73/7.07 (assert (forall ((K2 tptp.num)) (= (@ tptp.semiri5044797733671781792omplex (@ tptp.numeral_numeral_nat K2)) (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex K2)) (@ tptp.semiri5044797733671781792omplex (@ tptp.pred_numeral K2))))))
% 6.73/7.07 (assert (forall ((K2 tptp.num)) (= (@ tptp.semiri1406184849735516958ct_int (@ tptp.numeral_numeral_nat K2)) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int K2)) (@ tptp.semiri1406184849735516958ct_int (@ tptp.pred_numeral K2))))))
% 6.73/7.07 (assert (forall ((K2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat K2))) (= (@ tptp.semiri1408675320244567234ct_nat _let_1) (@ (@ tptp.times_times_nat _let_1) (@ tptp.semiri1408675320244567234ct_nat (@ tptp.pred_numeral K2)))))))
% 6.73/7.07 (assert (forall ((K2 tptp.num)) (= (@ tptp.semiri2265585572941072030t_real (@ tptp.numeral_numeral_nat K2)) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real K2)) (@ tptp.semiri2265585572941072030t_real (@ tptp.pred_numeral K2))))))
% 6.73/7.07 (assert (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))) (= (@ tptp.sin_complex (@ _let_1 X)) (@ (@ tptp.times_times_complex (@ _let_1 (@ tptp.sin_complex X))) (@ tptp.cos_complex X))))))
% 6.73/7.07 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (= (@ tptp.sin_real (@ _let_1 X)) (@ (@ tptp.times_times_real (@ _let_1 (@ tptp.sin_real X))) (@ tptp.cos_real X))))))
% 6.73/7.07 (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))))))
% 6.73/7.07 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.ord_less_eq_real (@ tptp.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))))))
% 6.73/7.07 (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))))))
% 6.73/7.07 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.ord_less_eq_int (@ tptp.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))))))
% 6.73/7.07 (assert (= tptp.unique5052692396658037445od_int (lambda ((M6 tptp.num) (N4 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N4))) (let ((_let_2 (@ tptp.numeral_numeral_int M6))) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.divide_divide_int _let_2) _let_1)) (@ (@ tptp.modulo_modulo_int _let_2) _let_1)))))))
% 6.73/7.07 (assert (forall ((P2 (-> tptp.code_integer tptp.code_integer Bool)) (X tptp.code_integer)) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) X3) (@ (@ P2 X3) (@ (@ tptp.power_8256067586552552935nteger X3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ P2 (@ tptp.abs_abs_Code_integer X)) (@ (@ tptp.power_8256067586552552935nteger X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))
% 6.73/7.07 (assert (forall ((P2 (-> tptp.real tptp.real Bool)) (X tptp.real)) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X3) (@ (@ P2 X3) (@ (@ tptp.power_power_real X3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ P2 (@ tptp.abs_abs_real X)) (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))
% 6.73/7.07 (assert (forall ((P2 (-> tptp.rat tptp.rat Bool)) (X tptp.rat)) (=> (forall ((X3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) X3) (@ (@ P2 X3) (@ (@ tptp.power_power_rat X3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ P2 (@ tptp.abs_abs_rat X)) (@ (@ tptp.power_power_rat X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))
% 6.73/7.07 (assert (forall ((P2 (-> tptp.int tptp.int Bool)) (X tptp.int)) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X3) (@ (@ P2 X3) (@ (@ tptp.power_power_int X3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ P2 (@ tptp.abs_abs_int X)) (@ (@ tptp.power_power_int X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))
% 6.73/7.07 (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))))))
% 6.73/7.07 (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))))))
% 6.73/7.07 (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))))))
% 6.73/7.07 (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))))))
% 6.73/7.07 (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))))
% 6.73/7.07 (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))))
% 6.73/7.07 (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))))
% 6.73/7.07 (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))))
% 6.73/7.07 (assert (= tptp.unique3479559517661332726nteger (lambda ((M6 tptp.num) (N4 tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger N4))) (let ((_let_2 (@ tptp.numera6620942414471956472nteger M6))) (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.divide6298287555418463151nteger _let_2) _let_1)) (@ (@ tptp.modulo364778990260209775nteger _let_2) _let_1)))))))
% 6.73/7.07 (assert (= tptp.unique5052692396658037445od_int (lambda ((M6 tptp.num) (N4 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N4))) (let ((_let_2 (@ tptp.numeral_numeral_int M6))) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.divide_divide_int _let_2) _let_1)) (@ (@ tptp.modulo_modulo_int _let_2) _let_1)))))))
% 6.73/7.07 (assert (= tptp.unique5055182867167087721od_nat (lambda ((M6 tptp.num) (N4 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N4))) (let ((_let_2 (@ tptp.numeral_numeral_nat M6))) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.divide_divide_nat _let_2) _let_1)) (@ (@ tptp.modulo_modulo_nat _let_2) _let_1)))))))
% 6.73/7.07 (assert (= tptp.unique5055182867167087721od_nat (lambda ((M6 tptp.num) (N4 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N4))) (let ((_let_2 (@ tptp.numeral_numeral_nat M6))) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.divide_divide_nat _let_2) _let_1)) (@ (@ tptp.modulo_modulo_nat _let_2) _let_1)))))))
% 6.73/7.07 (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))))))
% 6.73/7.07 (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))))))
% 6.73/7.07 (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))))))
% 6.73/7.07 (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))))))
% 6.73/7.07 (assert (forall ((I5 tptp.set_complex) (X (-> tptp.complex tptp.code_integer)) (A (-> tptp.complex tptp.code_integer)) (B tptp.code_integer) (Delta tptp.code_integer)) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) I5) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ X I3)))) (=> (= (@ (@ tptp.groups6621422865394947399nteger X) I5) tptp.one_one_Code_integer) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) I5) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger (@ A I3)) B))) Delta))) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.groups6621422865394947399nteger (lambda ((I tptp.complex)) (@ (@ tptp.times_3573771949741848930nteger (@ A I)) (@ X I)))) I5)) B))) Delta))))))
% 6.73/7.07 (assert (forall ((I5 tptp.set_real) (X (-> tptp.real tptp.code_integer)) (A (-> tptp.real tptp.code_integer)) (B tptp.code_integer) (Delta tptp.code_integer)) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) I5) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ X I3)))) (=> (= (@ (@ tptp.groups7713935264441627589nteger X) I5) tptp.one_one_Code_integer) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) I5) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger (@ A I3)) B))) Delta))) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.groups7713935264441627589nteger (lambda ((I tptp.real)) (@ (@ tptp.times_3573771949741848930nteger (@ A I)) (@ X I)))) I5)) B))) Delta))))))
% 6.73/7.07 (assert (forall ((I5 tptp.set_nat) (X (-> tptp.nat tptp.code_integer)) (A (-> tptp.nat tptp.code_integer)) (B tptp.code_integer) (Delta tptp.code_integer)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.member_nat I3) I5) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ X I3)))) (=> (= (@ (@ tptp.groups7501900531339628137nteger X) I5) tptp.one_one_Code_integer) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.member_nat I3) I5) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger (@ A I3)) B))) Delta))) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.groups7501900531339628137nteger (lambda ((I tptp.nat)) (@ (@ tptp.times_3573771949741848930nteger (@ A I)) (@ X I)))) I5)) B))) Delta))))))
% 6.73/7.07 (assert (forall ((I5 tptp.set_int) (X (-> tptp.int tptp.code_integer)) (A (-> tptp.int tptp.code_integer)) (B tptp.code_integer) (Delta tptp.code_integer)) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) I5) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ X I3)))) (=> (= (@ (@ tptp.groups7873554091576472773nteger X) I5) tptp.one_one_Code_integer) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) I5) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger (@ A I3)) B))) Delta))) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.groups7873554091576472773nteger (lambda ((I tptp.int)) (@ (@ tptp.times_3573771949741848930nteger (@ A I)) (@ X I)))) I5)) B))) Delta))))))
% 6.73/7.07 (assert (forall ((I5 tptp.set_complex) (X (-> tptp.complex tptp.real)) (A (-> tptp.complex tptp.real)) (B tptp.real) (Delta tptp.real)) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) I5) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ X I3)))) (=> (= (@ (@ tptp.groups5808333547571424918x_real X) I5) tptp.one_one_real) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) I5) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ A I3)) B))) Delta))) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ (@ tptp.groups5808333547571424918x_real (lambda ((I tptp.complex)) (@ (@ tptp.times_times_real (@ A I)) (@ X I)))) I5)) B))) Delta))))))
% 6.73/7.07 (assert (forall ((I5 tptp.set_real) (X (-> tptp.real tptp.real)) (A (-> tptp.real tptp.real)) (B tptp.real) (Delta tptp.real)) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) I5) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ X I3)))) (=> (= (@ (@ tptp.groups8097168146408367636l_real X) I5) tptp.one_one_real) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) I5) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ A I3)) B))) Delta))) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ (@ tptp.groups8097168146408367636l_real (lambda ((I tptp.real)) (@ (@ tptp.times_times_real (@ A I)) (@ X I)))) I5)) B))) Delta))))))
% 6.73/7.07 (assert (forall ((I5 tptp.set_int) (X (-> tptp.int tptp.real)) (A (-> tptp.int tptp.real)) (B tptp.real) (Delta tptp.real)) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) I5) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ X I3)))) (=> (= (@ (@ tptp.groups8778361861064173332t_real X) I5) tptp.one_one_real) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) I5) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ A I3)) B))) Delta))) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ (@ tptp.groups8778361861064173332t_real (lambda ((I tptp.int)) (@ (@ tptp.times_times_real (@ A I)) (@ X I)))) I5)) B))) Delta))))))
% 6.73/7.07 (assert (forall ((I5 tptp.set_complex) (X (-> tptp.complex tptp.rat)) (A (-> tptp.complex tptp.rat)) (B tptp.rat) (Delta tptp.rat)) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) I5) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ X I3)))) (=> (= (@ (@ tptp.groups5058264527183730370ex_rat X) I5) tptp.one_one_rat) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) I5) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ A I3)) B))) Delta))) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.groups5058264527183730370ex_rat (lambda ((I tptp.complex)) (@ (@ tptp.times_times_rat (@ A I)) (@ X I)))) I5)) B))) Delta))))))
% 6.73/7.07 (assert (forall ((I5 tptp.set_real) (X (-> tptp.real tptp.rat)) (A (-> tptp.real tptp.rat)) (B tptp.rat) (Delta tptp.rat)) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) I5) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ X I3)))) (=> (= (@ (@ tptp.groups1300246762558778688al_rat X) I5) tptp.one_one_rat) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) I5) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ A I3)) B))) Delta))) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.groups1300246762558778688al_rat (lambda ((I tptp.real)) (@ (@ tptp.times_times_rat (@ A I)) (@ X I)))) I5)) B))) Delta))))))
% 6.73/7.07 (assert (forall ((I5 tptp.set_nat) (X (-> tptp.nat tptp.rat)) (A (-> tptp.nat tptp.rat)) (B tptp.rat) (Delta tptp.rat)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.member_nat I3) I5) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ X I3)))) (=> (= (@ (@ tptp.groups2906978787729119204at_rat X) I5) tptp.one_one_rat) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.member_nat I3) I5) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ A I3)) B))) Delta))) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I tptp.nat)) (@ (@ tptp.times_times_rat (@ A I)) (@ X I)))) I5)) B))) Delta))))))
% 6.73/7.07 (assert (forall ((W2 tptp.complex) (Z3 tptp.complex)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.plus_plus_complex (@ tptp.cos_complex W2)) (@ tptp.cos_complex Z3)) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex _let_1) (@ tptp.cos_complex (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex W2) Z3)) _let_1)))) (@ tptp.cos_complex (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex W2) Z3)) _let_1)))))))
% 6.73/7.07 (assert (forall ((W2 tptp.real) (Z3 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.plus_plus_real (@ tptp.cos_real W2)) (@ tptp.cos_real Z3)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real _let_1) (@ tptp.cos_real (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real W2) Z3)) _let_1)))) (@ tptp.cos_real (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real W2) Z3)) _let_1)))))))
% 6.73/7.07 (assert (forall ((W2 tptp.complex) (Z3 tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.cos_complex W2)) (@ tptp.cos_complex Z3)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex (@ tptp.cos_complex (@ (@ tptp.minus_minus_complex W2) Z3))) (@ tptp.cos_complex (@ (@ tptp.plus_plus_complex W2) Z3)))) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))))
% 6.73/7.07 (assert (forall ((W2 tptp.real) (Z3 tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.cos_real W2)) (@ tptp.cos_real Z3)) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ tptp.cos_real (@ (@ tptp.minus_minus_real W2) Z3))) (@ tptp.cos_real (@ (@ tptp.plus_plus_real W2) Z3)))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))
% 6.73/7.07 (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))))))
% 6.73/7.07 (assert (forall ((W2 tptp.complex)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex _let_1)))) (= (@ tptp.cos_complex (@ _let_2 W2)) (@ (@ tptp.minus_minus_complex (@ _let_2 (@ (@ tptp.power_power_complex (@ tptp.cos_complex W2)) (@ tptp.numeral_numeral_nat _let_1)))) tptp.one_one_complex))))))
% 6.73/7.07 (assert (forall ((W2 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)))) (= (@ tptp.cos_real (@ _let_2 W2)) (@ (@ tptp.minus_minus_real (@ _let_2 (@ (@ tptp.power_power_real (@ tptp.cos_real W2)) (@ tptp.numeral_numeral_nat _let_1)))) tptp.one_one_real))))))
% 6.73/7.07 (assert (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.cos_complex X))) (let ((_let_2 (@ tptp.bit1 tptp.one))) (let ((_let_3 (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex _let_2)))) (= (@ tptp.cos_complex (@ _let_3 X)) (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 (@ tptp.bit0 tptp.one)))) (@ (@ tptp.power_power_complex _let_1) (@ tptp.numeral_numeral_nat _let_2)))) (@ _let_3 _let_1))))))))
% 6.73/7.07 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.cos_real X))) (let ((_let_2 (@ tptp.bit1 tptp.one))) (let ((_let_3 (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_2)))) (= (@ tptp.cos_real (@ _let_3 X)) (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 (@ tptp.bit0 tptp.one)))) (@ (@ tptp.power_power_real _let_1) (@ tptp.numeral_numeral_nat _let_2)))) (@ _let_3 _let_1))))))))
% 6.73/7.07 (assert (forall ((W2 tptp.complex) (Z3 tptp.complex)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.minus_minus_complex (@ tptp.cos_complex W2)) (@ tptp.cos_complex Z3)) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex _let_1) (@ tptp.sin_complex (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex W2) Z3)) _let_1)))) (@ tptp.sin_complex (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex Z3) W2)) _let_1)))))))
% 6.73/7.07 (assert (forall ((W2 tptp.real) (Z3 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.minus_minus_real (@ tptp.cos_real W2)) (@ tptp.cos_real Z3)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real _let_1) (@ tptp.sin_real (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real W2) Z3)) _let_1)))) (@ tptp.sin_real (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real Z3) W2)) _let_1)))))))
% 6.73/7.07 (assert (forall ((W2 tptp.complex) (Z3 tptp.complex)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.minus_minus_complex (@ tptp.sin_complex W2)) (@ tptp.sin_complex Z3)) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex _let_1) (@ tptp.sin_complex (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex W2) Z3)) _let_1)))) (@ tptp.cos_complex (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex W2) Z3)) _let_1)))))))
% 6.73/7.07 (assert (forall ((W2 tptp.real) (Z3 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.minus_minus_real (@ tptp.sin_real W2)) (@ tptp.sin_real Z3)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real _let_1) (@ tptp.sin_real (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real W2) Z3)) _let_1)))) (@ tptp.cos_real (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real W2) Z3)) _let_1)))))))
% 6.73/7.07 (assert (forall ((W2 tptp.complex) (Z3 tptp.complex)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.plus_plus_complex (@ tptp.sin_complex W2)) (@ tptp.sin_complex Z3)) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex _let_1) (@ tptp.sin_complex (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex W2) Z3)) _let_1)))) (@ tptp.cos_complex (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex W2) Z3)) _let_1)))))))
% 6.73/7.07 (assert (forall ((W2 tptp.real) (Z3 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.plus_plus_real (@ tptp.sin_real W2)) (@ tptp.sin_real Z3)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real _let_1) (@ tptp.sin_real (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real W2) Z3)) _let_1)))) (@ tptp.cos_real (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real W2) Z3)) _let_1)))))))
% 6.73/7.07 (assert (forall ((W2 tptp.complex) (Z3 tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.cos_complex W2)) (@ tptp.sin_complex Z3)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ tptp.sin_complex (@ (@ tptp.plus_plus_complex W2) Z3))) (@ tptp.sin_complex (@ (@ tptp.minus_minus_complex W2) Z3)))) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))))
% 6.73/7.07 (assert (forall ((W2 tptp.real) (Z3 tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.cos_real W2)) (@ tptp.sin_real Z3)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ tptp.sin_real (@ (@ tptp.plus_plus_real W2) Z3))) (@ tptp.sin_real (@ (@ tptp.minus_minus_real W2) Z3)))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))
% 6.73/7.07 (assert (forall ((W2 tptp.complex) (Z3 tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.sin_complex W2)) (@ tptp.cos_complex Z3)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex (@ tptp.sin_complex (@ (@ tptp.plus_plus_complex W2) Z3))) (@ tptp.sin_complex (@ (@ tptp.minus_minus_complex W2) Z3)))) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))))
% 6.73/7.07 (assert (forall ((W2 tptp.real) (Z3 tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.sin_real W2)) (@ tptp.cos_real Z3)) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ tptp.sin_real (@ (@ tptp.plus_plus_real W2) Z3))) (@ tptp.sin_real (@ (@ tptp.minus_minus_real W2) Z3)))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))
% 6.73/7.07 (assert (forall ((W2 tptp.complex) (Z3 tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.sin_complex W2)) (@ tptp.sin_complex Z3)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ tptp.cos_complex (@ (@ tptp.minus_minus_complex W2) Z3))) (@ tptp.cos_complex (@ (@ tptp.plus_plus_complex W2) Z3)))) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))))
% 6.73/7.07 (assert (forall ((W2 tptp.real) (Z3 tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.sin_real W2)) (@ tptp.sin_real Z3)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ tptp.cos_real (@ (@ tptp.minus_minus_real W2) Z3))) (@ tptp.cos_real (@ (@ tptp.plus_plus_real W2) Z3)))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))
% 6.73/7.07 (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 ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.cos_coeff M6)) (@ (@ tptp.power_power_real X) M6)))) (@ 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))))))))
% 6.73/7.07 (assert (forall ((X tptp.real)) (= (= (@ tptp.cos_real X) tptp.one_one_real) (or (exists ((X4 tptp.nat)) (= X (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real X4)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.pi))) (exists ((X4 tptp.nat)) (= X (@ tptp.uminus_uminus_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real X4)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.pi))))))))
% 6.73/7.07 (assert (forall ((X tptp.real) (M2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.plus_plus_real X))) (= (@ tptp.sin_real (@ _let_2 (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc M2))) tptp.pi)) _let_1))) (@ tptp.cos_real (@ _let_2 (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real M2)) tptp.pi)) _let_1))))))))
% 6.73/7.07 (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)))))))))))
% 6.73/7.07 (assert (forall ((X tptp.real)) (= (= (@ tptp.cos_real X) tptp.zero_zero_real) (or (exists ((N4 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (and (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat _let_1)) N4)) (= X (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N4)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1))))))) (exists ((N4 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (and (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat _let_1)) N4)) (= X (@ tptp.uminus_uminus_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N4)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1))))))))))))
% 6.73/7.07 (assert (forall ((X tptp.real) (M2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.plus_plus_real X))) (= (@ tptp.cos_real (@ _let_2 (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc M2))) tptp.pi)) _let_1))) (@ tptp.uminus_uminus_real (@ tptp.sin_real (@ _let_2 (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real M2)) tptp.pi)) _let_1)))))))))
% 6.73/7.07 (assert (forall ((X tptp.real)) (@ (@ tptp.sums_real (lambda ((N4 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N4))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N4)) (@ tptp.semiri2265585572941072030t_real _let_1))) (@ (@ tptp.power_power_real X) _let_1))))) (@ tptp.cos_real X))))
% 6.73/7.07 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)) tptp.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))))))))
% 6.73/7.07 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)) tptp.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))))))))))))
% 6.73/7.07 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) tptp.one_one_real) (@ tptp.topolo6980174941875973593q_real (lambda ((N4 tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat N4) (@ 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))))))))
% 6.73/7.07 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) tptp.one_one_real) (@ tptp.summable_real (lambda ((K3 tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat K3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_nat))) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) K3)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real _let_1))) (@ (@ tptp.power_power_real X) _let_1)))))))))
% 6.73/7.07 (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))))))))))
% 6.73/7.07 (assert (= (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 (@ tptp.bit0 tptp.one)))) (@ tptp.suminf_real (lambda ((K3 tptp.nat)) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) K3)) tptp.one_one_real)) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat K3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_nat)))))))
% 6.73/7.07 (assert (forall ((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.bit_se725231765392027082nd_int K2) L))) (let ((_let_5 (@ (@ tptp.insert_int tptp.zero_zero_int) (@ (@ tptp.insert_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.bot_bot_set_int)))) (let ((_let_6 (and (@ (@ tptp.member_int K2) _let_5) (@ (@ tptp.member_int L) _let_5)))) (=> (@ (@ tptp.accp_P1096762738010456898nt_int tptp.bit_and_int_rel) (@ (@ tptp.product_Pair_int_int K2) L)) (and (=> _let_6 (= _let_4 (@ tptp.uminus_uminus_int _let_3))) (=> (not _let_6) (= _let_4 (@ (@ tptp.plus_plus_int _let_3) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se725231765392027082nd_int (@ (@ tptp.divide_divide_int K2) _let_1)) (@ (@ tptp.divide_divide_int L) _let_1))))))))))))))))
% 6.73/7.07 (assert (forall ((N tptp.nat)) (= (@ tptp.tan_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) tptp.pi)) tptp.zero_zero_real)))
% 6.73/7.07 (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))))
% 6.73/7.07 (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))))
% 6.73/7.07 (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))))
% 6.73/7.07 (assert (forall ((M2 tptp.int) (N tptp.int)) (=> (= (@ tptp.abs_abs_int (@ (@ tptp.times_times_int M2) N)) tptp.one_one_int) (= (@ tptp.abs_abs_int M2) tptp.one_one_int))))
% 6.73/7.07 (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))))))
% 6.73/7.07 (assert (forall ((F2 (-> tptp.nat tptp.real)) (G2 (-> tptp.nat tptp.real))) (=> (exists ((N7 tptp.nat)) (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N7) N3) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ F2 N3))) (@ G2 N3))))) (=> (@ tptp.summable_real G2) (@ tptp.summable_real (lambda ((N4 tptp.nat)) (@ tptp.abs_abs_real (@ F2 N4))))))))
% 6.73/7.07 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= (@ tptp.ln_ln_real (@ (@ tptp.times_times_real X) Y)) (@ (@ tptp.plus_plus_real (@ tptp.ln_ln_real X)) (@ tptp.ln_ln_real Y))))))))
% 6.73/7.07 (assert (forall ((M2 tptp.int) (N tptp.int)) (=> (not (= M2 tptp.zero_zero_int)) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int M2) N)) M2) (= (@ tptp.abs_abs_int N) tptp.one_one_int)))))
% 6.73/7.07 (assert (forall ((F2 (-> tptp.nat tptp.real)) (K2 tptp.nat)) (=> (@ tptp.summable_real F2) (=> (forall ((D5 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.suc (@ tptp.suc tptp.zero_zero_nat))) D5))) (let ((_let_2 (@ tptp.plus_plus_nat K2))) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real (@ F2 (@ _let_2 _let_1))) (@ F2 (@ _let_2 (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat)))))))) (@ (@ tptp.ord_less_real (@ (@ tptp.groups6591440286371151544t_real F2) (@ tptp.set_ord_lessThan_nat K2))) (@ tptp.suminf_real F2))))))
% 6.73/7.07 (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))))))
% 6.73/7.07 (assert (forall ((F2 (-> tptp.nat tptp.real)) (Z3 tptp.real)) (=> (forall ((I3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ F2 I3)) tptp.one_one_real)) (=> (forall ((I3 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F2 I3))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Z3) (=> (@ (@ tptp.ord_less_real Z3) tptp.one_one_real) (@ tptp.summable_real (lambda ((I tptp.nat)) (@ (@ tptp.times_times_real (@ F2 I)) (@ (@ tptp.power_power_real Z3) I))))))))))
% 6.73/7.07 (assert (forall ((M2 tptp.nat) (N tptp.nat) (F2 (-> tptp.nat tptp.int)) (K2 tptp.int)) (=> (forall ((I3 tptp.nat)) (=> (and (@ (@ tptp.ord_less_eq_nat M2) I3) (@ (@ tptp.ord_less_nat I3) N)) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ F2 (@ tptp.suc I3))) (@ F2 I3)))) tptp.one_one_int))) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (=> (@ (@ tptp.ord_less_eq_int (@ F2 M2)) K2) (=> (@ (@ tptp.ord_less_eq_int K2) (@ F2 N)) (exists ((I3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat M2) I3) (@ (@ tptp.ord_less_eq_nat I3) N) (= (@ F2 I3) K2)))))))))
% 6.73/7.07 (assert (forall ((D tptp.int) (Z3 tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (@ (@ tptp.ord_less_int Z3) (@ (@ tptp.plus_plus_int X) (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int X) Z3))) tptp.one_one_int)) D))))))
% 6.73/7.07 (assert (forall ((D tptp.int) (X tptp.int) (Z3 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 Z3))) tptp.one_one_int)) D))) Z3)))))
% 6.73/7.07 (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 ((N4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N4)) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.plus_plus_nat N4) tptp.one_one_nat))))) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real X) tptp.one_one_real)) (@ tptp.suc N4))))))))))
% 6.73/7.07 (assert (forall ((N tptp.nat) (F2 (-> tptp.nat tptp.int)) (K2 tptp.int)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) N) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ F2 (@ tptp.suc I3))) (@ F2 I3)))) tptp.one_one_int))) (=> (@ (@ tptp.ord_less_eq_int (@ F2 tptp.zero_zero_nat)) K2) (=> (@ (@ tptp.ord_less_eq_int K2) (@ F2 N)) (exists ((I3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat I3) N) (= (@ F2 I3) K2))))))))
% 6.73/7.07 (assert (forall ((N tptp.nat) (F2 (-> tptp.nat tptp.int)) (K2 tptp.int)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) N) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ F2 (@ (@ tptp.plus_plus_nat I3) tptp.one_one_nat))) (@ F2 I3)))) tptp.one_one_int))) (=> (@ (@ tptp.ord_less_eq_int (@ F2 tptp.zero_zero_nat)) K2) (=> (@ (@ tptp.ord_less_eq_int K2) (@ F2 N)) (exists ((I3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat I3) N) (= (@ F2 I3) K2))))))))
% 6.73/7.07 (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)))))))))
% 6.73/7.07 (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)))))))))
% 6.73/7.07 (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)))))))))))))
% 6.73/7.07 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) tptp.one_one_real) (= (@ tptp.arctan X) (@ tptp.suminf_real (lambda ((K3 tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat K3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_nat))) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) K3)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real _let_1))) (@ (@ tptp.power_power_real X) _let_1))))))))))
% 6.73/7.07 (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 ((M6 tptp.nat)) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real X) M6)) (@ tptp.semiri2265585572941072030t_real M6)))) (@ 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)))))))))))
% 6.73/7.07 (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)))))))))))
% 6.73/7.07 (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))))))))
% 6.73/7.07 (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)))))))
% 6.73/7.07 (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))))))))
% 6.73/7.07 (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)))))))))
% 6.73/7.07 (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 ((M6 tptp.nat)) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real X) M6)) (@ tptp.semiri2265585572941072030t_real M6)))) (@ 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))))))))
% 6.73/7.07 (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)))))))
% 6.73/7.07 (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))))))))))))))))
% 6.73/7.07 (assert (= tptp.tanh_real (lambda ((X4 tptp.real)) (let ((_let_1 (@ tptp.exp_real (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) X4)))) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real tptp.one_one_real) _let_1)) (@ (@ tptp.plus_plus_real tptp.one_one_real) _let_1))))))
% 6.73/7.07 (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 ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.sin_coeff M6)) (@ (@ tptp.power_power_real X) M6)))) (@ tptp.set_ord_lessThan_nat N))))) (@ (@ tptp.times_times_real (@ tptp.inverse_inverse_real (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real X)) N)))))
% 6.73/7.07 (assert (forall ((M2 tptp.num)) (= (@ (@ tptp.unique5052692396658037445od_int (@ tptp.bitM M2)) (@ tptp.bit0 tptp.one)) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.minus_minus_int (@ tptp.numeral_numeral_int M2)) tptp.one_one_int)) tptp.one_one_int))))
% 6.73/7.07 (assert (forall ((K2 tptp.num)) (= (@ tptp.pred_numeral (@ tptp.bit0 K2)) (@ tptp.numeral_numeral_nat (@ tptp.bitM K2)))))
% 6.73/7.07 (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)))
% 6.73/7.07 (assert (forall ((X tptp.real) (I2 tptp.int)) (= (@ tptp.tan_real (@ (@ tptp.plus_plus_real X) (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real I2)) tptp.pi))) (@ tptp.tan_real X))))
% 6.73/7.07 (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)))
% 6.73/7.07 (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)))
% 6.73/7.07 (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))))))))
% 6.73/7.07 (assert (= tptp.real_V1485227260804924795R_real tptp.times_times_real))
% 6.73/7.07 (assert (= tptp.divide_divide_real (lambda ((X4 tptp.real) (Y4 tptp.real)) (@ (@ tptp.times_times_real X4) (@ tptp.inverse_inverse_real Y4)))))
% 6.73/7.07 (assert (forall ((N tptp.num)) (= (@ tptp.numeral_numeral_nat (@ tptp.bit0 N)) (@ tptp.suc (@ tptp.numeral_numeral_nat (@ tptp.bitM N))))))
% 6.73/7.07 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_num (@ tptp.bitM N)) tptp.one) (@ tptp.bit0 N))))
% 6.73/7.07 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_num tptp.one) (@ tptp.bitM N)) (@ tptp.bit0 N))))
% 6.73/7.07 (assert (forall ((P2 (-> tptp.real Bool)) (E tptp.real)) (=> (forall ((D5 tptp.real) (E2 tptp.real)) (=> (@ (@ tptp.ord_less_real D5) E2) (=> (@ P2 D5) (@ P2 E2)))) (=> (forall ((N3 tptp.nat)) (@ P2 (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N3))))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E) (@ P2 E))))))
% 6.73/7.07 (assert (forall ((P2 (-> tptp.real Bool)) (E tptp.real)) (=> (forall ((D5 tptp.real) (E2 tptp.real)) (=> (@ (@ tptp.ord_less_real D5) E2) (=> (@ P2 D5) (@ P2 E2)))) (=> (forall ((N3 tptp.nat)) (=> (not (= N3 tptp.zero_zero_nat)) (@ P2 (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real N3))))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E) (@ P2 E))))))
% 6.73/7.07 (assert (forall ((E tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) E) (exists ((N4 tptp.nat)) (let ((_let_1 (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real N4)))) (and (not (= N4 tptp.zero_zero_nat)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_real _let_1) E)))))))
% 6.73/7.07 (assert (forall ((X tptp.real)) (= (= (@ tptp.sin_real X) tptp.zero_zero_real) (exists ((I tptp.int)) (= X (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real I)) tptp.pi))))))
% 6.73/7.07 (assert (forall ((X tptp.real)) (= (= (@ tptp.cos_real X) tptp.one_one_real) (exists ((X4 tptp.int)) (= X (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real X4)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.pi))))))
% 6.73/7.07 (assert (forall ((X tptp.real)) (= (= (@ tptp.cos_real X) tptp.zero_zero_real) (exists ((I tptp.int)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (and (not (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int _let_1)) I)) (= X (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real I)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1))))))))))
% 6.73/7.07 (assert (forall ((X tptp.real)) (= (= (@ tptp.sin_real X) tptp.zero_zero_real) (exists ((I tptp.int)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (and (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int _let_1)) I) (= X (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real I)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1))))))))))
% 6.73/7.07 (assert (forall ((Z3 tptp.complex)) (=> (= (@ tptp.real_V1022390504157884413omplex Z3) 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 (= Z3 (@ (@ tptp.complex2 (@ tptp.cos_real T6)) (@ tptp.sin_real T6)))))))))))
% 6.73/7.07 (assert (forall ((Theta tptp.real)) (not (forall ((K 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 K)) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi))))))))))
% 6.73/7.07 (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.log2 _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)))))))
% 6.73/7.07 (assert (forall ((R3 tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real R3))) (= (@ (@ tptp.real_V2046097035970521341omplex R3) (@ (@ tptp.complex2 A) B)) (@ (@ tptp.complex2 (@ _let_1 A)) (@ _let_1 B))))))
% 6.73/7.07 (assert (forall ((A tptp.real) (B tptp.real) (C2 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 C2) D)) (@ (@ tptp.complex2 (@ (@ tptp.minus_minus_real (@ _let_2 C2)) (@ _let_1 D))) (@ (@ tptp.plus_plus_real (@ _let_2 D)) (@ _let_1 C2))))))))
% 6.73/7.07 (assert (forall ((A tptp.real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.log2 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)))))))))))
% 6.73/7.07 (assert (forall ((X tptp.real) (B tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.log2 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)))))))
% 6.73/7.07 (assert (forall ((M2 tptp.nat) (B tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real M2))) (=> (@ (@ 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) M2) (@ (@ tptp.ord_less_real (@ (@ tptp.log2 B) _let_1)) (@ tptp.semiri5074537144036343181t_real N))))))))
% 6.73/7.07 (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.log2 A) X) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.ln_ln_real B)) (@ tptp.ln_ln_real A))) (@ (@ tptp.log2 B) X)))))))))))
% 6.73/7.07 (assert (forall ((M2 tptp.nat) (B tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real M2))) (=> (@ (@ 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) M2) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.log2 B) _let_1)) (@ tptp.semiri5074537144036343181t_real N))))))))
% 6.73/7.07 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat _let_1)) N)) M2) (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.log2 (@ tptp.numeral_numeral_real _let_1)) (@ tptp.semiri5074537144036343181t_real M2)))))))
% 6.73/7.07 (assert (= tptp.unique5026877609467782581ep_nat (lambda ((L2 tptp.num) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((Q5 tptp.nat) (R tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Q5))) (let ((_let_2 (@ tptp.numeral_numeral_nat L2))) (@ (@ (@ tptp.if_Pro6206227464963214023at_nat (@ (@ tptp.ord_less_eq_nat _let_2) R)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat)) (@ (@ tptp.minus_minus_nat R) _let_2))) (@ (@ tptp.product_Pair_nat_nat _let_1) R)))))) __flatten_var_0))))
% 6.73/7.07 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (=> (@ (@ tptp.ord_less_nat M2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat _let_1)) N)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M2) (@ (@ tptp.ord_less_real (@ (@ tptp.log2 (@ tptp.numeral_numeral_real _let_1)) (@ tptp.semiri5074537144036343181t_real M2))) (@ tptp.semiri5074537144036343181t_real N)))))))
% 6.73/7.07 (assert (= tptp.unique5024387138958732305ep_int (lambda ((L2 tptp.num) (__flatten_var_0 tptp.product_prod_int_int)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((Q5 tptp.int) (R tptp.int)) (let ((_let_1 (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) Q5))) (let ((_let_2 (@ tptp.numeral_numeral_int L2))) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (@ (@ tptp.ord_less_eq_int _let_2) R)) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int)) (@ (@ tptp.minus_minus_int R) _let_2))) (@ (@ tptp.product_Pair_int_int _let_1) R)))))) __flatten_var_0))))
% 6.73/7.07 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (=> (@ (@ tptp.ord_less_eq_nat M2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat _let_1)) N)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M2) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.log2 (@ tptp.numeral_numeral_real _let_1)) (@ tptp.semiri5074537144036343181t_real M2))) (@ tptp.semiri5074537144036343181t_real N)))))))
% 6.73/7.07 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.log2 (@ 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)))))))
% 6.73/7.07 (assert (forall ((B tptp.nat) (K2 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) K2) (= (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.log2 (@ tptp.semiri5074537144036343181t_real B)) (@ tptp.semiri5074537144036343181t_real K2))) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int N)) tptp.one_one_int)) (and (@ (@ tptp.ord_less_nat (@ _let_1 N)) K2) (@ (@ tptp.ord_less_eq_nat K2) (@ _let_1 (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat))))))))))
% 6.73/7.07 (assert (forall ((B tptp.nat) (N tptp.nat) (K2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (=> (@ (@ tptp.ord_less_nat (@ _let_1 N)) K2) (=> (@ (@ tptp.ord_less_eq_nat K2) (@ _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.log2 (@ tptp.semiri5074537144036343181t_real B)) (@ tptp.semiri5074537144036343181t_real K2))) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int N)) tptp.one_one_int))))))))
% 6.73/7.07 (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.log2 (@ 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))))))))
% 6.73/7.07 (assert (= tptp.divmod_nat (lambda ((M6 tptp.nat) (N4 tptp.nat)) (@ (@ (@ tptp.if_Pro6206227464963214023at_nat (or (= N4 tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat M6) N4))) (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) M6)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((Q5 tptp.nat) (__flatten_var_0 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ tptp.suc Q5)) __flatten_var_0))) (@ (@ tptp.divmod_nat (@ (@ tptp.minus_minus_nat M6) N4)) N4))))))
% 6.73/7.07 (assert (forall ((B tptp.nat) (K2 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) K2) (= (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.log2 (@ tptp.semiri5074537144036343181t_real B)) (@ tptp.semiri5074537144036343181t_real K2))) (@ tptp.semiri1314217659103216013at_int N)) (and (@ (@ tptp.ord_less_eq_nat (@ _let_1 N)) K2) (@ (@ tptp.ord_less_nat K2) (@ _let_1 (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat))))))))))
% 6.73/7.07 (assert (= tptp.divide1717551699836669952omplex (lambda ((X4 tptp.complex) (Y4 tptp.complex)) (@ (@ tptp.times_times_complex X4) (@ tptp.invers8013647133539491842omplex Y4)))))
% 6.73/7.07 (assert (= tptp.nat_prod_encode (@ tptp.produc6842872674320459806at_nat (lambda ((M6 tptp.nat) (N4 tptp.nat)) (@ (@ tptp.plus_plus_nat (@ tptp.nat_triangle (@ (@ tptp.plus_plus_nat M6) N4))) M6)))))
% 6.73/7.07 (assert (= tptp.adjust_div (@ tptp.produc8211389475949308722nt_int (lambda ((Q5 tptp.int) (R tptp.int)) (@ (@ tptp.plus_plus_int Q5) (@ tptp.zero_n2684676970156552555ol_int (not (= R tptp.zero_zero_int))))))))
% 6.73/7.07 (assert (= tptp.divmod_nat (lambda ((M6 tptp.nat) (N4 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.divide_divide_nat M6) N4)) (@ (@ tptp.modulo_modulo_nat M6) N4)))))
% 6.73/7.07 (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.log2 (@ 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))))))))
% 6.73/7.07 (assert (forall ((B tptp.nat) (N tptp.nat) (K2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (=> (@ (@ tptp.ord_less_eq_nat (@ _let_1 N)) K2) (=> (@ (@ tptp.ord_less_nat K2) (@ _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.log2 (@ tptp.semiri5074537144036343181t_real B)) (@ tptp.semiri5074537144036343181t_real K2))) (@ tptp.semiri1314217659103216013at_int N))))))))
% 6.73/7.07 (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))))
% 6.73/7.07 (assert (forall ((L tptp.int) (K2 tptp.int) (N tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.modulo_modulo_nat M2) N)))) (let ((_let_2 (@ tptp.sgn_sgn_int L))) (let ((_let_3 (@ tptp.times_times_int _let_2))) (let ((_let_4 (@ tptp.sgn_sgn_int K2))) (let ((_let_5 (@ (@ tptp.times_times_int _let_4) (@ tptp.semiri1314217659103216013at_int M2)))) (let ((_let_6 (@ (@ tptp.modulo_modulo_int _let_5) (@ _let_3 (@ tptp.semiri1314217659103216013at_int 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) M2)))))) _let_1)))))))))))))))))
% 6.73/7.07 (assert (forall ((L tptp.int) (K2 tptp.int) (R3 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int L))) (= (@ _let_1 (@ (@ tptp.times_times_int K2) (@ tptp.sgn_sgn_int R3))) (or (@ _let_1 K2) (= R3 tptp.zero_zero_int))))))
% 6.73/7.07 (assert (forall ((L tptp.int) (R3 tptp.int) (K2 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int L))) (= (@ _let_1 (@ (@ tptp.times_times_int (@ tptp.sgn_sgn_int R3)) K2)) (or (@ _let_1 K2) (= R3 tptp.zero_zero_int))))))
% 6.73/7.07 (assert (forall ((L tptp.int) (R3 tptp.int) (K2 tptp.int)) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int L) (@ tptp.sgn_sgn_int R3))) K2) (and (@ (@ tptp.dvd_dvd_int L) K2) (=> (= R3 tptp.zero_zero_int) (= K2 tptp.zero_zero_int))))))
% 6.73/7.07 (assert (forall ((R3 tptp.int) (L tptp.int) (K2 tptp.int)) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int (@ tptp.sgn_sgn_int R3)) L)) K2) (and (@ (@ tptp.dvd_dvd_int L) K2) (=> (= R3 tptp.zero_zero_int) (= K2 tptp.zero_zero_int))))))
% 6.73/7.07 (assert (forall ((N tptp.nat)) (= (@ tptp.cot_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) tptp.pi)) tptp.zero_zero_real)))
% 6.73/7.07 (assert (forall ((K2 tptp.int)) (not (forall ((N3 tptp.nat) (L4 tptp.int)) (not (= K2 (@ (@ tptp.times_times_int (@ tptp.sgn_sgn_int L4)) (@ tptp.semiri1314217659103216013at_int N3))))))))
% 6.73/7.07 (assert (forall ((K2 tptp.int) (L tptp.int)) (=> (= (@ tptp.sgn_sgn_int K2) (@ tptp.sgn_sgn_int L)) (= (@ (@ tptp.divide_divide_int K2) L) (@ (@ tptp.divide_divide_int (@ tptp.abs_abs_int K2)) (@ tptp.abs_abs_int L))))))
% 6.73/7.07 (assert (forall ((V2 tptp.int) (K2 tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.abs_abs_int L))) (let ((_let_2 (@ tptp.abs_abs_int K2))) (let ((_let_3 (@ tptp.times_times_int (@ tptp.sgn_sgn_int V2)))) (=> (not (= V2 tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ _let_3 _let_2)) (@ _let_3 _let_1)) (@ (@ tptp.divide_divide_int _let_2) _let_1))))))))
% 6.73/7.07 (assert (forall ((L tptp.int) (K2 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int L) K2) (= (@ (@ tptp.divide_divide_int K2) L) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int (@ tptp.sgn_sgn_int K2)) (@ tptp.sgn_sgn_int L))) (@ (@ tptp.divide_divide_int (@ tptp.abs_abs_int K2)) (@ tptp.abs_abs_int L)))))))
% 6.73/7.07 (assert (forall ((R3 tptp.int) (L tptp.int) (K2 tptp.int) (Q2 tptp.int)) (=> (= (@ tptp.sgn_sgn_int R3) (@ tptp.sgn_sgn_int L)) (=> (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int R3)) (@ tptp.abs_abs_int L)) (=> (= K2 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int Q2) L)) R3)) (@ (@ (@ tptp.eucl_rel_int K2) L) (@ (@ tptp.product_Pair_int_int Q2) R3)))))))
% 6.73/7.07 (assert (= tptp.eucl_rel_int (lambda ((A13 tptp.int) (A24 tptp.int) (A32 tptp.product_prod_int_int)) (or (exists ((K3 tptp.int)) (and (= A13 K3) (= A24 tptp.zero_zero_int) (= A32 (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) K3)))) (exists ((L2 tptp.int) (K3 tptp.int) (Q5 tptp.int)) (and (= A13 K3) (= A24 L2) (= A32 (@ (@ tptp.product_Pair_int_int Q5) tptp.zero_zero_int)) (not (= L2 tptp.zero_zero_int)) (= K3 (@ (@ tptp.times_times_int Q5) L2)))) (exists ((R tptp.int) (L2 tptp.int) (K3 tptp.int) (Q5 tptp.int)) (and (= A13 K3) (= A24 L2) (= A32 (@ (@ tptp.product_Pair_int_int Q5) R)) (= (@ tptp.sgn_sgn_int R) (@ tptp.sgn_sgn_int L2)) (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int R)) (@ tptp.abs_abs_int L2)) (= K3 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int Q5) L2)) R))))))))
% 6.73/7.07 (assert (forall ((A12 tptp.int) (A23 tptp.int) (A33 tptp.product_prod_int_int)) (=> (@ (@ (@ tptp.eucl_rel_int A12) A23) A33) (=> (=> (= A23 tptp.zero_zero_int) (not (= A33 (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) A12)))) (=> (forall ((Q3 tptp.int)) (=> (= A33 (@ (@ tptp.product_Pair_int_int Q3) tptp.zero_zero_int)) (=> (not (= A23 tptp.zero_zero_int)) (not (= A12 (@ (@ tptp.times_times_int Q3) A23)))))) (not (forall ((R4 tptp.int) (Q3 tptp.int)) (=> (= A33 (@ (@ tptp.product_Pair_int_int Q3) R4)) (=> (= (@ tptp.sgn_sgn_int R4) (@ tptp.sgn_sgn_int A23)) (=> (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int R4)) (@ tptp.abs_abs_int A23)) (not (= A12 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int Q3) A23)) R4)))))))))))))
% 6.73/7.07 (assert (forall ((L tptp.int) (K2 tptp.int)) (=> (not (= L tptp.zero_zero_int)) (=> (not (= (@ tptp.sgn_sgn_int K2) (@ tptp.sgn_sgn_int L))) (= (@ (@ tptp.divide_divide_int K2) L) (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int (@ (@ tptp.divide_divide_int (@ tptp.abs_abs_int K2)) (@ tptp.abs_abs_int L)))) (@ tptp.zero_n2684676970156552555ol_int (not (@ (@ tptp.dvd_dvd_int L) K2)))))))))
% 6.73/7.07 (assert (forall ((L tptp.int) (K2 tptp.int) (N tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ (@ tptp.divide_divide_nat M2) N))) (let ((_let_2 (@ tptp.sgn_sgn_int L))) (let ((_let_3 (@ tptp.sgn_sgn_int K2))) (let ((_let_4 (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int _let_3) (@ tptp.semiri1314217659103216013at_int M2))) (@ (@ tptp.times_times_int _let_2) (@ tptp.semiri1314217659103216013at_int 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) M2)))))))))))))))))))
% 6.73/7.07 (assert (= tptp.bNF_Ca8459412986667044542atLess (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o tptp.ord_less_nat))))
% 6.73/7.07 (assert (= tptp.modulo_modulo_int (lambda ((K3 tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.abs_abs_int L2))) (let ((_let_2 (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.modulo_modulo_nat (@ tptp.nat2 (@ tptp.abs_abs_int K3))) (@ tptp.nat2 _let_1))))) (let ((_let_3 (@ tptp.sgn_sgn_int L2))) (let ((_let_4 (@ tptp.times_times_int _let_3))) (@ (@ (@ tptp.if_int (= L2 tptp.zero_zero_int)) K3) (@ (@ (@ tptp.if_int (= (@ tptp.sgn_sgn_int K3) _let_3)) (@ _let_4 _let_2)) (@ _let_4 (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int _let_1) (@ tptp.zero_n2684676970156552555ol_int (not (@ (@ tptp.dvd_dvd_int L2) K3))))) _let_2)))))))))))
% 6.73/7.07 (assert (forall ((X33 tptp.num)) (= (@ tptp.size_num (@ tptp.bit1 X33)) (@ (@ tptp.plus_plus_nat (@ tptp.size_num X33)) (@ tptp.suc tptp.zero_zero_nat)))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (assert (= (@ tptp.nat2 tptp.one_one_int) (@ tptp.suc tptp.zero_zero_nat)))
% 6.73/7.07 (assert (forall ((I2 tptp.int)) (= (= (@ tptp.nat2 I2) tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_int I2) tptp.zero_zero_int))))
% 6.73/7.07 (assert (forall ((Z3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Z3) tptp.zero_zero_int) (= (@ tptp.nat2 Z3) tptp.zero_zero_nat))))
% 6.73/7.07 (assert (forall ((K2 tptp.num)) (= (@ tptp.nat2 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K2))) tptp.zero_zero_nat)))
% 6.73/7.07 (assert (forall ((N tptp.nat)) (= (@ tptp.nat2 (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N))) tptp.zero_zero_nat)))
% 6.73/7.07 (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)))))
% 6.73/7.07 (assert (forall ((Z3 tptp.int)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.nat2 Z3)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z3))))
% 6.73/7.07 (assert (forall ((L tptp.int) (U tptp.int)) (= (@ tptp.finite_card_int (@ (@ tptp.set_or1266510415728281911st_int L) U)) (@ tptp.nat2 (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int U) L)) tptp.one_one_int)))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (assert (forall ((Z3 tptp.int)) (= (@ (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.nat2 Z3)) (@ (@ tptp.ord_less_int tptp.one_one_int) Z3))))
% 6.73/7.07 (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))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (assert (forall ((M2 tptp.nat) (N tptp.nat) (Q2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.bit_se2925701944663578781it_nat M2) Q2)) (@ (@ tptp.bit_se2925701944663578781it_nat N) Q2)))))
% 6.73/7.07 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.bit_se2925701944663578781it_nat N) M2)) M2)))
% 6.73/7.07 (assert (forall ((N tptp.nat) (K2 tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N))) (= (@ _let_1 (@ (@ tptp.times_times_int (@ _let_1 K2)) (@ _let_1 L))) (@ _let_1 (@ (@ tptp.times_times_int K2) L))))))
% 6.73/7.07 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat N) (@ tptp.bit_se2002935070580805687sk_nat N))))
% 6.73/7.07 (assert (= tptp.zero_zero_nat (@ tptp.nat2 tptp.zero_zero_int)))
% 6.73/7.07 (assert (forall ((M2 tptp.nat) (N tptp.nat) (K2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se2923211474154528505it_int M2) K2)) (@ (@ tptp.bit_se2923211474154528505it_int N) K2)))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (assert (forall ((W2 tptp.int) (Z3 tptp.int)) (= (@ tptp.nat2 (@ tptp.abs_abs_int (@ (@ tptp.times_times_int W2) Z3))) (@ (@ tptp.times_times_nat (@ tptp.nat2 (@ tptp.abs_abs_int W2))) (@ tptp.nat2 (@ tptp.abs_abs_int Z3))))))
% 6.73/7.07 (assert (= tptp.times_times_nat (lambda ((A5 tptp.nat) (B4 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int A5)) (@ tptp.semiri1314217659103216013at_int B4))))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (assert (forall ((W2 tptp.int) (Z3 tptp.int)) (=> (or (@ (@ tptp.ord_less_int tptp.zero_zero_int) W2) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z3)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.nat2 W2)) (@ tptp.nat2 Z3)) (@ (@ tptp.ord_less_eq_int W2) Z3)))))
% 6.73/7.07 (assert (forall ((M2 tptp.nat) (W2 tptp.int)) (let ((_let_1 (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) W2))) (= (= M2 (@ tptp.nat2 W2)) (and (=> _let_1 (= W2 (@ tptp.semiri1314217659103216013at_int M2))) (=> (not _let_1) (= M2 tptp.zero_zero_nat)))))))
% 6.73/7.07 (assert (forall ((W2 tptp.int) (M2 tptp.nat)) (let ((_let_1 (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) W2))) (= (= (@ tptp.nat2 W2) M2) (and (=> _let_1 (= W2 (@ tptp.semiri1314217659103216013at_int M2))) (=> (not _let_1) (= M2 tptp.zero_zero_nat)))))))
% 6.73/7.07 (assert (forall ((P2 (-> tptp.nat Bool)) (I2 tptp.int)) (= (@ P2 (@ tptp.nat2 I2)) (and (forall ((N4 tptp.nat)) (=> (= I2 (@ tptp.semiri1314217659103216013at_int N4)) (@ P2 N4))) (=> (@ (@ tptp.ord_less_int I2) tptp.zero_zero_int) (@ P2 tptp.zero_zero_nat))))))
% 6.73/7.07 (assert (forall ((K2 tptp.int) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K2) (= (@ (@ tptp.ord_less_eq_nat N) (@ tptp.nat2 K2)) (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int N)) K2)))))
% 6.73/7.07 (assert (forall ((Z3 tptp.int) (Z6 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z3) (= (@ tptp.nat2 (@ (@ tptp.times_times_int Z3) Z6)) (@ (@ tptp.times_times_nat (@ tptp.nat2 Z3)) (@ tptp.nat2 Z6))))))
% 6.73/7.07 (assert (= tptp.suc (lambda ((A5 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int A5)) tptp.one_one_int)))))
% 6.73/7.07 (assert (forall ((K2 tptp.int) (L tptp.int)) (@ (@ tptp.ord_less_eq_nat (@ tptp.nat2 (@ tptp.abs_abs_int (@ (@ tptp.plus_plus_int K2) L)))) (@ (@ tptp.plus_plus_nat (@ tptp.nat2 (@ tptp.abs_abs_int K2))) (@ tptp.nat2 (@ tptp.abs_abs_int L))))))
% 6.73/7.07 (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))))
% 6.73/7.07 (assert (forall ((K2 tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.abs_abs_int L))) (let ((_let_2 (@ tptp.abs_abs_int K2))) (= (@ (@ tptp.divide_divide_int _let_2) _let_1) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.divide_divide_nat (@ tptp.nat2 _let_2)) (@ tptp.nat2 _let_1))))))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (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))))))
% 6.73/7.07 (assert (forall ((K2 tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.abs_abs_int L))) (let ((_let_2 (@ tptp.abs_abs_int K2))) (= (@ (@ tptp.modulo_modulo_int _let_2) _let_1) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.modulo_modulo_nat (@ tptp.nat2 _let_2)) (@ tptp.nat2 _let_1))))))))
% 6.73/7.07 (assert (= (@ tptp.nat2 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.suc (@ tptp.suc tptp.zero_zero_nat))))
% 6.73/7.07 (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))))))
% 6.73/7.07 (assert (forall ((Z3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z3) (= (@ tptp.suc (@ tptp.nat2 Z3)) (@ tptp.nat2 (@ (@ tptp.plus_plus_int tptp.one_one_int) Z3))))))
% 6.73/7.07 (assert (forall ((Z3 tptp.int) (Z6 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Z3) tptp.zero_zero_int) (= (@ tptp.nat2 (@ (@ tptp.times_times_int Z3) Z6)) (@ (@ tptp.times_times_nat (@ tptp.nat2 (@ tptp.uminus_uminus_int Z3))) (@ tptp.nat2 (@ tptp.uminus_uminus_int Z6)))))))
% 6.73/7.07 (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))))))))
% 6.73/7.07 (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)))))
% 6.73/7.07 (assert (= (@ tptp.size_num tptp.one) tptp.zero_zero_nat))
% 6.73/7.07 (assert (forall ((Z6 tptp.int) (Z3 tptp.int)) (let ((_let_1 (@ (@ tptp.minus_minus_int Z3) Z6))) (let ((_let_2 (@ tptp.nat2 Z3))) (let ((_let_3 (@ (@ tptp.minus_minus_nat _let_2) (@ tptp.nat2 Z6)))) (let ((_let_4 (@ (@ tptp.ord_less_int Z6) tptp.zero_zero_int))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_int _let_1) tptp.zero_zero_int)) tptp.zero_zero_nat) (@ tptp.nat2 _let_1)))))))))))
% 6.73/7.07 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.bit_se2925701944663578781it_nat N) M2)) M2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) M2))))
% 6.73/7.07 (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))))
% 6.73/7.08 (assert (forall ((N tptp.nat) (K2 tptp.num)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.suc N)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 K2)))) (@ (@ tptp.times_times_int (@ (@ tptp.bit_se2923211474154528505it_int N) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K2)))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))))
% 6.73/7.08 (assert (forall ((Z3 tptp.int) (M2 tptp.nat)) (let ((_let_1 (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z3))) (= (@ (@ tptp.dvd_dvd_nat (@ tptp.nat2 Z3)) M2) (and (=> _let_1 (@ (@ tptp.dvd_dvd_int Z3) (@ tptp.semiri1314217659103216013at_int M2))) (=> (not _let_1) (= M2 tptp.zero_zero_nat)))))))
% 6.73/7.08 (assert (forall ((L tptp.num) (K2 tptp.num)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.numeral_numeral_nat L)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 K2)))) (@ (@ tptp.times_times_int (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.pred_numeral L)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K2)))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))))
% 6.73/7.08 (assert (forall ((N tptp.nat) (K2 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) K2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se2923211474154528505it_int N) K2)) (@ (@ tptp.minus_minus_int K2) _let_1)))))))
% 6.73/7.08 (assert (= tptp.bit_ri631733984087533419it_int (lambda ((N4 tptp.nat) (K3 tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N4))) (@ (@ tptp.minus_minus_int (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.suc N4)) (@ (@ tptp.plus_plus_int K3) _let_1))) _let_1)))))
% 6.73/7.08 (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))))))
% 6.73/7.08 (assert (forall ((X2 tptp.num)) (= (@ tptp.size_num (@ tptp.bit0 X2)) (@ (@ tptp.plus_plus_nat (@ tptp.size_num X2)) (@ tptp.suc tptp.zero_zero_nat)))))
% 6.73/7.08 (assert (forall ((L tptp.num) (K2 tptp.num)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.numeral_numeral_nat L)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 K2)))) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.pred_numeral L)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.inc K2))))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) tptp.one_one_int))))
% 6.73/7.08 (assert (forall ((N tptp.nat) (K2 tptp.num)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.suc N)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 K2)))) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.bit_se2923211474154528505it_int N) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.inc K2))))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) tptp.one_one_int))))
% 6.73/7.08 (assert (= tptp.bit_se1409905431419307370or_int (lambda ((K3 tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.uminus_uminus_int tptp.one_one_int))) (@ (@ (@ tptp.if_int (or (= K3 _let_2) (= L2 _let_2))) _let_2) (@ (@ (@ tptp.if_int (= K3 tptp.zero_zero_int)) L2) (@ (@ (@ tptp.if_int (= L2 tptp.zero_zero_int)) K3) (@ (@ tptp.plus_plus_int (@ (@ tptp.ord_max_int (@ (@ tptp.modulo_modulo_int K3) _let_1)) (@ (@ tptp.modulo_modulo_int L2) _let_1))) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se1409905431419307370or_int (@ (@ tptp.divide_divide_int K3) _let_1)) (@ (@ tptp.divide_divide_int L2) _let_1))))))))))))
% 6.73/7.08 (assert (= tptp.arctan (lambda ((X4 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 X4) (@ _let_2 (@ tptp.sqrt (@ _let_2 (@ (@ tptp.power_power_real X4) (@ tptp.numeral_numeral_nat _let_1)))))))))))))
% 6.73/7.08 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.sqrt A))) (= (@ (@ tptp.times_times_real _let_1) _let_1) (@ tptp.abs_abs_real A)))))
% 6.73/7.08 (assert (forall ((X tptp.real)) (= (@ tptp.sqrt (@ (@ tptp.times_times_real X) X)) (@ tptp.abs_abs_real X))))
% 6.73/7.08 (assert (forall ((K2 tptp.num)) (= (@ tptp.pred_numeral (@ tptp.inc K2)) (@ tptp.numeral_numeral_nat K2))))
% 6.73/7.08 (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)))))
% 6.73/7.08 (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)))))
% 6.73/7.08 (assert (forall ((P2 (-> tptp.num Bool)) (X tptp.num)) (=> (@ P2 tptp.one) (=> (forall ((X3 tptp.num)) (=> (@ P2 X3) (@ P2 (@ tptp.inc X3)))) (@ P2 X)))))
% 6.73/7.08 (assert (forall ((X tptp.num) (Y tptp.num)) (let ((_let_1 (@ tptp.plus_plus_num X))) (= (@ _let_1 (@ tptp.inc Y)) (@ tptp.inc (@ _let_1 Y))))))
% 6.73/7.08 (assert (= (@ tptp.inc tptp.one) (@ tptp.bit0 tptp.one)))
% 6.73/7.08 (assert (forall ((X tptp.num)) (= (@ tptp.inc (@ tptp.bit0 X)) (@ tptp.bit1 X))))
% 6.73/7.08 (assert (forall ((X tptp.num)) (= (@ tptp.inc (@ tptp.bit1 X)) (@ tptp.bit0 (@ tptp.inc X)))))
% 6.73/7.08 (assert (forall ((X tptp.num)) (= (@ (@ tptp.plus_plus_num X) tptp.one) (@ tptp.inc X))))
% 6.73/7.08 (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))))))
% 6.73/7.08 (assert (forall ((N tptp.num)) (= (@ tptp.inc (@ tptp.bitM N)) (@ tptp.bit0 N))))
% 6.73/7.08 (assert (forall ((N tptp.num)) (= (@ tptp.bitM (@ tptp.inc N)) (@ tptp.bit1 N))))
% 6.73/7.08 (assert (forall ((X tptp.num) (Y tptp.num)) (let ((_let_1 (@ tptp.times_times_num X))) (= (@ _let_1 (@ tptp.inc Y)) (@ (@ tptp.plus_plus_num (@ _let_1 Y)) X)))))
% 6.73/7.08 (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))))))))
% 6.73/7.08 (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)))))))))
% 6.73/7.08 (assert (= tptp.bit_se1409905431419307370or_int (lambda ((K3 tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_int _let_1))) (@ (@ tptp.plus_plus_int (@ tptp.zero_n2684676970156552555ol_int (or (not (@ _let_2 K3)) (not (@ _let_2 L2))))) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se1409905431419307370or_int (@ (@ tptp.divide_divide_int K3) _let_1)) (@ (@ tptp.divide_divide_int L2) _let_1)))))))))
% 6.73/7.08 (assert (= tptp.bit_ri631733984087533419it_int (lambda ((N4 tptp.nat) (K3 tptp.int)) (let ((_let_1 (@ tptp.suc N4))) (@ (@ tptp.minus_minus_int (@ (@ tptp.bit_se2923211474154528505it_int _let_1) K3)) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) _let_1)) (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.bit_se1146084159140164899it_int K3) N4))))))))
% 6.73/7.08 (assert (= (@ tptp.cis (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) tptp.one_one_complex))
% 6.73/7.08 (assert (forall ((N tptp.nat) (K2 tptp.int)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.suc N)) K2) (@ (@ 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 K2) N)))) (@ (@ tptp.bit_se2923211474154528505it_int N) K2)))))
% 6.73/7.08 (assert (= tptp.pi (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ tptp.the_real (lambda ((X4 tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4) (@ (@ tptp.ord_less_eq_real X4) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (= (@ tptp.cos_real X4) tptp.zero_zero_real)))))))
% 6.73/7.08 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 X)))) (= (@ (@ tptp.bit_se1412395901928357646or_nat _let_1) (@ tptp.suc tptp.zero_zero_nat)) _let_1))))
% 6.73/7.08 (assert (forall ((Y tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y)))) (= (@ (@ tptp.bit_se1412395901928357646or_nat (@ tptp.suc tptp.zero_zero_nat)) _let_1) _let_1))))
% 6.73/7.08 (assert (forall ((Y tptp.num)) (= (@ (@ tptp.bit_se1412395901928357646or_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Y))) (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y)))))
% 6.73/7.08 (assert (forall ((X tptp.num)) (= (@ (@ tptp.bit_se1412395901928357646or_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 X))) (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat (@ tptp.bit1 X)))))
% 6.73/7.08 (assert (forall ((W2 tptp.num) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 W2)))) (@ tptp.suc N)) (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int W2))) N))))
% 6.73/7.08 (assert (forall ((W2 tptp.num) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 W2)))) (@ tptp.suc N)) (not (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.numeral_numeral_int W2)) N)))))
% 6.73/7.08 (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)))))
% 6.73/7.08 (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)))))
% 6.73/7.08 (assert (forall ((M2 tptp.nat) (K2 tptp.int) (L tptp.int) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ (@ tptp.bit_concat_bit M2) K2) L)) N) (or (and (@ (@ tptp.ord_less_nat N) M2) (@ (@ tptp.bit_se1146084159140164899it_int K2) N)) (and (@ (@ tptp.ord_less_eq_nat M2) N) (@ (@ tptp.bit_se1146084159140164899it_int L) (@ (@ tptp.minus_minus_nat N) M2)))))))
% 6.73/7.08 (assert (forall ((K2 tptp.int)) (not (forall ((N3 tptp.nat)) (let ((_let_1 (@ tptp.bit_se1146084159140164899it_int K2))) (=> (forall ((M3 tptp.nat)) (let ((_let_1 (@ tptp.bit_se1146084159140164899it_int K2))) (=> (@ (@ tptp.ord_less_eq_nat N3) M3) (= (@ _let_1 M3) (@ _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)))))))))))
% 6.73/7.08 (assert (= tptp.bit_se7879613467334960850it_int (lambda ((N4 tptp.nat) (K3 tptp.int)) (@ (@ tptp.plus_plus_int K3) (@ (@ tptp.times_times_int (@ tptp.zero_n2684676970156552555ol_int (not (@ (@ tptp.bit_se1146084159140164899it_int K3) N4)))) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N4))))))
% 6.73/7.08 (assert (= tptp.bit_se4203085406695923979it_int (lambda ((N4 tptp.nat) (K3 tptp.int)) (@ (@ tptp.minus_minus_int K3) (@ (@ tptp.times_times_int (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.bit_se1146084159140164899it_int K3) N4))) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N4))))))
% 6.73/7.08 (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))))))
% 6.73/7.08 (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))))))
% 6.73/7.08 (assert (= tptp.bit_se1412395901928357646or_nat (lambda ((M6 tptp.nat) (N4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_nat _let_1))) (@ (@ tptp.plus_plus_nat (@ tptp.zero_n2687167440665602831ol_nat (or (not (@ _let_2 M6)) (not (@ _let_2 N4))))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se1412395901928357646or_nat (@ (@ tptp.divide_divide_nat M6) _let_1)) (@ (@ tptp.divide_divide_nat N4) _let_1)))))))))
% 6.73/7.08 (assert (= tptp.bit_se1412395901928357646or_nat (lambda ((M6 tptp.nat) (N4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_nat (= M6 tptp.zero_zero_nat)) N4) (@ (@ (@ tptp.if_nat (= N4 tptp.zero_zero_nat)) M6) (@ (@ tptp.plus_plus_nat (@ (@ tptp.ord_max_nat (@ (@ tptp.modulo_modulo_nat M6) _let_1)) (@ (@ tptp.modulo_modulo_nat N4) _let_1))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se1412395901928357646or_nat (@ (@ tptp.divide_divide_nat M6) _let_1)) (@ (@ tptp.divide_divide_nat N4) _let_1))))))))))
% 6.73/7.08 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ (@ tptp.bij_betw_nat_complex (lambda ((K3 tptp.nat)) (@ tptp.cis (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) (@ tptp.semiri5074537144036343181t_real K3))) (@ tptp.semiri5074537144036343181t_real N))))) (@ tptp.set_ord_lessThan_nat N)) (@ tptp.collect_complex (lambda ((Z4 tptp.complex)) (= (@ (@ tptp.power_power_complex Z4) N) tptp.one_one_complex)))))))
% 6.73/7.08 (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))))
% 6.73/7.08 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.suc N)))))
% 6.73/7.08 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.suc tptp.zero_zero_nat)) N) (= N tptp.zero_zero_nat))))
% 6.73/7.08 (assert (forall ((N tptp.num)) (not (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat N)))))
% 6.73/7.08 (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))))
% 6.73/7.08 (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))))
% 6.73/7.08 (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))))
% 6.73/7.08 (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))))
% 6.73/7.08 (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)))))))
% 6.73/7.08 (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)))))))
% 6.73/7.08 (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))))))
% 6.73/7.08 (assert (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex tptp.imaginary_unit))) (= (@ _let_1 (@ _let_1 X)) (@ tptp.uminus1482373934393186551omplex X)))))
% 6.73/7.08 (assert (forall ((Z3 tptp.complex) (N tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex N))) (= (@ (@ tptp.divide1717551699836669952omplex Z3) (@ (@ tptp.times_times_complex _let_1) tptp.imaginary_unit)) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.times_times_complex tptp.imaginary_unit) Z3))) _let_1)))))
% 6.73/7.08 (assert (forall ((X tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex X) tptp.imaginary_unit) (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex tptp.imaginary_unit)) X))))
% 6.73/7.08 (assert (= (@ (@ tptp.times_times_complex tptp.imaginary_unit) tptp.imaginary_unit) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))
% 6.73/7.08 (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)))))
% 6.73/7.08 (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)))))
% 6.73/7.08 (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)))))
% 6.73/7.08 (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)))))
% 6.73/7.08 (assert (forall ((W2 tptp.complex) (Z3 tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex tptp.imaginary_unit))) (= (= (@ _let_1 W2) Z3) (= W2 (@ tptp.uminus1482373934393186551omplex (@ _let_1 Z3)))))))
% 6.73/7.08 (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))))
% 6.73/7.08 (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))))
% 6.73/7.08 (assert (= tptp.bit_se6528837805403552850or_nat (lambda ((M6 tptp.nat) (N4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_nat (= M6 tptp.zero_zero_nat)) N4) (@ (@ (@ tptp.if_nat (= N4 tptp.zero_zero_nat)) M6) (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat M6) _let_1)) (@ (@ tptp.modulo_modulo_nat N4) _let_1))) _let_1)) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se6528837805403552850or_nat (@ (@ tptp.divide_divide_nat M6) _let_1)) (@ (@ tptp.divide_divide_nat N4) _let_1))))))))))
% 6.73/7.08 (assert (= tptp.bit_se6528837805403552850or_nat (lambda ((M6 tptp.nat) (N4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_nat _let_1))) (@ (@ tptp.plus_plus_nat (@ tptp.zero_n2687167440665602831ol_nat (not (= (not (@ _let_2 M6)) (not (@ _let_2 N4)))))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se6528837805403552850or_nat (@ (@ tptp.divide_divide_nat M6) _let_1)) (@ (@ tptp.divide_divide_nat N4) _let_1)))))))))
% 6.73/7.08 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X4 tptp.nat)) X4)) (@ (@ tptp.set_or4665077453230672383an_nat M2) 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 M2) (@ (@ tptp.minus_minus_nat M2) tptp.one_one_nat)))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 6.73/7.08 (assert (forall ((P2 (-> tptp.nat Bool))) (=> (@ P2 tptp.zero_zero_nat) (= (@ tptp.ord_Least_nat P2) tptp.zero_zero_nat))))
% 6.73/7.08 (assert (forall ((L tptp.nat) (U tptp.nat)) (@ tptp.finite_finite_nat (@ (@ tptp.set_or4665077453230672383an_nat L) U))))
% 6.73/7.08 (assert (forall ((L tptp.nat) (U tptp.nat)) (= (@ tptp.finite_card_nat (@ (@ tptp.set_or4665077453230672383an_nat L) U)) (@ (@ tptp.minus_minus_nat U) L))))
% 6.73/7.08 (assert (forall ((M2 tptp.nat)) (= (@ (@ tptp.set_or4665077453230672383an_nat M2) (@ tptp.suc M2)) (@ (@ tptp.insert_nat M2) tptp.bot_bot_set_nat))))
% 6.73/7.08 (assert (forall ((N tptp.nat) (P2 (-> tptp.nat Bool))) (= (forall ((M6 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M6) N) (@ P2 M6))) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N)) (@ P2 X4))))))
% 6.73/7.08 (assert (forall ((N tptp.nat) (P2 (-> tptp.nat Bool))) (= (exists ((M6 tptp.nat)) (and (@ (@ tptp.ord_less_nat M6) N) (@ P2 M6))) (exists ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N)) (@ P2 X4))))))
% 6.73/7.08 (assert (forall ((L tptp.nat) (U tptp.nat)) (= (@ (@ tptp.set_or4665077453230672383an_nat L) (@ tptp.suc U)) (@ (@ tptp.set_or1269000886237332187st_nat L) U))))
% 6.73/7.08 (assert (= tptp.set_ord_lessThan_nat (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat)))
% 6.73/7.08 (assert (forall ((M2 tptp.nat)) (= (@ (@ tptp.set_or4665077453230672383an_nat M2) tptp.zero_zero_nat) tptp.bot_bot_set_nat)))
% 6.73/7.08 (assert (forall ((P2 (-> tptp.nat Bool)) (N tptp.nat) (Q (-> tptp.nat Bool)) (M2 tptp.nat)) (=> (@ P2 N) (=> (@ Q M2) (=> (not (@ P2 tptp.zero_zero_nat)) (=> (forall ((K tptp.nat)) (= (@ P2 (@ tptp.suc K)) (@ Q K))) (= (@ tptp.ord_Least_nat P2) (@ tptp.suc (@ tptp.ord_Least_nat Q)))))))))
% 6.73/7.08 (assert (forall ((P2 (-> tptp.nat Bool)) (N tptp.nat)) (=> (@ P2 N) (=> (not (@ P2 tptp.zero_zero_nat)) (= (@ tptp.ord_Least_nat P2) (@ tptp.suc (@ tptp.ord_Least_nat (lambda ((M6 tptp.nat)) (@ P2 (@ tptp.suc M6))))))))))
% 6.73/7.08 (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))))))
% 6.73/7.08 (assert (forall ((N6 tptp.set_nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_set_nat N6) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N)) (@ tptp.finite_finite_nat N6))))
% 6.73/7.08 (assert (forall ((A4 tptp.set_nat) (K2 tptp.nat)) (let ((_let_1 (@ (@ tptp.set_or4665077453230672383an_nat K2) (@ (@ tptp.plus_plus_nat K2) (@ tptp.finite_card_nat A4))))) (=> (@ (@ tptp.ord_less_eq_set_nat A4) _let_1) (= A4 _let_1)))))
% 6.73/7.08 (assert (forall ((I2 tptp.nat) (J2 tptp.nat) (K2 tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat J2) K2))) (let ((_let_2 (@ tptp.set_or4665077453230672383an_nat I2))) (=> (@ (@ tptp.ord_less_eq_nat I2) J2) (= (@ _let_2 _let_1) (@ (@ tptp.sup_sup_set_nat (@ _let_2 J2)) (@ (@ tptp.set_or4665077453230672383an_nat J2) _let_1))))))))
% 6.73/7.08 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.set_or4665077453230672383an_nat M2))) (let ((_let_2 (@ _let_1 (@ tptp.suc N)))) (let ((_let_3 (@ (@ tptp.ord_less_eq_nat M2) N))) (and (=> _let_3 (= _let_2 (@ (@ tptp.insert_nat N) (@ _let_1 N)))) (=> (not _let_3) (= _let_2 tptp.bot_bot_set_nat))))))))
% 6.73/7.08 (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))))
% 6.73/7.08 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat tptp.suc) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N)) (@ tptp.semiri1408675320244567234ct_nat N))))
% 6.73/7.08 (assert (forall ((N6 tptp.set_nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_set_nat N6) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat N6)) N))))
% 6.73/7.08 (assert (forall ((S3 tptp.set_nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X4 tptp.nat)) X4)) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) (@ tptp.finite_card_nat S3)))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X4 tptp.nat)) X4)) S3))))
% 6.73/7.08 (assert (forall ((M2 tptp.nat) (K2 tptp.num)) (let ((_let_1 (@ tptp.set_or4665077453230672383an_nat M2))) (let ((_let_2 (@ _let_1 (@ tptp.numeral_numeral_nat K2)))) (let ((_let_3 (@ tptp.pred_numeral K2))) (let ((_let_4 (@ (@ tptp.ord_less_eq_nat M2) _let_3))) (and (=> _let_4 (= _let_2 (@ (@ tptp.insert_nat _let_3) (@ _let_1 _let_3)))) (=> (not _let_4) (= _let_2 tptp.bot_bot_set_nat)))))))))
% 6.73/7.08 (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)))))
% 6.73/7.08 (assert (= tptp.bit_se6526347334894502574or_int (lambda ((K3 tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_int _let_1))) (@ (@ tptp.plus_plus_int (@ tptp.zero_n2684676970156552555ol_int (not (= (not (@ _let_2 K3)) (not (@ _let_2 L2)))))) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se6526347334894502574or_int (@ (@ tptp.divide_divide_int K3) _let_1)) (@ (@ tptp.divide_divide_int L2) _let_1)))))))))
% 6.73/7.08 (assert (forall ((K2 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) K2)) (@ (@ tptp.minus_minus_nat (@ _let_1 K2)) tptp.one_one_nat)))))
% 6.73/7.08 (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 ((I3 tptp.nat) (J3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I3) J3) (=> (@ (@ tptp.ord_less_nat J3) N) (@ (@ tptp.ord_less_eq_nat (@ A I3)) (@ A J3))))) (=> (forall ((I3 tptp.nat) (J3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I3) J3) (=> (@ (@ tptp.ord_less_nat J3) N) (@ (@ tptp.ord_less_eq_nat (@ B J3)) (@ B I3))))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat N) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I tptp.nat)) (@ (@ tptp.times_times_nat (@ A I)) (@ B I)))) _let_1))) (@ (@ tptp.times_times_nat (@ (@ tptp.groups3542108847815614940at_nat A) _let_1)) (@ (@ tptp.groups3542108847815614940at_nat B) _let_1))))))))
% 6.73/7.08 (assert (= tptp.bit_se6526347334894502574or_int (lambda ((K3 tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.uminus_uminus_int tptp.one_one_int))) (@ (@ (@ tptp.if_int (= K3 _let_2)) (@ tptp.bit_ri7919022796975470100ot_int L2)) (@ (@ (@ tptp.if_int (= L2 _let_2)) (@ tptp.bit_ri7919022796975470100ot_int K3)) (@ (@ (@ tptp.if_int (= K3 tptp.zero_zero_int)) L2) (@ (@ (@ tptp.if_int (= L2 tptp.zero_zero_int)) K3) (@ (@ tptp.plus_plus_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ (@ tptp.modulo_modulo_int K3) _let_1)) (@ (@ tptp.modulo_modulo_int L2) _let_1)))) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se6526347334894502574or_int (@ (@ tptp.divide_divide_int K3) _let_1)) (@ (@ tptp.divide_divide_int L2) _let_1)))))))))))))
% 6.73/7.08 (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))
% 6.73/7.08 (assert (forall ((L tptp.int) (U tptp.int)) (@ tptp.finite_finite_int (@ (@ tptp.set_or4662586982721622107an_int L) U))))
% 6.73/7.08 (assert (forall ((L tptp.int) (U tptp.int)) (= (@ tptp.finite_card_int (@ (@ tptp.set_or4662586982721622107an_int L) U)) (@ tptp.nat2 (@ (@ tptp.minus_minus_int U) L)))))
% 6.73/7.08 (assert (= (@ tptp.exp_complex (@ (@ tptp.times_times_complex tptp.imaginary_unit) (@ tptp.real_V4546457046886955230omplex tptp.pi))) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))
% 6.73/7.08 (assert (= (@ tptp.exp_complex (@ (@ tptp.times_times_complex (@ tptp.real_V4546457046886955230omplex tptp.pi)) tptp.imaginary_unit)) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))
% 6.73/7.08 (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))
% 6.73/7.08 (assert (forall ((Z3 tptp.complex)) (exists ((A3 tptp.complex) (R4 tptp.real)) (= Z3 (@ (@ tptp.times_times_complex (@ tptp.real_V4546457046886955230omplex R4)) (@ tptp.exp_complex A3))))))
% 6.73/7.08 (assert (forall ((U tptp.int)) (@ tptp.finite_finite_int (@ (@ tptp.set_or4662586982721622107an_int tptp.zero_zero_int) U))))
% 6.73/7.08 (assert (forall ((L tptp.int) (U tptp.int)) (= (@ (@ tptp.set_or4662586982721622107an_int L) (@ (@ tptp.plus_plus_int U) tptp.one_one_int)) (@ (@ tptp.set_or1266510415728281911st_int L) U))))
% 6.73/7.08 (assert (forall ((X tptp.real) (Y tptp.real) (R3 tptp.real)) (= (@ (@ tptp.times_times_complex (@ (@ tptp.complex2 X) Y)) (@ tptp.real_V4546457046886955230omplex R3)) (@ (@ tptp.complex2 (@ (@ tptp.times_times_real X) R3)) (@ (@ tptp.times_times_real Y) R3)))))
% 6.73/7.08 (assert (forall ((R3 tptp.real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.times_times_real R3))) (= (@ (@ tptp.times_times_complex (@ tptp.real_V4546457046886955230omplex R3)) (@ (@ tptp.complex2 X) Y)) (@ (@ tptp.complex2 (@ _let_1 X)) (@ _let_1 Y))))))
% 6.73/7.08 (assert (= tptp.complex2 (lambda ((A5 tptp.real) (B4 tptp.real)) (@ (@ tptp.plus_plus_complex (@ tptp.real_V4546457046886955230omplex A5)) (@ (@ tptp.times_times_complex tptp.imaginary_unit) (@ tptp.real_V4546457046886955230omplex B4))))))
% 6.73/7.08 (assert (= tptp.cis (lambda ((B4 tptp.real)) (@ tptp.exp_complex (@ (@ tptp.times_times_complex tptp.imaginary_unit) (@ tptp.real_V4546457046886955230omplex B4))))))
% 6.73/7.08 (assert (forall ((U tptp.int)) (= (@ tptp.finite_card_int (@ (@ tptp.set_or4662586982721622107an_int tptp.zero_zero_int) U)) (@ tptp.nat2 U))))
% 6.73/7.08 (assert (forall ((R3 tptp.real)) (= (@ (@ tptp.times_times_complex (@ tptp.real_V4546457046886955230omplex R3)) tptp.imaginary_unit) (@ (@ tptp.complex2 tptp.zero_zero_real) R3))))
% 6.73/7.08 (assert (forall ((R3 tptp.real)) (= (@ (@ tptp.times_times_complex tptp.imaginary_unit) (@ tptp.real_V4546457046886955230omplex R3)) (@ (@ tptp.complex2 tptp.zero_zero_real) R3))))
% 6.73/7.08 (assert (forall ((Z3 tptp.complex)) (exists ((R4 tptp.real) (A3 tptp.real)) (= Z3 (@ (@ tptp.times_times_complex (@ tptp.real_V4546457046886955230omplex R4)) (@ (@ tptp.plus_plus_complex (@ tptp.real_V4546457046886955230omplex (@ tptp.cos_real A3))) (@ (@ tptp.times_times_complex tptp.imaginary_unit) (@ tptp.real_V4546457046886955230omplex (@ tptp.sin_real A3)))))))))
% 6.73/7.08 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 M2))) (@ 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 M2)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N)))))))
% 6.73/7.08 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 M2))) (@ 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 M2)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N)))))))
% 6.73/7.08 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit1 M2))) (@ 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 M2)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N)))))))
% 6.73/7.08 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int (@ tptp.bit0 M2))) (@ 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 M2)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N)))))))
% 6.73/7.08 (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)))
% 6.73/7.08 (assert (forall ((R3 tptp.real) (A tptp.real)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.times_times_complex (@ tptp.real_V4546457046886955230omplex R3)) (@ (@ 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 R3))))
% 6.73/7.08 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int (@ tptp.bit0 M2))) (@ 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 M2)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N))))))))
% 6.73/7.08 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit1 M2))) (@ 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 M2)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N))))))))
% 6.73/7.08 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int (@ tptp.bit1 M2))) (@ 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 M2)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N))))))))
% 6.73/7.08 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int (@ tptp.bit1 M2))) (@ 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 M2)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N))))))))
% 6.73/7.08 (assert (= tptp.bit_ri7919022796975470100ot_int (lambda ((K3 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (@ (@ tptp.plus_plus_int (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.dvd_dvd_int _let_1) K3))) (@ (@ tptp.times_times_int _let_1) (@ tptp.bit_ri7919022796975470100ot_int (@ (@ tptp.divide_divide_int K3) _let_1))))))))
% 6.73/7.08 (assert (= tptp.topolo4055970368930404560y_real (lambda ((X7 (-> tptp.nat tptp.real))) (forall ((J tptp.nat)) (exists ((M9 tptp.nat)) (forall ((M6 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M9) M6) (forall ((N4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M9) N4) (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ X7 M6)) (@ X7 N4)))) (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc J)))))))))))))
% 6.73/7.08 (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)))))
% 6.73/7.08 (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)))))
% 6.73/7.08 (assert (= tptp.unique4921790084139445826nteger (lambda ((L2 tptp.num) (__flatten_var_0 tptp.produc8923325533196201883nteger)) (@ (@ tptp.produc6916734918728496179nteger (lambda ((Q5 tptp.code_integer) (R tptp.code_integer)) (let ((_let_1 (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) Q5))) (let ((_let_2 (@ tptp.numera6620942414471956472nteger L2))) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (@ (@ tptp.ord_le3102999989581377725nteger _let_2) R)) (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.plus_p5714425477246183910nteger _let_1) tptp.one_one_Code_integer)) (@ (@ tptp.minus_8373710615458151222nteger R) _let_2))) (@ (@ tptp.produc1086072967326762835nteger _let_1) R)))))) __flatten_var_0))))
% 6.73/7.08 (assert (= tptp.divide1717551699836669952omplex (lambda ((A5 tptp.complex) (B4 tptp.complex)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex A5) (@ tptp.cnj B4))) (@ tptp.real_V4546457046886955230omplex (@ (@ tptp.power_power_real (@ tptp.real_V1022390504157884413omplex B4)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 6.73/7.08 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (=> (@ (@ tptp.accp_nat tptp.nat_list_decode_rel) _let_1) (= (@ tptp.nat_list_decode _let_1) (@ (@ tptp.produc2761476792215241774st_nat (lambda ((X4 tptp.nat) (Y4 tptp.nat)) (@ (@ tptp.cons_nat X4) (@ tptp.nat_list_decode Y4)))) (@ tptp.nat_prod_decode N)))))))
% 6.73/7.08 (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)))))
% 6.73/7.08 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (= (@ tptp.nat_list_decode X) (@ tptp.nat_list_decode Y)) (= X Y))))
% 6.73/7.08 (assert (forall ((K2 tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger K2) tptp.zero_z3403309356797280102nteger) tptp.zero_z3403309356797280102nteger)))
% 6.73/7.08 (assert (forall ((L tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger tptp.zero_z3403309356797280102nteger) L) tptp.zero_z3403309356797280102nteger)))
% 6.73/7.08 (assert (= tptp.zero_zero_nat tptp.zero_zero_nat))
% 6.73/7.08 (assert (forall ((N tptp.nat)) (= (@ tptp.nat_list_decode (@ tptp.suc N)) (@ (@ tptp.produc2761476792215241774st_nat (lambda ((X4 tptp.nat) (Y4 tptp.nat)) (@ (@ tptp.cons_nat X4) (@ tptp.nat_list_decode Y4)))) (@ tptp.nat_prod_decode N)))))
% 6.73/7.08 (assert (forall ((Z3 tptp.complex)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.times_times_complex Z3) (@ tptp.cnj Z3))) (@ (@ tptp.power_power_real (@ tptp.real_V1022390504157884413omplex Z3)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 6.73/7.08 (assert (forall ((Z3 tptp.complex)) (= (@ tptp.real_V4546457046886955230omplex (@ (@ tptp.power_power_real (@ tptp.real_V1022390504157884413omplex Z3)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.times_times_complex Z3) (@ tptp.cnj Z3)))))
% 6.73/7.08 (assert (= tptp.code_integer_of_int (lambda ((K3 tptp.int)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_int _let_1))) (let ((_let_3 (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger _let_1)) (@ tptp.code_integer_of_int (@ (@ tptp.divide_divide_int K3) _let_2))))) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.ord_less_int K3) tptp.zero_zero_int)) (@ tptp.uminus1351360451143612070nteger (@ tptp.code_integer_of_int (@ tptp.uminus_uminus_int K3)))) (@ (@ (@ tptp.if_Code_integer (= K3 tptp.zero_zero_int)) tptp.zero_z3403309356797280102nteger) (@ (@ (@ tptp.if_Code_integer (= (@ (@ tptp.modulo_modulo_int K3) _let_2) tptp.zero_zero_int)) _let_3) (@ (@ tptp.plus_p5714425477246183910nteger _let_3) tptp.one_one_Code_integer))))))))))
% 6.73/7.08 (assert (forall ((X tptp.nat) (Y tptp.list_nat)) (let ((_let_1 (@ tptp.accp_nat tptp.nat_list_decode_rel))) (=> (= (@ tptp.nat_list_decode X) Y) (=> (@ _let_1 X) (=> (=> (= X tptp.zero_zero_nat) (=> (= Y tptp.nil_nat) (not (@ _let_1 tptp.zero_zero_nat)))) (not (forall ((N3 tptp.nat)) (let ((_let_1 (@ tptp.suc N3))) (=> (= X _let_1) (=> (= Y (@ (@ tptp.produc2761476792215241774st_nat (lambda ((X4 tptp.nat) (Y4 tptp.nat)) (@ (@ tptp.cons_nat X4) (@ tptp.nat_list_decode Y4)))) (@ tptp.nat_prod_decode N3))) (not (@ (@ tptp.accp_nat tptp.nat_list_decode_rel) _let_1)))))))))))))
% 6.73/7.08 (assert (forall ((X tptp.nat) (Y tptp.list_nat)) (=> (= (@ tptp.nat_list_decode X) Y) (=> (=> (= X tptp.zero_zero_nat) (not (= Y tptp.nil_nat))) (not (forall ((N3 tptp.nat)) (=> (= X (@ tptp.suc N3)) (not (= Y (@ (@ tptp.produc2761476792215241774st_nat (lambda ((X4 tptp.nat) (Y4 tptp.nat)) (@ (@ tptp.cons_nat X4) (@ tptp.nat_list_decode Y4)))) (@ tptp.nat_prod_decode N3)))))))))))
% 6.73/7.08 (assert (forall ((Z3 tptp.complex) (W2 tptp.complex)) (let ((_let_1 (@ (@ tptp.times_times_complex Z3) (@ tptp.cnj W2)))) (= (@ (@ tptp.plus_plus_complex _let_1) (@ (@ tptp.times_times_complex (@ tptp.cnj Z3)) W2)) (@ tptp.real_V4546457046886955230omplex (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ tptp.re _let_1)))))))
% 6.73/7.08 (assert (forall ((X tptp.list_nat)) (=> (not (= X tptp.nil_nat)) (not (forall ((X3 tptp.nat) (Xs3 tptp.list_nat)) (not (= X (@ (@ tptp.cons_nat X3) Xs3))))))))
% 6.73/7.08 (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)))))
% 6.73/7.08 (assert (forall ((R3 tptp.real) (X tptp.complex)) (= (@ tptp.re (@ (@ tptp.real_V2046097035970521341omplex R3) X)) (@ (@ tptp.times_times_real R3) (@ tptp.re X)))))
% 6.73/7.08 (assert (= (@ tptp.nat_list_decode tptp.zero_zero_nat) tptp.nil_nat))
% 6.73/7.08 (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))))
% 6.73/7.08 (assert (= tptp.real_V1022390504157884413omplex (lambda ((Z4 tptp.complex)) (@ tptp.sqrt (@ tptp.re (@ (@ tptp.times_times_complex Z4) (@ tptp.cnj Z4)))))))
% 6.73/7.08 (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))))))))
% 6.73/7.08 (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))))
% 6.73/7.08 (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))))
% 6.73/7.08 (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))))))))
% 6.73/7.08 (assert (=> (@ (@ tptp.accp_nat tptp.nat_list_decode_rel) tptp.zero_zero_nat) (= (@ tptp.nat_list_decode tptp.zero_zero_nat) tptp.nil_nat)))
% 6.73/7.08 (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)))))
% 6.73/7.08 (assert (forall ((Z3 tptp.complex)) (= (@ (@ tptp.plus_plus_complex Z3) (@ tptp.cnj Z3)) (@ tptp.real_V4546457046886955230omplex (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ tptp.re Z3))))))
% 6.73/7.08 (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 ((X3 tptp.nat) (Xs3 tptp.list_nat)) (=> (= X (@ (@ tptp.cons_nat X3) Xs3)) (not (= Y (@ tptp.suc (@ tptp.nat_prod_encode (@ (@ tptp.product_Pair_nat_nat X3) (@ tptp.nat_list_encode Xs3)))))))))))))
% 6.73/7.08 (assert (= tptp.divide1717551699836669952omplex (lambda ((X4 tptp.complex) (Y4 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.im Y4))) (let ((_let_3 (@ tptp.re Y4))) (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 X4)))) (let ((_let_6 (@ tptp.times_times_real (@ tptp.im X4)))) (@ (@ 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)))))))))))
% 6.73/7.08 (assert (forall ((R3 tptp.complex) (Z3 tptp.complex)) (=> (@ (@ tptp.member_complex R3) tptp.real_V2521375963428798218omplex) (= (@ tptp.re (@ (@ tptp.divide1717551699836669952omplex R3) Z3)) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ tptp.re R3)) (@ tptp.re Z3))) (@ (@ tptp.power_power_real (@ tptp.real_V1022390504157884413omplex Z3)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 6.73/7.08 (assert (forall ((X tptp.list_nat)) (= (@ tptp.nat_list_decode (@ tptp.nat_list_encode X)) X)))
% 6.73/7.08 (assert (forall ((N tptp.nat)) (= (@ tptp.nat_list_encode (@ tptp.nat_list_decode N)) N)))
% 6.73/7.08 (assert (forall ((Z3 tptp.complex)) (= (@ tptp.im (@ (@ tptp.times_times_complex Z3) (@ tptp.cnj Z3))) tptp.zero_zero_real)))
% 6.73/7.08 (assert (forall ((Z3 tptp.complex)) (= (@ tptp.im (@ (@ tptp.times_times_complex tptp.imaginary_unit) Z3)) (@ tptp.re Z3))))
% 6.73/7.08 (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)))))))
% 6.73/7.08 (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)))))))
% 6.73/7.08 (assert (forall ((Z3 tptp.complex)) (= (@ tptp.re (@ (@ tptp.times_times_complex tptp.imaginary_unit) Z3)) (@ tptp.uminus_uminus_real (@ tptp.im Z3)))))
% 6.73/7.08 (assert (forall ((X tptp.list_nat) (Y tptp.list_nat)) (= (= (@ tptp.nat_list_encode X) (@ tptp.nat_list_encode Y)) (= X Y))))
% 6.73/7.08 (assert (forall ((R3 tptp.real) (X tptp.complex)) (= (@ tptp.im (@ (@ tptp.real_V2046097035970521341omplex R3) X)) (@ (@ tptp.times_times_real R3) (@ tptp.im X)))))
% 6.73/7.08 (assert (= (@ tptp.nat_list_encode tptp.nil_nat) tptp.zero_zero_nat))
% 6.73/7.08 (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))))))
% 6.73/7.08 (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))))))
% 6.73/7.08 (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))))
% 6.73/7.08 (assert (= tptp.real_V2046097035970521341omplex (lambda ((R tptp.real) (X4 tptp.complex)) (let ((_let_1 (@ tptp.times_times_real R))) (@ (@ tptp.complex2 (@ _let_1 (@ tptp.re X4))) (@ _let_1 (@ tptp.im X4)))))))
% 6.73/7.08 (assert (forall ((R3 tptp.complex) (Z3 tptp.complex)) (=> (@ (@ tptp.member_complex R3) tptp.real_V2521375963428798218omplex) (= (@ tptp.im (@ (@ tptp.divide1717551699836669952omplex R3) Z3)) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.re R3))) (@ tptp.im Z3))) (@ (@ tptp.power_power_real (@ tptp.real_V1022390504157884413omplex Z3)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 6.73/7.08 (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))))
% 6.73/7.08 (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))))))))
% 6.73/7.08 (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))))))))
% 6.73/7.08 (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))))
% 6.73/7.08 (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)))))
% 6.73/7.08 (assert (forall ((Z3 tptp.complex)) (= (@ tptp.re (@ tptp.exp_complex Z3)) (@ (@ tptp.times_times_real (@ tptp.exp_real (@ tptp.re Z3))) (@ tptp.cos_real (@ tptp.im Z3))))))
% 6.73/7.08 (assert (forall ((Z3 tptp.complex)) (= (@ tptp.im (@ tptp.exp_complex Z3)) (@ (@ tptp.times_times_real (@ tptp.exp_real (@ tptp.re Z3))) (@ tptp.sin_real (@ tptp.im Z3))))))
% 6.73/7.08 (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)))))))
% 6.73/7.08 (assert (= tptp.times_times_complex (lambda ((X4 tptp.complex) (Y4 tptp.complex)) (let ((_let_1 (@ tptp.re Y4))) (let ((_let_2 (@ tptp.times_times_real (@ tptp.im X4)))) (let ((_let_3 (@ tptp.im Y4))) (let ((_let_4 (@ tptp.times_times_real (@ tptp.re X4)))) (@ (@ 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))))))))))
% 6.73/7.08 (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)))))))))
% 6.73/7.08 (assert (= tptp.exp_complex (lambda ((Z4 tptp.complex)) (@ (@ tptp.times_times_complex (@ tptp.real_V4546457046886955230omplex (@ tptp.exp_real (@ tptp.re Z4)))) (@ tptp.cis (@ tptp.im Z4))))))
% 6.73/7.08 (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))))))
% 6.73/7.08 (assert (forall ((X tptp.nat) (Xs2 tptp.list_nat)) (= (@ tptp.nat_list_encode (@ (@ tptp.cons_nat X) Xs2)) (@ tptp.suc (@ tptp.nat_prod_encode (@ (@ tptp.product_Pair_nat_nat X) (@ tptp.nat_list_encode Xs2)))))))
% 6.73/7.08 (assert (forall ((Z3 tptp.complex)) (= (@ (@ tptp.minus_minus_complex Z3) (@ tptp.cnj Z3)) (@ (@ tptp.times_times_complex (@ tptp.real_V4546457046886955230omplex (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ tptp.im Z3)))) tptp.imaginary_unit))))
% 6.73/7.08 (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)))))))))
% 6.73/7.08 (assert (forall ((Z3 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.times_times_complex Z3) (@ tptp.cnj Z3)) (@ tptp.real_V4546457046886955230omplex (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real (@ tptp.re Z3)) _let_1)) (@ (@ tptp.power_power_real (@ tptp.im Z3)) _let_1)))))))
% 6.73/7.08 (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)))))))))
% 6.73/7.08 (assert (forall ((Z3 tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.abs_abs_real (@ tptp.re Z3))) (@ tptp.abs_abs_real (@ tptp.im Z3)))) (@ (@ tptp.times_times_real (@ tptp.sqrt (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.real_V1022390504157884413omplex Z3)))))
% 6.73/7.08 (assert (= tptp.csqrt (lambda ((Z4 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.re Z4))) (let ((_let_3 (@ tptp.real_V1022390504157884413omplex Z4))) (let ((_let_4 (@ tptp.im Z4))) (@ (@ 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)))))))))))
% 6.73/7.08 (assert (forall ((Z3 tptp.complex)) (let ((_let_1 (@ tptp.im Z3))) (= (@ tptp.im (@ tptp.csqrt Z3)) (@ (@ 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 Z3)) (@ tptp.re Z3))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))))))
% 6.73/7.08 (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))))))))))
% 6.73/7.08 (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)))))))
% 6.73/7.08 (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))))
% 6.73/7.08 (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))))
% 6.73/7.08 (assert (forall ((Nat tptp.nat)) (= (= Nat tptp.zero_zero_nat) (@ (@ (@ tptp.case_nat_o true) (lambda ((Uu3 tptp.nat)) false)) Nat))))
% 6.73/7.08 (assert (forall ((Nat tptp.nat)) (= (not (= Nat tptp.zero_zero_nat)) (@ (@ (@ tptp.case_nat_o false) (lambda ((Uu3 tptp.nat)) true)) Nat))))
% 6.73/7.08 (assert (forall ((M2 tptp.nat) (K2 tptp.int) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.bit_se545348938243370406it_int M2) K2)) N) (and (@ (@ tptp.ord_less_eq_nat M2) N) (@ (@ tptp.bit_se1146084159140164899it_int K2) (@ (@ tptp.minus_minus_nat N) M2))))))
% 6.73/7.08 (assert (forall ((M2 tptp.nat) (Q2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ (@ tptp.bit_se547839408752420682it_nat M2) Q2)) N) (and (@ (@ tptp.ord_less_eq_nat M2) N) (@ (@ tptp.bit_se1148574629649215175it_nat Q2) (@ (@ tptp.minus_minus_nat N) M2))))))
% 6.73/7.08 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M2)) N) (@ (@ (@ tptp.case_nat_o false) (@ tptp.ord_less_eq_nat M2)) N))))
% 6.73/7.08 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (= (@ (@ tptp.ord_max_nat M2) _let_1) (@ (@ (@ tptp.case_nat_nat _let_1) (lambda ((M7 tptp.nat)) (@ tptp.suc (@ (@ tptp.ord_max_nat M7) N)))) M2)))))
% 6.73/7.08 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (= (@ (@ tptp.ord_max_nat _let_1) M2) (@ (@ (@ tptp.case_nat_nat _let_1) (lambda ((M7 tptp.nat)) (@ tptp.suc (@ (@ tptp.ord_max_nat N) M7)))) M2)))))
% 6.73/7.08 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat M2))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ (@ tptp.case_nat_nat tptp.zero_zero_nat) (lambda ((K3 tptp.nat)) K3)) (@ _let_1 N))))))
% 6.73/7.08 (assert (= tptp.bit_se547839408752420682it_nat (lambda ((N4 tptp.nat) (M6 tptp.nat)) (@ (@ tptp.times_times_nat M6) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N4)))))
% 6.73/7.08 (assert (= tptp.bit_se545348938243370406it_int (lambda ((N4 tptp.nat) (K3 tptp.int)) (@ (@ tptp.times_times_int K3) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N4)))))
% 6.73/7.08 (assert (= tptp.pred (@ (@ tptp.case_nat_nat tptp.zero_zero_nat) (lambda ((X24 tptp.nat)) X24))))
% 6.73/7.08 (assert (forall ((K2 tptp.num)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat K2)) (@ tptp.product_snd_nat_nat (@ (@ tptp.unique5055182867167087721od_nat tptp.one) K2)))))
% 6.73/7.08 (assert (forall ((K2 tptp.num)) (= (@ (@ tptp.divide_divide_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat K2)) (@ tptp.product_fst_nat_nat (@ (@ tptp.unique5055182867167087721od_nat tptp.one) K2)))))
% 6.73/7.08 (assert (= tptp.code_nat_of_integer (lambda ((K3 tptp.code_integer)) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_le3102999989581377725nteger K3) tptp.zero_z3403309356797280102nteger)) tptp.zero_zero_nat) (@ (@ tptp.produc1555791787009142072er_nat (lambda ((L2 tptp.code_integer) (J tptp.code_integer)) (let ((_let_1 (@ tptp.code_nat_of_integer L2))) (let ((_let_2 (@ (@ tptp.plus_plus_nat _let_1) _let_1))) (@ (@ (@ tptp.if_nat (= J tptp.zero_z3403309356797280102nteger)) _let_2) (@ (@ tptp.plus_plus_nat _let_2) tptp.one_one_nat)))))) (@ (@ tptp.code_divmod_integer K3) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))))))
% 6.73/7.08 (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)))))
% 6.73/7.08 (assert (forall ((N tptp.nat) (K2 tptp.num)) (= (@ (@ tptp.bit_se8568078237143864401it_int (@ tptp.suc N)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 K2)))) (@ (@ tptp.bit_se8568078237143864401it_int N) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K2))))))
% 6.73/7.08 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ tptp.product_fst_nat_nat (@ (@ tptp.divmod_nat M2) N)) (@ (@ tptp.divide_divide_nat M2) N))))
% 6.73/7.08 (assert (forall ((K2 tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger K2) tptp.zero_z3403309356797280102nteger) (= (@ tptp.code_nat_of_integer K2) tptp.zero_zero_nat))))
% 6.73/7.08 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ tptp.product_snd_nat_nat (@ (@ tptp.divmod_nat M2) N)) (@ (@ tptp.modulo_modulo_nat M2) N))))
% 6.73/7.08 (assert (forall ((N tptp.nat) (K2 tptp.num)) (= (@ (@ tptp.bit_se8568078237143864401it_int (@ tptp.suc N)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 K2)))) (@ (@ tptp.bit_se8568078237143864401it_int N) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.inc K2)))))))
% 6.73/7.08 (assert (= (@ tptp.code_nat_of_integer tptp.zero_z3403309356797280102nteger) tptp.zero_zero_nat))
% 6.73/7.08 (assert (= tptp.code_int_of_integer (lambda ((K3 tptp.code_integer)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_le6747313008572928689nteger K3) tptp.zero_z3403309356797280102nteger)) (@ tptp.uminus_uminus_int (@ tptp.code_int_of_integer (@ tptp.uminus1351360451143612070nteger K3)))) (@ (@ (@ tptp.if_int (= K3 tptp.zero_z3403309356797280102nteger)) tptp.zero_zero_int) (@ (@ tptp.produc1553301316500091796er_int (lambda ((L2 tptp.code_integer) (J tptp.code_integer)) (let ((_let_1 (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.code_int_of_integer L2)))) (@ (@ (@ tptp.if_int (= J tptp.zero_z3403309356797280102nteger)) _let_1) (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int))))) (@ (@ tptp.code_divmod_integer K3) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))))))))
% 6.73/7.08 (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)))))
% 6.73/7.08 (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)))))))))))
% 6.73/7.08 (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))))))))))))))
% 6.73/7.08 (assert (= tptp.bezw (lambda ((X4 tptp.nat) (Y4 tptp.nat)) (let ((_let_1 (@ (@ tptp.bezw Y4) (@ (@ tptp.modulo_modulo_nat X4) Y4)))) (let ((_let_2 (@ tptp.product_snd_int_int _let_1))) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (= Y4 tptp.zero_zero_nat)) (@ (@ tptp.product_Pair_int_int tptp.one_one_int) tptp.zero_zero_int)) (@ (@ tptp.product_Pair_int_int _let_2) (@ (@ tptp.minus_minus_int (@ tptp.product_fst_int_int _let_1)) (@ (@ tptp.times_times_int _let_2) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.divide_divide_nat X4) Y4)))))))))))
% 6.73/7.08 (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))))))))
% 6.73/7.08 (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)))))))
% 6.73/7.08 (assert (forall ((M2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int M2)) (@ tptp.uminus_uminus_int _let_1)) (@ tptp.uminus_uminus_int (@ (@ tptp.adjust_mod _let_1) (@ tptp.product_snd_int_int (@ (@ tptp.unique5052692396658037445od_int M2) N))))))))
% 6.73/7.08 (assert (forall ((M2 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 M2))) _let_1) (@ (@ tptp.adjust_mod _let_1) (@ tptp.product_snd_int_int (@ (@ tptp.unique5052692396658037445od_int M2) N)))))))
% 6.73/7.08 (assert (= tptp.adjust_mod (lambda ((L2 tptp.int) (R tptp.int)) (@ (@ (@ tptp.if_int (= R tptp.zero_zero_int)) tptp.zero_zero_int) (@ (@ tptp.minus_minus_int L2) R)))))
% 6.73/7.08 (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)))))))))))
% 6.73/7.08 (assert (forall ((L tptp.int) (U tptp.int)) (= (@ tptp.finite_card_int (@ (@ tptp.set_or5832277885323065728an_int L) U)) (@ tptp.nat2 (@ (@ tptp.minus_minus_int U) (@ (@ tptp.plus_plus_int L) tptp.one_one_int))))))
% 6.73/7.08 (assert (forall ((L tptp.int) (U tptp.int)) (@ tptp.finite_finite_int (@ (@ tptp.set_or5832277885323065728an_int L) U))))
% 6.73/7.08 (assert (forall ((L tptp.int) (U tptp.int)) (= (@ (@ tptp.set_or4662586982721622107an_int (@ (@ tptp.plus_plus_int L) tptp.one_one_int)) U) (@ (@ tptp.set_or5832277885323065728an_int L) U))))
% 6.73/7.08 (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))))))))))
% 6.73/7.08 (assert (forall ((L tptp.nat) (U tptp.nat)) (@ tptp.finite_finite_nat (@ (@ tptp.set_or5834768355832116004an_nat L) U))))
% 6.73/7.08 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.compow_nat_nat N) tptp.suc) (@ tptp.plus_plus_nat N))))
% 6.73/7.08 (assert (forall ((L tptp.nat) (U tptp.nat)) (= (@ tptp.finite_card_nat (@ (@ tptp.set_or5834768355832116004an_nat L) U)) (@ (@ tptp.minus_minus_nat U) (@ tptp.suc L)))))
% 6.73/7.08 (assert (forall ((L tptp.nat) (U tptp.nat)) (= (@ (@ tptp.set_or4665077453230672383an_nat (@ tptp.suc L)) U) (@ (@ tptp.set_or5834768355832116004an_nat L) U))))
% 6.73/7.08 (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)))))
% 6.73/7.08 (assert (forall ((C2 tptp.complex) (N tptp.nat)) (=> (not (= C2 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 C2)))) (@ tptp.cis (@ (@ tptp.divide_divide_real (@ tptp.arg C2)) (@ tptp.semiri5074537144036343181t_real N)))))) (@ tptp.collect_complex (lambda ((Z4 tptp.complex)) (= (@ (@ tptp.power_power_complex Z4) N) tptp.one_one_complex)))) (@ tptp.collect_complex (lambda ((Z4 tptp.complex)) (= (@ (@ tptp.power_power_complex Z4) N) C2))))))))
% 6.73/7.08 (assert (@ (@ (@ (@ tptp.semila1623282765462674594er_nat tptp.ord_max_nat) tptp.zero_zero_nat) (lambda ((X4 tptp.nat) (Y4 tptp.nat)) (@ (@ tptp.ord_less_eq_nat Y4) X4))) (lambda ((X4 tptp.nat) (Y4 tptp.nat)) (@ (@ tptp.ord_less_nat Y4) X4))))
% 6.73/7.08 (assert (forall ((X tptp.real)) (= (@ (@ tptp.root (@ tptp.suc tptp.zero_zero_nat)) X) X)))
% 6.73/7.08 (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))))))
% 6.73/7.08 (assert (forall ((X tptp.real)) (= (@ (@ tptp.root tptp.zero_zero_nat) X) tptp.zero_zero_real)))
% 6.73/7.08 (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)))))
% 6.73/7.08 (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))))))
% 6.73/7.08 (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))))))
% 6.73/7.08 (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))))
% 6.73/7.08 (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)))))
% 6.73/7.08 (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))))))
% 6.73/7.08 (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)))))
% 6.73/7.08 (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))))))
% 6.73/7.08 (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)))))
% 6.73/7.08 (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))))))
% 6.73/7.08 (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)))))
% 6.73/7.08 (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))))))
% 6.73/7.08 (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)))))
% 6.73/7.08 (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)))))
% 6.73/7.08 (assert (forall ((M2 tptp.nat) (N tptp.nat) (X tptp.real)) (= (@ (@ tptp.root (@ (@ tptp.times_times_nat M2) N)) X) (@ (@ tptp.root M2) (@ (@ tptp.root N) X)))))
% 6.73/7.08 (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))))))
% 6.73/7.08 (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)))))))
% 6.73/7.08 (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)))))))
% 6.73/7.08 (assert (forall ((N tptp.nat) (X tptp.real) (K2 tptp.nat)) (let ((_let_1 (@ tptp.root N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ _let_1 (@ (@ tptp.power_power_real X) K2)) (@ (@ tptp.power_power_real (@ _let_1 X)) K2))))))
% 6.73/7.08 (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)))))))
% 6.73/7.08 (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)))))
% 6.73/7.08 (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)))))))
% 6.73/7.08 (assert (forall ((N tptp.nat) (N6 tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_nat N) N6) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X) (@ (@ tptp.ord_less_real (@ (@ tptp.root N6) X)) (@ (@ tptp.root N) X)))))))
% 6.73/7.08 (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)))))
% 6.73/7.08 (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))))))
% 6.73/7.08 (assert (forall ((N tptp.nat) (N6 tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_nat N) N6) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_real X) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ (@ tptp.root N) X)) (@ (@ tptp.root N6) X))))))))
% 6.73/7.08 (assert (forall ((N tptp.nat) (N6 tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_eq_nat N) N6) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.root N6) X)) (@ (@ tptp.root N) X)))))))
% 6.73/7.08 (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)))))
% 6.73/7.08 (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))))))
% 6.73/7.08 (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)))))
% 6.73/7.08 (assert (forall ((N tptp.nat) (N6 tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_eq_nat N) N6) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.root N) X)) (@ (@ tptp.root N6) X))))))))
% 6.73/7.08 (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)))))
% 6.73/7.08 (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))))
% 6.73/7.08 (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)))))))
% 6.73/7.08 (assert (forall ((N tptp.nat) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.log2 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))))))))
% 6.73/7.08 (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.log2 (@ (@ tptp.root N) B)) X) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.log2 B) X)))))))
% 6.73/7.08 (assert (forall ((P2 (-> tptp.real Bool)) (N tptp.nat) (X tptp.real)) (= (@ P2 (@ (@ tptp.root N) X)) (and (=> (= N tptp.zero_zero_nat) (@ P2 tptp.zero_zero_real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (forall ((Y4 tptp.real)) (=> (= (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real Y4)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real Y4)) N)) X) (@ P2 Y4))))))))
% 6.73/7.08 (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))))))))
% 6.73/7.08 (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))))))
% 6.73/7.08 (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))))))))
% 6.73/7.08 (assert (forall ((A tptp.real) (B tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.powr_real B))) (= (@ (@ tptp.divide_divide_real A) (@ _let_1 C2)) (@ (@ tptp.times_times_real A) (@ _let_1 (@ tptp.uminus_uminus_real C2)))))))
% 6.73/7.08 (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))))))
% 6.73/7.08 (assert (forall ((X tptp.real) (B tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.log2 B))) (=> (not (= X tptp.zero_zero_real)) (= (@ _let_1 (@ (@ tptp.powr_real X) Y)) (@ (@ tptp.times_times_real Y) (@ _let_1 X)))))))
% 6.73/7.08 (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)))))))
% 6.73/7.08 (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))))))
% 6.73/7.08 (assert (forall ((B tptp.real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.log2 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)))))))))))
% 6.73/7.08 (assert (forall ((B tptp.real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.log2 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))))))))))
% 6.73/7.08 (assert (forall ((B tptp.real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.log2 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))))))))))))
% 6.73/7.08 (assert (forall ((Xa2 tptp.product_prod_nat_nat) (X tptp.product_prod_nat_nat)) (= (@ (@ tptp.times_times_int (@ tptp.abs_Integ Xa2)) (@ tptp.abs_Integ X)) (@ tptp.abs_Integ (@ (@ (@ tptp.produc27273713700761075at_nat (lambda ((X4 tptp.nat) (Y4 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((U2 tptp.nat) (V3 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat Y4))) (let ((_let_2 (@ tptp.times_times_nat X4))) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat (@ _let_2 U2)) (@ _let_1 V3))) (@ (@ tptp.plus_plus_nat (@ _let_2 V3)) (@ _let_1 U2))))))) __flatten_var_0))) Xa2) X)))))
% 6.73/7.08 (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)))))))
% 6.73/7.08 (assert (forall ((Q2 tptp.num)) (= (@ tptp.num_of_nat (@ tptp.numeral_numeral_nat Q2)) Q2)))
% 6.73/7.08 (assert (forall ((Z3 tptp.int)) (not (forall ((X3 tptp.nat) (Y3 tptp.nat)) (not (= Z3 (@ tptp.abs_Integ (@ (@ tptp.product_Pair_nat_nat X3) Y3))))))))
% 6.73/7.08 (assert (= (@ tptp.num_of_nat tptp.zero_zero_nat) tptp.one))
% 6.73/7.08 (assert (= tptp.zero_zero_int (@ tptp.abs_Integ (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) tptp.zero_zero_nat))))
% 6.73/7.08 (assert (= tptp.semiri1314217659103216013at_int (lambda ((N4 tptp.nat)) (@ tptp.abs_Integ (@ (@ tptp.product_Pair_nat_nat N4) tptp.zero_zero_nat)))))
% 6.73/7.08 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.numeral_numeral_nat (@ tptp.num_of_nat N)) N))))
% 6.73/7.08 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) tptp.one_one_nat) (= (@ tptp.num_of_nat N) tptp.one))))
% 6.73/7.08 (assert (forall ((X tptp.product_prod_nat_nat)) (= (@ tptp.uminus_uminus_int (@ tptp.abs_Integ X)) (@ tptp.abs_Integ (@ (@ tptp.produc2626176000494625587at_nat (lambda ((X4 tptp.nat) (Y4 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat Y4) X4))) X)))))
% 6.73/7.08 (assert (= tptp.one_one_int (@ tptp.abs_Integ (@ (@ tptp.product_Pair_nat_nat tptp.one_one_nat) tptp.zero_zero_nat))))
% 6.73/7.08 (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))))))
% 6.73/7.08 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 M2) (=> (@ _let_1 N) (= (@ tptp.num_of_nat (@ (@ tptp.plus_plus_nat M2) N)) (@ (@ tptp.plus_plus_num (@ tptp.num_of_nat M2)) (@ tptp.num_of_nat N))))))))
% 6.73/7.08 (assert (forall ((Xa2 tptp.product_prod_nat_nat) (X tptp.product_prod_nat_nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.abs_Integ Xa2)) (@ tptp.abs_Integ X)) (@ (@ (@ tptp.produc8739625826339149834_nat_o (lambda ((X4 tptp.nat) (Y4 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc6081775807080527818_nat_o (lambda ((U2 tptp.nat) (V3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat X4) V3)) (@ (@ tptp.plus_plus_nat U2) Y4)))) __flatten_var_0))) Xa2) X))))
% 6.73/7.08 (assert (forall ((Xa2 tptp.product_prod_nat_nat) (X tptp.product_prod_nat_nat)) (= (@ (@ tptp.plus_plus_int (@ tptp.abs_Integ Xa2)) (@ tptp.abs_Integ X)) (@ tptp.abs_Integ (@ (@ (@ tptp.produc27273713700761075at_nat (lambda ((X4 tptp.nat) (Y4 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((U2 tptp.nat) (V3 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat X4) U2)) (@ (@ tptp.plus_plus_nat Y4) V3)))) __flatten_var_0))) Xa2) X)))))
% 6.73/7.08 (assert (forall ((Xa2 tptp.product_prod_nat_nat) (X tptp.product_prod_nat_nat)) (= (@ (@ tptp.minus_minus_int (@ tptp.abs_Integ Xa2)) (@ tptp.abs_Integ X)) (@ tptp.abs_Integ (@ (@ (@ tptp.produc27273713700761075at_nat (lambda ((X4 tptp.nat) (Y4 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((U2 tptp.nat) (V3 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat X4) V3)) (@ (@ tptp.plus_plus_nat Y4) U2)))) __flatten_var_0))) Xa2) X)))))
% 6.73/7.08 (assert (forall ((K2 tptp.nat)) (let ((_let_1 (@ tptp.suc K2))) (= (@ tptp.linord2614967742042102400et_nat (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.append_nat (@ tptp.linord2614967742042102400et_nat (@ tptp.set_ord_atMost_nat K2))) (@ (@ tptp.cons_nat _let_1) tptp.nil_nat))))))
% 6.73/7.08 (assert (forall ((K2 tptp.nat)) (= (@ tptp.linord2614967742042102400et_nat (@ tptp.set_ord_lessThan_nat (@ tptp.suc K2))) (@ (@ tptp.append_nat (@ tptp.linord2614967742042102400et_nat (@ tptp.set_ord_lessThan_nat K2))) (@ (@ tptp.cons_nat K2) tptp.nil_nat)))))
% 6.73/7.08 (assert (forall ((I2 tptp.nat) (J2 tptp.nat)) (let ((_let_1 (@ tptp.suc I2))) (=> (@ (@ tptp.ord_less_nat _let_1) J2) (= (@ tptp.linord2614967742042102400et_nat (@ (@ tptp.set_or5834768355832116004an_nat I2) J2)) (@ (@ tptp.cons_nat _let_1) (@ tptp.linord2614967742042102400et_nat (@ (@ tptp.set_or5834768355832116004an_nat _let_1) J2))))))))
% 6.73/7.08 (assert (forall ((N tptp.nat) (J2 tptp.nat) (I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) (@ (@ tptp.minus_minus_nat J2) (@ tptp.suc I2))) (= (@ (@ tptp.nth_nat (@ tptp.linord2614967742042102400et_nat (@ (@ tptp.set_or5834768355832116004an_nat I2) J2))) N) (@ tptp.suc (@ (@ tptp.plus_plus_nat I2) N))))))
% 6.73/7.08 (assert (= tptp.ord_less_eq_int (lambda ((X4 tptp.int) (Xa3 tptp.int)) (@ (@ (@ tptp.produc8739625826339149834_nat_o (lambda ((Y4 tptp.nat) (Z4 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc6081775807080527818_nat_o (lambda ((U2 tptp.nat) (V3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat Y4) V3)) (@ (@ tptp.plus_plus_nat U2) Z4)))) __flatten_var_0))) (@ tptp.rep_Integ X4)) (@ tptp.rep_Integ Xa3)))))
% 6.73/7.08 (assert (forall ((C2 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 C2) Y))) (and (=> _let_3 (= (@ (@ tptp.image_nat_nat (lambda ((I tptp.nat)) (@ (@ tptp.minus_minus_nat I) C2))) _let_1) (@ (@ tptp.set_or4665077453230672383an_nat (@ (@ tptp.minus_minus_nat X) C2)) (@ (@ tptp.minus_minus_nat Y) C2)))) (=> (not _let_3) (and (=> _let_2 (= (@ (@ tptp.image_nat_nat (lambda ((I tptp.nat)) (@ (@ tptp.minus_minus_nat I) C2))) _let_1) (@ (@ tptp.insert_nat tptp.zero_zero_nat) tptp.bot_bot_set_nat))) (=> (not _let_2) (= (@ (@ tptp.image_nat_nat (lambda ((I tptp.nat)) (@ (@ tptp.minus_minus_nat I) C2))) _let_1) tptp.bot_bot_set_nat))))))))))
% 6.73/7.08 (assert (forall ((M5 tptp.set_nat) (N6 tptp.set_nat)) (= (@ (@ (@ tptp.bij_betw_nat_nat tptp.suc) M5) N6) (= (@ (@ tptp.image_nat_nat tptp.suc) M5) N6))))
% 6.73/7.08 (assert (forall ((I2 tptp.nat) (J2 tptp.nat)) (= (@ (@ tptp.image_nat_nat tptp.suc) (@ (@ tptp.set_or1269000886237332187st_nat I2) J2)) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc I2)) (@ tptp.suc J2)))))
% 6.73/7.08 (assert (forall ((I2 tptp.nat) (J2 tptp.nat)) (= (@ (@ tptp.image_nat_nat tptp.suc) (@ (@ tptp.set_or4665077453230672383an_nat I2) J2)) (@ (@ tptp.set_or4665077453230672383an_nat (@ tptp.suc I2)) (@ tptp.suc J2)))))
% 6.73/7.08 (assert (forall ((A4 tptp.set_nat)) (not (@ (@ tptp.member_nat tptp.zero_zero_nat) (@ (@ tptp.image_nat_nat tptp.suc) A4)))))
% 6.73/7.08 (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))))
% 6.73/7.08 (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)))))
% 6.73/7.08 (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)))))))
% 6.73/7.08 (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)))))))
% 6.73/7.08 (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))))))
% 6.73/7.08 (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))))))
% 6.73/7.08 (assert (forall ((N tptp.nat) (J2 tptp.nat) (I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) (@ (@ tptp.minus_minus_nat J2) I2)) (= (@ (@ tptp.nth_nat (@ tptp.linord2614967742042102400et_nat (@ (@ tptp.set_or6659071591806873216st_nat I2) J2))) N) (@ tptp.suc (@ (@ tptp.plus_plus_nat I2) N))))))
% 6.73/7.08 (assert (= tptp.uminus_uminus_int (@ (@ (@ tptp.map_fu3667384564859982768at_int tptp.rep_Integ) tptp.abs_Integ) (@ tptp.produc2626176000494625587at_nat (lambda ((X4 tptp.nat) (Y4 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat Y4) X4))))))
% 6.73/7.08 (assert (forall ((P tptp.rat)) (= (@ tptp.quotient_of (@ tptp.inverse_inverse_rat P)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((A5 tptp.int) (B4 tptp.int)) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (= A5 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 A5)) B4)) (@ tptp.abs_abs_int A5))))) (@ tptp.quotient_of P)))))
% 6.73/7.08 (assert (forall ((L tptp.nat) (U tptp.nat)) (@ tptp.finite_finite_nat (@ (@ tptp.set_or6659071591806873216st_nat L) U))))
% 6.73/7.08 (assert (forall ((L tptp.nat) (U tptp.nat)) (= (@ tptp.finite_card_nat (@ (@ tptp.set_or6659071591806873216st_nat L) U)) (@ (@ tptp.minus_minus_nat U) L))))
% 6.73/7.08 (assert (= tptp.divide_divide_rat (lambda ((Q5 tptp.rat) (R tptp.rat)) (@ (@ tptp.times_times_rat Q5) (@ tptp.inverse_inverse_rat R)))))
% 6.73/7.08 (assert (= tptp.ord_less_eq_rat (lambda ((P5 tptp.rat) (Q5 tptp.rat)) (@ (@ tptp.produc4947309494688390418_int_o (lambda ((A5 tptp.int) (C3 tptp.int)) (@ (@ tptp.produc4947309494688390418_int_o (lambda ((B4 tptp.int) (D2 tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A5) D2)) (@ (@ tptp.times_times_int C3) B4)))) (@ tptp.quotient_of Q5)))) (@ tptp.quotient_of P5)))))
% 6.73/7.08 (assert (= tptp.ord_less_rat (lambda ((P5 tptp.rat) (Q5 tptp.rat)) (@ (@ tptp.produc4947309494688390418_int_o (lambda ((A5 tptp.int) (C3 tptp.int)) (@ (@ tptp.produc4947309494688390418_int_o (lambda ((B4 tptp.int) (D2 tptp.int)) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A5) D2)) (@ (@ tptp.times_times_int C3) B4)))) (@ tptp.quotient_of Q5)))) (@ tptp.quotient_of P5)))))
% 6.73/7.08 (assert (forall ((L tptp.nat) (U tptp.nat)) (= (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc L)) U) (@ (@ tptp.set_or6659071591806873216st_nat L) U))))
% 6.73/7.08 (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)))))
% 6.73/7.08 (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)))))
% 6.73/7.08 (assert (forall ((I2 tptp.nat) (J2 tptp.nat)) (let ((_let_1 (@ tptp.suc I2))) (=> (@ (@ tptp.ord_less_eq_nat _let_1) J2) (= (@ tptp.linord2614967742042102400et_nat (@ (@ tptp.set_or6659071591806873216st_nat I2) J2)) (@ (@ tptp.cons_nat _let_1) (@ tptp.linord2614967742042102400et_nat (@ (@ tptp.set_or6659071591806873216st_nat _let_1) J2))))))))
% 6.73/7.08 (assert (forall ((L tptp.int) (U tptp.int)) (= (@ (@ tptp.image_int_int (lambda ((X4 tptp.int)) (@ (@ tptp.plus_plus_int X4) L))) (@ (@ tptp.set_or4662586982721622107an_int tptp.zero_zero_int) (@ (@ tptp.minus_minus_int U) L))) (@ (@ tptp.set_or4662586982721622107an_int L) U))))
% 6.73/7.08 (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)))))))
% 6.73/7.08 (assert (= tptp.times_times_int (@ (@ (@ tptp.map_fu4960017516451851995nt_int tptp.rep_Integ) (@ (@ tptp.map_fu3667384564859982768at_int tptp.rep_Integ) tptp.abs_Integ)) (@ tptp.produc27273713700761075at_nat (lambda ((X4 tptp.nat) (Y4 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((U2 tptp.nat) (V3 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat Y4))) (let ((_let_2 (@ tptp.times_times_nat X4))) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat (@ _let_2 U2)) (@ _let_1 V3))) (@ (@ tptp.plus_plus_nat (@ _let_2 V3)) (@ _let_1 U2))))))) __flatten_var_0))))))
% 6.73/7.08 (assert (= tptp.minus_minus_int (@ (@ (@ tptp.map_fu4960017516451851995nt_int tptp.rep_Integ) (@ (@ tptp.map_fu3667384564859982768at_int tptp.rep_Integ) tptp.abs_Integ)) (@ tptp.produc27273713700761075at_nat (lambda ((X4 tptp.nat) (Y4 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((U2 tptp.nat) (V3 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat X4) V3)) (@ (@ tptp.plus_plus_nat Y4) U2)))) __flatten_var_0))))))
% 6.73/7.08 (assert (= tptp.plus_plus_int (@ (@ (@ tptp.map_fu4960017516451851995nt_int tptp.rep_Integ) (@ (@ tptp.map_fu3667384564859982768at_int tptp.rep_Integ) tptp.abs_Integ)) (@ tptp.produc27273713700761075at_nat (lambda ((X4 tptp.nat) (Y4 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((U2 tptp.nat) (V3 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat X4) U2)) (@ (@ tptp.plus_plus_nat Y4) V3)))) __flatten_var_0))))))
% 6.73/7.08 (assert (forall ((P tptp.rat) (Q2 tptp.rat)) (= (@ tptp.quotient_of (@ (@ tptp.minus_minus_rat P) Q2)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((A5 tptp.int) (C3 tptp.int)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((B4 tptp.int) (D2 tptp.int)) (@ tptp.normalize (@ (@ tptp.product_Pair_int_int (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int A5) D2)) (@ (@ tptp.times_times_int B4) C3))) (@ (@ tptp.times_times_int C3) D2))))) (@ tptp.quotient_of Q2)))) (@ tptp.quotient_of P)))))
% 6.73/7.08 (assert (forall ((L tptp.int) (U tptp.int)) (@ tptp.finite_finite_int (@ (@ tptp.set_or6656581121297822940st_int L) U))))
% 6.73/7.08 (assert (forall ((L tptp.int) (U tptp.int)) (= (@ tptp.finite_card_int (@ (@ tptp.set_or6656581121297822940st_int L) U)) (@ tptp.nat2 (@ (@ tptp.minus_minus_int U) L)))))
% 6.73/7.08 (assert (forall ((L tptp.int) (U tptp.int)) (= (@ (@ tptp.set_or1266510415728281911st_int (@ (@ tptp.plus_plus_int L) tptp.one_one_int)) U) (@ (@ tptp.set_or6656581121297822940st_int L) U))))
% 6.73/7.08 (assert (forall ((Q2 tptp.int) (S2 tptp.int) (P tptp.int) (R3 tptp.int)) (=> (not (= Q2 tptp.zero_zero_int)) (=> (not (= S2 tptp.zero_zero_int)) (=> (= (@ tptp.normalize (@ (@ tptp.product_Pair_int_int P) Q2)) (@ tptp.normalize (@ (@ tptp.product_Pair_int_int R3) S2))) (= (@ (@ tptp.times_times_int P) S2) (@ (@ tptp.times_times_int R3) Q2)))))))
% 6.73/7.08 (assert (forall ((P tptp.rat) (Q2 tptp.rat)) (= (@ tptp.quotient_of (@ (@ tptp.times_times_rat P) Q2)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((A5 tptp.int) (C3 tptp.int)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((B4 tptp.int) (D2 tptp.int)) (@ tptp.normalize (@ (@ tptp.product_Pair_int_int (@ (@ tptp.times_times_int A5) B4)) (@ (@ tptp.times_times_int C3) D2))))) (@ tptp.quotient_of Q2)))) (@ tptp.quotient_of P)))))
% 6.73/7.08 (assert (forall ((P tptp.rat) (Q2 tptp.rat)) (= (@ tptp.quotient_of (@ (@ tptp.divide_divide_rat P) Q2)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((A5 tptp.int) (C3 tptp.int)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((B4 tptp.int) (D2 tptp.int)) (@ tptp.normalize (@ (@ tptp.product_Pair_int_int (@ (@ tptp.times_times_int A5) D2)) (@ (@ tptp.times_times_int C3) B4))))) (@ tptp.quotient_of Q2)))) (@ tptp.quotient_of P)))))
% 6.73/7.08 (assert (forall ((P tptp.rat) (Q2 tptp.rat)) (= (@ tptp.quotient_of (@ (@ tptp.plus_plus_rat P) Q2)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((A5 tptp.int) (C3 tptp.int)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((B4 tptp.int) (D2 tptp.int)) (@ tptp.normalize (@ (@ tptp.product_Pair_int_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A5) D2)) (@ (@ tptp.times_times_int B4) C3))) (@ (@ tptp.times_times_int C3) D2))))) (@ tptp.quotient_of Q2)))) (@ tptp.quotient_of P)))))
% 6.73/7.08 (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 ((X3 tptp.nat) (Xs3 tptp.list_nat)) (let ((_let_1 (@ (@ tptp.cons_nat X3) Xs3))) (=> (= X _let_1) (=> (= Y (@ tptp.suc (@ tptp.nat_prod_encode (@ (@ tptp.product_Pair_nat_nat X3) (@ tptp.nat_list_encode Xs3))))) (not (@ (@ tptp.accp_list_nat tptp.nat_list_encode_rel) _let_1)))))))))))))
% 6.73/7.08 (assert (forall ((M2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N))) (let ((_let_2 (@ tptp.numeral_numeral_nat M2))) (let ((_let_3 (@ (@ tptp.upt _let_2) _let_1))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_2) _let_1))) (and (=> _let_4 (= _let_3 (@ (@ tptp.cons_nat _let_2) (@ (@ tptp.upt (@ tptp.suc _let_2)) _let_1)))) (=> (not _let_4) (= _let_3 tptp.nil_nat)))))))))
% 6.73/7.08 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ tptp.tl_nat (@ (@ tptp.upt M2) N)) (@ (@ tptp.upt (@ tptp.suc M2)) N))))
% 6.73/7.08 (assert (forall ((I2 tptp.nat) (J2 tptp.nat)) (= (@ tptp.size_size_list_nat (@ (@ tptp.upt I2) J2)) (@ (@ tptp.minus_minus_nat J2) I2))))
% 6.73/7.08 (assert (forall ((I2 tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat I2) M2))) (let ((_let_2 (@ tptp.upt I2))) (=> (@ (@ tptp.ord_less_eq_nat _let_1) N) (= (@ (@ tptp.take_nat M2) (@ _let_2 N)) (@ _let_2 _let_1)))))))
% 6.73/7.08 (assert (forall ((J2 tptp.nat) (I2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat J2) I2) (= (@ (@ tptp.upt I2) J2) tptp.nil_nat))))
% 6.73/7.08 (assert (forall ((I2 tptp.nat) (J2 tptp.nat)) (= (= (@ (@ tptp.upt I2) J2) tptp.nil_nat) (or (= J2 tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_nat J2) I2)))))
% 6.73/7.08 (assert (= tptp.set_or1269000886237332187st_nat (lambda ((N4 tptp.nat) (M6 tptp.nat)) (@ tptp.set_nat2 (@ (@ tptp.upt N4) (@ tptp.suc M6))))))
% 6.73/7.08 (assert (= tptp.set_ord_lessThan_nat (lambda ((N4 tptp.nat)) (@ tptp.set_nat2 (@ (@ tptp.upt tptp.zero_zero_nat) N4)))))
% 6.73/7.08 (assert (forall ((M2 tptp.nat) (N tptp.nat) (Ns tptp.list_nat) (Q2 tptp.nat)) (let ((_let_1 (@ (@ tptp.cons_nat N) Ns))) (= (= (@ (@ tptp.cons_nat M2) _let_1) (@ (@ tptp.upt M2) Q2)) (= _let_1 (@ (@ tptp.upt (@ tptp.suc M2)) Q2))))))
% 6.73/7.08 (assert (forall ((I2 tptp.nat)) (= (@ (@ tptp.upt I2) tptp.zero_zero_nat) tptp.nil_nat)))
% 6.73/7.08 (assert (= tptp.set_or6659071591806873216st_nat (lambda ((N4 tptp.nat) (M6 tptp.nat)) (@ tptp.set_nat2 (@ (@ tptp.upt (@ tptp.suc N4)) (@ tptp.suc M6))))))
% 6.73/7.08 (assert (= tptp.set_or5834768355832116004an_nat (lambda ((N4 tptp.nat) (M6 tptp.nat)) (@ tptp.set_nat2 (@ (@ tptp.upt (@ tptp.suc N4)) M6)))))
% 6.73/7.08 (assert (= tptp.set_ord_atMost_nat (lambda ((N4 tptp.nat)) (@ tptp.set_nat2 (@ (@ tptp.upt tptp.zero_zero_nat) (@ tptp.suc N4))))))
% 6.73/7.08 (assert (forall ((I2 tptp.nat) (J2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) J2) (= (@ (@ tptp.upt I2) J2) (@ (@ tptp.cons_nat I2) (@ (@ tptp.upt (@ tptp.suc I2)) J2))))))
% 6.73/7.08 (assert (forall ((I2 tptp.nat) (J2 tptp.nat) (K2 tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat J2) K2))) (let ((_let_2 (@ tptp.upt I2))) (=> (@ (@ tptp.ord_less_eq_nat I2) J2) (= (@ _let_2 _let_1) (@ (@ tptp.append_nat (@ _let_2 J2)) (@ (@ tptp.upt J2) _let_1))))))))
% 6.73/7.08 (assert (= tptp.upt (lambda ((I tptp.nat) (J tptp.nat)) (@ (@ (@ tptp.if_list_nat (@ (@ tptp.ord_less_nat I) J)) (@ (@ tptp.cons_nat I) (@ (@ tptp.upt (@ tptp.suc I)) J))) tptp.nil_nat))))
% 6.73/7.08 (assert (forall ((I2 tptp.nat) (J2 tptp.nat)) (let ((_let_1 (@ tptp.upt I2))) (let ((_let_2 (@ _let_1 (@ tptp.suc J2)))) (let ((_let_3 (@ (@ tptp.ord_less_eq_nat I2) J2))) (and (=> _let_3 (= _let_2 (@ (@ tptp.append_nat (@ _let_1 J2)) (@ (@ tptp.cons_nat J2) tptp.nil_nat)))) (=> (not _let_3) (= _let_2 tptp.nil_nat))))))))
% 6.73/7.08 (assert (forall ((I2 tptp.nat) (J2 tptp.nat)) (let ((_let_1 (@ tptp.upt I2))) (=> (@ (@ tptp.ord_less_eq_nat I2) J2) (= (@ _let_1 (@ tptp.suc J2)) (@ (@ tptp.append_nat (@ _let_1 J2)) (@ (@ tptp.cons_nat J2) tptp.nil_nat)))))))
% 6.73/7.08 (assert (@ tptp.order_mono_nat_nat tptp.suc))
% 6.73/7.08 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ tptp.order_mono_nat_nat (@ tptp.times_times_nat N)))))
% 6.73/7.08 (assert (forall ((K2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) K2) (@ tptp.order_mono_nat_nat (lambda ((M6 tptp.nat)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.power_power_nat K2) M6)) M6))))))
% 6.73/7.08 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ tptp.groups4561878855575611511st_nat (@ (@ tptp.upt M2) N)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X4 tptp.nat)) X4)) (@ (@ tptp.set_or4665077453230672383an_nat M2) N))))))
% 6.73/7.08 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.map_nat_nat tptp.suc) (@ (@ tptp.upt M2) N)) (@ (@ tptp.upt (@ tptp.suc M2)) (@ tptp.suc N)))))
% 6.73/7.08 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (= (@ (@ tptp.map_nat_nat (lambda ((I tptp.nat)) (@ (@ tptp.plus_plus_nat I) N))) (@ (@ tptp.upt tptp.zero_zero_nat) M2)) (@ (@ tptp.upt N) (@ (@ tptp.plus_plus_nat M2) N)))))
% 6.73/7.08 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.map_nat_nat (lambda ((N4 tptp.nat)) (@ (@ tptp.minus_minus_nat N4) (@ tptp.suc tptp.zero_zero_nat)))) (@ (@ tptp.upt (@ tptp.suc M2)) (@ tptp.suc N))) (@ (@ tptp.upt M2) N))))
% 6.73/7.08 (assert (forall ((M2 tptp.nat) (N6 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) M2) (= (@ tptp.finite_card_list_nat (@ tptp.collect_list_nat (lambda ((L2 tptp.list_nat)) (and (= (@ tptp.size_size_list_nat L2) M2) (= (@ tptp.groups4561878855575611511st_nat L2) N6))))) (@ (@ tptp.plus_plus_nat (@ tptp.finite_card_list_nat (@ tptp.collect_list_nat (lambda ((L2 tptp.list_nat)) (and (= (@ tptp.size_size_list_nat L2) (@ (@ tptp.minus_minus_nat M2) tptp.one_one_nat)) (= (@ tptp.groups4561878855575611511st_nat L2) N6)))))) (@ tptp.finite_card_list_nat (@ tptp.collect_list_nat (lambda ((L2 tptp.list_nat)) (and (= (@ tptp.size_size_list_nat L2) M2) (= (@ (@ tptp.plus_plus_nat (@ tptp.groups4561878855575611511st_nat L2)) tptp.one_one_nat) N6))))))))))
% 6.73/7.08 (assert (forall ((M2 tptp.nat) (N6 tptp.nat)) (= (@ tptp.finite_card_list_nat (@ tptp.collect_list_nat (lambda ((L2 tptp.list_nat)) (and (= (@ tptp.size_size_list_nat L2) M2) (= (@ tptp.groups4561878855575611511st_nat L2) N6))))) (@ (@ tptp.binomial (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat N6) M2)) tptp.one_one_nat)) N6))))
% 6.73/7.08 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.image_nat_nat (lambda ((M6 tptp.nat)) (@ (@ tptp.modulo_modulo_nat M6) N))) tptp.top_top_set_nat) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N)))))
% 6.73/7.08 (assert (= tptp.top_top_set_nat (@ (@ tptp.insert_nat tptp.zero_zero_nat) (@ (@ tptp.image_nat_nat tptp.suc) tptp.top_top_set_nat))))
% 6.73/7.08 (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)))))))
% 6.73/7.08 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (@ (@ tptp.sorted_wrt_nat tptp.ord_less_eq_nat) (@ (@ tptp.upt M2) N))))
% 6.73/7.08 (assert (= (@ (@ tptp.image_5846123807819985514at_nat tptp.nat_prod_decode) tptp.top_top_set_nat) tptp.top_to4669805908274784177at_nat))
% 6.73/7.08 (assert (@ (@ (@ tptp.bij_be8693218025023041337at_nat tptp.nat_prod_decode) tptp.top_top_set_nat) tptp.top_to4669805908274784177at_nat))
% 6.73/7.08 (assert (= (@ (@ tptp.image_nat_list_nat tptp.nat_list_decode) tptp.top_top_set_nat) tptp.top_top_set_list_nat))
% 6.73/7.08 (assert (@ (@ (@ tptp.bij_be6293887246118711976st_nat tptp.nat_list_decode) tptp.top_top_set_nat) tptp.top_top_set_list_nat))
% 6.73/7.08 (assert (= (@ (@ tptp.image_list_nat_nat tptp.nat_list_encode) tptp.top_top_set_list_nat) tptp.top_top_set_nat))
% 6.73/7.08 (assert (@ (@ (@ tptp.bij_be8532844293280997160at_nat tptp.nat_list_encode) tptp.top_top_set_list_nat) tptp.top_top_set_nat))
% 6.73/7.08 (assert (= (@ (@ tptp.image_2486076414777270412at_nat tptp.nat_prod_encode) tptp.top_to4669805908274784177at_nat) tptp.top_top_set_nat))
% 6.73/7.08 (assert (@ (@ (@ tptp.bij_be5333170631980326235at_nat tptp.nat_prod_encode) tptp.top_to4669805908274784177at_nat) tptp.top_top_set_nat))
% 6.73/7.08 (assert (forall ((Ns tptp.list_nat) (I2 tptp.nat)) (=> (@ (@ tptp.sorted_wrt_nat tptp.ord_less_nat) Ns) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_nat Ns)) (@ (@ tptp.ord_less_eq_nat I2) (@ (@ tptp.nth_nat Ns) I2))))))
% 6.73/7.08 (assert (= tptp.root (lambda ((N4 tptp.nat) (X4 tptp.real)) (@ (@ (@ tptp.if_real (= N4 tptp.zero_zero_nat)) tptp.zero_zero_real) (@ (@ (@ tptp.the_in5290026491893676941l_real tptp.top_top_set_real) (lambda ((Y4 tptp.real)) (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real Y4)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real Y4)) N4)))) X4)))))
% 6.73/7.08 (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))))))))
% 6.73/7.08 (assert (forall ((N tptp.nat) (X tptp.real) (D3 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 (= D3 _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) (= D3 (@ tptp.uminus_uminus_real _let_2)))) (=> (=> (not _let_4) _let_3) (@ (@ (@ tptp.has_fi5821293074295781190e_real _let_1) D3) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)))))))))))))
% 6.73/7.08 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X)) tptp.one_one_real) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((X9 tptp.real)) (@ tptp.suminf_real (lambda ((K3 tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat K3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_nat))) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) K3)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real _let_1))) (@ (@ tptp.power_power_real X9) _let_1)))))))) (@ tptp.suminf_real (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) K3)) (@ (@ tptp.power_power_real X) (@ (@ tptp.times_times_nat K3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)))))
% 6.73/7.08 (assert (forall ((G2 (-> tptp.real tptp.real)) (M2 tptp.real) (X tptp.real) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real))) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real G2) M2) _let_1) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((X4 tptp.real)) (@ (@ tptp.power_power_real (@ G2 X4)) N))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.power_power_real (@ G2 X)) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)))) M2)) _let_1)))))
% 6.73/7.08 (assert (forall ((Z3 tptp.real) (R3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Z3) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((Z4 tptp.real)) (@ (@ tptp.powr_real Z4) R3))) (@ (@ tptp.times_times_real R3) (@ (@ tptp.powr_real Z3) (@ (@ tptp.minus_minus_real R3) tptp.one_one_real)))) (@ (@ tptp.topolo2177554685111907308n_real Z3) tptp.top_top_set_real)))))
% 6.73/7.08 (assert (forall ((F2 (-> 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 ((X4 tptp.real)) (@ (@ F2 X4) N3))) (@ (@ F5 X0) N3)) (@ (@ tptp.topolo2177554685111907308n_real X0) tptp.top_top_set_real))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) (@ (@ tptp.set_or1633881224788618240n_real A) B)) (@ tptp.summable_real (@ F2 X3)))) (=> (@ (@ tptp.member_real X0) (@ (@ tptp.set_or1633881224788618240n_real A) B)) (=> (@ tptp.summable_real _let_1) (=> (@ tptp.summable_real L5) (=> (forall ((N3 tptp.nat) (X3 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ (@ tptp.set_or1633881224788618240n_real A) B))) (=> (@ (@ tptp.member_real X3) _let_1) (=> (@ (@ tptp.member_real Y3) _let_1) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ (@ F2 X3) N3)) (@ (@ F2 Y3) N3)))) (@ (@ tptp.times_times_real (@ L5 N3)) (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X3) Y3)))))))) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((X4 tptp.real)) (@ tptp.suminf_real (@ F2 X4)))) (@ tptp.suminf_real _let_1)) (@ (@ tptp.topolo2177554685111907308n_real X0) tptp.top_top_set_real)))))))))))
% 6.73/7.08 (assert (forall ((X tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ tptp.log2 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)))))
% 6.73/7.08 (assert (forall ((G2 (-> tptp.real tptp.real)) (M2 tptp.real) (X tptp.real) (R3 tptp.real)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real))) (let ((_let_2 (@ G2 X))) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real G2) M2) _let_1) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) _let_2) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((X4 tptp.real)) (@ (@ tptp.powr_real (@ G2 X4)) R3))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real R3) (@ (@ tptp.powr_real _let_2) (@ (@ tptp.minus_minus_real R3) (@ tptp.semiri5074537144036343181t_real tptp.one_one_nat))))) M2)) _let_1)))))))
% 6.73/7.08 (assert (forall ((G2 (-> tptp.real tptp.real)) (M2 tptp.real) (X tptp.real) (F2 (-> tptp.real tptp.real)) (R3 tptp.real)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real))) (let ((_let_2 (@ G2 X))) (let ((_let_3 (@ F2 X))) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real G2) M2) _let_1) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) _let_2) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F2) R3) _let_1) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((X4 tptp.real)) (@ (@ tptp.powr_real (@ G2 X4)) (@ F2 X4)))) (@ (@ tptp.times_times_real (@ (@ tptp.powr_real _let_2) _let_3)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real R3) (@ tptp.ln_ln_real _let_2))) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real M2) _let_3)) _let_2)))) _let_1)))))))))
% 6.73/7.08 (assert (forall ((R2 tptp.real) (F2 (-> tptp.nat tptp.real)) (X0 tptp.real)) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) (@ (@ tptp.set_or1633881224788618240n_real (@ tptp.uminus_uminus_real R2)) R2)) (@ tptp.summable_real (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ F2 N4)) (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N4)))) (@ (@ tptp.power_power_real X3) N4)))))) (=> (@ (@ tptp.member_real X0) (@ (@ tptp.set_or1633881224788618240n_real (@ tptp.uminus_uminus_real R2)) R2)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) R2) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((X4 tptp.real)) (@ tptp.suminf_real (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_real (@ F2 N4)) (@ (@ tptp.power_power_real X4) (@ tptp.suc N4))))))) (@ tptp.suminf_real (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ F2 N4)) (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N4)))) (@ (@ tptp.power_power_real X0) N4))))) (@ (@ tptp.topolo2177554685111907308n_real X0) tptp.top_top_set_real)))))))
% 6.73/7.08 (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)))))))
% 6.73/7.08 (assert (forall ((Diff (-> tptp.nat tptp.real tptp.real)) (F2 (-> tptp.real tptp.real)) (X tptp.real) (N tptp.nat)) (=> (= (@ Diff tptp.zero_zero_nat) F2) (=> (forall ((M tptp.nat) (X3 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M)) (@ (@ Diff (@ tptp.suc M)) X3)) (@ (@ tptp.topolo2177554685111907308n_real X3) 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)) (= (@ F2 X) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M6) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M6))) (@ (@ tptp.power_power_real X) M6)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T6)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X) N))))))))))
% 6.73/7.08 (assert (forall ((Diff (-> tptp.nat tptp.real tptp.real)) (F2 (-> tptp.real tptp.real)) (X tptp.real) (N tptp.nat)) (=> (and (= (@ Diff tptp.zero_zero_nat) F2) (forall ((M tptp.nat) (X3 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M)) (@ (@ Diff (@ tptp.suc M)) X3)) (@ (@ tptp.topolo2177554685111907308n_real X3) 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)) (= (@ F2 X) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M6) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M6))) (@ (@ tptp.power_power_real X) M6)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T6)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X) N)))))))))
% 6.73/7.08 (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)))))))
% 6.73/7.08 (assert (forall ((H tptp.real) (N tptp.nat) (Diff (-> tptp.nat tptp.real tptp.real)) (F2 (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real H) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (= (@ Diff tptp.zero_zero_nat) F2) (=> (forall ((M tptp.nat) (T6 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_eq_real H) T6) (@ (@ tptp.ord_less_eq_real T6) tptp.zero_zero_real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M)) (@ (@ Diff (@ tptp.suc M)) T6)) (@ (@ tptp.topolo2177554685111907308n_real T6) tptp.top_top_set_real)))) (exists ((T6 tptp.real)) (and (@ (@ tptp.ord_less_real H) T6) (@ (@ tptp.ord_less_real T6) tptp.zero_zero_real) (= (@ F2 H) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M6) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M6))) (@ (@ tptp.power_power_real H) M6)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T6)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real H) N))))))))))))
% 6.73/7.08 (assert (forall ((H tptp.real) (Diff (-> tptp.nat tptp.real tptp.real)) (F2 (-> tptp.real tptp.real)) (N tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H) (=> (= (@ Diff tptp.zero_zero_nat) F2) (=> (forall ((M tptp.nat) (T6 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T6) (@ (@ tptp.ord_less_eq_real T6) H)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M)) (@ (@ Diff (@ tptp.suc M)) 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) H) (= (@ F2 H) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M6) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M6))) (@ (@ tptp.power_power_real H) M6)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T6)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real H) N)))))))))))
% 6.73/7.08 (assert (forall ((H tptp.real) (N tptp.nat) (Diff (-> tptp.nat tptp.real tptp.real)) (F2 (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (= (@ Diff tptp.zero_zero_nat) F2) (=> (forall ((M tptp.nat) (T6 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T6) (@ (@ tptp.ord_less_eq_real T6) H)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M)) (@ (@ Diff (@ tptp.suc M)) 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) H) (= (@ F2 H) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M6) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M6))) (@ (@ tptp.power_power_real H) M6)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T6)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real H) N))))))))))))
% 6.73/7.08 (assert (forall ((Diff (-> tptp.nat tptp.real tptp.real)) (F2 (-> tptp.real tptp.real)) (N tptp.nat) (X tptp.real)) (=> (= (@ Diff tptp.zero_zero_nat) F2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (not (= X tptp.zero_zero_real)) (=> (forall ((M tptp.nat) (X3 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M)) (@ (@ Diff (@ tptp.suc M)) X3)) (@ (@ tptp.topolo2177554685111907308n_real X3) 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)) (= (@ F2 X) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M6) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M6))) (@ (@ tptp.power_power_real X) M6)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T6)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X) N)))))))))))))
% 6.73/7.08 (assert (forall ((Diff (-> tptp.nat tptp.real tptp.real)) (F2 (-> tptp.real tptp.real)) (N tptp.nat) (X tptp.real)) (=> (= (@ Diff tptp.zero_zero_nat) F2) (=> (forall ((M tptp.nat) (T6 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real T6)) (@ tptp.abs_abs_real X))) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M)) (@ (@ Diff (@ tptp.suc M)) 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)) (= (@ F2 X) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M6) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M6))) (@ (@ tptp.power_power_real X) M6)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T6)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X) N))))))))))
% 6.73/7.08 (assert (forall ((N tptp.nat) (Diff (-> tptp.nat tptp.real tptp.real)) (F2 (-> tptp.real tptp.real)) (A tptp.real) (B tptp.real) (C2 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (= (@ Diff tptp.zero_zero_nat) F2) (=> (forall ((M tptp.nat) (T6 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_eq_real A) T6) (@ (@ tptp.ord_less_eq_real T6) B)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M)) (@ (@ Diff (@ tptp.suc M)) T6)) (@ (@ tptp.topolo2177554685111907308n_real T6) tptp.top_top_set_real)))) (=> (@ (@ tptp.ord_less_real A) C2) (=> (@ (@ tptp.ord_less_eq_real C2) B) (exists ((T6 tptp.real)) (and (@ (@ tptp.ord_less_real A) T6) (@ (@ tptp.ord_less_real T6) C2) (= (@ F2 A) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M6) C2)) (@ tptp.semiri2265585572941072030t_real M6))) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real A) C2)) M6)))) (@ 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) C2)) N)))))))))))))
% 6.73/7.08 (assert (forall ((N tptp.nat) (Diff (-> tptp.nat tptp.real tptp.real)) (F2 (-> tptp.real tptp.real)) (A tptp.real) (B tptp.real) (C2 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (= (@ Diff tptp.zero_zero_nat) F2) (=> (forall ((M tptp.nat) (T6 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_eq_real A) T6) (@ (@ tptp.ord_less_eq_real T6) B)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M)) (@ (@ Diff (@ tptp.suc M)) T6)) (@ (@ tptp.topolo2177554685111907308n_real T6) tptp.top_top_set_real)))) (=> (@ (@ tptp.ord_less_eq_real A) C2) (=> (@ (@ tptp.ord_less_real C2) B) (exists ((T6 tptp.real)) (and (@ (@ tptp.ord_less_real C2) T6) (@ (@ tptp.ord_less_real T6) B) (= (@ F2 B) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M6) C2)) (@ tptp.semiri2265585572941072030t_real M6))) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real B) C2)) M6)))) (@ 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) C2)) N)))))))))))))
% 6.73/7.08 (assert (forall ((N tptp.nat) (Diff (-> tptp.nat tptp.real tptp.real)) (F2 (-> tptp.real tptp.real)) (A tptp.real) (B tptp.real) (C2 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) F2) (=> (forall ((M tptp.nat) (T6 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_eq_real A) T6) (@ (@ tptp.ord_less_eq_real T6) B)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M)) (@ (@ Diff (@ tptp.suc M)) T6)) (@ (@ tptp.topolo2177554685111907308n_real T6) tptp.top_top_set_real)))) (=> (@ _let_1 C2) (=> (@ (@ tptp.ord_less_eq_real C2) B) (=> (@ _let_1 X) (=> (@ (@ tptp.ord_less_eq_real X) B) (=> (not (= X C2)) (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 C2))) (and (=> _let_3 (and (@ _let_2 T6) (@ _let_1 C2))) (=> (not _let_3) (and (@ (@ tptp.ord_less_real C2) T6) (@ _let_1 X))) (= (@ F2 X) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M6) C2)) (@ tptp.semiri2265585572941072030t_real M6))) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real X) C2)) M6)))) (@ 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) C2)) N))))))))))))))))))))
% 6.73/7.08 (assert (forall ((N tptp.nat) (H tptp.real) (Diff (-> tptp.nat tptp.real tptp.real)) (K2 tptp.nat) (B5 tptp.real)) (=> (forall ((M tptp.nat) (T6 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T6) (@ (@ tptp.ord_less_eq_real T6) H)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M)) (@ (@ Diff (@ tptp.suc M)) T6)) (@ (@ tptp.topolo2177554685111907308n_real T6) tptp.top_top_set_real)))) (=> (= N (@ tptp.suc K2)) (forall ((M3 tptp.nat) (T7 tptp.real)) (let ((_let_1 (@ tptp.suc M3))) (let ((_let_2 (@ (@ tptp.minus_minus_nat N) _let_1))) (=> (and (@ (@ tptp.ord_less_nat M3) N) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T7) (@ (@ tptp.ord_less_eq_real T7) H)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((U2 tptp.real)) (let ((_let_1 (@ (@ tptp.minus_minus_nat N) M3))) (@ (@ tptp.minus_minus_real (@ (@ Diff M3) U2)) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((P5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff (@ (@ tptp.plus_plus_nat M3) P5)) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real P5))) (@ (@ tptp.power_power_real U2) P5)))) (@ tptp.set_ord_lessThan_nat _let_1))) (@ (@ tptp.times_times_real B5) (@ (@ 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 ((P5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff (@ (@ tptp.plus_plus_nat (@ tptp.suc M3)) P5)) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real P5))) (@ (@ tptp.power_power_real T7) P5)))) (@ tptp.set_ord_lessThan_nat _let_2))) (@ (@ tptp.times_times_real B5) (@ (@ 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))))))))))
% 6.73/7.08 (assert (forall ((N tptp.nat) (X tptp.real) (S2 tptp.set_real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((X4 tptp.real)) (@ (@ tptp.power_power_real X4) 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) S2))))
% 6.73/7.08 (assert (forall ((A tptp.real) (B tptp.real) (F2 (-> tptp.real tptp.real)) (K2 tptp.real)) (=> (not (= A B)) (=> (forall ((X3 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F2) K2) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real))) (= (@ (@ tptp.minus_minus_real (@ F2 B)) (@ F2 A)) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real B) A)) K2))))))
% 6.73/7.08 (assert (forall ((A tptp.real) (B tptp.real) (F2 (-> tptp.real tptp.real)) (F5 (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A) B) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) X3) (=> (@ (@ tptp.ord_less_eq_real X3) B) (@ (@ (@ tptp.has_fi5821293074295781190e_real F2) (@ F5 X3)) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real))))) (exists ((Z tptp.real)) (and (@ (@ tptp.ord_less_real A) Z) (@ (@ tptp.ord_less_real Z) B) (= (@ (@ tptp.minus_minus_real (@ F2 B)) (@ F2 A)) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real B) A)) (@ F5 Z)))))))))
% 6.73/7.08 (assert (forall ((A tptp.real) (B tptp.real) (F2 (-> tptp.real tptp.real)) (G2 (-> tptp.real tptp.real)) (G3 (-> tptp.real tptp.real)) (F5 (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A) B) (=> (forall ((Z tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) Z) (=> (@ (@ tptp.ord_less_eq_real Z) B) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real Z) tptp.top_top_set_real)) F2)))) (=> (forall ((Z tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) Z) (=> (@ (@ tptp.ord_less_eq_real Z) B) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real Z) tptp.top_top_set_real)) G2)))) (=> (forall ((Z tptp.real)) (=> (@ (@ tptp.ord_less_real A) Z) (=> (@ (@ tptp.ord_less_real Z) B) (@ (@ (@ tptp.has_fi5821293074295781190e_real G2) (@ G3 Z)) (@ (@ tptp.topolo2177554685111907308n_real Z) tptp.top_top_set_real))))) (=> (forall ((Z tptp.real)) (=> (@ (@ tptp.ord_less_real A) Z) (=> (@ (@ tptp.ord_less_real Z) B) (@ (@ (@ tptp.has_fi5821293074295781190e_real F2) (@ F5 Z)) (@ (@ tptp.topolo2177554685111907308n_real Z) tptp.top_top_set_real))))) (exists ((C tptp.real)) (and (@ (@ tptp.ord_less_real A) C) (@ (@ tptp.ord_less_real C) B) (= (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real (@ F2 B)) (@ F2 A))) (@ G3 C)) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real (@ G2 B)) (@ G2 A))) (@ F5 C))))))))))))
% 6.73/7.08 (assert (forall ((A (-> tptp.nat tptp.real))) (=> (@ (@ (@ tptp.filterlim_nat_real A) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (=> (@ tptp.topolo6980174941875973593q_real A) (=> (@ (@ tptp.ord_less_real (@ A tptp.zero_zero_nat)) tptp.zero_zero_real) (forall ((N8 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N8))) (@ (@ tptp.member_real (@ tptp.suminf_real (lambda ((I tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I)) (@ A I))))) (@ (@ tptp.set_or1222579329274155063t_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((I tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I)) (@ A I)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat)))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I)) (@ A I)))) (@ tptp.set_ord_lessThan_nat _let_1)))))))))))
% 6.73/7.08 (assert (forall ((A (-> tptp.nat tptp.real))) (=> (@ (@ (@ tptp.filterlim_nat_real A) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (=> (@ tptp.topolo6980174941875973593q_real A) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ A tptp.zero_zero_nat)) (forall ((N8 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N8))) (@ (@ tptp.member_real (@ tptp.suminf_real (lambda ((I tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I)) (@ A I))))) (@ (@ tptp.set_or1222579329274155063t_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((I tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I)) (@ A I)))) (@ tptp.set_ord_lessThan_nat _let_1))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I)) (@ A I)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat))))))))))))
% 6.73/7.08 (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 ((I tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I)) (@ A I))))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I)) (@ A I)))) (@ 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)))))))))
% 6.73/7.08 (assert (forall ((C2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C2) (@ (@ (@ tptp.filterlim_nat_nat (@ tptp.times_times_nat C2)) tptp.at_top_nat) tptp.at_top_nat))))
% 6.73/7.08 (assert (forall ((C2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C2) (@ (@ (@ tptp.filterlim_nat_nat (lambda ((X4 tptp.nat)) (@ (@ tptp.times_times_nat X4) C2))) tptp.at_top_nat) tptp.at_top_nat))))
% 6.73/7.08 (assert (forall ((F2 (-> tptp.nat tptp.real)) (G2 (-> tptp.nat tptp.real))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ F2 N3)) (@ F2 (@ tptp.suc N3)))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ G2 (@ tptp.suc N3))) (@ G2 N3))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ F2 N3)) (@ G2 N3))) (=> (@ (@ (@ tptp.filterlim_nat_real (lambda ((N4 tptp.nat)) (@ (@ tptp.minus_minus_real (@ F2 N4)) (@ G2 N4)))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (exists ((L4 tptp.real)) (let ((_let_1 (@ tptp.topolo2815343760600316023s_real L4))) (and (forall ((N8 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ F2 N8)) L4)) (@ (@ (@ tptp.filterlim_nat_real F2) _let_1) tptp.at_top_nat) (forall ((N8 tptp.nat)) (@ (@ tptp.ord_less_eq_real L4) (@ G2 N8))) (@ (@ (@ tptp.filterlim_nat_real G2) _let_1) tptp.at_top_nat))))))))))
% 6.73/7.08 (assert (forall ((X8 (-> tptp.nat tptp.real))) (=> (forall ((R4 tptp.real)) (exists ((N7 tptp.nat)) (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N7) N3) (@ (@ tptp.ord_less_real R4) (@ X8 N3)))))) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N4 tptp.nat)) (@ tptp.inverse_inverse_real (@ X8 N4)))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat))))
% 6.73/7.08 (assert (@ (@ (@ tptp.filterlim_nat_real (lambda ((N4 tptp.nat)) (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N4))))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat))
% 6.73/7.08 (assert (forall ((R3 tptp.real)) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N4 tptp.nat)) (@ (@ tptp.plus_plus_real R3) (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N4)))))) (@ tptp.topolo2815343760600316023s_real R3)) tptp.at_top_nat)))
% 6.73/7.08 (assert (forall ((F2 (-> tptp.nat tptp.real)) (L tptp.real)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ F2 N3)) (@ F2 (@ tptp.suc N3)))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ F2 N3)) L)) (=> (forall ((E2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E2) (exists ((N8 tptp.nat)) (@ (@ tptp.ord_less_eq_real L) (@ (@ tptp.plus_plus_real (@ F2 N8)) E2))))) (@ (@ (@ tptp.filterlim_nat_real F2) (@ tptp.topolo2815343760600316023s_real L)) tptp.at_top_nat))))))
% 6.73/7.08 (assert (forall ((R3 tptp.real)) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N4 tptp.nat)) (@ (@ tptp.plus_plus_real R3) (@ tptp.uminus_uminus_real (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N4))))))) (@ tptp.topolo2815343760600316023s_real R3)) tptp.at_top_nat)))
% 6.73/7.08 (assert (forall ((R3 tptp.real)) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_real R3) (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ tptp.uminus_uminus_real (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N4)))))))) (@ tptp.topolo2815343760600316023s_real R3)) tptp.at_top_nat)))
% 6.73/7.08 (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 ((N4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N4)) (@ A N4))))))))
% 6.73/7.08 (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 ((N4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N4)) (@ A N4)))))))))
% 6.73/7.08 (assert (forall ((Theta (-> tptp.nat tptp.real)) (Theta2 tptp.real)) (=> (@ (@ (@ tptp.filterlim_nat_real (lambda ((J tptp.nat)) (@ tptp.cos_real (@ (@ tptp.minus_minus_real (@ Theta J)) Theta2)))) (@ tptp.topolo2815343760600316023s_real tptp.one_one_real)) tptp.at_top_nat) (not (forall ((K (-> tptp.nat tptp.int))) (not (@ (@ (@ tptp.filterlim_nat_real (lambda ((J tptp.nat)) (@ (@ tptp.minus_minus_real (@ Theta J)) (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real (@ K J))) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi))))) (@ tptp.topolo2815343760600316023s_real Theta2)) tptp.at_top_nat)))))))
% 6.73/7.08 (assert (forall ((Theta (-> tptp.nat tptp.real))) (=> (@ (@ (@ tptp.filterlim_nat_real (lambda ((J tptp.nat)) (@ tptp.cos_real (@ Theta J)))) (@ tptp.topolo2815343760600316023s_real tptp.one_one_real)) tptp.at_top_nat) (exists ((K (-> tptp.nat tptp.int))) (@ (@ (@ tptp.filterlim_nat_real (lambda ((J tptp.nat)) (@ (@ tptp.minus_minus_real (@ Theta J)) (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real (@ K J))) (@ (@ 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)))))
% 6.73/7.08 (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 ((N4 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I)) (@ A I)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N4))))) (@ tptp.topolo2815343760600316023s_real (@ tptp.suminf_real (lambda ((I tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I)) (@ A I)))))) tptp.at_top_nat)))))
% 6.73/7.08 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) tptp.one_one_real) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N4 tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat N4) (@ 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))))
% 6.73/7.08 (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 ((I tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I)) (@ A I)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))) (@ tptp.suminf_real (lambda ((I tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I)) (@ A I))))))))))
% 6.73/7.08 (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 ((N4 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I)) (@ A I)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N4))))) (@ tptp.topolo2815343760600316023s_real (@ tptp.suminf_real (lambda ((I tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I)) (@ A I)))))) tptp.at_top_nat))))))
% 6.73/7.08 (assert (forall ((A (-> tptp.nat tptp.real))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ A (@ tptp.suc N3))) (@ A N3))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ A N3))) (=> (@ (@ (@ tptp.filterlim_nat_real A) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (exists ((L4 tptp.real)) (let ((_let_1 (@ tptp.topolo2815343760600316023s_real L4))) (and (forall ((N8 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((I tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I)) (@ A I)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N8)))) L4)) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N4 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I)) (@ A I)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N4))))) _let_1) tptp.at_top_nat) (forall ((N8 tptp.nat)) (@ (@ tptp.ord_less_eq_real L4) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I)) (@ A I)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N8)) tptp.one_one_nat))))) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N4 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I)) (@ A I)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N4)) tptp.one_one_nat))))) _let_1) tptp.at_top_nat)))))))))
% 6.73/7.08 (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 ((N4 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I)) (@ A I)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N4)) tptp.one_one_nat))))) (@ tptp.topolo2815343760600316023s_real (@ tptp.suminf_real (lambda ((I tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I)) (@ A I)))))) tptp.at_top_nat)))))
% 6.73/7.08 (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 ((N4 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I)) (@ A I)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N4)) tptp.one_one_nat))))) (@ tptp.topolo2815343760600316023s_real (@ tptp.suminf_real (lambda ((I tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I)) (@ A I)))))) tptp.at_top_nat))))))
% 6.73/7.08 (assert (= tptp.real_V5970128139526366754l_real (lambda ((F4 (-> tptp.real tptp.real))) (exists ((C3 tptp.real)) (= F4 (lambda ((X4 tptp.real)) (@ (@ tptp.times_times_real X4) C3)))))))
% 6.73/7.08 (assert (@ (@ (@ tptp.filterlim_nat_nat tptp.suc) tptp.at_top_nat) tptp.at_top_nat))
% 6.73/7.08 (assert (forall ((X tptp.real)) (@ (@ (@ tptp.filterlim_real_real (lambda ((Y4 tptp.real)) (@ (@ tptp.powr_real (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.times_times_real X) Y4))) (@ (@ tptp.divide_divide_real tptp.one_one_real) Y4)))) (@ tptp.topolo2815343760600316023s_real (@ tptp.exp_real X))) (@ (@ tptp.topolo2177554685111907308n_real tptp.zero_zero_real) (@ tptp.set_or5849166863359141190n_real tptp.zero_zero_real)))))
% 6.73/7.08 (assert (forall ((A tptp.real) (B tptp.real) (F2 (-> tptp.real tptp.real)) (G2 (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A) B) (=> (forall ((X3 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real A) X3) (@ (@ tptp.ord_less_eq_real X3) B)) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)) F2))) (=> (forall ((X3 tptp.real)) (=> (and (@ (@ tptp.ord_less_real A) X3) (@ (@ tptp.ord_less_real X3) B)) (@ (@ tptp.differ6690327859849518006l_real F2) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)))) (=> (forall ((X3 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real A) X3) (@ (@ tptp.ord_less_eq_real X3) B)) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)) G2))) (=> (forall ((X3 tptp.real)) (=> (and (@ (@ tptp.ord_less_real A) X3) (@ (@ tptp.ord_less_real X3) B)) (@ (@ tptp.differ6690327859849518006l_real G2) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)))) (exists ((G_c tptp.real) (F_c tptp.real) (C tptp.real)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real C) tptp.top_top_set_real))) (and (@ (@ (@ tptp.has_fi5821293074295781190e_real G2) G_c) _let_1) (@ (@ (@ tptp.has_fi5821293074295781190e_real F2) F_c) _let_1) (@ (@ tptp.ord_less_real A) C) (@ (@ tptp.ord_less_real C) B) (= (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real (@ F2 B)) (@ F2 A))) G_c) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real (@ G2 B)) (@ G2 A))) F_c))))))))))))
% 6.73/7.08 (assert (forall ((P2 (-> tptp.nat Bool))) (= (@ (@ tptp.eventually_nat (lambda ((I tptp.nat)) (@ P2 (@ tptp.suc I)))) tptp.at_top_nat) (@ (@ tptp.eventually_nat P2) tptp.at_top_nat))))
% 6.73/7.08 (assert (forall ((P2 (-> tptp.nat Bool))) (= (@ (@ tptp.eventually_nat P2) tptp.at_top_nat) (exists ((N5 tptp.nat)) (forall ((N4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N5) N4) (@ P2 N4)))))))
% 6.73/7.08 (assert (forall ((C2 tptp.nat) (P2 (-> tptp.nat Bool))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat C2) X3) (@ P2 X3))) (@ (@ tptp.eventually_nat P2) tptp.at_top_nat))))
% 6.73/7.08 (assert (forall ((F3 tptp.filter_nat)) (= (@ (@ tptp.ord_le2510731241096832064er_nat F3) tptp.at_top_nat) (forall ((N5 tptp.nat)) (@ (@ tptp.eventually_nat (@ tptp.ord_less_eq_nat N5)) F3)))))
% 6.73/7.08 (assert (= (@ tptp.set_ord_atLeast_nat tptp.zero_zero_nat) tptp.top_top_set_nat))
% 6.73/7.08 (assert (forall ((K2 tptp.nat)) (= (@ tptp.set_ord_atLeast_nat (@ tptp.suc K2)) (@ tptp.set_or1210151606488870762an_nat K2))))
% 6.73/7.08 (assert (= (@ tptp.set_or1210151606488870762an_nat tptp.zero_zero_nat) (@ (@ tptp.image_nat_nat tptp.suc) tptp.top_top_set_nat)))
% 6.73/7.08 (assert (forall ((K2 tptp.nat)) (let ((_let_1 (@ tptp.suc K2))) (= (@ tptp.set_or1210151606488870762an_nat _let_1) (@ (@ tptp.minus_minus_set_nat (@ tptp.set_or1210151606488870762an_nat K2)) (@ (@ tptp.insert_nat _let_1) tptp.bot_bot_set_nat))))))
% 6.73/7.08 (assert (forall ((K2 tptp.nat)) (= (@ tptp.set_ord_atLeast_nat (@ tptp.suc K2)) (@ (@ tptp.minus_minus_set_nat (@ tptp.set_ord_atLeast_nat K2)) (@ (@ tptp.insert_nat K2) tptp.bot_bot_set_nat)))))
% 6.73/7.08 (assert (forall ((N tptp.nat) (F2 (-> tptp.real tptp.real)) (F3 tptp.filter_real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ (@ tptp.filterlim_real_real F2) tptp.at_bot_real) F3) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (@ (@ (@ tptp.filterlim_real_real (lambda ((X4 tptp.real)) (@ (@ tptp.power_power_real (@ F2 X4)) N))) tptp.at_top_real) F3))))))
% 6.73/7.08 (assert (forall ((P2 (-> tptp.nat Bool)) (B tptp.nat)) (=> (exists ((X_1 tptp.nat)) (@ P2 X_1)) (=> (forall ((Y3 tptp.nat)) (=> (@ P2 Y3) (@ (@ tptp.ord_less_eq_nat Y3) B))) (@ P2 (@ tptp.order_Greatest_nat P2))))))
% 6.73/7.08 (assert (forall ((P2 (-> tptp.nat Bool)) (K2 tptp.nat) (B tptp.nat)) (=> (@ P2 K2) (=> (forall ((Y3 tptp.nat)) (=> (@ P2 Y3) (@ (@ tptp.ord_less_eq_nat Y3) B))) (@ (@ tptp.ord_less_eq_nat K2) (@ tptp.order_Greatest_nat P2))))))
% 6.73/7.08 (assert (forall ((P2 (-> tptp.nat Bool)) (K2 tptp.nat) (B tptp.nat)) (=> (@ P2 K2) (=> (forall ((Y3 tptp.nat)) (=> (@ P2 Y3) (@ (@ tptp.ord_less_eq_nat Y3) B))) (@ P2 (@ tptp.order_Greatest_nat P2))))))
% 6.73/7.08 (assert (forall ((N tptp.nat) (F2 (-> tptp.real tptp.real)) (F3 tptp.filter_real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ (@ tptp.filterlim_real_real F2) tptp.at_bot_real) F3) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (@ (@ (@ tptp.filterlim_real_real (lambda ((X4 tptp.real)) (@ (@ tptp.power_power_real (@ F2 X4)) N))) tptp.at_bot_real) F3))))))
% 6.73/7.08 (assert (forall ((A tptp.real) (B tptp.real) (F2 (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.topolo5044208981011980120l_real (@ (@ tptp.set_or1222579329274155063t_real A) B)) F2) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real A) X3) (=> (@ (@ tptp.ord_less_real X3) B) (@ (@ tptp.differ6690327859849518006l_real F2) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real))))) (exists ((L4 tptp.real) (Z tptp.real)) (and (@ (@ tptp.ord_less_real A) Z) (@ (@ tptp.ord_less_real Z) B) (@ (@ (@ tptp.has_fi5821293074295781190e_real F2) L4) (@ (@ tptp.topolo2177554685111907308n_real Z) tptp.top_top_set_real)) (= (@ (@ tptp.minus_minus_real (@ F2 B)) (@ F2 A)) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real B) A)) L4)))))))))
% 6.73/7.08 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.inj_on_real_real (lambda ((Y4 tptp.real)) (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real Y4)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real Y4)) N)))) tptp.top_top_set_real))))
% 6.73/7.08 (assert (= (@ tptp.comple7399068483239264473et_nat (@ (@ tptp.image_nat_set_nat tptp.set_ord_lessThan_nat) tptp.top_top_set_nat)) tptp.top_top_set_nat))
% 6.73/7.08 (assert (= (@ tptp.comple7399068483239264473et_nat (@ (@ tptp.image_nat_set_nat tptp.set_ord_atMost_nat) tptp.top_top_set_nat)) tptp.top_top_set_nat))
% 6.73/7.08 (assert (= (@ tptp.comple7399068483239264473et_nat (@ (@ tptp.image_nat_set_nat tptp.set_ord_atLeast_nat) tptp.top_top_set_nat)) tptp.top_top_set_nat))
% 6.73/7.08 (assert (= (@ tptp.complete_Sup_Sup_nat tptp.bot_bot_set_nat) tptp.zero_zero_nat))
% 6.73/7.08 (assert (forall ((A4 tptp.set_list_nat)) (@ (@ tptp.inj_on_list_nat_nat tptp.nat_list_encode) A4)))
% 6.73/7.08 (assert (forall ((A4 tptp.set_nat)) (@ (@ tptp.inj_on_nat_list_nat tptp.nat_list_decode) A4)))
% 6.73/7.08 (assert (forall ((A4 tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.inj_on2178005380612969504at_nat tptp.nat_prod_encode) A4)))
% 6.73/7.08 (assert (forall ((N6 tptp.set_nat)) (@ (@ tptp.inj_on_nat_nat tptp.suc) N6)))
% 6.73/7.08 (assert (forall ((A4 tptp.set_nat)) (@ (@ tptp.inj_on5538052773655684606at_nat tptp.nat_prod_decode) A4)))
% 6.73/7.08 (assert (forall ((N6 tptp.set_nat) (K2 tptp.nat)) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.member_nat N3) N6) (@ (@ tptp.ord_less_eq_nat K2) N3))) (@ (@ tptp.inj_on_nat_nat (lambda ((N4 tptp.nat)) (@ (@ tptp.minus_minus_nat N4) K2))) N6))))
% 6.73/7.08 (assert (@ (@ tptp.inj_on_set_nat_nat tptp.nat_set_encode) (@ tptp.collect_set_nat tptp.finite_finite_nat)))
% 6.73/7.08 (assert (= (@ tptp.comple7806235888213564991et_nat (@ (@ tptp.image_nat_set_nat tptp.set_or1210151606488870762an_nat) tptp.top_top_set_nat)) tptp.bot_bot_set_nat))
% 6.73/7.08 (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 ((M6 tptp.nat)) (@ tptp.collect_nat (lambda ((D2 tptp.nat)) (@ (@ tptp.dvd_dvd_nat D2) M6))))) M5)))))))))
% 6.73/7.08 (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))))
% 6.73/7.08 (assert (= tptp.complete_Sup_Sup_nat (lambda ((X7 tptp.set_nat)) (@ (@ (@ tptp.if_nat (= X7 tptp.bot_bot_set_nat)) tptp.zero_zero_nat) (@ tptp.lattic8265883725875713057ax_nat X7)))))
% 6.73/7.08 (assert (forall ((S3 tptp.set_nat)) (=> (@ tptp.finite_finite_nat S3) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat S3)) (@ tptp.suc (@ tptp.lattic8265883725875713057ax_nat S3))))))
% 6.73/7.08 (assert (= tptp.divide_divide_nat (lambda ((M6 tptp.nat) (N4 tptp.nat)) (@ (@ (@ tptp.if_nat (= N4 tptp.zero_zero_nat)) tptp.zero_zero_nat) (@ tptp.lattic8265883725875713057ax_nat (@ tptp.collect_nat (lambda ((K3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat K3) N4)) M6))))))))
% 6.73/7.08 (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) (TreeList 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) TreeList) Summary2)) (= Y (not (and (= Deg2 Xa2) (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList)) (@ (@ 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 TreeList) (@ (@ tptp.power_power_nat _let_1) _let_2)) (@ (@ (@ tptp.case_o184042715313410164at_nat (and (not (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) X7))) (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList)) (not (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X4) X7))))))) (@ 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 ((I tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat I) (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (= (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I)) X7)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I))))) (=> _let_2 (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList)) (not (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X4) X7)))))) (=> (not _let_2) (and (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList) Ma3) (forall ((X4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat X4) (@ (@ tptp.power_power_nat _let_1) Deg2)) (=> (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList) X4) (and (@ (@ tptp.ord_less_nat Mi3) X4) (@ (@ tptp.ord_less_eq_nat X4) Ma3)))))))))))))) Mima)))))))))))))
% 6.73/7.08 (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) (TreeList 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) TreeList) Summary2)) (not (and (= Deg2 Xa2) (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 TreeList)) (@ (@ tptp.vEBT_VEBT_valid X5) (@ (@ tptp.divide_divide_nat Deg2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.vEBT_VEBT_valid Summary2) _let_2) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList) (@ (@ tptp.power_power_nat _let_1) _let_2)) (@ (@ (@ tptp.case_o184042715313410164at_nat (and (not (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) X7))) (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList)) (not (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X4) X7))))))) (@ 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 ((I tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat I) (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (= (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I)) X7)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I))))) (=> _let_2 (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList)) (not (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X4) X7)))))) (=> (not _let_2) (and (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList) Ma3) (forall ((X4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat X4) (@ (@ tptp.power_power_nat _let_1) Deg2)) (=> (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList) X4) (and (@ (@ tptp.ord_less_nat Mi3) X4) (@ (@ tptp.ord_less_eq_nat X4) Ma3)))))))))))))) Mima))))))))))))
% 6.73/7.08 (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) (TreeList 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) TreeList) Summary2)) (and (= Deg2 Xa2) (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList)) (@ (@ 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 TreeList) (@ (@ tptp.power_power_nat _let_1) _let_2)) (@ (@ (@ tptp.case_o184042715313410164at_nat (and (not (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) X7))) (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList)) (not (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X4) X7))))))) (@ 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 ((I tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat I) (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (= (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I)) X7)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I))))) (=> _let_2 (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList)) (not (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X4) X7)))))) (=> (not _let_2) (and (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList) Ma3) (forall ((X4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat X4) (@ (@ tptp.power_power_nat _let_1) Deg2)) (=> (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList) X4) (and (@ (@ tptp.ord_less_nat Mi3) X4) (@ (@ tptp.ord_less_eq_nat X4) Ma3)))))))))))))) Mima)))))))))))
% 6.73/7.08 (assert (forall ((Mima2 tptp.option4927543243414619207at_nat) (Deg tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (Deg3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.minus_minus_nat Deg) (@ (@ tptp.divide_divide_nat Deg) _let_1)))) (= (@ (@ tptp.vEBT_VEBT_valid (@ (@ (@ (@ tptp.vEBT_Node Mima2) Deg) TreeList2) Summary)) Deg3) (and (= Deg Deg3) (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList2)) (@ (@ tptp.vEBT_VEBT_valid X4) (@ (@ tptp.divide_divide_nat Deg) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.vEBT_VEBT_valid Summary) _let_2) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList2) (@ (@ tptp.power_power_nat _let_1) _let_2)) (@ (@ (@ tptp.case_o184042715313410164at_nat (and (not (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary) X7))) (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X4) X7))))))) (@ 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 ((I tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat I) (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.minus_minus_nat Deg) (@ (@ tptp.divide_divide_nat Deg) _let_1)))) (= (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I)) X7)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary) I))))) (=> _let_2 (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X4) X7)))))) (=> (not _let_2) (and (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg) _let_1)) TreeList2) Ma3) (forall ((X4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat X4) (@ (@ tptp.power_power_nat _let_1) Deg)) (=> (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg) _let_1)) TreeList2) X4) (and (@ (@ tptp.ord_less_nat Mi3) X4) (@ (@ tptp.ord_less_eq_nat X4) Ma3)))))))))))))) Mima2)))))))
% 6.73/7.08 (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) (TreeList 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) TreeList) Summary2))) (=> (= X _let_3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_3) Xa2)) (and (= Deg2 Xa2) (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList)) (@ (@ 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 TreeList) (@ (@ tptp.power_power_nat _let_1) _let_2)) (@ (@ (@ tptp.case_o184042715313410164at_nat (and (not (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) X7))) (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList)) (not (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X4) X7))))))) (@ 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 ((I tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat I) (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (= (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I)) X7)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I))))) (=> _let_2 (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList)) (not (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X4) X7)))))) (=> (not _let_2) (and (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList) Ma3) (forall ((X4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat X4) (@ (@ tptp.power_power_nat _let_1) Deg2)) (=> (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList) X4) (and (@ (@ tptp.ord_less_nat Mi3) X4) (@ (@ tptp.ord_less_eq_nat X4) Ma3)))))))))))))) Mima))))))))))))))
% 6.73/7.08 (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) (TreeList 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) TreeList) Summary2))) (=> (= X _let_3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_3) Xa2)) (not (and (= Deg2 Xa2) (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 TreeList)) (@ (@ tptp.vEBT_VEBT_valid X5) (@ (@ tptp.divide_divide_nat Deg2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.vEBT_VEBT_valid Summary2) _let_2) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList) (@ (@ tptp.power_power_nat _let_1) _let_2)) (@ (@ (@ tptp.case_o184042715313410164at_nat (and (not (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) X7))) (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList)) (not (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X4) X7))))))) (@ 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 ((I tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat I) (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (= (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I)) X7)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I))))) (=> _let_2 (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList)) (not (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X4) X7)))))) (=> (not _let_2) (and (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList) Ma3) (forall ((X4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat X4) (@ (@ tptp.power_power_nat _let_1) Deg2)) (=> (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList) X4) (and (@ (@ tptp.ord_less_nat Mi3) X4) (@ (@ tptp.ord_less_eq_nat X4) Ma3)))))))))))))) Mima)))))))))))))))
% 6.73/7.08 (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) (TreeList tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Mima) Deg2) TreeList) Summary2))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_3 (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_2)))) (=> (= X _let_1) (=> (= Y (and (= Deg2 Xa2) (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList)) (@ (@ tptp.vEBT_VEBT_valid X4) (@ (@ tptp.divide_divide_nat Deg2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.vEBT_VEBT_valid Summary2) _let_3) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList) (@ (@ tptp.power_power_nat _let_2) _let_3)) (@ (@ (@ tptp.case_o184042715313410164at_nat (and (not (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) X7))) (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList)) (not (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X4) X7))))))) (@ 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 ((I tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat I) (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (= (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I)) X7)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I))))) (=> _let_2 (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList)) (not (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X4) X7)))))) (=> (not _let_2) (and (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList) Ma3) (forall ((X4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat X4) (@ (@ tptp.power_power_nat _let_1) Deg2)) (=> (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList) X4) (and (@ (@ tptp.ord_less_nat Mi3) X4) (@ (@ tptp.ord_less_eq_nat X4) Ma3)))))))))))))) Mima))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2)))))))))))))))
% 6.73/7.08 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_min_nat (@ tptp.suc M2)) (@ tptp.suc N)) (@ tptp.suc (@ (@ tptp.ord_min_nat M2) N)))))
% 6.73/7.08 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_min_nat tptp.zero_zero_nat) N) tptp.zero_zero_nat)))
% 6.73/7.08 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_min_nat N) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 6.73/7.08 (assert (forall ((M2 tptp.num)) (= (@ (@ tptp.bit_take_bit_num tptp.zero_zero_nat) M2) tptp.none_num)))
% 6.73/7.08 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_take_bit_num (@ tptp.suc N)) tptp.one) (@ tptp.some_num tptp.one))))
% 6.73/7.08 (assert (forall ((N tptp.nat) (M2 tptp.num)) (= (@ (@ tptp.bit_take_bit_num (@ tptp.suc N)) (@ tptp.bit0 M2)) (@ (@ (@ tptp.case_o6005452278849405969um_num tptp.none_num) (lambda ((Q5 tptp.num)) (@ tptp.some_num (@ tptp.bit0 Q5)))) (@ (@ tptp.bit_take_bit_num N) M2)))))
% 6.73/7.08 (assert (forall ((K2 tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_min_nat (@ tptp.numeral_numeral_nat K2)) (@ tptp.suc N)) (@ tptp.suc (@ (@ tptp.ord_min_nat (@ tptp.pred_numeral K2)) N)))))
% 6.73/7.08 (assert (forall ((N tptp.nat) (K2 tptp.num)) (= (@ (@ tptp.ord_min_nat (@ tptp.suc N)) (@ tptp.numeral_numeral_nat K2)) (@ tptp.suc (@ (@ tptp.ord_min_nat N) (@ tptp.pred_numeral K2))))))
% 6.73/7.08 (assert (forall ((N tptp.nat) (M2 tptp.num)) (= (@ (@ tptp.bit_take_bit_num (@ tptp.suc N)) (@ tptp.bit1 M2)) (@ tptp.some_num (@ (@ (@ tptp.case_option_num_num tptp.one) tptp.bit1) (@ (@ tptp.bit_take_bit_num N) M2))))))
% 6.73/7.08 (assert (forall ((M2 tptp.nat) (I2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_min_nat (@ (@ tptp.minus_minus_nat M2) I2)) (@ (@ tptp.minus_minus_nat N) I2)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.ord_min_nat M2) N)) I2))))
% 6.73/7.08 (assert (forall ((M2 tptp.nat) (N tptp.nat) (Q2 tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.ord_min_nat M2) N)) Q2) (@ (@ tptp.ord_min_nat (@ (@ tptp.times_times_nat M2) Q2)) (@ (@ tptp.times_times_nat N) Q2)))))
% 6.73/7.08 (assert (forall ((M2 tptp.nat) (N tptp.nat) (Q2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat M2))) (= (@ _let_1 (@ (@ tptp.ord_min_nat N) Q2)) (@ (@ tptp.ord_min_nat (@ _let_1 N)) (@ _let_1 Q2))))))
% 6.73/7.08 (assert (= tptp.inf_inf_nat tptp.ord_min_nat))
% 6.73/7.08 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (= (@ (@ tptp.ord_min_nat (@ tptp.suc N)) M2) (@ (@ (@ tptp.case_nat_nat tptp.zero_zero_nat) (lambda ((M7 tptp.nat)) (@ tptp.suc (@ (@ tptp.ord_min_nat N) M7)))) M2))))
% 6.73/7.08 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_min_nat M2) (@ tptp.suc N)) (@ (@ (@ tptp.case_nat_nat tptp.zero_zero_nat) (lambda ((M7 tptp.nat)) (@ tptp.suc (@ (@ tptp.ord_min_nat M7) N)))) M2))))
% 6.73/7.08 (assert (= tptp.bit_take_bit_num (lambda ((N4 tptp.nat) (M6 tptp.num)) (let ((_let_1 (@ (@ tptp.bit_se2925701944663578781it_nat N4) (@ tptp.numeral_numeral_nat M6)))) (@ (@ (@ tptp.if_option_num (= _let_1 tptp.zero_zero_nat)) tptp.none_num) (@ tptp.some_num (@ tptp.num_of_nat _let_1)))))))
% 6.73/7.08 (assert (= tptp.pred_nat (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((M6 tptp.nat) (N4 tptp.nat)) (= N4 (@ tptp.suc M6)))))))
% 6.73/7.08 (assert (= tptp.field_5140801741446780682s_real (@ tptp.collect_real (lambda ((Uu3 tptp.real)) (exists ((I tptp.int) (N4 tptp.nat)) (and (= Uu3 (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real I)) (@ tptp.semiri5074537144036343181t_real N4))) (not (= N4 tptp.zero_zero_nat))))))))
% 6.73/7.08 (assert (let ((_let_1 (@ (@ tptp.comp_nat_nat_nat tptp.suc) tptp.suc))) (= _let_1 _let_1)))
% 6.73/7.08 (assert (= tptp.code_divmod_integer (lambda ((K3 tptp.code_integer) (L2 tptp.code_integer)) (let ((_let_1 (@ (@ tptp.code_divmod_abs K3) L2))) (let ((_let_2 (@ tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger))) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (= K3 tptp.zero_z3403309356797280102nteger)) (@ _let_2 tptp.zero_z3403309356797280102nteger)) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (= L2 tptp.zero_z3403309356797280102nteger)) (@ _let_2 K3)) (@ (@ (@ (@ tptp.comp_C1593894019821074884nteger (@ (@ tptp.comp_C8797469213163452608nteger tptp.produc6499014454317279255nteger) tptp.times_3573771949741848930nteger)) tptp.sgn_sgn_Code_integer) L2) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (= (@ tptp.sgn_sgn_Code_integer K3) (@ tptp.sgn_sgn_Code_integer L2))) _let_1) (@ (@ tptp.produc6916734918728496179nteger (lambda ((R tptp.code_integer) (S6 tptp.code_integer)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger R))) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (= S6 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 L2)) S6)))))) _let_1))))))))))
% 6.73/7.08 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat M2) N)) (@ tptp.transi6264000038957366511cl_nat tptp.pred_nat)) (@ (@ tptp.ord_less_nat M2) N))))
% 6.73/7.08 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat M2) N)) (@ tptp.transi2905341329935302413cl_nat tptp.pred_nat)) (@ (@ tptp.ord_less_eq_nat M2) N))))
% 6.73/7.08 (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)))))))
% 6.73/7.08 (assert (forall ((X tptp.nat)) (= (@ (@ tptp.gcd_gcd_nat tptp.zero_zero_nat) X) X)))
% 6.73/7.08 (assert (forall ((X tptp.nat)) (= (@ (@ tptp.gcd_gcd_nat X) tptp.zero_zero_nat) X)))
% 6.73/7.08 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.gcd_gcd_nat A) tptp.zero_zero_nat) A)))
% 6.73/7.08 (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)))))
% 6.73/7.08 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.gcd_gcd_nat tptp.zero_zero_nat) A) A)))
% 6.73/7.08 (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)))))
% 6.73/7.08 (assert (forall ((M2 tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (@ (@ tptp.gcd_gcd_nat M2) _let_1) _let_1))))
% 6.73/7.08 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.gcd_gcd_nat M2) N)) (or (not (= M2 tptp.zero_zero_nat)) (not (= N tptp.zero_zero_nat))))))
% 6.73/7.08 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ (@ tptp.gcd_gcd_nat (@ (@ tptp.minus_minus_nat N) M2)) N) (@ (@ tptp.gcd_gcd_nat M2) N)))))
% 6.73/7.08 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M2) (= (@ (@ tptp.gcd_gcd_nat (@ (@ tptp.minus_minus_nat M2) N)) N) (@ (@ tptp.gcd_gcd_nat M2) N)))))
% 6.73/7.08 (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))))
% 6.73/7.08 (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))))
% 6.73/7.08 (assert (forall ((K2 tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K2))) (= (@ _let_1 (@ (@ tptp.gcd_gcd_nat M2) N)) (@ (@ tptp.gcd_gcd_nat (@ _let_1 M2)) (@ _let_1 N))))))
% 6.73/7.08 (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))))))
% 6.73/7.08 (assert (= tptp.gcd_gcd_nat (lambda ((X4 tptp.nat) (Y4 tptp.nat)) (@ (@ (@ tptp.if_nat (= Y4 tptp.zero_zero_nat)) X4) (@ (@ tptp.gcd_gcd_nat Y4) (@ (@ tptp.modulo_modulo_nat X4) Y4))))))
% 6.73/7.08 (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)))))))))
% 6.73/7.08 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (exists ((X3 tptp.nat) (Y3 tptp.nat)) (= (@ (@ tptp.times_times_nat A) X3) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat B) Y3)) (@ (@ tptp.gcd_gcd_nat A) B)))))))
% 6.73/7.08 (assert (forall ((B tptp.nat) (A tptp.nat)) (exists ((X3 tptp.nat) (Y3 tptp.nat)) (let ((_let_1 (@ (@ tptp.gcd_gcd_nat A) B))) (let ((_let_2 (@ tptp.times_times_nat A))) (let ((_let_3 (@ _let_2 Y3))) (let ((_let_4 (@ tptp.times_times_nat B))) (let ((_let_5 (@ _let_4 X3))) (let ((_let_6 (@ _let_4 Y3))) (let ((_let_7 (@ _let_2 X3))) (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)))))))))))))
% 6.73/7.08 (assert (forall ((N tptp.nat)) (= (@ tptp.field_nat (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((X4 tptp.nat) (Y4 tptp.nat)) (and (@ (@ tptp.ord_less_nat X4) N) (@ (@ tptp.ord_less_nat Y4) N) (@ (@ tptp.ord_less_eq_nat X4) Y4)))))) (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (@ (@ tptp.ord_less_nat X4) N))))))
% 6.73/7.08 (assert (@ (@ (@ (@ tptp.semila1623282765462674594er_nat tptp.gcd_gcd_nat) tptp.zero_zero_nat) tptp.dvd_dvd_nat) (lambda ((M6 tptp.nat) (N4 tptp.nat)) (and (@ (@ tptp.dvd_dvd_nat M6) N4) (not (= M6 N4))))))
% 6.73/7.08 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.gcd_gcd_nat M2) N) (@ tptp.lattic8265883725875713057ax_nat (@ tptp.collect_nat (lambda ((D2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat D2))) (and (@ _let_1 M2) (@ _let_1 N))))))))))
% 6.73/7.08 (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)))))))))
% 6.73/7.08 (assert (forall ((K2 tptp.int) (M2 tptp.int) (N tptp.int)) (let ((_let_1 (@ tptp.times_times_int K2))) (= (@ (@ tptp.times_times_int (@ tptp.abs_abs_int K2)) (@ (@ tptp.gcd_gcd_int M2) N)) (@ (@ tptp.gcd_gcd_int (@ _let_1 M2)) (@ _let_1 N))))))
% 6.73/7.08 (assert (forall ((X tptp.int) (Y tptp.int)) (exists ((U3 tptp.int) (V tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int U3) X)) (@ (@ tptp.times_times_int V) Y)) (@ (@ tptp.gcd_gcd_int X) Y)))))
% 6.73/7.08 (assert (forall ((F2 (-> tptp.nat tptp.nat)) (N tptp.nat)) (=> (@ tptp.order_5726023648592871131at_nat F2) (@ (@ tptp.ord_less_eq_nat N) (@ F2 N)))))
% 6.73/7.08 (assert (forall ((R3 tptp.real) (A tptp.real) (N tptp.nat)) (= (@ (@ tptp.power_power_complex (@ (@ tptp.rcis R3) A)) N) (@ (@ tptp.rcis (@ (@ tptp.power_power_real R3) N)) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) A)))))
% 6.73/7.08 (assert (forall ((R3 tptp.real) (A tptp.real)) (= (@ tptp.re (@ (@ tptp.rcis R3) A)) (@ (@ tptp.times_times_real R3) (@ tptp.cos_real A)))))
% 6.73/7.08 (assert (forall ((R3 tptp.real) (A tptp.real)) (= (@ tptp.im (@ (@ tptp.rcis R3) A)) (@ (@ tptp.times_times_real R3) (@ tptp.sin_real A)))))
% 6.73/7.08 (assert (forall ((R1 tptp.real) (A tptp.real) (R22 tptp.real) (B tptp.real)) (= (@ (@ tptp.times_times_complex (@ (@ tptp.rcis R1) A)) (@ (@ tptp.rcis R22) B)) (@ (@ tptp.rcis (@ (@ tptp.times_times_real R1) R22)) (@ (@ tptp.plus_plus_real A) B)))))
% 6.73/7.08 (assert (= tptp.rcis (lambda ((R tptp.real) (A5 tptp.real)) (@ (@ tptp.times_times_complex (@ tptp.real_V4546457046886955230omplex R)) (@ tptp.cis A5)))))
% 6.73/7.08 (assert (forall ((P2 (-> tptp.product_prod_nat_nat Bool))) (= (@ (@ tptp.eventu1038000079068216329at_nat P2) (@ (@ tptp.prod_filter_nat_nat tptp.at_top_nat) tptp.at_top_nat)) (exists ((N5 tptp.nat)) (forall ((M6 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N5) M6) (forall ((N4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N5) N4) (@ P2 (@ (@ tptp.product_Pair_nat_nat N4) M6))))))))))
% 6.73/7.08 (assert (forall ((N tptp.num)) (= (@ tptp.sqr (@ tptp.bit1 N)) (@ tptp.bit1 (@ tptp.bit0 (@ (@ tptp.plus_plus_num (@ tptp.sqr N)) N))))))
% 6.73/7.08 (assert (forall ((N tptp.num)) (= (@ tptp.sqr (@ tptp.bit0 N)) (@ tptp.bit0 (@ tptp.bit0 (@ tptp.sqr N))))))
% 6.73/7.08 (assert (= (@ tptp.sqr tptp.one) tptp.one))
% 6.73/7.08 (assert (= tptp.sqr (lambda ((X4 tptp.num)) (@ (@ tptp.times_times_num X4) X4))))
% 6.73/7.08 (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)))))
% 6.73/7.08 (assert (forall ((X tptp.num)) (= (@ (@ tptp.pow X) tptp.one) X)))
% 6.73/7.08 (assert (forall ((X tptp.num) (Y tptp.num)) (let ((_let_1 (@ tptp.pow X))) (= (@ _let_1 (@ tptp.bit0 Y)) (@ tptp.sqr (@ _let_1 Y))))))
% 6.73/7.08 (assert (forall ((N tptp.nat)) (@ tptp.bNF_We3818239936649020644el_nat (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((X4 tptp.nat) (Y4 tptp.nat)) (and (@ (@ tptp.ord_less_nat X4) N) (@ (@ tptp.ord_less_nat Y4) N) (@ (@ tptp.ord_less_eq_nat X4) Y4))))))))
% 6.73/7.08 (assert (forall ((M2 tptp.nat)) (= (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((I tptp.nat) (J tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I) J)) M2)))) (@ (@ tptp.produc457027306803732586at_nat (@ tptp.set_ord_atMost_nat M2)) (lambda ((R tptp.nat)) (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat M2) R)))))))
% 6.73/7.08 (assert (forall ((F3 tptp.set_nat)) (= (@ tptp.finite_finite_nat (@ (@ tptp.vimage_nat_nat tptp.suc) F3)) (@ tptp.finite_finite_nat F3))))
% 6.73/7.08 (assert (forall ((N tptp.nat)) (@ (@ tptp.algebr934650988132801477me_nat N) (@ tptp.suc tptp.zero_zero_nat))))
% 6.73/7.08 (assert (forall ((N tptp.nat)) (@ (@ tptp.algebr934650988132801477me_nat (@ tptp.suc tptp.zero_zero_nat)) N)))
% 6.73/7.08 (assert (forall ((N tptp.nat)) (@ (@ tptp.algebr934650988132801477me_nat (@ tptp.suc N)) N)))
% 6.73/7.08 (assert (forall ((N tptp.nat)) (@ (@ tptp.algebr934650988132801477me_nat N) (@ tptp.suc N))))
% 6.73/7.08 (assert (forall ((A tptp.nat) (D tptp.nat) (B tptp.nat) (C2 tptp.nat)) (=> (@ (@ tptp.algebr934650988132801477me_nat A) D) (=> (@ (@ tptp.algebr934650988132801477me_nat B) C2) (= (= (@ (@ tptp.times_times_nat A) C2) (@ (@ tptp.times_times_nat B) D)) (and (= A B) (= C2 D)))))))
% 6.73/7.08 (assert (forall ((N tptp.nat) (A4 tptp.set_nat)) (let ((_let_1 (@ tptp.vimage_nat_nat tptp.suc))) (= (@ _let_1 (@ (@ tptp.insert_nat (@ tptp.suc N)) A4)) (@ (@ tptp.insert_nat N) (@ _let_1 A4))))))
% 6.73/7.08 (assert (forall ((A4 tptp.set_nat)) (let ((_let_1 (@ tptp.vimage_nat_nat tptp.suc))) (= (@ _let_1 (@ (@ tptp.insert_nat tptp.zero_zero_nat) A4)) (@ _let_1 A4)))))
% 6.73/7.08 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.algebr934650988132801477me_nat (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) N))))
% 6.73/7.08 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.algebr934650988132801477me_nat N) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)))))
% 6.73/7.08 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.member_real X) tptp.field_5140801741446780682s_real) (not (forall ((M tptp.nat) (N3 tptp.nat)) (=> (not (= N3 tptp.zero_zero_nat)) (=> (= (@ tptp.abs_abs_real X) (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real M)) (@ tptp.semiri5074537144036343181t_real N3))) (not (@ (@ tptp.algebr934650988132801477me_nat M) N3)))))))))
% 6.73/7.08 (assert (forall ((X tptp.nat)) (= (@ tptp.nat_set_decode (@ (@ tptp.divide_divide_nat X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.vimage_nat_nat tptp.suc) (@ tptp.nat_set_decode X)))))
% 6.73/7.08 (assert (forall ((A4 tptp.set_nat)) (= (@ tptp.nat_set_encode (@ (@ tptp.vimage_nat_nat tptp.suc) A4)) (@ (@ tptp.divide_divide_nat (@ tptp.nat_set_encode A4)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 6.73/7.08 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat tptp.bNF_Ca8665028551170535155natLeq) (@ (@ tptp.produc457027306803732586at_nat (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (@ (@ tptp.ord_less_nat X4) N)))) (lambda ((Uu3 tptp.nat)) (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (@ (@ tptp.ord_less_nat X4) N)))))) (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((X4 tptp.nat) (Y4 tptp.nat)) (and (@ (@ tptp.ord_less_nat X4) N) (@ (@ tptp.ord_less_nat Y4) N) (@ (@ tptp.ord_less_eq_nat X4) Y4))))))))
% 6.73/7.08 (assert (= tptp.semiri1316708129612266289at_nat tptp.id_nat))
% 6.73/7.08 (assert (forall ((A tptp.int) (D tptp.int) (B tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.abs_abs_int D))) (let ((_let_2 (@ tptp.abs_abs_int C2))) (let ((_let_3 (@ tptp.abs_abs_int B))) (let ((_let_4 (@ tptp.abs_abs_int A))) (=> (@ (@ tptp.algebr932160517623751201me_int A) D) (=> (@ (@ tptp.algebr932160517623751201me_int B) C2) (= (= (@ (@ tptp.times_times_int _let_4) _let_2) (@ (@ tptp.times_times_int _let_3) _let_1)) (and (= _let_4 _let_3) (= _let_2 _let_1)))))))))))
% 6.73/7.08 (assert (@ (@ tptp.order_4473980167227706203on_nat (@ tptp.field_nat tptp.bNF_Ca8665028551170535155natLeq)) tptp.bNF_Ca8665028551170535155natLeq))
% 6.73/7.08 (assert (@ (@ tptp.total_on_nat (@ tptp.field_nat tptp.bNF_Ca8665028551170535155natLeq)) tptp.bNF_Ca8665028551170535155natLeq))
% 6.73/7.08 (assert (@ (@ tptp.refl_on_nat (@ tptp.field_nat tptp.bNF_Ca8665028551170535155natLeq)) tptp.bNF_Ca8665028551170535155natLeq))
% 6.73/7.08 (assert (= tptp.bNF_Ca8459412986667044542atLess (@ (@ tptp.minus_1356011639430497352at_nat tptp.bNF_Ca8665028551170535155natLeq) tptp.id_nat2)))
% 6.73/7.08 (assert (= (@ tptp.field_nat tptp.bNF_Ca8665028551170535155natLeq) tptp.top_top_set_nat))
% 6.73/7.08 (assert (= tptp.bNF_Ca8665028551170535155natLeq (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o tptp.ord_less_eq_nat))))
% 6.73/7.08 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat tptp.bNF_Ca8665028551170535155natLeq) (@ (@ tptp.produc457027306803732586at_nat (@ (@ tptp.order_underS_nat tptp.bNF_Ca8665028551170535155natLeq) N)) (lambda ((Uu3 tptp.nat)) (@ (@ tptp.order_underS_nat tptp.bNF_Ca8665028551170535155natLeq) N)))) (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((X4 tptp.nat) (Y4 tptp.nat)) (and (@ (@ tptp.ord_less_nat X4) N) (@ (@ tptp.ord_less_nat Y4) N) (@ (@ tptp.ord_less_eq_nat X4) Y4))))))))
% 6.73/7.08 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.order_underS_nat tptp.bNF_Ca8665028551170535155natLeq) N) (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (@ (@ tptp.ord_less_nat X4) N))))))
% 6.73/7.08 (assert (forall ((A tptp.nat) (B tptp.nat) (S2 tptp.nat) (T tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_nat S2) T) (@ (@ tptp.member8206827879206165904at_nat (@ (@ tptp.produc6161850002892822231at_nat (@ (@ tptp.product_Pair_nat_nat A) S2)) (@ (@ tptp.product_Pair_nat_nat B) T))) tptp.fun_pair_less)))))
% 6.73/7.08 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z3 tptp.nat)) (let ((_let_1 (@ tptp.product_Pair_nat_nat X))) (= (@ (@ tptp.member8206827879206165904at_nat (@ (@ tptp.produc6161850002892822231at_nat (@ _let_1 Y)) (@ _let_1 Z3))) tptp.fun_pair_less) (@ (@ tptp.ord_less_nat Y) Z3)))))
% 6.73/7.08 (assert (forall ((A tptp.nat) (B tptp.nat) (S2 tptp.nat) (T tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (@ (@ tptp.member8206827879206165904at_nat (@ (@ tptp.produc6161850002892822231at_nat (@ (@ tptp.product_Pair_nat_nat A) S2)) (@ (@ tptp.product_Pair_nat_nat B) T))) tptp.fun_pair_less))))
% 6.73/7.08 (assert (forall ((A tptp.nat) (B tptp.nat) (S2 tptp.nat) (T tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat S2) T) (@ (@ tptp.member8206827879206165904at_nat (@ (@ tptp.produc6161850002892822231at_nat (@ (@ tptp.product_Pair_nat_nat A) S2)) (@ (@ tptp.product_Pair_nat_nat B) T))) tptp.fun_pair_leq)))))
% 6.73/7.08 (assert (forall ((A tptp.nat) (B tptp.nat) (S2 tptp.nat) (T tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (@ (@ tptp.member8206827879206165904at_nat (@ (@ tptp.produc6161850002892822231at_nat (@ (@ tptp.product_Pair_nat_nat A) S2)) (@ (@ tptp.product_Pair_nat_nat B) T))) tptp.fun_pair_leq))))
% 6.73/7.08 (assert (forall ((I2 tptp.int) (J2 tptp.int)) (= (@ tptp.size_size_list_int (@ (@ tptp.upto I2) J2)) (@ tptp.nat2 (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int J2) I2)) tptp.one_one_int)))))
% 6.73/7.08 (assert (@ (@ (@ tptp.ordering_top_nat tptp.dvd_dvd_nat) (lambda ((M6 tptp.nat) (N4 tptp.nat)) (and (@ (@ tptp.dvd_dvd_nat M6) N4) (not (= M6 N4))))) tptp.zero_zero_nat))
% 6.73/7.08 (assert (@ (@ (@ tptp.ordering_top_nat (lambda ((X4 tptp.nat) (Y4 tptp.nat)) (@ (@ tptp.ord_less_eq_nat Y4) X4))) (lambda ((X4 tptp.nat) (Y4 tptp.nat)) (@ (@ tptp.ord_less_nat Y4) X4))) tptp.zero_zero_nat))
% 6.73/7.08 (assert (= tptp.ratrel (lambda ((X4 tptp.product_prod_int_int) (Y4 tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.product_snd_int_int X4))) (let ((_let_2 (@ tptp.product_snd_int_int Y4))) (and (not (= _let_1 tptp.zero_zero_int)) (not (= _let_2 tptp.zero_zero_int)) (= (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int X4)) _let_2) (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int Y4)) _let_1))))))))
% 6.73/7.08 (assert (= tptp.ratrel (lambda ((X4 tptp.product_prod_int_int) (Y4 tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.product_snd_int_int X4))) (let ((_let_2 (@ tptp.product_snd_int_int Y4))) (and (not (= _let_1 tptp.zero_zero_int)) (not (= _let_2 tptp.zero_zero_int)) (= (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int X4)) _let_2) (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int Y4)) _let_1))))))))
% 6.73/7.08 (assert (forall ((Xa2 tptp.product_prod_int_int) (X tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.product_snd_int_int X))) (let ((_let_2 (@ tptp.product_snd_int_int Xa2))) (=> (@ (@ tptp.ratrel Xa2) Xa2) (=> (@ (@ tptp.ratrel X) X) (= (@ (@ tptp.plus_plus_rat (@ tptp.abs_Rat Xa2)) (@ tptp.abs_Rat X)) (@ tptp.abs_Rat (@ (@ tptp.product_Pair_int_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int Xa2)) _let_1)) (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int X)) _let_2))) (@ (@ tptp.times_times_int _let_2) _let_1))))))))))
% 6.73/7.08 (assert (forall ((Xa2 tptp.product_prod_int_int) (X tptp.product_prod_int_int)) (=> (@ (@ tptp.ratrel Xa2) Xa2) (=> (@ (@ tptp.ratrel X) X) (= (@ (@ tptp.times_times_rat (@ tptp.abs_Rat Xa2)) (@ tptp.abs_Rat X)) (@ tptp.abs_Rat (@ (@ tptp.product_Pair_int_int (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int Xa2)) (@ tptp.product_fst_int_int X))) (@ (@ tptp.times_times_int (@ tptp.product_snd_int_int Xa2)) (@ tptp.product_snd_int_int X)))))))))
% 6.73/7.08 (assert (forall ((X tptp.product_prod_int_int)) (=> (@ (@ tptp.ratrel X) X) (= (@ tptp.positive (@ tptp.abs_Rat X)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int X)) (@ tptp.product_snd_int_int X)))))))
% 6.73/7.08 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ tptp.positive X) (=> (@ tptp.positive Y) (@ tptp.positive (@ (@ tptp.times_times_rat X) Y))))))
% 6.73/7.08 (assert (= tptp.positive (lambda ((X4 tptp.rat)) (let ((_let_1 (@ tptp.rep_Rat X4))) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int _let_1)) (@ tptp.product_snd_int_int _let_1)))))))
% 6.73/7.08 (assert (@ (@ (@ (@ tptp.bNF_re8699439704749558557nt_o_o tptp.ratrel) (lambda ((Y5 Bool) (Z2 Bool)) (= Y5 Z2))) (lambda ((X4 tptp.product_prod_int_int)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int X4)) (@ tptp.product_snd_int_int X4))))) (lambda ((X4 tptp.product_prod_int_int)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int X4)) (@ tptp.product_snd_int_int X4))))))
% 6.73/7.08 (assert (= tptp.positive (@ (@ (@ tptp.map_fu898904425404107465nt_o_o tptp.rep_Rat) tptp.id_o) (lambda ((X4 tptp.product_prod_int_int)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int X4)) (@ tptp.product_snd_int_int X4)))))))
% 6.73/7.08 (assert (@ (@ (@ (@ tptp.bNF_re578469030762574527_nat_o (lambda ((Y5 tptp.nat) (Z2 tptp.nat)) (= Y5 Z2))) (@ (@ tptp.bNF_re4705727531993890431at_o_o (lambda ((Y5 tptp.nat) (Z2 tptp.nat)) (= Y5 Z2))) (lambda ((Y5 Bool) (Z2 Bool)) (= Y5 Z2)))) tptp.ord_less_eq_nat) tptp.ord_less_eq_nat))
% 6.73/7.08 (assert (@ (@ (@ (@ tptp.bNF_re5653821019739307937at_nat (lambda ((Y5 tptp.nat) (Z2 tptp.nat)) (= Y5 Z2))) (lambda ((Y5 tptp.nat) (Z2 tptp.nat)) (= Y5 Z2))) tptp.suc) tptp.suc))
% 6.73/7.08 (assert (@ (@ (@ (@ tptp.bNF_re711492959462206631nt_int (lambda ((Y5 tptp.int) (Z2 tptp.int)) (= Y5 Z2))) (@ (@ tptp.bNF_re4712519889275205905nt_int (lambda ((Y5 tptp.int) (Z2 tptp.int)) (= Y5 Z2))) (lambda ((Y5 tptp.int) (Z2 tptp.int)) (= Y5 Z2)))) tptp.times_times_int) tptp.times_times_int))
% 6.73/7.08 (assert (@ (@ (@ (@ tptp.bNF_re1345281282404953727at_nat (lambda ((Y5 tptp.nat) (Z2 tptp.nat)) (= Y5 Z2))) (@ (@ tptp.bNF_re5653821019739307937at_nat (lambda ((Y5 tptp.nat) (Z2 tptp.nat)) (= Y5 Z2))) (lambda ((Y5 tptp.nat) (Z2 tptp.nat)) (= Y5 Z2)))) tptp.times_times_nat) tptp.times_times_nat))
% 6.73/7.08 (assert (@ (@ (@ (@ tptp.bNF_re5228765855967844073nt_int tptp.ratrel) (@ (@ tptp.bNF_re7145576690424134365nt_int tptp.ratrel) tptp.ratrel)) (lambda ((X4 tptp.product_prod_int_int) (Y4 tptp.product_prod_int_int)) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int X4)) (@ tptp.product_fst_int_int Y4))) (@ (@ tptp.times_times_int (@ tptp.product_snd_int_int X4)) (@ tptp.product_snd_int_int Y4))))) (lambda ((X4 tptp.product_prod_int_int) (Y4 tptp.product_prod_int_int)) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int X4)) (@ tptp.product_fst_int_int Y4))) (@ (@ tptp.times_times_int (@ tptp.product_snd_int_int X4)) (@ tptp.product_snd_int_int Y4))))))
% 6.73/7.08 (assert (@ (@ (@ (@ tptp.bNF_re5228765855967844073nt_int tptp.ratrel) (@ (@ tptp.bNF_re7145576690424134365nt_int tptp.ratrel) tptp.ratrel)) (lambda ((X4 tptp.product_prod_int_int) (Y4 tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.product_snd_int_int Y4))) (let ((_let_2 (@ tptp.product_snd_int_int X4))) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int X4)) _let_1)) (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int Y4)) _let_2))) (@ (@ tptp.times_times_int _let_2) _let_1)))))) (lambda ((X4 tptp.product_prod_int_int) (Y4 tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.product_snd_int_int Y4))) (let ((_let_2 (@ tptp.product_snd_int_int X4))) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int X4)) _let_1)) (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int Y4)) _let_2))) (@ (@ tptp.times_times_int _let_2) _let_1)))))))
% 6.73/7.08 (assert (@ (@ (@ (@ tptp.bNF_re7627151682743391978at_rat tptp.pcr_rat) (@ (@ tptp.bNF_re8279943556446156061nt_rat tptp.pcr_rat) tptp.pcr_rat)) (lambda ((X4 tptp.product_prod_int_int) (Y4 tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.product_snd_int_int Y4))) (let ((_let_2 (@ tptp.product_snd_int_int X4))) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int X4)) _let_1)) (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int Y4)) _let_2))) (@ (@ tptp.times_times_int _let_2) _let_1)))))) tptp.plus_plus_rat))
% 6.73/7.08 (assert (@ (@ (@ (@ tptp.bNF_re1494630372529172596at_o_o tptp.pcr_rat) (lambda ((Y5 Bool) (Z2 Bool)) (= Y5 Z2))) (lambda ((X4 tptp.product_prod_int_int)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int X4)) (@ tptp.product_snd_int_int X4))))) tptp.positive))
% 6.73/7.08 (assert (@ (@ (@ (@ tptp.bNF_re7627151682743391978at_rat tptp.pcr_rat) (@ (@ tptp.bNF_re8279943556446156061nt_rat tptp.pcr_rat) tptp.pcr_rat)) (lambda ((X4 tptp.product_prod_int_int) (Y4 tptp.product_prod_int_int)) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int X4)) (@ tptp.product_fst_int_int Y4))) (@ (@ tptp.times_times_int (@ tptp.product_snd_int_int X4)) (@ tptp.product_snd_int_int Y4))))) tptp.times_times_rat))
% 6.73/7.08 (assert (@ (@ (@ (@ tptp.bNF_re7408651293131936558nt_int tptp.pcr_int) (@ (@ tptp.bNF_re7400052026677387805at_int tptp.pcr_int) tptp.pcr_int)) (@ tptp.produc27273713700761075at_nat (lambda ((X4 tptp.nat) (Y4 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((U2 tptp.nat) (V3 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat Y4))) (let ((_let_2 (@ tptp.times_times_nat X4))) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat (@ _let_2 U2)) (@ _let_1 V3))) (@ (@ tptp.plus_plus_nat (@ _let_2 V3)) (@ _let_1 U2))))))) __flatten_var_0)))) tptp.times_times_int))
% 6.73/7.08 (assert (@ (@ (@ (@ tptp.bNF_re7408651293131936558nt_int tptp.pcr_int) (@ (@ tptp.bNF_re7400052026677387805at_int tptp.pcr_int) tptp.pcr_int)) (@ tptp.produc27273713700761075at_nat (lambda ((X4 tptp.nat) (Y4 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((U2 tptp.nat) (V3 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat X4) V3)) (@ (@ tptp.plus_plus_nat Y4) U2)))) __flatten_var_0)))) tptp.minus_minus_int))
% 6.73/7.08 (assert (@ (@ tptp.pcr_int (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) tptp.zero_zero_nat)) tptp.zero_zero_int))
% 6.73/7.08 (assert (@ (@ (@ (@ tptp.bNF_re6830278522597306478at_int (lambda ((Y5 tptp.nat) (Z2 tptp.nat)) (= Y5 Z2))) tptp.pcr_int) (lambda ((N4 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat N4) tptp.zero_zero_nat))) tptp.semiri1314217659103216013at_int))
% 6.73/7.08 (assert (@ (@ (@ (@ tptp.bNF_re7400052026677387805at_int tptp.pcr_int) tptp.pcr_int) (@ tptp.produc2626176000494625587at_nat (lambda ((X4 tptp.nat) (Y4 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat Y4) X4)))) tptp.uminus_uminus_int))
% 6.73/7.08 (assert (@ (@ tptp.pcr_int (@ (@ tptp.product_Pair_nat_nat tptp.one_one_nat) tptp.zero_zero_nat)) tptp.one_one_int))
% 6.73/7.08 (assert (@ (@ (@ (@ tptp.bNF_re717283939379294677_int_o tptp.pcr_int) (@ (@ tptp.bNF_re6644619430987730960nt_o_o tptp.pcr_int) (lambda ((Y5 Bool) (Z2 Bool)) (= Y5 Z2)))) (@ tptp.produc8739625826339149834_nat_o (lambda ((X4 tptp.nat) (Y4 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc6081775807080527818_nat_o (lambda ((U2 tptp.nat) (V3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat X4) V3)) (@ (@ tptp.plus_plus_nat U2) Y4)))) __flatten_var_0)))) tptp.ord_less_eq_int))
% 6.73/7.08 (assert (@ (@ (@ (@ tptp.bNF_re7408651293131936558nt_int tptp.pcr_int) (@ (@ tptp.bNF_re7400052026677387805at_int tptp.pcr_int) tptp.pcr_int)) (@ tptp.produc27273713700761075at_nat (lambda ((X4 tptp.nat) (Y4 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((U2 tptp.nat) (V3 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat X4) U2)) (@ (@ tptp.plus_plus_nat Y4) V3)))) __flatten_var_0)))) tptp.plus_plus_int))
% 6.73/7.08 (assert (@ (@ (@ (@ tptp.bNF_re3099431351363272937at_nat tptp.intrel) (@ (@ tptp.bNF_re2241393799969408733at_nat tptp.intrel) tptp.intrel)) (@ tptp.produc27273713700761075at_nat (lambda ((X4 tptp.nat) (Y4 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((U2 tptp.nat) (V3 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat Y4))) (let ((_let_2 (@ tptp.times_times_nat X4))) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat (@ _let_2 U2)) (@ _let_1 V3))) (@ (@ tptp.plus_plus_nat (@ _let_2 V3)) (@ _let_1 U2))))))) __flatten_var_0)))) (@ tptp.produc27273713700761075at_nat (lambda ((X4 tptp.nat) (Y4 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((U2 tptp.nat) (V3 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat Y4))) (let ((_let_2 (@ tptp.times_times_nat X4))) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat (@ _let_2 U2)) (@ _let_1 V3))) (@ (@ tptp.plus_plus_nat (@ _let_2 V3)) (@ _let_1 U2))))))) __flatten_var_0)))))
% 6.73/7.08 (assert (@ (@ (@ (@ tptp.bNF_re3099431351363272937at_nat tptp.intrel) (@ (@ tptp.bNF_re2241393799969408733at_nat tptp.intrel) tptp.intrel)) (@ tptp.produc27273713700761075at_nat (lambda ((X4 tptp.nat) (Y4 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((U2 tptp.nat) (V3 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat X4) V3)) (@ (@ tptp.plus_plus_nat Y4) U2)))) __flatten_var_0)))) (@ tptp.produc27273713700761075at_nat (lambda ((X4 tptp.nat) (Y4 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((U2 tptp.nat) (V3 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat X4) V3)) (@ (@ tptp.plus_plus_nat Y4) U2)))) __flatten_var_0)))))
% 6.73/7.08 (assert (forall ((X tptp.nat) (Y tptp.nat) (U tptp.nat) (V2 tptp.nat)) (= (@ (@ tptp.intrel (@ (@ tptp.product_Pair_nat_nat X) Y)) (@ (@ tptp.product_Pair_nat_nat U) V2)) (= (@ (@ tptp.plus_plus_nat X) V2) (@ (@ tptp.plus_plus_nat U) Y)))))
% 6.73/7.08 (assert (let ((_let_1 (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) tptp.zero_zero_nat))) (@ (@ tptp.intrel _let_1) _let_1)))
% 6.73/7.08 (assert (@ (@ (@ (@ tptp.bNF_re2241393799969408733at_nat tptp.intrel) tptp.intrel) (@ tptp.produc2626176000494625587at_nat (lambda ((X4 tptp.nat) (Y4 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat Y4) X4)))) (@ tptp.produc2626176000494625587at_nat (lambda ((X4 tptp.nat) (Y4 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat Y4) X4)))))
% 6.73/7.08 (assert (let ((_let_1 (@ (@ tptp.product_Pair_nat_nat tptp.one_one_nat) tptp.zero_zero_nat))) (@ (@ tptp.intrel _let_1) _let_1)))
% 6.73/7.08 (assert (@ (@ (@ (@ tptp.bNF_re4202695980764964119_nat_o tptp.intrel) (@ (@ tptp.bNF_re3666534408544137501at_o_o tptp.intrel) (lambda ((Y5 Bool) (Z2 Bool)) (= Y5 Z2)))) (@ tptp.produc8739625826339149834_nat_o (lambda ((X4 tptp.nat) (Y4 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc6081775807080527818_nat_o (lambda ((U2 tptp.nat) (V3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat X4) V3)) (@ (@ tptp.plus_plus_nat U2) Y4)))) __flatten_var_0)))) (@ tptp.produc8739625826339149834_nat_o (lambda ((X4 tptp.nat) (Y4 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc6081775807080527818_nat_o (lambda ((U2 tptp.nat) (V3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat X4) V3)) (@ (@ tptp.plus_plus_nat U2) Y4)))) __flatten_var_0)))))
% 6.73/7.08 (assert (@ (@ (@ (@ tptp.bNF_re3099431351363272937at_nat tptp.intrel) (@ (@ tptp.bNF_re2241393799969408733at_nat tptp.intrel) tptp.intrel)) (@ tptp.produc27273713700761075at_nat (lambda ((X4 tptp.nat) (Y4 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((U2 tptp.nat) (V3 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat X4) U2)) (@ (@ tptp.plus_plus_nat Y4) V3)))) __flatten_var_0)))) (@ tptp.produc27273713700761075at_nat (lambda ((X4 tptp.nat) (Y4 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((U2 tptp.nat) (V3 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat X4) U2)) (@ (@ tptp.plus_plus_nat Y4) V3)))) __flatten_var_0)))))
% 6.73/7.08 (assert (= tptp.ord_le2932123472753598470d_enat (lambda ((M6 tptp.extended_enat) (__flatten_var_0 tptp.extended_enat)) (@ (@ (@ tptp.extended_case_enat_o (lambda ((N1 tptp.nat)) (@ (@ (@ tptp.extended_case_enat_o (lambda ((M1 tptp.nat)) (@ (@ tptp.ord_less_eq_nat M1) N1))) false) M6))) true) __flatten_var_0))))
% 6.73/7.08 (assert (@ (@ tptp.order_2888998067076097458on_nat (@ tptp.field_nat tptp.bNF_Ca8665028551170535155natLeq)) tptp.bNF_Ca8665028551170535155natLeq))
% 6.73/7.08 (assert (forall ((N tptp.nat)) (@ (@ tptp.order_2888998067076097458on_nat (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (@ (@ tptp.ord_less_nat X4) N)))) (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((X4 tptp.nat) (Y4 tptp.nat)) (and (@ (@ tptp.ord_less_nat X4) N) (@ (@ tptp.ord_less_nat Y4) N) (@ (@ tptp.ord_less_eq_nat X4) Y4))))))))
% 6.73/7.08 (assert (forall ((N tptp.nat)) (@ (@ tptp.order_2888998067076097458on_nat (@ tptp.field_nat (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((X4 tptp.nat) (Y4 tptp.nat)) (and (@ (@ tptp.ord_less_nat X4) N) (@ (@ tptp.ord_less_nat Y4) N) (@ (@ tptp.ord_less_eq_nat X4) Y4))))))) (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((X4 tptp.nat) (Y4 tptp.nat)) (and (@ (@ tptp.ord_less_nat X4) N) (@ (@ tptp.ord_less_nat Y4) N) (@ (@ tptp.ord_less_eq_nat X4) Y4))))))))
% 6.73/7.08 (assert (@ (@ tptp.inj_on_nat_char tptp.unique3096191561947761185of_nat) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 tptp.one))))))))))))
% 6.73/7.08 (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)))))))))))))
% 6.73/7.08 (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))))))))))))
% 6.73/7.08 (assert (= tptp.plus_plus_rat (@ (@ (@ tptp.map_fu4333342158222067775at_rat tptp.rep_Rat) (@ (@ tptp.map_fu5673905371560938248nt_rat tptp.rep_Rat) tptp.abs_Rat)) (lambda ((X4 tptp.product_prod_int_int) (Y4 tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.product_snd_int_int Y4))) (let ((_let_2 (@ tptp.product_snd_int_int X4))) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int X4)) _let_1)) (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int Y4)) _let_2))) (@ (@ tptp.times_times_int _let_2) _let_1))))))))
% 6.73/7.08 (assert (forall ((B tptp.int) (D tptp.int) (A tptp.int) (C2 tptp.int)) (=> (not (= B tptp.zero_zero_int)) (=> (not (= D tptp.zero_zero_int)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.fract A) B)) (@ (@ tptp.fract C2) D)) (@ (@ tptp.fract (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int A) D)) (@ (@ tptp.times_times_int C2) B))) (@ (@ tptp.times_times_int B) D)))))))
% 6.73/7.08 (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))))))
% 6.73/7.08 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int) (D tptp.int)) (= (@ (@ tptp.times_times_rat (@ (@ tptp.fract A) B)) (@ (@ tptp.fract C2) D)) (@ (@ tptp.fract (@ (@ tptp.times_times_int A) C2)) (@ (@ tptp.times_times_int B) D)))))
% 6.73/7.08 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int) (D tptp.int)) (= (@ (@ tptp.divide_divide_rat (@ (@ tptp.fract A) B)) (@ (@ tptp.fract C2) D)) (@ (@ tptp.fract (@ (@ tptp.times_times_int A) D)) (@ (@ tptp.times_times_int B) C2)))))
% 6.73/7.08 (assert (forall ((B tptp.int) (D tptp.int) (A tptp.int) (C2 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 C2) 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 C2) B)) _let_1))))))))
% 6.73/7.08 (assert (forall ((B tptp.int) (D tptp.int) (A tptp.int) (C2 tptp.int)) (=> (not (= B tptp.zero_zero_int)) (=> (not (= D tptp.zero_zero_int)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.fract A) B)) (@ (@ tptp.fract C2) D)) (@ (@ tptp.fract (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) D)) (@ (@ tptp.times_times_int C2) B))) (@ (@ tptp.times_times_int B) D)))))))
% 6.73/7.08 (assert (forall ((B tptp.int) (D tptp.int) (A tptp.int) (C2 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 C2) 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 C2) B)) _let_1))))))))
% 6.73/7.08 (assert (forall ((C2 tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C2))) (=> (not (= C2 tptp.zero_zero_int)) (= (@ (@ tptp.fract (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.fract A) B))))))
% 6.73/7.08 (assert (forall ((B tptp.int) (D tptp.int) (A tptp.int) (C2 tptp.int)) (=> (not (= B tptp.zero_zero_int)) (=> (not (= D tptp.zero_zero_int)) (= (= (@ (@ tptp.fract A) B) (@ (@ tptp.fract C2) D)) (= (@ (@ tptp.times_times_int A) D) (@ (@ tptp.times_times_int C2) B)))))))
% 6.73/7.08 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ tptp.positive (@ (@ tptp.fract A) B)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.times_times_int A) B)))))
% 6.73/7.08 (assert (= tptp.times_times_rat (@ (@ (@ tptp.map_fu4333342158222067775at_rat tptp.rep_Rat) (@ (@ tptp.map_fu5673905371560938248nt_rat tptp.rep_Rat) tptp.abs_Rat)) (lambda ((X4 tptp.product_prod_int_int) (Y4 tptp.product_prod_int_int)) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int X4)) (@ tptp.product_fst_int_int Y4))) (@ (@ tptp.times_times_int (@ tptp.product_snd_int_int X4)) (@ tptp.product_snd_int_int Y4)))))))
% 6.73/7.08 (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))))))
% 6.73/7.08 (assert (forall ((X1 Bool) (X2 Bool) (X33 Bool) (X42 Bool) (X52 Bool) (X62 Bool) (X72 Bool) (X82 Bool)) (= (@ tptp.size_size_char (@ (@ (@ (@ (@ (@ (@ (@ tptp.char2 X1) X2) X33) X42) X52) X62) X72) X82)) tptp.zero_zero_nat)))
% 6.73/7.08 (assert (forall ((X1 Bool) (X2 Bool) (X33 Bool) (X42 Bool) (X52 Bool) (X62 Bool) (X72 Bool) (X82 Bool)) (= (@ tptp.size_char (@ (@ (@ (@ (@ (@ (@ (@ tptp.char2 X1) X2) X33) X42) X52) X62) X72) X82)) tptp.zero_zero_nat)))
% 6.73/7.08 (assert (forall ((M2 tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_le2932123472753598470d_enat (@ tptp.numera1916890842035813515d_enat M2)) (@ tptp.extended_enat2 N)) (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat M2)) N))))
% 6.73/7.08 (assert (forall ((N tptp.extended_enat)) (= (@ (@ tptp.minus_3235023915231533773d_enat N) (@ tptp.extended_enat2 tptp.zero_zero_nat)) N)))
% 6.73/7.08 (assert (forall ((N tptp.extended_enat)) (let ((_let_1 (@ tptp.extended_enat2 tptp.zero_zero_nat))) (= (@ (@ tptp.minus_3235023915231533773d_enat _let_1) N) _let_1))))
% 6.73/7.08 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.times_7803423173614009249d_enat (@ tptp.extended_enat2 M2)) (@ tptp.extended_enat2 N)) (@ tptp.extended_enat2 (@ (@ tptp.times_times_nat M2) N)))))
% 6.73/7.08 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_le2932123472753598470d_enat (@ tptp.extended_enat2 M2)) (@ tptp.extended_enat2 N)) (@ (@ tptp.ord_less_eq_nat M2) N))))
% 6.73/7.08 (assert (forall ((M2 tptp.nat) (N tptp.extended_enat)) (= (@ (@ tptp.ord_le2932123472753598470d_enat (@ tptp.extended_enat2 (@ tptp.suc M2))) N) (@ (@ tptp.ord_le72135733267957522d_enat (@ tptp.extended_enat2 M2)) N))))
% 6.73/7.08 (assert (forall ((X tptp.nat)) (= (= tptp.zero_z5237406670263579293d_enat (@ tptp.extended_enat2 X)) (= X tptp.zero_zero_nat))))
% 6.73/7.08 (assert (forall ((X tptp.nat)) (= (= (@ tptp.extended_enat2 X) tptp.zero_z5237406670263579293d_enat) (= X tptp.zero_zero_nat))))
% 6.73/7.08 (assert (= tptp.zero_z5237406670263579293d_enat (@ tptp.extended_enat2 tptp.zero_zero_nat)))
% 6.73/7.08 (assert (forall ((X tptp.extended_enat) (Y tptp.extended_enat) (N tptp.nat)) (= (@ (@ tptp.ord_le2932123472753598470d_enat (@ (@ tptp.plus_p3455044024723400733d_enat X) Y)) (@ tptp.extended_enat2 N)) (exists ((Y8 tptp.nat) (X9 tptp.nat)) (and (= X (@ tptp.extended_enat2 X9)) (= Y (@ tptp.extended_enat2 Y8)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat X9) Y8)) N))))))
% 6.73/7.08 (assert (forall ((Info2 tptp.option4927543243414619207at_nat) (Deg tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (N tptp.nat)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info2) Deg) TreeList2) Summary))) (=> (@ (@ tptp.vEBT_invar_vebt _let_1) N) (= (@ (@ tptp.vEBT_VEBT_elim_dead _let_1) (@ tptp.extended_enat2 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) _let_1)))))
% 6.73/7.08 (assert (forall ((Info2 tptp.option4927543243414619207at_nat) (Deg tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (L tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat L) (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.divide_divide_nat Deg) _let_1))))) (let ((_let_3 (@ (@ tptp.vEBT_Node Info2) Deg))) (= (@ (@ tptp.vEBT_VEBT_elim_dead (@ (@ _let_3 TreeList2) Summary)) (@ tptp.extended_enat2 L)) (@ (@ _let_3 (@ (@ tptp.take_VEBT_VEBT _let_2) (@ (@ tptp.map_VE8901447254227204932T_VEBT (lambda ((T2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.vEBT_VEBT_elim_dead T2) (@ tptp.extended_enat2 (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.divide_divide_nat Deg) _let_1))))))) TreeList2))) (@ (@ tptp.vEBT_VEBT_elim_dead Summary) (@ tptp.extended_enat2 _let_2)))))))))
% 6.73/7.08 (assert (forall ((M2 tptp.extended_enat) (N tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat))) (= (@ _let_1 (@ (@ tptp.times_7803423173614009249d_enat M2) N)) (and (@ _let_1 M2) (@ _let_1 N))))))
% 6.73/7.08 (assert (forall ((M2 tptp.extended_enat) (N tptp.extended_enat)) (= (= (@ (@ tptp.times_7803423173614009249d_enat M2) N) tptp.zero_z5237406670263579293d_enat) (or (= M2 tptp.zero_z5237406670263579293d_enat) (= N tptp.zero_z5237406670263579293d_enat)))))
% 6.73/7.08 (assert (forall ((A Bool) (B Bool) (Uu tptp.extended_enat)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A) B))) (= (@ (@ tptp.vEBT_VEBT_elim_dead _let_1) Uu) _let_1))))
% 6.73/7.08 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.extended_enat) (Y tptp.vEBT_VEBT)) (=> (= (@ (@ tptp.vEBT_VEBT_elim_dead X) Xa2) Y) (=> (forall ((A3 Bool) (B3 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A3) B3))) (=> (= X _let_1) (not (= Y _let_1))))) (=> (forall ((Info tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ tptp.vEBT_Node Info) Deg2))) (=> (= X (@ (@ _let_1 TreeList) Summary2)) (=> (= Xa2 tptp.extend5688581933313929465d_enat) (not (= Y (@ (@ _let_1 (@ (@ tptp.map_VE8901447254227204932T_VEBT (lambda ((T2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.vEBT_VEBT_elim_dead T2) (@ tptp.extended_enat2 (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.divide_divide_nat Deg2) _let_1))))))) TreeList)) (@ (@ tptp.vEBT_VEBT_elim_dead Summary2) tptp.extend5688581933313929465d_enat)))))))) (not (forall ((Info tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (=> (= X (@ (@ (@ (@ tptp.vEBT_Node Info) Deg2) TreeList) Summary2)) (forall ((L4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat L4) (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.divide_divide_nat Deg2) _let_1))))) (=> (= Xa2 (@ tptp.extended_enat2 L4)) (not (= Y (@ (@ (@ (@ tptp.vEBT_Node Info) Deg2) (@ (@ tptp.take_VEBT_VEBT _let_2) (@ (@ tptp.map_VE8901447254227204932T_VEBT (lambda ((T2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.vEBT_VEBT_elim_dead T2) (@ tptp.extended_enat2 (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.divide_divide_nat Deg2) _let_1))))))) TreeList))) (@ (@ tptp.vEBT_VEBT_elim_dead Summary2) (@ tptp.extended_enat2 _let_2)))))))))))))))))
% 6.73/7.08 (assert (forall ((Info2 tptp.option4927543243414619207at_nat) (Deg tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ tptp.vEBT_Node Info2) Deg))) (= (@ (@ tptp.vEBT_VEBT_elim_dead (@ (@ _let_1 TreeList2) Summary)) tptp.extend5688581933313929465d_enat) (@ (@ _let_1 (@ (@ tptp.map_VE8901447254227204932T_VEBT (lambda ((T2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.vEBT_VEBT_elim_dead T2) (@ tptp.extended_enat2 (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.divide_divide_nat Deg) _let_1))))))) TreeList2)) (@ (@ tptp.vEBT_VEBT_elim_dead Summary) tptp.extend5688581933313929465d_enat))))))
% 6.73/7.08 (assert (forall ((Info2 tptp.option4927543243414619207at_nat) (Deg tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (N tptp.nat)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info2) Deg) TreeList2) Summary))) (=> (@ (@ tptp.vEBT_invar_vebt _let_1) N) (= (@ (@ tptp.vEBT_VEBT_elim_dead _let_1) tptp.extend5688581933313929465d_enat) _let_1)))))
% 6.73/7.08 (assert (= (@ (@ tptp.times_7803423173614009249d_enat tptp.extend5688581933313929465d_enat) tptp.extend5688581933313929465d_enat) tptp.extend5688581933313929465d_enat))
% 6.73/7.08 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.times_7803423173614009249d_enat tptp.extend5688581933313929465d_enat) (@ tptp.extended_enat2 N)))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.zero_z5237406670263579293d_enat)) (=> (not _let_2) (= _let_1 tptp.extend5688581933313929465d_enat)))))))
% 6.73/7.08 (assert (forall ((M2 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_7803423173614009249d_enat (@ tptp.extended_enat2 M2)) tptp.extend5688581933313929465d_enat))) (let ((_let_2 (= M2 tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.zero_z5237406670263579293d_enat)) (=> (not _let_2) (= _let_1 tptp.extend5688581933313929465d_enat)))))))
% 6.73/7.08 (assert (forall ((A tptp.extended_enat) (B tptp.extended_enat)) (= (= (@ (@ tptp.times_7803423173614009249d_enat A) B) tptp.extend5688581933313929465d_enat) (or (and (= A tptp.extend5688581933313929465d_enat) (not (= B tptp.zero_z5237406670263579293d_enat))) (and (= B tptp.extend5688581933313929465d_enat) (not (= A tptp.zero_z5237406670263579293d_enat)))))))
% 6.73/7.08 (assert (forall ((X tptp.produc7272778201969148633d_enat)) (=> (forall ((A3 Bool) (B3 Bool) (Uu2 tptp.extended_enat)) (not (= X (@ (@ tptp.produc581526299967858633d_enat (@ (@ tptp.vEBT_Leaf A3) B3)) Uu2)))) (=> (forall ((Info tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (not (= X (@ (@ tptp.produc581526299967858633d_enat (@ (@ (@ (@ tptp.vEBT_Node Info) Deg2) TreeList) Summary2)) tptp.extend5688581933313929465d_enat)))) (not (forall ((Info tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT) (L4 tptp.nat)) (not (= X (@ (@ tptp.produc581526299967858633d_enat (@ (@ (@ (@ tptp.vEBT_Node Info) Deg2) TreeList) Summary2)) (@ tptp.extended_enat2 L4))))))))))
% 6.73/7.08 (assert (forall ((N tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat) N) (= (@ (@ tptp.times_7803423173614009249d_enat tptp.extend5688581933313929465d_enat) N) tptp.extend5688581933313929465d_enat))))
% 6.73/7.08 (assert (forall ((N tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat) N) (= (@ (@ tptp.times_7803423173614009249d_enat N) tptp.extend5688581933313929465d_enat) tptp.extend5688581933313929465d_enat))))
% 6.73/7.08 (assert (= tptp.times_7803423173614009249d_enat (lambda ((M6 tptp.extended_enat) (N4 tptp.extended_enat)) (@ (@ (@ tptp.extend3600170679010898289d_enat (lambda ((O tptp.nat)) (@ (@ (@ tptp.extend3600170679010898289d_enat (lambda ((P5 tptp.nat)) (@ tptp.extended_enat2 (@ (@ tptp.times_times_nat O) P5)))) (@ (@ (@ tptp.if_Extended_enat (= O tptp.zero_zero_nat)) tptp.zero_z5237406670263579293d_enat) tptp.extend5688581933313929465d_enat)) N4))) (@ (@ (@ tptp.if_Extended_enat (= N4 tptp.zero_z5237406670263579293d_enat)) tptp.zero_z5237406670263579293d_enat) tptp.extend5688581933313929465d_enat)) M6))))
% 6.73/7.08 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.extended_enat) (Y tptp.vEBT_VEBT)) (=> (= (@ (@ tptp.vEBT_VEBT_elim_dead X) Xa2) Y) (=> (@ (@ tptp.accp_P6183159247885693666d_enat tptp.vEBT_V312737461966249ad_rel) (@ (@ tptp.produc581526299967858633d_enat X) Xa2)) (=> (forall ((A3 Bool) (B3 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A3) B3))) (=> (= X _let_1) (=> (= Y _let_1) (not (@ (@ tptp.accp_P6183159247885693666d_enat tptp.vEBT_V312737461966249ad_rel) (@ (@ tptp.produc581526299967858633d_enat _let_1) Xa2))))))) (=> (forall ((Info tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ tptp.vEBT_Node Info) Deg2))) (let ((_let_2 (@ (@ _let_1 TreeList) Summary2))) (=> (= X _let_2) (=> (= Xa2 tptp.extend5688581933313929465d_enat) (=> (= Y (@ (@ _let_1 (@ (@ tptp.map_VE8901447254227204932T_VEBT (lambda ((T2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.vEBT_VEBT_elim_dead T2) (@ tptp.extended_enat2 (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.divide_divide_nat Deg2) _let_1))))))) TreeList)) (@ (@ tptp.vEBT_VEBT_elim_dead Summary2) tptp.extend5688581933313929465d_enat))) (not (@ (@ tptp.accp_P6183159247885693666d_enat tptp.vEBT_V312737461966249ad_rel) (@ (@ tptp.produc581526299967858633d_enat _let_2) tptp.extend5688581933313929465d_enat))))))))) (not (forall ((Info tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (=> (= X (@ (@ (@ (@ tptp.vEBT_Node Info) Deg2) TreeList) Summary2)) (forall ((L4 tptp.nat)) (let ((_let_1 (@ tptp.extended_enat2 L4))) (let ((_let_2 (@ (@ tptp.vEBT_Node Info) Deg2))) (let ((_let_3 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_4 (@ (@ tptp.divide_divide_nat L4) (@ (@ tptp.power_power_nat _let_3) (@ (@ tptp.divide_divide_nat Deg2) _let_3))))) (=> (= Xa2 _let_1) (=> (= Y (@ (@ _let_2 (@ (@ tptp.take_VEBT_VEBT _let_4) (@ (@ tptp.map_VE8901447254227204932T_VEBT (lambda ((T2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.vEBT_VEBT_elim_dead T2) (@ tptp.extended_enat2 (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.divide_divide_nat Deg2) _let_1))))))) TreeList))) (@ (@ tptp.vEBT_VEBT_elim_dead Summary2) (@ tptp.extended_enat2 _let_4)))) (not (@ (@ tptp.accp_P6183159247885693666d_enat tptp.vEBT_V312737461966249ad_rel) (@ (@ tptp.produc581526299967858633d_enat (@ (@ _let_2 TreeList) Summary2)) _let_1)))))))))))))))))))
% 6.73/7.08 (assert (= tptp.extended_eSuc (@ (@ tptp.extend3600170679010898289d_enat (lambda ((N4 tptp.nat)) (@ tptp.extended_enat2 (@ tptp.suc N4)))) tptp.extend5688581933313929465d_enat)))
% 6.73/7.08 (assert (= tptp.binomial (lambda ((N4 tptp.nat) (K3 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) N4))) (= (@ tptp.finite_card_nat K7) K3))))))))
% 6.73/7.08 (assert (forall ((Y tptp.nat) (X tptp.extended_enat)) (= (= (@ tptp.extended_enat2 Y) (@ tptp.extended_eSuc X)) (exists ((N4 tptp.nat)) (and (= Y (@ tptp.suc N4)) (= (@ tptp.extended_enat2 N4) X))))))
% 6.73/7.08 (assert (forall ((X tptp.extended_enat) (Y tptp.nat)) (= (= (@ tptp.extended_eSuc X) (@ tptp.extended_enat2 Y)) (exists ((N4 tptp.nat)) (and (= Y (@ tptp.suc N4)) (= X (@ tptp.extended_enat2 N4)))))))
% 6.73/7.08 (assert (forall ((N tptp.nat)) (= (@ tptp.extended_eSuc (@ tptp.extended_enat2 N)) (@ tptp.extended_enat2 (@ tptp.suc N)))))
% 6.73/7.08 (assert (forall ((M2 tptp.extended_enat) (N tptp.extended_enat)) (let ((_let_1 (@ tptp.times_7803423173614009249d_enat M2))) (= (@ _let_1 (@ tptp.extended_eSuc N)) (@ (@ tptp.plus_p3455044024723400733d_enat M2) (@ _let_1 N))))))
% 6.73/7.08 (assert (forall ((M2 tptp.extended_enat) (N tptp.extended_enat)) (= (@ (@ tptp.times_7803423173614009249d_enat (@ tptp.extended_eSuc M2)) N) (@ (@ tptp.plus_p3455044024723400733d_enat N) (@ (@ tptp.times_7803423173614009249d_enat M2) N)))))
% 6.73/7.08 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X) Y)) tptp.less_than) (@ (@ tptp.ord_less_nat X) Y))))
% 6.73/7.08 (assert (@ (@ (@ (@ tptp.bNF_re728719798268516973at_o_o tptp.realrel) (lambda ((Y5 Bool) (Z2 Bool)) (= Y5 Z2))) (lambda ((X7 (-> tptp.nat tptp.rat))) (exists ((R tptp.rat)) (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) R) (exists ((K3 tptp.nat)) (forall ((N4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K3) N4) (@ (@ tptp.ord_less_rat R) (@ X7 N4))))))))) (lambda ((X7 (-> tptp.nat tptp.rat))) (exists ((R tptp.rat)) (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) R) (exists ((K3 tptp.nat)) (forall ((N4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K3) N4) (@ (@ tptp.ord_less_rat R) (@ X7 N4))))))))))
% 6.73/7.08 (assert (forall ((Xs2 tptp.list_nat)) (= (@ tptp.gcd_Gcd_nat (@ tptp.set_nat2 Xs2)) (@ (@ (@ tptp.fold_nat_nat tptp.gcd_gcd_nat) Xs2) tptp.zero_zero_nat))))
% 6.73/7.08 (assert (@ (@ (@ (@ tptp.bNF_re1962705104956426057at_rat tptp.realrel) (@ (@ tptp.bNF_re895249473297799549at_rat tptp.realrel) tptp.realrel)) (lambda ((X7 (-> tptp.nat tptp.rat)) (Y9 (-> tptp.nat tptp.rat)) (N4 tptp.nat)) (@ (@ tptp.times_times_rat (@ X7 N4)) (@ Y9 N4)))) (lambda ((X7 (-> tptp.nat tptp.rat)) (Y9 (-> tptp.nat tptp.rat)) (N4 tptp.nat)) (@ (@ tptp.times_times_rat (@ X7 N4)) (@ Y9 N4)))))
% 6.73/7.08 (assert (@ (@ (@ (@ tptp.bNF_re4297313714947099218al_o_o tptp.pcr_real) (lambda ((Y5 Bool) (Z2 Bool)) (= Y5 Z2))) (lambda ((X7 (-> tptp.nat tptp.rat))) (exists ((R tptp.rat)) (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) R) (exists ((K3 tptp.nat)) (forall ((N4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K3) N4) (@ (@ tptp.ord_less_rat R) (@ X7 N4))))))))) tptp.positive2))
% 6.73/7.08 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ tptp.positive2 X) (=> (@ tptp.positive2 Y) (@ tptp.positive2 (@ (@ tptp.times_times_real X) Y))))))
% 6.73/7.08 (assert (@ (@ (@ (@ tptp.bNF_re4695409256820837752l_real tptp.pcr_real) (@ (@ tptp.bNF_re3023117138289059399t_real tptp.pcr_real) tptp.pcr_real)) (lambda ((X7 (-> tptp.nat tptp.rat)) (Y9 (-> tptp.nat tptp.rat)) (N4 tptp.nat)) (@ (@ tptp.times_times_rat (@ X7 N4)) (@ Y9 N4)))) tptp.times_times_real))
% 6.73/7.08 (assert (= tptp.positive2 (lambda ((X4 tptp.real)) (exists ((R tptp.rat)) (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) R) (exists ((K3 tptp.nat)) (forall ((N4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K3) N4) (@ (@ tptp.ord_less_rat R) (@ (@ tptp.rep_real X4) N4))))))))))
% 6.73/7.08 (assert (= tptp.positive2 (@ (@ (@ tptp.map_fu1856342031159181835at_o_o tptp.rep_real) tptp.id_o) (lambda ((X7 (-> tptp.nat tptp.rat))) (exists ((R tptp.rat)) (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) R) (exists ((K3 tptp.nat)) (forall ((N4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K3) N4) (@ (@ tptp.ord_less_rat R) (@ X7 N4)))))))))))
% 6.73/7.08 (assert (forall ((X (-> tptp.nat tptp.rat))) (=> (@ (@ tptp.realrel X) X) (= (@ tptp.positive2 (@ tptp.real2 X)) (exists ((R tptp.rat)) (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) R) (exists ((K3 tptp.nat)) (forall ((N4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K3) N4) (@ (@ tptp.ord_less_rat R) (@ X N4)))))))))))
% 6.73/7.08 (assert (forall ((Xa2 (-> tptp.nat tptp.rat)) (X (-> tptp.nat tptp.rat))) (=> (@ (@ tptp.realrel Xa2) Xa2) (=> (@ (@ tptp.realrel X) X) (= (@ (@ tptp.times_times_real (@ tptp.real2 Xa2)) (@ tptp.real2 X)) (@ tptp.real2 (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_rat (@ Xa2 N4)) (@ X N4)))))))))
% 6.73/7.08 (assert (forall ((X8 (-> tptp.nat tptp.rat)) (Y7 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X8) (=> (@ tptp.cauchy Y7) (= (@ (@ tptp.ord_less_eq_real (@ tptp.real2 X8)) (@ tptp.real2 Y7)) (forall ((R tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) R) (exists ((K3 tptp.nat)) (forall ((N4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K3) N4) (@ (@ tptp.ord_less_eq_rat (@ X8 N4)) (@ (@ tptp.plus_plus_rat (@ Y7 N4)) R))))))))))))
% 6.73/7.08 (assert (forall ((X8 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X8) (= (not (@ tptp.positive2 (@ tptp.real2 X8))) (forall ((R tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) R) (exists ((K3 tptp.nat)) (forall ((N4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K3) N4) (@ (@ tptp.ord_less_eq_rat (@ X8 N4)) R))))))))))
% 6.73/7.08 (assert (forall ((X8 (-> tptp.nat tptp.rat)) (Y7 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X8) (=> (@ tptp.cauchy Y7) (@ tptp.cauchy (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_rat (@ X8 N4)) (@ Y7 N4))))))))
% 6.73/7.08 (assert (forall ((X8 (-> tptp.nat tptp.rat)) (Y7 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X8) (=> (@ tptp.cauchy Y7) (= (@ (@ tptp.times_times_real (@ tptp.real2 X8)) (@ tptp.real2 Y7)) (@ tptp.real2 (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_rat (@ X8 N4)) (@ Y7 N4)))))))))
% 6.73/7.08 (assert (forall ((X8 (-> tptp.nat tptp.rat)) (R3 tptp.rat)) (=> (@ tptp.cauchy X8) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) R3) (exists ((K tptp.nat)) (forall ((M3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) M3) (forall ((N8 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N8) (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ X8 M3)) (@ X8 N8)))) R3))))))))))
% 6.73/7.08 (assert (forall ((X8 (-> tptp.nat tptp.rat))) (=> (forall ((R4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) R4) (exists ((K4 tptp.nat)) (forall ((M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K4) M) (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K4) N3) (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ X8 M)) (@ X8 N3)))) R4)))))))) (@ tptp.cauchy X8))))
% 6.73/7.08 (assert (= tptp.cauchy (lambda ((X7 (-> tptp.nat tptp.rat))) (forall ((R tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) R) (exists ((K3 tptp.nat)) (forall ((M6 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K3) M6) (forall ((N4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K3) N4) (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ X7 M6)) (@ X7 N4)))) R)))))))))))
% 6.73/7.08 (assert (forall ((X8 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X8) (= (@ tptp.positive2 (@ tptp.real2 X8)) (exists ((R tptp.rat)) (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) R) (exists ((K3 tptp.nat)) (forall ((N4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K3) N4) (@ (@ tptp.ord_less_rat R) (@ X8 N4)))))))))))
% 6.73/7.08 (assert (forall ((X8 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X8) (=> (not (@ tptp.vanishes X8)) (exists ((B3 tptp.rat)) (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) B3) (exists ((K tptp.nat)) (or (forall ((N8 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N8) (@ (@ tptp.ord_less_rat B3) (@ tptp.uminus_uminus_rat (@ X8 N8))))) (forall ((N8 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N8) (@ (@ tptp.ord_less_rat B3) (@ X8 N8))))))))))))
% 6.73/7.08 (assert (forall ((X8 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X8) (=> (not (@ tptp.vanishes X8)) (exists ((B3 tptp.rat)) (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) B3) (exists ((K tptp.nat)) (forall ((N8 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N8) (@ (@ tptp.ord_less_rat B3) (@ tptp.abs_abs_rat (@ X8 N8))))))))))))
% 6.73/7.08 (assert (forall ((X8 (-> tptp.nat tptp.rat)) (R3 tptp.rat)) (=> (@ tptp.vanishes X8) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) R3) (exists ((K tptp.nat)) (forall ((N8 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N8) (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat (@ X8 N8))) R3))))))))
% 6.73/7.08 (assert (forall ((X8 (-> tptp.nat tptp.rat))) (=> (forall ((R4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) R4) (exists ((K4 tptp.nat)) (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K4) N3) (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat (@ X8 N3))) R4)))))) (@ tptp.vanishes X8))))
% 6.73/7.08 (assert (= tptp.vanishes (lambda ((X7 (-> tptp.nat tptp.rat))) (forall ((R tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) R) (exists ((K3 tptp.nat)) (forall ((N4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K3) N4) (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat (@ X7 N4))) R)))))))))
% 6.73/7.08 (assert (forall ((X8 (-> tptp.nat tptp.rat)) (Y7 (-> tptp.nat tptp.rat))) (=> (exists ((A6 tptp.rat)) (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A6) (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat (@ X8 N3))) A6)))) (=> (@ tptp.vanishes Y7) (@ tptp.vanishes (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_rat (@ X8 N4)) (@ Y7 N4))))))))
% 6.73/7.08 (assert (= (@ (@ tptp.image_nat_int tptp.nat_int_decode) tptp.top_top_set_nat) tptp.top_top_set_int))
% 6.73/7.08 (assert (@ (@ (@ tptp.bij_betw_nat_int tptp.nat_int_decode) tptp.top_top_set_nat) tptp.top_top_set_int))
% 6.73/7.08 (assert (forall ((A4 tptp.set_nat)) (@ (@ tptp.inj_on_nat_int tptp.nat_int_decode) A4)))
% 6.73/7.08 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (= (@ tptp.nat_int_decode X) (@ tptp.nat_int_decode Y)) (= X Y))))
% 6.73/7.08 (assert (= tptp.nat_to_rat_surj (lambda ((N4 tptp.nat)) (@ (@ tptp.produc6207742614233964070at_rat (lambda ((A5 tptp.nat) (B4 tptp.nat)) (@ (@ tptp.fract (@ tptp.nat_int_decode A5)) (@ tptp.nat_int_decode B4)))) (@ tptp.nat_prod_decode N4)))))
% 6.73/7.08 (assert (@ (@ (@ tptp.bij_betw_int_nat tptp.nat_int_encode) tptp.top_top_set_int) tptp.top_top_set_nat))
% 6.73/7.08 (assert (forall ((X tptp.int)) (= (@ tptp.nat_int_decode (@ tptp.nat_int_encode X)) X)))
% 6.73/7.08 (assert (forall ((N tptp.nat)) (= (@ tptp.nat_int_encode (@ tptp.nat_int_decode N)) N)))
% 6.73/7.08 (assert (forall ((A4 tptp.set_int)) (@ (@ tptp.inj_on_int_nat tptp.nat_int_encode) A4)))
% 6.73/7.08 (assert (forall ((X tptp.int) (Y tptp.int)) (= (= (@ tptp.nat_int_encode X) (@ tptp.nat_int_encode Y)) (= X Y))))
% 6.73/7.08 (assert (= (@ (@ tptp.image_int_nat tptp.nat_int_encode) tptp.top_top_set_int) tptp.top_top_set_nat))
% 6.73/7.08 (assert (forall ((F2 (-> tptp.real tptp.real)) (R3 tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real R3))) (=> (@ tptp.real_V4572627801940501177l_real F2) (= (@ F2 (@ _let_1 B)) (@ _let_1 (@ F2 B)))))))
% 6.73/7.08 (assert (forall ((F2 (-> tptp.real tptp.real))) (=> (@ tptp.real_V4572627801940501177l_real F2) (not (forall ((C tptp.real)) (not (= F2 (@ tptp.times_times_real C))))))))
% 6.73/7.08 (assert (@ (@ tptp.order_5251275573222108571on_nat (@ tptp.field_nat tptp.bNF_Ca8665028551170535155natLeq)) tptp.bNF_Ca8665028551170535155natLeq))
% 6.73/7.08 (assert (@ (@ tptp.order_4861654808422542329on_nat (@ tptp.field_nat tptp.bNF_Ca8665028551170535155natLeq)) tptp.bNF_Ca8665028551170535155natLeq))
% 6.73/7.08 (assert (= tptp.ord_less_eq_int (@ (@ (@ tptp.map_fu434086159418415080_int_o tptp.rep_Integ) (@ (@ tptp.map_fu4826362097070443709at_o_o tptp.rep_Integ) tptp.id_o)) (@ tptp.produc8739625826339149834_nat_o (lambda ((X4 tptp.nat) (Y4 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc6081775807080527818_nat_o (lambda ((U2 tptp.nat) (V3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat X4) V3)) (@ (@ tptp.plus_plus_nat U2) Y4)))) __flatten_var_0))))))
% 6.73/7.08 (assert (= tptp.nat_int_encode (lambda ((I tptp.int)) (@ tptp.nat_sum_encode (@ (@ (@ tptp.if_Sum_sum_nat_nat (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) I)) (@ tptp.sum_Inl_nat_nat (@ tptp.nat2 I))) (@ tptp.sum_Inr_nat_nat (@ tptp.nat2 (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int I)) tptp.one_one_int))))))))
% 6.73/7.08 (assert (= (@ (@ tptp.image_1320371278474632150at_nat tptp.nat_sum_encode) tptp.top_to6661820994512907621at_nat) tptp.top_top_set_nat))
% 6.73/7.08 (assert (forall ((A4 tptp.set_Sum_sum_nat_nat)) (@ (@ tptp.inj_on6343450744447823682at_nat tptp.nat_sum_encode) A4)))
% 6.73/7.08 (assert (forall ((X tptp.sum_sum_nat_nat) (Y tptp.sum_sum_nat_nat)) (= (= (@ tptp.nat_sum_encode X) (@ tptp.nat_sum_encode Y)) (= X Y))))
% 6.73/7.08 (assert (@ (@ (@ tptp.bij_be5432664580149595207at_nat tptp.nat_sum_encode) tptp.top_to6661820994512907621at_nat) tptp.top_top_set_nat))
% 6.73/7.08 (assert (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat X))) (=> (@ _let_1 Y) (@ _let_1 (@ tptp.nat_sum_encode (@ tptp.sum_Inl_nat_nat Y)))))))
% 6.73/7.08 (assert (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat X))) (=> (@ _let_1 Y) (@ _let_1 (@ tptp.nat_sum_encode (@ tptp.sum_Inr_nat_nat Y)))))))
% 6.73/7.08 (assert (= tptp.nat_sum_decode (lambda ((N4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat N4) _let_1))) (@ (@ (@ tptp.if_Sum_sum_nat_nat (@ (@ tptp.dvd_dvd_nat _let_1) N4)) (@ tptp.sum_Inl_nat_nat _let_2)) (@ tptp.sum_Inr_nat_nat _let_2)))))))
% 6.73/7.08 (assert (forall ((X tptp.sum_sum_nat_nat)) (= (@ tptp.nat_sum_decode (@ tptp.nat_sum_encode X)) X)))
% 6.73/7.08 (assert (forall ((N tptp.nat)) (= (@ tptp.nat_sum_encode (@ tptp.nat_sum_decode N)) N)))
% 6.73/7.08 (assert (@ (@ (@ tptp.bij_be4790990086886966983at_nat tptp.nat_sum_decode) tptp.top_top_set_nat) tptp.top_to6661820994512907621at_nat))
% 6.73/7.08 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (= (@ tptp.nat_sum_decode X) (@ tptp.nat_sum_decode Y)) (= X Y))))
% 6.73/7.08 (assert (forall ((A4 tptp.set_nat)) (@ (@ tptp.inj_on5701776251185195458at_nat tptp.nat_sum_decode) A4)))
% 6.73/7.08 (assert (= (@ (@ tptp.image_678696785212003926at_nat tptp.nat_sum_decode) tptp.top_top_set_nat) tptp.top_to6661820994512907621at_nat))
% 6.73/7.08 (assert (forall ((A0 tptp.nat) (P2 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.accp_nat tptp.nth_item_rel))) (=> (@ _let_1 A0) (=> (=> (@ _let_1 tptp.zero_zero_nat) (@ P2 tptp.zero_zero_nat)) (=> (forall ((N3 tptp.nat)) (let ((_let_1 (@ tptp.suc N3))) (=> (@ (@ tptp.accp_nat tptp.nth_item_rel) _let_1) (=> (forall ((A6 tptp.nat) (Aa tptp.nat)) (=> (= (@ tptp.nat_sum_decode N3) (@ tptp.sum_Inl_nat_nat A6)) (=> (= (@ tptp.nat_sum_decode A6) (@ tptp.sum_Inl_nat_nat Aa)) (@ P2 Aa)))) (=> (forall ((A6 tptp.nat) (B6 tptp.nat)) (=> (= (@ tptp.nat_sum_decode N3) (@ tptp.sum_Inl_nat_nat A6)) (=> (= (@ tptp.nat_sum_decode A6) (@ tptp.sum_Inr_nat_nat B6)) (@ P2 B6)))) (=> (forall ((B6 tptp.nat) (Ba tptp.nat) (X5 tptp.nat) (Y6 tptp.nat)) (=> (= (@ tptp.nat_sum_decode N3) (@ tptp.sum_Inr_nat_nat B6)) (=> (= (@ tptp.nat_sum_decode B6) (@ tptp.sum_Inr_nat_nat Ba)) (=> (= (@ (@ tptp.product_Pair_nat_nat X5) Y6) (@ tptp.nat_prod_decode Ba)) (@ P2 X5))))) (=> (forall ((B6 tptp.nat) (Ba tptp.nat) (X5 tptp.nat) (Y6 tptp.nat)) (=> (= (@ tptp.nat_sum_decode N3) (@ tptp.sum_Inr_nat_nat B6)) (=> (= (@ tptp.nat_sum_decode B6) (@ tptp.sum_Inr_nat_nat Ba)) (=> (= (@ (@ tptp.product_Pair_nat_nat X5) Y6) (@ tptp.nat_prod_decode Ba)) (@ P2 Y6))))) (@ P2 _let_1)))))))) (@ P2 A0)))))))
% 6.73/7.08 (assert (= tptp.nat_int_decode (lambda ((N4 tptp.nat)) (@ (@ (@ tptp.sum_ca7763040182479039464nt_nat tptp.semiri1314217659103216013at_int) (lambda ((B4 tptp.nat)) (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int B4))) tptp.one_one_int))) (@ tptp.nat_sum_decode N4)))))
% 6.73/7.08 (assert (= tptp.nat_sum_encode (@ (@ tptp.sum_ca6763686470577984908at_nat (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (lambda ((B4 tptp.nat)) (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) B4))))))
% 6.73/7.08 (assert (= tptp.extended_enat2 (lambda ((N4 tptp.nat)) (@ tptp.extended_Abs_enat (@ tptp.some_nat N4)))))
% 6.73/7.08 (assert (forall ((F2 (-> tptp.nat tptp.real)) (M5 tptp.nat)) (=> (@ (@ tptp.bfun_nat_real (lambda ((N4 tptp.nat)) (@ F2 (@ (@ tptp.plus_plus_nat N4) M5)))) tptp.at_top_nat) (=> (forall ((M tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M5) M) (=> (@ (@ tptp.ord_less_eq_nat M) N3) (@ (@ tptp.ord_less_eq_real (@ F2 N3)) (@ F2 M))))) (@ tptp.topolo7531315842566124627t_real F2)))))
% 6.73/7.08 (assert (forall ((F2 (-> tptp.nat tptp.real)) (M5 tptp.nat)) (=> (@ (@ tptp.bfun_nat_real (lambda ((N4 tptp.nat)) (@ F2 (@ (@ tptp.plus_plus_nat N4) M5)))) tptp.at_top_nat) (=> (forall ((M tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M5) M) (=> (@ (@ tptp.ord_less_eq_nat M) N3) (@ (@ tptp.ord_less_eq_real (@ F2 M)) (@ F2 N3))))) (@ tptp.topolo7531315842566124627t_real F2)))))
% 6.73/7.08 (assert (forall ((X8 (-> tptp.nat tptp.real))) (=> (@ (@ tptp.bfun_nat_real X8) tptp.at_top_nat) (=> (forall ((M tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N3) (@ (@ tptp.ord_less_eq_real (@ X8 M)) (@ X8 N3)))) (@ tptp.topolo7531315842566124627t_real X8)))))
% 6.73/7.08 (assert (= tptp.gcd_lcm_int (lambda ((A5 tptp.int) (B4 tptp.int)) (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int (@ tptp.abs_abs_int A5)) (@ tptp.abs_abs_int B4))) (@ (@ tptp.gcd_gcd_int A5) B4)))))
% 6.73/7.08 (assert (forall ((M2 tptp.int) (N tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.abs_abs_int M2)) (@ tptp.abs_abs_int N)) (@ (@ tptp.times_times_int (@ (@ tptp.gcd_gcd_int M2) N)) (@ (@ tptp.gcd_lcm_int M2) N)))))
% 6.73/7.08 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (= (@ (@ tptp.gcd_lcm_nat M2) N) tptp.zero_zero_nat) (or (= M2 tptp.zero_zero_nat) (= N tptp.zero_zero_nat)))))
% 6.73/7.08 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (= (@ (@ tptp.gcd_lcm_nat M2) N) _let_1) (and (= M2 _let_1) (= N _let_1))))))
% 6.73/7.08 (assert (= tptp.times_times_nat (lambda ((M6 tptp.nat) (N4 tptp.nat)) (@ (@ tptp.times_times_nat (@ (@ tptp.gcd_gcd_nat M6) N4)) (@ (@ tptp.gcd_lcm_nat M6) N4)))))
% 6.73/7.08 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 M2) (=> (@ _let_1 N) (@ _let_1 (@ (@ tptp.gcd_lcm_nat M2) N)))))))
% 6.73/7.08 (assert (= tptp.gcd_lcm_Code_integer (lambda ((A5 tptp.code_integer) (B4 tptp.code_integer)) (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.times_3573771949741848930nteger (@ tptp.abs_abs_Code_integer A5)) (@ tptp.abs_abs_Code_integer B4))) (@ (@ tptp.gcd_gcd_Code_integer A5) B4)))))
% 6.73/7.08 (assert (= tptp.gcd_lcm_nat (lambda ((X4 tptp.nat) (Y4 tptp.nat)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat X4) Y4)) (@ (@ tptp.gcd_gcd_nat X4) Y4)))))
% 6.73/7.08 (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)) (=> (forall ((M tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.member_nat M) M5) (=> (@ (@ tptp.member_nat N3) M5) (@ (@ tptp.member_nat (@ (@ tptp.gcd_lcm_nat M) N3)) M5)))) (= (@ tptp.gcd_Lcm_nat M5) (@ tptp.lattic8265883725875713057ax_nat M5))))))))
% 6.73/7.08 (assert (forall ((A4 tptp.set_nat)) (=> (@ (@ tptp.member_nat tptp.zero_zero_nat) A4) (= (@ tptp.gcd_Lcm_nat A4) tptp.zero_zero_nat))))
% 6.73/7.08 (assert (forall ((A4 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A4) (= (= (@ tptp.gcd_Lcm_nat A4) tptp.zero_zero_nat) (@ (@ tptp.member_nat tptp.zero_zero_nat) A4)))))
% 6.73/7.08 (assert (forall ((M5 tptp.set_nat)) (=> (not (@ tptp.finite_finite_nat M5)) (= (@ tptp.gcd_Lcm_nat M5) tptp.zero_zero_nat))))
% 6.73/7.08 (assert (= tptp.gcd_Lcm_nat (lambda ((M9 tptp.set_nat)) (@ (@ (@ tptp.if_nat (@ tptp.finite_finite_nat M9)) (@ (@ (@ tptp.lattic7826324295020591184_F_nat tptp.gcd_lcm_nat) tptp.one_one_nat) M9)) tptp.zero_zero_nat))))
% 6.73/7.08 (assert (= (@ tptp.unit_f2748546683901255202or_nat tptp.zero_zero_nat) tptp.zero_zero_nat))
% 6.73/7.08 (assert (forall ((N tptp.nat)) (= (@ tptp.unit_f2748546683901255202or_nat (@ tptp.suc N)) tptp.one_one_nat)))
% 6.73/7.08 (assert (= tptp.unit_f2748546683901255202or_nat (lambda ((N4 tptp.nat)) (@ (@ (@ tptp.if_nat (= N4 tptp.zero_zero_nat)) tptp.zero_zero_nat) tptp.one_one_nat))))
% 6.73/7.08 (assert (= tptp.times_times_num (lambda ((M6 tptp.num) (N4 tptp.num)) (@ tptp.num_of_nat (@ (@ tptp.times_times_nat (@ tptp.nat_of_num M6)) (@ tptp.nat_of_num N4))))))
% 6.73/7.08 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.nat_of_num N))) (= (@ tptp.nat_of_num (@ tptp.bit0 N)) (@ (@ tptp.plus_plus_nat _let_1) _let_1)))))
% 6.73/7.08 (assert (= tptp.ord_less_eq_num (lambda ((M6 tptp.num) (N4 tptp.num)) (@ (@ tptp.ord_less_eq_nat (@ tptp.nat_of_num M6)) (@ tptp.nat_of_num N4)))))
% 6.73/7.08 (assert (= tptp.ord_less_num (lambda ((M6 tptp.num) (N4 tptp.num)) (@ (@ tptp.ord_less_nat (@ tptp.nat_of_num M6)) (@ tptp.nat_of_num N4)))))
% 6.73/7.08 (assert (forall ((X tptp.num)) (= (@ tptp.nat_of_num (@ tptp.inc X)) (@ tptp.suc (@ tptp.nat_of_num X)))))
% 6.73/7.08 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ tptp.nat_of_num (@ (@ tptp.times_times_num X) Y)) (@ (@ tptp.times_times_nat (@ tptp.nat_of_num X)) (@ tptp.nat_of_num Y)))))
% 6.73/7.08 (assert (= tptp.nat_of_num tptp.numeral_numeral_nat))
% 6.73/7.08 (assert (= (lambda ((Y5 tptp.num) (Z2 tptp.num)) (= Y5 Z2)) (lambda ((X4 tptp.num) (Y4 tptp.num)) (= (@ tptp.nat_of_num X4) (@ tptp.nat_of_num Y4)))))
% 6.73/7.08 (assert (forall ((X tptp.num)) (= (@ tptp.num_of_nat (@ tptp.nat_of_num X)) X)))
% 6.73/7.08 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.nat_of_num X))) (= (@ tptp.nat_of_num (@ tptp.bit0 X)) (@ (@ tptp.plus_plus_nat _let_1) _let_1)))))
% 6.73/7.08 (assert (forall ((X tptp.num)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.nat_of_num X))))
% 6.73/7.08 (assert (forall ((X tptp.num)) (not (= (@ tptp.nat_of_num X) tptp.zero_zero_nat))))
% 6.73/7.08 (assert (= (@ tptp.nat_of_num tptp.one) tptp.one_one_nat))
% 6.73/7.08 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ tptp.nat_of_num (@ (@ tptp.plus_plus_num X) Y)) (@ (@ tptp.plus_plus_nat (@ tptp.nat_of_num X)) (@ tptp.nat_of_num Y)))))
% 6.73/7.08 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.nat_of_num X))) (= (@ tptp.nat_of_num (@ tptp.sqr X)) (@ (@ tptp.times_times_nat _let_1) _let_1)))))
% 6.73/7.08 (assert (= (@ tptp.nat_of_num tptp.one) (@ tptp.suc tptp.zero_zero_nat)))
% 6.73/7.08 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.nat_of_num X))) (= (@ tptp.nat_of_num (@ tptp.bit1 X)) (@ tptp.suc (@ (@ tptp.plus_plus_nat _let_1) _let_1))))))
% 6.73/7.08 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.nat_of_num (@ tptp.num_of_nat N)) N))))
% 6.73/7.08 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.nat_of_num N))) (= (@ tptp.nat_of_num (@ tptp.bit1 N)) (@ tptp.suc (@ (@ tptp.plus_plus_nat _let_1) _let_1))))))
% 6.73/7.08 (assert (= tptp.plus_plus_num (lambda ((M6 tptp.num) (N4 tptp.num)) (@ tptp.num_of_nat (@ (@ tptp.plus_plus_nat (@ tptp.nat_of_num M6)) (@ tptp.nat_of_num N4))))))
% 6.73/7.08 (assert (@ tptp.trans_nat tptp.bNF_Ca8665028551170535155natLeq))
% 6.73/7.08 (assert (@ tptp.antisym_nat tptp.bNF_Ca8665028551170535155natLeq))
% 6.73/7.08 (assert (forall ((X tptp.option_nat) (Xa2 tptp.option_nat)) (=> (not (@ (@ tptp.vEBT_VEBT_lesseq X) Xa2)) (not (@ (@ (@ tptp.vEBT_V2881884560877996034ft_nat tptp.ord_less_eq_nat) X) Xa2)))))
% 6.73/7.08 (assert (forall ((X tptp.option_nat) (Xa2 tptp.option_nat)) (=> (@ (@ tptp.vEBT_VEBT_lesseq X) Xa2) (@ (@ (@ tptp.vEBT_V2881884560877996034ft_nat tptp.ord_less_eq_nat) X) Xa2))))
% 6.73/7.08 (assert (forall ((X tptp.option_nat) (Xa2 tptp.option_nat) (Y Bool)) (=> (= (@ (@ tptp.vEBT_VEBT_lesseq X) Xa2) Y) (= Y (@ (@ (@ tptp.vEBT_V2881884560877996034ft_nat tptp.ord_less_eq_nat) X) Xa2)))))
% 6.73/7.08 (assert (= tptp.vEBT_VEBT_lesseq (@ tptp.vEBT_V2881884560877996034ft_nat tptp.ord_less_eq_nat)))
% 6.73/7.08 (assert (= (@ tptp.code_integer_of_nat tptp.zero_zero_nat) tptp.zero_z3403309356797280102nteger))
% 6.73/7.08 (assert (forall ((N tptp.code_natural)) (let ((_let_1 (@ tptp.code_nat_of_natural N))) (=> (not (= N tptp.zero_z2226904508553997617atural)) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat _let_1) (@ tptp.suc tptp.zero_zero_nat))) _let_1)))))
% 6.73/7.08 (assert (forall ((X tptp.code_natural) (Xa2 tptp.code_natural)) (= (@ tptp.code_nat_of_natural (@ (@ tptp.times_2397367101498566445atural X) Xa2)) (@ (@ tptp.times_times_nat (@ tptp.code_nat_of_natural X)) (@ tptp.code_nat_of_natural Xa2)))))
% 6.73/7.08 (assert (= (@ tptp.code_nat_of_natural tptp.zero_z2226904508553997617atural) tptp.zero_zero_nat))
% 6.73/7.08 (assert (= tptp.ord_le1926595141338095240atural (lambda ((X4 tptp.code_natural) (Xa3 tptp.code_natural)) (@ (@ tptp.ord_less_eq_nat (@ tptp.code_nat_of_natural X4)) (@ tptp.code_nat_of_natural Xa3)))))
% 6.73/7.08 (assert (forall ((V2 tptp.code_natural) (W2 tptp.code_natural)) (let ((_let_1 (@ tptp.bit1 tptp.one))) (let ((_let_2 (@ tptp.bit1 _let_1))) (let ((_let_3 (@ tptp.bit0 _let_1))) (let ((_let_4 (@ tptp.numera5444537566228673987atural (@ tptp.bit0 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit1 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit0 _let_3)))))))))))))))) (let ((_let_5 (@ tptp.bit0 tptp.one))) (let ((_let_6 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit0 _let_5)))))) (let ((_let_7 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 _let_2)))))))))))))))))))))) (let ((_let_8 (@ (@ (@ tptp.minus_shift (@ tptp.numera5444537566228673987atural (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 _let_7)))))))))) (@ (@ tptp.times_2397367101498566445atural (@ (@ tptp.modulo8411746178871703098atural W2) _let_4)) (@ tptp.numera5444537566228673987atural (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit1 (@ tptp.bit0 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit0 (@ tptp.bit1 _let_6))))))))))))) (@ (@ tptp.times_2397367101498566445atural (@ (@ tptp.divide5121882707175180666atural W2) _let_4)) (@ tptp.numera5444537566228673987atural (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit0 _let_2)))))))))))))) (let ((_let_9 (@ tptp.numera5444537566228673987atural (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit1 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit1 (@ tptp.bit0 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit1 _let_3)))))))))))))))) (let ((_let_10 (@ tptp.bit1 (@ tptp.bit0 (@ tptp.bit1 (@ tptp.bit0 (@ tptp.bit1 (@ tptp.bit0 (@ tptp.bit1 _let_7))))))))) (let ((_let_11 (@ (@ (@ tptp.minus_shift (@ tptp.numera5444537566228673987atural (@ tptp.bit1 _let_10))) (@ (@ tptp.times_2397367101498566445atural (@ (@ tptp.modulo8411746178871703098atural V2) _let_9)) (@ tptp.numera5444537566228673987atural (@ tptp.bit0 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit1 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 _let_6))))))))))))) (@ (@ tptp.times_2397367101498566445atural (@ (@ tptp.divide5121882707175180666atural V2) _let_9)) (@ tptp.numera5444537566228673987atural (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit0 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 _let_5))))))))))))))))) (= (@ tptp.next (@ (@ tptp.produc3574140220909816553atural V2) W2)) (@ (@ tptp.produc6639722614265839536atural (@ (@ tptp.plus_p4538020629002901425atural (@ (@ (@ tptp.minus_shift (@ tptp.numera5444537566228673987atural (@ tptp.bit0 _let_10))) _let_11) (@ (@ tptp.plus_p4538020629002901425atural _let_8) tptp.one_one_Code_natural))) tptp.one_one_Code_natural)) (@ (@ tptp.produc3574140220909816553atural _let_11) _let_8))))))))))))))))
% 6.73/7.08 (assert (= tptp.range (lambda ((K3 tptp.code_natural) (__flatten_var_0 tptp.produc7822875418678951345atural)) (@ (@ (@ tptp.produc5538323210962509403atural (@ (@ (@ tptp.iterat8892046348760725948atural (@ (@ tptp.log (@ tptp.numera5444537566228673987atural (@ tptp.bit1 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit1 (@ tptp.bit0 (@ tptp.bit1 (@ tptp.bit0 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 tptp.one)))))))))))))))))))))))))))))))) K3)) (lambda ((L2 tptp.code_natural) (__flatten_var_0 tptp.produc7822875418678951345atural)) (@ (@ (@ tptp.produc5538323210962509403atural tptp.next) (lambda ((V3 tptp.code_natural) (__flatten_var_0 tptp.produc7822875418678951345atural)) (@ (@ tptp.produc6639722614265839536atural (@ (@ tptp.plus_p4538020629002901425atural V3) (@ (@ tptp.times_2397367101498566445atural L2) (@ tptp.numera5444537566228673987atural (@ tptp.bit1 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit1 (@ tptp.bit0 (@ tptp.bit1 (@ tptp.bit0 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 tptp.one)))))))))))))))))))))))))))))))))) __flatten_var_0))) __flatten_var_0))) tptp.one_one_Code_natural)) (lambda ((V3 tptp.code_natural) (__flatten_var_0 tptp.produc7822875418678951345atural)) (@ (@ tptp.produc6639722614265839536atural (@ (@ tptp.modulo8411746178871703098atural V3) K3)) __flatten_var_0))) __flatten_var_0))))
% 6.73/7.08 (assert (forall ((X tptp.code_natural)) (= (@ tptp.code_nat_of_natural (@ tptp.code_Suc X)) (@ tptp.suc (@ tptp.code_nat_of_natural X)))))
% 6.73/7.08 (assert (forall ((X tptp.nat)) (= (@ tptp.code_Suc (@ tptp.code_natural_of_nat X)) (@ tptp.code_natural_of_nat (@ tptp.suc X)))))
% 6.73/7.08 (assert (forall ((Xa2 tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_le1926595141338095240atural (@ tptp.code_natural_of_nat Xa2)) (@ tptp.code_natural_of_nat X)) (@ (@ tptp.ord_less_eq_nat Xa2) X))))
% 6.73/7.08 (assert (forall ((Xa2 tptp.nat) (X tptp.nat)) (= (@ (@ tptp.times_2397367101498566445atural (@ tptp.code_natural_of_nat Xa2)) (@ tptp.code_natural_of_nat X)) (@ tptp.code_natural_of_nat (@ (@ tptp.times_times_nat Xa2) X)))))
% 6.73/7.08 (assert (= tptp.ord_less_nat (@ tptp.transi2163837189807498211lp_nat (lambda ((M6 tptp.nat) (N4 tptp.nat)) (= N4 (@ tptp.suc M6))))))
% 6.73/7.08 (assert (= tptp.zero_z2226904508553997617atural (@ tptp.code_natural_of_nat tptp.zero_zero_nat)))
% 6.73/7.08 (assert (= tptp.code_Suc (@ (@ (@ tptp.map_fu1239815594074539274atural tptp.code_nat_of_natural) tptp.code_natural_of_nat) tptp.suc)))
% 6.73/7.08 (assert (= tptp.times_2397367101498566445atural (@ (@ (@ tptp.map_fu6549440983881763648atural tptp.code_nat_of_natural) (@ (@ tptp.map_fu1239815594074539274atural tptp.code_nat_of_natural) tptp.code_natural_of_nat)) tptp.times_times_nat)))
% 6.73/7.08 (assert (forall ((X tptp.typerep)) (not (= (@ tptp.size_size_typerep X) tptp.zero_zero_nat))))
% 6.73/7.08 (assert (forall ((X1 tptp.literal) (X2 tptp.list_typerep)) (= (@ tptp.size_size_typerep (@ (@ tptp.typerep2 X1) X2)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.size_list_typerep tptp.size_size_typerep) X2)) (@ tptp.suc tptp.zero_zero_nat)))))
% 6.73/7.08 (assert (forall ((X1 tptp.literal) (X2 tptp.list_typerep)) (= (@ tptp.size_typerep (@ (@ tptp.typerep2 X1) X2)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.size_list_typerep tptp.size_typerep) X2)) (@ tptp.suc tptp.zero_zero_nat)))))
% 6.73/7.08 (assert (@ (@ tptp.semila9081495762789891438tr_nat tptp.ord_max_nat) tptp.zero_zero_nat))
% 6.73/7.08 (assert (@ (@ tptp.semila9081495762789891438tr_nat tptp.gcd_gcd_nat) tptp.zero_zero_nat))
% 6.73/7.08 (assert (forall ((X tptp.rat) (Y tptp.rat)) (= (@ (@ tptp.times_times_real (@ tptp.ratreal X)) (@ tptp.ratreal Y)) (@ tptp.ratreal (@ (@ tptp.times_times_rat X) Y)))))
% 6.73/7.08 (assert (@ (@ tptp.monoid_nat tptp.ord_max_nat) tptp.zero_zero_nat))
% 6.73/7.08 (assert (@ (@ tptp.monoid_nat tptp.gcd_gcd_nat) tptp.zero_zero_nat))
% 6.73/7.08 (assert (@ (@ tptp.bNF_Ca1281551314933786834on_nat (@ tptp.field_nat tptp.bNF_Ca8665028551170535155natLeq)) tptp.bNF_Ca8665028551170535155natLeq))
% 6.73/7.08 (assert (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat (@ tptp.bNF_Ca3793111618940312692of_nat tptp.top_top_set_nat)) tptp.bNF_Ca8665028551170535155natLeq)) tptp.bNF_We5258908940166488438at_nat))
% 6.73/7.08 (assert (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat (@ tptp.bNF_Ca3793111618940312692of_nat (@ tptp.field_nat tptp.bNF_Ca8665028551170535155natLeq))) tptp.bNF_Ca8665028551170535155natLeq)) tptp.bNF_We5258908940166488438at_nat))
% 6.73/7.08 (assert (forall ((X tptp.int) (Y tptp.int)) (= (@ (@ (@ tptp.if_int false) X) Y) Y)))
% 6.73/7.08 (assert (forall ((X tptp.int) (Y tptp.int)) (= (@ (@ (@ tptp.if_int true) X) Y) X)))
% 6.73/7.08 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (@ (@ (@ tptp.if_nat false) X) Y) Y)))
% 6.73/7.08 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (@ (@ (@ tptp.if_nat true) X) Y) X)))
% 6.73/7.08 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ (@ tptp.if_num false) X) Y) Y)))
% 6.73/7.08 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ (@ tptp.if_num true) X) Y) X)))
% 6.73/7.08 (assert (forall ((X tptp.rat) (Y tptp.rat)) (= (@ (@ (@ tptp.if_rat false) X) Y) Y)))
% 6.73/7.08 (assert (forall ((X tptp.rat) (Y tptp.rat)) (= (@ (@ (@ tptp.if_rat true) X) Y) X)))
% 6.73/7.08 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ (@ tptp.if_real false) X) Y) Y)))
% 6.73/7.08 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ (@ tptp.if_real true) X) Y) X)))
% 6.73/7.08 (assert (forall ((X tptp.complex) (Y tptp.complex)) (= (@ (@ (@ tptp.if_complex false) X) Y) Y)))
% 6.73/7.08 (assert (forall ((X tptp.complex) (Y tptp.complex)) (= (@ (@ (@ tptp.if_complex true) X) Y) X)))
% 6.73/7.08 (assert (forall ((X tptp.extended_enat) (Y tptp.extended_enat)) (= (@ (@ (@ tptp.if_Extended_enat false) X) Y) Y)))
% 6.73/7.08 (assert (forall ((X tptp.extended_enat) (Y tptp.extended_enat)) (= (@ (@ (@ tptp.if_Extended_enat true) X) Y) X)))
% 6.73/7.08 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer)) (= (@ (@ (@ tptp.if_Code_integer false) X) Y) Y)))
% 104.61/105.05 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer)) (= (@ (@ (@ tptp.if_Code_integer true) X) Y) X)))
% 104.61/105.05 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat)) (= (@ (@ (@ tptp.if_set_nat false) X) Y) Y)))
% 104.61/105.05 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat)) (= (@ (@ (@ tptp.if_set_nat true) X) Y) X)))
% 104.61/105.05 (assert (forall ((X tptp.vEBT_VEBT) (Y tptp.vEBT_VEBT)) (= (@ (@ (@ tptp.if_VEBT_VEBT false) X) Y) Y)))
% 104.61/105.05 (assert (forall ((X tptp.vEBT_VEBT) (Y tptp.vEBT_VEBT)) (= (@ (@ (@ tptp.if_VEBT_VEBT true) X) Y) X)))
% 104.61/105.05 (assert (forall ((X tptp.list_nat) (Y tptp.list_nat)) (= (@ (@ (@ tptp.if_list_nat false) X) Y) Y)))
% 104.61/105.05 (assert (forall ((X tptp.list_nat) (Y tptp.list_nat)) (= (@ (@ (@ tptp.if_list_nat true) X) Y) X)))
% 104.61/105.05 (assert (forall ((X tptp.option_nat) (Y tptp.option_nat)) (= (@ (@ (@ tptp.if_option_nat false) X) Y) Y)))
% 104.61/105.05 (assert (forall ((X tptp.option_nat) (Y tptp.option_nat)) (= (@ (@ (@ tptp.if_option_nat true) X) Y) X)))
% 104.61/105.05 (assert (forall ((X tptp.option_num) (Y tptp.option_num)) (= (@ (@ (@ tptp.if_option_num false) X) Y) Y)))
% 104.61/105.05 (assert (forall ((X tptp.option_num) (Y tptp.option_num)) (= (@ (@ (@ tptp.if_option_num true) X) Y) X)))
% 104.61/105.05 (assert (forall ((X tptp.sum_sum_nat_nat) (Y tptp.sum_sum_nat_nat)) (= (@ (@ (@ tptp.if_Sum_sum_nat_nat false) X) Y) Y)))
% 104.61/105.05 (assert (forall ((X tptp.sum_sum_nat_nat) (Y tptp.sum_sum_nat_nat)) (= (@ (@ (@ tptp.if_Sum_sum_nat_nat true) X) Y) X)))
% 104.61/105.05 (assert (forall ((X tptp.product_prod_int_int) (Y tptp.product_prod_int_int)) (= (@ (@ (@ tptp.if_Pro3027730157355071871nt_int false) X) Y) Y)))
% 104.61/105.05 (assert (forall ((X tptp.product_prod_int_int) (Y tptp.product_prod_int_int)) (= (@ (@ (@ tptp.if_Pro3027730157355071871nt_int true) X) Y) X)))
% 104.61/105.05 (assert (forall ((X tptp.product_prod_nat_nat) (Y tptp.product_prod_nat_nat)) (= (@ (@ (@ tptp.if_Pro6206227464963214023at_nat false) X) Y) Y)))
% 104.61/105.05 (assert (forall ((X tptp.product_prod_nat_nat) (Y tptp.product_prod_nat_nat)) (= (@ (@ (@ tptp.if_Pro6206227464963214023at_nat true) X) Y) X)))
% 104.61/105.05 (assert (forall ((P2 Bool)) (or (= P2 true) (= P2 false))))
% 104.61/105.05 (assert (forall ((X tptp.produc8923325533196201883nteger) (Y tptp.produc8923325533196201883nteger)) (= (@ (@ (@ tptp.if_Pro6119634080678213985nteger false) X) Y) Y)))
% 104.61/105.05 (assert (forall ((X tptp.produc8923325533196201883nteger) (Y tptp.produc8923325533196201883nteger)) (= (@ (@ (@ tptp.if_Pro6119634080678213985nteger true) X) Y) X)))
% 104.61/105.05 (assert (not (= tptp.info (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat tptp.mi) tptp.ma)))))
% 104.61/105.05 (set-info :filename cvc5---1.0.5_3022)
% 104.61/105.05 (check-sat-assuming ( true ))
% 104.61/105.05 ------- get file name : TPTP file name is ITP276^3
% 104.61/105.05 ------- cvc5-thf : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_3022.smt2...
% 104.61/105.05 --- Run --ho-elim --full-saturate-quant at 10...
% 104.61/105.05 --- Run --ho-elim --no-e-matching --full-saturate-quant at 10...
% 104.61/105.05 --- Run --ho-elim --no-e-matching --enum-inst-sum --full-saturate-quant at 10...
% 104.61/105.05 --- Run --ho-elim --finite-model-find --uf-ss=no-minimal at 5...
% 104.61/105.05 --- Run --no-ho-matching --finite-model-find --uf-ss=no-minimal at 5...
% 104.61/105.05 --- Run --no-ho-matching --full-saturate-quant --enum-inst-interleave --ho-elim-store-ax at 10...
% 104.61/105.05 --- Run --no-ho-matching --full-saturate-quant --macros-quant-mode=all at 10...
% 104.61/105.05 --- Run --ho-elim --full-saturate-quant --enum-inst-interleave at 10...
% 104.61/105.05 --- Run --no-ho-matching --full-saturate-quant --ho-elim-store-ax at 10...
% 104.61/105.05 --- Run --ho-elim --no-ho-elim-store-ax --full-saturate-quant...
% 104.61/105.05 % SZS status Theorem for ITP276^3
% 104.61/105.05 % SZS output start Proof for ITP276^3
% 104.61/105.05 (
% 104.61/105.05 (let ((_let_1 (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat tptp.mi) tptp.ma)))) (let ((_let_2 (@ tptp.field_nat tptp.bNF_Ca8665028551170535155natLeq))) (let ((_let_3 (@ (@ tptp.map_fu1239815594074539274atural tptp.code_nat_of_natural) tptp.code_natural_of_nat))) (let ((_let_4 (= tptp.times_2397367101498566445atural (@ (@ (@ tptp.map_fu6549440983881763648atural tptp.code_nat_of_natural) _let_3) tptp.times_times_nat)))) (let ((_let_5 (= tptp.code_Suc (@ _let_3 tptp.suc)))) (let ((_let_6 (= tptp.zero_z2226904508553997617atural (@ tptp.code_natural_of_nat tptp.zero_zero_nat)))) (let ((_let_7 (= tptp.range (lambda ((K3 tptp.code_natural) (__flatten_var_0 tptp.produc7822875418678951345atural)) (@ (@ (@ tptp.produc5538323210962509403atural (@ (@ (@ tptp.iterat8892046348760725948atural (@ (@ tptp.log (@ tptp.numera5444537566228673987atural (@ tptp.bit1 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit1 (@ tptp.bit0 (@ tptp.bit1 (@ tptp.bit0 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 tptp.one)))))))))))))))))))))))))))))))) K3)) (lambda ((L2 tptp.code_natural) (__flatten_var_0 tptp.produc7822875418678951345atural)) (@ (@ (@ tptp.produc5538323210962509403atural tptp.next) (lambda ((V3 tptp.code_natural) (__flatten_var_0 tptp.produc7822875418678951345atural)) (@ (@ tptp.produc6639722614265839536atural (@ (@ tptp.plus_p4538020629002901425atural V3) (@ (@ tptp.times_2397367101498566445atural L2) (@ tptp.numera5444537566228673987atural (@ tptp.bit1 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit1 (@ tptp.bit0 (@ tptp.bit1 (@ tptp.bit0 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 tptp.one)))))))))))))))))))))))))))))))))) __flatten_var_0))) __flatten_var_0))) tptp.one_one_Code_natural)) (lambda ((V3 tptp.code_natural) (__flatten_var_0 tptp.produc7822875418678951345atural)) (@ (@ tptp.produc6639722614265839536atural (@ (@ tptp.modulo8411746178871703098atural V3) K3)) __flatten_var_0))) __flatten_var_0))))) (let ((_let_8 (= tptp.ord_le1926595141338095240atural (lambda ((X4 tptp.code_natural) (Xa3 tptp.code_natural)) (@ (@ tptp.ord_less_eq_nat (@ tptp.code_nat_of_natural X4)) (@ tptp.code_nat_of_natural Xa3)))))) (let ((_let_9 (= tptp.plus_plus_num (lambda ((M6 tptp.num) (N4 tptp.num)) (@ tptp.num_of_nat (@ (@ tptp.plus_plus_nat (@ tptp.nat_of_num M6)) (@ tptp.nat_of_num N4))))))) (let ((_let_10 (@ tptp.suc tptp.zero_zero_nat))) (let ((_let_11 (@ tptp.nat_of_num tptp.one))) (let ((_let_12 (= tptp.nat_of_num tptp.numeral_numeral_nat))) (let ((_let_13 (= tptp.ord_less_eq_num (lambda ((M6 tptp.num) (N4 tptp.num)) (@ (@ tptp.ord_less_eq_nat (@ tptp.nat_of_num M6)) (@ tptp.nat_of_num N4)))))) (let ((_let_14 (= tptp.times_times_num (lambda ((M6 tptp.num) (N4 tptp.num)) (@ tptp.num_of_nat (@ (@ tptp.times_times_nat (@ tptp.nat_of_num M6)) (@ tptp.nat_of_num N4))))))) (let ((_let_15 (= tptp.unit_f2748546683901255202or_nat (lambda ((N4 tptp.nat)) (@ (@ (@ tptp.if_nat (= N4 tptp.zero_zero_nat)) tptp.zero_zero_nat) tptp.one_one_nat))))) (let ((_let_16 (= tptp.gcd_Lcm_nat (lambda ((M9 tptp.set_nat)) (@ (@ (@ tptp.if_nat (@ tptp.finite_finite_nat M9)) (@ (@ (@ tptp.lattic7826324295020591184_F_nat tptp.gcd_lcm_nat) tptp.one_one_nat) M9)) tptp.zero_zero_nat))))) (let ((_let_17 (= tptp.gcd_lcm_nat (lambda ((X4 tptp.nat) (Y4 tptp.nat)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat X4) Y4)) (@ (@ tptp.gcd_gcd_nat X4) Y4)))))) (let ((_let_18 (= tptp.gcd_lcm_Code_integer (lambda ((A5 tptp.code_integer) (B4 tptp.code_integer)) (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.times_3573771949741848930nteger (@ tptp.abs_abs_Code_integer A5)) (@ tptp.abs_abs_Code_integer B4))) (@ (@ tptp.gcd_gcd_Code_integer A5) B4)))))) (let ((_let_19 (= tptp.gcd_lcm_int (lambda ((A5 tptp.int) (B4 tptp.int)) (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int (@ tptp.abs_abs_int A5)) (@ tptp.abs_abs_int B4))) (@ (@ tptp.gcd_gcd_int A5) B4)))))) (let ((_let_20 (= tptp.extended_enat2 (lambda ((N4 tptp.nat)) (@ tptp.extended_Abs_enat (@ tptp.some_nat N4)))))) (let ((_let_21 (@ tptp.bit0 tptp.one))) (let ((_let_22 (@ tptp.numeral_numeral_nat _let_21))) (let ((_let_23 (= tptp.nat_sum_encode (@ (@ tptp.sum_ca6763686470577984908at_nat (@ tptp.times_times_nat _let_22)) (lambda ((B4 tptp.nat)) (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) B4))))))) (let ((_let_24 (= tptp.nat_int_decode (lambda ((N4 tptp.nat)) (@ (@ (@ tptp.sum_ca7763040182479039464nt_nat tptp.semiri1314217659103216013at_int) (lambda ((B4 tptp.nat)) (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int B4))) tptp.one_one_int))) (@ tptp.nat_sum_decode N4)))))) (let ((_let_25 (@ (@ tptp.image_678696785212003926at_nat tptp.nat_sum_decode) tptp.top_top_set_nat))) (let ((_let_26 (= _let_25 tptp.top_to6661820994512907621at_nat))) (let ((_let_27 (= tptp.nat_sum_decode (lambda ((N4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat N4) _let_1))) (@ (@ (@ tptp.if_Sum_sum_nat_nat (@ (@ tptp.dvd_dvd_nat _let_1) N4)) (@ tptp.sum_Inl_nat_nat _let_2)) (@ tptp.sum_Inr_nat_nat _let_2)))))))) (let ((_let_28 (= tptp.nat_int_encode (lambda ((I tptp.int)) (@ tptp.nat_sum_encode (@ (@ (@ tptp.if_Sum_sum_nat_nat (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) I)) (@ tptp.sum_Inl_nat_nat (@ tptp.nat2 I))) (@ tptp.sum_Inr_nat_nat (@ tptp.nat2 (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int I)) tptp.one_one_int))))))))) (let ((_let_29 (= tptp.nat_to_rat_surj (lambda ((N4 tptp.nat)) (@ (@ tptp.produc6207742614233964070at_rat (lambda ((A5 tptp.nat) (B4 tptp.nat)) (@ (@ tptp.fract (@ tptp.nat_int_decode A5)) (@ tptp.nat_int_decode B4)))) (@ tptp.nat_prod_decode N4)))))) (let ((_let_30 (@ (@ tptp.image_nat_int tptp.nat_int_decode) tptp.top_top_set_nat))) (let ((_let_31 (= _let_30 tptp.top_top_set_int))) (let ((_let_32 (= tptp.vanishes (lambda ((X7 (-> tptp.nat tptp.rat))) (forall ((R tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) R) (exists ((K3 tptp.nat)) (forall ((N4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K3) N4) (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat (@ X7 N4))) R)))))))))) (let ((_let_33 (= tptp.cauchy (lambda ((X7 (-> tptp.nat tptp.rat))) (forall ((R tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) R) (exists ((K3 tptp.nat)) (forall ((M6 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K3) M6) (forall ((N4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K3) N4) (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ X7 M6)) (@ X7 N4)))) R)))))))))))) (let ((_let_34 (= tptp.positive2 (lambda ((X4 tptp.real)) (exists ((R tptp.rat)) (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) R) (exists ((K3 tptp.nat)) (forall ((N4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K3) N4) (@ (@ tptp.ord_less_rat R) (@ (@ tptp.rep_real X4) N4))))))))))) (let ((_let_35 (= tptp.binomial (lambda ((N4 tptp.nat) (K3 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) N4))) (= (@ tptp.finite_card_nat K7) K3))))))))) (let ((_let_36 (= tptp.extended_eSuc (@ (@ tptp.extend3600170679010898289d_enat (lambda ((N4 tptp.nat)) (@ tptp.extended_enat2 (@ tptp.suc N4)))) tptp.extend5688581933313929465d_enat)))) (let ((_let_37 (= tptp.times_7803423173614009249d_enat (lambda ((M6 tptp.extended_enat) (N4 tptp.extended_enat)) (@ (@ (@ tptp.extend3600170679010898289d_enat (lambda ((O tptp.nat)) (@ (@ (@ tptp.extend3600170679010898289d_enat (lambda ((P5 tptp.nat)) (@ tptp.extended_enat2 (@ (@ tptp.times_times_nat O) P5)))) (@ (@ (@ tptp.if_Extended_enat (= O tptp.zero_zero_nat)) tptp.zero_z5237406670263579293d_enat) tptp.extend5688581933313929465d_enat)) N4))) (@ (@ (@ tptp.if_Extended_enat (= N4 tptp.zero_z5237406670263579293d_enat)) tptp.zero_z5237406670263579293d_enat) tptp.extend5688581933313929465d_enat)) M6))))) (let ((_let_38 (= tptp.zero_z5237406670263579293d_enat (@ tptp.extended_enat2 tptp.zero_zero_nat)))) (let ((_let_39 (@ (@ tptp.map_fu4333342158222067775at_rat tptp.rep_Rat) (@ (@ tptp.map_fu5673905371560938248nt_rat tptp.rep_Rat) tptp.abs_Rat)))) (let ((_let_40 (= tptp.times_times_rat (@ _let_39 (lambda ((X4 tptp.product_prod_int_int) (Y4 tptp.product_prod_int_int)) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int X4)) (@ tptp.product_fst_int_int Y4))) (@ (@ tptp.times_times_int (@ tptp.product_snd_int_int X4)) (@ tptp.product_snd_int_int Y4)))))))) (let ((_let_41 (= tptp.plus_plus_rat (@ _let_39 (lambda ((X4 tptp.product_prod_int_int) (Y4 tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.product_snd_int_int Y4))) (let ((_let_2 (@ tptp.product_snd_int_int X4))) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int X4)) _let_1)) (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int Y4)) _let_2))) (@ (@ tptp.times_times_int _let_2) _let_1))))))))) (let ((_let_42 (@ tptp.bit0 _let_21))) (let ((_let_43 (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat))) (let ((_let_44 (@ _let_43 (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 _let_42)))))))))) (let ((_let_45 (= tptp.top_top_set_char (@ (@ tptp.image_nat_char tptp.unique3096191561947761185of_nat) _let_44)))) (let ((_let_46 (= tptp.ord_le2932123472753598470d_enat (lambda ((M6 tptp.extended_enat) (__flatten_var_0 tptp.extended_enat)) (@ (@ (@ tptp.extended_case_enat_o (lambda ((N1 tptp.nat)) (@ (@ (@ tptp.extended_case_enat_o (lambda ((M1 tptp.nat)) (@ (@ tptp.ord_less_eq_nat M1) N1))) false) M6))) true) __flatten_var_0))))) (let ((_let_47 (@ (@ tptp.bNF_re2241393799969408733at_nat tptp.intrel) tptp.intrel))) (let ((_let_48 (@ (@ tptp.bNF_re3099431351363272937at_nat tptp.intrel) _let_47))) (let ((_let_49 (@ (@ tptp.product_Pair_nat_nat tptp.one_one_nat) tptp.zero_zero_nat))) (let ((_let_50 (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) tptp.zero_zero_nat))) (let ((_let_51 (@ (@ tptp.bNF_re7400052026677387805at_int tptp.pcr_int) tptp.pcr_int))) (let ((_let_52 (@ (@ tptp.bNF_re7408651293131936558nt_int tptp.pcr_int) _let_51))) (let ((_let_53 (@ (@ tptp.bNF_re7627151682743391978at_rat tptp.pcr_rat) (@ (@ tptp.bNF_re8279943556446156061nt_rat tptp.pcr_rat) tptp.pcr_rat)))) (let ((_let_54 (@ (@ tptp.bNF_re5228765855967844073nt_int tptp.ratrel) (@ (@ tptp.bNF_re7145576690424134365nt_int tptp.ratrel) tptp.ratrel)))) (let ((_let_55 (= tptp.positive (lambda ((X4 tptp.rat)) (let ((_let_1 (@ tptp.rep_Rat X4))) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int _let_1)) (@ tptp.product_snd_int_int _let_1)))))))) (let ((_let_56 (= tptp.ratrel (lambda ((X4 tptp.product_prod_int_int) (Y4 tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.product_snd_int_int X4))) (let ((_let_2 (@ tptp.product_snd_int_int Y4))) (and (not (= _let_1 tptp.zero_zero_int)) (not (= _let_2 tptp.zero_zero_int)) (= (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int X4)) _let_2) (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int Y4)) _let_1))))))))) (let ((_let_57 (= tptp.bNF_Ca8665028551170535155natLeq (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o tptp.ord_less_eq_nat))))) (let ((_let_58 (= tptp.semiri1316708129612266289at_nat tptp.id_nat))) (let ((_let_59 (= tptp.sqr (lambda ((X4 tptp.num)) (@ (@ tptp.times_times_num X4) X4))))) (let ((_let_60 (= tptp.rcis (lambda ((R tptp.real) (A5 tptp.real)) (@ (@ tptp.times_times_complex (@ tptp.real_V4546457046886955230omplex R)) (@ tptp.cis A5)))))) (let ((_let_61 (= tptp.code_divmod_integer (lambda ((K3 tptp.code_integer) (L2 tptp.code_integer)) (let ((_let_1 (@ (@ tptp.code_divmod_abs K3) L2))) (let ((_let_2 (@ tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger))) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (= K3 tptp.zero_z3403309356797280102nteger)) (@ _let_2 tptp.zero_z3403309356797280102nteger)) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (= L2 tptp.zero_z3403309356797280102nteger)) (@ _let_2 K3)) (@ (@ (@ (@ tptp.comp_C1593894019821074884nteger (@ (@ tptp.comp_C8797469213163452608nteger tptp.produc6499014454317279255nteger) tptp.times_3573771949741848930nteger)) tptp.sgn_sgn_Code_integer) L2) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (= (@ tptp.sgn_sgn_Code_integer K3) (@ tptp.sgn_sgn_Code_integer L2))) _let_1) (@ (@ tptp.produc6916734918728496179nteger (lambda ((R tptp.code_integer) (S6 tptp.code_integer)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger R))) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (= S6 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 L2)) S6)))))) _let_1))))))))))) (let ((_let_62 (@ (@ tptp.comp_nat_nat_nat tptp.suc) tptp.suc))) (let ((_let_63 (= tptp.field_5140801741446780682s_real (@ tptp.collect_real (lambda ((Uu3 tptp.real)) (exists ((I tptp.int) (N4 tptp.nat)) (and (= Uu3 (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real I)) (@ tptp.semiri5074537144036343181t_real N4))) (not (= N4 tptp.zero_zero_nat))))))))) (let ((_let_64 (= tptp.pred_nat (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((M6 tptp.nat) (N4 tptp.nat)) (= N4 (@ tptp.suc M6)))))))) (let ((_let_65 (= tptp.bit_take_bit_num (lambda ((N4 tptp.nat) (M6 tptp.num)) (let ((_let_1 (@ (@ tptp.bit_se2925701944663578781it_nat N4) (@ tptp.numeral_numeral_nat M6)))) (@ (@ (@ tptp.if_option_num (= _let_1 tptp.zero_zero_nat)) tptp.none_num) (@ tptp.some_num (@ tptp.num_of_nat _let_1)))))))) (let ((_let_66 (= tptp.inf_inf_nat tptp.ord_min_nat))) (let ((_let_67 (= tptp.divide_divide_nat (lambda ((M6 tptp.nat) (N4 tptp.nat)) (@ (@ (@ tptp.if_nat (= N4 tptp.zero_zero_nat)) tptp.zero_zero_nat) (@ tptp.lattic8265883725875713057ax_nat (@ tptp.collect_nat (lambda ((K3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat K3) N4)) M6))))))))) (let ((_let_68 (= tptp.complete_Sup_Sup_nat (lambda ((X7 tptp.set_nat)) (@ (@ (@ tptp.if_nat (= X7 tptp.bot_bot_set_nat)) tptp.zero_zero_nat) (@ tptp.lattic8265883725875713057ax_nat X7)))))) (let ((_let_69 (@ (@ tptp.image_nat_nat tptp.suc) tptp.top_top_set_nat))) (let ((_let_70 (@ tptp.set_ord_atLeast_nat tptp.zero_zero_nat))) (let ((_let_71 (= _let_70 tptp.top_top_set_nat))) (let ((_let_72 (= tptp.real_V5970128139526366754l_real (lambda ((F4 (-> tptp.real tptp.real))) (exists ((C3 tptp.real)) (= F4 (lambda ((X4 tptp.real)) (@ (@ tptp.times_times_real X4) C3)))))))) (let ((_let_73 (= tptp.root (lambda ((N4 tptp.nat) (X4 tptp.real)) (@ (@ (@ tptp.if_real (= N4 tptp.zero_zero_nat)) tptp.zero_zero_real) (@ (@ (@ tptp.the_in5290026491893676941l_real tptp.top_top_set_real) (lambda ((Y4 tptp.real)) (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real Y4)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real Y4)) N4)))) X4)))))) (let ((_let_74 (= (@ (@ tptp.image_nat_list_nat tptp.nat_list_decode) tptp.top_top_set_nat) tptp.top_top_set_list_nat))) (let ((_let_75 (@ (@ tptp.image_5846123807819985514at_nat tptp.nat_prod_decode) tptp.top_top_set_nat))) (let ((_let_76 (= _let_75 tptp.top_to4669805908274784177at_nat))) (let ((_let_77 (@ tptp.insert_nat tptp.zero_zero_nat))) (let ((_let_78 (= tptp.set_or5834768355832116004an_nat (lambda ((N4 tptp.nat) (M6 tptp.nat)) (@ tptp.set_nat2 (@ (@ tptp.upt (@ tptp.suc N4)) M6)))))) (let ((_let_79 (= tptp.set_or6659071591806873216st_nat (lambda ((N4 tptp.nat) (M6 tptp.nat)) (@ tptp.set_nat2 (@ (@ tptp.upt (@ tptp.suc N4)) (@ tptp.suc M6))))))) (let ((_let_80 (= tptp.set_or1269000886237332187st_nat (lambda ((N4 tptp.nat) (M6 tptp.nat)) (@ tptp.set_nat2 (@ (@ tptp.upt N4) (@ tptp.suc M6))))))) (let ((_let_81 (@ (@ tptp.map_fu3667384564859982768at_int tptp.rep_Integ) tptp.abs_Integ))) (let ((_let_82 (@ (@ tptp.map_fu4960017516451851995nt_int tptp.rep_Integ) _let_81))) (let ((_let_83 (= tptp.plus_plus_int (@ _let_82 (@ tptp.produc27273713700761075at_nat (lambda ((X4 tptp.nat) (Y4 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((U2 tptp.nat) (V3 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat X4) U2)) (@ (@ tptp.plus_plus_nat Y4) V3)))) __flatten_var_0))))))) (let ((_let_84 (= tptp.divide_divide_rat (lambda ((Q5 tptp.rat) (R tptp.rat)) (@ (@ tptp.times_times_rat Q5) (@ tptp.inverse_inverse_rat R)))))) (let ((_let_85 (= tptp.uminus_uminus_int (@ _let_81 (@ tptp.produc2626176000494625587at_nat (lambda ((X4 tptp.nat) (Y4 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat Y4) X4))))))) (let ((_let_86 (= tptp.semiri1314217659103216013at_int (lambda ((N4 tptp.nat)) (@ tptp.abs_Integ (@ (@ tptp.product_Pair_nat_nat N4) tptp.zero_zero_nat)))))) (let ((_let_87 (@ tptp.num_of_nat tptp.zero_zero_nat))) (let ((_let_88 (= _let_87 tptp.one))) (let ((_let_89 (= tptp.adjust_mod (lambda ((L2 tptp.int) (R tptp.int)) (@ (@ (@ tptp.if_int (= R tptp.zero_zero_int)) tptp.zero_zero_int) (@ (@ tptp.minus_minus_int L2) R)))))) (let ((_let_90 (= tptp.pred (@ (@ tptp.case_nat_nat tptp.zero_zero_nat) (lambda ((X24 tptp.nat)) X24))))) (let ((_let_91 (= tptp.bit_se545348938243370406it_int (lambda ((N4 tptp.nat) (K3 tptp.int)) (@ (@ tptp.times_times_int K3) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N4)))))) (let ((_let_92 (= tptp.bit_se547839408752420682it_nat (lambda ((N4 tptp.nat) (M6 tptp.nat)) (@ (@ tptp.times_times_nat M6) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N4)))))) (let ((_let_93 (= tptp.csqrt (lambda ((Z4 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.re Z4))) (let ((_let_3 (@ tptp.real_V1022390504157884413omplex Z4))) (let ((_let_4 (@ tptp.im Z4))) (@ (@ tptp.complex2 (@ tptp.sqrt (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real _let_3) _let_2)) _let_1))) (@ (@ tptp.times_times_real (@ (@ (@ tptp.if_real (= _let_4 tptp.zero_zero_real)) tptp.one_one_real) (@ tptp.sgn_sgn_real _let_4))) (@ tptp.sqrt (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real _let_3) _let_2)) _let_1)))))))))))) (let ((_let_94 (= tptp.real_V2046097035970521341omplex (lambda ((R tptp.real) (X4 tptp.complex)) (let ((_let_1 (@ tptp.times_times_real R))) (@ (@ tptp.complex2 (@ _let_1 (@ tptp.re X4))) (@ _let_1 (@ tptp.im X4)))))))) (let ((_let_95 (@ tptp.nat_list_decode tptp.zero_zero_nat))) (let ((_let_96 (= _let_95 tptp.nil_nat))) (let ((_let_97 (= tptp.real_V1022390504157884413omplex (lambda ((Z4 tptp.complex)) (@ tptp.sqrt (@ tptp.re (@ (@ tptp.times_times_complex Z4) (@ tptp.cnj Z4)))))))) (let ((_let_98 (= tptp.unique4921790084139445826nteger (lambda ((L2 tptp.num) (__flatten_var_0 tptp.produc8923325533196201883nteger)) (@ (@ tptp.produc6916734918728496179nteger (lambda ((Q5 tptp.code_integer) (R tptp.code_integer)) (let ((_let_1 (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) Q5))) (let ((_let_2 (@ tptp.numera6620942414471956472nteger L2))) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (@ (@ tptp.ord_le3102999989581377725nteger _let_2) R)) (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.plus_p5714425477246183910nteger _let_1) tptp.one_one_Code_integer)) (@ (@ tptp.minus_8373710615458151222nteger R) _let_2))) (@ (@ tptp.produc1086072967326762835nteger _let_1) R)))))) __flatten_var_0))))) (let ((_let_99 (= tptp.topolo4055970368930404560y_real (lambda ((X7 (-> tptp.nat tptp.real))) (forall ((J tptp.nat)) (exists ((M9 tptp.nat)) (forall ((M6 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M9) M6) (forall ((N4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M9) N4) (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ X7 M6)) (@ X7 N4)))) (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc J)))))))))))))) (let ((_let_100 (= tptp.cis (lambda ((B4 tptp.real)) (@ tptp.exp_complex (@ (@ tptp.times_times_complex tptp.imaginary_unit) (@ tptp.real_V4546457046886955230omplex B4))))))) (let ((_let_101 (= tptp.complex2 (lambda ((A5 tptp.real) (B4 tptp.real)) (@ (@ tptp.plus_plus_complex (@ tptp.real_V4546457046886955230omplex A5)) (@ (@ tptp.times_times_complex tptp.imaginary_unit) (@ tptp.real_V4546457046886955230omplex B4))))))) (let ((_let_102 (@ tptp.real_V4546457046886955230omplex tptp.pi))) (let ((_let_103 (@ tptp.numera6690914467698888265omplex _let_21))) (let ((_let_104 (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))) (let ((_let_105 (@ tptp.times_times_complex _let_102))) (let ((_let_106 (@ tptp.times_times_complex tptp.imaginary_unit))) (let ((_let_107 (= tptp.bit_se4203085406695923979it_int (lambda ((N4 tptp.nat) (K3 tptp.int)) (@ (@ tptp.minus_minus_int K3) (@ (@ tptp.times_times_int (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.bit_se1146084159140164899it_int K3) N4))) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N4))))))) (let ((_let_108 (= tptp.bit_se7879613467334960850it_int (lambda ((N4 tptp.nat) (K3 tptp.int)) (@ (@ tptp.plus_plus_int K3) (@ (@ tptp.times_times_int (@ tptp.zero_n2684676970156552555ol_int (not (@ (@ tptp.bit_se1146084159140164899it_int K3) N4)))) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N4))))))) (let ((_let_109 (@ tptp.numeral_numeral_real _let_21))) (let ((_let_110 (@ tptp.times_times_real _let_109))) (let ((_let_111 (= tptp.pi (@ _let_110 (@ tptp.the_real (lambda ((X4 tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4) (@ (@ tptp.ord_less_eq_real X4) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (= (@ tptp.cos_real X4) tptp.zero_zero_real)))))))) (let ((_let_112 (@ _let_110 tptp.pi))) (let ((_let_113 (= tptp.bit_ri631733984087533419it_int (lambda ((N4 tptp.nat) (K3 tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N4))) (@ (@ tptp.minus_minus_int (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.suc N4)) (@ (@ tptp.plus_plus_int K3) _let_1))) _let_1)))))) (let ((_let_114 (@ tptp.suc _let_10))) (let ((_let_115 (@ tptp.numeral_numeral_int _let_21))) (let ((_let_116 (= tptp.times_times_nat (lambda ((A5 tptp.nat) (B4 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int A5)) (@ tptp.semiri1314217659103216013at_int B4))))))) (let ((_let_117 (= tptp.modulo_modulo_int (lambda ((K3 tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.abs_abs_int L2))) (let ((_let_2 (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.modulo_modulo_nat (@ tptp.nat2 (@ tptp.abs_abs_int K3))) (@ tptp.nat2 _let_1))))) (let ((_let_3 (@ tptp.sgn_sgn_int L2))) (let ((_let_4 (@ tptp.times_times_int _let_3))) (@ (@ (@ tptp.if_int (= L2 tptp.zero_zero_int)) K3) (@ (@ (@ tptp.if_int (= (@ tptp.sgn_sgn_int K3) _let_3)) (@ _let_4 _let_2)) (@ _let_4 (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int _let_1) (@ tptp.zero_n2684676970156552555ol_int (not (@ (@ tptp.dvd_dvd_int L2) K3))))) _let_2)))))))))))) (let ((_let_118 (= tptp.bNF_Ca8459412986667044542atLess (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o tptp.ord_less_nat))))) (let ((_let_119 (= tptp.eucl_rel_int (lambda ((A13 tptp.int) (A24 tptp.int) (A32 tptp.product_prod_int_int)) (or (exists ((K3 tptp.int)) (and (= A13 K3) (= A24 tptp.zero_zero_int) (= A32 (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) K3)))) (exists ((L2 tptp.int) (K3 tptp.int) (Q5 tptp.int)) (and (= A13 K3) (= A24 L2) (= A32 (@ (@ tptp.product_Pair_int_int Q5) tptp.zero_zero_int)) (not (= L2 tptp.zero_zero_int)) (= K3 (@ (@ tptp.times_times_int Q5) L2)))) (exists ((R tptp.int) (L2 tptp.int) (K3 tptp.int) (Q5 tptp.int)) (and (= A13 K3) (= A24 L2) (= A32 (@ (@ tptp.product_Pair_int_int Q5) R)) (= (@ tptp.sgn_sgn_int R) (@ tptp.sgn_sgn_int L2)) (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int R)) (@ tptp.abs_abs_int L2)) (= K3 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int Q5) L2)) R))))))))) (let ((_let_120 (= tptp.divmod_nat (lambda ((M6 tptp.nat) (N4 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.divide_divide_nat M6) N4)) (@ (@ tptp.modulo_modulo_nat M6) N4)))))) (let ((_let_121 (= tptp.adjust_div (@ tptp.produc8211389475949308722nt_int (lambda ((Q5 tptp.int) (R tptp.int)) (@ (@ tptp.plus_plus_int Q5) (@ tptp.zero_n2684676970156552555ol_int (not (= R tptp.zero_zero_int))))))))) (let ((_let_122 (= tptp.nat_prod_encode (@ tptp.produc6842872674320459806at_nat (lambda ((M6 tptp.nat) (N4 tptp.nat)) (@ (@ tptp.plus_plus_nat (@ tptp.nat_triangle (@ (@ tptp.plus_plus_nat M6) N4))) M6)))))) (let ((_let_123 (= tptp.divide1717551699836669952omplex (lambda ((X4 tptp.complex) (Y4 tptp.complex)) (@ (@ tptp.times_times_complex X4) (@ tptp.invers8013647133539491842omplex Y4)))))) (let ((_let_124 (= tptp.unique5024387138958732305ep_int (lambda ((L2 tptp.num) (__flatten_var_0 tptp.product_prod_int_int)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((Q5 tptp.int) (R tptp.int)) (let ((_let_1 (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) Q5))) (let ((_let_2 (@ tptp.numeral_numeral_int L2))) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (@ (@ tptp.ord_less_eq_int _let_2) R)) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int)) (@ (@ tptp.minus_minus_int R) _let_2))) (@ (@ tptp.product_Pair_int_int _let_1) R)))))) __flatten_var_0))))) (let ((_let_125 (= tptp.unique5026877609467782581ep_nat (lambda ((L2 tptp.num) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((Q5 tptp.nat) (R tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Q5))) (let ((_let_2 (@ tptp.numeral_numeral_nat L2))) (@ (@ (@ tptp.if_Pro6206227464963214023at_nat (@ (@ tptp.ord_less_eq_nat _let_2) R)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat)) (@ (@ tptp.minus_minus_nat R) _let_2))) (@ (@ tptp.product_Pair_nat_nat _let_1) R)))))) __flatten_var_0))))) (let ((_let_126 (= tptp.divide_divide_real (lambda ((X4 tptp.real) (Y4 tptp.real)) (@ (@ tptp.times_times_real X4) (@ tptp.inverse_inverse_real Y4)))))) (let ((_let_127 (= tptp.real_V1485227260804924795R_real tptp.times_times_real))) (let ((_let_128 (= tptp.tanh_real (lambda ((X4 tptp.real)) (let ((_let_1 (@ tptp.exp_real (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) X4)))) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real tptp.one_one_real) _let_1)) (@ (@ tptp.plus_plus_real tptp.one_one_real) _let_1))))))) (let ((_let_129 (@ tptp.bit1 tptp.one))) (let ((_let_130 (@ tptp.bit1 _let_129))) (let ((_let_131 (@ tptp.divide_divide_real tptp.one_one_real))) (let ((_let_132 (@ tptp.numeral_numeral_real (@ tptp.bit1 _let_21)))) (let ((_let_133 (@ tptp.numeral_numeral_real _let_42))) (let ((_let_134 (@ (@ tptp.divide_divide_real tptp.pi) _let_133))) (let ((_let_135 (@ tptp.numeral_numeral_real _let_129))) (let ((_let_136 (@ tptp.divide_divide_real _let_135))) (let ((_let_137 (= tptp.unique5055182867167087721od_nat (lambda ((M6 tptp.num) (N4 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N4))) (let ((_let_2 (@ tptp.numeral_numeral_nat M6))) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.divide_divide_nat _let_2) _let_1)) (@ (@ tptp.modulo_modulo_nat _let_2) _let_1)))))))) (let ((_let_138 (= tptp.unique3479559517661332726nteger (lambda ((M6 tptp.num) (N4 tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger N4))) (let ((_let_2 (@ tptp.numera6620942414471956472nteger M6))) (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.divide6298287555418463151nteger _let_2) _let_1)) (@ (@ tptp.modulo364778990260209775nteger _let_2) _let_1)))))))) (let ((_let_139 (= tptp.unique5052692396658037445od_int (lambda ((M6 tptp.num) (N4 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N4))) (let ((_let_2 (@ tptp.numeral_numeral_int M6))) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.divide_divide_int _let_2) _let_1)) (@ (@ tptp.modulo_modulo_int _let_2) _let_1)))))))) (let ((_let_140 (= tptp.abs_abs_rat (lambda ((A5 tptp.rat)) (@ (@ (@ tptp.if_rat (@ (@ tptp.ord_less_rat A5) tptp.zero_zero_rat)) (@ tptp.uminus_uminus_rat A5)) A5))))) (let ((_let_141 (= tptp.abs_abs_Code_integer (lambda ((A5 tptp.code_integer)) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.ord_le6747313008572928689nteger A5) tptp.zero_z3403309356797280102nteger)) (@ tptp.uminus1351360451143612070nteger A5)) A5))))) (let ((_let_142 (= tptp.abs_abs_real (lambda ((A5 tptp.real)) (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_real A5) tptp.zero_zero_real)) (@ tptp.uminus_uminus_real A5)) A5))))) (let ((_let_143 (= tptp.abs_abs_int (lambda ((A5 tptp.int)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_int A5) tptp.zero_zero_int)) (@ tptp.uminus_uminus_int A5)) A5))))) (let ((_let_144 (= tptp.numeral_numeral_nat (lambda ((K3 tptp.num)) (@ tptp.suc (@ tptp.pred_numeral K3)))))) (let ((_let_145 (= (@ tptp.abs_abs_int tptp.one_one_int) tptp.one_one_int))) (let ((_let_146 (= (@ tptp.abs_abs_real tptp.one_one_real) tptp.one_one_real))) (let ((_let_147 (= (@ tptp.abs_abs_Code_integer tptp.one_one_Code_integer) tptp.one_one_Code_integer))) (let ((_let_148 (= (@ tptp.abs_abs_rat tptp.one_one_rat) tptp.one_one_rat))) (let ((_let_149 (@ (@ tptp.times_times_real (@ _let_136 _let_109)) tptp.pi))) (let ((_let_150 (@ tptp.uminus_uminus_rat tptp.one_one_rat))) (let ((_let_151 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (let ((_let_152 (@ tptp.uminus_uminus_real tptp.one_one_real))) (let ((_let_153 (@ tptp.uminus_uminus_int tptp.one_one_int))) (let ((_let_154 (= (@ tptp.abs_abs_int tptp.zero_zero_int) tptp.zero_zero_int))) (let ((_let_155 (= (@ tptp.abs_abs_rat tptp.zero_zero_rat) tptp.zero_zero_rat))) (let ((_let_156 (= (@ tptp.abs_abs_real tptp.zero_zero_real) tptp.zero_zero_real))) (let ((_let_157 (= (@ tptp.abs_abs_Code_integer tptp.zero_z3403309356797280102nteger) tptp.zero_z3403309356797280102nteger))) (let ((_let_158 (@ tptp.numera6620942414471956472nteger _let_129))) (let ((_let_159 (@ tptp.numera6690914467698888265omplex _let_129))) (let ((_let_160 (@ tptp.numeral_numeral_int _let_129))) (let ((_let_161 (= tptp.sin_coeff (lambda ((N4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_real (@ (@ tptp.dvd_dvd_nat _let_1) N4)) 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 N4) (@ tptp.suc tptp.zero_zero_nat))) _let_1))) (@ tptp.semiri2265585572941072030t_real N4)))))))) (let ((_let_162 (= tptp.nat_set_decode (lambda ((X4 tptp.nat)) (@ tptp.collect_nat (lambda ((N4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (not (@ (@ tptp.dvd_dvd_nat _let_1) (@ (@ tptp.divide_divide_nat X4) (@ (@ tptp.power_power_nat _let_1) N4))))))))))) (let ((_let_163 (= tptp.semiri2265585572941072030t_real (lambda ((N4 tptp.nat)) (@ tptp.semiri5074537144036343181t_real (@ (@ (@ (@ tptp.set_fo2584398358068434914at_nat tptp.times_times_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N4) tptp.one_one_nat)))))) (let ((_let_164 (= tptp.semiri1408675320244567234ct_nat (lambda ((N4 tptp.nat)) (@ tptp.semiri1316708129612266289at_nat (@ (@ (@ (@ tptp.set_fo2584398358068434914at_nat tptp.times_times_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N4) tptp.one_one_nat)))))) (let ((_let_165 (= tptp.semiri1406184849735516958ct_int (lambda ((N4 tptp.nat)) (@ tptp.semiri1314217659103216013at_int (@ (@ (@ (@ tptp.set_fo2584398358068434914at_nat tptp.times_times_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N4) tptp.one_one_nat)))))) (let ((_let_166 (@ tptp.numera6620942414471956472nteger tptp.one))) (let ((_let_167 (@ tptp.numera6690914467698888265omplex tptp.one))) (let ((_let_168 (@ tptp.numeral_numeral_real tptp.one))) (let ((_let_169 (@ tptp.numeral_numeral_int tptp.one))) (let ((_let_170 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (let ((_let_171 (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger))) (let ((_let_172 (@ tptp.ord_less_real tptp.zero_zero_real))) (let ((_let_173 (@ tptp.ord_less_int tptp.zero_zero_int))) (let ((_let_174 (@ tptp.ord_less_rat _let_150))) (let ((_let_175 (@ tptp.ord_le6747313008572928689nteger _let_151))) (let ((_let_176 (@ tptp.ord_less_real _let_152))) (let ((_let_177 (@ tptp.ord_less_int _let_153))) (let ((_let_178 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_179 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (let ((_let_180 (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (let ((_let_181 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (let ((_let_182 (@ tptp.ord_less_eq_int _let_153))) (let ((_let_183 (@ tptp.ord_less_eq_rat _let_150))) (let ((_let_184 (@ tptp.ord_le3102999989581377725nteger _let_151))) (let ((_let_185 (@ tptp.ord_less_eq_real _let_152))) (let ((_let_186 (= tptp.minus_minus_rat (lambda ((A5 tptp.rat) (B4 tptp.rat)) (@ (@ tptp.plus_plus_rat A5) (@ tptp.uminus_uminus_rat B4)))))) (let ((_let_187 (= tptp.minus_8373710615458151222nteger (lambda ((A5 tptp.code_integer) (B4 tptp.code_integer)) (@ (@ tptp.plus_p5714425477246183910nteger A5) (@ tptp.uminus1351360451143612070nteger B4)))))) (let ((_let_188 (= tptp.minus_minus_complex (lambda ((A5 tptp.complex) (B4 tptp.complex)) (@ (@ tptp.plus_plus_complex A5) (@ tptp.uminus1482373934393186551omplex B4)))))) (let ((_let_189 (= tptp.minus_minus_real (lambda ((A5 tptp.real) (B4 tptp.real)) (@ (@ tptp.plus_plus_real A5) (@ tptp.uminus_uminus_real B4)))))) (let ((_let_190 (= tptp.minus_minus_int (lambda ((A5 tptp.int) (B4 tptp.int)) (@ (@ tptp.plus_plus_int A5) (@ tptp.uminus_uminus_int B4)))))) (let ((_let_191 (@ tptp.ord_less_rat tptp.one_one_rat))) (let ((_let_192 (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer))) (let ((_let_193 (@ tptp.ord_less_real tptp.one_one_real))) (let ((_let_194 (@ tptp.ord_less_int tptp.one_one_int))) (let ((_let_195 (@ tptp.ord_less_eq_int tptp.one_one_int))) (let ((_let_196 (@ tptp.ord_less_eq_rat tptp.one_one_rat))) (let ((_let_197 (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer))) (let ((_let_198 (@ tptp.ord_less_eq_real tptp.one_one_real))) (let ((_let_199 (@ tptp.numeral_numeral_rat _let_21))) (let ((_let_200 (@ tptp.uminus_uminus_rat _let_199))) (let ((_let_201 (@ tptp.numera6620942414471956472nteger _let_21))) (let ((_let_202 (@ tptp.uminus1351360451143612070nteger _let_201))) (let ((_let_203 (@ tptp.uminus1482373934393186551omplex _let_103))) (let ((_let_204 (@ tptp.uminus_uminus_real _let_109))) (let ((_let_205 (@ tptp.uminus_uminus_int _let_115))) (let ((_let_206 (@ tptp.minus_minus_rat _let_150))) (let ((_let_207 (@ tptp.minus_8373710615458151222nteger _let_151))) (let ((_let_208 (@ tptp.minus_minus_complex _let_104))) (let ((_let_209 (@ tptp.minus_minus_real _let_152))) (let ((_let_210 (@ tptp.minus_minus_int _let_153))) (let ((_let_211 (@ tptp.minus_minus_rat tptp.one_one_rat))) (let ((_let_212 (@ tptp.minus_8373710615458151222nteger tptp.one_one_Code_integer))) (let ((_let_213 (@ tptp.minus_minus_complex tptp.one_one_complex))) (let ((_let_214 (@ tptp.minus_minus_real tptp.one_one_real))) (let ((_let_215 (@ tptp.minus_minus_int tptp.one_one_int))) (let ((_let_216 (@ tptp.plus_plus_rat _let_150))) (let ((_let_217 (@ tptp.plus_p5714425477246183910nteger _let_151))) (let ((_let_218 (@ tptp.plus_plus_complex _let_104))) (let ((_let_219 (@ tptp.plus_plus_real _let_152))) (let ((_let_220 (@ tptp.plus_plus_int _let_153))) (let ((_let_221 (@ tptp.plus_plus_rat tptp.one_one_rat))) (let ((_let_222 (@ tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer))) (let ((_let_223 (@ tptp.plus_plus_complex tptp.one_one_complex))) (let ((_let_224 (@ tptp.plus_plus_real tptp.one_one_real))) (let ((_let_225 (@ tptp.plus_plus_int tptp.one_one_int))) (let ((_let_226 (= tptp.gbinomial_real (lambda ((A5 tptp.real) (K3 tptp.nat)) (@ (@ (@ tptp.if_real (= K3 tptp.zero_zero_nat)) tptp.one_one_real) (@ (@ tptp.divide_divide_real (@ (@ (@ (@ tptp.set_fo3111899725591712190t_real (lambda ((L2 tptp.nat) (__flatten_var_0 tptp.real)) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real A5) (@ tptp.semiri5074537144036343181t_real L2))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat K3) tptp.one_one_nat)) tptp.one_one_real)) (@ tptp.semiri2265585572941072030t_real K3))))))) (let ((_let_227 (= tptp.gbinomial_rat (lambda ((A5 tptp.rat) (K3 tptp.nat)) (@ (@ (@ tptp.if_rat (= K3 tptp.zero_zero_nat)) tptp.one_one_rat) (@ (@ tptp.divide_divide_rat (@ (@ (@ (@ tptp.set_fo1949268297981939178at_rat (lambda ((L2 tptp.nat) (__flatten_var_0 tptp.rat)) (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat A5) (@ tptp.semiri681578069525770553at_rat L2))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat K3) tptp.one_one_nat)) tptp.one_one_rat)) (@ tptp.semiri773545260158071498ct_rat K3))))))) (let ((_let_228 (= tptp.gbinomial_complex (lambda ((A5 tptp.complex) (K3 tptp.nat)) (@ (@ (@ tptp.if_complex (= K3 tptp.zero_zero_nat)) tptp.one_one_complex) (@ (@ tptp.divide1717551699836669952omplex (@ (@ (@ (@ tptp.set_fo1517530859248394432omplex (lambda ((L2 tptp.nat) (__flatten_var_0 tptp.complex)) (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex A5) (@ tptp.semiri8010041392384452111omplex L2))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat K3) tptp.one_one_nat)) tptp.one_one_complex)) (@ tptp.semiri5044797733671781792omplex K3))))))) (let ((_let_229 (= tptp.distinct_int (lambda ((Xs tptp.list_int)) (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_int Xs)) (forall ((J tptp.nat)) (let ((_let_1 (@ tptp.nth_int Xs))) (=> (@ (@ tptp.ord_less_nat J) (@ tptp.size_size_list_int Xs)) (=> (not (= I J)) (not (= (@ _let_1 I) (@ _let_1 J))))))))))))) (let ((_let_230 (= tptp.distinct_nat (lambda ((Xs tptp.list_nat)) (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_nat Xs)) (forall ((J tptp.nat)) (let ((_let_1 (@ tptp.nth_nat Xs))) (=> (@ (@ tptp.ord_less_nat J) (@ tptp.size_size_list_nat Xs)) (=> (not (= I J)) (not (= (@ _let_1 I) (@ _let_1 J))))))))))))) (let ((_let_231 (= tptp.distinct_o (lambda ((Xs tptp.list_o)) (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_o Xs)) (forall ((J tptp.nat)) (let ((_let_1 (@ tptp.nth_o Xs))) (=> (@ (@ tptp.ord_less_nat J) (@ tptp.size_size_list_o Xs)) (=> (not (= I J)) (not (= (@ _let_1 I) (@ _let_1 J))))))))))))) (let ((_let_232 (= tptp.distinct_VEBT_VEBT (lambda ((Xs tptp.list_VEBT_VEBT)) (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (forall ((J tptp.nat)) (let ((_let_1 (@ tptp.nth_VEBT_VEBT Xs))) (=> (@ (@ tptp.ord_less_nat J) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (=> (not (= I J)) (not (= (@ _let_1 I) (@ _let_1 J))))))))))))) (let ((_let_233 (= tptp.zero_n356916108424825756nteger (lambda ((P5 Bool)) (@ (@ (@ tptp.if_Code_integer P5) tptp.one_one_Code_integer) tptp.zero_z3403309356797280102nteger))))) (let ((_let_234 (= tptp.zero_n2684676970156552555ol_int (lambda ((P5 Bool)) (@ (@ (@ tptp.if_int P5) tptp.one_one_int) tptp.zero_zero_int))))) (let ((_let_235 (= tptp.zero_n2687167440665602831ol_nat (lambda ((P5 Bool)) (@ (@ (@ tptp.if_nat P5) tptp.one_one_nat) tptp.zero_zero_nat))))) (let ((_let_236 (= tptp.zero_n2052037380579107095ol_rat (lambda ((P5 Bool)) (@ (@ (@ tptp.if_rat P5) tptp.one_one_rat) tptp.zero_zero_rat))))) (let ((_let_237 (= tptp.zero_n3304061248610475627l_real (lambda ((P5 Bool)) (@ (@ (@ tptp.if_real P5) tptp.one_one_real) tptp.zero_zero_real))))) (let ((_let_238 (= tptp.zero_n1201886186963655149omplex (lambda ((P5 Bool)) (@ (@ (@ tptp.if_complex P5) tptp.one_one_complex) tptp.zero_zero_complex))))) (let ((_let_239 (= tptp.set_ord_atMost_nat (lambda ((U2 tptp.nat)) (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (@ (@ tptp.ord_less_eq_nat X4) U2))))))) (let ((_let_240 (= tptp.set_ord_atMost_int (lambda ((U2 tptp.int)) (@ tptp.collect_int (lambda ((X4 tptp.int)) (@ (@ tptp.ord_less_eq_int X4) U2))))))) (let ((_let_241 (= tptp.set_ord_atMost_num (lambda ((U2 tptp.num)) (@ tptp.collect_num (lambda ((X4 tptp.num)) (@ (@ tptp.ord_less_eq_num X4) U2))))))) (let ((_let_242 (= tptp.set_ord_atMost_rat (lambda ((U2 tptp.rat)) (@ tptp.collect_rat (lambda ((X4 tptp.rat)) (@ (@ tptp.ord_less_eq_rat X4) U2))))))) (let ((_let_243 (= tptp.set_or4236626031148496127et_nat (lambda ((U2 tptp.set_nat)) (@ tptp.collect_set_nat (lambda ((X4 tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat X4) U2))))))) (let ((_let_244 (= tptp.set_ord_atMost_real (lambda ((U2 tptp.real)) (@ tptp.collect_real (lambda ((X4 tptp.real)) (@ (@ tptp.ord_less_eq_real X4) U2))))))) (let ((_let_245 (= tptp.neg_numeral_dbl_int (lambda ((X4 tptp.int)) (@ (@ tptp.plus_plus_int X4) X4))))) (let ((_let_246 (= tptp.neg_numeral_dbl_rat (lambda ((X4 tptp.rat)) (@ (@ tptp.plus_plus_rat X4) X4))))) (let ((_let_247 (= tptp.neg_numeral_dbl_real (lambda ((X4 tptp.real)) (@ (@ tptp.plus_plus_real X4) X4))))) (let ((_let_248 (= tptp.set_ord_lessThan_nat (lambda ((U2 tptp.nat)) (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (@ (@ tptp.ord_less_nat X4) U2))))))) (let ((_let_249 (= tptp.set_ord_lessThan_int (lambda ((U2 tptp.int)) (@ tptp.collect_int (lambda ((X4 tptp.int)) (@ (@ tptp.ord_less_int X4) U2))))))) (let ((_let_250 (= tptp.set_ord_lessThan_num (lambda ((U2 tptp.num)) (@ tptp.collect_num (lambda ((X4 tptp.num)) (@ (@ tptp.ord_less_num X4) U2))))))) (let ((_let_251 (= tptp.set_ord_lessThan_rat (lambda ((U2 tptp.rat)) (@ tptp.collect_rat (lambda ((X4 tptp.rat)) (@ (@ tptp.ord_less_rat X4) U2))))))) (let ((_let_252 (= tptp.set_or5984915006950818249n_real (lambda ((U2 tptp.real)) (@ tptp.collect_real (lambda ((X4 tptp.real)) (@ (@ tptp.ord_less_real X4) U2))))))) (let ((_let_253 (= tptp.set_or890127255671739683et_nat (lambda ((U2 tptp.set_nat)) (@ tptp.collect_set_nat (lambda ((X4 tptp.set_nat)) (@ (@ tptp.ord_less_set_nat X4) U2))))))) (let ((_let_254 (= tptp.semiri1316708129612266289at_nat (lambda ((N4 tptp.nat)) (@ (@ (@ tptp.semiri8422978514062236437ux_nat (lambda ((I tptp.nat)) (@ (@ tptp.plus_plus_nat I) tptp.one_one_nat))) N4) tptp.zero_zero_nat))))) (let ((_let_255 (= tptp.semiri681578069525770553at_rat (lambda ((N4 tptp.nat)) (@ (@ (@ tptp.semiri7787848453975740701ux_rat (lambda ((I tptp.rat)) (@ (@ tptp.plus_plus_rat I) tptp.one_one_rat))) N4) tptp.zero_zero_rat))))) (let ((_let_256 (= tptp.comm_s4663373288045622133er_nat (lambda ((A5 tptp.nat) (N4 tptp.nat)) (@ (@ (@ tptp.if_nat (= N4 tptp.zero_zero_nat)) tptp.one_one_nat) (@ (@ (@ (@ tptp.set_fo2584398358068434914at_nat (lambda ((O tptp.nat) (__flatten_var_0 tptp.nat)) (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat A5) (@ tptp.semiri1316708129612266289at_nat O))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat N4) tptp.one_one_nat)) tptp.one_one_nat)))))) (let ((_let_257 (= tptp.comm_s4660882817536571857er_int (lambda ((A5 tptp.int) (N4 tptp.nat)) (@ (@ (@ tptp.if_int (= N4 tptp.zero_zero_nat)) tptp.one_one_int) (@ (@ (@ (@ tptp.set_fo2581907887559384638at_int (lambda ((O tptp.nat) (__flatten_var_0 tptp.int)) (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int A5) (@ tptp.semiri1314217659103216013at_int O))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat N4) tptp.one_one_nat)) tptp.one_one_int)))))) (let ((_let_258 (= tptp.comm_s7457072308508201937r_real (lambda ((A5 tptp.real) (N4 tptp.nat)) (@ (@ (@ tptp.if_real (= N4 tptp.zero_zero_nat)) tptp.one_one_real) (@ (@ (@ (@ tptp.set_fo3111899725591712190t_real (lambda ((O tptp.nat) (__flatten_var_0 tptp.real)) (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real A5) (@ tptp.semiri5074537144036343181t_real O))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat N4) tptp.one_one_nat)) tptp.one_one_real)))))) (let ((_let_259 (= tptp.comm_s4028243227959126397er_rat (lambda ((A5 tptp.rat) (N4 tptp.nat)) (@ (@ (@ tptp.if_rat (= N4 tptp.zero_zero_nat)) tptp.one_one_rat) (@ (@ (@ (@ tptp.set_fo1949268297981939178at_rat (lambda ((O tptp.nat) (__flatten_var_0 tptp.rat)) (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat A5) (@ tptp.semiri681578069525770553at_rat O))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat N4) tptp.one_one_nat)) tptp.one_one_rat)))))) (let ((_let_260 (= tptp.comm_s2602460028002588243omplex (lambda ((A5 tptp.complex) (N4 tptp.nat)) (@ (@ (@ tptp.if_complex (= N4 tptp.zero_zero_nat)) tptp.one_one_complex) (@ (@ (@ (@ tptp.set_fo1517530859248394432omplex (lambda ((O tptp.nat) (__flatten_var_0 tptp.complex)) (@ (@ tptp.times_times_complex (@ (@ tptp.plus_plus_complex A5) (@ tptp.semiri8010041392384452111omplex O))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat N4) tptp.one_one_nat)) tptp.one_one_complex)))))) (let ((_let_261 (= tptp.comm_s8582702949713902594nteger (lambda ((A5 tptp.code_integer) (N4 tptp.nat)) (@ (@ (@ tptp.if_Code_integer (= N4 tptp.zero_zero_nat)) tptp.one_one_Code_integer) (@ (@ (@ (@ tptp.set_fo1084959871951514735nteger (lambda ((O tptp.nat) (__flatten_var_0 tptp.code_integer)) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.plus_p5714425477246183910nteger A5) (@ tptp.semiri4939895301339042750nteger O))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat N4) tptp.one_one_nat)) tptp.one_one_Code_integer)))))) (let ((_let_262 (@ tptp.power_power_nat _let_22))) (let ((_let_263 (= tptp.nat_set_encode (@ tptp.groups3542108847815614940at_nat _let_262)))) (let ((_let_264 (= tptp.dvd_dvd_Code_natural (lambda ((A5 tptp.code_natural) (B4 tptp.code_natural)) (= (@ (@ tptp.modulo8411746178871703098atural B4) A5) tptp.zero_z2226904508553997617atural))))) (let ((_let_265 (= tptp.dvd_dvd_int (lambda ((B4 tptp.int) (A5 tptp.int)) (exists ((K3 tptp.int)) (= A5 (@ (@ tptp.times_times_int B4) K3))))))) (let ((_let_266 (= tptp.dvd_dvd_nat (lambda ((B4 tptp.nat) (A5 tptp.nat)) (exists ((K3 tptp.nat)) (= A5 (@ (@ tptp.times_times_nat B4) K3))))))) (let ((_let_267 (= tptp.dvd_dvd_rat (lambda ((A5 tptp.rat) (B4 tptp.rat)) (=> (= A5 tptp.zero_zero_rat) (= B4 tptp.zero_zero_rat)))))) (let ((_let_268 (= tptp.dvd_dvd_real (lambda ((A5 tptp.real) (B4 tptp.real)) (=> (= A5 tptp.zero_zero_real) (= B4 tptp.zero_zero_real)))))) (let ((_let_269 (= tptp.dvd_dvd_complex (lambda ((A5 tptp.complex) (B4 tptp.complex)) (=> (= A5 tptp.zero_zero_complex) (= B4 tptp.zero_zero_complex)))))) (let ((_let_270 (= tptp.modulo_modulo_nat (lambda ((M6 tptp.nat) (N4 tptp.nat)) (@ (@ tptp.minus_minus_nat M6) (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat M6) N4)) N4)))))) (let ((_let_271 (= tptp.vEBT_VEBT_low (lambda ((X4 tptp.nat) (N4 tptp.nat)) (@ (@ tptp.modulo_modulo_nat X4) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N4)))))) (let ((_let_272 (= tptp.vEBT_set_vebt (lambda ((T2 tptp.vEBT_VEBT)) (@ tptp.collect_nat (@ tptp.vEBT_V8194947554948674370ptions T2)))))) (let ((_let_273 (= tptp.sup_sup_nat tptp.ord_max_nat))) (let ((_let_274 (= tptp.ord_max_int (lambda ((A5 tptp.int) (B4 tptp.int)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_eq_int A5) B4)) B4) A5))))) (let ((_let_275 (= tptp.ord_max_nat (lambda ((A5 tptp.nat) (B4 tptp.nat)) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_eq_nat A5) B4)) B4) A5))))) (let ((_let_276 (= tptp.ord_max_num (lambda ((A5 tptp.num) (B4 tptp.num)) (@ (@ (@ tptp.if_num (@ (@ tptp.ord_less_eq_num A5) B4)) B4) A5))))) (let ((_let_277 (= tptp.ord_max_rat (lambda ((A5 tptp.rat) (B4 tptp.rat)) (@ (@ (@ tptp.if_rat (@ (@ tptp.ord_less_eq_rat A5) B4)) B4) A5))))) (let ((_let_278 (= tptp.ord_max_set_nat (lambda ((A5 tptp.set_nat) (B4 tptp.set_nat)) (@ (@ (@ tptp.if_set_nat (@ (@ tptp.ord_less_eq_set_nat A5) B4)) B4) A5))))) (let ((_let_279 (= tptp.vEBT_VEBT_set_vebt (lambda ((T2 tptp.vEBT_VEBT)) (@ tptp.collect_nat (@ tptp.vEBT_vebt_member T2)))))) (let ((_let_280 (= tptp.vEBT_V5917875025757280293ildren (lambda ((N4 tptp.nat) (TreeList4 tptp.list_VEBT_VEBT) (X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList4) (@ (@ tptp.vEBT_VEBT_high X4) N4))) (@ (@ tptp.vEBT_VEBT_low X4) N4)))))) (let ((_let_281 (= tptp.ord_less_eq_int (lambda ((X4 tptp.int) (Y4 tptp.int)) (= (@ (@ tptp.inf_inf_int X4) Y4) X4))))) (let ((_let_282 (= tptp.ord_less_eq_rat (lambda ((X4 tptp.rat) (Y4 tptp.rat)) (= (@ (@ tptp.inf_inf_rat X4) Y4) X4))))) (let ((_let_283 (= tptp.ord_less_eq_set_nat (lambda ((X4 tptp.set_nat) (Y4 tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat X4) Y4) X4))))) (let ((_let_284 (= tptp.ord_le3146513528884898305at_nat (lambda ((X4 tptp.set_Pr1261947904930325089at_nat) (Y4 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat X4) Y4) X4))))) (let ((_let_285 (= tptp.vEBT_VEBT_high (lambda ((X4 tptp.nat) (N4 tptp.nat)) (@ (@ tptp.divide_divide_nat X4) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N4)))))) (let ((_let_286 (= tptp.mi tptp.ma))) (let ((_let_287 (= (@ (@ tptp.divide_divide_int tptp.one_one_int) _let_115) tptp.zero_zero_int))) (let ((_let_288 (= (@ (@ tptp.divide_divide_nat tptp.one_one_nat) _let_22) tptp.zero_zero_nat))) (let ((_let_289 (= (@ (@ tptp.divide6298287555418463151nteger tptp.one_one_Code_integer) _let_201) tptp.zero_z3403309356797280102nteger))) (let ((_let_290 (= tptp.nat_triangle (lambda ((N4 tptp.nat)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat N4) (@ tptp.suc N4))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))) (let ((_let_291 (= (@ tptp.semiri1314217659103216013at_int tptp.zero_zero_nat) tptp.zero_zero_int))) (let ((_let_292 (@ tptp.numeral_numeral_nat tptp.one))) (let ((_let_293 (@ tptp.plus_plus_nat tptp.one_one_nat))) (let ((_let_294 (@ _let_293 tptp.one_one_nat))) (let ((_let_295 (= _let_294 _let_22))) (let ((_let_296 (= _let_292 tptp.one_one_nat))) (let ((_let_297 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (let ((_let_298 (= (@ tptp.numera1916890842035813515d_enat tptp.one) tptp.one_on7984719198319812577d_enat))) (let ((_let_299 (@ _let_225 tptp.one_one_int))) (let ((_let_300 (@ _let_224 tptp.one_one_real))) (let ((_let_301 (@ _let_221 tptp.one_one_rat))) (let ((_let_302 (@ _let_222 tptp.one_one_Code_integer))) (let ((_let_303 (@ tptp.semiri1314217659103216013at_int tptp.one_one_nat))) (let ((_let_304 (= _let_303 tptp.one_one_int))) (let ((_let_305 (@ tptp.semiri5074537144036343181t_real tptp.one_one_nat))) (let ((_let_306 (= _let_305 tptp.one_one_real))) (let ((_let_307 (@ tptp.semiri8010041392384452111omplex tptp.one_one_nat))) (let ((_let_308 (= _let_307 tptp.one_one_complex))) (let ((_let_309 (@ tptp.semiri4939895301339042750nteger tptp.one_one_nat))) (let ((_let_310 (= _let_309 tptp.one_one_Code_integer))) (let ((_let_311 (= tptp.vEBT_VEBT_bit_concat (lambda ((H2 tptp.nat) (L2 tptp.nat) (D2 tptp.nat)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat H2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) D2))) L2))))) (let ((_let_312 (@ (@ tptp.ord_less_eq_nat _let_22) tptp.deg))) (let ((_let_313 (@ _let_262 tptp.m))) (let ((_let_314 (= tptp.deg (@ (@ tptp.plus_plus_nat tptp.na) tptp.m)))) (let ((_let_315 (= tptp.neg_nu5851722552734809277nc_int (lambda ((X4 tptp.int)) (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int X4) X4)) tptp.one_one_int))))) (let ((_let_316 (= tptp.neg_nu5219082963157363817nc_rat (lambda ((X4 tptp.rat)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.plus_plus_rat X4) X4)) tptp.one_one_rat))))) (let ((_let_317 (= tptp.neg_nu8295874005876285629c_real (lambda ((X4 tptp.real)) (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real X4) X4)) tptp.one_one_real))))) (let ((_let_318 (= tptp.neg_nu8557863876264182079omplex (lambda ((X4 tptp.complex)) (@ (@ tptp.plus_plus_complex (@ (@ tptp.plus_plus_complex X4) X4)) tptp.one_one_complex))))) (let ((_let_319 (= tptp.neg_nu5831290666863070958nteger (lambda ((X4 tptp.code_integer)) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.plus_p5714425477246183910nteger X4) X4)) tptp.one_one_Code_integer))))) (let ((_let_320 (= tptp.vEBT_VEBT_power (@ tptp.vEBT_V4262088993061758097ft_nat tptp.power_power_nat)))) (let ((_let_321 (= tptp.neg_nu3811975205180677377ec_int (lambda ((X4 tptp.int)) (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int X4) X4)) tptp.one_one_int))))) (let ((_let_322 (= tptp.neg_nu3179335615603231917ec_rat (lambda ((X4 tptp.rat)) (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat X4) X4)) tptp.one_one_rat))))) (let ((_let_323 (= tptp.neg_nu6075765906172075777c_real (lambda ((X4 tptp.real)) (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real X4) X4)) tptp.one_one_real))))) (let ((_let_324 (= tptp.neg_nu6511756317524482435omplex (lambda ((X4 tptp.complex)) (@ (@ tptp.minus_minus_complex (@ (@ tptp.plus_plus_complex X4) X4)) tptp.one_one_complex))))) (let ((_let_325 (= tptp.neg_nu7757733837767384882nteger (lambda ((X4 tptp.code_integer)) (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.plus_p5714425477246183910nteger X4) X4)) tptp.one_one_Code_integer))))) (let ((_let_326 (= tptp.nat_prod_decode (@ tptp.nat_prod_decode_aux tptp.zero_zero_nat)))) (let ((_let_327 (@ tptp.gcd_Gcd_nat tptp.bot_bot_set_nat))) (let ((_let_328 (= _let_327 tptp.zero_zero_nat))) (let ((_let_329 (@ (@ tptp.vEBT_Leaf false) false))) (let ((_let_330 (= tptp.finite_finite_nat (lambda ((N5 tptp.set_nat)) (exists ((M6 tptp.nat)) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) N5) (@ (@ tptp.ord_less_nat X4) M6)))))))) (let ((_let_331 (= (@ _let_215 tptp.one_one_int) tptp.zero_zero_int))) (let ((_let_332 (= (@ _let_211 tptp.one_one_rat) tptp.zero_zero_rat))) (let ((_let_333 (= (@ _let_214 tptp.one_one_real) tptp.zero_zero_real))) (let ((_let_334 (= (@ _let_213 tptp.one_one_complex) tptp.zero_zero_complex))) (let ((_let_335 (= (@ _let_212 tptp.one_one_Code_integer) tptp.zero_z3403309356797280102nteger))) (let ((_let_336 (= tptp.vEBT_VEBT_add (@ tptp.vEBT_V4262088993061758097ft_nat tptp.plus_plus_nat)))) (let ((_let_337 (= tptp.vEBT_is_succ_in_set (lambda ((Xs tptp.set_nat) (X4 tptp.nat) (Y4 tptp.nat)) (and (@ (@ tptp.member_nat Y4) Xs) (@ (@ tptp.ord_less_nat X4) Y4) (forall ((Z4 tptp.nat)) (=> (@ (@ tptp.member_nat Z4) Xs) (=> (@ (@ tptp.ord_less_nat X4) Z4) (@ (@ tptp.ord_less_eq_nat Y4) Z4))))))))) (let ((_let_338 (= tptp.vEBT_is_pred_in_set (lambda ((Xs tptp.set_nat) (X4 tptp.nat) (Y4 tptp.nat)) (and (@ (@ tptp.member_nat Y4) Xs) (@ (@ tptp.ord_less_nat Y4) X4) (forall ((Z4 tptp.nat)) (=> (@ (@ tptp.member_nat Z4) Xs) (=> (@ (@ tptp.ord_less_nat Z4) X4) (@ (@ tptp.ord_less_eq_nat Z4) Y4))))))))) (let ((_let_339 (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))))))))) (let ((_let_340 (= tptp.ord_le6747313008572928689nteger (lambda ((A5 tptp.code_integer) (__flatten_var_0 tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.plus_p5714425477246183910nteger A5) tptp.one_one_Code_integer)) __flatten_var_0))))) (let ((_let_341 (= tptp.suc _let_293))) (let ((_let_342 (= tptp.bot_bot_nat tptp.zero_zero_nat))) (let ((_let_343 (= tptp.vEBT_V8194947554948674370ptions (lambda ((T2 tptp.vEBT_VEBT) (X4 tptp.nat)) (or (@ (@ tptp.vEBT_V5719532721284313246member T2) X4) (@ (@ tptp.vEBT_VEBT_membermima T2) X4)))))) (let ((_let_344 (@ tptp.vEBT_VEBT_set_vebt (@ (@ (@ (@ tptp.vEBT_Node _let_1) tptp.deg) tptp.treeList2) tptp.summary2)))) (let ((_let_345 (= tptp.m tptp.na))) (let ((_let_346 (= tptp.one_one_nat _let_10))) (let ((_let_347 (@ _let_178 tptp.one_one_int))) (let ((_let_348 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (let ((_let_349 (@ _let_348 tptp.one_one_nat))) (let ((_let_350 (@ _let_179 tptp.one_one_rat))) (let ((_let_351 (@ _let_181 tptp.one_one_real))) (let ((_let_352 (@ _let_180 tptp.one_one_Code_integer))) (let ((_let_353 (@ tptp.ord_less_eq_nat tptp.one_one_nat))) (let ((_let_354 (= tptp.ord_less_int (lambda ((X4 tptp.int) (Y4 tptp.int)) (and (@ (@ tptp.ord_less_eq_int X4) Y4) (not (= X4 Y4))))))) (let ((_let_355 (= tptp.ord_less_nat (lambda ((X4 tptp.nat) (Y4 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat X4) Y4) (not (= X4 Y4))))))) (let ((_let_356 (= tptp.ord_less_num (lambda ((X4 tptp.num) (Y4 tptp.num)) (and (@ (@ tptp.ord_less_eq_num X4) Y4) (not (= X4 Y4))))))) (let ((_let_357 (= tptp.ord_less_rat (lambda ((X4 tptp.rat) (Y4 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat X4) Y4) (not (= X4 Y4))))))) (let ((_let_358 (= tptp.ord_less_set_nat (lambda ((X4 tptp.set_nat) (Y4 tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat X4) Y4) (not (= X4 Y4))))))) (let ((_let_359 (= tptp.ord_less_real (lambda ((X4 tptp.real) (Y4 tptp.real)) (and (@ (@ tptp.ord_less_eq_real X4) Y4) (not (= X4 Y4))))))) (let ((_let_360 (@ _let_173 tptp.one_one_int))) (let ((_let_361 (@ _let_297 tptp.one_one_nat))) (let ((_let_362 (@ _let_170 tptp.one_one_rat))) (let ((_let_363 (@ _let_172 tptp.one_one_real))) (let ((_let_364 (@ _let_171 tptp.one_one_Code_integer))) (let ((_let_365 (@ tptp.ord_less_nat tptp.one_one_nat))) (let ((_let_366 (not (@ _let_365 tptp.zero_zero_nat)))) (let ((_let_367 (= tptp.vEBT_VEBT_valid tptp.vEBT_invar_vebt))) (let ((_let_368 (= tptp.vEBT_VEBT_mul (@ tptp.vEBT_V4262088993061758097ft_nat tptp.times_times_nat)))) (let ((_let_369 (= tptp.sa (@ (@ tptp.vEBT_Leaf tptp.a) tptp.b)))) (let ((_let_370 (forall ((N tptp.nat) (M2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) (@ tptp.suc M2)) (@ (@ tptp.ord_less_eq_nat N) M2))))) (let ((_let_371 (= tptp.deg _let_10))) (let ((_let_372 (= tptp.bNF_Ca8987285221972644271er_int (lambda ((R tptp.set_Pr4811707699266497531nteger) (As (-> tptp.code_integer tptp.int))) (forall ((I tptp.code_integer) (J tptp.code_integer)) (=> (@ (@ tptp.member157494554546826820nteger (@ (@ tptp.produc1086072967326762835nteger I) J)) R) (@ (@ tptp.ord_less_eq_int (@ As I)) (@ As J)))))))) (let ((_let_373 (= tptp.bNF_Ca1968104039914474786nt_nat (lambda ((R tptp.set_Pr958786334691620121nt_int) (As (-> tptp.int tptp.nat))) (forall ((I tptp.int) (J tptp.int)) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int I) J)) R) (@ (@ tptp.ord_less_eq_nat (@ As I)) (@ As J)))))))) (let ((_let_374 (= tptp.bNF_Ca968750328013420230at_nat (lambda ((R tptp.set_Pr1261947904930325089at_nat) (As (-> tptp.nat tptp.nat))) (forall ((I tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat I) J)) R) (@ (@ tptp.ord_less_eq_nat (@ As I)) (@ As J)))))))) (let ((_let_375 (= tptp.bNF_Ca8989775692481694547er_nat (lambda ((R tptp.set_Pr4811707699266497531nteger) (As (-> tptp.code_integer tptp.nat))) (forall ((I tptp.code_integer) (J tptp.code_integer)) (=> (@ (@ tptp.member157494554546826820nteger (@ (@ tptp.produc1086072967326762835nteger I) J)) R) (@ (@ tptp.ord_less_eq_nat (@ As I)) (@ As J)))))))) (let ((_let_376 (= tptp.bNF_Ca7748807862925029228nt_num (lambda ((R tptp.set_Pr958786334691620121nt_int) (As (-> tptp.int tptp.num))) (forall ((I tptp.int) (J tptp.int)) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int I) J)) R) (@ (@ tptp.ord_less_eq_num (@ As I)) (@ As J)))))))) (let ((_let_377 (= tptp.bNF_Ca6749454151023974672at_num (lambda ((R tptp.set_Pr1261947904930325089at_nat) (As (-> tptp.nat tptp.num))) (forall ((I tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat I) J)) R) (@ (@ tptp.ord_less_eq_num (@ As I)) (@ As J)))))))) (let ((_let_378 (= tptp.bNF_Ca5547107478637473181er_num (lambda ((R tptp.set_Pr4811707699266497531nteger) (As (-> tptp.code_integer tptp.num))) (forall ((I tptp.code_integer) (J tptp.code_integer)) (=> (@ (@ tptp.member157494554546826820nteger (@ (@ tptp.produc1086072967326762835nteger I) J)) R) (@ (@ tptp.ord_less_eq_num (@ As I)) (@ As J)))))))) (let ((_let_379 (= tptp.bNF_Ca1332973979827979050nt_rat (lambda ((R tptp.set_Pr958786334691620121nt_int) (As (-> tptp.int tptp.rat))) (forall ((I tptp.int) (J tptp.int)) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int I) J)) R) (@ (@ tptp.ord_less_eq_rat (@ As I)) (@ As J)))))))) (let ((_let_380 (= tptp.bNF_Ca333620267926924494at_rat (lambda ((R tptp.set_Pr1261947904930325089at_nat) (As (-> tptp.nat tptp.rat))) (forall ((I tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat I) J)) R) (@ (@ tptp.ord_less_eq_rat (@ As I)) (@ As J)))))))) (let ((_let_381 (= tptp.bNF_Ca8354645632395198811er_rat (lambda ((R tptp.set_Pr4811707699266497531nteger) (As (-> tptp.code_integer tptp.rat))) (forall ((I tptp.code_integer) (J tptp.code_integer)) (=> (@ (@ tptp.member157494554546826820nteger (@ (@ tptp.produc1086072967326762835nteger I) J)) R) (@ (@ tptp.ord_less_eq_rat (@ As I)) (@ As J)))))))) (let ((_let_382 (= tptp.ord_less_eq_nat (lambda ((X4 tptp.nat) (Y4 tptp.nat)) (@ (@ tptp.vEBT_VEBT_lesseq (@ tptp.some_nat X4)) (@ tptp.some_nat Y4)))))) (let ((_let_383 (= tptp.vEBT_VEBT_min_in_set (lambda ((Xs tptp.set_nat) (X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) Xs) (forall ((Y4 tptp.nat)) (=> (@ (@ tptp.member_nat Y4) Xs) (@ (@ tptp.ord_less_eq_nat X4) Y4)))))))) (let ((_let_384 (= tptp.vEBT_VEBT_max_in_set (lambda ((Xs tptp.set_nat) (X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) Xs) (forall ((Y4 tptp.nat)) (=> (@ (@ tptp.member_nat Y4) Xs) (@ (@ tptp.ord_less_eq_nat Y4) X4)))))))) (let ((_let_385 (ho_3709 k_3708 tptp.bot_bot_set_nat))) (let ((_let_386 (ho_3734 k_3733 _let_385))) (let ((_let_387 (ho_3763 k_3762 _let_386))) (let ((_let_388 (= k_3733 _let_387))) (let ((_let_389 (ho_3721 k_3720 _let_386))) (let ((_let_390 (ho_3734 k_3733 (ho_3732 k_3731 (ho_3730 k_3729 (ho_3728 k_3727 _let_385)))))) (let ((_let_391 (ho_3737 (ho_3736 k_3735 (ho_3721 k_3720 _let_390)) _let_389))) (let ((_let_392 (= _let_390 (ho_3734 _let_387 _let_386)))) (let ((_let_393 (ho_3737 (ho_3736 k_3735 (ho_3721 k_3720 (ho_3734 k_3733 _let_386))) _let_389))) (let ((_let_394 (@ tptp.suc _let_327))) (let ((_let_395 (@ tptp.plus_plus_nat _let_394))) (let ((_let_396 (EQ_RESOLVE (ASSUME :args (_let_384)) (MACRO_SR_EQ_INTRO :args (_let_384 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_397 (EQ_RESOLVE (ASSUME :args (_let_383)) (MACRO_SR_EQ_INTRO :args (_let_383 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_398 (ASSUME :args (_let_382)))) (let ((_let_399 (EQ_RESOLVE (ASSUME :args (_let_381)) (MACRO_SR_EQ_INTRO :args (_let_381 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_400 (EQ_RESOLVE (ASSUME :args (_let_380)) (MACRO_SR_EQ_INTRO :args (_let_380 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_401 (EQ_RESOLVE (ASSUME :args (_let_379)) (MACRO_SR_EQ_INTRO :args (_let_379 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_402 (EQ_RESOLVE (ASSUME :args (_let_378)) (MACRO_SR_EQ_INTRO :args (_let_378 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_403 (EQ_RESOLVE (ASSUME :args (_let_377)) (MACRO_SR_EQ_INTRO :args (_let_377 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_404 (EQ_RESOLVE (ASSUME :args (_let_376)) (MACRO_SR_EQ_INTRO :args (_let_376 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_405 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_375)) (MACRO_SR_EQ_INTRO :args (_let_375 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396) :args ((= tptp.bNF_Ca8989775692481694547er_nat (lambda ((R tptp.set_Pr4811707699266497531nteger) (As (-> tptp.code_integer tptp.nat))) (forall ((I tptp.code_integer) (J tptp.code_integer)) (or (not (@ (@ tptp.member157494554546826820nteger (@ (@ tptp.produc1086072967326762835nteger I) J)) R)) (@ (@ tptp.ord_less_eq_nat (@ As I)) (@ As J)))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_406 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_374)) (MACRO_SR_EQ_INTRO :args (_let_374 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396) :args ((= tptp.bNF_Ca968750328013420230at_nat (lambda ((R tptp.set_Pr1261947904930325089at_nat) (As (-> tptp.nat tptp.nat))) (forall ((I tptp.nat) (J tptp.nat)) (or (not (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat I) J)) R)) (@ (@ tptp.ord_less_eq_nat (@ As I)) (@ As J)))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_407 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_373)) (MACRO_SR_EQ_INTRO :args (_let_373 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396) :args ((= tptp.bNF_Ca1968104039914474786nt_nat (lambda ((R tptp.set_Pr958786334691620121nt_int) (As (-> tptp.int tptp.nat))) (forall ((I tptp.int) (J tptp.int)) (or (not (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int I) J)) R)) (@ (@ tptp.ord_less_eq_nat (@ As I)) (@ As J)))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_408 (EQ_RESOLVE (ASSUME :args (_let_372)) (MACRO_SR_EQ_INTRO :args (_let_372 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_409 (ASSUME :args (_let_371)))) (let ((_let_410 (ASSUME :args (_let_369)))) (let ((_let_411 (ASSUME :args (_let_368)))) (let ((_let_412 (ASSUME :args (_let_367)))) (let ((_let_413 (ASSUME :args (_let_359)))) (let ((_let_414 (ASSUME :args (_let_358)))) (let ((_let_415 (ASSUME :args (_let_357)))) (let ((_let_416 (ASSUME :args (_let_356)))) (let ((_let_417 (EQ_RESOLVE (ASSUME :args (_let_355)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396) :args (_let_355 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_418 (ASSUME :args (_let_354)))) (let ((_let_419 (ASSUME :args (_let_346)))) (let ((_let_420 (ASSUME :args (_let_345)))) (let ((_let_421 (ASSUME :args (_let_343)))) (let ((_let_422 (SYMM (ASSUME :args (_let_342))))) (let ((_let_423 (ASSUME :args (_let_340)))) (let ((_let_424 (AND_ELIM (EQ_RESOLVE (ASSUME :args (_let_339)) (MACRO_SR_EQ_INTRO :args (_let_339 SB_DEFAULT SBA_FIXPOINT))) :args (2)))) (let ((_let_425 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_338)) (MACRO_SR_EQ_INTRO :args (_let_338 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396) :args ((= tptp.vEBT_is_pred_in_set (lambda ((Xs tptp.set_nat) (X4 tptp.nat) (Y4 tptp.nat)) (and (@ (@ tptp.member_nat Y4) Xs) (@ (@ tptp.ord_less_nat Y4) X4) (forall ((Z4 tptp.nat)) (or (not (@ (@ tptp.member_nat Z4) Xs)) (not (@ (@ tptp.ord_less_nat Z4) X4)) (@ (@ tptp.ord_less_eq_nat Z4) Y4)))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_426 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_337)) (MACRO_SR_EQ_INTRO :args (_let_337 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396) :args ((= tptp.vEBT_is_succ_in_set (lambda ((Xs tptp.set_nat) (X4 tptp.nat) (Y4 tptp.nat)) (and (@ (@ tptp.member_nat Y4) Xs) (@ (@ tptp.ord_less_nat X4) Y4) (forall ((Z4 tptp.nat)) (or (not (@ (@ tptp.member_nat Z4) Xs)) (not (@ (@ tptp.ord_less_nat X4) Z4)) (@ (@ tptp.ord_less_eq_nat Y4) Z4)))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_427 (ASSUME :args (_let_336)))) (let ((_let_428 (SYMM (ASSUME :args (_let_335))))) (let ((_let_429 (SYMM (ASSUME :args (_let_334))))) (let ((_let_430 (SYMM (ASSUME :args (_let_333))))) (let ((_let_431 (SYMM (ASSUME :args (_let_332))))) (let ((_let_432 (SYMM (ASSUME :args (_let_331))))) (let ((_let_433 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_330)) (MACRO_SR_EQ_INTRO :args (_let_330 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396) :args ((= tptp.finite_finite_nat (lambda ((N5 tptp.set_nat)) (not (forall ((M6 tptp.nat)) (not (forall ((X4 tptp.nat)) (or (not (@ (@ tptp.member_nat X4) N5)) (@ (@ tptp.ord_less_nat X4) M6)))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_434 (EQ_RESOLVE (SYMM (ASSUME :args (_let_328))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396) :args ((= tptp.zero_zero_nat _let_327) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_435 (EQ_RESOLVE (ASSUME :args (_let_326)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396) :args (_let_326 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_436 (ASSUME :args (_let_325)))) (let ((_let_437 (ASSUME :args (_let_324)))) (let ((_let_438 (ASSUME :args (_let_323)))) (let ((_let_439 (ASSUME :args (_let_322)))) (let ((_let_440 (ASSUME :args (_let_321)))) (let ((_let_441 (ASSUME :args (_let_320)))) (let ((_let_442 (ASSUME :args (_let_319)))) (let ((_let_443 (ASSUME :args (_let_318)))) (let ((_let_444 (ASSUME :args (_let_317)))) (let ((_let_445 (ASSUME :args (_let_316)))) (let ((_let_446 (ASSUME :args (_let_315)))) (let ((_let_447 (ASSUME :args (_let_311)))) (let ((_let_448 (EQ_RESOLVE (SYMM (ASSUME :args (_let_310))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396) :args ((= tptp.one_one_Code_integer _let_309) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_449 (EQ_RESOLVE (SYMM (ASSUME :args (_let_308))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396) :args ((= tptp.one_one_complex _let_307) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_450 (EQ_RESOLVE (SYMM (ASSUME :args (_let_306))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396) :args ((= tptp.one_one_real _let_305) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_451 (EQ_RESOLVE (SYMM (ASSUME :args (_let_304))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396) :args ((= tptp.one_one_int _let_303) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_452 (SYMM (ASSUME :args (_let_298))))) (let ((_let_453 (ASSUME :args (_let_290)))) (let ((_let_454 (ASSUME :args (_let_285)))) (let ((_let_455 (EQ_RESOLVE (ASSUME :args (_let_284)) (MACRO_SR_EQ_INTRO :args (_let_284 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_456 (EQ_RESOLVE (ASSUME :args (_let_283)) (MACRO_SR_EQ_INTRO :args (_let_283 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_457 (EQ_RESOLVE (ASSUME :args (_let_282)) (MACRO_SR_EQ_INTRO :args (_let_282 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_458 (EQ_RESOLVE (ASSUME :args (_let_281)) (MACRO_SR_EQ_INTRO :args (_let_281 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_459 (EQ_RESOLVE (ASSUME :args (_let_280)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396) :args (_let_280 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_460 (ASSUME :args (_let_279)))) (let ((_let_461 (EQ_RESOLVE (ASSUME :args (_let_278)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396) :args (_let_278 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_462 (EQ_RESOLVE (ASSUME :args (_let_277)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396) :args (_let_277 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_463 (ASSUME :args (_let_276)))) (let ((_let_464 (EQ_RESOLVE (ASSUME :args (_let_275)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396) :args (_let_275 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_465 (EQ_RESOLVE (ASSUME :args (_let_274)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396) :args (_let_274 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_466 (EQ_RESOLVE (ASSUME :args (_let_273)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396) :args (_let_273 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_467 (EQ_RESOLVE (ASSUME :args (_let_272)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396) :args (_let_272 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_468 (ASSUME :args (_let_271)))) (let ((_let_469 (ASSUME :args (_let_270)))) (let ((_let_470 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_269)) (MACRO_SR_EQ_INTRO :args (_let_269 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396) :args ((= tptp.dvd_dvd_complex (lambda ((A5 tptp.complex) (B4 tptp.complex)) (=> (= tptp.zero_zero_complex A5) (= tptp.zero_zero_complex B4)))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_471 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_268)) (MACRO_SR_EQ_INTRO :args (_let_268 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396) :args ((= tptp.dvd_dvd_real (lambda ((A5 tptp.real) (B4 tptp.real)) (=> (= tptp.zero_zero_real A5) (= tptp.zero_zero_real B4)))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_472 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_267)) (MACRO_SR_EQ_INTRO :args (_let_267 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396) :args ((= tptp.dvd_dvd_rat (lambda ((A5 tptp.rat) (B4 tptp.rat)) (=> (= tptp.zero_zero_rat A5) (= tptp.zero_zero_rat B4)))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_473 (EQ_RESOLVE (ASSUME :args (_let_266)) (MACRO_SR_EQ_INTRO :args (_let_266 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_474 (EQ_RESOLVE (ASSUME :args (_let_265)) (MACRO_SR_EQ_INTRO :args (_let_265 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_475 (EQ_RESOLVE (ASSUME :args (_let_264)) (MACRO_SR_EQ_INTRO :args (_let_264 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_476 (ASSUME :args (_let_263)))) (let ((_let_477 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_261)) (MACRO_SR_EQ_INTRO :args (_let_261 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396) :args ((= tptp.comm_s8582702949713902594nteger (lambda ((A5 tptp.code_integer) (N4 tptp.nat)) (@ (@ (@ tptp.if_Code_integer (= tptp.zero_zero_nat N4)) tptp.one_one_Code_integer) (@ (@ (@ (@ tptp.set_fo1084959871951514735nteger (lambda ((O tptp.nat) (__flatten_var_0 tptp.code_integer)) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.plus_p5714425477246183910nteger A5) (@ tptp.semiri4939895301339042750nteger O))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat N4) tptp.one_one_nat)) tptp.one_one_Code_integer)))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_478 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_260)) (MACRO_SR_EQ_INTRO :args (_let_260 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396) :args ((= tptp.comm_s2602460028002588243omplex (lambda ((A5 tptp.complex) (N4 tptp.nat)) (@ (@ (@ tptp.if_complex (= tptp.zero_zero_nat N4)) tptp.one_one_complex) (@ (@ (@ (@ tptp.set_fo1517530859248394432omplex (lambda ((O tptp.nat) (__flatten_var_0 tptp.complex)) (@ (@ tptp.times_times_complex (@ (@ tptp.plus_plus_complex A5) (@ tptp.semiri8010041392384452111omplex O))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat N4) tptp.one_one_nat)) tptp.one_one_complex)))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_479 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_259)) (MACRO_SR_EQ_INTRO :args (_let_259 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396) :args ((= tptp.comm_s4028243227959126397er_rat (lambda ((A5 tptp.rat) (N4 tptp.nat)) (@ (@ (@ tptp.if_rat (= tptp.zero_zero_nat N4)) tptp.one_one_rat) (@ (@ (@ (@ tptp.set_fo1949268297981939178at_rat (lambda ((O tptp.nat) (__flatten_var_0 tptp.rat)) (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat A5) (@ tptp.semiri681578069525770553at_rat O))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat N4) tptp.one_one_nat)) tptp.one_one_rat)))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_480 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_258)) (MACRO_SR_EQ_INTRO :args (_let_258 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396) :args ((= tptp.comm_s7457072308508201937r_real (lambda ((A5 tptp.real) (N4 tptp.nat)) (@ (@ (@ tptp.if_real (= tptp.zero_zero_nat N4)) tptp.one_one_real) (@ (@ (@ (@ tptp.set_fo3111899725591712190t_real (lambda ((O tptp.nat) (__flatten_var_0 tptp.real)) (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real A5) (@ tptp.semiri5074537144036343181t_real O))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat N4) tptp.one_one_nat)) tptp.one_one_real)))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_481 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_257)) (MACRO_SR_EQ_INTRO :args (_let_257 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396) :args ((= tptp.comm_s4660882817536571857er_int (lambda ((A5 tptp.int) (N4 tptp.nat)) (@ (@ (@ tptp.if_int (= tptp.zero_zero_nat N4)) tptp.one_one_int) (@ (@ (@ (@ tptp.set_fo2581907887559384638at_int (lambda ((O tptp.nat) (__flatten_var_0 tptp.int)) (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int A5) (@ tptp.semiri1314217659103216013at_int O))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat N4) tptp.one_one_nat)) tptp.one_one_int)))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_482 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_256)) (MACRO_SR_EQ_INTRO :args (_let_256 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396) :args ((= tptp.comm_s4663373288045622133er_nat (lambda ((A5 tptp.nat) (N4 tptp.nat)) (@ (@ (@ tptp.if_nat (= tptp.zero_zero_nat N4)) tptp.one_one_nat) (@ (@ (@ (@ tptp.set_fo2584398358068434914at_nat (lambda ((O tptp.nat) (__flatten_var_0 tptp.nat)) (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat A5) (@ tptp.semiri1316708129612266289at_nat O))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat N4) tptp.one_one_nat)) tptp.one_one_nat)))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_483 (EQ_RESOLVE (ASSUME :args (_let_255)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396) :args (_let_255 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_484 (EQ_RESOLVE (ASSUME :args (_let_254)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396) :args (_let_254 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_485 (EQ_RESOLVE (ASSUME :args (_let_253)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396) :args (_let_253 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_486 (EQ_RESOLVE (ASSUME :args (_let_252)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396) :args (_let_252 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_487 (EQ_RESOLVE (ASSUME :args (_let_251)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396) :args (_let_251 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_488 (EQ_RESOLVE (ASSUME :args (_let_250)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396) :args (_let_250 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_489 (EQ_RESOLVE (ASSUME :args (_let_249)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396) :args (_let_249 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_490 (EQ_RESOLVE (ASSUME :args (_let_248)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396) :args (_let_248 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_491 (ASSUME :args (_let_247)))) (let ((_let_492 (ASSUME :args (_let_246)))) (let ((_let_493 (ASSUME :args (_let_245)))) (let ((_let_494 (ASSUME :args (_let_244)))) (let ((_let_495 (EQ_RESOLVE (ASSUME :args (_let_243)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396) :args (_let_243 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_496 (EQ_RESOLVE (ASSUME :args (_let_242)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396) :args (_let_242 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_497 (ASSUME :args (_let_241)))) (let ((_let_498 (EQ_RESOLVE (ASSUME :args (_let_240)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396) :args (_let_240 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_499 (EQ_RESOLVE (ASSUME :args (_let_239)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396) :args (_let_239 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_500 (EQ_RESOLVE (ASSUME :args (_let_238)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396) :args (_let_238 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_501 (EQ_RESOLVE (ASSUME :args (_let_237)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396) :args (_let_237 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_502 (EQ_RESOLVE (ASSUME :args (_let_236)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396) :args (_let_236 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_503 (EQ_RESOLVE (ASSUME :args (_let_235)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396) :args (_let_235 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_504 (EQ_RESOLVE (ASSUME :args (_let_234)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396) :args (_let_234 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_505 (EQ_RESOLVE (ASSUME :args (_let_233)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396) :args (_let_233 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_506 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_232)) (MACRO_SR_EQ_INTRO :args (_let_232 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396) :args ((= tptp.distinct_VEBT_VEBT (lambda ((Xs tptp.list_VEBT_VEBT)) (forall ((I tptp.nat) (BOUND_VARIABLE_216252 tptp.nat)) (let ((_let_1 (@ tptp.nth_VEBT_VEBT Xs))) (let ((_let_2 (@ tptp.size_s6755466524823107622T_VEBT Xs))) (or (not (@ (@ tptp.ord_less_nat I) _let_2)) (not (@ (@ tptp.ord_less_nat BOUND_VARIABLE_216252) _let_2)) (= I BOUND_VARIABLE_216252) (not (= (@ _let_1 I) (@ _let_1 BOUND_VARIABLE_216252))))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_507 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_231)) (MACRO_SR_EQ_INTRO :args (_let_231 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396) :args ((= tptp.distinct_o (lambda ((Xs tptp.list_o)) (forall ((I tptp.nat) (BOUND_VARIABLE_216284 tptp.nat)) (let ((_let_1 (@ tptp.nth_o Xs))) (let ((_let_2 (@ tptp.size_size_list_o Xs))) (or (not (@ (@ tptp.ord_less_nat I) _let_2)) (not (@ (@ tptp.ord_less_nat BOUND_VARIABLE_216284) _let_2)) (= I BOUND_VARIABLE_216284) (= (not (@ _let_1 I)) (@ _let_1 BOUND_VARIABLE_216284)))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_508 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_230)) (MACRO_SR_EQ_INTRO :args (_let_230 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396) :args ((= tptp.distinct_nat (lambda ((Xs tptp.list_nat)) (forall ((I tptp.nat) (BOUND_VARIABLE_216312 tptp.nat)) (let ((_let_1 (@ tptp.nth_nat Xs))) (let ((_let_2 (@ tptp.size_size_list_nat Xs))) (or (not (@ (@ tptp.ord_less_nat I) _let_2)) (not (@ (@ tptp.ord_less_nat BOUND_VARIABLE_216312) _let_2)) (= I BOUND_VARIABLE_216312) (not (= (@ _let_1 I) (@ _let_1 BOUND_VARIABLE_216312))))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_509 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_229)) (MACRO_SR_EQ_INTRO :args (_let_229 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396) :args ((= tptp.distinct_int (lambda ((Xs tptp.list_int)) (forall ((I tptp.nat) (BOUND_VARIABLE_216339 tptp.nat)) (let ((_let_1 (@ tptp.nth_int Xs))) (let ((_let_2 (@ tptp.size_size_list_int Xs))) (or (not (@ (@ tptp.ord_less_nat I) _let_2)) (not (@ (@ tptp.ord_less_nat BOUND_VARIABLE_216339) _let_2)) (= I BOUND_VARIABLE_216339) (not (= (@ _let_1 I) (@ _let_1 BOUND_VARIABLE_216339))))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_510 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_228)) (MACRO_SR_EQ_INTRO :args (_let_228 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396) :args ((= tptp.gbinomial_complex (lambda ((A5 tptp.complex) (K3 tptp.nat)) (@ (@ (@ tptp.if_complex (= tptp.zero_zero_nat K3)) tptp.one_one_complex) (@ (@ tptp.divide1717551699836669952omplex (@ (@ (@ (@ tptp.set_fo1517530859248394432omplex (lambda ((L2 tptp.nat) (__flatten_var_0 tptp.complex)) (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex A5) (@ tptp.semiri8010041392384452111omplex L2))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat K3) tptp.one_one_nat)) tptp.one_one_complex)) (@ tptp.semiri5044797733671781792omplex K3))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_511 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_227)) (MACRO_SR_EQ_INTRO :args (_let_227 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396) :args ((= tptp.gbinomial_rat (lambda ((A5 tptp.rat) (K3 tptp.nat)) (@ (@ (@ tptp.if_rat (= tptp.zero_zero_nat K3)) tptp.one_one_rat) (@ (@ tptp.divide_divide_rat (@ (@ (@ (@ tptp.set_fo1949268297981939178at_rat (lambda ((L2 tptp.nat) (__flatten_var_0 tptp.rat)) (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat A5) (@ tptp.semiri681578069525770553at_rat L2))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat K3) tptp.one_one_nat)) tptp.one_one_rat)) (@ tptp.semiri773545260158071498ct_rat K3))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_512 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_226)) (MACRO_SR_EQ_INTRO :args (_let_226 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396) :args ((= tptp.gbinomial_real (lambda ((A5 tptp.real) (K3 tptp.nat)) (@ (@ (@ tptp.if_real (= tptp.zero_zero_nat K3)) tptp.one_one_real) (@ (@ tptp.divide_divide_real (@ (@ (@ (@ tptp.set_fo3111899725591712190t_real (lambda ((L2 tptp.nat) (__flatten_var_0 tptp.real)) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real A5) (@ tptp.semiri5074537144036343181t_real L2))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat K3) tptp.one_one_nat)) tptp.one_one_real)) (@ tptp.semiri2265585572941072030t_real K3))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_513 (ASSUME :args (_let_190)))) (let ((_let_514 (ASSUME :args (_let_189)))) (let ((_let_515 (ASSUME :args (_let_188)))) (let ((_let_516 (ASSUME :args (_let_187)))) (let ((_let_517 (ASSUME :args (_let_186)))) (let ((_let_518 (EQ_RESOLVE (ASSUME :args (_let_165)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396) :args (_let_165 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_519 (EQ_RESOLVE (ASSUME :args (_let_164)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396) :args (_let_164 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_520 (EQ_RESOLVE (ASSUME :args (_let_163)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396) :args (_let_163 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_521 (EQ_RESOLVE (ASSUME :args (_let_162)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396) :args (_let_162 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_522 (EQ_RESOLVE (ASSUME :args (_let_161)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396) :args (_let_161 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_523 (ASSUME :args (_let_144)))) (let ((_let_524 (EQ_RESOLVE (ASSUME :args (_let_143)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396) :args (_let_143 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_525 (EQ_RESOLVE (ASSUME :args (_let_142)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396) :args (_let_142 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_526 (EQ_RESOLVE (ASSUME :args (_let_141)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396) :args (_let_141 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_527 (EQ_RESOLVE (ASSUME :args (_let_140)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396) :args (_let_140 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_528 (ASSUME :args (_let_139)))) (let ((_let_529 (ASSUME :args (_let_138)))) (let ((_let_530 (EQ_RESOLVE (ASSUME :args (_let_137)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396) :args (_let_137 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_531 (EQ_RESOLVE (ASSUME :args (_let_128)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396) :args (_let_128 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_532 (SYMM (ASSUME :args (_let_127))))) (let ((_let_533 (EQ_RESOLVE (ASSUME :args (_let_126)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396) :args (_let_126 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_534 (EQ_RESOLVE (ASSUME :args (_let_125)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396) :args (_let_125 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_535 (EQ_RESOLVE (ASSUME :args (_let_124)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396) :args (_let_124 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_536 (ASSUME :args (_let_123)))) (let ((_let_537 (EQ_RESOLVE (ASSUME :args (_let_122)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396) :args (_let_122 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_538 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_121)) (MACRO_SR_EQ_INTRO :args (_let_121 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396) :args ((= tptp.adjust_div (@ tptp.produc8211389475949308722nt_int (lambda ((Q5 tptp.int) (R tptp.int)) (@ (@ tptp.plus_plus_int Q5) (@ tptp.zero_n2684676970156552555ol_int (not (= tptp.zero_zero_int R))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_539 (EQ_RESOLVE (ASSUME :args (_let_120)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396) :args (_let_120 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_540 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_119)) (MACRO_SR_EQ_INTRO :args (_let_119 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396) :args ((= tptp.eucl_rel_int (lambda ((A13 tptp.int) (A24 tptp.int) (A32 tptp.product_prod_int_int)) (let ((_let_1 (= tptp.zero_zero_int A24))) (or (not (or (not _let_1) (not (= A32 (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) A13))))) (not (or _let_1 (forall ((Q5 tptp.int)) (or (not (= A32 (@ (@ tptp.product_Pair_int_int Q5) tptp.zero_zero_int))) (not (= A13 (@ (@ tptp.times_times_int Q5) A24))))))) (not (forall ((R tptp.int) (Q5 tptp.int)) (or (not (= A32 (@ (@ tptp.product_Pair_int_int Q5) R))) (not (= (@ tptp.sgn_sgn_int R) (@ tptp.sgn_sgn_int A24))) (not (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int R)) (@ tptp.abs_abs_int A24))) (not (= A13 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int Q5) A24)) R)))))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_541 (EQ_RESOLVE (ASSUME :args (_let_118)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396) :args (_let_118 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_542 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_117)) (MACRO_SR_EQ_INTRO :args (_let_117 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396) :args ((= tptp.modulo_modulo_int (lambda ((K3 tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.abs_abs_int L2))) (let ((_let_2 (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.modulo_modulo_nat (@ tptp.nat2 (@ tptp.abs_abs_int K3))) (@ tptp.nat2 _let_1))))) (let ((_let_3 (@ tptp.sgn_sgn_int L2))) (let ((_let_4 (@ tptp.times_times_int _let_3))) (@ (@ (@ tptp.if_int (= tptp.zero_zero_int L2)) K3) (@ (@ (@ tptp.if_int (= _let_3 (@ tptp.sgn_sgn_int K3))) (@ _let_4 _let_2)) (@ _let_4 (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int _let_1) (@ tptp.zero_n2684676970156552555ol_int (not (@ (@ tptp.dvd_dvd_int L2) K3))))) _let_2)))))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_543 (ASSUME :args (_let_116)))) (let ((_let_544 (EQ_RESOLVE (ASSUME :args (_let_113)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396) :args (_let_113 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_545 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_111)) (MACRO_SR_EQ_INTRO :args (_let_111 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396) :args ((= tptp.pi (@ _let_110 (@ tptp.the_real (lambda ((X4 tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4) (@ (@ tptp.ord_less_eq_real X4) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (= tptp.zero_zero_real (@ tptp.cos_real X4))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_546 (EQ_RESOLVE (ASSUME :args (_let_108)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396) :args (_let_108 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_547 (EQ_RESOLVE (ASSUME :args (_let_107)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396) :args (_let_107 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_548 (ASSUME :args (_let_101)))) (let ((_let_549 (ASSUME :args (_let_100)))) (let ((_let_550 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_99)) (MACRO_SR_EQ_INTRO :args (_let_99 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396) :args ((= tptp.topolo4055970368930404560y_real (lambda ((X7 (-> tptp.nat tptp.real))) (forall ((J tptp.nat)) (not (forall ((M9 tptp.nat)) (not (forall ((M6 tptp.nat) (BOUND_VARIABLE_225152 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat M9))) (or (not (@ _let_1 M6)) (not (@ _let_1 BOUND_VARIABLE_225152)) (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ X7 M6)) (@ X7 BOUND_VARIABLE_225152)))) (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc J))))))))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_551 (EQ_RESOLVE (ASSUME :args (_let_98)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396) :args (_let_98 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_552 (EQ_RESOLVE (SYMM (ASSUME :args (_let_96))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396) :args ((= tptp.nil_nat _let_95) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_553 (ASSUME :args (_let_97)))) (let ((_let_554 (EQ_RESOLVE (ASSUME :args (_let_94)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396) :args (_let_94 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_555 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_93)) (MACRO_SR_EQ_INTRO :args (_let_93 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396) :args ((= tptp.csqrt (lambda ((Z4 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.re Z4))) (let ((_let_3 (@ tptp.real_V1022390504157884413omplex Z4))) (let ((_let_4 (@ tptp.im Z4))) (@ (@ tptp.complex2 (@ tptp.sqrt (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real _let_3) _let_2)) _let_1))) (@ (@ tptp.times_times_real (@ (@ (@ tptp.if_real (= tptp.zero_zero_real _let_4)) tptp.one_one_real) (@ tptp.sgn_sgn_real _let_4))) (@ tptp.sqrt (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real _let_3) _let_2)) _let_1)))))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_556 (EQ_RESOLVE (ASSUME :args (_let_92)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396) :args (_let_92 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_557 (ASSUME :args (_let_91)))) (let ((_let_558 (EQ_RESOLVE (ASSUME :args (_let_90)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396) :args (_let_90 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_559 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_89)) (MACRO_SR_EQ_INTRO :args (_let_89 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396) :args ((= tptp.adjust_mod (lambda ((L2 tptp.int) (R tptp.int)) (@ (@ (@ tptp.if_int (= tptp.zero_zero_int R)) tptp.zero_zero_int) (@ (@ tptp.minus_minus_int L2) R)))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_560 (EQ_RESOLVE (SYMM (ASSUME :args (_let_88))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396) :args ((= tptp.one _let_87) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_561 (EQ_RESOLVE (ASSUME :args (_let_86)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396) :args (_let_86 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_562 (ASSUME :args (_let_85)))) (let ((_let_563 (ASSUME :args (_let_84)))) (let ((_let_564 (ASSUME :args (_let_83)))) (let ((_let_565 (ASSUME :args (_let_80)))) (let ((_let_566 (ASSUME :args (_let_79)))) (let ((_let_567 (ASSUME :args (_let_78)))) (let ((_let_568 (EQ_RESOLVE (SYMM (ASSUME :args (_let_76))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396) :args ((= tptp.top_to4669805908274784177at_nat _let_75) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_569 (SYMM (ASSUME :args (_let_74))))) (let ((_let_570 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_73)) (MACRO_SR_EQ_INTRO :args (_let_73 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396) :args ((= tptp.root (lambda ((N4 tptp.nat) (X4 tptp.real)) (@ (@ (@ tptp.if_real (= tptp.zero_zero_nat N4)) tptp.zero_zero_real) (@ (@ (@ tptp.the_in5290026491893676941l_real tptp.top_top_set_real) (lambda ((Y4 tptp.real)) (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real Y4)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real Y4)) N4)))) X4)))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_571 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_72)) (MACRO_SR_EQ_INTRO :args (_let_72 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396) :args ((= tptp.real_V5970128139526366754l_real (lambda ((F4 (-> tptp.real tptp.real))) (not (forall ((C3 tptp.real)) (not (= F4 (lambda ((X4 tptp.real)) (@ (@ tptp.times_times_real X4) C3)))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_572 (EQ_RESOLVE (SYMM (ASSUME :args (_let_71))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396) :args ((= tptp.top_top_set_nat _let_70) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_573 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_68)) (MACRO_SR_EQ_INTRO :args (_let_68 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396) :args ((= tptp.complete_Sup_Sup_nat (lambda ((X7 tptp.set_nat)) (@ (@ (@ tptp.if_nat (= tptp.bot_bot_set_nat X7)) tptp.zero_zero_nat) (@ tptp.lattic8265883725875713057ax_nat X7)))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_574 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_67)) (MACRO_SR_EQ_INTRO :args (_let_67 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396) :args ((= tptp.divide_divide_nat (lambda ((M6 tptp.nat) (N4 tptp.nat)) (@ (@ (@ tptp.if_nat (= tptp.zero_zero_nat N4)) tptp.zero_zero_nat) (@ tptp.lattic8265883725875713057ax_nat (@ tptp.collect_nat (lambda ((K3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat K3) N4)) M6))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_575 (ASSUME :args (_let_66)))) (let ((_let_576 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_65)) (MACRO_SR_EQ_INTRO :args (_let_65 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396) :args ((= tptp.bit_take_bit_num (lambda ((N4 tptp.nat) (M6 tptp.num)) (let ((_let_1 (@ (@ tptp.bit_se2925701944663578781it_nat N4) (@ tptp.numeral_numeral_nat M6)))) (@ (@ (@ tptp.if_option_num (= tptp.zero_zero_nat _let_1)) tptp.none_num) (@ tptp.some_num (@ tptp.num_of_nat _let_1)))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_577 (ASSUME :args (_let_64)))) (let ((_let_578 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_63)) (MACRO_SR_EQ_INTRO :args (_let_63 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396) :args ((= tptp.field_5140801741446780682s_real (@ tptp.collect_real (lambda ((Uu3 tptp.real)) (not (forall ((I tptp.int) (N4 tptp.nat)) (or (not (= Uu3 (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real I)) (@ tptp.semiri5074537144036343181t_real N4)))) (= tptp.zero_zero_nat N4))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_579 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_61)) (MACRO_SR_EQ_INTRO :args (_let_61 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396) :args ((= tptp.code_divmod_integer (lambda ((K3 tptp.code_integer) (L2 tptp.code_integer)) (let ((_let_1 (@ (@ tptp.code_divmod_abs K3) L2))) (let ((_let_2 (@ tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger))) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (= tptp.zero_z3403309356797280102nteger K3)) (@ _let_2 tptp.zero_z3403309356797280102nteger)) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (= tptp.zero_z3403309356797280102nteger L2)) (@ _let_2 K3)) (@ (@ (@ (@ tptp.comp_C1593894019821074884nteger (@ (@ tptp.comp_C8797469213163452608nteger tptp.produc6499014454317279255nteger) tptp.times_3573771949741848930nteger)) tptp.sgn_sgn_Code_integer) L2) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (= (@ tptp.sgn_sgn_Code_integer K3) (@ tptp.sgn_sgn_Code_integer L2))) _let_1) (@ (@ tptp.produc6916734918728496179nteger (lambda ((R tptp.code_integer) (S6 tptp.code_integer)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger R))) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (= tptp.zero_z3403309356797280102nteger S6)) (@ (@ 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 L2)) S6)))))) _let_1))))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_580 (EQ_RESOLVE (ASSUME :args (_let_60)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396) :args (_let_60 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_581 (ASSUME :args (_let_59)))) (let ((_let_582 (EQ_RESOLVE (SYMM (ASSUME :args (_let_58))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396) :args ((= tptp.id_nat tptp.semiri1316708129612266289at_nat) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_583 (EQ_RESOLVE (ASSUME :args (_let_57)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396) :args (_let_57 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_584 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_56)) (MACRO_SR_EQ_INTRO :args (_let_56 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396) :args ((= tptp.ratrel (lambda ((X4 tptp.product_prod_int_int) (Y4 tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.product_snd_int_int X4))) (let ((_let_2 (@ tptp.product_snd_int_int Y4))) (and (not (= tptp.zero_zero_int _let_1)) (not (= tptp.zero_zero_int _let_2)) (= (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int X4)) _let_2) (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int Y4)) _let_1))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_585 (EQ_RESOLVE (ASSUME :args (_let_55)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396) :args (_let_55 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_586 (EQ_RESOLVE (ASSUME :args (_let_46)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396) :args (_let_46 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_587 (EQ_RESOLVE (ASSUME :args (_let_45)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396) :args (_let_45 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_588 (EQ_RESOLVE (ASSUME :args (_let_41)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396) :args (_let_41 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_589 (ASSUME :args (_let_40)))) (let ((_let_590 (EQ_RESOLVE (ASSUME :args (_let_38)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396) :args (_let_38 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_591 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_37)) (MACRO_SR_EQ_INTRO :args (_let_37 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396) :args ((= tptp.times_7803423173614009249d_enat (lambda ((M6 tptp.extended_enat) (N4 tptp.extended_enat)) (@ (@ (@ tptp.extend3600170679010898289d_enat (lambda ((O tptp.nat)) (@ (@ (@ tptp.extend3600170679010898289d_enat (lambda ((P5 tptp.nat)) (@ tptp.extended_enat2 (@ (@ tptp.times_times_nat O) P5)))) (@ (@ (@ tptp.if_Extended_enat (= tptp.zero_zero_nat O)) tptp.zero_z5237406670263579293d_enat) tptp.extend5688581933313929465d_enat)) N4))) (@ (@ (@ tptp.if_Extended_enat (= tptp.zero_z5237406670263579293d_enat N4)) tptp.zero_z5237406670263579293d_enat) tptp.extend5688581933313929465d_enat)) M6))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_592 (ASSUME :args (_let_36)))) (let ((_let_593 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_35)) (MACRO_SR_EQ_INTRO :args (_let_35 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396) :args ((= tptp.binomial (lambda ((N4 tptp.nat) (K3 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) N4))) (= K3 (@ tptp.finite_card_nat K7)))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_594 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_34)) (MACRO_SR_EQ_INTRO :args (_let_34 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396) :args ((= tptp.positive2 (lambda ((X4 tptp.real)) (not (forall ((R tptp.rat) (BOUND_VARIABLE_229942 tptp.nat)) (or (not (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) R)) (not (forall ((N4 tptp.nat)) (or (not (@ (@ tptp.ord_less_eq_nat BOUND_VARIABLE_229942) N4)) (@ (@ tptp.ord_less_rat R) (@ (@ tptp.rep_real X4) N4)))))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_595 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_33)) (MACRO_SR_EQ_INTRO :args (_let_33 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396) :args ((= tptp.cauchy (lambda ((X7 (-> tptp.nat tptp.rat))) (forall ((R tptp.rat)) (or (not (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) R)) (not (forall ((K3 tptp.nat)) (not (forall ((M6 tptp.nat) (BOUND_VARIABLE_230163 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat K3))) (or (not (@ _let_1 M6)) (not (@ _let_1 BOUND_VARIABLE_230163)) (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ X7 M6)) (@ X7 BOUND_VARIABLE_230163)))) R))))))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_596 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_32)) (MACRO_SR_EQ_INTRO :args (_let_32 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396) :args ((= tptp.vanishes (lambda ((X7 (-> tptp.nat tptp.rat))) (forall ((R tptp.rat)) (or (not (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) R)) (not (forall ((K3 tptp.nat)) (not (forall ((N4 tptp.nat)) (or (not (@ (@ tptp.ord_less_eq_nat K3) N4)) (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat (@ X7 N4))) R)))))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_597 (EQ_RESOLVE (SYMM (ASSUME :args (_let_31))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396) :args ((= tptp.top_top_set_int _let_30) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_598 (EQ_RESOLVE (ASSUME :args (_let_29)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396) :args (_let_29 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_599 (EQ_RESOLVE (ASSUME :args (_let_28)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396) :args (_let_28 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_600 (EQ_RESOLVE (ASSUME :args (_let_27)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396) :args (_let_27 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_601 (EQ_RESOLVE (SYMM (ASSUME :args (_let_26))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396) :args ((= tptp.top_to6661820994512907621at_nat _let_25) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_602 (EQ_RESOLVE (ASSUME :args (_let_24)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396) :args (_let_24 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_603 (EQ_RESOLVE (ASSUME :args (_let_23)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396) :args (_let_23 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_604 (ASSUME :args (_let_20)))) (let ((_let_605 (EQ_RESOLVE (ASSUME :args (_let_19)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396) :args (_let_19 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_606 (EQ_RESOLVE (ASSUME :args (_let_18)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396) :args (_let_18 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_607 (EQ_RESOLVE (ASSUME :args (_let_17)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396) :args (_let_17 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_608 (EQ_RESOLVE (ASSUME :args (_let_16)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396) :args (_let_16 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_609 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_15)) (MACRO_SR_EQ_INTRO :args (_let_15 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396) :args ((= tptp.unit_f2748546683901255202or_nat (lambda ((N4 tptp.nat)) (@ (@ (@ tptp.if_nat (= tptp.zero_zero_nat N4)) tptp.zero_zero_nat) tptp.one_one_nat))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_610 (EQ_RESOLVE (ASSUME :args (_let_14)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396) :args (_let_14 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_611 (EQ_RESOLVE (ASSUME :args (_let_13)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396) :args (_let_13 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_612 (EQ_RESOLVE (ASSUME :args (_let_12)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396) :args (_let_12 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_613 (EQ_RESOLVE (ASSUME :args (_let_9)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396) :args (_let_9 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_614 (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396) :args (_let_8 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_615 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396) :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_616 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396) :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_617 (ASSUME :args (_let_5)))) (let ((_let_618 (AND_INTRO (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396) :args (_let_4 SB_DEFAULT SBA_FIXPOINT))) _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396))) (let ((_let_619 (EQ_RESOLVE (ASSUME :args (_let_341)) (TRANS (MACRO_SR_EQ_INTRO _let_618 :args (_let_341 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (= tptp.suc _let_395) _let_388))))))) (let ((_let_620 (@ tptp.some_nat _let_394))) (let ((_let_621 (@ tptp.suc (@ tptp.pred_numeral (@ tptp.bit0 (@ tptp.num_of_nat _let_327)))))) (let ((_let_622 (EQ_RESOLVE (ASSUME :args (_let_312)) (TRANS (MACRO_SR_EQ_INTRO _let_618 :args (_let_312 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (@ (@ tptp.vEBT_VEBT_lesseq (@ tptp.some_nat _let_621)) _let_620) _let_391))))))) (let ((_let_623 (EQ_RESOLVE (ASSUME :args (_let_295)) (TRANS (MACRO_SR_EQ_INTRO _let_618 :args (_let_295 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (= (@ _let_395 _let_394) _let_621) _let_392))))))) (let ((_let_624 (ho_3721 k_3720 _let_385))) (let ((_let_625 (ho_3737 (ho_3736 k_3735 _let_389) _let_624))) (let ((_let_626 (= _let_625 _let_393))) (let ((_let_627 (not _let_393))) (let ((_let_628 (forall ((N tptp.nat) (M2 tptp.nat)) (= (ho_3737 (ho_3736 k_3735 (ho_3721 k_3720 (ho_3734 k_3733 N))) (ho_3721 k_3720 (ho_3734 k_3733 M2))) (ho_3737 (ho_3736 k_3735 (ho_3721 k_3720 N)) (ho_3721 k_3720 M2)))))) (let ((_let_629 (EQ_RESOLVE (ASSUME :args (_let_370)) (TRANS (MACRO_SR_EQ_INTRO (AND_INTRO _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396) :args (_let_370 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((N tptp.nat) (M2 tptp.nat)) (= (@ (@ tptp.vEBT_VEBT_lesseq (@ tptp.some_nat N)) (@ tptp.some_nat M2)) (@ (@ tptp.vEBT_VEBT_lesseq (@ tptp.some_nat (@ tptp.suc N))) (@ tptp.some_nat (@ tptp.suc M2))))) _let_628))))))) (let ((_let_630 (= _let_385 _let_386))) (let ((_let_631 (not _let_625))) (let ((_let_632 (not _let_630))) (let ((_let_633 (not (= _let_327 _let_394)))) (let ((_let_634 (@ tptp.some_nat _let_327))) (let ((_let_635 (or))) (let ((_let_636 (ASSUME :args (_let_627)))) (let ((_let_637 (APPLY_UF ho_3721))) (let ((_let_638 (REFL :args (k_3720)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_636 _let_619 _let_623 _let_622) :args (_let_388 _let_391 _let_392 _let_627)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (TRUE_INTRO _let_622)) (CONG (CONG (REFL :args (k_3735)) (TRANS (CONG _let_638 (SYMM (SYMM _let_623)) :args _let_637) (CONG _let_638 (CONG (SYMM _let_619) (REFL :args (_let_386)) :args (APPLY_UF ho_3734)) :args _let_637)) :args (APPLY_UF ho_3736)) (REFL :args (_let_389)) :args (APPLY_UF ho_3737)) (FALSE_INTRO _let_636))) :args (_let_627 _let_388 _let_392 _let_391)) :args ((not (and _let_388 _let_391 _let_392 _let_627)) SB_LITERAL))) (CONG (REFL :args ((not _let_388))) (REFL :args ((not _let_391))) (REFL :args ((not _let_392))) (MACRO_SR_PRED_INTRO :args ((= (not _let_627) _let_393))) :args _let_635)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_626)) :args ((or _let_625 _let_627 (not _let_626)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (NOT_AND (EQ_RESOLVE (ASSUME :args (_let_366)) (TRANS (MACRO_SR_EQ_INTRO _let_618 :args (_let_366 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (not (and (@ (@ tptp.vEBT_VEBT_lesseq _let_620) _let_634) _let_633)) (not (and _let_625 _let_632)))))))) (CONG (REFL :args (_let_631)) (MACRO_SR_PRED_INTRO :args ((= (not _let_632) _let_630))) :args _let_635)) :args ((or _let_630 _let_631))) (AND_ELIM (EQ_RESOLVE (ASSUME :args (_let_361)) (TRANS (MACRO_SR_EQ_INTRO _let_618 :args (_let_361 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (and (@ (@ tptp.vEBT_VEBT_lesseq _let_634) _let_620) _let_633) (and (ho_3737 (ho_3736 k_3735 _let_624) _let_389) _let_632)))))) :args (1)) :args (_let_631 true _let_630)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_629 :args (_let_386 _let_385 QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_628)))) _let_629 :args (_let_626 false _let_628)) :args (_let_627 true _let_625 false _let_626)) _let_623 _let_622 _let_619 :args (false true _let_393 false _let_392 false _let_391 false _let_388)) :args ((@ (@ tptp.ord_less_eq_nat tptp.mi) tptp.ma) (forall ((X2 tptp.product_prod_nat_nat) (Y2 tptp.product_prod_nat_nat)) (= (= (@ 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tptp.nat) (N tptp.nat)) (= (not (@ (@ tptp.ord_less_eq_nat M2) N)) (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) M2))) (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) N))) (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.ord_less_eq_nat M2))) (= (@ _let_2 _let_1) (or (@ _let_2 N) (= M2 _let_1)))))) (forall ((N tptp.nat) (M4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) M4) (exists ((M tptp.nat)) (= M4 (@ tptp.suc M))))) (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat M2))) (=> (@ _let_1 N) (@ _let_1 (@ tptp.suc N))))) (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.ord_less_eq_nat M2))) (=> (@ _let_2 _let_1) (=> (not (@ _let_2 N)) (= M2 _let_1)))))) (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M2)) N) (@ (@ tptp.ord_less_eq_nat M2) N))) (forall ((Y tptp.set_nat) (X tptp.set_nat)) (=> (@ (@ 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(F2 (-> tptp.rat tptp.int)) (C2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (= (@ F2 B) C2) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y3) (@ (@ tptp.ord_less_eq_int (@ F2 X3)) (@ F2 Y3)))) (@ (@ tptp.ord_less_eq_int (@ F2 A)) C2))))) (forall ((A tptp.num) (B tptp.num) (F2 (-> tptp.num tptp.rat)) (C2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (= (@ F2 B) C2) (=> (forall ((X3 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y3) (@ (@ tptp.ord_less_eq_rat (@ F2 X3)) (@ F2 Y3)))) (@ (@ tptp.ord_less_eq_rat (@ F2 A)) C2))))) (forall ((A tptp.num) (B tptp.num) (F2 (-> tptp.num tptp.num)) (C2 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (= (@ F2 B) C2) (=> (forall ((X3 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y3) (@ (@ tptp.ord_less_eq_num (@ F2 X3)) (@ F2 Y3)))) (@ (@ tptp.ord_less_eq_num (@ F2 A)) C2))))) (forall ((A tptp.num) (B tptp.num) (F2 (-> tptp.num tptp.nat)) (C2 tptp.nat)) (=> (@ (@ 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tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) Y3) (@ (@ tptp.ord_less_eq_num (@ F2 X3)) (@ F2 Y3)))) (@ (@ tptp.ord_less_eq_num (@ F2 A)) C2))))) (forall ((A tptp.rat) (F2 (-> tptp.rat tptp.rat)) (B tptp.rat) (C2 tptp.rat)) (=> (= A (@ F2 B)) (=> (@ (@ tptp.ord_less_eq_rat B) C2) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y3) (@ (@ tptp.ord_less_eq_rat (@ F2 X3)) (@ F2 Y3)))) (@ (@ tptp.ord_less_eq_rat A) (@ F2 C2)))))) (forall ((A tptp.num) (F2 (-> tptp.rat tptp.num)) (B tptp.rat) (C2 tptp.rat)) (=> (= A (@ F2 B)) (=> (@ (@ tptp.ord_less_eq_rat B) C2) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y3) (@ (@ tptp.ord_less_eq_num (@ F2 X3)) (@ F2 Y3)))) (@ (@ tptp.ord_less_eq_num A) (@ F2 C2)))))) (forall ((A tptp.nat) (F2 (-> tptp.rat tptp.nat)) (B tptp.rat) (C2 tptp.rat)) (=> (= A (@ F2 B)) (=> (@ (@ tptp.ord_less_eq_rat B) C2) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y3) (@ (@ tptp.ord_less_eq_nat (@ F2 X3)) (@ F2 Y3)))) (@ (@ tptp.ord_less_eq_nat A) (@ F2 C2)))))) (forall ((A tptp.int) (F2 (-> tptp.rat tptp.int)) (B tptp.rat) (C2 tptp.rat)) (=> (= A (@ F2 B)) (=> (@ (@ tptp.ord_less_eq_rat B) C2) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y3) (@ (@ tptp.ord_less_eq_int (@ F2 X3)) (@ F2 Y3)))) (@ (@ tptp.ord_less_eq_int A) (@ F2 C2)))))) (forall ((A tptp.rat) (F2 (-> tptp.num tptp.rat)) (B tptp.num) (C2 tptp.num)) (=> (= A (@ F2 B)) (=> (@ (@ tptp.ord_less_eq_num B) C2) (=> (forall ((X3 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y3) (@ (@ tptp.ord_less_eq_rat (@ F2 X3)) (@ F2 Y3)))) (@ (@ tptp.ord_less_eq_rat A) (@ F2 C2)))))) (forall ((A tptp.num) (F2 (-> tptp.num tptp.num)) (B tptp.num) (C2 tptp.num)) (=> (= A (@ F2 B)) (=> (@ (@ tptp.ord_less_eq_num B) C2) (=> (forall ((X3 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y3) (@ (@ tptp.ord_less_eq_num (@ F2 X3)) (@ F2 Y3)))) (@ (@ 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(-> tptp.nat tptp.num)) (B tptp.nat) (C2 tptp.nat)) (=> (= A (@ F2 B)) (=> (@ (@ tptp.ord_less_eq_nat B) C2) (=> (forall ((X3 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) Y3) (@ (@ tptp.ord_less_eq_num (@ F2 X3)) (@ F2 Y3)))) (@ (@ tptp.ord_less_eq_num A) (@ F2 C2)))))) (forall ((X tptp.rat) (Y tptp.rat)) (or (@ (@ tptp.ord_less_eq_rat X) Y) (@ (@ tptp.ord_less_eq_rat Y) X))) (forall ((X tptp.num) (Y tptp.num)) (or (@ (@ tptp.ord_less_eq_num X) Y) (@ (@ tptp.ord_less_eq_num Y) X))) (forall ((X tptp.nat) (Y tptp.nat)) (or (@ (@ tptp.ord_less_eq_nat X) Y) (@ (@ tptp.ord_less_eq_nat Y) X))) (forall ((X tptp.int) (Y tptp.int)) (or (@ (@ tptp.ord_less_eq_int X) Y) (@ (@ tptp.ord_less_eq_int Y) X))) (forall ((X tptp.set_nat) (Y tptp.set_nat)) (=> (= X Y) (@ (@ tptp.ord_less_eq_set_nat X) Y))) (forall ((X tptp.rat) (Y tptp.rat)) (=> (= X Y) (@ (@ tptp.ord_less_eq_rat X) Y))) (forall ((X tptp.num) (Y tptp.num)) (=> (= X Y) (@ (@ tptp.ord_less_eq_num X) Y))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (= X Y) (@ (@ tptp.ord_less_eq_nat X) Y))) (forall ((X tptp.int) (Y tptp.int)) (=> (= X Y) (@ (@ tptp.ord_less_eq_int X) Y))) (forall ((A tptp.rat) (B tptp.rat) (F2 (-> tptp.rat tptp.rat)) (C2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat (@ F2 B)) C2) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y3) (@ (@ tptp.ord_less_eq_rat (@ F2 X3)) (@ F2 Y3)))) (@ (@ tptp.ord_less_eq_rat (@ F2 A)) C2))))) (forall ((A tptp.rat) (B tptp.rat) (F2 (-> tptp.rat tptp.num)) (C2 tptp.num)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_num (@ F2 B)) C2) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y3) (@ (@ tptp.ord_less_eq_num (@ F2 X3)) (@ F2 Y3)))) (@ (@ tptp.ord_less_eq_num (@ F2 A)) C2))))) (forall ((A tptp.rat) (B tptp.rat) (F2 (-> tptp.rat tptp.nat)) (C2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_nat (@ F2 B)) C2) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y3) (@ (@ tptp.ord_less_eq_nat (@ F2 X3)) (@ F2 Y3)))) (@ (@ tptp.ord_less_eq_nat (@ F2 A)) C2))))) (forall ((A tptp.rat) (B tptp.rat) (F2 (-> tptp.rat tptp.int)) (C2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_int (@ F2 B)) C2) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y3) (@ (@ tptp.ord_less_eq_int (@ F2 X3)) (@ F2 Y3)))) (@ (@ tptp.ord_less_eq_int (@ F2 A)) C2))))) (forall ((A tptp.num) (B tptp.num) (F2 (-> tptp.num tptp.rat)) (C2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (@ (@ tptp.ord_less_eq_rat (@ F2 B)) C2) (=> (forall ((X3 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y3) (@ (@ tptp.ord_less_eq_rat (@ F2 X3)) (@ F2 Y3)))) (@ (@ tptp.ord_less_eq_rat (@ F2 A)) C2))))) (forall ((A tptp.num) (B tptp.num) (F2 (-> tptp.num tptp.num)) (C2 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (@ (@ tptp.ord_less_eq_num (@ F2 B)) C2) (=> (forall ((X3 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y3) (@ (@ tptp.ord_less_eq_num (@ F2 X3)) (@ F2 Y3)))) (@ (@ tptp.ord_less_eq_num (@ F2 A)) C2))))) (forall ((A tptp.num) (B tptp.num) (F2 (-> tptp.num tptp.nat)) (C2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (@ (@ tptp.ord_less_eq_nat (@ F2 B)) C2) (=> (forall ((X3 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y3) (@ (@ tptp.ord_less_eq_nat (@ F2 X3)) (@ F2 Y3)))) (@ (@ tptp.ord_less_eq_nat (@ F2 A)) C2))))) (forall ((A tptp.num) (B tptp.num) (F2 (-> tptp.num tptp.int)) (C2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (@ (@ tptp.ord_less_eq_int (@ F2 B)) C2) (=> (forall ((X3 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y3) (@ (@ tptp.ord_less_eq_int (@ F2 X3)) (@ F2 Y3)))) (@ (@ tptp.ord_less_eq_int (@ F2 A)) C2))))) (forall ((A tptp.nat) (B tptp.nat) (F2 (-> tptp.nat tptp.rat)) (C2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_rat (@ F2 B)) C2) (=> (forall ((X3 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) Y3) (@ (@ tptp.ord_less_eq_rat (@ F2 X3)) (@ F2 Y3)))) (@ (@ tptp.ord_less_eq_rat (@ F2 A)) C2))))) (forall ((A tptp.nat) (B tptp.nat) (F2 (-> tptp.nat tptp.num)) (C2 tptp.num)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_num (@ F2 B)) C2) (=> (forall ((X3 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) Y3) (@ (@ tptp.ord_less_eq_num (@ F2 X3)) (@ F2 Y3)))) (@ (@ tptp.ord_less_eq_num (@ F2 A)) C2))))) (forall ((A tptp.rat) (F2 (-> tptp.rat tptp.rat)) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat A))) (=> (@ _let_1 (@ F2 B)) (=> (@ (@ tptp.ord_less_eq_rat B) C2) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y3) (@ (@ tptp.ord_less_eq_rat (@ F2 X3)) (@ F2 Y3)))) (@ _let_1 (@ F2 C2))))))) (forall ((A tptp.rat) (F2 (-> tptp.num tptp.rat)) (B tptp.num) (C2 tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_rat A))) (=> (@ _let_1 (@ F2 B)) (=> (@ (@ tptp.ord_less_eq_num B) C2) (=> (forall ((X3 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y3) (@ (@ tptp.ord_less_eq_rat (@ F2 X3)) (@ F2 Y3)))) (@ _let_1 (@ F2 C2))))))) (forall ((A tptp.rat) (F2 (-> tptp.nat tptp.rat)) (B tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_rat A))) (=> (@ _let_1 (@ F2 B)) (=> (@ (@ tptp.ord_less_eq_nat B) C2) (=> (forall ((X3 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) Y3) (@ (@ tptp.ord_less_eq_rat (@ F2 X3)) (@ F2 Y3)))) (@ _let_1 (@ F2 C2))))))) (forall ((A tptp.rat) (F2 (-> tptp.int tptp.rat)) (B tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_rat A))) (=> (@ _let_1 (@ F2 B)) (=> (@ (@ tptp.ord_less_eq_int B) C2) (=> (forall ((X3 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X3) Y3) (@ (@ tptp.ord_less_eq_rat (@ F2 X3)) (@ F2 Y3)))) (@ _let_1 (@ F2 C2))))))) (forall ((A tptp.num) (F2 (-> tptp.rat tptp.num)) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_num A))) (=> (@ _let_1 (@ F2 B)) (=> (@ (@ tptp.ord_less_eq_rat B) C2) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y3) (@ (@ tptp.ord_less_eq_num (@ F2 X3)) (@ F2 Y3)))) (@ _let_1 (@ F2 C2))))))) (forall ((A tptp.num) (F2 (-> tptp.num tptp.num)) (B tptp.num) (C2 tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_num A))) (=> (@ _let_1 (@ F2 B)) (=> (@ (@ tptp.ord_less_eq_num B) C2) (=> (forall ((X3 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y3) (@ (@ tptp.ord_less_eq_num (@ F2 X3)) (@ F2 Y3)))) (@ _let_1 (@ F2 C2))))))) (forall ((A tptp.num) (F2 (-> tptp.nat tptp.num)) (B tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_num A))) (=> (@ _let_1 (@ F2 B)) (=> (@ (@ tptp.ord_less_eq_nat B) C2) (=> (forall ((X3 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) Y3) (@ (@ tptp.ord_less_eq_num (@ F2 X3)) (@ F2 Y3)))) (@ _let_1 (@ F2 C2))))))) (forall ((A tptp.num) (F2 (-> tptp.int tptp.num)) (B tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_num A))) (=> (@ _let_1 (@ F2 B)) (=> (@ (@ tptp.ord_less_eq_int B) C2) (=> (forall ((X3 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X3) Y3) (@ (@ tptp.ord_less_eq_num (@ F2 X3)) (@ F2 Y3)))) (@ _let_1 (@ F2 C2))))))) (forall ((A tptp.nat) (F2 (-> tptp.rat tptp.nat)) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_nat A))) (=> (@ _let_1 (@ F2 B)) (=> (@ (@ tptp.ord_less_eq_rat B) C2) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y3) (@ (@ tptp.ord_less_eq_nat (@ F2 X3)) (@ F2 Y3)))) (@ _let_1 (@ F2 C2))))))) (forall ((A tptp.nat) (F2 (-> tptp.num tptp.nat)) (B tptp.num) (C2 tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_nat A))) (=> (@ _let_1 (@ F2 B)) (=> (@ (@ tptp.ord_less_eq_num B) C2) (=> (forall ((X3 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y3) (@ (@ tptp.ord_less_eq_nat (@ F2 X3)) (@ F2 Y3)))) (@ _let_1 (@ F2 C2))))))) (= (lambda ((Y5 tptp.set_nat) (Z2 tptp.set_nat)) (= Y5 Z2)) (lambda ((A5 tptp.set_nat) (B4 tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat A5) B4) (@ (@ tptp.ord_less_eq_set_nat B4) A5)))) (= (lambda ((Y5 tptp.rat) (Z2 tptp.rat)) (= Y5 Z2)) (lambda ((A5 tptp.rat) (B4 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat A5) B4) (@ (@ tptp.ord_less_eq_rat B4) A5)))) (= (lambda ((Y5 tptp.num) (Z2 tptp.num)) (= Y5 Z2)) (lambda ((A5 tptp.num) (B4 tptp.num)) (and (@ (@ tptp.ord_less_eq_num A5) B4) (@ (@ tptp.ord_less_eq_num B4) A5)))) (= (lambda ((Y5 tptp.nat) (Z2 tptp.nat)) (= Y5 Z2)) (lambda ((A5 tptp.nat) (B4 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat A5) B4) (@ (@ tptp.ord_less_eq_nat B4) A5)))) (= (lambda ((Y5 tptp.int) (Z2 tptp.int)) (= Y5 Z2)) (lambda ((A5 tptp.int) (B4 tptp.int)) (and (@ (@ tptp.ord_less_eq_int A5) B4) (@ (@ tptp.ord_less_eq_int B4) A5)))) (forall ((A tptp.set_nat) (B tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A) B) (=> (@ (@ tptp.ord_less_eq_set_nat B) A) (= A B)))) (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat B) A) (= A B)))) (forall ((A tptp.num) (B tptp.num)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (@ (@ tptp.ord_less_eq_num B) A) (= A B)))) (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat B) A) (= A B)))) (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_eq_int B) A) (= A B)))) (forall ((B tptp.set_nat) (A tptp.set_nat) (C2 tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat C2))) (=> (@ (@ tptp.ord_less_eq_set_nat B) A) (=> (@ _let_1 B) (@ _let_1 A))))) (forall ((B tptp.rat) (A tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat C2))) (=> (@ (@ tptp.ord_less_eq_rat B) A) (=> (@ _let_1 B) (@ _let_1 A))))) (forall ((B tptp.num) (A tptp.num) (C2 tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_num C2))) (=> (@ (@ tptp.ord_less_eq_num B) A) (=> (@ _let_1 B) (@ _let_1 A))))) (forall ((B tptp.nat) (A tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat C2))) (=> (@ (@ tptp.ord_less_eq_nat B) A) (=> (@ _let_1 B) (@ _let_1 A))))) (forall ((B tptp.int) (A tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int C2))) (=> (@ (@ tptp.ord_less_eq_int B) A) (=> (@ _let_1 B) (@ _let_1 A))))) (forall ((B tptp.set_nat) (A tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat B) A) (=> (@ (@ tptp.ord_less_eq_set_nat A) B) (= A B)))) (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat B) A) (=> (@ (@ tptp.ord_less_eq_rat A) B) (= A B)))) (forall ((B tptp.num) (A tptp.num)) (=> (@ (@ tptp.ord_less_eq_num B) A) (=> (@ (@ tptp.ord_less_eq_num A) B) (= A B)))) (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B) A) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= A B)))) (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B) A) (=> (@ (@ tptp.ord_less_eq_int A) B) (= A B)))) (= (lambda ((Y5 tptp.set_nat) (Z2 tptp.set_nat)) (= Y5 Z2)) (lambda ((A5 tptp.set_nat) (B4 tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat B4) A5) (@ (@ tptp.ord_less_eq_set_nat A5) B4)))) (= (lambda ((Y5 tptp.rat) (Z2 tptp.rat)) (= Y5 Z2)) (lambda ((A5 tptp.rat) (B4 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat B4) A5) (@ (@ tptp.ord_less_eq_rat A5) B4)))) (= (lambda ((Y5 tptp.num) (Z2 tptp.num)) (= Y5 Z2)) (lambda ((A5 tptp.num) (B4 tptp.num)) (and (@ (@ tptp.ord_less_eq_num B4) A5) (@ (@ tptp.ord_less_eq_num A5) B4)))) (= (lambda ((Y5 tptp.nat) (Z2 tptp.nat)) (= Y5 Z2)) (lambda ((A5 tptp.nat) (B4 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat B4) A5) (@ (@ tptp.ord_less_eq_nat A5) B4)))) (= (lambda ((Y5 tptp.int) (Z2 tptp.int)) (= Y5 Z2)) (lambda ((A5 tptp.int) (B4 tptp.int)) (and (@ (@ tptp.ord_less_eq_int B4) A5) (@ (@ tptp.ord_less_eq_int A5) B4)))) (forall ((P2 (-> tptp.rat tptp.rat Bool)) (A tptp.rat) (B tptp.rat)) (=> (forall ((A3 tptp.rat) (B3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A3) B3) (@ (@ P2 A3) B3))) (=> (forall ((A3 tptp.rat) (B3 tptp.rat)) (=> (@ (@ P2 B3) A3) (@ (@ P2 A3) B3))) (@ (@ P2 A) B)))) (forall ((P2 (-> tptp.num tptp.num Bool)) (A tptp.num) (B tptp.num)) (=> (forall ((A3 tptp.num) (B3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num A3) B3) (@ (@ P2 A3) B3))) (=> (forall ((A3 tptp.num) (B3 tptp.num)) (=> (@ (@ P2 B3) A3) (@ (@ P2 A3) B3))) (@ (@ P2 A) B)))) (forall ((P2 (-> tptp.nat tptp.nat Bool)) (A tptp.nat) (B tptp.nat)) (=> (forall ((A3 tptp.nat) (B3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A3) B3) (@ (@ P2 A3) B3))) (=> (forall ((A3 tptp.nat) (B3 tptp.nat)) (=> (@ (@ P2 B3) A3) (@ (@ P2 A3) B3))) (@ (@ P2 A) B)))) (forall ((P2 (-> tptp.int tptp.int Bool)) (A tptp.int) (B tptp.int)) (=> (forall ((A3 tptp.int) (B3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A3) B3) (@ (@ P2 A3) B3))) (=> (forall ((A3 tptp.int) (B3 tptp.int)) (=> (@ (@ P2 B3) A3) (@ (@ P2 A3) B3))) (@ (@ P2 A) B)))) (forall ((X tptp.set_nat) (Y tptp.set_nat) (Z3 tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_set_nat Y) Z3) (@ _let_1 Z3))))) (forall ((X tptp.rat) (Y tptp.rat) (Z3 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_rat Y) Z3) (@ _let_1 Z3))))) (forall ((X tptp.num) (Y tptp.num) (Z3 tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_num X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_num Y) Z3) (@ _let_1 Z3))))) (forall ((X tptp.nat) (Y tptp.nat) (Z3 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_nat Y) Z3) (@ _let_1 Z3))))) (forall ((X tptp.int) (Y tptp.int) (Z3 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_int Y) Z3) (@ _let_1 Z3))))) (forall ((A tptp.set_nat) (B tptp.set_nat) (C2 tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_set_nat B) C2) (@ _let_1 C2))))) (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_rat B) C2) (@ _let_1 C2))))) (forall ((A tptp.num) (B tptp.num) (C2 tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_num A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_num B) C2) (@ _let_1 C2))))) (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_nat B) C2) (@ _let_1 C2))))) (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_int B) C2) (@ _let_1 C2))))) (forall ((X tptp.set_nat) (Y tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat X) Y) (=> (@ (@ tptp.ord_less_eq_set_nat Y) X) (= X Y)))) (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X) Y) (=> (@ (@ tptp.ord_less_eq_rat Y) X) (= X Y)))) (forall ((X tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X) Y) (=> (@ (@ tptp.ord_less_eq_num Y) X) (= X Y)))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X) Y) (=> (@ (@ tptp.ord_less_eq_nat Y) X) (= X Y)))) (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X) Y) (=> (@ (@ tptp.ord_less_eq_int Y) X) (= X Y)))) (forall ((A tptp.set_nat) (B tptp.set_nat) (C2 tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat A))) (=> (@ _let_1 B) (=> (= B C2) (@ _let_1 C2))))) (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat A))) (=> (@ _let_1 B) (=> (= B C2) (@ _let_1 C2))))) (forall ((A tptp.num) (B tptp.num) (C2 tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_num A))) (=> (@ _let_1 B) (=> (= B C2) (@ _let_1 C2))))) (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat A))) (=> (@ _let_1 B) (=> (= B C2) (@ _let_1 C2))))) (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int A))) (=> (@ _let_1 B) (=> (= B C2) (@ _let_1 C2))))) (forall ((A tptp.set_nat) (B tptp.set_nat) (C2 tptp.set_nat)) (=> (= A B) (=> (@ (@ tptp.ord_less_eq_set_nat B) C2) (@ (@ tptp.ord_less_eq_set_nat A) C2)))) (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (=> (= A B) (=> (@ (@ tptp.ord_less_eq_rat B) C2) (@ (@ tptp.ord_less_eq_rat A) C2)))) (forall ((A tptp.num) (B tptp.num) (C2 tptp.num)) (=> (= A B) (=> (@ (@ tptp.ord_less_eq_num B) C2) (@ (@ tptp.ord_less_eq_num A) C2)))) (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (=> (= A B) (=> (@ (@ tptp.ord_less_eq_nat B) C2) (@ (@ tptp.ord_less_eq_nat A) C2)))) (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (=> (= A B) (=> (@ (@ tptp.ord_less_eq_int B) C2) (@ (@ tptp.ord_less_eq_int A) C2)))) (= (lambda ((Y5 tptp.set_nat) (Z2 tptp.set_nat)) (= Y5 Z2)) (lambda ((X4 tptp.set_nat) (Y4 tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat X4) Y4) (@ (@ tptp.ord_less_eq_set_nat Y4) X4)))) (= (lambda ((Y5 tptp.rat) (Z2 tptp.rat)) (= Y5 Z2)) (lambda ((X4 tptp.rat) (Y4 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat X4) Y4) (@ (@ tptp.ord_less_eq_rat Y4) X4)))) (= (lambda ((Y5 tptp.num) (Z2 tptp.num)) (= Y5 Z2)) (lambda ((X4 tptp.num) (Y4 tptp.num)) (and (@ (@ tptp.ord_less_eq_num X4) Y4) (@ (@ tptp.ord_less_eq_num Y4) X4)))) (= (lambda ((Y5 tptp.nat) (Z2 tptp.nat)) (= Y5 Z2)) (lambda ((X4 tptp.nat) (Y4 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat X4) Y4) (@ (@ tptp.ord_less_eq_nat Y4) X4)))) (= (lambda ((Y5 tptp.int) (Z2 tptp.int)) (= Y5 Z2)) (lambda ((X4 tptp.int) (Y4 tptp.int)) (and (@ (@ tptp.ord_less_eq_int X4) Y4) (@ (@ tptp.ord_less_eq_int Y4) X4)))) (forall ((X tptp.rat) (Y tptp.rat) (Z3 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 Z3))) (let ((_let_4 (@ _let_3 X))) (let ((_let_5 (@ tptp.ord_less_eq_rat Y))) (let ((_let_6 (@ _let_5 Z3))) (let ((_let_7 (@ _let_5 X))) (let ((_let_8 (@ _let_3 Y))) (let ((_let_9 (@ _let_1 Z3))) (=> (=> _let_2 (not _let_6)) (=> (=> _let_7 (not _let_9)) (=> (=> _let_9 (not _let_8)) (=> (=> _let_8 (not _let_7)) (=> (=> _let_6 (not _let_4)) (not (=> _let_4 (not _let_2)))))))))))))))))) (forall ((X tptp.num) (Y tptp.num) (Z3 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 Z3))) (let ((_let_4 (@ _let_3 X))) (let ((_let_5 (@ tptp.ord_less_eq_num Y))) (let ((_let_6 (@ _let_5 Z3))) (let ((_let_7 (@ _let_5 X))) (let ((_let_8 (@ _let_3 Y))) (let ((_let_9 (@ _let_1 Z3))) (=> (=> _let_2 (not _let_6)) (=> (=> _let_7 (not _let_9)) (=> (=> _let_9 (not _let_8)) (=> (=> _let_8 (not _let_7)) (=> (=> _let_6 (not _let_4)) (not (=> _let_4 (not _let_2)))))))))))))))))) (forall ((X tptp.nat) (Y tptp.nat) (Z3 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat X))) (let ((_let_2 (@ _let_1 Y))) (let ((_let_3 (@ tptp.ord_less_eq_nat Z3))) (let ((_let_4 (@ _let_3 X))) (let ((_let_5 (@ tptp.ord_less_eq_nat Y))) (let ((_let_6 (@ _let_5 Z3))) (let ((_let_7 (@ _let_5 X))) (let ((_let_8 (@ _let_3 Y))) (let ((_let_9 (@ _let_1 Z3))) (=> (=> _let_2 (not _let_6)) (=> (=> _let_7 (not _let_9)) (=> (=> _let_9 (not _let_8)) (=> (=> _let_8 (not _let_7)) (=> (=> _let_6 (not _let_4)) (not (=> _let_4 (not _let_2)))))))))))))))))) (forall ((X tptp.int) (Y tptp.int) (Z3 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int X))) (let ((_let_2 (@ _let_1 Y))) (let ((_let_3 (@ tptp.ord_less_eq_int Z3))) (let ((_let_4 (@ _let_3 X))) (let ((_let_5 (@ tptp.ord_less_eq_int Y))) (let ((_let_6 (@ _let_5 Z3))) (let ((_let_7 (@ _let_5 X))) (let ((_let_8 (@ _let_3 Y))) (let ((_let_9 (@ _let_1 Z3))) (=> (=> _let_2 (not _let_6)) (=> (=> _let_7 (not _let_9)) (=> (=> _let_9 (not _let_8)) (=> (=> _let_8 (not _let_7)) (=> (=> _let_6 (not _let_4)) (not (=> _let_4 (not _let_2)))))))))))))))))) (forall ((A tptp.rat) (B tptp.rat)) (= (not (@ (@ tptp.ord_less_eq_rat A) B)) (and (@ (@ tptp.ord_less_eq_rat B) A) (not (= B A))))) (forall ((A tptp.num) (B tptp.num)) (= (not (@ (@ tptp.ord_less_eq_num A) B)) (and (@ (@ tptp.ord_less_eq_num B) A) (not (= B A))))) (forall ((A tptp.nat) (B tptp.nat)) (= (not (@ (@ tptp.ord_less_eq_nat A) B)) (and (@ (@ tptp.ord_less_eq_nat B) A) (not (= B A))))) (forall ((A tptp.int) (B tptp.int)) (= (not (@ (@ tptp.ord_less_eq_int A) B)) (and (@ (@ tptp.ord_less_eq_int B) A) (not (= B A))))) (forall ((P2 (-> tptp.nat Bool)) (X tptp.nat) (M5 tptp.nat)) (=> (@ P2 X) (=> (forall ((X3 tptp.nat)) (=> (@ P2 X3) (@ (@ tptp.ord_less_eq_nat X3) M5))) (not (forall ((M tptp.nat)) (=> (@ P2 M) (not (forall ((X5 tptp.nat)) (=> (@ P2 X5) (@ (@ tptp.ord_less_eq_nat X5) M)))))))))) (forall ((P2 (-> tptp.nat Bool)) (K2 tptp.nat) (B tptp.nat)) (=> (@ P2 K2) (=> (forall ((Y3 tptp.nat)) (=> (@ P2 Y3) (@ (@ tptp.ord_less_eq_nat Y3) B))) (exists ((X3 tptp.nat)) (and (@ P2 X3) (forall ((Y6 tptp.nat)) (=> (@ P2 Y6) (@ (@ tptp.ord_less_eq_nat Y6) X3)))))))) (forall ((M2 tptp.nat) (N tptp.nat)) (or (@ (@ tptp.ord_less_eq_nat M2) N) (@ (@ tptp.ord_less_eq_nat N) M2))) (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (=> (@ (@ tptp.ord_less_eq_nat N) M2) (= M2 N)))) (forall ((M2 tptp.nat) (N tptp.nat)) (=> (= M2 N) (@ (@ tptp.ord_less_eq_nat M2) N))) (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) N)) (forall ((A tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A)) (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat N) tptp.zero_zero_nat) (= N tptp.zero_zero_nat))) (forall ((A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.zero_zero_nat) (= A tptp.zero_zero_nat))) (forall ((A tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat A) tptp.zero_zero_nat) (= A tptp.zero_zero_nat))) (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) N)) (forall ((N tptp.nat)) (=> (not (= N tptp.zero_zero_nat)) (exists ((M tptp.nat)) (= N (@ tptp.suc M))))) (forall ((M2 tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc M2)))) (forall ((M2 tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc M2)))) (forall ((M2 tptp.nat)) (not (= (@ tptp.suc M2) tptp.zero_zero_nat))) (forall ((P2 (-> tptp.nat Bool)) (K2 tptp.nat)) (=> (@ P2 K2) (=> (forall ((N3 tptp.nat)) (=> (@ P2 (@ tptp.suc N3)) (@ P2 N3))) (@ P2 tptp.zero_zero_nat)))) (forall ((P2 (-> tptp.nat tptp.nat Bool)) (M2 tptp.nat) (N tptp.nat)) (=> (forall ((X3 tptp.nat)) (@ (@ P2 X3) tptp.zero_zero_nat)) (=> (forall ((Y3 tptp.nat)) (@ (@ P2 tptp.zero_zero_nat) (@ tptp.suc Y3))) (=> (forall ((X3 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ P2 X3) Y3) (@ (@ P2 (@ tptp.suc X3)) (@ tptp.suc Y3)))) (@ (@ P2 M2) N))))) (forall ((X tptp.nat)) (=> (not (= X tptp.zero_zero_nat)) (not (forall ((N3 tptp.nat)) (not (= X (@ tptp.suc N3))))))) (forall ((X2 tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc X2)))) (forall ((Nat2 tptp.nat)) (not (= (@ tptp.suc Nat2) tptp.zero_zero_nat))) (forall ((Nat2 tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc Nat2)))) (forall ((Nat tptp.nat) (X2 tptp.nat)) (=> (= Nat (@ tptp.suc X2)) (not (= Nat tptp.zero_zero_nat)))) (forall ((Y tptp.nat)) (=> (not (= Y tptp.zero_zero_nat)) (not (forall ((Nat3 tptp.nat)) (not (= Y (@ tptp.suc Nat3))))))) (forall ((P2 (-> tptp.nat Bool)) (N tptp.nat)) (=> (@ P2 tptp.zero_zero_nat) (=> (forall ((N3 tptp.nat)) (=> (@ P2 N3) (@ P2 (@ tptp.suc N3)))) (@ P2 N)))) (@ (@ tptp.vEBT_invar_vebt tptp.sa) tptp.deg) (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat N) tptp.zero_zero_nat) (= N tptp.zero_zero_nat))) (forall ((X2 tptp.product_prod_nat_nat)) (= (@ tptp.size_s170228958280169651at_nat (@ tptp.some_P7363390416028606310at_nat X2)) (@ tptp.suc tptp.zero_zero_nat))) (forall ((X2 tptp.nat)) (= (@ tptp.size_size_option_nat (@ tptp.some_nat X2)) (@ tptp.suc tptp.zero_zero_nat))) (forall ((X2 tptp.num)) (= (@ tptp.size_size_option_num (@ tptp.some_num X2)) (@ tptp.suc tptp.zero_zero_nat))) (forall ((X tptp.nat)) (=> (not (= X tptp.zero_zero_nat)) (=> (not (= X (@ tptp.suc tptp.zero_zero_nat))) (not (forall ((Va tptp.nat)) (not (= X (@ tptp.suc (@ tptp.suc Va))))))))) (forall ((P2 (-> tptp.nat Bool))) (=> (not (@ P2 tptp.zero_zero_nat)) (=> (exists ((X_1 tptp.nat)) (@ P2 X_1)) (exists ((N3 tptp.nat)) (and (not (@ P2 N3)) (@ P2 (@ tptp.suc N3))))))) (@ _let_181 tptp.zero_zero_real) (@ _let_179 tptp.zero_zero_rat) (@ _let_348 tptp.zero_zero_nat) (@ _let_178 tptp.zero_zero_int) (forall ((X tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) X)) (forall ((Q2 tptp.code_integer) (R3 tptp.code_integer)) (= (@ tptp.unique5706413561485394159nteger (@ (@ tptp.produc1086072967326762835nteger Q2) R3)) (= R3 tptp.zero_z3403309356797280102nteger))) (forall ((Q2 tptp.nat) (R3 tptp.nat)) (= (@ tptp.unique6322359934112328802ux_nat (@ (@ tptp.product_Pair_nat_nat Q2) R3)) (= R3 tptp.zero_zero_nat))) (forall ((Q2 tptp.int) (R3 tptp.int)) (= (@ tptp.unique6319869463603278526ux_int (@ (@ tptp.product_Pair_int_int Q2) R3)) (= R3 tptp.zero_zero_int))) (forall ((M2 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 M2) N)) (and (@ _let_1 M2) (@ _let_1 N))))) _let_369 (forall ((T tptp.vEBT_VEBT)) (not (@ (@ tptp.vEBT_invar_vebt T) tptp.zero_zero_nat))) (forall ((T tptp.vEBT_VEBT)) (not (@ (@ tptp.vEBT_invar_vebt T) tptp.zero_zero_nat))) (forall ((A Bool) (B Bool)) (not (@ (@ tptp.vEBT_invar_vebt (@ (@ tptp.vEBT_Leaf A) B)) tptp.zero_zero_nat))) (forall ((X tptp.nat) (Y tptp.nat)) (= (= (@ tptp.nat_prod_decode X) (@ tptp.nat_prod_decode Y)) (= X Y))) (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (@ (@ tptp.vEBT_invar_vebt (@ (@ tptp.vEBT_VEBT_insert T) X)) N))) (forall ((M2 tptp.nat) (N tptp.nat)) (= (= (@ (@ tptp.times_times_nat M2) N) tptp.zero_zero_nat) (or (= M2 tptp.zero_zero_nat) (= N tptp.zero_zero_nat)))) (forall ((M2 tptp.nat)) (= (@ (@ tptp.times_times_nat M2) tptp.zero_zero_nat) tptp.zero_zero_nat)) (forall ((K2 tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K2))) (= (= (@ _let_1 M2) (@ _let_1 N)) (or (= M2 N) (= K2 tptp.zero_zero_nat))))) (forall ((M2 tptp.nat) (K2 tptp.nat) (N tptp.nat)) (= (= (@ (@ tptp.times_times_nat M2) K2) (@ (@ tptp.times_times_nat N) K2)) (or (= M2 N) (= K2 tptp.zero_zero_nat)))) (forall ((N tptp.nat)) (= (@ tptp.nat_prod_encode (@ tptp.nat_prod_decode N)) N)) (forall ((X tptp.product_prod_nat_nat)) (= (@ tptp.nat_prod_decode (@ tptp.nat_prod_encode X)) X)) (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (= _let_1 (@ (@ tptp.times_times_nat M2) N)) (and (= M2 _let_1) (= N _let_1))))) (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (= (@ (@ tptp.times_times_nat M2) N) _let_1) (and (= M2 _let_1) (= N _let_1))))) (forall ((B tptp.real) (A tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.times_times_real B))) (let ((_let_2 (@ tptp.times_times_real A))) (= (@ _let_1 (@ _let_2 C2)) (@ _let_2 (@ _let_1 C2)))))) (forall ((B tptp.rat) (A tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat B))) (let ((_let_2 (@ tptp.times_times_rat A))) (= (@ _let_1 (@ _let_2 C2)) (@ _let_2 (@ _let_1 C2)))))) (forall ((B tptp.nat) (A tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat B))) (let ((_let_2 (@ tptp.times_times_nat A))) (= (@ _let_1 (@ _let_2 C2)) (@ _let_2 (@ _let_1 C2)))))) (forall ((B tptp.int) (A tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int B))) (let ((_let_2 (@ tptp.times_times_int A))) (= (@ _let_1 (@ _let_2 C2)) (@ _let_2 (@ _let_1 C2)))))) (= tptp.times_times_real (lambda ((A5 tptp.real) (B4 tptp.real)) (@ (@ tptp.times_times_real B4) A5))) (= tptp.times_times_rat (lambda ((A5 tptp.rat) (B4 tptp.rat)) (@ (@ tptp.times_times_rat B4) A5))) (= tptp.times_times_nat (lambda ((A5 tptp.nat) (B4 tptp.nat)) (@ (@ tptp.times_times_nat B4) A5))) (= tptp.times_times_int (lambda ((A5 tptp.int) (B4 tptp.int)) (@ (@ tptp.times_times_int B4) A5))) (forall ((A tptp.real) (B tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.times_times_real A))) (= (@ (@ tptp.times_times_real (@ _let_1 B)) C2) (@ _let_1 (@ (@ tptp.times_times_real B) C2))))) (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat A))) (= (@ (@ tptp.times_times_rat (@ _let_1 B)) C2) (@ _let_1 (@ (@ tptp.times_times_rat B) C2))))) (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (= (@ (@ tptp.times_times_nat (@ _let_1 B)) C2) (@ _let_1 (@ (@ tptp.times_times_nat B) C2))))) (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (= (@ (@ tptp.times_times_int (@ _let_1 B)) C2) (@ _let_1 (@ (@ tptp.times_times_int B) C2))))) (forall ((A tptp.real) (B tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.times_times_real A))) (= (@ (@ tptp.times_times_real (@ _let_1 B)) C2) (@ _let_1 (@ (@ tptp.times_times_real B) C2))))) (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat A))) (= (@ (@ tptp.times_times_rat (@ _let_1 B)) C2) (@ _let_1 (@ (@ tptp.times_times_rat B) C2))))) (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (= (@ (@ tptp.times_times_nat (@ _let_1 B)) C2) (@ _let_1 (@ (@ tptp.times_times_nat B) C2))))) (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (= (@ (@ tptp.times_times_int (@ _let_1 B)) C2) (@ _let_1 (@ (@ tptp.times_times_int B) C2))))) (forall ((X tptp.list_VEBT_VEBT) (Y tptp.list_VEBT_VEBT)) (=> (not (= (@ tptp.size_s6755466524823107622T_VEBT X) (@ tptp.size_s6755466524823107622T_VEBT Y))) (not (= X Y)))) (forall ((X tptp.list_o) (Y tptp.list_o)) (=> (not (= (@ tptp.size_size_list_o X) (@ tptp.size_size_list_o Y))) (not (= X Y)))) (forall ((X tptp.list_nat) (Y tptp.list_nat)) (=> (not (= (@ tptp.size_size_list_nat X) (@ tptp.size_size_list_nat Y))) (not (= X Y)))) (forall ((X tptp.list_int) (Y tptp.list_int)) (=> (not (= (@ tptp.size_size_list_int X) (@ tptp.size_size_list_int Y))) (not (= X Y)))) (forall ((X tptp.num) (Y tptp.num)) (=> (not (= (@ tptp.size_size_num X) (@ tptp.size_size_num Y))) (not (= X Y)))) (forall ((K2 tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.suc K2)))) (= (= (@ _let_1 M2) (@ _let_1 N)) (= M2 N)))) (forall ((N tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.zero_zero_nat) N) tptp.zero_zero_nat)) (forall ((I2 tptp.nat) (J2 tptp.nat) (K2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K2))) (=> (@ (@ tptp.ord_less_eq_nat I2) J2) (@ (@ tptp.ord_less_eq_nat (@ _let_1 I2)) (@ _let_1 J2))))) (forall ((I2 tptp.nat) (J2 tptp.nat) (K2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat I2) K2)) (@ (@ tptp.times_times_nat J2) K2)))) (forall ((I2 tptp.nat) (J2 tptp.nat) (K2 tptp.nat) (L tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J2) (=> (@ (@ tptp.ord_less_eq_nat K2) L) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat I2) K2)) (@ (@ tptp.times_times_nat J2) L))))) (forall ((M2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat M2) (@ (@ tptp.times_times_nat M2) M2))) (forall ((M2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat M2))) (@ (@ tptp.ord_less_eq_nat M2) (@ _let_1 (@ _let_1 M2))))) (forall ((K2 tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.suc K2)))) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 M2)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat M2) N)))) (forall ((X tptp.complex)) (= (= tptp.zero_zero_complex X) (= X tptp.zero_zero_complex))) (forall ((X tptp.real)) (= (= tptp.zero_zero_real X) (= X tptp.zero_zero_real))) (forall ((X tptp.rat)) (= (= tptp.zero_zero_rat X) (= X tptp.zero_zero_rat))) (forall ((X tptp.nat)) (= (= tptp.zero_zero_nat X) (= X tptp.zero_zero_nat))) (forall ((X tptp.int)) (= (= tptp.zero_zero_int X) (= X tptp.zero_zero_int))) (forall ((A tptp.complex) (C2 tptp.complex) (B tptp.complex)) (= (= (@ (@ tptp.times_times_complex A) C2) (@ (@ tptp.times_times_complex B) C2)) (or (= C2 tptp.zero_zero_complex) (= A B)))) (forall ((A tptp.real) (C2 tptp.real) (B tptp.real)) (= (= (@ (@ tptp.times_times_real A) C2) (@ (@ tptp.times_times_real B) C2)) (or (= C2 tptp.zero_zero_real) (= A B)))) (forall ((A tptp.rat) (C2 tptp.rat) (B tptp.rat)) (= (= (@ (@ tptp.times_times_rat A) C2) (@ (@ tptp.times_times_rat B) C2)) (or (= C2 tptp.zero_zero_rat) (= A B)))) (forall ((A tptp.nat) (C2 tptp.nat) (B tptp.nat)) (= (= (@ (@ tptp.times_times_nat A) C2) (@ (@ tptp.times_times_nat B) C2)) (or (= C2 tptp.zero_zero_nat) (= A B)))) (forall ((A tptp.int) (C2 tptp.int) (B tptp.int)) (= (= (@ (@ tptp.times_times_int A) C2) (@ (@ tptp.times_times_int B) C2)) (or (= C2 tptp.zero_zero_int) (= A B)))) (forall ((C2 tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex C2))) (= (= (@ _let_1 A) (@ _let_1 B)) (or (= C2 tptp.zero_zero_complex) (= A B))))) (forall ((C2 tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real C2))) (= (= (@ _let_1 A) (@ _let_1 B)) (or (= C2 tptp.zero_zero_real) (= A B))))) (forall ((C2 tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C2))) (= (= (@ _let_1 A) (@ _let_1 B)) (or (= C2 tptp.zero_zero_rat) (= A B))))) (forall ((C2 tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C2))) (= (= (@ _let_1 A) (@ _let_1 B)) (or (= C2 tptp.zero_zero_nat) (= A B))))) (forall ((C2 tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C2))) (= (= (@ _let_1 A) (@ _let_1 B)) (or (= C2 tptp.zero_zero_int) (= A B))))) (forall ((A tptp.complex) (B tptp.complex)) (= (= (@ (@ tptp.times_times_complex A) B) tptp.zero_zero_complex) (or (= A tptp.zero_zero_complex) (= B tptp.zero_zero_complex)))) (forall ((A tptp.real) (B tptp.real)) (= (= (@ (@ tptp.times_times_real A) B) tptp.zero_zero_real) (or (= A tptp.zero_zero_real) (= B tptp.zero_zero_real)))) (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ (@ tptp.times_times_rat A) B) tptp.zero_zero_rat) (or (= A tptp.zero_zero_rat) (= B tptp.zero_zero_rat)))) (forall ((A tptp.nat) (B tptp.nat)) (= (= (@ (@ tptp.times_times_nat A) B) tptp.zero_zero_nat) (or (= A tptp.zero_zero_nat) (= B tptp.zero_zero_nat)))) (forall ((A tptp.int) (B tptp.int)) (= (= (@ (@ tptp.times_times_int A) B) tptp.zero_zero_int) (or (= A tptp.zero_zero_int) (= B tptp.zero_zero_int)))) (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex A) tptp.zero_zero_complex) tptp.zero_zero_complex)) (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real A) tptp.zero_zero_real) tptp.zero_zero_real)) (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat A) tptp.zero_zero_rat) tptp.zero_zero_rat)) (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat A) tptp.zero_zero_nat) tptp.zero_zero_nat)) (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int A) tptp.zero_zero_int) tptp.zero_zero_int)) (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex tptp.zero_zero_complex) A) tptp.zero_zero_complex)) (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real tptp.zero_zero_real) A) tptp.zero_zero_real)) (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat tptp.zero_zero_rat) A) tptp.zero_zero_rat)) (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)) (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int tptp.zero_zero_int) A) tptp.zero_zero_int)) (forall ((X tptp.nat) (Y tptp.nat) (Z3 tptp.nat)) (= (= (@ (@ tptp.times_times_nat X) Y) Z3) (= (@ (@ tptp.vEBT_VEBT_mul (@ tptp.some_nat X)) (@ tptp.some_nat Y)) (@ tptp.some_nat Z3)))) (forall ((A Bool) (B Bool)) (@ (@ tptp.vEBT_invar_vebt (@ (@ tptp.vEBT_Leaf A) B)) (@ tptp.suc tptp.zero_zero_nat))) (forall ((A tptp.real) (B tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.times_times_real C2))) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C2) (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B)))))) (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C2))) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C2) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B)))))) (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C2))) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C2) (@ (@ tptp.ord_less_eq_nat (@ _let_1 A)) (@ _let_1 B)))))) (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int C2))) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C2) (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B)))))) (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ (@ tptp.times_times_real A) B)) (or (and (@ _let_1 A) (@ _let_1 B)) (and (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real B) tptp.zero_zero_real)))))) (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (= (@ _let_1 (@ (@ tptp.times_times_rat A) B)) (or (and (@ _let_1 A) (@ _let_1 B)) (and (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat B) tptp.zero_zero_rat)))))) (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.times_times_int A) B)) (or (and (@ _let_1 A) (@ _let_1 B)) (and (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int B) tptp.zero_zero_int)))))) (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_eq_real B) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real B) A)) tptp.zero_zero_real)))) (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_eq_rat B) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat B) A)) tptp.zero_zero_rat)))) (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_eq_nat B) tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat B) A)) tptp.zero_zero_nat)))) (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_eq_int B) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int B) A)) tptp.zero_zero_int)))) (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) B) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) B)) tptp.zero_zero_real)))) (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) B) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) B)) tptp.zero_zero_rat)))) (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) B) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A) B)) tptp.zero_zero_nat)))) (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) B)) tptp.zero_zero_int)))) (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_eq_real B) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) B)) tptp.zero_zero_real)))) (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_eq_rat B) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) B)) tptp.zero_zero_rat)))) (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_eq_nat B) tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A) B)) tptp.zero_zero_nat)))) (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_eq_int B) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) B)) tptp.zero_zero_int)))) (forall ((X21 Bool) (X22 Bool) (Y21 Bool) (Y22 Bool)) (= (= (@ (@ tptp.vEBT_Leaf X21) X22) (@ (@ tptp.vEBT_Leaf Y21) Y22)) (and (= X21 Y21) (= X22 Y22)))) _let_368 (forall ((X21 Bool) (X22 Bool)) (= (@ tptp.size_size_VEBT_VEBT (@ (@ tptp.vEBT_Leaf X21) X22)) tptp.zero_zero_nat)) (forall ((A tptp.complex) (B tptp.complex)) (=> (not (= (@ (@ tptp.times_times_complex A) B) tptp.zero_zero_complex)) (and (not (= A tptp.zero_zero_complex)) (not (= B tptp.zero_zero_complex))))) (forall ((A tptp.real) (B tptp.real)) (=> (not (= (@ (@ tptp.times_times_real A) B) tptp.zero_zero_real)) (and (not (= A tptp.zero_zero_real)) (not (= B tptp.zero_zero_real))))) (forall ((A tptp.rat) (B tptp.rat)) (=> (not (= (@ (@ tptp.times_times_rat A) B) tptp.zero_zero_rat)) (and (not (= A tptp.zero_zero_rat)) (not (= B tptp.zero_zero_rat))))) (forall ((A tptp.nat) (B tptp.nat)) (=> (not (= (@ (@ tptp.times_times_nat A) B) tptp.zero_zero_nat)) (and (not (= A tptp.zero_zero_nat)) (not (= B tptp.zero_zero_nat))))) (forall ((A tptp.int) (B tptp.int)) (=> (not (= (@ (@ tptp.times_times_int A) B) tptp.zero_zero_int)) (and (not (= A tptp.zero_zero_int)) (not (= B tptp.zero_zero_int))))) (forall ((A tptp.complex) (B tptp.complex)) (=> (= (@ (@ tptp.times_times_complex A) B) tptp.zero_zero_complex) (or (= A tptp.zero_zero_complex) (= B tptp.zero_zero_complex)))) (forall ((A tptp.real) (B tptp.real)) (=> (= (@ (@ tptp.times_times_real A) B) tptp.zero_zero_real) (or (= A tptp.zero_zero_real) (= B tptp.zero_zero_real)))) (forall ((A tptp.rat) (B tptp.rat)) (=> (= (@ (@ tptp.times_times_rat A) B) tptp.zero_zero_rat) (or (= A tptp.zero_zero_rat) (= B tptp.zero_zero_rat)))) (forall ((A tptp.nat) (B tptp.nat)) (=> (= (@ (@ tptp.times_times_nat A) B) tptp.zero_zero_nat) (or (= A tptp.zero_zero_nat) (= B tptp.zero_zero_nat)))) (forall ((A tptp.int) (B tptp.int)) (=> (= (@ (@ tptp.times_times_int A) B) tptp.zero_zero_int) (or (= A tptp.zero_zero_int) (= B tptp.zero_zero_int)))) (forall ((A tptp.complex) (B tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (=> (not (= B tptp.zero_zero_complex)) (not (= (@ (@ tptp.times_times_complex A) B) tptp.zero_zero_complex))))) (forall ((A tptp.real) (B tptp.real)) (=> (not (= A tptp.zero_zero_real)) (=> (not (= B tptp.zero_zero_real)) (not (= (@ (@ tptp.times_times_real A) B) tptp.zero_zero_real))))) (forall ((A tptp.rat) (B tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (=> (not (= B tptp.zero_zero_rat)) (not (= (@ (@ tptp.times_times_rat A) B) tptp.zero_zero_rat))))) (forall ((A tptp.nat) (B tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (=> (not (= B tptp.zero_zero_nat)) (not (= (@ (@ tptp.times_times_nat A) B) tptp.zero_zero_nat))))) (forall ((A tptp.int) (B tptp.int)) (=> (not (= A tptp.zero_zero_int)) (=> (not (= B tptp.zero_zero_int)) (not (= (@ (@ tptp.times_times_int A) B) tptp.zero_zero_int))))) (forall ((C2 tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex C2))) (=> (not (= C2 tptp.zero_zero_complex)) (= (= (@ _let_1 A) (@ _let_1 B)) (= A B))))) (forall ((C2 tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real C2))) (=> (not (= C2 tptp.zero_zero_real)) (= (= (@ _let_1 A) (@ _let_1 B)) (= A B))))) (forall ((C2 tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C2))) (=> (not (= C2 tptp.zero_zero_rat)) (= (= (@ _let_1 A) (@ _let_1 B)) (= A B))))) (forall ((C2 tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C2))) (=> (not (= C2 tptp.zero_zero_nat)) (= (= (@ _let_1 A) (@ _let_1 B)) (= A B))))) (forall ((C2 tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C2))) (=> (not (= C2 tptp.zero_zero_int)) (= (= (@ _let_1 A) (@ _let_1 B)) (= A B))))) (forall ((C2 tptp.complex) (A tptp.complex) (B tptp.complex)) (=> (not (= C2 tptp.zero_zero_complex)) (= (= (@ (@ tptp.times_times_complex A) C2) (@ (@ tptp.times_times_complex B) C2)) (= A B)))) (forall ((C2 tptp.real) (A tptp.real) (B tptp.real)) (=> (not (= C2 tptp.zero_zero_real)) (= (= (@ (@ tptp.times_times_real A) C2) (@ (@ tptp.times_times_real B) C2)) (= A B)))) (forall ((C2 tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (not (= C2 tptp.zero_zero_rat)) (= (= (@ (@ tptp.times_times_rat A) C2) (@ (@ tptp.times_times_rat B) C2)) (= A B)))) (forall ((C2 tptp.nat) (A tptp.nat) (B tptp.nat)) (=> (not (= C2 tptp.zero_zero_nat)) (= (= (@ (@ tptp.times_times_nat A) C2) (@ (@ tptp.times_times_nat B) C2)) (= A B)))) (forall ((C2 tptp.int) (A tptp.int) (B tptp.int)) (=> (not (= C2 tptp.zero_zero_int)) (= (= (@ (@ tptp.times_times_int A) C2) (@ (@ tptp.times_times_int B) C2)) (= A B)))) (forall ((A tptp.real) (B tptp.real) (C2 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 C2) D) (=> (@ _let_1 B) (=> (@ _let_1 C2) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) C2)) (@ (@ tptp.times_times_real B) D)))))))) (forall ((A tptp.rat) (B tptp.rat) (C2 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 C2) D) (=> (@ _let_1 B) (=> (@ _let_1 C2) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C2)) (@ (@ tptp.times_times_rat B) D)))))))) (forall ((A tptp.nat) (B tptp.nat) (C2 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 C2) D) (=> (@ _let_1 B) (=> (@ _let_1 C2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A) C2)) (@ (@ tptp.times_times_nat B) D)))))))) (forall ((A tptp.int) (B tptp.int) (C2 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 C2) D) (=> (@ _let_1 B) (=> (@ _let_1 C2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) C2)) (@ (@ tptp.times_times_int B) D)))))))) (forall ((A tptp.real) (B tptp.real) (C2 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 C2) D) (=> (@ _let_1 A) (=> (@ _let_1 C2) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) C2)) (@ (@ tptp.times_times_real B) D)))))))) (forall ((A tptp.rat) (B tptp.rat) (C2 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 C2) D) (=> (@ _let_1 A) (=> (@ _let_1 C2) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C2)) (@ (@ tptp.times_times_rat B) D)))))))) (forall ((A tptp.nat) (B tptp.nat) (C2 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 C2) D) (=> (@ _let_1 A) (=> (@ _let_1 C2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A) C2)) (@ (@ tptp.times_times_nat B) D)))))))) (forall ((A tptp.int) (B tptp.int) (C2 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 C2) D) (=> (@ _let_1 A) (=> (@ _let_1 C2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) C2)) (@ (@ tptp.times_times_int B) D)))))))) (forall ((A tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.times_times_real A) A))) (forall ((A tptp.rat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.times_times_rat A) A))) (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.times_times_int A) A))) (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (or (and (@ _let_1 A) (@ _let_1 B)) (and (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real B) tptp.zero_zero_real))) (@ _let_1 (@ (@ tptp.times_times_real A) B))))) (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (or (and (@ _let_1 A) (@ _let_1 B)) (and (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat B) tptp.zero_zero_rat))) (@ _let_1 (@ (@ tptp.times_times_rat A) B))))) (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (or (and (@ _let_1 A) (@ _let_1 B)) (and (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int B) tptp.zero_zero_int))) (@ _let_1 (@ (@ tptp.times_times_int A) B))))) (forall ((B tptp.real) (A tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.times_times_real C2))) (=> (@ (@ tptp.ord_less_eq_real B) A) (=> (@ (@ tptp.ord_less_eq_real C2) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B)))))) (forall ((B tptp.rat) (A tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C2))) (=> (@ (@ tptp.ord_less_eq_rat B) A) (=> (@ (@ tptp.ord_less_eq_rat C2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B)))))) (forall ((B tptp.int) (A tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int C2))) (=> (@ (@ tptp.ord_less_eq_int B) A) (=> (@ (@ tptp.ord_less_eq_int C2) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B)))))) (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real B) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.times_times_real A) B))))) (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_rat B) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.times_times_rat A) B))))) (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_eq_int B) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.times_times_int A) B))))) (forall ((A tptp.real) (B tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.times_times_real C2))) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C2) (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B)))))) (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C2))) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C2) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B)))))) (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C2))) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C2) (@ (@ tptp.ord_less_eq_nat (@ _let_1 A)) (@ _let_1 B)))))) (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int C2))) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C2) (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B)))))) (forall ((B tptp.real) (A tptp.real) (C2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real B) A) (=> (@ (@ tptp.ord_less_eq_real C2) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) C2)) (@ (@ tptp.times_times_real B) C2))))) (forall ((B tptp.rat) (A tptp.rat) (C2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat B) A) (=> (@ (@ tptp.ord_less_eq_rat C2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C2)) (@ (@ tptp.times_times_rat B) C2))))) (forall ((B tptp.int) (A tptp.int) (C2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B) A) (=> (@ (@ tptp.ord_less_eq_int C2) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) C2)) (@ (@ tptp.times_times_int B) C2))))) (forall ((A tptp.real) (B tptp.real) (C2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C2) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) C2)) (@ (@ tptp.times_times_real B) C2))))) (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C2) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C2)) (@ (@ tptp.times_times_rat B) C2))))) (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A) C2)) (@ (@ tptp.times_times_nat B) C2))))) (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) C2)) (@ (@ tptp.times_times_int B) C2))))) (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) B)) tptp.zero_zero_real) (or (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_real B) tptp.zero_zero_real)) (and (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (@ _let_1 B)))))) (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) B)) tptp.zero_zero_rat) (or (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_rat B) tptp.zero_zero_rat)) (and (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat) (@ _let_1 B)))))) (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) B)) tptp.zero_zero_int) (or (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_int B) tptp.zero_zero_int)) (and (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int) (@ _let_1 B)))))) (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (or (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_real B) tptp.zero_zero_real)) (and (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (@ _let_1 B))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) B)) tptp.zero_zero_real)))) (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (or (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_rat B) tptp.zero_zero_rat)) (and (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat) (@ _let_1 B))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) B)) tptp.zero_zero_rat)))) (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (or (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_nat B) tptp.zero_zero_nat)) (and (@ (@ tptp.ord_less_eq_nat A) tptp.zero_zero_nat) (@ _let_1 B))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A) B)) tptp.zero_zero_nat)))) (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (or (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_int B) tptp.zero_zero_int)) (and (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int) (@ _let_1 B))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) B)) tptp.zero_zero_int)))) (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_times_real A) B)))))) (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_times_rat A) B)))))) (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_times_nat A) B)))))) (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_times_int A) B)))))) _let_367 (forall ((T tptp.vEBT_VEBT) (D tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) D) (@ (@ tptp.vEBT_VEBT_valid T) D))) (forall ((T tptp.vEBT_VEBT) (D tptp.nat)) (=> (@ (@ tptp.vEBT_VEBT_valid T) D) (@ (@ tptp.vEBT_invar_vebt T) D))) (forall ((T tptp.vEBT_VEBT)) (= (@ (@ tptp.vEBT_invar_vebt T) tptp.one_one_nat) (exists ((A5 Bool) (B4 Bool)) (= T (@ (@ tptp.vEBT_Leaf A5) B4))))) (forall ((T tptp.vEBT_VEBT)) (=> (@ (@ tptp.vEBT_invar_vebt T) tptp.one_one_nat) (exists ((A3 Bool) (B3 Bool)) (= T (@ (@ tptp.vEBT_Leaf A3) B3))))) (forall ((T tptp.vEBT_VEBT) (N tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (= N tptp.one_one_nat) (exists ((A3 Bool) (B3 Bool)) (= T (@ (@ tptp.vEBT_Leaf A3) B3)))))) (forall ((K2 tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K2))) (= (= (@ _let_1 M2) (@ _let_1 N)) (or (= K2 tptp.zero_zero_nat) (= M2 N))))) (forall ((T tptp.vEBT_VEBT) (N tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))) (forall ((X21 Bool) (X22 Bool)) (= (@ tptp.vEBT_size_VEBT (@ (@ tptp.vEBT_Leaf X21) X22)) tptp.zero_zero_nat)) (forall ((Tree tptp.vEBT_VEBT) (N tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt Tree) (@ tptp.suc (@ tptp.suc N))) (exists ((Info tptp.option4927543243414619207at_nat) (TreeList tptp.list_VEBT_VEBT) (S tptp.vEBT_VEBT)) (= Tree (@ (@ (@ (@ tptp.vEBT_Node Info) (@ tptp.suc (@ tptp.suc N))) TreeList) S))))) (= _let_344 (@ tptp.vEBT_VEBT_set_vebt tptp.sa)) (forall ((Info2 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 Info2) Deg) TreeList2) Summary)) N) (= Deg N))) (forall ((X11 tptp.option4927543243414619207at_nat) (X12 tptp.nat) (X13 tptp.list_VEBT_VEBT) (X14 tptp.vEBT_VEBT) (Y11 tptp.option4927543243414619207at_nat) (Y12 tptp.nat) (Y13 tptp.list_VEBT_VEBT) (Y14 tptp.vEBT_VEBT)) (= (= (@ (@ (@ (@ tptp.vEBT_Node X11) X12) X13) X14) (@ (@ (@ (@ tptp.vEBT_Node Y11) Y12) Y13) Y14)) (and (= X11 Y11) (= X12 Y12) (= X13 Y13) (= X14 Y14)))) (forall ((N tptp.nat)) (= (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)) (= N tptp.zero_zero_nat))) (forall ((A tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger tptp.one_one_Code_integer) A) A)) (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex tptp.one_one_complex) A) A)) (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real tptp.one_one_real) A) A)) (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat tptp.one_one_rat) A) A)) (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.one_one_nat) A) A)) (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int tptp.one_one_int) A) A)) (forall ((A tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger A) tptp.one_one_Code_integer) A)) (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex A) tptp.one_one_complex) A)) (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real A) tptp.one_one_real) A)) (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat A) tptp.one_one_rat) A)) (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat A) tptp.one_one_nat) A)) (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int A) tptp.one_one_int) A)) (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.suc M2)) (@ tptp.suc N)) (@ (@ tptp.ord_less_nat M2) N))) (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) N) (@ (@ tptp.ord_less_nat (@ tptp.suc M2)) (@ tptp.suc N)))) (forall ((N tptp.nat)) (@ (@ tptp.ord_less_nat N) (@ tptp.suc N))) (forall ((A tptp.nat)) (= (not (= A tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A))) (forall ((N tptp.nat)) (= (not (= N tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))) (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) tptp.zero_zero_nat))) (forall ((M2 tptp.nat) (N tptp.nat)) (= (= tptp.one_one_nat (@ (@ tptp.times_times_nat M2) N)) (and (= M2 tptp.one_one_nat) (= N tptp.one_one_nat)))) (forall ((M2 tptp.nat) (N tptp.nat)) (= (= (@ (@ tptp.times_times_nat M2) N) tptp.one_one_nat) (and (= M2 tptp.one_one_nat) (= N tptp.one_one_nat)))) (@ (@ tptp.vEBT_invar_vebt tptp.summary2) tptp.m) (forall ((C2 tptp.code_integer) (B tptp.code_integer)) (= (= C2 (@ (@ tptp.times_3573771949741848930nteger C2) B)) (or (= C2 tptp.zero_z3403309356797280102nteger) (= B tptp.one_one_Code_integer)))) (forall ((C2 tptp.complex) (B tptp.complex)) (= (= C2 (@ (@ tptp.times_times_complex C2) B)) (or (= C2 tptp.zero_zero_complex) (= B tptp.one_one_complex)))) (forall ((C2 tptp.real) (B tptp.real)) (= (= C2 (@ (@ tptp.times_times_real C2) B)) (or (= C2 tptp.zero_zero_real) (= B tptp.one_one_real)))) (forall ((C2 tptp.rat) (B tptp.rat)) (= (= C2 (@ (@ tptp.times_times_rat C2) B)) (or (= C2 tptp.zero_zero_rat) (= B tptp.one_one_rat)))) (forall ((C2 tptp.int) (B tptp.int)) (= (= C2 (@ (@ tptp.times_times_int C2) B)) (or (= C2 tptp.zero_zero_int) (= B tptp.one_one_int)))) (forall ((C2 tptp.code_integer) (A tptp.code_integer)) (= (= (@ (@ tptp.times_3573771949741848930nteger C2) A) C2) (or (= C2 tptp.zero_z3403309356797280102nteger) (= A tptp.one_one_Code_integer)))) (forall ((C2 tptp.complex) (A tptp.complex)) (= (= (@ (@ tptp.times_times_complex C2) A) C2) (or (= C2 tptp.zero_zero_complex) (= A tptp.one_one_complex)))) (forall ((C2 tptp.real) (A tptp.real)) (= (= (@ (@ tptp.times_times_real C2) A) C2) (or (= C2 tptp.zero_zero_real) (= A tptp.one_one_real)))) (forall ((C2 tptp.rat) (A tptp.rat)) (= (= (@ (@ tptp.times_times_rat C2) A) C2) (or (= C2 tptp.zero_zero_rat) (= A tptp.one_one_rat)))) (forall ((C2 tptp.int) (A tptp.int)) (= (= (@ (@ tptp.times_times_int C2) A) C2) (or (= C2 tptp.zero_zero_int) (= A tptp.one_one_int)))) (forall ((C2 tptp.code_integer) (B tptp.code_integer)) (= (= C2 (@ (@ tptp.times_3573771949741848930nteger B) C2)) (or (= C2 tptp.zero_z3403309356797280102nteger) (= B tptp.one_one_Code_integer)))) (forall ((C2 tptp.complex) (B tptp.complex)) (= (= C2 (@ (@ tptp.times_times_complex B) C2)) (or (= C2 tptp.zero_zero_complex) (= B tptp.one_one_complex)))) (forall ((C2 tptp.real) (B tptp.real)) (= (= C2 (@ (@ tptp.times_times_real B) C2)) (or (= C2 tptp.zero_zero_real) (= B tptp.one_one_real)))) (forall ((C2 tptp.rat) (B tptp.rat)) (= (= C2 (@ (@ tptp.times_times_rat B) C2)) (or (= C2 tptp.zero_zero_rat) (= B tptp.one_one_rat)))) (forall ((C2 tptp.int) (B tptp.int)) (= (= C2 (@ (@ tptp.times_times_int B) C2)) (or (= C2 tptp.zero_zero_int) (= B tptp.one_one_int)))) (forall ((A tptp.code_integer) (C2 tptp.code_integer)) (= (= (@ (@ tptp.times_3573771949741848930nteger A) C2) C2) (or (= C2 tptp.zero_z3403309356797280102nteger) (= A tptp.one_one_Code_integer)))) (forall ((A tptp.complex) (C2 tptp.complex)) (= (= (@ (@ tptp.times_times_complex A) C2) C2) (or (= C2 tptp.zero_zero_complex) (= A tptp.one_one_complex)))) (forall ((A tptp.real) (C2 tptp.real)) (= (= (@ (@ tptp.times_times_real A) C2) C2) (or (= C2 tptp.zero_zero_real) (= A tptp.one_one_real)))) (forall ((A tptp.rat) (C2 tptp.rat)) (= (= (@ (@ tptp.times_times_rat A) C2) C2) (or (= C2 tptp.zero_zero_rat) (= A tptp.one_one_rat)))) (forall ((A tptp.int) (C2 tptp.int)) (= (= (@ (@ tptp.times_times_int A) C2) C2) (or (= C2 tptp.zero_zero_int) (= A tptp.one_one_int)))) (forall ((N tptp.nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.suc N))) (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_nat N) (@ tptp.suc tptp.zero_zero_nat)) (= N tptp.zero_zero_nat))) (forall ((K2 tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K2))) (= (@ (@ tptp.ord_less_nat (@ _let_1 M2)) (@ _let_1 N)) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K2) (@ (@ tptp.ord_less_nat M2) N))))) (forall ((M2 tptp.nat) (K2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat M2) K2)) (@ (@ tptp.times_times_nat N) K2)) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K2) (@ (@ tptp.ord_less_nat M2) N)))) (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ (@ tptp.times_times_nat M2) N)) (and (@ _let_1 M2) (@ _let_1 N))))) (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_nat N) tptp.one_one_nat) (= N tptp.zero_zero_nat))) (forall ((K2 tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K2))) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 M2)) (@ _let_1 N)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K2) (@ (@ tptp.ord_less_eq_nat M2) N))))) (forall ((M2 tptp.nat) (K2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat M2) K2)) (@ (@ tptp.times_times_nat N) K2)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K2) (@ (@ tptp.ord_less_eq_nat M2) N)))) (forall ((T tptp.vEBT_VEBT) (N tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (= (@ tptp.vEBT_set_vebt T) (@ tptp.vEBT_VEBT_set_vebt T)))) (forall ((X tptp.real) (Y tptp.real)) (=> (not (= X Y)) (=> (not (@ (@ tptp.ord_less_real X) Y)) (@ (@ tptp.ord_less_real Y) X)))) (forall ((X tptp.rat) (Y tptp.rat)) (=> (not (= X Y)) (=> (not (@ (@ tptp.ord_less_rat X) Y)) (@ (@ tptp.ord_less_rat Y) X)))) (forall ((X tptp.int) (Y tptp.int)) (=> (not (= X Y)) (=> (not (@ (@ tptp.ord_less_int X) Y)) (@ (@ tptp.ord_less_int Y) X)))) (forall ((X tptp.real)) (exists ((Y3 tptp.real)) (@ (@ tptp.ord_less_real Y3) X))) (forall ((X tptp.rat)) (exists ((Y3 tptp.rat)) (@ (@ tptp.ord_less_rat Y3) X))) (forall ((X tptp.int)) (exists ((Y3 tptp.int)) (@ (@ tptp.ord_less_int Y3) X))) (forall ((X tptp.real)) (exists ((X_12 tptp.real)) (@ (@ tptp.ord_less_real X) X_12))) (forall ((X tptp.rat)) (exists ((X_12 tptp.rat)) (@ (@ tptp.ord_less_rat X) X_12))) (forall ((X tptp.nat)) (exists ((X_12 tptp.nat)) (@ (@ tptp.ord_less_nat X) X_12))) (forall ((X tptp.int)) (exists ((X_12 tptp.int)) (@ (@ tptp.ord_less_int X) X_12))) (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X) Y) (exists ((Z tptp.real)) (and (@ (@ tptp.ord_less_real X) Z) (@ (@ tptp.ord_less_real Z) Y))))) (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat X) Y) (exists ((Z tptp.rat)) (and (@ (@ tptp.ord_less_rat X) Z) (@ (@ tptp.ord_less_rat Z) Y))))) (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X) Y) (not (= X Y)))) (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat X) Y) (not (= X Y)))) (forall ((X tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_num X) Y) (not (= X Y)))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Y) (not (= X Y)))) (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int X) Y) (not (= X Y)))) (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (not (@ (@ tptp.ord_less_real B) A)))) (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (not (@ (@ tptp.ord_less_rat B) A)))) (forall ((A tptp.num) (B tptp.num)) (=> (@ (@ tptp.ord_less_num A) B) (not (@ (@ tptp.ord_less_num B) A)))) (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (not (@ (@ tptp.ord_less_nat B) A)))) (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (not (@ (@ tptp.ord_less_int B) A)))) (forall ((A tptp.real) (B tptp.real) (C2 tptp.real)) (=> (= A B) (=> (@ (@ tptp.ord_less_real B) C2) (@ (@ tptp.ord_less_real A) C2)))) (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (=> (= A B) (=> (@ (@ tptp.ord_less_rat B) C2) (@ (@ tptp.ord_less_rat A) C2)))) (forall ((A tptp.num) (B tptp.num) (C2 tptp.num)) (=> (= A B) (=> (@ (@ tptp.ord_less_num B) C2) (@ (@ tptp.ord_less_num A) C2)))) (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (=> (= A B) (=> (@ (@ tptp.ord_less_nat B) C2) (@ (@ tptp.ord_less_nat A) C2)))) (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (=> (= A B) (=> (@ (@ tptp.ord_less_int B) C2) (@ (@ tptp.ord_less_int A) C2)))) (forall ((A tptp.real) (B tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real A))) (=> (@ _let_1 B) (=> (= B C2) (@ _let_1 C2))))) (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A))) (=> (@ _let_1 B) (=> (= B C2) (@ _let_1 C2))))) (forall ((A tptp.num) (B tptp.num) (C2 tptp.num)) (let ((_let_1 (@ tptp.ord_less_num A))) (=> (@ _let_1 B) (=> (= B C2) (@ _let_1 C2))))) (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat A))) (=> (@ _let_1 B) (=> (= B C2) (@ _let_1 C2))))) (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int A))) (=> (@ _let_1 B) (=> (= B C2) (@ _let_1 C2))))) (forall ((P2 (-> tptp.nat Bool)) (A tptp.nat)) (=> (forall ((X3 tptp.nat)) (=> (forall ((Y6 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Y6) X3) (@ P2 Y6))) (@ P2 X3))) (@ P2 A))) (forall ((Y tptp.real) (X tptp.real)) (=> (not (@ (@ tptp.ord_less_real Y) X)) (= (not (@ (@ tptp.ord_less_real X) Y)) (= X Y)))) (forall ((Y tptp.rat) (X tptp.rat)) (=> (not (@ (@ tptp.ord_less_rat Y) X)) (= (not (@ (@ tptp.ord_less_rat X) Y)) (= X Y)))) (forall ((Y tptp.num) (X tptp.num)) (=> (not (@ (@ tptp.ord_less_num Y) X)) (= (not (@ (@ tptp.ord_less_num X) Y)) (= X Y)))) (forall ((Y tptp.nat) (X tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat Y) X)) (= (not (@ (@ tptp.ord_less_nat X) Y)) (= X Y)))) (forall ((Y tptp.int) (X tptp.int)) (=> (not (@ (@ tptp.ord_less_int Y) X)) (= (not (@ (@ tptp.ord_less_int X) Y)) (= X Y)))) (forall ((X tptp.real) (Y tptp.real)) (=> (not (@ (@ tptp.ord_less_real X) Y)) (=> (not (= X Y)) (@ (@ tptp.ord_less_real Y) X)))) (forall ((X tptp.rat) (Y tptp.rat)) (=> (not (@ (@ tptp.ord_less_rat X) Y)) (=> (not (= X Y)) (@ (@ tptp.ord_less_rat Y) X)))) (forall ((X tptp.num) (Y tptp.num)) (=> (not (@ (@ tptp.ord_less_num X) Y)) (=> (not (= X Y)) (@ (@ tptp.ord_less_num Y) X)))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat X) Y)) (=> (not (= X Y)) (@ (@ tptp.ord_less_nat Y) X)))) (forall ((X tptp.int) (Y tptp.int)) (=> (not (@ (@ tptp.ord_less_int X) Y)) (=> (not (= X Y)) (@ (@ tptp.ord_less_int Y) X)))) (forall ((B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real B) A) (not (@ (@ tptp.ord_less_real A) B)))) (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat B) A) (not (@ (@ tptp.ord_less_rat A) B)))) (forall ((B tptp.num) (A tptp.num)) (=> (@ (@ tptp.ord_less_num B) A) (not (@ (@ tptp.ord_less_num A) B)))) (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat B) A) (not (@ (@ tptp.ord_less_nat A) B)))) (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int B) A) (not (@ (@ tptp.ord_less_int A) B)))) (forall ((A tptp.real)) (not (@ (@ tptp.ord_less_real A) A))) (forall ((A tptp.rat)) (not (@ (@ tptp.ord_less_rat A) A))) (forall ((A tptp.num)) (not (@ (@ tptp.ord_less_num A) A))) (forall ((A tptp.nat)) (not (@ (@ tptp.ord_less_nat A) A))) (forall ((A tptp.int)) (not (@ (@ tptp.ord_less_int A) A))) (= (lambda ((P3 (-> tptp.nat Bool))) (exists ((X6 tptp.nat)) (@ P3 X6))) (lambda ((P4 (-> tptp.nat Bool))) (exists ((N4 tptp.nat)) (and (@ P4 N4) (forall ((M6 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M6) N4) (not (@ P4 M6)))))))) (forall ((P2 (-> tptp.real tptp.real Bool)) (A tptp.real) (B tptp.real)) (=> (forall ((A3 tptp.real) (B3 tptp.real)) (=> (@ (@ tptp.ord_less_real A3) B3) (@ (@ P2 A3) B3))) (=> (forall ((A3 tptp.real)) (@ (@ P2 A3) A3)) (=> (forall ((A3 tptp.real) (B3 tptp.real)) (=> (@ (@ P2 B3) A3) (@ (@ P2 A3) B3))) (@ (@ P2 A) B))))) (forall ((P2 (-> tptp.rat tptp.rat Bool)) (A tptp.rat) (B tptp.rat)) (=> (forall ((A3 tptp.rat) (B3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat A3) B3) (@ (@ P2 A3) B3))) (=> (forall ((A3 tptp.rat)) (@ (@ P2 A3) A3)) (=> (forall ((A3 tptp.rat) (B3 tptp.rat)) (=> (@ (@ P2 B3) A3) (@ (@ P2 A3) B3))) (@ (@ P2 A) B))))) (forall ((P2 (-> tptp.num tptp.num Bool)) (A tptp.num) (B tptp.num)) (=> (forall ((A3 tptp.num) (B3 tptp.num)) (=> (@ (@ tptp.ord_less_num A3) B3) (@ (@ P2 A3) B3))) (=> (forall ((A3 tptp.num)) (@ (@ P2 A3) A3)) (=> (forall ((A3 tptp.num) (B3 tptp.num)) (=> (@ (@ P2 B3) A3) (@ (@ P2 A3) B3))) (@ (@ P2 A) B))))) (forall ((P2 (-> tptp.nat tptp.nat Bool)) (A tptp.nat) (B tptp.nat)) (=> (forall ((A3 tptp.nat) (B3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A3) B3) (@ (@ P2 A3) B3))) (=> (forall ((A3 tptp.nat)) (@ (@ P2 A3) A3)) (=> (forall ((A3 tptp.nat) (B3 tptp.nat)) (=> (@ (@ P2 B3) A3) (@ (@ P2 A3) B3))) (@ (@ P2 A) B))))) (forall ((P2 (-> tptp.int tptp.int Bool)) (A tptp.int) (B tptp.int)) (=> (forall ((A3 tptp.int) (B3 tptp.int)) (=> (@ (@ tptp.ord_less_int A3) B3) (@ (@ P2 A3) B3))) (=> (forall ((A3 tptp.int)) (@ (@ P2 A3) A3)) (=> (forall ((A3 tptp.int) (B3 tptp.int)) (=> (@ (@ P2 B3) A3) (@ (@ P2 A3) B3))) (@ (@ P2 A) B))))) (forall ((A tptp.real) (B tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_real B) C2) (@ _let_1 C2))))) (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_rat B) C2) (@ _let_1 C2))))) (forall ((A tptp.num) (B tptp.num) (C2 tptp.num)) (let ((_let_1 (@ tptp.ord_less_num A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_num B) C2) (@ _let_1 C2))))) (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_nat B) C2) (@ _let_1 C2))))) (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_int B) C2) (@ _let_1 C2))))) (forall ((X tptp.real) (Y tptp.real)) (= (not (@ (@ tptp.ord_less_real X) Y)) (or (@ (@ tptp.ord_less_real Y) X) (= X Y)))) (forall ((X tptp.rat) (Y tptp.rat)) (= (not (@ (@ tptp.ord_less_rat X) Y)) (or (@ (@ tptp.ord_less_rat Y) X) (= X Y)))) (forall ((X tptp.num) (Y tptp.num)) (= (not (@ (@ tptp.ord_less_num X) Y)) (or (@ (@ tptp.ord_less_num Y) X) (= X Y)))) (forall ((X tptp.nat) (Y tptp.nat)) (= (not (@ (@ tptp.ord_less_nat X) Y)) (or (@ (@ tptp.ord_less_nat Y) X) (= X Y)))) (forall ((X tptp.int) (Y tptp.int)) (= (not (@ (@ tptp.ord_less_int X) Y)) (or (@ (@ tptp.ord_less_int Y) X) (= X Y)))) (forall ((B tptp.real) (A tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real C2))) (=> (@ (@ tptp.ord_less_real B) A) (=> (@ _let_1 B) (@ _let_1 A))))) (forall ((B tptp.rat) (A tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat C2))) (=> (@ (@ tptp.ord_less_rat B) A) (=> (@ _let_1 B) (@ _let_1 A))))) (forall ((B tptp.num) (A tptp.num) (C2 tptp.num)) (let ((_let_1 (@ tptp.ord_less_num C2))) (=> (@ (@ tptp.ord_less_num B) A) (=> (@ _let_1 B) (@ _let_1 A))))) (forall ((B tptp.nat) (A tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat C2))) (=> (@ (@ tptp.ord_less_nat B) A) (=> (@ _let_1 B) (@ _let_1 A))))) (forall ((B tptp.int) (A tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int C2))) (=> (@ (@ tptp.ord_less_int B) A) (=> (@ _let_1 B) (@ _let_1 A))))) (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (not (= A B)))) (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (not (= A B)))) (forall 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(=> (forall ((X3 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Y3) (@ (@ tptp.ord_less_rat (@ F2 X3)) (@ F2 Y3)))) (@ (@ tptp.ord_less_rat (@ F2 A)) C2))))) (forall ((A tptp.real) (B tptp.real) (F2 (-> tptp.real tptp.num)) (C2 tptp.num)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_num (@ F2 B)) C2) (=> (forall ((X3 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Y3) (@ (@ tptp.ord_less_num (@ F2 X3)) (@ F2 Y3)))) (@ (@ tptp.ord_less_num (@ F2 A)) C2))))) (forall ((A tptp.real) (B tptp.real) (F2 (-> tptp.real tptp.nat)) (C2 tptp.nat)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_nat (@ F2 B)) C2) (=> (forall ((X3 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Y3) (@ (@ tptp.ord_less_nat (@ F2 X3)) (@ F2 Y3)))) (@ (@ tptp.ord_less_nat (@ F2 A)) C2))))) (forall ((A tptp.real) (B tptp.real) (F2 (-> tptp.real tptp.int)) (C2 tptp.int)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_int (@ F2 B)) C2) (=> (forall ((X3 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Y3) (@ (@ tptp.ord_less_int (@ F2 X3)) (@ F2 Y3)))) (@ (@ tptp.ord_less_int (@ F2 A)) C2))))) (forall ((A tptp.rat) (B tptp.rat) (F2 (-> tptp.rat tptp.real)) (C2 tptp.real)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_real (@ F2 B)) C2) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y3) (@ (@ tptp.ord_less_real (@ F2 X3)) (@ F2 Y3)))) (@ (@ tptp.ord_less_real (@ F2 A)) C2))))) (forall ((A tptp.rat) (B tptp.rat) (F2 (-> tptp.rat tptp.rat)) (C2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_rat (@ F2 B)) C2) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y3) (@ (@ tptp.ord_less_rat (@ F2 X3)) (@ F2 Y3)))) (@ (@ tptp.ord_less_rat (@ F2 A)) C2))))) (forall ((A tptp.rat) (B tptp.rat) (F2 (-> tptp.rat tptp.num)) (C2 tptp.num)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_num (@ F2 B)) C2) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y3) (@ (@ tptp.ord_less_num (@ F2 X3)) (@ F2 Y3)))) (@ (@ tptp.ord_less_num (@ F2 A)) C2))))) (forall ((A tptp.rat) (B tptp.rat) (F2 (-> tptp.rat tptp.nat)) (C2 tptp.nat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_nat (@ F2 B)) C2) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y3) (@ (@ tptp.ord_less_nat (@ F2 X3)) (@ F2 Y3)))) (@ (@ tptp.ord_less_nat (@ F2 A)) C2))))) (forall ((A tptp.rat) (B tptp.rat) (F2 (-> tptp.rat tptp.int)) (C2 tptp.int)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_int (@ F2 B)) C2) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y3) (@ (@ tptp.ord_less_int (@ F2 X3)) (@ F2 Y3)))) (@ (@ tptp.ord_less_int (@ F2 A)) C2))))) (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X) Y) (not (@ (@ tptp.ord_less_real Y) X)))) (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat X) Y) (not (@ (@ tptp.ord_less_rat Y) X)))) (forall ((X tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_num X) Y) (not (@ (@ tptp.ord_less_num Y) X)))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Y) (not (@ (@ tptp.ord_less_nat Y) X)))) (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int X) Y) (not (@ (@ tptp.ord_less_int Y) X)))) (forall ((X tptp.real) (Y tptp.real) (P2 Bool)) (=> (@ (@ tptp.ord_less_real X) Y) (=> (@ (@ tptp.ord_less_real Y) X) P2))) (forall ((X tptp.rat) (Y tptp.rat) (P2 Bool)) (=> (@ (@ tptp.ord_less_rat X) Y) (=> (@ (@ tptp.ord_less_rat Y) X) P2))) (forall ((X tptp.num) (Y tptp.num) (P2 Bool)) (=> (@ (@ tptp.ord_less_num X) Y) (=> (@ (@ tptp.ord_less_num Y) X) P2))) (forall ((X tptp.nat) (Y tptp.nat) (P2 Bool)) (=> (@ (@ tptp.ord_less_nat X) Y) (=> (@ (@ tptp.ord_less_nat Y) X) P2))) (forall ((X tptp.int) (Y tptp.int) (P2 Bool)) (=> (@ (@ tptp.ord_less_int X) Y) (=> (@ (@ tptp.ord_less_int Y) X) P2))) (forall ((X tptp.real) (Y tptp.real)) (or (@ (@ tptp.ord_less_real X) Y) (= X Y) (@ (@ tptp.ord_less_real Y) X))) (forall ((X tptp.rat) (Y tptp.rat)) (or (@ (@ tptp.ord_less_rat X) Y) (= X Y) (@ (@ tptp.ord_less_rat Y) X))) (forall ((X tptp.num) (Y tptp.num)) (or (@ (@ tptp.ord_less_num X) Y) (= X Y) (@ (@ tptp.ord_less_num Y) X))) (forall ((X tptp.nat) (Y tptp.nat)) (or (@ (@ tptp.ord_less_nat X) Y) (= X Y) (@ (@ tptp.ord_less_nat Y) X))) (forall ((X tptp.int) (Y tptp.int)) (or (@ (@ tptp.ord_less_int X) Y) (= X Y) (@ (@ tptp.ord_less_int Y) X))) (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X) Y) (not (= X Y)))) (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat X) Y) (not (= X Y)))) (forall ((X tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_num X) Y) (not (= X Y)))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Y) (not (= X Y)))) (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int X) Y) (not (= X Y)))) (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X) Y) (not (= Y X)))) (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat X) Y) (not (= Y X)))) (forall ((X tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_num X) Y) (not (= Y X)))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Y) (not (= Y X)))) (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int X) Y) (not (= Y X)))) (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X) Y) (not (@ (@ tptp.ord_less_real Y) X)))) (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat X) Y) (not (@ (@ tptp.ord_less_rat Y) X)))) (forall ((X tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_num X) Y) (not (@ (@ tptp.ord_less_num Y) X)))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Y) (not (@ (@ tptp.ord_less_nat Y) X)))) (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int X) Y) (not (@ (@ tptp.ord_less_int Y) X)))) (not (@ _let_192 tptp.one_one_Code_integer)) (not (@ _let_193 tptp.one_one_real)) (not (@ _let_191 tptp.one_one_rat)) (not (@ _let_365 tptp.one_one_nat)) (not (@ _let_194 tptp.one_one_int)) (forall ((X tptp.code_integer)) (= (= tptp.one_one_Code_integer X) (= X tptp.one_one_Code_integer))) (forall ((X tptp.complex)) (= (= tptp.one_one_complex X) (= X tptp.one_one_complex))) (forall ((X tptp.real)) (= (= tptp.one_one_real X) (= X tptp.one_one_real))) (forall ((X tptp.nat)) (= (= tptp.one_one_nat X) (= X tptp.one_one_nat))) (forall ((X tptp.int)) (= (= tptp.one_one_int X) (= X tptp.one_one_int))) _let_364 _let_363 _let_362 _let_361 _let_360 (not (@ _let_192 tptp.zero_z3403309356797280102nteger)) (not (@ _let_193 tptp.zero_zero_real)) (not (@ _let_191 tptp.zero_zero_rat)) _let_366 (not (@ _let_194 tptp.zero_zero_int)) _let_364 _let_363 _let_362 _let_361 _let_360 (forall ((F2 (-> tptp.nat tptp.real)) (N tptp.nat) (M2 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_real (@ F2 N3)) (@ F2 (@ tptp.suc N3)))) (= (@ (@ tptp.ord_less_real (@ F2 N)) (@ F2 M2)) (@ (@ tptp.ord_less_nat N) M2)))) (forall ((F2 (-> tptp.nat tptp.rat)) (N tptp.nat) (M2 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_rat (@ F2 N3)) (@ F2 (@ tptp.suc N3)))) (= (@ (@ tptp.ord_less_rat (@ F2 N)) (@ F2 M2)) (@ (@ tptp.ord_less_nat N) M2)))) (forall ((F2 (-> tptp.nat tptp.num)) (N tptp.nat) (M2 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_num (@ F2 N3)) (@ F2 (@ tptp.suc N3)))) (= (@ (@ tptp.ord_less_num (@ F2 N)) (@ F2 M2)) (@ (@ tptp.ord_less_nat N) M2)))) (forall ((F2 (-> tptp.nat tptp.nat)) (N tptp.nat) (M2 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_nat (@ F2 N3)) (@ F2 (@ tptp.suc N3)))) (= (@ (@ tptp.ord_less_nat (@ F2 N)) (@ F2 M2)) (@ (@ tptp.ord_less_nat N) M2)))) (forall ((F2 (-> tptp.nat tptp.int)) (N tptp.nat) (M2 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_int (@ F2 N3)) (@ F2 (@ tptp.suc N3)))) (= (@ (@ tptp.ord_less_int (@ F2 N)) (@ F2 M2)) (@ (@ tptp.ord_less_nat N) M2)))) (forall ((F2 (-> tptp.nat tptp.real)) (N tptp.nat) (N2 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_real (@ F2 N3)) (@ F2 (@ tptp.suc N3)))) (=> (@ (@ tptp.ord_less_nat N) N2) (@ (@ tptp.ord_less_real (@ F2 N)) (@ F2 N2))))) (forall ((F2 (-> tptp.nat tptp.rat)) (N tptp.nat) (N2 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_rat (@ F2 N3)) (@ F2 (@ tptp.suc N3)))) (=> (@ (@ tptp.ord_less_nat N) N2) (@ (@ tptp.ord_less_rat (@ F2 N)) (@ F2 N2))))) (forall ((F2 (-> tptp.nat tptp.num)) (N tptp.nat) (N2 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_num (@ F2 N3)) (@ F2 (@ tptp.suc N3)))) (=> (@ (@ tptp.ord_less_nat N) N2) (@ (@ tptp.ord_less_num (@ F2 N)) (@ F2 N2))))) (forall ((F2 (-> tptp.nat tptp.nat)) (N tptp.nat) (N2 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_nat (@ F2 N3)) (@ F2 (@ tptp.suc N3)))) (=> (@ (@ tptp.ord_less_nat N) N2) (@ (@ tptp.ord_less_nat (@ F2 N)) (@ F2 N2))))) (forall ((F2 (-> tptp.nat tptp.int)) (N tptp.nat) (N2 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_int (@ F2 N3)) (@ F2 (@ tptp.suc N3)))) (=> (@ (@ tptp.ord_less_nat N) N2) (@ (@ tptp.ord_less_int (@ F2 N)) (@ F2 N2))))) (forall ((M2 tptp.code_integer) (N tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer))) (=> (@ _let_1 M2) (=> (@ _let_1 N) (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger M2) N)))))) (forall ((M2 tptp.real) (N tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ _let_1 M2) (=> (@ _let_1 N) (@ _let_1 (@ (@ tptp.times_times_real M2) N)))))) (forall ((M2 tptp.rat) (N tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.one_one_rat))) (=> (@ _let_1 M2) (=> (@ _let_1 N) (@ _let_1 (@ (@ tptp.times_times_rat M2) N)))))) (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.one_one_nat))) (=> (@ _let_1 M2) (=> (@ _let_1 N) (@ _let_1 (@ (@ tptp.times_times_nat M2) N)))))) (forall ((M2 tptp.int) (N tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.one_one_int))) (=> (@ _let_1 M2) (=> (@ _let_1 N) (@ _let_1 (@ (@ tptp.times_times_int M2) N)))))) (forall ((Uu Bool) (Uv Bool) (D tptp.nat)) (= (@ (@ tptp.vEBT_VEBT_valid (@ (@ tptp.vEBT_Leaf Uu) Uv)) D) (= D tptp.one_one_nat))) (forall ((N tptp.nat) (P2 (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ P2 tptp.one_one_nat) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N3) (=> (@ P2 N3) (@ P2 (@ tptp.suc N3))))) (@ P2 N))))) (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) Y) (or (@ (@ tptp.ord_less_real X) Y) (= X Y)))) (forall ((X tptp.set_nat) (Y tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat X) Y) (or (@ (@ tptp.ord_less_set_nat X) Y) (= X Y)))) (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X) Y) (or (@ (@ tptp.ord_less_rat X) Y) (= X Y)))) (forall ((X tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X) Y) (or (@ (@ tptp.ord_less_num X) Y) (= X Y)))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X) Y) (or (@ (@ tptp.ord_less_nat X) Y) (= X Y)))) (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X) Y) (or (@ (@ tptp.ord_less_int X) Y) (= X Y)))) (forall ((X tptp.real) (Y tptp.real)) (or (@ (@ tptp.ord_less_eq_real X) Y) (@ (@ tptp.ord_less_real Y) X))) (forall ((X tptp.rat) (Y tptp.rat)) (or (@ (@ tptp.ord_less_eq_rat X) Y) (@ (@ tptp.ord_less_rat Y) X))) (forall ((X tptp.num) (Y tptp.num)) (or (@ (@ tptp.ord_less_eq_num X) Y) (@ (@ tptp.ord_less_num Y) X))) (forall ((X tptp.nat) (Y tptp.nat)) (or (@ (@ tptp.ord_less_eq_nat X) Y) (@ (@ tptp.ord_less_nat Y) X))) (forall ((X tptp.int) (Y tptp.int)) (or (@ (@ tptp.ord_less_eq_int X) Y) (@ (@ tptp.ord_less_int Y) X))) (forall ((A tptp.real) (B tptp.real) (F2 (-> tptp.real tptp.real)) (C2 tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_eq_real (@ F2 B)) C2) (=> (forall ((X3 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Y3) (@ (@ tptp.ord_less_real (@ F2 X3)) (@ F2 Y3)))) (@ (@ tptp.ord_less_real (@ F2 A)) C2))))) (forall ((A tptp.rat) (B tptp.rat) (F2 (-> tptp.rat tptp.real)) (C2 tptp.real)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_eq_real (@ F2 B)) C2) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y3) (@ (@ tptp.ord_less_real (@ F2 X3)) (@ F2 Y3)))) (@ (@ tptp.ord_less_real (@ F2 A)) C2))))) (forall ((A tptp.num) (B tptp.num) (F2 (-> tptp.num tptp.real)) (C2 tptp.real)) (=> (@ (@ tptp.ord_less_num A) B) (=> (@ (@ tptp.ord_less_eq_real (@ F2 B)) C2) (=> (forall ((X3 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_num X3) Y3) (@ (@ tptp.ord_less_real (@ F2 X3)) (@ F2 Y3)))) (@ (@ tptp.ord_less_real (@ F2 A)) C2))))) (forall ((A tptp.nat) (B tptp.nat) (F2 (-> tptp.nat tptp.real)) (C2 tptp.real)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_eq_real (@ F2 B)) C2) (=> (forall ((X3 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Y3) (@ (@ tptp.ord_less_real (@ F2 X3)) (@ F2 Y3)))) (@ (@ tptp.ord_less_real (@ F2 A)) C2))))) (forall ((A tptp.int) (B tptp.int) (F2 (-> tptp.int tptp.real)) (C2 tptp.real)) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_eq_real (@ F2 B)) C2) (=> (forall ((X3 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Y3) (@ (@ tptp.ord_less_real (@ F2 X3)) (@ F2 Y3)))) (@ (@ tptp.ord_less_real (@ F2 A)) C2))))) (forall ((A tptp.real) (B tptp.real) (F2 (-> tptp.real tptp.rat)) (C2 tptp.rat)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_eq_rat (@ F2 B)) C2) (=> (forall ((X3 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Y3) (@ (@ tptp.ord_less_rat (@ F2 X3)) (@ F2 Y3)))) (@ (@ tptp.ord_less_rat (@ F2 A)) C2))))) (forall ((A tptp.rat) (B tptp.rat) (F2 (-> tptp.rat tptp.rat)) (C2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat (@ F2 B)) C2) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y3) (@ (@ tptp.ord_less_rat (@ F2 X3)) (@ F2 Y3)))) (@ (@ tptp.ord_less_rat (@ F2 A)) C2))))) (forall ((A tptp.num) (B tptp.num) (F2 (-> tptp.num tptp.rat)) (C2 tptp.rat)) (=> (@ (@ tptp.ord_less_num A) B) (=> (@ (@ tptp.ord_less_eq_rat (@ F2 B)) C2) (=> (forall ((X3 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_num X3) Y3) (@ (@ tptp.ord_less_rat (@ F2 X3)) (@ F2 Y3)))) (@ (@ tptp.ord_less_rat (@ F2 A)) C2))))) (forall ((A tptp.nat) (B tptp.nat) (F2 (-> tptp.nat tptp.rat)) (C2 tptp.rat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_eq_rat (@ F2 B)) C2) (=> (forall ((X3 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Y3) (@ (@ tptp.ord_less_rat (@ F2 X3)) (@ F2 Y3)))) (@ (@ tptp.ord_less_rat (@ F2 A)) C2))))) (forall ((A tptp.int) (B tptp.int) (F2 (-> tptp.int tptp.rat)) (C2 tptp.rat)) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_eq_rat (@ F2 B)) C2) (=> (forall ((X3 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Y3) (@ (@ tptp.ord_less_rat (@ F2 X3)) (@ F2 Y3)))) (@ (@ tptp.ord_less_rat (@ F2 A)) C2))))) (forall ((A tptp.real) (F2 (-> tptp.rat tptp.real)) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_real A))) (=> (@ _let_1 (@ F2 B)) (=> (@ (@ tptp.ord_less_eq_rat B) C2) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y3) (@ (@ tptp.ord_less_eq_real (@ F2 X3)) (@ F2 Y3)))) (@ _let_1 (@ F2 C2))))))) (forall ((A tptp.rat) (F2 (-> tptp.rat tptp.rat)) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A))) (=> (@ _let_1 (@ F2 B)) (=> (@ (@ tptp.ord_less_eq_rat B) C2) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y3) (@ (@ tptp.ord_less_eq_rat (@ F2 X3)) (@ F2 Y3)))) (@ _let_1 (@ F2 C2))))))) (forall ((A tptp.num) (F2 (-> tptp.rat tptp.num)) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_num A))) (=> (@ _let_1 (@ F2 B)) (=> (@ (@ tptp.ord_less_eq_rat B) C2) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y3) (@ (@ tptp.ord_less_eq_num (@ F2 X3)) (@ F2 Y3)))) (@ _let_1 (@ F2 C2))))))) (forall ((A tptp.nat) (F2 (-> tptp.rat tptp.nat)) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_nat A))) (=> (@ _let_1 (@ F2 B)) (=> (@ (@ tptp.ord_less_eq_rat B) C2) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y3) (@ (@ tptp.ord_less_eq_nat (@ F2 X3)) (@ F2 Y3)))) (@ _let_1 (@ F2 C2))))))) (forall ((A tptp.int) (F2 (-> tptp.rat tptp.int)) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_int A))) (=> (@ _let_1 (@ F2 B)) (=> (@ (@ tptp.ord_less_eq_rat B) C2) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y3) (@ (@ tptp.ord_less_eq_int (@ F2 X3)) (@ F2 Y3)))) (@ _let_1 (@ F2 C2))))))) (forall ((A tptp.real) (F2 (-> tptp.num tptp.real)) (B tptp.num) (C2 tptp.num)) (let ((_let_1 (@ tptp.ord_less_real A))) (=> (@ _let_1 (@ F2 B)) (=> (@ (@ tptp.ord_less_eq_num B) C2) (=> (forall ((X3 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y3) (@ (@ tptp.ord_less_eq_real (@ F2 X3)) (@ F2 Y3)))) (@ _let_1 (@ F2 C2))))))) (forall ((A tptp.rat) (F2 (-> tptp.num tptp.rat)) (B tptp.num) (C2 tptp.num)) (let ((_let_1 (@ tptp.ord_less_rat A))) (=> (@ _let_1 (@ F2 B)) (=> (@ (@ tptp.ord_less_eq_num B) C2) (=> (forall ((X3 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y3) (@ (@ tptp.ord_less_eq_rat (@ F2 X3)) (@ F2 Y3)))) (@ _let_1 (@ F2 C2))))))) (forall ((A tptp.num) (F2 (-> tptp.num tptp.num)) (B tptp.num) (C2 tptp.num)) (let ((_let_1 (@ tptp.ord_less_num A))) (=> (@ _let_1 (@ F2 B)) (=> (@ (@ tptp.ord_less_eq_num B) C2) (=> (forall ((X3 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y3) (@ (@ tptp.ord_less_eq_num (@ F2 X3)) (@ F2 Y3)))) (@ _let_1 (@ F2 C2))))))) (forall ((A tptp.nat) (F2 (-> tptp.num tptp.nat)) (B tptp.num) (C2 tptp.num)) (let ((_let_1 (@ tptp.ord_less_nat A))) (=> (@ _let_1 (@ F2 B)) (=> (@ (@ tptp.ord_less_eq_num B) C2) (=> (forall ((X3 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y3) (@ (@ tptp.ord_less_eq_nat (@ F2 X3)) (@ F2 Y3)))) (@ _let_1 (@ F2 C2))))))) (forall ((A tptp.int) (F2 (-> tptp.num tptp.int)) (B tptp.num) (C2 tptp.num)) (let ((_let_1 (@ tptp.ord_less_int A))) (=> (@ _let_1 (@ F2 B)) (=> (@ (@ tptp.ord_less_eq_num B) C2) (=> (forall ((X3 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y3) (@ (@ tptp.ord_less_eq_int (@ F2 X3)) (@ F2 Y3)))) (@ _let_1 (@ F2 C2))))))) (forall ((A tptp.rat) (B tptp.rat) (F2 (-> tptp.rat tptp.real)) (C2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_real (@ F2 B)) C2) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y3) (@ (@ tptp.ord_less_eq_real (@ F2 X3)) (@ F2 Y3)))) (@ (@ tptp.ord_less_real (@ F2 A)) C2))))) (forall ((A tptp.rat) (B tptp.rat) (F2 (-> tptp.rat tptp.rat)) (C2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_rat (@ F2 B)) C2) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y3) (@ (@ tptp.ord_less_eq_rat (@ F2 X3)) (@ F2 Y3)))) (@ (@ tptp.ord_less_rat (@ F2 A)) C2))))) (forall ((A tptp.rat) (B tptp.rat) (F2 (-> tptp.rat tptp.num)) (C2 tptp.num)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_num (@ F2 B)) C2) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y3) (@ (@ tptp.ord_less_eq_num (@ F2 X3)) (@ F2 Y3)))) (@ (@ tptp.ord_less_num (@ F2 A)) C2))))) (forall ((A tptp.rat) (B tptp.rat) (F2 (-> tptp.rat tptp.nat)) (C2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_nat (@ F2 B)) C2) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y3) (@ (@ tptp.ord_less_eq_nat (@ F2 X3)) (@ F2 Y3)))) (@ (@ tptp.ord_less_nat (@ F2 A)) C2))))) (forall ((A tptp.rat) (B tptp.rat) (F2 (-> tptp.rat tptp.int)) (C2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_int (@ F2 B)) C2) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y3) (@ (@ tptp.ord_less_eq_int (@ F2 X3)) (@ F2 Y3)))) (@ (@ tptp.ord_less_int (@ F2 A)) C2))))) (forall ((A tptp.num) (B tptp.num) (F2 (-> tptp.num tptp.real)) (C2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (@ (@ tptp.ord_less_real (@ F2 B)) C2) (=> (forall ((X3 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y3) (@ (@ tptp.ord_less_eq_real (@ F2 X3)) (@ F2 Y3)))) (@ (@ tptp.ord_less_real (@ F2 A)) C2))))) (forall ((A tptp.num) (B tptp.num) (F2 (-> tptp.num tptp.rat)) (C2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (@ (@ tptp.ord_less_rat (@ F2 B)) C2) (=> (forall ((X3 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y3) (@ (@ tptp.ord_less_eq_rat (@ F2 X3)) (@ F2 Y3)))) (@ (@ tptp.ord_less_rat (@ F2 A)) C2))))) (forall ((A tptp.num) (B tptp.num) (F2 (-> tptp.num tptp.num)) (C2 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (@ (@ tptp.ord_less_num (@ F2 B)) C2) (=> (forall ((X3 tptp.num) (Y3 tptp.num)) (=> (@ (@ 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(@ (@ tptp.ord_less_rat (@ F2 X3)) (@ F2 Y3)))) (@ (@ tptp.ord_less_rat A) (@ F2 C2)))))) (forall ((X tptp.real) (Y tptp.real) (Z3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_real Y) Z3) (@ _let_1 Z3))))) (forall ((X tptp.set_nat) (Y tptp.set_nat) (Z3 tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_set_nat X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_set_nat Y) Z3) (@ _let_1 Z3))))) (forall ((X tptp.rat) (Y tptp.rat) (Z3 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_rat Y) Z3) (@ _let_1 Z3))))) (forall ((X tptp.num) (Y tptp.num) (Z3 tptp.num)) (let ((_let_1 (@ tptp.ord_less_num X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_num Y) Z3) (@ _let_1 Z3))))) (forall ((X tptp.nat) (Y tptp.nat) (Z3 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_nat Y) Z3) (@ _let_1 Z3))))) (forall ((X tptp.int) (Y tptp.int) (Z3 tptp.int)) (let ((_let_1 (@ 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(=> (@ (@ tptp.ord_less_eq_set_nat A) B) (=> (not (= A B)) (@ (@ tptp.ord_less_set_nat A) B)))) (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (not (= A B)) (@ (@ tptp.ord_less_rat A) B)))) (forall ((A tptp.num) (B tptp.num)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (not (= A B)) (@ (@ tptp.ord_less_num A) B)))) (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (not (= A B)) (@ (@ tptp.ord_less_nat A) B)))) (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (not (= A B)) (@ (@ tptp.ord_less_int A) B)))) (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X) Y) (@ (@ tptp.ord_less_eq_real X) Y))) (forall ((X tptp.set_nat) (Y tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat X) Y) (@ (@ tptp.ord_less_eq_set_nat X) Y))) (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat X) Y) (@ (@ tptp.ord_less_eq_rat X) Y))) (forall ((X tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_num X) Y) (@ (@ tptp.ord_less_eq_num X) Y))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Y) (@ (@ tptp.ord_less_eq_nat X) Y))) (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int X) Y) (@ (@ tptp.ord_less_eq_int X) Y))) (forall ((X tptp.real) (Y tptp.real)) (= (not (@ (@ tptp.ord_less_real X) Y)) (@ (@ tptp.ord_less_eq_real Y) X))) (forall ((X tptp.rat) (Y tptp.rat)) (= (not (@ (@ tptp.ord_less_rat X) Y)) (@ (@ tptp.ord_less_eq_rat Y) X))) (forall ((X tptp.num) (Y tptp.num)) (= (not (@ (@ tptp.ord_less_num X) Y)) (@ (@ tptp.ord_less_eq_num Y) X))) (forall ((X tptp.nat) (Y tptp.nat)) (= (not (@ (@ tptp.ord_less_nat X) Y)) (@ (@ tptp.ord_less_eq_nat Y) X))) (forall ((X tptp.int) (Y tptp.int)) (= (not (@ (@ tptp.ord_less_int X) Y)) (@ (@ tptp.ord_less_eq_int Y) X))) (forall ((X tptp.real) (Y tptp.real)) (= (not (@ (@ tptp.ord_less_eq_real X) Y)) (@ (@ tptp.ord_less_real Y) X))) (forall ((X tptp.rat) (Y tptp.rat)) (= (not (@ (@ tptp.ord_less_eq_rat X) Y)) (@ (@ tptp.ord_less_rat Y) X))) (forall ((X tptp.num) (Y tptp.num)) (= (not (@ (@ tptp.ord_less_eq_num X) Y)) (@ (@ tptp.ord_less_num Y) X))) (forall ((X tptp.nat) (Y tptp.nat)) (= (not (@ (@ tptp.ord_less_eq_nat X) Y)) (@ (@ tptp.ord_less_nat Y) X))) (forall ((X tptp.int) (Y tptp.int)) (= (not (@ (@ tptp.ord_less_eq_int X) Y)) (@ (@ tptp.ord_less_int Y) X))) _let_359 _let_358 _let_357 _let_356 _let_355 _let_354 (= tptp.ord_less_eq_real (lambda ((X4 tptp.real) (Y4 tptp.real)) (or (@ (@ tptp.ord_less_real X4) Y4) (= X4 Y4)))) (= tptp.ord_less_eq_set_nat (lambda ((X4 tptp.set_nat) (Y4 tptp.set_nat)) (or (@ (@ tptp.ord_less_set_nat X4) Y4) (= X4 Y4)))) (= tptp.ord_less_eq_rat (lambda ((X4 tptp.rat) (Y4 tptp.rat)) (or (@ (@ tptp.ord_less_rat X4) Y4) (= X4 Y4)))) (= tptp.ord_less_eq_num (lambda ((X4 tptp.num) (Y4 tptp.num)) (or (@ (@ tptp.ord_less_num X4) Y4) (= X4 Y4)))) (= tptp.ord_less_eq_nat (lambda ((X4 tptp.nat) (Y4 tptp.nat)) (or (@ (@ tptp.ord_less_nat X4) Y4) (= X4 Y4)))) (= tptp.ord_less_eq_int (lambda ((X4 tptp.int) (Y4 tptp.int)) (or (@ (@ tptp.ord_less_int X4) Y4) (= X4 Y4)))) (forall ((B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real B) A) (@ (@ tptp.ord_less_eq_real B) A))) (forall ((B tptp.set_nat) (A tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat B) A) (@ (@ tptp.ord_less_eq_set_nat B) A))) (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat B) A) (@ (@ tptp.ord_less_eq_rat B) A))) (forall ((B tptp.num) (A tptp.num)) (=> (@ (@ tptp.ord_less_num B) A) (@ (@ tptp.ord_less_eq_num B) A))) (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat B) A) (@ (@ tptp.ord_less_eq_nat B) A))) (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int B) A) (@ (@ tptp.ord_less_eq_int B) A))) (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (@ (@ tptp.ord_less_eq_real A) B))) (forall ((A tptp.set_nat) (B tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat A) B) (@ (@ tptp.ord_less_eq_set_nat A) B))) (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (@ (@ tptp.ord_less_eq_rat A) B))) (forall ((A tptp.num) (B tptp.num)) (=> (@ (@ tptp.ord_less_num A) B) (@ (@ tptp.ord_less_eq_num A) B))) (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (@ (@ tptp.ord_less_eq_nat A) B))) (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (@ (@ tptp.ord_less_eq_int A) B))) (= tptp.ord_less_real (lambda ((B4 tptp.real) (A5 tptp.real)) (and (@ (@ tptp.ord_less_eq_real B4) A5) (not (@ (@ tptp.ord_less_eq_real A5) B4))))) (= tptp.ord_less_set_nat (lambda ((B4 tptp.set_nat) (A5 tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat B4) A5) (not (@ (@ tptp.ord_less_eq_set_nat A5) B4))))) (= tptp.ord_less_rat (lambda ((B4 tptp.rat) (A5 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat B4) A5) (not (@ (@ tptp.ord_less_eq_rat A5) B4))))) (= tptp.ord_less_num (lambda ((B4 tptp.num) (A5 tptp.num)) (and (@ (@ tptp.ord_less_eq_num B4) A5) (not (@ (@ tptp.ord_less_eq_num A5) B4))))) (= tptp.ord_less_nat (lambda ((B4 tptp.nat) (A5 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat B4) A5) (not (@ (@ tptp.ord_less_eq_nat A5) B4))))) (= tptp.ord_less_int (lambda ((B4 tptp.int) (A5 tptp.int)) (and (@ (@ tptp.ord_less_eq_int B4) A5) (not (@ (@ tptp.ord_less_eq_int A5) B4))))) (forall ((B tptp.real) (A tptp.real) (C2 tptp.real)) (=> (@ (@ tptp.ord_less_real B) A) (=> (@ (@ tptp.ord_less_eq_real C2) B) (@ (@ tptp.ord_less_real C2) A)))) (forall ((B tptp.set_nat) (A tptp.set_nat) (C2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat B) A) (=> (@ (@ tptp.ord_less_eq_set_nat C2) B) (@ (@ tptp.ord_less_set_nat C2) A)))) (forall ((B tptp.rat) (A tptp.rat) (C2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat B) A) (=> (@ (@ tptp.ord_less_eq_rat C2) B) (@ (@ tptp.ord_less_rat C2) A)))) (forall ((B tptp.num) (A tptp.num) (C2 tptp.num)) (=> (@ (@ tptp.ord_less_num B) A) (=> (@ (@ tptp.ord_less_eq_num C2) B) (@ (@ tptp.ord_less_num C2) A)))) (forall ((B tptp.nat) (A tptp.nat) (C2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat B) A) (=> (@ (@ tptp.ord_less_eq_nat C2) B) (@ (@ tptp.ord_less_nat C2) A)))) (forall ((B tptp.int) (A tptp.int) (C2 tptp.int)) (=> (@ (@ tptp.ord_less_int B) A) (=> (@ (@ tptp.ord_less_eq_int C2) B) (@ (@ tptp.ord_less_int C2) A)))) (forall ((B tptp.real) (A tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real C2))) (=> (@ (@ tptp.ord_less_eq_real B) A) (=> (@ _let_1 B) (@ _let_1 A))))) (forall ((B tptp.set_nat) (A tptp.set_nat) (C2 tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_set_nat C2))) (=> (@ (@ tptp.ord_less_eq_set_nat B) A) (=> (@ _let_1 B) (@ _let_1 A))))) (forall ((B tptp.rat) (A tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat C2))) (=> (@ (@ tptp.ord_less_eq_rat B) A) (=> (@ _let_1 B) (@ _let_1 A))))) (forall ((B tptp.num) (A tptp.num) (C2 tptp.num)) (let ((_let_1 (@ tptp.ord_less_num C2))) (=> (@ (@ tptp.ord_less_eq_num B) A) (=> (@ _let_1 B) (@ _let_1 A))))) (forall ((B tptp.nat) (A tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat C2))) (=> (@ (@ tptp.ord_less_eq_nat B) A) (=> (@ _let_1 B) (@ _let_1 A))))) (forall ((B tptp.int) (A tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int C2))) (=> (@ (@ tptp.ord_less_eq_int B) A) (=> (@ _let_1 B) (@ _let_1 A))))) (= tptp.ord_less_real (lambda ((B4 tptp.real) (A5 tptp.real)) (and (@ (@ tptp.ord_less_eq_real B4) A5) (not (= A5 B4))))) (= tptp.ord_less_set_nat (lambda ((B4 tptp.set_nat) (A5 tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat B4) A5) (not (= A5 B4))))) (= tptp.ord_less_rat (lambda ((B4 tptp.rat) (A5 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat B4) A5) (not (= A5 B4))))) (= tptp.ord_less_num (lambda ((B4 tptp.num) (A5 tptp.num)) (and (@ (@ tptp.ord_less_eq_num B4) A5) (not (= A5 B4))))) (= tptp.ord_less_nat (lambda ((B4 tptp.nat) (A5 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat B4) A5) (not (= A5 B4))))) (= tptp.ord_less_int (lambda ((B4 tptp.int) (A5 tptp.int)) (and (@ (@ tptp.ord_less_eq_int B4) A5) (not (= A5 B4))))) (= tptp.ord_less_eq_real (lambda ((B4 tptp.real) (A5 tptp.real)) (or (@ (@ tptp.ord_less_real B4) A5) (= A5 B4)))) (= tptp.ord_less_eq_set_nat (lambda ((B4 tptp.set_nat) (A5 tptp.set_nat)) (or (@ (@ tptp.ord_less_set_nat B4) A5) (= A5 B4)))) (= tptp.ord_less_eq_rat (lambda ((B4 tptp.rat) (A5 tptp.rat)) (or (@ (@ tptp.ord_less_rat B4) A5) (= A5 B4)))) (= tptp.ord_less_eq_num (lambda ((B4 tptp.num) (A5 tptp.num)) (or (@ (@ tptp.ord_less_num B4) A5) (= A5 B4)))) (= tptp.ord_less_eq_nat (lambda ((B4 tptp.nat) (A5 tptp.nat)) (or (@ (@ tptp.ord_less_nat B4) A5) (= A5 B4)))) (= tptp.ord_less_eq_int (lambda ((B4 tptp.int) (A5 tptp.int)) (or (@ (@ tptp.ord_less_int B4) A5) (= A5 B4)))) (forall ((X tptp.real) (Y tptp.real) (Z3 tptp.real)) (=> (@ (@ tptp.ord_less_real X) Y) (=> (forall ((W tptp.real)) (=> (@ (@ tptp.ord_less_real X) W) (=> (@ (@ tptp.ord_less_real W) Y) (@ (@ tptp.ord_less_eq_real W) Z3)))) (@ (@ tptp.ord_less_eq_real Y) Z3)))) (forall ((X tptp.rat) (Y tptp.rat) (Z3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X) Y) (=> (forall ((W tptp.rat)) (=> (@ (@ tptp.ord_less_rat X) W) (=> (@ (@ tptp.ord_less_rat W) Y) (@ (@ tptp.ord_less_eq_rat W) Z3)))) (@ (@ tptp.ord_less_eq_rat Y) Z3)))) (forall ((Z3 tptp.real) (X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real Z3) X) (=> (forall ((W tptp.real)) (=> (@ (@ tptp.ord_less_real Z3) W) (=> (@ (@ tptp.ord_less_real W) X) (@ (@ tptp.ord_less_eq_real Y) W)))) (@ (@ tptp.ord_less_eq_real Y) Z3)))) (forall ((Z3 tptp.rat) (X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z3) X) (=> (forall ((W tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z3) W) (=> (@ (@ tptp.ord_less_rat W) X) (@ (@ tptp.ord_less_eq_rat Y) W)))) (@ (@ tptp.ord_less_eq_rat Y) Z3)))) (= tptp.ord_less_real (lambda ((A5 tptp.real) (B4 tptp.real)) (and (@ (@ tptp.ord_less_eq_real A5) B4) (not (@ (@ tptp.ord_less_eq_real B4) A5))))) (= tptp.ord_less_set_nat (lambda ((A5 tptp.set_nat) (B4 tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat A5) B4) (not (@ (@ tptp.ord_less_eq_set_nat B4) A5))))) (= tptp.ord_less_rat (lambda ((A5 tptp.rat) (B4 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat A5) B4) (not (@ (@ tptp.ord_less_eq_rat B4) A5))))) (= tptp.ord_less_num (lambda ((A5 tptp.num) (B4 tptp.num)) (and (@ (@ tptp.ord_less_eq_num A5) B4) (not (@ (@ tptp.ord_less_eq_num B4) A5))))) (= tptp.ord_less_nat (lambda ((A5 tptp.nat) (B4 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat A5) B4) (not (@ (@ tptp.ord_less_eq_nat B4) A5))))) (= tptp.ord_less_int (lambda ((A5 tptp.int) (B4 tptp.int)) (and (@ (@ tptp.ord_less_eq_int A5) B4) (not (@ (@ tptp.ord_less_eq_int B4) A5))))) (forall ((A tptp.real) (B tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_real B) C2) (@ _let_1 C2))))) (forall ((A tptp.set_nat) (B tptp.set_nat) (C2 tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_set_nat A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_set_nat B) C2) (@ _let_1 C2))))) (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_rat B) C2) (@ _let_1 C2))))) (forall ((A tptp.num) (B tptp.num) (C2 tptp.num)) (let ((_let_1 (@ tptp.ord_less_num A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_num B) C2) (@ _let_1 C2))))) (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_nat B) C2) (@ _let_1 C2))))) (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_int B) C2) (@ _let_1 C2))))) (forall ((A tptp.real) (B tptp.real) (C2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_real B) C2) (@ (@ tptp.ord_less_real A) C2)))) (forall ((A tptp.set_nat) (B tptp.set_nat) (C2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A) B) (=> (@ (@ tptp.ord_less_set_nat B) C2) (@ (@ tptp.ord_less_set_nat A) C2)))) (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_rat B) C2) (@ (@ tptp.ord_less_rat A) C2)))) (forall ((A tptp.num) (B tptp.num) (C2 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (@ (@ tptp.ord_less_num B) C2) (@ (@ tptp.ord_less_num A) C2)))) (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_nat B) C2) (@ (@ tptp.ord_less_nat A) C2)))) (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_int B) C2) (@ (@ tptp.ord_less_int A) C2)))) (= tptp.ord_less_real (lambda ((A5 tptp.real) (B4 tptp.real)) (and (@ (@ tptp.ord_less_eq_real A5) B4) (not (= A5 B4))))) (= tptp.ord_less_set_nat (lambda ((A5 tptp.set_nat) (B4 tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat A5) B4) (not (= A5 B4))))) (= tptp.ord_less_rat (lambda ((A5 tptp.rat) (B4 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat A5) B4) (not (= A5 B4))))) (= tptp.ord_less_num (lambda ((A5 tptp.num) (B4 tptp.num)) (and (@ (@ tptp.ord_less_eq_num A5) B4) (not (= A5 B4))))) (= tptp.ord_less_nat (lambda ((A5 tptp.nat) (B4 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat A5) B4) (not (= A5 B4))))) (= tptp.ord_less_int (lambda ((A5 tptp.int) (B4 tptp.int)) (and (@ (@ tptp.ord_less_eq_int A5) B4) (not (= A5 B4))))) (= tptp.ord_less_eq_real (lambda ((A5 tptp.real) (B4 tptp.real)) (or (@ (@ tptp.ord_less_real A5) B4) (= A5 B4)))) (= tptp.ord_less_eq_set_nat (lambda ((A5 tptp.set_nat) (B4 tptp.set_nat)) (or (@ (@ tptp.ord_less_set_nat A5) B4) (= A5 B4)))) (= tptp.ord_less_eq_rat (lambda ((A5 tptp.rat) (B4 tptp.rat)) (or (@ (@ tptp.ord_less_rat A5) B4) (= A5 B4)))) (= tptp.ord_less_eq_num (lambda ((A5 tptp.num) (B4 tptp.num)) (or (@ (@ tptp.ord_less_num A5) B4) (= A5 B4)))) (= tptp.ord_less_eq_nat (lambda ((A5 tptp.nat) (B4 tptp.nat)) (or (@ (@ tptp.ord_less_nat A5) B4) (= A5 B4)))) (= tptp.ord_less_eq_int (lambda ((A5 tptp.int) (B4 tptp.int)) (or (@ (@ tptp.ord_less_int A5) B4) (= A5 B4)))) (forall ((Y tptp.real) (X tptp.real)) (=> (not (@ (@ tptp.ord_less_eq_real Y) X)) (@ (@ tptp.ord_less_real X) Y))) (forall ((Y tptp.rat) (X tptp.rat)) (=> (not (@ (@ tptp.ord_less_eq_rat Y) X)) (@ (@ tptp.ord_less_rat X) Y))) (forall ((Y tptp.num) (X tptp.num)) (=> (not (@ (@ tptp.ord_less_eq_num Y) X)) (@ (@ tptp.ord_less_num X) Y))) (forall ((Y tptp.nat) (X tptp.nat)) (=> (not (@ (@ tptp.ord_less_eq_nat Y) X)) (@ (@ tptp.ord_less_nat X) Y))) (forall ((Y tptp.int) (X tptp.int)) (=> (not (@ (@ tptp.ord_less_eq_int Y) X)) (@ (@ tptp.ord_less_int X) Y))) (= tptp.ord_less_real (lambda ((X4 tptp.real) (Y4 tptp.real)) (and (@ (@ tptp.ord_less_eq_real X4) Y4) (not (@ (@ tptp.ord_less_eq_real Y4) X4))))) (= tptp.ord_less_set_nat (lambda ((X4 tptp.set_nat) (Y4 tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat X4) Y4) (not (@ (@ tptp.ord_less_eq_set_nat Y4) X4))))) (= tptp.ord_less_rat (lambda ((X4 tptp.rat) (Y4 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat X4) Y4) (not (@ (@ tptp.ord_less_eq_rat Y4) X4))))) (= tptp.ord_less_num (lambda ((X4 tptp.num) (Y4 tptp.num)) (and (@ (@ tptp.ord_less_eq_num X4) Y4) (not (@ (@ tptp.ord_less_eq_num Y4) X4))))) (= tptp.ord_less_nat (lambda ((X4 tptp.nat) (Y4 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat X4) Y4) (not (@ (@ tptp.ord_less_eq_nat Y4) X4))))) (= tptp.ord_less_int (lambda ((X4 tptp.int) (Y4 tptp.int)) (and (@ (@ tptp.ord_less_eq_int X4) Y4) (not (@ (@ tptp.ord_less_eq_int Y4) X4))))) (forall ((Y tptp.real) (Z3 tptp.real)) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Y) (@ (@ tptp.ord_less_eq_real X3) Z3))) (@ (@ tptp.ord_less_eq_real Y) Z3))) (forall ((Y tptp.rat) (Z3 tptp.rat)) (=> (forall ((X3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y) (@ (@ tptp.ord_less_eq_rat X3) Z3))) (@ (@ tptp.ord_less_eq_rat Y) Z3))) (forall ((Z3 tptp.real) (Y tptp.real)) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real Z3) X3) (@ (@ tptp.ord_less_eq_real Y) X3))) (@ (@ tptp.ord_less_eq_real Y) Z3))) (forall ((Z3 tptp.rat) (Y tptp.rat)) (=> (forall ((X3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z3) X3) (@ (@ tptp.ord_less_eq_rat Y) X3))) (@ (@ tptp.ord_less_eq_rat Y) Z3))) (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) Y) (= (not (@ (@ tptp.ord_less_real X) Y)) (= X Y)))) (forall ((X tptp.set_nat) (Y tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat X) Y) (= (not (@ (@ tptp.ord_less_set_nat X) Y)) (= X Y)))) (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X) Y) (= (not (@ (@ tptp.ord_less_rat X) Y)) (= X Y)))) (forall ((X tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X) Y) (= (not (@ (@ tptp.ord_less_num X) Y)) (= X Y)))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X) Y) (= (not (@ (@ tptp.ord_less_nat X) Y)) (= X Y)))) (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X) Y) (= (not (@ (@ tptp.ord_less_int X) Y)) (= X Y)))) (forall ((X tptp.real) (Y tptp.real)) (=> (not (@ (@ tptp.ord_less_real X) Y)) (= (@ (@ tptp.ord_less_eq_real X) Y) (= X Y)))) (forall ((X tptp.set_nat) (Y tptp.set_nat)) (=> (not (@ (@ tptp.ord_less_set_nat X) Y)) (= (@ (@ tptp.ord_less_eq_set_nat X) Y) (= X Y)))) (forall ((X tptp.rat) (Y tptp.rat)) (=> (not (@ (@ tptp.ord_less_rat X) Y)) (= (@ (@ tptp.ord_less_eq_rat X) Y) (= X Y)))) (forall ((X tptp.num) (Y tptp.num)) (=> (not (@ (@ tptp.ord_less_num X) Y)) (= (@ (@ tptp.ord_less_eq_num X) Y) (= X Y)))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat X) Y)) (= (@ (@ tptp.ord_less_eq_nat X) Y) (= X Y)))) (forall ((X tptp.int) (Y tptp.int)) (=> (not (@ (@ tptp.ord_less_int X) Y)) (= (@ (@ tptp.ord_less_eq_int X) Y) (= X Y)))) (forall ((A tptp.real) (B tptp.real)) (= (not (@ (@ tptp.ord_less_real A) B)) (or (not (@ (@ tptp.ord_less_eq_real A) B)) (= A B)))) (forall ((A tptp.set_nat) (B tptp.set_nat)) (= (not (@ (@ tptp.ord_less_set_nat A) B)) (or (not (@ (@ tptp.ord_less_eq_set_nat A) B)) (= A B)))) (forall ((A tptp.rat) (B tptp.rat)) (= (not (@ (@ tptp.ord_less_rat A) B)) (or (not (@ (@ tptp.ord_less_eq_rat A) B)) (= A B)))) (forall ((A tptp.num) (B tptp.num)) (= (not (@ (@ tptp.ord_less_num A) B)) (or (not (@ (@ tptp.ord_less_eq_num A) B)) (= A B)))) (forall ((A tptp.nat) (B tptp.nat)) (= (not (@ (@ tptp.ord_less_nat A) B)) (or (not (@ (@ tptp.ord_less_eq_nat A) B)) (= A B)))) (forall ((A tptp.int) (B tptp.int)) (= (not (@ (@ tptp.ord_less_int A) B)) (or (not (@ (@ tptp.ord_less_eq_int A) B)) (= A B)))) (forall ((X tptp.real) (Y tptp.real)) (=> (not (@ (@ tptp.ord_less_real X) Y)) (@ (@ tptp.ord_less_eq_real Y) X))) (forall ((X tptp.rat) (Y tptp.rat)) (=> (not (@ (@ tptp.ord_less_rat X) Y)) (@ (@ tptp.ord_less_eq_rat Y) X))) (forall ((X tptp.num) (Y tptp.num)) (=> (not (@ (@ tptp.ord_less_num X) Y)) (@ (@ tptp.ord_less_eq_num Y) X))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat X) Y)) (@ (@ tptp.ord_less_eq_nat Y) X))) (forall ((X tptp.int) (Y tptp.int)) (=> (not (@ (@ tptp.ord_less_int X) Y)) (@ (@ tptp.ord_less_eq_int Y) X))) (forall ((Y tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real Y) X) (not (@ (@ tptp.ord_less_real X) Y)))) (forall ((Y tptp.set_nat) (X tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat Y) X) (not (@ (@ tptp.ord_less_set_nat X) Y)))) (forall ((Y tptp.rat) (X tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat Y) X) (not (@ (@ tptp.ord_less_rat X) Y)))) (forall ((Y tptp.num) (X tptp.num)) (=> (@ (@ tptp.ord_less_eq_num Y) X) (not (@ (@ tptp.ord_less_num X) Y)))) (forall ((Y tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Y) X) (not (@ (@ tptp.ord_less_nat X) Y)))) (forall ((Y tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Y) X) (not (@ (@ tptp.ord_less_int X) Y)))) (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (not (= N tptp.zero_zero_nat)))) (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) N) (not (= N tptp.zero_zero_nat)))) (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) tptp.zero_zero_nat))) (forall ((N tptp.nat)) (=> (not (= N tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))) (not (@ _let_172 tptp.zero_zero_real)) (not (@ _let_170 tptp.zero_zero_rat)) (not (@ _let_297 tptp.zero_zero_nat)) (not (@ _let_173 tptp.zero_zero_int)) (forall ((N tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat N))) (=> (not (@ _let_1 M2)) (= (@ _let_1 (@ tptp.suc M2)) (= N M2))))) (forall ((I2 tptp.nat) (J2 tptp.nat) (P2 (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_nat I2) J2) (=> (forall ((I3 tptp.nat)) (=> (= J2 (@ tptp.suc I3)) (@ P2 I3))) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) J2) (=> (@ P2 (@ tptp.suc I3)) (@ P2 I3)))) (@ P2 I2))))) (forall ((I2 tptp.nat) (J2 tptp.nat) (P2 (-> tptp.nat tptp.nat Bool))) (=> (@ (@ tptp.ord_less_nat I2) J2) (=> (forall ((I3 tptp.nat)) (@ (@ P2 I3) (@ tptp.suc I3))) (=> (forall ((I3 tptp.nat) (J3 tptp.nat) (K tptp.nat)) (let ((_let_1 (@ P2 I3))) (=> (@ (@ tptp.ord_less_nat I3) J3) (=> (@ (@ tptp.ord_less_nat J3) K) (=> (@ _let_1 J3) (=> (@ (@ P2 J3) K) (@ _let_1 K))))))) (@ (@ P2 I2) J2))))) (forall ((I2 tptp.nat) (J2 tptp.nat) (K2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) J2) (=> (@ (@ tptp.ord_less_nat J2) K2) (@ (@ tptp.ord_less_nat (@ tptp.suc I2)) K2)))) (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc M2)) (@ tptp.suc N)) (@ (@ tptp.ord_less_nat M2) N))) (forall ((N tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat N))) (=> (not (@ _let_1 M2)) (=> (@ _let_1 (@ tptp.suc M2)) (= M2 N))))) (forall ((N tptp.nat) (M2 tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.suc N)) M2) (exists ((M7 tptp.nat)) (and (= M2 (@ tptp.suc M7)) (@ (@ tptp.ord_less_nat N) M7))))) (forall ((N tptp.nat) (P2 (-> tptp.nat Bool))) (= (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.suc N)) (@ P2 I))) (and (@ P2 N) (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) N) (@ P2 I)))))) (forall ((M2 tptp.nat) (N tptp.nat)) (= (not (@ (@ tptp.ord_less_nat M2) N)) (@ (@ tptp.ord_less_nat N) (@ tptp.suc M2)))) (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat M2))) (= (@ _let_1 (@ tptp.suc N)) (or (@ _let_1 N) (= M2 N))))) (forall ((N tptp.nat) (P2 (-> tptp.nat Bool))) (= (exists ((I tptp.nat)) (and (@ (@ tptp.ord_less_nat I) (@ tptp.suc N)) (@ P2 I))) (or (@ P2 N) (exists ((I tptp.nat)) (and (@ (@ tptp.ord_less_nat I) N) (@ P2 I)))))) (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat M2))) (=> (@ _let_1 N) (@ _let_1 (@ tptp.suc N))))) (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat M2))) (=> (@ _let_1 (@ tptp.suc N)) (=> (not (@ _let_1 N)) (= M2 N))))) (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc M2))) (=> (@ (@ tptp.ord_less_nat M2) N) (=> (not (= _let_1 N)) (@ (@ tptp.ord_less_nat _let_1) N))))) (forall ((I2 tptp.nat) (K2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc I2)) K2) (not (forall ((J3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) J3) (not (= K2 (@ tptp.suc J3)))))))) (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc M2)) N) (@ (@ tptp.ord_less_nat M2) N))) (forall ((I2 tptp.nat) (K2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) K2) (=> (not (= K2 (@ tptp.suc I2))) (not (forall ((J3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) J3) (not (= K2 (@ tptp.suc J3))))))))) (forall ((X11 tptp.option4927543243414619207at_nat) (X12 tptp.nat) (X13 tptp.list_VEBT_VEBT) (X14 tptp.vEBT_VEBT) (X21 Bool) (X22 Bool)) (not (= (@ (@ (@ (@ tptp.vEBT_Node X11) X12) X13) X14) (@ (@ tptp.vEBT_Leaf X21) X22)))) (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) (X222 Bool)) (not (= Y (@ (@ tptp.vEBT_Leaf X212) X222))))))) (@ _let_197 tptp.one_one_Code_integer) (@ _let_198 tptp.one_one_real) (@ _let_196 tptp.one_one_rat) (@ _let_353 tptp.one_one_nat) (@ _let_195 tptp.one_one_int) (not (= tptp.zero_z3403309356797280102nteger tptp.one_one_Code_integer)) (not (= tptp.zero_zero_complex tptp.one_one_complex)) (not (= tptp.zero_zero_real tptp.one_one_real)) (not (= tptp.zero_zero_rat tptp.one_one_rat)) (not (= tptp.zero_zero_nat tptp.one_one_nat)) (not (= tptp.zero_zero_int tptp.one_one_int)) (forall ((A tptp.nat)) (not (@ (@ tptp.ord_less_nat A) tptp.zero_zero_nat))) (forall ((N tptp.nat)) (=> (not (= N tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))) (forall ((N tptp.nat)) (= (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)) (= N tptp.zero_zero_nat))) (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) tptp.zero_zero_nat))) (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) tptp.zero_zero_nat))) (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) N) (not (= N tptp.zero_zero_nat)))) (forall ((P2 (-> tptp.nat Bool)) (N tptp.nat)) (=> (@ P2 tptp.zero_zero_nat) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N3) (=> (not (@ P2 N3)) (exists ((M3 tptp.nat)) (and (@ (@ tptp.ord_less_nat M3) N3) (not (@ P2 M3))))))) (@ P2 N)))) (forall ((A tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger A) tptp.one_one_Code_integer) A)) (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex A) tptp.one_one_complex) A)) (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real A) tptp.one_one_real) A)) (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat A) tptp.one_one_rat) A)) (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat A) tptp.one_one_nat) A)) (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int A) tptp.one_one_int) A)) (forall ((A tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger tptp.one_one_Code_integer) A) A)) (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex tptp.one_one_complex) A) A)) (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real tptp.one_one_real) A) A)) (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat tptp.one_one_rat) A) A)) (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.one_one_nat) A) A)) (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int tptp.one_one_int) A) A)) (forall ((F2 (-> tptp.nat tptp.nat)) (I2 tptp.nat) (J2 tptp.nat)) (=> (forall ((I3 tptp.nat) (J3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) J3) (@ (@ tptp.ord_less_nat (@ F2 I3)) (@ F2 J3)))) (=> (@ (@ tptp.ord_less_eq_nat I2) J2) (@ (@ tptp.ord_less_eq_nat (@ F2 I2)) (@ F2 J2))))) (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (=> (not (= M2 N)) (@ (@ tptp.ord_less_nat M2) N)))) (forall ((M2 tptp.nat) (N tptp.nat)) (=> (or (@ (@ tptp.ord_less_nat M2) N) (= M2 N)) (@ (@ tptp.ord_less_eq_nat M2) N))) (= tptp.ord_less_eq_nat (lambda ((M6 tptp.nat) (N4 tptp.nat)) (or (@ (@ tptp.ord_less_nat M6) N4) (= M6 N4)))) (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) N) (@ (@ tptp.ord_less_eq_nat M2) N))) (= tptp.ord_less_nat (lambda ((M6 tptp.nat) (N4 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat M6) N4) (not (= M6 N4))))) (forall ((N tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.one_one_nat) N) N)) (forall ((N tptp.nat)) (= (@ (@ tptp.times_times_nat N) tptp.one_one_nat) N)) (forall ((K2 tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K2) (= (= (@ _let_1 M2) (@ _let_1 N)) (= M2 N))))) (forall ((K2 tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K2) (= (@ (@ tptp.ord_less_nat (@ _let_1 M2)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat M2) N))))) (forall ((A tptp.code_integer) (C2 tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.times_3573771949741848930nteger A) C2)) C2) (and (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) C2) (@ (@ tptp.ord_le6747313008572928689nteger A) tptp.one_one_Code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger C2) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) A))))) (forall ((A tptp.real) (C2 tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C2)) C2) (and (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C2) (@ (@ tptp.ord_less_real A) tptp.one_one_real)) (=> (@ (@ tptp.ord_less_eq_real C2) tptp.zero_zero_real) (@ (@ tptp.ord_less_real tptp.one_one_real) A))))) (forall ((A tptp.rat) (C2 tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C2)) C2) (and (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C2) (@ (@ tptp.ord_less_rat A) tptp.one_one_rat)) (=> (@ (@ tptp.ord_less_eq_rat C2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat tptp.one_one_rat) A))))) (forall ((A tptp.int) (C2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) C2)) C2) (and (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C2) (@ (@ tptp.ord_less_int A) tptp.one_one_int)) (=> (@ (@ tptp.ord_less_eq_int C2) tptp.zero_zero_int) (@ (@ tptp.ord_less_int tptp.one_one_int) A))))) (forall ((C2 tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger C2) (@ (@ tptp.times_3573771949741848930nteger B) C2)) (and (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) C2) (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) B)) (=> (@ (@ tptp.ord_le3102999989581377725nteger C2) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger B) tptp.one_one_Code_integer))))) (forall ((C2 tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_real C2) (@ (@ tptp.times_times_real B) C2)) (and (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C2) (@ (@ tptp.ord_less_real tptp.one_one_real) B)) (=> (@ (@ tptp.ord_less_eq_real C2) tptp.zero_zero_real) (@ (@ tptp.ord_less_real B) tptp.one_one_real))))) (forall ((C2 tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat C2) (@ (@ tptp.times_times_rat B) C2)) (and (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C2) (@ (@ tptp.ord_less_rat tptp.one_one_rat) B)) (=> (@ (@ tptp.ord_less_eq_rat C2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B) tptp.one_one_rat))))) (forall ((C2 tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_int C2) (@ (@ tptp.times_times_int B) C2)) (and (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C2) (@ (@ tptp.ord_less_int tptp.one_one_int) B)) (=> (@ (@ tptp.ord_less_eq_int C2) tptp.zero_zero_int) (@ (@ tptp.ord_less_int B) tptp.one_one_int))))) (forall ((C2 tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.times_3573771949741848930nteger C2) A)) C2) (and (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) C2) (@ (@ tptp.ord_le6747313008572928689nteger A) tptp.one_one_Code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger C2) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) A))))) (forall ((C2 tptp.real) (A tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real C2) A)) C2) (and (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C2) (@ (@ tptp.ord_less_real A) tptp.one_one_real)) (=> (@ (@ tptp.ord_less_eq_real C2) tptp.zero_zero_real) (@ (@ tptp.ord_less_real tptp.one_one_real) A))))) (forall ((C2 tptp.rat) (A tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat C2) A)) C2) (and (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C2) (@ (@ tptp.ord_less_rat A) tptp.one_one_rat)) (=> (@ (@ tptp.ord_less_eq_rat C2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat tptp.one_one_rat) A))))) (forall ((C2 tptp.int) (A tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int C2) A)) C2) (and (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C2) (@ (@ tptp.ord_less_int A) tptp.one_one_int)) (=> (@ (@ tptp.ord_less_eq_int C2) tptp.zero_zero_int) (@ (@ tptp.ord_less_int tptp.one_one_int) A))))) (forall ((C2 tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger C2) (@ (@ tptp.times_3573771949741848930nteger C2) B)) (and (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) C2) (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) B)) (=> (@ (@ tptp.ord_le3102999989581377725nteger C2) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger B) tptp.one_one_Code_integer))))) (forall ((C2 tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_real C2) (@ (@ tptp.times_times_real C2) B)) (and (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C2) (@ (@ tptp.ord_less_real tptp.one_one_real) B)) (=> (@ (@ tptp.ord_less_eq_real C2) tptp.zero_zero_real) (@ (@ tptp.ord_less_real B) tptp.one_one_real))))) (forall ((C2 tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat C2) (@ (@ tptp.times_times_rat C2) B)) (and (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C2) (@ (@ tptp.ord_less_rat tptp.one_one_rat) B)) (=> (@ (@ tptp.ord_less_eq_rat C2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B) tptp.one_one_rat))))) (forall ((C2 tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_int C2) (@ (@ tptp.times_times_int C2) B)) (and (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C2) (@ (@ tptp.ord_less_int tptp.one_one_int) B)) (=> (@ (@ tptp.ord_less_eq_int C2) tptp.zero_zero_int) (@ (@ tptp.ord_less_int B) tptp.one_one_int))))) (forall ((A tptp.code_integer) (C2 tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.times_3573771949741848930nteger A) C2)) C2) (and (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) C2) (@ (@ tptp.ord_le3102999989581377725nteger A) tptp.one_one_Code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger C2) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) A))))) (forall ((A tptp.real) (C2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) C2)) C2) (and (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C2) (@ (@ tptp.ord_less_eq_real A) tptp.one_one_real)) (=> (@ (@ tptp.ord_less_real C2) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) A))))) (forall ((A tptp.rat) (C2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C2)) C2) (and (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C2) (@ (@ tptp.ord_less_eq_rat A) tptp.one_one_rat)) (=> (@ (@ tptp.ord_less_rat C2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) A))))) (forall ((A tptp.int) (C2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) C2)) C2) (and (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C2) (@ (@ tptp.ord_less_eq_int A) tptp.one_one_int)) (=> (@ (@ tptp.ord_less_int C2) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) A))))) (forall ((C2 tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger C2) (@ (@ tptp.times_3573771949741848930nteger B) C2)) (and (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) C2) (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) B)) (=> (@ (@ tptp.ord_le6747313008572928689nteger C2) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le3102999989581377725nteger B) tptp.one_one_Code_integer))))) (forall ((C2 tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_eq_real C2) (@ (@ tptp.times_times_real B) C2)) (and (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C2) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) B)) (=> (@ (@ tptp.ord_less_real C2) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real B) tptp.one_one_real))))) (forall ((C2 tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat C2) (@ (@ tptp.times_times_rat B) C2)) (and (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C2) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) B)) (=> (@ (@ tptp.ord_less_rat C2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat B) tptp.one_one_rat))))) (forall ((C2 tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_int C2) (@ (@ tptp.times_times_int B) C2)) (and (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C2) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) B)) (=> (@ (@ tptp.ord_less_int C2) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int B) tptp.one_one_int))))) (forall ((C2 tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.times_3573771949741848930nteger C2) A)) C2) (and (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) C2) (@ (@ tptp.ord_le3102999989581377725nteger A) tptp.one_one_Code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger C2) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) A))))) (forall ((C2 tptp.real) (A tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real C2) A)) C2) (and (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C2) (@ (@ tptp.ord_less_eq_real A) tptp.one_one_real)) (=> (@ (@ tptp.ord_less_real C2) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) A))))) (forall ((C2 tptp.rat) (A tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat C2) A)) C2) (and (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C2) (@ (@ tptp.ord_less_eq_rat A) tptp.one_one_rat)) (=> (@ (@ tptp.ord_less_rat C2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) A))))) (forall ((C2 tptp.int) (A tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int C2) A)) C2) (and (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C2) (@ (@ tptp.ord_less_eq_int A) tptp.one_one_int)) (=> (@ (@ tptp.ord_less_int C2) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) A))))) (forall ((C2 tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger C2) (@ (@ tptp.times_3573771949741848930nteger C2) B)) (and (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) C2) (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) B)) (=> (@ (@ tptp.ord_le6747313008572928689nteger C2) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le3102999989581377725nteger B) tptp.one_one_Code_integer))))) (forall ((C2 tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_eq_real C2) (@ (@ tptp.times_times_real C2) B)) (and (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C2) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) B)) (=> (@ (@ tptp.ord_less_real C2) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real B) tptp.one_one_real))))) (forall ((C2 tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat C2) (@ (@ tptp.times_times_rat C2) B)) (and (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C2) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) B)) (=> (@ (@ tptp.ord_less_rat C2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat B) tptp.one_one_rat))))) (forall ((C2 tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_int C2) (@ (@ tptp.times_times_int C2) B)) (and (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C2) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) B)) (=> (@ (@ tptp.ord_less_int C2) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int B) tptp.one_one_int))))) (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real B) tptp.zero_zero_real) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.times_times_real A) B))))) (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat B) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.times_times_rat A) B))))) (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int B) tptp.zero_zero_int) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.times_times_int A) B))))) (forall ((A tptp.real)) (not (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) A)) tptp.zero_zero_real))) (forall ((A tptp.rat)) (not (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) A)) tptp.zero_zero_rat))) (forall ((A tptp.int)) (not (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) A)) tptp.zero_zero_int))) (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) B)) tptp.zero_zero_real) (or (and (@ _let_1 A) (@ (@ tptp.ord_less_real B) tptp.zero_zero_real)) (and (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (@ _let_1 B)))))) (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) B)) tptp.zero_zero_rat) (or (and (@ _let_1 A) (@ (@ tptp.ord_less_rat B) tptp.zero_zero_rat)) (and (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (@ _let_1 B)))))) (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (= (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) B)) tptp.zero_zero_int) (or (and (@ _let_1 A) (@ (@ tptp.ord_less_int B) tptp.zero_zero_int)) (and (@ (@ tptp.ord_less_int A) tptp.zero_zero_int) (@ _let_1 B)))))) (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) B) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) B)) tptp.zero_zero_real)))) (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) B) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) B)) tptp.zero_zero_rat)))) (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A) B)) tptp.zero_zero_nat)))) (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) B)) tptp.zero_zero_int)))) (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_real B) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) B)) tptp.zero_zero_real)))) (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_rat B) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) B)) tptp.zero_zero_rat)))) (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat B) tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A) B)) tptp.zero_zero_nat)))) (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int B) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) B)) tptp.zero_zero_int)))) (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_times_real A) B)))))) (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_times_rat A) B)))))) (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_times_nat A) B)))))) (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_times_int A) B)))))) (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_real B) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real B) A)) tptp.zero_zero_real)))) (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_rat B) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat B) A)) tptp.zero_zero_rat)))) (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat B) tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat B) A)) tptp.zero_zero_nat)))) (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int B) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int B) A)) tptp.zero_zero_int)))) (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ _let_1 (@ (@ tptp.times_times_real A) B)) (or (and (@ _let_1 A) (@ _let_1 B)) (and (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (@ (@ tptp.ord_less_real B) tptp.zero_zero_real)))))) (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (= (@ _let_1 (@ (@ tptp.times_times_rat A) B)) (or (and (@ _let_1 A) (@ _let_1 B)) (and (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B) tptp.zero_zero_rat)))))) (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.times_times_int A) B)) (or (and (@ _let_1 A) (@ _let_1 B)) (and (@ (@ tptp.ord_less_int A) tptp.zero_zero_int) (@ (@ tptp.ord_less_int B) tptp.zero_zero_int)))))) (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 (@ (@ tptp.times_times_real A) B)) (=> (@ _let_1 A) (@ _let_1 B))))) (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 (@ (@ tptp.times_times_rat A) B)) (=> (@ _let_1 A) (@ _let_1 B))))) (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 (@ (@ tptp.times_times_nat A) B)) (=> (@ _let_1 A) (@ _let_1 B))))) (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 (@ (@ tptp.times_times_int A) B)) (=> (@ _let_1 A) (@ _let_1 B))))) (forall ((B tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 (@ (@ tptp.times_times_real B) A)) (=> (@ _let_1 A) (@ _let_1 B))))) (forall ((B tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 (@ (@ tptp.times_times_rat B) A)) (=> (@ _let_1 A) (@ _let_1 B))))) (forall ((B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 (@ (@ tptp.times_times_nat B) A)) (=> (@ _let_1 A) (@ _let_1 B))))) (forall ((B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 (@ (@ tptp.times_times_int B) A)) (=> (@ _let_1 A) (@ _let_1 B))))) (forall ((C2 tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real C2))) (=> (@ (@ tptp.ord_less_real C2) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_real B) A))))) (forall ((C2 tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C2))) (=> (@ (@ tptp.ord_less_rat C2) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_rat B) A))))) (forall ((C2 tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C2))) (=> (@ (@ tptp.ord_less_int C2) tptp.zero_zero_int) (= (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_int B) A))))) (forall ((C2 tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real C2))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C2) (= (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_real A) B))))) (forall ((C2 tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C2))) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C2) (= (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_rat A) B))))) (forall ((C2 tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C2))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C2) (= (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_int A) B))))) (forall ((B tptp.real) (A tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.times_times_real C2))) (=> (@ (@ tptp.ord_less_real B) A) (=> (@ (@ tptp.ord_less_real C2) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B)))))) (forall ((B tptp.rat) (A tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C2))) (=> (@ (@ tptp.ord_less_rat B) A) (=> (@ (@ tptp.ord_less_rat C2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B)))))) (forall ((B tptp.int) (A tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int C2))) (=> (@ (@ tptp.ord_less_int B) A) (=> (@ (@ tptp.ord_less_int C2) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B)))))) (forall ((A tptp.real) (B tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.times_times_real C2))) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C2) (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B)))))) (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C2))) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C2) (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B)))))) (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C2))) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C2) (@ (@ tptp.ord_less_nat (@ _let_1 A)) (@ _let_1 B)))))) (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int C2))) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C2) (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B)))))) (forall ((C2 tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real C2))) (= (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B)) (or (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) C2) (@ (@ tptp.ord_less_real A) B)) (and (@ (@ tptp.ord_less_real C2) tptp.zero_zero_real) (@ (@ tptp.ord_less_real B) A)))))) (forall ((C2 tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C2))) (= (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B)) (or (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C2) (@ (@ tptp.ord_less_rat A) B)) (and (@ (@ tptp.ord_less_rat C2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B) A)))))) (forall ((C2 tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C2))) (= (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B)) (or (and (@ (@ tptp.ord_less_int tptp.zero_zero_int) C2) (@ (@ tptp.ord_less_int A) B)) (and (@ (@ tptp.ord_less_int C2) tptp.zero_zero_int) (@ (@ tptp.ord_less_int B) A)))))) (forall ((B tptp.real) (A tptp.real) (C2 tptp.real)) (=> (@ (@ tptp.ord_less_real B) A) (=> (@ (@ tptp.ord_less_real C2) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C2)) (@ (@ tptp.times_times_real B) C2))))) (forall ((B tptp.rat) (A tptp.rat) (C2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat B) A) (=> (@ (@ tptp.ord_less_rat C2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C2)) (@ (@ tptp.times_times_rat B) C2))))) (forall ((B tptp.int) (A tptp.int) (C2 tptp.int)) (=> (@ (@ tptp.ord_less_int B) A) (=> (@ (@ tptp.ord_less_int C2) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) C2)) (@ (@ tptp.times_times_int B) C2))))) (forall ((A tptp.real) (B tptp.real) (C2 tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C2) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C2)) (@ (@ tptp.times_times_real B) C2))))) (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C2) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C2)) (@ (@ tptp.times_times_rat B) C2))))) (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C2) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A) C2)) (@ (@ tptp.times_times_nat B) C2))))) (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C2) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) C2)) (@ (@ tptp.times_times_int B) C2))))) (forall ((A tptp.real) (C2 tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C2)) (@ (@ tptp.times_times_real B) C2)) (or (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) C2) (@ (@ tptp.ord_less_real A) B)) (and (@ (@ tptp.ord_less_real C2) tptp.zero_zero_real) (@ (@ tptp.ord_less_real B) A))))) (forall ((A tptp.rat) (C2 tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C2)) (@ (@ tptp.times_times_rat B) C2)) (or (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C2) (@ (@ tptp.ord_less_rat A) B)) (and (@ (@ tptp.ord_less_rat C2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B) A))))) (forall ((A tptp.int) (C2 tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) C2)) (@ (@ tptp.times_times_int B) C2)) (or (and (@ (@ tptp.ord_less_int tptp.zero_zero_int) C2) (@ (@ tptp.ord_less_int A) B)) (and (@ (@ tptp.ord_less_int C2) tptp.zero_zero_int) (@ (@ tptp.ord_less_int B) A))))) (forall ((A tptp.real) (B tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.times_times_real C2))) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C2) (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B)))))) (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C2))) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C2) (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B)))))) (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C2))) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C2) (@ (@ tptp.ord_less_nat (@ _let_1 A)) (@ _let_1 B)))))) (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int C2))) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C2) (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B)))))) (not (@ _let_197 tptp.zero_z3403309356797280102nteger)) (not (@ _let_198 tptp.zero_zero_real)) (not (@ _let_196 tptp.zero_zero_rat)) (not (@ _let_353 tptp.zero_zero_nat)) (not (@ _let_195 tptp.zero_zero_int)) _let_352 _let_351 _let_350 _let_349 _let_347 _let_352 _let_351 _let_350 _let_349 _let_347 (forall ((K2 tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K2) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 M2)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat M2) N))))) (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat M2) (@ tptp.suc N)) (or (= M2 tptp.zero_zero_nat) (exists ((J tptp.nat)) (and (= M2 (@ tptp.suc J)) (@ (@ tptp.ord_less_nat J) N)))))) (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (exists ((M tptp.nat)) (= N (@ tptp.suc M))))) (forall ((N tptp.nat) (P2 (-> tptp.nat Bool))) (= (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.suc N)) (@ P2 I))) (and (@ P2 tptp.zero_zero_nat) (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) N) (@ P2 (@ tptp.suc I))))))) (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (exists ((M6 tptp.nat)) (= N (@ tptp.suc M6))))) (forall ((N tptp.nat) (P2 (-> tptp.nat Bool))) (= (exists ((I tptp.nat)) (and (@ (@ tptp.ord_less_nat I) (@ tptp.suc N)) (@ P2 I))) (or (@ P2 tptp.zero_zero_nat) (exists ((I tptp.nat)) (and (@ (@ tptp.ord_less_nat I) N) (@ P2 (@ tptp.suc I))))))) (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (@ (@ tptp.ord_less_nat M2) (@ tptp.suc N)))) (= tptp.ord_less_nat (lambda ((N4 tptp.nat) (__flatten_var_0 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N4)) __flatten_var_0))) (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat M2) (@ tptp.suc N)) (@ (@ tptp.ord_less_eq_nat M2) N))) (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ (@ tptp.ord_less_nat N) (@ tptp.suc M2)) (= N M2)))) (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M2)) N) (@ (@ tptp.ord_less_nat M2) N))) (forall ((I2 tptp.nat) (J2 tptp.nat) (P2 (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat I2) J2) (=> (@ P2 J2) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) N3) (=> (@ (@ tptp.ord_less_nat N3) J2) (=> (@ P2 (@ tptp.suc N3)) (@ P2 N3))))) (@ P2 I2))))) (forall ((I2 tptp.nat) (J2 tptp.nat) (P2 (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat I2) J2) (=> (@ P2 I2) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) N3) (=> (@ (@ tptp.ord_less_nat N3) J2) (=> (@ P2 N3) (@ P2 (@ tptp.suc N3)))))) (@ P2 J2))))) (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M2)) N) (@ (@ tptp.ord_less_nat M2) N))) (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) N) (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M2)) N))) (forall ((P2 (-> tptp.nat Bool)) (N tptp.nat)) (=> (@ P2 N) (=> (not (@ P2 tptp.zero_zero_nat)) (exists ((K tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat K) N) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) K) (not (@ P2 I4)))) (@ P2 K)))))) (forall ((K2 tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.suc K2)))) (= (@ (@ tptp.ord_less_nat (@ _let_1 M2)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat M2) N)))) (forall ((I2 tptp.nat) (J2 tptp.nat) (K2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) J2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K2) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat I2) K2)) (@ (@ tptp.times_times_nat J2) K2))))) (forall ((I2 tptp.nat) (J2 tptp.nat) (K2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K2))) (=> (@ (@ tptp.ord_less_nat I2) J2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K2) (@ (@ tptp.ord_less_nat (@ _let_1 I2)) (@ _let_1 J2)))))) _let_346 (forall ((M2 tptp.nat) (N tptp.nat)) (=> (= M2 (@ (@ tptp.times_times_nat M2) N)) (or (= N tptp.one_one_nat) (= M2 tptp.zero_zero_nat)))) (forall ((A tptp.real) (B tptp.real) (C2 tptp.real) (D tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_eq_real C2) D) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C2) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C2)) (@ (@ tptp.times_times_real B) D))))))) (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat) (D tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat C2) D) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C2) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C2)) (@ (@ tptp.times_times_rat B) D))))))) (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat) (D tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat C2) D) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C2) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A) C2)) (@ (@ tptp.times_times_nat B) D))))))) (forall ((A tptp.int) (B tptp.int) (C2 tptp.int) (D tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_eq_int C2) D) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C2) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) C2)) (@ (@ tptp.times_times_int B) D))))))) (forall ((A tptp.real) (B tptp.real) (C2 tptp.real) (D tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_real C2) D) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C2) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C2)) (@ (@ tptp.times_times_real B) D))))))) (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat) (D tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_rat C2) D) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C2) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C2)) (@ (@ tptp.times_times_rat B) D))))))) (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat) (D tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_nat C2) D) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C2) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A) C2)) (@ (@ tptp.times_times_nat B) D))))))) (forall ((A tptp.int) (B tptp.int) (C2 tptp.int) (D tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_int C2) D) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C2) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) C2)) (@ (@ tptp.times_times_int B) D))))))) (forall ((A tptp.real) (C2 tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) C2)) (@ (@ tptp.times_times_real B) C2)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C2) (@ (@ tptp.ord_less_eq_real A) B)))) (forall ((A tptp.rat) (C2 tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C2)) (@ (@ tptp.times_times_rat B) C2)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C2) (@ (@ tptp.ord_less_eq_rat A) B)))) (forall ((A tptp.nat) (C2 tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A) C2)) (@ (@ tptp.times_times_nat B) C2)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C2) (@ (@ tptp.ord_less_eq_nat A) B)))) (forall ((A tptp.int) (C2 tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) C2)) (@ (@ tptp.times_times_int B) C2)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C2) (@ (@ tptp.ord_less_eq_int A) B)))) (forall ((C2 tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real C2))) (=> (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C2) (@ (@ tptp.ord_less_eq_real A) B))))) (forall ((C2 tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C2))) (=> (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C2) (@ (@ tptp.ord_less_eq_rat A) B))))) (forall ((C2 tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C2))) (=> (@ (@ tptp.ord_less_eq_nat (@ _let_1 A)) (@ _let_1 B)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C2) (@ (@ tptp.ord_less_eq_nat A) B))))) (forall ((C2 tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C2))) (=> (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C2) (@ (@ tptp.ord_less_eq_int A) B))))) (forall ((C2 tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real C2))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C2) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_real A) B))))) (forall ((C2 tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C2))) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C2) (= (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_rat A) B))))) (forall ((C2 tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C2))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C2) (= (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_int A) B))))) (forall ((C2 tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real C2))) (=> (@ (@ tptp.ord_less_real C2) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_real B) A))))) (forall ((C2 tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C2))) (=> (@ (@ tptp.ord_less_rat C2) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_rat B) A))))) (forall ((C2 tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C2))) (=> (@ (@ tptp.ord_less_int C2) tptp.zero_zero_int) (= (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_int B) A))))) (forall ((A tptp.real) (C2 tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C2)) (@ (@ tptp.times_times_real B) C2)) (and (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C2) (@ (@ tptp.ord_less_real A) B)) (=> (@ (@ tptp.ord_less_eq_real C2) tptp.zero_zero_real) (@ (@ tptp.ord_less_real B) A))))) (forall ((A tptp.rat) (C2 tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C2)) (@ (@ tptp.times_times_rat B) C2)) (and (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C2) (@ (@ tptp.ord_less_rat A) B)) (=> (@ (@ tptp.ord_less_eq_rat C2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B) A))))) (forall ((A tptp.int) (C2 tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) C2)) (@ (@ tptp.times_times_int B) C2)) (and (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C2) (@ (@ tptp.ord_less_int A) B)) (=> (@ (@ tptp.ord_less_eq_int C2) tptp.zero_zero_int) (@ (@ tptp.ord_less_int B) A))))) (forall ((A tptp.real) (B tptp.real) (C2 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 C2) D) (=> (@ _let_1 A) (=> (@ _let_1 C2) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C2)) (@ (@ tptp.times_times_real B) D)))))))) (forall ((A tptp.rat) (B tptp.rat) (C2 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 C2) D) (=> (@ _let_1 A) (=> (@ _let_1 C2) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C2)) (@ (@ tptp.times_times_rat B) D)))))))) (forall ((A tptp.nat) (B tptp.nat) (C2 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 C2) D) (=> (@ _let_1 A) (=> (@ _let_1 C2) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A) C2)) (@ (@ tptp.times_times_nat B) D)))))))) (forall ((A tptp.int) (B tptp.int) (C2 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 C2) D) (=> (@ _let_1 A) (=> (@ _let_1 C2) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) C2)) (@ (@ tptp.times_times_int B) D)))))))) (forall ((A tptp.real) (C2 tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C2)) (@ (@ tptp.times_times_real B) C2)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C2) (@ (@ tptp.ord_less_real A) B)))) (forall ((A tptp.rat) (C2 tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C2)) (@ (@ tptp.times_times_rat B) C2)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C2) (@ (@ tptp.ord_less_rat A) B)))) (forall ((A tptp.nat) (C2 tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A) C2)) (@ (@ tptp.times_times_nat B) C2)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C2) (@ (@ tptp.ord_less_nat A) B)))) (forall ((A tptp.int) (C2 tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) C2)) (@ (@ tptp.times_times_int B) C2)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C2) (@ (@ tptp.ord_less_int A) B)))) (forall ((C2 tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real C2))) (= (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B)) (and (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C2) (@ (@ tptp.ord_less_real A) B)) (=> (@ (@ tptp.ord_less_eq_real C2) tptp.zero_zero_real) (@ (@ tptp.ord_less_real B) A)))))) (forall ((C2 tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C2))) (= (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B)) (and (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C2) (@ (@ tptp.ord_less_rat A) B)) (=> (@ (@ tptp.ord_less_eq_rat C2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B) A)))))) (forall ((C2 tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C2))) (= (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B)) (and (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C2) (@ (@ tptp.ord_less_int A) B)) (=> (@ (@ tptp.ord_less_eq_int C2) tptp.zero_zero_int) (@ (@ tptp.ord_less_int B) A)))))) (forall ((A tptp.real) (B tptp.real) (C2 tptp.real) (D tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_real C2) D) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) B) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C2) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C2)) (@ (@ tptp.times_times_real B) D))))))) (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat) (D tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_rat C2) D) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) B) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C2) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C2)) (@ (@ tptp.times_times_rat B) D))))))) (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat) (D tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_nat C2) D) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C2) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A) C2)) (@ (@ tptp.times_times_nat B) D))))))) (forall ((A tptp.int) (B tptp.int) (C2 tptp.int) (D tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_int C2) D) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C2) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) C2)) (@ (@ tptp.times_times_int B) D))))))) (forall ((C2 tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real C2))) (=> (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C2) (@ (@ tptp.ord_less_real A) B))))) (forall ((C2 tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C2))) (=> (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C2) (@ (@ tptp.ord_less_rat A) B))))) (forall ((C2 tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C2))) (=> (@ (@ tptp.ord_less_nat (@ _let_1 A)) (@ _let_1 B)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C2) (@ (@ tptp.ord_less_nat A) B))))) (forall ((C2 tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C2))) (=> (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C2) (@ (@ tptp.ord_less_int A) B))))) (forall ((A tptp.real) (C2 tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) C2)) (@ (@ tptp.times_times_real B) C2)) (and (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C2) (@ (@ tptp.ord_less_eq_real A) B)) (=> (@ (@ tptp.ord_less_real C2) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real B) A))))) (forall ((A tptp.rat) (C2 tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C2)) (@ (@ tptp.times_times_rat B) C2)) (and (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C2) (@ (@ tptp.ord_less_eq_rat A) B)) (=> (@ (@ tptp.ord_less_rat C2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat B) A))))) (forall ((A tptp.int) (C2 tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) C2)) (@ (@ tptp.times_times_int B) C2)) (and (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C2) (@ (@ tptp.ord_less_eq_int A) B)) (=> (@ (@ tptp.ord_less_int C2) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int B) A))))) (forall ((C2 tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real C2))) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B)) (and (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C2) (@ (@ tptp.ord_less_eq_real A) B)) (=> (@ (@ tptp.ord_less_real C2) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real B) A)))))) (forall ((C2 tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C2))) (= (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B)) (and (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C2) (@ (@ tptp.ord_less_eq_rat A) B)) (=> (@ (@ tptp.ord_less_rat C2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat B) A)))))) (forall ((C2 tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C2))) (= (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B)) (and (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C2) (@ (@ tptp.ord_less_eq_int A) B)) (=> (@ (@ tptp.ord_less_int C2) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int B) A)))))) (forall ((X tptp.produc9072475918466114483BT_nat)) (=> (forall ((A3 Bool) (B3 Bool) (X3 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf A3) B3)) X3)))) (=> (forall ((Uu2 tptp.option4927543243414619207at_nat) (Uv2 tptp.list_VEBT_VEBT) (Uw tptp.vEBT_VEBT) (Ux tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node Uu2) tptp.zero_zero_nat) Uv2) Uw)) Ux)))) (not (forall ((Uy tptp.option4927543243414619207at_nat) (V tptp.nat) (TreeList tptp.list_VEBT_VEBT) (S tptp.vEBT_VEBT) (X3 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node Uy) (@ tptp.suc V)) TreeList) S)) X3)))))))) (forall ((C2 tptp.code_integer) (A tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger C2) tptp.one_one_Code_integer) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.times_3573771949741848930nteger A) C2)) A)))) (forall ((C2 tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_eq_real C2) tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) C2)) A)))) (forall ((C2 tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat C2) tptp.one_one_rat) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C2)) A)))) (forall ((C2 tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat C2) tptp.one_one_nat) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A) C2)) A)))) (forall ((C2 tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int C2) tptp.one_one_int) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) C2)) A)))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger A) tptp.one_one_Code_integer) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) B) (=> (@ (@ tptp.ord_le3102999989581377725nteger B) tptp.one_one_Code_integer) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.times_3573771949741848930nteger A) B)) tptp.one_one_Code_integer))))) (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) B) (=> (@ (@ tptp.ord_less_eq_real B) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) B)) tptp.one_one_real))))) (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) tptp.one_one_rat) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) B) (=> (@ (@ tptp.ord_less_eq_rat B) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) B)) tptp.one_one_rat))))) (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.one_one_nat) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) B) (=> (@ (@ tptp.ord_less_eq_nat B) tptp.one_one_nat) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A) B)) tptp.one_one_nat))))) (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) tptp.one_one_int) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B) (=> (@ (@ tptp.ord_less_eq_int B) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) B)) tptp.one_one_int))))) (forall ((X tptp.code_integer) (Y tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_le3102999989581377725nteger Y) tptp.one_one_Code_integer) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.times_3573771949741848930nteger X) Y)) X)))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real X) Y)) X)))))) (forall ((X tptp.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)))))) (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_int Y) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int X) Y)) X)))))) (forall ((X tptp.code_integer) (Y tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_le3102999989581377725nteger Y) tptp.one_one_Code_integer) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.times_3573771949741848930nteger Y) X)) X)))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real Y) X)) X)))))) (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)))))) (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_int Y) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int Y) X)) X)))))) (forall ((P2 (-> tptp.nat Bool)) (N tptp.nat)) (=> (@ P2 N) (=> (not (@ P2 tptp.zero_zero_nat)) (exists ((K tptp.nat)) (and (@ (@ tptp.ord_less_nat K) N) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I4) K) (not (@ P2 I4)))) (@ P2 (@ tptp.suc K))))))) (forall ((N tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)) M2) (@ (@ tptp.ord_less_nat N) (@ (@ tptp.times_times_nat N) M2))))) (forall ((N tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)) M2) (@ (@ tptp.ord_less_nat N) (@ (@ tptp.times_times_nat M2) N))))) (forall ((N tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)))) (=> (@ _let_1 N) (=> (@ _let_1 M2) (@ _let_1 (@ (@ tptp.times_times_nat M2) N)))))) (= tptp.ord_less_nat (lambda ((Y4 tptp.nat) (X4 tptp.nat)) (@ (@ tptp.vEBT_VEBT_greater (@ tptp.some_nat X4)) (@ tptp.some_nat Y4)))) (= tptp.ord_less_nat (lambda ((X4 tptp.nat) (Y4 tptp.nat)) (@ (@ tptp.vEBT_VEBT_less (@ tptp.some_nat X4)) (@ tptp.some_nat Y4)))) (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.vEBT_invar_vebt (@ tptp.vEBT_vebt_buildup N)) N))) (forall ((X tptp.real) (Y tptp.real)) (=> (forall ((Z tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Z) (=> (@ (@ tptp.ord_less_real Z) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real Z) X)) Y)))) (@ (@ tptp.ord_less_eq_real X) Y))) (forall ((X tptp.rat) (Y tptp.rat)) (=> (forall ((Z tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Z) (=> (@ (@ tptp.ord_less_rat Z) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat Z) X)) Y)))) (@ (@ tptp.ord_less_eq_rat X) Y))) (forall ((S2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.vEBT_invar_vebt S2) tptp.m) (=> (= (@ tptp.vEBT_VEBT_set_vebt tptp.summary2) (@ tptp.vEBT_VEBT_set_vebt S2)) (= S2 tptp.summary2)))) (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)))) (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))))) (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)))) (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))))) (forall ((Z3 tptp.real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.times_times_real Z3))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Z3) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_real X) Y))))) (forall ((Z3 tptp.rat) (X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat Z3))) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Z3) (= (@ (@ tptp.ord_less_eq_rat (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_rat X) Y))))) (forall ((Z3 tptp.int) (X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.times_times_int Z3))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z3) (= (@ (@ tptp.ord_less_eq_int (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_int X) Y))))) (forall ((Z3 tptp.real) (X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Z3) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real X) Z3)) (@ (@ tptp.times_times_real Y) Z3)) (@ (@ tptp.ord_less_eq_real X) Y)))) (forall ((Z3 tptp.rat) (X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Z3) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat X) Z3)) (@ (@ tptp.times_times_rat Y) Z3)) (@ (@ tptp.ord_less_eq_rat X) Y)))) (forall ((Z3 tptp.int) (X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z3) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int X) Z3)) (@ (@ tptp.times_times_int Y) Z3)) (@ (@ tptp.ord_less_eq_int X) Y)))) (forall ((T tptp.vEBT_VEBT) (H tptp.nat) (K2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.vEBT_invar_vebt T) H) (=> (@ (@ tptp.vEBT_invar_vebt K2) H) (=> (= (@ tptp.vEBT_VEBT_set_vebt T) (@ tptp.vEBT_VEBT_set_vebt K2)) (= (@ tptp.vEBT_vebt_mint T) (@ tptp.vEBT_vebt_mint K2)))))) (forall ((T tptp.vEBT_VEBT) (H tptp.nat) (K2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.vEBT_invar_vebt T) H) (=> (@ (@ tptp.vEBT_invar_vebt K2) H) (=> (= (@ tptp.vEBT_VEBT_set_vebt T) (@ tptp.vEBT_VEBT_set_vebt K2)) (= (@ tptp.vEBT_vebt_maxt T) (@ tptp.vEBT_vebt_maxt K2)))))) _let_345 (= (@ tptp.vEBT_vebt_buildup tptp.zero_zero_nat) _let_329) (= (@ tptp.vEBT_vebt_buildup _let_10) _let_329) (forall ((Z3 tptp.real) (X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Z3) (= (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real X) Z3)) (@ (@ tptp.times_times_real Y) Z3)) (@ (@ tptp.ord_less_real X) Y)))) (forall ((Z3 tptp.rat) (X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Z3) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat X) Z3)) (@ (@ tptp.times_times_rat Y) Z3)) (@ (@ tptp.ord_less_rat X) Y)))) (forall ((Z3 tptp.int) (X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z3) (= (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int X) Z3)) (@ (@ tptp.times_times_int Y) Z3)) (@ (@ tptp.ord_less_int X) Y)))) (forall ((Mi tptp.nat) (Ma tptp.nat) (Ux2 tptp.nat) (Uy2 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))) Ux2) Uy2) Uz)) (@ tptp.some_nat Ma))) (forall ((Mi tptp.nat) (Ma tptp.nat) (Ux2 tptp.nat) (Uy2 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))) Ux2) Uy2) Uz)) (@ tptp.some_nat Mi))) (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))))) (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))))) (forall ((N tptp.nat) (X tptp.nat)) (not (@ (@ tptp.vEBT_V5719532721284313246member (@ tptp.vEBT_vebt_buildup N)) X))) (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)))) (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)))) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.insert_nat tptp.mi) (@ (@ tptp.insert_nat tptp.ma) tptp.bot_bot_set_nat))) _let_344) (forall ((X tptp.produc9072475918466114483BT_nat)) (=> (forall ((A3 Bool) (B3 Bool) (X3 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf A3) B3)) X3)))) (not (forall ((Info tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT) (X3 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node Info) Deg2) TreeList) Summary2)) X3))))))) (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))))) (forall ((F2 (-> 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 F2) (@ tptp.some_P7363390416028606310at_nat A)) (@ tptp.some_P7363390416028606310at_nat B)) (@ tptp.some_P7363390416028606310at_nat (@ (@ F2 A) B)))) (forall ((F2 (-> tptp.num tptp.num tptp.num)) (A tptp.num) (B tptp.num)) (= (@ (@ (@ tptp.vEBT_V819420779217536731ft_num F2) (@ tptp.some_num A)) (@ tptp.some_num B)) (@ tptp.some_num (@ (@ F2 A) B)))) (forall ((F2 (-> tptp.nat tptp.nat tptp.nat)) (A tptp.nat) (B tptp.nat)) (= (@ (@ (@ tptp.vEBT_V4262088993061758097ft_nat F2) (@ tptp.some_nat A)) (@ tptp.some_nat B)) (@ tptp.some_nat (@ (@ F2 A) B)))) (forall ((N tptp.nat)) (= (@ tptp.vEBT_VEBT_set_vebt (@ tptp.vEBT_vebt_buildup N)) tptp.bot_bot_set_nat)) (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 ((Z4 tptp.nat)) (=> (and (@ (@ tptp.vEBT_vebt_member T) Z4) (@ (@ tptp.ord_less_nat Z4) X)) (@ (@ tptp.ord_less_eq_nat Z4) Y)))))) (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 ((Z4 tptp.nat)) (=> (and (@ (@ tptp.vEBT_vebt_member T) Z4) (@ (@ tptp.ord_less_nat X) Z4)) (@ (@ tptp.ord_less_eq_nat Y) Z4)))))) _let_314 (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 tptp.treeList2)) (and (@ (@ tptp.vEBT_invar_vebt X5) tptp.na) (forall ((Xa tptp.vEBT_VEBT)) (=> (@ (@ tptp.vEBT_invar_vebt Xa) tptp.na) (=> (= (@ tptp.vEBT_VEBT_set_vebt X5) (@ tptp.vEBT_VEBT_set_vebt Xa)) (= Xa X5))))))) (forall ((A tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A) tptp.bot_bot_set_int) (= A tptp.bot_bot_set_int))) (forall ((A tptp.set_real)) (=> (@ (@ tptp.ord_less_eq_set_real A) tptp.bot_bot_set_real) (= A tptp.bot_bot_set_real))) (forall ((A tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A) tptp.bot_bot_set_nat) (= A tptp.bot_bot_set_nat))) (forall ((A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.bot_bot_nat) (= A tptp.bot_bot_nat))) (forall ((A tptp.set_int)) (= (@ (@ tptp.ord_less_eq_set_int A) tptp.bot_bot_set_int) (= A tptp.bot_bot_set_int))) (forall ((A tptp.set_real)) (= (@ (@ tptp.ord_less_eq_set_real A) tptp.bot_bot_set_real) (= A tptp.bot_bot_set_real))) (forall ((A tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat A) tptp.bot_bot_set_nat) (= A tptp.bot_bot_set_nat))) (forall ((A tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat A) tptp.bot_bot_nat) (= A tptp.bot_bot_nat))) (forall ((A tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int tptp.bot_bot_set_int) A)) (forall ((A tptp.set_real)) (@ (@ tptp.ord_less_eq_set_real tptp.bot_bot_set_real) A)) (forall ((A tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat tptp.bot_bot_set_nat) A)) (forall ((A tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.bot_bot_nat) A)) (forall ((A tptp.set_nat)) (not (@ (@ tptp.ord_less_set_nat A) tptp.bot_bot_set_nat))) (forall ((A tptp.set_int)) (not (@ (@ tptp.ord_less_set_int A) tptp.bot_bot_set_int))) (forall ((A tptp.set_real)) (not (@ (@ tptp.ord_less_set_real A) tptp.bot_bot_set_real))) (forall ((A tptp.nat)) (not (@ (@ tptp.ord_less_nat A) tptp.bot_bot_nat))) (forall ((A tptp.set_nat)) (= (not (= A tptp.bot_bot_set_nat)) (@ (@ tptp.ord_less_set_nat tptp.bot_bot_set_nat) A))) (forall ((A tptp.set_int)) (= (not (= A tptp.bot_bot_set_int)) (@ (@ tptp.ord_less_set_int tptp.bot_bot_set_int) A))) (forall ((A tptp.set_real)) (= (not (= A tptp.bot_bot_set_real)) (@ (@ tptp.ord_less_set_real tptp.bot_bot_set_real) A))) (forall ((A tptp.nat)) (= (not (= A tptp.bot_bot_nat)) (@ (@ tptp.ord_less_nat tptp.bot_bot_nat) A))) (forall ((Uu tptp.option4927543243414619207at_nat) (Uv tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT) (Ux2 tptp.nat)) (not (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ (@ (@ tptp.vEBT_Node Uu) tptp.zero_zero_nat) Uv) Uw2)) Ux2))) (forall ((A Bool) (B Bool) (X tptp.nat)) (let ((_let_1 (= X tptp.one_one_nat))) (let ((_let_2 (= X tptp.zero_zero_nat))) (= (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.vEBT_Leaf A) B)) X) (and (=> _let_2 A) (=> (not _let_2) (and (=> _let_1 B) _let_1))))))) (forall ((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))))) (forall ((V2 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 V2)) (@ tptp.suc tptp.zero_zero_nat)) Vb) Vc)) X))) (forall ((A Bool) (B Bool) (X tptp.nat)) (let ((_let_1 (= X tptp.one_one_nat))) (let ((_let_2 (= X tptp.zero_zero_nat))) (= (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.vEBT_Leaf A) B)) X) (and (=> _let_2 A) (=> (not _let_2) (and (=> _let_1 B) _let_1))))))) (forall ((V2 tptp.product_prod_nat_nat) (Uy2 tptp.list_VEBT_VEBT) (Uz tptp.vEBT_VEBT) (X tptp.nat)) (not (@ (@ tptp.vEBT_vebt_member (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Uy2) Uz)) X))) (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)))) (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)))) (forall ((N tptp.nat) (X tptp.nat)) (not (@ (@ tptp.vEBT_VEBT_membermima (@ tptp.vEBT_vebt_buildup N)) X))) (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (= (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.vEBT_vebt_delete T) X)) Y) (and (not (= X Y)) (@ (@ tptp.vEBT_vebt_member T) Y))))) (forall ((X tptp.produc9072475918466114483BT_nat)) (=> (forall ((Uu2 Bool) (Uv2 Bool) (Uw tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf Uu2) Uv2)) Uw)))) (=> (forall ((Ux tptp.list_VEBT_VEBT) (Uy tptp.vEBT_VEBT) (Uz2 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) tptp.zero_zero_nat) Ux) Uy)) Uz2)))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va2 tptp.list_VEBT_VEBT) (Vb2 tptp.vEBT_VEBT) (X3 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) Va2) Vb2)) X3)))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (V tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT) (X3 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc V)) TreeList) Vc2)) X3)))) (not (forall ((V tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Vd tptp.vEBT_VEBT) (X3 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) (@ tptp.suc V)) TreeList) Vd)) X3)))))))))) (=> _let_286 (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 tptp.treeList2)) (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X5) X_1)))))) (forall ((X tptp.nat)) (=> (forall ((N3 tptp.nat)) (not (= X (@ (@ tptp.plus_plus_nat N3) N3)))) (not (forall ((N3 tptp.nat)) (not (= X (@ (@ tptp.plus_plus_nat N3) (@ tptp.suc N3)))))))) (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (@ (@ tptp.vEBT_invar_vebt (@ (@ tptp.vEBT_vebt_delete T) X)) N))) (forall ((T tptp.vEBT_VEBT) (X tptp.nat)) (=> (= (@ tptp.vEBT_vebt_maxt T) (@ tptp.some_nat X)) (@ (@ tptp.vEBT_V8194947554948674370ptions T) X))) (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))))) (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)))) (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)))) _let_343 (forall ((B tptp.real) (A tptp.real) (C2 tptp.real)) (= (= (@ (@ tptp.plus_plus_real B) A) (@ (@ tptp.plus_plus_real C2) A)) (= B C2))) (forall ((B tptp.rat) (A tptp.rat) (C2 tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat B) A) (@ (@ tptp.plus_plus_rat C2) A)) (= B C2))) (forall ((B tptp.nat) (A tptp.nat) (C2 tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat B) A) (@ (@ tptp.plus_plus_nat C2) A)) (= B C2))) (forall ((B tptp.int) (A tptp.int) (C2 tptp.int)) (= (= (@ (@ tptp.plus_plus_int B) A) (@ (@ tptp.plus_plus_int C2) A)) (= B C2))) (forall ((A tptp.real) (B tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A))) (= (= (@ _let_1 B) (@ _let_1 C2)) (= B C2)))) (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat A))) (= (= (@ _let_1 B) (@ _let_1 C2)) (= B C2)))) (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A))) (= (= (@ _let_1 B) (@ _let_1 C2)) (= B C2)))) (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A))) (= (= (@ _let_1 B) (@ _let_1 C2)) (= B C2)))) (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 ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X5) X_1))))) (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary) X_1))))))) (forall ((C2 tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real C2))) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_real A) B)))) (forall ((C2 tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat C2))) (= (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_rat A) B)))) (forall ((C2 tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C2))) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_nat A) B)))) (forall ((C2 tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C2))) (= (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_int A) B)))) (forall ((A tptp.real) (C2 tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A) C2)) (@ (@ tptp.plus_plus_real B) C2)) (@ (@ tptp.ord_less_eq_real A) B))) (forall ((A tptp.rat) (C2 tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A) C2)) (@ (@ tptp.plus_plus_rat B) C2)) (@ (@ tptp.ord_less_eq_rat A) B))) (forall ((A tptp.nat) (C2 tptp.nat) (B tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A) C2)) (@ (@ tptp.plus_plus_nat B) C2)) (@ (@ tptp.ord_less_eq_nat A) B))) (forall ((A tptp.int) (C2 tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A) C2)) (@ (@ tptp.plus_plus_int B) C2)) (@ (@ tptp.ord_less_eq_int A) B))) (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex A) tptp.zero_zero_complex) A)) (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real A) tptp.zero_zero_real) A)) (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat A) tptp.zero_zero_rat) A)) (forall ((A tptp.nat)) (= (@ (@ tptp.plus_plus_nat A) tptp.zero_zero_nat) A)) (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int A) tptp.zero_zero_int) A)) (forall ((A tptp.real)) (= (= tptp.zero_zero_real (@ (@ tptp.plus_plus_real A) A)) (= A tptp.zero_zero_real))) (forall ((A tptp.rat)) (= (= tptp.zero_zero_rat (@ (@ tptp.plus_plus_rat A) A)) (= A tptp.zero_zero_rat))) (forall ((A tptp.int)) (= (= tptp.zero_zero_int (@ (@ tptp.plus_plus_int A) A)) (= A tptp.zero_zero_int))) (forall ((B tptp.complex) (A tptp.complex)) (= (= (@ (@ tptp.plus_plus_complex B) A) A) (= B tptp.zero_zero_complex))) (forall ((B tptp.real) (A tptp.real)) (= (= (@ (@ tptp.plus_plus_real B) A) A) (= B tptp.zero_zero_real))) (forall ((B tptp.rat) (A tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat B) A) A) (= B tptp.zero_zero_rat))) (forall ((B tptp.nat) (A tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat B) A) A) (= B tptp.zero_zero_nat))) (forall ((B tptp.int) (A tptp.int)) (= (= (@ (@ tptp.plus_plus_int B) A) A) (= B tptp.zero_zero_int))) (forall ((A tptp.complex) (B tptp.complex)) (= (= (@ (@ tptp.plus_plus_complex A) B) A) (= B tptp.zero_zero_complex))) (forall ((A tptp.real) (B tptp.real)) (= (= (@ (@ tptp.plus_plus_real A) B) A) (= B tptp.zero_zero_real))) (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat A) B) A) (= B tptp.zero_zero_rat))) (forall ((A tptp.nat) (B tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat A) B) A) (= B tptp.zero_zero_nat))) (forall ((A tptp.int) (B tptp.int)) (= (= (@ (@ tptp.plus_plus_int A) B) A) (= B tptp.zero_zero_int))) (forall ((A tptp.complex) (B tptp.complex)) (= (= A (@ (@ 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tptp.zero_zero_int))) (forall ((X tptp.nat) (Y tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat X) Y) tptp.zero_zero_nat) (and (= X tptp.zero_zero_nat) (= Y tptp.zero_zero_nat)))) (forall ((X tptp.nat) (Y tptp.nat)) (= (= tptp.zero_zero_nat (@ (@ tptp.plus_plus_nat X) Y)) (and (= X tptp.zero_zero_nat) (= Y tptp.zero_zero_nat)))) (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex tptp.zero_zero_complex) A) A)) (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real tptp.zero_zero_real) A) A)) (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat tptp.zero_zero_rat) A) A)) (forall ((A tptp.nat)) (= (@ (@ tptp.plus_plus_nat tptp.zero_zero_nat) A) A)) (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int tptp.zero_zero_int) A) A)) (forall ((A tptp.real) (C2 tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) C2)) (@ (@ tptp.plus_plus_real B) C2)) (@ (@ tptp.ord_less_real A) B))) (forall ((A tptp.rat) (C2 tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ 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tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C2))) (= (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_int A) B)))) (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat M2))) (= (@ _let_1 (@ tptp.suc N)) (@ tptp.suc (@ _let_1 N))))) (forall ((M2 tptp.nat)) (= (@ (@ tptp.plus_plus_nat M2) tptp.zero_zero_nat) M2)) (forall ((M2 tptp.nat) (N tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat M2) N) tptp.zero_zero_nat) (and (= M2 tptp.zero_zero_nat) (= N tptp.zero_zero_nat)))) (forall ((K2 tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K2))) (= (@ (@ tptp.ord_less_nat (@ _let_1 M2)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat M2) N)))) (forall ((K2 tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K2))) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 M2)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat M2) N)))) (forall ((X tptp.option4927543243414619207at_nat)) (= (forall ((Y4 tptp.product_prod_nat_nat)) (not (= X (@ tptp.some_P7363390416028606310at_nat Y4)))) (= X tptp.none_P5556105721700978146at_nat))) (forall ((X tptp.option_nat)) (= (forall ((Y4 tptp.nat)) (not (= X (@ tptp.some_nat Y4)))) (= X tptp.none_nat))) (forall ((X tptp.option_num)) (= (forall ((Y4 tptp.num)) (not (= X (@ tptp.some_num Y4)))) (= X tptp.none_num))) (forall ((X tptp.option4927543243414619207at_nat)) (= (not (= X tptp.none_P5556105721700978146at_nat)) (exists ((Y4 tptp.product_prod_nat_nat)) (= X (@ tptp.some_P7363390416028606310at_nat Y4))))) (forall ((X tptp.option_nat)) (= (not (= X tptp.none_nat)) (exists ((Y4 tptp.nat)) (= X (@ tptp.some_nat Y4))))) (forall ((X tptp.option_num)) (= (not (= X tptp.none_num)) (exists ((Y4 tptp.num)) (= X (@ tptp.some_num Y4))))) (forall ((B tptp.real) (A tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real B) A)) B) (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real))) (forall ((B tptp.rat) (A tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat B) A)) B) (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat))) (forall ((B tptp.nat) (A tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat B) A)) B) (@ (@ tptp.ord_less_eq_nat A) tptp.zero_zero_nat))) (forall ((B tptp.int) (A tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int B) A)) B) (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int))) (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A) B)) B) (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real))) (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A) B)) B) (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat))) (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A) B)) B) (@ (@ tptp.ord_less_eq_nat A) tptp.zero_zero_nat))) (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A) B)) B) (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int))) (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_eq_real A) (@ (@ tptp.plus_plus_real A) B)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) B))) (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat A) (@ (@ tptp.plus_plus_rat A) B)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) B))) (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat A) (@ (@ tptp.plus_plus_nat A) B)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) B))) (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.plus_plus_int A) B)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B))) (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_eq_real A) (@ (@ tptp.plus_plus_real B) A)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) B))) (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat A) (@ (@ tptp.plus_plus_rat B) A)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) B))) (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat A) (@ (@ tptp.plus_plus_nat B) A)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) B))) (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.plus_plus_int B) A)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B))) (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A) A)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real))) (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A) A)) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat))) (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A) A)) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int))) (forall ((A tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ (@ tptp.plus_plus_real A) A)) (@ _let_1 A)))) (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat A) A)) (@ _let_1 A)))) (forall ((A tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.plus_plus_int A) A)) (@ _let_1 A)))) (forall ((A tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ _let_1 (@ (@ tptp.plus_plus_real A) A)) (@ _let_1 A)))) (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat A) A)) (@ _let_1 A)))) (forall ((A tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.plus_plus_int A) A)) (@ _let_1 A)))) (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) A)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real A) tptp.zero_zero_real))) (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) A)) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat))) (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) A)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int A) tptp.zero_zero_int))) (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_real A) (@ (@ tptp.plus_plus_real B) A)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) B))) (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat A) (@ (@ tptp.plus_plus_rat B) A)) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) B))) (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.ord_less_nat A) (@ (@ tptp.plus_plus_nat B) A)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B))) (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_int A) (@ (@ tptp.plus_plus_int B) A)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) B))) (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_real A) (@ (@ tptp.plus_plus_real A) B)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) B))) (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat A) (@ (@ tptp.plus_plus_rat A) B)) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) B))) (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.ord_less_nat A) (@ (@ tptp.plus_plus_nat A) B)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B))) (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_int A) (@ (@ tptp.plus_plus_int A) B)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) B))) (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) B)) B) (@ (@ tptp.ord_less_real A) tptp.zero_zero_real))) (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) B)) B) (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat))) (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) B)) B) (@ (@ tptp.ord_less_nat A) tptp.zero_zero_nat))) (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) B)) B) (@ (@ tptp.ord_less_int A) tptp.zero_zero_int))) (forall ((B tptp.real) (A tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real B) A)) B) (@ (@ tptp.ord_less_real A) tptp.zero_zero_real))) (forall ((B tptp.rat) (A tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat B) A)) B) (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat))) (forall ((B tptp.nat) (A tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat B) A)) B) (@ (@ tptp.ord_less_nat A) tptp.zero_zero_nat))) (forall ((B tptp.int) (A tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int B) A)) B) (@ (@ tptp.ord_less_int A) tptp.zero_zero_int))) (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M2) N)) (or (@ _let_1 M2) (@ _let_1 N))))) (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat M2))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.plus_plus_nat M2) (@ _let_1 N))))) (forall ((B tptp.real) (A tptp.real) (C2 tptp.real)) (=> (= (@ (@ tptp.plus_plus_real B) A) (@ (@ tptp.plus_plus_real C2) A)) (= B C2))) (forall ((B tptp.rat) (A tptp.rat) (C2 tptp.rat)) (=> (= (@ (@ tptp.plus_plus_rat B) A) (@ (@ tptp.plus_plus_rat C2) A)) (= B C2))) (forall ((B tptp.nat) (A tptp.nat) (C2 tptp.nat)) (=> (= (@ (@ tptp.plus_plus_nat B) A) (@ (@ tptp.plus_plus_nat C2) A)) (= B C2))) (forall ((B tptp.int) (A tptp.int) (C2 tptp.int)) (=> (= (@ (@ tptp.plus_plus_int B) A) (@ (@ tptp.plus_plus_int C2) A)) (= B C2))) (forall ((A tptp.real) (B tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A))) (=> (= (@ _let_1 B) (@ _let_1 C2)) (= B C2)))) (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat A))) (=> (= (@ _let_1 B) (@ _let_1 C2)) (= B C2)))) (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A))) (=> (= (@ _let_1 B) (@ _let_1 C2)) (= B C2)))) (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A))) (=> (= (@ _let_1 B) (@ _let_1 C2)) (= B C2)))) (forall ((B tptp.real) (A tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real B))) (let ((_let_2 (@ tptp.plus_plus_real A))) (= (@ _let_1 (@ _let_2 C2)) (@ _let_2 (@ _let_1 C2)))))) (forall ((B tptp.rat) (A tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat B))) (let ((_let_2 (@ tptp.plus_plus_rat A))) (= (@ _let_1 (@ _let_2 C2)) (@ _let_2 (@ _let_1 C2)))))) (forall ((B tptp.nat) (A tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat B))) (let ((_let_2 (@ tptp.plus_plus_nat A))) (= (@ _let_1 (@ _let_2 C2)) (@ _let_2 (@ _let_1 C2)))))) (forall ((B tptp.int) (A tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int B))) (let ((_let_2 (@ tptp.plus_plus_int A))) (= (@ _let_1 (@ _let_2 C2)) (@ _let_2 (@ _let_1 C2)))))) (= tptp.plus_plus_real (lambda ((A5 tptp.real) (B4 tptp.real)) (@ (@ tptp.plus_plus_real B4) A5))) (= tptp.plus_plus_rat (lambda ((A5 tptp.rat) (B4 tptp.rat)) (@ (@ tptp.plus_plus_rat B4) A5))) (= tptp.plus_plus_nat (lambda ((A5 tptp.nat) (B4 tptp.nat)) (@ (@ tptp.plus_plus_nat B4) A5))) (= tptp.plus_plus_int (lambda ((A5 tptp.int) (B4 tptp.int)) (@ (@ tptp.plus_plus_int B4) A5))) (forall ((B tptp.real) (A tptp.real) (C2 tptp.real)) (= (= (@ (@ tptp.plus_plus_real B) A) (@ (@ tptp.plus_plus_real C2) A)) (= B C2))) (forall ((B tptp.rat) (A tptp.rat) (C2 tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat B) A) (@ (@ tptp.plus_plus_rat C2) A)) (= B C2))) (forall ((B tptp.int) (A tptp.int) (C2 tptp.int)) (= (= (@ (@ tptp.plus_plus_int B) A) (@ (@ tptp.plus_plus_int C2) A)) (= B C2))) (forall ((A tptp.real) (B tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A))) (= (= (@ _let_1 B) (@ _let_1 C2)) (= B C2)))) (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat A))) (= (= (@ _let_1 B) (@ _let_1 C2)) (= B C2)))) (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A))) (= (= (@ _let_1 B) (@ _let_1 C2)) (= B C2)))) (forall ((A tptp.real) (B tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A))) (= (@ (@ tptp.plus_plus_real (@ _let_1 B)) C2) (@ _let_1 (@ (@ tptp.plus_plus_real B) C2))))) (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat A))) (= (@ (@ tptp.plus_plus_rat (@ _let_1 B)) C2) (@ _let_1 (@ (@ tptp.plus_plus_rat B) C2))))) (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A))) (= (@ (@ tptp.plus_plus_nat (@ _let_1 B)) C2) (@ _let_1 (@ (@ tptp.plus_plus_nat B) C2))))) (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A))) (= (@ (@ tptp.plus_plus_int (@ _let_1 B)) C2) (@ _let_1 (@ (@ tptp.plus_plus_int B) C2))))) (forall ((B5 tptp.real) (K2 tptp.real) (B tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A))) (let ((_let_2 (@ tptp.plus_plus_real K2))) (=> (= B5 (@ _let_2 B)) (= (@ _let_1 B5) (@ _let_2 (@ _let_1 B))))))) (forall ((B5 tptp.rat) (K2 tptp.rat) (B tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat A))) (let ((_let_2 (@ tptp.plus_plus_rat K2))) (=> (= B5 (@ _let_2 B)) (= (@ _let_1 B5) (@ _let_2 (@ _let_1 B))))))) (forall ((B5 tptp.nat) (K2 tptp.nat) (B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A))) (let ((_let_2 (@ tptp.plus_plus_nat K2))) (=> (= B5 (@ _let_2 B)) (= (@ _let_1 B5) (@ _let_2 (@ _let_1 B))))))) (forall ((B5 tptp.int) (K2 tptp.int) (B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A))) (let ((_let_2 (@ tptp.plus_plus_int K2))) (=> (= B5 (@ _let_2 B)) (= (@ _let_1 B5) (@ _let_2 (@ _let_1 B))))))) (forall ((A4 tptp.real) (K2 tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real K2))) (=> (= A4 (@ _let_1 A)) (= (@ (@ tptp.plus_plus_real A4) B) (@ _let_1 (@ (@ tptp.plus_plus_real A) B)))))) (forall ((A4 tptp.rat) (K2 tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat K2))) (=> (= A4 (@ _let_1 A)) (= (@ (@ tptp.plus_plus_rat A4) B) (@ _let_1 (@ (@ tptp.plus_plus_rat A) B)))))) (forall ((A4 tptp.nat) (K2 tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K2))) (=> (= A4 (@ _let_1 A)) (= (@ (@ tptp.plus_plus_nat A4) B) (@ _let_1 (@ (@ tptp.plus_plus_nat A) B)))))) (forall ((A4 tptp.int) (K2 tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int K2))) (=> (= A4 (@ _let_1 A)) (= (@ (@ tptp.plus_plus_int A4) B) (@ _let_1 (@ (@ tptp.plus_plus_int A) B)))))) (forall ((I2 tptp.real) (J2 tptp.real) (K2 tptp.real) (L tptp.real)) (=> (and (= I2 J2) (= K2 L)) (= (@ (@ tptp.plus_plus_real I2) K2) (@ (@ tptp.plus_plus_real J2) L)))) (forall ((I2 tptp.rat) (J2 tptp.rat) (K2 tptp.rat) (L tptp.rat)) (=> (and (= I2 J2) (= K2 L)) (= (@ (@ tptp.plus_plus_rat I2) K2) (@ (@ tptp.plus_plus_rat J2) L)))) (forall ((I2 tptp.nat) (J2 tptp.nat) (K2 tptp.nat) (L tptp.nat)) (=> (and (= I2 J2) (= K2 L)) (= (@ (@ tptp.plus_plus_nat I2) K2) (@ (@ tptp.plus_plus_nat J2) L)))) (forall ((I2 tptp.int) (J2 tptp.int) (K2 tptp.int) (L tptp.int)) (=> (and (= I2 J2) (= K2 L)) (= (@ (@ tptp.plus_plus_int I2) K2) (@ (@ tptp.plus_plus_int J2) L)))) (forall ((A tptp.real) (B tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A))) (= (@ (@ tptp.plus_plus_real (@ _let_1 B)) C2) (@ _let_1 (@ (@ tptp.plus_plus_real B) C2))))) (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat A))) (= (@ (@ tptp.plus_plus_rat (@ _let_1 B)) C2) (@ _let_1 (@ (@ tptp.plus_plus_rat B) C2))))) (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A))) (= (@ (@ tptp.plus_plus_int (@ _let_1 B)) C2) (@ _let_1 (@ (@ tptp.plus_plus_int B) C2))))) (forall ((A tptp.real) (B tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A))) (= (@ (@ tptp.plus_plus_real (@ _let_1 B)) C2) (@ _let_1 (@ (@ tptp.plus_plus_real B) C2))))) (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat A))) (= (@ (@ tptp.plus_plus_rat (@ _let_1 B)) C2) (@ _let_1 (@ (@ tptp.plus_plus_rat B) C2))))) (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A))) (= (@ (@ tptp.plus_plus_nat (@ _let_1 B)) C2) (@ _let_1 (@ (@ tptp.plus_plus_nat B) C2))))) (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A))) (= (@ (@ tptp.plus_plus_int (@ _let_1 B)) C2) (@ _let_1 (@ (@ tptp.plus_plus_int B) C2))))) _let_342 (forall ((Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT) (Uz tptp.nat)) (not (@ (@ tptp.vEBT_VEBT_membermima (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) tptp.zero_zero_nat) Ux2) Uy2)) Uz))) (forall ((I2 tptp.real) (J2 tptp.real) (K2 tptp.real) (L tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real I2) J2) (= K2 L)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real I2) K2)) (@ (@ tptp.plus_plus_real J2) L)))) (forall ((I2 tptp.rat) (J2 tptp.rat) (K2 tptp.rat) (L tptp.rat)) (=> (and (@ (@ tptp.ord_less_eq_rat I2) J2) (= K2 L)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat I2) K2)) (@ (@ tptp.plus_plus_rat J2) L)))) (forall ((I2 tptp.nat) (J2 tptp.nat) (K2 tptp.nat) (L tptp.nat)) (=> (and (@ (@ tptp.ord_less_eq_nat I2) J2) (= K2 L)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I2) K2)) (@ (@ tptp.plus_plus_nat J2) L)))) (forall ((I2 tptp.int) (J2 tptp.int) (K2 tptp.int) (L tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int I2) J2) (= K2 L)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int I2) K2)) (@ (@ tptp.plus_plus_int J2) L)))) (forall ((I2 tptp.real) (J2 tptp.real) (K2 tptp.real) (L tptp.real)) (=> (and (= I2 J2) (@ (@ tptp.ord_less_eq_real K2) L)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real I2) K2)) (@ (@ tptp.plus_plus_real J2) L)))) (forall ((I2 tptp.rat) (J2 tptp.rat) (K2 tptp.rat) (L tptp.rat)) (=> (and (= I2 J2) (@ (@ tptp.ord_less_eq_rat K2) L)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat I2) K2)) (@ (@ tptp.plus_plus_rat J2) L)))) (forall ((I2 tptp.nat) (J2 tptp.nat) (K2 tptp.nat) (L tptp.nat)) (=> (and (= I2 J2) (@ (@ tptp.ord_less_eq_nat K2) L)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I2) K2)) (@ (@ tptp.plus_plus_nat J2) L)))) (forall ((I2 tptp.int) (J2 tptp.int) (K2 tptp.int) (L tptp.int)) (=> (and (= I2 J2) (@ (@ tptp.ord_less_eq_int K2) L)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int I2) K2)) (@ (@ tptp.plus_plus_int J2) L)))) (forall ((I2 tptp.real) (J2 tptp.real) (K2 tptp.real) (L tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real I2) J2) (@ (@ tptp.ord_less_eq_real K2) L)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real I2) K2)) (@ (@ tptp.plus_plus_real J2) L)))) (forall ((I2 tptp.rat) (J2 tptp.rat) (K2 tptp.rat) (L tptp.rat)) (=> (and (@ (@ tptp.ord_less_eq_rat I2) J2) (@ (@ tptp.ord_less_eq_rat K2) L)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat I2) K2)) (@ (@ tptp.plus_plus_rat J2) L)))) (forall ((I2 tptp.nat) (J2 tptp.nat) (K2 tptp.nat) (L tptp.nat)) (=> (and (@ (@ tptp.ord_less_eq_nat I2) J2) (@ (@ tptp.ord_less_eq_nat K2) L)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I2) K2)) (@ (@ tptp.plus_plus_nat J2) L)))) (forall ((I2 tptp.int) (J2 tptp.int) (K2 tptp.int) (L tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int I2) J2) (@ (@ tptp.ord_less_eq_int K2) L)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int I2) K2)) (@ (@ tptp.plus_plus_int J2) L)))) (forall ((A tptp.real) (B tptp.real) (C2 tptp.real) (D tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real C2) D) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A) C2)) (@ (@ tptp.plus_plus_real B) D))))) (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat) (D tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat C2) D) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A) C2)) (@ (@ tptp.plus_plus_rat B) D))))) (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat) (D tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat C2) D) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A) C2)) (@ (@ tptp.plus_plus_nat B) D))))) (forall ((A tptp.int) (B tptp.int) (C2 tptp.int) (D tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_eq_int C2) D) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A) C2)) (@ (@ tptp.plus_plus_int B) D))))) (forall ((A tptp.real) (B tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real C2))) (=> (@ (@ tptp.ord_less_eq_real A) B) (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B))))) (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat C2))) (=> (@ (@ tptp.ord_less_eq_rat A) B) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B))))) (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C2))) (=> (@ (@ tptp.ord_less_eq_nat A) B) (@ (@ tptp.ord_less_eq_nat (@ _let_1 A)) (@ _let_1 B))))) (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C2))) (=> (@ (@ tptp.ord_less_eq_int A) B) (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B))))) (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (not (forall ((C tptp.nat)) (not (= B (@ (@ tptp.plus_plus_nat A) C))))))) (forall ((A tptp.real) (B tptp.real) (C2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A) C2)) (@ (@ tptp.plus_plus_real B) C2)))) (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A) C2)) (@ (@ tptp.plus_plus_rat B) C2)))) (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A) C2)) (@ (@ tptp.plus_plus_nat B) C2)))) (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A) C2)) (@ (@ tptp.plus_plus_int B) C2)))) (= tptp.ord_less_eq_nat (lambda ((A5 tptp.nat) (B4 tptp.nat)) (exists ((C3 tptp.nat)) (= B4 (@ (@ tptp.plus_plus_nat A5) C3))))) (forall ((C2 tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real C2))) (=> (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_real A) B)))) (forall ((C2 tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat C2))) (=> (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_rat A) B)))) (forall ((C2 tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C2))) (=> (@ (@ tptp.ord_less_eq_nat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_nat A) B)))) (forall ((C2 tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C2))) (=> (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_int A) B)))) (forall ((A tptp.real) (C2 tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A) C2)) (@ (@ tptp.plus_plus_real B) C2)) (@ (@ tptp.ord_less_eq_real A) B))) (forall ((A tptp.rat) (C2 tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A) C2)) (@ (@ tptp.plus_plus_rat B) C2)) (@ (@ tptp.ord_less_eq_rat A) B))) (forall ((A tptp.nat) (C2 tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A) C2)) (@ (@ tptp.plus_plus_nat B) C2)) (@ (@ tptp.ord_less_eq_nat A) B))) (forall ((A tptp.int) (C2 tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A) C2)) (@ (@ tptp.plus_plus_int B) C2)) (@ (@ tptp.ord_less_eq_int A) B))) (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex tptp.zero_zero_complex) A) A)) (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real tptp.zero_zero_real) A) A)) (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat tptp.zero_zero_rat) A) A)) (forall ((A tptp.nat)) (= (@ (@ tptp.plus_plus_nat tptp.zero_zero_nat) A) A)) (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int tptp.zero_zero_int) A) A)) (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex A) tptp.zero_zero_complex) A)) (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real A) tptp.zero_zero_real) A)) (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat A) tptp.zero_zero_rat) A)) (forall ((A tptp.nat)) (= (@ (@ tptp.plus_plus_nat A) tptp.zero_zero_nat) A)) (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int A) tptp.zero_zero_int) A)) (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex tptp.zero_zero_complex) A) A)) (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real tptp.zero_zero_real) A) A)) (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat tptp.zero_zero_rat) A) A)) (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int tptp.zero_zero_int) A) A)) (forall ((A tptp.real) (C2 tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) C2)) (@ (@ tptp.plus_plus_real B) C2)) (@ (@ tptp.ord_less_real A) B))) (forall ((A tptp.rat) (C2 tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) C2)) (@ (@ tptp.plus_plus_rat B) C2)) (@ (@ tptp.ord_less_rat A) B))) (forall ((A tptp.nat) (C2 tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) C2)) (@ (@ tptp.plus_plus_nat B) C2)) (@ (@ tptp.ord_less_nat A) B))) (forall ((A tptp.int) (C2 tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) C2)) (@ (@ tptp.plus_plus_int B) C2)) (@ (@ tptp.ord_less_int A) B))) (forall ((C2 tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real C2))) (=> (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_real A) B)))) (forall ((C2 tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat C2))) (=> (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_rat A) B)))) (forall ((C2 tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C2))) (=> (@ (@ tptp.ord_less_nat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_nat A) B)))) (forall ((C2 tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C2))) (=> (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_int A) B)))) (forall ((A tptp.real) (B tptp.real) (C2 tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) C2)) (@ (@ tptp.plus_plus_real B) C2)))) (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) C2)) (@ (@ tptp.plus_plus_rat B) C2)))) (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) C2)) (@ (@ tptp.plus_plus_nat B) C2)))) (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) C2)) (@ (@ tptp.plus_plus_int B) C2)))) (forall ((A tptp.real) (B tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real C2))) (=> (@ (@ tptp.ord_less_real A) B) (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B))))) (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat C2))) (=> (@ (@ tptp.ord_less_rat A) B) (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B))))) (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C2))) (=> (@ (@ tptp.ord_less_nat A) B) (@ (@ tptp.ord_less_nat (@ _let_1 A)) (@ _let_1 B))))) (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C2))) (=> (@ (@ tptp.ord_less_int A) B) (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B))))) (forall ((A tptp.real) (B tptp.real) (C2 tptp.real) (D tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_real C2) D) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) C2)) (@ (@ tptp.plus_plus_real B) D))))) (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat) (D tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_rat C2) D) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) C2)) (@ (@ tptp.plus_plus_rat B) D))))) (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat) (D tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_nat C2) D) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) C2)) (@ (@ tptp.plus_plus_nat B) D))))) (forall ((A tptp.int) (B tptp.int) (C2 tptp.int) (D tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_int C2) D) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) C2)) (@ (@ tptp.plus_plus_int B) D))))) (forall ((I2 tptp.real) (J2 tptp.real) (K2 tptp.real) (L tptp.real)) (=> (and (@ (@ tptp.ord_less_real I2) J2) (= K2 L)) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real I2) K2)) (@ (@ tptp.plus_plus_real J2) L)))) (forall ((I2 tptp.rat) (J2 tptp.rat) (K2 tptp.rat) (L tptp.rat)) (=> (and (@ (@ tptp.ord_less_rat I2) J2) (= K2 L)) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat I2) K2)) (@ (@ tptp.plus_plus_rat J2) L)))) (forall ((I2 tptp.nat) (J2 tptp.nat) (K2 tptp.nat) (L tptp.nat)) (=> (and (@ (@ tptp.ord_less_nat I2) J2) (= K2 L)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I2) K2)) (@ (@ tptp.plus_plus_nat J2) L)))) (forall ((I2 tptp.int) (J2 tptp.int) (K2 tptp.int) (L tptp.int)) (=> (and (@ (@ tptp.ord_less_int I2) J2) (= K2 L)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int I2) K2)) (@ (@ tptp.plus_plus_int J2) L)))) (forall ((I2 tptp.real) (J2 tptp.real) (K2 tptp.real) (L tptp.real)) (=> (and (= I2 J2) (@ (@ tptp.ord_less_real K2) L)) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real I2) K2)) (@ (@ tptp.plus_plus_real J2) L)))) (forall ((I2 tptp.rat) (J2 tptp.rat) (K2 tptp.rat) (L tptp.rat)) (=> (and (= I2 J2) (@ (@ tptp.ord_less_rat K2) L)) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat I2) K2)) (@ (@ tptp.plus_plus_rat J2) L)))) (forall ((I2 tptp.nat) (J2 tptp.nat) (K2 tptp.nat) (L tptp.nat)) (=> (and (= I2 J2) (@ (@ tptp.ord_less_nat K2) L)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I2) K2)) (@ (@ tptp.plus_plus_nat J2) L)))) (forall ((I2 tptp.int) (J2 tptp.int) (K2 tptp.int) (L tptp.int)) (=> (and (= I2 J2) (@ (@ tptp.ord_less_int K2) L)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int I2) K2)) (@ (@ tptp.plus_plus_int J2) L)))) (forall ((I2 tptp.real) (J2 tptp.real) (K2 tptp.real) (L tptp.real)) (=> (and (@ (@ tptp.ord_less_real I2) J2) (@ (@ tptp.ord_less_real K2) L)) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real I2) K2)) (@ (@ tptp.plus_plus_real J2) L)))) (forall ((I2 tptp.rat) (J2 tptp.rat) (K2 tptp.rat) (L tptp.rat)) (=> (and (@ (@ tptp.ord_less_rat I2) J2) (@ (@ tptp.ord_less_rat K2) L)) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat I2) K2)) (@ (@ tptp.plus_plus_rat J2) L)))) (forall ((I2 tptp.nat) (J2 tptp.nat) (K2 tptp.nat) (L tptp.nat)) (=> (and (@ (@ tptp.ord_less_nat I2) J2) (@ (@ tptp.ord_less_nat K2) L)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I2) K2)) (@ (@ tptp.plus_plus_nat J2) L)))) (forall ((I2 tptp.int) (J2 tptp.int) (K2 tptp.int) (L tptp.int)) (=> (and (@ (@ tptp.ord_less_int I2) J2) (@ (@ tptp.ord_less_int K2) L)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int I2) K2)) (@ (@ tptp.plus_plus_int J2) L)))) (forall ((A tptp.real) (B tptp.real) (C2 tptp.real)) (= (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real A) B)) C2) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) C2)) (@ (@ tptp.times_times_real B) C2)))) (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (= (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat A) B)) C2) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) C2)) (@ (@ tptp.times_times_rat B) C2)))) (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int A) B)) C2) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) C2)) (@ (@ tptp.times_times_int B) C2)))) (forall ((A tptp.real) (B tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.times_times_real A))) (= (@ _let_1 (@ (@ tptp.plus_plus_real B) C2)) (@ (@ tptp.plus_plus_real (@ _let_1 B)) (@ _let_1 C2))))) (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat B) C2)) (@ (@ tptp.plus_plus_rat (@ _let_1 B)) (@ _let_1 C2))))) (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (= (@ _let_1 (@ (@ tptp.plus_plus_int B) C2)) (@ (@ tptp.plus_plus_int (@ _let_1 B)) (@ _let_1 C2))))) (forall ((A tptp.real) (B tptp.real) (C2 tptp.real)) (= (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real A) B)) C2) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) C2)) (@ (@ tptp.times_times_real B) C2)))) (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (= (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat A) B)) C2) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) C2)) (@ (@ tptp.times_times_rat B) C2)))) (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat A) B)) C2) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat A) C2)) (@ (@ tptp.times_times_nat B) C2)))) (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int A) B)) C2) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) C2)) (@ (@ tptp.times_times_int B) C2)))) (forall ((A tptp.real) (B tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.times_times_real A))) (= (@ _let_1 (@ (@ tptp.plus_plus_real B) C2)) (@ (@ tptp.plus_plus_real (@ _let_1 B)) (@ _let_1 C2))))) (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat B) C2)) (@ (@ tptp.plus_plus_rat (@ _let_1 B)) (@ _let_1 C2))))) (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat B) C2)) (@ (@ tptp.plus_plus_nat (@ _let_1 B)) (@ _let_1 C2))))) (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (= (@ _let_1 (@ (@ tptp.plus_plus_int B) C2)) (@ (@ tptp.plus_plus_int (@ _let_1 B)) (@ _let_1 C2))))) (forall ((A tptp.real) (B tptp.real) (C2 tptp.real)) (= (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real A) B)) C2) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) C2)) (@ (@ tptp.times_times_real B) C2)))) (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (= (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat A) B)) C2) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) C2)) (@ (@ tptp.times_times_rat B) C2)))) (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat A) B)) C2) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat A) C2)) (@ (@ tptp.times_times_nat B) C2)))) (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int A) B)) C2) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) C2)) (@ (@ tptp.times_times_int B) C2)))) (forall ((A tptp.real) (E tptp.real) (B tptp.real) (C2 tptp.real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) E)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real B) E)) C2)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real A) B)) E)) C2))) (forall ((A tptp.rat) (E tptp.rat) (B tptp.rat) (C2 tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) E)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B) E)) C2)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat A) B)) E)) C2))) (forall ((A tptp.nat) (E tptp.nat) (B tptp.nat) (C2 tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat A) E)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat B) E)) C2)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat A) B)) E)) C2))) (forall ((A tptp.int) (E tptp.int) (B tptp.int) (C2 tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) E)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) E)) C2)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int A) B)) E)) C2))) (forall ((X tptp.option4927543243414619207at_nat) (P2 (-> tptp.option4927543243414619207at_nat tptp.option4927543243414619207at_nat Bool)) (Y tptp.option4927543243414619207at_nat)) (let ((_let_1 (@ (@ P2 X) Y))) (=> (=> (= X tptp.none_P5556105721700978146at_nat) _let_1) (=> (=> (= Y tptp.none_P5556105721700978146at_nat) _let_1) (=> (forall ((A3 tptp.product_prod_nat_nat) (B3 tptp.product_prod_nat_nat)) (=> (= X (@ tptp.some_P7363390416028606310at_nat A3)) (=> (= Y (@ tptp.some_P7363390416028606310at_nat B3)) (@ (@ P2 X) Y)))) _let_1))))) (forall ((X tptp.option4927543243414619207at_nat) (P2 (-> tptp.option4927543243414619207at_nat tptp.option_nat Bool)) (Y tptp.option_nat)) (let ((_let_1 (@ (@ P2 X) Y))) (=> (=> (= X tptp.none_P5556105721700978146at_nat) _let_1) (=> (=> (= Y tptp.none_nat) _let_1) (=> (forall ((A3 tptp.product_prod_nat_nat) (B3 tptp.nat)) (=> (= X (@ tptp.some_P7363390416028606310at_nat A3)) (=> (= Y (@ tptp.some_nat B3)) (@ (@ P2 X) Y)))) _let_1))))) (forall ((X tptp.option4927543243414619207at_nat) (P2 (-> tptp.option4927543243414619207at_nat tptp.option_num Bool)) (Y tptp.option_num)) (let ((_let_1 (@ (@ P2 X) Y))) (=> (=> (= X tptp.none_P5556105721700978146at_nat) _let_1) (=> (=> (= Y tptp.none_num) _let_1) (=> (forall ((A3 tptp.product_prod_nat_nat) (B3 tptp.num)) (=> (= X (@ tptp.some_P7363390416028606310at_nat A3)) (=> (= Y (@ tptp.some_num B3)) (@ (@ P2 X) Y)))) _let_1))))) (forall ((X tptp.option_nat) (P2 (-> tptp.option_nat tptp.option4927543243414619207at_nat Bool)) (Y tptp.option4927543243414619207at_nat)) (let ((_let_1 (@ (@ P2 X) Y))) (=> (=> (= X tptp.none_nat) _let_1) (=> (=> (= Y tptp.none_P5556105721700978146at_nat) _let_1) (=> (forall ((A3 tptp.nat) (B3 tptp.product_prod_nat_nat)) (=> (= X (@ tptp.some_nat A3)) (=> (= Y (@ tptp.some_P7363390416028606310at_nat B3)) (@ (@ P2 X) Y)))) _let_1))))) (forall ((X tptp.option_nat) (P2 (-> tptp.option_nat tptp.option_nat Bool)) (Y tptp.option_nat)) (let ((_let_1 (@ (@ P2 X) Y))) (=> (=> (= X tptp.none_nat) _let_1) (=> (=> (= Y tptp.none_nat) _let_1) (=> (forall ((A3 tptp.nat) (B3 tptp.nat)) (=> (= X (@ tptp.some_nat A3)) (=> (= Y (@ tptp.some_nat B3)) (@ (@ P2 X) Y)))) _let_1))))) (forall ((X tptp.option_nat) (P2 (-> tptp.option_nat tptp.option_num Bool)) (Y tptp.option_num)) (let ((_let_1 (@ (@ P2 X) Y))) (=> (=> (= X tptp.none_nat) _let_1) (=> (=> (= Y tptp.none_num) _let_1) (=> (forall ((A3 tptp.nat) (B3 tptp.num)) (=> (= X (@ tptp.some_nat A3)) (=> (= Y (@ tptp.some_num B3)) (@ (@ P2 X) Y)))) _let_1))))) (forall ((X tptp.option_num) (P2 (-> tptp.option_num tptp.option4927543243414619207at_nat Bool)) (Y tptp.option4927543243414619207at_nat)) (let ((_let_1 (@ (@ P2 X) Y))) (=> (=> (= X tptp.none_num) _let_1) (=> (=> (= Y tptp.none_P5556105721700978146at_nat) _let_1) (=> (forall ((A3 tptp.num) (B3 tptp.product_prod_nat_nat)) (=> (= X (@ tptp.some_num A3)) (=> (= Y (@ tptp.some_P7363390416028606310at_nat B3)) (@ (@ P2 X) Y)))) _let_1))))) (forall ((X tptp.option_num) (P2 (-> tptp.option_num tptp.option_nat Bool)) (Y tptp.option_nat)) (let ((_let_1 (@ (@ P2 X) Y))) (=> (=> (= X tptp.none_num) _let_1) (=> (=> (= Y tptp.none_nat) _let_1) (=> (forall ((A3 tptp.num) (B3 tptp.nat)) (=> (= X (@ tptp.some_num A3)) (=> (= Y (@ tptp.some_nat B3)) (@ (@ P2 X) Y)))) _let_1))))) (forall ((X tptp.option_num) (P2 (-> tptp.option_num tptp.option_num Bool)) (Y tptp.option_num)) (let ((_let_1 (@ (@ P2 X) Y))) (=> (=> (= X tptp.none_num) _let_1) (=> (=> (= Y tptp.none_num) _let_1) (=> (forall ((A3 tptp.num) (B3 tptp.num)) (=> (= X (@ tptp.some_num A3)) (=> (= Y (@ tptp.some_num B3)) (@ (@ P2 X) Y)))) _let_1))))) (= (lambda ((P3 (-> tptp.option4927543243414619207at_nat Bool))) (forall ((X6 tptp.option4927543243414619207at_nat)) (@ P3 X6))) (lambda ((P4 (-> tptp.option4927543243414619207at_nat Bool))) (and (@ P4 tptp.none_P5556105721700978146at_nat) (forall ((X4 tptp.product_prod_nat_nat)) (@ P4 (@ tptp.some_P7363390416028606310at_nat X4)))))) (= (lambda ((P3 (-> tptp.option_nat Bool))) (forall ((X6 tptp.option_nat)) (@ P3 X6))) (lambda ((P4 (-> tptp.option_nat Bool))) (and (@ P4 tptp.none_nat) (forall ((X4 tptp.nat)) (@ P4 (@ tptp.some_nat X4)))))) (= (lambda ((P3 (-> tptp.option_num Bool))) (forall ((X6 tptp.option_num)) (@ P3 X6))) (lambda ((P4 (-> tptp.option_num Bool))) (and (@ P4 tptp.none_num) (forall ((X4 tptp.num)) (@ P4 (@ tptp.some_num X4)))))) (= (lambda ((P3 (-> tptp.option4927543243414619207at_nat Bool))) (exists ((X6 tptp.option4927543243414619207at_nat)) (@ P3 X6))) (lambda ((P4 (-> tptp.option4927543243414619207at_nat Bool))) (or (@ P4 tptp.none_P5556105721700978146at_nat) (exists ((X4 tptp.product_prod_nat_nat)) (@ P4 (@ tptp.some_P7363390416028606310at_nat X4)))))) (= (lambda ((P3 (-> tptp.option_nat Bool))) (exists ((X6 tptp.option_nat)) (@ P3 X6))) (lambda ((P4 (-> tptp.option_nat Bool))) (or (@ P4 tptp.none_nat) (exists ((X4 tptp.nat)) (@ P4 (@ tptp.some_nat X4)))))) (= (lambda ((P3 (-> tptp.option_num Bool))) (exists ((X6 tptp.option_num)) (@ P3 X6))) (lambda ((P4 (-> tptp.option_num Bool))) (or (@ P4 tptp.none_num) (exists ((X4 tptp.num)) (@ P4 (@ tptp.some_num X4)))))) (forall ((Y tptp.option4927543243414619207at_nat)) (=> (not (= Y tptp.none_P5556105721700978146at_nat)) (not (forall ((X23 tptp.product_prod_nat_nat)) (not (= Y (@ tptp.some_P7363390416028606310at_nat X23))))))) (forall ((Y tptp.option_nat)) (=> (not (= Y tptp.none_nat)) (not (forall ((X23 tptp.nat)) (not (= Y (@ tptp.some_nat X23))))))) (forall ((Y tptp.option_num)) (=> (not (= Y tptp.none_num)) (not (forall ((X23 tptp.num)) (not (= Y (@ tptp.some_num X23))))))) (forall ((Option tptp.option4927543243414619207at_nat) (X2 tptp.product_prod_nat_nat)) (=> (= Option (@ tptp.some_P7363390416028606310at_nat X2)) (not (= Option tptp.none_P5556105721700978146at_nat)))) (forall ((Option tptp.option_nat) (X2 tptp.nat)) (=> (= Option (@ tptp.some_nat X2)) (not (= Option tptp.none_nat)))) (forall ((Option tptp.option_num) (X2 tptp.num)) (=> (= Option (@ tptp.some_num X2)) (not (= Option tptp.none_num)))) (forall ((X2 tptp.product_prod_nat_nat)) (not (= tptp.none_P5556105721700978146at_nat (@ tptp.some_P7363390416028606310at_nat X2)))) (forall ((X2 tptp.nat)) (not (= tptp.none_nat (@ tptp.some_nat X2)))) (forall ((X2 tptp.num)) (not (= tptp.none_num (@ tptp.some_num X2)))) (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 ((Uw (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)) (V tptp.product_prod_nat_nat)) (not (= X (@ (@ tptp.produc2899441246263362727at_nat Uw) (@ (@ tptp.produc488173922507101015at_nat (@ tptp.some_P7363390416028606310at_nat V)) tptp.none_P5556105721700978146at_nat))))) (not (forall ((F (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)) (A3 tptp.product_prod_nat_nat) (B3 tptp.product_prod_nat_nat)) (not (= X (@ (@ tptp.produc2899441246263362727at_nat F) (@ (@ tptp.produc488173922507101015at_nat (@ tptp.some_P7363390416028606310at_nat A3)) (@ tptp.some_P7363390416028606310at_nat B3)))))))))) (forall ((X tptp.produc8306885398267862888on_nat)) (=> (forall ((Uu2 (-> tptp.nat tptp.nat tptp.nat)) (Uv2 tptp.option_nat)) (not (= X (@ (@ tptp.produc8929957630744042906on_nat Uu2) (@ (@ tptp.produc5098337634421038937on_nat tptp.none_nat) Uv2))))) (=> (forall ((Uw (-> tptp.nat tptp.nat tptp.nat)) (V tptp.nat)) (not (= X (@ (@ tptp.produc8929957630744042906on_nat Uw) (@ (@ tptp.produc5098337634421038937on_nat (@ tptp.some_nat V)) tptp.none_nat))))) (not (forall ((F (-> tptp.nat tptp.nat tptp.nat)) (A3 tptp.nat) (B3 tptp.nat)) (not (= X (@ (@ tptp.produc8929957630744042906on_nat F) (@ (@ tptp.produc5098337634421038937on_nat (@ tptp.some_nat A3)) (@ tptp.some_nat B3)))))))))) (forall ((X tptp.produc1193250871479095198on_num)) (=> (forall ((Uu2 (-> tptp.num tptp.num tptp.num)) (Uv2 tptp.option_num)) (not (= X (@ (@ tptp.produc5778274026573060048on_num Uu2) (@ (@ tptp.produc8585076106096196333on_num tptp.none_num) Uv2))))) (=> (forall ((Uw (-> tptp.num tptp.num tptp.num)) (V tptp.num)) (not (= X (@ (@ tptp.produc5778274026573060048on_num Uw) (@ (@ tptp.produc8585076106096196333on_num (@ tptp.some_num V)) tptp.none_num))))) (not (forall ((F (-> tptp.num tptp.num tptp.num)) (A3 tptp.num) (B3 tptp.num)) (not (= X (@ (@ tptp.produc5778274026573060048on_num F) (@ (@ tptp.produc8585076106096196333on_num (@ tptp.some_num A3)) (@ tptp.some_num B3)))))))))) (forall ((X tptp.produc5491161045314408544at_nat)) (=> (forall ((Uu2 (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)) (Uv2 tptp.option4927543243414619207at_nat)) (not (= X (@ (@ tptp.produc3994169339658061776at_nat Uu2) (@ (@ tptp.produc488173922507101015at_nat tptp.none_P5556105721700978146at_nat) Uv2))))) (=> (forall ((Uw (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)) (V tptp.product_prod_nat_nat)) (not (= X (@ (@ tptp.produc3994169339658061776at_nat Uw) (@ (@ tptp.produc488173922507101015at_nat (@ tptp.some_P7363390416028606310at_nat V)) tptp.none_P5556105721700978146at_nat))))) (not (forall ((F (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)) (X3 tptp.product_prod_nat_nat) (Y3 tptp.product_prod_nat_nat)) (not (= X (@ (@ tptp.produc3994169339658061776at_nat F) (@ (@ tptp.produc488173922507101015at_nat (@ tptp.some_P7363390416028606310at_nat X3)) (@ tptp.some_P7363390416028606310at_nat Y3)))))))))) (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 ((Uw (-> tptp.nat tptp.nat Bool)) (V tptp.nat)) (not (= X (@ (@ tptp.produc4035269172776083154on_nat Uw) (@ (@ tptp.produc5098337634421038937on_nat (@ tptp.some_nat V)) tptp.none_nat))))) (not (forall ((F (-> tptp.nat tptp.nat Bool)) (X3 tptp.nat) (Y3 tptp.nat)) (not (= X (@ (@ tptp.produc4035269172776083154on_nat F) (@ (@ tptp.produc5098337634421038937on_nat (@ tptp.some_nat X3)) (@ tptp.some_nat Y3)))))))))) (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 ((Uw (-> tptp.num tptp.num Bool)) (V tptp.num)) (not (= X (@ (@ tptp.produc3576312749637752826on_num Uw) (@ (@ tptp.produc8585076106096196333on_num (@ tptp.some_num V)) tptp.none_num))))) (not (forall ((F (-> tptp.num tptp.num Bool)) (X3 tptp.num) (Y3 tptp.num)) (not (= X (@ (@ tptp.produc3576312749637752826on_num F) (@ (@ tptp.produc8585076106096196333on_num (@ tptp.some_num X3)) (@ tptp.some_num Y3)))))))))) (forall ((A4 tptp.nat) (K2 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K2))) (=> (= A4 (@ _let_1 A)) (= (@ tptp.suc A4) (@ _let_1 (@ tptp.suc A)))))) (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ tptp.suc M2)) N) (@ tptp.suc (@ (@ tptp.plus_plus_nat M2) N)))) (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ tptp.suc M2)) N) (@ (@ tptp.plus_plus_nat M2) (@ tptp.suc N)))) (forall ((M2 tptp.nat) (N tptp.nat)) (=> (= (@ (@ tptp.plus_plus_nat M2) N) M2) (= N tptp.zero_zero_nat))) (forall ((N tptp.nat)) (= (@ (@ tptp.plus_plus_nat tptp.zero_zero_nat) N) N)) (forall ((K2 tptp.nat) (L tptp.nat) (M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat K2) L) (=> (= (@ (@ tptp.plus_plus_nat M2) L) (@ (@ tptp.plus_plus_nat K2) N)) (@ (@ tptp.ord_less_nat M2) N)))) (forall ((I2 tptp.nat) (J2 tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat I2))) (=> (@ _let_1 J2) (@ _let_1 (@ (@ tptp.plus_plus_nat M2) J2))))) (forall ((I2 tptp.nat) (J2 tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat I2))) (=> (@ _let_1 J2) (@ _let_1 (@ (@ tptp.plus_plus_nat J2) M2))))) (forall ((I2 tptp.nat) (J2 tptp.nat) (K2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) J2) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I2) K2)) (@ (@ tptp.plus_plus_nat J2) K2)))) (forall ((J2 tptp.nat) (I2 tptp.nat)) (not (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat J2) I2)) I2))) (forall ((I2 tptp.nat) (J2 tptp.nat)) (not (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I2) J2)) I2))) (forall ((I2 tptp.nat) (J2 tptp.nat) (K2 tptp.nat) (L tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) J2) (=> (@ (@ tptp.ord_less_nat K2) L) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I2) K2)) (@ (@ tptp.plus_plus_nat J2) L))))) (forall ((I2 tptp.nat) (J2 tptp.nat) (K2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I2) J2)) K2) (@ (@ tptp.ord_less_nat I2) K2))) (forall ((M2 tptp.nat) (K2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat M2) K2)) N) (not (=> (@ (@ tptp.ord_less_eq_nat M2) N) (not (@ (@ tptp.ord_less_eq_nat K2) N)))))) (forall ((N tptp.nat) (M2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat N) (@ (@ tptp.plus_plus_nat N) M2))) (forall ((N tptp.nat) (M2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat N) (@ (@ tptp.plus_plus_nat M2) N))) (forall ((M2 tptp.nat) (K2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat M2) K2)) N) (@ (@ tptp.ord_less_eq_nat M2) N))) (forall ((M2 tptp.nat) (K2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat M2) K2)) N) (@ (@ tptp.ord_less_eq_nat K2) N))) (forall ((K2 tptp.nat) (L tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K2) L) (exists ((N3 tptp.nat)) (= L (@ (@ tptp.plus_plus_nat K2) N3))))) (forall ((I2 tptp.nat) (J2 tptp.nat) (K2 tptp.nat) (L tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J2) (=> (@ (@ tptp.ord_less_eq_nat K2) L) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I2) K2)) (@ (@ tptp.plus_plus_nat J2) L))))) (forall ((I2 tptp.nat) (J2 tptp.nat) (K2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I2) K2)) (@ (@ tptp.plus_plus_nat J2) K2)))) (forall ((I2 tptp.nat) (J2 tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat I2))) (=> (@ _let_1 J2) (@ _let_1 (@ (@ tptp.plus_plus_nat J2) M2))))) (forall ((I2 tptp.nat) (J2 tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat I2))) (=> (@ _let_1 J2) (@ _let_1 (@ (@ tptp.plus_plus_nat M2) J2))))) (= tptp.ord_less_eq_nat (lambda ((M6 tptp.nat) (N4 tptp.nat)) (exists ((K3 tptp.nat)) (= N4 (@ (@ tptp.plus_plus_nat M6) K3))))) (forall ((K2 tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K2))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M2) N)) (@ (@ tptp.plus_plus_nat (@ _let_1 M2)) (@ _let_1 N))))) (forall ((M2 tptp.nat) (N tptp.nat) (K2 tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat M2) N)) K2) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat M2) K2)) (@ (@ tptp.times_times_nat N) K2)))) (forall ((I2 tptp.nat) (U tptp.nat) (J2 tptp.nat) (K2 tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I2) U)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J2) U)) K2)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat I2) J2)) U)) K2))) (forall ((Uu Bool) (Uv Bool) (Uw2 tptp.nat)) (not (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.vEBT_Leaf Uu) Uv)) Uw2))) (forall ((A tptp.real) (C2 tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real C2) B) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A) C2)) B)))) (forall ((A tptp.rat) (C2 tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_rat C2) B) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A) C2)) B)))) (forall ((A tptp.nat) (C2 tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_eq_nat C2) B) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A) C2)) B)))) (forall ((A tptp.int) (C2 tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_eq_int C2) B) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A) C2)) B)))) (forall ((A tptp.real) (B tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real B))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ _let_1 C2) (@ _let_1 (@ (@ tptp.plus_plus_real A) C2)))))) (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat B))) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ _let_1 C2) (@ _let_1 (@ (@ tptp.plus_plus_rat A) C2)))))) (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat B))) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ _let_1 C2) (@ _let_1 (@ (@ tptp.plus_plus_nat A) C2)))))) (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int B))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ _let_1 C2) (@ _let_1 (@ (@ tptp.plus_plus_int A) C2)))))) (forall ((C2 tptp.real) (A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real C2) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real A) B) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A) C2)) B)))) (forall ((C2 tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat C2) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_rat A) B) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A) C2)) B)))) (forall ((C2 tptp.nat) (A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat C2) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_eq_nat A) B) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A) C2)) B)))) (forall ((C2 tptp.int) (A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int C2) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_eq_int A) B) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A) C2)) B)))) (forall ((C2 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) C2) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.plus_plus_real A) C2)))))) (forall ((C2 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) C2) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.plus_plus_rat A) C2)))))) (forall ((C2 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) C2) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.plus_plus_nat A) C2)))))) (forall ((C2 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) C2) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.plus_plus_int A) C2)))))) (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.plus_plus_real A) B)))))) (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.plus_plus_rat A) B)))))) (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.plus_plus_nat A) B)))))) (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.plus_plus_int A) B)))))) (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real B) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A) B)) tptp.zero_zero_real)))) (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_rat B) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A) B)) tptp.zero_zero_rat)))) (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_eq_nat B) tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A) B)) tptp.zero_zero_nat)))) (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_eq_int B) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A) B)) tptp.zero_zero_int)))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= (= (@ (@ tptp.plus_plus_real X) Y) tptp.zero_zero_real) (and (= X tptp.zero_zero_real) (= Y tptp.zero_zero_real))))))) (forall ((X tptp.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))))))) (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= (= (@ (@ tptp.plus_plus_nat X) Y) tptp.zero_zero_nat) (and (= X tptp.zero_zero_nat) (= Y tptp.zero_zero_nat))))))) (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= (= (@ (@ tptp.plus_plus_int X) Y) tptp.zero_zero_int) (and (= X tptp.zero_zero_int) (= Y tptp.zero_zero_int))))))) (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.zero_zero_real) (= (= (@ (@ tptp.plus_plus_real X) Y) tptp.zero_zero_real) (and (= X tptp.zero_zero_real) (= Y tptp.zero_zero_real)))))) (forall ((X tptp.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)))))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_eq_nat Y) tptp.zero_zero_nat) (= (= (@ (@ tptp.plus_plus_nat X) Y) tptp.zero_zero_nat) (and (= X tptp.zero_zero_nat) (= Y tptp.zero_zero_nat)))))) (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_eq_int Y) tptp.zero_zero_int) (= (= (@ (@ tptp.plus_plus_int X) Y) tptp.zero_zero_int) (and (= X tptp.zero_zero_int) (= Y tptp.zero_zero_int)))))) (forall ((A tptp.real) (B tptp.real) (C2 tptp.real) (D tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_eq_real C2) D) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) C2)) (@ (@ tptp.plus_plus_real B) D))))) (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat) (D tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat C2) D) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) C2)) (@ (@ tptp.plus_plus_rat B) D))))) (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat) (D tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat C2) D) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) C2)) (@ (@ tptp.plus_plus_nat B) D))))) (forall ((A tptp.int) (B tptp.int) (C2 tptp.int) (D tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_eq_int C2) D) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) C2)) (@ (@ tptp.plus_plus_int B) D))))) (forall ((A tptp.real) (B tptp.real) (C2 tptp.real) (D tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_real C2) D) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) C2)) (@ (@ tptp.plus_plus_real B) D))))) (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat) (D tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_rat C2) D) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) C2)) (@ (@ tptp.plus_plus_rat B) D))))) (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat) (D tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_nat C2) D) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) C2)) (@ (@ tptp.plus_plus_nat B) D))))) (forall ((A tptp.int) (B tptp.int) (C2 tptp.int) (D tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_int C2) D) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) C2)) (@ (@ tptp.plus_plus_int B) D))))) (forall ((I2 tptp.real) (J2 tptp.real) (K2 tptp.real) (L tptp.real)) (=> (and (@ (@ tptp.ord_less_real I2) J2) (@ (@ tptp.ord_less_eq_real K2) L)) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real I2) K2)) (@ (@ tptp.plus_plus_real J2) L)))) (forall ((I2 tptp.rat) (J2 tptp.rat) (K2 tptp.rat) (L tptp.rat)) (=> (and (@ (@ tptp.ord_less_rat I2) J2) (@ (@ tptp.ord_less_eq_rat K2) L)) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat I2) K2)) (@ (@ tptp.plus_plus_rat J2) L)))) (forall ((I2 tptp.nat) (J2 tptp.nat) (K2 tptp.nat) (L tptp.nat)) (=> (and (@ (@ tptp.ord_less_nat I2) J2) (@ (@ tptp.ord_less_eq_nat K2) L)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I2) K2)) (@ (@ tptp.plus_plus_nat J2) L)))) (forall ((I2 tptp.int) (J2 tptp.int) (K2 tptp.int) (L tptp.int)) (=> (and (@ (@ tptp.ord_less_int I2) J2) (@ (@ tptp.ord_less_eq_int K2) L)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int I2) K2)) (@ (@ tptp.plus_plus_int J2) L)))) (forall ((I2 tptp.real) (J2 tptp.real) (K2 tptp.real) (L tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real I2) J2) (@ (@ tptp.ord_less_real K2) L)) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real I2) K2)) (@ (@ tptp.plus_plus_real J2) L)))) (forall ((I2 tptp.rat) (J2 tptp.rat) (K2 tptp.rat) (L tptp.rat)) (=> (and (@ (@ tptp.ord_less_eq_rat I2) J2) (@ (@ tptp.ord_less_rat K2) L)) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat I2) K2)) (@ (@ tptp.plus_plus_rat J2) L)))) (forall ((I2 tptp.nat) (J2 tptp.nat) (K2 tptp.nat) (L tptp.nat)) (=> (and (@ (@ tptp.ord_less_eq_nat I2) J2) (@ (@ tptp.ord_less_nat K2) L)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I2) K2)) (@ (@ tptp.plus_plus_nat J2) L)))) (forall ((I2 tptp.int) (J2 tptp.int) (K2 tptp.int) (L tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int I2) J2) (@ (@ tptp.ord_less_int K2) L)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int I2) K2)) (@ (@ tptp.plus_plus_int J2) L)))) (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real X) Y)) tptp.zero_zero_real) (or (@ (@ tptp.ord_less_real X) tptp.zero_zero_real) (@ (@ tptp.ord_less_real Y) tptp.zero_zero_real)))) (forall ((X tptp.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)))) (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int X) Y)) tptp.zero_zero_int) (or (@ (@ tptp.ord_less_int X) tptp.zero_zero_int) (@ (@ tptp.ord_less_int Y) tptp.zero_zero_int)))) (forall ((A tptp.real) (B tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real B))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (@ _let_1 C2) (@ _let_1 (@ (@ tptp.plus_plus_real A) C2)))))) (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat B))) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (=> (@ _let_1 C2) (@ _let_1 (@ (@ tptp.plus_plus_rat A) C2)))))) (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat B))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A) (=> (@ _let_1 C2) (@ _let_1 (@ (@ tptp.plus_plus_nat A) C2)))))) (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int B))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (=> (@ _let_1 C2) (@ _let_1 (@ (@ tptp.plus_plus_int A) C2)))))) (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (not (forall ((C tptp.nat)) (=> (= B (@ (@ tptp.plus_plus_nat A) C)) (= C tptp.zero_zero_nat)))))) (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.plus_plus_real A) B)))))) (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.plus_plus_rat A) B)))))) (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.plus_plus_nat A) B)))))) (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.plus_plus_int A) B)))))) (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real B) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) B)) tptp.zero_zero_real)))) (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat B) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) B)) tptp.zero_zero_rat)))) (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_nat B) tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) B)) tptp.zero_zero_nat)))) (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int B) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) B)) tptp.zero_zero_int)))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A) B) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.plus_p5714425477246183910nteger A) tptp.one_one_Code_integer)) (@ (@ tptp.plus_p5714425477246183910nteger B) tptp.one_one_Code_integer)))) (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) tptp.one_one_real)) (@ (@ tptp.plus_plus_real B) tptp.one_one_real)))) (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) tptp.one_one_rat)) (@ (@ tptp.plus_plus_rat B) tptp.one_one_rat)))) (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) tptp.one_one_nat)) (@ (@ tptp.plus_plus_nat B) tptp.one_one_nat)))) (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) tptp.one_one_int)) (@ (@ tptp.plus_plus_int B) tptp.one_one_int)))) (forall ((A tptp.code_integer)) (@ (@ tptp.ord_le6747313008572928689nteger A) (@ (@ tptp.plus_p5714425477246183910nteger A) tptp.one_one_Code_integer))) (forall ((A tptp.real)) (@ (@ tptp.ord_less_real A) (@ (@ tptp.plus_plus_real A) tptp.one_one_real))) (forall ((A tptp.rat)) (@ (@ tptp.ord_less_rat A) (@ (@ tptp.plus_plus_rat A) tptp.one_one_rat))) (forall ((A tptp.nat)) (@ (@ tptp.ord_less_nat A) (@ (@ tptp.plus_plus_nat A) tptp.one_one_nat))) (forall ((A tptp.int)) (@ (@ tptp.ord_less_int A) (@ (@ tptp.plus_plus_int A) tptp.one_one_int))) (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (= (@ (@ tptp.plus_plus_nat M2) N) _let_1) (or (and (= M2 _let_1) (= N tptp.zero_zero_nat)) (and (= M2 tptp.zero_zero_nat) (= N _let_1)))))) (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (= _let_1 (@ (@ tptp.plus_plus_nat M2) N)) (or (and (= M2 _let_1) (= N tptp.zero_zero_nat)) (and (= M2 tptp.zero_zero_nat) (= N _let_1)))))) (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) N) (not (forall ((Q3 tptp.nat)) (not (= N (@ tptp.suc (@ (@ tptp.plus_plus_nat M2) Q3)))))))) (forall ((I2 tptp.nat) (M2 tptp.nat)) (@ (@ tptp.ord_less_nat I2) (@ tptp.suc (@ (@ tptp.plus_plus_nat I2) M2)))) (forall ((I2 tptp.nat) (M2 tptp.nat)) (@ (@ tptp.ord_less_nat I2) (@ tptp.suc (@ (@ tptp.plus_plus_nat M2) I2)))) (= tptp.ord_less_nat (lambda ((M6 tptp.nat) (N4 tptp.nat)) (exists ((K3 tptp.nat)) (= N4 (@ tptp.suc (@ (@ tptp.plus_plus_nat M6) K3)))))) (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) N) (exists ((K tptp.nat)) (= N (@ tptp.suc (@ (@ tptp.plus_plus_nat M2) K)))))) (forall ((I2 tptp.nat) (J2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) J2) (exists ((K tptp.nat)) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (@ (@ tptp.plus_plus_nat I2) K) J2))))) (forall ((F2 (-> tptp.nat tptp.nat)) (M2 tptp.nat) (K2 tptp.nat)) (=> (forall ((M tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N3) (@ (@ tptp.ord_less_nat (@ F2 M)) (@ F2 N3)))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ F2 M2)) K2)) (@ F2 (@ (@ tptp.plus_plus_nat M2) K2))))) (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.times_times_nat (@ tptp.suc M2)) N) (@ (@ tptp.plus_plus_nat N) (@ (@ tptp.times_times_nat M2) N)))) (= tptp.suc (lambda ((N4 tptp.nat)) (@ (@ tptp.plus_plus_nat N4) tptp.one_one_nat))) (= _let_293 tptp.suc) _let_341 (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 ((Uw tptp.nat) (Ux tptp.list_VEBT_VEBT) (Uy tptp.vEBT_VEBT)) (not (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uw) Ux) Uy)))) (not (forall ((Uz2 tptp.product_prod_nat_nat) (Va2 tptp.nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (not (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat Uz2)) Va2) Vb2) Vc2)))))))))) (forall ((Uw2 (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)) (V2 tptp.product_prod_nat_nat)) (= (@ (@ (@ tptp.vEBT_V1502963449132264192at_nat Uw2) (@ tptp.some_P7363390416028606310at_nat V2)) tptp.none_P5556105721700978146at_nat) tptp.none_P5556105721700978146at_nat)) (forall ((Uw2 (-> tptp.num tptp.num tptp.num)) (V2 tptp.num)) (= (@ (@ (@ tptp.vEBT_V819420779217536731ft_num Uw2) (@ tptp.some_num V2)) tptp.none_num) tptp.none_num)) (forall ((Uw2 (-> tptp.nat tptp.nat tptp.nat)) (V2 tptp.nat)) (= (@ (@ (@ tptp.vEBT_V4262088993061758097ft_nat Uw2) (@ tptp.some_nat V2)) tptp.none_nat) tptp.none_nat)) (forall ((X (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)) (Xa2 tptp.option4927543243414619207at_nat) (Xb tptp.option4927543243414619207at_nat) (Y tptp.option4927543243414619207at_nat)) (let ((_let_1 (not (= Y tptp.none_P5556105721700978146at_nat)))) (=> (= (@ (@ (@ tptp.vEBT_V1502963449132264192at_nat X) Xa2) Xb) Y) (=> (=> (= Xa2 tptp.none_P5556105721700978146at_nat) _let_1) (=> (=> (exists ((V tptp.product_prod_nat_nat)) (= Xa2 (@ tptp.some_P7363390416028606310at_nat V))) (=> (= Xb tptp.none_P5556105721700978146at_nat) _let_1)) (not (forall ((A3 tptp.product_prod_nat_nat)) (=> (= Xa2 (@ tptp.some_P7363390416028606310at_nat A3)) (forall ((B3 tptp.product_prod_nat_nat)) (=> (= Xb (@ tptp.some_P7363390416028606310at_nat B3)) (not (= Y (@ tptp.some_P7363390416028606310at_nat (@ (@ X A3) B3)))))))))))))) (forall ((X (-> tptp.num tptp.num tptp.num)) (Xa2 tptp.option_num) (Xb tptp.option_num) (Y tptp.option_num)) (let ((_let_1 (not (= Y tptp.none_num)))) (=> (= (@ (@ (@ tptp.vEBT_V819420779217536731ft_num X) Xa2) Xb) Y) (=> (=> (= Xa2 tptp.none_num) _let_1) (=> (=> (exists ((V tptp.num)) (= Xa2 (@ tptp.some_num V))) (=> (= Xb tptp.none_num) _let_1)) (not (forall ((A3 tptp.num)) (=> (= Xa2 (@ tptp.some_num A3)) (forall ((B3 tptp.num)) (=> (= Xb (@ tptp.some_num B3)) (not (= Y (@ tptp.some_num (@ (@ X A3) B3)))))))))))))) (forall ((X (-> tptp.nat tptp.nat tptp.nat)) (Xa2 tptp.option_nat) (Xb tptp.option_nat) (Y tptp.option_nat)) (let ((_let_1 (not (= Y tptp.none_nat)))) (=> (= (@ (@ (@ tptp.vEBT_V4262088993061758097ft_nat X) Xa2) Xb) Y) (=> (=> (= Xa2 tptp.none_nat) _let_1) (=> (=> (exists ((V tptp.nat)) (= Xa2 (@ tptp.some_nat V))) (=> (= Xb tptp.none_nat) _let_1)) (not (forall ((A3 tptp.nat)) (=> (= Xa2 (@ tptp.some_nat A3)) (forall ((B3 tptp.nat)) (=> (= Xb (@ tptp.some_nat B3)) (not (= Y (@ tptp.some_nat (@ (@ X A3) B3)))))))))))))) (forall ((X tptp.real) (Y tptp.real)) (=> (forall ((E2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E2) (@ (@ tptp.ord_less_eq_real X) (@ (@ tptp.plus_plus_real Y) E2)))) (@ (@ tptp.ord_less_eq_real X) Y))) (forall ((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))) (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real B) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) B)) tptp.zero_zero_real)))) (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_rat B) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) B)) tptp.zero_zero_rat)))) (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_eq_nat B) tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) B)) tptp.zero_zero_nat)))) (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_eq_int B) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) B)) tptp.zero_zero_int)))) (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.plus_plus_real A) B)))))) (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.plus_plus_rat A) B)))))) (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.plus_plus_nat A) B)))))) (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.plus_plus_int A) B)))))) (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real B) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) B)) tptp.zero_zero_real)))) (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat B) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) B)) tptp.zero_zero_rat)))) (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_nat B) tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) B)) tptp.zero_zero_nat)))) (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int B) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) B)) tptp.zero_zero_int)))) (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) B) (@ _let_1 (@ (@ tptp.plus_plus_real A) B)))))) (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 A) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) B) (@ _let_1 (@ (@ tptp.plus_plus_rat A) B)))))) (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 A) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) B) (@ _let_1 (@ (@ tptp.plus_plus_nat A) B)))))) (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 A) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B) (@ _let_1 (@ (@ tptp.plus_plus_int A) B)))))) (forall ((A tptp.real) (B tptp.real) (C2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_eq_real B) C2) (@ (@ tptp.ord_less_real B) (@ (@ tptp.plus_plus_real A) C2))))) (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_eq_rat B) C2) (@ (@ tptp.ord_less_rat B) (@ (@ tptp.plus_plus_rat A) C2))))) (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_eq_nat B) C2) (@ (@ tptp.ord_less_nat B) (@ (@ tptp.plus_plus_nat A) C2))))) (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_eq_int B) C2) (@ (@ tptp.ord_less_int B) (@ (@ tptp.plus_plus_int A) C2))))) (forall ((A tptp.real) (B tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real B))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ _let_1 C2) (@ _let_1 (@ (@ tptp.plus_plus_real A) C2)))))) (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat B))) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ _let_1 C2) (@ _let_1 (@ (@ tptp.plus_plus_rat A) C2)))))) (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat B))) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ _let_1 C2) (@ _let_1 (@ (@ tptp.plus_plus_nat A) C2)))))) (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int B))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ _let_1 C2) (@ _let_1 (@ (@ tptp.plus_plus_int A) C2)))))) (forall ((X tptp.real) (Y tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X) X)) (@ (@ tptp.times_times_real Y) Y)))) (forall ((X tptp.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)))) (forall ((X tptp.int) (Y tptp.int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int X) X)) (@ (@ tptp.times_times_int Y) Y)))) (forall ((X tptp.real) (Y tptp.real)) (not (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X) X)) (@ (@ tptp.times_times_real Y) Y))) tptp.zero_zero_real))) (forall ((X tptp.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))) (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))) _let_340 (= tptp.ord_less_nat (lambda ((A5 tptp.nat) (__flatten_var_0 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A5) tptp.one_one_nat)) __flatten_var_0))) (= tptp.ord_less_int (lambda ((A5 tptp.int) (__flatten_var_0 tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A5) tptp.one_one_int)) __flatten_var_0))) (@ _let_171 _let_302) (@ _let_172 _let_300) (@ _let_170 _let_301) (@ _let_297 _let_294) (@ _let_173 _let_299) (= (@ tptp.size_size_option_nat tptp.none_nat) _let_10) (= (@ tptp.size_s170228958280169651at_nat tptp.none_P5556105721700978146at_nat) _let_10) (= (@ tptp.size_size_option_num tptp.none_num) _let_10) (forall ((X tptp.code_integer) (A tptp.code_integer) (Y tptp.code_integer) (U tptp.code_integer) (V2 tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (=> (@ (@ tptp.ord_le3102999989581377725nteger X) A) (=> (@ (@ tptp.ord_le3102999989581377725nteger Y) A) (=> (@ _let_1 U) (=> (@ _let_1 V2) (=> (= (@ (@ tptp.plus_p5714425477246183910nteger U) V2) tptp.one_one_Code_integer) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger U) X)) (@ (@ tptp.times_3573771949741848930nteger V2) Y))) A)))))))) (forall ((X tptp.real) (A tptp.real) (Y tptp.real) (U tptp.real) (V2 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 V2) (=> (= (@ (@ tptp.plus_plus_real U) V2) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real U) X)) (@ (@ tptp.times_times_real V2) Y))) A)))))))) (forall ((X tptp.rat) (A tptp.rat) (Y tptp.rat) (U tptp.rat) (V2 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 V2) (=> (= (@ (@ tptp.plus_plus_rat U) V2) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat U) X)) (@ (@ tptp.times_times_rat V2) Y))) A)))))))) (forall ((X tptp.int) (A tptp.int) (Y tptp.int) (U tptp.int) (V2 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 V2) (=> (= (@ (@ tptp.plus_plus_int U) V2) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int U) X)) (@ (@ tptp.times_times_int V2) Y))) A)))))))) (forall ((X tptp.vEBT_VEBT) (Y tptp.option_nat)) (=> (= (@ tptp.vEBT_vebt_mint X) Y) (=> (forall ((A3 Bool) (B3 Bool)) (=> (= X (@ (@ tptp.vEBT_Leaf A3) B3)) (not (and (=> A3 (= Y (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A3) (and (=> B3 (= Y (@ tptp.some_nat tptp.one_one_nat))) (=> (not B3) (= Y tptp.none_nat)))))))) (=> (=> (exists ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw))) (not (= Y tptp.none_nat))) (not (forall ((Mi2 tptp.nat)) (=> (exists ((Ma2 tptp.nat) (Ux tptp.nat) (Uy tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) Ux) Uy) Uz2))) (not (= Y (@ tptp.some_nat Mi2)))))))))) (forall ((X tptp.vEBT_VEBT) (Y tptp.option_nat)) (=> (= (@ tptp.vEBT_vebt_maxt X) Y) (=> (forall ((A3 Bool) (B3 Bool)) (=> (= X (@ (@ tptp.vEBT_Leaf A3) B3)) (not (and (=> B3 (= Y (@ tptp.some_nat tptp.one_one_nat))) (=> (not B3) (and (=> A3 (= Y (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A3) (= Y tptp.none_nat)))))))) (=> (=> (exists ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw))) (not (= Y tptp.none_nat))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat)) (=> (exists ((Ux tptp.nat) (Uy tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) Ux) Uy) Uz2))) (not (= Y (@ tptp.some_nat Ma2)))))))))) (forall ((X tptp.vEBT_VEBT)) (=> (forall ((A3 Bool) (B3 Bool)) (not (= X (@ (@ tptp.vEBT_Leaf A3) B3)))) (=> (forall ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw tptp.vEBT_VEBT)) (not (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw)))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Ux tptp.nat) (Uy tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (not (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) Ux) Uy) Uz2)))))))) (forall ((X tptp.code_integer) (A tptp.code_integer) (Y tptp.code_integer) (U tptp.code_integer) (V2 tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (=> (@ (@ tptp.ord_le6747313008572928689nteger X) A) (=> (@ (@ tptp.ord_le6747313008572928689nteger Y) A) (=> (@ _let_1 U) (=> (@ _let_1 V2) (=> (= (@ (@ tptp.plus_p5714425477246183910nteger U) V2) tptp.one_one_Code_integer) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger U) X)) (@ (@ tptp.times_3573771949741848930nteger V2) Y))) A)))))))) (forall ((X tptp.real) (A tptp.real) (Y tptp.real) (U tptp.real) (V2 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 V2) (=> (= (@ (@ tptp.plus_plus_real U) V2) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real U) X)) (@ (@ tptp.times_times_real V2) Y))) A)))))))) (forall ((X tptp.rat) (A tptp.rat) (Y tptp.rat) (U tptp.rat) (V2 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 V2) (=> (= (@ (@ tptp.plus_plus_rat U) V2) tptp.one_one_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat U) X)) (@ (@ tptp.times_times_rat V2) Y))) A)))))))) (forall ((X tptp.int) (A tptp.int) (Y tptp.int) (U tptp.int) (V2 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 V2) (=> (= (@ (@ tptp.plus_plus_int U) V2) tptp.one_one_int) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int U) X)) (@ (@ tptp.times_times_int V2) Y))) A)))))))) (forall ((Mi tptp.nat) (Ma tptp.nat) (Va3 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) Va3) Vb)) X) (or (= X Mi) (= X Ma)))) (forall ((X tptp.produc9072475918466114483BT_nat)) (=> (forall ((A3 Bool) (B3 Bool) (X3 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf A3) B3)) X3)))) (=> (forall ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw tptp.vEBT_VEBT) (X3 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw)) X3)))) (=> (forall ((V tptp.product_prod_nat_nat) (Uy tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT) (X3 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V)) tptp.zero_zero_nat) Uy) Uz2)) X3)))) (=> (forall ((V tptp.product_prod_nat_nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT) (X3 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V)) (@ tptp.suc tptp.zero_zero_nat)) Vb2) Vc2)) X3)))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT) (X3 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc (@ tptp.suc Va))) TreeList) Summary2)) X3)))))))))) _let_339 (forall ((B Bool) (A Bool)) (let ((_let_1 (@ tptp.vEBT_vebt_maxt (@ (@ tptp.vEBT_Leaf A) B)))) (and (=> B (= _let_1 (@ tptp.some_nat tptp.one_one_nat))) (=> (not B) (and (=> A (= _let_1 (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A) (= _let_1 tptp.none_nat))))))) (forall ((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))))) (forall ((X tptp.produc9072475918466114483BT_nat)) (=> (forall ((Uu2 Bool) (Uv2 Bool)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf Uu2) Uv2)) tptp.zero_zero_nat)))) (=> (forall ((A3 Bool) (Uw Bool)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf A3) Uw)) (@ tptp.suc tptp.zero_zero_nat))))) (=> (forall ((A3 Bool) (B3 Bool) (Va tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf A3) B3)) (@ tptp.suc (@ tptp.suc Va)))))) (=> (forall ((Uy tptp.nat) (Uz2 tptp.list_VEBT_VEBT) (Va2 tptp.vEBT_VEBT) (Vb2 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uy) Uz2) Va2)) Vb2)))) (=> (forall ((V tptp.product_prod_nat_nat) (Vd tptp.list_VEBT_VEBT) (Ve tptp.vEBT_VEBT) (Vf tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V)) tptp.zero_zero_nat) Vd) Ve)) Vf)))) (=> (forall ((V tptp.product_prod_nat_nat) (Vh tptp.list_VEBT_VEBT) (Vi tptp.vEBT_VEBT) (Vj tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V)) (@ tptp.suc tptp.zero_zero_nat)) Vh) Vi)) Vj)))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT) (X3 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc (@ tptp.suc Va))) TreeList) Summary2)) X3)))))))))))) (forall ((X tptp.produc9072475918466114483BT_nat)) (=> (forall ((Uu2 Bool) (B3 Bool)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf Uu2) B3)) tptp.zero_zero_nat)))) (=> (forall ((Uv2 Bool) (Uw Bool) (N3 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf Uv2) Uw)) (@ tptp.suc N3))))) (=> (forall ((Ux tptp.nat) (Uy tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT) (Va2 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Ux) Uy) Uz2)) Va2)))) (=> (forall ((V tptp.product_prod_nat_nat) (Vc2 tptp.list_VEBT_VEBT) (Vd tptp.vEBT_VEBT) (Ve tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V)) tptp.zero_zero_nat) Vc2) Vd)) Ve)))) (=> (forall ((V tptp.product_prod_nat_nat) (Vg tptp.list_VEBT_VEBT) (Vh tptp.vEBT_VEBT) (Vi tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V)) (@ tptp.suc tptp.zero_zero_nat)) Vg) Vh)) Vi)))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT) (X3 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc (@ tptp.suc Va))) TreeList) Summary2)) X3))))))))))) (forall ((X tptp.produc9072475918466114483BT_nat)) (=> (forall ((A3 Bool) (B3 Bool)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf A3) B3)) tptp.zero_zero_nat)))) (=> (forall ((A3 Bool) (B3 Bool)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf A3) B3)) (@ tptp.suc tptp.zero_zero_nat))))) (=> (forall ((A3 Bool) (B3 Bool) (N3 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf A3) B3)) (@ tptp.suc (@ tptp.suc N3)))))) (=> (forall ((Deg2 tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT) (Uu2 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Deg2) TreeList) Summary2)) Uu2)))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (TrLst tptp.list_VEBT_VEBT) (Smry tptp.vEBT_VEBT) (X3 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) tptp.zero_zero_nat) TrLst) Smry)) X3)))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Tr tptp.list_VEBT_VEBT) (Sm tptp.vEBT_VEBT) (X3 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc tptp.zero_zero_nat)) Tr) Sm)) X3)))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT) (X3 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc (@ tptp.suc Va))) TreeList) Summary2)) X3)))))))))))) (forall ((X tptp.produc9072475918466114483BT_nat)) (=> (forall ((A3 Bool) (B3 Bool) (X3 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf A3) B3)) X3)))) (=> (forall ((Info tptp.option4927543243414619207at_nat) (Ts tptp.list_VEBT_VEBT) (S tptp.vEBT_VEBT) (X3 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node Info) tptp.zero_zero_nat) Ts) S)) X3)))) (=> (forall ((Info tptp.option4927543243414619207at_nat) (Ts tptp.list_VEBT_VEBT) (S tptp.vEBT_VEBT) (X3 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node Info) (@ tptp.suc tptp.zero_zero_nat)) Ts) S)) X3)))) (=> (forall ((V tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT) (X3 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) (@ tptp.suc (@ tptp.suc V))) TreeList) Summary2)) X3)))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT) (X3 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc (@ tptp.suc Va))) TreeList) Summary2)) X3)))))))))) (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)))) (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)))) (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)))) (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)))) (forall ((X tptp.real) (Y tptp.real)) (= (= (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X) X)) (@ (@ tptp.times_times_real Y) Y)) tptp.zero_zero_real) (and (= X tptp.zero_zero_real) (= Y tptp.zero_zero_real)))) (forall ((X tptp.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)))) (forall ((X tptp.int) (Y tptp.int)) (= (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int X) X)) (@ (@ tptp.times_times_int Y) Y)) tptp.zero_zero_int) (and (= X tptp.zero_zero_int) (= Y tptp.zero_zero_int)))) (forall ((Uv Bool) (Uw2 Bool) (N tptp.nat)) (= (@ (@ tptp.vEBT_vebt_succ (@ (@ tptp.vEBT_Leaf Uv) Uw2)) (@ tptp.suc N)) tptp.none_nat)) (forall ((Uu Bool) (Uv Bool)) (= (@ (@ tptp.vEBT_vebt_pred (@ (@ tptp.vEBT_Leaf Uu) Uv)) tptp.zero_zero_nat) tptp.none_nat)) (forall ((V2 tptp.product_prod_nat_nat) (Vc tptp.list_VEBT_VEBT) (Vd2 tptp.vEBT_VEBT) (Ve2 tptp.nat)) (= (@ (@ tptp.vEBT_vebt_succ (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Vc) Vd2)) Ve2) tptp.none_nat)) (forall ((V2 tptp.product_prod_nat_nat) (Vd2 tptp.list_VEBT_VEBT) (Ve2 tptp.vEBT_VEBT) (Vf2 tptp.nat)) (= (@ (@ tptp.vEBT_vebt_pred (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Vd2) Ve2)) Vf2) tptp.none_nat)) (forall ((V2 tptp.product_prod_nat_nat) (Vh2 tptp.list_VEBT_VEBT) (Vi2 tptp.vEBT_VEBT) (Vj2 tptp.nat)) (= (@ (@ tptp.vEBT_vebt_pred (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vh2) Vi2)) Vj2) tptp.none_nat)) (forall ((V2 tptp.product_prod_nat_nat) (Vg2 tptp.list_VEBT_VEBT) (Vh2 tptp.vEBT_VEBT) (Vi2 tptp.nat)) (= (@ (@ tptp.vEBT_vebt_succ (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vg2) Vh2)) Vi2) tptp.none_nat)) (forall ((A Bool) (Uw2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_vebt_pred (@ (@ tptp.vEBT_Leaf A) Uw2)) (@ tptp.suc tptp.zero_zero_nat)))) (and (=> A (= _let_1 (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A) (= _let_1 tptp.none_nat))))) (forall ((B Bool) (Uu Bool)) (let ((_let_1 (@ (@ tptp.vEBT_vebt_succ (@ (@ tptp.vEBT_Leaf Uu) B)) tptp.zero_zero_nat))) (and (=> B (= _let_1 (@ tptp.some_nat tptp.one_one_nat))) (=> (not B) (= _let_1 tptp.none_nat))))) (forall ((B Bool) (A Bool) (Va3 tptp.nat)) (let ((_let_1 (@ (@ tptp.vEBT_vebt_pred (@ (@ tptp.vEBT_Leaf A) B)) (@ tptp.suc (@ tptp.suc Va3))))) (and (=> B (= _let_1 (@ tptp.some_nat tptp.one_one_nat))) (=> (not B) (and (=> A (= _let_1 (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A) (= _let_1 tptp.none_nat))))))) (forall ((A Bool) (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))) (forall ((A Bool) (B Bool)) (= (@ (@ tptp.vEBT_vebt_delete (@ (@ tptp.vEBT_Leaf A) B)) tptp.zero_zero_nat) (@ (@ tptp.vEBT_Leaf false) B))) _let_338 _let_337 (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X) X)) (@ (@ tptp.times_times_real Y) Y))) tptp.zero_zero_real) (and (= X tptp.zero_zero_real) (= Y tptp.zero_zero_real)))) (forall ((X tptp.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)))) (forall ((X tptp.int) (Y tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int X) X)) (@ (@ tptp.times_times_int Y) Y))) tptp.zero_zero_int) (and (= X tptp.zero_zero_int) (= Y tptp.zero_zero_int)))) (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X) X)) (@ (@ tptp.times_times_real Y) Y))) (or (not (= X tptp.zero_zero_real)) (not (= Y tptp.zero_zero_real))))) (forall ((X tptp.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))))) (forall ((X tptp.int) (Y tptp.int)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int X) X)) (@ (@ tptp.times_times_int Y) Y))) (or (not (= X tptp.zero_zero_int)) (not (= Y tptp.zero_zero_int))))) (forall ((A Bool) (B Bool)) (let ((_let_1 (@ tptp.vEBT_Leaf A))) (= (@ (@ tptp.vEBT_vebt_delete (@ _let_1 B)) (@ tptp.suc tptp.zero_zero_nat)) (@ _let_1 false)))) (forall ((Mi tptp.nat) (Ma tptp.nat) (TrLst2 tptp.list_VEBT_VEBT) (Smry2 tptp.vEBT_VEBT) (X tptp.nat)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) tptp.zero_zero_nat) TrLst2) Smry2))) (= (@ (@ tptp.vEBT_vebt_delete _let_1) X) _let_1))) (forall ((Mi tptp.nat) (Ma tptp.nat) (Tr2 tptp.list_VEBT_VEBT) (Sm2 tptp.vEBT_VEBT) (X tptp.nat)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) (@ tptp.suc tptp.zero_zero_nat)) Tr2) Sm2))) (= (@ (@ tptp.vEBT_vebt_delete _let_1) X) _let_1))) _let_336 (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (= (@ tptp.vEBT_VEBT_set_vebt (@ (@ tptp.vEBT_vebt_delete T) X)) (@ (@ tptp.minus_minus_set_nat (@ tptp.vEBT_set_vebt T)) (@ (@ tptp.insert_nat X) tptp.bot_bot_set_nat))))) (forall ((A tptp.real)) (= (= (@ (@ tptp.plus_plus_real A) A) tptp.zero_zero_real) (= A tptp.zero_zero_real))) (forall ((A tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat A) A) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))) (forall ((A tptp.int)) (= (= (@ (@ tptp.plus_plus_int A) A) tptp.zero_zero_int) (= A tptp.zero_zero_int))) (forall ((X tptp.nat) (Y tptp.nat) (Z3 tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat X) Y) Z3) (= (@ (@ tptp.vEBT_VEBT_add (@ tptp.some_nat X)) (@ tptp.some_nat Y)) (@ tptp.some_nat Z3)))) (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (= (@ tptp.vEBT_VEBT_set_vebt (@ (@ tptp.vEBT_vebt_delete T) X)) (@ (@ tptp.minus_minus_set_nat (@ tptp.vEBT_VEBT_set_vebt T)) (@ (@ tptp.insert_nat X) tptp.bot_bot_set_nat))))) (forall ((X tptp.nat) (Z3 tptp.nat) (A4 tptp.set_nat) (B5 tptp.set_nat)) (=> (@ (@ tptp.ord_less_nat X) Z3) (=> (@ (@ tptp.vEBT_VEBT_max_in_set A4) Z3) (=> (@ tptp.finite_finite_nat B5) (=> (= A4 B5) (exists ((X_12 tptp.nat)) (@ (@ (@ tptp.vEBT_is_succ_in_set A4) X) X_12))))))) (forall ((Z3 tptp.nat) (X tptp.nat) (A4 tptp.set_nat)) (=> (@ (@ tptp.ord_less_nat Z3) X) (=> (@ (@ tptp.vEBT_VEBT_min_in_set A4) Z3) (=> (@ tptp.finite_finite_nat A4) (exists ((X_12 tptp.nat)) (@ (@ (@ tptp.vEBT_is_pred_in_set A4) X) X_12)))))) (forall ((X tptp.complex) (Xs2 tptp.list_complex)) (=> (@ (@ tptp.member_complex X) (@ tptp.set_complex2 Xs2)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_s3451745648224563538omplex Xs2)))) (forall ((X tptp.real) (Xs2 tptp.list_real)) (=> (@ (@ tptp.member_real X) (@ tptp.set_real2 Xs2)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_size_list_real Xs2)))) (forall ((X tptp.set_nat) (Xs2 tptp.list_set_nat)) (=> (@ (@ tptp.member_set_nat X) (@ tptp.set_set_nat2 Xs2)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_s3254054031482475050et_nat Xs2)))) (forall ((X tptp.vEBT_VEBT) (Xs2 tptp.list_VEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 Xs2)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_s6755466524823107622T_VEBT Xs2)))) (forall ((X Bool) (Xs2 tptp.list_o)) (=> (@ (@ tptp.member_o X) (@ tptp.set_o2 Xs2)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_size_list_o Xs2)))) (forall ((X tptp.nat) (Xs2 tptp.list_nat)) (=> (@ (@ tptp.member_nat X) (@ tptp.set_nat2 Xs2)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_size_list_nat Xs2)))) (forall ((X tptp.int) (Xs2 tptp.list_int)) (=> (@ (@ tptp.member_int X) (@ tptp.set_int2 Xs2)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_size_list_int Xs2)))) (forall ((X (-> tptp.product_prod_nat_nat tptp.nat)) (X2 tptp.product_prod_nat_nat)) (= (@ (@ tptp.size_o8335143837870341156at_nat X) (@ tptp.some_P7363390416028606310at_nat X2)) (@ (@ tptp.plus_plus_nat (@ X X2)) (@ tptp.suc tptp.zero_zero_nat)))) (forall ((X (-> tptp.nat tptp.nat)) (X2 tptp.nat)) (= (@ (@ tptp.size_option_nat X) (@ tptp.some_nat X2)) (@ (@ tptp.plus_plus_nat (@ X X2)) (@ tptp.suc tptp.zero_zero_nat)))) (forall ((X (-> tptp.num tptp.nat)) (X2 tptp.num)) (= (@ (@ tptp.size_option_num X) (@ tptp.some_num X2)) (@ (@ tptp.plus_plus_nat (@ X X2)) (@ tptp.suc tptp.zero_zero_nat)))) (forall ((R3 tptp.complex) (A tptp.complex) (B tptp.complex) (C2 tptp.complex) (D tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex R3))) (=> (not (= R3 tptp.zero_zero_complex)) (=> (and (= A B) (not (= C2 D))) (not (= (@ (@ tptp.plus_plus_complex A) (@ _let_1 C2)) (@ (@ tptp.plus_plus_complex B) (@ _let_1 D)))))))) (forall ((R3 tptp.real) (A tptp.real) (B tptp.real) (C2 tptp.real) (D tptp.real)) (let ((_let_1 (@ tptp.times_times_real R3))) (=> (not (= R3 tptp.zero_zero_real)) (=> (and (= A B) (not (= C2 D))) (not (= (@ (@ tptp.plus_plus_real A) (@ _let_1 C2)) (@ (@ tptp.plus_plus_real B) (@ _let_1 D)))))))) (forall ((R3 tptp.rat) (A tptp.rat) (B tptp.rat) (C2 tptp.rat) (D tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat R3))) (=> (not (= R3 tptp.zero_zero_rat)) (=> (and (= A B) (not (= C2 D))) (not (= (@ (@ tptp.plus_plus_rat A) (@ _let_1 C2)) (@ (@ tptp.plus_plus_rat B) (@ _let_1 D)))))))) (forall ((R3 tptp.nat) (A tptp.nat) (B tptp.nat) (C2 tptp.nat) (D tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat R3))) (=> (not (= R3 tptp.zero_zero_nat)) (=> (and (= A B) (not (= C2 D))) (not (= (@ (@ tptp.plus_plus_nat A) (@ _let_1 C2)) (@ (@ tptp.plus_plus_nat B) (@ _let_1 D)))))))) (forall ((R3 tptp.int) (A tptp.int) (B tptp.int) (C2 tptp.int) (D tptp.int)) (let ((_let_1 (@ tptp.times_times_int R3))) (=> (not (= R3 tptp.zero_zero_int)) (=> (and (= A B) (not (= C2 D))) (not (= (@ (@ tptp.plus_plus_int A) (@ _let_1 C2)) (@ (@ tptp.plus_plus_int B) (@ _let_1 D)))))))) (forall ((T tptp.vEBT_VEBT) (N tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (@ tptp.finite_finite_nat (@ tptp.vEBT_VEBT_set_vebt T)))) (forall ((Xs2 tptp.set_nat) (A tptp.nat)) (=> (not (exists ((X_12 tptp.nat)) (@ (@ (@ tptp.vEBT_is_pred_in_set Xs2) A) X_12))) (=> (@ tptp.finite_finite_nat Xs2) (not (exists ((X5 tptp.nat)) (and (@ (@ tptp.member_nat X5) Xs2) (@ (@ tptp.ord_less_nat X5) A))))))) (forall ((Xs2 tptp.set_nat) (A tptp.nat)) (=> (not (exists ((X_12 tptp.nat)) (@ (@ (@ tptp.vEBT_is_succ_in_set Xs2) A) X_12))) (=> (@ tptp.finite_finite_nat Xs2) (not (exists ((X5 tptp.nat)) (and (@ (@ tptp.member_nat X5) Xs2) (@ (@ tptp.ord_less_nat A) X5))))))) (forall ((A tptp.complex)) (= (@ (@ tptp.minus_minus_complex A) A) tptp.zero_zero_complex)) (forall ((A tptp.real)) (= (@ (@ tptp.minus_minus_real A) A) tptp.zero_zero_real)) (forall ((A tptp.rat)) (= (@ (@ tptp.minus_minus_rat A) A) tptp.zero_zero_rat)) (forall ((A tptp.int)) (= (@ (@ tptp.minus_minus_int A) A) tptp.zero_zero_int)) (forall ((A tptp.complex)) (= (@ (@ tptp.minus_minus_complex A) tptp.zero_zero_complex) A)) (forall ((A tptp.real)) (= (@ (@ tptp.minus_minus_real A) tptp.zero_zero_real) A)) (forall ((A tptp.rat)) (= (@ (@ tptp.minus_minus_rat A) tptp.zero_zero_rat) A)) (forall ((A tptp.int)) (= (@ (@ tptp.minus_minus_int A) tptp.zero_zero_int) A)) (forall ((A tptp.nat)) (= (@ (@ tptp.minus_minus_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)) (forall ((A tptp.complex)) (= (@ (@ tptp.minus_minus_complex A) tptp.zero_zero_complex) A)) (forall ((A tptp.real)) (= (@ (@ tptp.minus_minus_real A) tptp.zero_zero_real) A)) (forall ((A tptp.rat)) (= (@ (@ tptp.minus_minus_rat A) tptp.zero_zero_rat) A)) (forall ((A tptp.nat)) (= (@ (@ tptp.minus_minus_nat A) tptp.zero_zero_nat) A)) (forall ((A tptp.int)) (= (@ (@ tptp.minus_minus_int A) tptp.zero_zero_int) A)) (forall ((A tptp.complex)) (= (@ (@ tptp.minus_minus_complex A) A) tptp.zero_zero_complex)) (forall ((A tptp.real)) (= (@ (@ tptp.minus_minus_real A) A) tptp.zero_zero_real)) (forall ((A tptp.rat)) (= (@ (@ tptp.minus_minus_rat A) A) tptp.zero_zero_rat)) (forall ((A tptp.nat)) (= (@ (@ tptp.minus_minus_nat A) A) tptp.zero_zero_nat)) (forall ((A tptp.int)) (= (@ (@ tptp.minus_minus_int A) A) tptp.zero_zero_int)) (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A) B)) B) A)) (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A) B)) B) A)) (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat A) B)) B) A)) (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A) B)) B) A)) (forall ((A tptp.real) (C2 tptp.real) (B tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A) C2)) (@ (@ tptp.plus_plus_real B) C2)) (@ (@ tptp.minus_minus_real A) B))) (forall ((A tptp.rat) (C2 tptp.rat) (B tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A) C2)) (@ (@ tptp.plus_plus_rat B) C2)) (@ (@ tptp.minus_minus_rat A) B))) (forall ((A tptp.nat) (C2 tptp.nat) (B tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat A) C2)) (@ (@ tptp.plus_plus_nat B) C2)) (@ (@ tptp.minus_minus_nat A) B))) (forall ((A tptp.int) (C2 tptp.int) (B tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A) C2)) (@ (@ tptp.plus_plus_int B) C2)) (@ (@ tptp.minus_minus_int A) B))) (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A) B)) A) B)) (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A) B)) A) B)) (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat A) B)) A) B)) (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A) B)) A) B)) (forall ((C2 tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real C2))) (= (@ (@ tptp.minus_minus_real (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.minus_minus_real A) B)))) (forall ((C2 tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat C2))) (= (@ (@ tptp.minus_minus_rat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.minus_minus_rat A) B)))) (forall ((C2 tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C2))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.minus_minus_nat A) B)))) (forall ((C2 tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C2))) (= (@ (@ tptp.minus_minus_int (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.minus_minus_int A) B)))) (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.minus_minus_real A) B)) B) A)) (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.minus_minus_rat A) B)) B) A)) (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int A) B)) B) A)) (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A) B)) B) A)) (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A) B)) B) A)) (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A) B)) B) A)) (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.minus_minus_real A) B)) (@ (@ tptp.ord_less_eq_real B) A))) (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.minus_minus_rat A) B)) (@ (@ tptp.ord_less_eq_rat B) A))) (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.minus_minus_int A) B)) (@ (@ tptp.ord_less_eq_int B) A))) (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.minus_minus_real A) B)) (@ (@ tptp.ord_less_real B) A))) (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.minus_minus_rat A) B)) (@ (@ tptp.ord_less_rat B) A))) (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.minus_minus_int A) B)) (@ (@ tptp.ord_less_int B) A))) (forall ((B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_eq_real B) A) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.minus_minus_real A) B)) B) A))) (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat B) A) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.minus_minus_rat A) B)) B) A))) (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B) A) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat A) B)) B) A))) (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B) A) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int A) B)) B) A))) (forall ((B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_eq_real B) A) (= (@ (@ tptp.plus_plus_real B) (@ (@ tptp.minus_minus_real A) B)) A))) (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat B) A) (= (@ (@ tptp.plus_plus_rat B) (@ (@ tptp.minus_minus_rat A) B)) A))) (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B) A) (= (@ (@ tptp.plus_plus_nat B) (@ (@ tptp.minus_minus_nat A) B)) A))) (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B) A) (= (@ (@ tptp.plus_plus_int B) (@ (@ tptp.minus_minus_int A) B)) A))) (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.minus_minus_nat A) (@ (@ tptp.plus_plus_nat A) B)) tptp.zero_zero_nat)) _let_335 _let_334 _let_333 _let_332 _let_331 (forall ((Xs2 tptp.list_VEBT_VEBT) (Ys tptp.list_VEBT_VEBT)) (=> (not (= (@ tptp.size_s6755466524823107622T_VEBT Xs2) (@ tptp.size_s6755466524823107622T_VEBT Ys))) (not (= Xs2 Ys)))) (forall ((Xs2 tptp.list_o) (Ys tptp.list_o)) (=> (not (= (@ tptp.size_size_list_o Xs2) (@ tptp.size_size_list_o Ys))) (not (= Xs2 Ys)))) (forall ((Xs2 tptp.list_nat) (Ys tptp.list_nat)) (=> (not (= (@ tptp.size_size_list_nat Xs2) (@ tptp.size_size_list_nat Ys))) (not (= Xs2 Ys)))) (forall ((Xs2 tptp.list_int) (Ys tptp.list_int)) (=> (not (= (@ tptp.size_size_list_int Xs2) (@ tptp.size_size_list_int Ys))) (not (= Xs2 Ys)))) (forall ((N tptp.nat)) (exists ((Xs3 tptp.list_VEBT_VEBT)) (= (@ tptp.size_s6755466524823107622T_VEBT Xs3) N))) (forall ((N tptp.nat)) (exists ((Xs3 tptp.list_o)) (= (@ tptp.size_size_list_o Xs3) N))) (forall ((N tptp.nat)) (exists ((Xs3 tptp.list_nat)) (= (@ tptp.size_size_list_nat Xs3) N))) (forall ((N tptp.nat)) (exists ((Xs3 tptp.list_int)) (= (@ tptp.size_size_list_int Xs3) N))) (forall ((A tptp.rat) (C2 tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.minus_minus_rat A))) (= (@ (@ tptp.minus_minus_rat (@ _let_1 C2)) B) (@ (@ tptp.minus_minus_rat (@ _let_1 B)) C2)))) (forall ((A tptp.nat) (C2 tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat A))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 C2)) B) (@ (@ tptp.minus_minus_nat (@ _let_1 B)) C2)))) (forall ((A tptp.int) (C2 tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int A))) (= (@ (@ tptp.minus_minus_int (@ _let_1 C2)) B) (@ (@ tptp.minus_minus_int (@ _let_1 B)) C2)))) (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat) (D tptp.rat)) (=> (= (@ (@ tptp.minus_minus_rat A) B) (@ (@ tptp.minus_minus_rat C2) D)) (= (= A B) (= C2 D)))) (forall ((A tptp.int) (B tptp.int) (C2 tptp.int) (D tptp.int)) (=> (= (@ (@ tptp.minus_minus_int A) B) (@ (@ tptp.minus_minus_int C2) D)) (= (= A B) (= C2 D)))) (forall ((A tptp.rat) (B tptp.rat) (D tptp.rat) (C2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat D) C2) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat A) C2)) (@ (@ tptp.minus_minus_rat B) D))))) (forall ((A tptp.int) (B tptp.int) (D tptp.int) (C2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_eq_int D) C2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int A) C2)) (@ (@ tptp.minus_minus_int B) D))))) (forall ((B tptp.rat) (A tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.minus_minus_rat C2))) (=> (@ (@ tptp.ord_less_eq_rat B) A) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B))))) (forall ((B tptp.int) (A tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int C2))) (=> (@ (@ tptp.ord_less_eq_int B) A) (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B))))) (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat A) C2)) (@ (@ tptp.minus_minus_rat B) C2)))) (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int A) C2)) (@ (@ tptp.minus_minus_int B) C2)))) (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat) (D tptp.rat)) (=> (= (@ (@ tptp.minus_minus_rat A) B) (@ (@ tptp.minus_minus_rat C2) D)) (= (@ (@ tptp.ord_less_eq_rat A) B) (@ (@ tptp.ord_less_eq_rat C2) D)))) (forall ((A tptp.int) (B tptp.int) (C2 tptp.int) (D tptp.int)) (=> (= (@ (@ tptp.minus_minus_int A) B) (@ (@ tptp.minus_minus_int C2) D)) (= (@ (@ tptp.ord_less_eq_int A) B) (@ (@ tptp.ord_less_eq_int C2) D)))) (= (lambda ((Y5 tptp.complex) (Z2 tptp.complex)) (= Y5 Z2)) (lambda ((A5 tptp.complex) (B4 tptp.complex)) (= (@ (@ tptp.minus_minus_complex A5) B4) tptp.zero_zero_complex))) (= (lambda ((Y5 tptp.real) (Z2 tptp.real)) (= Y5 Z2)) (lambda ((A5 tptp.real) (B4 tptp.real)) (= (@ (@ tptp.minus_minus_real A5) B4) tptp.zero_zero_real))) (= (lambda ((Y5 tptp.rat) (Z2 tptp.rat)) (= Y5 Z2)) (lambda ((A5 tptp.rat) (B4 tptp.rat)) (= (@ (@ tptp.minus_minus_rat A5) B4) tptp.zero_zero_rat))) (= (lambda ((Y5 tptp.int) (Z2 tptp.int)) (= Y5 Z2)) (lambda ((A5 tptp.int) (B4 tptp.int)) (= (@ (@ tptp.minus_minus_int A5) B4) tptp.zero_zero_int))) (forall ((A tptp.real) (B tptp.real) (C2 tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real A) C2)) (@ (@ tptp.minus_minus_real B) C2)))) (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat A) C2)) (@ (@ tptp.minus_minus_rat B) C2)))) (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (@ (@ tptp.ord_less_int (@ (@ tptp.minus_minus_int A) C2)) (@ (@ tptp.minus_minus_int B) C2)))) (forall ((B tptp.real) (A tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.minus_minus_real C2))) (=> (@ (@ tptp.ord_less_real B) A) (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B))))) (forall ((B tptp.rat) (A tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.minus_minus_rat C2))) (=> (@ (@ tptp.ord_less_rat B) A) (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B))))) (forall ((B tptp.int) (A tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int C2))) (=> (@ (@ tptp.ord_less_int B) A) (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B))))) (forall ((A tptp.real) (B tptp.real) (C2 tptp.real) (D tptp.real)) (=> (= (@ (@ tptp.minus_minus_real A) B) (@ (@ tptp.minus_minus_real C2) D)) (= (@ (@ tptp.ord_less_real A) B) (@ (@ tptp.ord_less_real C2) D)))) (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat) (D tptp.rat)) (=> (= (@ (@ tptp.minus_minus_rat A) B) (@ (@ tptp.minus_minus_rat C2) D)) (= (@ (@ tptp.ord_less_rat A) B) (@ (@ tptp.ord_less_rat C2) D)))) (forall ((A tptp.int) (B tptp.int) (C2 tptp.int) (D tptp.int)) (=> (= (@ (@ tptp.minus_minus_int A) B) (@ (@ tptp.minus_minus_int C2) D)) (= (@ (@ tptp.ord_less_int A) B) (@ (@ tptp.ord_less_int C2) D)))) (forall ((A tptp.real) (B tptp.real) (D tptp.real) (C2 tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_real D) C2) (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real A) C2)) (@ (@ tptp.minus_minus_real B) D))))) (forall ((A tptp.rat) (B tptp.rat) (D tptp.rat) (C2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_rat D) C2) (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat A) C2)) (@ (@ tptp.minus_minus_rat B) D))))) (forall ((A tptp.int) (B tptp.int) (D tptp.int) (C2 tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_int D) C2) (@ (@ tptp.ord_less_int (@ (@ tptp.minus_minus_int A) C2)) (@ (@ tptp.minus_minus_int B) D))))) (forall ((A tptp.real) (B tptp.real) (C2 tptp.real)) (= (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real A) B)) C2) (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real A) C2)) (@ (@ tptp.times_times_real B) C2)))) (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (= (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat A) B)) C2) (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat A) C2)) (@ (@ tptp.times_times_rat B) C2)))) (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int A) B)) C2) (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int A) C2)) (@ (@ tptp.times_times_int B) C2)))) (forall ((A tptp.real) (B tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.times_times_real A))) (= (@ _let_1 (@ (@ tptp.minus_minus_real B) C2)) (@ (@ tptp.minus_minus_real (@ _let_1 B)) (@ _let_1 C2))))) (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat A))) (= (@ _let_1 (@ (@ tptp.minus_minus_rat B) C2)) (@ (@ tptp.minus_minus_rat (@ _let_1 B)) (@ _let_1 C2))))) (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (= (@ _let_1 (@ (@ tptp.minus_minus_int B) C2)) (@ (@ tptp.minus_minus_int (@ _let_1 B)) (@ _let_1 C2))))) (forall ((B tptp.real) (C2 tptp.real) (A tptp.real)) (= (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real B) C2)) A) (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real B) A)) (@ (@ tptp.times_times_real C2) A)))) (forall ((B tptp.rat) (C2 tptp.rat) (A tptp.rat)) (= (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat B) C2)) A) (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat B) A)) (@ (@ tptp.times_times_rat C2) A)))) (forall ((B tptp.nat) (C2 tptp.nat) (A tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat B) C2)) A) (@ (@ tptp.minus_minus_nat (@ (@ tptp.times_times_nat B) A)) (@ (@ tptp.times_times_nat C2) A)))) (forall ((B tptp.int) (C2 tptp.int) (A tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int B) C2)) A) (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int B) A)) (@ (@ tptp.times_times_int C2) A)))) (forall ((A tptp.real) (B tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.times_times_real A))) (= (@ _let_1 (@ (@ tptp.minus_minus_real B) C2)) (@ (@ tptp.minus_minus_real (@ _let_1 B)) (@ _let_1 C2))))) (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat A))) (= (@ _let_1 (@ (@ tptp.minus_minus_rat B) C2)) (@ (@ tptp.minus_minus_rat (@ _let_1 B)) (@ _let_1 C2))))) (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (= (@ _let_1 (@ (@ tptp.minus_minus_nat B) C2)) (@ (@ tptp.minus_minus_nat (@ _let_1 B)) (@ _let_1 C2))))) (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (= (@ _let_1 (@ (@ tptp.minus_minus_int B) C2)) (@ (@ tptp.minus_minus_int (@ _let_1 B)) (@ _let_1 C2))))) (forall ((A tptp.real) (B tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.minus_minus_real A))) (= (@ (@ tptp.minus_minus_real (@ _let_1 B)) C2) (@ _let_1 (@ (@ tptp.plus_plus_real B) C2))))) (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.minus_minus_rat A))) (= (@ (@ tptp.minus_minus_rat (@ _let_1 B)) C2) (@ _let_1 (@ (@ tptp.plus_plus_rat B) C2))))) (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat A))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 B)) C2) (@ _let_1 (@ (@ tptp.plus_plus_nat B) C2))))) (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int A))) (= (@ (@ tptp.minus_minus_int (@ _let_1 B)) C2) (@ _let_1 (@ (@ tptp.plus_plus_int B) C2))))) (forall ((C2 tptp.real) (B tptp.real) (A tptp.real)) (=> (= (@ (@ tptp.plus_plus_real C2) B) A) (= C2 (@ (@ tptp.minus_minus_real A) B)))) (forall ((C2 tptp.rat) (B tptp.rat) (A tptp.rat)) (=> (= (@ (@ tptp.plus_plus_rat C2) B) A) (= C2 (@ (@ tptp.minus_minus_rat A) B)))) (forall ((C2 tptp.nat) (B tptp.nat) (A tptp.nat)) (=> (= (@ (@ tptp.plus_plus_nat C2) B) A) (= C2 (@ (@ tptp.minus_minus_nat A) B)))) (forall ((C2 tptp.int) (B tptp.int) (A tptp.int)) (=> (= (@ (@ tptp.plus_plus_int C2) B) A) (= C2 (@ (@ tptp.minus_minus_int A) B)))) (forall ((A tptp.real) (B tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.minus_minus_real A))) (= (@ _let_1 (@ (@ tptp.plus_plus_real B) C2)) (@ (@ tptp.minus_minus_real (@ _let_1 C2)) B)))) (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.minus_minus_rat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat B) C2)) (@ (@ tptp.minus_minus_rat (@ _let_1 C2)) B)))) (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int A))) (= (@ _let_1 (@ (@ tptp.plus_plus_int B) C2)) (@ (@ tptp.minus_minus_int (@ _let_1 C2)) B)))) (forall ((A tptp.real) (B tptp.real) (C2 tptp.real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.minus_minus_real A) B)) C2) (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A) C2)) B))) (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.minus_minus_rat A) B)) C2) (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A) C2)) B))) (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int A) B)) C2) (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A) C2)) B))) (forall ((A tptp.real) (B tptp.real) (C2 tptp.real)) (= (@ (@ tptp.minus_minus_real A) (@ (@ tptp.minus_minus_real B) C2)) (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A) C2)) B))) (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (= (@ (@ tptp.minus_minus_rat A) (@ (@ tptp.minus_minus_rat B) C2)) (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A) C2)) B))) (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (= (@ (@ tptp.minus_minus_int A) (@ (@ tptp.minus_minus_int B) C2)) (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A) C2)) B))) (forall ((A tptp.real) (B tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A))) (= (@ _let_1 (@ (@ tptp.minus_minus_real B) C2)) (@ (@ tptp.minus_minus_real (@ _let_1 B)) C2)))) (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat A))) (= (@ _let_1 (@ (@ tptp.minus_minus_rat B) C2)) (@ (@ tptp.minus_minus_rat (@ _let_1 B)) C2)))) (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A))) (= (@ _let_1 (@ (@ tptp.minus_minus_int B) C2)) (@ (@ tptp.minus_minus_int (@ _let_1 B)) C2)))) (forall ((A tptp.real) (C2 tptp.real) (B tptp.real)) (= (= A (@ (@ tptp.minus_minus_real C2) B)) (= (@ (@ tptp.plus_plus_real A) B) C2))) (forall ((A tptp.rat) (C2 tptp.rat) (B tptp.rat)) (= (= A (@ (@ tptp.minus_minus_rat C2) B)) (= (@ (@ tptp.plus_plus_rat A) B) C2))) (forall ((A tptp.int) (C2 tptp.int) (B tptp.int)) (= (= A (@ (@ tptp.minus_minus_int C2) B)) (= (@ (@ tptp.plus_plus_int A) B) C2))) (forall ((A tptp.real) (B tptp.real) (C2 tptp.real)) (= (= (@ (@ tptp.minus_minus_real A) B) C2) (= A (@ (@ tptp.plus_plus_real C2) B)))) (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (= (= (@ (@ tptp.minus_minus_rat A) B) C2) (= A (@ (@ tptp.plus_plus_rat C2) B)))) (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (= (= (@ (@ tptp.minus_minus_int A) B) C2) (= A (@ (@ tptp.plus_plus_int C2) B)))) (forall ((A4 tptp.real) (K2 tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real K2))) (=> (= A4 (@ _let_1 A)) (= (@ (@ tptp.minus_minus_real A4) B) (@ _let_1 (@ (@ tptp.minus_minus_real A) B)))))) (forall ((A4 tptp.rat) (K2 tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat K2))) (=> (= A4 (@ _let_1 A)) (= (@ (@ tptp.minus_minus_rat A4) B) (@ _let_1 (@ (@ tptp.minus_minus_rat A) B)))))) (forall ((A4 tptp.int) (K2 tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int K2))) (=> (= A4 (@ _let_1 A)) (= (@ (@ tptp.minus_minus_int A4) B) (@ _let_1 (@ (@ tptp.minus_minus_int A) B)))))) _let_330 (forall ((N6 tptp.set_nat) (N tptp.nat)) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) N6) (@ (@ tptp.ord_less_nat X3) N))) (@ tptp.finite_finite_nat N6))) (= tptp.finite_finite_nat (lambda ((N5 tptp.set_nat)) (exists ((M6 tptp.nat)) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) N5) (@ (@ tptp.ord_less_eq_nat X4) M6)))))) (= tptp.ord_less_eq_real (lambda ((A5 tptp.real) (B4 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real A5) B4)) tptp.zero_zero_real))) (= tptp.ord_less_eq_rat (lambda ((A5 tptp.rat) (B4 tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat A5) B4)) tptp.zero_zero_rat))) (= tptp.ord_less_eq_int (lambda ((A5 tptp.int) (B4 tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int A5) B4)) tptp.zero_zero_int))) (= tptp.ord_less_real (lambda ((A5 tptp.real) (B4 tptp.real)) (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real A5) B4)) tptp.zero_zero_real))) (= tptp.ord_less_rat (lambda ((A5 tptp.rat) (B4 tptp.rat)) (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat A5) B4)) tptp.zero_zero_rat))) (= tptp.ord_less_int (lambda ((A5 tptp.int) (B4 tptp.int)) (@ (@ tptp.ord_less_int (@ (@ tptp.minus_minus_int A5) B4)) tptp.zero_zero_int))) (forall ((I2 tptp.real) (K2 tptp.real) (N tptp.real) (J2 tptp.real)) (let ((_let_1 (@ (@ tptp.ord_less_eq_real N) (@ (@ tptp.plus_plus_real J2) K2)))) (let ((_let_2 (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real I2) K2)) N))) (=> _let_2 (=> _let_1 (=> _let_2 (=> _let_1 (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real N) K2)) J2)))))))) (forall ((I2 tptp.rat) (K2 tptp.rat) (N tptp.rat) (J2 tptp.rat)) (let ((_let_1 (@ (@ tptp.ord_less_eq_rat N) (@ (@ tptp.plus_plus_rat J2) K2)))) (let ((_let_2 (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat I2) K2)) N))) (=> _let_2 (=> _let_1 (=> _let_2 (=> _let_1 (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat N) K2)) J2)))))))) (forall ((I2 tptp.nat) (K2 tptp.nat) (N tptp.nat) (J2 tptp.nat)) (let ((_let_1 (@ (@ tptp.ord_less_eq_nat N) (@ (@ tptp.plus_plus_nat J2) K2)))) (let ((_let_2 (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I2) K2)) N))) (=> _let_2 (=> _let_1 (=> _let_2 (=> _let_1 (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat N) K2)) J2)))))))) (forall ((I2 tptp.int) (K2 tptp.int) (N tptp.int) (J2 tptp.int)) (let ((_let_1 (@ (@ tptp.ord_less_eq_int N) (@ (@ tptp.plus_plus_int J2) K2)))) (let ((_let_2 (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int I2) K2)) N))) (=> _let_2 (=> _let_1 (=> _let_2 (=> _let_1 (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int N) K2)) J2)))))))) (forall ((I2 tptp.real) (K2 tptp.real) (N tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real I2) K2)) N) (@ (@ tptp.ord_less_eq_real I2) (@ (@ tptp.minus_minus_real N) K2)))) (forall ((I2 tptp.rat) (K2 tptp.rat) (N tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat I2) K2)) N) (@ (@ tptp.ord_less_eq_rat I2) (@ (@ tptp.minus_minus_rat N) K2)))) (forall ((I2 tptp.nat) (K2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I2) K2)) N) (@ (@ tptp.ord_less_eq_nat I2) (@ (@ tptp.minus_minus_nat N) K2)))) (forall ((I2 tptp.int) (K2 tptp.int) (N tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int I2) K2)) N) (@ (@ tptp.ord_less_eq_int I2) (@ (@ tptp.minus_minus_int N) K2)))) (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ (@ tptp.ord_less_eq_nat A) B))) (=> _let_1 (=> _let_1 (= (= (@ (@ tptp.minus_minus_nat B) A) C2) (= B (@ (@ tptp.plus_plus_nat C2) A))))))) (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= (@ (@ tptp.plus_plus_nat A) (@ (@ tptp.minus_minus_nat B) A)) B))) (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= (@ (@ tptp.minus_minus_nat C2) (@ (@ tptp.minus_minus_nat B) A)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat C2) A)) B)))) (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat B) C2)) A) (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat B) A)) C2)))) (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat B) A)) C2) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat B) C2)) A)))) (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C2))) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= (@ (@ tptp.minus_minus_nat (@ _let_1 B)) A) (@ _let_1 (@ (@ tptp.minus_minus_nat B) A)))))) (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C2))) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= (@ _let_1 (@ (@ tptp.minus_minus_nat B) A)) (@ (@ tptp.minus_minus_nat (@ _let_1 B)) A))))) (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= (@ (@ tptp.ord_less_eq_nat C2) (@ (@ tptp.minus_minus_nat B) A)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat C2) A)) B)))) (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (@ (@ tptp.ord_less_eq_nat C2) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat B) C2)) A)))) (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat B) A)) A) B))) (forall ((A tptp.real) (C2 tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_eq_real A) (@ (@ tptp.minus_minus_real C2) B)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A) B)) C2))) (forall ((A tptp.rat) (C2 tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat A) (@ (@ tptp.minus_minus_rat C2) B)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A) B)) C2))) (forall ((A tptp.int) (C2 tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.minus_minus_int C2) B)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A) B)) C2))) (forall ((A tptp.real) (B tptp.real) (C2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real A) B)) C2) (@ (@ tptp.ord_less_eq_real A) (@ (@ tptp.plus_plus_real C2) B)))) (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat A) B)) C2) (@ (@ tptp.ord_less_eq_rat A) (@ (@ tptp.plus_plus_rat C2) B)))) (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int A) B)) C2) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.plus_plus_int C2) B)))) (forall ((A tptp.real) (C2 tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_real A) (@ (@ tptp.minus_minus_real C2) B)) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) B)) C2))) (forall ((A tptp.rat) (C2 tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat A) (@ (@ tptp.minus_minus_rat C2) B)) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) B)) C2))) (forall ((A tptp.int) (C2 tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_int A) (@ (@ tptp.minus_minus_int C2) B)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) B)) C2))) (forall ((A tptp.real) (B tptp.real) (C2 tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real A) B)) C2) (@ (@ tptp.ord_less_real A) (@ (@ tptp.plus_plus_real C2) B)))) (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat A) B)) C2) (@ (@ tptp.ord_less_rat A) (@ (@ tptp.plus_plus_rat C2) B)))) (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.minus_minus_int A) B)) C2) (@ (@ tptp.ord_less_int A) (@ (@ tptp.plus_plus_int C2) B)))) (forall ((A tptp.real) (B tptp.real)) (=> (not (@ (@ tptp.ord_less_real A) B)) (= (@ (@ tptp.plus_plus_real B) (@ (@ tptp.minus_minus_real A) B)) A))) (forall ((A tptp.rat) (B tptp.rat)) (=> (not (@ (@ tptp.ord_less_rat A) B)) (= (@ (@ tptp.plus_plus_rat B) (@ (@ tptp.minus_minus_rat A) B)) A))) (forall ((A tptp.nat) (B tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat A) B)) (= (@ (@ tptp.plus_plus_nat B) (@ (@ tptp.minus_minus_nat A) B)) A))) (forall ((A tptp.int) (B tptp.int)) (=> (not (@ (@ tptp.ord_less_int A) B)) (= (@ (@ tptp.plus_plus_int B) (@ (@ tptp.minus_minus_int A) B)) A))) (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real X) X)) (@ (@ tptp.times_times_real Y) Y)) (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real X) Y)) (@ (@ tptp.minus_minus_real X) Y)))) (forall ((X tptp.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)))) (forall ((X tptp.int) (Y tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int X) X)) (@ (@ tptp.times_times_int Y) Y)) (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int X) Y)) (@ (@ tptp.minus_minus_int X) Y)))) (forall ((A tptp.real) (E tptp.real) (C2 tptp.real) (B tptp.real) (D tptp.real)) (= (= (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) E)) C2) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real B) E)) D)) (= C2 (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real B) A)) E)) D)))) (forall ((A tptp.rat) (E tptp.rat) (C2 tptp.rat) (B tptp.rat) (D tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) E)) C2) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B) E)) D)) (= C2 (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat B) A)) E)) D)))) (forall ((A tptp.int) (E tptp.int) (C2 tptp.int) (B tptp.int) (D tptp.int)) (= (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) E)) C2) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) E)) D)) (= C2 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int B) A)) E)) D)))) (forall ((A tptp.real) (E tptp.real) (C2 tptp.real) (B tptp.real) (D tptp.real)) (= (= (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) E)) C2) (@ (@ 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)) C2) D))) (forall ((A tptp.rat) (E tptp.rat) (C2 tptp.rat) (B tptp.rat) (D tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) E)) C2) (@ (@ 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)) C2) D))) (forall ((A tptp.int) (E tptp.int) (C2 tptp.int) (B tptp.int) (D tptp.int)) (= (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) E)) C2) (@ (@ 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)) C2) D))) (forall ((A tptp.real) (E tptp.real) (C2 tptp.real) (B tptp.real) (D tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) E)) C2)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real B) E)) D)) (@ (@ tptp.ord_less_eq_real C2) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real B) A)) E)) D)))) (forall ((A tptp.rat) (E tptp.rat) (C2 tptp.rat) (B tptp.rat) (D tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) E)) C2)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B) E)) D)) (@ (@ tptp.ord_less_eq_rat C2) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat B) A)) E)) D)))) (forall ((A tptp.int) (E tptp.int) (C2 tptp.int) (B tptp.int) (D tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) E)) C2)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) E)) D)) (@ (@ tptp.ord_less_eq_int C2) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int B) A)) E)) D)))) (forall ((A tptp.real) (E tptp.real) (C2 tptp.real) (B tptp.real) (D tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) E)) C2)) (@ (@ 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)) C2)) D))) (forall ((A tptp.rat) (E tptp.rat) (C2 tptp.rat) (B tptp.rat) (D tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) E)) C2)) (@ (@ 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)) C2)) D))) (forall ((A tptp.int) (E tptp.int) (C2 tptp.int) (B tptp.int) (D tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) E)) C2)) (@ (@ 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)) C2)) D))) (forall ((A tptp.real) (E tptp.real) (C2 tptp.real) (B tptp.real) (D tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) E)) C2)) (@ (@ 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)) C2)) D))) (forall ((A tptp.rat) (E tptp.rat) (C2 tptp.rat) (B tptp.rat) (D tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) E)) C2)) (@ (@ 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)) C2)) D))) (forall ((A tptp.int) (E tptp.int) (C2 tptp.int) (B tptp.int) (D tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) E)) C2)) (@ (@ 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)) C2)) D))) (forall ((A tptp.real) (E tptp.real) (C2 tptp.real) (B tptp.real) (D tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) E)) C2)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real B) E)) D)) (@ (@ tptp.ord_less_real C2) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real B) A)) E)) D)))) (forall ((A tptp.rat) (E tptp.rat) (C2 tptp.rat) (B tptp.rat) (D tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) E)) C2)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B) E)) D)) (@ (@ tptp.ord_less_rat C2) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat B) A)) E)) D)))) (forall ((A tptp.int) (E tptp.int) (C2 tptp.int) (B tptp.int) (D tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) E)) C2)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) E)) D)) (@ (@ tptp.ord_less_int C2) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int B) A)) E)) D)))) (forall ((X tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.times_3573771949741848930nteger X) X)) tptp.one_one_Code_integer) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.plus_p5714425477246183910nteger X) tptp.one_one_Code_integer)) (@ (@ tptp.minus_8373710615458151222nteger X) tptp.one_one_Code_integer)))) (forall ((X tptp.complex)) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex X) X)) tptp.one_one_complex) (@ (@ tptp.times_times_complex (@ (@ tptp.plus_plus_complex X) tptp.one_one_complex)) (@ (@ tptp.minus_minus_complex X) tptp.one_one_complex)))) (forall ((X tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real X) X)) tptp.one_one_real) (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real X) tptp.one_one_real)) (@ (@ tptp.minus_minus_real X) tptp.one_one_real)))) (forall ((X tptp.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)))) (forall ((X tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int X) X)) tptp.one_one_int) (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int X) tptp.one_one_int)) (@ (@ tptp.minus_minus_int X) tptp.one_one_int)))) (forall ((S3 tptp.set_complex) (P2 (-> tptp.set_complex Bool)) (F2 (-> tptp.complex tptp.rat))) (=> (@ tptp.finite3207457112153483333omplex S3) (=> (@ P2 tptp.bot_bot_set_complex) (=> (forall ((X3 tptp.complex) (S4 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex S4) (=> (forall ((Y6 tptp.complex)) (=> (@ (@ tptp.member_complex Y6) S4) (@ (@ tptp.ord_less_eq_rat (@ F2 Y6)) (@ F2 X3)))) (=> (@ P2 S4) (@ P2 (@ (@ tptp.insert_complex X3) S4)))))) (@ P2 S3))))) (forall ((S3 tptp.set_nat) (P2 (-> tptp.set_nat Bool)) (F2 (-> tptp.nat tptp.rat))) (=> (@ tptp.finite_finite_nat S3) (=> (@ P2 tptp.bot_bot_set_nat) (=> (forall ((X3 tptp.nat) (S4 tptp.set_nat)) (=> (@ tptp.finite_finite_nat S4) (=> (forall ((Y6 tptp.nat)) (=> (@ (@ tptp.member_nat Y6) S4) (@ (@ tptp.ord_less_eq_rat (@ F2 Y6)) (@ F2 X3)))) (=> (@ P2 S4) (@ P2 (@ (@ tptp.insert_nat X3) S4)))))) (@ P2 S3))))) (forall ((S3 tptp.set_int) (P2 (-> tptp.set_int Bool)) (F2 (-> tptp.int tptp.rat))) (=> (@ tptp.finite_finite_int S3) (=> (@ P2 tptp.bot_bot_set_int) (=> (forall ((X3 tptp.int) (S4 tptp.set_int)) (=> (@ tptp.finite_finite_int S4) (=> (forall ((Y6 tptp.int)) (=> (@ (@ tptp.member_int Y6) S4) (@ (@ tptp.ord_less_eq_rat (@ F2 Y6)) (@ F2 X3)))) (=> (@ P2 S4) (@ P2 (@ (@ tptp.insert_int X3) S4)))))) (@ P2 S3))))) (forall ((S3 tptp.set_real) (P2 (-> tptp.set_real Bool)) (F2 (-> tptp.real tptp.rat))) (=> (@ tptp.finite_finite_real S3) (=> (@ P2 tptp.bot_bot_set_real) (=> (forall ((X3 tptp.real) (S4 tptp.set_real)) (=> (@ tptp.finite_finite_real S4) (=> (forall ((Y6 tptp.real)) (=> (@ (@ tptp.member_real Y6) S4) (@ (@ tptp.ord_less_eq_rat (@ F2 Y6)) (@ F2 X3)))) (=> (@ P2 S4) (@ P2 (@ (@ tptp.insert_real X3) S4)))))) (@ P2 S3))))) (forall ((S3 tptp.set_complex) (P2 (-> tptp.set_complex Bool)) (F2 (-> tptp.complex tptp.num))) (=> (@ tptp.finite3207457112153483333omplex S3) (=> (@ P2 tptp.bot_bot_set_complex) (=> (forall ((X3 tptp.complex) (S4 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex S4) (=> (forall ((Y6 tptp.complex)) (=> (@ (@ tptp.member_complex Y6) S4) (@ (@ tptp.ord_less_eq_num (@ F2 Y6)) (@ F2 X3)))) (=> (@ P2 S4) (@ P2 (@ (@ tptp.insert_complex X3) S4)))))) (@ P2 S3))))) (forall ((S3 tptp.set_nat) (P2 (-> tptp.set_nat Bool)) (F2 (-> tptp.nat tptp.num))) (=> (@ tptp.finite_finite_nat S3) (=> (@ P2 tptp.bot_bot_set_nat) (=> (forall ((X3 tptp.nat) (S4 tptp.set_nat)) (=> (@ tptp.finite_finite_nat S4) (=> (forall ((Y6 tptp.nat)) (=> (@ (@ tptp.member_nat Y6) S4) (@ (@ tptp.ord_less_eq_num (@ F2 Y6)) (@ F2 X3)))) (=> (@ P2 S4) (@ P2 (@ (@ tptp.insert_nat X3) S4)))))) (@ P2 S3))))) (forall ((S3 tptp.set_int) (P2 (-> tptp.set_int Bool)) (F2 (-> tptp.int tptp.num))) (=> (@ tptp.finite_finite_int S3) (=> (@ P2 tptp.bot_bot_set_int) (=> (forall ((X3 tptp.int) (S4 tptp.set_int)) (=> (@ tptp.finite_finite_int S4) (=> (forall ((Y6 tptp.int)) (=> (@ (@ tptp.member_int Y6) S4) (@ (@ tptp.ord_less_eq_num (@ F2 Y6)) (@ F2 X3)))) (=> (@ P2 S4) (@ P2 (@ (@ tptp.insert_int X3) S4)))))) (@ P2 S3))))) (forall ((S3 tptp.set_real) (P2 (-> tptp.set_real Bool)) (F2 (-> tptp.real tptp.num))) (=> (@ tptp.finite_finite_real S3) (=> (@ P2 tptp.bot_bot_set_real) (=> (forall ((X3 tptp.real) (S4 tptp.set_real)) (=> (@ tptp.finite_finite_real S4) (=> (forall ((Y6 tptp.real)) (=> (@ (@ tptp.member_real Y6) S4) (@ (@ tptp.ord_less_eq_num (@ F2 Y6)) (@ F2 X3)))) (=> (@ P2 S4) (@ P2 (@ (@ tptp.insert_real X3) S4)))))) (@ P2 S3))))) (forall ((S3 tptp.set_complex) (P2 (-> tptp.set_complex Bool)) (F2 (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex S3) (=> (@ P2 tptp.bot_bot_set_complex) (=> (forall ((X3 tptp.complex) (S4 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex S4) (=> (forall ((Y6 tptp.complex)) (=> (@ (@ tptp.member_complex Y6) S4) (@ (@ tptp.ord_less_eq_nat (@ F2 Y6)) (@ F2 X3)))) (=> (@ P2 S4) (@ P2 (@ (@ tptp.insert_complex X3) S4)))))) (@ P2 S3))))) (forall ((S3 tptp.set_nat) (P2 (-> tptp.set_nat Bool)) (F2 (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_nat S3) (=> (@ P2 tptp.bot_bot_set_nat) (=> (forall ((X3 tptp.nat) (S4 tptp.set_nat)) (=> (@ tptp.finite_finite_nat S4) (=> (forall ((Y6 tptp.nat)) (=> (@ (@ tptp.member_nat Y6) S4) (@ (@ tptp.ord_less_eq_nat (@ F2 Y6)) (@ F2 X3)))) (=> (@ P2 S4) (@ P2 (@ (@ tptp.insert_nat X3) S4)))))) (@ P2 S3))))) (forall ((P2 (-> tptp.list_VEBT_VEBT Bool)) (Xs2 tptp.list_VEBT_VEBT)) (=> (forall ((Xs3 tptp.list_VEBT_VEBT)) (=> (forall ((Ys2 tptp.list_VEBT_VEBT)) (=> (@ (@ tptp.ord_less_nat (@ tptp.size_s6755466524823107622T_VEBT Ys2)) (@ tptp.size_s6755466524823107622T_VEBT Xs3)) (@ P2 Ys2))) (@ P2 Xs3))) (@ P2 Xs2))) (forall ((P2 (-> tptp.list_o Bool)) (Xs2 tptp.list_o)) (=> (forall ((Xs3 tptp.list_o)) (=> (forall ((Ys2 tptp.list_o)) (=> (@ (@ tptp.ord_less_nat (@ tptp.size_size_list_o Ys2)) (@ tptp.size_size_list_o Xs3)) (@ P2 Ys2))) (@ P2 Xs3))) (@ P2 Xs2))) (forall ((P2 (-> tptp.list_nat Bool)) (Xs2 tptp.list_nat)) (=> (forall ((Xs3 tptp.list_nat)) (=> (forall ((Ys2 tptp.list_nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.size_size_list_nat Ys2)) (@ tptp.size_size_list_nat Xs3)) (@ P2 Ys2))) (@ P2 Xs3))) (@ P2 Xs2))) (forall ((P2 (-> tptp.list_int Bool)) (Xs2 tptp.list_int)) (=> (forall ((Xs3 tptp.list_int)) (=> (forall ((Ys2 tptp.list_int)) (=> (@ (@ tptp.ord_less_nat (@ tptp.size_size_list_int Ys2)) (@ tptp.size_size_list_int Xs3)) (@ P2 Ys2))) (@ P2 Xs3))) (@ P2 Xs2))) (forall ((B tptp.complex) (A tptp.complex)) (= (= B (@ (@ tptp.plus_plus_complex B) A)) (= A tptp.zero_zero_complex))) (forall ((B tptp.real) (A tptp.real)) (= (= B (@ (@ tptp.plus_plus_real B) A)) (= A tptp.zero_zero_real))) (forall ((B tptp.rat) (A tptp.rat)) (= (= B (@ (@ tptp.plus_plus_rat B) A)) (= A tptp.zero_zero_rat))) (forall ((B tptp.nat) (A tptp.nat)) (= (= B (@ (@ tptp.plus_plus_nat B) A)) (= A tptp.zero_zero_nat))) (forall ((B tptp.int) (A tptp.int)) (= (= B (@ (@ tptp.plus_plus_int B) A)) (= A tptp.zero_zero_int))) (forall ((W2 tptp.real) (Y tptp.real) (X tptp.real) (Z3 tptp.real)) (let ((_let_1 (@ tptp.times_times_real X))) (let ((_let_2 (@ tptp.times_times_real W2))) (= (= (@ (@ tptp.plus_plus_real (@ _let_2 Y)) (@ _let_1 Z3)) (@ (@ tptp.plus_plus_real (@ _let_2 Z3)) (@ _let_1 Y))) (or (= W2 X) (= Y Z3)))))) (forall ((W2 tptp.rat) (Y tptp.rat) (X tptp.rat) (Z3 tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat X))) (let ((_let_2 (@ tptp.times_times_rat W2))) (= (= (@ (@ tptp.plus_plus_rat (@ _let_2 Y)) (@ _let_1 Z3)) (@ (@ tptp.plus_plus_rat (@ _let_2 Z3)) (@ _let_1 Y))) (or (= W2 X) (= Y Z3)))))) (forall ((W2 tptp.nat) (Y tptp.nat) (X tptp.nat) (Z3 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat X))) (let ((_let_2 (@ tptp.times_times_nat W2))) (= (= (@ (@ tptp.plus_plus_nat (@ _let_2 Y)) (@ _let_1 Z3)) (@ (@ tptp.plus_plus_nat (@ _let_2 Z3)) (@ _let_1 Y))) (or (= W2 X) (= Y Z3)))))) (forall ((W2 tptp.int) (Y tptp.int) (X tptp.int) (Z3 tptp.int)) (let ((_let_1 (@ tptp.times_times_int X))) (let ((_let_2 (@ tptp.times_times_int W2))) (= (= (@ (@ tptp.plus_plus_int (@ _let_2 Y)) (@ _let_1 Z3)) (@ (@ tptp.plus_plus_int (@ _let_2 Z3)) (@ _let_1 Y))) (or (= W2 X) (= Y Z3)))))) (forall ((A tptp.real) (B tptp.real) (C2 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 (= C2 D))) (not (= (@ (@ tptp.plus_plus_real (@ _let_2 C2)) (@ _let_1 D)) (@ (@ tptp.plus_plus_real (@ _let_2 D)) (@ _let_1 C2)))))))) (forall ((A tptp.rat) (B tptp.rat) (C2 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 (= C2 D))) (not (= (@ (@ tptp.plus_plus_rat (@ _let_2 C2)) (@ _let_1 D)) (@ (@ tptp.plus_plus_rat (@ _let_2 D)) (@ _let_1 C2)))))))) (forall ((A tptp.nat) (B tptp.nat) (C2 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 (= C2 D))) (not (= (@ (@ tptp.plus_plus_nat (@ _let_2 C2)) (@ _let_1 D)) (@ (@ tptp.plus_plus_nat (@ _let_2 D)) (@ _let_1 C2)))))))) (forall ((A tptp.int) (B tptp.int) (C2 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 (= C2 D))) (not (= (@ (@ tptp.plus_plus_int (@ _let_2 C2)) (@ _let_1 D)) (@ (@ tptp.plus_plus_int (@ _let_2 D)) (@ _let_1 C2)))))))) (forall ((X (-> tptp.nat tptp.nat))) (= (@ (@ tptp.size_option_nat X) tptp.none_nat) (@ tptp.suc tptp.zero_zero_nat))) (forall ((X (-> tptp.product_prod_nat_nat tptp.nat))) (= (@ (@ tptp.size_o8335143837870341156at_nat X) tptp.none_P5556105721700978146at_nat) (@ tptp.suc tptp.zero_zero_nat))) (forall ((X (-> tptp.num tptp.nat))) (= (@ (@ tptp.size_option_num X) tptp.none_num) (@ tptp.suc tptp.zero_zero_nat))) (forall ((A4 tptp.set_real)) (=> (@ tptp.finite_finite_real A4) (=> (not (= A4 tptp.bot_bot_set_real)) (exists ((X3 tptp.real)) (and (@ (@ tptp.member_real X3) A4) (forall ((Xa tptp.real)) (=> (@ (@ tptp.member_real Xa) A4) (=> (@ (@ tptp.ord_less_eq_real Xa) X3) (= X3 Xa))))))))) (forall ((A4 tptp.set_set_nat)) (=> (@ tptp.finite1152437895449049373et_nat A4) (=> (not (= A4 tptp.bot_bot_set_set_nat)) (exists ((X3 tptp.set_nat)) (and (@ (@ tptp.member_set_nat X3) A4) (forall ((Xa tptp.set_nat)) (=> (@ (@ tptp.member_set_nat Xa) A4) (=> (@ (@ tptp.ord_less_eq_set_nat Xa) X3) (= X3 Xa))))))))) (forall ((A4 tptp.set_rat)) (=> (@ tptp.finite_finite_rat A4) (=> (not (= A4 tptp.bot_bot_set_rat)) (exists ((X3 tptp.rat)) (and (@ (@ tptp.member_rat X3) A4) (forall ((Xa tptp.rat)) (=> (@ (@ tptp.member_rat Xa) A4) (=> (@ (@ tptp.ord_less_eq_rat Xa) X3) (= X3 Xa))))))))) (forall ((A4 tptp.set_num)) (=> (@ tptp.finite_finite_num A4) (=> (not (= A4 tptp.bot_bot_set_num)) (exists ((X3 tptp.num)) (and (@ (@ tptp.member_num X3) A4) (forall ((Xa tptp.num)) (=> (@ (@ tptp.member_num Xa) A4) (=> (@ (@ tptp.ord_less_eq_num Xa) X3) (= X3 Xa))))))))) (forall ((A4 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A4) (=> (not (= A4 tptp.bot_bot_set_nat)) (exists ((X3 tptp.nat)) (and (@ (@ tptp.member_nat X3) A4) (forall ((Xa tptp.nat)) (=> (@ (@ tptp.member_nat Xa) A4) (=> (@ (@ tptp.ord_less_eq_nat Xa) X3) (= X3 Xa))))))))) (forall ((A4 tptp.set_int)) (=> (@ tptp.finite_finite_int A4) (=> (not (= A4 tptp.bot_bot_set_int)) (exists ((X3 tptp.int)) (and (@ (@ tptp.member_int X3) A4) (forall ((Xa tptp.int)) (=> (@ (@ tptp.member_int Xa) A4) (=> (@ (@ tptp.ord_less_eq_int Xa) X3) (= X3 Xa))))))))) (forall ((A4 tptp.set_real)) (=> (@ tptp.finite_finite_real A4) (=> (not (= A4 tptp.bot_bot_set_real)) (exists ((X3 tptp.real)) (and (@ (@ tptp.member_real X3) A4) (forall ((Xa tptp.real)) (=> (@ (@ tptp.member_real Xa) A4) (=> (@ (@ tptp.ord_less_eq_real X3) Xa) (= X3 Xa))))))))) (forall ((A4 tptp.set_set_nat)) (=> (@ tptp.finite1152437895449049373et_nat A4) (=> (not (= A4 tptp.bot_bot_set_set_nat)) (exists ((X3 tptp.set_nat)) (and (@ (@ tptp.member_set_nat X3) A4) (forall ((Xa tptp.set_nat)) (=> (@ (@ tptp.member_set_nat Xa) A4) (=> (@ (@ tptp.ord_less_eq_set_nat X3) Xa) (= X3 Xa))))))))) (forall ((A4 tptp.set_rat)) (=> (@ tptp.finite_finite_rat A4) (=> (not (= A4 tptp.bot_bot_set_rat)) (exists ((X3 tptp.rat)) (and (@ (@ tptp.member_rat X3) A4) (forall ((Xa tptp.rat)) (=> (@ (@ tptp.member_rat Xa) A4) (=> (@ (@ tptp.ord_less_eq_rat X3) Xa) (= X3 Xa))))))))) (forall ((A4 tptp.set_num)) (=> (@ tptp.finite_finite_num A4) (=> (not (= A4 tptp.bot_bot_set_num)) (exists ((X3 tptp.num)) (and (@ (@ tptp.member_num X3) A4) (forall ((Xa tptp.num)) (=> (@ (@ tptp.member_num Xa) A4) (=> (@ (@ tptp.ord_less_eq_num X3) Xa) (= X3 Xa))))))))) (forall ((A4 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A4) (=> (not (= A4 tptp.bot_bot_set_nat)) (exists ((X3 tptp.nat)) (and (@ (@ tptp.member_nat X3) A4) (forall ((Xa tptp.nat)) (=> (@ (@ tptp.member_nat Xa) A4) (=> (@ (@ tptp.ord_less_eq_nat X3) Xa) (= X3 Xa))))))))) (forall ((A4 tptp.set_int)) (=> (@ tptp.finite_finite_int A4) (=> (not (= A4 tptp.bot_bot_set_int)) (exists ((X3 tptp.int)) (and (@ (@ tptp.member_int X3) A4) (forall ((Xa tptp.int)) (=> (@ (@ tptp.member_int Xa) A4) (=> (@ (@ tptp.ord_less_eq_int X3) Xa) (= X3 Xa))))))))) (forall ((X tptp.real) (Y tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real X))) (= (@ (@ tptp.minus_minus_real (@ _let_1 Y)) (@ (@ tptp.times_times_real A) B)) (@ (@ tptp.plus_plus_real (@ _let_1 (@ (@ tptp.minus_minus_real Y) B))) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real X) A)) B))))) (forall ((X tptp.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))))) (forall ((X tptp.int) (Y tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int X))) (= (@ (@ tptp.minus_minus_int (@ _let_1 Y)) (@ (@ tptp.times_times_int A) B)) (@ (@ tptp.plus_plus_int (@ _let_1 (@ (@ tptp.minus_minus_int Y) B))) (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int X) A)) B))))) (forall ((X tptp.set_int) (Y tptp.set_int)) (= (= (@ (@ tptp.minus_minus_set_int X) Y) tptp.bot_bot_set_int) (@ (@ tptp.ord_less_eq_set_int X) Y))) (forall ((X tptp.set_real) (Y tptp.set_real)) (= (= (@ (@ tptp.minus_minus_set_real X) Y) tptp.bot_bot_set_real) (@ (@ tptp.ord_less_eq_set_real X) Y))) (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat)) (= (= (@ (@ tptp.minus_1356011639430497352at_nat X) Y) tptp.bot_bo2099793752762293965at_nat) (@ (@ tptp.ord_le3146513528884898305at_nat X) Y))) (forall ((X tptp.set_nat) (Y tptp.set_nat)) (= (= (@ (@ tptp.minus_minus_set_nat X) Y) tptp.bot_bot_set_nat) (@ (@ tptp.ord_less_eq_set_nat X) Y))) (forall ((T tptp.vEBT_VEBT)) (=> (@ tptp.vEBT_VEBT_minNull T) (= (@ tptp.vEBT_vebt_mint T) tptp.none_nat))) (forall ((T tptp.vEBT_VEBT)) (=> (= (@ tptp.vEBT_vebt_mint T) tptp.none_nat) (@ tptp.vEBT_VEBT_minNull T))) (forall ((X tptp.vEBT_VEBT) (Y tptp.option_nat)) (=> (= (@ tptp.vEBT_vebt_maxt X) Y) (=> (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_vebt_maxt_rel) X) (=> (forall ((A3 Bool) (B3 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A3) B3))) (=> (= X _let_1) (=> (and (=> B3 (= Y (@ tptp.some_nat tptp.one_one_nat))) (=> (not B3) (and (=> A3 (= Y (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A3) (= Y tptp.none_nat))))) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_vebt_maxt_rel) _let_1)))))) (=> (forall ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw))) (=> (= 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) (Ux tptp.nat) (Uy 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))) Ux) Uy) Uz2))) (=> (= X _let_1) (=> (= Y (@ tptp.some_nat Ma2)) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_vebt_maxt_rel) _let_1)))))))))))) (forall ((X tptp.vEBT_VEBT) (Y tptp.option_nat)) (=> (= (@ tptp.vEBT_vebt_mint X) Y) (=> (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_vebt_mint_rel) X) (=> (forall ((A3 Bool) (B3 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A3) B3))) (=> (= X _let_1) (=> (and (=> A3 (= Y (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A3) (and (=> B3 (= Y (@ tptp.some_nat tptp.one_one_nat))) (=> (not B3) (= Y tptp.none_nat))))) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_vebt_mint_rel) _let_1)))))) (=> (forall ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw))) (=> (= 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) (Ux tptp.nat) (Uy 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))) Ux) Uy) Uz2))) (=> (= X _let_1) (=> (= Y (@ tptp.some_nat Mi2)) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_vebt_mint_rel) _let_1)))))))))))) (forall ((S3 tptp.set_nat)) (= (not (@ tptp.finite_finite_nat S3)) (forall ((M6 tptp.nat)) (exists ((N4 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat M6) N4) (@ (@ tptp.member_nat N4) S3)))))) (forall ((Xs2 tptp.list_complex) (P2 (-> tptp.complex Bool)) (N tptp.nat)) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ tptp.set_complex2 Xs2)) (@ P2 X3))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s3451745648224563538omplex Xs2)) (@ P2 (@ (@ tptp.nth_complex Xs2) N))))) (forall ((Xs2 tptp.list_real) (P2 (-> tptp.real Bool)) (N tptp.nat)) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) (@ tptp.set_real2 Xs2)) (@ P2 X3))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_real Xs2)) (@ P2 (@ (@ tptp.nth_real Xs2) N))))) (forall ((Xs2 tptp.list_set_nat) (P2 (-> tptp.set_nat Bool)) (N tptp.nat)) (=> (forall ((X3 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat X3) (@ tptp.set_set_nat2 Xs2)) (@ P2 X3))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s3254054031482475050et_nat Xs2)) (@ P2 (@ (@ tptp.nth_set_nat Xs2) N))))) (forall ((Xs2 tptp.list_VEBT_VEBT) (P2 (-> tptp.vEBT_VEBT Bool)) (N tptp.nat)) (=> (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 Xs2)) (@ P2 X3))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (@ P2 (@ (@ tptp.nth_VEBT_VEBT Xs2) N))))) (forall ((Xs2 tptp.list_o) (P2 (-> Bool Bool)) (N tptp.nat)) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) (@ tptp.set_o2 Xs2)) (@ P2 X3))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_o Xs2)) (@ P2 (@ (@ tptp.nth_o Xs2) N))))) (forall ((Xs2 tptp.list_nat) (P2 (-> tptp.nat Bool)) (N tptp.nat)) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ tptp.set_nat2 Xs2)) (@ P2 X3))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_nat Xs2)) (@ P2 (@ (@ tptp.nth_nat Xs2) N))))) (forall ((Xs2 tptp.list_int) (P2 (-> tptp.int Bool)) (N tptp.nat)) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ tptp.set_int2 Xs2)) (@ P2 X3))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_int Xs2)) (@ P2 (@ (@ tptp.nth_int Xs2) N))))) (forall ((T tptp.vEBT_VEBT)) (=> (not (@ tptp.vEBT_VEBT_minNull T)) (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions T) X_12)))) (forall ((T tptp.vEBT_VEBT) (X tptp.nat)) (=> (@ tptp.vEBT_VEBT_minNull T) (not (@ (@ tptp.vEBT_vebt_member T) X)))) (forall ((M2 tptp.nat) (N tptp.nat) (K2 tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat (@ tptp.suc M2)) N)) (@ tptp.suc K2)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat M2) N)) K2))) (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc M2)) (@ tptp.suc N)) (@ (@ tptp.minus_minus_nat M2) N))) (forall ((N tptp.nat)) (= (@ (@ tptp.minus_minus_nat tptp.zero_zero_nat) N) tptp.zero_zero_nat)) (forall ((M2 tptp.nat)) (= (@ (@ tptp.minus_minus_nat M2) M2) tptp.zero_zero_nat)) (forall ((I2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat N))) (=> (@ (@ tptp.ord_less_eq_nat I2) N) (= (@ _let_1 (@ _let_1 I2)) I2)))) (forall ((I2 tptp.nat) (J2 tptp.nat) (K2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat I2))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 J2)) K2) (@ _let_1 (@ (@ tptp.plus_plus_nat J2) K2))))) (forall ((N tptp.nat) (M2 tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat N) M2)) (@ (@ tptp.ord_less_nat M2) N))) (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ (@ tptp.minus_minus_nat M2) N) tptp.zero_zero_nat))) (forall ((M2 tptp.nat) (N tptp.nat)) (= (= (@ (@ tptp.minus_minus_nat M2) N) tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_nat M2) N))) (forall ((K2 tptp.nat) (J2 tptp.nat) (I2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat I2))) (=> (@ (@ tptp.ord_less_eq_nat K2) J2) (= (@ _let_1 (@ (@ tptp.minus_minus_nat J2) K2)) (@ (@ tptp.minus_minus_nat (@ _let_1 J2)) K2))))) (forall ((K2 tptp.nat) (J2 tptp.nat) (I2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K2) J2) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat J2) K2)) I2) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat J2) I2)) K2)))) (forall ((K2 tptp.nat) (J2 tptp.nat) (I2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K2) J2) (= (@ (@ tptp.minus_minus_nat I2) (@ (@ tptp.minus_minus_nat J2) K2)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat I2) K2)) J2)))) (forall ((N tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc N)) tptp.one_one_nat) N)) (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.suc (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat))) N))) (forall ((K2 tptp.nat) (J2 tptp.nat) (I2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K2) J2) (= (@ (@ tptp.minus_minus_nat I2) (@ tptp.suc (@ (@ tptp.minus_minus_nat J2) K2))) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat I2) K2)) (@ tptp.suc J2))))) (forall ((K2 tptp.nat) (J2 tptp.nat) (I2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K2) J2) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc (@ (@ tptp.minus_minus_nat J2) K2))) I2) (@ (@ tptp.minus_minus_nat (@ tptp.suc J2)) (@ (@ tptp.plus_plus_nat K2) I2))))) (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.suc (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) N))) (forall ((P2 (-> tptp.nat Bool)) (K2 tptp.nat) (I2 tptp.nat)) (=> (@ P2 K2) (=> (forall ((N3 tptp.nat)) (=> (@ P2 (@ tptp.suc N3)) (@ P2 N3))) (@ P2 (@ (@ tptp.minus_minus_nat K2) I2))))) (forall ((M2 tptp.nat)) (= (@ (@ tptp.minus_minus_nat M2) tptp.zero_zero_nat) M2)) (forall ((M2 tptp.nat) (N tptp.nat)) (=> (= (@ (@ tptp.minus_minus_nat M2) N) tptp.zero_zero_nat) (=> (= (@ (@ tptp.minus_minus_nat N) M2) tptp.zero_zero_nat) (= M2 N)))) (forall ((M2 tptp.nat) (N tptp.nat) (L tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat L))) (let ((_let_2 (@ tptp.ord_less_nat M2))) (=> (@ _let_2 N) (=> (@ _let_2 L) (@ (@ tptp.ord_less_nat (@ _let_1 N)) (@ _let_1 M2))))))) (forall ((J2 tptp.nat) (K2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat J2) K2) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat J2) N)) K2))) (forall ((M2 tptp.nat) (N tptp.nat) (L tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat L))) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (@ (@ tptp.ord_less_eq_nat (@ _let_1 N)) (@ _let_1 M2))))) (forall ((A tptp.nat) (C2 tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat B))) (let ((_let_2 (@ tptp.minus_minus_nat C2))) (=> (@ (@ tptp.ord_less_eq_nat A) C2) (=> (@ _let_1 C2) (= (@ (@ tptp.ord_less_eq_nat (@ _let_2 A)) (@ _let_2 B)) (@ _let_1 A))))))) (forall ((M2 tptp.nat) (N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat M2) N)) M2)) (forall ((M2 tptp.nat) (N tptp.nat) (L tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat M2) L)) (@ (@ tptp.minus_minus_nat N) L)))) (forall ((K2 tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat M2))) (let ((_let_2 (@ tptp.ord_less_eq_nat K2))) (=> (@ _let_2 M2) (=> (@ _let_2 N) (= (@ (@ tptp.minus_minus_nat (@ _let_1 K2)) (@ (@ tptp.minus_minus_nat N) K2)) (@ _let_1 N))))))) (forall ((K2 tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat K2))) (=> (@ _let_1 M2) (=> (@ _let_1 N) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat M2) K2)) (@ (@ tptp.minus_minus_nat N) K2)) (@ (@ tptp.ord_less_eq_nat M2) N)))))) (forall ((K2 tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat K2))) (=> (@ _let_1 M2) (=> (@ _let_1 N) (= (= (@ (@ tptp.minus_minus_nat M2) K2) (@ (@ tptp.minus_minus_nat N) K2)) (= M2 N)))))) (forall ((K2 tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K2))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 M2)) (@ _let_1 N)) (@ (@ tptp.minus_minus_nat M2) N)))) (forall ((M2 tptp.nat) (K2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M2) K2)) (@ (@ tptp.plus_plus_nat N) K2)) (@ (@ tptp.minus_minus_nat M2) N))) (forall ((N tptp.nat) (M2 tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat N) M2)) N) M2)) (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M2) N)) N) M2)) (forall ((M2 tptp.nat) (N tptp.nat) (K2 tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat M2) N)) K2) (@ (@ tptp.minus_minus_nat (@ (@ tptp.times_times_nat M2) K2)) (@ (@ tptp.times_times_nat N) K2)))) (forall ((K2 tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K2))) (= (@ _let_1 (@ (@ tptp.minus_minus_nat M2) N)) (@ (@ tptp.minus_minus_nat (@ _let_1 M2)) (@ _let_1 N))))) (@ tptp.vEBT_VEBT_minNull _let_329) (forall ((Uv Bool)) (not (@ tptp.vEBT_VEBT_minNull (@ (@ tptp.vEBT_Leaf true) Uv)))) (forall ((Uu Bool)) (not (@ tptp.vEBT_VEBT_minNull (@ (@ tptp.vEBT_Leaf Uu) true)))) (= (lambda ((Y5 tptp.list_VEBT_VEBT) (Z2 tptp.list_VEBT_VEBT)) (= Y5 Z2)) (lambda ((Xs tptp.list_VEBT_VEBT) (Ys3 tptp.list_VEBT_VEBT)) (and (= (@ tptp.size_s6755466524823107622T_VEBT Xs) (@ tptp.size_s6755466524823107622T_VEBT Ys3)) (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (= (@ (@ tptp.nth_VEBT_VEBT Xs) I) (@ (@ tptp.nth_VEBT_VEBT Ys3) I))))))) (= (lambda ((Y5 tptp.list_o) (Z2 tptp.list_o)) (= Y5 Z2)) (lambda ((Xs tptp.list_o) (Ys3 tptp.list_o)) (and (= (@ tptp.size_size_list_o Xs) (@ tptp.size_size_list_o Ys3)) (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_o Xs)) (= (@ (@ tptp.nth_o Xs) I) (@ (@ tptp.nth_o Ys3) I))))))) (= (lambda ((Y5 tptp.list_nat) (Z2 tptp.list_nat)) (= Y5 Z2)) (lambda ((Xs tptp.list_nat) (Ys3 tptp.list_nat)) (and (= (@ tptp.size_size_list_nat Xs) (@ tptp.size_size_list_nat Ys3)) (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_nat Xs)) (= (@ (@ tptp.nth_nat Xs) I) (@ (@ tptp.nth_nat Ys3) I))))))) (= (lambda ((Y5 tptp.list_int) (Z2 tptp.list_int)) (= Y5 Z2)) (lambda ((Xs tptp.list_int) (Ys3 tptp.list_int)) (and (= (@ tptp.size_size_list_int Xs) (@ tptp.size_size_list_int Ys3)) (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_int Xs)) (= (@ (@ tptp.nth_int Xs) I) (@ (@ tptp.nth_int Ys3) I))))))) (forall ((K2 tptp.nat) (P2 (-> tptp.nat tptp.vEBT_VEBT Bool))) (= (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) K2) (exists ((X7 tptp.vEBT_VEBT)) (@ (@ P2 I) X7)))) (exists ((Xs tptp.list_VEBT_VEBT)) (and (= (@ tptp.size_s6755466524823107622T_VEBT Xs) K2) (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) K2) (@ (@ P2 I) (@ (@ tptp.nth_VEBT_VEBT Xs) I)))))))) (forall ((K2 tptp.nat) (P2 (-> tptp.nat Bool Bool))) (= (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) K2) (exists ((X7 Bool)) (@ (@ P2 I) X7)))) (exists ((Xs tptp.list_o)) (and (= (@ tptp.size_size_list_o Xs) K2) (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) K2) (@ (@ P2 I) (@ (@ tptp.nth_o Xs) I)))))))) (forall ((K2 tptp.nat) (P2 (-> tptp.nat tptp.nat Bool))) (= (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) K2) (exists ((X7 tptp.nat)) (@ (@ P2 I) X7)))) (exists ((Xs tptp.list_nat)) (and (= (@ tptp.size_size_list_nat Xs) K2) (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) K2) (@ (@ P2 I) (@ (@ tptp.nth_nat Xs) I)))))))) (forall ((K2 tptp.nat) (P2 (-> tptp.nat tptp.int Bool))) (= (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) K2) (exists ((X7 tptp.int)) (@ (@ P2 I) X7)))) (exists ((Xs tptp.list_int)) (and (= (@ tptp.size_size_list_int Xs) K2) (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) K2) (@ (@ P2 I) (@ (@ tptp.nth_int Xs) I)))))))) (forall ((Xs2 tptp.list_VEBT_VEBT) (Ys tptp.list_VEBT_VEBT)) (=> (= (@ tptp.size_s6755466524823107622T_VEBT Xs2) (@ tptp.size_s6755466524823107622T_VEBT Ys)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (= (@ (@ tptp.nth_VEBT_VEBT Xs2) I3) (@ (@ tptp.nth_VEBT_VEBT Ys) I3)))) (= Xs2 Ys)))) (forall ((Xs2 tptp.list_o) (Ys tptp.list_o)) (=> (= (@ tptp.size_size_list_o Xs2) (@ tptp.size_size_list_o Ys)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_o Xs2)) (= (@ (@ tptp.nth_o Xs2) I3) (@ (@ tptp.nth_o Ys) I3)))) (= Xs2 Ys)))) (forall ((Xs2 tptp.list_nat) (Ys tptp.list_nat)) (=> (= (@ tptp.size_size_list_nat Xs2) (@ tptp.size_size_list_nat Ys)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_nat Xs2)) (= (@ (@ tptp.nth_nat Xs2) I3) (@ (@ tptp.nth_nat Ys) I3)))) (= Xs2 Ys)))) (forall ((Xs2 tptp.list_int) (Ys tptp.list_int)) (=> (= (@ tptp.size_size_list_int Xs2) (@ tptp.size_size_list_int Ys)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_int Xs2)) (= (@ (@ tptp.nth_int Xs2) I3) (@ (@ tptp.nth_int Ys) I3)))) (= Xs2 Ys)))) (forall ((M2 tptp.nat) (N tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat M2) N)) (@ tptp.suc M2))) (forall ((N tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat M2))) (=> (@ (@ tptp.ord_less_nat N) M2) (= (@ tptp.suc (@ _let_1 (@ tptp.suc N))) (@ _let_1 N))))) (forall ((N tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 N) (=> (@ _let_1 M2) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat M2) N)) M2))))) (forall ((N tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M2) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc M2)) N) (@ tptp.suc (@ (@ tptp.minus_minus_nat M2) N))))) (forall ((K2 tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat K2))) (=> (@ _let_1 M2) (=> (@ _let_1 N) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat M2) K2)) (@ (@ tptp.minus_minus_nat N) K2)) (@ (@ tptp.ord_less_nat M2) N)))))) (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat C2) A) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat A) C2)) (@ (@ tptp.minus_minus_nat B) C2))))) (forall ((N tptp.nat) (M2 tptp.nat)) (= (@ (@ tptp.minus_minus_nat N) (@ (@ tptp.plus_plus_nat N) M2)) tptp.zero_zero_nat)) (forall ((M5 tptp.set_list_VEBT_VEBT)) (=> (@ tptp.finite3004134309566078307T_VEBT M5) (exists ((N3 tptp.nat)) (forall ((X5 tptp.list_VEBT_VEBT)) (=> (@ (@ tptp.member2936631157270082147T_VEBT X5) M5) (@ (@ tptp.ord_less_nat (@ tptp.size_s6755466524823107622T_VEBT X5)) N3)))))) (forall ((M5 tptp.set_list_o)) (=> (@ tptp.finite_finite_list_o M5) (exists ((N3 tptp.nat)) (forall ((X5 tptp.list_o)) (=> (@ (@ tptp.member_list_o X5) M5) (@ (@ tptp.ord_less_nat (@ tptp.size_size_list_o X5)) N3)))))) (forall ((M5 tptp.set_list_nat)) (=> (@ tptp.finite8100373058378681591st_nat M5) (exists ((N3 tptp.nat)) (forall ((X5 tptp.list_nat)) (=> (@ (@ tptp.member_list_nat X5) M5) (@ (@ tptp.ord_less_nat (@ tptp.size_size_list_nat X5)) N3)))))) (forall ((M5 tptp.set_list_int)) (=> (@ tptp.finite3922522038869484883st_int M5) (exists ((N3 tptp.nat)) (forall ((X5 tptp.list_int)) (=> (@ (@ tptp.member_list_int X5) M5) (@ (@ tptp.ord_less_nat (@ tptp.size_size_list_int X5)) N3)))))) (forall ((I2 tptp.nat) (J2 tptp.nat) (K2 tptp.nat)) (= (@ (@ tptp.ord_less_nat I2) (@ (@ tptp.minus_minus_nat J2) K2)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I2) K2)) J2))) (forall ((M2 tptp.nat) (N tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat M2) N)) (= (@ (@ tptp.plus_plus_nat N) (@ (@ tptp.minus_minus_nat M2) N)) M2))) (forall ((J2 tptp.nat) (K2 tptp.nat) (I2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat J2) K2)) I2) (@ (@ tptp.ord_less_eq_nat J2) (@ (@ tptp.plus_plus_nat I2) K2)))) (forall ((K2 tptp.nat) (J2 tptp.nat) (I2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K2) J2) (= (@ (@ tptp.ord_less_eq_nat I2) (@ (@ tptp.minus_minus_nat J2) K2)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I2) K2)) J2)))) (forall ((K2 tptp.nat) (J2 tptp.nat) (I2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat I2))) (=> (@ (@ tptp.ord_less_eq_nat K2) J2) (= (@ (@ tptp.minus_minus_nat (@ _let_1 J2)) K2) (@ _let_1 (@ (@ tptp.minus_minus_nat J2) K2)))))) (forall ((K2 tptp.nat) (J2 tptp.nat) (I2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K2) J2) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat J2) I2)) K2) (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat J2) K2)) I2)))) (forall ((I2 tptp.nat) (J2 tptp.nat) (K2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J2) (= (= (@ (@ tptp.minus_minus_nat J2) I2) K2) (= J2 (@ (@ tptp.plus_plus_nat K2) I2))))) (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat M2))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.minus_minus_nat (@ _let_1 tptp.one_one_nat)) N)))) (forall ((Uz tptp.product_prod_nat_nat) (Va3 tptp.nat) (Vb tptp.list_VEBT_VEBT) (Vc tptp.vEBT_VEBT)) (not (@ tptp.vEBT_VEBT_minNull (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat Uz)) Va3) Vb) Vc)))) (forall ((N tptp.nat) (Xs2 tptp.list_complex)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s3451745648224563538omplex Xs2)) (@ (@ tptp.member_complex (@ (@ tptp.nth_complex Xs2) N)) (@ tptp.set_complex2 Xs2)))) (forall ((N tptp.nat) (Xs2 tptp.list_real)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_real Xs2)) (@ (@ tptp.member_real (@ (@ tptp.nth_real Xs2) N)) (@ tptp.set_real2 Xs2)))) (forall ((N tptp.nat) (Xs2 tptp.list_set_nat)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s3254054031482475050et_nat Xs2)) (@ (@ tptp.member_set_nat (@ (@ tptp.nth_set_nat Xs2) N)) (@ tptp.set_set_nat2 Xs2)))) (forall ((N tptp.nat) (Xs2 tptp.list_VEBT_VEBT)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (@ (@ tptp.member_VEBT_VEBT (@ (@ tptp.nth_VEBT_VEBT Xs2) N)) (@ tptp.set_VEBT_VEBT2 Xs2)))) (forall ((N tptp.nat) (Xs2 tptp.list_o)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_o Xs2)) (@ (@ tptp.member_o (@ (@ tptp.nth_o Xs2) N)) (@ tptp.set_o2 Xs2)))) (forall ((N tptp.nat) (Xs2 tptp.list_nat)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_nat Xs2)) (@ (@ tptp.member_nat (@ (@ tptp.nth_nat Xs2) N)) (@ tptp.set_nat2 Xs2)))) (forall ((N tptp.nat) (Xs2 tptp.list_int)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_int Xs2)) (@ (@ tptp.member_int (@ (@ tptp.nth_int Xs2) N)) (@ tptp.set_int2 Xs2)))) (forall ((N tptp.nat) (Xs2 tptp.list_VEBT_VEBT) (P2 (-> tptp.vEBT_VEBT Bool))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (=> (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 Xs2)) (@ P2 X3))) (@ P2 (@ (@ tptp.nth_VEBT_VEBT Xs2) N))))) (forall ((N tptp.nat) (Xs2 tptp.list_o) (P2 (-> Bool Bool))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_o Xs2)) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) (@ tptp.set_o2 Xs2)) (@ P2 X3))) (@ P2 (@ (@ tptp.nth_o Xs2) N))))) (forall ((N tptp.nat) (Xs2 tptp.list_nat) (P2 (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_nat Xs2)) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ tptp.set_nat2 Xs2)) (@ P2 X3))) (@ P2 (@ (@ tptp.nth_nat Xs2) N))))) (forall ((N tptp.nat) (Xs2 tptp.list_int) (P2 (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_int Xs2)) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ tptp.set_int2 Xs2)) (@ P2 X3))) (@ P2 (@ (@ tptp.nth_int Xs2) N))))) (forall ((X tptp.complex) (Xs2 tptp.list_complex)) (= (@ (@ tptp.member_complex X) (@ tptp.set_complex2 Xs2)) (exists ((I tptp.nat)) (and (@ (@ tptp.ord_less_nat I) (@ tptp.size_s3451745648224563538omplex Xs2)) (= (@ (@ tptp.nth_complex Xs2) I) X))))) (forall ((X tptp.real) (Xs2 tptp.list_real)) (= (@ (@ tptp.member_real X) (@ tptp.set_real2 Xs2)) (exists ((I tptp.nat)) (and (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_real Xs2)) (= (@ (@ tptp.nth_real Xs2) I) X))))) (forall ((X tptp.set_nat) (Xs2 tptp.list_set_nat)) (= (@ (@ tptp.member_set_nat X) (@ tptp.set_set_nat2 Xs2)) (exists ((I tptp.nat)) (and (@ (@ tptp.ord_less_nat I) (@ tptp.size_s3254054031482475050et_nat Xs2)) (= (@ (@ tptp.nth_set_nat Xs2) I) X))))) (forall ((X tptp.vEBT_VEBT) (Xs2 tptp.list_VEBT_VEBT)) (= (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 Xs2)) (exists ((I tptp.nat)) (and (@ (@ tptp.ord_less_nat I) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (= (@ (@ tptp.nth_VEBT_VEBT Xs2) I) X))))) (forall ((X Bool) (Xs2 tptp.list_o)) (= (@ (@ tptp.member_o X) (@ tptp.set_o2 Xs2)) (exists ((I tptp.nat)) (and (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_o Xs2)) (= (@ (@ tptp.nth_o Xs2) I) X))))) (forall ((X tptp.nat) (Xs2 tptp.list_nat)) (= (@ (@ tptp.member_nat X) (@ tptp.set_nat2 Xs2)) (exists ((I tptp.nat)) (and (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_nat Xs2)) (= (@ (@ tptp.nth_nat Xs2) I) X))))) (forall ((X tptp.int) (Xs2 tptp.list_int)) (= (@ (@ tptp.member_int X) (@ tptp.set_int2 Xs2)) (exists ((I tptp.nat)) (and (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_int Xs2)) (= (@ (@ tptp.nth_int Xs2) I) X))))) (forall ((Xs2 tptp.list_complex) (P2 (-> tptp.complex Bool)) (X tptp.complex)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_s3451745648224563538omplex Xs2)) (@ P2 (@ (@ tptp.nth_complex Xs2) I3)))) (=> (@ (@ tptp.member_complex X) (@ tptp.set_complex2 Xs2)) (@ P2 X)))) (forall ((Xs2 tptp.list_real) (P2 (-> tptp.real Bool)) (X tptp.real)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_real Xs2)) (@ P2 (@ (@ tptp.nth_real Xs2) I3)))) (=> (@ (@ tptp.member_real X) (@ tptp.set_real2 Xs2)) (@ P2 X)))) (forall ((Xs2 tptp.list_set_nat) (P2 (-> tptp.set_nat Bool)) (X tptp.set_nat)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_s3254054031482475050et_nat Xs2)) (@ P2 (@ (@ tptp.nth_set_nat Xs2) I3)))) (=> (@ (@ tptp.member_set_nat X) (@ tptp.set_set_nat2 Xs2)) (@ P2 X)))) (forall ((Xs2 tptp.list_VEBT_VEBT) (P2 (-> tptp.vEBT_VEBT Bool)) (X tptp.vEBT_VEBT)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (@ P2 (@ (@ tptp.nth_VEBT_VEBT Xs2) I3)))) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 Xs2)) (@ P2 X)))) (forall ((Xs2 tptp.list_o) (P2 (-> Bool Bool)) (X Bool)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_o Xs2)) (@ P2 (@ (@ tptp.nth_o Xs2) I3)))) (=> (@ (@ tptp.member_o X) (@ tptp.set_o2 Xs2)) (@ P2 X)))) (forall ((Xs2 tptp.list_nat) (P2 (-> tptp.nat Bool)) (X tptp.nat)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_nat Xs2)) (@ P2 (@ (@ tptp.nth_nat Xs2) I3)))) (=> (@ (@ tptp.member_nat X) (@ tptp.set_nat2 Xs2)) (@ P2 X)))) (forall ((Xs2 tptp.list_int) (P2 (-> tptp.int Bool)) (X tptp.int)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_int Xs2)) (@ P2 (@ (@ tptp.nth_int Xs2) I3)))) (=> (@ (@ tptp.member_int X) (@ tptp.set_int2 Xs2)) (@ P2 X)))) (forall ((Xs2 tptp.list_VEBT_VEBT) (P2 (-> tptp.vEBT_VEBT Bool))) (= (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 Xs2)) (@ P2 X4))) (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (@ P2 (@ (@ tptp.nth_VEBT_VEBT Xs2) I)))))) (forall ((Xs2 tptp.list_o) (P2 (-> Bool Bool))) (= (forall ((X4 Bool)) (=> (@ (@ tptp.member_o X4) (@ tptp.set_o2 Xs2)) (@ P2 X4))) (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_o Xs2)) (@ P2 (@ (@ tptp.nth_o Xs2) I)))))) (forall ((Xs2 tptp.list_nat) (P2 (-> tptp.nat Bool))) (= (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) (@ tptp.set_nat2 Xs2)) (@ P2 X4))) (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_nat Xs2)) (@ P2 (@ (@ tptp.nth_nat Xs2) I)))))) (forall ((Xs2 tptp.list_int) (P2 (-> tptp.int Bool))) (= (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) (@ tptp.set_int2 Xs2)) (@ P2 X4))) (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_int Xs2)) (@ P2 (@ (@ tptp.nth_int Xs2) I)))))) (forall ((N tptp.nat) (I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat N) (@ tptp.suc I2))) N))) (forall ((P2 (-> tptp.nat Bool)) (A tptp.nat) (B tptp.nat)) (= (@ P2 (@ (@ tptp.minus_minus_nat A) B)) (and (=> (@ (@ tptp.ord_less_nat A) B) (@ P2 tptp.zero_zero_nat)) (forall ((D2 tptp.nat)) (=> (= A (@ (@ tptp.plus_plus_nat B) D2)) (@ P2 D2)))))) (forall ((P2 (-> tptp.nat Bool)) (A tptp.nat) (B tptp.nat)) (= (@ P2 (@ (@ tptp.minus_minus_nat A) B)) (not (or (and (@ (@ tptp.ord_less_nat A) B) (not (@ P2 tptp.zero_zero_nat))) (exists ((D2 tptp.nat)) (and (= A (@ (@ tptp.plus_plus_nat B) D2)) (not (@ P2 D2)))))))) (forall ((K2 tptp.nat) (J2 tptp.nat) (I2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K2) J2) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat J2) K2)) I2) (@ (@ tptp.ord_less_nat J2) (@ (@ tptp.plus_plus_nat I2) K2))))) (forall ((J2 tptp.nat) (I2 tptp.nat) (U tptp.nat) (M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat J2) I2) (= (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I2) U)) M2) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J2) U)) N)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat I2) J2)) U)) M2) N)))) (forall ((I2 tptp.nat) (J2 tptp.nat) (U tptp.nat) (M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J2) (= (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I2) U)) M2) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J2) U)) N)) (= M2 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat J2) I2)) U)) N))))) (forall ((J2 tptp.nat) (I2 tptp.nat) (U tptp.nat) (M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat J2) I2) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I2) U)) M2)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J2) U)) N)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat I2) J2)) U)) M2)) N)))) (forall ((I2 tptp.nat) (J2 tptp.nat) (U tptp.nat) (M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J2) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I2) U)) M2)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J2) U)) N)) (@ (@ tptp.ord_less_eq_nat M2) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat J2) I2)) U)) N))))) (forall ((J2 tptp.nat) (I2 tptp.nat) (U tptp.nat) (M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat J2) I2) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I2) U)) M2)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J2) U)) N)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat I2) J2)) U)) M2)) N)))) (forall ((I2 tptp.nat) (J2 tptp.nat) (U tptp.nat) (M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J2) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I2) U)) M2)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J2) U)) N)) (@ (@ tptp.minus_minus_nat M2) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat J2) I2)) U)) N))))) (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) (Va2 tptp.nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (not (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat Uz2)) Va2) Vb2) Vc2))))))))) (forall ((X tptp.vEBT_VEBT)) (=> (@ tptp.vEBT_VEBT_minNull X) (=> (not (= X (@ (@ tptp.vEBT_Leaf false) false))) (not (forall ((Uw tptp.nat) (Ux tptp.list_VEBT_VEBT) (Uy tptp.vEBT_VEBT)) (not (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uw) Ux) Uy)))))))) (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= N (@ tptp.suc (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat))))) (forall ((N tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc M2)) N) (@ (@ tptp.minus_minus_nat M2) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat))))) (= tptp.plus_plus_nat (lambda ((M6 tptp.nat) (N4 tptp.nat)) (@ (@ (@ tptp.if_nat (= M6 tptp.zero_zero_nat)) N4) (@ tptp.suc (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat M6) tptp.one_one_nat)) N4))))) (forall ((J2 tptp.nat) (I2 tptp.nat) (U tptp.nat) (M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat J2) I2) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I2) U)) M2)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J2) U)) N)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat I2) J2)) U)) M2)) N)))) (forall ((I2 tptp.nat) (J2 tptp.nat) (U tptp.nat) (M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J2) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I2) U)) M2)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J2) U)) N)) (@ (@ tptp.ord_less_nat M2) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat J2) I2)) U)) N))))) (= tptp.times_times_nat (lambda ((M6 tptp.nat) (N4 tptp.nat)) (@ (@ (@ tptp.if_nat (= M6 tptp.zero_zero_nat)) tptp.zero_zero_nat) (@ (@ tptp.plus_plus_nat N4) (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat M6) tptp.one_one_nat)) N4))))) (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 ((Uw tptp.nat) (Ux tptp.list_VEBT_VEBT) (Uy tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uw) Ux) Uy))) _let_1) (not (=> (exists ((Uz2 tptp.product_prod_nat_nat) (Va2 tptp.nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat Uz2)) Va2) Vb2) Vc2))) Y))))))))) (forall ((D1 tptp.real) (D22 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 D1) (=> (@ _let_1 D22) (exists ((E2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real E2))) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) E2) (@ _let_1 D1) (@ _let_1 D22)))))))) (forall ((D1 tptp.rat) (D22 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 D1) (=> (@ _let_1 D22) (exists ((E2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat E2))) (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) E2) (@ _let_1 D1) (@ _let_1 D22)))))))) (forall ((A4 tptp.set_real) (A tptp.real)) (=> (@ tptp.finite_finite_real A4) (=> (@ (@ tptp.member_real A) A4) (exists ((X3 tptp.real)) (and (@ (@ tptp.member_real X3) A4) (@ (@ tptp.ord_less_eq_real X3) A) (forall ((Xa tptp.real)) (=> (@ (@ tptp.member_real Xa) A4) (=> (@ (@ tptp.ord_less_eq_real Xa) X3) (= X3 Xa))))))))) (forall ((A4 tptp.set_set_nat) (A tptp.set_nat)) (=> (@ tptp.finite1152437895449049373et_nat A4) (=> (@ (@ tptp.member_set_nat A) A4) (exists ((X3 tptp.set_nat)) (and (@ (@ tptp.member_set_nat X3) A4) (@ (@ tptp.ord_less_eq_set_nat X3) A) (forall ((Xa tptp.set_nat)) (=> (@ (@ tptp.member_set_nat Xa) A4) (=> (@ (@ tptp.ord_less_eq_set_nat Xa) X3) (= X3 Xa))))))))) (forall ((A4 tptp.set_rat) (A tptp.rat)) (=> (@ tptp.finite_finite_rat A4) (=> (@ (@ tptp.member_rat A) A4) (exists ((X3 tptp.rat)) (and (@ (@ tptp.member_rat X3) A4) (@ (@ tptp.ord_less_eq_rat X3) A) (forall ((Xa tptp.rat)) (=> (@ (@ tptp.member_rat Xa) A4) (=> (@ (@ tptp.ord_less_eq_rat Xa) X3) (= X3 Xa))))))))) (forall ((A4 tptp.set_num) (A tptp.num)) (=> (@ tptp.finite_finite_num A4) (=> (@ (@ tptp.member_num A) A4) (exists ((X3 tptp.num)) (and (@ (@ tptp.member_num X3) A4) (@ (@ tptp.ord_less_eq_num X3) A) (forall ((Xa tptp.num)) (=> (@ (@ tptp.member_num Xa) A4) (=> (@ (@ tptp.ord_less_eq_num Xa) X3) (= X3 Xa))))))))) (forall ((A4 tptp.set_nat) (A tptp.nat)) (=> (@ tptp.finite_finite_nat A4) (=> (@ (@ tptp.member_nat A) A4) (exists ((X3 tptp.nat)) (and (@ (@ tptp.member_nat X3) A4) (@ (@ tptp.ord_less_eq_nat X3) A) (forall ((Xa tptp.nat)) (=> (@ (@ tptp.member_nat Xa) A4) (=> (@ (@ tptp.ord_less_eq_nat Xa) X3) (= X3 Xa))))))))) (forall ((A4 tptp.set_int) (A tptp.int)) (=> (@ tptp.finite_finite_int A4) (=> (@ (@ tptp.member_int A) A4) (exists ((X3 tptp.int)) (and (@ (@ tptp.member_int X3) A4) (@ (@ tptp.ord_less_eq_int X3) A) (forall ((Xa tptp.int)) (=> (@ (@ tptp.member_int Xa) A4) (=> (@ (@ tptp.ord_less_eq_int Xa) X3) (= X3 Xa))))))))) (forall ((A4 tptp.set_real) (A tptp.real)) (=> (@ tptp.finite_finite_real A4) (=> (@ (@ tptp.member_real A) A4) (exists ((X3 tptp.real)) (and (@ (@ tptp.member_real X3) A4) (@ (@ tptp.ord_less_eq_real A) X3) (forall ((Xa tptp.real)) (=> (@ (@ tptp.member_real Xa) A4) (=> (@ (@ tptp.ord_less_eq_real X3) Xa) (= X3 Xa))))))))) (forall ((A4 tptp.set_set_nat) (A tptp.set_nat)) (=> (@ tptp.finite1152437895449049373et_nat A4) (=> (@ (@ tptp.member_set_nat A) A4) (exists ((X3 tptp.set_nat)) (and (@ (@ tptp.member_set_nat X3) A4) (@ (@ tptp.ord_less_eq_set_nat A) X3) (forall ((Xa tptp.set_nat)) (=> (@ (@ tptp.member_set_nat Xa) A4) (=> (@ (@ tptp.ord_less_eq_set_nat X3) Xa) (= X3 Xa))))))))) (forall ((A4 tptp.set_rat) (A tptp.rat)) (=> (@ tptp.finite_finite_rat A4) (=> (@ (@ tptp.member_rat A) A4) (exists ((X3 tptp.rat)) (and (@ (@ tptp.member_rat X3) A4) (@ (@ tptp.ord_less_eq_rat A) X3) (forall ((Xa tptp.rat)) (=> (@ (@ tptp.member_rat Xa) A4) (=> (@ (@ tptp.ord_less_eq_rat X3) Xa) (= X3 Xa))))))))) (forall ((A4 tptp.set_num) (A tptp.num)) (=> (@ tptp.finite_finite_num A4) (=> (@ (@ tptp.member_num A) A4) (exists ((X3 tptp.num)) (and (@ (@ tptp.member_num X3) A4) (@ (@ tptp.ord_less_eq_num A) X3) (forall ((Xa tptp.num)) (=> (@ (@ tptp.member_num Xa) A4) (=> (@ (@ tptp.ord_less_eq_num X3) Xa) (= X3 Xa))))))))) (forall ((A4 tptp.set_nat) (A tptp.nat)) (=> (@ tptp.finite_finite_nat A4) (=> (@ (@ tptp.member_nat A) A4) (exists ((X3 tptp.nat)) (and (@ (@ tptp.member_nat X3) A4) (@ (@ tptp.ord_less_eq_nat A) X3) (forall ((Xa tptp.nat)) (=> (@ (@ tptp.member_nat Xa) A4) (=> (@ (@ tptp.ord_less_eq_nat X3) Xa) (= X3 Xa))))))))) (forall ((A4 tptp.set_int) (A tptp.int)) (=> (@ tptp.finite_finite_int A4) (=> (@ (@ tptp.member_int A) A4) (exists ((X3 tptp.int)) (and (@ (@ tptp.member_int X3) A4) (@ (@ tptp.ord_less_eq_int A) X3) (forall ((Xa tptp.int)) (=> (@ (@ tptp.member_int Xa) A4) (=> (@ (@ tptp.ord_less_eq_int X3) Xa) (= X3 Xa))))))))) (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 ((Uw tptp.nat) (Ux tptp.list_VEBT_VEBT) (Uy tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uw) Ux) Uy))) (=> (= X _let_1) (=> Y (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel) _let_1)))))) (not (forall ((Uz2 tptp.product_prod_nat_nat) (Va2 tptp.nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat Uz2)) Va2) Vb2) Vc2))) (=> (= X _let_1) (=> (not Y) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel) _let_1)))))))))))))))) (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 ((Uw tptp.nat) (Ux tptp.list_VEBT_VEBT) (Uy tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uw) Ux) Uy))) (=> (= X _let_1) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel) _let_1)))))))))))) (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) (Va2 tptp.nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat Uz2)) Va2) Vb2) Vc2))) (=> (= X _let_1) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel) _let_1))))))))))) (forall ((M2 tptp.nat) (Xs2 tptp.list_VEBT_VEBT) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (= (@ (@ tptp.nth_Pr744662078594809490T_VEBT (@ (@ tptp.enumerate_VEBT_VEBT N) Xs2)) M2) (@ (@ tptp.produc599794634098209291T_VEBT (@ (@ tptp.plus_plus_nat N) M2)) (@ (@ tptp.nth_VEBT_VEBT Xs2) M2))))) (forall ((M2 tptp.nat) (Xs2 tptp.list_o) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) (@ tptp.size_size_list_o Xs2)) (= (@ (@ tptp.nth_Pr112076138515278198_nat_o (@ (@ tptp.enumerate_o N) Xs2)) M2) (@ (@ tptp.product_Pair_nat_o (@ (@ tptp.plus_plus_nat N) M2)) (@ (@ tptp.nth_o Xs2) M2))))) (forall ((M2 tptp.nat) (Xs2 tptp.list_nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) (@ tptp.size_size_list_nat Xs2)) (= (@ (@ tptp.nth_Pr7617993195940197384at_nat (@ (@ tptp.enumerate_nat N) Xs2)) M2) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat N) M2)) (@ (@ tptp.nth_nat Xs2) M2))))) (forall ((M2 tptp.nat) (Xs2 tptp.list_int) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) (@ tptp.size_size_list_int Xs2)) (= (@ (@ tptp.nth_Pr3440142176431000676at_int (@ (@ tptp.enumerate_int N) Xs2)) M2) (@ (@ tptp.product_Pair_nat_int (@ (@ tptp.plus_plus_nat N) M2)) (@ (@ tptp.nth_int Xs2) M2))))) (forall ((S3 tptp.set_complex) (Y tptp.complex) (F2 (-> tptp.complex tptp.rat))) (=> (@ tptp.finite3207457112153483333omplex S3) (=> (not (= S3 tptp.bot_bot_set_complex)) (=> (@ (@ tptp.member_complex Y) S3) (@ (@ tptp.ord_less_eq_rat (@ F2 (@ (@ tptp.lattic4729654577720512673ex_rat F2) S3))) (@ F2 Y)))))) (forall ((S3 tptp.set_nat) (Y tptp.nat) (F2 (-> tptp.nat tptp.rat))) (=> (@ tptp.finite_finite_nat S3) (=> (not (= S3 tptp.bot_bot_set_nat)) (=> (@ (@ tptp.member_nat Y) S3) (@ (@ tptp.ord_less_eq_rat (@ F2 (@ (@ tptp.lattic6811802900495863747at_rat F2) S3))) (@ F2 Y)))))) (forall ((S3 tptp.set_int) (Y tptp.int) (F2 (-> tptp.int tptp.rat))) (=> (@ tptp.finite_finite_int S3) (=> (not (= S3 tptp.bot_bot_set_int)) (=> (@ (@ tptp.member_int Y) S3) (@ (@ tptp.ord_less_eq_rat (@ F2 (@ (@ tptp.lattic7811156612396918303nt_rat F2) S3))) (@ F2 Y)))))) (forall ((S3 tptp.set_real) (Y tptp.real) (F2 (-> tptp.real tptp.rat))) (=> (@ tptp.finite_finite_real S3) (=> (not (= S3 tptp.bot_bot_set_real)) (=> (@ (@ tptp.member_real Y) S3) (@ (@ tptp.ord_less_eq_rat (@ F2 (@ (@ tptp.lattic4420706379359479199al_rat F2) S3))) (@ F2 Y)))))) (forall ((S3 tptp.set_complex) (Y tptp.complex) (F2 (-> tptp.complex tptp.num))) (=> (@ tptp.finite3207457112153483333omplex S3) (=> (not (= S3 tptp.bot_bot_set_complex)) (=> (@ (@ tptp.member_complex Y) S3) (@ (@ tptp.ord_less_eq_num (@ F2 (@ (@ tptp.lattic1922116423962787043ex_num F2) S3))) (@ F2 Y)))))) (forall ((S3 tptp.set_nat) (Y tptp.nat) (F2 (-> tptp.nat tptp.num))) (=> (@ tptp.finite_finite_nat S3) (=> (not (= S3 tptp.bot_bot_set_nat)) (=> (@ (@ tptp.member_nat Y) S3) (@ (@ tptp.ord_less_eq_num (@ F2 (@ (@ tptp.lattic4004264746738138117at_num F2) S3))) (@ F2 Y)))))) (forall ((S3 tptp.set_int) (Y tptp.int) (F2 (-> tptp.int tptp.num))) (=> (@ tptp.finite_finite_int S3) (=> (not (= S3 tptp.bot_bot_set_int)) (=> (@ (@ tptp.member_int Y) S3) (@ (@ tptp.ord_less_eq_num (@ F2 (@ (@ tptp.lattic5003618458639192673nt_num F2) S3))) (@ F2 Y)))))) (forall ((S3 tptp.set_real) (Y tptp.real) (F2 (-> tptp.real tptp.num))) (=> (@ tptp.finite_finite_real S3) (=> (not (= S3 tptp.bot_bot_set_real)) (=> (@ (@ tptp.member_real Y) S3) (@ (@ tptp.ord_less_eq_num (@ F2 (@ (@ tptp.lattic1613168225601753569al_num F2) S3))) (@ F2 Y)))))) (forall ((S3 tptp.set_complex) (Y tptp.complex) (F2 (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex S3) (=> (not (= S3 tptp.bot_bot_set_complex)) (=> (@ (@ tptp.member_complex Y) S3) (@ (@ tptp.ord_less_eq_nat (@ F2 (@ (@ tptp.lattic5364784637807008409ex_nat F2) S3))) (@ F2 Y)))))) (forall ((S3 tptp.set_nat) (Y tptp.nat) (F2 (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_nat S3) (=> (not (= S3 tptp.bot_bot_set_nat)) (=> (@ (@ tptp.member_nat Y) S3) (@ (@ tptp.ord_less_eq_nat (@ F2 (@ (@ tptp.lattic7446932960582359483at_nat F2) S3))) (@ F2 Y)))))) (forall ((P2 (-> tptp.nat tptp.nat Bool)) (A tptp.nat) (B tptp.nat)) (=> (forall ((A3 tptp.nat) (B3 tptp.nat)) (= (@ (@ P2 A3) B3) (@ (@ P2 B3) A3))) (=> (forall ((A3 tptp.nat)) (@ (@ P2 A3) tptp.zero_zero_nat)) (=> (forall ((A3 tptp.nat) (B3 tptp.nat)) (let ((_let_1 (@ P2 A3))) (=> (@ _let_1 B3) (@ _let_1 (@ (@ tptp.plus_plus_nat A3) B3))))) (@ (@ P2 A) B))))) (forall ((N tptp.nat) (P2 (-> tptp.nat Bool)) (M2 tptp.nat)) (=> (forall ((K tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) K) (@ P2 K))) (=> (forall ((K tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat K) I4) (@ P2 I4))) (@ P2 K)))) (@ P2 M2)))) (forall ((Xs2 tptp.list_list_VEBT_VEBT) (N tptp.nat)) (=> (forall ((X3 tptp.list_VEBT_VEBT)) (=> (@ (@ tptp.member2936631157270082147T_VEBT X3) (@ tptp.set_list_VEBT_VEBT2 Xs2)) (= (@ tptp.size_s6755466524823107622T_VEBT X3) N))) (= (@ tptp.size_s6755466524823107622T_VEBT (@ tptp.concat_VEBT_VEBT Xs2)) (@ (@ tptp.times_times_nat (@ tptp.size_s8217280938318005548T_VEBT Xs2)) N)))) (forall ((Xs2 tptp.list_list_o) (N tptp.nat)) (=> (forall ((X3 tptp.list_o)) (=> (@ (@ tptp.member_list_o X3) (@ tptp.set_list_o2 Xs2)) (= (@ tptp.size_size_list_o X3) N))) (= (@ tptp.size_size_list_o (@ tptp.concat_o Xs2)) (@ (@ tptp.times_times_nat (@ tptp.size_s2710708370519433104list_o Xs2)) N)))) (forall ((Xs2 tptp.list_list_nat) (N tptp.nat)) (=> (forall ((X3 tptp.list_nat)) (=> (@ (@ tptp.member_list_nat X3) (@ tptp.set_list_nat2 Xs2)) (= (@ tptp.size_size_list_nat X3) N))) (= (@ tptp.size_size_list_nat (@ tptp.concat_nat Xs2)) (@ (@ tptp.times_times_nat (@ tptp.size_s3023201423986296836st_nat Xs2)) N)))) (forall ((Xs2 tptp.list_list_int) (N tptp.nat)) (=> (forall ((X3 tptp.list_int)) (=> (@ (@ tptp.member_list_int X3) (@ tptp.set_list_int2 Xs2)) (= (@ tptp.size_size_list_int X3) N))) (= (@ tptp.size_size_list_int (@ tptp.concat_int Xs2)) (@ (@ tptp.times_times_nat (@ tptp.size_s533118279054570080st_int Xs2)) N)))) (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)))) (forall ((N tptp.nat) (Xs2 tptp.list_VEBT_VEBT)) (= (@ tptp.size_s4762443039079500285T_VEBT (@ (@ tptp.enumerate_VEBT_VEBT N) Xs2)) (@ tptp.size_s6755466524823107622T_VEBT Xs2))) (forall ((N tptp.nat) (Xs2 tptp.list_o)) (= (@ tptp.size_s6491369823275344609_nat_o (@ (@ tptp.enumerate_o N) Xs2)) (@ tptp.size_size_list_o Xs2))) (forall ((N tptp.nat) (Xs2 tptp.list_nat)) (= (@ tptp.size_s5460976970255530739at_nat (@ (@ tptp.enumerate_nat N) Xs2)) (@ tptp.size_size_list_nat Xs2))) (forall ((N tptp.nat) (Xs2 tptp.list_int)) (= (@ tptp.size_s2970893825323803983at_int (@ (@ tptp.enumerate_int N) Xs2)) (@ tptp.size_size_list_int Xs2))) (= (@ tptp.nat_triangle tptp.zero_zero_nat) tptp.zero_zero_nat) (forall ((I2 tptp.nat) (J2 tptp.nat) (K2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat I2))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 J2)) K2) (@ (@ tptp.minus_minus_nat (@ _let_1 K2)) J2)))) (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))))))))) (= tptp.nat_prod_decode_aux (lambda ((K3 tptp.nat) (M6 tptp.nat)) (let ((_let_1 (@ tptp.suc K3))) (@ (@ (@ tptp.if_Pro6206227464963214023at_nat (@ (@ tptp.ord_less_eq_nat M6) K3)) (@ (@ tptp.product_Pair_nat_nat M6) (@ (@ tptp.minus_minus_nat K3) M6))) (@ (@ tptp.nat_prod_decode_aux _let_1) (@ (@ tptp.minus_minus_nat M6) _let_1)))))) (forall ((K2 tptp.nat) (M2 tptp.nat)) (= (@ tptp.nat_prod_encode (@ (@ tptp.nat_prod_decode_aux K2) M2)) (@ (@ tptp.plus_plus_nat (@ tptp.nat_triangle K2)) M2))) (forall ((K2 tptp.nat) (M2 tptp.nat)) (= (@ tptp.nat_prod_decode (@ (@ tptp.plus_plus_nat (@ tptp.nat_triangle K2)) M2)) (@ (@ tptp.nat_prod_decode_aux K2) M2))) (forall ((Xs2 tptp.list_VEBT_VEBT) (Xss tptp.list_list_VEBT_VEBT)) (=> (@ (@ tptp.member2936631157270082147T_VEBT Xs2) (@ tptp.set_list_VEBT_VEBT2 (@ tptp.produc3021084454716106787T_VEBT Xss))) (= (@ tptp.size_s6755466524823107622T_VEBT Xs2) (@ tptp.size_s8217280938318005548T_VEBT Xss)))) (forall ((Xs2 tptp.list_o) (Xss tptp.list_list_o)) (=> (@ (@ tptp.member_list_o Xs2) (@ tptp.set_list_o2 (@ tptp.product_lists_o Xss))) (= (@ tptp.size_size_list_o Xs2) (@ tptp.size_s2710708370519433104list_o Xss)))) (forall ((Xs2 tptp.list_nat) (Xss tptp.list_list_nat)) (=> (@ (@ tptp.member_list_nat Xs2) (@ tptp.set_list_nat2 (@ tptp.product_lists_nat Xss))) (= (@ tptp.size_size_list_nat Xs2) (@ tptp.size_s3023201423986296836st_nat Xss)))) (forall ((Xs2 tptp.list_int) (Xss tptp.list_list_int)) (=> (@ (@ tptp.member_list_int Xs2) (@ tptp.set_list_int2 (@ tptp.product_lists_int Xss))) (= (@ tptp.size_size_list_int Xs2) (@ tptp.size_s533118279054570080st_int Xss)))) (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)))))) (forall ((P2 (-> tptp.real Bool)) (D3 tptp.real) (Q (-> tptp.real Bool))) (=> (forall ((X3 tptp.real) (K tptp.real)) (= (@ P2 X3) (@ P2 (@ (@ tptp.minus_minus_real X3) (@ (@ tptp.times_times_real K) D3))))) (=> (forall ((X3 tptp.real) (K tptp.real)) (= (@ Q X3) (@ Q (@ (@ tptp.minus_minus_real X3) (@ (@ tptp.times_times_real K) D3))))) (forall ((X5 tptp.real) (K4 tptp.real)) (let ((_let_1 (@ (@ tptp.minus_minus_real X5) (@ (@ tptp.times_times_real K4) D3)))) (= (or (@ P2 X5) (@ Q X5)) (or (@ P2 _let_1) (@ Q _let_1)))))))) (forall ((P2 (-> tptp.rat Bool)) (D3 tptp.rat) (Q (-> tptp.rat Bool))) (=> (forall ((X3 tptp.rat) (K tptp.rat)) (= (@ P2 X3) (@ P2 (@ (@ tptp.minus_minus_rat X3) (@ (@ tptp.times_times_rat K) D3))))) (=> (forall ((X3 tptp.rat) (K tptp.rat)) (= (@ Q X3) (@ Q (@ (@ tptp.minus_minus_rat X3) (@ (@ tptp.times_times_rat K) D3))))) (forall ((X5 tptp.rat) (K4 tptp.rat)) (let ((_let_1 (@ (@ tptp.minus_minus_rat X5) (@ (@ tptp.times_times_rat K4) D3)))) (= (or (@ P2 X5) (@ Q X5)) (or (@ P2 _let_1) (@ Q _let_1)))))))) (forall ((P2 (-> tptp.int Bool)) (D3 tptp.int) (Q (-> tptp.int Bool))) (=> (forall ((X3 tptp.int) (K tptp.int)) (= (@ P2 X3) (@ P2 (@ (@ tptp.minus_minus_int X3) (@ (@ tptp.times_times_int K) D3))))) (=> (forall ((X3 tptp.int) (K tptp.int)) (= (@ Q X3) (@ Q (@ (@ tptp.minus_minus_int X3) (@ (@ tptp.times_times_int K) D3))))) (forall ((X5 tptp.int) (K4 tptp.int)) (let ((_let_1 (@ (@ tptp.minus_minus_int X5) (@ (@ tptp.times_times_int K4) D3)))) (= (or (@ P2 X5) (@ Q X5)) (or (@ P2 _let_1) (@ Q _let_1)))))))) (forall ((P2 (-> tptp.real Bool)) (D3 tptp.real) (Q (-> tptp.real Bool))) (=> (forall ((X3 tptp.real) (K tptp.real)) (= (@ P2 X3) (@ P2 (@ (@ tptp.minus_minus_real X3) (@ (@ tptp.times_times_real K) D3))))) (=> (forall ((X3 tptp.real) (K tptp.real)) (= (@ Q X3) (@ Q (@ (@ tptp.minus_minus_real X3) (@ (@ tptp.times_times_real K) D3))))) (forall ((X5 tptp.real) (K4 tptp.real)) (let ((_let_1 (@ (@ tptp.minus_minus_real X5) (@ (@ tptp.times_times_real K4) D3)))) (= (and (@ P2 X5) (@ Q X5)) (and (@ P2 _let_1) (@ Q _let_1)))))))) (forall ((P2 (-> tptp.rat Bool)) (D3 tptp.rat) (Q (-> tptp.rat Bool))) (=> (forall ((X3 tptp.rat) (K tptp.rat)) (= (@ P2 X3) (@ P2 (@ (@ tptp.minus_minus_rat X3) (@ (@ tptp.times_times_rat K) D3))))) (=> (forall ((X3 tptp.rat) (K tptp.rat)) (= (@ Q X3) (@ Q (@ (@ tptp.minus_minus_rat X3) (@ (@ tptp.times_times_rat K) D3))))) (forall ((X5 tptp.rat) (K4 tptp.rat)) (let ((_let_1 (@ (@ tptp.minus_minus_rat X5) (@ (@ tptp.times_times_rat K4) D3)))) (= (and (@ P2 X5) (@ Q X5)) (and (@ P2 _let_1) (@ Q _let_1)))))))) (forall ((P2 (-> tptp.int Bool)) (D3 tptp.int) (Q (-> tptp.int Bool))) (=> (forall ((X3 tptp.int) (K tptp.int)) (= (@ P2 X3) (@ P2 (@ (@ tptp.minus_minus_int X3) (@ (@ tptp.times_times_int K) D3))))) (=> (forall ((X3 tptp.int) (K tptp.int)) (= (@ Q X3) (@ Q (@ (@ tptp.minus_minus_int X3) (@ (@ tptp.times_times_int K) D3))))) (forall ((X5 tptp.int) (K4 tptp.int)) (let ((_let_1 (@ (@ tptp.minus_minus_int X5) (@ (@ tptp.times_times_int K4) D3)))) (= (and (@ P2 X5) (@ Q X5)) (and (@ P2 _let_1) (@ Q _let_1)))))))) (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex A) tptp.zero_zero_complex) A)) (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real A) tptp.zero_zero_real) A)) (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat A) tptp.zero_zero_rat) A)) (forall ((A tptp.nat)) (= (@ (@ tptp.plus_plus_nat A) tptp.zero_zero_nat) A)) (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int A) tptp.zero_zero_int) A)) _let_328 (= (@ tptp.gcd_Gcd_int tptp.bot_bot_set_int) tptp.zero_zero_int) (forall ((A4 tptp.set_int)) (= (= (@ tptp.gcd_Gcd_int A4) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_set_int A4) (@ (@ tptp.insert_int tptp.zero_zero_int) tptp.bot_bot_set_int)))) (forall ((A4 tptp.set_nat)) (= (= (@ tptp.gcd_Gcd_nat A4) tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_set_nat A4) (@ (@ tptp.insert_nat tptp.zero_zero_nat) tptp.bot_bot_set_nat)))) (forall ((A tptp.rat) (B tptp.rat)) (or (= A B) (not (@ (@ tptp.ord_less_eq_rat A) B)) (not (@ (@ tptp.ord_less_eq_rat B) A)))) (forall ((A tptp.num) (B tptp.num)) (or (= A B) (not (@ (@ tptp.ord_less_eq_num A) B)) (not (@ (@ tptp.ord_less_eq_num B) A)))) (forall ((A tptp.nat) (B tptp.nat)) (or (= A B) (not (@ (@ tptp.ord_less_eq_nat A) B)) (not (@ (@ tptp.ord_less_eq_nat B) A)))) (forall ((A tptp.int) (B tptp.int)) (or (= A B) (not (@ (@ tptp.ord_less_eq_int A) B)) (not (@ (@ tptp.ord_less_eq_int B) A)))) (forall ((A tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat A) A)) (forall ((A tptp.rat)) (@ (@ tptp.ord_less_eq_rat A) A)) (forall ((A tptp.num)) (@ (@ tptp.ord_less_eq_num A) A)) (forall ((A tptp.nat)) (@ (@ tptp.ord_less_eq_nat A) A)) (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int A) A)) _let_326 (forall ((B2 tptp.real) (A2 tptp.real)) (= (not (@ (@ tptp.ord_less_eq_real B2) A2)) (@ (@ tptp.ord_less_real A2) B2))) (forall ((B2 tptp.rat) (A2 tptp.rat)) (= (not (@ (@ tptp.ord_less_eq_rat B2) A2)) (@ (@ tptp.ord_less_rat A2) B2))) (forall ((B2 tptp.num) (A2 tptp.num)) (= (not (@ (@ tptp.ord_less_eq_num B2) A2)) (@ (@ tptp.ord_less_num A2) B2))) (forall ((B2 tptp.nat) (A2 tptp.nat)) (= (not (@ (@ tptp.ord_less_eq_nat B2) A2)) (@ (@ tptp.ord_less_nat A2) B2))) (forall ((B2 tptp.int) (A2 tptp.int)) (= (not (@ (@ tptp.ord_less_eq_int B2) A2)) (@ (@ tptp.ord_less_int A2) B2))) (forall ((T tptp.real)) (exists ((Z tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real Z) X5) (not (@ (@ tptp.ord_less_eq_real X5) T)))))) (forall ((T tptp.rat)) (exists ((Z tptp.rat)) (forall ((X5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z) X5) (not (@ (@ tptp.ord_less_eq_rat X5) T)))))) (forall ((T tptp.num)) (exists ((Z tptp.num)) (forall ((X5 tptp.num)) (=> (@ (@ tptp.ord_less_num Z) X5) (not (@ (@ tptp.ord_less_eq_num X5) T)))))) (forall ((T tptp.nat)) (exists ((Z tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z) X5) (not (@ (@ tptp.ord_less_eq_nat X5) T)))))) (forall ((T tptp.int)) (exists ((Z tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int Z) X5) (not (@ (@ tptp.ord_less_eq_int X5) T)))))) (forall ((T tptp.real)) (exists ((Z tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real Z) X5) (@ (@ tptp.ord_less_eq_real T) X5))))) (forall ((T tptp.rat)) (exists ((Z tptp.rat)) (forall ((X5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z) X5) (@ (@ tptp.ord_less_eq_rat T) X5))))) (forall ((T tptp.num)) (exists ((Z tptp.num)) (forall ((X5 tptp.num)) (=> (@ (@ tptp.ord_less_num Z) X5) (@ (@ tptp.ord_less_eq_num T) X5))))) (forall ((T tptp.nat)) (exists ((Z tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z) X5) (@ (@ tptp.ord_less_eq_nat T) X5))))) (forall ((T tptp.int)) (exists ((Z tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int Z) X5) (@ (@ tptp.ord_less_eq_int T) X5))))) (forall ((T tptp.real)) (exists ((Z tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Z) (@ (@ tptp.ord_less_eq_real X5) T))))) (forall ((T tptp.rat)) (exists ((Z tptp.rat)) (forall ((X5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X5) Z) (@ (@ tptp.ord_less_eq_rat X5) T))))) (forall ((T tptp.num)) (exists ((Z tptp.num)) (forall ((X5 tptp.num)) (=> (@ (@ tptp.ord_less_num X5) Z) (@ (@ tptp.ord_less_eq_num X5) T))))) (forall ((T tptp.nat)) (exists ((Z tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Z) (@ (@ tptp.ord_less_eq_nat X5) T))))) (forall ((T tptp.int)) (exists ((Z tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int X5) Z) (@ (@ tptp.ord_less_eq_int X5) T))))) (forall ((T tptp.real)) (exists ((Z tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Z) (not (@ (@ tptp.ord_less_eq_real T) X5)))))) (forall ((T tptp.rat)) (exists ((Z tptp.rat)) (forall ((X5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X5) Z) (not (@ (@ tptp.ord_less_eq_rat T) X5)))))) (forall ((T tptp.num)) (exists ((Z tptp.num)) (forall ((X5 tptp.num)) (=> (@ (@ tptp.ord_less_num X5) Z) (not (@ (@ tptp.ord_less_eq_num T) X5)))))) (forall ((T tptp.nat)) (exists ((Z tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Z) (not (@ (@ tptp.ord_less_eq_nat T) X5)))))) (forall ((T tptp.int)) (exists ((Z tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int X5) Z) (not (@ (@ tptp.ord_less_eq_int T) X5)))))) (forall ((Xs2 tptp.list_VEBT_VEBT) (Ys tptp.list_VEBT_VEBT)) (= (@ tptp.size_s7466405169056248089T_VEBT (@ (@ tptp.produc4743750530478302277T_VEBT Xs2) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (@ tptp.size_s6755466524823107622T_VEBT Ys)))) (forall ((Xs2 tptp.list_VEBT_VEBT) (Ys tptp.list_o)) (= (@ tptp.size_s9168528473962070013VEBT_o (@ (@ tptp.product_VEBT_VEBT_o Xs2) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (@ tptp.size_size_list_o Ys)))) (forall ((Xs2 tptp.list_VEBT_VEBT) (Ys tptp.list_nat)) (= (@ tptp.size_s6152045936467909847BT_nat (@ (@ tptp.produc7295137177222721919BT_nat Xs2) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (@ tptp.size_size_list_nat Ys)))) (forall ((Xs2 tptp.list_VEBT_VEBT) (Ys tptp.list_int)) (= (@ tptp.size_s3661962791536183091BT_int (@ (@ tptp.produc7292646706713671643BT_int Xs2) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (@ tptp.size_size_list_int Ys)))) (forall ((Xs2 tptp.list_o) (Ys tptp.list_VEBT_VEBT)) (= (@ tptp.size_s4313452262239582901T_VEBT (@ (@ tptp.product_o_VEBT_VEBT Xs2) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_o Xs2)) (@ tptp.size_s6755466524823107622T_VEBT Ys)))) (forall ((Xs2 tptp.list_o) (Ys tptp.list_o)) (= (@ tptp.size_s1515746228057227161od_o_o (@ (@ tptp.product_o_o Xs2) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_o Xs2)) (@ tptp.size_size_list_o Ys)))) (forall ((Xs2 tptp.list_o) (Ys tptp.list_nat)) (= (@ tptp.size_s5443766701097040955_o_nat (@ (@ tptp.product_o_nat Xs2) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_o Xs2)) (@ tptp.size_size_list_nat Ys)))) (forall ((Xs2 tptp.list_o) (Ys tptp.list_int)) (= (@ tptp.size_s2953683556165314199_o_int (@ (@ tptp.product_o_int Xs2) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_o Xs2)) (@ tptp.size_size_list_int Ys)))) (forall ((Xs2 tptp.list_nat) (Ys tptp.list_VEBT_VEBT)) (= (@ tptp.size_s4762443039079500285T_VEBT (@ (@ tptp.produc7156399406898700509T_VEBT Xs2) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_nat Xs2)) (@ tptp.size_s6755466524823107622T_VEBT Ys)))) (forall ((Xs2 tptp.list_nat) (Ys tptp.list_o)) (= (@ tptp.size_s6491369823275344609_nat_o (@ (@ tptp.product_nat_o Xs2) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_nat Xs2)) (@ tptp.size_size_list_o Ys)))) (forall ((A tptp.real) (B tptp.real) (P2 (-> tptp.real Bool))) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ P2 A) (=> (not (@ P2 B)) (exists ((C tptp.real)) (and (@ (@ tptp.ord_less_eq_real A) C) (@ (@ tptp.ord_less_eq_real C) B) (forall ((X5 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real A) X5) (@ (@ tptp.ord_less_real X5) C)) (@ P2 X5))) (forall ((D4 tptp.real)) (=> (forall ((X3 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real A) X3) (@ (@ tptp.ord_less_real X3) D4)) (@ P2 X3))) (@ (@ tptp.ord_less_eq_real D4) C))))))))) (forall ((A tptp.nat) (B tptp.nat) (P2 (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ P2 A) (=> (not (@ P2 B)) (exists ((C tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat A) C) (@ (@ tptp.ord_less_eq_nat C) B) (forall ((X5 tptp.nat)) (=> (and (@ (@ tptp.ord_less_eq_nat A) X5) (@ (@ tptp.ord_less_nat X5) C)) (@ P2 X5))) (forall ((D4 tptp.nat)) (=> (forall ((X3 tptp.nat)) (=> (and (@ (@ tptp.ord_less_eq_nat A) X3) (@ (@ tptp.ord_less_nat X3) D4)) (@ P2 X3))) (@ (@ tptp.ord_less_eq_nat D4) C))))))))) (forall ((A tptp.int) (B tptp.int) (P2 (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ P2 A) (=> (not (@ P2 B)) (exists ((C tptp.int)) (and (@ (@ tptp.ord_less_eq_int A) C) (@ (@ tptp.ord_less_eq_int C) B) (forall ((X5 tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int A) X5) (@ (@ tptp.ord_less_int X5) C)) (@ P2 X5))) (forall ((D4 tptp.int)) (=> (forall ((X3 tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int A) X3) (@ (@ tptp.ord_less_int X3) D4)) (@ P2 X3))) (@ (@ tptp.ord_less_eq_int D4) C))))))))) (forall ((V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (X tptp.nat)) (let ((_let_1 (@ tptp.suc (@ tptp.suc V2)))) (= (@ (@ tptp.vEBT_vebt_insert (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1) TreeList2) Summary)) X) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat X) X))) _let_1) TreeList2) Summary)))) (forall ((I2 tptp.nat) (Xs2 tptp.list_Code_integer) (Ys tptp.list_Code_integer)) (let ((_let_1 (@ tptp.ord_less_nat I2))) (=> (@ _let_1 (@ tptp.size_s3445333598471063425nteger Xs2)) (=> (@ _let_1 (@ tptp.size_s3445333598471063425nteger Ys)) (= (@ (@ tptp.nth_Pr2304437835452373666nteger (@ (@ tptp.zip_Co3543743374963494515nteger Xs2) Ys)) I2) (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.nth_Code_integer Xs2) I2)) (@ (@ tptp.nth_Code_integer Ys) I2))))))) (forall ((I2 tptp.nat) (Xs2 tptp.list_VEBT_VEBT) (Ys tptp.list_VEBT_VEBT)) (let ((_let_1 (@ tptp.ord_less_nat I2))) (=> (@ _let_1 (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (=> (@ _let_1 (@ tptp.size_s6755466524823107622T_VEBT Ys)) (= (@ (@ tptp.nth_Pr4953567300277697838T_VEBT (@ (@ tptp.zip_VE537291747668921783T_VEBT Xs2) Ys)) I2) (@ (@ tptp.produc537772716801021591T_VEBT (@ (@ tptp.nth_VEBT_VEBT Xs2) I2)) (@ (@ tptp.nth_VEBT_VEBT Ys) I2))))))) (forall ((I2 tptp.nat) (Xs2 tptp.list_VEBT_VEBT) (Ys tptp.list_o)) (let ((_let_1 (@ tptp.ord_less_nat I2))) (=> (@ _let_1 (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (=> (@ _let_1 (@ tptp.size_size_list_o Ys)) (= (@ (@ tptp.nth_Pr4606735188037164562VEBT_o (@ (@ tptp.zip_VEBT_VEBT_o Xs2) Ys)) I2) (@ (@ tptp.produc8721562602347293563VEBT_o (@ (@ tptp.nth_VEBT_VEBT Xs2) I2)) (@ (@ tptp.nth_o Ys) I2))))))) (forall ((I2 tptp.nat) (Xs2 tptp.list_VEBT_VEBT) (Ys tptp.list_nat)) (let ((_let_1 (@ tptp.ord_less_nat I2))) (=> (@ _let_1 (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (=> (@ _let_1 (@ tptp.size_size_list_nat Ys)) (= (@ (@ tptp.nth_Pr1791586995822124652BT_nat (@ (@ tptp.zip_VEBT_VEBT_nat Xs2) Ys)) I2) (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.nth_VEBT_VEBT Xs2) I2)) (@ (@ tptp.nth_nat Ys) I2))))))) (forall ((I2 tptp.nat) (Xs2 tptp.list_VEBT_VEBT) (Ys tptp.list_int)) (let ((_let_1 (@ tptp.ord_less_nat I2))) (=> (@ _let_1 (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (=> (@ _let_1 (@ tptp.size_size_list_int Ys)) (= (@ (@ tptp.nth_Pr6837108013167703752BT_int (@ (@ tptp.zip_VEBT_VEBT_int Xs2) Ys)) I2) (@ (@ tptp.produc736041933913180425BT_int (@ (@ tptp.nth_VEBT_VEBT Xs2) I2)) (@ (@ tptp.nth_int Ys) I2))))))) (forall ((I2 tptp.nat) (Xs2 tptp.list_o) (Ys tptp.list_VEBT_VEBT)) (let ((_let_1 (@ tptp.ord_less_nat I2))) (=> (@ _let_1 (@ tptp.size_size_list_o Xs2)) (=> (@ _let_1 (@ tptp.size_s6755466524823107622T_VEBT Ys)) (= (@ (@ tptp.nth_Pr6777367263587873994T_VEBT (@ (@ tptp.zip_o_VEBT_VEBT Xs2) Ys)) I2) (@ (@ tptp.produc2982872950893828659T_VEBT (@ (@ tptp.nth_o Xs2) I2)) (@ (@ tptp.nth_VEBT_VEBT Ys) I2))))))) (forall ((I2 tptp.nat) (Xs2 tptp.list_o) (Ys tptp.list_o)) (let ((_let_1 (@ tptp.ord_less_nat I2))) (=> (@ _let_1 (@ tptp.size_size_list_o Xs2)) (=> (@ _let_1 (@ tptp.size_size_list_o Ys)) (= (@ (@ tptp.nth_Product_prod_o_o (@ (@ tptp.zip_o_o Xs2) Ys)) I2) (@ (@ tptp.product_Pair_o_o (@ (@ tptp.nth_o Xs2) I2)) (@ (@ tptp.nth_o Ys) I2))))))) (forall ((I2 tptp.nat) (Xs2 tptp.list_o) (Ys tptp.list_nat)) (let ((_let_1 (@ tptp.ord_less_nat I2))) (=> (@ _let_1 (@ tptp.size_size_list_o Xs2)) (=> (@ _let_1 (@ tptp.size_size_list_nat Ys)) (= (@ (@ tptp.nth_Pr5826913651314560976_o_nat (@ (@ tptp.zip_o_nat Xs2) Ys)) I2) (@ (@ tptp.product_Pair_o_nat (@ (@ tptp.nth_o Xs2) I2)) (@ (@ tptp.nth_nat Ys) I2))))))) (forall ((I2 tptp.nat) (Xs2 tptp.list_o) (Ys tptp.list_int)) (let ((_let_1 (@ tptp.ord_less_nat I2))) (=> (@ _let_1 (@ tptp.size_size_list_o Xs2)) (=> (@ _let_1 (@ tptp.size_size_list_int Ys)) (= (@ (@ tptp.nth_Pr1649062631805364268_o_int (@ (@ tptp.zip_o_int Xs2) Ys)) I2) (@ (@ tptp.product_Pair_o_int (@ (@ tptp.nth_o Xs2) I2)) (@ (@ tptp.nth_int Ys) I2))))))) (forall ((I2 tptp.nat) (Xs2 tptp.list_nat) (Ys tptp.list_VEBT_VEBT)) (let ((_let_1 (@ tptp.ord_less_nat I2))) (=> (@ _let_1 (@ tptp.size_size_list_nat Xs2)) (=> (@ _let_1 (@ tptp.size_s6755466524823107622T_VEBT Ys)) (= (@ (@ tptp.nth_Pr744662078594809490T_VEBT (@ (@ tptp.zip_nat_VEBT_VEBT Xs2) Ys)) I2) (@ (@ tptp.produc599794634098209291T_VEBT (@ (@ tptp.nth_nat Xs2) I2)) (@ (@ tptp.nth_VEBT_VEBT Ys) I2))))))) (forall ((X tptp.product_prod_nat_nat) (P2 (-> tptp.product_prod_nat_nat Bool)) (Xs2 tptp.list_P6011104703257516679at_nat)) (= (= (@ tptp.some_P7363390416028606310at_nat X) (@ (@ tptp.find_P8199882355184865565at_nat P2) Xs2)) (exists ((I tptp.nat)) (let ((_let_1 (@ (@ tptp.nth_Pr7617993195940197384at_nat Xs2) I))) (and (@ (@ tptp.ord_less_nat I) (@ tptp.size_s5460976970255530739at_nat Xs2)) (@ P2 _let_1) (= X _let_1) (forall ((J tptp.nat)) (=> (@ (@ tptp.ord_less_nat J) I) (not (@ P2 (@ (@ tptp.nth_Pr7617993195940197384at_nat Xs2) J)))))))))) (forall ((X tptp.num) (P2 (-> tptp.num Bool)) (Xs2 tptp.list_num)) (= (= (@ tptp.some_num X) (@ (@ tptp.find_num P2) Xs2)) (exists ((I tptp.nat)) (let ((_let_1 (@ (@ tptp.nth_num Xs2) I))) (and (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_num Xs2)) (@ P2 _let_1) (= X _let_1) (forall ((J tptp.nat)) (=> (@ (@ tptp.ord_less_nat J) I) (not (@ P2 (@ (@ tptp.nth_num Xs2) J)))))))))) (forall ((X tptp.vEBT_VEBT) (P2 (-> tptp.vEBT_VEBT Bool)) (Xs2 tptp.list_VEBT_VEBT)) (= (= (@ tptp.some_VEBT_VEBT X) (@ (@ tptp.find_VEBT_VEBT P2) Xs2)) (exists ((I tptp.nat)) (let ((_let_1 (@ (@ tptp.nth_VEBT_VEBT Xs2) I))) (and (@ (@ tptp.ord_less_nat I) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (@ P2 _let_1) (= X _let_1) (forall ((J tptp.nat)) (=> (@ (@ tptp.ord_less_nat J) I) (not (@ P2 (@ (@ tptp.nth_VEBT_VEBT Xs2) J)))))))))) (forall ((X Bool) (P2 (-> Bool Bool)) (Xs2 tptp.list_o)) (= (= (@ tptp.some_o X) (@ (@ tptp.find_o P2) Xs2)) (exists ((I tptp.nat)) (let ((_let_1 (@ (@ tptp.nth_o Xs2) I))) (and (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_o Xs2)) (@ P2 _let_1) (= X _let_1) (forall ((J tptp.nat)) (=> (@ (@ tptp.ord_less_nat J) I) (not (@ P2 (@ (@ tptp.nth_o Xs2) J)))))))))) (forall ((X tptp.nat) (P2 (-> tptp.nat Bool)) (Xs2 tptp.list_nat)) (= (= (@ tptp.some_nat X) (@ (@ tptp.find_nat P2) Xs2)) (exists ((I tptp.nat)) (let ((_let_1 (@ (@ tptp.nth_nat Xs2) I))) (and (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_nat Xs2)) (@ P2 _let_1) (= X _let_1) (forall ((J tptp.nat)) (=> (@ (@ tptp.ord_less_nat J) I) (not (@ P2 (@ (@ tptp.nth_nat Xs2) J)))))))))) (forall ((X tptp.int) (P2 (-> tptp.int Bool)) (Xs2 tptp.list_int)) (= (= (@ tptp.some_int X) (@ (@ tptp.find_int P2) Xs2)) (exists ((I tptp.nat)) (let ((_let_1 (@ (@ tptp.nth_int Xs2) I))) (and (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_int Xs2)) (@ P2 _let_1) (= X _let_1) (forall ((J tptp.nat)) (=> (@ (@ tptp.ord_less_nat J) I) (not (@ P2 (@ (@ tptp.nth_int Xs2) J)))))))))) (forall ((P2 (-> tptp.product_prod_nat_nat Bool)) (Xs2 tptp.list_P6011104703257516679at_nat) (X tptp.product_prod_nat_nat)) (= (= (@ (@ tptp.find_P8199882355184865565at_nat P2) Xs2) (@ tptp.some_P7363390416028606310at_nat X)) (exists ((I tptp.nat)) (let ((_let_1 (@ (@ tptp.nth_Pr7617993195940197384at_nat Xs2) I))) (and (@ (@ tptp.ord_less_nat I) (@ tptp.size_s5460976970255530739at_nat Xs2)) (@ P2 _let_1) (= X _let_1) (forall ((J tptp.nat)) (=> (@ (@ tptp.ord_less_nat J) I) (not (@ P2 (@ (@ tptp.nth_Pr7617993195940197384at_nat Xs2) J)))))))))) (forall ((P2 (-> tptp.num Bool)) (Xs2 tptp.list_num) (X tptp.num)) (= (= (@ (@ tptp.find_num P2) Xs2) (@ tptp.some_num X)) (exists ((I tptp.nat)) (let ((_let_1 (@ (@ tptp.nth_num Xs2) I))) (and (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_num Xs2)) (@ P2 _let_1) (= X _let_1) (forall ((J tptp.nat)) (=> (@ (@ tptp.ord_less_nat J) I) (not (@ P2 (@ (@ tptp.nth_num Xs2) J)))))))))) (forall ((P2 (-> tptp.vEBT_VEBT Bool)) (Xs2 tptp.list_VEBT_VEBT) (X tptp.vEBT_VEBT)) (= (= (@ (@ tptp.find_VEBT_VEBT P2) Xs2) (@ tptp.some_VEBT_VEBT X)) (exists ((I tptp.nat)) (let ((_let_1 (@ (@ tptp.nth_VEBT_VEBT Xs2) I))) (and (@ (@ tptp.ord_less_nat I) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (@ P2 _let_1) (= X _let_1) (forall ((J tptp.nat)) (=> (@ (@ tptp.ord_less_nat J) I) (not (@ P2 (@ (@ tptp.nth_VEBT_VEBT Xs2) J)))))))))) (forall ((P2 (-> Bool Bool)) (Xs2 tptp.list_o) (X Bool)) (= (= (@ (@ tptp.find_o P2) Xs2) (@ tptp.some_o X)) (exists ((I tptp.nat)) (let ((_let_1 (@ (@ tptp.nth_o Xs2) I))) (and (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_o Xs2)) (@ P2 _let_1) (= X _let_1) (forall ((J tptp.nat)) (=> (@ (@ tptp.ord_less_nat J) I) (not (@ P2 (@ (@ tptp.nth_o Xs2) J)))))))))) (forall ((P2 (-> tptp.nat Bool)) (Xs2 tptp.list_nat) (X tptp.nat)) (= (= (@ (@ tptp.find_nat P2) Xs2) (@ tptp.some_nat X)) (exists ((I tptp.nat)) (let ((_let_1 (@ (@ tptp.nth_nat Xs2) I))) (and (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_nat Xs2)) (@ P2 _let_1) (= X _let_1) (forall ((J tptp.nat)) (=> (@ (@ tptp.ord_less_nat J) I) (not (@ P2 (@ (@ tptp.nth_nat Xs2) J)))))))))) (forall ((P2 (-> tptp.int Bool)) (Xs2 tptp.list_int) (X tptp.int)) (= (= (@ (@ tptp.find_int P2) Xs2) (@ tptp.some_int X)) (exists ((I tptp.nat)) (let ((_let_1 (@ (@ tptp.nth_int Xs2) I))) (and (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_int Xs2)) (@ P2 _let_1) (= X _let_1) (forall ((J tptp.nat)) (=> (@ (@ tptp.ord_less_nat J) I) (not (@ P2 (@ (@ tptp.nth_int Xs2) J)))))))))) (forall ((N tptp.nat) (X tptp.vEBT_VEBT) (Xs2 tptp.list_VEBT_VEBT)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.nth_VEBT_VEBT (@ (@ tptp.cons_VEBT_VEBT X) Xs2)) N) (@ (@ tptp.nth_VEBT_VEBT Xs2) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat))))) (forall ((N tptp.nat) (X tptp.nat) (Xs2 tptp.list_nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.nth_nat (@ (@ tptp.cons_nat X) Xs2)) N) (@ (@ tptp.nth_nat Xs2) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat))))) (forall ((Xs2 tptp.list_VEBT_VEBT)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_s6755466524823107622T_VEBT Xs2)) tptp.one_one_nat) (= (@ tptp.rotate1_VEBT_VEBT Xs2) Xs2))) (forall ((Xs2 tptp.list_o)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_o Xs2)) tptp.one_one_nat) (= (@ tptp.rotate1_o Xs2) Xs2))) (forall ((Xs2 tptp.list_nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_nat Xs2)) tptp.one_one_nat) (= (@ tptp.rotate1_nat Xs2) Xs2))) (forall ((Xs2 tptp.list_int)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_int Xs2)) tptp.one_one_nat) (= (@ tptp.rotate1_int Xs2) Xs2))) (forall ((Xs2 tptp.list_VEBT_VEBT)) (= (@ tptp.size_s6755466524823107622T_VEBT (@ tptp.rotate1_VEBT_VEBT Xs2)) (@ tptp.size_s6755466524823107622T_VEBT Xs2))) (forall ((Xs2 tptp.list_o)) (= (@ tptp.size_size_list_o (@ tptp.rotate1_o Xs2)) (@ tptp.size_size_list_o Xs2))) (forall ((Xs2 tptp.list_nat)) (= (@ tptp.size_size_list_nat (@ tptp.rotate1_nat Xs2)) (@ tptp.size_size_list_nat Xs2))) (forall ((Xs2 tptp.list_int)) (= (@ tptp.size_size_list_int (@ tptp.rotate1_int Xs2)) (@ tptp.size_size_list_int Xs2))) (forall ((X tptp.vEBT_VEBT) (Xs2 tptp.list_VEBT_VEBT) (N tptp.nat)) (= (@ (@ tptp.nth_VEBT_VEBT (@ (@ tptp.cons_VEBT_VEBT X) Xs2)) (@ tptp.suc N)) (@ (@ tptp.nth_VEBT_VEBT Xs2) N))) (forall ((X tptp.nat) (Xs2 tptp.list_nat) (N tptp.nat)) (= (@ (@ tptp.nth_nat (@ (@ tptp.cons_nat X) Xs2)) (@ tptp.suc N)) (@ (@ tptp.nth_nat Xs2) N))) (forall ((X tptp.vEBT_VEBT) (Xs2 tptp.list_VEBT_VEBT)) (= (@ (@ tptp.nth_VEBT_VEBT (@ (@ tptp.cons_VEBT_VEBT X) Xs2)) tptp.zero_zero_nat) X)) (forall ((X tptp.nat) (Xs2 tptp.list_nat)) (= (@ (@ tptp.nth_nat (@ (@ tptp.cons_nat X) Xs2)) tptp.zero_zero_nat) X)) (forall ((X tptp.code_integer) (Xs2 tptp.list_Code_integer) (Y tptp.code_integer) (Ys tptp.list_Code_integer)) (= (@ (@ tptp.zip_Co3543743374963494515nteger (@ (@ tptp.cons_Code_integer X) Xs2)) (@ (@ tptp.cons_Code_integer Y) Ys)) (@ (@ tptp.cons_P9044669534377732177nteger (@ (@ tptp.produc1086072967326762835nteger X) Y)) (@ (@ tptp.zip_Co3543743374963494515nteger Xs2) Ys)))) (forall ((X tptp.product_prod_nat_nat) (Xs2 tptp.list_P6011104703257516679at_nat) (Y tptp.product_prod_nat_nat) (Ys tptp.list_P6011104703257516679at_nat)) (= (@ (@ tptp.zip_Pr4664179122662387191at_nat (@ (@ tptp.cons_P6512896166579812791at_nat X) Xs2)) (@ (@ tptp.cons_P6512896166579812791at_nat Y) Ys)) (@ (@ tptp.cons_P8732206157123786781at_nat (@ (@ tptp.produc6161850002892822231at_nat X) Y)) (@ (@ tptp.zip_Pr4664179122662387191at_nat Xs2) Ys)))) (forall ((X tptp.set_Pr1261947904930325089at_nat) (Xs2 tptp.list_s1210847774152347623at_nat) (Y tptp.set_Pr1261947904930325089at_nat) (Ys tptp.list_s1210847774152347623at_nat)) (= (@ (@ tptp.zip_se5600341670672612855at_nat (@ (@ tptp.cons_s6881495754146722583at_nat X) Xs2)) (@ (@ tptp.cons_s6881495754146722583at_nat Y) Ys)) (@ (@ tptp.cons_P3940603068885512221at_nat (@ (@ tptp.produc2922128104949294807at_nat X) Y)) (@ (@ tptp.zip_se5600341670672612855at_nat Xs2) Ys)))) (forall ((X tptp.nat) (Xs2 tptp.list_nat) (Y tptp.nat) (Ys tptp.list_nat)) (= (@ (@ tptp.zip_nat_nat (@ (@ tptp.cons_nat X) Xs2)) (@ (@ tptp.cons_nat Y) Ys)) (@ (@ tptp.cons_P6512896166579812791at_nat (@ (@ tptp.product_Pair_nat_nat X) Y)) (@ (@ tptp.zip_nat_nat Xs2) Ys)))) (forall ((X tptp.int) (Xs2 tptp.list_int) (Y tptp.int) (Ys tptp.list_int)) (= (@ (@ tptp.zip_int_int (@ (@ tptp.cons_int X) Xs2)) (@ (@ tptp.cons_int Y) Ys)) (@ (@ tptp.cons_P3334398858971670639nt_int (@ (@ tptp.product_Pair_int_int X) Y)) (@ (@ tptp.zip_int_int Xs2) Ys)))) (forall ((N tptp.nat) (X tptp.nat) (Xs2 tptp.list_nat)) (= (@ (@ tptp.enumerate_nat N) (@ (@ tptp.cons_nat X) Xs2)) (@ (@ tptp.cons_P6512896166579812791at_nat (@ (@ tptp.product_Pair_nat_nat N) X)) (@ (@ tptp.enumerate_nat (@ tptp.suc N)) Xs2)))) (forall ((Xs2 tptp.list_Code_integer) (Ys tptp.list_Code_integer) (Xy tptp.produc8923325533196201883nteger) (Xys tptp.list_P5578671422887162913nteger)) (=> (= (@ (@ tptp.zip_Co3543743374963494515nteger Xs2) Ys) (@ (@ tptp.cons_P9044669534377732177nteger Xy) Xys)) (not (forall ((X3 tptp.code_integer) (Xs4 tptp.list_Code_integer)) (=> (= Xs2 (@ (@ tptp.cons_Code_integer X3) Xs4)) (forall ((Y3 tptp.code_integer) (Ys4 tptp.list_Code_integer)) (=> (= Ys (@ (@ 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tptp.set_Code_integer2 Ys)))) (forall ((X tptp.product_prod_nat_nat) (Y tptp.product_prod_nat_nat) (Xs2 tptp.list_P6011104703257516679at_nat) (Ys tptp.list_P6011104703257516679at_nat)) (=> (@ (@ tptp.member8206827879206165904at_nat (@ (@ tptp.produc6161850002892822231at_nat X) Y)) (@ tptp.set_Pr5518436109238095868at_nat (@ (@ tptp.zip_Pr4664179122662387191at_nat Xs2) Ys))) (@ (@ tptp.member8440522571783428010at_nat Y) (@ tptp.set_Pr5648618587558075414at_nat Ys)))) (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat) (Xs2 tptp.list_s1210847774152347623at_nat) (Ys tptp.list_s1210847774152347623at_nat)) (=> (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat X) Y)) (@ tptp.set_Pr3765526544606949372at_nat (@ (@ tptp.zip_se5600341670672612855at_nat Xs2) Ys))) (@ (@ tptp.member2643936169264416010at_nat Y) (@ tptp.set_se5049602875457034614at_nat Ys)))) (forall ((X tptp.nat) (Y tptp.nat) (Xs2 tptp.list_nat) (Ys 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(=> (@ (@ tptp.member7849222048561428706l_real (@ (@ tptp.produc4511245868158468465l_real X) Y)) (@ tptp.set_Pr5999470521830281550l_real (@ (@ tptp.zip_real_real Xs2) Ys))) (not (=> (@ (@ tptp.member_real X) (@ tptp.set_real2 Xs2)) (not (@ (@ tptp.member_real Y) (@ tptp.set_real2 Ys))))))) (forall ((X tptp.real) (Y tptp.int) (Xs2 tptp.list_real) (Ys tptp.list_int)) (=> (@ (@ tptp.member1627681773268152802al_int (@ (@ tptp.produc3179012173361985393al_int X) Y)) (@ tptp.set_Pr8219819362198175822al_int (@ (@ tptp.zip_real_int Xs2) Ys))) (not (=> (@ (@ tptp.member_real X) (@ tptp.set_real2 Xs2)) (not (@ (@ tptp.member_int Y) (@ tptp.set_int2 Ys))))))) (forall ((X tptp.int) (Y tptp.complex) (Xs2 tptp.list_int) (Ys tptp.list_complex)) (=> (@ (@ tptp.member8811922270175639012omplex (@ (@ tptp.produc7948753499206759283omplex X) Y)) (@ tptp.set_Pr3989287306472219216omplex (@ (@ tptp.zip_int_complex Xs2) Ys))) (not (=> (@ (@ tptp.member_int X) (@ tptp.set_int2 Xs2)) (not (@ (@ 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tptp.list_P6011104703257516679at_nat)) (= (@ (@ tptp.member8206827879206165904at_nat (@ (@ tptp.produc6161850002892822231at_nat A) B)) (@ tptp.set_Pr5518436109238095868at_nat (@ (@ tptp.zip_Pr4664179122662387191at_nat Xs2) Xs2))) (and (@ (@ tptp.member8440522571783428010at_nat A) (@ tptp.set_Pr5648618587558075414at_nat Xs2)) (= A B)))) (forall ((A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat) (Xs2 tptp.list_s1210847774152347623at_nat)) (= (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat A) B)) (@ tptp.set_Pr3765526544606949372at_nat (@ (@ tptp.zip_se5600341670672612855at_nat Xs2) Xs2))) (and (@ (@ tptp.member2643936169264416010at_nat A) (@ tptp.set_se5049602875457034614at_nat Xs2)) (= A B)))) (forall ((A tptp.nat) (B tptp.nat) (Xs2 tptp.list_nat)) (= (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat A) B)) (@ tptp.set_Pr5648618587558075414at_nat (@ (@ tptp.zip_nat_nat Xs2) Xs2))) (and (@ (@ 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Ys3)) (= (@ tptp.size_size_list_nat Ys3) N))))) (forall ((N tptp.nat) (Xs2 tptp.list_int)) (= (= (@ tptp.suc N) (@ tptp.size_size_list_int Xs2)) (exists ((Y4 tptp.int) (Ys3 tptp.list_int)) (and (= Xs2 (@ (@ tptp.cons_int Y4) Ys3)) (= (@ tptp.size_size_list_int Ys3) N))))) (forall ((Xs2 tptp.list_VEBT_VEBT) (N tptp.nat)) (= (= (@ tptp.size_s6755466524823107622T_VEBT Xs2) (@ tptp.suc N)) (exists ((Y4 tptp.vEBT_VEBT) (Ys3 tptp.list_VEBT_VEBT)) (and (= Xs2 (@ (@ tptp.cons_VEBT_VEBT Y4) Ys3)) (= (@ tptp.size_s6755466524823107622T_VEBT Ys3) N))))) (forall ((Xs2 tptp.list_o) (N tptp.nat)) (= (= (@ tptp.size_size_list_o Xs2) (@ tptp.suc N)) (exists ((Y4 Bool) (Ys3 tptp.list_o)) (and (= Xs2 (@ (@ tptp.cons_o Y4) Ys3)) (= (@ tptp.size_size_list_o Ys3) N))))) (forall ((Xs2 tptp.list_nat) (N tptp.nat)) (= (= (@ tptp.size_size_list_nat Xs2) (@ tptp.suc N)) (exists ((Y4 tptp.nat) (Ys3 tptp.list_nat)) (and (= Xs2 (@ (@ tptp.cons_nat Y4) Ys3)) (= (@ tptp.size_size_list_nat Ys3) N))))) (forall ((Xs2 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tptp.member_complex X) (@ tptp.set_complex2 Xs2)) (not (forall ((Y3 tptp.vEBT_VEBT)) (not (@ (@ tptp.member1978952105866562066T_VEBT (@ (@ tptp.produc2757191886755552429T_VEBT X) Y3)) (@ tptp.set_Pr5158653123227461798T_VEBT (@ (@ tptp.zip_co9157518722488180109T_VEBT Xs2) Ys))))))))) (forall ((Xs2 tptp.list_real) (Ys tptp.list_VEBT_VEBT) (X tptp.real)) (=> (= (@ tptp.size_size_list_real Xs2) (@ tptp.size_s6755466524823107622T_VEBT Ys)) (=> (@ (@ tptp.member_real X) (@ tptp.set_real2 Xs2)) (not (forall ((Y3 tptp.vEBT_VEBT)) (not (@ (@ tptp.member7262085504369356948T_VEBT (@ (@ tptp.produc6931449550656315951T_VEBT X) Y3)) (@ tptp.set_Pr8897343066327330088T_VEBT (@ (@ tptp.zip_real_VEBT_VEBT Xs2) Ys))))))))) (forall ((Xs2 tptp.list_complex) (Ys tptp.list_o) (X tptp.complex)) (=> (= (@ tptp.size_s3451745648224563538omplex Xs2) (@ tptp.size_size_list_o Ys)) (=> (@ (@ tptp.member_complex X) (@ tptp.set_complex2 Xs2)) (not (forall ((Y3 Bool)) (not (@ (@ tptp.member6487239523555734774plex_o (@ (@ tptp.produc2908979694703026321plex_o X) Y3)) (@ tptp.set_Pr6829704231520703882plex_o (@ (@ tptp.zip_complex_o Xs2) Ys))))))))) (forall ((Xs2 tptp.list_real) (Ys tptp.list_o) (X tptp.real)) (=> (= (@ tptp.size_size_list_real Xs2) (@ tptp.size_size_list_o Ys)) (=> (@ (@ tptp.member_real X) (@ tptp.set_real2 Xs2)) (not (forall ((Y3 Bool)) (not (@ (@ tptp.member772602641336174712real_o (@ (@ tptp.product_Pair_real_o X) Y3)) (@ tptp.set_Pr5196769464307566348real_o (@ (@ tptp.zip_real_o Xs2) Ys))))))))) (forall ((Xs2 tptp.list_complex) (Ys tptp.list_nat) (X tptp.complex)) (=> (= (@ tptp.size_s3451745648224563538omplex Xs2) (@ tptp.size_size_list_nat Ys)) (=> (@ (@ tptp.member_complex X) (@ tptp.set_complex2 Xs2)) (not (forall ((Y3 tptp.nat)) (not (@ (@ tptp.member4772924384108857480ex_nat (@ (@ tptp.produc1369629321580543767ex_nat X) Y3)) (@ tptp.set_Pr9173661457260213492ex_nat (@ (@ tptp.zip_complex_nat Xs2) Ys))))))))) (forall ((Xs2 tptp.list_real) (Ys tptp.list_nat) (X tptp.real)) (=> (= (@ tptp.size_size_list_real Xs2) (@ tptp.size_size_list_nat Ys)) (=> (@ (@ tptp.member_real X) (@ tptp.set_real2 Xs2)) (not (forall ((Y3 tptp.nat)) (not (@ (@ tptp.member5805532792777349510al_nat (@ (@ tptp.produc3181502643871035669al_nat X) Y3)) (@ tptp.set_Pr3174298344852596722al_nat (@ (@ tptp.zip_real_nat Xs2) Ys))))))))) (forall ((Xs2 tptp.list_complex) (Ys tptp.list_int) (X tptp.complex)) (=> (= (@ tptp.size_s3451745648224563538omplex Xs2) (@ tptp.size_size_list_int Ys)) (=> (@ (@ tptp.member_complex X) (@ tptp.set_complex2 Xs2)) (not (forall ((Y3 tptp.int)) (not (@ (@ tptp.member595073364599660772ex_int (@ (@ tptp.produc1367138851071493491ex_int X) Y3)) (@ tptp.set_Pr4995810437751016784ex_int (@ (@ tptp.zip_complex_int Xs2) Ys))))))))) (forall ((Xs2 tptp.list_real) (Ys tptp.list_int) (X tptp.real)) (=> (= (@ tptp.size_size_list_real Xs2) (@ tptp.size_size_list_int Ys)) (=> (@ (@ tptp.member_real X) (@ tptp.set_real2 Xs2)) (not (forall ((Y3 tptp.int)) (not (@ (@ tptp.member1627681773268152802al_int (@ (@ tptp.produc3179012173361985393al_int X) Y3)) (@ tptp.set_Pr8219819362198175822al_int (@ (@ tptp.zip_real_int Xs2) Ys))))))))) (forall ((Xs2 tptp.list_VEBT_VEBT) (Ys tptp.list_VEBT_VEBT) (X tptp.vEBT_VEBT)) (=> (= (@ tptp.size_s6755466524823107622T_VEBT Xs2) (@ tptp.size_s6755466524823107622T_VEBT Ys)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 Xs2)) (not (forall ((Y3 tptp.vEBT_VEBT)) (not (@ (@ tptp.member568628332442017744T_VEBT (@ (@ tptp.produc537772716801021591T_VEBT X) Y3)) (@ tptp.set_Pr9182192707038809660T_VEBT (@ (@ tptp.zip_VE537291747668921783T_VEBT Xs2) Ys))))))))) (forall ((Xs2 tptp.list_Code_integer) (Ys tptp.list_Code_integer) (Y tptp.code_integer)) (=> (= (@ tptp.size_s3445333598471063425nteger Xs2) (@ tptp.size_s3445333598471063425nteger Ys)) (=> (@ (@ tptp.member_Code_integer Y) (@ tptp.set_Code_integer2 Ys)) (not (forall ((X3 tptp.code_integer)) (not (@ (@ tptp.member157494554546826820nteger (@ (@ tptp.produc1086072967326762835nteger X3) Y)) (@ tptp.set_Pr920681315882439344nteger (@ (@ tptp.zip_Co3543743374963494515nteger Xs2) Ys))))))))) (forall ((Xs2 tptp.list_VEBT_VEBT) (Ys tptp.list_complex) (Y tptp.complex)) (=> (= (@ tptp.size_s6755466524823107622T_VEBT Xs2) (@ tptp.size_s3451745648224563538omplex Ys)) (=> (@ (@ tptp.member_complex Y) (@ tptp.set_complex2 Ys)) (not (forall ((X3 tptp.vEBT_VEBT)) (not (@ (@ tptp.member3207599676835851048omplex (@ (@ tptp.produc5617778602380981643omplex X3) Y)) (@ tptp.set_Pr6387300694196750780omplex (@ (@ tptp.zip_VE2794733401258833515omplex Xs2) Ys))))))))) (forall ((Xs2 tptp.list_VEBT_VEBT) (Ys tptp.list_real) (Y tptp.real)) (=> (= (@ tptp.size_s6755466524823107622T_VEBT Xs2) (@ tptp.size_size_list_real Ys)) (=> (@ (@ tptp.member_real Y) (@ tptp.set_real2 Ys)) (not (forall ((X3 tptp.vEBT_VEBT)) (not (@ (@ tptp.member8675245146396747942T_real (@ (@ tptp.produc8117437818029410057T_real X3) Y)) (@ tptp.set_Pr1087130671499945274T_real (@ (@ tptp.zip_VEBT_VEBT_real Xs2) Ys))))))))) (forall ((Xs2 tptp.list_VEBT_VEBT) (Ys tptp.list_VEBT_VEBT) (Y tptp.vEBT_VEBT)) (=> (= (@ tptp.size_s6755466524823107622T_VEBT Xs2) (@ tptp.size_s6755466524823107622T_VEBT Ys)) (=> (@ (@ tptp.member_VEBT_VEBT Y) (@ tptp.set_VEBT_VEBT2 Ys)) (not (forall ((X3 tptp.vEBT_VEBT)) (not (@ (@ tptp.member568628332442017744T_VEBT (@ (@ tptp.produc537772716801021591T_VEBT X3) Y)) (@ tptp.set_Pr9182192707038809660T_VEBT (@ (@ tptp.zip_VE537291747668921783T_VEBT Xs2) Ys))))))))) (forall ((Xs2 tptp.list_VEBT_VEBT) (Ys tptp.list_o) (Y Bool)) (=> (= (@ tptp.size_s6755466524823107622T_VEBT Xs2) (@ tptp.size_size_list_o Ys)) (=> (@ (@ tptp.member_o Y) (@ tptp.set_o2 Ys)) (not (forall ((X3 tptp.vEBT_VEBT)) (not (@ (@ tptp.member3307348790968139188VEBT_o (@ (@ tptp.produc8721562602347293563VEBT_o X3) Y)) (@ tptp.set_Pr7708085864119495200VEBT_o (@ (@ tptp.zip_VEBT_VEBT_o Xs2) Ys))))))))) (forall ((Xs2 tptp.list_VEBT_VEBT) (Ys tptp.list_nat) (Y tptp.nat)) (=> (= (@ tptp.size_s6755466524823107622T_VEBT Xs2) (@ tptp.size_size_list_nat Ys)) (=> (@ (@ tptp.member_nat Y) (@ tptp.set_nat2 Ys)) (not (forall ((X3 tptp.vEBT_VEBT)) (not (@ (@ tptp.member373505688050248522BT_nat (@ (@ tptp.produc738532404422230701BT_nat X3) Y)) (@ tptp.set_Pr7031586669278753246BT_nat (@ (@ tptp.zip_VEBT_VEBT_nat Xs2) Ys))))))))) (forall ((Xs2 tptp.list_VEBT_VEBT) (Ys tptp.list_int) (Y tptp.int)) (=> (= (@ tptp.size_s6755466524823107622T_VEBT Xs2) (@ tptp.size_size_list_int Ys)) (=> (@ (@ tptp.member_int Y) (@ tptp.set_int2 Ys)) (not (forall ((X3 tptp.vEBT_VEBT)) (not (@ (@ tptp.member5419026705395827622BT_int (@ (@ tptp.produc736041933913180425BT_int X3) Y)) (@ tptp.set_Pr2853735649769556538BT_int (@ (@ tptp.zip_VEBT_VEBT_int Xs2) Ys))))))))) (forall ((Xs2 tptp.list_o) (Ys tptp.list_complex) (Y tptp.complex)) (=> (= (@ tptp.size_size_list_o Xs2) (@ tptp.size_s3451745648224563538omplex Ys)) (=> (@ (@ tptp.member_complex Y) (@ tptp.set_complex2 Ys)) (not (forall ((X3 Bool)) (not (@ (@ tptp.member1046615901120239500omplex (@ (@ tptp.produc414345526774272751omplex X3) Y)) (@ tptp.set_Pr1389080609085208608omplex (@ (@ tptp.zip_o_complex Xs2) Ys))))))))) (forall ((Xs2 tptp.list_o) (Ys tptp.list_real) (Y tptp.real)) (=> (= (@ tptp.size_size_list_o Xs2) (@ tptp.size_size_list_real Ys)) (=> (@ (@ tptp.member_real Y) (@ tptp.set_real2 Ys)) (not (forall ((X3 Bool)) (not (@ (@ tptp.member7400031367953476362o_real (@ (@ tptp.product_Pair_o_real X3) Y)) (@ tptp.set_Pr2600826154070092190o_real (@ (@ tptp.zip_o_real Xs2) Ys))))))))) (forall ((Xs2 tptp.list_o) (Ys tptp.list_VEBT_VEBT) (Y tptp.vEBT_VEBT)) (=> (= (@ tptp.size_size_list_o Xs2) (@ tptp.size_s6755466524823107622T_VEBT Ys)) (=> (@ (@ tptp.member_VEBT_VEBT Y) (@ tptp.set_VEBT_VEBT2 Ys)) (not (forall ((X3 Bool)) (not (@ (@ tptp.member5477980866518848620T_VEBT (@ (@ tptp.produc2982872950893828659T_VEBT X3) Y)) (@ tptp.set_Pr655345902815428824T_VEBT (@ (@ tptp.zip_o_VEBT_VEBT Xs2) Ys))))))))) (forall ((N tptp.nat) (Xs2 tptp.list_VEBT_VEBT)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (exists ((X4 tptp.vEBT_VEBT) (Ys3 tptp.list_VEBT_VEBT)) (and (= Xs2 (@ (@ tptp.cons_VEBT_VEBT X4) Ys3)) (@ (@ tptp.ord_less_eq_nat N) (@ tptp.size_s6755466524823107622T_VEBT Ys3)))))) (forall ((N tptp.nat) (Xs2 tptp.list_o)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) (@ tptp.size_size_list_o Xs2)) (exists ((X4 Bool) (Ys3 tptp.list_o)) (and (= Xs2 (@ (@ tptp.cons_o X4) Ys3)) (@ (@ tptp.ord_less_eq_nat N) (@ tptp.size_size_list_o Ys3)))))) (forall ((N tptp.nat) (Xs2 tptp.list_nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) (@ tptp.size_size_list_nat Xs2)) (exists ((X4 tptp.nat) (Ys3 tptp.list_nat)) (and (= Xs2 (@ (@ tptp.cons_nat X4) Ys3)) (@ (@ tptp.ord_less_eq_nat N) (@ tptp.size_size_list_nat Ys3)))))) (forall ((N tptp.nat) (Xs2 tptp.list_int)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) (@ tptp.size_size_list_int Xs2)) (exists ((X4 tptp.int) (Ys3 tptp.list_int)) (and (= Xs2 (@ (@ tptp.cons_int X4) Ys3)) (@ (@ tptp.ord_less_eq_nat N) (@ tptp.size_size_list_int Ys3)))))) (forall ((A Bool) (B Bool) (X tptp.nat)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A) B))) (= (@ (@ tptp.vEBT_VEBT_insert _let_1) X) (@ (@ tptp.vEBT_vebt_insert _let_1) X)))) (forall ((Info2 tptp.option4927543243414619207at_nat) (Ts2 tptp.list_VEBT_VEBT) (S2 tptp.vEBT_VEBT) (X tptp.nat)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info2) (@ tptp.suc tptp.zero_zero_nat)) Ts2) S2))) (= (@ (@ tptp.vEBT_vebt_insert _let_1) X) _let_1))) (forall ((X tptp.nat) (A Bool) (B Bool)) (let ((_let_1 (@ tptp.vEBT_Leaf A))) (let ((_let_2 (@ _let_1 B))) (let ((_let_3 (@ (@ tptp.vEBT_vebt_insert _let_2) X))) (let ((_let_4 (= X tptp.one_one_nat))) (let ((_let_5 (= X tptp.zero_zero_nat))) (and (=> _let_5 (= _let_3 (@ (@ tptp.vEBT_Leaf true) B))) (=> (not _let_5) (and (=> _let_4 (= _let_3 (@ _let_1 true))) (=> (not _let_4) (= _let_3 _let_2))))))))))) (forall ((X21 tptp.vEBT_VEBT) (X22 tptp.list_VEBT_VEBT)) (= (@ tptp.size_s6755466524823107622T_VEBT (@ (@ tptp.cons_VEBT_VEBT X21) X22)) (@ (@ tptp.plus_plus_nat (@ tptp.size_s6755466524823107622T_VEBT X22)) (@ tptp.suc tptp.zero_zero_nat)))) (forall ((X21 Bool) (X22 tptp.list_o)) (= (@ tptp.size_size_list_o (@ (@ tptp.cons_o X21) X22)) (@ (@ tptp.plus_plus_nat (@ tptp.size_size_list_o X22)) (@ tptp.suc tptp.zero_zero_nat)))) (forall ((X21 tptp.nat) (X22 tptp.list_nat)) (= (@ tptp.size_size_list_nat (@ (@ tptp.cons_nat X21) X22)) (@ (@ tptp.plus_plus_nat (@ tptp.size_size_list_nat X22)) (@ tptp.suc tptp.zero_zero_nat)))) (forall ((X21 tptp.int) (X22 tptp.list_int)) (= (@ tptp.size_size_list_int (@ (@ tptp.cons_int X21) X22)) (@ (@ tptp.plus_plus_nat (@ tptp.size_size_list_int X22)) (@ tptp.suc tptp.zero_zero_nat)))) (forall ((N tptp.nat) (X tptp.vEBT_VEBT) (Xs2 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.nth_VEBT_VEBT (@ (@ tptp.cons_VEBT_VEBT X) Xs2)) N))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 X)) (=> (not _let_2) (= _let_1 (@ (@ tptp.nth_VEBT_VEBT Xs2) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)))))))) (forall ((N tptp.nat) (X tptp.nat) (Xs2 tptp.list_nat)) (let ((_let_1 (@ (@ tptp.nth_nat (@ (@ tptp.cons_nat X) Xs2)) N))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 X)) (=> (not _let_2) (= _let_1 (@ (@ tptp.nth_nat Xs2) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)))))))) (forall ((X tptp.complex) (Xs2 tptp.list_complex) (N tptp.nat)) (=> (not (@ (@ tptp.member_complex X) (@ tptp.set_complex2 Xs2))) (=> (@ (@ tptp.ord_less_eq_nat N) (@ tptp.size_s3451745648224563538omplex Xs2)) (= (= (@ (@ tptp.nth_complex (@ (@ tptp.cons_complex X) Xs2)) N) X) (= N tptp.zero_zero_nat))))) (forall ((X tptp.real) (Xs2 tptp.list_real) (N tptp.nat)) (=> (not (@ (@ tptp.member_real X) (@ tptp.set_real2 Xs2))) (=> (@ (@ tptp.ord_less_eq_nat N) (@ tptp.size_size_list_real Xs2)) (= (= (@ (@ tptp.nth_real (@ (@ tptp.cons_real X) Xs2)) N) X) (= N tptp.zero_zero_nat))))) (forall ((X tptp.set_nat) (Xs2 tptp.list_set_nat) (N tptp.nat)) (=> (not (@ (@ tptp.member_set_nat X) (@ tptp.set_set_nat2 Xs2))) (=> (@ (@ tptp.ord_less_eq_nat N) (@ tptp.size_s3254054031482475050et_nat Xs2)) (= (= (@ (@ tptp.nth_set_nat (@ (@ tptp.cons_set_nat X) Xs2)) N) X) (= N tptp.zero_zero_nat))))) (forall ((X tptp.vEBT_VEBT) (Xs2 tptp.list_VEBT_VEBT) (N tptp.nat)) (=> (not (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 Xs2))) (=> (@ (@ tptp.ord_less_eq_nat N) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (= (= (@ (@ tptp.nth_VEBT_VEBT (@ (@ tptp.cons_VEBT_VEBT X) Xs2)) N) X) (= N tptp.zero_zero_nat))))) (forall ((X Bool) (Xs2 tptp.list_o) (N tptp.nat)) (=> (not (@ (@ tptp.member_o X) (@ tptp.set_o2 Xs2))) (=> (@ (@ tptp.ord_less_eq_nat N) (@ tptp.size_size_list_o Xs2)) (= (= (@ (@ tptp.nth_o (@ (@ tptp.cons_o X) Xs2)) N) X) (= N tptp.zero_zero_nat))))) (forall ((X tptp.nat) (Xs2 tptp.list_nat) (N tptp.nat)) (=> (not (@ (@ tptp.member_nat X) (@ tptp.set_nat2 Xs2))) (=> (@ (@ tptp.ord_less_eq_nat N) (@ tptp.size_size_list_nat Xs2)) (= (= (@ (@ tptp.nth_nat (@ (@ tptp.cons_nat X) Xs2)) N) X) (= N tptp.zero_zero_nat))))) (forall ((X tptp.int) (Xs2 tptp.list_int) (N tptp.nat)) (=> (not (@ (@ tptp.member_int X) (@ tptp.set_int2 Xs2))) (=> (@ (@ tptp.ord_less_eq_nat N) (@ tptp.size_size_list_int Xs2)) (= (= (@ (@ tptp.nth_int (@ (@ tptp.cons_int X) Xs2)) N) X) (= N tptp.zero_zero_nat))))) (forall ((X tptp.vEBT_VEBT) (Y tptp.vEBT_VEBT) (Xs2 tptp.list_VEBT_VEBT) (N tptp.nat)) (=> (not (= X Y)) (= (= (@ (@ tptp.nth_VEBT_VEBT (@ (@ tptp.cons_VEBT_VEBT X) Xs2)) N) Y) (and (= (@ (@ tptp.nth_VEBT_VEBT Xs2) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) Y) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))) (forall ((X tptp.nat) (Y tptp.nat) (Xs2 tptp.list_nat) (N tptp.nat)) (=> (not (= X Y)) (= (= (@ (@ tptp.nth_nat (@ (@ tptp.cons_nat X) Xs2)) N) Y) (and (= (@ (@ tptp.nth_nat Xs2) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) Y) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))) (forall ((X tptp.vEBT_VEBT) (Xs2 tptp.list_VEBT_VEBT)) (= (@ tptp.size_s6755466524823107622T_VEBT (@ (@ tptp.cons_VEBT_VEBT X) Xs2)) (@ tptp.suc (@ tptp.size_s6755466524823107622T_VEBT Xs2)))) (forall ((X Bool) (Xs2 tptp.list_o)) (= (@ tptp.size_size_list_o (@ (@ tptp.cons_o X) Xs2)) (@ tptp.suc (@ tptp.size_size_list_o Xs2)))) (forall ((X tptp.nat) (Xs2 tptp.list_nat)) (= (@ tptp.size_size_list_nat (@ (@ tptp.cons_nat X) Xs2)) (@ tptp.suc (@ tptp.size_size_list_nat Xs2)))) (forall ((X tptp.int) (Xs2 tptp.list_int)) (= (@ tptp.size_size_list_int (@ (@ tptp.cons_int X) Xs2)) (@ tptp.suc (@ tptp.size_size_list_int Xs2)))) (= (@ tptp.neg_nu5831290666863070958nteger tptp.zero_z3403309356797280102nteger) tptp.one_one_Code_integer) (= (@ tptp.neg_nu8557863876264182079omplex tptp.zero_zero_complex) tptp.one_one_complex) (= (@ tptp.neg_nu8295874005876285629c_real tptp.zero_zero_real) tptp.one_one_real) (= (@ tptp.neg_nu5219082963157363817nc_rat tptp.zero_zero_rat) tptp.one_one_rat) (= (@ tptp.neg_nu5851722552734809277nc_int tptp.zero_zero_int) tptp.one_one_int) (forall ((S3 tptp.set_nat) (N tptp.nat)) (let ((_let_1 (@ tptp.infini8530281810654367211te_nat S3))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.infini8530281810654367211te_nat (@ (@ tptp.minus_minus_set_nat S3) (@ (@ tptp.insert_nat (@ _let_1 tptp.zero_zero_nat)) tptp.bot_bot_set_nat))) N)))) _let_325 _let_324 _let_323 _let_322 _let_321 (forall ((A4 tptp.set_int)) (= (= (@ tptp.semiri4256215615220890538in_int A4) tptp.zero_zero_int) (and (@ (@ tptp.ord_less_eq_set_int A4) (@ (@ tptp.insert_int tptp.zero_zero_int) tptp.bot_bot_set_int)) (@ tptp.finite_finite_int A4)))) (forall ((A4 tptp.set_nat)) (= (= (@ tptp.semiri4258706085729940814in_nat A4) tptp.zero_zero_nat) (and (@ (@ tptp.ord_less_eq_set_nat A4) (@ (@ tptp.insert_nat tptp.zero_zero_nat) tptp.bot_bot_set_nat)) (@ tptp.finite_finite_nat A4)))) (forall ((B tptp.code_integer) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger B))) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) B) (=> (@ (@ tptp.ord_le6747313008572928689nteger B) tptp.one_one_Code_integer) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ _let_1 M2)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat N) M2)))))) (forall ((B tptp.real) (M2 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 M2)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat N) M2)))))) (forall ((B tptp.rat) (M2 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 M2)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat N) M2)))))) (forall ((B tptp.nat) (M2 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 M2)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat N) M2)))))) (forall ((B tptp.int) (M2 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 M2)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat N) M2)))))) (forall ((N tptp.nat) (Y tptp.set_real) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_real Y)) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_real (@ (@ tptp.insert_real X) Y))) N)))) (forall ((N tptp.nat) (Y tptp.set_nat) (X tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat Y)) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat (@ (@ tptp.insert_nat X) Y))) N)))) (forall ((N tptp.nat) (Y tptp.set_complex) (X tptp.complex)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_complex Y)) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_complex (@ (@ tptp.insert_complex X) Y))) N)))) (forall ((N tptp.nat) (Y tptp.set_int) (X tptp.int)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_int Y)) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_int (@ (@ tptp.insert_int X) Y))) N)))) (forall ((N tptp.nat) (Y tptp.set_list_nat) (X tptp.list_nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_list_nat Y)) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_list_nat (@ (@ tptp.insert_list_nat X) Y))) N)))) (forall ((N tptp.nat) (Y tptp.set_set_nat) (X tptp.set_nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_set_nat Y)) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_set_nat (@ (@ tptp.insert_set_nat X) Y))) N)))) (forall ((X tptp.complex) (Xs2 tptp.list_complex)) (=> (not (@ (@ tptp.member_complex X) (@ tptp.set_complex2 Xs2))) (= (@ (@ tptp.count_list_complex Xs2) X) tptp.zero_zero_nat))) (forall ((X tptp.real) (Xs2 tptp.list_real)) (=> (not (@ (@ tptp.member_real X) (@ tptp.set_real2 Xs2))) (= (@ (@ tptp.count_list_real Xs2) X) tptp.zero_zero_nat))) (forall ((X tptp.set_nat) (Xs2 tptp.list_set_nat)) (=> (not (@ (@ tptp.member_set_nat X) (@ tptp.set_set_nat2 Xs2))) (= (@ (@ tptp.count_list_set_nat Xs2) X) tptp.zero_zero_nat))) (forall ((X tptp.int) (Xs2 tptp.list_int)) (=> (not (@ (@ tptp.member_int X) (@ tptp.set_int2 Xs2))) (= (@ (@ tptp.count_list_int Xs2) X) tptp.zero_zero_nat))) (forall ((X tptp.vEBT_VEBT) (Xs2 tptp.list_VEBT_VEBT)) (=> (not (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 Xs2))) (= (@ (@ tptp.count_list_VEBT_VEBT Xs2) X) tptp.zero_zero_nat))) (forall ((X tptp.nat) (Xs2 tptp.list_nat)) (=> (not (@ (@ tptp.member_nat X) (@ tptp.set_nat2 Xs2))) (= (@ (@ tptp.count_list_nat Xs2) X) tptp.zero_zero_nat))) (forall ((M2 tptp.code_integer) (Ms tptp.list_Code_integer) (N tptp.code_integer) (Ns tptp.list_Code_integer) (R3 tptp.set_Pr4811707699266497531nteger)) (let ((_let_1 (@ tptp.lenlex_Code_integer R3))) (let ((_let_2 (@ tptp.size_s3445333598471063425nteger Ns))) (let ((_let_3 (@ tptp.size_s3445333598471063425nteger Ms))) (= (@ (@ tptp.member749217712838834276nteger (@ (@ tptp.produc750622340256944499nteger (@ (@ tptp.cons_Code_integer M2) Ms)) (@ (@ tptp.cons_Code_integer N) Ns))) _let_1) (or (@ (@ tptp.ord_less_nat _let_3) _let_2) (and (= _let_3 _let_2) (@ (@ tptp.member157494554546826820nteger (@ (@ tptp.produc1086072967326762835nteger M2) N)) R3)) (and (= M2 N) (@ (@ tptp.member749217712838834276nteger (@ (@ tptp.produc750622340256944499nteger Ms) Ns)) _let_1)))))))) (forall ((M2 tptp.product_prod_nat_nat) (Ms tptp.list_P6011104703257516679at_nat) (N tptp.product_prod_nat_nat) (Ns tptp.list_P6011104703257516679at_nat) (R3 tptp.set_Pr8693737435421807431at_nat)) (let ((_let_1 (@ tptp.lenlex325483962726685836at_nat R3))) (let ((_let_2 (@ tptp.size_s5460976970255530739at_nat Ns))) (let ((_let_3 (@ tptp.size_s5460976970255530739at_nat Ms))) (= (@ (@ tptp.member6693912407220327184at_nat (@ (@ tptp.produc5943733680697469783at_nat (@ (@ tptp.cons_P6512896166579812791at_nat M2) Ms)) (@ (@ tptp.cons_P6512896166579812791at_nat N) Ns))) _let_1) (or (@ (@ tptp.ord_less_nat _let_3) _let_2) (and (= _let_3 _let_2) (@ (@ tptp.member8206827879206165904at_nat (@ (@ tptp.produc6161850002892822231at_nat M2) N)) R3)) (and (= M2 N) (@ (@ tptp.member6693912407220327184at_nat (@ (@ tptp.produc5943733680697469783at_nat Ms) Ns)) _let_1)))))))) (forall ((M2 tptp.set_Pr1261947904930325089at_nat) (Ms tptp.list_s1210847774152347623at_nat) (N tptp.set_Pr1261947904930325089at_nat) (Ns tptp.list_s1210847774152347623at_nat) (R3 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.lenlex1357538814655152620at_nat R3))) (let ((_let_2 (@ tptp.size_s8736152011456118867at_nat Ns))) (let ((_let_3 (@ tptp.size_s8736152011456118867at_nat Ms))) (= (@ (@ tptp.member4080735728053443344at_nat (@ (@ tptp.produc7536900900485677911at_nat (@ (@ tptp.cons_s6881495754146722583at_nat M2) Ms)) (@ (@ tptp.cons_s6881495754146722583at_nat N) Ns))) _let_1) (or (@ (@ tptp.ord_less_nat _let_3) _let_2) (and (= _let_3 _let_2) (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat M2) N)) R3)) (and (= M2 N) (@ (@ tptp.member4080735728053443344at_nat (@ (@ tptp.produc7536900900485677911at_nat Ms) Ns)) _let_1)))))))) (forall ((M2 tptp.vEBT_VEBT) (Ms tptp.list_VEBT_VEBT) (N tptp.vEBT_VEBT) (Ns tptp.list_VEBT_VEBT) (R3 tptp.set_Pr6192946355708809607T_VEBT)) (let ((_let_1 (@ tptp.lenlex_VEBT_VEBT R3))) (let ((_let_2 (@ tptp.size_s6755466524823107622T_VEBT Ns))) (let ((_let_3 (@ tptp.size_s6755466524823107622T_VEBT Ms))) (= (@ (@ tptp.member4439316823752958928T_VEBT (@ (@ tptp.produc3897820843166775703T_VEBT (@ (@ tptp.cons_VEBT_VEBT M2) Ms)) (@ (@ tptp.cons_VEBT_VEBT N) Ns))) _let_1) (or (@ (@ tptp.ord_less_nat _let_3) _let_2) (and (= _let_3 _let_2) (@ (@ tptp.member568628332442017744T_VEBT (@ (@ tptp.produc537772716801021591T_VEBT M2) N)) R3)) (and (= M2 N) (@ (@ tptp.member4439316823752958928T_VEBT (@ (@ tptp.produc3897820843166775703T_VEBT Ms) Ns)) _let_1)))))))) (forall ((M2 Bool) (Ms tptp.list_o) (N Bool) (Ns tptp.list_o) (R3 tptp.set_Product_prod_o_o)) (let ((_let_1 (@ tptp.lenlex_o R3))) (let ((_let_2 (@ tptp.size_size_list_o Ns))) (let ((_let_3 (@ tptp.size_size_list_o Ms))) (= (@ (@ tptp.member4159035015898711888list_o (@ (@ tptp.produc8435520187683070743list_o (@ (@ tptp.cons_o M2) Ms)) (@ (@ tptp.cons_o N) Ns))) _let_1) (or (@ (@ tptp.ord_less_nat _let_3) _let_2) (and (= _let_3 _let_2) (@ (@ tptp.member7466972457876170832od_o_o (@ (@ tptp.product_Pair_o_o M2) N)) R3)) (and (= M2 N) (@ (@ tptp.member4159035015898711888list_o (@ (@ tptp.produc8435520187683070743list_o Ms) Ns)) _let_1)))))))) (forall ((M2 tptp.nat) (Ms tptp.list_nat) (N tptp.nat) (Ns tptp.list_nat) (R3 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.lenlex_nat R3))) (let ((_let_2 (@ tptp.size_size_list_nat Ns))) (let ((_let_3 (@ tptp.size_size_list_nat Ms))) (= (@ (@ tptp.member7340969449405702474st_nat (@ (@ tptp.produc2694037385005941721st_nat (@ (@ tptp.cons_nat M2) Ms)) (@ (@ tptp.cons_nat N) Ns))) _let_1) (or (@ (@ tptp.ord_less_nat _let_3) _let_2) (and (= _let_3 _let_2) (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat M2) N)) R3)) (and (= M2 N) (@ (@ tptp.member7340969449405702474st_nat (@ (@ tptp.produc2694037385005941721st_nat Ms) Ns)) _let_1)))))))) (forall ((M2 tptp.int) (Ms tptp.list_int) (N tptp.int) (Ns tptp.list_int) (R3 tptp.set_Pr958786334691620121nt_int)) (let ((_let_1 (@ tptp.lenlex_int R3))) (let ((_let_2 (@ tptp.size_size_list_int Ns))) (let ((_let_3 (@ tptp.size_size_list_int Ms))) (= (@ (@ tptp.member6698963635872716290st_int (@ (@ tptp.produc364263696895485585st_int (@ (@ tptp.cons_int M2) Ms)) (@ (@ tptp.cons_int N) Ns))) _let_1) (or (@ (@ tptp.ord_less_nat _let_3) _let_2) (and (= _let_3 _let_2) (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int M2) N)) R3)) (and (= M2 N) (@ (@ tptp.member6698963635872716290st_int (@ (@ tptp.produc364263696895485585st_int Ms) Ns)) _let_1)))))))) (forall ((X tptp.nat) (Y tptp.nat) (Z3 tptp.nat)) (= (= (@ (@ tptp.power_power_nat X) Y) Z3) (= (@ (@ tptp.vEBT_VEBT_power (@ tptp.some_nat X)) (@ tptp.some_nat Y)) (@ tptp.some_nat Z3)))) _let_320 (forall ((X tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (= (@ (@ tptp.power_power_nat X) M2) _let_1) (or (= M2 tptp.zero_zero_nat) (= X _let_1))))) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (@ (@ tptp.power_power_nat _let_1) N) _let_1))) (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))))) (= (@ tptp.neg_nu7757733837767384882nteger tptp.one_one_Code_integer) tptp.one_one_Code_integer) (= (@ tptp.neg_nu6511756317524482435omplex tptp.one_one_complex) tptp.one_one_complex) (= (@ tptp.neg_nu6075765906172075777c_real tptp.one_one_real) tptp.one_one_real) (= (@ tptp.neg_nu3811975205180677377ec_int tptp.one_one_int) tptp.one_one_int) (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_rat tptp.zero_zero_rat) (@ tptp.suc N)) tptp.zero_zero_rat)) (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_nat tptp.zero_zero_nat) (@ tptp.suc N)) tptp.zero_zero_nat)) (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_real tptp.zero_zero_real) (@ tptp.suc N)) tptp.zero_zero_real)) (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_int tptp.zero_zero_int) (@ tptp.suc N)) tptp.zero_zero_int)) (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_complex tptp.zero_zero_complex) (@ tptp.suc N)) tptp.zero_zero_complex)) (forall ((A tptp.nat)) (= (@ (@ tptp.power_power_nat A) (@ tptp.suc tptp.zero_zero_nat)) A)) (forall ((A tptp.real)) (= (@ (@ tptp.power_power_real A) (@ tptp.suc tptp.zero_zero_nat)) A)) (forall ((A tptp.int)) (= (@ (@ tptp.power_power_int A) (@ tptp.suc tptp.zero_zero_nat)) A)) (forall ((A tptp.complex)) (= (@ (@ tptp.power_power_complex A) (@ tptp.suc tptp.zero_zero_nat)) A)) (= (@ tptp.finite_card_complex tptp.bot_bot_set_complex) tptp.zero_zero_nat) (= (@ tptp.finite_card_list_nat tptp.bot_bot_set_list_nat) tptp.zero_zero_nat) (= (@ tptp.finite_card_set_nat tptp.bot_bot_set_set_nat) tptp.zero_zero_nat) (= (@ tptp.finite_card_nat tptp.bot_bot_set_nat) tptp.zero_zero_nat) (= (@ tptp.finite_card_int tptp.bot_bot_set_int) tptp.zero_zero_nat) (= (@ tptp.finite_card_real tptp.bot_bot_set_real) tptp.zero_zero_nat) (forall ((A4 tptp.set_list_nat)) (=> (not (@ tptp.finite8100373058378681591st_nat A4)) (= (@ tptp.finite_card_list_nat A4) tptp.zero_zero_nat))) (forall ((A4 tptp.set_set_nat)) (=> (not (@ tptp.finite1152437895449049373et_nat A4)) (= (@ tptp.finite_card_set_nat A4) tptp.zero_zero_nat))) (forall ((A4 tptp.set_nat)) (=> (not (@ tptp.finite_finite_nat A4)) (= (@ tptp.finite_card_nat A4) tptp.zero_zero_nat))) (forall ((A4 tptp.set_int)) (=> (not (@ tptp.finite_finite_int A4)) (= (@ tptp.finite_card_int A4) tptp.zero_zero_nat))) (forall ((A4 tptp.set_complex)) (=> (not (@ tptp.finite3207457112153483333omplex A4)) (= (@ tptp.finite_card_complex A4) tptp.zero_zero_nat))) (= (@ tptp.semiri4258706085729940814in_nat tptp.bot_bot_set_nat) tptp.zero_zero_nat) (= (@ tptp.semiri4256215615220890538in_int tptp.bot_bot_set_int) tptp.zero_zero_int) (forall ((A tptp.rat) (N tptp.nat)) (= (= (@ (@ tptp.power_power_rat A) N) tptp.zero_zero_rat) (and (= A tptp.zero_zero_rat) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)))) (forall ((A tptp.nat) (N tptp.nat)) (= (= (@ (@ tptp.power_power_nat A) N) tptp.zero_zero_nat) (and (= A tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)))) (forall ((A tptp.real) (N tptp.nat)) (= (= (@ (@ tptp.power_power_real A) N) tptp.zero_zero_real) (and (= A tptp.zero_zero_real) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)))) (forall ((A tptp.int) (N tptp.nat)) (= (= (@ (@ tptp.power_power_int A) N) tptp.zero_zero_int) (and (= A tptp.zero_zero_int) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)))) (forall ((A tptp.complex) (N tptp.nat)) (= (= (@ (@ tptp.power_power_complex A) N) tptp.zero_zero_complex) (and (= A tptp.zero_zero_complex) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)))) (forall ((A4 tptp.set_list_nat)) (=> (@ tptp.finite8100373058378681591st_nat A4) (= (= (@ tptp.finite_card_list_nat A4) tptp.zero_zero_nat) (= A4 tptp.bot_bot_set_list_nat)))) (forall ((A4 tptp.set_set_nat)) (=> (@ tptp.finite1152437895449049373et_nat A4) (= (= (@ tptp.finite_card_set_nat A4) tptp.zero_zero_nat) (= A4 tptp.bot_bot_set_set_nat)))) (forall ((A4 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex A4) (= (= (@ tptp.finite_card_complex A4) tptp.zero_zero_nat) (= A4 tptp.bot_bot_set_complex)))) (forall ((A4 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A4) (= (= (@ tptp.finite_card_nat A4) tptp.zero_zero_nat) (= A4 tptp.bot_bot_set_nat)))) (forall ((A4 tptp.set_int)) (=> (@ tptp.finite_finite_int A4) (= (= (@ tptp.finite_card_int A4) tptp.zero_zero_nat) (= A4 tptp.bot_bot_set_int)))) (forall ((A4 tptp.set_real)) (=> (@ tptp.finite_finite_real A4) (= (= (@ tptp.finite_card_real A4) tptp.zero_zero_nat) (= A4 tptp.bot_bot_set_real)))) (forall ((A4 tptp.set_real) (X tptp.real)) (=> (@ tptp.finite_finite_real A4) (=> (not (@ (@ tptp.member_real X) A4)) (= (@ tptp.finite_card_real (@ (@ tptp.insert_real X) A4)) (@ tptp.suc (@ tptp.finite_card_real A4)))))) (forall ((A4 tptp.set_list_nat) (X tptp.list_nat)) (=> (@ tptp.finite8100373058378681591st_nat A4) (=> (not (@ (@ tptp.member_list_nat X) A4)) (= (@ tptp.finite_card_list_nat (@ (@ tptp.insert_list_nat X) A4)) (@ tptp.suc (@ tptp.finite_card_list_nat A4)))))) (forall ((A4 tptp.set_set_nat) (X tptp.set_nat)) (=> (@ tptp.finite1152437895449049373et_nat A4) (=> (not (@ (@ tptp.member_set_nat X) A4)) (= (@ tptp.finite_card_set_nat (@ (@ tptp.insert_set_nat X) A4)) (@ tptp.suc (@ tptp.finite_card_set_nat A4)))))) (forall ((A4 tptp.set_nat) (X tptp.nat)) (=> (@ tptp.finite_finite_nat A4) (=> (not (@ (@ tptp.member_nat X) A4)) (= (@ tptp.finite_card_nat (@ (@ tptp.insert_nat X) A4)) (@ tptp.suc (@ tptp.finite_card_nat A4)))))) (forall ((A4 tptp.set_int) (X tptp.int)) (=> (@ tptp.finite_finite_int A4) (=> (not (@ (@ tptp.member_int X) A4)) (= (@ tptp.finite_card_int (@ (@ tptp.insert_int X) A4)) (@ tptp.suc (@ tptp.finite_card_int A4)))))) (forall ((A4 tptp.set_complex) (X tptp.complex)) (=> (@ tptp.finite3207457112153483333omplex A4) (=> (not (@ (@ tptp.member_complex X) A4)) (= (@ tptp.finite_card_complex (@ (@ tptp.insert_complex X) A4)) (@ tptp.suc (@ tptp.finite_card_complex A4)))))) (forall ((B tptp.code_integer) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger B))) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) B) (=> (@ (@ tptp.ord_le6747313008572928689nteger B) tptp.one_one_Code_integer) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ _let_1 M2)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat N) M2)))))) (forall ((B tptp.real) (M2 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 M2)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat N) M2)))))) (forall ((B tptp.rat) (M2 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 M2)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat N) M2)))))) (forall ((B tptp.nat) (M2 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 M2)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat N) M2)))))) (forall ((B tptp.int) (M2 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 M2)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat N) M2)))))) (forall ((B tptp.code_integer) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger B))) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) B) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_nat X) Y))))) (forall ((B tptp.real) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.power_power_real B))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_nat X) Y))))) (forall ((B tptp.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))))) (forall ((B tptp.nat) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) B) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_nat X) Y))))) (forall ((B tptp.int) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.power_power_int B))) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) B) (= (@ (@ tptp.ord_less_eq_int (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_nat X) Y))))) (forall ((A tptp.real) (B tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real A) N)) (@ (@ tptp.power_power_real B) N)) (@ (@ tptp.ord_less_eq_real A) B))))))) (forall ((A tptp.rat) (B tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 A) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat A) N)) (@ (@ tptp.power_power_rat B) N)) (@ (@ tptp.ord_less_eq_rat A) B))))))) (forall ((A tptp.nat) (B tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ _let_1 A) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat A) N)) (@ (@ tptp.power_power_nat B) N)) (@ (@ tptp.ord_less_eq_nat A) B))))))) (forall ((A tptp.int) (B tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 A) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A) N)) (@ (@ tptp.power_power_int B) N)) (@ (@ tptp.ord_less_eq_int A) B))))))) (forall ((A tptp.rat) (N tptp.nat)) (=> (not (= A tptp.zero_zero_rat)) (not (= (@ (@ tptp.power_power_rat A) N) tptp.zero_zero_rat)))) (forall ((A tptp.nat) (N tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (not (= (@ (@ tptp.power_power_nat A) N) tptp.zero_zero_nat)))) (forall ((A tptp.real) (N tptp.nat)) (=> (not (= A tptp.zero_zero_real)) (not (= (@ (@ tptp.power_power_real A) N) tptp.zero_zero_real)))) (forall ((A tptp.int) (N tptp.nat)) (=> (not (= A tptp.zero_zero_int)) (not 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_let_2 _let_1)))))) (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)))))) (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)))))) (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)))) (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)))) (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)))) (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)))) (forall ((A tptp.int) (B tptp.int) (N tptp.nat)) (= (@ (@ tptp.power_power_int (@ (@ tptp.times_times_int A) B)) N) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int A) N)) (@ (@ tptp.power_power_int B) N)))) (forall ((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)))) (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)))) (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)))) (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)))) (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)))) (forall ((A tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (= (@ _let_1 (@ (@ tptp.times_times_nat M2) N)) (@ (@ tptp.power_power_nat (@ _let_1 M2)) N)))) (forall ((A tptp.real) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A))) (= (@ _let_1 (@ (@ tptp.times_times_nat M2) N)) (@ (@ tptp.power_power_real (@ _let_1 M2)) N)))) (forall ((A tptp.int) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (= (@ _let_1 (@ (@ tptp.times_times_nat M2) N)) (@ (@ tptp.power_power_int (@ _let_1 M2)) N)))) (forall ((A tptp.complex) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex A))) (= (@ _let_1 (@ (@ tptp.times_times_nat M2) N)) (@ (@ tptp.power_power_complex (@ _let_1 M2)) N)))) (forall ((S3 tptp.set_nat) (N tptp.nat)) (=> (@ tptp.finite_finite_nat S3) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.finite_card_nat S3)) (@ (@ tptp.ord_less_eq_nat N) (@ (@ tptp.infini8530281810654367211te_nat S3) N))))) (forall ((R3 tptp.set_Pr4811707699266497531nteger) (Xs2 tptp.list_Code_integer)) (=> (forall ((X3 tptp.code_integer)) (not (@ (@ tptp.member157494554546826820nteger (@ (@ tptp.produc1086072967326762835nteger X3) X3)) R3))) (not (@ (@ tptp.member749217712838834276nteger (@ (@ tptp.produc750622340256944499nteger Xs2) Xs2)) (@ tptp.lenlex_Code_integer R3))))) (forall ((R3 tptp.set_Pr8693737435421807431at_nat) (Xs2 tptp.list_P6011104703257516679at_nat)) (=> (forall ((X3 tptp.product_prod_nat_nat)) (not (@ (@ tptp.member8206827879206165904at_nat (@ (@ tptp.produc6161850002892822231at_nat X3) X3)) R3))) (not (@ (@ tptp.member6693912407220327184at_nat (@ (@ tptp.produc5943733680697469783at_nat Xs2) Xs2)) (@ tptp.lenlex325483962726685836at_nat R3))))) (forall ((R3 tptp.set_Pr4329608150637261639at_nat) (Xs2 tptp.list_s1210847774152347623at_nat)) (=> (forall ((X3 tptp.set_Pr1261947904930325089at_nat)) (not (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat X3) X3)) R3))) (not (@ (@ tptp.member4080735728053443344at_nat (@ (@ tptp.produc7536900900485677911at_nat Xs2) Xs2)) (@ tptp.lenlex1357538814655152620at_nat R3))))) (forall ((R3 tptp.set_Pr1261947904930325089at_nat) (Xs2 tptp.list_nat)) (=> (forall ((X3 tptp.nat)) (not (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X3) X3)) R3))) (not (@ (@ tptp.member7340969449405702474st_nat (@ (@ tptp.produc2694037385005941721st_nat Xs2) Xs2)) (@ tptp.lenlex_nat R3))))) (forall ((R3 tptp.set_Pr958786334691620121nt_int) (Xs2 tptp.list_int)) (=> (forall ((X3 tptp.int)) (not (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X3) X3)) R3))) (not (@ (@ tptp.member6698963635872716290st_int (@ (@ tptp.produc364263696895485585st_int Xs2) Xs2)) (@ tptp.lenlex_int R3))))) (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_real A) N))))) (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_rat A) N))))) (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_nat A) N))))) (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_int A) N))))) (forall ((A tptp.real) (B tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real A) N)) (@ (@ tptp.power_power_real B) N))))) (forall ((A tptp.rat) (B tptp.rat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat A) N)) (@ (@ tptp.power_power_rat B) N))))) (forall ((A tptp.nat) (B tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat A) N)) (@ (@ tptp.power_power_nat B) N))))) (forall ((A tptp.int) (B tptp.int) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A) N)) (@ (@ tptp.power_power_int B) N))))) (forall ((S3 tptp.set_nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.infini8530281810654367211te_nat S3))) (=> (@ tptp.finite_finite_nat S3) (=> (@ (@ tptp.ord_less_nat _let_1) (@ tptp.finite_card_nat S3)) (@ (@ tptp.ord_less_nat (@ _let_2 N)) (@ _let_2 _let_1))))))) (forall ((B5 tptp.set_real) (A4 tptp.set_real) (R3 (-> tptp.real tptp.real Bool))) (=> (@ tptp.finite_finite_real B5) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) A4) (exists ((B6 tptp.real)) (and (@ (@ tptp.member_real B6) B5) (@ (@ R3 A3) B6))))) (=> (forall ((A1 tptp.real) (A22 tptp.real) (B3 tptp.real)) (=> (@ (@ tptp.member_real A1) A4) (=> (@ (@ tptp.member_real A22) A4) (=> (@ (@ tptp.member_real B3) B5) (=> (@ (@ R3 A1) B3) (=> (@ (@ R3 A22) B3) (= A1 A22))))))) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_real A4)) (@ tptp.finite_card_real B5)))))) (forall ((B5 tptp.set_real) (A4 tptp.set_nat) (R3 (-> tptp.nat tptp.real Bool))) (=> (@ tptp.finite_finite_real B5) (=> (forall ((A3 tptp.nat)) (=> (@ (@ tptp.member_nat A3) A4) (exists ((B6 tptp.real)) (and (@ (@ tptp.member_real B6) B5) (@ (@ R3 A3) B6))))) (=> (forall ((A1 tptp.nat) (A22 tptp.nat) (B3 tptp.real)) (=> (@ (@ tptp.member_nat A1) A4) (=> (@ (@ tptp.member_nat A22) A4) (=> (@ (@ tptp.member_real B3) B5) (=> (@ (@ R3 A1) B3) (=> (@ (@ R3 A22) B3) (= A1 A22))))))) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat A4)) (@ tptp.finite_card_real B5)))))) (forall ((B5 tptp.set_real) (A4 tptp.set_complex) (R3 (-> tptp.complex tptp.real Bool))) (=> (@ tptp.finite_finite_real B5) (=> (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) A4) (exists ((B6 tptp.real)) (and (@ (@ tptp.member_real B6) B5) (@ (@ R3 A3) B6))))) (=> (forall ((A1 tptp.complex) (A22 tptp.complex) (B3 tptp.real)) (=> (@ (@ tptp.member_complex A1) A4) (=> (@ (@ tptp.member_complex A22) A4) (=> (@ (@ tptp.member_real B3) B5) (=> (@ (@ R3 A1) B3) (=> (@ (@ R3 A22) B3) (= A1 A22))))))) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_complex A4)) (@ tptp.finite_card_real B5)))))) (forall ((B5 tptp.set_real) (A4 tptp.set_int) (R3 (-> tptp.int tptp.real Bool))) (=> (@ tptp.finite_finite_real B5) (=> (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) A4) (exists ((B6 tptp.real)) (and (@ (@ tptp.member_real B6) B5) (@ (@ R3 A3) B6))))) (=> (forall ((A1 tptp.int) (A22 tptp.int) (B3 tptp.real)) (=> (@ (@ tptp.member_int A1) A4) (=> (@ (@ tptp.member_int A22) A4) (=> (@ (@ tptp.member_real B3) B5) (=> (@ (@ R3 A1) B3) (=> (@ (@ R3 A22) B3) (= A1 A22))))))) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_int A4)) (@ tptp.finite_card_real B5)))))) (forall ((B5 tptp.set_nat) (A4 tptp.set_real) (R3 (-> tptp.real tptp.nat Bool))) (=> (@ tptp.finite_finite_nat B5) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) A4) (exists ((B6 tptp.nat)) (and (@ (@ tptp.member_nat B6) B5) (@ (@ R3 A3) B6))))) (=> (forall ((A1 tptp.real) (A22 tptp.real) (B3 tptp.nat)) (=> (@ (@ tptp.member_real A1) A4) (=> (@ (@ tptp.member_real A22) A4) (=> (@ (@ tptp.member_nat B3) B5) (=> (@ (@ R3 A1) B3) (=> (@ (@ R3 A22) B3) (= A1 A22))))))) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_real A4)) (@ tptp.finite_card_nat B5)))))) (forall ((B5 tptp.set_nat) (A4 tptp.set_nat) (R3 (-> tptp.nat tptp.nat Bool))) (=> (@ tptp.finite_finite_nat B5) (=> (forall ((A3 tptp.nat)) (=> (@ (@ tptp.member_nat A3) A4) (exists ((B6 tptp.nat)) (and (@ (@ tptp.member_nat B6) B5) (@ (@ R3 A3) B6))))) (=> (forall ((A1 tptp.nat) (A22 tptp.nat) (B3 tptp.nat)) (=> (@ (@ tptp.member_nat A1) A4) (=> (@ (@ tptp.member_nat A22) A4) (=> (@ (@ tptp.member_nat B3) B5) (=> (@ (@ R3 A1) B3) (=> (@ (@ R3 A22) B3) (= A1 A22))))))) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat A4)) (@ tptp.finite_card_nat B5)))))) (forall ((B5 tptp.set_nat) (A4 tptp.set_complex) (R3 (-> tptp.complex tptp.nat Bool))) (=> (@ tptp.finite_finite_nat B5) (=> (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) A4) (exists ((B6 tptp.nat)) (and (@ (@ tptp.member_nat B6) B5) (@ (@ R3 A3) B6))))) (=> (forall ((A1 tptp.complex) (A22 tptp.complex) (B3 tptp.nat)) (=> (@ (@ tptp.member_complex A1) A4) (=> (@ (@ tptp.member_complex A22) A4) (=> (@ (@ tptp.member_nat B3) B5) (=> (@ (@ R3 A1) B3) (=> (@ (@ R3 A22) B3) (= A1 A22))))))) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_complex A4)) (@ tptp.finite_card_nat B5)))))) (forall ((B5 tptp.set_nat) (A4 tptp.set_int) (R3 (-> tptp.int tptp.nat Bool))) (=> (@ tptp.finite_finite_nat B5) (=> (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) A4) (exists ((B6 tptp.nat)) (and (@ (@ tptp.member_nat B6) B5) (@ (@ R3 A3) B6))))) (=> (forall ((A1 tptp.int) (A22 tptp.int) (B3 tptp.nat)) (=> (@ (@ tptp.member_int A1) A4) (=> (@ (@ tptp.member_int A22) A4) (=> (@ (@ tptp.member_nat B3) B5) (=> (@ (@ R3 A1) B3) (=> (@ (@ R3 A22) B3) (= A1 A22))))))) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_int A4)) (@ tptp.finite_card_nat B5)))))) (forall ((B5 tptp.set_int) (A4 tptp.set_real) (R3 (-> tptp.real tptp.int Bool))) (=> (@ tptp.finite_finite_int B5) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) A4) (exists ((B6 tptp.int)) (and (@ (@ tptp.member_int B6) B5) (@ (@ R3 A3) B6))))) (=> (forall ((A1 tptp.real) (A22 tptp.real) (B3 tptp.int)) (=> (@ (@ tptp.member_real A1) A4) (=> (@ (@ tptp.member_real A22) A4) (=> (@ (@ tptp.member_int B3) B5) (=> (@ (@ R3 A1) B3) (=> (@ (@ R3 A22) B3) (= A1 A22))))))) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_real A4)) (@ tptp.finite_card_int B5)))))) (forall ((B5 tptp.set_int) (A4 tptp.set_nat) (R3 (-> tptp.nat tptp.int Bool))) (=> (@ tptp.finite_finite_int B5) (=> (forall ((A3 tptp.nat)) (=> (@ (@ tptp.member_nat A3) A4) (exists ((B6 tptp.int)) (and (@ (@ tptp.member_int B6) B5) (@ (@ R3 A3) B6))))) (=> (forall ((A1 tptp.nat) (A22 tptp.nat) (B3 tptp.int)) (=> (@ (@ tptp.member_nat A1) A4) (=> (@ (@ tptp.member_nat A22) A4) (=> (@ (@ tptp.member_int B3) B5) (=> (@ (@ R3 A1) B3) (=> (@ (@ R3 A22) B3) (= A1 A22))))))) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat A4)) (@ tptp.finite_card_int B5)))))) (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_real A) N))))) (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_rat A) N))))) (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_nat A) N))))) (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_int A) N))))) (forall ((A4 tptp.set_real) (X tptp.real)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_real A4)) (@ tptp.finite_card_real (@ (@ tptp.insert_real X) A4)))) (forall ((A4 tptp.set_nat) (X tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat A4)) (@ tptp.finite_card_nat (@ (@ tptp.insert_nat X) A4)))) (forall ((A4 tptp.set_complex) (X tptp.complex)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_complex A4)) (@ tptp.finite_card_complex (@ (@ tptp.insert_complex X) A4)))) (forall ((A4 tptp.set_int) (X tptp.int)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_int A4)) (@ tptp.finite_card_int (@ (@ tptp.insert_int X) A4)))) (forall ((A4 tptp.set_list_nat) (X tptp.list_nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_list_nat A4)) (@ tptp.finite_card_list_nat (@ (@ tptp.insert_list_nat X) A4)))) (forall ((A4 tptp.set_set_nat) (X tptp.set_nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_set_nat A4)) (@ tptp.finite_card_set_nat (@ (@ tptp.insert_set_nat X) A4)))) (forall ((A tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_8256067586552552935nteger A) N))))) (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.one_one_real))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_real A) N))))) (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.one_one_rat))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_rat A) N))))) (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.one_one_nat))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_nat A) N))))) (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.one_one_int))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_int A) N))))) (forall ((X tptp.code_integer) (Y tptp.code_integer) (N tptp.nat)) (=> (= (@ (@ tptp.times_3573771949741848930nteger X) Y) tptp.one_one_Code_integer) (= (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.power_8256067586552552935nteger X) N)) (@ (@ tptp.power_8256067586552552935nteger Y) N)) tptp.one_one_Code_integer))) (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))) (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))) (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))) (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))) (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))) (forall ((X8 tptp.set_nat) (Y7 tptp.set_nat)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.finite_card_nat X8)) (= (@ (@ tptp.infini8530281810654367211te_nat X8) I3) (@ (@ tptp.infini8530281810654367211te_nat Y7) I3)))) (=> (@ tptp.finite_finite_nat X8) (=> (@ tptp.finite_finite_nat Y7) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat X8)) (@ tptp.finite_card_nat Y7)) (@ (@ tptp.ord_less_eq_set_nat X8) Y7)))))) (forall ((A tptp.complex) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex A))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_complex A) (@ _let_1 N))))) (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_real A) (@ _let_1 N))))) (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat A))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_rat A) (@ _let_1 N))))) (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_nat A) (@ _let_1 N))))) (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_int A) (@ _let_1 N))))) (forall ((A tptp.complex) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex A))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_complex (@ _let_1 N)) A)))) (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_real (@ _let_1 N)) A)))) (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat A))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_rat (@ _let_1 N)) A)))) (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_nat (@ _let_1 N)) A)))) (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_int (@ _let_1 N)) A)))) (forall ((A tptp.code_integer)) (= (@ (@ tptp.power_8256067586552552935nteger A) tptp.zero_zero_nat) tptp.one_one_Code_integer)) (forall ((A tptp.nat)) (= (@ (@ tptp.power_power_nat A) tptp.zero_zero_nat) tptp.one_one_nat)) (forall ((A tptp.real)) (= (@ (@ tptp.power_power_real A) tptp.zero_zero_nat) tptp.one_one_real)) (forall ((A tptp.int)) (= (@ (@ tptp.power_power_int A) tptp.zero_zero_nat) tptp.one_one_int)) (forall ((A tptp.complex)) (= (@ (@ tptp.power_power_complex A) tptp.zero_zero_nat) tptp.one_one_complex)) (forall ((A tptp.complex) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M2) N)) (@ (@ tptp.times_times_complex (@ _let_1 M2)) (@ _let_1 N))))) (forall ((A tptp.real) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M2) N)) (@ (@ tptp.times_times_real (@ _let_1 M2)) (@ _let_1 N))))) (forall ((A tptp.rat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M2) N)) (@ (@ tptp.times_times_rat (@ _let_1 M2)) (@ _let_1 N))))) (forall ((A tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M2) N)) (@ (@ tptp.times_times_nat (@ _let_1 M2)) (@ _let_1 N))))) (forall ((A tptp.int) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M2) N)) (@ (@ tptp.times_times_int (@ _let_1 M2)) (@ _let_1 N))))) (forall ((I2 tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat I2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) I2) (=> (@ (@ tptp.ord_less_nat (@ _let_1 M2)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat M2) N))))) (forall ((S3 tptp.set_nat) (N tptp.nat)) (=> (not (@ tptp.finite_finite_nat S3)) (@ (@ tptp.ord_less_eq_nat N) (@ (@ tptp.infini8530281810654367211te_nat S3) N)))) (forall ((A4 tptp.set_list_nat)) (= (= (@ tptp.finite_card_list_nat A4) tptp.zero_zero_nat) (or (= A4 tptp.bot_bot_set_list_nat) (not (@ tptp.finite8100373058378681591st_nat A4))))) (forall ((A4 tptp.set_set_nat)) (= (= (@ tptp.finite_card_set_nat A4) tptp.zero_zero_nat) (or (= A4 tptp.bot_bot_set_set_nat) (not (@ tptp.finite1152437895449049373et_nat A4))))) (forall ((A4 tptp.set_complex)) (= (= (@ tptp.finite_card_complex A4) tptp.zero_zero_nat) (or (= A4 tptp.bot_bot_set_complex) (not (@ tptp.finite3207457112153483333omplex A4))))) (forall ((A4 tptp.set_nat)) (= (= (@ tptp.finite_card_nat A4) tptp.zero_zero_nat) (or (= A4 tptp.bot_bot_set_nat) (not (@ tptp.finite_finite_nat A4))))) (forall ((A4 tptp.set_int)) (= (= (@ tptp.finite_card_int A4) tptp.zero_zero_nat) (or (= A4 tptp.bot_bot_set_int) (not (@ tptp.finite_finite_int A4))))) (forall ((A4 tptp.set_real)) (= (= (@ tptp.finite_card_real A4) tptp.zero_zero_nat) (or (= A4 tptp.bot_bot_set_real) (not (@ tptp.finite_finite_real A4))))) (forall ((A4 tptp.set_list_nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.finite_card_list_nat A4)) (@ tptp.finite8100373058378681591st_nat A4))) (forall ((A4 tptp.set_set_nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.finite_card_set_nat A4)) (@ tptp.finite1152437895449049373et_nat A4))) (forall ((A4 tptp.set_nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.finite_card_nat A4)) (@ tptp.finite_finite_nat A4))) (forall ((A4 tptp.set_int)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.finite_card_int A4)) (@ tptp.finite_finite_int A4))) (forall ((A4 tptp.set_complex)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.finite_card_complex A4)) (@ tptp.finite3207457112153483333omplex A4))) (forall ((A4 tptp.set_real) (X tptp.real)) (let ((_let_1 (@ tptp.finite_card_real A4))) (let ((_let_2 (@ tptp.finite_card_real (@ (@ tptp.insert_real X) A4)))) (let ((_let_3 (@ (@ tptp.member_real X) A4))) (=> (@ tptp.finite_finite_real A4) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ tptp.suc _let_1))))))))) (forall ((A4 tptp.set_list_nat) (X tptp.list_nat)) (let ((_let_1 (@ tptp.finite_card_list_nat A4))) (let ((_let_2 (@ tptp.finite_card_list_nat (@ (@ tptp.insert_list_nat X) A4)))) (let ((_let_3 (@ (@ tptp.member_list_nat X) A4))) (=> (@ tptp.finite8100373058378681591st_nat A4) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ tptp.suc _let_1))))))))) (forall ((A4 tptp.set_set_nat) (X tptp.set_nat)) (let ((_let_1 (@ tptp.finite_card_set_nat A4))) (let ((_let_2 (@ tptp.finite_card_set_nat (@ (@ tptp.insert_set_nat X) A4)))) (let ((_let_3 (@ (@ tptp.member_set_nat X) A4))) (=> (@ tptp.finite1152437895449049373et_nat A4) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ tptp.suc _let_1))))))))) (forall ((A4 tptp.set_nat) (X tptp.nat)) (let ((_let_1 (@ tptp.finite_card_nat A4))) (let ((_let_2 (@ tptp.finite_card_nat (@ (@ tptp.insert_nat X) A4)))) (let ((_let_3 (@ (@ tptp.member_nat X) A4))) (=> (@ tptp.finite_finite_nat A4) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ tptp.suc _let_1))))))))) (forall ((A4 tptp.set_int) (X tptp.int)) (let ((_let_1 (@ tptp.finite_card_int A4))) (let ((_let_2 (@ tptp.finite_card_int (@ (@ tptp.insert_int X) A4)))) (let ((_let_3 (@ (@ tptp.member_int X) A4))) (=> (@ tptp.finite_finite_int A4) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ tptp.suc _let_1))))))))) (forall ((A4 tptp.set_complex) (X tptp.complex)) (let ((_let_1 (@ tptp.finite_card_complex A4))) (let ((_let_2 (@ tptp.finite_card_complex (@ (@ tptp.insert_complex X) A4)))) (let ((_let_3 (@ (@ tptp.member_complex X) A4))) (=> (@ tptp.finite3207457112153483333omplex A4) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ tptp.suc _let_1))))))))) (forall ((A4 tptp.set_real) (K2 tptp.nat)) (= (= (@ tptp.finite_card_real A4) (@ tptp.suc K2)) (exists ((B4 tptp.real) (B7 tptp.set_real)) (and (= A4 (@ (@ tptp.insert_real B4) B7)) (not (@ (@ tptp.member_real B4) B7)) (= (@ tptp.finite_card_real B7) K2) (@ tptp.finite_finite_real B7))))) (forall ((A4 tptp.set_list_nat) (K2 tptp.nat)) (= (= (@ tptp.finite_card_list_nat A4) (@ tptp.suc K2)) (exists ((B4 tptp.list_nat) (B7 tptp.set_list_nat)) (and (= A4 (@ (@ tptp.insert_list_nat B4) B7)) (not (@ (@ tptp.member_list_nat B4) B7)) (= (@ tptp.finite_card_list_nat B7) K2) (@ tptp.finite8100373058378681591st_nat B7))))) (forall ((A4 tptp.set_set_nat) (K2 tptp.nat)) (= (= (@ tptp.finite_card_set_nat A4) (@ tptp.suc K2)) (exists ((B4 tptp.set_nat) (B7 tptp.set_set_nat)) (and (= A4 (@ (@ tptp.insert_set_nat B4) B7)) (not (@ (@ tptp.member_set_nat B4) B7)) (= (@ tptp.finite_card_set_nat B7) K2) (@ tptp.finite1152437895449049373et_nat B7))))) (forall ((A4 tptp.set_nat) (K2 tptp.nat)) (= (= (@ tptp.finite_card_nat A4) (@ tptp.suc K2)) (exists ((B4 tptp.nat) (B7 tptp.set_nat)) (and (= A4 (@ (@ tptp.insert_nat B4) B7)) (not (@ (@ tptp.member_nat B4) B7)) (= (@ tptp.finite_card_nat B7) K2) (@ tptp.finite_finite_nat B7))))) (forall ((A4 tptp.set_int) (K2 tptp.nat)) (= (= (@ tptp.finite_card_int A4) (@ tptp.suc K2)) (exists ((B4 tptp.int) (B7 tptp.set_int)) (and (= A4 (@ (@ tptp.insert_int B4) B7)) (not (@ (@ tptp.member_int B4) B7)) (= (@ tptp.finite_card_int B7) K2) (@ tptp.finite_finite_int B7))))) (forall ((A4 tptp.set_complex) (K2 tptp.nat)) (= (= (@ tptp.finite_card_complex A4) (@ tptp.suc K2)) (exists ((B4 tptp.complex) (B7 tptp.set_complex)) (and (= A4 (@ (@ tptp.insert_complex B4) B7)) (not (@ (@ tptp.member_complex B4) B7)) (= (@ tptp.finite_card_complex B7) K2) (@ tptp.finite3207457112153483333omplex B7))))) (forall ((A tptp.real) (N tptp.nat) (B tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real A) N)) (@ (@ tptp.power_power_real B) N)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) B) (@ (@ tptp.ord_less_real A) B)))) (forall ((A tptp.rat) (N tptp.nat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat A) N)) (@ (@ tptp.power_power_rat B) N)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) B) (@ (@ tptp.ord_less_rat A) B)))) (forall ((A tptp.nat) (N tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat A) N)) (@ (@ tptp.power_power_nat B) N)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) B) (@ (@ tptp.ord_less_nat A) B)))) (forall ((A tptp.int) (N tptp.nat) (B tptp.int)) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int A) N)) (@ (@ tptp.power_power_int B) N)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B) (@ (@ tptp.ord_less_int A) B)))) (forall ((B5 tptp.set_list_nat) (A4 tptp.set_list_nat)) (=> (@ tptp.finite8100373058378681591st_nat B5) (=> (@ (@ tptp.ord_le6045566169113846134st_nat A4) B5) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_list_nat A4)) (@ tptp.finite_card_list_nat B5))))) (forall ((B5 tptp.set_set_nat) (A4 tptp.set_set_nat)) (=> (@ tptp.finite1152437895449049373et_nat B5) (=> (@ (@ tptp.ord_le6893508408891458716et_nat A4) B5) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_set_nat A4)) (@ tptp.finite_card_set_nat B5))))) (forall ((B5 tptp.set_int) (A4 tptp.set_int)) (=> (@ tptp.finite_finite_int B5) (=> (@ (@ tptp.ord_less_eq_set_int A4) B5) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_int A4)) (@ tptp.finite_card_int B5))))) (forall ((B5 tptp.set_complex) (A4 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex B5) (=> (@ (@ tptp.ord_le211207098394363844omplex A4) B5) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_complex A4)) (@ tptp.finite_card_complex B5))))) (forall ((B5 tptp.set_nat) (A4 tptp.set_nat)) (=> (@ tptp.finite_finite_nat B5) (=> (@ (@ tptp.ord_less_eq_set_nat A4) B5) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat A4)) (@ tptp.finite_card_nat B5))))) (forall ((B5 tptp.set_list_nat) (A4 tptp.set_list_nat)) (=> (@ tptp.finite8100373058378681591st_nat B5) (=> (@ (@ tptp.ord_le6045566169113846134st_nat A4) B5) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_list_nat B5)) (@ tptp.finite_card_list_nat A4)) (= A4 B5))))) (forall ((B5 tptp.set_set_nat) (A4 tptp.set_set_nat)) (=> (@ tptp.finite1152437895449049373et_nat B5) (=> (@ (@ tptp.ord_le6893508408891458716et_nat A4) B5) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_set_nat B5)) (@ tptp.finite_card_set_nat A4)) (= A4 B5))))) (forall ((B5 tptp.set_int) (A4 tptp.set_int)) (=> (@ tptp.finite_finite_int B5) (=> (@ (@ tptp.ord_less_eq_set_int A4) B5) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_int B5)) (@ tptp.finite_card_int A4)) (= A4 B5))))) (forall ((B5 tptp.set_complex) (A4 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex B5) (=> (@ (@ tptp.ord_le211207098394363844omplex A4) B5) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_complex B5)) (@ tptp.finite_card_complex A4)) (= A4 B5))))) (forall ((B5 tptp.set_nat) (A4 tptp.set_nat)) (=> (@ tptp.finite_finite_nat B5) (=> (@ (@ tptp.ord_less_eq_set_nat A4) B5) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat B5)) (@ tptp.finite_card_nat A4)) (= A4 B5))))) (forall ((F3 tptp.set_list_nat) (C4 tptp.nat)) (=> (forall ((G tptp.set_list_nat)) (=> (@ (@ tptp.ord_le6045566169113846134st_nat G) F3) (=> (@ tptp.finite8100373058378681591st_nat G) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_list_nat G)) C4)))) (and (@ tptp.finite8100373058378681591st_nat F3) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_list_nat F3)) C4)))) (forall ((F3 tptp.set_set_nat) (C4 tptp.nat)) (=> (forall ((G tptp.set_set_nat)) (=> (@ (@ tptp.ord_le6893508408891458716et_nat G) F3) (=> (@ tptp.finite1152437895449049373et_nat G) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_set_nat G)) C4)))) (and (@ tptp.finite1152437895449049373et_nat F3) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_set_nat F3)) C4)))) (forall ((F3 tptp.set_int) (C4 tptp.nat)) (=> (forall ((G tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int G) F3) (=> (@ tptp.finite_finite_int G) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_int G)) C4)))) (and (@ tptp.finite_finite_int F3) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_int F3)) C4)))) (forall ((F3 tptp.set_complex) (C4 tptp.nat)) (=> (forall ((G tptp.set_complex)) (=> (@ (@ tptp.ord_le211207098394363844omplex G) F3) (=> (@ tptp.finite3207457112153483333omplex G) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_complex G)) C4)))) (and (@ tptp.finite3207457112153483333omplex F3) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_complex F3)) C4)))) (forall ((F3 tptp.set_nat) (C4 tptp.nat)) (=> (forall ((G tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat G) F3) (=> (@ tptp.finite_finite_nat G) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat G)) C4)))) (and (@ tptp.finite_finite_nat F3) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat F3)) C4)))) (forall ((N tptp.nat) (S3 tptp.set_list_nat)) (=> (@ (@ tptp.ord_less_eq_nat N) (@ tptp.finite_card_list_nat S3)) (not (forall ((T3 tptp.set_list_nat)) (=> (@ (@ tptp.ord_le6045566169113846134st_nat T3) S3) (=> (= (@ tptp.finite_card_list_nat T3) N) (not (@ tptp.finite8100373058378681591st_nat T3)))))))) (forall ((N tptp.nat) (S3 tptp.set_set_nat)) (=> (@ (@ tptp.ord_less_eq_nat N) (@ tptp.finite_card_set_nat S3)) (not (forall ((T3 tptp.set_set_nat)) (=> (@ (@ tptp.ord_le6893508408891458716et_nat T3) S3) (=> (= (@ tptp.finite_card_set_nat T3) N) (not (@ tptp.finite1152437895449049373et_nat T3)))))))) (forall ((N tptp.nat) (S3 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_nat N) (@ tptp.finite_card_int S3)) (not (forall ((T3 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int T3) S3) (=> (= (@ tptp.finite_card_int T3) N) (not (@ tptp.finite_finite_int T3)))))))) (forall ((N tptp.nat) (S3 tptp.set_complex)) (=> (@ (@ tptp.ord_less_eq_nat N) (@ tptp.finite_card_complex S3)) (not (forall ((T3 tptp.set_complex)) (=> (@ (@ tptp.ord_le211207098394363844omplex T3) S3) (=> (= (@ tptp.finite_card_complex T3) N) (not (@ tptp.finite3207457112153483333omplex T3)))))))) (forall ((N tptp.nat) (S3 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_nat N) (@ tptp.finite_card_nat S3)) (not (forall ((T3 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat T3) S3) (=> (= (@ tptp.finite_card_nat T3) N) (not (@ tptp.finite_finite_nat T3)))))))) (forall ((A tptp.code_integer) (N tptp.nat)) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A) (=> (@ (@ tptp.ord_le3102999989581377725nteger A) tptp.one_one_Code_integer) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.power_8256067586552552935nteger A) N)) tptp.one_one_Code_integer)))) (forall ((A tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_eq_real A) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real A) N)) tptp.one_one_real)))) (forall ((A tptp.rat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_eq_rat A) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat A) N)) tptp.one_one_rat)))) (forall ((A tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.one_one_nat) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat A) N)) tptp.one_one_nat)))) (forall ((A tptp.int) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_eq_int A) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A) N)) tptp.one_one_int)))) (forall ((A tptp.real) (N tptp.nat) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (let ((_let_2 (@ tptp.suc N))) (=> (= (@ (@ tptp.power_power_real A) _let_2) (@ (@ tptp.power_power_real B) _let_2)) (=> (@ _let_1 A) (=> (@ _let_1 B) (= A B))))))) (forall ((A tptp.rat) (N tptp.nat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (let ((_let_2 (@ tptp.suc N))) (=> (= (@ (@ tptp.power_power_rat A) _let_2) (@ (@ tptp.power_power_rat B) _let_2)) (=> (@ _let_1 A) (=> (@ _let_1 B) (= A B))))))) (forall ((A tptp.nat) (N tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (let ((_let_2 (@ tptp.suc N))) (=> (= (@ (@ tptp.power_power_nat A) _let_2) (@ (@ tptp.power_power_nat B) _let_2)) (=> (@ _let_1 A) (=> (@ _let_1 B) (= A B))))))) (forall ((A tptp.int) (N tptp.nat) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_2 (@ tptp.suc N))) (=> (= (@ (@ tptp.power_power_int A) _let_2) (@ (@ tptp.power_power_int B) _let_2)) (=> (@ _let_1 A) (=> (@ _let_1 B) (= A B))))))) (forall ((A tptp.real) (N tptp.nat) (B tptp.real)) (let ((_let_1 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real A) _let_1)) (@ (@ tptp.power_power_real B) _let_1)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) B) (@ (@ tptp.ord_less_eq_real A) B))))) (forall ((A tptp.rat) (N tptp.nat) (B tptp.rat)) (let ((_let_1 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat A) _let_1)) (@ (@ tptp.power_power_rat B) _let_1)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) B) (@ (@ tptp.ord_less_eq_rat A) B))))) (forall ((A tptp.nat) (N tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat A) _let_1)) (@ (@ tptp.power_power_nat B) _let_1)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) B) (@ (@ tptp.ord_less_eq_nat A) B))))) (forall ((A tptp.int) (N tptp.nat) (B tptp.int)) (let ((_let_1 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A) _let_1)) (@ (@ tptp.power_power_int B) _let_1)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B) (@ (@ tptp.ord_less_eq_int A) B))))) (forall ((A tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_8256067586552552935nteger A) N))) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) A) (@ (@ tptp.ord_le6747313008572928689nteger _let_1) (@ (@ tptp.times_3573771949741848930nteger A) _let_1))))) (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))))) (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))))) (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))))) (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))))) (forall ((A tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger A) (@ (@ tptp.power_8256067586552552935nteger A) N)))))) (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.times_times_real A) (@ (@ tptp.power_power_real A) N)))))) (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.one_one_rat))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.times_times_rat A) (@ (@ tptp.power_power_rat A) N)))))) (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.one_one_nat))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.times_times_nat A) (@ (@ tptp.power_power_nat A) N)))))) (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int tptp.one_one_int))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.times_times_int A) (@ (@ tptp.power_power_int A) N)))))) (forall ((A4 tptp.set_list_nat) (B5 tptp.set_list_nat)) (=> (@ tptp.finite8100373058378681591st_nat A4) (=> (@ tptp.finite8100373058378681591st_nat B5) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_list_nat A4)) (@ tptp.finite_card_list_nat B5)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_list_nat (@ (@ tptp.minus_7954133019191499631st_nat A4) B5))) (@ tptp.finite_card_list_nat (@ (@ tptp.minus_7954133019191499631st_nat B5) A4))))))) (forall ((A4 tptp.set_set_nat) (B5 tptp.set_set_nat)) (=> (@ tptp.finite1152437895449049373et_nat A4) (=> (@ tptp.finite1152437895449049373et_nat B5) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_set_nat A4)) (@ tptp.finite_card_set_nat B5)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_set_nat (@ (@ tptp.minus_2163939370556025621et_nat A4) B5))) (@ tptp.finite_card_set_nat (@ (@ tptp.minus_2163939370556025621et_nat B5) A4))))))) (forall ((A4 tptp.set_int) (B5 tptp.set_int)) (=> (@ tptp.finite_finite_int A4) (=> (@ tptp.finite_finite_int B5) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_int A4)) (@ tptp.finite_card_int B5)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_int (@ (@ tptp.minus_minus_set_int A4) B5))) (@ tptp.finite_card_int (@ (@ tptp.minus_minus_set_int B5) A4))))))) (forall ((A4 tptp.set_complex) (B5 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex A4) (=> (@ tptp.finite3207457112153483333omplex B5) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_complex A4)) (@ tptp.finite_card_complex B5)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_complex (@ (@ tptp.minus_811609699411566653omplex A4) B5))) (@ tptp.finite_card_complex (@ (@ tptp.minus_811609699411566653omplex B5) A4))))))) (forall ((A4 tptp.set_Pr1261947904930325089at_nat) (B5 tptp.set_Pr1261947904930325089at_nat)) (=> (@ tptp.finite6177210948735845034at_nat A4) (=> (@ tptp.finite6177210948735845034at_nat B5) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite711546835091564841at_nat A4)) (@ tptp.finite711546835091564841at_nat B5)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite711546835091564841at_nat (@ (@ tptp.minus_1356011639430497352at_nat A4) B5))) (@ tptp.finite711546835091564841at_nat (@ (@ tptp.minus_1356011639430497352at_nat B5) A4))))))) (forall ((A4 tptp.set_nat) (B5 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A4) (=> (@ tptp.finite_finite_nat B5) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat A4)) (@ tptp.finite_card_nat B5)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat (@ (@ tptp.minus_minus_set_nat A4) B5))) (@ tptp.finite_card_nat (@ (@ tptp.minus_minus_set_nat B5) A4))))))) (forall ((Xs2 tptp.list_complex)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_complex (@ tptp.set_complex2 Xs2))) (@ tptp.size_s3451745648224563538omplex Xs2))) (forall ((Xs2 tptp.list_list_nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_list_nat (@ tptp.set_list_nat2 Xs2))) (@ tptp.size_s3023201423986296836st_nat Xs2))) (forall ((Xs2 tptp.list_set_nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_set_nat (@ tptp.set_set_nat2 Xs2))) (@ tptp.size_s3254054031482475050et_nat Xs2))) (forall ((Xs2 tptp.list_VEBT_VEBT)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite7802652506058667612T_VEBT (@ tptp.set_VEBT_VEBT2 Xs2))) (@ tptp.size_s6755466524823107622T_VEBT Xs2))) (forall ((Xs2 tptp.list_o)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_o (@ tptp.set_o2 Xs2))) (@ tptp.size_size_list_o Xs2))) (forall ((Xs2 tptp.list_nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat (@ tptp.set_nat2 Xs2))) (@ tptp.size_size_list_nat Xs2))) (forall ((Xs2 tptp.list_int)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_int (@ tptp.set_int2 Xs2))) (@ tptp.size_size_list_int Xs2))) (forall ((A tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_8256067586552552935nteger A) (@ tptp.suc N)))))) (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_real A) (@ tptp.suc N)))))) (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.one_one_rat))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_rat A) (@ tptp.suc N)))))) (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.one_one_nat))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_nat A) (@ tptp.suc N)))))) (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int tptp.one_one_int))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_int A) (@ tptp.suc N)))))) (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_8256067586552552935nteger tptp.zero_z3403309356797280102nteger) N))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_Code_integer)) (=> (not _let_2) (= _let_1 tptp.zero_z3403309356797280102nteger)))))) (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_rat tptp.zero_zero_rat) N))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_rat)) (=> (not _let_2) (= _let_1 tptp.zero_zero_rat)))))) (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat tptp.zero_zero_nat) N))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_nat)) (=> (not _let_2) (= _let_1 tptp.zero_zero_nat)))))) (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_real tptp.zero_zero_real) N))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_real)) (=> (not _let_2) (= _let_1 tptp.zero_zero_real)))))) (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int tptp.zero_zero_int) N))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_int)) (=> (not _let_2) (= _let_1 tptp.zero_zero_int)))))) (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_complex tptp.zero_zero_complex) N))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_complex)) (=> (not _let_2) (= _let_1 tptp.zero_zero_complex)))))) (forall ((N tptp.nat) (N6 tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger A))) (=> (@ (@ tptp.ord_less_eq_nat N) N6) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) A) (@ (@ tptp.ord_le3102999989581377725nteger (@ _let_1 N)) (@ _let_1 N6)))))) (forall ((N tptp.nat) (N6 tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_eq_nat N) N6) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) A) (@ (@ tptp.ord_less_eq_real (@ _let_1 N)) (@ _let_1 N6)))))) (forall ((N tptp.nat) (N6 tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat A))) (=> (@ (@ tptp.ord_less_eq_nat N) N6) (=> (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) A) (@ (@ tptp.ord_less_eq_rat (@ _let_1 N)) (@ _let_1 N6)))))) (forall ((N tptp.nat) (N6 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_eq_nat N) N6) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) A) (@ (@ tptp.ord_less_eq_nat (@ _let_1 N)) (@ _let_1 N6)))))) (forall ((N tptp.nat) (N6 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_eq_nat N) N6) (=> (@ (@ tptp.ord_less_eq_int tptp.one_one_int) A) (@ (@ tptp.ord_less_eq_int (@ _let_1 N)) (@ _let_1 N6)))))) (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.power_power_rat tptp.zero_zero_rat) N) tptp.zero_zero_rat))) (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.power_power_nat tptp.zero_zero_nat) N) tptp.zero_zero_nat))) (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.power_power_real tptp.zero_zero_real) N) tptp.zero_zero_real))) (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.power_power_int tptp.zero_zero_int) N) tptp.zero_zero_int))) (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.power_power_complex tptp.zero_zero_complex) N) tptp.zero_zero_complex))) (forall ((Ms tptp.list_VEBT_VEBT) (Ns tptp.list_VEBT_VEBT) (R3 tptp.set_Pr6192946355708809607T_VEBT)) (=> (@ (@ tptp.member4439316823752958928T_VEBT (@ (@ tptp.produc3897820843166775703T_VEBT Ms) Ns)) (@ tptp.lenlex_VEBT_VEBT R3)) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_s6755466524823107622T_VEBT Ms)) (@ tptp.size_s6755466524823107622T_VEBT Ns)))) (forall ((Ms tptp.list_o) (Ns tptp.list_o) (R3 tptp.set_Product_prod_o_o)) (=> (@ (@ tptp.member4159035015898711888list_o (@ (@ tptp.produc8435520187683070743list_o Ms) Ns)) (@ tptp.lenlex_o R3)) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_o Ms)) (@ tptp.size_size_list_o Ns)))) (forall ((Ms tptp.list_nat) (Ns tptp.list_nat) (R3 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.member7340969449405702474st_nat (@ (@ tptp.produc2694037385005941721st_nat Ms) Ns)) (@ tptp.lenlex_nat R3)) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_nat Ms)) (@ tptp.size_size_list_nat Ns)))) (forall ((Ms tptp.list_int) (Ns tptp.list_int) (R3 tptp.set_Pr958786334691620121nt_int)) (=> (@ (@ tptp.member6698963635872716290st_int (@ (@ tptp.produc364263696895485585st_int Ms) Ns)) (@ tptp.lenlex_int R3)) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_int Ms)) (@ tptp.size_size_list_int Ns)))) (forall ((N tptp.nat) (K2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)) N) (@ (@ tptp.ord_less_nat K2) (@ (@ tptp.power_power_nat N) K2)))) (forall ((I2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat (@ tptp.suc tptp.zero_zero_nat)))) (=> (@ _let_1 I2) (@ _let_1 (@ (@ tptp.power_power_nat I2) N))))) (forall ((S3 tptp.set_nat) (N tptp.nat)) (let ((_let_1 (@ tptp.infini8530281810654367211te_nat S3))) (=> (not (@ tptp.finite_finite_nat S3)) (@ (@ tptp.ord_less_nat (@ _let_1 N)) (@ _let_1 (@ tptp.suc N)))))) (forall ((A4 tptp.set_list_nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.finite_card_list_nat A4)) (and (not (= A4 tptp.bot_bot_set_list_nat)) (@ tptp.finite8100373058378681591st_nat A4)))) (forall ((A4 tptp.set_set_nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.finite_card_set_nat A4)) (and (not (= A4 tptp.bot_bot_set_set_nat)) (@ tptp.finite1152437895449049373et_nat A4)))) (forall ((A4 tptp.set_complex)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.finite_card_complex A4)) (and (not (= A4 tptp.bot_bot_set_complex)) (@ tptp.finite3207457112153483333omplex A4)))) (forall ((A4 tptp.set_nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.finite_card_nat A4)) (and (not (= A4 tptp.bot_bot_set_nat)) (@ tptp.finite_finite_nat A4)))) (forall ((A4 tptp.set_int)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.finite_card_int A4)) (and (not (= A4 tptp.bot_bot_set_int)) (@ tptp.finite_finite_int A4)))) (forall ((A4 tptp.set_real)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.finite_card_real A4)) (and (not (= A4 tptp.bot_bot_set_real)) (@ tptp.finite_finite_real A4)))) (forall ((A4 tptp.set_complex)) (= (= (@ tptp.finite_card_complex A4) (@ tptp.suc tptp.zero_zero_nat)) (exists ((X4 tptp.complex)) (= A4 (@ (@ tptp.insert_complex X4) tptp.bot_bot_set_complex))))) (forall ((A4 tptp.set_list_nat)) (= (= (@ tptp.finite_card_list_nat A4) (@ tptp.suc tptp.zero_zero_nat)) (exists ((X4 tptp.list_nat)) (= A4 (@ (@ tptp.insert_list_nat X4) tptp.bot_bot_set_list_nat))))) (forall ((A4 tptp.set_set_nat)) (= (= (@ tptp.finite_card_set_nat A4) (@ tptp.suc tptp.zero_zero_nat)) (exists ((X4 tptp.set_nat)) (= A4 (@ (@ tptp.insert_set_nat X4) tptp.bot_bot_set_set_nat))))) (forall ((A4 tptp.set_nat)) (= (= (@ tptp.finite_card_nat A4) (@ tptp.suc tptp.zero_zero_nat)) (exists ((X4 tptp.nat)) (= A4 (@ (@ tptp.insert_nat X4) tptp.bot_bot_set_nat))))) (forall ((A4 tptp.set_int)) (= (= (@ tptp.finite_card_int A4) (@ tptp.suc tptp.zero_zero_nat)) (exists ((X4 tptp.int)) (= A4 (@ (@ tptp.insert_int X4) tptp.bot_bot_set_int))))) (forall ((A4 tptp.set_real)) (= (= (@ tptp.finite_card_real A4) (@ tptp.suc tptp.zero_zero_nat)) (exists ((X4 tptp.real)) (= A4 (@ (@ tptp.insert_real X4) tptp.bot_bot_set_real))))) (forall ((A4 tptp.set_complex) (K2 tptp.nat)) (=> (= (@ tptp.finite_card_complex A4) (@ tptp.suc K2)) (exists ((B3 tptp.complex) (B8 tptp.set_complex)) (and (= A4 (@ (@ tptp.insert_complex B3) B8)) (not (@ (@ tptp.member_complex B3) B8)) (= (@ tptp.finite_card_complex B8) K2) (=> (= K2 tptp.zero_zero_nat) (= B8 tptp.bot_bot_set_complex)))))) (forall ((A4 tptp.set_list_nat) (K2 tptp.nat)) (=> (= (@ tptp.finite_card_list_nat A4) (@ tptp.suc K2)) (exists ((B3 tptp.list_nat) (B8 tptp.set_list_nat)) (and (= A4 (@ (@ tptp.insert_list_nat B3) B8)) (not (@ (@ tptp.member_list_nat B3) B8)) (= (@ tptp.finite_card_list_nat B8) K2) (=> (= K2 tptp.zero_zero_nat) (= B8 tptp.bot_bot_set_list_nat)))))) (forall ((A4 tptp.set_set_nat) (K2 tptp.nat)) (=> (= (@ tptp.finite_card_set_nat A4) (@ tptp.suc K2)) (exists ((B3 tptp.set_nat) (B8 tptp.set_set_nat)) (and (= A4 (@ (@ tptp.insert_set_nat B3) B8)) (not (@ (@ tptp.member_set_nat B3) B8)) (= (@ tptp.finite_card_set_nat B8) K2) (=> (= K2 tptp.zero_zero_nat) (= B8 tptp.bot_bot_set_set_nat)))))) (forall ((A4 tptp.set_nat) (K2 tptp.nat)) (=> (= (@ tptp.finite_card_nat A4) (@ tptp.suc K2)) (exists ((B3 tptp.nat) (B8 tptp.set_nat)) (and (= A4 (@ (@ tptp.insert_nat B3) B8)) (not (@ (@ tptp.member_nat B3) B8)) (= (@ tptp.finite_card_nat B8) K2) (=> (= K2 tptp.zero_zero_nat) (= B8 tptp.bot_bot_set_nat)))))) (forall ((A4 tptp.set_int) (K2 tptp.nat)) (=> (= (@ tptp.finite_card_int A4) (@ tptp.suc K2)) (exists ((B3 tptp.int) (B8 tptp.set_int)) (and (= A4 (@ (@ tptp.insert_int B3) B8)) (not (@ (@ tptp.member_int B3) B8)) (= (@ tptp.finite_card_int B8) K2) (=> (= K2 tptp.zero_zero_nat) (= B8 tptp.bot_bot_set_int)))))) (forall ((A4 tptp.set_real) (K2 tptp.nat)) (=> (= (@ tptp.finite_card_real A4) (@ tptp.suc K2)) (exists ((B3 tptp.real) (B8 tptp.set_real)) (and (= A4 (@ (@ tptp.insert_real B3) B8)) (not (@ (@ tptp.member_real B3) B8)) (= (@ tptp.finite_card_real B8) K2) (=> (= K2 tptp.zero_zero_nat) (= B8 tptp.bot_bot_set_real)))))) (forall ((A4 tptp.set_complex) (K2 tptp.nat)) (= (= (@ tptp.finite_card_complex A4) (@ tptp.suc K2)) (exists ((B4 tptp.complex) (B7 tptp.set_complex)) (and (= A4 (@ (@ tptp.insert_complex B4) B7)) (not (@ (@ tptp.member_complex B4) B7)) (= (@ tptp.finite_card_complex B7) K2) (=> (= K2 tptp.zero_zero_nat) (= B7 tptp.bot_bot_set_complex)))))) (forall ((A4 tptp.set_list_nat) (K2 tptp.nat)) (= (= (@ tptp.finite_card_list_nat A4) (@ tptp.suc K2)) (exists ((B4 tptp.list_nat) (B7 tptp.set_list_nat)) (and (= A4 (@ (@ tptp.insert_list_nat B4) B7)) (not (@ (@ tptp.member_list_nat B4) B7)) (= (@ tptp.finite_card_list_nat B7) K2) (=> (= K2 tptp.zero_zero_nat) (= B7 tptp.bot_bot_set_list_nat)))))) (forall ((A4 tptp.set_set_nat) (K2 tptp.nat)) (= (= (@ tptp.finite_card_set_nat A4) (@ tptp.suc K2)) (exists ((B4 tptp.set_nat) (B7 tptp.set_set_nat)) (and (= A4 (@ (@ tptp.insert_set_nat B4) B7)) (not (@ (@ tptp.member_set_nat B4) B7)) (= (@ tptp.finite_card_set_nat B7) K2) (=> (= K2 tptp.zero_zero_nat) (= B7 tptp.bot_bot_set_set_nat)))))) (forall ((A4 tptp.set_nat) (K2 tptp.nat)) (= (= (@ tptp.finite_card_nat A4) (@ tptp.suc K2)) (exists ((B4 tptp.nat) (B7 tptp.set_nat)) (and (= A4 (@ (@ tptp.insert_nat B4) B7)) (not (@ (@ tptp.member_nat B4) B7)) (= (@ tptp.finite_card_nat B7) K2) (=> (= K2 tptp.zero_zero_nat) (= B7 tptp.bot_bot_set_nat)))))) (forall ((A4 tptp.set_int) (K2 tptp.nat)) (= (= (@ tptp.finite_card_int A4) (@ tptp.suc K2)) (exists ((B4 tptp.int) (B7 tptp.set_int)) (and (= A4 (@ (@ tptp.insert_int B4) B7)) (not (@ (@ tptp.member_int B4) B7)) (= (@ tptp.finite_card_int B7) K2) (=> (= K2 tptp.zero_zero_nat) (= B7 tptp.bot_bot_set_int)))))) (forall ((A4 tptp.set_real) (K2 tptp.nat)) (= (= (@ tptp.finite_card_real A4) (@ tptp.suc K2)) (exists ((B4 tptp.real) (B7 tptp.set_real)) (and (= A4 (@ (@ tptp.insert_real B4) B7)) (not (@ (@ tptp.member_real B4) B7)) (= (@ tptp.finite_card_real B7) K2) (=> (= K2 tptp.zero_zero_nat) (= B7 tptp.bot_bot_set_real)))))) (forall ((A4 tptp.set_list_nat)) (=> (@ tptp.finite8100373058378681591st_nat A4) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_list_nat A4)) (@ tptp.suc tptp.zero_zero_nat)) (forall ((X4 tptp.list_nat)) (=> (@ (@ tptp.member_list_nat X4) A4) (forall ((Y4 tptp.list_nat)) (=> (@ (@ tptp.member_list_nat Y4) A4) (= X4 Y4)))))))) (forall ((A4 tptp.set_set_nat)) (=> (@ tptp.finite1152437895449049373et_nat A4) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_set_nat A4)) (@ tptp.suc tptp.zero_zero_nat)) (forall ((X4 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat X4) A4) (forall ((Y4 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat Y4) A4) (= X4 Y4)))))))) (forall ((A4 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A4) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat A4)) (@ tptp.suc tptp.zero_zero_nat)) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) A4) (forall ((Y4 tptp.nat)) (=> (@ (@ tptp.member_nat Y4) A4) (= X4 Y4)))))))) (forall ((A4 tptp.set_int)) (=> (@ tptp.finite_finite_int A4) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_int A4)) (@ tptp.suc tptp.zero_zero_nat)) (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) A4) (forall ((Y4 tptp.int)) (=> (@ (@ tptp.member_int Y4) A4) (= X4 Y4)))))))) (forall ((A4 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex A4) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_complex A4)) (@ tptp.suc tptp.zero_zero_nat)) (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) A4) (forall ((Y4 tptp.complex)) (=> (@ (@ tptp.member_complex Y4) A4) (= X4 Y4)))))))) (forall ((N tptp.nat) (A4 tptp.set_real)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) (@ tptp.finite_card_real A4)) (exists ((A5 tptp.real) (B7 tptp.set_real)) (and (= A4 (@ (@ tptp.insert_real A5) B7)) (not (@ (@ tptp.member_real A5) B7)) (@ (@ tptp.ord_less_eq_nat N) (@ tptp.finite_card_real B7)) (@ tptp.finite_finite_real B7))))) (forall ((N tptp.nat) (A4 tptp.set_list_nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) (@ tptp.finite_card_list_nat A4)) (exists ((A5 tptp.list_nat) (B7 tptp.set_list_nat)) (and (= A4 (@ (@ tptp.insert_list_nat A5) B7)) (not (@ (@ tptp.member_list_nat A5) B7)) (@ (@ tptp.ord_less_eq_nat N) (@ tptp.finite_card_list_nat B7)) (@ tptp.finite8100373058378681591st_nat B7))))) (forall ((N tptp.nat) (A4 tptp.set_set_nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) (@ tptp.finite_card_set_nat A4)) (exists ((A5 tptp.set_nat) (B7 tptp.set_set_nat)) (and (= A4 (@ (@ tptp.insert_set_nat A5) B7)) (not (@ (@ tptp.member_set_nat A5) B7)) (@ (@ tptp.ord_less_eq_nat N) (@ tptp.finite_card_set_nat B7)) (@ tptp.finite1152437895449049373et_nat B7))))) (forall ((N tptp.nat) (A4 tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) (@ tptp.finite_card_nat A4)) (exists ((A5 tptp.nat) (B7 tptp.set_nat)) (and (= A4 (@ (@ tptp.insert_nat A5) B7)) (not (@ (@ tptp.member_nat A5) B7)) (@ (@ tptp.ord_less_eq_nat N) (@ tptp.finite_card_nat B7)) (@ tptp.finite_finite_nat B7))))) (forall ((N tptp.nat) (A4 tptp.set_int)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) (@ tptp.finite_card_int A4)) (exists ((A5 tptp.int) (B7 tptp.set_int)) (and (= A4 (@ (@ tptp.insert_int A5) B7)) (not (@ (@ tptp.member_int A5) B7)) (@ (@ tptp.ord_less_eq_nat N) (@ tptp.finite_card_int B7)) (@ tptp.finite_finite_int B7))))) (forall ((N tptp.nat) (A4 tptp.set_complex)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) (@ tptp.finite_card_complex A4)) (exists ((A5 tptp.complex) (B7 tptp.set_complex)) (and (= A4 (@ (@ tptp.insert_complex A5) B7)) (not (@ (@ tptp.member_complex A5) B7)) (@ (@ tptp.ord_less_eq_nat N) (@ tptp.finite_card_complex B7)) (@ tptp.finite3207457112153483333omplex B7))))) (forall ((A tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_8256067586552552935nteger A) N))) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A) (=> (@ (@ tptp.ord_le6747313008572928689nteger A) tptp.one_one_Code_integer) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.times_3573771949741848930nteger A) _let_1)) _let_1))))) (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_real A) N))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_real A) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) _let_1)) _let_1))))) (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_rat A) N))) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_rat A) tptp.one_one_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) _let_1)) _let_1))))) (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat A) N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat A) tptp.one_one_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A) _let_1)) _let_1))))) (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int A) N))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int A) tptp.one_one_int) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) _let_1)) _let_1))))) (forall ((A tptp.code_integer) (N tptp.nat)) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A) (=> (@ (@ tptp.ord_le3102999989581377725nteger A) tptp.one_one_Code_integer) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.power_8256067586552552935nteger A) (@ tptp.suc N))) A)))) (forall ((A tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_eq_real A) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real A) (@ tptp.suc N))) A)))) (forall ((A tptp.rat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_eq_rat A) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat A) (@ tptp.suc N))) A)))) (forall ((A tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.one_one_nat) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat A) (@ tptp.suc N))) A)))) (forall ((A tptp.int) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_eq_int A) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A) (@ tptp.suc N))) A)))) (forall ((A tptp.code_integer) (N tptp.nat)) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A) (=> (@ (@ tptp.ord_le6747313008572928689nteger A) tptp.one_one_Code_integer) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.power_8256067586552552935nteger A) (@ tptp.suc N))) tptp.one_one_Code_integer)))) (forall ((A tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_real A) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real A) (@ tptp.suc N))) tptp.one_one_real)))) (forall ((A tptp.rat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_rat A) tptp.one_one_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat A) (@ tptp.suc N))) tptp.one_one_rat)))) (forall ((A tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat A) tptp.one_one_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat A) (@ tptp.suc N))) tptp.one_one_nat)))) (forall ((A tptp.int) (N tptp.nat)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int A) tptp.one_one_int) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int A) (@ tptp.suc N))) tptp.one_one_int)))) (forall ((A4 tptp.set_complex) (X tptp.complex)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_complex (@ (@ tptp.minus_811609699411566653omplex A4) (@ (@ tptp.insert_complex X) tptp.bot_bot_set_complex)))) (@ tptp.finite_card_complex A4))) (forall ((A4 tptp.set_list_nat) (X tptp.list_nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_list_nat (@ (@ tptp.minus_7954133019191499631st_nat A4) (@ (@ tptp.insert_list_nat X) tptp.bot_bot_set_list_nat)))) (@ tptp.finite_card_list_nat A4))) (forall ((A4 tptp.set_set_nat) (X tptp.set_nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_set_nat (@ (@ tptp.minus_2163939370556025621et_nat A4) (@ (@ tptp.insert_set_nat X) tptp.bot_bot_set_set_nat)))) (@ tptp.finite_card_set_nat A4))) (forall ((A4 tptp.set_int) (X tptp.int)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_int (@ (@ tptp.minus_minus_set_int A4) (@ (@ tptp.insert_int X) tptp.bot_bot_set_int)))) (@ tptp.finite_card_int A4))) (forall ((A4 tptp.set_real) (X tptp.real)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_real (@ (@ tptp.minus_minus_set_real A4) (@ (@ tptp.insert_real X) tptp.bot_bot_set_real)))) (@ tptp.finite_card_real A4))) (forall ((A4 tptp.set_Pr1261947904930325089at_nat) (X tptp.product_prod_nat_nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite711546835091564841at_nat (@ (@ tptp.minus_1356011639430497352at_nat A4) (@ (@ tptp.insert8211810215607154385at_nat X) tptp.bot_bo2099793752762293965at_nat)))) (@ tptp.finite711546835091564841at_nat A4))) (forall ((A4 tptp.set_nat) (X tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat (@ (@ tptp.minus_minus_set_nat A4) (@ (@ tptp.insert_nat X) tptp.bot_bot_set_nat)))) (@ tptp.finite_card_nat A4))) (forall ((N tptp.nat) (N6 tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger A))) (=> (@ (@ tptp.ord_less_nat N) N6) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A) (=> (@ (@ tptp.ord_le6747313008572928689nteger A) tptp.one_one_Code_integer) (@ (@ tptp.ord_le6747313008572928689nteger (@ _let_1 N6)) (@ _let_1 N))))))) (forall ((N tptp.nat) (N6 tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_nat N) N6) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_real A) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ _let_1 N6)) (@ _let_1 N))))))) (forall ((N tptp.nat) (N6 tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat A))) (=> (@ (@ tptp.ord_less_nat N) N6) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_rat A) tptp.one_one_rat) (@ (@ tptp.ord_less_rat (@ _let_1 N6)) (@ _let_1 N))))))) (forall ((N tptp.nat) (N6 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_nat N) N6) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat A) tptp.one_one_nat) (@ (@ tptp.ord_less_nat (@ _let_1 N6)) (@ _let_1 N))))))) (forall ((N tptp.nat) (N6 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_nat N) N6) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int A) tptp.one_one_int) (@ (@ tptp.ord_less_int (@ _let_1 N6)) (@ _let_1 N))))))) (forall ((N tptp.nat) (N6 tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger A))) (=> (@ (@ tptp.ord_less_eq_nat N) N6) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A) (=> (@ (@ tptp.ord_le3102999989581377725nteger A) tptp.one_one_Code_integer) (@ (@ tptp.ord_le3102999989581377725nteger (@ _let_1 N6)) (@ _let_1 N))))))) (forall ((N tptp.nat) (N6 tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_eq_nat N) N6) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_eq_real A) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ _let_1 N6)) (@ _let_1 N))))))) (forall ((N tptp.nat) (N6 tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat A))) (=> (@ (@ tptp.ord_less_eq_nat N) N6) (=> (@ (@ 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 N6)) (@ _let_1 N))))))) (forall ((N tptp.nat) (N6 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_eq_nat N) N6) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.one_one_nat) (@ (@ tptp.ord_less_eq_nat (@ _let_1 N6)) (@ _let_1 N))))))) (forall ((N tptp.nat) (N6 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_eq_nat N) N6) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_eq_int A) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ _let_1 N6)) (@ _let_1 N))))))) (forall ((A tptp.code_integer) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger A))) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) A) (=> (@ (@ tptp.ord_le3102999989581377725nteger (@ _let_1 M2)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat M2) N))))) (forall ((A tptp.real) (M2 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 M2)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat M2) N))))) (forall ((A tptp.rat) (M2 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 M2)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat M2) N))))) (forall ((A tptp.nat) (M2 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 M2)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat M2) N))))) (forall ((A tptp.int) (M2 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 M2)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat M2) N))))) (forall ((N tptp.nat) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (= (@ (@ tptp.power_power_real A) N) (@ (@ tptp.power_power_real B) N)) (= A B))))))) (forall ((N tptp.nat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (= (@ (@ tptp.power_power_rat A) N) (@ (@ tptp.power_power_rat B) N)) (= A B))))))) (forall ((N tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (= (@ (@ tptp.power_power_nat A) N) (@ (@ tptp.power_power_nat B) N)) (= A B))))))) (forall ((N tptp.nat) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (= (@ (@ tptp.power_power_int A) N) (@ (@ tptp.power_power_int B) N)) (= A B))))))) (forall ((A tptp.real) (N tptp.nat) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (= (@ (@ tptp.power_power_real A) N) (@ (@ tptp.power_power_real B) N)) (=> (@ _let_1 A) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= A B))))))) (forall ((A tptp.rat) (N tptp.nat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (= (@ (@ tptp.power_power_rat A) N) (@ (@ tptp.power_power_rat B) N)) (=> (@ _let_1 A) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= A B))))))) (forall ((A tptp.nat) (N tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (= (@ (@ tptp.power_power_nat A) N) (@ (@ tptp.power_power_nat B) N)) (=> (@ _let_1 A) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= A B))))))) (forall ((A tptp.int) (N tptp.nat) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (= (@ (@ tptp.power_power_int A) N) (@ (@ tptp.power_power_int B) N)) (=> (@ _let_1 A) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= A B))))))) (forall ((B5 tptp.set_list_nat) (A4 tptp.set_list_nat)) (=> (@ tptp.finite8100373058378681591st_nat B5) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat (@ tptp.finite_card_list_nat A4)) (@ tptp.finite_card_list_nat B5))) (@ tptp.finite_card_list_nat (@ (@ tptp.minus_7954133019191499631st_nat A4) B5))))) (forall ((B5 tptp.set_set_nat) (A4 tptp.set_set_nat)) (=> (@ tptp.finite1152437895449049373et_nat B5) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat (@ tptp.finite_card_set_nat A4)) (@ tptp.finite_card_set_nat B5))) (@ tptp.finite_card_set_nat (@ (@ tptp.minus_2163939370556025621et_nat A4) B5))))) (forall ((B5 tptp.set_int) (A4 tptp.set_int)) (=> (@ tptp.finite_finite_int B5) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat (@ tptp.finite_card_int A4)) (@ tptp.finite_card_int B5))) (@ tptp.finite_card_int (@ (@ tptp.minus_minus_set_int A4) B5))))) (forall ((B5 tptp.set_complex) (A4 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex B5) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat (@ tptp.finite_card_complex A4)) (@ tptp.finite_card_complex B5))) (@ tptp.finite_card_complex (@ (@ tptp.minus_811609699411566653omplex A4) B5))))) (forall ((B5 tptp.set_Pr1261947904930325089at_nat) (A4 tptp.set_Pr1261947904930325089at_nat)) (=> (@ tptp.finite6177210948735845034at_nat B5) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat (@ tptp.finite711546835091564841at_nat A4)) (@ tptp.finite711546835091564841at_nat B5))) (@ tptp.finite711546835091564841at_nat (@ (@ tptp.minus_1356011639430497352at_nat A4) B5))))) (forall ((B5 tptp.set_nat) (A4 tptp.set_nat)) (=> (@ tptp.finite_finite_nat B5) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat (@ tptp.finite_card_nat A4)) (@ tptp.finite_card_nat B5))) (@ tptp.finite_card_nat (@ (@ tptp.minus_minus_set_nat A4) B5))))) (forall ((A tptp.code_integer) (N tptp.nat)) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_le3102999989581377725nteger A) (@ (@ tptp.power_8256067586552552935nteger A) N))))) (forall ((A tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_eq_real A) (@ (@ tptp.power_power_real A) N))))) (forall ((A tptp.rat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_eq_rat A) (@ (@ tptp.power_power_rat A) N))))) (forall ((A tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_eq_nat A) (@ (@ tptp.power_power_nat A) N))))) (forall ((A tptp.int) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int tptp.one_one_int) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.power_power_int A) N))))) (forall ((A tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer))) (=> (@ _let_1 A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ _let_1 (@ (@ tptp.power_8256067586552552935nteger A) N)))))) (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ _let_1 A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ _let_1 (@ (@ tptp.power_power_real A) N)))))) (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.one_one_rat))) (=> (@ _let_1 A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ _let_1 (@ (@ tptp.power_power_rat A) N)))))) (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.one_one_nat))) (=> (@ _let_1 A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ _let_1 (@ (@ tptp.power_power_nat A) N)))))) (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int tptp.one_one_int))) (=> (@ _let_1 A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ _let_1 (@ (@ tptp.power_power_int A) N)))))) (forall ((Xs2 tptp.list_VEBT_VEBT) (X tptp.vEBT_VEBT)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.count_list_VEBT_VEBT Xs2) X)) (@ tptp.size_s6755466524823107622T_VEBT Xs2))) (forall ((Xs2 tptp.list_o) (X Bool)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.count_list_o Xs2) X)) (@ tptp.size_size_list_o Xs2))) (forall ((Xs2 tptp.list_nat) (X tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.count_list_nat Xs2) X)) (@ tptp.size_size_list_nat Xs2))) (forall ((Xs2 tptp.list_int) (X tptp.int)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.count_list_int Xs2) X)) (@ tptp.size_size_list_int Xs2))) _let_319 _let_318 _let_317 _let_316 _let_315 (forall ((A4 tptp.set_list_nat) (X tptp.list_nat)) (=> (@ tptp.finite8100373058378681591st_nat A4) (=> (@ (@ tptp.member_list_nat X) A4) (= (@ tptp.finite_card_list_nat A4) (@ tptp.suc (@ tptp.finite_card_list_nat (@ (@ tptp.minus_7954133019191499631st_nat A4) (@ (@ tptp.insert_list_nat X) tptp.bot_bot_set_list_nat)))))))) (forall ((A4 tptp.set_set_nat) (X tptp.set_nat)) (=> (@ tptp.finite1152437895449049373et_nat A4) (=> (@ (@ tptp.member_set_nat X) A4) (= (@ tptp.finite_card_set_nat A4) (@ tptp.suc (@ tptp.finite_card_set_nat (@ (@ tptp.minus_2163939370556025621et_nat A4) (@ (@ tptp.insert_set_nat X) tptp.bot_bot_set_set_nat)))))))) (forall ((A4 tptp.set_complex) (X tptp.complex)) (=> (@ tptp.finite3207457112153483333omplex A4) (=> (@ (@ tptp.member_complex X) A4) (= (@ tptp.finite_card_complex A4) (@ tptp.suc (@ tptp.finite_card_complex (@ (@ tptp.minus_811609699411566653omplex A4) (@ (@ tptp.insert_complex X) tptp.bot_bot_set_complex)))))))) (forall ((A4 tptp.set_int) (X tptp.int)) (=> (@ tptp.finite_finite_int A4) (=> (@ (@ tptp.member_int X) A4) (= (@ tptp.finite_card_int A4) (@ tptp.suc (@ tptp.finite_card_int (@ (@ tptp.minus_minus_set_int A4) (@ (@ tptp.insert_int X) tptp.bot_bot_set_int)))))))) (forall ((A4 tptp.set_real) (X tptp.real)) (=> (@ tptp.finite_finite_real A4) (=> (@ (@ tptp.member_real X) A4) (= (@ tptp.finite_card_real A4) (@ tptp.suc (@ tptp.finite_card_real (@ (@ tptp.minus_minus_set_real A4) (@ (@ tptp.insert_real X) tptp.bot_bot_set_real)))))))) (forall ((A4 tptp.set_Pr1261947904930325089at_nat) (X tptp.product_prod_nat_nat)) (=> (@ tptp.finite6177210948735845034at_nat A4) (=> (@ (@ tptp.member8440522571783428010at_nat X) A4) (= (@ tptp.finite711546835091564841at_nat A4) (@ tptp.suc (@ tptp.finite711546835091564841at_nat (@ (@ tptp.minus_1356011639430497352at_nat A4) (@ (@ tptp.insert8211810215607154385at_nat X) tptp.bot_bo2099793752762293965at_nat)))))))) (forall ((A4 tptp.set_nat) (X tptp.nat)) (=> (@ tptp.finite_finite_nat A4) (=> (@ (@ tptp.member_nat X) A4) (= (@ tptp.finite_card_nat A4) (@ tptp.suc (@ tptp.finite_card_nat (@ (@ tptp.minus_minus_set_nat A4) (@ (@ tptp.insert_nat X) tptp.bot_bot_set_nat)))))))) (forall ((A4 tptp.set_list_nat) (X tptp.list_nat)) (let ((_let_1 (@ tptp.insert_list_nat X))) (=> (@ tptp.finite8100373058378681591st_nat A4) (= (@ tptp.finite_card_list_nat (@ _let_1 A4)) (@ tptp.suc (@ tptp.finite_card_list_nat (@ (@ tptp.minus_7954133019191499631st_nat A4) (@ _let_1 tptp.bot_bot_set_list_nat)))))))) (forall ((A4 tptp.set_set_nat) (X tptp.set_nat)) (let ((_let_1 (@ tptp.insert_set_nat X))) (=> (@ tptp.finite1152437895449049373et_nat A4) (= (@ tptp.finite_card_set_nat (@ _let_1 A4)) (@ tptp.suc (@ tptp.finite_card_set_nat (@ (@ tptp.minus_2163939370556025621et_nat A4) (@ _let_1 tptp.bot_bot_set_set_nat)))))))) (forall ((A4 tptp.set_complex) (X tptp.complex)) (let ((_let_1 (@ tptp.insert_complex X))) (=> (@ tptp.finite3207457112153483333omplex A4) (= (@ tptp.finite_card_complex (@ _let_1 A4)) (@ tptp.suc (@ tptp.finite_card_complex (@ (@ tptp.minus_811609699411566653omplex A4) (@ _let_1 tptp.bot_bot_set_complex)))))))) (forall ((A4 tptp.set_int) (X tptp.int)) (let ((_let_1 (@ tptp.insert_int X))) (=> (@ tptp.finite_finite_int A4) (= (@ tptp.finite_card_int (@ _let_1 A4)) (@ tptp.suc (@ tptp.finite_card_int (@ (@ tptp.minus_minus_set_int A4) (@ _let_1 tptp.bot_bot_set_int)))))))) (forall ((A4 tptp.set_real) (X tptp.real)) (let ((_let_1 (@ tptp.insert_real X))) (=> (@ tptp.finite_finite_real A4) (= (@ tptp.finite_card_real (@ _let_1 A4)) (@ tptp.suc (@ tptp.finite_card_real (@ (@ tptp.minus_minus_set_real A4) (@ _let_1 tptp.bot_bot_set_real)))))))) (forall ((A4 tptp.set_Pr1261947904930325089at_nat) (X tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.insert8211810215607154385at_nat X))) (=> (@ tptp.finite6177210948735845034at_nat A4) (= (@ tptp.finite711546835091564841at_nat (@ _let_1 A4)) (@ tptp.suc (@ tptp.finite711546835091564841at_nat (@ (@ tptp.minus_1356011639430497352at_nat A4) (@ _let_1 tptp.bot_bo2099793752762293965at_nat)))))))) (forall ((A4 tptp.set_nat) (X tptp.nat)) (let ((_let_1 (@ tptp.insert_nat X))) (=> (@ tptp.finite_finite_nat A4) (= (@ tptp.finite_card_nat (@ _let_1 A4)) (@ tptp.suc (@ tptp.finite_card_nat (@ (@ tptp.minus_minus_set_nat A4) (@ _let_1 tptp.bot_bot_set_nat)))))))) (forall ((A4 tptp.set_list_nat) (X tptp.list_nat)) (=> (@ tptp.finite8100373058378681591st_nat A4) (=> (@ (@ tptp.member_list_nat X) A4) (= (@ tptp.suc (@ tptp.finite_card_list_nat (@ (@ tptp.minus_7954133019191499631st_nat A4) (@ (@ tptp.insert_list_nat X) tptp.bot_bot_set_list_nat)))) (@ tptp.finite_card_list_nat A4))))) (forall ((A4 tptp.set_set_nat) (X tptp.set_nat)) (=> (@ tptp.finite1152437895449049373et_nat A4) (=> (@ (@ tptp.member_set_nat X) A4) (= (@ tptp.suc (@ tptp.finite_card_set_nat (@ (@ tptp.minus_2163939370556025621et_nat A4) (@ (@ tptp.insert_set_nat X) tptp.bot_bot_set_set_nat)))) (@ tptp.finite_card_set_nat A4))))) (forall ((A4 tptp.set_complex) (X tptp.complex)) (=> (@ tptp.finite3207457112153483333omplex A4) (=> (@ (@ tptp.member_complex X) A4) (= (@ tptp.suc (@ tptp.finite_card_complex (@ (@ tptp.minus_811609699411566653omplex A4) (@ (@ tptp.insert_complex X) tptp.bot_bot_set_complex)))) (@ tptp.finite_card_complex A4))))) (forall ((A4 tptp.set_int) (X tptp.int)) (=> (@ tptp.finite_finite_int A4) (=> (@ (@ tptp.member_int X) A4) (= (@ tptp.suc (@ tptp.finite_card_int (@ (@ tptp.minus_minus_set_int A4) (@ (@ tptp.insert_int X) tptp.bot_bot_set_int)))) (@ tptp.finite_card_int A4))))) (forall ((A4 tptp.set_real) (X tptp.real)) (=> (@ tptp.finite_finite_real A4) (=> (@ (@ tptp.member_real X) A4) (= (@ tptp.suc (@ tptp.finite_card_real (@ (@ tptp.minus_minus_set_real A4) (@ (@ tptp.insert_real X) tptp.bot_bot_set_real)))) (@ tptp.finite_card_real A4))))) (forall ((A4 tptp.set_Pr1261947904930325089at_nat) (X tptp.product_prod_nat_nat)) (=> (@ tptp.finite6177210948735845034at_nat A4) (=> (@ (@ tptp.member8440522571783428010at_nat X) A4) (= (@ tptp.suc (@ tptp.finite711546835091564841at_nat (@ (@ tptp.minus_1356011639430497352at_nat A4) (@ (@ tptp.insert8211810215607154385at_nat X) tptp.bot_bo2099793752762293965at_nat)))) (@ tptp.finite711546835091564841at_nat A4))))) (forall ((A4 tptp.set_nat) (X tptp.nat)) (=> (@ tptp.finite_finite_nat A4) (=> (@ (@ tptp.member_nat X) A4) (= (@ tptp.suc (@ tptp.finite_card_nat (@ (@ tptp.minus_minus_set_nat A4) (@ (@ tptp.insert_nat X) tptp.bot_bot_set_nat)))) (@ tptp.finite_card_nat A4))))) (forall ((A tptp.real) (B tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real A) N)) (@ (@ tptp.power_power_real B) N)))))) (forall ((A tptp.rat) (B tptp.rat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat A) N)) (@ (@ tptp.power_power_rat B) N)))))) (forall ((A tptp.nat) (B tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat A) N)) (@ (@ tptp.power_power_nat B) N)))))) (forall ((A tptp.int) (B tptp.int) (N tptp.nat)) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int A) N)) (@ (@ tptp.power_power_int B) N)))))) (= tptp.power_8256067586552552935nteger (lambda ((P5 tptp.code_integer) (M6 tptp.nat)) (@ (@ (@ tptp.if_Code_integer (= M6 tptp.zero_zero_nat)) tptp.one_one_Code_integer) (@ (@ tptp.times_3573771949741848930nteger P5) (@ (@ tptp.power_8256067586552552935nteger P5) (@ (@ tptp.minus_minus_nat M6) tptp.one_one_nat)))))) (= tptp.power_power_complex (lambda ((P5 tptp.complex) (M6 tptp.nat)) (@ (@ (@ tptp.if_complex (= M6 tptp.zero_zero_nat)) tptp.one_one_complex) (@ (@ tptp.times_times_complex P5) (@ (@ tptp.power_power_complex P5) (@ (@ tptp.minus_minus_nat M6) tptp.one_one_nat)))))) (= tptp.power_power_real (lambda ((P5 tptp.real) (M6 tptp.nat)) (@ (@ (@ tptp.if_real (= M6 tptp.zero_zero_nat)) tptp.one_one_real) (@ (@ tptp.times_times_real P5) (@ (@ tptp.power_power_real P5) (@ (@ tptp.minus_minus_nat M6) tptp.one_one_nat)))))) (= tptp.power_power_rat (lambda ((P5 tptp.rat) (M6 tptp.nat)) (@ (@ (@ tptp.if_rat (= M6 tptp.zero_zero_nat)) tptp.one_one_rat) (@ (@ tptp.times_times_rat P5) (@ (@ tptp.power_power_rat P5) (@ (@ tptp.minus_minus_nat M6) tptp.one_one_nat)))))) (= tptp.power_power_nat (lambda ((P5 tptp.nat) (M6 tptp.nat)) (@ (@ (@ tptp.if_nat (= M6 tptp.zero_zero_nat)) tptp.one_one_nat) (@ (@ tptp.times_times_nat P5) (@ (@ tptp.power_power_nat P5) (@ (@ tptp.minus_minus_nat M6) tptp.one_one_nat)))))) (= tptp.power_power_int (lambda ((P5 tptp.int) (M6 tptp.nat)) (@ (@ (@ tptp.if_int (= M6 tptp.zero_zero_nat)) tptp.one_one_int) (@ (@ tptp.times_times_int P5) (@ (@ tptp.power_power_int P5) (@ (@ tptp.minus_minus_nat M6) tptp.one_one_nat)))))) (forall ((N tptp.nat) (A tptp.complex)) (let ((_let_1 (@ tptp.power_power_complex A))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.times_times_complex (@ _let_1 (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat))) A) (@ _let_1 N))))) (forall ((N tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.times_times_real (@ _let_1 (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat))) A) (@ _let_1 N))))) (forall ((N tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat A))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.times_times_rat (@ _let_1 (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat))) A) (@ _let_1 N))))) (forall ((N tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.times_times_nat (@ _let_1 (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat))) A) (@ _let_1 N))))) (forall ((N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.times_times_int (@ _let_1 (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat))) A) (@ _let_1 N))))) (forall ((X tptp.code_integer) (Xs2 tptp.list_Code_integer) (Y tptp.code_integer) (Ys tptp.list_Code_integer) (R3 tptp.set_Pr4811707699266497531nteger)) (let ((_let_1 (@ tptp.lex_Code_integer R3))) (= (@ (@ tptp.member749217712838834276nteger (@ (@ tptp.produc750622340256944499nteger (@ (@ tptp.cons_Code_integer X) Xs2)) (@ (@ tptp.cons_Code_integer Y) Ys))) _let_1) (or (and (@ (@ tptp.member157494554546826820nteger (@ (@ tptp.produc1086072967326762835nteger X) Y)) R3) (= (@ tptp.size_s3445333598471063425nteger Xs2) (@ tptp.size_s3445333598471063425nteger Ys))) (and (= X Y) (@ (@ tptp.member749217712838834276nteger (@ (@ tptp.produc750622340256944499nteger Xs2) Ys)) _let_1)))))) (forall ((X tptp.product_prod_nat_nat) (Xs2 tptp.list_P6011104703257516679at_nat) (Y tptp.product_prod_nat_nat) (Ys tptp.list_P6011104703257516679at_nat) (R3 tptp.set_Pr8693737435421807431at_nat)) (let ((_let_1 (@ tptp.lex_Pr8571645452597969515at_nat R3))) (= (@ (@ tptp.member6693912407220327184at_nat (@ (@ tptp.produc5943733680697469783at_nat (@ (@ tptp.cons_P6512896166579812791at_nat X) Xs2)) (@ (@ tptp.cons_P6512896166579812791at_nat Y) Ys))) _let_1) (or (and (@ (@ tptp.member8206827879206165904at_nat (@ (@ tptp.produc6161850002892822231at_nat X) Y)) R3) (= (@ tptp.size_s5460976970255530739at_nat Xs2) (@ tptp.size_s5460976970255530739at_nat Ys))) (and (= X Y) (@ (@ tptp.member6693912407220327184at_nat (@ (@ tptp.produc5943733680697469783at_nat Xs2) Ys)) _let_1)))))) (forall ((X tptp.set_Pr1261947904930325089at_nat) (Xs2 tptp.list_s1210847774152347623at_nat) (Y tptp.set_Pr1261947904930325089at_nat) (Ys tptp.list_s1210847774152347623at_nat) (R3 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.lex_se2245640040323279819at_nat R3))) (= (@ (@ tptp.member4080735728053443344at_nat (@ (@ tptp.produc7536900900485677911at_nat (@ (@ tptp.cons_s6881495754146722583at_nat X) Xs2)) (@ (@ tptp.cons_s6881495754146722583at_nat Y) Ys))) _let_1) (or (and (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat X) Y)) R3) (= (@ tptp.size_s8736152011456118867at_nat Xs2) (@ tptp.size_s8736152011456118867at_nat Ys))) (and (= X Y) (@ (@ tptp.member4080735728053443344at_nat (@ (@ tptp.produc7536900900485677911at_nat Xs2) Ys)) _let_1)))))) (forall ((X tptp.vEBT_VEBT) (Xs2 tptp.list_VEBT_VEBT) (Y tptp.vEBT_VEBT) (Ys tptp.list_VEBT_VEBT) (R3 tptp.set_Pr6192946355708809607T_VEBT)) (let ((_let_1 (@ tptp.lex_VEBT_VEBT R3))) (= (@ (@ tptp.member4439316823752958928T_VEBT (@ (@ tptp.produc3897820843166775703T_VEBT (@ (@ tptp.cons_VEBT_VEBT X) Xs2)) (@ (@ tptp.cons_VEBT_VEBT Y) Ys))) _let_1) (or (and (@ (@ tptp.member568628332442017744T_VEBT (@ (@ tptp.produc537772716801021591T_VEBT X) Y)) R3) (= (@ tptp.size_s6755466524823107622T_VEBT Xs2) (@ tptp.size_s6755466524823107622T_VEBT Ys))) (and (= X Y) (@ (@ tptp.member4439316823752958928T_VEBT (@ (@ tptp.produc3897820843166775703T_VEBT Xs2) Ys)) _let_1)))))) (forall ((X Bool) (Xs2 tptp.list_o) (Y Bool) (Ys tptp.list_o) (R3 tptp.set_Product_prod_o_o)) (let ((_let_1 (@ tptp.lex_o R3))) (= (@ (@ tptp.member4159035015898711888list_o (@ (@ tptp.produc8435520187683070743list_o (@ (@ tptp.cons_o X) Xs2)) (@ (@ tptp.cons_o Y) Ys))) _let_1) (or (and (@ (@ tptp.member7466972457876170832od_o_o (@ (@ tptp.product_Pair_o_o X) Y)) R3) (= (@ tptp.size_size_list_o Xs2) (@ tptp.size_size_list_o Ys))) (and (= X Y) (@ (@ tptp.member4159035015898711888list_o (@ (@ tptp.produc8435520187683070743list_o Xs2) Ys)) _let_1)))))) (forall ((X tptp.nat) (Xs2 tptp.list_nat) (Y tptp.nat) (Ys tptp.list_nat) (R3 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.lex_nat R3))) (= (@ (@ tptp.member7340969449405702474st_nat (@ (@ tptp.produc2694037385005941721st_nat (@ (@ tptp.cons_nat X) Xs2)) (@ (@ tptp.cons_nat Y) Ys))) _let_1) (or (and (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X) Y)) R3) (= (@ tptp.size_size_list_nat Xs2) (@ tptp.size_size_list_nat Ys))) (and (= X Y) (@ (@ tptp.member7340969449405702474st_nat (@ (@ tptp.produc2694037385005941721st_nat Xs2) Ys)) _let_1)))))) (forall ((X tptp.int) (Xs2 tptp.list_int) (Y tptp.int) (Ys tptp.list_int) (R3 tptp.set_Pr958786334691620121nt_int)) (let ((_let_1 (@ tptp.lex_int R3))) (= (@ (@ tptp.member6698963635872716290st_int (@ (@ tptp.produc364263696895485585st_int (@ (@ tptp.cons_int X) Xs2)) (@ (@ tptp.cons_int Y) Ys))) _let_1) (or (and (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X) Y)) R3) (= (@ tptp.size_size_list_int Xs2) (@ tptp.size_size_list_int Ys))) (and (= X Y) (@ (@ tptp.member6698963635872716290st_int (@ (@ tptp.produc364263696895485585st_int Xs2) Ys)) _let_1)))))) (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 ((X3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) X3) (= (@ (@ tptp.power_power_real X3) N) A) (forall ((Y6 tptp.real)) (=> (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y6) (= (@ (@ tptp.power_power_real Y6) N) A)) (= Y6 X3)))))))) (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 ((R4 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) R4) (= (@ (@ tptp.power_power_real R4) N) A)))))) (and (= tptp.sa (@ (@ (@ (@ tptp.vEBT_Node tptp.info) tptp.deg) tptp.treeList) tptp.summary)) _let_314 (= (@ tptp.size_s6755466524823107622T_VEBT tptp.treeList) _let_313) (@ (@ tptp.vEBT_invar_vebt tptp.summary) tptp.m) (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 tptp.treeList)) (@ (@ tptp.vEBT_invar_vebt X5) tptp.na)))) (forall ((Xs2 tptp.list_Code_integer) (Ys tptp.list_Code_integer) (R3 tptp.set_Pr4811707699266497531nteger)) (= (@ (@ tptp.member749217712838834276nteger (@ (@ tptp.produc750622340256944499nteger Xs2) Ys)) (@ tptp.listre5734910445319291053nteger R3)) (and (= (@ tptp.size_s3445333598471063425nteger Xs2) (@ tptp.size_s3445333598471063425nteger Ys)) (forall ((N4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N4) (@ tptp.size_s3445333598471063425nteger Xs2)) (@ (@ tptp.member157494554546826820nteger (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.nth_Code_integer Xs2) N4)) (@ (@ tptp.nth_Code_integer Ys) N4))) R3)))))) (forall ((Xs2 tptp.list_VEBT_VEBT) (Ys tptp.list_VEBT_VEBT) (R3 tptp.set_Pr6192946355708809607T_VEBT)) (= (@ (@ tptp.member4439316823752958928T_VEBT (@ (@ tptp.produc3897820843166775703T_VEBT Xs2) Ys)) (@ tptp.listre1230615542750757617T_VEBT R3)) (and (= (@ tptp.size_s6755466524823107622T_VEBT Xs2) (@ tptp.size_s6755466524823107622T_VEBT Ys)) (forall ((N4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N4) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (@ (@ tptp.member568628332442017744T_VEBT (@ (@ tptp.produc537772716801021591T_VEBT (@ (@ tptp.nth_VEBT_VEBT Xs2) N4)) (@ (@ tptp.nth_VEBT_VEBT Ys) N4))) R3)))))) (forall ((Xs2 tptp.list_VEBT_VEBT) (Ys tptp.list_o) (R3 tptp.set_Pr3175402225741728619VEBT_o)) (= (@ (@ tptp.member3126162362653435956list_o (@ (@ tptp.produc2717590391345394939list_o Xs2) Ys)) (@ tptp.listrel_VEBT_VEBT_o R3)) (and (= (@ tptp.size_s6755466524823107622T_VEBT Xs2) (@ tptp.size_size_list_o Ys)) (forall ((N4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N4) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (@ (@ tptp.member3307348790968139188VEBT_o (@ (@ tptp.produc8721562602347293563VEBT_o (@ (@ tptp.nth_VEBT_VEBT Xs2) N4)) (@ (@ tptp.nth_o Ys) N4))) R3)))))) (forall ((Xs2 tptp.list_VEBT_VEBT) (Ys tptp.list_nat) (R3 tptp.set_Pr7556676689462069481BT_nat)) (= (@ (@ tptp.member6193324644334088288st_nat (@ (@ tptp.produc5570133714943300547st_nat Xs2) Ys)) (@ tptp.listre5900670229112895443BT_nat R3)) (and (= (@ tptp.size_s6755466524823107622T_VEBT Xs2) (@ tptp.size_size_list_nat Ys)) (forall ((N4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N4) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (@ (@ tptp.member373505688050248522BT_nat (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.nth_VEBT_VEBT Xs2) N4)) (@ (@ tptp.nth_nat Ys) N4))) R3)))))) (forall ((Xs2 tptp.list_VEBT_VEBT) (Ys tptp.list_int) (R3 tptp.set_Pr5066593544530342725BT_int)) (= (@ (@ tptp.member3703241499402361532st_int (@ (@ tptp.produc1392282695434103839st_int Xs2) Ys)) (@ tptp.listre5898179758603845167BT_int R3)) (and (= (@ tptp.size_s6755466524823107622T_VEBT Xs2) (@ tptp.size_size_list_int Ys)) (forall ((N4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N4) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (@ (@ tptp.member5419026705395827622BT_int (@ (@ tptp.produc736041933913180425BT_int (@ (@ 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tptp.member7466972457876170832od_o_o (@ (@ tptp.product_Pair_o_o (@ (@ tptp.nth_o Xs2) N4)) (@ (@ tptp.nth_o Ys) N4))) R3)))))) (forall ((Xs2 tptp.list_o) (Ys tptp.list_nat) (R3 tptp.set_Pr2101469702781467981_o_nat)) (= (@ (@ tptp.member1519744053835550788st_nat (@ (@ tptp.produc7128876500814652583st_nat Xs2) Ys)) (@ tptp.listrel_o_nat R3)) (and (= (@ tptp.size_size_list_o Xs2) (@ tptp.size_size_list_nat Ys)) (forall ((N4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N4) (@ tptp.size_size_list_o Xs2)) (@ (@ tptp.member2802428098988154798_o_nat (@ (@ tptp.product_Pair_o_nat (@ (@ tptp.nth_o Xs2) N4)) (@ (@ tptp.nth_nat Ys) N4))) R3)))))) (forall ((Xs2 tptp.list_o) (Ys tptp.list_int) (R3 tptp.set_Pr8834758594704517033_o_int)) (= (@ (@ tptp.member8253032945758599840st_int (@ (@ tptp.produc2951025481305455875st_int Xs2) Ys)) (@ tptp.listrel_o_int R3)) (and (= (@ tptp.size_size_list_o Xs2) (@ tptp.size_size_list_int Ys)) (forall ((N4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N4) (@ tptp.size_size_list_o Xs2)) (@ (@ tptp.member7847949116333733898_o_int (@ (@ tptp.product_Pair_o_int (@ (@ tptp.nth_o Xs2) N4)) (@ (@ tptp.nth_int Ys) N4))) R3)))))) (forall ((Xs2 tptp.list_nat) (Ys tptp.list_VEBT_VEBT) (R3 tptp.set_Pr6167073792073659919T_VEBT)) (= (@ (@ tptp.member5968030670617646438T_VEBT (@ (@ tptp.produc8335345208264861441T_VEBT Xs2) Ys)) (@ tptp.listre5761932458788874033T_VEBT R3)) (and (= (@ tptp.size_size_list_nat Xs2) (@ tptp.size_s6755466524823107622T_VEBT Ys)) (forall ((N4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N4) (@ tptp.size_size_list_nat Xs2)) (@ (@ tptp.member8549952807677709168T_VEBT (@ (@ tptp.produc599794634098209291T_VEBT (@ (@ tptp.nth_nat Xs2) N4)) (@ (@ tptp.nth_VEBT_VEBT Ys) N4))) R3)))))) (forall ((X tptp.code_integer) (Y tptp.code_integer) (F2 (-> tptp.code_integer tptp.nat)) (Fs tptp.list_C4705013386053401436er_nat)) (let ((_let_1 (@ tptp.member157494554546826820nteger (@ (@ tptp.produc1086072967326762835nteger X) Y)))) (let ((_let_2 (@ F2 Y))) (let ((_let_3 (@ F2 X))) (= (@ _let_1 (@ tptp.measur8870801148506250077nteger (@ (@ tptp.cons_C1897838848541180310er_nat F2) Fs))) (or (@ (@ tptp.ord_less_nat _let_3) _let_2) (and (= _let_3 _let_2) (@ _let_1 (@ tptp.measur8870801148506250077nteger Fs))))))))) (forall ((X tptp.product_prod_nat_nat) (Y tptp.product_prod_nat_nat) (F2 (-> tptp.product_prod_nat_nat tptp.nat)) (Fs tptp.list_P9162950289778280392at_nat)) (let ((_let_1 (@ tptp.member8206827879206165904at_nat (@ (@ tptp.produc6161850002892822231at_nat X) Y)))) (let ((_let_2 (@ F2 Y))) (let ((_let_3 (@ F2 X))) (= (@ _let_1 (@ tptp.measur2679027848233739777at_nat (@ (@ tptp.cons_P4861729644591583992at_nat F2) Fs))) (or (@ (@ tptp.ord_less_nat _let_3) _let_2) (and (= _let_3 _let_2) (@ _let_1 (@ tptp.measur2679027848233739777at_nat Fs))))))))) (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat) (F2 (-> tptp.set_Pr1261947904930325089at_nat tptp.nat)) (Fs tptp.list_s9130966667114977576at_nat)) (let ((_let_1 (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat X) Y)))) (let ((_let_2 (@ F2 Y))) (let ((_let_3 (@ F2 X))) (= (@ _let_1 (@ tptp.measur2694323259624372065at_nat (@ (@ tptp.cons_s2538900923071588440at_nat F2) Fs))) (or (@ (@ tptp.ord_less_nat _let_3) _let_2) (and (= _let_3 _let_2) (@ _let_1 (@ tptp.measur2694323259624372065at_nat Fs))))))))) (forall ((X tptp.nat) (Y tptp.nat) (F2 (-> tptp.nat tptp.nat)) (Fs tptp.list_nat_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X) Y)))) (let ((_let_2 (@ F2 Y))) (let ((_let_3 (@ F2 X))) (= (@ _let_1 (@ tptp.measures_nat (@ (@ tptp.cons_nat_nat F2) Fs))) (or (@ (@ tptp.ord_less_nat _let_3) _let_2) (and (= _let_3 _let_2) (@ _let_1 (@ tptp.measures_nat Fs))))))))) (forall ((X tptp.int) (Y tptp.int) (F2 (-> tptp.int tptp.nat)) (Fs tptp.list_int_nat)) (let ((_let_1 (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X) Y)))) (let ((_let_2 (@ F2 Y))) (let ((_let_3 (@ F2 X))) (= (@ _let_1 (@ tptp.measures_int (@ (@ tptp.cons_int_nat F2) Fs))) (or (@ (@ tptp.ord_less_nat _let_3) _let_2) (and (= _let_3 _let_2) (@ _let_1 (@ tptp.measures_int Fs))))))))) (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)))) (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)))) (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)))) (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))))) (not (forall ((TreeList3 tptp.list_VEBT_VEBT) (Summary3 tptp.vEBT_VEBT) (Info tptp.option4927543243414619207at_nat)) (not (and (= tptp.sa (@ (@ (@ (@ tptp.vEBT_Node Info) tptp.deg) TreeList3) Summary3)) (= tptp.deg (@ (@ tptp.plus_plus_nat tptp.na) tptp.m)) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.m)) (@ (@ tptp.vEBT_invar_vebt Summary3) tptp.m) (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 TreeList3)) (@ (@ tptp.vEBT_invar_vebt X5) tptp.na))))))) (forall ((I2 tptp.nat) (N tptp.nat) (P2 (-> tptp.nat Bool)) (X tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) N) (=> (@ P2 X) (@ P2 (@ (@ tptp.nth_nat (@ (@ tptp.replicate_nat N) X)) I2))))) (forall ((I2 tptp.nat) (N tptp.nat) (P2 (-> tptp.vEBT_VEBT Bool)) (X tptp.vEBT_VEBT)) (=> (@ (@ tptp.ord_less_nat I2) N) (=> (@ P2 X) (@ P2 (@ (@ tptp.nth_VEBT_VEBT (@ (@ tptp.replicate_VEBT_VEBT N) X)) I2))))) (forall ((M2 tptp.num) (N tptp.num)) (= (= (@ tptp.numera1916890842035813515d_enat M2) (@ tptp.numera1916890842035813515d_enat N)) (= M2 N))) (forall ((M2 tptp.num) (N tptp.num)) (= (= (@ tptp.numera6690914467698888265omplex M2) (@ tptp.numera6690914467698888265omplex N)) (= M2 N))) (forall ((M2 tptp.num) (N tptp.num)) (= (= (@ tptp.numeral_numeral_real M2) (@ tptp.numeral_numeral_real N)) (= M2 N))) (forall ((M2 tptp.num) (N tptp.num)) (= (= (@ tptp.numeral_numeral_nat M2) (@ tptp.numeral_numeral_nat N)) (= M2 N))) (forall ((M2 tptp.num) (N tptp.num)) (= (= (@ tptp.numeral_numeral_int M2) (@ tptp.numeral_numeral_int N)) (= M2 N))) (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_num (@ tptp.bit0 M2)) (@ tptp.bit0 N)) (@ tptp.bit0 (@ tptp.bit0 (@ (@ tptp.times_times_num M2) N))))) (forall ((M2 tptp.num)) (= (@ (@ tptp.times_times_num M2) tptp.one) M2)) (forall ((N tptp.num)) (= (@ (@ tptp.times_times_num tptp.one) N) N)) (@ (@ tptp.ord_less_nat tptp.ma) (@ _let_262 tptp.deg)) (= (@ tptp.size_s6755466524823107622T_VEBT tptp.treeList2) _let_313) (forall ((M2 tptp.nat) (N tptp.nat)) (= (= (@ tptp.semiri5074537144036343181t_real M2) (@ tptp.semiri5074537144036343181t_real N)) (= M2 N))) (forall ((M2 tptp.nat) (N tptp.nat)) (= (= (@ tptp.semiri1314217659103216013at_int M2) (@ tptp.semiri1314217659103216013at_int N)) (= M2 N))) (forall ((M2 tptp.nat) (N tptp.nat)) (= (= (@ tptp.semiri1316708129612266289at_nat M2) (@ tptp.semiri1316708129612266289at_nat N)) (= M2 N))) _let_312 (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.m)) (= (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT tptp.treeList2) I4)) X7)) (@ (@ tptp.vEBT_V8194947554948674370ptions tptp.summary2) I4)))) (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))))) (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_invar_vebt (@ (@ tptp.vEBT_vebt_insert T) X)) N)))) (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_le2932123472753598470d_enat (@ tptp.numera1916890842035813515d_enat M2)) (@ tptp.numera1916890842035813515d_enat N)) (@ (@ tptp.ord_less_eq_num M2) N))) (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real M2)) (@ tptp.numeral_numeral_real N)) (@ (@ tptp.ord_less_eq_num M2) N))) (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.numeral_numeral_rat M2)) (@ tptp.numeral_numeral_rat N)) (@ (@ tptp.ord_less_eq_num M2) N))) (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat M2)) (@ tptp.numeral_numeral_nat N)) (@ (@ tptp.ord_less_eq_num M2) N))) (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int M2)) (@ tptp.numeral_numeral_int N)) (@ (@ tptp.ord_less_eq_num M2) N))) (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_rat (@ tptp.numeral_numeral_rat M2)) (@ tptp.numeral_numeral_rat N)) (@ (@ tptp.ord_less_num M2) N))) (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_le72135733267957522d_enat (@ tptp.numera1916890842035813515d_enat M2)) (@ tptp.numera1916890842035813515d_enat N)) (@ (@ tptp.ord_less_num M2) N))) (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real M2)) (@ tptp.numeral_numeral_real N)) (@ (@ tptp.ord_less_num M2) N))) (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_nat (@ tptp.numeral_numeral_nat M2)) (@ tptp.numeral_numeral_nat N)) (@ (@ tptp.ord_less_num M2) N))) (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int M2)) (@ tptp.numeral_numeral_int N)) (@ (@ tptp.ord_less_num M2) N))) (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat M2)) (@ tptp.numeral_numeral_rat N)) (@ tptp.numeral_numeral_rat (@ (@ tptp.times_times_num M2) N)))) (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.times_7803423173614009249d_enat (@ tptp.numera1916890842035813515d_enat M2)) (@ tptp.numera1916890842035813515d_enat N)) (@ tptp.numera1916890842035813515d_enat (@ (@ tptp.times_times_num M2) N)))) (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex M2)) (@ tptp.numera6690914467698888265omplex N)) (@ tptp.numera6690914467698888265omplex (@ (@ tptp.times_times_num M2) N)))) (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real M2)) (@ tptp.numeral_numeral_real N)) (@ tptp.numeral_numeral_real (@ (@ tptp.times_times_num M2) N)))) (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat M2)) (@ tptp.numeral_numeral_nat N)) (@ tptp.numeral_numeral_nat (@ (@ tptp.times_times_num M2) N)))) (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int M2)) (@ tptp.numeral_numeral_int N)) (@ tptp.numeral_numeral_int (@ (@ tptp.times_times_num M2) N)))) (forall ((V2 tptp.num) (W2 tptp.num) (Z3 tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat V2)) (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat W2)) Z3)) (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat (@ (@ tptp.times_times_num V2) W2))) Z3))) (forall ((V2 tptp.num) (W2 tptp.num) (Z3 tptp.extended_enat)) (= (@ (@ tptp.times_7803423173614009249d_enat (@ tptp.numera1916890842035813515d_enat V2)) (@ (@ tptp.times_7803423173614009249d_enat (@ tptp.numera1916890842035813515d_enat W2)) Z3)) (@ (@ tptp.times_7803423173614009249d_enat (@ tptp.numera1916890842035813515d_enat (@ (@ tptp.times_times_num V2) W2))) Z3))) (forall ((V2 tptp.num) (W2 tptp.num) (Z3 tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex V2)) (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex W2)) Z3)) (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ (@ tptp.times_times_num V2) W2))) Z3))) (forall ((V2 tptp.num) (W2 tptp.num) (Z3 tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real V2)) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real W2)) Z3)) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ (@ tptp.times_times_num V2) W2))) Z3))) (forall ((V2 tptp.num) (W2 tptp.num) (Z3 tptp.nat)) (= (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat V2)) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat W2)) Z3)) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ (@ tptp.times_times_num V2) W2))) Z3))) (forall ((V2 tptp.num) (W2 tptp.num) (Z3 tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int V2)) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int W2)) Z3)) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ (@ tptp.times_times_num V2) W2))) Z3))) (forall ((V2 tptp.num) (W2 tptp.num) (Z3 tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ tptp.numeral_numeral_rat V2)) (@ (@ tptp.plus_plus_rat (@ tptp.numeral_numeral_rat W2)) Z3)) (@ (@ tptp.plus_plus_rat (@ tptp.numeral_numeral_rat (@ (@ tptp.plus_plus_num V2) W2))) Z3))) (forall ((V2 tptp.num) (W2 tptp.num) (Z3 tptp.extended_enat)) (= (@ (@ tptp.plus_p3455044024723400733d_enat (@ tptp.numera1916890842035813515d_enat V2)) (@ (@ tptp.plus_p3455044024723400733d_enat (@ tptp.numera1916890842035813515d_enat W2)) Z3)) (@ (@ tptp.plus_p3455044024723400733d_enat (@ tptp.numera1916890842035813515d_enat (@ (@ tptp.plus_plus_num V2) W2))) Z3))) (forall ((V2 tptp.num) (W2 tptp.num) (Z3 tptp.complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.numera6690914467698888265omplex V2)) (@ (@ tptp.plus_plus_complex (@ tptp.numera6690914467698888265omplex W2)) Z3)) (@ (@ tptp.plus_plus_complex (@ tptp.numera6690914467698888265omplex (@ (@ tptp.plus_plus_num V2) W2))) Z3))) (forall ((V2 tptp.num) (W2 tptp.num) (Z3 tptp.real)) (= (@ (@ tptp.plus_plus_real (@ tptp.numeral_numeral_real V2)) (@ (@ tptp.plus_plus_real (@ tptp.numeral_numeral_real W2)) Z3)) (@ (@ tptp.plus_plus_real (@ tptp.numeral_numeral_real (@ (@ tptp.plus_plus_num V2) W2))) Z3))) (forall ((V2 tptp.num) (W2 tptp.num) (Z3 tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat V2)) (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat W2)) Z3)) (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num V2) W2))) Z3))) (forall ((V2 tptp.num) (W2 tptp.num) (Z3 tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.numeral_numeral_int V2)) (@ (@ tptp.plus_plus_int (@ tptp.numeral_numeral_int W2)) Z3)) (@ (@ tptp.plus_plus_int (@ tptp.numeral_numeral_int (@ (@ tptp.plus_plus_num V2) W2))) Z3))) (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.plus_plus_rat (@ tptp.numeral_numeral_rat M2)) (@ tptp.numeral_numeral_rat N)) (@ tptp.numeral_numeral_rat (@ (@ tptp.plus_plus_num M2) N)))) (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.plus_p3455044024723400733d_enat (@ tptp.numera1916890842035813515d_enat M2)) (@ tptp.numera1916890842035813515d_enat N)) (@ tptp.numera1916890842035813515d_enat (@ (@ tptp.plus_plus_num M2) N)))) (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.plus_plus_complex (@ tptp.numera6690914467698888265omplex M2)) (@ tptp.numera6690914467698888265omplex N)) (@ tptp.numera6690914467698888265omplex (@ (@ tptp.plus_plus_num M2) N)))) (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.plus_plus_real (@ tptp.numeral_numeral_real M2)) (@ tptp.numeral_numeral_real N)) (@ tptp.numeral_numeral_real (@ (@ tptp.plus_plus_num M2) N)))) (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat M2)) (@ tptp.numeral_numeral_nat N)) (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M2) N)))) (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.plus_plus_int (@ tptp.numeral_numeral_int M2)) (@ tptp.numeral_numeral_int N)) (@ tptp.numeral_numeral_int (@ (@ tptp.plus_plus_num M2) N)))) (forall ((N tptp.num)) (= (@ (@ tptp.times_times_num (@ tptp.bit0 tptp.one)) N) (@ tptp.bit0 N))) (forall ((A tptp.nat) (M2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.power_power_nat A))) (= (@ (@ tptp.power_power_nat (@ _let_1 (@ tptp.numeral_numeral_nat M2))) (@ tptp.numeral_numeral_nat N)) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.times_times_num M2) N)))))) (forall ((A tptp.real) (M2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.power_power_real A))) (= (@ (@ tptp.power_power_real (@ _let_1 (@ tptp.numeral_numeral_nat M2))) (@ tptp.numeral_numeral_nat N)) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.times_times_num M2) N)))))) (forall ((A tptp.int) (M2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.power_power_int A))) (= (@ (@ tptp.power_power_int (@ _let_1 (@ tptp.numeral_numeral_nat M2))) (@ tptp.numeral_numeral_nat N)) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.times_times_num M2) N)))))) (forall ((A tptp.complex) (M2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.power_power_complex A))) (= (@ (@ tptp.power_power_complex (@ _let_1 (@ tptp.numeral_numeral_nat M2))) (@ tptp.numeral_numeral_nat N)) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.times_times_num M2) N)))))) (forall ((X tptp.nat) (Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList2) Summary))) (=> (or (= X Mi) (= X Ma)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Deg) (= (@ (@ tptp.vEBT_vebt_insert _let_1) X) _let_1))))) (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (= (@ tptp.some_nat M2) (@ tptp.vEBT_vebt_mint T)) (@ (@ tptp.ord_less_nat M2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))) (forall ((X tptp.real)) (= (not (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.times_times_real X) X))) (= X tptp.zero_zero_real))) (forall ((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)))) (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))))))) (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))))) (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))))) (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)))))))) (forall ((M2 tptp.nat) (X tptp.vEBT_VEBT) (N tptp.nat) (Y tptp.vEBT_VEBT)) (= (= (@ (@ tptp.replicate_VEBT_VEBT M2) X) (@ (@ tptp.replicate_VEBT_VEBT N) Y)) (and (= M2 N) (=> (not (= M2 tptp.zero_zero_nat)) (= X Y))))) (forall ((N tptp.nat) (X tptp.vEBT_VEBT)) (= (@ tptp.size_s6755466524823107622T_VEBT (@ (@ tptp.replicate_VEBT_VEBT N) X)) N)) (forall ((N tptp.nat) (X Bool)) (= (@ tptp.size_size_list_o (@ (@ tptp.replicate_o N) X)) N)) (forall ((N tptp.nat) (X tptp.nat)) (= (@ tptp.size_size_list_nat (@ (@ tptp.replicate_nat N) X)) N)) (forall ((N tptp.nat) (X tptp.int)) (= (@ tptp.size_size_list_int (@ (@ tptp.replicate_int N) X)) N)) (forall ((X tptp.nat) (Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList2) Summary))) (=> (or (@ (@ tptp.ord_less_nat X) Mi) (@ (@ tptp.ord_less_nat Ma) X)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Deg) (= (@ (@ tptp.vEBT_vebt_delete _let_1) X) _let_1))))) (forall ((X tptp.nat) (Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (=> (and (= X Mi) (= X Ma)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Deg) (= (@ (@ tptp.vEBT_vebt_delete (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList2) Summary)) X) (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Deg) TreeList2) Summary))))) (forall ((TreeList2 tptp.list_VEBT_VEBT) (N tptp.nat) (M2 tptp.nat)) (=> (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList2)) (@ (@ tptp.vEBT_invar_vebt X3) N))) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M2)) (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N)))) (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))))) (forall ((Deg tptp.nat) (Ma tptp.nat) (X tptp.nat) (Mi tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Deg) (=> (@ (@ tptp.ord_less_nat Ma) X) (= (@ (@ tptp.vEBT_vebt_pred (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList2) Summary)) X) (@ tptp.some_nat Ma))))) (forall ((Deg tptp.nat) (X tptp.nat) (Mi tptp.nat) (Ma tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Deg) (=> (@ (@ tptp.ord_less_nat X) Mi) (= (@ (@ tptp.vEBT_vebt_succ (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList2) Summary)) X) (@ tptp.some_nat Mi))))) _let_311 (forall ((V2 tptp.num) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat V2)))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat B) C2)) (@ (@ tptp.plus_plus_rat (@ _let_1 B)) (@ _let_1 C2))))) (forall ((V2 tptp.num) (B tptp.extended_enat) (C2 tptp.extended_enat)) (let ((_let_1 (@ tptp.times_7803423173614009249d_enat (@ tptp.numera1916890842035813515d_enat V2)))) (= (@ _let_1 (@ (@ tptp.plus_p3455044024723400733d_enat B) C2)) (@ (@ tptp.plus_p3455044024723400733d_enat (@ _let_1 B)) (@ _let_1 C2))))) (forall ((V2 tptp.num) (B tptp.complex) (C2 tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex V2)))) (= (@ _let_1 (@ (@ tptp.plus_plus_complex B) C2)) (@ (@ tptp.plus_plus_complex (@ _let_1 B)) (@ _let_1 C2))))) (forall ((V2 tptp.num) (B tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.times_times_real (@ tptp.numeral_numeral_real V2)))) (= (@ _let_1 (@ (@ tptp.plus_plus_real B) C2)) (@ (@ tptp.plus_plus_real (@ _let_1 B)) (@ _let_1 C2))))) (forall ((V2 tptp.num) (B tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat V2)))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat B) C2)) (@ (@ tptp.plus_plus_nat (@ _let_1 B)) (@ _let_1 C2))))) (forall ((V2 tptp.num) (B tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int (@ tptp.numeral_numeral_int V2)))) (= (@ _let_1 (@ (@ tptp.plus_plus_int B) C2)) (@ (@ tptp.plus_plus_int (@ _let_1 B)) (@ _let_1 C2))))) (forall ((A tptp.rat) (B tptp.rat) (V2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat V2))) (= (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat A) B)) _let_1) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) _let_1)) (@ (@ tptp.times_times_rat B) _let_1))))) (forall ((A tptp.extended_enat) (B tptp.extended_enat) (V2 tptp.num)) (let ((_let_1 (@ tptp.numera1916890842035813515d_enat V2))) (= (@ (@ tptp.times_7803423173614009249d_enat (@ (@ tptp.plus_p3455044024723400733d_enat A) B)) _let_1) (@ (@ tptp.plus_p3455044024723400733d_enat (@ (@ tptp.times_7803423173614009249d_enat A) _let_1)) (@ (@ tptp.times_7803423173614009249d_enat B) _let_1))))) (forall ((A tptp.complex) (B tptp.complex) (V2 tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex V2))) (= (@ (@ tptp.times_times_complex (@ (@ tptp.plus_plus_complex A) B)) _let_1) (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex A) _let_1)) (@ (@ tptp.times_times_complex B) _let_1))))) (forall ((A tptp.real) (B tptp.real) (V2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real V2))) (= (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real A) B)) _let_1) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) _let_1)) (@ (@ tptp.times_times_real B) _let_1))))) (forall ((A tptp.nat) (B tptp.nat) (V2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat V2))) (= (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat A) B)) _let_1) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat A) _let_1)) (@ (@ tptp.times_times_nat B) _let_1))))) (forall ((A tptp.int) (B tptp.int) (V2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int V2))) (= (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int A) B)) _let_1) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) _let_1)) (@ (@ tptp.times_times_int B) _let_1))))) (forall ((N tptp.num)) (= (= (@ tptp.numera6620942414471956472nteger N) tptp.one_one_Code_integer) (= N tptp.one))) (forall ((N tptp.num)) (= (= (@ tptp.numera1916890842035813515d_enat N) tptp.one_on7984719198319812577d_enat) (= N tptp.one))) (forall ((N tptp.num)) (= (= (@ tptp.numera6690914467698888265omplex N) tptp.one_one_complex) (= N tptp.one))) (forall ((N tptp.num)) (= (= (@ tptp.numeral_numeral_real N) tptp.one_one_real) (= N tptp.one))) (forall ((N tptp.num)) (= (= (@ tptp.numeral_numeral_nat N) tptp.one_one_nat) (= N tptp.one))) (forall ((N tptp.num)) (= (= (@ tptp.numeral_numeral_int N) tptp.one_one_int) (= N tptp.one))) (forall ((N tptp.num)) (= (= tptp.one_one_Code_integer (@ tptp.numera6620942414471956472nteger N)) (= tptp.one N))) (forall ((N tptp.num)) (= (= tptp.one_on7984719198319812577d_enat (@ tptp.numera1916890842035813515d_enat N)) (= tptp.one N))) (forall ((N tptp.num)) (= (= tptp.one_one_complex (@ tptp.numera6690914467698888265omplex N)) (= tptp.one N))) (forall ((N tptp.num)) (= (= tptp.one_one_real (@ tptp.numeral_numeral_real N)) (= tptp.one N))) (forall ((N tptp.num)) (= (= tptp.one_one_nat (@ tptp.numeral_numeral_nat N)) (= tptp.one N))) (forall ((N tptp.num)) (= (= tptp.one_one_int (@ tptp.numeral_numeral_int N)) (= tptp.one N))) (forall ((A tptp.rat) (B tptp.rat) (V2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat V2))) (= (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat A) B)) _let_1) (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat A) _let_1)) (@ (@ tptp.times_times_rat B) _let_1))))) (forall ((A tptp.complex) (B tptp.complex) (V2 tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex V2))) (= (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex A) B)) _let_1) (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex A) _let_1)) (@ (@ tptp.times_times_complex B) _let_1))))) (forall ((A tptp.real) (B tptp.real) (V2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real V2))) (= (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real A) B)) _let_1) (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real A) _let_1)) (@ (@ tptp.times_times_real B) _let_1))))) (forall ((A tptp.int) (B tptp.int) (V2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int V2))) (= (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int A) B)) _let_1) (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int A) _let_1)) (@ (@ tptp.times_times_int B) _let_1))))) (forall ((V2 tptp.num) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat V2)))) (= (@ _let_1 (@ (@ tptp.minus_minus_rat B) C2)) (@ (@ tptp.minus_minus_rat (@ _let_1 B)) (@ _let_1 C2))))) (forall ((V2 tptp.num) (B tptp.complex) (C2 tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex V2)))) (= (@ _let_1 (@ (@ tptp.minus_minus_complex B) C2)) (@ (@ tptp.minus_minus_complex (@ _let_1 B)) (@ _let_1 C2))))) (forall ((V2 tptp.num) (B tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.times_times_real (@ tptp.numeral_numeral_real V2)))) (= (@ _let_1 (@ (@ tptp.minus_minus_real B) C2)) (@ (@ tptp.minus_minus_real (@ _let_1 B)) (@ _let_1 C2))))) (forall ((V2 tptp.num) (B tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int (@ tptp.numeral_numeral_int V2)))) (= (@ _let_1 (@ (@ tptp.minus_minus_int B) C2)) (@ (@ tptp.minus_minus_int (@ _let_1 B)) (@ _let_1 C2))))) (forall ((K2 tptp.num)) (= (@ (@ tptp.power_power_rat tptp.zero_zero_rat) (@ tptp.numeral_numeral_nat K2)) tptp.zero_zero_rat)) (forall ((K2 tptp.num)) (= (@ (@ tptp.power_power_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat K2)) tptp.zero_zero_nat)) (forall ((K2 tptp.num)) (= (@ (@ tptp.power_power_real tptp.zero_zero_real) (@ tptp.numeral_numeral_nat K2)) tptp.zero_zero_real)) (forall ((K2 tptp.num)) (= (@ (@ tptp.power_power_int tptp.zero_zero_int) (@ tptp.numeral_numeral_nat K2)) tptp.zero_zero_int)) (forall ((K2 tptp.num)) (= (@ (@ tptp.power_power_complex tptp.zero_zero_complex) (@ tptp.numeral_numeral_nat K2)) tptp.zero_zero_complex)) (forall ((N tptp.num)) (= (@ tptp.suc (@ tptp.numeral_numeral_nat N)) (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num N) tptp.one)))) (forall ((A tptp.complex) (M2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.power_power_complex A))) (= (@ (@ tptp.times_times_complex (@ _let_1 (@ tptp.numeral_numeral_nat M2))) (@ _let_1 (@ tptp.numeral_numeral_nat N))) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M2) N)))))) (forall ((A tptp.real) (M2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.power_power_real A))) (= (@ (@ tptp.times_times_real (@ _let_1 (@ tptp.numeral_numeral_nat M2))) (@ _let_1 (@ tptp.numeral_numeral_nat N))) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M2) N)))))) (forall ((A tptp.rat) (M2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.power_power_rat A))) (= (@ (@ tptp.times_times_rat (@ _let_1 (@ tptp.numeral_numeral_nat M2))) (@ _let_1 (@ tptp.numeral_numeral_nat N))) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M2) N)))))) (forall ((A tptp.nat) (M2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.power_power_nat A))) (= (@ (@ tptp.times_times_nat (@ _let_1 (@ tptp.numeral_numeral_nat M2))) (@ _let_1 (@ tptp.numeral_numeral_nat N))) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M2) N)))))) (forall ((A tptp.int) (M2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.power_power_int A))) (= (@ (@ tptp.times_times_int (@ _let_1 (@ tptp.numeral_numeral_nat M2))) (@ _let_1 (@ tptp.numeral_numeral_nat N))) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M2) N)))))) (forall ((A tptp.complex) (M2 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 M2))) (@ (@ 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 M2) N)))) B)))) (forall ((A tptp.real) (M2 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 M2))) (@ (@ 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 M2) N)))) B)))) (forall ((A tptp.rat) (M2 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 M2))) (@ (@ 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 M2) N)))) B)))) (forall ((A tptp.nat) (M2 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 M2))) (@ (@ 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 M2) N)))) B)))) (forall ((A tptp.int) (M2 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 M2))) (@ (@ 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 M2) N)))) B)))) (forall ((M2 tptp.nat)) (= (= (@ tptp.semiri8010041392384452111omplex M2) tptp.zero_zero_complex) (= M2 tptp.zero_zero_nat))) (forall ((M2 tptp.nat)) (= (= (@ tptp.semiri681578069525770553at_rat M2) tptp.zero_zero_rat) (= M2 tptp.zero_zero_nat))) (forall ((M2 tptp.nat)) (= (= (@ tptp.semiri5074537144036343181t_real M2) tptp.zero_zero_real) (= M2 tptp.zero_zero_nat))) (forall ((M2 tptp.nat)) (= (= (@ tptp.semiri1314217659103216013at_int M2) tptp.zero_zero_int) (= M2 tptp.zero_zero_nat))) (forall ((M2 tptp.nat)) (= (= (@ tptp.semiri1316708129612266289at_nat M2) tptp.zero_zero_nat) (= M2 tptp.zero_zero_nat))) (forall ((N tptp.nat)) (= (= tptp.zero_zero_complex (@ tptp.semiri8010041392384452111omplex N)) (= tptp.zero_zero_nat N))) (forall ((N tptp.nat)) (= (= tptp.zero_zero_rat (@ tptp.semiri681578069525770553at_rat N)) (= tptp.zero_zero_nat N))) (forall ((N tptp.nat)) (= (= tptp.zero_zero_real (@ tptp.semiri5074537144036343181t_real N)) (= tptp.zero_zero_nat N))) (forall ((N tptp.nat)) (= (= tptp.zero_zero_int (@ tptp.semiri1314217659103216013at_int N)) (= tptp.zero_zero_nat N))) (forall ((N tptp.nat)) (= (= tptp.zero_zero_nat (@ tptp.semiri1316708129612266289at_nat N)) (= tptp.zero_zero_nat N))) (= (@ tptp.semiri8010041392384452111omplex tptp.zero_zero_nat) tptp.zero_zero_complex) (= (@ tptp.semiri681578069525770553at_rat tptp.zero_zero_nat) tptp.zero_zero_rat) (= (@ tptp.semiri5074537144036343181t_real tptp.zero_zero_nat) tptp.zero_zero_real) _let_291 (= (@ tptp.semiri1316708129612266289at_nat tptp.zero_zero_nat) tptp.zero_zero_nat) (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_rat (@ tptp.semiri681578069525770553at_rat M2)) (@ tptp.semiri681578069525770553at_rat N)) (@ (@ tptp.ord_less_nat M2) N))) (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real M2)) (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.ord_less_nat M2) N))) (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int M2)) (@ tptp.semiri1314217659103216013at_int N)) (@ (@ tptp.ord_less_nat M2) N))) (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.semiri1316708129612266289at_nat M2)) (@ tptp.semiri1316708129612266289at_nat N)) (@ (@ tptp.ord_less_nat M2) N))) (forall ((N tptp.num)) (= (@ tptp.semiri4216267220026989637d_enat (@ tptp.numeral_numeral_nat N)) (@ tptp.numera1916890842035813515d_enat N))) (forall ((N tptp.num)) (= (@ tptp.semiri8010041392384452111omplex (@ tptp.numeral_numeral_nat N)) (@ tptp.numera6690914467698888265omplex N))) (forall ((N tptp.num)) (= (@ tptp.semiri5074537144036343181t_real (@ tptp.numeral_numeral_nat N)) (@ tptp.numeral_numeral_real N))) (forall ((N tptp.num)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.numeral_numeral_nat N)) (@ tptp.numeral_numeral_int N))) (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N))) (= (@ tptp.semiri1316708129612266289at_nat _let_1) _let_1))) (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real M2)) (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.ord_less_eq_nat M2) N))) (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.semiri681578069525770553at_rat M2)) (@ tptp.semiri681578069525770553at_rat N)) (@ (@ tptp.ord_less_eq_nat M2) N))) (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1316708129612266289at_nat M2)) (@ tptp.semiri1316708129612266289at_nat N)) (@ (@ tptp.ord_less_eq_nat M2) N))) (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int M2)) (@ tptp.semiri1314217659103216013at_int N)) (@ (@ tptp.ord_less_eq_nat M2) N))) (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.plus_plus_nat M2) N)) (@ (@ tptp.plus_plus_rat (@ tptp.semiri681578069525770553at_rat M2)) (@ tptp.semiri681578069525770553at_rat N)))) (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.plus_plus_nat M2) N)) (@ (@ tptp.plus_plus_real (@ tptp.semiri5074537144036343181t_real M2)) (@ tptp.semiri5074537144036343181t_real N)))) (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.plus_plus_nat M2) N)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int M2)) (@ tptp.semiri1314217659103216013at_int N)))) (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.plus_plus_nat M2) N)) (@ (@ tptp.plus_plus_nat (@ tptp.semiri1316708129612266289at_nat M2)) (@ tptp.semiri1316708129612266289at_nat N)))) (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.times_times_nat M2) N)) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat M2)) (@ tptp.semiri681578069525770553at_rat N)))) (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.times_times_nat M2) N)) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real M2)) (@ tptp.semiri5074537144036343181t_real N)))) (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.times_times_nat M2) N)) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int M2)) (@ tptp.semiri1314217659103216013at_int N)))) (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.times_times_nat M2) N)) (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat M2)) (@ tptp.semiri1316708129612266289at_nat N)))) (forall ((N tptp.nat)) (= (= (@ tptp.semiri4939895301339042750nteger N) tptp.one_one_Code_integer) (= N tptp.one_one_nat))) (forall ((N tptp.nat)) (= (= (@ tptp.semiri8010041392384452111omplex N) tptp.one_one_complex) (= N tptp.one_one_nat))) (forall ((N tptp.nat)) (= (= (@ tptp.semiri5074537144036343181t_real N) tptp.one_one_real) (= N tptp.one_one_nat))) (forall ((N tptp.nat)) (= (= (@ tptp.semiri1314217659103216013at_int N) tptp.one_one_int) (= N tptp.one_one_nat))) (forall ((N tptp.nat)) (= (= (@ tptp.semiri1316708129612266289at_nat N) tptp.one_one_nat) (= N tptp.one_one_nat))) (forall ((N tptp.nat)) (= (= tptp.one_one_Code_integer (@ tptp.semiri4939895301339042750nteger N)) (= N tptp.one_one_nat))) (forall ((N tptp.nat)) (= (= tptp.one_one_complex (@ tptp.semiri8010041392384452111omplex N)) (= N tptp.one_one_nat))) (forall ((N tptp.nat)) (= (= tptp.one_one_real (@ tptp.semiri5074537144036343181t_real N)) (= N tptp.one_one_nat))) (forall ((N tptp.nat)) (= (= tptp.one_one_int (@ tptp.semiri1314217659103216013at_int N)) (= N tptp.one_one_nat))) (forall ((N tptp.nat)) (= (= tptp.one_one_nat (@ tptp.semiri1316708129612266289at_nat N)) (= N tptp.one_one_nat))) _let_310 _let_308 _let_306 _let_304 (= (@ tptp.semiri1316708129612266289at_nat tptp.one_one_nat) tptp.one_one_nat) (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))))) (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))))) (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))))) (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))))) (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))))) (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))))) (forall ((N tptp.nat) (A tptp.nat) (P2 (-> tptp.nat Bool))) (= (exists ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) (@ tptp.set_nat2 (@ (@ tptp.replicate_nat N) A))) (@ P2 X4))) (and (@ P2 A) (not (= N tptp.zero_zero_nat))))) (forall ((N tptp.nat) (A tptp.vEBT_VEBT) (P2 (-> tptp.vEBT_VEBT Bool))) (= (exists ((X4 tptp.vEBT_VEBT)) (and (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 (@ (@ tptp.replicate_VEBT_VEBT N) A))) (@ P2 X4))) (and (@ P2 A) (not (= N tptp.zero_zero_nat))))) (forall ((N tptp.nat) (A tptp.nat) (P2 (-> tptp.nat Bool))) (= (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) (@ tptp.set_nat2 (@ (@ tptp.replicate_nat N) A))) (@ P2 X4))) (or (@ P2 A) (= N tptp.zero_zero_nat)))) (forall ((N tptp.nat) (A tptp.vEBT_VEBT) (P2 (-> tptp.vEBT_VEBT Bool))) (= (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 (@ (@ tptp.replicate_VEBT_VEBT N) A))) (@ P2 X4))) (or (@ P2 A) (= N tptp.zero_zero_nat)))) (forall ((N tptp.num)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.numera6620942414471956472nteger N)) tptp.one_one_Code_integer) (@ (@ tptp.ord_less_eq_num N) tptp.one))) (forall ((N tptp.num)) (= (@ (@ tptp.ord_le2932123472753598470d_enat (@ tptp.numera1916890842035813515d_enat N)) tptp.one_on7984719198319812577d_enat) (@ (@ tptp.ord_less_eq_num N) tptp.one))) (forall ((N tptp.num)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real N)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_num N) tptp.one))) (forall ((N tptp.num)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.numeral_numeral_rat N)) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_num N) tptp.one))) (forall ((N tptp.num)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat N)) tptp.one_one_nat) (@ (@ tptp.ord_less_eq_num N) tptp.one))) (forall ((N tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int N)) tptp.one_one_int) (@ (@ tptp.ord_less_eq_num N) tptp.one))) (forall ((N tptp.num)) (= (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) (@ tptp.numera6620942414471956472nteger N)) (@ (@ tptp.ord_less_num tptp.one) N))) (forall ((N tptp.num)) (= (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat N)) (@ (@ tptp.ord_less_num tptp.one) N))) (forall ((N tptp.num)) (= (@ (@ tptp.ord_le72135733267957522d_enat tptp.one_on7984719198319812577d_enat) (@ tptp.numera1916890842035813515d_enat N)) (@ (@ tptp.ord_less_num tptp.one) N))) (forall ((N tptp.num)) (= (@ (@ tptp.ord_less_real tptp.one_one_real) (@ tptp.numeral_numeral_real N)) (@ (@ tptp.ord_less_num tptp.one) N))) (forall ((N tptp.num)) (= (@ (@ tptp.ord_less_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat N)) (@ (@ tptp.ord_less_num tptp.one) N))) (forall ((N tptp.num)) (= (@ (@ tptp.ord_less_int tptp.one_one_int) (@ tptp.numeral_numeral_int N)) (@ (@ tptp.ord_less_num tptp.one) N))) (forall ((N tptp.num)) (= (@ (@ tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer) (@ tptp.numera6620942414471956472nteger N)) (@ tptp.numera6620942414471956472nteger (@ (@ tptp.plus_plus_num tptp.one) N)))) (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat N)) (@ tptp.numeral_numeral_rat (@ (@ tptp.plus_plus_num tptp.one) N)))) (forall ((N tptp.num)) (= (@ (@ tptp.plus_p3455044024723400733d_enat tptp.one_on7984719198319812577d_enat) (@ tptp.numera1916890842035813515d_enat N)) (@ tptp.numera1916890842035813515d_enat (@ (@ tptp.plus_plus_num tptp.one) N)))) (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_complex tptp.one_one_complex) (@ tptp.numera6690914467698888265omplex N)) (@ tptp.numera6690914467698888265omplex (@ (@ tptp.plus_plus_num tptp.one) N)))) (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ tptp.numeral_numeral_real N)) (@ tptp.numeral_numeral_real (@ (@ tptp.plus_plus_num tptp.one) N)))) (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat N)) (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num tptp.one) N)))) (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ tptp.numeral_numeral_int N)) (@ tptp.numeral_numeral_int (@ (@ tptp.plus_plus_num tptp.one) N)))) (forall ((N tptp.num)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.numera6620942414471956472nteger N)) tptp.one_one_Code_integer) (@ tptp.numera6620942414471956472nteger (@ (@ tptp.plus_plus_num N) tptp.one)))) (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_rat (@ tptp.numeral_numeral_rat N)) tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ (@ tptp.plus_plus_num N) tptp.one)))) (forall ((N tptp.num)) (= (@ (@ tptp.plus_p3455044024723400733d_enat (@ tptp.numera1916890842035813515d_enat N)) tptp.one_on7984719198319812577d_enat) (@ tptp.numera1916890842035813515d_enat (@ (@ tptp.plus_plus_num N) tptp.one)))) (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_complex (@ tptp.numera6690914467698888265omplex N)) tptp.one_one_complex) (@ tptp.numera6690914467698888265omplex (@ (@ tptp.plus_plus_num N) tptp.one)))) (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_real (@ tptp.numeral_numeral_real N)) tptp.one_one_real) (@ tptp.numeral_numeral_real (@ (@ tptp.plus_plus_num N) tptp.one)))) (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat N)) tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num N) tptp.one)))) (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_int (@ tptp.numeral_numeral_int N)) tptp.one_one_int) (@ tptp.numeral_numeral_int (@ (@ tptp.plus_plus_num N) tptp.one)))) (forall ((M2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real M2)) tptp.zero_zero_real) (= M2 tptp.zero_zero_nat))) (forall ((M2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.semiri681578069525770553at_rat M2)) tptp.zero_zero_rat) (= M2 tptp.zero_zero_nat))) (forall ((M2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1316708129612266289at_nat M2)) tptp.zero_zero_nat) (= M2 tptp.zero_zero_nat))) (forall ((M2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int M2)) tptp.zero_zero_int) (= M2 tptp.zero_zero_nat))) (forall ((M2 tptp.nat)) (= (@ tptp.semiri4939895301339042750nteger (@ tptp.suc M2)) (@ (@ tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer) (@ tptp.semiri4939895301339042750nteger M2)))) (forall ((M2 tptp.nat)) (= (@ tptp.semiri8010041392384452111omplex (@ tptp.suc M2)) (@ (@ tptp.plus_plus_complex tptp.one_one_complex) (@ tptp.semiri8010041392384452111omplex M2)))) (forall ((M2 tptp.nat)) (= (@ tptp.semiri681578069525770553at_rat (@ tptp.suc M2)) (@ (@ tptp.plus_plus_rat tptp.one_one_rat) (@ tptp.semiri681578069525770553at_rat M2)))) (forall ((M2 tptp.nat)) (= (@ tptp.semiri5074537144036343181t_real (@ tptp.suc M2)) (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real M2)))) (forall ((M2 tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.suc M2)) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ tptp.semiri1314217659103216013at_int M2)))) (forall ((M2 tptp.nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ tptp.suc M2)) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ tptp.semiri1316708129612266289at_nat M2)))) (= _let_302 _let_201) (= _let_301 _let_199) (= (@ (@ tptp.plus_p3455044024723400733d_enat tptp.one_on7984719198319812577d_enat) tptp.one_on7984719198319812577d_enat) (@ tptp.numera1916890842035813515d_enat _let_21)) (= (@ _let_223 tptp.one_one_complex) _let_103) (= _let_300 _let_109) _let_295 (= _let_299 _let_115) (forall ((A tptp.rat)) (= (= (@ (@ tptp.power_power_rat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))) (forall ((A tptp.nat)) (= (= (@ (@ tptp.power_power_nat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_nat) (= A tptp.zero_zero_nat))) (forall ((A tptp.real)) (= (= (@ (@ tptp.power_power_real A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_real) (= A tptp.zero_zero_real))) (forall ((A tptp.int)) (= (= (@ (@ tptp.power_power_int A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_int) (= A tptp.zero_zero_int))) (forall ((A tptp.complex)) (= (= (@ (@ tptp.power_power_complex A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_complex) (= A tptp.zero_zero_complex))) (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.semiri681578069525770553at_rat N)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))) (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))) (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.semiri1314217659103216013at_int N)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ tptp.semiri1316708129612266289at_nat N)) (@ _let_1 N)))) (forall ((N tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (@ tptp.suc (@ tptp.suc N)))) (forall ((N tptp.nat)) (= (@ (@ tptp.plus_plus_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.suc (@ tptp.suc N)))) (= (@ tptp.suc tptp.one_one_nat) _let_22) (forall ((B tptp.nat) (W2 tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real B)) W2)) (@ tptp.semiri5074537144036343181t_real X)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat B) W2)) X))) (forall ((B tptp.nat) (W2 tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat (@ tptp.semiri681578069525770553at_rat B)) W2)) (@ tptp.semiri681578069525770553at_rat X)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat B) W2)) X))) (forall ((B tptp.nat) (W2 tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat B)) W2)) (@ tptp.semiri1316708129612266289at_nat X)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat B) W2)) X))) (forall ((B tptp.nat) (W2 tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int B)) W2)) (@ tptp.semiri1314217659103216013at_int X)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat B) W2)) X))) (forall ((X tptp.nat) (B tptp.nat) (W2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real X)) (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real B)) W2)) (@ (@ tptp.ord_less_eq_nat X) (@ (@ tptp.power_power_nat B) W2)))) (forall ((X tptp.nat) (B tptp.nat) (W2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.semiri681578069525770553at_rat X)) (@ (@ tptp.power_power_rat (@ tptp.semiri681578069525770553at_rat B)) W2)) (@ (@ tptp.ord_less_eq_nat X) (@ (@ tptp.power_power_nat B) W2)))) (forall ((X tptp.nat) (B tptp.nat) (W2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1316708129612266289at_nat X)) (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat B)) W2)) (@ (@ tptp.ord_less_eq_nat X) (@ (@ tptp.power_power_nat B) W2)))) (forall ((X tptp.nat) (B tptp.nat) (W2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int X)) (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int B)) W2)) (@ (@ tptp.ord_less_eq_nat X) (@ (@ tptp.power_power_nat B) W2)))) (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)))) (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)))) (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)))) (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)))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_2 X) (=> (@ _let_2 Y) (= (= (@ (@ tptp.power_power_real X) _let_1) (@ (@ tptp.power_power_real Y) _let_1)) (= X Y))))))) (forall ((X tptp.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))))))) (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ _let_2 X) (=> (@ _let_2 Y) (= (= (@ (@ tptp.power_power_nat X) _let_1) (@ (@ tptp.power_power_nat Y) _let_1)) (= X Y))))))) (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_2 X) (=> (@ _let_2 Y) (= (= (@ (@ tptp.power_power_int X) _let_1) (@ (@ tptp.power_power_int Y) _let_1)) (= X Y))))))) (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.zero_zero_real) (= A tptp.zero_zero_real))) (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))) (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.zero_zero_int) (= A tptp.zero_zero_int))) (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.power_power_real A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (not (= A tptp.zero_zero_real)))) (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.power_power_rat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (not (= A tptp.zero_zero_rat)))) (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.power_power_int A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (not (= A tptp.zero_zero_int)))) (forall ((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))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)) tptp.zero_zero_real) (and (= X tptp.zero_zero_real) (= Y tptp.zero_zero_real))))) (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int X) _let_1)) (@ (@ tptp.power_power_int Y) _let_1)) tptp.zero_zero_int) (and (= X tptp.zero_zero_int) (= Y tptp.zero_zero_int))))) (forall ((I2 tptp.num) (N tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real I2)) N)) (@ tptp.semiri5074537144036343181t_real X)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N)) X))) (forall ((I2 tptp.num) (N tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat I2)) N)) (@ tptp.semiri681578069525770553at_rat X)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N)) X))) (forall ((I2 tptp.num) (N tptp.nat) (X tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N)))) (= (@ _let_1 (@ tptp.semiri1316708129612266289at_nat X)) (@ _let_1 X)))) (forall ((I2 tptp.num) (N tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int I2)) N)) (@ tptp.semiri1314217659103216013at_int X)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N)) X))) (forall ((X tptp.nat) (I2 tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real X)) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real I2)) N)) (@ (@ tptp.ord_less_eq_nat X) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N)))) (forall ((X tptp.nat) (I2 tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.semiri681578069525770553at_rat X)) (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat I2)) N)) (@ (@ tptp.ord_less_eq_nat X) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N)))) (forall ((X tptp.nat) (I2 tptp.num) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N))) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1316708129612266289at_nat X)) _let_1) (@ (@ tptp.ord_less_eq_nat X) _let_1)))) (forall ((X tptp.nat) (I2 tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int X)) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int I2)) N)) (@ (@ tptp.ord_less_eq_nat X) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N)))) (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat M2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) N) (@ (@ tptp.ord_less_eq_nat M2) N))) (forall ((M2 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 M2) _let_1)) (@ (@ tptp.power_power_nat N) _let_1)) (@ (@ tptp.ord_less_eq_nat M2) N)))) (forall ((K2 tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) K2) (@ (@ tptp.ord_less_eq_nat M2) (@ (@ tptp.power_power_nat K2) M2)))) (forall ((S3 tptp.set_nat)) (= (= (@ tptp.finite_card_nat S3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (exists ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) S3) (exists ((Y4 tptp.nat)) (and (@ (@ tptp.member_nat Y4) S3) (not (= X4 Y4)) (forall ((Z4 tptp.nat)) (=> (@ (@ tptp.member_nat Z4) S3) (or (= Z4 X4) (= Z4 Y4)))))))))) (forall ((S3 tptp.set_complex)) (= (= (@ tptp.finite_card_complex S3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (exists ((X4 tptp.complex)) (and (@ (@ tptp.member_complex X4) S3) (exists ((Y4 tptp.complex)) (and (@ (@ tptp.member_complex Y4) S3) (not (= X4 Y4)) (forall ((Z4 tptp.complex)) (=> (@ (@ tptp.member_complex Z4) S3) (or (= Z4 X4) (= Z4 Y4)))))))))) (forall ((S3 tptp.set_int)) (= (= (@ tptp.finite_card_int S3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (exists ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) S3) (exists ((Y4 tptp.int)) (and (@ (@ tptp.member_int Y4) S3) (not (= X4 Y4)) (forall ((Z4 tptp.int)) (=> (@ (@ tptp.member_int Z4) S3) (or (= Z4 X4) (= Z4 Y4)))))))))) (forall ((S3 tptp.set_list_nat)) (= (= (@ tptp.finite_card_list_nat S3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (exists ((X4 tptp.list_nat)) (and (@ (@ tptp.member_list_nat X4) S3) (exists ((Y4 tptp.list_nat)) (and (@ (@ tptp.member_list_nat Y4) S3) (not (= X4 Y4)) (forall ((Z4 tptp.list_nat)) (=> (@ (@ tptp.member_list_nat Z4) S3) (or (= Z4 X4) (= Z4 Y4)))))))))) (forall ((S3 tptp.set_set_nat)) (= (= (@ tptp.finite_card_set_nat S3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (exists ((X4 tptp.set_nat)) (and (@ (@ tptp.member_set_nat X4) S3) (exists ((Y4 tptp.set_nat)) (and (@ (@ tptp.member_set_nat Y4) S3) (not (= X4 Y4)) (forall ((Z4 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat Z4) S3) (or (= Z4 X4) (= Z4 Y4)))))))))) (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (forall ((Y6 tptp.real)) (exists ((N3 tptp.nat)) (@ (@ tptp.ord_less_real Y6) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N3)) X)))))) (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_num tptp.one) N) (@ (@ tptp.plus_plus_num N) tptp.one))) (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat N))) (= (@ tptp.numeral_numeral_rat (@ tptp.bit0 N)) (@ (@ tptp.plus_plus_rat _let_1) _let_1)))) (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numera1916890842035813515d_enat N))) (= (@ tptp.numera1916890842035813515d_enat (@ tptp.bit0 N)) (@ (@ tptp.plus_p3455044024723400733d_enat _let_1) _let_1)))) (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex N))) (= (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 N)) (@ (@ tptp.plus_plus_complex _let_1) _let_1)))) (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real N))) (= (@ tptp.numeral_numeral_real (@ tptp.bit0 N)) (@ (@ tptp.plus_plus_real _let_1) _let_1)))) (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N))) (= (@ tptp.numeral_numeral_nat (@ tptp.bit0 N)) (@ (@ tptp.plus_plus_nat _let_1) _let_1)))) (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (= (@ tptp.numeral_numeral_int (@ tptp.bit0 N)) (@ (@ tptp.plus_plus_int _let_1) _let_1)))) (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat A) (@ tptp.numeral_numeral_rat tptp.one)) A)) (forall ((A tptp.extended_enat)) (= (@ (@ tptp.times_7803423173614009249d_enat A) (@ tptp.numera1916890842035813515d_enat tptp.one)) A)) (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex A) (@ tptp.numera6690914467698888265omplex tptp.one)) A)) (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real A) (@ tptp.numeral_numeral_real tptp.one)) A)) (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat A) (@ tptp.numeral_numeral_nat tptp.one)) A)) (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int A) (@ tptp.numeral_numeral_int tptp.one)) A)) (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat tptp.one)) A) A)) (forall ((A tptp.extended_enat)) (= (@ (@ tptp.times_7803423173614009249d_enat (@ tptp.numera1916890842035813515d_enat tptp.one)) A) A)) (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex tptp.one)) A) A)) (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real tptp.one)) A) A)) (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat tptp.one)) A) A)) (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int tptp.one)) A) A)) (= _let_166 tptp.one_one_Code_integer) _let_298 (= _let_167 tptp.one_one_complex) (= _let_168 tptp.one_one_real) _let_296 (= _let_169 tptp.one_one_int) (@ _let_297 _let_22) _let_296 (forall ((X tptp.num)) (= (@ (@ tptp.ord_less_eq_num X) tptp.one) (= X tptp.one))) (forall ((Z3 tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))) Z3) (@ (@ tptp.plus_plus_rat Z3) Z3))) (forall ((Z3 tptp.extended_enat)) (= (@ (@ tptp.times_7803423173614009249d_enat (@ tptp.numera1916890842035813515d_enat (@ tptp.bit0 tptp.one))) Z3) (@ (@ tptp.plus_p3455044024723400733d_enat Z3) Z3))) (forall ((Z3 tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))) Z3) (@ (@ tptp.plus_plus_complex Z3) Z3))) (forall ((Z3 tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) Z3) (@ (@ tptp.plus_plus_real Z3) Z3))) (forall ((Z3 tptp.nat)) (= (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Z3) (@ (@ tptp.plus_plus_nat Z3) Z3))) (forall ((Z3 tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) Z3) (@ (@ tptp.plus_plus_int Z3) Z3))) (forall ((Z3 tptp.rat)) (= (@ (@ tptp.times_times_rat Z3) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_plus_rat Z3) Z3))) (forall ((Z3 tptp.extended_enat)) (= (@ (@ tptp.times_7803423173614009249d_enat Z3) (@ tptp.numera1916890842035813515d_enat (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_p3455044024723400733d_enat Z3) Z3))) (forall ((Z3 tptp.complex)) (= (@ (@ tptp.times_times_complex Z3) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_plus_complex Z3) Z3))) (forall ((Z3 tptp.real)) (= (@ (@ tptp.times_times_real Z3) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_plus_real Z3) Z3))) (forall ((Z3 tptp.nat)) (= (@ (@ tptp.times_times_nat Z3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_plus_nat Z3) Z3))) (forall ((Z3 tptp.int)) (= (@ (@ tptp.times_times_int Z3) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_plus_int Z3) Z3))) (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat A))) (= (@ _let_1 (@ _let_1 B)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))) A)) B)))) (forall ((A tptp.extended_enat) (B tptp.extended_enat)) (let ((_let_1 (@ tptp.plus_p3455044024723400733d_enat A))) (= (@ _let_1 (@ _let_1 B)) (@ (@ tptp.plus_p3455044024723400733d_enat (@ (@ tptp.times_7803423173614009249d_enat (@ tptp.numera1916890842035813515d_enat (@ tptp.bit0 tptp.one))) A)) B)))) (forall ((A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.plus_plus_complex A))) (= (@ _let_1 (@ _let_1 B)) (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))) A)) B)))) (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A))) (= (@ _let_1 (@ _let_1 B)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) A)) B)))) (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A))) (= (@ _let_1 (@ _let_1 B)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) A)) B)))) (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A))) (= (@ _let_1 (@ _let_1 B)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) A)) B)))) (= (@ (@ tptp.power_power_rat tptp.zero_zero_rat) _let_22) tptp.zero_zero_rat) (= (@ (@ tptp.power_power_nat tptp.zero_zero_nat) _let_22) tptp.zero_zero_nat) (= (@ (@ tptp.power_power_real tptp.zero_zero_real) _let_22) tptp.zero_zero_real) (= (@ (@ tptp.power_power_int tptp.zero_zero_int) _let_22) tptp.zero_zero_int) (= (@ (@ tptp.power_power_complex tptp.zero_zero_complex) _let_22) tptp.zero_zero_complex) (forall ((A tptp.complex)) (= (@ (@ tptp.power_power_complex A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.times_times_complex A) A))) (forall ((A tptp.real)) (= (@ (@ tptp.power_power_real A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.times_times_real A) A))) (forall ((A tptp.rat)) (= (@ (@ tptp.power_power_rat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.times_times_rat A) A))) (forall ((A tptp.nat)) (= (@ (@ tptp.power_power_nat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.times_times_nat A) A))) (forall ((A tptp.int)) (= (@ (@ tptp.power_power_int A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.times_times_int A) A))) (forall ((X tptp.complex)) (= (@ (@ tptp.power_power_complex X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 tptp.one)))) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex X) X)) X)) X))) (forall ((X tptp.real)) (= (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 tptp.one)))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real X) X)) X)) X))) (forall ((X tptp.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))) (forall ((X tptp.nat)) (= (@ (@ tptp.power_power_nat X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 tptp.one)))) (@ (@ tptp.times_times_nat (@ (@ tptp.times_times_nat (@ (@ tptp.times_times_nat X) X)) X)) X))) (forall ((X tptp.int)) (= (@ (@ tptp.power_power_int X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 tptp.one)))) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int X) X)) X)) X))) (= _let_22 _let_114) (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_nat A))) (= (@ _let_2 (@ (@ tptp.times_times_nat _let_1) N)) (@ (@ tptp.power_power_nat (@ _let_2 N)) _let_1))))) (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_real A))) (= (@ _let_2 (@ (@ tptp.times_times_nat _let_1) N)) (@ (@ tptp.power_power_real (@ _let_2 N)) _let_1))))) (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_int A))) (= (@ _let_2 (@ (@ tptp.times_times_nat _let_1) N)) (@ (@ tptp.power_power_int (@ _let_2 N)) _let_1))))) (forall ((A tptp.complex) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_complex A))) (= (@ _let_2 (@ (@ tptp.times_times_nat _let_1) N)) (@ (@ tptp.power_power_complex (@ _let_2 N)) _let_1))))) (forall ((K2 tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat K2))) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) K2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat M2) N)) (@ (@ tptp.minus_minus_nat (@ _let_1 M2)) (@ _let_1 N)))))) _let_295 (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)))))) (forall ((X tptp.extended_enat) (Y tptp.extended_enat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ (@ tptp.power_8040749407984259932d_enat (@ (@ tptp.plus_p3455044024723400733d_enat X) Y)) _let_2) (@ (@ tptp.plus_p3455044024723400733d_enat (@ (@ tptp.plus_p3455044024723400733d_enat (@ (@ tptp.power_8040749407984259932d_enat X) _let_2)) (@ (@ tptp.power_8040749407984259932d_enat Y) _let_2))) (@ (@ tptp.times_7803423173614009249d_enat (@ (@ tptp.times_7803423173614009249d_enat (@ tptp.numera1916890842035813515d_enat _let_1)) X)) Y)))))) (forall ((X tptp.complex) (Y tptp.complex)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ (@ tptp.power_power_complex (@ (@ tptp.plus_plus_complex X) Y)) _let_2) (@ (@ tptp.plus_plus_complex (@ (@ tptp.plus_plus_complex (@ (@ tptp.power_power_complex X) _let_2)) (@ (@ tptp.power_power_complex Y) _let_2))) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex _let_1)) X)) Y)))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real X) Y)) _let_2) (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_2)) (@ (@ tptp.power_power_real Y) _let_2))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) X)) Y)))))) (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_nat (@ (@ tptp.plus_plus_nat X) Y)) _let_1) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.power_power_nat X) _let_1)) (@ (@ tptp.power_power_nat Y) _let_1))) (@ (@ tptp.times_times_nat (@ (@ tptp.times_times_nat _let_1) X)) Y))))) (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ (@ tptp.power_power_int (@ (@ tptp.plus_plus_int X) Y)) _let_2) (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int X) _let_2)) (@ (@ tptp.power_power_int Y) _let_2))) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int _let_1)) X)) Y)))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) X)) Y)) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_2)) (@ (@ tptp.power_power_real Y) _let_2)))))) (forall ((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)))))) (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)))))) (forall ((X tptp.complex) (Y tptp.complex)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ (@ tptp.power_power_complex (@ (@ tptp.minus_minus_complex X) Y)) _let_2) (@ (@ tptp.minus_minus_complex (@ (@ tptp.plus_plus_complex (@ (@ tptp.power_power_complex X) _let_2)) (@ (@ tptp.power_power_complex Y) _let_2))) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex _let_1)) X)) Y)))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real X) Y)) _let_2) (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_2)) (@ (@ tptp.power_power_real Y) _let_2))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) X)) Y)))))) (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ (@ tptp.power_power_int (@ (@ tptp.minus_minus_int X) Y)) _let_2) (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int X) _let_2)) (@ (@ tptp.power_power_int Y) _let_2))) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int _let_1)) X)) Y)))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (@ (@ tptp.ord_less_eq_real X) Y))))) (forall ((X tptp.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))))) (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat X) _let_1)) (@ (@ tptp.power_power_nat Y) _let_1)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) Y) (@ (@ tptp.ord_less_eq_nat X) Y))))) (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int X) _let_1)) (@ (@ tptp.power_power_int Y) _let_1)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y) (@ (@ tptp.ord_less_eq_int X) Y))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (= (@ (@ tptp.power_power_real X) _let_2) (@ (@ tptp.power_power_real Y) _let_2)) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= X Y))))))) (forall ((X tptp.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))))))) (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (= (@ (@ tptp.power_power_nat X) _let_2) (@ (@ tptp.power_power_nat Y) _let_2)) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= X Y))))))) (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (= (@ (@ tptp.power_power_int X) _let_2) (@ (@ tptp.power_power_int Y) _let_2)) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= X Y))))))) (forall ((A tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.power_power_real A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (forall ((A tptp.rat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.power_power_rat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.power_power_int A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (forall ((A tptp.real)) (not (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.zero_zero_real))) (forall ((A tptp.rat)) (not (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.zero_zero_rat))) (forall ((A tptp.int)) (not (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.zero_zero_int))) (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (or (= N tptp.zero_zero_nat) (= N (@ tptp.suc tptp.zero_zero_nat))))) (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (or (= N tptp.zero_zero_nat) (= N (@ tptp.suc tptp.zero_zero_nat))))) (forall ((S3 tptp.set_complex)) (= (= (@ tptp.finite_card_complex S3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (exists ((X4 tptp.complex) (Y4 tptp.complex)) (and (= S3 (@ (@ tptp.insert_complex X4) (@ (@ tptp.insert_complex Y4) tptp.bot_bot_set_complex))) (not (= X4 Y4)))))) (forall ((S3 tptp.set_list_nat)) (= (= (@ tptp.finite_card_list_nat S3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (exists ((X4 tptp.list_nat) (Y4 tptp.list_nat)) (and (= S3 (@ (@ tptp.insert_list_nat X4) (@ (@ tptp.insert_list_nat Y4) tptp.bot_bot_set_list_nat))) (not (= X4 Y4)))))) (forall ((S3 tptp.set_set_nat)) (= (= (@ tptp.finite_card_set_nat S3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (exists ((X4 tptp.set_nat) (Y4 tptp.set_nat)) (and (= S3 (@ (@ tptp.insert_set_nat X4) (@ (@ tptp.insert_set_nat Y4) tptp.bot_bot_set_set_nat))) (not (= X4 Y4)))))) (forall ((S3 tptp.set_nat)) (= (= (@ tptp.finite_card_nat S3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (exists ((X4 tptp.nat) (Y4 tptp.nat)) (and (= S3 (@ (@ tptp.insert_nat X4) (@ (@ tptp.insert_nat Y4) tptp.bot_bot_set_nat))) (not (= X4 Y4)))))) (forall ((S3 tptp.set_int)) (= (= (@ tptp.finite_card_int S3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (exists ((X4 tptp.int) (Y4 tptp.int)) (and (= S3 (@ (@ tptp.insert_int X4) (@ (@ tptp.insert_int Y4) tptp.bot_bot_set_int))) (not (= X4 Y4)))))) (forall ((S3 tptp.set_real)) (= (= (@ tptp.finite_card_real S3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (exists ((X4 tptp.real) (Y4 tptp.real)) (and (= S3 (@ (@ tptp.insert_real X4) (@ (@ tptp.insert_real Y4) tptp.bot_bot_set_real))) (not (= X4 Y4)))))) (= _let_292 _let_10) (forall ((V2 tptp.num) (N tptp.nat)) (= (@ tptp.suc (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat V2)) N)) (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num V2) tptp.one))) N))) (forall ((X tptp.real)) (exists ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real X) (@ tptp.semiri5074537144036343181t_real N3)))) (forall ((X tptp.rat)) (exists ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_rat X) (@ tptp.semiri681578069525770553at_rat N3)))) (forall ((X tptp.rat)) (exists ((N3 tptp.nat)) (@ (@ tptp.ord_less_rat X) (@ tptp.semiri681578069525770553at_rat N3)))) (forall ((X tptp.real)) (exists ((N3 tptp.nat)) (@ (@ tptp.ord_less_real X) (@ tptp.semiri5074537144036343181t_real N3)))) (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)))) (forall ((X tptp.nat) (Y tptp.real)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real X))) (= (@ (@ tptp.times_times_real _let_1) Y) (@ (@ tptp.times_times_real Y) _let_1)))) (forall ((X tptp.nat) (Y tptp.int)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int X))) (= (@ (@ tptp.times_times_int _let_1) Y) (@ (@ tptp.times_times_int Y) _let_1)))) (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.semiri1316708129612266289at_nat X))) (= (@ (@ tptp.times_times_nat _let_1) Y) (@ (@ tptp.times_times_nat Y) _let_1)))) (= tptp.ord_less_int (lambda ((W3 tptp.int) (Z4 tptp.int)) (exists ((N4 tptp.nat)) (= Z4 (@ (@ tptp.plus_plus_int W3) (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N4))))))) (forall ((N tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int N)) tptp.one_one_int))) (forall ((A tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.suc A)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int A)) tptp.one_one_int))) (forall ((N tptp.num)) (not (= tptp.zero_zero_rat (@ tptp.numeral_numeral_rat N)))) (forall ((N tptp.num)) (not (= tptp.zero_z5237406670263579293d_enat (@ tptp.numera1916890842035813515d_enat N)))) (forall ((N tptp.num)) (not (= tptp.zero_zero_complex (@ tptp.numera6690914467698888265omplex N)))) (forall ((N tptp.num)) (not (= tptp.zero_zero_real (@ tptp.numeral_numeral_real N)))) (forall ((N tptp.num)) (not (= tptp.zero_zero_nat (@ tptp.numeral_numeral_nat N)))) (forall ((N tptp.num)) (not (= tptp.zero_zero_int (@ tptp.numeral_numeral_int N)))) _let_291 (= tptp.ord_less_eq_nat (lambda ((N4 tptp.nat) (M6 tptp.nat)) (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real N4)) (@ (@ tptp.plus_plus_real (@ tptp.semiri5074537144036343181t_real M6)) tptp.one_one_real)))) (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int M2)) (@ tptp.semiri1314217659103216013at_int N)) (@ (@ tptp.ord_less_eq_nat M2) N))) (= tptp.ord_less_eq_nat (lambda ((A5 tptp.nat) (B4 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int A5)) (@ tptp.semiri1314217659103216013at_int B4)))) (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)))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (@ (@ tptp.ord_less_real X) Y))))) (forall ((X tptp.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))))) (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat X) _let_1)) (@ (@ tptp.power_power_nat Y) _let_1)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) Y) (@ (@ tptp.ord_less_nat X) Y))))) (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int X) _let_1)) (@ (@ tptp.power_power_int Y) _let_1)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y) (@ (@ tptp.ord_less_int X) Y))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1))) tptp.zero_zero_real) (and (= X tptp.zero_zero_real) (= Y tptp.zero_zero_real))))) (forall ((X tptp.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))))) (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int X) _let_1)) (@ (@ tptp.power_power_int Y) _let_1))) tptp.zero_zero_int) (and (= X tptp.zero_zero_int) (= Y tptp.zero_zero_int))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1))))) (forall ((X tptp.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))))) (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int X) _let_1)) (@ (@ tptp.power_power_int Y) _let_1))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1))) (or (not (= X tptp.zero_zero_real)) (not (= Y tptp.zero_zero_real)))))) (forall ((X tptp.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)))))) (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int X) _let_1)) (@ (@ tptp.power_power_int Y) _let_1))) (or (not (= X tptp.zero_zero_int)) (not (= Y tptp.zero_zero_int)))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (not (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1))) tptp.zero_zero_real)))) (forall ((X tptp.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)))) (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)))) (= (@ tptp.size_size_num tptp.one) tptp.zero_zero_nat) (forall ((A tptp.real) (N tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.power_power_real A) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))) (forall ((A tptp.rat) (N tptp.nat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.power_power_rat A) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))) (forall ((A tptp.int) (N tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.power_power_int A) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))) (forall ((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)))))) (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)))))) (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)))))) (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)))))) (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)))))) (forall ((B tptp.nat) (K2 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) K2) (exists ((N3 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (and (@ (@ tptp.ord_less_eq_nat (@ _let_1 N3)) K2) (@ (@ tptp.ord_less_nat K2) (@ _let_1 (@ (@ tptp.plus_plus_nat N3) tptp.one_one_nat))))))))) (forall ((B tptp.nat) (K2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (@ _let_1 B) (=> (@ _let_1 K2) (exists ((N3 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (and (@ (@ tptp.ord_less_nat (@ _let_1 N3)) K2) (@ (@ tptp.ord_less_eq_nat K2) (@ _let_1 (@ (@ tptp.plus_plus_nat N3) tptp.one_one_nat)))))))))) (forall ((Deg tptp.nat) (X tptp.nat) (Info2 tptp.option4927543243414619207at_nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info2) Deg) TreeList2) Summary))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_insert _let_1) X))) (let ((_let_3 (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Deg)) X))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ (@ tptp.vEBT_vebt_insert _let_1) X)))))))) (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 (@ (@ tptp.power_power_real A) (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))) (@ _let_1 A)))) (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 (@ (@ tptp.power_power_rat A) (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))) (@ _let_1 A)))) (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 (@ (@ tptp.power_power_int A) (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))) (@ _let_1 A)))) (forall ((A tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real A) (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))) tptp.zero_zero_real))) (forall ((A tptp.rat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat A) (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))) tptp.zero_zero_rat))) (forall ((A tptp.int) (N tptp.nat)) (=> (@ (@ tptp.ord_less_int A) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int A) (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))) tptp.zero_zero_int))) (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y tptp.vEBT_VEBT)) (=> (= (@ (@ tptp.vEBT_VEBT_insert X) Xa2) Y) (=> (forall ((A3 Bool) (B3 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A3) B3))) (=> (= X _let_1) (not (= Y (@ (@ tptp.vEBT_vebt_insert _let_1) Xa2)))))) (not (forall ((Info tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info) Deg2) TreeList) Summary2))) (let ((_let_2 (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Deg2)) Xa2))) (=> (= X _let_1) (not (and (=> _let_2 (= Y _let_1)) (=> (not _let_2) (= Y (@ (@ tptp.vEBT_vebt_insert _let_1) Xa2))))))))))))) (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.semiri5074537144036343181t_real N))) (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.semiri681578069525770553at_rat N))) (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ tptp.semiri1316708129612266289at_nat N))) (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.semiri1314217659103216013at_int N))) (forall ((M2 tptp.nat)) (not (@ (@ tptp.ord_less_rat (@ tptp.semiri681578069525770553at_rat M2)) tptp.zero_zero_rat))) (forall ((M2 tptp.nat)) (not (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real M2)) tptp.zero_zero_real))) (forall ((M2 tptp.nat)) (not (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int M2)) tptp.zero_zero_int))) (forall ((M2 tptp.nat)) (not (@ (@ tptp.ord_less_nat (@ tptp.semiri1316708129612266289at_nat M2)) tptp.zero_zero_nat))) (forall ((N tptp.nat)) (not (= (@ tptp.semiri8010041392384452111omplex (@ tptp.suc N)) tptp.zero_zero_complex))) (forall ((N tptp.nat)) (not (= (@ tptp.semiri681578069525770553at_rat (@ tptp.suc N)) tptp.zero_zero_rat))) (forall ((N tptp.nat)) (not (= (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N)) tptp.zero_zero_real))) (forall ((N tptp.nat)) (not (= (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N)) tptp.zero_zero_int))) (forall ((N tptp.nat)) (not (= (@ tptp.semiri1316708129612266289at_nat (@ tptp.suc N)) tptp.zero_zero_nat))) (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_rat (@ tptp.semiri681578069525770553at_rat M2)) (@ tptp.semiri681578069525770553at_rat N)) (@ (@ tptp.ord_less_nat M2) N))) (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real M2)) (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.ord_less_nat M2) N))) (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int M2)) (@ tptp.semiri1314217659103216013at_int N)) (@ (@ tptp.ord_less_nat M2) N))) (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.semiri1316708129612266289at_nat M2)) (@ tptp.semiri1316708129612266289at_nat N)) (@ (@ tptp.ord_less_nat M2) N))) (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) N) (@ (@ tptp.ord_less_rat (@ tptp.semiri681578069525770553at_rat M2)) (@ tptp.semiri681578069525770553at_rat N)))) (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) N) (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real M2)) (@ tptp.semiri5074537144036343181t_real N)))) (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) N) (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int M2)) (@ tptp.semiri1314217659103216013at_int N)))) (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) N) (@ (@ tptp.ord_less_nat (@ tptp.semiri1316708129612266289at_nat M2)) (@ tptp.semiri1316708129612266289at_nat N)))) (forall ((I2 tptp.nat) (J2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J2) (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real I2)) (@ tptp.semiri5074537144036343181t_real J2)))) (forall ((I2 tptp.nat) (J2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J2) (@ (@ tptp.ord_less_eq_rat (@ tptp.semiri681578069525770553at_rat I2)) (@ tptp.semiri681578069525770553at_rat J2)))) (forall ((I2 tptp.nat) (J2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J2) (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1316708129612266289at_nat I2)) (@ tptp.semiri1316708129612266289at_nat J2)))) (forall ((I2 tptp.nat) (J2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J2) (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int I2)) (@ tptp.semiri1314217659103216013at_int J2)))) (forall ((N tptp.num)) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ tptp.numera1916890842035813515d_enat N))) (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.numeral_numeral_real N))) (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.numeral_numeral_rat N))) (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat N))) (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.numeral_numeral_int N))) (forall ((N tptp.num)) (not (@ (@ tptp.ord_le2932123472753598470d_enat (@ tptp.numera1916890842035813515d_enat N)) tptp.zero_z5237406670263579293d_enat))) (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real N)) tptp.zero_zero_real))) (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_eq_rat (@ tptp.numeral_numeral_rat N)) tptp.zero_zero_rat))) (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat N)) tptp.zero_zero_nat))) (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int N)) tptp.zero_zero_int))) (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_rat (@ tptp.numeral_numeral_rat N)) tptp.zero_zero_rat))) (forall ((N tptp.num)) (not (@ (@ tptp.ord_le72135733267957522d_enat (@ tptp.numera1916890842035813515d_enat N)) tptp.zero_z5237406670263579293d_enat))) (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real N)) tptp.zero_zero_real))) (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_nat (@ tptp.numeral_numeral_nat N)) tptp.zero_zero_nat))) (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int N)) tptp.zero_zero_int))) (forall ((N tptp.num)) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.numeral_numeral_rat N))) (forall ((N tptp.num)) (@ (@ tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat) (@ tptp.numera1916890842035813515d_enat N))) (forall ((N tptp.num)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.numeral_numeral_real N))) (forall ((N tptp.num)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat N))) (forall ((N tptp.num)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.numeral_numeral_int N))) (forall ((N tptp.nat) (X tptp.nat)) (= (@ (@ tptp.replicate_nat (@ tptp.suc N)) X) (@ (@ tptp.cons_nat X) (@ (@ tptp.replicate_nat N) X)))) (forall ((N tptp.nat) (X tptp.vEBT_VEBT)) (= (@ (@ tptp.replicate_VEBT_VEBT (@ tptp.suc N)) X) (@ (@ tptp.cons_VEBT_VEBT X) (@ (@ tptp.replicate_VEBT_VEBT N) X)))) (forall ((X tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 C2) (=> (forall ((M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real M)) X)) C2))) (= X tptp.zero_zero_real)))))) (forall ((N tptp.num)) (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (@ tptp.numera6620942414471956472nteger N))) (forall ((N tptp.num)) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.one_on7984719198319812577d_enat) (@ tptp.numera1916890842035813515d_enat N))) (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.numeral_numeral_real N))) (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat N))) (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat N))) (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.numeral_numeral_int N))) (forall ((K2 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K2) (not (forall ((N3 tptp.nat)) (=> (= K2 (@ tptp.semiri1314217659103216013at_int N3)) (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N3))))))) (forall ((K2 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K2) (exists ((N3 tptp.nat)) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N3) (= K2 (@ tptp.semiri1314217659103216013at_int N3)))))) (forall ((I2 tptp.int) (J2 tptp.int) (K2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int K2)))) (=> (@ (@ tptp.ord_less_int I2) J2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K2) (@ (@ tptp.ord_less_int (@ _let_1 I2)) (@ _let_1 J2)))))) (forall ((N tptp.num)) (not (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.numera6620942414471956472nteger N)) tptp.one_one_Code_integer))) (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_rat (@ tptp.numeral_numeral_rat N)) tptp.one_one_rat))) (forall ((N tptp.num)) (not (@ (@ tptp.ord_le72135733267957522d_enat (@ tptp.numera1916890842035813515d_enat N)) tptp.one_on7984719198319812577d_enat))) (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real N)) tptp.one_one_real))) (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_nat (@ tptp.numeral_numeral_nat N)) tptp.one_one_nat))) (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int N)) tptp.one_one_int))) (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger X))) (= (@ (@ tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer) _let_1) (@ (@ tptp.plus_p5714425477246183910nteger _let_1) tptp.one_one_Code_integer)))) (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)))) (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numera1916890842035813515d_enat X))) (= (@ (@ tptp.plus_p3455044024723400733d_enat tptp.one_on7984719198319812577d_enat) _let_1) (@ (@ tptp.plus_p3455044024723400733d_enat _let_1) tptp.one_on7984719198319812577d_enat)))) (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex X))) (= (@ (@ tptp.plus_plus_complex tptp.one_one_complex) _let_1) (@ (@ tptp.plus_plus_complex _let_1) tptp.one_one_complex)))) (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real X))) (= (@ (@ tptp.plus_plus_real tptp.one_one_real) _let_1) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real)))) (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat X))) (= (@ (@ tptp.plus_plus_nat tptp.one_one_nat) _let_1) (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat)))) (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int X))) (= (@ (@ tptp.plus_plus_int tptp.one_one_int) _let_1) (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int)))) (forall ((Xs2 tptp.list_VEBT_VEBT) (X tptp.vEBT_VEBT)) (=> (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 Xs2)) (= X3 X))) (= (@ (@ tptp.replicate_VEBT_VEBT (@ tptp.size_s6755466524823107622T_VEBT Xs2)) X) Xs2))) (forall ((Xs2 tptp.list_o) (X Bool)) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) (@ tptp.set_o2 Xs2)) (= X3 X))) (= (@ (@ tptp.replicate_o (@ tptp.size_size_list_o Xs2)) X) Xs2))) (forall ((Xs2 tptp.list_nat) (X tptp.nat)) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ tptp.set_nat2 Xs2)) (= X3 X))) (= (@ (@ tptp.replicate_nat (@ tptp.size_size_list_nat Xs2)) X) Xs2))) (forall ((Xs2 tptp.list_int) (X tptp.int)) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ tptp.set_int2 Xs2)) (= X3 X))) (= (@ (@ tptp.replicate_int (@ tptp.size_size_list_int Xs2)) X) Xs2))) (forall ((Xs2 tptp.list_complex) (N tptp.nat) (X tptp.complex)) (=> (= (@ tptp.size_s3451745648224563538omplex Xs2) N) (=> (forall ((Y3 tptp.complex)) (=> (@ (@ tptp.member_complex Y3) (@ tptp.set_complex2 Xs2)) (= Y3 X))) (= Xs2 (@ (@ tptp.replicate_complex N) X))))) (forall ((Xs2 tptp.list_real) (N tptp.nat) (X tptp.real)) (=> (= (@ tptp.size_size_list_real Xs2) N) (=> (forall ((Y3 tptp.real)) (=> (@ (@ tptp.member_real Y3) (@ tptp.set_real2 Xs2)) (= Y3 X))) (= Xs2 (@ (@ tptp.replicate_real N) X))))) (forall ((Xs2 tptp.list_set_nat) (N tptp.nat) (X tptp.set_nat)) (=> (= (@ tptp.size_s3254054031482475050et_nat Xs2) N) (=> (forall ((Y3 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat Y3) (@ tptp.set_set_nat2 Xs2)) (= Y3 X))) (= Xs2 (@ (@ tptp.replicate_set_nat N) X))))) (forall ((Xs2 tptp.list_VEBT_VEBT) (N tptp.nat) (X tptp.vEBT_VEBT)) (=> (= (@ tptp.size_s6755466524823107622T_VEBT Xs2) N) (=> (forall ((Y3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT Y3) (@ tptp.set_VEBT_VEBT2 Xs2)) (= Y3 X))) (= Xs2 (@ (@ tptp.replicate_VEBT_VEBT N) X))))) (forall ((Xs2 tptp.list_o) (N tptp.nat) (X Bool)) (=> (= (@ tptp.size_size_list_o Xs2) N) (=> (forall ((Y3 Bool)) (=> (@ (@ tptp.member_o Y3) (@ tptp.set_o2 Xs2)) (= Y3 X))) (= Xs2 (@ (@ tptp.replicate_o N) X))))) (forall ((Xs2 tptp.list_nat) (N tptp.nat) (X tptp.nat)) (=> (= (@ tptp.size_size_list_nat Xs2) N) (=> (forall ((Y3 tptp.nat)) (=> (@ (@ tptp.member_nat Y3) (@ tptp.set_nat2 Xs2)) (= Y3 X))) (= Xs2 (@ (@ tptp.replicate_nat N) X))))) (forall ((Xs2 tptp.list_int) (N tptp.nat) (X tptp.int)) (=> (= (@ tptp.size_size_list_int Xs2) N) (=> (forall ((Y3 tptp.int)) (=> (@ (@ tptp.member_int Y3) (@ tptp.set_int2 Xs2)) (= Y3 X))) (= Xs2 (@ (@ tptp.replicate_int N) X))))) (forall ((TreeList2 tptp.list_VEBT_VEBT) (N tptp.nat) (Summary tptp.vEBT_VEBT) (M2 tptp.nat) (Deg tptp.nat)) (=> (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList2)) (@ (@ tptp.vEBT_invar_vebt X3) N))) (=> (@ (@ tptp.vEBT_invar_vebt Summary) M2) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M2)) (=> (= M2 N) (=> (= Deg (@ (@ tptp.plus_plus_nat N) M2)) (=> (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary) X_12))) (=> (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X3) X_12))))) (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Deg) TreeList2) Summary)) Deg))))))))) (forall ((TreeList2 tptp.list_VEBT_VEBT) (N tptp.nat) (Summary tptp.vEBT_VEBT) (M2 tptp.nat) (Deg tptp.nat)) (=> (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList2)) (@ (@ tptp.vEBT_invar_vebt X3) N))) (=> (@ (@ tptp.vEBT_invar_vebt Summary) M2) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M2)) (=> (= M2 (@ tptp.suc N)) (=> (= Deg (@ (@ tptp.plus_plus_nat N) M2)) (=> (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary) X_12))) (=> (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X3) X_12))))) (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Deg) TreeList2) Summary)) Deg))))))))) (forall ((Xs2 tptp.list_VEBT_VEBT) (Ys tptp.list_VEBT_VEBT) (R3 tptp.set_Pr6192946355708809607T_VEBT)) (=> (@ (@ tptp.member4439316823752958928T_VEBT (@ (@ tptp.produc3897820843166775703T_VEBT Xs2) Ys)) (@ tptp.listre1230615542750757617T_VEBT R3)) (= (@ tptp.size_s6755466524823107622T_VEBT Xs2) (@ tptp.size_s6755466524823107622T_VEBT Ys)))) (forall ((Xs2 tptp.list_VEBT_VEBT) (Ys tptp.list_o) (R3 tptp.set_Pr3175402225741728619VEBT_o)) (=> (@ (@ tptp.member3126162362653435956list_o (@ (@ tptp.produc2717590391345394939list_o Xs2) Ys)) (@ tptp.listrel_VEBT_VEBT_o R3)) (= (@ tptp.size_s6755466524823107622T_VEBT Xs2) (@ tptp.size_size_list_o Ys)))) (forall ((Xs2 tptp.list_VEBT_VEBT) (Ys tptp.list_nat) (R3 tptp.set_Pr7556676689462069481BT_nat)) (=> (@ (@ tptp.member6193324644334088288st_nat (@ (@ tptp.produc5570133714943300547st_nat Xs2) Ys)) (@ tptp.listre5900670229112895443BT_nat R3)) (= (@ tptp.size_s6755466524823107622T_VEBT Xs2) (@ tptp.size_size_list_nat Ys)))) (forall ((Xs2 tptp.list_VEBT_VEBT) (Ys tptp.list_int) (R3 tptp.set_Pr5066593544530342725BT_int)) (=> (@ (@ tptp.member3703241499402361532st_int (@ (@ tptp.produc1392282695434103839st_int Xs2) Ys)) (@ tptp.listre5898179758603845167BT_int R3)) (= (@ tptp.size_s6755466524823107622T_VEBT Xs2) (@ tptp.size_size_list_int Ys)))) (forall ((Xs2 tptp.list_o) (Ys tptp.list_VEBT_VEBT) (R3 tptp.set_Pr7543698050874017315T_VEBT)) (=> (@ (@ tptp.member1087064965665443052T_VEBT (@ (@ tptp.produc6043759678074843571T_VEBT Xs2) Ys)) (@ tptp.listrel_o_VEBT_VEBT R3)) (= (@ tptp.size_size_list_o Xs2) (@ tptp.size_s6755466524823107622T_VEBT Ys)))) (forall ((Xs2 tptp.list_o) (Ys tptp.list_o) (R3 tptp.set_Product_prod_o_o)) (=> (@ (@ tptp.member4159035015898711888list_o (@ (@ tptp.produc8435520187683070743list_o Xs2) Ys)) (@ tptp.listrel_o_o R3)) (= (@ tptp.size_size_list_o Xs2) (@ tptp.size_size_list_o Ys)))) (forall ((Xs2 tptp.list_o) (Ys tptp.list_nat) (R3 tptp.set_Pr2101469702781467981_o_nat)) (=> (@ (@ tptp.member1519744053835550788st_nat (@ (@ tptp.produc7128876500814652583st_nat Xs2) Ys)) (@ tptp.listrel_o_nat R3)) (= (@ tptp.size_size_list_o Xs2) (@ tptp.size_size_list_nat Ys)))) (forall ((Xs2 tptp.list_o) (Ys tptp.list_int) (R3 tptp.set_Pr8834758594704517033_o_int)) (=> (@ (@ tptp.member8253032945758599840st_int (@ (@ tptp.produc2951025481305455875st_int Xs2) Ys)) (@ tptp.listrel_o_int R3)) (= (@ tptp.size_size_list_o Xs2) (@ tptp.size_size_list_int Ys)))) (forall ((Xs2 tptp.list_nat) (Ys tptp.list_VEBT_VEBT) (R3 tptp.set_Pr6167073792073659919T_VEBT)) (=> (@ (@ tptp.member5968030670617646438T_VEBT (@ (@ tptp.produc8335345208264861441T_VEBT Xs2) Ys)) (@ tptp.listre5761932458788874033T_VEBT R3)) (= (@ tptp.size_size_list_nat Xs2) (@ tptp.size_s6755466524823107622T_VEBT Ys)))) (forall ((Xs2 tptp.list_nat) (Ys tptp.list_o) (R3 tptp.set_Pr3149072824959771635_nat_o)) (=> (@ (@ tptp.member6688923169008879818list_o (@ (@ tptp.produc699922362453767013list_o Xs2) Ys)) (@ tptp.listrel_nat_o R3)) (= (@ tptp.size_size_list_nat Xs2) (@ tptp.size_size_list_o Ys)))) (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))))) (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (exists ((N3 tptp.nat)) (@ (@ tptp.ord_less_real Y) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N3)) X))))) (forall ((N tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M2) (= (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.minus_minus_nat M2) N)) (@ (@ tptp.minus_minus_rat (@ tptp.semiri681578069525770553at_rat M2)) (@ tptp.semiri681578069525770553at_rat N))))) (forall ((N tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M2) (= (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.minus_minus_nat M2) N)) (@ (@ tptp.minus_minus_real (@ tptp.semiri5074537144036343181t_real M2)) (@ tptp.semiri5074537144036343181t_real N))))) (forall ((N tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M2) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.minus_minus_nat M2) N)) (@ (@ tptp.minus_minus_int (@ tptp.semiri1314217659103216013at_int M2)) (@ tptp.semiri1314217659103216013at_int N))))) (forall ((N tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M2) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.minus_minus_nat M2) N)) (@ (@ tptp.minus_minus_nat (@ tptp.semiri1316708129612266289at_nat M2)) (@ tptp.semiri1316708129612266289at_nat N))))) (forall ((P2 (-> tptp.int Bool)) (X tptp.nat) (Y tptp.nat)) (= (@ P2 (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.minus_minus_nat X) Y))) (and (=> (@ (@ tptp.ord_less_eq_nat Y) X) (@ P2 (@ (@ tptp.minus_minus_int (@ tptp.semiri1314217659103216013at_int X)) (@ tptp.semiri1314217659103216013at_int Y)))) (=> (@ (@ tptp.ord_less_nat X) Y) (@ P2 tptp.zero_zero_int))))) (forall ((X2 tptp.num)) (= (@ tptp.size_size_num (@ tptp.bit0 X2)) (@ (@ tptp.plus_plus_nat (@ tptp.size_size_num X2)) (@ tptp.suc tptp.zero_zero_nat)))) (forall ((A tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (exists ((R4 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) R4) (= (@ (@ tptp.power_power_real R4) (@ tptp.suc N)) A))))) (forall ((Xs2 tptp.list_Code_integer) (Y tptp.code_integer) (Ys tptp.list_Code_integer) (R3 tptp.set_Pr4811707699266497531nteger)) (=> (@ (@ tptp.member749217712838834276nteger (@ (@ tptp.produc750622340256944499nteger Xs2) (@ (@ tptp.cons_Code_integer Y) Ys))) (@ tptp.listre5734910445319291053nteger R3)) (not (forall ((X3 tptp.code_integer) (Xs3 tptp.list_Code_integer)) (=> (= Xs2 (@ (@ tptp.cons_Code_integer X3) Xs3)) (=> (@ (@ tptp.member157494554546826820nteger (@ (@ tptp.produc1086072967326762835nteger X3) Y)) R3) (not (@ (@ tptp.member749217712838834276nteger (@ (@ tptp.produc750622340256944499nteger Xs3) Ys)) (@ tptp.listre5734910445319291053nteger R3))))))))) (forall ((Xs2 tptp.list_P6011104703257516679at_nat) (Y tptp.product_prod_nat_nat) (Ys tptp.list_P6011104703257516679at_nat) (R3 tptp.set_Pr8693737435421807431at_nat)) (=> (@ (@ tptp.member6693912407220327184at_nat (@ (@ tptp.produc5943733680697469783at_nat Xs2) (@ (@ tptp.cons_P6512896166579812791at_nat Y) Ys))) (@ tptp.listre818007680106770737at_nat R3)) (not (forall ((X3 tptp.product_prod_nat_nat) (Xs3 tptp.list_P6011104703257516679at_nat)) (=> (= Xs2 (@ (@ tptp.cons_P6512896166579812791at_nat X3) Xs3)) (=> (@ (@ tptp.member8206827879206165904at_nat (@ (@ tptp.produc6161850002892822231at_nat X3) Y)) R3) (not (@ (@ tptp.member6693912407220327184at_nat (@ (@ tptp.produc5943733680697469783at_nat Xs3) Ys)) (@ tptp.listre818007680106770737at_nat R3))))))))) (forall ((Xs2 tptp.list_s1210847774152347623at_nat) (Y tptp.set_Pr1261947904930325089at_nat) (Ys tptp.list_s1210847774152347623at_nat) (R3 tptp.set_Pr4329608150637261639at_nat)) (=> (@ (@ tptp.member4080735728053443344at_nat (@ (@ tptp.produc7536900900485677911at_nat Xs2) (@ (@ tptp.cons_s6881495754146722583at_nat Y) Ys))) (@ tptp.listre2047417242196832561at_nat R3)) (not (forall ((X3 tptp.set_Pr1261947904930325089at_nat) (Xs3 tptp.list_s1210847774152347623at_nat)) (=> (= Xs2 (@ (@ tptp.cons_s6881495754146722583at_nat X3) Xs3)) (=> (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat X3) Y)) R3) (not (@ (@ tptp.member4080735728053443344at_nat (@ (@ tptp.produc7536900900485677911at_nat Xs3) Ys)) (@ tptp.listre2047417242196832561at_nat R3))))))))) (forall ((Xs2 tptp.list_nat) (Y tptp.nat) (Ys tptp.list_nat) (R3 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.member7340969449405702474st_nat (@ (@ tptp.produc2694037385005941721st_nat Xs2) (@ (@ tptp.cons_nat Y) Ys))) (@ tptp.listrel_nat_nat R3)) (not (forall ((X3 tptp.nat) (Xs3 tptp.list_nat)) (=> (= Xs2 (@ (@ tptp.cons_nat X3) Xs3)) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X3) Y)) R3) (not (@ (@ tptp.member7340969449405702474st_nat (@ (@ tptp.produc2694037385005941721st_nat Xs3) Ys)) (@ tptp.listrel_nat_nat R3))))))))) (forall ((Xs2 tptp.list_int) (Y tptp.int) (Ys tptp.list_int) (R3 tptp.set_Pr958786334691620121nt_int)) (=> (@ (@ tptp.member6698963635872716290st_int (@ (@ tptp.produc364263696895485585st_int Xs2) (@ (@ tptp.cons_int Y) Ys))) (@ tptp.listrel_int_int R3)) (not (forall ((X3 tptp.int) (Xs3 tptp.list_int)) (=> (= Xs2 (@ (@ tptp.cons_int X3) Xs3)) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X3) Y)) R3) (not (@ (@ tptp.member6698963635872716290st_int (@ (@ tptp.produc364263696895485585st_int Xs3) Ys)) (@ tptp.listrel_int_int R3))))))))) (forall ((Y tptp.code_integer) (Ys tptp.list_Code_integer) (Xs2 tptp.list_Code_integer) (R3 tptp.set_Pr4811707699266497531nteger)) (=> (@ (@ tptp.member749217712838834276nteger (@ (@ tptp.produc750622340256944499nteger (@ (@ tptp.cons_Code_integer Y) Ys)) Xs2)) (@ tptp.listre5734910445319291053nteger R3)) (not (forall ((Y3 tptp.code_integer) (Ys5 tptp.list_Code_integer)) (=> (= Xs2 (@ (@ tptp.cons_Code_integer Y3) Ys5)) (=> (@ (@ tptp.member157494554546826820nteger (@ (@ tptp.produc1086072967326762835nteger Y) Y3)) R3) (not (@ (@ tptp.member749217712838834276nteger (@ (@ tptp.produc750622340256944499nteger Ys) Ys5)) (@ tptp.listre5734910445319291053nteger R3))))))))) (forall ((Y tptp.product_prod_nat_nat) (Ys tptp.list_P6011104703257516679at_nat) (Xs2 tptp.list_P6011104703257516679at_nat) (R3 tptp.set_Pr8693737435421807431at_nat)) (=> (@ (@ tptp.member6693912407220327184at_nat (@ (@ tptp.produc5943733680697469783at_nat (@ (@ tptp.cons_P6512896166579812791at_nat Y) Ys)) Xs2)) (@ tptp.listre818007680106770737at_nat R3)) (not (forall ((Y3 tptp.product_prod_nat_nat) (Ys5 tptp.list_P6011104703257516679at_nat)) (=> (= Xs2 (@ (@ tptp.cons_P6512896166579812791at_nat Y3) Ys5)) (=> (@ (@ tptp.member8206827879206165904at_nat (@ (@ tptp.produc6161850002892822231at_nat Y) Y3)) R3) (not (@ (@ tptp.member6693912407220327184at_nat (@ (@ tptp.produc5943733680697469783at_nat Ys) Ys5)) (@ tptp.listre818007680106770737at_nat R3))))))))) (forall ((Y tptp.set_Pr1261947904930325089at_nat) (Ys tptp.list_s1210847774152347623at_nat) (Xs2 tptp.list_s1210847774152347623at_nat) (R3 tptp.set_Pr4329608150637261639at_nat)) (=> (@ (@ tptp.member4080735728053443344at_nat (@ (@ tptp.produc7536900900485677911at_nat (@ (@ tptp.cons_s6881495754146722583at_nat Y) Ys)) Xs2)) (@ tptp.listre2047417242196832561at_nat R3)) (not (forall ((Y3 tptp.set_Pr1261947904930325089at_nat) (Ys5 tptp.list_s1210847774152347623at_nat)) (=> (= Xs2 (@ (@ tptp.cons_s6881495754146722583at_nat Y3) Ys5)) (=> (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat Y) Y3)) R3) (not (@ (@ tptp.member4080735728053443344at_nat (@ (@ tptp.produc7536900900485677911at_nat Ys) Ys5)) (@ tptp.listre2047417242196832561at_nat R3))))))))) (forall ((Y tptp.nat) (Ys tptp.list_nat) (Xs2 tptp.list_nat) (R3 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.member7340969449405702474st_nat (@ (@ tptp.produc2694037385005941721st_nat (@ (@ tptp.cons_nat Y) Ys)) Xs2)) (@ tptp.listrel_nat_nat R3)) (not (forall ((Y3 tptp.nat) (Ys5 tptp.list_nat)) (=> (= Xs2 (@ (@ tptp.cons_nat Y3) Ys5)) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat Y) Y3)) R3) (not (@ (@ tptp.member7340969449405702474st_nat (@ (@ tptp.produc2694037385005941721st_nat Ys) Ys5)) (@ tptp.listrel_nat_nat R3))))))))) (forall ((Y tptp.int) (Ys tptp.list_int) (Xs2 tptp.list_int) (R3 tptp.set_Pr958786334691620121nt_int)) (=> (@ (@ tptp.member6698963635872716290st_int (@ (@ tptp.produc364263696895485585st_int (@ (@ tptp.cons_int Y) Ys)) Xs2)) (@ tptp.listrel_int_int R3)) (not (forall ((Y3 tptp.int) (Ys5 tptp.list_int)) (=> (= Xs2 (@ (@ tptp.cons_int Y3) Ys5)) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int Y) Y3)) R3) (not (@ (@ tptp.member6698963635872716290st_int (@ (@ tptp.produc364263696895485585st_int Ys) Ys5)) (@ tptp.listrel_int_int R3))))))))) (forall ((X tptp.code_integer) (Y tptp.code_integer) (R3 tptp.set_Pr4811707699266497531nteger) (Xs2 tptp.list_Code_integer) (Ys tptp.list_Code_integer)) (let ((_let_1 (@ tptp.listre5734910445319291053nteger R3))) (=> (@ (@ tptp.member157494554546826820nteger (@ (@ tptp.produc1086072967326762835nteger X) Y)) R3) (=> (@ (@ tptp.member749217712838834276nteger (@ (@ tptp.produc750622340256944499nteger Xs2) Ys)) _let_1) (@ (@ tptp.member749217712838834276nteger (@ (@ tptp.produc750622340256944499nteger (@ (@ tptp.cons_Code_integer X) Xs2)) (@ (@ tptp.cons_Code_integer Y) Ys))) _let_1))))) (forall ((X tptp.product_prod_nat_nat) (Y tptp.product_prod_nat_nat) (R3 tptp.set_Pr8693737435421807431at_nat) (Xs2 tptp.list_P6011104703257516679at_nat) (Ys tptp.list_P6011104703257516679at_nat)) (let ((_let_1 (@ tptp.listre818007680106770737at_nat R3))) (=> (@ (@ tptp.member8206827879206165904at_nat (@ (@ tptp.produc6161850002892822231at_nat X) Y)) R3) (=> (@ (@ tptp.member6693912407220327184at_nat (@ (@ tptp.produc5943733680697469783at_nat Xs2) Ys)) _let_1) (@ (@ tptp.member6693912407220327184at_nat (@ (@ tptp.produc5943733680697469783at_nat (@ (@ tptp.cons_P6512896166579812791at_nat X) Xs2)) (@ (@ tptp.cons_P6512896166579812791at_nat Y) Ys))) _let_1))))) (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat) (R3 tptp.set_Pr4329608150637261639at_nat) (Xs2 tptp.list_s1210847774152347623at_nat) (Ys tptp.list_s1210847774152347623at_nat)) (let ((_let_1 (@ tptp.listre2047417242196832561at_nat R3))) (=> (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat X) Y)) R3) (=> (@ (@ tptp.member4080735728053443344at_nat (@ (@ tptp.produc7536900900485677911at_nat Xs2) Ys)) _let_1) (@ (@ tptp.member4080735728053443344at_nat (@ (@ tptp.produc7536900900485677911at_nat (@ (@ tptp.cons_s6881495754146722583at_nat X) Xs2)) (@ (@ tptp.cons_s6881495754146722583at_nat Y) Ys))) _let_1))))) (forall ((X tptp.nat) (Y tptp.nat) (R3 tptp.set_Pr1261947904930325089at_nat) (Xs2 tptp.list_nat) (Ys tptp.list_nat)) (let ((_let_1 (@ tptp.listrel_nat_nat R3))) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X) Y)) R3) (=> (@ (@ tptp.member7340969449405702474st_nat (@ (@ tptp.produc2694037385005941721st_nat Xs2) Ys)) _let_1) (@ (@ tptp.member7340969449405702474st_nat (@ (@ tptp.produc2694037385005941721st_nat (@ (@ tptp.cons_nat X) Xs2)) (@ (@ tptp.cons_nat Y) Ys))) _let_1))))) (forall ((X tptp.int) (Y tptp.int) (R3 tptp.set_Pr958786334691620121nt_int) (Xs2 tptp.list_int) (Ys tptp.list_int)) (let ((_let_1 (@ tptp.listrel_int_int R3))) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X) Y)) R3) (=> (@ (@ tptp.member6698963635872716290st_int (@ (@ tptp.produc364263696895485585st_int Xs2) Ys)) _let_1) (@ (@ tptp.member6698963635872716290st_int (@ (@ tptp.produc364263696895485585st_int (@ (@ tptp.cons_int X) Xs2)) (@ (@ tptp.cons_int Y) Ys))) _let_1))))) (forall ((F2 (-> tptp.code_integer tptp.nat)) (X tptp.code_integer) (Y tptp.code_integer) (Fs tptp.list_C4705013386053401436er_nat)) (=> (@ (@ tptp.ord_less_nat (@ F2 X)) (@ F2 Y)) (@ (@ tptp.member157494554546826820nteger (@ (@ tptp.produc1086072967326762835nteger X) Y)) (@ tptp.measur8870801148506250077nteger (@ (@ tptp.cons_C1897838848541180310er_nat F2) Fs))))) (forall ((F2 (-> tptp.product_prod_nat_nat tptp.nat)) (X tptp.product_prod_nat_nat) (Y tptp.product_prod_nat_nat) (Fs tptp.list_P9162950289778280392at_nat)) (=> (@ (@ tptp.ord_less_nat (@ F2 X)) (@ F2 Y)) (@ (@ tptp.member8206827879206165904at_nat (@ (@ tptp.produc6161850002892822231at_nat X) Y)) (@ tptp.measur2679027848233739777at_nat (@ (@ tptp.cons_P4861729644591583992at_nat F2) Fs))))) (forall ((F2 (-> tptp.set_Pr1261947904930325089at_nat tptp.nat)) (X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat) (Fs tptp.list_s9130966667114977576at_nat)) (=> (@ (@ tptp.ord_less_nat (@ F2 X)) (@ F2 Y)) (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat X) Y)) (@ tptp.measur2694323259624372065at_nat (@ (@ tptp.cons_s2538900923071588440at_nat F2) Fs))))) (forall ((F2 (-> tptp.nat tptp.nat)) (X tptp.nat) (Y tptp.nat) (Fs tptp.list_nat_nat)) (=> (@ (@ tptp.ord_less_nat (@ F2 X)) (@ F2 Y)) (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X) Y)) (@ tptp.measures_nat (@ (@ tptp.cons_nat_nat F2) Fs))))) (forall ((F2 (-> tptp.int tptp.nat)) (X tptp.int) (Y tptp.int) (Fs tptp.list_int_nat)) (=> (@ (@ tptp.ord_less_nat (@ F2 X)) (@ F2 Y)) (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X) Y)) (@ tptp.measures_int (@ (@ tptp.cons_int_nat F2) Fs))))) (forall ((F2 (-> tptp.code_integer tptp.nat)) (X tptp.code_integer) (Y tptp.code_integer) (Fs tptp.list_C4705013386053401436er_nat)) (let ((_let_1 (@ tptp.member157494554546826820nteger (@ (@ tptp.produc1086072967326762835nteger X) Y)))) (=> (@ (@ tptp.ord_less_eq_nat (@ F2 X)) (@ F2 Y)) (=> (@ _let_1 (@ tptp.measur8870801148506250077nteger Fs)) (@ _let_1 (@ tptp.measur8870801148506250077nteger (@ (@ tptp.cons_C1897838848541180310er_nat F2) Fs))))))) (forall ((F2 (-> tptp.product_prod_nat_nat tptp.nat)) (X tptp.product_prod_nat_nat) (Y tptp.product_prod_nat_nat) (Fs tptp.list_P9162950289778280392at_nat)) (let ((_let_1 (@ tptp.member8206827879206165904at_nat (@ (@ tptp.produc6161850002892822231at_nat X) Y)))) (=> (@ (@ tptp.ord_less_eq_nat (@ F2 X)) (@ F2 Y)) (=> (@ _let_1 (@ tptp.measur2679027848233739777at_nat Fs)) (@ _let_1 (@ tptp.measur2679027848233739777at_nat (@ (@ tptp.cons_P4861729644591583992at_nat F2) Fs))))))) (forall ((F2 (-> tptp.set_Pr1261947904930325089at_nat tptp.nat)) (X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat) (Fs tptp.list_s9130966667114977576at_nat)) (let ((_let_1 (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat X) Y)))) (=> (@ (@ tptp.ord_less_eq_nat (@ F2 X)) (@ F2 Y)) (=> (@ _let_1 (@ tptp.measur2694323259624372065at_nat Fs)) (@ _let_1 (@ tptp.measur2694323259624372065at_nat (@ (@ tptp.cons_s2538900923071588440at_nat F2) Fs))))))) (forall ((F2 (-> tptp.nat tptp.nat)) (X tptp.nat) (Y tptp.nat) (Fs tptp.list_nat_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X) Y)))) (=> (@ (@ tptp.ord_less_eq_nat (@ F2 X)) (@ F2 Y)) (=> (@ _let_1 (@ tptp.measures_nat Fs)) (@ _let_1 (@ tptp.measures_nat (@ (@ tptp.cons_nat_nat F2) Fs))))))) (forall ((F2 (-> tptp.int tptp.nat)) (X tptp.int) (Y tptp.int) (Fs tptp.list_int_nat)) (let ((_let_1 (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X) Y)))) (=> (@ (@ tptp.ord_less_eq_nat (@ F2 X)) (@ F2 Y)) (=> (@ _let_1 (@ tptp.measures_int Fs)) (@ _let_1 (@ tptp.measures_int (@ (@ tptp.cons_int_nat F2) Fs))))))) (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))) (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))) (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))) (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))) (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))))))) (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))))))) (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))))))) (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))))))) (forall ((X tptp.nat) (Xs2 tptp.list_nat) (N tptp.nat) (Y tptp.nat)) (= (= (@ (@ tptp.cons_nat X) Xs2) (@ (@ tptp.replicate_nat N) Y)) (and (= X Y) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= Xs2 (@ (@ tptp.replicate_nat (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) X))))) (forall ((X tptp.vEBT_VEBT) (Xs2 tptp.list_VEBT_VEBT) (N tptp.nat) (Y tptp.vEBT_VEBT)) (= (= (@ (@ tptp.cons_VEBT_VEBT X) Xs2) (@ (@ tptp.replicate_VEBT_VEBT N) Y)) (and (= X Y) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= Xs2 (@ (@ tptp.replicate_VEBT_VEBT (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) X))))) (forall ((L tptp.num) (R3 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 L) (@ (@ tptp.product_Pair_nat_nat Q2) R3)))) (let ((_let_3 (@ tptp.numeral_numeral_nat L))) (let ((_let_4 (@ (@ tptp.ord_less_eq_nat _let_3) R3))) (and (=> _let_4 (= _let_2 (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat)) (@ (@ tptp.minus_minus_nat R3) _let_3)))) (=> (not _let_4) (= _let_2 (@ (@ tptp.product_Pair_nat_nat _let_1) R3))))))))) (forall ((L tptp.num) (R3 tptp.int) (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 L) (@ (@ tptp.product_Pair_int_int Q2) R3)))) (let ((_let_3 (@ tptp.numeral_numeral_int L))) (let ((_let_4 (@ (@ tptp.ord_less_eq_int _let_3) R3))) (and (=> _let_4 (= _let_2 (@ (@ tptp.product_Pair_int_int (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int)) (@ (@ tptp.minus_minus_int R3) _let_3)))) (=> (not _let_4) (= _let_2 (@ (@ tptp.product_Pair_int_int _let_1) R3))))))))) (forall ((L tptp.num) (R3 tptp.code_integer) (Q2 tptp.code_integer)) (let ((_let_1 (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) Q2))) (let ((_let_2 (@ (@ tptp.unique4921790084139445826nteger L) (@ (@ tptp.produc1086072967326762835nteger Q2) R3)))) (let ((_let_3 (@ tptp.numera6620942414471956472nteger L))) (let ((_let_4 (@ (@ tptp.ord_le3102999989581377725nteger _let_3) R3))) (and (=> _let_4 (= _let_2 (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.plus_p5714425477246183910nteger _let_1) tptp.one_one_Code_integer)) (@ (@ tptp.minus_8373710615458151222nteger R3) _let_3)))) (=> (not _let_4) (= _let_2 (@ (@ tptp.produc1086072967326762835nteger _let_1) R3))))))))) (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 ((M tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (and (= (@ tptp.some_nat M) (@ tptp.vEBT_vebt_mint Summary)) (@ (@ tptp.ord_less_nat M) (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.minus_minus_nat N) (@ (@ tptp.divide_divide_nat N) _let_1))))))))))) (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.sup_sup_set_nat (@ tptp.vEBT_set_vebt T)) (@ (@ tptp.insert_nat X) tptp.bot_bot_set_nat)) (@ tptp.vEBT_set_vebt (@ (@ tptp.vEBT_vebt_insert T) X)))))) (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.sup_sup_set_nat (@ tptp.vEBT_VEBT_set_vebt T)) (@ (@ tptp.insert_nat X) tptp.bot_bot_set_nat)) (@ tptp.vEBT_VEBT_set_vebt (@ (@ tptp.vEBT_vebt_insert T) X)))))) (forall ((T tptp.vEBT_VEBT) (N tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.vEBT_VEBT_set_vebt T)) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) tptp.one_one_nat))))) (forall ((P2 (-> tptp.nat Bool)) (N tptp.nat)) (=> (@ P2 tptp.zero_zero_nat) (=> (forall ((N3 tptp.nat)) (=> (@ P2 N3) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N3) (@ P2 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N3))))) (=> (forall ((N3 tptp.nat)) (=> (@ P2 N3) (@ P2 (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N3))))) (@ P2 N))))) (forall ((P2 (-> tptp.nat Bool)) (N tptp.nat)) (=> (@ P2 tptp.zero_zero_nat) (=> (@ P2 tptp.one_one_nat) (=> (forall ((N3 tptp.nat)) (=> (@ P2 N3) (@ P2 (@ (@ tptp.plus_plus_nat N3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ P2 N))))) (forall ((N tptp.nat) (M2 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) M2)) tptp.zero_zero_nat))))) (forall ((N tptp.nat) (M2 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) M2)) tptp.zero_zero_int))))) (forall ((M2 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 M2) N)) tptp.zero_zero_nat)) (not (= (@ _let_1 M2) tptp.zero_zero_nat))))) (forall ((M2 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 M2) N)) tptp.zero_zero_int)) (not (= (@ _let_1 M2) tptp.zero_zero_int))))) (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.divide_divide_nat (@ _let_1 (@ (@ tptp.plus_plus_nat A) B))) (@ _let_1 A)) (@ _let_1 B)))) (forall ((B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_eq_nat B) A) (= (@ _let_1 (@ (@ tptp.minus_minus_nat A) B)) (@ (@ tptp.divide_divide_nat (@ _let_1 A)) (@ _let_1 B)))))) (forall ((A tptp.nat)) (= (@ (@ tptp.divide_divide_nat A) tptp.zero_zero_nat) tptp.zero_zero_nat)) (forall ((A tptp.int)) (= (@ (@ tptp.divide_divide_int A) tptp.zero_zero_int) tptp.zero_zero_int)) (forall ((A tptp.nat)) (= (@ (@ tptp.divide_divide_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)) (forall ((A tptp.int)) (= (@ (@ tptp.divide_divide_int tptp.zero_zero_int) A) tptp.zero_zero_int)) (forall ((A tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) tptp.zero_zero_complex) tptp.zero_zero_complex)) (forall ((A tptp.real)) (= (@ (@ tptp.divide_divide_real A) tptp.zero_zero_real) tptp.zero_zero_real)) (forall ((A tptp.rat)) (= (@ (@ tptp.divide_divide_rat A) tptp.zero_zero_rat) tptp.zero_zero_rat)) (forall ((A tptp.nat)) (= (@ (@ tptp.divide_divide_nat A) tptp.zero_zero_nat) tptp.zero_zero_nat)) (forall ((A tptp.int)) (= (@ (@ tptp.divide_divide_int A) tptp.zero_zero_int) tptp.zero_zero_int)) (forall ((A tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex tptp.zero_zero_complex) A) tptp.zero_zero_complex)) (forall ((A tptp.real)) (= (@ (@ tptp.divide_divide_real tptp.zero_zero_real) A) tptp.zero_zero_real)) (forall ((A tptp.rat)) (= (@ (@ tptp.divide_divide_rat tptp.zero_zero_rat) A) tptp.zero_zero_rat)) (forall ((A tptp.nat)) (= (@ (@ tptp.divide_divide_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)) (forall ((A tptp.int)) (= (@ (@ tptp.divide_divide_int tptp.zero_zero_int) A) tptp.zero_zero_int)) (forall ((A tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) tptp.zero_zero_complex) tptp.zero_zero_complex)) (forall ((A tptp.real)) (= (@ (@ tptp.divide_divide_real A) tptp.zero_zero_real) tptp.zero_zero_real)) (forall ((A tptp.rat)) (= (@ (@ tptp.divide_divide_rat A) tptp.zero_zero_rat) tptp.zero_zero_rat)) (forall ((A tptp.complex) (C2 tptp.complex) (B tptp.complex)) (= (= (@ (@ tptp.divide1717551699836669952omplex A) C2) (@ (@ tptp.divide1717551699836669952omplex B) C2)) (or (= C2 tptp.zero_zero_complex) (= A B)))) (forall ((A tptp.real) (C2 tptp.real) (B tptp.real)) (= (= (@ (@ tptp.divide_divide_real A) C2) (@ (@ tptp.divide_divide_real B) C2)) (or (= C2 tptp.zero_zero_real) (= A B)))) (forall ((A tptp.rat) (C2 tptp.rat) (B tptp.rat)) (= (= (@ (@ tptp.divide_divide_rat A) C2) (@ (@ tptp.divide_divide_rat B) C2)) (or (= C2 tptp.zero_zero_rat) (= A B)))) (forall ((C2 tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.divide1717551699836669952omplex C2))) (= (= (@ _let_1 A) (@ _let_1 B)) (or (= C2 tptp.zero_zero_complex) (= A B))))) (forall ((C2 tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.divide_divide_real C2))) (= (= (@ _let_1 A) (@ _let_1 B)) (or (= C2 tptp.zero_zero_real) (= A B))))) (forall ((C2 tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.divide_divide_rat C2))) (= (= (@ _let_1 A) (@ _let_1 B)) (or (= C2 tptp.zero_zero_rat) (= A B))))) (forall ((A tptp.complex) (B tptp.complex)) (= (= (@ (@ tptp.divide1717551699836669952omplex A) B) tptp.zero_zero_complex) (or (= A tptp.zero_zero_complex) (= B tptp.zero_zero_complex)))) (forall ((A tptp.real) (B tptp.real)) (= (= (@ (@ tptp.divide_divide_real A) B) tptp.zero_zero_real) (or (= A tptp.zero_zero_real) (= B tptp.zero_zero_real)))) (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ (@ tptp.divide_divide_rat A) B) tptp.zero_zero_rat) (or (= A tptp.zero_zero_rat) (= B tptp.zero_zero_rat)))) (forall ((A tptp.complex) (B tptp.complex) (C2 tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex A))) (= (@ _let_1 (@ (@ tptp.divide1717551699836669952omplex B) C2)) (@ (@ tptp.divide1717551699836669952omplex (@ _let_1 B)) C2)))) (forall ((A tptp.real) (B tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.times_times_real A))) (= (@ _let_1 (@ (@ tptp.divide_divide_real B) C2)) (@ (@ tptp.divide_divide_real (@ _let_1 B)) C2)))) (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat A))) (= (@ _let_1 (@ (@ tptp.divide_divide_rat B) C2)) (@ (@ tptp.divide_divide_rat (@ _let_1 B)) C2)))) (forall ((A tptp.complex) (B tptp.complex) (C2 tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) (@ (@ tptp.divide1717551699836669952omplex B) C2)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex A) C2)) B))) (forall ((A tptp.real) (B tptp.real) (C2 tptp.real)) (= (@ (@ tptp.divide_divide_real A) (@ (@ tptp.divide_divide_real B) C2)) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real A) C2)) B))) (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (= (@ (@ tptp.divide_divide_rat A) (@ (@ tptp.divide_divide_rat B) C2)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat A) C2)) B))) (forall ((A tptp.complex) (B tptp.complex) (C2 tptp.complex)) (let ((_let_1 (@ tptp.divide1717551699836669952omplex A))) (= (@ (@ tptp.divide1717551699836669952omplex (@ _let_1 B)) C2) (@ _let_1 (@ (@ tptp.times_times_complex B) C2))))) (forall ((A tptp.real) (B tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.divide_divide_real A))) (= (@ (@ tptp.divide_divide_real (@ _let_1 B)) C2) (@ _let_1 (@ (@ tptp.times_times_real B) C2))))) (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.divide_divide_rat A))) (= (@ (@ tptp.divide_divide_rat (@ _let_1 B)) C2) (@ _let_1 (@ (@ tptp.times_times_rat B) C2))))) (forall ((B tptp.complex) (C2 tptp.complex) (A tptp.complex)) (= (@ (@ tptp.times_times_complex (@ (@ tptp.divide1717551699836669952omplex B) C2)) A) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex B) A)) C2))) (forall ((B tptp.real) (C2 tptp.real) (A tptp.real)) (= (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real B) C2)) A) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real B) A)) C2))) (forall ((B tptp.rat) (C2 tptp.rat) (A tptp.rat)) (= (@ (@ tptp.times_times_rat (@ (@ tptp.divide_divide_rat B) C2)) A) (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat B) A)) C2))) (forall ((A tptp.code_integer)) (= (@ (@ tptp.divide6298287555418463151nteger A) tptp.one_one_Code_integer) A)) (forall ((A tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) tptp.one_one_complex) A)) (forall ((A tptp.real)) (= (@ (@ tptp.divide_divide_real A) tptp.one_one_real) A)) (forall ((A tptp.rat)) (= (@ (@ tptp.divide_divide_rat A) tptp.one_one_rat) A)) (forall ((A tptp.nat)) (= (@ (@ tptp.divide_divide_nat A) tptp.one_one_nat) A)) (forall ((A tptp.int)) (= (@ (@ tptp.divide_divide_int A) tptp.one_one_int) A)) (forall ((I2 tptp.set_nat) (L tptp.set_nat) (U tptp.set_nat)) (= (@ (@ tptp.member_set_nat I2) (@ (@ tptp.set_or4548717258645045905et_nat L) U)) (and (@ (@ tptp.ord_less_eq_set_nat L) I2) (@ (@ tptp.ord_less_eq_set_nat I2) U)))) (forall ((I2 tptp.rat) (L tptp.rat) (U tptp.rat)) (= (@ (@ tptp.member_rat I2) (@ (@ tptp.set_or633870826150836451st_rat L) U)) (and (@ (@ tptp.ord_less_eq_rat L) I2) (@ (@ tptp.ord_less_eq_rat I2) U)))) (forall ((I2 tptp.num) (L tptp.num) (U tptp.num)) (= (@ (@ tptp.member_num I2) (@ (@ tptp.set_or7049704709247886629st_num L) U)) (and (@ (@ tptp.ord_less_eq_num L) I2) (@ (@ tptp.ord_less_eq_num I2) U)))) (forall ((I2 tptp.nat) (L tptp.nat) (U tptp.nat)) (= (@ (@ tptp.member_nat I2) (@ (@ tptp.set_or1269000886237332187st_nat L) U)) (and (@ (@ tptp.ord_less_eq_nat L) I2) (@ (@ tptp.ord_less_eq_nat I2) U)))) (forall ((I2 tptp.int) (L tptp.int) (U tptp.int)) (= (@ (@ tptp.member_int I2) (@ (@ tptp.set_or1266510415728281911st_int L) U)) (and (@ (@ tptp.ord_less_eq_int L) I2) (@ (@ tptp.ord_less_eq_int I2) U)))) (forall ((I2 tptp.real) (L tptp.real) (U tptp.real)) (= (@ (@ tptp.member_real I2) (@ (@ tptp.set_or1222579329274155063t_real L) U)) (and (@ (@ tptp.ord_less_eq_real L) I2) (@ (@ tptp.ord_less_eq_real I2) U)))) (forall ((L tptp.set_nat) (H tptp.set_nat) (L3 tptp.set_nat) (H3 tptp.set_nat)) (= (= (@ (@ tptp.set_or4548717258645045905et_nat L) H) (@ (@ tptp.set_or4548717258645045905et_nat L3) H3)) (or (and (= L L3) (= H H3)) (and (not (@ (@ tptp.ord_less_eq_set_nat L) H)) (not (@ (@ tptp.ord_less_eq_set_nat L3) H3)))))) (forall ((L tptp.rat) (H tptp.rat) (L3 tptp.rat) (H3 tptp.rat)) (= (= (@ (@ tptp.set_or633870826150836451st_rat L) H) (@ (@ tptp.set_or633870826150836451st_rat L3) H3)) (or (and (= L L3) (= H H3)) (and (not (@ (@ tptp.ord_less_eq_rat L) H)) (not (@ (@ tptp.ord_less_eq_rat L3) H3)))))) (forall ((L tptp.num) (H tptp.num) (L3 tptp.num) (H3 tptp.num)) (= (= (@ (@ tptp.set_or7049704709247886629st_num L) H) (@ (@ tptp.set_or7049704709247886629st_num L3) H3)) (or (and (= L L3) (= H H3)) (and (not (@ (@ tptp.ord_less_eq_num L) H)) (not (@ (@ tptp.ord_less_eq_num L3) H3)))))) (forall ((L tptp.nat) (H tptp.nat) (L3 tptp.nat) (H3 tptp.nat)) (= (= (@ (@ tptp.set_or1269000886237332187st_nat L) H) (@ (@ tptp.set_or1269000886237332187st_nat L3) H3)) (or (and (= L L3) (= H H3)) (and (not (@ (@ tptp.ord_less_eq_nat L) H)) (not (@ (@ tptp.ord_less_eq_nat L3) H3)))))) (forall ((L tptp.int) (H tptp.int) (L3 tptp.int) (H3 tptp.int)) (= (= (@ (@ tptp.set_or1266510415728281911st_int L) H) (@ (@ tptp.set_or1266510415728281911st_int L3) H3)) (or (and (= L L3) (= H H3)) (and (not (@ (@ tptp.ord_less_eq_int L) H)) (not (@ (@ tptp.ord_less_eq_int L3) H3)))))) (forall ((L tptp.real) (H tptp.real) (L3 tptp.real) (H3 tptp.real)) (= (= (@ (@ tptp.set_or1222579329274155063t_real L) H) (@ (@ tptp.set_or1222579329274155063t_real L3) H3)) (or (and (= L L3) (= H H3)) (and (not (@ (@ tptp.ord_less_eq_real L) H)) (not (@ (@ tptp.ord_less_eq_real L3) H3)))))) (forall ((L tptp.nat) (U tptp.nat)) (@ tptp.finite_finite_nat (@ (@ tptp.set_or1269000886237332187st_nat L) U))) (forall ((A tptp.complex) (B tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex A) B)) A) B))) (forall ((A tptp.real) (B tptp.real)) (=> (not (= A tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real A) B)) A) B))) (forall ((A tptp.rat) (B tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat A) B)) A) B))) (forall ((A tptp.nat) (B tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat A) B)) A) B))) (forall ((A tptp.int) (B tptp.int)) (=> (not (= A tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int A) B)) A) B))) (forall ((B tptp.complex) (A tptp.complex)) (=> (not (= B tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex A) B)) B) A))) (forall ((B tptp.real) (A tptp.real)) (=> (not (= B tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real A) B)) B) A))) (forall ((B tptp.rat) (A tptp.rat)) (=> (not (= B tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat A) B)) B) A))) (forall ((B tptp.nat) (A tptp.nat)) (=> (not (= B tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat A) B)) B) A))) (forall ((B tptp.int) (A tptp.int)) (=> (not (= B tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int A) B)) B) A))) (forall ((C2 tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex C2))) (let ((_let_2 (@ (@ tptp.divide1717551699836669952omplex (@ _let_1 A)) (@ _let_1 B)))) (let ((_let_3 (= C2 tptp.zero_zero_complex))) (and (=> _let_3 (= _let_2 tptp.zero_zero_complex)) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide1717551699836669952omplex A) B)))))))) (forall ((C2 tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real C2))) (let ((_let_2 (@ (@ tptp.divide_divide_real (@ _let_1 A)) (@ _let_1 B)))) (let ((_let_3 (= C2 tptp.zero_zero_real))) (and (=> _let_3 (= _let_2 tptp.zero_zero_real)) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_real A) B)))))))) (forall ((C2 tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C2))) (let ((_let_2 (@ (@ tptp.divide_divide_rat (@ _let_1 A)) (@ _let_1 B)))) (let ((_let_3 (= C2 tptp.zero_zero_rat))) (and (=> _let_3 (= _let_2 tptp.zero_zero_rat)) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_rat A) B)))))))) (forall ((C2 tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex C2))) (=> (not (= C2 tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.divide1717551699836669952omplex A) B))))) (forall ((C2 tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real C2))) (=> (not (= C2 tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.divide_divide_real A) B))))) (forall ((C2 tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C2))) (=> (not (= C2 tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.divide_divide_rat A) B))))) (forall ((C2 tptp.complex) (A tptp.complex) (B tptp.complex)) (=> (not (= C2 tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex C2) A)) (@ (@ tptp.times_times_complex B) C2)) (@ (@ tptp.divide1717551699836669952omplex A) B)))) (forall ((C2 tptp.real) (A tptp.real) (B tptp.real)) (=> (not (= C2 tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real C2) A)) (@ (@ tptp.times_times_real B) C2)) (@ (@ tptp.divide_divide_real A) B)))) (forall ((C2 tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (not (= C2 tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat C2) A)) (@ (@ tptp.times_times_rat B) C2)) (@ (@ tptp.divide_divide_rat A) B)))) (forall ((C2 tptp.complex) (A tptp.complex) (B tptp.complex)) (=> (not (= C2 tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex A) C2)) (@ (@ tptp.times_times_complex B) C2)) (@ (@ tptp.divide1717551699836669952omplex A) B)))) (forall ((C2 tptp.real) (A tptp.real) (B tptp.real)) (=> (not (= C2 tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real A) C2)) (@ (@ tptp.times_times_real B) C2)) (@ (@ tptp.divide_divide_real A) B)))) (forall ((C2 tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (not (= C2 tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat A) C2)) (@ (@ tptp.times_times_rat B) C2)) (@ (@ tptp.divide_divide_rat A) B)))) (forall ((C2 tptp.complex) (A tptp.complex) (B tptp.complex)) (=> (not (= C2 tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex A) C2)) (@ (@ tptp.times_times_complex C2) B)) (@ (@ tptp.divide1717551699836669952omplex A) B)))) (forall ((C2 tptp.real) (A tptp.real) (B tptp.real)) (=> (not (= C2 tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real A) C2)) (@ (@ tptp.times_times_real C2) B)) (@ (@ tptp.divide_divide_real A) B)))) (forall ((C2 tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (not (= C2 tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat A) C2)) (@ (@ tptp.times_times_rat C2) B)) (@ (@ tptp.divide_divide_rat A) B)))) (forall ((A tptp.code_integer)) (=> (not (= A tptp.zero_z3403309356797280102nteger)) (= (@ (@ tptp.divide6298287555418463151nteger A) A) tptp.one_one_Code_integer))) (forall ((A tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) A) tptp.one_one_complex))) (forall ((A tptp.real)) (=> (not (= A tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real A) A) tptp.one_one_real))) (forall ((A tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat A) A) tptp.one_one_rat))) (forall ((A tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat A) A) tptp.one_one_nat))) (forall ((A tptp.int)) (=> (not (= A tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int A) A) tptp.one_one_int))) (forall ((A tptp.real)) (= (= tptp.zero_zero_real (@ (@ tptp.divide_divide_real tptp.one_one_real) A)) (= A tptp.zero_zero_real))) (forall ((A tptp.rat)) (= (= tptp.zero_zero_rat (@ (@ tptp.divide_divide_rat tptp.one_one_rat) A)) (= A tptp.zero_zero_rat))) (forall ((A tptp.real)) (= (= (@ (@ tptp.divide_divide_real tptp.one_one_real) A) tptp.zero_zero_real) (= A tptp.zero_zero_real))) (forall ((A tptp.rat)) (= (= (@ (@ tptp.divide_divide_rat tptp.one_one_rat) A) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))) (forall ((B tptp.real) (A tptp.real)) (= (= tptp.one_one_real (@ (@ tptp.divide_divide_real B) A)) (and (not (= A tptp.zero_zero_real)) (= A B)))) (forall ((B tptp.rat) (A tptp.rat)) (= (= tptp.one_one_rat (@ (@ tptp.divide_divide_rat B) A)) (and (not (= A tptp.zero_zero_rat)) (= A B)))) (forall ((B tptp.real) (A tptp.real)) (= (= (@ (@ tptp.divide_divide_real B) A) tptp.one_one_real) (and (not (= A tptp.zero_zero_real)) (= A B)))) (forall ((B tptp.rat) (A tptp.rat)) (= (= (@ (@ tptp.divide_divide_rat B) A) tptp.one_one_rat) (and (not (= A tptp.zero_zero_rat)) (= A B)))) (forall ((A tptp.complex)) (let ((_let_1 (@ (@ tptp.divide1717551699836669952omplex A) A))) (let ((_let_2 (= A tptp.zero_zero_complex))) (and (=> _let_2 (= _let_1 tptp.zero_zero_complex)) (=> (not _let_2) (= _let_1 tptp.one_one_complex)))))) (forall ((A tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real A) A))) (let ((_let_2 (= A tptp.zero_zero_real))) (and (=> _let_2 (= _let_1 tptp.zero_zero_real)) (=> (not _let_2) (= _let_1 tptp.one_one_real)))))) (forall ((A tptp.rat)) (let ((_let_1 (@ (@ tptp.divide_divide_rat A) A))) (let ((_let_2 (= A tptp.zero_zero_rat))) (and (=> _let_2 (= _let_1 tptp.zero_zero_rat)) (=> (not _let_2) (= _let_1 tptp.one_one_rat)))))) (forall ((A tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) A) tptp.one_one_complex))) (forall ((A tptp.real)) (=> (not (= A tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real A) A) tptp.one_one_real))) (forall ((A tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat A) A) tptp.one_one_rat))) (forall ((A tptp.complex) (B tptp.complex)) (= (= tptp.one_one_complex (@ (@ tptp.divide1717551699836669952omplex A) B)) (and (not (= B tptp.zero_zero_complex)) (= A B)))) (forall ((A tptp.real) (B tptp.real)) (= (= tptp.one_one_real (@ (@ tptp.divide_divide_real A) B)) (and (not (= B tptp.zero_zero_real)) (= A B)))) (forall ((A tptp.rat) (B tptp.rat)) (= (= tptp.one_one_rat (@ (@ tptp.divide_divide_rat A) B)) (and (not (= B tptp.zero_zero_rat)) (= A B)))) (forall ((A tptp.complex) (B tptp.complex)) (= (= (@ (@ tptp.divide1717551699836669952omplex A) B) tptp.one_one_complex) (and (not (= B tptp.zero_zero_complex)) (= A B)))) (forall ((A tptp.real) (B tptp.real)) (= (= (@ (@ tptp.divide_divide_real A) B) tptp.one_one_real) (and (not (= B tptp.zero_zero_real)) (= A B)))) (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ (@ tptp.divide_divide_rat A) B) tptp.one_one_rat) (and (not (= B tptp.zero_zero_rat)) (= A B)))) (forall ((A tptp.set_nat) (B tptp.set_nat)) (= (= (@ (@ tptp.set_or4548717258645045905et_nat A) B) tptp.bot_bot_set_set_nat) (not (@ (@ tptp.ord_less_eq_set_nat A) B)))) (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ (@ tptp.set_or633870826150836451st_rat A) B) tptp.bot_bot_set_rat) (not (@ (@ tptp.ord_less_eq_rat A) B)))) (forall ((A tptp.num) (B tptp.num)) (= (= (@ (@ tptp.set_or7049704709247886629st_num A) B) tptp.bot_bot_set_num) (not (@ (@ tptp.ord_less_eq_num A) B)))) (forall ((A tptp.nat) (B tptp.nat)) (= (= (@ (@ tptp.set_or1269000886237332187st_nat A) B) tptp.bot_bot_set_nat) (not (@ (@ tptp.ord_less_eq_nat A) B)))) (forall ((A tptp.int) (B tptp.int)) (= (= (@ (@ tptp.set_or1266510415728281911st_int A) B) tptp.bot_bot_set_int) (not (@ (@ tptp.ord_less_eq_int A) B)))) (forall ((A tptp.real) (B tptp.real)) (= (= (@ (@ tptp.set_or1222579329274155063t_real A) B) tptp.bot_bot_set_real) (not (@ (@ tptp.ord_less_eq_real A) B)))) (forall ((A tptp.set_nat) (B tptp.set_nat)) (= (= tptp.bot_bot_set_set_nat (@ (@ tptp.set_or4548717258645045905et_nat A) B)) (not (@ (@ tptp.ord_less_eq_set_nat A) B)))) (forall ((A tptp.rat) (B tptp.rat)) (= (= tptp.bot_bot_set_rat (@ (@ tptp.set_or633870826150836451st_rat A) B)) (not (@ (@ tptp.ord_less_eq_rat A) B)))) (forall ((A tptp.num) (B tptp.num)) (= (= tptp.bot_bot_set_num (@ (@ tptp.set_or7049704709247886629st_num A) B)) (not (@ (@ tptp.ord_less_eq_num A) B)))) (forall ((A tptp.nat) (B tptp.nat)) (= (= tptp.bot_bot_set_nat (@ (@ tptp.set_or1269000886237332187st_nat A) B)) (not (@ (@ tptp.ord_less_eq_nat A) B)))) (forall ((A tptp.int) (B tptp.int)) (= (= tptp.bot_bot_set_int (@ (@ tptp.set_or1266510415728281911st_int A) B)) (not (@ (@ tptp.ord_less_eq_int A) B)))) (forall ((A tptp.real) (B tptp.real)) (= (= tptp.bot_bot_set_real (@ (@ tptp.set_or1222579329274155063t_real A) B)) (not (@ (@ tptp.ord_less_eq_real A) B)))) (forall ((A tptp.set_nat) (B tptp.set_nat) (C2 tptp.set_nat) (D tptp.set_nat)) (= (@ (@ tptp.ord_le6893508408891458716et_nat (@ (@ tptp.set_or4548717258645045905et_nat A) B)) (@ (@ tptp.set_or4548717258645045905et_nat C2) D)) (or (not (@ (@ tptp.ord_less_eq_set_nat A) B)) (and (@ (@ tptp.ord_less_eq_set_nat C2) A) (@ (@ tptp.ord_less_eq_set_nat B) D))))) (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat) (D tptp.rat)) (= (@ (@ tptp.ord_less_eq_set_rat (@ (@ tptp.set_or633870826150836451st_rat A) B)) (@ (@ tptp.set_or633870826150836451st_rat C2) D)) (or (not (@ (@ tptp.ord_less_eq_rat A) B)) (and (@ (@ tptp.ord_less_eq_rat C2) A) (@ (@ tptp.ord_less_eq_rat B) D))))) (forall ((A tptp.num) (B tptp.num) (C2 tptp.num) (D tptp.num)) (= (@ (@ tptp.ord_less_eq_set_num (@ (@ tptp.set_or7049704709247886629st_num A) B)) (@ (@ tptp.set_or7049704709247886629st_num C2) D)) (or (not (@ (@ tptp.ord_less_eq_num A) B)) (and (@ (@ tptp.ord_less_eq_num C2) A) (@ (@ tptp.ord_less_eq_num B) D))))) (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat) (D tptp.nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.set_or1269000886237332187st_nat A) B)) (@ (@ tptp.set_or1269000886237332187st_nat C2) D)) (or (not (@ (@ tptp.ord_less_eq_nat A) B)) (and (@ (@ tptp.ord_less_eq_nat C2) A) (@ (@ tptp.ord_less_eq_nat B) D))))) (forall ((A tptp.int) (B tptp.int) (C2 tptp.int) (D tptp.int)) (= (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.set_or1266510415728281911st_int A) B)) (@ (@ tptp.set_or1266510415728281911st_int C2) D)) (or (not (@ (@ tptp.ord_less_eq_int A) B)) (and (@ (@ tptp.ord_less_eq_int C2) A) (@ (@ tptp.ord_less_eq_int B) D))))) (forall ((A tptp.real) (B tptp.real) (C2 tptp.real) (D tptp.real)) (= (@ (@ tptp.ord_less_eq_set_real (@ (@ tptp.set_or1222579329274155063t_real A) B)) (@ (@ tptp.set_or1222579329274155063t_real C2) D)) (or (not (@ (@ tptp.ord_less_eq_real A) B)) (and (@ (@ tptp.ord_less_eq_real C2) A) (@ (@ tptp.ord_less_eq_real B) D))))) (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat B) A) (= (@ (@ tptp.set_or633870826150836451st_rat A) B) tptp.bot_bot_set_rat))) (forall ((B tptp.num) (A tptp.num)) (=> (@ (@ tptp.ord_less_num B) A) (= (@ (@ tptp.set_or7049704709247886629st_num A) B) tptp.bot_bot_set_num))) (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat B) A) (= (@ (@ tptp.set_or1269000886237332187st_nat A) B) tptp.bot_bot_set_nat))) (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int B) A) (= (@ (@ tptp.set_or1266510415728281911st_int A) B) tptp.bot_bot_set_int))) (forall ((B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real B) A) (= (@ (@ tptp.set_or1222579329274155063t_real A) B) tptp.bot_bot_set_real))) (forall ((A tptp.rat) (B tptp.rat)) (= (not (@ tptp.finite_finite_rat (@ (@ tptp.set_or633870826150836451st_rat A) B))) (@ (@ tptp.ord_less_rat A) B))) (forall ((A tptp.real) (B tptp.real)) (= (not (@ tptp.finite_finite_real (@ (@ tptp.set_or1222579329274155063t_real A) B))) (@ (@ tptp.ord_less_real A) B))) (forall ((A tptp.nat)) (= (@ (@ tptp.set_or1269000886237332187st_nat A) A) (@ (@ tptp.insert_nat A) tptp.bot_bot_set_nat))) (forall ((A tptp.int)) (= (@ (@ tptp.set_or1266510415728281911st_int A) A) (@ (@ tptp.insert_int A) tptp.bot_bot_set_int))) (forall ((A tptp.real)) (= (@ (@ tptp.set_or1222579329274155063t_real A) A) (@ (@ tptp.insert_real A) tptp.bot_bot_set_real))) (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (= (= (@ (@ tptp.set_or1269000886237332187st_nat A) B) (@ (@ tptp.insert_nat C2) tptp.bot_bot_set_nat)) (and (= A B) (= B C2)))) (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (= (= (@ (@ tptp.set_or1266510415728281911st_int A) B) (@ (@ tptp.insert_int C2) tptp.bot_bot_set_int)) (and (= A B) (= B C2)))) (forall ((A tptp.real) (B tptp.real) (C2 tptp.real)) (= (= (@ (@ tptp.set_or1222579329274155063t_real A) B) (@ (@ tptp.insert_real C2) tptp.bot_bot_set_real)) (and (= A B) (= B C2)))) (forall ((K2 tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K2))) (let ((_let_2 (@ (@ tptp.divide_divide_nat (@ _let_1 M2)) (@ _let_1 N)))) (let ((_let_3 (= K2 tptp.zero_zero_nat))) (and (=> _let_3 (= _let_2 tptp.zero_zero_nat)) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_nat M2) N)))))))) (forall ((A tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ (@ tptp.divide_divide_real tptp.one_one_real) A)) (@ _let_1 A)))) (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (= (@ _let_1 (@ (@ tptp.divide_divide_rat tptp.one_one_rat) A)) (@ _let_1 A)))) (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real tptp.one_one_real) A)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real))) (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat tptp.one_one_rat) A)) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat))) (forall ((A tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ _let_1 (@ (@ tptp.divide_divide_real tptp.one_one_real) A)) (@ _let_1 A)))) (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (= (@ _let_1 (@ (@ tptp.divide_divide_rat tptp.one_one_rat) A)) (@ _let_1 A)))) (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (= (@ (@ tptp.ord_less_real tptp.one_one_real) (@ (@ tptp.divide_divide_real B) A)) (@ (@ tptp.ord_less_real A) B)))) (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (= (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ (@ tptp.divide_divide_rat B) A)) (@ (@ tptp.ord_less_rat A) B)))) (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_real tptp.one_one_real) (@ (@ tptp.divide_divide_real B) A)) (@ (@ tptp.ord_less_real B) A)))) (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ (@ tptp.divide_divide_rat B) A)) (@ (@ tptp.ord_less_rat B) A)))) (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real B) A)) tptp.one_one_real) (@ (@ tptp.ord_less_real B) A)))) (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat B) A)) tptp.one_one_rat) (@ (@ tptp.ord_less_rat B) A)))) (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_real A))) (=> (@ _let_1 tptp.zero_zero_real) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real B) A)) tptp.one_one_real) (@ _let_1 B))))) (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A))) (=> (@ _let_1 tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat B) A)) tptp.one_one_rat) (@ _let_1 B))))) (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real tptp.one_one_real) A)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real A) tptp.zero_zero_real))) (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat tptp.one_one_rat) A)) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat))) (forall ((B tptp.real) (W2 tptp.num) (A tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real W2))) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real B) _let_1)) A) (@ (@ tptp.ord_less_eq_real B) (@ (@ tptp.times_times_real A) _let_1))))) (forall ((B tptp.rat) (W2 tptp.num) (A tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_rat W2))) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat B) _let_1)) A) (@ (@ tptp.ord_less_eq_rat B) (@ (@ tptp.times_times_rat A) _let_1))))) (forall ((A tptp.real) (B tptp.real) (W2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real W2))) (= (@ (@ tptp.ord_less_eq_real A) (@ (@ tptp.divide_divide_real B) _let_1)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) _let_1)) B)))) (forall ((A tptp.rat) (B tptp.rat) (W2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat W2))) (= (@ (@ tptp.ord_less_eq_rat A) (@ (@ tptp.divide_divide_rat B) _let_1)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) _let_1)) B)))) (forall ((B tptp.complex) (W2 tptp.num) (A tptp.complex)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex W2))) (let ((_let_2 (= _let_1 tptp.zero_zero_complex))) (= (= (@ (@ tptp.divide1717551699836669952omplex B) _let_1) A) (and (=> (not _let_2) (= B (@ (@ tptp.times_times_complex A) _let_1))) (=> _let_2 (= A tptp.zero_zero_complex))))))) (forall ((B tptp.real) (W2 tptp.num) (A tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real W2))) (let ((_let_2 (= _let_1 tptp.zero_zero_real))) (= (= (@ (@ tptp.divide_divide_real B) _let_1) A) (and (=> (not _let_2) (= B (@ (@ tptp.times_times_real A) _let_1))) (=> _let_2 (= A tptp.zero_zero_real))))))) (forall ((B tptp.rat) (W2 tptp.num) (A tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_rat W2))) (let ((_let_2 (= _let_1 tptp.zero_zero_rat))) (= (= (@ (@ tptp.divide_divide_rat B) _let_1) A) (and (=> (not _let_2) (= B (@ (@ tptp.times_times_rat A) _let_1))) (=> _let_2 (= A tptp.zero_zero_rat))))))) (forall ((A tptp.complex) (B tptp.complex) (W2 tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex W2))) (let ((_let_2 (= _let_1 tptp.zero_zero_complex))) (= (= A (@ (@ tptp.divide1717551699836669952omplex B) _let_1)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_complex A) _let_1) B)) (=> _let_2 (= A tptp.zero_zero_complex))))))) (forall ((A tptp.real) (B tptp.real) (W2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real W2))) (let ((_let_2 (= _let_1 tptp.zero_zero_real))) (= (= A (@ (@ tptp.divide_divide_real B) _let_1)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_real A) _let_1) B)) (=> _let_2 (= A tptp.zero_zero_real))))))) (forall ((A tptp.rat) (B tptp.rat) (W2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat W2))) (let ((_let_2 (= _let_1 tptp.zero_zero_rat))) (= (= A (@ (@ tptp.divide_divide_rat B) _let_1)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_rat A) _let_1) B)) (=> _let_2 (= A tptp.zero_zero_rat))))))) (forall ((A tptp.real) (B tptp.real) (W2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real W2))) (= (@ (@ tptp.ord_less_real A) (@ (@ tptp.divide_divide_real B) _let_1)) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) _let_1)) B)))) (forall ((A tptp.rat) (B tptp.rat) (W2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat W2))) (= (@ (@ tptp.ord_less_rat A) (@ (@ tptp.divide_divide_rat B) _let_1)) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) _let_1)) B)))) (forall ((B tptp.real) (W2 tptp.num) (A tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real W2))) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real B) _let_1)) A) (@ (@ tptp.ord_less_real B) (@ (@ tptp.times_times_real A) _let_1))))) (forall ((B tptp.rat) (W2 tptp.num) (A tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_rat W2))) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat B) _let_1)) A) (@ (@ tptp.ord_less_rat B) (@ (@ tptp.times_times_rat A) _let_1))))) (forall ((A tptp.complex) (B tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) (@ (@ tptp.times_times_complex A) B)) (@ (@ tptp.divide1717551699836669952omplex tptp.one_one_complex) B)))) (forall ((A tptp.real) (B tptp.real)) (=> (not (= A tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real A) (@ (@ tptp.times_times_real A) B)) (@ (@ tptp.divide_divide_real tptp.one_one_real) B)))) (forall ((A tptp.rat) (B tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat A) (@ (@ tptp.times_times_rat A) B)) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) B)))) (forall ((B tptp.complex) (A tptp.complex)) (=> (not (= B tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex B) (@ (@ tptp.times_times_complex A) B)) (@ (@ tptp.divide1717551699836669952omplex tptp.one_one_complex) A)))) (forall ((B tptp.real) (A tptp.real)) (=> (not (= B tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real B) (@ (@ tptp.times_times_real A) B)) (@ (@ tptp.divide_divide_real tptp.one_one_real) A)))) (forall ((B tptp.rat) (A tptp.rat)) (=> (not (= B tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat B) (@ (@ tptp.times_times_rat A) B)) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) A)))) (forall ((N tptp.num) (M2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real N)) (@ tptp.semiri5074537144036343181t_real M2)) (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat N)) M2))) (forall ((L tptp.nat) (U tptp.nat)) (= (@ tptp.finite_card_nat (@ (@ tptp.set_or1269000886237332187st_nat L) U)) (@ (@ tptp.minus_minus_nat (@ tptp.suc U)) L))) (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (= (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ (@ tptp.divide_divide_real B) A)) (@ (@ tptp.ord_less_eq_real A) B)))) (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (= (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ (@ tptp.divide_divide_rat B) A)) (@ (@ tptp.ord_less_eq_rat A) B)))) (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ (@ tptp.divide_divide_real B) A)) (@ (@ tptp.ord_less_eq_real B) A)))) (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ (@ tptp.divide_divide_rat B) A)) (@ (@ tptp.ord_less_eq_rat B) A)))) (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real B) A)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real B) A)))) (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat B) A)) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat B) A)))) (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real B) A)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real A) B)))) (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat B) A)) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat A) B)))) _let_289 _let_288 _let_287 (forall ((D tptp.int) (P2 (-> tptp.int Bool)) (K2 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (=> (forall ((X3 tptp.int)) (=> (@ P2 X3) (@ P2 (@ (@ tptp.minus_minus_int X3) D)))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K2) (forall ((X5 tptp.int)) (=> (@ P2 X5) (@ P2 (@ (@ tptp.minus_minus_int X5) (@ (@ tptp.times_times_int K2) D))))))))) (forall ((D tptp.int) (P1 (-> tptp.int Bool)) (P2 (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (=> (forall ((X3 tptp.int) (K tptp.int)) (= (@ P1 X3) (@ P1 (@ (@ tptp.minus_minus_int X3) (@ (@ tptp.times_times_int K) D))))) (=> (exists ((Z5 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Z5) (= (@ P2 X3) (@ P1 X3))))) (=> (exists ((X_1 tptp.int)) (@ P1 X_1)) (exists ((X_12 tptp.int)) (@ P2 X_12))))))) (forall ((D tptp.int) (P6 (-> tptp.int Bool)) (P2 (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (=> (forall ((X3 tptp.int) (K tptp.int)) (= (@ P6 X3) (@ P6 (@ (@ tptp.minus_minus_int X3) (@ (@ tptp.times_times_int K) D))))) (=> (exists ((Z5 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int Z5) X3) (= (@ P2 X3) (@ P6 X3))))) (=> (exists ((X_1 tptp.int)) (@ P6 X_1)) (exists ((X_12 tptp.int)) (@ P2 X_12))))))) (forall ((L tptp.int)) (= (@ (@ tptp.times_times_int tptp.zero_zero_int) L) tptp.zero_zero_int)) (forall ((K2 tptp.int)) (= (@ (@ tptp.times_times_int K2) tptp.zero_zero_int) tptp.zero_zero_int)) (forall ((M2 tptp.int) (N tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) M2) (= (= (@ (@ tptp.times_times_int M2) N) tptp.one_one_int) (and (= M2 tptp.one_one_int) (= N tptp.one_one_int))))) (forall ((I2 tptp.int) (J2 tptp.int) (K2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int K2))) (=> (@ (@ tptp.ord_less_int I2) J2) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K2) (@ (@ tptp.ord_less_int (@ _let_1 I2)) (@ _let_1 J2)))))) (forall ((B tptp.int) (Q4 tptp.int) (R5 tptp.int) (Q2 tptp.int) (R3 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int B))) (let ((_let_2 (@ tptp.times_times_int B))) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ _let_2 Q4)) R5)) (@ (@ tptp.plus_plus_int (@ _let_2 Q2)) R3)) (=> (@ (@ tptp.ord_less_eq_int R3) tptp.zero_zero_int) (=> (@ _let_1 R3) (=> (@ _let_1 R5) (@ (@ tptp.ord_less_eq_int Q2) Q4)))))))) (forall ((B tptp.int) (Q4 tptp.int) (R5 tptp.int) (Q2 tptp.int) (R3 tptp.int)) (let ((_let_1 (@ tptp.times_times_int B))) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ _let_1 Q4)) R5)) (@ (@ tptp.plus_plus_int (@ _let_1 Q2)) R3)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) R5) (=> (@ (@ tptp.ord_less_int R5) B) (=> (@ (@ tptp.ord_less_int R3) B) (@ (@ tptp.ord_less_eq_int Q4) Q2))))))) (forall ((B tptp.int) (Q2 tptp.int) (R3 tptp.int) (B2 tptp.int) (Q4 tptp.int) (R5 tptp.int)) (let ((_let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B2) Q4)) R5))) (=> (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) Q2)) R3) _let_1) (=> (@ (@ tptp.ord_less_int _let_1) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int R3) B) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) R5) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B2) (=> (@ (@ tptp.ord_less_eq_int B2) B) (@ (@ tptp.ord_less_eq_int Q4) Q2))))))))) (forall ((B tptp.int) (Q2 tptp.int) (R3 tptp.int) (B2 tptp.int) (Q4 tptp.int) (R5 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 B2) Q4)) R5))) (=> (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) Q2)) R3) _let_2) (=> (@ _let_1 _let_2) (=> (@ (@ tptp.ord_less_int R5) B2) (=> (@ _let_1 R3) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B2) (=> (@ (@ tptp.ord_less_eq_int B2) B) (@ (@ tptp.ord_less_eq_int Q2) Q4)))))))))) (forall ((B2 tptp.int) (Q4 tptp.int) (R5 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B2) Q4)) R5)) (=> (@ (@ tptp.ord_less_int R5) B2) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B2) (@ _let_1 Q4)))))) (forall ((D tptp.int) (P2 (-> tptp.int Bool)) (K2 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (=> (forall ((X3 tptp.int)) (=> (@ P2 X3) (@ P2 (@ (@ tptp.plus_plus_int X3) D)))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K2) (forall ((X5 tptp.int)) (=> (@ P2 X5) (@ P2 (@ (@ tptp.plus_plus_int X5) (@ (@ tptp.times_times_int K2) D))))))))) (forall ((L tptp.rat) (M2 tptp.rat) (U tptp.rat)) (let ((_let_1 (@ tptp.set_or633870826150836451st_rat L))) (=> (@ (@ tptp.ord_less_eq_rat L) M2) (=> (@ (@ tptp.ord_less_eq_rat M2) U) (= (@ (@ tptp.sup_sup_set_rat (@ _let_1 M2)) (@ (@ tptp.set_or633870826150836451st_rat M2) U)) (@ _let_1 U)))))) (forall ((L tptp.num) (M2 tptp.num) (U tptp.num)) (let ((_let_1 (@ tptp.set_or7049704709247886629st_num L))) (=> (@ (@ tptp.ord_less_eq_num L) M2) (=> (@ (@ tptp.ord_less_eq_num M2) U) (= (@ (@ tptp.sup_sup_set_num (@ _let_1 M2)) (@ (@ tptp.set_or7049704709247886629st_num M2) U)) (@ _let_1 U)))))) (forall ((L tptp.nat) (M2 tptp.nat) (U tptp.nat)) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat L))) (=> (@ (@ tptp.ord_less_eq_nat L) M2) (=> (@ (@ tptp.ord_less_eq_nat M2) U) (= (@ (@ tptp.sup_sup_set_nat (@ _let_1 M2)) (@ (@ tptp.set_or1269000886237332187st_nat M2) U)) (@ _let_1 U)))))) (forall ((L tptp.int) (M2 tptp.int) (U tptp.int)) (let ((_let_1 (@ tptp.set_or1266510415728281911st_int L))) (=> (@ (@ tptp.ord_less_eq_int L) M2) (=> (@ (@ tptp.ord_less_eq_int M2) U) (= (@ (@ tptp.sup_sup_set_int (@ _let_1 M2)) (@ (@ tptp.set_or1266510415728281911st_int M2) U)) (@ _let_1 U)))))) (forall ((L tptp.real) (M2 tptp.real) (U tptp.real)) (let ((_let_1 (@ tptp.set_or1222579329274155063t_real L))) (=> (@ (@ tptp.ord_less_eq_real L) M2) (=> (@ (@ tptp.ord_less_eq_real M2) U) (= (@ (@ tptp.sup_sup_set_real (@ _let_1 M2)) (@ (@ tptp.set_or1222579329274155063t_real M2) U)) (@ _let_1 U)))))) (forall ((W2 tptp.int) (Z1 tptp.int) (Z22 tptp.int)) (let ((_let_1 (@ tptp.times_times_int W2))) (= (@ _let_1 (@ (@ tptp.plus_plus_int Z1) Z22)) (@ (@ tptp.plus_plus_int (@ _let_1 Z1)) (@ _let_1 Z22))))) (forall ((Z1 tptp.int) (Z22 tptp.int) (W2 tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int Z1) Z22)) W2) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int Z1) W2)) (@ (@ tptp.times_times_int Z22) W2)))) (forall ((Z1 tptp.int) (Z22 tptp.int) (W2 tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int Z1) Z22)) W2) (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int Z1) W2)) (@ (@ tptp.times_times_int Z22) W2)))) (forall ((W2 tptp.int) (Z1 tptp.int) (Z22 tptp.int)) (let ((_let_1 (@ tptp.times_times_int W2))) (= (@ _let_1 (@ (@ tptp.minus_minus_int Z1) Z22)) (@ (@ tptp.minus_minus_int (@ _let_1 Z1)) (@ _let_1 Z22))))) (forall ((A tptp.complex) (B tptp.complex) (C2 tptp.complex)) (let ((_let_1 (@ tptp.divide1717551699836669952omplex A))) (= (@ (@ tptp.divide1717551699836669952omplex (@ _let_1 B)) C2) (@ _let_1 (@ (@ tptp.times_times_complex C2) B))))) (forall ((A tptp.real) (B tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.divide_divide_real A))) (= (@ (@ tptp.divide_divide_real (@ _let_1 B)) C2) (@ _let_1 (@ (@ tptp.times_times_real C2) B))))) (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.divide_divide_rat A))) (= (@ (@ tptp.divide_divide_rat (@ _let_1 B)) C2) (@ _let_1 (@ (@ tptp.times_times_rat C2) B))))) (forall ((X tptp.complex) (Y tptp.complex) (Z3 tptp.complex) (W2 tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.divide1717551699836669952omplex X) Y)) (@ (@ tptp.divide1717551699836669952omplex Z3) W2)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex X) W2)) (@ (@ tptp.times_times_complex Y) Z3)))) (forall ((X tptp.real) (Y tptp.real) (Z3 tptp.real) (W2 tptp.real)) (= (@ (@ tptp.divide_divide_real (@ (@ tptp.divide_divide_real X) Y)) (@ (@ tptp.divide_divide_real Z3) W2)) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real X) W2)) (@ (@ tptp.times_times_real Y) Z3)))) (forall ((X tptp.rat) (Y tptp.rat) (Z3 tptp.rat) (W2 tptp.rat)) (= (@ (@ tptp.divide_divide_rat (@ (@ tptp.divide_divide_rat X) Y)) (@ (@ tptp.divide_divide_rat Z3) W2)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat X) W2)) (@ (@ tptp.times_times_rat Y) Z3)))) (forall ((X tptp.complex) (Y tptp.complex) (Z3 tptp.complex) (W2 tptp.complex)) (= (@ (@ tptp.times_times_complex (@ (@ tptp.divide1717551699836669952omplex X) Y)) (@ (@ tptp.divide1717551699836669952omplex Z3) W2)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex X) Z3)) (@ (@ tptp.times_times_complex Y) W2)))) (forall ((X tptp.real) (Y tptp.real) (Z3 tptp.real) (W2 tptp.real)) (= (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real X) Y)) (@ (@ tptp.divide_divide_real Z3) W2)) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real X) Z3)) (@ (@ tptp.times_times_real Y) W2)))) (forall ((X tptp.rat) (Y tptp.rat) (Z3 tptp.rat) (W2 tptp.rat)) (= (@ (@ tptp.times_times_rat (@ (@ tptp.divide_divide_rat X) Y)) (@ (@ tptp.divide_divide_rat Z3) W2)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat X) Z3)) (@ (@ tptp.times_times_rat Y) W2)))) (forall ((A tptp.set_nat) (B tptp.set_nat) (C2 tptp.set_nat) (D tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat C2))) (= (@ (@ tptp.ord_less_set_set_nat (@ (@ tptp.set_or4548717258645045905et_nat A) B)) (@ (@ tptp.set_or4548717258645045905et_nat C2) D)) (and (or (not (@ (@ tptp.ord_less_eq_set_nat A) B)) (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_set_nat B) D) (or (@ (@ tptp.ord_less_set_nat C2) A) (@ (@ tptp.ord_less_set_nat B) D)))) (@ _let_1 D))))) (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat) (D tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat C2))) (= (@ (@ tptp.ord_less_set_rat (@ (@ tptp.set_or633870826150836451st_rat A) B)) (@ (@ tptp.set_or633870826150836451st_rat C2) 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 C2) A) (@ (@ tptp.ord_less_rat B) D)))) (@ _let_1 D))))) (forall ((A tptp.num) (B tptp.num) (C2 tptp.num) (D tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_num C2))) (= (@ (@ tptp.ord_less_set_num (@ (@ tptp.set_or7049704709247886629st_num A) B)) (@ (@ tptp.set_or7049704709247886629st_num C2) 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 C2) A) (@ (@ tptp.ord_less_num B) D)))) (@ _let_1 D))))) (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat) (D tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat C2))) (= (@ (@ tptp.ord_less_set_nat (@ (@ tptp.set_or1269000886237332187st_nat A) B)) (@ (@ tptp.set_or1269000886237332187st_nat C2) 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 C2) A) (@ (@ tptp.ord_less_nat B) D)))) (@ _let_1 D))))) (forall ((A tptp.int) (B tptp.int) (C2 tptp.int) (D tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int C2))) (= (@ (@ tptp.ord_less_set_int (@ (@ tptp.set_or1266510415728281911st_int A) B)) (@ (@ tptp.set_or1266510415728281911st_int C2) 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 C2) A) (@ (@ tptp.ord_less_int B) D)))) (@ _let_1 D))))) (forall ((A tptp.real) (B tptp.real) (C2 tptp.real) (D tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real C2))) (= (@ (@ tptp.ord_less_set_real (@ (@ tptp.set_or1222579329274155063t_real A) B)) (@ (@ tptp.set_or1222579329274155063t_real C2) 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 C2) A) (@ (@ tptp.ord_less_real B) D)))) (@ _let_1 D))))) (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (not (@ tptp.finite_finite_rat (@ (@ tptp.set_or633870826150836451st_rat A) B))))) (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (not (@ tptp.finite_finite_real (@ (@ tptp.set_or1222579329274155063t_real A) B))))) (forall ((A tptp.nat) (B tptp.nat)) (=> (= A B) (= (@ (@ tptp.set_or1269000886237332187st_nat A) B) (@ (@ tptp.insert_nat A) tptp.bot_bot_set_nat)))) (forall ((A tptp.int) (B tptp.int)) (=> (= A B) (= (@ (@ tptp.set_or1266510415728281911st_int A) B) (@ (@ tptp.insert_int A) tptp.bot_bot_set_int)))) (forall ((A tptp.real) (B tptp.real)) (=> (= A B) (= (@ (@ tptp.set_or1222579329274155063t_real A) B) (@ (@ tptp.insert_real A) tptp.bot_bot_set_real)))) (forall ((A tptp.real) (B tptp.real) (C2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real C2) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real B) C2)) (@ (@ tptp.divide_divide_real A) C2))))) (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat C2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat B) C2)) (@ (@ tptp.divide_divide_rat A) C2))))) (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.divide_divide_real X) Y))))) (forall ((X tptp.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))))) (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real X) Y)) tptp.zero_zero_real)))) (forall ((X tptp.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)))) (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real X) Y)) tptp.zero_zero_real)))) (forall ((X tptp.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)))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (@ _let_1 (@ (@ tptp.divide_divide_real X) Y)))))) (forall ((X tptp.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)))))) (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ (@ tptp.divide_divide_real A) B)) (or (and (@ _let_1 A) (@ _let_1 B)) (and (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real B) tptp.zero_zero_real)))))) (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (= (@ _let_1 (@ (@ tptp.divide_divide_rat A) B)) (or (and (@ _let_1 A) (@ _let_1 B)) (and (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat B) tptp.zero_zero_rat)))))) (forall ((A tptp.real) (B tptp.real) (C2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C2) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real A) C2)) (@ (@ tptp.divide_divide_real B) C2))))) (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C2) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat A) C2)) (@ (@ tptp.divide_divide_rat B) C2))))) (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real A) B)) tptp.zero_zero_real) (or (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_real B) tptp.zero_zero_real)) (and (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (@ _let_1 B)))))) (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat A) B)) tptp.zero_zero_rat) (or (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_rat B) tptp.zero_zero_rat)) (and (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat) (@ _let_1 B)))))) (forall ((B tptp.real) (A tptp.real) (C2 tptp.real)) (=> (@ (@ tptp.ord_less_real B) A) (=> (@ (@ tptp.ord_less_real C2) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real A) C2)) (@ (@ tptp.divide_divide_real B) C2))))) (forall ((B tptp.rat) (A tptp.rat) (C2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat B) A) (=> (@ (@ tptp.ord_less_rat C2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat A) C2)) (@ (@ tptp.divide_divide_rat B) C2))))) (forall ((A tptp.real) (B tptp.real) (C2 tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C2) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real A) C2)) (@ (@ tptp.divide_divide_real B) C2))))) (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C2) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat A) C2)) (@ (@ tptp.divide_divide_rat B) C2))))) (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ _let_1 (@ (@ tptp.divide_divide_real A) B)) (or (and (@ _let_1 A) (@ _let_1 B)) (and (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (@ (@ tptp.ord_less_real B) tptp.zero_zero_real)))))) (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (= (@ _let_1 (@ (@ tptp.divide_divide_rat A) B)) (or (and (@ _let_1 A) (@ _let_1 B)) (and (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B) tptp.zero_zero_rat)))))) (forall ((A tptp.real) (C2 tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real A) C2)) (@ (@ tptp.divide_divide_real B) C2)) (and (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C2) (@ (@ tptp.ord_less_real A) B)) (=> (@ (@ tptp.ord_less_real C2) tptp.zero_zero_real) (@ (@ tptp.ord_less_real B) A)) (not (= C2 tptp.zero_zero_real))))) (forall ((A tptp.rat) (C2 tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat A) C2)) (@ (@ tptp.divide_divide_rat B) C2)) (and (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C2) (@ (@ tptp.ord_less_rat A) B)) (=> (@ (@ tptp.ord_less_rat C2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B) A)) (not (= C2 tptp.zero_zero_rat))))) (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real A) B)) tptp.zero_zero_real) (or (and (@ _let_1 A) (@ (@ tptp.ord_less_real B) tptp.zero_zero_real)) (and (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (@ _let_1 B)))))) (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat A) B)) tptp.zero_zero_rat) (or (and (@ _let_1 A) (@ (@ tptp.ord_less_rat B) tptp.zero_zero_rat)) (and (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (@ _let_1 B)))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (@ _let_1 (@ (@ tptp.divide_divide_real X) Y)))))) (forall ((X tptp.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)))))) (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_real Y) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real X) Y)) tptp.zero_zero_real)))) (forall ((X tptp.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)))) (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real X) Y)) tptp.zero_zero_real)))) (forall ((X tptp.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)))) (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real Y) tptp.zero_zero_real) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.divide_divide_real X) Y))))) (forall ((X tptp.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))))) (forall ((N tptp.nat) (P2 (-> tptp.nat Bool))) (= (forall ((M6 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M6) N) (@ P2 M6))) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)) (@ P2 X4))))) (forall ((N tptp.nat) (P2 (-> tptp.nat Bool))) (= (exists ((M6 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat M6) N) (@ P2 M6))) (exists ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)) (@ P2 X4))))) (forall ((Y tptp.complex) (Z3 tptp.complex) (X tptp.complex) (W2 tptp.complex)) (=> (not (= Y tptp.zero_zero_complex)) (=> (not (= Z3 tptp.zero_zero_complex)) (= (= (@ (@ tptp.divide1717551699836669952omplex X) Y) (@ (@ tptp.divide1717551699836669952omplex W2) Z3)) (= (@ (@ tptp.times_times_complex X) Z3) (@ (@ tptp.times_times_complex W2) Y)))))) (forall ((Y tptp.real) (Z3 tptp.real) (X tptp.real) (W2 tptp.real)) (=> (not (= Y tptp.zero_zero_real)) (=> (not (= Z3 tptp.zero_zero_real)) (= (= (@ (@ tptp.divide_divide_real X) Y) (@ (@ tptp.divide_divide_real W2) Z3)) (= (@ (@ tptp.times_times_real X) Z3) (@ (@ tptp.times_times_real W2) Y)))))) (forall ((Y tptp.rat) (Z3 tptp.rat) (X tptp.rat) (W2 tptp.rat)) (=> (not (= Y tptp.zero_zero_rat)) (=> (not (= Z3 tptp.zero_zero_rat)) (= (= (@ (@ tptp.divide_divide_rat X) Y) (@ (@ tptp.divide_divide_rat W2) Z3)) (= (@ (@ tptp.times_times_rat X) Z3) (@ (@ tptp.times_times_rat W2) Y)))))) (forall ((B tptp.complex) (C2 tptp.complex) (A tptp.complex)) (let ((_let_1 (= C2 tptp.zero_zero_complex))) (= (= (@ (@ tptp.divide1717551699836669952omplex B) C2) A) (and (=> (not _let_1) (= B (@ (@ tptp.times_times_complex A) C2))) (=> _let_1 (= A tptp.zero_zero_complex)))))) (forall ((B tptp.real) (C2 tptp.real) (A tptp.real)) (let ((_let_1 (= C2 tptp.zero_zero_real))) (= (= (@ (@ tptp.divide_divide_real B) C2) A) (and (=> (not _let_1) (= B (@ (@ tptp.times_times_real A) C2))) (=> _let_1 (= A tptp.zero_zero_real)))))) (forall ((B tptp.rat) (C2 tptp.rat) (A tptp.rat)) (let ((_let_1 (= C2 tptp.zero_zero_rat))) (= (= (@ (@ tptp.divide_divide_rat B) C2) A) (and (=> (not _let_1) (= B (@ (@ tptp.times_times_rat A) C2))) (=> _let_1 (= A tptp.zero_zero_rat)))))) (forall ((A tptp.complex) (B tptp.complex) (C2 tptp.complex)) (let ((_let_1 (= C2 tptp.zero_zero_complex))) (= (= A (@ (@ tptp.divide1717551699836669952omplex B) C2)) (and (=> (not _let_1) (= (@ (@ tptp.times_times_complex A) C2) B)) (=> _let_1 (= A tptp.zero_zero_complex)))))) (forall ((A tptp.real) (B tptp.real) (C2 tptp.real)) (let ((_let_1 (= C2 tptp.zero_zero_real))) (= (= A (@ (@ tptp.divide_divide_real B) C2)) (and (=> (not _let_1) (= (@ (@ tptp.times_times_real A) C2) B)) (=> _let_1 (= A tptp.zero_zero_real)))))) (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (= C2 tptp.zero_zero_rat))) (= (= A (@ (@ tptp.divide_divide_rat B) C2)) (and (=> (not _let_1) (= (@ (@ tptp.times_times_rat A) C2) B)) (=> _let_1 (= A tptp.zero_zero_rat)))))) (forall ((C2 tptp.complex) (B tptp.complex) (A tptp.complex)) (=> (not (= C2 tptp.zero_zero_complex)) (=> (= B (@ (@ tptp.times_times_complex A) C2)) (= (@ (@ tptp.divide1717551699836669952omplex B) C2) A)))) (forall ((C2 tptp.real) (B tptp.real) (A tptp.real)) (=> (not (= C2 tptp.zero_zero_real)) (=> (= B (@ (@ tptp.times_times_real A) C2)) (= (@ (@ tptp.divide_divide_real B) C2) A)))) (forall ((C2 tptp.rat) (B tptp.rat) (A tptp.rat)) (=> (not (= C2 tptp.zero_zero_rat)) (=> (= B (@ (@ tptp.times_times_rat A) C2)) (= (@ (@ tptp.divide_divide_rat B) C2) A)))) (forall ((C2 tptp.complex) (A tptp.complex) (B tptp.complex)) (=> (not (= C2 tptp.zero_zero_complex)) (=> (= (@ (@ tptp.times_times_complex A) C2) B) (= A (@ (@ tptp.divide1717551699836669952omplex B) C2))))) (forall ((C2 tptp.real) (A tptp.real) (B tptp.real)) (=> (not (= C2 tptp.zero_zero_real)) (=> (= (@ (@ tptp.times_times_real A) C2) B) (= A (@ (@ tptp.divide_divide_real B) C2))))) (forall ((C2 tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (not (= C2 tptp.zero_zero_rat)) (=> (= (@ (@ tptp.times_times_rat A) C2) B) (= A (@ (@ tptp.divide_divide_rat B) C2))))) (forall ((C2 tptp.complex) (B tptp.complex) (A tptp.complex)) (=> (not (= C2 tptp.zero_zero_complex)) (= (= (@ (@ tptp.divide1717551699836669952omplex B) C2) A) (= B (@ (@ tptp.times_times_complex A) C2))))) (forall ((C2 tptp.real) (B tptp.real) (A tptp.real)) (=> (not (= C2 tptp.zero_zero_real)) (= (= (@ (@ tptp.divide_divide_real B) C2) A) (= B (@ (@ tptp.times_times_real A) C2))))) (forall ((C2 tptp.rat) (B tptp.rat) (A tptp.rat)) (=> (not (= C2 tptp.zero_zero_rat)) (= (= (@ (@ tptp.divide_divide_rat B) C2) A) (= B (@ (@ tptp.times_times_rat A) C2))))) (forall ((C2 tptp.complex) (A tptp.complex) (B tptp.complex)) (=> (not (= C2 tptp.zero_zero_complex)) (= (= A (@ (@ tptp.divide1717551699836669952omplex B) C2)) (= (@ (@ tptp.times_times_complex A) C2) B)))) (forall ((C2 tptp.real) (A tptp.real) (B tptp.real)) (=> (not (= C2 tptp.zero_zero_real)) (= (= A (@ (@ tptp.divide_divide_real B) C2)) (= (@ (@ tptp.times_times_real A) C2) B)))) (forall ((C2 tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (not (= C2 tptp.zero_zero_rat)) (= (= A (@ (@ tptp.divide_divide_rat B) C2)) (= (@ (@ tptp.times_times_rat A) C2) B)))) (forall ((B tptp.complex) (A tptp.complex)) (=> (not (= B tptp.zero_zero_complex)) (= (= (@ (@ tptp.divide1717551699836669952omplex A) B) tptp.one_one_complex) (= A B)))) (forall ((B tptp.real) (A tptp.real)) (=> (not (= B tptp.zero_zero_real)) (= (= (@ (@ tptp.divide_divide_real A) B) tptp.one_one_real) (= A B)))) (forall ((B tptp.rat) (A tptp.rat)) (=> (not (= B tptp.zero_zero_rat)) (= (= (@ (@ tptp.divide_divide_rat A) B) tptp.one_one_rat) (= A B)))) (forall ((A tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) (@ tptp.numera6690914467698888265omplex tptp.one)) A)) (forall ((A tptp.real)) (= (@ (@ tptp.divide_divide_real A) (@ tptp.numeral_numeral_real tptp.one)) A)) (forall ((A tptp.rat)) (= (@ (@ tptp.divide_divide_rat A) (@ tptp.numeral_numeral_rat tptp.one)) A)) (forall ((B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_nat B) A) (@ _let_1 (@ (@ tptp.divide_divide_nat A) B)))))) (forall ((B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_int B) A) (@ _let_1 (@ (@ tptp.divide_divide_int A) B)))))) (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat A) B) (= (@ (@ tptp.divide_divide_nat A) B) tptp.zero_zero_nat)))) (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int A) B) (= (@ (@ tptp.divide_divide_int A) B) tptp.zero_zero_int)))) (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real X) Y)) tptp.zero_zero_real)))) (forall ((X tptp.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)))) (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real Y) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.divide_divide_real X) Y))))) (forall ((X tptp.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))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (@ _let_1 (@ (@ tptp.divide_divide_real X) Y)))))) (forall ((X tptp.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)))))) (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_real Y) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real X) Y)) tptp.zero_zero_real)))) (forall ((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)))) (forall ((A tptp.real) (C2 tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real A) C2)) (@ (@ tptp.divide_divide_real B) C2)) (and (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C2) (@ (@ tptp.ord_less_eq_real A) B)) (=> (@ (@ tptp.ord_less_real C2) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real B) A))))) (forall ((A tptp.rat) (C2 tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat A) C2)) (@ (@ tptp.divide_divide_rat B) C2)) (and (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C2) (@ (@ tptp.ord_less_eq_rat A) B)) (=> (@ (@ tptp.ord_less_rat C2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat B) A))))) (forall ((X tptp.real) (Y tptp.real) (W2 tptp.real) (Z3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ (@ tptp.ord_less_eq_real X) Y) (=> (@ _let_1 W2) (=> (@ (@ tptp.ord_less_real W2) Z3) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real X) Z3)) (@ (@ tptp.divide_divide_real Y) W2)))))))) (forall ((X tptp.rat) (Y tptp.rat) (W2 tptp.rat) (Z3 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 W2) (=> (@ (@ tptp.ord_less_rat W2) Z3) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat X) Z3)) (@ (@ tptp.divide_divide_rat Y) W2)))))))) (forall ((X tptp.real) (Y tptp.real) (W2 tptp.real) (Z3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_real X) Y) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) W2) (=> (@ (@ tptp.ord_less_eq_real W2) Z3) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real X) Z3)) (@ (@ tptp.divide_divide_real Y) W2))))))) (forall ((X tptp.rat) (Y tptp.rat) (W2 tptp.rat) (Z3 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) W2) (=> (@ (@ tptp.ord_less_eq_rat W2) Z3) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat X) Z3)) (@ (@ tptp.divide_divide_rat Y) W2))))))) (forall ((Y tptp.real) (X tptp.real) (W2 tptp.real) (Z3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (=> (@ (@ tptp.ord_less_eq_real X) Y) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) W2) (=> (@ (@ tptp.ord_less_eq_real W2) Z3) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real X) Z3)) (@ (@ tptp.divide_divide_real Y) W2))))))) (forall ((Y tptp.rat) (X tptp.rat) (W2 tptp.rat) (Z3 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) W2) (=> (@ (@ tptp.ord_less_eq_rat W2) Z3) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat X) Z3)) (@ (@ tptp.divide_divide_rat Y) W2))))))) (forall ((C2 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) C2) (= (@ _let_1 (@ (@ tptp.times_times_nat B) C2)) (@ (@ tptp.divide_divide_nat (@ _let_1 B)) C2))))) (forall ((C2 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) C2) (= (@ _let_1 (@ (@ tptp.times_times_int B) C2)) (@ (@ tptp.divide_divide_int (@ _let_1 B)) C2))))) (forall ((B tptp.real) (C2 tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (let ((_let_2 (@ (@ tptp.ord_less_real C2) tptp.zero_zero_real))) (let ((_let_3 (@ (@ tptp.times_times_real A) C2))) (let ((_let_4 (@ _let_1 C2))) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real B) C2)) A) (and (=> _let_4 (@ (@ tptp.ord_less_real B) _let_3)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_real _let_3) B)) (=> (not _let_2) (@ _let_1 A))))))))))) (forall ((B tptp.rat) (C2 tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (let ((_let_2 (@ (@ tptp.ord_less_rat C2) tptp.zero_zero_rat))) (let ((_let_3 (@ (@ tptp.times_times_rat A) C2))) (let ((_let_4 (@ _let_1 C2))) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat B) C2)) A) (and (=> _let_4 (@ (@ tptp.ord_less_rat B) _let_3)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_rat _let_3) B)) (=> (not _let_2) (@ _let_1 A))))))))))) (forall ((A tptp.real) (B tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real A))) (let ((_let_2 (@ (@ tptp.ord_less_real C2) tptp.zero_zero_real))) (let ((_let_3 (@ (@ tptp.times_times_real A) C2))) (let ((_let_4 (@ (@ tptp.ord_less_real tptp.zero_zero_real) C2))) (= (@ _let_1 (@ (@ tptp.divide_divide_real B) C2)) (and (=> _let_4 (@ (@ tptp.ord_less_real _let_3) B)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_real B) _let_3)) (=> (not _let_2) (@ _let_1 tptp.zero_zero_real))))))))))) (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A))) (let ((_let_2 (@ (@ tptp.ord_less_rat C2) tptp.zero_zero_rat))) (let ((_let_3 (@ (@ tptp.times_times_rat A) C2))) (let ((_let_4 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C2))) (= (@ _let_1 (@ (@ tptp.divide_divide_rat B) C2)) (and (=> _let_4 (@ (@ tptp.ord_less_rat _let_3) B)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_rat B) _let_3)) (=> (not _let_2) (@ _let_1 tptp.zero_zero_rat))))))))))) (forall ((C2 tptp.real) (B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real C2) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real B) C2)) A) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C2)) B)))) (forall ((C2 tptp.rat) (B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat C2) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat B) C2)) A) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C2)) B)))) (forall ((C2 tptp.real) (A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real C2) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_real A) (@ (@ tptp.divide_divide_real B) C2)) (@ (@ tptp.ord_less_real B) (@ (@ tptp.times_times_real A) C2))))) (forall ((C2 tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat C2) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_rat A) (@ (@ tptp.divide_divide_rat B) C2)) (@ (@ tptp.ord_less_rat B) (@ (@ tptp.times_times_rat A) C2))))) (forall ((C2 tptp.real) (B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C2) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real B) C2)) A) (@ (@ tptp.ord_less_real B) (@ (@ tptp.times_times_real A) C2))))) (forall ((C2 tptp.rat) (B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C2) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat B) C2)) A) (@ (@ tptp.ord_less_rat B) (@ (@ tptp.times_times_rat A) C2))))) (forall ((C2 tptp.real) (A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C2) (= (@ (@ tptp.ord_less_real A) (@ (@ tptp.divide_divide_real B) C2)) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C2)) B)))) (forall ((C2 tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C2) (= (@ (@ tptp.ord_less_rat A) (@ (@ tptp.divide_divide_rat B) C2)) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C2)) B)))) (forall ((Y tptp.real) (X tptp.real) (Z3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (=> (@ (@ tptp.ord_less_real X) (@ (@ tptp.times_times_real Z3) Y)) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real X) Y)) Z3)))) (forall ((Y tptp.rat) (X tptp.rat) (Z3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y) (=> (@ (@ tptp.ord_less_rat X) (@ (@ tptp.times_times_rat Z3) Y)) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat X) Y)) Z3)))) (forall ((Y tptp.real) (Z3 tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real Z3) Y)) X) (@ (@ tptp.ord_less_real Z3) (@ (@ tptp.divide_divide_real X) Y))))) (forall ((Y tptp.rat) (Z3 tptp.rat) (X tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat Z3) Y)) X) (@ (@ tptp.ord_less_rat Z3) (@ (@ tptp.divide_divide_rat X) Y))))) (forall ((B tptp.real) (A tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.divide_divide_real C2))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_real B) A) (=> (@ _let_2 C2) (=> (@ _let_2 (@ (@ tptp.times_times_real A) B)) (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B)))))))) (forall ((B tptp.rat) (A tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.divide_divide_rat C2))) (let ((_let_2 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ (@ tptp.ord_less_rat B) A) (=> (@ _let_2 C2) (=> (@ _let_2 (@ (@ tptp.times_times_rat A) B)) (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B)))))))) (forall ((A tptp.real) (B tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.divide_divide_real C2))) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_real C2) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.times_times_real A) B)) (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B))))))) (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.divide_divide_rat C2))) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_rat C2) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.times_times_rat A) B)) (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B))))))) (forall ((B tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.ord_less_real A))) (= (@ (@ tptp.ord_less_real tptp.one_one_real) (@ (@ tptp.divide_divide_real B) A)) (or (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (@ _let_1 B)) (and (@ _let_1 tptp.zero_zero_real) (@ (@ tptp.ord_less_real B) A)))))) (forall ((B tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A))) (= (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ (@ tptp.divide_divide_rat B) A)) (or (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (@ _let_1 B)) (and (@ _let_1 tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B) A)))))) (forall ((B tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.ord_less_real A))) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real B) A)) tptp.one_one_real) (or (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (@ (@ tptp.ord_less_real B) A)) (and (@ _let_1 tptp.zero_zero_real) (@ _let_1 B)) (= A tptp.zero_zero_real))))) (forall ((B tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A))) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat B) A)) tptp.one_one_rat) (or (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (@ (@ tptp.ord_less_rat B) A)) (and (@ _let_1 tptp.zero_zero_rat) (@ _let_1 B)) (= A tptp.zero_zero_rat))))) (forall ((B tptp.complex) (C2 tptp.complex) (W2 tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex W2))) (let ((_let_2 (= C2 tptp.zero_zero_complex))) (= (= (@ (@ tptp.divide1717551699836669952omplex B) C2) _let_1) (and (=> (not _let_2) (= B (@ (@ tptp.times_times_complex _let_1) C2))) (=> _let_2 (= _let_1 tptp.zero_zero_complex))))))) (forall ((B tptp.real) (C2 tptp.real) (W2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real W2))) (let ((_let_2 (= C2 tptp.zero_zero_real))) (= (= (@ (@ tptp.divide_divide_real B) C2) _let_1) (and (=> (not _let_2) (= B (@ (@ tptp.times_times_real _let_1) C2))) (=> _let_2 (= _let_1 tptp.zero_zero_real))))))) (forall ((B tptp.rat) (C2 tptp.rat) (W2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat W2))) (let ((_let_2 (= C2 tptp.zero_zero_rat))) (= (= (@ (@ tptp.divide_divide_rat B) C2) _let_1) (and (=> (not _let_2) (= B (@ (@ tptp.times_times_rat _let_1) C2))) (=> _let_2 (= _let_1 tptp.zero_zero_rat))))))) (forall ((W2 tptp.num) (B tptp.complex) (C2 tptp.complex)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex W2))) (let ((_let_2 (= C2 tptp.zero_zero_complex))) (= (= _let_1 (@ (@ tptp.divide1717551699836669952omplex B) C2)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_complex _let_1) C2) B)) (=> _let_2 (= _let_1 tptp.zero_zero_complex))))))) (forall ((W2 tptp.num) (B tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real W2))) (let ((_let_2 (= C2 tptp.zero_zero_real))) (= (= _let_1 (@ (@ tptp.divide_divide_real B) C2)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_real _let_1) C2) B)) (=> _let_2 (= _let_1 tptp.zero_zero_real))))))) (forall ((W2 tptp.num) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_rat W2))) (let ((_let_2 (= C2 tptp.zero_zero_rat))) (= (= _let_1 (@ (@ tptp.divide_divide_rat B) C2)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_rat _let_1) C2) B)) (=> _let_2 (= _let_1 tptp.zero_zero_rat))))))) (forall ((Z3 tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ (@ tptp.plus_plus_complex (@ (@ tptp.divide1717551699836669952omplex A) Z3)) B))) (let ((_let_2 (= Z3 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) Z3))) Z3))))))) (forall ((Z3 tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ (@ tptp.plus_plus_real (@ (@ tptp.divide_divide_real A) Z3)) B))) (let ((_let_2 (= Z3 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) Z3))) Z3))))))) (forall ((Z3 tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ (@ tptp.plus_plus_rat (@ (@ tptp.divide_divide_rat A) Z3)) B))) (let ((_let_2 (= Z3 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) Z3))) Z3))))))) (forall ((Z3 tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ (@ tptp.plus_plus_complex A) (@ (@ tptp.divide1717551699836669952omplex B) Z3)))) (let ((_let_2 (= Z3 tptp.zero_zero_complex))) (and (=> _let_2 (= _let_1 A)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex A) Z3)) B)) Z3))))))) (forall ((Z3 tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ (@ tptp.plus_plus_real A) (@ (@ tptp.divide_divide_real B) Z3)))) (let ((_let_2 (= Z3 tptp.zero_zero_real))) (and (=> _let_2 (= _let_1 A)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) Z3)) B)) Z3))))))) (forall ((Z3 tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ (@ tptp.plus_plus_rat A) (@ (@ tptp.divide_divide_rat B) Z3)))) (let ((_let_2 (= Z3 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) Z3)) B)) Z3))))))) (forall ((Y tptp.complex) (Z3 tptp.complex) (X tptp.complex) (W2 tptp.complex)) (=> (not (= Y tptp.zero_zero_complex)) (=> (not (= Z3 tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.divide1717551699836669952omplex X) Y)) (@ (@ tptp.divide1717551699836669952omplex W2) Z3)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex X) Z3)) (@ (@ tptp.times_times_complex W2) Y))) (@ (@ tptp.times_times_complex Y) Z3)))))) (forall ((Y tptp.real) (Z3 tptp.real) (X tptp.real) (W2 tptp.real)) (=> (not (= Y tptp.zero_zero_real)) (=> (not (= Z3 tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.divide_divide_real X) Y)) (@ (@ tptp.divide_divide_real W2) Z3)) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X) Z3)) (@ (@ tptp.times_times_real W2) Y))) (@ (@ tptp.times_times_real Y) Z3)))))) (forall ((Y tptp.rat) (Z3 tptp.rat) (X tptp.rat) (W2 tptp.rat)) (=> (not (= Y tptp.zero_zero_rat)) (=> (not (= Z3 tptp.zero_zero_rat)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.divide_divide_rat X) Y)) (@ (@ tptp.divide_divide_rat W2) Z3)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X) Z3)) (@ (@ tptp.times_times_rat W2) Y))) (@ (@ tptp.times_times_rat Y) Z3)))))) (forall ((Y tptp.complex) (X tptp.complex) (Z3 tptp.complex)) (=> (not (= Y tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.divide1717551699836669952omplex X) Y)) Z3) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex X) (@ (@ tptp.times_times_complex Z3) Y))) Y)))) (forall ((Y tptp.real) (X tptp.real) (Z3 tptp.real)) (=> (not (= Y tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.divide_divide_real X) Y)) Z3) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X) (@ (@ tptp.times_times_real Z3) Y))) Y)))) (forall ((Y tptp.rat) (X tptp.rat) (Z3 tptp.rat)) (=> (not (= Y tptp.zero_zero_rat)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.divide_divide_rat X) Y)) Z3) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat X) (@ (@ tptp.times_times_rat Z3) Y))) Y)))) (forall ((Y tptp.complex) (Z3 tptp.complex) (X tptp.complex)) (=> (not (= Y tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex Z3) (@ (@ tptp.divide1717551699836669952omplex X) Y)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex X) (@ (@ tptp.times_times_complex Z3) Y))) Y)))) (forall ((Y tptp.real) (Z3 tptp.real) (X tptp.real)) (=> (not (= Y tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real Z3) (@ (@ tptp.divide_divide_real X) Y)) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X) (@ (@ tptp.times_times_real Z3) Y))) Y)))) (forall ((Y tptp.rat) (Z3 tptp.rat) (X tptp.rat)) (=> (not (= Y tptp.zero_zero_rat)) (= (@ (@ tptp.plus_plus_rat Z3) (@ (@ tptp.divide_divide_rat X) Y)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat X) (@ (@ tptp.times_times_rat Z3) Y))) Y)))) (forall ((Z3 tptp.complex) (X tptp.complex) (Y tptp.complex)) (=> (not (= Z3 tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex X) (@ (@ tptp.divide1717551699836669952omplex Y) Z3)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex X) Z3)) Y)) Z3)))) (forall ((Z3 tptp.real) (X tptp.real) (Y tptp.real)) (=> (not (= Z3 tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real X) (@ (@ tptp.divide_divide_real Y) Z3)) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X) Z3)) Y)) Z3)))) (forall ((Z3 tptp.rat) (X tptp.rat) (Y tptp.rat)) (=> (not (= Z3 tptp.zero_zero_rat)) (= (@ (@ tptp.plus_plus_rat X) (@ (@ tptp.divide_divide_rat Y) Z3)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X) Z3)) Y)) Z3)))) (forall ((Z3 tptp.complex) (X tptp.complex) (Y tptp.complex)) (=> (not (= Z3 tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.divide1717551699836669952omplex X) Z3)) Y) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex X) (@ (@ tptp.times_times_complex Y) Z3))) Z3)))) (forall ((Z3 tptp.real) (X tptp.real) (Y tptp.real)) (=> (not (= Z3 tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.divide_divide_real X) Z3)) Y) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X) (@ (@ tptp.times_times_real Y) Z3))) Z3)))) (forall ((Z3 tptp.rat) (X tptp.rat) (Y tptp.rat)) (=> (not (= Z3 tptp.zero_zero_rat)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.divide_divide_rat X) Z3)) Y) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat X) (@ (@ tptp.times_times_rat Y) Z3))) Z3)))) (forall ((Z3 tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ (@ tptp.minus_minus_complex A) (@ (@ tptp.divide1717551699836669952omplex B) Z3)))) (let ((_let_2 (= Z3 tptp.zero_zero_complex))) (and (=> _let_2 (= _let_1 A)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex A) Z3)) B)) Z3))))))) (forall ((Z3 tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ (@ tptp.minus_minus_real A) (@ (@ tptp.divide_divide_real B) Z3)))) (let ((_let_2 (= Z3 tptp.zero_zero_real))) (and (=> _let_2 (= _let_1 A)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real A) Z3)) B)) Z3))))))) (forall ((Z3 tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ (@ tptp.minus_minus_rat A) (@ (@ tptp.divide_divide_rat B) Z3)))) (let ((_let_2 (= Z3 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) Z3)) B)) Z3))))))) (forall ((Y tptp.complex) (Z3 tptp.complex) (X tptp.complex) (W2 tptp.complex)) (=> (not (= Y tptp.zero_zero_complex)) (=> (not (= Z3 tptp.zero_zero_complex)) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.divide1717551699836669952omplex X) Y)) (@ (@ tptp.divide1717551699836669952omplex W2) Z3)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex X) Z3)) (@ (@ tptp.times_times_complex W2) Y))) (@ (@ tptp.times_times_complex Y) Z3)))))) (forall ((Y tptp.real) (Z3 tptp.real) (X tptp.real) (W2 tptp.real)) (=> (not (= Y tptp.zero_zero_real)) (=> (not (= Z3 tptp.zero_zero_real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real X) Y)) (@ (@ tptp.divide_divide_real W2) Z3)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real X) Z3)) (@ (@ tptp.times_times_real W2) Y))) (@ (@ tptp.times_times_real Y) Z3)))))) (forall ((Y tptp.rat) (Z3 tptp.rat) (X tptp.rat) (W2 tptp.rat)) (=> (not (= Y tptp.zero_zero_rat)) (=> (not (= Z3 tptp.zero_zero_rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.divide_divide_rat X) Y)) (@ (@ tptp.divide_divide_rat W2) Z3)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat X) Z3)) (@ (@ tptp.times_times_rat W2) Y))) (@ (@ tptp.times_times_rat Y) Z3)))))) (forall ((Z3 tptp.complex) (X tptp.complex) (Y tptp.complex)) (=> (not (= Z3 tptp.zero_zero_complex)) (= (@ (@ tptp.minus_minus_complex X) (@ (@ tptp.divide1717551699836669952omplex Y) Z3)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex X) Z3)) Y)) Z3)))) (forall ((Z3 tptp.real) (X tptp.real) (Y tptp.real)) (=> (not (= Z3 tptp.zero_zero_real)) (= (@ (@ tptp.minus_minus_real X) (@ (@ tptp.divide_divide_real Y) Z3)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real X) Z3)) Y)) Z3)))) (forall ((Z3 tptp.rat) (X tptp.rat) (Y tptp.rat)) (=> (not (= Z3 tptp.zero_zero_rat)) (= (@ (@ tptp.minus_minus_rat X) (@ (@ tptp.divide_divide_rat Y) Z3)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat X) Z3)) Y)) Z3)))) (forall ((Z3 tptp.complex) (X tptp.complex) (Y tptp.complex)) (=> (not (= Z3 tptp.zero_zero_complex)) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.divide1717551699836669952omplex X) Z3)) Y) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex X) (@ (@ tptp.times_times_complex Y) Z3))) Z3)))) (forall ((Z3 tptp.real) (X tptp.real) (Y tptp.real)) (=> (not (= Z3 tptp.zero_zero_real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real X) Z3)) Y) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real X) (@ (@ tptp.times_times_real Y) Z3))) Z3)))) (forall ((Z3 tptp.rat) (X tptp.rat) (Y tptp.rat)) (=> (not (= Z3 tptp.zero_zero_rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.divide_divide_rat X) Z3)) Y) (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat X) (@ (@ tptp.times_times_rat Y) Z3))) Z3)))) (forall ((A4 tptp.set_complex) (B5 tptp.set_complex)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_complex (@ (@ tptp.sup_sup_set_complex A4) B5))) (@ (@ tptp.plus_plus_nat (@ tptp.finite_card_complex A4)) (@ tptp.finite_card_complex B5)))) (forall ((A4 tptp.set_int) (B5 tptp.set_int)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_int (@ (@ tptp.sup_sup_set_int A4) B5))) (@ (@ tptp.plus_plus_nat (@ tptp.finite_card_int A4)) (@ tptp.finite_card_int B5)))) (forall ((A4 tptp.set_list_nat) (B5 tptp.set_list_nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_list_nat (@ (@ tptp.sup_sup_set_list_nat A4) B5))) (@ (@ tptp.plus_plus_nat (@ tptp.finite_card_list_nat A4)) (@ tptp.finite_card_list_nat B5)))) (forall ((A4 tptp.set_set_nat) (B5 tptp.set_set_nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_set_nat (@ (@ tptp.sup_sup_set_set_nat A4) B5))) (@ (@ tptp.plus_plus_nat (@ tptp.finite_card_set_nat A4)) (@ tptp.finite_card_set_nat B5)))) (forall ((A4 tptp.set_nat) (B5 tptp.set_nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat (@ (@ tptp.sup_sup_set_nat A4) B5))) (@ (@ tptp.plus_plus_nat (@ tptp.finite_card_nat A4)) (@ tptp.finite_card_nat B5)))) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat))) (let ((_let_2 (@ tptp.suc N))) (= (@ _let_1 _let_2) (@ (@ tptp.insert_nat _let_2) (@ _let_1 N)))))) (forall ((K2 tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K2) (= (@ (@ tptp.divide_divide_nat (@ _let_1 M2)) (@ _let_1 N)) (@ (@ tptp.divide_divide_nat M2) N))))) (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ (@ tptp.set_or1269000886237332187st_nat M2) N) (@ (@ tptp.insert_nat M2) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M2)) N))))) (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat M2))) (let ((_let_2 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_nat M2) _let_2) (= (@ _let_1 _let_2) (@ (@ tptp.insert_nat _let_2) (@ _let_1 N))))))) (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ (@ tptp.insert_nat M2) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M2)) N)) (@ (@ tptp.set_or1269000886237332187st_nat M2) N)))) (forall ((N6 tptp.set_nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_set_nat N6) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)) (@ tptp.finite_finite_nat N6))) (forall ((B tptp.real) (C2 tptp.real) (A tptp.real)) (let ((_let_1 (@ (@ tptp.ord_less_real C2) tptp.zero_zero_real))) (let ((_let_2 (@ (@ tptp.times_times_real A) C2))) (let ((_let_3 (@ (@ tptp.ord_less_real tptp.zero_zero_real) C2))) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real B) C2)) A) (and (=> _let_3 (@ (@ tptp.ord_less_eq_real B) _let_2)) (=> (not _let_3) (and (=> _let_1 (@ (@ tptp.ord_less_eq_real _let_2) B)) (=> (not _let_1) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A)))))))))) (forall ((B tptp.rat) (C2 tptp.rat) (A tptp.rat)) (let ((_let_1 (@ (@ tptp.ord_less_rat C2) tptp.zero_zero_rat))) (let ((_let_2 (@ (@ tptp.times_times_rat A) C2))) (let ((_let_3 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C2))) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat B) C2)) A) (and (=> _let_3 (@ (@ tptp.ord_less_eq_rat B) _let_2)) (=> (not _let_3) (and (=> _let_1 (@ (@ tptp.ord_less_eq_rat _let_2) B)) (=> (not _let_1) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A)))))))))) (forall ((A tptp.real) (B tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real A))) (let ((_let_2 (@ (@ tptp.ord_less_real C2) tptp.zero_zero_real))) (let ((_let_3 (@ (@ tptp.times_times_real A) C2))) (let ((_let_4 (@ (@ tptp.ord_less_real tptp.zero_zero_real) C2))) (= (@ _let_1 (@ (@ tptp.divide_divide_real B) C2)) (and (=> _let_4 (@ (@ tptp.ord_less_eq_real _let_3) B)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_eq_real B) _let_3)) (=> (not _let_2) (@ _let_1 tptp.zero_zero_real))))))))))) (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat A))) (let ((_let_2 (@ (@ tptp.ord_less_rat C2) tptp.zero_zero_rat))) (let ((_let_3 (@ (@ tptp.times_times_rat A) C2))) (let ((_let_4 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C2))) (= (@ _let_1 (@ (@ tptp.divide_divide_rat B) C2)) (and (=> _let_4 (@ (@ tptp.ord_less_eq_rat _let_3) B)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_eq_rat B) _let_3)) (=> (not _let_2) (@ _let_1 tptp.zero_zero_rat))))))))))) (forall ((B tptp.real) (A tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.divide_divide_real C2))) (=> (@ (@ tptp.ord_less_eq_real B) A) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.times_times_real A) B)) (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B))))))) (forall ((B tptp.rat) (A tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.divide_divide_rat C2))) (=> (@ (@ tptp.ord_less_eq_rat B) A) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C2) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.times_times_rat A) B)) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B))))))) (forall ((C2 tptp.real) (B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real C2) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real B) C2)) A) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) C2)) B)))) (forall ((C2 tptp.rat) (B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat C2) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat B) C2)) A) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C2)) B)))) (forall ((C2 tptp.real) (A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real C2) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_eq_real A) (@ (@ tptp.divide_divide_real B) C2)) (@ (@ tptp.ord_less_eq_real B) (@ (@ tptp.times_times_real A) C2))))) (forall ((C2 tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat C2) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_eq_rat A) (@ (@ tptp.divide_divide_rat B) C2)) (@ (@ tptp.ord_less_eq_rat B) (@ (@ tptp.times_times_rat A) C2))))) (forall ((C2 tptp.real) (B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C2) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real B) C2)) A) (@ (@ tptp.ord_less_eq_real B) (@ (@ tptp.times_times_real A) C2))))) (forall ((C2 tptp.rat) (B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C2) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat B) C2)) A) (@ (@ tptp.ord_less_eq_rat B) (@ (@ tptp.times_times_rat A) C2))))) (forall ((C2 tptp.real) (A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C2) (= (@ (@ tptp.ord_less_eq_real A) (@ (@ tptp.divide_divide_real B) C2)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) C2)) B)))) (forall ((C2 tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C2) (= (@ (@ tptp.ord_less_eq_rat A) (@ (@ tptp.divide_divide_rat B) C2)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C2)) B)))) (forall ((Y tptp.real) (X tptp.real) (Z3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (=> (@ (@ tptp.ord_less_eq_real X) (@ (@ tptp.times_times_real Z3) Y)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real X) Y)) Z3)))) (forall ((Y tptp.rat) (X tptp.rat) (Z3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y) (=> (@ (@ tptp.ord_less_eq_rat X) (@ (@ tptp.times_times_rat Z3) Y)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat X) Y)) Z3)))) (forall ((Y tptp.real) (Z3 tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real Z3) Y)) X) (@ (@ tptp.ord_less_eq_real Z3) (@ (@ tptp.divide_divide_real X) Y))))) (forall ((Y tptp.rat) (Z3 tptp.rat) (X tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y) (=> (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat Z3) Y)) X) (@ (@ tptp.ord_less_eq_rat Z3) (@ (@ tptp.divide_divide_rat X) Y))))) (forall ((A tptp.real) (B tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.divide_divide_real C2))) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real C2) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.times_times_real A) B)) (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B))))))) (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.divide_divide_rat C2))) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat C2) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.times_times_rat A) B)) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B))))))) (forall ((B tptp.real) (A tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real B) A)) tptp.one_one_real) (or (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (@ (@ tptp.ord_less_eq_real B) A)) (and (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real A) B)) (= A tptp.zero_zero_real)))) (forall ((B tptp.rat) (A tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat B) A)) tptp.one_one_rat) (or (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (@ (@ tptp.ord_less_eq_rat B) A)) (and (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat A) B)) (= A tptp.zero_zero_rat)))) (forall ((B tptp.real) (A tptp.real)) (= (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ (@ tptp.divide_divide_real B) A)) (or (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (@ (@ tptp.ord_less_eq_real A) B)) (and (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real B) A))))) (forall ((B tptp.rat) (A tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ (@ tptp.divide_divide_rat B) A)) (or (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (@ (@ tptp.ord_less_eq_rat A) B)) (and (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat B) A))))) (forall ((B tptp.real) (C2 tptp.real) (W2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real W2))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (let ((_let_3 (@ (@ tptp.ord_less_real C2) tptp.zero_zero_real))) (let ((_let_4 (@ (@ tptp.times_times_real _let_1) C2))) (let ((_let_5 (@ _let_2 C2))) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real B) C2)) _let_1) (and (=> _let_5 (@ (@ tptp.ord_less_real B) _let_4)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_real _let_4) B)) (=> (not _let_3) (@ _let_2 _let_1)))))))))))) (forall ((B tptp.rat) (C2 tptp.rat) (W2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat W2))) (let ((_let_2 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (let ((_let_3 (@ (@ tptp.ord_less_rat C2) tptp.zero_zero_rat))) (let ((_let_4 (@ (@ tptp.times_times_rat _let_1) C2))) (let ((_let_5 (@ _let_2 C2))) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat B) C2)) _let_1) (and (=> _let_5 (@ (@ tptp.ord_less_rat B) _let_4)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_rat _let_4) B)) (=> (not _let_3) (@ _let_2 _let_1)))))))))))) (forall ((W2 tptp.num) (B tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real W2))) (let ((_let_2 (@ tptp.ord_less_real _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_real C2) tptp.zero_zero_real))) (let ((_let_4 (@ (@ tptp.times_times_real _let_1) C2))) (let ((_let_5 (@ (@ tptp.ord_less_real tptp.zero_zero_real) C2))) (= (@ _let_2 (@ (@ tptp.divide_divide_real B) C2)) (and (=> _let_5 (@ (@ tptp.ord_less_real _let_4) B)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_real B) _let_4)) (=> (not _let_3) (@ _let_2 tptp.zero_zero_real)))))))))))) (forall ((W2 tptp.num) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_rat W2))) (let ((_let_2 (@ tptp.ord_less_rat _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_rat C2) tptp.zero_zero_rat))) (let ((_let_4 (@ (@ tptp.times_times_rat _let_1) C2))) (let ((_let_5 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C2))) (= (@ _let_2 (@ (@ tptp.divide_divide_rat B) C2)) (and (=> _let_5 (@ (@ tptp.ord_less_rat _let_4) B)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_rat B) _let_4)) (=> (not _let_3) (@ _let_2 tptp.zero_zero_rat)))))))))))) (forall ((Y tptp.real) (Z3 tptp.real) (X tptp.real) (W2 tptp.real)) (=> (not (= Y tptp.zero_zero_real)) (=> (not (= Z3 tptp.zero_zero_real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real X) Y)) (@ (@ tptp.divide_divide_real W2) Z3)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real X) Z3)) (@ (@ tptp.times_times_real W2) Y))) (@ (@ tptp.times_times_real Y) Z3))) tptp.zero_zero_real))))) (forall ((Y tptp.rat) (Z3 tptp.rat) (X tptp.rat) (W2 tptp.rat)) (=> (not (= Y tptp.zero_zero_rat)) (=> (not (= Z3 tptp.zero_zero_rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat X) Y)) (@ (@ tptp.divide_divide_rat W2) Z3)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat X) Z3)) (@ (@ tptp.times_times_rat W2) Y))) (@ (@ tptp.times_times_rat Y) Z3))) tptp.zero_zero_rat))))) (forall ((Y tptp.real) (Z3 tptp.real) (X tptp.real) (W2 tptp.real)) (=> (not (= Y tptp.zero_zero_real)) (=> (not (= Z3 tptp.zero_zero_real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real X) Y)) (@ (@ tptp.divide_divide_real W2) Z3)) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real X) Z3)) (@ (@ tptp.times_times_real W2) Y))) (@ (@ tptp.times_times_real Y) Z3))) tptp.zero_zero_real))))) (forall ((Y tptp.rat) (Z3 tptp.rat) (X tptp.rat) (W2 tptp.rat)) (=> (not (= Y tptp.zero_zero_rat)) (=> (not (= Z3 tptp.zero_zero_rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat X) Y)) (@ (@ tptp.divide_divide_rat W2) Z3)) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat X) Z3)) (@ (@ tptp.times_times_rat W2) Y))) (@ (@ tptp.times_times_rat Y) Z3))) tptp.zero_zero_rat))))) (forall ((A tptp.complex) (N tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex A))) (=> (not (= A tptp.zero_zero_complex)) (=> (@ (@ tptp.ord_less_eq_nat N) M2) (= (@ _let_1 (@ (@ tptp.minus_minus_nat M2) N)) (@ (@ tptp.divide1717551699836669952omplex (@ _let_1 M2)) (@ _let_1 N))))))) (forall ((A tptp.real) (N tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (not (= A tptp.zero_zero_real)) (=> (@ (@ tptp.ord_less_eq_nat N) M2) (= (@ _let_1 (@ (@ tptp.minus_minus_nat M2) N)) (@ (@ tptp.divide_divide_real (@ _let_1 M2)) (@ _let_1 N))))))) (forall ((A tptp.rat) (N tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat A))) (=> (not (= A tptp.zero_zero_rat)) (=> (@ (@ tptp.ord_less_eq_nat N) M2) (= (@ _let_1 (@ (@ tptp.minus_minus_nat M2) N)) (@ (@ tptp.divide_divide_rat (@ _let_1 M2)) (@ _let_1 N))))))) (forall ((A tptp.nat) (N tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (not (= A tptp.zero_zero_nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M2) (= (@ _let_1 (@ (@ tptp.minus_minus_nat M2) N)) (@ (@ tptp.divide_divide_nat (@ _let_1 M2)) (@ _let_1 N))))))) (forall ((A tptp.int) (N tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (not (= A tptp.zero_zero_int)) (=> (@ (@ tptp.ord_less_eq_nat N) M2) (= (@ _let_1 (@ (@ tptp.minus_minus_nat M2) N)) (@ (@ tptp.divide_divide_int (@ _let_1 M2)) (@ _let_1 N))))))) (forall ((N tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (not (@ (@ tptp.ord_less_nat M2) N)) (= (@ (@ tptp.divide_divide_nat M2) N) (@ tptp.suc (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat M2) N)) N)))))) (forall ((X tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 _let_1))) (@ (@ tptp.power_power_real X) _let_2)) (@ (@ tptp.power_power_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) X)) _let_2))))) (forall ((A tptp.real) (C2 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) C2))) (@ (@ 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 C2) _let_2))))))) (forall ((B tptp.real) (C2 tptp.real) (W2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real W2))) (let ((_let_2 (@ (@ tptp.ord_less_real C2) tptp.zero_zero_real))) (let ((_let_3 (@ (@ tptp.times_times_real _let_1) C2))) (let ((_let_4 (@ (@ tptp.ord_less_real tptp.zero_zero_real) C2))) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real B) C2)) _let_1) (and (=> _let_4 (@ (@ tptp.ord_less_eq_real B) _let_3)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_eq_real _let_3) B)) (=> (not _let_2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1))))))))))) (forall ((B tptp.rat) (C2 tptp.rat) (W2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat W2))) (let ((_let_2 (@ (@ tptp.ord_less_rat C2) tptp.zero_zero_rat))) (let ((_let_3 (@ (@ tptp.times_times_rat _let_1) C2))) (let ((_let_4 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C2))) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat B) C2)) _let_1) (and (=> _let_4 (@ (@ tptp.ord_less_eq_rat B) _let_3)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_eq_rat _let_3) B)) (=> (not _let_2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1))))))))))) (forall ((W2 tptp.num) (B tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real W2))) (let ((_let_2 (@ tptp.ord_less_eq_real _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_real C2) tptp.zero_zero_real))) (let ((_let_4 (@ (@ tptp.times_times_real _let_1) C2))) (let ((_let_5 (@ (@ tptp.ord_less_real tptp.zero_zero_real) C2))) (= (@ _let_2 (@ (@ tptp.divide_divide_real B) C2)) (and (=> _let_5 (@ (@ tptp.ord_less_eq_real _let_4) B)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_eq_real B) _let_4)) (=> (not _let_3) (@ _let_2 tptp.zero_zero_real)))))))))))) (forall ((W2 tptp.num) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_rat W2))) (let ((_let_2 (@ tptp.ord_less_eq_rat _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_rat C2) tptp.zero_zero_rat))) (let ((_let_4 (@ (@ tptp.times_times_rat _let_1) C2))) (let ((_let_5 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C2))) (= (@ _let_2 (@ (@ tptp.divide_divide_rat B) C2)) (and (=> _let_5 (@ (@ tptp.ord_less_eq_rat _let_4) B)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_eq_rat B) _let_4)) (=> (not _let_3) (@ _let_2 tptp.zero_zero_rat)))))))))))) (forall ((A tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.divide_divide_real A) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))) (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.divide_divide_rat A) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))))) (forall ((A tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ _let_1 (@ (@ tptp.divide_divide_real A) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ _let_1 A)))) (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (= (@ _let_1 (@ (@ tptp.divide_divide_rat A) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one)))) (@ _let_1 A)))) (forall ((U tptp.real) (V2 tptp.real) (R3 tptp.real) (S2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real U) V2) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) R3) (=> (@ (@ tptp.ord_less_eq_real R3) S2) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real U) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real R3) (@ (@ tptp.minus_minus_real V2) U))) S2))) V2))))) (forall ((U tptp.rat) (V2 tptp.rat) (R3 tptp.rat) (S2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat U) V2) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) R3) (=> (@ (@ tptp.ord_less_eq_rat R3) S2) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat U) (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat R3) (@ (@ tptp.minus_minus_rat V2) U))) S2))) V2))))) (forall ((E tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) E) (not (forall ((N3 tptp.nat)) (not (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat tptp.one_one_rat) (@ tptp.semiri681578069525770553at_rat (@ tptp.suc N3)))) E)))))) (forall ((E tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E) (not (forall ((N3 tptp.nat)) (not (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N3)))) E)))))) (forall ((N tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_real tptp.one_one_real))) (=> (@ (@ tptp.ord_less_eq_nat N) M2) (=> (not (= N tptp.zero_zero_nat)) (@ (@ tptp.ord_less_eq_real (@ _let_1 (@ tptp.semiri5074537144036343181t_real M2))) (@ _let_1 (@ tptp.semiri5074537144036343181t_real N))))))) (forall ((N tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_rat tptp.one_one_rat))) (=> (@ (@ tptp.ord_less_eq_nat N) M2) (=> (not (= N tptp.zero_zero_nat)) (@ (@ tptp.ord_less_eq_rat (@ _let_1 (@ tptp.semiri681578069525770553at_rat M2))) (@ _let_1 (@ tptp.semiri681578069525770553at_rat N))))))) _let_290 (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))))))))) (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))))))))) (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (not (= (@ _let_1 M2) (@ tptp.suc (@ _let_1 N)))))) (forall ((M2 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 M2)) (@ _let_1 N))))) (forall ((M2 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 M2) N)) tptp.zero_zero_nat)) (not (= (@ _let_1 N) tptp.zero_zero_nat))))) (forall ((M2 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 M2) N)) tptp.zero_zero_int)) (not (= (@ _let_1 N) tptp.zero_zero_int))))) _let_289 _let_288 _let_287 (forall ((M2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.divide_divide_nat (@ tptp.suc (@ tptp.suc M2))) _let_1) (@ tptp.suc (@ (@ tptp.divide_divide_nat M2) _let_1))))) (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (= (@ tptp.vEBT_set_vebt (@ (@ tptp.vEBT_VEBT_insert T) X)) (@ (@ tptp.inf_inf_set_nat (@ (@ tptp.sup_sup_set_nat (@ tptp.vEBT_set_vebt T)) (@ (@ tptp.insert_nat X) tptp.bot_bot_set_nat))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) tptp.one_one_nat)))))) (forall ((N tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat M2) N)) N) M2))) (forall ((N tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat N) M2)) N) M2))) (forall ((B tptp.nat) (A tptp.nat) (C2 tptp.nat)) (=> (not (= B tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat A) (@ (@ tptp.times_times_nat C2) B))) B) (@ (@ tptp.plus_plus_nat C2) (@ (@ tptp.divide_divide_nat A) B))))) (forall ((B tptp.int) (A tptp.int) (C2 tptp.int)) (=> (not (= B tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int A) (@ (@ tptp.times_times_int C2) B))) B) (@ (@ tptp.plus_plus_int C2) (@ (@ tptp.divide_divide_int A) B))))) (forall ((B tptp.nat) (A tptp.nat) (C2 tptp.nat)) (=> (not (= B tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat A) (@ (@ tptp.times_times_nat B) C2))) B) (@ (@ tptp.plus_plus_nat C2) (@ (@ tptp.divide_divide_nat A) B))))) (forall ((B tptp.int) (A tptp.int) (C2 tptp.int)) (=> (not (= B tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int A) (@ (@ tptp.times_times_int B) C2))) B) (@ (@ tptp.plus_plus_int C2) (@ (@ tptp.divide_divide_int A) B))))) (forall ((B tptp.nat) (C2 tptp.nat) (A tptp.nat)) (=> (not (= B tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat C2) B)) A)) B) (@ (@ tptp.plus_plus_nat C2) (@ (@ tptp.divide_divide_nat A) B))))) (forall ((B tptp.int) (C2 tptp.int) (A tptp.int)) (=> (not (= B tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int C2) B)) A)) B) (@ (@ tptp.plus_plus_int C2) (@ (@ tptp.divide_divide_int A) B))))) (forall ((V2 tptp.num) (W2 tptp.num)) (= (@ (@ tptp.divide_divide_int (@ tptp.numeral_numeral_int (@ tptp.bit0 V2))) (@ tptp.numeral_numeral_int (@ tptp.bit0 W2))) (@ (@ tptp.divide_divide_int (@ tptp.numeral_numeral_int V2)) (@ tptp.numeral_numeral_int W2)))) (forall ((R3 tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.times_times_real R3))) (= (@ (@ tptp.divide_divide_real (@ _let_1 A)) (@ _let_1 R3)) (@ (@ tptp.divide_divide_real A) R3)))) (forall ((C2 tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C2))) (let ((_let_2 (@ (@ tptp.divide_divide_nat (@ _let_1 A)) (@ _let_1 B)))) (let ((_let_3 (= C2 tptp.zero_zero_nat))) (and (=> _let_3 (= _let_2 tptp.zero_zero_nat)) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_nat A) B)))))))) (forall ((C2 tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C2))) (let ((_let_2 (@ (@ tptp.divide_divide_int (@ _let_1 A)) (@ _let_1 B)))) (let ((_let_3 (= C2 tptp.zero_zero_int))) (and (=> _let_3 (= _let_2 tptp.zero_zero_int)) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_int A) B)))))))) (forall ((C2 tptp.nat) (A tptp.nat) (B tptp.nat)) (=> (not (= C2 tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat A) C2)) (@ (@ tptp.times_times_nat B) C2)) (@ (@ tptp.divide_divide_nat A) B)))) (forall ((C2 tptp.int) (A tptp.int) (B tptp.int)) (=> (not (= C2 tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int A) C2)) (@ (@ tptp.times_times_int B) C2)) (@ (@ tptp.divide_divide_int A) B)))) (forall ((C2 tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C2))) (=> (not (= C2 tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.divide_divide_nat A) B))))) (forall ((C2 tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C2))) (=> (not (= C2 tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.divide_divide_int A) B))))) (forall ((M2 tptp.nat)) (= (@ (@ tptp.divide_divide_nat M2) (@ tptp.suc tptp.zero_zero_nat)) M2)) (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) N) (= (@ (@ tptp.divide_divide_nat M2) N) tptp.zero_zero_nat))) (forall ((B tptp.nat) (C2 tptp.nat) (A tptp.nat)) (=> (not (= B tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat B) C2)) A)) B) (@ (@ tptp.plus_plus_nat C2) (@ (@ tptp.divide_divide_nat A) B))))) (forall ((B tptp.int) (C2 tptp.int) (A tptp.int)) (=> (not (= B tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) C2)) A)) B) (@ (@ tptp.plus_plus_int C2) (@ (@ tptp.divide_divide_int A) B))))) (forall ((C2 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) C2) (= (@ _let_1 (@ (@ tptp.times_times_int B) C2)) (@ (@ tptp.divide_divide_int (@ _let_1 B)) C2))))) (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (@ (@ tptp.ord_less_int (@ (@ tptp.divide_divide_int A) B)) tptp.zero_zero_int)))) (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int B) tptp.zero_zero_int) (= (@ (@ tptp.ord_less_int (@ (@ tptp.divide_divide_int A) B)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int tptp.zero_zero_int) A)))) (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (= (@ (@ tptp.ord_less_int (@ (@ tptp.divide_divide_int A) B)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int A) tptp.zero_zero_int)))) (forall ((A tptp.nat) (B tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.divide_divide_nat A) B)) (@ (@ tptp.divide_divide_int (@ tptp.semiri1314217659103216013at_int A)) (@ tptp.semiri1314217659103216013at_int B)))) (forall ((M2 tptp.int) (N tptp.int)) (let ((_let_1 (@ tptp.set_or1266510415728281911st_int M2))) (let ((_let_2 (@ (@ tptp.plus_plus_int tptp.one_one_int) N))) (=> (@ (@ tptp.ord_less_eq_int M2) _let_2) (= (@ _let_1 _let_2) (@ (@ tptp.insert_int _let_2) (@ _let_1 N))))))) (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (= (@ _let_1 (@ (@ tptp.divide_divide_int A) B)) (and (@ (@ tptp.ord_less_eq_int B) A) (@ _let_1 B)))))) (forall ((B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (= (@ _let_1 (@ (@ tptp.divide_divide_int A) B)) (@ _let_1 A))))) (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int B) tptp.zero_zero_int) (= (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.divide_divide_int A) B)) (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int)))) (forall ((K2 tptp.int) (I2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 K2) (= (@ _let_1 (@ (@ tptp.divide_divide_int I2) K2)) (@ (@ tptp.ord_less_eq_int K2) I2))))) (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.divide_divide_int A) B)) tptp.zero_zero_int)))) (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int B) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.divide_divide_int A) B)) tptp.zero_zero_int)))) (forall ((L tptp.int) (K2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_eq_int L) K2) (=> (@ _let_1 L) (@ _let_1 (@ (@ tptp.divide_divide_int K2) L)))))) (forall ((K2 tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.divide_divide_int K2) L)) (or (= K2 tptp.zero_zero_int) (= L tptp.zero_zero_int) (and (@ _let_1 K2) (@ _let_1 L)) (and (@ (@ tptp.ord_less_int K2) tptp.zero_zero_int) (@ (@ tptp.ord_less_int L) tptp.zero_zero_int)))))) (forall ((A tptp.int) (B2 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) B2) (=> (@ (@ tptp.ord_less_eq_int B2) B) (@ (@ tptp.ord_less_eq_int (@ _let_1 B2)) (@ _let_1 B))))))) (forall ((A tptp.int) (A2 tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) A2) (=> (@ (@ tptp.ord_less_int B) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.divide_divide_int A2) B)) (@ (@ tptp.divide_divide_int A) B))))) (forall ((I2 tptp.int) (K2 tptp.int)) (= (= (@ (@ tptp.divide_divide_int I2) K2) tptp.zero_zero_int) (or (= K2 tptp.zero_zero_int) (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) I2) (@ (@ tptp.ord_less_int I2) K2)) (and (@ (@ tptp.ord_less_eq_int I2) tptp.zero_zero_int) (@ (@ tptp.ord_less_int K2) I2))))) (forall ((A tptp.int) (B2 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) B2) (=> (@ (@ tptp.ord_less_eq_int B2) B) (@ (@ tptp.ord_less_eq_int (@ _let_1 B)) (@ _let_1 B2))))))) (forall ((A tptp.int) (A2 tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) A2) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.divide_divide_int A) B)) (@ (@ tptp.divide_divide_int A2) B))))) (forall ((X tptp.int) (K2 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) X) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) K2) (@ (@ tptp.ord_less_int (@ (@ tptp.divide_divide_int X) K2)) X)))) (forall ((D tptp.int) (P2 (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (=> (forall ((X3 tptp.int) (K tptp.int)) (= (@ P2 X3) (@ P2 (@ (@ tptp.minus_minus_int X3) (@ (@ tptp.times_times_int K) D))))) (= (exists ((X7 tptp.int)) (@ P2 X7)) (exists ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D)) (@ P2 X4))))))) (forall ((P2 (-> tptp.int Bool)) (N tptp.int) (K2 tptp.int)) (= (@ P2 (@ (@ tptp.divide_divide_int N) K2)) (and (=> (= K2 tptp.zero_zero_int) (@ P2 tptp.zero_zero_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K2) (forall ((I tptp.int) (J tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) J) (@ (@ tptp.ord_less_int J) K2) (= N (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int K2) I)) J))) (@ P2 I)))) (=> (@ (@ tptp.ord_less_int K2) tptp.zero_zero_int) (forall ((I tptp.int) (J tptp.int)) (=> (and (@ (@ tptp.ord_less_int K2) J) (@ (@ tptp.ord_less_eq_int J) tptp.zero_zero_int) (= N (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int K2) I)) J))) (@ P2 I))))))) (forall ((A tptp.int) (B tptp.int) (Q2 tptp.int) (R3 tptp.int)) (=> (= A (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) Q2)) R3)) (=> (@ (@ tptp.ord_less_eq_int R3) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int B) R3) (= (@ (@ tptp.divide_divide_int A) B) Q2))))) (forall ((A tptp.int) (B tptp.int) (Q2 tptp.int) (R3 tptp.int)) (=> (= A (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) Q2)) R3)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) R3) (=> (@ (@ tptp.ord_less_int R3) B) (= (@ (@ tptp.divide_divide_int A) B) Q2))))) (forall ((D3 tptp.int) (P2 (-> tptp.int Bool)) (P6 (-> tptp.int Bool)) (B5 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D3) (=> (exists ((Z5 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Z5) (= (@ P2 X3) (@ P6 X3))))) (=> (forall ((X3 tptp.int)) (=> (forall ((Xa tptp.int)) (=> (@ (@ tptp.member_int Xa) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D3)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) B5) (not (= X3 (@ (@ tptp.plus_plus_int Xb2) Xa))))))) (=> (@ P2 X3) (@ P2 (@ (@ tptp.minus_minus_int X3) D3))))) (=> (forall ((X3 tptp.int) (K tptp.int)) (= (@ P6 X3) (@ P6 (@ (@ tptp.minus_minus_int X3) (@ (@ tptp.times_times_int K) D3))))) (= (exists ((X7 tptp.int)) (@ P2 X7)) (or (exists ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D3)) (@ P6 X4))) (exists ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D3)) (exists ((Y4 tptp.int)) (and (@ (@ tptp.member_int Y4) B5) (@ P2 (@ (@ tptp.plus_plus_int Y4) X4))))))))))))) (forall ((D3 tptp.int) (P2 (-> tptp.int Bool)) (P6 (-> tptp.int Bool)) (A4 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D3) (=> (exists ((Z5 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int Z5) X3) (= (@ P2 X3) (@ P6 X3))))) (=> (forall ((X3 tptp.int)) (=> (forall ((Xa tptp.int)) (=> (@ (@ tptp.member_int Xa) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D3)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) A4) (not (= X3 (@ (@ tptp.minus_minus_int Xb2) Xa))))))) (=> (@ P2 X3) (@ P2 (@ (@ tptp.plus_plus_int X3) D3))))) (=> (forall ((X3 tptp.int) (K tptp.int)) (= (@ P6 X3) (@ P6 (@ (@ tptp.minus_minus_int X3) (@ (@ tptp.times_times_int K) D3))))) (= (exists ((X7 tptp.int)) (@ P2 X7)) (or (exists ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D3)) (@ P6 X4))) (exists ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D3)) (exists ((Y4 tptp.int)) (and (@ (@ tptp.member_int Y4) A4) (@ P2 (@ (@ tptp.minus_minus_int Y4) X4))))))))))))) (forall ((M2 tptp.nat) (K2 tptp.int)) (let ((_let_1 (@ tptp.power_power_int K2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M2) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K2) (= (@ (@ tptp.divide_divide_int (@ _let_1 M2)) K2) (@ _let_1 (@ (@ tptp.minus_minus_nat M2) (@ tptp.suc tptp.zero_zero_nat)))))))) (forall ((L tptp.int) (K2 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) L) (=> (@ (@ tptp.ord_less_eq_int L) K2) (= (@ (@ tptp.divide_divide_int K2) L) (@ (@ tptp.plus_plus_int (@ (@ tptp.divide_divide_int (@ (@ tptp.minus_minus_int K2) L)) L)) tptp.one_one_int))))) (forall ((M2 tptp.nat) (N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.divide_divide_nat M2) N)) M2)) (forall ((M2 tptp.nat) (N tptp.nat) (K2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.divide_divide_nat M2) K2)) (@ (@ tptp.divide_divide_nat N) K2)))) (forall ((M2 tptp.nat) (N tptp.nat) (Q2 tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat M2))) (= (@ _let_1 (@ (@ tptp.times_times_nat N) Q2)) (@ (@ tptp.divide_divide_nat (@ _let_1 N)) Q2)))) (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ _let_1 B))) (@ _let_1 A)) (@ (@ tptp.divide_divide_int B) A))))) (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ _let_1 B))) (@ _let_1 A)) (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int B) tptp.one_one_int)) A))))) (forall ((A tptp.int) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int N))) (let ((_let_2 (@ tptp.semiri1314217659103216013at_int M2))) (let ((_let_3 (@ tptp.divide_divide_int A))) (= (@ _let_3 (@ (@ tptp.times_times_int _let_2) _let_1)) (@ (@ tptp.divide_divide_int (@ _let_3 _let_2)) _let_1)))))) (forall ((A tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri1316708129612266289at_nat N))) (let ((_let_2 (@ tptp.semiri1316708129612266289at_nat M2))) (let ((_let_3 (@ tptp.divide_divide_nat A))) (= (@ _let_3 (@ (@ tptp.times_times_nat _let_2) _let_1)) (@ (@ tptp.divide_divide_nat (@ _let_3 _let_2)) _let_1)))))) (forall ((M2 tptp.nat) (N tptp.nat)) (= (= (@ (@ tptp.divide_divide_nat M2) N) tptp.zero_zero_nat) (or (@ (@ tptp.ord_less_nat M2) N) (= N tptp.zero_zero_nat)))) (forall ((M2 tptp.nat) (N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.divide_divide_nat M2) N)) (@ (@ tptp.divide_divide_nat (@ tptp.suc M2)) N))) (forall ((M2 tptp.nat) (I2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) (@ (@ tptp.times_times_nat I2) N)) (@ (@ tptp.ord_less_nat (@ (@ tptp.divide_divide_nat M2) N)) I2))) (forall ((N tptp.nat) (M2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat N) (@ (@ tptp.divide_divide_nat M2) N))) M2)) (forall ((M2 tptp.nat) (N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat M2) N)) N)) M2)) (forall ((A tptp.nat) (K2 tptp.num) (L tptp.num)) (let ((_let_1 (@ tptp.divide_divide_nat A))) (= (@ (@ tptp.divide_divide_nat (@ _let_1 (@ tptp.numeral_numeral_nat K2))) (@ tptp.numeral_numeral_nat L)) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.times_times_num K2) L)))))) (forall ((A tptp.int) (K2 tptp.num) (L tptp.num)) (let ((_let_1 (@ tptp.divide_divide_int A))) (= (@ (@ tptp.divide_divide_int (@ _let_1 (@ tptp.numeral_numeral_int K2))) (@ tptp.numeral_numeral_int L)) (@ _let_1 (@ tptp.numeral_numeral_int (@ (@ tptp.times_times_num K2) L)))))) (forall ((B tptp.code_integer) (A tptp.code_integer)) (=> (not (= B tptp.zero_z3403309356797280102nteger)) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.plus_p5714425477246183910nteger B) A)) B) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.divide6298287555418463151nteger A) B)) tptp.one_one_Code_integer)))) (forall ((B tptp.nat) (A tptp.nat)) (=> (not (= B tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat B) A)) B) (@ (@ tptp.plus_plus_nat (@ (@ tptp.divide_divide_nat A) B)) tptp.one_one_nat)))) (forall ((B tptp.int) (A tptp.int)) (=> (not (= B tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int B) A)) B) (@ (@ tptp.plus_plus_int (@ (@ tptp.divide_divide_int A) B)) tptp.one_one_int)))) (forall ((B tptp.code_integer) (A tptp.code_integer)) (=> (not (= B tptp.zero_z3403309356797280102nteger)) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B)) B) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.divide6298287555418463151nteger A) B)) tptp.one_one_Code_integer)))) (forall ((B tptp.nat) (A tptp.nat)) (=> (not (= B tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat A) B)) B) (@ (@ tptp.plus_plus_nat (@ (@ tptp.divide_divide_nat A) B)) tptp.one_one_nat)))) (forall ((B tptp.int) (A tptp.int)) (=> (not (= B tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int A) B)) B) (@ (@ tptp.plus_plus_int (@ (@ tptp.divide_divide_int A) B)) tptp.one_one_int)))) (forall ((M2 tptp.nat) (N tptp.nat) (K2 tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat K2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M2) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (@ (@ tptp.ord_less_eq_nat (@ _let_1 N)) (@ _let_1 M2)))))) (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ (@ tptp.divide_divide_nat M2) N)) (and (@ (@ tptp.ord_less_eq_nat N) M2) (@ _let_1 N))))) (forall ((Q2 tptp.nat) (M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) Q2) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.divide_divide_nat M2) Q2)) N) (@ (@ tptp.ord_less_nat M2) (@ (@ tptp.times_times_nat N) Q2))))) (forall ((N tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) N) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M2) (@ (@ tptp.ord_less_nat (@ (@ tptp.divide_divide_nat M2) N)) M2)))) (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M2) (= (= (@ (@ tptp.divide_divide_nat M2) N) M2) (= N tptp.one_one_nat)))) (= tptp.divide_divide_nat (lambda ((M6 tptp.nat) (N4 tptp.nat)) (@ (@ (@ tptp.if_nat (or (@ (@ tptp.ord_less_nat M6) N4) (= N4 tptp.zero_zero_nat))) tptp.zero_zero_nat) (@ tptp.suc (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat M6) N4)) N4))))) (forall ((N tptp.nat) (Q2 tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat N))) (=> (@ (@ tptp.ord_less_eq_nat (@ _let_1 Q2)) M2) (=> (@ (@ tptp.ord_less_nat M2) (@ _let_1 (@ tptp.suc Q2))) (= (@ (@ tptp.divide_divide_nat M2) N) Q2))))) (forall ((Q2 tptp.nat) (M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) Q2) (= (@ (@ tptp.ord_less_eq_nat M2) (@ (@ tptp.divide_divide_nat N) Q2)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat M2) Q2)) N)))) (forall ((N tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_nat M2) (@ (@ tptp.plus_plus_nat N) (@ (@ tptp.times_times_nat N) (@ (@ tptp.divide_divide_nat M2) N)))))) (forall ((N tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_nat M2) (@ (@ tptp.plus_plus_nat N) (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat M2) N)) N))))) (forall ((P2 (-> tptp.nat Bool)) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (= N tptp.zero_zero_nat))) (= (@ P2 (@ (@ tptp.divide_divide_nat M2) N)) (and (=> _let_1 (@ P2 tptp.zero_zero_nat)) (=> (not _let_1) (forall ((I tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_nat J) N) (=> (= M2 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat N) I)) J)) (@ P2 I))))))))) (forall ((A tptp.code_integer) (N tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger A))) (let ((_let_2 (@ (@ tptp.divide6298287555418463151nteger (@ _let_1 M2)) (@ _let_1 N)))) (let ((_let_3 (@ (@ tptp.ord_less_eq_nat N) M2))) (=> (not (= A tptp.zero_z3403309356797280102nteger)) (and (=> _let_3 (= _let_2 (@ _let_1 (@ (@ tptp.minus_minus_nat M2) N)))) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide6298287555418463151nteger tptp.one_one_Code_integer) (@ _let_1 (@ (@ tptp.minus_minus_nat N) M2))))))))))) (forall ((A tptp.nat) (N tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (let ((_let_2 (@ (@ tptp.divide_divide_nat (@ _let_1 M2)) (@ _let_1 N)))) (let ((_let_3 (@ (@ tptp.ord_less_eq_nat N) M2))) (=> (not (= A tptp.zero_zero_nat)) (and (=> _let_3 (= _let_2 (@ _let_1 (@ (@ tptp.minus_minus_nat M2) N)))) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_nat tptp.one_one_nat) (@ _let_1 (@ (@ tptp.minus_minus_nat N) M2))))))))))) (forall ((A tptp.int) (N tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (let ((_let_2 (@ (@ tptp.divide_divide_int (@ _let_1 M2)) (@ _let_1 N)))) (let ((_let_3 (@ (@ tptp.ord_less_eq_nat N) M2))) (=> (not (= A tptp.zero_zero_int)) (and (=> _let_3 (= _let_2 (@ _let_1 (@ (@ tptp.minus_minus_nat M2) N)))) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_int tptp.one_one_int) (@ _let_1 (@ (@ tptp.minus_minus_nat N) M2))))))))))) (forall ((N tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_eq_nat N) M2) (= (@ (@ tptp.divide_divide_nat M2) N) (@ tptp.suc (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat M2) N)) N)))))) (forall ((P2 (-> tptp.nat Bool)) (M2 tptp.nat) (N tptp.nat)) (= (@ P2 (@ (@ tptp.divide_divide_nat M2) N)) (or (and (= N tptp.zero_zero_nat) (@ P2 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)) M2) (@ (@ tptp.ord_less_nat M2) (@ _let_1 (@ tptp.suc Q5))) (@ P2 Q5))))))) (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)) N) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.divide_divide_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 N) (@ _let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc N)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))) (forall ((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)))) (forall ((Deg tptp.nat) (Mi tptp.nat) (X tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Ma tptp.nat) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_nat _let_1) Deg) (=> (@ (@ tptp.ord_less_eq_nat Mi) X) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_s6755466524823107622T_VEBT TreeList2)) (@ (@ tptp.vEBT_VEBT_high X) (@ (@ tptp.divide_divide_nat Deg) _let_1))) (= (@ (@ tptp.vEBT_vebt_succ (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList2) Summary)) X) tptp.none_nat)))))) (forall ((Deg tptp.nat) (X tptp.nat) (Ma tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Mi tptp.nat) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_nat _let_1) Deg) (=> (@ (@ tptp.ord_less_eq_nat X) Ma) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_s6755466524823107622T_VEBT TreeList2)) (@ (@ tptp.vEBT_VEBT_high X) (@ (@ tptp.divide_divide_nat Deg) _let_1))) (= (@ (@ tptp.vEBT_vebt_pred (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList2) Summary)) X) tptp.none_nat)))))) (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se2793503036327961859nteger tptp.zero_zero_nat) A) (@ (@ tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer) (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.divide6298287555418463151nteger A) _let_1)))))) (forall ((A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se7882103937844011126it_nat tptp.zero_zero_nat) A) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.divide_divide_nat A) _let_1)))))) (forall ((A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se7879613467334960850it_int tptp.zero_zero_nat) A) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.divide_divide_int A) _let_1)))))) (=> (not _let_286) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.m)) (and (=> (= (@ (@ tptp.vEBT_VEBT_high tptp.ma) tptp.na) I4) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT tptp.treeList2) I4)) (@ (@ tptp.vEBT_VEBT_low tptp.ma) tptp.na))) (forall ((X5 tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X5) tptp.na) I4) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT tptp.treeList2) I4)) (@ (@ tptp.vEBT_VEBT_low X5) tptp.na))) (and (@ (@ tptp.ord_less_nat tptp.mi) X5) (@ (@ tptp.ord_less_eq_nat X5) tptp.ma)))))))) (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_le2932123472753598470d_enat (@ tptp.numera1916890842035813515d_enat M2)) (@ tptp.numera1916890842035813515d_enat N)) (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat M2)) (@ tptp.numeral_numeral_nat N)))) (forall ((X tptp.set_nat) (Y tptp.set_nat) (Z3 tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.sup_sup_set_nat X) Y)) Z3) (and (@ (@ tptp.ord_less_eq_set_nat X) Z3) (@ (@ tptp.ord_less_eq_set_nat Y) Z3)))) (forall ((X tptp.rat) (Y tptp.rat) (Z3 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.sup_sup_rat X) Y)) Z3) (and (@ (@ tptp.ord_less_eq_rat X) Z3) (@ (@ tptp.ord_less_eq_rat Y) Z3)))) (forall ((X tptp.nat) (Y tptp.nat) (Z3 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.sup_sup_nat X) Y)) Z3) (and (@ (@ tptp.ord_less_eq_nat X) Z3) (@ (@ tptp.ord_less_eq_nat Y) Z3)))) (forall ((X tptp.int) (Y tptp.int) (Z3 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.sup_sup_int X) Y)) Z3) (and (@ (@ tptp.ord_less_eq_int X) Z3) (@ (@ tptp.ord_less_eq_int Y) Z3)))) (forall ((B tptp.set_nat) (C2 tptp.set_nat) (A tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.sup_sup_set_nat B) C2)) A) (and (@ (@ tptp.ord_less_eq_set_nat B) A) (@ (@ tptp.ord_less_eq_set_nat C2) A)))) (forall ((B tptp.rat) (C2 tptp.rat) (A tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.sup_sup_rat B) C2)) A) (and (@ (@ tptp.ord_less_eq_rat B) A) (@ (@ tptp.ord_less_eq_rat C2) A)))) (forall ((B tptp.nat) (C2 tptp.nat) (A tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.sup_sup_nat B) C2)) A) (and (@ (@ tptp.ord_less_eq_nat B) A) (@ (@ tptp.ord_less_eq_nat C2) A)))) (forall ((B tptp.int) (C2 tptp.int) (A tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.sup_sup_int B) C2)) A) (and (@ (@ tptp.ord_less_eq_int B) A) (@ (@ tptp.ord_less_eq_int C2) A)))) (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)) (forall ((L tptp.int) (U tptp.int)) (@ tptp.finite_finite_int (@ (@ tptp.set_or1266510415728281911st_int L) U))) _let_285 (forall ((Ma tptp.nat) (N tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_nat Ma) (@ _let_1 (@ (@ tptp.plus_plus_nat N) M2))) (@ (@ tptp.ord_less_nat (@ (@ tptp.vEBT_VEBT_high Ma) N)) (@ _let_1 M2))))) (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)))) (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)))) (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat) (Z3 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.ord_le3146513528884898305at_nat X))) (= (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat Y) Z3)) (and (@ _let_1 Y) (@ _let_1 Z3))))) (forall ((X tptp.set_nat) (Y tptp.set_nat) (Z3 tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat X))) (= (@ _let_1 (@ (@ tptp.inf_inf_set_nat Y) Z3)) (and (@ _let_1 Y) (@ _let_1 Z3))))) (forall ((X tptp.rat) (Y tptp.rat) (Z3 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat X))) (= (@ _let_1 (@ (@ tptp.inf_inf_rat Y) Z3)) (and (@ _let_1 Y) (@ _let_1 Z3))))) (forall ((X tptp.nat) (Y tptp.nat) (Z3 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat X))) (= (@ _let_1 (@ (@ tptp.inf_inf_nat Y) Z3)) (and (@ _let_1 Y) (@ _let_1 Z3))))) (forall ((X tptp.int) (Y tptp.int) (Z3 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int X))) (= (@ _let_1 (@ (@ tptp.inf_inf_int Y) Z3)) (and (@ _let_1 Y) (@ _let_1 Z3))))) (forall ((A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat) (C2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.ord_le3146513528884898305at_nat A))) (= (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat B) C2)) (and (@ _let_1 B) (@ _let_1 C2))))) (forall ((A tptp.set_nat) (B tptp.set_nat) (C2 tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat A))) (= (@ _let_1 (@ (@ tptp.inf_inf_set_nat B) C2)) (and (@ _let_1 B) (@ _let_1 C2))))) (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat A))) (= (@ _let_1 (@ (@ tptp.inf_inf_rat B) C2)) (and (@ _let_1 B) (@ _let_1 C2))))) (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat A))) (= (@ _let_1 (@ (@ tptp.inf_inf_nat B) C2)) (and (@ _let_1 B) (@ _let_1 C2))))) (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int A))) (= (@ _let_1 (@ (@ tptp.inf_inf_int B) C2)) (and (@ _let_1 B) (@ _let_1 C2))))) (forall ((Info2 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 Info2) 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)))))))) (forall ((Deg tptp.nat) (Mi tptp.nat) (Ma tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (X tptp.nat)) (let ((_let_1 (@ (@ tptp.divide_divide_nat Deg) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) Deg) (=> (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList2) Summary)) X) (or (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) (@ (@ tptp.vEBT_VEBT_high X) _let_1))) (@ (@ tptp.vEBT_VEBT_low X) _let_1)) (= X Mi) (= X Ma)))))) (forall ((Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (X tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat Deg) _let_1))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high X) _let_2))) (=> (@ (@ tptp.vEBT_vebt_member (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList2) Summary)) X) (and (@ (@ tptp.ord_less_eq_nat _let_1) Deg) (or (= X Mi) (= X Ma) (and (@ (@ tptp.ord_less_nat X) Ma) (@ (@ tptp.ord_less_nat Mi) X) (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)) (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_3)) (@ (@ tptp.vEBT_VEBT_low X) _let_2)))))))))) (forall ((X tptp.nat) (Deg tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Mi tptp.nat) (Ma tptp.nat) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat Deg) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high X) _let_1))) (=> (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) Deg) (=> (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_2)) (@ (@ tptp.vEBT_VEBT_low X) _let_1)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList2) Summary)) X))))))) (forall ((X tptp.nat) (N tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ (@ tptp.ord_less_nat X) (@ _let_1 (@ (@ tptp.plus_plus_nat N) M2))) (=> (@ _let_2 N) (=> (@ _let_2 M2) (@ (@ tptp.ord_less_nat (@ (@ tptp.vEBT_VEBT_low X) N)) (@ _let_1 N)))))))) (forall ((X tptp.nat) (N tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ (@ tptp.ord_less_nat X) (@ _let_1 (@ (@ tptp.plus_plus_nat N) M2))) (=> (@ _let_2 N) (=> (@ _let_2 M2) (@ (@ tptp.ord_less_nat (@ (@ tptp.vEBT_VEBT_high X) N)) (@ _let_1 M2)))))))) (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.inf_in2572325071724192079at_nat X) Y)) Y)) (forall ((X tptp.set_nat) (Y tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.inf_inf_set_nat X) Y)) Y)) (forall ((X tptp.rat) (Y tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.inf_inf_rat X) Y)) Y)) (forall ((X tptp.nat) (Y tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.inf_inf_nat X) Y)) Y)) (forall ((X tptp.int) (Y tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.inf_inf_int X) Y)) Y)) (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.inf_in2572325071724192079at_nat X) Y)) X)) (forall ((X tptp.set_nat) (Y tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.inf_inf_set_nat X) Y)) X)) (forall ((X tptp.rat) (Y tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.inf_inf_rat X) Y)) X)) (forall ((X tptp.nat) (Y tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.inf_inf_nat X) Y)) X)) (forall ((X tptp.int) (Y tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.inf_inf_int X) Y)) X)) (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y 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tptp.inf_inf_int A) B) B))) (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_le3146513528884898305at_nat X) Y) (= (@ (@ tptp.inf_in2572325071724192079at_nat X) Y) X))) (forall ((X tptp.set_nat) (Y tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat X) Y) (= (@ (@ tptp.inf_inf_set_nat X) Y) X))) (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X) Y) (= (@ (@ tptp.inf_inf_rat X) Y) X))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X) Y) (= (@ (@ tptp.inf_inf_nat X) Y) X))) (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X) Y) (= (@ (@ tptp.inf_inf_int X) Y) X))) (forall ((Y tptp.set_Pr1261947904930325089at_nat) (X tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_le3146513528884898305at_nat Y) X) (= (@ (@ tptp.inf_in2572325071724192079at_nat X) Y) Y))) (forall ((Y tptp.set_nat) (X tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat Y) X) (= (@ (@ tptp.inf_inf_set_nat X) Y) Y))) (forall ((Y tptp.rat) (X tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat Y) X) (= (@ (@ tptp.inf_inf_rat X) Y) Y))) (forall ((Y tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Y) X) (= (@ (@ tptp.inf_inf_nat X) Y) Y))) (forall ((Y tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Y) X) (= (@ (@ tptp.inf_inf_int X) Y) Y))) (forall ((A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat) (C2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.ord_le3146513528884898305at_nat A))) (=> (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat B) C2)) (not (=> (@ _let_1 B) (not (@ _let_1 C2))))))) (forall ((A tptp.set_nat) (B tptp.set_nat) (C2 tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat A))) (=> (@ _let_1 (@ (@ tptp.inf_inf_set_nat B) C2)) (not (=> (@ _let_1 B) (not (@ _let_1 C2))))))) (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat A))) (=> (@ _let_1 (@ (@ tptp.inf_inf_rat B) C2)) (not (=> (@ _let_1 B) (not (@ _let_1 C2))))))) (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat A))) (=> (@ _let_1 (@ (@ tptp.inf_inf_nat B) C2)) (not (=> (@ _let_1 B) (not (@ _let_1 C2))))))) (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int A))) (=> (@ _let_1 (@ (@ tptp.inf_inf_int B) C2)) (not (=> (@ _let_1 B) (not (@ _let_1 C2))))))) (forall ((A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat) (C2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.ord_le3146513528884898305at_nat A))) (=> (@ _let_1 B) (=> (@ _let_1 C2) (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat B) C2)))))) (forall ((A tptp.set_nat) (B tptp.set_nat) (C2 tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat A))) (=> (@ _let_1 B) (=> (@ _let_1 C2) (@ _let_1 (@ (@ tptp.inf_inf_set_nat B) C2)))))) (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat A))) (=> (@ _let_1 B) (=> (@ _let_1 C2) (@ _let_1 (@ (@ tptp.inf_inf_rat B) C2)))))) (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat A))) (=> (@ _let_1 B) (=> (@ _let_1 C2) (@ _let_1 (@ (@ tptp.inf_inf_nat B) C2)))))) (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int A))) (=> (@ _let_1 B) (=> (@ _let_1 C2) (@ _let_1 (@ (@ tptp.inf_inf_int B) C2)))))) (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat) (Z3 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.ord_le3146513528884898305at_nat X))) (=> (@ _let_1 Y) (=> (@ _let_1 Z3) (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat Y) Z3)))))) (forall ((X tptp.set_nat) (Y tptp.set_nat) (Z3 tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat X))) (=> (@ _let_1 Y) (=> (@ _let_1 Z3) (@ _let_1 (@ (@ tptp.inf_inf_set_nat Y) Z3)))))) (forall ((X tptp.rat) (Y tptp.rat) (Z3 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat X))) (=> (@ _let_1 Y) (=> (@ _let_1 Z3) (@ _let_1 (@ (@ tptp.inf_inf_rat Y) Z3)))))) (forall ((X tptp.nat) (Y tptp.nat) (Z3 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat X))) (=> (@ _let_1 Y) (=> (@ _let_1 Z3) (@ _let_1 (@ (@ tptp.inf_inf_nat Y) Z3)))))) (forall ((X tptp.int) (Y tptp.int) (Z3 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int X))) (=> (@ _let_1 Y) (=> (@ _let_1 Z3) (@ _let_1 (@ (@ tptp.inf_inf_int Y) Z3)))))) (= tptp.ord_le3146513528884898305at_nat (lambda ((A5 tptp.set_Pr1261947904930325089at_nat) (B4 tptp.set_Pr1261947904930325089at_nat)) (= A5 (@ (@ tptp.inf_in2572325071724192079at_nat A5) B4)))) (= tptp.ord_less_eq_set_nat (lambda ((A5 tptp.set_nat) (B4 tptp.set_nat)) (= A5 (@ (@ tptp.inf_inf_set_nat A5) B4)))) (= tptp.ord_less_eq_rat (lambda ((A5 tptp.rat) (B4 tptp.rat)) (= A5 (@ (@ tptp.inf_inf_rat A5) B4)))) (= tptp.ord_less_eq_nat (lambda ((A5 tptp.nat) (B4 tptp.nat)) (= A5 (@ (@ tptp.inf_inf_nat A5) B4)))) (= tptp.ord_less_eq_int (lambda ((A5 tptp.int) (B4 tptp.int)) (= A5 (@ (@ tptp.inf_inf_int A5) B4)))) (forall ((A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.inf_in2572325071724192079at_nat A) B)) A)) (forall ((A tptp.set_nat) (B tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.inf_inf_set_nat A) B)) A)) (forall ((A tptp.rat) (B tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.inf_inf_rat A) B)) A)) (forall ((A tptp.nat) (B tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.inf_inf_nat A) B)) A)) (forall ((A tptp.int) (B tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.inf_inf_int A) B)) A)) (forall ((A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.inf_in2572325071724192079at_nat A) B)) B)) (forall ((A tptp.set_nat) (B tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.inf_inf_set_nat A) B)) B)) (forall ((A tptp.rat) (B tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.inf_inf_rat A) B)) B)) (forall ((A tptp.nat) (B tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.inf_inf_nat A) B)) B)) (forall ((A tptp.int) (B tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.inf_inf_int A) B)) B)) (= tptp.ord_le3146513528884898305at_nat (lambda ((A5 tptp.set_Pr1261947904930325089at_nat) (B4 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat A5) B4) A5))) (= tptp.ord_less_eq_set_nat (lambda ((A5 tptp.set_nat) (B4 tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat A5) B4) A5))) (= tptp.ord_less_eq_rat (lambda ((A5 tptp.rat) (B4 tptp.rat)) (= (@ (@ tptp.inf_inf_rat A5) B4) A5))) (= tptp.ord_less_eq_nat (lambda ((A5 tptp.nat) (B4 tptp.nat)) (= (@ (@ tptp.inf_inf_nat A5) B4) A5))) (= tptp.ord_less_eq_int (lambda ((A5 tptp.int) (B4 tptp.int)) (= (@ (@ tptp.inf_inf_int A5) B4) A5))) (= tptp.ord_le3146513528884898305at_nat (lambda ((B4 tptp.set_Pr1261947904930325089at_nat) (A5 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat A5) B4) B4))) (= tptp.ord_less_eq_set_nat (lambda ((B4 tptp.set_nat) (A5 tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat A5) B4) B4))) (= tptp.ord_less_eq_rat (lambda ((B4 tptp.rat) (A5 tptp.rat)) (= (@ (@ tptp.inf_inf_rat A5) B4) B4))) (= tptp.ord_less_eq_nat (lambda ((B4 tptp.nat) (A5 tptp.nat)) (= (@ (@ tptp.inf_inf_nat A5) B4) B4))) (= tptp.ord_less_eq_int (lambda ((B4 tptp.int) (A5 tptp.int)) (= (@ (@ tptp.inf_inf_int A5) B4) B4))) (forall ((A tptp.set_Pr1261947904930325089at_nat) (C2 tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_le3146513528884898305at_nat A) C2) (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.inf_in2572325071724192079at_nat A) B)) C2))) (forall ((A tptp.set_nat) (C2 tptp.set_nat) (B tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A) C2) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.inf_inf_set_nat A) B)) C2))) (forall ((A tptp.rat) (C2 tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) C2) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.inf_inf_rat A) B)) C2))) (forall ((A tptp.nat) (C2 tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) C2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.inf_inf_nat A) B)) C2))) (forall ((A tptp.int) (C2 tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) C2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.inf_inf_int A) B)) C2))) (forall ((B tptp.set_Pr1261947904930325089at_nat) (C2 tptp.set_Pr1261947904930325089at_nat) (A tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_le3146513528884898305at_nat B) C2) (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.inf_in2572325071724192079at_nat A) B)) C2))) (forall ((B tptp.set_nat) (C2 tptp.set_nat) (A tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat B) C2) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.inf_inf_set_nat A) B)) C2))) (forall ((B tptp.rat) (C2 tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat B) C2) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.inf_inf_rat A) B)) C2))) (forall ((B tptp.nat) (C2 tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B) C2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.inf_inf_nat A) B)) C2))) (forall ((B tptp.int) (C2 tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B) C2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.inf_inf_int A) B)) C2))) (forall ((C2 tptp.set_nat) (B tptp.set_nat) (A tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat C2))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.sup_sup_set_nat A) B))))) (forall ((C2 tptp.rat) (B tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat C2))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.sup_sup_rat A) B))))) (forall ((C2 tptp.nat) (B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat C2))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.sup_sup_nat A) B))))) (forall ((C2 tptp.int) (B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int C2))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.sup_sup_int A) B))))) (forall ((C2 tptp.set_nat) (A tptp.set_nat) (B tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat C2))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.sup_sup_set_nat A) B))))) (forall ((C2 tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat C2))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.sup_sup_rat A) B))))) (forall ((C2 tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat C2))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.sup_sup_nat A) B))))) (forall ((C2 tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int C2))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.sup_sup_int A) B))))) (= tptp.ord_less_eq_set_nat (lambda ((A5 tptp.set_nat) (B4 tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat A5) B4) B4))) (= tptp.ord_less_eq_rat (lambda ((A5 tptp.rat) (B4 tptp.rat)) (= (@ (@ tptp.sup_sup_rat A5) B4) B4))) (= tptp.ord_less_eq_nat (lambda ((A5 tptp.nat) (B4 tptp.nat)) (= (@ (@ tptp.sup_sup_nat A5) B4) B4))) (= tptp.ord_less_eq_int (lambda ((A5 tptp.int) (B4 tptp.int)) (= (@ (@ tptp.sup_sup_int A5) B4) B4))) (= tptp.ord_less_eq_set_nat (lambda ((B4 tptp.set_nat) (A5 tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat A5) B4) A5))) (= tptp.ord_less_eq_rat (lambda ((B4 tptp.rat) (A5 tptp.rat)) (= (@ (@ tptp.sup_sup_rat A5) B4) A5))) (= tptp.ord_less_eq_nat (lambda ((B4 tptp.nat) (A5 tptp.nat)) (= (@ (@ tptp.sup_sup_nat A5) B4) A5))) (= tptp.ord_less_eq_int (lambda ((B4 tptp.int) (A5 tptp.int)) (= (@ (@ tptp.sup_sup_int A5) B4) A5))) (forall ((B tptp.set_nat) (A tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat B) (@ (@ tptp.sup_sup_set_nat A) B))) (forall ((B tptp.rat) (A tptp.rat)) (@ (@ tptp.ord_less_eq_rat B) (@ (@ tptp.sup_sup_rat A) B))) (forall ((B tptp.nat) (A tptp.nat)) (@ (@ tptp.ord_less_eq_nat B) (@ (@ tptp.sup_sup_nat A) B))) (forall ((B tptp.int) (A tptp.int)) (@ (@ tptp.ord_less_eq_int B) (@ (@ tptp.sup_sup_int A) B))) (forall ((A tptp.set_nat) (B tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat A) (@ (@ tptp.sup_sup_set_nat A) B))) (forall ((A tptp.rat) (B tptp.rat)) (@ (@ tptp.ord_less_eq_rat A) (@ (@ tptp.sup_sup_rat A) B))) (forall ((A tptp.nat) (B tptp.nat)) (@ (@ tptp.ord_less_eq_nat A) (@ (@ tptp.sup_sup_nat A) B))) (forall ((A tptp.int) (B tptp.int)) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.sup_sup_int A) B))) (= tptp.ord_less_eq_set_nat (lambda ((B4 tptp.set_nat) (A5 tptp.set_nat)) (= A5 (@ (@ tptp.sup_sup_set_nat A5) B4)))) (= tptp.ord_less_eq_rat (lambda ((B4 tptp.rat) (A5 tptp.rat)) (= A5 (@ (@ tptp.sup_sup_rat A5) B4)))) (= tptp.ord_less_eq_nat (lambda ((B4 tptp.nat) (A5 tptp.nat)) (= A5 (@ (@ tptp.sup_sup_nat A5) B4)))) (= tptp.ord_less_eq_int (lambda ((B4 tptp.int) (A5 tptp.int)) (= A5 (@ (@ tptp.sup_sup_int A5) B4)))) (forall ((B tptp.set_nat) (A tptp.set_nat) (C2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat B) A) (=> (@ (@ tptp.ord_less_eq_set_nat C2) A) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.sup_sup_set_nat B) C2)) A)))) (forall ((B tptp.rat) (A tptp.rat) (C2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat B) A) (=> (@ (@ tptp.ord_less_eq_rat C2) A) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.sup_sup_rat B) C2)) A)))) (forall ((B tptp.nat) (A tptp.nat) (C2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B) A) (=> (@ (@ tptp.ord_less_eq_nat C2) A) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.sup_sup_nat B) C2)) A)))) (forall ((B tptp.int) (A tptp.int) (C2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B) A) (=> (@ (@ tptp.ord_less_eq_int C2) A) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.sup_sup_int B) C2)) A)))) (forall ((B tptp.set_nat) (C2 tptp.set_nat) (A tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.sup_sup_set_nat B) C2)) A) (not (=> (@ (@ tptp.ord_less_eq_set_nat B) A) (not (@ (@ tptp.ord_less_eq_set_nat C2) A)))))) (forall ((B tptp.rat) (C2 tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.sup_sup_rat B) C2)) A) (not (=> (@ (@ tptp.ord_less_eq_rat B) A) (not (@ (@ tptp.ord_less_eq_rat C2) A)))))) (forall ((B tptp.nat) (C2 tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.sup_sup_nat B) C2)) A) (not (=> (@ (@ tptp.ord_less_eq_nat B) A) (not (@ (@ tptp.ord_less_eq_nat C2) A)))))) (forall ((B tptp.int) (C2 tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.sup_sup_int B) C2)) A) (not (=> (@ (@ tptp.ord_less_eq_int B) A) (not (@ (@ tptp.ord_less_eq_int C2) A)))))) (forall ((X tptp.set_nat) (Y tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat X) Y) (= (@ (@ tptp.sup_sup_set_nat X) Y) Y))) (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X) Y) (= (@ (@ tptp.sup_sup_rat X) Y) Y))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X) Y) (= (@ (@ tptp.sup_sup_nat X) Y) Y))) (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X) Y) (= (@ (@ tptp.sup_sup_int X) Y) Y))) (forall ((Y tptp.set_nat) (X tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat Y) X) (= (@ (@ tptp.sup_sup_set_nat X) Y) X))) (forall ((Y tptp.rat) (X tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat Y) X) (= (@ (@ tptp.sup_sup_rat X) Y) X))) (forall ((Y tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Y) X) (= (@ (@ tptp.sup_sup_nat X) Y) X))) (forall ((Y tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Y) X) (= (@ (@ tptp.sup_sup_int X) Y) X))) (forall ((A tptp.set_nat) (B tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A) B) (= (@ (@ tptp.sup_sup_set_nat A) B) B))) (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (= (@ (@ tptp.sup_sup_rat A) B) B))) (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= (@ (@ tptp.sup_sup_nat A) B) B))) (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (= (@ (@ tptp.sup_sup_int A) B) B))) (forall ((B tptp.set_nat) (A tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat B) A) (= (@ (@ tptp.sup_sup_set_nat A) B) A))) (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat B) A) (= (@ (@ tptp.sup_sup_rat A) B) A))) (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B) A) (= (@ (@ tptp.sup_sup_nat A) B) A))) (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B) A) (= (@ (@ tptp.sup_sup_int A) B) A))) (forall ((F2 (-> tptp.set_nat tptp.set_nat tptp.set_nat)) (X tptp.set_nat) (Y tptp.set_nat)) (=> (forall ((X3 tptp.set_nat) (Y3 tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat X3) (@ (@ F2 X3) Y3))) (=> (forall ((X3 tptp.set_nat) (Y3 tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat Y3) (@ (@ F2 X3) Y3))) (=> (forall ((X3 tptp.set_nat) (Y3 tptp.set_nat) (Z tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat Y3) X3) (=> (@ (@ tptp.ord_less_eq_set_nat Z) X3) (@ (@ tptp.ord_less_eq_set_nat (@ (@ F2 Y3) Z)) X3)))) (= (@ (@ tptp.sup_sup_set_nat X) Y) (@ (@ F2 X) Y)))))) (forall ((F2 (-> tptp.rat tptp.rat tptp.rat)) (X tptp.rat) (Y tptp.rat)) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (@ (@ tptp.ord_less_eq_rat X3) (@ (@ F2 X3) Y3))) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (@ (@ tptp.ord_less_eq_rat Y3) (@ (@ F2 X3) Y3))) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat) (Z tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat Y3) X3) (=> (@ (@ tptp.ord_less_eq_rat Z) X3) (@ (@ tptp.ord_less_eq_rat (@ (@ F2 Y3) Z)) X3)))) (= (@ (@ tptp.sup_sup_rat X) Y) (@ (@ F2 X) Y)))))) (forall ((F2 (-> tptp.nat tptp.nat tptp.nat)) (X tptp.nat) (Y tptp.nat)) (=> (forall ((X3 tptp.nat) (Y3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat X3) (@ (@ F2 X3) Y3))) (=> (forall ((X3 tptp.nat) (Y3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat Y3) (@ (@ F2 X3) Y3))) (=> (forall ((X3 tptp.nat) (Y3 tptp.nat) (Z tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Y3) X3) (=> (@ (@ tptp.ord_less_eq_nat Z) X3) (@ (@ tptp.ord_less_eq_nat (@ (@ F2 Y3) Z)) X3)))) (= (@ (@ tptp.sup_sup_nat X) Y) (@ (@ F2 X) Y)))))) (forall ((F2 (-> tptp.int tptp.int tptp.int)) (X tptp.int) (Y tptp.int)) (=> (forall ((X3 tptp.int) (Y3 tptp.int)) (@ (@ tptp.ord_less_eq_int X3) (@ (@ F2 X3) Y3))) (=> (forall ((X3 tptp.int) (Y3 tptp.int)) (@ (@ tptp.ord_less_eq_int Y3) (@ (@ F2 X3) Y3))) (=> (forall ((X3 tptp.int) (Y3 tptp.int) (Z tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Y3) X3) (=> (@ (@ tptp.ord_less_eq_int Z) X3) (@ (@ tptp.ord_less_eq_int (@ (@ F2 Y3) Z)) X3)))) (= (@ (@ tptp.sup_sup_int X) Y) (@ (@ F2 X) Y)))))) (forall ((A tptp.set_nat) (B tptp.set_nat)) (=> (= A (@ (@ tptp.sup_sup_set_nat A) B)) (@ (@ tptp.ord_less_eq_set_nat B) A))) (forall ((A tptp.rat) (B tptp.rat)) (=> (= A (@ (@ tptp.sup_sup_rat A) B)) (@ (@ tptp.ord_less_eq_rat B) A))) (forall ((A tptp.nat) (B tptp.nat)) (=> (= A (@ (@ tptp.sup_sup_nat A) B)) (@ (@ tptp.ord_less_eq_nat B) A))) (forall ((A tptp.int) (B tptp.int)) (=> (= A (@ (@ tptp.sup_sup_int A) B)) (@ (@ tptp.ord_less_eq_int B) A))) (forall ((B tptp.set_nat) (A tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat B) A) (= A (@ (@ tptp.sup_sup_set_nat A) B)))) (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat B) A) (= A (@ (@ tptp.sup_sup_rat A) B)))) (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B) A) (= A (@ (@ tptp.sup_sup_nat A) B)))) (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B) A) (= A (@ (@ tptp.sup_sup_int A) B)))) (= tptp.ord_less_eq_set_nat (lambda ((X4 tptp.set_nat) (Y4 tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat X4) Y4) Y4))) (= tptp.ord_less_eq_rat (lambda ((X4 tptp.rat) (Y4 tptp.rat)) (= (@ (@ tptp.sup_sup_rat X4) Y4) Y4))) (= tptp.ord_less_eq_nat (lambda ((X4 tptp.nat) (Y4 tptp.nat)) (= (@ (@ tptp.sup_sup_nat X4) Y4) Y4))) (= tptp.ord_less_eq_int (lambda ((X4 tptp.int) (Y4 tptp.int)) (= (@ (@ tptp.sup_sup_int X4) Y4) Y4))) (forall ((Y tptp.set_nat) (X tptp.set_nat) (Z3 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat Y) X) (=> (@ (@ tptp.ord_less_eq_set_nat Z3) X) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.sup_sup_set_nat Y) Z3)) X)))) (forall ((Y tptp.rat) (X tptp.rat) (Z3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat Y) X) (=> (@ (@ tptp.ord_less_eq_rat Z3) X) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.sup_sup_rat Y) Z3)) X)))) (forall ((Y tptp.nat) (X tptp.nat) (Z3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Y) X) (=> (@ (@ tptp.ord_less_eq_nat Z3) X) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.sup_sup_nat Y) Z3)) X)))) (forall ((Y tptp.int) (X tptp.int) (Z3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Y) X) (=> (@ (@ tptp.ord_less_eq_int Z3) X) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.sup_sup_int Y) Z3)) X)))) (forall ((A tptp.set_nat) (C2 tptp.set_nat) (B tptp.set_nat) (D tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A) C2) (=> (@ (@ tptp.ord_less_eq_set_nat B) D) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.sup_sup_set_nat A) B)) (@ (@ tptp.sup_sup_set_nat C2) D))))) (forall ((A tptp.rat) (C2 tptp.rat) (B tptp.rat) (D tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) C2) (=> (@ (@ tptp.ord_less_eq_rat B) D) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.sup_sup_rat A) B)) (@ (@ tptp.sup_sup_rat C2) D))))) (forall ((A tptp.nat) (C2 tptp.nat) (B tptp.nat) (D tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) C2) (=> (@ (@ tptp.ord_less_eq_nat B) D) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.sup_sup_nat A) B)) (@ (@ tptp.sup_sup_nat C2) D))))) (forall ((A tptp.int) (C2 tptp.int) (B tptp.int) (D tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) C2) (=> (@ (@ tptp.ord_less_eq_int B) D) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.sup_sup_int A) B)) (@ (@ tptp.sup_sup_int C2) D))))) (forall ((C2 tptp.set_nat) (A tptp.set_nat) (D tptp.set_nat) (B tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat C2) A) (=> (@ (@ tptp.ord_less_eq_set_nat D) B) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.sup_sup_set_nat C2) D)) (@ (@ tptp.sup_sup_set_nat A) B))))) (forall ((C2 tptp.rat) (A tptp.rat) (D tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat C2) A) (=> (@ (@ tptp.ord_less_eq_rat D) B) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.sup_sup_rat C2) D)) (@ (@ tptp.sup_sup_rat A) B))))) (forall ((C2 tptp.nat) (A tptp.nat) (D tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat C2) A) (=> (@ (@ tptp.ord_less_eq_nat D) B) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.sup_sup_nat C2) D)) (@ (@ tptp.sup_sup_nat A) B))))) (forall ((C2 tptp.int) (A tptp.int) (D tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int C2) A) (=> (@ (@ tptp.ord_less_eq_int D) B) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.sup_sup_int C2) D)) (@ (@ tptp.sup_sup_int A) B))))) (forall ((X tptp.set_nat) (B tptp.set_nat) (A tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat X))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.sup_sup_set_nat A) B))))) (forall ((X tptp.rat) (B tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat X))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.sup_sup_rat A) B))))) (forall ((X tptp.nat) (B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat X))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.sup_sup_nat A) B))))) (forall ((X tptp.int) (B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int X))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.sup_sup_int A) B))))) (forall ((X tptp.set_nat) (A tptp.set_nat) (B tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat X))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.sup_sup_set_nat A) B))))) (forall ((X tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat X))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.sup_sup_rat A) B))))) (forall ((X tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat X))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.sup_sup_nat A) B))))) (forall ((X tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int X))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.sup_sup_int A) B))))) (forall ((Y tptp.set_nat) (X tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat Y) (@ (@ tptp.sup_sup_set_nat X) Y))) (forall ((Y tptp.rat) (X tptp.rat)) (@ (@ tptp.ord_less_eq_rat Y) (@ (@ tptp.sup_sup_rat X) Y))) (forall ((Y tptp.nat) (X tptp.nat)) (@ (@ tptp.ord_less_eq_nat Y) (@ (@ tptp.sup_sup_nat X) Y))) (forall ((Y tptp.int) (X tptp.int)) (@ (@ tptp.ord_less_eq_int Y) (@ (@ tptp.sup_sup_int X) Y))) (forall ((X tptp.set_nat) (Y tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat X) (@ (@ tptp.sup_sup_set_nat X) Y))) (forall ((X tptp.rat) (Y tptp.rat)) (@ (@ tptp.ord_less_eq_rat X) (@ (@ tptp.sup_sup_rat X) Y))) (forall ((X tptp.nat) (Y tptp.nat)) (@ (@ tptp.ord_less_eq_nat X) (@ (@ tptp.sup_sup_nat X) Y))) (forall ((X tptp.int) (Y tptp.int)) (@ (@ tptp.ord_less_eq_int X) (@ (@ tptp.sup_sup_int X) Y))) (forall ((A tptp.set_nat) (X tptp.set_nat) (B tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A) X) (=> (@ (@ tptp.ord_less_eq_set_nat B) X) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.sup_sup_set_nat A) B)) X)))) (forall ((A tptp.rat) (X tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) X) (=> (@ (@ tptp.ord_less_eq_rat B) X) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.sup_sup_rat A) B)) X)))) (forall ((A tptp.nat) (X tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) X) (=> (@ (@ tptp.ord_less_eq_nat B) X) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.sup_sup_nat A) B)) X)))) (forall ((A tptp.int) (X tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) X) (=> (@ (@ tptp.ord_less_eq_int B) X) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.sup_sup_int A) B)) X)))) (forall ((A tptp.set_nat) (B tptp.set_nat) (X tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.sup_sup_set_nat A) B)) X) (not (=> (@ (@ tptp.ord_less_eq_set_nat A) X) (not (@ (@ tptp.ord_less_eq_set_nat B) X)))))) (forall ((A tptp.rat) (B tptp.rat) (X tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.sup_sup_rat A) B)) X) (not (=> (@ (@ tptp.ord_less_eq_rat A) X) (not (@ (@ tptp.ord_less_eq_rat B) X)))))) (forall ((A tptp.nat) (B tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.sup_sup_nat A) B)) X) (not (=> (@ (@ tptp.ord_less_eq_nat A) X) (not (@ (@ tptp.ord_less_eq_nat B) X)))))) (forall ((A tptp.int) (B tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.sup_sup_int A) B)) X) (not (=> (@ (@ tptp.ord_less_eq_int A) X) (not (@ (@ tptp.ord_less_eq_int B) X)))))) (forall ((X tptp.set_nat) (Y tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat X) (@ (@ tptp.sup_sup_set_nat X) Y))) (forall ((X tptp.rat) (Y tptp.rat)) (@ (@ tptp.ord_less_eq_rat X) (@ (@ tptp.sup_sup_rat X) Y))) (forall ((X tptp.nat) (Y tptp.nat)) (@ (@ tptp.ord_less_eq_nat X) (@ (@ tptp.sup_sup_nat X) Y))) (forall ((X tptp.int) (Y tptp.int)) (@ (@ tptp.ord_less_eq_int X) (@ (@ tptp.sup_sup_int X) Y))) (forall ((Y tptp.set_nat) (X tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat Y) (@ (@ tptp.sup_sup_set_nat X) Y))) (forall ((Y tptp.rat) (X tptp.rat)) (@ (@ tptp.ord_less_eq_rat Y) (@ (@ tptp.sup_sup_rat X) Y))) (forall ((Y tptp.nat) (X tptp.nat)) (@ (@ tptp.ord_less_eq_nat Y) (@ (@ tptp.sup_sup_nat X) Y))) (forall ((Y tptp.int) (X tptp.int)) (@ (@ tptp.ord_less_eq_int Y) (@ (@ tptp.sup_sup_int X) Y))) (forall ((TreeList2 tptp.list_VEBT_VEBT) (N tptp.nat) (Summary tptp.vEBT_VEBT) (M2 tptp.nat) (Deg tptp.nat) (Mi tptp.nat) (Ma tptp.nat)) (let ((_let_1 (= Mi Ma))) (let ((_let_2 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList2)) (@ (@ tptp.vEBT_invar_vebt X3) N))) (=> (@ (@ tptp.vEBT_invar_vebt Summary) M2) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList2) (@ _let_2 M2)) (=> (= M2 N) (=> (= Deg (@ (@ tptp.plus_plus_nat N) M2)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M2)) (= (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I3)) X7)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary) I3)))) (=> (=> _let_1 (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X3) X_12)))))) (=> (@ (@ tptp.ord_less_eq_nat Mi) Ma) (=> (@ (@ tptp.ord_less_nat Ma) (@ _let_2 Deg)) (=> (=> (not _let_1) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M2)) (and (=> (= (@ (@ tptp.vEBT_VEBT_high Ma) N) I3) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I3)) (@ (@ tptp.vEBT_VEBT_low Ma) N))) (forall ((X3 tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X3) N) I3) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I3)) (@ (@ tptp.vEBT_VEBT_low X3) N))) (and (@ (@ tptp.ord_less_nat Mi) X3) (@ (@ tptp.ord_less_eq_nat X3) Ma)))))))) (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList2) Summary)) Deg)))))))))))))) (forall ((TreeList2 tptp.list_VEBT_VEBT) (N tptp.nat) (Summary tptp.vEBT_VEBT) (M2 tptp.nat) (Deg tptp.nat) (Mi tptp.nat) (Ma tptp.nat)) (let ((_let_1 (= Mi Ma))) (let ((_let_2 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList2)) (@ (@ tptp.vEBT_invar_vebt X3) N))) (=> (@ (@ tptp.vEBT_invar_vebt Summary) M2) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList2) (@ _let_2 M2)) (=> (= M2 (@ tptp.suc N)) (=> (= Deg (@ (@ tptp.plus_plus_nat N) M2)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M2)) (= (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I3)) X7)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary) I3)))) (=> (=> _let_1 (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X3) X_12)))))) (=> (@ (@ tptp.ord_less_eq_nat Mi) Ma) (=> (@ (@ tptp.ord_less_nat Ma) (@ _let_2 Deg)) (=> (=> (not _let_1) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M2)) (and (=> (= (@ (@ tptp.vEBT_VEBT_high Ma) N) I3) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I3)) (@ (@ tptp.vEBT_VEBT_low Ma) N))) (forall ((X3 tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X3) N) I3) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I3)) (@ (@ tptp.vEBT_VEBT_low X3) N))) (and (@ (@ tptp.ord_less_nat Mi) X3) (@ (@ tptp.ord_less_eq_nat X3) Ma)))))))) (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList2) Summary)) Deg)))))))))))))) (forall ((A12 tptp.vEBT_VEBT) (A23 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt A12) A23) (=> (=> (exists ((A3 Bool) (B3 Bool)) (= A12 (@ (@ tptp.vEBT_Leaf A3) B3))) (not (= A23 (@ tptp.suc tptp.zero_zero_nat)))) (=> (forall ((TreeList tptp.list_VEBT_VEBT) (N3 tptp.nat) (Summary2 tptp.vEBT_VEBT) (M tptp.nat) (Deg2 tptp.nat)) (=> (= A12 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Deg2) TreeList) Summary2)) (=> (= A23 Deg2) (=> (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 TreeList)) (@ (@ tptp.vEBT_invar_vebt X5) N3))) (=> (@ (@ tptp.vEBT_invar_vebt Summary2) M) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M)) (=> (= M N3) (=> (= Deg2 (@ (@ tptp.plus_plus_nat N3) M)) (=> (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) X_1))) (not (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 TreeList)) (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X5) X_1))))))))))))))) (=> (forall ((TreeList tptp.list_VEBT_VEBT) (N3 tptp.nat) (Summary2 tptp.vEBT_VEBT) (M tptp.nat) (Deg2 tptp.nat)) (=> (= A12 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Deg2) TreeList) Summary2)) (=> (= A23 Deg2) (=> (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 TreeList)) (@ (@ tptp.vEBT_invar_vebt X5) N3))) (=> (@ (@ tptp.vEBT_invar_vebt Summary2) M) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M)) (=> (= M (@ tptp.suc N3)) (=> (= Deg2 (@ (@ tptp.plus_plus_nat N3) M)) (=> (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) X_1))) (not (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 TreeList)) (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X5) X_1))))))))))))))) (=> (forall ((TreeList tptp.list_VEBT_VEBT) (N3 tptp.nat) (Summary2 tptp.vEBT_VEBT) (M 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) TreeList) Summary2)) (=> (= A23 Deg2) (=> (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 TreeList)) (@ (@ tptp.vEBT_invar_vebt X5) N3))) (=> (@ (@ tptp.vEBT_invar_vebt Summary2) M) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList) (@ _let_2 M)) (=> (= M N3) (=> (= Deg2 (@ (@ tptp.plus_plus_nat N3) M)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M)) (= (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I4)) X7)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I4)))) (=> (=> _let_1 (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 TreeList)) (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X5) X_1)))))) (=> (@ (@ tptp.ord_less_eq_nat Mi2) Ma2) (=> (@ (@ tptp.ord_less_nat Ma2) (@ _let_2 Deg2)) (not (=> (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 Ma2) N3) I4) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I4)) (@ (@ tptp.vEBT_VEBT_low Ma2) N3))) (forall ((X5 tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X5) N3) I4) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I4)) (@ (@ tptp.vEBT_VEBT_low X5) N3))) (and (@ (@ tptp.ord_less_nat Mi2) X5) (@ (@ tptp.ord_less_eq_nat X5) Ma2))))))))))))))))))))))) (not (forall ((TreeList tptp.list_VEBT_VEBT) (N3 tptp.nat) (Summary2 tptp.vEBT_VEBT) (M 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) TreeList) Summary2)) (=> (= A23 Deg2) (=> (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 TreeList)) (@ (@ tptp.vEBT_invar_vebt X5) N3))) (=> (@ (@ tptp.vEBT_invar_vebt Summary2) M) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList) (@ _let_2 M)) (=> (= M (@ tptp.suc N3)) (=> (= Deg2 (@ (@ tptp.plus_plus_nat N3) M)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M)) (= (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I4)) X7)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I4)))) (=> (=> _let_1 (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 TreeList)) (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X5) X_1)))))) (=> (@ (@ tptp.ord_less_eq_nat Mi2) Ma2) (=> (@ (@ tptp.ord_less_nat Ma2) (@ _let_2 Deg2)) (not (=> (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 Ma2) N3) I4) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I4)) (@ (@ tptp.vEBT_VEBT_low Ma2) N3))) (forall ((X5 tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X5) N3) I4) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I4)) (@ (@ tptp.vEBT_VEBT_low X5) N3))) (and (@ (@ tptp.ord_less_nat Mi2) X5) (@ (@ tptp.ord_less_eq_nat X5) Ma2)))))))))))))))))))))))))))))) (= tptp.vEBT_invar_vebt (lambda ((A13 tptp.vEBT_VEBT) (A24 tptp.nat)) (or (and (exists ((A5 Bool) (B4 Bool)) (= A13 (@ (@ tptp.vEBT_Leaf A5) B4))) (= A24 (@ tptp.suc tptp.zero_zero_nat))) (exists ((TreeList4 tptp.list_VEBT_VEBT) (N4 tptp.nat) (Summary4 tptp.vEBT_VEBT)) (and (= A13 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) A24) TreeList4) Summary4)) (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList4)) (@ (@ tptp.vEBT_invar_vebt X4) N4))) (@ (@ tptp.vEBT_invar_vebt Summary4) N4) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList4) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N4)) (= A24 (@ (@ tptp.plus_plus_nat N4) N4)) (not (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary4) X7))) (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList4)) (not (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X4) X7))))))) (exists ((TreeList4 tptp.list_VEBT_VEBT) (N4 tptp.nat) (Summary4 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc N4))) (and (= A13 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) A24) TreeList4) Summary4)) (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList4)) (@ (@ tptp.vEBT_invar_vebt X4) N4))) (@ (@ tptp.vEBT_invar_vebt Summary4) _let_1) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList4) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_1)) (= A24 (@ (@ tptp.plus_plus_nat N4) _let_1)) (not (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary4) X7))) (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList4)) (not (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X4) X7)))))))) (exists ((TreeList4 tptp.list_VEBT_VEBT) (N4 tptp.nat) (Summary4 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 (= A13 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi3) Ma3))) A24) TreeList4) Summary4)) (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList4)) (@ (@ tptp.vEBT_invar_vebt X4) N4))) (@ (@ tptp.vEBT_invar_vebt Summary4) N4) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList4) (@ _let_2 N4)) (= A24 (@ (@ tptp.plus_plus_nat N4) N4)) (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N4)) (= (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList4) I)) X7)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary4) I)))) (=> _let_1 (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList4)) (not (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X4) X7)))))) (@ (@ tptp.ord_less_eq_nat Mi3) Ma3) (@ (@ tptp.ord_less_nat Ma3) (@ _let_2 A24)) (=> (not _let_1) (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N4)) (and (=> (= (@ (@ tptp.vEBT_VEBT_high Ma3) N4) I) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList4) I)) (@ (@ tptp.vEBT_VEBT_low Ma3) N4))) (forall ((X4 tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X4) N4) I) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList4) I)) (@ (@ tptp.vEBT_VEBT_low X4) N4))) (and (@ (@ tptp.ord_less_nat Mi3) X4) (@ (@ tptp.ord_less_eq_nat X4) Ma3)))))))))))) (exists ((TreeList4 tptp.list_VEBT_VEBT) (N4 tptp.nat) (Summary4 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 N4))) (and (= A13 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi3) Ma3))) A24) TreeList4) Summary4)) (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList4)) (@ (@ tptp.vEBT_invar_vebt X4) N4))) (@ (@ tptp.vEBT_invar_vebt Summary4) _let_3) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList4) (@ _let_2 _let_3)) (= A24 (@ (@ tptp.plus_plus_nat N4) _let_3)) (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.suc N4))) (= (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList4) I)) X7)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary4) I)))) (=> _let_1 (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList4)) (not (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X4) X7)))))) (@ (@ tptp.ord_less_eq_nat Mi3) Ma3) (@ (@ tptp.ord_less_nat Ma3) (@ _let_2 A24)) (=> (not _let_1) (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.suc N4))) (and (=> (= (@ (@ tptp.vEBT_VEBT_high Ma3) N4) I) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList4) I)) (@ (@ tptp.vEBT_VEBT_low Ma3) N4))) (forall ((X4 tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X4) N4) I) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList4) I)) (@ (@ tptp.vEBT_VEBT_low X4) N4))) (and (@ (@ tptp.ord_less_nat Mi3) X4) (@ (@ tptp.ord_less_eq_nat X4) Ma3)))))))))))))))) (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat) (Z3 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.inf_in2572325071724192079at_nat X))) (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.sup_su6327502436637775413at_nat (@ _let_1 Y)) (@ _let_1 Z3))) (@ _let_1 (@ (@ tptp.sup_su6327502436637775413at_nat Y) Z3))))) (forall ((X tptp.set_nat) (Y tptp.set_nat) (Z3 tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat X))) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.sup_sup_set_nat (@ _let_1 Y)) (@ _let_1 Z3))) (@ _let_1 (@ (@ tptp.sup_sup_set_nat Y) Z3))))) (forall ((X tptp.rat) (Y tptp.rat) (Z3 tptp.rat)) (let ((_let_1 (@ tptp.inf_inf_rat X))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.sup_sup_rat (@ _let_1 Y)) (@ _let_1 Z3))) (@ _let_1 (@ (@ tptp.sup_sup_rat Y) Z3))))) (forall ((X tptp.nat) (Y tptp.nat) (Z3 tptp.nat)) (let ((_let_1 (@ tptp.inf_inf_nat X))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.sup_sup_nat (@ _let_1 Y)) (@ _let_1 Z3))) (@ _let_1 (@ (@ tptp.sup_sup_nat Y) Z3))))) (forall ((X tptp.int) (Y tptp.int) (Z3 tptp.int)) (let ((_let_1 (@ tptp.inf_inf_int X))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.sup_sup_int (@ _let_1 Y)) (@ _let_1 Z3))) (@ _let_1 (@ (@ tptp.sup_sup_int Y) Z3))))) (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat) (Z3 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.sup_su6327502436637775413at_nat X))) (@ (@ tptp.ord_le3146513528884898305at_nat (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat Y) Z3))) (@ (@ tptp.inf_in2572325071724192079at_nat (@ _let_1 Y)) (@ _let_1 Z3))))) (forall ((X tptp.set_nat) (Y tptp.set_nat) (Z3 tptp.set_nat)) (let ((_let_1 (@ tptp.sup_sup_set_nat X))) (@ (@ tptp.ord_less_eq_set_nat (@ _let_1 (@ (@ tptp.inf_inf_set_nat Y) Z3))) (@ (@ tptp.inf_inf_set_nat (@ _let_1 Y)) (@ _let_1 Z3))))) (forall ((X tptp.rat) (Y tptp.rat) (Z3 tptp.rat)) (let ((_let_1 (@ tptp.sup_sup_rat X))) (@ (@ tptp.ord_less_eq_rat (@ _let_1 (@ (@ tptp.inf_inf_rat Y) Z3))) (@ (@ tptp.inf_inf_rat (@ _let_1 Y)) (@ _let_1 Z3))))) (forall ((X tptp.nat) (Y tptp.nat) (Z3 tptp.nat)) (let ((_let_1 (@ tptp.sup_sup_nat X))) (@ (@ tptp.ord_less_eq_nat (@ _let_1 (@ (@ tptp.inf_inf_nat Y) Z3))) (@ (@ tptp.inf_inf_nat (@ _let_1 Y)) (@ _let_1 Z3))))) (forall ((X tptp.int) (Y tptp.int) (Z3 tptp.int)) (let ((_let_1 (@ tptp.sup_sup_int X))) (@ (@ tptp.ord_less_eq_int (@ _let_1 (@ (@ tptp.inf_inf_int Y) Z3))) (@ (@ tptp.inf_inf_int (@ _let_1 Y)) (@ _let_1 Z3))))) _let_280 (forall ((Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (N tptp.nat) (Va3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat Va3) _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 Va3))) (=> (not (@ (@ tptp.ord_less_nat Ma) Mi)) (=> (not (= Ma Mi)) (@ (@ tptp.ord_less_nat (@ (@ tptp.vEBT_VEBT_high (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_3) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.power_power_nat _let_1) _let_2)))) (@ tptp.the_nat (@ tptp.vEBT_vebt_mint (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_3))))) (@ tptp.suc _let_2))) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))))))))) (forall ((Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (=> (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList2) Summary)) Deg) (=> (not (= Mi Ma)) (= (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt Summary)) (@ (@ tptp.vEBT_VEBT_high Ma) (@ (@ tptp.divide_divide_nat Deg) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))) (forall ((A4 tptp.set_nat) (N tptp.nat)) (=> (@ tptp.finite_finite_nat A4) (=> (not (@ (@ tptp.member_nat N) A4)) (= (@ tptp.nat_set_encode (@ (@ tptp.insert_nat N) A4)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (@ tptp.nat_set_encode A4)))))) (forall ((A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se4205575877204974255it_nat tptp.zero_zero_nat) A) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.divide_divide_nat A) _let_1))))) (forall ((A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se4203085406695923979it_int tptp.zero_zero_nat) A) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.divide_divide_int A) _let_1))))) (forall ((X tptp.nat) (Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (Xn tptp.nat) (H tptp.nat) (Summary tptp.vEBT_VEBT) (TreeList2 tptp.list_VEBT_VEBT) (L 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 H) (=> (= 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) L) (=> (@ (@ tptp.ord_less_nat _let_5) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)) (=> (= Newnode (@ (@ tptp.vEBT_vebt_delete (@ _let_4 H)) L)) (=> (= Newlist (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList2) H) 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 H) _let_3)) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ (@ tptp.nth_VEBT_VEBT Newlist) H))))) Ma)))) Deg) Newlist) Summary))))))))))))))))))) (forall ((Mi tptp.nat) (X tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (H tptp.nat) (L 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 H) (=> (= (@ (@ tptp.vEBT_VEBT_low X) _let_2) L) (=> (= Newnode (@ (@ tptp.vEBT_vebt_delete (@ (@ tptp.nth_VEBT_VEBT TreeList2) H)) L)) (=> (not (@ tptp.vEBT_VEBT_minNull Newnode)) (=> (= Newlist (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList2) H) 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 H) (@ (@ tptp.power_power_nat _let_1) _let_2))) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ (@ tptp.nth_VEBT_VEBT Newlist) H))))) Ma)))) Deg) Newlist) Summary)))))))))))))))) (forall ((B tptp.int) (A tptp.int) (Q2 tptp.int) (R3 tptp.int)) (let ((_let_1 (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.product_Pair_int_int 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 R3)) (@ (@ (@ tptp.eucl_rel_int (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ _let_1 A))) (@ _let_1 B)) (@ _let_2 (@ (@ tptp.minus_minus_int (@ _let_1 R3)) tptp.one_one_int)))))))) (forall ((Xs2 tptp.list_VEBT_VEBT) (I2 tptp.nat) (X tptp.vEBT_VEBT)) (= (@ tptp.size_s6755466524823107622T_VEBT (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs2) I2) X)) (@ tptp.size_s6755466524823107622T_VEBT Xs2))) (forall ((Xs2 tptp.list_o) (I2 tptp.nat) (X Bool)) (= (@ tptp.size_size_list_o (@ (@ (@ tptp.list_update_o Xs2) I2) X)) (@ tptp.size_size_list_o Xs2))) (forall ((Xs2 tptp.list_nat) (I2 tptp.nat) (X tptp.nat)) (= (@ tptp.size_size_list_nat (@ (@ (@ tptp.list_update_nat Xs2) I2) X)) (@ tptp.size_size_list_nat Xs2))) (forall ((Xs2 tptp.list_int) (I2 tptp.nat) (X tptp.int)) (= (@ tptp.size_size_list_int (@ (@ (@ tptp.list_update_int Xs2) I2) X)) (@ tptp.size_size_list_int Xs2))) (forall ((Option tptp.option4927543243414619207at_nat)) (=> (not (= Option tptp.none_P5556105721700978146at_nat)) (= (@ tptp.some_P7363390416028606310at_nat (@ tptp.the_Pr8591224930841456533at_nat Option)) Option))) (forall ((Option tptp.option_nat)) (=> (not (= Option tptp.none_nat)) (= (@ tptp.some_nat (@ tptp.the_nat Option)) Option))) (forall ((Option tptp.option_num)) (=> (not (= Option tptp.none_num)) (= (@ tptp.some_num (@ tptp.the_num Option)) Option))) (forall ((Xs2 tptp.list_VEBT_VEBT) (I2 tptp.nat) (X tptp.vEBT_VEBT)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_s6755466524823107622T_VEBT Xs2)) I2) (= (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs2) I2) X) Xs2))) (forall ((Xs2 tptp.list_o) (I2 tptp.nat) (X Bool)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_o Xs2)) I2) (= (@ (@ (@ tptp.list_update_o Xs2) I2) X) Xs2))) (forall ((Xs2 tptp.list_nat) (I2 tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_nat Xs2)) I2) (= (@ (@ (@ tptp.list_update_nat Xs2) I2) X) Xs2))) (forall ((Xs2 tptp.list_int) (I2 tptp.nat) (X tptp.int)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_int Xs2)) I2) (= (@ (@ (@ tptp.list_update_int Xs2) I2) X) Xs2))) (= (@ tptp.nat_set_encode tptp.bot_bot_set_nat) tptp.zero_zero_nat) (forall ((I2 tptp.nat) (Xs2 tptp.list_VEBT_VEBT) (X tptp.vEBT_VEBT)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (= (@ (@ tptp.nth_VEBT_VEBT (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs2) I2) X)) I2) X))) (forall ((I2 tptp.nat) (Xs2 tptp.list_o) (X Bool)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_o Xs2)) (= (@ (@ tptp.nth_o (@ (@ (@ tptp.list_update_o Xs2) I2) X)) I2) X))) (forall ((I2 tptp.nat) (Xs2 tptp.list_nat) (X tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_nat Xs2)) (= (@ (@ tptp.nth_nat (@ (@ (@ tptp.list_update_nat Xs2) I2) X)) I2) X))) (forall ((I2 tptp.nat) (Xs2 tptp.list_int) (X tptp.int)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_int Xs2)) (= (@ (@ tptp.nth_int (@ (@ (@ tptp.list_update_int Xs2) I2) X)) I2) X))) (forall ((I2 tptp.nat) (Xs2 tptp.list_VEBT_VEBT) (J2 tptp.nat)) (let ((_let_1 (@ tptp.nth_VEBT_VEBT Xs2))) (let ((_let_2 (@ tptp.size_s6755466524823107622T_VEBT Xs2))) (=> (@ (@ tptp.ord_less_nat I2) _let_2) (=> (@ (@ tptp.ord_less_nat J2) _let_2) (= (@ tptp.set_VEBT_VEBT2 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs2) I2) (@ _let_1 J2))) J2) (@ _let_1 I2))) (@ tptp.set_VEBT_VEBT2 Xs2))))))) (forall ((I2 tptp.nat) (Xs2 tptp.list_o) (J2 tptp.nat)) (let ((_let_1 (@ tptp.nth_o Xs2))) (let ((_let_2 (@ tptp.size_size_list_o Xs2))) (=> (@ (@ tptp.ord_less_nat I2) _let_2) (=> (@ (@ tptp.ord_less_nat J2) _let_2) (= (@ tptp.set_o2 (@ (@ (@ tptp.list_update_o (@ (@ (@ tptp.list_update_o Xs2) I2) (@ _let_1 J2))) J2) (@ _let_1 I2))) (@ tptp.set_o2 Xs2))))))) (forall ((I2 tptp.nat) (Xs2 tptp.list_nat) (J2 tptp.nat)) (let ((_let_1 (@ tptp.nth_nat Xs2))) (let ((_let_2 (@ tptp.size_size_list_nat Xs2))) (=> (@ (@ tptp.ord_less_nat I2) _let_2) (=> (@ (@ tptp.ord_less_nat J2) _let_2) (= (@ tptp.set_nat2 (@ (@ (@ tptp.list_update_nat (@ (@ (@ tptp.list_update_nat Xs2) I2) (@ _let_1 J2))) J2) (@ _let_1 I2))) (@ tptp.set_nat2 Xs2))))))) (forall ((I2 tptp.nat) (Xs2 tptp.list_int) (J2 tptp.nat)) (let ((_let_1 (@ tptp.nth_int Xs2))) (let ((_let_2 (@ tptp.size_size_list_int Xs2))) (=> (@ (@ tptp.ord_less_nat I2) _let_2) (=> (@ (@ tptp.ord_less_nat J2) _let_2) (= (@ tptp.set_int2 (@ (@ (@ tptp.list_update_int (@ (@ (@ tptp.list_update_int Xs2) I2) (@ _let_1 J2))) J2) (@ _let_1 I2))) (@ tptp.set_int2 Xs2))))))) (forall ((A tptp.int) (B tptp.int) (Q2 tptp.int) (R3 tptp.int) (Q4 tptp.int) (R5 tptp.int)) (let ((_let_1 (@ (@ tptp.eucl_rel_int A) B))) (=> (@ _let_1 (@ (@ tptp.product_Pair_int_int Q2) R3)) (=> (@ _let_1 (@ (@ tptp.product_Pair_int_int Q4) R5)) (= Q2 Q4))))) (forall ((A tptp.int) (B tptp.int) (Q2 tptp.int) (R3 tptp.int) (Q4 tptp.int) (R5 tptp.int)) (let ((_let_1 (@ (@ tptp.eucl_rel_int A) B))) (=> (@ _let_1 (@ (@ tptp.product_Pair_int_int Q2) R3)) (=> (@ _let_1 (@ (@ tptp.product_Pair_int_int Q4) R5)) (= R3 R5))))) (forall ((Xs2 tptp.list_VEBT_VEBT) (I2 tptp.nat) (X tptp.vEBT_VEBT) (Ys tptp.list_VEBT_VEBT) (Y tptp.vEBT_VEBT)) (= (@ (@ tptp.zip_VE537291747668921783T_VEBT (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs2) I2) X)) (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Ys) I2) Y)) (@ (@ (@ tptp.list_u6961636818849549845T_VEBT (@ (@ tptp.zip_VE537291747668921783T_VEBT Xs2) Ys)) I2) (@ (@ tptp.produc537772716801021591T_VEBT X) Y)))) (forall ((Xs2 tptp.list_Code_integer) (I2 tptp.nat) (X tptp.code_integer) (Ys tptp.list_Code_integer) (Y tptp.code_integer)) (= (@ (@ tptp.zip_Co3543743374963494515nteger (@ (@ (@ tptp.list_u5447711078246177391nteger Xs2) I2) X)) (@ (@ (@ tptp.list_u5447711078246177391nteger Ys) I2) Y)) (@ (@ (@ tptp.list_u2254550707601501961nteger (@ (@ tptp.zip_Co3543743374963494515nteger Xs2) Ys)) I2) (@ (@ tptp.produc1086072967326762835nteger X) Y)))) (forall ((Xs2 tptp.list_P6011104703257516679at_nat) (I2 tptp.nat) (X tptp.product_prod_nat_nat) (Ys tptp.list_P6011104703257516679at_nat) (Y tptp.product_prod_nat_nat)) (= (@ (@ tptp.zip_Pr4664179122662387191at_nat (@ (@ (@ tptp.list_u6180841689913720943at_nat Xs2) I2) X)) (@ (@ (@ tptp.list_u6180841689913720943at_nat Ys) I2) Y)) (@ (@ (@ tptp.list_u5003261594476800725at_nat (@ (@ tptp.zip_Pr4664179122662387191at_nat Xs2) Ys)) I2) (@ (@ tptp.produc6161850002892822231at_nat X) Y)))) (forall ((Xs2 tptp.list_s1210847774152347623at_nat) (I2 tptp.nat) (X tptp.set_Pr1261947904930325089at_nat) (Ys tptp.list_s1210847774152347623at_nat) (Y tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.zip_se5600341670672612855at_nat (@ (@ (@ tptp.list_u8444657558853818831at_nat Xs2) I2) X)) (@ (@ (@ tptp.list_u8444657558853818831at_nat Ys) I2) Y)) (@ (@ (@ tptp.list_u4696772448584712917at_nat (@ (@ tptp.zip_se5600341670672612855at_nat Xs2) Ys)) I2) (@ (@ tptp.produc2922128104949294807at_nat X) Y)))) (forall ((Xs2 tptp.list_nat) (I2 tptp.nat) (X tptp.nat) (Ys tptp.list_nat) (Y tptp.nat)) (= (@ (@ tptp.zip_nat_nat (@ (@ (@ tptp.list_update_nat Xs2) I2) X)) (@ (@ (@ tptp.list_update_nat Ys) I2) Y)) (@ (@ (@ tptp.list_u6180841689913720943at_nat (@ (@ tptp.zip_nat_nat Xs2) Ys)) I2) (@ (@ tptp.product_Pair_nat_nat X) Y)))) (forall ((Xs2 tptp.list_int) (I2 tptp.nat) (X tptp.int) (Ys tptp.list_int) (Y tptp.int)) (= (@ (@ tptp.zip_int_int (@ (@ (@ tptp.list_update_int Xs2) I2) X)) (@ (@ (@ tptp.list_update_int Ys) I2) Y)) (@ (@ (@ tptp.list_u3002344382305578791nt_int (@ (@ tptp.zip_int_int Xs2) Ys)) I2) (@ (@ tptp.product_Pair_int_int X) Y)))) (forall ((X2 tptp.product_prod_nat_nat)) (= (@ tptp.the_Pr8591224930841456533at_nat (@ tptp.some_P7363390416028606310at_nat X2)) X2)) (forall ((X2 tptp.nat)) (= (@ tptp.the_nat (@ tptp.some_nat X2)) X2)) (forall ((X2 tptp.num)) (= (@ tptp.the_num (@ tptp.some_num X2)) X2)) (forall ((Option tptp.option_nat) (Option2 tptp.option_nat)) (let ((_let_1 (= Option2 tptp.none_nat))) (let ((_let_2 (= Option tptp.none_nat))) (=> (= _let_2 _let_1) (=> (=> (not _let_2) (=> (not _let_1) (= (@ tptp.the_nat Option) (@ tptp.the_nat Option2)))) (= Option Option2)))))) (forall ((Option tptp.option4927543243414619207at_nat) (Option2 tptp.option4927543243414619207at_nat)) (let ((_let_1 (= Option2 tptp.none_P5556105721700978146at_nat))) (let ((_let_2 (= Option tptp.none_P5556105721700978146at_nat))) (=> (= _let_2 _let_1) (=> (=> (not _let_2) (=> (not _let_1) (= (@ tptp.the_Pr8591224930841456533at_nat Option) (@ tptp.the_Pr8591224930841456533at_nat Option2)))) (= Option Option2)))))) (forall ((Option tptp.option_num) (Option2 tptp.option_num)) (let ((_let_1 (= Option2 tptp.none_num))) (let ((_let_2 (= Option tptp.none_num))) (=> (= _let_2 _let_1) (=> (=> (not _let_2) (=> (not _let_1) (= (@ tptp.the_num Option) (@ tptp.the_num Option2)))) (= Option Option2)))))) (forall ((K2 tptp.int)) (@ (@ (@ tptp.eucl_rel_int K2) tptp.zero_zero_int) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) K2))) (forall ((K2 tptp.int) (L tptp.int) (Q2 tptp.int) (R3 tptp.int)) (=> (@ (@ (@ tptp.eucl_rel_int K2) L) (@ (@ tptp.product_Pair_int_int Q2) R3)) (= (@ (@ tptp.divide_divide_int K2) L) Q2))) (forall ((X tptp.nat) (Xs2 tptp.list_nat) (I2 tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.cons_nat X))) (= (@ (@ (@ tptp.list_update_nat (@ _let_1 Xs2)) (@ tptp.suc I2)) Y) (@ _let_1 (@ (@ (@ tptp.list_update_nat Xs2) I2) Y))))) (forall ((X tptp.vEBT_VEBT) (Xs2 tptp.list_VEBT_VEBT) (I2 tptp.nat) (Y tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.cons_VEBT_VEBT X))) (= (@ (@ (@ tptp.list_u1324408373059187874T_VEBT (@ _let_1 Xs2)) (@ tptp.suc I2)) Y) (@ _let_1 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs2) I2) Y))))) (forall ((X tptp.nat) (Xs2 tptp.list_nat) (Y tptp.nat)) (= (@ (@ (@ tptp.list_update_nat (@ (@ tptp.cons_nat X) Xs2)) tptp.zero_zero_nat) Y) (@ (@ tptp.cons_nat Y) Xs2))) (forall ((X tptp.vEBT_VEBT) (Xs2 tptp.list_VEBT_VEBT) (Y tptp.vEBT_VEBT)) (= (@ (@ (@ tptp.list_u1324408373059187874T_VEBT (@ (@ tptp.cons_VEBT_VEBT X) Xs2)) tptp.zero_zero_nat) Y) (@ (@ tptp.cons_VEBT_VEBT Y) Xs2))) (forall ((A4 tptp.set_nat) (B5 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A4) (=> (@ tptp.finite_finite_nat B5) (= (= (@ tptp.nat_set_encode A4) (@ tptp.nat_set_encode B5)) (= A4 B5))))) (forall ((Option tptp.option4927543243414619207at_nat)) (=> (not (= Option tptp.none_P5556105721700978146at_nat)) (= Option (@ tptp.some_P7363390416028606310at_nat (@ tptp.the_Pr8591224930841456533at_nat Option))))) (forall ((Option tptp.option_nat)) (=> (not (= Option tptp.none_nat)) (= Option (@ tptp.some_nat (@ tptp.the_nat Option))))) (forall ((Option tptp.option_num)) (=> (not (= Option tptp.none_num)) (= Option (@ tptp.some_num (@ tptp.the_num Option))))) (forall ((L tptp.int) (K2 tptp.int) (Q2 tptp.int)) (=> (not (= L tptp.zero_zero_int)) (=> (= K2 (@ (@ tptp.times_times_int Q2) L)) (@ (@ (@ tptp.eucl_rel_int K2) L) (@ (@ tptp.product_Pair_int_int Q2) tptp.zero_zero_int))))) (forall ((N tptp.nat) (Xs2 tptp.list_complex) (X tptp.complex)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s3451745648224563538omplex Xs2)) (@ (@ tptp.member_complex X) (@ tptp.set_complex2 (@ (@ (@ tptp.list_update_complex Xs2) N) X))))) (forall ((N tptp.nat) (Xs2 tptp.list_real) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_real Xs2)) (@ (@ tptp.member_real X) (@ tptp.set_real2 (@ (@ (@ tptp.list_update_real Xs2) N) X))))) (forall ((N tptp.nat) (Xs2 tptp.list_set_nat) (X tptp.set_nat)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s3254054031482475050et_nat Xs2)) (@ (@ tptp.member_set_nat X) (@ tptp.set_set_nat2 (@ (@ (@ tptp.list_update_set_nat Xs2) N) X))))) (forall ((N tptp.nat) (Xs2 tptp.list_VEBT_VEBT) (X tptp.vEBT_VEBT)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs2) N) X))))) (forall ((N tptp.nat) (Xs2 tptp.list_o) (X Bool)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_o Xs2)) (@ (@ tptp.member_o X) (@ tptp.set_o2 (@ (@ (@ tptp.list_update_o Xs2) N) X))))) (forall ((N tptp.nat) (Xs2 tptp.list_nat) (X tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_nat Xs2)) (@ (@ tptp.member_nat X) (@ tptp.set_nat2 (@ (@ (@ tptp.list_update_nat Xs2) N) X))))) (forall ((N tptp.nat) (Xs2 tptp.list_int) (X tptp.int)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_int Xs2)) (@ (@ tptp.member_int X) (@ tptp.set_int2 (@ (@ (@ tptp.list_update_int Xs2) N) X))))) (forall ((I2 tptp.nat) (Xs2 tptp.list_VEBT_VEBT) (X tptp.vEBT_VEBT)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (= (= (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs2) I2) X) Xs2) (= (@ (@ tptp.nth_VEBT_VEBT Xs2) I2) X)))) (forall ((I2 tptp.nat) (Xs2 tptp.list_o) (X Bool)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_o Xs2)) (= (= (@ (@ (@ tptp.list_update_o Xs2) I2) X) Xs2) (= (@ (@ tptp.nth_o Xs2) I2) X)))) (forall ((I2 tptp.nat) (Xs2 tptp.list_nat) (X tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_nat Xs2)) (= (= (@ (@ (@ tptp.list_update_nat Xs2) I2) X) Xs2) (= (@ (@ tptp.nth_nat Xs2) I2) X)))) (forall ((I2 tptp.nat) (Xs2 tptp.list_int) (X tptp.int)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_int Xs2)) (= (= (@ (@ (@ tptp.list_update_int Xs2) I2) X) Xs2) (= (@ (@ tptp.nth_int Xs2) I2) X)))) (forall ((I2 tptp.nat) (Xs2 tptp.list_VEBT_VEBT) (J2 tptp.nat) (X tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ tptp.nth_VEBT_VEBT (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs2) I2) X)) J2))) (let ((_let_2 (= I2 J2))) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (and (=> _let_2 (= _let_1 X)) (=> (not _let_2) (= _let_1 (@ (@ tptp.nth_VEBT_VEBT Xs2) J2)))))))) (forall ((I2 tptp.nat) (Xs2 tptp.list_o) (X Bool) (J2 tptp.nat)) (let ((_let_1 (= I2 J2))) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_o Xs2)) (= (@ (@ tptp.nth_o (@ (@ (@ tptp.list_update_o Xs2) I2) X)) J2) (and (=> _let_1 X) (=> (not _let_1) (@ (@ tptp.nth_o Xs2) J2))))))) (forall ((I2 tptp.nat) (Xs2 tptp.list_nat) (J2 tptp.nat) (X tptp.nat)) (let ((_let_1 (@ (@ tptp.nth_nat (@ (@ (@ tptp.list_update_nat Xs2) I2) X)) J2))) (let ((_let_2 (= I2 J2))) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_nat Xs2)) (and (=> _let_2 (= _let_1 X)) (=> (not _let_2) (= _let_1 (@ (@ tptp.nth_nat Xs2) J2)))))))) (forall ((I2 tptp.nat) (Xs2 tptp.list_int) (J2 tptp.nat) (X tptp.int)) (let ((_let_1 (@ (@ tptp.nth_int (@ (@ (@ tptp.list_update_int Xs2) I2) X)) J2))) (let ((_let_2 (= I2 J2))) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_int Xs2)) (and (=> _let_2 (= _let_1 X)) (=> (not _let_2) (= _let_1 (@ (@ tptp.nth_int Xs2) J2)))))))) (forall ((A4 tptp.set_nat)) (=> (not (@ tptp.finite_finite_nat A4)) (= (@ tptp.nat_set_encode A4) tptp.zero_zero_nat))) (forall ((K2 tptp.int) (L tptp.int) (Q2 tptp.int) (R3 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int L))) (let ((_let_2 (@ _let_1 tptp.zero_zero_int))) (let ((_let_3 (@ (@ tptp.ord_less_int tptp.zero_zero_int) L))) (= (@ (@ (@ tptp.eucl_rel_int K2) L) (@ (@ tptp.product_Pair_int_int Q2) R3)) (and (= K2 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int L) Q2)) R3)) (=> _let_3 (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) R3) (@ (@ tptp.ord_less_int R3) L))) (=> (not _let_3) (and (=> _let_2 (and (@ _let_1 R3) (@ (@ tptp.ord_less_eq_int R3) tptp.zero_zero_int))) (=> (not _let_2) (= Q2 tptp.zero_zero_int)))))))))) (forall ((B tptp.int) (A tptp.int) (Q2 tptp.int) (R3 tptp.int)) (let ((_let_1 (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.plus_plus_int tptp.one_one_int))) (let ((_let_3 (@ tptp.product_Pair_int_int Q2))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B) (=> (@ (@ (@ tptp.eucl_rel_int A) B) (@ _let_3 R3)) (@ (@ (@ tptp.eucl_rel_int (@ _let_2 (@ _let_1 A))) (@ _let_1 B)) (@ _let_3 (@ _let_2 (@ _let_1 R3)))))))))) (forall ((Mi tptp.nat) (Deg tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (X tptp.nat) (Ma tptp.nat) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat Deg) _let_1))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high Mi) _let_2))) (let ((_let_4 (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_3))) (=> (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)) (=> (@ (@ tptp.ord_less_nat X) Mi) (=> (@ (@ tptp.ord_less_eq_nat _let_1) Deg) (=> (not (= X Ma)) (= (@ (@ tptp.vEBT_vebt_insert (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList2) Summary)) X) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat X) (@ (@ tptp.ord_max_nat Mi) Ma)))) Deg) (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList2) _let_3) (@ (@ tptp.vEBT_vebt_insert _let_4) (@ (@ tptp.vEBT_VEBT_low Mi) _let_2)))) (@ (@ (@ tptp.if_VEBT_VEBT (@ tptp.vEBT_VEBT_minNull _let_4)) (@ (@ tptp.vEBT_vebt_insert Summary) _let_3)) Summary)))))))))))) (forall ((X tptp.nat) (Deg tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Mi tptp.nat) (Ma tptp.nat) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat Deg) _let_1))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high X) _let_2))) (let ((_let_4 (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_3))) (let ((_let_5 (@ tptp.product_Pair_nat_nat Mi))) (=> (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)) (=> (@ (@ tptp.ord_less_nat Mi) X) (=> (@ (@ tptp.ord_less_eq_nat _let_1) Deg) (=> (not (= X Ma)) (= (@ (@ tptp.vEBT_vebt_insert (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_5 Ma))) Deg) TreeList2) Summary)) X) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_5 (@ (@ tptp.ord_max_nat X) Ma)))) Deg) (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList2) _let_3) (@ (@ tptp.vEBT_vebt_insert _let_4) (@ (@ tptp.vEBT_VEBT_low X) _let_2)))) (@ (@ (@ tptp.if_VEBT_VEBT (@ tptp.vEBT_VEBT_minNull _let_4)) (@ (@ tptp.vEBT_vebt_insert Summary) _let_3)) Summary))))))))))))) (forall ((Deg tptp.nat) (X tptp.nat) (Ma tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Mi tptp.nat) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat Deg) _let_1))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high X) _let_2))) (let ((_let_4 (@ (@ tptp.vEBT_vebt_pred Summary) _let_3))) (let ((_let_5 (@ tptp.nth_VEBT_VEBT TreeList2))) (let ((_let_6 (@ tptp.vEBT_VEBT_mul (@ tptp.some_nat (@ (@ tptp.power_power_nat _let_1) _let_2))))) (let ((_let_7 (@ (@ tptp.vEBT_VEBT_low X) _let_2))) (let ((_let_8 (@ _let_5 _let_3))) (let ((_let_9 (@ tptp.vEBT_vebt_mint _let_8))) (=> (@ (@ tptp.ord_less_eq_nat _let_1) Deg) (=> (@ (@ tptp.ord_less_eq_nat X) Ma) (=> (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)) (= (@ (@ tptp.vEBT_vebt_pred (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList2) Summary)) X) (@ (@ (@ tptp.if_option_nat (and (not (= _let_9 tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_greater (@ tptp.some_nat _let_7)) _let_9))) (@ (@ tptp.vEBT_VEBT_add (@ _let_6 (@ tptp.some_nat _let_3))) (@ (@ tptp.vEBT_vebt_pred _let_8) _let_7))) (@ (@ (@ tptp.if_option_nat (= _let_4 tptp.none_nat)) (@ (@ (@ tptp.if_option_nat (@ (@ tptp.ord_less_nat Mi) X)) (@ tptp.some_nat Mi)) tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_add (@ _let_6 _let_4)) (@ tptp.vEBT_vebt_maxt (@ _let_5 (@ tptp.the_nat _let_4)))))))))))))))))))) (forall ((Deg tptp.nat) (X tptp.nat) (Ma tptp.nat) (Mi tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat Deg) _let_1))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high X) _let_2))) (let ((_let_4 (@ (@ tptp.vEBT_vebt_pred Summary) _let_3))) (let ((_let_5 (@ tptp.nth_VEBT_VEBT TreeList2))) (let ((_let_6 (@ tptp.vEBT_VEBT_mul (@ tptp.some_nat (@ (@ tptp.power_power_nat _let_1) _let_2))))) (let ((_let_7 (@ (@ tptp.vEBT_VEBT_low X) _let_2))) (let ((_let_8 (@ _let_5 _let_3))) (let ((_let_9 (@ tptp.vEBT_vebt_mint _let_8))) (=> (@ (@ tptp.ord_less_eq_nat _let_1) Deg) (=> (@ (@ tptp.ord_less_eq_nat X) Ma) (= (@ (@ tptp.vEBT_vebt_pred (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList2) Summary)) X) (@ (@ (@ tptp.if_option_nat (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList2))) (@ (@ (@ tptp.if_option_nat (and (not (= _let_9 tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_greater (@ tptp.some_nat _let_7)) _let_9))) (@ (@ tptp.vEBT_VEBT_add (@ _let_6 (@ tptp.some_nat _let_3))) (@ (@ tptp.vEBT_vebt_pred _let_8) _let_7))) (@ (@ (@ tptp.if_option_nat (= _let_4 tptp.none_nat)) (@ (@ (@ tptp.if_option_nat (@ (@ tptp.ord_less_nat Mi) X)) (@ tptp.some_nat Mi)) tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_add (@ _let_6 _let_4)) (@ tptp.vEBT_vebt_maxt (@ _let_5 (@ tptp.the_nat _let_4))))))) tptp.none_nat)))))))))))))) (forall ((Deg tptp.nat) (Mi tptp.nat) (X tptp.nat) (Ma tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat Deg) _let_1))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high X) _let_2))) (let ((_let_4 (@ (@ tptp.vEBT_vebt_succ Summary) _let_3))) (let ((_let_5 (@ tptp.nth_VEBT_VEBT TreeList2))) (let ((_let_6 (@ tptp.vEBT_VEBT_mul (@ tptp.some_nat (@ (@ tptp.power_power_nat _let_1) _let_2))))) (let ((_let_7 (@ (@ tptp.vEBT_VEBT_low X) _let_2))) (let ((_let_8 (@ _let_5 _let_3))) (let ((_let_9 (@ tptp.vEBT_vebt_maxt _let_8))) (=> (@ (@ tptp.ord_less_eq_nat _let_1) Deg) (=> (@ (@ tptp.ord_less_eq_nat Mi) X) (= (@ (@ tptp.vEBT_vebt_succ (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList2) Summary)) X) (@ (@ (@ tptp.if_option_nat (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList2))) (@ (@ (@ tptp.if_option_nat (and (not (= _let_9 tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_less (@ tptp.some_nat _let_7)) _let_9))) (@ (@ tptp.vEBT_VEBT_add (@ _let_6 (@ tptp.some_nat _let_3))) (@ (@ tptp.vEBT_vebt_succ _let_8) _let_7))) (@ (@ (@ tptp.if_option_nat (= _let_4 tptp.none_nat)) tptp.none_nat) (@ (@ tptp.vEBT_VEBT_add (@ _let_6 _let_4)) (@ tptp.vEBT_vebt_mint (@ _let_5 (@ tptp.the_nat _let_4))))))) tptp.none_nat)))))))))))))) (forall ((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)))))))))))))))))))) (forall ((Mi tptp.nat) (X tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList2) Summary))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_3 (@ (@ tptp.divide_divide_nat Deg) _let_2))) (let ((_let_4 (@ tptp.the_nat (@ tptp.vEBT_vebt_mint Summary)))) (let ((_let_5 (@ tptp.nth_VEBT_VEBT TreeList2))) (let ((_let_6 (@ (@ tptp.power_power_nat _let_2) _let_3))) (let ((_let_7 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_4) _let_6)) (@ tptp.the_nat (@ tptp.vEBT_vebt_mint (@ _let_5 _let_4)))))) (let ((_let_8 (= X Mi))) (let ((_let_9 (@ tptp.if_nat _let_8))) (let ((_let_10 (@ (@ _let_9 _let_7) X))) (let ((_let_11 (@ (@ tptp.vEBT_VEBT_high _let_10) _let_3))) (let ((_let_12 (@ (@ tptp.vEBT_vebt_delete (@ _let_5 _let_11)) (@ (@ tptp.vEBT_VEBT_low _let_10) _let_3)))) (let ((_let_13 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList2) _let_11) _let_12))) (let ((_let_14 (@ tptp.nth_VEBT_VEBT _let_13))) (let ((_let_15 (@ tptp.if_nat (and (=> _let_8 (= _let_7 Ma)) (=> (not _let_8) (= X Ma)))))) (let ((_let_16 (@ (@ _let_9 _let_10) Mi))) (let ((_let_17 (@ tptp.product_Pair_nat_nat _let_16))) (let ((_let_18 (@ (@ tptp.vEBT_vebt_delete Summary) _let_11))) (let ((_let_19 (@ tptp.vEBT_vebt_maxt _let_18))) (let ((_let_20 (@ tptp.the_nat _let_19))) (=> (and (@ (@ tptp.ord_less_eq_nat Mi) X) (@ (@ tptp.ord_less_eq_nat X) Ma)) (=> (not (= Mi Ma)) (=> (@ (@ tptp.ord_less_eq_nat _let_2) Deg) (= (@ (@ tptp.vEBT_vebt_delete _let_1) X) (@ (@ (@ tptp.if_VEBT_VEBT (@ (@ tptp.ord_less_nat _let_11) (@ tptp.size_s6755466524823107622T_VEBT TreeList2))) (@ (@ (@ tptp.if_VEBT_VEBT (@ tptp.vEBT_VEBT_minNull _let_12)) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_17 (@ (@ _let_15 (@ (@ (@ tptp.if_nat (= _let_19 tptp.none_nat)) _let_16) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_6) _let_20)) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ _let_14 _let_20)))))) Ma)))) Deg) _let_13) _let_18)) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_17 (@ (@ _let_15 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_11) _let_6)) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ _let_14 _let_11))))) Ma)))) Deg) _let_13) Summary))) _let_1)))))))))))))))))))))))))) (forall ((X tptp.nat) (Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (Xn tptp.nat) (H tptp.nat) (Summary tptp.vEBT_VEBT) (TreeList2 tptp.list_VEBT_VEBT) (L tptp.nat)) (let ((_let_1 (@ tptp.nth_VEBT_VEBT TreeList2))) (let ((_let_2 (@ (@ tptp.vEBT_vebt_delete (@ _let_1 H)) L))) (let ((_let_3 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList2) H) _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) H))) (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 H) (=> (= 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) L) (=> (@ (@ 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 H) _let_7)) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ _let_4 H))))) Ma)))) Deg) _let_3) Summary))))))))))))))))))))))))) _let_279 (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 ((Y4 tptp.nat)) (and (@ (@ tptp.vEBT_vebt_member T) Y4) (@ (@ tptp.ord_less_nat Y4) X)))) tptp.bot_bot_set_nat)))) (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 ((Y4 tptp.nat)) (and (@ (@ tptp.vEBT_vebt_member T) Y4) (@ (@ tptp.ord_less_nat X) Y4)))) tptp.bot_bot_set_nat)))) (forall ((B tptp.rat) (C2 tptp.rat) (A tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.ord_max_rat B) C2)) A) (and (@ (@ tptp.ord_less_eq_rat B) A) (@ (@ tptp.ord_less_eq_rat C2) A)))) (forall ((B tptp.num) (C2 tptp.num) (A tptp.num)) (= (@ (@ tptp.ord_less_eq_num (@ (@ tptp.ord_max_num B) C2)) A) (and (@ (@ tptp.ord_less_eq_num B) A) (@ (@ tptp.ord_less_eq_num C2) A)))) (forall ((B tptp.nat) (C2 tptp.nat) (A tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.ord_max_nat B) C2)) A) (and (@ (@ tptp.ord_less_eq_nat B) A) (@ (@ tptp.ord_less_eq_nat C2) A)))) (forall ((B tptp.int) (C2 tptp.int) (A tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.ord_max_int B) C2)) A) (and (@ (@ tptp.ord_less_eq_int B) A) (@ (@ tptp.ord_less_eq_int C2) A)))) (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (= (@ (@ tptp.ord_max_rat A) B) B))) (forall ((A tptp.num) (B tptp.num)) (=> (@ (@ tptp.ord_less_eq_num A) B) (= (@ (@ tptp.ord_max_num A) B) B))) (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= (@ (@ tptp.ord_max_nat A) B) B))) (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (= (@ (@ tptp.ord_max_int A) B) B))) (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat B) A) (= (@ (@ tptp.ord_max_rat A) B) A))) (forall ((B tptp.num) (A tptp.num)) (=> (@ (@ tptp.ord_less_eq_num B) A) (= (@ (@ tptp.ord_max_num A) B) A))) (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B) A) (= (@ (@ tptp.ord_max_nat A) B) A))) (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B) A) (= (@ (@ tptp.ord_max_int A) B) A))) (forall ((X tptp.set_nat)) (= (@ (@ tptp.ord_max_set_nat tptp.bot_bot_set_nat) X) X)) (forall ((X tptp.set_int)) (= (@ (@ tptp.ord_max_set_int tptp.bot_bot_set_int) X) X)) (forall ((X tptp.set_real)) (= (@ (@ tptp.ord_max_set_real tptp.bot_bot_set_real) X) X)) (forall ((X tptp.nat)) (= (@ (@ tptp.ord_max_nat tptp.bot_bot_nat) X) X)) (forall ((X tptp.set_nat)) (= (@ (@ tptp.ord_max_set_nat X) tptp.bot_bot_set_nat) X)) (forall ((X tptp.set_int)) (= (@ (@ tptp.ord_max_set_int X) tptp.bot_bot_set_int) X)) (forall ((X tptp.set_real)) (= (@ (@ tptp.ord_max_set_real X) tptp.bot_bot_set_real) X)) (forall ((X tptp.nat)) (= (@ (@ tptp.ord_max_nat X) tptp.bot_bot_nat) X)) (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_max_nat (@ tptp.suc M2)) (@ tptp.suc N)) (@ tptp.suc (@ (@ tptp.ord_max_nat M2) N)))) (forall ((A tptp.nat) (B tptp.nat)) (= (= (@ (@ tptp.ord_max_nat A) B) tptp.zero_zero_nat) (and (= A tptp.zero_zero_nat) (= B tptp.zero_zero_nat)))) (forall ((A tptp.nat)) (= (@ (@ tptp.ord_max_nat tptp.zero_zero_nat) A) A)) (forall ((A tptp.nat) (B tptp.nat)) (= (= tptp.zero_zero_nat (@ (@ tptp.ord_max_nat A) B)) (and (= A tptp.zero_zero_nat) (= B tptp.zero_zero_nat)))) (forall ((A tptp.nat)) (= (@ (@ tptp.ord_max_nat A) tptp.zero_zero_nat) A)) (forall ((N tptp.nat)) (= (@ (@ tptp.ord_max_nat tptp.zero_zero_nat) N) N)) (forall ((N tptp.nat)) (= (@ (@ tptp.ord_max_nat N) tptp.zero_zero_nat) N)) (forall ((K2 tptp.nat)) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_nat N4) K2))))) (forall ((U tptp.num) (V2 tptp.num)) (let ((_let_1 (@ tptp.numera1916890842035813515d_enat U))) (let ((_let_2 (@ tptp.numera1916890842035813515d_enat V2))) (let ((_let_3 (@ (@ tptp.ord_ma741700101516333627d_enat _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_le2932123472753598470d_enat _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))) (forall ((U tptp.num) (V2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real U))) (let ((_let_2 (@ tptp.numeral_numeral_real V2))) (let ((_let_3 (@ (@ tptp.ord_max_real _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_eq_real _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))) (forall ((U tptp.num) (V2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat U))) (let ((_let_2 (@ tptp.numeral_numeral_rat V2))) (let ((_let_3 (@ (@ tptp.ord_max_rat _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_eq_rat _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))) (forall ((U tptp.num) (V2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat U))) (let ((_let_2 (@ tptp.numeral_numeral_nat V2))) (let ((_let_3 (@ (@ tptp.ord_max_nat _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_eq_nat _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))) (forall ((U tptp.num) (V2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int U))) (let ((_let_2 (@ tptp.numeral_numeral_int V2))) (let ((_let_3 (@ (@ tptp.ord_max_int _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_eq_int _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))) (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat X))) (= (@ (@ tptp.ord_max_rat tptp.zero_zero_rat) _let_1) _let_1))) (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numera1916890842035813515d_enat X))) (= (@ (@ tptp.ord_ma741700101516333627d_enat tptp.zero_z5237406670263579293d_enat) _let_1) _let_1))) (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real X))) (= (@ (@ tptp.ord_max_real tptp.zero_zero_real) _let_1) _let_1))) (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat X))) (= (@ (@ tptp.ord_max_nat tptp.zero_zero_nat) _let_1) _let_1))) (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int X))) (= (@ (@ tptp.ord_max_int tptp.zero_zero_int) _let_1) _let_1))) (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat X))) (= (@ (@ tptp.ord_max_rat _let_1) tptp.zero_zero_rat) _let_1))) (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numera1916890842035813515d_enat X))) (= (@ (@ tptp.ord_ma741700101516333627d_enat _let_1) tptp.zero_z5237406670263579293d_enat) _let_1))) (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real X))) (= (@ (@ tptp.ord_max_real _let_1) tptp.zero_zero_real) _let_1))) (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat X))) (= (@ (@ tptp.ord_max_nat _let_1) tptp.zero_zero_nat) _let_1))) (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int X))) (= (@ (@ tptp.ord_max_int _let_1) tptp.zero_zero_int) _let_1))) (= (@ (@ tptp.ord_max_Code_integer tptp.one_one_Code_integer) tptp.zero_z3403309356797280102nteger) tptp.one_one_Code_integer) (= (@ (@ tptp.ord_max_real tptp.one_one_real) tptp.zero_zero_real) tptp.one_one_real) (= (@ (@ tptp.ord_max_rat tptp.one_one_rat) tptp.zero_zero_rat) tptp.one_one_rat) (= (@ (@ tptp.ord_max_nat tptp.one_one_nat) tptp.zero_zero_nat) tptp.one_one_nat) (= (@ (@ tptp.ord_max_int tptp.one_one_int) tptp.zero_zero_int) tptp.one_one_int) (= (@ (@ tptp.ord_max_Code_integer tptp.zero_z3403309356797280102nteger) tptp.one_one_Code_integer) tptp.one_one_Code_integer) (= (@ (@ tptp.ord_max_real tptp.zero_zero_real) tptp.one_one_real) tptp.one_one_real) (= (@ (@ tptp.ord_max_rat tptp.zero_zero_rat) tptp.one_one_rat) tptp.one_one_rat) (= (@ (@ tptp.ord_max_nat tptp.zero_zero_nat) tptp.one_one_nat) tptp.one_one_nat) (= (@ (@ tptp.ord_max_int tptp.zero_zero_int) tptp.one_one_int) tptp.one_one_int) (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger X))) (= (@ (@ tptp.ord_max_Code_integer tptp.one_one_Code_integer) _let_1) _let_1))) (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numera1916890842035813515d_enat X))) (= (@ (@ tptp.ord_ma741700101516333627d_enat tptp.one_on7984719198319812577d_enat) _let_1) _let_1))) (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real X))) (= (@ (@ tptp.ord_max_real tptp.one_one_real) _let_1) _let_1))) (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat X))) (= (@ (@ tptp.ord_max_nat tptp.one_one_nat) _let_1) _let_1))) (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int X))) (= (@ (@ tptp.ord_max_int tptp.one_one_int) _let_1) _let_1))) (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger X))) (= (@ (@ tptp.ord_max_Code_integer _let_1) tptp.one_one_Code_integer) _let_1))) (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numera1916890842035813515d_enat X))) (= (@ (@ tptp.ord_ma741700101516333627d_enat _let_1) tptp.one_on7984719198319812577d_enat) _let_1))) (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real X))) (= (@ (@ tptp.ord_max_real _let_1) tptp.one_one_real) _let_1))) (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat X))) (= (@ (@ tptp.ord_max_nat _let_1) tptp.one_one_nat) _let_1))) (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int X))) (= (@ (@ tptp.ord_max_int _let_1) tptp.one_one_int) _let_1))) (forall ((N tptp.nat)) (= (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((I tptp.nat)) (@ (@ tptp.ord_less_eq_nat I) N)))) (@ tptp.suc N))) (forall ((Mi tptp.nat) (X tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (H tptp.nat) (L tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ tptp.vEBT_vebt_delete (@ (@ tptp.nth_VEBT_VEBT TreeList2) H)) L))) (let ((_let_2 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList2) H) _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) H))) (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 H) (=> (= (@ (@ tptp.vEBT_VEBT_low X) _let_5) L) (=> (@ (@ 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 H) _let_6)) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ _let_3 H))))) Ma)))) Deg) _let_2) Summary)))))))))))))))))))))) (forall ((Mi tptp.nat) (X tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (H tptp.nat) (L 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 H) (=> (= (@ (@ tptp.vEBT_VEBT_low X) _let_4) L) (=> (= Newnode (@ (@ tptp.vEBT_vebt_delete (@ (@ tptp.nth_VEBT_VEBT TreeList2) H)) L)) (=> (@ tptp.vEBT_VEBT_minNull Newnode) (=> (= Sn (@ (@ tptp.vEBT_vebt_delete Summary) H)) (=> (= Newlist (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList2) H) Newnode)) (=> (@ (@ tptp.ord_less_nat _let_6) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)) (= (@ (@ tptp.vEBT_vebt_delete (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_5 Ma))) Deg) TreeList2) Summary)) X) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_5 (@ (@ (@ tptp.if_nat (= X Ma)) (@ (@ (@ tptp.if_nat (= _let_1 tptp.none_nat)) Mi) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.power_power_nat _let_3) _let_4)) _let_2)) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ (@ tptp.nth_VEBT_VEBT Newlist) _let_2)))))) Ma)))) Deg) Newlist) Sn))))))))))))))))))) (forall ((Mi tptp.nat) (X tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (H tptp.nat) (L 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) H))) (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 H) (=> (= (@ (@ tptp.vEBT_VEBT_low X) _let_3) L) (=> (= Newnode (@ (@ tptp.vEBT_vebt_delete (@ (@ tptp.nth_VEBT_VEBT TreeList2) H)) L)) (=> (= Newlist (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList2) H) 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 H) _let_4)) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ _let_1 H))))) Ma)))) Deg) Newlist) Summary))))))))))))))))))))))))) (forall ((X tptp.nat) (Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList2) Summary))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_3 (@ (@ tptp.divide_divide_nat Deg) _let_2))) (let ((_let_4 (@ tptp.the_nat (@ tptp.vEBT_vebt_mint Summary)))) (let ((_let_5 (@ tptp.nth_VEBT_VEBT TreeList2))) (let ((_let_6 (@ (@ tptp.power_power_nat _let_2) _let_3))) (let ((_let_7 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_4) _let_6)) (@ tptp.the_nat (@ tptp.vEBT_vebt_mint (@ _let_5 _let_4)))))) (let ((_let_8 (@ (@ tptp.vEBT_VEBT_high _let_7) _let_3))) (let ((_let_9 (@ (@ tptp.vEBT_vebt_delete (@ _let_5 _let_8)) (@ (@ tptp.vEBT_VEBT_low _let_7) _let_3)))) (let ((_let_10 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList2) _let_8) _let_9))) (let ((_let_11 (@ tptp.nth_VEBT_VEBT _let_10))) (let ((_let_12 (@ tptp.if_nat (= _let_7 Ma)))) (let ((_let_13 (@ tptp.product_Pair_nat_nat _let_7))) (let ((_let_14 (@ (@ tptp.vEBT_vebt_delete Summary) _let_8))) (let ((_let_15 (@ tptp.vEBT_vebt_maxt _let_14))) (let ((_let_16 (@ tptp.the_nat _let_15))) (=> (and (= X Mi) (@ (@ tptp.ord_less_nat X) Ma)) (=> (not (= Mi Ma)) (=> (@ (@ tptp.ord_less_eq_nat _let_2) Deg) (= (@ (@ tptp.vEBT_vebt_delete _let_1) X) (@ (@ (@ tptp.if_VEBT_VEBT (@ (@ tptp.ord_less_nat _let_8) (@ tptp.size_s6755466524823107622T_VEBT TreeList2))) (@ (@ (@ tptp.if_VEBT_VEBT (@ tptp.vEBT_VEBT_minNull _let_9)) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_13 (@ (@ _let_12 (@ (@ (@ tptp.if_nat (= _let_15 tptp.none_nat)) _let_7) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_6) _let_16)) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ _let_11 _let_16)))))) Ma)))) Deg) _let_10) _let_14)) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_13 (@ (@ _let_12 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_8) _let_6)) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ _let_11 _let_8))))) Ma)))) Deg) _let_10) Summary))) _let_1)))))))))))))))))))))) (forall ((X tptp.nat) (Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (Xn tptp.nat) (H tptp.nat) (Summary tptp.vEBT_VEBT) (TreeList2 tptp.list_VEBT_VEBT) (L 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 H) (=> (= 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) L) (=> (@ (@ tptp.ord_less_nat _let_7) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)) (=> (= Newnode (@ (@ tptp.vEBT_vebt_delete (@ _let_6 H)) L)) (=> (= Newlist (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList2) H) Newnode)) (=> (@ tptp.vEBT_VEBT_minNull Newnode) (=> (= Sn (@ (@ tptp.vEBT_vebt_delete Summary) H)) (= (@ (@ tptp.vEBT_vebt_delete (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList2) Summary)) X) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Xn) (@ (@ (@ tptp.if_nat (= Xn Ma)) (@ (@ (@ tptp.if_nat (= _let_1 tptp.none_nat)) Xn) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_5) _let_2)) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ (@ tptp.nth_VEBT_VEBT Newlist) _let_2)))))) Ma)))) Deg) Newlist) Sn)))))))))))))))))))))) (forall ((X tptp.nat) (Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (Xn tptp.nat) (H tptp.nat) (Summary tptp.vEBT_VEBT) (TreeList2 tptp.list_VEBT_VEBT) (L 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) H))) (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 H) (=> (= 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) L) (=> (@ (@ tptp.ord_less_nat _let_13) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)) (=> (= Newnode (@ (@ tptp.vEBT_vebt_delete (@ _let_12 H)) L)) (=> (= Newlist (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList2) H) 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 H) _let_4)) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ _let_1 H))))) Ma)))) Deg) Newlist) Summary)))))))))))))))))))))))))))) (forall ((X tptp.nat) (Y tptp.nat)) (= (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.ord_max_nat X) Y)) (@ (@ tptp.ord_max_real (@ tptp.semiri5074537144036343181t_real X)) (@ tptp.semiri5074537144036343181t_real Y)))) (forall ((X tptp.nat) (Y tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.ord_max_nat X) Y)) (@ (@ tptp.ord_max_int (@ tptp.semiri1314217659103216013at_int X)) (@ tptp.semiri1314217659103216013at_int Y)))) (forall ((X tptp.nat) (Y tptp.nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.ord_max_nat X) Y)) (@ (@ tptp.ord_max_nat (@ tptp.semiri1316708129612266289at_nat X)) (@ tptp.semiri1316708129612266289at_nat Y)))) _let_278 _let_277 _let_276 _let_275 _let_274 _let_273 (= (lambda ((H2 tptp.complex)) tptp.zero_zero_complex) (@ tptp.times_times_complex tptp.zero_zero_complex)) (= (lambda ((H2 tptp.real)) tptp.zero_zero_real) (@ tptp.times_times_real tptp.zero_zero_real)) (= (lambda ((H2 tptp.rat)) tptp.zero_zero_rat) (@ tptp.times_times_rat tptp.zero_zero_rat)) (= (lambda ((H2 tptp.nat)) tptp.zero_zero_nat) (@ tptp.times_times_nat tptp.zero_zero_nat)) (= (lambda ((H2 tptp.int)) tptp.zero_zero_int) (@ tptp.times_times_int tptp.zero_zero_int)) (= (lambda ((X4 tptp.code_integer)) X4) (@ tptp.times_3573771949741848930nteger tptp.one_one_Code_integer)) (= (lambda ((X4 tptp.complex)) X4) (@ tptp.times_times_complex tptp.one_one_complex)) (= (lambda ((X4 tptp.real)) X4) (@ tptp.times_times_real tptp.one_one_real)) (= (lambda ((X4 tptp.rat)) X4) (@ tptp.times_times_rat tptp.one_one_rat)) (= (lambda ((X4 tptp.nat)) X4) (@ tptp.times_times_nat tptp.one_one_nat)) (= (lambda ((X4 tptp.int)) X4) (@ tptp.times_times_int tptp.one_one_int)) (forall ((P2 (-> tptp.nat Bool)) (I2 tptp.nat)) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((K3 tptp.nat)) (and (@ P2 K3) (@ (@ tptp.ord_less_nat K3) I2)))))) (forall ((F2 (-> tptp.nat tptp.nat)) (U tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat N3) (@ F2 N3))) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ F2 N4)) U)))))) (forall ((C2 tptp.rat) (A tptp.rat) (D tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat C2) A) (=> (@ (@ tptp.ord_less_eq_rat D) B) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.ord_max_rat C2) D)) (@ (@ tptp.ord_max_rat A) B))))) (forall ((C2 tptp.num) (A tptp.num) (D tptp.num) (B tptp.num)) (=> (@ (@ tptp.ord_less_eq_num C2) A) (=> (@ (@ tptp.ord_less_eq_num D) B) (@ (@ tptp.ord_less_eq_num (@ (@ tptp.ord_max_num C2) D)) (@ (@ tptp.ord_max_num A) B))))) (forall ((C2 tptp.nat) (A tptp.nat) (D tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat C2) A) (=> (@ (@ tptp.ord_less_eq_nat D) B) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.ord_max_nat C2) D)) (@ (@ tptp.ord_max_nat A) B))))) (forall ((C2 tptp.int) (A tptp.int) (D tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int C2) A) (=> (@ (@ tptp.ord_less_eq_int D) B) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.ord_max_int C2) D)) (@ (@ tptp.ord_max_int A) B))))) (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat B) A) (= A (@ (@ tptp.ord_max_rat A) B)))) (forall ((B tptp.num) (A tptp.num)) (=> (@ (@ tptp.ord_less_eq_num B) A) (= A (@ (@ tptp.ord_max_num A) B)))) (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B) A) (= A (@ (@ tptp.ord_max_nat A) B)))) (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B) A) (= A (@ (@ tptp.ord_max_int A) B)))) (forall ((A tptp.rat) (B tptp.rat)) (=> (= A (@ (@ tptp.ord_max_rat A) B)) (@ (@ tptp.ord_less_eq_rat B) A))) (forall ((A tptp.num) (B tptp.num)) (=> (= A (@ (@ tptp.ord_max_num A) B)) (@ (@ tptp.ord_less_eq_num B) A))) (forall ((A tptp.nat) (B tptp.nat)) (=> (= A (@ (@ tptp.ord_max_nat A) B)) (@ (@ tptp.ord_less_eq_nat B) A))) (forall ((A tptp.int) (B tptp.int)) (=> (= A (@ (@ tptp.ord_max_int A) B)) (@ (@ tptp.ord_less_eq_int B) A))) (forall ((B tptp.rat) (C2 tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.ord_max_rat B) C2)) A) (not (=> (@ (@ tptp.ord_less_eq_rat B) A) (not (@ (@ tptp.ord_less_eq_rat C2) A)))))) (forall ((B tptp.num) (C2 tptp.num) (A tptp.num)) (=> (@ (@ tptp.ord_less_eq_num (@ (@ tptp.ord_max_num B) C2)) A) (not (=> (@ (@ tptp.ord_less_eq_num B) A) (not (@ (@ tptp.ord_less_eq_num C2) A)))))) (forall ((B tptp.nat) (C2 tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.ord_max_nat B) C2)) A) (not (=> (@ (@ tptp.ord_less_eq_nat B) A) (not (@ (@ tptp.ord_less_eq_nat C2) A)))))) (forall ((B tptp.int) (C2 tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.ord_max_int B) C2)) A) (not (=> (@ (@ tptp.ord_less_eq_int B) A) (not (@ (@ tptp.ord_less_eq_int C2) A)))))) (forall ((B tptp.rat) (A tptp.rat) (C2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat B) A) (=> (@ (@ tptp.ord_less_eq_rat C2) A) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.ord_max_rat B) C2)) A)))) (forall ((B tptp.num) (A tptp.num) (C2 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num B) A) (=> (@ (@ tptp.ord_less_eq_num C2) A) (@ (@ tptp.ord_less_eq_num (@ (@ tptp.ord_max_num B) C2)) A)))) (forall ((B tptp.nat) (A tptp.nat) (C2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B) A) (=> (@ (@ tptp.ord_less_eq_nat C2) A) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.ord_max_nat B) C2)) A)))) (forall ((B tptp.int) (A tptp.int) (C2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B) A) (=> (@ (@ tptp.ord_less_eq_int C2) A) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.ord_max_int B) C2)) A)))) (= tptp.ord_less_eq_rat (lambda ((B4 tptp.rat) (A5 tptp.rat)) (= A5 (@ (@ tptp.ord_max_rat A5) B4)))) (= tptp.ord_less_eq_num (lambda ((B4 tptp.num) (A5 tptp.num)) (= A5 (@ (@ tptp.ord_max_num A5) B4)))) (= tptp.ord_less_eq_nat (lambda ((B4 tptp.nat) (A5 tptp.nat)) (= A5 (@ (@ tptp.ord_max_nat A5) B4)))) (= tptp.ord_less_eq_int (lambda ((B4 tptp.int) (A5 tptp.int)) (= A5 (@ (@ tptp.ord_max_int A5) B4)))) (forall ((A tptp.rat) (B tptp.rat)) (@ (@ tptp.ord_less_eq_rat A) (@ (@ tptp.ord_max_rat A) B))) (forall ((A tptp.num) (B tptp.num)) (@ (@ tptp.ord_less_eq_num A) (@ (@ tptp.ord_max_num A) B))) (forall ((A tptp.nat) (B tptp.nat)) (@ (@ tptp.ord_less_eq_nat A) (@ (@ tptp.ord_max_nat A) B))) (forall ((A tptp.int) (B tptp.int)) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.ord_max_int A) B))) (forall ((B tptp.rat) (A tptp.rat)) (@ (@ tptp.ord_less_eq_rat B) (@ (@ tptp.ord_max_rat A) B))) (forall ((B tptp.num) (A tptp.num)) (@ (@ tptp.ord_less_eq_num B) (@ (@ tptp.ord_max_num A) B))) (forall ((B tptp.nat) (A tptp.nat)) (@ (@ tptp.ord_less_eq_nat B) (@ (@ tptp.ord_max_nat A) B))) (forall ((B tptp.int) (A tptp.int)) (@ (@ tptp.ord_less_eq_int B) (@ (@ tptp.ord_max_int A) B))) (forall ((Z3 tptp.rat) (X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat Z3))) (= (@ _let_1 (@ (@ tptp.ord_max_rat X) Y)) (or (@ _let_1 X) (@ _let_1 Y))))) (forall ((Z3 tptp.num) (X tptp.num) (Y tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_num Z3))) (= (@ _let_1 (@ (@ tptp.ord_max_num X) Y)) (or (@ _let_1 X) (@ _let_1 Y))))) (forall ((Z3 tptp.nat) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat Z3))) (= (@ _let_1 (@ (@ tptp.ord_max_nat X) Y)) (or (@ _let_1 X) (@ _let_1 Y))))) (forall ((Z3 tptp.int) (X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int Z3))) (= (@ _let_1 (@ (@ tptp.ord_max_int X) Y)) (or (@ _let_1 X) (@ _let_1 Y))))) (= tptp.ord_less_eq_rat (lambda ((B4 tptp.rat) (A5 tptp.rat)) (= (@ (@ tptp.ord_max_rat A5) B4) A5))) (= tptp.ord_less_eq_num (lambda ((B4 tptp.num) (A5 tptp.num)) (= (@ (@ tptp.ord_max_num A5) B4) A5))) (= tptp.ord_less_eq_nat (lambda ((B4 tptp.nat) (A5 tptp.nat)) (= (@ (@ tptp.ord_max_nat A5) B4) A5))) (= tptp.ord_less_eq_int (lambda ((B4 tptp.int) (A5 tptp.int)) (= (@ (@ tptp.ord_max_int A5) B4) A5))) (= tptp.ord_less_eq_rat (lambda ((A5 tptp.rat) (B4 tptp.rat)) (= (@ (@ tptp.ord_max_rat A5) B4) B4))) (= tptp.ord_less_eq_num (lambda ((A5 tptp.num) (B4 tptp.num)) (= (@ (@ tptp.ord_max_num A5) B4) B4))) (= tptp.ord_less_eq_nat (lambda ((A5 tptp.nat) (B4 tptp.nat)) (= (@ (@ tptp.ord_max_nat A5) B4) B4))) (= tptp.ord_less_eq_int (lambda ((A5 tptp.int) (B4 tptp.int)) (= (@ (@ tptp.ord_max_int A5) B4) B4))) (forall ((C2 tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat C2))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.ord_max_rat A) B))))) (forall ((C2 tptp.num) (A tptp.num) (B tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_num C2))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.ord_max_num A) B))))) (forall ((C2 tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat C2))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.ord_max_nat A) B))))) (forall ((C2 tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int C2))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.ord_max_int A) B))))) (forall ((C2 tptp.rat) (B tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat C2))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.ord_max_rat A) B))))) (forall ((C2 tptp.num) (B tptp.num) (A tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_num C2))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.ord_max_num A) B))))) (forall ((C2 tptp.nat) (B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat C2))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.ord_max_nat A) B))))) (forall ((C2 tptp.int) (B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int C2))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.ord_max_int A) B))))) (forall ((X tptp.set_nat) (Y tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat X) Y) (= (@ (@ tptp.ord_max_set_nat X) Y) Y))) (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X) Y) (= (@ (@ tptp.ord_max_rat X) Y) Y))) (forall ((X tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X) Y) (= (@ (@ tptp.ord_max_num X) Y) Y))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X) Y) (= (@ (@ tptp.ord_max_nat X) Y) Y))) (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X) Y) (= (@ (@ tptp.ord_max_int X) Y) Y))) (forall ((Y tptp.set_nat) (X tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat Y) X) (= (@ (@ tptp.ord_max_set_nat X) Y) X))) (forall ((Y tptp.rat) (X tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat Y) X) (= (@ (@ tptp.ord_max_rat X) Y) X))) (forall ((Y tptp.num) (X tptp.num)) (=> (@ (@ tptp.ord_less_eq_num Y) X) (= (@ (@ tptp.ord_max_num X) Y) X))) (forall ((Y tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Y) X) (= (@ (@ tptp.ord_max_nat X) Y) X))) (forall ((Y tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Y) X) (= (@ (@ tptp.ord_max_int X) Y) X))) (= tptp.ord_max_set_nat (lambda ((A5 tptp.set_nat) (B4 tptp.set_nat)) (@ (@ (@ tptp.if_set_nat (@ (@ tptp.ord_less_eq_set_nat A5) B4)) B4) A5))) (= tptp.ord_max_rat (lambda ((A5 tptp.rat) (B4 tptp.rat)) (@ (@ (@ tptp.if_rat (@ (@ tptp.ord_less_eq_rat A5) B4)) B4) A5))) (= tptp.ord_max_num (lambda ((A5 tptp.num) (B4 tptp.num)) (@ (@ (@ tptp.if_num (@ (@ tptp.ord_less_eq_num A5) B4)) B4) A5))) (= tptp.ord_max_nat (lambda ((A5 tptp.nat) (B4 tptp.nat)) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_eq_nat A5) B4)) B4) A5))) (= tptp.ord_max_int (lambda ((A5 tptp.int) (B4 tptp.int)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_eq_int A5) B4)) B4) A5))) (forall ((X tptp.real) (Y tptp.real) (Z3 tptp.real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.ord_max_real X) Y)) Z3) (@ (@ tptp.ord_max_real (@ (@ tptp.plus_plus_real X) Z3)) (@ (@ tptp.plus_plus_real Y) Z3)))) (forall ((X tptp.rat) (Y tptp.rat) (Z3 tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.ord_max_rat X) Y)) Z3) (@ (@ tptp.ord_max_rat (@ (@ tptp.plus_plus_rat X) Z3)) (@ (@ tptp.plus_plus_rat Y) Z3)))) (forall ((X tptp.nat) (Y tptp.nat) (Z3 tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.ord_max_nat X) Y)) Z3) (@ (@ tptp.ord_max_nat (@ (@ tptp.plus_plus_nat X) Z3)) (@ (@ tptp.plus_plus_nat Y) Z3)))) (forall ((X tptp.int) (Y tptp.int) (Z3 tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.ord_max_int X) Y)) Z3) (@ (@ tptp.ord_max_int (@ (@ tptp.plus_plus_int X) Z3)) (@ (@ tptp.plus_plus_int Y) Z3)))) (forall ((X tptp.real) (Y tptp.real) (Z3 tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real X))) (= (@ _let_1 (@ (@ tptp.ord_max_real Y) Z3)) (@ (@ tptp.ord_max_real (@ _let_1 Y)) (@ _let_1 Z3))))) (forall ((X tptp.rat) (Y tptp.rat) (Z3 tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat X))) (= (@ _let_1 (@ (@ tptp.ord_max_rat Y) Z3)) (@ (@ tptp.ord_max_rat (@ _let_1 Y)) (@ _let_1 Z3))))) (forall ((X tptp.nat) (Y tptp.nat) (Z3 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat X))) (= (@ _let_1 (@ (@ tptp.ord_max_nat Y) Z3)) (@ (@ tptp.ord_max_nat (@ _let_1 Y)) (@ _let_1 Z3))))) (forall ((X tptp.int) (Y tptp.int) (Z3 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int X))) (= (@ _let_1 (@ (@ tptp.ord_max_int Y) Z3)) (@ (@ tptp.ord_max_int (@ _let_1 Y)) (@ _let_1 Z3))))) (forall ((X tptp.rat) (Y tptp.rat) (Z3 tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.ord_max_rat X) Y)) Z3) (@ (@ tptp.ord_max_rat (@ (@ tptp.minus_minus_rat X) Z3)) (@ (@ tptp.minus_minus_rat Y) Z3)))) (forall ((X tptp.int) (Y tptp.int) (Z3 tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.ord_max_int X) Y)) Z3) (@ (@ tptp.ord_max_int (@ (@ tptp.minus_minus_int X) Z3)) (@ (@ tptp.minus_minus_int Y) Z3)))) (forall ((M2 tptp.nat) (N tptp.nat) (Q2 tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.ord_max_nat M2) N)) Q2) (@ (@ tptp.ord_max_nat (@ (@ tptp.plus_plus_nat M2) Q2)) (@ (@ tptp.plus_plus_nat N) Q2)))) (forall ((M2 tptp.nat) (N tptp.nat) (Q2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat M2))) (= (@ _let_1 (@ (@ tptp.ord_max_nat N) Q2)) (@ (@ tptp.ord_max_nat (@ _let_1 N)) (@ _let_1 Q2))))) _let_272 (forall ((M2 tptp.nat) (N tptp.nat) (Q2 tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.ord_max_nat M2) N)) Q2) (@ (@ tptp.ord_max_nat (@ (@ tptp.times_times_nat M2) Q2)) (@ (@ tptp.times_times_nat N) Q2)))) (forall ((M2 tptp.nat) (N tptp.nat) (Q2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat M2))) (= (@ _let_1 (@ (@ tptp.ord_max_nat N) Q2)) (@ (@ tptp.ord_max_nat (@ _let_1 N)) (@ _let_1 Q2))))) (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat N))) (= (@ tptp.numeral_numeral_rat (@ tptp.bit0 N)) (@ (@ tptp.plus_plus_rat _let_1) _let_1)))) (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numera1916890842035813515d_enat N))) (= (@ tptp.numera1916890842035813515d_enat (@ tptp.bit0 N)) (@ (@ tptp.plus_p3455044024723400733d_enat _let_1) _let_1)))) (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex N))) (= (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 N)) (@ (@ tptp.plus_plus_complex _let_1) _let_1)))) (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real N))) (= (@ tptp.numeral_numeral_real (@ tptp.bit0 N)) (@ (@ tptp.plus_plus_real _let_1) _let_1)))) (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N))) (= (@ tptp.numeral_numeral_nat (@ tptp.bit0 N)) (@ (@ tptp.plus_plus_nat _let_1) _let_1)))) (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (= (@ tptp.numeral_numeral_int (@ tptp.bit0 N)) (@ (@ tptp.plus_plus_int _let_1) _let_1)))) (= tptp.ord_less_eq_nat (lambda ((A5 tptp.nat) (B4 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int A5)) (@ tptp.semiri1314217659103216013at_int B4)))) (forall ((Z3 tptp.complex) (W2 tptp.num)) (let ((_let_1 (@ tptp.power_power_complex Z3))) (let ((_let_2 (@ _let_1 (@ tptp.numeral_numeral_nat W2)))) (= (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 W2))) (@ (@ tptp.times_times_complex _let_2) _let_2))))) (forall ((Z3 tptp.real) (W2 tptp.num)) (let ((_let_1 (@ tptp.power_power_real Z3))) (let ((_let_2 (@ _let_1 (@ tptp.numeral_numeral_nat W2)))) (= (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 W2))) (@ (@ tptp.times_times_real _let_2) _let_2))))) (forall ((Z3 tptp.rat) (W2 tptp.num)) (let ((_let_1 (@ tptp.power_power_rat Z3))) (let ((_let_2 (@ _let_1 (@ tptp.numeral_numeral_nat W2)))) (= (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 W2))) (@ (@ tptp.times_times_rat _let_2) _let_2))))) (forall ((Z3 tptp.nat) (W2 tptp.num)) (let ((_let_1 (@ tptp.power_power_nat Z3))) (let ((_let_2 (@ _let_1 (@ tptp.numeral_numeral_nat W2)))) (= (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 W2))) (@ (@ tptp.times_times_nat _let_2) _let_2))))) (forall ((Z3 tptp.int) (W2 tptp.num)) (let ((_let_1 (@ tptp.power_power_int Z3))) (let ((_let_2 (@ _let_1 (@ tptp.numeral_numeral_nat W2)))) (= (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 W2))) (@ (@ tptp.times_times_int _let_2) _let_2))))) (forall ((M5 tptp.set_nat) (I2 tptp.nat)) (=> (@ (@ tptp.member_nat tptp.zero_zero_nat) M5) (not (= (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((K3 tptp.nat)) (and (@ (@ tptp.member_nat K3) M5) (@ (@ tptp.ord_less_nat K3) (@ tptp.suc I2)))))) tptp.zero_zero_nat)))) (forall ((M5 tptp.set_nat) (I2 tptp.nat)) (=> (@ (@ tptp.member_nat tptp.zero_zero_nat) M5) (= (@ tptp.suc (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((K3 tptp.nat)) (and (@ (@ tptp.member_nat (@ tptp.suc K3)) M5) (@ (@ tptp.ord_less_nat K3) I2)))))) (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((K3 tptp.nat)) (and (@ (@ tptp.member_nat K3) M5) (@ (@ tptp.ord_less_nat K3) (@ tptp.suc I2))))))))) (forall ((M5 tptp.set_nat) (I2 tptp.nat)) (=> (not (@ (@ tptp.member_nat tptp.zero_zero_nat) M5)) (= (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((K3 tptp.nat)) (and (@ (@ tptp.member_nat (@ tptp.suc K3)) M5) (@ (@ tptp.ord_less_nat K3) I2))))) (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((K3 tptp.nat)) (and (@ (@ tptp.member_nat K3) M5) (@ (@ tptp.ord_less_nat K3) (@ tptp.suc I2))))))))) (forall ((N tptp.nat) (M2 tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat N) M2)) M2) (@ (@ tptp.ord_max_nat N) M2))) (forall ((A4 tptp.set_complex) (N tptp.nat)) (=> (@ tptp.finite3207457112153483333omplex A4) (@ tptp.finite8712137658972009173omplex (@ tptp.collect_list_complex (lambda ((Xs tptp.list_complex)) (and (@ (@ tptp.ord_le211207098394363844omplex (@ tptp.set_complex2 Xs)) A4) (= (@ tptp.size_s3451745648224563538omplex Xs) N))))))) (forall ((A4 tptp.set_VEBT_VEBT) (N tptp.nat)) (=> (@ tptp.finite5795047828879050333T_VEBT A4) (@ tptp.finite3004134309566078307T_VEBT (@ tptp.collec5608196760682091941T_VEBT (lambda ((Xs tptp.list_VEBT_VEBT)) (and (@ (@ tptp.ord_le4337996190870823476T_VEBT (@ tptp.set_VEBT_VEBT2 Xs)) A4) (= (@ tptp.size_s6755466524823107622T_VEBT Xs) N))))))) (forall ((A4 tptp.set_o) (N tptp.nat)) (=> (@ tptp.finite_finite_o A4) (@ tptp.finite_finite_list_o (@ tptp.collect_list_o (lambda ((Xs tptp.list_o)) (and (@ (@ tptp.ord_less_eq_set_o (@ tptp.set_o2 Xs)) A4) (= (@ tptp.size_size_list_o Xs) N))))))) (forall ((A4 tptp.set_int) (N tptp.nat)) (=> (@ tptp.finite_finite_int A4) (@ tptp.finite3922522038869484883st_int (@ tptp.collect_list_int (lambda ((Xs tptp.list_int)) (and (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_int2 Xs)) A4) (= (@ tptp.size_size_list_int Xs) N))))))) (forall ((A4 tptp.set_nat) (N tptp.nat)) (=> (@ tptp.finite_finite_nat A4) (@ tptp.finite8100373058378681591st_nat (@ tptp.collect_list_nat (lambda ((Xs tptp.list_nat)) (and (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_nat2 Xs)) A4) (= (@ tptp.size_size_list_nat Xs) N))))))) (forall ((A4 tptp.set_list_nat) (N tptp.nat)) (=> (@ tptp.finite8100373058378681591st_nat A4) (= (@ tptp.finite7325466520557071688st_nat (@ tptp.collec5989764272469232197st_nat (lambda ((Xs tptp.list_list_nat)) (and (@ (@ tptp.ord_le6045566169113846134st_nat (@ tptp.set_list_nat2 Xs)) A4) (= (@ tptp.size_s3023201423986296836st_nat Xs) N))))) (@ (@ tptp.power_power_nat (@ tptp.finite_card_list_nat A4)) N)))) (forall ((A4 tptp.set_set_nat) (N tptp.nat)) (=> (@ tptp.finite1152437895449049373et_nat A4) (= (@ tptp.finite5631907774883551598et_nat (@ tptp.collect_list_set_nat (lambda ((Xs tptp.list_set_nat)) (and (@ (@ tptp.ord_le6893508408891458716et_nat (@ tptp.set_set_nat2 Xs)) A4) (= (@ tptp.size_s3254054031482475050et_nat Xs) N))))) (@ (@ tptp.power_power_nat (@ tptp.finite_card_set_nat A4)) N)))) (forall ((A4 tptp.set_complex) (N tptp.nat)) (=> (@ tptp.finite3207457112153483333omplex A4) (= (@ tptp.finite5120063068150530198omplex (@ tptp.collect_list_complex (lambda ((Xs tptp.list_complex)) (and (@ (@ tptp.ord_le211207098394363844omplex (@ tptp.set_complex2 Xs)) A4) (= (@ tptp.size_s3451745648224563538omplex Xs) N))))) (@ (@ tptp.power_power_nat (@ tptp.finite_card_complex A4)) N)))) (forall ((A4 tptp.set_VEBT_VEBT) (N tptp.nat)) (=> (@ tptp.finite5795047828879050333T_VEBT A4) (= (@ tptp.finite5915292604075114978T_VEBT (@ tptp.collec5608196760682091941T_VEBT (lambda ((Xs tptp.list_VEBT_VEBT)) (and (@ (@ tptp.ord_le4337996190870823476T_VEBT (@ tptp.set_VEBT_VEBT2 Xs)) A4) (= (@ tptp.size_s6755466524823107622T_VEBT Xs) N))))) (@ (@ tptp.power_power_nat (@ tptp.finite7802652506058667612T_VEBT A4)) N)))) (forall ((A4 tptp.set_o) (N tptp.nat)) (=> (@ tptp.finite_finite_o A4) (= (@ tptp.finite_card_list_o (@ tptp.collect_list_o (lambda ((Xs tptp.list_o)) (and (@ (@ tptp.ord_less_eq_set_o (@ tptp.set_o2 Xs)) A4) (= (@ tptp.size_size_list_o Xs) N))))) (@ (@ tptp.power_power_nat (@ tptp.finite_card_o A4)) N)))) (forall ((A4 tptp.set_int) (N tptp.nat)) (=> (@ tptp.finite_finite_int A4) (= (@ tptp.finite_card_list_int (@ tptp.collect_list_int (lambda ((Xs tptp.list_int)) (and (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_int2 Xs)) A4) (= (@ tptp.size_size_list_int Xs) N))))) (@ (@ tptp.power_power_nat (@ tptp.finite_card_int A4)) N)))) (forall ((A4 tptp.set_nat) (N tptp.nat)) (=> (@ tptp.finite_finite_nat A4) (= (@ tptp.finite_card_list_nat (@ tptp.collect_list_nat (lambda ((Xs tptp.list_nat)) (and (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_nat2 Xs)) A4) (= (@ tptp.size_size_list_nat Xs) N))))) (@ (@ tptp.power_power_nat (@ tptp.finite_card_nat A4)) N)))) (forall ((A4 tptp.set_complex) (N tptp.nat)) (=> (@ tptp.finite3207457112153483333omplex A4) (@ tptp.finite8712137658972009173omplex (@ tptp.collect_list_complex (lambda ((Xs tptp.list_complex)) (and (@ (@ tptp.ord_le211207098394363844omplex (@ tptp.set_complex2 Xs)) A4) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_s3451745648224563538omplex Xs)) N))))))) (forall ((A4 tptp.set_VEBT_VEBT) (N tptp.nat)) (=> (@ tptp.finite5795047828879050333T_VEBT A4) (@ tptp.finite3004134309566078307T_VEBT (@ tptp.collec5608196760682091941T_VEBT (lambda ((Xs tptp.list_VEBT_VEBT)) (and (@ (@ tptp.ord_le4337996190870823476T_VEBT (@ tptp.set_VEBT_VEBT2 Xs)) A4) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_s6755466524823107622T_VEBT Xs)) N))))))) (forall ((A4 tptp.set_o) (N tptp.nat)) (=> (@ tptp.finite_finite_o A4) (@ tptp.finite_finite_list_o (@ tptp.collect_list_o (lambda ((Xs tptp.list_o)) (and (@ (@ tptp.ord_less_eq_set_o (@ tptp.set_o2 Xs)) A4) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_o Xs)) N))))))) (forall ((A4 tptp.set_int) (N tptp.nat)) (=> (@ tptp.finite_finite_int A4) (@ tptp.finite3922522038869484883st_int (@ tptp.collect_list_int (lambda ((Xs tptp.list_int)) (and (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_int2 Xs)) A4) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_int Xs)) N))))))) (forall ((A4 tptp.set_nat) (N tptp.nat)) (=> (@ tptp.finite_finite_nat A4) (@ tptp.finite8100373058378681591st_nat (@ tptp.collect_list_nat (lambda ((Xs tptp.list_nat)) (and (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_nat2 Xs)) A4) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_nat Xs)) N))))))) (forall ((Mi tptp.nat) (Ma tptp.nat) (Va3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (X tptp.nat)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va3)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) _let_1) TreeList2) Summary))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_4 (@ tptp.if_nat (@ (@ tptp.ord_less_nat X) Mi)))) (let ((_let_5 (@ (@ _let_4 Mi) X))) (let ((_let_6 (@ (@ tptp.vEBT_VEBT_high _let_5) _let_3))) (let ((_let_7 (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_6))) (= (@ (@ tptp.vEBT_vebt_insert _let_2) X) (@ (@ (@ tptp.if_VEBT_VEBT (and (@ (@ tptp.ord_less_nat _let_6) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)) (not (or (= X Mi) (= X Ma))))) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat (@ (@ _let_4 X) Mi)) (@ (@ tptp.ord_max_nat _let_5) Ma)))) _let_1) (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList2) _let_6) (@ (@ tptp.vEBT_vebt_insert _let_7) (@ (@ tptp.vEBT_VEBT_low _let_5) _let_3)))) (@ (@ (@ tptp.if_VEBT_VEBT (@ tptp.vEBT_VEBT_minNull _let_7)) (@ (@ tptp.vEBT_vebt_insert Summary) _let_6)) Summary))) _let_2)))))))))) (forall ((Uy2 tptp.option4927543243414619207at_nat) (V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (S2 tptp.vEBT_VEBT) (X tptp.nat)) (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 X) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (= (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ (@ (@ tptp.vEBT_Node Uy2) _let_1) TreeList2) S2)) X) (and (=> _let_4 (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_3)) (@ (@ tptp.vEBT_VEBT_low X) _let_2))) _let_4))))))) (forall ((V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Vd2 tptp.vEBT_VEBT) (X tptp.nat)) (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 X) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (= (@ (@ tptp.vEBT_VEBT_membermima (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1) TreeList2) Vd2)) X) (and (=> _let_4 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_3)) (@ (@ tptp.vEBT_VEBT_low X) _let_2))) _let_4))))))) (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y tptp.vEBT_VEBT)) (=> (= (@ (@ tptp.vEBT_vebt_insert X) Xa2) Y) (=> (forall ((A3 Bool) (B3 Bool)) (let ((_let_1 (@ tptp.vEBT_Leaf A3))) (let ((_let_2 (@ _let_1 B3))) (let ((_let_3 (= Xa2 tptp.one_one_nat))) (let ((_let_4 (= Xa2 tptp.zero_zero_nat))) (=> (= X _let_2) (not (and (=> _let_4 (= Y (@ (@ tptp.vEBT_Leaf true) B3))) (=> (not _let_4) (and (=> _let_3 (= Y (@ _let_1 true))) (=> (not _let_3) (= Y _let_2)))))))))))) (=> (forall ((Info tptp.option4927543243414619207at_nat) (Ts tptp.list_VEBT_VEBT) (S tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info) tptp.zero_zero_nat) Ts) S))) (=> (= X _let_1) (not (= Y _let_1))))) (=> (forall ((Info tptp.option4927543243414619207at_nat) (Ts tptp.list_VEBT_VEBT) (S tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info) (@ tptp.suc tptp.zero_zero_nat)) Ts) S))) (=> (= X _let_1) (not (= Y _let_1))))) (=> (forall ((V tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc V)))) (=> (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1) TreeList) Summary2)) (not (= Y (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Xa2) Xa2))) _let_1) TreeList) Summary2)))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList) 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 TreeList) _let_6))) (=> (= X _let_2) (not (= Y (@ (@ (@ tptp.if_VEBT_VEBT (and (@ (@ tptp.ord_less_nat _let_6) (@ tptp.size_s6755466524823107622T_VEBT TreeList)) (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 TreeList) _let_6) (@ (@ tptp.vEBT_vebt_insert _let_7) (@ (@ tptp.vEBT_VEBT_low _let_5) _let_3)))) (@ (@ (@ tptp.if_VEBT_VEBT (@ tptp.vEBT_VEBT_minNull _let_7)) (@ (@ tptp.vEBT_vebt_insert Summary2) _let_6)) Summary2))) _let_2))))))))))))))))))) (forall ((Mi tptp.nat) (Ma tptp.nat) (Va3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (X tptp.nat)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va3)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high X) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (let ((_let_5 (not (@ (@ tptp.ord_less_nat Ma) X)))) (let ((_let_6 (not (@ (@ tptp.ord_less_nat X) Mi)))) (= (@ (@ tptp.vEBT_vebt_member (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) _let_1) TreeList2) Summary)) X) (=> (not (= X Mi)) (=> (not (= X Ma)) (and _let_6 (=> _let_6 (and _let_5 (=> _let_5 (and (=> _let_4 (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_3)) (@ (@ tptp.vEBT_VEBT_low X) _let_2))) _let_4))))))))))))))) (forall ((Mi tptp.nat) (Ma tptp.nat) (V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Vc tptp.vEBT_VEBT) (X tptp.nat)) (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 X) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (= (@ (@ tptp.vEBT_VEBT_membermima (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) _let_1) TreeList2) Vc)) X) (or (= X Mi) (= X Ma) (and (=> _let_4 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_3)) (@ (@ tptp.vEBT_VEBT_low X) _let_2))) _let_4)))))))) (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (not (@ (@ tptp.vEBT_V5719532721284313246member X) Xa2)) (=> (forall ((A3 Bool) (B3 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (=> (= X (@ (@ tptp.vEBT_Leaf A3) B3)) (and (=> _let_2 A3) (=> (not _let_2) (and (=> _let_1 B3) _let_1))))))) (=> (forall ((Uu2 tptp.option4927543243414619207at_nat) (Uv2 tptp.list_VEBT_VEBT) (Uw tptp.vEBT_VEBT)) (not (= X (@ (@ (@ (@ tptp.vEBT_Node Uu2) tptp.zero_zero_nat) Uv2) Uw)))) (not (forall ((Uy tptp.option4927543243414619207at_nat) (V tptp.nat) (TreeList tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V)) (@ 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 TreeList)))) (=> (exists ((S tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node Uy) (@ tptp.suc V)) TreeList) S))) (and (=> _let_3 (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3))))))))))) (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (@ (@ tptp.vEBT_V5719532721284313246member X) Xa2) (=> (forall ((A3 Bool) (B3 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (=> (= X (@ (@ tptp.vEBT_Leaf A3) B3)) (not (and (=> _let_2 A3) (=> (not _let_2) (and (=> _let_1 B3) _let_1)))))))) (not (forall ((Uy tptp.option4927543243414619207at_nat) (V tptp.nat) (TreeList tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V)) (@ 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 TreeList)))) (=> (exists ((S tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node Uy) (@ tptp.suc V)) TreeList) S))) (not (and (=> _let_3 (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3))))))))))) (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y Bool)) (=> (= (@ (@ tptp.vEBT_V5719532721284313246member X) Xa2) Y) (=> (forall ((A3 Bool) (B3 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (=> (= X (@ (@ tptp.vEBT_Leaf A3) B3)) (= Y (not (and (=> _let_2 A3) (=> (not _let_2) (and (=> _let_1 B3) _let_1))))))))) (=> (=> (exists ((Uu2 tptp.option4927543243414619207at_nat) (Uv2 tptp.list_VEBT_VEBT) (Uw tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node Uu2) tptp.zero_zero_nat) Uv2) Uw))) Y) (not (forall ((Uy tptp.option4927543243414619207at_nat) (V tptp.nat) (TreeList tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V)) (@ 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 TreeList)))) (=> (exists ((S tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node Uy) (@ tptp.suc V)) TreeList) S))) (= Y (not (and (=> _let_3 (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3))))))))))))) (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (@ (@ tptp.vEBT_VEBT_membermima X) Xa2) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat)) (=> (exists ((Va2 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) Va2) Vb2))) (not (or (= Xa2 Mi2) (= Xa2 Ma2))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (V tptp.nat) (TreeList tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V)) (@ 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 TreeList)))) (=> (exists ((Vc2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc V)) TreeList) Vc2))) (not (or (= Xa2 Mi2) (= Xa2 Ma2) (and (=> _let_3 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3)))))))) (not (forall ((V tptp.nat) (TreeList tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V)) (@ 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 TreeList)))) (=> (exists ((Vd tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) (@ tptp.suc V)) TreeList) Vd))) (not (and (=> _let_3 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3)))))))))))) (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (@ (@ tptp.vEBT_vebt_member X) Xa2) (=> (forall ((A3 Bool) (B3 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (=> (= X (@ (@ tptp.vEBT_Leaf A3) B3)) (not (and (=> _let_2 A3) (=> (not _let_2) (and (=> _let_1 B3) _let_1)))))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va tptp.nat) (TreeList tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc (@ tptp.suc Va))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList)))) (let ((_let_4 (not (@ (@ tptp.ord_less_nat Ma2) Xa2)))) (let ((_let_5 (not (@ (@ tptp.ord_less_nat Xa2) Mi2)))) (=> (exists ((Summary2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc (@ tptp.suc Va))) TreeList) 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 TreeList) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3))))))))))))))))))) (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (not (@ (@ tptp.vEBT_VEBT_membermima X) Xa2)) (=> (forall ((Uu2 Bool) (Uv2 Bool)) (not (= X (@ (@ tptp.vEBT_Leaf Uu2) Uv2)))) (=> (forall ((Ux tptp.list_VEBT_VEBT) (Uy tptp.vEBT_VEBT)) (not (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) tptp.zero_zero_nat) Ux) Uy)))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat)) (=> (exists ((Va2 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) Va2) Vb2))) (or (= Xa2 Mi2) (= Xa2 Ma2)))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (V tptp.nat) (TreeList tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V)) (@ 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 TreeList)))) (=> (exists ((Vc2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc V)) TreeList) Vc2))) (or (= Xa2 Mi2) (= Xa2 Ma2) (and (=> _let_3 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3))))))) (not (forall ((V tptp.nat) (TreeList tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V)) (@ 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 TreeList)))) (=> (exists ((Vd tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) (@ tptp.suc V)) TreeList) Vd))) (and (=> _let_3 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3))))))))))))) (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y Bool)) (=> (= (@ (@ tptp.vEBT_VEBT_membermima X) Xa2) Y) (=> (=> (exists ((Uu2 Bool) (Uv2 Bool)) (= X (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) Y) (=> (=> (exists ((Ux tptp.list_VEBT_VEBT) (Uy tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) tptp.zero_zero_nat) Ux) Uy))) Y) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat)) (=> (exists ((Va2 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) Va2) Vb2))) (= Y (not (or (= Xa2 Mi2) (= Xa2 Ma2)))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (V tptp.nat) (TreeList tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V)) (@ 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 TreeList)))) (=> (exists ((Vc2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc V)) TreeList) Vc2))) (= Y (not (or (= Xa2 Mi2) (= Xa2 Ma2) (and (=> _let_3 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3))))))))) (not (forall ((V tptp.nat) (TreeList tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V)) (@ 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 TreeList)))) (=> (exists ((Vd tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) (@ tptp.suc V)) TreeList) Vd))) (= Y (not (and (=> _let_3 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3))))))))))))))) (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (not (@ (@ tptp.vEBT_vebt_member X) Xa2)) (=> (forall ((A3 Bool) (B3 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (=> (= X (@ (@ tptp.vEBT_Leaf A3) B3)) (and (=> _let_2 A3) (=> (not _let_2) (and (=> _let_1 B3) _let_1))))))) (=> (forall ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw tptp.vEBT_VEBT)) (not (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw)))) (=> (forall ((V tptp.product_prod_nat_nat) (Uy tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (not (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V)) tptp.zero_zero_nat) Uy) Uz2)))) (=> (forall ((V tptp.product_prod_nat_nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (not (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V)) (@ tptp.suc tptp.zero_zero_nat)) Vb2) Vc2)))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va tptp.nat) (TreeList tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc (@ tptp.suc Va))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList)))) (let ((_let_4 (not (@ (@ tptp.ord_less_nat Ma2) Xa2)))) (let ((_let_5 (not (@ (@ tptp.ord_less_nat Xa2) Mi2)))) (=> (exists ((Summary2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc (@ tptp.suc Va))) TreeList) 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 TreeList) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3))))))))))))))))))))) (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y Bool)) (=> (= (@ (@ tptp.vEBT_vebt_member X) Xa2) Y) (=> (forall ((A3 Bool) (B3 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (=> (= X (@ (@ tptp.vEBT_Leaf A3) B3)) (= Y (not (and (=> _let_2 A3) (=> (not _let_2) (and (=> _let_1 B3) _let_1))))))))) (=> (=> (exists ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw))) Y) (=> (=> (exists ((V tptp.product_prod_nat_nat) (Uy tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ 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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 TreeList) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3))))))))))))))))))))))) (forall ((Ma tptp.nat) (X tptp.nat) (Mi tptp.nat) (Va3 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 Va3)))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_2) _let_1))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_high X) _let_3))) (let ((_let_5 (@ (@ tptp.vEBT_vebt_pred Summary) _let_4))) (let ((_let_6 (@ tptp.nth_VEBT_VEBT TreeList2))) (let ((_let_7 (@ tptp.vEBT_VEBT_mul (@ tptp.some_nat (@ (@ tptp.power_power_nat _let_1) _let_3))))) (let ((_let_8 (@ (@ tptp.vEBT_VEBT_low X) _let_3))) (let ((_let_9 (@ _let_6 _let_4))) (let ((_let_10 (@ tptp.vEBT_vebt_mint _let_9))) (let ((_let_11 (@ (@ tptp.vEBT_vebt_pred (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) _let_2) TreeList2) Summary)) X))) (let ((_let_12 (@ (@ tptp.ord_less_nat Ma) X))) (and (=> _let_12 (= _let_11 (@ tptp.some_nat Ma))) (=> (not _let_12) (= _let_11 (@ (@ (@ tptp.if_option_nat (@ (@ tptp.ord_less_nat _let_4) (@ tptp.size_s6755466524823107622T_VEBT TreeList2))) (@ (@ (@ tptp.if_option_nat (and (not (= _let_10 tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_greater (@ tptp.some_nat _let_8)) _let_10))) (@ (@ tptp.vEBT_VEBT_add (@ _let_7 (@ tptp.some_nat _let_4))) (@ (@ tptp.vEBT_vebt_pred _let_9) _let_8))) (@ (@ (@ tptp.if_option_nat (= _let_5 tptp.none_nat)) (@ (@ (@ tptp.if_option_nat (@ (@ tptp.ord_less_nat Mi) X)) (@ tptp.some_nat Mi)) tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_add (@ _let_7 _let_5)) (@ tptp.vEBT_vebt_maxt (@ _let_6 (@ tptp.the_nat _let_5))))))) tptp.none_nat))))))))))))))))) (forall ((X tptp.nat) (Mi tptp.nat) (Ma tptp.nat) (Va3 tptp.nat) 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(@ 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))))))))))))))))) (forall ((X tptp.nat) (Mi tptp.nat) (Ma tptp.nat) (Va3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va3)))) (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 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_let_20))) (let ((_let_22 (@ tptp.the_nat _let_21))) (let ((_let_23 (@ (@ tptp.vEBT_vebt_delete _let_2) X))) (let ((_let_24 (and _let_9 _let_16))) (let ((_let_25 (or (@ (@ tptp.ord_less_nat X) Mi) (@ (@ tptp.ord_less_nat Ma) X)))) (and (=> _let_25 (= _let_23 _let_2)) (=> (not _let_25) (and (=> _let_24 (= _let_23 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1) TreeList2) Summary))) (=> (not _let_24) (= _let_23 (@ (@ (@ tptp.if_VEBT_VEBT (@ (@ tptp.ord_less_nat _let_12) (@ tptp.size_s6755466524823107622T_VEBT TreeList2))) (@ (@ (@ tptp.if_VEBT_VEBT (@ tptp.vEBT_VEBT_minNull _let_13)) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_19 (@ (@ _let_17 (@ (@ (@ tptp.if_nat (= _let_21 tptp.none_nat)) _let_18) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_7) _let_22)) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ _let_15 _let_22)))))) Ma)))) _let_1) _let_14) _let_20)) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_19 (@ (@ _let_17 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_12) _let_7)) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ _let_15 _let_12))))) Ma)))) _let_1) _let_14) Summary))) _let_2)))))))))))))))))))))))))))))))) (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y tptp.vEBT_VEBT)) (=> (= (@ (@ tptp.vEBT_vebt_delete X) Xa2) Y) (=> (forall ((A3 Bool) (B3 Bool)) (=> (= X (@ (@ tptp.vEBT_Leaf A3) B3)) (=> (= Xa2 tptp.zero_zero_nat) (not (= Y (@ (@ tptp.vEBT_Leaf false) B3)))))) (=> (forall ((A3 Bool)) (=> (exists ((B3 Bool)) (= X (@ (@ tptp.vEBT_Leaf A3) B3))) (=> (= Xa2 (@ tptp.suc tptp.zero_zero_nat)) (not (= Y (@ (@ tptp.vEBT_Leaf A3) false)))))) (=> (forall ((A3 Bool) (B3 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A3) B3))) (=> (= X _let_1) (=> (exists ((N3 tptp.nat)) (= Xa2 (@ tptp.suc (@ tptp.suc N3)))) (not (= Y _let_1)))))) (=> (forall ((Deg2 tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node 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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 TreeList))) (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 TreeList) _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) TreeList) Summary2))) (=> (not _let_23) (= Y (@ (@ (@ tptp.if_VEBT_VEBT (@ (@ tptp.ord_less_nat _let_12) (@ tptp.size_s6755466524823107622T_VEBT TreeList))) (@ (@ (@ tptp.if_VEBT_VEBT (@ tptp.vEBT_VEBT_minNull _let_13)) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_19 (@ (@ _let_17 (@ (@ (@ tptp.if_nat (= _let_21 tptp.none_nat)) _let_18) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_7) _let_22)) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ _let_15 _let_22)))))) Ma2)))) _let_1) _let_14) _let_20)) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_19 (@ (@ _let_17 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_12) _let_7)) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ _let_15 _let_12))))) Ma2)))) _let_1) _let_14) Summary2))) _let_2)))))))))))))))))))))))))))))))))))))))))) (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y tptp.option_nat)) (let ((_let_1 (not (= Y tptp.none_nat)))) (=> (= (@ (@ tptp.vEBT_vebt_succ X) Xa2) Y) (=> (forall ((Uu2 Bool) (B3 Bool)) (=> (= X (@ (@ tptp.vEBT_Leaf Uu2) B3)) (=> (= Xa2 tptp.zero_zero_nat) (not (and (=> B3 (= Y (@ tptp.some_nat tptp.one_one_nat))) (=> (not B3) (= Y tptp.none_nat))))))) (=> (=> (exists ((Uv2 Bool) (Uw Bool)) (= X (@ (@ tptp.vEBT_Leaf Uv2) Uw))) (=> (exists ((N3 tptp.nat)) (= Xa2 (@ tptp.suc N3))) _let_1)) (=> (=> (exists ((Ux tptp.nat) (Uy tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Ux) Uy) Uz2))) _let_1) (=> (=> (exists ((V tptp.product_prod_nat_nat) (Vc2 tptp.list_VEBT_VEBT) (Vd tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V)) tptp.zero_zero_nat) Vc2) Vd))) _let_1) (=> (=> (exists ((V tptp.product_prod_nat_nat) (Vg tptp.list_VEBT_VEBT) (Vh tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V)) (@ tptp.suc tptp.zero_zero_nat)) Vg) Vh))) _let_1) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va tptp.nat) (TreeList 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 Va)))) (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 TreeList))) (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) TreeList) 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 TreeList))) (@ (@ (@ tptp.if_option_nat (and (not (= _let_10 tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_less (@ tptp.some_nat _let_8)) _let_10))) (@ (@ tptp.vEBT_VEBT_add (@ _let_7 (@ tptp.some_nat _let_4))) (@ (@ tptp.vEBT_vebt_succ _let_9) _let_8))) (@ (@ (@ tptp.if_option_nat (= _let_5 tptp.none_nat)) tptp.none_nat) (@ (@ tptp.vEBT_VEBT_add (@ _let_7 _let_5)) (@ tptp.vEBT_vebt_mint (@ _let_6 (@ tptp.the_nat _let_5))))))) tptp.none_nat))))))))))))))))))))))))))) (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y tptp.option_nat)) (let ((_let_1 (not (= Y tptp.none_nat)))) (=> (= (@ (@ tptp.vEBT_vebt_pred X) Xa2) Y) (=> (=> (exists ((Uu2 Bool) (Uv2 Bool)) (= X (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) (=> (= Xa2 tptp.zero_zero_nat) _let_1)) (=> (forall ((A3 Bool)) (=> (exists ((Uw Bool)) (= X (@ (@ tptp.vEBT_Leaf A3) Uw))) (=> (= Xa2 (@ tptp.suc tptp.zero_zero_nat)) (not (and (=> A3 (= Y (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A3) (= Y tptp.none_nat))))))) (=> (forall ((A3 Bool) (B3 Bool)) (=> (= X (@ (@ tptp.vEBT_Leaf A3) B3)) (=> (exists ((Va tptp.nat)) (= Xa2 (@ tptp.suc (@ tptp.suc Va)))) (not (and (=> B3 (= Y (@ tptp.some_nat tptp.one_one_nat))) (=> (not B3) (and (=> A3 (= Y (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A3) (= Y tptp.none_nat))))))))) (=> (=> (exists ((Uy tptp.nat) (Uz2 tptp.list_VEBT_VEBT) (Va2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uy) Uz2) Va2))) _let_1) (=> (=> (exists ((V tptp.product_prod_nat_nat) (Vd tptp.list_VEBT_VEBT) (Ve tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V)) tptp.zero_zero_nat) Vd) Ve))) _let_1) (=> (=> (exists ((V tptp.product_prod_nat_nat) (Vh tptp.list_VEBT_VEBT) (Vi tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V)) (@ tptp.suc tptp.zero_zero_nat)) Vh) Vi))) _let_1) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va tptp.nat) (TreeList 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 Va)))) (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 TreeList))) (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) TreeList) 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 TreeList))) (@ (@ (@ tptp.if_option_nat (and (not (= _let_10 tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_greater (@ tptp.some_nat _let_8)) _let_10))) (@ (@ tptp.vEBT_VEBT_add (@ _let_7 (@ tptp.some_nat _let_4))) (@ (@ tptp.vEBT_vebt_pred _let_9) _let_8))) (@ (@ (@ tptp.if_option_nat (= _let_5 tptp.none_nat)) (@ (@ (@ tptp.if_option_nat (@ (@ tptp.ord_less_nat Mi2) Xa2)) (@ tptp.some_nat Mi2)) tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_add (@ _let_7 _let_5)) (@ tptp.vEBT_vebt_maxt (@ _let_6 (@ tptp.the_nat _let_5))))))) tptp.none_nat)))))))))))))))))))))))))))) (forall ((N tptp.nat) (C2 tptp.complex)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((Z4 tptp.complex)) (= (@ (@ tptp.power_power_complex Z4) N) C2)))))) (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_real (@ tptp.collect_real (lambda ((Z4 tptp.real)) (= (@ (@ tptp.power_power_real Z4) N) tptp.one_one_real))))) N))) (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_complex (@ tptp.collect_complex (lambda ((Z4 tptp.complex)) (= (@ (@ tptp.power_power_complex Z4) N) tptp.one_one_complex))))) N))) (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N) (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((Z4 tptp.real)) (= (@ (@ tptp.power_power_real Z4) N) tptp.one_one_real)))))) (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N) (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((Z4 tptp.complex)) (= (@ (@ tptp.power_power_complex Z4) N) tptp.one_one_complex)))))) (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y tptp.option_nat)) (=> (= (@ (@ tptp.vEBT_vebt_succ X) Xa2) Y) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_succ_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa2)) (=> (forall ((Uu2 Bool) (B3 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu2) B3))) (=> (= X _let_1) (=> (= Xa2 tptp.zero_zero_nat) (=> (and (=> B3 (= Y (@ tptp.some_nat tptp.one_one_nat))) (=> (not B3) (= Y tptp.none_nat))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_succ_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) tptp.zero_zero_nat)))))))) (=> (forall ((Uv2 Bool) (Uw Bool)) (=> (= X (@ (@ tptp.vEBT_Leaf Uv2) Uw)) (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) Uw)) _let_1))))))))) (=> (forall ((Ux tptp.nat) (Uy tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Ux) Uy) 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 ((V tptp.product_prod_nat_nat) (Vc2 tptp.list_VEBT_VEBT) (Vd tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V)) tptp.zero_zero_nat) Vc2) Vd))) (=> (= X _let_1) (=> (= Y tptp.none_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_succ_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((V tptp.product_prod_nat_nat) (Vg tptp.list_VEBT_VEBT) (Vh tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V)) (@ tptp.suc tptp.zero_zero_nat)) Vg) Vh))) (=> (= X _let_1) (=> (= Y tptp.none_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_succ_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList) 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 TreeList))) (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 TreeList))) (@ (@ (@ tptp.if_option_nat (and (not (= _let_11 tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_less (@ tptp.some_nat _let_9)) _let_11))) (@ (@ tptp.vEBT_VEBT_add (@ _let_8 (@ tptp.some_nat _let_5))) (@ (@ tptp.vEBT_vebt_succ _let_10) _let_9))) (@ (@ (@ tptp.if_option_nat (= _let_6 tptp.none_nat)) tptp.none_nat) (@ (@ tptp.vEBT_VEBT_add (@ _let_8 _let_6)) (@ tptp.vEBT_vebt_mint (@ _let_7 (@ tptp.the_nat _let_6))))))) tptp.none_nat)))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_succ_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa2))))))))))))))))))))))))))) (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y tptp.option_nat)) (=> (= (@ (@ tptp.vEBT_vebt_pred X) Xa2) Y) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_pred_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa2)) (=> (forall ((Uu2 Bool) (Uv2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) (=> (= X _let_1) (=> (= Xa2 tptp.zero_zero_nat) (=> (= Y tptp.none_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_pred_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) tptp.zero_zero_nat)))))))) (=> (forall ((A3 Bool) (Uw Bool)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (let ((_let_2 (@ (@ tptp.vEBT_Leaf A3) Uw))) (=> (= X _let_2) (=> (= Xa2 _let_1) (=> (and (=> A3 (= Y (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A3) (= Y tptp.none_nat))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_pred_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) _let_1))))))))) (=> (forall ((A3 Bool) (B3 Bool)) (=> (= X (@ (@ tptp.vEBT_Leaf A3) B3)) (forall ((Va tptp.nat)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va)))) (=> (= Xa2 _let_1) (=> (and (=> B3 (= Y (@ tptp.some_nat tptp.one_one_nat))) (=> (not B3) (and (=> A3 (= Y (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A3) (= Y tptp.none_nat))))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_pred_rel) (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf A3) B3)) _let_1))))))))) (=> (forall ((Uy tptp.nat) (Uz2 tptp.list_VEBT_VEBT) (Va2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uy) Uz2) Va2))) (=> (= X _let_1) (=> (= Y tptp.none_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_pred_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((V tptp.product_prod_nat_nat) (Vd tptp.list_VEBT_VEBT) (Ve tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V)) tptp.zero_zero_nat) Vd) Ve))) (=> (= X _let_1) (=> (= Y tptp.none_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_pred_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((V tptp.product_prod_nat_nat) (Vh tptp.list_VEBT_VEBT) (Vi tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V)) (@ tptp.suc tptp.zero_zero_nat)) Vh) Vi))) (=> (= X _let_1) (=> (= Y tptp.none_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_pred_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList) 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 TreeList))) (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 TreeList))) (@ (@ (@ tptp.if_option_nat (and (not (= _let_11 tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_greater (@ tptp.some_nat _let_9)) _let_11))) (@ (@ tptp.vEBT_VEBT_add (@ _let_8 (@ tptp.some_nat _let_5))) (@ (@ tptp.vEBT_vebt_pred _let_10) _let_9))) (@ (@ (@ tptp.if_option_nat (= _let_6 tptp.none_nat)) (@ (@ (@ tptp.if_option_nat (@ (@ tptp.ord_less_nat Mi2) Xa2)) (@ tptp.some_nat Mi2)) tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_add (@ _let_8 _let_6)) (@ tptp.vEBT_vebt_maxt (@ _let_7 (@ tptp.the_nat _let_6))))))) tptp.none_nat)))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_pred_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa2)))))))))))))))))))))))))))) (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y tptp.vEBT_VEBT)) (=> (= (@ (@ tptp.vEBT_vebt_delete X) Xa2) Y) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_delete_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa2)) (=> (forall ((A3 Bool) (B3 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A3) B3))) (=> (= X _let_1) (=> (= Xa2 tptp.zero_zero_nat) (=> (= Y (@ (@ tptp.vEBT_Leaf false) B3)) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_delete_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) tptp.zero_zero_nat)))))))) (=> (forall ((A3 Bool) (B3 Bool)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (let ((_let_2 (@ tptp.vEBT_Leaf A3))) (let ((_let_3 (@ _let_2 B3))) (=> (= X _let_3) (=> (= Xa2 _let_1) (=> (= Y (@ _let_2 false)) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_delete_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_3) _let_1)))))))))) (=> (forall ((A3 Bool) (B3 Bool)) (=> (= X (@ (@ tptp.vEBT_Leaf A3) B3)) (forall ((N3 tptp.nat)) (let ((_let_1 (@ tptp.suc (@ tptp.suc N3)))) (let ((_let_2 (@ (@ tptp.vEBT_Leaf A3) B3))) (=> (= Xa2 _let_1) (=> (= Y _let_2) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_delete_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) _let_1)))))))))) (=> (forall ((Deg2 tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Deg2) TreeList) Summary2))) (=> (= X _let_1) (=> (= Y _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_delete_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (TrLst tptp.list_VEBT_VEBT) (Smry tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) tptp.zero_zero_nat) TrLst) Smry))) (=> (= X _let_1) (=> (= Y _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_delete_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Tr tptp.list_VEBT_VEBT) (Sm tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc tptp.zero_zero_nat)) Tr) Sm))) (=> (= X _let_1) (=> (= Y _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_delete_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList) 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 TreeList))) (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 TreeList) _let_12) _let_13))) (let ((_let_15 (@ 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(@ _let_17 (@ (@ (@ tptp.if_nat (= _let_21 tptp.none_nat)) _let_18) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_7) _let_22)) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ _let_15 _let_22)))))) Ma2)))) _let_1) _let_14) _let_20)) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_19 (@ (@ _let_17 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_12) _let_7)) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ _let_15 _let_12))))) Ma2)))) _let_1) _let_14) Summary2))) _let_2)))))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_delete_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa2)))))))))))))))))))))))))))))))))))))))) (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y tptp.vEBT_VEBT)) (=> (= (@ (@ tptp.vEBT_vebt_insert X) Xa2) Y) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_insert_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa2)) (=> (forall ((A3 Bool) (B3 Bool)) (let ((_let_1 (@ tptp.vEBT_Leaf A3))) (let ((_let_2 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tptp.vEBT_vebt_insert_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa2))))))))))))))))))))) _let_271 (forall ((A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)) (forall ((A tptp.int)) (= (@ (@ tptp.modulo_modulo_int tptp.zero_zero_int) A) tptp.zero_zero_int)) (forall ((A tptp.code_natural)) (= (@ (@ tptp.modulo8411746178871703098atural tptp.zero_z2226904508553997617atural) A) tptp.zero_z2226904508553997617atural)) (forall ((A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat A) tptp.zero_zero_nat) A)) (forall ((A tptp.int)) (= (@ (@ tptp.modulo_modulo_int A) tptp.zero_zero_int) A)) (forall ((A tptp.code_natural)) (= (@ (@ tptp.modulo8411746178871703098atural A) tptp.zero_z2226904508553997617atural) A)) (forall ((A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat A) A) tptp.zero_zero_nat)) (forall ((A tptp.int)) (= (@ (@ tptp.modulo_modulo_int A) A) tptp.zero_zero_int)) (forall ((A tptp.code_natural)) (= (@ (@ tptp.modulo8411746178871703098atural A) 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tptp.plus_p4538020629002901425atural (@ (@ tptp.times_2397367101498566445atural C2) B)) A)) B) (@ (@ tptp.modulo8411746178871703098atural A) B))) (forall ((B tptp.nat) (C2 tptp.nat) (A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat B) C2)) A)) B) (@ (@ tptp.modulo_modulo_nat A) B))) (forall ((B tptp.int) (C2 tptp.int) (A tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) C2)) A)) B) (@ (@ tptp.modulo_modulo_int A) B))) (forall ((B tptp.code_natural) (C2 tptp.code_natural) (A tptp.code_natural)) (= (@ (@ tptp.modulo8411746178871703098atural (@ (@ tptp.plus_p4538020629002901425atural (@ (@ tptp.times_2397367101498566445atural B) C2)) A)) B) (@ (@ tptp.modulo8411746178871703098atural A) B))) (forall ((M2 tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat M2) (@ tptp.suc tptp.zero_zero_nat)) tptp.zero_zero_nat)) (forall ((N tptp.nat) (K2 tptp.nat) (M2 tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat N) K2)) M2))) N) (@ (@ tptp.modulo_modulo_nat (@ tptp.suc M2)) N))) (forall ((K2 tptp.nat) (N tptp.nat) (M2 tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat K2) N)) M2))) N) (@ (@ tptp.modulo_modulo_nat (@ tptp.suc M2)) N))) (forall ((M2 tptp.nat) (N tptp.nat) (K2 tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ (@ tptp.plus_plus_nat M2) (@ (@ tptp.times_times_nat N) K2)))) N) (@ (@ tptp.modulo_modulo_nat (@ tptp.suc M2)) N))) (forall ((M2 tptp.nat) (K2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ (@ tptp.plus_plus_nat M2) (@ (@ tptp.times_times_nat K2) N)))) N) (@ (@ tptp.modulo_modulo_nat (@ tptp.suc M2)) N))) (forall ((M2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ tptp.suc M2))) _let_1) (@ (@ tptp.modulo_modulo_nat M2) _let_1)))) (forall ((K2 tptp.num) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat K2))) (=> (not (= _let_1 tptp.one_one_nat)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ (@ tptp.times_times_nat _let_1) N))) _let_1) tptp.one_one_nat)))) (forall ((A tptp.code_integer)) (let ((_let_1 (@ (@ tptp.modulo364778990260209775nteger A) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (= (not (= _let_1 tptp.zero_z3403309356797280102nteger)) (= _let_1 tptp.one_one_Code_integer)))) (forall ((A tptp.nat)) (let ((_let_1 (@ (@ tptp.modulo_modulo_nat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (not (= _let_1 tptp.zero_zero_nat)) (= _let_1 tptp.one_one_nat)))) (forall ((A tptp.int)) (let ((_let_1 (@ (@ tptp.modulo_modulo_int A) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (not (= _let_1 tptp.zero_zero_int)) (= _let_1 tptp.one_one_int)))) (forall ((A tptp.code_natural)) (let ((_let_1 (@ (@ tptp.modulo8411746178871703098atural A) (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one))))) (= (not (= _let_1 tptp.zero_z2226904508553997617atural)) (= _let_1 tptp.one_one_Code_natural)))) (forall ((A tptp.code_integer)) (let ((_let_1 (@ (@ tptp.modulo364778990260209775nteger A) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (= (not (= _let_1 tptp.one_one_Code_integer)) (= _let_1 tptp.zero_z3403309356797280102nteger)))) (forall ((A tptp.nat)) (let ((_let_1 (@ (@ tptp.modulo_modulo_nat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (not (= _let_1 tptp.one_one_nat)) (= _let_1 tptp.zero_zero_nat)))) (forall ((A tptp.int)) (let ((_let_1 (@ (@ tptp.modulo_modulo_int A) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (not (= _let_1 tptp.one_one_int)) (= _let_1 tptp.zero_zero_int)))) (forall ((A tptp.code_natural)) (let ((_let_1 (@ (@ tptp.modulo8411746178871703098atural A) (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one))))) (= (not (= _let_1 tptp.one_one_Code_natural)) (= _let_1 tptp.zero_z2226904508553997617atural)))) (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.modulo_modulo_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (not (= _let_1 (@ tptp.suc tptp.zero_zero_nat))) (= _let_1 tptp.zero_zero_nat)))) (forall ((M2 tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat M2) M2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_nat)) (forall ((M2 tptp.nat)) (let ((_let_1 (@ (@ tptp.modulo_modulo_nat M2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) _let_1) (= _let_1 tptp.one_one_nat)))) (forall ((A tptp.nat) (C2 tptp.nat) (B tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat (@ (@ tptp.modulo_modulo_nat A) C2)) (@ (@ tptp.modulo_modulo_nat B) C2))) C2) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat A) B)) C2))) (forall ((A tptp.int) (C2 tptp.int) (B tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int (@ (@ tptp.modulo_modulo_int A) C2)) (@ (@ tptp.modulo_modulo_int B) C2))) C2) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int A) B)) C2))) (forall ((A tptp.code_natural) (C2 tptp.code_natural) (B tptp.code_natural)) (= (@ (@ tptp.modulo8411746178871703098atural (@ (@ tptp.times_2397367101498566445atural (@ (@ tptp.modulo8411746178871703098atural A) C2)) (@ (@ tptp.modulo8411746178871703098atural B) C2))) C2) (@ (@ tptp.modulo8411746178871703098atural (@ (@ tptp.times_2397367101498566445atural A) B)) C2))) (forall ((A tptp.nat) (C2 tptp.nat) (A2 tptp.nat) (B tptp.nat) (B2 tptp.nat)) (=> (= (@ (@ tptp.modulo_modulo_nat A) C2) (@ (@ tptp.modulo_modulo_nat A2) C2)) (=> (= (@ (@ tptp.modulo_modulo_nat B) C2) (@ (@ tptp.modulo_modulo_nat B2) C2)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat A) B)) C2) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat A2) B2)) C2))))) (forall ((A tptp.int) (C2 tptp.int) (A2 tptp.int) (B tptp.int) (B2 tptp.int)) (=> (= (@ (@ tptp.modulo_modulo_int A) C2) (@ (@ tptp.modulo_modulo_int A2) C2)) (=> (= (@ (@ tptp.modulo_modulo_int B) C2) (@ (@ tptp.modulo_modulo_int B2) C2)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int A) B)) C2) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int A2) B2)) C2))))) (forall ((A tptp.code_natural) (C2 tptp.code_natural) (A2 tptp.code_natural) (B tptp.code_natural) (B2 tptp.code_natural)) (=> (= (@ (@ tptp.modulo8411746178871703098atural A) C2) (@ (@ tptp.modulo8411746178871703098atural A2) C2)) (=> (= (@ (@ tptp.modulo8411746178871703098atural B) C2) (@ (@ tptp.modulo8411746178871703098atural B2) C2)) (= (@ (@ tptp.modulo8411746178871703098atural (@ (@ tptp.times_2397367101498566445atural A) B)) C2) (@ (@ tptp.modulo8411746178871703098atural (@ (@ tptp.times_2397367101498566445atural A2) B2)) C2))))) (forall ((A tptp.nat) (C2 tptp.nat) (B tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat A) C2)) (@ (@ tptp.times_times_nat B) C2)) (@ (@ tptp.times_times_nat (@ (@ tptp.modulo_modulo_nat A) B)) C2))) (forall ((A tptp.int) (C2 tptp.int) (B tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int A) C2)) (@ (@ tptp.times_times_int B) C2)) (@ (@ tptp.times_times_int (@ (@ tptp.modulo_modulo_int A) B)) C2))) (forall ((A tptp.code_natural) (C2 tptp.code_natural) (B tptp.code_natural)) (= (@ (@ tptp.modulo8411746178871703098atural (@ (@ tptp.times_2397367101498566445atural A) C2)) (@ (@ tptp.times_2397367101498566445atural B) C2)) (@ (@ tptp.times_2397367101498566445atural (@ (@ tptp.modulo8411746178871703098atural A) B)) C2))) (forall ((C2 tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C2))) (= (@ _let_1 (@ (@ tptp.modulo_modulo_nat A) B)) (@ (@ tptp.modulo_modulo_nat (@ _let_1 A)) (@ _let_1 B))))) (forall ((C2 tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C2))) (= (@ _let_1 (@ (@ tptp.modulo_modulo_int A) B)) (@ (@ tptp.modulo_modulo_int (@ _let_1 A)) (@ _let_1 B))))) (forall ((C2 tptp.code_natural) (A tptp.code_natural) (B tptp.code_natural)) (let ((_let_1 (@ tptp.times_2397367101498566445atural C2))) (= (@ _let_1 (@ (@ tptp.modulo8411746178871703098atural A) B)) (@ (@ tptp.modulo8411746178871703098atural (@ _let_1 A)) (@ _let_1 B))))) (forall ((A tptp.nat) (C2 tptp.nat) (B tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat (@ (@ tptp.modulo_modulo_nat A) C2)) B)) C2) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat A) B)) C2))) (forall ((A tptp.int) (C2 tptp.int) (B tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int (@ (@ tptp.modulo_modulo_int A) C2)) B)) C2) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int A) B)) C2))) (forall ((A tptp.code_natural) (C2 tptp.code_natural) (B tptp.code_natural)) (= (@ (@ tptp.modulo8411746178871703098atural (@ (@ tptp.times_2397367101498566445atural (@ (@ tptp.modulo8411746178871703098atural A) C2)) B)) C2) (@ (@ tptp.modulo8411746178871703098atural (@ (@ tptp.times_2397367101498566445atural A) B)) C2))) (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (= (@ (@ tptp.modulo_modulo_nat (@ _let_1 (@ (@ tptp.modulo_modulo_nat B) C2))) C2) (@ (@ tptp.modulo_modulo_nat (@ _let_1 B)) C2)))) (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (= (@ (@ tptp.modulo_modulo_int (@ _let_1 (@ (@ tptp.modulo_modulo_int B) C2))) C2) (@ (@ tptp.modulo_modulo_int (@ _let_1 B)) C2)))) (forall ((A tptp.code_natural) (B tptp.code_natural) (C2 tptp.code_natural)) (let ((_let_1 (@ tptp.times_2397367101498566445atural A))) (= (@ (@ tptp.modulo8411746178871703098atural (@ _let_1 (@ (@ tptp.modulo8411746178871703098atural B) C2))) C2) (@ (@ tptp.modulo8411746178871703098atural (@ _let_1 B)) C2)))) (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ tptp.suc (@ (@ tptp.modulo_modulo_nat M2) N)))) N) (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ tptp.suc M2))) N))) (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ (@ tptp.modulo_modulo_nat M2) N))) N) (@ (@ tptp.modulo_modulo_nat (@ tptp.suc M2)) N))) (forall ((M2 tptp.nat) (N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.modulo_modulo_nat M2) N)) M2)) (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.modulo_modulo_nat A) B)) A))) (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.modulo_modulo_int A) B)) A))) (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B) (@ (@ tptp.ord_less_nat (@ (@ tptp.modulo_modulo_nat A) B)) B))) (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (@ (@ tptp.ord_less_int (@ (@ tptp.modulo_modulo_int A) B)) B))) (forall ((A tptp.nat) (B tptp.nat)) (= (= (@ (@ tptp.modulo_modulo_nat A) B) A) (= (@ (@ tptp.divide_divide_nat A) B) tptp.zero_zero_nat))) (forall ((A tptp.int) (B tptp.int)) (= (= (@ (@ tptp.modulo_modulo_int A) B) A) (= (@ (@ tptp.divide_divide_int A) B) tptp.zero_zero_int))) (forall ((A tptp.code_natural) (B tptp.code_natural)) (= (= (@ (@ tptp.modulo8411746178871703098atural A) B) A) (= (@ (@ tptp.divide5121882707175180666atural A) B) tptp.zero_z2226904508553997617atural))) (forall ((M2 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 M2))) _let_2) (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 N))) _let_2)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat M2)) _let_1) (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat N)) _let_1)))))) (forall ((M2 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 M2))) _let_2) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N))) _let_2)) (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int M2)) _let_1) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int N)) _let_1)))))) (forall ((M2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat tptp.one))) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat M2)) _let_1) (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat N)) _let_1)))) (forall ((M2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int tptp.one))) (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int M2)) _let_1) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int N)) _let_1)))) (forall ((A tptp.int) (C2 tptp.int) (B tptp.int)) (=> (= (@ (@ tptp.modulo_modulo_int A) C2) (@ (@ tptp.modulo_modulo_int B) C2)) (not (forall ((D5 tptp.int)) (not (= B (@ (@ tptp.plus_plus_int A) (@ (@ tptp.times_times_int C2) D5)))))))) (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc (@ (@ tptp.modulo_modulo_nat M2) N)))) (let ((_let_2 (@ (@ tptp.modulo_modulo_nat (@ tptp.suc M2)) N))) (let ((_let_3 (= _let_1 N))) (and (=> _let_3 (= _let_2 tptp.zero_zero_nat)) (=> (not _let_3) (= _let_2 _let_1))))))) (forall ((P2 (-> tptp.nat Bool)) (N tptp.nat) (P tptp.nat) (M2 tptp.nat)) (=> (@ P2 N) (=> (@ (@ tptp.ord_less_nat N) P) (=> (@ (@ tptp.ord_less_nat M2) P) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N3) P) (=> (@ P2 N3) (@ P2 (@ (@ tptp.modulo_modulo_nat (@ tptp.suc N3)) P))))) (@ P2 M2)))))) (forall ((N tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_nat (@ (@ tptp.modulo_modulo_nat M2) N)) N))) (forall ((P2 (-> tptp.nat tptp.nat Bool)) (M2 tptp.nat) (N tptp.nat)) (=> (forall ((M tptp.nat)) (@ (@ P2 M) tptp.zero_zero_nat)) (=> (forall ((M tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N3) (=> (@ (@ P2 N3) (@ (@ tptp.modulo_modulo_nat M) N3)) (@ (@ P2 M) N3)))) (@ (@ P2 M2) N)))) (forall ((M2 tptp.nat) (N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.modulo_modulo_nat M2) (@ tptp.suc N))) N)) (forall ((M2 tptp.nat) (D tptp.nat)) (=> (= (@ (@ tptp.modulo_modulo_nat M2) D) tptp.zero_zero_nat) (exists ((Q3 tptp.nat)) (= M2 (@ (@ tptp.times_times_nat D) Q3))))) (forall ((M2 tptp.nat) (N tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat M2) N)) (= (@ (@ tptp.modulo_modulo_nat M2) N) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.minus_minus_nat M2) N)) N)))) (forall ((N tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M2) (= (@ (@ tptp.modulo_modulo_nat M2) N) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.minus_minus_nat M2) N)) N)))) (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))))))) (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat A) B) (= (@ (@ tptp.modulo_modulo_nat A) B) A)))) (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int A) B) (= (@ (@ tptp.modulo_modulo_int A) B) A)))) (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ (@ tptp.modulo_modulo_nat A) B)))) (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.modulo_modulo_int A) B)))) (forall ((N tptp.num) (Q2 tptp.num)) (= (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 N))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Q2))) tptp.zero_zero_nat) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat N)) (@ tptp.numeral_numeral_nat Q2)) tptp.zero_zero_nat))) (forall ((N tptp.num) (Q2 tptp.num)) (= (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N))) (@ tptp.numeral_numeral_int (@ tptp.bit0 Q2))) tptp.zero_zero_int) (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int N)) (@ tptp.numeral_numeral_int Q2)) tptp.zero_zero_int))) (forall ((N tptp.num)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat N)) (@ tptp.numeral_numeral_nat tptp.one)) tptp.zero_zero_nat)) (forall ((N tptp.num)) (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int N)) (@ tptp.numeral_numeral_int tptp.one)) tptp.zero_zero_int)) (forall ((Q2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 Q2)))) (not (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat tptp.one)) _let_1) (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 N))) _let_1))))) (forall ((Q2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 Q2)))) (not (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int tptp.one)) _let_1) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N))) _let_1))))) (forall ((M2 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 M2))) _let_1) (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat tptp.one)) _let_1))))) (forall ((M2 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 M2))) _let_1) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int tptp.one)) _let_1))))) (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (= (@ (@ tptp.divide_divide_nat (@ _let_1 B)) C2) (@ (@ tptp.plus_plus_nat (@ _let_1 (@ (@ tptp.divide_divide_nat B) C2))) (@ (@ tptp.divide_divide_nat (@ _let_1 (@ (@ tptp.modulo_modulo_nat B) C2))) C2))))) (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (= (@ (@ tptp.divide_divide_int (@ _let_1 B)) C2) (@ (@ tptp.plus_plus_int (@ _let_1 (@ (@ tptp.divide_divide_int B) C2))) (@ (@ tptp.divide_divide_int (@ _let_1 (@ (@ tptp.modulo_modulo_int B) C2))) C2))))) (forall ((A tptp.code_natural) (B tptp.code_natural) (C2 tptp.code_natural)) (let ((_let_1 (@ tptp.times_2397367101498566445atural A))) (= (@ (@ tptp.divide5121882707175180666atural (@ _let_1 B)) C2) (@ (@ tptp.plus_p4538020629002901425atural (@ _let_1 (@ (@ tptp.divide5121882707175180666atural B) C2))) (@ (@ tptp.divide5121882707175180666atural (@ _let_1 (@ (@ tptp.modulo8411746178871703098atural B) C2))) C2))))) (forall ((B tptp.nat) (A tptp.nat) (C2 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))) C2) (@ (@ tptp.plus_plus_nat A) C2))) (forall ((B tptp.int) (A tptp.int) (C2 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))) C2) (@ (@ tptp.plus_plus_int A) C2))) (forall ((B tptp.code_natural) (A tptp.code_natural) (C2 tptp.code_natural)) (= (@ (@ tptp.plus_p4538020629002901425atural (@ (@ tptp.plus_p4538020629002901425atural (@ (@ tptp.times_2397367101498566445atural B) (@ (@ tptp.divide5121882707175180666atural A) B))) (@ (@ tptp.modulo8411746178871703098atural A) B))) C2) (@ (@ tptp.plus_p4538020629002901425atural A) C2))) (forall ((A tptp.nat) (B tptp.nat) (C2 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))) C2) (@ (@ tptp.plus_plus_nat A) C2))) (forall ((A tptp.int) (B tptp.int) (C2 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))) C2) (@ (@ tptp.plus_plus_int A) C2))) (forall ((A tptp.code_natural) (B tptp.code_natural) (C2 tptp.code_natural)) (= (@ (@ tptp.plus_p4538020629002901425atural (@ (@ tptp.plus_p4538020629002901425atural (@ (@ tptp.times_2397367101498566445atural (@ (@ tptp.divide5121882707175180666atural A) B)) B)) (@ (@ tptp.modulo8411746178871703098atural A) B))) C2) (@ (@ tptp.plus_p4538020629002901425atural A) C2))) (forall ((A tptp.nat) (B tptp.nat)) (= A (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat A) B)) B)) (@ (@ tptp.modulo_modulo_nat A) B)))) (forall ((A tptp.int) (B tptp.int)) (= A (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int A) B)) B)) (@ (@ tptp.modulo_modulo_int A) B)))) (forall ((A tptp.code_natural) (B tptp.code_natural)) (= A (@ (@ tptp.plus_p4538020629002901425atural (@ (@ tptp.times_2397367101498566445atural (@ (@ tptp.divide5121882707175180666atural A) B)) B)) (@ (@ tptp.modulo8411746178871703098atural A) B)))) (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat A) B)) B)) (@ (@ tptp.modulo_modulo_nat A) B)) A)) (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int A) B)) B)) (@ (@ tptp.modulo_modulo_int A) B)) A)) (forall ((A tptp.code_natural) (B tptp.code_natural)) (= (@ (@ tptp.plus_p4538020629002901425atural (@ (@ tptp.times_2397367101498566445atural (@ (@ tptp.divide5121882707175180666atural A) B)) B)) (@ (@ tptp.modulo8411746178871703098atural A) B)) A)) (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat A) B)) (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat A) B)) B)) A)) (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.modulo_modulo_int A) B)) (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int A) B)) B)) A)) (forall ((A tptp.code_natural) (B tptp.code_natural)) (= (@ (@ tptp.plus_p4538020629002901425atural (@ (@ tptp.modulo8411746178871703098atural A) B)) (@ (@ tptp.times_2397367101498566445atural (@ (@ tptp.divide5121882707175180666atural A) B)) B)) A)) (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat A) B)) (@ (@ tptp.times_times_nat B) (@ (@ tptp.divide_divide_nat A) B))) A)) (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.modulo_modulo_int A) B)) (@ (@ tptp.times_times_int B) (@ (@ tptp.divide_divide_int A) B))) A)) (forall ((A tptp.code_natural) (B tptp.code_natural)) (= (@ (@ tptp.plus_p4538020629002901425atural (@ (@ tptp.modulo8411746178871703098atural A) B)) (@ (@ tptp.times_2397367101498566445atural B) (@ (@ tptp.divide5121882707175180666atural A) B))) A)) (forall ((B tptp.nat) (A tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat B) (@ (@ tptp.divide_divide_nat A) B))) (@ (@ tptp.modulo_modulo_nat A) B)) A)) (forall ((B tptp.int) (A tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) (@ (@ tptp.divide_divide_int A) B))) (@ (@ tptp.modulo_modulo_int A) B)) A)) (forall ((B tptp.code_natural) (A tptp.code_natural)) (= (@ (@ tptp.plus_p4538020629002901425atural (@ (@ tptp.times_2397367101498566445atural B) (@ (@ tptp.divide5121882707175180666atural A) B))) (@ (@ tptp.modulo8411746178871703098atural A) B)) A)) (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.minus_minus_nat A) (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat A) B)) B)) (@ (@ tptp.modulo_modulo_nat A) B))) (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.minus_minus_int A) (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int A) B)) B)) (@ (@ tptp.modulo_modulo_int A) B))) (forall ((A tptp.code_natural) (B tptp.code_natural)) (= (@ (@ tptp.minus_7197305767214868737atural A) (@ (@ tptp.times_2397367101498566445atural (@ (@ tptp.divide5121882707175180666atural A) B)) B)) (@ (@ tptp.modulo8411746178871703098atural A) B))) (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.minus_minus_nat A) (@ (@ tptp.modulo_modulo_nat A) B)) (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat A) B)) B))) (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.minus_minus_int A) (@ (@ tptp.modulo_modulo_int A) B)) (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int A) B)) B))) (forall ((A tptp.code_natural) (B tptp.code_natural)) (= (@ (@ tptp.minus_7197305767214868737atural A) (@ (@ tptp.modulo8411746178871703098atural A) B)) (@ (@ tptp.times_2397367101498566445atural (@ (@ tptp.divide5121882707175180666atural A) B)) B))) (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.minus_minus_nat A) (@ (@ tptp.modulo_modulo_nat A) B)) (@ (@ tptp.times_times_nat B) (@ (@ tptp.divide_divide_nat A) B)))) (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.minus_minus_int A) (@ (@ tptp.modulo_modulo_int A) B)) (@ (@ tptp.times_times_int B) (@ (@ tptp.divide_divide_int A) B)))) (forall ((A tptp.code_natural) (B tptp.code_natural)) (= (@ (@ tptp.minus_7197305767214868737atural A) (@ (@ tptp.modulo8411746178871703098atural A) B)) (@ (@ tptp.times_2397367101498566445atural B) (@ (@ tptp.divide5121882707175180666atural A) B)))) (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.minus_minus_nat A) (@ (@ tptp.times_times_nat B) (@ (@ tptp.divide_divide_nat A) B))) (@ (@ tptp.modulo_modulo_nat A) B))) (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.minus_minus_int A) (@ (@ tptp.times_times_int B) (@ (@ tptp.divide_divide_int A) B))) (@ (@ tptp.modulo_modulo_int A) B))) (forall ((A tptp.code_natural) (B tptp.code_natural)) (= (@ (@ tptp.minus_7197305767214868737atural A) (@ (@ tptp.times_2397367101498566445atural B) (@ (@ tptp.divide5121882707175180666atural A) B))) (@ (@ tptp.modulo8411746178871703098atural A) B))) (forall ((N tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.modulo_modulo_nat M2) N)) N))) (forall ((A4 tptp.nat) (B5 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat A4) B5) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (= (@ (@ tptp.modulo_modulo_nat A4) N) tptp.zero_zero_nat) (=> (= (@ (@ tptp.modulo_modulo_nat B5) N) tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.divide_divide_nat A4) N)) (@ (@ tptp.divide_divide_nat B5) N))))))) (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))))))) (forall ((M2 tptp.nat) (Q2 tptp.nat) (N tptp.nat)) (=> (= (@ (@ tptp.modulo_modulo_nat M2) Q2) (@ (@ tptp.modulo_modulo_nat N) Q2)) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (not (forall ((S tptp.nat)) (not (= N (@ (@ tptp.plus_plus_nat M2) (@ (@ tptp.times_times_nat Q2) S))))))))) (forall ((M2 tptp.nat) (Q2 tptp.nat) (N tptp.nat)) (=> (= (@ (@ tptp.modulo_modulo_nat M2) Q2) (@ (@ tptp.modulo_modulo_nat N) Q2)) (=> (@ (@ tptp.ord_less_eq_nat N) M2) (not (forall ((S tptp.nat)) (not (= M2 (@ (@ tptp.plus_plus_nat N) (@ (@ tptp.times_times_nat Q2) S))))))))) (forall ((M2 tptp.nat) (N tptp.nat) (Q2 tptp.nat)) (let ((_let_1 (@ tptp.modulo_modulo_nat M2))) (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 M2) N)) Q2))) (@ _let_1 N)))))) (forall ((A4 tptp.nat) (N tptp.nat)) (= A4 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat A4) N)) N)) (@ (@ tptp.modulo_modulo_nat A4) N)))) _let_270 (forall ((A tptp.code_natural) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri3763490453095760265atural M2))) (let ((_let_2 (@ tptp.modulo8411746178871703098atural A))) (let ((_let_3 (@ tptp.semiri3763490453095760265atural N))) (let ((_let_4 (@ tptp.times_2397367101498566445atural _let_1))) (= (@ _let_2 (@ _let_4 _let_3)) (@ (@ tptp.plus_p4538020629002901425atural (@ _let_4 (@ (@ tptp.modulo8411746178871703098atural (@ (@ tptp.divide5121882707175180666atural A) _let_1)) _let_3))) (@ _let_2 _let_1)))))))) (forall ((A tptp.int) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int M2))) (let ((_let_2 (@ tptp.modulo_modulo_int A))) (let ((_let_3 (@ tptp.semiri1314217659103216013at_int N))) (let ((_let_4 (@ tptp.times_times_int _let_1))) (= (@ _let_2 (@ _let_4 _let_3)) (@ (@ tptp.plus_plus_int (@ _let_4 (@ (@ tptp.modulo_modulo_int (@ (@ tptp.divide_divide_int A) _let_1)) _let_3))) (@ _let_2 _let_1)))))))) (forall ((A tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri1316708129612266289at_nat M2))) (let ((_let_2 (@ tptp.modulo_modulo_nat A))) (let ((_let_3 (@ tptp.semiri1316708129612266289at_nat N))) (let ((_let_4 (@ tptp.times_times_nat _let_1))) (= (@ _let_2 (@ _let_4 _let_3)) (@ (@ tptp.plus_plus_nat (@ _let_4 (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.divide_divide_nat A) _let_1)) _let_3))) (@ _let_2 _let_1)))))))) (forall ((P2 (-> tptp.nat Bool)) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (= N tptp.zero_zero_nat))) (= (@ P2 (@ (@ tptp.modulo_modulo_nat M2) N)) (and (=> _let_1 (@ P2 M2)) (=> (not _let_1) (forall ((I tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_nat J) N) (=> (= M2 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat N) I)) J)) (@ P2 J))))))))) (forall ((C2 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) C2) (= (@ _let_1 (@ _let_2 C2)) (@ (@ tptp.plus_plus_nat (@ _let_2 (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.divide_divide_nat A) B)) C2))) (@ _let_1 B))))))) (forall ((C2 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) C2) (= (@ _let_1 (@ _let_2 C2)) (@ (@ tptp.plus_plus_int (@ _let_2 (@ (@ tptp.modulo_modulo_int (@ (@ tptp.divide_divide_int A) B)) C2))) (@ _let_1 B))))))) (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)) M2) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ (@ tptp.times_times_nat M2) N))) M2) tptp.one_one_nat))) (forall ((N tptp.nat) (Xs2 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ tptp.size_s6755466524823107622T_VEBT Xs2))) (=> (@ (@ tptp.ord_less_nat N) _let_1) (= (@ (@ tptp.nth_VEBT_VEBT (@ tptp.rotate1_VEBT_VEBT Xs2)) N) (@ (@ tptp.nth_VEBT_VEBT Xs2) (@ (@ tptp.modulo_modulo_nat (@ tptp.suc N)) _let_1)))))) (forall ((N tptp.nat) (Xs2 tptp.list_o)) (let ((_let_1 (@ tptp.size_size_list_o Xs2))) (=> (@ (@ tptp.ord_less_nat N) _let_1) (= (@ (@ tptp.nth_o (@ tptp.rotate1_o Xs2)) N) (@ (@ tptp.nth_o Xs2) (@ (@ tptp.modulo_modulo_nat (@ tptp.suc N)) _let_1)))))) (forall ((N tptp.nat) (Xs2 tptp.list_nat)) (let ((_let_1 (@ tptp.size_size_list_nat Xs2))) (=> (@ (@ tptp.ord_less_nat N) _let_1) (= (@ (@ tptp.nth_nat (@ tptp.rotate1_nat Xs2)) N) (@ (@ tptp.nth_nat Xs2) (@ (@ tptp.modulo_modulo_nat (@ tptp.suc N)) _let_1)))))) (forall ((N tptp.nat) (Xs2 tptp.list_int)) (let ((_let_1 (@ tptp.size_size_list_int Xs2))) (=> (@ (@ tptp.ord_less_nat N) _let_1) (= (@ (@ tptp.nth_int (@ tptp.rotate1_int Xs2)) N) (@ (@ tptp.nth_int Xs2) (@ (@ tptp.modulo_modulo_nat (@ tptp.suc N)) _let_1)))))) (forall ((B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.modulo_modulo_nat A))) (let ((_let_2 (@ _let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) B)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B) (=> (@ (@ tptp.ord_less_nat _let_2) B) (= _let_2 (@ _let_1 B))))))) (forall ((B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.modulo_modulo_int A))) (let ((_let_2 (@ _let_1 (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) B)))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (=> (@ (@ tptp.ord_less_int _let_2) B) (= _let_2 (@ _let_1 B))))))) (forall ((A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (= (@ (@ tptp.divide_divide_nat A) _let_1) A) (= (@ (@ tptp.plus_plus_nat A) (@ (@ tptp.modulo_modulo_nat A) _let_1)) tptp.zero_zero_nat)))) (forall ((A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (=> (= (@ (@ tptp.divide_divide_int A) _let_1) A) (= (@ (@ tptp.plus_plus_int A) (@ (@ tptp.modulo_modulo_int A) _let_1)) tptp.zero_zero_int)))) (forall ((A tptp.code_natural)) (let ((_let_1 (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one)))) (=> (= (@ (@ tptp.divide5121882707175180666atural A) _let_1) A) (= (@ (@ tptp.plus_p4538020629002901425atural A) (@ (@ tptp.modulo8411746178871703098atural A) _let_1)) tptp.zero_z2226904508553997617atural)))) (forall ((A4 tptp.nat) (B5 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat A4) B5) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.divide_divide_nat A4) N)) (@ (@ (@ tptp.if_nat (= (@ (@ tptp.modulo_modulo_nat B5) N) tptp.zero_zero_nat)) tptp.one_one_nat) tptp.zero_zero_nat))) (@ (@ tptp.divide_divide_nat B5) N))))) (forall ((B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat A))) (let ((_let_2 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ _let_2 B))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.modulo_modulo_nat A) _let_3)) B) (= (@ _let_2 (@ _let_1 _let_3)) (@ _let_1 B)))))))) (forall ((B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A))) (let ((_let_2 (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ _let_2 B))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.modulo_modulo_int A) _let_3)) B) (= (@ _let_2 (@ _let_1 _let_3)) (@ _let_1 B)))))))) (forall ((M2 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 M2))) (=> (@ (@ tptp.ord_less_eq_nat M2) 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) M2)))) _let_2)))))) (forall ((M2 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 M2))) (=> (@ (@ tptp.ord_less_eq_nat M2) 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) M2)))) _let_2)))))) (forall ((M2 tptp.nat) (N tptp.nat) (A tptp.code_natural)) (let ((_let_1 (@ tptp.power_7079662738309270450atural (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 M2))) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ (@ tptp.modulo8411746178871703098atural (@ (@ tptp.times_2397367101498566445atural A) _let_2)) (@ _let_1 N)) (@ (@ tptp.times_2397367101498566445atural (@ (@ tptp.modulo8411746178871703098atural A) (@ _let_1 (@ (@ tptp.minus_minus_nat N) M2)))) _let_2)))))) (forall ((M2 tptp.nat) (X tptp.nat)) (let ((_let_1 (@ tptp.modulo_modulo_nat X))) (let ((_let_2 (@ _let_1 M2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M2)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M2) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) X) (or (= _let_3 _let_2) (= _let_3 (@ (@ tptp.plus_plus_nat _let_2) M2))))))))) (forall ((M2 tptp.int) (X tptp.int)) (let ((_let_1 (@ tptp.modulo_modulo_int X))) (let ((_let_2 (@ _let_1 M2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) M2)))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) M2) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X) (or (= _let_3 _let_2) (= _let_3 (@ (@ tptp.plus_plus_int _let_2) M2))))))))) (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.modulo_modulo_nat A))) (let ((_let_2 (@ _let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) B)))) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B) (=> (@ (@ tptp.ord_less_eq_nat B) _let_2) (= (@ (@ tptp.minus_minus_nat _let_2) B) (@ _let_1 B)))))))) (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.modulo_modulo_int A))) (let ((_let_2 (@ _let_1 (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) B)))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (=> (@ (@ tptp.ord_less_eq_int B) _let_2) (= (@ (@ tptp.minus_minus_int _let_2) B) (@ _let_1 B)))))))) (forall ((N tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se4205575877204974255it_nat (@ tptp.suc N)) A) (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat A) _let_1)) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se4205575877204974255it_nat N) (@ (@ tptp.divide_divide_nat A) _let_1))))))) (forall ((N tptp.nat) (A tptp.code_natural)) (let ((_let_1 (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se7083795435491715335atural (@ tptp.suc N)) A) (@ (@ tptp.plus_p4538020629002901425atural (@ (@ tptp.modulo8411746178871703098atural A) _let_1)) (@ (@ tptp.times_2397367101498566445atural _let_1) (@ (@ tptp.bit_se7083795435491715335atural N) (@ (@ tptp.divide5121882707175180666atural A) _let_1))))))) (forall ((N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se4203085406695923979it_int (@ tptp.suc N)) A) (@ (@ tptp.plus_plus_int (@ (@ tptp.modulo_modulo_int A) _let_1)) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se4203085406695923979it_int N) (@ (@ tptp.divide_divide_int A) _let_1))))))) (forall ((N tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_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))))))) (forall ((N tptp.nat) (A tptp.code_natural)) (let ((_let_1 (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se1617098188084679374atural (@ tptp.suc N)) A) (@ (@ tptp.plus_p4538020629002901425atural (@ (@ tptp.modulo8411746178871703098atural A) _let_1)) (@ (@ tptp.times_2397367101498566445atural _let_1) (@ (@ tptp.bit_se1617098188084679374atural N) (@ (@ tptp.divide5121882707175180666atural A) _let_1))))))) (forall ((N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se7879613467334960850it_int (@ tptp.suc N)) A) (@ (@ tptp.plus_plus_int (@ (@ tptp.modulo_modulo_int A) _let_1)) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se7879613467334960850it_int N) (@ (@ tptp.divide_divide_int A) _let_1))))))) (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.finite_card_complex (@ tptp.collect_complex (lambda ((Z4 tptp.complex)) (= (@ (@ tptp.power_power_complex Z4) N) tptp.one_one_complex)))) N))) (forall ((C2 tptp.complex) (N tptp.nat)) (=> (not (= C2 tptp.zero_zero_complex)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.finite_card_complex (@ tptp.collect_complex (lambda ((Z4 tptp.complex)) (= (@ (@ tptp.power_power_complex Z4) N) C2)))) N)))) (forall ((N tptp.nat) (Xs2 tptp.list_Code_integer) (Ys tptp.list_Code_integer)) (let ((_let_1 (@ tptp.size_s3445333598471063425nteger Ys))) (=> (@ (@ tptp.ord_less_nat N) (@ (@ tptp.times_times_nat (@ tptp.size_s3445333598471063425nteger Xs2)) _let_1)) (= (@ (@ tptp.nth_Pr2304437835452373666nteger (@ (@ tptp.produc8792966785426426881nteger Xs2) Ys)) N) (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.nth_Code_integer Xs2) (@ (@ tptp.divide_divide_nat N) _let_1))) (@ (@ tptp.nth_Code_integer Ys) (@ (@ tptp.modulo_modulo_nat N) _let_1))))))) (forall ((N tptp.nat) (Xs2 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 Xs2)) _let_1)) (= (@ (@ tptp.nth_Pr4953567300277697838T_VEBT (@ (@ tptp.produc4743750530478302277T_VEBT Xs2) Ys)) N) (@ (@ tptp.produc537772716801021591T_VEBT (@ (@ tptp.nth_VEBT_VEBT Xs2) (@ (@ tptp.divide_divide_nat N) _let_1))) (@ (@ tptp.nth_VEBT_VEBT Ys) (@ (@ tptp.modulo_modulo_nat N) _let_1))))))) (forall ((N tptp.nat) (Xs2 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 Xs2)) _let_1)) (= (@ (@ tptp.nth_Pr4606735188037164562VEBT_o (@ (@ tptp.product_VEBT_VEBT_o Xs2) Ys)) N) (@ (@ tptp.produc8721562602347293563VEBT_o (@ (@ tptp.nth_VEBT_VEBT Xs2) (@ (@ tptp.divide_divide_nat N) _let_1))) (@ (@ tptp.nth_o Ys) (@ (@ tptp.modulo_modulo_nat N) _let_1))))))) (forall ((N tptp.nat) (Xs2 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 Xs2)) _let_1)) (= (@ (@ tptp.nth_Pr1791586995822124652BT_nat (@ (@ tptp.produc7295137177222721919BT_nat Xs2) Ys)) N) (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.nth_VEBT_VEBT Xs2) (@ (@ tptp.divide_divide_nat N) _let_1))) (@ (@ tptp.nth_nat Ys) (@ (@ tptp.modulo_modulo_nat N) _let_1))))))) (forall ((N tptp.nat) (Xs2 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 Xs2)) _let_1)) (= (@ (@ tptp.nth_Pr6837108013167703752BT_int (@ (@ tptp.produc7292646706713671643BT_int Xs2) Ys)) N) (@ (@ tptp.produc736041933913180425BT_int (@ (@ tptp.nth_VEBT_VEBT Xs2) (@ (@ tptp.divide_divide_nat N) _let_1))) (@ (@ tptp.nth_int Ys) (@ (@ tptp.modulo_modulo_nat N) _let_1))))))) (forall ((N tptp.nat) (Xs2 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 Xs2)) _let_1)) (= (@ (@ tptp.nth_Pr6777367263587873994T_VEBT (@ (@ tptp.product_o_VEBT_VEBT Xs2) Ys)) N) (@ (@ tptp.produc2982872950893828659T_VEBT (@ (@ tptp.nth_o Xs2) (@ (@ tptp.divide_divide_nat N) _let_1))) (@ (@ tptp.nth_VEBT_VEBT Ys) (@ (@ tptp.modulo_modulo_nat N) _let_1))))))) (forall ((N tptp.nat) (Xs2 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 Xs2)) _let_1)) (= (@ (@ tptp.nth_Product_prod_o_o (@ (@ tptp.product_o_o Xs2) Ys)) N) (@ (@ tptp.product_Pair_o_o (@ (@ tptp.nth_o Xs2) (@ (@ tptp.divide_divide_nat N) _let_1))) (@ (@ tptp.nth_o Ys) (@ (@ tptp.modulo_modulo_nat N) _let_1))))))) (forall ((N tptp.nat) (Xs2 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 Xs2)) _let_1)) (= (@ (@ tptp.nth_Pr5826913651314560976_o_nat (@ (@ tptp.product_o_nat Xs2) Ys)) N) (@ (@ tptp.product_Pair_o_nat (@ (@ tptp.nth_o Xs2) (@ (@ tptp.divide_divide_nat N) _let_1))) (@ (@ tptp.nth_nat Ys) (@ (@ tptp.modulo_modulo_nat N) _let_1))))))) (forall ((N tptp.nat) (Xs2 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 Xs2)) _let_1)) (= (@ (@ tptp.nth_Pr1649062631805364268_o_int (@ (@ tptp.product_o_int Xs2) Ys)) N) (@ (@ tptp.product_Pair_o_int (@ (@ tptp.nth_o Xs2) (@ (@ tptp.divide_divide_nat N) _let_1))) (@ (@ tptp.nth_int Ys) (@ (@ tptp.modulo_modulo_nat N) _let_1))))))) (forall ((N tptp.nat) (Xs2 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 Xs2)) _let_1)) (= (@ (@ tptp.nth_Pr744662078594809490T_VEBT (@ (@ tptp.produc7156399406898700509T_VEBT Xs2) Ys)) N) (@ (@ tptp.produc599794634098209291T_VEBT (@ (@ tptp.nth_nat Xs2) (@ (@ tptp.divide_divide_nat N) _let_1))) (@ (@ tptp.nth_VEBT_VEBT Ys) (@ (@ tptp.modulo_modulo_nat N) _let_1))))))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.divide6298287555418463151nteger A))) (let ((_let_2 (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ _let_2 B))) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) B) (=> (@ (@ tptp.ord_le3102999989581377725nteger B) (@ (@ tptp.modulo364778990260209775nteger A) _let_3)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ _let_2 (@ _let_1 _let_3))) tptp.one_one_Code_integer) (@ _let_1 B))))))))) (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat A))) (let ((_let_2 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ _let_2 B))) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B) (=> (@ (@ tptp.ord_less_eq_nat B) (@ (@ tptp.modulo_modulo_nat A) _let_3)) (= (@ (@ tptp.plus_plus_nat (@ _let_2 (@ _let_1 _let_3))) tptp.one_one_nat) (@ _let_1 B))))))))) (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A))) (let ((_let_2 (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ _let_2 B))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (=> (@ (@ tptp.ord_less_eq_int B) (@ (@ tptp.modulo_modulo_int A) _let_3)) (= (@ (@ tptp.plus_plus_int (@ _let_2 (@ _let_1 _let_3))) tptp.one_one_int) (@ _let_1 B))))))))) (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y tptp.vEBT_VEBT)) (=> (= (@ (@ tptp.vEBT_VEBT_insert X) Xa2) Y) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_insert_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa2)) (=> (forall ((A3 Bool) (B3 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A3) B3))) (=> (= X _let_1) (=> (= Y (@ (@ tptp.vEBT_vebt_insert _let_1) Xa2)) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_insert_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (not (forall ((Info tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info) Deg2) TreeList) Summary2))) (let ((_let_2 (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Deg2)) Xa2))) (=> (= X _let_1) (=> (and (=> _let_2 (= Y _let_1)) (=> (not _let_2) (= Y (@ (@ tptp.vEBT_vebt_insert _let_1) Xa2)))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_insert_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))))))))) (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y Bool)) (=> (= (@ (@ tptp.vEBT_vebt_member X) Xa2) Y) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa2)) (=> (forall ((A3 Bool) (B3 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A3) B3))) (let ((_let_2 (= Xa2 tptp.one_one_nat))) (let ((_let_3 (= Xa2 tptp.zero_zero_nat))) (=> (= X _let_1) (=> (= Y (and (=> _let_3 A3) (=> (not _let_3) (and (=> _let_2 B3) _let_2)))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))))) (=> (forall ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw))) (=> (= X _let_1) (=> (not Y) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((V tptp.product_prod_nat_nat) (Uy tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V)) tptp.zero_zero_nat) Uy) Uz2))) (=> (= X _let_1) (=> (not Y) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((V tptp.product_prod_nat_nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V)) (@ tptp.suc tptp.zero_zero_nat)) Vb2) Vc2))) (=> (= X _let_1) (=> (not Y) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList) 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 TreeList)))) (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 TreeList) _let_4)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_3))) _let_5)))))))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa2))))))))))))))))))))) (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (not (@ (@ tptp.vEBT_vebt_member X) Xa2)) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa2)) (=> (forall ((A3 Bool) (B3 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (let ((_let_3 (@ (@ tptp.vEBT_Leaf A3) B3))) (=> (= X _let_3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_3) Xa2)) (and (=> _let_2 A3) (=> (not _let_2) (and (=> _let_1 B3) _let_1))))))))) (=> (forall ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw))) (=> (= X _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2)))))) (=> (forall ((V tptp.product_prod_nat_nat) (Uy tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V)) tptp.zero_zero_nat) Uy) Uz2))) (=> (= X _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2)))))) (=> (forall ((V tptp.product_prod_nat_nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V)) (@ tptp.suc tptp.zero_zero_nat)) Vb2) Vc2))) (=> (= X _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2)))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList)))) (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) TreeList) 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 TreeList) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_2))) _let_4))))))))))))))))))))))))) (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y Bool)) (=> (= (@ (@ tptp.vEBT_V5719532721284313246member X) Xa2) Y) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa2)) (=> (forall ((A3 Bool) (B3 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A3) B3))) (let ((_let_2 (= Xa2 tptp.one_one_nat))) (let ((_let_3 (= Xa2 tptp.zero_zero_nat))) (=> (= X _let_1) (=> (= Y (and (=> _let_3 A3) (=> (not _let_3) (and (=> _let_2 B3) _let_2)))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))))) (=> (forall ((Uu2 tptp.option4927543243414619207at_nat) (Uv2 tptp.list_VEBT_VEBT) (Uw tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Uu2) tptp.zero_zero_nat) Uv2) Uw))) (=> (= X _let_1) (=> (not Y) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (not (forall ((Uy tptp.option4927543243414619207at_nat) (V tptp.nat) (TreeList tptp.list_VEBT_VEBT) (S tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node Uy) _let_1) TreeList) S))) (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 TreeList)))) (=> (= X _let_2) (=> (= Y (and (=> _let_5 (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_4)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_3))) _let_5)) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa2))))))))))))))))) (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (@ (@ tptp.vEBT_V5719532721284313246member X) Xa2) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa2)) (=> (forall ((A3 Bool) (B3 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (let ((_let_3 (@ (@ tptp.vEBT_Leaf A3) B3))) (=> (= X _let_3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_3) Xa2)) (not (and (=> _let_2 A3) (=> (not _let_2) (and (=> _let_1 B3) _let_1)))))))))) (not (forall ((Uy tptp.option4927543243414619207at_nat) (V tptp.nat) (TreeList tptp.list_VEBT_VEBT) (S tptp.vEBT_VEBT)) (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 Xa2) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList)))) (let ((_let_5 (@ (@ (@ (@ tptp.vEBT_Node Uy) _let_1) TreeList) S))) (=> (= 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 TreeList) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_2))) _let_4))))))))))))))) (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (not (@ (@ tptp.vEBT_V5719532721284313246member X) Xa2)) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa2)) (=> (forall ((A3 Bool) (B3 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (let ((_let_3 (@ (@ tptp.vEBT_Leaf A3) B3))) (=> (= X _let_3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_3) Xa2)) (and (=> _let_2 A3) (=> (not _let_2) (and (=> _let_1 B3) _let_1))))))))) (=> (forall ((Uu2 tptp.option4927543243414619207at_nat) (Uv2 tptp.list_VEBT_VEBT) (Uw tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Uu2) tptp.zero_zero_nat) Uv2) Uw))) (=> (= X _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2)))))) (not (forall ((Uy tptp.option4927543243414619207at_nat) (V tptp.nat) (TreeList tptp.list_VEBT_VEBT) (S tptp.vEBT_VEBT)) (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 Xa2) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList)))) (let ((_let_5 (@ (@ (@ (@ tptp.vEBT_Node Uy) _let_1) TreeList) S))) (=> (= 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 TreeList) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_2))) _let_4))))))))))))))) (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (@ (@ tptp.vEBT_vebt_member X) Xa2) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa2)) (=> (forall ((A3 Bool) (B3 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (let ((_let_3 (@ (@ tptp.vEBT_Leaf A3) B3))) (=> (= X _let_3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_3) Xa2)) (not (and (=> _let_2 A3) (=> (not _let_2) (and (=> _let_1 B3) _let_1)))))))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList)))) (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) TreeList) 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 TreeList) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_2))) _let_4))))))))))))))))))))))) (forall ((V2 tptp.num) (W2 tptp.num)) (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit0 V2))) (@ tptp.numeral_numeral_int (@ tptp.bit0 W2))) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int V2)) (@ tptp.numeral_numeral_int W2))))) (forall ((M2 tptp.int) (K2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) M2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.modulo_modulo_int M2) K2)) M2))) (forall ((M2 tptp.int) (D tptp.int)) (= (= (@ (@ tptp.modulo_modulo_int M2) D) tptp.zero_zero_int) (exists ((Q5 tptp.int)) (= M2 (@ (@ tptp.times_times_int D) Q5))))) (forall ((M2 tptp.int) (D tptp.int)) (=> (= (@ (@ tptp.modulo_modulo_int M2) D) tptp.zero_zero_int) (exists ((Q3 tptp.int)) (= M2 (@ (@ tptp.times_times_int D) Q3))))) (forall ((A tptp.nat) (B tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.modulo_modulo_nat A) B)) (@ (@ tptp.modulo_modulo_int (@ tptp.semiri1314217659103216013at_int A)) (@ tptp.semiri1314217659103216013at_int B)))) (forall ((K2 tptp.int) (L tptp.int) (Q2 tptp.int) (R3 tptp.int)) (=> (@ (@ (@ tptp.eucl_rel_int K2) L) (@ (@ tptp.product_Pair_int_int Q2) R3)) (= (@ (@ tptp.modulo_modulo_int K2) L) R3))) (forall ((B tptp.int) (A tptp.int)) (let ((_let_1 (@ (@ tptp.modulo_modulo_int A) B))) (let ((_let_2 (@ tptp.ord_less_int B))) (=> (@ _let_2 tptp.zero_zero_int) (and (@ (@ tptp.ord_less_eq_int _let_1) tptp.zero_zero_int) (@ _let_2 _let_1)))))) (forall ((B tptp.int) (A tptp.int)) (let ((_let_1 (@ (@ tptp.modulo_modulo_int A) B))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) _let_1) (@ (@ tptp.ord_less_int _let_1) B))))) (forall ((I2 tptp.int) (K2 tptp.int)) (= (= (@ (@ tptp.modulo_modulo_int I2) K2) I2) (or (= K2 tptp.zero_zero_int) (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) I2) (@ (@ tptp.ord_less_int I2) K2)) (and (@ (@ tptp.ord_less_eq_int I2) tptp.zero_zero_int) (@ (@ tptp.ord_less_int K2) I2))))) (forall ((A4 tptp.int) (N tptp.int)) (= A4 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int A4) N)) N)) (@ (@ tptp.modulo_modulo_int A4) N)))) (forall ((K2 tptp.int) (L tptp.int)) (@ (@ (@ tptp.eucl_rel_int K2) L) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.divide_divide_int K2) L)) (@ (@ tptp.modulo_modulo_int K2) L)))) (forall ((L tptp.int) (K2 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) L) (=> (@ (@ tptp.ord_less_eq_int L) K2) (= (@ (@ tptp.modulo_modulo_int K2) L) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.minus_minus_int K2) L)) L))))) (forall ((A tptp.int) (B tptp.int) (Q2 tptp.int) (R3 tptp.int)) (=> (= A (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) Q2)) R3)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) R3) (=> (@ (@ tptp.ord_less_int R3) B) (= (@ (@ tptp.modulo_modulo_int A) B) R3))))) (forall ((A tptp.int) (B tptp.int) (Q2 tptp.int) (R3 tptp.int)) (=> (= A (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) Q2)) R3)) (=> (@ (@ tptp.ord_less_eq_int R3) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int B) R3) (= (@ (@ tptp.modulo_modulo_int A) B) R3))))) (forall ((P2 (-> tptp.int Bool)) (N tptp.int) (K2 tptp.int)) (= (@ P2 (@ (@ tptp.modulo_modulo_int N) K2)) (and (=> (= K2 tptp.zero_zero_int) (@ P2 N)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K2) (forall ((I tptp.int) (J tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) J) (@ (@ tptp.ord_less_int J) K2) (= N (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int K2) I)) J))) (@ P2 J)))) (=> (@ (@ tptp.ord_less_int K2) tptp.zero_zero_int) (forall ((I tptp.int) (J tptp.int)) (=> (and (@ (@ tptp.ord_less_int K2) J) (@ (@ tptp.ord_less_eq_int J) tptp.zero_zero_int) (= N (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int K2) I)) J))) (@ P2 J))))))) (forall ((C2 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) C2) (= (@ _let_1 (@ _let_2 C2)) (@ (@ tptp.plus_plus_int (@ _let_2 (@ (@ tptp.modulo_modulo_int (@ (@ tptp.divide_divide_int A) B)) C2))) (@ _let_1 B))))))) (forall ((K2 tptp.int) (P2 (-> tptp.int tptp.int Bool)) (N tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K2) (= (@ (@ P2 (@ (@ tptp.divide_divide_int N) K2)) (@ (@ tptp.modulo_modulo_int N) K2)) (forall ((I tptp.int) (J tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) J) (@ (@ tptp.ord_less_int J) K2) (= N (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int K2) I)) J))) (@ (@ P2 I) J)))))) (forall ((K2 tptp.int) (P2 (-> tptp.int tptp.int Bool)) (N tptp.int)) (=> (@ (@ tptp.ord_less_int K2) tptp.zero_zero_int) (= (@ (@ P2 (@ (@ tptp.divide_divide_int N) K2)) (@ (@ tptp.modulo_modulo_int N) K2)) (forall ((I tptp.int) (J tptp.int)) (=> (and (@ (@ tptp.ord_less_int K2) J) (@ (@ tptp.ord_less_eq_int J) tptp.zero_zero_int) (= N (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int K2) I)) J))) (@ (@ P2 I) J)))))) (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.plus_plus_int tptp.one_one_int))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (= (@ (@ tptp.modulo_modulo_int (@ _let_2 (@ _let_1 B))) (@ _let_1 A)) (@ _let_2 (@ _let_1 (@ (@ tptp.modulo_modulo_int B) A)))))))) (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ _let_1 B))) (@ _let_1 A)) (@ (@ tptp.minus_minus_int (@ _let_1 (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int B) tptp.one_one_int)) A))) tptp.one_one_int))))) (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 ((Ux tptp.list_VEBT_VEBT) (Uy tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) tptp.zero_zero_nat) Ux) Uy))) (=> (= 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) (Va2 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) Va2) 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) (V tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList) 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 TreeList)))) (=> (= X _let_2) (=> (= Y (or (= Xa2 Mi2) (= Xa2 Ma2) (and (=> _let_5 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList) _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 ((V tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Vd tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1) TreeList) Vd))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_3))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_4) (@ tptp.size_s6755466524823107622T_VEBT TreeList)))) (=> (= X _let_2) (=> (= Y (and (=> _let_5 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_4)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_3))) _let_5)) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa2))))))))))))))))))) (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (not (@ (@ tptp.vEBT_VEBT_membermima X) Xa2)) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa2)) (=> (forall ((Uu2 Bool) (Uv2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) (=> (= X _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2)))))) (=> (forall ((Ux tptp.list_VEBT_VEBT) (Uy tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) tptp.zero_zero_nat) Ux) Uy))) (=> (= 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) (Va2 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) Va2) 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) (V tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (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 Xa2) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList)))) (let ((_let_5 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList) 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 TreeList) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_2))) _let_4)))))))))) (not (forall ((V tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Vd tptp.vEBT_VEBT)) (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 Xa2) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList)))) (let ((_let_5 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1) TreeList) Vd))) (=> (= X _let_5) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_5) Xa2)) (and (=> _let_4 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_2))) _let_4))))))))))))))))) (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (@ (@ tptp.vEBT_VEBT_membermima X) Xa2) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa2)) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va2 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) Va2) 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) (V tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (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 Xa2) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList)))) (let ((_let_5 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList) 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 TreeList) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_2))) _let_4))))))))))) (not (forall ((V tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Vd tptp.vEBT_VEBT)) (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 Xa2) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList)))) (let ((_let_5 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1) TreeList) Vd))) (=> (= X _let_5) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_5) Xa2)) (not (and (=> _let_4 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_2))) _let_4)))))))))))))))) (= (@ tptp.arcosh_real tptp.one_one_real) tptp.zero_zero_real) (forall ((H tptp.real) (Z3 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 Z3))) (let ((_let_5 (@ (@ tptp.plus_plus_real Z3) H))) (=> (not (= H tptp.zero_zero_real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real Z3)) K5) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real _let_5)) K5) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real _let_5) N)) (@ _let_4 N))) H)) (@ _let_3 (@ _let_4 _let_2))))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ _let_3 (@ tptp.semiri5074537144036343181t_real _let_2))) (@ (@ tptp.power_power_real K5) (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ tptp.real_V7735802525324610683m_real H)))))))))))) (forall ((H tptp.complex) (Z3 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 Z3))) (let ((_let_4 (@ (@ tptp.plus_plus_complex Z3) H))) (=> (not (= H tptp.zero_zero_complex)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex Z3)) K5) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex _let_4)) K5) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ (@ tptp.power_power_complex _let_4) N)) (@ _let_3 N))) H)) (@ (@ 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 H))))))))))) (forall ((N tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se2161824704523386999it_nat (@ tptp.suc N)) A) (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat A) _let_1)) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se2161824704523386999it_nat N) (@ (@ tptp.divide_divide_nat A) _let_1))))))) (forall ((N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se2159334234014336723it_int (@ tptp.suc N)) A) (@ (@ tptp.plus_plus_int (@ (@ tptp.modulo_modulo_int A) _let_1)) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se2159334234014336723it_int N) (@ (@ tptp.divide_divide_int A) _let_1))))))) (forall ((N tptp.nat) (A tptp.code_natural)) (let ((_let_1 (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se168947363167071951atural (@ tptp.suc N)) A) (@ (@ tptp.plus_p4538020629002901425atural (@ (@ tptp.modulo8411746178871703098atural A) _let_1)) (@ (@ tptp.times_2397367101498566445atural _let_1) (@ (@ tptp.bit_se168947363167071951atural N) (@ (@ tptp.divide5121882707175180666atural A) _let_1))))))) (= (@ tptp.artanh_real tptp.zero_zero_real) tptp.zero_zero_real) (forall ((W2 tptp.num) (A tptp.real)) (let ((_let_1 (@ tptp.times_times_real (@ tptp.numeral_numeral_real W2)))) (= (@ tptp.real_V7735802525324610683m_real (@ _let_1 A)) (@ _let_1 (@ tptp.real_V7735802525324610683m_real A))))) (forall ((W2 tptp.num) (A tptp.complex)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex W2)) A)) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real W2)) (@ tptp.real_V1022390504157884413omplex A)))) (forall ((A tptp.real) (W2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real W2))) (= (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.times_times_real A) _let_1)) (@ (@ tptp.times_times_real (@ tptp.real_V7735802525324610683m_real A)) _let_1)))) (forall ((A tptp.complex) (W2 tptp.num)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.times_times_complex A) (@ tptp.numera6690914467698888265omplex W2))) (@ (@ tptp.times_times_real (@ tptp.real_V1022390504157884413omplex A)) (@ tptp.numeral_numeral_real W2)))) (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real X)) tptp.zero_zero_real) (= X tptp.zero_zero_real))) (forall ((X tptp.complex)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex X)) tptp.zero_zero_real) (= X tptp.zero_zero_complex))) (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.real_V7735802525324610683m_real X)) (not (= X tptp.zero_zero_real)))) (forall ((X tptp.complex)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.real_V1022390504157884413omplex X)) (not (= X tptp.zero_zero_complex)))) (= (@ tptp.real_V7735802525324610683m_real tptp.zero_zero_real) tptp.zero_zero_real) (= (@ tptp.real_V1022390504157884413omplex tptp.zero_zero_complex) tptp.zero_zero_real) (forall ((X tptp.real)) (= (= (@ tptp.real_V7735802525324610683m_real X) tptp.zero_zero_real) (= X tptp.zero_zero_real))) (forall ((X tptp.complex)) (= (= (@ tptp.real_V1022390504157884413omplex X) tptp.zero_zero_real) (= X tptp.zero_zero_complex))) (forall ((Z3 tptp.real) (W2 tptp.real) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real Z3)) tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real W2)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real Z3) M2)) (@ (@ tptp.power_power_real W2) M2)))) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real M2)) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real Z3) W2))))))) (forall ((Z3 tptp.complex) (W2 tptp.complex) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex Z3)) tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex W2)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex (@ (@ tptp.power_power_complex Z3) M2)) (@ (@ tptp.power_power_complex W2) M2)))) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real M2)) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex Z3) W2))))))) (forall ((X tptp.real) (Y tptp.real)) (= (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.times_times_real X) Y)) (@ (@ tptp.times_times_real (@ tptp.real_V7735802525324610683m_real X)) (@ tptp.real_V7735802525324610683m_real Y)))) (forall ((X tptp.complex) (Y tptp.complex)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.times_times_complex X) Y)) (@ (@ tptp.times_times_real (@ tptp.real_V1022390504157884413omplex X)) (@ tptp.real_V1022390504157884413omplex Y)))) (forall ((B tptp.real) (A tptp.real)) (=> (not (= B tptp.zero_zero_real)) (= (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.divide_divide_real A) B)) (@ (@ tptp.divide_divide_real (@ tptp.real_V7735802525324610683m_real A)) (@ tptp.real_V7735802525324610683m_real B))))) (forall ((B tptp.complex) (A tptp.complex)) (=> (not (= B tptp.zero_zero_complex)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.divide1717551699836669952omplex A) B)) (@ (@ tptp.divide_divide_real (@ tptp.real_V1022390504157884413omplex A)) (@ tptp.real_V1022390504157884413omplex B))))) (forall ((W2 tptp.real) (N tptp.nat) (Z3 tptp.real)) (=> (= (@ (@ tptp.power_power_real W2) N) (@ (@ tptp.power_power_real Z3) N)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.real_V7735802525324610683m_real W2) (@ tptp.real_V7735802525324610683m_real Z3))))) (forall ((W2 tptp.complex) (N tptp.nat) (Z3 tptp.complex)) (=> (= (@ (@ tptp.power_power_complex W2) N) (@ (@ tptp.power_power_complex Z3) N)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.real_V1022390504157884413omplex W2) (@ tptp.real_V1022390504157884413omplex Z3))))) (forall ((X tptp.real) (R3 tptp.real) (Y tptp.real) (S2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real X)) R3) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real Y)) S2) (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.times_times_real X) Y))) (@ (@ tptp.times_times_real R3) S2))))) (forall ((X tptp.complex) (R3 tptp.real) (Y tptp.complex) (S2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex X)) R3) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex Y)) S2) (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.times_times_complex X) Y))) (@ (@ tptp.times_times_real R3) S2))))) (forall ((X tptp.real) (Y tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.times_times_real X) Y))) (@ (@ tptp.times_times_real (@ tptp.real_V7735802525324610683m_real X)) (@ tptp.real_V7735802525324610683m_real Y)))) (forall ((X tptp.complex) (Y tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.times_times_complex X) Y))) (@ (@ tptp.times_times_real (@ tptp.real_V1022390504157884413omplex X)) (@ tptp.real_V1022390504157884413omplex Y)))) (forall ((W2 tptp.real) (N tptp.nat)) (=> (= (@ (@ tptp.power_power_real W2) N) tptp.one_one_real) (or (= (@ tptp.real_V7735802525324610683m_real W2) tptp.one_one_real) (= N tptp.zero_zero_nat)))) (forall ((W2 tptp.complex) (N tptp.nat)) (=> (= (@ (@ tptp.power_power_complex W2) N) tptp.one_one_complex) (or (= (@ tptp.real_V1022390504157884413omplex W2) tptp.one_one_real) (= N tptp.zero_zero_nat)))) (= (@ tptp.arsinh_real tptp.zero_zero_real) tptp.zero_zero_real) (forall ((X tptp.nat) (Y tptp.vEBT_VEBT)) (let ((_let_1 (not (= Y (@ (@ tptp.vEBT_Leaf false) false))))) (=> (= (@ tptp.vEBT_vebt_buildup X) Y) (=> (=> (= X tptp.zero_zero_nat) _let_1) (=> (=> (= X (@ tptp.suc tptp.zero_zero_nat)) _let_1) (not (forall ((Va tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_2) _let_1))) (let ((_let_4 (@ tptp.suc _let_3))) (let ((_let_5 (@ tptp.vEBT_vebt_buildup _let_3))) (let ((_let_6 (@ tptp.power_power_nat _let_1))) (let ((_let_7 (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_2))) (let ((_let_8 (@ (@ tptp.dvd_dvd_nat _let_1) _let_2))) (=> (= X _let_2) (not (and (=> _let_8 (= Y (@ (@ _let_7 (@ (@ tptp.replicate_VEBT_VEBT (@ _let_6 _let_3)) _let_5)) _let_5))) (=> (not _let_8) (= Y (@ (@ _let_7 (@ (@ tptp.replicate_VEBT_VEBT (@ _let_6 _let_4)) _let_5)) (@ tptp.vEBT_vebt_buildup _let_4)))))))))))))))))))))) (forall ((I5 tptp.set_real) (X (-> tptp.real tptp.code_integer)) (Y (-> tptp.real tptp.code_integer))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I tptp.real)) (and (@ (@ tptp.member_real I) I5) (not (= (@ X I) tptp.one_one_Code_integer)))))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I tptp.real)) (and (@ (@ tptp.member_real I) I5) (not (= (@ Y I) tptp.one_one_Code_integer)))))) (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I tptp.real)) (and (@ (@ tptp.member_real I) I5) (not (= (@ (@ tptp.times_3573771949741848930nteger (@ X I)) (@ Y I)) tptp.one_one_Code_integer))))))))) (forall ((I5 tptp.set_nat) (X (-> tptp.nat tptp.code_integer)) (Y (-> tptp.nat tptp.code_integer))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I tptp.nat)) (and (@ (@ tptp.member_nat I) I5) (not (= (@ X I) tptp.one_one_Code_integer)))))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I tptp.nat)) (and (@ (@ tptp.member_nat I) I5) (not (= (@ Y I) tptp.one_one_Code_integer)))))) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I tptp.nat)) (and (@ (@ tptp.member_nat I) I5) (not (= (@ (@ tptp.times_3573771949741848930nteger (@ X I)) (@ Y I)) tptp.one_one_Code_integer))))))))) (forall ((I5 tptp.set_int) (X (-> tptp.int tptp.code_integer)) (Y (-> tptp.int tptp.code_integer))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I tptp.int)) (and (@ (@ tptp.member_int I) I5) (not (= (@ X I) tptp.one_one_Code_integer)))))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I tptp.int)) (and (@ (@ tptp.member_int I) I5) (not (= (@ Y I) tptp.one_one_Code_integer)))))) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I tptp.int)) (and (@ (@ tptp.member_int I) I5) (not (= (@ (@ tptp.times_3573771949741848930nteger (@ X I)) (@ Y I)) tptp.one_one_Code_integer))))))))) (forall ((I5 tptp.set_complex) (X (-> tptp.complex tptp.code_integer)) (Y (-> tptp.complex tptp.code_integer))) (=> (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I tptp.complex)) (and (@ (@ tptp.member_complex I) I5) (not (= (@ X I) tptp.one_one_Code_integer)))))) (=> (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I tptp.complex)) (and (@ (@ tptp.member_complex I) I5) (not (= (@ Y I) tptp.one_one_Code_integer)))))) (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I tptp.complex)) (and (@ (@ tptp.member_complex I) I5) (not (= (@ (@ tptp.times_3573771949741848930nteger (@ X I)) (@ Y I)) tptp.one_one_Code_integer))))))))) (forall ((I5 tptp.set_real) (X (-> tptp.real tptp.complex)) (Y (-> tptp.real tptp.complex))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I tptp.real)) (and (@ (@ tptp.member_real I) I5) (not (= (@ X I) tptp.one_one_complex)))))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I tptp.real)) (and (@ (@ tptp.member_real I) I5) (not (= (@ Y I) tptp.one_one_complex)))))) (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I tptp.real)) (and (@ (@ tptp.member_real I) I5) (not (= (@ (@ tptp.times_times_complex (@ X I)) (@ Y I)) tptp.one_one_complex))))))))) (forall ((I5 tptp.set_nat) (X (-> tptp.nat tptp.complex)) (Y (-> tptp.nat tptp.complex))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I tptp.nat)) (and (@ (@ tptp.member_nat I) I5) (not (= (@ X I) tptp.one_one_complex)))))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I tptp.nat)) (and (@ (@ tptp.member_nat I) I5) (not (= (@ Y I) tptp.one_one_complex)))))) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I tptp.nat)) (and (@ (@ tptp.member_nat I) I5) (not (= (@ (@ tptp.times_times_complex (@ X I)) (@ Y I)) tptp.one_one_complex))))))))) (forall ((I5 tptp.set_int) (X (-> tptp.int tptp.complex)) (Y (-> tptp.int tptp.complex))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I tptp.int)) (and (@ (@ tptp.member_int I) I5) (not (= (@ X I) tptp.one_one_complex)))))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I tptp.int)) (and (@ (@ tptp.member_int I) I5) (not (= (@ Y I) tptp.one_one_complex)))))) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I tptp.int)) (and (@ (@ tptp.member_int I) I5) (not (= (@ (@ tptp.times_times_complex (@ X I)) (@ Y I)) tptp.one_one_complex))))))))) (forall ((I5 tptp.set_complex) (X (-> tptp.complex tptp.complex)) (Y (-> tptp.complex tptp.complex))) (=> (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I tptp.complex)) (and (@ (@ tptp.member_complex I) I5) (not (= (@ X I) tptp.one_one_complex)))))) (=> (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I tptp.complex)) (and (@ (@ tptp.member_complex I) I5) (not (= (@ Y I) tptp.one_one_complex)))))) (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I tptp.complex)) (and (@ (@ tptp.member_complex I) I5) (not (= (@ (@ tptp.times_times_complex (@ X I)) (@ Y I)) tptp.one_one_complex))))))))) (forall ((I5 tptp.set_real) (X (-> tptp.real tptp.real)) (Y (-> tptp.real tptp.real))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I tptp.real)) (and (@ (@ tptp.member_real I) I5) (not (= (@ X I) tptp.one_one_real)))))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I tptp.real)) (and (@ (@ tptp.member_real I) I5) (not (= (@ Y I) tptp.one_one_real)))))) (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I tptp.real)) (and (@ (@ tptp.member_real I) I5) (not (= (@ (@ tptp.times_times_real (@ X I)) (@ Y I)) tptp.one_one_real))))))))) (forall ((I5 tptp.set_nat) (X (-> tptp.nat tptp.real)) (Y (-> tptp.nat tptp.real))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I tptp.nat)) (and (@ (@ tptp.member_nat I) I5) (not (= (@ X I) tptp.one_one_real)))))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I tptp.nat)) (and (@ (@ tptp.member_nat I) I5) (not (= (@ Y I) tptp.one_one_real)))))) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I tptp.nat)) (and (@ (@ tptp.member_nat I) I5) (not (= (@ (@ tptp.times_times_real (@ X I)) (@ Y I)) tptp.one_one_real))))))))) (forall ((N tptp.nat) (M2 tptp.nat) (X tptp.complex)) (let ((_let_1 (@ tptp.power_power_complex X))) (let ((_let_2 (@ (@ tptp.groups2073611262835488442omplex _let_1) (@ (@ tptp.set_or1269000886237332187st_nat M2) N)))) (let ((_let_3 (= X tptp.one_one_complex))) (let ((_let_4 (@ (@ tptp.ord_less_nat N) M2))) (and (=> _let_4 (= _let_2 tptp.zero_zero_complex)) (=> (not _let_4) (and (=> _let_3 (= _let_2 (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat)) M2)))) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ _let_1 M2)) (@ _let_1 (@ tptp.suc N)))) (@ (@ tptp.minus_minus_complex tptp.one_one_complex) X)))))))))))) (forall ((N tptp.nat) (M2 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 M2) N)))) (let ((_let_3 (= X tptp.one_one_rat))) (let ((_let_4 (@ (@ tptp.ord_less_nat N) M2))) (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)) M2)))) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ _let_1 M2)) (@ _let_1 (@ tptp.suc N)))) (@ (@ tptp.minus_minus_rat tptp.one_one_rat) X)))))))))))) (forall ((N tptp.nat) (M2 tptp.nat) (X tptp.real)) (let ((_let_1 (@ tptp.power_power_real X))) (let ((_let_2 (@ (@ tptp.groups6591440286371151544t_real _let_1) (@ (@ tptp.set_or1269000886237332187st_nat M2) N)))) (let ((_let_3 (= X tptp.one_one_real))) (let ((_let_4 (@ (@ tptp.ord_less_nat N) M2))) (and (=> _let_4 (= _let_2 tptp.zero_zero_real)) (=> (not _let_4) (and (=> _let_3 (= _let_2 (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat)) M2)))) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ _let_1 M2)) (@ _let_1 (@ tptp.suc N)))) (@ (@ tptp.minus_minus_real tptp.one_one_real) X)))))))))))) (forall ((I5 tptp.set_real) (X (-> tptp.real tptp.complex)) (Y (-> tptp.real tptp.complex))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I tptp.real)) (and (@ (@ tptp.member_real I) I5) (not (= (@ X I) tptp.zero_zero_complex)))))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I tptp.real)) (and (@ (@ tptp.member_real I) I5) (not (= (@ Y I) tptp.zero_zero_complex)))))) (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I tptp.real)) (and (@ (@ tptp.member_real I) I5) (not (= (@ (@ tptp.plus_plus_complex (@ X I)) (@ Y I)) tptp.zero_zero_complex))))))))) (forall ((I5 tptp.set_nat) (X (-> tptp.nat tptp.complex)) (Y (-> tptp.nat tptp.complex))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I tptp.nat)) (and (@ (@ tptp.member_nat I) I5) (not (= (@ X I) tptp.zero_zero_complex)))))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I tptp.nat)) (and (@ (@ tptp.member_nat I) I5) (not (= (@ Y I) tptp.zero_zero_complex)))))) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I tptp.nat)) (and (@ (@ tptp.member_nat I) I5) (not (= (@ (@ tptp.plus_plus_complex (@ X I)) (@ Y I)) tptp.zero_zero_complex))))))))) (forall ((I5 tptp.set_int) (X (-> tptp.int tptp.complex)) (Y (-> tptp.int tptp.complex))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I tptp.int)) (and (@ (@ tptp.member_int I) I5) (not (= (@ X I) tptp.zero_zero_complex)))))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I tptp.int)) (and (@ (@ tptp.member_int I) I5) (not (= (@ Y I) tptp.zero_zero_complex)))))) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I tptp.int)) (and (@ (@ tptp.member_int I) I5) (not (= (@ (@ tptp.plus_plus_complex (@ X I)) (@ Y I)) tptp.zero_zero_complex))))))))) (forall ((I5 tptp.set_complex) (X (-> tptp.complex tptp.complex)) (Y (-> tptp.complex tptp.complex))) (=> (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I tptp.complex)) (and (@ (@ tptp.member_complex I) I5) (not (= (@ X I) tptp.zero_zero_complex)))))) (=> (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I tptp.complex)) (and (@ (@ tptp.member_complex I) I5) (not (= (@ Y I) tptp.zero_zero_complex)))))) (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I tptp.complex)) (and (@ (@ tptp.member_complex I) I5) (not (= (@ (@ tptp.plus_plus_complex (@ X I)) (@ Y I)) tptp.zero_zero_complex))))))))) (forall ((I5 tptp.set_real) (X (-> tptp.real tptp.real)) (Y (-> tptp.real tptp.real))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I tptp.real)) (and (@ (@ tptp.member_real I) I5) (not (= (@ X I) tptp.zero_zero_real)))))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I tptp.real)) (and (@ (@ tptp.member_real I) I5) (not (= (@ Y I) tptp.zero_zero_real)))))) (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I tptp.real)) (and (@ (@ tptp.member_real I) I5) (not (= (@ (@ tptp.plus_plus_real (@ X I)) (@ Y I)) tptp.zero_zero_real))))))))) (forall ((I5 tptp.set_nat) (X (-> tptp.nat tptp.real)) (Y (-> tptp.nat tptp.real))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I tptp.nat)) (and (@ (@ tptp.member_nat I) I5) (not (= (@ X I) tptp.zero_zero_real)))))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I tptp.nat)) (and (@ (@ tptp.member_nat I) I5) (not (= (@ Y I) tptp.zero_zero_real)))))) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I tptp.nat)) (and (@ (@ tptp.member_nat I) I5) (not (= (@ (@ tptp.plus_plus_real (@ X I)) (@ Y I)) tptp.zero_zero_real))))))))) (forall ((I5 tptp.set_int) (X (-> tptp.int tptp.real)) (Y (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I tptp.int)) (and (@ (@ tptp.member_int I) I5) (not (= (@ X I) tptp.zero_zero_real)))))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I tptp.int)) (and (@ (@ tptp.member_int I) I5) (not (= (@ Y I) tptp.zero_zero_real)))))) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I tptp.int)) (and (@ (@ tptp.member_int I) I5) (not (= (@ (@ tptp.plus_plus_real (@ X I)) (@ Y I)) tptp.zero_zero_real))))))))) (forall ((I5 tptp.set_complex) (X (-> tptp.complex tptp.real)) (Y (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I tptp.complex)) (and (@ (@ tptp.member_complex I) I5) (not (= (@ X I) tptp.zero_zero_real)))))) (=> (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I tptp.complex)) (and (@ (@ tptp.member_complex I) I5) (not (= (@ Y I) tptp.zero_zero_real)))))) (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I tptp.complex)) (and (@ (@ tptp.member_complex I) I5) (not (= (@ (@ tptp.plus_plus_real (@ X I)) (@ Y I)) tptp.zero_zero_real))))))))) (forall ((I5 tptp.set_real) (X (-> tptp.real tptp.rat)) (Y (-> tptp.real tptp.rat))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I tptp.real)) (and (@ (@ tptp.member_real I) I5) (not (= (@ X I) tptp.zero_zero_rat)))))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I tptp.real)) (and (@ (@ tptp.member_real I) I5) (not (= (@ Y I) tptp.zero_zero_rat)))))) (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I tptp.real)) (and (@ (@ tptp.member_real I) I5) (not (= (@ (@ tptp.plus_plus_rat (@ X I)) (@ Y I)) tptp.zero_zero_rat))))))))) (forall ((I5 tptp.set_nat) (X (-> tptp.nat tptp.rat)) (Y (-> tptp.nat tptp.rat))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I tptp.nat)) (and (@ (@ tptp.member_nat I) I5) (not (= (@ X I) tptp.zero_zero_rat)))))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I tptp.nat)) (and (@ (@ tptp.member_nat I) I5) (not (= (@ Y I) tptp.zero_zero_rat)))))) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I tptp.nat)) (and (@ (@ tptp.member_nat I) I5) (not (= (@ (@ tptp.plus_plus_rat (@ X I)) (@ Y I)) tptp.zero_zero_rat))))))))) (forall ((Z3 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real Z3)) tptp.one_one_real) (@ (@ tptp.sums_real (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N4))) (@ (@ tptp.power_power_real Z3) N4)))) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real tptp.one_one_real) Z3)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))) (forall ((Z3 tptp.complex)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex Z3)) tptp.one_one_real) (@ (@ tptp.sums_complex (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex (@ tptp.suc N4))) (@ (@ tptp.power_power_complex Z3) N4)))) (@ (@ tptp.divide1717551699836669952omplex tptp.one_one_complex) (@ (@ tptp.power_power_complex (@ (@ tptp.minus_minus_complex tptp.one_one_complex) Z3)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))) (forall ((Z3 tptp.complex) (N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numera6690914467698888265omplex _let_1))) (let ((_let_3 (@ tptp.numeral_numeral_nat _let_1))) (let ((_let_4 (@ (@ tptp.times_times_nat _let_3) N))) (= (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.times_times_complex _let_2) Z3)) _let_4) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.power_power_nat _let_3) _let_4))) (@ (@ tptp.comm_s2602460028002588243omplex Z3) N))) (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.plus_plus_complex Z3) (@ (@ tptp.divide1717551699836669952omplex tptp.one_one_complex) _let_2))) N)))))))) (forall ((Z3 tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_rat _let_1))) (let ((_let_3 (@ tptp.numeral_numeral_nat _let_1))) (let ((_let_4 (@ (@ tptp.times_times_nat _let_3) N))) (= (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.times_times_rat _let_2) Z3)) _let_4) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.power_power_nat _let_3) _let_4))) (@ (@ tptp.comm_s4028243227959126397er_rat Z3) N))) (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.plus_plus_rat Z3) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) _let_2))) N)))))))) (forall ((Z3 tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_real _let_1))) (let ((_let_3 (@ tptp.numeral_numeral_nat _let_1))) (let ((_let_4 (@ (@ tptp.times_times_nat _let_3) N))) (= (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.times_times_real _let_2) Z3)) _let_4) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.power_power_nat _let_3) _let_4))) (@ (@ tptp.comm_s7457072308508201937r_real Z3) N))) (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.plus_plus_real Z3) (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_2))) N)))))))) (forall ((A tptp.complex)) (@ (@ tptp.dvd_dvd_complex A) tptp.zero_zero_complex)) (forall ((A tptp.real)) (@ (@ tptp.dvd_dvd_real A) tptp.zero_zero_real)) (forall ((A tptp.rat)) (@ (@ tptp.dvd_dvd_rat A) tptp.zero_zero_rat)) (forall ((A tptp.nat)) (@ (@ tptp.dvd_dvd_nat A) tptp.zero_zero_nat)) (forall ((A tptp.int)) (@ (@ tptp.dvd_dvd_int A) tptp.zero_zero_int)) (forall ((A tptp.complex)) (= (@ (@ tptp.dvd_dvd_complex tptp.zero_zero_complex) A) (= A tptp.zero_zero_complex))) (forall ((A tptp.real)) (= (@ (@ tptp.dvd_dvd_real tptp.zero_zero_real) A) (= A tptp.zero_zero_real))) (forall ((A tptp.rat)) (= (@ (@ tptp.dvd_dvd_rat tptp.zero_zero_rat) A) (= A tptp.zero_zero_rat))) (forall ((A tptp.nat)) (= (@ (@ tptp.dvd_dvd_nat tptp.zero_zero_nat) A) (= A tptp.zero_zero_nat))) (forall ((A tptp.int)) (= (@ (@ tptp.dvd_dvd_int tptp.zero_zero_int) A) (= A tptp.zero_zero_int))) (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real A))) (= (@ _let_1 (@ (@ tptp.plus_plus_real B) A)) (@ _let_1 B)))) (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat B) A)) (@ _let_1 B)))) (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat B) A)) (@ _let_1 B)))) (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (= (@ _let_1 (@ (@ tptp.plus_plus_int B) A)) (@ _let_1 B)))) (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real A))) (= (@ _let_1 (@ (@ tptp.plus_plus_real A) B)) (@ _let_1 B)))) (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat A) B)) (@ _let_1 B)))) (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat A) B)) (@ _let_1 B)))) (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (= (@ _let_1 (@ (@ tptp.plus_plus_int A) B)) (@ _let_1 B)))) (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (=> (@ _let_1 B) (=> (@ _let_1 C2) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.divide_divide_nat B) A)) (@ (@ tptp.divide_divide_nat C2) A)) (@ (@ tptp.dvd_dvd_nat B) C2)))))) (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (=> (@ _let_1 B) (=> (@ _let_1 C2) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.divide_divide_int B) A)) (@ (@ tptp.divide_divide_int C2) A)) (@ (@ tptp.dvd_dvd_int B) C2)))))) (forall ((M2 tptp.nat)) (= (@ (@ tptp.dvd_dvd_nat M2) tptp.one_one_nat) (= M2 tptp.one_one_nat))) (forall ((A4 tptp.set_nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((Uu3 tptp.nat)) tptp.zero_zero_nat)) A4) tptp.zero_zero_nat)) (forall ((A4 tptp.set_int)) (= (@ (@ tptp.groups4538972089207619220nt_int (lambda ((Uu3 tptp.int)) tptp.zero_zero_int)) A4) tptp.zero_zero_int)) (forall ((A4 tptp.set_nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((Uu3 tptp.nat)) tptp.zero_zero_real)) A4) tptp.zero_zero_real)) (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat B) A)) (@ (@ tptp.times_times_nat C2) A)) (@ (@ tptp.dvd_dvd_nat B) C2)))) (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (=> (not (= A tptp.zero_zero_int)) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int B) A)) (@ (@ tptp.times_times_int C2) A)) (@ (@ tptp.dvd_dvd_int B) C2)))) (forall ((A tptp.nat) (B tptp.nat) (C2 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 C2)) (@ (@ tptp.dvd_dvd_nat B) C2))))) (forall ((A tptp.int) (B tptp.int) (C2 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 C2)) (@ (@ tptp.dvd_dvd_int B) C2))))) (forall ((A tptp.complex) (C2 tptp.complex) (B tptp.complex)) (= (@ (@ tptp.dvd_dvd_complex (@ (@ tptp.times_times_complex A) C2)) (@ (@ tptp.times_times_complex B) C2)) (or (= C2 tptp.zero_zero_complex) (@ (@ tptp.dvd_dvd_complex A) B)))) (forall ((A tptp.real) (C2 tptp.real) (B tptp.real)) (= (@ (@ tptp.dvd_dvd_real (@ (@ tptp.times_times_real A) C2)) (@ (@ tptp.times_times_real B) C2)) (or (= C2 tptp.zero_zero_real) (@ (@ tptp.dvd_dvd_real A) B)))) (forall ((A tptp.rat) (C2 tptp.rat) (B tptp.rat)) (= (@ (@ tptp.dvd_dvd_rat (@ (@ tptp.times_times_rat A) C2)) (@ (@ tptp.times_times_rat B) C2)) (or (= C2 tptp.zero_zero_rat) (@ (@ tptp.dvd_dvd_rat A) B)))) (forall ((A tptp.int) (C2 tptp.int) (B tptp.int)) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A) C2)) (@ (@ tptp.times_times_int B) C2)) (or (= C2 tptp.zero_zero_int) (@ (@ tptp.dvd_dvd_int A) B)))) (forall ((C2 tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex C2))) (= (@ (@ tptp.dvd_dvd_complex (@ _let_1 A)) (@ _let_1 B)) (or (= C2 tptp.zero_zero_complex) (@ (@ tptp.dvd_dvd_complex A) B))))) (forall ((C2 tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real C2))) (= (@ (@ tptp.dvd_dvd_real (@ _let_1 A)) (@ _let_1 B)) (or (= C2 tptp.zero_zero_real) (@ (@ tptp.dvd_dvd_real A) B))))) (forall ((C2 tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C2))) (= (@ (@ tptp.dvd_dvd_rat (@ _let_1 A)) (@ _let_1 B)) (or (= C2 tptp.zero_zero_rat) (@ (@ tptp.dvd_dvd_rat A) B))))) (forall ((C2 tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C2))) (= (@ (@ tptp.dvd_dvd_int (@ _let_1 A)) (@ _let_1 B)) (or (= C2 tptp.zero_zero_int) (@ (@ tptp.dvd_dvd_int A) B))))) (forall ((A tptp.real) (B tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real A))) (= (@ _let_1 (@ (@ tptp.plus_plus_real B) (@ (@ tptp.times_times_real C2) A))) (@ _let_1 B)))) (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat B) (@ (@ tptp.times_times_rat C2) A))) (@ _let_1 B)))) (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat B) (@ (@ tptp.times_times_nat C2) A))) (@ _let_1 B)))) (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (= (@ _let_1 (@ (@ tptp.plus_plus_int B) (@ (@ tptp.times_times_int C2) A))) (@ _let_1 B)))) (forall ((A tptp.real) (C2 tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real A))) (= (@ _let_1 (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real C2) A)) B)) (@ _let_1 B)))) (forall ((A tptp.rat) (C2 tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat C2) A)) B)) (@ _let_1 B)))) (forall ((A tptp.nat) (C2 tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat C2) A)) B)) (@ _let_1 B)))) (forall ((A tptp.int) (C2 tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (= (@ _let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int C2) A)) B)) (@ _let_1 B)))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer) (=> (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer) (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.times_3573771949741848930nteger A) B)) tptp.one_one_Code_integer)))) (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (=> (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat A) B)) tptp.one_one_nat)))) (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (=> (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A) B)) tptp.one_one_int)))) (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) B) (= (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat B) A)) A) B))) (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) B) (= (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int B) A)) A) B))) (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) B) (= (@ (@ tptp.times_times_nat A) (@ (@ tptp.divide_divide_nat B) A)) B))) (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) B) (= (@ (@ tptp.times_times_int A) (@ (@ tptp.divide_divide_int B) A)) B))) (forall ((C2 tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat C2))) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat A) B)) C2) (@ (@ tptp.plus_plus_nat (@ (@ tptp.divide_divide_nat A) C2)) (@ (@ tptp.divide_divide_nat B) C2))))))) (forall ((C2 tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int C2))) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int A) B)) C2) (@ (@ tptp.plus_plus_int (@ (@ tptp.divide_divide_int A) C2)) (@ (@ tptp.divide_divide_int B) C2))))))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer) (=> (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer) (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.divide6298287555418463151nteger A) B)) tptp.one_one_Code_integer)))) (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (=> (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.divide_divide_nat A) B)) tptp.one_one_nat)))) (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (=> (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.divide_divide_int A) B)) tptp.one_one_int)))) (forall ((A tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer) (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.divide6298287555418463151nteger tptp.one_one_Code_integer) A)) tptp.one_one_Code_integer))) (forall ((A tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.divide_divide_nat tptp.one_one_nat) A)) tptp.one_one_nat))) (forall ((A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.divide_divide_int tptp.one_one_int) A)) tptp.one_one_int))) (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.divide6298287555418463151nteger tptp.one_one_Code_integer))) (=> (@ (@ tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer) (= (@ _let_1 (@ _let_1 A)) A)))) (forall ((A tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat tptp.one_one_nat))) (=> (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (= (@ _let_1 (@ _let_1 A)) A)))) (forall ((A tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int tptp.one_one_int))) (=> (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (= (@ _let_1 (@ _let_1 A)) A)))) (forall ((G2 (-> tptp.nat tptp.complex))) (= (@ (@ tptp.groups2073611262835488442omplex G2) tptp.bot_bot_set_nat) tptp.zero_zero_complex)) (forall ((G2 (-> tptp.nat tptp.rat))) (= (@ (@ tptp.groups2906978787729119204at_rat G2) tptp.bot_bot_set_nat) tptp.zero_zero_rat)) (forall ((G2 (-> tptp.nat tptp.int))) (= (@ (@ tptp.groups3539618377306564664at_int G2) tptp.bot_bot_set_nat) tptp.zero_zero_int)) (forall ((G2 (-> tptp.int tptp.complex))) (= (@ (@ tptp.groups3049146728041665814omplex G2) tptp.bot_bot_set_int) tptp.zero_zero_complex)) (forall ((G2 (-> tptp.int tptp.real))) (= (@ (@ tptp.groups8778361861064173332t_real G2) tptp.bot_bot_set_int) tptp.zero_zero_real)) (forall ((G2 (-> tptp.int tptp.rat))) (= (@ (@ tptp.groups3906332499630173760nt_rat G2) tptp.bot_bot_set_int) tptp.zero_zero_rat)) (forall ((G2 (-> tptp.int tptp.nat))) (= (@ (@ tptp.groups4541462559716669496nt_nat G2) tptp.bot_bot_set_int) tptp.zero_zero_nat)) (forall ((G2 (-> tptp.real tptp.complex))) (= (@ (@ tptp.groups5754745047067104278omplex G2) tptp.bot_bot_set_real) tptp.zero_zero_complex)) (forall ((G2 (-> tptp.real tptp.real))) (= (@ (@ tptp.groups8097168146408367636l_real G2) tptp.bot_bot_set_real) tptp.zero_zero_real)) (forall ((G2 (-> tptp.real tptp.rat))) (= (@ (@ tptp.groups1300246762558778688al_rat G2) tptp.bot_bot_set_real) tptp.zero_zero_rat)) (forall ((A4 tptp.set_nat) (G2 (-> tptp.nat tptp.complex))) (=> (not (@ tptp.finite_finite_nat A4)) (= (@ (@ tptp.groups2073611262835488442omplex G2) A4) tptp.zero_zero_complex))) (forall ((A4 tptp.set_int) (G2 (-> tptp.int tptp.complex))) (=> (not (@ tptp.finite_finite_int A4)) (= (@ (@ tptp.groups3049146728041665814omplex G2) A4) tptp.zero_zero_complex))) (forall ((A4 tptp.set_complex) (G2 (-> tptp.complex tptp.complex))) (=> (not (@ tptp.finite3207457112153483333omplex A4)) (= (@ (@ tptp.groups7754918857620584856omplex G2) A4) tptp.zero_zero_complex))) (forall ((A4 tptp.set_int) (G2 (-> tptp.int tptp.real))) (=> (not (@ tptp.finite_finite_int A4)) (= (@ (@ tptp.groups8778361861064173332t_real G2) A4) tptp.zero_zero_real))) (forall ((A4 tptp.set_complex) (G2 (-> tptp.complex tptp.real))) (=> (not (@ tptp.finite3207457112153483333omplex A4)) (= (@ (@ tptp.groups5808333547571424918x_real G2) A4) tptp.zero_zero_real))) (forall ((A4 tptp.set_nat) (G2 (-> tptp.nat tptp.rat))) (=> (not (@ tptp.finite_finite_nat A4)) (= (@ (@ tptp.groups2906978787729119204at_rat G2) A4) tptp.zero_zero_rat))) (forall ((A4 tptp.set_int) (G2 (-> tptp.int tptp.rat))) (=> (not (@ tptp.finite_finite_int A4)) (= (@ (@ tptp.groups3906332499630173760nt_rat G2) A4) tptp.zero_zero_rat))) (forall ((A4 tptp.set_complex) (G2 (-> tptp.complex tptp.rat))) (=> (not (@ tptp.finite3207457112153483333omplex A4)) (= (@ (@ tptp.groups5058264527183730370ex_rat G2) A4) tptp.zero_zero_rat))) (forall ((A4 tptp.set_int) (G2 (-> tptp.int tptp.nat))) (=> (not (@ tptp.finite_finite_int A4)) (= (@ (@ tptp.groups4541462559716669496nt_nat G2) A4) tptp.zero_zero_nat))) (forall ((A4 tptp.set_complex) (G2 (-> tptp.complex tptp.nat))) (=> (not (@ tptp.finite3207457112153483333omplex A4)) (= (@ (@ tptp.groups5693394587270226106ex_nat G2) A4) tptp.zero_zero_nat))) (forall ((F3 tptp.set_int) (F2 (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int F3) (= (= (@ (@ tptp.groups4541462559716669496nt_nat F2) F3) tptp.zero_zero_nat) (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) F3) (= (@ F2 X4) tptp.zero_zero_nat)))))) (forall ((F3 tptp.set_complex) (F2 (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex F3) (= (= (@ (@ tptp.groups5693394587270226106ex_nat F2) F3) tptp.zero_zero_nat) (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) F3) (= (@ F2 X4) tptp.zero_zero_nat)))))) (forall ((F3 tptp.set_nat) (F2 (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_nat F3) (= (= (@ (@ tptp.groups3542108847815614940at_nat F2) F3) tptp.zero_zero_nat) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) F3) (= (@ F2 X4) tptp.zero_zero_nat)))))) (forall ((C2 tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int C2))) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.minus_minus_int A) B)) C2) (@ (@ tptp.minus_minus_int (@ (@ tptp.divide_divide_int A) C2)) (@ (@ tptp.divide_divide_int B) C2))))))) (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) B) (= (@ (@ tptp.modulo_modulo_nat B) A) tptp.zero_zero_nat))) (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) B) (= (@ (@ tptp.modulo_modulo_int B) A) tptp.zero_zero_int))) (forall ((A tptp.code_natural) (B tptp.code_natural)) (=> (@ (@ tptp.dvd_dvd_Code_natural A) B) (= (@ (@ tptp.modulo8411746178871703098atural B) A) tptp.zero_z2226904508553997617atural))) (forall ((K2 tptp.nat)) (@ (@ tptp.dvd_dvd_nat (@ tptp.suc tptp.zero_zero_nat)) K2)) (forall ((M2 tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (@ (@ tptp.dvd_dvd_nat M2) _let_1) (= M2 _let_1)))) (forall ((K2 tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K2))) (= (@ (@ tptp.dvd_dvd_nat (@ _let_1 M2)) (@ _let_1 N)) (or (= K2 tptp.zero_zero_nat) (@ (@ tptp.dvd_dvd_nat M2) N))))) (forall ((A tptp.code_integer)) (= (@ (@ tptp.comm_s8582702949713902594nteger A) tptp.zero_zero_nat) tptp.one_one_Code_integer)) (forall ((A tptp.complex)) (= (@ (@ tptp.comm_s2602460028002588243omplex A) tptp.zero_zero_nat) tptp.one_one_complex)) (forall ((A tptp.real)) (= (@ (@ tptp.comm_s7457072308508201937r_real A) tptp.zero_zero_nat) tptp.one_one_real)) (forall ((A tptp.nat)) (= (@ (@ tptp.comm_s4663373288045622133er_nat A) tptp.zero_zero_nat) tptp.one_one_nat)) (forall ((A tptp.int)) (= (@ (@ tptp.comm_s4660882817536571857er_int A) tptp.zero_zero_nat) tptp.one_one_int)) (forall ((S3 tptp.set_real) (A tptp.real) (B (-> tptp.real tptp.complex))) (let ((_let_1 (@ (@ tptp.member_real A) S3))) (=> (@ tptp.finite_finite_real S3) (and (=> _let_1 (= (@ (@ tptp.groups5754745047067104278omplex (lambda ((K3 tptp.real)) (@ (@ (@ tptp.if_complex (= K3 A)) (@ B K3)) tptp.zero_zero_complex))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups5754745047067104278omplex (lambda ((K3 tptp.real)) (@ (@ (@ tptp.if_complex (= K3 A)) (@ B K3)) tptp.zero_zero_complex))) S3) tptp.zero_zero_complex)))))) (forall ((S3 tptp.set_nat) (A tptp.nat) (B (-> tptp.nat tptp.complex))) (let ((_let_1 (@ (@ tptp.member_nat A) S3))) (=> (@ tptp.finite_finite_nat S3) (and (=> _let_1 (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((K3 tptp.nat)) (@ (@ (@ tptp.if_complex (= K3 A)) (@ B K3)) tptp.zero_zero_complex))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((K3 tptp.nat)) (@ (@ (@ tptp.if_complex (= K3 A)) (@ B K3)) tptp.zero_zero_complex))) S3) tptp.zero_zero_complex)))))) (forall ((S3 tptp.set_int) (A tptp.int) (B (-> tptp.int tptp.complex))) (let ((_let_1 (@ (@ tptp.member_int A) S3))) (=> (@ tptp.finite_finite_int S3) (and (=> _let_1 (= (@ (@ tptp.groups3049146728041665814omplex (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_complex (= K3 A)) (@ B K3)) tptp.zero_zero_complex))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups3049146728041665814omplex (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_complex (= K3 A)) (@ B K3)) tptp.zero_zero_complex))) S3) tptp.zero_zero_complex)))))) (forall ((S3 tptp.set_complex) (A tptp.complex) (B (-> tptp.complex tptp.complex))) (let ((_let_1 (@ (@ tptp.member_complex A) S3))) (=> (@ tptp.finite3207457112153483333omplex S3) (and (=> _let_1 (= (@ (@ tptp.groups7754918857620584856omplex (lambda ((K3 tptp.complex)) (@ (@ (@ tptp.if_complex (= K3 A)) (@ B K3)) tptp.zero_zero_complex))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups7754918857620584856omplex (lambda ((K3 tptp.complex)) (@ (@ (@ tptp.if_complex (= K3 A)) (@ B K3)) tptp.zero_zero_complex))) S3) tptp.zero_zero_complex)))))) (forall ((S3 tptp.set_real) (A tptp.real) (B (-> tptp.real tptp.real))) (let ((_let_1 (@ (@ tptp.member_real A) S3))) (=> (@ tptp.finite_finite_real S3) (and (=> _let_1 (= (@ (@ tptp.groups8097168146408367636l_real (lambda ((K3 tptp.real)) (@ (@ (@ tptp.if_real (= K3 A)) (@ B K3)) tptp.zero_zero_real))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups8097168146408367636l_real (lambda ((K3 tptp.real)) (@ (@ (@ tptp.if_real (= K3 A)) (@ B K3)) tptp.zero_zero_real))) S3) tptp.zero_zero_real)))))) (forall ((S3 tptp.set_int) (A tptp.int) (B (-> tptp.int tptp.real))) (let ((_let_1 (@ (@ tptp.member_int A) S3))) (=> (@ tptp.finite_finite_int S3) (and (=> _let_1 (= (@ (@ tptp.groups8778361861064173332t_real (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_real (= K3 A)) (@ B K3)) tptp.zero_zero_real))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups8778361861064173332t_real (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_real (= K3 A)) (@ B K3)) tptp.zero_zero_real))) S3) tptp.zero_zero_real)))))) (forall ((S3 tptp.set_complex) (A tptp.complex) (B (-> tptp.complex tptp.real))) (let ((_let_1 (@ (@ tptp.member_complex A) S3))) (=> (@ tptp.finite3207457112153483333omplex S3) (and (=> _let_1 (= (@ (@ tptp.groups5808333547571424918x_real (lambda ((K3 tptp.complex)) (@ (@ (@ tptp.if_real (= K3 A)) (@ B K3)) tptp.zero_zero_real))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups5808333547571424918x_real (lambda ((K3 tptp.complex)) (@ (@ (@ tptp.if_real (= K3 A)) (@ B K3)) tptp.zero_zero_real))) S3) tptp.zero_zero_real)))))) (forall ((S3 tptp.set_real) (A tptp.real) (B (-> tptp.real tptp.rat))) (let ((_let_1 (@ (@ tptp.member_real A) S3))) (=> (@ tptp.finite_finite_real S3) (and (=> _let_1 (= (@ (@ tptp.groups1300246762558778688al_rat (lambda ((K3 tptp.real)) (@ (@ (@ tptp.if_rat (= K3 A)) (@ B K3)) tptp.zero_zero_rat))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups1300246762558778688al_rat (lambda ((K3 tptp.real)) (@ (@ (@ tptp.if_rat (= K3 A)) (@ B K3)) tptp.zero_zero_rat))) S3) tptp.zero_zero_rat)))))) (forall ((S3 tptp.set_nat) (A tptp.nat) (B (-> tptp.nat tptp.rat))) (let ((_let_1 (@ (@ tptp.member_nat A) S3))) (=> (@ tptp.finite_finite_nat S3) (and (=> _let_1 (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ (@ tptp.if_rat (= K3 A)) (@ B K3)) tptp.zero_zero_rat))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ (@ tptp.if_rat (= K3 A)) (@ B K3)) tptp.zero_zero_rat))) S3) tptp.zero_zero_rat)))))) (forall ((S3 tptp.set_int) (A tptp.int) (B (-> tptp.int tptp.rat))) (let ((_let_1 (@ (@ tptp.member_int A) S3))) (=> (@ tptp.finite_finite_int S3) (and (=> _let_1 (= (@ (@ tptp.groups3906332499630173760nt_rat (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_rat (= K3 A)) (@ B K3)) tptp.zero_zero_rat))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups3906332499630173760nt_rat (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_rat (= K3 A)) (@ B K3)) tptp.zero_zero_rat))) S3) tptp.zero_zero_rat)))))) (forall ((S3 tptp.set_real) (A tptp.real) (B (-> tptp.real tptp.complex))) (let ((_let_1 (@ (@ tptp.member_real A) S3))) (=> (@ tptp.finite_finite_real S3) (and (=> _let_1 (= (@ (@ tptp.groups5754745047067104278omplex (lambda ((K3 tptp.real)) (@ (@ (@ tptp.if_complex (= A K3)) (@ B K3)) tptp.zero_zero_complex))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups5754745047067104278omplex (lambda ((K3 tptp.real)) (@ (@ (@ tptp.if_complex (= A K3)) (@ B K3)) tptp.zero_zero_complex))) S3) tptp.zero_zero_complex)))))) (forall ((S3 tptp.set_nat) (A tptp.nat) (B (-> tptp.nat tptp.complex))) (let ((_let_1 (@ (@ tptp.member_nat A) S3))) (=> (@ tptp.finite_finite_nat S3) (and (=> _let_1 (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((K3 tptp.nat)) (@ (@ (@ tptp.if_complex (= A K3)) (@ B K3)) tptp.zero_zero_complex))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((K3 tptp.nat)) (@ (@ (@ tptp.if_complex (= A K3)) (@ B K3)) tptp.zero_zero_complex))) S3) tptp.zero_zero_complex)))))) (forall ((S3 tptp.set_int) (A tptp.int) (B (-> tptp.int tptp.complex))) (let ((_let_1 (@ (@ tptp.member_int A) S3))) (=> (@ tptp.finite_finite_int S3) (and (=> _let_1 (= (@ (@ tptp.groups3049146728041665814omplex (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_complex (= A K3)) (@ B K3)) tptp.zero_zero_complex))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups3049146728041665814omplex (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_complex (= A K3)) (@ B K3)) tptp.zero_zero_complex))) S3) tptp.zero_zero_complex)))))) (forall ((S3 tptp.set_complex) (A tptp.complex) (B (-> tptp.complex tptp.complex))) (let ((_let_1 (@ (@ tptp.member_complex A) S3))) (=> (@ tptp.finite3207457112153483333omplex S3) (and (=> _let_1 (= (@ (@ tptp.groups7754918857620584856omplex (lambda ((K3 tptp.complex)) (@ (@ (@ tptp.if_complex (= A K3)) (@ B K3)) tptp.zero_zero_complex))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups7754918857620584856omplex (lambda ((K3 tptp.complex)) (@ (@ (@ tptp.if_complex (= A K3)) (@ B K3)) tptp.zero_zero_complex))) S3) tptp.zero_zero_complex)))))) (forall ((S3 tptp.set_real) (A tptp.real) (B (-> tptp.real tptp.real))) (let ((_let_1 (@ (@ tptp.member_real A) S3))) (=> (@ tptp.finite_finite_real S3) (and (=> _let_1 (= (@ (@ tptp.groups8097168146408367636l_real (lambda ((K3 tptp.real)) (@ (@ (@ tptp.if_real (= A K3)) (@ B K3)) tptp.zero_zero_real))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups8097168146408367636l_real (lambda ((K3 tptp.real)) (@ (@ (@ tptp.if_real (= A K3)) (@ B K3)) tptp.zero_zero_real))) S3) tptp.zero_zero_real)))))) (forall ((S3 tptp.set_int) (A tptp.int) (B (-> tptp.int tptp.real))) (let ((_let_1 (@ (@ tptp.member_int A) S3))) (=> (@ tptp.finite_finite_int S3) (and (=> _let_1 (= (@ (@ tptp.groups8778361861064173332t_real (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_real (= A K3)) (@ B K3)) tptp.zero_zero_real))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups8778361861064173332t_real (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_real (= A K3)) (@ B K3)) tptp.zero_zero_real))) S3) tptp.zero_zero_real)))))) (forall ((S3 tptp.set_complex) (A tptp.complex) (B (-> tptp.complex tptp.real))) (let ((_let_1 (@ (@ tptp.member_complex A) S3))) (=> (@ tptp.finite3207457112153483333omplex S3) (and (=> _let_1 (= (@ (@ tptp.groups5808333547571424918x_real (lambda ((K3 tptp.complex)) (@ (@ (@ tptp.if_real (= A K3)) (@ B K3)) tptp.zero_zero_real))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups5808333547571424918x_real (lambda ((K3 tptp.complex)) (@ (@ (@ tptp.if_real (= A K3)) (@ B K3)) tptp.zero_zero_real))) S3) tptp.zero_zero_real)))))) (forall ((S3 tptp.set_real) (A tptp.real) (B (-> tptp.real tptp.rat))) (let ((_let_1 (@ (@ tptp.member_real A) S3))) (=> (@ tptp.finite_finite_real S3) (and (=> _let_1 (= (@ (@ tptp.groups1300246762558778688al_rat (lambda ((K3 tptp.real)) (@ (@ (@ tptp.if_rat (= A K3)) (@ B K3)) tptp.zero_zero_rat))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups1300246762558778688al_rat (lambda ((K3 tptp.real)) (@ (@ (@ tptp.if_rat (= A K3)) (@ B K3)) tptp.zero_zero_rat))) S3) tptp.zero_zero_rat)))))) (forall ((S3 tptp.set_nat) (A tptp.nat) (B (-> tptp.nat tptp.rat))) (let ((_let_1 (@ (@ tptp.member_nat A) S3))) (=> (@ tptp.finite_finite_nat S3) (and (=> _let_1 (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ (@ tptp.if_rat (= A K3)) (@ B K3)) tptp.zero_zero_rat))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ (@ tptp.if_rat (= A K3)) (@ B K3)) tptp.zero_zero_rat))) S3) tptp.zero_zero_rat)))))) (forall ((S3 tptp.set_int) (A tptp.int) (B (-> tptp.int tptp.rat))) (let ((_let_1 (@ (@ tptp.member_int A) S3))) (=> (@ tptp.finite_finite_int S3) (and (=> _let_1 (= (@ (@ tptp.groups3906332499630173760nt_rat (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_rat (= A K3)) (@ B K3)) tptp.zero_zero_rat))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups3906332499630173760nt_rat (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_rat (= A K3)) (@ B K3)) tptp.zero_zero_rat))) S3) tptp.zero_zero_rat)))))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer) (= (@ (@ tptp.times_3573771949741848930nteger B) (@ (@ tptp.divide6298287555418463151nteger tptp.one_one_Code_integer) A)) (@ (@ tptp.divide6298287555418463151nteger B) A)))) (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (= (@ (@ tptp.times_times_nat B) (@ (@ tptp.divide_divide_nat tptp.one_one_nat) A)) (@ (@ tptp.divide_divide_nat B) A)))) (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (= (@ (@ tptp.times_times_int B) (@ (@ tptp.divide_divide_int tptp.one_one_int) A)) (@ (@ tptp.divide_divide_int B) A)))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer) (= (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.divide6298287555418463151nteger B) A)) A) B))) (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (= (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat B) A)) A) B))) (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (= (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int B) A)) A) B))) (forall ((N tptp.nat) (A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.power_power_nat A) N)) (@ (@ tptp.power_power_nat B) N)) (@ (@ tptp.dvd_dvd_nat A) B)))) (forall ((N tptp.nat) (A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.power_power_int A) N)) (@ (@ tptp.power_power_int B) N)) (@ (@ tptp.dvd_dvd_int A) B)))) (forall ((Y tptp.rat) (A4 tptp.set_nat)) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((X4 tptp.nat)) Y)) A4) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat (@ tptp.finite_card_nat A4))) Y))) (forall ((Y tptp.rat) (A4 tptp.set_complex)) (= (@ (@ tptp.groups5058264527183730370ex_rat (lambda ((X4 tptp.complex)) Y)) A4) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat (@ tptp.finite_card_complex A4))) Y))) (forall ((Y tptp.rat) (A4 tptp.set_int)) (= (@ (@ tptp.groups3906332499630173760nt_rat (lambda ((X4 tptp.int)) Y)) A4) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat (@ tptp.finite_card_int A4))) Y))) (forall ((Y tptp.real) (A4 tptp.set_complex)) (= (@ (@ tptp.groups5808333547571424918x_real (lambda ((X4 tptp.complex)) Y)) A4) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ tptp.finite_card_complex A4))) Y))) (forall ((Y tptp.real) (A4 tptp.set_int)) (= (@ (@ tptp.groups8778361861064173332t_real (lambda ((X4 tptp.int)) Y)) A4) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ tptp.finite_card_int A4))) Y))) (forall ((Y tptp.int) (A4 tptp.set_nat)) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((X4 tptp.nat)) Y)) A4) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int (@ tptp.finite_card_nat A4))) Y))) (forall ((Y tptp.int) (A4 tptp.set_complex)) (= (@ (@ tptp.groups5690904116761175830ex_int (lambda ((X4 tptp.complex)) Y)) A4) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int (@ tptp.finite_card_complex A4))) Y))) (forall ((Y tptp.nat) (A4 tptp.set_complex)) (= (@ (@ tptp.groups5693394587270226106ex_nat (lambda ((X4 tptp.complex)) Y)) A4) (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat (@ tptp.finite_card_complex A4))) Y))) (forall ((Y tptp.nat) (A4 tptp.set_int)) (= (@ (@ tptp.groups4541462559716669496nt_nat (lambda ((X4 tptp.int)) Y)) A4) (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat (@ tptp.finite_card_int A4))) Y))) (forall ((Y tptp.nat) (A4 tptp.set_nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X4 tptp.nat)) Y)) A4) (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat (@ tptp.finite_card_nat A4))) Y))) (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.times_times_nat A) B)) (or (@ _let_1 A) (@ _let_1 B))))) (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.times_times_int A) B)) (or (@ _let_1 A) (@ _let_1 B))))) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ tptp.suc (@ tptp.suc N))) (@ _let_1 N)))) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ tptp.suc N)) (not (@ _let_1 N))))) (forall ((A (-> tptp.nat tptp.complex)) (X tptp.complex)) (= (@ (@ tptp.sums_complex (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_complex (@ A N4)) (@ (@ tptp.power_power_complex tptp.zero_zero_complex) N4)))) X) (= (@ A tptp.zero_zero_nat) X))) (forall ((A (-> tptp.nat tptp.real)) (X tptp.real)) (= (@ (@ tptp.sums_real (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_real (@ A N4)) (@ (@ tptp.power_power_real tptp.zero_zero_real) N4)))) X) (= (@ A tptp.zero_zero_nat) X))) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.dvd_dvd_nat _let_1) N) (= (@ (@ tptp.divide_divide_nat (@ tptp.suc N)) _let_1) (@ (@ tptp.divide_divide_nat N) _let_1))))) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (not (@ (@ tptp.dvd_dvd_nat _let_1) N)) (= (@ (@ tptp.divide_divide_nat (@ tptp.suc N)) _let_1) (@ tptp.suc (@ (@ tptp.divide_divide_nat N) _let_1)))))) (forall ((N tptp.nat) (M2 tptp.nat) (G2 (-> tptp.nat tptp.complex))) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M2))) (let ((_let_3 (@ tptp.groups2073611262835488442omplex G2))) (let ((_let_4 (@ _let_3 (@ _let_2 _let_1)))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_1) M2))) (and (=> _let_5 (= _let_4 tptp.zero_zero_complex)) (=> (not _let_5) (= _let_4 (@ (@ tptp.plus_plus_complex (@ _let_3 (@ _let_2 N))) (@ G2 _let_1))))))))))) (forall ((N tptp.nat) (M2 tptp.nat) (G2 (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M2))) (let ((_let_3 (@ tptp.groups2906978787729119204at_rat G2))) (let ((_let_4 (@ _let_3 (@ _let_2 _let_1)))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_1) M2))) (and (=> _let_5 (= _let_4 tptp.zero_zero_rat)) (=> (not _let_5) (= _let_4 (@ (@ tptp.plus_plus_rat (@ _let_3 (@ _let_2 N))) (@ G2 _let_1))))))))))) (forall ((N tptp.nat) (M2 tptp.nat) (G2 (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M2))) (let ((_let_3 (@ tptp.groups3539618377306564664at_int G2))) (let ((_let_4 (@ _let_3 (@ _let_2 _let_1)))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_1) M2))) (and (=> _let_5 (= _let_4 tptp.zero_zero_int)) (=> (not _let_5) (= _let_4 (@ (@ tptp.plus_plus_int (@ _let_3 (@ _let_2 N))) (@ G2 _let_1))))))))))) (forall ((N tptp.nat) (M2 tptp.nat) (G2 (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M2))) (let ((_let_3 (@ tptp.groups3542108847815614940at_nat G2))) (let ((_let_4 (@ _let_3 (@ _let_2 _let_1)))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_1) M2))) (and (=> _let_5 (= _let_4 tptp.zero_zero_nat)) (=> (not _let_5) (= _let_4 (@ (@ tptp.plus_plus_nat (@ _let_3 (@ _let_2 N))) (@ G2 _let_1))))))))))) (forall ((N tptp.nat) (M2 tptp.nat) (G2 (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M2))) (let ((_let_3 (@ tptp.groups6591440286371151544t_real G2))) (let ((_let_4 (@ _let_3 (@ _let_2 _let_1)))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_1) M2))) (and (=> _let_5 (= _let_4 tptp.zero_zero_real)) (=> (not _let_5) (= _let_4 (@ (@ tptp.plus_plus_real (@ _let_3 (@ _let_2 N))) (@ G2 _let_1))))))))))) (forall ((A4 tptp.set_nat) (C2 (-> tptp.nat tptp.complex))) (let ((_let_1 (and (@ tptp.finite_finite_nat A4) (@ (@ tptp.member_nat tptp.zero_zero_nat) A4)))) (and (=> _let_1 (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I tptp.nat)) (@ (@ tptp.times_times_complex (@ C2 I)) (@ (@ tptp.power_power_complex tptp.zero_zero_complex) I)))) A4) (@ C2 tptp.zero_zero_nat))) (=> (not _let_1) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I tptp.nat)) (@ (@ tptp.times_times_complex (@ C2 I)) (@ (@ tptp.power_power_complex tptp.zero_zero_complex) I)))) A4) tptp.zero_zero_complex))))) (forall ((A4 tptp.set_nat) (C2 (-> tptp.nat tptp.rat))) (let ((_let_1 (and (@ tptp.finite_finite_nat A4) (@ (@ tptp.member_nat tptp.zero_zero_nat) A4)))) (and (=> _let_1 (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I tptp.nat)) (@ (@ tptp.times_times_rat (@ C2 I)) (@ (@ tptp.power_power_rat tptp.zero_zero_rat) I)))) A4) (@ C2 tptp.zero_zero_nat))) (=> (not _let_1) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I tptp.nat)) (@ (@ tptp.times_times_rat (@ C2 I)) (@ (@ tptp.power_power_rat tptp.zero_zero_rat) I)))) A4) tptp.zero_zero_rat))))) (forall ((A4 tptp.set_nat) (C2 (-> tptp.nat tptp.real))) (let ((_let_1 (and (@ tptp.finite_finite_nat A4) (@ (@ tptp.member_nat tptp.zero_zero_nat) A4)))) (and (=> _let_1 (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I tptp.nat)) (@ (@ tptp.times_times_real (@ C2 I)) (@ (@ tptp.power_power_real tptp.zero_zero_real) I)))) A4) (@ C2 tptp.zero_zero_nat))) (=> (not _let_1) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I tptp.nat)) (@ (@ tptp.times_times_real (@ C2 I)) (@ (@ tptp.power_power_real tptp.zero_zero_real) I)))) A4) tptp.zero_zero_real))))) (forall ((A tptp.real) (W2 tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (let ((_let_2 (@ tptp.numeral_numeral_nat W2))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_2))) (= (@ _let_1 (@ (@ tptp.power_power_real A) _let_2)) (or _let_3 (and (not _let_3) (@ _let_1 A)))))))) (forall ((A tptp.rat) (W2 tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (let ((_let_2 (@ tptp.numeral_numeral_nat W2))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_2))) (= (@ _let_1 (@ (@ tptp.power_power_rat A) _let_2)) (or _let_3 (and (not _let_3) (@ _let_1 A)))))))) (forall ((A tptp.int) (W2 tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_2 (@ tptp.numeral_numeral_nat W2))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_2))) (= (@ _let_1 (@ (@ tptp.power_power_int A) _let_2)) (or _let_3 (and (not _let_3) (@ _let_1 A)))))))) (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.power_power_nat A) N)) (and (@ _let_1 A) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))) (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.power_power_int A) N)) (and (@ _let_1 A) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))) (forall ((A tptp.real) (N tptp.nat)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real A) N)) tptp.zero_zero_real) (and (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (@ (@ tptp.ord_less_real A) tptp.zero_zero_real)))) (forall ((A tptp.rat) (N tptp.nat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat A) N)) tptp.zero_zero_rat) (and (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat)))) (forall ((A tptp.int) (N tptp.nat)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int A) N)) tptp.zero_zero_int) (and (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (@ (@ tptp.ord_less_int A) tptp.zero_zero_int)))) (forall ((A tptp.real) (W2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat W2))) (= (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real A) _let_1)) tptp.zero_zero_real) (and (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_1)) (@ (@ tptp.ord_less_real A) tptp.zero_zero_real))))) (forall ((A tptp.rat) (W2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat W2))) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat A) _let_1)) tptp.zero_zero_rat) (and (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_1)) (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat))))) (forall ((A tptp.int) (W2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat W2))) (= (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int A) _let_1)) tptp.zero_zero_int) (and (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_1)) (@ (@ tptp.ord_less_int A) tptp.zero_zero_int))))) (forall ((N tptp.nat)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (= (@ tptp.suc (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat))) N))) (forall ((A4 tptp.set_nat) (C2 (-> tptp.nat tptp.complex)) (D (-> tptp.nat tptp.complex))) (let ((_let_1 (and (@ tptp.finite_finite_nat A4) (@ (@ tptp.member_nat tptp.zero_zero_nat) A4)))) (and (=> _let_1 (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I tptp.nat)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex (@ C2 I)) (@ (@ tptp.power_power_complex tptp.zero_zero_complex) I))) (@ D I)))) A4) (@ (@ tptp.divide1717551699836669952omplex (@ C2 tptp.zero_zero_nat)) (@ D tptp.zero_zero_nat)))) (=> (not _let_1) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I tptp.nat)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex (@ C2 I)) (@ (@ tptp.power_power_complex tptp.zero_zero_complex) I))) (@ D I)))) A4) tptp.zero_zero_complex))))) (forall ((A4 tptp.set_nat) (C2 (-> tptp.nat tptp.rat)) (D (-> tptp.nat tptp.rat))) (let ((_let_1 (and (@ tptp.finite_finite_nat A4) (@ (@ tptp.member_nat tptp.zero_zero_nat) A4)))) (and (=> _let_1 (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I tptp.nat)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat (@ C2 I)) (@ (@ tptp.power_power_rat tptp.zero_zero_rat) I))) (@ D I)))) A4) (@ (@ tptp.divide_divide_rat (@ C2 tptp.zero_zero_nat)) (@ D tptp.zero_zero_nat)))) (=> (not _let_1) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I tptp.nat)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat (@ C2 I)) (@ (@ tptp.power_power_rat tptp.zero_zero_rat) I))) (@ D I)))) A4) tptp.zero_zero_rat))))) (forall ((A4 tptp.set_nat) (C2 (-> tptp.nat tptp.real)) (D (-> tptp.nat tptp.real))) (let ((_let_1 (and (@ tptp.finite_finite_nat A4) (@ (@ tptp.member_nat tptp.zero_zero_nat) A4)))) (and (=> _let_1 (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I tptp.nat)) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ C2 I)) (@ (@ tptp.power_power_real tptp.zero_zero_real) I))) (@ D I)))) A4) (@ (@ tptp.divide_divide_real (@ C2 tptp.zero_zero_nat)) (@ D tptp.zero_zero_nat)))) (=> (not _let_1) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I tptp.nat)) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ C2 I)) (@ (@ tptp.power_power_real tptp.zero_zero_real) I))) (@ D I)))) A4) tptp.zero_zero_real))))) (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (=> (not (@ (@ tptp.dvd_dvd_Code_integer _let_1) A)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.divide6298287555418463151nteger A) _let_1))) tptp.one_one_Code_integer) A)))) (forall ((A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (not (@ (@ tptp.dvd_dvd_nat _let_1) A)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.divide_divide_nat A) _let_1))) tptp.one_one_nat) A)))) (forall ((A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (=> (not (@ (@ tptp.dvd_dvd_int _let_1) A)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.divide_divide_int A) _let_1))) tptp.one_one_int) A)))) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.dvd_dvd_Code_integer _let_1) (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.power_8256067586552552935nteger _let_1) N)) tptp.one_one_Code_integer)) (= N tptp.zero_zero_nat)))) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.dvd_dvd_nat _let_1) (@ (@ tptp.minus_minus_nat (@ (@ tptp.power_power_nat _let_1) N)) tptp.one_one_nat)) (= N tptp.zero_zero_nat)))) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.dvd_dvd_int _let_1) (@ (@ tptp.minus_minus_int (@ (@ tptp.power_power_int _let_1) N)) tptp.one_one_int)) (= N tptp.zero_zero_nat)))) (forall ((A tptp.real) (W2 tptp.num)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (let ((_let_2 (@ tptp.numeral_numeral_nat W2))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_2))) (= (@ _let_1 (@ (@ tptp.power_power_real A) _let_2)) (or (= _let_2 tptp.zero_zero_nat) (and _let_3 (not (= A tptp.zero_zero_real))) (and (not _let_3) (@ _let_1 A)))))))) (forall ((A tptp.rat) (W2 tptp.num)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (let ((_let_2 (@ tptp.numeral_numeral_nat W2))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_2))) (= (@ _let_1 (@ (@ tptp.power_power_rat A) _let_2)) (or (= _let_2 tptp.zero_zero_nat) (and _let_3 (not (= A tptp.zero_zero_rat))) (and (not _let_3) (@ _let_1 A)))))))) (forall ((A tptp.int) (W2 tptp.num)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (let ((_let_2 (@ tptp.numeral_numeral_nat W2))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_2))) (= (@ _let_1 (@ (@ tptp.power_power_int A) _let_2)) (or (= _let_2 tptp.zero_zero_nat) (and _let_3 (not (= A tptp.zero_zero_int))) (and (not _let_3) (@ _let_1 A)))))))) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (not (@ (@ tptp.dvd_dvd_nat _let_1) N)) (= (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.divide_divide_nat N) _let_1)) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat))))) (forall ((A tptp.real) (W2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat W2))) (let ((_let_2 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_1))) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real A) _let_1)) tptp.zero_zero_real) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) _let_1) (or (and (not _let_2) (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real)) (and _let_2 (= A tptp.zero_zero_real)))))))) (forall ((A tptp.rat) (W2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat W2))) (let ((_let_2 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_1))) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat A) _let_1)) tptp.zero_zero_rat) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) _let_1) (or (and (not _let_2) (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat)) (and _let_2 (= A tptp.zero_zero_rat)))))))) (forall ((A tptp.int) (W2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat W2))) (let ((_let_2 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_1))) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A) _let_1)) tptp.zero_zero_int) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) _let_1) (or (and (not _let_2) (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int)) (and _let_2 (= A tptp.zero_zero_int)))))))) (forall ((A tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.power_8256067586552552935nteger _let_1) N))) (=> (@ (@ tptp.dvd_dvd_Code_integer _let_1) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer) A)) _let_2) (@ (@ tptp.divide6298287555418463151nteger A) _let_2))))))) (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.power_power_nat _let_1) N))) (=> (@ (@ tptp.dvd_dvd_nat _let_1) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat tptp.one_one_nat) A)) _let_2) (@ (@ tptp.divide_divide_nat A) _let_2))))))) (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.power_power_int _let_1) N))) (=> (@ (@ tptp.dvd_dvd_int _let_1) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int tptp.one_one_int) A)) _let_2) (@ (@ tptp.divide_divide_int A) _let_2))))))) (forall ((A tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.power_8256067586552552935nteger _let_1) N))) (let ((_let_3 (@ tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer))) (=> (@ (@ tptp.dvd_dvd_Code_integer _let_1) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.modulo364778990260209775nteger (@ _let_3 A)) _let_2) (@ _let_3 (@ (@ tptp.modulo364778990260209775nteger A) _let_2))))))))) (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.power_power_nat _let_1) N))) (let ((_let_3 (@ tptp.plus_plus_nat tptp.one_one_nat))) (=> (@ (@ tptp.dvd_dvd_nat _let_1) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.modulo_modulo_nat (@ _let_3 A)) _let_2) (@ _let_3 (@ (@ tptp.modulo_modulo_nat A) _let_2))))))))) (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.power_power_int _let_1) N))) (let ((_let_3 (@ tptp.plus_plus_int tptp.one_one_int))) (=> (@ (@ tptp.dvd_dvd_int _let_1) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.modulo_modulo_int (@ _let_3 A)) _let_2) (@ _let_3 (@ (@ tptp.modulo_modulo_int A) _let_2))))))))) (forall ((A tptp.code_natural) (N tptp.nat)) (let ((_let_1 (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.power_7079662738309270450atural _let_1) N))) (let ((_let_3 (@ tptp.plus_p4538020629002901425atural tptp.one_one_Code_natural))) (=> (@ (@ tptp.dvd_dvd_Code_natural _let_1) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.modulo8411746178871703098atural (@ _let_3 A)) _let_2) (@ _let_3 (@ (@ tptp.modulo8411746178871703098atural A) _let_2))))))))) (forall ((A4 tptp.set_nat) (G2 (-> tptp.nat tptp.nat))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A4) (= (@ G2 X3) tptp.zero_zero_nat))) (= (@ (@ tptp.groups3542108847815614940at_nat G2) A4) tptp.zero_zero_nat))) (forall ((A4 tptp.set_int) (G2 (-> tptp.int tptp.int))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A4) (= (@ G2 X3) tptp.zero_zero_int))) (= (@ (@ tptp.groups4538972089207619220nt_int G2) A4) tptp.zero_zero_int))) (forall ((A4 tptp.set_nat) (G2 (-> tptp.nat tptp.real))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A4) (= (@ G2 X3) tptp.zero_zero_real))) (= (@ (@ tptp.groups6591440286371151544t_real G2) A4) tptp.zero_zero_real))) (forall ((G2 (-> tptp.complex tptp.complex)) (A4 tptp.set_complex)) (=> (not (= (@ (@ tptp.groups7754918857620584856omplex G2) A4) tptp.zero_zero_complex)) (not (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) A4) (= (@ G2 A3) tptp.zero_zero_complex)))))) (forall ((G2 (-> tptp.real tptp.complex)) (A4 tptp.set_real)) (=> (not (= (@ (@ tptp.groups5754745047067104278omplex G2) A4) tptp.zero_zero_complex)) (not (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) A4) (= (@ G2 A3) tptp.zero_zero_complex)))))) (forall ((G2 (-> tptp.nat tptp.complex)) (A4 tptp.set_nat)) (=> (not (= (@ (@ tptp.groups2073611262835488442omplex G2) A4) tptp.zero_zero_complex)) (not (forall ((A3 tptp.nat)) (=> (@ (@ tptp.member_nat A3) A4) (= (@ G2 A3) tptp.zero_zero_complex)))))) (forall ((G2 (-> tptp.int tptp.complex)) (A4 tptp.set_int)) (=> (not (= (@ (@ tptp.groups3049146728041665814omplex G2) A4) tptp.zero_zero_complex)) (not (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) A4) (= (@ G2 A3) tptp.zero_zero_complex)))))) (forall ((G2 (-> tptp.complex tptp.real)) (A4 tptp.set_complex)) (=> (not (= (@ (@ tptp.groups5808333547571424918x_real G2) A4) tptp.zero_zero_real)) (not (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) A4) (= (@ G2 A3) tptp.zero_zero_real)))))) (forall ((G2 (-> tptp.real tptp.real)) (A4 tptp.set_real)) (=> (not (= (@ (@ tptp.groups8097168146408367636l_real G2) A4) tptp.zero_zero_real)) (not (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) A4) (= (@ G2 A3) tptp.zero_zero_real)))))) (forall ((G2 (-> tptp.int tptp.real)) (A4 tptp.set_int)) (=> (not (= (@ (@ tptp.groups8778361861064173332t_real G2) A4) tptp.zero_zero_real)) (not (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) A4) (= (@ G2 A3) tptp.zero_zero_real)))))) (forall ((G2 (-> tptp.complex tptp.rat)) (A4 tptp.set_complex)) (=> (not (= (@ (@ tptp.groups5058264527183730370ex_rat G2) A4) tptp.zero_zero_rat)) (not (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) A4) (= (@ G2 A3) tptp.zero_zero_rat)))))) (forall ((G2 (-> tptp.real tptp.rat)) (A4 tptp.set_real)) (=> (not (= (@ (@ tptp.groups1300246762558778688al_rat G2) A4) tptp.zero_zero_rat)) (not (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) A4) (= (@ G2 A3) tptp.zero_zero_rat)))))) (forall ((G2 (-> tptp.nat tptp.rat)) (A4 tptp.set_nat)) (=> (not (= (@ (@ tptp.groups2906978787729119204at_rat G2) A4) tptp.zero_zero_rat)) (not (forall ((A3 tptp.nat)) (=> (@ (@ tptp.member_nat A3) A4) (= (@ G2 A3) tptp.zero_zero_rat)))))) (forall ((K5 tptp.set_complex) (F2 (-> tptp.complex tptp.rat)) (G2 (-> tptp.complex tptp.rat))) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) K5) (@ (@ tptp.ord_less_eq_rat (@ F2 I3)) (@ G2 I3)))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups5058264527183730370ex_rat F2) K5)) (@ (@ tptp.groups5058264527183730370ex_rat G2) K5)))) (forall ((K5 tptp.set_real) (F2 (-> tptp.real tptp.rat)) (G2 (-> tptp.real tptp.rat))) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) K5) (@ (@ tptp.ord_less_eq_rat (@ F2 I3)) (@ G2 I3)))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups1300246762558778688al_rat F2) K5)) (@ (@ tptp.groups1300246762558778688al_rat G2) K5)))) (forall ((K5 tptp.set_nat) (F2 (-> tptp.nat tptp.rat)) (G2 (-> tptp.nat tptp.rat))) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.member_nat I3) K5) (@ (@ tptp.ord_less_eq_rat (@ F2 I3)) (@ G2 I3)))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups2906978787729119204at_rat F2) K5)) (@ (@ tptp.groups2906978787729119204at_rat G2) K5)))) (forall ((K5 tptp.set_int) (F2 (-> tptp.int tptp.rat)) (G2 (-> tptp.int tptp.rat))) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) K5) (@ (@ tptp.ord_less_eq_rat (@ F2 I3)) (@ G2 I3)))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups3906332499630173760nt_rat F2) K5)) (@ (@ tptp.groups3906332499630173760nt_rat G2) K5)))) (forall ((K5 tptp.set_complex) (F2 (-> tptp.complex tptp.nat)) (G2 (-> tptp.complex tptp.nat))) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) K5) (@ (@ tptp.ord_less_eq_nat (@ F2 I3)) (@ G2 I3)))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups5693394587270226106ex_nat F2) K5)) (@ (@ tptp.groups5693394587270226106ex_nat G2) K5)))) (forall ((K5 tptp.set_real) (F2 (-> tptp.real tptp.nat)) (G2 (-> tptp.real tptp.nat))) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) K5) (@ (@ tptp.ord_less_eq_nat (@ F2 I3)) (@ G2 I3)))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups1935376822645274424al_nat F2) K5)) (@ (@ tptp.groups1935376822645274424al_nat G2) K5)))) (forall ((K5 tptp.set_int) (F2 (-> tptp.int tptp.nat)) (G2 (-> tptp.int tptp.nat))) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) K5) (@ (@ tptp.ord_less_eq_nat (@ F2 I3)) (@ G2 I3)))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups4541462559716669496nt_nat F2) K5)) (@ (@ tptp.groups4541462559716669496nt_nat G2) K5)))) (forall ((K5 tptp.set_complex) (F2 (-> tptp.complex tptp.int)) (G2 (-> tptp.complex tptp.int))) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) K5) (@ (@ tptp.ord_less_eq_int (@ F2 I3)) (@ G2 I3)))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.groups5690904116761175830ex_int F2) K5)) (@ (@ tptp.groups5690904116761175830ex_int G2) K5)))) (forall ((K5 tptp.set_real) (F2 (-> tptp.real tptp.int)) (G2 (-> tptp.real tptp.int))) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) K5) (@ (@ tptp.ord_less_eq_int (@ F2 I3)) (@ G2 I3)))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.groups1932886352136224148al_int F2) K5)) (@ (@ tptp.groups1932886352136224148al_int G2) K5)))) (forall ((K5 tptp.set_nat) (F2 (-> tptp.nat tptp.int)) (G2 (-> tptp.nat tptp.int))) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.member_nat I3) K5) (@ (@ tptp.ord_less_eq_int (@ F2 I3)) (@ G2 I3)))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.groups3539618377306564664at_int F2) K5)) (@ (@ tptp.groups3539618377306564664at_int G2) K5)))) (forall ((R3 tptp.nat) (F2 (-> tptp.nat tptp.nat)) (A4 tptp.set_nat)) (= (@ (@ tptp.times_times_nat R3) (@ (@ tptp.groups3542108847815614940at_nat F2) A4)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_nat R3) (@ F2 N4)))) A4))) (forall ((R3 tptp.int) (F2 (-> tptp.int tptp.int)) (A4 tptp.set_int)) (= (@ (@ tptp.times_times_int R3) (@ (@ tptp.groups4538972089207619220nt_int F2) A4)) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((N4 tptp.int)) (@ (@ tptp.times_times_int R3) (@ F2 N4)))) A4))) (forall ((R3 tptp.real) (F2 (-> tptp.nat tptp.real)) (A4 tptp.set_nat)) (= (@ (@ tptp.times_times_real R3) (@ (@ tptp.groups6591440286371151544t_real F2) A4)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_real R3) (@ F2 N4)))) A4))) (forall ((F2 (-> tptp.nat tptp.nat)) (A4 tptp.set_nat) (R3 tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.groups3542108847815614940at_nat F2) A4)) R3) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_nat (@ F2 N4)) R3))) A4))) (forall ((F2 (-> tptp.int tptp.int)) (A4 tptp.set_int) (R3 tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.groups4538972089207619220nt_int F2) A4)) R3) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((N4 tptp.int)) (@ (@ tptp.times_times_int (@ F2 N4)) R3))) A4))) (forall ((F2 (-> tptp.nat tptp.real)) (A4 tptp.set_nat) (R3 tptp.real)) (= (@ (@ tptp.times_times_real (@ (@ tptp.groups6591440286371151544t_real F2) A4)) R3) (@ (@ tptp.groups6591440286371151544t_real (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_real (@ F2 N4)) R3))) A4))) (forall ((F2 (-> tptp.nat tptp.nat)) (A4 tptp.set_nat) (G2 (-> tptp.nat tptp.nat)) (B5 tptp.set_nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.groups3542108847815614940at_nat F2) A4)) (@ (@ tptp.groups3542108847815614940at_nat G2) B5)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I tptp.nat)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((J tptp.nat)) (@ (@ tptp.times_times_nat (@ F2 I)) (@ G2 J)))) B5))) A4))) (forall ((F2 (-> tptp.int tptp.int)) (A4 tptp.set_int) (G2 (-> tptp.int tptp.int)) (B5 tptp.set_int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.groups4538972089207619220nt_int F2) A4)) (@ (@ tptp.groups4538972089207619220nt_int G2) B5)) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((I tptp.int)) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((J tptp.int)) (@ (@ tptp.times_times_int (@ F2 I)) (@ G2 J)))) B5))) A4))) (forall ((F2 (-> tptp.nat tptp.real)) (A4 tptp.set_nat) (G2 (-> tptp.nat tptp.real)) (B5 tptp.set_nat)) (= (@ (@ tptp.times_times_real (@ (@ tptp.groups6591440286371151544t_real F2) A4)) (@ (@ tptp.groups6591440286371151544t_real G2) B5)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((J tptp.nat)) (@ (@ tptp.times_times_real (@ F2 I)) (@ G2 J)))) B5))) A4))) (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat M2) N) (=> (@ (@ tptp.dvd_dvd_nat N) M2) (= M2 N)))) (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (=> (@ _let_1 B) (=> (@ (@ tptp.dvd_dvd_nat B) C2) (@ _let_1 C2))))) (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (=> (@ _let_1 B) (=> (@ (@ tptp.dvd_dvd_int B) C2) (@ _let_1 C2))))) (forall ((A tptp.nat)) (@ (@ tptp.dvd_dvd_nat A) A)) (forall ((A tptp.int)) (@ (@ tptp.dvd_dvd_int A) A)) _let_269 _let_268 _let_267 (forall ((A tptp.complex)) (=> (@ (@ tptp.dvd_dvd_complex tptp.zero_zero_complex) A) (= A tptp.zero_zero_complex))) (forall ((A tptp.real)) (=> (@ (@ tptp.dvd_dvd_real tptp.zero_zero_real) A) (= A tptp.zero_zero_real))) (forall ((A tptp.rat)) (=> (@ (@ tptp.dvd_dvd_rat tptp.zero_zero_rat) A) (= A tptp.zero_zero_rat))) (forall ((A tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat tptp.zero_zero_nat) A) (= A tptp.zero_zero_nat))) (forall ((A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int tptp.zero_zero_int) A) (= A tptp.zero_zero_int))) (forall ((P tptp.nat) (A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat P) (@ (@ tptp.times_times_nat A) B)) (not (forall ((X3 tptp.nat) (Y3 tptp.nat)) (=> (= P (@ (@ tptp.times_times_nat X3) Y3)) (=> (@ (@ tptp.dvd_dvd_nat X3) A) (not (@ (@ tptp.dvd_dvd_nat Y3) B)))))))) (forall ((P tptp.int) (A tptp.int) (B tptp.int)) (=> (@ (@ tptp.dvd_dvd_int P) (@ (@ tptp.times_times_int A) B)) (not (forall ((X3 tptp.int) (Y3 tptp.int)) (=> (= P (@ (@ tptp.times_times_int X3) Y3)) (=> (@ (@ tptp.dvd_dvd_int X3) A) (not (@ (@ tptp.dvd_dvd_int Y3) B)))))))) (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) (@ (@ tptp.times_times_nat B) C2)) (exists ((B9 tptp.nat) (C5 tptp.nat)) (and (= A (@ (@ tptp.times_times_nat B9) C5)) (@ (@ tptp.dvd_dvd_nat B9) B) (@ (@ tptp.dvd_dvd_nat C5) C2))))) (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) (@ (@ tptp.times_times_int B) C2)) (exists ((B9 tptp.int) (C5 tptp.int)) (and (= A (@ (@ tptp.times_times_int B9) C5)) (@ (@ tptp.dvd_dvd_int B9) B) (@ (@ tptp.dvd_dvd_int C5) C2))))) (forall ((B tptp.real) (A tptp.real)) (=> (@ (@ tptp.dvd_dvd_real B) A) (not (forall ((K tptp.real)) (not (= A (@ (@ tptp.times_times_real B) K))))))) (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.dvd_dvd_rat B) A) (not (forall ((K tptp.rat)) (not (= A (@ (@ tptp.times_times_rat B) K))))))) (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B) A) (not (forall ((K tptp.nat)) (not (= A (@ (@ tptp.times_times_nat B) K))))))) (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B) A) (not (forall ((K tptp.int)) (not (= A (@ (@ tptp.times_times_int B) K))))))) (forall ((A tptp.real) (B tptp.real) (K2 tptp.real)) (=> (= A (@ (@ tptp.times_times_real B) K2)) (@ (@ tptp.dvd_dvd_real B) A))) (forall ((A tptp.rat) (B tptp.rat) (K2 tptp.rat)) (=> (= A (@ (@ tptp.times_times_rat B) K2)) (@ (@ tptp.dvd_dvd_rat B) A))) (forall ((A tptp.nat) (B tptp.nat) (K2 tptp.nat)) (=> (= A (@ (@ tptp.times_times_nat B) K2)) (@ (@ tptp.dvd_dvd_nat B) A))) (forall ((A tptp.int) (B tptp.int) (K2 tptp.int)) (=> (= A (@ (@ tptp.times_times_int B) K2)) (@ (@ tptp.dvd_dvd_int B) A))) (= tptp.dvd_dvd_real (lambda ((B4 tptp.real) (A5 tptp.real)) (exists ((K3 tptp.real)) (= A5 (@ (@ tptp.times_times_real B4) K3))))) (= tptp.dvd_dvd_rat (lambda ((B4 tptp.rat) (A5 tptp.rat)) (exists ((K3 tptp.rat)) (= A5 (@ (@ tptp.times_times_rat B4) K3))))) _let_266 _let_265 (forall ((A tptp.real) (C2 tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real A))) (=> (@ _let_1 C2) (@ _let_1 (@ (@ tptp.times_times_real B) C2))))) (forall ((A tptp.rat) (C2 tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat A))) (=> (@ _let_1 C2) (@ _let_1 (@ (@ tptp.times_times_rat B) C2))))) (forall ((A tptp.nat) (C2 tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (=> (@ _let_1 C2) (@ _let_1 (@ (@ tptp.times_times_nat B) C2))))) (forall ((A tptp.int) (C2 tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (=> (@ _let_1 C2) (@ _let_1 (@ (@ tptp.times_times_int B) C2))))) (forall ((A tptp.real) (B tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real A))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_times_real B) C2))))) (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat A))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_times_rat B) C2))))) (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_times_nat B) C2))))) (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_times_int B) C2))))) (forall ((A tptp.real) (B tptp.real) (C2 tptp.real)) (=> (@ (@ tptp.dvd_dvd_real (@ (@ tptp.times_times_real A) B)) C2) (@ (@ tptp.dvd_dvd_real A) C2))) (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (=> (@ (@ tptp.dvd_dvd_rat (@ (@ tptp.times_times_rat A) B)) C2) (@ (@ tptp.dvd_dvd_rat A) C2))) (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat A) B)) C2) (@ (@ tptp.dvd_dvd_nat A) C2))) (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A) B)) C2) (@ (@ tptp.dvd_dvd_int A) C2))) (forall ((A tptp.real) (B tptp.real)) (@ (@ tptp.dvd_dvd_real A) (@ (@ tptp.times_times_real A) B))) (forall ((A tptp.rat) (B tptp.rat)) (@ (@ tptp.dvd_dvd_rat A) (@ (@ tptp.times_times_rat A) B))) (forall ((A tptp.nat) (B tptp.nat)) (@ (@ tptp.dvd_dvd_nat A) (@ (@ tptp.times_times_nat A) B))) (forall ((A tptp.int) (B tptp.int)) (@ (@ tptp.dvd_dvd_int A) (@ (@ tptp.times_times_int A) B))) (forall ((A tptp.real) (B tptp.real) (C2 tptp.real) (D tptp.real)) (=> (@ (@ tptp.dvd_dvd_real A) B) (=> (@ (@ tptp.dvd_dvd_real C2) D) (@ (@ tptp.dvd_dvd_real (@ (@ tptp.times_times_real A) C2)) (@ (@ tptp.times_times_real B) D))))) (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat) (D tptp.rat)) (=> (@ (@ tptp.dvd_dvd_rat A) B) (=> (@ (@ tptp.dvd_dvd_rat C2) D) (@ (@ tptp.dvd_dvd_rat (@ (@ tptp.times_times_rat A) C2)) (@ (@ tptp.times_times_rat B) D))))) (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat) (D tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) B) (=> (@ (@ tptp.dvd_dvd_nat C2) D) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat A) C2)) (@ (@ tptp.times_times_nat B) D))))) (forall ((A tptp.int) (B tptp.int) (C2 tptp.int) (D tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) B) (=> (@ (@ tptp.dvd_dvd_int C2) D) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A) C2)) (@ (@ tptp.times_times_int B) D))))) (forall ((A tptp.real) (B tptp.real) (C2 tptp.real)) (=> (@ (@ tptp.dvd_dvd_real (@ (@ tptp.times_times_real A) B)) C2) (@ (@ tptp.dvd_dvd_real B) C2))) (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (=> (@ (@ tptp.dvd_dvd_rat (@ (@ tptp.times_times_rat A) B)) C2) (@ (@ tptp.dvd_dvd_rat B) C2))) (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat A) B)) C2) (@ (@ tptp.dvd_dvd_nat B) C2))) (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A) B)) C2) (@ (@ tptp.dvd_dvd_int B) C2))) (forall ((A tptp.real) (B tptp.real)) (@ (@ tptp.dvd_dvd_real A) (@ (@ tptp.times_times_real B) A))) (forall ((A tptp.rat) (B tptp.rat)) (@ (@ tptp.dvd_dvd_rat A) (@ (@ tptp.times_times_rat B) A))) (forall ((A tptp.nat) (B tptp.nat)) (@ (@ tptp.dvd_dvd_nat A) (@ (@ tptp.times_times_nat B) A))) (forall ((A tptp.int) (B tptp.int)) (@ (@ tptp.dvd_dvd_int A) (@ (@ tptp.times_times_int B) A))) (forall ((A tptp.real) (B tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real A))) (=> (@ _let_1 B) (= (@ _let_1 (@ (@ tptp.plus_plus_real B) C2)) (@ _let_1 C2))))) (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat A))) (=> (@ _let_1 B) (= (@ _let_1 (@ (@ tptp.plus_plus_rat B) C2)) (@ _let_1 C2))))) (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (=> (@ _let_1 B) (= (@ _let_1 (@ (@ tptp.plus_plus_nat B) C2)) (@ _let_1 C2))))) (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (=> (@ _let_1 B) (= (@ _let_1 (@ (@ tptp.plus_plus_int B) C2)) (@ _let_1 C2))))) (forall ((A tptp.real) (C2 tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real A))) (=> (@ _let_1 C2) (= (@ _let_1 (@ (@ tptp.plus_plus_real B) C2)) (@ _let_1 B))))) (forall ((A tptp.rat) (C2 tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat A))) (=> (@ _let_1 C2) (= (@ _let_1 (@ (@ tptp.plus_plus_rat B) C2)) (@ _let_1 B))))) (forall ((A tptp.nat) (C2 tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (=> (@ _let_1 C2) (= (@ _let_1 (@ (@ tptp.plus_plus_nat B) C2)) (@ _let_1 B))))) (forall ((A tptp.int) (C2 tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (=> (@ _let_1 C2) (= (@ _let_1 (@ (@ tptp.plus_plus_int B) C2)) (@ _let_1 B))))) (forall ((A tptp.real) (B tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real A))) (=> (@ _let_1 B) (=> (@ _let_1 C2) (@ _let_1 (@ (@ tptp.plus_plus_real B) C2)))))) (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat A))) (=> (@ _let_1 B) (=> (@ _let_1 C2) (@ _let_1 (@ (@ tptp.plus_plus_rat B) C2)))))) (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (=> (@ _let_1 B) (=> (@ _let_1 C2) (@ _let_1 (@ (@ tptp.plus_plus_nat B) C2)))))) (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (=> (@ _let_1 B) (=> (@ _let_1 C2) (@ _let_1 (@ (@ tptp.plus_plus_int B) C2)))))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer A))) (=> (@ _let_1 B) (=> (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer) (@ _let_1 tptp.one_one_Code_integer))))) (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (=> (@ _let_1 B) (=> (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat) (@ _let_1 tptp.one_one_nat))))) (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (=> (@ _let_1 B) (=> (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int) (@ _let_1 tptp.one_one_int))))) (forall ((B tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer B))) (=> (@ _let_1 tptp.one_one_Code_integer) (@ _let_1 A)))) (forall ((B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat B))) (=> (@ _let_1 tptp.one_one_nat) (@ _let_1 A)))) (forall ((B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int B))) (=> (@ _let_1 tptp.one_one_int) (@ _let_1 A)))) (forall ((A tptp.code_integer)) (@ (@ tptp.dvd_dvd_Code_integer tptp.one_one_Code_integer) A)) (forall ((A tptp.complex)) (@ (@ tptp.dvd_dvd_complex tptp.one_one_complex) A)) (forall ((A tptp.real)) (@ (@ tptp.dvd_dvd_real tptp.one_one_real) A)) (forall ((A tptp.nat)) (@ (@ tptp.dvd_dvd_nat tptp.one_one_nat) A)) (forall ((A tptp.int)) (@ (@ tptp.dvd_dvd_int tptp.one_one_int) A)) (forall ((X tptp.rat) (Y tptp.rat) (Z3 tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat X))) (=> (@ _let_1 Y) (=> (@ _let_1 Z3) (@ _let_1 (@ (@ tptp.minus_minus_rat Y) Z3)))))) (forall ((X tptp.int) (Y tptp.int) (Z3 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int X))) (=> (@ _let_1 Y) (=> (@ _let_1 Z3) (@ _let_1 (@ (@ tptp.minus_minus_int Y) Z3)))))) (forall ((D tptp.nat) (B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat A))) (=> (@ (@ tptp.dvd_dvd_nat D) B) (=> (@ (@ tptp.dvd_dvd_nat B) A) (= (@ (@ tptp.divide_divide_nat (@ _let_1 D)) (@ (@ tptp.divide_divide_nat B) D)) (@ _let_1 B)))))) (forall ((D tptp.int) (B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A))) (=> (@ (@ tptp.dvd_dvd_int D) B) (=> (@ (@ tptp.dvd_dvd_int B) A) (= (@ (@ tptp.divide_divide_int (@ _let_1 D)) (@ (@ tptp.divide_divide_int B) D)) (@ _let_1 B)))))) (forall ((A tptp.complex) (C2 tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.dvd_dvd_complex C2))) (=> (= (@ (@ tptp.divide1717551699836669952omplex A) C2) (@ (@ tptp.divide1717551699836669952omplex B) C2)) (=> (@ _let_1 A) (=> (@ _let_1 B) (= A B)))))) (forall ((A tptp.real) (C2 tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real C2))) (=> (= (@ (@ tptp.divide_divide_real A) C2) (@ (@ tptp.divide_divide_real B) C2)) (=> (@ _let_1 A) (=> (@ _let_1 B) (= A B)))))) (forall ((A tptp.rat) (C2 tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat C2))) (=> (= (@ (@ tptp.divide_divide_rat A) C2) (@ (@ tptp.divide_divide_rat B) C2)) (=> (@ _let_1 A) (=> (@ _let_1 B) (= A B)))))) (forall ((A tptp.nat) (C2 tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat C2))) (=> (= (@ (@ tptp.divide_divide_nat A) C2) (@ (@ tptp.divide_divide_nat B) C2)) (=> (@ _let_1 A) (=> (@ _let_1 B) (= A B)))))) (forall ((A tptp.int) (C2 tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int C2))) (=> (= (@ (@ tptp.divide_divide_int A) C2) (@ (@ tptp.divide_divide_int B) C2)) (=> (@ _let_1 A) (=> (@ _let_1 B) (= A B)))))) (forall ((C2 tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.dvd_dvd_complex C2))) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (= (@ (@ tptp.divide1717551699836669952omplex A) C2) (@ (@ tptp.divide1717551699836669952omplex B) C2)) (= A B)))))) (forall ((C2 tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real C2))) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (= (@ (@ tptp.divide_divide_real A) C2) (@ (@ tptp.divide_divide_real B) C2)) (= A B)))))) (forall ((C2 tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat C2))) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (= (@ (@ tptp.divide_divide_rat A) C2) (@ (@ tptp.divide_divide_rat B) C2)) (= A B)))))) (forall ((C2 tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat C2))) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (= (@ (@ tptp.divide_divide_nat A) C2) (@ (@ tptp.divide_divide_nat B) C2)) (= A B)))))) (forall ((C2 tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int C2))) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (= (@ (@ tptp.divide_divide_int A) C2) (@ (@ tptp.divide_divide_int B) C2)) (= A B)))))) (forall ((A tptp.nat)) (@ (@ tptp.dvd_dvd_nat A) tptp.zero_zero_nat)) (forall ((A tptp.nat)) (not (and (@ (@ tptp.dvd_dvd_nat tptp.zero_zero_nat) A) (not (= tptp.zero_zero_nat A))))) (forall ((A tptp.nat)) (= (@ (@ tptp.dvd_dvd_nat tptp.zero_zero_nat) A) (= A tptp.zero_zero_nat))) (forall ((A tptp.nat)) (let ((_let_1 (not (= A tptp.zero_zero_nat)))) (= _let_1 (and (@ (@ tptp.dvd_dvd_nat A) tptp.zero_zero_nat) _let_1)))) (forall ((A tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat tptp.zero_zero_nat) A) (= A tptp.zero_zero_nat))) (forall ((C2 tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat C2))) (=> (@ _let_1 (@ (@ tptp.modulo_modulo_nat A) B)) (=> (@ _let_1 B) (@ _let_1 A))))) (forall ((C2 tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int C2))) (=> (@ _let_1 (@ (@ tptp.modulo_modulo_int A) B)) (=> (@ _let_1 B) (@ _let_1 A))))) (forall ((C2 tptp.code_natural) (A tptp.code_natural) (B tptp.code_natural)) (let ((_let_1 (@ tptp.dvd_dvd_Code_natural C2))) (=> (@ _let_1 (@ (@ tptp.modulo8411746178871703098atural A) B)) (=> (@ _let_1 B) (@ _let_1 A))))) (forall ((C2 tptp.nat) (B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat C2))) (=> (@ _let_1 B) (= (@ _let_1 (@ (@ tptp.modulo_modulo_nat A) B)) (@ _let_1 A))))) (forall ((C2 tptp.int) (B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int C2))) (=> (@ _let_1 B) (= (@ _let_1 (@ (@ tptp.modulo_modulo_int A) B)) (@ _let_1 A))))) (forall ((C2 tptp.code_natural) (B tptp.code_natural) (A tptp.code_natural)) (let ((_let_1 (@ tptp.dvd_dvd_Code_natural C2))) (=> (@ _let_1 B) (= (@ _let_1 (@ (@ tptp.modulo8411746178871703098atural A) B)) (@ _let_1 A))))) (forall ((A4 tptp.set_complex) (F2 (-> tptp.complex tptp.real))) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) A4) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F2 X3)))) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.groups5808333547571424918x_real F2) A4)))) (forall ((A4 tptp.set_real) (F2 (-> tptp.real tptp.real))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) A4) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F2 X3)))) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.groups8097168146408367636l_real F2) A4)))) (forall ((A4 tptp.set_int) (F2 (-> tptp.int tptp.real))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A4) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F2 X3)))) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.groups8778361861064173332t_real F2) A4)))) (forall ((A4 tptp.set_complex) (F2 (-> tptp.complex tptp.rat))) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) A4) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F2 X3)))) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.groups5058264527183730370ex_rat F2) A4)))) (forall ((A4 tptp.set_real) (F2 (-> tptp.real tptp.rat))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) A4) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F2 X3)))) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.groups1300246762558778688al_rat F2) A4)))) (forall ((A4 tptp.set_nat) (F2 (-> tptp.nat tptp.rat))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A4) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F2 X3)))) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.groups2906978787729119204at_rat F2) A4)))) (forall ((A4 tptp.set_int) (F2 (-> tptp.int tptp.rat))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A4) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F2 X3)))) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.groups3906332499630173760nt_rat F2) A4)))) (forall ((A4 tptp.set_complex) (F2 (-> tptp.complex tptp.nat))) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) A4) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F2 X3)))) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ (@ tptp.groups5693394587270226106ex_nat F2) A4)))) (forall ((A4 tptp.set_real) (F2 (-> tptp.real tptp.nat))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) A4) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F2 X3)))) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ (@ tptp.groups1935376822645274424al_nat F2) A4)))) (forall ((A4 tptp.set_int) (F2 (-> tptp.int tptp.nat))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A4) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F2 X3)))) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ (@ tptp.groups4541462559716669496nt_nat F2) A4)))) (forall ((A4 tptp.set_complex) (F2 (-> tptp.complex tptp.real))) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) A4) (@ (@ tptp.ord_less_eq_real (@ F2 X3)) tptp.zero_zero_real))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups5808333547571424918x_real F2) A4)) tptp.zero_zero_real))) (forall ((A4 tptp.set_real) (F2 (-> tptp.real tptp.real))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) A4) (@ (@ tptp.ord_less_eq_real (@ F2 X3)) tptp.zero_zero_real))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups8097168146408367636l_real F2) A4)) tptp.zero_zero_real))) (forall ((A4 tptp.set_int) (F2 (-> tptp.int tptp.real))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A4) (@ (@ tptp.ord_less_eq_real (@ F2 X3)) tptp.zero_zero_real))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups8778361861064173332t_real F2) A4)) tptp.zero_zero_real))) (forall ((A4 tptp.set_complex) (F2 (-> tptp.complex tptp.rat))) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) A4) (@ (@ tptp.ord_less_eq_rat (@ F2 X3)) tptp.zero_zero_rat))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups5058264527183730370ex_rat F2) A4)) tptp.zero_zero_rat))) (forall ((A4 tptp.set_real) (F2 (-> tptp.real tptp.rat))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) A4) (@ (@ tptp.ord_less_eq_rat (@ F2 X3)) tptp.zero_zero_rat))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups1300246762558778688al_rat F2) A4)) tptp.zero_zero_rat))) (forall ((A4 tptp.set_nat) (F2 (-> tptp.nat tptp.rat))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A4) (@ (@ tptp.ord_less_eq_rat (@ F2 X3)) tptp.zero_zero_rat))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups2906978787729119204at_rat F2) A4)) tptp.zero_zero_rat))) (forall ((A4 tptp.set_int) (F2 (-> tptp.int tptp.rat))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A4) (@ (@ tptp.ord_less_eq_rat (@ F2 X3)) tptp.zero_zero_rat))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups3906332499630173760nt_rat F2) A4)) tptp.zero_zero_rat))) (forall ((A4 tptp.set_complex) (F2 (-> tptp.complex tptp.nat))) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) A4) (@ (@ tptp.ord_less_eq_nat (@ F2 X3)) tptp.zero_zero_nat))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups5693394587270226106ex_nat F2) A4)) tptp.zero_zero_nat))) (forall ((A4 tptp.set_real) (F2 (-> tptp.real tptp.nat))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) A4) (@ (@ tptp.ord_less_eq_nat (@ F2 X3)) tptp.zero_zero_nat))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups1935376822645274424al_nat F2) A4)) tptp.zero_zero_nat))) (forall ((A4 tptp.set_int) (F2 (-> tptp.int tptp.nat))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A4) (@ (@ tptp.ord_less_eq_nat (@ F2 X3)) tptp.zero_zero_nat))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups4541462559716669496nt_nat F2) A4)) tptp.zero_zero_nat))) (forall ((K2 tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat K2))) (=> (@ _let_1 M2) (=> (@ _let_1 N) (@ _let_1 (@ (@ tptp.minus_minus_nat M2) N)))))) (forall ((F2 (-> tptp.real tptp.rat)) (I5 tptp.set_real) (G2 (-> tptp.real tptp.rat)) (I2 tptp.real)) (=> (= (@ (@ tptp.groups1300246762558778688al_rat F2) I5) (@ (@ tptp.groups1300246762558778688al_rat G2) I5)) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) I5) (@ (@ tptp.ord_less_eq_rat (@ F2 I3)) (@ G2 I3)))) (=> (@ (@ tptp.member_real I2) I5) (=> (@ tptp.finite_finite_real I5) (= (@ F2 I2) (@ G2 I2))))))) (forall ((F2 (-> tptp.nat tptp.rat)) (I5 tptp.set_nat) (G2 (-> tptp.nat tptp.rat)) (I2 tptp.nat)) (=> (= (@ (@ tptp.groups2906978787729119204at_rat F2) I5) (@ (@ tptp.groups2906978787729119204at_rat G2) I5)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.member_nat I3) I5) (@ (@ tptp.ord_less_eq_rat (@ F2 I3)) (@ G2 I3)))) (=> (@ (@ tptp.member_nat I2) I5) (=> (@ tptp.finite_finite_nat I5) (= (@ F2 I2) (@ G2 I2))))))) (forall ((F2 (-> tptp.int tptp.rat)) (I5 tptp.set_int) (G2 (-> tptp.int tptp.rat)) (I2 tptp.int)) (=> (= (@ (@ tptp.groups3906332499630173760nt_rat F2) I5) (@ (@ tptp.groups3906332499630173760nt_rat G2) I5)) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) I5) (@ (@ tptp.ord_less_eq_rat (@ F2 I3)) (@ G2 I3)))) (=> (@ (@ tptp.member_int I2) I5) (=> (@ tptp.finite_finite_int I5) (= (@ F2 I2) (@ G2 I2))))))) (forall ((F2 (-> tptp.complex tptp.rat)) (I5 tptp.set_complex) (G2 (-> tptp.complex tptp.rat)) (I2 tptp.complex)) (=> (= (@ (@ tptp.groups5058264527183730370ex_rat F2) I5) (@ (@ tptp.groups5058264527183730370ex_rat G2) I5)) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) I5) (@ (@ tptp.ord_less_eq_rat (@ F2 I3)) (@ G2 I3)))) (=> (@ (@ tptp.member_complex I2) I5) (=> (@ tptp.finite3207457112153483333omplex I5) (= (@ F2 I2) (@ G2 I2))))))) (forall ((F2 (-> tptp.real tptp.nat)) (I5 tptp.set_real) (G2 (-> tptp.real tptp.nat)) (I2 tptp.real)) (=> (= (@ (@ tptp.groups1935376822645274424al_nat F2) I5) (@ (@ tptp.groups1935376822645274424al_nat G2) I5)) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) I5) (@ (@ tptp.ord_less_eq_nat (@ F2 I3)) (@ G2 I3)))) (=> (@ (@ tptp.member_real I2) I5) (=> (@ tptp.finite_finite_real I5) (= (@ F2 I2) (@ G2 I2))))))) (forall ((F2 (-> tptp.int tptp.nat)) (I5 tptp.set_int) (G2 (-> tptp.int tptp.nat)) (I2 tptp.int)) (=> (= (@ (@ tptp.groups4541462559716669496nt_nat F2) I5) (@ (@ tptp.groups4541462559716669496nt_nat G2) I5)) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) I5) (@ (@ tptp.ord_less_eq_nat (@ F2 I3)) (@ G2 I3)))) (=> (@ (@ tptp.member_int I2) I5) (=> (@ tptp.finite_finite_int I5) (= (@ F2 I2) (@ G2 I2))))))) (forall ((F2 (-> tptp.complex tptp.nat)) (I5 tptp.set_complex) (G2 (-> tptp.complex tptp.nat)) (I2 tptp.complex)) (=> (= (@ (@ tptp.groups5693394587270226106ex_nat F2) I5) (@ (@ tptp.groups5693394587270226106ex_nat G2) I5)) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) I5) (@ (@ tptp.ord_less_eq_nat (@ F2 I3)) (@ G2 I3)))) (=> (@ (@ tptp.member_complex I2) I5) (=> (@ tptp.finite3207457112153483333omplex I5) (= (@ F2 I2) (@ G2 I2))))))) (forall ((F2 (-> tptp.real tptp.int)) (I5 tptp.set_real) (G2 (-> tptp.real tptp.int)) (I2 tptp.real)) (=> (= (@ (@ tptp.groups1932886352136224148al_int F2) I5) (@ (@ tptp.groups1932886352136224148al_int G2) I5)) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) I5) (@ (@ tptp.ord_less_eq_int (@ F2 I3)) (@ G2 I3)))) (=> (@ (@ tptp.member_real I2) I5) (=> (@ tptp.finite_finite_real I5) (= (@ F2 I2) (@ G2 I2))))))) (forall ((F2 (-> tptp.nat tptp.int)) (I5 tptp.set_nat) (G2 (-> tptp.nat tptp.int)) (I2 tptp.nat)) (=> (= (@ (@ tptp.groups3539618377306564664at_int F2) I5) (@ (@ tptp.groups3539618377306564664at_int G2) I5)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.member_nat I3) I5) (@ (@ tptp.ord_less_eq_int (@ F2 I3)) (@ G2 I3)))) (=> (@ (@ tptp.member_nat I2) I5) (=> (@ tptp.finite_finite_nat I5) (= (@ F2 I2) (@ G2 I2))))))) (forall ((F2 (-> tptp.complex tptp.int)) (I5 tptp.set_complex) (G2 (-> tptp.complex tptp.int)) (I2 tptp.complex)) (=> (= (@ (@ tptp.groups5690904116761175830ex_int F2) I5) (@ (@ tptp.groups5690904116761175830ex_int G2) I5)) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) I5) (@ (@ tptp.ord_less_eq_int (@ F2 I3)) (@ G2 I3)))) (=> (@ (@ tptp.member_complex I2) I5) (=> (@ tptp.finite3207457112153483333omplex I5) (= (@ F2 I2) (@ G2 I2))))))) (forall ((A4 tptp.set_nat) (F2 (-> tptp.nat tptp.nat)) (G2 (-> tptp.nat tptp.nat))) (=> (not (@ (@ tptp.member_nat tptp.zero_zero_nat) A4)) (=> (forall ((X3 tptp.nat)) (let ((_let_1 (@ tptp.suc X3))) (=> (@ (@ tptp.member_nat _let_1) A4) (= (@ F2 _let_1) (@ G2 _let_1))))) (= (@ (@ tptp.groups3542108847815614940at_nat F2) A4) (@ (@ tptp.groups3542108847815614940at_nat G2) A4))))) (forall ((A4 tptp.set_nat) (F2 (-> tptp.nat tptp.real)) (G2 (-> tptp.nat tptp.real))) (=> (not (@ (@ tptp.member_nat tptp.zero_zero_nat) A4)) (=> (forall ((X3 tptp.nat)) (let ((_let_1 (@ tptp.suc X3))) (=> (@ (@ tptp.member_nat _let_1) A4) (= (@ F2 _let_1) (@ G2 _let_1))))) (= (@ (@ tptp.groups6591440286371151544t_real F2) A4) (@ (@ tptp.groups6591440286371151544t_real G2) A4))))) (forall ((A4 tptp.set_real) (G2 (-> tptp.real tptp.complex)) (P2 (-> tptp.real Bool))) (=> (@ tptp.finite_finite_real A4) (= (@ (@ tptp.groups5754745047067104278omplex G2) (@ tptp.collect_real (lambda ((X4 tptp.real)) (and (@ (@ tptp.member_real X4) A4) (@ P2 X4))))) (@ (@ tptp.groups5754745047067104278omplex (lambda ((X4 tptp.real)) (@ (@ (@ tptp.if_complex (@ P2 X4)) (@ G2 X4)) tptp.zero_zero_complex))) A4)))) (forall ((A4 tptp.set_nat) (G2 (-> tptp.nat tptp.complex)) (P2 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat A4) (= (@ (@ tptp.groups2073611262835488442omplex G2) (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) A4) (@ P2 X4))))) (@ (@ tptp.groups2073611262835488442omplex (lambda ((X4 tptp.nat)) (@ (@ (@ tptp.if_complex (@ P2 X4)) (@ G2 X4)) tptp.zero_zero_complex))) A4)))) (forall ((A4 tptp.set_int) (G2 (-> tptp.int tptp.complex)) (P2 (-> tptp.int Bool))) (=> (@ tptp.finite_finite_int A4) (= (@ (@ tptp.groups3049146728041665814omplex G2) (@ tptp.collect_int (lambda ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) A4) (@ P2 X4))))) (@ (@ tptp.groups3049146728041665814omplex (lambda ((X4 tptp.int)) (@ (@ (@ tptp.if_complex (@ P2 X4)) (@ G2 X4)) tptp.zero_zero_complex))) A4)))) (forall ((A4 tptp.set_complex) (G2 (-> tptp.complex tptp.complex)) (P2 (-> tptp.complex Bool))) (=> (@ tptp.finite3207457112153483333omplex A4) (= (@ (@ tptp.groups7754918857620584856omplex G2) (@ tptp.collect_complex (lambda ((X4 tptp.complex)) (and (@ (@ tptp.member_complex X4) A4) (@ P2 X4))))) (@ (@ tptp.groups7754918857620584856omplex (lambda ((X4 tptp.complex)) (@ (@ (@ tptp.if_complex (@ P2 X4)) (@ G2 X4)) tptp.zero_zero_complex))) A4)))) (forall ((A4 tptp.set_real) (G2 (-> tptp.real tptp.real)) (P2 (-> tptp.real Bool))) (=> (@ tptp.finite_finite_real A4) (= (@ (@ tptp.groups8097168146408367636l_real G2) (@ tptp.collect_real (lambda ((X4 tptp.real)) (and (@ (@ tptp.member_real X4) A4) (@ P2 X4))))) (@ (@ tptp.groups8097168146408367636l_real (lambda ((X4 tptp.real)) (@ (@ (@ tptp.if_real (@ P2 X4)) (@ G2 X4)) tptp.zero_zero_real))) A4)))) (forall ((A4 tptp.set_int) (G2 (-> tptp.int tptp.real)) (P2 (-> tptp.int Bool))) (=> (@ tptp.finite_finite_int A4) (= (@ (@ tptp.groups8778361861064173332t_real G2) (@ tptp.collect_int (lambda ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) A4) (@ P2 X4))))) (@ (@ tptp.groups8778361861064173332t_real (lambda ((X4 tptp.int)) (@ (@ (@ tptp.if_real (@ P2 X4)) (@ G2 X4)) tptp.zero_zero_real))) A4)))) (forall ((A4 tptp.set_complex) (G2 (-> tptp.complex tptp.real)) (P2 (-> tptp.complex Bool))) (=> (@ tptp.finite3207457112153483333omplex A4) (= (@ (@ tptp.groups5808333547571424918x_real G2) (@ tptp.collect_complex (lambda ((X4 tptp.complex)) (and (@ (@ tptp.member_complex X4) A4) (@ P2 X4))))) (@ (@ tptp.groups5808333547571424918x_real (lambda ((X4 tptp.complex)) (@ (@ (@ tptp.if_real (@ P2 X4)) (@ G2 X4)) tptp.zero_zero_real))) A4)))) (forall ((A4 tptp.set_real) (G2 (-> tptp.real tptp.rat)) (P2 (-> tptp.real Bool))) (=> (@ tptp.finite_finite_real A4) (= (@ (@ tptp.groups1300246762558778688al_rat G2) (@ tptp.collect_real (lambda ((X4 tptp.real)) (and (@ (@ tptp.member_real X4) A4) (@ P2 X4))))) (@ (@ tptp.groups1300246762558778688al_rat (lambda ((X4 tptp.real)) (@ (@ (@ tptp.if_rat (@ P2 X4)) (@ G2 X4)) tptp.zero_zero_rat))) A4)))) (forall ((A4 tptp.set_nat) (G2 (-> tptp.nat tptp.rat)) (P2 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat A4) (= (@ (@ tptp.groups2906978787729119204at_rat G2) (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) A4) (@ P2 X4))))) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((X4 tptp.nat)) (@ (@ (@ tptp.if_rat (@ P2 X4)) (@ G2 X4)) tptp.zero_zero_rat))) A4)))) (forall ((A4 tptp.set_int) (G2 (-> tptp.int tptp.rat)) (P2 (-> tptp.int Bool))) (=> (@ tptp.finite_finite_int A4) (= (@ (@ tptp.groups3906332499630173760nt_rat G2) (@ tptp.collect_int (lambda ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) A4) (@ P2 X4))))) (@ (@ tptp.groups3906332499630173760nt_rat (lambda ((X4 tptp.int)) (@ (@ (@ tptp.if_rat (@ P2 X4)) (@ G2 X4)) tptp.zero_zero_rat))) A4)))) (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))) (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_eq_set_real (@ tptp.collect_real (lambda ((C3 tptp.real)) (@ (@ tptp.dvd_dvd_real C3) A)))) (@ tptp.collect_real (lambda ((C3 tptp.real)) (@ (@ tptp.dvd_dvd_real C3) B)))) (@ (@ tptp.dvd_dvd_real A) B))) (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))) (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))) (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))))) (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_set_real (@ tptp.collect_real (lambda ((C3 tptp.real)) (@ (@ tptp.dvd_dvd_real C3) A)))) (@ tptp.collect_real (lambda ((C3 tptp.real)) (@ (@ tptp.dvd_dvd_real C3) B)))) (and (@ (@ tptp.dvd_dvd_real A) B) (not (@ (@ tptp.dvd_dvd_real B) A))))) (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.ord_less_set_nat (@ tptp.collect_nat (lambda ((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))))) (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))))) (forall ((S2 tptp.set_int) (T tptp.set_int) (G2 (-> tptp.int tptp.real)) (I2 (-> tptp.int tptp.int)) (F2 (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int S2) (=> (@ tptp.finite_finite_int T) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) T) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ G2 X3)))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) S2) (exists ((Xa tptp.int)) (and (@ (@ tptp.member_int Xa) T) (= (@ I2 Xa) X3) (@ (@ tptp.ord_less_eq_real (@ F2 X3)) (@ G2 Xa)))))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups8778361861064173332t_real F2) S2)) (@ (@ tptp.groups8778361861064173332t_real G2) T))))))) (forall ((S2 tptp.set_int) (T tptp.set_complex) (G2 (-> tptp.complex tptp.real)) (I2 (-> tptp.complex tptp.int)) (F2 (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int S2) (=> (@ tptp.finite3207457112153483333omplex T) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) T) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ G2 X3)))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) S2) (exists ((Xa tptp.complex)) (and (@ (@ tptp.member_complex Xa) T) (= (@ I2 Xa) X3) (@ (@ tptp.ord_less_eq_real (@ F2 X3)) (@ G2 Xa)))))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups8778361861064173332t_real F2) S2)) (@ (@ tptp.groups5808333547571424918x_real G2) T))))))) (forall ((S2 tptp.set_complex) (T tptp.set_int) (G2 (-> tptp.int tptp.real)) (I2 (-> tptp.int tptp.complex)) (F2 (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex S2) (=> (@ tptp.finite_finite_int T) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) T) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ G2 X3)))) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) S2) (exists ((Xa tptp.int)) (and (@ (@ tptp.member_int Xa) T) (= (@ I2 Xa) X3) (@ (@ tptp.ord_less_eq_real (@ F2 X3)) (@ G2 Xa)))))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups5808333547571424918x_real F2) S2)) (@ (@ tptp.groups8778361861064173332t_real G2) T))))))) (forall ((S2 tptp.set_complex) (T tptp.set_complex) (G2 (-> tptp.complex tptp.real)) (I2 (-> tptp.complex tptp.complex)) (F2 (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex S2) (=> (@ tptp.finite3207457112153483333omplex T) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) T) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ G2 X3)))) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) S2) (exists ((Xa tptp.complex)) (and (@ (@ tptp.member_complex Xa) T) (= (@ I2 Xa) X3) (@ (@ tptp.ord_less_eq_real (@ F2 X3)) (@ G2 Xa)))))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups5808333547571424918x_real F2) S2)) (@ (@ tptp.groups5808333547571424918x_real G2) T))))))) (forall ((S2 tptp.set_nat) (T tptp.set_nat) (G2 (-> tptp.nat tptp.rat)) (I2 (-> tptp.nat tptp.nat)) (F2 (-> tptp.nat tptp.rat))) (=> (@ tptp.finite_finite_nat S2) (=> (@ tptp.finite_finite_nat T) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) T) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ G2 X3)))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) S2) (exists ((Xa tptp.nat)) (and (@ (@ tptp.member_nat Xa) T) (= (@ I2 Xa) X3) (@ (@ tptp.ord_less_eq_rat (@ F2 X3)) (@ G2 Xa)))))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups2906978787729119204at_rat F2) S2)) (@ (@ tptp.groups2906978787729119204at_rat G2) T))))))) (forall ((S2 tptp.set_nat) (T tptp.set_int) (G2 (-> tptp.int tptp.rat)) (I2 (-> tptp.int tptp.nat)) (F2 (-> tptp.nat tptp.rat))) (=> (@ tptp.finite_finite_nat S2) (=> (@ tptp.finite_finite_int T) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) T) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ G2 X3)))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) S2) (exists ((Xa tptp.int)) (and (@ (@ tptp.member_int Xa) T) (= (@ I2 Xa) X3) (@ (@ tptp.ord_less_eq_rat (@ F2 X3)) (@ G2 Xa)))))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups2906978787729119204at_rat F2) S2)) (@ (@ tptp.groups3906332499630173760nt_rat G2) T))))))) (forall ((S2 tptp.set_nat) (T tptp.set_complex) (G2 (-> tptp.complex tptp.rat)) (I2 (-> tptp.complex tptp.nat)) (F2 (-> tptp.nat tptp.rat))) (=> (@ tptp.finite_finite_nat S2) (=> (@ tptp.finite3207457112153483333omplex T) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) T) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ G2 X3)))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) S2) (exists ((Xa tptp.complex)) (and (@ (@ tptp.member_complex Xa) T) (= (@ I2 Xa) X3) (@ (@ tptp.ord_less_eq_rat (@ F2 X3)) (@ G2 Xa)))))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups2906978787729119204at_rat F2) S2)) (@ (@ tptp.groups5058264527183730370ex_rat G2) T))))))) (forall ((S2 tptp.set_int) (T tptp.set_nat) (G2 (-> tptp.nat tptp.rat)) (I2 (-> tptp.nat tptp.int)) (F2 (-> tptp.int tptp.rat))) (=> (@ tptp.finite_finite_int S2) (=> (@ tptp.finite_finite_nat T) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) T) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ G2 X3)))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) S2) (exists ((Xa tptp.nat)) (and (@ (@ tptp.member_nat Xa) T) (= (@ I2 Xa) X3) (@ (@ tptp.ord_less_eq_rat (@ F2 X3)) (@ G2 Xa)))))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups3906332499630173760nt_rat F2) S2)) (@ (@ tptp.groups2906978787729119204at_rat G2) T))))))) (forall ((S2 tptp.set_int) (T tptp.set_int) (G2 (-> tptp.int tptp.rat)) (I2 (-> tptp.int tptp.int)) (F2 (-> tptp.int tptp.rat))) (=> (@ tptp.finite_finite_int S2) (=> (@ tptp.finite_finite_int T) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) T) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ G2 X3)))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) S2) (exists ((Xa tptp.int)) (and (@ (@ tptp.member_int Xa) T) (= (@ I2 Xa) X3) (@ (@ tptp.ord_less_eq_rat (@ F2 X3)) (@ G2 Xa)))))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups3906332499630173760nt_rat F2) S2)) (@ (@ tptp.groups3906332499630173760nt_rat G2) T))))))) (forall ((S2 tptp.set_int) (T tptp.set_complex) (G2 (-> tptp.complex tptp.rat)) (I2 (-> tptp.complex tptp.int)) (F2 (-> tptp.int tptp.rat))) (=> (@ tptp.finite_finite_int S2) (=> (@ tptp.finite3207457112153483333omplex T) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) T) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ G2 X3)))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) S2) (exists ((Xa tptp.complex)) (and (@ (@ tptp.member_complex Xa) T) (= (@ I2 Xa) X3) (@ (@ tptp.ord_less_eq_rat (@ F2 X3)) (@ G2 Xa)))))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups3906332499630173760nt_rat F2) S2)) (@ (@ tptp.groups5058264527183730370ex_rat G2) T))))))) (forall ((A4 tptp.set_real) (F2 (-> tptp.real tptp.real))) (=> (@ tptp.finite_finite_real A4) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) A4) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F2 X3)))) (= (= (@ (@ tptp.groups8097168146408367636l_real F2) A4) tptp.zero_zero_real) (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) A4) (= (@ F2 X4) tptp.zero_zero_real))))))) (forall ((A4 tptp.set_int) (F2 (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int A4) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A4) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F2 X3)))) (= (= (@ (@ tptp.groups8778361861064173332t_real F2) A4) tptp.zero_zero_real) (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) A4) (= (@ F2 X4) tptp.zero_zero_real))))))) (forall ((A4 tptp.set_complex) (F2 (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex A4) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) A4) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F2 X3)))) (= (= (@ (@ tptp.groups5808333547571424918x_real F2) A4) tptp.zero_zero_real) (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) A4) (= (@ F2 X4) tptp.zero_zero_real))))))) (forall ((A4 tptp.set_real) (F2 (-> tptp.real tptp.rat))) (=> (@ tptp.finite_finite_real A4) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) A4) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F2 X3)))) (= (= (@ (@ tptp.groups1300246762558778688al_rat F2) A4) tptp.zero_zero_rat) (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) A4) (= (@ F2 X4) tptp.zero_zero_rat))))))) (forall ((A4 tptp.set_nat) (F2 (-> tptp.nat tptp.rat))) (=> (@ tptp.finite_finite_nat A4) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A4) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F2 X3)))) (= (= (@ (@ tptp.groups2906978787729119204at_rat F2) A4) tptp.zero_zero_rat) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) A4) (= (@ F2 X4) tptp.zero_zero_rat))))))) (forall ((A4 tptp.set_int) (F2 (-> tptp.int tptp.rat))) (=> (@ tptp.finite_finite_int A4) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A4) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F2 X3)))) (= (= (@ (@ tptp.groups3906332499630173760nt_rat F2) A4) tptp.zero_zero_rat) (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) A4) (= (@ F2 X4) tptp.zero_zero_rat))))))) (forall ((A4 tptp.set_complex) (F2 (-> tptp.complex tptp.rat))) (=> (@ tptp.finite3207457112153483333omplex A4) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) A4) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F2 X3)))) (= (= (@ (@ tptp.groups5058264527183730370ex_rat F2) A4) tptp.zero_zero_rat) (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) A4) (= (@ F2 X4) tptp.zero_zero_rat))))))) (forall ((A4 tptp.set_real) (F2 (-> tptp.real tptp.nat))) (=> (@ tptp.finite_finite_real A4) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) A4) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F2 X3)))) (= (= (@ (@ tptp.groups1935376822645274424al_nat F2) A4) tptp.zero_zero_nat) (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) A4) (= (@ F2 X4) tptp.zero_zero_nat))))))) (forall ((A4 tptp.set_int) (F2 (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int A4) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A4) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F2 X3)))) (= (= (@ (@ tptp.groups4541462559716669496nt_nat F2) A4) tptp.zero_zero_nat) (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) A4) (= (@ F2 X4) tptp.zero_zero_nat))))))) (forall ((A4 tptp.set_complex) (F2 (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex A4) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) A4) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F2 X3)))) (= (= (@ (@ tptp.groups5693394587270226106ex_nat F2) A4) tptp.zero_zero_nat) (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) A4) (= (@ F2 X4) tptp.zero_zero_nat))))))) (forall ((A4 tptp.set_int) (F2 (-> tptp.int tptp.real)) (G2 (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int A4) (=> (forall ((X3 tptp.int)) (=> (@ (@ 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tptp.member_nat X3) A4) (@ (@ tptp.ord_less_eq_rat (@ F2 X3)) (@ G2 X3)))) (=> (exists ((X5 tptp.nat)) (and (@ (@ tptp.member_nat X5) A4) (@ (@ tptp.ord_less_rat (@ F2 X5)) (@ G2 X5)))) (@ (@ tptp.ord_less_rat (@ (@ tptp.groups2906978787729119204at_rat F2) A4)) (@ (@ tptp.groups2906978787729119204at_rat G2) A4)))))) (forall ((A4 tptp.set_int) (F2 (-> tptp.int tptp.rat)) (G2 (-> tptp.int tptp.rat))) (=> (@ tptp.finite_finite_int A4) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A4) (@ (@ tptp.ord_less_eq_rat (@ F2 X3)) (@ G2 X3)))) (=> (exists ((X5 tptp.int)) (and (@ (@ tptp.member_int X5) A4) (@ (@ tptp.ord_less_rat (@ F2 X5)) (@ G2 X5)))) (@ (@ tptp.ord_less_rat (@ (@ tptp.groups3906332499630173760nt_rat F2) A4)) (@ (@ tptp.groups3906332499630173760nt_rat G2) A4)))))) (forall ((A4 tptp.set_complex) (F2 (-> tptp.complex tptp.rat)) (G2 (-> tptp.complex tptp.rat))) (=> (@ tptp.finite3207457112153483333omplex A4) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) A4) (@ (@ tptp.ord_less_eq_rat (@ F2 X3)) (@ G2 X3)))) (=> (exists ((X5 tptp.complex)) (and (@ (@ tptp.member_complex X5) A4) (@ (@ tptp.ord_less_rat (@ F2 X5)) (@ G2 X5)))) (@ (@ tptp.ord_less_rat (@ (@ tptp.groups5058264527183730370ex_rat F2) A4)) (@ (@ tptp.groups5058264527183730370ex_rat G2) A4)))))) (forall ((A4 tptp.set_int) (F2 (-> tptp.int tptp.nat)) (G2 (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int A4) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A4) (@ (@ tptp.ord_less_eq_nat (@ F2 X3)) (@ G2 X3)))) (=> (exists ((X5 tptp.int)) (and (@ (@ tptp.member_int X5) A4) (@ (@ tptp.ord_less_nat (@ F2 X5)) (@ G2 X5)))) (@ (@ tptp.ord_less_nat (@ (@ tptp.groups4541462559716669496nt_nat F2) A4)) (@ (@ tptp.groups4541462559716669496nt_nat G2) A4)))))) (forall ((A4 tptp.set_complex) (F2 (-> tptp.complex tptp.nat)) (G2 (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex A4) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) A4) (@ 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(@ tptp.member_int A3) (@ (@ tptp.minus_minus_set_int S3) S5)) (@ (@ tptp.member_int (@ J2 A3)) (@ (@ tptp.minus_minus_set_int T5) T4)))) (=> (forall ((B3 tptp.int)) (=> (@ (@ tptp.member_int B3) (@ (@ tptp.minus_minus_set_int T5) T4)) (= (@ J2 (@ I2 B3)) B3))) (=> (forall ((B3 tptp.int)) (=> (@ (@ tptp.member_int B3) (@ (@ tptp.minus_minus_set_int T5) T4)) (@ (@ tptp.member_int (@ I2 B3)) (@ (@ tptp.minus_minus_set_int S3) S5)))) (=> (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) S5) (= (@ G2 A3) tptp.zero_zero_complex))) (=> (forall ((B3 tptp.int)) (=> (@ (@ tptp.member_int B3) T4) (= (@ H B3) tptp.zero_zero_complex))) (=> (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) S3) (= (@ H (@ J2 A3)) (@ G2 A3)))) (= (@ (@ tptp.groups3049146728041665814omplex G2) S3) (@ (@ tptp.groups3049146728041665814omplex H) T5)))))))))))) (forall ((S5 tptp.set_int) (T4 tptp.set_complex) (S3 tptp.set_int) (I2 (-> tptp.complex tptp.int)) (J2 (-> tptp.int tptp.complex)) (T5 tptp.set_complex) (G2 (-> tptp.int tptp.complex)) (H (-> tptp.complex tptp.complex))) (=> (@ tptp.finite_finite_int S5) (=> (@ tptp.finite3207457112153483333omplex T4) (=> (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) (@ (@ tptp.minus_minus_set_int S3) S5)) (= (@ I2 (@ J2 A3)) A3))) (=> (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) (@ (@ tptp.minus_minus_set_int S3) S5)) (@ (@ tptp.member_complex (@ J2 A3)) (@ (@ tptp.minus_811609699411566653omplex T5) T4)))) (=> (forall ((B3 tptp.complex)) (=> (@ (@ tptp.member_complex B3) (@ (@ tptp.minus_811609699411566653omplex T5) T4)) (= (@ J2 (@ I2 B3)) B3))) (=> (forall ((B3 tptp.complex)) (=> (@ (@ tptp.member_complex B3) (@ (@ tptp.minus_811609699411566653omplex T5) T4)) (@ (@ tptp.member_int (@ I2 B3)) (@ (@ tptp.minus_minus_set_int S3) S5)))) (=> (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) S5) (= (@ G2 A3) tptp.zero_zero_complex))) (=> (forall ((B3 tptp.complex)) (=> (@ (@ tptp.member_complex B3) T4) (= (@ H B3) tptp.zero_zero_complex))) (=> (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) S3) (= (@ H (@ J2 A3)) (@ G2 A3)))) (= (@ (@ tptp.groups3049146728041665814omplex G2) S3) (@ (@ tptp.groups7754918857620584856omplex H) T5)))))))))))) (forall ((S5 tptp.set_complex) (T4 tptp.set_real) (S3 tptp.set_complex) (I2 (-> tptp.real tptp.complex)) (J2 (-> tptp.complex tptp.real)) (T5 tptp.set_real) (G2 (-> tptp.complex tptp.complex)) (H (-> tptp.real tptp.complex))) (=> (@ tptp.finite3207457112153483333omplex S5) (=> (@ tptp.finite_finite_real T4) (=> (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) (@ (@ tptp.minus_811609699411566653omplex S3) S5)) (= (@ I2 (@ J2 A3)) A3))) (=> (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) (@ (@ tptp.minus_811609699411566653omplex S3) S5)) (@ (@ tptp.member_real (@ J2 A3)) (@ (@ tptp.minus_minus_set_real T5) T4)))) (=> (forall ((B3 tptp.real)) (=> (@ (@ tptp.member_real B3) (@ (@ tptp.minus_minus_set_real T5) T4)) (= (@ J2 (@ I2 B3)) B3))) (=> (forall ((B3 tptp.real)) (=> (@ (@ tptp.member_real B3) (@ (@ tptp.minus_minus_set_real T5) T4)) (@ (@ tptp.member_complex (@ I2 B3)) (@ (@ tptp.minus_811609699411566653omplex S3) S5)))) (=> (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) S5) (= (@ G2 A3) tptp.zero_zero_complex))) (=> (forall ((B3 tptp.real)) (=> (@ (@ tptp.member_real B3) T4) (= (@ H B3) tptp.zero_zero_complex))) (=> (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) S3) (= (@ H (@ J2 A3)) (@ G2 A3)))) (= (@ (@ tptp.groups7754918857620584856omplex G2) S3) (@ (@ tptp.groups5754745047067104278omplex H) T5)))))))))))) (forall ((S5 tptp.set_complex) (T4 tptp.set_int) (S3 tptp.set_complex) (I2 (-> tptp.int tptp.complex)) (J2 (-> tptp.complex tptp.int)) (T5 tptp.set_int) (G2 (-> tptp.complex tptp.complex)) (H (-> tptp.int tptp.complex))) (=> (@ tptp.finite3207457112153483333omplex S5) (=> (@ tptp.finite_finite_int T4) (=> (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) (@ (@ tptp.minus_811609699411566653omplex S3) S5)) (= (@ I2 (@ J2 A3)) A3))) (=> (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) (@ (@ tptp.minus_811609699411566653omplex S3) S5)) (@ (@ tptp.member_int (@ J2 A3)) (@ (@ tptp.minus_minus_set_int T5) T4)))) (=> (forall ((B3 tptp.int)) (=> (@ (@ tptp.member_int B3) (@ (@ tptp.minus_minus_set_int T5) T4)) (= (@ J2 (@ I2 B3)) B3))) (=> (forall ((B3 tptp.int)) (=> (@ (@ tptp.member_int B3) (@ (@ tptp.minus_minus_set_int T5) T4)) (@ (@ tptp.member_complex (@ I2 B3)) (@ (@ tptp.minus_811609699411566653omplex S3) S5)))) (=> (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) S5) (= (@ G2 A3) tptp.zero_zero_complex))) (=> (forall ((B3 tptp.int)) (=> (@ (@ tptp.member_int B3) T4) (= (@ H B3) tptp.zero_zero_complex))) (=> (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) S3) (= (@ H (@ J2 A3)) (@ G2 A3)))) (= (@ (@ tptp.groups7754918857620584856omplex G2) S3) (@ (@ tptp.groups3049146728041665814omplex H) T5)))))))))))) (forall ((S5 tptp.set_complex) (T4 tptp.set_complex) (S3 tptp.set_complex) (I2 (-> tptp.complex tptp.complex)) (J2 (-> tptp.complex tptp.complex)) (T5 tptp.set_complex) (G2 (-> tptp.complex tptp.complex)) (H (-> tptp.complex tptp.complex))) (=> (@ tptp.finite3207457112153483333omplex S5) (=> (@ tptp.finite3207457112153483333omplex T4) (=> (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) (@ (@ tptp.minus_811609699411566653omplex S3) S5)) (= (@ I2 (@ J2 A3)) A3))) (=> (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) (@ (@ tptp.minus_811609699411566653omplex S3) S5)) (@ (@ tptp.member_complex (@ J2 A3)) (@ (@ tptp.minus_811609699411566653omplex T5) T4)))) (=> (forall ((B3 tptp.complex)) (=> (@ (@ tptp.member_complex B3) (@ (@ tptp.minus_811609699411566653omplex T5) T4)) (= (@ J2 (@ I2 B3)) B3))) (=> (forall ((B3 tptp.complex)) (=> (@ (@ tptp.member_complex B3) (@ (@ tptp.minus_811609699411566653omplex T5) T4)) (@ (@ tptp.member_complex (@ I2 B3)) (@ (@ tptp.minus_811609699411566653omplex S3) S5)))) (=> (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) S5) (= (@ G2 A3) tptp.zero_zero_complex))) (=> (forall ((B3 tptp.complex)) (=> (@ (@ tptp.member_complex B3) T4) (= (@ H B3) tptp.zero_zero_complex))) (=> (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) S3) (= (@ H (@ J2 A3)) (@ G2 A3)))) (= (@ (@ tptp.groups7754918857620584856omplex G2) S3) (@ (@ tptp.groups7754918857620584856omplex H) T5)))))))))))) (forall ((S5 tptp.set_real) (T4 tptp.set_real) (S3 tptp.set_real) (I2 (-> tptp.real tptp.real)) (J2 (-> tptp.real tptp.real)) (T5 tptp.set_real) (G2 (-> tptp.real tptp.real)) (H (-> tptp.real tptp.real))) (=> (@ tptp.finite_finite_real S5) (=> (@ tptp.finite_finite_real T4) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) (@ (@ tptp.minus_minus_set_real S3) S5)) (= (@ I2 (@ J2 A3)) A3))) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) (@ (@ tptp.minus_minus_set_real S3) S5)) (@ (@ tptp.member_real (@ J2 A3)) (@ (@ tptp.minus_minus_set_real T5) T4)))) (=> (forall ((B3 tptp.real)) (=> (@ (@ tptp.member_real B3) (@ (@ tptp.minus_minus_set_real T5) T4)) (= (@ J2 (@ I2 B3)) B3))) (=> (forall ((B3 tptp.real)) (=> (@ (@ tptp.member_real B3) (@ (@ tptp.minus_minus_set_real T5) T4)) (@ (@ tptp.member_real (@ I2 B3)) (@ (@ tptp.minus_minus_set_real S3) S5)))) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) S5) (= (@ G2 A3) tptp.zero_zero_real))) (=> (forall ((B3 tptp.real)) (=> (@ (@ tptp.member_real B3) T4) (= (@ H B3) tptp.zero_zero_real))) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) S3) (= (@ H (@ J2 A3)) (@ G2 A3)))) (= (@ (@ tptp.groups8097168146408367636l_real G2) S3) (@ (@ tptp.groups8097168146408367636l_real H) T5)))))))))))) (not (@ (@ tptp.dvd_dvd_Code_integer tptp.zero_z3403309356797280102nteger) tptp.one_one_Code_integer)) (not (@ (@ tptp.dvd_dvd_nat tptp.zero_zero_nat) tptp.one_one_nat)) (not (@ (@ tptp.dvd_dvd_int tptp.zero_zero_int) tptp.one_one_int)) (forall ((B tptp.complex) (A tptp.complex)) (=> (@ (@ tptp.dvd_dvd_complex B) A) (= (= (@ (@ tptp.divide1717551699836669952omplex A) B) tptp.zero_zero_complex) (= A tptp.zero_zero_complex)))) (forall ((B tptp.real) (A tptp.real)) (=> (@ (@ tptp.dvd_dvd_real B) A) (= (= (@ (@ tptp.divide_divide_real A) B) tptp.zero_zero_real) (= A tptp.zero_zero_real)))) (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.dvd_dvd_rat B) A) (= (= (@ (@ tptp.divide_divide_rat A) B) tptp.zero_zero_rat) (= A tptp.zero_zero_rat)))) (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B) A) (= (= (@ (@ tptp.divide_divide_nat A) B) tptp.zero_zero_nat) (= A tptp.zero_zero_nat)))) (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B) A) (= (= (@ (@ tptp.divide_divide_int A) B) tptp.zero_zero_int) (= A tptp.zero_zero_int)))) (forall ((A tptp.code_integer) (B tptp.code_integer) (C2 tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer) (= (= (@ (@ tptp.times_3573771949741848930nteger B) A) (@ (@ tptp.times_3573771949741848930nteger C2) A)) (= B C2)))) (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (= (= (@ (@ tptp.times_times_nat B) A) (@ (@ tptp.times_times_nat C2) A)) (= B C2)))) (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (= (= (@ (@ tptp.times_times_int B) A) (@ (@ tptp.times_times_int C2) A)) (= B C2)))) (forall ((A tptp.code_integer) (B tptp.code_integer) (C2 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 C2)) (= B C2))))) (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (=> (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (= (= (@ _let_1 B) (@ _let_1 C2)) (= B C2))))) (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (=> (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (= (= (@ _let_1 B) (@ _let_1 C2)) (= B C2))))) (forall ((A tptp.code_integer) (B tptp.code_integer) (C2 tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer) (= (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.times_3573771949741848930nteger A) B)) C2) (@ (@ tptp.dvd_dvd_Code_integer B) C2)))) (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat A) B)) C2) (@ (@ tptp.dvd_dvd_nat B) C2)))) (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A) B)) C2) (@ (@ tptp.dvd_dvd_int B) C2)))) (forall ((B tptp.code_integer) (A tptp.code_integer) (C2 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) C2)) (@ _let_1 C2))))) (forall ((B tptp.nat) (A tptp.nat) (C2 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) C2)) (@ _let_1 C2))))) (forall ((B tptp.int) (A tptp.int) (C2 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) C2)) (@ _let_1 C2))))) (forall ((B tptp.code_integer) (A tptp.code_integer) (C2 tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer) (= (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.times_3573771949741848930nteger A) B)) C2) (@ (@ tptp.dvd_dvd_Code_integer A) C2)))) (forall ((B tptp.nat) (A tptp.nat) (C2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat A) B)) C2) (@ (@ tptp.dvd_dvd_nat A) C2)))) (forall ((B tptp.int) (A tptp.int) (C2 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A) B)) C2) (@ (@ tptp.dvd_dvd_int A) C2)))) (forall ((B tptp.code_integer) (A tptp.code_integer) (C2 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 C2) B)) (@ _let_1 C2))))) (forall ((B tptp.nat) (A tptp.nat) (C2 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 C2) B)) (@ _let_1 C2))))) (forall ((B tptp.int) (A tptp.int) (C2 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 C2) B)) (@ _let_1 C2))))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.times_3573771949741848930nteger A) B)) tptp.one_one_Code_integer) (and (@ (@ tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer) (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer)))) (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat A) B)) tptp.one_one_nat) (and (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat)))) (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A) B)) tptp.one_one_int) (and (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int)))) (forall ((C2 tptp.nat) (B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat C2) B) (= (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat B) C2)) A) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat B) A)) C2)))) (forall ((C2 tptp.int) (B tptp.int) (A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int C2) B) (= (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int B) C2)) A) (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int B) A)) C2)))) (forall ((C2 tptp.nat) (B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (=> (@ (@ tptp.dvd_dvd_nat C2) B) (= (@ _let_1 (@ (@ tptp.divide_divide_nat B) C2)) (@ (@ tptp.divide_divide_nat (@ _let_1 B)) C2))))) (forall ((C2 tptp.int) (B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (=> (@ (@ tptp.dvd_dvd_int C2) B) (= (@ _let_1 (@ (@ tptp.divide_divide_int B) C2)) (@ (@ tptp.divide_divide_int (@ _let_1 B)) C2))))) (forall ((C2 tptp.nat) (B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat A))) (=> (@ (@ tptp.dvd_dvd_nat C2) B) (=> (@ (@ tptp.dvd_dvd_nat B) A) (= (@ _let_1 (@ (@ tptp.divide_divide_nat B) C2)) (@ (@ tptp.times_times_nat (@ _let_1 B)) C2)))))) (forall ((C2 tptp.int) (B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A))) (=> (@ (@ tptp.dvd_dvd_int C2) B) (=> (@ (@ tptp.dvd_dvd_int B) A) (= (@ _let_1 (@ (@ tptp.divide_divide_int B) C2)) (@ (@ tptp.times_times_int (@ _let_1 B)) C2)))))) (forall ((B tptp.nat) (C2 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat A))) (let ((_let_2 (@ (@ tptp.times_times_nat B) C2))) (=> (@ (@ tptp.dvd_dvd_nat _let_2) A) (= (@ _let_1 _let_2) (@ (@ tptp.divide_divide_nat (@ _let_1 B)) C2)))))) (forall ((B tptp.int) (C2 tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A))) (let ((_let_2 (@ (@ tptp.times_times_int B) C2))) (=> (@ (@ tptp.dvd_dvd_int _let_2) A) (= (@ _let_1 _let_2) (@ (@ tptp.divide_divide_int (@ _let_1 B)) C2)))))) (forall ((A tptp.nat) (C2 tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat A) C2)) B) (@ (@ tptp.dvd_dvd_nat A) (@ (@ tptp.divide_divide_nat B) C2)))) (forall ((A tptp.int) (C2 tptp.int) (B tptp.int)) (=> (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A) C2)) B) (@ (@ tptp.dvd_dvd_int A) (@ (@ tptp.divide_divide_int B) C2)))) (forall ((B tptp.nat) (A tptp.nat) (D tptp.nat) (C2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B) A) (=> (@ (@ tptp.dvd_dvd_nat D) C2) (= (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat A) B)) (@ (@ tptp.divide_divide_nat C2) D)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat A) C2)) (@ (@ tptp.times_times_nat B) D)))))) (forall ((B tptp.int) (A tptp.int) (D tptp.int) (C2 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B) A) (=> (@ (@ tptp.dvd_dvd_int D) C2) (= (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int A) B)) (@ (@ tptp.divide_divide_int C2) D)) (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int A) C2)) (@ (@ tptp.times_times_int B) D)))))) (forall ((A tptp.code_integer) (B tptp.code_integer) (C2 tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer) (= (= (@ (@ tptp.divide6298287555418463151nteger B) A) (@ (@ tptp.divide6298287555418463151nteger C2) A)) (= B C2)))) (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (= (= (@ (@ tptp.divide_divide_nat B) A) (@ (@ tptp.divide_divide_nat C2) A)) (= B C2)))) (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (= (= (@ (@ tptp.divide_divide_int B) A) (@ (@ tptp.divide_divide_int C2) A)) (= B C2)))) (forall ((B tptp.code_integer) (A tptp.code_integer) (C2 tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer) (= (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.divide6298287555418463151nteger A) B)) C2) (@ (@ tptp.dvd_dvd_Code_integer A) C2)))) (forall ((B tptp.nat) (A tptp.nat) (C2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.divide_divide_nat A) B)) C2) (@ (@ tptp.dvd_dvd_nat A) C2)))) (forall ((B tptp.int) (A tptp.int) (C2 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.divide_divide_int A) B)) C2) (@ (@ tptp.dvd_dvd_int A) C2)))) (forall ((B tptp.code_integer) (A tptp.code_integer) (C2 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 C2) B)) (@ _let_1 C2))))) (forall ((B tptp.nat) (A tptp.nat) (C2 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 C2) B)) (@ _let_1 C2))))) (forall ((B tptp.int) (A tptp.int) (C2 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 C2) B)) (@ _let_1 C2))))) (forall ((A tptp.nat) (B tptp.nat)) (= (= (@ (@ tptp.modulo_modulo_nat A) B) tptp.zero_zero_nat) (@ (@ tptp.dvd_dvd_nat B) A))) (forall ((A tptp.int) (B tptp.int)) (= (= (@ (@ tptp.modulo_modulo_int A) B) tptp.zero_zero_int) (@ (@ tptp.dvd_dvd_int B) A))) (forall ((A tptp.code_natural) (B tptp.code_natural)) (= (= (@ (@ tptp.modulo8411746178871703098atural A) B) tptp.zero_z2226904508553997617atural) (@ (@ tptp.dvd_dvd_Code_natural B) A))) (= tptp.dvd_dvd_nat (lambda ((A5 tptp.nat) (B4 tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat B4) A5) tptp.zero_zero_nat))) (= tptp.dvd_dvd_int (lambda ((A5 tptp.int) (B4 tptp.int)) (= (@ (@ tptp.modulo_modulo_int B4) A5) tptp.zero_zero_int))) _let_264 (forall ((A tptp.nat) (B tptp.nat)) (=> (= (@ (@ tptp.modulo_modulo_nat A) B) tptp.zero_zero_nat) (@ (@ tptp.dvd_dvd_nat B) A))) (forall ((A tptp.int) (B tptp.int)) (=> (= (@ (@ tptp.modulo_modulo_int A) B) tptp.zero_zero_int) (@ (@ tptp.dvd_dvd_int B) A))) (forall ((A tptp.code_natural) (B tptp.code_natural)) (=> (= (@ (@ tptp.modulo8411746178871703098atural A) B) tptp.zero_z2226904508553997617atural) (@ (@ tptp.dvd_dvd_Code_natural B) A))) (forall ((X tptp.nat) (Y tptp.nat) (N tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat X) Y) (=> (@ (@ tptp.ord_less_eq_nat N) M2) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.power_power_nat X) N)) (@ (@ tptp.power_power_nat Y) M2))))) (forall ((X tptp.real) (Y tptp.real) (N tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_real X) Y) (=> (@ (@ tptp.ord_less_eq_nat N) M2) (@ (@ tptp.dvd_dvd_real (@ (@ tptp.power_power_real X) N)) (@ (@ tptp.power_power_real Y) M2))))) (forall ((X tptp.int) (Y tptp.int) (N tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_int X) Y) (=> (@ (@ tptp.ord_less_eq_nat N) M2) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.power_power_int X) N)) (@ (@ tptp.power_power_int Y) M2))))) (forall ((X tptp.complex) (Y tptp.complex) (N tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_complex X) Y) (=> (@ (@ tptp.ord_less_eq_nat N) M2) (@ (@ tptp.dvd_dvd_complex (@ (@ tptp.power_power_complex X) N)) (@ (@ tptp.power_power_complex Y) M2))))) (forall ((A tptp.nat) (N tptp.nat) (B tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.dvd_dvd_nat (@ _let_1 N)) B) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (@ (@ tptp.dvd_dvd_nat (@ _let_1 M2)) B))))) (forall ((A tptp.real) (N tptp.nat) (B tptp.real) (M2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.dvd_dvd_real (@ _let_1 N)) B) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (@ (@ tptp.dvd_dvd_real (@ _let_1 M2)) B))))) (forall ((A tptp.int) (N tptp.nat) (B tptp.int) (M2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.dvd_dvd_int (@ _let_1 N)) B) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (@ (@ tptp.dvd_dvd_int (@ _let_1 M2)) B))))) (forall ((A tptp.complex) (N tptp.nat) (B tptp.complex) (M2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex A))) (=> (@ (@ tptp.dvd_dvd_complex (@ _let_1 N)) B) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (@ (@ tptp.dvd_dvd_complex (@ _let_1 M2)) B))))) (forall ((M2 tptp.nat) (N tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (@ (@ tptp.dvd_dvd_nat (@ _let_1 M2)) (@ _let_1 N))))) (forall ((M2 tptp.nat) (N tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (@ (@ tptp.dvd_dvd_real (@ _let_1 M2)) (@ _let_1 N))))) (forall ((M2 tptp.nat) (N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (@ (@ tptp.dvd_dvd_int (@ _let_1 M2)) (@ _let_1 N))))) (forall ((M2 tptp.nat) (N tptp.nat) (A tptp.complex)) (let ((_let_1 (@ tptp.power_power_complex A))) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (@ (@ tptp.dvd_dvd_complex (@ _let_1 M2)) (@ _let_1 N))))) (forall ((B tptp.nat) (A tptp.nat)) (@ (@ tptp.dvd_dvd_nat B) (@ (@ tptp.minus_minus_nat A) (@ (@ tptp.modulo_modulo_nat A) B)))) (forall ((B tptp.int) (A tptp.int)) (@ (@ tptp.dvd_dvd_int B) (@ (@ tptp.minus_minus_int A) (@ (@ tptp.modulo_modulo_int A) B)))) (forall ((B tptp.code_natural) (A tptp.code_natural)) (@ (@ tptp.dvd_dvd_Code_natural B) (@ (@ tptp.minus_7197305767214868737atural A) (@ (@ tptp.modulo8411746178871703098atural A) B)))) (forall ((N tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 N) (=> (@ (@ tptp.dvd_dvd_nat M2) N) (@ _let_1 M2))))) (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M2) (=> (@ (@ tptp.ord_less_nat M2) N) (not (@ (@ tptp.dvd_dvd_nat N) M2))))) (forall ((X tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X) (@ _let_1 (@ (@ tptp.comm_s7457072308508201937r_real X) N))))) (forall ((X tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 X) (@ _let_1 (@ (@ tptp.comm_s4028243227959126397er_rat X) N))))) (forall ((X tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 X) (@ _let_1 (@ (@ tptp.comm_s4663373288045622133er_nat X) N))))) (forall ((X tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 X) (@ _let_1 (@ (@ tptp.comm_s4660882817536571857er_int X) N))))) (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat M2))) (= (@ _let_1 (@ (@ tptp.minus_minus_nat N) M2)) (or (@ (@ tptp.ord_less_nat N) M2) (@ _let_1 N))))) (forall ((S2 tptp.set_real) (F2 (-> tptp.real tptp.real)) (I2 tptp.real)) (=> (@ tptp.finite_finite_real S2) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) S2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F2 I3)))) (=> (= (@ (@ tptp.groups8097168146408367636l_real F2) S2) tptp.zero_zero_real) (=> (@ (@ tptp.member_real I2) S2) (= (@ F2 I2) tptp.zero_zero_real)))))) (forall ((S2 tptp.set_int) (F2 (-> tptp.int tptp.real)) (I2 tptp.int)) (=> (@ tptp.finite_finite_int S2) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) S2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F2 I3)))) (=> (= (@ (@ tptp.groups8778361861064173332t_real F2) S2) tptp.zero_zero_real) (=> (@ (@ tptp.member_int I2) S2) (= (@ F2 I2) tptp.zero_zero_real)))))) (forall ((S2 tptp.set_complex) (F2 (-> tptp.complex tptp.real)) (I2 tptp.complex)) (=> (@ tptp.finite3207457112153483333omplex S2) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) S2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F2 I3)))) (=> (= (@ (@ tptp.groups5808333547571424918x_real F2) S2) tptp.zero_zero_real) (=> (@ (@ tptp.member_complex I2) S2) (= (@ F2 I2) tptp.zero_zero_real)))))) (forall ((S2 tptp.set_real) (F2 (-> tptp.real tptp.rat)) (I2 tptp.real)) (=> (@ tptp.finite_finite_real S2) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) S2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F2 I3)))) (=> (= (@ (@ tptp.groups1300246762558778688al_rat F2) S2) tptp.zero_zero_rat) (=> (@ (@ tptp.member_real I2) S2) (= (@ F2 I2) tptp.zero_zero_rat)))))) (forall ((S2 tptp.set_nat) (F2 (-> tptp.nat tptp.rat)) (I2 tptp.nat)) (=> (@ tptp.finite_finite_nat S2) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.member_nat I3) S2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F2 I3)))) (=> (= (@ (@ tptp.groups2906978787729119204at_rat F2) S2) tptp.zero_zero_rat) (=> (@ (@ tptp.member_nat I2) S2) (= (@ F2 I2) tptp.zero_zero_rat)))))) (forall ((S2 tptp.set_int) (F2 (-> tptp.int tptp.rat)) (I2 tptp.int)) (=> (@ tptp.finite_finite_int S2) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) S2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F2 I3)))) (=> (= (@ (@ tptp.groups3906332499630173760nt_rat F2) S2) tptp.zero_zero_rat) (=> (@ (@ tptp.member_int I2) S2) (= (@ F2 I2) tptp.zero_zero_rat)))))) (forall ((S2 tptp.set_complex) (F2 (-> tptp.complex tptp.rat)) (I2 tptp.complex)) (=> (@ tptp.finite3207457112153483333omplex S2) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) S2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F2 I3)))) (=> (= (@ (@ tptp.groups5058264527183730370ex_rat F2) S2) tptp.zero_zero_rat) (=> (@ (@ tptp.member_complex I2) S2) (= (@ F2 I2) tptp.zero_zero_rat)))))) (forall ((S2 tptp.set_real) (F2 (-> tptp.real tptp.nat)) (I2 tptp.real)) (=> (@ tptp.finite_finite_real S2) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) S2) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F2 I3)))) (=> (= (@ (@ tptp.groups1935376822645274424al_nat F2) S2) tptp.zero_zero_nat) (=> (@ (@ tptp.member_real I2) S2) (= (@ F2 I2) tptp.zero_zero_nat)))))) (forall ((S2 tptp.set_int) (F2 (-> tptp.int tptp.nat)) (I2 tptp.int)) (=> (@ tptp.finite_finite_int S2) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) S2) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F2 I3)))) (=> (= (@ (@ tptp.groups4541462559716669496nt_nat F2) S2) tptp.zero_zero_nat) (=> (@ (@ tptp.member_int I2) S2) (= (@ F2 I2) tptp.zero_zero_nat)))))) (forall ((S2 tptp.set_complex) (F2 (-> tptp.complex tptp.nat)) (I2 tptp.complex)) (=> (@ tptp.finite3207457112153483333omplex S2) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) S2) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F2 I3)))) (=> (= (@ (@ tptp.groups5693394587270226106ex_nat F2) S2) tptp.zero_zero_nat) (=> (@ (@ tptp.member_complex I2) S2) (= (@ F2 I2) tptp.zero_zero_nat)))))) (forall ((S2 tptp.set_real) (F2 (-> tptp.real tptp.real)) (B5 tptp.real) (I2 tptp.real)) (=> (@ tptp.finite_finite_real S2) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) S2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F2 I3)))) (=> (= (@ (@ tptp.groups8097168146408367636l_real F2) S2) B5) (=> (@ (@ tptp.member_real I2) S2) (@ (@ tptp.ord_less_eq_real (@ F2 I2)) B5)))))) (forall ((S2 tptp.set_int) (F2 (-> tptp.int tptp.real)) (B5 tptp.real) (I2 tptp.int)) (=> (@ tptp.finite_finite_int S2) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) S2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F2 I3)))) (=> (= (@ (@ tptp.groups8778361861064173332t_real F2) S2) B5) (=> (@ (@ tptp.member_int I2) S2) (@ (@ tptp.ord_less_eq_real (@ F2 I2)) B5)))))) (forall ((S2 tptp.set_complex) (F2 (-> tptp.complex tptp.real)) (B5 tptp.real) (I2 tptp.complex)) (=> (@ tptp.finite3207457112153483333omplex S2) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) S2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F2 I3)))) (=> (= (@ (@ tptp.groups5808333547571424918x_real F2) S2) B5) (=> (@ (@ tptp.member_complex I2) S2) (@ (@ tptp.ord_less_eq_real (@ F2 I2)) B5)))))) (forall ((S2 tptp.set_real) (F2 (-> tptp.real tptp.rat)) (B5 tptp.rat) (I2 tptp.real)) (=> (@ tptp.finite_finite_real S2) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) S2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F2 I3)))) (=> (= (@ (@ tptp.groups1300246762558778688al_rat F2) S2) B5) (=> (@ (@ tptp.member_real I2) S2) (@ (@ tptp.ord_less_eq_rat (@ F2 I2)) B5)))))) (forall ((S2 tptp.set_nat) (F2 (-> tptp.nat tptp.rat)) (B5 tptp.rat) (I2 tptp.nat)) (=> (@ tptp.finite_finite_nat S2) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.member_nat I3) S2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F2 I3)))) (=> (= (@ (@ tptp.groups2906978787729119204at_rat F2) S2) B5) (=> (@ (@ tptp.member_nat I2) S2) (@ (@ tptp.ord_less_eq_rat (@ F2 I2)) B5)))))) (forall ((S2 tptp.set_int) (F2 (-> tptp.int tptp.rat)) (B5 tptp.rat) (I2 tptp.int)) (=> (@ tptp.finite_finite_int S2) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) S2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F2 I3)))) (=> (= (@ (@ tptp.groups3906332499630173760nt_rat F2) S2) B5) (=> (@ (@ tptp.member_int I2) S2) (@ (@ tptp.ord_less_eq_rat (@ F2 I2)) B5)))))) (forall ((S2 tptp.set_complex) (F2 (-> tptp.complex tptp.rat)) (B5 tptp.rat) (I2 tptp.complex)) (=> (@ tptp.finite3207457112153483333omplex S2) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) S2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F2 I3)))) (=> (= (@ (@ tptp.groups5058264527183730370ex_rat F2) S2) B5) (=> (@ (@ tptp.member_complex I2) S2) (@ (@ tptp.ord_less_eq_rat (@ F2 I2)) B5)))))) (forall ((S2 tptp.set_real) (F2 (-> tptp.real tptp.nat)) (B5 tptp.nat) (I2 tptp.real)) (=> (@ tptp.finite_finite_real S2) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) S2) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F2 I3)))) (=> (= (@ (@ tptp.groups1935376822645274424al_nat F2) S2) B5) (=> (@ (@ tptp.member_real I2) S2) (@ (@ tptp.ord_less_eq_nat (@ F2 I2)) B5)))))) (forall ((S2 tptp.set_int) (F2 (-> tptp.int tptp.nat)) (B5 tptp.nat) (I2 tptp.int)) (=> (@ tptp.finite_finite_int S2) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) S2) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F2 I3)))) (=> (= (@ (@ tptp.groups4541462559716669496nt_nat F2) S2) B5) (=> (@ (@ tptp.member_int I2) S2) (@ (@ tptp.ord_less_eq_nat (@ F2 I2)) B5)))))) (forall ((S2 tptp.set_complex) (F2 (-> tptp.complex tptp.nat)) (B5 tptp.nat) (I2 tptp.complex)) (=> (@ tptp.finite3207457112153483333omplex S2) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) S2) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F2 I3)))) (=> (= (@ (@ tptp.groups5693394587270226106ex_nat F2) S2) B5) (=> (@ (@ tptp.member_complex I2) S2) (@ (@ tptp.ord_less_eq_nat (@ F2 I2)) B5)))))) (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat M2))) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ _let_1 N) (@ _let_1 (@ (@ tptp.minus_minus_nat N) M2)))))) (forall ((K2 tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat K2))) (=> (@ _let_1 (@ (@ tptp.minus_minus_nat M2) N)) (=> (@ _let_1 M2) (=> (@ (@ tptp.ord_less_eq_nat N) M2) (@ _let_1 N)))))) (forall ((K2 tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat K2))) (=> (@ _let_1 (@ (@ tptp.minus_minus_nat M2) N)) (=> (@ _let_1 N) (=> (@ (@ tptp.ord_less_eq_nat N) M2) (@ _let_1 M2)))))) (forall ((A tptp.complex) (N tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.comm_s2602460028002588243omplex A))) (=> (= (@ _let_1 N) tptp.zero_zero_complex) (=> (@ (@ tptp.ord_less_eq_nat N) M2) (= (@ _let_1 M2) tptp.zero_zero_complex))))) (forall ((A tptp.real) (N tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.comm_s7457072308508201937r_real A))) (=> (= (@ _let_1 N) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_nat N) M2) (= (@ _let_1 M2) tptp.zero_zero_real))))) (forall ((A tptp.rat) (N tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.comm_s4028243227959126397er_rat A))) (=> (= (@ _let_1 N) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_nat N) M2) (= (@ _let_1 M2) tptp.zero_zero_rat))))) (forall ((A tptp.complex) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.comm_s2602460028002588243omplex A))) (=> (not (= (@ _let_1 M2) tptp.zero_zero_complex)) (=> (@ (@ tptp.ord_less_eq_nat N) M2) (not (= (@ _let_1 N) tptp.zero_zero_complex)))))) (forall ((A tptp.real) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.comm_s7457072308508201937r_real A))) (=> (not (= (@ _let_1 M2) tptp.zero_zero_real)) (=> (@ (@ tptp.ord_less_eq_nat N) M2) (not (= (@ _let_1 N) tptp.zero_zero_real)))))) (forall ((A tptp.rat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.comm_s4028243227959126397er_rat A))) (=> (not (= (@ _let_1 M2) tptp.zero_zero_rat)) (=> (@ (@ tptp.ord_less_eq_nat N) M2) (not (= (@ _let_1 N) tptp.zero_zero_rat)))))) (forall ((A tptp.nat) (B tptp.nat)) (exists ((D5 tptp.nat) (X3 tptp.nat) (Y3 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (let ((_let_2 (@ tptp.times_times_nat B))) (let ((_let_3 (@ tptp.dvd_dvd_nat D5))) (and (@ _let_3 A) (@ _let_3 B) (or (= (@ _let_1 X3) (@ (@ tptp.plus_plus_nat (@ _let_2 Y3)) D5)) (= (@ _let_2 X3) (@ (@ tptp.plus_plus_nat (@ _let_1 Y3)) D5))))))))) (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 ((X3 tptp.nat) (Y3 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (let ((_let_2 (@ (@ tptp.plus_plus_nat A) B))) (let ((_let_3 (@ tptp.times_times_nat _let_2))) (let ((_let_4 (@ tptp.dvd_dvd_nat D))) (and (@ _let_4 A) (@ _let_4 _let_2) (or (= (@ _let_1 X3) (@ (@ tptp.plus_plus_nat (@ _let_3 Y3)) D)) (= (@ _let_3 X3) (@ (@ tptp.plus_plus_nat (@ _let_1 Y3)) D)))))))))))))))) (forall ((A tptp.nat) (B tptp.nat)) (exists ((D5 tptp.nat) (X3 tptp.nat) (Y3 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (let ((_let_2 (@ tptp.times_times_nat B))) (let ((_let_3 (@ tptp.dvd_dvd_nat D5))) (and (@ _let_3 A) (@ _let_3 B) (or (= (@ (@ tptp.minus_minus_nat (@ _let_1 X3)) (@ _let_2 Y3)) D5) (= (@ (@ tptp.minus_minus_nat (@ _let_2 X3)) (@ _let_1 Y3)) D5)))))))) (forall ((A4 tptp.set_real) (G2 (-> tptp.real tptp.complex)) (B5 tptp.set_real)) (=> (@ tptp.finite_finite_real A4) (= (@ (@ tptp.groups5754745047067104278omplex G2) (@ (@ tptp.inf_inf_set_real A4) B5)) (@ (@ tptp.groups5754745047067104278omplex (lambda ((X4 tptp.real)) (@ (@ (@ tptp.if_complex (@ (@ tptp.member_real X4) B5)) (@ G2 X4)) tptp.zero_zero_complex))) A4)))) (forall ((A4 tptp.set_int) (G2 (-> tptp.int tptp.complex)) (B5 tptp.set_int)) (=> (@ tptp.finite_finite_int A4) (= (@ (@ tptp.groups3049146728041665814omplex G2) (@ (@ tptp.inf_inf_set_int A4) B5)) (@ (@ tptp.groups3049146728041665814omplex (lambda ((X4 tptp.int)) (@ (@ (@ tptp.if_complex (@ (@ tptp.member_int X4) B5)) (@ G2 X4)) tptp.zero_zero_complex))) A4)))) (forall ((A4 tptp.set_complex) (G2 (-> tptp.complex tptp.complex)) (B5 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex A4) (= (@ (@ tptp.groups7754918857620584856omplex G2) (@ (@ tptp.inf_inf_set_complex A4) B5)) (@ (@ tptp.groups7754918857620584856omplex (lambda ((X4 tptp.complex)) (@ (@ (@ tptp.if_complex (@ (@ tptp.member_complex X4) B5)) (@ G2 X4)) tptp.zero_zero_complex))) A4)))) (forall ((A4 tptp.set_real) (G2 (-> tptp.real tptp.real)) (B5 tptp.set_real)) (=> (@ tptp.finite_finite_real A4) (= (@ (@ tptp.groups8097168146408367636l_real G2) (@ (@ tptp.inf_inf_set_real A4) B5)) (@ (@ tptp.groups8097168146408367636l_real (lambda ((X4 tptp.real)) (@ (@ (@ tptp.if_real (@ (@ tptp.member_real X4) B5)) (@ G2 X4)) tptp.zero_zero_real))) A4)))) (forall ((A4 tptp.set_int) (G2 (-> tptp.int tptp.real)) (B5 tptp.set_int)) (=> (@ tptp.finite_finite_int A4) (= (@ (@ tptp.groups8778361861064173332t_real G2) (@ (@ tptp.inf_inf_set_int A4) B5)) (@ (@ tptp.groups8778361861064173332t_real (lambda ((X4 tptp.int)) (@ (@ (@ tptp.if_real (@ (@ tptp.member_int X4) B5)) (@ G2 X4)) tptp.zero_zero_real))) A4)))) (forall ((A4 tptp.set_complex) (G2 (-> tptp.complex tptp.real)) (B5 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex A4) (= (@ (@ tptp.groups5808333547571424918x_real G2) (@ (@ tptp.inf_inf_set_complex A4) B5)) (@ (@ tptp.groups5808333547571424918x_real (lambda ((X4 tptp.complex)) (@ (@ (@ tptp.if_real (@ (@ tptp.member_complex X4) B5)) (@ G2 X4)) tptp.zero_zero_real))) A4)))) (forall ((A4 tptp.set_real) (G2 (-> tptp.real tptp.rat)) (B5 tptp.set_real)) (=> (@ tptp.finite_finite_real A4) (= (@ (@ tptp.groups1300246762558778688al_rat G2) (@ (@ tptp.inf_inf_set_real A4) B5)) (@ (@ tptp.groups1300246762558778688al_rat (lambda ((X4 tptp.real)) (@ (@ (@ tptp.if_rat (@ (@ tptp.member_real X4) B5)) (@ G2 X4)) tptp.zero_zero_rat))) A4)))) (forall ((A4 tptp.set_int) (G2 (-> tptp.int tptp.rat)) (B5 tptp.set_int)) (=> (@ tptp.finite_finite_int A4) (= (@ (@ tptp.groups3906332499630173760nt_rat G2) (@ (@ tptp.inf_inf_set_int A4) B5)) (@ (@ tptp.groups3906332499630173760nt_rat (lambda ((X4 tptp.int)) (@ (@ (@ tptp.if_rat (@ (@ tptp.member_int X4) B5)) (@ G2 X4)) tptp.zero_zero_rat))) A4)))) (forall ((A4 tptp.set_complex) (G2 (-> tptp.complex tptp.rat)) (B5 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex A4) (= (@ (@ tptp.groups5058264527183730370ex_rat G2) (@ (@ tptp.inf_inf_set_complex A4) B5)) (@ (@ tptp.groups5058264527183730370ex_rat (lambda ((X4 tptp.complex)) (@ (@ (@ tptp.if_rat (@ (@ tptp.member_complex X4) B5)) (@ G2 X4)) tptp.zero_zero_rat))) A4)))) (forall ((A4 tptp.set_real) (G2 (-> tptp.real tptp.nat)) (B5 tptp.set_real)) (=> (@ tptp.finite_finite_real A4) (= (@ (@ tptp.groups1935376822645274424al_nat G2) (@ (@ tptp.inf_inf_set_real A4) B5)) (@ (@ tptp.groups1935376822645274424al_nat (lambda ((X4 tptp.real)) (@ (@ (@ tptp.if_nat (@ (@ tptp.member_real X4) B5)) (@ G2 X4)) tptp.zero_zero_nat))) A4)))) (forall ((A4 tptp.set_real) (G2 (-> tptp.real tptp.complex))) (let ((_let_1 (@ tptp.groups5754745047067104278omplex G2))) (=> (@ tptp.finite_finite_real A4) (= (@ _let_1 (@ (@ tptp.minus_minus_set_real A4) (@ tptp.collect_real (lambda ((X4 tptp.real)) (= (@ G2 X4) tptp.zero_zero_complex))))) (@ _let_1 A4))))) (forall ((A4 tptp.set_int) (G2 (-> tptp.int tptp.complex))) (let ((_let_1 (@ tptp.groups3049146728041665814omplex G2))) (=> (@ tptp.finite_finite_int A4) (= (@ _let_1 (@ (@ tptp.minus_minus_set_int A4) (@ tptp.collect_int (lambda ((X4 tptp.int)) (= (@ G2 X4) tptp.zero_zero_complex))))) (@ _let_1 A4))))) (forall ((A4 tptp.set_complex) (G2 (-> tptp.complex tptp.complex))) (let ((_let_1 (@ tptp.groups7754918857620584856omplex G2))) (=> (@ tptp.finite3207457112153483333omplex A4) (= (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A4) (@ tptp.collect_complex (lambda ((X4 tptp.complex)) (= (@ G2 X4) tptp.zero_zero_complex))))) (@ _let_1 A4))))) (forall ((A4 tptp.set_real) (G2 (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.groups8097168146408367636l_real G2))) (=> (@ tptp.finite_finite_real A4) (= (@ _let_1 (@ (@ tptp.minus_minus_set_real A4) (@ tptp.collect_real (lambda ((X4 tptp.real)) (= (@ G2 X4) tptp.zero_zero_real))))) (@ _let_1 A4))))) (forall ((A4 tptp.set_int) (G2 (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups8778361861064173332t_real G2))) (=> (@ tptp.finite_finite_int A4) (= (@ _let_1 (@ (@ tptp.minus_minus_set_int A4) (@ tptp.collect_int (lambda ((X4 tptp.int)) (= (@ G2 X4) tptp.zero_zero_real))))) (@ _let_1 A4))))) (forall ((A4 tptp.set_complex) (G2 (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups5808333547571424918x_real G2))) (=> (@ tptp.finite3207457112153483333omplex A4) (= (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A4) (@ tptp.collect_complex (lambda ((X4 tptp.complex)) (= (@ G2 X4) tptp.zero_zero_real))))) (@ _let_1 A4))))) (forall ((A4 tptp.set_real) (G2 (-> tptp.real tptp.rat))) (let ((_let_1 (@ tptp.groups1300246762558778688al_rat G2))) (=> (@ tptp.finite_finite_real A4) (= (@ _let_1 (@ (@ tptp.minus_minus_set_real A4) (@ tptp.collect_real (lambda ((X4 tptp.real)) (= (@ G2 X4) tptp.zero_zero_rat))))) (@ _let_1 A4))))) (forall ((A4 tptp.set_int) (G2 (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups3906332499630173760nt_rat G2))) (=> (@ tptp.finite_finite_int A4) (= (@ _let_1 (@ (@ tptp.minus_minus_set_int A4) (@ tptp.collect_int (lambda ((X4 tptp.int)) (= (@ G2 X4) tptp.zero_zero_rat))))) (@ _let_1 A4))))) (forall ((A4 tptp.set_complex) (G2 (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups5058264527183730370ex_rat G2))) (=> (@ tptp.finite3207457112153483333omplex A4) (= (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A4) (@ tptp.collect_complex (lambda ((X4 tptp.complex)) (= (@ G2 X4) tptp.zero_zero_rat))))) (@ _let_1 A4))))) (forall ((A4 tptp.set_real) (G2 (-> tptp.real tptp.nat))) (let ((_let_1 (@ tptp.groups1935376822645274424al_nat G2))) (=> (@ tptp.finite_finite_real A4) (= (@ _let_1 (@ (@ tptp.minus_minus_set_real A4) (@ tptp.collect_real (lambda ((X4 tptp.real)) (= (@ G2 X4) tptp.zero_zero_nat))))) (@ _let_1 A4))))) (forall ((G2 (-> tptp.nat tptp.nat)) (M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat G2) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M2)) (@ tptp.suc N))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I tptp.nat)) (@ G2 (@ tptp.suc I)))) (@ (@ tptp.set_or1269000886237332187st_nat M2) N)))) (forall ((G2 (-> tptp.nat tptp.real)) (M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real G2) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M2)) (@ tptp.suc N))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I tptp.nat)) (@ G2 (@ tptp.suc I)))) (@ (@ tptp.set_or1269000886237332187st_nat M2) N)))) (forall ((G2 (-> tptp.nat tptp.nat)) (M2 tptp.nat) (K2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat G2) (@ (@ tptp.set_or1269000886237332187st_nat (@ (@ tptp.plus_plus_nat M2) K2)) (@ (@ tptp.plus_plus_nat N) K2))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I tptp.nat)) (@ G2 (@ (@ tptp.plus_plus_nat I) K2)))) (@ (@ tptp.set_or1269000886237332187st_nat M2) N)))) (forall ((G2 (-> tptp.nat tptp.real)) (M2 tptp.nat) (K2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real G2) (@ (@ tptp.set_or1269000886237332187st_nat (@ (@ tptp.plus_plus_nat M2) K2)) (@ (@ tptp.plus_plus_nat N) K2))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I tptp.nat)) (@ G2 (@ (@ tptp.plus_plus_nat I) K2)))) (@ (@ tptp.set_or1269000886237332187st_nat M2) N)))) (forall ((I5 tptp.set_real) (I2 tptp.real) (F2 (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ tptp.finite_finite_real I5) (=> (@ (@ tptp.member_real I2) I5) (=> (@ _let_1 (@ F2 I2)) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) I5) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F2 I3)))) (@ _let_1 (@ (@ tptp.groups8097168146408367636l_real F2) I5)))))))) (forall ((I5 tptp.set_int) (I2 tptp.int) (F2 (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ tptp.finite_finite_int I5) (=> (@ (@ tptp.member_int I2) I5) (=> (@ _let_1 (@ F2 I2)) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) I5) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F2 I3)))) (@ _let_1 (@ (@ tptp.groups8778361861064173332t_real F2) I5)))))))) (forall ((I5 tptp.set_complex) (I2 tptp.complex) (F2 (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ tptp.finite3207457112153483333omplex I5) (=> (@ (@ tptp.member_complex I2) I5) (=> (@ _let_1 (@ F2 I2)) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) I5) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F2 I3)))) (@ _let_1 (@ (@ tptp.groups5808333547571424918x_real F2) I5)))))))) (forall ((I5 tptp.set_real) (I2 tptp.real) (F2 (-> tptp.real tptp.rat))) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ tptp.finite_finite_real I5) (=> (@ (@ tptp.member_real I2) I5) (=> (@ _let_1 (@ F2 I2)) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) I5) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F2 I3)))) (@ _let_1 (@ (@ tptp.groups1300246762558778688al_rat F2) I5)))))))) (forall ((I5 tptp.set_nat) (I2 tptp.nat) (F2 (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ tptp.finite_finite_nat I5) (=> (@ (@ tptp.member_nat I2) I5) (=> (@ _let_1 (@ F2 I2)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.member_nat I3) I5) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F2 I3)))) (@ _let_1 (@ (@ tptp.groups2906978787729119204at_rat F2) I5)))))))) (forall ((I5 tptp.set_int) (I2 tptp.int) (F2 (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ tptp.finite_finite_int I5) (=> (@ (@ tptp.member_int I2) I5) (=> (@ _let_1 (@ F2 I2)) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) I5) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F2 I3)))) (@ _let_1 (@ (@ tptp.groups3906332499630173760nt_rat F2) I5)))))))) (forall ((I5 tptp.set_complex) (I2 tptp.complex) (F2 (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ tptp.finite3207457112153483333omplex I5) (=> (@ (@ tptp.member_complex I2) I5) (=> (@ _let_1 (@ F2 I2)) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) I5) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F2 I3)))) (@ _let_1 (@ (@ tptp.groups5058264527183730370ex_rat F2) I5)))))))) (forall ((I5 tptp.set_real) (I2 tptp.real) (F2 (-> tptp.real tptp.nat))) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ tptp.finite_finite_real I5) (=> (@ (@ tptp.member_real I2) I5) (=> (@ _let_1 (@ F2 I2)) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) I5) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F2 I3)))) (@ _let_1 (@ (@ tptp.groups1935376822645274424al_nat F2) I5)))))))) (forall ((I5 tptp.set_int) (I2 tptp.int) (F2 (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ tptp.finite_finite_int I5) (=> (@ (@ tptp.member_int I2) I5) (=> (@ _let_1 (@ F2 I2)) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) I5) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F2 I3)))) (@ _let_1 (@ (@ tptp.groups4541462559716669496nt_nat F2) I5)))))))) (forall ((I5 tptp.set_complex) (I2 tptp.complex) (F2 (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ tptp.finite3207457112153483333omplex I5) (=> (@ (@ tptp.member_complex I2) I5) (=> (@ _let_1 (@ F2 I2)) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) I5) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F2 I3)))) (@ _let_1 (@ (@ tptp.groups5693394587270226106ex_nat F2) I5)))))))) (forall ((I5 tptp.set_complex) (F2 (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex I5) (=> (not (= I5 tptp.bot_bot_set_complex)) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) I5) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F2 I3)))) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.groups5808333547571424918x_real F2) I5)))))) (forall ((I5 tptp.set_int) (F2 (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int I5) (=> (not (= I5 tptp.bot_bot_set_int)) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) I5) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F2 I3)))) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.groups8778361861064173332t_real F2) I5)))))) (forall ((I5 tptp.set_real) (F2 (-> tptp.real tptp.real))) (=> (@ tptp.finite_finite_real I5) (=> (not (= I5 tptp.bot_bot_set_real)) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) I5) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F2 I3)))) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.groups8097168146408367636l_real F2) I5)))))) (forall ((I5 tptp.set_complex) (F2 (-> tptp.complex tptp.rat))) (=> (@ tptp.finite3207457112153483333omplex I5) (=> (not (= I5 tptp.bot_bot_set_complex)) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) I5) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ F2 I3)))) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.groups5058264527183730370ex_rat F2) I5)))))) (forall ((I5 tptp.set_nat) (F2 (-> tptp.nat tptp.rat))) (=> (@ tptp.finite_finite_nat I5) (=> (not (= I5 tptp.bot_bot_set_nat)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.member_nat I3) I5) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ F2 I3)))) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.groups2906978787729119204at_rat F2) I5)))))) (forall ((I5 tptp.set_int) (F2 (-> tptp.int tptp.rat))) (=> (@ tptp.finite_finite_int I5) (=> (not (= I5 tptp.bot_bot_set_int)) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) I5) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ F2 I3)))) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.groups3906332499630173760nt_rat F2) I5)))))) (forall ((I5 tptp.set_real) (F2 (-> tptp.real tptp.rat))) (=> (@ tptp.finite_finite_real I5) (=> (not (= I5 tptp.bot_bot_set_real)) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) I5) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ F2 I3)))) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.groups1300246762558778688al_rat F2) I5)))))) (forall ((I5 tptp.set_complex) (F2 (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex I5) (=> (not (= I5 tptp.bot_bot_set_complex)) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) I5) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F2 I3)))) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.groups5693394587270226106ex_nat F2) I5)))))) (forall ((I5 tptp.set_int) (F2 (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int I5) (=> (not (= I5 tptp.bot_bot_set_int)) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) I5) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F2 I3)))) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.groups4541462559716669496nt_nat F2) I5)))))) (forall ((I5 tptp.set_real) (F2 (-> tptp.real tptp.nat))) (=> (@ tptp.finite_finite_real I5) (=> (not (= I5 tptp.bot_bot_set_real)) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) I5) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F2 I3)))) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.groups1935376822645274424al_nat F2) I5)))))) (forall ((A4 tptp.set_real) (K5 tptp.real) (F2 (-> tptp.real tptp.real))) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) A4) (@ (@ tptp.ord_less_eq_real K5) (@ F2 I3)))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ tptp.finite_card_real A4))) K5)) (@ (@ tptp.groups8097168146408367636l_real F2) A4)))) (forall ((A4 tptp.set_complex) (K5 tptp.real) (F2 (-> tptp.complex tptp.real))) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) A4) (@ (@ tptp.ord_less_eq_real K5) (@ F2 I3)))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ tptp.finite_card_complex A4))) K5)) (@ (@ tptp.groups5808333547571424918x_real F2) A4)))) (forall ((A4 tptp.set_int) (K5 tptp.real) (F2 (-> tptp.int tptp.real))) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) A4) (@ (@ tptp.ord_less_eq_real K5) (@ F2 I3)))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ tptp.finite_card_int A4))) K5)) (@ (@ tptp.groups8778361861064173332t_real F2) A4)))) (forall ((A4 tptp.set_real) (K5 tptp.rat) (F2 (-> tptp.real tptp.rat))) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) A4) (@ (@ tptp.ord_less_eq_rat K5) (@ F2 I3)))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat (@ tptp.finite_card_real A4))) K5)) (@ (@ tptp.groups1300246762558778688al_rat F2) A4)))) (forall ((A4 tptp.set_nat) (K5 tptp.rat) (F2 (-> tptp.nat tptp.rat))) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.member_nat I3) A4) (@ (@ tptp.ord_less_eq_rat K5) (@ F2 I3)))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat (@ tptp.finite_card_nat A4))) K5)) (@ (@ tptp.groups2906978787729119204at_rat F2) A4)))) (forall ((A4 tptp.set_complex) (K5 tptp.rat) (F2 (-> tptp.complex tptp.rat))) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) A4) (@ (@ tptp.ord_less_eq_rat K5) (@ F2 I3)))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat (@ tptp.finite_card_complex A4))) K5)) (@ (@ tptp.groups5058264527183730370ex_rat F2) A4)))) (forall ((A4 tptp.set_int) (K5 tptp.rat) (F2 (-> tptp.int tptp.rat))) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) A4) (@ (@ tptp.ord_less_eq_rat K5) (@ F2 I3)))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat (@ tptp.finite_card_int A4))) K5)) (@ (@ tptp.groups3906332499630173760nt_rat F2) A4)))) (forall ((A4 tptp.set_real) (K5 tptp.nat) (F2 (-> tptp.real tptp.nat))) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) A4) (@ (@ tptp.ord_less_eq_nat K5) (@ F2 I3)))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat (@ tptp.finite_card_real A4))) K5)) (@ (@ tptp.groups1935376822645274424al_nat F2) A4)))) (forall ((A4 tptp.set_complex) (K5 tptp.nat) (F2 (-> tptp.complex tptp.nat))) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) A4) (@ (@ tptp.ord_less_eq_nat K5) (@ F2 I3)))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat (@ tptp.finite_card_complex A4))) K5)) (@ (@ tptp.groups5693394587270226106ex_nat F2) A4)))) (forall ((A4 tptp.set_int) (K5 tptp.nat) (F2 (-> tptp.int tptp.nat))) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) A4) (@ (@ tptp.ord_less_eq_nat K5) (@ F2 I3)))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat (@ tptp.finite_card_int A4))) K5)) (@ (@ tptp.groups4541462559716669496nt_nat F2) A4)))) (forall ((A4 tptp.set_real) (F2 (-> tptp.real tptp.real)) (K5 tptp.real)) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) A4) (@ (@ tptp.ord_less_eq_real (@ F2 I3)) K5))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups8097168146408367636l_real F2) A4)) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ tptp.finite_card_real A4))) K5)))) (forall ((A4 tptp.set_complex) (F2 (-> tptp.complex tptp.real)) (K5 tptp.real)) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) A4) (@ (@ tptp.ord_less_eq_real (@ F2 I3)) K5))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups5808333547571424918x_real F2) A4)) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ tptp.finite_card_complex A4))) K5)))) (forall ((A4 tptp.set_int) (F2 (-> tptp.int tptp.real)) (K5 tptp.real)) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) A4) (@ (@ tptp.ord_less_eq_real (@ F2 I3)) K5))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups8778361861064173332t_real F2) A4)) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ tptp.finite_card_int A4))) K5)))) (forall ((A4 tptp.set_real) (F2 (-> tptp.real tptp.rat)) (K5 tptp.rat)) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) A4) (@ (@ tptp.ord_less_eq_rat (@ F2 I3)) K5))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups1300246762558778688al_rat F2) A4)) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat (@ tptp.finite_card_real A4))) K5)))) (forall ((A4 tptp.set_nat) (F2 (-> tptp.nat tptp.rat)) (K5 tptp.rat)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.member_nat I3) A4) (@ (@ tptp.ord_less_eq_rat (@ F2 I3)) K5))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups2906978787729119204at_rat F2) A4)) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat (@ tptp.finite_card_nat A4))) K5)))) (forall ((A4 tptp.set_complex) (F2 (-> tptp.complex tptp.rat)) (K5 tptp.rat)) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) A4) (@ (@ tptp.ord_less_eq_rat (@ F2 I3)) K5))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups5058264527183730370ex_rat F2) A4)) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat (@ tptp.finite_card_complex A4))) K5)))) (forall ((A4 tptp.set_int) (F2 (-> tptp.int tptp.rat)) (K5 tptp.rat)) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) A4) (@ (@ tptp.ord_less_eq_rat (@ F2 I3)) K5))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups3906332499630173760nt_rat F2) A4)) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat (@ tptp.finite_card_int A4))) K5)))) (forall ((A4 tptp.set_real) (F2 (-> tptp.real tptp.nat)) (K5 tptp.nat)) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) A4) (@ (@ tptp.ord_less_eq_nat (@ F2 I3)) K5))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups1935376822645274424al_nat F2) A4)) (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat (@ tptp.finite_card_real A4))) K5)))) (forall ((A4 tptp.set_complex) (F2 (-> tptp.complex tptp.nat)) (K5 tptp.nat)) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) A4) (@ (@ tptp.ord_less_eq_nat (@ F2 I3)) K5))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups5693394587270226106ex_nat F2) A4)) (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat (@ tptp.finite_card_complex A4))) K5)))) (forall ((A4 tptp.set_int) (F2 (-> tptp.int tptp.nat)) (K5 tptp.nat)) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) A4) (@ (@ tptp.ord_less_eq_nat (@ F2 I3)) K5))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups4541462559716669496nt_nat F2) A4)) (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat (@ tptp.finite_card_int A4))) K5)))) (forall ((T5 tptp.set_real) (S3 tptp.set_real) (G2 (-> tptp.real tptp.complex)) (H (-> tptp.real tptp.complex))) (=> (@ tptp.finite_finite_real T5) (=> (@ (@ tptp.ord_less_eq_set_real S3) T5) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) (@ (@ tptp.minus_minus_set_real T5) S3)) (= (@ G2 X3) tptp.zero_zero_complex))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) S3) (= (@ G2 X3) (@ H X3)))) (= (@ (@ tptp.groups5754745047067104278omplex G2) T5) (@ (@ tptp.groups5754745047067104278omplex H) S3))))))) (forall ((T5 tptp.set_int) (S3 tptp.set_int) (G2 (-> tptp.int tptp.complex)) (H (-> tptp.int tptp.complex))) (=> (@ tptp.finite_finite_int T5) (=> (@ (@ tptp.ord_less_eq_set_int S3) T5) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.minus_minus_set_int T5) S3)) (= (@ G2 X3) tptp.zero_zero_complex))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) S3) (= (@ G2 X3) (@ H X3)))) (= (@ (@ tptp.groups3049146728041665814omplex G2) T5) (@ (@ tptp.groups3049146728041665814omplex H) S3))))))) (forall ((T5 tptp.set_complex) (S3 tptp.set_complex) (G2 (-> tptp.complex tptp.complex)) (H (-> tptp.complex tptp.complex))) (=> (@ tptp.finite3207457112153483333omplex T5) (=> (@ (@ tptp.ord_le211207098394363844omplex S3) T5) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ (@ tptp.minus_811609699411566653omplex T5) S3)) (= (@ G2 X3) tptp.zero_zero_complex))) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) S3) (= (@ G2 X3) (@ H X3)))) (= (@ (@ tptp.groups7754918857620584856omplex G2) T5) (@ (@ tptp.groups7754918857620584856omplex H) S3))))))) (forall ((T5 tptp.set_real) (S3 tptp.set_real) (G2 (-> tptp.real tptp.real)) (H (-> tptp.real tptp.real))) (=> (@ tptp.finite_finite_real T5) (=> (@ (@ tptp.ord_less_eq_set_real S3) T5) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) (@ (@ tptp.minus_minus_set_real T5) S3)) (= (@ G2 X3) tptp.zero_zero_real))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) S3) (= (@ G2 X3) (@ H X3)))) (= (@ (@ tptp.groups8097168146408367636l_real G2) T5) (@ (@ tptp.groups8097168146408367636l_real H) S3))))))) (forall ((T5 tptp.set_int) (S3 tptp.set_int) (G2 (-> tptp.int tptp.real)) (H (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int T5) (=> (@ (@ tptp.ord_less_eq_set_int S3) T5) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.minus_minus_set_int T5) S3)) (= (@ G2 X3) tptp.zero_zero_real))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) S3) (= (@ G2 X3) (@ H X3)))) (= (@ (@ tptp.groups8778361861064173332t_real G2) T5) (@ (@ tptp.groups8778361861064173332t_real H) S3))))))) (forall ((T5 tptp.set_complex) (S3 tptp.set_complex) (G2 (-> tptp.complex tptp.real)) (H (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex T5) (=> (@ (@ tptp.ord_le211207098394363844omplex S3) T5) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ (@ tptp.minus_811609699411566653omplex T5) S3)) (= (@ G2 X3) tptp.zero_zero_real))) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) S3) (= (@ G2 X3) (@ H X3)))) (= (@ (@ tptp.groups5808333547571424918x_real G2) T5) (@ (@ tptp.groups5808333547571424918x_real H) S3))))))) (forall ((T5 tptp.set_real) (S3 tptp.set_real) (G2 (-> tptp.real tptp.rat)) (H (-> tptp.real tptp.rat))) (=> (@ tptp.finite_finite_real T5) (=> (@ (@ tptp.ord_less_eq_set_real S3) T5) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) (@ (@ tptp.minus_minus_set_real T5) S3)) (= (@ G2 X3) tptp.zero_zero_rat))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) S3) (= (@ G2 X3) (@ H X3)))) (= (@ (@ tptp.groups1300246762558778688al_rat G2) T5) (@ (@ tptp.groups1300246762558778688al_rat H) S3))))))) (forall ((T5 tptp.set_int) (S3 tptp.set_int) (G2 (-> tptp.int tptp.rat)) (H (-> tptp.int tptp.rat))) (=> (@ tptp.finite_finite_int T5) (=> (@ (@ tptp.ord_less_eq_set_int S3) T5) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.minus_minus_set_int T5) S3)) (= (@ G2 X3) tptp.zero_zero_rat))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) S3) (= (@ G2 X3) (@ H X3)))) (= (@ (@ tptp.groups3906332499630173760nt_rat G2) T5) (@ (@ tptp.groups3906332499630173760nt_rat H) S3))))))) (forall ((T5 tptp.set_complex) (S3 tptp.set_complex) (G2 (-> tptp.complex tptp.rat)) (H (-> tptp.complex tptp.rat))) (=> (@ tptp.finite3207457112153483333omplex T5) (=> (@ (@ tptp.ord_le211207098394363844omplex S3) T5) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ (@ tptp.minus_811609699411566653omplex T5) S3)) (= (@ G2 X3) tptp.zero_zero_rat))) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) S3) (= (@ G2 X3) (@ H X3)))) (= (@ (@ tptp.groups5058264527183730370ex_rat G2) T5) (@ (@ tptp.groups5058264527183730370ex_rat H) S3))))))) (forall ((T5 tptp.set_real) (S3 tptp.set_real) (G2 (-> tptp.real tptp.nat)) (H (-> tptp.real tptp.nat))) (=> (@ tptp.finite_finite_real T5) (=> (@ (@ tptp.ord_less_eq_set_real S3) T5) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) (@ (@ tptp.minus_minus_set_real T5) S3)) (= (@ G2 X3) tptp.zero_zero_nat))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) S3) (= (@ G2 X3) (@ H X3)))) (= (@ (@ tptp.groups1935376822645274424al_nat G2) T5) (@ (@ tptp.groups1935376822645274424al_nat H) S3))))))) (forall ((T5 tptp.set_real) (S3 tptp.set_real) (H (-> tptp.real tptp.complex)) (G2 (-> tptp.real tptp.complex))) (=> (@ tptp.finite_finite_real T5) (=> (@ (@ tptp.ord_less_eq_set_real S3) T5) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) (@ (@ tptp.minus_minus_set_real T5) S3)) (= (@ H X3) tptp.zero_zero_complex))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) S3) (= (@ G2 X3) (@ H X3)))) (= (@ (@ tptp.groups5754745047067104278omplex G2) S3) (@ (@ tptp.groups5754745047067104278omplex H) T5))))))) (forall ((T5 tptp.set_int) (S3 tptp.set_int) (H (-> tptp.int tptp.complex)) (G2 (-> tptp.int tptp.complex))) (=> (@ tptp.finite_finite_int T5) (=> (@ (@ tptp.ord_less_eq_set_int S3) T5) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.minus_minus_set_int T5) S3)) (= (@ H X3) tptp.zero_zero_complex))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) S3) (= (@ G2 X3) (@ H X3)))) (= (@ (@ tptp.groups3049146728041665814omplex G2) S3) (@ (@ tptp.groups3049146728041665814omplex H) T5))))))) (forall ((T5 tptp.set_complex) (S3 tptp.set_complex) (H (-> tptp.complex tptp.complex)) (G2 (-> tptp.complex tptp.complex))) (=> (@ tptp.finite3207457112153483333omplex T5) (=> (@ (@ tptp.ord_le211207098394363844omplex S3) T5) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ (@ tptp.minus_811609699411566653omplex T5) S3)) (= (@ H X3) tptp.zero_zero_complex))) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) S3) (= (@ G2 X3) (@ H X3)))) (= (@ (@ tptp.groups7754918857620584856omplex G2) S3) (@ (@ tptp.groups7754918857620584856omplex H) T5))))))) (forall ((T5 tptp.set_real) (S3 tptp.set_real) (H (-> tptp.real tptp.real)) (G2 (-> tptp.real tptp.real))) (=> (@ tptp.finite_finite_real T5) (=> (@ (@ tptp.ord_less_eq_set_real S3) T5) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) (@ (@ tptp.minus_minus_set_real T5) S3)) (= (@ H X3) tptp.zero_zero_real))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) S3) (= (@ G2 X3) (@ H X3)))) (= (@ (@ tptp.groups8097168146408367636l_real G2) S3) (@ (@ tptp.groups8097168146408367636l_real H) T5))))))) (forall ((T5 tptp.set_int) (S3 tptp.set_int) (H (-> tptp.int tptp.real)) (G2 (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int T5) (=> (@ (@ tptp.ord_less_eq_set_int S3) T5) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.minus_minus_set_int T5) S3)) (= (@ H X3) tptp.zero_zero_real))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) S3) (= (@ G2 X3) (@ H X3)))) (= (@ (@ tptp.groups8778361861064173332t_real G2) S3) (@ (@ tptp.groups8778361861064173332t_real H) T5))))))) (forall ((T5 tptp.set_complex) (S3 tptp.set_complex) (H (-> tptp.complex tptp.real)) (G2 (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex T5) (=> (@ (@ tptp.ord_le211207098394363844omplex S3) T5) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ (@ tptp.minus_811609699411566653omplex T5) S3)) (= (@ H X3) tptp.zero_zero_real))) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) S3) (= (@ G2 X3) (@ H X3)))) (= (@ (@ tptp.groups5808333547571424918x_real G2) S3) (@ (@ tptp.groups5808333547571424918x_real H) T5))))))) (forall ((T5 tptp.set_real) (S3 tptp.set_real) (H (-> tptp.real tptp.rat)) (G2 (-> tptp.real tptp.rat))) (=> (@ tptp.finite_finite_real T5) (=> (@ (@ tptp.ord_less_eq_set_real S3) T5) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) (@ (@ tptp.minus_minus_set_real T5) S3)) (= (@ H X3) tptp.zero_zero_rat))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) S3) (= (@ G2 X3) (@ H X3)))) (= (@ (@ tptp.groups1300246762558778688al_rat G2) S3) (@ (@ tptp.groups1300246762558778688al_rat H) T5))))))) (forall ((T5 tptp.set_int) (S3 tptp.set_int) (H (-> tptp.int tptp.rat)) (G2 (-> tptp.int tptp.rat))) (=> (@ tptp.finite_finite_int T5) (=> (@ (@ tptp.ord_less_eq_set_int S3) T5) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.minus_minus_set_int T5) S3)) (= (@ H X3) tptp.zero_zero_rat))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) S3) (= (@ G2 X3) (@ H X3)))) (= (@ (@ tptp.groups3906332499630173760nt_rat G2) S3) (@ (@ tptp.groups3906332499630173760nt_rat H) T5))))))) (forall ((T5 tptp.set_complex) (S3 tptp.set_complex) (H (-> tptp.complex tptp.rat)) (G2 (-> tptp.complex tptp.rat))) (=> (@ tptp.finite3207457112153483333omplex T5) (=> (@ (@ tptp.ord_le211207098394363844omplex S3) T5) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ (@ tptp.minus_811609699411566653omplex T5) S3)) (= (@ H X3) tptp.zero_zero_rat))) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) S3) (= (@ G2 X3) (@ H X3)))) (= (@ (@ tptp.groups5058264527183730370ex_rat G2) S3) (@ (@ tptp.groups5058264527183730370ex_rat H) T5))))))) (forall ((T5 tptp.set_real) (S3 tptp.set_real) (H (-> tptp.real tptp.nat)) (G2 (-> tptp.real tptp.nat))) (=> (@ tptp.finite_finite_real T5) (=> (@ (@ tptp.ord_less_eq_set_real S3) T5) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) (@ (@ tptp.minus_minus_set_real T5) S3)) (= (@ H X3) tptp.zero_zero_nat))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) S3) (= (@ G2 X3) (@ H X3)))) (= (@ (@ tptp.groups1935376822645274424al_nat G2) S3) (@ (@ tptp.groups1935376822645274424al_nat H) T5))))))) (forall ((T5 tptp.set_int) (S3 tptp.set_int) (G2 (-> tptp.int tptp.complex))) (let ((_let_1 (@ tptp.groups3049146728041665814omplex G2))) (=> (@ tptp.finite_finite_int T5) (=> (@ (@ tptp.ord_less_eq_set_int S3) T5) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.minus_minus_set_int T5) S3)) (= (@ G2 X3) tptp.zero_zero_complex))) (= (@ _let_1 T5) (@ _let_1 S3))))))) (forall ((T5 tptp.set_complex) (S3 tptp.set_complex) (G2 (-> tptp.complex tptp.complex))) (let ((_let_1 (@ tptp.groups7754918857620584856omplex G2))) (=> (@ tptp.finite3207457112153483333omplex T5) (=> (@ (@ tptp.ord_le211207098394363844omplex S3) T5) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ (@ tptp.minus_811609699411566653omplex T5) S3)) (= (@ G2 X3) tptp.zero_zero_complex))) (= (@ _let_1 T5) (@ _let_1 S3))))))) (forall ((T5 tptp.set_int) (S3 tptp.set_int) (G2 (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups8778361861064173332t_real G2))) (=> (@ tptp.finite_finite_int T5) (=> (@ (@ tptp.ord_less_eq_set_int S3) T5) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.minus_minus_set_int T5) S3)) (= (@ G2 X3) tptp.zero_zero_real))) (= (@ _let_1 T5) (@ _let_1 S3))))))) (forall ((T5 tptp.set_complex) (S3 tptp.set_complex) (G2 (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups5808333547571424918x_real G2))) (=> (@ tptp.finite3207457112153483333omplex T5) (=> (@ (@ tptp.ord_le211207098394363844omplex S3) T5) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ (@ tptp.minus_811609699411566653omplex T5) S3)) (= (@ G2 X3) tptp.zero_zero_real))) (= (@ _let_1 T5) (@ _let_1 S3))))))) (forall ((T5 tptp.set_int) (S3 tptp.set_int) (G2 (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups3906332499630173760nt_rat G2))) (=> (@ tptp.finite_finite_int T5) (=> (@ (@ tptp.ord_less_eq_set_int S3) T5) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.minus_minus_set_int T5) S3)) (= (@ G2 X3) tptp.zero_zero_rat))) (= (@ _let_1 T5) (@ _let_1 S3))))))) (forall ((T5 tptp.set_complex) (S3 tptp.set_complex) (G2 (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups5058264527183730370ex_rat G2))) (=> (@ tptp.finite3207457112153483333omplex T5) (=> (@ (@ tptp.ord_le211207098394363844omplex S3) T5) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ (@ tptp.minus_811609699411566653omplex T5) S3)) (= (@ G2 X3) tptp.zero_zero_rat))) (= (@ _let_1 T5) (@ _let_1 S3))))))) (forall ((T5 tptp.set_int) (S3 tptp.set_int) (G2 (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups4541462559716669496nt_nat G2))) (=> (@ tptp.finite_finite_int T5) (=> (@ (@ tptp.ord_less_eq_set_int S3) T5) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.minus_minus_set_int T5) S3)) (= (@ G2 X3) tptp.zero_zero_nat))) (= (@ _let_1 T5) (@ _let_1 S3))))))) (forall ((T5 tptp.set_complex) (S3 tptp.set_complex) (G2 (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups5693394587270226106ex_nat G2))) (=> (@ tptp.finite3207457112153483333omplex T5) (=> (@ (@ tptp.ord_le211207098394363844omplex S3) T5) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ (@ tptp.minus_811609699411566653omplex T5) S3)) (= (@ G2 X3) tptp.zero_zero_nat))) (= (@ _let_1 T5) (@ _let_1 S3))))))) (forall ((T5 tptp.set_complex) (S3 tptp.set_complex) (G2 (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.groups5690904116761175830ex_int G2))) (=> (@ tptp.finite3207457112153483333omplex T5) (=> (@ (@ tptp.ord_le211207098394363844omplex S3) T5) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ (@ tptp.minus_811609699411566653omplex T5) S3)) (= (@ G2 X3) tptp.zero_zero_int))) (= (@ _let_1 T5) (@ _let_1 S3))))))) (forall ((T5 tptp.set_nat) (S3 tptp.set_nat) (G2 (-> tptp.nat tptp.complex))) (let ((_let_1 (@ tptp.groups2073611262835488442omplex G2))) (=> (@ tptp.finite_finite_nat T5) (=> (@ (@ tptp.ord_less_eq_set_nat S3) T5) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ (@ tptp.minus_minus_set_nat T5) S3)) (= (@ G2 X3) tptp.zero_zero_complex))) (= (@ _let_1 T5) (@ _let_1 S3))))))) (forall ((T5 tptp.set_int) (S3 tptp.set_int) (G2 (-> tptp.int tptp.complex))) (let ((_let_1 (@ tptp.groups3049146728041665814omplex G2))) (=> (@ tptp.finite_finite_int T5) (=> (@ (@ tptp.ord_less_eq_set_int S3) T5) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.minus_minus_set_int T5) S3)) (= (@ G2 X3) tptp.zero_zero_complex))) (= (@ _let_1 S3) (@ _let_1 T5))))))) (forall ((T5 tptp.set_complex) (S3 tptp.set_complex) (G2 (-> tptp.complex tptp.complex))) (let ((_let_1 (@ tptp.groups7754918857620584856omplex G2))) (=> (@ tptp.finite3207457112153483333omplex T5) (=> (@ (@ tptp.ord_le211207098394363844omplex S3) T5) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ (@ tptp.minus_811609699411566653omplex T5) S3)) (= (@ G2 X3) tptp.zero_zero_complex))) (= (@ _let_1 S3) (@ _let_1 T5))))))) (forall ((T5 tptp.set_int) (S3 tptp.set_int) (G2 (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups8778361861064173332t_real G2))) (=> (@ tptp.finite_finite_int T5) (=> (@ (@ tptp.ord_less_eq_set_int S3) T5) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.minus_minus_set_int T5) S3)) (= (@ G2 X3) tptp.zero_zero_real))) (= (@ _let_1 S3) (@ _let_1 T5))))))) (forall ((T5 tptp.set_complex) (S3 tptp.set_complex) (G2 (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups5808333547571424918x_real G2))) (=> (@ tptp.finite3207457112153483333omplex T5) (=> (@ (@ tptp.ord_le211207098394363844omplex S3) T5) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ (@ tptp.minus_811609699411566653omplex T5) S3)) (= (@ G2 X3) tptp.zero_zero_real))) (= (@ _let_1 S3) (@ _let_1 T5))))))) (forall ((T5 tptp.set_int) (S3 tptp.set_int) (G2 (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups3906332499630173760nt_rat G2))) (=> (@ tptp.finite_finite_int T5) (=> (@ (@ tptp.ord_less_eq_set_int S3) T5) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.minus_minus_set_int T5) S3)) (= (@ G2 X3) tptp.zero_zero_rat))) (= (@ _let_1 S3) (@ _let_1 T5))))))) (forall ((T5 tptp.set_complex) (S3 tptp.set_complex) (G2 (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups5058264527183730370ex_rat G2))) (=> (@ tptp.finite3207457112153483333omplex T5) (=> (@ (@ tptp.ord_le211207098394363844omplex S3) T5) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ (@ tptp.minus_811609699411566653omplex T5) S3)) (= (@ G2 X3) tptp.zero_zero_rat))) (= (@ _let_1 S3) (@ _let_1 T5))))))) (forall ((T5 tptp.set_int) (S3 tptp.set_int) (G2 (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups4541462559716669496nt_nat G2))) (=> (@ tptp.finite_finite_int T5) (=> (@ (@ tptp.ord_less_eq_set_int S3) T5) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.minus_minus_set_int T5) S3)) (= (@ G2 X3) tptp.zero_zero_nat))) (= (@ _let_1 S3) (@ _let_1 T5))))))) (forall ((T5 tptp.set_complex) (S3 tptp.set_complex) (G2 (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups5693394587270226106ex_nat G2))) (=> (@ tptp.finite3207457112153483333omplex T5) (=> (@ (@ tptp.ord_le211207098394363844omplex S3) T5) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ (@ tptp.minus_811609699411566653omplex T5) S3)) (= (@ G2 X3) tptp.zero_zero_nat))) (= (@ _let_1 S3) (@ _let_1 T5))))))) (forall ((T5 tptp.set_complex) (S3 tptp.set_complex) (G2 (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.groups5690904116761175830ex_int G2))) (=> (@ tptp.finite3207457112153483333omplex T5) (=> (@ (@ tptp.ord_le211207098394363844omplex S3) T5) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ (@ tptp.minus_811609699411566653omplex T5) S3)) (= (@ G2 X3) tptp.zero_zero_int))) (= (@ _let_1 S3) (@ _let_1 T5))))))) (forall ((T5 tptp.set_nat) (S3 tptp.set_nat) (G2 (-> tptp.nat tptp.complex))) (let ((_let_1 (@ tptp.groups2073611262835488442omplex G2))) (=> (@ tptp.finite_finite_nat T5) (=> (@ (@ tptp.ord_less_eq_set_nat S3) T5) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ (@ tptp.minus_minus_set_nat T5) S3)) (= (@ G2 X3) tptp.zero_zero_complex))) (= (@ _let_1 S3) (@ _let_1 T5))))))) (forall ((C4 tptp.set_real) (A4 tptp.set_real) (B5 tptp.set_real) (G2 (-> tptp.real tptp.complex)) (H (-> tptp.real tptp.complex))) (let ((_let_1 (@ tptp.groups5754745047067104278omplex H))) (let ((_let_2 (@ tptp.groups5754745047067104278omplex G2))) (=> (@ tptp.finite_finite_real C4) (=> (@ (@ tptp.ord_less_eq_set_real A4) C4) (=> (@ (@ tptp.ord_less_eq_set_real B5) C4) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) (@ (@ tptp.minus_minus_set_real C4) A4)) (= (@ G2 A3) tptp.zero_zero_complex))) (=> (forall ((B3 tptp.real)) (=> (@ (@ tptp.member_real B3) (@ (@ tptp.minus_minus_set_real C4) B5)) (= (@ H B3) tptp.zero_zero_complex))) (=> (= (@ _let_2 C4) (@ _let_1 C4)) (= (@ _let_2 A4) (@ _let_1 B5))))))))))) (forall ((C4 tptp.set_int) (A4 tptp.set_int) (B5 tptp.set_int) (G2 (-> tptp.int tptp.complex)) (H (-> tptp.int tptp.complex))) (let ((_let_1 (@ tptp.groups3049146728041665814omplex H))) (let ((_let_2 (@ tptp.groups3049146728041665814omplex G2))) (=> (@ tptp.finite_finite_int C4) (=> (@ (@ tptp.ord_less_eq_set_int A4) C4) (=> (@ (@ tptp.ord_less_eq_set_int B5) C4) (=> (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) (@ (@ tptp.minus_minus_set_int C4) A4)) (= (@ G2 A3) tptp.zero_zero_complex))) (=> (forall ((B3 tptp.int)) (=> (@ (@ tptp.member_int B3) (@ (@ tptp.minus_minus_set_int C4) B5)) (= (@ H B3) tptp.zero_zero_complex))) (=> (= (@ _let_2 C4) (@ _let_1 C4)) (= (@ _let_2 A4) (@ _let_1 B5))))))))))) (forall ((C4 tptp.set_complex) (A4 tptp.set_complex) (B5 tptp.set_complex) (G2 (-> tptp.complex tptp.complex)) (H (-> tptp.complex tptp.complex))) (let ((_let_1 (@ tptp.groups7754918857620584856omplex H))) (let ((_let_2 (@ tptp.groups7754918857620584856omplex G2))) (=> (@ tptp.finite3207457112153483333omplex C4) (=> (@ (@ tptp.ord_le211207098394363844omplex A4) C4) (=> (@ (@ tptp.ord_le211207098394363844omplex B5) C4) (=> (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) (@ (@ tptp.minus_811609699411566653omplex C4) A4)) (= (@ G2 A3) tptp.zero_zero_complex))) (=> (forall ((B3 tptp.complex)) (=> (@ (@ tptp.member_complex B3) (@ (@ tptp.minus_811609699411566653omplex C4) B5)) (= (@ H B3) tptp.zero_zero_complex))) (=> (= (@ _let_2 C4) (@ _let_1 C4)) (= (@ _let_2 A4) (@ _let_1 B5))))))))))) (forall ((C4 tptp.set_real) (A4 tptp.set_real) (B5 tptp.set_real) (G2 (-> tptp.real tptp.real)) (H (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.groups8097168146408367636l_real H))) (let ((_let_2 (@ tptp.groups8097168146408367636l_real G2))) (=> (@ tptp.finite_finite_real C4) (=> (@ (@ tptp.ord_less_eq_set_real A4) C4) (=> (@ (@ tptp.ord_less_eq_set_real B5) C4) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) (@ (@ tptp.minus_minus_set_real C4) A4)) (= (@ G2 A3) tptp.zero_zero_real))) (=> (forall ((B3 tptp.real)) (=> (@ (@ tptp.member_real B3) (@ (@ tptp.minus_minus_set_real C4) B5)) (= (@ H B3) tptp.zero_zero_real))) (=> (= (@ _let_2 C4) (@ _let_1 C4)) (= (@ _let_2 A4) (@ _let_1 B5))))))))))) (forall ((C4 tptp.set_int) (A4 tptp.set_int) (B5 tptp.set_int) (G2 (-> tptp.int tptp.real)) (H (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups8778361861064173332t_real H))) (let ((_let_2 (@ tptp.groups8778361861064173332t_real G2))) (=> (@ tptp.finite_finite_int C4) (=> (@ (@ tptp.ord_less_eq_set_int A4) C4) (=> (@ (@ tptp.ord_less_eq_set_int B5) C4) (=> (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) (@ (@ tptp.minus_minus_set_int C4) A4)) (= (@ G2 A3) tptp.zero_zero_real))) (=> (forall ((B3 tptp.int)) (=> (@ (@ tptp.member_int B3) (@ (@ tptp.minus_minus_set_int C4) B5)) (= (@ H B3) tptp.zero_zero_real))) (=> (= (@ _let_2 C4) (@ _let_1 C4)) (= (@ _let_2 A4) (@ _let_1 B5))))))))))) (forall ((C4 tptp.set_complex) (A4 tptp.set_complex) (B5 tptp.set_complex) (G2 (-> tptp.complex tptp.real)) (H (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups5808333547571424918x_real H))) (let ((_let_2 (@ tptp.groups5808333547571424918x_real G2))) (=> (@ tptp.finite3207457112153483333omplex C4) (=> (@ (@ tptp.ord_le211207098394363844omplex A4) C4) (=> (@ (@ tptp.ord_le211207098394363844omplex B5) C4) (=> (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) (@ (@ tptp.minus_811609699411566653omplex C4) A4)) (= (@ G2 A3) tptp.zero_zero_real))) (=> (forall ((B3 tptp.complex)) (=> (@ (@ tptp.member_complex B3) (@ (@ tptp.minus_811609699411566653omplex C4) B5)) (= (@ H B3) tptp.zero_zero_real))) (=> (= (@ _let_2 C4) (@ _let_1 C4)) (= (@ _let_2 A4) (@ _let_1 B5))))))))))) (forall ((C4 tptp.set_real) (A4 tptp.set_real) (B5 tptp.set_real) (G2 (-> tptp.real tptp.rat)) (H (-> tptp.real tptp.rat))) (let ((_let_1 (@ tptp.groups1300246762558778688al_rat H))) (let ((_let_2 (@ tptp.groups1300246762558778688al_rat G2))) (=> (@ tptp.finite_finite_real C4) (=> (@ (@ tptp.ord_less_eq_set_real A4) C4) (=> (@ (@ tptp.ord_less_eq_set_real B5) C4) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) (@ (@ tptp.minus_minus_set_real C4) A4)) (= (@ G2 A3) tptp.zero_zero_rat))) (=> (forall ((B3 tptp.real)) (=> (@ (@ tptp.member_real B3) (@ (@ tptp.minus_minus_set_real C4) B5)) (= (@ H B3) tptp.zero_zero_rat))) (=> (= (@ _let_2 C4) (@ _let_1 C4)) (= (@ _let_2 A4) (@ _let_1 B5))))))))))) (forall ((C4 tptp.set_int) (A4 tptp.set_int) (B5 tptp.set_int) (G2 (-> tptp.int tptp.rat)) (H (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups3906332499630173760nt_rat H))) (let ((_let_2 (@ tptp.groups3906332499630173760nt_rat G2))) (=> (@ tptp.finite_finite_int C4) (=> (@ (@ tptp.ord_less_eq_set_int A4) C4) (=> (@ (@ tptp.ord_less_eq_set_int B5) C4) (=> (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) (@ (@ tptp.minus_minus_set_int C4) A4)) (= (@ G2 A3) tptp.zero_zero_rat))) (=> (forall ((B3 tptp.int)) (=> (@ (@ tptp.member_int B3) (@ (@ tptp.minus_minus_set_int C4) B5)) (= (@ H B3) tptp.zero_zero_rat))) (=> (= (@ _let_2 C4) (@ _let_1 C4)) (= (@ _let_2 A4) (@ _let_1 B5))))))))))) (forall ((C4 tptp.set_complex) (A4 tptp.set_complex) (B5 tptp.set_complex) (G2 (-> tptp.complex tptp.rat)) (H (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups5058264527183730370ex_rat H))) (let ((_let_2 (@ tptp.groups5058264527183730370ex_rat G2))) (=> (@ tptp.finite3207457112153483333omplex C4) (=> (@ (@ tptp.ord_le211207098394363844omplex A4) C4) (=> (@ (@ tptp.ord_le211207098394363844omplex B5) C4) (=> (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) (@ (@ tptp.minus_811609699411566653omplex C4) A4)) (= (@ G2 A3) tptp.zero_zero_rat))) (=> (forall ((B3 tptp.complex)) (=> (@ (@ tptp.member_complex B3) (@ (@ tptp.minus_811609699411566653omplex C4) B5)) (= (@ H B3) tptp.zero_zero_rat))) (=> (= (@ _let_2 C4) (@ _let_1 C4)) (= (@ _let_2 A4) (@ _let_1 B5))))))))))) (forall ((C4 tptp.set_real) (A4 tptp.set_real) (B5 tptp.set_real) (G2 (-> tptp.real tptp.nat)) (H (-> tptp.real tptp.nat))) (let ((_let_1 (@ tptp.groups1935376822645274424al_nat H))) (let ((_let_2 (@ tptp.groups1935376822645274424al_nat G2))) (=> (@ tptp.finite_finite_real C4) (=> (@ (@ tptp.ord_less_eq_set_real A4) C4) (=> (@ (@ tptp.ord_less_eq_set_real B5) C4) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) (@ (@ tptp.minus_minus_set_real C4) A4)) (= (@ G2 A3) tptp.zero_zero_nat))) (=> (forall ((B3 tptp.real)) (=> (@ (@ tptp.member_real B3) (@ (@ tptp.minus_minus_set_real C4) B5)) (= (@ H B3) tptp.zero_zero_nat))) (=> (= (@ _let_2 C4) (@ _let_1 C4)) (= (@ _let_2 A4) (@ _let_1 B5))))))))))) (forall ((C4 tptp.set_real) (A4 tptp.set_real) (B5 tptp.set_real) (G2 (-> tptp.real tptp.complex)) (H (-> tptp.real tptp.complex))) (let ((_let_1 (@ tptp.groups5754745047067104278omplex H))) (let ((_let_2 (@ tptp.groups5754745047067104278omplex G2))) (=> (@ tptp.finite_finite_real C4) (=> (@ (@ tptp.ord_less_eq_set_real A4) C4) (=> (@ (@ tptp.ord_less_eq_set_real B5) C4) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) (@ (@ tptp.minus_minus_set_real C4) A4)) (= (@ G2 A3) tptp.zero_zero_complex))) (=> (forall ((B3 tptp.real)) (=> (@ (@ tptp.member_real B3) (@ (@ tptp.minus_minus_set_real C4) B5)) (= (@ H B3) tptp.zero_zero_complex))) (= (= (@ _let_2 A4) (@ _let_1 B5)) (= (@ _let_2 C4) (@ _let_1 C4))))))))))) (forall ((C4 tptp.set_int) (A4 tptp.set_int) (B5 tptp.set_int) (G2 (-> tptp.int tptp.complex)) (H (-> tptp.int tptp.complex))) (let ((_let_1 (@ tptp.groups3049146728041665814omplex H))) (let ((_let_2 (@ tptp.groups3049146728041665814omplex G2))) (=> (@ tptp.finite_finite_int C4) (=> (@ (@ tptp.ord_less_eq_set_int A4) C4) (=> (@ (@ tptp.ord_less_eq_set_int B5) C4) (=> (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) (@ (@ tptp.minus_minus_set_int C4) A4)) (= (@ G2 A3) tptp.zero_zero_complex))) (=> (forall ((B3 tptp.int)) (=> (@ (@ tptp.member_int B3) (@ (@ tptp.minus_minus_set_int C4) B5)) (= (@ H B3) tptp.zero_zero_complex))) (= (= (@ _let_2 A4) (@ _let_1 B5)) (= (@ _let_2 C4) (@ _let_1 C4))))))))))) (forall ((C4 tptp.set_complex) (A4 tptp.set_complex) (B5 tptp.set_complex) (G2 (-> tptp.complex tptp.complex)) (H (-> tptp.complex tptp.complex))) (let ((_let_1 (@ tptp.groups7754918857620584856omplex H))) (let ((_let_2 (@ tptp.groups7754918857620584856omplex G2))) (=> (@ tptp.finite3207457112153483333omplex C4) (=> (@ (@ tptp.ord_le211207098394363844omplex A4) C4) (=> (@ (@ tptp.ord_le211207098394363844omplex B5) C4) (=> (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) (@ (@ tptp.minus_811609699411566653omplex C4) A4)) (= (@ G2 A3) tptp.zero_zero_complex))) (=> (forall ((B3 tptp.complex)) (=> (@ (@ tptp.member_complex B3) (@ (@ tptp.minus_811609699411566653omplex C4) B5)) (= (@ H B3) tptp.zero_zero_complex))) (= (= (@ _let_2 A4) (@ _let_1 B5)) (= (@ _let_2 C4) (@ _let_1 C4))))))))))) (forall ((C4 tptp.set_real) (A4 tptp.set_real) (B5 tptp.set_real) (G2 (-> tptp.real tptp.real)) (H (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.groups8097168146408367636l_real H))) (let ((_let_2 (@ tptp.groups8097168146408367636l_real G2))) (=> (@ tptp.finite_finite_real C4) (=> (@ (@ tptp.ord_less_eq_set_real A4) C4) (=> (@ (@ tptp.ord_less_eq_set_real B5) C4) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) (@ (@ tptp.minus_minus_set_real C4) A4)) (= (@ G2 A3) tptp.zero_zero_real))) (=> (forall ((B3 tptp.real)) (=> (@ (@ tptp.member_real B3) (@ (@ tptp.minus_minus_set_real C4) B5)) (= (@ H B3) tptp.zero_zero_real))) (= (= (@ _let_2 A4) (@ _let_1 B5)) (= (@ _let_2 C4) (@ _let_1 C4))))))))))) (forall ((C4 tptp.set_int) (A4 tptp.set_int) (B5 tptp.set_int) (G2 (-> tptp.int tptp.real)) (H (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups8778361861064173332t_real H))) (let ((_let_2 (@ tptp.groups8778361861064173332t_real G2))) (=> (@ tptp.finite_finite_int C4) (=> (@ (@ tptp.ord_less_eq_set_int A4) C4) (=> (@ (@ tptp.ord_less_eq_set_int B5) C4) (=> (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) (@ (@ tptp.minus_minus_set_int C4) A4)) (= (@ G2 A3) tptp.zero_zero_real))) (=> (forall ((B3 tptp.int)) (=> (@ (@ tptp.member_int B3) (@ (@ tptp.minus_minus_set_int C4) B5)) (= (@ H B3) tptp.zero_zero_real))) (= (= (@ _let_2 A4) (@ _let_1 B5)) (= (@ _let_2 C4) (@ _let_1 C4))))))))))) (forall ((C4 tptp.set_complex) (A4 tptp.set_complex) (B5 tptp.set_complex) (G2 (-> tptp.complex tptp.real)) (H (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups5808333547571424918x_real H))) (let ((_let_2 (@ tptp.groups5808333547571424918x_real G2))) (=> (@ tptp.finite3207457112153483333omplex C4) (=> (@ (@ tptp.ord_le211207098394363844omplex A4) C4) (=> (@ (@ tptp.ord_le211207098394363844omplex B5) C4) (=> (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) (@ (@ tptp.minus_811609699411566653omplex C4) A4)) (= (@ G2 A3) tptp.zero_zero_real))) (=> (forall ((B3 tptp.complex)) (=> (@ (@ tptp.member_complex B3) (@ (@ tptp.minus_811609699411566653omplex C4) B5)) (= (@ H B3) tptp.zero_zero_real))) (= (= (@ _let_2 A4) (@ _let_1 B5)) (= (@ _let_2 C4) (@ _let_1 C4))))))))))) (forall ((C4 tptp.set_real) (A4 tptp.set_real) (B5 tptp.set_real) (G2 (-> tptp.real tptp.rat)) (H (-> tptp.real tptp.rat))) (let ((_let_1 (@ tptp.groups1300246762558778688al_rat H))) (let ((_let_2 (@ tptp.groups1300246762558778688al_rat G2))) (=> (@ tptp.finite_finite_real C4) (=> (@ (@ tptp.ord_less_eq_set_real A4) C4) (=> (@ (@ tptp.ord_less_eq_set_real B5) C4) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) (@ (@ tptp.minus_minus_set_real C4) A4)) (= (@ G2 A3) tptp.zero_zero_rat))) (=> (forall ((B3 tptp.real)) (=> (@ (@ tptp.member_real B3) (@ (@ tptp.minus_minus_set_real C4) B5)) (= (@ H B3) tptp.zero_zero_rat))) (= (= (@ _let_2 A4) (@ _let_1 B5)) (= (@ _let_2 C4) (@ _let_1 C4))))))))))) (forall ((C4 tptp.set_int) (A4 tptp.set_int) (B5 tptp.set_int) (G2 (-> tptp.int tptp.rat)) (H (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups3906332499630173760nt_rat H))) (let ((_let_2 (@ tptp.groups3906332499630173760nt_rat G2))) (=> (@ tptp.finite_finite_int C4) (=> (@ (@ tptp.ord_less_eq_set_int A4) C4) (=> (@ (@ tptp.ord_less_eq_set_int B5) C4) (=> (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) (@ (@ tptp.minus_minus_set_int C4) A4)) (= (@ G2 A3) tptp.zero_zero_rat))) (=> (forall ((B3 tptp.int)) (=> (@ (@ tptp.member_int B3) (@ (@ tptp.minus_minus_set_int C4) B5)) (= (@ H B3) tptp.zero_zero_rat))) (= (= (@ _let_2 A4) (@ _let_1 B5)) (= (@ _let_2 C4) (@ _let_1 C4))))))))))) (forall ((C4 tptp.set_complex) (A4 tptp.set_complex) (B5 tptp.set_complex) (G2 (-> tptp.complex tptp.rat)) (H (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups5058264527183730370ex_rat H))) (let ((_let_2 (@ tptp.groups5058264527183730370ex_rat G2))) (=> (@ tptp.finite3207457112153483333omplex C4) (=> (@ (@ tptp.ord_le211207098394363844omplex A4) C4) (=> (@ (@ tptp.ord_le211207098394363844omplex B5) C4) (=> (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) (@ (@ tptp.minus_811609699411566653omplex C4) A4)) (= (@ G2 A3) tptp.zero_zero_rat))) (=> (forall ((B3 tptp.complex)) (=> (@ (@ tptp.member_complex B3) (@ (@ tptp.minus_811609699411566653omplex C4) B5)) (= (@ H B3) tptp.zero_zero_rat))) (= (= (@ _let_2 A4) (@ _let_1 B5)) (= (@ _let_2 C4) (@ _let_1 C4))))))))))) (forall ((C4 tptp.set_real) (A4 tptp.set_real) (B5 tptp.set_real) (G2 (-> tptp.real tptp.nat)) (H (-> tptp.real tptp.nat))) (let ((_let_1 (@ tptp.groups1935376822645274424al_nat H))) (let ((_let_2 (@ tptp.groups1935376822645274424al_nat G2))) (=> (@ tptp.finite_finite_real C4) (=> (@ (@ tptp.ord_less_eq_set_real A4) C4) (=> (@ (@ tptp.ord_less_eq_set_real B5) C4) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) (@ (@ tptp.minus_minus_set_real C4) A4)) (= (@ G2 A3) tptp.zero_zero_nat))) (=> (forall ((B3 tptp.real)) (=> (@ (@ tptp.member_real B3) (@ (@ tptp.minus_minus_set_real C4) B5)) (= (@ H B3) tptp.zero_zero_nat))) (= (= (@ _let_2 A4) (@ _let_1 B5)) (= (@ _let_2 C4) (@ _let_1 C4))))))))))) (forall ((T5 tptp.set_real) (S3 tptp.set_real) (H (-> tptp.real tptp.complex)) (G2 (-> tptp.real tptp.complex))) (=> (@ tptp.finite_finite_real T5) (=> (@ tptp.finite_finite_real S3) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) (@ (@ tptp.minus_minus_set_real T5) S3)) (= (@ H I3) tptp.zero_zero_complex))) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) (@ (@ tptp.minus_minus_set_real S3) T5)) (= (@ G2 I3) tptp.zero_zero_complex))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) (@ (@ tptp.inf_inf_set_real S3) T5)) (= (@ G2 X3) (@ H X3)))) (= (@ (@ tptp.groups5754745047067104278omplex G2) S3) (@ (@ tptp.groups5754745047067104278omplex H) T5)))))))) (forall ((T5 tptp.set_int) (S3 tptp.set_int) (H (-> tptp.int tptp.complex)) (G2 (-> tptp.int tptp.complex))) (=> (@ tptp.finite_finite_int T5) (=> (@ tptp.finite_finite_int S3) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) (@ (@ tptp.minus_minus_set_int T5) S3)) (= (@ H I3) tptp.zero_zero_complex))) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) (@ (@ tptp.minus_minus_set_int S3) T5)) (= (@ G2 I3) tptp.zero_zero_complex))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.inf_inf_set_int S3) T5)) (= (@ G2 X3) (@ H X3)))) (= (@ (@ tptp.groups3049146728041665814omplex G2) S3) (@ (@ tptp.groups3049146728041665814omplex H) T5)))))))) (forall ((T5 tptp.set_complex) (S3 tptp.set_complex) (H (-> tptp.complex tptp.complex)) (G2 (-> tptp.complex tptp.complex))) (=> (@ tptp.finite3207457112153483333omplex T5) (=> (@ tptp.finite3207457112153483333omplex S3) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) (@ (@ tptp.minus_811609699411566653omplex T5) S3)) (= (@ H I3) tptp.zero_zero_complex))) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) (@ (@ tptp.minus_811609699411566653omplex S3) T5)) (= (@ G2 I3) tptp.zero_zero_complex))) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ (@ tptp.inf_inf_set_complex S3) T5)) (= (@ G2 X3) (@ H X3)))) (= (@ (@ tptp.groups7754918857620584856omplex G2) S3) (@ (@ tptp.groups7754918857620584856omplex H) T5)))))))) (forall ((T5 tptp.set_real) (S3 tptp.set_real) (H (-> tptp.real tptp.real)) (G2 (-> tptp.real tptp.real))) (=> (@ tptp.finite_finite_real T5) (=> (@ tptp.finite_finite_real S3) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) (@ (@ tptp.minus_minus_set_real T5) S3)) (= (@ H I3) tptp.zero_zero_real))) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) (@ (@ tptp.minus_minus_set_real S3) T5)) (= (@ G2 I3) tptp.zero_zero_real))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) (@ (@ tptp.inf_inf_set_real S3) T5)) (= (@ G2 X3) (@ H X3)))) (= (@ (@ tptp.groups8097168146408367636l_real G2) S3) (@ (@ tptp.groups8097168146408367636l_real H) T5)))))))) (forall ((T5 tptp.set_int) (S3 tptp.set_int) (H (-> tptp.int tptp.real)) (G2 (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int T5) (=> (@ tptp.finite_finite_int S3) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) (@ (@ tptp.minus_minus_set_int T5) S3)) (= (@ H I3) tptp.zero_zero_real))) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) (@ (@ tptp.minus_minus_set_int S3) T5)) (= (@ G2 I3) tptp.zero_zero_real))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.inf_inf_set_int S3) T5)) (= (@ G2 X3) (@ H X3)))) (= (@ (@ tptp.groups8778361861064173332t_real G2) S3) (@ (@ tptp.groups8778361861064173332t_real H) T5)))))))) (forall ((T5 tptp.set_complex) (S3 tptp.set_complex) (H (-> tptp.complex tptp.real)) (G2 (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex T5) (=> (@ tptp.finite3207457112153483333omplex S3) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) (@ (@ tptp.minus_811609699411566653omplex T5) S3)) (= (@ H I3) tptp.zero_zero_real))) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) (@ (@ tptp.minus_811609699411566653omplex S3) T5)) (= (@ G2 I3) tptp.zero_zero_real))) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ (@ tptp.inf_inf_set_complex S3) T5)) (= (@ G2 X3) (@ H X3)))) (= (@ (@ tptp.groups5808333547571424918x_real G2) S3) (@ (@ tptp.groups5808333547571424918x_real H) T5)))))))) (forall ((T5 tptp.set_real) (S3 tptp.set_real) (H (-> tptp.real tptp.rat)) (G2 (-> tptp.real tptp.rat))) (=> (@ tptp.finite_finite_real T5) (=> (@ tptp.finite_finite_real S3) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) (@ (@ tptp.minus_minus_set_real T5) S3)) (= (@ H I3) tptp.zero_zero_rat))) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) (@ (@ tptp.minus_minus_set_real S3) T5)) (= (@ G2 I3) tptp.zero_zero_rat))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) (@ (@ tptp.inf_inf_set_real S3) T5)) (= (@ G2 X3) (@ H X3)))) (= (@ (@ tptp.groups1300246762558778688al_rat G2) S3) (@ (@ tptp.groups1300246762558778688al_rat H) T5)))))))) (forall ((T5 tptp.set_int) (S3 tptp.set_int) (H (-> tptp.int tptp.rat)) (G2 (-> tptp.int tptp.rat))) (=> (@ tptp.finite_finite_int T5) (=> (@ tptp.finite_finite_int S3) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) (@ (@ tptp.minus_minus_set_int T5) S3)) (= (@ H I3) tptp.zero_zero_rat))) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) (@ (@ tptp.minus_minus_set_int S3) T5)) (= (@ G2 I3) tptp.zero_zero_rat))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.inf_inf_set_int S3) T5)) (= (@ G2 X3) (@ H X3)))) (= (@ (@ tptp.groups3906332499630173760nt_rat G2) S3) (@ (@ tptp.groups3906332499630173760nt_rat H) T5)))))))) (forall ((T5 tptp.set_complex) (S3 tptp.set_complex) (H (-> tptp.complex tptp.rat)) (G2 (-> tptp.complex tptp.rat))) (=> (@ tptp.finite3207457112153483333omplex T5) (=> (@ tptp.finite3207457112153483333omplex S3) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) (@ (@ tptp.minus_811609699411566653omplex T5) S3)) (= (@ H I3) tptp.zero_zero_rat))) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) (@ (@ tptp.minus_811609699411566653omplex S3) T5)) (= (@ G2 I3) tptp.zero_zero_rat))) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ (@ tptp.inf_inf_set_complex S3) T5)) (= (@ G2 X3) (@ H X3)))) (= (@ (@ tptp.groups5058264527183730370ex_rat G2) S3) (@ (@ tptp.groups5058264527183730370ex_rat H) T5)))))))) (forall ((T5 tptp.set_real) (S3 tptp.set_real) (H (-> tptp.real tptp.nat)) (G2 (-> tptp.real tptp.nat))) (=> (@ tptp.finite_finite_real T5) (=> (@ tptp.finite_finite_real S3) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) (@ (@ tptp.minus_minus_set_real T5) S3)) (= (@ H I3) tptp.zero_zero_nat))) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) (@ (@ tptp.minus_minus_set_real S3) T5)) (= (@ G2 I3) tptp.zero_zero_nat))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) (@ (@ tptp.inf_inf_set_real S3) T5)) (= (@ G2 X3) (@ H X3)))) (= (@ (@ tptp.groups1935376822645274424al_nat G2) S3) (@ (@ tptp.groups1935376822645274424al_nat H) T5)))))))) (forall ((P2 (-> tptp.complex Bool)) (L tptp.complex)) (= (exists ((X4 tptp.complex)) (@ P2 (@ (@ tptp.times_times_complex L) X4))) (exists ((X4 tptp.complex)) (and (@ (@ tptp.dvd_dvd_complex L) (@ (@ tptp.plus_plus_complex X4) tptp.zero_zero_complex)) (@ P2 X4))))) (forall ((P2 (-> tptp.real Bool)) (L tptp.real)) (= (exists ((X4 tptp.real)) (@ P2 (@ (@ tptp.times_times_real L) X4))) (exists ((X4 tptp.real)) (and (@ (@ tptp.dvd_dvd_real L) (@ (@ tptp.plus_plus_real X4) tptp.zero_zero_real)) (@ P2 X4))))) (forall ((P2 (-> tptp.rat Bool)) (L tptp.rat)) (= (exists ((X4 tptp.rat)) (@ P2 (@ (@ tptp.times_times_rat L) X4))) (exists ((X4 tptp.rat)) (and (@ (@ tptp.dvd_dvd_rat L) (@ (@ tptp.plus_plus_rat X4) tptp.zero_zero_rat)) (@ P2 X4))))) (forall ((P2 (-> tptp.nat Bool)) (L tptp.nat)) (= (exists ((X4 tptp.nat)) (@ P2 (@ (@ tptp.times_times_nat L) X4))) (exists ((X4 tptp.nat)) (and (@ (@ tptp.dvd_dvd_nat L) (@ (@ tptp.plus_plus_nat X4) tptp.zero_zero_nat)) (@ P2 X4))))) (forall ((P2 (-> tptp.int Bool)) (L tptp.int)) (= (exists ((X4 tptp.int)) (@ P2 (@ (@ tptp.times_times_int L) X4))) (exists ((X4 tptp.int)) (and (@ (@ tptp.dvd_dvd_int L) (@ (@ tptp.plus_plus_int X4) tptp.zero_zero_int)) (@ P2 X4))))) (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 ((C tptp.code_integer)) (not (= B (@ (@ tptp.times_3573771949741848930nteger A) C)))))))) (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (not (=> (not (= A tptp.zero_zero_nat)) (forall ((C tptp.nat)) (not (= B (@ (@ tptp.times_times_nat A) C)))))))) (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (not (=> (not (= A tptp.zero_zero_int)) (forall ((C tptp.int)) (not (= B (@ (@ tptp.times_times_int A) C)))))))) (forall ((A tptp.nat) (C2 tptp.nat) (B tptp.nat) (D tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (=> (not (= C2 tptp.zero_zero_nat)) (=> (@ (@ tptp.dvd_dvd_nat A) B) (=> (@ (@ tptp.dvd_dvd_nat C2) D) (= (= (@ (@ tptp.divide_divide_nat B) A) (@ (@ tptp.divide_divide_nat D) C2)) (= (@ (@ tptp.times_times_nat B) C2) (@ (@ tptp.times_times_nat A) D)))))))) (forall ((A tptp.int) (C2 tptp.int) (B tptp.int) (D tptp.int)) (=> (not (= A tptp.zero_zero_int)) (=> (not (= C2 tptp.zero_zero_int)) (=> (@ (@ tptp.dvd_dvd_int A) B) (=> (@ (@ tptp.dvd_dvd_int C2) D) (= (= (@ (@ tptp.divide_divide_int B) A) (@ (@ tptp.divide_divide_int D) C2)) (= (@ (@ tptp.times_times_int B) C2) (@ (@ tptp.times_times_int A) D)))))))) (forall ((C2 tptp.nat) (B tptp.nat) (A tptp.nat)) (=> (not (= C2 tptp.zero_zero_nat)) (=> (@ (@ tptp.dvd_dvd_nat C2) B) (= (@ (@ tptp.dvd_dvd_nat A) (@ (@ tptp.divide_divide_nat B) C2)) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat A) C2)) B))))) (forall ((C2 tptp.int) (B tptp.int) (A tptp.int)) (=> (not (= C2 tptp.zero_zero_int)) (=> (@ (@ tptp.dvd_dvd_int C2) B) (= (@ (@ tptp.dvd_dvd_int A) (@ (@ tptp.divide_divide_int B) C2)) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A) C2)) B))))) (forall ((B tptp.nat) (A tptp.nat) (C2 tptp.nat)) (=> (not (= B tptp.zero_zero_nat)) (=> (@ (@ tptp.dvd_dvd_nat B) A) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.divide_divide_nat A) B)) C2) (@ (@ tptp.dvd_dvd_nat A) (@ (@ tptp.times_times_nat C2) B)))))) (forall ((B tptp.int) (A tptp.int) (C2 tptp.int)) (=> (not (= B tptp.zero_zero_int)) (=> (@ (@ tptp.dvd_dvd_int B) A) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.divide_divide_int A) B)) C2) (@ (@ tptp.dvd_dvd_int A) (@ (@ tptp.times_times_int C2) B)))))) (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (=> (@ (@ tptp.dvd_dvd_nat A) B) (= (= (@ (@ tptp.divide_divide_nat B) A) C2) (= B (@ (@ tptp.times_times_nat C2) A)))))) (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (=> (not (= A tptp.zero_zero_int)) (=> (@ (@ tptp.dvd_dvd_int A) B) (= (= (@ (@ tptp.divide_divide_int B) A) C2) (= B (@ (@ tptp.times_times_int C2) A)))))) (forall ((B tptp.code_integer) (A tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer) (= (= (@ (@ tptp.divide6298287555418463151nteger A) B) tptp.zero_z3403309356797280102nteger) (= A tptp.zero_z3403309356797280102nteger)))) (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat) (= (= (@ (@ tptp.divide_divide_nat A) B) tptp.zero_zero_nat) (= A tptp.zero_zero_nat)))) (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int) (= (= (@ (@ tptp.divide_divide_int A) B) tptp.zero_zero_int) (= A tptp.zero_zero_int)))) (forall ((D tptp.real) (D3 tptp.real) (T tptp.real)) (=> (@ (@ tptp.dvd_dvd_real D) D3) (forall ((X5 tptp.real) (K4 tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real D))) (= (not (@ _let_1 (@ (@ tptp.plus_plus_real X5) T))) (not (@ _let_1 (@ (@ tptp.plus_plus_real (@ (@ tptp.minus_minus_real X5) (@ (@ tptp.times_times_real K4) D3))) T)))))))) (forall ((D tptp.rat) (D3 tptp.rat) (T tptp.rat)) (=> (@ (@ tptp.dvd_dvd_rat D) D3) (forall ((X5 tptp.rat) (K4 tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat D))) (= (not (@ _let_1 (@ (@ tptp.plus_plus_rat X5) T))) (not (@ _let_1 (@ (@ tptp.plus_plus_rat (@ (@ tptp.minus_minus_rat X5) (@ (@ tptp.times_times_rat K4) D3))) T)))))))) (forall ((D tptp.int) (D3 tptp.int) (T tptp.int)) (=> (@ (@ tptp.dvd_dvd_int D) D3) (forall ((X5 tptp.int) (K4 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int D))) (= (not (@ _let_1 (@ (@ tptp.plus_plus_int X5) T))) (not (@ _let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int X5) (@ (@ tptp.times_times_int K4) D3))) T)))))))) (forall ((D tptp.real) (D3 tptp.real) (T tptp.real)) (=> (@ (@ tptp.dvd_dvd_real D) D3) (forall ((X5 tptp.real) (K4 tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real D))) (= (@ _let_1 (@ (@ tptp.plus_plus_real X5) T)) (@ _let_1 (@ (@ tptp.plus_plus_real (@ (@ tptp.minus_minus_real X5) (@ (@ tptp.times_times_real K4) D3))) T))))))) (forall ((D tptp.rat) (D3 tptp.rat) (T tptp.rat)) (=> (@ (@ tptp.dvd_dvd_rat D) D3) (forall ((X5 tptp.rat) (K4 tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat D))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat X5) T)) (@ _let_1 (@ (@ tptp.plus_plus_rat (@ (@ tptp.minus_minus_rat X5) (@ (@ tptp.times_times_rat K4) D3))) T))))))) (forall ((D tptp.int) (D3 tptp.int) (T tptp.int)) (=> (@ (@ tptp.dvd_dvd_int D) D3) (forall ((X5 tptp.int) (K4 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int D))) (= (@ _let_1 (@ (@ tptp.plus_plus_int X5) T)) (@ _let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int X5) (@ (@ tptp.times_times_int K4) D3))) T))))))) (forall ((B tptp.code_integer) (A tptp.code_integer) (C2 tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer) (= (= (@ (@ tptp.divide6298287555418463151nteger A) B) C2) (= A (@ (@ tptp.times_3573771949741848930nteger C2) B))))) (forall ((B tptp.nat) (A tptp.nat) (C2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat) (= (= (@ (@ tptp.divide_divide_nat A) B) C2) (= A (@ (@ tptp.times_times_nat C2) B))))) (forall ((B tptp.int) (A tptp.int) (C2 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int) (= (= (@ (@ tptp.divide_divide_int A) B) C2) (= A (@ (@ tptp.times_times_int C2) B))))) (forall ((B tptp.code_integer) (A tptp.code_integer) (C2 tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer) (= (= A (@ (@ tptp.divide6298287555418463151nteger C2) B)) (= (@ (@ tptp.times_3573771949741848930nteger A) B) C2)))) (forall ((B tptp.nat) (A tptp.nat) (C2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat) (= (= A (@ (@ tptp.divide_divide_nat C2) B)) (= (@ (@ tptp.times_times_nat A) B) C2)))) (forall ((B tptp.int) (A tptp.int) (C2 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int) (= (= A (@ (@ tptp.divide_divide_int C2) B)) (= (@ (@ tptp.times_times_int A) B) C2)))) (forall ((C2 tptp.code_integer) (B tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.divide6298287555418463151nteger A))) (=> (@ (@ tptp.dvd_dvd_Code_integer C2) tptp.one_one_Code_integer) (=> (@ (@ tptp.dvd_dvd_Code_integer B) A) (= (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger B) C2)) (@ (@ tptp.divide6298287555418463151nteger (@ _let_1 B)) C2)))))) (forall ((C2 tptp.nat) (B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat A))) (=> (@ (@ tptp.dvd_dvd_nat C2) tptp.one_one_nat) (=> (@ (@ tptp.dvd_dvd_nat B) A) (= (@ _let_1 (@ (@ tptp.times_times_nat B) C2)) (@ (@ tptp.divide_divide_nat (@ _let_1 B)) C2)))))) (forall ((C2 tptp.int) (B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A))) (=> (@ (@ tptp.dvd_dvd_int C2) tptp.one_one_int) (=> (@ (@ tptp.dvd_dvd_int B) A) (= (@ _let_1 (@ (@ tptp.times_times_int B) C2)) (@ (@ tptp.divide_divide_int (@ _let_1 B)) C2)))))) (forall ((B tptp.code_integer) (A tptp.code_integer) (C2 tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer) (= (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.divide6298287555418463151nteger A) B)) C2) (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.times_3573771949741848930nteger A) C2)) B)))) (forall ((B tptp.nat) (A tptp.nat) (C2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat) (= (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat A) B)) C2) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat A) C2)) B)))) (forall ((B tptp.int) (A tptp.int) (C2 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int) (= (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int A) B)) C2) (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int A) C2)) B)))) (forall ((C2 tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger A))) (=> (@ (@ tptp.dvd_dvd_Code_integer C2) tptp.one_one_Code_integer) (= (@ _let_1 (@ (@ tptp.divide6298287555418463151nteger B) C2)) (@ (@ tptp.divide6298287555418463151nteger (@ _let_1 B)) C2))))) (forall ((C2 tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (=> (@ (@ tptp.dvd_dvd_nat C2) tptp.one_one_nat) (= (@ _let_1 (@ (@ tptp.divide_divide_nat B) C2)) (@ (@ tptp.divide_divide_nat (@ _let_1 B)) C2))))) (forall ((C2 tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (=> (@ (@ tptp.dvd_dvd_int C2) tptp.one_one_int) (= (@ _let_1 (@ (@ tptp.divide_divide_int B) C2)) (@ (@ tptp.divide_divide_int (@ _let_1 B)) C2))))) (forall ((B tptp.code_integer) (C2 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 C2) tptp.one_one_Code_integer) (= (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger B) C2)) (@ (@ tptp.divide6298287555418463151nteger (@ _let_1 B)) C2)))))) (forall ((B tptp.nat) (C2 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 C2) tptp.one_one_nat) (= (@ _let_1 (@ (@ tptp.times_times_nat B) C2)) (@ (@ tptp.divide_divide_nat (@ _let_1 B)) C2)))))) (forall ((B tptp.int) (C2 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 C2) tptp.one_one_int) (= (@ _let_1 (@ (@ tptp.times_times_int B) C2)) (@ (@ tptp.divide_divide_int (@ _let_1 B)) C2)))))) (forall ((A tptp.code_integer) (N tptp.nat)) (= (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.power_8256067586552552935nteger A) N)) tptp.one_one_Code_integer) (or (@ (@ tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer) (= N tptp.zero_zero_nat)))) (forall ((A tptp.nat) (N tptp.nat)) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.power_power_nat A) N)) tptp.one_one_nat) (or (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (= N tptp.zero_zero_nat)))) (forall ((A tptp.int) (N tptp.nat)) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.power_power_int A) N)) tptp.one_one_int) (or (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (= N tptp.zero_zero_nat)))) (forall ((B tptp.code_integer) (A tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer) (= (@ (@ tptp.modulo364778990260209775nteger A) B) tptp.zero_z3403309356797280102nteger))) (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat) (= (@ (@ tptp.modulo_modulo_nat A) B) tptp.zero_zero_nat))) (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int) (= (@ (@ tptp.modulo_modulo_int A) B) tptp.zero_zero_int))) (forall ((B tptp.code_natural) (A tptp.code_natural)) (=> (@ (@ tptp.dvd_dvd_Code_natural B) tptp.one_one_Code_natural) (= (@ (@ tptp.modulo8411746178871703098atural A) B) tptp.zero_z2226904508553997617atural))) (forall ((X tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.comm_s7457072308508201937r_real X) N)))) (forall ((X tptp.rat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) X) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.comm_s4028243227959126397er_rat X) N)))) (forall ((X tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) X) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ (@ tptp.comm_s4663373288045622133er_nat X) N)))) (forall ((X tptp.int) (N tptp.nat)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) X) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.comm_s4660882817536571857er_int X) N)))) (forall ((K2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat K2) N) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_eq_nat K2) N)))) (forall ((K2 tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K2))) (=> (@ (@ tptp.dvd_dvd_nat (@ _let_1 M2)) (@ _let_1 N)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K2) (@ (@ tptp.dvd_dvd_nat M2) N))))) (forall ((K2 tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K2) (= (@ (@ tptp.dvd_dvd_nat (@ _let_1 M2)) (@ _let_1 N)) (@ (@ tptp.dvd_dvd_nat M2) N))))) (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.comm_s8582702949713902594nteger tptp.zero_z3403309356797280102nteger) N))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_Code_integer)) (=> (not _let_2) (= _let_1 tptp.zero_z3403309356797280102nteger)))))) (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.comm_s2602460028002588243omplex tptp.zero_zero_complex) N))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_complex)) (=> (not _let_2) (= _let_1 tptp.zero_zero_complex)))))) (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.comm_s7457072308508201937r_real tptp.zero_zero_real) N))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_real)) (=> (not _let_2) (= _let_1 tptp.zero_zero_real)))))) (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.comm_s4028243227959126397er_rat tptp.zero_zero_rat) N))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_rat)) (=> (not _let_2) (= _let_1 tptp.zero_zero_rat)))))) (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.comm_s4663373288045622133er_nat tptp.zero_zero_nat) N))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_nat)) (=> (not _let_2) (= _let_1 tptp.zero_zero_nat)))))) (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.comm_s4660882817536571857er_int tptp.zero_zero_int) N))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_int)) (=> (not _let_2) (= _let_1 tptp.zero_zero_int)))))) (forall ((A tptp.nat) (B tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (exists ((D5 tptp.nat) (X3 tptp.nat) (Y3 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat D5))) (and (@ _let_1 A) (@ _let_1 B) (= (@ (@ tptp.times_times_nat A) X3) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat B) Y3)) D5))))))) (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.modulo_modulo_nat M2) N)) (not (@ (@ tptp.dvd_dvd_nat N) M2)))) (forall ((N tptp.nat) (M2 tptp.nat) (Q2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M2) (= (= (@ (@ tptp.modulo_modulo_nat M2) Q2) (@ (@ tptp.modulo_modulo_nat N) Q2)) (@ (@ tptp.dvd_dvd_nat Q2) (@ (@ tptp.minus_minus_nat M2) N))))) (forall ((X tptp.complex) (M2 tptp.nat) (I5 tptp.set_nat)) (let ((_let_1 (@ tptp.power_power_complex X))) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I tptp.nat)) (@ (@ tptp.power_power_complex X) (@ (@ tptp.plus_plus_nat M2) I)))) I5) (@ (@ tptp.times_times_complex (@ _let_1 M2)) (@ (@ tptp.groups2073611262835488442omplex _let_1) I5))))) (forall ((X tptp.rat) (M2 tptp.nat) (I5 tptp.set_nat)) (let ((_let_1 (@ tptp.power_power_rat X))) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I tptp.nat)) (@ (@ tptp.power_power_rat X) (@ (@ tptp.plus_plus_nat M2) I)))) I5) (@ (@ tptp.times_times_rat (@ _let_1 M2)) (@ (@ tptp.groups2906978787729119204at_rat _let_1) I5))))) (forall ((X tptp.int) (M2 tptp.nat) (I5 tptp.set_nat)) (let ((_let_1 (@ tptp.power_power_int X))) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((I tptp.nat)) (@ (@ tptp.power_power_int X) (@ (@ tptp.plus_plus_nat M2) I)))) I5) (@ (@ tptp.times_times_int (@ _let_1 M2)) (@ (@ tptp.groups3539618377306564664at_int _let_1) I5))))) (forall ((X tptp.real) (M2 tptp.nat) (I5 tptp.set_nat)) (let ((_let_1 (@ tptp.power_power_real X))) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I tptp.nat)) (@ (@ tptp.power_power_real X) (@ (@ tptp.plus_plus_nat M2) I)))) I5) (@ (@ tptp.times_times_real (@ _let_1 M2)) (@ (@ tptp.groups6591440286371151544t_real _let_1) I5))))) (forall ((B5 tptp.set_real) (A4 tptp.set_real) (F2 (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.groups8097168146408367636l_real F2))) (=> (@ tptp.finite_finite_real B5) (=> (@ (@ tptp.ord_less_eq_set_real A4) B5) (=> (forall ((B3 tptp.real)) (=> (@ (@ tptp.member_real B3) (@ (@ tptp.minus_minus_set_real B5) A4)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F2 B3)))) (@ (@ tptp.ord_less_eq_real (@ _let_1 A4)) (@ _let_1 B5))))))) (forall ((B5 tptp.set_int) (A4 tptp.set_int) (F2 (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups8778361861064173332t_real F2))) (=> (@ tptp.finite_finite_int B5) (=> (@ (@ tptp.ord_less_eq_set_int A4) B5) (=> (forall ((B3 tptp.int)) (=> (@ (@ tptp.member_int B3) (@ (@ tptp.minus_minus_set_int B5) A4)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F2 B3)))) (@ (@ tptp.ord_less_eq_real (@ _let_1 A4)) (@ _let_1 B5))))))) (forall ((B5 tptp.set_complex) (A4 tptp.set_complex) (F2 (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups5808333547571424918x_real F2))) (=> (@ tptp.finite3207457112153483333omplex B5) (=> (@ (@ tptp.ord_le211207098394363844omplex A4) B5) (=> (forall ((B3 tptp.complex)) (=> (@ (@ tptp.member_complex B3) (@ (@ tptp.minus_811609699411566653omplex B5) A4)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F2 B3)))) (@ (@ tptp.ord_less_eq_real (@ _let_1 A4)) (@ _let_1 B5))))))) (forall ((B5 tptp.set_real) (A4 tptp.set_real) (F2 (-> tptp.real tptp.rat))) (let ((_let_1 (@ tptp.groups1300246762558778688al_rat F2))) (=> (@ tptp.finite_finite_real B5) (=> (@ (@ tptp.ord_less_eq_set_real A4) B5) (=> (forall ((B3 tptp.real)) (=> (@ (@ tptp.member_real B3) (@ (@ tptp.minus_minus_set_real B5) A4)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F2 B3)))) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A4)) (@ _let_1 B5))))))) (forall ((B5 tptp.set_int) (A4 tptp.set_int) (F2 (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups3906332499630173760nt_rat F2))) (=> (@ tptp.finite_finite_int B5) (=> (@ (@ tptp.ord_less_eq_set_int A4) B5) (=> (forall ((B3 tptp.int)) (=> (@ (@ tptp.member_int B3) (@ (@ tptp.minus_minus_set_int B5) A4)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F2 B3)))) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A4)) (@ _let_1 B5))))))) (forall ((B5 tptp.set_complex) (A4 tptp.set_complex) (F2 (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups5058264527183730370ex_rat F2))) (=> (@ tptp.finite3207457112153483333omplex B5) (=> (@ (@ tptp.ord_le211207098394363844omplex A4) B5) (=> (forall ((B3 tptp.complex)) (=> (@ (@ tptp.member_complex B3) (@ (@ tptp.minus_811609699411566653omplex B5) A4)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F2 B3)))) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A4)) (@ _let_1 B5))))))) (forall ((B5 tptp.set_real) (A4 tptp.set_real) (F2 (-> tptp.real tptp.nat))) (let ((_let_1 (@ tptp.groups1935376822645274424al_nat F2))) (=> (@ tptp.finite_finite_real B5) (=> (@ (@ tptp.ord_less_eq_set_real A4) B5) (=> (forall ((B3 tptp.real)) (=> (@ (@ tptp.member_real B3) (@ (@ tptp.minus_minus_set_real B5) A4)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F2 B3)))) (@ (@ tptp.ord_less_eq_nat (@ _let_1 A4)) (@ _let_1 B5))))))) (forall ((B5 tptp.set_int) (A4 tptp.set_int) (F2 (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups4541462559716669496nt_nat F2))) (=> (@ tptp.finite_finite_int B5) (=> (@ (@ tptp.ord_less_eq_set_int A4) B5) (=> (forall ((B3 tptp.int)) (=> (@ (@ tptp.member_int B3) (@ (@ tptp.minus_minus_set_int B5) A4)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F2 B3)))) (@ (@ tptp.ord_less_eq_nat (@ _let_1 A4)) (@ _let_1 B5))))))) (forall ((B5 tptp.set_complex) (A4 tptp.set_complex) (F2 (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups5693394587270226106ex_nat F2))) (=> (@ tptp.finite3207457112153483333omplex B5) (=> (@ (@ tptp.ord_le211207098394363844omplex A4) B5) (=> (forall ((B3 tptp.complex)) (=> (@ (@ tptp.member_complex B3) (@ (@ tptp.minus_811609699411566653omplex B5) A4)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F2 B3)))) (@ (@ tptp.ord_less_eq_nat (@ _let_1 A4)) (@ _let_1 B5))))))) (forall ((B5 tptp.set_real) (A4 tptp.set_real) (F2 (-> tptp.real tptp.int))) (let ((_let_1 (@ tptp.groups1932886352136224148al_int F2))) (=> (@ tptp.finite_finite_real B5) (=> (@ (@ tptp.ord_less_eq_set_real A4) B5) (=> (forall ((B3 tptp.real)) (=> (@ (@ tptp.member_real B3) (@ (@ tptp.minus_minus_set_real B5) A4)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F2 B3)))) (@ (@ tptp.ord_less_eq_int (@ _let_1 A4)) (@ _let_1 B5))))))) (forall ((A4 tptp.set_int) (B5 tptp.set_int) (G2 (-> tptp.int tptp.complex))) (let ((_let_1 (@ tptp.groups3049146728041665814omplex G2))) (=> (@ tptp.finite_finite_int A4) (=> (@ tptp.finite_finite_int B5) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.inf_inf_set_int A4) B5)) (= (@ G2 X3) tptp.zero_zero_complex))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_int A4) B5)) (@ (@ tptp.plus_plus_complex (@ _let_1 A4)) (@ _let_1 B5)))))))) (forall ((A4 tptp.set_complex) (B5 tptp.set_complex) (G2 (-> tptp.complex tptp.complex))) (let ((_let_1 (@ tptp.groups7754918857620584856omplex G2))) (=> (@ tptp.finite3207457112153483333omplex A4) (=> (@ tptp.finite3207457112153483333omplex B5) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ (@ tptp.inf_inf_set_complex A4) B5)) (= (@ G2 X3) tptp.zero_zero_complex))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_complex A4) B5)) (@ (@ tptp.plus_plus_complex (@ _let_1 A4)) (@ _let_1 B5)))))))) (forall ((A4 tptp.set_int) (B5 tptp.set_int) (G2 (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups8778361861064173332t_real G2))) (=> (@ tptp.finite_finite_int A4) (=> (@ tptp.finite_finite_int B5) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.inf_inf_set_int A4) B5)) (= (@ G2 X3) tptp.zero_zero_real))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_int A4) B5)) (@ (@ tptp.plus_plus_real (@ _let_1 A4)) (@ _let_1 B5)))))))) (forall ((A4 tptp.set_complex) (B5 tptp.set_complex) (G2 (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups5808333547571424918x_real G2))) (=> (@ tptp.finite3207457112153483333omplex A4) (=> (@ tptp.finite3207457112153483333omplex B5) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ (@ tptp.inf_inf_set_complex A4) B5)) (= (@ G2 X3) tptp.zero_zero_real))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_complex A4) B5)) (@ (@ tptp.plus_plus_real (@ _let_1 A4)) (@ _let_1 B5)))))))) (forall ((A4 tptp.set_int) (B5 tptp.set_int) (G2 (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups3906332499630173760nt_rat G2))) (=> (@ tptp.finite_finite_int A4) (=> (@ tptp.finite_finite_int B5) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.inf_inf_set_int A4) B5)) (= (@ G2 X3) tptp.zero_zero_rat))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_int A4) B5)) (@ (@ tptp.plus_plus_rat (@ _let_1 A4)) (@ _let_1 B5)))))))) (forall ((A4 tptp.set_complex) (B5 tptp.set_complex) (G2 (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups5058264527183730370ex_rat G2))) (=> (@ tptp.finite3207457112153483333omplex A4) (=> (@ tptp.finite3207457112153483333omplex B5) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ (@ tptp.inf_inf_set_complex A4) B5)) (= (@ G2 X3) tptp.zero_zero_rat))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_complex A4) B5)) (@ (@ tptp.plus_plus_rat (@ _let_1 A4)) (@ _let_1 B5)))))))) (forall ((A4 tptp.set_int) (B5 tptp.set_int) (G2 (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups4541462559716669496nt_nat G2))) (=> (@ tptp.finite_finite_int A4) (=> (@ tptp.finite_finite_int B5) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.inf_inf_set_int A4) B5)) (= (@ G2 X3) tptp.zero_zero_nat))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_int A4) B5)) (@ (@ tptp.plus_plus_nat (@ _let_1 A4)) (@ _let_1 B5)))))))) (forall ((A4 tptp.set_complex) (B5 tptp.set_complex) (G2 (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups5693394587270226106ex_nat G2))) (=> (@ tptp.finite3207457112153483333omplex A4) (=> (@ tptp.finite3207457112153483333omplex B5) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ (@ tptp.inf_inf_set_complex A4) B5)) (= (@ G2 X3) tptp.zero_zero_nat))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_complex A4) B5)) (@ (@ tptp.plus_plus_nat (@ _let_1 A4)) (@ _let_1 B5)))))))) (forall ((A4 tptp.set_complex) (B5 tptp.set_complex) (G2 (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.groups5690904116761175830ex_int G2))) (=> (@ tptp.finite3207457112153483333omplex A4) (=> (@ tptp.finite3207457112153483333omplex B5) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ (@ tptp.inf_inf_set_complex A4) B5)) (= (@ G2 X3) tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_complex A4) B5)) (@ (@ tptp.plus_plus_int (@ _let_1 A4)) (@ _let_1 B5)))))))) (forall ((A4 tptp.set_nat) (B5 tptp.set_nat) (G2 (-> tptp.nat tptp.complex))) (let ((_let_1 (@ tptp.groups2073611262835488442omplex G2))) (=> (@ tptp.finite_finite_nat A4) (=> (@ tptp.finite_finite_nat B5) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ (@ tptp.inf_inf_set_nat A4) B5)) (= (@ G2 X3) tptp.zero_zero_complex))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_nat A4) B5)) (@ (@ tptp.plus_plus_complex (@ _let_1 A4)) (@ _let_1 B5)))))))) (forall ((G2 (-> tptp.nat tptp.nat)) (N tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat N) M2))) (= (@ (@ tptp.groups3542108847815614940at_nat G2) _let_1) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I tptp.nat)) (@ G2 (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M2) N)) I)))) _let_1)))) (forall ((G2 (-> tptp.nat tptp.real)) (N tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat N) M2))) (= (@ (@ tptp.groups6591440286371151544t_real G2) _let_1) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I tptp.nat)) (@ G2 (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M2) N)) I)))) _let_1)))) (forall ((M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M2) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((D2 tptp.nat)) (@ (@ tptp.dvd_dvd_nat D2) M2)))))) (forall ((A (-> tptp.nat tptp.complex))) (@ (@ tptp.sums_complex (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_complex (@ A N4)) (@ (@ tptp.power_power_complex tptp.zero_zero_complex) N4)))) (@ A tptp.zero_zero_nat))) (forall ((A (-> tptp.nat tptp.real))) (@ (@ tptp.sums_real (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_real (@ A N4)) (@ (@ tptp.power_power_real tptp.zero_zero_real) N4)))) (@ A tptp.zero_zero_nat))) (forall ((F2 (-> tptp.nat tptp.complex)) (K2 tptp.nat)) (let ((_let_1 (@ tptp.groups2073611262835488442omplex F2))) (=> (= (@ F2 tptp.zero_zero_nat) tptp.zero_zero_complex) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) K2)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) K2)))))) (forall ((F2 (-> tptp.nat tptp.rat)) (K2 tptp.nat)) (let ((_let_1 (@ tptp.groups2906978787729119204at_rat F2))) (=> (= (@ F2 tptp.zero_zero_nat) tptp.zero_zero_rat) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) K2)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) K2)))))) (forall ((F2 (-> tptp.nat tptp.int)) (K2 tptp.nat)) (let ((_let_1 (@ tptp.groups3539618377306564664at_int F2))) (=> (= (@ F2 tptp.zero_zero_nat) tptp.zero_zero_int) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) K2)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) K2)))))) (forall ((F2 (-> tptp.nat tptp.nat)) (K2 tptp.nat)) (let ((_let_1 (@ tptp.groups3542108847815614940at_nat F2))) (=> (= (@ F2 tptp.zero_zero_nat) tptp.zero_zero_nat) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) K2)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) K2)))))) (forall ((F2 (-> tptp.nat tptp.real)) (K2 tptp.nat)) (let ((_let_1 (@ tptp.groups6591440286371151544t_real F2))) (=> (= (@ F2 tptp.zero_zero_nat) tptp.zero_zero_real) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) K2)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) K2)))))) (forall ((G2 (-> 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 G2))) (= (@ _let_3 (@ _let_2 _let_1)) (@ (@ tptp.plus_plus_rat (@ _let_3 (@ _let_2 N))) (@ G2 _let_1))))))) (forall ((G2 (-> 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 G2))) (= (@ _let_3 (@ _let_2 _let_1)) (@ (@ tptp.plus_plus_int (@ _let_3 (@ _let_2 N))) (@ G2 _let_1))))))) (forall ((G2 (-> 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 G2))) (= (@ _let_3 (@ _let_2 _let_1)) (@ (@ tptp.plus_plus_nat (@ _let_3 (@ _let_2 N))) (@ G2 _let_1))))))) (forall ((G2 (-> 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 G2))) (= (@ _let_3 (@ _let_2 _let_1)) (@ (@ tptp.plus_plus_real (@ _let_3 (@ _let_2 N))) (@ G2 _let_1))))))) (forall ((M2 tptp.nat) (N tptp.nat) (G2 (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups2906978787729119204at_rat G2))) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M2) N)) (@ (@ tptp.plus_plus_rat (@ G2 M2)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M2)) N))))))) (forall ((M2 tptp.nat) (N tptp.nat) (G2 (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.groups3539618377306564664at_int G2))) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M2) N)) (@ (@ tptp.plus_plus_int (@ G2 M2)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M2)) N))))))) (forall ((M2 tptp.nat) (N tptp.nat) (G2 (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.groups3542108847815614940at_nat G2))) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M2) N)) (@ (@ tptp.plus_plus_nat (@ G2 M2)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M2)) N))))))) (forall ((M2 tptp.nat) (N tptp.nat) (G2 (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.groups6591440286371151544t_real G2))) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M2) N)) (@ (@ tptp.plus_plus_real (@ G2 M2)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M2)) N))))))) (forall ((M2 tptp.nat) (N tptp.nat) (G2 (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat M2))) (let ((_let_2 (@ tptp.groups2906978787729119204at_rat G2))) (let ((_let_3 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_nat M2) _let_3) (= (@ _let_2 (@ _let_1 _let_3)) (@ (@ tptp.plus_plus_rat (@ G2 _let_3)) (@ _let_2 (@ _let_1 N))))))))) (forall ((M2 tptp.nat) (N tptp.nat) (G2 (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat M2))) (let ((_let_2 (@ tptp.groups3539618377306564664at_int G2))) (let ((_let_3 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_nat M2) _let_3) (= (@ _let_2 (@ _let_1 _let_3)) (@ (@ tptp.plus_plus_int (@ G2 _let_3)) (@ _let_2 (@ _let_1 N))))))))) (forall ((M2 tptp.nat) (N tptp.nat) (G2 (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat M2))) (let ((_let_2 (@ tptp.groups3542108847815614940at_nat G2))) (let ((_let_3 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_nat M2) _let_3) (= (@ _let_2 (@ _let_1 _let_3)) (@ (@ tptp.plus_plus_nat (@ G2 _let_3)) (@ _let_2 (@ _let_1 N))))))))) (forall ((M2 tptp.nat) (N tptp.nat) (G2 (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat M2))) (let ((_let_2 (@ tptp.groups6591440286371151544t_real G2))) (let ((_let_3 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_nat M2) _let_3) (= (@ _let_2 (@ _let_1 _let_3)) (@ (@ tptp.plus_plus_real (@ G2 _let_3)) (@ _let_2 (@ _let_1 N))))))))) (@ (@ tptp.dvd_dvd_nat _let_22) tptp.zero_zero_nat) (@ (@ tptp.dvd_dvd_int _let_115) tptp.zero_zero_int) (forall ((A tptp.code_integer) (C2 tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer) (not (=> (not (= A tptp.zero_z3403309356797280102nteger)) (forall ((B3 tptp.code_integer)) (let ((_let_1 (@ tptp.divide6298287555418463151nteger tptp.one_one_Code_integer))) (=> (not (= B3 tptp.zero_z3403309356797280102nteger)) (=> (@ (@ tptp.dvd_dvd_Code_integer B3) tptp.one_one_Code_integer) (=> (= (@ _let_1 A) B3) (=> (= (@ _let_1 B3) A) (=> (= (@ (@ tptp.times_3573771949741848930nteger A) B3) tptp.one_one_Code_integer) (not (= (@ (@ tptp.divide6298287555418463151nteger C2) A) (@ (@ tptp.times_3573771949741848930nteger C2) B3)))))))))))))) (forall ((A tptp.nat) (C2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (not (=> (not (= A tptp.zero_zero_nat)) (forall ((B3 tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat tptp.one_one_nat))) (=> (not (= B3 tptp.zero_zero_nat)) (=> (@ (@ tptp.dvd_dvd_nat B3) tptp.one_one_nat) (=> (= (@ _let_1 A) B3) (=> (= (@ _let_1 B3) A) (=> (= (@ (@ tptp.times_times_nat A) B3) tptp.one_one_nat) (not (= (@ (@ tptp.divide_divide_nat C2) A) (@ (@ tptp.times_times_nat C2) B3)))))))))))))) (forall ((A tptp.int) (C2 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (not (=> (not (= A tptp.zero_zero_int)) (forall ((B3 tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int tptp.one_one_int))) (=> (not (= B3 tptp.zero_zero_int)) (=> (@ (@ tptp.dvd_dvd_int B3) tptp.one_one_int) (=> (= (@ _let_1 A) B3) (=> (= (@ _let_1 B3) A) (=> (= (@ (@ tptp.times_times_int A) B3) tptp.one_one_int) (not (= (@ (@ tptp.divide_divide_int C2) A) (@ (@ tptp.times_times_int C2) B3)))))))))))))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (not (= A tptp.zero_z3403309356797280102nteger)) (=> (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer) (= (@ (@ tptp.divide6298287555418463151nteger A) (@ (@ tptp.times_3573771949741848930nteger A) B)) (@ (@ tptp.divide6298287555418463151nteger tptp.one_one_Code_integer) B))))) (forall ((A tptp.nat) (B tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (=> (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat) (= (@ (@ tptp.divide_divide_nat A) (@ (@ tptp.times_times_nat A) B)) (@ (@ tptp.divide_divide_nat tptp.one_one_nat) B))))) (forall ((A tptp.int) (B tptp.int)) (=> (not (= A tptp.zero_zero_int)) (=> (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int) (= (@ (@ tptp.divide_divide_int A) (@ (@ tptp.times_times_int A) B)) (@ (@ tptp.divide_divide_int tptp.one_one_int) B))))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (not (= A tptp.zero_z3403309356797280102nteger)) (=> (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer) (= (@ (@ tptp.divide6298287555418463151nteger A) (@ (@ tptp.times_3573771949741848930nteger B) A)) (@ (@ tptp.divide6298287555418463151nteger tptp.one_one_Code_integer) B))))) (forall ((A tptp.nat) (B tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (=> (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat) (= (@ (@ tptp.divide_divide_nat A) (@ (@ tptp.times_times_nat B) A)) (@ (@ tptp.divide_divide_nat tptp.one_one_nat) B))))) (forall ((A tptp.int) (B tptp.int)) (=> (not (= A tptp.zero_zero_int)) (=> (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int) (= (@ (@ tptp.divide_divide_int A) (@ (@ tptp.times_times_int B) A)) (@ (@ tptp.divide_divide_int tptp.one_one_int) B))))) (forall ((A tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) A) (not (forall ((B3 tptp.nat)) (not (= A (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) B3))))))) (forall ((A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) A) (not (forall ((B3 tptp.int)) (not (= A (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) B3))))))) (forall ((X tptp.code_integer) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger X))) (=> (not (= X tptp.zero_z3403309356797280102nteger)) (= (@ (@ tptp.dvd_dvd_Code_integer (@ _let_1 M2)) (@ _let_1 N)) (or (@ (@ tptp.dvd_dvd_Code_integer X) tptp.one_one_Code_integer) (@ (@ tptp.ord_less_eq_nat M2) N)))))) (forall ((X tptp.nat) (M2 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 M2)) (@ _let_1 N)) (or (@ (@ tptp.dvd_dvd_nat X) tptp.one_one_nat) (@ (@ tptp.ord_less_eq_nat M2) N)))))) (forall ((X tptp.int) (M2 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 M2)) (@ _let_1 N)) (or (@ (@ tptp.dvd_dvd_int X) tptp.one_one_int) (@ (@ tptp.ord_less_eq_nat M2) N)))))) (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)))) (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)))) (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)))) (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)))) (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)))) (forall ((B5 tptp.set_real) (A4 tptp.set_real) (B tptp.real) (F2 (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.groups8097168146408367636l_real F2))) (=> (@ tptp.finite_finite_real B5) (=> (@ (@ tptp.ord_less_eq_set_real A4) B5) (=> (@ (@ tptp.member_real B) (@ (@ tptp.minus_minus_set_real B5) A4)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F2 B)) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) B5) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F2 X3)))) (@ (@ tptp.ord_less_real (@ _let_1 A4)) (@ _let_1 B5))))))))) (forall ((B5 tptp.set_int) (A4 tptp.set_int) (B tptp.int) (F2 (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups8778361861064173332t_real F2))) (=> (@ tptp.finite_finite_int B5) (=> (@ (@ tptp.ord_less_eq_set_int A4) B5) (=> (@ (@ tptp.member_int B) (@ (@ tptp.minus_minus_set_int B5) A4)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F2 B)) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) B5) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F2 X3)))) (@ (@ tptp.ord_less_real (@ _let_1 A4)) (@ _let_1 B5))))))))) (forall ((B5 tptp.set_complex) (A4 tptp.set_complex) (B tptp.complex) (F2 (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups5808333547571424918x_real F2))) (=> (@ tptp.finite3207457112153483333omplex B5) (=> (@ (@ tptp.ord_le211207098394363844omplex A4) B5) (=> (@ (@ tptp.member_complex B) (@ (@ tptp.minus_811609699411566653omplex B5) A4)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F2 B)) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) B5) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F2 X3)))) (@ (@ tptp.ord_less_real (@ _let_1 A4)) (@ _let_1 B5))))))))) (forall ((B5 tptp.set_real) (A4 tptp.set_real) (B tptp.real) (F2 (-> tptp.real tptp.rat))) (let ((_let_1 (@ tptp.groups1300246762558778688al_rat F2))) (=> (@ tptp.finite_finite_real B5) (=> (@ (@ tptp.ord_less_eq_set_real A4) B5) (=> (@ (@ tptp.member_real B) (@ (@ tptp.minus_minus_set_real B5) A4)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ F2 B)) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) B5) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F2 X3)))) (@ (@ tptp.ord_less_rat (@ _let_1 A4)) (@ _let_1 B5))))))))) (forall ((B5 tptp.set_int) (A4 tptp.set_int) (B tptp.int) (F2 (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups3906332499630173760nt_rat F2))) (=> (@ tptp.finite_finite_int B5) (=> (@ (@ tptp.ord_less_eq_set_int A4) B5) (=> (@ (@ tptp.member_int B) (@ (@ tptp.minus_minus_set_int B5) A4)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ F2 B)) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) B5) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F2 X3)))) (@ (@ tptp.ord_less_rat (@ _let_1 A4)) (@ _let_1 B5))))))))) (forall ((B5 tptp.set_complex) (A4 tptp.set_complex) (B tptp.complex) (F2 (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups5058264527183730370ex_rat F2))) (=> (@ tptp.finite3207457112153483333omplex B5) (=> (@ (@ tptp.ord_le211207098394363844omplex A4) B5) (=> (@ (@ tptp.member_complex B) (@ (@ tptp.minus_811609699411566653omplex B5) A4)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ F2 B)) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) B5) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F2 X3)))) (@ (@ tptp.ord_less_rat (@ _let_1 A4)) (@ _let_1 B5))))))))) (forall ((B5 tptp.set_real) (A4 tptp.set_real) (B tptp.real) (F2 (-> tptp.real tptp.nat))) (let ((_let_1 (@ tptp.groups1935376822645274424al_nat F2))) (=> (@ tptp.finite_finite_real B5) (=> (@ (@ tptp.ord_less_eq_set_real A4) B5) (=> (@ (@ tptp.member_real B) (@ (@ tptp.minus_minus_set_real B5) A4)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F2 B)) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) B5) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F2 X3)))) (@ (@ tptp.ord_less_nat (@ _let_1 A4)) (@ _let_1 B5))))))))) (forall ((B5 tptp.set_int) (A4 tptp.set_int) (B tptp.int) (F2 (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups4541462559716669496nt_nat F2))) (=> (@ tptp.finite_finite_int B5) (=> (@ (@ tptp.ord_less_eq_set_int A4) B5) (=> (@ (@ tptp.member_int B) (@ (@ tptp.minus_minus_set_int B5) A4)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F2 B)) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) B5) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F2 X3)))) (@ (@ tptp.ord_less_nat (@ _let_1 A4)) (@ _let_1 B5))))))))) (forall ((B5 tptp.set_complex) (A4 tptp.set_complex) (B tptp.complex) (F2 (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups5693394587270226106ex_nat F2))) (=> (@ tptp.finite3207457112153483333omplex B5) (=> (@ (@ tptp.ord_le211207098394363844omplex A4) B5) (=> (@ (@ tptp.member_complex B) (@ (@ tptp.minus_811609699411566653omplex B5) A4)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F2 B)) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) B5) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F2 X3)))) (@ (@ tptp.ord_less_nat (@ _let_1 A4)) (@ _let_1 B5))))))))) (forall ((B5 tptp.set_real) (A4 tptp.set_real) (B tptp.real) (F2 (-> tptp.real tptp.int))) (let ((_let_1 (@ tptp.groups1932886352136224148al_int F2))) (=> (@ tptp.finite_finite_real B5) (=> (@ (@ tptp.ord_less_eq_set_real A4) B5) (=> (@ (@ tptp.member_real B) (@ (@ tptp.minus_minus_set_real B5) A4)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ F2 B)) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) B5) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F2 X3)))) (@ (@ tptp.ord_less_int (@ _let_1 A4)) (@ _let_1 B5))))))))) (forall ((I2 tptp.complex) (A4 tptp.set_complex) (F2 (-> tptp.complex tptp.real))) (=> (@ (@ tptp.member_complex I2) A4) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ (@ tptp.minus_811609699411566653omplex A4) (@ (@ tptp.insert_complex I2) tptp.bot_bot_set_complex))) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F2 X3)))) (=> (@ tptp.finite3207457112153483333omplex A4) (@ (@ tptp.ord_less_eq_real (@ F2 I2)) (@ (@ tptp.groups5808333547571424918x_real F2) A4)))))) (forall ((I2 tptp.int) (A4 tptp.set_int) (F2 (-> tptp.int tptp.real))) (=> (@ (@ tptp.member_int I2) A4) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.minus_minus_set_int A4) (@ (@ tptp.insert_int I2) tptp.bot_bot_set_int))) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F2 X3)))) (=> (@ tptp.finite_finite_int A4) (@ (@ tptp.ord_less_eq_real (@ F2 I2)) (@ (@ tptp.groups8778361861064173332t_real F2) A4)))))) (forall ((I2 tptp.real) (A4 tptp.set_real) (F2 (-> tptp.real tptp.real))) (=> (@ (@ tptp.member_real I2) A4) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) (@ (@ tptp.minus_minus_set_real A4) (@ (@ tptp.insert_real I2) tptp.bot_bot_set_real))) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F2 X3)))) (=> (@ tptp.finite_finite_real A4) (@ (@ tptp.ord_less_eq_real (@ F2 I2)) (@ (@ tptp.groups8097168146408367636l_real F2) A4)))))) (forall ((I2 tptp.complex) (A4 tptp.set_complex) (F2 (-> tptp.complex tptp.rat))) (=> (@ (@ tptp.member_complex I2) A4) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ (@ tptp.minus_811609699411566653omplex A4) (@ (@ tptp.insert_complex I2) tptp.bot_bot_set_complex))) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F2 X3)))) (=> (@ tptp.finite3207457112153483333omplex A4) (@ (@ tptp.ord_less_eq_rat (@ F2 I2)) (@ (@ tptp.groups5058264527183730370ex_rat F2) A4)))))) (forall ((I2 tptp.int) (A4 tptp.set_int) (F2 (-> tptp.int tptp.rat))) (=> (@ (@ tptp.member_int I2) A4) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.minus_minus_set_int A4) (@ (@ tptp.insert_int I2) tptp.bot_bot_set_int))) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F2 X3)))) (=> (@ tptp.finite_finite_int A4) (@ (@ tptp.ord_less_eq_rat (@ F2 I2)) (@ (@ tptp.groups3906332499630173760nt_rat F2) A4)))))) (forall ((I2 tptp.real) (A4 tptp.set_real) (F2 (-> tptp.real tptp.rat))) (=> (@ (@ tptp.member_real I2) A4) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) (@ (@ tptp.minus_minus_set_real A4) (@ (@ tptp.insert_real I2) tptp.bot_bot_set_real))) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F2 X3)))) (=> (@ tptp.finite_finite_real A4) (@ (@ tptp.ord_less_eq_rat (@ F2 I2)) (@ (@ tptp.groups1300246762558778688al_rat F2) A4)))))) (forall ((I2 tptp.nat) (A4 tptp.set_nat) (F2 (-> tptp.nat tptp.rat))) (=> (@ (@ tptp.member_nat I2) A4) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ (@ tptp.minus_minus_set_nat A4) (@ (@ tptp.insert_nat I2) tptp.bot_bot_set_nat))) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F2 X3)))) (=> (@ tptp.finite_finite_nat A4) (@ (@ tptp.ord_less_eq_rat (@ F2 I2)) (@ (@ tptp.groups2906978787729119204at_rat F2) A4)))))) (forall ((I2 tptp.complex) (A4 tptp.set_complex) (F2 (-> tptp.complex tptp.nat))) (=> (@ (@ tptp.member_complex I2) A4) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ (@ tptp.minus_811609699411566653omplex A4) (@ (@ tptp.insert_complex I2) tptp.bot_bot_set_complex))) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F2 X3)))) (=> (@ tptp.finite3207457112153483333omplex A4) (@ (@ tptp.ord_less_eq_nat (@ F2 I2)) (@ (@ tptp.groups5693394587270226106ex_nat F2) A4)))))) (forall ((I2 tptp.int) (A4 tptp.set_int) (F2 (-> tptp.int tptp.nat))) (=> (@ (@ tptp.member_int I2) A4) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.minus_minus_set_int A4) (@ (@ tptp.insert_int I2) tptp.bot_bot_set_int))) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F2 X3)))) (=> (@ tptp.finite_finite_int A4) (@ (@ tptp.ord_less_eq_nat (@ F2 I2)) (@ (@ tptp.groups4541462559716669496nt_nat F2) A4)))))) (forall ((I2 tptp.real) (A4 tptp.set_real) (F2 (-> tptp.real tptp.nat))) (=> (@ (@ tptp.member_real I2) A4) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) (@ (@ tptp.minus_minus_set_real A4) (@ (@ tptp.insert_real I2) tptp.bot_bot_set_real))) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F2 X3)))) (=> (@ tptp.finite_finite_real A4) (@ (@ tptp.ord_less_eq_nat (@ F2 I2)) (@ (@ tptp.groups1935376822645274424al_nat F2) A4)))))) (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_nat _let_1))) (=> (= (@ (@ tptp.divide_divide_nat X) _let_1) (@ (@ tptp.divide_divide_nat Y) _let_1)) (=> (= (@ _let_2 X) (@ _let_2 Y)) (= X Y)))))) (forall ((A4 tptp.set_real) (F2 (-> tptp.real tptp.rat)) (K5 tptp.rat)) (let ((_let_1 (@ tptp.finite_card_real A4))) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) A4) (@ (@ tptp.ord_less_rat (@ F2 I3)) K5))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) _let_1) (@ (@ tptp.ord_less_rat (@ (@ tptp.groups1300246762558778688al_rat F2) A4)) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat _let_1)) K5)))))) (forall ((A4 tptp.set_nat) (F2 (-> tptp.nat tptp.rat)) (K5 tptp.rat)) (let ((_let_1 (@ tptp.finite_card_nat A4))) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.member_nat I3) A4) (@ (@ tptp.ord_less_rat (@ F2 I3)) K5))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) _let_1) (@ (@ tptp.ord_less_rat (@ (@ tptp.groups2906978787729119204at_rat F2) A4)) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat _let_1)) K5)))))) (forall ((A4 tptp.set_complex) (F2 (-> tptp.complex tptp.rat)) (K5 tptp.rat)) (let ((_let_1 (@ tptp.finite_card_complex A4))) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) A4) (@ (@ tptp.ord_less_rat (@ F2 I3)) K5))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) _let_1) (@ (@ tptp.ord_less_rat (@ (@ tptp.groups5058264527183730370ex_rat F2) A4)) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat _let_1)) K5)))))) (forall ((A4 tptp.set_int) (F2 (-> tptp.int tptp.rat)) (K5 tptp.rat)) (let ((_let_1 (@ tptp.finite_card_int A4))) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) A4) (@ (@ tptp.ord_less_rat (@ F2 I3)) K5))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) _let_1) (@ (@ tptp.ord_less_rat (@ (@ tptp.groups3906332499630173760nt_rat F2) A4)) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat _let_1)) K5)))))) (forall ((A4 tptp.set_real) (F2 (-> tptp.real tptp.real)) (K5 tptp.real)) (let ((_let_1 (@ tptp.finite_card_real A4))) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) A4) (@ (@ tptp.ord_less_real (@ F2 I3)) K5))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) _let_1) (@ (@ tptp.ord_less_real (@ (@ tptp.groups8097168146408367636l_real F2) A4)) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real _let_1)) K5)))))) (forall ((A4 tptp.set_complex) (F2 (-> tptp.complex tptp.real)) (K5 tptp.real)) (let ((_let_1 (@ tptp.finite_card_complex A4))) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) A4) (@ (@ tptp.ord_less_real (@ F2 I3)) K5))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) _let_1) (@ (@ tptp.ord_less_real (@ (@ tptp.groups5808333547571424918x_real F2) A4)) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real _let_1)) K5)))))) (forall ((A4 tptp.set_int) (F2 (-> tptp.int tptp.real)) (K5 tptp.real)) (let ((_let_1 (@ tptp.finite_card_int A4))) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) A4) (@ (@ tptp.ord_less_real (@ F2 I3)) K5))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) _let_1) (@ (@ tptp.ord_less_real (@ (@ tptp.groups8778361861064173332t_real F2) A4)) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real _let_1)) K5)))))) (forall ((A4 tptp.set_real) (F2 (-> tptp.real tptp.int)) (K5 tptp.int)) (let ((_let_1 (@ tptp.finite_card_real A4))) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) A4) (@ (@ tptp.ord_less_int (@ F2 I3)) K5))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) _let_1) (@ (@ tptp.ord_less_int (@ (@ tptp.groups1932886352136224148al_int F2) A4)) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int _let_1)) K5)))))) (forall ((A4 tptp.set_nat) (F2 (-> tptp.nat tptp.int)) (K5 tptp.int)) (let ((_let_1 (@ tptp.finite_card_nat A4))) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.member_nat I3) A4) (@ (@ tptp.ord_less_int (@ F2 I3)) K5))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) _let_1) (@ (@ tptp.ord_less_int (@ (@ tptp.groups3539618377306564664at_int F2) A4)) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int _let_1)) K5)))))) (forall ((A4 tptp.set_complex) (F2 (-> tptp.complex tptp.int)) (K5 tptp.int)) (let ((_let_1 (@ tptp.finite_card_complex A4))) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) A4) (@ (@ tptp.ord_less_int (@ F2 I3)) K5))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) _let_1) (@ (@ tptp.ord_less_int (@ (@ tptp.groups5690904116761175830ex_int F2) A4)) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int _let_1)) K5)))))) (forall ((A4 tptp.set_complex) (F2 (-> tptp.complex tptp.real)) (K5 tptp.real)) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) A4) (@ (@ tptp.ord_less_eq_real (@ F2 I3)) (@ (@ tptp.divide_divide_real K5) (@ tptp.semiri5074537144036343181t_real (@ tptp.finite_card_complex A4)))))) (=> (@ tptp.finite3207457112153483333omplex A4) (=> (not (= A4 tptp.bot_bot_set_complex)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups5808333547571424918x_real F2) A4)) K5))))) (forall ((A4 tptp.set_int) (F2 (-> tptp.int tptp.real)) (K5 tptp.real)) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) A4) (@ (@ tptp.ord_less_eq_real (@ F2 I3)) (@ (@ tptp.divide_divide_real K5) (@ tptp.semiri5074537144036343181t_real (@ tptp.finite_card_int A4)))))) (=> (@ tptp.finite_finite_int A4) (=> (not (= A4 tptp.bot_bot_set_int)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups8778361861064173332t_real F2) A4)) K5))))) (forall ((A4 tptp.set_real) (F2 (-> tptp.real tptp.real)) (K5 tptp.real)) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) A4) (@ (@ tptp.ord_less_eq_real (@ F2 I3)) (@ (@ tptp.divide_divide_real K5) (@ tptp.semiri5074537144036343181t_real (@ tptp.finite_card_real A4)))))) (=> (@ tptp.finite_finite_real A4) (=> (not (= A4 tptp.bot_bot_set_real)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups8097168146408367636l_real F2) A4)) K5))))) (forall ((A4 tptp.set_complex) (F2 (-> tptp.complex tptp.rat)) (K5 tptp.rat)) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) A4) (@ (@ tptp.ord_less_eq_rat (@ F2 I3)) (@ (@ tptp.divide_divide_rat K5) (@ tptp.semiri681578069525770553at_rat (@ tptp.finite_card_complex A4)))))) (=> (@ tptp.finite3207457112153483333omplex A4) (=> (not (= A4 tptp.bot_bot_set_complex)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups5058264527183730370ex_rat F2) A4)) K5))))) (forall ((A4 tptp.set_nat) (F2 (-> tptp.nat tptp.rat)) (K5 tptp.rat)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.member_nat I3) A4) (@ (@ tptp.ord_less_eq_rat (@ F2 I3)) (@ (@ tptp.divide_divide_rat K5) (@ tptp.semiri681578069525770553at_rat (@ tptp.finite_card_nat A4)))))) (=> (@ tptp.finite_finite_nat A4) (=> (not (= A4 tptp.bot_bot_set_nat)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups2906978787729119204at_rat F2) A4)) K5))))) (forall ((A4 tptp.set_int) (F2 (-> tptp.int tptp.rat)) (K5 tptp.rat)) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) A4) (@ (@ tptp.ord_less_eq_rat (@ F2 I3)) (@ (@ tptp.divide_divide_rat K5) (@ tptp.semiri681578069525770553at_rat (@ tptp.finite_card_int A4)))))) (=> (@ tptp.finite_finite_int A4) (=> (not (= A4 tptp.bot_bot_set_int)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups3906332499630173760nt_rat F2) A4)) K5))))) (forall ((A4 tptp.set_real) (F2 (-> tptp.real tptp.rat)) (K5 tptp.rat)) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) A4) (@ (@ tptp.ord_less_eq_rat (@ F2 I3)) (@ (@ tptp.divide_divide_rat K5) (@ tptp.semiri681578069525770553at_rat (@ tptp.finite_card_real A4)))))) (=> (@ tptp.finite_finite_real A4) (=> (not (= A4 tptp.bot_bot_set_real)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups1300246762558778688al_rat F2) A4)) K5))))) (forall ((A4 tptp.set_nat) (F2 (-> tptp.nat tptp.real)) (K5 tptp.real)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.member_nat I3) A4) (@ (@ tptp.ord_less_eq_real (@ F2 I3)) (@ (@ tptp.divide_divide_real K5) (@ tptp.semiri5074537144036343181t_real (@ tptp.finite_card_nat A4)))))) (=> (@ tptp.finite_finite_nat A4) (=> (not (= A4 tptp.bot_bot_set_nat)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups6591440286371151544t_real F2) A4)) K5))))) (forall ((A4 tptp.set_list_nat) (F2 (-> tptp.list_nat tptp.real)) (K5 tptp.real)) (=> (forall ((I3 tptp.list_nat)) (=> (@ (@ tptp.member_list_nat I3) A4) (@ (@ tptp.ord_less_eq_real (@ F2 I3)) (@ (@ tptp.divide_divide_real K5) (@ tptp.semiri5074537144036343181t_real (@ tptp.finite_card_list_nat A4)))))) (=> (@ tptp.finite8100373058378681591st_nat A4) (=> (not (= A4 tptp.bot_bot_set_list_nat)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups8399112307953289288t_real F2) A4)) K5))))) (forall ((A4 tptp.set_set_nat) (F2 (-> tptp.set_nat tptp.real)) (K5 tptp.real)) (=> (forall ((I3 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat I3) A4) (@ (@ tptp.ord_less_eq_real (@ F2 I3)) (@ (@ tptp.divide_divide_real K5) (@ tptp.semiri5074537144036343181t_real (@ tptp.finite_card_set_nat A4)))))) (=> (@ tptp.finite1152437895449049373et_nat A4) (=> (not (= A4 tptp.bot_bot_set_set_nat)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups5107569545109728110t_real F2) A4)) K5))))) (forall ((A tptp.code_integer) (N tptp.nat)) (= (@ (@ tptp.comm_s8582702949713902594nteger A) (@ tptp.suc N)) (@ (@ tptp.times_3573771949741848930nteger A) (@ (@ tptp.comm_s8582702949713902594nteger (@ (@ tptp.plus_p5714425477246183910nteger A) tptp.one_one_Code_integer)) N)))) (forall ((A tptp.complex) (N tptp.nat)) (= (@ (@ tptp.comm_s2602460028002588243omplex A) (@ tptp.suc N)) (@ (@ tptp.times_times_complex A) (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.plus_plus_complex A) tptp.one_one_complex)) N)))) (forall ((A tptp.real) (N tptp.nat)) (= (@ (@ tptp.comm_s7457072308508201937r_real A) (@ tptp.suc N)) (@ (@ tptp.times_times_real A) (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.plus_plus_real A) tptp.one_one_real)) N)))) (forall ((A tptp.rat) (N tptp.nat)) (= (@ (@ tptp.comm_s4028243227959126397er_rat A) (@ tptp.suc N)) (@ (@ tptp.times_times_rat A) (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.plus_plus_rat A) tptp.one_one_rat)) N)))) (forall ((A tptp.nat) (N tptp.nat)) (= (@ (@ tptp.comm_s4663373288045622133er_nat A) (@ tptp.suc N)) (@ (@ tptp.times_times_nat A) (@ (@ tptp.comm_s4663373288045622133er_nat (@ (@ tptp.plus_plus_nat A) tptp.one_one_nat)) N)))) (forall ((A tptp.int) (N tptp.nat)) (= (@ (@ tptp.comm_s4660882817536571857er_int A) (@ tptp.suc N)) (@ (@ tptp.times_times_int A) (@ (@ tptp.comm_s4660882817536571857er_int (@ (@ tptp.plus_plus_int A) tptp.one_one_int)) N)))) (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M2) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat M2) N)) M2) (= N tptp.one_one_nat)))) (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M2) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat N) M2)) M2) (= N tptp.one_one_nat)))) (forall ((Z3 tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.comm_s4028243227959126397er_rat Z3))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat Z3) (@ tptp.semiri681578069525770553at_rat N))) (@ _let_1 N))))) (forall ((Z3 tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.comm_s7457072308508201937r_real Z3))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real Z3) (@ tptp.semiri5074537144036343181t_real N))) (@ _let_1 N))))) (forall ((Z3 tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.comm_s4660882817536571857er_int Z3))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int Z3) (@ tptp.semiri1314217659103216013at_int N))) (@ _let_1 N))))) (forall ((Z3 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.comm_s4663373288045622133er_nat Z3))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat Z3) (@ tptp.semiri1316708129612266289at_nat N))) (@ _let_1 N))))) (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.comm_s4028243227959126397er_rat A))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_rat (@ _let_1 N)) (@ (@ tptp.plus_plus_rat A) (@ tptp.semiri681578069525770553at_rat N)))))) (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.comm_s7457072308508201937r_real A))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_real (@ _let_1 N)) (@ (@ tptp.plus_plus_real A) (@ tptp.semiri5074537144036343181t_real N)))))) (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.comm_s4660882817536571857er_int A))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_int (@ _let_1 N)) (@ (@ tptp.plus_plus_int A) (@ tptp.semiri1314217659103216013at_int N)))))) (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.comm_s4663373288045622133er_nat A))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_nat (@ _let_1 N)) (@ (@ tptp.plus_plus_nat A) (@ tptp.semiri1316708129612266289at_nat N)))))) (forall ((Q2 tptp.nat) (N tptp.nat) (R3 tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat R3) M2))) (let ((_let_2 (@ tptp.dvd_dvd_nat M2))) (let ((_let_3 (@ tptp.ord_less_eq_nat Q2))) (=> (@ _let_3 N) (=> (@ _let_3 _let_1) (= (@ _let_2 (@ (@ tptp.minus_minus_nat N) Q2)) (@ _let_2 (@ (@ tptp.plus_plus_nat N) (@ (@ tptp.minus_minus_nat _let_1) Q2)))))))))) (forall ((I2 tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat I2))) (=> (@ (@ tptp.dvd_dvd_nat (@ _let_1 M2)) (@ _let_1 N)) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) I2) (@ (@ tptp.ord_less_eq_nat M2) N))))) (forall ((Z3 tptp.rat) (N tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.comm_s4028243227959126397er_rat Z3))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N) M2)) (@ (@ tptp.times_times_rat (@ _let_1 N)) (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.plus_plus_rat Z3) (@ tptp.semiri681578069525770553at_rat N))) M2))))) (forall ((Z3 tptp.real) (N tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.comm_s7457072308508201937r_real Z3))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N) M2)) (@ (@ tptp.times_times_real (@ _let_1 N)) (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.plus_plus_real Z3) (@ tptp.semiri5074537144036343181t_real N))) M2))))) (forall ((Z3 tptp.int) (N tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.comm_s4660882817536571857er_int Z3))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N) M2)) (@ (@ tptp.times_times_int (@ _let_1 N)) (@ (@ tptp.comm_s4660882817536571857er_int (@ (@ tptp.plus_plus_int Z3) (@ tptp.semiri1314217659103216013at_int N))) M2))))) (forall ((Z3 tptp.nat) (N tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.comm_s4663373288045622133er_nat Z3))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N) M2)) (@ (@ tptp.times_times_nat (@ _let_1 N)) (@ (@ tptp.comm_s4663373288045622133er_nat (@ (@ tptp.plus_plus_nat Z3) (@ tptp.semiri1316708129612266289at_nat N))) M2))))) (forall ((R3 tptp.nat) (N tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat R3) N) (=> (@ (@ tptp.ord_less_eq_nat R3) M2) (=> (@ (@ tptp.dvd_dvd_nat N) (@ (@ tptp.minus_minus_nat M2) R3)) (= (@ (@ tptp.modulo_modulo_nat M2) N) R3))))) (forall ((M2 tptp.nat) (N tptp.nat) (G2 (-> tptp.nat tptp.rat))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M2) N))) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.groups2906978787729119204at_rat G2) _let_1)) (@ G2 (@ tptp.suc N))) (@ (@ tptp.plus_plus_rat (@ G2 M2)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I tptp.nat)) (@ G2 (@ tptp.suc I)))) _let_1)))))) (forall ((M2 tptp.nat) (N tptp.nat) (G2 (-> tptp.nat tptp.int))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M2) N))) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.groups3539618377306564664at_int G2) _let_1)) (@ G2 (@ tptp.suc N))) (@ (@ tptp.plus_plus_int (@ G2 M2)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I tptp.nat)) (@ G2 (@ tptp.suc I)))) _let_1)))))) (forall ((M2 tptp.nat) (N tptp.nat) (G2 (-> tptp.nat tptp.nat))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M2) N))) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.groups3542108847815614940at_nat G2) _let_1)) (@ G2 (@ tptp.suc N))) (@ (@ tptp.plus_plus_nat (@ G2 M2)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I tptp.nat)) (@ G2 (@ tptp.suc I)))) _let_1)))))) (forall ((M2 tptp.nat) (N tptp.nat) (G2 (-> tptp.nat tptp.real))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M2) N))) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real G2) _let_1)) (@ G2 (@ tptp.suc N))) (@ (@ tptp.plus_plus_real (@ G2 M2)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I tptp.nat)) (@ G2 (@ tptp.suc I)))) _let_1)))))) (forall ((M2 tptp.nat) (N tptp.nat) (F2 (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_nat M2) _let_1) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I tptp.nat)) (@ (@ tptp.minus_minus_rat (@ F2 (@ tptp.suc I))) (@ F2 I)))) (@ (@ tptp.set_or1269000886237332187st_nat M2) N)) (@ (@ tptp.minus_minus_rat (@ F2 _let_1)) (@ F2 M2)))))) (forall ((M2 tptp.nat) (N tptp.nat) (F2 (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_nat M2) _let_1) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((I tptp.nat)) (@ (@ tptp.minus_minus_int (@ F2 (@ tptp.suc I))) (@ F2 I)))) (@ (@ tptp.set_or1269000886237332187st_nat M2) N)) (@ (@ tptp.minus_minus_int (@ F2 _let_1)) (@ F2 M2)))))) (forall ((M2 tptp.nat) (N tptp.nat) (F2 (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_nat M2) _let_1) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I tptp.nat)) (@ (@ tptp.minus_minus_real (@ F2 (@ tptp.suc I))) (@ F2 I)))) (@ (@ tptp.set_or1269000886237332187st_nat M2) N)) (@ (@ tptp.minus_minus_real (@ F2 _let_1)) (@ F2 M2)))))) (forall ((S3 tptp.set_real) (F2 (-> tptp.real tptp.complex)) (K5 tptp.real)) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) S3) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ F2 X3))) K5))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.groups5754745047067104278omplex F2) S3))) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ tptp.finite_card_real S3))) K5)))) (forall ((S3 tptp.set_nat) (F2 (-> tptp.nat tptp.complex)) (K5 tptp.real)) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) S3) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ F2 X3))) K5))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.groups2073611262835488442omplex F2) S3))) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ tptp.finite_card_nat S3))) K5)))) (forall ((S3 tptp.set_complex) (F2 (-> tptp.complex tptp.complex)) (K5 tptp.real)) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) S3) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ F2 X3))) K5))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.groups7754918857620584856omplex F2) S3))) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ tptp.finite_card_complex S3))) K5)))) (forall ((S3 tptp.set_int) (F2 (-> tptp.int tptp.complex)) (K5 tptp.real)) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) S3) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ F2 X3))) K5))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.groups3049146728041665814omplex F2) S3))) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ tptp.finite_card_int S3))) K5)))) (forall ((S3 tptp.set_list_nat) (F2 (-> tptp.list_nat tptp.complex)) (K5 tptp.real)) (=> (forall ((X3 tptp.list_nat)) (=> (@ (@ tptp.member_list_nat X3) S3) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ F2 X3))) K5))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.groups6529277132148336714omplex F2) S3))) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ tptp.finite_card_list_nat S3))) K5)))) (forall ((S3 tptp.set_set_nat) (F2 (-> tptp.set_nat tptp.complex)) (K5 tptp.real)) (=> (forall ((X3 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat X3) S3) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ F2 X3))) K5))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.groups8255218700646806128omplex F2) S3))) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ tptp.finite_card_set_nat S3))) K5)))) (forall ((S3 tptp.set_nat) (F2 (-> tptp.nat tptp.real)) (K5 tptp.real)) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) S3) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ F2 X3))) K5))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.groups6591440286371151544t_real F2) S3))) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ tptp.finite_card_nat S3))) K5)))) (forall ((M2 tptp.nat) (N tptp.nat) (G2 (-> tptp.nat tptp.rat)) (P tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N))) (let ((_let_2 (@ _let_1 P))) (let ((_let_3 (@ _let_1 tptp.one_one_nat))) (let ((_let_4 (@ tptp.groups2906978787729119204at_rat G2))) (let ((_let_5 (@ tptp.set_or1269000886237332187st_nat M2))) (=> (@ (@ tptp.ord_less_eq_nat M2) _let_3) (= (@ _let_4 (@ _let_5 _let_2)) (@ (@ tptp.plus_plus_rat (@ _let_4 (@ _let_5 N))) (@ _let_4 (@ (@ tptp.set_or1269000886237332187st_nat _let_3) _let_2))))))))))) (forall ((M2 tptp.nat) (N tptp.nat) (G2 (-> tptp.nat tptp.int)) (P tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N))) (let ((_let_2 (@ _let_1 P))) (let ((_let_3 (@ _let_1 tptp.one_one_nat))) (let ((_let_4 (@ tptp.groups3539618377306564664at_int G2))) (let ((_let_5 (@ tptp.set_or1269000886237332187st_nat M2))) (=> (@ (@ tptp.ord_less_eq_nat M2) _let_3) (= (@ _let_4 (@ _let_5 _let_2)) (@ (@ tptp.plus_plus_int (@ _let_4 (@ _let_5 N))) (@ _let_4 (@ (@ tptp.set_or1269000886237332187st_nat _let_3) _let_2))))))))))) (forall ((M2 tptp.nat) (N tptp.nat) (G2 (-> tptp.nat tptp.nat)) (P tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N))) (let ((_let_2 (@ _let_1 P))) (let ((_let_3 (@ _let_1 tptp.one_one_nat))) (let ((_let_4 (@ tptp.groups3542108847815614940at_nat G2))) (let ((_let_5 (@ tptp.set_or1269000886237332187st_nat M2))) (=> (@ (@ tptp.ord_less_eq_nat M2) _let_3) (= (@ _let_4 (@ _let_5 _let_2)) (@ (@ tptp.plus_plus_nat (@ _let_4 (@ _let_5 N))) (@ _let_4 (@ (@ tptp.set_or1269000886237332187st_nat _let_3) _let_2))))))))))) (forall ((M2 tptp.nat) (N tptp.nat) (G2 (-> tptp.nat tptp.real)) (P tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N))) (let ((_let_2 (@ _let_1 P))) (let ((_let_3 (@ _let_1 tptp.one_one_nat))) (let ((_let_4 (@ tptp.groups6591440286371151544t_real G2))) (let ((_let_5 (@ tptp.set_or1269000886237332187st_nat M2))) (=> (@ (@ tptp.ord_less_eq_nat M2) _let_3) (= (@ _let_4 (@ _let_5 _let_2)) (@ (@ tptp.plus_plus_real (@ _let_4 (@ _let_5 N))) (@ _let_4 (@ (@ tptp.set_or1269000886237332187st_nat _let_3) _let_2))))))))))) (forall ((A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.dvd_dvd_nat _let_1) A) (= (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.divide_divide_nat A) _let_1)) A)))) (forall ((A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.dvd_dvd_int _let_1) A) (= (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.divide_divide_int A) _let_1)) A)))) (forall ((A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.dvd_dvd_nat _let_1) A) (= (@ (@ tptp.modulo_modulo_nat A) _let_1) tptp.zero_zero_nat)))) (forall ((A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.dvd_dvd_int _let_1) A) (= (@ (@ tptp.modulo_modulo_int A) _let_1) tptp.zero_zero_int)))) (forall ((A tptp.code_natural)) (let ((_let_1 (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.dvd_dvd_Code_natural _let_1) A) (= (@ (@ tptp.modulo8411746178871703098atural A) _let_1) tptp.zero_z2226904508553997617atural)))) (forall ((N tptp.nat) (A tptp.real) (B tptp.real)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (=> (@ (@ tptp.ord_less_eq_real A) B) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real A) N)) (@ (@ tptp.power_power_real B) N))))) (forall ((N tptp.nat) (A tptp.rat) (B tptp.rat)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat A) N)) (@ (@ tptp.power_power_rat B) N))))) (forall ((N tptp.nat) (A tptp.int) (B tptp.int)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (=> (@ (@ tptp.ord_less_eq_int A) B) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A) N)) (@ (@ tptp.power_power_int B) N))))) (forall ((N tptp.nat)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))) (forall ((K2 tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat K2))) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) K2) (= (@ (@ tptp.dvd_dvd_nat (@ _let_1 M2)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat M2) N))))) (forall ((M2 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se4205575877204974255it_nat M2) A)) (or (@ _let_1 A) (= M2 tptp.zero_zero_nat))))) (forall ((M2 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se4203085406695923979it_int M2) A)) (or (@ _let_1 A) (= M2 tptp.zero_zero_nat))))) _let_263 (forall ((M2 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se7882103937844011126it_nat M2) A)) (and (@ _let_1 A) (not (= M2 tptp.zero_zero_nat)))))) (forall ((M2 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se7879613467334960850it_int M2) A)) (and (@ _let_1 A) (not (= M2 tptp.zero_zero_nat)))))) (forall ((M2 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se2161824704523386999it_nat M2) A)) (not (= (@ _let_1 A) (= M2 tptp.zero_zero_nat)))))) (forall ((M2 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se2159334234014336723it_int M2) A)) (not (= (@ _let_1 A) (= M2 tptp.zero_zero_nat)))))) (forall ((M2 tptp.nat) (N tptp.nat) (Z3 tptp.rat)) (let ((_let_1 (@ tptp.comm_s4028243227959126397er_rat Z3))) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ _let_1 N) (@ (@ tptp.times_times_rat (@ _let_1 M2)) (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.plus_plus_rat Z3) (@ tptp.semiri681578069525770553at_rat M2))) (@ (@ tptp.minus_minus_nat N) M2))))))) (forall ((M2 tptp.nat) (N tptp.nat) (Z3 tptp.real)) (let ((_let_1 (@ tptp.comm_s7457072308508201937r_real Z3))) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ _let_1 N) (@ (@ tptp.times_times_real (@ _let_1 M2)) (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.plus_plus_real Z3) (@ tptp.semiri5074537144036343181t_real M2))) (@ (@ tptp.minus_minus_nat N) M2))))))) (forall ((M2 tptp.nat) (N tptp.nat) (Z3 tptp.int)) (let ((_let_1 (@ tptp.comm_s4660882817536571857er_int Z3))) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ _let_1 N) (@ (@ tptp.times_times_int (@ _let_1 M2)) (@ (@ tptp.comm_s4660882817536571857er_int (@ (@ tptp.plus_plus_int Z3) (@ tptp.semiri1314217659103216013at_int M2))) (@ (@ tptp.minus_minus_nat N) M2))))))) (forall ((M2 tptp.nat) (N tptp.nat) (Z3 tptp.nat)) (let ((_let_1 (@ tptp.comm_s4663373288045622133er_nat Z3))) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ _let_1 N) (@ (@ tptp.times_times_nat (@ _let_1 M2)) (@ (@ tptp.comm_s4663373288045622133er_nat (@ (@ tptp.plus_plus_nat Z3) (@ tptp.semiri1316708129612266289at_nat M2))) (@ (@ tptp.minus_minus_nat N) M2))))))) (forall ((A tptp.code_integer)) (=> (not (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) A)) (not (forall ((B3 tptp.code_integer)) (not (= A (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) B3)) tptp.one_one_Code_integer))))))) (forall ((A tptp.nat)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) A)) (not (forall ((B3 tptp.nat)) (not (= A (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) B3)) tptp.one_one_nat))))))) (forall ((A tptp.int)) (=> (not (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) A)) (not (forall ((B3 tptp.int)) (not (= A (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) B3)) tptp.one_one_int))))))) (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.modulo364778990260209775nteger A) _let_1))) (let ((_let_3 (@ (@ tptp.dvd_dvd_Code_integer _let_1) A))) (and (=> _let_3 (= _let_2 tptp.zero_z3403309356797280102nteger)) (=> (not _let_3) (= _let_2 tptp.one_one_Code_integer))))))) (forall ((A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.modulo_modulo_nat A) _let_1))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat _let_1) A))) (and (=> _let_3 (= _let_2 tptp.zero_zero_nat)) (=> (not _let_3) (= _let_2 tptp.one_one_nat))))))) (forall ((A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.modulo_modulo_int A) _let_1))) (let ((_let_3 (@ (@ tptp.dvd_dvd_int _let_1) A))) (and (=> _let_3 (= _let_2 tptp.zero_zero_int)) (=> (not _let_3) (= _let_2 tptp.one_one_int))))))) (forall ((A tptp.code_natural)) (let ((_let_1 (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.modulo8411746178871703098atural A) _let_1))) (let ((_let_3 (@ (@ tptp.dvd_dvd_Code_natural _let_1) A))) (and (=> _let_3 (= _let_2 tptp.zero_z2226904508553997617atural)) (=> (not _let_3) (= _let_2 tptp.one_one_Code_natural))))))) (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.modulo364778990260209775nteger A) _let_1))) (let ((_let_3 (@ (@ tptp.dvd_dvd_Code_integer _let_1) A))) (=> (=> _let_3 (not (= _let_2 tptp.zero_z3403309356797280102nteger))) (not (=> (not _let_3) (not (= _let_2 tptp.one_one_Code_integer))))))))) (forall ((A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.modulo_modulo_nat A) _let_1))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat _let_1) A))) (=> (=> _let_3 (not (= _let_2 tptp.zero_zero_nat))) (not (=> (not _let_3) (not (= _let_2 tptp.one_one_nat))))))))) (forall ((A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.modulo_modulo_int A) _let_1))) (let ((_let_3 (@ (@ tptp.dvd_dvd_int _let_1) A))) (=> (=> _let_3 (not (= _let_2 tptp.zero_zero_int))) (not (=> (not _let_3) (not (= _let_2 tptp.one_one_int))))))))) (forall ((A tptp.code_natural)) (let ((_let_1 (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.modulo8411746178871703098atural A) _let_1))) (let ((_let_3 (@ (@ tptp.dvd_dvd_Code_natural _let_1) A))) (=> (=> _let_3 (not (= _let_2 tptp.zero_z2226904508553997617atural))) (not (=> (not _let_3) (not (= _let_2 tptp.one_one_Code_natural))))))))) (forall ((N tptp.nat) (A tptp.real)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.power_power_real A) N)))) (forall ((N tptp.nat) (A tptp.rat)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.power_power_rat A) N)))) (forall ((N tptp.nat) (A tptp.int)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.power_power_int A) N)))) (forall ((N tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (= (@ _let_1 (@ (@ tptp.power_power_real A) N)) (@ _let_1 A))))) (forall ((N tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (= (@ _let_1 (@ (@ tptp.power_power_rat A) N)) (@ _let_1 A))))) (forall ((N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (= (@ _let_1 (@ (@ tptp.power_power_int A) N)) (@ _let_1 A))))) (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (let ((_let_2 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (= (@ _let_1 (@ (@ tptp.power_power_real A) N)) (or _let_2 (and (not _let_2) (@ _let_1 A))))))) (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (let ((_let_2 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (= (@ _let_1 (@ (@ tptp.power_power_rat A) N)) (or _let_2 (and (not _let_2) (@ _let_1 A))))))) (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_2 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (= (@ _let_1 (@ (@ tptp.power_power_int A) N)) (or _let_2 (and (not _let_2) (@ _let_1 A))))))) (forall ((M2 tptp.nat) (N tptp.nat) (F2 (-> tptp.nat tptp.complex))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M2) N))) (let ((_let_2 (@ (@ tptp.ord_less_eq_nat M2) N))) (and (=> _let_2 (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((K3 tptp.nat)) (@ (@ tptp.minus_minus_complex (@ F2 K3)) (@ F2 (@ (@ tptp.plus_plus_nat K3) tptp.one_one_nat))))) _let_1) (@ (@ tptp.minus_minus_complex (@ F2 M2)) (@ F2 (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat))))) (=> (not _let_2) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((K3 tptp.nat)) (@ (@ tptp.minus_minus_complex (@ F2 K3)) (@ F2 (@ (@ tptp.plus_plus_nat K3) tptp.one_one_nat))))) _let_1) tptp.zero_zero_complex)))))) (forall ((M2 tptp.nat) (N tptp.nat) (F2 (-> tptp.nat tptp.rat))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M2) N))) (let ((_let_2 (@ (@ tptp.ord_less_eq_nat M2) N))) (and (=> _let_2 (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ tptp.minus_minus_rat (@ F2 K3)) (@ F2 (@ (@ tptp.plus_plus_nat K3) tptp.one_one_nat))))) _let_1) (@ (@ tptp.minus_minus_rat (@ F2 M2)) (@ F2 (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat))))) (=> (not _let_2) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ tptp.minus_minus_rat (@ F2 K3)) (@ F2 (@ (@ tptp.plus_plus_nat K3) tptp.one_one_nat))))) _let_1) tptp.zero_zero_rat)))))) (forall ((M2 tptp.nat) (N tptp.nat) (F2 (-> tptp.nat tptp.int))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M2) N))) (let ((_let_2 (@ (@ tptp.ord_less_eq_nat M2) N))) (and (=> _let_2 (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((K3 tptp.nat)) (@ (@ tptp.minus_minus_int (@ F2 K3)) (@ F2 (@ (@ tptp.plus_plus_nat K3) tptp.one_one_nat))))) _let_1) (@ (@ tptp.minus_minus_int (@ F2 M2)) (@ F2 (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat))))) (=> (not _let_2) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((K3 tptp.nat)) (@ (@ tptp.minus_minus_int (@ F2 K3)) (@ F2 (@ (@ tptp.plus_plus_nat K3) tptp.one_one_nat))))) _let_1) tptp.zero_zero_int)))))) (forall ((M2 tptp.nat) (N tptp.nat) (F2 (-> tptp.nat tptp.real))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M2) N))) (let ((_let_2 (@ (@ tptp.ord_less_eq_nat M2) N))) (and (=> _let_2 (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.minus_minus_real (@ F2 K3)) (@ F2 (@ (@ tptp.plus_plus_nat K3) tptp.one_one_nat))))) _let_1) (@ (@ tptp.minus_minus_real (@ F2 M2)) (@ F2 (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat))))) (=> (not _let_2) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.minus_minus_real (@ F2 K3)) (@ F2 (@ (@ tptp.plus_plus_nat K3) tptp.one_one_nat))))) _let_1) tptp.zero_zero_real)))))) (forall ((M2 tptp.nat) (N tptp.nat) (F2 (-> tptp.nat tptp.rat))) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ tptp.minus_minus_rat (@ F2 K3)) (@ F2 (@ (@ tptp.minus_minus_nat K3) tptp.one_one_nat))))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M2)) N)) (@ (@ tptp.minus_minus_rat (@ F2 N)) (@ F2 M2))))) (forall ((M2 tptp.nat) (N tptp.nat) (F2 (-> tptp.nat tptp.int))) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((K3 tptp.nat)) (@ (@ tptp.minus_minus_int (@ F2 K3)) (@ F2 (@ (@ tptp.minus_minus_nat K3) tptp.one_one_nat))))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M2)) N)) (@ (@ tptp.minus_minus_int (@ F2 N)) (@ F2 M2))))) (forall ((M2 tptp.nat) (N tptp.nat) (F2 (-> tptp.nat tptp.real))) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.minus_minus_real (@ F2 K3)) (@ F2 (@ (@ tptp.minus_minus_nat K3) tptp.one_one_nat))))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M2)) N)) (@ (@ tptp.minus_minus_real (@ F2 N)) (@ F2 M2))))) (forall ((A4 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A4) (= (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.nat_set_encode A4)) (not (@ (@ tptp.member_nat tptp.zero_zero_nat) A4))))) (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (let ((_let_2 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (= (@ _let_1 (@ (@ tptp.power_power_real A) N)) (or (= N tptp.zero_zero_nat) (and _let_2 (not (= A tptp.zero_zero_real))) (and (not _let_2) (@ _let_1 A))))))) (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (let ((_let_2 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (= (@ _let_1 (@ (@ tptp.power_power_rat A) N)) (or (= N tptp.zero_zero_nat) (and _let_2 (not (= A tptp.zero_zero_rat))) (and (not _let_2) (@ _let_1 A))))))) (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (let ((_let_2 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (= (@ _let_1 (@ (@ tptp.power_power_int A) N)) (or (= N tptp.zero_zero_nat) (and _let_2 (not (= A tptp.zero_zero_int))) (and (not _let_2) (@ _let_1 A))))))) (forall ((M2 tptp.nat) (N tptp.nat) (X tptp.code_integer)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger X))) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.minus_8373710615458151222nteger tptp.one_one_Code_integer) X)) (@ (@ tptp.groups7501900531339628137nteger _let_1) (@ (@ tptp.set_or1269000886237332187st_nat M2) N))) (@ (@ tptp.minus_8373710615458151222nteger (@ _let_1 M2)) (@ _let_1 (@ tptp.suc N))))))) (forall ((M2 tptp.nat) (N tptp.nat) (X tptp.complex)) (let ((_let_1 (@ tptp.power_power_complex X))) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex tptp.one_one_complex) X)) (@ (@ tptp.groups2073611262835488442omplex _let_1) (@ (@ tptp.set_or1269000886237332187st_nat M2) N))) (@ (@ tptp.minus_minus_complex (@ _let_1 M2)) (@ _let_1 (@ tptp.suc N))))))) (forall ((M2 tptp.nat) (N tptp.nat) (X tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat X))) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat tptp.one_one_rat) X)) (@ (@ tptp.groups2906978787729119204at_rat _let_1) (@ (@ tptp.set_or1269000886237332187st_nat M2) N))) (@ (@ tptp.minus_minus_rat (@ _let_1 M2)) (@ _let_1 (@ tptp.suc N))))))) (forall ((M2 tptp.nat) (N tptp.nat) (X tptp.int)) (let ((_let_1 (@ tptp.power_power_int X))) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int tptp.one_one_int) X)) (@ (@ tptp.groups3539618377306564664at_int _let_1) (@ (@ tptp.set_or1269000886237332187st_nat M2) N))) (@ (@ tptp.minus_minus_int (@ _let_1 M2)) (@ _let_1 (@ tptp.suc N))))))) (forall ((M2 tptp.nat) (N tptp.nat) (X tptp.real)) (let ((_let_1 (@ tptp.power_power_real X))) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real tptp.one_one_real) X)) (@ (@ tptp.groups6591440286371151544t_real _let_1) (@ (@ tptp.set_or1269000886237332187st_nat M2) N))) (@ (@ tptp.minus_minus_real (@ _let_1 M2)) (@ _let_1 (@ tptp.suc N))))))) (forall ((G2 (-> tptp.nat tptp.rat)) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.groups2906978787729119204at_rat G2) (@ (@ tptp.set_or1269000886237332187st_nat (@ _let_1 M2)) (@ tptp.suc (@ _let_1 N)))) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I))) (@ (@ tptp.plus_plus_rat (@ G2 _let_1)) (@ G2 (@ tptp.suc _let_1)))))) (@ (@ tptp.set_or1269000886237332187st_nat M2) N))))) (forall ((G2 (-> tptp.nat tptp.int)) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.groups3539618377306564664at_int G2) (@ (@ tptp.set_or1269000886237332187st_nat (@ _let_1 M2)) (@ tptp.suc (@ _let_1 N)))) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I))) (@ (@ tptp.plus_plus_int (@ G2 _let_1)) (@ G2 (@ tptp.suc _let_1)))))) (@ (@ tptp.set_or1269000886237332187st_nat M2) N))))) (forall ((G2 (-> tptp.nat tptp.nat)) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.groups3542108847815614940at_nat G2) (@ (@ tptp.set_or1269000886237332187st_nat (@ _let_1 M2)) (@ tptp.suc (@ _let_1 N)))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I))) (@ (@ tptp.plus_plus_nat (@ G2 _let_1)) (@ G2 (@ tptp.suc _let_1)))))) (@ (@ tptp.set_or1269000886237332187st_nat M2) N))))) (forall ((G2 (-> tptp.nat tptp.real)) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.groups6591440286371151544t_real G2) (@ (@ tptp.set_or1269000886237332187st_nat (@ _let_1 M2)) (@ tptp.suc (@ _let_1 N)))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I))) (@ (@ tptp.plus_plus_real (@ G2 _let_1)) (@ G2 (@ tptp.suc _let_1)))))) (@ (@ tptp.set_or1269000886237332187st_nat M2) N))))) (forall ((M2 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 M2)) tptp.one_one_Code_integer)) (@ _let_2 N))) (@ (@ tptp.ord_less_eq_nat M2) N))))) (forall ((M2 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 M2)) tptp.one_one_nat)) (@ _let_2 N))) (@ (@ tptp.ord_less_eq_nat M2) N))))) (forall ((M2 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 M2)) tptp.one_one_int)) (@ _let_2 N))) (@ (@ tptp.ord_less_eq_nat M2) N))))) (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real A) N)) tptp.zero_zero_real) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (or (and (not _let_1) (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real)) (and _let_1 (= A tptp.zero_zero_real))))))) (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat A) N)) tptp.zero_zero_rat) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (or (and (not _let_1) (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat)) (and _let_1 (= A tptp.zero_zero_rat))))))) (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A) N)) tptp.zero_zero_int) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (or (and (not _let_1) (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int)) (and _let_1 (= A tptp.zero_zero_int))))))) (forall ((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))))))) (forall ((N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X4 tptp.nat)) X4)) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat N) (@ tptp.suc N))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (let ((_let_3 (@ tptp.suc tptp.zero_zero_nat))) (=> (= (@ (@ tptp.modulo_modulo_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 _let_1))) _let_3) (@ (@ tptp.dvd_dvd_nat _let_2) (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat N) _let_3)) _let_2))))))) (forall ((M2 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 M2)) tptp.one_one_Code_integer)) _let_3)) (or (= _let_3 tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_less_eq_nat M2) N))))))) (forall ((M2 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 M2)) tptp.one_one_nat)) _let_3)) (or (= _let_3 tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_nat M2) N))))))) (forall ((M2 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 M2)) tptp.one_one_int)) _let_3)) (or (= _let_3 tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_nat M2) N))))))) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri4939895301339042750nteger N))) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups7501900531339628137nteger tptp.semiri4939895301339042750nteger) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N))) (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.plus_p5714425477246183910nteger _let_1) tptp.one_one_Code_integer))))) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri681578069525770553at_rat N))) (= (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups2906978787729119204at_rat tptp.semiri681578069525770553at_rat) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N))) (@ (@ tptp.times_times_rat _let_1) (@ (@ tptp.plus_plus_rat _let_1) tptp.one_one_rat))))) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri4216267220026989637d_enat N))) (= (@ (@ tptp.times_7803423173614009249d_enat (@ tptp.numera1916890842035813515d_enat (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups7108830773950497114d_enat tptp.semiri4216267220026989637d_enat) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N))) (@ (@ tptp.times_7803423173614009249d_enat _let_1) (@ (@ tptp.plus_p3455044024723400733d_enat _let_1) tptp.one_on7984719198319812577d_enat))))) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri8010041392384452111omplex N))) (= (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups2073611262835488442omplex tptp.semiri8010041392384452111omplex) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N))) (@ (@ tptp.times_times_complex _let_1) (@ (@ tptp.plus_plus_complex _let_1) tptp.one_one_complex))))) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int N))) (= (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups3539618377306564664at_int tptp.semiri1314217659103216013at_int) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N))) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int))))) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri1316708129612266289at_nat N))) (= (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups3542108847815614940at_nat tptp.semiri1316708129612266289at_nat) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat))))) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real N))) (= (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups6591440286371151544t_real tptp.semiri5074537144036343181t_real) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N))) (@ (@ tptp.times_times_real _let_1) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real))))) (forall ((A tptp.code_integer) (D tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri4939895301339042750nteger N))) (let ((_let_2 (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (= (@ _let_2 (@ (@ tptp.groups7501900531339628137nteger (lambda ((I tptp.nat)) (@ (@ tptp.plus_p5714425477246183910nteger A) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.semiri4939895301339042750nteger I)) D)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N))) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.plus_p5714425477246183910nteger _let_1) tptp.one_one_Code_integer)) (@ (@ tptp.plus_p5714425477246183910nteger (@ _let_2 A)) (@ (@ tptp.times_3573771949741848930nteger _let_1) D))))))) (forall ((A tptp.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 ((I tptp.nat)) (@ (@ tptp.plus_plus_rat A) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat I)) D)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N))) (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat _let_1) tptp.one_one_rat)) (@ (@ tptp.plus_plus_rat (@ _let_2 A)) (@ (@ tptp.times_times_rat _let_1) D))))))) (forall ((A tptp.extended_enat) (D tptp.extended_enat) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri4216267220026989637d_enat N))) (let ((_let_2 (@ tptp.times_7803423173614009249d_enat (@ tptp.numera1916890842035813515d_enat (@ tptp.bit0 tptp.one))))) (= (@ _let_2 (@ (@ tptp.groups7108830773950497114d_enat (lambda ((I tptp.nat)) (@ (@ tptp.plus_p3455044024723400733d_enat A) (@ (@ tptp.times_7803423173614009249d_enat (@ tptp.semiri4216267220026989637d_enat I)) D)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N))) (@ (@ tptp.times_7803423173614009249d_enat (@ (@ tptp.plus_p3455044024723400733d_enat _let_1) tptp.one_on7984719198319812577d_enat)) (@ (@ tptp.plus_p3455044024723400733d_enat (@ _let_2 A)) (@ (@ tptp.times_7803423173614009249d_enat _let_1) D))))))) (forall ((A tptp.complex) (D tptp.complex) (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 ((I tptp.nat)) (@ (@ tptp.plus_plus_complex A) (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex I)) D)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N))) (@ (@ tptp.times_times_complex (@ (@ tptp.plus_plus_complex _let_1) tptp.one_one_complex)) (@ (@ tptp.plus_plus_complex (@ _let_2 A)) (@ (@ tptp.times_times_complex _let_1) D))))))) (forall ((A tptp.int) (D tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int N))) (let ((_let_2 (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_2 (@ (@ tptp.groups3539618377306564664at_int (lambda ((I tptp.nat)) (@ (@ tptp.plus_plus_int A) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int I)) D)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N))) (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int)) (@ (@ tptp.plus_plus_int (@ _let_2 A)) (@ (@ tptp.times_times_int _let_1) D))))))) (forall ((A tptp.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 ((I tptp.nat)) (@ (@ tptp.plus_plus_nat A) (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat I)) D)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N))) (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat)) (@ (@ tptp.plus_plus_nat (@ _let_2 A)) (@ (@ tptp.times_times_nat _let_1) D))))))) (forall ((A tptp.real) (D tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real N))) (let ((_let_2 (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (= (@ _let_2 (@ (@ tptp.groups6591440286371151544t_real (lambda ((I tptp.nat)) (@ (@ tptp.plus_plus_real A) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real I)) D)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N))) (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real)) (@ (@ tptp.plus_plus_real (@ _let_2 A)) (@ (@ tptp.times_times_real _let_1) D))))))) (forall ((A tptp.nat) (D tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I tptp.nat)) (@ (@ tptp.plus_plus_nat A) (@ (@ tptp.times_times_nat I) D)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat (@ tptp.suc N)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_1) A)) (@ (@ tptp.times_times_nat N) D)))) _let_1)))) (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X4 tptp.nat)) X4)) (@ (@ tptp.set_or1269000886237332187st_nat M2) 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 M2) (@ (@ tptp.minus_minus_nat M2) tptp.one_one_nat)))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (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))))) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri4939895301339042750nteger N))) (= (@ (@ tptp.groups7501900531339628137nteger tptp.semiri4939895301339042750nteger) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)) (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.plus_p5714425477246183910nteger _let_1) tptp.one_one_Code_integer))) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))))) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int N))) (= (@ (@ tptp.groups3539618377306564664at_int tptp.semiri1314217659103216013at_int) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)) (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))))) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri1316708129612266289at_nat N))) (= (@ (@ tptp.groups3542108847815614940at_nat tptp.semiri1316708129612266289at_nat) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (forall ((A tptp.code_integer) (D tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.semiri4939895301339042750nteger N))) (= (@ (@ tptp.groups7501900531339628137nteger (lambda ((I tptp.nat)) (@ (@ tptp.plus_p5714425477246183910nteger A) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.semiri4939895301339042750nteger I)) D)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)) (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.plus_p5714425477246183910nteger _let_2) tptp.one_one_Code_integer)) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger _let_1) A)) (@ (@ tptp.times_3573771949741848930nteger _let_2) D)))) _let_1))))) (forall ((A tptp.int) (D tptp.int) (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 ((I tptp.nat)) (@ (@ tptp.plus_plus_int A) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int I)) D)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)) (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int _let_2) tptp.one_one_int)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int _let_1) A)) (@ (@ tptp.times_times_int _let_2) D)))) _let_1))))) (forall ((A tptp.nat) (D tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.semiri1316708129612266289at_nat N))) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I tptp.nat)) (@ (@ tptp.plus_plus_nat A) (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat I)) D)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat _let_2) tptp.one_one_nat)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_1) A)) (@ (@ tptp.times_times_nat _let_2) D)))) _let_1))))) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri4939895301339042750nteger N))) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups7501900531339628137nteger tptp.semiri4939895301339042750nteger) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N))) (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.plus_p5714425477246183910nteger _let_1) tptp.one_one_Code_integer))))) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri681578069525770553at_rat N))) (= (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups2906978787729119204at_rat tptp.semiri681578069525770553at_rat) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N))) (@ (@ tptp.times_times_rat _let_1) (@ (@ tptp.plus_plus_rat _let_1) tptp.one_one_rat))))) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri4216267220026989637d_enat N))) (= (@ (@ tptp.times_7803423173614009249d_enat (@ tptp.numera1916890842035813515d_enat (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups7108830773950497114d_enat tptp.semiri4216267220026989637d_enat) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N))) (@ (@ tptp.times_7803423173614009249d_enat _let_1) (@ (@ tptp.plus_p3455044024723400733d_enat _let_1) tptp.one_on7984719198319812577d_enat))))) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri8010041392384452111omplex N))) (= (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups2073611262835488442omplex tptp.semiri8010041392384452111omplex) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N))) (@ (@ tptp.times_times_complex _let_1) (@ (@ tptp.plus_plus_complex _let_1) tptp.one_one_complex))))) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int N))) (= (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups3539618377306564664at_int tptp.semiri1314217659103216013at_int) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N))) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int))))) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri1316708129612266289at_nat N))) (= (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups3542108847815614940at_nat tptp.semiri1316708129612266289at_nat) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat))))) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real N))) (= (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups6591440286371151544t_real tptp.semiri5074537144036343181t_real) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N))) (@ (@ tptp.times_times_real _let_1) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real))))) (forall ((A tptp.nat) (M2 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 M2))) _let_4)) (or (@ (@ tptp.ord_less_nat N) M2) (= _let_4 tptp.zero_zero_nat) (and (@ (@ tptp.ord_less_eq_nat M2) N) (@ _let_3 (@ (@ tptp.divide_divide_nat A) (@ _let_2 (@ (@ tptp.minus_minus_nat N) M2)))))))))))) (forall ((A tptp.int) (M2 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 M2))) _let_4)) (or (@ (@ tptp.ord_less_nat N) M2) (= _let_4 tptp.zero_zero_int) (and (@ (@ tptp.ord_less_eq_nat M2) N) (@ _let_3 (@ (@ tptp.divide_divide_int A) (@ _let_2 (@ (@ tptp.minus_minus_nat N) M2)))))))))))) (forall ((X tptp.complex) (M2 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 M2) (@ (@ tptp.plus_plus_nat M2) 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 M2)) (@ _let_1 (@ _let_2 (@ tptp.suc N))))) (@ _let_1 X)))))))))) (forall ((X tptp.rat) (M2 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 M2) (@ (@ tptp.plus_plus_nat M2) 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 M2)) (@ _let_1 (@ _let_2 (@ tptp.suc N))))) (@ _let_1 X)))))))))) (forall ((X tptp.real) (M2 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 M2) (@ (@ tptp.plus_plus_nat M2) 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 M2)) (@ _let_1 (@ _let_2 (@ tptp.suc N))))) (@ _let_1 X)))))))))) (forall ((Va3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.suc (@ tptp.suc Va3)))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_2) _let_1))) (let ((_let_4 (@ tptp.suc _let_3))) (let ((_let_5 (@ tptp.vEBT_vebt_buildup _let_3))) (let ((_let_6 (@ tptp.power_power_nat _let_1))) (let ((_let_7 (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_2))) (let ((_let_8 (@ tptp.vEBT_vebt_buildup _let_2))) (let ((_let_9 (@ (@ tptp.dvd_dvd_nat _let_1) _let_2))) (and (=> _let_9 (= _let_8 (@ (@ _let_7 (@ (@ tptp.replicate_VEBT_VEBT (@ _let_6 _let_3)) _let_5)) _let_5))) (=> (not _let_9) (= _let_8 (@ (@ _let_7 (@ (@ tptp.replicate_VEBT_VEBT (@ _let_6 _let_4)) _let_5)) (@ tptp.vEBT_vebt_buildup _let_4))))))))))))))) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri4939895301339042750nteger N))) (= (@ (@ tptp.groups7501900531339628137nteger tptp.semiri4939895301339042750nteger) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N)) (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.plus_p5714425477246183910nteger _let_1) tptp.one_one_Code_integer))) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))))) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int N))) (= (@ (@ tptp.groups3539618377306564664at_int tptp.semiri1314217659103216013at_int) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N)) (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))))) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri1316708129612266289at_nat N))) (= (@ (@ tptp.groups3542108847815614940at_nat tptp.semiri1316708129612266289at_nat) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.sums_real (lambda ((N4 tptp.nat)) (@ (@ tptp.power_power_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.suc N4)))) tptp.one_one_real) (@ (@ tptp.sums_complex (lambda ((N4 tptp.nat)) tptp.zero_zero_complex)) tptp.zero_zero_complex) (@ (@ tptp.sums_real (lambda ((N4 tptp.nat)) tptp.zero_zero_real)) tptp.zero_zero_real) (@ (@ tptp.sums_nat (lambda ((N4 tptp.nat)) tptp.zero_zero_nat)) tptp.zero_zero_nat) (@ (@ tptp.sums_int (lambda ((N4 tptp.nat)) tptp.zero_zero_int)) tptp.zero_zero_int) (forall ((M2 tptp.nat) (Z3 tptp.complex)) (@ (@ tptp.sums_complex (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ (@ tptp.if_complex (= N4 M2)) tptp.one_one_complex) tptp.zero_zero_complex)) (@ (@ tptp.power_power_complex Z3) N4)))) (@ (@ tptp.power_power_complex Z3) M2))) (forall ((M2 tptp.nat) (Z3 tptp.real)) (@ (@ tptp.sums_real (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ (@ tptp.if_real (= N4 M2)) tptp.one_one_real) tptp.zero_zero_real)) (@ (@ tptp.power_power_real Z3) N4)))) (@ (@ tptp.power_power_real Z3) M2))) (forall ((M2 tptp.nat) (Z3 tptp.int)) (@ (@ tptp.sums_int (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_int (@ (@ (@ tptp.if_int (= N4 M2)) tptp.one_one_int) tptp.zero_zero_int)) (@ (@ tptp.power_power_int Z3) N4)))) (@ (@ tptp.power_power_int Z3) M2))) (forall ((A4 tptp.set_nat) (F2 (-> tptp.nat tptp.complex))) (=> (@ tptp.finite_finite_nat A4) (@ (@ tptp.sums_complex (lambda ((R tptp.nat)) (@ (@ (@ tptp.if_complex (@ (@ tptp.member_nat R) A4)) (@ F2 R)) tptp.zero_zero_complex))) (@ (@ tptp.groups2073611262835488442omplex F2) A4)))) (forall ((A4 tptp.set_nat) (F2 (-> tptp.nat tptp.int))) (=> (@ tptp.finite_finite_nat A4) (@ (@ tptp.sums_int (lambda ((R tptp.nat)) (@ (@ (@ tptp.if_int (@ (@ tptp.member_nat R) A4)) (@ F2 R)) tptp.zero_zero_int))) (@ (@ tptp.groups3539618377306564664at_int F2) A4)))) (forall ((A4 tptp.set_nat) (F2 (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_nat A4) (@ (@ tptp.sums_nat (lambda ((R tptp.nat)) (@ (@ (@ tptp.if_nat (@ (@ tptp.member_nat R) A4)) (@ F2 R)) tptp.zero_zero_nat))) (@ (@ tptp.groups3542108847815614940at_nat F2) A4)))) (forall ((A4 tptp.set_nat) (F2 (-> tptp.nat tptp.real))) (=> (@ tptp.finite_finite_nat A4) (@ (@ tptp.sums_real (lambda ((R tptp.nat)) (@ (@ (@ tptp.if_real (@ (@ tptp.member_nat R) A4)) (@ F2 R)) tptp.zero_zero_real))) (@ (@ tptp.groups6591440286371151544t_real F2) A4)))) (forall ((P2 (-> tptp.nat Bool)) (F2 (-> tptp.nat tptp.complex))) (let ((_let_1 (@ tptp.collect_nat P2))) (=> (@ tptp.finite_finite_nat _let_1) (@ (@ tptp.sums_complex (lambda ((R tptp.nat)) (@ (@ (@ tptp.if_complex (@ P2 R)) (@ F2 R)) tptp.zero_zero_complex))) (@ (@ tptp.groups2073611262835488442omplex F2) _let_1))))) (forall ((P2 (-> tptp.nat Bool)) (F2 (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.collect_nat P2))) (=> (@ tptp.finite_finite_nat _let_1) (@ (@ tptp.sums_int (lambda ((R tptp.nat)) (@ (@ (@ tptp.if_int (@ P2 R)) (@ F2 R)) tptp.zero_zero_int))) (@ (@ tptp.groups3539618377306564664at_int F2) _let_1))))) (forall ((P2 (-> tptp.nat Bool)) (F2 (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.collect_nat P2))) (=> (@ tptp.finite_finite_nat _let_1) (@ (@ tptp.sums_nat (lambda ((R tptp.nat)) (@ (@ (@ tptp.if_nat (@ P2 R)) (@ F2 R)) tptp.zero_zero_nat))) (@ (@ tptp.groups3542108847815614940at_nat F2) _let_1))))) (forall ((P2 (-> tptp.nat Bool)) (F2 (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.collect_nat P2))) (=> (@ tptp.finite_finite_nat _let_1) (@ (@ tptp.sums_real (lambda ((R tptp.nat)) (@ (@ (@ tptp.if_real (@ P2 R)) (@ F2 R)) tptp.zero_zero_real))) (@ (@ tptp.groups6591440286371151544t_real F2) _let_1))))) (forall ((N6 tptp.set_nat) (F2 (-> tptp.nat tptp.complex))) (=> (@ tptp.finite_finite_nat N6) (=> (forall ((N3 tptp.nat)) (=> (not (@ (@ tptp.member_nat N3) N6)) (= (@ F2 N3) tptp.zero_zero_complex))) (@ (@ tptp.sums_complex F2) (@ (@ tptp.groups2073611262835488442omplex F2) N6))))) (forall ((N6 tptp.set_nat) (F2 (-> tptp.nat tptp.int))) (=> (@ tptp.finite_finite_nat N6) (=> (forall ((N3 tptp.nat)) (=> (not (@ (@ tptp.member_nat N3) N6)) (= (@ F2 N3) tptp.zero_zero_int))) (@ (@ tptp.sums_int F2) (@ (@ tptp.groups3539618377306564664at_int F2) N6))))) (forall ((N6 tptp.set_nat) (F2 (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_nat N6) (=> (forall ((N3 tptp.nat)) (=> (not (@ (@ tptp.member_nat N3) N6)) (= (@ F2 N3) tptp.zero_zero_nat))) (@ (@ tptp.sums_nat F2) (@ (@ tptp.groups3542108847815614940at_nat F2) N6))))) (forall ((N6 tptp.set_nat) (F2 (-> tptp.nat tptp.real))) (=> (@ tptp.finite_finite_nat N6) (=> (forall ((N3 tptp.nat)) (=> (not (@ (@ tptp.member_nat N3) N6)) (= (@ F2 N3) tptp.zero_zero_real))) (@ (@ tptp.sums_real F2) (@ (@ tptp.groups6591440286371151544t_real F2) N6))))) (forall ((N tptp.nat) (F2 (-> tptp.nat tptp.complex)) (S2 tptp.complex)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) N) (= (@ F2 I3) tptp.zero_zero_complex))) (= (@ (@ tptp.sums_complex (lambda ((I tptp.nat)) (@ F2 (@ (@ tptp.plus_plus_nat I) N)))) S2) (@ (@ tptp.sums_complex F2) S2)))) (forall ((N tptp.nat) (F2 (-> tptp.nat tptp.real)) (S2 tptp.real)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) N) (= (@ F2 I3) tptp.zero_zero_real))) (= (@ (@ tptp.sums_real (lambda ((I tptp.nat)) (@ F2 (@ (@ tptp.plus_plus_nat I) N)))) S2) (@ (@ tptp.sums_real F2) S2)))) (forall ((K2 tptp.int) (M2 tptp.int) (T tptp.int)) (let ((_let_1 (@ tptp.times_times_int K2))) (=> (not (= K2 tptp.zero_zero_int)) (= (@ (@ tptp.dvd_dvd_int M2) T) (@ (@ tptp.dvd_dvd_int (@ _let_1 M2)) (@ _let_1 T)))))) (forall ((K2 tptp.int) (M2 tptp.int) (N tptp.int)) (let ((_let_1 (@ tptp.times_times_int K2))) (=> (@ (@ tptp.dvd_dvd_int (@ _let_1 M2)) (@ _let_1 N)) (=> (not (= K2 tptp.zero_zero_int)) (@ (@ tptp.dvd_dvd_int M2) N))))) (forall ((A tptp.int) (D tptp.int) (X tptp.int) (T tptp.int) (C2 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 C2) D))) T))))))) (forall ((K2 tptp.int) (N tptp.int) (M2 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int K2))) (= (@ _let_1 (@ (@ tptp.plus_plus_int N) (@ (@ tptp.times_times_int K2) M2))) (@ _let_1 N)))) (forall ((A4 tptp.set_complex) (G2 (-> tptp.complex tptp.nat)) (F2 (-> tptp.complex tptp.nat))) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) A4) (@ (@ tptp.ord_less_eq_nat (@ G2 X3)) (@ F2 X3)))) (= (@ (@ tptp.groups5693394587270226106ex_nat (lambda ((X4 tptp.complex)) (@ (@ tptp.minus_minus_nat (@ F2 X4)) (@ G2 X4)))) A4) (@ (@ tptp.minus_minus_nat (@ (@ tptp.groups5693394587270226106ex_nat F2) A4)) (@ (@ tptp.groups5693394587270226106ex_nat G2) A4))))) (forall ((A4 tptp.set_real) (G2 (-> tptp.real tptp.nat)) (F2 (-> tptp.real tptp.nat))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) A4) (@ (@ tptp.ord_less_eq_nat (@ G2 X3)) (@ F2 X3)))) (= (@ (@ tptp.groups1935376822645274424al_nat (lambda ((X4 tptp.real)) (@ (@ tptp.minus_minus_nat (@ F2 X4)) (@ G2 X4)))) A4) (@ (@ tptp.minus_minus_nat (@ (@ tptp.groups1935376822645274424al_nat F2) A4)) (@ (@ tptp.groups1935376822645274424al_nat G2) A4))))) (forall ((A4 tptp.set_set_nat) (G2 (-> tptp.set_nat tptp.nat)) (F2 (-> tptp.set_nat tptp.nat))) (=> (forall ((X3 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat X3) A4) (@ (@ tptp.ord_less_eq_nat (@ G2 X3)) (@ F2 X3)))) (= (@ (@ tptp.groups8294997508430121362at_nat (lambda ((X4 tptp.set_nat)) (@ (@ tptp.minus_minus_nat (@ F2 X4)) (@ G2 X4)))) A4) (@ (@ tptp.minus_minus_nat (@ (@ tptp.groups8294997508430121362at_nat F2) A4)) (@ (@ tptp.groups8294997508430121362at_nat G2) A4))))) (forall ((A4 tptp.set_int) (G2 (-> tptp.int tptp.nat)) (F2 (-> tptp.int tptp.nat))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A4) (@ (@ tptp.ord_less_eq_nat (@ G2 X3)) (@ F2 X3)))) (= (@ (@ tptp.groups4541462559716669496nt_nat (lambda ((X4 tptp.int)) (@ (@ tptp.minus_minus_nat (@ F2 X4)) (@ G2 X4)))) A4) (@ (@ tptp.minus_minus_nat (@ (@ tptp.groups4541462559716669496nt_nat F2) A4)) (@ (@ tptp.groups4541462559716669496nt_nat G2) A4))))) (forall ((A4 tptp.set_nat) (G2 (-> tptp.nat tptp.nat)) (F2 (-> tptp.nat tptp.nat))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A4) (@ (@ tptp.ord_less_eq_nat (@ G2 X3)) (@ F2 X3)))) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X4 tptp.nat)) (@ (@ tptp.minus_minus_nat (@ F2 X4)) (@ G2 X4)))) A4) (@ (@ tptp.minus_minus_nat (@ (@ tptp.groups3542108847815614940at_nat F2) A4)) (@ (@ tptp.groups3542108847815614940at_nat G2) A4))))) (forall ((A4 tptp.set_int) (F2 (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int A4) (= (= (@ (@ tptp.groups4541462559716669496nt_nat F2) A4) (@ tptp.suc tptp.zero_zero_nat)) (exists ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) A4) (= (@ F2 X4) (@ tptp.suc tptp.zero_zero_nat)) (forall ((Y4 tptp.int)) (=> (@ (@ tptp.member_int Y4) A4) (=> (not (= X4 Y4)) (= (@ F2 Y4) tptp.zero_zero_nat))))))))) (forall ((A4 tptp.set_complex) (F2 (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex A4) (= (= (@ (@ tptp.groups5693394587270226106ex_nat F2) A4) (@ tptp.suc tptp.zero_zero_nat)) (exists ((X4 tptp.complex)) (and (@ (@ tptp.member_complex X4) A4) (= (@ F2 X4) (@ tptp.suc tptp.zero_zero_nat)) (forall ((Y4 tptp.complex)) (=> (@ (@ tptp.member_complex Y4) A4) (=> (not (= X4 Y4)) (= (@ F2 Y4) tptp.zero_zero_nat))))))))) (forall ((A4 tptp.set_nat) (F2 (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_nat A4) (= (= (@ (@ tptp.groups3542108847815614940at_nat F2) A4) (@ tptp.suc tptp.zero_zero_nat)) (exists ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) A4) (= (@ F2 X4) (@ tptp.suc tptp.zero_zero_nat)) (forall ((Y4 tptp.nat)) (=> (@ (@ tptp.member_nat Y4) A4) (=> (not (= X4 Y4)) (= (@ F2 Y4) tptp.zero_zero_nat))))))))) (forall ((F2 (-> tptp.nat tptp.nat)) (A4 tptp.set_nat) (N tptp.nat)) (=> (= (@ (@ tptp.groups3542108847815614940at_nat F2) A4) (@ tptp.suc N)) (exists ((X3 tptp.nat)) (and (@ (@ tptp.member_nat X3) A4) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F2 X3)))))) (forall ((A4 tptp.set_int) (F2 (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int A4) (= (= (@ (@ tptp.groups4541462559716669496nt_nat F2) A4) tptp.one_one_nat) (exists ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) A4) (= (@ F2 X4) tptp.one_one_nat) (forall ((Y4 tptp.int)) (=> (@ (@ tptp.member_int Y4) A4) (=> (not (= X4 Y4)) (= (@ F2 Y4) tptp.zero_zero_nat))))))))) (forall ((A4 tptp.set_complex) (F2 (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex A4) (= (= (@ (@ tptp.groups5693394587270226106ex_nat F2) A4) tptp.one_one_nat) (exists ((X4 tptp.complex)) (and (@ (@ tptp.member_complex X4) A4) (= (@ F2 X4) tptp.one_one_nat) (forall ((Y4 tptp.complex)) (=> (@ (@ tptp.member_complex Y4) A4) (=> (not (= X4 Y4)) (= (@ F2 Y4) tptp.zero_zero_nat))))))))) (forall ((A4 tptp.set_nat) (F2 (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_nat A4) (= (= (@ (@ tptp.groups3542108847815614940at_nat F2) A4) tptp.one_one_nat) (exists ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) A4) (= (@ F2 X4) tptp.one_one_nat) (forall ((Y4 tptp.nat)) (=> (@ (@ tptp.member_nat Y4) A4) (=> (not (= X4 Y4)) (= (@ F2 Y4) tptp.zero_zero_nat))))))))) (forall ((F2 (-> tptp.complex tptp.nat)) (A4 tptp.set_complex)) (= (@ (@ tptp.groups5693394587270226106ex_nat (lambda ((X4 tptp.complex)) (@ tptp.suc (@ F2 X4)))) A4) (@ (@ tptp.plus_plus_nat (@ (@ tptp.groups5693394587270226106ex_nat F2) A4)) (@ tptp.finite_card_complex A4)))) (forall ((F2 (-> tptp.int tptp.nat)) (A4 tptp.set_int)) (= (@ (@ tptp.groups4541462559716669496nt_nat (lambda ((X4 tptp.int)) (@ tptp.suc (@ F2 X4)))) A4) (@ (@ tptp.plus_plus_nat (@ (@ tptp.groups4541462559716669496nt_nat F2) A4)) (@ tptp.finite_card_int A4)))) (forall ((F2 (-> tptp.list_nat tptp.nat)) (A4 tptp.set_list_nat)) (= (@ (@ tptp.groups4396056296759096172at_nat (lambda ((X4 tptp.list_nat)) (@ tptp.suc (@ F2 X4)))) A4) (@ (@ tptp.plus_plus_nat (@ (@ tptp.groups4396056296759096172at_nat F2) A4)) (@ tptp.finite_card_list_nat A4)))) (forall ((F2 (-> tptp.set_nat tptp.nat)) (A4 tptp.set_set_nat)) (= (@ (@ tptp.groups8294997508430121362at_nat (lambda ((X4 tptp.set_nat)) (@ tptp.suc (@ F2 X4)))) A4) (@ (@ tptp.plus_plus_nat (@ (@ tptp.groups8294997508430121362at_nat F2) A4)) (@ tptp.finite_card_set_nat A4)))) (forall ((F2 (-> tptp.nat tptp.nat)) (A4 tptp.set_nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X4 tptp.nat)) (@ tptp.suc (@ F2 X4)))) A4) (@ (@ tptp.plus_plus_nat (@ (@ tptp.groups3542108847815614940at_nat F2) A4)) (@ tptp.finite_card_nat A4)))) (forall ((S3 tptp.set_real) (T5 tptp.set_real) (R2 (-> tptp.real tptp.real Bool)) (K2 tptp.nat)) (=> (@ tptp.finite_finite_real S3) (=> (@ tptp.finite_finite_real T5) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) T5) (= (@ tptp.finite_card_real (@ tptp.collect_real (lambda ((I tptp.real)) (and (@ (@ tptp.member_real I) S3) (@ (@ R2 I) X3))))) K2))) (= (@ (@ tptp.groups1935376822645274424al_nat (lambda ((I tptp.real)) (@ tptp.finite_card_real (@ tptp.collect_real (lambda ((J tptp.real)) (and (@ (@ tptp.member_real J) T5) (@ (@ R2 I) J))))))) S3) (@ (@ tptp.times_times_nat K2) (@ tptp.finite_card_real T5))))))) (forall ((S3 tptp.set_real) (T5 tptp.set_nat) (R2 (-> tptp.real tptp.nat Bool)) (K2 tptp.nat)) (=> (@ tptp.finite_finite_real S3) (=> (@ tptp.finite_finite_nat T5) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) T5) (= (@ tptp.finite_card_real (@ tptp.collect_real (lambda ((I tptp.real)) (and (@ (@ tptp.member_real I) S3) (@ (@ R2 I) X3))))) K2))) (= (@ (@ tptp.groups1935376822645274424al_nat (lambda ((I tptp.real)) (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((J tptp.nat)) (and (@ (@ tptp.member_nat J) T5) (@ (@ R2 I) J))))))) S3) (@ (@ tptp.times_times_nat K2) (@ tptp.finite_card_nat T5))))))) (forall ((S3 tptp.set_real) (T5 tptp.set_int) (R2 (-> tptp.real tptp.int Bool)) (K2 tptp.nat)) (=> (@ tptp.finite_finite_real S3) (=> (@ tptp.finite_finite_int T5) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) T5) (= (@ tptp.finite_card_real (@ tptp.collect_real (lambda ((I tptp.real)) (and (@ (@ tptp.member_real I) S3) (@ (@ R2 I) X3))))) K2))) (= (@ (@ tptp.groups1935376822645274424al_nat (lambda ((I tptp.real)) (@ tptp.finite_card_int (@ tptp.collect_int (lambda ((J tptp.int)) (and (@ (@ tptp.member_int J) T5) (@ (@ R2 I) J))))))) S3) (@ (@ tptp.times_times_nat K2) (@ tptp.finite_card_int T5))))))) (forall ((S3 tptp.set_real) (T5 tptp.set_complex) (R2 (-> tptp.real tptp.complex Bool)) (K2 tptp.nat)) (=> (@ tptp.finite_finite_real S3) (=> (@ tptp.finite3207457112153483333omplex T5) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) T5) (= (@ tptp.finite_card_real (@ tptp.collect_real (lambda ((I tptp.real)) (and (@ (@ tptp.member_real I) S3) (@ (@ R2 I) X3))))) K2))) (= (@ (@ tptp.groups1935376822645274424al_nat (lambda ((I tptp.real)) (@ tptp.finite_card_complex (@ tptp.collect_complex (lambda ((J tptp.complex)) (and (@ (@ tptp.member_complex J) T5) (@ (@ R2 I) J))))))) S3) (@ (@ tptp.times_times_nat K2) (@ tptp.finite_card_complex T5))))))) (forall ((S3 tptp.set_int) (T5 tptp.set_real) (R2 (-> tptp.int tptp.real Bool)) (K2 tptp.nat)) (=> (@ tptp.finite_finite_int S3) (=> (@ tptp.finite_finite_real T5) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) T5) (= (@ tptp.finite_card_int (@ tptp.collect_int (lambda ((I tptp.int)) (and (@ (@ tptp.member_int I) S3) (@ (@ R2 I) X3))))) K2))) (= (@ (@ tptp.groups4541462559716669496nt_nat (lambda ((I tptp.int)) (@ tptp.finite_card_real (@ tptp.collect_real (lambda ((J tptp.real)) (and (@ (@ tptp.member_real J) T5) (@ (@ R2 I) J))))))) S3) (@ (@ tptp.times_times_nat K2) (@ tptp.finite_card_real T5))))))) (forall ((S3 tptp.set_int) (T5 tptp.set_nat) (R2 (-> tptp.int tptp.nat Bool)) (K2 tptp.nat)) (=> (@ tptp.finite_finite_int S3) (=> (@ tptp.finite_finite_nat T5) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) T5) (= (@ tptp.finite_card_int (@ tptp.collect_int (lambda ((I tptp.int)) (and (@ (@ tptp.member_int I) S3) (@ (@ R2 I) X3))))) K2))) (= (@ (@ tptp.groups4541462559716669496nt_nat (lambda ((I tptp.int)) (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((J tptp.nat)) (and (@ (@ tptp.member_nat J) T5) (@ (@ R2 I) J))))))) S3) (@ (@ tptp.times_times_nat K2) (@ tptp.finite_card_nat T5))))))) (forall ((S3 tptp.set_int) (T5 tptp.set_int) (R2 (-> tptp.int tptp.int Bool)) (K2 tptp.nat)) (=> (@ tptp.finite_finite_int S3) (=> (@ tptp.finite_finite_int T5) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) T5) (= (@ tptp.finite_card_int (@ tptp.collect_int (lambda ((I tptp.int)) (and (@ (@ tptp.member_int I) S3) (@ (@ R2 I) X3))))) K2))) (= (@ (@ tptp.groups4541462559716669496nt_nat (lambda ((I tptp.int)) (@ tptp.finite_card_int (@ tptp.collect_int (lambda ((J tptp.int)) (and (@ (@ tptp.member_int J) T5) (@ (@ R2 I) J))))))) S3) (@ (@ tptp.times_times_nat K2) (@ tptp.finite_card_int T5))))))) (forall ((S3 tptp.set_int) (T5 tptp.set_complex) (R2 (-> tptp.int tptp.complex Bool)) (K2 tptp.nat)) (=> (@ tptp.finite_finite_int S3) (=> (@ tptp.finite3207457112153483333omplex T5) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) T5) (= (@ tptp.finite_card_int (@ tptp.collect_int (lambda ((I tptp.int)) (and (@ (@ tptp.member_int I) S3) (@ (@ R2 I) X3))))) K2))) (= (@ (@ tptp.groups4541462559716669496nt_nat (lambda ((I tptp.int)) (@ tptp.finite_card_complex (@ tptp.collect_complex (lambda ((J tptp.complex)) (and (@ (@ tptp.member_complex J) T5) (@ (@ R2 I) J))))))) S3) (@ (@ tptp.times_times_nat K2) (@ tptp.finite_card_complex T5))))))) (forall ((S3 tptp.set_complex) (T5 tptp.set_real) (R2 (-> tptp.complex tptp.real Bool)) (K2 tptp.nat)) (=> (@ tptp.finite3207457112153483333omplex S3) (=> (@ tptp.finite_finite_real T5) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) T5) (= (@ tptp.finite_card_complex (@ tptp.collect_complex (lambda ((I tptp.complex)) (and (@ (@ tptp.member_complex I) S3) (@ (@ R2 I) X3))))) K2))) (= (@ (@ tptp.groups5693394587270226106ex_nat (lambda ((I tptp.complex)) (@ tptp.finite_card_real (@ tptp.collect_real (lambda ((J tptp.real)) (and (@ (@ tptp.member_real J) T5) (@ (@ R2 I) J))))))) S3) (@ (@ tptp.times_times_nat K2) (@ tptp.finite_card_real T5))))))) (forall ((S3 tptp.set_complex) (T5 tptp.set_nat) (R2 (-> tptp.complex tptp.nat Bool)) (K2 tptp.nat)) (=> (@ tptp.finite3207457112153483333omplex S3) (=> (@ tptp.finite_finite_nat T5) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) T5) (= (@ tptp.finite_card_complex (@ tptp.collect_complex (lambda ((I tptp.complex)) (and (@ (@ tptp.member_complex I) S3) (@ (@ R2 I) X3))))) K2))) (= (@ (@ tptp.groups5693394587270226106ex_nat (lambda ((I tptp.complex)) (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((J tptp.nat)) (and (@ (@ tptp.member_nat J) T5) (@ (@ R2 I) J))))))) S3) (@ (@ tptp.times_times_nat K2) (@ tptp.finite_card_nat T5))))))) (forall ((K2 tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.modulo_modulo_int K2) L)) (or (@ (@ tptp.dvd_dvd_int L) K2) (and (= L tptp.zero_zero_int) (@ _let_1 K2)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) L))))) (forall ((Xs2 tptp.list_complex) (X8 tptp.set_complex)) (=> (@ (@ tptp.ord_le211207098394363844omplex (@ tptp.set_complex2 Xs2)) X8) (=> (@ tptp.finite3207457112153483333omplex X8) (= (@ (@ tptp.groups5693394587270226106ex_nat (@ tptp.count_list_complex Xs2)) X8) (@ tptp.size_s3451745648224563538omplex Xs2))))) (forall ((Xs2 tptp.list_VEBT_VEBT) (X8 tptp.set_VEBT_VEBT)) (=> (@ (@ tptp.ord_le4337996190870823476T_VEBT (@ tptp.set_VEBT_VEBT2 Xs2)) X8) (=> (@ tptp.finite5795047828879050333T_VEBT X8) (= (@ (@ tptp.groups771621172384141258BT_nat (@ tptp.count_list_VEBT_VEBT Xs2)) X8) (@ tptp.size_s6755466524823107622T_VEBT Xs2))))) (forall ((Xs2 tptp.list_o) (X8 tptp.set_o)) (=> (@ (@ tptp.ord_less_eq_set_o (@ tptp.set_o2 Xs2)) X8) (=> (@ tptp.finite_finite_o X8) (= (@ (@ tptp.groups8507830703676809646_o_nat (@ tptp.count_list_o Xs2)) X8) (@ tptp.size_size_list_o Xs2))))) (forall ((Xs2 tptp.list_int) (X8 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_int2 Xs2)) X8) (=> (@ tptp.finite_finite_int X8) (= (@ (@ tptp.groups4541462559716669496nt_nat (@ tptp.count_list_int Xs2)) X8) (@ tptp.size_size_list_int Xs2))))) (forall ((Xs2 tptp.list_nat) (X8 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_nat2 Xs2)) X8) (=> (@ tptp.finite_finite_nat X8) (= (@ (@ tptp.groups3542108847815614940at_nat (@ tptp.count_list_nat Xs2)) X8) (@ tptp.size_size_list_nat Xs2))))) (forall ((F2 (-> tptp.nat tptp.real)) (G2 (-> tptp.nat tptp.real)) (S2 tptp.real) (T tptp.real)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ F2 N3)) (@ G2 N3))) (=> (@ (@ tptp.sums_real F2) S2) (=> (@ (@ tptp.sums_real G2) T) (@ (@ tptp.ord_less_eq_real S2) T))))) (forall ((F2 (-> tptp.nat tptp.nat)) (G2 (-> tptp.nat tptp.nat)) (S2 tptp.nat) (T tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ F2 N3)) (@ G2 N3))) (=> (@ (@ tptp.sums_nat F2) S2) (=> (@ (@ tptp.sums_nat G2) T) (@ (@ tptp.ord_less_eq_nat S2) T))))) (forall ((F2 (-> tptp.nat tptp.int)) (G2 (-> tptp.nat tptp.int)) (S2 tptp.int) (T tptp.int)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ F2 N3)) (@ G2 N3))) (=> (@ (@ tptp.sums_int F2) S2) (=> (@ (@ tptp.sums_int G2) T) (@ (@ tptp.ord_less_eq_int S2) T))))) (forall ((F2 (-> tptp.nat tptp.complex))) (=> (forall ((N3 tptp.nat)) (= (@ F2 N3) tptp.zero_zero_complex)) (@ (@ tptp.sums_complex F2) tptp.zero_zero_complex))) (forall ((F2 (-> tptp.nat tptp.real))) (=> (forall ((N3 tptp.nat)) (= (@ F2 N3) tptp.zero_zero_real)) (@ (@ tptp.sums_real F2) tptp.zero_zero_real))) (forall ((F2 (-> tptp.nat tptp.nat))) (=> (forall ((N3 tptp.nat)) (= (@ F2 N3) tptp.zero_zero_nat)) (@ (@ tptp.sums_nat F2) tptp.zero_zero_nat))) (forall ((F2 (-> tptp.nat tptp.int))) (=> (forall ((N3 tptp.nat)) (= (@ F2 N3) tptp.zero_zero_int)) (@ (@ tptp.sums_int F2) tptp.zero_zero_int))) (forall ((I2 tptp.nat) (F2 (-> tptp.nat tptp.complex))) (@ (@ tptp.sums_complex (lambda ((R tptp.nat)) (@ (@ (@ tptp.if_complex (= R I2)) (@ F2 R)) tptp.zero_zero_complex))) (@ F2 I2))) (forall ((I2 tptp.nat) (F2 (-> tptp.nat tptp.real))) (@ (@ tptp.sums_real (lambda ((R tptp.nat)) (@ (@ (@ tptp.if_real (= R I2)) (@ F2 R)) tptp.zero_zero_real))) (@ F2 I2))) (forall ((I2 tptp.nat) (F2 (-> tptp.nat tptp.nat))) (@ (@ tptp.sums_nat (lambda ((R tptp.nat)) (@ (@ (@ tptp.if_nat (= R I2)) (@ F2 R)) tptp.zero_zero_nat))) (@ F2 I2))) (forall ((I2 tptp.nat) (F2 (-> tptp.nat tptp.int))) (@ (@ tptp.sums_int (lambda ((R tptp.nat)) (@ (@ (@ tptp.if_int (= R I2)) (@ F2 R)) tptp.zero_zero_int))) (@ F2 I2))) (forall ((F2 (-> tptp.nat tptp.real)) (A tptp.real) (C2 tptp.real)) (=> (@ (@ tptp.sums_real F2) A) (@ (@ tptp.sums_real (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_real (@ F2 N4)) C2))) (@ (@ tptp.times_times_real A) C2)))) (forall ((F2 (-> tptp.nat tptp.real)) (A tptp.real) (C2 tptp.real)) (=> (@ (@ tptp.sums_real F2) A) (@ (@ tptp.sums_real (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_real C2) (@ F2 N4)))) (@ (@ tptp.times_times_real C2) A)))) (forall ((M2 tptp.int) (N tptp.int)) (=> (@ (@ tptp.ord_less_eq_int M2) N) (= (@ (@ tptp.groups4538972089207619220nt_int (lambda ((X4 tptp.int)) X4)) (@ (@ tptp.set_or1266510415728281911st_int M2) 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 M2) (@ (@ tptp.minus_minus_int M2) tptp.one_one_int)))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))))) (forall ((C2 tptp.complex) (F2 (-> tptp.nat tptp.complex)) (D tptp.complex)) (=> (not (= C2 tptp.zero_zero_complex)) (= (@ (@ tptp.sums_complex (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_complex C2) (@ F2 N4)))) (@ (@ tptp.times_times_complex C2) D)) (@ (@ tptp.sums_complex F2) D)))) (forall ((C2 tptp.real) (F2 (-> tptp.nat tptp.real)) (D tptp.real)) (=> (not (= C2 tptp.zero_zero_real)) (= (@ (@ tptp.sums_real (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_real C2) (@ F2 N4)))) (@ (@ tptp.times_times_real C2) D)) (@ (@ tptp.sums_real F2) D)))) (forall ((C2 tptp.complex) (F2 (-> tptp.nat tptp.complex)) (D tptp.complex)) (=> (not (= C2 tptp.zero_zero_complex)) (= (@ (@ tptp.sums_complex (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_complex (@ F2 N4)) C2))) (@ (@ tptp.times_times_complex D) C2)) (@ (@ tptp.sums_complex F2) D)))) (forall ((C2 tptp.real) (F2 (-> tptp.nat tptp.real)) (D tptp.real)) (=> (not (= C2 tptp.zero_zero_real)) (= (@ (@ tptp.sums_real (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_real (@ F2 N4)) C2))) (@ (@ tptp.times_times_real D) C2)) (@ (@ tptp.sums_real F2) D)))) (forall ((C2 tptp.complex) (F2 (-> tptp.nat tptp.complex)) (A tptp.complex)) (=> (@ (@ tptp.sums_complex (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_complex C2) (@ F2 N4)))) A) (=> (not (= C2 tptp.zero_zero_complex)) (@ (@ tptp.sums_complex F2) (@ (@ tptp.divide1717551699836669952omplex A) C2))))) (forall ((C2 tptp.real) (F2 (-> tptp.nat tptp.real)) (A tptp.real)) (=> (@ (@ tptp.sums_real (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_real C2) (@ F2 N4)))) A) (=> (not (= C2 tptp.zero_zero_real)) (@ (@ tptp.sums_real F2) (@ (@ tptp.divide_divide_real A) C2))))) (forall ((F2 (-> tptp.nat tptp.complex)) (S2 tptp.complex)) (=> (= (@ F2 tptp.zero_zero_nat) tptp.zero_zero_complex) (=> (@ (@ tptp.sums_complex (lambda ((N4 tptp.nat)) (@ F2 (@ tptp.suc N4)))) S2) (@ (@ tptp.sums_complex F2) S2)))) (forall ((F2 (-> tptp.nat tptp.real)) (S2 tptp.real)) (=> (= (@ F2 tptp.zero_zero_nat) tptp.zero_zero_real) (=> (@ (@ tptp.sums_real (lambda ((N4 tptp.nat)) (@ F2 (@ tptp.suc N4)))) S2) (@ (@ tptp.sums_real F2) S2)))) (forall ((F2 (-> tptp.nat tptp.real)) (S2 tptp.real)) (= (@ (@ tptp.sums_real (lambda ((N4 tptp.nat)) (@ F2 (@ tptp.suc N4)))) S2) (@ (@ tptp.sums_real F2) (@ (@ tptp.plus_plus_real S2) (@ F2 tptp.zero_zero_nat))))) (forall ((F2 (-> tptp.nat tptp.real)) (L tptp.real)) (=> (@ (@ tptp.sums_real (lambda ((N4 tptp.nat)) (@ F2 (@ tptp.suc N4)))) L) (@ (@ tptp.sums_real F2) (@ (@ tptp.plus_plus_real L) (@ F2 tptp.zero_zero_nat))))) (forall ((F2 (-> tptp.nat tptp.nat)) (L tptp.nat)) (=> (@ (@ tptp.sums_nat (lambda ((N4 tptp.nat)) (@ F2 (@ tptp.suc N4)))) L) (@ (@ tptp.sums_nat F2) (@ (@ tptp.plus_plus_nat L) (@ F2 tptp.zero_zero_nat))))) (forall ((F2 (-> tptp.nat tptp.int)) (L tptp.int)) (=> (@ (@ tptp.sums_int (lambda ((N4 tptp.nat)) (@ F2 (@ tptp.suc N4)))) L) (@ (@ tptp.sums_int F2) (@ (@ tptp.plus_plus_int L) (@ F2 tptp.zero_zero_nat))))) (forall ((Z3 tptp.complex) (N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.suc N))) (= (@ (@ tptp.times_times_complex (@ (@ tptp.comm_s2602460028002588243omplex Z3) _let_2)) (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.plus_plus_complex Z3) (@ (@ tptp.divide1717551699836669952omplex tptp.one_one_complex) (@ tptp.numera6690914467698888265omplex _let_1)))) _let_2)) (@ (@ tptp.groups6464643781859351333omplex (lambda ((K3 tptp.nat)) (@ (@ tptp.plus_plus_complex Z3) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.semiri8010041392384452111omplex K3)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat _let_1)) N)) tptp.one_one_nat))))))) (forall ((Z3 tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.suc N))) (= (@ (@ tptp.times_times_rat (@ (@ tptp.comm_s4028243227959126397er_rat Z3) _let_2)) (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.plus_plus_rat Z3) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat _let_1)))) _let_2)) (@ (@ tptp.groups73079841787564623at_rat (lambda ((K3 tptp.nat)) (@ (@ tptp.plus_plus_rat Z3) (@ (@ tptp.divide_divide_rat (@ tptp.semiri681578069525770553at_rat K3)) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat _let_1)) N)) tptp.one_one_nat))))))) (forall ((Z3 tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.suc N))) (= (@ (@ tptp.times_times_real (@ (@ tptp.comm_s7457072308508201937r_real Z3) _let_2)) (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.plus_plus_real Z3) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real _let_1)))) _let_2)) (@ (@ tptp.groups129246275422532515t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.plus_plus_real Z3) (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real K3)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat _let_1)) N)) tptp.one_one_nat))))))) (forall ((H tptp.complex) (Z3 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 Z3))) (=> (not (= H tptp.zero_zero_complex)) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ (@ tptp.power_power_complex (@ (@ tptp.plus_plus_complex Z3) H)) N)) (@ _let_2 N))) H)) (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex N)) (@ _let_2 _let_1))) (@ (@ tptp.times_times_complex H) (@ (@ tptp.groups2073611262835488442omplex (lambda ((P5 tptp.nat)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((Q5 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex (@ (@ tptp.plus_plus_complex Z3) H)) Q5)) (@ (@ tptp.power_power_complex Z3) (@ (@ 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))) P5))))) (@ tptp.set_ord_lessThan_nat _let_1)))))))) (forall ((H tptp.rat) (Z3 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 Z3))) (=> (not (= H tptp.zero_zero_rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.power_power_rat (@ (@ tptp.plus_plus_rat Z3) H)) N)) (@ _let_2 N))) H)) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat N)) (@ _let_2 _let_1))) (@ (@ tptp.times_times_rat H) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((P5 tptp.nat)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((Q5 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ (@ tptp.plus_plus_rat Z3) H)) Q5)) (@ (@ tptp.power_power_rat Z3) (@ (@ 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))) P5))))) (@ tptp.set_ord_lessThan_nat _let_1)))))))) (forall ((H tptp.real) (Z3 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 Z3))) (=> (not (= H tptp.zero_zero_real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real Z3) H)) N)) (@ _let_2 N))) H)) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ _let_2 _let_1))) (@ (@ tptp.times_times_real H) (@ (@ tptp.groups6591440286371151544t_real (lambda ((P5 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((Q5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real Z3) H)) Q5)) (@ (@ tptp.power_power_real Z3) (@ (@ 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))) P5))))) (@ tptp.set_ord_lessThan_nat _let_1)))))))) _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 (= tptp.semiri4939895301339042750nteger (lambda ((N4 tptp.nat)) (@ (@ (@ tptp.semiri4055485073559036834nteger (lambda ((I tptp.code_integer)) (@ (@ tptp.plus_p5714425477246183910nteger I) tptp.one_one_Code_integer))) N4) tptp.zero_z3403309356797280102nteger))) (= tptp.semiri8010041392384452111omplex (lambda ((N4 tptp.nat)) (@ (@ (@ tptp.semiri2816024913162550771omplex (lambda ((I tptp.complex)) (@ (@ tptp.plus_plus_complex I) tptp.one_one_complex))) N4) tptp.zero_zero_complex))) _let_255 (= tptp.semiri5074537144036343181t_real (lambda ((N4 tptp.nat)) (@ (@ (@ tptp.semiri7260567687927622513x_real (lambda ((I tptp.real)) (@ (@ tptp.plus_plus_real I) tptp.one_one_real))) N4) tptp.zero_zero_real))) (= tptp.semiri1314217659103216013at_int (lambda ((N4 tptp.nat)) (@ (@ (@ tptp.semiri8420488043553186161ux_int (lambda ((I tptp.int)) (@ (@ tptp.plus_plus_int I) tptp.one_one_int))) N4) tptp.zero_zero_int))) _let_254 (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real (@ tptp.bit0 _let_1))) N)) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) (@ tptp.semiri5074537144036343181t_real N)))) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.binomial (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat _let_1)) N)) N)))))) (forall ((N tptp.nat) (K2 tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ (@ tptp.bit_concat_bit (@ tptp.suc N)) K2) L) (@ (@ tptp.plus_plus_int (@ (@ tptp.modulo_modulo_int K2) _let_1)) (@ (@ tptp.times_times_int _let_1) (@ (@ (@ tptp.bit_concat_bit N) (@ (@ tptp.divide_divide_int K2) _let_1)) L)))))) (= (@ tptp.neg_nu8804712462038260780nteger tptp.one_one_Code_integer) _let_201) (= (@ tptp.neg_nu7009210354673126013omplex tptp.one_one_complex) _let_103) (= (@ tptp.neg_numeral_dbl_real tptp.one_one_real) _let_109) (= (@ tptp.neg_numeral_dbl_int tptp.one_one_int) _let_115) (forall ((X tptp.nat) (Y tptp.nat)) (= (= (@ tptp.set_ord_lessThan_nat X) (@ tptp.set_ord_lessThan_nat Y)) (= X Y))) (forall ((I2 tptp.set_nat) (K2 tptp.set_nat)) (= (@ (@ tptp.member_set_nat I2) (@ tptp.set_or890127255671739683et_nat K2)) (@ (@ tptp.ord_less_set_nat I2) K2))) (forall ((I2 tptp.real) (K2 tptp.real)) (= (@ (@ tptp.member_real I2) (@ tptp.set_or5984915006950818249n_real K2)) (@ (@ tptp.ord_less_real I2) K2))) (forall ((I2 tptp.rat) (K2 tptp.rat)) (= (@ (@ tptp.member_rat I2) (@ tptp.set_ord_lessThan_rat K2)) (@ (@ tptp.ord_less_rat I2) K2))) (forall ((I2 tptp.num) (K2 tptp.num)) (= (@ (@ tptp.member_num I2) (@ tptp.set_ord_lessThan_num K2)) (@ (@ tptp.ord_less_num I2) K2))) (forall ((I2 tptp.int) (K2 tptp.int)) (= (@ (@ tptp.member_int I2) (@ tptp.set_ord_lessThan_int K2)) (@ (@ tptp.ord_less_int I2) K2))) (forall ((I2 tptp.nat) (K2 tptp.nat)) (= (@ (@ tptp.member_nat I2) (@ tptp.set_ord_lessThan_nat K2)) (@ (@ tptp.ord_less_nat I2) K2))) (forall ((K2 tptp.nat)) (@ tptp.finite_finite_nat (@ tptp.set_ord_lessThan_nat K2))) (forall ((K2 tptp.int) (L tptp.int)) (= (@ (@ (@ tptp.bit_concat_bit tptp.zero_zero_nat) K2) L) L)) (forall ((U tptp.nat)) (= (@ tptp.finite_card_nat (@ tptp.set_ord_lessThan_nat U)) U)) (= (@ tptp.neg_nu7009210354673126013omplex tptp.zero_zero_complex) tptp.zero_zero_complex) (= (@ tptp.neg_numeral_dbl_real tptp.zero_zero_real) tptp.zero_zero_real) (= (@ tptp.neg_numeral_dbl_rat tptp.zero_zero_rat) tptp.zero_zero_rat) (= (@ tptp.neg_numeral_dbl_int tptp.zero_zero_int) tptp.zero_zero_int) (forall ((A4 tptp.set_nat) (F2 (-> tptp.nat tptp.complex))) (=> (@ tptp.finite_finite_nat A4) (= (= (@ (@ tptp.groups6464643781859351333omplex F2) A4) tptp.zero_zero_complex) (exists ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) A4) (= (@ F2 X4) tptp.zero_zero_complex)))))) (forall ((A4 tptp.set_int) (F2 (-> tptp.int tptp.complex))) (=> (@ tptp.finite_finite_int A4) (= (= (@ (@ tptp.groups7440179247065528705omplex F2) A4) tptp.zero_zero_complex) (exists ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) A4) (= (@ F2 X4) tptp.zero_zero_complex)))))) (forall ((A4 tptp.set_complex) (F2 (-> tptp.complex tptp.complex))) (=> (@ tptp.finite3207457112153483333omplex A4) (= (= (@ (@ tptp.groups3708469109370488835omplex F2) A4) tptp.zero_zero_complex) (exists ((X4 tptp.complex)) (and (@ (@ tptp.member_complex X4) A4) (= (@ F2 X4) tptp.zero_zero_complex)))))) (forall ((A4 tptp.set_nat) (F2 (-> tptp.nat tptp.real))) (=> (@ tptp.finite_finite_nat A4) (= (= (@ (@ tptp.groups129246275422532515t_real F2) A4) tptp.zero_zero_real) (exists ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) A4) (= (@ F2 X4) tptp.zero_zero_real)))))) (forall ((A4 tptp.set_int) (F2 (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int A4) (= (= (@ (@ tptp.groups2316167850115554303t_real F2) A4) tptp.zero_zero_real) (exists ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) A4) (= (@ F2 X4) tptp.zero_zero_real)))))) (forall ((A4 tptp.set_complex) (F2 (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex A4) (= (= (@ (@ tptp.groups766887009212190081x_real F2) A4) tptp.zero_zero_real) (exists ((X4 tptp.complex)) (and (@ (@ tptp.member_complex X4) A4) (= (@ F2 X4) tptp.zero_zero_real)))))) (forall ((A4 tptp.set_nat) (F2 (-> tptp.nat tptp.rat))) (=> (@ tptp.finite_finite_nat A4) (= (= (@ (@ tptp.groups73079841787564623at_rat F2) A4) tptp.zero_zero_rat) (exists ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) A4) (= (@ F2 X4) tptp.zero_zero_rat)))))) (forall ((A4 tptp.set_int) (F2 (-> tptp.int tptp.rat))) (=> (@ tptp.finite_finite_int A4) (= (= (@ (@ tptp.groups1072433553688619179nt_rat F2) A4) tptp.zero_zero_rat) (exists ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) A4) (= (@ F2 X4) tptp.zero_zero_rat)))))) (forall ((A4 tptp.set_complex) (F2 (-> tptp.complex tptp.rat))) (=> (@ tptp.finite3207457112153483333omplex A4) (= (= (@ (@ tptp.groups225925009352817453ex_rat F2) A4) tptp.zero_zero_rat) (exists ((X4 tptp.complex)) (and (@ (@ tptp.member_complex X4) A4) (= (@ F2 X4) tptp.zero_zero_rat)))))) (forall ((A4 tptp.set_int) (F2 (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int A4) (= (= (@ (@ tptp.groups1707563613775114915nt_nat F2) A4) tptp.zero_zero_nat) (exists ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) A4) (= (@ F2 X4) tptp.zero_zero_nat)))))) (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))) (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.ord_less_eq_set_num (@ tptp.set_ord_lessThan_num X)) (@ tptp.set_ord_lessThan_num Y)) (@ (@ tptp.ord_less_eq_num X) Y))) (forall ((X tptp.int) (Y tptp.int)) (= (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_ord_lessThan_int X)) (@ tptp.set_ord_lessThan_int Y)) (@ (@ tptp.ord_less_eq_int X) Y))) (forall ((X tptp.nat) (Y tptp.nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_ord_lessThan_nat X)) (@ tptp.set_ord_lessThan_nat Y)) (@ (@ tptp.ord_less_eq_nat X) Y))) (= (@ tptp.set_ord_lessThan_nat tptp.zero_zero_nat) tptp.bot_bot_set_nat) (forall ((K2 tptp.num)) (= (@ tptp.neg_nu7009210354673126013omplex (@ tptp.numera6690914467698888265omplex K2)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 K2)))) (forall ((K2 tptp.num)) (= (@ tptp.neg_numeral_dbl_real (@ tptp.numeral_numeral_real K2)) (@ tptp.numeral_numeral_real (@ tptp.bit0 K2)))) (forall ((K2 tptp.num)) (= (@ tptp.neg_numeral_dbl_int (@ tptp.numeral_numeral_int K2)) (@ tptp.numeral_numeral_int (@ tptp.bit0 K2)))) (forall ((A4 tptp.set_real) (X tptp.real) (G2 (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.groups1681761925125756287l_real G2))) (=> (@ tptp.finite_finite_real A4) (=> (not (@ (@ tptp.member_real X) A4)) (= (@ _let_1 (@ (@ tptp.insert_real X) A4)) (@ (@ tptp.times_times_real (@ G2 X)) (@ _let_1 A4))))))) (forall ((A4 tptp.set_nat) (X tptp.nat) (G2 (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.groups129246275422532515t_real G2))) (=> (@ tptp.finite_finite_nat A4) (=> (not (@ (@ tptp.member_nat X) A4)) (= (@ _let_1 (@ (@ tptp.insert_nat X) A4)) (@ (@ tptp.times_times_real (@ G2 X)) (@ _let_1 A4))))))) (forall ((A4 tptp.set_int) (X tptp.int) (G2 (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups2316167850115554303t_real G2))) (=> (@ tptp.finite_finite_int A4) (=> (not (@ (@ tptp.member_int X) A4)) (= (@ _let_1 (@ (@ tptp.insert_int X) A4)) (@ (@ tptp.times_times_real (@ G2 X)) (@ _let_1 A4))))))) (forall ((A4 tptp.set_complex) (X tptp.complex) (G2 (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups766887009212190081x_real G2))) (=> (@ tptp.finite3207457112153483333omplex A4) (=> (not (@ (@ tptp.member_complex X) A4)) (= (@ _let_1 (@ (@ tptp.insert_complex X) A4)) (@ (@ tptp.times_times_real (@ G2 X)) (@ _let_1 A4))))))) (forall ((A4 tptp.set_real) (X tptp.real) (G2 (-> tptp.real tptp.rat))) (let ((_let_1 (@ tptp.groups4061424788464935467al_rat G2))) (=> (@ tptp.finite_finite_real A4) (=> (not (@ (@ tptp.member_real X) A4)) (= (@ _let_1 (@ (@ tptp.insert_real X) A4)) (@ (@ tptp.times_times_rat (@ G2 X)) (@ _let_1 A4))))))) (forall ((A4 tptp.set_nat) (X tptp.nat) (G2 (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups73079841787564623at_rat G2))) (=> (@ tptp.finite_finite_nat A4) (=> (not (@ (@ tptp.member_nat X) A4)) (= (@ _let_1 (@ (@ tptp.insert_nat X) A4)) (@ (@ tptp.times_times_rat (@ G2 X)) (@ _let_1 A4))))))) (forall ((A4 tptp.set_int) (X tptp.int) (G2 (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups1072433553688619179nt_rat G2))) (=> (@ tptp.finite_finite_int A4) (=> (not (@ (@ tptp.member_int X) A4)) (= (@ _let_1 (@ (@ tptp.insert_int X) A4)) (@ (@ tptp.times_times_rat (@ G2 X)) (@ _let_1 A4))))))) (forall ((A4 tptp.set_complex) (X tptp.complex) (G2 (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups225925009352817453ex_rat G2))) (=> (@ tptp.finite3207457112153483333omplex A4) (=> (not (@ (@ tptp.member_complex X) A4)) (= (@ _let_1 (@ (@ tptp.insert_complex X) A4)) (@ (@ tptp.times_times_rat (@ G2 X)) (@ _let_1 A4))))))) (forall ((A4 tptp.set_real) (X tptp.real) (G2 (-> tptp.real tptp.nat))) (let ((_let_1 (@ tptp.groups4696554848551431203al_nat G2))) (=> (@ tptp.finite_finite_real A4) (=> (not (@ (@ tptp.member_real X) A4)) (= (@ _let_1 (@ (@ tptp.insert_real X) A4)) (@ (@ tptp.times_times_nat (@ G2 X)) (@ _let_1 A4))))))) (forall ((A4 tptp.set_int) (X tptp.int) (G2 (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups1707563613775114915nt_nat G2))) (=> (@ tptp.finite_finite_int A4) (=> (not (@ (@ tptp.member_int X) A4)) (= (@ _let_1 (@ (@ tptp.insert_int X) A4)) (@ (@ tptp.times_times_nat (@ G2 X)) (@ _let_1 A4))))))) (forall ((G2 (-> tptp.nat tptp.rat)) (N tptp.nat)) (let ((_let_1 (@ tptp.groups2906978787729119204at_rat G2))) (= (@ _let_1 (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) (@ (@ tptp.plus_plus_rat (@ _let_1 (@ tptp.set_ord_lessThan_nat N))) (@ G2 N))))) (forall ((G2 (-> tptp.nat tptp.int)) (N tptp.nat)) (let ((_let_1 (@ tptp.groups3539618377306564664at_int G2))) (= (@ _let_1 (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) (@ (@ tptp.plus_plus_int (@ _let_1 (@ tptp.set_ord_lessThan_nat N))) (@ G2 N))))) (forall ((G2 (-> tptp.nat tptp.nat)) (N tptp.nat)) (let ((_let_1 (@ tptp.groups3542108847815614940at_nat G2))) (= (@ _let_1 (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) (@ (@ tptp.plus_plus_nat (@ _let_1 (@ tptp.set_ord_lessThan_nat N))) (@ G2 N))))) (forall ((G2 (-> tptp.nat tptp.real)) (N tptp.nat)) (let ((_let_1 (@ tptp.groups6591440286371151544t_real G2))) (= (@ _let_1 (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) (@ (@ tptp.plus_plus_real (@ _let_1 (@ tptp.set_ord_lessThan_nat N))) (@ G2 N))))) (forall ((K2 tptp.int)) (let ((_let_1 (@ (@ tptp.insert_int K2) tptp.bot_bot_set_int))) (= (@ (@ tptp.minus_minus_set_int _let_1) (@ tptp.set_ord_lessThan_int K2)) _let_1))) (forall ((K2 tptp.real)) (let ((_let_1 (@ (@ tptp.insert_real K2) tptp.bot_bot_set_real))) (= (@ (@ tptp.minus_minus_set_real _let_1) (@ tptp.set_or5984915006950818249n_real K2)) _let_1))) (forall ((K2 tptp.nat)) (let ((_let_1 (@ (@ tptp.insert_nat K2) tptp.bot_bot_set_nat))) (= (@ (@ tptp.minus_minus_set_nat _let_1) (@ tptp.set_ord_lessThan_nat K2)) _let_1))) (forall ((G2 (-> tptp.nat tptp.real)) (N tptp.nat)) (let ((_let_1 (@ tptp.groups129246275422532515t_real G2))) (= (@ _let_1 (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) (@ (@ tptp.times_times_real (@ _let_1 (@ tptp.set_ord_lessThan_nat N))) (@ G2 N))))) (forall ((G2 (-> tptp.nat tptp.rat)) (N tptp.nat)) (let ((_let_1 (@ tptp.groups73079841787564623at_rat G2))) (= (@ _let_1 (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) (@ (@ tptp.times_times_rat (@ _let_1 (@ tptp.set_ord_lessThan_nat N))) (@ G2 N))))) (forall ((G2 (-> tptp.nat tptp.int)) (N tptp.nat)) (let ((_let_1 (@ tptp.groups705719431365010083at_int G2))) (= (@ _let_1 (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) (@ (@ tptp.times_times_int (@ _let_1 (@ tptp.set_ord_lessThan_nat N))) (@ G2 N))))) (forall ((G2 (-> tptp.nat tptp.nat)) (N tptp.nat)) (let ((_let_1 (@ tptp.groups708209901874060359at_nat G2))) (= (@ _let_1 (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) (@ (@ tptp.times_times_nat (@ _let_1 (@ tptp.set_ord_lessThan_nat N))) (@ G2 N))))) (forall ((N tptp.nat) (M2 tptp.nat) (G2 (-> tptp.nat tptp.code_integer))) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M2))) (let ((_let_3 (@ tptp.groups3455450783089532116nteger G2))) (let ((_let_4 (@ _let_3 (@ _let_2 _let_1)))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_1) M2))) (and (=> _let_5 (= _let_4 tptp.one_one_Code_integer)) (=> (not _let_5) (= _let_4 (@ (@ tptp.times_3573771949741848930nteger (@ _let_3 (@ _let_2 N))) (@ G2 _let_1))))))))))) (forall ((N tptp.nat) (M2 tptp.nat) (G2 (-> tptp.nat tptp.complex))) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M2))) (let ((_let_3 (@ tptp.groups6464643781859351333omplex G2))) (let ((_let_4 (@ _let_3 (@ _let_2 _let_1)))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_1) M2))) (and (=> _let_5 (= _let_4 tptp.one_one_complex)) (=> (not _let_5) (= _let_4 (@ (@ tptp.times_times_complex (@ _let_3 (@ _let_2 N))) (@ G2 _let_1))))))))))) (forall ((N tptp.nat) (M2 tptp.nat) (G2 (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M2))) (let ((_let_3 (@ tptp.groups129246275422532515t_real G2))) (let ((_let_4 (@ _let_3 (@ _let_2 _let_1)))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_1) M2))) (and (=> _let_5 (= _let_4 tptp.one_one_real)) (=> (not _let_5) (= _let_4 (@ (@ tptp.times_times_real (@ _let_3 (@ _let_2 N))) (@ G2 _let_1))))))))))) (forall ((N tptp.nat) (M2 tptp.nat) (G2 (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M2))) (let ((_let_3 (@ tptp.groups73079841787564623at_rat G2))) (let ((_let_4 (@ _let_3 (@ _let_2 _let_1)))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_1) M2))) (and (=> _let_5 (= _let_4 tptp.one_one_rat)) (=> (not _let_5) (= _let_4 (@ (@ tptp.times_times_rat (@ _let_3 (@ _let_2 N))) (@ G2 _let_1))))))))))) (forall ((N tptp.nat) (M2 tptp.nat) (G2 (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M2))) (let ((_let_3 (@ tptp.groups705719431365010083at_int G2))) (let ((_let_4 (@ _let_3 (@ _let_2 _let_1)))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_1) M2))) (and (=> _let_5 (= _let_4 tptp.one_one_int)) (=> (not _let_5) (= _let_4 (@ (@ tptp.times_times_int (@ _let_3 (@ _let_2 N))) (@ G2 _let_1))))))))))) (forall ((N tptp.nat) (M2 tptp.nat) (G2 (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M2))) (let ((_let_3 (@ tptp.groups708209901874060359at_nat G2))) (let ((_let_4 (@ _let_3 (@ _let_2 _let_1)))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_1) M2))) (and (=> _let_5 (= _let_4 tptp.one_one_nat)) (=> (not _let_5) (= _let_4 (@ (@ tptp.times_times_nat (@ _let_3 (@ _let_2 N))) (@ G2 _let_1))))))))))) (forall ((G2 (-> tptp.nat tptp.int)) (N tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat N))) (= (@ (@ tptp.groups705719431365010083at_int (lambda ((I tptp.nat)) (@ G2 (@ (@ tptp.minus_minus_nat N) (@ tptp.suc I))))) _let_1) (@ (@ tptp.groups705719431365010083at_int G2) _let_1)))) (forall ((G2 (-> tptp.nat tptp.nat)) (N tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat N))) (= (@ (@ tptp.groups708209901874060359at_nat (lambda ((I tptp.nat)) (@ G2 (@ (@ tptp.minus_minus_nat N) (@ tptp.suc I))))) _let_1) (@ (@ tptp.groups708209901874060359at_nat G2) _let_1)))) (forall ((X tptp.int)) (not (= (@ tptp.set_ord_lessThan_int X) tptp.bot_bot_set_int))) (forall ((X tptp.real)) (not (= (@ tptp.set_or5984915006950818249n_real X) tptp.bot_bot_set_real))) (forall ((A tptp.int)) (not (@ tptp.finite_finite_int (@ tptp.set_ord_lessThan_int A)))) (forall ((G2 (-> tptp.nat tptp.int)) (H (-> tptp.nat tptp.int)) (A4 tptp.set_nat)) (= (@ (@ tptp.groups705719431365010083at_int (lambda ((X4 tptp.nat)) (@ (@ tptp.times_times_int (@ G2 X4)) (@ H X4)))) A4) (@ (@ tptp.times_times_int (@ (@ tptp.groups705719431365010083at_int G2) A4)) (@ (@ tptp.groups705719431365010083at_int H) A4)))) (forall ((G2 (-> tptp.int tptp.int)) (H (-> tptp.int tptp.int)) (A4 tptp.set_int)) (= (@ (@ tptp.groups1705073143266064639nt_int (lambda ((X4 tptp.int)) (@ (@ tptp.times_times_int (@ G2 X4)) (@ H X4)))) A4) (@ (@ tptp.times_times_int (@ (@ tptp.groups1705073143266064639nt_int G2) A4)) (@ (@ tptp.groups1705073143266064639nt_int H) A4)))) (forall ((G2 (-> tptp.nat tptp.nat)) (H (-> tptp.nat tptp.nat)) (A4 tptp.set_nat)) (= (@ (@ tptp.groups708209901874060359at_nat (lambda ((X4 tptp.nat)) (@ (@ tptp.times_times_nat (@ G2 X4)) (@ H X4)))) A4) (@ (@ tptp.times_times_nat (@ (@ tptp.groups708209901874060359at_nat G2) A4)) (@ (@ tptp.groups708209901874060359at_nat H) A4)))) _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 (forall ((G2 (-> tptp.nat tptp.real)) (N tptp.nat)) (= (@ (@ tptp.groups129246275422532515t_real G2) (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) (@ (@ tptp.times_times_real (@ G2 tptp.zero_zero_nat)) (@ (@ tptp.groups129246275422532515t_real (lambda ((I tptp.nat)) (@ G2 (@ tptp.suc I)))) (@ tptp.set_ord_lessThan_nat N))))) (forall ((G2 (-> tptp.nat tptp.rat)) (N tptp.nat)) (= (@ (@ tptp.groups73079841787564623at_rat G2) (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) (@ (@ tptp.times_times_rat (@ G2 tptp.zero_zero_nat)) (@ (@ tptp.groups73079841787564623at_rat (lambda ((I tptp.nat)) (@ G2 (@ tptp.suc I)))) (@ tptp.set_ord_lessThan_nat N))))) (forall ((G2 (-> tptp.nat tptp.int)) (N tptp.nat)) (= (@ (@ tptp.groups705719431365010083at_int G2) (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) (@ (@ tptp.times_times_int (@ G2 tptp.zero_zero_nat)) (@ (@ tptp.groups705719431365010083at_int (lambda ((I tptp.nat)) (@ G2 (@ tptp.suc I)))) (@ tptp.set_ord_lessThan_nat N))))) (forall ((G2 (-> tptp.nat tptp.nat)) (N tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat G2) (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) (@ (@ tptp.times_times_nat (@ G2 tptp.zero_zero_nat)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I tptp.nat)) (@ G2 (@ tptp.suc I)))) (@ tptp.set_ord_lessThan_nat N))))) (forall ((G2 (-> tptp.nat tptp.int)) (N tptp.nat)) (= (@ (@ tptp.groups705719431365010083at_int G2) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N)) (@ (@ tptp.groups705719431365010083at_int (lambda ((K3 tptp.nat)) (@ G2 (@ tptp.suc K3)))) (@ tptp.set_ord_lessThan_nat N)))) (forall ((G2 (-> tptp.nat tptp.nat)) (N tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat G2) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((K3 tptp.nat)) (@ G2 (@ tptp.suc K3)))) (@ tptp.set_ord_lessThan_nat N)))) (forall ((A4 tptp.set_complex) (F2 (-> tptp.complex tptp.real)) (G2 (-> tptp.complex tptp.real))) (=> (forall ((I3 tptp.complex)) (let ((_let_1 (@ F2 I3))) (=> (@ (@ tptp.member_complex I3) A4) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) (@ G2 I3)))))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups766887009212190081x_real F2) A4)) (@ (@ tptp.groups766887009212190081x_real G2) A4)))) (forall ((A4 tptp.set_real) (F2 (-> tptp.real tptp.real)) (G2 (-> tptp.real tptp.real))) (=> (forall ((I3 tptp.real)) (let ((_let_1 (@ F2 I3))) (=> (@ (@ tptp.member_real I3) A4) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) (@ G2 I3)))))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups1681761925125756287l_real F2) A4)) (@ (@ tptp.groups1681761925125756287l_real G2) A4)))) (forall ((A4 tptp.set_nat) (F2 (-> tptp.nat tptp.real)) (G2 (-> tptp.nat tptp.real))) (=> (forall ((I3 tptp.nat)) (let ((_let_1 (@ F2 I3))) (=> (@ (@ tptp.member_nat I3) A4) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) (@ G2 I3)))))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups129246275422532515t_real F2) A4)) (@ (@ tptp.groups129246275422532515t_real G2) A4)))) (forall ((A4 tptp.set_int) (F2 (-> tptp.int tptp.real)) (G2 (-> tptp.int tptp.real))) (=> (forall ((I3 tptp.int)) (let ((_let_1 (@ F2 I3))) (=> (@ (@ tptp.member_int I3) A4) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) (@ G2 I3)))))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups2316167850115554303t_real F2) A4)) (@ (@ tptp.groups2316167850115554303t_real G2) A4)))) (forall ((A4 tptp.set_complex) (F2 (-> tptp.complex tptp.rat)) (G2 (-> tptp.complex tptp.rat))) (=> (forall ((I3 tptp.complex)) (let ((_let_1 (@ F2 I3))) (=> (@ (@ tptp.member_complex I3) A4) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1) (@ (@ tptp.ord_less_eq_rat _let_1) (@ G2 I3)))))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups225925009352817453ex_rat F2) A4)) (@ (@ tptp.groups225925009352817453ex_rat G2) A4)))) (forall ((A4 tptp.set_real) (F2 (-> tptp.real tptp.rat)) (G2 (-> tptp.real tptp.rat))) (=> (forall ((I3 tptp.real)) (let ((_let_1 (@ F2 I3))) (=> (@ (@ tptp.member_real I3) A4) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1) (@ (@ tptp.ord_less_eq_rat _let_1) (@ G2 I3)))))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups4061424788464935467al_rat F2) A4)) (@ (@ tptp.groups4061424788464935467al_rat G2) A4)))) (forall ((A4 tptp.set_nat) (F2 (-> tptp.nat tptp.rat)) (G2 (-> tptp.nat tptp.rat))) (=> (forall ((I3 tptp.nat)) (let ((_let_1 (@ F2 I3))) (=> (@ (@ tptp.member_nat I3) A4) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1) (@ (@ tptp.ord_less_eq_rat _let_1) (@ G2 I3)))))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups73079841787564623at_rat F2) A4)) (@ (@ tptp.groups73079841787564623at_rat G2) A4)))) (forall ((A4 tptp.set_int) (F2 (-> tptp.int tptp.rat)) (G2 (-> tptp.int tptp.rat))) (=> (forall ((I3 tptp.int)) (let ((_let_1 (@ F2 I3))) (=> (@ (@ tptp.member_int I3) A4) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1) (@ (@ tptp.ord_less_eq_rat _let_1) (@ G2 I3)))))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups1072433553688619179nt_rat F2) A4)) (@ (@ tptp.groups1072433553688619179nt_rat G2) A4)))) (forall ((A4 tptp.set_complex) (F2 (-> tptp.complex tptp.nat)) (G2 (-> tptp.complex tptp.nat))) (=> (forall ((I3 tptp.complex)) (let ((_let_1 (@ F2 I3))) (=> (@ (@ tptp.member_complex I3) A4) (and (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) _let_1) (@ (@ tptp.ord_less_eq_nat _let_1) (@ G2 I3)))))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups861055069439313189ex_nat F2) A4)) (@ (@ tptp.groups861055069439313189ex_nat G2) A4)))) (forall ((A4 tptp.set_real) (F2 (-> tptp.real tptp.nat)) (G2 (-> tptp.real tptp.nat))) (=> (forall ((I3 tptp.real)) (let ((_let_1 (@ F2 I3))) (=> (@ (@ tptp.member_real I3) A4) (and (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) _let_1) (@ (@ tptp.ord_less_eq_nat _let_1) (@ G2 I3)))))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups4696554848551431203al_nat F2) A4)) (@ (@ tptp.groups4696554848551431203al_nat G2) A4)))) (forall ((A4 tptp.set_nat) (F2 (-> tptp.nat tptp.int))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A4) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F2 X3)))) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.groups705719431365010083at_int F2) A4)))) (forall ((A4 tptp.set_int) (F2 (-> tptp.int tptp.int))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A4) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F2 X3)))) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.groups1705073143266064639nt_int F2) A4)))) (forall ((A4 tptp.set_nat) (F2 (-> tptp.nat tptp.nat))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A4) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F2 X3)))) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ (@ tptp.groups708209901874060359at_nat F2) A4)))) (forall ((A4 tptp.set_nat) (F2 (-> tptp.nat tptp.int))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A4) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ F2 X3)))) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.groups705719431365010083at_int F2) A4)))) (forall ((A4 tptp.set_int) (F2 (-> tptp.int tptp.int))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A4) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ F2 X3)))) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.groups1705073143266064639nt_int F2) A4)))) (forall ((A4 tptp.set_nat) (F2 (-> tptp.nat tptp.nat))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A4) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F2 X3)))) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.groups708209901874060359at_nat F2) A4)))) (forall ((A4 tptp.set_complex) (F2 (-> tptp.complex tptp.code_integer))) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) A4) (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (@ F2 X3)))) (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (@ (@ tptp.groups8682486955453173170nteger F2) A4)))) (forall ((A4 tptp.set_real) (F2 (-> tptp.real tptp.code_integer))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) A4) (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (@ F2 X3)))) (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (@ (@ tptp.groups6225526099057966256nteger F2) A4)))) (forall ((A4 tptp.set_nat) (F2 (-> tptp.nat tptp.code_integer))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A4) (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (@ F2 X3)))) (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (@ (@ tptp.groups3455450783089532116nteger F2) A4)))) (forall ((A4 tptp.set_int) (F2 (-> tptp.int tptp.code_integer))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A4) (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (@ F2 X3)))) (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (@ (@ tptp.groups3827104343326376752nteger F2) A4)))) (forall ((A4 tptp.set_complex) (F2 (-> tptp.complex tptp.real))) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) A4) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F2 X3)))) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ (@ tptp.groups766887009212190081x_real F2) A4)))) (forall ((A4 tptp.set_real) (F2 (-> tptp.real tptp.real))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) A4) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F2 X3)))) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ (@ tptp.groups1681761925125756287l_real F2) A4)))) (forall ((A4 tptp.set_nat) (F2 (-> tptp.nat tptp.real))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A4) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F2 X3)))) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ (@ tptp.groups129246275422532515t_real F2) A4)))) (forall ((A4 tptp.set_int) (F2 (-> tptp.int tptp.real))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A4) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F2 X3)))) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ (@ tptp.groups2316167850115554303t_real F2) A4)))) (forall ((A4 tptp.set_complex) (F2 (-> tptp.complex tptp.rat))) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) A4) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ F2 X3)))) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ (@ tptp.groups225925009352817453ex_rat F2) A4)))) (forall ((A4 tptp.set_real) (F2 (-> tptp.real tptp.rat))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) A4) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ F2 X3)))) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ (@ tptp.groups4061424788464935467al_rat F2) A4)))) (forall ((A4 tptp.set_nat) (F2 (-> tptp.nat tptp.complex))) (=> (@ tptp.finite_finite_nat A4) (=> (exists ((X5 tptp.nat)) (and (@ (@ tptp.member_nat X5) A4) (= (@ F2 X5) tptp.zero_zero_complex))) (= (@ (@ tptp.groups6464643781859351333omplex F2) A4) tptp.zero_zero_complex)))) (forall ((A4 tptp.set_int) (F2 (-> tptp.int tptp.complex))) (=> (@ tptp.finite_finite_int A4) (=> (exists ((X5 tptp.int)) (and (@ (@ tptp.member_int X5) A4) (= (@ F2 X5) tptp.zero_zero_complex))) (= (@ (@ tptp.groups7440179247065528705omplex F2) A4) tptp.zero_zero_complex)))) (forall ((A4 tptp.set_complex) (F2 (-> tptp.complex tptp.complex))) (=> (@ tptp.finite3207457112153483333omplex A4) (=> (exists ((X5 tptp.complex)) (and (@ (@ tptp.member_complex X5) A4) (= (@ F2 X5) tptp.zero_zero_complex))) (= (@ (@ tptp.groups3708469109370488835omplex F2) A4) tptp.zero_zero_complex)))) (forall ((A4 tptp.set_nat) (F2 (-> tptp.nat tptp.real))) (=> (@ tptp.finite_finite_nat A4) (=> (exists ((X5 tptp.nat)) (and (@ (@ tptp.member_nat X5) A4) (= (@ F2 X5) tptp.zero_zero_real))) (= (@ (@ tptp.groups129246275422532515t_real F2) A4) tptp.zero_zero_real)))) (forall ((A4 tptp.set_int) (F2 (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int A4) (=> (exists ((X5 tptp.int)) (and (@ (@ tptp.member_int X5) A4) (= (@ F2 X5) tptp.zero_zero_real))) (= (@ (@ tptp.groups2316167850115554303t_real F2) A4) tptp.zero_zero_real)))) (forall ((A4 tptp.set_complex) (F2 (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex A4) (=> (exists ((X5 tptp.complex)) (and (@ (@ tptp.member_complex X5) A4) (= (@ F2 X5) tptp.zero_zero_real))) (= (@ (@ tptp.groups766887009212190081x_real F2) A4) tptp.zero_zero_real)))) (forall ((A4 tptp.set_nat) (F2 (-> tptp.nat tptp.rat))) (=> (@ tptp.finite_finite_nat A4) (=> (exists ((X5 tptp.nat)) (and (@ (@ tptp.member_nat X5) A4) (= (@ F2 X5) tptp.zero_zero_rat))) (= (@ (@ tptp.groups73079841787564623at_rat F2) A4) tptp.zero_zero_rat)))) (forall ((A4 tptp.set_int) (F2 (-> tptp.int tptp.rat))) (=> (@ tptp.finite_finite_int A4) (=> (exists ((X5 tptp.int)) (and (@ (@ tptp.member_int X5) A4) (= (@ F2 X5) tptp.zero_zero_rat))) (= (@ (@ tptp.groups1072433553688619179nt_rat F2) A4) tptp.zero_zero_rat)))) (forall ((A4 tptp.set_complex) (F2 (-> tptp.complex tptp.rat))) (=> (@ tptp.finite3207457112153483333omplex A4) (=> (exists ((X5 tptp.complex)) (and (@ (@ tptp.member_complex X5) A4) (= (@ F2 X5) tptp.zero_zero_rat))) (= (@ (@ tptp.groups225925009352817453ex_rat F2) A4) tptp.zero_zero_rat)))) (forall ((A4 tptp.set_int) (F2 (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int A4) (=> (exists ((X5 tptp.int)) (and (@ (@ tptp.member_int X5) A4) (= (@ F2 X5) tptp.zero_zero_nat))) (= (@ (@ tptp.groups1707563613775114915nt_nat F2) A4) tptp.zero_zero_nat)))) (forall ((F2 (-> tptp.nat tptp.code_integer)) (A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.groups3455450783089532116nteger F2) (@ (@ tptp.set_or1269000886237332187st_nat A) B)) (@ (@ (@ (@ tptp.set_fo1084959871951514735nteger (lambda ((A5 tptp.nat) (__flatten_var_0 tptp.code_integer)) (@ (@ tptp.times_3573771949741848930nteger (@ F2 A5)) __flatten_var_0))) A) B) tptp.one_one_Code_integer))) (forall ((F2 (-> tptp.nat tptp.complex)) (A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.groups6464643781859351333omplex F2) (@ (@ tptp.set_or1269000886237332187st_nat A) B)) (@ (@ (@ (@ tptp.set_fo1517530859248394432omplex (lambda ((A5 tptp.nat) (__flatten_var_0 tptp.complex)) (@ (@ tptp.times_times_complex (@ F2 A5)) __flatten_var_0))) A) B) tptp.one_one_complex))) (forall ((F2 (-> tptp.nat tptp.real)) (A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.groups129246275422532515t_real F2) (@ (@ tptp.set_or1269000886237332187st_nat A) B)) (@ (@ (@ (@ tptp.set_fo3111899725591712190t_real (lambda ((A5 tptp.nat) (__flatten_var_0 tptp.real)) (@ (@ tptp.times_times_real (@ F2 A5)) __flatten_var_0))) A) B) tptp.one_one_real))) (forall ((F2 (-> tptp.nat tptp.rat)) (A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.groups73079841787564623at_rat F2) (@ (@ tptp.set_or1269000886237332187st_nat A) B)) (@ (@ (@ (@ tptp.set_fo1949268297981939178at_rat (lambda ((A5 tptp.nat) (__flatten_var_0 tptp.rat)) (@ (@ tptp.times_times_rat (@ F2 A5)) __flatten_var_0))) A) B) tptp.one_one_rat))) (forall ((F2 (-> tptp.nat tptp.int)) (A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.groups705719431365010083at_int F2) (@ (@ tptp.set_or1269000886237332187st_nat A) B)) (@ (@ (@ (@ tptp.set_fo2581907887559384638at_int (lambda ((A5 tptp.nat) (__flatten_var_0 tptp.int)) (@ (@ tptp.times_times_int (@ F2 A5)) __flatten_var_0))) A) B) tptp.one_one_int))) (forall ((F2 (-> tptp.nat tptp.nat)) (A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat F2) (@ (@ tptp.set_or1269000886237332187st_nat A) B)) (@ (@ (@ (@ tptp.set_fo2584398358068434914at_nat (lambda ((A5 tptp.nat) (__flatten_var_0 tptp.nat)) (@ (@ tptp.times_times_nat (@ F2 A5)) __flatten_var_0))) A) B) tptp.one_one_nat))) (forall ((N tptp.nat)) (= (= (@ tptp.set_ord_lessThan_nat N) tptp.bot_bot_set_nat) (= N tptp.bot_bot_nat))) (forall ((M2 tptp.real) (N tptp.real)) (= (@ (@ tptp.ord_less_set_real (@ tptp.set_or5984915006950818249n_real M2)) (@ tptp.set_or5984915006950818249n_real N)) (@ (@ tptp.ord_less_real M2) N))) (forall ((M2 tptp.rat) (N tptp.rat)) (= (@ (@ tptp.ord_less_set_rat (@ tptp.set_ord_lessThan_rat M2)) (@ tptp.set_ord_lessThan_rat N)) (@ (@ tptp.ord_less_rat M2) N))) (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_set_num (@ tptp.set_ord_lessThan_num M2)) (@ tptp.set_ord_lessThan_num N)) (@ (@ tptp.ord_less_num M2) N))) (forall ((M2 tptp.int) (N tptp.int)) (= (@ (@ tptp.ord_less_set_int (@ tptp.set_ord_lessThan_int M2)) (@ tptp.set_ord_lessThan_int N)) (@ (@ tptp.ord_less_int M2) N))) (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_set_nat (@ tptp.set_ord_lessThan_nat M2)) (@ tptp.set_ord_lessThan_nat N)) (@ (@ tptp.ord_less_nat M2) N))) (forall ((K2 tptp.nat)) (= (@ tptp.set_ord_lessThan_nat (@ tptp.suc K2)) (@ (@ tptp.insert_nat K2) (@ tptp.set_ord_lessThan_nat K2)))) (forall ((N tptp.nat)) (= (= (@ tptp.set_ord_lessThan_nat N) tptp.bot_bot_set_nat) (= N tptp.zero_zero_nat))) _let_247 _let_246 _let_245 (forall ((G2 (-> tptp.nat tptp.int)) (M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups705719431365010083at_int G2) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M2)) (@ tptp.suc N))) (@ (@ tptp.groups705719431365010083at_int (lambda ((I tptp.nat)) (@ G2 (@ tptp.suc I)))) (@ (@ tptp.set_or1269000886237332187st_nat M2) N)))) (forall ((G2 (-> tptp.nat tptp.nat)) (M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat G2) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M2)) (@ tptp.suc N))) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I tptp.nat)) (@ G2 (@ tptp.suc I)))) (@ (@ tptp.set_or1269000886237332187st_nat M2) N)))) (forall ((G2 (-> tptp.nat tptp.int)) (M2 tptp.nat) (K2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups705719431365010083at_int G2) (@ (@ tptp.set_or1269000886237332187st_nat (@ (@ tptp.plus_plus_nat M2) K2)) (@ (@ tptp.plus_plus_nat N) K2))) (@ (@ tptp.groups705719431365010083at_int (lambda ((I tptp.nat)) (@ G2 (@ (@ tptp.plus_plus_nat I) K2)))) (@ (@ tptp.set_or1269000886237332187st_nat M2) N)))) (forall ((G2 (-> tptp.nat tptp.nat)) (M2 tptp.nat) (K2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat G2) (@ (@ tptp.set_or1269000886237332187st_nat (@ (@ tptp.plus_plus_nat M2) K2)) (@ (@ tptp.plus_plus_nat N) K2))) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I tptp.nat)) (@ G2 (@ (@ tptp.plus_plus_nat I) K2)))) (@ (@ tptp.set_or1269000886237332187st_nat M2) N)))) (forall ((A4 tptp.set_complex) (F2 (-> tptp.complex tptp.code_integer))) (=> (forall ((X3 tptp.complex)) (let ((_let_1 (@ F2 X3))) (=> (@ (@ tptp.member_complex X3) A4) (and (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) _let_1) (@ (@ tptp.ord_le3102999989581377725nteger _let_1) tptp.one_one_Code_integer))))) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.groups8682486955453173170nteger F2) A4)) tptp.one_one_Code_integer))) (forall ((A4 tptp.set_real) (F2 (-> tptp.real tptp.code_integer))) (=> (forall ((X3 tptp.real)) (let ((_let_1 (@ F2 X3))) (=> (@ (@ tptp.member_real X3) A4) (and (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) _let_1) (@ (@ tptp.ord_le3102999989581377725nteger _let_1) tptp.one_one_Code_integer))))) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.groups6225526099057966256nteger F2) A4)) tptp.one_one_Code_integer))) (forall ((A4 tptp.set_nat) (F2 (-> tptp.nat tptp.code_integer))) (=> (forall ((X3 tptp.nat)) (let ((_let_1 (@ F2 X3))) (=> (@ (@ tptp.member_nat X3) A4) (and (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) _let_1) (@ (@ tptp.ord_le3102999989581377725nteger _let_1) tptp.one_one_Code_integer))))) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.groups3455450783089532116nteger F2) A4)) tptp.one_one_Code_integer))) (forall ((A4 tptp.set_int) (F2 (-> tptp.int tptp.code_integer))) (=> (forall ((X3 tptp.int)) (let ((_let_1 (@ F2 X3))) (=> (@ (@ tptp.member_int X3) A4) (and (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) _let_1) (@ (@ tptp.ord_le3102999989581377725nteger _let_1) tptp.one_one_Code_integer))))) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.groups3827104343326376752nteger F2) A4)) tptp.one_one_Code_integer))) (forall ((A4 tptp.set_complex) (F2 (-> tptp.complex tptp.real))) (=> (forall ((X3 tptp.complex)) (let ((_let_1 (@ F2 X3))) (=> (@ (@ tptp.member_complex X3) A4) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) tptp.one_one_real))))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups766887009212190081x_real F2) A4)) tptp.one_one_real))) (forall ((A4 tptp.set_real) (F2 (-> tptp.real tptp.real))) (=> (forall ((X3 tptp.real)) (let ((_let_1 (@ F2 X3))) (=> (@ (@ tptp.member_real X3) A4) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) tptp.one_one_real))))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups1681761925125756287l_real F2) A4)) tptp.one_one_real))) (forall ((A4 tptp.set_nat) (F2 (-> tptp.nat tptp.real))) (=> (forall ((X3 tptp.nat)) (let ((_let_1 (@ F2 X3))) (=> (@ (@ tptp.member_nat X3) A4) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) tptp.one_one_real))))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups129246275422532515t_real F2) A4)) tptp.one_one_real))) (forall ((A4 tptp.set_int) (F2 (-> tptp.int tptp.real))) (=> (forall ((X3 tptp.int)) (let ((_let_1 (@ F2 X3))) (=> (@ (@ tptp.member_int X3) A4) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) tptp.one_one_real))))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups2316167850115554303t_real F2) A4)) tptp.one_one_real))) (forall ((A4 tptp.set_complex) (F2 (-> tptp.complex tptp.rat))) (=> (forall ((X3 tptp.complex)) (let ((_let_1 (@ F2 X3))) (=> (@ (@ tptp.member_complex X3) A4) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1) (@ (@ tptp.ord_less_eq_rat _let_1) tptp.one_one_rat))))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups225925009352817453ex_rat F2) A4)) tptp.one_one_rat))) (forall ((A4 tptp.set_real) (F2 (-> tptp.real tptp.rat))) (=> (forall ((X3 tptp.real)) (let ((_let_1 (@ F2 X3))) (=> (@ (@ tptp.member_real X3) A4) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1) (@ (@ tptp.ord_less_eq_rat _let_1) tptp.one_one_rat))))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups4061424788464935467al_rat F2) A4)) tptp.one_one_rat))) (forall ((R2 (-> tptp.code_integer tptp.code_integer Bool)) (S3 tptp.set_nat) (H (-> tptp.nat tptp.code_integer)) (G2 (-> tptp.nat tptp.code_integer))) (=> (@ (@ R2 tptp.one_one_Code_integer) tptp.one_one_Code_integer) (=> (forall ((X15 tptp.code_integer) (Y15 tptp.code_integer) (X23 tptp.code_integer) (Y23 tptp.code_integer)) (=> (and (@ (@ R2 X15) X23) (@ (@ R2 Y15) Y23)) (@ (@ R2 (@ (@ tptp.times_3573771949741848930nteger X15) Y15)) (@ (@ tptp.times_3573771949741848930nteger X23) Y23)))) (=> (@ tptp.finite_finite_nat S3) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) S3) (@ (@ R2 (@ H X3)) (@ G2 X3)))) (@ (@ R2 (@ (@ tptp.groups3455450783089532116nteger H) S3)) (@ (@ tptp.groups3455450783089532116nteger G2) S3))))))) (forall ((R2 (-> tptp.code_integer tptp.code_integer Bool)) (S3 tptp.set_int) (H (-> tptp.int tptp.code_integer)) (G2 (-> tptp.int tptp.code_integer))) (=> (@ (@ R2 tptp.one_one_Code_integer) tptp.one_one_Code_integer) (=> (forall ((X15 tptp.code_integer) (Y15 tptp.code_integer) (X23 tptp.code_integer) (Y23 tptp.code_integer)) (=> (and (@ (@ R2 X15) X23) (@ (@ R2 Y15) Y23)) (@ (@ R2 (@ (@ tptp.times_3573771949741848930nteger X15) Y15)) (@ (@ tptp.times_3573771949741848930nteger X23) Y23)))) (=> (@ tptp.finite_finite_int S3) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) S3) (@ (@ R2 (@ H X3)) (@ G2 X3)))) (@ (@ R2 (@ (@ tptp.groups3827104343326376752nteger H) S3)) (@ (@ tptp.groups3827104343326376752nteger G2) S3))))))) (forall ((R2 (-> tptp.code_integer tptp.code_integer Bool)) (S3 tptp.set_complex) (H (-> tptp.complex tptp.code_integer)) (G2 (-> tptp.complex tptp.code_integer))) (=> (@ (@ R2 tptp.one_one_Code_integer) tptp.one_one_Code_integer) (=> (forall ((X15 tptp.code_integer) (Y15 tptp.code_integer) (X23 tptp.code_integer) (Y23 tptp.code_integer)) (=> (and (@ (@ R2 X15) X23) (@ (@ R2 Y15) Y23)) (@ (@ R2 (@ (@ tptp.times_3573771949741848930nteger X15) Y15)) (@ (@ tptp.times_3573771949741848930nteger X23) Y23)))) (=> (@ tptp.finite3207457112153483333omplex S3) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) S3) (@ (@ R2 (@ H X3)) (@ G2 X3)))) (@ (@ R2 (@ (@ tptp.groups8682486955453173170nteger H) S3)) (@ (@ tptp.groups8682486955453173170nteger G2) S3))))))) (forall ((R2 (-> tptp.complex tptp.complex Bool)) (S3 tptp.set_nat) (H (-> tptp.nat tptp.complex)) (G2 (-> tptp.nat tptp.complex))) (=> (@ (@ R2 tptp.one_one_complex) tptp.one_one_complex) (=> (forall ((X15 tptp.complex) (Y15 tptp.complex) (X23 tptp.complex) (Y23 tptp.complex)) (=> (and (@ (@ R2 X15) X23) (@ (@ R2 Y15) Y23)) (@ (@ R2 (@ (@ tptp.times_times_complex X15) Y15)) (@ (@ tptp.times_times_complex X23) Y23)))) (=> (@ tptp.finite_finite_nat S3) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) S3) (@ (@ R2 (@ H X3)) (@ G2 X3)))) (@ (@ R2 (@ (@ tptp.groups6464643781859351333omplex H) S3)) (@ (@ tptp.groups6464643781859351333omplex G2) S3))))))) (forall ((R2 (-> tptp.complex tptp.complex Bool)) (S3 tptp.set_int) (H (-> tptp.int tptp.complex)) (G2 (-> tptp.int tptp.complex))) (=> (@ (@ R2 tptp.one_one_complex) tptp.one_one_complex) (=> (forall ((X15 tptp.complex) (Y15 tptp.complex) (X23 tptp.complex) (Y23 tptp.complex)) (=> (and (@ (@ R2 X15) X23) (@ (@ R2 Y15) Y23)) (@ (@ R2 (@ (@ tptp.times_times_complex X15) Y15)) (@ (@ tptp.times_times_complex X23) Y23)))) (=> (@ tptp.finite_finite_int S3) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) S3) (@ (@ R2 (@ H X3)) (@ G2 X3)))) (@ (@ R2 (@ (@ tptp.groups7440179247065528705omplex H) S3)) (@ (@ tptp.groups7440179247065528705omplex G2) S3))))))) (forall ((R2 (-> tptp.complex tptp.complex Bool)) (S3 tptp.set_complex) (H (-> tptp.complex tptp.complex)) (G2 (-> tptp.complex tptp.complex))) (=> (@ (@ R2 tptp.one_one_complex) tptp.one_one_complex) (=> (forall ((X15 tptp.complex) (Y15 tptp.complex) (X23 tptp.complex) (Y23 tptp.complex)) (=> (and (@ (@ R2 X15) X23) (@ (@ R2 Y15) Y23)) (@ (@ R2 (@ (@ tptp.times_times_complex X15) Y15)) (@ (@ tptp.times_times_complex X23) Y23)))) (=> (@ tptp.finite3207457112153483333omplex S3) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) S3) (@ (@ R2 (@ H X3)) (@ G2 X3)))) (@ (@ R2 (@ (@ tptp.groups3708469109370488835omplex H) S3)) (@ (@ tptp.groups3708469109370488835omplex G2) S3))))))) (forall ((R2 (-> tptp.real tptp.real Bool)) (S3 tptp.set_nat) (H (-> tptp.nat tptp.real)) (G2 (-> tptp.nat tptp.real))) (=> (@ (@ R2 tptp.one_one_real) tptp.one_one_real) (=> (forall ((X15 tptp.real) (Y15 tptp.real) (X23 tptp.real) (Y23 tptp.real)) (=> (and (@ (@ R2 X15) X23) (@ (@ R2 Y15) Y23)) (@ (@ R2 (@ (@ tptp.times_times_real X15) Y15)) (@ (@ tptp.times_times_real X23) Y23)))) (=> (@ tptp.finite_finite_nat S3) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) S3) (@ (@ R2 (@ H X3)) (@ G2 X3)))) (@ (@ R2 (@ (@ tptp.groups129246275422532515t_real H) S3)) (@ (@ tptp.groups129246275422532515t_real G2) S3))))))) (forall ((R2 (-> tptp.real tptp.real Bool)) (S3 tptp.set_int) (H (-> tptp.int tptp.real)) (G2 (-> tptp.int tptp.real))) (=> (@ (@ R2 tptp.one_one_real) tptp.one_one_real) (=> (forall ((X15 tptp.real) (Y15 tptp.real) (X23 tptp.real) (Y23 tptp.real)) (=> (and (@ (@ R2 X15) X23) (@ (@ R2 Y15) Y23)) (@ (@ R2 (@ (@ tptp.times_times_real X15) Y15)) (@ (@ tptp.times_times_real X23) Y23)))) (=> (@ tptp.finite_finite_int S3) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) S3) (@ (@ R2 (@ H X3)) (@ G2 X3)))) (@ (@ R2 (@ (@ tptp.groups2316167850115554303t_real H) S3)) (@ (@ tptp.groups2316167850115554303t_real G2) S3))))))) (forall ((R2 (-> tptp.real tptp.real Bool)) (S3 tptp.set_complex) (H (-> tptp.complex tptp.real)) (G2 (-> tptp.complex tptp.real))) (=> (@ (@ R2 tptp.one_one_real) tptp.one_one_real) (=> (forall ((X15 tptp.real) (Y15 tptp.real) (X23 tptp.real) (Y23 tptp.real)) (=> (and (@ (@ R2 X15) X23) (@ (@ R2 Y15) Y23)) (@ (@ R2 (@ (@ tptp.times_times_real X15) Y15)) (@ (@ tptp.times_times_real X23) Y23)))) (=> (@ tptp.finite3207457112153483333omplex S3) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) S3) (@ (@ R2 (@ H X3)) (@ G2 X3)))) (@ (@ R2 (@ (@ tptp.groups766887009212190081x_real H) S3)) (@ (@ tptp.groups766887009212190081x_real G2) S3))))))) (forall ((R2 (-> tptp.rat tptp.rat Bool)) (S3 tptp.set_nat) (H (-> tptp.nat tptp.rat)) (G2 (-> tptp.nat tptp.rat))) (=> (@ (@ R2 tptp.one_one_rat) tptp.one_one_rat) (=> (forall ((X15 tptp.rat) (Y15 tptp.rat) (X23 tptp.rat) (Y23 tptp.rat)) (=> (and (@ (@ R2 X15) X23) (@ (@ R2 Y15) Y23)) (@ (@ R2 (@ (@ tptp.times_times_rat X15) Y15)) (@ (@ tptp.times_times_rat X23) Y23)))) (=> (@ tptp.finite_finite_nat S3) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) S3) (@ (@ R2 (@ H X3)) (@ G2 X3)))) (@ (@ R2 (@ (@ tptp.groups73079841787564623at_rat H) S3)) (@ (@ tptp.groups73079841787564623at_rat G2) S3))))))) (forall ((A4 tptp.set_real) (X tptp.real) (G2 (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.groups1681761925125756287l_real G2))) (let ((_let_2 (@ _let_1 A4))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_real X) A4)))) (let ((_let_4 (@ (@ tptp.member_real X) A4))) (=> (@ tptp.finite_finite_real A4) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.times_times_real (@ G2 X)) _let_2)))))))))) (forall ((A4 tptp.set_nat) (X tptp.nat) (G2 (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.groups129246275422532515t_real G2))) (let ((_let_2 (@ _let_1 A4))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_nat X) A4)))) (let ((_let_4 (@ (@ tptp.member_nat X) A4))) (=> (@ tptp.finite_finite_nat A4) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.times_times_real (@ G2 X)) _let_2)))))))))) (forall ((A4 tptp.set_int) (X tptp.int) (G2 (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups2316167850115554303t_real G2))) (let ((_let_2 (@ _let_1 A4))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_int X) A4)))) (let ((_let_4 (@ (@ tptp.member_int X) A4))) (=> (@ tptp.finite_finite_int A4) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.times_times_real (@ G2 X)) _let_2)))))))))) (forall ((A4 tptp.set_complex) (X tptp.complex) (G2 (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups766887009212190081x_real G2))) (let ((_let_2 (@ _let_1 A4))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_complex X) A4)))) (let ((_let_4 (@ (@ tptp.member_complex X) A4))) (=> (@ tptp.finite3207457112153483333omplex A4) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.times_times_real (@ G2 X)) _let_2)))))))))) (forall ((A4 tptp.set_real) (X tptp.real) (G2 (-> tptp.real tptp.rat))) (let ((_let_1 (@ tptp.groups4061424788464935467al_rat G2))) (let ((_let_2 (@ _let_1 A4))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_real X) A4)))) (let ((_let_4 (@ (@ tptp.member_real X) A4))) (=> (@ tptp.finite_finite_real A4) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.times_times_rat (@ G2 X)) _let_2)))))))))) (forall ((A4 tptp.set_nat) (X tptp.nat) (G2 (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups73079841787564623at_rat G2))) (let ((_let_2 (@ _let_1 A4))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_nat X) A4)))) (let ((_let_4 (@ (@ tptp.member_nat X) A4))) (=> (@ tptp.finite_finite_nat A4) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.times_times_rat (@ G2 X)) _let_2)))))))))) (forall ((A4 tptp.set_int) (X tptp.int) (G2 (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups1072433553688619179nt_rat G2))) (let ((_let_2 (@ _let_1 A4))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_int X) A4)))) (let ((_let_4 (@ (@ tptp.member_int X) A4))) (=> (@ tptp.finite_finite_int A4) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.times_times_rat (@ G2 X)) _let_2)))))))))) (forall ((A4 tptp.set_complex) (X tptp.complex) (G2 (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups225925009352817453ex_rat G2))) (let ((_let_2 (@ _let_1 A4))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_complex X) A4)))) (let ((_let_4 (@ (@ tptp.member_complex X) A4))) (=> (@ tptp.finite3207457112153483333omplex A4) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.times_times_rat (@ G2 X)) _let_2)))))))))) (forall ((A4 tptp.set_real) (X tptp.real) (G2 (-> tptp.real tptp.nat))) (let ((_let_1 (@ tptp.groups4696554848551431203al_nat G2))) (let ((_let_2 (@ _let_1 A4))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_real X) A4)))) (let ((_let_4 (@ (@ tptp.member_real X) A4))) (=> (@ tptp.finite_finite_real A4) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.times_times_nat (@ G2 X)) _let_2)))))))))) (forall ((A4 tptp.set_int) (X tptp.int) (G2 (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups1707563613775114915nt_nat G2))) (let ((_let_2 (@ _let_1 A4))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_int X) A4)))) (let ((_let_4 (@ (@ tptp.member_int X) A4))) (=> (@ tptp.finite_finite_int A4) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.times_times_nat (@ G2 X)) _let_2)))))))))) (forall ((L tptp.nat) (U tptp.nat)) (= (@ (@ tptp.inf_inf_set_nat (@ tptp.set_ord_lessThan_nat L)) (@ (@ tptp.set_or1269000886237332187st_nat L) U)) tptp.bot_bot_set_nat)) (forall ((L tptp.int) (U tptp.int)) (= (@ (@ tptp.inf_inf_set_int (@ tptp.set_ord_lessThan_int L)) (@ (@ tptp.set_or1266510415728281911st_int L) U)) tptp.bot_bot_set_int)) (forall ((L tptp.real) (U tptp.real)) (= (@ (@ tptp.inf_inf_set_real (@ tptp.set_or5984915006950818249n_real L)) (@ (@ tptp.set_or1222579329274155063t_real L) U)) tptp.bot_bot_set_real)) (forall ((G2 (-> tptp.nat tptp.int)) (N tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat N) M2))) (= (@ (@ tptp.groups705719431365010083at_int G2) _let_1) (@ (@ tptp.groups705719431365010083at_int (lambda ((I tptp.nat)) (@ G2 (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M2) N)) I)))) _let_1)))) (forall ((G2 (-> tptp.nat tptp.nat)) (N tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat N) M2))) (= (@ (@ tptp.groups708209901874060359at_nat G2) _let_1) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I tptp.nat)) (@ G2 (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M2) N)) I)))) _let_1)))) (forall ((G2 (-> tptp.nat tptp.nat)) (N tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat N))) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I tptp.nat)) (@ G2 (@ (@ tptp.minus_minus_nat N) (@ tptp.suc I))))) _let_1) (@ (@ tptp.groups3542108847815614940at_nat G2) _let_1)))) (forall ((G2 (-> tptp.nat tptp.real)) (N tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat N))) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I tptp.nat)) (@ G2 (@ (@ tptp.minus_minus_nat N) (@ tptp.suc I))))) _let_1) (@ (@ tptp.groups6591440286371151544t_real G2) _let_1)))) (forall ((Q (-> tptp.nat tptp.nat)) (P2 (-> tptp.nat tptp.nat)) (N tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat N))) (=> (forall ((X3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ Q X3)) (@ P2 X3))) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.groups3542108847815614940at_nat P2) _let_1)) (@ (@ tptp.groups3542108847815614940at_nat Q) _let_1)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X4 tptp.nat)) (@ (@ tptp.minus_minus_nat (@ P2 X4)) (@ Q X4)))) _let_1))))) (forall ((I5 tptp.set_real) (I2 tptp.real) (F2 (-> tptp.real tptp.code_integer))) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer))) (=> (@ tptp.finite_finite_real I5) (=> (@ (@ tptp.member_real I2) I5) (=> (@ _let_1 (@ F2 I2)) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) I5) (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (@ F2 I3)))) (@ _let_1 (@ (@ tptp.groups6225526099057966256nteger F2) I5)))))))) (forall ((I5 tptp.set_nat) (I2 tptp.nat) (F2 (-> tptp.nat tptp.code_integer))) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer))) (=> (@ tptp.finite_finite_nat I5) (=> (@ (@ tptp.member_nat I2) I5) (=> (@ _let_1 (@ F2 I2)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.member_nat I3) I5) (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (@ F2 I3)))) (@ _let_1 (@ (@ tptp.groups3455450783089532116nteger F2) I5)))))))) (forall ((I5 tptp.set_int) (I2 tptp.int) (F2 (-> tptp.int tptp.code_integer))) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer))) (=> (@ tptp.finite_finite_int I5) (=> (@ (@ tptp.member_int I2) I5) (=> (@ _let_1 (@ F2 I2)) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) I5) (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (@ F2 I3)))) (@ _let_1 (@ (@ tptp.groups3827104343326376752nteger F2) I5)))))))) (forall ((I5 tptp.set_complex) (I2 tptp.complex) (F2 (-> tptp.complex tptp.code_integer))) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer))) (=> (@ tptp.finite3207457112153483333omplex I5) (=> (@ (@ tptp.member_complex I2) I5) (=> (@ _let_1 (@ F2 I2)) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) I5) (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (@ F2 I3)))) (@ _let_1 (@ (@ tptp.groups8682486955453173170nteger F2) I5)))))))) (forall ((I5 tptp.set_real) (I2 tptp.real) (F2 (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ tptp.finite_finite_real I5) (=> (@ (@ tptp.member_real I2) I5) (=> (@ _let_1 (@ F2 I2)) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) I5) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F2 I3)))) (@ _let_1 (@ (@ tptp.groups1681761925125756287l_real F2) I5)))))))) (forall ((I5 tptp.set_nat) (I2 tptp.nat) (F2 (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ tptp.finite_finite_nat I5) (=> (@ (@ tptp.member_nat I2) I5) (=> (@ _let_1 (@ F2 I2)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.member_nat I3) I5) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F2 I3)))) (@ _let_1 (@ (@ tptp.groups129246275422532515t_real F2) I5)))))))) (forall ((I5 tptp.set_int) (I2 tptp.int) (F2 (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ tptp.finite_finite_int I5) (=> (@ (@ tptp.member_int I2) I5) (=> (@ _let_1 (@ F2 I2)) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) I5) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F2 I3)))) (@ _let_1 (@ (@ tptp.groups2316167850115554303t_real F2) I5)))))))) (forall ((I5 tptp.set_complex) (I2 tptp.complex) (F2 (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ tptp.finite3207457112153483333omplex I5) (=> (@ (@ tptp.member_complex I2) I5) (=> (@ _let_1 (@ F2 I2)) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) I5) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F2 I3)))) (@ _let_1 (@ (@ tptp.groups766887009212190081x_real F2) I5)))))))) (forall ((I5 tptp.set_real) (I2 tptp.real) (F2 (-> tptp.real tptp.rat))) (let ((_let_1 (@ tptp.ord_less_rat tptp.one_one_rat))) (=> (@ tptp.finite_finite_real I5) (=> (@ (@ tptp.member_real I2) I5) (=> (@ _let_1 (@ F2 I2)) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) I5) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ F2 I3)))) (@ _let_1 (@ (@ tptp.groups4061424788464935467al_rat F2) I5)))))))) (forall ((I5 tptp.set_nat) (I2 tptp.nat) (F2 (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.ord_less_rat tptp.one_one_rat))) (=> (@ tptp.finite_finite_nat I5) (=> (@ (@ tptp.member_nat I2) I5) (=> (@ _let_1 (@ F2 I2)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.member_nat I3) I5) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ F2 I3)))) (@ _let_1 (@ (@ tptp.groups73079841787564623at_rat F2) I5)))))))) (forall ((B5 tptp.set_int) (A4 tptp.set_int) (G2 (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups2316167850115554303t_real G2))) (=> (@ (@ tptp.ord_less_eq_set_int B5) A4) (=> (@ tptp.finite_finite_int A4) (= (@ _let_1 A4) (@ (@ tptp.times_times_real (@ _let_1 (@ (@ tptp.minus_minus_set_int A4) B5))) (@ _let_1 B5))))))) (forall ((B5 tptp.set_complex) (A4 tptp.set_complex) (G2 (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups766887009212190081x_real G2))) (=> (@ (@ tptp.ord_le211207098394363844omplex B5) A4) (=> (@ tptp.finite3207457112153483333omplex A4) (= (@ _let_1 A4) (@ (@ tptp.times_times_real (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A4) B5))) (@ _let_1 B5))))))) (forall ((B5 tptp.set_int) (A4 tptp.set_int) (G2 (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups1072433553688619179nt_rat G2))) (=> (@ (@ tptp.ord_less_eq_set_int B5) A4) (=> (@ tptp.finite_finite_int A4) (= (@ _let_1 A4) (@ (@ tptp.times_times_rat (@ _let_1 (@ (@ tptp.minus_minus_set_int A4) B5))) (@ _let_1 B5))))))) (forall ((B5 tptp.set_complex) (A4 tptp.set_complex) (G2 (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups225925009352817453ex_rat G2))) (=> (@ (@ tptp.ord_le211207098394363844omplex B5) A4) (=> (@ tptp.finite3207457112153483333omplex A4) (= (@ _let_1 A4) (@ (@ tptp.times_times_rat (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A4) B5))) (@ _let_1 B5))))))) (forall ((B5 tptp.set_int) (A4 tptp.set_int) (G2 (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups1707563613775114915nt_nat G2))) (=> (@ (@ tptp.ord_less_eq_set_int B5) A4) (=> (@ tptp.finite_finite_int A4) (= (@ _let_1 A4) (@ (@ tptp.times_times_nat (@ _let_1 (@ (@ tptp.minus_minus_set_int A4) B5))) (@ _let_1 B5))))))) (forall ((B5 tptp.set_complex) (A4 tptp.set_complex) (G2 (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups861055069439313189ex_nat G2))) (=> (@ (@ tptp.ord_le211207098394363844omplex B5) A4) (=> (@ tptp.finite3207457112153483333omplex A4) (= (@ _let_1 A4) (@ (@ tptp.times_times_nat (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A4) B5))) (@ _let_1 B5))))))) (forall ((B5 tptp.set_complex) (A4 tptp.set_complex) (G2 (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.groups858564598930262913ex_int G2))) (=> (@ (@ tptp.ord_le211207098394363844omplex B5) A4) (=> (@ tptp.finite3207457112153483333omplex A4) (= (@ _let_1 A4) (@ (@ tptp.times_times_int (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A4) B5))) (@ _let_1 B5))))))) (forall ((B5 tptp.set_nat) (A4 tptp.set_nat) (G2 (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.groups129246275422532515t_real G2))) (=> (@ (@ tptp.ord_less_eq_set_nat B5) A4) (=> (@ tptp.finite_finite_nat A4) (= (@ _let_1 A4) (@ (@ tptp.times_times_real (@ _let_1 (@ (@ tptp.minus_minus_set_nat A4) B5))) (@ _let_1 B5))))))) (forall ((B5 tptp.set_nat) (A4 tptp.set_nat) (G2 (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups73079841787564623at_rat G2))) (=> (@ (@ tptp.ord_less_eq_set_nat B5) A4) (=> (@ tptp.finite_finite_nat A4) (= (@ _let_1 A4) (@ (@ tptp.times_times_rat (@ _let_1 (@ (@ tptp.minus_minus_set_nat A4) B5))) (@ _let_1 B5))))))) (forall ((B5 tptp.set_nat) (A4 tptp.set_nat) (G2 (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.groups705719431365010083at_int G2))) (=> (@ (@ tptp.ord_less_eq_set_nat B5) A4) (=> (@ tptp.finite_finite_nat A4) (= (@ _let_1 A4) (@ (@ tptp.times_times_int (@ _let_1 (@ (@ tptp.minus_minus_set_nat A4) B5))) (@ _let_1 B5))))))) (forall ((A4 tptp.set_int) (B5 tptp.set_int) (G2 (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups2316167850115554303t_real G2))) (=> (@ tptp.finite_finite_int A4) (=> (@ tptp.finite_finite_int B5) (= (@ (@ tptp.times_times_real (@ _let_1 (@ (@ tptp.sup_sup_set_int A4) B5))) (@ _let_1 (@ (@ tptp.inf_inf_set_int A4) B5))) (@ (@ tptp.times_times_real (@ _let_1 A4)) (@ _let_1 B5))))))) (forall ((A4 tptp.set_complex) (B5 tptp.set_complex) (G2 (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups766887009212190081x_real G2))) (=> (@ tptp.finite3207457112153483333omplex A4) (=> (@ tptp.finite3207457112153483333omplex B5) (= (@ (@ tptp.times_times_real (@ _let_1 (@ (@ tptp.sup_sup_set_complex A4) B5))) (@ _let_1 (@ (@ tptp.inf_inf_set_complex A4) B5))) (@ (@ tptp.times_times_real (@ _let_1 A4)) (@ _let_1 B5))))))) (forall ((A4 tptp.set_nat) (B5 tptp.set_nat) (G2 (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.groups129246275422532515t_real G2))) (=> (@ tptp.finite_finite_nat A4) (=> (@ tptp.finite_finite_nat B5) (= (@ (@ tptp.times_times_real (@ _let_1 (@ (@ tptp.sup_sup_set_nat A4) B5))) (@ _let_1 (@ (@ tptp.inf_inf_set_nat A4) B5))) (@ (@ tptp.times_times_real (@ _let_1 A4)) (@ _let_1 B5))))))) (forall ((A4 tptp.set_int) (B5 tptp.set_int) (G2 (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups1072433553688619179nt_rat G2))) (=> (@ tptp.finite_finite_int A4) (=> (@ tptp.finite_finite_int B5) (= (@ (@ tptp.times_times_rat (@ _let_1 (@ (@ tptp.sup_sup_set_int A4) B5))) (@ _let_1 (@ (@ tptp.inf_inf_set_int A4) B5))) (@ (@ tptp.times_times_rat (@ _let_1 A4)) (@ _let_1 B5))))))) (forall ((A4 tptp.set_complex) (B5 tptp.set_complex) (G2 (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups225925009352817453ex_rat G2))) (=> (@ tptp.finite3207457112153483333omplex A4) (=> (@ tptp.finite3207457112153483333omplex B5) (= (@ (@ tptp.times_times_rat (@ _let_1 (@ (@ tptp.sup_sup_set_complex A4) B5))) (@ _let_1 (@ (@ tptp.inf_inf_set_complex A4) B5))) (@ (@ tptp.times_times_rat (@ _let_1 A4)) (@ _let_1 B5))))))) (forall ((A4 tptp.set_nat) (B5 tptp.set_nat) (G2 (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups73079841787564623at_rat G2))) (=> (@ tptp.finite_finite_nat A4) (=> (@ tptp.finite_finite_nat B5) (= (@ (@ tptp.times_times_rat (@ _let_1 (@ (@ tptp.sup_sup_set_nat A4) B5))) (@ _let_1 (@ (@ tptp.inf_inf_set_nat A4) B5))) (@ (@ tptp.times_times_rat (@ _let_1 A4)) (@ _let_1 B5))))))) (forall ((A4 tptp.set_int) (B5 tptp.set_int) (G2 (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups1707563613775114915nt_nat G2))) (=> (@ tptp.finite_finite_int A4) (=> (@ tptp.finite_finite_int B5) (= (@ (@ tptp.times_times_nat (@ _let_1 (@ (@ tptp.sup_sup_set_int A4) B5))) (@ _let_1 (@ (@ tptp.inf_inf_set_int A4) B5))) (@ (@ tptp.times_times_nat (@ _let_1 A4)) (@ _let_1 B5))))))) (forall ((A4 tptp.set_complex) (B5 tptp.set_complex) (G2 (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups861055069439313189ex_nat G2))) (=> (@ tptp.finite3207457112153483333omplex A4) (=> (@ tptp.finite3207457112153483333omplex B5) (= (@ (@ tptp.times_times_nat (@ _let_1 (@ (@ tptp.sup_sup_set_complex A4) B5))) (@ _let_1 (@ (@ tptp.inf_inf_set_complex A4) B5))) (@ (@ tptp.times_times_nat (@ _let_1 A4)) (@ _let_1 B5))))))) (forall ((A4 tptp.set_complex) (B5 tptp.set_complex) (G2 (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.groups858564598930262913ex_int G2))) (=> (@ tptp.finite3207457112153483333omplex A4) (=> (@ tptp.finite3207457112153483333omplex B5) (= (@ (@ tptp.times_times_int (@ _let_1 (@ (@ tptp.sup_sup_set_complex A4) B5))) (@ _let_1 (@ (@ tptp.inf_inf_set_complex A4) B5))) (@ (@ tptp.times_times_int (@ _let_1 A4)) (@ _let_1 B5))))))) (forall ((A4 tptp.set_nat) (B5 tptp.set_nat) (G2 (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.groups705719431365010083at_int G2))) (=> (@ tptp.finite_finite_nat A4) (=> (@ tptp.finite_finite_nat B5) (= (@ (@ tptp.times_times_int (@ _let_1 (@ (@ tptp.sup_sup_set_nat A4) B5))) (@ _let_1 (@ (@ tptp.inf_inf_set_nat A4) B5))) (@ (@ tptp.times_times_int (@ _let_1 A4)) (@ _let_1 B5))))))) (forall ((A4 tptp.set_int) (G2 (-> tptp.int tptp.real)) (B5 tptp.set_int)) (let ((_let_1 (@ tptp.groups2316167850115554303t_real G2))) (=> (@ tptp.finite_finite_int A4) (= (@ _let_1 A4) (@ (@ tptp.times_times_real (@ _let_1 (@ (@ tptp.inf_inf_set_int A4) B5))) (@ _let_1 (@ (@ tptp.minus_minus_set_int A4) B5))))))) (forall ((A4 tptp.set_complex) (G2 (-> tptp.complex tptp.real)) (B5 tptp.set_complex)) (let ((_let_1 (@ tptp.groups766887009212190081x_real G2))) (=> (@ tptp.finite3207457112153483333omplex A4) (= (@ _let_1 A4) (@ (@ tptp.times_times_real (@ _let_1 (@ (@ tptp.inf_inf_set_complex A4) B5))) (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A4) B5))))))) (forall ((A4 tptp.set_nat) (G2 (-> tptp.nat tptp.real)) (B5 tptp.set_nat)) (let ((_let_1 (@ tptp.groups129246275422532515t_real G2))) (=> (@ tptp.finite_finite_nat A4) (= (@ _let_1 A4) (@ (@ tptp.times_times_real (@ _let_1 (@ (@ tptp.inf_inf_set_nat A4) B5))) (@ _let_1 (@ (@ tptp.minus_minus_set_nat A4) B5))))))) (forall ((A4 tptp.set_int) (G2 (-> tptp.int tptp.rat)) (B5 tptp.set_int)) (let ((_let_1 (@ tptp.groups1072433553688619179nt_rat G2))) (=> (@ tptp.finite_finite_int A4) (= (@ _let_1 A4) (@ (@ tptp.times_times_rat (@ _let_1 (@ (@ tptp.inf_inf_set_int A4) B5))) (@ _let_1 (@ (@ tptp.minus_minus_set_int A4) B5))))))) (forall ((A4 tptp.set_complex) (G2 (-> tptp.complex tptp.rat)) (B5 tptp.set_complex)) (let ((_let_1 (@ tptp.groups225925009352817453ex_rat G2))) (=> (@ tptp.finite3207457112153483333omplex A4) (= (@ _let_1 A4) (@ (@ tptp.times_times_rat (@ _let_1 (@ (@ tptp.inf_inf_set_complex A4) B5))) (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A4) B5))))))) (forall ((A4 tptp.set_nat) (G2 (-> tptp.nat tptp.rat)) (B5 tptp.set_nat)) (let ((_let_1 (@ tptp.groups73079841787564623at_rat G2))) (=> (@ tptp.finite_finite_nat A4) (= (@ _let_1 A4) (@ (@ tptp.times_times_rat (@ _let_1 (@ (@ tptp.inf_inf_set_nat A4) B5))) (@ _let_1 (@ (@ tptp.minus_minus_set_nat A4) B5))))))) (forall ((A4 tptp.set_int) (G2 (-> tptp.int tptp.nat)) (B5 tptp.set_int)) (let ((_let_1 (@ tptp.groups1707563613775114915nt_nat G2))) (=> (@ tptp.finite_finite_int A4) (= (@ _let_1 A4) (@ (@ tptp.times_times_nat (@ _let_1 (@ (@ tptp.inf_inf_set_int A4) B5))) (@ _let_1 (@ (@ tptp.minus_minus_set_int A4) B5))))))) (forall ((A4 tptp.set_complex) (G2 (-> tptp.complex tptp.nat)) (B5 tptp.set_complex)) (let ((_let_1 (@ tptp.groups861055069439313189ex_nat G2))) (=> (@ tptp.finite3207457112153483333omplex A4) (= (@ _let_1 A4) (@ (@ tptp.times_times_nat (@ _let_1 (@ (@ tptp.inf_inf_set_complex A4) B5))) (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A4) B5))))))) (forall ((A4 tptp.set_complex) (G2 (-> tptp.complex tptp.int)) (B5 tptp.set_complex)) (let ((_let_1 (@ tptp.groups858564598930262913ex_int G2))) (=> (@ tptp.finite3207457112153483333omplex A4) (= (@ _let_1 A4) (@ (@ tptp.times_times_int (@ _let_1 (@ (@ tptp.inf_inf_set_complex A4) B5))) (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A4) B5))))))) (forall ((A4 tptp.set_nat) (G2 (-> tptp.nat tptp.int)) (B5 tptp.set_nat)) (let ((_let_1 (@ tptp.groups705719431365010083at_int G2))) (=> (@ tptp.finite_finite_nat A4) (= (@ _let_1 A4) (@ (@ tptp.times_times_int (@ _let_1 (@ (@ tptp.inf_inf_set_nat A4) B5))) (@ _let_1 (@ (@ tptp.minus_minus_set_nat A4) B5))))))) (forall ((G2 (-> tptp.nat tptp.real)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat))) (let ((_let_3 (@ tptp.groups129246275422532515t_real G2))) (= (@ _let_3 (@ _let_2 _let_1)) (@ (@ tptp.times_times_real (@ _let_3 (@ _let_2 N))) (@ G2 _let_1))))))) (forall ((G2 (-> tptp.nat tptp.rat)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat))) (let ((_let_3 (@ tptp.groups73079841787564623at_rat G2))) (= (@ _let_3 (@ _let_2 _let_1)) (@ (@ tptp.times_times_rat (@ _let_3 (@ _let_2 N))) (@ G2 _let_1))))))) (forall ((G2 (-> tptp.nat tptp.int)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat))) (let ((_let_3 (@ tptp.groups705719431365010083at_int G2))) (= (@ _let_3 (@ _let_2 _let_1)) (@ (@ tptp.times_times_int (@ _let_3 (@ _let_2 N))) (@ G2 _let_1))))))) (forall ((G2 (-> tptp.nat tptp.nat)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat))) (let ((_let_3 (@ tptp.groups708209901874060359at_nat G2))) (= (@ _let_3 (@ _let_2 _let_1)) (@ (@ tptp.times_times_nat (@ _let_3 (@ _let_2 N))) (@ G2 _let_1))))))) (forall ((M2 tptp.nat) (N tptp.nat) (G2 (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.groups129246275422532515t_real G2))) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M2) N)) (@ (@ tptp.times_times_real (@ G2 M2)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M2)) N))))))) (forall ((M2 tptp.nat) (N tptp.nat) (G2 (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups73079841787564623at_rat G2))) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M2) N)) (@ (@ tptp.times_times_rat (@ G2 M2)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M2)) N))))))) (forall ((M2 tptp.nat) (N tptp.nat) (G2 (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.groups705719431365010083at_int G2))) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M2) N)) (@ (@ tptp.times_times_int (@ G2 M2)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M2)) N))))))) (forall ((M2 tptp.nat) (N tptp.nat) (G2 (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.groups708209901874060359at_nat G2))) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M2) N)) (@ (@ tptp.times_times_nat (@ G2 M2)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M2)) N))))))) (forall ((M2 tptp.nat) (N tptp.nat) (G2 (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat M2))) (let ((_let_2 (@ tptp.groups129246275422532515t_real G2))) (let ((_let_3 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_nat M2) _let_3) (= (@ _let_2 (@ _let_1 _let_3)) (@ (@ tptp.times_times_real (@ G2 _let_3)) (@ _let_2 (@ _let_1 N))))))))) (forall ((M2 tptp.nat) (N tptp.nat) (G2 (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat M2))) (let ((_let_2 (@ tptp.groups73079841787564623at_rat G2))) (let ((_let_3 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_nat M2) _let_3) (= (@ _let_2 (@ _let_1 _let_3)) (@ (@ tptp.times_times_rat (@ G2 _let_3)) (@ _let_2 (@ _let_1 N))))))))) (forall ((M2 tptp.nat) (N tptp.nat) (G2 (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat M2))) (let ((_let_2 (@ tptp.groups705719431365010083at_int G2))) (let ((_let_3 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_nat M2) _let_3) (= (@ _let_2 (@ _let_1 _let_3)) (@ (@ tptp.times_times_int (@ G2 _let_3)) (@ _let_2 (@ _let_1 N))))))))) (forall ((M2 tptp.nat) (N tptp.nat) (G2 (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat M2))) (let ((_let_2 (@ tptp.groups708209901874060359at_nat G2))) (let ((_let_3 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_nat M2) _let_3) (= (@ _let_2 (@ _let_1 _let_3)) (@ (@ tptp.times_times_nat (@ G2 _let_3)) (@ _let_2 (@ _let_1 N))))))))) (forall ((X tptp.real) (K2 tptp.real)) (let ((_let_1 (@ (@ tptp.insert_real X) tptp.bot_bot_set_real))) (let ((_let_2 (@ (@ tptp.inf_inf_set_real (@ tptp.set_or5984915006950818249n_real K2)) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_real X) K2))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 tptp.bot_bot_set_real))))))) (forall ((X tptp.rat) (K2 tptp.rat)) (let ((_let_1 (@ (@ tptp.insert_rat X) tptp.bot_bot_set_rat))) (let ((_let_2 (@ (@ tptp.inf_inf_set_rat (@ tptp.set_ord_lessThan_rat K2)) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_rat X) K2))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 tptp.bot_bot_set_rat))))))) (forall ((X tptp.num) (K2 tptp.num)) (let ((_let_1 (@ (@ tptp.insert_num X) tptp.bot_bot_set_num))) (let ((_let_2 (@ (@ tptp.inf_inf_set_num (@ tptp.set_ord_lessThan_num K2)) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_num X) K2))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 tptp.bot_bot_set_num))))))) (forall ((X tptp.int) (K2 tptp.int)) (let ((_let_1 (@ (@ tptp.insert_int X) tptp.bot_bot_set_int))) (let ((_let_2 (@ (@ tptp.inf_inf_set_int (@ tptp.set_ord_lessThan_int K2)) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_int X) K2))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 tptp.bot_bot_set_int))))))) (forall ((X tptp.nat) (K2 tptp.nat)) (let ((_let_1 (@ (@ tptp.insert_nat X) tptp.bot_bot_set_nat))) (let ((_let_2 (@ (@ tptp.inf_inf_set_nat (@ tptp.set_ord_lessThan_nat K2)) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat X) K2))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 tptp.bot_bot_set_nat))))))) (forall ((M2 tptp.nat) (N tptp.nat) (G2 (-> tptp.nat tptp.real))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M2) N))) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ (@ tptp.times_times_real (@ (@ tptp.groups129246275422532515t_real G2) _let_1)) (@ G2 (@ tptp.suc N))) (@ (@ tptp.times_times_real (@ G2 M2)) (@ (@ tptp.groups129246275422532515t_real (lambda ((I tptp.nat)) (@ G2 (@ tptp.suc I)))) _let_1)))))) (forall ((M2 tptp.nat) (N tptp.nat) (G2 (-> tptp.nat tptp.rat))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M2) N))) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ (@ tptp.times_times_rat (@ (@ tptp.groups73079841787564623at_rat G2) _let_1)) (@ G2 (@ tptp.suc N))) (@ (@ tptp.times_times_rat (@ G2 M2)) (@ (@ tptp.groups73079841787564623at_rat (lambda ((I tptp.nat)) (@ G2 (@ tptp.suc I)))) _let_1)))))) (forall ((M2 tptp.nat) (N tptp.nat) (G2 (-> tptp.nat tptp.int))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M2) N))) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ (@ tptp.times_times_int (@ (@ tptp.groups705719431365010083at_int G2) _let_1)) (@ G2 (@ tptp.suc N))) (@ (@ tptp.times_times_int (@ G2 M2)) (@ (@ tptp.groups705719431365010083at_int (lambda ((I tptp.nat)) (@ G2 (@ tptp.suc I)))) _let_1)))))) (forall ((M2 tptp.nat) (N tptp.nat) (G2 (-> tptp.nat tptp.nat))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M2) N))) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ (@ tptp.times_times_nat (@ (@ tptp.groups708209901874060359at_nat G2) _let_1)) (@ G2 (@ tptp.suc N))) (@ (@ tptp.times_times_nat (@ G2 M2)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I tptp.nat)) (@ G2 (@ tptp.suc I)))) _let_1)))))) (forall ((G2 (-> tptp.nat tptp.rat)) (N tptp.nat)) (= (@ (@ tptp.groups2906978787729119204at_rat G2) (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) (@ (@ tptp.plus_plus_rat (@ G2 tptp.zero_zero_nat)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I tptp.nat)) (@ G2 (@ tptp.suc I)))) (@ tptp.set_ord_lessThan_nat N))))) (forall ((G2 (-> tptp.nat tptp.int)) (N tptp.nat)) (= (@ (@ tptp.groups3539618377306564664at_int G2) (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) (@ (@ tptp.plus_plus_int (@ G2 tptp.zero_zero_nat)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I tptp.nat)) (@ G2 (@ tptp.suc I)))) (@ tptp.set_ord_lessThan_nat N))))) (forall ((G2 (-> tptp.nat tptp.nat)) (N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat G2) (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) (@ (@ tptp.plus_plus_nat (@ G2 tptp.zero_zero_nat)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I tptp.nat)) (@ G2 (@ tptp.suc I)))) (@ tptp.set_ord_lessThan_nat N))))) (forall ((G2 (-> tptp.nat tptp.real)) (N tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real G2) (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) (@ (@ tptp.plus_plus_real (@ G2 tptp.zero_zero_nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I tptp.nat)) (@ G2 (@ tptp.suc I)))) (@ tptp.set_ord_lessThan_nat N))))) (forall ((F2 (-> tptp.nat tptp.rat)) (M2 tptp.nat)) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((N4 tptp.nat)) (@ (@ tptp.minus_minus_rat (@ F2 N4)) (@ F2 (@ tptp.suc N4))))) (@ tptp.set_ord_lessThan_nat M2)) (@ (@ tptp.minus_minus_rat (@ F2 tptp.zero_zero_nat)) (@ F2 M2)))) (forall ((F2 (-> tptp.nat tptp.int)) (M2 tptp.nat)) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((N4 tptp.nat)) (@ (@ tptp.minus_minus_int (@ F2 N4)) (@ F2 (@ tptp.suc N4))))) (@ tptp.set_ord_lessThan_nat M2)) (@ (@ tptp.minus_minus_int (@ F2 tptp.zero_zero_nat)) (@ F2 M2)))) (forall ((F2 (-> tptp.nat tptp.real)) (M2 tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((N4 tptp.nat)) (@ (@ tptp.minus_minus_real (@ F2 N4)) (@ F2 (@ tptp.suc N4))))) (@ tptp.set_ord_lessThan_nat M2)) (@ (@ tptp.minus_minus_real (@ F2 tptp.zero_zero_nat)) (@ F2 M2)))) (forall ((F2 (-> tptp.nat tptp.rat)) (M2 tptp.nat)) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((N4 tptp.nat)) (@ (@ tptp.minus_minus_rat (@ F2 (@ tptp.suc N4))) (@ F2 N4)))) (@ tptp.set_ord_lessThan_nat M2)) (@ (@ tptp.minus_minus_rat (@ F2 M2)) (@ F2 tptp.zero_zero_nat)))) (forall ((F2 (-> tptp.nat tptp.int)) (M2 tptp.nat)) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((N4 tptp.nat)) (@ (@ tptp.minus_minus_int (@ F2 (@ tptp.suc N4))) (@ F2 N4)))) (@ tptp.set_ord_lessThan_nat M2)) (@ (@ tptp.minus_minus_int (@ F2 M2)) (@ F2 tptp.zero_zero_nat)))) (forall ((F2 (-> tptp.nat tptp.real)) (M2 tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((N4 tptp.nat)) (@ (@ tptp.minus_minus_real (@ F2 (@ tptp.suc N4))) (@ F2 N4)))) (@ tptp.set_ord_lessThan_nat M2)) (@ (@ tptp.minus_minus_real (@ F2 M2)) (@ F2 tptp.zero_zero_nat)))) (forall ((F2 (-> tptp.nat tptp.rat)) (N tptp.nat) (R3 tptp.rat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat N))) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.groups2906978787729119204at_rat F2) _let_1)) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat N)) R3)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I tptp.nat)) (@ (@ tptp.minus_minus_rat (@ F2 I)) R3))) _let_1)))) (forall ((F2 (-> tptp.nat tptp.int)) (N tptp.nat) (R3 tptp.int)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat N))) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.groups3539618377306564664at_int F2) _let_1)) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int N)) R3)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I tptp.nat)) (@ (@ tptp.minus_minus_int (@ F2 I)) R3))) _let_1)))) (forall ((F2 (-> tptp.nat tptp.real)) (N tptp.nat) (R3 tptp.real)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat N))) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.groups6591440286371151544t_real F2) _let_1)) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) R3)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I tptp.nat)) (@ (@ tptp.minus_minus_real (@ F2 I)) R3))) _let_1)))) (forall ((G2 (-> tptp.nat tptp.nat)) (N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat G2) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K3 tptp.nat)) (@ G2 (@ tptp.suc K3)))) (@ tptp.set_ord_lessThan_nat N)))) (forall ((G2 (-> tptp.nat tptp.real)) (N tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real G2) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ G2 (@ tptp.suc K3)))) (@ tptp.set_ord_lessThan_nat N)))) (forall ((A4 tptp.set_complex) (F2 (-> tptp.complex tptp.real)) (G2 (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex A4) (=> (forall ((I3 tptp.complex)) (let ((_let_1 (@ F2 I3))) (=> (@ (@ tptp.member_complex I3) A4) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_real _let_1) (@ G2 I3)))))) (=> (not (= A4 tptp.bot_bot_set_complex)) (@ (@ tptp.ord_less_real (@ (@ tptp.groups766887009212190081x_real F2) A4)) (@ (@ tptp.groups766887009212190081x_real G2) A4)))))) (forall ((A4 tptp.set_nat) (F2 (-> tptp.nat tptp.real)) (G2 (-> tptp.nat tptp.real))) (=> (@ tptp.finite_finite_nat A4) (=> (forall ((I3 tptp.nat)) (let ((_let_1 (@ F2 I3))) (=> (@ (@ tptp.member_nat I3) A4) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_real _let_1) (@ G2 I3)))))) (=> (not (= A4 tptp.bot_bot_set_nat)) (@ (@ tptp.ord_less_real (@ (@ tptp.groups129246275422532515t_real F2) A4)) (@ (@ tptp.groups129246275422532515t_real G2) A4)))))) (forall ((A4 tptp.set_int) (F2 (-> tptp.int tptp.real)) (G2 (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int A4) (=> (forall ((I3 tptp.int)) (let ((_let_1 (@ F2 I3))) (=> (@ (@ tptp.member_int I3) A4) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_real _let_1) (@ G2 I3)))))) (=> (not (= A4 tptp.bot_bot_set_int)) (@ (@ tptp.ord_less_real (@ (@ tptp.groups2316167850115554303t_real F2) A4)) (@ (@ tptp.groups2316167850115554303t_real G2) A4)))))) (forall ((A4 tptp.set_real) (F2 (-> tptp.real tptp.real)) (G2 (-> tptp.real tptp.real))) (=> (@ tptp.finite_finite_real A4) (=> (forall ((I3 tptp.real)) (let ((_let_1 (@ F2 I3))) (=> (@ (@ tptp.member_real I3) A4) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_real _let_1) (@ G2 I3)))))) (=> (not (= A4 tptp.bot_bot_set_real)) (@ (@ tptp.ord_less_real (@ (@ tptp.groups1681761925125756287l_real F2) A4)) (@ (@ tptp.groups1681761925125756287l_real G2) A4)))))) (forall ((A4 tptp.set_complex) (F2 (-> tptp.complex tptp.rat)) (G2 (-> tptp.complex tptp.rat))) (=> (@ tptp.finite3207457112153483333omplex A4) (=> (forall ((I3 tptp.complex)) (let ((_let_1 (@ F2 I3))) (=> (@ (@ tptp.member_complex I3) A4) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1) (@ (@ tptp.ord_less_rat _let_1) (@ G2 I3)))))) (=> (not (= A4 tptp.bot_bot_set_complex)) (@ (@ tptp.ord_less_rat (@ (@ tptp.groups225925009352817453ex_rat F2) A4)) (@ (@ tptp.groups225925009352817453ex_rat G2) A4)))))) (forall ((A4 tptp.set_nat) (F2 (-> tptp.nat tptp.rat)) (G2 (-> tptp.nat tptp.rat))) (=> (@ tptp.finite_finite_nat A4) (=> (forall ((I3 tptp.nat)) (let ((_let_1 (@ F2 I3))) (=> (@ (@ tptp.member_nat I3) A4) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1) (@ (@ tptp.ord_less_rat _let_1) (@ G2 I3)))))) (=> (not (= A4 tptp.bot_bot_set_nat)) (@ (@ tptp.ord_less_rat (@ (@ tptp.groups73079841787564623at_rat F2) A4)) (@ (@ tptp.groups73079841787564623at_rat G2) A4)))))) (forall ((A4 tptp.set_int) (F2 (-> tptp.int tptp.rat)) (G2 (-> tptp.int tptp.rat))) (=> (@ tptp.finite_finite_int A4) (=> (forall ((I3 tptp.int)) (let ((_let_1 (@ F2 I3))) (=> (@ (@ tptp.member_int I3) A4) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1) (@ (@ tptp.ord_less_rat _let_1) (@ G2 I3)))))) (=> (not (= A4 tptp.bot_bot_set_int)) (@ (@ tptp.ord_less_rat (@ (@ tptp.groups1072433553688619179nt_rat F2) A4)) (@ (@ tptp.groups1072433553688619179nt_rat G2) A4)))))) (forall ((A4 tptp.set_real) (F2 (-> tptp.real tptp.rat)) (G2 (-> tptp.real tptp.rat))) (=> (@ tptp.finite_finite_real A4) (=> (forall ((I3 tptp.real)) (let ((_let_1 (@ F2 I3))) (=> (@ (@ tptp.member_real I3) A4) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1) (@ (@ tptp.ord_less_rat _let_1) (@ G2 I3)))))) (=> (not (= A4 tptp.bot_bot_set_real)) (@ (@ tptp.ord_less_rat (@ (@ tptp.groups4061424788464935467al_rat F2) A4)) (@ (@ tptp.groups4061424788464935467al_rat G2) A4)))))) (forall ((A4 tptp.set_complex) (F2 (-> tptp.complex tptp.nat)) (G2 (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex A4) (=> (forall ((I3 tptp.complex)) (let ((_let_1 (@ F2 I3))) (=> (@ (@ tptp.member_complex I3) A4) (and (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) _let_1) (@ (@ tptp.ord_less_nat _let_1) (@ G2 I3)))))) (=> (not (= A4 tptp.bot_bot_set_complex)) (@ (@ tptp.ord_less_nat (@ (@ tptp.groups861055069439313189ex_nat F2) A4)) (@ (@ tptp.groups861055069439313189ex_nat G2) A4)))))) (forall ((A4 tptp.set_int) (F2 (-> tptp.int tptp.nat)) (G2 (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int A4) (=> (forall ((I3 tptp.int)) (let ((_let_1 (@ F2 I3))) (=> (@ (@ tptp.member_int I3) A4) (and (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) _let_1) (@ (@ tptp.ord_less_nat _let_1) (@ G2 I3)))))) (=> (not (= A4 tptp.bot_bot_set_int)) (@ (@ tptp.ord_less_nat (@ (@ tptp.groups1707563613775114915nt_nat F2) A4)) (@ (@ tptp.groups1707563613775114915nt_nat G2) A4)))))) (forall ((A4 tptp.set_complex) (X tptp.complex) (G2 (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups766887009212190081x_real G2))) (=> (@ tptp.finite3207457112153483333omplex A4) (=> (@ (@ tptp.member_complex X) A4) (= (@ _let_1 A4) (@ (@ tptp.times_times_real (@ G2 X)) (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A4) (@ (@ tptp.insert_complex X) tptp.bot_bot_set_complex))))))))) (forall ((A4 tptp.set_int) (X tptp.int) (G2 (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups2316167850115554303t_real G2))) (=> (@ tptp.finite_finite_int A4) (=> (@ (@ tptp.member_int X) A4) (= (@ _let_1 A4) (@ (@ tptp.times_times_real (@ G2 X)) (@ _let_1 (@ (@ tptp.minus_minus_set_int A4) (@ (@ tptp.insert_int X) tptp.bot_bot_set_int))))))))) (forall ((A4 tptp.set_real) (X tptp.real) (G2 (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.groups1681761925125756287l_real G2))) (=> (@ tptp.finite_finite_real A4) (=> (@ (@ tptp.member_real X) A4) (= (@ _let_1 A4) (@ (@ tptp.times_times_real (@ G2 X)) (@ _let_1 (@ (@ tptp.minus_minus_set_real A4) (@ (@ tptp.insert_real X) tptp.bot_bot_set_real))))))))) (forall ((A4 tptp.set_nat) (X tptp.nat) (G2 (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.groups129246275422532515t_real G2))) (=> (@ tptp.finite_finite_nat A4) (=> (@ (@ tptp.member_nat X) A4) (= (@ _let_1 A4) (@ (@ tptp.times_times_real (@ G2 X)) (@ _let_1 (@ (@ tptp.minus_minus_set_nat A4) (@ (@ tptp.insert_nat X) tptp.bot_bot_set_nat))))))))) (forall ((A4 tptp.set_complex) (X tptp.complex) (G2 (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups225925009352817453ex_rat G2))) (=> (@ tptp.finite3207457112153483333omplex A4) (=> (@ (@ tptp.member_complex X) A4) (= (@ _let_1 A4) (@ (@ tptp.times_times_rat (@ G2 X)) (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A4) (@ (@ tptp.insert_complex X) tptp.bot_bot_set_complex))))))))) (forall ((A4 tptp.set_int) (X tptp.int) (G2 (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups1072433553688619179nt_rat G2))) (=> (@ tptp.finite_finite_int A4) (=> (@ (@ tptp.member_int X) A4) (= (@ _let_1 A4) (@ (@ tptp.times_times_rat (@ G2 X)) (@ _let_1 (@ (@ tptp.minus_minus_set_int A4) (@ (@ tptp.insert_int X) tptp.bot_bot_set_int))))))))) (forall ((A4 tptp.set_real) (X tptp.real) (G2 (-> tptp.real tptp.rat))) (let ((_let_1 (@ tptp.groups4061424788464935467al_rat G2))) (=> (@ tptp.finite_finite_real A4) (=> (@ (@ tptp.member_real X) A4) (= (@ _let_1 A4) (@ (@ tptp.times_times_rat (@ G2 X)) (@ _let_1 (@ (@ tptp.minus_minus_set_real A4) (@ (@ tptp.insert_real X) tptp.bot_bot_set_real))))))))) (forall ((A4 tptp.set_nat) (X tptp.nat) (G2 (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups73079841787564623at_rat G2))) (=> (@ tptp.finite_finite_nat A4) (=> (@ (@ tptp.member_nat X) A4) (= (@ _let_1 A4) (@ (@ tptp.times_times_rat (@ G2 X)) (@ _let_1 (@ (@ tptp.minus_minus_set_nat A4) (@ (@ tptp.insert_nat X) tptp.bot_bot_set_nat))))))))) (forall ((A4 tptp.set_complex) (X tptp.complex) (G2 (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups861055069439313189ex_nat G2))) (=> (@ tptp.finite3207457112153483333omplex A4) (=> (@ (@ tptp.member_complex X) A4) (= (@ _let_1 A4) (@ (@ tptp.times_times_nat (@ G2 X)) (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A4) (@ (@ tptp.insert_complex X) tptp.bot_bot_set_complex))))))))) (forall ((A4 tptp.set_int) (X tptp.int) (G2 (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups1707563613775114915nt_nat G2))) (=> (@ tptp.finite_finite_int A4) (=> (@ (@ tptp.member_int X) A4) (= (@ _let_1 A4) (@ (@ tptp.times_times_nat (@ G2 X)) (@ _let_1 (@ (@ tptp.minus_minus_set_int A4) (@ (@ tptp.insert_int X) tptp.bot_bot_set_int))))))))) (forall ((A4 tptp.set_complex) (G2 (-> tptp.complex tptp.real)) (X tptp.complex)) (let ((_let_1 (@ tptp.insert_complex X))) (let ((_let_2 (@ tptp.groups766887009212190081x_real G2))) (=> (@ tptp.finite3207457112153483333omplex A4) (= (@ _let_2 (@ _let_1 A4)) (@ (@ tptp.times_times_real (@ G2 X)) (@ _let_2 (@ (@ tptp.minus_811609699411566653omplex A4) (@ _let_1 tptp.bot_bot_set_complex))))))))) (forall ((A4 tptp.set_int) (G2 (-> tptp.int tptp.real)) (X tptp.int)) (let ((_let_1 (@ tptp.insert_int X))) (let ((_let_2 (@ tptp.groups2316167850115554303t_real G2))) (=> (@ tptp.finite_finite_int A4) (= (@ _let_2 (@ _let_1 A4)) (@ (@ tptp.times_times_real (@ G2 X)) (@ _let_2 (@ (@ tptp.minus_minus_set_int A4) (@ _let_1 tptp.bot_bot_set_int))))))))) (forall ((A4 tptp.set_real) (G2 (-> tptp.real tptp.real)) (X tptp.real)) (let ((_let_1 (@ tptp.insert_real X))) (let ((_let_2 (@ tptp.groups1681761925125756287l_real G2))) (=> (@ tptp.finite_finite_real A4) (= (@ _let_2 (@ _let_1 A4)) (@ (@ tptp.times_times_real (@ G2 X)) (@ _let_2 (@ (@ tptp.minus_minus_set_real A4) (@ _let_1 tptp.bot_bot_set_real))))))))) (forall ((A4 tptp.set_nat) (G2 (-> tptp.nat tptp.real)) (X tptp.nat)) (let ((_let_1 (@ tptp.insert_nat X))) (let ((_let_2 (@ tptp.groups129246275422532515t_real G2))) (=> (@ tptp.finite_finite_nat A4) (= (@ _let_2 (@ _let_1 A4)) (@ (@ tptp.times_times_real (@ G2 X)) (@ _let_2 (@ (@ tptp.minus_minus_set_nat A4) (@ _let_1 tptp.bot_bot_set_nat))))))))) (forall ((A4 tptp.set_complex) (G2 (-> tptp.complex tptp.rat)) (X tptp.complex)) (let ((_let_1 (@ tptp.insert_complex X))) (let ((_let_2 (@ tptp.groups225925009352817453ex_rat G2))) (=> (@ tptp.finite3207457112153483333omplex A4) (= (@ _let_2 (@ _let_1 A4)) (@ (@ tptp.times_times_rat (@ G2 X)) (@ _let_2 (@ (@ tptp.minus_811609699411566653omplex A4) (@ _let_1 tptp.bot_bot_set_complex))))))))) (forall ((A4 tptp.set_int) (G2 (-> tptp.int tptp.rat)) (X tptp.int)) (let ((_let_1 (@ tptp.insert_int X))) (let ((_let_2 (@ tptp.groups1072433553688619179nt_rat G2))) (=> (@ tptp.finite_finite_int A4) (= (@ _let_2 (@ _let_1 A4)) (@ (@ tptp.times_times_rat (@ G2 X)) (@ _let_2 (@ (@ tptp.minus_minus_set_int A4) (@ _let_1 tptp.bot_bot_set_int))))))))) (forall ((A4 tptp.set_real) (G2 (-> tptp.real tptp.rat)) (X tptp.real)) (let ((_let_1 (@ tptp.insert_real X))) (let ((_let_2 (@ tptp.groups4061424788464935467al_rat G2))) (=> (@ tptp.finite_finite_real A4) (= (@ _let_2 (@ _let_1 A4)) (@ (@ tptp.times_times_rat (@ G2 X)) (@ _let_2 (@ (@ tptp.minus_minus_set_real A4) (@ _let_1 tptp.bot_bot_set_real))))))))) (forall ((A4 tptp.set_nat) (G2 (-> tptp.nat tptp.rat)) (X tptp.nat)) (let ((_let_1 (@ tptp.insert_nat X))) (let ((_let_2 (@ tptp.groups73079841787564623at_rat G2))) (=> (@ tptp.finite_finite_nat A4) (= (@ _let_2 (@ _let_1 A4)) (@ (@ tptp.times_times_rat (@ G2 X)) (@ _let_2 (@ (@ tptp.minus_minus_set_nat A4) (@ _let_1 tptp.bot_bot_set_nat))))))))) (forall ((A4 tptp.set_complex) (G2 (-> tptp.complex tptp.nat)) (X tptp.complex)) (let ((_let_1 (@ tptp.insert_complex X))) (let ((_let_2 (@ tptp.groups861055069439313189ex_nat G2))) (=> (@ tptp.finite3207457112153483333omplex A4) (= (@ _let_2 (@ _let_1 A4)) (@ (@ tptp.times_times_nat (@ G2 X)) (@ _let_2 (@ (@ tptp.minus_811609699411566653omplex A4) (@ _let_1 tptp.bot_bot_set_complex))))))))) (forall ((A4 tptp.set_int) (G2 (-> tptp.int tptp.nat)) (X tptp.int)) (let ((_let_1 (@ tptp.insert_int X))) (let ((_let_2 (@ tptp.groups1707563613775114915nt_nat G2))) (=> (@ tptp.finite_finite_int A4) (= (@ _let_2 (@ _let_1 A4)) (@ (@ tptp.times_times_nat (@ G2 X)) (@ _let_2 (@ (@ tptp.minus_minus_set_int A4) (@ _let_1 tptp.bot_bot_set_int))))))))) (forall ((A4 tptp.set_int) (B5 tptp.set_int) (G2 (-> tptp.int tptp.code_integer))) (let ((_let_1 (@ tptp.groups3827104343326376752nteger G2))) (=> (@ tptp.finite_finite_int A4) (=> (@ tptp.finite_finite_int B5) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.inf_inf_set_int A4) B5)) (= (@ G2 X3) tptp.one_one_Code_integer))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_int A4) B5)) (@ (@ tptp.times_3573771949741848930nteger (@ _let_1 A4)) (@ _let_1 B5)))))))) (forall ((A4 tptp.set_complex) (B5 tptp.set_complex) (G2 (-> tptp.complex tptp.code_integer))) (let ((_let_1 (@ tptp.groups8682486955453173170nteger G2))) (=> (@ tptp.finite3207457112153483333omplex A4) (=> (@ tptp.finite3207457112153483333omplex B5) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ (@ tptp.inf_inf_set_complex A4) B5)) (= (@ G2 X3) tptp.one_one_Code_integer))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_complex A4) B5)) (@ (@ tptp.times_3573771949741848930nteger (@ _let_1 A4)) (@ _let_1 B5)))))))) (forall ((A4 tptp.set_int) (B5 tptp.set_int) (G2 (-> tptp.int tptp.complex))) (let ((_let_1 (@ tptp.groups7440179247065528705omplex G2))) (=> (@ tptp.finite_finite_int A4) (=> (@ tptp.finite_finite_int B5) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.inf_inf_set_int A4) B5)) (= (@ G2 X3) tptp.one_one_complex))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_int A4) B5)) (@ (@ tptp.times_times_complex (@ _let_1 A4)) (@ _let_1 B5)))))))) (forall ((A4 tptp.set_complex) (B5 tptp.set_complex) (G2 (-> tptp.complex tptp.complex))) (let ((_let_1 (@ tptp.groups3708469109370488835omplex G2))) (=> (@ tptp.finite3207457112153483333omplex A4) (=> (@ tptp.finite3207457112153483333omplex B5) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ (@ tptp.inf_inf_set_complex A4) B5)) (= (@ G2 X3) tptp.one_one_complex))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_complex A4) B5)) (@ (@ tptp.times_times_complex (@ _let_1 A4)) (@ _let_1 B5)))))))) (forall ((A4 tptp.set_nat) (B5 tptp.set_nat) (G2 (-> tptp.nat tptp.code_integer))) (let ((_let_1 (@ tptp.groups3455450783089532116nteger G2))) (=> (@ tptp.finite_finite_nat A4) (=> (@ tptp.finite_finite_nat B5) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ (@ tptp.inf_inf_set_nat A4) B5)) (= (@ G2 X3) tptp.one_one_Code_integer))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_nat A4) B5)) (@ (@ tptp.times_3573771949741848930nteger (@ _let_1 A4)) (@ _let_1 B5)))))))) (forall ((A4 tptp.set_nat) (B5 tptp.set_nat) (G2 (-> tptp.nat tptp.complex))) (let ((_let_1 (@ tptp.groups6464643781859351333omplex G2))) (=> (@ tptp.finite_finite_nat A4) (=> (@ tptp.finite_finite_nat B5) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ (@ tptp.inf_inf_set_nat A4) B5)) (= (@ G2 X3) tptp.one_one_complex))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_nat A4) B5)) (@ (@ tptp.times_times_complex (@ _let_1 A4)) (@ _let_1 B5)))))))) (forall ((A4 tptp.set_int) (B5 tptp.set_int) (G2 (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups2316167850115554303t_real G2))) (=> (@ tptp.finite_finite_int A4) (=> (@ tptp.finite_finite_int B5) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.inf_inf_set_int A4) B5)) (= (@ G2 X3) tptp.one_one_real))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_int A4) B5)) (@ (@ tptp.times_times_real (@ _let_1 A4)) (@ _let_1 B5)))))))) (forall ((A4 tptp.set_complex) (B5 tptp.set_complex) (G2 (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups766887009212190081x_real G2))) (=> (@ tptp.finite3207457112153483333omplex A4) (=> (@ tptp.finite3207457112153483333omplex B5) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ (@ tptp.inf_inf_set_complex A4) B5)) (= (@ G2 X3) tptp.one_one_real))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_complex A4) B5)) (@ (@ tptp.times_times_real (@ _let_1 A4)) (@ _let_1 B5)))))))) (forall ((A4 tptp.set_nat) (B5 tptp.set_nat) (G2 (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.groups129246275422532515t_real G2))) (=> (@ tptp.finite_finite_nat A4) (=> (@ tptp.finite_finite_nat B5) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ (@ tptp.inf_inf_set_nat A4) B5)) (= (@ G2 X3) tptp.one_one_real))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_nat A4) B5)) (@ (@ tptp.times_times_real (@ _let_1 A4)) (@ _let_1 B5)))))))) (forall ((A4 tptp.set_int) (B5 tptp.set_int) (G2 (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups1072433553688619179nt_rat G2))) (=> (@ tptp.finite_finite_int A4) (=> (@ tptp.finite_finite_int B5) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.inf_inf_set_int A4) B5)) (= (@ G2 X3) tptp.one_one_rat))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_int A4) B5)) (@ (@ tptp.times_times_rat (@ _let_1 A4)) (@ _let_1 B5)))))))) (forall ((A4 tptp.set_complex) (B5 tptp.set_complex) (G2 (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups766887009212190081x_real G2))) (=> (@ tptp.finite3207457112153483333omplex A4) (=> (@ tptp.finite3207457112153483333omplex B5) (=> (= (@ (@ tptp.inf_inf_set_complex A4) B5) tptp.bot_bot_set_complex) (= (@ _let_1 (@ (@ tptp.sup_sup_set_complex A4) B5)) (@ (@ tptp.times_times_real (@ _let_1 A4)) (@ _let_1 B5)))))))) (forall ((A4 tptp.set_nat) (B5 tptp.set_nat) (G2 (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.groups129246275422532515t_real G2))) (=> (@ tptp.finite_finite_nat A4) (=> (@ tptp.finite_finite_nat B5) (=> (= (@ (@ tptp.inf_inf_set_nat A4) B5) tptp.bot_bot_set_nat) (= (@ _let_1 (@ (@ tptp.sup_sup_set_nat A4) B5)) (@ (@ tptp.times_times_real (@ _let_1 A4)) (@ _let_1 B5)))))))) (forall ((A4 tptp.set_int) (B5 tptp.set_int) (G2 (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups2316167850115554303t_real G2))) (=> (@ tptp.finite_finite_int A4) (=> (@ tptp.finite_finite_int B5) (=> (= (@ (@ tptp.inf_inf_set_int A4) B5) tptp.bot_bot_set_int) (= (@ _let_1 (@ (@ tptp.sup_sup_set_int A4) B5)) (@ (@ tptp.times_times_real (@ _let_1 A4)) (@ _let_1 B5)))))))) (forall ((A4 tptp.set_real) (B5 tptp.set_real) (G2 (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.groups1681761925125756287l_real G2))) (=> (@ tptp.finite_finite_real A4) (=> (@ tptp.finite_finite_real B5) (=> (= (@ (@ tptp.inf_inf_set_real A4) B5) tptp.bot_bot_set_real) (= (@ _let_1 (@ (@ tptp.sup_sup_set_real A4) B5)) (@ (@ tptp.times_times_real (@ _let_1 A4)) (@ _let_1 B5)))))))) (forall ((A4 tptp.set_complex) (B5 tptp.set_complex) (G2 (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups225925009352817453ex_rat G2))) (=> (@ tptp.finite3207457112153483333omplex A4) (=> (@ tptp.finite3207457112153483333omplex B5) (=> (= (@ (@ tptp.inf_inf_set_complex A4) B5) tptp.bot_bot_set_complex) (= (@ _let_1 (@ (@ tptp.sup_sup_set_complex A4) B5)) (@ (@ tptp.times_times_rat (@ _let_1 A4)) (@ _let_1 B5)))))))) (forall ((A4 tptp.set_nat) (B5 tptp.set_nat) (G2 (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups73079841787564623at_rat G2))) (=> (@ tptp.finite_finite_nat A4) (=> (@ tptp.finite_finite_nat B5) (=> (= (@ (@ tptp.inf_inf_set_nat A4) B5) tptp.bot_bot_set_nat) (= (@ _let_1 (@ (@ tptp.sup_sup_set_nat A4) B5)) (@ (@ tptp.times_times_rat (@ _let_1 A4)) (@ _let_1 B5)))))))) (forall ((A4 tptp.set_int) (B5 tptp.set_int) (G2 (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups1072433553688619179nt_rat G2))) (=> (@ tptp.finite_finite_int A4) (=> (@ tptp.finite_finite_int B5) (=> (= (@ (@ tptp.inf_inf_set_int A4) B5) tptp.bot_bot_set_int) (= (@ _let_1 (@ (@ tptp.sup_sup_set_int A4) B5)) (@ (@ tptp.times_times_rat (@ _let_1 A4)) (@ _let_1 B5)))))))) (forall ((A4 tptp.set_real) (B5 tptp.set_real) (G2 (-> tptp.real tptp.rat))) (let ((_let_1 (@ tptp.groups4061424788464935467al_rat G2))) (=> (@ tptp.finite_finite_real A4) (=> (@ tptp.finite_finite_real B5) (=> (= (@ (@ tptp.inf_inf_set_real A4) B5) tptp.bot_bot_set_real) (= (@ _let_1 (@ (@ tptp.sup_sup_set_real A4) B5)) (@ (@ tptp.times_times_rat (@ _let_1 A4)) (@ _let_1 B5)))))))) (forall ((A4 tptp.set_complex) (B5 tptp.set_complex) (G2 (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups861055069439313189ex_nat G2))) (=> (@ tptp.finite3207457112153483333omplex A4) (=> (@ tptp.finite3207457112153483333omplex B5) (=> (= (@ (@ tptp.inf_inf_set_complex A4) B5) tptp.bot_bot_set_complex) (= (@ _let_1 (@ (@ tptp.sup_sup_set_complex A4) B5)) (@ (@ tptp.times_times_nat (@ _let_1 A4)) (@ _let_1 B5)))))))) (forall ((A4 tptp.set_int) (B5 tptp.set_int) (G2 (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups1707563613775114915nt_nat G2))) (=> (@ tptp.finite_finite_int A4) (=> (@ tptp.finite_finite_int B5) (=> (= (@ (@ tptp.inf_inf_set_int A4) B5) tptp.bot_bot_set_int) (= (@ _let_1 (@ (@ tptp.sup_sup_set_int A4) B5)) (@ (@ tptp.times_times_nat (@ _let_1 A4)) (@ _let_1 B5)))))))) (forall ((N tptp.nat) (K2 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 K2)) (@ _let_1 N)))) (forall ((K2 tptp.nat) (K6 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.binomial N))) (=> (@ (@ tptp.ord_less_eq_nat K2) 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 K2)) (@ _let_1 K6)))))) (forall ((K2 tptp.nat) (K6 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.binomial N))) (=> (@ (@ tptp.ord_less_eq_nat K2) K6) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.divide_divide_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) K2) (=> (@ (@ tptp.ord_less_eq_nat K6) N) (@ (@ tptp.ord_less_eq_nat (@ _let_1 K6)) (@ _let_1 K2))))))) (forall ((N tptp.nat) (K2 tptp.nat)) (let ((_let_1 (@ tptp.binomial N))) (@ (@ tptp.ord_less_eq_nat (@ _let_1 K2)) (@ _let_1 (@ (@ tptp.divide_divide_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))) (forall ((A4 tptp.set_int) (B5 tptp.set_int) (G2 (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups2316167850115554303t_real G2))) (=> (@ tptp.finite_finite_int A4) (=> (@ tptp.finite_finite_int B5) (= (@ _let_1 (@ (@ tptp.sup_sup_set_int A4) B5)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ _let_1 (@ (@ tptp.minus_minus_set_int A4) B5))) (@ _let_1 (@ (@ tptp.minus_minus_set_int B5) A4)))) (@ _let_1 (@ (@ tptp.inf_inf_set_int A4) B5)))))))) (forall ((A4 tptp.set_complex) (B5 tptp.set_complex) (G2 (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups766887009212190081x_real G2))) (=> (@ tptp.finite3207457112153483333omplex A4) (=> (@ tptp.finite3207457112153483333omplex B5) (= (@ _let_1 (@ (@ tptp.sup_sup_set_complex A4) B5)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A4) B5))) (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex B5) A4)))) (@ _let_1 (@ (@ tptp.inf_inf_set_complex A4) B5)))))))) (forall ((A4 tptp.set_nat) (B5 tptp.set_nat) (G2 (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.groups129246275422532515t_real G2))) (=> (@ tptp.finite_finite_nat A4) (=> (@ tptp.finite_finite_nat B5) (= (@ _let_1 (@ (@ tptp.sup_sup_set_nat A4) B5)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ _let_1 (@ (@ tptp.minus_minus_set_nat A4) B5))) (@ _let_1 (@ (@ tptp.minus_minus_set_nat B5) A4)))) (@ _let_1 (@ (@ tptp.inf_inf_set_nat A4) B5)))))))) (forall ((A4 tptp.set_int) (B5 tptp.set_int) (G2 (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups1072433553688619179nt_rat G2))) (=> (@ tptp.finite_finite_int A4) (=> (@ tptp.finite_finite_int B5) (= (@ _let_1 (@ (@ tptp.sup_sup_set_int A4) B5)) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ _let_1 (@ (@ tptp.minus_minus_set_int A4) B5))) (@ _let_1 (@ (@ tptp.minus_minus_set_int B5) A4)))) (@ _let_1 (@ (@ tptp.inf_inf_set_int A4) B5)))))))) (forall ((A4 tptp.set_complex) (B5 tptp.set_complex) (G2 (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups225925009352817453ex_rat G2))) (=> (@ tptp.finite3207457112153483333omplex A4) (=> (@ tptp.finite3207457112153483333omplex B5) (= (@ _let_1 (@ (@ tptp.sup_sup_set_complex A4) B5)) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A4) B5))) (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex B5) A4)))) (@ _let_1 (@ (@ tptp.inf_inf_set_complex A4) B5)))))))) (forall ((A4 tptp.set_nat) (B5 tptp.set_nat) (G2 (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups73079841787564623at_rat G2))) (=> (@ tptp.finite_finite_nat A4) (=> (@ tptp.finite_finite_nat B5) (= (@ _let_1 (@ (@ tptp.sup_sup_set_nat A4) B5)) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ _let_1 (@ (@ tptp.minus_minus_set_nat A4) B5))) (@ _let_1 (@ (@ tptp.minus_minus_set_nat B5) A4)))) (@ _let_1 (@ (@ tptp.inf_inf_set_nat A4) B5)))))))) (forall ((A4 tptp.set_int) (B5 tptp.set_int) (G2 (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups1707563613775114915nt_nat G2))) (=> (@ tptp.finite_finite_int A4) (=> (@ tptp.finite_finite_int B5) (= (@ _let_1 (@ (@ tptp.sup_sup_set_int A4) B5)) (@ (@ tptp.times_times_nat (@ (@ tptp.times_times_nat (@ _let_1 (@ (@ tptp.minus_minus_set_int A4) B5))) (@ _let_1 (@ (@ tptp.minus_minus_set_int B5) A4)))) (@ _let_1 (@ (@ tptp.inf_inf_set_int A4) B5)))))))) (forall ((A4 tptp.set_complex) (B5 tptp.set_complex) (G2 (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups861055069439313189ex_nat G2))) (=> (@ tptp.finite3207457112153483333omplex A4) (=> (@ tptp.finite3207457112153483333omplex B5) (= (@ _let_1 (@ (@ tptp.sup_sup_set_complex A4) B5)) (@ (@ tptp.times_times_nat (@ (@ tptp.times_times_nat (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A4) B5))) (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex B5) A4)))) (@ _let_1 (@ (@ tptp.inf_inf_set_complex A4) B5)))))))) (forall ((A4 tptp.set_complex) (B5 tptp.set_complex) (G2 (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.groups858564598930262913ex_int G2))) (=> (@ tptp.finite3207457112153483333omplex A4) (=> (@ tptp.finite3207457112153483333omplex B5) (= (@ _let_1 (@ (@ tptp.sup_sup_set_complex A4) B5)) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A4) B5))) (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex B5) A4)))) (@ _let_1 (@ (@ tptp.inf_inf_set_complex A4) B5)))))))) (forall ((A4 tptp.set_nat) (B5 tptp.set_nat) (G2 (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.groups705719431365010083at_int G2))) (=> (@ tptp.finite_finite_nat A4) (=> (@ tptp.finite_finite_nat B5) (= (@ _let_1 (@ (@ tptp.sup_sup_set_nat A4) B5)) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int (@ _let_1 (@ (@ tptp.minus_minus_set_nat A4) B5))) (@ _let_1 (@ (@ tptp.minus_minus_set_nat B5) A4)))) (@ _let_1 (@ (@ tptp.inf_inf_set_nat A4) B5)))))))) (forall ((M2 tptp.nat) (N tptp.nat) (G2 (-> tptp.nat tptp.real)) (P tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N))) (let ((_let_2 (@ _let_1 P))) (let ((_let_3 (@ _let_1 tptp.one_one_nat))) (let ((_let_4 (@ tptp.groups129246275422532515t_real G2))) (let ((_let_5 (@ tptp.set_or1269000886237332187st_nat M2))) (=> (@ (@ tptp.ord_less_eq_nat M2) _let_3) (= (@ _let_4 (@ _let_5 _let_2)) (@ (@ tptp.times_times_real (@ _let_4 (@ _let_5 N))) (@ _let_4 (@ (@ tptp.set_or1269000886237332187st_nat _let_3) _let_2))))))))))) (forall ((M2 tptp.nat) (N tptp.nat) (G2 (-> tptp.nat tptp.rat)) (P tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N))) (let ((_let_2 (@ _let_1 P))) (let ((_let_3 (@ _let_1 tptp.one_one_nat))) (let ((_let_4 (@ tptp.groups73079841787564623at_rat G2))) (let ((_let_5 (@ tptp.set_or1269000886237332187st_nat M2))) (=> (@ (@ tptp.ord_less_eq_nat M2) _let_3) (= (@ _let_4 (@ _let_5 _let_2)) (@ (@ tptp.times_times_rat (@ _let_4 (@ _let_5 N))) (@ _let_4 (@ (@ tptp.set_or1269000886237332187st_nat _let_3) _let_2))))))))))) (forall ((M2 tptp.nat) (N tptp.nat) (G2 (-> tptp.nat tptp.int)) (P tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N))) (let ((_let_2 (@ _let_1 P))) (let ((_let_3 (@ _let_1 tptp.one_one_nat))) (let ((_let_4 (@ tptp.groups705719431365010083at_int G2))) (let ((_let_5 (@ tptp.set_or1269000886237332187st_nat M2))) (=> (@ (@ tptp.ord_less_eq_nat M2) _let_3) (= (@ _let_4 (@ _let_5 _let_2)) (@ (@ tptp.times_times_int (@ _let_4 (@ _let_5 N))) (@ _let_4 (@ (@ tptp.set_or1269000886237332187st_nat _let_3) _let_2))))))))))) (forall ((M2 tptp.nat) (N tptp.nat) (G2 (-> tptp.nat tptp.nat)) (P tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N))) (let ((_let_2 (@ _let_1 P))) (let ((_let_3 (@ _let_1 tptp.one_one_nat))) (let ((_let_4 (@ tptp.groups708209901874060359at_nat G2))) (let ((_let_5 (@ tptp.set_or1269000886237332187st_nat M2))) (=> (@ (@ tptp.ord_less_eq_nat M2) _let_3) (= (@ _let_4 (@ _let_5 _let_2)) (@ (@ tptp.times_times_nat (@ _let_4 (@ _let_5 N))) (@ _let_4 (@ (@ tptp.set_or1269000886237332187st_nat _let_3) _let_2))))))))))) (= tptp.set_fo2584398358068434914at_nat (lambda ((F4 (-> tptp.nat tptp.nat tptp.nat)) (A5 tptp.nat) (B4 tptp.nat) (Acc2 tptp.nat)) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat B4) A5)) Acc2) (@ (@ (@ (@ tptp.set_fo2584398358068434914at_nat F4) (@ (@ tptp.plus_plus_nat A5) tptp.one_one_nat)) B4) (@ (@ F4 A5) Acc2))))) (forall ((X (-> tptp.nat tptp.nat tptp.nat)) (Xa2 tptp.nat) (Xb tptp.nat) (Xc tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.set_fo2584398358068434914at_nat X))) (let ((_let_2 (@ (@ tptp.ord_less_nat Xb) Xa2))) (=> (= (@ (@ (@ _let_1 Xa2) Xb) Xc) Y) (and (=> _let_2 (= Y Xc)) (=> (not _let_2) (= Y (@ (@ (@ _let_1 (@ (@ tptp.plus_plus_nat Xa2) tptp.one_one_nat)) Xb) (@ (@ X Xa2) Xc))))))))) (forall ((S3 tptp.set_complex) (A tptp.complex) (B (-> tptp.complex tptp.real)) (C2 (-> tptp.complex tptp.real))) (let ((_let_1 (@ (@ tptp.groups766887009212190081x_real C2) (@ (@ tptp.minus_811609699411566653omplex S3) (@ (@ tptp.insert_complex A) tptp.bot_bot_set_complex))))) (let ((_let_2 (@ (@ tptp.member_complex A) S3))) (=> (@ tptp.finite3207457112153483333omplex S3) (and (=> _let_2 (= (@ (@ tptp.groups766887009212190081x_real (lambda ((K3 tptp.complex)) (@ (@ (@ tptp.if_real (= K3 A)) (@ B K3)) (@ C2 K3)))) S3) (@ (@ tptp.times_times_real (@ B A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups766887009212190081x_real (lambda ((K3 tptp.complex)) (@ (@ (@ tptp.if_real (= K3 A)) (@ B K3)) (@ C2 K3)))) S3) _let_1))))))) (forall ((S3 tptp.set_int) (A tptp.int) (B (-> tptp.int tptp.real)) (C2 (-> tptp.int tptp.real))) (let ((_let_1 (@ (@ tptp.groups2316167850115554303t_real C2) (@ (@ tptp.minus_minus_set_int S3) (@ (@ tptp.insert_int A) tptp.bot_bot_set_int))))) (let ((_let_2 (@ (@ tptp.member_int A) S3))) (=> (@ tptp.finite_finite_int S3) (and (=> _let_2 (= (@ (@ tptp.groups2316167850115554303t_real (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_real (= K3 A)) (@ B K3)) (@ C2 K3)))) S3) (@ (@ tptp.times_times_real (@ B A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups2316167850115554303t_real (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_real (= K3 A)) (@ B K3)) (@ C2 K3)))) S3) _let_1))))))) (forall ((S3 tptp.set_real) (A tptp.real) (B (-> tptp.real tptp.real)) (C2 (-> tptp.real tptp.real))) (let ((_let_1 (@ (@ tptp.groups1681761925125756287l_real C2) (@ (@ tptp.minus_minus_set_real S3) (@ (@ tptp.insert_real A) tptp.bot_bot_set_real))))) (let ((_let_2 (@ (@ tptp.member_real A) S3))) (=> (@ tptp.finite_finite_real S3) (and (=> _let_2 (= (@ (@ tptp.groups1681761925125756287l_real (lambda ((K3 tptp.real)) (@ (@ (@ tptp.if_real (= K3 A)) (@ B K3)) (@ C2 K3)))) S3) (@ (@ tptp.times_times_real (@ B A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups1681761925125756287l_real (lambda ((K3 tptp.real)) (@ (@ (@ tptp.if_real (= K3 A)) (@ B K3)) (@ C2 K3)))) S3) _let_1))))))) (forall ((S3 tptp.set_nat) (A tptp.nat) (B (-> tptp.nat tptp.real)) (C2 (-> tptp.nat tptp.real))) (let ((_let_1 (@ (@ tptp.groups129246275422532515t_real C2) (@ (@ tptp.minus_minus_set_nat S3) (@ (@ tptp.insert_nat A) tptp.bot_bot_set_nat))))) (let ((_let_2 (@ (@ tptp.member_nat A) S3))) (=> (@ tptp.finite_finite_nat S3) (and (=> _let_2 (= (@ (@ tptp.groups129246275422532515t_real (lambda ((K3 tptp.nat)) (@ (@ (@ tptp.if_real (= K3 A)) (@ B K3)) (@ C2 K3)))) S3) (@ (@ tptp.times_times_real (@ B A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups129246275422532515t_real (lambda ((K3 tptp.nat)) (@ (@ (@ tptp.if_real (= K3 A)) (@ B K3)) (@ C2 K3)))) S3) _let_1))))))) (forall ((S3 tptp.set_complex) (A tptp.complex) (B (-> tptp.complex tptp.rat)) (C2 (-> tptp.complex tptp.rat))) (let ((_let_1 (@ (@ tptp.groups225925009352817453ex_rat C2) (@ (@ tptp.minus_811609699411566653omplex S3) (@ (@ tptp.insert_complex A) tptp.bot_bot_set_complex))))) (let ((_let_2 (@ (@ tptp.member_complex A) S3))) (=> (@ tptp.finite3207457112153483333omplex S3) (and (=> _let_2 (= (@ (@ tptp.groups225925009352817453ex_rat (lambda ((K3 tptp.complex)) (@ (@ (@ tptp.if_rat (= K3 A)) (@ B K3)) (@ C2 K3)))) S3) (@ (@ tptp.times_times_rat (@ B A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups225925009352817453ex_rat (lambda ((K3 tptp.complex)) (@ (@ (@ tptp.if_rat (= K3 A)) (@ B K3)) (@ C2 K3)))) S3) _let_1))))))) (forall ((S3 tptp.set_int) (A tptp.int) (B (-> tptp.int tptp.rat)) (C2 (-> tptp.int tptp.rat))) (let ((_let_1 (@ (@ tptp.groups1072433553688619179nt_rat C2) (@ (@ tptp.minus_minus_set_int S3) (@ (@ tptp.insert_int A) tptp.bot_bot_set_int))))) (let ((_let_2 (@ (@ tptp.member_int A) S3))) (=> (@ tptp.finite_finite_int S3) (and (=> _let_2 (= (@ (@ tptp.groups1072433553688619179nt_rat (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_rat (= K3 A)) (@ B K3)) (@ C2 K3)))) S3) (@ (@ tptp.times_times_rat (@ B A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups1072433553688619179nt_rat (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_rat (= K3 A)) (@ B K3)) (@ C2 K3)))) S3) _let_1))))))) (forall ((S3 tptp.set_real) (A tptp.real) (B (-> tptp.real tptp.rat)) (C2 (-> tptp.real tptp.rat))) (let ((_let_1 (@ (@ tptp.groups4061424788464935467al_rat C2) (@ (@ tptp.minus_minus_set_real S3) (@ (@ tptp.insert_real A) tptp.bot_bot_set_real))))) (let ((_let_2 (@ (@ tptp.member_real A) S3))) (=> (@ tptp.finite_finite_real S3) (and (=> _let_2 (= (@ (@ tptp.groups4061424788464935467al_rat (lambda ((K3 tptp.real)) (@ (@ (@ tptp.if_rat (= K3 A)) (@ B K3)) (@ C2 K3)))) S3) (@ (@ tptp.times_times_rat (@ B A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups4061424788464935467al_rat (lambda ((K3 tptp.real)) (@ (@ (@ tptp.if_rat (= K3 A)) (@ B K3)) (@ C2 K3)))) S3) _let_1))))))) (forall ((S3 tptp.set_nat) (A tptp.nat) (B (-> tptp.nat tptp.rat)) (C2 (-> tptp.nat tptp.rat))) (let ((_let_1 (@ (@ tptp.groups73079841787564623at_rat C2) (@ (@ tptp.minus_minus_set_nat S3) (@ (@ tptp.insert_nat A) tptp.bot_bot_set_nat))))) (let ((_let_2 (@ (@ tptp.member_nat A) S3))) (=> (@ tptp.finite_finite_nat S3) (and (=> _let_2 (= (@ (@ tptp.groups73079841787564623at_rat (lambda ((K3 tptp.nat)) (@ (@ (@ tptp.if_rat (= K3 A)) (@ B K3)) (@ C2 K3)))) S3) (@ (@ tptp.times_times_rat (@ B A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups73079841787564623at_rat (lambda ((K3 tptp.nat)) (@ (@ (@ tptp.if_rat (= K3 A)) (@ B K3)) (@ C2 K3)))) S3) _let_1))))))) (forall ((S3 tptp.set_complex) (A tptp.complex) (B (-> tptp.complex tptp.nat)) (C2 (-> tptp.complex tptp.nat))) (let ((_let_1 (@ (@ tptp.groups861055069439313189ex_nat C2) (@ (@ tptp.minus_811609699411566653omplex S3) (@ (@ tptp.insert_complex A) tptp.bot_bot_set_complex))))) (let ((_let_2 (@ (@ tptp.member_complex A) S3))) (=> (@ tptp.finite3207457112153483333omplex S3) (and (=> _let_2 (= (@ (@ tptp.groups861055069439313189ex_nat (lambda ((K3 tptp.complex)) (@ (@ (@ tptp.if_nat (= K3 A)) (@ B K3)) (@ C2 K3)))) S3) (@ (@ tptp.times_times_nat (@ B A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups861055069439313189ex_nat (lambda ((K3 tptp.complex)) (@ (@ (@ tptp.if_nat (= K3 A)) (@ B K3)) (@ C2 K3)))) S3) _let_1))))))) (forall ((S3 tptp.set_int) (A tptp.int) (B (-> tptp.int tptp.nat)) (C2 (-> tptp.int tptp.nat))) (let ((_let_1 (@ (@ tptp.groups1707563613775114915nt_nat C2) (@ (@ tptp.minus_minus_set_int S3) (@ (@ tptp.insert_int A) tptp.bot_bot_set_int))))) (let ((_let_2 (@ (@ tptp.member_int A) S3))) (=> (@ tptp.finite_finite_int S3) (and (=> _let_2 (= (@ (@ tptp.groups1707563613775114915nt_nat (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_nat (= K3 A)) (@ B K3)) (@ C2 K3)))) S3) (@ (@ tptp.times_times_nat (@ B A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups1707563613775114915nt_nat (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_nat (= K3 A)) (@ B K3)) (@ C2 K3)))) S3) _let_1))))))) (forall ((X tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger X))) (= (@ (@ tptp.minus_8373710615458151222nteger (@ _let_1 N)) tptp.one_one_Code_integer) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.minus_8373710615458151222nteger X) tptp.one_one_Code_integer)) (@ (@ tptp.groups7501900531339628137nteger _let_1) (@ tptp.set_ord_lessThan_nat N)))))) (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)))))) (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)))))) (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)))))) (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)))))) (forall ((X tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger X))) (let ((_let_2 (@ tptp.minus_8373710615458151222nteger tptp.one_one_Code_integer))) (= (@ _let_2 (@ _let_1 N)) (@ (@ tptp.times_3573771949741848930nteger (@ _let_2 X)) (@ (@ tptp.groups7501900531339628137nteger _let_1) (@ tptp.set_ord_lessThan_nat N))))))) (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))))))) (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))))))) (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))))))) (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))))))) (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)))))) (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)))))) (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)))))) (forall ((B5 tptp.set_real) (A4 tptp.set_real) (F2 (-> tptp.real tptp.code_integer))) (let ((_let_1 (@ tptp.groups6225526099057966256nteger F2))) (=> (@ tptp.finite_finite_real B5) (=> (@ (@ tptp.ord_less_eq_set_real A4) B5) (=> (forall ((B3 tptp.real)) (=> (@ (@ tptp.member_real B3) (@ (@ tptp.minus_minus_set_real B5) A4)) (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (@ F2 B3)))) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) A4) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ F2 A3)))) (@ (@ tptp.ord_le3102999989581377725nteger (@ _let_1 A4)) (@ _let_1 B5)))))))) (forall ((B5 tptp.set_int) (A4 tptp.set_int) (F2 (-> tptp.int tptp.code_integer))) (let ((_let_1 (@ tptp.groups3827104343326376752nteger F2))) (=> (@ tptp.finite_finite_int B5) (=> (@ (@ tptp.ord_less_eq_set_int A4) B5) (=> (forall ((B3 tptp.int)) (=> (@ (@ tptp.member_int B3) (@ (@ tptp.minus_minus_set_int B5) A4)) (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (@ F2 B3)))) (=> (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) A4) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ F2 A3)))) (@ (@ tptp.ord_le3102999989581377725nteger (@ _let_1 A4)) (@ _let_1 B5)))))))) (forall ((B5 tptp.set_complex) (A4 tptp.set_complex) (F2 (-> tptp.complex tptp.code_integer))) (let ((_let_1 (@ tptp.groups8682486955453173170nteger F2))) (=> (@ tptp.finite3207457112153483333omplex B5) (=> (@ (@ tptp.ord_le211207098394363844omplex A4) B5) (=> (forall ((B3 tptp.complex)) (=> (@ (@ tptp.member_complex B3) (@ (@ tptp.minus_811609699411566653omplex B5) A4)) (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (@ F2 B3)))) (=> (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) A4) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ F2 A3)))) (@ (@ tptp.ord_le3102999989581377725nteger (@ _let_1 A4)) (@ _let_1 B5)))))))) (forall ((B5 tptp.set_real) (A4 tptp.set_real) (F2 (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.groups1681761925125756287l_real F2))) (=> (@ tptp.finite_finite_real B5) (=> (@ (@ tptp.ord_less_eq_set_real A4) B5) (=> (forall ((B3 tptp.real)) (=> (@ (@ tptp.member_real B3) (@ (@ tptp.minus_minus_set_real B5) A4)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F2 B3)))) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) A4) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F2 A3)))) (@ (@ tptp.ord_less_eq_real (@ _let_1 A4)) (@ _let_1 B5)))))))) (forall ((B5 tptp.set_int) (A4 tptp.set_int) (F2 (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups2316167850115554303t_real F2))) (=> (@ tptp.finite_finite_int B5) (=> (@ (@ tptp.ord_less_eq_set_int A4) B5) (=> (forall ((B3 tptp.int)) (=> (@ (@ tptp.member_int B3) (@ (@ tptp.minus_minus_set_int B5) A4)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F2 B3)))) (=> (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) A4) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F2 A3)))) (@ (@ tptp.ord_less_eq_real (@ _let_1 A4)) (@ _let_1 B5)))))))) (forall ((B5 tptp.set_complex) (A4 tptp.set_complex) (F2 (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups766887009212190081x_real F2))) (=> (@ tptp.finite3207457112153483333omplex B5) (=> (@ (@ tptp.ord_le211207098394363844omplex A4) B5) (=> (forall ((B3 tptp.complex)) (=> (@ (@ tptp.member_complex B3) (@ (@ tptp.minus_811609699411566653omplex B5) A4)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F2 B3)))) (=> (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) A4) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F2 A3)))) (@ (@ tptp.ord_less_eq_real (@ _let_1 A4)) (@ _let_1 B5)))))))) (forall ((B5 tptp.set_real) (A4 tptp.set_real) (F2 (-> tptp.real tptp.rat))) (let ((_let_1 (@ tptp.groups4061424788464935467al_rat F2))) (=> (@ tptp.finite_finite_real B5) (=> (@ (@ tptp.ord_less_eq_set_real A4) B5) (=> (forall ((B3 tptp.real)) (=> (@ (@ tptp.member_real B3) (@ (@ tptp.minus_minus_set_real B5) A4)) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ F2 B3)))) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) A4) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F2 A3)))) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A4)) (@ _let_1 B5)))))))) (forall ((B5 tptp.set_int) (A4 tptp.set_int) (F2 (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups1072433553688619179nt_rat F2))) (=> (@ tptp.finite_finite_int B5) (=> (@ (@ tptp.ord_less_eq_set_int A4) B5) (=> (forall ((B3 tptp.int)) (=> (@ (@ tptp.member_int B3) (@ (@ tptp.minus_minus_set_int B5) A4)) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ F2 B3)))) (=> (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) A4) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F2 A3)))) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A4)) (@ _let_1 B5)))))))) (forall ((B5 tptp.set_complex) (A4 tptp.set_complex) (F2 (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups225925009352817453ex_rat F2))) (=> (@ tptp.finite3207457112153483333omplex B5) (=> (@ (@ tptp.ord_le211207098394363844omplex A4) B5) (=> (forall ((B3 tptp.complex)) (=> (@ (@ tptp.member_complex B3) (@ (@ tptp.minus_811609699411566653omplex B5) A4)) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ F2 B3)))) (=> (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) A4) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F2 A3)))) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A4)) (@ _let_1 B5)))))))) (forall ((B5 tptp.set_real) (A4 tptp.set_real) (F2 (-> tptp.real tptp.int))) (let ((_let_1 (@ tptp.groups4694064378042380927al_int F2))) (=> (@ tptp.finite_finite_real B5) (=> (@ (@ tptp.ord_less_eq_set_real A4) B5) (=> (forall ((B3 tptp.real)) (=> (@ (@ tptp.member_real B3) (@ (@ tptp.minus_minus_set_real B5) A4)) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ F2 B3)))) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) A4) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F2 A3)))) (@ (@ tptp.ord_less_eq_int (@ _let_1 A4)) (@ _let_1 B5)))))))) (forall ((A4 tptp.set_real) (F2 (-> tptp.real tptp.code_integer)) (N tptp.code_integer) (K2 tptp.nat)) (=> (forall ((I3 tptp.real)) (let ((_let_1 (@ F2 I3))) (=> (@ (@ tptp.member_real I3) A4) (and (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) _let_1) (@ (@ tptp.ord_le3102999989581377725nteger _let_1) N))))) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_real A4)) K2) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) N) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.groups6225526099057966256nteger F2) A4)) (@ (@ tptp.power_8256067586552552935nteger N) K2)))))) (forall ((A4 tptp.set_nat) (F2 (-> tptp.nat tptp.code_integer)) (N tptp.code_integer) (K2 tptp.nat)) (=> (forall ((I3 tptp.nat)) (let ((_let_1 (@ F2 I3))) (=> (@ (@ tptp.member_nat I3) A4) (and (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) _let_1) (@ (@ tptp.ord_le3102999989581377725nteger _let_1) N))))) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat A4)) K2) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) N) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.groups3455450783089532116nteger F2) A4)) (@ (@ tptp.power_8256067586552552935nteger N) K2)))))) (forall ((A4 tptp.set_complex) (F2 (-> tptp.complex tptp.code_integer)) (N tptp.code_integer) (K2 tptp.nat)) (=> (forall ((I3 tptp.complex)) (let ((_let_1 (@ F2 I3))) (=> (@ (@ tptp.member_complex I3) A4) (and (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) _let_1) (@ (@ tptp.ord_le3102999989581377725nteger _let_1) N))))) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_complex A4)) K2) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) N) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.groups8682486955453173170nteger F2) A4)) (@ (@ tptp.power_8256067586552552935nteger N) K2)))))) (forall ((A4 tptp.set_int) (F2 (-> tptp.int tptp.code_integer)) (N tptp.code_integer) (K2 tptp.nat)) (=> (forall ((I3 tptp.int)) (let ((_let_1 (@ F2 I3))) (=> (@ (@ tptp.member_int I3) A4) (and (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) _let_1) (@ (@ tptp.ord_le3102999989581377725nteger _let_1) N))))) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_int A4)) K2) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) N) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.groups3827104343326376752nteger F2) A4)) (@ (@ tptp.power_8256067586552552935nteger N) K2)))))) (forall ((A4 tptp.set_real) (F2 (-> tptp.real tptp.real)) (N tptp.real) (K2 tptp.nat)) (=> (forall ((I3 tptp.real)) (let ((_let_1 (@ F2 I3))) (=> (@ (@ tptp.member_real I3) A4) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) N))))) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_real A4)) K2) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) N) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups1681761925125756287l_real F2) A4)) (@ (@ tptp.power_power_real N) K2)))))) (forall ((A4 tptp.set_nat) (F2 (-> tptp.nat tptp.real)) (N tptp.real) (K2 tptp.nat)) (=> (forall ((I3 tptp.nat)) (let ((_let_1 (@ F2 I3))) (=> (@ (@ tptp.member_nat I3) A4) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) N))))) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat A4)) K2) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) N) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups129246275422532515t_real F2) A4)) (@ (@ tptp.power_power_real N) K2)))))) (forall ((A4 tptp.set_complex) (F2 (-> tptp.complex tptp.real)) (N tptp.real) (K2 tptp.nat)) (=> (forall ((I3 tptp.complex)) (let ((_let_1 (@ F2 I3))) (=> (@ (@ tptp.member_complex I3) A4) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) N))))) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_complex A4)) K2) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) N) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups766887009212190081x_real F2) A4)) (@ (@ tptp.power_power_real N) K2)))))) (forall ((A4 tptp.set_int) (F2 (-> tptp.int tptp.real)) (N tptp.real) (K2 tptp.nat)) (=> (forall ((I3 tptp.int)) (let ((_let_1 (@ F2 I3))) (=> (@ (@ tptp.member_int I3) A4) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) N))))) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_int A4)) K2) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) N) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups2316167850115554303t_real F2) A4)) (@ (@ tptp.power_power_real N) K2)))))) (forall ((A4 tptp.set_real) (F2 (-> tptp.real tptp.rat)) (N tptp.rat) (K2 tptp.nat)) (=> (forall ((I3 tptp.real)) (let ((_let_1 (@ F2 I3))) (=> (@ (@ tptp.member_real I3) A4) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1) (@ (@ tptp.ord_less_eq_rat _let_1) N))))) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_real A4)) K2) (=> (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) N) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups4061424788464935467al_rat F2) A4)) (@ (@ tptp.power_power_rat N) K2)))))) (forall ((A4 tptp.set_nat) (F2 (-> tptp.nat tptp.rat)) (N tptp.rat) (K2 tptp.nat)) (=> (forall ((I3 tptp.nat)) (let ((_let_1 (@ F2 I3))) (=> (@ (@ tptp.member_nat I3) A4) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1) (@ (@ tptp.ord_less_eq_rat _let_1) N))))) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat A4)) K2) (=> (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) N) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups73079841787564623at_rat F2) A4)) (@ (@ tptp.power_power_rat N) K2)))))) (forall ((A4 tptp.set_int) (B5 tptp.set_int) (F2 (-> tptp.int tptp.complex))) (let ((_let_1 (@ tptp.groups7440179247065528705omplex F2))) (=> (@ tptp.finite_finite_int A4) (=> (@ tptp.finite_finite_int B5) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.inf_inf_set_int A4) B5)) (not (= (@ F2 X3) tptp.zero_zero_complex)))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_int A4) B5)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex (@ _let_1 A4)) (@ _let_1 B5))) (@ _let_1 (@ (@ tptp.inf_inf_set_int A4) B5))))))))) (forall ((A4 tptp.set_complex) (B5 tptp.set_complex) (F2 (-> tptp.complex tptp.complex))) (let ((_let_1 (@ tptp.groups3708469109370488835omplex F2))) (=> (@ tptp.finite3207457112153483333omplex A4) (=> (@ tptp.finite3207457112153483333omplex B5) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ (@ tptp.inf_inf_set_complex A4) B5)) (not (= (@ F2 X3) tptp.zero_zero_complex)))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_complex A4) B5)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex (@ _let_1 A4)) (@ _let_1 B5))) (@ _let_1 (@ (@ tptp.inf_inf_set_complex A4) B5))))))))) (forall ((A4 tptp.set_nat) (B5 tptp.set_nat) (F2 (-> tptp.nat tptp.complex))) (let ((_let_1 (@ tptp.groups6464643781859351333omplex F2))) (=> (@ tptp.finite_finite_nat A4) (=> (@ tptp.finite_finite_nat B5) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ (@ tptp.inf_inf_set_nat A4) B5)) (not (= (@ F2 X3) tptp.zero_zero_complex)))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_nat A4) B5)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex (@ _let_1 A4)) (@ _let_1 B5))) (@ _let_1 (@ (@ tptp.inf_inf_set_nat A4) B5))))))))) (forall ((A4 tptp.set_int) (B5 tptp.set_int) (F2 (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups2316167850115554303t_real F2))) (=> (@ tptp.finite_finite_int A4) (=> (@ tptp.finite_finite_int B5) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.inf_inf_set_int A4) B5)) (not (= (@ F2 X3) tptp.zero_zero_real)))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_int A4) B5)) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ _let_1 A4)) (@ _let_1 B5))) (@ _let_1 (@ (@ tptp.inf_inf_set_int A4) B5))))))))) (forall ((A4 tptp.set_complex) (B5 tptp.set_complex) (F2 (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups766887009212190081x_real F2))) (=> (@ tptp.finite3207457112153483333omplex A4) (=> (@ tptp.finite3207457112153483333omplex B5) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ (@ tptp.inf_inf_set_complex A4) B5)) (not (= (@ F2 X3) tptp.zero_zero_real)))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_complex A4) B5)) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ _let_1 A4)) (@ _let_1 B5))) (@ _let_1 (@ (@ tptp.inf_inf_set_complex A4) B5))))))))) (forall ((A4 tptp.set_nat) (B5 tptp.set_nat) (F2 (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.groups129246275422532515t_real F2))) (=> (@ tptp.finite_finite_nat A4) (=> (@ tptp.finite_finite_nat B5) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ (@ tptp.inf_inf_set_nat A4) B5)) (not (= (@ F2 X3) tptp.zero_zero_real)))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_nat A4) B5)) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ _let_1 A4)) (@ _let_1 B5))) (@ _let_1 (@ (@ tptp.inf_inf_set_nat A4) B5))))))))) (forall ((A4 tptp.set_int) (B5 tptp.set_int) (F2 (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups1072433553688619179nt_rat F2))) (=> (@ tptp.finite_finite_int A4) (=> (@ tptp.finite_finite_int B5) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.inf_inf_set_int A4) B5)) (not (= (@ F2 X3) tptp.zero_zero_rat)))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_int A4) B5)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat (@ _let_1 A4)) (@ _let_1 B5))) (@ _let_1 (@ (@ tptp.inf_inf_set_int A4) B5))))))))) (forall ((A4 tptp.set_complex) (B5 tptp.set_complex) (F2 (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups225925009352817453ex_rat F2))) (=> (@ tptp.finite3207457112153483333omplex A4) (=> (@ tptp.finite3207457112153483333omplex B5) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ (@ tptp.inf_inf_set_complex A4) B5)) (not (= (@ F2 X3) tptp.zero_zero_rat)))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_complex A4) B5)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat (@ _let_1 A4)) (@ _let_1 B5))) (@ _let_1 (@ (@ tptp.inf_inf_set_complex A4) B5))))))))) (forall ((A4 tptp.set_nat) (B5 tptp.set_nat) (F2 (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups73079841787564623at_rat F2))) (=> (@ tptp.finite_finite_nat A4) (=> (@ tptp.finite_finite_nat B5) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ (@ tptp.inf_inf_set_nat A4) B5)) (not (= (@ F2 X3) tptp.zero_zero_rat)))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_nat A4) B5)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat (@ _let_1 A4)) (@ _let_1 B5))) (@ _let_1 (@ (@ tptp.inf_inf_set_nat A4) B5))))))))) (forall ((A4 tptp.set_Pr1261947904930325089at_nat) (B5 tptp.set_Pr1261947904930325089at_nat) (F2 (-> tptp.product_prod_nat_nat tptp.complex))) (let ((_let_1 (@ tptp.groups8110221916422527690omplex F2))) (=> (@ tptp.finite6177210948735845034at_nat A4) (=> (@ tptp.finite6177210948735845034at_nat B5) (=> (forall ((X3 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat X3) (@ (@ tptp.inf_in2572325071724192079at_nat A4) B5)) (not (= (@ F2 X3) tptp.zero_zero_complex)))) (= (@ _let_1 (@ (@ tptp.sup_su6327502436637775413at_nat A4) B5)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex (@ _let_1 A4)) (@ _let_1 B5))) (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat A4) B5))))))))) (forall ((A4 tptp.set_complex) (F2 (-> tptp.complex tptp.complex)) (A tptp.complex)) (let ((_let_1 (@ tptp.groups3708469109370488835omplex F2))) (let ((_let_2 (@ _let_1 A4))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A4) (@ (@ tptp.insert_complex A) tptp.bot_bot_set_complex))))) (let ((_let_4 (@ (@ tptp.member_complex A) A4))) (let ((_let_5 (@ F2 A))) (=> (@ tptp.finite3207457112153483333omplex A4) (=> (not (= _let_5 tptp.zero_zero_complex)) (and (=> _let_4 (= _let_3 (@ (@ tptp.divide1717551699836669952omplex _let_2) _let_5))) (=> (not _let_4) (= _let_3 _let_2))))))))))) (forall ((A4 tptp.set_int) (F2 (-> tptp.int tptp.complex)) (A tptp.int)) (let ((_let_1 (@ tptp.groups7440179247065528705omplex F2))) (let ((_let_2 (@ _let_1 A4))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_minus_set_int A4) (@ (@ tptp.insert_int A) tptp.bot_bot_set_int))))) (let ((_let_4 (@ (@ tptp.member_int A) A4))) (let ((_let_5 (@ F2 A))) (=> (@ tptp.finite_finite_int A4) (=> (not (= _let_5 tptp.zero_zero_complex)) (and (=> _let_4 (= _let_3 (@ (@ tptp.divide1717551699836669952omplex _let_2) _let_5))) (=> (not _let_4) (= _let_3 _let_2))))))))))) (forall ((A4 tptp.set_real) (F2 (-> tptp.real tptp.complex)) (A tptp.real)) (let ((_let_1 (@ tptp.groups713298508707869441omplex F2))) (let ((_let_2 (@ _let_1 A4))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_minus_set_real A4) (@ (@ tptp.insert_real A) tptp.bot_bot_set_real))))) (let ((_let_4 (@ (@ tptp.member_real A) A4))) (let ((_let_5 (@ F2 A))) (=> (@ tptp.finite_finite_real A4) (=> (not (= _let_5 tptp.zero_zero_complex)) (and (=> _let_4 (= _let_3 (@ (@ tptp.divide1717551699836669952omplex _let_2) _let_5))) (=> (not _let_4) (= _let_3 _let_2))))))))))) (forall ((A4 tptp.set_nat) (F2 (-> tptp.nat tptp.complex)) (A tptp.nat)) (let ((_let_1 (@ tptp.groups6464643781859351333omplex F2))) (let ((_let_2 (@ _let_1 A4))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_minus_set_nat A4) (@ (@ tptp.insert_nat A) tptp.bot_bot_set_nat))))) (let ((_let_4 (@ (@ tptp.member_nat A) A4))) (let ((_let_5 (@ F2 A))) (=> (@ tptp.finite_finite_nat A4) (=> (not (= _let_5 tptp.zero_zero_complex)) (and (=> _let_4 (= _let_3 (@ (@ tptp.divide1717551699836669952omplex _let_2) _let_5))) (=> (not _let_4) (= _let_3 _let_2))))))))))) (forall ((A4 tptp.set_complex) (F2 (-> tptp.complex tptp.real)) (A tptp.complex)) (let ((_let_1 (@ tptp.groups766887009212190081x_real F2))) (let ((_let_2 (@ _let_1 A4))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A4) (@ (@ tptp.insert_complex A) tptp.bot_bot_set_complex))))) (let ((_let_4 (@ (@ tptp.member_complex A) A4))) (let ((_let_5 (@ F2 A))) (=> (@ tptp.finite3207457112153483333omplex A4) (=> (not (= _let_5 tptp.zero_zero_real)) (and (=> _let_4 (= _let_3 (@ (@ tptp.divide_divide_real _let_2) _let_5))) (=> (not _let_4) (= _let_3 _let_2))))))))))) (forall ((A4 tptp.set_int) (F2 (-> tptp.int tptp.real)) (A tptp.int)) (let ((_let_1 (@ tptp.groups2316167850115554303t_real F2))) (let ((_let_2 (@ _let_1 A4))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_minus_set_int A4) (@ (@ tptp.insert_int A) tptp.bot_bot_set_int))))) (let ((_let_4 (@ (@ tptp.member_int A) A4))) (let ((_let_5 (@ F2 A))) (=> (@ tptp.finite_finite_int A4) (=> (not (= _let_5 tptp.zero_zero_real)) (and (=> _let_4 (= _let_3 (@ (@ tptp.divide_divide_real _let_2) _let_5))) (=> (not _let_4) (= _let_3 _let_2))))))))))) (forall ((A4 tptp.set_real) (F2 (-> tptp.real tptp.real)) (A tptp.real)) (let ((_let_1 (@ tptp.groups1681761925125756287l_real F2))) (let ((_let_2 (@ _let_1 A4))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_minus_set_real A4) (@ (@ tptp.insert_real A) tptp.bot_bot_set_real))))) (let ((_let_4 (@ (@ tptp.member_real A) A4))) (let ((_let_5 (@ F2 A))) (=> (@ tptp.finite_finite_real A4) (=> (not (= _let_5 tptp.zero_zero_real)) (and (=> _let_4 (= _let_3 (@ (@ tptp.divide_divide_real _let_2) _let_5))) (=> (not _let_4) (= _let_3 _let_2))))))))))) (forall ((A4 tptp.set_nat) (F2 (-> tptp.nat tptp.real)) (A tptp.nat)) (let ((_let_1 (@ tptp.groups129246275422532515t_real F2))) (let ((_let_2 (@ _let_1 A4))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_minus_set_nat A4) (@ (@ tptp.insert_nat A) tptp.bot_bot_set_nat))))) (let ((_let_4 (@ (@ tptp.member_nat A) A4))) (let ((_let_5 (@ F2 A))) (=> (@ tptp.finite_finite_nat A4) (=> (not (= _let_5 tptp.zero_zero_real)) (and (=> _let_4 (= _let_3 (@ (@ tptp.divide_divide_real _let_2) _let_5))) (=> (not _let_4) (= _let_3 _let_2))))))))))) (forall ((A4 tptp.set_complex) (F2 (-> tptp.complex tptp.rat)) (A tptp.complex)) (let ((_let_1 (@ tptp.groups225925009352817453ex_rat F2))) (let ((_let_2 (@ _let_1 A4))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A4) (@ (@ tptp.insert_complex A) tptp.bot_bot_set_complex))))) (let ((_let_4 (@ (@ tptp.member_complex A) A4))) (let ((_let_5 (@ F2 A))) (=> (@ tptp.finite3207457112153483333omplex A4) (=> (not (= _let_5 tptp.zero_zero_rat)) (and (=> _let_4 (= _let_3 (@ (@ tptp.divide_divide_rat _let_2) _let_5))) (=> (not _let_4) (= _let_3 _let_2))))))))))) (forall ((A4 tptp.set_int) (F2 (-> tptp.int tptp.rat)) (A tptp.int)) (let ((_let_1 (@ tptp.groups1072433553688619179nt_rat F2))) (let ((_let_2 (@ _let_1 A4))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_minus_set_int A4) (@ (@ tptp.insert_int A) tptp.bot_bot_set_int))))) (let ((_let_4 (@ (@ tptp.member_int A) A4))) (let ((_let_5 (@ F2 A))) (=> (@ tptp.finite_finite_int A4) (=> (not (= _let_5 tptp.zero_zero_rat)) (and (=> _let_4 (= _let_3 (@ (@ tptp.divide_divide_rat _let_2) _let_5))) (=> (not _let_4) (= _let_3 _let_2))))))))))) (forall ((K2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.binomial N))) (=> (@ (@ tptp.ord_less_nat K2) (@ (@ tptp.divide_divide_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_nat (@ _let_1 K2)) (@ _let_1 (@ tptp.suc K2)))))) (forall ((K2 tptp.nat) (K6 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.binomial N))) (=> (@ (@ tptp.ord_less_nat K2) K6) (=> (@ (@ tptp.ord_less_eq_nat N) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) K2)) (=> (@ (@ tptp.ord_less_eq_nat K6) N) (@ (@ tptp.ord_less_nat (@ _let_1 K6)) (@ _let_1 K2))))))) (forall ((K2 tptp.nat) (K6 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.binomial N))) (=> (@ (@ tptp.ord_less_nat K2) 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 K2)) (@ _let_1 K6)))))) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat N) _let_1))) (let ((_let_3 (@ tptp.binomial N))) (=> (not (@ (@ tptp.dvd_dvd_nat _let_1) N)) (= (@ _let_3 (@ tptp.suc _let_2)) (@ _let_3 _let_2))))))) (forall ((S3 tptp.set_real) (A tptp.real) (B (-> tptp.real tptp.complex)) (C2 tptp.complex)) (let ((_let_1 (@ tptp.finite_card_real S3))) (let ((_let_2 (@ tptp.power_power_complex C2))) (let ((_let_3 (@ (@ tptp.member_real A) S3))) (=> (@ tptp.finite_finite_real S3) (and (=> _let_3 (= (@ (@ tptp.groups713298508707869441omplex (lambda ((K3 tptp.real)) (@ (@ (@ tptp.if_complex (= K3 A)) (@ B K3)) C2))) S3) (@ (@ tptp.times_times_complex (@ B A)) (@ _let_2 (@ (@ tptp.minus_minus_nat _let_1) tptp.one_one_nat))))) (=> (not _let_3) (= (@ (@ tptp.groups713298508707869441omplex (lambda ((K3 tptp.real)) (@ (@ (@ tptp.if_complex (= K3 A)) (@ B K3)) C2))) S3) (@ _let_2 _let_1))))))))) (forall ((S3 tptp.set_nat) (A tptp.nat) (B (-> tptp.nat tptp.complex)) (C2 tptp.complex)) (let ((_let_1 (@ tptp.finite_card_nat S3))) (let ((_let_2 (@ tptp.power_power_complex C2))) (let ((_let_3 (@ (@ tptp.member_nat A) S3))) (=> (@ tptp.finite_finite_nat S3) (and (=> _let_3 (= (@ (@ tptp.groups6464643781859351333omplex (lambda ((K3 tptp.nat)) (@ (@ (@ tptp.if_complex (= K3 A)) (@ B K3)) C2))) S3) (@ (@ tptp.times_times_complex (@ B A)) (@ _let_2 (@ (@ tptp.minus_minus_nat _let_1) tptp.one_one_nat))))) (=> (not _let_3) (= (@ (@ tptp.groups6464643781859351333omplex (lambda ((K3 tptp.nat)) (@ (@ (@ tptp.if_complex (= K3 A)) (@ B K3)) C2))) S3) (@ _let_2 _let_1))))))))) (forall ((S3 tptp.set_int) (A tptp.int) (B (-> tptp.int tptp.complex)) (C2 tptp.complex)) (let ((_let_1 (@ tptp.finite_card_int S3))) (let ((_let_2 (@ tptp.power_power_complex C2))) (let ((_let_3 (@ (@ tptp.member_int A) S3))) (=> (@ tptp.finite_finite_int S3) (and (=> _let_3 (= (@ (@ tptp.groups7440179247065528705omplex (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_complex (= K3 A)) (@ B K3)) C2))) S3) (@ (@ tptp.times_times_complex (@ B A)) (@ _let_2 (@ (@ tptp.minus_minus_nat _let_1) tptp.one_one_nat))))) (=> (not _let_3) (= (@ (@ tptp.groups7440179247065528705omplex (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_complex (= K3 A)) (@ B K3)) C2))) S3) (@ _let_2 _let_1))))))))) (forall ((S3 tptp.set_complex) (A tptp.complex) (B (-> tptp.complex tptp.complex)) (C2 tptp.complex)) (let ((_let_1 (@ tptp.finite_card_complex S3))) (let ((_let_2 (@ tptp.power_power_complex C2))) (let ((_let_3 (@ (@ tptp.member_complex A) S3))) (=> (@ tptp.finite3207457112153483333omplex S3) (and (=> _let_3 (= (@ (@ tptp.groups3708469109370488835omplex (lambda ((K3 tptp.complex)) (@ (@ (@ tptp.if_complex (= K3 A)) (@ B K3)) C2))) S3) (@ (@ tptp.times_times_complex (@ B A)) (@ _let_2 (@ (@ tptp.minus_minus_nat _let_1) tptp.one_one_nat))))) (=> (not _let_3) (= (@ (@ tptp.groups3708469109370488835omplex (lambda ((K3 tptp.complex)) (@ (@ (@ tptp.if_complex (= K3 A)) (@ B K3)) C2))) S3) (@ _let_2 _let_1))))))))) (forall ((S3 tptp.set_real) (A tptp.real) (B (-> tptp.real tptp.real)) (C2 tptp.real)) (let ((_let_1 (@ tptp.finite_card_real S3))) (let ((_let_2 (@ tptp.power_power_real C2))) (let ((_let_3 (@ (@ tptp.member_real A) S3))) (=> (@ tptp.finite_finite_real S3) (and (=> _let_3 (= (@ (@ tptp.groups1681761925125756287l_real (lambda ((K3 tptp.real)) (@ (@ (@ tptp.if_real (= K3 A)) (@ B K3)) C2))) S3) (@ (@ tptp.times_times_real (@ B A)) (@ _let_2 (@ (@ tptp.minus_minus_nat _let_1) tptp.one_one_nat))))) (=> (not _let_3) (= (@ (@ tptp.groups1681761925125756287l_real (lambda ((K3 tptp.real)) (@ (@ (@ tptp.if_real (= K3 A)) (@ B K3)) C2))) S3) (@ _let_2 _let_1))))))))) (forall ((S3 tptp.set_nat) (A tptp.nat) (B (-> tptp.nat tptp.real)) (C2 tptp.real)) (let ((_let_1 (@ tptp.finite_card_nat S3))) (let ((_let_2 (@ tptp.power_power_real C2))) (let ((_let_3 (@ (@ tptp.member_nat A) S3))) (=> (@ tptp.finite_finite_nat S3) (and (=> _let_3 (= (@ (@ tptp.groups129246275422532515t_real (lambda ((K3 tptp.nat)) (@ (@ (@ tptp.if_real (= K3 A)) (@ B K3)) C2))) S3) (@ (@ tptp.times_times_real (@ B A)) (@ _let_2 (@ (@ tptp.minus_minus_nat _let_1) tptp.one_one_nat))))) (=> (not _let_3) (= (@ (@ tptp.groups129246275422532515t_real (lambda ((K3 tptp.nat)) (@ (@ (@ tptp.if_real (= K3 A)) (@ B K3)) C2))) S3) (@ _let_2 _let_1))))))))) (forall ((S3 tptp.set_int) (A tptp.int) (B (-> tptp.int tptp.real)) (C2 tptp.real)) (let ((_let_1 (@ tptp.finite_card_int S3))) (let ((_let_2 (@ tptp.power_power_real C2))) (let ((_let_3 (@ (@ tptp.member_int A) S3))) (=> (@ tptp.finite_finite_int S3) (and (=> _let_3 (= (@ (@ tptp.groups2316167850115554303t_real (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_real (= K3 A)) (@ B K3)) C2))) S3) (@ (@ tptp.times_times_real (@ B A)) (@ _let_2 (@ (@ tptp.minus_minus_nat _let_1) tptp.one_one_nat))))) (=> (not _let_3) (= (@ (@ tptp.groups2316167850115554303t_real (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_real (= K3 A)) (@ B K3)) C2))) S3) (@ _let_2 _let_1))))))))) (forall ((S3 tptp.set_complex) (A tptp.complex) (B (-> tptp.complex tptp.real)) (C2 tptp.real)) (let ((_let_1 (@ tptp.finite_card_complex S3))) (let ((_let_2 (@ tptp.power_power_real C2))) (let ((_let_3 (@ (@ tptp.member_complex A) S3))) (=> (@ tptp.finite3207457112153483333omplex S3) (and (=> _let_3 (= (@ (@ tptp.groups766887009212190081x_real (lambda ((K3 tptp.complex)) (@ (@ (@ tptp.if_real (= K3 A)) (@ B K3)) C2))) S3) (@ (@ tptp.times_times_real (@ B A)) (@ _let_2 (@ (@ tptp.minus_minus_nat _let_1) tptp.one_one_nat))))) (=> (not _let_3) (= (@ (@ tptp.groups766887009212190081x_real (lambda ((K3 tptp.complex)) (@ (@ (@ tptp.if_real (= K3 A)) (@ B K3)) C2))) S3) (@ _let_2 _let_1))))))))) (forall ((S3 tptp.set_real) (A tptp.real) (B (-> tptp.real tptp.rat)) (C2 tptp.rat)) (let ((_let_1 (@ tptp.finite_card_real S3))) (let ((_let_2 (@ tptp.power_power_rat C2))) (let ((_let_3 (@ (@ tptp.member_real A) S3))) (=> (@ tptp.finite_finite_real S3) (and (=> _let_3 (= (@ (@ tptp.groups4061424788464935467al_rat (lambda ((K3 tptp.real)) (@ (@ (@ tptp.if_rat (= K3 A)) (@ B K3)) C2))) S3) (@ (@ tptp.times_times_rat (@ B A)) (@ _let_2 (@ (@ tptp.minus_minus_nat _let_1) tptp.one_one_nat))))) (=> (not _let_3) (= (@ (@ tptp.groups4061424788464935467al_rat (lambda ((K3 tptp.real)) (@ (@ (@ tptp.if_rat (= K3 A)) (@ B K3)) C2))) S3) (@ _let_2 _let_1))))))))) (forall ((S3 tptp.set_nat) (A tptp.nat) (B (-> tptp.nat tptp.rat)) (C2 tptp.rat)) (let ((_let_1 (@ tptp.finite_card_nat S3))) (let ((_let_2 (@ tptp.power_power_rat C2))) (let ((_let_3 (@ (@ tptp.member_nat A) S3))) (=> (@ tptp.finite_finite_nat S3) (and (=> _let_3 (= (@ (@ tptp.groups73079841787564623at_rat (lambda ((K3 tptp.nat)) (@ (@ (@ tptp.if_rat (= K3 A)) (@ B K3)) C2))) S3) (@ (@ tptp.times_times_rat (@ B A)) (@ _let_2 (@ (@ tptp.minus_minus_nat _let_1) tptp.one_one_nat))))) (=> (not _let_3) (= (@ (@ tptp.groups73079841787564623at_rat (lambda ((K3 tptp.nat)) (@ (@ (@ tptp.if_rat (= K3 A)) (@ B K3)) C2))) S3) (@ _let_2 _let_1))))))))) (forall ((A tptp.rat) (N tptp.nat)) (= (@ (@ tptp.comm_s4028243227959126397er_rat A) (@ tptp.suc N)) (@ (@ tptp.groups73079841787564623at_rat (lambda ((I tptp.nat)) (@ (@ tptp.plus_plus_rat A) (@ tptp.semiri681578069525770553at_rat I)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)))) (forall ((A tptp.real) (N tptp.nat)) (= (@ (@ tptp.comm_s7457072308508201937r_real A) (@ tptp.suc N)) (@ (@ tptp.groups129246275422532515t_real (lambda ((I tptp.nat)) (@ (@ tptp.plus_plus_real A) (@ tptp.semiri5074537144036343181t_real I)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)))) (forall ((A tptp.int) (N tptp.nat)) (= (@ (@ tptp.comm_s4660882817536571857er_int A) (@ tptp.suc N)) (@ (@ tptp.groups705719431365010083at_int (lambda ((I tptp.nat)) (@ (@ tptp.plus_plus_int A) (@ tptp.semiri1314217659103216013at_int I)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)))) (forall ((A tptp.nat) (N tptp.nat)) (= (@ (@ tptp.comm_s4663373288045622133er_nat A) (@ tptp.suc N)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I tptp.nat)) (@ (@ tptp.plus_plus_nat A) (@ tptp.semiri1316708129612266289at_nat I)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)))) (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)))))))))) (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)))))))))) (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)))))))))) (forall ((Z3 tptp.complex) (H tptp.complex) (M2 tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat M2))) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((P5 tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex Z3))) (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex (@ (@ tptp.plus_plus_complex Z3) H)) (@ (@ tptp.minus_minus_nat M2) P5))) (@ _let_1 P5))) (@ _let_1 M2))))) _let_1) (@ (@ tptp.groups2073611262835488442omplex (lambda ((P5 tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat M2) P5))) (let ((_let_2 (@ tptp.power_power_complex Z3))) (@ (@ tptp.times_times_complex (@ _let_2 P5)) (@ (@ tptp.minus_minus_complex (@ (@ tptp.power_power_complex (@ (@ tptp.plus_plus_complex Z3) H)) _let_1)) (@ _let_2 _let_1))))))) _let_1)))) (forall ((Z3 tptp.rat) (H tptp.rat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat M2))) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((P5 tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat Z3))) (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ (@ tptp.plus_plus_rat Z3) H)) (@ (@ tptp.minus_minus_nat M2) P5))) (@ _let_1 P5))) (@ _let_1 M2))))) _let_1) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((P5 tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat M2) P5))) (let ((_let_2 (@ tptp.power_power_rat Z3))) (@ (@ tptp.times_times_rat (@ _let_2 P5)) (@ (@ tptp.minus_minus_rat (@ (@ tptp.power_power_rat (@ (@ tptp.plus_plus_rat Z3) H)) _let_1)) (@ _let_2 _let_1))))))) _let_1)))) (forall ((Z3 tptp.int) (H tptp.int) (M2 tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat M2))) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((P5 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int Z3))) (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ (@ tptp.plus_plus_int Z3) H)) (@ (@ tptp.minus_minus_nat M2) P5))) (@ _let_1 P5))) (@ _let_1 M2))))) _let_1) (@ (@ tptp.groups3539618377306564664at_int (lambda ((P5 tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat M2) P5))) (let ((_let_2 (@ tptp.power_power_int Z3))) (@ (@ tptp.times_times_int (@ _let_2 P5)) (@ (@ tptp.minus_minus_int (@ (@ tptp.power_power_int (@ (@ tptp.plus_plus_int Z3) H)) _let_1)) (@ _let_2 _let_1))))))) _let_1)))) (forall ((Z3 tptp.real) (H tptp.real) (M2 tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat M2))) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((P5 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real Z3))) (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real Z3) H)) (@ (@ tptp.minus_minus_nat M2) P5))) (@ _let_1 P5))) (@ _let_1 M2))))) _let_1) (@ (@ tptp.groups6591440286371151544t_real (lambda ((P5 tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat M2) P5))) (let ((_let_2 (@ tptp.power_power_real Z3))) (@ (@ tptp.times_times_real (@ _let_2 P5)) (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real Z3) H)) _let_1)) (@ _let_2 _let_1))))))) _let_1)))) (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 ((P5 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex X) P5)) (@ (@ tptp.power_power_complex Y) (@ (@ tptp.minus_minus_nat N) P5))))) (@ tptp.set_ord_lessThan_nat _let_1)))))) (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 ((P5 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat X) P5)) (@ (@ tptp.power_power_rat Y) (@ (@ tptp.minus_minus_nat N) P5))))) (@ tptp.set_ord_lessThan_nat _let_1)))))) (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 ((P5 tptp.nat)) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int X) P5)) (@ (@ tptp.power_power_int Y) (@ (@ tptp.minus_minus_nat N) P5))))) (@ tptp.set_ord_lessThan_nat _let_1)))))) (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 ((P5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real X) P5)) (@ (@ tptp.power_power_real Y) (@ (@ tptp.minus_minus_nat N) P5))))) (@ tptp.set_ord_lessThan_nat _let_1)))))) (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 ((I tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex Y) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc I)))) (@ (@ tptp.power_power_complex X) I)))) (@ tptp.set_ord_lessThan_nat N))))) (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 ((I tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat Y) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc I)))) (@ (@ tptp.power_power_rat X) I)))) (@ tptp.set_ord_lessThan_nat N))))) (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 ((I tptp.nat)) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int Y) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc I)))) (@ (@ tptp.power_power_int X) I)))) (@ tptp.set_ord_lessThan_nat N))))) (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 ((I tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real Y) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc I)))) (@ (@ tptp.power_power_real X) I)))) (@ tptp.set_ord_lessThan_nat N))))) (forall ((N tptp.nat) (F2 (-> tptp.nat tptp.rat)) (K5 tptp.rat) (K2 tptp.nat)) (=> (forall ((P7 tptp.nat)) (=> (@ (@ tptp.ord_less_nat P7) N) (@ (@ tptp.ord_less_eq_rat (@ F2 P7)) K5))) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) K5) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups2906978787729119204at_rat F2) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.minus_minus_nat N) K2)))) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat N)) K5))))) (forall ((N tptp.nat) (F2 (-> tptp.nat tptp.int)) (K5 tptp.int) (K2 tptp.nat)) (=> (forall ((P7 tptp.nat)) (=> (@ (@ tptp.ord_less_nat P7) N) (@ (@ tptp.ord_less_eq_int (@ F2 P7)) K5))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K5) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.groups3539618377306564664at_int F2) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.minus_minus_nat N) K2)))) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int N)) K5))))) (forall ((N tptp.nat) (F2 (-> tptp.nat tptp.nat)) (K5 tptp.nat) (K2 tptp.nat)) (=> (forall ((P7 tptp.nat)) (=> (@ (@ tptp.ord_less_nat P7) N) (@ (@ tptp.ord_less_eq_nat (@ F2 P7)) K5))) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) K5) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups3542108847815614940at_nat F2) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.minus_minus_nat N) K2)))) (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat N)) K5))))) (forall ((N tptp.nat) (F2 (-> tptp.nat tptp.real)) (K5 tptp.real) (K2 tptp.nat)) (=> (forall ((P7 tptp.nat)) (=> (@ (@ tptp.ord_less_nat P7) N) (@ (@ tptp.ord_less_eq_real (@ F2 P7)) K5))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) K5) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups6591440286371151544t_real F2) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.minus_minus_nat N) K2)))) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) K5))))) (forall ((G2 (-> tptp.nat tptp.real)) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.groups129246275422532515t_real G2) (@ (@ tptp.set_or1269000886237332187st_nat (@ _let_1 M2)) (@ tptp.suc (@ _let_1 N)))) (@ (@ tptp.groups129246275422532515t_real (lambda ((I tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I))) (@ (@ tptp.times_times_real (@ G2 _let_1)) (@ G2 (@ tptp.suc _let_1)))))) (@ (@ tptp.set_or1269000886237332187st_nat M2) N))))) (forall ((G2 (-> tptp.nat tptp.rat)) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.groups73079841787564623at_rat G2) (@ (@ tptp.set_or1269000886237332187st_nat (@ _let_1 M2)) (@ tptp.suc (@ _let_1 N)))) (@ (@ tptp.groups73079841787564623at_rat (lambda ((I tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I))) (@ (@ tptp.times_times_rat (@ G2 _let_1)) (@ G2 (@ tptp.suc _let_1)))))) (@ (@ tptp.set_or1269000886237332187st_nat M2) N))))) (forall ((G2 (-> tptp.nat tptp.int)) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.groups705719431365010083at_int G2) (@ (@ tptp.set_or1269000886237332187st_nat (@ _let_1 M2)) (@ tptp.suc (@ _let_1 N)))) (@ (@ tptp.groups705719431365010083at_int (lambda ((I tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I))) (@ (@ tptp.times_times_int (@ G2 _let_1)) (@ G2 (@ tptp.suc _let_1)))))) (@ (@ tptp.set_or1269000886237332187st_nat M2) N))))) (forall ((G2 (-> tptp.nat tptp.nat)) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.groups708209901874060359at_nat G2) (@ (@ tptp.set_or1269000886237332187st_nat (@ _let_1 M2)) (@ tptp.suc (@ _let_1 N)))) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I))) (@ (@ tptp.times_times_nat (@ G2 _let_1)) (@ G2 (@ tptp.suc _let_1)))))) (@ (@ tptp.set_or1269000886237332187st_nat M2) N))))) (forall ((F2 (-> tptp.nat tptp.complex)) (A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.groups2073611262835488442omplex F2) (@ (@ tptp.set_or1269000886237332187st_nat A) B)) (@ (@ (@ (@ tptp.set_fo1517530859248394432omplex (lambda ((A5 tptp.nat) (__flatten_var_0 tptp.complex)) (@ (@ tptp.plus_plus_complex (@ F2 A5)) __flatten_var_0))) A) B) tptp.zero_zero_complex))) (forall ((F2 (-> tptp.nat tptp.rat)) (A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.groups2906978787729119204at_rat F2) (@ (@ tptp.set_or1269000886237332187st_nat A) B)) (@ (@ (@ (@ tptp.set_fo1949268297981939178at_rat (lambda ((A5 tptp.nat) (__flatten_var_0 tptp.rat)) (@ (@ tptp.plus_plus_rat (@ F2 A5)) __flatten_var_0))) A) B) tptp.zero_zero_rat))) (forall ((F2 (-> tptp.nat tptp.int)) (A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.groups3539618377306564664at_int F2) (@ (@ tptp.set_or1269000886237332187st_nat A) B)) (@ (@ (@ (@ tptp.set_fo2581907887559384638at_int (lambda ((A5 tptp.nat) (__flatten_var_0 tptp.int)) (@ (@ tptp.plus_plus_int (@ F2 A5)) __flatten_var_0))) A) B) tptp.zero_zero_int))) (forall ((F2 (-> tptp.nat tptp.nat)) (A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat F2) (@ (@ tptp.set_or1269000886237332187st_nat A) B)) (@ (@ (@ (@ tptp.set_fo2584398358068434914at_nat (lambda ((A5 tptp.nat) (__flatten_var_0 tptp.nat)) (@ (@ tptp.plus_plus_nat (@ F2 A5)) __flatten_var_0))) A) B) tptp.zero_zero_nat))) (forall ((F2 (-> tptp.nat tptp.real)) (A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real F2) (@ (@ tptp.set_or1269000886237332187st_nat A) B)) (@ (@ (@ (@ tptp.set_fo3111899725591712190t_real (lambda ((A5 tptp.nat) (__flatten_var_0 tptp.real)) (@ (@ tptp.plus_plus_real (@ F2 A5)) __flatten_var_0))) A) B) tptp.zero_zero_real))) (forall ((A tptp.rat) (N tptp.nat)) (= (@ (@ tptp.comm_s4028243227959126397er_rat A) (@ tptp.suc N)) (@ (@ tptp.groups73079841787564623at_rat (lambda ((I tptp.nat)) (@ (@ tptp.plus_plus_rat A) (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.minus_minus_nat N) I))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)))) (forall ((A tptp.real) (N tptp.nat)) (= (@ (@ tptp.comm_s7457072308508201937r_real A) (@ tptp.suc N)) (@ (@ tptp.groups129246275422532515t_real (lambda ((I tptp.nat)) (@ (@ tptp.plus_plus_real A) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.minus_minus_nat N) I))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)))) (forall ((A tptp.int) (N tptp.nat)) (= (@ (@ tptp.comm_s4660882817536571857er_int A) (@ tptp.suc N)) (@ (@ tptp.groups705719431365010083at_int (lambda ((I tptp.nat)) (@ (@ tptp.plus_plus_int A) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.minus_minus_nat N) I))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)))) (forall ((A tptp.nat) (N tptp.nat)) (= (@ (@ tptp.comm_s4663373288045622133er_nat A) (@ tptp.suc N)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I tptp.nat)) (@ (@ tptp.plus_plus_nat A) (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.minus_minus_nat N) I))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)))) (forall ((X tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_8373710615458151222nteger tptp.one_one_Code_integer))) (= (@ _let_1 (@ (@ tptp.power_8256067586552552935nteger X) N)) (@ (@ tptp.times_3573771949741848930nteger (@ _let_1 X)) (@ (@ tptp.groups7501900531339628137nteger (lambda ((I tptp.nat)) (@ (@ tptp.power_8256067586552552935nteger X) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc I))))) (@ tptp.set_ord_lessThan_nat N)))))) (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 ((I tptp.nat)) (@ (@ tptp.power_power_complex X) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc I))))) (@ tptp.set_ord_lessThan_nat N)))))) (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 ((I tptp.nat)) (@ (@ tptp.power_power_rat X) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc I))))) (@ tptp.set_ord_lessThan_nat N)))))) (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 ((I tptp.nat)) (@ (@ tptp.power_power_int X) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc I))))) (@ tptp.set_ord_lessThan_nat N)))))) (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 ((I tptp.nat)) (@ (@ tptp.power_power_real X) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc I))))) (@ tptp.set_ord_lessThan_nat N)))))) (forall ((F2 (-> tptp.nat tptp.real)) (G2 (-> tptp.nat tptp.real)) (N tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat N))) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I tptp.nat)) (@ (@ (@ tptp.if_real (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I)) (@ F2 I)) (@ G2 I)))) (@ 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 ((I tptp.nat)) (@ F2 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I)))) _let_1)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I tptp.nat)) (@ G2 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I)) tptp.one_one_nat)))) _let_1))))) (forall ((N tptp.nat) (K2 tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.binomial N) K2)) (@ (@ tptp.ord_less_eq_nat K2) N))) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.binomial N) _let_1) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat N) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat))) _let_1)))) (forall ((N tptp.nat)) (= (@ (@ tptp.binomial N) tptp.zero_zero_nat) tptp.one_one_nat)) (forall ((N tptp.nat) (K2 tptp.nat)) (let ((_let_1 (@ tptp.suc K2))) (let ((_let_2 (@ tptp.binomial N))) (= (@ (@ tptp.binomial (@ tptp.suc N)) _let_1) (@ (@ tptp.plus_plus_nat (@ _let_2 K2)) (@ _let_2 _let_1)))))) (forall ((N tptp.nat) (K2 tptp.nat)) (= (= (@ (@ tptp.binomial N) K2) tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat N) K2))) (forall ((N tptp.nat)) (= (@ (@ tptp.binomial N) (@ tptp.suc tptp.zero_zero_nat)) N)) (forall ((K2 tptp.nat)) (= (@ (@ tptp.binomial tptp.zero_zero_nat) (@ tptp.suc K2)) tptp.zero_zero_nat)) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (= (@ (@ tptp.binomial _let_1) N) _let_1))) (forall ((A4 tptp.set_int) (F2 (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int A4) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.groups1707563613775114915nt_nat F2) A4)) (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) A4) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F2 X4))))))) (forall ((A4 tptp.set_complex) (F2 (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex A4) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.groups861055069439313189ex_nat F2) A4)) (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) A4) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F2 X4))))))) (forall ((A4 tptp.set_nat) (F2 (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_nat A4) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.groups708209901874060359at_nat F2) A4)) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) A4) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F2 X4))))))) (forall ((I2 tptp.nat) (J2 tptp.nat)) (= (@ (@ tptp.groups705719431365010083at_int tptp.semiri1314217659103216013at_int) (@ (@ tptp.set_or1269000886237332187st_nat I2) J2)) (@ (@ tptp.groups1705073143266064639nt_int (lambda ((X4 tptp.int)) X4)) (@ (@ tptp.set_or1266510415728281911st_int (@ tptp.semiri1314217659103216013at_int I2)) (@ tptp.semiri1314217659103216013at_int J2))))) (forall ((I2 tptp.nat) (J2 tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat I2) J2))) (= (@ (@ tptp.groups705719431365010083at_int tptp.semiri1314217659103216013at_int) (@ (@ tptp.set_or1269000886237332187st_nat I2) _let_1)) (@ (@ tptp.groups1705073143266064639nt_int (lambda ((X4 tptp.int)) X4)) (@ (@ tptp.set_or1266510415728281911st_int (@ tptp.semiri1314217659103216013at_int I2)) (@ tptp.semiri1314217659103216013at_int _let_1)))))) (forall ((N tptp.nat) (K2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) K2) (= (@ (@ tptp.binomial N) K2) tptp.zero_zero_nat))) (forall ((K2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.suc K2))) (= (@ (@ tptp.times_times_nat _let_2) (@ (@ tptp.binomial _let_1) _let_2)) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.binomial N) K2)))))) (forall ((N tptp.nat) (K2 tptp.nat)) (let ((_let_1 (@ tptp.suc K2))) (let ((_let_2 (@ tptp.suc N))) (= (@ (@ tptp.times_times_nat _let_2) (@ (@ tptp.binomial N) K2)) (@ (@ tptp.times_times_nat (@ (@ tptp.binomial _let_2) _let_1)) _let_1))))) (forall ((K2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.binomial N))) (=> (@ (@ tptp.ord_less_eq_nat K2) N) (= (@ _let_1 K2) (@ _let_1 (@ (@ tptp.minus_minus_nat N) K2)))))) (forall ((M2 tptp.nat) (R3 tptp.nat) (K2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat M2))) (let ((_let_2 (@ _let_1 R3))) (let ((_let_3 (@ tptp.binomial (@ (@ tptp.plus_plus_nat _let_2) K2)))) (let ((_let_4 (@ _let_1 K2))) (= (@ (@ tptp.times_times_nat (@ _let_3 _let_4)) (@ (@ tptp.binomial _let_4) K2)) (@ (@ tptp.times_times_nat (@ _let_3 K2)) (@ (@ tptp.binomial _let_2) M2)))))))) (forall ((R3 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat R3) N) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.binomial N) R3)) (@ (@ tptp.power_power_nat N) R3)))) (forall ((K2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K2) N) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.binomial N) K2)))) (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.binomial (@ tptp.suc (@ (@ tptp.plus_plus_nat A) B))))) (let ((_let_2 (@ tptp.suc A))) (= (@ (@ tptp.times_times_nat _let_2) (@ _let_1 _let_2)) (@ (@ tptp.times_times_nat (@ tptp.suc B)) (@ _let_1 A)))))) (forall ((N tptp.nat) (K2 tptp.nat)) (let ((_let_1 (@ tptp.suc K2))) (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) K2))) _let_1))))) (forall ((K2 tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.binomial N))) (=> (@ (@ tptp.ord_less_eq_nat K2) M2) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ (@ tptp.times_times_nat (@ _let_1 M2)) (@ (@ tptp.binomial M2) K2)) (@ (@ tptp.times_times_nat (@ _let_1 K2)) (@ (@ tptp.binomial (@ (@ tptp.minus_minus_nat N) K2)) (@ (@ tptp.minus_minus_nat M2) K2)))))))) (forall ((N tptp.nat) (K2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat N))) (= (@ (@ tptp.times_times_nat (@ _let_1 K2)) (@ (@ tptp.binomial N) K2)) (@ (@ tptp.times_times_nat N) (@ (@ tptp.binomial (@ _let_1 tptp.one_one_nat)) K2))))) (forall ((K2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc K2))) (= (@ (@ 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)) K2))))) (forall ((F2 (-> tptp.nat tptp.nat)) (Mm tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K3 tptp.nat)) (@ F2 (@ tptp.suc K3)))) (@ tptp.set_ord_lessThan_nat Mm)) (@ (@ tptp.groups3542108847815614940at_nat F2) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) Mm)))) (forall ((F2 (-> tptp.nat tptp.real)) (Mm tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ F2 (@ tptp.suc K3)))) (@ tptp.set_ord_lessThan_nat Mm)) (@ (@ tptp.groups6591440286371151544t_real F2) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) Mm)))) (forall ((K2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K2) N) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real N)) (@ tptp.semiri5074537144036343181t_real K2))) K2)) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.binomial N) K2))))) (forall ((K2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K2) N) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat (@ (@ tptp.divide_divide_rat (@ tptp.semiri681578069525770553at_rat N)) (@ tptp.semiri681578069525770553at_rat K2))) K2)) (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.binomial N) K2))))) (forall ((N tptp.nat) (K2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.binomial N) K2)) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (forall ((N tptp.nat) (K2 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 K2) (= (@ (@ tptp.binomial N) K2) (@ (@ tptp.plus_plus_nat (@ _let_1 (@ (@ tptp.minus_minus_nat K2) tptp.one_one_nat))) (@ _let_1 K2)))))))) (forall ((K2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K2) (= (@ (@ tptp.times_times_nat K2) (@ (@ tptp.binomial N) K2)) (@ (@ tptp.times_times_nat N) (@ (@ tptp.binomial (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) (@ (@ tptp.minus_minus_nat K2) tptp.one_one_nat)))))) (forall ((N tptp.nat) (K2 tptp.nat)) (let ((_let_1 (@ tptp.binomial (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)))) (let ((_let_2 (@ tptp.suc K2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.binomial N) _let_2) (@ (@ tptp.plus_plus_nat (@ _let_1 _let_2)) (@ _let_1 K2))))))) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.times_times_rat _let_1) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I tptp.nat)) (@ (@ (@ tptp.if_rat (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I))) (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.binomial N) I))) tptp.zero_zero_rat))) (@ tptp.set_ord_atMost_nat N))) (@ (@ tptp.power_power_rat _let_1) N))))) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.times_times_complex _let_1) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I tptp.nat)) (@ (@ (@ tptp.if_complex (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I))) (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.binomial N) I))) tptp.zero_zero_complex))) (@ tptp.set_ord_atMost_nat N))) (@ (@ tptp.power_power_complex _let_1) N))))) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I tptp.nat)) (@ (@ (@ tptp.if_int (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I))) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.binomial N) I))) tptp.zero_zero_int))) (@ tptp.set_ord_atMost_nat N))) (@ (@ tptp.power_power_int _let_1) N))))) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.times_times_real _let_1) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I tptp.nat)) (@ (@ (@ tptp.if_real (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I))) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.binomial N) I))) tptp.zero_zero_real))) (@ tptp.set_ord_atMost_nat N))) (@ (@ tptp.power_power_real _let_1) N))))) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.times_times_rat _let_1) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I tptp.nat)) (@ (@ (@ tptp.if_rat (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I)) (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.binomial N) I))) tptp.zero_zero_rat))) (@ tptp.set_ord_atMost_nat N))) (@ (@ tptp.power_power_rat _let_1) N))))) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.times_times_complex _let_1) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I tptp.nat)) (@ (@ (@ tptp.if_complex (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I)) (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.binomial N) I))) tptp.zero_zero_complex))) (@ tptp.set_ord_atMost_nat N))) (@ (@ tptp.power_power_complex _let_1) N))))) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I tptp.nat)) (@ (@ (@ tptp.if_int (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I)) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.binomial N) I))) tptp.zero_zero_int))) (@ tptp.set_ord_atMost_nat N))) (@ (@ tptp.power_power_int _let_1) N))))) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.times_times_real _let_1) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I tptp.nat)) (@ (@ (@ tptp.if_real (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I)) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.binomial N) I))) tptp.zero_zero_real))) (@ tptp.set_ord_atMost_nat N))) (@ (@ tptp.power_power_real _let_1) N))))) (forall ((A4 tptp.set_list_nat) (K2 tptp.nat)) (let ((_let_1 (@ tptp.finite_card_list_nat A4))) (=> (@ tptp.finite8100373058378681591st_nat A4) (=> (@ (@ tptp.ord_less_eq_nat K2) _let_1) (= (@ tptp.finite7325466520557071688st_nat (@ tptp.collec5989764272469232197st_nat (lambda ((Xs tptp.list_list_nat)) (and (= (@ tptp.size_s3023201423986296836st_nat Xs) K2) (@ tptp.distinct_list_nat Xs) (@ (@ tptp.ord_le6045566169113846134st_nat (@ tptp.set_list_nat2 Xs)) A4))))) (@ (@ tptp.groups708209901874060359at_nat (lambda ((X4 tptp.nat)) X4)) (@ (@ tptp.set_or1269000886237332187st_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat _let_1) K2)) tptp.one_one_nat)) _let_1))))))) (forall ((A4 tptp.set_set_nat) (K2 tptp.nat)) (let ((_let_1 (@ tptp.finite_card_set_nat A4))) (=> (@ tptp.finite1152437895449049373et_nat A4) (=> (@ (@ tptp.ord_less_eq_nat K2) _let_1) (= (@ tptp.finite5631907774883551598et_nat (@ tptp.collect_list_set_nat (lambda ((Xs tptp.list_set_nat)) (and (= (@ tptp.size_s3254054031482475050et_nat Xs) K2) (@ tptp.distinct_set_nat Xs) (@ (@ tptp.ord_le6893508408891458716et_nat (@ tptp.set_set_nat2 Xs)) A4))))) (@ (@ tptp.groups708209901874060359at_nat (lambda ((X4 tptp.nat)) X4)) (@ (@ tptp.set_or1269000886237332187st_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat _let_1) K2)) tptp.one_one_nat)) _let_1))))))) (forall ((A4 tptp.set_complex) (K2 tptp.nat)) (let ((_let_1 (@ tptp.finite_card_complex A4))) (=> (@ tptp.finite3207457112153483333omplex A4) (=> (@ (@ tptp.ord_less_eq_nat K2) _let_1) (= (@ tptp.finite5120063068150530198omplex (@ tptp.collect_list_complex (lambda ((Xs tptp.list_complex)) (and (= (@ tptp.size_s3451745648224563538omplex Xs) K2) (@ tptp.distinct_complex Xs) (@ (@ tptp.ord_le211207098394363844omplex (@ tptp.set_complex2 Xs)) A4))))) (@ (@ tptp.groups708209901874060359at_nat (lambda ((X4 tptp.nat)) X4)) (@ (@ tptp.set_or1269000886237332187st_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat _let_1) K2)) tptp.one_one_nat)) _let_1))))))) (forall ((A4 tptp.set_VEBT_VEBT) (K2 tptp.nat)) (let ((_let_1 (@ tptp.finite7802652506058667612T_VEBT A4))) (=> (@ tptp.finite5795047828879050333T_VEBT A4) (=> (@ (@ tptp.ord_less_eq_nat K2) _let_1) (= (@ tptp.finite5915292604075114978T_VEBT (@ tptp.collec5608196760682091941T_VEBT (lambda ((Xs tptp.list_VEBT_VEBT)) (and (= (@ tptp.size_s6755466524823107622T_VEBT Xs) K2) (@ tptp.distinct_VEBT_VEBT Xs) (@ (@ tptp.ord_le4337996190870823476T_VEBT (@ tptp.set_VEBT_VEBT2 Xs)) A4))))) (@ (@ tptp.groups708209901874060359at_nat (lambda ((X4 tptp.nat)) X4)) (@ (@ tptp.set_or1269000886237332187st_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat _let_1) K2)) tptp.one_one_nat)) _let_1))))))) (forall ((A4 tptp.set_o) (K2 tptp.nat)) (let ((_let_1 (@ tptp.finite_card_o A4))) (=> (@ tptp.finite_finite_o A4) (=> (@ (@ tptp.ord_less_eq_nat K2) _let_1) (= (@ tptp.finite_card_list_o (@ tptp.collect_list_o (lambda ((Xs tptp.list_o)) (and (= (@ tptp.size_size_list_o Xs) K2) (@ tptp.distinct_o Xs) (@ (@ tptp.ord_less_eq_set_o (@ tptp.set_o2 Xs)) A4))))) (@ (@ tptp.groups708209901874060359at_nat (lambda ((X4 tptp.nat)) X4)) (@ (@ tptp.set_or1269000886237332187st_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat _let_1) K2)) tptp.one_one_nat)) _let_1))))))) (forall ((A4 tptp.set_int) (K2 tptp.nat)) (let ((_let_1 (@ tptp.finite_card_int A4))) (=> (@ tptp.finite_finite_int A4) (=> (@ (@ tptp.ord_less_eq_nat K2) _let_1) (= (@ tptp.finite_card_list_int (@ tptp.collect_list_int (lambda ((Xs tptp.list_int)) (and (= (@ tptp.size_size_list_int Xs) K2) (@ tptp.distinct_int Xs) (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_int2 Xs)) A4))))) (@ (@ tptp.groups708209901874060359at_nat (lambda ((X4 tptp.nat)) X4)) (@ (@ tptp.set_or1269000886237332187st_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat _let_1) K2)) tptp.one_one_nat)) _let_1))))))) (forall ((A4 tptp.set_nat) (K2 tptp.nat)) (let ((_let_1 (@ tptp.finite_card_nat A4))) (=> (@ tptp.finite_finite_nat A4) (=> (@ (@ tptp.ord_less_eq_nat K2) _let_1) (= (@ tptp.finite_card_list_nat (@ tptp.collect_list_nat (lambda ((Xs tptp.list_nat)) (and (= (@ tptp.size_size_list_nat Xs) K2) (@ tptp.distinct_nat Xs) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_nat2 Xs)) A4))))) (@ (@ tptp.groups708209901874060359at_nat (lambda ((X4 tptp.nat)) X4)) (@ (@ tptp.set_or1269000886237332187st_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat _let_1) K2)) tptp.one_one_nat)) _let_1))))))) (forall ((R3 tptp.complex) (M2 tptp.nat)) (let ((_let_1 (@ tptp.suc M2))) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.gbinomial_complex R3) K3)) (@ (@ tptp.minus_minus_complex (@ (@ tptp.divide1717551699836669952omplex R3) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) (@ tptp.semiri8010041392384452111omplex K3))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) M2)) (@ (@ tptp.times_times_complex (@ (@ tptp.divide1717551699836669952omplex (@ tptp.semiri8010041392384452111omplex _let_1)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) (@ (@ tptp.gbinomial_complex R3) _let_1))))) (forall ((R3 tptp.rat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.suc M2))) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.gbinomial_rat R3) K3)) (@ (@ tptp.minus_minus_rat (@ (@ tptp.divide_divide_rat R3) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one)))) (@ tptp.semiri681578069525770553at_rat K3))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) M2)) (@ (@ tptp.times_times_rat (@ (@ tptp.divide_divide_rat (@ tptp.semiri681578069525770553at_rat _let_1)) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.gbinomial_rat R3) _let_1))))) (forall ((R3 tptp.real) (M2 tptp.nat)) (let ((_let_1 (@ tptp.suc M2))) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.gbinomial_real R3) K3)) (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real R3) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.semiri5074537144036343181t_real K3))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) M2)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real _let_1)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ (@ tptp.gbinomial_real R3) _let_1))))) (forall ((X tptp.nat) (Y tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (let ((_let_2 (@ tptp.accp_nat tptp.vEBT_v4011308405150292612up_rel))) (let ((_let_3 (= Y (@ (@ tptp.vEBT_Leaf false) false)))) (=> (= (@ tptp.vEBT_vebt_buildup X) Y) (=> (@ _let_2 X) (=> (=> (= X tptp.zero_zero_nat) (=> _let_3 (not (@ _let_2 tptp.zero_zero_nat)))) (=> (=> (= X _let_1) (=> _let_3 (not (@ _let_2 _let_1)))) (not (forall ((Va tptp.nat)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_1) _let_2))) (let ((_let_4 (@ tptp.suc _let_3))) (let ((_let_5 (@ tptp.vEBT_vebt_buildup _let_3))) (let ((_let_6 (@ tptp.power_power_nat _let_2))) (let ((_let_7 (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1))) (let ((_let_8 (@ (@ tptp.dvd_dvd_nat _let_2) _let_1))) (=> (= X _let_1) (=> (and (=> _let_8 (= Y (@ (@ _let_7 (@ (@ tptp.replicate_VEBT_VEBT (@ _let_6 _let_3)) _let_5)) _let_5))) (=> (not _let_8) (= Y (@ (@ _let_7 (@ (@ tptp.replicate_VEBT_VEBT (@ _let_6 _let_4)) _let_5)) (@ tptp.vEBT_vebt_buildup _let_4))))) (not (@ (@ tptp.accp_nat tptp.vEBT_v4011308405150292612up_rel) _let_1)))))))))))))))))))))) (forall ((A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se2161824704523386999it_nat tptp.zero_zero_nat) A) (@ (@ tptp.plus_plus_nat (@ tptp.zero_n2687167440665602831ol_nat (@ (@ tptp.dvd_dvd_nat _let_1) A))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.divide_divide_nat A) _let_1)))))) (forall ((A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se2159334234014336723it_int tptp.zero_zero_nat) A) (@ (@ tptp.plus_plus_int (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.dvd_dvd_int _let_1) A))) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.divide_divide_int A) _let_1)))))) (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se1345352211410354436nteger tptp.zero_zero_nat) A) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.zero_n356916108424825756nteger (@ (@ tptp.dvd_dvd_Code_integer _let_1) A))) (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.divide6298287555418463151nteger A) _let_1)))))) (forall ((X tptp.nat) (Y tptp.nat)) (= (= (@ tptp.set_ord_atMost_nat X) (@ tptp.set_ord_atMost_nat Y)) (= X Y))) (forall ((I2 tptp.real) (K2 tptp.real)) (= (@ (@ tptp.member_real I2) (@ tptp.set_ord_atMost_real K2)) (@ (@ tptp.ord_less_eq_real I2) K2))) (forall ((I2 tptp.set_nat) (K2 tptp.set_nat)) (= (@ (@ tptp.member_set_nat I2) (@ tptp.set_or4236626031148496127et_nat K2)) (@ (@ tptp.ord_less_eq_set_nat I2) K2))) (forall ((I2 tptp.rat) (K2 tptp.rat)) (= (@ (@ tptp.member_rat I2) (@ tptp.set_ord_atMost_rat K2)) (@ (@ tptp.ord_less_eq_rat I2) K2))) (forall ((I2 tptp.num) (K2 tptp.num)) (= (@ (@ tptp.member_num I2) (@ tptp.set_ord_atMost_num K2)) (@ (@ tptp.ord_less_eq_num I2) K2))) (forall ((I2 tptp.int) (K2 tptp.int)) (= (@ (@ tptp.member_int I2) (@ tptp.set_ord_atMost_int K2)) (@ (@ tptp.ord_less_eq_int I2) K2))) (forall ((I2 tptp.nat) (K2 tptp.nat)) (= (@ (@ tptp.member_nat I2) (@ tptp.set_ord_atMost_nat K2)) (@ (@ tptp.ord_less_eq_nat I2) K2))) (forall ((P2 Bool) (Q Bool)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.zero_n2052037380579107095ol_rat P2)) (@ tptp.zero_n2052037380579107095ol_rat Q)) (=> P2 Q))) (forall ((P2 Bool) (Q Bool)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.zero_n2687167440665602831ol_nat P2)) (@ tptp.zero_n2687167440665602831ol_nat Q)) (=> P2 Q))) (forall ((P2 Bool) (Q Bool)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.zero_n2684676970156552555ol_int P2)) (@ tptp.zero_n2684676970156552555ol_int Q)) (=> P2 Q))) (forall ((P2 Bool) (Q Bool)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.zero_n356916108424825756nteger P2)) (@ tptp.zero_n356916108424825756nteger Q)) (=> P2 Q))) (= (@ tptp.zero_n1201886186963655149omplex false) tptp.zero_zero_complex) (= (@ tptp.zero_n3304061248610475627l_real false) tptp.zero_zero_real) (= (@ tptp.zero_n2052037380579107095ol_rat false) tptp.zero_zero_rat) (= (@ tptp.zero_n2687167440665602831ol_nat false) tptp.zero_zero_nat) (= (@ tptp.zero_n2684676970156552555ol_int false) tptp.zero_zero_int) (= (@ tptp.zero_n356916108424825756nteger false) tptp.zero_z3403309356797280102nteger) (forall ((P2 Bool)) (= (= (@ tptp.zero_n1201886186963655149omplex P2) tptp.zero_zero_complex) (not P2))) (forall ((P2 Bool)) (= (= (@ tptp.zero_n3304061248610475627l_real P2) tptp.zero_zero_real) (not P2))) (forall ((P2 Bool)) (= (= (@ tptp.zero_n2052037380579107095ol_rat P2) tptp.zero_zero_rat) (not P2))) (forall ((P2 Bool)) (= (= (@ tptp.zero_n2687167440665602831ol_nat P2) tptp.zero_zero_nat) (not P2))) (forall ((P2 Bool)) (= (= (@ tptp.zero_n2684676970156552555ol_int P2) tptp.zero_zero_int) (not P2))) (forall ((P2 Bool)) (= (= (@ tptp.zero_n356916108424825756nteger P2) tptp.zero_z3403309356797280102nteger) (not P2))) (forall ((P2 Bool) (Q Bool)) (= (@ (@ tptp.ord_less_real (@ tptp.zero_n3304061248610475627l_real P2)) (@ tptp.zero_n3304061248610475627l_real Q)) (and (not P2) Q))) (forall ((P2 Bool) (Q Bool)) (= (@ (@ tptp.ord_less_rat (@ tptp.zero_n2052037380579107095ol_rat P2)) (@ tptp.zero_n2052037380579107095ol_rat Q)) (and (not P2) Q))) (forall ((P2 Bool) (Q Bool)) (= (@ (@ tptp.ord_less_nat (@ tptp.zero_n2687167440665602831ol_nat P2)) (@ tptp.zero_n2687167440665602831ol_nat Q)) (and (not P2) Q))) (forall ((P2 Bool) (Q Bool)) (= (@ (@ tptp.ord_less_int (@ tptp.zero_n2684676970156552555ol_int P2)) (@ tptp.zero_n2684676970156552555ol_int Q)) (and (not P2) Q))) (forall ((P2 Bool) (Q Bool)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.zero_n356916108424825756nteger P2)) (@ tptp.zero_n356916108424825756nteger Q)) (and (not P2) Q))) (forall ((P2 Bool)) (= (= (@ tptp.zero_n1201886186963655149omplex P2) tptp.one_one_complex) P2)) (forall ((P2 Bool)) (= (= (@ tptp.zero_n3304061248610475627l_real P2) tptp.one_one_real) P2)) (forall ((P2 Bool)) (= (= (@ tptp.zero_n2687167440665602831ol_nat P2) tptp.one_one_nat) P2)) (forall ((P2 Bool)) (= (= (@ tptp.zero_n2684676970156552555ol_int P2) tptp.one_one_int) P2)) (forall ((P2 Bool)) (= (= (@ tptp.zero_n356916108424825756nteger P2) tptp.one_one_Code_integer) P2)) (= (@ tptp.zero_n1201886186963655149omplex true) tptp.one_one_complex) (= (@ tptp.zero_n3304061248610475627l_real true) tptp.one_one_real) (= (@ tptp.zero_n2687167440665602831ol_nat true) tptp.one_one_nat) (= (@ tptp.zero_n2684676970156552555ol_int true) tptp.one_one_int) (= (@ tptp.zero_n356916108424825756nteger true) tptp.one_one_Code_integer) (forall ((P2 Bool)) (= (@ tptp.semiri5074537144036343181t_real (@ tptp.zero_n2687167440665602831ol_nat P2)) (@ tptp.zero_n3304061248610475627l_real P2))) (forall ((P2 Bool)) (let ((_let_1 (@ tptp.zero_n2687167440665602831ol_nat P2))) (= (@ tptp.semiri1316708129612266289at_nat _let_1) _let_1))) (forall ((P2 Bool)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.zero_n2687167440665602831ol_nat P2)) (@ tptp.zero_n2684676970156552555ol_int P2))) (forall ((P2 Bool)) (= (@ tptp.semiri4939895301339042750nteger (@ tptp.zero_n2687167440665602831ol_nat P2)) (@ tptp.zero_n356916108424825756nteger P2))) (forall ((P2 Bool) (Q Bool)) (= (@ tptp.zero_n2687167440665602831ol_nat (or P2 Q)) (@ (@ tptp.ord_max_nat (@ tptp.zero_n2687167440665602831ol_nat P2)) (@ tptp.zero_n2687167440665602831ol_nat Q)))) (forall ((P2 Bool) (Q Bool)) (= (@ tptp.zero_n2684676970156552555ol_int (or P2 Q)) (@ (@ tptp.ord_max_int (@ tptp.zero_n2684676970156552555ol_int P2)) (@ tptp.zero_n2684676970156552555ol_int Q)))) (forall ((P2 Bool) (Q Bool)) (= (@ tptp.zero_n356916108424825756nteger (or P2 Q)) (@ (@ tptp.ord_max_Code_integer (@ tptp.zero_n356916108424825756nteger P2)) (@ tptp.zero_n356916108424825756nteger Q)))) (forall ((K2 tptp.nat)) (@ tptp.finite_finite_nat (@ tptp.set_ord_atMost_nat K2))) (forall ((P2 Bool)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.zero_n3304061248610475627l_real P2)) P2)) (forall ((P2 Bool)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.zero_n2052037380579107095ol_rat P2)) P2)) (forall ((P2 Bool)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.zero_n2687167440665602831ol_nat P2)) P2)) (forall ((P2 Bool)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.zero_n2684676970156552555ol_int P2)) P2)) (forall ((P2 Bool)) (= (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ tptp.zero_n356916108424825756nteger P2)) P2)) (forall ((X tptp.set_nat) (Y tptp.set_nat)) (= (@ (@ tptp.ord_le6893508408891458716et_nat (@ tptp.set_or4236626031148496127et_nat X)) (@ tptp.set_or4236626031148496127et_nat Y)) (@ (@ tptp.ord_less_eq_set_nat X) Y))) (forall ((X tptp.rat) (Y tptp.rat)) (= (@ (@ tptp.ord_less_eq_set_rat (@ tptp.set_ord_atMost_rat X)) (@ tptp.set_ord_atMost_rat Y)) (@ (@ tptp.ord_less_eq_rat X) Y))) (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.ord_less_eq_set_num (@ tptp.set_ord_atMost_num X)) (@ tptp.set_ord_atMost_num Y)) (@ (@ tptp.ord_less_eq_num X) Y))) (forall ((X tptp.int) (Y tptp.int)) (= (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_ord_atMost_int X)) (@ tptp.set_ord_atMost_int Y)) (@ (@ tptp.ord_less_eq_int X) Y))) (forall ((X tptp.nat) (Y tptp.nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_ord_atMost_nat X)) (@ tptp.set_ord_atMost_nat Y)) (@ (@ tptp.ord_less_eq_nat X) Y))) (forall ((P2 Bool)) (= (@ (@ tptp.ord_less_real (@ tptp.zero_n3304061248610475627l_real P2)) tptp.one_one_real) (not P2))) (forall ((P2 Bool)) (= (@ (@ tptp.ord_less_rat (@ tptp.zero_n2052037380579107095ol_rat P2)) tptp.one_one_rat) (not P2))) (forall ((P2 Bool)) (= (@ (@ tptp.ord_less_nat (@ tptp.zero_n2687167440665602831ol_nat P2)) tptp.one_one_nat) (not P2))) (forall ((P2 Bool)) (= (@ (@ tptp.ord_less_int (@ tptp.zero_n2684676970156552555ol_int P2)) tptp.one_one_int) (not P2))) (forall ((P2 Bool)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.zero_n356916108424825756nteger P2)) tptp.one_one_Code_integer) (not P2))) (forall ((P2 Bool)) (= (@ tptp.zero_n1201886186963655149omplex (not P2)) (@ (@ tptp.minus_minus_complex tptp.one_one_complex) (@ tptp.zero_n1201886186963655149omplex P2)))) (forall ((P2 Bool)) (= (@ tptp.zero_n3304061248610475627l_real (not P2)) (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ tptp.zero_n3304061248610475627l_real P2)))) (forall ((P2 Bool)) (= (@ tptp.zero_n2052037380579107095ol_rat (not P2)) (@ (@ tptp.minus_minus_rat tptp.one_one_rat) (@ tptp.zero_n2052037380579107095ol_rat P2)))) (forall ((P2 Bool)) (= (@ tptp.zero_n2684676970156552555ol_int (not P2)) (@ (@ tptp.minus_minus_int tptp.one_one_int) (@ tptp.zero_n2684676970156552555ol_int P2)))) (forall ((P2 Bool)) (= (@ tptp.zero_n356916108424825756nteger (not P2)) (@ (@ tptp.minus_8373710615458151222nteger tptp.one_one_Code_integer) (@ tptp.zero_n356916108424825756nteger P2)))) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (@ (@ tptp.modulo_modulo_nat _let_1) N) (@ tptp.zero_n2687167440665602831ol_nat (not (= N _let_1)))))) (forall ((K2 tptp.nat)) (= (@ (@ tptp.gbinomial_complex tptp.zero_zero_complex) (@ tptp.suc K2)) tptp.zero_zero_complex)) (forall ((K2 tptp.nat)) (= (@ (@ tptp.gbinomial_real tptp.zero_zero_real) (@ tptp.suc K2)) tptp.zero_zero_real)) (forall ((K2 tptp.nat)) (= (@ (@ tptp.gbinomial_rat tptp.zero_zero_rat) (@ tptp.suc K2)) tptp.zero_zero_rat)) (forall ((K2 tptp.nat)) (= (@ (@ tptp.gbinomial_nat tptp.zero_zero_nat) (@ tptp.suc K2)) tptp.zero_zero_nat)) (forall ((K2 tptp.nat)) (= (@ (@ tptp.gbinomial_int tptp.zero_zero_int) (@ tptp.suc K2)) tptp.zero_zero_int)) (forall ((A tptp.code_integer)) (= (@ (@ tptp.gbinom8545251970709558553nteger A) tptp.zero_zero_nat) tptp.one_one_Code_integer)) (forall ((A tptp.complex)) (= (@ (@ tptp.gbinomial_complex A) tptp.zero_zero_nat) tptp.one_one_complex)) (forall ((A tptp.real)) (= (@ (@ tptp.gbinomial_real A) tptp.zero_zero_nat) tptp.one_one_real)) (forall ((A tptp.nat)) (= (@ (@ tptp.gbinomial_nat A) tptp.zero_zero_nat) tptp.one_one_nat)) (forall ((A tptp.int)) (= (@ (@ tptp.gbinomial_int A) tptp.zero_zero_nat) tptp.one_one_int)) (forall ((U tptp.nat)) (= (@ tptp.finite_card_nat (@ tptp.set_ord_atMost_nat U)) (@ tptp.suc U))) (forall ((L tptp.set_nat) (H tptp.set_nat) (H3 tptp.set_nat)) (= (@ (@ tptp.ord_le6893508408891458716et_nat (@ (@ tptp.set_or4548717258645045905et_nat L) H)) (@ tptp.set_or4236626031148496127et_nat H3)) (or (not (@ (@ tptp.ord_less_eq_set_nat L) H)) (@ (@ tptp.ord_less_eq_set_nat H) H3)))) (forall ((L tptp.rat) (H tptp.rat) (H3 tptp.rat)) (= (@ (@ tptp.ord_less_eq_set_rat (@ (@ tptp.set_or633870826150836451st_rat L) H)) (@ tptp.set_ord_atMost_rat H3)) (or (not (@ (@ tptp.ord_less_eq_rat L) H)) (@ (@ tptp.ord_less_eq_rat H) H3)))) (forall ((L tptp.num) (H tptp.num) (H3 tptp.num)) (= (@ (@ tptp.ord_less_eq_set_num (@ (@ tptp.set_or7049704709247886629st_num L) H)) (@ tptp.set_ord_atMost_num H3)) (or (not (@ (@ tptp.ord_less_eq_num L) H)) (@ (@ tptp.ord_less_eq_num H) H3)))) (forall ((L tptp.nat) (H tptp.nat) (H3 tptp.nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.set_or1269000886237332187st_nat L) H)) (@ tptp.set_ord_atMost_nat H3)) (or (not (@ (@ tptp.ord_less_eq_nat L) H)) (@ (@ tptp.ord_less_eq_nat H) H3)))) (forall ((L tptp.int) (H tptp.int) (H3 tptp.int)) (= (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.set_or1266510415728281911st_int L) H)) (@ tptp.set_ord_atMost_int H3)) (or (not (@ (@ tptp.ord_less_eq_int L) H)) (@ (@ tptp.ord_less_eq_int H) H3)))) (forall ((L tptp.real) (H tptp.real) (H3 tptp.real)) (= (@ (@ tptp.ord_less_eq_set_real (@ (@ tptp.set_or1222579329274155063t_real L) H)) (@ tptp.set_ord_atMost_real H3)) (or (not (@ (@ tptp.ord_less_eq_real L) H)) (@ (@ tptp.ord_less_eq_real H) H3)))) (forall ((G2 (-> tptp.nat tptp.rat)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.groups2906978787729119204at_rat G2))) (= (@ _let_2 (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.plus_plus_rat (@ _let_2 (@ tptp.set_ord_atMost_nat N))) (@ G2 _let_1)))))) (forall ((G2 (-> tptp.nat tptp.int)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.groups3539618377306564664at_int G2))) (= (@ _let_2 (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.plus_plus_int (@ _let_2 (@ tptp.set_ord_atMost_nat N))) (@ G2 _let_1)))))) (forall ((G2 (-> tptp.nat tptp.nat)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.groups3542108847815614940at_nat G2))) (= (@ _let_2 (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.plus_plus_nat (@ _let_2 (@ tptp.set_ord_atMost_nat N))) (@ G2 _let_1)))))) (forall ((G2 (-> tptp.nat tptp.real)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.groups6591440286371151544t_real G2))) (= (@ _let_2 (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.plus_plus_real (@ _let_2 (@ tptp.set_ord_atMost_nat N))) (@ G2 _let_1)))))) (forall ((G2 (-> tptp.nat tptp.real)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.groups129246275422532515t_real G2))) (= (@ _let_2 (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.times_times_real (@ _let_2 (@ tptp.set_ord_atMost_nat N))) (@ G2 _let_1)))))) (forall ((G2 (-> tptp.nat tptp.rat)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.groups73079841787564623at_rat G2))) (= (@ _let_2 (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.times_times_rat (@ _let_2 (@ tptp.set_ord_atMost_nat N))) (@ G2 _let_1)))))) (forall ((G2 (-> tptp.nat tptp.int)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.groups705719431365010083at_int G2))) (= (@ _let_2 (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.times_times_int (@ _let_2 (@ tptp.set_ord_atMost_nat N))) (@ G2 _let_1)))))) (forall ((G2 (-> tptp.nat tptp.nat)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.groups708209901874060359at_nat G2))) (= (@ _let_2 (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.times_times_nat (@ _let_2 (@ tptp.set_ord_atMost_nat N))) (@ G2 _let_1)))))) (= (@ tptp.set_ord_atMost_nat tptp.zero_zero_nat) (@ _let_77 tptp.bot_bot_set_nat)) (forall ((I2 tptp.nat) (Xs2 tptp.list_VEBT_VEBT) (J2 tptp.nat)) (let ((_let_1 (@ tptp.nth_VEBT_VEBT Xs2))) (let ((_let_2 (@ tptp.size_s6755466524823107622T_VEBT Xs2))) (=> (@ (@ tptp.ord_less_nat I2) _let_2) (=> (@ (@ tptp.ord_less_nat J2) _let_2) (= (@ tptp.distinct_VEBT_VEBT (@ (@ (@ tptp.list_u1324408373059187874T_VEBT (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs2) I2) (@ _let_1 J2))) J2) (@ _let_1 I2))) (@ tptp.distinct_VEBT_VEBT Xs2))))))) (forall ((I2 tptp.nat) (Xs2 tptp.list_o) (J2 tptp.nat)) (let ((_let_1 (@ tptp.nth_o Xs2))) (let ((_let_2 (@ tptp.size_size_list_o Xs2))) (=> (@ (@ tptp.ord_less_nat I2) _let_2) (=> (@ (@ tptp.ord_less_nat J2) _let_2) (= (@ tptp.distinct_o (@ (@ (@ tptp.list_update_o (@ (@ (@ tptp.list_update_o Xs2) I2) (@ _let_1 J2))) J2) (@ _let_1 I2))) (@ tptp.distinct_o Xs2))))))) (forall ((I2 tptp.nat) (Xs2 tptp.list_nat) (J2 tptp.nat)) (let ((_let_1 (@ tptp.nth_nat Xs2))) (let ((_let_2 (@ tptp.size_size_list_nat Xs2))) (=> (@ (@ tptp.ord_less_nat I2) _let_2) (=> (@ (@ tptp.ord_less_nat J2) _let_2) (= (@ tptp.distinct_nat (@ (@ (@ tptp.list_update_nat (@ (@ (@ tptp.list_update_nat Xs2) I2) (@ _let_1 J2))) J2) (@ _let_1 I2))) (@ tptp.distinct_nat Xs2))))))) (forall ((I2 tptp.nat) (Xs2 tptp.list_int) (J2 tptp.nat)) (let ((_let_1 (@ tptp.nth_int Xs2))) (let ((_let_2 (@ tptp.size_size_list_int Xs2))) (=> (@ (@ tptp.ord_less_nat I2) _let_2) (=> (@ (@ tptp.ord_less_nat J2) _let_2) (= (@ tptp.distinct_int (@ (@ (@ tptp.list_update_int (@ (@ (@ tptp.list_update_int Xs2) I2) (@ _let_1 J2))) J2) (@ _let_1 I2))) (@ tptp.distinct_int Xs2))))))) (forall ((A4 tptp.set_real) (F2 (-> tptp.real tptp.real)) (P2 (-> tptp.real Bool))) (=> (@ tptp.finite_finite_real A4) (= (@ (@ tptp.groups8097168146408367636l_real (lambda ((X4 tptp.real)) (@ (@ tptp.times_times_real (@ F2 X4)) (@ tptp.zero_n3304061248610475627l_real (@ P2 X4))))) A4) (@ (@ tptp.groups8097168146408367636l_real F2) (@ (@ tptp.inf_inf_set_real A4) (@ tptp.collect_real P2)))))) (forall ((A4 tptp.set_int) (F2 (-> tptp.int tptp.real)) (P2 (-> tptp.int Bool))) (=> (@ tptp.finite_finite_int A4) (= (@ (@ tptp.groups8778361861064173332t_real (lambda ((X4 tptp.int)) (@ (@ tptp.times_times_real (@ F2 X4)) (@ tptp.zero_n3304061248610475627l_real (@ P2 X4))))) A4) (@ (@ tptp.groups8778361861064173332t_real F2) (@ (@ tptp.inf_inf_set_int A4) (@ tptp.collect_int P2)))))) (forall ((A4 tptp.set_complex) (F2 (-> tptp.complex tptp.real)) (P2 (-> tptp.complex Bool))) (=> (@ tptp.finite3207457112153483333omplex A4) (= (@ (@ tptp.groups5808333547571424918x_real (lambda ((X4 tptp.complex)) (@ (@ tptp.times_times_real (@ F2 X4)) (@ tptp.zero_n3304061248610475627l_real (@ P2 X4))))) A4) (@ (@ tptp.groups5808333547571424918x_real F2) (@ (@ tptp.inf_inf_set_complex A4) (@ tptp.collect_complex P2)))))) (forall ((A4 tptp.set_real) (F2 (-> tptp.real tptp.rat)) (P2 (-> tptp.real Bool))) (=> (@ tptp.finite_finite_real A4) (= (@ (@ tptp.groups1300246762558778688al_rat (lambda ((X4 tptp.real)) (@ (@ tptp.times_times_rat (@ F2 X4)) (@ tptp.zero_n2052037380579107095ol_rat (@ P2 X4))))) A4) (@ (@ tptp.groups1300246762558778688al_rat F2) (@ (@ tptp.inf_inf_set_real A4) (@ tptp.collect_real P2)))))) (forall ((A4 tptp.set_int) (F2 (-> tptp.int tptp.rat)) (P2 (-> tptp.int Bool))) (=> (@ tptp.finite_finite_int A4) (= (@ (@ tptp.groups3906332499630173760nt_rat (lambda ((X4 tptp.int)) (@ (@ tptp.times_times_rat (@ F2 X4)) (@ tptp.zero_n2052037380579107095ol_rat (@ P2 X4))))) A4) (@ (@ tptp.groups3906332499630173760nt_rat F2) (@ (@ tptp.inf_inf_set_int A4) (@ tptp.collect_int P2)))))) (forall ((A4 tptp.set_complex) (F2 (-> tptp.complex tptp.rat)) (P2 (-> tptp.complex Bool))) (=> (@ tptp.finite3207457112153483333omplex A4) (= (@ (@ tptp.groups5058264527183730370ex_rat (lambda ((X4 tptp.complex)) (@ (@ tptp.times_times_rat (@ F2 X4)) (@ tptp.zero_n2052037380579107095ol_rat (@ P2 X4))))) A4) (@ (@ tptp.groups5058264527183730370ex_rat F2) (@ (@ tptp.inf_inf_set_complex A4) (@ tptp.collect_complex P2)))))) (forall ((A4 tptp.set_nat) (F2 (-> tptp.nat tptp.rat)) (P2 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat A4) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((X4 tptp.nat)) (@ (@ tptp.times_times_rat (@ F2 X4)) (@ tptp.zero_n2052037380579107095ol_rat (@ P2 X4))))) A4) (@ (@ tptp.groups2906978787729119204at_rat F2) (@ (@ tptp.inf_inf_set_nat A4) (@ tptp.collect_nat P2)))))) (forall ((A4 tptp.set_real) (F2 (-> tptp.real tptp.nat)) (P2 (-> tptp.real Bool))) (=> (@ tptp.finite_finite_real A4) (= (@ (@ tptp.groups1935376822645274424al_nat (lambda ((X4 tptp.real)) (@ (@ tptp.times_times_nat (@ F2 X4)) (@ tptp.zero_n2687167440665602831ol_nat (@ P2 X4))))) A4) (@ (@ tptp.groups1935376822645274424al_nat F2) (@ (@ tptp.inf_inf_set_real A4) (@ tptp.collect_real P2)))))) (forall ((A4 tptp.set_int) (F2 (-> tptp.int tptp.nat)) (P2 (-> tptp.int Bool))) (=> (@ tptp.finite_finite_int A4) (= (@ (@ tptp.groups4541462559716669496nt_nat (lambda ((X4 tptp.int)) (@ (@ tptp.times_times_nat (@ F2 X4)) (@ tptp.zero_n2687167440665602831ol_nat (@ P2 X4))))) A4) (@ (@ tptp.groups4541462559716669496nt_nat F2) (@ (@ tptp.inf_inf_set_int A4) (@ tptp.collect_int P2)))))) (forall ((A4 tptp.set_complex) (F2 (-> tptp.complex tptp.nat)) (P2 (-> tptp.complex Bool))) (=> (@ tptp.finite3207457112153483333omplex A4) (= (@ (@ tptp.groups5693394587270226106ex_nat (lambda ((X4 tptp.complex)) (@ (@ tptp.times_times_nat (@ F2 X4)) (@ tptp.zero_n2687167440665602831ol_nat (@ P2 X4))))) A4) (@ (@ tptp.groups5693394587270226106ex_nat F2) (@ (@ tptp.inf_inf_set_complex A4) (@ tptp.collect_complex P2)))))) (forall ((A4 tptp.set_real) (P2 (-> tptp.real Bool)) (F2 (-> tptp.real tptp.real))) (=> (@ tptp.finite_finite_real A4) (= (@ (@ tptp.groups8097168146408367636l_real (lambda ((X4 tptp.real)) (@ (@ tptp.times_times_real (@ tptp.zero_n3304061248610475627l_real (@ P2 X4))) (@ F2 X4)))) A4) (@ (@ tptp.groups8097168146408367636l_real F2) (@ (@ tptp.inf_inf_set_real A4) (@ tptp.collect_real P2)))))) (forall ((A4 tptp.set_int) (P2 (-> tptp.int Bool)) (F2 (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int A4) (= (@ (@ tptp.groups8778361861064173332t_real (lambda ((X4 tptp.int)) (@ (@ tptp.times_times_real (@ tptp.zero_n3304061248610475627l_real (@ P2 X4))) (@ F2 X4)))) A4) (@ (@ tptp.groups8778361861064173332t_real F2) (@ (@ tptp.inf_inf_set_int A4) (@ tptp.collect_int P2)))))) (forall ((A4 tptp.set_complex) (P2 (-> tptp.complex Bool)) (F2 (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex A4) (= (@ (@ tptp.groups5808333547571424918x_real (lambda ((X4 tptp.complex)) (@ (@ tptp.times_times_real (@ tptp.zero_n3304061248610475627l_real (@ P2 X4))) (@ F2 X4)))) A4) (@ (@ tptp.groups5808333547571424918x_real F2) (@ (@ tptp.inf_inf_set_complex A4) (@ tptp.collect_complex P2)))))) (forall ((A4 tptp.set_real) (P2 (-> tptp.real Bool)) (F2 (-> tptp.real tptp.rat))) (=> (@ tptp.finite_finite_real A4) (= (@ (@ tptp.groups1300246762558778688al_rat (lambda ((X4 tptp.real)) (@ (@ tptp.times_times_rat (@ tptp.zero_n2052037380579107095ol_rat (@ P2 X4))) (@ F2 X4)))) A4) (@ (@ tptp.groups1300246762558778688al_rat F2) (@ (@ tptp.inf_inf_set_real A4) (@ tptp.collect_real P2)))))) (forall ((A4 tptp.set_int) (P2 (-> tptp.int Bool)) (F2 (-> tptp.int tptp.rat))) (=> (@ tptp.finite_finite_int A4) (= (@ (@ tptp.groups3906332499630173760nt_rat (lambda ((X4 tptp.int)) (@ (@ tptp.times_times_rat (@ tptp.zero_n2052037380579107095ol_rat (@ P2 X4))) (@ F2 X4)))) A4) (@ (@ tptp.groups3906332499630173760nt_rat F2) (@ (@ tptp.inf_inf_set_int A4) (@ tptp.collect_int P2)))))) (forall ((A4 tptp.set_complex) (P2 (-> tptp.complex Bool)) (F2 (-> tptp.complex tptp.rat))) (=> (@ tptp.finite3207457112153483333omplex A4) (= (@ (@ tptp.groups5058264527183730370ex_rat (lambda ((X4 tptp.complex)) (@ (@ tptp.times_times_rat (@ tptp.zero_n2052037380579107095ol_rat (@ P2 X4))) (@ F2 X4)))) A4) (@ (@ tptp.groups5058264527183730370ex_rat F2) (@ (@ tptp.inf_inf_set_complex A4) (@ tptp.collect_complex P2)))))) (forall ((A4 tptp.set_nat) (P2 (-> tptp.nat Bool)) (F2 (-> tptp.nat tptp.rat))) (=> (@ tptp.finite_finite_nat A4) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((X4 tptp.nat)) (@ (@ tptp.times_times_rat (@ tptp.zero_n2052037380579107095ol_rat (@ P2 X4))) (@ F2 X4)))) A4) (@ (@ tptp.groups2906978787729119204at_rat F2) (@ (@ tptp.inf_inf_set_nat A4) (@ tptp.collect_nat P2)))))) (forall ((A4 tptp.set_real) (P2 (-> tptp.real Bool)) (F2 (-> tptp.real tptp.nat))) (=> (@ tptp.finite_finite_real A4) (= (@ (@ tptp.groups1935376822645274424al_nat (lambda ((X4 tptp.real)) (@ (@ tptp.times_times_nat (@ tptp.zero_n2687167440665602831ol_nat (@ P2 X4))) (@ F2 X4)))) A4) (@ (@ tptp.groups1935376822645274424al_nat F2) (@ (@ tptp.inf_inf_set_real A4) (@ tptp.collect_real P2)))))) (forall ((A4 tptp.set_int) (P2 (-> tptp.int Bool)) (F2 (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int A4) (= (@ (@ tptp.groups4541462559716669496nt_nat (lambda ((X4 tptp.int)) (@ (@ tptp.times_times_nat (@ tptp.zero_n2687167440665602831ol_nat (@ P2 X4))) (@ F2 X4)))) A4) (@ (@ tptp.groups4541462559716669496nt_nat F2) (@ (@ tptp.inf_inf_set_int A4) (@ tptp.collect_int P2)))))) (forall ((A4 tptp.set_complex) (P2 (-> tptp.complex Bool)) (F2 (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex A4) (= (@ (@ tptp.groups5693394587270226106ex_nat (lambda ((X4 tptp.complex)) (@ (@ tptp.times_times_nat (@ tptp.zero_n2687167440665602831ol_nat (@ P2 X4))) (@ F2 X4)))) A4) (@ (@ tptp.groups5693394587270226106ex_nat F2) (@ (@ tptp.inf_inf_set_complex A4) (@ tptp.collect_complex P2)))))) (forall ((B Bool)) (= (@ (@ tptp.divide_divide_nat (@ tptp.zero_n2687167440665602831ol_nat B)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_nat)) (forall ((B Bool)) (= (@ (@ tptp.divide_divide_int (@ tptp.zero_n2684676970156552555ol_int B)) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) tptp.zero_zero_int)) (forall ((B Bool)) (= (@ (@ tptp.divide6298287555418463151nteger (@ tptp.zero_n356916108424825756nteger B)) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) tptp.zero_z3403309356797280102nteger)) (forall ((A4 tptp.set_complex) (N tptp.nat)) (=> (@ tptp.finite3207457112153483333omplex A4) (@ tptp.finite8712137658972009173omplex (@ tptp.collect_list_complex (lambda ((Xs tptp.list_complex)) (and (= (@ tptp.size_s3451745648224563538omplex Xs) N) (@ tptp.distinct_complex Xs) (@ (@ tptp.ord_le211207098394363844omplex (@ tptp.set_complex2 Xs)) A4))))))) (forall ((A4 tptp.set_VEBT_VEBT) (N tptp.nat)) (=> (@ tptp.finite5795047828879050333T_VEBT A4) (@ tptp.finite3004134309566078307T_VEBT (@ tptp.collec5608196760682091941T_VEBT (lambda ((Xs tptp.list_VEBT_VEBT)) (and (= (@ tptp.size_s6755466524823107622T_VEBT Xs) N) (@ tptp.distinct_VEBT_VEBT Xs) (@ (@ tptp.ord_le4337996190870823476T_VEBT (@ tptp.set_VEBT_VEBT2 Xs)) A4))))))) (forall ((A4 tptp.set_o) (N tptp.nat)) (=> (@ tptp.finite_finite_o A4) (@ tptp.finite_finite_list_o (@ tptp.collect_list_o (lambda ((Xs tptp.list_o)) (and (= (@ tptp.size_size_list_o Xs) N) (@ tptp.distinct_o Xs) (@ (@ tptp.ord_less_eq_set_o (@ tptp.set_o2 Xs)) A4))))))) (forall ((A4 tptp.set_int) (N tptp.nat)) (=> (@ tptp.finite_finite_int A4) (@ tptp.finite3922522038869484883st_int (@ tptp.collect_list_int (lambda ((Xs tptp.list_int)) (and (= (@ tptp.size_size_list_int Xs) N) (@ tptp.distinct_int Xs) (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_int2 Xs)) A4))))))) (forall ((A4 tptp.set_nat) (N tptp.nat)) (=> (@ tptp.finite_finite_nat A4) (@ tptp.finite8100373058378681591st_nat (@ tptp.collect_list_nat (lambda ((Xs tptp.list_nat)) (and (= (@ tptp.size_size_list_nat Xs) N) (@ tptp.distinct_nat Xs) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_nat2 Xs)) A4))))))) (forall ((N tptp.nat)) (= (@ (@ tptp.divide_divide_nat tptp.one_one_nat) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (@ tptp.zero_n2687167440665602831ol_nat (= N tptp.zero_zero_nat)))) (forall ((N tptp.nat)) (= (@ (@ tptp.divide_divide_int tptp.one_one_int) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)) (@ tptp.zero_n2684676970156552555ol_int (= N tptp.zero_zero_nat)))) (forall ((N tptp.nat)) (= (@ (@ tptp.divide6298287555418463151nteger tptp.one_one_Code_integer) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) N)) (@ tptp.zero_n356916108424825756nteger (= N tptp.zero_zero_nat)))) (forall ((N tptp.nat)) (= (@ (@ tptp.divide_divide_nat tptp.one_one_nat) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (@ tptp.zero_n2687167440665602831ol_nat (= N tptp.zero_zero_nat)))) (forall ((N tptp.nat)) (= (@ (@ tptp.divide_divide_int tptp.one_one_int) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)) (@ tptp.zero_n2684676970156552555ol_int (= N tptp.zero_zero_nat)))) (forall ((N tptp.nat)) (= (@ (@ tptp.divide6298287555418463151nteger tptp.one_one_Code_integer) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) N)) (@ tptp.zero_n356916108424825756nteger (= N tptp.zero_zero_nat)))) (forall ((N tptp.nat)) (= (@ (@ tptp.modulo8411746178871703098atural tptp.one_one_Code_natural) (@ (@ tptp.power_7079662738309270450atural (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one))) N)) (@ tptp.zero_n8403883297036319079atural (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)))) (forall ((N tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat tptp.one_one_nat) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (@ tptp.zero_n2687167440665602831ol_nat (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)))) (forall ((N tptp.nat)) (= (@ (@ tptp.modulo_modulo_int tptp.one_one_int) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)) (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)))) (forall ((N tptp.nat)) (= (@ (@ tptp.modulo364778990260209775nteger tptp.one_one_Code_integer) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) N)) (@ tptp.zero_n356916108424825756nteger (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)))) (forall ((P Bool) (Q2 Bool)) (= (= (@ tptp.zero_n2687167440665602831ol_nat P) (@ tptp.zero_n2687167440665602831ol_nat Q2)) (= P Q2))) (forall ((P Bool) (Q2 Bool)) (= (= (@ tptp.zero_n2684676970156552555ol_int P) (@ tptp.zero_n2684676970156552555ol_int Q2)) (= P Q2))) (forall ((P Bool) (Q2 Bool)) (= (= (@ tptp.zero_n356916108424825756nteger P) (@ tptp.zero_n356916108424825756nteger Q2)) (= P Q2))) (forall ((P2 Bool) (Q Bool)) (= (@ tptp.zero_n3304061248610475627l_real (and P2 Q)) (@ (@ tptp.times_times_real (@ tptp.zero_n3304061248610475627l_real P2)) (@ tptp.zero_n3304061248610475627l_real Q)))) (forall ((P2 Bool) (Q Bool)) (= (@ tptp.zero_n2052037380579107095ol_rat (and P2 Q)) (@ (@ tptp.times_times_rat (@ tptp.zero_n2052037380579107095ol_rat P2)) (@ tptp.zero_n2052037380579107095ol_rat Q)))) (forall ((P2 Bool) (Q Bool)) (= (@ tptp.zero_n2687167440665602831ol_nat (and P2 Q)) (@ (@ tptp.times_times_nat (@ tptp.zero_n2687167440665602831ol_nat P2)) (@ tptp.zero_n2687167440665602831ol_nat Q)))) (forall ((P2 Bool) (Q Bool)) (= (@ tptp.zero_n2684676970156552555ol_int (and P2 Q)) (@ (@ tptp.times_times_int (@ tptp.zero_n2684676970156552555ol_int P2)) (@ tptp.zero_n2684676970156552555ol_int Q)))) (forall ((P2 Bool) (Q Bool)) (= (@ tptp.zero_n356916108424825756nteger (and P2 Q)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.zero_n356916108424825756nteger P2)) (@ tptp.zero_n356916108424825756nteger Q)))) (forall ((H tptp.int)) (not (= tptp.bot_bot_set_int (@ tptp.set_ord_atMost_int H)))) (forall ((H tptp.real)) (not (= tptp.bot_bot_set_real (@ tptp.set_ord_atMost_real H)))) (forall ((H tptp.nat)) (not (= tptp.bot_bot_set_nat (@ tptp.set_ord_atMost_nat H)))) (forall ((A tptp.int)) (not (@ tptp.finite_finite_int (@ tptp.set_ord_atMost_int A)))) (forall ((H3 tptp.int) (L tptp.int) (H tptp.int)) (not (= (@ tptp.set_ord_atMost_int H3) (@ (@ tptp.set_or1266510415728281911st_int L) H)))) (forall ((H3 tptp.real) (L tptp.real) (H tptp.real)) (not (= (@ tptp.set_ord_atMost_real H3) (@ (@ tptp.set_or1222579329274155063t_real L) H)))) _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 (forall ((P2 Bool)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.zero_n3304061248610475627l_real P2))) (forall ((P2 Bool)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.zero_n2052037380579107095ol_rat P2))) (forall ((P2 Bool)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ tptp.zero_n2687167440665602831ol_nat P2))) (forall ((P2 Bool)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.zero_n2684676970156552555ol_int P2))) (forall ((P2 Bool)) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ tptp.zero_n356916108424825756nteger P2))) (forall ((P2 Bool)) (@ (@ tptp.ord_less_eq_real (@ tptp.zero_n3304061248610475627l_real P2)) tptp.one_one_real)) (forall ((P2 Bool)) (@ (@ tptp.ord_less_eq_rat (@ tptp.zero_n2052037380579107095ol_rat P2)) tptp.one_one_rat)) (forall ((P2 Bool)) (@ (@ tptp.ord_less_eq_nat (@ tptp.zero_n2687167440665602831ol_nat P2)) tptp.one_one_nat)) (forall ((P2 Bool)) (@ (@ tptp.ord_less_eq_int (@ tptp.zero_n2684676970156552555ol_int P2)) tptp.one_one_int)) (forall ((P2 Bool)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.zero_n356916108424825756nteger P2)) tptp.one_one_Code_integer)) _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 (forall ((P2 (-> tptp.complex Bool)) (P Bool)) (= (@ P2 (@ tptp.zero_n1201886186963655149omplex P)) (and (=> P (@ P2 tptp.one_one_complex)) (=> (not P) (@ P2 tptp.zero_zero_complex))))) (forall ((P2 (-> tptp.real Bool)) (P Bool)) (= (@ P2 (@ tptp.zero_n3304061248610475627l_real P)) (and (=> P (@ P2 tptp.one_one_real)) (=> (not P) (@ P2 tptp.zero_zero_real))))) (forall ((P2 (-> tptp.rat Bool)) (P Bool)) (= (@ P2 (@ tptp.zero_n2052037380579107095ol_rat P)) (and (=> P (@ P2 tptp.one_one_rat)) (=> (not P) (@ P2 tptp.zero_zero_rat))))) (forall ((P2 (-> tptp.nat Bool)) (P Bool)) (= (@ P2 (@ tptp.zero_n2687167440665602831ol_nat P)) (and (=> P (@ P2 tptp.one_one_nat)) (=> (not P) (@ P2 tptp.zero_zero_nat))))) (forall ((P2 (-> tptp.int Bool)) (P Bool)) (= (@ P2 (@ tptp.zero_n2684676970156552555ol_int P)) (and (=> P (@ P2 tptp.one_one_int)) (=> (not P) (@ P2 tptp.zero_zero_int))))) (forall ((P2 (-> tptp.code_integer Bool)) (P Bool)) (= (@ P2 (@ tptp.zero_n356916108424825756nteger P)) (and (=> P (@ P2 tptp.one_one_Code_integer)) (=> (not P) (@ P2 tptp.zero_z3403309356797280102nteger))))) (forall ((P2 (-> tptp.complex Bool)) (P Bool)) (= (@ P2 (@ tptp.zero_n1201886186963655149omplex P)) (not (or (and P (not (@ P2 tptp.one_one_complex))) (and (not P) (not (@ P2 tptp.zero_zero_complex))))))) (forall ((P2 (-> tptp.real Bool)) (P Bool)) (= (@ P2 (@ tptp.zero_n3304061248610475627l_real P)) (not (or (and P (not (@ P2 tptp.one_one_real))) (and (not P) (not (@ P2 tptp.zero_zero_real))))))) (forall ((P2 (-> tptp.rat Bool)) (P Bool)) (= (@ P2 (@ tptp.zero_n2052037380579107095ol_rat P)) (not (or (and P (not (@ P2 tptp.one_one_rat))) (and (not P) (not (@ P2 tptp.zero_zero_rat))))))) (forall ((P2 (-> tptp.nat Bool)) (P Bool)) (= (@ P2 (@ tptp.zero_n2687167440665602831ol_nat P)) (not (or (and P (not (@ P2 tptp.one_one_nat))) (and (not P) (not (@ P2 tptp.zero_zero_nat))))))) (forall ((P2 (-> tptp.int Bool)) (P Bool)) (= (@ P2 (@ tptp.zero_n2684676970156552555ol_int P)) (not (or (and P (not (@ P2 tptp.one_one_int))) (and (not P) (not (@ P2 tptp.zero_zero_int))))))) (forall ((P2 (-> tptp.code_integer Bool)) (P Bool)) (= (@ P2 (@ tptp.zero_n356916108424825756nteger P)) (not (or (and P (not (@ P2 tptp.one_one_Code_integer))) (and (not P) (not (@ P2 tptp.zero_z3403309356797280102nteger))))))) (= tptp.set_ord_atMost_nat (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat)) (forall ((K2 tptp.nat)) (= (@ tptp.set_ord_lessThan_nat (@ tptp.suc K2)) (@ tptp.set_ord_atMost_nat K2))) (forall ((K2 tptp.nat)) (let ((_let_1 (@ tptp.suc K2))) (= (@ tptp.set_ord_atMost_nat _let_1) (@ (@ tptp.insert_nat _let_1) (@ tptp.set_ord_atMost_nat K2))))) (forall ((H tptp.int) (L3 tptp.int) (H3 tptp.int)) (not (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_ord_atMost_int H)) (@ (@ tptp.set_or1266510415728281911st_int L3) H3)))) (forall ((H tptp.real) (L3 tptp.real) (H3 tptp.real)) (not (@ (@ tptp.ord_less_eq_set_real (@ tptp.set_ord_atMost_real H)) (@ (@ tptp.set_or1222579329274155063t_real L3) H3)))) (forall ((Xs2 tptp.list_VEBT_VEBT) (I2 tptp.nat) (J2 tptp.nat)) (let ((_let_1 (@ tptp.nth_VEBT_VEBT Xs2))) (let ((_let_2 (@ tptp.size_s6755466524823107622T_VEBT Xs2))) (=> (@ tptp.distinct_VEBT_VEBT Xs2) (=> (@ (@ tptp.ord_less_nat I2) _let_2) (=> (@ (@ tptp.ord_less_nat J2) _let_2) (= (= (@ _let_1 I2) (@ _let_1 J2)) (= I2 J2)))))))) (forall ((Xs2 tptp.list_o) (I2 tptp.nat) (J2 tptp.nat)) (let ((_let_1 (@ tptp.nth_o Xs2))) (let ((_let_2 (@ tptp.size_size_list_o Xs2))) (=> (@ tptp.distinct_o Xs2) (=> (@ (@ tptp.ord_less_nat I2) _let_2) (=> (@ (@ tptp.ord_less_nat J2) _let_2) (= (= (@ _let_1 I2) (@ _let_1 J2)) (= I2 J2)))))))) (forall ((Xs2 tptp.list_nat) (I2 tptp.nat) (J2 tptp.nat)) (let ((_let_1 (@ tptp.nth_nat Xs2))) (let ((_let_2 (@ tptp.size_size_list_nat Xs2))) (=> (@ tptp.distinct_nat Xs2) (=> (@ (@ tptp.ord_less_nat I2) _let_2) (=> (@ (@ tptp.ord_less_nat J2) _let_2) (= (= (@ _let_1 I2) (@ _let_1 J2)) (= I2 J2)))))))) (forall ((Xs2 tptp.list_int) (I2 tptp.nat) (J2 tptp.nat)) (let ((_let_1 (@ tptp.nth_int Xs2))) (let ((_let_2 (@ tptp.size_size_list_int Xs2))) (=> (@ tptp.distinct_int Xs2) (=> (@ (@ tptp.ord_less_nat I2) _let_2) (=> (@ (@ tptp.ord_less_nat J2) _let_2) (= (= (@ _let_1 I2) (@ _let_1 J2)) (= I2 J2)))))))) _let_232 _let_231 _let_230 _let_229 (forall ((Xs2 tptp.list_complex)) (=> (= (@ tptp.finite_card_complex (@ tptp.set_complex2 Xs2)) (@ tptp.size_s3451745648224563538omplex Xs2)) (@ tptp.distinct_complex Xs2))) (forall ((Xs2 tptp.list_list_nat)) (=> (= (@ tptp.finite_card_list_nat (@ tptp.set_list_nat2 Xs2)) (@ tptp.size_s3023201423986296836st_nat Xs2)) (@ tptp.distinct_list_nat Xs2))) (forall ((Xs2 tptp.list_set_nat)) (=> (= (@ tptp.finite_card_set_nat (@ tptp.set_set_nat2 Xs2)) (@ tptp.size_s3254054031482475050et_nat Xs2)) (@ tptp.distinct_set_nat Xs2))) (forall ((Xs2 tptp.list_VEBT_VEBT)) (=> (= (@ tptp.finite7802652506058667612T_VEBT (@ tptp.set_VEBT_VEBT2 Xs2)) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (@ tptp.distinct_VEBT_VEBT Xs2))) (forall ((Xs2 tptp.list_o)) (=> (= (@ tptp.finite_card_o (@ tptp.set_o2 Xs2)) (@ tptp.size_size_list_o Xs2)) (@ tptp.distinct_o Xs2))) (forall ((Xs2 tptp.list_nat)) (=> (= (@ tptp.finite_card_nat (@ tptp.set_nat2 Xs2)) (@ tptp.size_size_list_nat Xs2)) (@ tptp.distinct_nat Xs2))) (forall ((Xs2 tptp.list_int)) (=> (= (@ tptp.finite_card_int (@ tptp.set_int2 Xs2)) (@ tptp.size_size_list_int Xs2)) (@ tptp.distinct_int Xs2))) (forall ((Xs2 tptp.list_complex)) (=> (@ tptp.distinct_complex Xs2) (= (@ tptp.finite_card_complex (@ tptp.set_complex2 Xs2)) (@ tptp.size_s3451745648224563538omplex Xs2)))) (forall ((Xs2 tptp.list_list_nat)) (=> (@ tptp.distinct_list_nat Xs2) (= (@ tptp.finite_card_list_nat (@ tptp.set_list_nat2 Xs2)) (@ tptp.size_s3023201423986296836st_nat Xs2)))) (forall ((Xs2 tptp.list_set_nat)) (=> (@ tptp.distinct_set_nat Xs2) (= (@ tptp.finite_card_set_nat (@ tptp.set_set_nat2 Xs2)) (@ tptp.size_s3254054031482475050et_nat Xs2)))) (forall ((Xs2 tptp.list_VEBT_VEBT)) (=> (@ tptp.distinct_VEBT_VEBT Xs2) (= (@ tptp.finite7802652506058667612T_VEBT (@ tptp.set_VEBT_VEBT2 Xs2)) (@ tptp.size_s6755466524823107622T_VEBT Xs2)))) (forall ((Xs2 tptp.list_o)) (=> (@ tptp.distinct_o Xs2) (= (@ tptp.finite_card_o (@ tptp.set_o2 Xs2)) (@ tptp.size_size_list_o Xs2)))) (forall ((Xs2 tptp.list_nat)) (=> (@ tptp.distinct_nat Xs2) (= (@ tptp.finite_card_nat (@ tptp.set_nat2 Xs2)) (@ tptp.size_size_list_nat Xs2)))) (forall ((Xs2 tptp.list_int)) (=> (@ tptp.distinct_int Xs2) (= (@ tptp.finite_card_int (@ tptp.set_int2 Xs2)) (@ tptp.size_size_list_int Xs2)))) (forall ((A tptp.complex) (K2 tptp.nat)) (let ((_let_1 (@ tptp.suc K2))) (let ((_let_2 (@ tptp.gbinomial_complex A))) (= (@ (@ tptp.gbinomial_complex (@ (@ tptp.plus_plus_complex A) tptp.one_one_complex)) _let_1) (@ (@ tptp.plus_plus_complex (@ _let_2 K2)) (@ _let_2 _let_1)))))) (forall ((A tptp.real) (K2 tptp.nat)) (let ((_let_1 (@ tptp.suc K2))) (let ((_let_2 (@ tptp.gbinomial_real A))) (= (@ (@ tptp.gbinomial_real (@ (@ tptp.plus_plus_real A) tptp.one_one_real)) _let_1) (@ (@ tptp.plus_plus_real (@ _let_2 K2)) (@ _let_2 _let_1)))))) (forall ((A tptp.rat) (K2 tptp.nat)) (let ((_let_1 (@ tptp.suc K2))) (let ((_let_2 (@ tptp.gbinomial_rat A))) (= (@ (@ tptp.gbinomial_rat (@ (@ tptp.plus_plus_rat A) tptp.one_one_rat)) _let_1) (@ (@ tptp.plus_plus_rat (@ _let_2 K2)) (@ _let_2 _let_1)))))) (forall ((K2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.gbinomial_real (@ tptp.semiri5074537144036343181t_real N)))) (=> (@ (@ tptp.ord_less_eq_nat K2) N) (= (@ _let_1 K2) (@ _let_1 (@ (@ tptp.minus_minus_nat N) K2)))))) (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_eq_set_real (@ tptp.set_ord_atMost_real A)) (@ tptp.set_or5984915006950818249n_real B)) (@ (@ tptp.ord_less_real A) B))) (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_set_rat (@ tptp.set_ord_atMost_rat A)) (@ tptp.set_ord_lessThan_rat B)) (@ (@ tptp.ord_less_rat A) B))) (forall ((A tptp.num) (B tptp.num)) (= (@ (@ tptp.ord_less_eq_set_num (@ tptp.set_ord_atMost_num A)) (@ tptp.set_ord_lessThan_num B)) (@ (@ tptp.ord_less_num A) B))) (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_ord_atMost_int A)) (@ tptp.set_ord_lessThan_int B)) (@ (@ tptp.ord_less_int A) B))) (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_ord_atMost_nat A)) (@ tptp.set_ord_lessThan_nat B)) (@ (@ tptp.ord_less_nat A) B))) (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K3 tptp.nat)) (@ (@ tptp.binomial K3) M2))) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.binomial (@ tptp.suc N)) (@ tptp.suc M2)))) (forall ((Xs2 tptp.list_complex) (X tptp.complex)) (=> (@ tptp.distinct_complex Xs2) (=> (@ (@ tptp.member_complex X) (@ tptp.set_complex2 Xs2)) (exists ((X3 tptp.nat)) (and (@ (@ tptp.ord_less_nat X3) (@ tptp.size_s3451745648224563538omplex Xs2)) (= (@ (@ tptp.nth_complex Xs2) X3) X) (forall ((Y6 tptp.nat)) (=> (and (@ (@ tptp.ord_less_nat Y6) (@ tptp.size_s3451745648224563538omplex Xs2)) (= (@ (@ tptp.nth_complex Xs2) Y6) X)) (= Y6 X3)))))))) (forall ((Xs2 tptp.list_real) (X tptp.real)) (=> (@ tptp.distinct_real Xs2) (=> (@ (@ tptp.member_real X) (@ tptp.set_real2 Xs2)) (exists ((X3 tptp.nat)) (and (@ (@ tptp.ord_less_nat X3) (@ tptp.size_size_list_real Xs2)) (= (@ (@ tptp.nth_real Xs2) X3) X) (forall ((Y6 tptp.nat)) (=> (and (@ (@ tptp.ord_less_nat Y6) (@ tptp.size_size_list_real Xs2)) (= (@ (@ tptp.nth_real Xs2) Y6) X)) (= Y6 X3)))))))) (forall ((Xs2 tptp.list_set_nat) (X tptp.set_nat)) (=> (@ tptp.distinct_set_nat Xs2) (=> (@ (@ tptp.member_set_nat X) (@ tptp.set_set_nat2 Xs2)) (exists ((X3 tptp.nat)) (and (@ (@ tptp.ord_less_nat X3) (@ tptp.size_s3254054031482475050et_nat Xs2)) (= (@ (@ tptp.nth_set_nat Xs2) X3) X) (forall ((Y6 tptp.nat)) (=> (and (@ (@ tptp.ord_less_nat Y6) (@ tptp.size_s3254054031482475050et_nat Xs2)) (= (@ (@ tptp.nth_set_nat Xs2) Y6) X)) (= Y6 X3)))))))) (forall ((Xs2 tptp.list_VEBT_VEBT) (X tptp.vEBT_VEBT)) (=> (@ tptp.distinct_VEBT_VEBT Xs2) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 Xs2)) (exists ((X3 tptp.nat)) (and (@ (@ tptp.ord_less_nat X3) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (= (@ (@ tptp.nth_VEBT_VEBT Xs2) X3) X) (forall ((Y6 tptp.nat)) (=> (and (@ (@ tptp.ord_less_nat Y6) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (= (@ (@ tptp.nth_VEBT_VEBT Xs2) Y6) X)) (= Y6 X3)))))))) (forall ((Xs2 tptp.list_o) (X Bool)) (=> (@ tptp.distinct_o Xs2) (=> (@ (@ tptp.member_o X) (@ tptp.set_o2 Xs2)) (exists ((X3 tptp.nat)) (and (@ (@ tptp.ord_less_nat X3) (@ tptp.size_size_list_o Xs2)) (= (@ (@ tptp.nth_o Xs2) X3) X) (forall ((Y6 tptp.nat)) (=> (and (@ (@ tptp.ord_less_nat Y6) (@ tptp.size_size_list_o Xs2)) (= (@ (@ tptp.nth_o Xs2) Y6) X)) (= Y6 X3)))))))) (forall ((Xs2 tptp.list_nat) (X tptp.nat)) (=> (@ tptp.distinct_nat Xs2) (=> (@ (@ tptp.member_nat X) (@ tptp.set_nat2 Xs2)) (exists ((X3 tptp.nat)) (and (@ (@ tptp.ord_less_nat X3) (@ tptp.size_size_list_nat Xs2)) (= (@ (@ tptp.nth_nat Xs2) X3) X) (forall ((Y6 tptp.nat)) (=> (and (@ (@ tptp.ord_less_nat Y6) (@ tptp.size_size_list_nat Xs2)) (= (@ (@ tptp.nth_nat Xs2) Y6) X)) (= Y6 X3)))))))) (forall ((Xs2 tptp.list_int) (X tptp.int)) (=> (@ tptp.distinct_int Xs2) (=> (@ (@ tptp.member_int X) (@ tptp.set_int2 Xs2)) (exists ((X3 tptp.nat)) (and (@ (@ tptp.ord_less_nat X3) (@ tptp.size_size_list_int Xs2)) (= (@ (@ tptp.nth_int Xs2) X3) X) (forall ((Y6 tptp.nat)) (=> (and (@ (@ tptp.ord_less_nat Y6) (@ tptp.size_size_list_int Xs2)) (= (@ (@ tptp.nth_int Xs2) Y6) X)) (= Y6 X3)))))))) (forall ((M2 tptp.nat) (A tptp.complex) (X tptp.complex) (Y tptp.complex)) (let ((_let_1 (@ tptp.set_ord_atMost_nat M2))) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ (@ tptp.gbinomial_complex (@ (@ tptp.plus_plus_complex (@ tptp.semiri8010041392384452111omplex M2)) A)) K3)) (@ (@ tptp.power_power_complex X) K3))) (@ (@ tptp.power_power_complex Y) (@ (@ tptp.minus_minus_nat M2) K3))))) _let_1) (@ (@ tptp.groups2073611262835488442omplex (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ (@ tptp.gbinomial_complex (@ (@ tptp.minus_minus_complex (@ (@ tptp.plus_plus_complex (@ tptp.semiri8010041392384452111omplex K3)) A)) tptp.one_one_complex)) K3)) (@ (@ tptp.power_power_complex X) K3))) (@ (@ tptp.power_power_complex (@ (@ tptp.plus_plus_complex X) Y)) (@ (@ tptp.minus_minus_nat M2) K3))))) _let_1)))) (forall ((M2 tptp.nat) (A tptp.rat) (X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.set_ord_atMost_nat M2))) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ (@ tptp.gbinomial_rat (@ (@ tptp.plus_plus_rat (@ tptp.semiri681578069525770553at_rat M2)) A)) K3)) (@ (@ tptp.power_power_rat X) K3))) (@ (@ tptp.power_power_rat Y) (@ (@ tptp.minus_minus_nat M2) K3))))) _let_1) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ (@ tptp.gbinomial_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat (@ tptp.semiri681578069525770553at_rat K3)) A)) tptp.one_one_rat)) K3)) (@ (@ tptp.power_power_rat X) K3))) (@ (@ tptp.power_power_rat (@ (@ tptp.plus_plus_rat X) Y)) (@ (@ tptp.minus_minus_nat M2) K3))))) _let_1)))) (forall ((M2 tptp.nat) (A tptp.real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.set_ord_atMost_nat M2))) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.gbinomial_real (@ (@ tptp.plus_plus_real (@ tptp.semiri5074537144036343181t_real M2)) A)) K3)) (@ (@ tptp.power_power_real X) K3))) (@ (@ tptp.power_power_real Y) (@ (@ tptp.minus_minus_nat M2) K3))))) _let_1) (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.gbinomial_real (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real (@ tptp.semiri5074537144036343181t_real K3)) A)) tptp.one_one_real)) K3)) (@ (@ tptp.power_power_real X) K3))) (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real X) Y)) (@ (@ tptp.minus_minus_nat M2) K3))))) _let_1)))) (forall ((A tptp.complex) (K2 tptp.nat)) (let ((_let_1 (@ tptp.gbinomial_complex (@ (@ tptp.minus_minus_complex A) tptp.one_one_complex)))) (let ((_let_2 (@ tptp.suc K2))) (= (@ (@ tptp.gbinomial_complex A) _let_2) (@ (@ tptp.plus_plus_complex (@ _let_1 _let_2)) (@ _let_1 K2)))))) (forall ((A tptp.real) (K2 tptp.nat)) (let ((_let_1 (@ tptp.gbinomial_real (@ (@ tptp.minus_minus_real A) tptp.one_one_real)))) (let ((_let_2 (@ tptp.suc K2))) (= (@ (@ tptp.gbinomial_real A) _let_2) (@ (@ tptp.plus_plus_real (@ _let_1 _let_2)) (@ _let_1 K2)))))) (forall ((A tptp.rat) (K2 tptp.nat)) (let ((_let_1 (@ tptp.gbinomial_rat (@ (@ tptp.minus_minus_rat A) tptp.one_one_rat)))) (let ((_let_2 (@ tptp.suc K2))) (= (@ (@ tptp.gbinomial_rat A) _let_2) (@ (@ tptp.plus_plus_rat (@ _let_1 _let_2)) (@ _let_1 K2)))))) (forall ((A tptp.complex) (K2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_complex A))) (= (@ (@ tptp.times_times_complex (@ _let_1 (@ tptp.semiri8010041392384452111omplex K2))) (@ (@ tptp.gbinomial_complex A) K2)) (@ (@ tptp.times_times_complex A) (@ (@ tptp.gbinomial_complex (@ _let_1 tptp.one_one_complex)) K2))))) (forall ((A tptp.rat) (K2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_rat A))) (= (@ (@ tptp.times_times_rat (@ _let_1 (@ tptp.semiri681578069525770553at_rat K2))) (@ (@ tptp.gbinomial_rat A) K2)) (@ (@ tptp.times_times_rat A) (@ (@ tptp.gbinomial_rat (@ _let_1 tptp.one_one_rat)) K2))))) (forall ((A tptp.real) (K2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_real A))) (= (@ (@ tptp.times_times_real (@ _let_1 (@ tptp.semiri5074537144036343181t_real K2))) (@ (@ tptp.gbinomial_real A) K2)) (@ (@ tptp.times_times_real A) (@ (@ tptp.gbinomial_real (@ _let_1 tptp.one_one_real)) K2))))) (forall ((K2 tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real K2))) (=> (@ (@ tptp.ord_less_eq_real _let_1) A) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ (@ tptp.divide_divide_real A) _let_1)) K2)) (@ (@ tptp.gbinomial_real A) K2))))) (forall ((K2 tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.semiri681578069525770553at_rat K2))) (=> (@ (@ tptp.ord_less_eq_rat _let_1) A) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat (@ (@ tptp.divide_divide_rat A) _let_1)) K2)) (@ (@ tptp.gbinomial_rat A) K2))))) (forall ((A tptp.rat) (K2 tptp.nat)) (let ((_let_1 (@ tptp.suc K2))) (let ((_let_2 (@ tptp.gbinomial_rat A))) (let ((_let_3 (@ _let_2 K2))) (= (@ (@ tptp.times_times_rat _let_3) A) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat K2)) _let_3)) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat _let_1)) (@ _let_2 _let_1)))))))) (forall ((A tptp.real) (K2 tptp.nat)) (let ((_let_1 (@ tptp.suc K2))) (let ((_let_2 (@ tptp.gbinomial_real A))) (let ((_let_3 (@ _let_2 K2))) (= (@ (@ tptp.times_times_real _let_3) A) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real K2)) _let_3)) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real _let_1)) (@ _let_2 _let_1)))))))) (forall ((A tptp.rat) (K2 tptp.nat)) (let ((_let_1 (@ tptp.suc K2))) (let ((_let_2 (@ tptp.gbinomial_rat A))) (let ((_let_3 (@ _let_2 K2))) (= (@ (@ tptp.times_times_rat A) _let_3) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat K2)) _let_3)) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat _let_1)) (@ _let_2 _let_1)))))))) (forall ((A tptp.real) (K2 tptp.nat)) (let ((_let_1 (@ tptp.suc K2))) (let ((_let_2 (@ tptp.gbinomial_real A))) (let ((_let_3 (@ _let_2 K2))) (= (@ (@ tptp.times_times_real A) _let_3) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real K2)) _let_3)) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real _let_1)) (@ _let_2 _let_1)))))))) (forall ((G2 (-> tptp.nat tptp.rat)) (N tptp.nat)) (= (@ (@ tptp.groups2906978787729119204at_rat G2) (@ tptp.set_ord_atMost_nat (@ tptp.suc N))) (@ (@ tptp.plus_plus_rat (@ G2 tptp.zero_zero_nat)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I tptp.nat)) (@ G2 (@ tptp.suc I)))) (@ tptp.set_ord_atMost_nat N))))) (forall ((G2 (-> tptp.nat tptp.int)) (N tptp.nat)) (= (@ (@ tptp.groups3539618377306564664at_int G2) (@ tptp.set_ord_atMost_nat (@ tptp.suc N))) (@ (@ tptp.plus_plus_int (@ G2 tptp.zero_zero_nat)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I tptp.nat)) (@ G2 (@ tptp.suc I)))) (@ tptp.set_ord_atMost_nat N))))) (forall ((G2 (-> tptp.nat tptp.nat)) (N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat G2) (@ tptp.set_ord_atMost_nat (@ tptp.suc N))) (@ (@ tptp.plus_plus_nat (@ G2 tptp.zero_zero_nat)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I tptp.nat)) (@ G2 (@ tptp.suc I)))) (@ tptp.set_ord_atMost_nat N))))) (forall ((G2 (-> tptp.nat tptp.real)) (N tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real G2) (@ tptp.set_ord_atMost_nat (@ tptp.suc N))) (@ (@ tptp.plus_plus_real (@ G2 tptp.zero_zero_nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I tptp.nat)) (@ G2 (@ tptp.suc I)))) (@ tptp.set_ord_atMost_nat N))))) (forall ((F2 (-> tptp.nat tptp.rat)) (I2 tptp.nat)) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I tptp.nat)) (@ (@ tptp.minus_minus_rat (@ F2 I)) (@ F2 (@ tptp.suc I))))) (@ tptp.set_ord_atMost_nat I2)) (@ (@ tptp.minus_minus_rat (@ F2 tptp.zero_zero_nat)) (@ F2 (@ tptp.suc I2))))) (forall ((F2 (-> tptp.nat tptp.int)) (I2 tptp.nat)) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((I tptp.nat)) (@ (@ tptp.minus_minus_int (@ F2 I)) (@ F2 (@ tptp.suc I))))) (@ tptp.set_ord_atMost_nat I2)) (@ (@ tptp.minus_minus_int (@ F2 tptp.zero_zero_nat)) (@ F2 (@ tptp.suc I2))))) (forall ((F2 (-> tptp.nat tptp.real)) (I2 tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I tptp.nat)) (@ (@ tptp.minus_minus_real (@ F2 I)) (@ F2 (@ tptp.suc I))))) (@ tptp.set_ord_atMost_nat I2)) (@ (@ tptp.minus_minus_real (@ F2 tptp.zero_zero_nat)) (@ F2 (@ tptp.suc I2))))) (forall ((C2 (-> tptp.nat tptp.complex)) (N tptp.nat) (D (-> tptp.nat tptp.complex))) (= (forall ((X4 tptp.complex)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N))) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I tptp.nat)) (@ (@ tptp.times_times_complex (@ C2 I)) (@ (@ tptp.power_power_complex X4) I)))) _let_1) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I tptp.nat)) (@ (@ tptp.times_times_complex (@ D I)) (@ (@ tptp.power_power_complex X4) I)))) _let_1)))) (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) N) (= (@ C2 I) (@ D I)))))) (forall ((C2 (-> tptp.nat tptp.real)) (N tptp.nat) (D (-> tptp.nat tptp.real))) (= (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N))) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I tptp.nat)) (@ (@ tptp.times_times_real (@ C2 I)) (@ (@ tptp.power_power_real X4) I)))) _let_1) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I tptp.nat)) (@ (@ tptp.times_times_real (@ D I)) (@ (@ tptp.power_power_real X4) I)))) _let_1)))) (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) N) (= (@ C2 I) (@ D I)))))) (forall ((G2 (-> tptp.nat tptp.real)) (N tptp.nat)) (= (@ (@ tptp.groups129246275422532515t_real G2) (@ tptp.set_ord_atMost_nat (@ tptp.suc N))) (@ (@ tptp.times_times_real (@ G2 tptp.zero_zero_nat)) (@ (@ tptp.groups129246275422532515t_real (lambda ((I tptp.nat)) (@ G2 (@ tptp.suc I)))) (@ tptp.set_ord_atMost_nat N))))) (forall ((G2 (-> tptp.nat tptp.rat)) (N tptp.nat)) (= (@ (@ tptp.groups73079841787564623at_rat G2) (@ tptp.set_ord_atMost_nat (@ tptp.suc N))) (@ (@ tptp.times_times_rat (@ G2 tptp.zero_zero_nat)) (@ (@ tptp.groups73079841787564623at_rat (lambda ((I tptp.nat)) (@ G2 (@ tptp.suc I)))) (@ tptp.set_ord_atMost_nat N))))) (forall ((G2 (-> tptp.nat tptp.int)) (N tptp.nat)) (= (@ (@ tptp.groups705719431365010083at_int G2) (@ tptp.set_ord_atMost_nat (@ tptp.suc N))) (@ (@ tptp.times_times_int (@ G2 tptp.zero_zero_nat)) (@ (@ tptp.groups705719431365010083at_int (lambda ((I tptp.nat)) (@ G2 (@ tptp.suc I)))) (@ tptp.set_ord_atMost_nat N))))) (forall ((G2 (-> tptp.nat tptp.nat)) (N tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat G2) (@ tptp.set_ord_atMost_nat (@ tptp.suc N))) (@ (@ tptp.times_times_nat (@ G2 tptp.zero_zero_nat)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I tptp.nat)) (@ G2 (@ tptp.suc I)))) (@ tptp.set_ord_atMost_nat N))))) (forall ((A (-> tptp.nat tptp.nat tptp.nat)) (N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I tptp.nat)) (@ (@ tptp.groups3542108847815614940at_nat (@ A I)) (@ tptp.set_ord_lessThan_nat I)))) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((J tptp.nat)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I tptp.nat)) (@ (@ A I) J))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc J)) N)))) (@ tptp.set_ord_lessThan_nat N)))) (forall ((A (-> tptp.nat tptp.nat tptp.real)) (N tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (@ A I)) (@ tptp.set_ord_lessThan_nat I)))) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((J tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I tptp.nat)) (@ (@ A I) J))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc J)) N)))) (@ tptp.set_ord_lessThan_nat N)))) (forall ((L tptp.rat) (U tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat L) U) (= (@ (@ tptp.sup_sup_set_rat (@ tptp.set_ord_lessThan_rat L)) (@ (@ tptp.set_or633870826150836451st_rat L) U)) (@ tptp.set_ord_atMost_rat U)))) (forall ((L tptp.num) (U tptp.num)) (=> (@ (@ tptp.ord_less_eq_num L) U) (= (@ (@ tptp.sup_sup_set_num (@ tptp.set_ord_lessThan_num L)) (@ (@ tptp.set_or7049704709247886629st_num L) U)) (@ tptp.set_ord_atMost_num U)))) (forall ((L tptp.nat) (U tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat L) U) (= (@ (@ tptp.sup_sup_set_nat (@ tptp.set_ord_lessThan_nat L)) (@ (@ tptp.set_or1269000886237332187st_nat L) U)) (@ tptp.set_ord_atMost_nat U)))) (forall ((L tptp.int) (U tptp.int)) (=> (@ (@ tptp.ord_less_eq_int L) U) (= (@ (@ tptp.sup_sup_set_int (@ tptp.set_ord_lessThan_int L)) (@ (@ tptp.set_or1266510415728281911st_int L) U)) (@ tptp.set_ord_atMost_int U)))) (forall ((L tptp.real) (U tptp.real)) (=> (@ (@ tptp.ord_less_eq_real L) U) (= (@ (@ tptp.sup_sup_set_real (@ tptp.set_or5984915006950818249n_real L)) (@ (@ tptp.set_or1222579329274155063t_real L) U)) (@ tptp.set_ord_atMost_real U)))) (forall ((U tptp.int)) (= (@ (@ tptp.sup_sup_set_int (@ tptp.set_ord_lessThan_int U)) (@ (@ tptp.insert_int U) tptp.bot_bot_set_int)) (@ tptp.set_ord_atMost_int U))) (forall ((U tptp.real)) (= (@ (@ tptp.sup_sup_set_real (@ tptp.set_or5984915006950818249n_real U)) (@ (@ tptp.insert_real U) tptp.bot_bot_set_real)) (@ tptp.set_ord_atMost_real U))) (forall ((U tptp.nat)) (= (@ (@ tptp.sup_sup_set_nat (@ tptp.set_ord_lessThan_nat U)) (@ (@ tptp.insert_nat U) tptp.bot_bot_set_nat)) (@ tptp.set_ord_atMost_nat U))) (forall ((A (-> tptp.nat tptp.nat tptp.int)) (N tptp.nat)) (= (@ (@ tptp.groups705719431365010083at_int (lambda ((I tptp.nat)) (@ (@ tptp.groups705719431365010083at_int (@ A I)) (@ tptp.set_ord_lessThan_nat I)))) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.groups705719431365010083at_int (lambda ((J tptp.nat)) (@ (@ tptp.groups705719431365010083at_int (lambda ((I tptp.nat)) (@ (@ A I) J))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc J)) N)))) (@ tptp.set_ord_lessThan_nat N)))) (forall ((A (-> tptp.nat tptp.nat tptp.nat)) (N tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat (lambda ((I tptp.nat)) (@ (@ tptp.groups708209901874060359at_nat (@ A I)) (@ tptp.set_ord_lessThan_nat I)))) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((J tptp.nat)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I tptp.nat)) (@ (@ A I) J))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc J)) N)))) (@ tptp.set_ord_lessThan_nat N)))) (forall ((R3 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K3 tptp.nat)) (@ (@ tptp.binomial (@ (@ tptp.plus_plus_nat R3) K3)) K3))) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.binomial (@ tptp.suc (@ (@ tptp.plus_plus_nat R3) N))) N))) (forall ((K2 tptp.nat) (A tptp.complex)) (let ((_let_1 (@ (@ tptp.plus_plus_complex A) tptp.one_one_complex))) (let ((_let_2 (@ tptp.suc K2))) (= (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex _let_2)) (@ (@ tptp.gbinomial_complex _let_1) _let_2)) (@ (@ tptp.times_times_complex _let_1) (@ (@ tptp.gbinomial_complex A) K2)))))) (forall ((K2 tptp.nat) (A tptp.rat)) (let ((_let_1 (@ (@ tptp.plus_plus_rat A) tptp.one_one_rat))) (let ((_let_2 (@ tptp.suc K2))) (= (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat _let_2)) (@ (@ tptp.gbinomial_rat _let_1) _let_2)) (@ (@ tptp.times_times_rat _let_1) (@ (@ tptp.gbinomial_rat A) K2)))))) (forall ((K2 tptp.nat) (A tptp.real)) (let ((_let_1 (@ (@ tptp.plus_plus_real A) tptp.one_one_real))) (let ((_let_2 (@ tptp.suc K2))) (= (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real _let_2)) (@ (@ tptp.gbinomial_real _let_1) _let_2)) (@ (@ tptp.times_times_real _let_1) (@ (@ tptp.gbinomial_real A) K2)))))) (forall ((K2 tptp.nat) (A tptp.complex)) (let ((_let_1 (@ tptp.suc K2))) (= (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex _let_1)) (@ (@ tptp.gbinomial_complex A) _let_1)) (@ (@ tptp.times_times_complex A) (@ (@ tptp.gbinomial_complex (@ (@ tptp.minus_minus_complex A) tptp.one_one_complex)) K2))))) (forall ((K2 tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.suc K2))) (= (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat _let_1)) (@ (@ tptp.gbinomial_rat A) _let_1)) (@ (@ tptp.times_times_rat A) (@ (@ tptp.gbinomial_rat (@ (@ tptp.minus_minus_rat A) tptp.one_one_rat)) K2))))) (forall ((K2 tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.suc K2))) (= (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real _let_1)) (@ (@ tptp.gbinomial_real A) _let_1)) (@ (@ tptp.times_times_real A) (@ (@ tptp.gbinomial_real (@ (@ tptp.minus_minus_real A) tptp.one_one_real)) K2))))) (forall ((K2 tptp.nat) (M2 tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.gbinomial_rat A))) (=> (@ (@ tptp.ord_less_eq_nat K2) M2) (= (@ (@ tptp.times_times_rat (@ _let_1 M2)) (@ (@ tptp.gbinomial_rat (@ tptp.semiri681578069525770553at_rat M2)) K2)) (@ (@ tptp.times_times_rat (@ _let_1 K2)) (@ (@ tptp.gbinomial_rat (@ (@ tptp.minus_minus_rat A) (@ tptp.semiri681578069525770553at_rat K2))) (@ (@ tptp.minus_minus_nat M2) K2))))))) (forall ((K2 tptp.nat) (M2 tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.gbinomial_real A))) (=> (@ (@ tptp.ord_less_eq_nat K2) M2) (= (@ (@ tptp.times_times_real (@ _let_1 M2)) (@ (@ tptp.gbinomial_real (@ tptp.semiri5074537144036343181t_real M2)) K2)) (@ (@ tptp.times_times_real (@ _let_1 K2)) (@ (@ tptp.gbinomial_real (@ (@ tptp.minus_minus_real A) (@ tptp.semiri5074537144036343181t_real K2))) (@ (@ tptp.minus_minus_nat M2) K2))))))) (forall ((C2 (-> tptp.nat tptp.complex)) (N tptp.nat) (K2 tptp.nat)) (=> (forall ((W tptp.complex)) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I tptp.nat)) (@ (@ tptp.times_times_complex (@ C2 I)) (@ (@ tptp.power_power_complex W) I)))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_complex)) (=> (@ (@ tptp.ord_less_eq_nat K2) N) (= (@ C2 K2) tptp.zero_zero_complex)))) (forall ((C2 (-> tptp.nat tptp.real)) (N tptp.nat) (K2 tptp.nat)) (=> (forall ((W tptp.real)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I tptp.nat)) (@ (@ tptp.times_times_real (@ C2 I)) (@ (@ tptp.power_power_real W) I)))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_real)) (=> (@ (@ tptp.ord_less_eq_nat K2) N) (= (@ C2 K2) tptp.zero_zero_real)))) (forall ((C2 (-> tptp.nat tptp.complex)) (N tptp.nat)) (= (forall ((X4 tptp.complex)) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I tptp.nat)) (@ (@ tptp.times_times_complex (@ C2 I)) (@ (@ tptp.power_power_complex X4) I)))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_complex)) (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) N) (= (@ C2 I) tptp.zero_zero_complex))))) (forall ((C2 (-> tptp.nat tptp.real)) (N tptp.nat)) (= (forall ((X4 tptp.real)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I tptp.nat)) (@ (@ tptp.times_times_real (@ C2 I)) (@ (@ tptp.power_power_real X4) I)))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_real)) (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) N) (= (@ C2 I) tptp.zero_zero_real))))) (forall ((G2 (-> tptp.nat tptp.rat)) (N tptp.nat)) (= (@ (@ tptp.groups2906978787729119204at_rat G2) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.plus_plus_rat (@ G2 tptp.zero_zero_nat)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I tptp.nat)) (@ G2 (@ tptp.suc I)))) (@ tptp.set_ord_lessThan_nat N))))) (forall ((G2 (-> tptp.nat tptp.int)) (N tptp.nat)) (= (@ (@ tptp.groups3539618377306564664at_int G2) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.plus_plus_int (@ G2 tptp.zero_zero_nat)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I tptp.nat)) (@ G2 (@ tptp.suc I)))) (@ tptp.set_ord_lessThan_nat N))))) (forall ((G2 (-> tptp.nat tptp.nat)) (N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat G2) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.plus_plus_nat (@ G2 tptp.zero_zero_nat)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I tptp.nat)) (@ G2 (@ tptp.suc I)))) (@ tptp.set_ord_lessThan_nat N))))) (forall ((G2 (-> tptp.nat tptp.real)) (N tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real G2) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.plus_plus_real (@ G2 tptp.zero_zero_nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I tptp.nat)) (@ G2 (@ tptp.suc I)))) (@ tptp.set_ord_lessThan_nat N))))) (forall ((F2 (-> tptp.nat tptp.rat)) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat M2) N))) (let ((_let_2 (@ tptp.groups2906978787729119204at_rat F2))) (= (@ _let_2 (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.plus_plus_rat (@ _let_2 (@ tptp.set_ord_atMost_nat M2))) (@ _let_2 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M2)) _let_1))))))) (forall ((F2 (-> tptp.nat tptp.int)) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat M2) N))) (let ((_let_2 (@ tptp.groups3539618377306564664at_int F2))) (= (@ _let_2 (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.plus_plus_int (@ _let_2 (@ tptp.set_ord_atMost_nat M2))) (@ _let_2 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M2)) _let_1))))))) (forall ((F2 (-> tptp.nat tptp.nat)) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat M2) N))) (let ((_let_2 (@ tptp.groups3542108847815614940at_nat F2))) (= (@ _let_2 (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.plus_plus_nat (@ _let_2 (@ tptp.set_ord_atMost_nat M2))) (@ _let_2 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M2)) _let_1))))))) (forall ((F2 (-> tptp.nat tptp.real)) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat M2) N))) (let ((_let_2 (@ tptp.groups6591440286371151544t_real F2))) (= (@ _let_2 (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.plus_plus_real (@ _let_2 (@ tptp.set_ord_atMost_nat M2))) (@ _let_2 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M2)) _let_1))))))) (forall ((G2 (-> tptp.nat tptp.real)) (N tptp.nat)) (= (@ (@ tptp.groups129246275422532515t_real G2) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.times_times_real (@ G2 tptp.zero_zero_nat)) (@ (@ tptp.groups129246275422532515t_real (lambda ((I tptp.nat)) (@ G2 (@ tptp.suc I)))) (@ tptp.set_ord_lessThan_nat N))))) (forall ((G2 (-> tptp.nat tptp.rat)) (N tptp.nat)) (= (@ (@ tptp.groups73079841787564623at_rat G2) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.times_times_rat (@ G2 tptp.zero_zero_nat)) (@ (@ tptp.groups73079841787564623at_rat (lambda ((I tptp.nat)) (@ G2 (@ tptp.suc I)))) (@ tptp.set_ord_lessThan_nat N))))) (forall ((G2 (-> tptp.nat tptp.int)) (N tptp.nat)) (= (@ (@ tptp.groups705719431365010083at_int G2) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.times_times_int (@ G2 tptp.zero_zero_nat)) (@ (@ tptp.groups705719431365010083at_int (lambda ((I tptp.nat)) (@ G2 (@ tptp.suc I)))) (@ tptp.set_ord_lessThan_nat N))))) (forall ((G2 (-> tptp.nat tptp.nat)) (N tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat G2) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.times_times_nat (@ G2 tptp.zero_zero_nat)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I tptp.nat)) (@ G2 (@ tptp.suc I)))) (@ tptp.set_ord_lessThan_nat N))))) (forall ((M2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_rat _let_1))) (= (@ (@ tptp.groups2906978787729119204at_rat (@ tptp.gbinomial_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat _let_2) (@ tptp.semiri681578069525770553at_rat M2))) tptp.one_one_rat))) (@ tptp.set_ord_atMost_nat M2)) (@ (@ tptp.power_power_rat _let_2) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat _let_1)) M2)))))) (forall ((M2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numera6690914467698888265omplex _let_1))) (= (@ (@ tptp.groups2073611262835488442omplex (@ tptp.gbinomial_complex (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex _let_2) (@ tptp.semiri8010041392384452111omplex M2))) tptp.one_one_complex))) (@ tptp.set_ord_atMost_nat M2)) (@ (@ tptp.power_power_complex _let_2) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat _let_1)) M2)))))) (forall ((M2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_real _let_1))) (= (@ (@ tptp.groups6591440286371151544t_real (@ tptp.gbinomial_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real _let_2) (@ tptp.semiri5074537144036343181t_real M2))) tptp.one_one_real))) (@ tptp.set_ord_atMost_nat M2)) (@ (@ tptp.power_power_real _let_2) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat _let_1)) M2)))))) (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K3 tptp.nat)) (@ (@ tptp.binomial (@ (@ tptp.minus_minus_nat N) K3)) (@ (@ tptp.minus_minus_nat M2) K3)))) (@ tptp.set_ord_atMost_nat M2)) (@ (@ tptp.binomial (@ tptp.suc N)) M2)))) (forall ((M2 tptp.nat) (N tptp.nat) (R3 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_nat (@ (@ tptp.binomial M2) K3)) (@ (@ tptp.binomial N) (@ (@ tptp.minus_minus_nat R3) K3))))) (@ tptp.set_ord_atMost_nat R3)) (@ (@ tptp.binomial (@ (@ tptp.plus_plus_nat M2) N)) R3))) (forall ((P2 (-> tptp.nat Bool)) (A tptp.nat)) (=> (forall ((A3 tptp.nat)) (=> (= (@ (@ tptp.divide_divide_nat A3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) A3) (@ P2 A3))) (=> (forall ((A3 tptp.nat) (B3 Bool)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.plus_plus_nat (@ tptp.zero_n2687167440665602831ol_nat B3)) (@ (@ tptp.times_times_nat _let_1) A3)))) (=> (@ P2 A3) (=> (= (@ (@ tptp.divide_divide_nat _let_2) _let_1) A3) (@ P2 _let_2)))))) (@ P2 A)))) (forall ((P2 (-> tptp.int Bool)) (A tptp.int)) (=> (forall ((A3 tptp.int)) (=> (= (@ (@ tptp.divide_divide_int A3) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) A3) (@ P2 A3))) (=> (forall ((A3 tptp.int) (B3 Bool)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.plus_plus_int (@ tptp.zero_n2684676970156552555ol_int B3)) (@ (@ tptp.times_times_int _let_1) A3)))) (=> (@ P2 A3) (=> (= (@ (@ tptp.divide_divide_int _let_2) _let_1) A3) (@ P2 _let_2)))))) (@ P2 A)))) (forall ((P2 (-> tptp.code_integer Bool)) (A tptp.code_integer)) (=> (forall ((A3 tptp.code_integer)) (=> (= (@ (@ tptp.divide6298287555418463151nteger A3) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) A3) (@ P2 A3))) (=> (forall ((A3 tptp.code_integer) (B3 Bool)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.zero_n356916108424825756nteger B3)) (@ (@ tptp.times_3573771949741848930nteger _let_1) A3)))) (=> (@ P2 A3) (=> (= (@ (@ tptp.divide6298287555418463151nteger _let_2) _let_1) A3) (@ P2 _let_2)))))) (@ P2 A)))) (forall ((A tptp.complex) (M2 tptp.nat)) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.gbinomial_complex A) K3)) (@ (@ tptp.minus_minus_complex (@ (@ tptp.divide1717551699836669952omplex A) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) (@ tptp.semiri8010041392384452111omplex K3))))) (@ tptp.set_ord_atMost_nat M2)) (@ (@ tptp.times_times_complex (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex (@ tptp.semiri8010041392384452111omplex M2)) tptp.one_one_complex)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) (@ (@ tptp.gbinomial_complex A) (@ (@ tptp.plus_plus_nat M2) tptp.one_one_nat))))) (forall ((A tptp.rat) (M2 tptp.nat)) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.gbinomial_rat A) K3)) (@ (@ tptp.minus_minus_rat (@ (@ tptp.divide_divide_rat A) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one)))) (@ tptp.semiri681578069525770553at_rat K3))))) (@ tptp.set_ord_atMost_nat M2)) (@ (@ tptp.times_times_rat (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat (@ tptp.semiri681578069525770553at_rat M2)) tptp.one_one_rat)) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.gbinomial_rat A) (@ (@ tptp.plus_plus_nat M2) tptp.one_one_nat))))) (forall ((A tptp.real) (M2 tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.gbinomial_real A) K3)) (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real A) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.semiri5074537144036343181t_real K3))))) (@ tptp.set_ord_atMost_nat M2)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ tptp.semiri5074537144036343181t_real M2)) tptp.one_one_real)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ (@ tptp.gbinomial_real A) (@ (@ tptp.plus_plus_nat M2) tptp.one_one_nat))))) (forall ((A tptp.complex) (K2 tptp.nat)) (let ((_let_1 (@ tptp.suc K2))) (let ((_let_2 (@ (@ tptp.plus_plus_complex A) tptp.one_one_complex))) (= (@ (@ tptp.gbinomial_complex _let_2) _let_1) (@ (@ tptp.times_times_complex (@ (@ tptp.divide1717551699836669952omplex _let_2) (@ tptp.semiri8010041392384452111omplex _let_1))) (@ (@ tptp.gbinomial_complex A) K2)))))) (forall ((A tptp.rat) (K2 tptp.nat)) (let ((_let_1 (@ tptp.suc K2))) (let ((_let_2 (@ (@ tptp.plus_plus_rat A) tptp.one_one_rat))) (= (@ (@ tptp.gbinomial_rat _let_2) _let_1) (@ (@ tptp.times_times_rat (@ (@ tptp.divide_divide_rat _let_2) (@ tptp.semiri681578069525770553at_rat _let_1))) (@ (@ tptp.gbinomial_rat A) K2)))))) (forall ((A tptp.real) (K2 tptp.nat)) (let ((_let_1 (@ tptp.suc K2))) (let ((_let_2 (@ (@ tptp.plus_plus_real A) tptp.one_one_real))) (= (@ (@ tptp.gbinomial_real _let_2) _let_1) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real _let_2) (@ tptp.semiri5074537144036343181t_real _let_1))) (@ (@ tptp.gbinomial_real A) K2)))))) (forall ((A tptp.complex) (K2 tptp.nat)) (let ((_let_1 (@ tptp.suc K2))) (let ((_let_2 (@ (@ tptp.plus_plus_complex A) tptp.one_one_complex))) (= (@ (@ tptp.gbinomial_complex _let_2) _let_1) (@ (@ tptp.times_times_complex (@ (@ tptp.gbinomial_complex A) K2)) (@ (@ tptp.divide1717551699836669952omplex _let_2) (@ tptp.semiri8010041392384452111omplex _let_1))))))) (forall ((A tptp.rat) (K2 tptp.nat)) (let ((_let_1 (@ tptp.suc K2))) (let ((_let_2 (@ (@ tptp.plus_plus_rat A) tptp.one_one_rat))) (= (@ (@ tptp.gbinomial_rat _let_2) _let_1) (@ (@ tptp.times_times_rat (@ (@ tptp.gbinomial_rat A) K2)) (@ (@ tptp.divide_divide_rat _let_2) (@ tptp.semiri681578069525770553at_rat _let_1))))))) (forall ((A tptp.real) (K2 tptp.nat)) (let ((_let_1 (@ tptp.suc K2))) (let ((_let_2 (@ (@ tptp.plus_plus_real A) tptp.one_one_real))) (= (@ (@ tptp.gbinomial_real _let_2) _let_1) (@ (@ tptp.times_times_real (@ (@ tptp.gbinomial_real A) K2)) (@ (@ tptp.divide_divide_real _let_2) (@ tptp.semiri5074537144036343181t_real _let_1))))))) (forall ((X tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger X))) (let ((_let_2 (@ tptp.minus_8373710615458151222nteger tptp.one_one_Code_integer))) (= (@ (@ tptp.times_3573771949741848930nteger (@ _let_2 X)) (@ (@ tptp.groups7501900531339628137nteger _let_1) (@ tptp.set_ord_atMost_nat N))) (@ _let_2 (@ _let_1 (@ tptp.suc N))))))) (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))) (= (@ (@ tptp.times_times_complex (@ _let_2 X)) (@ (@ tptp.groups2073611262835488442omplex _let_1) (@ tptp.set_ord_atMost_nat N))) (@ _let_2 (@ _let_1 (@ tptp.suc N))))))) (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))) (= (@ (@ tptp.times_times_rat (@ _let_2 X)) (@ (@ tptp.groups2906978787729119204at_rat _let_1) (@ tptp.set_ord_atMost_nat N))) (@ _let_2 (@ _let_1 (@ tptp.suc N))))))) (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))) (= (@ (@ tptp.times_times_int (@ _let_2 X)) (@ (@ tptp.groups3539618377306564664at_int _let_1) (@ tptp.set_ord_atMost_nat N))) (@ _let_2 (@ _let_1 (@ tptp.suc N))))))) (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))) (= (@ (@ tptp.times_times_real (@ _let_2 X)) (@ (@ tptp.groups6591440286371151544t_real _let_1) (@ tptp.set_ord_atMost_nat N))) (@ _let_2 (@ _let_1 (@ tptp.suc N))))))) (forall ((C2 (-> tptp.nat tptp.complex)) (N tptp.nat)) (= (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((X4 tptp.complex)) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I tptp.nat)) (@ (@ tptp.times_times_complex (@ C2 I)) (@ (@ tptp.power_power_complex X4) I)))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_complex)))) (exists ((I tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat I) N) (not (= (@ C2 I) tptp.zero_zero_complex)))))) (forall ((C2 (-> tptp.nat tptp.real)) (N tptp.nat)) (= (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((X4 tptp.real)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I tptp.nat)) (@ (@ tptp.times_times_real (@ C2 I)) (@ (@ tptp.power_power_real X4) I)))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_real)))) (exists ((I tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat I) N) (not (= (@ C2 I) tptp.zero_zero_real)))))) (forall ((C2 (-> tptp.nat tptp.complex)) (K2 tptp.nat) (N tptp.nat)) (=> (not (= (@ C2 K2) tptp.zero_zero_complex)) (=> (@ (@ tptp.ord_less_eq_nat K2) N) (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((Z4 tptp.complex)) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I tptp.nat)) (@ (@ tptp.times_times_complex (@ C2 I)) (@ (@ tptp.power_power_complex Z4) I)))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_complex))))))) (forall ((C2 (-> tptp.nat tptp.real)) (K2 tptp.nat) (N tptp.nat)) (=> (not (= (@ C2 K2) tptp.zero_zero_real)) (=> (@ (@ tptp.ord_less_eq_nat K2) N) (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((Z4 tptp.real)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I tptp.nat)) (@ (@ tptp.times_times_real (@ C2 I)) (@ (@ tptp.power_power_real Z4) I)))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_real))))))) (forall ((C2 (-> tptp.nat tptp.complex)) (K2 tptp.nat) (N tptp.nat)) (=> (not (= (@ C2 K2) tptp.zero_zero_complex)) (=> (@ (@ tptp.ord_less_eq_nat K2) N) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_complex (@ tptp.collect_complex (lambda ((Z4 tptp.complex)) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I tptp.nat)) (@ (@ tptp.times_times_complex (@ C2 I)) (@ (@ tptp.power_power_complex Z4) I)))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_complex))))) N)))) (forall ((C2 (-> tptp.nat tptp.real)) (K2 tptp.nat) (N tptp.nat)) (=> (not (= (@ C2 K2) tptp.zero_zero_real)) (=> (@ (@ tptp.ord_less_eq_nat K2) N) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_real (@ tptp.collect_real (lambda ((Z4 tptp.real)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I tptp.nat)) (@ (@ tptp.times_times_real (@ C2 I)) (@ (@ tptp.power_power_real Z4) I)))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_real))))) N)))) (forall ((C2 (-> tptp.nat tptp.complex)) (A tptp.complex) (N tptp.nat)) (=> (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I tptp.nat)) (@ (@ tptp.times_times_complex (@ C2 I)) (@ (@ tptp.power_power_complex A) I)))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_complex) (not (forall ((B3 (-> tptp.nat tptp.complex))) (not (forall ((Z5 tptp.complex)) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I tptp.nat)) (@ (@ tptp.times_times_complex (@ C2 I)) (@ (@ tptp.power_power_complex Z5) I)))) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex Z5) A)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I tptp.nat)) (@ (@ tptp.times_times_complex (@ B3 I)) (@ (@ tptp.power_power_complex Z5) I)))) (@ tptp.set_ord_lessThan_nat N)))))))))) (forall ((C2 (-> tptp.nat tptp.rat)) (A tptp.rat) (N tptp.nat)) (=> (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I tptp.nat)) (@ (@ tptp.times_times_rat (@ C2 I)) (@ (@ tptp.power_power_rat A) I)))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_rat) (not (forall ((B3 (-> tptp.nat tptp.rat))) (not (forall ((Z5 tptp.rat)) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I tptp.nat)) (@ (@ tptp.times_times_rat (@ C2 I)) (@ (@ tptp.power_power_rat Z5) I)))) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat Z5) A)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I tptp.nat)) (@ (@ tptp.times_times_rat (@ B3 I)) (@ (@ tptp.power_power_rat Z5) I)))) (@ tptp.set_ord_lessThan_nat N)))))))))) (forall ((C2 (-> tptp.nat tptp.int)) (A tptp.int) (N tptp.nat)) (=> (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((I tptp.nat)) (@ (@ tptp.times_times_int (@ C2 I)) (@ (@ tptp.power_power_int A) I)))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_int) (not (forall ((B3 (-> tptp.nat tptp.int))) (not (forall ((Z5 tptp.int)) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((I tptp.nat)) (@ (@ tptp.times_times_int (@ C2 I)) (@ (@ tptp.power_power_int Z5) I)))) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int Z5) A)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I tptp.nat)) (@ (@ tptp.times_times_int (@ B3 I)) (@ (@ tptp.power_power_int Z5) I)))) (@ tptp.set_ord_lessThan_nat N)))))))))) (forall ((C2 (-> tptp.nat tptp.real)) (A tptp.real) (N tptp.nat)) (=> (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I tptp.nat)) (@ (@ tptp.times_times_real (@ C2 I)) (@ (@ tptp.power_power_real A) I)))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_real) (not (forall ((B3 (-> tptp.nat tptp.real))) (not (forall ((Z5 tptp.real)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I tptp.nat)) (@ (@ tptp.times_times_real (@ C2 I)) (@ (@ tptp.power_power_real Z5) I)))) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real Z5) A)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I tptp.nat)) (@ (@ tptp.times_times_real (@ B3 I)) (@ (@ tptp.power_power_real Z5) I)))) (@ tptp.set_ord_lessThan_nat N)))))))))) (forall ((C2 (-> tptp.nat tptp.complex)) (N tptp.nat) (A tptp.complex)) (exists ((B3 (-> tptp.nat tptp.complex))) (forall ((Z5 tptp.complex)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N))) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I tptp.nat)) (@ (@ tptp.times_times_complex (@ C2 I)) (@ (@ tptp.power_power_complex Z5) I)))) _let_1) (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex Z5) A)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I tptp.nat)) (@ (@ tptp.times_times_complex (@ B3 I)) (@ (@ tptp.power_power_complex Z5) I)))) (@ tptp.set_ord_lessThan_nat N)))) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I tptp.nat)) (@ (@ tptp.times_times_complex (@ C2 I)) (@ (@ tptp.power_power_complex A) I)))) _let_1))))))) (forall ((C2 (-> tptp.nat tptp.rat)) (N tptp.nat) (A tptp.rat)) (exists ((B3 (-> tptp.nat tptp.rat))) (forall ((Z5 tptp.rat)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N))) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I tptp.nat)) (@ (@ tptp.times_times_rat (@ C2 I)) (@ (@ tptp.power_power_rat Z5) I)))) _let_1) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat Z5) A)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I tptp.nat)) (@ (@ tptp.times_times_rat (@ B3 I)) (@ (@ tptp.power_power_rat Z5) I)))) (@ tptp.set_ord_lessThan_nat N)))) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I tptp.nat)) (@ (@ tptp.times_times_rat (@ C2 I)) (@ (@ tptp.power_power_rat A) I)))) _let_1))))))) (forall ((C2 (-> tptp.nat tptp.int)) (N tptp.nat) (A tptp.int)) (exists ((B3 (-> tptp.nat tptp.int))) (forall ((Z5 tptp.int)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N))) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((I tptp.nat)) (@ (@ tptp.times_times_int (@ C2 I)) (@ (@ tptp.power_power_int Z5) I)))) _let_1) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int Z5) A)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I tptp.nat)) (@ (@ tptp.times_times_int (@ B3 I)) (@ (@ tptp.power_power_int Z5) I)))) (@ tptp.set_ord_lessThan_nat N)))) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I tptp.nat)) (@ (@ tptp.times_times_int (@ C2 I)) (@ (@ tptp.power_power_int A) I)))) _let_1))))))) (forall ((C2 (-> tptp.nat tptp.real)) (N tptp.nat) (A tptp.real)) (exists ((B3 (-> tptp.nat tptp.real))) (forall ((Z5 tptp.real)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N))) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I tptp.nat)) (@ (@ tptp.times_times_real (@ C2 I)) (@ (@ tptp.power_power_real Z5) I)))) _let_1) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real Z5) A)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I tptp.nat)) (@ (@ tptp.times_times_real (@ B3 I)) (@ (@ tptp.power_power_real Z5) I)))) (@ tptp.set_ord_lessThan_nat N)))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I tptp.nat)) (@ (@ tptp.times_times_real (@ C2 I)) (@ (@ tptp.power_power_real A) I)))) _let_1))))))) (forall ((M2 tptp.nat) (N tptp.nat) (X tptp.complex)) (let ((_let_1 (@ tptp.power_power_complex X))) (let ((_let_2 (@ tptp.groups2073611262835488442omplex _let_1))) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ _let_2 (@ (@ tptp.set_or1269000886237332187st_nat M2) N)) (@ (@ tptp.times_times_complex (@ _let_1 M2)) (@ _let_2 (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat N) M2))))))))) (forall ((M2 tptp.nat) (N tptp.nat) (X tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat X))) (let ((_let_2 (@ tptp.groups2906978787729119204at_rat _let_1))) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ _let_2 (@ (@ tptp.set_or1269000886237332187st_nat M2) N)) (@ (@ tptp.times_times_rat (@ _let_1 M2)) (@ _let_2 (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat N) M2))))))))) (forall ((M2 tptp.nat) (N tptp.nat) (X tptp.int)) (let ((_let_1 (@ tptp.power_power_int X))) (let ((_let_2 (@ tptp.groups3539618377306564664at_int _let_1))) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ _let_2 (@ (@ tptp.set_or1269000886237332187st_nat M2) N)) (@ (@ tptp.times_times_int (@ _let_1 M2)) (@ _let_2 (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat N) M2))))))))) (forall ((M2 tptp.nat) (N tptp.nat) (X tptp.real)) (let ((_let_1 (@ tptp.power_power_real X))) (let ((_let_2 (@ tptp.groups6591440286371151544t_real _let_1))) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ _let_2 (@ (@ tptp.set_or1269000886237332187st_nat M2) N)) (@ (@ tptp.times_times_real (@ _let_1 M2)) (@ _let_2 (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat N) M2))))))))) (forall ((A tptp.nat) (B tptp.nat) (N tptp.nat)) (= (@ (@ tptp.power_power_nat (@ (@ tptp.plus_plus_nat A) B)) N) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_nat (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.binomial N) K3))) (@ (@ tptp.power_power_nat A) K3))) (@ (@ tptp.power_power_nat B) (@ (@ tptp.minus_minus_nat N) K3))))) (@ tptp.set_ord_atMost_nat N)))) (forall ((N tptp.nat)) (= (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N) (@ (@ tptp.minus_minus_set_nat (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.insert_nat tptp.zero_zero_nat) tptp.bot_bot_set_nat)))) (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_7079662738309270450atural (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 M2))) (= (@ (@ tptp.modulo8411746178871703098atural _let_2) (@ _let_1 N)) (@ (@ tptp.times_2397367101498566445atural (@ tptp.zero_n8403883297036319079atural (@ (@ tptp.ord_less_nat M2) N))) _let_2))))) (forall ((M2 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 M2))) (= (@ (@ tptp.modulo_modulo_nat _let_2) (@ _let_1 N)) (@ (@ tptp.times_times_nat (@ tptp.zero_n2687167440665602831ol_nat (@ (@ tptp.ord_less_nat M2) N))) _let_2))))) (forall ((M2 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 M2))) (= (@ (@ tptp.modulo_modulo_int _let_2) (@ _let_1 N)) (@ (@ tptp.times_times_int (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.ord_less_nat M2) N))) _let_2))))) (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 M2))) (= (@ (@ tptp.modulo364778990260209775nteger _let_2) (@ _let_1 N)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.zero_n356916108424825756nteger (@ (@ tptp.ord_less_nat M2) N))) _let_2))))) (forall ((K2 tptp.nat) (A tptp.complex)) (let ((_let_1 (@ tptp.gbinomial_complex (@ (@ tptp.minus_minus_complex A) tptp.one_one_complex)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K2) (= (@ (@ tptp.gbinomial_complex A) K2) (@ (@ tptp.plus_plus_complex (@ _let_1 (@ (@ tptp.minus_minus_nat K2) tptp.one_one_nat))) (@ _let_1 K2)))))) (forall ((K2 tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.gbinomial_real (@ (@ tptp.minus_minus_real A) tptp.one_one_real)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K2) (= (@ (@ tptp.gbinomial_real A) K2) (@ (@ tptp.plus_plus_real (@ _let_1 (@ (@ tptp.minus_minus_nat K2) tptp.one_one_nat))) (@ _let_1 K2)))))) (forall ((K2 tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.gbinomial_rat (@ (@ tptp.minus_minus_rat A) tptp.one_one_rat)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K2) (= (@ (@ tptp.gbinomial_rat A) K2) (@ (@ tptp.plus_plus_rat (@ _let_1 (@ (@ tptp.minus_minus_nat K2) tptp.one_one_nat))) (@ _let_1 K2)))))) (forall ((G2 (-> tptp.nat tptp.rat)) (N tptp.nat)) (= (@ (@ tptp.groups2906978787729119204at_rat G2) (@ tptp.set_ord_atMost_nat (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I))) (@ (@ tptp.plus_plus_rat (@ G2 _let_1)) (@ G2 (@ tptp.suc _let_1)))))) (@ tptp.set_ord_atMost_nat N)))) (forall ((G2 (-> tptp.nat tptp.int)) (N tptp.nat)) (= (@ (@ tptp.groups3539618377306564664at_int G2) (@ tptp.set_ord_atMost_nat (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I))) (@ (@ tptp.plus_plus_int (@ G2 _let_1)) (@ G2 (@ tptp.suc _let_1)))))) (@ tptp.set_ord_atMost_nat N)))) (forall ((G2 (-> tptp.nat tptp.nat)) (N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat G2) (@ tptp.set_ord_atMost_nat (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I))) (@ (@ tptp.plus_plus_nat (@ G2 _let_1)) (@ G2 (@ tptp.suc _let_1)))))) (@ tptp.set_ord_atMost_nat N)))) (forall ((G2 (-> tptp.nat tptp.real)) (N tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real G2) (@ tptp.set_ord_atMost_nat (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I))) (@ (@ tptp.plus_plus_real (@ G2 _let_1)) (@ G2 (@ tptp.suc _let_1)))))) (@ tptp.set_ord_atMost_nat N)))) (forall ((C2 (-> tptp.nat tptp.complex)) (K2 tptp.nat) (N tptp.nat)) (=> (not (= (@ C2 K2) tptp.zero_zero_complex)) (=> (@ (@ tptp.ord_less_eq_nat K2) N) (and (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((Z4 tptp.complex)) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I tptp.nat)) (@ (@ tptp.times_times_complex (@ C2 I)) (@ (@ tptp.power_power_complex Z4) I)))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_complex)))) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_complex (@ tptp.collect_complex (lambda ((Z4 tptp.complex)) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I tptp.nat)) (@ (@ tptp.times_times_complex (@ C2 I)) (@ (@ tptp.power_power_complex Z4) I)))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_complex))))) N))))) (forall ((C2 (-> tptp.nat tptp.real)) (K2 tptp.nat) (N tptp.nat)) (=> (not (= (@ C2 K2) tptp.zero_zero_real)) (=> (@ (@ tptp.ord_less_eq_nat K2) N) (and (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((Z4 tptp.real)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I tptp.nat)) (@ (@ tptp.times_times_real (@ C2 I)) (@ (@ tptp.power_power_real Z4) I)))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_real)))) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_real (@ tptp.collect_real (lambda ((Z4 tptp.real)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I tptp.nat)) (@ (@ tptp.times_times_real (@ C2 I)) (@ (@ tptp.power_power_real Z4) I)))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_real))))) N))))) (forall ((M2 tptp.nat) (A (-> tptp.nat tptp.complex)) (N tptp.nat) (B (-> tptp.nat tptp.complex)) (X tptp.complex)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) I3) (= (@ A I3) tptp.zero_zero_complex))) (=> (forall ((J3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) J3) (= (@ B J3) tptp.zero_zero_complex))) (= (@ (@ tptp.times_times_complex (@ (@ tptp.groups2073611262835488442omplex (lambda ((I tptp.nat)) (@ (@ tptp.times_times_complex (@ A I)) (@ (@ tptp.power_power_complex X) I)))) (@ tptp.set_ord_atMost_nat M2))) (@ (@ tptp.groups2073611262835488442omplex (lambda ((J tptp.nat)) (@ (@ tptp.times_times_complex (@ B J)) (@ (@ tptp.power_power_complex X) J)))) (@ tptp.set_ord_atMost_nat N))) (@ (@ tptp.groups2073611262835488442omplex (lambda ((R tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.groups2073611262835488442omplex (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_complex (@ A K3)) (@ B (@ (@ tptp.minus_minus_nat R) K3))))) (@ tptp.set_ord_atMost_nat R))) (@ (@ tptp.power_power_complex X) R)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.plus_plus_nat M2) N))))))) (forall ((M2 tptp.nat) (A (-> tptp.nat tptp.rat)) (N tptp.nat) (B (-> tptp.nat tptp.rat)) (X tptp.rat)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) I3) (= (@ A I3) tptp.zero_zero_rat))) (=> (forall ((J3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) J3) (= (@ B J3) tptp.zero_zero_rat))) (= (@ (@ tptp.times_times_rat (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I tptp.nat)) (@ (@ tptp.times_times_rat (@ A I)) (@ (@ tptp.power_power_rat X) I)))) (@ tptp.set_ord_atMost_nat M2))) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((J tptp.nat)) (@ (@ tptp.times_times_rat (@ B J)) (@ (@ tptp.power_power_rat X) J)))) (@ tptp.set_ord_atMost_nat N))) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((R tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_rat (@ A K3)) (@ B (@ (@ tptp.minus_minus_nat R) K3))))) (@ tptp.set_ord_atMost_nat R))) (@ (@ tptp.power_power_rat X) R)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.plus_plus_nat M2) N))))))) (forall ((M2 tptp.nat) (A (-> tptp.nat tptp.int)) (N tptp.nat) (B (-> tptp.nat tptp.int)) (X tptp.int)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) I3) (= (@ A I3) tptp.zero_zero_int))) (=> (forall ((J3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) J3) (= (@ B J3) tptp.zero_zero_int))) (= (@ (@ tptp.times_times_int (@ (@ tptp.groups3539618377306564664at_int (lambda ((I tptp.nat)) (@ (@ tptp.times_times_int (@ A I)) (@ (@ tptp.power_power_int X) I)))) (@ tptp.set_ord_atMost_nat M2))) (@ (@ tptp.groups3539618377306564664at_int (lambda ((J tptp.nat)) (@ (@ tptp.times_times_int (@ B J)) (@ (@ tptp.power_power_int X) J)))) (@ tptp.set_ord_atMost_nat N))) (@ (@ tptp.groups3539618377306564664at_int (lambda ((R tptp.nat)) (@ (@ tptp.times_times_int (@ (@ tptp.groups3539618377306564664at_int (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_int (@ A K3)) (@ B (@ (@ tptp.minus_minus_nat R) K3))))) (@ tptp.set_ord_atMost_nat R))) (@ (@ tptp.power_power_int X) R)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.plus_plus_nat M2) N))))))) (forall ((M2 tptp.nat) (A (-> tptp.nat tptp.real)) (N tptp.nat) (B (-> tptp.nat tptp.real)) (X tptp.real)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) I3) (= (@ A I3) tptp.zero_zero_real))) (=> (forall ((J3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) J3) (= (@ B J3) tptp.zero_zero_real))) (= (@ (@ tptp.times_times_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((I tptp.nat)) (@ (@ tptp.times_times_real (@ A I)) (@ (@ tptp.power_power_real X) I)))) (@ tptp.set_ord_atMost_nat M2))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((J tptp.nat)) (@ (@ tptp.times_times_real (@ B J)) (@ (@ tptp.power_power_real X) J)))) (@ tptp.set_ord_atMost_nat N))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((R tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_real (@ A K3)) (@ B (@ (@ tptp.minus_minus_nat R) K3))))) (@ tptp.set_ord_atMost_nat R))) (@ (@ tptp.power_power_real X) R)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.plus_plus_nat M2) N))))))) (forall ((G2 (-> tptp.nat tptp.real)) (N tptp.nat)) (= (@ (@ tptp.groups129246275422532515t_real G2) (@ tptp.set_ord_atMost_nat (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))) (@ (@ tptp.groups129246275422532515t_real (lambda ((I tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I))) (@ (@ tptp.times_times_real (@ G2 _let_1)) (@ G2 (@ tptp.suc _let_1)))))) (@ tptp.set_ord_atMost_nat N)))) (forall ((G2 (-> tptp.nat tptp.rat)) (N tptp.nat)) (= (@ (@ tptp.groups73079841787564623at_rat G2) (@ tptp.set_ord_atMost_nat (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))) (@ (@ tptp.groups73079841787564623at_rat (lambda ((I tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I))) (@ (@ tptp.times_times_rat (@ G2 _let_1)) (@ G2 (@ tptp.suc _let_1)))))) (@ tptp.set_ord_atMost_nat N)))) (forall ((G2 (-> tptp.nat tptp.int)) (N tptp.nat)) (= (@ (@ tptp.groups705719431365010083at_int G2) (@ tptp.set_ord_atMost_nat (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))) (@ (@ tptp.groups705719431365010083at_int (lambda ((I tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I))) (@ (@ tptp.times_times_int (@ G2 _let_1)) (@ G2 (@ tptp.suc _let_1)))))) (@ tptp.set_ord_atMost_nat N)))) (forall ((G2 (-> tptp.nat tptp.nat)) (N tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat G2) (@ tptp.set_ord_atMost_nat (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I))) (@ (@ tptp.times_times_nat (@ G2 _let_1)) (@ G2 (@ tptp.suc _let_1)))))) (@ tptp.set_ord_atMost_nat N)))) (forall ((C2 (-> tptp.nat tptp.complex)) (N tptp.nat) (K2 tptp.complex)) (= (forall ((X4 tptp.complex)) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I tptp.nat)) (@ (@ tptp.times_times_complex (@ C2 I)) (@ (@ tptp.power_power_complex X4) I)))) (@ tptp.set_ord_atMost_nat N)) K2)) (and (= (@ C2 tptp.zero_zero_nat) K2) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N)) (= (@ C2 X4) tptp.zero_zero_complex)))))) (forall ((C2 (-> tptp.nat tptp.real)) (N tptp.nat) (K2 tptp.real)) (= (forall ((X4 tptp.real)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I tptp.nat)) (@ (@ tptp.times_times_real (@ C2 I)) (@ (@ tptp.power_power_real X4) I)))) (@ tptp.set_ord_atMost_nat N)) K2)) (and (= (@ C2 tptp.zero_zero_nat) K2) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N)) (= (@ C2 X4) tptp.zero_zero_real)))))) (forall ((A tptp.complex) (B tptp.complex) (N tptp.nat)) (= (@ (@ tptp.power_power_complex (@ (@ tptp.plus_plus_complex A) B)) N) (@ (@ tptp.groups2073611262835488442omplex (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.binomial N) K3))) (@ (@ tptp.power_power_complex A) K3))) (@ (@ tptp.power_power_complex B) (@ (@ tptp.minus_minus_nat N) K3))))) (@ tptp.set_ord_atMost_nat N)))) (forall ((A tptp.rat) (B tptp.rat) (N tptp.nat)) (= (@ (@ tptp.power_power_rat (@ (@ tptp.plus_plus_rat A) B)) N) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.binomial N) K3))) (@ (@ tptp.power_power_rat A) K3))) (@ (@ tptp.power_power_rat B) (@ (@ tptp.minus_minus_nat N) K3))))) (@ tptp.set_ord_atMost_nat N)))) (forall ((A tptp.int) (B tptp.int) (N tptp.nat)) (= (@ (@ tptp.power_power_int (@ (@ tptp.plus_plus_int A) B)) N) (@ (@ tptp.groups3539618377306564664at_int (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.binomial N) K3))) (@ (@ tptp.power_power_int A) K3))) (@ (@ tptp.power_power_int B) (@ (@ tptp.minus_minus_nat N) K3))))) (@ tptp.set_ord_atMost_nat N)))) (forall ((A tptp.nat) (B tptp.nat) (N tptp.nat)) (= (@ (@ tptp.power_power_nat (@ (@ tptp.plus_plus_nat A) B)) N) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_nat (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.binomial N) K3))) (@ (@ tptp.power_power_nat A) K3))) (@ (@ tptp.power_power_nat B) (@ (@ tptp.minus_minus_nat N) K3))))) (@ tptp.set_ord_atMost_nat N)))) (forall ((A tptp.real) (B tptp.real) (N tptp.nat)) (= (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real A) B)) N) (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.binomial N) K3))) (@ (@ tptp.power_power_real A) K3))) (@ (@ tptp.power_power_real B) (@ (@ tptp.minus_minus_nat N) K3))))) (@ tptp.set_ord_atMost_nat N)))) (forall ((A tptp.rat) (B tptp.rat) (N tptp.nat)) (= (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.plus_plus_rat A) B)) N) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.binomial N) K3))) (@ (@ tptp.comm_s4028243227959126397er_rat A) K3))) (@ (@ tptp.comm_s4028243227959126397er_rat B) (@ (@ tptp.minus_minus_nat N) K3))))) (@ tptp.set_ord_atMost_nat N)))) (forall ((A tptp.int) (B tptp.int) (N tptp.nat)) (= (@ (@ tptp.comm_s4660882817536571857er_int (@ (@ tptp.plus_plus_int A) B)) N) (@ (@ tptp.groups3539618377306564664at_int (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.binomial N) K3))) (@ (@ tptp.comm_s4660882817536571857er_int A) K3))) (@ (@ tptp.comm_s4660882817536571857er_int B) (@ (@ tptp.minus_minus_nat N) K3))))) (@ tptp.set_ord_atMost_nat N)))) (forall ((A tptp.real) (B tptp.real) (N tptp.nat)) (= (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.plus_plus_real A) B)) N) (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.binomial N) K3))) (@ (@ tptp.comm_s7457072308508201937r_real A) K3))) (@ (@ tptp.comm_s7457072308508201937r_real B) (@ (@ tptp.minus_minus_nat N) K3))))) (@ tptp.set_ord_atMost_nat N)))) (forall ((M2 tptp.nat) (A (-> tptp.nat tptp.nat)) (N tptp.nat) (B (-> tptp.nat tptp.nat)) (X tptp.nat)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) I3) (= (@ A I3) tptp.zero_zero_nat))) (=> (forall ((J3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) J3) (= (@ B J3) tptp.zero_zero_nat))) (= (@ (@ tptp.times_times_nat (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I tptp.nat)) (@ (@ tptp.times_times_nat (@ A I)) (@ (@ tptp.power_power_nat X) I)))) (@ tptp.set_ord_atMost_nat M2))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((J tptp.nat)) (@ (@ tptp.times_times_nat (@ B J)) (@ (@ tptp.power_power_nat X) J)))) (@ tptp.set_ord_atMost_nat N))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((R tptp.nat)) (@ (@ tptp.times_times_nat (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_nat (@ A K3)) (@ B (@ (@ tptp.minus_minus_nat R) K3))))) (@ tptp.set_ord_atMost_nat R))) (@ (@ tptp.power_power_nat X) R)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.plus_plus_nat M2) N))))))) (forall ((N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K3 tptp.nat)) (@ (@ tptp.power_power_nat (@ (@ tptp.binomial N) K3)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.binomial (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) N))) (forall ((Xs2 tptp.list_VEBT_VEBT) (N tptp.nat) (X tptp.vEBT_VEBT)) (=> (@ tptp.distinct_VEBT_VEBT Xs2) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (= (@ tptp.set_VEBT_VEBT2 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs2) N) X)) (@ (@ tptp.insert_VEBT_VEBT X) (@ (@ tptp.minus_5127226145743854075T_VEBT (@ tptp.set_VEBT_VEBT2 Xs2)) (@ (@ tptp.insert_VEBT_VEBT (@ (@ tptp.nth_VEBT_VEBT Xs2) N)) tptp.bot_bo8194388402131092736T_VEBT))))))) (forall ((Xs2 tptp.list_o) (N tptp.nat) (X Bool)) (=> (@ tptp.distinct_o Xs2) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_o Xs2)) (= (@ tptp.set_o2 (@ (@ (@ tptp.list_update_o Xs2) N) X)) (@ (@ tptp.insert_o X) (@ (@ tptp.minus_minus_set_o (@ tptp.set_o2 Xs2)) (@ (@ tptp.insert_o (@ (@ tptp.nth_o Xs2) N)) tptp.bot_bot_set_o))))))) (forall ((Xs2 tptp.list_int) (N tptp.nat) (X tptp.int)) (=> (@ tptp.distinct_int Xs2) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_int Xs2)) (= (@ tptp.set_int2 (@ (@ (@ tptp.list_update_int Xs2) N) X)) (@ (@ tptp.insert_int X) (@ (@ tptp.minus_minus_set_int (@ tptp.set_int2 Xs2)) (@ (@ tptp.insert_int (@ (@ tptp.nth_int Xs2) N)) tptp.bot_bot_set_int))))))) (forall ((Xs2 tptp.list_real) (N tptp.nat) (X tptp.real)) (=> (@ tptp.distinct_real Xs2) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_real Xs2)) (= (@ tptp.set_real2 (@ (@ (@ tptp.list_update_real Xs2) N) X)) (@ (@ tptp.insert_real X) (@ (@ tptp.minus_minus_set_real (@ tptp.set_real2 Xs2)) (@ (@ tptp.insert_real (@ (@ tptp.nth_real Xs2) N)) tptp.bot_bot_set_real))))))) (forall ((Xs2 tptp.list_P6011104703257516679at_nat) (N tptp.nat) (X tptp.product_prod_nat_nat)) (=> (@ tptp.distin6923225563576452346at_nat Xs2) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s5460976970255530739at_nat Xs2)) (= (@ tptp.set_Pr5648618587558075414at_nat (@ (@ (@ tptp.list_u6180841689913720943at_nat Xs2) N) X)) (@ (@ tptp.insert8211810215607154385at_nat X) (@ (@ tptp.minus_1356011639430497352at_nat (@ tptp.set_Pr5648618587558075414at_nat Xs2)) (@ (@ tptp.insert8211810215607154385at_nat (@ (@ tptp.nth_Pr7617993195940197384at_nat Xs2) N)) tptp.bot_bo2099793752762293965at_nat))))))) (forall ((Xs2 tptp.list_nat) (N tptp.nat) (X tptp.nat)) (=> (@ tptp.distinct_nat Xs2) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_nat Xs2)) (= (@ tptp.set_nat2 (@ (@ (@ tptp.list_update_nat Xs2) N) X)) (@ (@ tptp.insert_nat X) (@ (@ tptp.minus_minus_set_nat (@ tptp.set_nat2 Xs2)) (@ (@ tptp.insert_nat (@ (@ tptp.nth_nat Xs2) N)) tptp.bot_bot_set_nat))))))) (forall ((P tptp.nat) (K2 tptp.nat) (G2 (-> tptp.nat tptp.complex)) (H (-> tptp.nat tptp.complex))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) P) (=> (@ (@ tptp.ord_less_eq_nat K2) P) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((J tptp.nat)) (@ (@ (@ tptp.if_complex (@ (@ tptp.ord_less_nat J) K2)) (@ G2 J)) (@ (@ (@ tptp.if_complex (= J K2)) tptp.zero_zero_complex) (@ H (@ (@ tptp.minus_minus_nat J) (@ tptp.suc tptp.zero_zero_nat))))))) (@ tptp.set_ord_atMost_nat P)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((J tptp.nat)) (@ (@ (@ tptp.if_complex (@ (@ tptp.ord_less_nat J) K2)) (@ G2 J)) (@ H J)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat P) (@ tptp.suc tptp.zero_zero_nat)))))))) (forall ((P tptp.nat) (K2 tptp.nat) (G2 (-> tptp.nat tptp.rat)) (H (-> tptp.nat tptp.rat))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) P) (=> (@ (@ tptp.ord_less_eq_nat K2) P) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((J tptp.nat)) (@ (@ (@ tptp.if_rat (@ (@ tptp.ord_less_nat J) K2)) (@ G2 J)) (@ (@ (@ tptp.if_rat (= J K2)) tptp.zero_zero_rat) (@ H (@ (@ tptp.minus_minus_nat J) (@ tptp.suc tptp.zero_zero_nat))))))) (@ tptp.set_ord_atMost_nat P)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((J tptp.nat)) (@ (@ (@ tptp.if_rat (@ (@ tptp.ord_less_nat J) K2)) (@ G2 J)) (@ H J)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat P) (@ tptp.suc tptp.zero_zero_nat)))))))) (forall ((P tptp.nat) (K2 tptp.nat) (G2 (-> tptp.nat tptp.int)) (H (-> tptp.nat tptp.int))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) P) (=> (@ (@ tptp.ord_less_eq_nat K2) P) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((J tptp.nat)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_nat J) K2)) (@ G2 J)) (@ (@ (@ tptp.if_int (= J K2)) tptp.zero_zero_int) (@ H (@ (@ tptp.minus_minus_nat J) (@ tptp.suc tptp.zero_zero_nat))))))) (@ tptp.set_ord_atMost_nat P)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((J tptp.nat)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_nat J) K2)) (@ G2 J)) (@ H J)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat P) (@ tptp.suc tptp.zero_zero_nat)))))))) (forall ((P tptp.nat) (K2 tptp.nat) (G2 (-> tptp.nat tptp.nat)) (H (-> tptp.nat tptp.nat))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) P) (=> (@ (@ tptp.ord_less_eq_nat K2) P) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((J tptp.nat)) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat J) K2)) (@ G2 J)) (@ (@ (@ tptp.if_nat (= J K2)) tptp.zero_zero_nat) (@ H (@ (@ tptp.minus_minus_nat J) (@ tptp.suc tptp.zero_zero_nat))))))) (@ tptp.set_ord_atMost_nat P)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((J tptp.nat)) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat J) K2)) (@ G2 J)) (@ H J)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat P) (@ tptp.suc tptp.zero_zero_nat)))))))) (forall ((P tptp.nat) (K2 tptp.nat) (G2 (-> tptp.nat tptp.real)) (H (-> tptp.nat tptp.real))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) P) (=> (@ (@ tptp.ord_less_eq_nat K2) P) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((J tptp.nat)) (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_nat J) K2)) (@ G2 J)) (@ (@ (@ tptp.if_real (= J K2)) tptp.zero_zero_real) (@ H (@ (@ tptp.minus_minus_nat J) (@ tptp.suc tptp.zero_zero_nat))))))) (@ tptp.set_ord_atMost_nat P)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((J tptp.nat)) (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_nat J) K2)) (@ G2 J)) (@ H J)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat P) (@ tptp.suc tptp.zero_zero_nat)))))))) (forall ((P tptp.nat) (K2 tptp.nat) (G2 (-> tptp.nat tptp.code_integer)) (H (-> tptp.nat tptp.code_integer))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) P) (=> (@ (@ tptp.ord_less_eq_nat K2) P) (= (@ (@ tptp.groups3455450783089532116nteger (lambda ((J tptp.nat)) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.ord_less_nat J) K2)) (@ G2 J)) (@ (@ (@ tptp.if_Code_integer (= J K2)) tptp.one_one_Code_integer) (@ H (@ (@ tptp.minus_minus_nat J) (@ tptp.suc tptp.zero_zero_nat))))))) (@ tptp.set_ord_atMost_nat P)) (@ (@ tptp.groups3455450783089532116nteger (lambda ((J tptp.nat)) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.ord_less_nat J) K2)) (@ G2 J)) (@ H J)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat P) (@ tptp.suc tptp.zero_zero_nat)))))))) (forall ((P tptp.nat) (K2 tptp.nat) (G2 (-> tptp.nat tptp.complex)) (H (-> tptp.nat tptp.complex))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) P) (=> (@ (@ tptp.ord_less_eq_nat K2) P) (= (@ (@ tptp.groups6464643781859351333omplex (lambda ((J tptp.nat)) (@ (@ (@ tptp.if_complex (@ (@ tptp.ord_less_nat J) K2)) (@ G2 J)) (@ (@ (@ tptp.if_complex (= J K2)) tptp.one_one_complex) (@ H (@ (@ tptp.minus_minus_nat J) (@ tptp.suc tptp.zero_zero_nat))))))) (@ tptp.set_ord_atMost_nat P)) (@ (@ tptp.groups6464643781859351333omplex (lambda ((J tptp.nat)) (@ (@ (@ tptp.if_complex (@ (@ tptp.ord_less_nat J) K2)) (@ G2 J)) (@ H J)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat P) (@ tptp.suc tptp.zero_zero_nat)))))))) (forall ((P tptp.nat) (K2 tptp.nat) (G2 (-> tptp.nat tptp.real)) (H (-> tptp.nat tptp.real))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) P) (=> (@ (@ tptp.ord_less_eq_nat K2) P) (= (@ (@ tptp.groups129246275422532515t_real (lambda ((J tptp.nat)) (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_nat J) K2)) (@ G2 J)) (@ (@ (@ tptp.if_real (= J K2)) tptp.one_one_real) (@ H (@ (@ tptp.minus_minus_nat J) (@ tptp.suc tptp.zero_zero_nat))))))) (@ tptp.set_ord_atMost_nat P)) (@ (@ tptp.groups129246275422532515t_real (lambda ((J tptp.nat)) (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_nat J) K2)) (@ G2 J)) (@ H J)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat P) (@ tptp.suc tptp.zero_zero_nat)))))))) (forall ((P tptp.nat) (K2 tptp.nat) (G2 (-> tptp.nat tptp.int)) (H (-> tptp.nat tptp.int))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) P) (=> (@ (@ tptp.ord_less_eq_nat K2) P) (= (@ (@ tptp.groups705719431365010083at_int (lambda ((J tptp.nat)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_nat J) K2)) (@ G2 J)) (@ (@ (@ tptp.if_int (= J K2)) tptp.one_one_int) (@ H (@ (@ tptp.minus_minus_nat J) (@ tptp.suc tptp.zero_zero_nat))))))) (@ tptp.set_ord_atMost_nat P)) (@ (@ tptp.groups705719431365010083at_int (lambda ((J tptp.nat)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_nat J) K2)) (@ G2 J)) (@ H J)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat P) (@ tptp.suc tptp.zero_zero_nat)))))))) (forall ((P tptp.nat) (K2 tptp.nat) (G2 (-> tptp.nat tptp.nat)) (H (-> tptp.nat tptp.nat))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) P) (=> (@ (@ tptp.ord_less_eq_nat K2) P) (= (@ (@ tptp.groups708209901874060359at_nat (lambda ((J tptp.nat)) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat J) K2)) (@ G2 J)) (@ (@ (@ tptp.if_nat (= J K2)) tptp.one_one_nat) (@ H (@ (@ tptp.minus_minus_nat J) (@ tptp.suc tptp.zero_zero_nat))))))) (@ tptp.set_ord_atMost_nat P)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((J tptp.nat)) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat J) K2)) (@ G2 J)) (@ H J)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat P) (@ tptp.suc tptp.zero_zero_nat)))))))) (forall ((K2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((J tptp.nat)) (@ (@ tptp.gbinomial_complex (@ tptp.semiri8010041392384452111omplex J)) K2))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)) (@ (@ tptp.gbinomial_complex (@ (@ tptp.plus_plus_complex (@ tptp.semiri8010041392384452111omplex N)) tptp.one_one_complex)) (@ (@ tptp.plus_plus_nat K2) tptp.one_one_nat)))) (forall ((K2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((J tptp.nat)) (@ (@ tptp.gbinomial_rat (@ tptp.semiri681578069525770553at_rat J)) K2))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)) (@ (@ tptp.gbinomial_rat (@ (@ tptp.plus_plus_rat (@ tptp.semiri681578069525770553at_rat N)) tptp.one_one_rat)) (@ (@ tptp.plus_plus_nat K2) tptp.one_one_nat)))) (forall ((K2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((J tptp.nat)) (@ (@ tptp.gbinomial_real (@ tptp.semiri5074537144036343181t_real J)) K2))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)) (@ (@ tptp.gbinomial_real (@ (@ tptp.plus_plus_real (@ tptp.semiri5074537144036343181t_real N)) tptp.one_one_real)) (@ (@ tptp.plus_plus_nat K2) tptp.one_one_nat)))) (forall ((M2 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 M2))) (= (@ (@ 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) M2)))) (@ _let_1 (@ (@ tptp.minus_minus_nat M2) N))))))) (forall ((M2 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 M2))) (= (@ (@ 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) M2)))) (@ _let_1 (@ (@ tptp.minus_minus_nat M2) N))))))) (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 M2))) (= (@ (@ 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) M2)))) (@ _let_1 (@ (@ tptp.minus_minus_nat M2) N))))))) (forall ((K2 tptp.nat) (A tptp.complex)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K2) (= (@ (@ tptp.gbinomial_complex A) K2) (@ (@ tptp.times_times_complex (@ (@ tptp.divide1717551699836669952omplex A) (@ tptp.semiri8010041392384452111omplex K2))) (@ (@ tptp.gbinomial_complex (@ (@ tptp.minus_minus_complex A) tptp.one_one_complex)) (@ (@ tptp.minus_minus_nat K2) tptp.one_one_nat)))))) (forall ((K2 tptp.nat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K2) (= (@ (@ tptp.gbinomial_rat A) K2) (@ (@ tptp.times_times_rat (@ (@ tptp.divide_divide_rat A) (@ tptp.semiri681578069525770553at_rat K2))) (@ (@ tptp.gbinomial_rat (@ (@ tptp.minus_minus_rat A) tptp.one_one_rat)) (@ (@ tptp.minus_minus_nat K2) tptp.one_one_nat)))))) (forall ((K2 tptp.nat) (A tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K2) (= (@ (@ tptp.gbinomial_real A) K2) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real A) (@ tptp.semiri5074537144036343181t_real K2))) (@ (@ tptp.gbinomial_real (@ (@ tptp.minus_minus_real A) tptp.one_one_real)) (@ (@ tptp.minus_minus_nat K2) tptp.one_one_nat)))))) (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_atMost_nat N)))) (let ((_let_4 (= X tptp.one_one_complex))) (and (=> _let_4 (= _let_3 (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat)))) (=> (not _let_4) (= _let_3 (@ (@ tptp.divide1717551699836669952omplex (@ _let_1 (@ _let_2 (@ tptp.suc N)))) (@ _let_1 X)))))))))) (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_atMost_nat N)))) (let ((_let_4 (= X tptp.one_one_rat))) (and (=> _let_4 (= _let_3 (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat)))) (=> (not _let_4) (= _let_3 (@ (@ tptp.divide_divide_rat (@ _let_1 (@ _let_2 (@ tptp.suc N)))) (@ _let_1 X)))))))))) (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_atMost_nat N)))) (let ((_let_4 (= X tptp.one_one_real))) (and (=> _let_4 (= _let_3 (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat)))) (=> (not _let_4) (= _let_3 (@ (@ tptp.divide_divide_real (@ _let_1 (@ _let_2 (@ tptp.suc N)))) (@ _let_1 X)))))))))) (forall ((N tptp.nat) (A (-> tptp.nat tptp.complex)) (X tptp.complex) (Y tptp.complex)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.groups2073611262835488442omplex (lambda ((I tptp.nat)) (@ (@ tptp.times_times_complex (@ A I)) (@ (@ tptp.power_power_complex X) I)))) _let_1)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I tptp.nat)) (@ (@ tptp.times_times_complex (@ A I)) (@ (@ tptp.power_power_complex Y) I)))) _let_1)) (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex X) Y)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((J tptp.nat)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ A (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat J) K3)) tptp.one_one_nat))) (@ (@ tptp.power_power_complex Y) K3))) (@ (@ tptp.power_power_complex X) J)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.minus_minus_nat N) J))))) (@ tptp.set_ord_lessThan_nat N))))))) (forall ((N tptp.nat) (A (-> tptp.nat tptp.rat)) (X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I tptp.nat)) (@ (@ tptp.times_times_rat (@ A I)) (@ (@ tptp.power_power_rat X) I)))) _let_1)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I tptp.nat)) (@ (@ tptp.times_times_rat (@ A I)) (@ (@ tptp.power_power_rat Y) I)))) _let_1)) (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat X) Y)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((J tptp.nat)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ A (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat J) K3)) tptp.one_one_nat))) (@ (@ tptp.power_power_rat Y) K3))) (@ (@ tptp.power_power_rat X) J)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.minus_minus_nat N) J))))) (@ tptp.set_ord_lessThan_nat N))))))) (forall ((N tptp.nat) (A (-> tptp.nat tptp.int)) (X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.groups3539618377306564664at_int (lambda ((I tptp.nat)) (@ (@ tptp.times_times_int (@ A I)) (@ (@ tptp.power_power_int X) I)))) _let_1)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I tptp.nat)) (@ (@ tptp.times_times_int (@ A I)) (@ (@ tptp.power_power_int Y) I)))) _let_1)) (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int X) Y)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((J tptp.nat)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int (@ A (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat J) K3)) tptp.one_one_nat))) (@ (@ tptp.power_power_int Y) K3))) (@ (@ tptp.power_power_int X) J)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.minus_minus_nat N) J))))) (@ tptp.set_ord_lessThan_nat N))))))) (forall ((N tptp.nat) (A (-> tptp.nat tptp.real)) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((I tptp.nat)) (@ (@ tptp.times_times_real (@ A I)) (@ (@ tptp.power_power_real X) I)))) _let_1)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I tptp.nat)) (@ (@ tptp.times_times_real (@ A I)) (@ (@ tptp.power_power_real Y) I)))) _let_1)) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real X) Y)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((J tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ A (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat J) K3)) tptp.one_one_nat))) (@ (@ tptp.power_power_real Y) K3))) (@ (@ tptp.power_power_real X) J)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.minus_minus_nat N) J))))) (@ tptp.set_ord_lessThan_nat N))))))) (forall ((M2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.times_times_nat _let_1) M2))) (= (@ (@ tptp.groups3542108847815614940at_nat (@ tptp.binomial (@ (@ tptp.plus_plus_nat _let_2) tptp.one_one_nat))) (@ tptp.set_ord_atMost_nat M2)) (@ (@ tptp.power_power_nat _let_1) _let_2))))) (forall ((N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I tptp.nat)) (@ (@ tptp.times_times_nat I) (@ (@ tptp.binomial N) I)))) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.times_times_nat N) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat))))) (forall ((A4 tptp.set_list_nat) (N tptp.nat)) (=> (@ tptp.finite8100373058378681591st_nat A4) (= (@ tptp.finite7325466520557071688st_nat (@ tptp.collec5989764272469232197st_nat (lambda ((Xs tptp.list_list_nat)) (and (@ (@ tptp.ord_le6045566169113846134st_nat (@ tptp.set_list_nat2 Xs)) A4) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_s3023201423986296836st_nat Xs)) N))))) (@ (@ tptp.groups3542108847815614940at_nat (@ tptp.power_power_nat (@ tptp.finite_card_list_nat A4))) (@ tptp.set_ord_atMost_nat N))))) (forall ((A4 tptp.set_set_nat) (N tptp.nat)) (=> (@ tptp.finite1152437895449049373et_nat A4) (= (@ tptp.finite5631907774883551598et_nat (@ tptp.collect_list_set_nat (lambda ((Xs tptp.list_set_nat)) (and (@ (@ tptp.ord_le6893508408891458716et_nat (@ tptp.set_set_nat2 Xs)) A4) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_s3254054031482475050et_nat Xs)) N))))) (@ (@ tptp.groups3542108847815614940at_nat (@ tptp.power_power_nat (@ tptp.finite_card_set_nat A4))) (@ tptp.set_ord_atMost_nat N))))) (forall ((A4 tptp.set_complex) (N tptp.nat)) (=> (@ tptp.finite3207457112153483333omplex A4) (= (@ tptp.finite5120063068150530198omplex (@ tptp.collect_list_complex (lambda ((Xs tptp.list_complex)) (and (@ (@ tptp.ord_le211207098394363844omplex (@ tptp.set_complex2 Xs)) A4) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_s3451745648224563538omplex Xs)) N))))) (@ (@ tptp.groups3542108847815614940at_nat (@ tptp.power_power_nat (@ tptp.finite_card_complex A4))) (@ tptp.set_ord_atMost_nat N))))) (forall ((A4 tptp.set_VEBT_VEBT) (N tptp.nat)) (=> (@ tptp.finite5795047828879050333T_VEBT A4) (= (@ tptp.finite5915292604075114978T_VEBT (@ tptp.collec5608196760682091941T_VEBT (lambda ((Xs tptp.list_VEBT_VEBT)) (and (@ (@ tptp.ord_le4337996190870823476T_VEBT (@ tptp.set_VEBT_VEBT2 Xs)) A4) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_s6755466524823107622T_VEBT Xs)) N))))) (@ (@ tptp.groups3542108847815614940at_nat (@ tptp.power_power_nat (@ tptp.finite7802652506058667612T_VEBT A4))) (@ tptp.set_ord_atMost_nat N))))) (forall ((A4 tptp.set_o) (N tptp.nat)) (=> (@ tptp.finite_finite_o A4) (= (@ tptp.finite_card_list_o (@ tptp.collect_list_o (lambda ((Xs tptp.list_o)) (and (@ (@ tptp.ord_less_eq_set_o (@ tptp.set_o2 Xs)) A4) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_o Xs)) N))))) (@ (@ tptp.groups3542108847815614940at_nat (@ tptp.power_power_nat (@ tptp.finite_card_o A4))) (@ tptp.set_ord_atMost_nat N))))) (forall ((A4 tptp.set_int) (N tptp.nat)) (=> (@ tptp.finite_finite_int A4) (= (@ tptp.finite_card_list_int (@ tptp.collect_list_int (lambda ((Xs tptp.list_int)) (and (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_int2 Xs)) A4) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_int Xs)) N))))) (@ (@ tptp.groups3542108847815614940at_nat (@ tptp.power_power_nat (@ tptp.finite_card_int A4))) (@ tptp.set_ord_atMost_nat N))))) (forall ((A4 tptp.set_nat) (N tptp.nat)) (=> (@ tptp.finite_finite_nat A4) (= (@ tptp.finite_card_list_nat (@ tptp.collect_list_nat (lambda ((Xs tptp.list_nat)) (and (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_nat2 Xs)) A4) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_nat Xs)) N))))) (@ (@ tptp.groups3542108847815614940at_nat (@ tptp.power_power_nat (@ tptp.finite_card_nat A4))) (@ tptp.set_ord_atMost_nat N))))) (forall ((E tptp.real) (C2 (-> tptp.nat tptp.complex)) (N tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E) (exists ((M8 tptp.real)) (forall ((Z5 tptp.complex)) (let ((_let_1 (@ tptp.real_V1022390504157884413omplex Z5))) (=> (@ (@ tptp.ord_less_eq_real M8) _let_1) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.groups2073611262835488442omplex (lambda ((I tptp.nat)) (@ (@ tptp.times_times_complex (@ C2 I)) (@ (@ tptp.power_power_complex Z5) I)))) (@ tptp.set_ord_atMost_nat N)))) (@ (@ tptp.times_times_real E) (@ (@ tptp.power_power_real _let_1) (@ tptp.suc N)))))))))) (forall ((E tptp.real) (C2 (-> tptp.nat tptp.real)) (N tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E) (exists ((M8 tptp.real)) (forall ((Z5 tptp.real)) (let ((_let_1 (@ tptp.real_V7735802525324610683m_real Z5))) (=> (@ (@ tptp.ord_less_eq_real M8) _let_1) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((I tptp.nat)) (@ (@ tptp.times_times_real (@ C2 I)) (@ (@ tptp.power_power_real Z5) I)))) (@ tptp.set_ord_atMost_nat N)))) (@ (@ tptp.times_times_real E) (@ (@ tptp.power_power_real _let_1) (@ tptp.suc N)))))))))) (forall ((N tptp.nat) (A (-> tptp.nat tptp.complex)) (X tptp.complex) (Y tptp.complex)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.groups2073611262835488442omplex (lambda ((I tptp.nat)) (@ (@ tptp.times_times_complex (@ A I)) (@ (@ tptp.power_power_complex X) I)))) _let_1)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I tptp.nat)) (@ (@ tptp.times_times_complex (@ A I)) (@ (@ tptp.power_power_complex Y) I)))) _let_1)) (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex X) Y)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((J tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.groups2073611262835488442omplex (lambda ((I tptp.nat)) (@ (@ tptp.times_times_complex (@ A I)) (@ (@ tptp.power_power_complex Y) (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat I) J)) tptp.one_one_nat))))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc J)) N))) (@ (@ tptp.power_power_complex X) J)))) (@ tptp.set_ord_lessThan_nat N))))))) (forall ((N tptp.nat) (A (-> tptp.nat tptp.rat)) (X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I tptp.nat)) (@ (@ tptp.times_times_rat (@ A I)) (@ (@ tptp.power_power_rat X) I)))) _let_1)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I tptp.nat)) (@ (@ tptp.times_times_rat (@ A I)) (@ (@ tptp.power_power_rat Y) I)))) _let_1)) (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat X) Y)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((J tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I tptp.nat)) (@ (@ tptp.times_times_rat (@ A I)) (@ (@ tptp.power_power_rat Y) (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat I) J)) tptp.one_one_nat))))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc J)) N))) (@ (@ tptp.power_power_rat X) J)))) (@ tptp.set_ord_lessThan_nat N))))))) (forall ((N tptp.nat) (A (-> tptp.nat tptp.int)) (X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.groups3539618377306564664at_int (lambda ((I tptp.nat)) (@ (@ tptp.times_times_int (@ A I)) (@ (@ tptp.power_power_int X) I)))) _let_1)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I tptp.nat)) (@ (@ tptp.times_times_int (@ A I)) (@ (@ tptp.power_power_int Y) I)))) _let_1)) (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int X) Y)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((J tptp.nat)) (@ (@ tptp.times_times_int (@ (@ tptp.groups3539618377306564664at_int (lambda ((I tptp.nat)) (@ (@ tptp.times_times_int (@ A I)) (@ (@ tptp.power_power_int Y) (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat I) J)) tptp.one_one_nat))))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc J)) N))) (@ (@ tptp.power_power_int X) J)))) (@ tptp.set_ord_lessThan_nat N))))))) (forall ((N tptp.nat) (A (-> tptp.nat tptp.real)) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((I tptp.nat)) (@ (@ tptp.times_times_real (@ A I)) (@ (@ tptp.power_power_real X) I)))) _let_1)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I tptp.nat)) (@ (@ tptp.times_times_real (@ A I)) (@ (@ tptp.power_power_real Y) I)))) _let_1)) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real X) Y)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((J tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((I tptp.nat)) (@ (@ tptp.times_times_real (@ A I)) (@ (@ tptp.power_power_real Y) (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat I) J)) tptp.one_one_nat))))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc J)) N))) (@ (@ tptp.power_power_real X) J)))) (@ tptp.set_ord_lessThan_nat N))))))) (forall ((K2 tptp.nat) (A4 tptp.set_complex)) (let ((_let_1 (@ tptp.finite_card_complex A4))) (=> (@ (@ tptp.ord_less_nat K2) _let_1) (= (@ tptp.finite5120063068150530198omplex (@ tptp.collect_list_complex (lambda ((Xs tptp.list_complex)) (and (= (@ tptp.size_s3451745648224563538omplex Xs) K2) (@ tptp.distinct_complex Xs) (@ (@ tptp.ord_le211207098394363844omplex (@ tptp.set_complex2 Xs)) A4))))) (@ (@ tptp.groups708209901874060359at_nat (lambda ((X4 tptp.nat)) X4)) (@ (@ tptp.set_or1269000886237332187st_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat _let_1) K2)) tptp.one_one_nat)) _let_1)))))) (forall ((K2 tptp.nat) (A4 tptp.set_list_nat)) (let ((_let_1 (@ tptp.finite_card_list_nat A4))) (=> (@ (@ tptp.ord_less_nat K2) _let_1) (= (@ tptp.finite7325466520557071688st_nat (@ tptp.collec5989764272469232197st_nat (lambda ((Xs tptp.list_list_nat)) (and (= (@ tptp.size_s3023201423986296836st_nat Xs) K2) (@ tptp.distinct_list_nat Xs) (@ (@ tptp.ord_le6045566169113846134st_nat (@ tptp.set_list_nat2 Xs)) A4))))) (@ (@ tptp.groups708209901874060359at_nat (lambda ((X4 tptp.nat)) X4)) (@ (@ tptp.set_or1269000886237332187st_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat _let_1) K2)) tptp.one_one_nat)) _let_1)))))) (forall ((K2 tptp.nat) (A4 tptp.set_set_nat)) (let ((_let_1 (@ tptp.finite_card_set_nat A4))) (=> (@ (@ tptp.ord_less_nat K2) _let_1) (= (@ tptp.finite5631907774883551598et_nat (@ tptp.collect_list_set_nat (lambda ((Xs tptp.list_set_nat)) (and (= (@ tptp.size_s3254054031482475050et_nat Xs) K2) (@ tptp.distinct_set_nat Xs) (@ (@ tptp.ord_le6893508408891458716et_nat (@ tptp.set_set_nat2 Xs)) A4))))) (@ (@ tptp.groups708209901874060359at_nat (lambda ((X4 tptp.nat)) X4)) (@ (@ tptp.set_or1269000886237332187st_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat _let_1) K2)) tptp.one_one_nat)) _let_1)))))) (forall ((K2 tptp.nat) (A4 tptp.set_VEBT_VEBT)) (let ((_let_1 (@ tptp.finite7802652506058667612T_VEBT A4))) (=> (@ (@ tptp.ord_less_nat K2) _let_1) (= (@ tptp.finite5915292604075114978T_VEBT (@ tptp.collec5608196760682091941T_VEBT (lambda ((Xs tptp.list_VEBT_VEBT)) (and (= (@ tptp.size_s6755466524823107622T_VEBT Xs) K2) (@ tptp.distinct_VEBT_VEBT Xs) (@ (@ tptp.ord_le4337996190870823476T_VEBT (@ tptp.set_VEBT_VEBT2 Xs)) A4))))) (@ (@ tptp.groups708209901874060359at_nat (lambda ((X4 tptp.nat)) X4)) (@ (@ tptp.set_or1269000886237332187st_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat _let_1) K2)) tptp.one_one_nat)) _let_1)))))) (forall ((K2 tptp.nat) (A4 tptp.set_o)) (let ((_let_1 (@ tptp.finite_card_o A4))) (=> (@ (@ tptp.ord_less_nat K2) _let_1) (= (@ tptp.finite_card_list_o (@ tptp.collect_list_o (lambda ((Xs tptp.list_o)) (and (= (@ tptp.size_size_list_o Xs) K2) (@ tptp.distinct_o Xs) (@ (@ tptp.ord_less_eq_set_o (@ tptp.set_o2 Xs)) A4))))) (@ (@ tptp.groups708209901874060359at_nat (lambda ((X4 tptp.nat)) X4)) (@ (@ tptp.set_or1269000886237332187st_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat _let_1) K2)) tptp.one_one_nat)) _let_1)))))) (forall ((K2 tptp.nat) (A4 tptp.set_int)) (let ((_let_1 (@ tptp.finite_card_int A4))) (=> (@ (@ tptp.ord_less_nat K2) _let_1) (= (@ tptp.finite_card_list_int (@ tptp.collect_list_int (lambda ((Xs tptp.list_int)) (and (= (@ tptp.size_size_list_int Xs) K2) (@ tptp.distinct_int Xs) (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_int2 Xs)) A4))))) (@ (@ tptp.groups708209901874060359at_nat (lambda ((X4 tptp.nat)) X4)) (@ (@ tptp.set_or1269000886237332187st_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat _let_1) K2)) tptp.one_one_nat)) _let_1)))))) (forall ((K2 tptp.nat) (A4 tptp.set_nat)) (let ((_let_1 (@ tptp.finite_card_nat A4))) (=> (@ (@ tptp.ord_less_nat K2) _let_1) (= (@ tptp.finite_card_list_nat (@ tptp.collect_list_nat (lambda ((Xs tptp.list_nat)) (and (= (@ tptp.size_size_list_nat Xs) K2) (@ tptp.distinct_nat Xs) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_nat2 Xs)) A4))))) (@ (@ tptp.groups708209901874060359at_nat (lambda ((X4 tptp.nat)) X4)) (@ (@ tptp.set_or1269000886237332187st_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat _let_1) K2)) tptp.one_one_nat)) _let_1)))))) (forall ((Q2 tptp.int) (R3 tptp.int)) (= (@ tptp.adjust_div (@ (@ tptp.product_Pair_int_int Q2) R3)) (@ (@ tptp.plus_plus_int Q2) (@ tptp.zero_n2684676970156552555ol_int (not (= R3 tptp.zero_zero_int)))))) (forall ((A0 tptp.nat) (P2 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.accp_nat tptp.nat_list_decode_rel))) (=> (@ _let_1 A0) (=> (=> (@ _let_1 tptp.zero_zero_nat) (@ P2 tptp.zero_zero_nat)) (=> (forall ((N3 tptp.nat)) (let ((_let_1 (@ tptp.suc N3))) (=> (@ (@ tptp.accp_nat tptp.nat_list_decode_rel) _let_1) (=> (forall ((X5 tptp.nat) (Y6 tptp.nat)) (=> (= (@ (@ tptp.product_Pair_nat_nat X5) Y6) (@ tptp.nat_prod_decode N3)) (@ P2 Y6))) (@ P2 _let_1))))) (@ P2 A0)))))) _let_228 _let_227 _let_226 (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) I)) (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.binomial N) I))))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_complex))) (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.groups7501900531339628137nteger (lambda ((I tptp.nat)) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) I)) (@ tptp.semiri4939895301339042750nteger (@ (@ tptp.binomial N) I))))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_z3403309356797280102nteger))) (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) I)) (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.binomial N) I))))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_rat))) (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((I tptp.nat)) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) I)) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.binomial N) I))))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_int))) (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I)) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.binomial N) I))))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_real))) (forall ((N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.suc N)) A) (@ (@ tptp.plus_plus_int (@ (@ tptp.modulo_modulo_int A) _let_1)) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_ri631733984087533419it_int N) (@ (@ tptp.divide_divide_int A) _let_1))))))) (forall ((X tptp.nat)) (= (@ (@ tptp.member_nat tptp.zero_zero_nat) (@ tptp.nat_set_decode X)) (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) X)))) (forall ((A tptp.int)) (= (@ tptp.uminus_uminus_int (@ tptp.uminus_uminus_int A)) A)) (forall ((A tptp.real)) (= (@ tptp.uminus_uminus_real (@ tptp.uminus_uminus_real A)) A)) (forall ((A tptp.complex)) (= (@ tptp.uminus1482373934393186551omplex (@ tptp.uminus1482373934393186551omplex A)) A)) (forall ((A tptp.code_integer)) (= (@ tptp.uminus1351360451143612070nteger (@ tptp.uminus1351360451143612070nteger A)) A)) (forall ((A tptp.rat)) (= (@ tptp.uminus_uminus_rat (@ tptp.uminus_uminus_rat A)) A)) (forall ((A tptp.int) (B tptp.int)) (= (= (@ tptp.uminus_uminus_int A) (@ tptp.uminus_uminus_int B)) (= A B))) (forall ((A tptp.real) (B tptp.real)) (= (= (@ tptp.uminus_uminus_real A) (@ tptp.uminus_uminus_real B)) (= A B))) (forall ((A tptp.complex) (B tptp.complex)) (= (= (@ tptp.uminus1482373934393186551omplex A) (@ tptp.uminus1482373934393186551omplex B)) (= A B))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= (@ tptp.uminus1351360451143612070nteger A) (@ tptp.uminus1351360451143612070nteger B)) (= A B))) (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ tptp.uminus_uminus_rat A) (@ tptp.uminus_uminus_rat B)) (= A B))) (= tptp.semiri1316708129612266289at_nat (lambda ((N4 tptp.nat)) N4)) (forall ((X tptp.set_nat) (Y tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ tptp.uminus5710092332889474511et_nat X)) (@ tptp.uminus5710092332889474511et_nat Y)) (@ (@ tptp.ord_less_eq_set_nat Y) X))) (forall ((B tptp.real) (A tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real B)) (@ tptp.uminus_uminus_real A)) (@ (@ tptp.ord_less_eq_real A) B))) (forall ((B tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger A)) (@ (@ tptp.ord_le3102999989581377725nteger A) B))) (forall ((B tptp.rat) (A tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat B)) (@ tptp.uminus_uminus_rat A)) (@ (@ tptp.ord_less_eq_rat A) B))) (forall ((B tptp.int) (A tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int B)) (@ tptp.uminus_uminus_int A)) (@ (@ tptp.ord_less_eq_int A) B))) (forall ((A tptp.int)) (= (= (@ tptp.uminus_uminus_int A) A) (= A tptp.zero_zero_int))) (forall ((A tptp.real)) (= (= (@ tptp.uminus_uminus_real A) A) (= A tptp.zero_zero_real))) (forall ((A tptp.code_integer)) (= (= (@ tptp.uminus1351360451143612070nteger A) A) (= A tptp.zero_z3403309356797280102nteger))) (forall ((A tptp.rat)) (= (= (@ tptp.uminus_uminus_rat A) A) (= A tptp.zero_zero_rat))) (forall ((A tptp.int)) (= (= A (@ tptp.uminus_uminus_int A)) (= A tptp.zero_zero_int))) (forall ((A tptp.real)) (= (= A (@ tptp.uminus_uminus_real A)) (= A tptp.zero_zero_real))) (forall ((A tptp.code_integer)) (= (= A (@ tptp.uminus1351360451143612070nteger A)) (= A tptp.zero_z3403309356797280102nteger))) (forall ((A tptp.rat)) (= (= A (@ tptp.uminus_uminus_rat A)) (= A tptp.zero_zero_rat))) (forall ((A tptp.int)) (= (= (@ tptp.uminus_uminus_int A) tptp.zero_zero_int) (= A tptp.zero_zero_int))) (forall ((A tptp.real)) (= (= (@ tptp.uminus_uminus_real A) tptp.zero_zero_real) (= A tptp.zero_zero_real))) (forall ((A tptp.complex)) (= (= (@ tptp.uminus1482373934393186551omplex A) tptp.zero_zero_complex) (= A tptp.zero_zero_complex))) (forall ((A tptp.code_integer)) (= (= (@ tptp.uminus1351360451143612070nteger A) tptp.zero_z3403309356797280102nteger) (= A tptp.zero_z3403309356797280102nteger))) (forall ((A tptp.rat)) (= (= (@ tptp.uminus_uminus_rat A) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))) (forall ((A tptp.int)) (= (= tptp.zero_zero_int (@ tptp.uminus_uminus_int A)) (= tptp.zero_zero_int A))) (forall ((A tptp.real)) (= (= tptp.zero_zero_real (@ tptp.uminus_uminus_real A)) (= tptp.zero_zero_real A))) (forall ((A tptp.complex)) (= (= tptp.zero_zero_complex (@ tptp.uminus1482373934393186551omplex A)) (= tptp.zero_zero_complex A))) (forall ((A tptp.code_integer)) (= (= tptp.zero_z3403309356797280102nteger (@ tptp.uminus1351360451143612070nteger A)) (= tptp.zero_z3403309356797280102nteger A))) (forall ((A tptp.rat)) (= (= tptp.zero_zero_rat (@ tptp.uminus_uminus_rat A)) (= tptp.zero_zero_rat A))) (= (@ tptp.uminus_uminus_int tptp.zero_zero_int) tptp.zero_zero_int) (= (@ tptp.uminus_uminus_real tptp.zero_zero_real) tptp.zero_zero_real) (= (@ tptp.uminus1482373934393186551omplex tptp.zero_zero_complex) tptp.zero_zero_complex) (= (@ tptp.uminus1351360451143612070nteger tptp.zero_z3403309356797280102nteger) tptp.zero_z3403309356797280102nteger) (= (@ tptp.uminus_uminus_rat tptp.zero_zero_rat) tptp.zero_zero_rat) (forall ((B tptp.int) (A tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int B)) (@ tptp.uminus_uminus_int A)) (@ (@ tptp.ord_less_int A) B))) (forall ((B tptp.real) (A tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real B)) (@ tptp.uminus_uminus_real A)) (@ (@ tptp.ord_less_real A) B))) (forall ((B tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger A)) (@ (@ tptp.ord_le6747313008572928689nteger A) B))) (forall ((B tptp.rat) (A tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat B)) (@ tptp.uminus_uminus_rat A)) (@ (@ tptp.ord_less_rat A) B))) (forall ((M2 tptp.num) (N tptp.num)) (= (= (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) (= M2 N))) (forall ((M2 tptp.num) (N tptp.num)) (= (= (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M2)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))) (= M2 N))) (forall ((M2 tptp.num) (N tptp.num)) (= (= (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex M2)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N))) (= M2 N))) (forall ((M2 tptp.num) (N tptp.num)) (= (= (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M2)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))) (= M2 N))) (forall ((M2 tptp.num) (N tptp.num)) (= (= (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M2)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))) (= M2 N))) (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (= (@ _let_1 (@ tptp.uminus_uminus_int B)) (@ tptp.uminus_uminus_int (@ _let_1 B))))) (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real A))) (= (@ _let_1 (@ tptp.uminus_uminus_real B)) (@ tptp.uminus_uminus_real (@ _let_1 B))))) (forall ((A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex A))) (= (@ _let_1 (@ tptp.uminus1482373934393186551omplex B)) (@ tptp.uminus1482373934393186551omplex (@ _let_1 B))))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger A))) (= (@ _let_1 (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger (@ _let_1 B))))) (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat A))) (= (@ _let_1 (@ tptp.uminus_uminus_rat B)) (@ tptp.uminus_uminus_rat (@ _let_1 B))))) (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int A)) (@ tptp.uminus_uminus_int B)) (@ (@ tptp.times_times_int A) B))) (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real A)) (@ tptp.uminus_uminus_real B)) (@ (@ tptp.times_times_real A) B))) (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex A)) (@ tptp.uminus1482373934393186551omplex B)) (@ (@ tptp.times_times_complex A) B))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger A)) (@ tptp.uminus1351360451143612070nteger B)) (@ (@ tptp.times_3573771949741848930nteger A) B))) (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat A)) (@ tptp.uminus_uminus_rat B)) (@ (@ tptp.times_times_rat A) B))) (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int A)) B) (@ tptp.uminus_uminus_int (@ (@ tptp.times_times_int A) B)))) (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real A)) B) (@ tptp.uminus_uminus_real (@ (@ tptp.times_times_real A) B)))) (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex A)) B) (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.times_times_complex A) B)))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger A)) B) (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.times_3573771949741848930nteger A) B)))) (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat A)) B) (@ tptp.uminus_uminus_rat (@ (@ tptp.times_times_rat A) B)))) (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.plus_plus_int A) (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int A)) B)) B)) (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.plus_plus_real A) (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A)) B)) B)) (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.plus_plus_complex A) (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex A)) B)) B)) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger A) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger A)) B)) B)) (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.plus_plus_rat A) (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat A)) B)) B)) (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int A)) (@ (@ tptp.plus_plus_int A) B)) B)) (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A)) (@ (@ tptp.plus_plus_real A) B)) B)) (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex A)) (@ (@ tptp.plus_plus_complex A) B)) B)) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger A)) (@ (@ tptp.plus_p5714425477246183910nteger A) B)) B)) (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat A)) (@ (@ tptp.plus_plus_rat A) B)) B)) (forall ((A tptp.int) (B tptp.int)) (= (@ tptp.uminus_uminus_int (@ (@ tptp.plus_plus_int A) B)) (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int A)) (@ tptp.uminus_uminus_int B)))) (forall ((A tptp.real) (B tptp.real)) (= (@ tptp.uminus_uminus_real (@ (@ tptp.plus_plus_real A) B)) (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A)) (@ tptp.uminus_uminus_real B)))) (forall ((A tptp.complex) (B tptp.complex)) (= (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.plus_plus_complex A) B)) (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex A)) (@ tptp.uminus1482373934393186551omplex B)))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B)) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger A)) (@ tptp.uminus1351360451143612070nteger B)))) (forall ((A tptp.rat) (B tptp.rat)) (= (@ tptp.uminus_uminus_rat (@ (@ tptp.plus_plus_rat A) B)) (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat A)) (@ tptp.uminus_uminus_rat B)))) (forall ((A tptp.int) (B tptp.int)) (= (@ tptp.uminus_uminus_int (@ (@ tptp.minus_minus_int A) B)) (@ (@ tptp.minus_minus_int B) A))) (forall ((A tptp.real) (B tptp.real)) (= (@ tptp.uminus_uminus_real (@ (@ tptp.minus_minus_real A) B)) (@ (@ tptp.minus_minus_real B) A))) (forall ((A tptp.complex) (B tptp.complex)) (= (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.minus_minus_complex A) B)) (@ (@ tptp.minus_minus_complex B) A))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.minus_8373710615458151222nteger A) B)) (@ (@ tptp.minus_8373710615458151222nteger B) A))) (forall ((A tptp.rat) (B tptp.rat)) (= (@ tptp.uminus_uminus_rat (@ (@ tptp.minus_minus_rat A) B)) (@ (@ tptp.minus_minus_rat B) A))) (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int X))) (= (@ _let_1 (@ tptp.uminus_uminus_int Y)) (@ _let_1 Y)))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real X))) (= (@ _let_1 (@ tptp.uminus_uminus_real Y)) (@ _let_1 Y)))) (forall ((X tptp.complex) (Y tptp.complex)) (let ((_let_1 (@ tptp.dvd_dvd_complex X))) (= (@ _let_1 (@ tptp.uminus1482373934393186551omplex Y)) (@ _let_1 Y)))) (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)))) (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)))) (forall ((X tptp.int) (Y tptp.int)) (= (@ (@ tptp.dvd_dvd_int (@ tptp.uminus_uminus_int X)) Y) (@ (@ tptp.dvd_dvd_int X) Y))) (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ tptp.dvd_dvd_real (@ tptp.uminus_uminus_real X)) Y) (@ (@ tptp.dvd_dvd_real X) Y))) (forall ((X tptp.complex) (Y tptp.complex)) (= (@ (@ tptp.dvd_dvd_complex (@ tptp.uminus1482373934393186551omplex X)) Y) (@ (@ tptp.dvd_dvd_complex X) Y))) (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))) (forall ((X tptp.rat) (Y tptp.rat)) (= (@ (@ tptp.dvd_dvd_rat (@ tptp.uminus_uminus_rat X)) Y) (@ (@ tptp.dvd_dvd_rat X) Y))) (forall ((N tptp.nat) (M2 tptp.nat)) (= (= (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N)) (@ tptp.semiri1314217659103216013at_int M2)) (and (= N tptp.zero_zero_nat) (= M2 tptp.zero_zero_nat)))) (forall ((N tptp.nat)) (= (@ (@ tptp.bit_ri631733984087533419it_int N) tptp.zero_zero_int) tptp.zero_zero_int)) (forall ((N tptp.nat)) (= (@ tptp.nat_set_encode (@ tptp.nat_set_decode N)) N)) (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real A)) A) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A))) (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger A)) A) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A))) (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat A)) A) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A))) (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int A)) A) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A))) (forall ((A tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real A))) (= (@ _let_1 (@ tptp.uminus_uminus_real A)) (@ _let_1 tptp.zero_zero_real)))) (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger A))) (= (@ _let_1 (@ tptp.uminus1351360451143612070nteger A)) (@ _let_1 tptp.zero_z3403309356797280102nteger)))) (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat A))) (= (@ _let_1 (@ tptp.uminus_uminus_rat A)) (@ _let_1 tptp.zero_zero_rat)))) (forall ((A tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int A))) (= (@ _let_1 (@ tptp.uminus_uminus_int A)) (@ _let_1 tptp.zero_zero_int)))) (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real A)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A))) (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger A)) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A))) (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat A)) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A))) (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int A)) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A))) (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.uminus_uminus_real A)) (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real))) (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger A)) (@ (@ tptp.ord_le3102999989581377725nteger A) tptp.zero_z3403309356797280102nteger))) (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.uminus_uminus_rat A)) (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat))) (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int A)) (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int))) (forall ((A tptp.int)) (let ((_let_1 (@ tptp.ord_less_int A))) (= (@ _let_1 (@ tptp.uminus_uminus_int A)) (@ _let_1 tptp.zero_zero_int)))) (forall ((A tptp.real)) (let ((_let_1 (@ tptp.ord_less_real A))) (= (@ _let_1 (@ tptp.uminus_uminus_real A)) (@ _let_1 tptp.zero_zero_real)))) (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger A))) (= (@ _let_1 (@ tptp.uminus1351360451143612070nteger A)) (@ _let_1 tptp.zero_z3403309356797280102nteger)))) (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A))) (= (@ _let_1 (@ tptp.uminus_uminus_rat A)) (@ _let_1 tptp.zero_zero_rat)))) (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int A)) A) (@ (@ tptp.ord_less_int tptp.zero_zero_int) A))) (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real A)) A) (@ (@ tptp.ord_less_real tptp.zero_zero_real) A))) (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger A)) A) (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A))) (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat A)) A) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A))) (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int A)) (@ (@ tptp.ord_less_int A) tptp.zero_zero_int))) (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.uminus_uminus_real A)) (@ (@ tptp.ord_less_real A) tptp.zero_zero_real))) (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger A)) (@ (@ tptp.ord_le6747313008572928689nteger A) tptp.zero_z3403309356797280102nteger))) (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.uminus_uminus_rat A)) (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat))) (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int A)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int tptp.zero_zero_int) A))) (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real A)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real tptp.zero_zero_real) A))) (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger A)) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A))) (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat A)) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A))) (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int A) (@ tptp.uminus_uminus_int A)) tptp.zero_zero_int)) (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real A) (@ tptp.uminus_uminus_real A)) tptp.zero_zero_real)) (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex A) (@ tptp.uminus1482373934393186551omplex A)) tptp.zero_zero_complex)) (forall ((A tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger A) (@ tptp.uminus1351360451143612070nteger A)) tptp.zero_z3403309356797280102nteger)) (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat A) (@ tptp.uminus_uminus_rat A)) tptp.zero_zero_rat)) (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int A)) A) tptp.zero_zero_int)) (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A)) A) tptp.zero_zero_real)) (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex A)) A) tptp.zero_zero_complex)) (forall ((A tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger A)) A) tptp.zero_z3403309356797280102nteger)) (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat A)) A) tptp.zero_zero_rat)) (forall ((B tptp.int)) (= (@ (@ tptp.minus_minus_int tptp.zero_zero_int) B) (@ tptp.uminus_uminus_int B))) (forall ((B tptp.real)) (= (@ (@ tptp.minus_minus_real tptp.zero_zero_real) B) (@ tptp.uminus_uminus_real B))) (forall ((B tptp.complex)) (= (@ (@ tptp.minus_minus_complex tptp.zero_zero_complex) B) (@ tptp.uminus1482373934393186551omplex B))) (forall ((B tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger tptp.zero_z3403309356797280102nteger) B) (@ tptp.uminus1351360451143612070nteger B))) (forall ((B tptp.rat)) (= (@ (@ tptp.minus_minus_rat tptp.zero_zero_rat) B) (@ tptp.uminus_uminus_rat B))) (forall ((A tptp.int)) (= (@ (@ tptp.minus_minus_int tptp.zero_zero_int) A) (@ tptp.uminus_uminus_int A))) (forall ((A tptp.real)) (= (@ (@ tptp.minus_minus_real tptp.zero_zero_real) A) (@ tptp.uminus_uminus_real A))) (forall ((A tptp.complex)) (= (@ (@ tptp.minus_minus_complex tptp.zero_zero_complex) A) (@ tptp.uminus1482373934393186551omplex A))) (forall ((A tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger tptp.zero_z3403309356797280102nteger) A) (@ tptp.uminus1351360451143612070nteger A))) (forall ((A tptp.rat)) (= (@ (@ tptp.minus_minus_rat tptp.zero_zero_rat) A) (@ tptp.uminus_uminus_rat A))) (forall ((M2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (let ((_let_2 (@ tptp.numeral_numeral_int M2))) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int _let_2)) (@ tptp.uminus_uminus_int _let_1)) (@ tptp.uminus_uminus_int (@ (@ tptp.plus_plus_int _let_2) _let_1)))))) (forall ((M2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real N))) (let ((_let_2 (@ tptp.numeral_numeral_real M2))) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real _let_2)) (@ tptp.uminus_uminus_real _let_1)) (@ tptp.uminus_uminus_real (@ (@ tptp.plus_plus_real _let_2) _let_1)))))) (forall ((M2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex N))) (let ((_let_2 (@ tptp.numera6690914467698888265omplex M2))) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex _let_2)) (@ tptp.uminus1482373934393186551omplex _let_1)) (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.plus_plus_complex _let_2) _let_1)))))) (forall ((M2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger N))) (let ((_let_2 (@ tptp.numera6620942414471956472nteger M2))) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger _let_2)) (@ tptp.uminus1351360451143612070nteger _let_1)) (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.plus_p5714425477246183910nteger _let_2) _let_1)))))) (forall ((M2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat N))) (let ((_let_2 (@ tptp.numeral_numeral_rat M2))) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat _let_2)) (@ tptp.uminus_uminus_rat _let_1)) (@ tptp.uminus_uminus_rat (@ (@ tptp.plus_plus_rat _let_2) _let_1)))))) (forall ((Z3 tptp.int)) (= (@ (@ tptp.times_times_int Z3) (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.uminus_uminus_int Z3))) (forall ((Z3 tptp.real)) (= (@ (@ tptp.times_times_real Z3) (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.uminus_uminus_real Z3))) (forall ((Z3 tptp.complex)) (= (@ (@ tptp.times_times_complex Z3) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ tptp.uminus1482373934393186551omplex Z3))) (forall ((Z3 tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger Z3) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.uminus1351360451143612070nteger Z3))) (forall ((Z3 tptp.rat)) (= (@ (@ tptp.times_times_rat Z3) (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.uminus_uminus_rat Z3))) (forall ((Z3 tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int tptp.one_one_int)) Z3) (@ tptp.uminus_uminus_int Z3))) (forall ((Z3 tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Z3) (@ tptp.uminus_uminus_real Z3))) (forall ((Z3 tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) Z3) (@ tptp.uminus1482373934393186551omplex Z3))) (forall ((Z3 tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) Z3) (@ tptp.uminus1351360451143612070nteger Z3))) (forall ((Z3 tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) Z3) (@ tptp.uminus_uminus_rat Z3))) (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.minus_minus_int A) (@ tptp.uminus_uminus_int B)) (@ (@ tptp.plus_plus_int A) B))) (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.minus_minus_real A) (@ tptp.uminus_uminus_real B)) (@ (@ tptp.plus_plus_real A) B))) (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.minus_minus_complex A) (@ tptp.uminus1482373934393186551omplex B)) (@ (@ tptp.plus_plus_complex A) B))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger A) (@ tptp.uminus1351360451143612070nteger B)) (@ (@ tptp.plus_p5714425477246183910nteger A) B))) (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.minus_minus_rat A) (@ tptp.uminus_uminus_rat B)) (@ (@ tptp.plus_plus_rat A) B))) (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int A)) B) (@ (@ tptp.minus_minus_int B) A))) (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A)) B) (@ (@ tptp.minus_minus_real B) A))) (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex A)) B) (@ (@ tptp.minus_minus_complex B) A))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger A)) B) (@ (@ tptp.minus_8373710615458151222nteger B) A))) (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat A)) B) (@ (@ tptp.minus_minus_rat B) A))) (= (@ tptp.semiri3624122377584611663nteger tptp.zero_zero_nat) tptp.one_one_Code_integer) (= (@ tptp.semiri5044797733671781792omplex tptp.zero_zero_nat) tptp.one_one_complex) (= (@ tptp.semiri1406184849735516958ct_int tptp.zero_zero_nat) tptp.one_one_int) (= (@ tptp.semiri1408675320244567234ct_nat tptp.zero_zero_nat) tptp.one_one_nat) (= (@ tptp.semiri2265585572941072030t_real tptp.zero_zero_nat) tptp.one_one_real) (forall ((N tptp.nat) (M2 tptp.nat)) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N)))) (@ tptp.semiri1314217659103216013at_int M2))) (forall ((N tptp.nat)) (= (@ (@ tptp.bit_ri6519982836138164636nteger (@ tptp.suc N)) tptp.one_one_Code_integer) tptp.one_one_Code_integer)) (forall ((N tptp.nat)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.suc N)) tptp.one_one_int) tptp.one_one_int)) (forall ((K2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int K2))) (= (@ tptp.neg_numeral_dbl_int (@ tptp.uminus_uminus_int _let_1)) (@ tptp.uminus_uminus_int (@ tptp.neg_numeral_dbl_int _let_1))))) (forall ((K2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real K2))) (= (@ tptp.neg_numeral_dbl_real (@ tptp.uminus_uminus_real _let_1)) (@ tptp.uminus_uminus_real (@ tptp.neg_numeral_dbl_real _let_1))))) (forall ((K2 tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex K2))) (= (@ tptp.neg_nu7009210354673126013omplex (@ tptp.uminus1482373934393186551omplex _let_1)) (@ tptp.uminus1482373934393186551omplex (@ tptp.neg_nu7009210354673126013omplex _let_1))))) (forall ((K2 tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger K2))) (= (@ tptp.neg_nu8804712462038260780nteger (@ tptp.uminus1351360451143612070nteger _let_1)) (@ tptp.uminus1351360451143612070nteger (@ tptp.neg_nu8804712462038260780nteger _let_1))))) (forall ((K2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat K2))) (= (@ tptp.neg_numeral_dbl_rat (@ tptp.uminus_uminus_rat _let_1)) (@ tptp.uminus_uminus_rat (@ tptp.neg_numeral_dbl_rat _let_1))))) (= (@ tptp.neg_nu5851722552734809277nc_int _let_153) _let_153) (= (@ tptp.neg_nu8295874005876285629c_real _let_152) _let_152) (= (@ tptp.neg_nu8557863876264182079omplex _let_104) _let_104) (= (@ tptp.neg_nu5831290666863070958nteger _let_151) _let_151) (= (@ tptp.neg_nu5219082963157363817nc_rat _let_150) _let_150) (= (@ tptp.nat_set_decode tptp.zero_zero_nat) tptp.bot_bot_set_nat) (forall ((A4 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A4) (= (@ tptp.nat_set_decode (@ tptp.nat_set_encode A4)) A4))) (= (@ _let_225 _let_153) tptp.zero_zero_int) (= (@ _let_224 _let_152) tptp.zero_zero_real) (= (@ _let_223 _let_104) tptp.zero_zero_complex) (= (@ _let_222 _let_151) tptp.zero_z3403309356797280102nteger) (= (@ _let_221 _let_150) tptp.zero_zero_rat) (= (@ _let_220 tptp.one_one_int) tptp.zero_zero_int) (= (@ _let_219 tptp.one_one_real) tptp.zero_zero_real) (= (@ _let_218 tptp.one_one_complex) tptp.zero_zero_complex) (= (@ _let_217 tptp.one_one_Code_integer) tptp.zero_z3403309356797280102nteger) (= (@ _let_216 tptp.one_one_rat) tptp.zero_zero_rat) (= (@ _let_210 _let_153) tptp.zero_zero_int) (= (@ _let_209 _let_152) tptp.zero_zero_real) (= (@ _let_208 _let_104) tptp.zero_zero_complex) (= (@ _let_207 _let_151) tptp.zero_z3403309356797280102nteger) (= (@ _let_206 _let_150) tptp.zero_zero_rat) (forall ((N tptp.num)) (= (= (@ tptp.uminus_uminus_int tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) (= N tptp.one))) (forall ((N tptp.num)) (= (= (@ tptp.uminus_uminus_real tptp.one_one_real) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))) (= N tptp.one))) (forall ((N tptp.num)) (= (= (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N))) (= N tptp.one))) (forall ((N tptp.num)) (= (= (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))) (= N tptp.one))) (forall ((N tptp.num)) (= (= (@ tptp.uminus_uminus_rat tptp.one_one_rat) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))) (= N tptp.one))) (forall ((N tptp.num)) (= (= (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N)) (@ tptp.uminus_uminus_int tptp.one_one_int)) (= N tptp.one))) (forall ((N tptp.num)) (= (= (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N)) (@ tptp.uminus_uminus_real tptp.one_one_real)) (= N tptp.one))) (forall ((N tptp.num)) (= (= (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N)) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (= N tptp.one))) (forall ((N tptp.num)) (= (= (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N)) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (= N tptp.one))) (forall ((N tptp.num)) (= (= (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N)) (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (= N tptp.one))) (forall ((N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) N)))) (= (@ _let_1 (@ _let_1 A)) A))) (forall ((N tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N)))) (= (@ _let_1 (@ _let_1 A)) A))) (forall ((N tptp.nat) (A tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) N)))) (= (@ _let_1 (@ _let_1 A)) A))) (forall ((N tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) N)))) (= (@ _let_1 (@ _let_1 A)) A))) (forall ((N tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) N)))) (= (@ _let_1 (@ _let_1 A)) A))) (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) N))) (= (@ (@ tptp.times_times_int _let_1) _let_1) tptp.one_one_int))) (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N))) (= (@ (@ tptp.times_times_real _let_1) _let_1) tptp.one_one_real))) (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) N))) (= (@ (@ tptp.times_times_complex _let_1) _let_1) tptp.one_one_complex))) (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) N))) (= (@ (@ tptp.times_3573771949741848930nteger _let_1) _let_1) tptp.one_one_Code_integer))) (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) N))) (= (@ (@ tptp.times_times_rat _let_1) _let_1) tptp.one_one_rat))) (forall ((A tptp.int)) (= (@ (@ tptp.modulo_modulo_int A) (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.zero_zero_int)) (forall ((A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger A) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.zero_z3403309356797280102nteger)) (forall ((U tptp.num) (V2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real U))) (let ((_let_2 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V2)))) (let ((_let_3 (@ (@ tptp.ord_max_real _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_eq_real _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))) (forall ((U tptp.num) (V2 tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger U))) (let ((_let_2 (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger V2)))) (let ((_let_3 (@ (@ tptp.ord_max_Code_integer _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_le3102999989581377725nteger _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))) (forall ((U tptp.num) (V2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat U))) (let ((_let_2 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V2)))) (let ((_let_3 (@ (@ tptp.ord_max_rat _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_eq_rat _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))) (forall ((U tptp.num) (V2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int U))) (let ((_let_2 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V2)))) (let ((_let_3 (@ (@ tptp.ord_max_int _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_eq_int _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))) (forall ((U tptp.num) (V2 tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real U)))) (let ((_let_2 (@ tptp.numeral_numeral_real V2))) (let ((_let_3 (@ (@ tptp.ord_max_real _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_eq_real _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))) (forall ((U tptp.num) (V2 tptp.num)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger U)))) (let ((_let_2 (@ tptp.numera6620942414471956472nteger V2))) (let ((_let_3 (@ (@ tptp.ord_max_Code_integer _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_le3102999989581377725nteger _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))) (forall ((U tptp.num) (V2 tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat U)))) (let ((_let_2 (@ tptp.numeral_numeral_rat V2))) (let ((_let_3 (@ (@ tptp.ord_max_rat _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_eq_rat _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))) (forall ((U tptp.num) (V2 tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int U)))) (let ((_let_2 (@ tptp.numeral_numeral_int V2))) (let ((_let_3 (@ (@ tptp.ord_max_int _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_eq_int _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))) (forall ((U tptp.num) (V2 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 V2)))) (let ((_let_3 (@ (@ tptp.ord_max_real _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_eq_real _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))) (forall ((U tptp.num) (V2 tptp.num)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger U)))) (let ((_let_2 (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger V2)))) (let ((_let_3 (@ (@ tptp.ord_max_Code_integer _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_le3102999989581377725nteger _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))) (forall ((U tptp.num) (V2 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 V2)))) (let ((_let_3 (@ (@ tptp.ord_max_rat _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_eq_rat _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))) (forall ((U tptp.num) (V2 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 V2)))) (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)))))))) (= (@ tptp.semiri3624122377584611663nteger _let_10) tptp.one_one_Code_integer) (= (@ tptp.semiri5044797733671781792omplex _let_10) tptp.one_one_complex) (= (@ tptp.semiri1406184849735516958ct_int _let_10) tptp.one_one_int) (= (@ tptp.semiri1408675320244567234ct_nat _let_10) tptp.one_one_nat) (= (@ tptp.semiri2265585572941072030t_real _let_10) tptp.one_one_real) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (= (@ tptp.semiri773545260158071498ct_rat _let_1) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat _let_1)) (@ tptp.semiri773545260158071498ct_rat N))))) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (= (@ tptp.semiri1406184849735516958ct_int _let_1) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int _let_1)) (@ tptp.semiri1406184849735516958ct_int N))))) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (= (@ tptp.semiri1408675320244567234ct_nat _let_1) (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat _let_1)) (@ tptp.semiri1408675320244567234ct_nat N))))) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (= (@ tptp.semiri2265585572941072030t_real _let_1) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real _let_1)) (@ tptp.semiri2265585572941072030t_real N))))) (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M2))) (@ tptp.numeral_numeral_int N)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.plus_plus_num M2) N))))) (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M2))) (@ tptp.numeral_numeral_real N)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ (@ tptp.plus_plus_num M2) N))))) (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex M2))) (@ tptp.numera6690914467698888265omplex N)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ (@ tptp.plus_plus_num M2) N))))) (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M2))) (@ tptp.numera6620942414471956472nteger N)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ (@ tptp.plus_plus_num M2) N))))) (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M2))) (@ tptp.numeral_numeral_rat N)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ (@ tptp.plus_plus_num M2) N))))) (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.minus_minus_int (@ tptp.numeral_numeral_int M2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) (@ tptp.numeral_numeral_int (@ (@ tptp.plus_plus_num M2) N)))) (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.minus_minus_real (@ tptp.numeral_numeral_real M2)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))) (@ tptp.numeral_numeral_real (@ (@ tptp.plus_plus_num M2) N)))) (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.minus_minus_complex (@ tptp.numera6690914467698888265omplex M2)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N))) (@ tptp.numera6690914467698888265omplex (@ (@ tptp.plus_plus_num M2) N)))) (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.numera6620942414471956472nteger M2)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))) (@ tptp.numera6620942414471956472nteger (@ (@ tptp.plus_plus_num M2) N)))) (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.minus_minus_rat (@ tptp.numeral_numeral_rat M2)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))) (@ tptp.numeral_numeral_rat (@ (@ tptp.plus_plus_num M2) N)))) (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int M2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.times_times_num M2) N))))) (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real M2)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ (@ tptp.times_times_num M2) N))))) (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex M2)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N))) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ (@ tptp.times_times_num M2) N))))) (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger M2)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ (@ tptp.times_times_num M2) N))))) (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat M2)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ (@ tptp.times_times_num M2) N))))) (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M2))) (@ tptp.numeral_numeral_int N)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.times_times_num M2) N))))) (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M2))) (@ tptp.numeral_numeral_real N)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ (@ tptp.times_times_num M2) N))))) (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex M2))) (@ tptp.numera6690914467698888265omplex N)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ (@ tptp.times_times_num M2) N))))) (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M2))) (@ tptp.numera6620942414471956472nteger N)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ (@ tptp.times_times_num M2) N))))) (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M2))) (@ tptp.numeral_numeral_rat N)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ (@ tptp.times_times_num M2) N))))) (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M2))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) (@ tptp.numeral_numeral_int (@ (@ tptp.times_times_num M2) N)))) (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M2))) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))) (@ tptp.numeral_numeral_real (@ (@ tptp.times_times_num M2) N)))) (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex M2))) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N))) (@ tptp.numera6690914467698888265omplex (@ (@ tptp.times_times_num M2) N)))) (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M2))) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))) (@ tptp.numera6620942414471956472nteger (@ (@ tptp.times_times_num M2) N)))) (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M2))) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))) (@ tptp.numeral_numeral_rat (@ (@ tptp.times_times_num M2) N)))) (forall ((V2 tptp.num) (W2 tptp.num) (Y tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V2))) (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int W2))) Y)) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ (@ tptp.times_times_num V2) W2))) Y))) (forall ((V2 tptp.num) (W2 tptp.num) (Y tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V2))) (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W2))) Y)) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ (@ tptp.times_times_num V2) W2))) Y))) (forall ((V2 tptp.num) (W2 tptp.num) (Y tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex V2))) (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W2))) Y)) (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ (@ tptp.times_times_num V2) W2))) Y))) (forall ((V2 tptp.num) (W2 tptp.num) (Y tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger V2))) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger W2))) Y)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ (@ tptp.times_times_num V2) W2))) Y))) (forall ((V2 tptp.num) (W2 tptp.num) (Y tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V2))) (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W2))) Y)) (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat (@ (@ tptp.times_times_num V2) W2))) Y))) (forall ((V2 tptp.num) (W2 tptp.num) (Y tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int V2)) (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int W2))) Y)) (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.times_times_num V2) W2)))) Y))) (forall ((V2 tptp.num) (W2 tptp.num) (Y tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real V2)) (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W2))) Y)) (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ (@ tptp.times_times_num V2) W2)))) Y))) (forall ((V2 tptp.num) (W2 tptp.num) (Y tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex V2)) (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W2))) Y)) (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ (@ tptp.times_times_num V2) W2)))) Y))) (forall ((V2 tptp.num) (W2 tptp.num) (Y tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger V2)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger W2))) Y)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ (@ tptp.times_times_num V2) W2)))) Y))) (forall ((V2 tptp.num) (W2 tptp.num) (Y tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat V2)) (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W2))) Y)) (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ (@ tptp.times_times_num V2) W2)))) Y))) (forall ((V2 tptp.num) (W2 tptp.num) (Y tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V2))) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int W2)) Y)) (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.times_times_num V2) W2)))) Y))) (forall ((V2 tptp.num) (W2 tptp.num) (Y tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V2))) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real W2)) Y)) (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ (@ tptp.times_times_num V2) W2)))) Y))) (forall ((V2 tptp.num) (W2 tptp.num) (Y tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex V2))) (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex W2)) Y)) (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ (@ tptp.times_times_num V2) W2)))) Y))) (forall ((V2 tptp.num) (W2 tptp.num) (Y tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger V2))) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger W2)) Y)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ (@ tptp.times_times_num V2) W2)))) Y))) (forall ((V2 tptp.num) (W2 tptp.num) (Y tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V2))) (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat W2)) Y)) (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ (@ tptp.times_times_num V2) W2)))) Y))) (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M2))) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))) (@ (@ tptp.ord_less_eq_num N) M2))) (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M2))) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))) (@ (@ tptp.ord_less_eq_num N) M2))) (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M2))) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))) (@ (@ tptp.ord_less_eq_num N) M2))) (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M2))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) (@ (@ tptp.ord_less_eq_num N) M2))) (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M2))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) (@ (@ tptp.ord_less_num N) M2))) (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M2))) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))) (@ (@ tptp.ord_less_num N) M2))) (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M2))) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))) (@ (@ tptp.ord_less_num N) M2))) (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M2))) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))) (@ (@ tptp.ord_less_num N) M2))) (= (@ tptp.neg_nu3811975205180677377ec_int tptp.zero_zero_int) _let_153) (= (@ tptp.neg_nu6075765906172075777c_real tptp.zero_zero_real) _let_152) (= (@ tptp.neg_nu6511756317524482435omplex tptp.zero_zero_complex) _let_104) (= (@ tptp.neg_nu7757733837767384882nteger tptp.zero_z3403309356797280102nteger) _let_151) (= (@ tptp.neg_nu3179335615603231917ec_rat tptp.zero_zero_rat) _let_150) (forall ((M2 tptp.num)) (= (not (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M2)))) (not (= M2 tptp.one)))) (forall ((M2 tptp.num)) (= (not (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M2)))) (not (= M2 tptp.one)))) (forall ((M2 tptp.num)) (= (not (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M2)))) (not (= M2 tptp.one)))) (forall ((M2 tptp.num)) (= (not (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M2)))) (not (= M2 tptp.one)))) (forall ((B tptp.real) (W2 tptp.num) (A tptp.real)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W2)))) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real B) _let_1)) A) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) _let_1)) B)))) (forall ((B tptp.rat) (W2 tptp.num) (A tptp.rat)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W2)))) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat B) _let_1)) A) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) _let_1)) B)))) (forall ((A tptp.real) (B tptp.real) (W2 tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W2)))) (= (@ (@ tptp.ord_less_eq_real A) (@ (@ tptp.divide_divide_real B) _let_1)) (@ (@ tptp.ord_less_eq_real B) (@ (@ tptp.times_times_real A) _let_1))))) (forall ((A tptp.rat) (B tptp.rat) (W2 tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W2)))) (= (@ (@ tptp.ord_less_eq_rat A) (@ (@ tptp.divide_divide_rat B) _let_1)) (@ (@ tptp.ord_less_eq_rat B) (@ (@ tptp.times_times_rat A) _let_1))))) (forall ((B tptp.real) (W2 tptp.num) (A tptp.real)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W2)))) (let ((_let_2 (= _let_1 tptp.zero_zero_real))) (= (= (@ (@ tptp.divide_divide_real B) _let_1) A) (and (=> (not _let_2) (= B (@ (@ tptp.times_times_real A) _let_1))) (=> _let_2 (= A tptp.zero_zero_real))))))) (forall ((B tptp.complex) (W2 tptp.num) (A tptp.complex)) (let ((_let_1 (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W2)))) (let ((_let_2 (= _let_1 tptp.zero_zero_complex))) (= (= (@ (@ tptp.divide1717551699836669952omplex B) _let_1) A) (and (=> (not _let_2) (= B (@ (@ tptp.times_times_complex A) _let_1))) (=> _let_2 (= A tptp.zero_zero_complex))))))) (forall ((B tptp.rat) (W2 tptp.num) (A tptp.rat)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W2)))) (let ((_let_2 (= _let_1 tptp.zero_zero_rat))) (= (= (@ (@ tptp.divide_divide_rat B) _let_1) A) (and (=> (not _let_2) (= B (@ (@ tptp.times_times_rat A) _let_1))) (=> _let_2 (= A tptp.zero_zero_rat))))))) (forall ((A tptp.real) (B tptp.real) (W2 tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W2)))) (let ((_let_2 (= _let_1 tptp.zero_zero_real))) (= (= A (@ (@ tptp.divide_divide_real B) _let_1)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_real A) _let_1) B)) (=> _let_2 (= A tptp.zero_zero_real))))))) (forall ((A tptp.complex) (B tptp.complex) (W2 tptp.num)) (let ((_let_1 (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W2)))) (let ((_let_2 (= _let_1 tptp.zero_zero_complex))) (= (= A (@ (@ tptp.divide1717551699836669952omplex B) _let_1)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_complex A) _let_1) B)) (=> _let_2 (= A tptp.zero_zero_complex))))))) (forall ((A tptp.rat) (B tptp.rat) (W2 tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W2)))) (let ((_let_2 (= _let_1 tptp.zero_zero_rat))) (= (= A (@ (@ tptp.divide_divide_rat B) _let_1)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_rat A) _let_1) B)) (=> _let_2 (= A tptp.zero_zero_rat))))))) (forall ((M2 tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M2))) (@ tptp.uminus_uminus_int tptp.one_one_int)) (not (= M2 tptp.one)))) (forall ((M2 tptp.num)) (= (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M2))) (@ tptp.uminus_uminus_real tptp.one_one_real)) (not (= M2 tptp.one)))) (forall ((M2 tptp.num)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M2))) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (not (= M2 tptp.one)))) (forall ((M2 tptp.num)) (= (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M2))) (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (not (= M2 tptp.one)))) (forall ((A tptp.real) (B tptp.real) (W2 tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W2)))) (= (@ (@ tptp.ord_less_real A) (@ (@ tptp.divide_divide_real B) _let_1)) (@ (@ tptp.ord_less_real B) (@ (@ tptp.times_times_real A) _let_1))))) (forall ((A tptp.rat) (B tptp.rat) (W2 tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W2)))) (= (@ (@ tptp.ord_less_rat A) (@ (@ tptp.divide_divide_rat B) _let_1)) (@ (@ tptp.ord_less_rat B) (@ (@ tptp.times_times_rat A) _let_1))))) (forall ((B tptp.real) (W2 tptp.num) (A tptp.real)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W2)))) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real B) _let_1)) A) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) _let_1)) B)))) (forall ((B tptp.rat) (W2 tptp.num) (A tptp.rat)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W2)))) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat B) _let_1)) A) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) _let_1)) B)))) (forall ((K2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int K2))) (= (@ tptp.neg_nu3811975205180677377ec_int (@ tptp.uminus_uminus_int _let_1)) (@ tptp.uminus_uminus_int (@ tptp.neg_nu5851722552734809277nc_int _let_1))))) (forall ((K2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real K2))) (= (@ tptp.neg_nu6075765906172075777c_real (@ tptp.uminus_uminus_real _let_1)) (@ tptp.uminus_uminus_real (@ tptp.neg_nu8295874005876285629c_real _let_1))))) (forall ((K2 tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex K2))) (= (@ tptp.neg_nu6511756317524482435omplex (@ tptp.uminus1482373934393186551omplex _let_1)) (@ tptp.uminus1482373934393186551omplex (@ tptp.neg_nu8557863876264182079omplex _let_1))))) (forall ((K2 tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger K2))) (= (@ tptp.neg_nu7757733837767384882nteger (@ tptp.uminus1351360451143612070nteger _let_1)) (@ tptp.uminus1351360451143612070nteger (@ tptp.neg_nu5831290666863070958nteger _let_1))))) (forall ((K2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat K2))) (= (@ tptp.neg_nu3179335615603231917ec_rat (@ tptp.uminus_uminus_rat _let_1)) (@ tptp.uminus_uminus_rat (@ tptp.neg_nu5219082963157363817nc_rat _let_1))))) (forall ((K2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int K2))) (= (@ tptp.neg_nu5851722552734809277nc_int (@ tptp.uminus_uminus_int _let_1)) (@ tptp.uminus_uminus_int (@ tptp.neg_nu3811975205180677377ec_int _let_1))))) (forall ((K2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real K2))) (= (@ tptp.neg_nu8295874005876285629c_real (@ tptp.uminus_uminus_real _let_1)) (@ tptp.uminus_uminus_real (@ tptp.neg_nu6075765906172075777c_real _let_1))))) (forall ((K2 tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex K2))) (= (@ tptp.neg_nu8557863876264182079omplex (@ tptp.uminus1482373934393186551omplex _let_1)) (@ tptp.uminus1482373934393186551omplex (@ tptp.neg_nu6511756317524482435omplex _let_1))))) (forall ((K2 tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger K2))) (= (@ tptp.neg_nu5831290666863070958nteger (@ tptp.uminus1351360451143612070nteger _let_1)) (@ tptp.uminus1351360451143612070nteger (@ tptp.neg_nu7757733837767384882nteger _let_1))))) (forall ((K2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat K2))) (= (@ tptp.neg_nu5219082963157363817nc_rat (@ tptp.uminus_uminus_rat _let_1)) (@ tptp.uminus_uminus_rat (@ tptp.neg_nu3179335615603231917ec_rat _let_1))))) (forall ((N tptp.nat) (K2 tptp.num)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.suc N)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 K2)))) (@ (@ tptp.times_times_int (@ (@ tptp.bit_ri631733984087533419it_int N) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K2)))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (forall ((N tptp.nat) (K2 tptp.num)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.suc N)) (@ tptp.numeral_numeral_int (@ tptp.bit0 K2))) (@ (@ tptp.times_times_int (@ (@ tptp.bit_ri631733984087533419it_int N) (@ tptp.numeral_numeral_int K2))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_220 _let_153) _let_205) (= (@ _let_219 _let_152) _let_204) (= (@ _let_218 _let_104) _let_203) (= (@ _let_217 _let_151) _let_202) (= (@ _let_216 _let_150) _let_200) (= (@ _let_215 _let_153) _let_115) (= (@ _let_214 _let_152) _let_109) (= (@ _let_213 _let_104) _let_103) (= (@ _let_212 _let_151) _let_201) (= (@ _let_211 _let_150) _let_199) (= (@ _let_210 tptp.one_one_int) _let_205) (= (@ _let_209 tptp.one_one_real) _let_204) (= (@ _let_208 tptp.one_one_complex) _let_203) (= (@ _let_207 tptp.one_one_Code_integer) _let_202) (= (@ _let_206 tptp.one_one_rat) _let_200) (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int A)) _let_1) (@ (@ tptp.power_power_int A) _let_1)))) (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (= (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real A)) _let_1) (@ (@ tptp.power_power_real A) _let_1)))) (forall ((A tptp.complex) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (= (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex A)) _let_1) (@ (@ tptp.power_power_complex A) _let_1)))) (forall ((A tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger A)) _let_1) (@ (@ tptp.power_8256067586552552935nteger A) _let_1)))) (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (= (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat A)) _let_1) (@ (@ tptp.power_power_rat A) _let_1)))) (forall ((M2 tptp.num)) (= (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M2))) tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.plus_plus_num M2) tptp.one))))) (forall ((M2 tptp.num)) (= (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M2))) tptp.one_one_real) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ (@ tptp.plus_plus_num M2) tptp.one))))) (forall ((M2 tptp.num)) (= (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex M2))) tptp.one_one_complex) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ (@ tptp.plus_plus_num M2) tptp.one))))) (forall ((M2 tptp.num)) (= (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M2))) tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ (@ tptp.plus_plus_num M2) tptp.one))))) (forall ((M2 tptp.num)) (= (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M2))) tptp.one_one_rat) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ (@ tptp.plus_plus_num M2) tptp.one))))) (forall ((N tptp.num)) (= (@ (@ tptp.minus_minus_int tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) (@ tptp.numeral_numeral_int (@ (@ tptp.plus_plus_num tptp.one) N)))) (forall ((N tptp.num)) (= (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))) (@ tptp.numeral_numeral_real (@ (@ tptp.plus_plus_num tptp.one) N)))) (forall ((N tptp.num)) (= (@ (@ tptp.minus_minus_complex tptp.one_one_complex) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N))) (@ tptp.numera6690914467698888265omplex (@ (@ tptp.plus_plus_num tptp.one) N)))) (forall ((N tptp.num)) (= (@ (@ tptp.minus_8373710615458151222nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))) (@ tptp.numera6620942414471956472nteger (@ (@ tptp.plus_plus_num tptp.one) N)))) (forall ((N tptp.num)) (= (@ (@ tptp.minus_minus_rat tptp.one_one_rat) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))) (@ tptp.numeral_numeral_rat (@ (@ tptp.plus_plus_num tptp.one) N)))) (forall ((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))))))) (= (@ tptp.neg_numeral_dbl_int _let_153) _let_205) (= (@ tptp.neg_numeral_dbl_real _let_152) _let_204) (= (@ tptp.neg_nu7009210354673126013omplex _let_104) _let_203) (= (@ tptp.neg_nu8804712462038260780nteger _let_151) _let_202) (= (@ tptp.neg_numeral_dbl_rat _let_150) _let_200) (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) tptp.one_one_int)) (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) tptp.one_one_real)) (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) tptp.one_one_complex)) (forall ((N tptp.nat)) (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) tptp.one_one_Code_integer)) (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) tptp.one_one_rat)) (forall ((A tptp.code_integer)) (= (@ (@ tptp.bit_ri6519982836138164636nteger tptp.zero_zero_nat) A) (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.modulo364778990260209775nteger A) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))))) (forall ((A tptp.int)) (= (@ (@ tptp.bit_ri631733984087533419it_int tptp.zero_zero_nat) A) (@ tptp.uminus_uminus_int (@ (@ tptp.modulo_modulo_int A) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))))) (forall ((A tptp.int) (B tptp.int)) (= (= A (@ tptp.uminus_uminus_int B)) (= B (@ tptp.uminus_uminus_int A)))) (forall ((A tptp.real) (B tptp.real)) (= (= A (@ tptp.uminus_uminus_real B)) (= B (@ tptp.uminus_uminus_real A)))) (forall ((A tptp.complex) (B tptp.complex)) (= (= A (@ tptp.uminus1482373934393186551omplex B)) (= B (@ tptp.uminus1482373934393186551omplex A)))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= A (@ tptp.uminus1351360451143612070nteger B)) (= B (@ tptp.uminus1351360451143612070nteger A)))) (forall ((A tptp.rat) (B tptp.rat)) (= (= A (@ tptp.uminus_uminus_rat B)) (= B (@ tptp.uminus_uminus_rat A)))) (forall ((A tptp.int) (B tptp.int)) (= (= (@ tptp.uminus_uminus_int A) B) (= (@ tptp.uminus_uminus_int B) A))) (forall ((A tptp.real) (B tptp.real)) (= (= (@ tptp.uminus_uminus_real A) B) (= (@ tptp.uminus_uminus_real B) A))) (forall ((A tptp.complex) (B tptp.complex)) (= (= (@ tptp.uminus1482373934393186551omplex A) B) (= (@ tptp.uminus1482373934393186551omplex B) A))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= (@ tptp.uminus1351360451143612070nteger A) B) (= (@ tptp.uminus1351360451143612070nteger B) A))) (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ tptp.uminus_uminus_rat A) B) (= (@ tptp.uminus_uminus_rat B) A))) (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1408675320244567234ct_nat M2)) (@ tptp.semiri1408675320244567234ct_nat N)))) (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat N) (@ tptp.semiri1408675320244567234ct_nat N))) (forall ((N tptp.nat)) (not (= (@ tptp.semiri5044797733671781792omplex N) tptp.zero_zero_complex))) (forall ((N tptp.nat)) (not (= (@ tptp.semiri773545260158071498ct_rat N) tptp.zero_zero_rat))) (forall ((N tptp.nat)) (not (= (@ tptp.semiri1406184849735516958ct_int N) tptp.zero_zero_int))) (forall ((N tptp.nat)) (not (= (@ tptp.semiri1408675320244567234ct_nat N) tptp.zero_zero_nat))) (forall ((N tptp.nat)) (not (= (@ tptp.semiri2265585572941072030t_real N) tptp.zero_zero_real))) (forall ((Y tptp.set_nat) (X tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat (@ tptp.uminus5710092332889474511et_nat Y)) X) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.uminus5710092332889474511et_nat X)) Y))) (forall ((Y tptp.set_nat) (X tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat Y) (@ tptp.uminus5710092332889474511et_nat X)) (@ (@ tptp.ord_less_eq_set_nat X) (@ tptp.uminus5710092332889474511et_nat Y)))) (forall ((X tptp.set_nat) (Y tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat X) Y) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.uminus5710092332889474511et_nat Y)) (@ tptp.uminus5710092332889474511et_nat X)))) (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real B)) (@ tptp.uminus_uminus_real A)))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger A) B) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger A)))) (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat B)) (@ tptp.uminus_uminus_rat A)))) (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int B)) (@ tptp.uminus_uminus_int A)))) (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real A)) B) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real B)) A))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger A)) B) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger B)) A))) (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat A)) B) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat B)) A))) (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int A)) B) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int B)) A))) (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_eq_real A) (@ tptp.uminus_uminus_real B)) (@ (@ tptp.ord_less_eq_real B) (@ tptp.uminus_uminus_real A)))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger A) (@ tptp.uminus1351360451143612070nteger B)) (@ (@ tptp.ord_le3102999989581377725nteger B) (@ tptp.uminus1351360451143612070nteger A)))) (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat A) (@ tptp.uminus_uminus_rat B)) (@ (@ tptp.ord_less_eq_rat B) (@ tptp.uminus_uminus_rat A)))) (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_int A) (@ tptp.uminus_uminus_int B)) (@ (@ tptp.ord_less_eq_int B) (@ tptp.uminus_uminus_int A)))) (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_int A) (@ tptp.uminus_uminus_int B)) (@ (@ tptp.ord_less_int B) (@ tptp.uminus_uminus_int A)))) (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_real A) (@ tptp.uminus_uminus_real B)) (@ (@ tptp.ord_less_real B) (@ tptp.uminus_uminus_real A)))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger A) (@ tptp.uminus1351360451143612070nteger B)) (@ (@ tptp.ord_le6747313008572928689nteger B) (@ tptp.uminus1351360451143612070nteger A)))) (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat A) (@ tptp.uminus_uminus_rat B)) (@ (@ tptp.ord_less_rat B) (@ tptp.uminus_uminus_rat A)))) (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int A)) B) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int B)) A))) (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real A)) B) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real B)) A))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger A)) B) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger B)) A))) (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat A)) B) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat B)) A))) (forall ((M2 tptp.num) (N tptp.num)) (not (= (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M2)) (@ tptp.numeral_numeral_int N)))) (forall ((M2 tptp.num) (N tptp.num)) (not (= (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M2)) (@ tptp.numeral_numeral_real N)))) (forall ((M2 tptp.num) (N tptp.num)) (not (= (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex M2)) (@ tptp.numera6690914467698888265omplex N)))) (forall ((M2 tptp.num) (N tptp.num)) (not (= (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M2)) (@ tptp.numera6620942414471956472nteger N)))) (forall ((M2 tptp.num) (N tptp.num)) (not (= (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M2)) (@ tptp.numeral_numeral_rat N)))) (forall ((M2 tptp.num) (N tptp.num)) (not (= (@ tptp.numeral_numeral_int M2) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))))) (forall ((M2 tptp.num) (N tptp.num)) (not (= (@ tptp.numeral_numeral_real M2) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))))) (forall ((M2 tptp.num) (N tptp.num)) (not (= (@ tptp.numera6690914467698888265omplex M2) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N))))) (forall ((M2 tptp.num) (N tptp.num)) (not (= (@ tptp.numera6620942414471956472nteger M2) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))))) (forall ((M2 tptp.num) (N tptp.num)) (not (= (@ tptp.numeral_numeral_rat M2) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))))) (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int A)) B) (@ (@ tptp.times_times_int A) (@ tptp.uminus_uminus_int B)))) (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real A)) B) (@ (@ tptp.times_times_real A) (@ tptp.uminus_uminus_real B)))) (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex A)) B) (@ (@ tptp.times_times_complex A) (@ tptp.uminus1482373934393186551omplex B)))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger A)) B) (@ (@ tptp.times_3573771949741848930nteger A) (@ tptp.uminus1351360451143612070nteger B)))) (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat A)) B) (@ (@ tptp.times_times_rat A) (@ tptp.uminus_uminus_rat B)))) (forall ((A tptp.int) (B tptp.int)) (= (= (@ (@ tptp.times_times_int A) A) (@ (@ tptp.times_times_int B) B)) (or (= A B) (= A (@ tptp.uminus_uminus_int B))))) (forall ((A tptp.real) (B tptp.real)) (= (= (@ (@ tptp.times_times_real A) A) (@ (@ tptp.times_times_real B) B)) (or (= A B) (= A (@ tptp.uminus_uminus_real B))))) (forall ((A tptp.complex) (B tptp.complex)) (= (= (@ (@ tptp.times_times_complex A) A) (@ (@ tptp.times_times_complex B) B)) (or (= A B) (= A (@ 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tptp.uminus1482373934393186551omplex A)))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B)) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger A)))) (forall ((A tptp.rat) (B tptp.rat)) (= (@ tptp.uminus_uminus_rat (@ (@ tptp.plus_plus_rat A) B)) (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat B)) (@ tptp.uminus_uminus_rat A)))) (forall ((A4 tptp.int) (K2 tptp.int) (A tptp.int)) (=> (= A4 (@ (@ tptp.plus_plus_int K2) A)) (= (@ tptp.uminus_uminus_int A4) (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int K2)) (@ tptp.uminus_uminus_int A))))) (forall ((A4 tptp.real) (K2 tptp.real) (A tptp.real)) (=> (= A4 (@ (@ tptp.plus_plus_real K2) A)) (= (@ tptp.uminus_uminus_real A4) (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real K2)) (@ tptp.uminus_uminus_real A))))) (forall ((A4 tptp.complex) (K2 tptp.complex) (A tptp.complex)) (=> (= A4 (@ (@ tptp.plus_plus_complex K2) A)) (= (@ tptp.uminus1482373934393186551omplex A4) (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex K2)) (@ tptp.uminus1482373934393186551omplex A))))) (forall ((A4 tptp.code_integer) (K2 tptp.code_integer) (A tptp.code_integer)) (=> (= A4 (@ (@ tptp.plus_p5714425477246183910nteger K2) A)) (= (@ tptp.uminus1351360451143612070nteger A4) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger K2)) (@ tptp.uminus1351360451143612070nteger A))))) (forall ((A4 tptp.rat) (K2 tptp.rat) (A tptp.rat)) (=> (= A4 (@ (@ tptp.plus_plus_rat K2) A)) (= (@ tptp.uminus_uminus_rat A4) (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat K2)) (@ tptp.uminus_uminus_rat A))))) (forall ((A tptp.int) (B tptp.int)) (= (@ tptp.uminus_uminus_int (@ (@ tptp.plus_plus_int A) B)) (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int B)) (@ tptp.uminus_uminus_int A)))) (forall ((A tptp.real) (B tptp.real)) (= (@ tptp.uminus_uminus_real (@ (@ tptp.plus_plus_real A) B)) (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real B)) (@ tptp.uminus_uminus_real A)))) (forall ((A tptp.complex) (B tptp.complex)) (= (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.plus_plus_complex A) B)) (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex B)) (@ tptp.uminus1482373934393186551omplex A)))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B)) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger A)))) (forall ((A tptp.rat) (B tptp.rat)) (= (@ tptp.uminus_uminus_rat (@ (@ tptp.plus_plus_rat A) B)) (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat B)) (@ tptp.uminus_uminus_rat A)))) (not (= tptp.one_one_int _let_153)) (not (= tptp.one_one_real _let_152)) (not (= tptp.one_one_complex _let_104)) (not (= tptp.one_one_Code_integer _let_151)) (not (= tptp.one_one_rat _let_150)) (forall ((B tptp.int) (A tptp.int)) (= (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int B)) A) (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int A)) B))) (forall ((B tptp.real) (A tptp.real)) (= (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real B)) A) (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real A)) B))) (forall ((B tptp.complex) (A tptp.complex)) (= (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex B)) A) (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex A)) B))) (forall ((B tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger B)) A) (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger A)) B))) (forall ((B tptp.rat) (A tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat B)) A) (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat A)) B))) (forall ((N tptp.nat) (K2 tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.bit_ri631733984087533419it_int N))) (= (@ _let_1 (@ (@ tptp.times_times_int (@ _let_1 K2)) (@ _let_1 L))) (@ _let_1 (@ (@ tptp.times_times_int K2) L))))) (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M2) (=> (@ (@ tptp.ord_less_nat M2) N) (@ (@ tptp.ord_less_nat (@ tptp.semiri1408675320244567234ct_nat M2)) (@ tptp.semiri1408675320244567234ct_nat N))))) (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.semiri773545260158071498ct_rat N))) (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.semiri1406184849735516958ct_int N))) (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ tptp.semiri1408675320244567234ct_nat N))) (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.semiri2265585572941072030t_real N))) (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_rat (@ 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tptp.ord_le6747313008572928689nteger (@ tptp.numera6620942414471956472nteger M2)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))))) (forall ((M2 tptp.num) (N tptp.num)) (not (@ (@ tptp.ord_less_rat (@ tptp.numeral_numeral_rat M2)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))))) (forall ((M2 tptp.num) (N tptp.num)) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M2))) (@ tptp.numeral_numeral_int N))) (forall ((M2 tptp.num) (N tptp.num)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M2))) (@ tptp.numeral_numeral_real N))) (forall ((M2 tptp.num) (N tptp.num)) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M2))) (@ tptp.numera6620942414471956472nteger N))) (forall ((M2 tptp.num) (N tptp.num)) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M2))) (@ tptp.numeral_numeral_rat N))) (not (@ _let_198 _let_152)) (not (@ _let_197 _let_151)) (not (@ _let_196 _let_150)) (not (@ _let_195 _let_153)) (@ _let_185 tptp.one_one_real) (@ _let_184 tptp.one_one_Code_integer) (@ _let_183 tptp.one_one_rat) (@ _let_182 tptp.one_one_int) (forall ((A tptp.int) (B tptp.int)) (= (= (@ (@ tptp.plus_plus_int A) B) tptp.zero_zero_int) (= B (@ tptp.uminus_uminus_int A)))) (forall ((A tptp.real) (B tptp.real)) (= (= (@ (@ tptp.plus_plus_real A) B) tptp.zero_zero_real) (= B (@ tptp.uminus_uminus_real A)))) (forall ((A tptp.complex) (B tptp.complex)) (= (= (@ (@ tptp.plus_plus_complex A) B) tptp.zero_zero_complex) (= B (@ tptp.uminus1482373934393186551omplex A)))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= (@ (@ tptp.plus_p5714425477246183910nteger A) B) tptp.zero_z3403309356797280102nteger) (= B (@ tptp.uminus1351360451143612070nteger A)))) (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat A) B) tptp.zero_zero_rat) (= B (@ tptp.uminus_uminus_rat A)))) (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int A)) A) tptp.zero_zero_int)) (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A)) A) tptp.zero_zero_real)) (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex A)) A) tptp.zero_zero_complex)) (forall ((A tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger A)) A) tptp.zero_z3403309356797280102nteger)) (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat A)) A) tptp.zero_zero_rat)) (forall ((A tptp.int) (B tptp.int)) (=> (= (@ (@ tptp.plus_plus_int A) B) tptp.zero_zero_int) (= (@ tptp.uminus_uminus_int A) B))) (forall ((A tptp.real) (B tptp.real)) (=> (= (@ (@ tptp.plus_plus_real A) B) tptp.zero_zero_real) (= (@ tptp.uminus_uminus_real A) B))) (forall ((A tptp.complex) (B tptp.complex)) (=> (= (@ (@ tptp.plus_plus_complex A) B) tptp.zero_zero_complex) (= (@ tptp.uminus1482373934393186551omplex A) B))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (= (@ (@ tptp.plus_p5714425477246183910nteger A) B) tptp.zero_z3403309356797280102nteger) (= (@ tptp.uminus1351360451143612070nteger A) B))) (forall ((A tptp.rat) (B tptp.rat)) (=> (= (@ (@ tptp.plus_plus_rat A) B) tptp.zero_zero_rat) (= (@ tptp.uminus_uminus_rat A) B))) (forall ((A tptp.int) (B tptp.int)) (= (= A (@ tptp.uminus_uminus_int B)) (= (@ (@ tptp.plus_plus_int A) B) tptp.zero_zero_int))) (forall ((A tptp.real) (B tptp.real)) (= (= A (@ tptp.uminus_uminus_real B)) (= (@ (@ tptp.plus_plus_real A) B) tptp.zero_zero_real))) (forall ((A tptp.complex) (B tptp.complex)) (= (= A (@ tptp.uminus1482373934393186551omplex B)) (= (@ (@ tptp.plus_plus_complex A) B) tptp.zero_zero_complex))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= A (@ tptp.uminus1351360451143612070nteger B)) (= (@ (@ tptp.plus_p5714425477246183910nteger A) B) tptp.zero_z3403309356797280102nteger))) (forall ((A tptp.rat) (B tptp.rat)) (= (= A (@ tptp.uminus_uminus_rat B)) (= (@ (@ tptp.plus_plus_rat A) B) tptp.zero_zero_rat))) (forall ((A tptp.int) (B tptp.int)) (= (= (@ tptp.uminus_uminus_int A) B) (= (@ (@ tptp.plus_plus_int A) B) tptp.zero_zero_int))) (forall ((A tptp.real) (B tptp.real)) (= (= (@ tptp.uminus_uminus_real A) B) (= (@ (@ tptp.plus_plus_real A) B) tptp.zero_zero_real))) (forall ((A tptp.complex) (B tptp.complex)) (= (= (@ tptp.uminus1482373934393186551omplex A) B) (= (@ (@ tptp.plus_plus_complex A) B) tptp.zero_zero_complex))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= (@ tptp.uminus1351360451143612070nteger A) B) (= (@ (@ tptp.plus_p5714425477246183910nteger A) B) tptp.zero_z3403309356797280102nteger))) (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ tptp.uminus_uminus_rat A) B) (= (@ (@ tptp.plus_plus_rat A) B) tptp.zero_zero_rat))) (not (= tptp.zero_zero_int _let_153)) (not (= tptp.zero_zero_real _let_152)) (not (= tptp.zero_zero_complex _let_104)) (not (= tptp.zero_z3403309356797280102nteger _let_151)) (not (= tptp.zero_zero_rat _let_150)) (not (@ _let_194 _let_153)) (not (@ _let_193 _let_152)) (not (@ _let_192 _let_151)) (not (@ _let_191 _let_150)) (@ _let_177 tptp.one_one_int) (@ _let_176 tptp.one_one_real) (@ _let_175 tptp.one_one_Code_integer) (@ _let_174 tptp.one_one_rat) (forall ((W2 tptp.num) (X tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int W2))) (= (@ (@ tptp.times_times_int _let_1) (@ tptp.uminus_uminus_int X)) (@ (@ tptp.times_times_int X) (@ tptp.uminus_uminus_int _let_1))))) (forall ((W2 tptp.num) (X tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real W2))) (= (@ (@ tptp.times_times_real _let_1) (@ tptp.uminus_uminus_real X)) (@ (@ tptp.times_times_real X) (@ tptp.uminus_uminus_real _let_1))))) (forall ((W2 tptp.num) (X tptp.complex)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex W2))) (= (@ (@ tptp.times_times_complex _let_1) (@ tptp.uminus1482373934393186551omplex X)) (@ (@ tptp.times_times_complex X) (@ tptp.uminus1482373934393186551omplex _let_1))))) (forall ((W2 tptp.num) (X tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger W2))) (= (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ tptp.uminus1351360451143612070nteger X)) (@ (@ tptp.times_3573771949741848930nteger X) (@ tptp.uminus1351360451143612070nteger _let_1))))) (forall ((W2 tptp.num) (X tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_rat W2))) (= (@ (@ tptp.times_times_rat _let_1) (@ tptp.uminus_uminus_rat X)) (@ (@ tptp.times_times_rat X) (@ tptp.uminus_uminus_rat _let_1))))) (forall ((B tptp.real) (A tptp.real)) (=> (not (= B tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real A)) (@ tptp.uminus_uminus_real B)) (@ (@ tptp.divide_divide_real A) B)))) (forall ((B tptp.complex) (A tptp.complex)) (=> (not (= B tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ tptp.uminus1482373934393186551omplex A)) (@ tptp.uminus1482373934393186551omplex B)) (@ (@ tptp.divide1717551699836669952omplex A) B)))) (forall ((B tptp.rat) (A tptp.rat)) (=> (not (= B tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat (@ tptp.uminus_uminus_rat A)) (@ tptp.uminus_uminus_rat B)) (@ (@ tptp.divide_divide_rat A) B)))) (forall ((B tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.divide_divide_real A))) (=> (not (= B tptp.zero_zero_real)) (= (@ tptp.uminus_uminus_real (@ _let_1 B)) (@ _let_1 (@ tptp.uminus_uminus_real B)))))) (forall ((B tptp.complex) (A tptp.complex)) (let ((_let_1 (@ tptp.divide1717551699836669952omplex A))) (=> (not (= B tptp.zero_zero_complex)) (= (@ tptp.uminus1482373934393186551omplex (@ _let_1 B)) (@ _let_1 (@ tptp.uminus1482373934393186551omplex B)))))) (forall ((B tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.divide_divide_rat A))) (=> (not (= B tptp.zero_zero_rat)) (= (@ tptp.uminus_uminus_rat (@ _let_1 B)) (@ _let_1 (@ tptp.uminus_uminus_rat B)))))) (forall ((N tptp.num)) (not (= tptp.one_one_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))))) (forall ((N tptp.num)) (not (= tptp.one_one_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))))) (forall ((N tptp.num)) (not (= tptp.one_one_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N))))) (forall ((N tptp.num)) (not (= tptp.one_one_Code_integer (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))))) (forall ((N tptp.num)) (not (= tptp.one_one_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))))) (forall ((N tptp.num)) (not (= (@ tptp.numeral_numeral_int N) (@ tptp.uminus_uminus_int tptp.one_one_int)))) (forall ((N tptp.num)) (not (= (@ tptp.numeral_numeral_real N) (@ tptp.uminus_uminus_real tptp.one_one_real)))) (forall ((N tptp.num)) (not (= (@ tptp.numera6690914467698888265omplex N) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))) (forall ((N tptp.num)) (not (= (@ tptp.numera6620942414471956472nteger N) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))) (forall ((N tptp.num)) (not (= (@ tptp.numeral_numeral_rat N) (@ tptp.uminus_uminus_rat tptp.one_one_rat)))) (forall ((X tptp.int)) (= (= (@ (@ tptp.times_times_int X) X) tptp.one_one_int) (or (= X tptp.one_one_int) (= X (@ tptp.uminus_uminus_int tptp.one_one_int))))) (forall ((X tptp.real)) (= (= (@ (@ tptp.times_times_real X) X) tptp.one_one_real) (or (= X tptp.one_one_real) (= X (@ tptp.uminus_uminus_real tptp.one_one_real))))) (forall ((X tptp.complex)) (= (= (@ (@ tptp.times_times_complex X) X) tptp.one_one_complex) (or (= X tptp.one_one_complex) (= X (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))))) (forall ((X tptp.code_integer)) (= (= (@ (@ tptp.times_3573771949741848930nteger X) X) tptp.one_one_Code_integer) (or (= X tptp.one_one_Code_integer) (= X (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))) (forall ((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))))) (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (@ (@ tptp.ord_less_eq_rat (@ tptp.semiri773545260158071498ct_rat M2)) (@ tptp.semiri773545260158071498ct_rat N)))) (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1406184849735516958ct_int M2)) (@ tptp.semiri1406184849735516958ct_int N)))) (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1408675320244567234ct_nat M2)) (@ tptp.semiri1408675320244567234ct_nat N)))) (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (@ (@ tptp.ord_less_eq_real (@ tptp.semiri2265585572941072030t_real M2)) (@ tptp.semiri2265585572941072030t_real N)))) _let_190 _let_189 _let_188 _let_187 _let_186 (= tptp.minus_minus_int (lambda ((A5 tptp.int) (B4 tptp.int)) (@ (@ tptp.plus_plus_int A5) (@ tptp.uminus_uminus_int B4)))) (= tptp.minus_minus_real (lambda ((A5 tptp.real) (B4 tptp.real)) (@ (@ tptp.plus_plus_real A5) (@ tptp.uminus_uminus_real B4)))) (= tptp.minus_minus_complex (lambda ((A5 tptp.complex) (B4 tptp.complex)) (@ (@ tptp.plus_plus_complex A5) (@ tptp.uminus1482373934393186551omplex B4)))) (= tptp.minus_8373710615458151222nteger (lambda ((A5 tptp.code_integer) (B4 tptp.code_integer)) (@ (@ tptp.plus_p5714425477246183910nteger A5) (@ tptp.uminus1351360451143612070nteger B4)))) (= tptp.minus_minus_rat (lambda ((A5 tptp.rat) (B4 tptp.rat)) (@ (@ tptp.plus_plus_rat A5) (@ tptp.uminus_uminus_rat B4)))) (forall ((B5 tptp.int) (K2 tptp.int) (B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int A))) (=> (= B5 (@ (@ tptp.plus_plus_int K2) B)) (= (@ _let_1 B5) (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int K2)) (@ _let_1 B)))))) (forall ((B5 tptp.real) (K2 tptp.real) (B tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.minus_minus_real A))) (=> (= B5 (@ (@ tptp.plus_plus_real K2) B)) (= (@ _let_1 B5) (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real K2)) (@ _let_1 B)))))) (forall ((B5 tptp.complex) (K2 tptp.complex) (B tptp.complex) (A tptp.complex)) (let ((_let_1 (@ tptp.minus_minus_complex A))) (=> (= B5 (@ (@ tptp.plus_plus_complex K2) B)) (= (@ _let_1 B5) (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex K2)) (@ _let_1 B)))))) (forall ((B5 tptp.code_integer) (K2 tptp.code_integer) (B tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.minus_8373710615458151222nteger A))) (=> (= B5 (@ (@ tptp.plus_p5714425477246183910nteger K2) B)) (= (@ _let_1 B5) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger K2)) (@ _let_1 B)))))) (forall ((B5 tptp.rat) (K2 tptp.rat) (B tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.minus_minus_rat A))) (=> (= B5 (@ (@ tptp.plus_plus_rat K2) B)) (= (@ _let_1 B5) (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat K2)) (@ _let_1 B)))))) (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B) A) (= (@ (@ tptp.divide_divide_int (@ tptp.uminus_uminus_int A)) B) (@ tptp.uminus_uminus_int (@ (@ tptp.divide_divide_int A) B))))) (forall ((B tptp.real) (A tptp.real)) (=> (@ (@ tptp.dvd_dvd_real B) A) (= (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real A)) B) (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real A) B))))) (forall ((B tptp.complex) (A tptp.complex)) (=> (@ (@ tptp.dvd_dvd_complex B) A) (= (@ (@ tptp.divide1717551699836669952omplex (@ tptp.uminus1482373934393186551omplex A)) B) (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex A) B))))) (forall ((B tptp.code_integer) (A tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer B) A) (= (@ (@ tptp.divide6298287555418463151nteger (@ tptp.uminus1351360451143612070nteger A)) B) (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.divide6298287555418463151nteger A) B))))) (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.dvd_dvd_rat B) A) (= (@ (@ tptp.divide_divide_rat (@ tptp.uminus_uminus_rat A)) B) (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat A) B))))) (forall ((B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A))) (=> (@ (@ tptp.dvd_dvd_int B) A) (= (@ _let_1 (@ tptp.uminus_uminus_int B)) (@ tptp.uminus_uminus_int (@ _let_1 B)))))) (forall ((B tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.divide_divide_real A))) (=> (@ (@ tptp.dvd_dvd_real B) A) (= (@ _let_1 (@ tptp.uminus_uminus_real B)) (@ tptp.uminus_uminus_real (@ _let_1 B)))))) (forall ((B tptp.complex) (A tptp.complex)) (let ((_let_1 (@ tptp.divide1717551699836669952omplex A))) (=> (@ (@ tptp.dvd_dvd_complex B) A) (= (@ _let_1 (@ tptp.uminus1482373934393186551omplex B)) (@ tptp.uminus1482373934393186551omplex (@ _let_1 B)))))) (forall ((B tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.divide6298287555418463151nteger A))) (=> (@ (@ tptp.dvd_dvd_Code_integer B) A) (= (@ _let_1 (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger (@ _let_1 B)))))) (forall ((B tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.divide_divide_rat A))) (=> (@ (@ tptp.dvd_dvd_rat B) A) (= (@ _let_1 (@ tptp.uminus_uminus_rat B)) (@ tptp.uminus_uminus_rat (@ _let_1 B)))))) (forall ((N tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M2) (@ (@ tptp.dvd_dvd_int (@ tptp.semiri1406184849735516958ct_int N)) (@ tptp.semiri1406184849735516958ct_int M2)))) (forall ((N tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M2) (@ (@ tptp.dvd_dvd_nat (@ tptp.semiri1408675320244567234ct_nat N)) (@ tptp.semiri1408675320244567234ct_nat M2)))) (forall ((N tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M2) (@ (@ tptp.dvd_dvd_real (@ tptp.semiri2265585572941072030t_real N)) (@ tptp.semiri2265585572941072030t_real M2)))) (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))) (forall ((P2 (-> tptp.int Bool)) (Z3 tptp.int)) (=> (forall ((N3 tptp.nat)) (@ P2 (@ tptp.semiri1314217659103216013at_int N3))) (=> (forall ((N3 tptp.nat)) (@ P2 (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N3))))) (@ P2 Z3)))) (forall ((Z3 tptp.int)) (=> (forall ((N3 tptp.nat)) (not (= Z3 (@ tptp.semiri1314217659103216013at_int N3)))) (not (forall ((N3 tptp.nat)) (not (= Z3 (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N3))))))))) (forall ((M2 tptp.int) (N tptp.int)) (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (= (@ (@ tptp.times_times_int M2) N) tptp.one_one_int) (or (and (= M2 tptp.one_one_int) (= N tptp.one_one_int)) (and (= M2 _let_1) (= N _let_1)))))) (forall ((M2 tptp.int) (N tptp.int)) (=> (= (@ (@ tptp.times_times_int M2) N) tptp.one_one_int) (or (= M2 tptp.one_one_int) (= M2 (@ tptp.uminus_uminus_int tptp.one_one_int))))) (forall ((K2 tptp.int) (L tptp.int)) (=> (not (= (@ (@ tptp.modulo_modulo_int (@ tptp.uminus_uminus_int K2)) L) tptp.zero_zero_int)) (not (= (@ (@ tptp.modulo_modulo_int K2) L) tptp.zero_zero_int)))) (forall ((K2 tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.modulo_modulo_int K2))) (=> (not (= (@ _let_1 (@ tptp.uminus_uminus_int L)) tptp.zero_zero_int)) (not (= (@ _let_1 L) tptp.zero_zero_int))))) (forall ((N tptp.nat)) (= (@ (@ tptp.comm_s2602460028002588243omplex (@ tptp.uminus1482373934393186551omplex (@ tptp.semiri8010041392384452111omplex N))) N) (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) N)) (@ tptp.semiri5044797733671781792omplex N)))) (forall ((N tptp.nat)) (= (@ (@ tptp.comm_s8582702949713902594nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.semiri4939895301339042750nteger N))) N) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) N)) (@ tptp.semiri3624122377584611663nteger N)))) (forall ((N tptp.nat)) (= (@ (@ tptp.comm_s4028243227959126397er_rat (@ tptp.uminus_uminus_rat (@ tptp.semiri681578069525770553at_rat N))) N) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) N)) (@ tptp.semiri773545260158071498ct_rat N)))) (forall ((N tptp.nat)) (= (@ (@ tptp.comm_s4660882817536571857er_int (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N))) N) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) N)) (@ tptp.semiri1406184849735516958ct_int N)))) (forall ((N tptp.nat)) (= (@ (@ tptp.comm_s7457072308508201937r_real (@ tptp.uminus_uminus_real (@ tptp.semiri5074537144036343181t_real N))) N) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N)) (@ tptp.semiri2265585572941072030t_real N)))) (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.semiri1408675320244567234ct_nat N))) (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) M2) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (@ (@ tptp.dvd_dvd_nat M2) (@ tptp.semiri1408675320244567234ct_nat N))))) (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))))) (forall ((N tptp.num)) (not (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))))) (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))))) (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))))) (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))) tptp.zero_zero_real)) (forall ((N tptp.num)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))) tptp.zero_z3403309356797280102nteger)) (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))) tptp.zero_zero_rat)) (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) tptp.zero_zero_int)) (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))))) (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))))) (forall ((N tptp.num)) (not (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))))) (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))))) (forall ((N tptp.num)) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) tptp.zero_zero_int)) (forall ((N tptp.num)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))) tptp.zero_zero_real)) (forall ((N tptp.num)) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))) tptp.zero_z3403309356797280102nteger)) (forall ((N tptp.num)) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))) tptp.zero_zero_rat)) (@ _let_185 tptp.zero_zero_real) (@ _let_184 tptp.zero_z3403309356797280102nteger) (@ _let_183 tptp.zero_zero_rat) (@ _let_182 tptp.zero_zero_int) (not (@ _let_181 _let_152)) (not (@ _let_180 _let_151)) (not (@ _let_179 _let_150)) (not (@ _let_178 _let_153)) (@ _let_177 tptp.zero_zero_int) (@ _let_176 tptp.zero_zero_real) (@ _let_175 tptp.zero_z3403309356797280102nteger) (@ _let_174 tptp.zero_zero_rat) (not (@ _let_173 _let_153)) (not (@ _let_172 _let_152)) (not (@ _let_171 _let_151)) (not (@ _let_170 _let_150)) (forall ((M2 tptp.num)) (not (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M2))))) (forall ((M2 tptp.num)) (not (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M2))))) (forall ((M2 tptp.num)) (not (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M2))))) (forall ((M2 tptp.num)) (not (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M2))))) (forall ((M2 tptp.num)) (not (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real M2)) (@ tptp.uminus_uminus_real tptp.one_one_real)))) (forall ((M2 tptp.num)) (not (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.numera6620942414471956472nteger M2)) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))) (forall ((M2 tptp.num)) (not (@ (@ tptp.ord_less_eq_rat (@ tptp.numeral_numeral_rat M2)) (@ tptp.uminus_uminus_rat tptp.one_one_rat)))) (forall ((M2 tptp.num)) (not (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int M2)) (@ tptp.uminus_uminus_int tptp.one_one_int)))) (forall ((M2 tptp.num)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M2))) (@ tptp.uminus_uminus_real tptp.one_one_real))) (forall ((M2 tptp.num)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M2))) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (forall ((M2 tptp.num)) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M2))) (@ tptp.uminus_uminus_rat tptp.one_one_rat))) (forall ((M2 tptp.num)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M2))) (@ tptp.uminus_uminus_int tptp.one_one_int))) (forall ((M2 tptp.num)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.numeral_numeral_real M2))) (forall ((M2 tptp.num)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.numera6620942414471956472nteger M2))) (forall ((M2 tptp.num)) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.numeral_numeral_rat M2))) (forall ((M2 tptp.num)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.numeral_numeral_int M2))) (forall ((M2 tptp.num)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M2))) tptp.one_one_real)) (forall ((M2 tptp.num)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M2))) tptp.one_one_Code_integer)) (forall ((M2 tptp.num)) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M2))) tptp.one_one_rat)) (forall ((M2 tptp.num)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M2))) tptp.one_one_int)) (= tptp.gbinomial_complex (lambda ((A5 tptp.complex) (K3 tptp.nat)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) K3)) (@ (@ tptp.comm_s2602460028002588243omplex (@ tptp.uminus1482373934393186551omplex A5)) K3))) (@ tptp.semiri5044797733671781792omplex K3)))) (= tptp.gbinomial_rat (lambda ((A5 tptp.rat) (K3 tptp.nat)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) K3)) (@ (@ tptp.comm_s4028243227959126397er_rat (@ tptp.uminus_uminus_rat A5)) K3))) (@ tptp.semiri773545260158071498ct_rat K3)))) (= tptp.gbinomial_real (lambda ((A5 tptp.real) (K3 tptp.nat)) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) K3)) (@ (@ tptp.comm_s7457072308508201937r_real (@ tptp.uminus_uminus_real A5)) K3))) (@ tptp.semiri2265585572941072030t_real K3)))) (forall ((M2 tptp.num)) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M2))) tptp.one_one_int)) (forall ((M2 tptp.num)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M2))) tptp.one_one_real)) (forall ((M2 tptp.num)) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M2))) tptp.one_one_Code_integer)) (forall ((M2 tptp.num)) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M2))) tptp.one_one_rat)) (forall ((M2 tptp.num)) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.numeral_numeral_int M2))) (forall ((M2 tptp.num)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.numeral_numeral_real M2))) (forall ((M2 tptp.num)) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.numera6620942414471956472nteger M2))) (forall ((M2 tptp.num)) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.numeral_numeral_rat M2))) (forall ((M2 tptp.num)) (not (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int M2)) (@ tptp.uminus_uminus_int tptp.one_one_int)))) (forall ((M2 tptp.num)) (not (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real M2)) (@ tptp.uminus_uminus_real tptp.one_one_real)))) (forall ((M2 tptp.num)) (not (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.numera6620942414471956472nteger M2)) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))) (forall ((M2 tptp.num)) (not (@ (@ tptp.ord_less_rat (@ tptp.numeral_numeral_rat M2)) (@ tptp.uminus_uminus_rat tptp.one_one_rat)))) (forall ((M2 tptp.num)) (not (@ (@ tptp.ord_less_int tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M2))))) (forall ((M2 tptp.num)) (not (@ (@ tptp.ord_less_real tptp.one_one_real) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M2))))) (forall ((M2 tptp.num)) (not (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M2))))) (forall ((M2 tptp.num)) (not (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M2))))) (forall ((M2 tptp.num)) (not (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M2))))) (forall ((M2 tptp.num)) (not (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M2))))) (forall ((M2 tptp.num)) (not (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M2))))) (forall ((M2 tptp.num)) (not (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M2))))) (forall ((A tptp.real) (B tptp.real) (C2 tptp.real)) (let ((_let_1 (= C2 tptp.zero_zero_real))) (= (= A (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B) C2))) (and (=> (not _let_1) (= (@ (@ tptp.times_times_real A) C2) (@ tptp.uminus_uminus_real B))) (=> _let_1 (= A tptp.zero_zero_real)))))) (forall ((A tptp.complex) (B tptp.complex) (C2 tptp.complex)) (let ((_let_1 (= C2 tptp.zero_zero_complex))) (= (= A (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex B) C2))) (and (=> (not _let_1) (= (@ (@ tptp.times_times_complex A) C2) (@ tptp.uminus1482373934393186551omplex B))) (=> _let_1 (= A tptp.zero_zero_complex)))))) (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (= C2 tptp.zero_zero_rat))) (= (= A (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C2))) (and (=> (not _let_1) (= (@ (@ tptp.times_times_rat A) C2) (@ tptp.uminus_uminus_rat B))) (=> _let_1 (= A tptp.zero_zero_rat)))))) (forall ((B tptp.real) (C2 tptp.real) (A tptp.real)) (let ((_let_1 (= C2 tptp.zero_zero_real))) (= (= (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B) C2)) A) (and (=> (not _let_1) (= (@ tptp.uminus_uminus_real B) (@ (@ tptp.times_times_real A) C2))) (=> _let_1 (= A tptp.zero_zero_real)))))) (forall ((B tptp.complex) (C2 tptp.complex) (A tptp.complex)) (let ((_let_1 (= C2 tptp.zero_zero_complex))) (= (= (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex B) C2)) A) (and (=> (not _let_1) (= (@ tptp.uminus1482373934393186551omplex B) (@ (@ tptp.times_times_complex A) C2))) (=> _let_1 (= A tptp.zero_zero_complex)))))) (forall ((B tptp.rat) (C2 tptp.rat) (A tptp.rat)) (let ((_let_1 (= C2 tptp.zero_zero_rat))) (= (= (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C2)) A) (and (=> (not _let_1) (= (@ tptp.uminus_uminus_rat B) (@ (@ tptp.times_times_rat A) C2))) (=> _let_1 (= A tptp.zero_zero_rat)))))) (forall ((B tptp.real) (A tptp.real) (C2 tptp.real)) (=> (not (= B tptp.zero_zero_real)) (= (= (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real A) B)) C2) (= (@ tptp.uminus_uminus_real A) (@ (@ tptp.times_times_real C2) B))))) (forall ((B tptp.complex) (A tptp.complex) (C2 tptp.complex)) (=> (not (= B tptp.zero_zero_complex)) (= (= (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex A) B)) C2) (= (@ tptp.uminus1482373934393186551omplex A) (@ (@ tptp.times_times_complex C2) B))))) (forall ((B tptp.rat) (A tptp.rat) (C2 tptp.rat)) (=> (not (= B tptp.zero_zero_rat)) (= (= (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat A) B)) C2) (= (@ tptp.uminus_uminus_rat A) (@ (@ tptp.times_times_rat C2) B))))) (forall ((B tptp.real) (C2 tptp.real) (A tptp.real)) (=> (not (= B tptp.zero_zero_real)) (= (= C2 (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real A) B))) (= (@ (@ tptp.times_times_real C2) B) (@ tptp.uminus_uminus_real A))))) (forall ((B tptp.complex) (C2 tptp.complex) (A tptp.complex)) (=> (not (= B tptp.zero_zero_complex)) (= (= C2 (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex A) B))) (= (@ (@ tptp.times_times_complex C2) B) (@ tptp.uminus1482373934393186551omplex A))))) (forall ((B tptp.rat) (C2 tptp.rat) (A tptp.rat)) (=> (not (= B tptp.zero_zero_rat)) (= (= C2 (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat A) B))) (= (@ (@ tptp.times_times_rat C2) B) (@ tptp.uminus_uminus_rat A))))) (forall ((B tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int tptp.one))) B) (@ tptp.uminus_uminus_int B))) (forall ((B tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real tptp.one))) B) (@ tptp.uminus_uminus_real B))) (forall ((B tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex tptp.one))) B) (@ tptp.uminus1482373934393186551omplex B))) (forall ((B tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger tptp.one))) B) (@ tptp.uminus1351360451143612070nteger B))) (forall ((B tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat tptp.one))) B) (@ tptp.uminus_uminus_rat B))) (forall ((B tptp.int)) (= (@ (@ tptp.times_times_int B) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int tptp.one))) (@ tptp.uminus_uminus_int B))) (forall ((B tptp.real)) (= (@ (@ tptp.times_times_real B) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real tptp.one))) (@ tptp.uminus_uminus_real B))) (forall ((B tptp.complex)) (= (@ (@ tptp.times_times_complex B) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex tptp.one))) (@ tptp.uminus1482373934393186551omplex B))) (forall ((B tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger B) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger tptp.one))) (@ tptp.uminus1351360451143612070nteger B))) (forall ((B tptp.rat)) (= (@ (@ tptp.times_times_rat B) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat tptp.one))) (@ tptp.uminus_uminus_rat B))) (forall ((A tptp.real) (B tptp.real)) (= (= (@ (@ tptp.divide_divide_real A) B) (@ tptp.uminus_uminus_real tptp.one_one_real)) (and (not (= B tptp.zero_zero_real)) (= A (@ tptp.uminus_uminus_real B))))) (forall ((A tptp.complex) (B tptp.complex)) (= (= (@ (@ tptp.divide1717551699836669952omplex A) B) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (and (not (= B tptp.zero_zero_complex)) (= A (@ tptp.uminus1482373934393186551omplex B))))) (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ (@ tptp.divide_divide_rat A) B) (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (and (not (= B tptp.zero_zero_rat)) (= A (@ tptp.uminus_uminus_rat B))))) (= (@ tptp.uminus_uminus_int _let_169) _let_153) (= (@ tptp.uminus_uminus_real _let_168) _let_152) (= (@ tptp.uminus1482373934393186551omplex _let_167) _let_104) (= (@ tptp.uminus1351360451143612070nteger _let_166) _let_151) (= (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat tptp.one)) _let_150) (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M2) (=> (@ (@ tptp.ord_less_nat M2) N) (@ (@ tptp.ord_less_rat (@ tptp.semiri773545260158071498ct_rat M2)) (@ tptp.semiri773545260158071498ct_rat N))))) (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M2) (=> (@ (@ tptp.ord_less_nat M2) N) (@ (@ tptp.ord_less_int (@ tptp.semiri1406184849735516958ct_int M2)) (@ tptp.semiri1406184849735516958ct_int N))))) (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M2) (=> (@ (@ tptp.ord_less_nat M2) N) (@ (@ tptp.ord_less_nat (@ tptp.semiri1408675320244567234ct_nat M2)) (@ tptp.semiri1408675320244567234ct_nat N))))) (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M2) (=> (@ (@ tptp.ord_less_nat M2) N) (@ (@ tptp.ord_less_real (@ tptp.semiri2265585572941072030t_real M2)) (@ tptp.semiri2265585572941072030t_real N))))) (forall ((A tptp.int) (N tptp.nat)) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int A)) N) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) N)) (@ (@ tptp.power_power_int A) N)))) (forall ((A tptp.real) (N tptp.nat)) (= (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real A)) N) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N)) (@ (@ tptp.power_power_real A) N)))) (forall ((A tptp.complex) (N tptp.nat)) (= (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex A)) N) (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) N)) (@ (@ tptp.power_power_complex A) N)))) (forall ((A tptp.code_integer) (N tptp.nat)) (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger A)) N) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) N)) (@ (@ tptp.power_8256067586552552935nteger A) N)))) (forall ((A tptp.rat) (N tptp.nat)) (= (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat A)) N) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) N)) (@ (@ tptp.power_power_rat A) N)))) (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat)) (= (= (@ (@ tptp.inf_in2572325071724192079at_nat X) Y) tptp.bot_bo2099793752762293965at_nat) (@ (@ tptp.ord_le3146513528884898305at_nat X) (@ tptp.uminus6524753893492686040at_nat Y)))) (forall ((X tptp.set_int) (Y tptp.set_int)) (= (= (@ (@ tptp.inf_inf_set_int X) Y) tptp.bot_bot_set_int) (@ (@ tptp.ord_less_eq_set_int X) (@ tptp.uminus1532241313380277803et_int Y)))) (forall ((X tptp.set_real) (Y tptp.set_real)) (= (= (@ (@ tptp.inf_inf_set_real X) Y) tptp.bot_bot_set_real) (@ (@ tptp.ord_less_eq_set_real X) (@ tptp.uminus612125837232591019t_real Y)))) (forall ((X tptp.set_nat) (Y tptp.set_nat)) (= (= (@ (@ tptp.inf_inf_set_nat X) Y) tptp.bot_bot_set_nat) (@ (@ tptp.ord_less_eq_set_nat X) (@ tptp.uminus5710092332889474511et_nat Y)))) (forall ((K2 tptp.nat) (N tptp.nat)) (@ (@ tptp.dvd_dvd_rat (@ (@ tptp.times_times_rat (@ tptp.semiri773545260158071498ct_rat K2)) (@ tptp.semiri773545260158071498ct_rat N))) (@ tptp.semiri773545260158071498ct_rat (@ (@ tptp.plus_plus_nat K2) N)))) (forall ((K2 tptp.nat) (N tptp.nat)) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int (@ tptp.semiri1406184849735516958ct_int K2)) (@ tptp.semiri1406184849735516958ct_int N))) (@ tptp.semiri1406184849735516958ct_int (@ (@ tptp.plus_plus_nat K2) N)))) (forall ((K2 tptp.nat) (N tptp.nat)) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat (@ tptp.semiri1408675320244567234ct_nat K2)) (@ tptp.semiri1408675320244567234ct_nat N))) (@ tptp.semiri1408675320244567234ct_nat (@ (@ tptp.plus_plus_nat K2) N)))) (forall ((K2 tptp.nat) (N tptp.nat)) (@ (@ tptp.dvd_dvd_real (@ (@ tptp.times_times_real (@ tptp.semiri2265585572941072030t_real K2)) (@ tptp.semiri2265585572941072030t_real N))) (@ tptp.semiri2265585572941072030t_real (@ (@ tptp.plus_plus_nat K2) N)))) (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ (@ tptp.modulo_modulo_int (@ tptp.semiri1406184849735516958ct_int N)) (@ tptp.semiri1406184849735516958ct_int M2)) tptp.zero_zero_int))) (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ (@ tptp.modulo8411746178871703098atural (@ tptp.semiri2447717529341329178atural N)) (@ tptp.semiri2447717529341329178atural M2)) tptp.zero_z2226904508553997617atural))) (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.semiri1408675320244567234ct_nat N)) (@ tptp.semiri1408675320244567234ct_nat M2)) tptp.zero_zero_nat))) (forall ((P tptp.set_Pr1261947904930325089at_nat) (Q2 tptp.set_Pr1261947904930325089at_nat) (R3 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.ord_le3146513528884898305at_nat P) (@ (@ tptp.sup_su6327502436637775413at_nat Q2) R3)) (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.inf_in2572325071724192079at_nat P) (@ tptp.uminus6524753893492686040at_nat Q2))) R3))) (forall ((P tptp.set_nat) (Q2 tptp.set_nat) (R3 tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat P) (@ (@ tptp.sup_sup_set_nat Q2) R3)) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.inf_inf_set_nat P) (@ tptp.uminus5710092332889474511et_nat Q2))) R3))) (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat) (Z3 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.inf_in2572325071724192079at_nat X) (@ tptp.uminus6524753893492686040at_nat Y))) Z3) (@ (@ tptp.ord_le3146513528884898305at_nat X) (@ (@ tptp.sup_su6327502436637775413at_nat Y) Z3)))) (forall ((X tptp.set_nat) (Y tptp.set_nat) (Z3 tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.inf_inf_set_nat X) (@ tptp.uminus5710092332889474511et_nat Y))) Z3) (@ (@ tptp.ord_less_eq_set_nat X) (@ (@ tptp.sup_sup_set_nat Y) Z3)))) (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat) (Z3 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.inf_in2572325071724192079at_nat X) Y)) Z3) (@ (@ tptp.ord_le3146513528884898305at_nat X) (@ (@ tptp.sup_su6327502436637775413at_nat (@ tptp.uminus6524753893492686040at_nat Y)) Z3)))) (forall ((X tptp.set_nat) (Y tptp.set_nat) (Z3 tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.inf_inf_set_nat X) Y)) Z3) (@ (@ tptp.ord_less_eq_set_nat X) (@ (@ tptp.sup_sup_set_nat (@ tptp.uminus5710092332889474511et_nat Y)) Z3)))) (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.semiri773545260158071498ct_rat N)) (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.power_power_nat N) N)))) (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1406184849735516958ct_int N)) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.power_power_nat N) N)))) (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1408675320244567234ct_nat N)) (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.power_power_nat N) N)))) (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.semiri2265585572941072030t_real N)) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.power_power_nat N) N)))) (forall ((M2 tptp.int)) (=> (forall ((N3 tptp.nat)) (not (= M2 (@ tptp.semiri1314217659103216013at_int N3)))) (not (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N3) (not (= M2 (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N3))))))))) (forall ((N tptp.nat) (M2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int N)) (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int M2))) (and (= N tptp.zero_zero_nat) (= M2 tptp.zero_zero_nat)))) (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ (@ tptp.modulo_modulo_int A) B))) (let ((_let_2 (@ (@ tptp.modulo_modulo_int (@ tptp.uminus_uminus_int A)) B))) (let ((_let_3 (= _let_1 tptp.zero_zero_int))) (and (=> _let_3 (= _let_2 tptp.zero_zero_int)) (=> (not _let_3) (= _let_2 (@ (@ tptp.minus_minus_int B) _let_1)))))))) (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.modulo_modulo_int A))) (let ((_let_2 (@ _let_1 B))) (let ((_let_3 (@ _let_1 (@ tptp.uminus_uminus_int B)))) (let ((_let_4 (= _let_2 tptp.zero_zero_int))) (and (=> _let_4 (= _let_3 tptp.zero_zero_int)) (=> (not _let_4) (= _let_3 (@ (@ tptp.minus_minus_int _let_2) B))))))))) (forall ((R3 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat R3) N) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.divide_divide_nat (@ tptp.semiri1408675320244567234ct_nat N)) (@ tptp.semiri1408675320244567234ct_nat (@ (@ tptp.minus_minus_nat N) R3)))) (@ (@ tptp.power_power_nat N) R3)))) (forall ((K2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K2) N) (= (@ (@ tptp.times_times_nat (@ (@ tptp.times_times_nat (@ tptp.semiri1408675320244567234ct_nat K2)) (@ tptp.semiri1408675320244567234ct_nat (@ (@ tptp.minus_minus_nat N) K2)))) (@ (@ tptp.binomial N) K2)) (@ tptp.semiri1408675320244567234ct_nat N)))) (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_set_nat (@ tptp.nat_set_decode M2)) (@ tptp.nat_set_decode N)) (@ (@ tptp.ord_less_eq_nat M2) N))) (forall ((A tptp.real) (B tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real A))) (let ((_let_2 (@ (@ tptp.ord_less_real C2) tptp.zero_zero_real))) (let ((_let_3 (@ (@ tptp.times_times_real A) C2))) (let ((_let_4 (@ tptp.uminus_uminus_real B))) (let ((_let_5 (@ (@ tptp.ord_less_real tptp.zero_zero_real) C2))) (= (@ _let_1 (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B) C2))) (and (=> _let_5 (@ (@ tptp.ord_less_real _let_3) _let_4)) (=> (not _let_5) (and (=> _let_2 (@ (@ tptp.ord_less_real _let_4) _let_3)) (=> (not _let_2) (@ _let_1 tptp.zero_zero_real)))))))))))) (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A))) (let ((_let_2 (@ (@ tptp.ord_less_rat C2) tptp.zero_zero_rat))) (let ((_let_3 (@ (@ tptp.times_times_rat A) C2))) (let ((_let_4 (@ tptp.uminus_uminus_rat B))) (let ((_let_5 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C2))) (= (@ _let_1 (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C2))) (and (=> _let_5 (@ (@ tptp.ord_less_rat _let_3) _let_4)) (=> (not _let_5) (and (=> _let_2 (@ (@ tptp.ord_less_rat _let_4) _let_3)) (=> (not _let_2) (@ _let_1 tptp.zero_zero_rat)))))))))))) (forall ((B tptp.real) (C2 tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (let ((_let_2 (@ (@ tptp.ord_less_real C2) tptp.zero_zero_real))) (let ((_let_3 (@ tptp.uminus_uminus_real B))) (let ((_let_4 (@ (@ tptp.times_times_real A) C2))) (let ((_let_5 (@ _let_1 C2))) (= (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B) C2))) A) (and (=> _let_5 (@ (@ tptp.ord_less_real _let_3) _let_4)) (=> (not _let_5) (and (=> _let_2 (@ (@ tptp.ord_less_real _let_4) _let_3)) (=> (not _let_2) (@ _let_1 A)))))))))))) (forall ((B tptp.rat) (C2 tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (let ((_let_2 (@ (@ tptp.ord_less_rat C2) tptp.zero_zero_rat))) (let ((_let_3 (@ tptp.uminus_uminus_rat B))) (let ((_let_4 (@ (@ tptp.times_times_rat A) C2))) (let ((_let_5 (@ _let_1 C2))) (= (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C2))) A) (and (=> _let_5 (@ (@ tptp.ord_less_rat _let_3) _let_4)) (=> (not _let_5) (and (=> _let_2 (@ (@ tptp.ord_less_rat _let_4) _let_3)) (=> (not _let_2) (@ _let_1 A)))))))))))) (forall ((C2 tptp.real) (A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real C2) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_real A) (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B) C2))) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real B)) (@ (@ tptp.times_times_real A) C2))))) (forall ((C2 tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat C2) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_rat A) (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C2))) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat B)) (@ (@ tptp.times_times_rat A) C2))))) (forall ((C2 tptp.real) (B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real C2) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B) C2))) A) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C2)) (@ tptp.uminus_uminus_real B))))) (forall ((C2 tptp.rat) (B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat C2) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C2))) A) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C2)) (@ tptp.uminus_uminus_rat B))))) (forall ((C2 tptp.real) (A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C2) (= (@ (@ tptp.ord_less_real A) (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B) C2))) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C2)) (@ tptp.uminus_uminus_real B))))) (forall ((C2 tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C2) (= (@ (@ tptp.ord_less_rat A) (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C2))) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C2)) (@ tptp.uminus_uminus_rat B))))) (forall ((C2 tptp.real) (B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C2) (= (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B) C2))) A) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real B)) (@ (@ tptp.times_times_real A) C2))))) (forall ((C2 tptp.rat) (B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C2) (= (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C2))) A) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat B)) (@ (@ tptp.times_times_rat A) C2))))) (forall ((W2 tptp.num) (B tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W2)))) (let ((_let_2 (= C2 tptp.zero_zero_real))) (= (= _let_1 (@ (@ tptp.divide_divide_real B) C2)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_real _let_1) C2) B)) (=> _let_2 (= _let_1 tptp.zero_zero_real))))))) (forall ((W2 tptp.num) (B tptp.complex) (C2 tptp.complex)) (let ((_let_1 (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W2)))) (let ((_let_2 (= C2 tptp.zero_zero_complex))) (= (= _let_1 (@ (@ tptp.divide1717551699836669952omplex B) C2)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_complex _let_1) C2) B)) (=> _let_2 (= _let_1 tptp.zero_zero_complex))))))) (forall ((W2 tptp.num) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W2)))) (let ((_let_2 (= C2 tptp.zero_zero_rat))) (= (= _let_1 (@ (@ tptp.divide_divide_rat B) C2)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_rat _let_1) C2) B)) (=> _let_2 (= _let_1 tptp.zero_zero_rat))))))) (forall ((B tptp.real) (C2 tptp.real) (W2 tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W2)))) (let ((_let_2 (= C2 tptp.zero_zero_real))) (= (= (@ (@ tptp.divide_divide_real B) C2) _let_1) (and (=> (not _let_2) (= B (@ (@ tptp.times_times_real _let_1) C2))) (=> _let_2 (= _let_1 tptp.zero_zero_real))))))) (forall ((B tptp.complex) (C2 tptp.complex) (W2 tptp.num)) (let ((_let_1 (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W2)))) (let ((_let_2 (= C2 tptp.zero_zero_complex))) (= (= (@ (@ tptp.divide1717551699836669952omplex B) C2) _let_1) (and (=> (not _let_2) (= B (@ (@ tptp.times_times_complex _let_1) C2))) (=> _let_2 (= _let_1 tptp.zero_zero_complex))))))) (forall ((B tptp.rat) (C2 tptp.rat) (W2 tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W2)))) (let ((_let_2 (= C2 tptp.zero_zero_rat))) (= (= (@ (@ tptp.divide_divide_rat B) C2) _let_1) (and (=> (not _let_2) (= B (@ (@ tptp.times_times_rat _let_1) C2))) (=> _let_2 (= _let_1 tptp.zero_zero_rat))))))) (forall ((Z3 tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real A) Z3))) B))) (let ((_let_2 (= Z3 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) Z3))) Z3))))))) (forall ((Z3 tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex A) Z3))) B))) (let ((_let_2 (= Z3 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) Z3))) Z3))))))) (forall ((Z3 tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat A) Z3))) B))) (let ((_let_2 (= Z3 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) Z3))) Z3))))))) (forall ((Z3 tptp.real) (X tptp.real) (Y tptp.real)) (=> (not (= Z3 tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real X) Z3))) Y) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real X)) (@ (@ tptp.times_times_real Y) Z3))) Z3)))) (forall ((Z3 tptp.complex) (X tptp.complex) (Y tptp.complex)) (=> (not (= Z3 tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex X) Z3))) Y) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex X)) (@ (@ tptp.times_times_complex Y) Z3))) Z3)))) (forall ((Z3 tptp.rat) (X tptp.rat) (Y tptp.rat)) (=> (not (= Z3 tptp.zero_zero_rat)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat X) Z3))) Y) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat X)) (@ (@ tptp.times_times_rat Y) Z3))) Z3)))) (forall ((K2 tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_int K2) (@ tptp.uminus_uminus_int (@ _let_1 N))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int K2) (@ _let_1 (@ tptp.suc N)))) (@ (@ tptp.bit_ri631733984087533419it_int N) K2))))) (forall ((Z3 tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real A) Z3))) B))) (let ((_let_2 (= Z3 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) Z3))) Z3))))))) (forall ((Z3 tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex A) Z3))) B))) (let ((_let_2 (= Z3 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) Z3))) Z3))))))) (forall ((Z3 tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat A) Z3))) B))) (let ((_let_2 (= Z3 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) Z3))) Z3))))))) (forall ((Z3 tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real A) Z3)) B))) (let ((_let_2 (= Z3 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) Z3))) Z3))))))) (forall ((Z3 tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ (@ tptp.minus_minus_complex (@ (@ tptp.divide1717551699836669952omplex A) Z3)) B))) (let ((_let_2 (= Z3 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) Z3))) Z3))))))) (forall ((Z3 tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ (@ tptp.minus_minus_rat (@ (@ tptp.divide_divide_rat A) Z3)) B))) (let ((_let_2 (= Z3 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) Z3))) Z3))))))) (forall ((Z3 tptp.real) (X tptp.real) (Y tptp.real)) (=> (not (= Z3 tptp.zero_zero_real)) (= (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real X) Z3))) Y) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real X)) (@ (@ tptp.times_times_real Y) Z3))) Z3)))) (forall ((Z3 tptp.complex) (X tptp.complex) (Y tptp.complex)) (=> (not (= Z3 tptp.zero_zero_complex)) (= (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex X) Z3))) Y) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex X)) (@ (@ tptp.times_times_complex Y) Z3))) Z3)))) (forall ((Z3 tptp.rat) (X tptp.rat) (Y tptp.rat)) (=> (not (= Z3 tptp.zero_zero_rat)) (= (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat X) Z3))) Y) (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat X)) (@ (@ tptp.times_times_rat Y) Z3))) Z3)))) (forall ((K2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K2) N) (@ (@ tptp.dvd_dvd_rat (@ (@ tptp.times_times_rat (@ tptp.semiri773545260158071498ct_rat K2)) (@ tptp.semiri773545260158071498ct_rat (@ (@ tptp.minus_minus_nat N) K2)))) (@ tptp.semiri773545260158071498ct_rat N)))) (forall ((K2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K2) N) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int (@ tptp.semiri1406184849735516958ct_int K2)) (@ tptp.semiri1406184849735516958ct_int (@ (@ tptp.minus_minus_nat N) K2)))) (@ tptp.semiri1406184849735516958ct_int N)))) (forall ((K2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K2) N) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat (@ tptp.semiri1408675320244567234ct_nat K2)) (@ tptp.semiri1408675320244567234ct_nat (@ (@ tptp.minus_minus_nat N) K2)))) (@ tptp.semiri1408675320244567234ct_nat N)))) (forall ((K2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K2) N) (@ (@ tptp.dvd_dvd_real (@ (@ tptp.times_times_real (@ tptp.semiri2265585572941072030t_real K2)) (@ tptp.semiri2265585572941072030t_real (@ (@ tptp.minus_minus_nat N) K2)))) (@ tptp.semiri2265585572941072030t_real N)))) (forall ((K2 tptp.int)) (=> (not (= K2 tptp.zero_zero_int)) (=> (forall ((N3 tptp.nat)) (=> (= K2 (@ tptp.semiri1314217659103216013at_int N3)) (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N3)))) (not (forall ((N3 tptp.nat)) (=> (= K2 (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N3))) (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N3)))))))) (forall ((N tptp.nat) (K2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) K2) (= (@ (@ tptp.comm_s2602460028002588243omplex (@ tptp.uminus1482373934393186551omplex (@ tptp.semiri8010041392384452111omplex N))) K2) tptp.zero_zero_complex))) (forall ((N tptp.nat) (K2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) K2) (= (@ (@ tptp.comm_s8582702949713902594nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.semiri4939895301339042750nteger N))) K2) tptp.zero_z3403309356797280102nteger))) (forall ((N tptp.nat) (K2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) K2) (= (@ (@ tptp.comm_s4028243227959126397er_rat (@ tptp.uminus_uminus_rat (@ tptp.semiri681578069525770553at_rat N))) K2) tptp.zero_zero_rat))) (forall ((N tptp.nat) (K2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) K2) (= (@ (@ tptp.comm_s7457072308508201937r_real (@ tptp.uminus_uminus_real (@ tptp.semiri5074537144036343181t_real N))) K2) tptp.zero_zero_real))) (forall ((N tptp.nat) (K2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) K2) (= (@ (@ tptp.comm_s4660882817536571857er_int (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N))) K2) tptp.zero_zero_int))) (forall ((N tptp.nat) (K2 tptp.nat)) (= (= (@ (@ tptp.comm_s2602460028002588243omplex (@ tptp.uminus1482373934393186551omplex (@ tptp.semiri8010041392384452111omplex N))) K2) tptp.zero_zero_complex) (@ (@ tptp.ord_less_nat N) K2))) (forall ((N tptp.nat) (K2 tptp.nat)) (= (= (@ (@ tptp.comm_s8582702949713902594nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.semiri4939895301339042750nteger N))) K2) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_less_nat N) K2))) (forall ((N tptp.nat) (K2 tptp.nat)) (= (= (@ (@ tptp.comm_s4028243227959126397er_rat (@ tptp.uminus_uminus_rat (@ tptp.semiri681578069525770553at_rat N))) K2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_nat N) K2))) (forall ((N tptp.nat) (K2 tptp.nat)) (= (= (@ (@ tptp.comm_s7457072308508201937r_real (@ tptp.uminus_uminus_real (@ tptp.semiri5074537144036343181t_real N))) K2) tptp.zero_zero_real) (@ (@ tptp.ord_less_nat N) K2))) (forall ((N tptp.nat) (K2 tptp.nat)) (= (= (@ (@ tptp.comm_s4660882817536571857er_int (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N))) K2) tptp.zero_zero_int) (@ (@ tptp.ord_less_nat N) K2))) (forall ((A tptp.complex) (N tptp.nat)) (= (= (@ (@ tptp.comm_s2602460028002588243omplex A) N) tptp.zero_zero_complex) (exists ((K3 tptp.nat)) (and (@ (@ tptp.ord_less_nat K3) N) (= A (@ tptp.uminus1482373934393186551omplex (@ tptp.semiri8010041392384452111omplex K3))))))) (forall ((A tptp.rat) (N tptp.nat)) (= (= (@ (@ tptp.comm_s4028243227959126397er_rat A) N) tptp.zero_zero_rat) (exists ((K3 tptp.nat)) (and (@ (@ tptp.ord_less_nat K3) N) (= A (@ tptp.uminus_uminus_rat (@ tptp.semiri681578069525770553at_rat K3))))))) (forall ((A tptp.real) (N tptp.nat)) (= (= (@ (@ tptp.comm_s7457072308508201937r_real A) N) tptp.zero_zero_real) (exists ((K3 tptp.nat)) (and (@ (@ tptp.ord_less_nat K3) N) (= A (@ tptp.uminus_uminus_real (@ tptp.semiri5074537144036343181t_real K3))))))) (forall ((K2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K2) N) (not (= (@ (@ tptp.comm_s2602460028002588243omplex (@ tptp.uminus1482373934393186551omplex (@ tptp.semiri8010041392384452111omplex N))) K2) tptp.zero_zero_complex)))) (forall ((K2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K2) N) (not (= (@ (@ tptp.comm_s8582702949713902594nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.semiri4939895301339042750nteger N))) K2) tptp.zero_z3403309356797280102nteger)))) (forall ((K2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K2) N) (not (= (@ (@ tptp.comm_s4028243227959126397er_rat (@ tptp.uminus_uminus_rat (@ tptp.semiri681578069525770553at_rat N))) K2) tptp.zero_zero_rat)))) (forall ((K2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K2) N) (not (= (@ (@ tptp.comm_s7457072308508201937r_real (@ tptp.uminus_uminus_real (@ tptp.semiri5074537144036343181t_real N))) K2) tptp.zero_zero_real)))) (forall ((K2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K2) N) (not (= (@ (@ tptp.comm_s4660882817536571857er_int (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N))) K2) tptp.zero_zero_int)))) (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N)))))) (forall ((X tptp.int)) (=> (@ (@ tptp.ord_less_int X) tptp.zero_zero_int) (exists ((N3 tptp.nat)) (= X (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N3))))))) (forall ((N tptp.nat)) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N)))) tptp.zero_zero_int)) (forall ((B tptp.int)) (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (= (@ (@ tptp.divide_divide_int _let_1) B) _let_1)))) (forall ((A4 tptp.set_real) (P2 (-> tptp.real Bool)) (H (-> tptp.real tptp.real)) (G2 (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.collect_real P2))) (let ((_let_2 (@ tptp.inf_inf_set_real A4))) (=> (@ tptp.finite_finite_real A4) (= (@ (@ tptp.groups1681761925125756287l_real (lambda ((X4 tptp.real)) (@ (@ (@ tptp.if_real (@ P2 X4)) (@ H X4)) (@ G2 X4)))) A4) (@ (@ tptp.times_times_real (@ (@ tptp.groups1681761925125756287l_real H) (@ _let_2 _let_1))) (@ (@ tptp.groups1681761925125756287l_real G2) (@ _let_2 (@ tptp.uminus612125837232591019t_real _let_1))))))))) (forall ((A4 tptp.set_int) (P2 (-> tptp.int Bool)) (H (-> tptp.int tptp.real)) (G2 (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.collect_int P2))) (let ((_let_2 (@ tptp.inf_inf_set_int A4))) (=> (@ tptp.finite_finite_int A4) (= (@ (@ tptp.groups2316167850115554303t_real (lambda ((X4 tptp.int)) (@ (@ (@ tptp.if_real (@ P2 X4)) (@ H X4)) (@ G2 X4)))) A4) (@ (@ tptp.times_times_real (@ (@ tptp.groups2316167850115554303t_real H) (@ _let_2 _let_1))) (@ (@ tptp.groups2316167850115554303t_real G2) (@ _let_2 (@ tptp.uminus1532241313380277803et_int _let_1))))))))) (forall ((A4 tptp.set_complex) (P2 (-> tptp.complex Bool)) (H (-> tptp.complex tptp.real)) (G2 (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.collect_complex P2))) (let ((_let_2 (@ tptp.inf_inf_set_complex A4))) (=> (@ tptp.finite3207457112153483333omplex A4) (= (@ (@ tptp.groups766887009212190081x_real (lambda ((X4 tptp.complex)) (@ (@ (@ tptp.if_real (@ P2 X4)) (@ H X4)) (@ G2 X4)))) A4) (@ (@ tptp.times_times_real (@ (@ tptp.groups766887009212190081x_real H) (@ _let_2 _let_1))) (@ (@ tptp.groups766887009212190081x_real G2) (@ _let_2 (@ tptp.uminus8566677241136511917omplex _let_1))))))))) (forall ((A4 tptp.set_nat) (P2 (-> tptp.nat Bool)) (H (-> tptp.nat tptp.real)) (G2 (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.collect_nat P2))) (let ((_let_2 (@ tptp.inf_inf_set_nat A4))) (=> (@ tptp.finite_finite_nat A4) (= (@ (@ tptp.groups129246275422532515t_real (lambda ((X4 tptp.nat)) (@ (@ (@ tptp.if_real (@ P2 X4)) (@ H X4)) (@ G2 X4)))) A4) (@ (@ tptp.times_times_real (@ (@ tptp.groups129246275422532515t_real H) (@ _let_2 _let_1))) (@ (@ tptp.groups129246275422532515t_real G2) (@ _let_2 (@ tptp.uminus5710092332889474511et_nat _let_1))))))))) (forall ((A4 tptp.set_real) (P2 (-> tptp.real Bool)) (H (-> tptp.real tptp.rat)) (G2 (-> tptp.real tptp.rat))) (let ((_let_1 (@ tptp.collect_real P2))) (let ((_let_2 (@ tptp.inf_inf_set_real A4))) (=> (@ tptp.finite_finite_real A4) (= (@ (@ tptp.groups4061424788464935467al_rat (lambda ((X4 tptp.real)) (@ (@ (@ tptp.if_rat (@ P2 X4)) (@ H X4)) (@ G2 X4)))) A4) (@ (@ tptp.times_times_rat (@ (@ tptp.groups4061424788464935467al_rat H) (@ _let_2 _let_1))) (@ (@ tptp.groups4061424788464935467al_rat G2) (@ _let_2 (@ tptp.uminus612125837232591019t_real _let_1))))))))) (forall ((A4 tptp.set_int) (P2 (-> tptp.int Bool)) (H (-> tptp.int tptp.rat)) (G2 (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.collect_int P2))) (let ((_let_2 (@ tptp.inf_inf_set_int A4))) (=> (@ tptp.finite_finite_int A4) (= (@ (@ tptp.groups1072433553688619179nt_rat (lambda ((X4 tptp.int)) (@ (@ (@ tptp.if_rat (@ P2 X4)) (@ H X4)) (@ G2 X4)))) A4) (@ (@ tptp.times_times_rat (@ (@ tptp.groups1072433553688619179nt_rat H) (@ _let_2 _let_1))) (@ (@ tptp.groups1072433553688619179nt_rat G2) (@ _let_2 (@ tptp.uminus1532241313380277803et_int _let_1))))))))) (forall ((A4 tptp.set_complex) (P2 (-> tptp.complex Bool)) (H (-> tptp.complex tptp.rat)) (G2 (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.collect_complex P2))) (let ((_let_2 (@ tptp.inf_inf_set_complex A4))) (=> (@ tptp.finite3207457112153483333omplex A4) (= (@ (@ tptp.groups225925009352817453ex_rat (lambda ((X4 tptp.complex)) (@ (@ (@ tptp.if_rat (@ P2 X4)) (@ H X4)) (@ G2 X4)))) A4) (@ (@ tptp.times_times_rat (@ (@ tptp.groups225925009352817453ex_rat H) (@ _let_2 _let_1))) (@ (@ tptp.groups225925009352817453ex_rat G2) (@ _let_2 (@ tptp.uminus8566677241136511917omplex _let_1))))))))) (forall ((A4 tptp.set_nat) (P2 (-> tptp.nat Bool)) (H (-> tptp.nat tptp.rat)) (G2 (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.collect_nat P2))) (let ((_let_2 (@ tptp.inf_inf_set_nat A4))) (=> (@ tptp.finite_finite_nat A4) (= (@ (@ tptp.groups73079841787564623at_rat (lambda ((X4 tptp.nat)) (@ (@ (@ tptp.if_rat (@ P2 X4)) (@ H X4)) (@ G2 X4)))) A4) (@ (@ tptp.times_times_rat (@ (@ tptp.groups73079841787564623at_rat H) (@ _let_2 _let_1))) (@ (@ tptp.groups73079841787564623at_rat G2) (@ _let_2 (@ tptp.uminus5710092332889474511et_nat _let_1))))))))) (forall ((A4 tptp.set_real) (P2 (-> tptp.real Bool)) (H (-> tptp.real tptp.nat)) (G2 (-> tptp.real tptp.nat))) (let ((_let_1 (@ tptp.collect_real P2))) (let ((_let_2 (@ tptp.inf_inf_set_real A4))) (=> (@ tptp.finite_finite_real A4) (= (@ (@ tptp.groups4696554848551431203al_nat (lambda ((X4 tptp.real)) (@ (@ (@ tptp.if_nat (@ P2 X4)) (@ H X4)) (@ G2 X4)))) A4) (@ (@ tptp.times_times_nat (@ (@ tptp.groups4696554848551431203al_nat H) (@ _let_2 _let_1))) (@ (@ tptp.groups4696554848551431203al_nat G2) (@ _let_2 (@ tptp.uminus612125837232591019t_real _let_1))))))))) (forall ((A4 tptp.set_int) (P2 (-> tptp.int Bool)) (H (-> tptp.int tptp.nat)) (G2 (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.collect_int P2))) (let ((_let_2 (@ tptp.inf_inf_set_int A4))) (=> (@ tptp.finite_finite_int A4) (= (@ (@ tptp.groups1707563613775114915nt_nat (lambda ((X4 tptp.int)) (@ (@ (@ tptp.if_nat (@ P2 X4)) (@ H X4)) (@ G2 X4)))) A4) (@ (@ tptp.times_times_nat (@ (@ tptp.groups1707563613775114915nt_nat H) (@ _let_2 _let_1))) (@ (@ tptp.groups1707563613775114915nt_nat G2) (@ _let_2 (@ tptp.uminus1532241313380277803et_int _let_1))))))))) (forall ((K2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K2) N) (= (@ (@ tptp.binomial N) K2) (@ (@ tptp.divide_divide_nat (@ tptp.semiri1408675320244567234ct_nat N)) (@ (@ tptp.times_times_nat (@ tptp.semiri1408675320244567234ct_nat K2)) (@ tptp.semiri1408675320244567234ct_nat (@ (@ tptp.minus_minus_nat N) K2))))))) (forall ((A tptp.real) (B tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real A))) (let ((_let_2 (@ (@ tptp.ord_less_real C2) tptp.zero_zero_real))) (let ((_let_3 (@ (@ tptp.times_times_real A) C2))) (let ((_let_4 (@ tptp.uminus_uminus_real B))) (let ((_let_5 (@ (@ tptp.ord_less_real tptp.zero_zero_real) C2))) (= (@ _let_1 (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B) C2))) (and (=> _let_5 (@ (@ tptp.ord_less_eq_real _let_3) _let_4)) (=> (not _let_5) (and (=> _let_2 (@ (@ tptp.ord_less_eq_real _let_4) _let_3)) (=> (not _let_2) (@ _let_1 tptp.zero_zero_real)))))))))))) (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat A))) (let ((_let_2 (@ (@ tptp.ord_less_rat C2) tptp.zero_zero_rat))) (let ((_let_3 (@ (@ tptp.times_times_rat A) C2))) (let ((_let_4 (@ tptp.uminus_uminus_rat B))) (let ((_let_5 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C2))) (= (@ _let_1 (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C2))) (and (=> _let_5 (@ (@ tptp.ord_less_eq_rat _let_3) _let_4)) (=> (not _let_5) (and (=> _let_2 (@ (@ tptp.ord_less_eq_rat _let_4) _let_3)) (=> (not _let_2) (@ _let_1 tptp.zero_zero_rat)))))))))))) (forall ((B tptp.real) (C2 tptp.real) (A tptp.real)) (let ((_let_1 (@ (@ tptp.ord_less_real C2) tptp.zero_zero_real))) (let ((_let_2 (@ tptp.uminus_uminus_real B))) (let ((_let_3 (@ (@ tptp.times_times_real A) C2))) (let ((_let_4 (@ (@ tptp.ord_less_real tptp.zero_zero_real) C2))) (= (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B) C2))) A) (and (=> _let_4 (@ (@ tptp.ord_less_eq_real _let_2) _let_3)) (=> (not _let_4) (and (=> _let_1 (@ (@ tptp.ord_less_eq_real _let_3) _let_2)) (=> (not _let_1) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A))))))))))) (forall ((B tptp.rat) (C2 tptp.rat) (A tptp.rat)) (let ((_let_1 (@ (@ tptp.ord_less_rat C2) tptp.zero_zero_rat))) (let ((_let_2 (@ tptp.uminus_uminus_rat B))) (let ((_let_3 (@ (@ tptp.times_times_rat A) C2))) (let ((_let_4 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C2))) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C2))) A) (and (=> _let_4 (@ (@ tptp.ord_less_eq_rat _let_2) _let_3)) (=> (not _let_4) (and (=> _let_1 (@ (@ tptp.ord_less_eq_rat _let_3) _let_2)) (=> (not _let_1) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A))))))))))) (forall ((C2 tptp.real) (A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real C2) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_eq_real A) (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B) C2))) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real B)) (@ (@ tptp.times_times_real A) C2))))) (forall ((C2 tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat C2) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_eq_rat A) (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C2))) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat B)) (@ (@ tptp.times_times_rat A) C2))))) (forall ((C2 tptp.real) (B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real C2) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B) C2))) A) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) C2)) (@ tptp.uminus_uminus_real B))))) (forall ((C2 tptp.rat) (B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat C2) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C2))) A) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C2)) (@ tptp.uminus_uminus_rat B))))) (forall ((C2 tptp.real) (A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C2) (= (@ (@ tptp.ord_less_eq_real A) (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B) C2))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) C2)) (@ tptp.uminus_uminus_real B))))) (forall ((C2 tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C2) (= (@ (@ tptp.ord_less_eq_rat A) (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C2))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C2)) (@ tptp.uminus_uminus_rat B))))) (forall ((C2 tptp.real) (B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C2) (= (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B) C2))) A) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real B)) (@ (@ tptp.times_times_real A) C2))))) (forall ((C2 tptp.rat) (B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C2) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C2))) A) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat B)) (@ (@ tptp.times_times_rat A) C2))))) (forall ((B tptp.real) (C2 tptp.real) (W2 tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W2)))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (let ((_let_3 (@ (@ tptp.ord_less_real C2) tptp.zero_zero_real))) (let ((_let_4 (@ (@ tptp.times_times_real _let_1) C2))) (let ((_let_5 (@ _let_2 C2))) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real B) C2)) _let_1) (and (=> _let_5 (@ (@ tptp.ord_less_real B) _let_4)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_real _let_4) B)) (=> (not _let_3) (@ _let_2 _let_1)))))))))))) (forall ((B tptp.rat) (C2 tptp.rat) (W2 tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W2)))) (let ((_let_2 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (let ((_let_3 (@ (@ tptp.ord_less_rat C2) tptp.zero_zero_rat))) (let ((_let_4 (@ (@ tptp.times_times_rat _let_1) C2))) (let ((_let_5 (@ _let_2 C2))) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat B) C2)) _let_1) (and (=> _let_5 (@ (@ tptp.ord_less_rat B) _let_4)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_rat _let_4) B)) (=> (not _let_3) (@ _let_2 _let_1)))))))))))) (forall ((W2 tptp.num) (B tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W2)))) (let ((_let_2 (@ tptp.ord_less_real _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_real C2) tptp.zero_zero_real))) (let ((_let_4 (@ (@ tptp.times_times_real _let_1) C2))) (let ((_let_5 (@ (@ tptp.ord_less_real tptp.zero_zero_real) C2))) (= (@ _let_2 (@ (@ tptp.divide_divide_real B) C2)) (and (=> _let_5 (@ (@ tptp.ord_less_real _let_4) B)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_real B) _let_4)) (=> (not _let_3) (@ _let_2 tptp.zero_zero_real)))))))))))) (forall ((W2 tptp.num) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W2)))) (let ((_let_2 (@ tptp.ord_less_rat _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_rat C2) tptp.zero_zero_rat))) (let ((_let_4 (@ (@ tptp.times_times_rat _let_1) C2))) (let ((_let_5 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C2))) (= (@ _let_2 (@ (@ tptp.divide_divide_rat B) C2)) (and (=> _let_5 (@ (@ tptp.ord_less_rat _let_4) B)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_rat B) _let_4)) (=> (not _let_3) (@ _let_2 tptp.zero_zero_rat)))))))))))) (forall ((K2 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 K2) N) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N) K2)) (@ _let_1 (@ (@ tptp.minus_minus_nat N) K2)))))) (forall ((K2 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 K2) N) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N) K2)) (@ _let_1 (@ (@ tptp.minus_minus_nat N) K2)))))) (forall ((K2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))) (=> (@ (@ tptp.ord_less_eq_nat K2) N) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N) K2)) (@ _let_1 (@ (@ tptp.minus_minus_nat N) K2)))))) (forall ((K2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))) (=> (@ (@ tptp.ord_less_eq_nat K2) N) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N) K2)) (@ _let_1 (@ (@ tptp.minus_minus_nat N) K2)))))) (forall ((K2 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 K2) N) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N) K2)) (@ _let_1 (@ (@ tptp.minus_minus_nat N) K2)))))) (forall ((K2 tptp.int)) (=> (@ (@ tptp.ord_less_int K2) tptp.zero_zero_int) (not (forall ((N3 tptp.nat)) (=> (= K2 (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N3))) (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N3))))))) (forall ((L tptp.int) (K2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) L) (= (@ (@ tptp.modulo_modulo_int (@ tptp.uminus_uminus_int K2)) L) (@ (@ tptp.minus_minus_int (@ (@ tptp.minus_minus_int L) tptp.one_one_int)) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.minus_minus_int K2) tptp.one_one_int)) L))))) (forall ((B tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (= (@ (@ tptp.modulo_modulo_int (@ tptp.uminus_uminus_int tptp.one_one_int)) B) (@ (@ tptp.minus_minus_int B) tptp.one_one_int)))) (forall ((B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.uminus_uminus_int (@ (@ tptp.divide_divide_int A) B)))) (let ((_let_2 (@ (@ tptp.divide_divide_int (@ tptp.uminus_uminus_int A)) B))) (let ((_let_3 (= (@ (@ tptp.modulo_modulo_int A) B) tptp.zero_zero_int))) (=> (not (= B tptp.zero_zero_int)) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ (@ tptp.minus_minus_int _let_1) tptp.one_one_int))))))))) (forall ((B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A))) (let ((_let_2 (@ tptp.uminus_uminus_int (@ _let_1 B)))) (let ((_let_3 (@ _let_1 (@ tptp.uminus_uminus_int B)))) (let ((_let_4 (= (@ (@ tptp.modulo_modulo_int A) B) tptp.zero_zero_int))) (=> (not (= B tptp.zero_zero_int)) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.minus_minus_int _let_2) tptp.one_one_int)))))))))) (forall ((N tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M2) (= (@ tptp.semiri1408675320244567234ct_nat M2) (@ (@ tptp.times_times_nat (@ tptp.semiri1408675320244567234ct_nat N)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((X4 tptp.nat)) X4)) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc N)) M2)))))) (= tptp.bit_ri6519982836138164636nteger (lambda ((N4 tptp.nat) (A5 tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.modulo364778990260209775nteger A5) _let_1))) (@ (@ (@ tptp.if_Code_integer (= N4 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 N4) tptp.one_one_nat)) (@ (@ tptp.divide6298287555418463151nteger A5) _let_1))))))))) (= tptp.bit_ri631733984087533419it_int (lambda ((N4 tptp.nat) (A5 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.modulo_modulo_int A5) _let_1))) (@ (@ (@ tptp.if_int (= N4 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 N4) tptp.one_one_nat)) (@ (@ tptp.divide_divide_int A5) _let_1))))))))) (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))))) (forall ((A tptp.int) (B tptp.int) (Q2 tptp.int) (R3 tptp.int)) (let ((_let_1 (@ tptp.if_int (= R3 tptp.zero_zero_int)))) (let ((_let_2 (@ tptp.uminus_uminus_int Q2))) (=> (@ (@ (@ tptp.eucl_rel_int A) B) (@ (@ tptp.product_Pair_int_int Q2) R3)) (=> (not (= B tptp.zero_zero_int)) (@ (@ (@ tptp.eucl_rel_int (@ tptp.uminus_uminus_int A)) B) (@ (@ tptp.product_Pair_int_int (@ (@ _let_1 _let_2) (@ (@ tptp.minus_minus_int _let_2) tptp.one_one_int))) (@ (@ _let_1 tptp.zero_zero_int) (@ (@ tptp.minus_minus_int B) R3))))))))) (forall ((B tptp.real) (C2 tptp.real) (W2 tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W2)))) (let ((_let_2 (@ (@ tptp.ord_less_real C2) tptp.zero_zero_real))) (let ((_let_3 (@ (@ tptp.times_times_real _let_1) C2))) (let ((_let_4 (@ (@ tptp.ord_less_real tptp.zero_zero_real) C2))) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real B) C2)) _let_1) (and (=> _let_4 (@ (@ tptp.ord_less_eq_real B) _let_3)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_eq_real _let_3) B)) (=> (not _let_2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1))))))))))) (forall ((B tptp.rat) (C2 tptp.rat) (W2 tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W2)))) (let ((_let_2 (@ (@ tptp.ord_less_rat C2) tptp.zero_zero_rat))) (let ((_let_3 (@ (@ tptp.times_times_rat _let_1) C2))) (let ((_let_4 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C2))) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat B) C2)) _let_1) (and (=> _let_4 (@ (@ tptp.ord_less_eq_rat B) _let_3)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_eq_rat _let_3) B)) (=> (not _let_2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1))))))))))) (forall ((W2 tptp.num) (B tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W2)))) (let ((_let_2 (@ tptp.ord_less_eq_real _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_real C2) tptp.zero_zero_real))) (let ((_let_4 (@ (@ tptp.times_times_real _let_1) C2))) (let ((_let_5 (@ (@ tptp.ord_less_real tptp.zero_zero_real) C2))) (= (@ _let_2 (@ (@ tptp.divide_divide_real B) C2)) (and (=> _let_5 (@ (@ tptp.ord_less_eq_real _let_4) B)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_eq_real B) _let_4)) (=> (not _let_3) (@ _let_2 tptp.zero_zero_real)))))))))))) (forall ((W2 tptp.num) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W2)))) (let ((_let_2 (@ tptp.ord_less_eq_rat _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_rat C2) tptp.zero_zero_rat))) (let ((_let_4 (@ (@ tptp.times_times_rat _let_1) C2))) (let ((_let_5 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C2))) (= (@ _let_2 (@ (@ tptp.divide_divide_rat B) C2)) (and (=> _let_5 (@ (@ tptp.ord_less_eq_rat _let_4) B)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_eq_rat B) _let_4)) (=> (not _let_3) (@ _let_2 tptp.zero_zero_rat)))))))))))) (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_real)))) (forall ((X tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) X) (=> (@ (@ tptp.ord_le3102999989581377725nteger X) tptp.one_one_Code_integer) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.power_8256067586552552935nteger X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_Code_integer)))) (forall ((X tptp.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)))) (forall ((X tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int tptp.one_one_int)) X) (=> (@ (@ tptp.ord_less_eq_int X) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_int)))) (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int A)) N))) (= (@ (@ tptp.times_times_int _let_1) _let_1) (@ (@ tptp.power_power_int A) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))) (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real A)) N))) (= (@ (@ tptp.times_times_real _let_1) _let_1) (@ (@ tptp.power_power_real A) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))) (forall ((A tptp.complex) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex A)) N))) (= (@ (@ tptp.times_times_complex _let_1) _let_1) (@ (@ tptp.power_power_complex A) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))) (forall ((A tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger A)) N))) (= (@ (@ tptp.times_3573771949741848930nteger _let_1) _let_1) (@ (@ tptp.power_8256067586552552935nteger A) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))) (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat A)) N))) (= (@ (@ tptp.times_times_rat _let_1) _let_1) (@ (@ tptp.power_power_rat A) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))) (= tptp.semiri3624122377584611663nteger (lambda ((M6 tptp.nat)) (@ (@ (@ tptp.if_Code_integer (= M6 tptp.zero_zero_nat)) tptp.one_one_Code_integer) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.semiri4939895301339042750nteger M6)) (@ tptp.semiri3624122377584611663nteger (@ (@ tptp.minus_minus_nat M6) tptp.one_one_nat)))))) (= tptp.semiri5044797733671781792omplex (lambda ((M6 tptp.nat)) (@ (@ (@ tptp.if_complex (= M6 tptp.zero_zero_nat)) tptp.one_one_complex) (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex M6)) (@ tptp.semiri5044797733671781792omplex (@ (@ tptp.minus_minus_nat M6) tptp.one_one_nat)))))) (= tptp.semiri773545260158071498ct_rat (lambda ((M6 tptp.nat)) (@ (@ (@ tptp.if_rat (= M6 tptp.zero_zero_nat)) tptp.one_one_rat) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat M6)) (@ tptp.semiri773545260158071498ct_rat (@ (@ tptp.minus_minus_nat M6) tptp.one_one_nat)))))) (= tptp.semiri1406184849735516958ct_int (lambda ((M6 tptp.nat)) (@ (@ (@ tptp.if_int (= M6 tptp.zero_zero_nat)) tptp.one_one_int) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int M6)) (@ tptp.semiri1406184849735516958ct_int (@ (@ tptp.minus_minus_nat M6) tptp.one_one_nat)))))) (= tptp.semiri1408675320244567234ct_nat (lambda ((M6 tptp.nat)) (@ (@ (@ tptp.if_nat (= M6 tptp.zero_zero_nat)) tptp.one_one_nat) (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat M6)) (@ tptp.semiri1408675320244567234ct_nat (@ (@ tptp.minus_minus_nat M6) tptp.one_one_nat)))))) (= tptp.semiri2265585572941072030t_real (lambda ((M6 tptp.nat)) (@ (@ (@ tptp.if_real (= M6 tptp.zero_zero_nat)) tptp.one_one_real) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real M6)) (@ tptp.semiri2265585572941072030t_real (@ (@ tptp.minus_minus_nat M6) tptp.one_one_nat)))))) _let_165 _let_164 _let_163 (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.semiri773545260158071498ct_rat N) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat N)) (@ tptp.semiri773545260158071498ct_rat (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)))))) (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.semiri1406184849735516958ct_int N) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int N)) (@ tptp.semiri1406184849735516958ct_int (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)))))) (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.semiri1408675320244567234ct_nat N) (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat N)) (@ tptp.semiri1408675320244567234ct_nat (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)))))) (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.semiri2265585572941072030t_real N) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ tptp.semiri2265585572941072030t_real (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)))))) (forall ((R3 tptp.complex) (K2 tptp.nat)) (let ((_let_1 (@ tptp.uminus1482373934393186551omplex R3))) (= (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex R3) (@ tptp.semiri8010041392384452111omplex K2))) (@ (@ tptp.comm_s2602460028002588243omplex _let_1) K2)) (@ (@ tptp.times_times_complex R3) (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.plus_plus_complex _let_1) tptp.one_one_complex)) K2))))) (forall ((R3 tptp.code_integer) (K2 tptp.nat)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger R3))) (= (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.minus_8373710615458151222nteger R3) (@ tptp.semiri4939895301339042750nteger K2))) (@ (@ tptp.comm_s8582702949713902594nteger _let_1) K2)) (@ (@ tptp.times_3573771949741848930nteger R3) (@ (@ tptp.comm_s8582702949713902594nteger (@ (@ tptp.plus_p5714425477246183910nteger _let_1) tptp.one_one_Code_integer)) K2))))) (forall ((R3 tptp.rat) (K2 tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_rat R3))) (= (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat R3) (@ tptp.semiri681578069525770553at_rat K2))) (@ (@ tptp.comm_s4028243227959126397er_rat _let_1) K2)) (@ (@ tptp.times_times_rat R3) (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.plus_plus_rat _let_1) tptp.one_one_rat)) K2))))) (forall ((R3 tptp.real) (K2 tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_real R3))) (= (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real R3) (@ tptp.semiri5074537144036343181t_real K2))) (@ (@ tptp.comm_s7457072308508201937r_real _let_1) K2)) (@ (@ tptp.times_times_real R3) (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real)) K2))))) (forall ((R3 tptp.int) (K2 tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_int R3))) (= (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int R3) (@ tptp.semiri1314217659103216013at_int K2))) (@ (@ tptp.comm_s4660882817536571857er_int _let_1) K2)) (@ (@ tptp.times_times_int R3) (@ (@ tptp.comm_s4660882817536571857er_int (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int)) K2))))) (forall ((K2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))) (= (@ (@ tptp.times_times_complex (@ _let_1 K2)) (@ (@ tptp.gbinomial_complex (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.semiri8010041392384452111omplex N))) tptp.one_one_complex)) K2)) (@ (@ tptp.times_times_complex (@ _let_1 N)) (@ (@ tptp.gbinomial_complex (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.semiri8010041392384452111omplex K2))) tptp.one_one_complex)) N))))) (forall ((K2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)))) (= (@ (@ tptp.times_times_rat (@ _let_1 K2)) (@ (@ tptp.gbinomial_rat (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat (@ tptp.semiri681578069525770553at_rat N))) tptp.one_one_rat)) K2)) (@ (@ tptp.times_times_rat (@ _let_1 N)) (@ (@ tptp.gbinomial_rat (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat (@ tptp.semiri681578069525770553at_rat K2))) tptp.one_one_rat)) N))))) (forall ((K2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)))) (= (@ (@ tptp.times_times_real (@ _let_1 K2)) (@ (@ tptp.gbinomial_real (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real (@ tptp.semiri5074537144036343181t_real N))) tptp.one_one_real)) K2)) (@ (@ tptp.times_times_real (@ _let_1 N)) (@ (@ tptp.gbinomial_real (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real (@ tptp.semiri5074537144036343181t_real K2))) tptp.one_one_real)) N))))) (= tptp.gbinomial_complex (lambda ((A5 tptp.complex) (K3 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) K3)) (@ (@ tptp.gbinomial_complex (@ (@ tptp.minus_minus_complex (@ (@ tptp.minus_minus_complex (@ tptp.semiri8010041392384452111omplex K3)) A5)) tptp.one_one_complex)) K3)))) (= tptp.gbinomial_rat (lambda ((A5 tptp.rat) (K3 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) K3)) (@ (@ tptp.gbinomial_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.minus_minus_rat (@ tptp.semiri681578069525770553at_rat K3)) A5)) tptp.one_one_rat)) K3)))) (= tptp.gbinomial_real (lambda ((A5 tptp.real) (K3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) K3)) (@ (@ tptp.gbinomial_real (@ (@ tptp.minus_minus_real (@ (@ tptp.minus_minus_real (@ tptp.semiri5074537144036343181t_real K3)) A5)) tptp.one_one_real)) K3)))) (forall ((K2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K2) N) (= (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.binomial N) K2)) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.semiri5044797733671781792omplex N)) (@ (@ tptp.times_times_complex (@ tptp.semiri5044797733671781792omplex K2)) (@ tptp.semiri5044797733671781792omplex (@ (@ tptp.minus_minus_nat N) K2))))))) (forall ((K2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K2) N) (= (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.binomial N) K2)) (@ (@ tptp.divide_divide_rat (@ tptp.semiri773545260158071498ct_rat N)) (@ (@ tptp.times_times_rat (@ tptp.semiri773545260158071498ct_rat K2)) (@ tptp.semiri773545260158071498ct_rat (@ (@ tptp.minus_minus_nat N) K2))))))) (forall ((K2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K2) N) (= (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.binomial N) K2)) (@ (@ tptp.divide_divide_real (@ tptp.semiri2265585572941072030t_real N)) (@ (@ tptp.times_times_real (@ tptp.semiri2265585572941072030t_real K2)) (@ tptp.semiri2265585572941072030t_real (@ (@ tptp.minus_minus_nat N) K2))))))) (forall ((K2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K2) N) (= (@ (@ tptp.times_times_complex (@ tptp.semiri5044797733671781792omplex K2)) (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.binomial N) K2))) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.semiri5044797733671781792omplex N)) (@ tptp.semiri5044797733671781792omplex (@ (@ tptp.minus_minus_nat N) K2)))))) (forall ((K2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K2) N) (= (@ (@ tptp.times_times_rat (@ tptp.semiri773545260158071498ct_rat K2)) (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.binomial N) K2))) (@ (@ tptp.divide_divide_rat (@ tptp.semiri773545260158071498ct_rat N)) (@ tptp.semiri773545260158071498ct_rat (@ (@ tptp.minus_minus_nat N) K2)))))) (forall ((K2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K2) N) (= (@ (@ tptp.times_times_real (@ tptp.semiri2265585572941072030t_real K2)) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.binomial N) K2))) (@ (@ tptp.divide_divide_real (@ tptp.semiri2265585572941072030t_real N)) (@ tptp.semiri2265585572941072030t_real (@ (@ tptp.minus_minus_nat N) K2)))))) (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))))) (forall ((N tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M2) (= (@ (@ tptp.divide_divide_nat (@ tptp.semiri1408675320244567234ct_nat M2)) (@ tptp.semiri1408675320244567234ct_nat N)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((X4 tptp.nat)) X4)) (@ (@ tptp.set_or1269000886237332187st_nat (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat)) M2))))) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (@ (@ tptp.power_power_int _let_1) (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) _let_1))) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_real tptp.one_one_real))) (= (@ (@ tptp.power_power_real _let_1) (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) _let_1))) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))) (= (@ (@ tptp.power_power_complex _let_1) (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) _let_1))) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (= (@ (@ tptp.power_8256067586552552935nteger _let_1) (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) _let_1))) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_rat tptp.one_one_rat))) (= (@ (@ tptp.power_power_rat _let_1) (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) _let_1))) (forall ((A tptp.complex) (K2 tptp.nat)) (= (@ (@ tptp.gbinomial_complex (@ tptp.uminus1482373934393186551omplex A)) K2) (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) K2)) (@ (@ tptp.gbinomial_complex (@ (@ tptp.minus_minus_complex (@ (@ tptp.plus_plus_complex A) (@ tptp.semiri8010041392384452111omplex K2))) tptp.one_one_complex)) K2)))) (forall ((A tptp.rat) (K2 tptp.nat)) (= (@ (@ tptp.gbinomial_rat (@ tptp.uminus_uminus_rat A)) K2) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) K2)) (@ (@ tptp.gbinomial_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A) (@ tptp.semiri681578069525770553at_rat K2))) tptp.one_one_rat)) K2)))) (forall ((A tptp.real) (K2 tptp.nat)) (= (@ (@ tptp.gbinomial_real (@ tptp.uminus_uminus_real A)) K2) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) K2)) (@ (@ tptp.gbinomial_real (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A) (@ tptp.semiri5074537144036343181t_real K2))) tptp.one_one_real)) K2)))) (forall ((N tptp.nat) (K2 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)) K2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_ri631733984087533419it_int N) K2)) (@ (@ tptp.minus_minus_int K2) (@ _let_1 (@ tptp.suc N))))))) (forall ((B tptp.complex) (K2 tptp.nat)) (= (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.plus_plus_complex (@ (@ tptp.minus_minus_complex B) (@ tptp.semiri8010041392384452111omplex K2))) tptp.one_one_complex)) K2) (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) K2)) (@ (@ tptp.comm_s2602460028002588243omplex (@ tptp.uminus1482373934393186551omplex B)) K2)))) (forall ((B tptp.code_integer) (K2 tptp.nat)) (= (@ (@ tptp.comm_s8582702949713902594nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.minus_8373710615458151222nteger B) (@ tptp.semiri4939895301339042750nteger K2))) tptp.one_one_Code_integer)) K2) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) K2)) (@ (@ tptp.comm_s8582702949713902594nteger (@ tptp.uminus1351360451143612070nteger B)) K2)))) (forall ((B tptp.rat) (K2 tptp.nat)) (= (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.minus_minus_rat B) (@ tptp.semiri681578069525770553at_rat K2))) tptp.one_one_rat)) K2) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) K2)) (@ (@ tptp.comm_s4028243227959126397er_rat (@ tptp.uminus_uminus_rat B)) K2)))) (forall ((B tptp.real) (K2 tptp.nat)) (= (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.plus_plus_real (@ (@ tptp.minus_minus_real B) (@ tptp.semiri5074537144036343181t_real K2))) tptp.one_one_real)) K2) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) K2)) (@ (@ tptp.comm_s7457072308508201937r_real (@ tptp.uminus_uminus_real B)) K2)))) (forall ((B tptp.int) (K2 tptp.nat)) (= (@ (@ tptp.comm_s4660882817536571857er_int (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int B) (@ tptp.semiri1314217659103216013at_int K2))) tptp.one_one_int)) K2) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) K2)) (@ (@ tptp.comm_s4660882817536571857er_int (@ tptp.uminus_uminus_int B)) K2)))) (forall ((B tptp.complex) (K2 tptp.nat)) (= (@ (@ tptp.comm_s2602460028002588243omplex (@ tptp.uminus1482373934393186551omplex B)) K2) (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) K2)) (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.plus_plus_complex (@ (@ tptp.minus_minus_complex B) (@ tptp.semiri8010041392384452111omplex K2))) tptp.one_one_complex)) K2)))) (forall ((B tptp.code_integer) (K2 tptp.nat)) (= (@ (@ tptp.comm_s8582702949713902594nteger (@ tptp.uminus1351360451143612070nteger B)) K2) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) K2)) (@ (@ tptp.comm_s8582702949713902594nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.minus_8373710615458151222nteger B) (@ tptp.semiri4939895301339042750nteger K2))) tptp.one_one_Code_integer)) K2)))) (forall ((B tptp.rat) (K2 tptp.nat)) (= (@ (@ tptp.comm_s4028243227959126397er_rat (@ tptp.uminus_uminus_rat B)) K2) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) K2)) (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.minus_minus_rat B) (@ tptp.semiri681578069525770553at_rat K2))) tptp.one_one_rat)) K2)))) (forall ((B tptp.real) (K2 tptp.nat)) (= (@ (@ tptp.comm_s7457072308508201937r_real (@ tptp.uminus_uminus_real B)) K2) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) K2)) (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.plus_plus_real (@ (@ tptp.minus_minus_real B) (@ tptp.semiri5074537144036343181t_real K2))) tptp.one_one_real)) K2)))) (forall ((B tptp.int) (K2 tptp.nat)) (= (@ (@ tptp.comm_s4660882817536571857er_int (@ tptp.uminus_uminus_int B)) K2) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) K2)) (@ (@ tptp.comm_s4660882817536571857er_int (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int B) (@ tptp.semiri1314217659103216013at_int K2))) tptp.one_one_int)) K2)))) (forall ((P2 (-> tptp.int Bool)) (K2 tptp.int)) (=> (@ P2 tptp.zero_zero_int) (=> (@ P2 (@ tptp.uminus_uminus_int tptp.one_one_int)) (=> (forall ((K tptp.int)) (=> (@ P2 K) (=> (not (= K tptp.zero_zero_int)) (@ P2 (@ (@ tptp.times_times_int K) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))))) (=> (forall ((K tptp.int)) (=> (@ P2 K) (=> (not (= K (@ tptp.uminus_uminus_int tptp.one_one_int))) (@ P2 (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ (@ tptp.times_times_int K) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))))))) (@ P2 K2)))))) (forall ((A tptp.complex) (M2 tptp.nat)) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.gbinomial_complex A) K3)) (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) K3)))) (@ tptp.set_ord_atMost_nat M2)) (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) M2)) (@ (@ tptp.gbinomial_complex (@ (@ tptp.minus_minus_complex A) tptp.one_one_complex)) M2)))) (forall ((A tptp.rat) (M2 tptp.nat)) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.gbinomial_rat A) K3)) (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) K3)))) (@ tptp.set_ord_atMost_nat M2)) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) M2)) (@ (@ tptp.gbinomial_rat (@ (@ tptp.minus_minus_rat A) tptp.one_one_rat)) M2)))) (forall ((A tptp.real) (M2 tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.gbinomial_real A) K3)) (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) K3)))) (@ tptp.set_ord_atMost_nat M2)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) M2)) (@ (@ tptp.gbinomial_real (@ (@ tptp.minus_minus_real A) tptp.one_one_real)) M2)))) (forall ((A tptp.complex) (K2 tptp.nat)) (let ((_let_1 (@ tptp.suc K2))) (= (@ (@ tptp.gbinomial_complex A) _let_1) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.groups6464643781859351333omplex (lambda ((I tptp.nat)) (@ (@ tptp.minus_minus_complex A) (@ tptp.semiri8010041392384452111omplex I)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) K2))) (@ tptp.semiri5044797733671781792omplex _let_1))))) (forall ((A tptp.rat) (K2 tptp.nat)) (let ((_let_1 (@ tptp.suc K2))) (= (@ (@ tptp.gbinomial_rat A) _let_1) (@ (@ tptp.divide_divide_rat (@ (@ tptp.groups73079841787564623at_rat (lambda ((I tptp.nat)) (@ (@ tptp.minus_minus_rat A) (@ tptp.semiri681578069525770553at_rat I)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) K2))) (@ tptp.semiri773545260158071498ct_rat _let_1))))) (forall ((A tptp.real) (K2 tptp.nat)) (let ((_let_1 (@ tptp.suc K2))) (= (@ (@ tptp.gbinomial_real A) _let_1) (@ (@ tptp.divide_divide_real (@ (@ tptp.groups129246275422532515t_real (lambda ((I tptp.nat)) (@ (@ tptp.minus_minus_real A) (@ tptp.semiri5074537144036343181t_real I)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) K2))) (@ tptp.semiri2265585572941072030t_real _let_1))))) (forall ((A tptp.int) (K2 tptp.nat)) (let ((_let_1 (@ tptp.suc K2))) (= (@ (@ tptp.gbinomial_int A) _let_1) (@ (@ tptp.divide_divide_int (@ (@ tptp.groups705719431365010083at_int (lambda ((I tptp.nat)) (@ (@ tptp.minus_minus_int A) (@ tptp.semiri1314217659103216013at_int I)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) K2))) (@ tptp.semiri1406184849735516958ct_int _let_1))))) (forall ((A tptp.nat) (K2 tptp.nat)) (let ((_let_1 (@ tptp.suc K2))) (= (@ (@ tptp.gbinomial_nat A) _let_1) (@ (@ tptp.divide_divide_nat (@ (@ tptp.groups708209901874060359at_nat (lambda ((I tptp.nat)) (@ (@ tptp.minus_minus_nat A) (@ tptp.semiri1316708129612266289at_nat I)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) K2))) (@ tptp.semiri1408675320244567234ct_nat _let_1))))) (forall ((M2 tptp.nat) (A tptp.complex) (X tptp.complex) (Y tptp.complex)) (let ((_let_1 (@ tptp.set_ord_atMost_nat M2))) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ (@ tptp.gbinomial_complex (@ (@ tptp.plus_plus_complex (@ tptp.semiri8010041392384452111omplex M2)) A)) K3)) (@ (@ tptp.power_power_complex X) K3))) (@ (@ tptp.power_power_complex Y) (@ (@ tptp.minus_minus_nat M2) K3))))) _let_1) (@ (@ tptp.groups2073611262835488442omplex (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ (@ tptp.gbinomial_complex (@ tptp.uminus1482373934393186551omplex A)) K3)) (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex X)) K3))) (@ (@ tptp.power_power_complex (@ (@ tptp.plus_plus_complex X) Y)) (@ (@ tptp.minus_minus_nat M2) K3))))) _let_1)))) (forall ((M2 tptp.nat) (A tptp.rat) (X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.set_ord_atMost_nat M2))) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ (@ tptp.gbinomial_rat (@ (@ tptp.plus_plus_rat (@ tptp.semiri681578069525770553at_rat M2)) A)) K3)) (@ (@ tptp.power_power_rat X) K3))) (@ (@ tptp.power_power_rat Y) (@ (@ tptp.minus_minus_nat M2) K3))))) _let_1) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ (@ tptp.gbinomial_rat (@ tptp.uminus_uminus_rat A)) K3)) (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat X)) K3))) (@ (@ tptp.power_power_rat (@ (@ tptp.plus_plus_rat X) Y)) (@ (@ tptp.minus_minus_nat M2) K3))))) _let_1)))) (forall ((M2 tptp.nat) (A tptp.real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.set_ord_atMost_nat M2))) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.gbinomial_real (@ (@ tptp.plus_plus_real (@ tptp.semiri5074537144036343181t_real M2)) A)) K3)) (@ (@ tptp.power_power_real X) K3))) (@ (@ tptp.power_power_real Y) (@ (@ tptp.minus_minus_nat M2) K3))))) _let_1) (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.gbinomial_real (@ tptp.uminus_uminus_real A)) K3)) (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real X)) K3))) (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real X) Y)) (@ (@ tptp.minus_minus_nat M2) K3))))) _let_1)))) (forall ((N tptp.nat) (Z3 tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N) (= (= (@ (@ tptp.power_power_int Z3) N) A) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((I tptp.nat)) (@ (@ tptp.times_times_int (@ (@ (@ tptp.if_int (= I tptp.zero_zero_nat)) (@ tptp.uminus_uminus_int A)) (@ (@ (@ tptp.if_int (= I N)) tptp.one_one_int) tptp.zero_zero_int))) (@ (@ tptp.power_power_int Z3) I)))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_int)))) (forall ((N tptp.nat) (Z3 tptp.complex) (A tptp.complex)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N) (= (= (@ (@ tptp.power_power_complex Z3) N) A) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ (@ tptp.if_complex (= I tptp.zero_zero_nat)) (@ tptp.uminus1482373934393186551omplex A)) (@ (@ (@ tptp.if_complex (= I N)) tptp.one_one_complex) tptp.zero_zero_complex))) (@ (@ tptp.power_power_complex Z3) I)))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_complex)))) (forall ((N tptp.nat) (Z3 tptp.code_integer) (A tptp.code_integer)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N) (= (= (@ (@ tptp.power_8256067586552552935nteger Z3) N) A) (= (@ (@ tptp.groups7501900531339628137nteger (lambda ((I tptp.nat)) (@ (@ tptp.times_3573771949741848930nteger (@ (@ (@ tptp.if_Code_integer (= I tptp.zero_zero_nat)) (@ tptp.uminus1351360451143612070nteger A)) (@ (@ (@ tptp.if_Code_integer (= I N)) tptp.one_one_Code_integer) tptp.zero_z3403309356797280102nteger))) (@ (@ tptp.power_8256067586552552935nteger Z3) I)))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_z3403309356797280102nteger)))) (forall ((N tptp.nat) (Z3 tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N) (= (= (@ (@ tptp.power_power_rat Z3) N) A) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ (@ tptp.if_rat (= I tptp.zero_zero_nat)) (@ tptp.uminus_uminus_rat A)) (@ (@ (@ tptp.if_rat (= I N)) tptp.one_one_rat) tptp.zero_zero_rat))) (@ (@ tptp.power_power_rat Z3) I)))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_rat)))) (forall ((N tptp.nat) (Z3 tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N) (= (= (@ (@ tptp.power_power_real Z3) N) A) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I tptp.nat)) (@ (@ tptp.times_times_real (@ (@ (@ tptp.if_real (= I tptp.zero_zero_nat)) (@ tptp.uminus_uminus_real A)) (@ (@ (@ tptp.if_real (= I N)) tptp.one_one_real) tptp.zero_zero_real))) (@ (@ tptp.power_power_real Z3) I)))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_real)))) (forall ((N tptp.nat) (Z3 tptp.nat)) (let ((_let_1 (@ tptp.nat_set_decode Z3))) (=> (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)) Z3)) (@ (@ tptp.insert_nat N) _let_1))))) (forall ((N tptp.nat)) (=> (not (= N tptp.one_one_nat)) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) I)) (@ tptp.semiri8010041392384452111omplex I))) (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.binomial N) I))))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_complex))) (forall ((N tptp.nat)) (=> (not (= N tptp.one_one_nat)) (= (@ (@ tptp.groups7501900531339628137nteger (lambda ((I tptp.nat)) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) I)) (@ tptp.semiri4939895301339042750nteger I))) (@ tptp.semiri4939895301339042750nteger (@ (@ tptp.binomial N) I))))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_z3403309356797280102nteger))) (forall ((N tptp.nat)) (=> (not (= N tptp.one_one_nat)) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) I)) (@ tptp.semiri681578069525770553at_rat I))) (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.binomial N) I))))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_rat))) (forall ((N tptp.nat)) (=> (not (= N tptp.one_one_nat)) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((I tptp.nat)) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) I)) (@ tptp.semiri1314217659103216013at_int I))) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.binomial N) I))))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_int))) (forall ((N tptp.nat)) (=> (not (= N tptp.one_one_nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I)) (@ tptp.semiri5074537144036343181t_real I))) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.binomial N) I))))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_real))) _let_162 (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numera6690914467698888265omplex _let_1))) (let ((_let_3 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat _let_1)) N))) (= (@ tptp.semiri5044797733671781792omplex _let_3) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex _let_2) _let_3)) (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.divide1717551699836669952omplex tptp.one_one_complex) _let_2)) N))) (@ tptp.semiri5044797733671781792omplex N))))))) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_rat _let_1))) (let ((_let_3 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat _let_1)) N))) (= (@ tptp.semiri773545260158071498ct_rat _let_3) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat _let_2) _let_3)) (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.divide_divide_rat tptp.one_one_rat) _let_2)) N))) (@ tptp.semiri773545260158071498ct_rat N))))))) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_real _let_1))) (let ((_let_3 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat _let_1)) N))) (= (@ tptp.semiri2265585572941072030t_real _let_3) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real _let_2) _let_3)) (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_2)) N))) (@ tptp.semiri2265585572941072030t_real N))))))) (= tptp.binomial (lambda ((N4 tptp.nat) (K3 tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat N4) K3))) (let ((_let_2 (@ tptp.ord_less_nat N4))) (@ (@ (@ tptp.if_nat (@ _let_2 K3)) tptp.zero_zero_nat) (@ (@ (@ tptp.if_nat (@ _let_2 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) K3))) (@ (@ tptp.binomial N4) _let_1)) (@ (@ tptp.divide_divide_nat (@ (@ (@ (@ tptp.set_fo2584398358068434914at_nat tptp.times_times_nat) (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat)) N4) tptp.one_one_nat)) (@ tptp.semiri1408675320244567234ct_nat K3)))))))) (forall ((H tptp.real) (F2 (-> tptp.real tptp.real)) (J2 (-> tptp.nat tptp.real)) (N tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H) (exists ((B8 tptp.real)) (= (@ F2 H) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ J2 M6)) (@ tptp.semiri2265585572941072030t_real M6))) (@ (@ tptp.power_power_real H) M6)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real B8) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real H) N)) (@ tptp.semiri2265585572941072030t_real N)))))))) (forall ((X tptp.real) (N tptp.nat) (Diff (-> tptp.nat tptp.complex tptp.real))) (=> (= X tptp.zero_zero_real) (=> (not (= N tptp.zero_zero_nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M6) tptp.zero_zero_complex)) (@ tptp.semiri2265585572941072030t_real M6))) (@ (@ tptp.power_power_real X) M6)))) (@ tptp.set_ord_lessThan_nat N)) (@ (@ Diff tptp.zero_zero_nat) tptp.zero_zero_complex))))) (forall ((X tptp.real) (N tptp.nat) (Diff (-> tptp.nat tptp.real tptp.real))) (=> (= X tptp.zero_zero_real) (=> (not (= N tptp.zero_zero_nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M6) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M6))) (@ (@ tptp.power_power_real X) M6)))) (@ tptp.set_ord_lessThan_nat N)) (@ (@ Diff tptp.zero_zero_nat) tptp.zero_zero_real))))) (forall ((X tptp.real) (N tptp.nat) (Diff (-> tptp.nat tptp.rat tptp.real))) (=> (= X tptp.zero_zero_real) (=> (not (= N tptp.zero_zero_nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M6) tptp.zero_zero_rat)) (@ tptp.semiri2265585572941072030t_real M6))) (@ (@ tptp.power_power_real X) M6)))) (@ tptp.set_ord_lessThan_nat N)) (@ (@ Diff tptp.zero_zero_nat) tptp.zero_zero_rat))))) (forall ((X tptp.real) (N tptp.nat) (Diff (-> tptp.nat tptp.nat tptp.real))) (=> (= X tptp.zero_zero_real) (=> (not (= N tptp.zero_zero_nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M6) tptp.zero_zero_nat)) (@ tptp.semiri2265585572941072030t_real M6))) (@ (@ tptp.power_power_real X) M6)))) (@ tptp.set_ord_lessThan_nat N)) (@ (@ Diff tptp.zero_zero_nat) tptp.zero_zero_nat))))) (forall ((X tptp.real) (N tptp.nat) (Diff (-> tptp.nat tptp.int tptp.real))) (=> (= X tptp.zero_zero_real) (=> (not (= N tptp.zero_zero_nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M6) tptp.zero_zero_int)) (@ tptp.semiri2265585572941072030t_real M6))) (@ (@ tptp.power_power_real X) M6)))) (@ tptp.set_ord_lessThan_nat N)) (@ (@ Diff tptp.zero_zero_nat) tptp.zero_zero_int))))) _let_161 (forall ((N tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.suc M2))) (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 M2) N)))))))) (forall ((X tptp.real)) (@ (@ tptp.sums_real (lambda ((N4 tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N4)) tptp.one_one_nat))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N4)) (@ tptp.semiri2265585572941072030t_real _let_1))) (@ (@ tptp.power_power_real X) _let_1))))) (@ tptp.sin_real X))) (= tptp.bit_se725231765392027082nd_int (lambda ((K3 tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_int _let_1))) (let ((_let_3 (@ tptp.zero_n2684676970156552555ol_int (and (not (@ _let_2 K3)) (not (@ _let_2 L2)))))) (let ((_let_4 (@ (@ tptp.insert_int tptp.zero_zero_int) (@ (@ tptp.insert_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.bot_bot_set_int)))) (@ (@ (@ tptp.if_int (and (@ (@ tptp.member_int K3) _let_4) (@ (@ tptp.member_int L2) _let_4))) (@ tptp.uminus_uminus_int _let_3)) (@ (@ tptp.plus_plus_int _let_3) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se725231765392027082nd_int (@ (@ tptp.divide_divide_int K3) _let_1)) (@ (@ tptp.divide_divide_int L2) _let_1))))))))))) (= (@ tptp.sin_complex tptp.zero_zero_complex) tptp.zero_zero_complex) (= (@ tptp.sin_real tptp.zero_zero_real) tptp.zero_zero_real) (forall ((X tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int X) tptp.zero_zero_int) tptp.zero_zero_int)) (forall ((X tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.zero_zero_int) X) tptp.zero_zero_int)) (forall ((A tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.zero_zero_int) A) tptp.zero_zero_int)) (forall ((A tptp.nat)) (= (@ (@ tptp.bit_se727722235901077358nd_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)) (forall ((A tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int A) tptp.zero_zero_int) tptp.zero_zero_int)) (forall ((A tptp.nat)) (= (@ (@ tptp.bit_se727722235901077358nd_nat A) tptp.zero_zero_nat) tptp.zero_zero_nat)) (= (@ tptp.sin_coeff tptp.zero_zero_nat) tptp.zero_zero_real) (forall ((X tptp.num)) (= (@ (@ tptp.bit_se3949692690581998587nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 X))) tptp.one_one_Code_integer) tptp.zero_z3403309356797280102nteger)) (forall ((X tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 X))) tptp.one_one_int) tptp.zero_zero_int)) (forall ((X tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 X))) tptp.one_one_nat) tptp.zero_zero_nat)) (forall ((Y tptp.num)) (= (@ (@ tptp.bit_se3949692690581998587nteger tptp.one_one_Code_integer) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 Y))) tptp.zero_z3403309356797280102nteger)) (forall ((Y tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 Y))) tptp.zero_zero_int)) (forall ((Y tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Y))) tptp.zero_zero_nat)) (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 X))) (@ tptp.numeral_numeral_int (@ tptp.bit0 Y))) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int X)) (@ tptp.numeral_numeral_int Y))))) (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 X))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Y))) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat X)) (@ tptp.numeral_numeral_nat Y))))) (= tptp.bit_se725231765392027082nd_int (lambda ((K3 tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_int _let_1))) (@ (@ tptp.plus_plus_int (@ tptp.zero_n2684676970156552555ol_int (and (not (@ _let_2 K3)) (not (@ _let_2 L2))))) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se725231765392027082nd_int (@ (@ tptp.divide_divide_int K3) _let_1)) (@ (@ tptp.divide_divide_int L2) _let_1)))))))) (= tptp.bit_se725231765392027082nd_int (lambda ((K3 tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.uminus_uminus_int tptp.one_one_int))) (@ (@ (@ tptp.if_int (or (= K3 tptp.zero_zero_int) (= L2 tptp.zero_zero_int))) tptp.zero_zero_int) (@ (@ (@ tptp.if_int (= K3 _let_2)) L2) (@ (@ (@ tptp.if_int (= L2 _let_2)) K3) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.modulo_modulo_int K3) _let_1)) (@ (@ tptp.modulo_modulo_int L2) _let_1))) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se725231765392027082nd_int (@ (@ tptp.divide_divide_int K3) _let_1)) (@ (@ tptp.divide_divide_int L2) _let_1))))))))))) (forall ((X tptp.int) (Xa2 tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_int _let_1))) (let ((_let_3 (@ tptp.zero_n2684676970156552555ol_int (and (not (@ _let_2 X)) (not (@ _let_2 Xa2)))))) (let ((_let_4 (@ (@ tptp.insert_int tptp.zero_zero_int) (@ (@ tptp.insert_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.bot_bot_set_int)))) (let ((_let_5 (and (@ (@ tptp.member_int X) _let_4) (@ (@ tptp.member_int Xa2) _let_4)))) (=> (= (@ (@ tptp.bit_se725231765392027082nd_int X) Xa2) Y) (and (=> _let_5 (= Y (@ tptp.uminus_uminus_int _let_3))) (=> (not _let_5) (= Y (@ (@ tptp.plus_plus_int _let_3) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se725231765392027082nd_int (@ (@ tptp.divide_divide_int X) _let_1)) (@ (@ tptp.divide_divide_int Xa2) _let_1)))))))))))))) (forall ((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 ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.sin_coeff M6)) (@ (@ tptp.power_power_real X) M6)))) (@ 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))))))))) (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 ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.sin_coeff M6)) (@ (@ tptp.power_power_real X) M6)))) (@ 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)))))))) (forall ((N tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.cos_coeff M6)) (@ (@ tptp.power_power_real tptp.zero_zero_real) M6)))) (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) tptp.one_one_real)) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ tptp.sin_real (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat _let_1)) N)))) tptp.pi)) (@ tptp.numeral_numeral_real _let_1))) (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N)))) (forall ((X tptp.real) (N tptp.nat)) (exists ((T6 tptp.real)) (= (@ tptp.sin_real X) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.sin_coeff M6)) (@ (@ tptp.power_power_real X) M6)))) (@ tptp.set_ord_lessThan_nat 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)))))) (forall ((N tptp.nat) (K2 tptp.num)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.suc N)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 K2)))) (@ (@ 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 K2))) tptp.one_one_int))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) tptp.one_one_int))) (forall ((M2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.times_times_num (@ tptp.bit1 M2)))) (= (@ _let_1 (@ tptp.bit0 N)) (@ tptp.bit0 (@ _let_1 N))))) (forall ((M2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.bit1 N))) (= (@ (@ tptp.times_times_num (@ tptp.bit0 M2)) _let_1) (@ tptp.bit0 (@ (@ tptp.times_times_num M2) _let_1))))) (= (@ tptp.cos_coeff tptp.zero_zero_nat) tptp.one_one_real) (forall ((K2 tptp.num)) (= (@ tptp.neg_nu8557863876264182079omplex (@ tptp.numera6690914467698888265omplex K2)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit1 K2)))) (forall ((K2 tptp.num)) (= (@ tptp.neg_nu8295874005876285629c_real (@ tptp.numeral_numeral_real K2)) (@ tptp.numeral_numeral_real (@ tptp.bit1 K2)))) (forall ((K2 tptp.num)) (= (@ tptp.neg_nu5851722552734809277nc_int (@ tptp.numeral_numeral_int K2)) (@ tptp.numeral_numeral_int (@ tptp.bit1 K2)))) (forall ((Y tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Y))) tptp.zero_zero_nat)) (forall ((X tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 X))) (@ tptp.suc tptp.zero_zero_nat)) tptp.zero_zero_nat)) (forall ((V2 tptp.num) (W2 tptp.num)) (= (@ (@ tptp.divide_divide_int (@ tptp.numeral_numeral_int (@ tptp.bit1 V2))) (@ tptp.numeral_numeral_int (@ tptp.bit0 W2))) (@ (@ tptp.divide_divide_int (@ tptp.numeral_numeral_int V2)) (@ tptp.numeral_numeral_int W2)))) (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_num (@ tptp.bit1 M2)) (@ tptp.bit1 N)) (@ tptp.bit1 (@ (@ tptp.plus_plus_num (@ (@ tptp.plus_plus_num M2) N)) (@ tptp.bit0 (@ (@ tptp.times_times_num M2) N)))))) (forall ((X tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 X))) (@ tptp.suc tptp.zero_zero_nat)) tptp.one_one_nat)) (forall ((Y tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y))) tptp.one_one_nat)) (forall ((N tptp.nat)) (= (@ tptp.sin_real (@ (@ tptp.times_times_real tptp.pi) (@ tptp.semiri5074537144036343181t_real N))) tptp.zero_zero_real)) (forall ((N tptp.nat)) (= (@ tptp.sin_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) tptp.pi)) tptp.zero_zero_real)) (= (@ tptp.neg_nu5831290666863070958nteger tptp.one_one_Code_integer) _let_158) (= (@ tptp.neg_nu8557863876264182079omplex tptp.one_one_complex) _let_159) (= (@ tptp.neg_nu8295874005876285629c_real tptp.one_one_real) _let_135) (= (@ tptp.neg_nu5851722552734809277nc_int tptp.one_one_int) _let_160) (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 X))) (@ tptp.numeral_numeral_int (@ tptp.bit1 Y))) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int X)) (@ tptp.numeral_numeral_int Y))))) (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 X))) (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y))) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat X)) (@ tptp.numeral_numeral_nat Y))))) (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit1 X))) (@ tptp.numeral_numeral_int (@ tptp.bit0 Y))) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int X)) (@ tptp.numeral_numeral_int Y))))) (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 X))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Y))) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat X)) (@ tptp.numeral_numeral_nat Y))))) (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.suc tptp.zero_zero_nat)) N) (@ (@ tptp.modulo_modulo_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se727722235901077358nd_nat N) (@ tptp.suc tptp.zero_zero_nat)) (@ (@ tptp.modulo_modulo_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat M2))) (= (@ _let_1 (@ tptp.suc (@ tptp.suc (@ tptp.suc N)))) (@ _let_1 (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) N))))) (forall ((M2 tptp.nat) (V2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat V2))) (= (@ (@ tptp.divide_divide_nat (@ tptp.suc (@ tptp.suc (@ tptp.suc M2)))) _let_1) (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) M2)) _let_1)))) (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.modulo_modulo_nat M2))) (= (@ _let_1 (@ tptp.suc (@ tptp.suc (@ tptp.suc N)))) (@ _let_1 (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) N))))) (forall ((M2 tptp.nat) (V2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat V2))) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ tptp.suc (@ tptp.suc M2)))) _let_1) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) M2)) _let_1)))) (= (@ tptp.neg_nu3811975205180677377ec_int _let_153) (@ tptp.uminus_uminus_int _let_160)) (= (@ tptp.neg_nu6075765906172075777c_real _let_152) (@ tptp.uminus_uminus_real _let_135)) (= (@ tptp.neg_nu6511756317524482435omplex _let_104) (@ tptp.uminus1482373934393186551omplex _let_159)) (= (@ tptp.neg_nu7757733837767384882nteger _let_151) (@ tptp.uminus1351360451143612070nteger _let_158)) (= (@ tptp.neg_nu3179335615603231917ec_rat _let_150) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat _let_129))) (= (@ tptp.sin_real _let_112) tptp.zero_zero_real) (forall ((X tptp.real)) (= (@ tptp.sin_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) X)) (@ tptp.uminus_uminus_real (@ tptp.sin_real X)))) (forall ((X tptp.real)) (= (@ tptp.sin_real (@ (@ tptp.plus_plus_real X) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi))) (@ tptp.sin_real X))) (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se3949692690581998587nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 X))) (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 Y))) (@ (@ tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se3949692690581998587nteger (@ tptp.numera6620942414471956472nteger X)) (@ tptp.numera6620942414471956472nteger Y)))))) (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit1 X))) (@ tptp.numeral_numeral_int (@ tptp.bit1 Y))) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int X)) (@ tptp.numeral_numeral_int Y)))))) (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 X))) (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y))) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat X)) (@ tptp.numeral_numeral_nat Y)))))) (forall ((V2 tptp.num) (W2 tptp.num)) (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit1 V2))) (@ tptp.numeral_numeral_int (@ tptp.bit0 W2))) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int V2)) (@ tptp.numeral_numeral_int W2)))) tptp.one_one_int))) (forall ((N tptp.nat)) (= (@ tptp.sin_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ tptp.semiri5074537144036343181t_real N))) tptp.pi)) tptp.zero_zero_real)) (forall ((N tptp.nat) (K2 tptp.num)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.suc N)) (@ tptp.numeral_numeral_int (@ tptp.bit1 K2))) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.bit_ri631733984087533419it_int N) (@ tptp.numeral_numeral_int K2))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) tptp.one_one_int))) (= (@ tptp.sin_real _let_149) _let_152) (forall ((Y tptp.num)) (=> (not (= Y tptp.one)) (=> (forall ((X23 tptp.num)) (not (= Y (@ tptp.bit0 X23)))) (not (forall ((X32 tptp.num)) (not (= Y (@ tptp.bit1 X32)))))))) (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger N))) (= (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 N)) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.plus_p5714425477246183910nteger _let_1) _let_1)) tptp.one_one_Code_integer)))) (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat N))) (= (@ tptp.numeral_numeral_rat (@ tptp.bit1 N)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.plus_plus_rat _let_1) _let_1)) tptp.one_one_rat)))) (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numera1916890842035813515d_enat N))) (= (@ tptp.numera1916890842035813515d_enat (@ tptp.bit1 N)) (@ (@ tptp.plus_p3455044024723400733d_enat (@ (@ tptp.plus_p3455044024723400733d_enat _let_1) _let_1)) tptp.one_on7984719198319812577d_enat)))) (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex N))) (= (@ tptp.numera6690914467698888265omplex (@ tptp.bit1 N)) (@ (@ tptp.plus_plus_complex (@ (@ tptp.plus_plus_complex _let_1) _let_1)) tptp.one_one_complex)))) (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real N))) (= (@ tptp.numeral_numeral_real (@ tptp.bit1 N)) (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real _let_1) _let_1)) tptp.one_one_real)))) (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N))) (= (@ tptp.numeral_numeral_nat (@ tptp.bit1 N)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat _let_1) _let_1)) tptp.one_one_nat)))) (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (= (@ tptp.numeral_numeral_int (@ tptp.bit1 N)) (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int _let_1) _let_1)) tptp.one_one_int)))) (forall ((N tptp.num)) (= (@ tptp.numeral_numeral_nat (@ tptp.bit1 N)) (@ tptp.suc (@ tptp.numeral_numeral_nat (@ tptp.bit0 N))))) (forall ((M2 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 M2))) _let_2) (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 N))) _let_2)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat M2)) _let_1) (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat N)) _let_1)))))) (forall ((M2 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 M2))) _let_2) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N))) _let_2)) (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int M2)) _let_1) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int N)) _let_1)))))) (forall ((M2 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 M2))) _let_1) (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 N))) _let_1))))) (forall ((M2 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 M2))) _let_1) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N))) _let_1))))) (forall ((M2 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 M2))) _let_1) (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 N))) _let_1))))) (forall ((M2 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 M2))) _let_1) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N))) _let_1))))) (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger N))) (= (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 N)) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.plus_p5714425477246183910nteger _let_1) _let_1)) tptp.one_one_Code_integer)))) (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat N))) (= (@ tptp.numeral_numeral_rat (@ tptp.bit1 N)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.plus_plus_rat _let_1) _let_1)) tptp.one_one_rat)))) (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numera1916890842035813515d_enat N))) (= (@ tptp.numera1916890842035813515d_enat (@ tptp.bit1 N)) (@ (@ tptp.plus_p3455044024723400733d_enat (@ (@ tptp.plus_p3455044024723400733d_enat _let_1) _let_1)) tptp.one_on7984719198319812577d_enat)))) (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex N))) (= (@ tptp.numera6690914467698888265omplex (@ tptp.bit1 N)) (@ (@ tptp.plus_plus_complex (@ (@ tptp.plus_plus_complex _let_1) _let_1)) tptp.one_one_complex)))) (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real N))) (= (@ tptp.numeral_numeral_real (@ tptp.bit1 N)) (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real _let_1) _let_1)) tptp.one_one_real)))) (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N))) (= (@ tptp.numeral_numeral_nat (@ tptp.bit1 N)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat _let_1) _let_1)) tptp.one_one_nat)))) (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (= (@ tptp.numeral_numeral_int (@ tptp.bit1 N)) (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int _let_1) _let_1)) tptp.one_one_int)))) (forall ((Z3 tptp.complex) (W2 tptp.num)) (let ((_let_1 (@ tptp.power_power_complex Z3))) (let ((_let_2 (@ _let_1 (@ tptp.numeral_numeral_nat W2)))) (= (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 W2))) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex Z3) _let_2)) _let_2))))) (forall ((Z3 tptp.real) (W2 tptp.num)) (let ((_let_1 (@ tptp.power_power_real Z3))) (let ((_let_2 (@ _let_1 (@ tptp.numeral_numeral_nat W2)))) (= (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 W2))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real Z3) _let_2)) _let_2))))) (forall ((Z3 tptp.rat) (W2 tptp.num)) (let ((_let_1 (@ tptp.power_power_rat Z3))) (let ((_let_2 (@ _let_1 (@ tptp.numeral_numeral_nat W2)))) (= (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 W2))) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat Z3) _let_2)) _let_2))))) (forall ((Z3 tptp.nat) (W2 tptp.num)) (let ((_let_1 (@ tptp.power_power_nat Z3))) (let ((_let_2 (@ _let_1 (@ tptp.numeral_numeral_nat W2)))) (= (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 W2))) (@ (@ tptp.times_times_nat (@ (@ tptp.times_times_nat Z3) _let_2)) _let_2))))) (forall ((Z3 tptp.int) (W2 tptp.num)) (let ((_let_1 (@ tptp.power_power_int Z3))) (let ((_let_2 (@ _let_1 (@ tptp.numeral_numeral_nat W2)))) (= (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 W2))) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int Z3) _let_2)) _let_2))))) (forall ((N tptp.num) (Q2 tptp.num)) (not (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 N))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Q2))) tptp.zero_zero_nat))) (forall ((N tptp.num) (Q2 tptp.num)) (not (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N))) (@ tptp.numeral_numeral_int (@ tptp.bit0 Q2))) tptp.zero_zero_int))) (forall ((A tptp.complex)) (= (@ (@ tptp.power_power_complex A) (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex A) A)) A))) (forall ((A tptp.real)) (= (@ (@ tptp.power_power_real A) (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real A) A)) A))) (forall ((A tptp.rat)) (= (@ (@ tptp.power_power_rat A) (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat A) A)) A))) (forall ((A tptp.nat)) (= (@ (@ tptp.power_power_nat A) (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) (@ (@ tptp.times_times_nat (@ (@ tptp.times_times_nat A) A)) A))) (forall ((A tptp.int)) (= (@ (@ tptp.power_power_int A) (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int A) A)) A))) (= (@ tptp.numeral_numeral_nat _let_129) (@ tptp.suc _let_114)) (forall ((N tptp.nat)) (= (@ tptp.suc (@ tptp.suc (@ tptp.suc N))) (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) N))) (forall ((X33 tptp.num)) (= (@ tptp.size_size_num (@ tptp.bit1 X33)) (@ (@ tptp.plus_plus_nat (@ tptp.size_size_num X33)) (@ tptp.suc tptp.zero_zero_nat)))) (forall ((Q2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 Q2)))) (= (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat tptp.one)) _let_1) (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 N))) _let_1)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat N)) (@ tptp.numeral_numeral_nat Q2)) tptp.zero_zero_nat)))) (forall ((Q2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 Q2)))) (= (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int tptp.one)) _let_1) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N))) _let_1)) (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int N)) (@ tptp.numeral_numeral_int Q2)) tptp.zero_zero_int)))) (forall ((M2 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 M2))) _let_1) (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat tptp.one)) _let_1)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat M2)) (@ tptp.numeral_numeral_nat Q2)) tptp.zero_zero_nat)))) (forall ((M2 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 M2))) _let_1) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int tptp.one)) _let_1)) (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int M2)) (@ tptp.numeral_numeral_int Q2)) tptp.zero_zero_int)))) (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.divide_divide_nat (@ tptp.suc (@ tptp.suc (@ tptp.suc M2)))) N) (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) M2)) N))) (forall ((S3 tptp.set_complex)) (= (= (@ tptp.finite_card_complex S3) (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) (exists ((X4 tptp.complex) (Y4 tptp.complex) (Z4 tptp.complex)) (and (= S3 (@ (@ tptp.insert_complex X4) (@ (@ tptp.insert_complex Y4) (@ (@ tptp.insert_complex Z4) tptp.bot_bot_set_complex)))) (not (= X4 Y4)) (not (= Y4 Z4)) (not (= X4 Z4)))))) (forall ((S3 tptp.set_list_nat)) (= (= (@ tptp.finite_card_list_nat S3) (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) (exists ((X4 tptp.list_nat) (Y4 tptp.list_nat) (Z4 tptp.list_nat)) (and (= S3 (@ (@ tptp.insert_list_nat X4) (@ (@ tptp.insert_list_nat Y4) (@ (@ tptp.insert_list_nat Z4) tptp.bot_bot_set_list_nat)))) (not (= X4 Y4)) (not (= Y4 Z4)) (not (= X4 Z4)))))) (forall ((S3 tptp.set_set_nat)) (= (= (@ tptp.finite_card_set_nat S3) (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) (exists ((X4 tptp.set_nat) (Y4 tptp.set_nat) (Z4 tptp.set_nat)) (and (= S3 (@ (@ tptp.insert_set_nat X4) (@ (@ tptp.insert_set_nat Y4) (@ (@ tptp.insert_set_nat Z4) tptp.bot_bot_set_set_nat)))) (not (= X4 Y4)) (not (= Y4 Z4)) (not (= X4 Z4)))))) (forall ((S3 tptp.set_nat)) (= (= (@ tptp.finite_card_nat S3) (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) (exists ((X4 tptp.nat) (Y4 tptp.nat) (Z4 tptp.nat)) (and (= S3 (@ (@ tptp.insert_nat X4) (@ (@ tptp.insert_nat Y4) (@ (@ tptp.insert_nat Z4) tptp.bot_bot_set_nat)))) (not (= X4 Y4)) (not (= Y4 Z4)) (not (= X4 Z4)))))) (forall ((S3 tptp.set_int)) (= (= (@ tptp.finite_card_int S3) (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) (exists ((X4 tptp.int) (Y4 tptp.int) (Z4 tptp.int)) (and (= S3 (@ (@ tptp.insert_int X4) (@ (@ tptp.insert_int Y4) (@ (@ tptp.insert_int Z4) tptp.bot_bot_set_int)))) (not (= X4 Y4)) (not (= Y4 Z4)) (not (= X4 Z4)))))) (forall ((S3 tptp.set_real)) (= (= (@ tptp.finite_card_real S3) (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) (exists ((X4 tptp.real) (Y4 tptp.real) (Z4 tptp.real)) (and (= S3 (@ (@ tptp.insert_real X4) (@ (@ tptp.insert_real Y4) (@ (@ tptp.insert_real Z4) tptp.bot_bot_set_real)))) (not (= X4 Y4)) (not (= Y4 Z4)) (not (= X4 Z4)))))) (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ tptp.suc (@ tptp.suc M2)))) N) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) M2)) N))) (forall ((M2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ (@ tptp.modulo_modulo_nat M2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 _let_1))))) (or (= _let_2 tptp.zero_zero_nat) (= _let_2 tptp.one_one_nat) (= _let_2 (@ tptp.numeral_numeral_nat _let_1)) (= _let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))))))) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_112)) tptp.pi) (forall ((N tptp.nat)) (=> (not (= N tptp.zero_zero_nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.sin_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.semiri5074537144036343181t_real N)))))) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (= (@ tptp.sin_coeff _let_1) (@ (@ tptp.divide_divide_real (@ tptp.cos_coeff N)) (@ tptp.semiri5074537144036343181t_real _let_1))))) (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.pi) X) (=> (@ (@ tptp.ord_less_real X) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) (@ (@ tptp.ord_less_real (@ tptp.sin_real X)) tptp.zero_zero_real)))) (= tptp.bit_se727722235901077358nd_nat (lambda ((M6 tptp.nat) (N4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_nat (or (= M6 tptp.zero_zero_nat) (= N4 tptp.zero_zero_nat))) tptp.zero_zero_nat) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.modulo_modulo_nat M6) _let_1)) (@ (@ tptp.modulo_modulo_nat N4) _let_1))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se727722235901077358nd_nat (@ (@ tptp.divide_divide_nat M6) _let_1)) (@ (@ tptp.divide_divide_nat N4) _let_1)))))))) (= tptp.bit_se727722235901077358nd_nat (lambda ((M6 tptp.nat) (N4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_nat _let_1))) (@ (@ tptp.plus_plus_nat (@ tptp.zero_n2687167440665602831ol_nat (and (not (@ _let_2 M6)) (not (@ _let_2 N4))))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se727722235901077358nd_nat (@ (@ tptp.divide_divide_nat M6) _let_1)) (@ (@ tptp.divide_divide_nat N4) _let_1)))))))) (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.pi) X) (=> (@ (@ tptp.ord_less_real X) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) (@ (@ tptp.ord_less_eq_real (@ tptp.sin_real X)) tptp.zero_zero_real)))) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (= (@ tptp.cos_coeff _let_1) (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real (@ tptp.sin_coeff N))) (@ tptp.semiri5074537144036343181t_real _let_1))))) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (=> (= (@ (@ tptp.modulo_modulo_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 _let_1))) (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) (not (@ (@ tptp.dvd_dvd_nat _let_2) (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat))) _let_2))))))) (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.sin_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.semiri5074537144036343181t_real N)))))) (forall ((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)))))))))) (forall ((X tptp.real)) (= (= (@ tptp.sin_real X) tptp.zero_zero_real) (or (exists ((N4 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (and (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat _let_1)) N4) (= X (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N4)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1))))))) (exists ((N4 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (and (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat _let_1)) N4) (= X (@ tptp.uminus_uminus_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N4)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1))))))))))) (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 ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.cos_coeff M6)) (@ (@ tptp.power_power_real X) M6)))) (@ 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))))))))) (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 ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.cos_coeff M6)) (@ (@ tptp.power_power_real X) M6)))) (@ 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))))))))) (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 ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.sin_coeff M6)) (@ (@ tptp.power_power_real X) M6)))) (@ 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))))))) (forall ((L tptp.num) (K2 tptp.num)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.numeral_numeral_nat L)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 K2)))) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.pred_numeral L)) (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K2))) tptp.one_one_int))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) tptp.one_one_int))) (forall ((M2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.bit1 N))) (let ((_let_2 (@ tptp.bit1 M2))) (let ((_let_3 (@ tptp.unique5055182867167087721od_nat _let_2))) (let ((_let_4 (@ _let_3 _let_1))) (let ((_let_5 (@ (@ tptp.ord_less_num M2) N))) (and (=> _let_5 (= _let_4 (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat _let_2)))) (=> (not _let_5) (= _let_4 (@ (@ tptp.unique5026877609467782581ep_nat _let_1) (@ _let_3 (@ tptp.bit0 _let_1)))))))))))) (forall ((M2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.bit1 N))) (let ((_let_2 (@ tptp.bit1 M2))) (let ((_let_3 (@ tptp.unique5052692396658037445od_int _let_2))) (let ((_let_4 (@ _let_3 _let_1))) (let ((_let_5 (@ (@ tptp.ord_less_num M2) N))) (and (=> _let_5 (= _let_4 (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) (@ tptp.numeral_numeral_int _let_2)))) (=> (not _let_5) (= _let_4 (@ (@ tptp.unique5024387138958732305ep_int _let_1) (@ _let_3 (@ tptp.bit0 _let_1)))))))))))) (forall ((M2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.bit1 N))) (let ((_let_2 (@ tptp.bit1 M2))) (let ((_let_3 (@ tptp.unique3479559517661332726nteger _let_2))) (let ((_let_4 (@ _let_3 _let_1))) (let ((_let_5 (@ (@ tptp.ord_less_num M2) N))) (and (=> _let_5 (= _let_4 (@ (@ tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger) (@ tptp.numera6620942414471956472nteger _let_2)))) (=> (not _let_5) (= _let_4 (@ (@ tptp.unique4921790084139445826nteger _let_1) (@ _let_3 (@ tptp.bit0 _let_1)))))))))))) (forall ((M2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.bit1 N))) (let ((_let_2 (@ tptp.bit0 M2))) (let ((_let_3 (@ tptp.unique5055182867167087721od_nat _let_2))) (let ((_let_4 (@ _let_3 _let_1))) (let ((_let_5 (@ (@ tptp.ord_less_eq_num M2) N))) (and (=> _let_5 (= _let_4 (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat _let_2)))) (=> (not _let_5) (= _let_4 (@ (@ tptp.unique5026877609467782581ep_nat _let_1) (@ _let_3 (@ tptp.bit0 _let_1)))))))))))) (forall ((M2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.bit1 N))) (let ((_let_2 (@ tptp.bit0 M2))) (let ((_let_3 (@ tptp.unique5052692396658037445od_int _let_2))) (let ((_let_4 (@ _let_3 _let_1))) (let ((_let_5 (@ (@ tptp.ord_less_eq_num M2) N))) (and (=> _let_5 (= _let_4 (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) (@ tptp.numeral_numeral_int _let_2)))) (=> (not _let_5) (= _let_4 (@ (@ tptp.unique5024387138958732305ep_int _let_1) (@ _let_3 (@ tptp.bit0 _let_1)))))))))))) (forall ((M2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.bit1 N))) (let ((_let_2 (@ tptp.bit0 M2))) (let ((_let_3 (@ tptp.unique3479559517661332726nteger _let_2))) (let ((_let_4 (@ _let_3 _let_1))) (let ((_let_5 (@ (@ tptp.ord_less_eq_num M2) N))) (and (=> _let_5 (= _let_4 (@ (@ tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger) (@ tptp.numera6620942414471956472nteger _let_2)))) (=> (not _let_5) (= _let_4 (@ (@ tptp.unique4921790084139445826nteger _let_1) (@ _let_3 (@ tptp.bit0 _let_1)))))))))))) (forall ((A tptp.real)) (let ((_let_1 (@ tptp.abs_abs_real A))) (= (@ tptp.abs_abs_real _let_1) _let_1))) (forall ((A tptp.int)) (let ((_let_1 (@ tptp.abs_abs_int A))) (= (@ tptp.abs_abs_int _let_1) _let_1))) (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.abs_abs_Code_integer A))) (= (@ tptp.abs_abs_Code_integer _let_1) _let_1))) (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.abs_abs_rat A))) (= (@ tptp.abs_abs_rat _let_1) _let_1))) (forall ((A tptp.real)) (let ((_let_1 (@ tptp.abs_abs_real A))) (= (@ tptp.abs_abs_real _let_1) _let_1))) (forall ((A tptp.int)) (let ((_let_1 (@ tptp.abs_abs_int A))) (= (@ tptp.abs_abs_int _let_1) _let_1))) (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.abs_abs_Code_integer A))) (= (@ tptp.abs_abs_Code_integer _let_1) _let_1))) (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.abs_abs_rat A))) (= (@ tptp.abs_abs_rat _let_1) _let_1))) _let_157 (= (@ tptp.abs_abs_complex tptp.zero_zero_complex) tptp.zero_zero_complex) _let_156 _let_155 _let_154 (forall ((A tptp.code_integer)) (= (= tptp.zero_z3403309356797280102nteger (@ tptp.abs_abs_Code_integer A)) (= A tptp.zero_z3403309356797280102nteger))) (forall ((A tptp.real)) (= (= tptp.zero_zero_real (@ tptp.abs_abs_real A)) (= A tptp.zero_zero_real))) (forall ((A tptp.rat)) (= (= tptp.zero_zero_rat (@ tptp.abs_abs_rat A)) (= A tptp.zero_zero_rat))) (forall ((A tptp.int)) (= (= tptp.zero_zero_int (@ tptp.abs_abs_int A)) (= A tptp.zero_zero_int))) (forall ((A tptp.code_integer)) (= (= (@ tptp.abs_abs_Code_integer A) tptp.zero_z3403309356797280102nteger) (= A tptp.zero_z3403309356797280102nteger))) (forall ((A tptp.real)) (= (= (@ tptp.abs_abs_real A) tptp.zero_zero_real) (= A tptp.zero_zero_real))) (forall ((A tptp.rat)) (= (= (@ tptp.abs_abs_rat A) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))) (forall ((A tptp.int)) (= (= (@ tptp.abs_abs_int A) tptp.zero_zero_int) (= A tptp.zero_zero_int))) _let_157 _let_156 _let_155 _let_154 (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger N))) (= (@ tptp.abs_abs_Code_integer _let_1) _let_1))) (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat N))) (= (@ tptp.abs_abs_rat _let_1) _let_1))) (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real N))) (= (@ tptp.abs_abs_real _let_1) _let_1))) (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (= (@ tptp.abs_abs_int _let_1) _let_1))) (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.abs_abs_Code_integer A))) (= (@ (@ tptp.times_3573771949741848930nteger _let_1) _let_1) (@ (@ tptp.times_3573771949741848930nteger A) A)))) (forall ((A tptp.real)) (let ((_let_1 (@ tptp.abs_abs_real A))) (= (@ (@ tptp.times_times_real _let_1) _let_1) (@ (@ tptp.times_times_real A) A)))) (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.abs_abs_rat A))) (= (@ (@ tptp.times_times_rat _let_1) _let_1) (@ (@ tptp.times_times_rat A) A)))) (forall ((A tptp.int)) (let ((_let_1 (@ tptp.abs_abs_int A))) (= (@ (@ tptp.times_times_int _let_1) _let_1) (@ (@ tptp.times_times_int A) A)))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.abs_abs_Code_integer A)) (@ tptp.abs_abs_Code_integer B)))) (= (@ tptp.abs_abs_Code_integer _let_1) _let_1))) (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ (@ tptp.plus_plus_real (@ tptp.abs_abs_real A)) (@ tptp.abs_abs_real B)))) (= (@ tptp.abs_abs_real _let_1) _let_1))) (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ (@ tptp.plus_plus_rat (@ tptp.abs_abs_rat A)) (@ tptp.abs_abs_rat B)))) (= (@ tptp.abs_abs_rat _let_1) _let_1))) (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ (@ tptp.plus_plus_int (@ tptp.abs_abs_int A)) (@ tptp.abs_abs_int B)))) (= (@ tptp.abs_abs_int _let_1) _let_1))) _let_148 _let_147 (= (@ tptp.abs_abs_complex tptp.one_one_complex) tptp.one_one_complex) _let_146 _let_145 (forall ((A tptp.int)) (= (@ tptp.abs_abs_int (@ tptp.uminus_uminus_int A)) (@ tptp.abs_abs_int A))) (forall ((A tptp.real)) (= (@ tptp.abs_abs_real (@ tptp.uminus_uminus_real A)) (@ tptp.abs_abs_real A))) (forall ((A tptp.code_integer)) (= (@ tptp.abs_abs_Code_integer (@ tptp.uminus1351360451143612070nteger A)) (@ tptp.abs_abs_Code_integer A))) (forall ((A tptp.rat)) (= (@ tptp.abs_abs_rat (@ tptp.uminus_uminus_rat A)) (@ tptp.abs_abs_rat A))) (forall ((A tptp.int)) (= (@ tptp.abs_abs_int (@ tptp.uminus_uminus_int A)) (@ tptp.abs_abs_int A))) (forall ((A tptp.real)) (= (@ tptp.abs_abs_real (@ tptp.uminus_uminus_real A)) (@ tptp.abs_abs_real A))) (forall ((A tptp.complex)) (= (@ tptp.abs_abs_complex (@ tptp.uminus1482373934393186551omplex A)) (@ tptp.abs_abs_complex A))) (forall ((A tptp.code_integer)) (= (@ tptp.abs_abs_Code_integer (@ tptp.uminus1351360451143612070nteger A)) (@ tptp.abs_abs_Code_integer A))) (forall ((A tptp.rat)) (= (@ tptp.abs_abs_rat (@ tptp.uminus_uminus_rat A)) (@ tptp.abs_abs_rat A))) (forall ((M2 tptp.real) (K2 tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real M2))) (= (@ _let_1 (@ tptp.abs_abs_real K2)) (@ _let_1 K2)))) (forall ((M2 tptp.int) (K2 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int M2))) (= (@ _let_1 (@ tptp.abs_abs_int K2)) (@ _let_1 K2)))) (forall ((M2 tptp.code_integer) (K2 tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer M2))) (= (@ _let_1 (@ tptp.abs_abs_Code_integer K2)) (@ _let_1 K2)))) (forall ((M2 tptp.rat) (K2 tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat M2))) (= (@ _let_1 (@ tptp.abs_abs_rat K2)) (@ _let_1 K2)))) (forall ((M2 tptp.real) (K2 tptp.real)) (= (@ (@ tptp.dvd_dvd_real (@ tptp.abs_abs_real M2)) K2) (@ (@ tptp.dvd_dvd_real M2) K2))) (forall ((M2 tptp.int) (K2 tptp.int)) (= (@ (@ tptp.dvd_dvd_int (@ tptp.abs_abs_int M2)) K2) (@ (@ tptp.dvd_dvd_int M2) K2))) (forall ((M2 tptp.code_integer) (K2 tptp.code_integer)) (= (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.abs_abs_Code_integer M2)) K2) (@ (@ tptp.dvd_dvd_Code_integer M2) K2))) (forall ((M2 tptp.rat) (K2 tptp.rat)) (= (@ (@ tptp.dvd_dvd_rat (@ tptp.abs_abs_rat M2)) K2) (@ (@ tptp.dvd_dvd_rat M2) K2))) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri4939895301339042750nteger N))) (= (@ tptp.abs_abs_Code_integer _let_1) _let_1))) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri681578069525770553at_rat N))) (= (@ tptp.abs_abs_rat _let_1) _let_1))) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real N))) (= (@ tptp.abs_abs_real _let_1) _let_1))) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int N))) (= (@ tptp.abs_abs_int _let_1) _let_1))) (forall ((P2 Bool)) (let ((_let_1 (@ tptp.zero_n3304061248610475627l_real P2))) (= (@ tptp.abs_abs_real _let_1) _let_1))) (forall ((P2 Bool)) (let ((_let_1 (@ tptp.zero_n2052037380579107095ol_rat P2))) (= (@ tptp.abs_abs_rat _let_1) _let_1))) (forall ((P2 Bool)) (let ((_let_1 (@ tptp.zero_n2684676970156552555ol_int P2))) (= (@ tptp.abs_abs_int _let_1) _let_1))) (forall ((P2 Bool)) (let ((_let_1 (@ tptp.zero_n356916108424825756nteger P2))) (= (@ tptp.abs_abs_Code_integer _let_1) _let_1))) (forall ((A tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A) (= (@ tptp.abs_abs_Code_integer A) A))) (forall ((A tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (= (@ tptp.abs_abs_real A) A))) (forall ((A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (= (@ tptp.abs_abs_rat A) A))) (forall ((A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (= (@ tptp.abs_abs_int A) A))) (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer A)) A) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A))) (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real A)) A) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A))) (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat A)) A) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A))) (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int A)) A) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A))) (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer A)) tptp.zero_z3403309356797280102nteger) (= A tptp.zero_z3403309356797280102nteger))) (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real A)) tptp.zero_zero_real) (= A tptp.zero_zero_real))) (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat A)) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))) (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int A)) tptp.zero_zero_int) (= A tptp.zero_zero_int))) (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ tptp.abs_abs_Code_integer A)) (not (= A tptp.zero_z3403309356797280102nteger)))) (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.abs_abs_real A)) (not (= A tptp.zero_zero_real)))) (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.abs_abs_rat A)) (not (= A tptp.zero_zero_rat)))) (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.abs_abs_int A)) (not (= A tptp.zero_zero_int)))) (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (= (@ tptp.abs_abs_int (@ tptp.uminus_uminus_int _let_1)) _let_1))) (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real N))) (= (@ tptp.abs_abs_real (@ tptp.uminus_uminus_real _let_1)) _let_1))) (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger N))) (= (@ tptp.abs_abs_Code_integer (@ tptp.uminus1351360451143612070nteger _let_1)) _let_1))) (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat N))) (= (@ tptp.abs_abs_rat (@ tptp.uminus_uminus_rat _let_1)) _let_1))) (= (@ tptp.abs_abs_int _let_153) tptp.one_one_int) (= (@ tptp.abs_abs_real _let_152) tptp.one_one_real) (= (@ tptp.abs_abs_Code_integer _let_151) tptp.one_one_Code_integer) (= (@ tptp.abs_abs_rat _let_150) tptp.one_one_rat) (= (@ tptp.cos_complex tptp.zero_zero_complex) tptp.one_one_complex) (= (@ tptp.cos_real tptp.zero_zero_real) tptp.one_one_real) (= (@ tptp.pred_numeral tptp.one) tptp.zero_zero_nat) (forall ((K2 tptp.num) (N tptp.nat)) (= (= (@ tptp.numeral_numeral_nat K2) (@ tptp.suc N)) (= (@ tptp.pred_numeral K2) N))) (forall ((N tptp.nat) (K2 tptp.num)) (= (= (@ tptp.suc N) (@ tptp.numeral_numeral_nat K2)) (= N (@ tptp.pred_numeral K2)))) (forall ((F2 (-> tptp.int tptp.int)) (A4 tptp.set_int)) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.groups4538972089207619220nt_int F2) A4))) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((I tptp.int)) (@ tptp.abs_abs_int (@ F2 I)))) A4))) (forall ((F2 (-> tptp.nat tptp.real)) (A4 tptp.set_nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.groups6591440286371151544t_real F2) A4))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I tptp.nat)) (@ tptp.abs_abs_real (@ F2 I)))) A4))) (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real A) (@ tptp.abs_abs_real B))) tptp.zero_zero_real) (or (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (= B tptp.zero_zero_real)))) (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat A) (@ tptp.abs_abs_rat B))) tptp.zero_zero_rat) (or (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat) (= B tptp.zero_zero_rat)))) (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ (@ tptp.divide_divide_real A) (@ tptp.abs_abs_real B))) (or (@ _let_1 A) (= B tptp.zero_zero_real))))) (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (= (@ _let_1 (@ (@ tptp.divide_divide_rat A) (@ tptp.abs_abs_rat B))) (or (@ _let_1 A) (= B tptp.zero_zero_rat))))) (forall ((A tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (= (@ tptp.abs_abs_real A) (@ tptp.uminus_uminus_real A)))) (forall ((A tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger A) tptp.zero_z3403309356797280102nteger) (= (@ tptp.abs_abs_Code_integer A) (@ tptp.uminus1351360451143612070nteger A)))) (forall ((A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat) (= (@ tptp.abs_abs_rat A) (@ tptp.uminus_uminus_rat A)))) (forall ((A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int) (= (@ tptp.abs_abs_int A) (@ tptp.uminus_uminus_int A)))) (forall ((N tptp.nat) (K2 tptp.num)) (= (@ (@ tptp.ord_less_nat (@ tptp.suc N)) (@ tptp.numeral_numeral_nat K2)) (@ (@ tptp.ord_less_nat N) (@ tptp.pred_numeral K2)))) (forall ((K2 tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.numeral_numeral_nat K2)) (@ tptp.suc N)) (@ (@ tptp.ord_less_nat (@ tptp.pred_numeral K2)) N))) (forall ((K2 tptp.num)) (= (@ tptp.pred_numeral (@ tptp.bit1 K2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 K2)))) (forall ((K2 tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat K2)) (@ tptp.suc N)) (@ (@ tptp.ord_less_eq_nat (@ tptp.pred_numeral K2)) N))) (forall ((N tptp.nat) (K2 tptp.num)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) (@ tptp.numeral_numeral_nat K2)) (@ (@ tptp.ord_less_eq_nat N) (@ tptp.pred_numeral K2)))) (forall ((K2 tptp.num) (N tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ tptp.numeral_numeral_nat K2)) (@ tptp.suc N)) (@ (@ tptp.minus_minus_nat (@ tptp.pred_numeral K2)) N))) (forall ((N tptp.nat) (K2 tptp.num)) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc N)) (@ tptp.numeral_numeral_nat K2)) (@ (@ tptp.minus_minus_nat N) (@ tptp.pred_numeral K2)))) (forall ((N tptp.nat) (K2 tptp.num)) (= (@ (@ tptp.ord_max_nat (@ tptp.suc N)) (@ tptp.numeral_numeral_nat K2)) (@ tptp.suc (@ (@ tptp.ord_max_nat N) (@ tptp.pred_numeral K2))))) (forall ((K2 tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_max_nat (@ tptp.numeral_numeral_nat K2)) (@ tptp.suc N)) (@ tptp.suc (@ (@ tptp.ord_max_nat (@ tptp.pred_numeral K2)) N)))) (forall ((F2 (-> tptp.int tptp.int)) (A4 tptp.set_int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((I tptp.int)) (@ tptp.abs_abs_int (@ F2 I)))) A4))) (forall ((F2 (-> tptp.nat tptp.real)) (A4 tptp.set_nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I tptp.nat)) (@ tptp.abs_abs_real (@ F2 I)))) A4))) (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.divide_divide_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M2))) (@ tptp.numeral_numeral_int N)) (@ tptp.uminus_uminus_int (@ tptp.adjust_div (@ (@ tptp.unique5052692396658037445od_int M2) N))))) (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.divide_divide_int (@ tptp.numeral_numeral_int M2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) (@ tptp.uminus_uminus_int (@ tptp.adjust_div (@ (@ tptp.unique5052692396658037445od_int M2) N))))) (forall ((A tptp.code_integer) (N tptp.nat)) (= (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.abs_abs_Code_integer A)) N)) (or (not (= A tptp.zero_z3403309356797280102nteger)) (= N tptp.zero_zero_nat)))) (forall ((A tptp.real) (N tptp.nat)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real A)) N)) (or (not (= A tptp.zero_zero_real)) (= N tptp.zero_zero_nat)))) (forall ((A tptp.rat) (N tptp.nat)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.power_power_rat (@ tptp.abs_abs_rat A)) N)) (or (not (= A tptp.zero_zero_rat)) (= N tptp.zero_zero_nat)))) (forall ((A tptp.int) (N tptp.nat)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.power_power_int (@ tptp.abs_abs_int A)) N)) (or (not (= A tptp.zero_zero_int)) (= N tptp.zero_zero_nat)))) (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.sin_complex X))) (let ((_let_2 (@ tptp.cos_complex X))) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex _let_2) _let_2)) (@ (@ tptp.times_times_complex _let_1) _let_1)) tptp.one_one_complex)))) (forall ((X tptp.real)) (let ((_let_1 (@ tptp.sin_real X))) (let ((_let_2 (@ tptp.cos_real X))) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real _let_2) _let_2)) (@ (@ tptp.times_times_real _let_1) _let_1)) tptp.one_one_real)))) (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int M2)) (@ tptp.numeral_numeral_int N)) (@ tptp.unique6319869463603278526ux_int (@ (@ tptp.unique5052692396658037445od_int N) M2)))) (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat M2)) (@ tptp.numeral_numeral_nat N)) (@ tptp.unique6322359934112328802ux_nat (@ (@ tptp.unique5055182867167087721od_nat N) M2)))) (forall ((M2 tptp.num)) (= (@ (@ tptp.unique3479559517661332726nteger M2) tptp.one) (@ (@ tptp.produc1086072967326762835nteger (@ tptp.numera6620942414471956472nteger M2)) tptp.zero_z3403309356797280102nteger))) (forall ((M2 tptp.num)) (= (@ (@ tptp.unique5052692396658037445od_int M2) tptp.one) (@ (@ tptp.product_Pair_int_int (@ tptp.numeral_numeral_int M2)) tptp.zero_zero_int))) (forall ((M2 tptp.num)) (= (@ (@ tptp.unique5055182867167087721od_nat M2) tptp.one) (@ (@ tptp.product_Pair_nat_nat (@ tptp.numeral_numeral_nat M2)) tptp.zero_zero_nat))) (forall ((N tptp.num)) (= (@ (@ tptp.unique3479559517661332726nteger tptp.one) (@ tptp.bit0 N)) (@ (@ tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger) (@ tptp.numera6620942414471956472nteger tptp.one)))) (forall ((N tptp.num)) (= (@ (@ tptp.unique5052692396658037445od_int tptp.one) (@ tptp.bit0 N)) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) (@ tptp.numeral_numeral_int tptp.one)))) (forall ((N tptp.num)) (= (@ (@ tptp.unique5055182867167087721od_nat tptp.one) (@ tptp.bit0 N)) (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat tptp.one)))) (forall ((N tptp.num)) (= (@ (@ tptp.unique3479559517661332726nteger tptp.one) (@ tptp.bit1 N)) (@ (@ tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger) (@ tptp.numera6620942414471956472nteger tptp.one)))) (forall ((N tptp.num)) (= (@ (@ tptp.unique5052692396658037445od_int tptp.one) (@ tptp.bit1 N)) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) (@ tptp.numeral_numeral_int tptp.one)))) (forall ((N tptp.num)) (= (@ (@ tptp.unique5055182867167087721od_nat tptp.one) (@ tptp.bit1 N)) (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat tptp.one)))) (forall ((N tptp.num)) (= (@ (@ tptp.divide_divide_int tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) (@ tptp.uminus_uminus_int (@ tptp.adjust_div (@ (@ tptp.unique5052692396658037445od_int tptp.one) N))))) (forall ((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))))) (= (@ tptp.cos_real _let_112) tptp.one_one_real) (forall ((X tptp.real)) (= (@ tptp.cos_real (@ (@ tptp.plus_plus_real X) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi))) (@ tptp.cos_real X))) (forall ((X tptp.real)) (= (@ tptp.cos_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) X)) (@ tptp.cos_real X))) (forall ((L tptp.num) (K2 tptp.num)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.numeral_numeral_nat L)) (@ tptp.numeral_numeral_int (@ tptp.bit0 K2))) (@ (@ tptp.times_times_int (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.pred_numeral L)) (@ tptp.numeral_numeral_int K2))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (forall ((N tptp.nat)) (= (@ tptp.cos_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) tptp.pi)) (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N))) (forall ((N tptp.nat)) (= (@ tptp.cos_real (@ (@ tptp.times_times_real tptp.pi) (@ tptp.semiri5074537144036343181t_real N))) (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N))) (forall ((N tptp.nat)) (= (@ tptp.cos_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ tptp.semiri5074537144036343181t_real N))) tptp.pi)) tptp.one_one_real)) (forall ((L tptp.num) (K2 tptp.num)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.numeral_numeral_nat L)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 K2)))) (@ (@ tptp.times_times_int (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.pred_numeral L)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K2)))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ tptp.cos_real _let_149) tptp.zero_zero_real) (forall ((L tptp.num) (K2 tptp.num)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.numeral_numeral_nat L)) (@ tptp.numeral_numeral_int (@ tptp.bit1 K2))) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.pred_numeral L)) (@ tptp.numeral_numeral_int K2))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) tptp.one_one_int))) (forall ((M2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ tptp.cos_real (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real tptp.pi) (@ tptp.semiri5074537144036343181t_real (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat _let_1)) M2))))) (@ tptp.numeral_numeral_real _let_1))) tptp.zero_zero_real))) (forall ((A tptp.real)) (@ (@ tptp.ord_less_eq_real A) (@ tptp.abs_abs_real A))) (forall ((A tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger A) (@ tptp.abs_abs_Code_integer A))) (forall ((A tptp.rat)) (@ (@ tptp.ord_less_eq_rat A) (@ tptp.abs_abs_rat A))) (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int A) (@ tptp.abs_abs_int A))) (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real A)) B) (@ (@ tptp.ord_less_eq_real A) B))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer A)) B) (@ (@ tptp.ord_le3102999989581377725nteger A) B))) (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat A)) B) (@ (@ tptp.ord_less_eq_rat A) B))) (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int A)) B) (@ (@ tptp.ord_less_eq_int A) B))) (forall ((A tptp.code_integer)) (= (= (@ tptp.abs_abs_Code_integer A) tptp.zero_z3403309356797280102nteger) (= A tptp.zero_z3403309356797280102nteger))) (forall ((A tptp.complex)) (= (= (@ tptp.abs_abs_complex A) tptp.zero_zero_complex) (= A tptp.zero_zero_complex))) (forall ((A tptp.real)) (= (= (@ tptp.abs_abs_real A) tptp.zero_zero_real) (= A tptp.zero_zero_real))) (forall ((A tptp.rat)) (= (= (@ tptp.abs_abs_rat A) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))) (forall ((A tptp.int)) (= (= (@ tptp.abs_abs_int A) tptp.zero_zero_int) (= A tptp.zero_zero_int))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ tptp.abs_abs_Code_integer (@ (@ tptp.times_3573771949741848930nteger A) B)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.abs_abs_Code_integer A)) (@ tptp.abs_abs_Code_integer B)))) (forall ((A tptp.real) (B tptp.real)) (= (@ tptp.abs_abs_real (@ (@ tptp.times_times_real A) B)) (@ (@ tptp.times_times_real (@ tptp.abs_abs_real A)) (@ tptp.abs_abs_real B)))) (forall ((A tptp.rat) (B tptp.rat)) (= (@ tptp.abs_abs_rat (@ (@ tptp.times_times_rat A) B)) (@ (@ tptp.times_times_rat (@ tptp.abs_abs_rat A)) (@ tptp.abs_abs_rat B)))) (forall ((A tptp.int) (B tptp.int)) (= (@ tptp.abs_abs_int (@ (@ tptp.times_times_int A) B)) (@ (@ tptp.times_times_int (@ tptp.abs_abs_int A)) (@ tptp.abs_abs_int B)))) _let_148 _let_147 _let_146 _let_145 (forall ((A tptp.real) (B tptp.real)) (= (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real A) B)) (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real B) A)))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger A) B)) (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger B) A)))) (forall ((A tptp.rat) (B tptp.rat)) (= (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat A) B)) (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat B) A)))) (forall ((A tptp.int) (B tptp.int)) (= (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int A) B)) (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int B) A)))) (forall ((X tptp.int) (Y tptp.int)) (= (= (@ tptp.abs_abs_int X) (@ tptp.abs_abs_int Y)) (or (= X Y) (= X (@ tptp.uminus_uminus_int Y))))) (forall ((X tptp.real) (Y tptp.real)) (= (= (@ tptp.abs_abs_real X) (@ tptp.abs_abs_real Y)) (or (= X Y) (= X (@ tptp.uminus_uminus_real Y))))) (forall ((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))))) (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))))) (forall ((L tptp.real) (K2 tptp.real)) (=> (= (@ tptp.abs_abs_real L) (@ tptp.abs_abs_real K2)) (@ (@ tptp.dvd_dvd_real L) K2))) (forall ((L tptp.int) (K2 tptp.int)) (=> (= (@ tptp.abs_abs_int L) (@ tptp.abs_abs_int K2)) (@ (@ tptp.dvd_dvd_int L) K2))) (forall ((L tptp.code_integer) (K2 tptp.code_integer)) (=> (= (@ tptp.abs_abs_Code_integer L) (@ tptp.abs_abs_Code_integer K2)) (@ (@ tptp.dvd_dvd_Code_integer L) K2))) (forall ((L tptp.rat) (K2 tptp.rat)) (=> (= (@ tptp.abs_abs_rat L) (@ tptp.abs_abs_rat K2)) (@ (@ tptp.dvd_dvd_rat L) K2))) (forall ((A tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ tptp.abs_abs_Code_integer A))) (forall ((A tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.abs_abs_real A))) (forall ((A tptp.rat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.abs_abs_rat A))) (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.abs_abs_int A))) (forall ((A tptp.code_integer)) (not (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.abs_abs_Code_integer A)) tptp.zero_z3403309356797280102nteger))) (forall ((A tptp.real)) (not (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real A)) tptp.zero_zero_real))) (forall ((A tptp.rat)) (not (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat A)) tptp.zero_zero_rat))) (forall ((A tptp.int)) (not (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int A)) tptp.zero_zero_int))) (forall ((A tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A) (= (@ tptp.abs_abs_Code_integer A) A))) (forall ((A tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (= (@ tptp.abs_abs_real A) A))) (forall ((A tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (= (@ tptp.abs_abs_rat A) A))) (forall ((A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (= (@ tptp.abs_abs_int A) A))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.plus_p5714425477246183910nteger A) B))) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.abs_abs_Code_integer A)) (@ tptp.abs_abs_Code_integer B)))) (forall ((A tptp.real) (B tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.plus_plus_real A) B))) (@ (@ tptp.plus_plus_real (@ tptp.abs_abs_real A)) (@ tptp.abs_abs_real B)))) (forall ((A tptp.rat) (B tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.plus_plus_rat A) B))) (@ (@ tptp.plus_plus_rat (@ tptp.abs_abs_rat A)) (@ tptp.abs_abs_rat B)))) (forall ((A tptp.int) (B tptp.int)) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.plus_plus_int A) B))) (@ (@ tptp.plus_plus_int (@ tptp.abs_abs_int A)) (@ tptp.abs_abs_int B)))) (forall ((A tptp.code_integer) (C2 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) C2) (=> (@ (@ tptp.ord_le6747313008572928689nteger _let_1) D) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.times_3573771949741848930nteger _let_2) _let_1)) (@ (@ tptp.times_3573771949741848930nteger C2) D))))))) (forall ((A tptp.real) (C2 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) C2) (=> (@ (@ tptp.ord_less_real _let_1) D) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real _let_2) _let_1)) (@ (@ tptp.times_times_real C2) D))))))) (forall ((A tptp.rat) (C2 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) C2) (=> (@ (@ tptp.ord_less_rat _let_1) D) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat _let_2) _let_1)) (@ (@ tptp.times_times_rat C2) D))))))) (forall ((A tptp.int) (C2 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) C2) (=> (@ (@ tptp.ord_less_int _let_1) D) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int _let_2) _let_1)) (@ (@ tptp.times_times_int C2) D))))))) (forall ((A tptp.real) (B tptp.real)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ tptp.abs_abs_real A)) (@ tptp.abs_abs_real B))) (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real B) A)))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.abs_abs_Code_integer A)) (@ tptp.abs_abs_Code_integer B))) (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger B) A)))) (forall ((A tptp.rat) (B tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat (@ tptp.abs_abs_rat A)) (@ tptp.abs_abs_rat B))) (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat B) A)))) (forall ((A tptp.int) (B tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int (@ tptp.abs_abs_int A)) (@ tptp.abs_abs_int B))) (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int B) A)))) (forall ((A tptp.real) (B tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ tptp.abs_abs_real A)) (@ tptp.abs_abs_real B)))) (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real A) B)))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.abs_abs_Code_integer A)) (@ tptp.abs_abs_Code_integer B)))) (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger A) B)))) (forall ((A tptp.rat) (B tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ tptp.abs_abs_rat A)) (@ tptp.abs_abs_rat B)))) (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat A) B)))) (forall ((A tptp.int) (B tptp.int)) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ tptp.abs_abs_int A)) (@ tptp.abs_abs_int B)))) (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int A) B)))) (forall ((A tptp.real) (B tptp.real)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ tptp.abs_abs_real A)) (@ tptp.abs_abs_real B))) (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real A) B)))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.abs_abs_Code_integer A)) (@ tptp.abs_abs_Code_integer B))) (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger A) B)))) (forall ((A tptp.rat) (B tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat (@ tptp.abs_abs_rat A)) (@ tptp.abs_abs_rat B))) (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat A) B)))) (forall ((A tptp.int) (B tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int (@ tptp.abs_abs_int A)) (@ tptp.abs_abs_int B))) (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int A) B)))) (forall ((B tptp.real) (A tptp.real)) (=> (not (= B tptp.zero_zero_real)) (= (@ tptp.abs_abs_real (@ (@ tptp.divide_divide_real A) B)) (@ (@ tptp.divide_divide_real (@ tptp.abs_abs_real A)) (@ tptp.abs_abs_real B))))) (forall ((B tptp.rat) (A tptp.rat)) (=> (not (= B tptp.zero_zero_rat)) (= (@ tptp.abs_abs_rat (@ (@ tptp.divide_divide_rat A) B)) (@ (@ tptp.divide_divide_rat (@ tptp.abs_abs_rat A)) (@ tptp.abs_abs_rat B))))) (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real A)) B) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real A)) B)))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger A) B) (=> (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger A)) B) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer A)) B)))) (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat A)) B) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat A)) B)))) (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int A)) B) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int A)) B)))) (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real A)) B) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real A)) B))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer A)) B) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger A)) B))) (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat A)) B) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat A)) B))) (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int A)) B) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int A)) B))) (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real A)) B) (and (@ (@ tptp.ord_less_eq_real A) B) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real A)) B)))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer A)) B) (and (@ (@ tptp.ord_le3102999989581377725nteger A) B) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger A)) B)))) (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat A)) B) (and (@ (@ tptp.ord_less_eq_rat A) B) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat A)) B)))) (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int A)) B) (and (@ (@ tptp.ord_less_eq_int A) B) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int A)) B)))) (forall ((A tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real A)) (@ tptp.abs_abs_real A))) (forall ((A tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger A)) (@ tptp.abs_abs_Code_integer A))) (forall ((A tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat A)) (@ tptp.abs_abs_rat A))) (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int A)) (@ tptp.abs_abs_int A))) (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int A)) B) (and (@ (@ tptp.ord_less_int A) B) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int A)) B)))) (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real A)) B) (and (@ (@ tptp.ord_less_real A) B) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real A)) B)))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.abs_abs_Code_integer A)) B) (and (@ (@ tptp.ord_le6747313008572928689nteger A) B) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger A)) B)))) (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat A)) B) (and (@ (@ tptp.ord_less_rat A) B) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat A)) B)))) (forall ((X tptp.real) (Y tptp.real)) (exists ((R4 tptp.real) (A3 tptp.real)) (let ((_let_1 (@ tptp.times_times_real R4))) (and (= X (@ _let_1 (@ tptp.cos_real A3))) (= Y (@ _let_1 (@ tptp.sin_real A3))))))) _let_144 (forall ((X tptp.real) (Y tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.sin_real X)) (@ tptp.sin_real Y))) (@ (@ tptp.times_times_real (@ tptp.cos_real X)) (@ tptp.cos_real Y))))) tptp.one_one_real)) (forall ((X tptp.real)) (=> (forall ((E2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E2) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) E2))) (= X tptp.zero_zero_real))) (forall ((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))) (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))))) (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (= (@ (@ tptp.times_times_real (@ tptp.abs_abs_real Y)) X) (@ tptp.abs_abs_real (@ (@ tptp.times_times_real Y) X))))) (forall ((X tptp.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))))) (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X) (= (@ (@ tptp.times_times_int (@ tptp.abs_abs_int Y)) X) (@ tptp.abs_abs_int (@ (@ tptp.times_times_int Y) X))))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (=> (and (or (@ _let_1 A) (@ (@ tptp.ord_le3102999989581377725nteger A) tptp.zero_z3403309356797280102nteger)) (or (@ _let_1 B) (@ (@ tptp.ord_le3102999989581377725nteger B) tptp.zero_z3403309356797280102nteger))) (= (@ tptp.abs_abs_Code_integer (@ (@ tptp.times_3573771949741848930nteger A) B)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.abs_abs_Code_integer A)) (@ tptp.abs_abs_Code_integer B)))))) (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (and (or (@ _let_1 A) (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real)) (or (@ _let_1 B) (@ (@ tptp.ord_less_eq_real B) tptp.zero_zero_real))) (= (@ tptp.abs_abs_real (@ (@ tptp.times_times_real A) B)) (@ (@ tptp.times_times_real (@ tptp.abs_abs_real A)) (@ tptp.abs_abs_real B)))))) (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (and (or (@ _let_1 A) (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat)) (or (@ _let_1 B) (@ (@ tptp.ord_less_eq_rat B) tptp.zero_zero_rat))) (= (@ tptp.abs_abs_rat (@ (@ tptp.times_times_rat A) B)) (@ (@ tptp.times_times_rat (@ tptp.abs_abs_rat A)) (@ tptp.abs_abs_rat B)))))) (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (and (or (@ _let_1 A) (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int)) (or (@ _let_1 B) (@ (@ tptp.ord_less_eq_int B) tptp.zero_zero_int))) (= (@ tptp.abs_abs_int (@ (@ tptp.times_times_int A) B)) (@ (@ tptp.times_times_int (@ tptp.abs_abs_int A)) (@ tptp.abs_abs_int B)))))) (forall ((X tptp.complex)) (=> (= (@ tptp.cos_complex X) tptp.one_one_complex) (= (@ tptp.sin_complex X) tptp.zero_zero_complex))) (forall ((X tptp.real)) (=> (= (@ tptp.cos_real X) tptp.one_one_real) (= (@ tptp.sin_real X) tptp.zero_zero_real))) (forall ((A tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ tptp.abs_abs_real A))) tptp.zero_zero_real)) (forall ((A tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.abs_abs_Code_integer A))) tptp.zero_z3403309356797280102nteger)) (forall ((A tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ tptp.abs_abs_rat A))) tptp.zero_zero_rat)) (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.abs_abs_int A))) tptp.zero_zero_int)) (forall ((A tptp.real) (B tptp.real)) (= (= A (@ tptp.abs_abs_real B)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (or (= B A) (= B (@ tptp.uminus_uminus_real A)))))) (forall ((